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in Value Space: Orthogonal Complement Matters", + "text_level": 1, + "bbox": [ + 192, + 130, + 803, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuan Wang $^{1*}$ , Ouxiang Li $^{1*}$ , Tingting Mu $^{2}$ , Yanbin Hao $^{3\\dagger}$ , Kuien Liu $^{4}$ , Xiang Wang $^{1}$ , Xiangnan He $^{1\\dagger}$", + "bbox": [ + 104, + 202, + 897, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Science and Technology of China, 2The University of Manchester,", + "bbox": [ + 256, + 223, + 738, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Hefei University of Technology, $^{4}$ Institute of Software Chinese Academy of Sciences", + "bbox": [ + 238, + 239, + 756, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wy1001, lioox}@mail.ustc.edu.cn, haoyanbin@hotmail.com, xiangnanhe@gmail.com", + "bbox": [ + 156, + 258, + 836, + 273 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c96b13d5b89e107e6e7a944c0ad34490c3acaee3b620c7da1b5d9e095e489dbd.jpg", + "image_caption": [ + "(a) Erasure Efficacy and Prior Preservation" + ], + "image_footnote": [], + "bbox": [ + 94, + 284, + 588, + 547 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cdea46124456ecfd27cc2aa05ef91abc3e90be8bca8e901c2686dd917f1eaf16.jpg", + "image_caption": [ + "(b) Transferability", + "Figure 1. The proposed Adaptive Value Decomposer (AdaVD) demonstrates a satisfactory balance between erasure efficacy and prior preservation and an effective transferability across T2I diffusion models. (a) Compared to SLD [39], AdaVD enables precise concept erasure without compromising prior knowledge for non-target concepts at both single- and multi-concept erasure. This is facilitated by a precise disentanglement of target semantics (e.g., \"Snoopy\") and a robust preservation of non-target ones (e.g., \"Teddy\"), with visualization interpretation marked by $\\diamond$ . (b) AdaVD can be transferred to various T2I models, e.g., SDXL [31], DreamShaper [6], Chilloutmix [5]." + ], + "image_footnote": [], + "bbox": [ + 589, + 285, + 903, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 647, + 326, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent success of text-to-image (T2I) generation and its increasing practical applications, enabled by diffusion models, require urgent consideration of erasing unwanted concepts, e.g., copyrighted, offensive, and unsafe ones, from the pre-trained models in a precise, timely, and low-cost manner. The twofold demand of concept erasure includes not only a precise removal of the target concept (i.e., erasure efficacy) but also a minimal change on non-target content (i.e., prior preservation), during generation. Existing methods face challenges in maintaining an effective balance between erasure efficacy and prior preservation, and they can be computationally costly. To improve, we propose a precise, fast, and low-cost concept era", + "bbox": [ + 88, + 667, + 485, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sure method, called Adaptive Vaule Decomposer (AdaVD), which is training-free. Our method is grounded in a classical linear algebraic operation of computing orthogonal complement, implemented in the value space of each cross-attention layer within the UNet of diffusion models. We design a shift factor to adaptively navigate the erasure strength, enhancing effectively prior preservation without sacrificing erasure efficacy. Extensive comparative experiments with both training-based and training-free state of the arts demonstrate that the proposed AdaVD excels in both single and multiple concept erasure, showing 2 to 10 times of improvement in prior preservation than the second best, meanwhile achieving the best or near best erasure efficacy. AdaVD supports a series of diffusion models and downstream image generation tasks, with code available on: https://github.com/WYuan1001/AdaVD.", + "bbox": [ + 511, + 648, + 908, + 891 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contributions.", + "bbox": [ + 107, + 875, + 227, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 109, + 887, + 241, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28759", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 89, + 222, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recent advancements of text-to-image (T2I) diffusion models [11, 17, 18, 30, 36, 50, 52] have enabled users to effortlessly generate high-quality images with simple textual prompts. However, such generations would inevitably introduce copyrighted [10, 22, 42, 44] or offensive [23, 39] concepts, caused by the noisy training data scraped from web [9, 40]. Because it is very costly to re-train large generative models from scratch, it is vital to develop low-cost techniques to precisely erase unwanted semantic concepts in images, i.e., concept erasure. This task aims at a precise erasure of visual content w.r.t. target concepts from generated images (i.e., erasure efficacy), while a faithful preservation of irrelevant content w.r.t. the prompts comprising non-target concepts (i.e., prior preservation), safeguarding a secure T2I generation for diffusion models.", + "bbox": [ + 89, + 114, + 480, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A representative category of concept erasure methods is training-based, which fine-tunes a subset of model parameters by formulating meticulous erasing objective functions [12, 20, 26, 27]. Despite good erasure efficacy, they exhibit considerable practical limitations when being deployed. For instance, they require expensive individual fine-tuning to erase each concept, which thereby limits their real-time usage. As an example, it is unacceptable for online T2I platforms to be costly to erase newly emerging concepts, where copyrighted or offensive concepts could arise unexpectedly, with no means to produce a complete list of concepts to erase in advance. Moreover, these methods suffer from a limited balance between erasure efficacy and prior preservation, due to their reliance on regularization terms to trade off prior preservation.", + "bbox": [ + 89, + 342, + 482, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An alternative category of concept erasure methods is training-free, such as Negative Prompt (NP) [2], Safe Latent Diffusion (SLD) [39], and SuppressEOT [24], which enable real-time erasure. They intervene in the image generation process, exhibiting a range of drawbacks. For instance, NP was initially designed to enhance image quality and can result in compromised erasure efficacy; while SuppressEOT requires the user to specify the location of the target concept within the prompt, thus, it is not suitable for erasure applications that require full automation. Therefore, both NP and SuppressEOT fall short as independent tools for concept erasure. Regarding SLD, it does not perform well at retaining prior knowledge of non-target concepts as illustrated in Fig. 1, failing in precise concept erasure. Limited by their drawbacks, current training-free methods are not robust enough to act as an independent concept erasure tool and to be applied in continual erasure of multiple concepts.", + "bbox": [ + 89, + 568, + 482, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this light, we advance concept erasure techniques for T2I generation, by developing a precise, fast, and low-cost method called Adaptive Value Decomposer (AdaVD). It is a training-free method, capable of precisely erasing the target concepts and satisfactorily preserving non-target priors", + "bbox": [ + 89, + 825, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with low computational overhead. Our core design builds on a classical linear algebraic operation, i.e., projection onto the orthogonal complement of the semantic space of the target concepts. We conduct this projection-based decomposition in the cross-attention value space, disentangling target semantics from the original prompts. To improve the erasure precision and prior preservation, we further refine the decomposition by adaptively allocating token-wise shifts. These shifts are designed to differentiate the strong and specific alignments from the weak and general alignments between prompt tokens and visual content associated with the target concept. Guided by these shifts, the strong and specific alignments are erased for precision while the weak and general alignments are retained for prior preservation.", + "bbox": [ + 511, + 90, + 903, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 1 (a) demonstrates the erased results for both target and non-target concepts. It shows that our AdaVD can precisely locate and erase the components indicated by the target semantics, meanwhile keeping the non-target priors maximally unaffected. Empirical evaluation shows that AdaVD excels in prior preservation, outperforming the second best by a 2- to 10-fold improvement across various nontarget concepts, and meanwhile maintains exceptional erasure efficacy, consistently achieving the best or near-best performance. Our contributions are summarized below:", + "bbox": [ + 511, + 303, + 903, + 453 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel and effective erasing operation by exploiting the projection onto the orthogonal complement of the target concept in the cross-attention value space, to disentangle semantics carried by the target concept.", + "- An adaptive erasing mechanism through a dynamic shift factor, which can effectively minimize the impact on prior knowledge, without compromising the erasure efficacy.", + "- A precise, fast, and low-cost concept erasure technique AdaVD, which works in a training-free manner and supports a series of T2I diffusion models, capable of precise concept erasure.", + "- Extensive experiments that demonstrate the superiority of AdaVA against state-of-the-art (SOTA) methods, achieving 2 to 10 times of improvement in prior preservation while maintaining precise erasure efficacy." + ], + "bbox": [ + 511, + 454, + 903, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 511, + 693, + 663, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Re-training and Blocking: The most straightforward way to erase a target concept from a pre-trained T2I model is to exclude the training data relevant to this concept and retrain the model from scratch, as in Stable Diffusion (SD) v2.0 [3]. For this, an Not Safe For Work (NSFW) detector [8, 21, 38] can be used to filter unsafe data from LAION-5B [41] prior to the training. However, this approach is time-consuming, requires specialized detectors, and can introduce biases [43]. An alternative solution is to block the prompts of concerns and restrict the outputs of concerns, by using filters [43] and safety checkers [1, 35]. Yet, such safeguards are fragile and easy to bypass [46, 49], especially", + "bbox": [ + 511, + 719, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28760", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "when being confronted with crafted malicious prompts [39]. Training-based: A more effective group of concept erasure solutions fine-tune pre-trained generative models, teaching them to \"forget\" a target concept, e.g., Erased Stable Diffusion (ESD) [12]. However, since the ESD design does not consider prior preservation, both target and non-target concepts are adversely affected. To improve, new training techniques have been developed, e.g., ConAbl [20], SA [14], UCE [13], EraseDiff [48], SPM [27] and MACE [26]. They improve prior preservation through regularization but still fall short in achieving both precise erasure and robust prior preservation. Moreover, for every new target concept to be erased, a separate fine-tuning is required. This is time-consuming, making real-time erasure impractical, especially for highly interactive platforms where unsafe or inappropriate concepts can emerge unexpectedly.", + "bbox": [ + 89, + 90, + 480, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training-free: With largely reduced computing costs, training-free methods are gaining increasing attention. NP [2] and SLD [39] pioneer training-free concept erasure by adjusting classifier-free guidance [17], leading the generation towards a direction away from the target concepts. However, NP lacks fine-grained control over target concepts and compromises prior preservation. SLD also compromises the prior knowledge during its generation, disrupting the overall generating quality of non-target concepts. SuppressEOT [24], akin to image editing techniques [15], removes target concepts based on user-specified textual positions. Its user-involved design makes it more suitable for editing tasks, but not for system-wide erasing tasks that require full automation. Benefiting from orthogonal decompositions in value spaces, the proposed training-free method AdaVD achieves not only precise concept erasure but also satisfactory prior preservation. It supports multi-concept erasure, is compatible across different versions of stable diffusion, and consistently demonstrates superior performance. The training-free method SAFREE [51], concurrent to ours, also uses orthogonal decomposition but operates differently on text embeddings, supported by masking, projection, Fourier transforms, and a hard control of removal strength. We compare performance with it in the appendix.", + "bbox": [ + 91, + 333, + 483, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 709, + 181, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concept erasure in T2I generation aims at a successful removal of the visual content indicated by textual concepts (i.e., target concepts), meanwhile a satisfactory preservation of the visual content irrelevant to these concepts (i.e., prior knowledge). It is challenging to achieve simultaneously satisfactory erasure efficacy and prior preservation. To advance this field, we propose a precise, fast, and low-cost concept erasure method, termed AdaVD and illustrated in Fig. 2 (c). The method is training-free, and its core design builds on a classical linear algebraic operation, i.e., orthogonal complement. This simple but elegant geometric", + "bbox": [ + 89, + 734, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "operation is able to guide effectively the image generation, enabling a precise removal of the target concepts from the image content meanwhile a satisfactory preservation of the non-target content.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary on T2I Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 161, + 834, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current T2I models usually include an image compression network [19] and a conditional latent diffusion model [36] that performs sequential denoising with a UNet [37] in the latent space. The UNet takes as inputs the noise latent variable $\\mathbf{z}_t$ , timestep $t$ , and embedding $\\mathbf{C}$ of the textual prompt from a pre-trained CLIP model [33], and predicts the noise $\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C})$ . In training-free concept erasure, the noise is additionally conditioned on the target concept with text embedding $\\mathbf{C}_t$ , predicted by $\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C}, \\mathbf{C}_t)$ .", + "bbox": [ + 511, + 183, + 903, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interactions between the image and text modalities are enabled by cross-attention (CA) layers [36, 47] within the UNet, which align the latent representation of the noisy image with the semantic detail of the textual prompt. Each CA layer computes an attention map $\\mathbf{A} = \\mathrm{softmax}\\left(\\frac{\\mathbf{Q}\\mathbf{K}^T}{\\sqrt{d}}\\right)$ with a latent feature dimension $d$ . The queries $\\mathbf{Q}$ are computed from the noisy image features, while both keys $\\mathbf{K}$ and values $\\mathbf{V}$ from the text embeddings $\\mathbf{C}$ , using different projection matrices. The layer output is a weighted aggregation of $\\mathbf{A}$ and $\\mathbf{V}$ . More details on CA layers are in Appendix A.", + "bbox": [ + 511, + 319, + 903, + 476 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It has been recognized that the keys in CA layers mostly act as the \"Where\" pathway, governing the layout of the attention map and determining the compositional structure of the generated images, while the values as the \"What\" pathway, controlling the content and visual appearance of images [45]. Because the goal of concept erasure is to modify the visual content of the generated images, we propose to conduct value decompositions into subspaces, which are uniquely constructed by exploiting the target concept and its orthogonal complement in an adaptive fashion. We demonstrate that information offered by the orthogonal complement can be used to generate successfully high-quality images with the target concept precisely erased.", + "bbox": [ + 511, + 477, + 905, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Token-wise Target Embedding Pre-processing", + "text_level": 1, + "bbox": [ + 511, + 681, + 901, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a textual example, which can be either a target concept to erase or an original prompt, its embedding is computed at the token level by a CLIP text encoder. Each tokenized example is padded with [SOT] as the prefix and [EOT] at the end, with [EOT] filling any remaining positions to maintain a fixed token length of $l$ . Each token is characterized by an embedding vector of dimension $D_{c}$ .", + "bbox": [ + 511, + 704, + 903, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We focus on the embedding of a target concept $\\mathbf{C}_t\\in$ $\\mathbb{R}^{l\\times D_c}$ , and denote each column of $\\mathbf{C}_t^T$ by $c_{t}^{j}$ that corresponds to a token vector where $j\\in \\{1,2,\\dots ,l\\}$ . To facilitate a precise erasure, we emphasize the key information carried by a target concept by proposing an embedding duplication. Specifically, the embedding of the last sub", + "bbox": [ + 511, + 810, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28761", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4cda90f0a533aee68d3b154ae598bde49c37ebab0d734efbca4245b1090bbf63.jpg", + "image_caption": [ + "Figure 2. Overview of our Adaptive Value Decomposer (AdaVD) in erasing the target concept \"Snoopy\". (a) First, we token-wisely duplicate the last subject token of the target embedding encoded by the text encoder, except for [SOT]. (b) Then, the pre-processed target embedding and corresponding prompt embedding are jointly fed into CA layers within the UNet as conditions, to disentangle target semantics from the original image at each timestep. (c) In each CA layer, we perform token-wise orthogonal value decomposition with an adaptive token-wise shift. The new value is subsequently multiplied by the attention map, producing the erased output for this CA layer." + ], + "image_footnote": [], + "bbox": [ + 93, + 78, + 903, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ject token within its prompt content excluding [SOT] and [EOT], replaces all the token positions except for [SOT], as illustrated in Fig. 2 (a). For instance, the single-token concept \"snoopy\" has a modified embedding matrix corresponding to \"[SOT], snoopy, snoopy, ..., snoopy\", while the multi-token concept \"Van Gogh\" to \"[SOT], gogh, gogh, ..., gogh\". Benefiting from the causal attention mechanism used by the CLIP text encoder, the last subject token is able to \"see\" all the prompt content and contains key information [28], therefore is sufficient for erasure calculation. The modified embedding matrix $\\tilde{\\mathbf{C}}_t$ is fed into a CA layer to compute the value matrix $\\tilde{\\mathbf{V}}_t \\in \\mathbb{R}^{l \\times d}$ via a linear projection using the projection matrix $\\mathbf{W}_{\\mathrm{V}} \\in \\mathbb{R}^{D_c \\times d}$ , as", + "bbox": [ + 88, + 316, + 485, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {V}} _ {t} = \\tilde {\\mathbf {C}} _ {t} \\mathbf {W} _ {\\mathrm {V}} = \\left[ c _ {t} ^ {1}, \\underbrace {c _ {t} ^ {k} , \\dots , c _ {t} ^ {k}} _ {l - 1} \\right] ^ {T} \\mathbf {W} _ {\\mathrm {V}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 523, + 482, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The token vector $c_{t}^{1}$ corresponds to [SOT] and $c_{t}^{k}$ to the last subject token. The total token number is still $l$ .", + "bbox": [ + 89, + 598, + 482, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Orthogonal Value Decomposition", + "text_level": 1, + "bbox": [ + 89, + 641, + 382, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a conditional latent diffusion model trained for standard T2I generation, our proposed erasing operation works by projecting the original textual prompt onto the orthogonal complement of the subspace spanned by the target concepts to erase, and it is implemented in the value space learned at each CA layer of the UNet. It supports both single-concept and multi-concept erasure.", + "bbox": [ + 89, + 664, + 482, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We do not apply any erasing operation to [SOT], as it primarily serves as a prefix and does not carry useful information to distinguish the semantic content. We start from the modified value matrix $\\tilde{\\mathbf{V}}_t$ in Eq. (1), and use $\\tilde{\\boldsymbol{v}}_t^j$ to denote the $j$ -th column of $\\tilde{\\mathbf{V}}_t^T$ . The exclusion of [SOT] in the erasure calculation is equivalent to replacing the value vector in the first row of $\\tilde{\\mathbf{V}}_t$ by a zero vector, resulting in $\\mathbf{V}_t = \\left[0,\\tilde{\\boldsymbol{v}}_t^2,\\tilde{\\boldsymbol{v}}_t^3,\\dots,\\tilde{\\boldsymbol{v}}_t^l\\right]^T$ to use in the erasing operation.", + "bbox": [ + 89, + 771, + 482, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1. Single-concept Erasure", + "text_level": 1, + "bbox": [ + 511, + 316, + 720, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our erasing operation works with $\\mathbf{V}_t^T$ , where each column of $\\mathbf{V}_t^T$ corresponds to the erased value vector for token position $j$ and is denoted as $\\pmb{v}_t^j$ , and with the value matrix $\\mathbf{V} \\in \\mathbb{R}^{l \\times d}$ computed from the original prompt, where each column of $\\mathbf{V}^T$ is referred to as the original value vector for the token position $j$ , denoted by $\\pmb{v}^j$ . To remove the effect of the target concept from the original prompt, for each token position, we project the original value vector $\\pmb{v}^j$ onto the orthogonal complement of the span of the erased value vector $\\pmb{v}_t^j$ , and denote this orthogonal complement by $\\mathrm{span}^\\perp(\\pmb{v}_t^j)$ . This results in the following modified value vector:", + "bbox": [ + 511, + 334, + 906, + 507 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\operatorname {s p a n} ^ {\\perp} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)} \\boldsymbol {v} ^ {j} = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\operatorname {s p a n} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)}\\right) \\boldsymbol {v} ^ {j} \\tag {2} \\\\ = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j} \\boldsymbol {v} _ {t} ^ {j T}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 516, + 906, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{P}_{\\mathbb{X}}\\pmb{x}$ denotes the orthogonal projection of a vector $\\pmb{x}$ onto the space $\\mathbb{X}$ , and $\\mathbf{I}_d$ is an identity matrix of size $d$ . The modified value vector $\\pmb{v}_r^j$ is used, instead of $\\pmb{v}^j$ , to calculate the output of the CA layer, as illustrated in Fig. 2 (c). Since $\\pmb{v}_t^1 = \\mathbf{0}$ , it has $\\pmb{v}_r^1 = \\pmb{v}^1$ , meaning that no erasure is performed for [SOT].", + "bbox": [ + 511, + 589, + 905, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2. Multi-concept Erasure", + "text_level": 1, + "bbox": [ + 511, + 686, + 718, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We generalize the above operation to erase a set of $n$ target concepts, and their corresponding modified value matrices are denoted by $\\{\\mathbf{V}_t^h\\in \\mathbb{R}^{l\\times d}\\}_{h = 1}^n$ . We use $\\pmb{v}_{t}^{h,j}$ to denote the $j$ -th column of $\\left(\\mathbf{V}_t^h\\right)^T$ , referred to as the erased value vector for the $j$ -th token position of the $h$ -th target concept. Our erasing operation can naturally be extended to projecting the original prompt to the orthogonal complement of the span of the $n$ erased value vectors $\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n$ , denoted by $\\mathrm{span}^\\perp \\left(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n\\right)$ . To calculate the projection, we first conduct the Gram-Schmidt orthogonalization to obtain a set of $n$ orthonormal basis vectors $\\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h = 1}^n$", + "bbox": [ + 511, + 705, + 906, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28762", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for the span of $\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n$ . Here, we assume the value vectors in $\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n$ are linearly independent and they form a basis. Such an assumption is reasonable because the multiple concepts to erase should be semantically different in practice, otherwise, a single-concept erasure would be sufficient. The desired projection is then computed by", + "bbox": [ + 89, + 88, + 483, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {v} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} \\tag {3} \\\\ = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\text {s p a n}} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)\\right) \\boldsymbol {v} ^ {j} \\\\ = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\left(\\boldsymbol {o} _ {t} ^ {h, j}\\right) ^ {T} \\boldsymbol {v} ^ {j} \\boldsymbol {o} _ {t} ^ {h, j}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 210, + 482, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As an addition, we provide in Appendix B an alternative way to compute $\\mathbf{P}_{\\mathrm{span}^{\\perp}\\left(\\left\\{\\boldsymbol{v}_t^{h,j}\\right\\}_{h=1}^n\\right)} \\boldsymbol{v}^j$ that does not require Gram-Schmidt orthogonalization but matrix inverse.", + "bbox": [ + 89, + 316, + 483, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Adaptive Erasing Shift", + "text_level": 1, + "bbox": [ + 89, + 378, + 303, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, given a pair of textual prompts and a target concept to erase, their token-wise relevance can vary across different token positions. The different tokens of the prompt carry information with different intensities and focuses and thus can have quite different effects on image generation. As an example, we compare the generated images in each subfigure of Fig. 3, using different versions of the value matrix $\\mathbf{V}$ for the same prompt. We separate the values corresponding to the [EOT] tokens and the remaining, expressing it as $\\mathbf{V} = [\\mathbf{V}_{\\text {content }}, \\mathbf{V}_{[\\text {EOT}]}\\]$ . Herein, we include [SOT] within $\\mathbf{V}_{\\text {content }}$ for simplicity. We obtain three versions of $\\mathbf{V}$ by (1) keeping it as what it is, (2) setting $\\mathbf{V}_{[\\text {EOT}]}$ as zero, and (3) setting $\\mathbf{V}_{\\text {content }}$ as zero. Fig. 3 shows that the prompt content carries more featured information than those [EOT] tokens. This motivates us to further improve the design in Eqs. (2) and (3), by enabling adaptive adjustment of the erasing operation at the token level.", + "bbox": [ + 89, + 401, + 483, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We discover that, although a projection onto the orthogonal complement of the target concept is effective at erasing this concept itself, it can sometimes affect the prior preservation due to an excessive removal of information. Therefore, our adaptive design is focused on improving the prior preservation. When semantics carried by a prompt token are less relevant to a target token, we intend to perform less erasure to protect the prior image content. According to [32], angular information plays a more critical role in conveying semantics than magnitude during image generation. These motivate us to exploit the cosine similarity between the value vectors of a prompt token and a target token and use it to derive a shift factor to adjust the erasing strength along the identified erasing direction, which we refer to as the erasing shift. In general, we let the factor reduce when the cosine similarity becomes smaller.", + "bbox": [ + 89, + 659, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d87e906a1e21539b4d747b4682b0d70b9c016535e8172ad57e97103f95183f90.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
(1) Instance(2) Art style
A nice photo of SnoopyAn night scene in Van Gogh style
[Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]][Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]]
", + "bbox": [ + 517, + 90, + 903, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 3. We analyze the contribution of different tokens in text-visual alignment by separately masking the value of content tokens and [EOT] tokens, where content tokens carry more featured information than those [EOT] tokens.", + "bbox": [ + 511, + 186, + 906, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We denote the shift factor by $\\delta (\\cdot ,\\cdot):\\mathbb{R}^d\\times \\mathbb{R}^d\\to \\mathbb{R}$ which is a function of two value vectors. Using it, we revise the erasing operation in Eq. (2) for a single concept to", + "bbox": [ + 511, + 248, + 906, + 295 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\delta (\\boldsymbol {v} _ {t} ^ {j} , \\boldsymbol {v} ^ {j}) \\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 301, + 903, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While for multiple concepts, Eq. (3) is revised to", + "bbox": [ + 513, + 352, + 839, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\delta \\left(\\boldsymbol {v} _ {t} ^ {h, j}, \\boldsymbol {v} ^ {j}\\right) \\left(\\sum_ {k = 1} ^ {n} w _ {h k} \\left(\\boldsymbol {o} _ {t} ^ {k, j}\\right) ^ {T} \\boldsymbol {v} ^ {j}\\right) \\boldsymbol {v} _ {t} ^ {h, j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 375, + 903, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{hk}$ is the $hk$ -th element of the projection matrix that transforms the basis $\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n$ to the orthonormal basis $\\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h=1}^n$ . For a single target concept, it is straightforward to introduce the shift factor, as in Eq. (4). However, in the case of erasing multiple concepts, the derivation of a shifted operation is less straightforward, as the orthonormal basis does not carry meaningful semantics, thus a transformation back to the value vectors of the target tokens is needed. We explain in Appendix B how to derive Eq. (5) from Eq. (3). The revised erasing operations result in the proposal AdaVD.", + "bbox": [ + 511, + 428, + 905, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our shift factor design builds on the sigmoid function. Given two input vectors $\\pmb{x}, \\pmb{y} \\in \\mathbb{R}^d$ , we formulate it as", + "bbox": [ + 511, + 611, + 903, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta (\\boldsymbol {x}, \\boldsymbol {y}) = \\frac {s}{1 + e ^ {- p (\\cos (\\boldsymbol {x} , \\boldsymbol {y}) - \\epsilon)}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 648, + 903, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The cosine threshold $\\epsilon$ allows a strong erasure when exceeding the threshold. A negative cosine similarity indicates a very weak relevance between the target and prompt tokens, suggesting no erasure is required. Therefore, we set $0 < \\epsilon < 1$ to quantify and filter the relatively weak relevance indicated by a positive but small cosine similarity. The hyper-parameter $s > 0$ controls the factor scale, while $p > 0$ controls the increasing rate of the $\\delta$ value against the cosine value. In Appendix C.2, we provide hyper-parameter implementation details and a comprehensive analysis.", + "bbox": [ + 511, + 681, + 906, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Result Analysis", + "text_level": 1, + "bbox": [ + 511, + 844, + 815, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct extensive experiments to evaluate the proposed AdaVD for erasing a diverse range of target concepts, cov", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28763", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ering specific instances, art styles, NSFW content, and celebrity. We compare with SOTA training-based methods including ConAbl [20], ESD [12], SPM [27] and MACE [26] and SOTA training-free methods including NP [2] and SLD [39]. We also demonstrate the time efficiency and interpretability of AdaVD, along with its wider usage in other downstream image generation tasks coupled with a series of diffusion models.", + "bbox": [ + 89, + 90, + 480, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 217, + 279, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation: We employ SD v1.4 [2] to generate images using the DPM-solver sampler [25] over 30 sampling steps with classifier-free guidance [17] of 7.5. All the compared methods are implemented following their default configurations available from their official repository. Further implementation details are provided in Appendix C.1.", + "bbox": [ + 89, + 238, + 482, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Data: Adopting the same evaluation protocol from SPM [27], we assess the methods based on 80 instance templates, 30 art style templates, and 25 celebrity templates, and benchmark each method by generating 10 images per template per concept in evaluation. To assess the performance of NSFW erasure, we use the I2P benchmark [39].", + "bbox": [ + 89, + 330, + 482, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance Metrics: We follow the widely used evaluation metrics for concept erasure, including the CLIP score (CS) [33] to assess erasure efficacy and the Fréchet inception distance (FID) [16] to assess prior preservation. CS calculates the cosine similarity between a textual prompt and the generated image [33]. We examine two CS values before and after erasing and compare the CS value after the erasure. When the prompts contain the target concepts, a more reduced CS indicates a more effective erasure of the target concepts. FID measures the distance between images generated before and after erasing [16]. A lower FID indicates a better alignment between the two images. Thus, for non-target concepts, lower FID values indicate better prior preservation. Overall, a precise concept erasure should have a low CS for prompts containing the target concepts and a low FID for prompts composed of non-target concepts.", + "bbox": [ + 89, + 420, + 482, + 661 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Summary: Results on instance and art style concept erasure are reported in Sections 4.2 and 4.3, while results on celebrity and NSFW erasure are reported in Appendices D.3 and D.2. Additional analyses, including extended quantitative results, comparisons with SuppressEOT [24], performance on different versions of SD, and further discussions, are presented in the Appendix.", + "bbox": [ + 89, + 662, + 482, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. On Instance Concept Erasure", + "text_level": 1, + "bbox": [ + 89, + 773, + 354, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first conduct the experiment with erasing a single concept \"Snoopy\". Six types of prompts were tested, of which one contains \"Snoopy\" and the other five contain only nontarget concepts. The results are compared in the top block of Table 1. It can be seen that our proposed AdaVD achieves the lowest CS and FID scores in all cases. Particularly, its FID is $33\\%$ lower than that of the second-best method. It", + "bbox": [ + 89, + 794, + 482, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/70b3bc140c0c1c94223a3607294363f8784805ecc9102b574e269c37592db714.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ConceptSnoopyMickeySpongebobPikachuDogLegislator
CSCSCSCSCSCS
SD v1.428.5126.5727.43---
", + "bbox": [ + 514, + 88, + 901, + 130 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2f4d0f304e9ab896dc21454f8f312d365c6d1b68845532cf0b641312b2cf5601.jpg", + "table_caption": [ + "Erase Snoopy" + ], + "table_footnote": [], + "table_body": "
CS ↓FID ↓FID ↓FID ↓FID ↓FID ↓
ConAbl25.3838.4441.5929.6827.7627.36
MACE20.78118.01111.9081.9943.2765.97
SPM23.8933.0634.7023.8919.6118.26
NP23.6659.5878.7452.3767.5155.22
SLD27.8448.1255.3638.7441.9549.08
Ours20.285.728.565.792.326.07
", + "bbox": [ + 516, + 141, + 901, + 232 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0b1f1c7ac4eca739d6e7c08441a0c5b17612b623a87aa5e04307d4a311c6867d.jpg", + "table_caption": [ + "Erase Snoopy and Mickey" + ], + "table_footnote": [], + "table_body": "
CS ↓CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl24.2624.0846.3239.6330.5727.49
MACE20.7420.7151.49110.6752.0777.13
SPM23.1622.8141.5831.7721.9623.69
NP23.5924.8581.4150.1065.9358.88
SLD27.7626.7454.5939.2441.6250.13
Ours20.2919.939.345.842.416.43
", + "bbox": [ + 516, + 243, + 901, + 335 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/78864e8502d76fa9adf302a6b0ee6667a584f2d3d07383aae22f0f1c8805d814.jpg", + "table_caption": [ + "Erase Snoopy and Mickey and Spongebob" + ], + "table_footnote": [], + "table_body": "
CS ↓CS ↓CS ↓FID ↓FID ↓FID ↓
ConAb123.9423.6425.0451.2031.5930.03
MACE20.4820.5021.5999.6847.4670.38
SPM22.8122.3520.8239.8322.6825.31
NP24.2924.7625.3164.7565.1059.33
SLD27.8426.7127.6039.4142.3249.88
Ours19.3919.7320.346.852.797.26
", + "bbox": [ + 516, + 347, + 901, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of single- and multi-instance erasure. The best and second-best results are marked in bold and underlined, respectively. Our AdaVD consistently achieves the lowest CS and the lowest FID in all cases, indicating superior prior preservation without compromising erasure efficacy.", + "bbox": [ + 511, + 444, + 903, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "improves over SOTA by significantly enhanced prior preservation without compromising the erasure precision, as exemplified in Fig. 4. It can be observed from Fig. 4 that methods such as SPM, NP, and SLD fail to fully erase \"Snoopy\" which can be found from the ear and the shape characteristic of the generated image after erasure. MACE can successfully erase the \"Snoopy\" concept. But all the competing methods suffer from degraded image quality in non-target concept generation, e.g., \"Spongebob\".", + "bbox": [ + 511, + 523, + 903, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then compare the performance for multi-concept erasure, experimenting with two cases, of which one erases two concepts of \"Snoopy\" and \"Mickey\" together and the other erases three concepts of \"Snoopy\", \"Mickey\" and \"Spongebob\" together. Results are reported in the bottom two blocks of Table 1 and visualized in the second and third sections of Fig. 4. Similarly, our AdaVD achieves the lowest CS and FID scores across all cases. This verifies that AdaVD is capable of handling more complex multi-concept erasure and simultaneously fighting against catastrophic forgetting. Conversely, other methods struggle to consistently perform well for multi-concept erasure. For example, when erasing \"Snoopy\" and \"Mickey\" together, the image quality for non-target concepts like \"Spongebob\" and \"Legislator\" shows apparent degradation in Fig. 4. SLD, in particular, fails to maintain its erasure ability even", + "bbox": [ + 511, + 659, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28764", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/981afa5437dd2d868a4b8b3d7b447bbad39ba2abe30385b94855e975bc03c8e8.jpg", + "image_caption": [ + "Concepts", + "Figure 4. Qualitative comparison of single- and multi-instance erasure. Both training-based and training-free methods show limitations in prior preservation. In contrast, our AdaVD demonstrates considerable performance in maintaining prior knowledge without compromising erasure efficacy across both single- and multi-concept erasure tasks." + ], + "image_footnote": [], + "bbox": [ + 96, + 109, + 400, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75a06f1f2167ad016df0c89dd9fac0f340016b5236785945d884a965e9608427.jpg", + "image_caption": [ + "Snoopy, Miekey, Spongebob, Dog, Legislator" + ], + "image_footnote": [], + "bbox": [ + 413, + 116, + 650, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a909be6fd1116f13c631dd30380ed0f04cc1411ee17fc66325b1dcd593323cc3.jpg", + "image_caption": [ + "Snoopy, Mickey, Spongebob, Dog, Legislator" + ], + "image_footnote": [], + "bbox": [ + 663, + 116, + 898, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3be4de8fc996c55eaf22558d95bf67bb080e91b951ad1ddf537739e6c7215883.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of art style erasure. Our AdaVD can effectively remove the target concept \"Van Gogh\" while preserving non-target styles like \"Picasso\" and \"Monet\"." + ], + "image_footnote": [], + "bbox": [ + 93, + 377, + 480, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "when dealing with 2-concept erasure. In Appendix G, we report more experimental results for erasing up to 40 concepts, where our AdaVD can extend to erase dozens of concepts in practice, maintaining consistent erasure efficacy and prior preservation, as shown in Fig. 1.", + "bbox": [ + 89, + 566, + 483, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. On Art Style Erasure", + "text_level": 1, + "bbox": [ + 89, + 650, + 290, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We experiment with erasing specific art style, including \"Van Gogh\", \"Picasso\" and \"Monet\". Results are reported in Table 2, and visual comparisons are provided in Fig. 5. Our AdaVD exhibits superior prior preservation, and achieves the lowest or closed-to-lowest CS and FID scores, demonstrating strong prior preservation without sacrificing erasure efficacy. Other methods show different drawbacks as observed from the results. For instance, although NP achieves notably better precision in art style removal as compared to instance removal, Fig. 5 shows that it still struggles to fully erase the \"Van Gogh\" style. Also, SLD fails to erase the \"Van Gogh\" style. These two methods also degrade generation quality for non-target styles, such as \"Picasso\" and \"Monet\", showing harmful effects on non-target concepts directly, as evidenced in both Fig. 5 and", + "bbox": [ + 89, + 674, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7084dff46ee1614088623e3acfcafc92737aaa8773952b6716adf77c7c62fba9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ConceptVan GoghPicassoMonetAndy WarholCaravaggio
CSCSCSCSCS
SD v1.429.2129.0629.02--
", + "bbox": [ + 514, + 375, + 903, + 417 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6f91548e04707919764abd086294c7dfc5c0b74485eba2af0d8986a5e148f52f.jpg", + "table_caption": [ + "Erase Van Gogh" + ], + "table_footnote": [], + "table_body": "
CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl28.8071.71138.7270.3073.10
MACE27.7465.7769.7983.3775.41
SPM24.7862.2532.2758.3061.50
NP24.90141.56124.52127.85136.32
SLD27.48103.96109.11103.89119.32
Ours24.876.822.668.366.84
", + "bbox": [ + 514, + 429, + 903, + 522 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/21449d38c5d27030a32b66155c30392f20cba17e282d68a110e786e7c4b1c262.jpg", + "table_caption": [ + "Erase Picasso" + ], + "table_footnote": [], + "table_body": "
FID ↓CS ↓FID ↓FID ↓FID ↓
ConAbl58.6227.72140.3473.3567.44
MACE60.4627.1149.9276.1072.85
SPM38.7926.697.7652.0051.40
NP111.3526.1491.11116.24121.82
SLD98.2127.0393.0197.00110.05
Ours5.4926.992.339.387.05
", + "bbox": [ + 514, + 532, + 903, + 627 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f5d995e1ad4d7caed3d5e16af15ae439534e19b3b7452a5c29a0c47fada1931b.jpg", + "table_caption": [ + "Erase Monet" + ], + "table_footnote": [], + "table_body": "
FID ↓FID ↓CS ↓FID ↓FID ↓
ConAbl141.52132.1024.53208.38186.26
MACE76.9069.3526.8988.3581.72
SPM41.0329.7127.0031.9025.99
NP137.21126.7524.47127.22135.83
SLD94.4892.8825.73100.90114.87
Ours6.946.5026.308.467.19
", + "bbox": [ + 514, + 638, + 903, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison of art style erasure. AdaVD achieves a superior balance between erasure efficacy and prior preservation, especially excelling in prior preservation.", + "bbox": [ + 511, + 738, + 906, + 780 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Both MACE and SPM are effective in erasing the target concept, however, their prior preservation is somehow less satisfactory, which is particularly noticeable in the generated images in \"Monet\" style. Differently, AdaVD can effectively and consistently remove the target concept and meanwhile preserve satisfactorily the prior content, as confirmed by Table 2 and Fig. 5.", + "bbox": [ + 511, + 795, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28765", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6d2c8c4fe4c078aac0018bd1ef87ac4932ab5e7add486311b7d915be8582038f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Data PreparationModel FinetuneImage GenerationTotal Time
ConAbl929011200.910419
SPM0728501.772867
MACE3032320.9544
SLD001.414
Ours401.822
", + "bbox": [ + 94, + 88, + 478, + 183 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Time consumption of 10-concept erasure. We calculate the time cost (s) to erase 10 concepts and generate 10 images using one NVIDIA A40 GPU. Compared with training-based methods, AdaVD exhibits exceptional efficiency in real-time erasure.", + "bbox": [ + 89, + 188, + 482, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Further Analysis", + "text_level": 1, + "bbox": [ + 89, + 253, + 256, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Time Consumption: The computational cost of concept erasure primarily arises from three components, including (1) data preparation time required by training-based methods for preparing training data and by AdaVD for basis computation; (2) model fine-tuning time required by training-based methods; and (3) image generation time required by all methods. In Table 3, we compare the total time consumption of different methods, as well as their time spent on each component. The two training-free methods of SLD and AdaVD are significantly faster as no fine-tuning is needed. Our AdaVD costs slightly more time than SLD, i.e., 0.8 extra seconds per image due to its basis computation, and a total of 8 extra seconds for generating 10 images. But this mild increase yields a significant performance gain, succeeding in precise concept erasure.", + "bbox": [ + 88, + 277, + 482, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interpreting Erased Components by Visualization: Our AdaVD generates images by replacing the original value vector $\\pmb{v}^j$ with $\\pmb{v}_r^j$ via orthogonal complement operation. To empirically interpret the rationale behind our method, we visualize the erased component, $\\pmb{v}^j - \\pmb{v}_r^j$ . Fig. 6 presents three cases of erasing the target concepts \"Mickey\", \"Van Gogh\" and \"Bruce Lee\", where AdaVD successfully erases these target concepts while robustly preserving prior knowledge of non-target concepts. In the first row, as shown in the middle column of each block, the erased components consistently align with the corresponding target semantics when dealing with the target concepts. In the second row of non-target concepts, conversely, the erased components do not contain any informative pattern, indicating that they carry no meaningful semantics, and therefore exert minimal impact on the prior knowledge.", + "bbox": [ + 89, + 506, + 482, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Downstream Applications: We conduct additional experiments to showcase the versatile applications of our AdaVD across various generative tasks, including (1) implicit concept erasure: by removing the implicit concepts of \"rainy\" and \"foggy\"; (2) image editing: by removing the appearance concepts of \"glasses\" and \"mustache\"; and (3) attribute suppression: by removing the coupled color concept of \"red\". Additionally, we integrate AdaVD with a series of diffusion models, including Chilloutmix [5], DreamShaper [6], RealisticVision [7], and SD v2.1 [4], alongside SD", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3346c4cac0a6e6af7b4a49634547ff2ee55c92f9821d5381aba83ce134a97e3.jpg", + "image_caption": [ + "Figure 6. Visualization of erased components. In each block, we compare both target (1st row) and non-target concept (2nd row) by visualizing the original image (1st column), erased component (2nd column), and generation by our AdaVD (3rd column)." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 903, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51eaea3c18fd219431b9ecaf1f0b969ee652f7282c56a080a4dbcf9aa308259e.jpg", + "image_caption": [ + "Figure 7. Downstream applications. We extend AdaVD to versatile generation tasks, including (1) implicit concept erasure, (2) image editing, and (3) attribute suppression, indicating its significant potential for broad applications." + ], + "image_footnote": [], + "bbox": [ + 517, + 250, + 903, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "v1.4. As illustrated in Fig. 7, despite the absence of explicit mention for \"rainy\" and \"foggy\", AdaVD can still effectively erase these concepts in image semantic space. Meanwhile, AdaVD also precisely removes \"glasses\" and \"mustache\" with minimal changes to other details, highlighting its potential in image editing applications. For attribute suppression, AdaVD successfully eliminates the color attribute \"red\" from objects such as apples and roses, demonstrating its capability to decouple strongly coupled concepts, e.g., \"roses are red\" embedded in the model's prior knowledge.", + "bbox": [ + 511, + 465, + 906, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 511, + 623, + 782, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented AdaVD, a precise, fast, and low-cost method for erasing unwanted concepts. The idea of leveraging the classical linear algebraic orthogonal complement operation and an adaptive erasing shift design is novel, and has successfully achieved a precise concept erasure. Extensive experiments have demonstrated both high erasure efficacy and strong prior preservation of AdaVD for both single- and multi-concept erasure. Moreover, AdaVD exhibits excellent interpretability through visualizing its erased components and strong capability in solving downstream tasks. It has been an intriguing discovery that the orthogonal complement of the value vectors of the target concepts is effective at erasing their inherent semantics. Despite the empirical success, we will seek to establish a rigorous theoretical understanding of the accumulative effect of applying this linear algebraic operation layer-wise for concept erasure in the future.", + "bbox": [ + 511, + 643, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28766", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 259, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the National Science and Technology Major Project (2023ZD0121102) and the National Natural Science Foundation of China (U24B20180).", + "bbox": [ + 89, + 114, + 485, + 160 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 174, + 187, + 191 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Safety checker nested in stable diffusion. https://huggingface.co/CompVis/stable-diffusion-safety-checker, 2022.2", + "[2] Stable diffusion. https://huggingface.co/ CompVis/stable-diffusion-v1-4, 2022.2,3,6", + "[3] Stable diffusion v2.0. https://huggingface.co/stabilityai/stable-diffusion-2, 2022.2", + "[4] Stable diffusion v2.1. https://huggingface.co/stabilityai/stable-diffusion-2-1, 2022.8", + "[5] Chilloutmix. https://huggingface.co/swl-models/chilloutmix, 2023.1,8,18", + "[6] Dreamshaper. https://huggingface.co/Lykon/DreamShaper, 2023.1,8,18,22", + "[7] Realisticvision. https://huggingface.co/SG161222/Realistic_Vision_V5.1_noVAE, 2023.8,18,22", + "[8] Praneeth Bedapudi. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023. 2" + ], + "bbox": [ + 516, + 92, + 903, + 727 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28768", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Precise, Fast, and Low-cost Concept Erasure in Value Space_ Orthogonal Complement Matters/cf17c55d-6d37-44b9-b018-ae4df3534d26_model.json b/2025/Precise, Fast, and Low-cost Concept Erasure in Value Space_ Orthogonal Complement Matters/cf17c55d-6d37-44b9-b018-ae4df3534d26_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b93df5b715c8fc0ea1d8aff17862b85e70cd8d44 --- /dev/null +++ b/2025/Precise, Fast, and Low-cost Concept Erasure in Value Space_ Orthogonal Complement Matters/cf17c55d-6d37-44b9-b018-ae4df3534d26_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.194, + 0.131, + 0.804, + 0.177 + ], + "angle": 0, + "content": "Precise, Fast, and Low-cost Concept Erasure in Value Space: Orthogonal Complement Matters" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.203, + 0.898, + 0.223 + ], + "angle": 0, + "content": "Yuan Wang\\(^{1*}\\), Ouxiang Li\\(^{1*}\\), Tingting Mu\\(^{2}\\), Yanbin Hao\\(^{3\\dagger}\\), Kuien Liu\\(^{4}\\), Xiang Wang\\(^{1}\\), Xiangnan He\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.224, + 0.74, + 0.239 + ], + "angle": 0, + "content": "1University of Science and Technology of China, 2The University of Manchester," + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.241, + 0.757, + 0.256 + ], + "angle": 0, + "content": "\\(^{3}\\)Hefei University of Technology, \\(^{4}\\) Institute of Software Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.26, + 0.837, + 0.275 + ], + "angle": 0, + "content": "{wy1001, lioox}@mail.ustc.edu.cn, haoyanbin@hotmail.com, xiangnanhe@gmail.com" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.285, + 0.589, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.552, + 0.471, + 0.565 + ], + "angle": 0, + "content": "(a) Erasure Efficacy and Prior Preservation" + }, + { + "type": "image", + "bbox": [ + 0.59, + 0.286, + 0.905, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.693, + 0.552, + 0.802, + 0.566 + ], + "angle": 0, + "content": "(b) Transferability" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.568, + 0.907, + 0.64 + ], + "angle": 0, + "content": "Figure 1. The proposed Adaptive Value Decomposer (AdaVD) demonstrates a satisfactory balance between erasure efficacy and prior preservation and an effective transferability across T2I diffusion models. (a) Compared to SLD [39], AdaVD enables precise concept erasure without compromising prior knowledge for non-target concepts at both single- and multi-concept erasure. This is facilitated by a precise disentanglement of target semantics (e.g., \"Snoopy\") and a robust preservation of non-target ones (e.g., \"Teddy\"), with visualization interpretation marked by \\(\\diamond\\). (b) AdaVD can be transferred to various T2I models, e.g., SDXL [31], DreamShaper [6], Chilloutmix [5]." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.648, + 0.327, + 0.664 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.669, + 0.486, + 0.866 + ], + "angle": 0, + "content": "Recent success of text-to-image (T2I) generation and its increasing practical applications, enabled by diffusion models, require urgent consideration of erasing unwanted concepts, e.g., copyrighted, offensive, and unsafe ones, from the pre-trained models in a precise, timely, and low-cost manner. The twofold demand of concept erasure includes not only a precise removal of the target concept (i.e., erasure efficacy) but also a minimal change on non-target content (i.e., prior preservation), during generation. Existing methods face challenges in maintaining an effective balance between erasure efficacy and prior preservation, and they can be computationally costly. To improve, we propose a precise, fast, and low-cost concept era" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.65, + 0.909, + 0.892 + ], + "angle": 0, + "content": "sure method, called Adaptive Vaule Decomposer (AdaVD), which is training-free. Our method is grounded in a classical linear algebraic operation of computing orthogonal complement, implemented in the value space of each cross-attention layer within the UNet of diffusion models. We design a shift factor to adaptively navigate the erasure strength, enhancing effectively prior preservation without sacrificing erasure efficacy. Extensive comparative experiments with both training-based and training-free state of the arts demonstrate that the proposed AdaVD excels in both single and multiple concept erasure, showing 2 to 10 times of improvement in prior preservation than the second best, meanwhile achieving the best or near best erasure efficacy. AdaVD supports a series of diffusion models and downstream image generation tasks, with code available on: https://github.com/WYuan1001/AdaVD." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.228, + 0.888 + ], + "angle": 0, + "content": "*Equal Contributions." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.242, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.242, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "28759" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.223, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.482, + 0.341 + ], + "angle": 0, + "content": "The recent advancements of text-to-image (T2I) diffusion models [11, 17, 18, 30, 36, 50, 52] have enabled users to effortlessly generate high-quality images with simple textual prompts. However, such generations would inevitably introduce copyrighted [10, 22, 42, 44] or offensive [23, 39] concepts, caused by the noisy training data scraped from web [9, 40]. Because it is very costly to re-train large generative models from scratch, it is vital to develop low-cost techniques to precisely erase unwanted semantic concepts in images, i.e., concept erasure. This task aims at a precise erasure of visual content w.r.t. target concepts from generated images (i.e., erasure efficacy), while a faithful preservation of irrelevant content w.r.t. the prompts comprising non-target concepts (i.e., prior preservation), safeguarding a secure T2I generation for diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.343, + 0.483, + 0.569 + ], + "angle": 0, + "content": "A representative category of concept erasure methods is training-based, which fine-tunes a subset of model parameters by formulating meticulous erasing objective functions [12, 20, 26, 27]. Despite good erasure efficacy, they exhibit considerable practical limitations when being deployed. For instance, they require expensive individual fine-tuning to erase each concept, which thereby limits their real-time usage. As an example, it is unacceptable for online T2I platforms to be costly to erase newly emerging concepts, where copyrighted or offensive concepts could arise unexpectedly, with no means to produce a complete list of concepts to erase in advance. Moreover, these methods suffer from a limited balance between erasure efficacy and prior preservation, due to their reliance on regularization terms to trade off prior preservation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.483, + 0.825 + ], + "angle": 0, + "content": "An alternative category of concept erasure methods is training-free, such as Negative Prompt (NP) [2], Safe Latent Diffusion (SLD) [39], and SuppressEOT [24], which enable real-time erasure. They intervene in the image generation process, exhibiting a range of drawbacks. For instance, NP was initially designed to enhance image quality and can result in compromised erasure efficacy; while SuppressEOT requires the user to specify the location of the target concept within the prompt, thus, it is not suitable for erasure applications that require full automation. Therefore, both NP and SuppressEOT fall short as independent tools for concept erasure. Regarding SLD, it does not perform well at retaining prior knowledge of non-target concepts as illustrated in Fig. 1, failing in precise concept erasure. Limited by their drawbacks, current training-free methods are not robust enough to act as an independent concept erasure tool and to be applied in continual erasure of multiple concepts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.902 + ], + "angle": 0, + "content": "In this light, we advance concept erasure techniques for T2I generation, by developing a precise, fast, and low-cost method called Adaptive Value Decomposer (AdaVD). It is a training-free method, capable of precisely erasing the target concepts and satisfactorily preserving non-target priors" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.303 + ], + "angle": 0, + "content": "with low computational overhead. Our core design builds on a classical linear algebraic operation, i.e., projection onto the orthogonal complement of the semantic space of the target concepts. We conduct this projection-based decomposition in the cross-attention value space, disentangling target semantics from the original prompts. To improve the erasure precision and prior preservation, we further refine the decomposition by adaptively allocating token-wise shifts. These shifts are designed to differentiate the strong and specific alignments from the weak and general alignments between prompt tokens and visual content associated with the target concept. Guided by these shifts, the strong and specific alignments are erased for precision while the weak and general alignments are retained for prior preservation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.304, + 0.905, + 0.454 + ], + "angle": 0, + "content": "Fig. 1 (a) demonstrates the erased results for both target and non-target concepts. It shows that our AdaVD can precisely locate and erase the components indicated by the target semantics, meanwhile keeping the non-target priors maximally unaffected. Empirical evaluation shows that AdaVD excels in prior preservation, outperforming the second best by a 2- to 10-fold improvement across various nontarget concepts, and meanwhile maintains exceptional erasure efficacy, consistently achieving the best or near-best performance. Our contributions are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.455, + 0.905, + 0.514 + ], + "angle": 0, + "content": "- A novel and effective erasing operation by exploiting the projection onto the orthogonal complement of the target concept in the cross-attention value space, to disentangle semantics carried by the target concept." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.515, + 0.905, + 0.559 + ], + "angle": 0, + "content": "- An adaptive erasing mechanism through a dynamic shift factor, which can effectively minimize the impact on prior knowledge, without compromising the erasure efficacy." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.561, + 0.905, + 0.619 + ], + "angle": 0, + "content": "- A precise, fast, and low-cost concept erasure technique AdaVD, which works in a training-free manner and supports a series of T2I diffusion models, capable of precise concept erasure." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.62, + 0.905, + 0.68 + ], + "angle": 0, + "content": "- Extensive experiments that demonstrate the superiority of AdaVA against state-of-the-art (SOTA) methods, achieving 2 to 10 times of improvement in prior preservation while maintaining precise erasure efficacy." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.455, + 0.905, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.694, + 0.664, + 0.71 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Re-training and Blocking: The most straightforward way to erase a target concept from a pre-trained T2I model is to exclude the training data relevant to this concept and retrain the model from scratch, as in Stable Diffusion (SD) v2.0 [3]. For this, an Not Safe For Work (NSFW) detector [8, 21, 38] can be used to filter unsafe data from LAION-5B [41] prior to the training. However, this approach is time-consuming, requires specialized detectors, and can introduce biases [43]. An alternative solution is to block the prompts of concerns and restrict the outputs of concerns, by using filters [43] and safety checkers [1, 35]. Yet, such safeguards are fragile and easy to bypass [46, 49], especially" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28760" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.333 + ], + "angle": 0, + "content": "when being confronted with crafted malicious prompts [39]. Training-based: A more effective group of concept erasure solutions fine-tune pre-trained generative models, teaching them to \"forget\" a target concept, e.g., Erased Stable Diffusion (ESD) [12]. However, since the ESD design does not consider prior preservation, both target and non-target concepts are adversely affected. To improve, new training techniques have been developed, e.g., ConAbl [20], SA [14], UCE [13], EraseDiff [48], SPM [27] and MACE [26]. They improve prior preservation through regularization but still fall short in achieving both precise erasure and robust prior preservation. Moreover, for every new target concept to be erased, a separate fine-tuning is required. This is time-consuming, making real-time erasure impractical, especially for highly interactive platforms where unsafe or inappropriate concepts can emerge unexpectedly." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.334, + 0.485, + 0.697 + ], + "angle": 0, + "content": "Training-free: With largely reduced computing costs, training-free methods are gaining increasing attention. NP [2] and SLD [39] pioneer training-free concept erasure by adjusting classifier-free guidance [17], leading the generation towards a direction away from the target concepts. However, NP lacks fine-grained control over target concepts and compromises prior preservation. SLD also compromises the prior knowledge during its generation, disrupting the overall generating quality of non-target concepts. SuppressEOT [24], akin to image editing techniques [15], removes target concepts based on user-specified textual positions. Its user-involved design makes it more suitable for editing tasks, but not for system-wide erasing tasks that require full automation. Benefiting from orthogonal decompositions in value spaces, the proposed training-free method AdaVD achieves not only precise concept erasure but also satisfactory prior preservation. It supports multi-concept erasure, is compatible across different versions of stable diffusion, and consistently demonstrates superior performance. The training-free method SAFREE [51], concurrent to ours, also uses orthogonal decomposition but operates differently on text embeddings, supported by masking, projection, Fourier transforms, and a hard control of removal strength. We compare performance with it in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.182, + 0.725 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Concept erasure in T2I generation aims at a successful removal of the visual content indicated by textual concepts (i.e., target concepts), meanwhile a satisfactory preservation of the visual content irrelevant to these concepts (i.e., prior knowledge). It is challenging to achieve simultaneously satisfactory erasure efficacy and prior preservation. To advance this field, we propose a precise, fast, and low-cost concept erasure method, termed AdaVD and illustrated in Fig. 2 (c). The method is training-free, and its core design builds on a classical linear algebraic operation, i.e., orthogonal complement. This simple but elegant geometric" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "operation is able to guide effectively the image generation, enabling a precise removal of the target concepts from the image content meanwhile a satisfactory preservation of the non-target content." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.162, + 0.835, + 0.178 + ], + "angle": 0, + "content": "3.1. Preliminary on T2I Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.184, + 0.905, + 0.32 + ], + "angle": 0, + "content": "Current T2I models usually include an image compression network [19] and a conditional latent diffusion model [36] that performs sequential denoising with a UNet [37] in the latent space. The UNet takes as inputs the noise latent variable \\(\\mathbf{z}_t\\), timestep \\(t\\), and embedding \\(\\mathbf{C}\\) of the textual prompt from a pre-trained CLIP model [33], and predicts the noise \\(\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C})\\). In training-free concept erasure, the noise is additionally conditioned on the target concept with text embedding \\(\\mathbf{C}_t\\), predicted by \\(\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C}, \\mathbf{C}_t)\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.32, + 0.905, + 0.477 + ], + "angle": 0, + "content": "Interactions between the image and text modalities are enabled by cross-attention (CA) layers [36, 47] within the UNet, which align the latent representation of the noisy image with the semantic detail of the textual prompt. Each CA layer computes an attention map \\(\\mathbf{A} = \\mathrm{softmax}\\left(\\frac{\\mathbf{Q}\\mathbf{K}^T}{\\sqrt{d}}\\right)\\) with a latent feature dimension \\(d\\). The queries \\(\\mathbf{Q}\\) are computed from the noisy image features, while both keys \\(\\mathbf{K}\\) and values \\(\\mathbf{V}\\) from the text embeddings \\(\\mathbf{C}\\), using different projection matrices. The layer output is a weighted aggregation of \\(\\mathbf{A}\\) and \\(\\mathbf{V}\\). More details on CA layers are in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.906, + 0.675 + ], + "angle": 0, + "content": "It has been recognized that the keys in CA layers mostly act as the \"Where\" pathway, governing the layout of the attention map and determining the compositional structure of the generated images, while the values as the \"What\" pathway, controlling the content and visual appearance of images [45]. Because the goal of concept erasure is to modify the visual content of the generated images, we propose to conduct value decompositions into subspaces, which are uniquely constructed by exploiting the target concept and its orthogonal complement in an adaptive fashion. We demonstrate that information offered by the orthogonal complement can be used to generate successfully high-quality images with the target concept precisely erased." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.683, + 0.902, + 0.699 + ], + "angle": 0, + "content": "3.2. Token-wise Target Embedding Pre-processing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.905, + 0.81 + ], + "angle": 0, + "content": "Given a textual example, which can be either a target concept to erase or an original prompt, its embedding is computed at the token level by a CLIP text encoder. Each tokenized example is padded with [SOT] as the prefix and [EOT] at the end, with [EOT] filling any remaining positions to maintain a fixed token length of \\( l \\). Each token is characterized by an embedding vector of dimension \\( D_{c} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.905, + 0.901 + ], + "angle": 0, + "content": "We focus on the embedding of a target concept \\(\\mathbf{C}_t\\in\\) \\(\\mathbb{R}^{l\\times D_c}\\) , and denote each column of \\(\\mathbf{C}_t^T\\) by \\(c_{t}^{j}\\) that corresponds to a token vector where \\(j\\in \\{1,2,\\dots ,l\\}\\) . To facilitate a precise erasure, we emphasize the key information carried by a target concept by proposing an embedding duplication. Specifically, the embedding of the last sub" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28761" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.079, + 0.904, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.236, + 0.907, + 0.309 + ], + "angle": 0, + "content": "Figure 2. Overview of our Adaptive Value Decomposer (AdaVD) in erasing the target concept \"Snoopy\". (a) First, we token-wisely duplicate the last subject token of the target embedding encoded by the text encoder, except for [SOT]. (b) Then, the pre-processed target embedding and corresponding prompt embedding are jointly fed into CA layers within the UNet as conditions, to disentangle target semantics from the original image at each timestep. (c) In each CA layer, we perform token-wise orthogonal value decomposition with an adaptive token-wise shift. The new value is subsequently multiplied by the attention map, producing the erased output for this CA layer." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.317, + 0.486, + 0.514 + ], + "angle": 0, + "content": "ject token within its prompt content excluding [SOT] and [EOT], replaces all the token positions except for [SOT], as illustrated in Fig. 2 (a). For instance, the single-token concept \"snoopy\" has a modified embedding matrix corresponding to \"[SOT], snoopy, snoopy, ..., snoopy\", while the multi-token concept \"Van Gogh\" to \"[SOT], gogh, gogh, ..., gogh\". Benefiting from the causal attention mechanism used by the CLIP text encoder, the last subject token is able to \"see\" all the prompt content and contains key information [28], therefore is sufficient for erasure calculation. The modified embedding matrix \\(\\tilde{\\mathbf{C}}_t\\) is fed into a CA layer to compute the value matrix \\(\\tilde{\\mathbf{V}}_t \\in \\mathbb{R}^{l \\times d}\\) via a linear projection using the projection matrix \\(\\mathbf{W}_{\\mathrm{V}} \\in \\mathbb{R}^{D_c \\times d}\\), as" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.525, + 0.483, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {V}} _ {t} = \\tilde {\\mathbf {C}} _ {t} \\mathbf {W} _ {\\mathrm {V}} = \\left[ c _ {t} ^ {1}, \\underbrace {c _ {t} ^ {k} , \\dots , c _ {t} ^ {k}} _ {l - 1} \\right] ^ {T} \\mathbf {W} _ {\\mathrm {V}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.63 + ], + "angle": 0, + "content": "The token vector \\( c_{t}^{1} \\) corresponds to [SOT] and \\( c_{t}^{k} \\) to the last subject token. The total token number is still \\( l \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.642, + 0.383, + 0.659 + ], + "angle": 0, + "content": "3.3. Orthogonal Value Decomposition" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.665, + 0.483, + 0.771 + ], + "angle": 0, + "content": "Given a conditional latent diffusion model trained for standard T2I generation, our proposed erasing operation works by projecting the original textual prompt onto the orthogonal complement of the subspace spanned by the target concepts to erase, and it is implemented in the value space learned at each CA layer of the UNet. It supports both single-concept and multi-concept erasure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.772, + 0.483, + 0.906 + ], + "angle": 0, + "content": "We do not apply any erasing operation to [SOT], as it primarily serves as a prefix and does not carry useful information to distinguish the semantic content. We start from the modified value matrix \\(\\tilde{\\mathbf{V}}_t\\) in Eq. (1), and use \\(\\tilde{\\boldsymbol{v}}_t^j\\) to denote the \\(j\\)-th column of \\(\\tilde{\\mathbf{V}}_t^T\\). The exclusion of [SOT] in the erasure calculation is equivalent to replacing the value vector in the first row of \\(\\tilde{\\mathbf{V}}_t\\) by a zero vector, resulting in \\(\\mathbf{V}_t = \\left[0,\\tilde{\\boldsymbol{v}}_t^2,\\tilde{\\boldsymbol{v}}_t^3,\\dots,\\tilde{\\boldsymbol{v}}_t^l\\right]^T\\) to use in the erasing operation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.317, + 0.722, + 0.332 + ], + "angle": 0, + "content": "3.3.1. Single-concept Erasure" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.335, + 0.907, + 0.508 + ], + "angle": 0, + "content": "Our erasing operation works with \\(\\mathbf{V}_t^T\\), where each column of \\(\\mathbf{V}_t^T\\) corresponds to the erased value vector for token position \\(j\\) and is denoted as \\(\\pmb{v}_t^j\\), and with the value matrix \\(\\mathbf{V} \\in \\mathbb{R}^{l \\times d}\\) computed from the original prompt, where each column of \\(\\mathbf{V}^T\\) is referred to as the original value vector for the token position \\(j\\), denoted by \\(\\pmb{v}^j\\). To remove the effect of the target concept from the original prompt, for each token position, we project the original value vector \\(\\pmb{v}^j\\) onto the orthogonal complement of the span of the erased value vector \\(\\pmb{v}_t^j\\), and denote this orthogonal complement by \\(\\mathrm{span}^\\perp(\\pmb{v}_t^j)\\). This results in the following modified value vector:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.517, + 0.907, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\operatorname {s p a n} ^ {\\perp} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)} \\boldsymbol {v} ^ {j} = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\operatorname {s p a n} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)}\\right) \\boldsymbol {v} ^ {j} \\tag {2} \\\\ = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j} \\boldsymbol {v} _ {t} ^ {j T}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.906, + 0.68 + ], + "angle": 0, + "content": "where \\(\\mathbf{P}_{\\mathbb{X}}\\pmb{x}\\) denotes the orthogonal projection of a vector \\(\\pmb{x}\\) onto the space \\(\\mathbb{X}\\), and \\(\\mathbf{I}_d\\) is an identity matrix of size \\(d\\). The modified value vector \\(\\pmb{v}_r^j\\) is used, instead of \\(\\pmb{v}^j\\), to calculate the output of the CA layer, as illustrated in Fig. 2 (c). Since \\(\\pmb{v}_t^1 = \\mathbf{0}\\), it has \\(\\pmb{v}_r^1 = \\pmb{v}^1\\), meaning that no erasure is performed for [SOT]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.688, + 0.719, + 0.702 + ], + "angle": 0, + "content": "3.3.2. Multi-concept Erasure" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.706, + 0.907, + 0.906 + ], + "angle": 0, + "content": "We generalize the above operation to erase a set of \\(n\\) target concepts, and their corresponding modified value matrices are denoted by \\(\\{\\mathbf{V}_t^h\\in \\mathbb{R}^{l\\times d}\\}_{h = 1}^n\\). We use \\(\\pmb{v}_{t}^{h,j}\\) to denote the \\(j\\)-th column of \\(\\left(\\mathbf{V}_t^h\\right)^T\\), referred to as the erased value vector for the \\(j\\)-th token position of the \\(h\\)-th target concept. Our erasing operation can naturally be extended to projecting the original prompt to the orthogonal complement of the span of the \\(n\\) erased value vectors \\(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n\\), denoted by \\(\\mathrm{span}^\\perp \\left(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n\\right)\\). To calculate the projection, we first conduct the Gram-Schmidt orthogonalization to obtain a set of \\(n\\) orthonormal basis vectors \\(\\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h = 1}^n\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28762" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.089, + 0.485, + 0.199 + ], + "angle": 0, + "content": "for the span of \\(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n\\). Here, we assume the value vectors in \\(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n\\) are linearly independent and they form a basis. Such an assumption is reasonable because the multiple concepts to erase should be semantically different in practice, otherwise, a single-concept erasure would be sufficient. The desired projection is then computed by" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.212, + 0.483, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {v} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} \\tag {3} \\\\ = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\text {s p a n}} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)\\right) \\boldsymbol {v} ^ {j} \\\\ = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\left(\\boldsymbol {o} _ {t} ^ {h, j}\\right) ^ {T} \\boldsymbol {v} ^ {j} \\boldsymbol {o} _ {t} ^ {h, j}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.317, + 0.484, + 0.368 + ], + "angle": 0, + "content": "As an addition, we provide in Appendix B an alternative way to compute \\(\\mathbf{P}_{\\mathrm{span}^{\\perp}\\left(\\left\\{\\boldsymbol{v}_t^{h,j}\\right\\}_{h=1}^n\\right)} \\boldsymbol{v}^j\\) that does not require Gram-Schmidt orthogonalization but matrix inverse." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.379, + 0.304, + 0.395 + ], + "angle": 0, + "content": "3.4. Adaptive Erasing Shift" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.484, + 0.658 + ], + "angle": 0, + "content": "In practice, given a pair of textual prompts and a target concept to erase, their token-wise relevance can vary across different token positions. The different tokens of the prompt carry information with different intensities and focuses and thus can have quite different effects on image generation. As an example, we compare the generated images in each subfigure of Fig. 3, using different versions of the value matrix \\(\\mathbf{V}\\) for the same prompt. We separate the values corresponding to the [EOT] tokens and the remaining, expressing it as \\(\\mathbf{V} = [\\mathbf{V}_{\\text {content }}, \\mathbf{V}_{[\\text {EOT}]}\\]\\). Herein, we include [SOT] within \\(\\mathbf{V}_{\\text {content }}\\) for simplicity. We obtain three versions of \\(\\mathbf{V}\\) by (1) keeping it as what it is, (2) setting \\(\\mathbf{V}_{[\\text {EOT}]}\\) as zero, and (3) setting \\(\\mathbf{V}_{\\text {content }}\\) as zero. Fig. 3 shows that the prompt content carries more featured information than those [EOT] tokens. This motivates us to further improve the design in Eqs. (2) and (3), by enabling adaptive adjustment of the erasing operation at the token level." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We discover that, although a projection onto the orthogonal complement of the target concept is effective at erasing this concept itself, it can sometimes affect the prior preservation due to an excessive removal of information. Therefore, our adaptive design is focused on improving the prior preservation. When semantics carried by a prompt token are less relevant to a target token, we intend to perform less erasure to protect the prior image content. According to [32], angular information plays a more critical role in conveying semantics than magnitude during image generation. These motivate us to exploit the cosine similarity between the value vectors of a prompt token and a target token and use it to derive a shift factor to adjust the erasing strength along the identified erasing direction, which we refer to as the erasing shift. In general, we let the factor reduce when the cosine similarity becomes smaller." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "
(1) Instance(2) Art style
A nice photo of SnoopyAn night scene in Van Gogh style
[Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]][Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]]
" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.187, + 0.907, + 0.243 + ], + "angle": 0, + "content": "Figure 3. We analyze the contribution of different tokens in text-visual alignment by separately masking the value of content tokens and [EOT] tokens, where content tokens carry more featured information than those [EOT] tokens." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.249, + 0.907, + 0.296 + ], + "angle": 0, + "content": "We denote the shift factor by \\(\\delta (\\cdot ,\\cdot):\\mathbb{R}^d\\times \\mathbb{R}^d\\to \\mathbb{R}\\) which is a function of two value vectors. Using it, we revise the erasing operation in Eq. (2) for a single concept to" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.303, + 0.905, + 0.348 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\delta (\\boldsymbol {v} _ {t} ^ {j} , \\boldsymbol {v} ^ {j}) \\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.353, + 0.84, + 0.369 + ], + "angle": 0, + "content": "While for multiple concepts, Eq. (3) is revised to" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.375, + 0.905, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\delta \\left(\\boldsymbol {v} _ {t} ^ {h, j}, \\boldsymbol {v} ^ {j}\\right) \\left(\\sum_ {k = 1} ^ {n} w _ {h k} \\left(\\boldsymbol {o} _ {t} ^ {k, j}\\right) ^ {T} \\boldsymbol {v} ^ {j}\\right) \\boldsymbol {v} _ {t} ^ {h, j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.906, + 0.612 + ], + "angle": 0, + "content": "where \\( w_{hk} \\) is the \\( hk \\)-th element of the projection matrix that transforms the basis \\( \\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n \\) to the orthonormal basis \\( \\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h=1}^n \\). For a single target concept, it is straightforward to introduce the shift factor, as in Eq. (4). However, in the case of erasing multiple concepts, the derivation of a shifted operation is less straightforward, as the orthonormal basis does not carry meaningful semantics, thus a transformation back to the value vectors of the target tokens is needed. We explain in Appendix B how to derive Eq. (5) from Eq. (3). The revised erasing operations result in the proposal AdaVD." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.612, + 0.904, + 0.643 + ], + "angle": 0, + "content": "Our shift factor design builds on the sigmoid function. Given two input vectors \\( \\pmb{x}, \\pmb{y} \\in \\mathbb{R}^d \\), we formulate it as" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.649, + 0.905, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\delta (\\boldsymbol {x}, \\boldsymbol {y}) = \\frac {s}{1 + e ^ {- p (\\cos (\\boldsymbol {x} , \\boldsymbol {y}) - \\epsilon)}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.682, + 0.907, + 0.835 + ], + "angle": 0, + "content": "The cosine threshold \\(\\epsilon\\) allows a strong erasure when exceeding the threshold. A negative cosine similarity indicates a very weak relevance between the target and prompt tokens, suggesting no erasure is required. Therefore, we set \\(0 < \\epsilon < 1\\) to quantify and filter the relatively weak relevance indicated by a positive but small cosine similarity. The hyper-parameter \\(s > 0\\) controls the factor scale, while \\(p > 0\\) controls the increasing rate of the \\(\\delta\\) value against the cosine value. In Appendix C.2, we provide hyper-parameter implementation details and a comprehensive analysis." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.845, + 0.816, + 0.863 + ], + "angle": 0, + "content": "4. Experiments and Result Analysis" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "We conduct extensive experiments to evaluate the proposed AdaVD for erasing a diverse range of target concepts, cov" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28763" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.211 + ], + "angle": 0, + "content": "ering specific instances, art styles, NSFW content, and celebrity. We compare with SOTA training-based methods including ConAbl [20], ESD [12], SPM [27] and MACE [26] and SOTA training-free methods including NP [2] and SLD [39]. We also demonstrate the time efficiency and interpretability of AdaVD, along with its wider usage in other downstream image generation tasks coupled with a series of diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.218, + 0.281, + 0.234 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.239, + 0.483, + 0.33 + ], + "angle": 0, + "content": "Implementation: We employ SD v1.4 [2] to generate images using the DPM-solver sampler [25] over 30 sampling steps with classifier-free guidance [17] of 7.5. All the compared methods are implemented following their default configurations available from their official repository. Further implementation details are provided in Appendix C.1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.331, + 0.483, + 0.42 + ], + "angle": 0, + "content": "Evaluation Data: Adopting the same evaluation protocol from SPM [27], we assess the methods based on 80 instance templates, 30 art style templates, and 25 celebrity templates, and benchmark each method by generating 10 images per template per concept in evaluation. To assess the performance of NSFW erasure, we use the I2P benchmark [39]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.421, + 0.483, + 0.662 + ], + "angle": 0, + "content": "Performance Metrics: We follow the widely used evaluation metrics for concept erasure, including the CLIP score (CS) [33] to assess erasure efficacy and the Fréchet inception distance (FID) [16] to assess prior preservation. CS calculates the cosine similarity between a textual prompt and the generated image [33]. We examine two CS values before and after erasing and compare the CS value after the erasure. When the prompts contain the target concepts, a more reduced CS indicates a more effective erasure of the target concepts. FID measures the distance between images generated before and after erasing [16]. A lower FID indicates a better alignment between the two images. Thus, for non-target concepts, lower FID values indicate better prior preservation. Overall, a precise concept erasure should have a low CS for prompts containing the target concepts and a low FID for prompts composed of non-target concepts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.663, + 0.483, + 0.768 + ], + "angle": 0, + "content": "Summary: Results on instance and art style concept erasure are reported in Sections 4.2 and 4.3, while results on celebrity and NSFW erasure are reported in Appendices D.3 and D.2. Additional analyses, including extended quantitative results, comparisons with SuppressEOT [24], performance on different versions of SD, and further discussions, are presented in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.774, + 0.355, + 0.789 + ], + "angle": 0, + "content": "4.2. On Instance Concept Erasure" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.9 + ], + "angle": 0, + "content": "We first conduct the experiment with erasing a single concept \"Snoopy\". Six types of prompts were tested, of which one contains \"Snoopy\" and the other five contain only nontarget concepts. The results are compared in the top block of Table 1. It can be seen that our proposed AdaVD achieves the lowest CS and FID scores in all cases. Particularly, its FID is \\(33\\%\\) lower than that of the second-best method. It" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.089, + 0.903, + 0.131 + ], + "angle": 0, + "content": "
ConceptSnoopyMickeySpongebobPikachuDogLegislator
CSCSCSCSCSCS
SD v1.428.5126.5727.43---
" + }, + { + "type": "table_caption", + "bbox": [ + 0.675, + 0.132, + 0.744, + 0.142 + ], + "angle": 0, + "content": "Erase Snoopy" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.142, + 0.902, + 0.233 + ], + "angle": 0, + "content": "
CS ↓FID ↓FID ↓FID ↓FID ↓FID ↓
ConAbl25.3838.4441.5929.6827.7627.36
MACE20.78118.01111.9081.9943.2765.97
SPM23.8933.0634.7023.8919.6118.26
NP23.6659.5878.7452.3767.5155.22
SLD27.8448.1255.3638.7441.9549.08
Ours20.285.728.565.792.326.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.645, + 0.234, + 0.774, + 0.244 + ], + "angle": 0, + "content": "Erase Snoopy and Mickey" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.244, + 0.902, + 0.336 + ], + "angle": 0, + "content": "
CS ↓CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl24.2624.0846.3239.6330.5727.49
MACE20.7420.7151.49110.6752.0777.13
SPM23.1622.8141.5831.7721.9623.69
NP23.5924.8581.4150.1065.9358.88
SLD27.7626.7454.5939.2441.6250.13
Ours20.2919.939.345.842.416.43
" + }, + { + "type": "table_caption", + "bbox": [ + 0.606, + 0.337, + 0.812, + 0.348 + ], + "angle": 0, + "content": "Erase Snoopy and Mickey and Spongebob" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.348, + 0.902, + 0.44 + ], + "angle": 0, + "content": "
CS ↓CS ↓CS ↓FID ↓FID ↓FID ↓
ConAb123.9423.6425.0451.2031.5930.03
MACE20.4820.5021.5999.6847.4670.38
SPM22.8122.3520.8239.8322.6825.31
NP24.2924.7625.3164.7565.1059.33
SLD27.8426.7127.6039.4142.3249.88
Ours19.3919.7320.346.852.797.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.445, + 0.905, + 0.515 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of single- and multi-instance erasure. The best and second-best results are marked in bold and underlined, respectively. Our AdaVD consistently achieves the lowest CS and the lowest FID in all cases, indicating superior prior preservation without compromising erasure efficacy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.524, + 0.905, + 0.659 + ], + "angle": 0, + "content": "improves over SOTA by significantly enhanced prior preservation without compromising the erasure precision, as exemplified in Fig. 4. It can be observed from Fig. 4 that methods such as SPM, NP, and SLD fail to fully erase \"Snoopy\" which can be found from the ear and the shape characteristic of the generated image after erasure. MACE can successfully erase the \"Snoopy\" concept. But all the competing methods suffer from degraded image quality in non-target concept generation, e.g., \"Spongebob\"." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We then compare the performance for multi-concept erasure, experimenting with two cases, of which one erases two concepts of \"Snoopy\" and \"Mickey\" together and the other erases three concepts of \"Snoopy\", \"Mickey\" and \"Spongebob\" together. Results are reported in the bottom two blocks of Table 1 and visualized in the second and third sections of Fig. 4. Similarly, our AdaVD achieves the lowest CS and FID scores across all cases. This verifies that AdaVD is capable of handling more complex multi-concept erasure and simultaneously fighting against catastrophic forgetting. Conversely, other methods struggle to consistently perform well for multi-concept erasure. For example, when erasing \"Snoopy\" and \"Mickey\" together, the image quality for non-target concepts like \"Spongebob\" and \"Legislator\" shows apparent degradation in Fig. 4. SLD, in particular, fails to maintain its erasure ability even" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28764" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.097, + 0.15, + 0.11 + ], + "angle": 0, + "content": "Concepts" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.111, + 0.401, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.46, + 0.091, + 0.603, + 0.116 + ], + "angle": 0, + "content": "Snoopy, Miekey, Spongebob, Dog, Legislator" + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.117, + 0.651, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.091, + 0.853, + 0.116 + ], + "angle": 0, + "content": "Snoopy, Mickey, Spongebob, Dog, Legislator" + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.117, + 0.9, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.328, + 0.907, + 0.37 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of single- and multi-instance erasure. Both training-based and training-free methods show limitations in prior preservation. In contrast, our AdaVD demonstrates considerable performance in maintaining prior knowledge without compromising erasure efficacy across both single- and multi-concept erasure tasks." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.378, + 0.481, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.517, + 0.483, + 0.56 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of art style erasure. Our AdaVD can effectively remove the target concept \"Van Gogh\" while preserving non-target styles like \"Picasso\" and \"Monet\"." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.567, + 0.484, + 0.643 + ], + "angle": 0, + "content": "when dealing with 2-concept erasure. In Appendix G, we report more experimental results for erasing up to 40 concepts, where our AdaVD can extend to erase dozens of concepts in practice, maintaining consistent erasure efficacy and prior preservation, as shown in Fig. 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.651, + 0.292, + 0.667 + ], + "angle": 0, + "content": "4.3. On Art Style Erasure" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We experiment with erasing specific art style, including \"Van Gogh\", \"Picasso\" and \"Monet\". Results are reported in Table 2, and visual comparisons are provided in Fig. 5. Our AdaVD exhibits superior prior preservation, and achieves the lowest or closed-to-lowest CS and FID scores, demonstrating strong prior preservation without sacrificing erasure efficacy. Other methods show different drawbacks as observed from the results. For instance, although NP achieves notably better precision in art style removal as compared to instance removal, Fig. 5 shows that it still struggles to fully erase the \"Van Gogh\" style. Also, SLD fails to erase the \"Van Gogh\" style. These two methods also degrade generation quality for non-target styles, such as \"Picasso\" and \"Monet\", showing harmful effects on non-target concepts directly, as evidenced in both Fig. 5 and" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.376, + 0.905, + 0.418 + ], + "angle": 0, + "content": "
ConceptVan GoghPicassoMonetAndy WarholCaravaggio
CSCSCSCSCS
SD v1.429.2129.0629.02--
" + }, + { + "type": "table_caption", + "bbox": [ + 0.667, + 0.419, + 0.754, + 0.43 + ], + "angle": 0, + "content": "Erase Van Gogh" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.43, + 0.905, + 0.523 + ], + "angle": 0, + "content": "
CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl28.8071.71138.7270.3073.10
MACE27.7465.7769.7983.3775.41
SPM24.7862.2532.2758.3061.50
NP24.90141.56124.52127.85136.32
SLD27.48103.96109.11103.89119.32
Ours24.876.822.668.366.84
" + }, + { + "type": "table_caption", + "bbox": [ + 0.673, + 0.524, + 0.747, + 0.533 + ], + "angle": 0, + "content": "Erase Picasso" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.534, + 0.905, + 0.628 + ], + "angle": 0, + "content": "
FID ↓CS ↓FID ↓FID ↓FID ↓
ConAbl58.6227.72140.3473.3567.44
MACE60.4627.1149.9276.1072.85
SPM38.7926.697.7652.0051.40
NP111.3526.1491.11116.24121.82
SLD98.2127.0393.0197.00110.05
Ours5.4926.992.339.387.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.676, + 0.629, + 0.746, + 0.638 + ], + "angle": 0, + "content": "Erase Monet" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.639, + 0.904, + 0.733 + ], + "angle": 0, + "content": "
FID ↓FID ↓CS ↓FID ↓FID ↓
ConAbl141.52132.1024.53208.38186.26
MACE76.9069.3526.8988.3581.72
SPM41.0329.7127.0031.9025.99
NP137.21126.7524.47127.22135.83
SLD94.4892.8825.73100.90114.87
Ours6.946.5026.308.467.19
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.739, + 0.907, + 0.781 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison of art style erasure. AdaVD achieves a superior balance between erasure efficacy and prior preservation, especially excelling in prior preservation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Table 2. Both MACE and SPM are effective in erasing the target concept, however, their prior preservation is somehow less satisfactory, which is particularly noticeable in the generated images in \"Monet\" style. Differently, AdaVD can effectively and consistently remove the target concept and meanwhile preserve satisfactorily the prior content, as confirmed by Table 2 and Fig. 5." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28765" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.48, + 0.184 + ], + "angle": 0, + "content": "
Data PreparationModel FinetuneImage GenerationTotal Time
ConAbl929011200.910419
SPM0728501.772867
MACE3032320.9544
SLD001.414
Ours401.822
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.189, + 0.483, + 0.245 + ], + "angle": 0, + "content": "Table 3. Time consumption of 10-concept erasure. We calculate the time cost (s) to erase 10 concepts and generate 10 images using one NVIDIA A40 GPU. Compared with training-based methods, AdaVD exhibits exceptional efficiency in real-time erasure." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.254, + 0.258, + 0.27 + ], + "angle": 0, + "content": "4.4. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.278, + 0.483, + 0.504 + ], + "angle": 0, + "content": "Time Consumption: The computational cost of concept erasure primarily arises from three components, including (1) data preparation time required by training-based methods for preparing training data and by AdaVD for basis computation; (2) model fine-tuning time required by training-based methods; and (3) image generation time required by all methods. In Table 3, we compare the total time consumption of different methods, as well as their time spent on each component. The two training-free methods of SLD and AdaVD are significantly faster as no fine-tuning is needed. Our AdaVD costs slightly more time than SLD, i.e., 0.8 extra seconds per image due to its basis computation, and a total of 8 extra seconds for generating 10 images. But this mild increase yields a significant performance gain, succeeding in precise concept erasure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.507, + 0.483, + 0.748 + ], + "angle": 0, + "content": "Interpreting Erased Components by Visualization: Our AdaVD generates images by replacing the original value vector \\(\\pmb{v}^j\\) with \\(\\pmb{v}_r^j\\) via orthogonal complement operation. To empirically interpret the rationale behind our method, we visualize the erased component, \\(\\pmb{v}^j - \\pmb{v}_r^j\\). Fig. 6 presents three cases of erasing the target concepts \"Mickey\", \"Van Gogh\" and \"Bruce Lee\", where AdaVD successfully erases these target concepts while robustly preserving prior knowledge of non-target concepts. In the first row, as shown in the middle column of each block, the erased components consistently align with the corresponding target semantics when dealing with the target concepts. In the second row of non-target concepts, conversely, the erased components do not contain any informative pattern, indicating that they carry no meaningful semantics, and therefore exert minimal impact on the prior knowledge." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Downstream Applications: We conduct additional experiments to showcase the versatile applications of our AdaVD across various generative tasks, including (1) implicit concept erasure: by removing the implicit concepts of \"rainy\" and \"foggy\"; (2) image editing: by removing the appearance concepts of \"glasses\" and \"mustache\"; and (3) attribute suppression: by removing the coupled color concept of \"red\". Additionally, we integrate AdaVD with a series of diffusion models, including Chilloutmix [5], DreamShaper [6], RealisticVision [7], and SD v2.1 [4], alongside SD" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.905, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.187, + 0.907, + 0.243 + ], + "angle": 0, + "content": "Figure 6. Visualization of erased components. In each block, we compare both target (1st row) and non-target concept (2nd row) by visualizing the original image (1st column), erased component (2nd column), and generation by our AdaVD (3rd column)." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.251, + 0.905, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.403, + 0.907, + 0.46 + ], + "angle": 0, + "content": "Figure 7. Downstream applications. We extend AdaVD to versatile generation tasks, including (1) implicit concept erasure, (2) image editing, and (3) attribute suppression, indicating its significant potential for broad applications." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.907, + 0.618 + ], + "angle": 0, + "content": "v1.4. As illustrated in Fig. 7, despite the absence of explicit mention for \"rainy\" and \"foggy\", AdaVD can still effectively erase these concepts in image semantic space. Meanwhile, AdaVD also precisely removes \"glasses\" and \"mustache\" with minimal changes to other details, highlighting its potential in image editing applications. For attribute suppression, AdaVD successfully eliminates the color attribute \"red\" from objects such as apples and roses, demonstrating its capability to decouple strongly coupled concepts, e.g., \"roses are red\" embedded in the model's prior knowledge." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.624, + 0.783, + 0.639 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.909, + 0.901 + ], + "angle": 0, + "content": "We have presented AdaVD, a precise, fast, and low-cost method for erasing unwanted concepts. The idea of leveraging the classical linear algebraic orthogonal complement operation and an adaptive erasing shift design is novel, and has successfully achieved a precise concept erasure. Extensive experiments have demonstrated both high erasure efficacy and strong prior preservation of AdaVD for both single- and multi-concept erasure. Moreover, AdaVD exhibits excellent interpretability through visualizing its erased components and strong capability in solving downstream tasks. It has been an intriguing discovery that the orthogonal complement of the value vectors of the target concepts is effective at erasing their inherent semantics. Despite the empirical success, we will seek to establish a rigorous theoretical understanding of the accumulative effect of applying this linear algebraic operation layer-wise for concept erasure in the future." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28766" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.26, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.486, + 0.161 + ], + "angle": 0, + "content": "This work is supported by the National Science and Technology Major Project (2023ZD0121102) and the National Natural Science Foundation of China (U24B20180)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.175, + 0.188, + 0.192 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.201, + 0.482, + 0.242 + ], + "angle": 0, + "content": "[1] Safety checker nested in stable diffusion. https://huggingface.co/CompVis/stable-diffusion-safety-checker, 2022.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.245, + 0.482, + 0.272 + ], + "angle": 0, + "content": "[2] Stable diffusion. https://huggingface.co/ CompVis/stable-diffusion-v1-4, 2022.2,3,6" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.274, + 0.482, + 0.3 + ], + "angle": 0, + "content": "[3] Stable diffusion v2.0. https://huggingface.co/stabilityai/stable-diffusion-2, 2022.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.303, + 0.482, + 0.33 + ], + "angle": 0, + "content": "[4] Stable diffusion v2.1. https://huggingface.co/stabilityai/stable-diffusion-2-1, 2022.8" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.332, + 0.482, + 0.359 + ], + "angle": 0, + "content": "[5] Chilloutmix. https://huggingface.co/swl-models/chilloutmix, 2023.1,8,18" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.362, + 0.482, + 0.388 + ], + "angle": 0, + "content": "[6] Dreamshaper. https://huggingface.co/Lykon/DreamShaper, 2023.1,8,18,22" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.391, + 0.482, + 0.431 + ], + "angle": 0, + "content": "[7] Realisticvision. https://huggingface.co/SG161222/Realistic_Vision_V5.1_noVAE, 2023.8,18,22" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.434, + 0.482, + 0.473 + ], + "angle": 0, + "content": "[8] Praneeth Bedapudi. 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The proposed Adaptive Value Decomposer (AdaVD) demonstrates a satisfactory balance between erasure efficacy and prior preservation and an effective transferability across T2I diffusion models. (a) Compared to SLD [39], AdaVD enables precise concept erasure without compromising prior knowledge for non-target concepts at both single- and multi-concept erasure. This is facilitated by a precise disentanglement of target semantics (e.g., "Snoopy") and a robust preservation of non-target ones (e.g., "Teddy"), with visualization interpretation marked by $\diamond$ . (b) AdaVD can be transferred to various T2I models, e.g., SDXL [31], DreamShaper [6], Chilloutmix [5]. + +# Abstract + +Recent success of text-to-image (T2I) generation and its increasing practical applications, enabled by diffusion models, require urgent consideration of erasing unwanted concepts, e.g., copyrighted, offensive, and unsafe ones, from the pre-trained models in a precise, timely, and low-cost manner. The twofold demand of concept erasure includes not only a precise removal of the target concept (i.e., erasure efficacy) but also a minimal change on non-target content (i.e., prior preservation), during generation. Existing methods face challenges in maintaining an effective balance between erasure efficacy and prior preservation, and they can be computationally costly. To improve, we propose a precise, fast, and low-cost concept era + +sure method, called Adaptive Vaule Decomposer (AdaVD), which is training-free. Our method is grounded in a classical linear algebraic operation of computing orthogonal complement, implemented in the value space of each cross-attention layer within the UNet of diffusion models. We design a shift factor to adaptively navigate the erasure strength, enhancing effectively prior preservation without sacrificing erasure efficacy. Extensive comparative experiments with both training-based and training-free state of the arts demonstrate that the proposed AdaVD excels in both single and multiple concept erasure, showing 2 to 10 times of improvement in prior preservation than the second best, meanwhile achieving the best or near best erasure efficacy. AdaVD supports a series of diffusion models and downstream image generation tasks, with code available on: https://github.com/WYuan1001/AdaVD. + +# 1. Introduction + +The recent advancements of text-to-image (T2I) diffusion models [11, 17, 18, 30, 36, 50, 52] have enabled users to effortlessly generate high-quality images with simple textual prompts. However, such generations would inevitably introduce copyrighted [10, 22, 42, 44] or offensive [23, 39] concepts, caused by the noisy training data scraped from web [9, 40]. Because it is very costly to re-train large generative models from scratch, it is vital to develop low-cost techniques to precisely erase unwanted semantic concepts in images, i.e., concept erasure. This task aims at a precise erasure of visual content w.r.t. target concepts from generated images (i.e., erasure efficacy), while a faithful preservation of irrelevant content w.r.t. the prompts comprising non-target concepts (i.e., prior preservation), safeguarding a secure T2I generation for diffusion models. + +A representative category of concept erasure methods is training-based, which fine-tunes a subset of model parameters by formulating meticulous erasing objective functions [12, 20, 26, 27]. Despite good erasure efficacy, they exhibit considerable practical limitations when being deployed. For instance, they require expensive individual fine-tuning to erase each concept, which thereby limits their real-time usage. As an example, it is unacceptable for online T2I platforms to be costly to erase newly emerging concepts, where copyrighted or offensive concepts could arise unexpectedly, with no means to produce a complete list of concepts to erase in advance. Moreover, these methods suffer from a limited balance between erasure efficacy and prior preservation, due to their reliance on regularization terms to trade off prior preservation. + +An alternative category of concept erasure methods is training-free, such as Negative Prompt (NP) [2], Safe Latent Diffusion (SLD) [39], and SuppressEOT [24], which enable real-time erasure. They intervene in the image generation process, exhibiting a range of drawbacks. For instance, NP was initially designed to enhance image quality and can result in compromised erasure efficacy; while SuppressEOT requires the user to specify the location of the target concept within the prompt, thus, it is not suitable for erasure applications that require full automation. Therefore, both NP and SuppressEOT fall short as independent tools for concept erasure. Regarding SLD, it does not perform well at retaining prior knowledge of non-target concepts as illustrated in Fig. 1, failing in precise concept erasure. Limited by their drawbacks, current training-free methods are not robust enough to act as an independent concept erasure tool and to be applied in continual erasure of multiple concepts. + +In this light, we advance concept erasure techniques for T2I generation, by developing a precise, fast, and low-cost method called Adaptive Value Decomposer (AdaVD). It is a training-free method, capable of precisely erasing the target concepts and satisfactorily preserving non-target priors + +with low computational overhead. Our core design builds on a classical linear algebraic operation, i.e., projection onto the orthogonal complement of the semantic space of the target concepts. We conduct this projection-based decomposition in the cross-attention value space, disentangling target semantics from the original prompts. To improve the erasure precision and prior preservation, we further refine the decomposition by adaptively allocating token-wise shifts. These shifts are designed to differentiate the strong and specific alignments from the weak and general alignments between prompt tokens and visual content associated with the target concept. Guided by these shifts, the strong and specific alignments are erased for precision while the weak and general alignments are retained for prior preservation. + +Fig. 1 (a) demonstrates the erased results for both target and non-target concepts. It shows that our AdaVD can precisely locate and erase the components indicated by the target semantics, meanwhile keeping the non-target priors maximally unaffected. Empirical evaluation shows that AdaVD excels in prior preservation, outperforming the second best by a 2- to 10-fold improvement across various nontarget concepts, and meanwhile maintains exceptional erasure efficacy, consistently achieving the best or near-best performance. Our contributions are summarized below: + +- A novel and effective erasing operation by exploiting the projection onto the orthogonal complement of the target concept in the cross-attention value space, to disentangle semantics carried by the target concept. +- An adaptive erasing mechanism through a dynamic shift factor, which can effectively minimize the impact on prior knowledge, without compromising the erasure efficacy. +- A precise, fast, and low-cost concept erasure technique AdaVD, which works in a training-free manner and supports a series of T2I diffusion models, capable of precise concept erasure. +- Extensive experiments that demonstrate the superiority of AdaVA against state-of-the-art (SOTA) methods, achieving 2 to 10 times of improvement in prior preservation while maintaining precise erasure efficacy. + +# 2. Related Works + +Re-training and Blocking: The most straightforward way to erase a target concept from a pre-trained T2I model is to exclude the training data relevant to this concept and retrain the model from scratch, as in Stable Diffusion (SD) v2.0 [3]. For this, an Not Safe For Work (NSFW) detector [8, 21, 38] can be used to filter unsafe data from LAION-5B [41] prior to the training. However, this approach is time-consuming, requires specialized detectors, and can introduce biases [43]. An alternative solution is to block the prompts of concerns and restrict the outputs of concerns, by using filters [43] and safety checkers [1, 35]. Yet, such safeguards are fragile and easy to bypass [46, 49], especially + +when being confronted with crafted malicious prompts [39]. Training-based: A more effective group of concept erasure solutions fine-tune pre-trained generative models, teaching them to "forget" a target concept, e.g., Erased Stable Diffusion (ESD) [12]. However, since the ESD design does not consider prior preservation, both target and non-target concepts are adversely affected. To improve, new training techniques have been developed, e.g., ConAbl [20], SA [14], UCE [13], EraseDiff [48], SPM [27] and MACE [26]. They improve prior preservation through regularization but still fall short in achieving both precise erasure and robust prior preservation. Moreover, for every new target concept to be erased, a separate fine-tuning is required. This is time-consuming, making real-time erasure impractical, especially for highly interactive platforms where unsafe or inappropriate concepts can emerge unexpectedly. + +Training-free: With largely reduced computing costs, training-free methods are gaining increasing attention. NP [2] and SLD [39] pioneer training-free concept erasure by adjusting classifier-free guidance [17], leading the generation towards a direction away from the target concepts. However, NP lacks fine-grained control over target concepts and compromises prior preservation. SLD also compromises the prior knowledge during its generation, disrupting the overall generating quality of non-target concepts. SuppressEOT [24], akin to image editing techniques [15], removes target concepts based on user-specified textual positions. Its user-involved design makes it more suitable for editing tasks, but not for system-wide erasing tasks that require full automation. Benefiting from orthogonal decompositions in value spaces, the proposed training-free method AdaVD achieves not only precise concept erasure but also satisfactory prior preservation. It supports multi-concept erasure, is compatible across different versions of stable diffusion, and consistently demonstrates superior performance. The training-free method SAFREE [51], concurrent to ours, also uses orthogonal decomposition but operates differently on text embeddings, supported by masking, projection, Fourier transforms, and a hard control of removal strength. We compare performance with it in the appendix. + +# 3. Method + +Concept erasure in T2I generation aims at a successful removal of the visual content indicated by textual concepts (i.e., target concepts), meanwhile a satisfactory preservation of the visual content irrelevant to these concepts (i.e., prior knowledge). It is challenging to achieve simultaneously satisfactory erasure efficacy and prior preservation. To advance this field, we propose a precise, fast, and low-cost concept erasure method, termed AdaVD and illustrated in Fig. 2 (c). The method is training-free, and its core design builds on a classical linear algebraic operation, i.e., orthogonal complement. This simple but elegant geometric + +operation is able to guide effectively the image generation, enabling a precise removal of the target concepts from the image content meanwhile a satisfactory preservation of the non-target content. + +# 3.1. Preliminary on T2I Diffusion Models + +Current T2I models usually include an image compression network [19] and a conditional latent diffusion model [36] that performs sequential denoising with a UNet [37] in the latent space. The UNet takes as inputs the noise latent variable $\mathbf{z}_t$ , timestep $t$ , and embedding $\mathbf{C}$ of the textual prompt from a pre-trained CLIP model [33], and predicts the noise $\epsilon_{\theta}(\mathbf{z}_t, t, \mathbf{C})$ . In training-free concept erasure, the noise is additionally conditioned on the target concept with text embedding $\mathbf{C}_t$ , predicted by $\epsilon_{\theta}(\mathbf{z}_t, t, \mathbf{C}, \mathbf{C}_t)$ . + +Interactions between the image and text modalities are enabled by cross-attention (CA) layers [36, 47] within the UNet, which align the latent representation of the noisy image with the semantic detail of the textual prompt. Each CA layer computes an attention map $\mathbf{A} = \mathrm{softmax}\left(\frac{\mathbf{Q}\mathbf{K}^T}{\sqrt{d}}\right)$ with a latent feature dimension $d$ . The queries $\mathbf{Q}$ are computed from the noisy image features, while both keys $\mathbf{K}$ and values $\mathbf{V}$ from the text embeddings $\mathbf{C}$ , using different projection matrices. The layer output is a weighted aggregation of $\mathbf{A}$ and $\mathbf{V}$ . More details on CA layers are in Appendix A. + +It has been recognized that the keys in CA layers mostly act as the "Where" pathway, governing the layout of the attention map and determining the compositional structure of the generated images, while the values as the "What" pathway, controlling the content and visual appearance of images [45]. Because the goal of concept erasure is to modify the visual content of the generated images, we propose to conduct value decompositions into subspaces, which are uniquely constructed by exploiting the target concept and its orthogonal complement in an adaptive fashion. We demonstrate that information offered by the orthogonal complement can be used to generate successfully high-quality images with the target concept precisely erased. + +# 3.2. Token-wise Target Embedding Pre-processing + +Given a textual example, which can be either a target concept to erase or an original prompt, its embedding is computed at the token level by a CLIP text encoder. Each tokenized example is padded with [SOT] as the prefix and [EOT] at the end, with [EOT] filling any remaining positions to maintain a fixed token length of $l$ . Each token is characterized by an embedding vector of dimension $D_{c}$ . + +We focus on the embedding of a target concept $\mathbf{C}_t\in$ $\mathbb{R}^{l\times D_c}$ , and denote each column of $\mathbf{C}_t^T$ by $c_{t}^{j}$ that corresponds to a token vector where $j\in \{1,2,\dots ,l\}$ . To facilitate a precise erasure, we emphasize the key information carried by a target concept by proposing an embedding duplication. Specifically, the embedding of the last sub + +![](images/4cda90f0a533aee68d3b154ae598bde49c37ebab0d734efbca4245b1090bbf63.jpg) +Figure 2. Overview of our Adaptive Value Decomposer (AdaVD) in erasing the target concept "Snoopy". (a) First, we token-wisely duplicate the last subject token of the target embedding encoded by the text encoder, except for [SOT]. (b) Then, the pre-processed target embedding and corresponding prompt embedding are jointly fed into CA layers within the UNet as conditions, to disentangle target semantics from the original image at each timestep. (c) In each CA layer, we perform token-wise orthogonal value decomposition with an adaptive token-wise shift. The new value is subsequently multiplied by the attention map, producing the erased output for this CA layer. + +ject token within its prompt content excluding [SOT] and [EOT], replaces all the token positions except for [SOT], as illustrated in Fig. 2 (a). For instance, the single-token concept "snoopy" has a modified embedding matrix corresponding to "[SOT], snoopy, snoopy, ..., snoopy", while the multi-token concept "Van Gogh" to "[SOT], gogh, gogh, ..., gogh". Benefiting from the causal attention mechanism used by the CLIP text encoder, the last subject token is able to "see" all the prompt content and contains key information [28], therefore is sufficient for erasure calculation. The modified embedding matrix $\tilde{\mathbf{C}}_t$ is fed into a CA layer to compute the value matrix $\tilde{\mathbf{V}}_t \in \mathbb{R}^{l \times d}$ via a linear projection using the projection matrix $\mathbf{W}_{\mathrm{V}} \in \mathbb{R}^{D_c \times d}$ , as + +$$ +\tilde {\mathbf {V}} _ {t} = \tilde {\mathbf {C}} _ {t} \mathbf {W} _ {\mathrm {V}} = \left[ c _ {t} ^ {1}, \underbrace {c _ {t} ^ {k} , \dots , c _ {t} ^ {k}} _ {l - 1} \right] ^ {T} \mathbf {W} _ {\mathrm {V}}. \tag {1} +$$ + +The token vector $c_{t}^{1}$ corresponds to [SOT] and $c_{t}^{k}$ to the last subject token. The total token number is still $l$ . + +# 3.3. Orthogonal Value Decomposition + +Given a conditional latent diffusion model trained for standard T2I generation, our proposed erasing operation works by projecting the original textual prompt onto the orthogonal complement of the subspace spanned by the target concepts to erase, and it is implemented in the value space learned at each CA layer of the UNet. It supports both single-concept and multi-concept erasure. + +We do not apply any erasing operation to [SOT], as it primarily serves as a prefix and does not carry useful information to distinguish the semantic content. We start from the modified value matrix $\tilde{\mathbf{V}}_t$ in Eq. (1), and use $\tilde{\boldsymbol{v}}_t^j$ to denote the $j$ -th column of $\tilde{\mathbf{V}}_t^T$ . The exclusion of [SOT] in the erasure calculation is equivalent to replacing the value vector in the first row of $\tilde{\mathbf{V}}_t$ by a zero vector, resulting in $\mathbf{V}_t = \left[0,\tilde{\boldsymbol{v}}_t^2,\tilde{\boldsymbol{v}}_t^3,\dots,\tilde{\boldsymbol{v}}_t^l\right]^T$ to use in the erasing operation. + +# 3.3.1. Single-concept Erasure + +Our erasing operation works with $\mathbf{V}_t^T$ , where each column of $\mathbf{V}_t^T$ corresponds to the erased value vector for token position $j$ and is denoted as $\pmb{v}_t^j$ , and with the value matrix $\mathbf{V} \in \mathbb{R}^{l \times d}$ computed from the original prompt, where each column of $\mathbf{V}^T$ is referred to as the original value vector for the token position $j$ , denoted by $\pmb{v}^j$ . To remove the effect of the target concept from the original prompt, for each token position, we project the original value vector $\pmb{v}^j$ onto the orthogonal complement of the span of the erased value vector $\pmb{v}_t^j$ , and denote this orthogonal complement by $\mathrm{span}^\perp(\pmb{v}_t^j)$ . This results in the following modified value vector: + +$$ +\begin{array}{l} \boldsymbol {v} _ {r} ^ {j} = \mathbf {P} _ {\operatorname {s p a n} ^ {\perp} \left(\boldsymbol {v} _ {t} ^ {j}\right)} \boldsymbol {v} ^ {j} = \left(\mathbf {I} _ {d} - \mathbf {P} _ {\operatorname {s p a n} \left(\boldsymbol {v} _ {t} ^ {j}\right)}\right) \boldsymbol {v} ^ {j} \tag {2} \\ = \boldsymbol {v} ^ {j} - \frac {\boldsymbol {v} _ {t} ^ {j} \boldsymbol {v} _ {t} ^ {j T}}{\boldsymbol {v} _ {t} ^ {j T} \boldsymbol {v} _ {t} ^ {j}} \boldsymbol {v} ^ {j} = \boldsymbol {v} ^ {j} - \frac {\boldsymbol {v} _ {t} ^ {j T} \boldsymbol {v} ^ {j}}{\boldsymbol {v} _ {t} ^ {j T} \boldsymbol {v} _ {t} ^ {j}} \boldsymbol {v} _ {t} ^ {j}, \\ \end{array} +$$ + +where $\mathbf{P}_{\mathbb{X}}\pmb{x}$ denotes the orthogonal projection of a vector $\pmb{x}$ onto the space $\mathbb{X}$ , and $\mathbf{I}_d$ is an identity matrix of size $d$ . The modified value vector $\pmb{v}_r^j$ is used, instead of $\pmb{v}^j$ , to calculate the output of the CA layer, as illustrated in Fig. 2 (c). Since $\pmb{v}_t^1 = \mathbf{0}$ , it has $\pmb{v}_r^1 = \pmb{v}^1$ , meaning that no erasure is performed for [SOT]. + +# 3.3.2. Multi-concept Erasure + +We generalize the above operation to erase a set of $n$ target concepts, and their corresponding modified value matrices are denoted by $\{\mathbf{V}_t^h\in \mathbb{R}^{l\times d}\}_{h = 1}^n$ . We use $\pmb{v}_{t}^{h,j}$ to denote the $j$ -th column of $\left(\mathbf{V}_t^h\right)^T$ , referred to as the erased value vector for the $j$ -th token position of the $h$ -th target concept. Our erasing operation can naturally be extended to projecting the original prompt to the orthogonal complement of the span of the $n$ erased value vectors $\left\{\pmb{v}_t^{h,j}\right\}_{h = 1}^n$ , denoted by $\mathrm{span}^\perp \left(\left\{\pmb{v}_t^{h,j}\right\}_{h = 1}^n\right)$ . To calculate the projection, we first conduct the Gram-Schmidt orthogonalization to obtain a set of $n$ orthonormal basis vectors $\left\{\pmb{o}_t^{h,j}\right\}_{h = 1}^n$ + +for the span of $\left\{\pmb{v}_t^{h,j}\right\}_{h=1}^n$ . Here, we assume the value vectors in $\left\{\pmb{v}_t^{h,j}\right\}_{h=1}^n$ are linearly independent and they form a basis. Such an assumption is reasonable because the multiple concepts to erase should be semantically different in practice, otherwise, a single-concept erasure would be sufficient. The desired projection is then computed by + +$$ +\begin{array}{l} \boldsymbol {v} _ {r} ^ {j} = \mathbf {P} _ {\text {s p a n} ^ {\perp} \left(\left\{\boldsymbol {v} _ {t} ^ {h, j} \right\} _ {h = 1} ^ {n}\right)} \boldsymbol {v} ^ {j} = \mathbf {P} _ {\text {s p a n} ^ {\perp} \left(\left\{\boldsymbol {o} _ {t} ^ {h, j} \right\} _ {h = 1} ^ {n}\right)} \boldsymbol {v} ^ {j} \tag {3} \\ = \left(\mathbf {I} _ {d} - \mathbf {P} _ {\text {s p a n}} \left(\left\{\boldsymbol {o} _ {t} ^ {h, j} \right\} _ {h = 1} ^ {n}\right)\right) \boldsymbol {v} ^ {j} \\ = \boldsymbol {v} ^ {j} - \sum_ {h = 1} ^ {n} \left(\boldsymbol {o} _ {t} ^ {h, j}\right) ^ {T} \boldsymbol {v} ^ {j} \boldsymbol {o} _ {t} ^ {h, j}. \\ \end{array} +$$ + +As an addition, we provide in Appendix B an alternative way to compute $\mathbf{P}_{\mathrm{span}^{\perp}\left(\left\{\boldsymbol{v}_t^{h,j}\right\}_{h=1}^n\right)} \boldsymbol{v}^j$ that does not require Gram-Schmidt orthogonalization but matrix inverse. + +# 3.4. Adaptive Erasing Shift + +In practice, given a pair of textual prompts and a target concept to erase, their token-wise relevance can vary across different token positions. The different tokens of the prompt carry information with different intensities and focuses and thus can have quite different effects on image generation. As an example, we compare the generated images in each subfigure of Fig. 3, using different versions of the value matrix $\mathbf{V}$ for the same prompt. We separate the values corresponding to the [EOT] tokens and the remaining, expressing it as $\mathbf{V} = [\mathbf{V}_{\text {content }}, \mathbf{V}_{[\text {EOT}]}\]$ . Herein, we include [SOT] within $\mathbf{V}_{\text {content }}$ for simplicity. We obtain three versions of $\mathbf{V}$ by (1) keeping it as what it is, (2) setting $\mathbf{V}_{[\text {EOT}]}$ as zero, and (3) setting $\mathbf{V}_{\text {content }}$ as zero. Fig. 3 shows that the prompt content carries more featured information than those [EOT] tokens. This motivates us to further improve the design in Eqs. (2) and (3), by enabling adaptive adjustment of the erasing operation at the token level. + +We discover that, although a projection onto the orthogonal complement of the target concept is effective at erasing this concept itself, it can sometimes affect the prior preservation due to an excessive removal of information. Therefore, our adaptive design is focused on improving the prior preservation. When semantics carried by a prompt token are less relevant to a target token, we intend to perform less erasure to protect the prior image content. According to [32], angular information plays a more critical role in conveying semantics than magnitude during image generation. These motivate us to exploit the cosine similarity between the value vectors of a prompt token and a target token and use it to derive a shift factor to adjust the erasing strength along the identified erasing direction, which we refer to as the erasing shift. In general, we let the factor reduce when the cosine similarity becomes smaller. + +
(1) Instance(2) Art style
A nice photo of SnoopyAn night scene in Van Gogh style
[Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]][Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]]
+ +Figure 3. We analyze the contribution of different tokens in text-visual alignment by separately masking the value of content tokens and [EOT] tokens, where content tokens carry more featured information than those [EOT] tokens. + +We denote the shift factor by $\delta (\cdot ,\cdot):\mathbb{R}^d\times \mathbb{R}^d\to \mathbb{R}$ which is a function of two value vectors. Using it, we revise the erasing operation in Eq. (2) for a single concept to + +$$ +\boldsymbol {v} _ {r} ^ {j} = \boldsymbol {v} ^ {j} - \frac {\delta (\boldsymbol {v} _ {t} ^ {j} , \boldsymbol {v} ^ {j}) \boldsymbol {v} _ {t} ^ {j T} \boldsymbol {v} ^ {j}}{\boldsymbol {v} _ {t} ^ {j T} \boldsymbol {v} _ {t} ^ {j}} \boldsymbol {v} _ {t} ^ {j}. \tag {4} +$$ + +While for multiple concepts, Eq. (3) is revised to + +$$ +\boldsymbol {v} _ {r} ^ {j} = \boldsymbol {v} ^ {j} - \sum_ {h = 1} ^ {n} \delta \left(\boldsymbol {v} _ {t} ^ {h, j}, \boldsymbol {v} ^ {j}\right) \left(\sum_ {k = 1} ^ {n} w _ {h k} \left(\boldsymbol {o} _ {t} ^ {k, j}\right) ^ {T} \boldsymbol {v} ^ {j}\right) \boldsymbol {v} _ {t} ^ {h, j}, \tag {5} +$$ + +where $w_{hk}$ is the $hk$ -th element of the projection matrix that transforms the basis $\left\{\pmb{v}_t^{h,j}\right\}_{h=1}^n$ to the orthonormal basis $\left\{\pmb{o}_t^{h,j}\right\}_{h=1}^n$ . For a single target concept, it is straightforward to introduce the shift factor, as in Eq. (4). However, in the case of erasing multiple concepts, the derivation of a shifted operation is less straightforward, as the orthonormal basis does not carry meaningful semantics, thus a transformation back to the value vectors of the target tokens is needed. We explain in Appendix B how to derive Eq. (5) from Eq. (3). The revised erasing operations result in the proposal AdaVD. + +Our shift factor design builds on the sigmoid function. Given two input vectors $\pmb{x}, \pmb{y} \in \mathbb{R}^d$ , we formulate it as + +$$ +\delta (\boldsymbol {x}, \boldsymbol {y}) = \frac {s}{1 + e ^ {- p (\cos (\boldsymbol {x} , \boldsymbol {y}) - \epsilon)}}. \tag {6} +$$ + +The cosine threshold $\epsilon$ allows a strong erasure when exceeding the threshold. A negative cosine similarity indicates a very weak relevance between the target and prompt tokens, suggesting no erasure is required. Therefore, we set $0 < \epsilon < 1$ to quantify and filter the relatively weak relevance indicated by a positive but small cosine similarity. The hyper-parameter $s > 0$ controls the factor scale, while $p > 0$ controls the increasing rate of the $\delta$ value against the cosine value. In Appendix C.2, we provide hyper-parameter implementation details and a comprehensive analysis. + +# 4. Experiments and Result Analysis + +We conduct extensive experiments to evaluate the proposed AdaVD for erasing a diverse range of target concepts, cov + +ering specific instances, art styles, NSFW content, and celebrity. We compare with SOTA training-based methods including ConAbl [20], ESD [12], SPM [27] and MACE [26] and SOTA training-free methods including NP [2] and SLD [39]. We also demonstrate the time efficiency and interpretability of AdaVD, along with its wider usage in other downstream image generation tasks coupled with a series of diffusion models. + +# 4.1. Experimental Setup + +Implementation: We employ SD v1.4 [2] to generate images using the DPM-solver sampler [25] over 30 sampling steps with classifier-free guidance [17] of 7.5. All the compared methods are implemented following their default configurations available from their official repository. Further implementation details are provided in Appendix C.1. + +Evaluation Data: Adopting the same evaluation protocol from SPM [27], we assess the methods based on 80 instance templates, 30 art style templates, and 25 celebrity templates, and benchmark each method by generating 10 images per template per concept in evaluation. To assess the performance of NSFW erasure, we use the I2P benchmark [39]. + +Performance Metrics: We follow the widely used evaluation metrics for concept erasure, including the CLIP score (CS) [33] to assess erasure efficacy and the Fréchet inception distance (FID) [16] to assess prior preservation. CS calculates the cosine similarity between a textual prompt and the generated image [33]. We examine two CS values before and after erasing and compare the CS value after the erasure. When the prompts contain the target concepts, a more reduced CS indicates a more effective erasure of the target concepts. FID measures the distance between images generated before and after erasing [16]. A lower FID indicates a better alignment between the two images. Thus, for non-target concepts, lower FID values indicate better prior preservation. Overall, a precise concept erasure should have a low CS for prompts containing the target concepts and a low FID for prompts composed of non-target concepts. + +Summary: Results on instance and art style concept erasure are reported in Sections 4.2 and 4.3, while results on celebrity and NSFW erasure are reported in Appendices D.3 and D.2. Additional analyses, including extended quantitative results, comparisons with SuppressEOT [24], performance on different versions of SD, and further discussions, are presented in the Appendix. + +# 4.2. On Instance Concept Erasure + +We first conduct the experiment with erasing a single concept "Snoopy". Six types of prompts were tested, of which one contains "Snoopy" and the other five contain only nontarget concepts. The results are compared in the top block of Table 1. It can be seen that our proposed AdaVD achieves the lowest CS and FID scores in all cases. Particularly, its FID is $33\%$ lower than that of the second-best method. It + +
ConceptSnoopyMickeySpongebobPikachuDogLegislator
CSCSCSCSCSCS
SD v1.428.5126.5727.43---
+ +Erase Snoopy + +
CS ↓FID ↓FID ↓FID ↓FID ↓FID ↓
ConAbl25.3838.4441.5929.6827.7627.36
MACE20.78118.01111.9081.9943.2765.97
SPM23.8933.0634.7023.8919.6118.26
NP23.6659.5878.7452.3767.5155.22
SLD27.8448.1255.3638.7441.9549.08
Ours20.285.728.565.792.326.07
+ +Erase Snoopy and Mickey + +
CS ↓CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl24.2624.0846.3239.6330.5727.49
MACE20.7420.7151.49110.6752.0777.13
SPM23.1622.8141.5831.7721.9623.69
NP23.5924.8581.4150.1065.9358.88
SLD27.7626.7454.5939.2441.6250.13
Ours20.2919.939.345.842.416.43
+ +Erase Snoopy and Mickey and Spongebob + +
CS ↓CS ↓CS ↓FID ↓FID ↓FID ↓
ConAb123.9423.6425.0451.2031.5930.03
MACE20.4820.5021.5999.6847.4670.38
SPM22.8122.3520.8239.8322.6825.31
NP24.2924.7625.3164.7565.1059.33
SLD27.8426.7127.6039.4142.3249.88
Ours19.3919.7320.346.852.797.26
+ +Table 1. Quantitative comparison of single- and multi-instance erasure. The best and second-best results are marked in bold and underlined, respectively. Our AdaVD consistently achieves the lowest CS and the lowest FID in all cases, indicating superior prior preservation without compromising erasure efficacy. + +improves over SOTA by significantly enhanced prior preservation without compromising the erasure precision, as exemplified in Fig. 4. It can be observed from Fig. 4 that methods such as SPM, NP, and SLD fail to fully erase "Snoopy" which can be found from the ear and the shape characteristic of the generated image after erasure. MACE can successfully erase the "Snoopy" concept. But all the competing methods suffer from degraded image quality in non-target concept generation, e.g., "Spongebob". + +We then compare the performance for multi-concept erasure, experimenting with two cases, of which one erases two concepts of "Snoopy" and "Mickey" together and the other erases three concepts of "Snoopy", "Mickey" and "Spongebob" together. Results are reported in the bottom two blocks of Table 1 and visualized in the second and third sections of Fig. 4. Similarly, our AdaVD achieves the lowest CS and FID scores across all cases. This verifies that AdaVD is capable of handling more complex multi-concept erasure and simultaneously fighting against catastrophic forgetting. Conversely, other methods struggle to consistently perform well for multi-concept erasure. For example, when erasing "Snoopy" and "Mickey" together, the image quality for non-target concepts like "Spongebob" and "Legislator" shows apparent degradation in Fig. 4. SLD, in particular, fails to maintain its erasure ability even + +![](images/981afa5437dd2d868a4b8b3d7b447bbad39ba2abe30385b94855e975bc03c8e8.jpg) +Concepts +Figure 4. Qualitative comparison of single- and multi-instance erasure. Both training-based and training-free methods show limitations in prior preservation. In contrast, our AdaVD demonstrates considerable performance in maintaining prior knowledge without compromising erasure efficacy across both single- and multi-concept erasure tasks. + +![](images/75a06f1f2167ad016df0c89dd9fac0f340016b5236785945d884a965e9608427.jpg) +Snoopy, Miekey, Spongebob, Dog, Legislator + +![](images/a909be6fd1116f13c631dd30380ed0f04cc1411ee17fc66325b1dcd593323cc3.jpg) +Snoopy, Mickey, Spongebob, Dog, Legislator + +![](images/3be4de8fc996c55eaf22558d95bf67bb080e91b951ad1ddf537739e6c7215883.jpg) +Figure 5. Qualitative comparison of art style erasure. Our AdaVD can effectively remove the target concept "Van Gogh" while preserving non-target styles like "Picasso" and "Monet". + +when dealing with 2-concept erasure. In Appendix G, we report more experimental results for erasing up to 40 concepts, where our AdaVD can extend to erase dozens of concepts in practice, maintaining consistent erasure efficacy and prior preservation, as shown in Fig. 1. + +# 4.3. On Art Style Erasure + +We experiment with erasing specific art style, including "Van Gogh", "Picasso" and "Monet". Results are reported in Table 2, and visual comparisons are provided in Fig. 5. Our AdaVD exhibits superior prior preservation, and achieves the lowest or closed-to-lowest CS and FID scores, demonstrating strong prior preservation without sacrificing erasure efficacy. Other methods show different drawbacks as observed from the results. For instance, although NP achieves notably better precision in art style removal as compared to instance removal, Fig. 5 shows that it still struggles to fully erase the "Van Gogh" style. Also, SLD fails to erase the "Van Gogh" style. These two methods also degrade generation quality for non-target styles, such as "Picasso" and "Monet", showing harmful effects on non-target concepts directly, as evidenced in both Fig. 5 and + +
ConceptVan GoghPicassoMonetAndy WarholCaravaggio
CSCSCSCSCS
SD v1.429.2129.0629.02--
+ +Erase Van Gogh + +
CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl28.8071.71138.7270.3073.10
MACE27.7465.7769.7983.3775.41
SPM24.7862.2532.2758.3061.50
NP24.90141.56124.52127.85136.32
SLD27.48103.96109.11103.89119.32
Ours24.876.822.668.366.84
+ +Erase Picasso + +
FID ↓CS ↓FID ↓FID ↓FID ↓
ConAbl58.6227.72140.3473.3567.44
MACE60.4627.1149.9276.1072.85
SPM38.7926.697.7652.0051.40
NP111.3526.1491.11116.24121.82
SLD98.2127.0393.0197.00110.05
Ours5.4926.992.339.387.05
+ +Erase Monet + +
FID ↓FID ↓CS ↓FID ↓FID ↓
ConAbl141.52132.1024.53208.38186.26
MACE76.9069.3526.8988.3581.72
SPM41.0329.7127.0031.9025.99
NP137.21126.7524.47127.22135.83
SLD94.4892.8825.73100.90114.87
Ours6.946.5026.308.467.19
+ +Table 2. Quantitative comparison of art style erasure. AdaVD achieves a superior balance between erasure efficacy and prior preservation, especially excelling in prior preservation. + +Table 2. Both MACE and SPM are effective in erasing the target concept, however, their prior preservation is somehow less satisfactory, which is particularly noticeable in the generated images in "Monet" style. Differently, AdaVD can effectively and consistently remove the target concept and meanwhile preserve satisfactorily the prior content, as confirmed by Table 2 and Fig. 5. + +
Data PreparationModel FinetuneImage GenerationTotal Time
ConAbl929011200.910419
SPM0728501.772867
MACE3032320.9544
SLD001.414
Ours401.822
+ +Table 3. Time consumption of 10-concept erasure. We calculate the time cost (s) to erase 10 concepts and generate 10 images using one NVIDIA A40 GPU. Compared with training-based methods, AdaVD exhibits exceptional efficiency in real-time erasure. + +# 4.4. Further Analysis + +Time Consumption: The computational cost of concept erasure primarily arises from three components, including (1) data preparation time required by training-based methods for preparing training data and by AdaVD for basis computation; (2) model fine-tuning time required by training-based methods; and (3) image generation time required by all methods. In Table 3, we compare the total time consumption of different methods, as well as their time spent on each component. The two training-free methods of SLD and AdaVD are significantly faster as no fine-tuning is needed. Our AdaVD costs slightly more time than SLD, i.e., 0.8 extra seconds per image due to its basis computation, and a total of 8 extra seconds for generating 10 images. But this mild increase yields a significant performance gain, succeeding in precise concept erasure. + +Interpreting Erased Components by Visualization: Our AdaVD generates images by replacing the original value vector $\pmb{v}^j$ with $\pmb{v}_r^j$ via orthogonal complement operation. To empirically interpret the rationale behind our method, we visualize the erased component, $\pmb{v}^j - \pmb{v}_r^j$ . Fig. 6 presents three cases of erasing the target concepts "Mickey", "Van Gogh" and "Bruce Lee", where AdaVD successfully erases these target concepts while robustly preserving prior knowledge of non-target concepts. In the first row, as shown in the middle column of each block, the erased components consistently align with the corresponding target semantics when dealing with the target concepts. In the second row of non-target concepts, conversely, the erased components do not contain any informative pattern, indicating that they carry no meaningful semantics, and therefore exert minimal impact on the prior knowledge. + +Downstream Applications: We conduct additional experiments to showcase the versatile applications of our AdaVD across various generative tasks, including (1) implicit concept erasure: by removing the implicit concepts of "rainy" and "foggy"; (2) image editing: by removing the appearance concepts of "glasses" and "mustache"; and (3) attribute suppression: by removing the coupled color concept of "red". Additionally, we integrate AdaVD with a series of diffusion models, including Chilloutmix [5], DreamShaper [6], RealisticVision [7], and SD v2.1 [4], alongside SD + +![](images/e3346c4cac0a6e6af7b4a49634547ff2ee55c92f9821d5381aba83ce134a97e3.jpg) +Figure 6. Visualization of erased components. In each block, we compare both target (1st row) and non-target concept (2nd row) by visualizing the original image (1st column), erased component (2nd column), and generation by our AdaVD (3rd column). + +![](images/51eaea3c18fd219431b9ecaf1f0b969ee652f7282c56a080a4dbcf9aa308259e.jpg) +Figure 7. Downstream applications. We extend AdaVD to versatile generation tasks, including (1) implicit concept erasure, (2) image editing, and (3) attribute suppression, indicating its significant potential for broad applications. + +v1.4. As illustrated in Fig. 7, despite the absence of explicit mention for "rainy" and "foggy", AdaVD can still effectively erase these concepts in image semantic space. Meanwhile, AdaVD also precisely removes "glasses" and "mustache" with minimal changes to other details, highlighting its potential in image editing applications. For attribute suppression, AdaVD successfully eliminates the color attribute "red" from objects such as apples and roses, demonstrating its capability to decouple strongly coupled concepts, e.g., "roses are red" embedded in the model's prior knowledge. + +# 5. Conclusion and Future Work + +We have presented AdaVD, a precise, fast, and low-cost method for erasing unwanted concepts. The idea of leveraging the classical linear algebraic orthogonal complement operation and an adaptive erasing shift design is novel, and has successfully achieved a precise concept erasure. Extensive experiments have demonstrated both high erasure efficacy and strong prior preservation of AdaVD for both single- and multi-concept erasure. Moreover, AdaVD exhibits excellent interpretability through visualizing its erased components and strong capability in solving downstream tasks. It has been an intriguing discovery that the orthogonal complement of the value vectors of the target concepts is effective at erasing their inherent semantics. Despite the empirical success, we will seek to establish a rigorous theoretical understanding of the accumulative effect of applying this linear algebraic operation layer-wise for concept erasure in the future. + +# Acknowledgements + +This work is supported by the National Science and Technology Major Project (2023ZD0121102) and the National Natural Science Foundation of China (U24B20180). + +# References + +[1] Safety checker nested in stable diffusion. https://huggingface.co/CompVis/stable-diffusion-safety-checker, 2022.2 +[2] Stable diffusion. https://huggingface.co/ CompVis/stable-diffusion-v1-4, 2022.2,3,6 +[3] Stable diffusion v2.0. https://huggingface.co/stabilityai/stable-diffusion-2, 2022.2 +[4] Stable diffusion v2.1. https://huggingface.co/stabilityai/stable-diffusion-2-1, 2022.8 +[5] Chilloutmix. https://huggingface.co/swl-models/chilloutmix, 2023.1,8,18 +[6] Dreamshaper. https://huggingface.co/Lykon/DreamShaper, 2023.1,8,18,22 +[7] Realisticvision. https://huggingface.co/SG161222/Realistic_Vision_V5.1_noVAE, 2023.8,18,22 +[8] Praneeth Bedapudi. 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+ } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 449, + 555, + 506 + ], + "lines": [ + { + "bbox": [ + 54, + 449, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 54, + 449, + 555, + 506 + ], + "type": "text", + "content": "Figure 1. The proposed Adaptive Value Decomposer (AdaVD) demonstrates a satisfactory balance between erasure efficacy and prior preservation and an effective transferability across T2I diffusion models. (a) Compared to SLD [39], AdaVD enables precise concept erasure without compromising prior knowledge for non-target concepts at both single- and multi-concept erasure. This is facilitated by a precise disentanglement of target semantics (e.g., \"Snoopy\") and a robust preservation of non-target ones (e.g., \"Teddy\"), with visualization interpretation marked by " + }, + { + "bbox": [ + 54, + 449, + 555, + 506 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 54, + 449, + 555, + 506 + ], + "type": "text", + "content": ". (b) AdaVD can be transferred to various T2I models, e.g., SDXL [31], DreamShaper [6], Chilloutmix [5]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 152, + 513, + 200, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 513, + 200, + 525 + ], + "spans": [ + { + "bbox": [ + 152, + 513, + 200, + 525 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 54, + 529, + 297, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 529, + 297, + 685 + ], + "spans": [ + { + "bbox": [ + 54, + 529, + 297, + 685 + ], + "type": "text", + "content": "Recent success of text-to-image (T2I) generation and its increasing practical applications, enabled by diffusion models, require urgent consideration of erasing unwanted concepts, e.g., copyrighted, offensive, and unsafe ones, from the pre-trained models in a precise, timely, and low-cost manner. The twofold demand of concept erasure includes not only a precise removal of the target concept (i.e., erasure efficacy) but also a minimal change on non-target content (i.e., prior preservation), during generation. Existing methods face challenges in maintaining an effective balance between erasure efficacy and prior preservation, and they can be computationally costly. To improve, we propose a precise, fast, and low-cost concept era" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 514, + 556, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 556, + 706 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 556, + 706 + ], + "type": "text", + "content": "sure method, called Adaptive Vaule Decomposer (AdaVD), which is training-free. Our method is grounded in a classical linear algebraic operation of computing orthogonal complement, implemented in the value space of each cross-attention layer within the UNet of diffusion models. We design a shift factor to adaptively navigate the erasure strength, enhancing effectively prior preservation without sacrificing erasure efficacy. Extensive comparative experiments with both training-based and training-free state of the arts demonstrate that the proposed AdaVD excels in both single and multiple concept erasure, showing 2 to 10 times of improvement in prior preservation than the second best, meanwhile achieving the best or near best erasure efficacy. AdaVD supports a series of diffusion models and downstream image generation tasks, with code available on: https://github.com/WYuan1001/AdaVD." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 139, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 139, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 139, + 703 + ], + "type": "text", + "content": "*Equal Contributions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28759" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 294, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 294, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 294, + 270 + ], + "type": "text", + "content": "The recent advancements of text-to-image (T2I) diffusion models [11, 17, 18, 30, 36, 50, 52] have enabled users to effortlessly generate high-quality images with simple textual prompts. However, such generations would inevitably introduce copyrighted [10, 22, 42, 44] or offensive [23, 39] concepts, caused by the noisy training data scraped from web [9, 40]. Because it is very costly to re-train large generative models from scratch, it is vital to develop low-cost techniques to precisely erase unwanted semantic concepts in images, i.e., concept erasure. This task aims at a precise erasure of visual content w.r.t. target concepts from generated images (i.e., erasure efficacy), while a faithful preservation of irrelevant content w.r.t. the prompts comprising non-target concepts (i.e., prior preservation), safeguarding a secure T2I generation for diffusion models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 271, + 295, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 271, + 295, + 450 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 295, + 450 + ], + "type": "text", + "content": "A representative category of concept erasure methods is training-based, which fine-tunes a subset of model parameters by formulating meticulous erasing objective functions [12, 20, 26, 27]. Despite good erasure efficacy, they exhibit considerable practical limitations when being deployed. For instance, they require expensive individual fine-tuning to erase each concept, which thereby limits their real-time usage. As an example, it is unacceptable for online T2I platforms to be costly to erase newly emerging concepts, where copyrighted or offensive concepts could arise unexpectedly, with no means to produce a complete list of concepts to erase in advance. Moreover, these methods suffer from a limited balance between erasure efficacy and prior preservation, due to their reliance on regularization terms to trade off prior preservation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 450, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 295, + 653 + ], + "type": "text", + "content": "An alternative category of concept erasure methods is training-free, such as Negative Prompt (NP) [2], Safe Latent Diffusion (SLD) [39], and SuppressEOT [24], which enable real-time erasure. They intervene in the image generation process, exhibiting a range of drawbacks. For instance, NP was initially designed to enhance image quality and can result in compromised erasure efficacy; while SuppressEOT requires the user to specify the location of the target concept within the prompt, thus, it is not suitable for erasure applications that require full automation. Therefore, both NP and SuppressEOT fall short as independent tools for concept erasure. Regarding SLD, it does not perform well at retaining prior knowledge of non-target concepts as illustrated in Fig. 1, failing in precise concept erasure. Limited by their drawbacks, current training-free methods are not robust enough to act as an independent concept erasure tool and to be applied in continual erasure of multiple concepts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "content": "In this light, we advance concept erasure techniques for T2I generation, by developing a precise, fast, and low-cost method called Adaptive Value Decomposer (AdaVD). It is a training-free method, capable of precisely erasing the target concepts and satisfactorily preserving non-target priors" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "content": "with low computational overhead. Our core design builds on a classical linear algebraic operation, i.e., projection onto the orthogonal complement of the semantic space of the target concepts. We conduct this projection-based decomposition in the cross-attention value space, disentangling target semantics from the original prompts. To improve the erasure precision and prior preservation, we further refine the decomposition by adaptively allocating token-wise shifts. These shifts are designed to differentiate the strong and specific alignments from the weak and general alignments between prompt tokens and visual content associated with the target concept. Guided by these shifts, the strong and specific alignments are erased for precision while the weak and general alignments are retained for prior preservation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 240, + 553, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 553, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 553, + 359 + ], + "type": "text", + "content": "Fig. 1 (a) demonstrates the erased results for both target and non-target concepts. It shows that our AdaVD can precisely locate and erase the components indicated by the target semantics, meanwhile keeping the non-target priors maximally unaffected. Empirical evaluation shows that AdaVD excels in prior preservation, outperforming the second best by a 2- to 10-fold improvement across various nontarget concepts, and meanwhile maintains exceptional erasure efficacy, consistently achieving the best or near-best performance. Our contributions are summarized below:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 360, + 553, + 538 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 313, + 360, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 553, + 407 + ], + "type": "text", + "content": "- A novel and effective erasing operation by exploiting the projection onto the orthogonal complement of the target concept in the cross-attention value space, to disentangle semantics carried by the target concept." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 407, + 553, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 553, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 553, + 442 + ], + "type": "text", + "content": "- An adaptive erasing mechanism through a dynamic shift factor, which can effectively minimize the impact on prior knowledge, without compromising the erasure efficacy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 444, + 553, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 553, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 553, + 490 + ], + "type": "text", + "content": "- A precise, fast, and low-cost concept erasure technique AdaVD, which works in a training-free manner and supports a series of T2I diffusion models, capable of precise concept erasure." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 491, + 553, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 553, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 553, + 538 + ], + "type": "text", + "content": "- Extensive experiments that demonstrate the superiority of AdaVA against state-of-the-art (SOTA) methods, achieving 2 to 10 times of improvement in prior preservation while maintaining precise erasure efficacy." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 549, + 406, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 549, + 406, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 549, + 406, + 562 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "content": "Re-training and Blocking: The most straightforward way to erase a target concept from a pre-trained T2I model is to exclude the training data relevant to this concept and retrain the model from scratch, as in Stable Diffusion (SD) v2.0 [3]. For this, an Not Safe For Work (NSFW) detector [8, 21, 38] can be used to filter unsafe data from LAION-5B [41] prior to the training. However, this approach is time-consuming, requires specialized detectors, and can introduce biases [43]. An alternative solution is to block the prompts of concerns and restrict the outputs of concerns, by using filters [43] and safety checkers [1, 35]. Yet, such safeguards are fragile and easy to bypass [46, 49], especially" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28760" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "content": "when being confronted with crafted malicious prompts [39]. Training-based: A more effective group of concept erasure solutions fine-tune pre-trained generative models, teaching them to \"forget\" a target concept, e.g., Erased Stable Diffusion (ESD) [12]. However, since the ESD design does not consider prior preservation, both target and non-target concepts are adversely affected. To improve, new training techniques have been developed, e.g., ConAbl [20], SA [14], UCE [13], EraseDiff [48], SPM [27] and MACE [26]. They improve prior preservation through regularization but still fall short in achieving both precise erasure and robust prior preservation. Moreover, for every new target concept to be erased, a separate fine-tuning is required. This is time-consuming, making real-time erasure impractical, especially for highly interactive platforms where unsafe or inappropriate concepts can emerge unexpectedly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 264, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 264, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 56, + 264, + 296, + 552 + ], + "type": "text", + "content": "Training-free: With largely reduced computing costs, training-free methods are gaining increasing attention. NP [2] and SLD [39] pioneer training-free concept erasure by adjusting classifier-free guidance [17], leading the generation towards a direction away from the target concepts. However, NP lacks fine-grained control over target concepts and compromises prior preservation. SLD also compromises the prior knowledge during its generation, disrupting the overall generating quality of non-target concepts. SuppressEOT [24], akin to image editing techniques [15], removes target concepts based on user-specified textual positions. Its user-involved design makes it more suitable for editing tasks, but not for system-wide erasing tasks that require full automation. Benefiting from orthogonal decompositions in value spaces, the proposed training-free method AdaVD achieves not only precise concept erasure but also satisfactory prior preservation. It supports multi-concept erasure, is compatible across different versions of stable diffusion, and consistently demonstrates superior performance. The training-free method SAFREE [51], concurrent to ours, also uses orthogonal decomposition but operates differently on text embeddings, supported by masking, projection, Fourier transforms, and a hard control of removal strength. We compare performance with it in the appendix." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "content": "Concept erasure in T2I generation aims at a successful removal of the visual content indicated by textual concepts (i.e., target concepts), meanwhile a satisfactory preservation of the visual content irrelevant to these concepts (i.e., prior knowledge). It is challenging to achieve simultaneously satisfactory erasure efficacy and prior preservation. To advance this field, we propose a precise, fast, and low-cost concept erasure method, termed AdaVD and illustrated in Fig. 2 (c). The method is training-free, and its core design builds on a classical linear algebraic operation, i.e., orthogonal complement. This simple but elegant geometric" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "operation is able to guide effectively the image generation, enabling a precise removal of the target concepts from the image content meanwhile a satisfactory preservation of the non-target content." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 128, + 511, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 128, + 511, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 128, + 511, + 140 + ], + "type": "text", + "content": "3.1. Preliminary on T2I Diffusion Models" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": "Current T2I models usually include an image compression network [19] and a conditional latent diffusion model [36] that performs sequential denoising with a UNet [37] in the latent space. The UNet takes as inputs the noise latent variable " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": ", timestep " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": ", and embedding " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": " of the textual prompt from a pre-trained CLIP model [33], and predicts the noise " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C})" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": ". In training-free concept erasure, the noise is additionally conditioned on the target concept with text embedding " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": ", predicted by " + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t, t, \\mathbf{C}, \\mathbf{C}_t)" + }, + { + "bbox": [ + 313, + 145, + 553, + 253 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": "Interactions between the image and text modalities are enabled by cross-attention (CA) layers [36, 47] within the UNet, which align the latent representation of the noisy image with the semantic detail of the textual prompt. Each CA layer computes an attention map " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{A} = \\mathrm{softmax}\\left(\\frac{\\mathbf{Q}\\mathbf{K}^T}{\\sqrt{d}}\\right)" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": " with a latent feature dimension " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": ". The queries " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": " are computed from the noisy image features, while both keys " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": " and values " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": " from the text embeddings " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": ", using different projection matrices. The layer output is a weighted aggregation of " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 253, + 553, + 377 + ], + "type": "text", + "content": ". More details on CA layers are in Appendix A." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 378, + 554, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 554, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 554, + 534 + ], + "type": "text", + "content": "It has been recognized that the keys in CA layers mostly act as the \"Where\" pathway, governing the layout of the attention map and determining the compositional structure of the generated images, while the values as the \"What\" pathway, controlling the content and visual appearance of images [45]. Because the goal of concept erasure is to modify the visual content of the generated images, we propose to conduct value decompositions into subspaces, which are uniquely constructed by exploiting the target concept and its orthogonal complement in an adaptive fashion. We demonstrate that information offered by the orthogonal complement can be used to generate successfully high-quality images with the target concept precisely erased." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 540, + 552, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 552, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 552, + 553 + ], + "type": "text", + "content": "3.2. Token-wise Target Embedding Pre-processing" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "text", + "content": "Given a textual example, which can be either a target concept to erase or an original prompt, its embedding is computed at the token level by a CLIP text encoder. Each tokenized example is padded with [SOT] as the prefix and [EOT] at the end, with [EOT] filling any remaining positions to maintain a fixed token length of " + }, + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "text", + "content": ". Each token is characterized by an embedding vector of dimension " + }, + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 313, + 558, + 553, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": "We focus on the embedding of a target concept " + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t\\in" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{l\\times D_c}" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": " , and denote each column of " + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t^T" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "c_{t}^{j}" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": " that corresponds to a token vector where " + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "j\\in \\{1,2,\\dots ,l\\}" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": " . To facilitate a precise erasure, we emphasize the key information carried by a target concept by proposing an embedding duplication. Specifically, the embedding of the last sub" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28761" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 62, + 553, + 184 + ], + "blocks": [ + { + "bbox": [ + 57, + 62, + 553, + 184 + ], + "lines": [ + { + "bbox": [ + 57, + 62, + 553, + 184 + ], + "spans": [ + { + "bbox": [ + 57, + 62, + 553, + 184 + ], + "type": "image", + "image_path": "4cda90f0a533aee68d3b154ae598bde49c37ebab0d734efbca4245b1090bbf63.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 186, + 555, + 244 + ], + "lines": [ + { + "bbox": [ + 54, + 186, + 555, + 244 + ], + "spans": [ + { + "bbox": [ + 54, + 186, + 555, + 244 + ], + "type": "text", + "content": "Figure 2. Overview of our Adaptive Value Decomposer (AdaVD) in erasing the target concept \"Snoopy\". (a) First, we token-wisely duplicate the last subject token of the target embedding encoded by the text encoder, except for [SOT]. (b) Then, the pre-processed target embedding and corresponding prompt embedding are jointly fed into CA layers within the UNet as conditions, to disentangle target semantics from the original image at each timestep. (c) In each CA layer, we perform token-wise orthogonal value decomposition with an adaptive token-wise shift. The new value is subsequently multiplied by the attention map, producing the erased output for this CA layer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "spans": [ + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "text", + "content": "ject token within its prompt content excluding [SOT] and [EOT], replaces all the token positions except for [SOT], as illustrated in Fig. 2 (a). For instance, the single-token concept \"snoopy\" has a modified embedding matrix corresponding to \"[SOT], snoopy, snoopy, ..., snoopy\", while the multi-token concept \"Van Gogh\" to \"[SOT], gogh, gogh, ..., gogh\". Benefiting from the causal attention mechanism used by the CLIP text encoder, the last subject token is able to \"see\" all the prompt content and contains key information [28], therefore is sufficient for erasure calculation. The modified embedding matrix " + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{C}}_t" + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "text", + "content": " is fed into a CA layer to compute the value matrix " + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{V}}_t \\in \\mathbb{R}^{l \\times d}" + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "text", + "content": " via a linear projection using the projection matrix " + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{V}} \\in \\mathbb{R}^{D_c \\times d}" + }, + { + "bbox": [ + 54, + 251, + 297, + 407 + ], + "type": "text", + "content": ", as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 415, + 295, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 415, + 295, + 464 + ], + "spans": [ + { + "bbox": [ + 91, + 415, + 295, + 464 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {V}} _ {t} = \\tilde {\\mathbf {C}} _ {t} \\mathbf {W} _ {\\mathrm {V}} = \\left[ c _ {t} ^ {1}, \\underbrace {c _ {t} ^ {k} , \\dots , c _ {t} ^ {k}} _ {l - 1} \\right] ^ {T} \\mathbf {W} _ {\\mathrm {V}}. \\tag {1}", + "image_path": "1372ec28149745897602f60ce6e1aa3be4126e24abb9382066387ad08d2dfdae.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "text", + "content": "The token vector " + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "inline_equation", + "content": "c_{t}^{1}" + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "text", + "content": " corresponds to [SOT] and " + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "inline_equation", + "content": "c_{t}^{k}" + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "text", + "content": " to the last subject token. The total token number is still " + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 474, + 295, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 508, + 234, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 234, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 234, + 521 + ], + "type": "text", + "content": "3.3. Orthogonal Value Decomposition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 526, + 295, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 526, + 295, + 610 + ], + "spans": [ + { + "bbox": [ + 55, + 526, + 295, + 610 + ], + "type": "text", + "content": "Given a conditional latent diffusion model trained for standard T2I generation, our proposed erasing operation works by projecting the original textual prompt onto the orthogonal complement of the subspace spanned by the target concepts to erase, and it is implemented in the value space learned at each CA layer of the UNet. It supports both single-concept and multi-concept erasure." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": "We do not apply any erasing operation to [SOT], as it primarily serves as a prefix and does not carry useful information to distinguish the semantic content. We start from the modified value matrix " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{V}}_t" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": " in Eq. (1), and use " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{v}}_t^j" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": " to denote the " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": "-th column of " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{V}}_t^T" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": ". The exclusion of [SOT] in the erasure calculation is equivalent to replacing the value vector in the first row of " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{V}}_t" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": " by a zero vector, resulting in " + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_t = \\left[0,\\tilde{\\boldsymbol{v}}_t^2,\\tilde{\\boldsymbol{v}}_t^3,\\dots,\\tilde{\\boldsymbol{v}}_t^l\\right]^T" + }, + { + "bbox": [ + 55, + 611, + 295, + 717 + ], + "type": "text", + "content": " to use in the erasing operation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 251, + 441, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 441, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 441, + 262 + ], + "type": "text", + "content": "3.3.1. Single-concept Erasure" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": "Our erasing operation works with " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_t^T" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ", where each column of " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_t^T" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": " corresponds to the erased value vector for token position " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": " and is denoted as " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\pmb{v}_t^j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ", and with the value matrix " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{l \\times d}" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": " computed from the original prompt, where each column of " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^T" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": " is referred to as the original value vector for the token position " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ". To remove the effect of the target concept from the original prompt, for each token position, we project the original value vector " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": " onto the orthogonal complement of the span of the erased value vector " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\pmb{v}_t^j" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ", and denote this orthogonal complement by " + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "inline_equation", + "content": "\\mathrm{span}^\\perp(\\pmb{v}_t^j)" + }, + { + "bbox": [ + 313, + 265, + 555, + 402 + ], + "type": "text", + "content": ". This results in the following modified value vector:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 409, + 555, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 409, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 317, + 409, + 555, + 460 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\operatorname {s p a n} ^ {\\perp} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)} \\boldsymbol {v} ^ {j} = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\operatorname {s p a n} \\left(\\boldsymbol {v} _ {t} ^ {j}\\right)}\\right) \\boldsymbol {v} ^ {j} \\tag {2} \\\\ = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j} \\boldsymbol {v} _ {t} ^ {j T}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}, \\\\ \\end{array}", + "image_path": "caf4aac0ea60dfd85155e2faa67f3840540739293d252ff0c71753cd8bcb61c4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathbb{X}}\\pmb{x}" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": " denotes the orthogonal projection of a vector " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": " onto the space " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\mathbb{X}" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_d" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": " is an identity matrix of size " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": ". The modified value vector " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\pmb{v}_r^j" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": " is used, instead of " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": ", to calculate the output of the CA layer, as illustrated in Fig. 2 (c). Since " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\pmb{v}_t^1 = \\mathbf{0}" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": ", it has " + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\pmb{v}_r^1 = \\pmb{v}^1" + }, + { + "bbox": [ + 313, + 467, + 554, + 538 + ], + "type": "text", + "content": ", meaning that no erasure is performed for [SOT]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 544, + 440, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 440, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 440, + 555 + ], + "type": "text", + "content": "3.3.2. Multi-concept Erasure" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": "We generalize the above operation to erase a set of " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": " target concepts, and their corresponding modified value matrices are denoted by " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{V}_t^h\\in \\mathbb{R}^{l\\times d}\\}_{h = 1}^n" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{t}^{h,j}" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": " to denote the " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": "-th column of " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\left(\\mathbf{V}_t^h\\right)^T" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": ", referred to as the erased value vector for the " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": "-th token position of the " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": "-th target concept. Our erasing operation can naturally be extended to projecting the original prompt to the orthogonal complement of the span of the " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": " erased value vectors " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\mathrm{span}^\\perp \\left(\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h = 1}^n\\right)" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": ". To calculate the projection, we first conduct the Gram-Schmidt orthogonalization to obtain a set of " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "text", + "content": " orthonormal basis vectors " + }, + { + "bbox": [ + 313, + 559, + 555, + 717 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h = 1}^n" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28762" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "text", + "content": "for the span of " + }, + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n" + }, + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "text", + "content": ". Here, we assume the value vectors in " + }, + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n" + }, + { + "bbox": [ + 55, + 70, + 296, + 157 + ], + "type": "text", + "content": " are linearly independent and they form a basis. Such an assumption is reasonable because the multiple concepts to erase should be semantically different in practice, otherwise, a single-concept erasure would be sufficient. The desired projection is then computed by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 167, + 295, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 167, + 295, + 240 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 295, + 240 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {v} _ {r} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {v} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} = \\mathbf {P} _ {\\text {s p a n} ^ {\\perp} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)} \\boldsymbol {v} ^ {j} \\tag {3} \\\\ = \\left(\\mathbf {I} _ {d} - \\mathbf {P} _ {\\text {s p a n}} \\left(\\left\\{\\boldsymbol {o} _ {t} ^ {h, j} \\right\\} _ {h = 1} ^ {n}\\right)\\right) \\boldsymbol {v} ^ {j} \\\\ = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\left(\\boldsymbol {o} _ {t} ^ {h, j}\\right) ^ {T} \\boldsymbol {v} ^ {j} \\boldsymbol {o} _ {t} ^ {h, j}. \\\\ \\end{array}", + "image_path": "bd7c1efec56daa4b75098f2bcef4a712a146bab9328c94f2103808fa93d1a0ea.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 251, + 296, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 291 + ], + "type": "text", + "content": "As an addition, we provide in Appendix B an alternative way to compute " + }, + { + "bbox": [ + 55, + 251, + 296, + 291 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{span}^{\\perp}\\left(\\left\\{\\boldsymbol{v}_t^{h,j}\\right\\}_{h=1}^n\\right)} \\boldsymbol{v}^j" + }, + { + "bbox": [ + 55, + 251, + 296, + 291 + ], + "type": "text", + "content": " that does not require Gram-Schmidt orthogonalization but matrix inverse." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 300, + 186, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 186, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 186, + 312 + ], + "type": "text", + "content": "3.4. Adaptive Erasing Shift" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": "In practice, given a pair of textual prompts and a target concept to erase, their token-wise relevance can vary across different token positions. The different tokens of the prompt carry information with different intensities and focuses and thus can have quite different effects on image generation. As an example, we compare the generated images in each subfigure of Fig. 3, using different versions of the value matrix " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": " for the same prompt. We separate the values corresponding to the [EOT] tokens and the remaining, expressing it as " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = [\\mathbf{V}_{\\text {content }}, \\mathbf{V}_{[\\text {EOT}]}\\]" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": ". Herein, we include [SOT] within " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\text {content }}" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": " for simplicity. We obtain three versions of " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": " by (1) keeping it as what it is, (2) setting " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{[\\text {EOT}]}" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": " as zero, and (3) setting " + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\text {content }}" + }, + { + "bbox": [ + 55, + 318, + 296, + 521 + ], + "type": "text", + "content": " as zero. Fig. 3 shows that the prompt content carries more featured information than those [EOT] tokens. This motivates us to further improve the design in Eqs. (2) and (3), by enabling adaptive adjustment of the erasing operation at the token level." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": "We discover that, although a projection onto the orthogonal complement of the target concept is effective at erasing this concept itself, it can sometimes affect the prior preservation due to an excessive removal of information. Therefore, our adaptive design is focused on improving the prior preservation. When semantics carried by a prompt token are less relevant to a target token, we intend to perform less erasure to protect the prior image content. According to [32], angular information plays a more critical role in conveying semantics than magnitude during image generation. These motivate us to exploit the cosine similarity between the value vectors of a prompt token and a target token and use it to derive a shift factor to adjust the erasing strength along the identified erasing direction, which we refer to as the erasing shift. In general, we let the factor reduce when the cosine similarity becomes smaller." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 317, + 72, + 553, + 144 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 144 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 144 + ], + "type": "table", + "html": "
(1) Instance(2) Art style
A nice photo of SnoopyAn night scene in Van Gogh style
[Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]][Vcontent, V[EOT]][Vcontent, 0][0, V[EOT]]
", + "image_path": "d87e906a1e21539b4d747b4682b0d70b9c016535e8172ad57e97103f95183f90.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "type": "text", + "content": "Figure 3. We analyze the contribution of different tokens in text-visual alignment by separately masking the value of content tokens and [EOT] tokens, where content tokens carry more featured information than those [EOT] tokens." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 197, + 555, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 555, + 234 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 555, + 234 + ], + "type": "text", + "content": "We denote the shift factor by " + }, + { + "bbox": [ + 313, + 197, + 555, + 234 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot ,\\cdot):\\mathbb{R}^d\\times \\mathbb{R}^d\\to \\mathbb{R}" + }, + { + "bbox": [ + 313, + 197, + 555, + 234 + ], + "type": "text", + "content": " which is a function of two value vectors. Using it, we revise the erasing operation in Eq. (2) for a single concept to" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 365, + 239, + 553, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 239, + 553, + 275 + ], + "spans": [ + { + "bbox": [ + 365, + 239, + 553, + 275 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\frac {\\delta (\\boldsymbol {v} _ {t} ^ {j} , \\boldsymbol {v} ^ {j}) \\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} ^ {j}}{\\boldsymbol {v} _ {t} ^ {j T} \\boldsymbol {v} _ {t} ^ {j}} \\boldsymbol {v} _ {t} ^ {j}. \\tag {4}", + "image_path": "361c41bf252a7441108e244b7288d8b919feb43851f8fc70e564dbf48ad221f6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 279, + 514, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 279, + 514, + 292 + ], + "spans": [ + { + "bbox": [ + 314, + 279, + 514, + 292 + ], + "type": "text", + "content": "While for multiple concepts, Eq. (3) is revised to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 297, + 553, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 297, + 553, + 339 + ], + "spans": [ + { + "bbox": [ + 315, + 297, + 553, + 339 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {r} ^ {j} = \\boldsymbol {v} ^ {j} - \\sum_ {h = 1} ^ {n} \\delta \\left(\\boldsymbol {v} _ {t} ^ {h, j}, \\boldsymbol {v} ^ {j}\\right) \\left(\\sum_ {k = 1} ^ {n} w _ {h k} \\left(\\boldsymbol {o} _ {t} ^ {k, j}\\right) ^ {T} \\boldsymbol {v} ^ {j}\\right) \\boldsymbol {v} _ {t} ^ {h, j}, \\tag {5}", + "image_path": "0f2a7172360aa87c18c5f9c46d1b41b6e2726e840e1e8f682cfbf720bb5f1f92.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "inline_equation", + "content": "w_{hk}" + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "inline_equation", + "content": "hk" + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "content": "-th element of the projection matrix that transforms the basis " + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{v}_t^{h,j}\\right\\}_{h=1}^n" + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "content": " to the orthonormal basis " + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "inline_equation", + "content": "\\left\\{\\pmb{o}_t^{h,j}\\right\\}_{h=1}^n" + }, + { + "bbox": [ + 313, + 339, + 554, + 484 + ], + "type": "text", + "content": ". For a single target concept, it is straightforward to introduce the shift factor, as in Eq. (4). However, in the case of erasing multiple concepts, the derivation of a shifted operation is less straightforward, as the orthonormal basis does not carry meaningful semantics, thus a transformation back to the value vectors of the target tokens is needed. We explain in Appendix B how to derive Eq. (5) from Eq. (3). The revised erasing operations result in the proposal AdaVD." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 484, + 553, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 553, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 553, + 509 + ], + "type": "text", + "content": "Our shift factor design builds on the sigmoid function. Given two input vectors " + }, + { + "bbox": [ + 313, + 484, + 553, + 509 + ], + "type": "inline_equation", + "content": "\\pmb{x}, \\pmb{y} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 484, + 553, + 509 + ], + "type": "text", + "content": ", we formulate it as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 369, + 514, + 553, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 514, + 553, + 536 + ], + "spans": [ + { + "bbox": [ + 369, + 514, + 553, + 536 + ], + "type": "interline_equation", + "content": "\\delta (\\boldsymbol {x}, \\boldsymbol {y}) = \\frac {s}{1 + e ^ {- p (\\cos (\\boldsymbol {x} , \\boldsymbol {y}) - \\epsilon)}}. \\tag {6}", + "image_path": "ef6d7194e9678c818c90e17670159cd58540897238743edcd4a4b36e111795cb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": "The cosine threshold " + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": " allows a strong erasure when exceeding the threshold. A negative cosine similarity indicates a very weak relevance between the target and prompt tokens, suggesting no erasure is required. Therefore, we set " + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "inline_equation", + "content": "0 < \\epsilon < 1" + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": " to quantify and filter the relatively weak relevance indicated by a positive but small cosine similarity. The hyper-parameter " + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "inline_equation", + "content": "s > 0" + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": " controls the factor scale, while " + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "inline_equation", + "content": "p > 0" + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": " controls the increasing rate of the " + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 540, + 555, + 661 + ], + "type": "text", + "content": " value against the cosine value. In Appendix C.2, we provide hyper-parameter implementation details and a comprehensive analysis." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 669, + 499, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 499, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 499, + 683 + ], + "type": "text", + "content": "4. Experiments and Result Analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "We conduct extensive experiments to evaluate the proposed AdaVD for erasing a diverse range of target concepts, cov" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28763" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": "ering specific instances, art styles, NSFW content, and celebrity. We compare with SOTA training-based methods including ConAbl [20], ESD [12], SPM [27] and MACE [26] and SOTA training-free methods including NP [2] and SLD [39]. We also demonstrate the time efficiency and interpretability of AdaVD, along with its wider usage in other downstream image generation tasks coupled with a series of diffusion models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 172, + 171, + 185 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 172, + 171, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 172, + 171, + 185 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 189, + 295, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 189, + 295, + 261 + ], + "spans": [ + { + "bbox": [ + 55, + 189, + 295, + 261 + ], + "type": "text", + "content": "Implementation: We employ SD v1.4 [2] to generate images using the DPM-solver sampler [25] over 30 sampling steps with classifier-free guidance [17] of 7.5. All the compared methods are implemented following their default configurations available from their official repository. Further implementation details are provided in Appendix C.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 262, + 295, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 295, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 295, + 332 + ], + "type": "text", + "content": "Evaluation Data: Adopting the same evaluation protocol from SPM [27], we assess the methods based on 80 instance templates, 30 art style templates, and 25 celebrity templates, and benchmark each method by generating 10 images per template per concept in evaluation. To assess the performance of NSFW erasure, we use the I2P benchmark [39]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 333, + 295, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 333, + 295, + 524 + ], + "spans": [ + { + "bbox": [ + 55, + 333, + 295, + 524 + ], + "type": "text", + "content": "Performance Metrics: We follow the widely used evaluation metrics for concept erasure, including the CLIP score (CS) [33] to assess erasure efficacy and the Fréchet inception distance (FID) [16] to assess prior preservation. CS calculates the cosine similarity between a textual prompt and the generated image [33]. We examine two CS values before and after erasing and compare the CS value after the erasure. When the prompts contain the target concepts, a more reduced CS indicates a more effective erasure of the target concepts. FID measures the distance between images generated before and after erasing [16]. A lower FID indicates a better alignment between the two images. Thus, for non-target concepts, lower FID values indicate better prior preservation. Overall, a precise concept erasure should have a low CS for prompts containing the target concepts and a low FID for prompts composed of non-target concepts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 525, + 295, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 295, + 608 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 295, + 608 + ], + "type": "text", + "content": "Summary: Results on instance and art style concept erasure are reported in Sections 4.2 and 4.3, while results on celebrity and NSFW erasure are reported in Appendices D.3 and D.2. Additional analyses, including extended quantitative results, comparisons with SuppressEOT [24], performance on different versions of SD, and further discussions, are presented in the Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 613, + 217, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 613, + 217, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 613, + 217, + 624 + ], + "type": "text", + "content": "4.2. On Instance Concept Erasure" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 629, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 712 + ], + "type": "text", + "content": "We first conduct the experiment with erasing a single concept \"Snoopy\". Six types of prompts were tested, of which one contains \"Snoopy\" and the other five contain only nontarget concepts. The results are compared in the top block of Table 1. It can be seen that our proposed AdaVD achieves the lowest CS and FID scores in all cases. Particularly, its FID is " + }, + { + "bbox": [ + 55, + 629, + 295, + 712 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 55, + 629, + 295, + 712 + ], + "type": "text", + "content": " lower than that of the second-best method. It" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 552, + 103 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 552, + 103 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 552, + 103 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 552, + 103 + ], + "type": "table", + "html": "
ConceptSnoopyMickeySpongebobPikachuDogLegislator
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", + "image_path": "70b3bc140c0c1c94223a3607294363f8784805ecc9102b574e269c37592db714.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 112, + 552, + 184 + ], + "blocks": [ + { + "bbox": [ + 413, + 104, + 455, + 112 + ], + "lines": [ + { + "bbox": [ + 413, + 104, + 455, + 112 + ], + "spans": [ + { + "bbox": [ + 413, + 104, + 455, + 112 + ], + "type": "text", + "content": "Erase Snoopy" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 112, + 552, + 184 + ], + "lines": [ + { + "bbox": [ + 316, + 112, + 552, + 184 + ], + "spans": [ + { + "bbox": [ + 316, + 112, + 552, + 184 + ], + "type": "table", + "html": "
CS ↓FID ↓FID ↓FID ↓FID ↓FID ↓
ConAbl25.3838.4441.5929.6827.7627.36
MACE20.78118.01111.9081.9943.2765.97
SPM23.8933.0634.7023.8919.6118.26
NP23.6659.5878.7452.3767.5155.22
SLD27.8448.1255.3638.7441.9549.08
Ours20.285.728.565.792.326.07
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CS ↓CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl24.2624.0846.3239.6330.5727.49
MACE20.7420.7151.49110.6752.0777.13
SPM23.1622.8141.5831.7721.9623.69
NP23.5924.8581.4150.1065.9358.88
SLD27.7626.7454.5939.2441.6250.13
Ours20.2919.939.345.842.416.43
", + "image_path": "0b1f1c7ac4eca739d6e7c08441a0c5b17612b623a87aa5e04307d4a311c6867d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 316, + 275, + 552, + 348 + ], + "blocks": [ + { + "bbox": [ + 370, + 266, + 496, + 275 + ], + "lines": [ + { + "bbox": [ + 370, + 266, + 496, + 275 + ], + "spans": [ + { + "bbox": [ + 370, + 266, + 496, + 275 + ], + "type": "text", + "content": "Erase Snoopy and Mickey and Spongebob" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 275, + 552, + 348 + ], + "lines": [ + { + "bbox": [ + 316, + 275, + 552, + 348 + ], + "spans": [ + { + "bbox": [ + 316, + 275, + 552, + 348 + ], + "type": "table", + "html": "
CS ↓CS ↓CS ↓FID ↓FID ↓FID ↓
ConAb123.9423.6425.0451.2031.5930.03
MACE20.4820.5021.5999.6847.4670.38
SPM22.8122.3520.8239.8322.6825.31
NP24.2924.7625.3164.7565.1059.33
SLD27.8426.7127.6039.4142.3249.88
Ours19.3919.7320.346.852.797.26
", + "image_path": "78864e8502d76fa9adf302a6b0ee6667a584f2d3d07383aae22f0f1c8805d814.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 352, + 553, + 407 + ], + "lines": [ + { + "bbox": [ + 313, + 352, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 553, + 407 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of single- and multi-instance erasure. The best and second-best results are marked in bold and underlined, respectively. Our AdaVD consistently achieves the lowest CS and the lowest FID in all cases, indicating superior prior preservation without compromising erasure efficacy." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 415, + 553, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 553, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 553, + 521 + ], + "type": "text", + "content": "improves over SOTA by significantly enhanced prior preservation without compromising the erasure precision, as exemplified in Fig. 4. It can be observed from Fig. 4 that methods such as SPM, NP, and SLD fail to fully erase \"Snoopy\" which can be found from the ear and the shape characteristic of the generated image after erasure. MACE can successfully erase the \"Snoopy\" concept. But all the competing methods suffer from degraded image quality in non-target concept generation, e.g., \"Spongebob\"." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": "We then compare the performance for multi-concept erasure, experimenting with two cases, of which one erases two concepts of \"Snoopy\" and \"Mickey\" together and the other erases three concepts of \"Snoopy\", \"Mickey\" and \"Spongebob\" together. Results are reported in the bottom two blocks of Table 1 and visualized in the second and third sections of Fig. 4. Similarly, our AdaVD achieves the lowest CS and FID scores across all cases. This verifies that AdaVD is capable of handling more complex multi-concept erasure and simultaneously fighting against catastrophic forgetting. Conversely, other methods struggle to consistently perform well for multi-concept erasure. For example, when erasing \"Snoopy\" and \"Mickey\" together, the image quality for non-target concepts like \"Spongebob\" and \"Legislator\" shows apparent degradation in Fig. 4. SLD, in particular, fails to maintain its erasure ability even" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28764" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 87, + 245, + 255 + ], + "blocks": [ + { + "bbox": [ + 59, + 76, + 91, + 87 + ], + "lines": [ + { + "bbox": [ + 59, + 76, + 91, + 87 + ], + "spans": [ + { + "bbox": [ + 59, + 76, + 91, + 87 + ], + "type": "text", + "content": "Concepts" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 87, + 245, + 255 + ], + "lines": [ + { + "bbox": [ + 59, + 87, + 245, + 255 + ], + "spans": [ + { + "bbox": [ + 59, + 87, + 245, + 255 + ], + "type": "image", + "image_path": "981afa5437dd2d868a4b8b3d7b447bbad39ba2abe30385b94855e975bc03c8e8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 259, + 555, + 293 + ], + "lines": [ + { + "bbox": [ + 55, + 259, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 259, + 555, + 293 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of single- and multi-instance erasure. Both training-based and training-free methods show limitations in prior preservation. In contrast, our AdaVD demonstrates considerable performance in maintaining prior knowledge without compromising erasure efficacy across both single- and multi-concept erasure tasks." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 253, + 92, + 398, + 255 + ], + "blocks": [ + { + "bbox": [ + 281, + 72, + 369, + 91 + ], + "lines": [ + { + "bbox": [ + 281, + 72, + 369, + 91 + ], + "spans": [ + { + "bbox": [ + 281, + 72, + 369, + 91 + ], + "type": "text", + "content": "Snoopy, Miekey, Spongebob, Dog, Legislator" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 253, + 92, + 398, + 255 + ], + "lines": [ + { + "bbox": [ + 253, + 92, + 398, + 255 + ], + "spans": [ + { + "bbox": [ + 253, + 92, + 398, + 255 + ], + "type": "image", + "image_path": "75a06f1f2167ad016df0c89dd9fac0f340016b5236785945d884a965e9608427.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 406, + 92, + 550, + 255 + ], + "blocks": [ + { + "bbox": [ + 433, + 72, + 522, + 91 + ], + "lines": [ + { + "bbox": [ + 433, + 72, + 522, + 91 + ], + "spans": [ + { + "bbox": [ + 433, + 72, + 522, + 91 + ], + "type": "text", + "content": "Snoopy, Mickey, Spongebob, Dog, Legislator" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 406, + 92, + 550, + 255 + ], + "lines": [ + { + "bbox": [ + 406, + 92, + 550, + 255 + ], + "spans": [ + { + "bbox": [ + 406, + 92, + 550, + 255 + ], + "type": "image", + "image_path": "a909be6fd1116f13c631dd30380ed0f04cc1411ee17fc66325b1dcd593323cc3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 57, + 299, + 294, + 405 + ], + "blocks": [ + { + "bbox": [ + 57, + 299, + 294, + 405 + ], + "lines": [ + { + "bbox": [ + 57, + 299, + 294, + 405 + ], + "spans": [ + { + "bbox": [ + 57, + 299, + 294, + 405 + ], + "type": "image", + "image_path": "3be4de8fc996c55eaf22558d95bf67bb080e91b951ad1ddf537739e6c7215883.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 409, + 295, + 443 + ], + "lines": [ + { + "bbox": [ + 55, + 409, + 295, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 295, + 443 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of art style erasure. Our AdaVD can effectively remove the target concept \"Van Gogh\" while preserving non-target styles like \"Picasso\" and \"Monet\"." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "text", + "content": "when dealing with 2-concept erasure. In Appendix G, we report more experimental results for erasing up to 40 concepts, where our AdaVD can extend to erase dozens of concepts in practice, maintaining consistent erasure efficacy and prior preservation, as shown in Fig. 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 515, + 178, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 178, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 178, + 528 + ], + "type": "text", + "content": "4.3. On Art Style Erasure" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": "We experiment with erasing specific art style, including \"Van Gogh\", \"Picasso\" and \"Monet\". Results are reported in Table 2, and visual comparisons are provided in Fig. 5. Our AdaVD exhibits superior prior preservation, and achieves the lowest or closed-to-lowest CS and FID scores, demonstrating strong prior preservation without sacrificing erasure efficacy. Other methods show different drawbacks as observed from the results. For instance, although NP achieves notably better precision in art style removal as compared to instance removal, Fig. 5 shows that it still struggles to fully erase the \"Van Gogh\" style. Also, SLD fails to erase the \"Van Gogh\" style. These two methods also degrade generation quality for non-target styles, such as \"Picasso\" and \"Monet\", showing harmful effects on non-target concepts directly, as evidenced in both Fig. 5 and" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 297, + 553, + 331 + ], + "blocks": [ + { + "bbox": [ + 315, + 297, + 553, + 331 + ], + "lines": [ + { + "bbox": [ + 315, + 297, + 553, + 331 + ], + "spans": [ + { + "bbox": [ + 315, + 297, + 553, + 331 + ], + "type": "table", + "html": "
ConceptVan GoghPicassoMonetAndy WarholCaravaggio
CSCSCSCSCS
SD v1.429.2129.0629.02--
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CS ↓FID ↓FID ↓FID ↓FID ↓
ConAbl28.8071.71138.7270.3073.10
MACE27.7465.7769.7983.3775.41
SPM24.7862.2532.2758.3061.50
NP24.90141.56124.52127.85136.32
SLD27.48103.96109.11103.89119.32
Ours24.876.822.668.366.84
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FID ↓CS ↓FID ↓FID ↓FID ↓
ConAbl58.6227.72140.3473.3567.44
MACE60.4627.1149.9276.1072.85
SPM38.7926.697.7652.0051.40
NP111.3526.1491.11116.24121.82
SLD98.2127.0393.0197.00110.05
Ours5.4926.992.339.387.05
", + "image_path": "21449d38c5d27030a32b66155c30392f20cba17e282d68a110e786e7c4b1c262.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 315, + 506, + 553, + 580 + ], + "blocks": [ + { + "bbox": [ + 413, + 498, + 456, + 505 + ], + "lines": [ + { + "bbox": [ + 413, + 498, + 456, + 505 + ], + "spans": [ + { + "bbox": [ + 413, + 498, + 456, + 505 + ], + "type": "text", + "content": "Erase Monet" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 506, + 553, + 580 + ], + "lines": [ + { + "bbox": [ + 315, + 506, + 553, + 580 + ], + "spans": [ + { + "bbox": [ + 315, + 506, + 553, + 580 + ], + "type": "table", + "html": "
FID ↓FID ↓CS ↓FID ↓FID ↓
ConAbl141.52132.1024.53208.38186.26
MACE76.9069.3526.8988.3581.72
SPM41.0329.7127.0031.9025.99
NP137.21126.7524.47127.22135.83
SLD94.4892.8825.73100.90114.87
Ours6.946.5026.308.467.19
", + "image_path": "f5d995e1ad4d7caed3d5e16af15ae439534e19b3b7452a5c29a0c47fada1931b.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 585, + 555, + 618 + ], + "lines": [ + { + "bbox": [ + 313, + 585, + 555, + 618 + ], + "spans": [ + { + "bbox": [ + 313, + 585, + 555, + 618 + ], + "type": "text", + "content": "Table 2. Quantitative comparison of art style erasure. AdaVD achieves a superior balance between erasure efficacy and prior preservation, especially excelling in prior preservation." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 630, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 555, + 715 + ], + "type": "text", + "content": "Table 2. Both MACE and SPM are effective in erasing the target concept, however, their prior preservation is somehow less satisfactory, which is particularly noticeable in the generated images in \"Monet\" style. Differently, AdaVD can effectively and consistently remove the target concept and meanwhile preserve satisfactorily the prior content, as confirmed by Table 2 and Fig. 5." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28765" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 293, + 145 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 293, + 145 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 293, + 145 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 293, + 145 + ], + "type": "table", + "html": "
Data PreparationModel FinetuneImage GenerationTotal Time
ConAbl929011200.910419
SPM0728501.772867
MACE3032320.9544
SLD001.414
Ours401.822
", + "image_path": "6d2c8c4fe4c078aac0018bd1ef87ac4932ab5e7add486311b7d915be8582038f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 149, + 295, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 149, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 149, + 295, + 194 + ], + "type": "text", + "content": "Table 3. Time consumption of 10-concept erasure. We calculate the time cost (s) to erase 10 concepts and generate 10 images using one NVIDIA A40 GPU. Compared with training-based methods, AdaVD exhibits exceptional efficiency in real-time erasure." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 201, + 157, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 201, + 157, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 157, + 213 + ], + "type": "text", + "content": "4.4. Further Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 220, + 295, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 220, + 295, + 399 + ], + "spans": [ + { + "bbox": [ + 54, + 220, + 295, + 399 + ], + "type": "text", + "content": "Time Consumption: The computational cost of concept erasure primarily arises from three components, including (1) data preparation time required by training-based methods for preparing training data and by AdaVD for basis computation; (2) model fine-tuning time required by training-based methods; and (3) image generation time required by all methods. In Table 3, we compare the total time consumption of different methods, as well as their time spent on each component. The two training-free methods of SLD and AdaVD are significantly faster as no fine-tuning is needed. Our AdaVD costs slightly more time than SLD, i.e., 0.8 extra seconds per image due to its basis computation, and a total of 8 extra seconds for generating 10 images. But this mild increase yields a significant performance gain, succeeding in precise concept erasure." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "text", + "content": "Interpreting Erased Components by Visualization: Our AdaVD generates images by replacing the original value vector " + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j" + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\pmb{v}_r^j" + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "text", + "content": " via orthogonal complement operation. To empirically interpret the rationale behind our method, we visualize the erased component, " + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j - \\pmb{v}_r^j" + }, + { + "bbox": [ + 55, + 401, + 295, + 592 + ], + "type": "text", + "content": ". Fig. 6 presents three cases of erasing the target concepts \"Mickey\", \"Van Gogh\" and \"Bruce Lee\", where AdaVD successfully erases these target concepts while robustly preserving prior knowledge of non-target concepts. In the first row, as shown in the middle column of each block, the erased components consistently align with the corresponding target semantics when dealing with the target concepts. In the second row of non-target concepts, conversely, the erased components do not contain any informative pattern, indicating that they carry no meaningful semantics, and therefore exert minimal impact on the prior knowledge." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "Downstream Applications: We conduct additional experiments to showcase the versatile applications of our AdaVD across various generative tasks, including (1) implicit concept erasure: by removing the implicit concepts of \"rainy\" and \"foggy\"; (2) image editing: by removing the appearance concepts of \"glasses\" and \"mustache\"; and (3) attribute suppression: by removing the coupled color concept of \"red\". Additionally, we integrate AdaVD with a series of diffusion models, including Chilloutmix [5], DreamShaper [6], RealisticVision [7], and SD v2.1 [4], alongside SD" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 553, + 140 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 140 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 140 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 140 + ], + "type": "image", + "image_path": "e3346c4cac0a6e6af7b4a49634547ff2ee55c92f9821d5381aba83ce134a97e3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "lines": [ + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 148, + 555, + 192 + ], + "type": "text", + "content": "Figure 6. Visualization of erased components. In each block, we compare both target (1st row) and non-target concept (2nd row) by visualizing the original image (1st column), erased component (2nd column), and generation by our AdaVD (3rd column)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 198, + 553, + 312 + ], + "blocks": [ + { + "bbox": [ + 317, + 198, + 553, + 312 + ], + "lines": [ + { + "bbox": [ + 317, + 198, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 198, + 553, + 312 + ], + "type": "image", + "image_path": "51eaea3c18fd219431b9ecaf1f0b969ee652f7282c56a080a4dbcf9aa308259e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 319, + 555, + 364 + ], + "lines": [ + { + "bbox": [ + 313, + 319, + 555, + 364 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 555, + 364 + ], + "type": "text", + "content": "Figure 7. Downstream applications. We extend AdaVD to versatile generation tasks, including (1) implicit concept erasure, (2) image editing, and (3) attribute suppression, indicating its significant potential for broad applications." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 369, + 555, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 489 + ], + "type": "text", + "content": "v1.4. As illustrated in Fig. 7, despite the absence of explicit mention for \"rainy\" and \"foggy\", AdaVD can still effectively erase these concepts in image semantic space. Meanwhile, AdaVD also precisely removes \"glasses\" and \"mustache\" with minimal changes to other details, highlighting its potential in image editing applications. For attribute suppression, AdaVD successfully eliminates the color attribute \"red\" from objects such as apples and roses, demonstrating its capability to decouple strongly coupled concepts, e.g., \"roses are red\" embedded in the model's prior knowledge." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 494, + 479, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 479, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 479, + 506 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "type": "text", + "content": "We have presented AdaVD, a precise, fast, and low-cost method for erasing unwanted concepts. The idea of leveraging the classical linear algebraic orthogonal complement operation and an adaptive erasing shift design is novel, and has successfully achieved a precise concept erasure. Extensive experiments have demonstrated both high erasure efficacy and strong prior preservation of AdaVD for both single- and multi-concept erasure. Moreover, AdaVD exhibits excellent interpretability through visualizing its erased components and strong capability in solving downstream tasks. It has been an intriguing discovery that the orthogonal complement of the value vectors of the target concepts is effective at erasing their inherent semantics. Despite the empirical success, we will seek to establish a rigorous theoretical understanding of the accumulative effect of applying this linear algebraic operation layer-wise for concept erasure in the future." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28766" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 159, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 159, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 159, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "type": "text", + "content": "This work is supported by the National Science and Technology Major Project (2023ZD0121102) and the National Natural Science Foundation of China (U24B20180)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 138, + 115, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 138, + 115, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 138, + 115, + 152 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 159, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 61, + 159, + 294, + 191 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 159, + 294, + 191 + ], + "spans": [ + { + "bbox": [ + 61, + 159, + 294, + 191 + ], + "type": "text", + "content": "[1] Safety checker nested in stable diffusion. https://huggingface.co/CompVis/stable-diffusion-safety-checker, 2022.2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 194, + 294, + 215 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 194, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 62, + 194, + 294, + 215 + ], + "type": "text", + "content": "[2] Stable diffusion. https://huggingface.co/ CompVis/stable-diffusion-v1-4, 2022.2,3,6" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 217, + 294, + 237 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 217, + 294, + 237 + ], + "spans": [ + { + "bbox": [ + 62, + 217, + 294, + 237 + ], + "type": "text", + "content": "[3] Stable diffusion v2.0. https://huggingface.co/stabilityai/stable-diffusion-2, 2022.2" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 239, + 294, + 261 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 239, + 294, + 261 + ], + "spans": [ + { + "bbox": [ + 62, + 239, + 294, + 261 + ], + "type": "text", + "content": "[4] Stable diffusion v2.1. https://huggingface.co/stabilityai/stable-diffusion-2-1, 2022.8" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 62, + 262, + 294, + 284 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 262, + 294, + 284 + ], + "spans": [ + { + "bbox": [ + 62, + 262, + 294, + 284 + ], + "type": "text", + "content": "[5] Chilloutmix. https://huggingface.co/swl-models/chilloutmix, 2023.1,8,18" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 286, + 294, + 307 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 286, + 294, + 307 + ], + "spans": [ + { + "bbox": [ + 62, + 286, + 294, + 307 + ], + "type": "text", + "content": "[6] Dreamshaper. https://huggingface.co/Lykon/DreamShaper, 2023.1,8,18,22" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 309, + 294, + 341 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 309, + 294, + 341 + ], + "spans": [ + { + "bbox": [ + 62, + 309, + 294, + 341 + ], + "type": "text", + "content": "[7] Realisticvision. https://huggingface.co/SG161222/Realistic_Vision_V5.1_noVAE, 2023.8,18,22" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 62, + 343, + 294, + 374 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 343, + 294, + 374 + ], + "spans": [ + { + "bbox": [ + 62, + 343, + 294, + 374 + ], + "type": "text", + "content": "[8] Praneeth Bedapudi. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023. 2" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28768" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_content_list.json b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..06e36081b6186b659c9bb6361a951b0e386ebcbb --- /dev/null +++ b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_content_list.json @@ -0,0 +1,1680 @@ +[ + { + "type": "text", + "text": "PreciseCam: Precise Camera Control for Text-to-Image Generation", + "text_level": 1, + "bbox": [ + 156, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Edurne Bernal-Berdun1, Ana Serrano1, Belen Masia1, Matheus Gadelha2, Yannick Hold-Geoffroy2, Xin Sun2, Diego Gutierrez1", + "bbox": [ + 207, + 180, + 787, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Universidad de Zaragoza, I3A {edurnebernal, anase, bmasia, diegog}@unizar.es", + "bbox": [ + 107, + 239, + 522, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Adobe Research {gadelha, holdgeof, xinsun}@adobe.com", + "bbox": [ + 558, + 239, + 885, + 277 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db30796ef700bfffffb1c306c1ff80a2e116b20a30148cd1a9883bde85c2a193.jpg", + "image_caption": [ + "Figure 1. Our approach enhances the artistic expression of text-to-image generative models by incorporating precise control over camera angles and lens distortion effects. Left: Our input consists of a standard text prompt along with extrinsic (roll and pitch) and intrinsic (vertical field of view and distortion $\\xi$ ) camera parameters, which are translated into a suitable and efficient representation for learning camera views. Right: Examples varying roll (top) and pitch (bottom) with the same prompt, while keeping the remaining camera parameters fixed." + ], + "image_footnote": [], + "bbox": [ + 133, + 310, + 867, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 574, + 326, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Images as an artistic medium often rely on specific camera angles and lens distortions to convey ideas or emotions; however, such precise control is missing in current text-to-image models. We propose an efficient and general solution that allows precise control over the camera when generating both photographic and artistic images. Unlike prior methods that rely on predefined shots, we rely solely on four simple extrinsic and intrinsic camera parameters, removing the need for pre-existing geometry, reference 3D objects, and multi-view data. We also present a novel dataset with more than 57,000 images, along with their text prompts and ground-truth camera parameters. Our evaluation shows precise camera control in text-to-image generation, surpassing traditional prompt engineering approaches.", + "bbox": [ + 88, + 606, + 485, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 844, + 220, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Images are versatile mediums where content and camera language are crucial. Different camera parameters can con", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vey dramatically different messages; for example, a low angle may portray dominance or epicness, while a Dutch angle (about 45 degrees) creates unease or tension.", + "bbox": [ + 511, + 575, + 906, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-image (T2I) diffusion models have the ability to generate detailed images based on prompts. However, they often produce a flat horizon in the center of the image, which can limit creative expression. This limitation can hinder graphic designers, artists, and photographers from effectively conveying emotions, sensations, or messages. To unlock the capabilities of generative models, it is essential to have precise control over camera parameters.", + "bbox": [ + 509, + 623, + 906, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Camera views are defined by intrinsic and extrinsic parameters such as field of view (FoV), pitch, roll, etc. However, most text-to-image models are not designed for precise camera view control, making prompt engineering the primary method to achieve desired visual results. This time-consuming approach requires significant expertise and offers limited control.", + "bbox": [ + 509, + 747, + 908, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models like Firefly [2] have allowed users to control camera views with general instructions such as wide angle or closeup. However, these controls are im", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2724", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/72a720cf0230c8b8c537e27d2370453dd55de0ebd6429db62f00712c4644535e.jpg", + "image_caption": [ + "Figure 2. Red boxes: Current approaches rely on trial-and-error prompt engineering or generalistic tags, offering limited camera control in text-to-image generative AI. Others use 3D representations of the scenes, from which depth or edge maps are obtained, but this imposes strict constraints on the resulting image, limiting flexibility. Green box: Our method relies on two extrinsic and two intrinsic camera parameters, user-provided; we then obtain the effects that such camera parameters impose on the appearance of each pixel in the final image, encoded in a 2D PF-US map (see text for details). This allows for precise, fine-tuned camera control, thus enhancing creativity." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 906, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "precise, limiting artistic options. While precise camera control has been explored through 3D information from multiview images, such images are often unavailable, and creating comprehensive 3D representations for all possible camera configurations is not feasible. This results in challenges when generating multiple objects, cluttered scenes, or coherent backgrounds. An alternative is training ControlNet on depth or edge maps, which imposes strict constraints limiting flexibility (see Fig. 2).", + "bbox": [ + 88, + 353, + 480, + 489 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we aim to provide a general solution to the problem of precise camera view control, which expands artistic freedom in generative AI. We do not focus solely on well-known photographic shots; instead, we offer simple, direct control of both intrinsic and extrinsic camera parameters, which allows us to achieve a broad spectrum of possible camera views while maintaining precise control (see Fig. 2 (green box)). Instead of representing a 3D scene, which has the limitations we discussed above, we identify the essential effects that such camera parameters impose on the appearance of each pixel in the final image, thus overcoming the requirement to rely on multi-view images and using only simple, single-view images.", + "bbox": [ + 89, + 491, + 482, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve our goal, we rely on two extrinsic parameters, roll and pitch rotations, and two intrinsic parameters, vertical FoV (vFoV) and geometrical distortion of the camera $(\\xi)$ . Combined with a user-provided prompt, these parameters serve as inputs to our model to generate images with the intended camera view. We adopt the Unified Spherical (US) camera model [5], which allows us to translate these camera parameters into a Perspective Field (PF) representation [24], which is easy to store and interpret. The PF-US encodes the camera parameters as per-pixel information, describing the pixels' up-vector (opposed to the gravity direction) and distance to the horizon, allowing us to encode per-pixel appearance from roll, pitch, vFoV, and $\\xi$ parameters. We then adopt ControlNet [54] to guide our image", + "bbox": [ + 89, + 689, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "generation according to the resulting PF-US. Our model, PreciseCam, archives precise camera view control, while the content remains fully determined by the text prompt.", + "bbox": [ + 511, + 353, + 903, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, we have created a novel dataset of 57,380 single-view RGB images, along with their ground-truth camera parameters and prompt descriptions. Our dataset spans a comprehensive range of camera parameters and a diversity of scenes, making it specifically suitable for the camera control problem we address.", + "bbox": [ + 511, + 400, + 905, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Last, while our approach is primarily designed for image generation, it opens up new possibilities for video generation, as absolute camera control conditioning is currently being overlooked. Our method can create a precise initial camera position, from which relative camera control can subsequently be applied. Alternatively, we showcase how our model tailored for images can be leveraged to apply limited absolute camera control on videos. Our code and model are publicly available at https://graphics.unizar.es/projects/PreciseCam2024.", + "bbox": [ + 511, + 492, + 905, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 662, + 653, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conditional image generation. Seminal work in conditional image generation leveraged local image statistics [13, 14, 21] and retrieved information from large image datasets [10, 15, 19, 25]. Later deep learning techniques allowed faster, more flexible, and more customized image synthesis within specific domains [9, 23, 35, 43, 44, 52, 53]. Those models were limited in their ability to generate high-quality images and to support open-ended generation tasks. With the advent of large-scale image and text datasets, autoregressive [50] and especially diffusion models [37-39] were proposed as an effective solution to create high-quality images from a virtually unbounded set of text descriptions. Despite these advancements, text remains a limited modality for controlling image generation. Recent methods in", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2725", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "produced modifications to the diffusion process, enhancing controllability by allowing users to incorporate additional guidance through color [31], hand-crafted terms [16, 34], and spatially localized prompts [3, 4, 12, 51]. While these methods offer improved control in the generative process, they lack support for more granular guidance, such as structural cues like edges or depth maps.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Camera control on diffusion generation. While some works have addressed camera control for image generation, this area remains underexplored. Kumari et al. [27] proposed a method that introduces camera control without relying on prompt engineering. They refine a text-to-image diffusion model by conditioning it on a 3D object representation, enabling the generation of various camera viewpoints in new backgrounds. Their NeRF-based method needs multi-view images of a specific object to generate novel views, but it struggles with extreme angles or prompts with other objects. Cheng et al. [11] introduced Continuous 3D Words, which allows control over attributes like object position and lighting by mapping them to the token embedding domain. However, it struggles with complex prompts and tends to replicate poses from the training set. Their camera control is limited to the \"dolly zoom\", which adjusts field of view and distance simultaneously, lacking independent control. On the other hand, Voynov et al. [42] incorporated lens geometry into the generative pipeline to control camera distortion for effects like fish-eye images but did not address extrinsic parameters such as roll or pitch. In contrast, our general approach generates images of any object, scene, or landscape while preserving the model's ability to handle complex prompts and produce various artistic styles and multi-object scenes.", + "bbox": [ + 91, + 217, + 483, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Closely related to our work are methods that train networks to guide the generative process using inputs like depth, edges, normals, and segmentation maps [32, 54]. However, these methods still overlook a critical aspect of image creation: controlling the camera used to obtain that image. It is common for practitioners to reason about image editing operations using camera abstractions – what the image would look like if one changes the camera pitch, roll, field of view, etc. To address this gap, we propose a novel approach that incorporates fine-grained camera controls into diffusion adapters like ControlNet [54], expanding the versatility and usability of image generation to scenarios where precise camera control is paramount. Last, recent works focus on relative camera view control for video generation [20, 45, 46, 48, 49]. These methods adjust camera movement relative to the first frame but lack control over initial camera position. Our method provides control over this starting camera orientation, enabling horizon positioning and gravity alignment.", + "bbox": [ + 89, + 613, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Approach", + "text_level": 1, + "bbox": [ + 513, + 89, + 661, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed framework for precise camera view control in text-to-image generation takes as input a text prompt $p$ and a camera view specified by a set $\\Omega$ of four parameters, and generates images $I$ according to both. The four camera parameters (roll, pitch, vFoV, and distortion $\\xi$ ) are provided by the user through simple sliders; they are both intuitive and expressive enough to allow for precise camera control. These parameters, together with the camera view representation used by our model, are presented in Sec. 3.1.", + "bbox": [ + 511, + 114, + 903, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-conditioned image generation is performed by means of a diffusion model $\\mathcal{D}$ , while we achieve camera view conditioning via a ControlNet-based module, as described in Sec. 3.2. The model is trained with a new dataset featuring ground-truth camera view specification (Sec. 3.3).", + "bbox": [ + 511, + 251, + 903, + 327 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Precise Camera View Representation", + "text_level": 1, + "bbox": [ + 511, + 335, + 834, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To enable a precise camera view specification, we adopt the Perspective Field (PF) representation [24], which was originally designed for single-image camera calibration. For any arbitrary projection function $\\mathcal{P}(\\mathbf{X}) = \\mathbf{x}$ mapping a 3D point $\\mathbf{X}$ to an image pixel $\\mathbf{x}$ , PF assigns each pixel $\\mathbf{x}$ an up-vector $\\mathbf{u}_{\\mathbf{x}}$ and a latitude angle $\\varphi_{\\mathbf{x}}$ . Since each pixel $\\mathbf{x}$ originates from a light ray $\\mathbf{R}$ emitted from $\\mathbf{X}$ , the up-vector $\\mathbf{u}_{\\mathbf{x}}$ represents the projection of the up direction of $\\mathbf{X}$ (which is opposite to the gravity vector $\\mathbf{g}$ at $\\mathbf{X}$ ), while the latitude $\\varphi_{x}$ measures the angle between the light ray $\\mathbf{R}$ and the horizontal world plane. In particular:", + "bbox": [ + 511, + 358, + 906, + 512 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {u} _ {\\mathbf {x}} = \\lim _ {c \\rightarrow 0} \\frac {\\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X})}{\\| \\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X}) \\| _ {2}}, \\text {a n d} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 520, + 903, + 550 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\varphi_ {\\mathbf {x}} = \\arcsin \\left(\\frac {\\mathbf {R} \\cdot \\mathbf {g}}{\\| \\mathbf {R} \\| _ {2}}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 553, + 903, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to enhance creativity and expressivity beyond the commonly used pinhole model in generative AI, including precisely-controlled wide-angle or fisheye cameras. To achieve this, we take advantage of the flexibility of PF to support different camera models through their respective $\\mathcal{P}(X)$ functions, and employ the Unified Spherical (US) camera model [5, 8], which allows camera models beyond the pinhole camera to be encoded within the PF. The projection function $\\mathcal{P}(X)$ of the US model is defined as:", + "bbox": [ + 511, + 585, + 905, + 712 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} (\\mathbf {X}) = \\mathbf {x} = (u, v),\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 717, + 733, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu = \\frac {x f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + u _ {0}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 737, + 903, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv = \\frac {y f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + v _ {0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 770, + 812, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Where $(x,y,z)$ are the 3D point world coordinates, $(u_0,v_0)$ are the principal point coordinates in the image, $f$ is the focal length, and $\\xi$ is a distortion parameter ranging between 0 and 1, with $\\xi = 0$ being a pinhole camera.", + "bbox": [ + 511, + 810, + 903, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We choose to represent our camera view with two intrinsic parameters: vertical FoV (which is in turn defined", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2726", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/854d0d28e50ed05b55e939e30010bacb471d4e5d86269854b21658ab53bac3b1.jpg", + "image_caption": [ + "Figure 3. Left and center: PF-US camera view representation. PF-US camera parameters (roll, pitch, vertical FoV, and distortion $\\xi$ ) and associated maps corresponding to two example images. PF-US maps encode, for each pixel, a latitude value $\\varphi_{\\mathbf{x}}$ (blue-red color map with contour lines) and a unit up-vector $\\mathbf{u}_{\\mathbf{x}}$ (green arrows). Right: Dataset generation. We generate training data in the form of images with ground-truth PF-US maps by leveraging $360^{\\circ}$ images. We sample our camera parameters and obtain the corresponding cropped region for each sampled quartet (as examples, the highlighted regions in red and yellow yield the two examples shown on the left)." + ], + "image_footnote": [], + "bbox": [ + 93, + 99, + 395, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f2fa8caaa41bc79b45a8bf9892c5e49e91cc80729e1658330b749b98af1a6454.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 397, + 99, + 697, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e11d32d6f95dc658e6dbf7264763b53aaed6f2b5a5280d6c2180f413b2a82c39.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 99, + 903, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by the focal length $f$ and distortion $\\xi$ , as well as two extrinsic parameters: roll and pitch rotations with respect to the horizon. These four parameters conform the set $\\Omega = (\\mathrm{roll},\\mathrm{pitch},\\mathrm{vFoV},\\xi)$ , which is expressive enough to represent a wide range of camera configurations, while being intuitive to users. The four parameters are then transformed, by means of the PF-US representation (Eqs. 1-3), into per-pixel up-vectors and latitude values, yielding the corresponding PF-US maps (see Fig. 3, left and center, for two different illustrative examples).", + "bbox": [ + 88, + 325, + 480, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resulting PF-US maps provide local information about how camera parameters affect the appearance of each pixel, allowing the model to learn this relationship without the need for heavy 3D representations. Finally, note that yaw rotation is excluded; given a 2D image, we can define up or down directions based on the horizon, but there is no such reference to define left or right directions. By leaving yaw information out, we allow the model to focus on the relevant camera parameters that affect image formation.", + "bbox": [ + 88, + 477, + 482, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning Camera View Control", + "text_level": 1, + "bbox": [ + 89, + 619, + 372, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to introduce precise camera view control in text-to-image diffusion models, while preserving their generalization capabilities. This requires a method that minimally disrupts their generation pipeline, already trained on large, quality datasets, adding only the essential information needed to achieve the desired camera view. To do this, we adopt the ControlNet approach to condition image generation [54]: it provides a framework for guiding diffusion models to adhere to a specific condition, and has delivered impressive results conditioning generation with poses, depth, edges, or normal maps, among others.", + "bbox": [ + 88, + 643, + 482, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the generation process, ControlNet ensures that the generated images align with both the prompt and the conditioning input, in our case the PF-US map. We use Stable Diffusion XL (SDXL) [36] as our base text-to-image model, although our approach is compatible with any other UNet-based diffusion model. Our ControlNet setup in", + "bbox": [ + 88, + 810, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b5532014a382bbab00a76c78c1bb1accb846f51561067acfbf26c418a5e7d2ec.jpg", + "image_caption": [ + "Figure 4. Training of our proposed approach for precise camera control. Text-to-image generation with a UNet-based diffusion model (SDXL in our implementation) is conditioned with a PF-US map representing the desired camera parameters; conditioning is learned by means of a ControlNet-based module. During inference, only the middle block output of this module is injected into SDXL (shown in red, see text for more details)." + ], + "image_footnote": [], + "bbox": [ + 513, + 321, + 908, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "volves duplicating the encoder and middle block layers of the original SDXL model. While SDXL remains frozen during training to preserve its generalization abilities, ControlNet is initialized with the same weights and trained (see Sec. A of the supplementary material for training details).", + "bbox": [ + 511, + 744, + 906, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 4 illustrates this. To incorporate ControlNet's output into SDXL, its residuals are passed through a zero-convolution layer (1×1 convolution layer with all-zero initial weights) before being added to the residuals of the original SDXL model. During training, ControlNet outputs are", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Roll=0°, Pitch=30°, vFoV=35°, $\\xi = 0.1$", + "bbox": [ + 148, + 87, + 341, + 98 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Roll=30°, Pitch=-60°, vFov=100°, $\\xi = 0.9$", + "bbox": [ + 442, + 88, + 653, + 99 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2727", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "added to the UNet bottleneck and to the decoder skip connections, as in the original implementation. At inference time, however, we find that injecting the ControlNet output only in the bottleneck (marked in red in Fig. 4) improves generation consistency without being detrimental to condition adherence [6]. Our ablation study (Sec. 4) shows how various ControlNet outputs affect the generation process.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Dataset Generation", + "text_level": 1, + "bbox": [ + 89, + 209, + 274, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train our framework, we need a diverse dataset of RGB images with corresponding text prompts and PF-US camera parameters, represented as triplets $(I_i, p_i, \\Omega_i)$ .", + "bbox": [ + 89, + 233, + 482, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Jin et al. [24] provide data featuring RGB images and ground-truth PF representations. However, they primarily depict urban outdoor scenes and, more importantly, do not cover the full range of camera parameters; for example, they include only minimal distortions (low $\\xi$ values) and avoid large vertical FoVs. A possible alternative would be to use their PF estimation model and apply it to an existing dataset. However, the resulting estimations lack sufficient accuracy for our training purposes, hindering our model's ability to learn view control across the full spectrum of camera parameters (refer to Sec. B of the supplementary material).", + "bbox": [ + 89, + 279, + 482, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We thus generate our own dataset with ground truth PF-US representations by leveraging $360^{\\circ}$ images. We sample our set of camera parameters (see Sec. B of the supplementary material) and obtain, for each sampled quartet, the corresponding areas cropped from the $360^{\\circ}$ images, and their PF-US maps (as described in Sec. 3.1). Fig. 3 (right) shows two of the resulting regions, with boundaries highlighted in orange and yellow, respectively. Sampling ranges for each camera parameter are: roll $\\in (-90^{\\circ}, 90^{\\circ})$ , pitch $\\in (-90^{\\circ}, 90^{\\circ})$ , vFoV $\\in [15^{\\circ}, 140^{\\circ}]$ and $\\xi \\in (0, 1)$ .", + "bbox": [ + 89, + 446, + 482, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To maximize diversity in the images, we use six different $360^{\\circ}$ image datasets: 360-SOD [28], CVRG-Pano [33], F-360iSOD [55], Poly Haven HDRIs [18], Sitzmann et al. [40], and 360cities [1]. These feature a mix of outdoor and indoor scenes, containing both natural and urban settings with a diverse array of activities and environments. Please refer to Sec. B.1 of the supplementary material for an analysis of our dataset, highlighting its extended camera coverage and content diversity.", + "bbox": [ + 89, + 598, + 482, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From the resulting $(I, \\Omega)$ pairs, we use BLIP-2 [29] to generate a descriptive text prompt $p_i$ for each image $I_i$ . While BLIP-2 may sometimes provide inaccurate descriptions, this is not an issue for our training: we do not train the text-to-image model itself, but the conditioning module instead, which needs to learn the camera view independently of the prompt. These inaccurate prompts are akin to the ControlNet technique of introducing empty strings as the prompt during training. Our final dataset is comprised of 57,380 RGB images with associated text prompts and ground-truth PF-US parameters.", + "bbox": [ + 89, + 734, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Results", + "text_level": 1, + "bbox": [ + 513, + 90, + 599, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our precise control of camera parameters against baseline methods, demonstrating that our approach can manage both artistic and realistic styles. Then, we analyze the robustness of our model, including camera conditioning and an ablation study on residuals for improved control and quality. Finally, we showcase various applications such as background generation for object rendering, video generation, and enhanced control with multiple ControlNets. For further results and details, please see the supplementary material.", + "bbox": [ + 511, + 114, + 903, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Camera control. PreciseCam enables precise control over extrinsic (roll and pitch rotations) and intrinsic (vFoV and distortion $\\xi$ ) camera parameters. Fig. 5 illustrates control over extrinsic parameters. In it, roll (top row) and pitch (bottom row) are varied while the remaining parameters are held constant. The images follow the conditioning, and a high degree of consistency is maintained through camera variations. Similarly, in Fig. 6, we show intrinsic parameter control by varying the vertical field of view vFoV (left) or the distortion $\\xi$ (right), while keeping all the other parameters fixed. In the PF-US maps (see Sec. 3.1), larger vFoV leads to increased latitude values, whereas $\\xi$ mainly affects the up vectors. The generated images follow the PF-US maps, effectively translating camera settings into visual outcomes. There is a lack of reliable metrics in the literature for evaluating the camera parameters of generated images, which makes it challenging to assess PreciseCam's accuracy. Nevertheless, we include a quantitative evaluation of the camera view in Sec. F of the supplementary material, based on Perspective Fields [24]. Additionally, Sec. C of the supplementary material includes more examples of systematic variation of camera parameters for a variety of prompts, illustrating the disentanglement between camera parameters and prompt of PreciseCam. Our ControlNet-based architecture, combined with our diverse dataset, effectively disentangles the camera parameters from image semantics.", + "bbox": [ + 511, + 273, + 906, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparisons. We compare our approach to two alternative methods: prompt-engineered SDXL and Adobe Firefly, a state-of-the-art diffusion model with preset style tags. Fig. 8 illustrates this comparison. Despite prompt engineering efforts, SDXL's ability to control camera perspectives remains limited, and it often struggles to consistently interpret complex camera-related prompts. Adobe Firefly includes predefined style tags for shot specification, such as close-up, shot from above, shot from below, and wide angle, supporting basic camera control. Nevertheless, while Firefly's tags do introduce some perspective variations, the control enabled by these tags is limited, and insufficient even when combined with prompt specification. In contrast, our model is able to control camera views precisely in both realistic (top row) and artistic (bottom row) styles.", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2728", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a14581c2cdb3b49f1da75539e65a4c122f7ef3effc9671a8150a3c1fd07edd4e.jpg", + "image_caption": [ + "A digital art depiction of a castle floating in the ocean, with glowing bluish clouds. The castle's towers are impossibly tall and the colors soft, with reflections from the light of an ethereal sun." + ], + "image_footnote": [], + "bbox": [ + 212, + 88, + 349, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/acbdec47b716c433a910cb3a524d83510e9094a722c9598c1965ffea8e93b1e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 88, + 488, + 196 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f9f222ee1274f912ac94eaf61f8812d1dc05332bad499f89798bacc570215d63.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 88, + 627, + 196 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2b9411883ce0027d0945ab6092f0cadbb5242f35362c5d5aec8872c28b9066dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 88, + 766, + 196 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7fe40c990e349c023ce4f09bd9c7afbd48736ad58c57e9d4f8a13a0121a0830.jpg", + "image_caption": [ + "Figure 7. Our model achieves prompt adherence on par with SDXL, as reflected in the table by comparable CLIP and BLIP scores (see text for details), while enabling camera control that SDXL cannot provide. Images show an example result from SDXL with prompt engineering (left), and from our model (right)." + ], + "image_footnote": [], + "bbox": [ + 767, + 88, + 905, + 196 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a716a447f5cc9a9f03b7c350beae1c4651beac8d4cde1d824af4e70cb6d31972.jpg", + "image_caption": [ + "A photorealistic digital art of a futuristic cityscape at sunset. Every detail, like the reflective glass skyscrapers, is rendered with high clarity. The colors are warm and saturated, with a glowing orange sky." + ], + "image_footnote": [], + "bbox": [ + 212, + 208, + 349, + 318 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/81264e045d68165de0d9d728f0d777c8764aab4f854aab4618d4680b0ef6e5b2.jpg", + "image_caption": [ + "Figure 5. Extrinsic Parameter Control. Images generated by varying the extrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Top row: Variation in pitch, effectively shifting the view from looking downward to upward; fixed parameters are (roll, vFoV, $\\xi$ ) = (0°, 80°, 0.1). Right: Variation in roll, tilting the view from left to right; (pitch, vFoV, $\\xi$ ) = (0°, 80°, 0.1). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text." + ], + "image_footnote": [], + "bbox": [ + 351, + 208, + 488, + 318 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b4796de98117765e7f83bf9a141e79051fab61930d289453c392b03863f9eb67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 208, + 627, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c35c004ebc4d73629ae3ed41947a5aaedc2116623205608baf529356770d4b3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 209, + 766, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d16baa69ab7a3958fea0d6f88ba3b555b415ce8b47659116cf2008a2f1fc5231.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 209, + 905, + 318 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c31975495654f8b843dcc3ea929537498eb3bafa864c35b5ebe631c8269f794f.jpg", + "image_caption": [ + "A photograph of a comfortable nursery with soft pastel colors, a rocking chair, a crib by the window, and shelves with neatly organized baby essentials." + ], + "image_footnote": [], + "bbox": [ + 91, + 397, + 220, + 500 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22acd96d10bd984395facc1f0392724282c51c0d4e01fb16c5b28be5b1d7f5ac.jpg", + "image_caption": [ + "Figure 6. Intrinsic Parameter Control. Images generated by varying the intrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Left: Variation in the vertical field of view (vFoV); fixed parameters are (roll, pitch, $\\xi$ ) = (0°, 0°, 0.1). Right: Variation in distortion ( $\\xi$ ); (roll, pitch, vFoV) = (0°, 0°, 120°). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text." + ], + "image_footnote": [], + "bbox": [ + 222, + 398, + 349, + 500 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/65474c0e768bb223293678758e12d4463935ecc6570d395904ef93c04ca20cae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 398, + 482, + 500 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a196c40866c8a2248031583dbf5f9db1ec9359992f965ca4aeb9d0caae9ae41c.jpg", + "image_caption": [ + "A narrow alleyway in an old European village, depicted in a vintage lithograph style, with intricate line work and a muted color palette." + ], + "image_footnote": [], + "bbox": [ + 513, + 397, + 642, + 500 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aad747a8d44a9a9323be0a38b1578f2b270343bf8df255f739ce6d2058fae594.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 398, + 772, + 500 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/422881caabb0cf22c190f8bf73126f771241042957b7b2c7703ccac3f17a1dcf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 398, + 905, + 500 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/28f53c8a72ae84ab501cce8f6f00739d9a3a6ba7687da3acc39fc2b1679736e5.jpg", + "table_caption": [], + "table_footnote": [ + "Prompt: Two enormous steampunk-style airships engaged in combat over a foggy cityscape. Gears, steam, and mechanical components are exposed on the airships, while cannons fire plumes of smoke and sparks. Below, the city is filled with smokesstacks and towering clock towers." + ], + "table_body": "
CLIP ScoreBLIP Score
SDXL + Prompt Engineering0.557 (0.039)0.299 (0.025)
(Ours) PreciseCam0.543 (0.039)0.292 (0.026)
Prompt +\nOpen with\na angle,\nof -70.Prompt +\nRoll = 0°\nPitch = -70°\nvFoV = 70\nξ = 0.1.
", + "bbox": [ + 130, + 607, + 444, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we conducted a user study with 34 participants to compare the camera view precision of the models, revealing that our model significantly outperformed SDXL and Adobe Firefly in aligning with the desired camera view (see Sec. E of the supplementary material). We also evaluate whether our model maintains, despite the inclusion of camera control, the text prompt adherence exhibited by SDXL. To do this, we compare our results to those of the baseline SDXL by computing, for each method, CLIP and BLIP scores [22], which are commonly used to evaluate prompt relevance in generated images. The comparison is done over 2,940 images generated with each method (ours and baseline SDXL). For the baseline SDXL, we use prompt engineering, specifying the desired view to encourage distinct camera perspectives (see Sec. D of the supplementary material). Our approach achieves comparable scores to SDXL (Fig. 7 shows mean and standard deviation), suggesting that our model is able to maintain prompt alignment while providing precise camera view control.", + "bbox": [ + 511, + 612, + 906, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2729", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/844169732971a6f667bfc5b7e07899f060d12d3dcf036bc46ed22323ae401c4b.jpg", + "image_caption": [ + "SDXL", + "A photograph of a street cafe scene at twilight with people enjoying drinks, a shot from below." + ], + "image_footnote": [], + "bbox": [ + 117, + 99, + 223, + 179 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d8cf3a8bbc2087bf02095bdd0d1a0d5b4557b6daa256ec392383db48d6716dc.jpg", + "image_caption": [ + "Firefly Image 3", + "A photograph of a street cafe scene at twilight with people enjoying drinks.", + "+ tag: shot from below" + ], + "image_footnote": [], + "bbox": [ + 243, + 99, + 348, + 179 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9f80f4d17d4c61695c9359bdb42ada0ecd2020d0744cd15bca52ef2b2e6a02c7.jpg", + "image_caption": [ + "Ours", + "A photograph of a street cafe scene at twilight with people enjoying drinks.", + "+ roll=0°, pitch=40°." + ], + "image_footnote": [], + "bbox": [ + 352, + 97, + 470, + 179 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/550a011d2fabd42cd77014949469285e6db493dd0c4addca1f15936a216d716c.jpg", + "image_caption": [ + "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, a shot from below." + ], + "image_footnote": [], + "bbox": [ + 117, + 253, + 227, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/664c6987f844a57b739780921faf116c7e24d06f7533c87373397aafa42250b3.jpg", + "image_caption": [ + "A street cafe scene at twilight withpeople enjoying drinks , depicted ina lively watercolor and ink stylewith loose lines and warm , glowingcolors + tag : shot from below" + ], + "image_footnote": [], + "bbox": [ + 243, + 253, + 352, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2a11c39171838cea261d98f34b79fb197edc4efc880c47e2bbd03c51849ed6c7.jpg", + "image_caption": [ + "vFoV=70°, $\\xi = 0.1$", + "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors.", + "+ roll = 0°, pitch = 40°, vFOV = 70°, $\\xi = 0.1$" + ], + "image_footnote": [], + "bbox": [ + 354, + 250, + 470, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9aea71119c654db33524b72619e13d15ca6942600f8b92f3f4ca82416e1d3468.jpg", + "image_caption": [ + "SDXL", + "A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene." + ], + "image_footnote": [], + "bbox": [ + 516, + 99, + 620, + 178 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7230325751787558521aa87dcc467c99979307c0e4e24b5ccbd827efe9bfa89f.jpg", + "image_caption": [ + "Firefly Image 3", + "A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene" + ], + "image_footnote": [], + "bbox": [ + 640, + 98, + 745, + 178 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eba7b50e407f47e32b224011a559d49e1f531eaab9bc51811fbfcf1b56c6e12d.jpg", + "image_caption": [ + "Ours", + "A photograph of a street cafe scene at twilight with people enjoying drinks.", + "+ roll $= -30^{\\circ}$ pitch $= 40^{\\circ}$ $\\mathrm{VFOV} = 0^{\\circ}$ $\\xi = 0.1$" + ], + "image_footnote": [], + "bbox": [ + 753, + 97, + 870, + 179 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f70326fae5ec5f4c460aaee82ce6737400e3ae47d2e2a6488adf2f45d3b5d228.jpg", + "image_caption": [ + "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene." + ], + "image_footnote": [], + "bbox": [ + 516, + 255, + 624, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/37daadcfdd4004ea9e1eea36d871c55a516f72d0d5373012f9709ec66067d03d.jpg", + "image_caption": [ + "+ tag: shot from below", + "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a groundlevel camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene + tag: shot from below" + ], + "image_footnote": [], + "bbox": [ + 640, + 253, + 750, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44e24d3f700c925beab25dbde17c6e7e09f7ee01b843f97794c8a7698d587de6.jpg", + "image_caption": [ + "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors. + roll $= -30^{\\circ}$ pitch $= 40^{\\circ}$ vFoV $= 70^{\\circ}$ $\\xi = 0.1$" + ], + "image_footnote": [], + "bbox": [ + 753, + 250, + 880, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Model analysis", + "text_level": 1, + "bbox": [ + 89, + 534, + 241, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Camera conditioning adherence. To assess the stability of our model's camera conditioning, we generate images using the same PF-US maps and prompts but vary the input noise. Results show consistent camera conditioning (please refer to Sec. G of the supplementary material for examples).", + "bbox": [ + 89, + 560, + 483, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation: Influence of the residuals' contributions. In our framework, the ControlNet-based module generates residual outputs that can be injected into the main model in various layers. We observe that residuals from the middle block (bottleneck) effectively achieve adherence to the camera conditioning, while preserving the image quality achieved by the base model (SDXL). The injection of residuals at additional levels can introduce distortions and hinder semantic integrity preservation, as shown in Fig. 9. This aligns with the findings of previous works that use ControlNet for conditioning diffusion models [6]. Therefore, in our model, we use only the mid-level residuals during inference; these are key for adhering to camera conditions without disrupting the generative capabilities of the base model (SDXL), providing a good trade-off between effective camera control and high-quality image generation.", + "bbox": [ + 89, + 659, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8de14a3043388b405b75940bcb01f4ab9a54f086aae789cb6624e0f286b1c720.jpg", + "image_caption": [ + "Figure 8. Comparison of our model with SDXL and Adobe Firefly (Firefly tags are in dark blue background; prompt engineering, when present, in bold and dark blue text). Four examples are shown: the top half depicts realistic styles, while the bottom half depicts artistic styles; the left half examples intend a shot from below, and the right half a tilted view from below. SDXL struggles in all cases. Firefly successfully produces the shot from below in the realistic style due to its matching tag, but fails in the artistic version of it; for more complex perspectives, like the tilted view from below, Firefly lacks a tag for this view, and fails to produce a valid result despite the efforts with the prompt. Our approach achieves reliable camera control across both styles and perspectives." + ], + "image_footnote": [], + "bbox": [ + 535, + 530, + 648, + 627 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/425c8d85f1a2fc64543f00aa2340fe6241d95a0a2f680c3650518d3ea29dc68d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 531, + 766, + 627 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75be72c9cdc211c4bce4fa525e0749b49df6f921c7d92ffd5252ce511dba8350.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 531, + 879, + 627 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d39b480f44a0389418c18cf669a5ae77b97751ebe5a8c21a50bf64a54fec0c7.jpg", + "image_caption": [ + "Residuals: Middle + C", + "A majestic white stag standing in a misty forest. Its antlers are massive and covered in moss and glowing crystals. Its fur is smooth and white, almost glowing under the pale morning light.", + "Figure 9. Image generation conditioned by the text prompt (bottom) and fixed camera parameters, for different injections of residual outputs of the ControlNet-based module into the main SDXL model. Middle block residuals injected at the bottleneck (ours) enable precise camera control with minimal impact on image quality, while deeper residuals introduce distortions, reducing overall image quality." + ], + "image_footnote": [], + "bbox": [ + 535, + 638, + 648, + 724 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cc46c89f4dfb92447a1a5da0d7e1e559a30819a0385e60ba7942155685c346be.jpg", + "image_caption": [ + "Residuals: Middle + C + B" + ], + "image_footnote": [], + "bbox": [ + 653, + 638, + 766, + 724 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/10897ccdd39afa460c0c1bef784bb5c9bb63a373d3bcebc6cc8c876e0911e198.jpg", + "image_caption": [ + "Residuals: Middle + C + B + A" + ], + "image_footnote": [], + "bbox": [ + 767, + 638, + 883, + 724 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2730", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c4239aa35b14b23b4591725c5975c0151258dba0a08e25912555a609632303a5.jpg", + "image_caption": [ + "Figure 10. Background generation without and with camera control. Our method can generate a background that aligns with the object's perspective (shown on the left), ensuring seamless integration. The baseline approach (SDXL, center) lacks perspective consistency, while the background generated with our method aligns well with the object (right)." + ], + "image_footnote": [], + "bbox": [ + 93, + 85, + 480, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fa7ee707259458809b68d32c9e6a0b38dc69184baf2864d3035842623c0feb61.jpg", + "image_caption": [ + "Figure 11. Video generation results showing two examples of frame-by-frame camera control. Camera parameters are specified to achieve a zoom-in effect (top) and an anti-clockwise rotation (bottom). Frames progress from left to right over time." + ], + "image_footnote": [], + "bbox": [ + 91, + 301, + 480, + 452 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Applications", + "text_level": 1, + "bbox": [ + 89, + 539, + 223, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Background generation for object rendering. Precise-Cam can be used to generate backgrounds that match the perspective of a given object. By aligning the background's perspective with the object's viewpoint, our model can be used to create visually coherent scenes where the object appears naturally embedded, as shown in Fig. 10.", + "bbox": [ + 89, + 565, + 482, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Video generation. Our model can be used to condition the camera view on each frame of a video to specify the desired perspectives throughout the sequence, as illustrated in Fig. 11. Each frame is guided by our four camera parameters through a custom-trained adapter [30] for Stable Video Diffusion [7], ensuring consistent perspective control across frames. Alternatively, our method can be used to condition the initial frame of a video sequence, after which existing methods for relative camera view control can guide the trajectory for the remaining frames [20, 45, 46, 48, 49]. While these existing methods establish movement relative to the first frame, they lack control over the initial camera position that sets the starting perspective for the entire video. Our approach addresses this gap by enabling precise control over the initial camera position to anchor the video sequence.", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bdf8b9ae5f4cb869bbb41cc9c180650e0cc69a6cc508a464c522e896a9209389.jpg", + "image_caption": [ + "Figure 12. Limitations. Left: The model may occasionally incorrectly position objects or people in a vertical, standing orientation (like the man on the boat), as it is more frequent. Right: In the presence of conflicts between the prompt and the desired camera view, the model may produce semantically incoherent outputs." + ], + "image_footnote": [], + "bbox": [ + 516, + 87, + 903, + 214 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Extended control with multiple ControlNets. Additionally, our approach is compatible with other ControlNets, allowing additional conditioning on the final output to achieve complex effects. For instance, combining our model with depth, Canny edges, and pose control can allow for simultaneous control over camera view, subject positioning, and scene structure [54]. Please refer to Sec. H of the supplementary material for further details and examples.", + "bbox": [ + 511, + 315, + 906, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 449, + 633, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present PreciseCam, a framework for precise camera control in text-to-image diffusion-based generation, along with a novel dataset. Our experiments show precise and consistent camera control, far exceeding existing methods such as prompt engineering, even with artistic images not found in our dataset (e.g., Fig. 8). Additionally, we provide proof-of-concept applications for enhancing creative expression, background generation for object compositing, and video generation.", + "bbox": [ + 511, + 474, + 905, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite our dataset covering a wide range of camera parameters and content, PreciseCam may struggle with extreme roll due to the backbone's tendency to align objects vertically (Fig. 12, left). While our model retains SDXL's ability to generate images that match prompts, conflicts between the prompt and camera view (Fig. 12, right) can cause incoherent outputs. We hope our work helps develop new tools to unlock artistic generative imaging.", + "bbox": [ + 511, + 611, + 905, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 511, + 739, + 681, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Dario Lanza and Nestor Monzon and the Graphics and Imaging Lab members. This research was funded by grant PID2022-141539NB-I00, funded by MI-CIU/AEI/10.13039/501100011033, and by ERDF, EU. It has also been partially funded by the Government of Aragon's Departamento de Empleo, Ciencia y Universidades (project ref Proy-T25-24). Additionally, Edurne Bernal-Berdun was supported by a Governor de Aragon predoctoral grant program (2021-2025).", + "bbox": [ + 511, + 763, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2731", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] 360cities. 360cities dataset. https://www.360cities.net/. 5, 1", + "[2] Adobe. Firefly. https://www.adobe.com/products/firefly.html. 1", + "[3] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Ji-aming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, et al. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint arXiv:2211.01324, 2022. 3", + "[4] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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In ICIP, 2020. 5, 1" + ], + "bbox": [ + 516, + 92, + 903, + 486 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2733", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_model.json b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c35f43350cceb9290ece1fc15e17630d60f6b9fa --- /dev/null +++ b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_model.json @@ -0,0 +1,2563 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.157, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "PreciseCam: Precise Camera Control for Text-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.181, + 0.788, + 0.219 + ], + "angle": 0, + "content": "Edurne Bernal-Berdun1, Ana Serrano1, Belen Masia1, Matheus Gadelha2, Yannick Hold-Geoffroy2, Xin Sun2, Diego Gutierrez1" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.241, + 0.524, + 0.278 + ], + "angle": 0, + "content": "1Universidad de Zaragoza, I3A {edurnebernal, anase, bmasia, diegog}@unizar.es" + }, + { + "type": "text", + "bbox": [ + 0.559, + 0.241, + 0.887, + 0.278 + ], + "angle": 0, + "content": "2Adobe Research {gadelha, holdgeof, xinsun}@adobe.com" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.311, + 0.868, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.506, + 0.907, + 0.565 + ], + "angle": 0, + "content": "Figure 1. Our approach enhances the artistic expression of text-to-image generative models by incorporating precise control over camera angles and lens distortion effects. Left: Our input consists of a standard text prompt along with extrinsic (roll and pitch) and intrinsic (vertical field of view and distortion \\(\\xi\\)) camera parameters, which are translated into a suitable and efficient representation for learning camera views. Right: Examples varying roll (top) and pitch (bottom) with the same prompt, while keeping the remaining camera parameters fixed." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.575, + 0.327, + 0.591 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.607, + 0.486, + 0.82 + ], + "angle": 0, + "content": "Images as an artistic medium often rely on specific camera angles and lens distortions to convey ideas or emotions; however, such precise control is missing in current text-to-image models. We propose an efficient and general solution that allows precise control over the camera when generating both photographic and artistic images. Unlike prior methods that rely on predefined shots, we rely solely on four simple extrinsic and intrinsic camera parameters, removing the need for pre-existing geometry, reference 3D objects, and multi-view data. We also present a novel dataset with more than 57,000 images, along with their text prompts and ground-truth camera parameters. Our evaluation shows precise camera control in text-to-image generation, surpassing traditional prompt engineering approaches." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.222, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Images are versatile mediums where content and camera language are crucial. Different camera parameters can con" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.576, + 0.907, + 0.621 + ], + "angle": 0, + "content": "vey dramatically different messages; for example, a low angle may portray dominance or epicness, while a Dutch angle (about 45 degrees) creates unease or tension." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.624, + 0.907, + 0.746 + ], + "angle": 0, + "content": "Text-to-image (T2I) diffusion models have the ability to generate detailed images based on prompts. However, they often produce a flat horizon in the center of the image, which can limit creative expression. This limitation can hinder graphic designers, artists, and photographers from effectively conveying emotions, sensations, or messages. To unlock the capabilities of generative models, it is essential to have precise control over camera parameters." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.748, + 0.909, + 0.852 + ], + "angle": 0, + "content": "Camera views are defined by intrinsic and extrinsic parameters such as field of view (FoV), pitch, roll, etc. However, most text-to-image models are not designed for precise camera view control, making prompt engineering the primary method to achieve desired visual results. This time-consuming approach requires significant expertise and offers limited control." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recently, diffusion models like Firefly [2] have allowed users to control camera views with general instructions such as wide angle or closeup. However, these controls are im" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2724" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.086, + 0.907, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.258, + 0.907, + 0.329 + ], + "angle": 0, + "content": "Figure 2. Red boxes: Current approaches rely on trial-and-error prompt engineering or generalistic tags, offering limited camera control in text-to-image generative AI. Others use 3D representations of the scenes, from which depth or edge maps are obtained, but this imposes strict constraints on the resulting image, limiting flexibility. Green box: Our method relies on two extrinsic and two intrinsic camera parameters, user-provided; we then obtain the effects that such camera parameters impose on the appearance of each pixel in the final image, encoded in a 2D PF-US map (see text for details). This allows for precise, fine-tuned camera control, thus enhancing creativity." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.354, + 0.482, + 0.49 + ], + "angle": 0, + "content": "precise, limiting artistic options. While precise camera control has been explored through 3D information from multiview images, such images are often unavailable, and creating comprehensive 3D representations for all possible camera configurations is not feasible. This results in challenges when generating multiple objects, cluttered scenes, or coherent backgrounds. An alternative is training ControlNet on depth or edge maps, which imposes strict constraints limiting flexibility (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.483, + 0.688 + ], + "angle": 0, + "content": "In this work, we aim to provide a general solution to the problem of precise camera view control, which expands artistic freedom in generative AI. We do not focus solely on well-known photographic shots; instead, we offer simple, direct control of both intrinsic and extrinsic camera parameters, which allows us to achieve a broad spectrum of possible camera views while maintaining precise control (see Fig. 2 (green box)). Instead of representing a 3D scene, which has the limitations we discussed above, we identify the essential effects that such camera parameters impose on the appearance of each pixel in the final image, thus overcoming the requirement to rely on multi-view images and using only simple, single-view images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.902 + ], + "angle": 0, + "content": "To achieve our goal, we rely on two extrinsic parameters, roll and pitch rotations, and two intrinsic parameters, vertical FoV (vFoV) and geometrical distortion of the camera \\((\\xi)\\). Combined with a user-provided prompt, these parameters serve as inputs to our model to generate images with the intended camera view. We adopt the Unified Spherical (US) camera model [5], which allows us to translate these camera parameters into a Perspective Field (PF) representation [24], which is easy to store and interpret. The PF-US encodes the camera parameters as per-pixel information, describing the pixels' up-vector (opposed to the gravity direction) and distance to the horizon, allowing us to encode per-pixel appearance from roll, pitch, vFoV, and \\(\\xi\\) parameters. We then adopt ControlNet [54] to guide our image" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.354, + 0.905, + 0.4 + ], + "angle": 0, + "content": "generation according to the resulting PF-US. Our model, PreciseCam, archives precise camera view control, while the content remains fully determined by the text prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.401, + 0.906, + 0.492 + ], + "angle": 0, + "content": "In addition, we have created a novel dataset of 57,380 single-view RGB images, along with their ground-truth camera parameters and prompt descriptions. Our dataset spans a comprehensive range of camera parameters and a diversity of scenes, making it specifically suitable for the camera control problem we address." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.493, + 0.906, + 0.645 + ], + "angle": 0, + "content": "Last, while our approach is primarily designed for image generation, it opens up new possibilities for video generation, as absolute camera control conditioning is currently being overlooked. Our method can create a precise initial camera position, from which relative camera control can subsequently be applied. Alternatively, we showcase how our model tailored for images can be leveraged to apply limited absolute camera control on videos. Our code and model are publicly available at https://graphics.unizar.es/projects/PreciseCam2024." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.663, + 0.655, + 0.679 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Conditional image generation. Seminal work in conditional image generation leveraged local image statistics [13, 14, 21] and retrieved information from large image datasets [10, 15, 19, 25]. Later deep learning techniques allowed faster, more flexible, and more customized image synthesis within specific domains [9, 23, 35, 43, 44, 52, 53]. Those models were limited in their ability to generate high-quality images and to support open-ended generation tasks. With the advent of large-scale image and text datasets, autoregressive [50] and especially diffusion models [37-39] were proposed as an effective solution to create high-quality images from a virtually unbounded set of text descriptions. Despite these advancements, text remains a limited modality for controlling image generation. Recent methods in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2725" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "produced modifications to the diffusion process, enhancing controllability by allowing users to incorporate additional guidance through color [31], hand-crafted terms [16, 34], and spatially localized prompts [3, 4, 12, 51]. While these methods offer improved control in the generative process, they lack support for more granular guidance, such as structural cues like edges or depth maps." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.218, + 0.485, + 0.595 + ], + "angle": 0, + "content": "Camera control on diffusion generation. While some works have addressed camera control for image generation, this area remains underexplored. Kumari et al. [27] proposed a method that introduces camera control without relying on prompt engineering. They refine a text-to-image diffusion model by conditioning it on a 3D object representation, enabling the generation of various camera viewpoints in new backgrounds. Their NeRF-based method needs multi-view images of a specific object to generate novel views, but it struggles with extreme angles or prompts with other objects. Cheng et al. [11] introduced Continuous 3D Words, which allows control over attributes like object position and lighting by mapping them to the token embedding domain. However, it struggles with complex prompts and tends to replicate poses from the training set. Their camera control is limited to the \"dolly zoom\", which adjusts field of view and distance simultaneously, lacking independent control. On the other hand, Voynov et al. [42] incorporated lens geometry into the generative pipeline to control camera distortion for effects like fish-eye images but did not address extrinsic parameters such as roll or pitch. In contrast, our general approach generates images of any object, scene, or landscape while preserving the model's ability to handle complex prompts and produce various artistic styles and multi-object scenes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Closely related to our work are methods that train networks to guide the generative process using inputs like depth, edges, normals, and segmentation maps [32, 54]. However, these methods still overlook a critical aspect of image creation: controlling the camera used to obtain that image. It is common for practitioners to reason about image editing operations using camera abstractions – what the image would look like if one changes the camera pitch, roll, field of view, etc. To address this gap, we propose a novel approach that incorporates fine-grained camera controls into diffusion adapters like ControlNet [54], expanding the versatility and usability of image generation to scenarios where precise camera control is paramount. Last, recent works focus on relative camera view control for video generation [20, 45, 46, 48, 49]. These methods adjust camera movement relative to the first frame but lack control over initial camera position. Our method provides control over this starting camera orientation, enabling horizon positioning and gravity alignment." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.662, + 0.108 + ], + "angle": 0, + "content": "3. Our Approach" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.905, + 0.251 + ], + "angle": 0, + "content": "Our proposed framework for precise camera view control in text-to-image generation takes as input a text prompt \\( p \\) and a camera view specified by a set \\( \\Omega \\) of four parameters, and generates images \\( I \\) according to both. The four camera parameters (roll, pitch, vFoV, and distortion \\( \\xi \\)) are provided by the user through simple sliders; they are both intuitive and expressive enough to allow for precise camera control. These parameters, together with the camera view representation used by our model, are presented in Sec. 3.1." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.252, + 0.905, + 0.328 + ], + "angle": 0, + "content": "Text-conditioned image generation is performed by means of a diffusion model \\(\\mathcal{D}\\), while we achieve camera view conditioning via a ControlNet-based module, as described in Sec. 3.2. The model is trained with a new dataset featuring ground-truth camera view specification (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.337, + 0.835, + 0.353 + ], + "angle": 0, + "content": "3.1. Precise Camera View Representation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.359, + 0.907, + 0.513 + ], + "angle": 0, + "content": "To enable a precise camera view specification, we adopt the Perspective Field (PF) representation [24], which was originally designed for single-image camera calibration. For any arbitrary projection function \\(\\mathcal{P}(\\mathbf{X}) = \\mathbf{x}\\) mapping a 3D point \\(\\mathbf{X}\\) to an image pixel \\(\\mathbf{x}\\), PF assigns each pixel \\(\\mathbf{x}\\) an up-vector \\(\\mathbf{u}_{\\mathbf{x}}\\) and a latitude angle \\(\\varphi_{\\mathbf{x}}\\). Since each pixel \\(\\mathbf{x}\\) originates from a light ray \\(\\mathbf{R}\\) emitted from \\(\\mathbf{X}\\), the up-vector \\(\\mathbf{u}_{\\mathbf{x}}\\) represents the projection of the up direction of \\(\\mathbf{X}\\) (which is opposite to the gravity vector \\(\\mathbf{g}\\) at \\(\\mathbf{X}\\)), while the latitude \\(\\varphi_{x}\\) measures the angle between the light ray \\(\\mathbf{R}\\) and the horizontal world plane. In particular:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.521, + 0.905, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\mathbf {u} _ {\\mathbf {x}} = \\lim _ {c \\rightarrow 0} \\frac {\\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X})}{\\| \\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X}) \\| _ {2}}, \\text {a n d} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.554, + 0.905, + 0.584 + ], + "angle": 0, + "content": "\\[\n\\varphi_ {\\mathbf {x}} = \\arcsin \\left(\\frac {\\mathbf {R} \\cdot \\mathbf {g}}{\\| \\mathbf {R} \\| _ {2}}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.587, + 0.906, + 0.713 + ], + "angle": 0, + "content": "We aim to enhance creativity and expressivity beyond the commonly used pinhole model in generative AI, including precisely-controlled wide-angle or fisheye cameras. To achieve this, we take advantage of the flexibility of PF to support different camera models through their respective \\(\\mathcal{P}(X)\\) functions, and employ the Unified Spherical (US) camera model [5, 8], which allows camera models beyond the pinhole camera to be encoded within the PF. The projection function \\(\\mathcal{P}(X)\\) of the US model is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.718, + 0.735, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} (\\mathbf {X}) = \\mathbf {x} = (u, v),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.738, + 0.905, + 0.768 + ], + "angle": 0, + "content": "\\[\nu = \\frac {x f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + u _ {0}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.771, + 0.813, + 0.802 + ], + "angle": 0, + "content": "\\[\nv = \\frac {y f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + v _ {0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.811, + 0.905, + 0.87 + ], + "angle": 0, + "content": "Where \\((x,y,z)\\) are the 3D point world coordinates, \\((u_0,v_0)\\) are the principal point coordinates in the image, \\(f\\) is the focal length, and \\(\\xi\\) is a distortion parameter ranging between 0 and 1, with \\(\\xi = 0\\) being a pinhole camera." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "We choose to represent our camera view with two intrinsic parameters: vertical FoV (which is in turn defined" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2726" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.15, + 0.088, + 0.342, + 0.099 + ], + "angle": 0, + "content": "Roll=0°, Pitch=30°, vFoV=35°, \\(\\xi = 0.1\\)" + }, + { + "type": "header", + "bbox": [ + 0.443, + 0.089, + 0.654, + 0.1 + ], + "angle": 0, + "content": "Roll=30°, Pitch=-60°, vFov=100°, \\(\\xi = 0.9\\)" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.101, + 0.396, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.398, + 0.101, + 0.699, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.101, + 0.905, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.23, + 0.908, + 0.3 + ], + "angle": 0, + "content": "Figure 3. Left and center: PF-US camera view representation. PF-US camera parameters (roll, pitch, vertical FoV, and distortion \\(\\xi\\)) and associated maps corresponding to two example images. PF-US maps encode, for each pixel, a latitude value \\(\\varphi_{\\mathbf{x}}\\) (blue-red color map with contour lines) and a unit up-vector \\(\\mathbf{u}_{\\mathbf{x}}\\) (green arrows). Right: Dataset generation. We generate training data in the form of images with ground-truth PF-US maps by leveraging \\(360^{\\circ}\\) images. We sample our camera parameters and obtain the corresponding cropped region for each sampled quartet (as examples, the highlighted regions in red and yellow yield the two examples shown on the left)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.326, + 0.482, + 0.476 + ], + "angle": 0, + "content": "by the focal length \\( f \\) and distortion \\( \\xi \\), as well as two extrinsic parameters: roll and pitch rotations with respect to the horizon. These four parameters conform the set \\( \\Omega = (\\mathrm{roll},\\mathrm{pitch},\\mathrm{vFoV},\\xi) \\), which is expressive enough to represent a wide range of camera configurations, while being intuitive to users. The four parameters are then transformed, by means of the PF-US representation (Eqs. 1-3), into per-pixel up-vectors and latitude values, yielding the corresponding PF-US maps (see Fig. 3, left and center, for two different illustrative examples)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.478, + 0.483, + 0.613 + ], + "angle": 0, + "content": "The resulting PF-US maps provide local information about how camera parameters affect the appearance of each pixel, allowing the model to learn this relationship without the need for heavy 3D representations. Finally, note that yaw rotation is excluded; given a 2D image, we can define up or down directions based on the horizon, but there is no such reference to define left or right directions. By leaving yaw information out, we allow the model to focus on the relevant camera parameters that affect image formation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.621, + 0.373, + 0.637 + ], + "angle": 0, + "content": "3.2. Learning Camera View Control" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.644, + 0.483, + 0.81 + ], + "angle": 0, + "content": "We aim to introduce precise camera view control in text-to-image diffusion models, while preserving their generalization capabilities. This requires a method that minimally disrupts their generation pipeline, already trained on large, quality datasets, adding only the essential information needed to achieve the desired camera view. To do this, we adopt the ControlNet approach to condition image generation [54]: it provides a framework for guiding diffusion models to adhere to a specific condition, and has delivered impressive results conditioning generation with poses, depth, edges, or normal maps, among others." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.811, + 0.484, + 0.901 + ], + "angle": 0, + "content": "During the generation process, ControlNet ensures that the generated images align with both the prompt and the conditioning input, in our case the PF-US map. We use Stable Diffusion XL (SDXL) [36] as our base text-to-image model, although our approach is compatible with any other UNet-based diffusion model. Our ControlNet setup in" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.322, + 0.909, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.621, + 0.908, + 0.718 + ], + "angle": 0, + "content": "Figure 4. Training of our proposed approach for precise camera control. Text-to-image generation with a UNet-based diffusion model (SDXL in our implementation) is conditioned with a PF-US map representing the desired camera parameters; conditioning is learned by means of a ControlNet-based module. During inference, only the middle block output of this module is injected into SDXL (shown in red, see text for more details)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.745, + 0.907, + 0.821 + ], + "angle": 0, + "content": "volves duplicating the encoder and middle block layers of the original SDXL model. While SDXL remains frozen during training to preserve its generalization abilities, ControlNet is initialized with the same weights and trained (see Sec. A of the supplementary material for training details)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Fig. 4 illustrates this. To incorporate ControlNet's output into SDXL, its residuals are passed through a zero-convolution layer (1×1 convolution layer with all-zero initial weights) before being added to the residuals of the original SDXL model. During training, ControlNet outputs are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2727" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "added to the UNet bottleneck and to the decoder skip connections, as in the original implementation. At inference time, however, we find that injecting the ControlNet output only in the bottleneck (marked in red in Fig. 4) improves generation consistency without being detrimental to condition adherence [6]. Our ablation study (Sec. 4) shows how various ControlNet outputs affect the generation process." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.21, + 0.276, + 0.224 + ], + "angle": 0, + "content": "3.3. Dataset Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.234, + 0.483, + 0.279 + ], + "angle": 0, + "content": "To train our framework, we need a diverse dataset of RGB images with corresponding text prompts and PF-US camera parameters, represented as triplets \\((I_i, p_i, \\Omega_i)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.483, + 0.446 + ], + "angle": 0, + "content": "Jin et al. [24] provide data featuring RGB images and ground-truth PF representations. However, they primarily depict urban outdoor scenes and, more importantly, do not cover the full range of camera parameters; for example, they include only minimal distortions (low \\(\\xi\\) values) and avoid large vertical FoVs. A possible alternative would be to use their PF estimation model and apply it to an existing dataset. However, the resulting estimations lack sufficient accuracy for our training purposes, hindering our model's ability to learn view control across the full spectrum of camera parameters (refer to Sec. B of the supplementary material)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.447, + 0.483, + 0.597 + ], + "angle": 0, + "content": "We thus generate our own dataset with ground truth PF-US representations by leveraging \\(360^{\\circ}\\) images. We sample our set of camera parameters (see Sec. B of the supplementary material) and obtain, for each sampled quartet, the corresponding areas cropped from the \\(360^{\\circ}\\) images, and their PF-US maps (as described in Sec. 3.1). Fig. 3 (right) shows two of the resulting regions, with boundaries highlighted in orange and yellow, respectively. Sampling ranges for each camera parameter are: roll \\(\\in (-90^{\\circ}, 90^{\\circ})\\), pitch \\(\\in (-90^{\\circ}, 90^{\\circ})\\), vFoV \\(\\in [15^{\\circ}, 140^{\\circ}]\\) and \\(\\xi \\in (0, 1)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.734 + ], + "angle": 0, + "content": "To maximize diversity in the images, we use six different \\(360^{\\circ}\\) image datasets: 360-SOD [28], CVRG-Pano [33], F-360iSOD [55], Poly Haven HDRIs [18], Sitzmann et al. [40], and 360cities [1]. These feature a mix of outdoor and indoor scenes, containing both natural and urban settings with a diverse array of activities and environments. Please refer to Sec. B.1 of the supplementary material for an analysis of our dataset, highlighting its extended camera coverage and content diversity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.902 + ], + "angle": 0, + "content": "From the resulting \\((I, \\Omega)\\) pairs, we use BLIP-2 [29] to generate a descriptive text prompt \\(p_i\\) for each image \\(I_i\\). While BLIP-2 may sometimes provide inaccurate descriptions, this is not an issue for our training: we do not train the text-to-image model itself, but the conditioning module instead, which needs to learn the camera view independently of the prompt. These inaccurate prompts are akin to the ControlNet technique of introducing empty strings as the prompt during training. Our final dataset is comprised of 57,380 RGB images with associated text prompts and ground-truth PF-US parameters." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.6, + 0.105 + ], + "angle": 0, + "content": "4. Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.905, + 0.267 + ], + "angle": 0, + "content": "We evaluate our precise control of camera parameters against baseline methods, demonstrating that our approach can manage both artistic and realistic styles. Then, we analyze the robustness of our model, including camera conditioning and an ablation study on residuals for improved control and quality. Finally, we showcase various applications such as background generation for object rendering, video generation, and enhanced control with multiple ControlNets. For further results and details, please see the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.274, + 0.907, + 0.668 + ], + "angle": 0, + "content": "Camera control. PreciseCam enables precise control over extrinsic (roll and pitch rotations) and intrinsic (vFoV and distortion \\(\\xi\\)) camera parameters. Fig. 5 illustrates control over extrinsic parameters. In it, roll (top row) and pitch (bottom row) are varied while the remaining parameters are held constant. The images follow the conditioning, and a high degree of consistency is maintained through camera variations. Similarly, in Fig. 6, we show intrinsic parameter control by varying the vertical field of view vFoV (left) or the distortion \\(\\xi\\) (right), while keeping all the other parameters fixed. In the PF-US maps (see Sec. 3.1), larger vFoV leads to increased latitude values, whereas \\(\\xi\\) mainly affects the up vectors. The generated images follow the PF-US maps, effectively translating camera settings into visual outcomes. There is a lack of reliable metrics in the literature for evaluating the camera parameters of generated images, which makes it challenging to assess PreciseCam's accuracy. Nevertheless, we include a quantitative evaluation of the camera view in Sec. F of the supplementary material, based on Perspective Fields [24]. Additionally, Sec. C of the supplementary material includes more examples of systematic variation of camera parameters for a variety of prompts, illustrating the disentanglement between camera parameters and prompt of PreciseCam. Our ControlNet-based architecture, combined with our diverse dataset, effectively disentangles the camera parameters from image semantics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Comparisons. We compare our approach to two alternative methods: prompt-engineered SDXL and Adobe Firefly, a state-of-the-art diffusion model with preset style tags. Fig. 8 illustrates this comparison. Despite prompt engineering efforts, SDXL's ability to control camera perspectives remains limited, and it often struggles to consistently interpret complex camera-related prompts. Adobe Firefly includes predefined style tags for shot specification, such as close-up, shot from above, shot from below, and wide angle, supporting basic camera control. Nevertheless, while Firefly's tags do introduce some perspective variations, the control enabled by these tags is limited, and insufficient even when combined with prompt specification. In contrast, our model is able to control camera views precisely in both realistic (top row) and artistic (bottom row) styles." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2728" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.089, + 0.21, + 0.165 + ], + "angle": 0, + "content": "A digital art depiction of a castle floating in the ocean, with glowing bluish clouds. The castle's towers are impossibly tall and the colors soft, with reflections from the light of an ethereal sun." + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.089, + 0.351, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.089, + 0.49, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.089, + 0.628, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.089, + 0.767, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.089, + 0.906, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.209, + 0.21, + 0.295 + ], + "angle": 0, + "content": "A photorealistic digital art of a futuristic cityscape at sunset. Every detail, like the reflective glass skyscrapers, is rendered with high clarity. The colors are warm and saturated, with a glowing orange sky." + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.209, + 0.351, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.209, + 0.49, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.209, + 0.628, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.21, + 0.767, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.21, + 0.906, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.329, + 0.907, + 0.386 + ], + "angle": 0, + "content": "Figure 5. Extrinsic Parameter Control. Images generated by varying the extrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Top row: Variation in pitch, effectively shifting the view from looking downward to upward; fixed parameters are (roll, vFoV, \\(\\xi\\)) = (0°, 80°, 0.1). Right: Variation in roll, tilting the view from left to right; (pitch, vFoV, \\(\\xi\\)) = (0°, 80°, 0.1). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.398, + 0.222, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.399, + 0.351, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.399, + 0.483, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.502, + 0.483, + 0.525 + ], + "angle": 0, + "content": "A photograph of a comfortable nursery with soft pastel colors, a rocking chair, a crib by the window, and shelves with neatly organized baby essentials." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.398, + 0.643, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.399, + 0.774, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.399, + 0.906, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.502, + 0.906, + 0.524 + ], + "angle": 0, + "content": "A narrow alleyway in an old European village, depicted in a vintage lithograph style, with intricate line work and a muted color palette." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.536, + 0.907, + 0.592 + ], + "angle": 0, + "content": "Figure 6. Intrinsic Parameter Control. Images generated by varying the intrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Left: Variation in the vertical field of view (vFoV); fixed parameters are (roll, pitch, \\(\\xi\\)) = (0°, 0°, 0.1). Right: Variation in distortion (\\(\\xi\\)); (roll, pitch, vFoV) = (0°, 0°, 120°). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text." + }, + { + "type": "table", + "bbox": [ + 0.132, + 0.608, + 0.445, + 0.741 + ], + "angle": 0, + "content": "
CLIP ScoreBLIP Score
SDXL + Prompt Engineering0.557 (0.039)0.299 (0.025)
(Ours) PreciseCam0.543 (0.039)0.292 (0.026)
Prompt +\nOpen with\na angle,\nof -70.Prompt +\nRoll = 0°\nPitch = -70°\nvFoV = 70\nξ = 0.1.
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.091, + 0.741, + 0.473, + 0.774 + ], + "angle": 0, + "content": "Prompt: Two enormous steampunk-style airships engaged in combat over a foggy cityscape. Gears, steam, and mechanical components are exposed on the airships, while cannons fire plumes of smoke and sparks. Below, the city is filled with smokesstacks and towering clock towers." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.784, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Figure 7. Our model achieves prompt adherence on par with SDXL, as reflected in the table by comparable CLIP and BLIP scores (see text for details), while enabling camera control that SDXL cannot provide. Images show an example result from SDXL with prompt engineering (left), and from our model (right)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Additionally, we conducted a user study with 34 participants to compare the camera view precision of the models, revealing that our model significantly outperformed SDXL and Adobe Firefly in aligning with the desired camera view (see Sec. E of the supplementary material). We also evaluate whether our model maintains, despite the inclusion of camera control, the text prompt adherence exhibited by SDXL. To do this, we compare our results to those of the baseline SDXL by computing, for each method, CLIP and BLIP scores [22], which are commonly used to evaluate prompt relevance in generated images. The comparison is done over 2,940 images generated with each method (ours and baseline SDXL). For the baseline SDXL, we use prompt engineering, specifying the desired view to encourage distinct camera perspectives (see Sec. D of the supplementary material). Our approach achieves comparable scores to SDXL (Fig. 7 shows mean and standard deviation), suggesting that our model is able to maintain prompt alignment while providing precise camera view control." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2729" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.158, + 0.089, + 0.186, + 0.098 + ], + "angle": 0, + "content": "SDXL" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.1, + 0.225, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.182, + 0.232, + 0.211 + ], + "angle": 0, + "content": "A photograph of a street cafe scene at twilight with people enjoying drinks, a shot from below." + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.089, + 0.33, + 0.098 + ], + "angle": 0, + "content": "Firefly Image 3" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.1, + 0.349, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.182, + 0.341, + 0.21 + ], + "angle": 0, + "content": "A photograph of a street cafe scene at twilight with people enjoying drinks." + }, + { + "type": "image_caption", + "bbox": [ + 0.246, + 0.211, + 0.328, + 0.22 + ], + "angle": 0, + "content": "+ tag: shot from below" + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.089, + 0.431, + 0.098 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.098, + 0.471, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.355, + 0.181, + 0.482, + 0.201 + ], + "angle": 0, + "content": "A photograph of a street cafe scene at twilight with people enjoying drinks." + }, + { + "type": "image_caption", + "bbox": [ + 0.374, + 0.204, + 0.451, + 0.211 + ], + "angle": 0, + "content": "+ roll=0°, pitch=40°." + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.212, + 0.45, + 0.221 + ], + "angle": 0, + "content": "vFoV=70°, \\(\\xi = 0.1\\)" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.255, + 0.228, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.338, + 0.231, + 0.386 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, a shot from below." + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.255, + 0.353, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.338, + 0.356, + 0.386 + ], + "angle": 0, + "content": "A street cafe scene at twilight withpeople enjoying drinks , depicted ina lively watercolor and ink stylewith loose lines and warm , glowingcolors + tag : shot from below" + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.251, + 0.471, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.358, + 0.338, + 0.484, + 0.376 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors." + }, + { + "type": "image_caption", + "bbox": [ + 0.374, + 0.378, + 0.451, + 0.394 + ], + "angle": 0, + "content": "+ roll = 0°, pitch = 40°, vFOV = 70°, \\(\\xi = 0.1\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.089, + 0.58, + 0.098 + ], + "angle": 0, + "content": "SDXL" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.1, + 0.622, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.181, + 0.624, + 0.24 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene." + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.089, + 0.726, + 0.098 + ], + "angle": 0, + "content": "Firefly Image 3" + }, + { + "type": "image", + "bbox": [ + 0.641, + 0.099, + 0.746, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.181, + 0.748, + 0.24 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene" + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.24, + 0.719, + 0.248 + ], + "angle": 0, + "content": "+ tag: shot from below" + }, + { + "type": "image_caption", + "bbox": [ + 0.806, + 0.089, + 0.829, + 0.098 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.098, + 0.872, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.754, + 0.181, + 0.88, + 0.201 + ], + "angle": 0, + "content": "A photograph of a street cafe scene at twilight with people enjoying drinks." + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.204, + 0.859, + 0.221 + ], + "angle": 0, + "content": "+ roll \\(= -30^{\\circ}\\) pitch \\(= 40^{\\circ}\\) \\(\\mathrm{VFOV} = 0^{\\circ}\\) \\(\\xi = 0.1\\)" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.256, + 0.625, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.338, + 0.627, + 0.424 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene." + }, + { + "type": "image", + "bbox": [ + 0.641, + 0.255, + 0.75, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.338, + 0.751, + 0.425 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a groundlevel camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene + tag: shot from below" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.25, + 0.882, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.76, + 0.338, + 0.885, + 0.395 + ], + "angle": 0, + "content": "A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors. + roll \\(= -30^{\\circ}\\) pitch \\(= 40^{\\circ}\\) vFoV \\(= 70^{\\circ}\\) \\(\\xi = 0.1\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.435, + 0.907, + 0.518 + ], + "angle": 0, + "content": "Figure 8. Comparison of our model with SDXL and Adobe Firefly (Firefly tags are in dark blue background; prompt engineering, when present, in bold and dark blue text). Four examples are shown: the top half depicts realistic styles, while the bottom half depicts artistic styles; the left half examples intend a shot from below, and the right half a tilted view from below. SDXL struggles in all cases. Firefly successfully produces the shot from below in the realistic style due to its matching tag, but fails in the artistic version of it; for more complex perspectives, like the tilted view from below, Firefly lacks a tag for this view, and fails to produce a valid result despite the efforts with the prompt. Our approach achieves reliable camera control across both styles and perspectives." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.535, + 0.242, + 0.55 + ], + "angle": 0, + "content": "4.1. Model analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.561, + 0.484, + 0.637 + ], + "angle": 0, + "content": "Camera conditioning adherence. To assess the stability of our model's camera conditioning, we generate images using the same PF-US maps and prompts but vary the input noise. Results show consistent camera conditioning (please refer to Sec. G of the supplementary material for examples)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Ablation: Influence of the residuals' contributions. In our framework, the ControlNet-based module generates residual outputs that can be injected into the main model in various layers. We observe that residuals from the middle block (bottleneck) effectively achieve adherence to the camera conditioning, while preserving the image quality achieved by the base model (SDXL). The injection of residuals at additional levels can introduce distortions and hinder semantic integrity preservation, as shown in Fig. 9. This aligns with the findings of previous works that use ControlNet for conditioning diffusion models [6]. Therefore, in our model, we use only the mid-level residuals during inference; these are key for adhering to camera conditions without disrupting the generative capabilities of the base model (SDXL), providing a good trade-off between effective camera control and high-quality image generation." + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.531, + 0.65, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.631, + 0.636, + 0.638 + ], + "angle": 0, + "content": "Residuals: Middle + C" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.532, + 0.767, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.631, + 0.762, + 0.639 + ], + "angle": 0, + "content": "Residuals: Middle + C + B" + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.532, + 0.88, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.77, + 0.631, + 0.885, + 0.639 + ], + "angle": 0, + "content": "Residuals: Middle + C + B + A" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.639, + 0.65, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.727, + 0.884, + 0.747 + ], + "angle": 0, + "content": "A majestic white stag standing in a misty forest. Its antlers are massive and covered in moss and glowing crystals. Its fur is smooth and white, almost glowing under the pale morning light." + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.639, + 0.767, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.639, + 0.885, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.758, + 0.907, + 0.856 + ], + "angle": 0, + "content": "Figure 9. Image generation conditioned by the text prompt (bottom) and fixed camera parameters, for different injections of residual outputs of the ControlNet-based module into the main SDXL model. Middle block residuals injected at the bottleneck (ours) enable precise camera control with minimal impact on image quality, while deeper residuals introduce distortions, reducing overall image quality." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2730" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.087, + 0.482, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.209, + 0.483, + 0.293 + ], + "angle": 0, + "content": "Figure 10. Background generation without and with camera control. Our method can generate a background that aligns with the object's perspective (shown on the left), ensuring seamless integration. The baseline approach (SDXL, center) lacks perspective consistency, while the background generated with our method aligns well with the object (right)." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.302, + 0.482, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.464, + 0.483, + 0.52 + ], + "angle": 0, + "content": "Figure 11. Video generation results showing two examples of frame-by-frame camera control. Camera parameters are specified to achieve a zoom-in effect (top) and an anti-clockwise rotation (bottom). Frames progress from left to right over time." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.54, + 0.225, + 0.557 + ], + "angle": 0, + "content": "4.2. Applications" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.566, + 0.483, + 0.657 + ], + "angle": 0, + "content": "Background generation for object rendering. Precise-Cam can be used to generate backgrounds that match the perspective of a given object. By aligning the background's perspective with the object's viewpoint, our model can be used to create visually coherent scenes where the object appears naturally embedded, as shown in Fig. 10." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Video generation. Our model can be used to condition the camera view on each frame of a video to specify the desired perspectives throughout the sequence, as illustrated in Fig. 11. Each frame is guided by our four camera parameters through a custom-trained adapter [30] for Stable Video Diffusion [7], ensuring consistent perspective control across frames. Alternatively, our method can be used to condition the initial frame of a video sequence, after which existing methods for relative camera view control can guide the trajectory for the remaining frames [20, 45, 46, 48, 49]. While these existing methods establish movement relative to the first frame, they lack control over the initial camera position that sets the starting perspective for the entire video. Our approach addresses this gap by enabling precise control over the initial camera position to anchor the video sequence." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.088, + 0.905, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.226, + 0.905, + 0.296 + ], + "angle": 0, + "content": "Figure 12. Limitations. Left: The model may occasionally incorrectly position objects or people in a vertical, standing orientation (like the man on the boat), as it is more frequent. Right: In the presence of conflicts between the prompt and the desired camera view, the model may produce semantically incoherent outputs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.316, + 0.907, + 0.437 + ], + "angle": 0, + "content": "Extended control with multiple ControlNets. Additionally, our approach is compatible with other ControlNets, allowing additional conditioning on the final output to achieve complex effects. For instance, combining our model with depth, Canny edges, and pose control can allow for simultaneous control over camera view, subject positioning, and scene structure [54]. Please refer to Sec. H of the supplementary material for further details and examples." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.45, + 0.634, + 0.466 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.906, + 0.61 + ], + "angle": 0, + "content": "We present PreciseCam, a framework for precise camera control in text-to-image diffusion-based generation, along with a novel dataset. Our experiments show precise and consistent camera control, far exceeding existing methods such as prompt engineering, even with artistic images not found in our dataset (e.g., Fig. 8). Additionally, we provide proof-of-concept applications for enhancing creative expression, background generation for object compositing, and video generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.906, + 0.732 + ], + "angle": 0, + "content": "Despite our dataset covering a wide range of camera parameters and content, PreciseCam may struggle with extreme roll due to the backbone's tendency to align objects vertically (Fig. 12, left). While our model retains SDXL's ability to generate images that match prompts, conflicts between the prompt and camera view (Fig. 12, right) can cause incoherent outputs. We hope our work helps develop new tools to unlock artistic generative imaging." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.74, + 0.682, + 0.758 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We thank Dario Lanza and Nestor Monzon and the Graphics and Imaging Lab members. This research was funded by grant PID2022-141539NB-I00, funded by MI-CIU/AEI/10.13039/501100011033, and by ERDF, EU. It has also been partially funded by the Government of Aragon's Departamento de Empleo, Ciencia y Universidades (project ref Proy-T25-24). Additionally, Edurne Bernal-Berdun was supported by a Governor de Aragon predoctoral grant program (2021-2025)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2731" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.129 + ], + "angle": 0, + "content": "[1] 360cities. 360cities dataset. https://www.360cities.net/. 5, 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.131, + 0.485, + 0.157 + ], + "angle": 0, + "content": "[2] Adobe. 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In ICIP, 2020. 5, 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2733" + } + ] +] \ No newline at end of file diff --git a/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_origin.pdf b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bb00d2313767552df6d8f46deca9780596fb83f0 --- /dev/null +++ b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/f1c3bc77-cc18-4660-8f04-34981ca422eb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:52b0d7a3ed31268db8b14770f74aa967b632ef22b6dac664c948a0dc9e986529 +size 10044033 diff --git a/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/full.md b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..674333eb4a759d0541ab6bb8eb26ebdd3e85ecf9 --- /dev/null +++ b/2025/PreciseCam_ Precise Camera Control for Text-to-Image Generation/full.md @@ -0,0 +1,346 @@ +# PreciseCam: Precise Camera Control for Text-to-Image Generation + +Edurne Bernal-Berdun1, Ana Serrano1, Belen Masia1, Matheus Gadelha2, Yannick Hold-Geoffroy2, Xin Sun2, Diego Gutierrez1 + +1Universidad de Zaragoza, I3A {edurnebernal, anase, bmasia, diegog}@unizar.es + +2Adobe Research {gadelha, holdgeof, xinsun}@adobe.com + +![](images/db30796ef700bfffffb1c306c1ff80a2e116b20a30148cd1a9883bde85c2a193.jpg) +Figure 1. Our approach enhances the artistic expression of text-to-image generative models by incorporating precise control over camera angles and lens distortion effects. Left: Our input consists of a standard text prompt along with extrinsic (roll and pitch) and intrinsic (vertical field of view and distortion $\xi$ ) camera parameters, which are translated into a suitable and efficient representation for learning camera views. Right: Examples varying roll (top) and pitch (bottom) with the same prompt, while keeping the remaining camera parameters fixed. + +# Abstract + +Images as an artistic medium often rely on specific camera angles and lens distortions to convey ideas or emotions; however, such precise control is missing in current text-to-image models. We propose an efficient and general solution that allows precise control over the camera when generating both photographic and artistic images. Unlike prior methods that rely on predefined shots, we rely solely on four simple extrinsic and intrinsic camera parameters, removing the need for pre-existing geometry, reference 3D objects, and multi-view data. We also present a novel dataset with more than 57,000 images, along with their text prompts and ground-truth camera parameters. Our evaluation shows precise camera control in text-to-image generation, surpassing traditional prompt engineering approaches. + +# 1. Introduction + +Images are versatile mediums where content and camera language are crucial. Different camera parameters can con + +vey dramatically different messages; for example, a low angle may portray dominance or epicness, while a Dutch angle (about 45 degrees) creates unease or tension. + +Text-to-image (T2I) diffusion models have the ability to generate detailed images based on prompts. However, they often produce a flat horizon in the center of the image, which can limit creative expression. This limitation can hinder graphic designers, artists, and photographers from effectively conveying emotions, sensations, or messages. To unlock the capabilities of generative models, it is essential to have precise control over camera parameters. + +Camera views are defined by intrinsic and extrinsic parameters such as field of view (FoV), pitch, roll, etc. However, most text-to-image models are not designed for precise camera view control, making prompt engineering the primary method to achieve desired visual results. This time-consuming approach requires significant expertise and offers limited control. + +Recently, diffusion models like Firefly [2] have allowed users to control camera views with general instructions such as wide angle or closeup. However, these controls are im + +![](images/72a720cf0230c8b8c537e27d2370453dd55de0ebd6429db62f00712c4644535e.jpg) +Figure 2. Red boxes: Current approaches rely on trial-and-error prompt engineering or generalistic tags, offering limited camera control in text-to-image generative AI. Others use 3D representations of the scenes, from which depth or edge maps are obtained, but this imposes strict constraints on the resulting image, limiting flexibility. Green box: Our method relies on two extrinsic and two intrinsic camera parameters, user-provided; we then obtain the effects that such camera parameters impose on the appearance of each pixel in the final image, encoded in a 2D PF-US map (see text for details). This allows for precise, fine-tuned camera control, thus enhancing creativity. + +precise, limiting artistic options. While precise camera control has been explored through 3D information from multiview images, such images are often unavailable, and creating comprehensive 3D representations for all possible camera configurations is not feasible. This results in challenges when generating multiple objects, cluttered scenes, or coherent backgrounds. An alternative is training ControlNet on depth or edge maps, which imposes strict constraints limiting flexibility (see Fig. 2). + +In this work, we aim to provide a general solution to the problem of precise camera view control, which expands artistic freedom in generative AI. We do not focus solely on well-known photographic shots; instead, we offer simple, direct control of both intrinsic and extrinsic camera parameters, which allows us to achieve a broad spectrum of possible camera views while maintaining precise control (see Fig. 2 (green box)). Instead of representing a 3D scene, which has the limitations we discussed above, we identify the essential effects that such camera parameters impose on the appearance of each pixel in the final image, thus overcoming the requirement to rely on multi-view images and using only simple, single-view images. + +To achieve our goal, we rely on two extrinsic parameters, roll and pitch rotations, and two intrinsic parameters, vertical FoV (vFoV) and geometrical distortion of the camera $(\xi)$ . Combined with a user-provided prompt, these parameters serve as inputs to our model to generate images with the intended camera view. We adopt the Unified Spherical (US) camera model [5], which allows us to translate these camera parameters into a Perspective Field (PF) representation [24], which is easy to store and interpret. The PF-US encodes the camera parameters as per-pixel information, describing the pixels' up-vector (opposed to the gravity direction) and distance to the horizon, allowing us to encode per-pixel appearance from roll, pitch, vFoV, and $\xi$ parameters. We then adopt ControlNet [54] to guide our image + +generation according to the resulting PF-US. Our model, PreciseCam, archives precise camera view control, while the content remains fully determined by the text prompt. + +In addition, we have created a novel dataset of 57,380 single-view RGB images, along with their ground-truth camera parameters and prompt descriptions. Our dataset spans a comprehensive range of camera parameters and a diversity of scenes, making it specifically suitable for the camera control problem we address. + +Last, while our approach is primarily designed for image generation, it opens up new possibilities for video generation, as absolute camera control conditioning is currently being overlooked. Our method can create a precise initial camera position, from which relative camera control can subsequently be applied. Alternatively, we showcase how our model tailored for images can be leveraged to apply limited absolute camera control on videos. Our code and model are publicly available at https://graphics.unizar.es/projects/PreciseCam2024. + +# 2. Related Work + +Conditional image generation. Seminal work in conditional image generation leveraged local image statistics [13, 14, 21] and retrieved information from large image datasets [10, 15, 19, 25]. Later deep learning techniques allowed faster, more flexible, and more customized image synthesis within specific domains [9, 23, 35, 43, 44, 52, 53]. Those models were limited in their ability to generate high-quality images and to support open-ended generation tasks. With the advent of large-scale image and text datasets, autoregressive [50] and especially diffusion models [37-39] were proposed as an effective solution to create high-quality images from a virtually unbounded set of text descriptions. Despite these advancements, text remains a limited modality for controlling image generation. Recent methods in + +produced modifications to the diffusion process, enhancing controllability by allowing users to incorporate additional guidance through color [31], hand-crafted terms [16, 34], and spatially localized prompts [3, 4, 12, 51]. While these methods offer improved control in the generative process, they lack support for more granular guidance, such as structural cues like edges or depth maps. + +Camera control on diffusion generation. While some works have addressed camera control for image generation, this area remains underexplored. Kumari et al. [27] proposed a method that introduces camera control without relying on prompt engineering. They refine a text-to-image diffusion model by conditioning it on a 3D object representation, enabling the generation of various camera viewpoints in new backgrounds. Their NeRF-based method needs multi-view images of a specific object to generate novel views, but it struggles with extreme angles or prompts with other objects. Cheng et al. [11] introduced Continuous 3D Words, which allows control over attributes like object position and lighting by mapping them to the token embedding domain. However, it struggles with complex prompts and tends to replicate poses from the training set. Their camera control is limited to the "dolly zoom", which adjusts field of view and distance simultaneously, lacking independent control. On the other hand, Voynov et al. [42] incorporated lens geometry into the generative pipeline to control camera distortion for effects like fish-eye images but did not address extrinsic parameters such as roll or pitch. In contrast, our general approach generates images of any object, scene, or landscape while preserving the model's ability to handle complex prompts and produce various artistic styles and multi-object scenes. + +Closely related to our work are methods that train networks to guide the generative process using inputs like depth, edges, normals, and segmentation maps [32, 54]. However, these methods still overlook a critical aspect of image creation: controlling the camera used to obtain that image. It is common for practitioners to reason about image editing operations using camera abstractions – what the image would look like if one changes the camera pitch, roll, field of view, etc. To address this gap, we propose a novel approach that incorporates fine-grained camera controls into diffusion adapters like ControlNet [54], expanding the versatility and usability of image generation to scenarios where precise camera control is paramount. Last, recent works focus on relative camera view control for video generation [20, 45, 46, 48, 49]. These methods adjust camera movement relative to the first frame but lack control over initial camera position. Our method provides control over this starting camera orientation, enabling horizon positioning and gravity alignment. + +# 3. Our Approach + +Our proposed framework for precise camera view control in text-to-image generation takes as input a text prompt $p$ and a camera view specified by a set $\Omega$ of four parameters, and generates images $I$ according to both. The four camera parameters (roll, pitch, vFoV, and distortion $\xi$ ) are provided by the user through simple sliders; they are both intuitive and expressive enough to allow for precise camera control. These parameters, together with the camera view representation used by our model, are presented in Sec. 3.1. + +Text-conditioned image generation is performed by means of a diffusion model $\mathcal{D}$ , while we achieve camera view conditioning via a ControlNet-based module, as described in Sec. 3.2. The model is trained with a new dataset featuring ground-truth camera view specification (Sec. 3.3). + +# 3.1. Precise Camera View Representation + +To enable a precise camera view specification, we adopt the Perspective Field (PF) representation [24], which was originally designed for single-image camera calibration. For any arbitrary projection function $\mathcal{P}(\mathbf{X}) = \mathbf{x}$ mapping a 3D point $\mathbf{X}$ to an image pixel $\mathbf{x}$ , PF assigns each pixel $\mathbf{x}$ an up-vector $\mathbf{u}_{\mathbf{x}}$ and a latitude angle $\varphi_{\mathbf{x}}$ . Since each pixel $\mathbf{x}$ originates from a light ray $\mathbf{R}$ emitted from $\mathbf{X}$ , the up-vector $\mathbf{u}_{\mathbf{x}}$ represents the projection of the up direction of $\mathbf{X}$ (which is opposite to the gravity vector $\mathbf{g}$ at $\mathbf{X}$ ), while the latitude $\varphi_{x}$ measures the angle between the light ray $\mathbf{R}$ and the horizontal world plane. In particular: + +$$ +\mathbf {u} _ {\mathbf {x}} = \lim _ {c \rightarrow 0} \frac {\mathcal {P} (\mathbf {X} - c \mathbf {g}) - \mathcal {P} (\mathbf {X})}{\| \mathcal {P} (\mathbf {X} - c \mathbf {g}) - \mathcal {P} (\mathbf {X}) \| _ {2}}, \text {a n d} \tag {1} +$$ + +$$ +\varphi_ {\mathbf {x}} = \arcsin \left(\frac {\mathbf {R} \cdot \mathbf {g}}{\| \mathbf {R} \| _ {2}}\right). \tag {2} +$$ + +We aim to enhance creativity and expressivity beyond the commonly used pinhole model in generative AI, including precisely-controlled wide-angle or fisheye cameras. To achieve this, we take advantage of the flexibility of PF to support different camera models through their respective $\mathcal{P}(X)$ functions, and employ the Unified Spherical (US) camera model [5, 8], which allows camera models beyond the pinhole camera to be encoded within the PF. The projection function $\mathcal{P}(X)$ of the US model is defined as: + +$$ +\mathcal {P} (\mathbf {X}) = \mathbf {x} = (u, v), +$$ + +$$ +u = \frac {x f}{\xi \sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + u _ {0}, \tag {3} +$$ + +$$ +v = \frac {y f}{\xi \sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + v _ {0}. +$$ + +Where $(x,y,z)$ are the 3D point world coordinates, $(u_0,v_0)$ are the principal point coordinates in the image, $f$ is the focal length, and $\xi$ is a distortion parameter ranging between 0 and 1, with $\xi = 0$ being a pinhole camera. + +We choose to represent our camera view with two intrinsic parameters: vertical FoV (which is in turn defined + +![](images/854d0d28e50ed05b55e939e30010bacb471d4e5d86269854b21658ab53bac3b1.jpg) +Figure 3. Left and center: PF-US camera view representation. PF-US camera parameters (roll, pitch, vertical FoV, and distortion $\xi$ ) and associated maps corresponding to two example images. PF-US maps encode, for each pixel, a latitude value $\varphi_{\mathbf{x}}$ (blue-red color map with contour lines) and a unit up-vector $\mathbf{u}_{\mathbf{x}}$ (green arrows). Right: Dataset generation. We generate training data in the form of images with ground-truth PF-US maps by leveraging $360^{\circ}$ images. We sample our camera parameters and obtain the corresponding cropped region for each sampled quartet (as examples, the highlighted regions in red and yellow yield the two examples shown on the left). + +![](images/f2fa8caaa41bc79b45a8bf9892c5e49e91cc80729e1658330b749b98af1a6454.jpg) + +![](images/e11d32d6f95dc658e6dbf7264763b53aaed6f2b5a5280d6c2180f413b2a82c39.jpg) + +by the focal length $f$ and distortion $\xi$ , as well as two extrinsic parameters: roll and pitch rotations with respect to the horizon. These four parameters conform the set $\Omega = (\mathrm{roll},\mathrm{pitch},\mathrm{vFoV},\xi)$ , which is expressive enough to represent a wide range of camera configurations, while being intuitive to users. The four parameters are then transformed, by means of the PF-US representation (Eqs. 1-3), into per-pixel up-vectors and latitude values, yielding the corresponding PF-US maps (see Fig. 3, left and center, for two different illustrative examples). + +The resulting PF-US maps provide local information about how camera parameters affect the appearance of each pixel, allowing the model to learn this relationship without the need for heavy 3D representations. Finally, note that yaw rotation is excluded; given a 2D image, we can define up or down directions based on the horizon, but there is no such reference to define left or right directions. By leaving yaw information out, we allow the model to focus on the relevant camera parameters that affect image formation. + +# 3.2. Learning Camera View Control + +We aim to introduce precise camera view control in text-to-image diffusion models, while preserving their generalization capabilities. This requires a method that minimally disrupts their generation pipeline, already trained on large, quality datasets, adding only the essential information needed to achieve the desired camera view. To do this, we adopt the ControlNet approach to condition image generation [54]: it provides a framework for guiding diffusion models to adhere to a specific condition, and has delivered impressive results conditioning generation with poses, depth, edges, or normal maps, among others. + +During the generation process, ControlNet ensures that the generated images align with both the prompt and the conditioning input, in our case the PF-US map. We use Stable Diffusion XL (SDXL) [36] as our base text-to-image model, although our approach is compatible with any other UNet-based diffusion model. Our ControlNet setup in + +![](images/b5532014a382bbab00a76c78c1bb1accb846f51561067acfbf26c418a5e7d2ec.jpg) +Figure 4. Training of our proposed approach for precise camera control. Text-to-image generation with a UNet-based diffusion model (SDXL in our implementation) is conditioned with a PF-US map representing the desired camera parameters; conditioning is learned by means of a ControlNet-based module. During inference, only the middle block output of this module is injected into SDXL (shown in red, see text for more details). + +volves duplicating the encoder and middle block layers of the original SDXL model. While SDXL remains frozen during training to preserve its generalization abilities, ControlNet is initialized with the same weights and trained (see Sec. A of the supplementary material for training details). + +Fig. 4 illustrates this. To incorporate ControlNet's output into SDXL, its residuals are passed through a zero-convolution layer (1×1 convolution layer with all-zero initial weights) before being added to the residuals of the original SDXL model. During training, ControlNet outputs are + +added to the UNet bottleneck and to the decoder skip connections, as in the original implementation. At inference time, however, we find that injecting the ControlNet output only in the bottleneck (marked in red in Fig. 4) improves generation consistency without being detrimental to condition adherence [6]. Our ablation study (Sec. 4) shows how various ControlNet outputs affect the generation process. + +# 3.3. Dataset Generation + +To train our framework, we need a diverse dataset of RGB images with corresponding text prompts and PF-US camera parameters, represented as triplets $(I_i, p_i, \Omega_i)$ . + +Jin et al. [24] provide data featuring RGB images and ground-truth PF representations. However, they primarily depict urban outdoor scenes and, more importantly, do not cover the full range of camera parameters; for example, they include only minimal distortions (low $\xi$ values) and avoid large vertical FoVs. A possible alternative would be to use their PF estimation model and apply it to an existing dataset. However, the resulting estimations lack sufficient accuracy for our training purposes, hindering our model's ability to learn view control across the full spectrum of camera parameters (refer to Sec. B of the supplementary material). + +We thus generate our own dataset with ground truth PF-US representations by leveraging $360^{\circ}$ images. We sample our set of camera parameters (see Sec. B of the supplementary material) and obtain, for each sampled quartet, the corresponding areas cropped from the $360^{\circ}$ images, and their PF-US maps (as described in Sec. 3.1). Fig. 3 (right) shows two of the resulting regions, with boundaries highlighted in orange and yellow, respectively. Sampling ranges for each camera parameter are: roll $\in (-90^{\circ}, 90^{\circ})$ , pitch $\in (-90^{\circ}, 90^{\circ})$ , vFoV $\in [15^{\circ}, 140^{\circ}]$ and $\xi \in (0, 1)$ . + +To maximize diversity in the images, we use six different $360^{\circ}$ image datasets: 360-SOD [28], CVRG-Pano [33], F-360iSOD [55], Poly Haven HDRIs [18], Sitzmann et al. [40], and 360cities [1]. These feature a mix of outdoor and indoor scenes, containing both natural and urban settings with a diverse array of activities and environments. Please refer to Sec. B.1 of the supplementary material for an analysis of our dataset, highlighting its extended camera coverage and content diversity. + +From the resulting $(I, \Omega)$ pairs, we use BLIP-2 [29] to generate a descriptive text prompt $p_i$ for each image $I_i$ . While BLIP-2 may sometimes provide inaccurate descriptions, this is not an issue for our training: we do not train the text-to-image model itself, but the conditioning module instead, which needs to learn the camera view independently of the prompt. These inaccurate prompts are akin to the ControlNet technique of introducing empty strings as the prompt during training. Our final dataset is comprised of 57,380 RGB images with associated text prompts and ground-truth PF-US parameters. + +# 4. Results + +We evaluate our precise control of camera parameters against baseline methods, demonstrating that our approach can manage both artistic and realistic styles. Then, we analyze the robustness of our model, including camera conditioning and an ablation study on residuals for improved control and quality. Finally, we showcase various applications such as background generation for object rendering, video generation, and enhanced control with multiple ControlNets. For further results and details, please see the supplementary material. + +Camera control. PreciseCam enables precise control over extrinsic (roll and pitch rotations) and intrinsic (vFoV and distortion $\xi$ ) camera parameters. Fig. 5 illustrates control over extrinsic parameters. In it, roll (top row) and pitch (bottom row) are varied while the remaining parameters are held constant. The images follow the conditioning, and a high degree of consistency is maintained through camera variations. Similarly, in Fig. 6, we show intrinsic parameter control by varying the vertical field of view vFoV (left) or the distortion $\xi$ (right), while keeping all the other parameters fixed. In the PF-US maps (see Sec. 3.1), larger vFoV leads to increased latitude values, whereas $\xi$ mainly affects the up vectors. The generated images follow the PF-US maps, effectively translating camera settings into visual outcomes. There is a lack of reliable metrics in the literature for evaluating the camera parameters of generated images, which makes it challenging to assess PreciseCam's accuracy. Nevertheless, we include a quantitative evaluation of the camera view in Sec. F of the supplementary material, based on Perspective Fields [24]. Additionally, Sec. C of the supplementary material includes more examples of systematic variation of camera parameters for a variety of prompts, illustrating the disentanglement between camera parameters and prompt of PreciseCam. Our ControlNet-based architecture, combined with our diverse dataset, effectively disentangles the camera parameters from image semantics. + +Comparisons. We compare our approach to two alternative methods: prompt-engineered SDXL and Adobe Firefly, a state-of-the-art diffusion model with preset style tags. Fig. 8 illustrates this comparison. Despite prompt engineering efforts, SDXL's ability to control camera perspectives remains limited, and it often struggles to consistently interpret complex camera-related prompts. Adobe Firefly includes predefined style tags for shot specification, such as close-up, shot from above, shot from below, and wide angle, supporting basic camera control. Nevertheless, while Firefly's tags do introduce some perspective variations, the control enabled by these tags is limited, and insufficient even when combined with prompt specification. In contrast, our model is able to control camera views precisely in both realistic (top row) and artistic (bottom row) styles. + +![](images/a14581c2cdb3b49f1da75539e65a4c122f7ef3effc9671a8150a3c1fd07edd4e.jpg) +A digital art depiction of a castle floating in the ocean, with glowing bluish clouds. The castle's towers are impossibly tall and the colors soft, with reflections from the light of an ethereal sun. + +![](images/acbdec47b716c433a910cb3a524d83510e9094a722c9598c1965ffea8e93b1e5.jpg) + +![](images/f9f222ee1274f912ac94eaf61f8812d1dc05332bad499f89798bacc570215d63.jpg) + +![](images/2b9411883ce0027d0945ab6092f0cadbb5242f35362c5d5aec8872c28b9066dc.jpg) + +![](images/b7fe40c990e349c023ce4f09bd9c7afbd48736ad58c57e9d4f8a13a0121a0830.jpg) +Figure 7. Our model achieves prompt adherence on par with SDXL, as reflected in the table by comparable CLIP and BLIP scores (see text for details), while enabling camera control that SDXL cannot provide. Images show an example result from SDXL with prompt engineering (left), and from our model (right). + +![](images/a716a447f5cc9a9f03b7c350beae1c4651beac8d4cde1d824af4e70cb6d31972.jpg) +A photorealistic digital art of a futuristic cityscape at sunset. Every detail, like the reflective glass skyscrapers, is rendered with high clarity. The colors are warm and saturated, with a glowing orange sky. + +![](images/81264e045d68165de0d9d728f0d777c8764aab4f854aab4618d4680b0ef6e5b2.jpg) +Figure 5. Extrinsic Parameter Control. Images generated by varying the extrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Top row: Variation in pitch, effectively shifting the view from looking downward to upward; fixed parameters are (roll, vFoV, $\xi$ ) = (0°, 80°, 0.1). Right: Variation in roll, tilting the view from left to right; (pitch, vFoV, $\xi$ ) = (0°, 80°, 0.1). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text. + +![](images/b4796de98117765e7f83bf9a141e79051fab61930d289453c392b03863f9eb67.jpg) + +![](images/c35c004ebc4d73629ae3ed41947a5aaedc2116623205608baf529356770d4b3b.jpg) + +![](images/d16baa69ab7a3958fea0d6f88ba3b555b415ce8b47659116cf2008a2f1fc5231.jpg) + +![](images/c31975495654f8b843dcc3ea929537498eb3bafa864c35b5ebe631c8269f794f.jpg) +A photograph of a comfortable nursery with soft pastel colors, a rocking chair, a crib by the window, and shelves with neatly organized baby essentials. + +![](images/22acd96d10bd984395facc1f0392724282c51c0d4e01fb16c5b28be5b1d7f5ac.jpg) +Figure 6. Intrinsic Parameter Control. Images generated by varying the intrinsic camera parameters while keeping the rest of the conditioning fixed, showing consistent adherence to the camera specification. Left: Variation in the vertical field of view (vFoV); fixed parameters are (roll, pitch, $\xi$ ) = (0°, 0°, 0.1). Right: Variation in distortion ( $\xi$ ); (roll, pitch, vFoV) = (0°, 0°, 120°). Insets show the corresponding PF-US maps, and text prompts are shown in italicized text. + +![](images/65474c0e768bb223293678758e12d4463935ecc6570d395904ef93c04ca20cae.jpg) + +![](images/a196c40866c8a2248031583dbf5f9db1ec9359992f965ca4aeb9d0caae9ae41c.jpg) +A narrow alleyway in an old European village, depicted in a vintage lithograph style, with intricate line work and a muted color palette. + +![](images/aad747a8d44a9a9323be0a38b1578f2b270343bf8df255f739ce6d2058fae594.jpg) + +![](images/422881caabb0cf22c190f8bf73126f771241042957b7b2c7703ccac3f17a1dcf.jpg) + +
CLIP ScoreBLIP Score
SDXL + Prompt Engineering0.557 (0.039)0.299 (0.025)
(Ours) PreciseCam0.543 (0.039)0.292 (0.026)
Prompt + +Open with +a angle, +of -70.Prompt + +Roll = 0° +Pitch = -70° +vFoV = 70 +ξ = 0.1.
+ +Prompt: Two enormous steampunk-style airships engaged in combat over a foggy cityscape. Gears, steam, and mechanical components are exposed on the airships, while cannons fire plumes of smoke and sparks. Below, the city is filled with smokesstacks and towering clock towers. + +Additionally, we conducted a user study with 34 participants to compare the camera view precision of the models, revealing that our model significantly outperformed SDXL and Adobe Firefly in aligning with the desired camera view (see Sec. E of the supplementary material). We also evaluate whether our model maintains, despite the inclusion of camera control, the text prompt adherence exhibited by SDXL. To do this, we compare our results to those of the baseline SDXL by computing, for each method, CLIP and BLIP scores [22], which are commonly used to evaluate prompt relevance in generated images. The comparison is done over 2,940 images generated with each method (ours and baseline SDXL). For the baseline SDXL, we use prompt engineering, specifying the desired view to encourage distinct camera perspectives (see Sec. D of the supplementary material). Our approach achieves comparable scores to SDXL (Fig. 7 shows mean and standard deviation), suggesting that our model is able to maintain prompt alignment while providing precise camera view control. + +![](images/844169732971a6f667bfc5b7e07899f060d12d3dcf036bc46ed22323ae401c4b.jpg) +SDXL +A photograph of a street cafe scene at twilight with people enjoying drinks, a shot from below. + +![](images/7d8cf3a8bbc2087bf02095bdd0d1a0d5b4557b6daa256ec392383db48d6716dc.jpg) +Firefly Image 3 +A photograph of a street cafe scene at twilight with people enjoying drinks. ++ tag: shot from below + +![](images/9f80f4d17d4c61695c9359bdb42ada0ecd2020d0744cd15bca52ef2b2e6a02c7.jpg) +Ours +A photograph of a street cafe scene at twilight with people enjoying drinks. ++ roll=0°, pitch=40°. + +![](images/550a011d2fabd42cd77014949469285e6db493dd0c4addca1f15936a216d716c.jpg) +A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, a shot from below. + +![](images/664c6987f844a57b739780921faf116c7e24d06f7533c87373397aafa42250b3.jpg) +A street cafe scene at twilight withpeople enjoying drinks , depicted ina lively watercolor and ink stylewith loose lines and warm , glowingcolors + tag : shot from below + +![](images/2a11c39171838cea261d98f34b79fb197edc4efc880c47e2bbd03c51849ed6c7.jpg) +vFoV=70°, $\xi = 0.1$ +A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors. ++ roll = 0°, pitch = 40°, vFOV = 70°, $\xi = 0.1$ + +![](images/9aea71119c654db33524b72619e13d15ca6942600f8b92f3f4ca82416e1d3468.jpg) +SDXL +A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene. + +![](images/7230325751787558521aa87dcc467c99979307c0e4e24b5ccbd827efe9bfa89f.jpg) +Firefly Image 3 +A street cafe scene at twilight with people enjoying drinks, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene + +![](images/eba7b50e407f47e32b224011a559d49e1f531eaab9bc51811fbfcf1b56c6e12d.jpg) +Ours +A photograph of a street cafe scene at twilight with people enjoying drinks. ++ roll $= -30^{\circ}$ pitch $= 40^{\circ}$ $\mathrm{VFOV} = 0^{\circ}$ $\xi = 0.1$ + +![](images/f70326fae5ec5f4c460aaee82ce6737400e3ae47d2e2a6488adf2f45d3b5d228.jpg) +A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a ground-level camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene. + +![](images/37daadcfdd4004ea9e1eea36d871c55a516f72d0d5373012f9709ec66067d03d.jpg) ++ tag: shot from below +A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors, captured from a groundlevel camera angle with the camera tilted to the left for a dynamic perspective, a rotated scene + tag: shot from below + +![](images/44e24d3f700c925beab25dbde17c6e7e09f7ee01b843f97794c8a7698d587de6.jpg) +A street cafe scene at twilight with people enjoying drinks, depicted in a lively watercolor and ink style with loose lines and warm, glowing colors. + roll $= -30^{\circ}$ pitch $= 40^{\circ}$ vFoV $= 70^{\circ}$ $\xi = 0.1$ + +# 4.1. Model analysis + +Camera conditioning adherence. To assess the stability of our model's camera conditioning, we generate images using the same PF-US maps and prompts but vary the input noise. Results show consistent camera conditioning (please refer to Sec. G of the supplementary material for examples). + +Ablation: Influence of the residuals' contributions. In our framework, the ControlNet-based module generates residual outputs that can be injected into the main model in various layers. We observe that residuals from the middle block (bottleneck) effectively achieve adherence to the camera conditioning, while preserving the image quality achieved by the base model (SDXL). The injection of residuals at additional levels can introduce distortions and hinder semantic integrity preservation, as shown in Fig. 9. This aligns with the findings of previous works that use ControlNet for conditioning diffusion models [6]. Therefore, in our model, we use only the mid-level residuals during inference; these are key for adhering to camera conditions without disrupting the generative capabilities of the base model (SDXL), providing a good trade-off between effective camera control and high-quality image generation. + +![](images/8de14a3043388b405b75940bcb01f4ab9a54f086aae789cb6624e0f286b1c720.jpg) +Figure 8. Comparison of our model with SDXL and Adobe Firefly (Firefly tags are in dark blue background; prompt engineering, when present, in bold and dark blue text). Four examples are shown: the top half depicts realistic styles, while the bottom half depicts artistic styles; the left half examples intend a shot from below, and the right half a tilted view from below. SDXL struggles in all cases. Firefly successfully produces the shot from below in the realistic style due to its matching tag, but fails in the artistic version of it; for more complex perspectives, like the tilted view from below, Firefly lacks a tag for this view, and fails to produce a valid result despite the efforts with the prompt. Our approach achieves reliable camera control across both styles and perspectives. + +![](images/425c8d85f1a2fc64543f00aa2340fe6241d95a0a2f680c3650518d3ea29dc68d.jpg) + +![](images/75be72c9cdc211c4bce4fa525e0749b49df6f921c7d92ffd5252ce511dba8350.jpg) + +![](images/7d39b480f44a0389418c18cf669a5ae77b97751ebe5a8c21a50bf64a54fec0c7.jpg) +Residuals: Middle + C +A majestic white stag standing in a misty forest. Its antlers are massive and covered in moss and glowing crystals. Its fur is smooth and white, almost glowing under the pale morning light. +Figure 9. Image generation conditioned by the text prompt (bottom) and fixed camera parameters, for different injections of residual outputs of the ControlNet-based module into the main SDXL model. Middle block residuals injected at the bottleneck (ours) enable precise camera control with minimal impact on image quality, while deeper residuals introduce distortions, reducing overall image quality. + +![](images/cc46c89f4dfb92447a1a5da0d7e1e559a30819a0385e60ba7942155685c346be.jpg) +Residuals: Middle + C + B + +![](images/10897ccdd39afa460c0c1bef784bb5c9bb63a373d3bcebc6cc8c876e0911e198.jpg) +Residuals: Middle + C + B + A + +![](images/c4239aa35b14b23b4591725c5975c0151258dba0a08e25912555a609632303a5.jpg) +Figure 10. Background generation without and with camera control. Our method can generate a background that aligns with the object's perspective (shown on the left), ensuring seamless integration. The baseline approach (SDXL, center) lacks perspective consistency, while the background generated with our method aligns well with the object (right). + +![](images/fa7ee707259458809b68d32c9e6a0b38dc69184baf2864d3035842623c0feb61.jpg) +Figure 11. Video generation results showing two examples of frame-by-frame camera control. Camera parameters are specified to achieve a zoom-in effect (top) and an anti-clockwise rotation (bottom). Frames progress from left to right over time. + +# 4.2. Applications + +Background generation for object rendering. Precise-Cam can be used to generate backgrounds that match the perspective of a given object. By aligning the background's perspective with the object's viewpoint, our model can be used to create visually coherent scenes where the object appears naturally embedded, as shown in Fig. 10. + +Video generation. Our model can be used to condition the camera view on each frame of a video to specify the desired perspectives throughout the sequence, as illustrated in Fig. 11. Each frame is guided by our four camera parameters through a custom-trained adapter [30] for Stable Video Diffusion [7], ensuring consistent perspective control across frames. Alternatively, our method can be used to condition the initial frame of a video sequence, after which existing methods for relative camera view control can guide the trajectory for the remaining frames [20, 45, 46, 48, 49]. While these existing methods establish movement relative to the first frame, they lack control over the initial camera position that sets the starting perspective for the entire video. Our approach addresses this gap by enabling precise control over the initial camera position to anchor the video sequence. + +![](images/bdf8b9ae5f4cb869bbb41cc9c180650e0cc69a6cc508a464c522e896a9209389.jpg) +Figure 12. Limitations. Left: The model may occasionally incorrectly position objects or people in a vertical, standing orientation (like the man on the boat), as it is more frequent. Right: In the presence of conflicts between the prompt and the desired camera view, the model may produce semantically incoherent outputs. + +Extended control with multiple ControlNets. Additionally, our approach is compatible with other ControlNets, allowing additional conditioning on the final output to achieve complex effects. For instance, combining our model with depth, Canny edges, and pose control can allow for simultaneous control over camera view, subject positioning, and scene structure [54]. Please refer to Sec. H of the supplementary material for further details and examples. + +# 5. Conclusion + +We present PreciseCam, a framework for precise camera control in text-to-image diffusion-based generation, along with a novel dataset. Our experiments show precise and consistent camera control, far exceeding existing methods such as prompt engineering, even with artistic images not found in our dataset (e.g., Fig. 8). Additionally, we provide proof-of-concept applications for enhancing creative expression, background generation for object compositing, and video generation. + +Despite our dataset covering a wide range of camera parameters and content, PreciseCam may struggle with extreme roll due to the backbone's tendency to align objects vertically (Fig. 12, left). While our model retains SDXL's ability to generate images that match prompts, conflicts between the prompt and camera view (Fig. 12, right) can cause incoherent outputs. We hope our work helps develop new tools to unlock artistic generative imaging. + +# Acknowledgements + +We thank Dario Lanza and Nestor Monzon and the Graphics and Imaging Lab members. This research was funded by grant PID2022-141539NB-I00, funded by MI-CIU/AEI/10.13039/501100011033, and by ERDF, EU. It has also been partially funded by the Government of Aragon's Departamento de Empleo, Ciencia y Universidades (project ref Proy-T25-24). Additionally, Edurne Bernal-Berdun was supported by a Governor de Aragon predoctoral grant program (2021-2025). + +# References + +[1] 360cities. 360cities dataset. https://www.360cities.net/. 5, 1 +[2] Adobe. Firefly. https://www.adobe.com/products/firefly.html. 1 +[3] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Ji-aming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, et al. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint arXiv:2211.01324, 2022. 3 +[4] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. Multidiffusion: Fusing diffusion paths for controlled image generation. 2023. 3 +[5] Joao P Barreto. 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Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Images are versatile mediums where content and camera language are crucial. 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This limitation can hinder graphic designers, artists, and photographers from effectively conveying emotions, sensations, or messages. To unlock the capabilities of generative models, it is essential to have precise control over camera parameters." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 592, + 556, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 592, + 556, + 674 + ], + "spans": [ + { + "bbox": [ + 312, + 592, + 556, + 674 + ], + "type": "text", + "content": "Camera views are defined by intrinsic and extrinsic parameters such as field of view (FoV), pitch, roll, etc. However, most text-to-image models are not designed for precise camera view control, making prompt engineering the primary method to achieve desired visual results. This time-consuming approach requires significant expertise and offers limited control." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "Recently, diffusion models like Firefly [2] have allowed users to control camera views with general instructions such as wide angle or closeup. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2724" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 555, + 196 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 555, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 555, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 555, + 196 + ], + "type": "image", + "image_path": "72a720cf0230c8b8c537e27d2370453dd55de0ebd6429db62f00712c4644535e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 204, + 555, + 260 + ], + "lines": [ + { + "bbox": [ + 54, + 204, + 555, + 260 + ], + "spans": [ + { + "bbox": [ + 54, + 204, + 555, + 260 + ], + "type": "text", + "content": "Figure 2. Red boxes: Current approaches rely on trial-and-error prompt engineering or generalistic tags, offering limited camera control in text-to-image generative AI. Others use 3D representations of the scenes, from which depth or edge maps are obtained, but this imposes strict constraints on the resulting image, limiting flexibility. Green box: Our method relies on two extrinsic and two intrinsic camera parameters, user-provided; we then obtain the effects that such camera parameters impose on the appearance of each pixel in the final image, encoded in a 2D PF-US map (see text for details). This allows for precise, fine-tuned camera control, thus enhancing creativity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 280, + 294, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 280, + 294, + 388 + ], + "spans": [ + { + "bbox": [ + 54, + 280, + 294, + 388 + ], + "type": "text", + "content": "precise, limiting artistic options. While precise camera control has been explored through 3D information from multiview images, such images are often unavailable, and creating comprehensive 3D representations for all possible camera configurations is not feasible. This results in challenges when generating multiple objects, cluttered scenes, or coherent backgrounds. An alternative is training ControlNet on depth or edge maps, which imposes strict constraints limiting flexibility (see Fig. 2)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 389, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 295, + 544 + ], + "type": "text", + "content": "In this work, we aim to provide a general solution to the problem of precise camera view control, which expands artistic freedom in generative AI. We do not focus solely on well-known photographic shots; instead, we offer simple, direct control of both intrinsic and extrinsic camera parameters, which allows us to achieve a broad spectrum of possible camera views while maintaining precise control (see Fig. 2 (green box)). Instead of representing a 3D scene, which has the limitations we discussed above, we identify the essential effects that such camera parameters impose on the appearance of each pixel in the final image, thus overcoming the requirement to rely on multi-view images and using only simple, single-view images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": "To achieve our goal, we rely on two extrinsic parameters, roll and pitch rotations, and two intrinsic parameters, vertical FoV (vFoV) and geometrical distortion of the camera " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "(\\xi)" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": ". Combined with a user-provided prompt, these parameters serve as inputs to our model to generate images with the intended camera view. We adopt the Unified Spherical (US) camera model [5], which allows us to translate these camera parameters into a Perspective Field (PF) representation [24], which is easy to store and interpret. The PF-US encodes the camera parameters as per-pixel information, describing the pixels' up-vector (opposed to the gravity direction) and distance to the horizon, allowing us to encode per-pixel appearance from roll, pitch, vFoV, and " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": " parameters. We then adopt ControlNet [54] to guide our image" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 280, + 553, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 553, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 553, + 316 + ], + "type": "text", + "content": "generation according to the resulting PF-US. Our model, PreciseCam, archives precise camera view control, while the content remains fully determined by the text prompt." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 317, + 554, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 317, + 554, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 317, + 554, + 389 + ], + "type": "text", + "content": "In addition, we have created a novel dataset of 57,380 single-view RGB images, along with their ground-truth camera parameters and prompt descriptions. Our dataset spans a comprehensive range of camera parameters and a diversity of scenes, making it specifically suitable for the camera control problem we address." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 390, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 554, + 510 + ], + "type": "text", + "content": "Last, while our approach is primarily designed for image generation, it opens up new possibilities for video generation, as absolute camera control conditioning is currently being overlooked. Our method can create a precise initial camera position, from which relative camera control can subsequently be applied. Alternatively, we showcase how our model tailored for images can be leveraged to apply limited absolute camera control on videos. Our code and model are publicly available at https://graphics.unizar.es/projects/PreciseCam2024." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 525, + 400, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 525, + 400, + 537 + ], + "spans": [ + { + "bbox": [ + 314, + 525, + 400, + 537 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "Conditional image generation. Seminal work in conditional image generation leveraged local image statistics [13, 14, 21] and retrieved information from large image datasets [10, 15, 19, 25]. Later deep learning techniques allowed faster, more flexible, and more customized image synthesis within specific domains [9, 23, 35, 43, 44, 52, 53]. Those models were limited in their ability to generate high-quality images and to support open-ended generation tasks. With the advent of large-scale image and text datasets, autoregressive [50] and especially diffusion models [37-39] were proposed as an effective solution to create high-quality images from a virtually unbounded set of text descriptions. Despite these advancements, text remains a limited modality for controlling image generation. Recent methods in" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2725" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "produced modifications to the diffusion process, enhancing controllability by allowing users to incorporate additional guidance through color [31], hand-crafted terms [16, 34], and spatially localized prompts [3, 4, 12, 51]. While these methods offer improved control in the generative process, they lack support for more granular guidance, such as structural cues like edges or depth maps." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 172, + 296, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 172, + 296, + 471 + ], + "spans": [ + { + "bbox": [ + 56, + 172, + 296, + 471 + ], + "type": "text", + "content": "Camera control on diffusion generation. While some works have addressed camera control for image generation, this area remains underexplored. Kumari et al. [27] proposed a method that introduces camera control without relying on prompt engineering. They refine a text-to-image diffusion model by conditioning it on a 3D object representation, enabling the generation of various camera viewpoints in new backgrounds. Their NeRF-based method needs multi-view images of a specific object to generate novel views, but it struggles with extreme angles or prompts with other objects. Cheng et al. [11] introduced Continuous 3D Words, which allows control over attributes like object position and lighting by mapping them to the token embedding domain. However, it struggles with complex prompts and tends to replicate poses from the training set. Their camera control is limited to the \"dolly zoom\", which adjusts field of view and distance simultaneously, lacking independent control. On the other hand, Voynov et al. [42] incorporated lens geometry into the generative pipeline to control camera distortion for effects like fish-eye images but did not address extrinsic parameters such as roll or pitch. In contrast, our general approach generates images of any object, scene, or landscape while preserving the model's ability to handle complex prompts and produce various artistic styles and multi-object scenes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 486, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 714 + ], + "type": "text", + "content": "Closely related to our work are methods that train networks to guide the generative process using inputs like depth, edges, normals, and segmentation maps [32, 54]. However, these methods still overlook a critical aspect of image creation: controlling the camera used to obtain that image. It is common for practitioners to reason about image editing operations using camera abstractions – what the image would look like if one changes the camera pitch, roll, field of view, etc. To address this gap, we propose a novel approach that incorporates fine-grained camera controls into diffusion adapters like ControlNet [54], expanding the versatility and usability of image generation to scenarios where precise camera control is paramount. Last, recent works focus on relative camera view control for video generation [20, 45, 46, 48, 49]. These methods adjust camera movement relative to the first frame but lack control over initial camera position. Our method provides control over this starting camera orientation, enabling horizon positioning and gravity alignment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 314, + 71, + 405, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 405, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 405, + 85 + ], + "type": "text", + "content": "3. Our Approach" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "content": "Our proposed framework for precise camera view control in text-to-image generation takes as input a text prompt " + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "content": " and a camera view specified by a set " + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "content": " of four parameters, and generates images " + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "content": " according to both. The four camera parameters (roll, pitch, vFoV, and distortion " + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 91, + 553, + 198 + ], + "type": "text", + "content": ") are provided by the user through simple sliders; they are both intuitive and expressive enough to allow for precise camera control. These parameters, together with the camera view representation used by our model, are presented in Sec. 3.1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 199, + 553, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 199, + 553, + 259 + ], + "spans": [ + { + "bbox": [ + 313, + 199, + 553, + 259 + ], + "type": "text", + "content": "Text-conditioned image generation is performed by means of a diffusion model " + }, + { + "bbox": [ + 313, + 199, + 553, + 259 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 199, + 553, + 259 + ], + "type": "text", + "content": ", while we achieve camera view conditioning via a ControlNet-based module, as described in Sec. 3.2. The model is trained with a new dataset featuring ground-truth camera view specification (Sec. 3.3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 266, + 511, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 511, + 279 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 511, + 279 + ], + "type": "text", + "content": "3.1. Precise Camera View Representation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": "To enable a precise camera view specification, we adopt the Perspective Field (PF) representation [24], which was originally designed for single-image camera calibration. For any arbitrary projection function " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\mathbf{X}) = \\mathbf{x}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " mapping a 3D point " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " to an image pixel " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": ", PF assigns each pixel " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " an up-vector " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " and a latitude angle " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\varphi_{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": ". Since each pixel " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " originates from a light ray " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " emitted from " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": ", the up-vector " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " represents the projection of the up direction of " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " (which is opposite to the gravity vector " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": "), while the latitude " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\varphi_{x}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " measures the angle between the light ray " + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 313, + 284, + 555, + 406 + ], + "type": "text", + "content": " and the horizontal world plane. In particular:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 358, + 412, + 553, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 412, + 553, + 436 + ], + "spans": [ + { + "bbox": [ + 358, + 412, + 553, + 436 + ], + "type": "interline_equation", + "content": "\\mathbf {u} _ {\\mathbf {x}} = \\lim _ {c \\rightarrow 0} \\frac {\\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X})}{\\| \\mathcal {P} (\\mathbf {X} - c \\mathbf {g}) - \\mathcal {P} (\\mathbf {X}) \\| _ {2}}, \\text {a n d} \\tag {1}", + "image_path": "c4b528575f51136a6abe15a16a0d2386793af2b6e5cee1813b208643561a4d48.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 388, + 438, + 553, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 438, + 553, + 462 + ], + "spans": [ + { + "bbox": [ + 388, + 438, + 553, + 462 + ], + "type": "interline_equation", + "content": "\\varphi_ {\\mathbf {x}} = \\arcsin \\left(\\frac {\\mathbf {R} \\cdot \\mathbf {g}}{\\| \\mathbf {R} \\| _ {2}}\\right). \\tag {2}", + "image_path": "00ffc21a8c06f6180fde8a4efa1fe8c8f32ffc74f7a09952717acbad212ada7d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "text", + "content": "We aim to enhance creativity and expressivity beyond the commonly used pinhole model in generative AI, including precisely-controlled wide-angle or fisheye cameras. To achieve this, we take advantage of the flexibility of PF to support different camera models through their respective " + }, + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(X)" + }, + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "text", + "content": " functions, and employ the Unified Spherical (US) camera model [5, 8], which allows camera models beyond the pinhole camera to be encoded within the PF. The projection function " + }, + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(X)" + }, + { + "bbox": [ + 313, + 464, + 554, + 564 + ], + "type": "text", + "content": " of the US model is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 370, + 568, + 449, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 568, + 449, + 582 + ], + "spans": [ + { + "bbox": [ + 370, + 568, + 449, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {P} (\\mathbf {X}) = \\mathbf {x} = (u, v),", + "image_path": "fa99fc472ff10a28832d2aac5d363118588ac4b1c64c3efe96e1754cd22f116e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 388, + 584, + 553, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 584, + 553, + 608 + ], + "spans": [ + { + "bbox": [ + 388, + 584, + 553, + 608 + ], + "type": "interline_equation", + "content": "u = \\frac {x f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + u _ {0}, \\tag {3}", + "image_path": "ce8ffcd5bedc2bba908ca57cdb22188d1e86f585afe5a80add8ef9e21e5ba7de.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 388, + 610, + 497, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 610, + 497, + 635 + ], + "spans": [ + { + "bbox": [ + 388, + 610, + 497, + 635 + ], + "type": "interline_equation", + "content": "v = \\frac {y f}{\\xi \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}} + z} + v _ {0}.", + "image_path": "97a0016d460c1c6cba8bba356f036a9fa94865f61e01955afcb104aaec40137e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": " are the 3D point world coordinates, " + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "inline_equation", + "content": "(u_0,v_0)" + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": " are the principal point coordinates in the image, " + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": " is the focal length, and " + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": " is a distortion parameter ranging between 0 and 1, with " + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\xi = 0" + }, + { + "bbox": [ + 313, + 642, + 553, + 689 + ], + "type": "text", + "content": " being a pinhole camera." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "We choose to represent our camera view with two intrinsic parameters: vertical FoV (which is in turn defined" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2726" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 79, + 242, + 173 + ], + "blocks": [ + { + "bbox": [ + 57, + 79, + 242, + 173 + ], + "lines": [ + { + "bbox": [ + 57, + 79, + 242, + 173 + ], + "spans": [ + { + "bbox": [ + 57, + 79, + 242, + 173 + ], + "type": "image", + "image_path": "854d0d28e50ed05b55e939e30010bacb471d4e5d86269854b21658ab53bac3b1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "lines": [ + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "spans": [ + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "text", + "content": "Figure 3. Left and center: PF-US camera view representation. PF-US camera parameters (roll, pitch, vertical FoV, and distortion " + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "text", + "content": ") and associated maps corresponding to two example images. PF-US maps encode, for each pixel, a latitude value " + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "inline_equation", + "content": "\\varphi_{\\mathbf{x}}" + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "text", + "content": " (blue-red color map with contour lines) and a unit up-vector " + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{\\mathbf{x}}" + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "text", + "content": " (green arrows). Right: Dataset generation. We generate training data in the form of images with ground-truth PF-US maps by leveraging " + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 54, + 182, + 555, + 237 + ], + "type": "text", + "content": " images. We sample our camera parameters and obtain the corresponding cropped region for each sampled quartet (as examples, the highlighted regions in red and yellow yield the two examples shown on the left)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 243, + 79, + 427, + 173 + ], + "blocks": [ + { + "bbox": [ + 243, + 79, + 427, + 173 + ], + "lines": [ + { + "bbox": [ + 243, + 79, + 427, + 173 + ], + "spans": [ + { + "bbox": [ + 243, + 79, + 427, + 173 + ], + "type": "image", + "image_path": "f2fa8caaa41bc79b45a8bf9892c5e49e91cc80729e1658330b749b98af1a6454.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 433, + 79, + 553, + 175 + ], + "blocks": [ + { + "bbox": [ + 433, + 79, + 553, + 175 + ], + "lines": [ + { + "bbox": [ + 433, + 79, + 553, + 175 + ], + "spans": [ + { + "bbox": [ + 433, + 79, + 553, + 175 + ], + "type": "image", + "image_path": "e11d32d6f95dc658e6dbf7264763b53aaed6f2b5a5280d6c2180f413b2a82c39.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "text", + "content": "by the focal length " + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "text", + "content": " and distortion " + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "text", + "content": ", as well as two extrinsic parameters: roll and pitch rotations with respect to the horizon. These four parameters conform the set " + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "inline_equation", + "content": "\\Omega = (\\mathrm{roll},\\mathrm{pitch},\\mathrm{vFoV},\\xi)" + }, + { + "bbox": [ + 54, + 258, + 294, + 376 + ], + "type": "text", + "content": ", which is expressive enough to represent a wide range of camera configurations, while being intuitive to users. The four parameters are then transformed, by means of the PF-US representation (Eqs. 1-3), into per-pixel up-vectors and latitude values, yielding the corresponding PF-US maps (see Fig. 3, left and center, for two different illustrative examples)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 378, + 295, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 378, + 295, + 485 + ], + "spans": [ + { + "bbox": [ + 54, + 378, + 295, + 485 + ], + "type": "text", + "content": "The resulting PF-US maps provide local information about how camera parameters affect the appearance of each pixel, allowing the model to learn this relationship without the need for heavy 3D representations. Finally, note that yaw rotation is excluded; given a 2D image, we can define up or down directions based on the horizon, but there is no such reference to define left or right directions. By leaving yaw information out, we allow the model to focus on the relevant camera parameters that affect image formation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 491, + 228, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 228, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 228, + 504 + ], + "type": "text", + "content": "3.2. Learning Camera View Control" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "text", + "content": "We aim to introduce precise camera view control in text-to-image diffusion models, while preserving their generalization capabilities. This requires a method that minimally disrupts their generation pipeline, already trained on large, quality datasets, adding only the essential information needed to achieve the desired camera view. To do this, we adopt the ControlNet approach to condition image generation [54]: it provides a framework for guiding diffusion models to adhere to a specific condition, and has delivered impressive results conditioning generation with poses, depth, edges, or normal maps, among others." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 642, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 642, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 642, + 296, + 713 + ], + "type": "text", + "content": "During the generation process, ControlNet ensures that the generated images align with both the prompt and the conditioning input, in our case the PF-US map. We use Stable Diffusion XL (SDXL) [36] as our base text-to-image model, although our approach is compatible with any other UNet-based diffusion model. Our ControlNet setup in" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 314, + 255, + 556, + 484 + ], + "blocks": [ + { + "bbox": [ + 314, + 255, + 556, + 484 + ], + "lines": [ + { + "bbox": [ + 314, + 255, + 556, + 484 + ], + "spans": [ + { + "bbox": [ + 314, + 255, + 556, + 484 + ], + "type": "image", + "image_path": "b5532014a382bbab00a76c78c1bb1accb846f51561067acfbf26c418a5e7d2ec.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 491, + 555, + 568 + ], + "lines": [ + { + "bbox": [ + 313, + 491, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 555, + 568 + ], + "type": "text", + "content": "Figure 4. Training of our proposed approach for precise camera control. Text-to-image generation with a UNet-based diffusion model (SDXL in our implementation) is conditioned with a PF-US map representing the desired camera parameters; conditioning is learned by means of a ControlNet-based module. During inference, only the middle block output of this module is injected into SDXL (shown in red, see text for more details)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 590, + 555, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 650 + ], + "type": "text", + "content": "volves duplicating the encoder and middle block layers of the original SDXL model. While SDXL remains frozen during training to preserve its generalization abilities, ControlNet is initialized with the same weights and trained (see Sec. A of the supplementary material for training details)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "Fig. 4 illustrates this. To incorporate ControlNet's output into SDXL, its residuals are passed through a zero-convolution layer (1×1 convolution layer with all-zero initial weights) before being added to the residuals of the original SDXL model. During training, ControlNet outputs are" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 91, + 69, + 209, + 78 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 69, + 209, + 78 + ], + "spans": [ + { + "bbox": [ + 91, + 69, + 209, + 78 + ], + "type": "text", + "content": "Roll=0°, Pitch=30°, vFoV=35°, " + }, + { + "bbox": [ + 91, + 69, + 209, + 78 + ], + "type": "inline_equation", + "content": "\\xi = 0.1" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 271, + 70, + 400, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 271, + 70, + 400, + 79 + ], + "spans": [ + { + "bbox": [ + 271, + 70, + 400, + 79 + ], + "type": "text", + "content": "Roll=30°, Pitch=-60°, vFov=100°, " + }, + { + "bbox": [ + 271, + 70, + 400, + 79 + ], + "type": "inline_equation", + "content": "\\xi = 0.9" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2727" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "added to the UNet bottleneck and to the decoder skip connections, as in the original implementation. At inference time, however, we find that injecting the ControlNet output only in the bottleneck (marked in red in Fig. 4) improves generation consistency without being detrimental to condition adherence [6]. Our ablation study (Sec. 4) shows how various ControlNet outputs affect the generation process." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 166, + 168, + 177 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 166, + 168, + 177 + ], + "spans": [ + { + "bbox": [ + 55, + 166, + 168, + 177 + ], + "type": "text", + "content": "3.3. Dataset Generation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 185, + 295, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 185, + 295, + 220 + ], + "spans": [ + { + "bbox": [ + 55, + 185, + 295, + 220 + ], + "type": "text", + "content": "To train our framework, we need a diverse dataset of RGB images with corresponding text prompts and PF-US camera parameters, represented as triplets " + }, + { + "bbox": [ + 55, + 185, + 295, + 220 + ], + "type": "inline_equation", + "content": "(I_i, p_i, \\Omega_i)" + }, + { + "bbox": [ + 55, + 185, + 295, + 220 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 221, + 295, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 295, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 295, + 353 + ], + "type": "text", + "content": "Jin et al. [24] provide data featuring RGB images and ground-truth PF representations. However, they primarily depict urban outdoor scenes and, more importantly, do not cover the full range of camera parameters; for example, they include only minimal distortions (low " + }, + { + "bbox": [ + 55, + 221, + 295, + 353 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 55, + 221, + 295, + 353 + ], + "type": "text", + "content": " values) and avoid large vertical FoVs. A possible alternative would be to use their PF estimation model and apply it to an existing dataset. However, the resulting estimations lack sufficient accuracy for our training purposes, hindering our model's ability to learn view control across the full spectrum of camera parameters (refer to Sec. B of the supplementary material)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": "We thus generate our own dataset with ground truth PF-US representations by leveraging " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": " images. We sample our set of camera parameters (see Sec. B of the supplementary material) and obtain, for each sampled quartet, the corresponding areas cropped from the " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": " images, and their PF-US maps (as described in Sec. 3.1). Fig. 3 (right) shows two of the resulting regions, with boundaries highlighted in orange and yellow, respectively. Sampling ranges for each camera parameter are: roll " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\in (-90^{\\circ}, 90^{\\circ})" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": ", pitch " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\in (-90^{\\circ}, 90^{\\circ})" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": ", vFoV " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\in [15^{\\circ}, 140^{\\circ}]" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\xi \\in (0, 1)" + }, + { + "bbox": [ + 55, + 354, + 295, + 472 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 474, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 581 + ], + "type": "text", + "content": "To maximize diversity in the images, we use six different " + }, + { + "bbox": [ + 55, + 474, + 295, + 581 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 474, + 295, + 581 + ], + "type": "text", + "content": " image datasets: 360-SOD [28], CVRG-Pano [33], F-360iSOD [55], Poly Haven HDRIs [18], Sitzmann et al. [40], and 360cities [1]. These feature a mix of outdoor and indoor scenes, containing both natural and urban settings with a diverse array of activities and environments. Please refer to Sec. B.1 of the supplementary material for an analysis of our dataset, highlighting its extended camera coverage and content diversity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": "From the resulting " + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "(I, \\Omega)" + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": " pairs, we use BLIP-2 [29] to generate a descriptive text prompt " + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": " for each image " + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": ". While BLIP-2 may sometimes provide inaccurate descriptions, this is not an issue for our training: we do not train the text-to-image model itself, but the conditioning module instead, which needs to learn the camera view independently of the prompt. These inaccurate prompts are akin to the ControlNet technique of introducing empty strings as the prompt during training. Our final dataset is comprised of 57,380 RGB images with associated text prompts and ground-truth PF-US parameters." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 72, + 367, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 367, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 367, + 83 + ], + "type": "text", + "content": "4. Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 91, + 553, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 211 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 211 + ], + "type": "text", + "content": "We evaluate our precise control of camera parameters against baseline methods, demonstrating that our approach can manage both artistic and realistic styles. Then, we analyze the robustness of our model, including camera conditioning and an ablation study on residuals for improved control and quality. Finally, we showcase various applications such as background generation for object rendering, video generation, and enhanced control with multiple ControlNets. For further results and details, please see the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "text", + "content": "Camera control. PreciseCam enables precise control over extrinsic (roll and pitch rotations) and intrinsic (vFoV and distortion " + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "text", + "content": ") camera parameters. Fig. 5 illustrates control over extrinsic parameters. In it, roll (top row) and pitch (bottom row) are varied while the remaining parameters are held constant. The images follow the conditioning, and a high degree of consistency is maintained through camera variations. Similarly, in Fig. 6, we show intrinsic parameter control by varying the vertical field of view vFoV (left) or the distortion " + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "text", + "content": " (right), while keeping all the other parameters fixed. In the PF-US maps (see Sec. 3.1), larger vFoV leads to increased latitude values, whereas " + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 217, + 555, + 529 + ], + "type": "text", + "content": " mainly affects the up vectors. The generated images follow the PF-US maps, effectively translating camera settings into visual outcomes. There is a lack of reliable metrics in the literature for evaluating the camera parameters of generated images, which makes it challenging to assess PreciseCam's accuracy. Nevertheless, we include a quantitative evaluation of the camera view in Sec. F of the supplementary material, based on Perspective Fields [24]. Additionally, Sec. C of the supplementary material includes more examples of systematic variation of camera parameters for a variety of prompts, illustrating the disentanglement between camera parameters and prompt of PreciseCam. Our ControlNet-based architecture, combined with our diverse dataset, effectively disentangles the camera parameters from image semantics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "Comparisons. We compare our approach to two alternative methods: prompt-engineered SDXL and Adobe Firefly, a state-of-the-art diffusion model with preset style tags. Fig. 8 illustrates this comparison. Despite prompt engineering efforts, SDXL's ability to control camera perspectives remains limited, and it often struggles to consistently interpret complex camera-related prompts. Adobe Firefly includes predefined style tags for shot specification, such as close-up, shot from above, shot from below, and wide angle, supporting basic camera control. Nevertheless, while Firefly's tags do introduce some perspective variations, the control enabled by these tags is limited, and insufficient even when combined with prompt specification. 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CLIP ScoreBLIP Score
SDXL + Prompt Engineering0.557 (0.039)0.299 (0.025)
(Ours) PreciseCam0.543 (0.039)0.292 (0.026)
Prompt +\nOpen with\na angle,\nof -70.Prompt +\nRoll = 0°\nPitch = -70°\nvFoV = 70\nξ = 0.1.
", + "image_path": "28f53c8a72ae84ab501cce8f6f00739d9a3a6ba7687da3acc39fc2b1679736e5.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 586, + 289, + 613 + ], + "lines": [ + { + "bbox": [ + 55, + 586, + 289, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 289, + 613 + ], + "type": "text", + "content": "Prompt: Two enormous steampunk-style airships engaged in combat over a foggy cityscape. Gears, steam, and mechanical components are exposed on the airships, while cannons fire plumes of smoke and sparks. Below, the city is filled with smokesstacks and towering clock towers." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 485, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 555, + 712 + ], + "type": "text", + "content": "Additionally, we conducted a user study with 34 participants to compare the camera view precision of the models, revealing that our model significantly outperformed SDXL and Adobe Firefly in aligning with the desired camera view (see Sec. E of the supplementary material). We also evaluate whether our model maintains, despite the inclusion of camera control, the text prompt adherence exhibited by SDXL. To do this, we compare our results to those of the baseline SDXL by computing, for each method, CLIP and BLIP scores [22], which are commonly used to evaluate prompt relevance in generated images. The comparison is done over 2,940 images generated with each method (ours and baseline SDXL). For the baseline SDXL, we use prompt engineering, specifying the desired view to encourage distinct camera perspectives (see Sec. D of the supplementary material). 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"type": "inline_equation", + "content": "= 70^{\\circ}" + }, + { + "bbox": [ + 465, + 267, + 541, + 312 + ], + "type": "inline_equation", + "content": "\\xi = 0.1" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "bbox": [ + 55, + 423, + 148, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 148, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 148, + 435 + ], + "type": "text", + "content": "4.1. Model analysis" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 55, + 444, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 444, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 296, + 504 + ], + "type": "text", + "content": "Camera conditioning adherence. To assess the stability of our model's camera conditioning, we generate images using the same PF-US maps and prompts but vary the input noise. Results show consistent camera conditioning (please refer to Sec. G of the supplementary material for examples)." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": "Ablation: Influence of the residuals' contributions. In our framework, the ControlNet-based module generates residual outputs that can be injected into the main model in various layers. We observe that residuals from the middle block (bottleneck) effectively achieve adherence to the camera conditioning, while preserving the image quality achieved by the base model (SDXL). The injection of residuals at additional levels can introduce distortions and hinder semantic integrity preservation, as shown in Fig. 9. This aligns with the findings of previous works that use ControlNet for conditioning diffusion models [6]. Therefore, in our model, we use only the mid-level residuals during inference; these are key for adhering to camera conditions without disrupting the generative capabilities of the base model (SDXL), providing a good trade-off between effective camera control and high-quality image generation." + } + ] + } + ], + "index": 39 + }, + { + "type": "image", + "bbox": [ + 328, + 420, + 397, + 497 + ], + "blocks": [ + { + "bbox": [ + 55, + 344, + 555, + 410 + ], + "lines": [ + { + "bbox": [ + 55, + 344, + 555, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 555, + 410 + ], + "type": "text", + "content": "Figure 8. Comparison of our model with SDXL and Adobe Firefly (Firefly tags are in dark blue background; prompt engineering, when present, in bold and dark blue text). Four examples are shown: the top half depicts realistic styles, while the bottom half depicts artistic styles; the left half examples intend a shot from below, and the right half a tilted view from below. SDXL struggles in all cases. Firefly successfully produces the shot from below in the realistic style due to its matching tag, but fails in the artistic version of it; for more complex perspectives, like the tilted view from below, Firefly lacks a tag for this view, and fails to produce a valid result despite the efforts with the prompt. Our approach achieves reliable camera control across both styles and perspectives." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 328, + 420, + 397, + 497 + ], + "lines": [ + { + "bbox": [ + 328, + 420, + 397, + 497 + ], + "spans": [ + { + "bbox": [ + 328, + 420, + 397, + 497 + ], + "type": "image", + "image_path": "8de14a3043388b405b75940bcb01f4ab9a54f086aae789cb6624e0f286b1c720.jpg" + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_body" + } + ], + "index": 40 + }, + { + "type": "image", + "bbox": [ + 400, + 421, + 469, + 497 + ], + "blocks": [ + { + "bbox": [ + 400, + 421, + 469, + 497 + ], + "lines": [ + { + "bbox": [ + 400, + 421, + 469, + 497 + ], + "spans": [ + { + "bbox": [ + 400, + 421, + 469, + 497 + ], + "type": "image", + "image_path": "425c8d85f1a2fc64543f00aa2340fe6241d95a0a2f680c3650518d3ea29dc68d.jpg" + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "image_body" + } + ], + "index": 42 + }, + { + "type": "image", + "bbox": [ + 471, + 421, + 538, + 497 + ], + "blocks": [ + { + "bbox": [ + 471, + 421, + 538, + 497 + ], + "lines": [ + { + "bbox": [ + 471, + 421, + 538, + 497 + ], + "spans": [ + { + "bbox": [ + 471, + 421, + 538, + 497 + ], + "type": "image", + "image_path": "75be72c9cdc211c4bce4fa525e0749b49df6f921c7d92ffd5252ce511dba8350.jpg" + } + ] + } + ], + "index": 44, + "angle": 0, + "type": "image_body" + } + ], + "index": 44 + }, + { + "type": "image", + "bbox": [ + 328, + 506, + 397, + 574 + ], + "blocks": [ + { + "bbox": [ + 335, + 499, + 389, + 505 + ], + "lines": [ + { + "bbox": [ + 335, + 499, + 389, + 505 + ], + "spans": [ + { + "bbox": [ + 335, + 499, + 389, + 505 + ], + "type": "text", + "content": "Residuals: Middle + C" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 328, + 506, + 397, + 574 + ], + "lines": [ + { + "bbox": [ + 328, + 506, + 397, + 574 + ], + "spans": [ + { + "bbox": [ + 328, + 506, + 397, + 574 + ], + "type": "image", + "image_path": "7d39b480f44a0389418c18cf669a5ae77b97751ebe5a8c21a50bf64a54fec0c7.jpg" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 327, + 575, + 541, + 591 + ], + "lines": [ + { + "bbox": [ + 327, + 575, + 541, + 591 + ], + "spans": [ + { + "bbox": [ + 327, + 575, + 541, + 591 + ], + "type": "text", + "content": "A majestic white stag standing in a misty forest. Its antlers are massive and covered in moss and glowing crystals. Its fur is smooth and white, almost glowing under the pale morning light." + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 600, + 555, + 677 + ], + "lines": [ + { + "bbox": [ + 313, + 600, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 555, + 677 + ], + "type": "text", + "content": "Figure 9. Image generation conditioned by the text prompt (bottom) and fixed camera parameters, for different injections of residual outputs of the ControlNet-based module into the main SDXL model. Middle block residuals injected at the bottleneck (ours) enable precise camera control with minimal impact on image quality, while deeper residuals introduce distortions, reducing overall image quality." + } + ] + } + ], + "index": 50, + "angle": 0, + "type": "image_caption" + } + ], + "index": 46 + }, + { + "type": "image", + "bbox": [ + 400, + 506, + 469, + 574 + ], + "blocks": [ + { + "bbox": [ + 403, + 499, + 466, + 506 + ], + "lines": [ + { + "bbox": [ + 403, + 499, + 466, + 506 + ], + "spans": [ + { + "bbox": [ + 403, + 499, + 466, + 506 + ], + "type": "text", + "content": "Residuals: Middle + C + B" + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 400, + 506, + 469, + 574 + ], + "lines": [ + { + "bbox": [ + 400, + 506, + 469, + 574 + ], + "spans": [ + { + "bbox": [ + 400, + 506, + 469, + 574 + ], + "type": "image", + "image_path": "cc46c89f4dfb92447a1a5da0d7e1e559a30819a0385e60ba7942155685c346be.jpg" + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "image_body" + } + ], + "index": 48 + }, + { + "type": "image", + "bbox": [ + 470, + 506, + 541, + 574 + ], + "blocks": [ + { + "bbox": [ + 471, + 499, + 541, + 506 + ], + "lines": [ + { + "bbox": [ + 471, + 499, + 541, + 506 + ], + "spans": [ + { + "bbox": [ + 471, + 499, + 541, + 506 + ], + "type": "text", + "content": "Residuals: Middle + C + B + A" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 470, + 506, + 541, + 574 + ], + "lines": [ + { + "bbox": [ + 470, + 506, + 541, + 574 + ], + "spans": [ + { + "bbox": [ + 470, + 506, + 541, + 574 + ], + "type": "image", + "image_path": "10897ccdd39afa460c0c1bef784bb5c9bb63a373d3bcebc6cc8c876e0911e198.jpg" + } + ] + } + ], + "index": 49, + "angle": 0, + "type": "image_body" + } + ], + "index": 49 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2730" + } + ] + } + ], + "index": 51 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 68, + 294, + 157 + ], + "blocks": [ + { + "bbox": [ + 57, + 68, + 294, + 157 + ], + "lines": [ + { + "bbox": [ + 57, + 68, + 294, + 157 + ], + "spans": [ + { + "bbox": [ + 57, + 68, + 294, + 157 + ], + "type": "image", + "image_path": "c4239aa35b14b23b4591725c5975c0151258dba0a08e25912555a609632303a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 165, + 295, + 232 + ], + "lines": [ + { + "bbox": [ + 55, + 165, + 295, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 165, + 295, + 232 + ], + "type": "text", + "content": "Figure 10. Background generation without and with camera control. Our method can generate a background that aligns with the object's perspective (shown on the left), ensuring seamless integration. The baseline approach (SDXL, center) lacks perspective consistency, while the background generated with our method aligns well with the object (right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 239, + 294, + 358 + ], + "blocks": [ + { + "bbox": [ + 56, + 239, + 294, + 358 + ], + "lines": [ + { + "bbox": [ + 56, + 239, + 294, + 358 + ], + "spans": [ + { + "bbox": [ + 56, + 239, + 294, + 358 + ], + "type": "image", + "image_path": "fa7ee707259458809b68d32c9e6a0b38dc69184baf2864d3035842623c0feb61.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 367, + 295, + 411 + ], + "lines": [ + { + "bbox": [ + 55, + 367, + 295, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 367, + 295, + 411 + ], + "type": "text", + "content": "Figure 11. Video generation results showing two examples of frame-by-frame camera control. Camera parameters are specified to achieve a zoom-in effect (top) and an anti-clockwise rotation (bottom). Frames progress from left to right over time." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 427, + 137, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 137, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 137, + 441 + ], + "type": "text", + "content": "4.2. Applications" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 448, + 295, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 295, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 295, + 520 + ], + "type": "text", + "content": "Background generation for object rendering. Precise-Cam can be used to generate backgrounds that match the perspective of a given object. By aligning the background's perspective with the object's viewpoint, our model can be used to create visually coherent scenes where the object appears naturally embedded, as shown in Fig. 10." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "Video generation. Our model can be used to condition the camera view on each frame of a video to specify the desired perspectives throughout the sequence, as illustrated in Fig. 11. Each frame is guided by our four camera parameters through a custom-trained adapter [30] for Stable Video Diffusion [7], ensuring consistent perspective control across frames. Alternatively, our method can be used to condition the initial frame of a video sequence, after which existing methods for relative camera view control can guide the trajectory for the remaining frames [20, 45, 46, 48, 49]. While these existing methods establish movement relative to the first frame, they lack control over the initial camera position that sets the starting perspective for the entire video. Our approach addresses this gap by enabling precise control over the initial camera position to anchor the video sequence." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 316, + 69, + 553, + 170 + ], + "blocks": [ + { + "bbox": [ + 316, + 69, + 553, + 170 + ], + "lines": [ + { + "bbox": [ + 316, + 69, + 553, + 170 + ], + "spans": [ + { + "bbox": [ + 316, + 69, + 553, + 170 + ], + "type": "image", + "image_path": "bdf8b9ae5f4cb869bbb41cc9c180650e0cc69a6cc508a464c522e896a9209389.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 178, + 553, + 234 + ], + "lines": [ + { + "bbox": [ + 313, + 178, + 553, + 234 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 553, + 234 + ], + "type": "text", + "content": "Figure 12. Limitations. Left: The model may occasionally incorrectly position objects or people in a vertical, standing orientation (like the man on the boat), as it is more frequent. Right: In the presence of conflicts between the prompt and the desired camera view, the model may produce semantically incoherent outputs." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 250, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 250, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 250, + 555, + 346 + ], + "type": "text", + "content": "Extended control with multiple ControlNets. Additionally, our approach is compatible with other ControlNets, allowing additional conditioning on the final output to achieve complex effects. For instance, combining our model with depth, Canny edges, and pose control can allow for simultaneous control over camera view, subject positioning, and scene structure [54]. Please refer to Sec. H of the supplementary material for further details and examples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 356, + 388, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 388, + 369 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 388, + 369 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 376, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 554, + 483 + ], + "type": "text", + "content": "We present PreciseCam, a framework for precise camera control in text-to-image diffusion-based generation, along with a novel dataset. Our experiments show precise and consistent camera control, far exceeding existing methods such as prompt engineering, even with artistic images not found in our dataset (e.g., Fig. 8). Additionally, we provide proof-of-concept applications for enhancing creative expression, background generation for object compositing, and video generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 484, + 554, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 554, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 554, + 579 + ], + "type": "text", + "content": "Despite our dataset covering a wide range of camera parameters and content, PreciseCam may struggle with extreme roll due to the backbone's tendency to align objects vertically (Fig. 12, left). While our model retains SDXL's ability to generate images that match prompts, conflicts between the prompt and camera view (Fig. 12, right) can cause incoherent outputs. We hope our work helps develop new tools to unlock artistic generative imaging." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 586, + 417, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 586, + 417, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 586, + 417, + 600 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": "We thank Dario Lanza and Nestor Monzon and the Graphics and Imaging Lab members. This research was funded by grant PID2022-141539NB-I00, funded by MI-CIU/AEI/10.13039/501100011033, and by ERDF, EU. It has also been partially funded by the Government of Aragon's Departamento de Empleo, Ciencia y Universidades (project ref Proy-T25-24). Additionally, Edurne Bernal-Berdun was supported by a Governor de Aragon predoctoral grant program (2021-2025)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2731" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 102 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 102 + ], + "type": "text", + "content": "[1] 360cities. 360cities dataset. https://www.360cities.net/. 5, 1" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 103, + 296, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 103, + 296, + 124 + ], + "spans": [ + { + "bbox": [ + 61, + 103, + 296, + 124 + ], + "type": "text", + "content": "[2] Adobe. 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In ICIP, 2020. 5, 1" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2733" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_content_list.json b/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0721080ffff52a0b9b70e301b25ff7a3ce581e5d --- /dev/null +++ b/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_content_list.json @@ -0,0 +1,1737 @@ +[ + { + "type": "text", + "text": "Preconditioners for the Stochastic Training of Neural Fields", + "text_level": 1, + "bbox": [ + 197, + 130, + 800, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shin-Fang Chng* Hemanth Saratchandran* Simon Lucey Australian Institute of Machine Learning, University of Adelaide.", + "bbox": [ + 238, + 186, + 756, + 226 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f2676f0f0acd62834581f8c58d29d3ce15aafba1dd115570b1c7aedbd815852.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 104, + 237, + 359, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/98d530d00b07a93992ae517d56dfd9c61422e76b34fb9bf840b49bf7c4864b8c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 237, + 622, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/02037b7175d32bc0bfea5a93a3d359cc7cf76f3fdc52f2f7575d3ae33ddbb664.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 630, + 238, + 892, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/537e4158e7b78132f19498bf8c6adbbdbd699892331b78ea1794aa78a2d41da2.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 96, + 441, + 228, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3e074a9b15914298b4e84453d6b2aa726f59f1deb6429ded1c2c51ee4946ea41.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 230, + 441, + 362, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f48bb816e0475b8e2007e2957a64776554d46eeb5ca950bc0c427a81cf65a15d.jpg", + "image_caption": [ + "(b)", + "(f)" + ], + "image_footnote": [], + "bbox": [ + 369, + 433, + 495, + 542 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/06efefc0e5f01d7495223ac7d8bf473a440e3fc6e7eec35978eedc4357cbdf62.jpg", + "image_caption": [ + "(g)" + ], + "image_footnote": [], + "bbox": [ + 503, + 433, + 627, + 542 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/afd613ce835f0a692876b5aa77ff37d2935909186131a2f6abd83ca5944a3d9e.jpg", + "image_caption": [ + "(h)", + "Figure 1. We demonstrate that curvature-aware preconditioners can significantly accelerate training convergence for neural fields with suitable activations. Specifically, ESGD (a curvature-aware preconditioned gradient descent algorithm [14]) improves convergence for wavelet, sine, and Gaussian activations, while Adam performs better for ReLU network with positional encoding (ReLU(PE)). In a $2D$ image reconstruction task (Fig. 1a), a wavelet-based neural field trained with ESGD achieves 29.36 PSNR (Fig. 1e) at the $10^{\\mathrm{th}}$ epoch, outperforming Adam's 26.61 PSNR (Fig. 1d). In a $3D$ binary occupancy task (Fig. 1b), ESGD enables faster convergence for sine activations, as shown by the improved armadillo mesh reconstruction at the $1000^{\\mathrm{th}}$ epoch (Fig. 1g vs. Fig. 1f). In a Neural Radiance Fields (NeRF) task (Fig. 1c), a Gaussian-based model trained with ESGD achieves lower reconstruction error (Fig. 1i, 0.0695) compared to Adam (Fig. 1h, 0.0743), as seen in the error map (darker areas indicate lower error; zoom in $4\\times$ for clarity)." + ], + "image_footnote": [], + "bbox": [ + 630, + 441, + 761, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6227585b6f4660dad18edd1d71ade7cdfa90928eea6dbc06e8b5ef853bd4ec6b.jpg", + "image_caption": [ + "(i)" + ], + "image_footnote": [], + "bbox": [ + 764, + 441, + 897, + 544 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 681, + 326, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effec", + "bbox": [ + 88, + 713, + 485, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF) $^{1}$ .", + "bbox": [ + 511, + 684, + 906, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 742, + 645, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, neural fields, also known as implicit neural representations, have garnered significant attention in machine learning and computer graphics [8, 9, 25, 32, 53-55, 57]. Unlike traditional grid-based representations [6, 17, 56, 64], neural fields implicitly encode shapes and objects through neural networks. These representations are", + "bbox": [ + 511, + 767, + 906, + 859 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ *Equal contribution.> Correspondence to: Shin-Fang Chng .", + "bbox": [ + 89, + 873, + 482, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Source code is available at https://github.com/sfchng/preconditioner_neural_fields.git.", + "bbox": [ + 511, + 867, + 903, + 893 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27222", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "highly efficient for capturing complex, high-resolution signals, making them well-suited for tasks such as image synthesis [9, 55], shape modeling [32, 53], and robotics [10, 59].", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Classically, neural fields trained with ReLU activations suffer from spectral bias and limited fidelity [40]. To address this, positional encoding (PE) layers [58] were introduced but at the cost of increased model complexity and noisy gradients. More recent work has explored non-standard activations, such as sine [54], Gaussian [41] and wavelets [49] which enable high-frequency encoding without positional encodings and produce well-behaved gradients [50].", + "bbox": [ + 89, + 152, + 486, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While neural fields have enabled realistic and efficient representations of continuous signals, progress on minimizing the training time of such representations remains a significant research challenge. Currently, the Adam optimizer is the de facto algorithm for training neural fields, particularly in applications involving datasets where a stochastic training regime is essential. Yet, the preference for Adam over simpler alternatives such as stochastic gradient descent (SGD) has not been rigorously justified for neural fields, despite its widespread adoption. Notably, [50] demonstrated substantial gains in training speed for neural fields using second-order optimizers such as L-BFGS [34]. However, second-order methods are often impractical for stochastic settings [50], limiting their effectiveness for large-scale data, where stochastic training is essential.", + "bbox": [ + 89, + 272, + 485, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we approach neural field training from the perspective of preconditioning. Preconditioners improve convergence by reducing the condition number of the optimization problem [4, 34, 46]. We develop a theoretical framework linking Adam's performance to its implicit use of a diagonal preconditioner derived from the Gauss-Newton matrix and proceed to identify conditions under which curvature-aware diagonal preconditioners, such as those in ESGD (equilibrated stochastic gradient descent) [14], enhance training for neural fields with sine, Gaussian, or wavelet activations. For ReLU activations, we show that such preconditioning provides limited benefit.", + "bbox": [ + 89, + 500, + 491, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our experiments validate the proposed framework across a range of tasks, including 2D image reconstruction, 3D binary occupancy, and Neural Radiance Fields (NeRF). As demonstrated in Fig. 1, ESGD consistently outperforms Adam for neural fields with wavelet, sine, and Gaussian activations, which, as predicted by our theory, is due to their better-conditioned Hessians. In contrast, Adam performs better for ReLU-PE activations, which are associated with poorly conditioned Hessians. Furthermore, we evaluated other curvature-aware algorithms, including ESGD, Ada-Hessian [62], Shampoo [21], and K-FAC [30], offering valuable insights into their effectiveness in stochastic training settings.", + "bbox": [ + 89, + 680, + 495, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are:", + "bbox": [ + 109, + 877, + 294, + 891 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We present a theoretical framework for preconditioning in neural field training, uncovering key conditions and highlighting when preconditioning is beneficial.", + "2. We empirically validate our framework, demonstrating the superiority of curvature-aware algorithms like ESGD over Adam across diverse tasks, including image reconstruction, 3D shape modeling, and NeRF." + ], + "bbox": [ + 514, + 90, + 903, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 514, + 210, + 653, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Fields represent signals as weights within a neural network, using low-dimensional coordinates to maintain smoothness in the output [64]. The influential work by Mildenhall et al. [32] showcased the potential of neural fields for novel view synthesis, demonstrating their impressive generalization capabilities. Since then, neural fields have seen widespread application across image view synthesis, shape reconstruction, and robotics [7, 11, 12, 15, 18, 33, 35, 36, 38, 42, 47, 48, 54, 60, 63, 65]. Traditionally, these approaches integrate a positional embedding layer to counteract the spectral bias introduced by ReLU activations [40]. However, recent work has explored alternative, non-standard activations such as sine [54], Gaussian [41], wavelets [49], and sinc [51]. These activations have shown to outperform conventional approaches in various vision tasks, delivering enhanced performance in capturing high-frequency details and reducing reliance on positional embeddings [12, 29, 41, 49, 54, 61].", + "bbox": [ + 511, + 234, + 916, + 507 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Preconditioners were initially introduced in numerical linear algebra [20, 46] to transform ill-conditioned linear systems into well-conditioned forms, thereby accelerating the convergence of iterative solvers. Over time, preconditioning techniques have become integral to machine learning, where they enhance the efficiency and performance of optimization algorithms. Early applications in machine learning can be traced to foundational optimization methods, such as the conjugate gradient method and its variants [34]. As machine learning problems have grown more complex—often involving sparse matrices, non-convex objectives, and large-scale datasets—researchers have developed specialized preconditioning strategies to meet these unique challenges [3, 24, 39, 43]. Many widely-used optimizers incorporate preconditioning, including methods like ADMM [27], mirror descent [2], quasi-Newton methods [5, 19, 34], and adaptive optimizers [14, 16, 21, 30, 62]. These preconditioned optimizers have become essential for addressing the complex landscapes of modern machine learning models, driving improvements in both convergence speed and solution quality.", + "bbox": [ + 511, + 525, + 910, + 843 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27223", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Notation", + "text_level": 1, + "bbox": [ + 89, + 89, + 189, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The neural fields we consider in this paper will be defined by a depth $L$ neural network with layer widths $\\{n_1,\\dots ,n_L\\}$ . We let $X\\in \\mathbb{R}^{N\\times n_0}$ denote the training data, with $n_0$ being the dimension of the input and $N$ being the number of training samples. The output at layer $k$ will be denoted by $F_{k}$ and is defined by", + "bbox": [ + 89, + 114, + 485, + 205 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF _ {k} = \\left\\{ \\begin{array}{l l} F _ {L - 1} W _ {L} + b _ {L}, & k = L \\\\ \\phi \\left(F _ {k - 1} W _ {k} + b _ {k}\\right), & k \\in [ L - 1 ] \\\\ X, & k = 0 \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 213, + 482, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the weights $W_{k} \\in \\mathbb{R}^{n_{k - 1} \\times n_{k}}$ and the biases $b_{k} \\in \\mathbb{R}^{n_{k}}$ and $\\phi$ is an activation applied component wise. The notation $[m]$ is defined by $[m] = \\{1, \\dots, m\\}$ . We will denote the loss function that we train the neural fields with by $\\mathcal{L}$ . In many experiments in the paper this will be the MSE loss [37]. Our theoretical results will be primarily for the case where $\\phi$ is given by one of the activation sine, Gaussian, wavelet or ReLU. For more details on how these activations are used within the context of neural fields we refer the reader to [41, 49, 54].", + "bbox": [ + 89, + 276, + 483, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Theoretical Framework", + "text_level": 1, + "bbox": [ + 89, + 440, + 316, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overview of Preconditioners", + "text_level": 1, + "bbox": [ + 89, + 465, + 346, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preconditioning enhances optimization convergence and efficiency by regulating curvature, particularly in stochastic gradient descent (SGD) [14, 39]. High curvature directions in SGD require a small learning rate to avoid overshooting, leading to slow progress in low curvature directions.", + "bbox": [ + 89, + 487, + 483, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For general objective functions $f$ on parameters $\\mathbf{x} \\in \\mathbb{R}^n$ . Preconditioning is done by employing a linear change of parameters $\\widetilde{\\mathbf{x}} = D^{\\frac{1}{2}}\\mathbf{x}$ , where in practise $D^{\\frac{1}{2}}$ is a non-singular matrix. With this change of parameters a new objective function $\\widetilde{f}$ , defined on $\\widetilde{\\mathbf{x}}$ , can be defined as", + "bbox": [ + 89, + 563, + 483, + 638 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {f} (\\widetilde {\\mathbf {x}}) = f (\\mathbf {x}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 238, + 643, + 482, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denoting the gradient of the original objective function by $\\nabla f$ and its Hessian by $H(f) = \\nabla^2 f(\\mathbf{x})$ . The chain rule gives", + "bbox": [ + 89, + 671, + 483, + 717 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla \\widetilde {f} (\\widetilde {\\mathbf {x}}) = D ^ {- \\frac {1}{2}} \\nabla f \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 723, + 480, + 743 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH (\\widetilde {f}) (\\widetilde {\\mathbf {x}}) = \\left(D ^ {- \\frac {1}{2}}\\right) ^ {T} \\left(H (f) (\\mathbf {x})\\right) \\left(D ^ {- \\frac {1}{2}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 746, + 482, + 766 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Equation (3) exhibits the key idea of training with a preconditioner. If we consider gradient descent on the transformed parameter space, a gradient descent iteration takes the form", + "bbox": [ + 89, + 773, + 483, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {x}} _ {t} = \\widetilde {\\mathbf {x}} _ {t - 1} - \\eta \\nabla_ {\\widetilde {\\mathbf {x}} _ {t - 1}} \\widetilde {f} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 830, + 482, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Applying equations (2) and (3) this corresponds to doing the update", + "bbox": [ + 89, + 853, + 482, + 882 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\mathbf {x} _ {t - 1} - \\eta D ^ {- \\frac {1}{2}} \\nabla_ {\\mathbf {x} _ {t - 1}} f. \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 883, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main endeavour of preconditioning for optimization is to find a preconditioning matrix $D$ such that the new Hessian, given by equation (4), has equal curvature in all directions. This will allow the update (6) to move faster along small curvature directions, leading to faster convergence. Algorithm 1 gives the basic pseudocode for preconditioned SGD.", + "bbox": [ + 511, + 90, + 906, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1 Preconditioned SGD", + "text_level": 1, + "bbox": [ + 514, + 208, + 741, + 222 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Require: initial point $x_0$ , iterations $N$ , learning rate $\\eta$ , preconditioner $D$ .", + "bbox": [ + 514, + 227, + 903, + 257 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {f o r} t = 0, \\dots , N \\mathbf {d o} \\\\ g _ {t} \\leftarrow \\nabla_ {x _ {t}} f \\\\ D _ {t} \\leftarrow D (x _ {t}) \\\\ x _ {t + 1} \\leftarrow x _ {t} - \\eta D (x _ {t}) ^ {- \\frac {1}{2}} g _ {t} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 257, + 733, + 320 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 531, + 320, + 584, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "From Eq. (4) we see that the best preconditioner to use would be the absolute value of the Hessian itself. In the case of a positive definite Hessian, this is precisely what Newton's method does [34]. The main issue with this preconditioner is that the cost of storing and inverting the preconditioner will be $\\mathcal{O}(n^3)$ for an objective function of $n$ parameters [34]. This will be extremely costly for the training of overparameterized neural networks whose Hessians are extremely large.", + "bbox": [ + 511, + 354, + 906, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We list some of the main preconditioners that are being used in the literature.", + "bbox": [ + 511, + 489, + 905, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diagonal Preconditioners: are matrices that represent some form of a diagonal approximation of the Hessian. Examples include the Jacobi preconditioner, which is given by $D^{J} = |\\operatorname{diag}(H)|$ , where $|\\cdot|$ is element-wise absolute value and $H$ is the Hessian. In practical settings, the absolute value is taken so that the preconditioner is positive semidefinite. The equilibration preconditioner is a diagonal matrix which has the 2-norm of each row (or column) on the diagonal: $D^{E} = ||H_{i,\\cdot}||$ . The preconditioners $D^{J}$ and $D^{E}$ are known as curvature-aware preconditioners as they seek to give a good approximation to the Hessian. Diagonal preconditioners are often used because of their ability to be stored and inverted in linear time. Diagonal preconditioners are also known as adaptive learning rates in the literature. The algorithm Equilibrated Stochastic Gradient Descent (ESGD) [14] employs $D^{E}$ as a preconditioner to condition stochastic gradient descent. In [14], it is shown that applying ESGD leads to faster training times for autoencoder tasks when compared to vanilla SGD, RMSProp [45] and a preconditioned SGD using $D^{J}$ as preconditioner. AdaHessian [62] is a recent algorithm that applies a diagonal preconditioner in the setting of moving averages and thus can be seen as a way of enhancing the Adam optimizer [23].", + "bbox": [ + 511, + 537, + 921, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27224", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Kronecker Factored Preconditioners: are preconditioners of the form $D = A^T A$ , where $A = A_1 \\otimes \\dots \\otimes A_k$ and $\\otimes$ denotes the Kronecker product. The algorithm K-FAC [30] employs a Kronecker factored preconditioner.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Others: There are several second order optimisation algorithms that use preconditioners that do not fall into the above three categories such as, The Gauss-Newton method, The Conjugate Gradient method, Limited memory Broyden-Fisher-Golfarb-Shanno (L-BFGS) [34]. It was shown in [50] that these algorithms do not train well in stochastic settings.", + "bbox": [ + 89, + 152, + 482, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Condition Number", + "text_level": 1, + "bbox": [ + 89, + 265, + 272, + 279 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Sec. 4.1, we explained that SGD will move faster through the loss landscape when the curvatures in each direction are similar. The regularity of the loss landscape at a point is quantified via the condition number of the Hessian.", + "bbox": [ + 89, + 286, + 483, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 4.1. Given a matrix $A$ we define the condition number $\\kappa$ of $A$ by", + "bbox": [ + 89, + 354, + 483, + 386 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\kappa (A) := \\frac {\\sigma_ {\\operatorname* {m a x}} (A)}{\\sigma_ {\\operatorname* {m i n}} (A)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 391, + 482, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ is the eigenvalue. Using Eq. (4) we observe that if we take a preconditioner $D$ such that $\\kappa((D^{-\\frac{1}{2}})^T(H(f)(\\mathbf{x}))(D^{-\\frac{1}{2}}))$ is closer to 1 than $\\kappa(H)$ , then this implies that the preconditioner $D$ is regularising the curvatures of the landscape to be equal in each direction, which yields a better training landscape for a gradient descent based algorithm [34].", + "bbox": [ + 89, + 431, + 488, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To empirically illustrate the concept of preconditioning, we examined a one-dimensional curve fitting scenario. Specifically, we considered a feedforward network with two hidden layers, each containing 16 neurons, tasked with fitting the signal $f(x) = \\sin (2\\pi x) + \\sin (6\\pi x)$ using a Gaussian activation [41]. During optimization with gradient descent, we applied two types of preconditioners: an equilibrated preconditioner $D^{E}$ and a Jacobi preconditioner $D^{J}$ . At each optimization step, we computed both the original Hessian associated with gradient descent and the transformed Hessian using Eq. (4). As shown in Fig. 2, the results demonstrate that applying either the Jacobi or equilibrated preconditioner consistently reduced the condition number of the Hessian compared to the unconditioned case, highlighting the effectiveness of preconditioning in improving optimization.", + "bbox": [ + 89, + 539, + 496, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Training with Adam", + "text_level": 1, + "bbox": [ + 89, + 787, + 284, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we aim to explain why training with Adam is generally more efficient than training with SGD for a variety of neural fields. While this observation is well-known within the community, we include it here to provide context and motivation for the theoretical framework developed in Sec. 4.4.", + "bbox": [ + 89, + 809, + 483, + 898 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fe616343aaaaf14f1b2f781a3e345cc821e2cb7f36418bffc191dc7c022ff1b9.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 705, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3564b6ecda338ae5406efeb8cc3a2ff62c726bcdbc3f09389813ac4fd13e9847.jpg", + "image_caption": [ + "(b)", + "Figure 2. Fig. 2a compares the condition number (7) on a 1D signal regression task before (dotted line) and after (solid line) applying equilibrated $D^{E}$ and Jacobi $D^{J}$ preconditioners. The equilibrated preconditioner significantly reduces the Hessian's condition number, as shown by the larger gap between the yellow solid and dotted lines compared to the green solid and dotted lines representing the Jacobi preconditioner, thus achieves faster convergence as seen in Fig. 2b." + ], + "image_footnote": [], + "bbox": [ + 709, + 95, + 897, + 203 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an objective function $L(\\theta) = |f(\\theta)|^2$ for a nonlinear function $f$ . The Jacobian $J_{L}$ of $L$ can be computed via the chain rule: $J_{L} = 2J_{f}^{T}f$ , where $J_{f}$ denotes the Jacobian of $f$ . The Hessian of $L$ , $H_{L}$ , can be computed by an application of the chain rule", + "bbox": [ + 511, + 356, + 905, + 434 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH _ {L} = 2 J _ {f} ^ {T} J _ {f} + 2 H _ {f} f. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 441, + 903, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can then approximate the Hessian $H_{L}$ by the term $2J_{f}^{T}J_{f}$ . Leading to the first order approximation", + "bbox": [ + 511, + 472, + 911, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH _ {L} \\approx 2 J _ {f} ^ {T} J _ {f} = \\frac {1}{2 | f | ^ {2}} J _ {L} ^ {T} J _ {L} = \\frac {1}{2 L} J _ {L} ^ {T} J _ {L}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 512, + 903, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eq. (9) yields the basic idea of the Gauss-Newton method. By taking the Gauss-Newton matrix $J_{L}^{T}J_{L}$ as an approximation to the Hessian $H_{L}$ , we can perform an optimization update that uses the step: $\\Delta_{GN} = -\\frac{1}{J^TJ}\\nabla L$ . The Gauss-Newton matrix is in general only positive semi-definite. Therefore, when implementing the algorithm one often adds a small damping factor $\\lambda$ so the implemented step is $\\Delta_{GN} = -\\frac{1}{J^TJ + \\lambda}\\nabla L$ . A similar derivation can be made for more general loss functions used in non-linear least squares type regression problems [34]. It follows that the Gauss-Newton method can be seen as a preconditioned SGD that uses a first order (first derivatives) Hessian approximate preconditioner given by the Gauss-Newton matrix $J^T J$ .", + "bbox": [ + 511, + 551, + 921, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the above observations we now show how to view Adam as an optimizer that applies a diagonal preconditioner. The Adam optimizer involves two key steps. The first is to compute a first moment estimate of the form $m_{t} = \\beta_{1}m_{t - 1} + (1 - \\beta_{1})g_{t}$ , where $g_{t}$ is the gradient of a given objective function $f$ at iteration $t$ , and $m_0 = 0$ . The second is to compute a second moment estimate $v_{t} = \\beta_{2}v_{t - 1} + (1 - \\beta_{2})g_{t}^{2}$ , where $g_{t}^{2} = g_{t}\\odot g_{t},\\odot$ denotes the Hadamard product, and $v_{0} = 0$ . The numbers $0 < \\beta_{1} < \\beta_{2} < 1$ are hyperparameters. The algorithm then applies a bias correction to the above first", + "bbox": [ + 511, + 750, + 910, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27225", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/150a19ddfd5b7786e5637b7114b6a8adf18d154c731103e64cb80fc8f8bd4033.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 361, + 262 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9104b3424b2530ee19492f45e26433bb81312bbda42839a4ad5d8c84ba4a153a.jpg", + "image_caption": [ + "(b)", + "Figure 3. Comparison of training convergence for neural fields with different activations – ReLU with positional encoding (ReLU (PE)), wavelet, sine and Gaussian – using Adam and SGD optimizers across three tasks: 2D image reconstruction (Fig. 3a), 3D binary occupancy reconstruction (Fig. 3b), and NeRF (Fig. 3c). In all cases, the Adam optimizer outperforms SGD, indicating that leveraging curvature information facilitates faster convergence." + ], + "image_footnote": [], + "bbox": [ + 370, + 90, + 625, + 262 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a3ce407e507e7c7aeed26f594909ebd161892fabe90e4a90cbd26e5f8d8354ea.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 633, + 98, + 893, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and second moment estimates, and then takes a moving average to perform an update step based on $-\\frac{m_t}{\\sqrt{v_t}}$ , see [23] for details.", + "bbox": [ + 89, + 362, + 482, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the following discussion, we will only focus on analyzing the second raw moment estimate, as this is related to the Gauss-Newton matrix. Given an objective function $f$ , observe that we can express $g_t^2 = g_t \\odot g_t = \\text{Diag}(J^T J)$ , where $J$ denotes the Jacobian of $f$ . Thus the second raw moment estimate of Adam can be recast as:", + "bbox": [ + 89, + 409, + 483, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {t} = \\beta_ {2} v _ {t - 1} + (1 - \\beta_ {2}) \\operatorname {D i a g} \\left(J _ {t} ^ {T} J _ {t}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 508, + 480, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $J_{t}$ denotes the Jacobian at iteration $t$ . Thus we see that Adam applies a preconditioner given by the diagonal of the Gauss-Newton matrix. Since the Gauss-Newton matrix can be seen as a first order approximation to the Hessian, Adam can be seen as using an approximation to curvature to adapt the learning rate for faster optimization. This suggests that Adam can outperform SGD which employs no preconditioner.", + "bbox": [ + 89, + 539, + 483, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We empirically validated this insight across three distinct neural field tasks: image reconstruction, binary occupancy, and NeRF. For each task, we compared the performance of ReLU(PE) activated networks trained with both SGD and Adam against networks using wavelet, sine, and Gaussian activations. As shown in Fig. 3, Adam consistently outperforms SGD in all cases. This suggests that Adam's use of a preconditioner significantly enhances its performance for neural field applications, see Sec. 5 for the details of the architectures and experimental setup.", + "bbox": [ + 89, + 660, + 483, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Main theorems", + "text_level": 1, + "bbox": [ + 89, + 821, + 243, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Sec. 4.3, we discussed how Adam can be viewed as applying a diagonal preconditioner based on the diagonal of the Gauss-Newton matrix, which uses first derivatives to", + "bbox": [ + 89, + 843, + 483, + 888 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/71d26ca2e77dcbbabd3e3142c48014e425ca4beee0f006629c287e2a095b594a.jpg", + "image_caption": [ + "Figure 4. Percentage sparsity of Hessian-vector product matrices across all layers throughout the training process of a 2D image reconstruction task, using ESGD to train networks with different activations. The x-axis ranges from 0 to 1, with values closer to 1 indicating higher sparsity." + ], + "image_footnote": [], + "bbox": [ + 566, + 361, + 852, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "approximate the Hessian matrix. Here, we aim to identify the architectural properties that enable effective training of neural fields with diagonal preconditioners that give a better approximation to the Hessian. Our primary theorems demonstrate that the choice of activation function is crucial for enabling efficient training with such preconditioners, highlighting its central role in achieving effective curvature-aware optimization for neural fields.", + "bbox": [ + 511, + 625, + 905, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recall Sec. 4.1 that diagonal preconditioners such as the equilibrated precondition $D^{E}$ or the Jacobi preconditioner $D^{J}$ all involve the Hessian matrix. In the context of neural networks the Hessian of the loss landscape is often an extremely large matrix. Thus in practical settings one often replaces the Hessian with a Hessian vector product which is much cheaper to store [34].", + "bbox": [ + 511, + 744, + 906, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our first theorem shows that the Hessian vector product of the loss landscape associated to a sine, Gaussian, wavelet or sinc activated neural field produces a dense vector.", + "bbox": [ + 511, + 851, + 905, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27226", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 4.2. Let $F$ denote a sine, Gaussian, wavelet or sinc activated neural field. Let $\\mathcal{L}(\\theta)$ denote the MSE loss associated to $F$ and a training set $(X,Y)$ . Let $H$ denote the Hessian of $\\mathcal{L}$ at a fixed parameter point $\\theta$ . Then given a non-zero vector $v$ the Hessian vector product $Hv$ will be a dense vector.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While it may seem rather costly for a sine- or Gaussian-activated INR to have dense Hessian vector products when applied to the MSE loss function, we point out that the cost is much less than storing a dense Hessian.", + "bbox": [ + 89, + 191, + 483, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 4.3. Let $F$ denote a ReLU/ReLU(PE)-activated neural field. Let $\\mathcal{L}(\\theta)$ denote the MSE loss associated to $F$ and a training set $(X, Y)$ . Let $H$ denote the Hessian of $\\mathcal{L}$ at a fixed parameter point $\\theta$ . Then given a non-zero vector $v$ the Hessian vector product $Hv$ will be a sparse vector.", + "bbox": [ + 89, + 262, + 483, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 4.2 and Theorem 4.3 also hold for the binary cross-entropy loss. The proofs of Theorem 4.2 and Theorem 4.3 are given in the Supplementary material.", + "bbox": [ + 89, + 347, + 482, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 4.3 implies that when applying a preconditioner, built from a Hessian vector product, to a ReLU/ReLU(PE) INR, such as ESGD [14] or AdaHessian [62], only a few components of the gradient will be scaled during the update step. This means that the preconditioner will not be adding much to the optimization process. On the other hand, Theorem 4.2 implies that applying a preconditioner built from the Hessian to the gradient of the MSE loss of a sine, Gaussian and wavelet-activated neural field should help optimization as many of the gradient components will get scaled by a quantity depending on the curvature of the loss landscape. This yields a clear difference between ReLU/ReLU(PE) activated neural fields and those activated with a sine, Gaussian, wavelet activation. In particular, Theorem 4.2 implies that neural fields admitting a sine, Gaussian, wavelet activation have the ability to be trained efficiently with a diagonal curvature aware preconditioner such as the equilibrated preconditioner $D^{E}$ defined in Sec. 4.1.", + "bbox": [ + 89, + 393, + 483, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 4 shows the results of a Hessian vector product of the MSE loss of a ReLU(PE) and Gaussian neural field for an image reconstruction task for the weights in all layers of the network layer throughout training. The random vector was chosen from a Rademacher distribution and the reported figures are given as the mean of the Hessian of all layers averaged over all iterations of training. As demonstrated by the experiment, the ReLU(PE) network generates a sparse Hessian-vector product, as predicted by Theorem 4.3, while the Gaussian network produces a dense vector, as indicated by Theorem 4.2. Furthermore, as we will observe in Sec. 5, this sparsity helps explain why Adam performs well for neural fields with ReLU (ReLU(PE)) activations, whereas an algorithm like ESGD [14] does not. This is because Adam does not rely on Hessian-vector product.", + "bbox": [ + 89, + 665, + 483, + 891 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 89, + 645, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared various preconditioners over popular benchmarks [22, 28, 50, 52, 54]: 2D image reconstruction, 3D shape reconstruction and novel view synthesis with NeRF. Our primary focus was on curvature-aware preconditioners that are well-suited for the stochastic training of neural network. Specifically, we compared the following methods: ESGD $[14]^2$ , AdaHessian $[62]^3$ , Shampoo $[21]^4$ , and Kronecker-based preconditioner $[30]^5$ . We provide the details of each algorithm including the reproducibility details of each experiment and machines we used to run each experiment in the supplementary material. In the main paper, we focused on analyzing Gaussian networks, see supplementary material for additional analysis for other non-traditional activations and other neural field tasks.", + "bbox": [ + 511, + 114, + 934, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark for AdaHessian We observed that in the implementation of AdaHessian, an equilibrated preconditioner $D^{E}$ is utilized, even though the paper primarily focuses on using a Jacobi preconditioner [14]. Therefore, we introduced a Jacobi preconditioner $D^{J}$ into AdaHessian, which we refer to as AdaHessian(J). We use the term AdaHessian(E) for the original implementation.", + "bbox": [ + 511, + 332, + 906, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark for ESGD We further modified the ESGD by applying the squared Hessian diagonal preconditioner in two settings: using an exponential moving average (ESGD) and using an infinity norm (ESGD-max) [23]. We also opted to recompute the $D^{E}$ for every $N$ iterations for computational efficiency, we use $N = 100$ for all the experiments.", + "bbox": [ + 511, + 443, + 906, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Image Reconstruction", + "text_level": 1, + "bbox": [ + 511, + 544, + 718, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated on a 2D image reconstruction task, where given pixel coordinates $\\mathbf{x} \\in \\mathbb{R}^2$ , we optimized a neural network to regress the corresponding RGB values $c \\in \\mathbb{R}^3$ . We used a 5-layer Gaussian-activated network with 256 neurons. We used $\\sigma = 0.05$ for the Gaussian activation. We trained the network using mini-batches of size 512. We compared the training convergence of different preconditioners and the Adam optimizer on the lion instance from the DIV2K dataset [1] in Fig. 5a. Additional results on the rest of the DIV2K dataset are provided in the supplementary material. As predicted by Theorem 4.2, Gaussian network equipped with the dense Hessian-vector product exhibits faster convergence when optimized with curvature-aware preconditioned methods compared to Adam. Notably, ESGD demonstrates faster convergence and has comparable training time and memory usage per iteration compared to Adam.", + "bbox": [ + 511, + 566, + 908, + 821 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://github.com/crowsonkb/esgd", + "bbox": [ + 532, + 830, + 725, + 844 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3https://github.com/amirgholami/adahes", + "bbox": [ + 532, + 844, + 745, + 856 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "4https://github.com/google-research/google-", + "bbox": [ + 532, + 856, + 764, + 868 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "research/tree/master/scalable_shampoo/pytorch", + "bbox": [ + 514, + 868, + 764, + 880 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "5https://github.com/Thrandis/EKFAC-pytorch", + "bbox": [ + 532, + 880, + 774, + 893 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27227", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/99f8da22605ca54d3f70f804bee1b6eba7543f4e1d988b4497c36a9357accd50.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 214, + 93, + 493, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/87496d8c5dd8a872aa627cf97ed9b257a395f62be382dfa107f31eda11a4a87a.jpg", + "image_caption": [ + "(b)", + "Figure 5. Comparison of training convergence and computational complexity for various preconditioners. We evaluated a Gaussian-activated neural field on the lion instance from the DIV2K dataset. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: We provide the time-based comparisons in the supplementary material (Sec 3.1). Similar analysis for other activations and additional instances from the DIV2K dataset are available in the supplementary material (Sec. 3.2)." + ], + "image_footnote": [], + "bbox": [ + 503, + 90, + 781, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ESGD and AdaHessian obtain Hessian information by computing Hessian-vector products, which makes them very computational efficient. Each Hessian-vector product is generally as fast as a single gradient computation, as demonstrated in Fig. 5b. In contrast, other preconditioners, particularly Shampoo are more computationally expensive because they involve Kronecker product computations for preconditioner matrices, see supp. material for details.", + "bbox": [ + 89, + 386, + 483, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. 3D Binary Occupancy Reconstruction", + "text_level": 1, + "bbox": [ + 89, + 516, + 416, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluated on learning a binary occupancy field, where given 3D point coordinates $\\mathbf{x} \\in \\mathbb{R}^3$ , we optimized a neural network to represent the occupancy field of 3D shapes. Following existing works [22], we sampled one million 3D points for training - one-third of the points were sampled uniformly within the volume, and the remaining two-thirds of the points were sampled near the mesh surface and perturbed with random Gaussian noise using sigma of 0.1 and 0.01, respectively [22]. We trained the network using binary cross-entropy (BCE) loss, which compares the predicted occupancy and the true occupancy. We used a 5-layer Gaussian network with 256 neurons and $\\sigma = 0.09$ . We trained the network using mini-batches of size 50000.", + "bbox": [ + 89, + 537, + 482, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compared the training convergence of different preconditioners and the Adam optimizer on the armadillo instance from the Stanford 3D Scanning dataset. Fig. 6 shows that ESGD exhibits superior convergence than other preconditioner-type optimizers. We showcase a qualitative result comparing the mesh reconstruction of ESGD and Adam given the same number of iteration in Fig. 7. Interestingly, when dealing with higher mode signals, both AdaHessian and Shampoo no longer demonstrated superior convergence,", + "bbox": [ + 89, + 734, + 491, + 872 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "unlike in the 2D image reconstruction task in Fig. 5a. We speculate that the local Hessians may become noisy with higher mode signals, thereby impacting the gradient updates. In contrast, this noise did not significantly affect ESGD's convergence because its preconditioner updates were performed every $N$ iterations. Hence, we will focus on comparing Adam and ESGD for the experiments in the following section.", + "bbox": [ + 511, + 386, + 913, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Neural Radiance Fields (NeRF)", + "text_level": 1, + "bbox": [ + 511, + 516, + 790, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Neural Radiance Fields (NeRF) have recently emerged as a pioneering approach in novel view synthesis, utilizing neural networks to model volumetric fields of 3D scenes using", + "bbox": [ + 511, + 537, + 906, + 584 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ea9ea563ce0c03cf9e8472dc52508e1d0380337a68ef3344324c413917a4da05.jpg", + "image_caption": [ + "Figure 6. Comparison of training convergence for various preconditioners. We evaluated a Gaussian-activated neural field on a 3D binary occupancy reconstruction task on the armadillo instance. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: Similar analysis for other activations are available in the supplementary material." + ], + "image_footnote": [], + "bbox": [ + 557, + 609, + 859, + 789 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "6http://graphics.stanford.edu/data/3Dscanrep/", + "bbox": [ + 107, + 878, + 351, + 893 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27228", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b5c0a6fd6c06cbf1fc0384f66b0566c6cfb376edaf8b902907187374cc9f13d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SceneTrain PSNRIteration ↓Time (s)↓Adam TestIteration ↓Time (s)↓ESGD Test
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
fern25.38200K368.4324.380.740.28120K270.8124.410.740.30
flower29.17200K469.3125.670.780.12120K263.9325.650.780.13
horns24.9560K130.8221.820.700.34120K227.5820.780.630.44
orchids23.3200K501.9019.560.610.24120K269.0119.740.610.21
room31.20110K194.0531.600.930.12140K201.8830.520.900.20
fortress30.18140K333.7028.930.810.15140K334.5628.60.800.17
leaves21.36200K482.3419.560.610.24120K271.2519.430.590.25
trex25.5080K164.9622.040.710.31120K209.2522.210.750.23
", + "bbox": [ + 91, + 88, + 936, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Quantitative results of NeRF on all instances from the LLFF dataset [31]. The reported time solely refers to the optimization update step. Note: Results for the Blender synthetic [32] and BLEFF [60] datasets are available in supplementary material.", + "bbox": [ + 89, + 281, + 906, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/58924fec6d51fdaf675756065544bbb0fdd50e69b56253961a237a7bec04c21a.jpg", + "image_caption": [ + "(a)", + "Figure 7. Qualitative results for the dragon instance from Stanford 3D Scanning dataset. Compared to the Gaussian-based neural field trained with Adam (Fig. 7a), ESGD (Fig. 7b) has reconstructed the shapes with significantly improved fidelity at epoch 500 (zoom in $4 \\times$ for better visibility). Note: Qualitative results for the rest of the instances from Stanford 3D Scanning Dataset are available in supplementary material." + ], + "image_footnote": [], + "bbox": [ + 99, + 340, + 279, + 472 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9973ee219ba2dc58b28c0fad3cfc16fd83922fdaedec8a11e53452f4d5482c23.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 290, + 340, + 468, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "multi-view 2D images [12, 13, 26, 32, 44]. Specifically, given 3D points $\\mathbf{x} \\in \\mathbb{R}^3$ and viewing direction, NeRF estimates the 5D radiance field of a 3D scene which maps each input 3D coordinate to its corresponding volume density $\\sigma \\in \\mathbb{R}$ and directional emitted color $\\mathbf{c} \\in \\mathbb{R}^3$ [12, 26, 32]. We used an 8-layer Gaussian-activated network with 256 neurons and $\\sigma = 0.1$ . Recall that in the previous section we demonstrated that ESGD exhibited superior performance in terms of convergence and computational complexity compared to other preconditioners. Therefore, we focused on comparing Adam and ESGD here. We determined the same training PSNR at which both model converged and reported the corresponding optimization metrics, including the number of iterations and the total time taken for the update computation. We evaluated the PSNR on a hold-out test scene. Table 1. shows that ESGD achieves on average faster convergence than Adam, see more results in the supp. material.", + "bbox": [ + 89, + 619, + 482, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 511, + 335, + 635, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While our work theoretically established the suitability of curvature-aware preconditioners for training neural fields with non-traditional activations such as sine, Gaussian, and wavelets, it also highlighted their ineffectiveness for neural fields employing ReLU-PE activations. Specifically, we showed that Adam performs well for ReLU-PE due to its use of a diagonal preconditioner derived from the Gauss-Newton matrix, rather than relying on Hessian vector products. However, this raises an important limitation of our work: we did not explore whether alternative preconditioners, potentially more effective than the Gauss-Newton matrix, could be developed to improve the training of ReLU-PE activated neural fields beyond what Adam achieves. This is particularly relevant since ReLU-PE remains widely used in practical applications. This question represents an avenue for future research, which we leave it as future work.", + "bbox": [ + 511, + 359, + 906, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 614, + 633, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We explored the impact of preconditioners on the stochastic training of neural fields, developing a theoretical framework based on Hessian-vector products. Our analysis demonstrates that curvature-aware preconditioners can significantly accelerate training for neural fields with non-traditional activations, such as sine, Gaussian, and wavelet. Experimental validation across various tasks—including image reconstruction, shape modeling, and neural radiance fields—using ESGD and AdaHessian confirmed these benefits. In contrast, for neural fields with ReLU or ReLU-PE activations, our theory predicted no significant advantage from curvature-aware preconditioning, highlighting the activation-dependent nature of these methods. For practitioners employing activations like sine, Gaussian, or wavelet, robust curvature-aware algorithms provide an efficient approach for stochastic training across diverse applications.", + "bbox": [ + 511, + 640, + 913, + 883 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27229", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12786-12796, 2022. 2" + ], + "bbox": [ + 91, + 92, + 480, + 652 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "27232", + "bbox": [ + 478, + 943, + 517, + 954 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_model.json b/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c2feb1f773e8fe40ee8048c9a05c8259a0b15e08 --- /dev/null +++ b/2025/Preconditioners for the Stochastic Training of Neural Fields/b8f2c34c-ad8b-45bc-bfac-d02839f8ad19_model.json @@ -0,0 +1,2587 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.198, + 0.131, + 0.802, + 0.154 + ], + "angle": 0, + "content": "Preconditioners for the Stochastic Training of Neural Fields" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.187, + 0.757, + 0.227 + ], + "angle": 0, + "content": "Shin-Fang Chng* Hemanth Saratchandran* Simon Lucey Australian Institute of Machine Learning, University of Adelaide." + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.238, + 0.361, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.224, + 0.422, + 0.241, + 0.433 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.238, + 0.624, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.486, + 0.422, + 0.504, + 0.433 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.239, + 0.893, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.754, + 0.422, + 0.771, + 0.433 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.442, + 0.23, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.548, + 0.172, + 0.557 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.442, + 0.364, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.289, + 0.548, + 0.305, + 0.557 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.434, + 0.496, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.424, + 0.548, + 0.439, + 0.557 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.434, + 0.629, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.548, + 0.573, + 0.558 + ], + "angle": 0, + "content": "(g)" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.442, + 0.763, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.548, + 0.706, + 0.557 + ], + "angle": 0, + "content": "(h)" + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.442, + 0.898, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.548, + 0.838, + 0.557 + ], + "angle": 0, + "content": "(i)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.559, + 0.907, + 0.671 + ], + "angle": 0, + "content": "Figure 1. We demonstrate that curvature-aware preconditioners can significantly accelerate training convergence for neural fields with suitable activations. Specifically, ESGD (a curvature-aware preconditioned gradient descent algorithm [14]) improves convergence for wavelet, sine, and Gaussian activations, while Adam performs better for ReLU network with positional encoding (ReLU(PE)). In a \\(2D\\) image reconstruction task (Fig. 1a), a wavelet-based neural field trained with ESGD achieves 29.36 PSNR (Fig. 1e) at the \\(10^{\\mathrm{th}}\\) epoch, outperforming Adam's 26.61 PSNR (Fig. 1d). In a \\(3D\\) binary occupancy task (Fig. 1b), ESGD enables faster convergence for sine activations, as shown by the improved armadillo mesh reconstruction at the \\(1000^{\\mathrm{th}}\\) epoch (Fig. 1g vs. Fig. 1f). In a Neural Radiance Fields (NeRF) task (Fig. 1c), a Gaussian-based model trained with ESGD achieves lower reconstruction error (Fig. 1i, 0.0695) compared to Adam (Fig. 1h, 0.0743), as seen in the error map (darker areas indicate lower error; zoom in \\(4\\times\\) for clarity)." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.683, + 0.327, + 0.699 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.714, + 0.486, + 0.866 + ], + "angle": 0, + "content": "Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effec" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.685, + 0.907, + 0.714 + ], + "angle": 0, + "content": "tiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF) \\(^{1}\\)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.743, + 0.646, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.768, + 0.907, + 0.86 + ], + "angle": 0, + "content": "In recent years, neural fields, also known as implicit neural representations, have garnered significant attention in machine learning and computer graphics [8, 9, 25, 32, 53-55, 57]. Unlike traditional grid-based representations [6, 17, 56, 64], neural fields implicitly encode shapes and objects through neural networks. These representations are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.874, + 0.483, + 0.899 + ], + "angle": 0, + "content": "\\(^{1}\\) *Equal contribution.> Correspondence to: Shin-Fang Chng ." + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.868, + 0.905, + 0.894 + ], + "angle": 0, + "content": "Source code is available at https://github.com/sfchng/preconditioner_neural_fields.git." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "27222" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "highly efficient for capturing complex, high-resolution signals, making them well-suited for tasks such as image synthesis [9, 55], shape modeling [32, 53], and robotics [10, 59]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.488, + 0.272 + ], + "angle": 0, + "content": "Classically, neural fields trained with ReLU activations suffer from spectral bias and limited fidelity [40]. To address this, positional encoding (PE) layers [58] were introduced but at the cost of increased model complexity and noisy gradients. More recent work has explored non-standard activations, such as sine [54], Gaussian [41] and wavelets [49] which enable high-frequency encoding without positional encodings and produce well-behaved gradients [50]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.273, + 0.486, + 0.499 + ], + "angle": 0, + "content": "While neural fields have enabled realistic and efficient representations of continuous signals, progress on minimizing the training time of such representations remains a significant research challenge. Currently, the Adam optimizer is the de facto algorithm for training neural fields, particularly in applications involving datasets where a stochastic training regime is essential. Yet, the preference for Adam over simpler alternatives such as stochastic gradient descent (SGD) has not been rigorously justified for neural fields, despite its widespread adoption. Notably, [50] demonstrated substantial gains in training speed for neural fields using second-order optimizers such as L-BFGS [34]. However, second-order methods are often impractical for stochastic settings [50], limiting their effectiveness for large-scale data, where stochastic training is essential." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.493, + 0.68 + ], + "angle": 0, + "content": "In this paper, we approach neural field training from the perspective of preconditioning. Preconditioners improve convergence by reducing the condition number of the optimization problem [4, 34, 46]. We develop a theoretical framework linking Adam's performance to its implicit use of a diagonal preconditioner derived from the Gauss-Newton matrix and proceed to identify conditions under which curvature-aware diagonal preconditioners, such as those in ESGD (equilibrated stochastic gradient descent) [14], enhance training for neural fields with sine, Gaussian, or wavelet activations. For ReLU activations, we show that such preconditioning provides limited benefit." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.681, + 0.496, + 0.877 + ], + "angle": 0, + "content": "Our experiments validate the proposed framework across a range of tasks, including 2D image reconstruction, 3D binary occupancy, and Neural Radiance Fields (NeRF). As demonstrated in Fig. 1, ESGD consistently outperforms Adam for neural fields with wavelet, sine, and Gaussian activations, which, as predicted by our theory, is due to their better-conditioned Hessians. In contrast, Adam performs better for ReLU-PE activations, which are associated with poorly conditioned Hessians. Furthermore, we evaluated other curvature-aware algorithms, including ESGD, Ada-Hessian [62], Shampoo [21], and K-FAC [30], offering valuable insights into their effectiveness in stochastic training settings." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.878, + 0.295, + 0.892 + ], + "angle": 0, + "content": "Our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "1. We present a theoretical framework for preconditioning in neural field training, uncovering key conditions and highlighting when preconditioning is beneficial." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.137, + 0.905, + 0.197 + ], + "angle": 0, + "content": "2. We empirically validate our framework, demonstrating the superiority of curvature-aware algorithms like ESGD over Adam across diverse tasks, including image reconstruction, 3D shape modeling, and NeRF." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.092, + 0.905, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.211, + 0.655, + 0.227 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.236, + 0.918, + 0.508 + ], + "angle": 0, + "content": "Neural Fields represent signals as weights within a neural network, using low-dimensional coordinates to maintain smoothness in the output [64]. The influential work by Mildenhall et al. [32] showcased the potential of neural fields for novel view synthesis, demonstrating their impressive generalization capabilities. Since then, neural fields have seen widespread application across image view synthesis, shape reconstruction, and robotics [7, 11, 12, 15, 18, 33, 35, 36, 38, 42, 47, 48, 54, 60, 63, 65]. Traditionally, these approaches integrate a positional embedding layer to counteract the spectral bias introduced by ReLU activations [40]. However, recent work has explored alternative, non-standard activations such as sine [54], Gaussian [41], wavelets [49], and sinc [51]. These activations have shown to outperform conventional approaches in various vision tasks, delivering enhanced performance in capturing high-frequency details and reducing reliance on positional embeddings [12, 29, 41, 49, 54, 61]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.526, + 0.911, + 0.844 + ], + "angle": 0, + "content": "Preconditioners were initially introduced in numerical linear algebra [20, 46] to transform ill-conditioned linear systems into well-conditioned forms, thereby accelerating the convergence of iterative solvers. Over time, preconditioning techniques have become integral to machine learning, where they enhance the efficiency and performance of optimization algorithms. Early applications in machine learning can be traced to foundational optimization methods, such as the conjugate gradient method and its variants [34]. As machine learning problems have grown more complex—often involving sparse matrices, non-convex objectives, and large-scale datasets—researchers have developed specialized preconditioning strategies to meet these unique challenges [3, 24, 39, 43]. Many widely-used optimizers incorporate preconditioning, including methods like ADMM [27], mirror descent [2], quasi-Newton methods [5, 19, 34], and adaptive optimizers [14, 16, 21, 30, 62]. These preconditioned optimizers have become essential for addressing the complex landscapes of modern machine learning models, driving improvements in both convergence speed and solution quality." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "27223" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.191, + 0.106 + ], + "angle": 0, + "content": "3. Notation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.486, + 0.207 + ], + "angle": 0, + "content": "The neural fields we consider in this paper will be defined by a depth \\(L\\) neural network with layer widths \\(\\{n_1,\\dots ,n_L\\}\\). We let \\(X\\in \\mathbb{R}^{N\\times n_0}\\) denote the training data, with \\(n_0\\) being the dimension of the input and \\(N\\) being the number of training samples. The output at layer \\(k\\) will be denoted by \\(F_{k}\\) and is defined by" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.214, + 0.483, + 0.268 + ], + "angle": 0, + "content": "\\[\nF _ {k} = \\left\\{ \\begin{array}{l l} F _ {L - 1} W _ {L} + b _ {L}, & k = L \\\\ \\phi \\left(F _ {k - 1} W _ {k} + b _ {k}\\right), & k \\in [ L - 1 ] \\\\ X, & k = 0 \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.277, + 0.485, + 0.43 + ], + "angle": 0, + "content": "where the weights \\( W_{k} \\in \\mathbb{R}^{n_{k - 1} \\times n_{k}} \\) and the biases \\( b_{k} \\in \\mathbb{R}^{n_{k}} \\) and \\( \\phi \\) is an activation applied component wise. The notation \\( [m] \\) is defined by \\( [m] = \\{1, \\dots, m\\} \\). We will denote the loss function that we train the neural fields with by \\( \\mathcal{L} \\). In many experiments in the paper this will be the MSE loss [37]. Our theoretical results will be primarily for the case where \\( \\phi \\) is given by one of the activation sine, Gaussian, wavelet or ReLU. For more details on how these activations are used within the context of neural fields we refer the reader to [41, 49, 54]." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.441, + 0.317, + 0.456 + ], + "angle": 0, + "content": "4. Theoretical Framework" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.466, + 0.347, + 0.48 + ], + "angle": 0, + "content": "4.1. Overview of Preconditioners" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.488, + 0.484, + 0.563 + ], + "angle": 0, + "content": "Preconditioning enhances optimization convergence and efficiency by regulating curvature, particularly in stochastic gradient descent (SGD) [14, 39]. High curvature directions in SGD require a small learning rate to avoid overshooting, leading to slow progress in low curvature directions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.564, + 0.484, + 0.64 + ], + "angle": 0, + "content": "For general objective functions \\( f \\) on parameters \\( \\mathbf{x} \\in \\mathbb{R}^n \\). Preconditioning is done by employing a linear change of parameters \\( \\widetilde{\\mathbf{x}} = D^{\\frac{1}{2}}\\mathbf{x} \\), where in practise \\( D^{\\frac{1}{2}} \\) is a non-singular matrix. With this change of parameters a new objective function \\( \\widetilde{f} \\), defined on \\( \\widetilde{\\mathbf{x}} \\), can be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.24, + 0.645, + 0.483, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\widetilde {f} (\\widetilde {\\mathbf {x}}) = f (\\mathbf {x}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.484, + 0.718 + ], + "angle": 0, + "content": "Denoting the gradient of the original objective function by \\(\\nabla f\\) and its Hessian by \\(H(f) = \\nabla^2 f(\\mathbf{x})\\). The chain rule gives" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.724, + 0.482, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\nabla \\widetilde {f} (\\widetilde {\\mathbf {x}}) = D ^ {- \\frac {1}{2}} \\nabla f \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.747, + 0.483, + 0.767 + ], + "angle": 0, + "content": "\\[\nH (\\widetilde {f}) (\\widetilde {\\mathbf {x}}) = \\left(D ^ {- \\frac {1}{2}}\\right) ^ {T} \\left(H (f) (\\mathbf {x})\\right) \\left(D ^ {- \\frac {1}{2}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.774, + 0.484, + 0.831 + ], + "angle": 0, + "content": "Equation (3) exhibits the key idea of training with a preconditioner. If we consider gradient descent on the transformed parameter space, a gradient descent iteration takes the form" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.832, + 0.483, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {x}} _ {t} = \\widetilde {\\mathbf {x}} _ {t - 1} - \\eta \\nabla_ {\\widetilde {\\mathbf {x}} _ {t - 1}} \\widetilde {f} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.854, + 0.483, + 0.883 + ], + "angle": 0, + "content": "Applying equations (2) and (3) this corresponds to doing the update" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.884, + 0.483, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\mathbf {x} _ {t - 1} - \\eta D ^ {- \\frac {1}{2}} \\nabla_ {\\mathbf {x} _ {t - 1}} f. \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.198 + ], + "angle": 0, + "content": "The main endeavour of preconditioning for optimization is to find a preconditioning matrix \\( D \\) such that the new Hessian, given by equation (4), has equal curvature in all directions. This will allow the update (6) to move faster along small curvature directions, leading to faster convergence. Algorithm 1 gives the basic pseudocode for preconditioned SGD." + }, + { + "type": "title", + "bbox": [ + 0.516, + 0.209, + 0.743, + 0.223 + ], + "angle": 0, + "content": "Algorithm 1 Preconditioned SGD" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.228, + 0.905, + 0.258 + ], + "angle": 0, + "content": "Require: initial point \\( x_0 \\), iterations \\( N \\), learning rate \\( \\eta \\), preconditioner \\( D \\)." + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.258, + 0.735, + 0.321 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {f o r} t = 0, \\dots , N \\mathbf {d o} \\\\ g _ {t} \\leftarrow \\nabla_ {x _ {t}} f \\\\ D _ {t} \\leftarrow D (x _ {t}) \\\\ x _ {t + 1} \\leftarrow x _ {t} - \\eta D (x _ {t}) ^ {- \\frac {1}{2}} g _ {t} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.321, + 0.586, + 0.333 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.355, + 0.907, + 0.49 + ], + "angle": 0, + "content": "From Eq. (4) we see that the best preconditioner to use would be the absolute value of the Hessian itself. In the case of a positive definite Hessian, this is precisely what Newton's method does [34]. The main issue with this preconditioner is that the cost of storing and inverting the preconditioner will be \\(\\mathcal{O}(n^3)\\) for an objective function of \\(n\\) parameters [34]. This will be extremely costly for the training of overparameterized neural networks whose Hessians are extremely large." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.491, + 0.906, + 0.52 + ], + "angle": 0, + "content": "We list some of the main preconditioners that are being used in the literature." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.539, + 0.922, + 0.903 + ], + "angle": 0, + "content": "Diagonal Preconditioners: are matrices that represent some form of a diagonal approximation of the Hessian. Examples include the Jacobi preconditioner, which is given by \\( D^{J} = |\\operatorname{diag}(H)| \\), where \\( |\\cdot| \\) is element-wise absolute value and \\( H \\) is the Hessian. In practical settings, the absolute value is taken so that the preconditioner is positive semidefinite. The equilibration preconditioner is a diagonal matrix which has the 2-norm of each row (or column) on the diagonal: \\( D^{E} = ||H_{i,\\cdot}|| \\). The preconditioners \\( D^{J} \\) and \\( D^{E} \\) are known as curvature-aware preconditioners as they seek to give a good approximation to the Hessian. Diagonal preconditioners are often used because of their ability to be stored and inverted in linear time. Diagonal preconditioners are also known as adaptive learning rates in the literature. The algorithm Equilibrated Stochastic Gradient Descent (ESGD) [14] employs \\( D^{E} \\) as a preconditioner to condition stochastic gradient descent. In [14], it is shown that applying ESGD leads to faster training times for autoencoder tasks when compared to vanilla SGD, RMSProp [45] and a preconditioned SGD using \\( D^{J} \\) as preconditioner. AdaHessian [62] is a recent algorithm that applies a diagonal preconditioner in the setting of moving averages and thus can be seen as a way of enhancing the Adam optimizer [23]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "27224" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "Kronecker Factored Preconditioners: are preconditioners of the form \\( D = A^T A \\), where \\( A = A_1 \\otimes \\dots \\otimes A_k \\) and \\( \\otimes \\) denotes the Kronecker product. The algorithm K-FAC [30] employs a Kronecker factored preconditioner." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.258 + ], + "angle": 0, + "content": "Others: There are several second order optimisation algorithms that use preconditioners that do not fall into the above three categories such as, The Gauss-Newton method, The Conjugate Gradient method, Limited memory Broyden-Fisher-Golfarb-Shanno (L-BFGS) [34]. It was shown in [50] that these algorithms do not train well in stochastic settings." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.266, + 0.273, + 0.28 + ], + "angle": 0, + "content": "4.2. Condition Number" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.287, + 0.484, + 0.349 + ], + "angle": 0, + "content": "In Sec. 4.1, we explained that SGD will move faster through the loss landscape when the curvatures in each direction are similar. The regularity of the loss landscape at a point is quantified via the condition number of the Hessian." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.355, + 0.484, + 0.387 + ], + "angle": 0, + "content": "Definition 4.1. Given a matrix \\( A \\) we define the condition number \\( \\kappa \\) of \\( A \\) by" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.392, + 0.483, + 0.426 + ], + "angle": 0, + "content": "\\[\n\\kappa (A) := \\frac {\\sigma_ {\\operatorname* {m a x}} (A)}{\\sigma_ {\\operatorname* {m i n}} (A)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.432, + 0.489, + 0.538 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the eigenvalue. Using Eq. (4) we observe that if we take a preconditioner \\(D\\) such that \\(\\kappa((D^{-\\frac{1}{2}})^T(H(f)(\\mathbf{x}))(D^{-\\frac{1}{2}}))\\) is closer to 1 than \\(\\kappa(H)\\), then this implies that the preconditioner \\(D\\) is regularising the curvatures of the landscape to be equal in each direction, which yields a better training landscape for a gradient descent based algorithm [34]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.497, + 0.78 + ], + "angle": 0, + "content": "To empirically illustrate the concept of preconditioning, we examined a one-dimensional curve fitting scenario. Specifically, we considered a feedforward network with two hidden layers, each containing 16 neurons, tasked with fitting the signal \\( f(x) = \\sin (2\\pi x) + \\sin (6\\pi x) \\) using a Gaussian activation [41]. During optimization with gradient descent, we applied two types of preconditioners: an equilibrated preconditioner \\( D^{E} \\) and a Jacobi preconditioner \\( D^{J} \\). At each optimization step, we computed both the original Hessian associated with gradient descent and the transformed Hessian using Eq. (4). As shown in Fig. 2, the results demonstrate that applying either the Jacobi or equilibrated preconditioner consistently reduced the condition number of the Hessian compared to the unconditioned case, highlighting the effectiveness of preconditioning in improving optimization." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.285, + 0.804 + ], + "angle": 0, + "content": "4.3. Training with Adam" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.9 + ], + "angle": 0, + "content": "In this section, we aim to explain why training with Adam is generally more efficient than training with SGD for a variety of neural fields. While this observation is well-known within the community, we include it here to provide context and motivation for the theoretical framework developed in Sec. 4.4." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.092, + 0.707, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.21, + 0.621, + 0.221 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.097, + 0.898, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.209, + 0.814, + 0.22 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.222, + 0.905, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Fig. 2a compares the condition number (7) on a 1D signal regression task before (dotted line) and after (solid line) applying equilibrated \\( D^{E} \\) and Jacobi \\( D^{J} \\) preconditioners. The equilibrated preconditioner significantly reduces the Hessian's condition number, as shown by the larger gap between the yellow solid and dotted lines compared to the green solid and dotted lines representing the Jacobi preconditioner, thus achieves faster convergence as seen in Fig. 2b." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.906, + 0.435 + ], + "angle": 0, + "content": "Given an objective function \\( L(\\theta) = |f(\\theta)|^2 \\) for a nonlinear function \\( f \\). The Jacobian \\( J_{L} \\) of \\( L \\) can be computed via the chain rule: \\( J_{L} = 2J_{f}^{T}f \\), where \\( J_{f} \\) denotes the Jacobian of \\( f \\). The Hessian of \\( L \\), \\( H_{L} \\), can be computed by an application of the chain rule" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.443, + 0.905, + 0.462 + ], + "angle": 0, + "content": "\\[\nH _ {L} = 2 J _ {f} ^ {T} J _ {f} + 2 H _ {f} f. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.473, + 0.913, + 0.504 + ], + "angle": 0, + "content": "We can then approximate the Hessian \\(H_{L}\\) by the term \\(2J_{f}^{T}J_{f}\\). Leading to the first order approximation" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.513, + 0.905, + 0.545 + ], + "angle": 0, + "content": "\\[\nH _ {L} \\approx 2 J _ {f} ^ {T} J _ {f} = \\frac {1}{2 | f | ^ {2}} J _ {L} ^ {T} J _ {L} = \\frac {1}{2 L} J _ {L} ^ {T} J _ {L}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.922, + 0.75 + ], + "angle": 0, + "content": "Eq. (9) yields the basic idea of the Gauss-Newton method. By taking the Gauss-Newton matrix \\( J_{L}^{T}J_{L} \\) as an approximation to the Hessian \\( H_{L} \\), we can perform an optimization update that uses the step: \\( \\Delta_{GN} = -\\frac{1}{J^TJ}\\nabla L \\). The Gauss-Newton matrix is in general only positive semi-definite. Therefore, when implementing the algorithm one often adds a small damping factor \\( \\lambda \\) so the implemented step is \\( \\Delta_{GN} = -\\frac{1}{J^TJ + \\lambda}\\nabla L \\). A similar derivation can be made for more general loss functions used in non-linear least squares type regression problems [34]. It follows that the Gauss-Newton method can be seen as a preconditioned SGD that uses a first order (first derivatives) Hessian approximate preconditioner given by the Gauss-Newton matrix \\( J^T J \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.911, + 0.902 + ], + "angle": 0, + "content": "Using the above observations we now show how to view Adam as an optimizer that applies a diagonal preconditioner. The Adam optimizer involves two key steps. The first is to compute a first moment estimate of the form \\( m_{t} = \\beta_{1}m_{t - 1} + (1 - \\beta_{1})g_{t} \\), where \\( g_{t} \\) is the gradient of a given objective function \\( f \\) at iteration \\( t \\), and \\( m_0 = 0 \\). The second is to compute a second moment estimate \\( v_{t} = \\beta_{2}v_{t - 1} + (1 - \\beta_{2})g_{t}^{2} \\), where \\( g_{t}^{2} = g_{t}\\odot g_{t},\\odot \\) denotes the Hadamard product, and \\( v_{0} = 0 \\). The numbers \\( 0 < \\beta_{1} < \\beta_{2} < 1 \\) are hyperparameters. The algorithm then applies a bias correction to the above first" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "27225" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.091, + 0.362, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.269, + 0.24, + 0.28 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.092, + 0.627, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.488, + 0.268, + 0.506, + 0.279 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.099, + 0.895, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.756, + 0.269, + 0.772, + 0.279 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.28, + 0.908, + 0.337 + ], + "angle": 0, + "content": "Figure 3. Comparison of training convergence for neural fields with different activations – ReLU with positional encoding (ReLU (PE)), wavelet, sine and Gaussian – using Adam and SGD optimizers across three tasks: 2D image reconstruction (Fig. 3a), 3D binary occupancy reconstruction (Fig. 3b), and NeRF (Fig. 3c). In all cases, the Adam optimizer outperforms SGD, indicating that leveraging curvature information facilitates faster convergence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.363, + 0.483, + 0.408 + ], + "angle": 0, + "content": "and second moment estimates, and then takes a moving average to perform an update step based on \\(-\\frac{m_t}{\\sqrt{v_t}}\\), see [23] for details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.5 + ], + "angle": 0, + "content": "For the following discussion, we will only focus on analyzing the second raw moment estimate, as this is related to the Gauss-Newton matrix. Given an objective function \\( f \\), observe that we can express \\( g_t^2 = g_t \\odot g_t = \\text{Diag}(J^T J) \\), where \\( J \\) denotes the Jacobian of \\( f \\). Thus the second raw moment estimate of Adam can be recast as:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.51, + 0.482, + 0.53 + ], + "angle": 0, + "content": "\\[\nv _ {t} = \\beta_ {2} v _ {t - 1} + (1 - \\beta_ {2}) \\operatorname {D i a g} \\left(J _ {t} ^ {T} J _ {t}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.484, + 0.66 + ], + "angle": 0, + "content": "where \\( J_{t} \\) denotes the Jacobian at iteration \\( t \\). Thus we see that Adam applies a preconditioner given by the diagonal of the Gauss-Newton matrix. Since the Gauss-Newton matrix can be seen as a first order approximation to the Hessian, Adam can be seen as using an approximation to curvature to adapt the learning rate for faster optimization. This suggests that Adam can outperform SGD which employs no preconditioner." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.661, + 0.484, + 0.812 + ], + "angle": 0, + "content": "We empirically validated this insight across three distinct neural field tasks: image reconstruction, binary occupancy, and NeRF. For each task, we compared the performance of ReLU(PE) activated networks trained with both SGD and Adam against networks using wavelet, sine, and Gaussian activations. As shown in Fig. 3, Adam consistently outperforms SGD in all cases. This suggests that Adam's use of a preconditioner significantly enhances its performance for neural field applications, see Sec. 5 for the details of the architectures and experimental setup." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.822, + 0.245, + 0.836 + ], + "angle": 0, + "content": "4.4. Main theorems" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.844, + 0.484, + 0.889 + ], + "angle": 0, + "content": "In Sec. 4.3, we discussed how Adam can be viewed as applying a diagonal preconditioner based on the diagonal of the Gauss-Newton matrix, which uses first derivatives to" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.362, + 0.853, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.53, + 0.907, + 0.599 + ], + "angle": 0, + "content": "Figure 4. Percentage sparsity of Hessian-vector product matrices across all layers throughout the training process of a 2D image reconstruction task, using ESGD to train networks with different activations. The x-axis ranges from 0 to 1, with values closer to 1 indicating higher sparsity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.906, + 0.746 + ], + "angle": 0, + "content": "approximate the Hessian matrix. Here, we aim to identify the architectural properties that enable effective training of neural fields with diagonal preconditioners that give a better approximation to the Hessian. Our primary theorems demonstrate that the choice of activation function is crucial for enabling efficient training with such preconditioners, highlighting its central role in achieving effective curvature-aware optimization for neural fields." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.746, + 0.907, + 0.852 + ], + "angle": 0, + "content": "Recall Sec. 4.1 that diagonal preconditioners such as the equilibrated precondition \\( D^{E} \\) or the Jacobi preconditioner \\( D^{J} \\) all involve the Hessian matrix. In the context of neural networks the Hessian of the loss landscape is often an extremely large matrix. Thus in practical settings one often replaces the Hessian with a Hessian vector product which is much cheaper to store [34]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.852, + 0.906, + 0.898 + ], + "angle": 0, + "content": "Our first theorem shows that the Hessian vector product of the loss landscape associated to a sine, Gaussian, wavelet or sinc activated neural field produces a dense vector." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "27226" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "Theorem 4.2. Let \\( F \\) denote a sine, Gaussian, wavelet or sinc activated neural field. Let \\( \\mathcal{L}(\\theta) \\) denote the MSE loss associated to \\( F \\) and a training set \\( (X,Y) \\). Let \\( H \\) denote the Hessian of \\( \\mathcal{L} \\) at a fixed parameter point \\( \\theta \\). Then given a non-zero vector \\( v \\) the Hessian vector product \\( Hv \\) will be a dense vector." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.192, + 0.485, + 0.254 + ], + "angle": 0, + "content": "While it may seem rather costly for a sine- or Gaussian-activated INR to have dense Hessian vector products when applied to the MSE loss function, we point out that the cost is much less than storing a dense Hessian." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.263, + 0.484, + 0.34 + ], + "angle": 0, + "content": "Theorem 4.3. Let \\( F \\) denote a ReLU/ReLU(PE)-activated neural field. Let \\( \\mathcal{L}(\\theta) \\) denote the MSE loss associated to \\( F \\) and a training set \\( (X, Y) \\). Let \\( H \\) denote the Hessian of \\( \\mathcal{L} \\) at a fixed parameter point \\( \\theta \\). Then given a non-zero vector \\( v \\) the Hessian vector product \\( Hv \\) will be a sparse vector." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.348, + 0.483, + 0.394 + ], + "angle": 0, + "content": "Theorem 4.2 and Theorem 4.3 also hold for the binary cross-entropy loss. The proofs of Theorem 4.2 and Theorem 4.3 are given in the Supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.394, + 0.485, + 0.664 + ], + "angle": 0, + "content": "Theorem 4.3 implies that when applying a preconditioner, built from a Hessian vector product, to a ReLU/ReLU(PE) INR, such as ESGD [14] or AdaHessian [62], only a few components of the gradient will be scaled during the update step. This means that the preconditioner will not be adding much to the optimization process. On the other hand, Theorem 4.2 implies that applying a preconditioner built from the Hessian to the gradient of the MSE loss of a sine, Gaussian and wavelet-activated neural field should help optimization as many of the gradient components will get scaled by a quantity depending on the curvature of the loss landscape. This yields a clear difference between ReLU/ReLU(PE) activated neural fields and those activated with a sine, Gaussian, wavelet activation. In particular, Theorem 4.2 implies that neural fields admitting a sine, Gaussian, wavelet activation have the ability to be trained efficiently with a diagonal curvature aware preconditioner such as the equilibrated preconditioner \\( D^{E} \\) defined in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.666, + 0.484, + 0.892 + ], + "angle": 0, + "content": "Fig. 4 shows the results of a Hessian vector product of the MSE loss of a ReLU(PE) and Gaussian neural field for an image reconstruction task for the weights in all layers of the network layer throughout training. The random vector was chosen from a Rademacher distribution and the reported figures are given as the mean of the Hessian of all layers averaged over all iterations of training. As demonstrated by the experiment, the ReLU(PE) network generates a sparse Hessian-vector product, as predicted by Theorem 4.3, while the Gaussian network produces a dense vector, as indicated by Theorem 4.2. Furthermore, as we will observe in Sec. 5, this sparsity helps explain why Adam performs well for neural fields with ReLU (ReLU(PE)) activations, whereas an algorithm like ESGD [14] does not. This is because Adam does not rely on Hessian-vector product." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.646, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.935, + 0.327 + ], + "angle": 0, + "content": "We compared various preconditioners over popular benchmarks [22, 28, 50, 52, 54]: 2D image reconstruction, 3D shape reconstruction and novel view synthesis with NeRF. Our primary focus was on curvature-aware preconditioners that are well-suited for the stochastic training of neural network. Specifically, we compared the following methods: ESGD \\([14]^2\\), AdaHessian \\([62]^3\\), Shampoo \\([21]^4\\), and Kronecker-based preconditioner \\([30]^5\\). We provide the details of each algorithm including the reproducibility details of each experiment and machines we used to run each experiment in the supplementary material. In the main paper, we focused on analyzing Gaussian networks, see supplementary material for additional analysis for other non-traditional activations and other neural field tasks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.333, + 0.907, + 0.439 + ], + "angle": 0, + "content": "Remark for AdaHessian We observed that in the implementation of AdaHessian, an equilibrated preconditioner \\( D^{E} \\) is utilized, even though the paper primarily focuses on using a Jacobi preconditioner [14]. Therefore, we introduced a Jacobi preconditioner \\( D^{J} \\) into AdaHessian, which we refer to as AdaHessian(J). We use the term AdaHessian(E) for the original implementation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.444, + 0.907, + 0.535 + ], + "angle": 0, + "content": "Remark for ESGD We further modified the ESGD by applying the squared Hessian diagonal preconditioner in two settings: using an exponential moving average (ESGD) and using an infinity norm (ESGD-max) [23]. We also opted to recompute the \\( D^{E} \\) for every \\( N \\) iterations for computational efficiency, we use \\( N = 100 \\) for all the experiments." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.545, + 0.72, + 0.56 + ], + "angle": 0, + "content": "5.1. Image Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.909, + 0.822 + ], + "angle": 0, + "content": "We evaluated on a 2D image reconstruction task, where given pixel coordinates \\(\\mathbf{x} \\in \\mathbb{R}^2\\), we optimized a neural network to regress the corresponding RGB values \\(c \\in \\mathbb{R}^3\\). We used a 5-layer Gaussian-activated network with 256 neurons. We used \\(\\sigma = 0.05\\) for the Gaussian activation. We trained the network using mini-batches of size 512. We compared the training convergence of different preconditioners and the Adam optimizer on the lion instance from the DIV2K dataset [1] in Fig. 5a. Additional results on the rest of the DIV2K dataset are provided in the supplementary material. As predicted by Theorem 4.2, Gaussian network equipped with the dense Hessian-vector product exhibits faster convergence when optimized with curvature-aware preconditioned methods compared to Adam. Notably, ESGD demonstrates faster convergence and has comparable training time and memory usage per iteration compared to Adam." + }, + { + "type": "page_footnote", + "bbox": [ + 0.533, + 0.832, + 0.726, + 0.845 + ], + "angle": 0, + "content": "\\(^{2}\\)https://github.com/crowsonkb/esgd" + }, + { + "type": "page_footnote", + "bbox": [ + 0.534, + 0.845, + 0.746, + 0.857 + ], + "angle": 0, + "content": "3https://github.com/amirgholami/adahes" + }, + { + "type": "page_footnote", + "bbox": [ + 0.534, + 0.857, + 0.765, + 0.869 + ], + "angle": 0, + "content": "4https://github.com/google-research/google-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.869, + 0.765, + 0.881 + ], + "angle": 0, + "content": "research/tree/master/scalable_shampoo/pytorch" + }, + { + "type": "page_footnote", + "bbox": [ + 0.534, + 0.881, + 0.776, + 0.894 + ], + "angle": 0, + "content": "5https://github.com/Thrandis/EKFAC-pytorch" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.832, + 0.776, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "27227" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.215, + 0.094, + 0.495, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.279, + 0.362, + 0.291 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.092, + 0.782, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.279, + 0.649, + 0.29 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.291, + 0.907, + 0.361 + ], + "angle": 0, + "content": "Figure 5. Comparison of training convergence and computational complexity for various preconditioners. We evaluated a Gaussian-activated neural field on the lion instance from the DIV2K dataset. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: We provide the time-based comparisons in the supplementary material (Sec 3.1). Similar analysis for other activations and additional instances from the DIV2K dataset are available in the supplementary material (Sec. 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.387, + 0.484, + 0.509 + ], + "angle": 0, + "content": "ESGD and AdaHessian obtain Hessian information by computing Hessian-vector products, which makes them very computational efficient. Each Hessian-vector product is generally as fast as a single gradient computation, as demonstrated in Fig. 5b. In contrast, other preconditioners, particularly Shampoo are more computationally expensive because they involve Kronecker product computations for preconditioner matrices, see supp. material for details." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.517, + 0.418, + 0.533 + ], + "angle": 0, + "content": "5.2. 3D Binary Occupancy Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.483, + 0.735 + ], + "angle": 0, + "content": "We evaluated on learning a binary occupancy field, where given 3D point coordinates \\(\\mathbf{x} \\in \\mathbb{R}^3\\), we optimized a neural network to represent the occupancy field of 3D shapes. Following existing works [22], we sampled one million 3D points for training - one-third of the points were sampled uniformly within the volume, and the remaining two-thirds of the points were sampled near the mesh surface and perturbed with random Gaussian noise using sigma of 0.1 and 0.01, respectively [22]. We trained the network using binary cross-entropy (BCE) loss, which compares the predicted occupancy and the true occupancy. We used a 5-layer Gaussian network with 256 neurons and \\(\\sigma = 0.09\\). We trained the network using mini-batches of size 50000." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.736, + 0.493, + 0.873 + ], + "angle": 0, + "content": "We compared the training convergence of different preconditioners and the Adam optimizer on the armadillo instance from the Stanford 3D Scanning dataset. Fig. 6 shows that ESGD exhibits superior convergence than other preconditioner-type optimizers. We showcase a qualitative result comparing the mesh reconstruction of ESGD and Adam given the same number of iteration in Fig. 7. Interestingly, when dealing with higher mode signals, both AdaHessian and Shampoo no longer demonstrated superior convergence," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.387, + 0.915, + 0.508 + ], + "angle": 0, + "content": "unlike in the 2D image reconstruction task in Fig. 5a. We speculate that the local Hessians may become noisy with higher mode signals, thereby impacting the gradient updates. In contrast, this noise did not significantly affect ESGD's convergence because its preconditioner updates were performed every \\(N\\) iterations. Hence, we will focus on comparing Adam and ESGD for the experiments in the following section." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.517, + 0.791, + 0.533 + ], + "angle": 0, + "content": "5.3. Neural Radiance Fields (NeRF)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.539, + 0.907, + 0.585 + ], + "angle": 0, + "content": "Neural Radiance Fields (NeRF) have recently emerged as a pioneering approach in novel view synthesis, utilizing neural networks to model volumetric fields of 3D scenes using" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.61, + 0.861, + 0.79 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.792, + 0.907, + 0.889 + ], + "angle": 0, + "content": "Figure 6. Comparison of training convergence for various preconditioners. We evaluated a Gaussian-activated neural field on a 3D binary occupancy reconstruction task on the armadillo instance. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: Similar analysis for other activations are available in the supplementary material." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.88, + 0.352, + 0.894 + ], + "angle": 0, + "content": "6http://graphics.stanford.edu/data/3Dscanrep/" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "27228" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.937, + 0.273 + ], + "angle": 0, + "content": "
SceneTrain PSNRIteration ↓Time (s)↓Adam TestIteration ↓Time (s)↓ESGD Test
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
fern25.38200K368.4324.380.740.28120K270.8124.410.740.30
flower29.17200K469.3125.670.780.12120K263.9325.650.780.13
horns24.9560K130.8221.820.700.34120K227.5820.780.630.44
orchids23.3200K501.9019.560.610.24120K269.0119.740.610.21
room31.20110K194.0531.600.930.12140K201.8830.520.900.20
fortress30.18140K333.7028.930.810.15140K334.5628.60.800.17
leaves21.36200K482.3419.560.610.24120K271.2519.430.590.25
trex25.5080K164.9622.040.710.31120K209.2522.210.750.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.282, + 0.908, + 0.312 + ], + "angle": 0, + "content": "Table 1. Quantitative results of NeRF on all instances from the LLFF dataset [31]. The reported time solely refers to the optimization update step. Note: Results for the Blender synthetic [32] and BLEFF [60] datasets are available in supplementary material." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.342, + 0.28, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.18, + 0.486, + 0.198, + 0.496 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.342, + 0.47, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.485, + 0.391, + 0.496 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.497, + 0.483, + 0.595 + ], + "angle": 0, + "content": "Figure 7. Qualitative results for the dragon instance from Stanford 3D Scanning dataset. Compared to the Gaussian-based neural field trained with Adam (Fig. 7a), ESGD (Fig. 7b) has reconstructed the shapes with significantly improved fidelity at epoch 500 (zoom in \\(4 \\times\\) for better visibility). Note: Qualitative results for the rest of the instances from Stanford 3D Scanning Dataset are available in supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.62, + 0.483, + 0.879 + ], + "angle": 0, + "content": "multi-view 2D images [12, 13, 26, 32, 44]. Specifically, given 3D points \\(\\mathbf{x} \\in \\mathbb{R}^3\\) and viewing direction, NeRF estimates the 5D radiance field of a 3D scene which maps each input 3D coordinate to its corresponding volume density \\(\\sigma \\in \\mathbb{R}\\) and directional emitted color \\(\\mathbf{c} \\in \\mathbb{R}^3\\) [12, 26, 32]. We used an 8-layer Gaussian-activated network with 256 neurons and \\(\\sigma = 0.1\\). Recall that in the previous section we demonstrated that ESGD exhibited superior performance in terms of convergence and computational complexity compared to other preconditioners. Therefore, we focused on comparing Adam and ESGD here. We determined the same training PSNR at which both model converged and reported the corresponding optimization metrics, including the number of iterations and the total time taken for the update computation. We evaluated the PSNR on a hold-out test scene. Table 1. shows that ESGD achieves on average faster convergence than Adam, see more results in the supp. material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.336, + 0.637, + 0.351 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.361, + 0.908, + 0.603 + ], + "angle": 0, + "content": "While our work theoretically established the suitability of curvature-aware preconditioners for training neural fields with non-traditional activations such as sine, Gaussian, and wavelets, it also highlighted their ineffectiveness for neural fields employing ReLU-PE activations. Specifically, we showed that Adam performs well for ReLU-PE due to its use of a diagonal preconditioner derived from the Gauss-Newton matrix, rather than relying on Hessian vector products. However, this raises an important limitation of our work: we did not explore whether alternative preconditioners, potentially more effective than the Gauss-Newton matrix, could be developed to improve the training of ReLU-PE activated neural fields beyond what Adam achieves. This is particularly relevant since ReLU-PE remains widely used in practical applications. This question represents an avenue for future research, which we leave it as future work." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.616, + 0.634, + 0.632 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.641, + 0.914, + 0.884 + ], + "angle": 0, + "content": "We explored the impact of preconditioners on the stochastic training of neural fields, developing a theoretical framework based on Hessian-vector products. Our analysis demonstrates that curvature-aware preconditioners can significantly accelerate training for neural fields with non-traditional activations, such as sine, Gaussian, and wavelet. Experimental validation across various tasks—including image reconstruction, shape modeling, and neural radiance fields—using ESGD and AdaHessian confirmed these benefits. In contrast, for neural fields with ReLU or ReLU-PE activations, our theory predicted no significant advantage from curvature-aware preconditioning, highlighting the activation-dependent nature of these methods. For practitioners employing activations like sine, Gaussian, or wavelet, robust curvature-aware algorithms provide an efficient approach for stochastic training across diverse applications." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "27229" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. 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We demonstrate that curvature-aware preconditioners can significantly accelerate training convergence for neural fields with suitable activations. Specifically, ESGD (a curvature-aware preconditioned gradient descent algorithm [14]) improves convergence for wavelet, sine, and Gaussian activations, while Adam performs better for ReLU network with positional encoding (ReLU(PE)). In a $2D$ image reconstruction task (Fig. 1a), a wavelet-based neural field trained with ESGD achieves 29.36 PSNR (Fig. 1e) at the $10^{\mathrm{th}}$ epoch, outperforming Adam's 26.61 PSNR (Fig. 1d). In a $3D$ binary occupancy task (Fig. 1b), ESGD enables faster convergence for sine activations, as shown by the improved armadillo mesh reconstruction at the $1000^{\mathrm{th}}$ epoch (Fig. 1g vs. Fig. 1f). In a Neural Radiance Fields (NeRF) task (Fig. 1c), a Gaussian-based model trained with ESGD achieves lower reconstruction error (Fig. 1i, 0.0695) compared to Adam (Fig. 1h, 0.0743), as seen in the error map (darker areas indicate lower error; zoom in $4\times$ for clarity). + +![](images/6227585b6f4660dad18edd1d71ade7cdfa90928eea6dbc06e8b5ef853bd4ec6b.jpg) +(i) + +# Abstract + +Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effec + +tiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF) $^{1}$ . + +# 1. Introduction + +In recent years, neural fields, also known as implicit neural representations, have garnered significant attention in machine learning and computer graphics [8, 9, 25, 32, 53-55, 57]. Unlike traditional grid-based representations [6, 17, 56, 64], neural fields implicitly encode shapes and objects through neural networks. These representations are + +highly efficient for capturing complex, high-resolution signals, making them well-suited for tasks such as image synthesis [9, 55], shape modeling [32, 53], and robotics [10, 59]. + +Classically, neural fields trained with ReLU activations suffer from spectral bias and limited fidelity [40]. To address this, positional encoding (PE) layers [58] were introduced but at the cost of increased model complexity and noisy gradients. More recent work has explored non-standard activations, such as sine [54], Gaussian [41] and wavelets [49] which enable high-frequency encoding without positional encodings and produce well-behaved gradients [50]. + +While neural fields have enabled realistic and efficient representations of continuous signals, progress on minimizing the training time of such representations remains a significant research challenge. Currently, the Adam optimizer is the de facto algorithm for training neural fields, particularly in applications involving datasets where a stochastic training regime is essential. Yet, the preference for Adam over simpler alternatives such as stochastic gradient descent (SGD) has not been rigorously justified for neural fields, despite its widespread adoption. Notably, [50] demonstrated substantial gains in training speed for neural fields using second-order optimizers such as L-BFGS [34]. However, second-order methods are often impractical for stochastic settings [50], limiting their effectiveness for large-scale data, where stochastic training is essential. + +In this paper, we approach neural field training from the perspective of preconditioning. Preconditioners improve convergence by reducing the condition number of the optimization problem [4, 34, 46]. We develop a theoretical framework linking Adam's performance to its implicit use of a diagonal preconditioner derived from the Gauss-Newton matrix and proceed to identify conditions under which curvature-aware diagonal preconditioners, such as those in ESGD (equilibrated stochastic gradient descent) [14], enhance training for neural fields with sine, Gaussian, or wavelet activations. For ReLU activations, we show that such preconditioning provides limited benefit. + +Our experiments validate the proposed framework across a range of tasks, including 2D image reconstruction, 3D binary occupancy, and Neural Radiance Fields (NeRF). As demonstrated in Fig. 1, ESGD consistently outperforms Adam for neural fields with wavelet, sine, and Gaussian activations, which, as predicted by our theory, is due to their better-conditioned Hessians. In contrast, Adam performs better for ReLU-PE activations, which are associated with poorly conditioned Hessians. Furthermore, we evaluated other curvature-aware algorithms, including ESGD, Ada-Hessian [62], Shampoo [21], and K-FAC [30], offering valuable insights into their effectiveness in stochastic training settings. + +Our main contributions are: + +1. We present a theoretical framework for preconditioning in neural field training, uncovering key conditions and highlighting when preconditioning is beneficial. +2. We empirically validate our framework, demonstrating the superiority of curvature-aware algorithms like ESGD over Adam across diverse tasks, including image reconstruction, 3D shape modeling, and NeRF. + +# 2. Related Work + +Neural Fields represent signals as weights within a neural network, using low-dimensional coordinates to maintain smoothness in the output [64]. The influential work by Mildenhall et al. [32] showcased the potential of neural fields for novel view synthesis, demonstrating their impressive generalization capabilities. Since then, neural fields have seen widespread application across image view synthesis, shape reconstruction, and robotics [7, 11, 12, 15, 18, 33, 35, 36, 38, 42, 47, 48, 54, 60, 63, 65]. Traditionally, these approaches integrate a positional embedding layer to counteract the spectral bias introduced by ReLU activations [40]. However, recent work has explored alternative, non-standard activations such as sine [54], Gaussian [41], wavelets [49], and sinc [51]. These activations have shown to outperform conventional approaches in various vision tasks, delivering enhanced performance in capturing high-frequency details and reducing reliance on positional embeddings [12, 29, 41, 49, 54, 61]. + +Preconditioners were initially introduced in numerical linear algebra [20, 46] to transform ill-conditioned linear systems into well-conditioned forms, thereby accelerating the convergence of iterative solvers. Over time, preconditioning techniques have become integral to machine learning, where they enhance the efficiency and performance of optimization algorithms. Early applications in machine learning can be traced to foundational optimization methods, such as the conjugate gradient method and its variants [34]. As machine learning problems have grown more complex—often involving sparse matrices, non-convex objectives, and large-scale datasets—researchers have developed specialized preconditioning strategies to meet these unique challenges [3, 24, 39, 43]. Many widely-used optimizers incorporate preconditioning, including methods like ADMM [27], mirror descent [2], quasi-Newton methods [5, 19, 34], and adaptive optimizers [14, 16, 21, 30, 62]. These preconditioned optimizers have become essential for addressing the complex landscapes of modern machine learning models, driving improvements in both convergence speed and solution quality. + +# 3. Notation + +The neural fields we consider in this paper will be defined by a depth $L$ neural network with layer widths $\{n_1,\dots ,n_L\}$ . We let $X\in \mathbb{R}^{N\times n_0}$ denote the training data, with $n_0$ being the dimension of the input and $N$ being the number of training samples. The output at layer $k$ will be denoted by $F_{k}$ and is defined by + +$$ +F _ {k} = \left\{ \begin{array}{l l} F _ {L - 1} W _ {L} + b _ {L}, & k = L \\ \phi \left(F _ {k - 1} W _ {k} + b _ {k}\right), & k \in [ L - 1 ] \\ X, & k = 0 \end{array} \right. \tag {1} +$$ + +where the weights $W_{k} \in \mathbb{R}^{n_{k - 1} \times n_{k}}$ and the biases $b_{k} \in \mathbb{R}^{n_{k}}$ and $\phi$ is an activation applied component wise. The notation $[m]$ is defined by $[m] = \{1, \dots, m\}$ . We will denote the loss function that we train the neural fields with by $\mathcal{L}$ . In many experiments in the paper this will be the MSE loss [37]. Our theoretical results will be primarily for the case where $\phi$ is given by one of the activation sine, Gaussian, wavelet or ReLU. For more details on how these activations are used within the context of neural fields we refer the reader to [41, 49, 54]. + +# 4. Theoretical Framework + +# 4.1. Overview of Preconditioners + +Preconditioning enhances optimization convergence and efficiency by regulating curvature, particularly in stochastic gradient descent (SGD) [14, 39]. High curvature directions in SGD require a small learning rate to avoid overshooting, leading to slow progress in low curvature directions. + +For general objective functions $f$ on parameters $\mathbf{x} \in \mathbb{R}^n$ . Preconditioning is done by employing a linear change of parameters $\widetilde{\mathbf{x}} = D^{\frac{1}{2}}\mathbf{x}$ , where in practise $D^{\frac{1}{2}}$ is a non-singular matrix. With this change of parameters a new objective function $\widetilde{f}$ , defined on $\widetilde{\mathbf{x}}$ , can be defined as + +$$ +\widetilde {f} (\widetilde {\mathbf {x}}) = f (\mathbf {x}). \tag {2} +$$ + +Denoting the gradient of the original objective function by $\nabla f$ and its Hessian by $H(f) = \nabla^2 f(\mathbf{x})$ . The chain rule gives + +$$ +\nabla \widetilde {f} (\widetilde {\mathbf {x}}) = D ^ {- \frac {1}{2}} \nabla f \tag {3} +$$ + +$$ +H (\widetilde {f}) (\widetilde {\mathbf {x}}) = \left(D ^ {- \frac {1}{2}}\right) ^ {T} \left(H (f) (\mathbf {x})\right) \left(D ^ {- \frac {1}{2}}\right). \tag {4} +$$ + +Equation (3) exhibits the key idea of training with a preconditioner. If we consider gradient descent on the transformed parameter space, a gradient descent iteration takes the form + +$$ +\widetilde {\mathbf {x}} _ {t} = \widetilde {\mathbf {x}} _ {t - 1} - \eta \nabla_ {\widetilde {\mathbf {x}} _ {t - 1}} \widetilde {f} \tag {5} +$$ + +Applying equations (2) and (3) this corresponds to doing the update + +$$ +\mathbf {x} _ {t} = \mathbf {x} _ {t - 1} - \eta D ^ {- \frac {1}{2}} \nabla_ {\mathbf {x} _ {t - 1}} f. \qquad (6) +$$ + +The main endeavour of preconditioning for optimization is to find a preconditioning matrix $D$ such that the new Hessian, given by equation (4), has equal curvature in all directions. This will allow the update (6) to move faster along small curvature directions, leading to faster convergence. Algorithm 1 gives the basic pseudocode for preconditioned SGD. + +# Algorithm 1 Preconditioned SGD + +Require: initial point $x_0$ , iterations $N$ , learning rate $\eta$ , preconditioner $D$ . + +$$ +\begin{array}{l} \mathbf {f o r} t = 0, \dots , N \mathbf {d o} \\ g _ {t} \leftarrow \nabla_ {x _ {t}} f \\ D _ {t} \leftarrow D (x _ {t}) \\ x _ {t + 1} \leftarrow x _ {t} - \eta D (x _ {t}) ^ {- \frac {1}{2}} g _ {t} \\ \end{array} +$$ + +end for + +From Eq. (4) we see that the best preconditioner to use would be the absolute value of the Hessian itself. In the case of a positive definite Hessian, this is precisely what Newton's method does [34]. The main issue with this preconditioner is that the cost of storing and inverting the preconditioner will be $\mathcal{O}(n^3)$ for an objective function of $n$ parameters [34]. This will be extremely costly for the training of overparameterized neural networks whose Hessians are extremely large. + +We list some of the main preconditioners that are being used in the literature. + +Diagonal Preconditioners: are matrices that represent some form of a diagonal approximation of the Hessian. Examples include the Jacobi preconditioner, which is given by $D^{J} = |\operatorname{diag}(H)|$ , where $|\cdot|$ is element-wise absolute value and $H$ is the Hessian. In practical settings, the absolute value is taken so that the preconditioner is positive semidefinite. The equilibration preconditioner is a diagonal matrix which has the 2-norm of each row (or column) on the diagonal: $D^{E} = ||H_{i,\cdot}||$ . The preconditioners $D^{J}$ and $D^{E}$ are known as curvature-aware preconditioners as they seek to give a good approximation to the Hessian. Diagonal preconditioners are often used because of their ability to be stored and inverted in linear time. Diagonal preconditioners are also known as adaptive learning rates in the literature. The algorithm Equilibrated Stochastic Gradient Descent (ESGD) [14] employs $D^{E}$ as a preconditioner to condition stochastic gradient descent. In [14], it is shown that applying ESGD leads to faster training times for autoencoder tasks when compared to vanilla SGD, RMSProp [45] and a preconditioned SGD using $D^{J}$ as preconditioner. AdaHessian [62] is a recent algorithm that applies a diagonal preconditioner in the setting of moving averages and thus can be seen as a way of enhancing the Adam optimizer [23]. + +Kronecker Factored Preconditioners: are preconditioners of the form $D = A^T A$ , where $A = A_1 \otimes \dots \otimes A_k$ and $\otimes$ denotes the Kronecker product. The algorithm K-FAC [30] employs a Kronecker factored preconditioner. + +Others: There are several second order optimisation algorithms that use preconditioners that do not fall into the above three categories such as, The Gauss-Newton method, The Conjugate Gradient method, Limited memory Broyden-Fisher-Golfarb-Shanno (L-BFGS) [34]. It was shown in [50] that these algorithms do not train well in stochastic settings. + +# 4.2. Condition Number + +In Sec. 4.1, we explained that SGD will move faster through the loss landscape when the curvatures in each direction are similar. The regularity of the loss landscape at a point is quantified via the condition number of the Hessian. + +Definition 4.1. Given a matrix $A$ we define the condition number $\kappa$ of $A$ by + +$$ +\kappa (A) := \frac {\sigma_ {\operatorname* {m a x}} (A)}{\sigma_ {\operatorname* {m i n}} (A)}, \tag {7} +$$ + +where $\sigma$ is the eigenvalue. Using Eq. (4) we observe that if we take a preconditioner $D$ such that $\kappa((D^{-\frac{1}{2}})^T(H(f)(\mathbf{x}))(D^{-\frac{1}{2}}))$ is closer to 1 than $\kappa(H)$ , then this implies that the preconditioner $D$ is regularising the curvatures of the landscape to be equal in each direction, which yields a better training landscape for a gradient descent based algorithm [34]. + +To empirically illustrate the concept of preconditioning, we examined a one-dimensional curve fitting scenario. Specifically, we considered a feedforward network with two hidden layers, each containing 16 neurons, tasked with fitting the signal $f(x) = \sin (2\pi x) + \sin (6\pi x)$ using a Gaussian activation [41]. During optimization with gradient descent, we applied two types of preconditioners: an equilibrated preconditioner $D^{E}$ and a Jacobi preconditioner $D^{J}$ . At each optimization step, we computed both the original Hessian associated with gradient descent and the transformed Hessian using Eq. (4). As shown in Fig. 2, the results demonstrate that applying either the Jacobi or equilibrated preconditioner consistently reduced the condition number of the Hessian compared to the unconditioned case, highlighting the effectiveness of preconditioning in improving optimization. + +# 4.3. Training with Adam + +In this section, we aim to explain why training with Adam is generally more efficient than training with SGD for a variety of neural fields. While this observation is well-known within the community, we include it here to provide context and motivation for the theoretical framework developed in Sec. 4.4. + +![](images/fe616343aaaaf14f1b2f781a3e345cc821e2cb7f36418bffc191dc7c022ff1b9.jpg) +(a) + +![](images/3564b6ecda338ae5406efeb8cc3a2ff62c726bcdbc3f09389813ac4fd13e9847.jpg) +(b) +Figure 2. Fig. 2a compares the condition number (7) on a 1D signal regression task before (dotted line) and after (solid line) applying equilibrated $D^{E}$ and Jacobi $D^{J}$ preconditioners. The equilibrated preconditioner significantly reduces the Hessian's condition number, as shown by the larger gap between the yellow solid and dotted lines compared to the green solid and dotted lines representing the Jacobi preconditioner, thus achieves faster convergence as seen in Fig. 2b. + +Given an objective function $L(\theta) = |f(\theta)|^2$ for a nonlinear function $f$ . The Jacobian $J_{L}$ of $L$ can be computed via the chain rule: $J_{L} = 2J_{f}^{T}f$ , where $J_{f}$ denotes the Jacobian of $f$ . The Hessian of $L$ , $H_{L}$ , can be computed by an application of the chain rule + +$$ +H _ {L} = 2 J _ {f} ^ {T} J _ {f} + 2 H _ {f} f. \tag {8} +$$ + +We can then approximate the Hessian $H_{L}$ by the term $2J_{f}^{T}J_{f}$ . Leading to the first order approximation + +$$ +H _ {L} \approx 2 J _ {f} ^ {T} J _ {f} = \frac {1}{2 | f | ^ {2}} J _ {L} ^ {T} J _ {L} = \frac {1}{2 L} J _ {L} ^ {T} J _ {L}. \tag {9} +$$ + +Eq. (9) yields the basic idea of the Gauss-Newton method. By taking the Gauss-Newton matrix $J_{L}^{T}J_{L}$ as an approximation to the Hessian $H_{L}$ , we can perform an optimization update that uses the step: $\Delta_{GN} = -\frac{1}{J^TJ}\nabla L$ . The Gauss-Newton matrix is in general only positive semi-definite. Therefore, when implementing the algorithm one often adds a small damping factor $\lambda$ so the implemented step is $\Delta_{GN} = -\frac{1}{J^TJ + \lambda}\nabla L$ . A similar derivation can be made for more general loss functions used in non-linear least squares type regression problems [34]. It follows that the Gauss-Newton method can be seen as a preconditioned SGD that uses a first order (first derivatives) Hessian approximate preconditioner given by the Gauss-Newton matrix $J^T J$ . + +Using the above observations we now show how to view Adam as an optimizer that applies a diagonal preconditioner. The Adam optimizer involves two key steps. The first is to compute a first moment estimate of the form $m_{t} = \beta_{1}m_{t - 1} + (1 - \beta_{1})g_{t}$ , where $g_{t}$ is the gradient of a given objective function $f$ at iteration $t$ , and $m_0 = 0$ . The second is to compute a second moment estimate $v_{t} = \beta_{2}v_{t - 1} + (1 - \beta_{2})g_{t}^{2}$ , where $g_{t}^{2} = g_{t}\odot g_{t},\odot$ denotes the Hadamard product, and $v_{0} = 0$ . The numbers $0 < \beta_{1} < \beta_{2} < 1$ are hyperparameters. The algorithm then applies a bias correction to the above first + +![](images/150a19ddfd5b7786e5637b7114b6a8adf18d154c731103e64cb80fc8f8bd4033.jpg) +(a) + +![](images/9104b3424b2530ee19492f45e26433bb81312bbda42839a4ad5d8c84ba4a153a.jpg) +(b) +Figure 3. Comparison of training convergence for neural fields with different activations – ReLU with positional encoding (ReLU (PE)), wavelet, sine and Gaussian – using Adam and SGD optimizers across three tasks: 2D image reconstruction (Fig. 3a), 3D binary occupancy reconstruction (Fig. 3b), and NeRF (Fig. 3c). In all cases, the Adam optimizer outperforms SGD, indicating that leveraging curvature information facilitates faster convergence. + +![](images/a3ce407e507e7c7aeed26f594909ebd161892fabe90e4a90cbd26e5f8d8354ea.jpg) +(c) + +and second moment estimates, and then takes a moving average to perform an update step based on $-\frac{m_t}{\sqrt{v_t}}$ , see [23] for details. + +For the following discussion, we will only focus on analyzing the second raw moment estimate, as this is related to the Gauss-Newton matrix. Given an objective function $f$ , observe that we can express $g_t^2 = g_t \odot g_t = \text{Diag}(J^T J)$ , where $J$ denotes the Jacobian of $f$ . Thus the second raw moment estimate of Adam can be recast as: + +$$ +v _ {t} = \beta_ {2} v _ {t - 1} + (1 - \beta_ {2}) \operatorname {D i a g} \left(J _ {t} ^ {T} J _ {t}\right) \tag {10} +$$ + +where $J_{t}$ denotes the Jacobian at iteration $t$ . Thus we see that Adam applies a preconditioner given by the diagonal of the Gauss-Newton matrix. Since the Gauss-Newton matrix can be seen as a first order approximation to the Hessian, Adam can be seen as using an approximation to curvature to adapt the learning rate for faster optimization. This suggests that Adam can outperform SGD which employs no preconditioner. + +We empirically validated this insight across three distinct neural field tasks: image reconstruction, binary occupancy, and NeRF. For each task, we compared the performance of ReLU(PE) activated networks trained with both SGD and Adam against networks using wavelet, sine, and Gaussian activations. As shown in Fig. 3, Adam consistently outperforms SGD in all cases. This suggests that Adam's use of a preconditioner significantly enhances its performance for neural field applications, see Sec. 5 for the details of the architectures and experimental setup. + +# 4.4. Main theorems + +In Sec. 4.3, we discussed how Adam can be viewed as applying a diagonal preconditioner based on the diagonal of the Gauss-Newton matrix, which uses first derivatives to + +![](images/71d26ca2e77dcbbabd3e3142c48014e425ca4beee0f006629c287e2a095b594a.jpg) +Figure 4. Percentage sparsity of Hessian-vector product matrices across all layers throughout the training process of a 2D image reconstruction task, using ESGD to train networks with different activations. The x-axis ranges from 0 to 1, with values closer to 1 indicating higher sparsity. + +approximate the Hessian matrix. Here, we aim to identify the architectural properties that enable effective training of neural fields with diagonal preconditioners that give a better approximation to the Hessian. Our primary theorems demonstrate that the choice of activation function is crucial for enabling efficient training with such preconditioners, highlighting its central role in achieving effective curvature-aware optimization for neural fields. + +Recall Sec. 4.1 that diagonal preconditioners such as the equilibrated precondition $D^{E}$ or the Jacobi preconditioner $D^{J}$ all involve the Hessian matrix. In the context of neural networks the Hessian of the loss landscape is often an extremely large matrix. Thus in practical settings one often replaces the Hessian with a Hessian vector product which is much cheaper to store [34]. + +Our first theorem shows that the Hessian vector product of the loss landscape associated to a sine, Gaussian, wavelet or sinc activated neural field produces a dense vector. + +Theorem 4.2. Let $F$ denote a sine, Gaussian, wavelet or sinc activated neural field. Let $\mathcal{L}(\theta)$ denote the MSE loss associated to $F$ and a training set $(X,Y)$ . Let $H$ denote the Hessian of $\mathcal{L}$ at a fixed parameter point $\theta$ . Then given a non-zero vector $v$ the Hessian vector product $Hv$ will be a dense vector. + +While it may seem rather costly for a sine- or Gaussian-activated INR to have dense Hessian vector products when applied to the MSE loss function, we point out that the cost is much less than storing a dense Hessian. + +Theorem 4.3. Let $F$ denote a ReLU/ReLU(PE)-activated neural field. Let $\mathcal{L}(\theta)$ denote the MSE loss associated to $F$ and a training set $(X, Y)$ . Let $H$ denote the Hessian of $\mathcal{L}$ at a fixed parameter point $\theta$ . Then given a non-zero vector $v$ the Hessian vector product $Hv$ will be a sparse vector. + +Theorem 4.2 and Theorem 4.3 also hold for the binary cross-entropy loss. The proofs of Theorem 4.2 and Theorem 4.3 are given in the Supplementary material. + +Theorem 4.3 implies that when applying a preconditioner, built from a Hessian vector product, to a ReLU/ReLU(PE) INR, such as ESGD [14] or AdaHessian [62], only a few components of the gradient will be scaled during the update step. This means that the preconditioner will not be adding much to the optimization process. On the other hand, Theorem 4.2 implies that applying a preconditioner built from the Hessian to the gradient of the MSE loss of a sine, Gaussian and wavelet-activated neural field should help optimization as many of the gradient components will get scaled by a quantity depending on the curvature of the loss landscape. This yields a clear difference between ReLU/ReLU(PE) activated neural fields and those activated with a sine, Gaussian, wavelet activation. In particular, Theorem 4.2 implies that neural fields admitting a sine, Gaussian, wavelet activation have the ability to be trained efficiently with a diagonal curvature aware preconditioner such as the equilibrated preconditioner $D^{E}$ defined in Sec. 4.1. + +Fig. 4 shows the results of a Hessian vector product of the MSE loss of a ReLU(PE) and Gaussian neural field for an image reconstruction task for the weights in all layers of the network layer throughout training. The random vector was chosen from a Rademacher distribution and the reported figures are given as the mean of the Hessian of all layers averaged over all iterations of training. As demonstrated by the experiment, the ReLU(PE) network generates a sparse Hessian-vector product, as predicted by Theorem 4.3, while the Gaussian network produces a dense vector, as indicated by Theorem 4.2. Furthermore, as we will observe in Sec. 5, this sparsity helps explain why Adam performs well for neural fields with ReLU (ReLU(PE)) activations, whereas an algorithm like ESGD [14] does not. This is because Adam does not rely on Hessian-vector product. + +# 5. Experiments + +We compared various preconditioners over popular benchmarks [22, 28, 50, 52, 54]: 2D image reconstruction, 3D shape reconstruction and novel view synthesis with NeRF. Our primary focus was on curvature-aware preconditioners that are well-suited for the stochastic training of neural network. Specifically, we compared the following methods: ESGD $[14]^2$ , AdaHessian $[62]^3$ , Shampoo $[21]^4$ , and Kronecker-based preconditioner $[30]^5$ . We provide the details of each algorithm including the reproducibility details of each experiment and machines we used to run each experiment in the supplementary material. In the main paper, we focused on analyzing Gaussian networks, see supplementary material for additional analysis for other non-traditional activations and other neural field tasks. + +Remark for AdaHessian We observed that in the implementation of AdaHessian, an equilibrated preconditioner $D^{E}$ is utilized, even though the paper primarily focuses on using a Jacobi preconditioner [14]. Therefore, we introduced a Jacobi preconditioner $D^{J}$ into AdaHessian, which we refer to as AdaHessian(J). We use the term AdaHessian(E) for the original implementation. + +Remark for ESGD We further modified the ESGD by applying the squared Hessian diagonal preconditioner in two settings: using an exponential moving average (ESGD) and using an infinity norm (ESGD-max) [23]. We also opted to recompute the $D^{E}$ for every $N$ iterations for computational efficiency, we use $N = 100$ for all the experiments. + +# 5.1. Image Reconstruction + +We evaluated on a 2D image reconstruction task, where given pixel coordinates $\mathbf{x} \in \mathbb{R}^2$ , we optimized a neural network to regress the corresponding RGB values $c \in \mathbb{R}^3$ . We used a 5-layer Gaussian-activated network with 256 neurons. We used $\sigma = 0.05$ for the Gaussian activation. We trained the network using mini-batches of size 512. We compared the training convergence of different preconditioners and the Adam optimizer on the lion instance from the DIV2K dataset [1] in Fig. 5a. Additional results on the rest of the DIV2K dataset are provided in the supplementary material. As predicted by Theorem 4.2, Gaussian network equipped with the dense Hessian-vector product exhibits faster convergence when optimized with curvature-aware preconditioned methods compared to Adam. Notably, ESGD demonstrates faster convergence and has comparable training time and memory usage per iteration compared to Adam. + +![](images/99f8da22605ca54d3f70f804bee1b6eba7543f4e1d988b4497c36a9357accd50.jpg) +(a) + +![](images/87496d8c5dd8a872aa627cf97ed9b257a395f62be382dfa107f31eda11a4a87a.jpg) +(b) +Figure 5. Comparison of training convergence and computational complexity for various preconditioners. We evaluated a Gaussian-activated neural field on the lion instance from the DIV2K dataset. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: We provide the time-based comparisons in the supplementary material (Sec 3.1). Similar analysis for other activations and additional instances from the DIV2K dataset are available in the supplementary material (Sec. 3.2). + +ESGD and AdaHessian obtain Hessian information by computing Hessian-vector products, which makes them very computational efficient. Each Hessian-vector product is generally as fast as a single gradient computation, as demonstrated in Fig. 5b. In contrast, other preconditioners, particularly Shampoo are more computationally expensive because they involve Kronecker product computations for preconditioner matrices, see supp. material for details. + +# 5.2. 3D Binary Occupancy Reconstruction + +We evaluated on learning a binary occupancy field, where given 3D point coordinates $\mathbf{x} \in \mathbb{R}^3$ , we optimized a neural network to represent the occupancy field of 3D shapes. Following existing works [22], we sampled one million 3D points for training - one-third of the points were sampled uniformly within the volume, and the remaining two-thirds of the points were sampled near the mesh surface and perturbed with random Gaussian noise using sigma of 0.1 and 0.01, respectively [22]. We trained the network using binary cross-entropy (BCE) loss, which compares the predicted occupancy and the true occupancy. We used a 5-layer Gaussian network with 256 neurons and $\sigma = 0.09$ . We trained the network using mini-batches of size 50000. + +We compared the training convergence of different preconditioners and the Adam optimizer on the armadillo instance from the Stanford 3D Scanning dataset. Fig. 6 shows that ESGD exhibits superior convergence than other preconditioner-type optimizers. We showcase a qualitative result comparing the mesh reconstruction of ESGD and Adam given the same number of iteration in Fig. 7. Interestingly, when dealing with higher mode signals, both AdaHessian and Shampoo no longer demonstrated superior convergence, + +unlike in the 2D image reconstruction task in Fig. 5a. We speculate that the local Hessians may become noisy with higher mode signals, thereby impacting the gradient updates. In contrast, this noise did not significantly affect ESGD's convergence because its preconditioner updates were performed every $N$ iterations. Hence, we will focus on comparing Adam and ESGD for the experiments in the following section. + +# 5.3. Neural Radiance Fields (NeRF) + +Neural Radiance Fields (NeRF) have recently emerged as a pioneering approach in novel view synthesis, utilizing neural networks to model volumetric fields of 3D scenes using + +![](images/ea9ea563ce0c03cf9e8472dc52508e1d0380337a68ef3344324c413917a4da05.jpg) +Figure 6. Comparison of training convergence for various preconditioners. We evaluated a Gaussian-activated neural field on a 3D binary occupancy reconstruction task on the armadillo instance. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: Similar analysis for other activations are available in the supplementary material. + +
SceneTrain PSNRIteration ↓Time (s)↓Adam TestIteration ↓Time (s)↓ESGD Test
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
fern25.38200K368.4324.380.740.28120K270.8124.410.740.30
flower29.17200K469.3125.670.780.12120K263.9325.650.780.13
horns24.9560K130.8221.820.700.34120K227.5820.780.630.44
orchids23.3200K501.9019.560.610.24120K269.0119.740.610.21
room31.20110K194.0531.600.930.12140K201.8830.520.900.20
fortress30.18140K333.7028.930.810.15140K334.5628.60.800.17
leaves21.36200K482.3419.560.610.24120K271.2519.430.590.25
trex25.5080K164.9622.040.710.31120K209.2522.210.750.23
+ +Table 1. Quantitative results of NeRF on all instances from the LLFF dataset [31]. The reported time solely refers to the optimization update step. Note: Results for the Blender synthetic [32] and BLEFF [60] datasets are available in supplementary material. + +![](images/58924fec6d51fdaf675756065544bbb0fdd50e69b56253961a237a7bec04c21a.jpg) +(a) +Figure 7. Qualitative results for the dragon instance from Stanford 3D Scanning dataset. Compared to the Gaussian-based neural field trained with Adam (Fig. 7a), ESGD (Fig. 7b) has reconstructed the shapes with significantly improved fidelity at epoch 500 (zoom in $4 \times$ for better visibility). Note: Qualitative results for the rest of the instances from Stanford 3D Scanning Dataset are available in supplementary material. + +![](images/9973ee219ba2dc58b28c0fad3cfc16fd83922fdaedec8a11e53452f4d5482c23.jpg) +(b) + +multi-view 2D images [12, 13, 26, 32, 44]. Specifically, given 3D points $\mathbf{x} \in \mathbb{R}^3$ and viewing direction, NeRF estimates the 5D radiance field of a 3D scene which maps each input 3D coordinate to its corresponding volume density $\sigma \in \mathbb{R}$ and directional emitted color $\mathbf{c} \in \mathbb{R}^3$ [12, 26, 32]. We used an 8-layer Gaussian-activated network with 256 neurons and $\sigma = 0.1$ . Recall that in the previous section we demonstrated that ESGD exhibited superior performance in terms of convergence and computational complexity compared to other preconditioners. Therefore, we focused on comparing Adam and ESGD here. We determined the same training PSNR at which both model converged and reported the corresponding optimization metrics, including the number of iterations and the total time taken for the update computation. We evaluated the PSNR on a hold-out test scene. Table 1. shows that ESGD achieves on average faster convergence than Adam, see more results in the supp. material. + +# 6. Limitations + +While our work theoretically established the suitability of curvature-aware preconditioners for training neural fields with non-traditional activations such as sine, Gaussian, and wavelets, it also highlighted their ineffectiveness for neural fields employing ReLU-PE activations. Specifically, we showed that Adam performs well for ReLU-PE due to its use of a diagonal preconditioner derived from the Gauss-Newton matrix, rather than relying on Hessian vector products. However, this raises an important limitation of our work: we did not explore whether alternative preconditioners, potentially more effective than the Gauss-Newton matrix, could be developed to improve the training of ReLU-PE activated neural fields beyond what Adam achieves. This is particularly relevant since ReLU-PE remains widely used in practical applications. This question represents an avenue for future research, which we leave it as future work. + +# 7. Conclusion + +We explored the impact of preconditioners on the stochastic training of neural fields, developing a theoretical framework based on Hessian-vector products. Our analysis demonstrates that curvature-aware preconditioners can significantly accelerate training for neural fields with non-traditional activations, such as sine, Gaussian, and wavelet. Experimental validation across various tasks—including image reconstruction, shape modeling, and neural radiance fields—using ESGD and AdaHessian confirmed these benefits. In contrast, for neural fields with ReLU or ReLU-PE activations, our theory predicted no significant advantage from curvature-aware preconditioning, highlighting the activation-dependent nature of these methods. 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We demonstrate that curvature-aware preconditioners can significantly accelerate training convergence for neural fields with suitable activations. Specifically, ESGD (a curvature-aware preconditioned gradient descent algorithm [14]) improves convergence for wavelet, sine, and Gaussian activations, while Adam performs better for ReLU network with positional encoding (ReLU(PE)). In a " + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "inline_equation", + "content": "2D" + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "text", + "content": " image reconstruction task (Fig. 1a), a wavelet-based neural field trained with ESGD achieves 29.36 PSNR (Fig. 1e) at the " + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "inline_equation", + "content": "10^{\\mathrm{th}}" + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "text", + "content": " epoch, outperforming Adam's 26.61 PSNR (Fig. 1d). In a " + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "inline_equation", + "content": "3D" + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "text", + "content": " binary occupancy task (Fig. 1b), ESGD enables faster convergence for sine activations, as shown by the improved armadillo mesh reconstruction at the " + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "inline_equation", + "content": "1000^{\\mathrm{th}}" + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "text", + "content": " epoch (Fig. 1g vs. Fig. 1f). In a Neural Radiance Fields (NeRF) task (Fig. 1c), a Gaussian-based model trained with ESGD achieves lower reconstruction error (Fig. 1i, 0.0695) compared to Adam (Fig. 1h, 0.0743), as seen in the error map (darker areas indicate lower error; zoom in " + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 55, + 442, + 555, + 531 + ], + "type": "text", + "content": " for clarity)." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 468, + 350, + 549, + 431 + ], + "blocks": [ + { + "bbox": [ + 468, + 350, + 549, + 431 + ], + "lines": [ + { + "bbox": [ + 468, + 350, + 549, + 431 + ], + "spans": [ + { + "bbox": [ + 468, + 350, + 549, + 431 + ], + "type": "image", + "image_path": "6227585b6f4660dad18edd1d71ade7cdfa90928eea6dbc06e8b5ef853bd4ec6b.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 504, + 434, + 512, + 441 + ], + "lines": [ + { + "bbox": [ + 504, + 434, + 512, + 441 + ], + "spans": [ + { + "bbox": [ + 504, + 434, + 512, + 441 + ], + "type": "text", + "content": "(i)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 151, + 540, + 200, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 540, + 200, + 553 + ], + "spans": [ + { + "bbox": [ + 151, + 540, + 200, + 553 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 54, + 565, + 297, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 565, + 297, + 685 + ], + "spans": [ + { + "bbox": [ + 54, + 565, + 297, + 685 + ], + "type": "text", + "content": "Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effec" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 542, + 555, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 555, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 555, + 565 + ], + "type": "text", + "content": "tiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF) " + }, + { + "bbox": [ + 313, + 542, + 555, + 565 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 313, + 542, + 555, + 565 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 588, + 395, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 588, + 395, + 601 + ], + "spans": [ + { + "bbox": [ + 314, + 588, + 395, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 608, + 555, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 555, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 555, + 681 + ], + "type": "text", + "content": "In recent years, neural fields, also known as implicit neural representations, have garnered significant attention in machine learning and computer graphics [8, 9, 25, 32, 53-55, 57]. Unlike traditional grid-based representations [6, 17, 56, 64], neural fields implicitly encode shapes and objects through neural networks. These representations are" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 692, + 295, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 692, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 692, + 295, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 55, + 692, + 295, + 712 + ], + "type": "text", + "content": " *Equal contribution.> Correspondence to: Shin-Fang Chng ." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 687, + 553, + 708 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 687, + 553, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 687, + 553, + 708 + ], + "type": "text", + "content": "Source code is available at https://github.com/sfchng/preconditioner_neural_fields.git." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "27222" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "highly efficient for capturing complex, high-resolution signals, making them well-suited for tasks such as image synthesis [9, 55], shape modeling [32, 53], and robotics [10, 59]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 298, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 298, + 215 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 298, + 215 + ], + "type": "text", + "content": "Classically, neural fields trained with ReLU activations suffer from spectral bias and limited fidelity [40]. To address this, positional encoding (PE) layers [58] were introduced but at the cost of increased model complexity and noisy gradients. More recent work has explored non-standard activations, such as sine [54], Gaussian [41] and wavelets [49] which enable high-frequency encoding without positional encodings and produce well-behaved gradients [50]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 216, + 297, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 216, + 297, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 297, + 395 + ], + "type": "text", + "content": "While neural fields have enabled realistic and efficient representations of continuous signals, progress on minimizing the training time of such representations remains a significant research challenge. Currently, the Adam optimizer is the de facto algorithm for training neural fields, particularly in applications involving datasets where a stochastic training regime is essential. Yet, the preference for Adam over simpler alternatives such as stochastic gradient descent (SGD) has not been rigorously justified for neural fields, despite its widespread adoption. Notably, [50] demonstrated substantial gains in training speed for neural fields using second-order optimizers such as L-BFGS [34]. However, second-order methods are often impractical for stochastic settings [50], limiting their effectiveness for large-scale data, where stochastic training is essential." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 301, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 301, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 301, + 538 + ], + "type": "text", + "content": "In this paper, we approach neural field training from the perspective of preconditioning. Preconditioners improve convergence by reducing the condition number of the optimization problem [4, 34, 46]. We develop a theoretical framework linking Adam's performance to its implicit use of a diagonal preconditioner derived from the Gauss-Newton matrix and proceed to identify conditions under which curvature-aware diagonal preconditioners, such as those in ESGD (equilibrated stochastic gradient descent) [14], enhance training for neural fields with sine, Gaussian, or wavelet activations. For ReLU activations, we show that such preconditioning provides limited benefit." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 539, + 303, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 539, + 303, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 303, + 694 + ], + "type": "text", + "content": "Our experiments validate the proposed framework across a range of tasks, including 2D image reconstruction, 3D binary occupancy, and Neural Radiance Fields (NeRF). As demonstrated in Fig. 1, ESGD consistently outperforms Adam for neural fields with wavelet, sine, and Gaussian activations, which, as predicted by our theory, is due to their better-conditioned Hessians. In contrast, Adam performs better for ReLU-PE activations, which are associated with poorly conditioned Hessians. Furthermore, we evaluated other curvature-aware algorithms, including ESGD, Ada-Hessian [62], Shampoo [21], and K-FAC [30], offering valuable insights into their effectiveness in stochastic training settings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 695, + 180, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 695, + 180, + 706 + ], + "spans": [ + { + "bbox": [ + 67, + 695, + 180, + 706 + ], + "type": "text", + "content": "Our main contributions are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 72, + 553, + 156 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 315, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 553, + 108 + ], + "type": "text", + "content": "1. We present a theoretical framework for preconditioning in neural field training, uncovering key conditions and highlighting when preconditioning is beneficial." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 108, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 108, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 315, + 108, + 553, + 156 + ], + "type": "text", + "content": "2. We empirically validate our framework, demonstrating the superiority of curvature-aware algorithms like ESGD over Adam across diverse tasks, including image reconstruction, 3D shape modeling, and NeRF." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 167, + 400, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 167, + 400, + 179 + ], + "spans": [ + { + "bbox": [ + 315, + 167, + 400, + 179 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 186, + 561, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 186, + 561, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 561, + 402 + ], + "type": "text", + "content": "Neural Fields represent signals as weights within a neural network, using low-dimensional coordinates to maintain smoothness in the output [64]. The influential work by Mildenhall et al. [32] showcased the potential of neural fields for novel view synthesis, demonstrating their impressive generalization capabilities. Since then, neural fields have seen widespread application across image view synthesis, shape reconstruction, and robotics [7, 11, 12, 15, 18, 33, 35, 36, 38, 42, 47, 48, 54, 60, 63, 65]. Traditionally, these approaches integrate a positional embedding layer to counteract the spectral bias introduced by ReLU activations [40]. However, recent work has explored alternative, non-standard activations such as sine [54], Gaussian [41], wavelets [49], and sinc [51]. These activations have shown to outperform conventional approaches in various vision tasks, delivering enhanced performance in capturing high-frequency details and reducing reliance on positional embeddings [12, 29, 41, 49, 54, 61]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 416, + 557, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 416, + 557, + 668 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 557, + 668 + ], + "type": "text", + "content": "Preconditioners were initially introduced in numerical linear algebra [20, 46] to transform ill-conditioned linear systems into well-conditioned forms, thereby accelerating the convergence of iterative solvers. Over time, preconditioning techniques have become integral to machine learning, where they enhance the efficiency and performance of optimization algorithms. Early applications in machine learning can be traced to foundational optimization methods, such as the conjugate gradient method and its variants [34]. As machine learning problems have grown more complex—often involving sparse matrices, non-convex objectives, and large-scale datasets—researchers have developed specialized preconditioning strategies to meet these unique challenges [3, 24, 39, 43]. Many widely-used optimizers incorporate preconditioning, including methods like ADMM [27], mirror descent [2], quasi-Newton methods [5, 19, 34], and adaptive optimizers [14, 16, 21, 30, 62]. These preconditioned optimizers have become essential for addressing the complex landscapes of modern machine learning models, driving improvements in both convergence speed and solution quality." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "27223" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 116, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 116, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 116, + 83 + ], + "type": "text", + "content": "3. Notation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": "The neural fields we consider in this paper will be defined by a depth " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " neural network with layer widths " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "\\{n_1,\\dots ,n_L\\}" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": ". We let " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "X\\in \\mathbb{R}^{N\\times n_0}" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " denote the training data, with " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "n_0" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " being the dimension of the input and " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " being the number of training samples. The output at layer " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " will be denoted by " + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "inline_equation", + "content": "F_{k}" + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": " and is defined by" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 91, + 169, + 295, + 212 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 169, + 295, + 212 + ], + "spans": [ + { + "bbox": [ + 91, + 169, + 295, + 212 + ], + "type": "interline_equation", + "content": "F _ {k} = \\left\\{ \\begin{array}{l l} F _ {L - 1} W _ {L} + b _ {L}, & k = L \\\\ \\phi \\left(F _ {k - 1} W _ {k} + b _ {k}\\right), & k \\in [ L - 1 ] \\\\ X, & k = 0 \\end{array} \\right. \\tag {1}", + "image_path": "052ccc3f47fb39fe889015541193a86f613798cfb2782355bc1463e77cc4893d.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "spans": [ + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": "where the weights " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "W_{k} \\in \\mathbb{R}^{n_{k - 1} \\times n_{k}}" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": " and the biases " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "b_{k} \\in \\mathbb{R}^{n_{k}}" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": " is an activation applied component wise. The notation " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "[m]" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": " is defined by " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "[m] = \\{1, \\dots, m\\}" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": ". We will denote the loss function that we train the neural fields with by " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": ". In many experiments in the paper this will be the MSE loss [37]. Our theoretical results will be primarily for the case where " + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 219, + 296, + 340 + ], + "type": "text", + "content": " is given by one of the activation sine, Gaussian, wavelet or ReLU. For more details on how these activations are used within the context of neural fields we refer the reader to [41, 49, 54]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 349, + 194, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 194, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 194, + 361 + ], + "type": "text", + "content": "4. Theoretical Framework" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 369, + 212, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 212, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 212, + 380 + ], + "type": "text", + "content": "4.1. Overview of Preconditioners" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 386, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 386, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 386, + 296, + 445 + ], + "type": "text", + "content": "Preconditioning enhances optimization convergence and efficiency by regulating curvature, particularly in stochastic gradient descent (SGD) [14, 39]. High curvature directions in SGD require a small learning rate to avoid overshooting, leading to slow progress in low curvature directions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": "For general objective functions " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": " on parameters " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": ". Preconditioning is done by employing a linear change of parameters " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}} = D^{\\frac{1}{2}}\\mathbf{x}" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": ", where in practise " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "D^{\\frac{1}{2}}" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": " is a non-singular matrix. With this change of parameters a new objective function " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\widetilde{f}" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": ", defined on " + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}" + }, + { + "bbox": [ + 55, + 446, + 296, + 506 + ], + "type": "text", + "content": ", can be defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 146, + 510, + 295, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 510, + 295, + 526 + ], + "spans": [ + { + "bbox": [ + 146, + 510, + 295, + 526 + ], + "type": "interline_equation", + "content": "\\widetilde {f} (\\widetilde {\\mathbf {x}}) = f (\\mathbf {x}). \\tag {2}", + "image_path": "ff583f033008c626e98580dcb9a1356dfb661096947bdd50397a70e4052a5cf3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "text", + "content": "Denoting the gradient of the original objective function by " + }, + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\nabla f" + }, + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "text", + "content": " and its Hessian by " + }, + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "inline_equation", + "content": "H(f) = \\nabla^2 f(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 532, + 296, + 568 + ], + "type": "text", + "content": ". The chain rule gives" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 573, + 294, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 573, + 294, + 589 + ], + "spans": [ + { + "bbox": [ + 102, + 573, + 294, + 589 + ], + "type": "interline_equation", + "content": "\\nabla \\widetilde {f} (\\widetilde {\\mathbf {x}}) = D ^ {- \\frac {1}{2}} \\nabla f \\tag {3}", + "image_path": "62d4bf0369b45b3a9141660ea4d5cf885ed5c84b4358fa6765d63bc915717906.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 95, + 591, + 295, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 591, + 295, + 607 + ], + "spans": [ + { + "bbox": [ + 95, + 591, + 295, + 607 + ], + "type": "interline_equation", + "content": "H (\\widetilde {f}) (\\widetilde {\\mathbf {x}}) = \\left(D ^ {- \\frac {1}{2}}\\right) ^ {T} \\left(H (f) (\\mathbf {x})\\right) \\left(D ^ {- \\frac {1}{2}}\\right). \\tag {4}", + "image_path": "26cabf4b12b24772cb50ef30d895dec103dd01b4e4dcb7732576387fa712a433.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 613, + 296, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 613, + 296, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 613, + 296, + 658 + ], + "type": "text", + "content": "Equation (3) exhibits the key idea of training with a preconditioner. If we consider gradient descent on the transformed parameter space, a gradient descent iteration takes the form" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 129, + 658, + 295, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 658, + 295, + 673 + ], + "spans": [ + { + "bbox": [ + 129, + 658, + 295, + 673 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {x}} _ {t} = \\widetilde {\\mathbf {x}} _ {t - 1} - \\eta \\nabla_ {\\widetilde {\\mathbf {x}} _ {t - 1}} \\widetilde {f} \\tag {5}", + "image_path": "b72e0bf48cca31ceee624255b5a6afd43fdaddf19d0e564e4f15c684e655d29e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 676, + 295, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 676, + 295, + 699 + ], + "spans": [ + { + "bbox": [ + 55, + 676, + 295, + 699 + ], + "type": "text", + "content": "Applying equations (2) and (3) this corresponds to doing the update" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 117, + 700, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 700, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 117, + 700, + 295, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\mathbf {x} _ {t - 1} - \\eta D ^ {- \\frac {1}{2}} \\nabla_ {\\mathbf {x} _ {t - 1}} f. \\qquad (6)", + "image_path": "8f7a3f26b615090ec2ef2e967d9dd88e60bf945d6aae59f32fa6eccd29da5c61.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 72, + 555, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 156 + ], + "type": "text", + "content": "The main endeavour of preconditioning for optimization is to find a preconditioning matrix " + }, + { + "bbox": [ + 313, + 72, + 555, + 156 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 72, + 555, + 156 + ], + "type": "text", + "content": " such that the new Hessian, given by equation (4), has equal curvature in all directions. This will allow the update (6) to move faster along small curvature directions, leading to faster convergence. Algorithm 1 gives the basic pseudocode for preconditioned SGD." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 165, + 454, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 165, + 454, + 176 + ], + "spans": [ + { + "bbox": [ + 315, + 165, + 454, + 176 + ], + "type": "text", + "content": "Algorithm 1 Preconditioned SGD" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "content": "Require: initial point " + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "content": ", iterations " + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "content": ", learning rate " + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "content": ", preconditioner " + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 315, + 180, + 553, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 325, + 204, + 449, + 254 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 204, + 449, + 254 + ], + "spans": [ + { + "bbox": [ + 325, + 204, + 449, + 254 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {f o r} t = 0, \\dots , N \\mathbf {d o} \\\\ g _ {t} \\leftarrow \\nabla_ {x _ {t}} f \\\\ D _ {t} \\leftarrow D (x _ {t}) \\\\ x _ {t + 1} \\leftarrow x _ {t} - \\eta D (x _ {t}) ^ {- \\frac {1}{2}} g _ {t} \\\\ \\end{array}", + "image_path": "ccede33255ba354054a03531241c6b3ad68221d9e95e15c236567e5dc10cee4e.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 325, + 254, + 358, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 254, + 358, + 263 + ], + "spans": [ + { + "bbox": [ + 325, + 254, + 358, + 263 + ], + "type": "text", + "content": "end for" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "text", + "content": "From Eq. (4) we see that the best preconditioner to use would be the absolute value of the Hessian itself. In the case of a positive definite Hessian, this is precisely what Newton's method does [34]. The main issue with this preconditioner is that the cost of storing and inverting the preconditioner will be " + }, + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n^3)" + }, + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "text", + "content": " for an objective function of " + }, + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 281, + 555, + 388 + ], + "type": "text", + "content": " parameters [34]. This will be extremely costly for the training of overparameterized neural networks whose Hessians are extremely large." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 388, + 554, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 554, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 554, + 411 + ], + "type": "text", + "content": "We list some of the main preconditioners that are being used in the literature." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": "Diagonal Preconditioners: are matrices that represent some form of a diagonal approximation of the Hessian. Examples include the Jacobi preconditioner, which is given by " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{J} = |\\operatorname{diag}(H)|" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " is element-wise absolute value and " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " is the Hessian. In practical settings, the absolute value is taken so that the preconditioner is positive semidefinite. The equilibration preconditioner is a diagonal matrix which has the 2-norm of each row (or column) on the diagonal: " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{E} = ||H_{i,\\cdot}||" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": ". The preconditioners " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " are known as curvature-aware preconditioners as they seek to give a good approximation to the Hessian. Diagonal preconditioners are often used because of their ability to be stored and inverted in linear time. Diagonal preconditioners are also known as adaptive learning rates in the literature. The algorithm Equilibrated Stochastic Gradient Descent (ESGD) [14] employs " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " as a preconditioner to condition stochastic gradient descent. In [14], it is shown that applying ESGD leads to faster training times for autoencoder tasks when compared to vanilla SGD, RMSProp [45] and a preconditioned SGD using " + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 313, + 426, + 564, + 715 + ], + "type": "text", + "content": " as preconditioner. AdaHessian [62] is a recent algorithm that applies a diagonal preconditioner in the setting of moving averages and thus can be seen as a way of enhancing the Adam optimizer [23]." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "27224" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "Kronecker Factored Preconditioners: are preconditioners of the form " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "D = A^T A" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "A = A_1 \\otimes \\dots \\otimes A_k" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " denotes the Kronecker product. The algorithm K-FAC [30] employs a Kronecker factored preconditioner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 204 + ], + "type": "text", + "content": "Others: There are several second order optimisation algorithms that use preconditioners that do not fall into the above three categories such as, The Gauss-Newton method, The Conjugate Gradient method, Limited memory Broyden-Fisher-Golfarb-Shanno (L-BFGS) [34]. It was shown in [50] that these algorithms do not train well in stochastic settings." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 210, + 167, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 210, + 167, + 221 + ], + "spans": [ + { + "bbox": [ + 55, + 210, + 167, + 221 + ], + "type": "text", + "content": "4.2. Condition Number" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 227, + 296, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 227, + 296, + 276 + ], + "spans": [ + { + "bbox": [ + 55, + 227, + 296, + 276 + ], + "type": "text", + "content": "In Sec. 4.1, we explained that SGD will move faster through the loss landscape when the curvatures in each direction are similar. The regularity of the loss landscape at a point is quantified via the condition number of the Hessian." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "text", + "content": "Definition 4.1. Given a matrix " + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "text", + "content": " we define the condition number " + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 281, + 296, + 306 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 310, + 295, + 337 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 310, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 134, + 310, + 295, + 337 + ], + "type": "interline_equation", + "content": "\\kappa (A) := \\frac {\\sigma_ {\\operatorname* {m a x}} (A)}{\\sigma_ {\\operatorname* {m i n}} (A)}, \\tag {7}", + "image_path": "562aba9e3b32f65c936f25951c1a7509022b7e1715fe9f63180e253df309be8d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": " is the eigenvalue. Using Eq. (4) we observe that if we take a preconditioner " + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "inline_equation", + "content": "\\kappa((D^{-\\frac{1}{2}})^T(H(f)(\\mathbf{x}))(D^{-\\frac{1}{2}}))" + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": " is closer to 1 than " + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "inline_equation", + "content": "\\kappa(H)" + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": ", then this implies that the preconditioner " + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 342, + 299, + 426 + ], + "type": "text", + "content": " is regularising the curvatures of the landscape to be equal in each direction, which yields a better training landscape for a gradient descent based algorithm [34]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "text", + "content": "To empirically illustrate the concept of preconditioning, we examined a one-dimensional curve fitting scenario. Specifically, we considered a feedforward network with two hidden layers, each containing 16 neurons, tasked with fitting the signal " + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "inline_equation", + "content": "f(x) = \\sin (2\\pi x) + \\sin (6\\pi x)" + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "text", + "content": " using a Gaussian activation [41]. During optimization with gradient descent, we applied two types of preconditioners: an equilibrated preconditioner " + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "text", + "content": " and a Jacobi preconditioner " + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 55, + 427, + 304, + 617 + ], + "type": "text", + "content": ". At each optimization step, we computed both the original Hessian associated with gradient descent and the transformed Hessian using Eq. (4). As shown in Fig. 2, the results demonstrate that applying either the Jacobi or equilibrated preconditioner consistently reduced the condition number of the Hessian compared to the unconditioned case, highlighting the effectiveness of preconditioning in improving optimization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 624, + 174, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 174, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 174, + 636 + ], + "type": "text", + "content": "4.3. Training with Adam" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 641, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 712 + ], + "type": "text", + "content": "In this section, we aim to explain why training with Adam is generally more efficient than training with SGD for a variety of neural fields. While this observation is well-known within the community, we include it here to provide context and motivation for the theoretical framework developed in Sec. 4.4." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 432, + 162 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 432, + 162 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 432, + 162 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 432, + 162 + ], + "type": "image", + "image_path": "fe616343aaaaf14f1b2f781a3e345cc821e2cb7f36418bffc191dc7c022ff1b9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 369, + 166, + 380, + 175 + ], + "lines": [ + { + "bbox": [ + 369, + 166, + 380, + 175 + ], + "spans": [ + { + "bbox": [ + 369, + 166, + 380, + 175 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 434, + 76, + 549, + 161 + ], + "blocks": [ + { + "bbox": [ + 434, + 76, + 549, + 161 + ], + "lines": [ + { + "bbox": [ + 434, + 76, + 549, + 161 + ], + "spans": [ + { + "bbox": [ + 434, + 76, + 549, + 161 + ], + "type": "image", + "image_path": "3564b6ecda338ae5406efeb8cc3a2ff62c726bcdbc3f09389813ac4fd13e9847.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 487, + 165, + 498, + 174 + ], + "lines": [ + { + "bbox": [ + 487, + 165, + 498, + 174 + ], + "spans": [ + { + "bbox": [ + 487, + 165, + 498, + 174 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "lines": [ + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "type": "text", + "content": "Figure 2. Fig. 2a compares the condition number (7) on a 1D signal regression task before (dotted line) and after (solid line) applying equilibrated " + }, + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "type": "text", + "content": " and Jacobi " + }, + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 313, + 175, + 553, + 262 + ], + "type": "text", + "content": " preconditioners. The equilibrated preconditioner significantly reduces the Hessian's condition number, as shown by the larger gap between the yellow solid and dotted lines compared to the green solid and dotted lines representing the Jacobi preconditioner, thus achieves faster convergence as seen in Fig. 2b." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": "Given an objective function " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "L(\\theta) = |f(\\theta)|^2" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": " for a nonlinear function " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": ". The Jacobian " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "J_{L}" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": " can be computed via the chain rule: " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "J_{L} = 2J_{f}^{T}f" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "J_{f}" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": " denotes the Jacobian of " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": ". The Hessian of " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "inline_equation", + "content": "H_{L}" + }, + { + "bbox": [ + 313, + 282, + 554, + 344 + ], + "type": "text", + "content": ", can be computed by an application of the chain rule" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 385, + 350, + 553, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 350, + 553, + 365 + ], + "spans": [ + { + "bbox": [ + 385, + 350, + 553, + 365 + ], + "type": "interline_equation", + "content": "H _ {L} = 2 J _ {f} ^ {T} J _ {f} + 2 H _ {f} f. \\tag {8}", + "image_path": "1206e54ff84b8c014b60167f868a92855419e3f1ab6338c95a3a6d38bc423e3e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "text", + "content": "We can then approximate the Hessian " + }, + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "inline_equation", + "content": "H_{L}" + }, + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "text", + "content": " by the term " + }, + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "inline_equation", + "content": "2J_{f}^{T}J_{f}" + }, + { + "bbox": [ + 313, + 374, + 558, + 399 + ], + "type": "text", + "content": ". Leading to the first order approximation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 347, + 406, + 553, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 406, + 553, + 431 + ], + "spans": [ + { + "bbox": [ + 347, + 406, + 553, + 431 + ], + "type": "interline_equation", + "content": "H _ {L} \\approx 2 J _ {f} ^ {T} J _ {f} = \\frac {1}{2 | f | ^ {2}} J _ {L} ^ {T} J _ {L} = \\frac {1}{2 L} J _ {L} ^ {T} J _ {L}. \\tag {9}", + "image_path": "2912f66488238c1a71b03b54d71962e2617c414ce0bf0de697eabb0b648ba15e.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": "Eq. (9) yields the basic idea of the Gauss-Newton method. By taking the Gauss-Newton matrix " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "J_{L}^{T}J_{L}" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": " as an approximation to the Hessian " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "H_{L}" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": ", we can perform an optimization update that uses the step: " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "\\Delta_{GN} = -\\frac{1}{J^TJ}\\nabla L" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": ". The Gauss-Newton matrix is in general only positive semi-definite. Therefore, when implementing the algorithm one often adds a small damping factor " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": " so the implemented step is " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "\\Delta_{GN} = -\\frac{1}{J^TJ + \\lambda}\\nabla L" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": ". A similar derivation can be made for more general loss functions used in non-linear least squares type regression problems [34]. It follows that the Gauss-Newton method can be seen as a preconditioned SGD that uses a first order (first derivatives) Hessian approximate preconditioner given by the Gauss-Newton matrix " + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "inline_equation", + "content": "J^T J" + }, + { + "bbox": [ + 313, + 437, + 564, + 594 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": "Using the above observations we now show how to view Adam as an optimizer that applies a diagonal preconditioner. The Adam optimizer involves two key steps. The first is to compute a first moment estimate of the form " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "m_{t} = \\beta_{1}m_{t - 1} + (1 - \\beta_{1})g_{t}" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": " is the gradient of a given objective function " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": " at iteration " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "m_0 = 0" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ". The second is to compute a second moment estimate " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "v_{t} = \\beta_{2}v_{t - 1} + (1 - \\beta_{2})g_{t}^{2}" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "g_{t}^{2} = g_{t}\\odot g_{t},\\odot" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": " denotes the Hadamard product, and " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "v_{0} = 0" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ". The numbers " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "0 < \\beta_{1} < \\beta_{2} < 1" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": " are hyperparameters. The algorithm then applies a bias correction to the above first" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "27225" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 221, + 208 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 221, + 208 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 221, + 208 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 221, + 208 + ], + "type": "image", + "image_path": "150a19ddfd5b7786e5637b7114b6a8adf18d154c731103e64cb80fc8f8bd4033.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 213, + 146, + 221 + ], + "lines": [ + { + "bbox": [ + 135, + 213, + 146, + 221 + ], + "spans": [ + { + "bbox": [ + 135, + 213, + 146, + 221 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 227, + 72, + 383, + 208 + ], + "blocks": [ + { + "bbox": [ + 227, + 72, + 383, + 208 + ], + "lines": [ + { + "bbox": [ + 227, + 72, + 383, + 208 + ], + "spans": [ + { + "bbox": [ + 227, + 72, + 383, + 208 + ], + "type": "image", + "image_path": "9104b3424b2530ee19492f45e26433bb81312bbda42839a4ad5d8c84ba4a153a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 298, + 212, + 309, + 220 + ], + "lines": [ + { + "bbox": [ + 298, + 212, + 309, + 220 + ], + "spans": [ + { + "bbox": [ + 298, + 212, + 309, + 220 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 221, + 555, + 266 + ], + "lines": [ + { + "bbox": [ + 55, + 221, + 555, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 555, + 266 + ], + "type": "text", + "content": "Figure 3. Comparison of training convergence for neural fields with different activations – ReLU with positional encoding (ReLU (PE)), wavelet, sine and Gaussian – using Adam and SGD optimizers across three tasks: 2D image reconstruction (Fig. 3a), 3D binary occupancy reconstruction (Fig. 3b), and NeRF (Fig. 3c). In all cases, the Adam optimizer outperforms SGD, indicating that leveraging curvature information facilitates faster convergence." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 388, + 78, + 547, + 208 + ], + "blocks": [ + { + "bbox": [ + 388, + 78, + 547, + 208 + ], + "lines": [ + { + "bbox": [ + 388, + 78, + 547, + 208 + ], + "spans": [ + { + "bbox": [ + 388, + 78, + 547, + 208 + ], + "type": "image", + "image_path": "a3ce407e507e7c7aeed26f594909ebd161892fabe90e4a90cbd26e5f8d8354ea.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 462, + 213, + 472, + 220 + ], + "lines": [ + { + "bbox": [ + 462, + 213, + 472, + 220 + ], + "spans": [ + { + "bbox": [ + 462, + 213, + 472, + 220 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 287, + 295, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 287, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 287, + 295, + 323 + ], + "type": "text", + "content": "and second moment estimates, and then takes a moving average to perform an update step based on " + }, + { + "bbox": [ + 55, + 287, + 295, + 323 + ], + "type": "inline_equation", + "content": "-\\frac{m_t}{\\sqrt{v_t}}" + }, + { + "bbox": [ + 55, + 287, + 295, + 323 + ], + "type": "text", + "content": ", see [23] for details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "content": "For the following discussion, we will only focus on analyzing the second raw moment estimate, as this is related to the Gauss-Newton matrix. Given an objective function " + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "content": ", observe that we can express " + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "inline_equation", + "content": "g_t^2 = g_t \\odot g_t = \\text{Diag}(J^T J)" + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "content": " denotes the Jacobian of " + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 324, + 296, + 396 + ], + "type": "text", + "content": ". Thus the second raw moment estimate of Adam can be recast as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 99, + 403, + 294, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 403, + 294, + 419 + ], + "spans": [ + { + "bbox": [ + 99, + 403, + 294, + 419 + ], + "type": "interline_equation", + "content": "v _ {t} = \\beta_ {2} v _ {t - 1} + (1 - \\beta_ {2}) \\operatorname {D i a g} \\left(J _ {t} ^ {T} J _ {t}\\right) \\tag {10}", + "image_path": "3539fb3b65dec2cb2ad8c418a499aa1776e3ea71d4794b5a2079c6b3d4926537.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "inline_equation", + "content": "J_{t}" + }, + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "text", + "content": " denotes the Jacobian at iteration " + }, + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 427, + 296, + 522 + ], + "type": "text", + "content": ". Thus we see that Adam applies a preconditioner given by the diagonal of the Gauss-Newton matrix. Since the Gauss-Newton matrix can be seen as a first order approximation to the Hessian, Adam can be seen as using an approximation to curvature to adapt the learning rate for faster optimization. This suggests that Adam can outperform SGD which employs no preconditioner." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 523, + 296, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 523, + 296, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 523, + 296, + 643 + ], + "type": "text", + "content": "We empirically validated this insight across three distinct neural field tasks: image reconstruction, binary occupancy, and NeRF. For each task, we compared the performance of ReLU(PE) activated networks trained with both SGD and Adam against networks using wavelet, sine, and Gaussian activations. As shown in Fig. 3, Adam consistently outperforms SGD in all cases. This suggests that Adam's use of a preconditioner significantly enhances its performance for neural field applications, see Sec. 5 for the details of the architectures and experimental setup." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 651, + 149, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 149, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 149, + 662 + ], + "type": "text", + "content": "4.4. Main theorems" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 668, + 296, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 668, + 296, + 704 + ], + "spans": [ + { + "bbox": [ + 55, + 668, + 296, + 704 + ], + "type": "text", + "content": "In Sec. 4.3, we discussed how Adam can be viewed as applying a diagonal preconditioner based on the diagonal of the Gauss-Newton matrix, which uses first derivatives to" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 347, + 286, + 522, + 417 + ], + "blocks": [ + { + "bbox": [ + 347, + 286, + 522, + 417 + ], + "lines": [ + { + "bbox": [ + 347, + 286, + 522, + 417 + ], + "spans": [ + { + "bbox": [ + 347, + 286, + 522, + 417 + ], + "type": "image", + "image_path": "71d26ca2e77dcbbabd3e3142c48014e425ca4beee0f006629c287e2a095b594a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 419, + 555, + 474 + ], + "lines": [ + { + "bbox": [ + 313, + 419, + 555, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 555, + 474 + ], + "type": "text", + "content": "Figure 4. Percentage sparsity of Hessian-vector product matrices across all layers throughout the training process of a 2D image reconstruction task, using ESGD to train networks with different activations. The x-axis ranges from 0 to 1, with values closer to 1 indicating higher sparsity." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 495, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 554, + 590 + ], + "type": "text", + "content": "approximate the Hessian matrix. Here, we aim to identify the architectural properties that enable effective training of neural fields with diagonal preconditioners that give a better approximation to the Hessian. Our primary theorems demonstrate that the choice of activation function is crucial for enabling efficient training with such preconditioners, highlighting its central role in achieving effective curvature-aware optimization for neural fields." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": "Recall Sec. 4.1 that diagonal preconditioners such as the equilibrated precondition " + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": " or the Jacobi preconditioner " + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": " all involve the Hessian matrix. In the context of neural networks the Hessian of the loss landscape is often an extremely large matrix. Thus in practical settings one often replaces the Hessian with a Hessian vector product which is much cheaper to store [34]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 674, + 554, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 674, + 554, + 711 + ], + "spans": [ + { + "bbox": [ + 313, + 674, + 554, + 711 + ], + "type": "text", + "content": "Our first theorem shows that the Hessian vector product of the loss landscape associated to a sine, Gaussian, wavelet or sinc activated neural field produces a dense vector." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "27226" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "Theorem 4.2. Let " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " denote a sine, Gaussian, wavelet or sinc activated neural field. Let " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta)" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " denote the MSE loss associated to " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " and a training set " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "(X,Y)" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " denote the Hessian of " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " at a fixed parameter point " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": ". Then given a non-zero vector " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " the Hessian vector product " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "Hv" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " will be a dense vector." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 152, + 296, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 152, + 296, + 201 + ], + "spans": [ + { + "bbox": [ + 55, + 152, + 296, + 201 + ], + "type": "text", + "content": "While it may seem rather costly for a sine- or Gaussian-activated INR to have dense Hessian vector products when applied to the MSE loss function, we point out that the cost is much less than storing a dense Hessian." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "spans": [ + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": "Theorem 4.3. Let " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " denote a ReLU/ReLU(PE)-activated neural field. Let " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta)" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " denote the MSE loss associated to " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " and a training set " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "(X, Y)" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " denote the Hessian of " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " at a fixed parameter point " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": ". Then given a non-zero vector " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " the Hessian vector product " + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "inline_equation", + "content": "Hv" + }, + { + "bbox": [ + 55, + 208, + 296, + 269 + ], + "type": "text", + "content": " will be a sparse vector." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "text", + "content": "Theorem 4.2 and Theorem 4.3 also hold for the binary cross-entropy loss. The proofs of Theorem 4.2 and Theorem 4.3 are given in the Supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 312, + 296, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 296, + 525 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 296, + 525 + ], + "type": "text", + "content": "Theorem 4.3 implies that when applying a preconditioner, built from a Hessian vector product, to a ReLU/ReLU(PE) INR, such as ESGD [14] or AdaHessian [62], only a few components of the gradient will be scaled during the update step. This means that the preconditioner will not be adding much to the optimization process. On the other hand, Theorem 4.2 implies that applying a preconditioner built from the Hessian to the gradient of the MSE loss of a sine, Gaussian and wavelet-activated neural field should help optimization as many of the gradient components will get scaled by a quantity depending on the curvature of the loss landscape. This yields a clear difference between ReLU/ReLU(PE) activated neural fields and those activated with a sine, Gaussian, wavelet activation. In particular, Theorem 4.2 implies that neural fields admitting a sine, Gaussian, wavelet activation have the ability to be trained efficiently with a diagonal curvature aware preconditioner such as the equilibrated preconditioner " + }, + { + "bbox": [ + 55, + 312, + 296, + 525 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 55, + 312, + 296, + 525 + ], + "type": "text", + "content": " defined in Sec. 4.1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 527, + 296, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 527, + 296, + 706 + ], + "spans": [ + { + "bbox": [ + 55, + 527, + 296, + 706 + ], + "type": "text", + "content": "Fig. 4 shows the results of a Hessian vector product of the MSE loss of a ReLU(PE) and Gaussian neural field for an image reconstruction task for the weights in all layers of the network layer throughout training. The random vector was chosen from a Rademacher distribution and the reported figures are given as the mean of the Hessian of all layers averaged over all iterations of training. As demonstrated by the experiment, the ReLU(PE) network generates a sparse Hessian-vector product, as predicted by Theorem 4.3, while the Gaussian network produces a dense vector, as indicated by Theorem 4.2. Furthermore, as we will observe in Sec. 5, this sparsity helps explain why Adam performs well for neural fields with ReLU (ReLU(PE)) activations, whereas an algorithm like ESGD [14] does not. This is because Adam does not rely on Hessian-vector product." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 71, + 395, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 395, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 395, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "content": "We compared various preconditioners over popular benchmarks [22, 28, 50, 52, 54]: 2D image reconstruction, 3D shape reconstruction and novel view synthesis with NeRF. Our primary focus was on curvature-aware preconditioners that are well-suited for the stochastic training of neural network. Specifically, we compared the following methods: ESGD " + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "inline_equation", + "content": "[14]^2" + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "content": ", AdaHessian " + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "inline_equation", + "content": "[62]^3" + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "content": ", Shampoo " + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "inline_equation", + "content": "[21]^4" + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "content": ", and Kronecker-based preconditioner " + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "inline_equation", + "content": "[30]^5" + }, + { + "bbox": [ + 313, + 91, + 572, + 258 + ], + "type": "text", + "content": ". We provide the details of each algorithm including the reproducibility details of each experiment and machines we used to run each experiment in the supplementary material. In the main paper, we focused on analyzing Gaussian networks, see supplementary material for additional analysis for other non-traditional activations and other neural field tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "text", + "content": "Remark for AdaHessian We observed that in the implementation of AdaHessian, an equilibrated preconditioner " + }, + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "text", + "content": " is utilized, even though the paper primarily focuses on using a Jacobi preconditioner [14]. Therefore, we introduced a Jacobi preconditioner " + }, + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "inline_equation", + "content": "D^{J}" + }, + { + "bbox": [ + 313, + 263, + 555, + 347 + ], + "type": "text", + "content": " into AdaHessian, which we refer to as AdaHessian(J). We use the term AdaHessian(E) for the original implementation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "text", + "content": "Remark for ESGD We further modified the ESGD by applying the squared Hessian diagonal preconditioner in two settings: using an exponential moving average (ESGD) and using an infinity norm (ESGD-max) [23]. We also opted to recompute the " + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "inline_equation", + "content": "D^{E}" + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "text", + "content": " for every " + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "text", + "content": " iterations for computational efficiency, we use " + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "inline_equation", + "content": "N = 100" + }, + { + "bbox": [ + 313, + 351, + 555, + 423 + ], + "type": "text", + "content": " for all the experiments." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 431, + 440, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 440, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 440, + 443 + ], + "type": "text", + "content": "5.1. Image Reconstruction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "text", + "content": "We evaluated on a 2D image reconstruction task, where given pixel coordinates " + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "text", + "content": ", we optimized a neural network to regress the corresponding RGB values " + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "text", + "content": ". We used a 5-layer Gaussian-activated network with 256 neurons. We used " + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "inline_equation", + "content": "\\sigma = 0.05" + }, + { + "bbox": [ + 313, + 449, + 556, + 651 + ], + "type": "text", + "content": " for the Gaussian activation. We trained the network using mini-batches of size 512. We compared the training convergence of different preconditioners and the Adam optimizer on the lion instance from the DIV2K dataset [1] in Fig. 5a. Additional results on the rest of the DIV2K dataset are provided in the supplementary material. As predicted by Theorem 4.2, Gaussian network equipped with the dense Hessian-vector product exhibits faster convergence when optimized with curvature-aware preconditioned methods compared to Adam. Notably, ESGD demonstrates faster convergence and has comparable training time and memory usage per iteration compared to Adam." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 326, + 658, + 444, + 669 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 658, + 444, + 669 + ], + "spans": [ + { + "bbox": [ + 326, + 658, + 444, + 669 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 326, + 658, + 444, + 669 + ], + "type": "text", + "content": "https://github.com/crowsonkb/esgd" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 326, + 669, + 456, + 678 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 669, + 456, + 678 + ], + "spans": [ + { + "bbox": [ + 326, + 669, + 456, + 678 + ], + "type": "text", + "content": "3https://github.com/amirgholami/adahes" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 678, + 468, + 688 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 678, + 468, + 688 + ], + "spans": [ + { + "bbox": [ + 326, + 678, + 468, + 688 + ], + "type": "text", + "content": "4https://github.com/google-research/google-" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 688, + 468, + 697 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 688, + 468, + 697 + ], + "spans": [ + { + "bbox": [ + 315, + 688, + 468, + 697 + ], + "type": "text", + "content": "research/tree/master/scalable_shampoo/pytorch" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 697, + 474, + 708 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 697, + 474, + 708 + ], + "spans": [ + { + "bbox": [ + 326, + 697, + 474, + 708 + ], + "type": "text", + "content": "5https://github.com/Thrandis/EKFAC-pytorch" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "27227" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 131, + 74, + 302, + 217 + ], + "blocks": [ + { + "bbox": [ + 131, + 74, + 302, + 217 + ], + "lines": [ + { + "bbox": [ + 131, + 74, + 302, + 217 + ], + "spans": [ + { + "bbox": [ + 131, + 74, + 302, + 217 + ], + "type": "image", + "image_path": "99f8da22605ca54d3f70f804bee1b6eba7543f4e1d988b4497c36a9357accd50.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 220, + 221, + 230 + ], + "lines": [ + { + "bbox": [ + 211, + 220, + 221, + 230 + ], + "spans": [ + { + "bbox": [ + 211, + 220, + 221, + 230 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 308, + 72, + 478, + 217 + ], + "blocks": [ + { + "bbox": [ + 308, + 72, + 478, + 217 + ], + "lines": [ + { + "bbox": [ + 308, + 72, + 478, + 217 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 478, + 217 + ], + "type": "image", + "image_path": "87496d8c5dd8a872aa627cf97ed9b257a395f62be382dfa107f31eda11a4a87a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 387, + 220, + 397, + 229 + ], + "lines": [ + { + "bbox": [ + 387, + 220, + 397, + 229 + ], + "spans": [ + { + "bbox": [ + 387, + 220, + 397, + 229 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 230, + 555, + 285 + ], + "lines": [ + { + "bbox": [ + 55, + 230, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 555, + 285 + ], + "type": "text", + "content": "Figure 5. Comparison of training convergence and computational complexity for various preconditioners. We evaluated a Gaussian-activated neural field on the lion instance from the DIV2K dataset. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: We provide the time-based comparisons in the supplementary material (Sec 3.1). Similar analysis for other activations and additional instances from the DIV2K dataset are available in the supplementary material (Sec. 3.2)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 306, + 296, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 306, + 296, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 306, + 296, + 403 + ], + "type": "text", + "content": "ESGD and AdaHessian obtain Hessian information by computing Hessian-vector products, which makes them very computational efficient. Each Hessian-vector product is generally as fast as a single gradient computation, as demonstrated in Fig. 5b. In contrast, other preconditioners, particularly Shampoo are more computationally expensive because they involve Kronecker product computations for preconditioner matrices, see supp. material for details." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 409, + 255, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 409, + 255, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 255, + 422 + ], + "type": "text", + "content": "5.2. 3D Binary Occupancy Reconstruction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "text", + "content": "We evaluated on learning a binary occupancy field, where given 3D point coordinates " + }, + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "text", + "content": ", we optimized a neural network to represent the occupancy field of 3D shapes. Following existing works [22], we sampled one million 3D points for training - one-third of the points were sampled uniformly within the volume, and the remaining two-thirds of the points were sampled near the mesh surface and perturbed with random Gaussian noise using sigma of 0.1 and 0.01, respectively [22]. We trained the network using binary cross-entropy (BCE) loss, which compares the predicted occupancy and the true occupancy. We used a 5-layer Gaussian network with 256 neurons and " + }, + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "inline_equation", + "content": "\\sigma = 0.09" + }, + { + "bbox": [ + 55, + 426, + 295, + 582 + ], + "type": "text", + "content": ". We trained the network using mini-batches of size 50000." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 301, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 301, + 691 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 301, + 691 + ], + "type": "text", + "content": "We compared the training convergence of different preconditioners and the Adam optimizer on the armadillo instance from the Stanford 3D Scanning dataset. Fig. 6 shows that ESGD exhibits superior convergence than other preconditioner-type optimizers. We showcase a qualitative result comparing the mesh reconstruction of ESGD and Adam given the same number of iteration in Fig. 7. Interestingly, when dealing with higher mode signals, both AdaHessian and Shampoo no longer demonstrated superior convergence," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 306, + 559, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 306, + 559, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 306, + 559, + 402 + ], + "type": "text", + "content": "unlike in the 2D image reconstruction task in Fig. 5a. We speculate that the local Hessians may become noisy with higher mode signals, thereby impacting the gradient updates. In contrast, this noise did not significantly affect ESGD's convergence because its preconditioner updates were performed every " + }, + { + "bbox": [ + 313, + 306, + 559, + 402 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 306, + 559, + 402 + ], + "type": "text", + "content": " iterations. Hence, we will focus on comparing Adam and ESGD for the experiments in the following section." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 409, + 484, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 484, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 484, + 422 + ], + "type": "text", + "content": "5.3. Neural Radiance Fields (NeRF)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 426, + 555, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 463 + ], + "type": "text", + "content": "Neural Radiance Fields (NeRF) have recently emerged as a pioneering approach in novel view synthesis, utilizing neural networks to model volumetric fields of 3D scenes using" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 341, + 483, + 526, + 625 + ], + "blocks": [ + { + "bbox": [ + 341, + 483, + 526, + 625 + ], + "lines": [ + { + "bbox": [ + 341, + 483, + 526, + 625 + ], + "spans": [ + { + "bbox": [ + 341, + 483, + 526, + 625 + ], + "type": "image", + "image_path": "ea9ea563ce0c03cf9e8472dc52508e1d0380337a68ef3344324c413917a4da05.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 627, + 555, + 704 + ], + "lines": [ + { + "bbox": [ + 313, + 627, + 555, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 627, + 555, + 704 + ], + "type": "text", + "content": "Figure 6. Comparison of training convergence for various preconditioners. We evaluated a Gaussian-activated neural field on a 3D binary occupancy reconstruction task on the armadillo instance. ESGD demonstrates superior convergence compared to other preconditioners, striking a balance between accuracy and computational efficiency. Note: Similar analysis for other activations are available in the supplementary material." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 696, + 215, + 708 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 696, + 215, + 708 + ], + "spans": [ + { + "bbox": [ + 66, + 696, + 215, + 708 + ], + "type": "text", + "content": "6http://graphics.stanford.edu/data/3Dscanrep/" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "27228" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 573, + 216 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 573, + 216 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 573, + 216 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 573, + 216 + ], + "type": "table", + "html": "
SceneTrain PSNRIteration ↓Time (s)↓Adam TestIteration ↓Time (s)↓ESGD Test
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
fern25.38200K368.4324.380.740.28120K270.8124.410.740.30
flower29.17200K469.3125.670.780.12120K263.9325.650.780.13
horns24.9560K130.8221.820.700.34120K227.5820.780.630.44
orchids23.3200K501.9019.560.610.24120K269.0119.740.610.21
room31.20110K194.0531.600.930.12140K201.8830.520.900.20
fortress30.18140K333.7028.930.810.15140K334.5628.60.800.17
leaves21.36200K482.3419.560.610.24120K271.2519.430.590.25
trex25.5080K164.9622.040.710.31120K209.2522.210.750.23
", + "image_path": "4b5c0a6fd6c06cbf1fc0384f66b0566c6cfb376edaf8b902907187374cc9f13d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 223, + 555, + 247 + ], + "lines": [ + { + "bbox": [ + 55, + 223, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 555, + 247 + ], + "type": "text", + "content": "Table 1. Quantitative results of NeRF on all instances from the LLFF dataset [31]. The reported time solely refers to the optimization update step. Note: Results for the Blender synthetic [32] and BLEFF [60] datasets are available in supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 61, + 270, + 171, + 374 + ], + "blocks": [ + { + "bbox": [ + 61, + 270, + 171, + 374 + ], + "lines": [ + { + "bbox": [ + 61, + 270, + 171, + 374 + ], + "spans": [ + { + "bbox": [ + 61, + 270, + 171, + 374 + ], + "type": "image", + "image_path": "58924fec6d51fdaf675756065544bbb0fdd50e69b56253961a237a7bec04c21a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 110, + 384, + 121, + 392 + ], + "lines": [ + { + "bbox": [ + 110, + 384, + 121, + 392 + ], + "spans": [ + { + "bbox": [ + 110, + 384, + 121, + 392 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 393, + 295, + 471 + ], + "lines": [ + { + "bbox": [ + 55, + 393, + 295, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 295, + 471 + ], + "type": "text", + "content": "Figure 7. Qualitative results for the dragon instance from Stanford 3D Scanning dataset. Compared to the Gaussian-based neural field trained with Adam (Fig. 7a), ESGD (Fig. 7b) has reconstructed the shapes with significantly improved fidelity at epoch 500 (zoom in " + }, + { + "bbox": [ + 55, + 393, + 295, + 471 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 55, + 393, + 295, + 471 + ], + "type": "text", + "content": " for better visibility). Note: Qualitative results for the rest of the instances from Stanford 3D Scanning Dataset are available in supplementary material." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 178, + 270, + 287, + 373 + ], + "blocks": [ + { + "bbox": [ + 178, + 270, + 287, + 373 + ], + "lines": [ + { + "bbox": [ + 178, + 270, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 178, + 270, + 287, + 373 + ], + "type": "image", + "image_path": "9973ee219ba2dc58b28c0fad3cfc16fd83922fdaedec8a11e53452f4d5482c23.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 228, + 384, + 239, + 392 + ], + "lines": [ + { + "bbox": [ + 228, + 384, + 239, + 392 + ], + "spans": [ + { + "bbox": [ + 228, + 384, + 239, + 392 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "content": "multi-view 2D images [12, 13, 26, 32, 44]. Specifically, given 3D points " + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "content": " and viewing direction, NeRF estimates the 5D radiance field of a 3D scene which maps each input 3D coordinate to its corresponding volume density " + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}" + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "content": " and directional emitted color " + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "content": " [12, 26, 32]. We used an 8-layer Gaussian-activated network with 256 neurons and " + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "inline_equation", + "content": "\\sigma = 0.1" + }, + { + "bbox": [ + 55, + 491, + 295, + 696 + ], + "type": "text", + "content": ". Recall that in the previous section we demonstrated that ESGD exhibited superior performance in terms of convergence and computational complexity compared to other preconditioners. Therefore, we focused on comparing Adam and ESGD here. We determined the same training PSNR at which both model converged and reported the corresponding optimization metrics, including the number of iterations and the total time taken for the update computation. We evaluated the PSNR on a hold-out test scene. Table 1. shows that ESGD achieves on average faster convergence than Adam, see more results in the supp. material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 266, + 389, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 389, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 389, + 277 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 285, + 555, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 555, + 477 + ], + "type": "text", + "content": "While our work theoretically established the suitability of curvature-aware preconditioners for training neural fields with non-traditional activations such as sine, Gaussian, and wavelets, it also highlighted their ineffectiveness for neural fields employing ReLU-PE activations. Specifically, we showed that Adam performs well for ReLU-PE due to its use of a diagonal preconditioner derived from the Gauss-Newton matrix, rather than relying on Hessian vector products. However, this raises an important limitation of our work: we did not explore whether alternative preconditioners, potentially more effective than the Gauss-Newton matrix, could be developed to improve the training of ReLU-PE activated neural fields beyond what Adam achieves. This is particularly relevant since ReLU-PE remains widely used in practical applications. This question represents an avenue for future research, which we leave it as future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 487, + 388, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 388, + 500 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 388, + 500 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 507, + 559, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 507, + 559, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 507, + 559, + 700 + ], + "type": "text", + "content": "We explored the impact of preconditioners on the stochastic training of neural fields, developing a theoretical framework based on Hessian-vector products. Our analysis demonstrates that curvature-aware preconditioners can significantly accelerate training for neural fields with non-traditional activations, such as sine, Gaussian, and wavelet. Experimental validation across various tasks—including image reconstruction, shape modeling, and neural radiance fields—using ESGD and AdaHessian confirmed these benefits. In contrast, for neural fields with ReLU or ReLU-PE activations, our theory predicted no significant advantage from curvature-aware preconditioning, highlighting the activation-dependent nature of these methods. For practitioners employing activations like sine, Gaussian, or wavelet, robust curvature-aware algorithms provide an efficient approach for stochastic training across diverse applications." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "27229" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 706 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing", + "text_level": 1, + "bbox": [ + 140, + 128, + 857, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yoonjeon Kim $^{1,*}$ Soohyun Ryu $^{1,*}$", + "bbox": [ + 189, + 200, + 488, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Joowon Kim1 June Yong Yang1", + "bbox": [ + 189, + 220, + 477, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yeonsung Jung1 Hyunkoo Lee1", + "bbox": [ + 511, + 203, + 792, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jaeryong Hwang² Eunho Yang1,3,\\dagger", + "bbox": [ + 500, + 220, + 805, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ KAIST $^{2}$ Republic of Korea Naval Academy $^{3}$ AITRICS", + "bbox": [ + 230, + 244, + 759, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://augclip.github.io/", + "bbox": [ + 380, + 273, + 609, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 241, + 323, + 331, + 339 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The development of vision-language and generative models has significantly advanced text-guided image editing, which seeks the preservation of core elements in the source image while implementing modifications based on the target text. However, existing metrics have a context-blindness problem, indiscriminately applying the same evaluation criteria on completely different pairs of source image and target text, biasing towards either modification or preservation. Directional CLIP similarity, the only metric that considers both source image and target text, is also biased towards modification aspects and attends to irrelevant editing regions of the image. We propose AugCLIP, a context-aware metric that adaptively coordinates preservation and modification aspects, depending on the specific context of a given source image and target text. This is done by deriving the CLIP representation of an ideally edited image, that preserves the source image with necessary modifications to align with target text. More specifically, using a multi-modal large language model, AugCLIP augments the textual descriptions of the source and target, then calculates a modification vector through a hyperplane that separates source and target attributes in CLIP space. Extensive experiments on five benchmark datasets, encompassing a diverse range of editing scenarios, show that AugCLIP aligns remarkably well with human evaluation standards, outperforming existing metrics. The code is available at https://github.com/augclip/augclip_eval.", + "bbox": [ + 89, + 354, + 485, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 821, + 243, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building on advancements in vision-language models [7, 19, 24], recent generative models [2, 8, 12] have", + "bbox": [ + 89, + 845, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8c9eebbd2925c824938d973906dafb48c22165ddd0370f1de1e63043f81a15ac.jpg", + "image_caption": [ + "\"Turn into Ironman\"", + "Figure 1. Context Blindness Problem of Existing Evaluation Metrics. Evaluation metrics should consider the specific context of a given source image and target text. However, existing metrics exhibit context-blindness, applying the same criteria of either 'preserve' (P) or 'modify' (M) across the entire image. Our proposed metric, AugCLIP, is a context-aware metric that flexibly applies different criteria to local regions of the image." + ], + "image_footnote": [], + "bbox": [ + 521, + 338, + 633, + 424 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sitting down", + "bbox": [ + 638, + 343, + 720, + 356 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tree in behind", + "bbox": [ + 643, + 366, + 718, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Preserve", + "bbox": [ + 656, + 381, + 702, + 392 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Orange T-shirt Red armor suit", + "bbox": [ + 643, + 397, + 720, + 416 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Blue cap", + "bbox": [ + 658, + 420, + 705, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ironman mask", + "bbox": [ + 651, + 431, + 709, + 440 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Modify", + "bbox": [ + 658, + 440, + 700, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(a) Given Context", + "bbox": [ + 531, + 469, + 620, + 481 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) Guideline", + "bbox": [ + 640, + 469, + 704, + 481 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Preserve or Modify ?", + "bbox": [ + 745, + 325, + 883, + 339 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "P√ M X m △ P", + "bbox": [ + 733, + 340, + 883, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "P√ M X m△ P√", + "bbox": [ + 743, + 364, + 883, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "P X M√ M√ M√", + "bbox": [ + 743, + 398, + 883, + 410 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "P×M√M", + "bbox": [ + 736, + 420, + 883, + 441 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Presv.Modif. CLIP.. AugCLIP", + "bbox": [ + 733, + 441, + 893, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Metric Metric", + "bbox": [ + 733, + 450, + 800, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(c) Evaluation Standard of Metrics", + "bbox": [ + 728, + 469, + 898, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "been widely utilized as creative tools for image editing via text instructions. Text-guided image editing models enable the modification of images in response to textual guidance, ensuring that changes are aligned with the provided instructions. The primary objective of these models is to apply the necessary modifications guided by the target text while preserving most of the source image.", + "bbox": [ + 509, + 635, + 906, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the remarkable advancements in editing models, there has been a lack of rigorous evaluation methods, tailored specifically for text-guided image editing. Consequently, most studies [1, 2, 6, 9, 13, 15, 26] have heavily relied on human evaluation, which provides balanced consideration of preservation and modification aspects. However, as it is costly and impractical for real-world applications, researchers have adapted automatic evaluation metrics [3, 10, 11, 29] originally", + "bbox": [ + 511, + 756, + 908, + 893 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 0, + 810, + 18 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 723, + 30 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 754, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution,† Corresponding Author.", + "bbox": [ + 109, + 886, + 388, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23474", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "designed for other vision tasks, such as image generation or captioning.", + "bbox": [ + 89, + 90, + 480, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In text-guided editing scenarios, it is essential to assess which elements in the source to preserve and which in the target to modify into, based on the specific context of the given source image and target text (see Fig. 1(a)-(b) for example). Existing metrics, however, exhibit context blindness, meaning preservation-centric metrics completely ignore the target context while modification-centric metrics do not account for the source context. As shown in Fig. 1(c), preservation- and modification-centric metrics apply a fixed standard across the entire image, regardless of the true editing requirement of the given context. Even combining them fails to overcome the context blindness problem.", + "bbox": [ + 88, + 121, + 482, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among existing metrics, directional CLIP similarity [6] is unique because it provides a method to consider both the source image and target text in the evaluation. Even this metric suffers from a context-blindness problem, using a fixed standard without considering the specific relationship between the source image and target text. We show that directional CLIP similarity tends to prioritize modification over preservation, and often focuses on peripheral parts rather than regions that are edited as guided by target text, in Sec. 3. These observations underscore the need for a context-aware metric to dynamically adjust the evaluation standard, balancing both aspects in response to diverse editing contexts.", + "bbox": [ + 91, + 318, + 483, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on our comprehensive analysis, we propose a novel context-aware metric, AugCLIP, which evaluates the quality of the edited image by comparing it with an estimated representation of a well-edited image. To balance preservation and modification, a well-edited image is represented by a minimum modification on the source image, while matching the target text. We use multi-modal large language models (MLLMs) to extract attributes that capture various visual aspects of the source image and target text. With these attributes, we derive a hyperplane that separates the source and target to derive the ideal modification as a projection to this hyperplane. AugCLIP evaluates how closely the edited image aligns with the estimated ideal image in CLIP space.", + "bbox": [ + 91, + 530, + 483, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our metric AugCLIP demonstrates remarkable improvement in alignment with human judgment on diverse editing scenarios such as object, attribute, and style alteration compared to all other existing metrics. Moreover, our metric is even applicable to personalized generation, the DreamBooth dataset, where the objective is to identify an object in the source image and edit it into a completely novel context. This shows the flexibility of AugCLIP, which seamlessly applies to", + "bbox": [ + 89, + 755, + 482, + 891 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a variety of editing directions. Notably, our metric excels in identifying minor differences between the source image and the edited image, showing superb ability in complex image editing scenarios such as MagicBrush.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The major contributions are summarized as follows.", + "bbox": [ + 535, + 152, + 903, + 166 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We point out the unreliability of current evaluation metrics in text-guided image editing, noting their inability to balance preservation and modification effectively due to inherent context blindness.", + "- We introduce AugCLIP, a context-aware metric for image editing by automatically augmenting descriptions via MLLM and estimating a balanced representation of preservation and modification, which takes into account the relative importance of each description.", + "- AugCLIP demonstrates a significantly high correlation with human evaluations across various editing scenarios, even in complex applications where existing metrics struggle." + ], + "bbox": [ + 516, + 167, + 903, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background on Existing Metrics", + "text_level": 1, + "bbox": [ + 511, + 391, + 854, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the context of text-guided image editing, evaluation metrics should assess the quality of edited images in terms of both preservation of the source image and modification towards the target text.", + "bbox": [ + 511, + 416, + 903, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Preservation-Centric Metrics FID [11], LPIPS [29], and L2 distance measure feature-level distance between images. These metrics are primarily used in image generation tasks to compare the distributions of real and generated images. When applied to editing scenarios, they assess the distance between the source and edited images, completely ignoring the target text guiding the editing process. Segmentation consistency (SC) [13] measures the structural change. Additionally, DINO similarity (DINO) and CLIP-I evaluate the semantic similarity between the source and edited images within the DINO [3] and CLIP [24] embedding spaces, also focusing solely on preservation.", + "bbox": [ + 511, + 494, + 906, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modification-Centric Metrics To assess how well an edited image aligns with the target text, the primary approach involves using a pre-trained multimodal model [24]. CLIPScore (CLIP-T) [10] is the most widely adopted metric in this category, measuring the similarity between the edited image and the target text. This metric completely ignores the source image that should be considered for the preservation aspect.", + "bbox": [ + 511, + 708, + 903, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Holistic Evaluation of Preservation and Modification Directional CLIP similarity $(\\mathrm{CLIP}_{\\mathrm{dir}})$ [6] is unique among existing metrics as it assesses both", + "bbox": [ + 511, + 847, + 903, + 893 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23475", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1c8ce8f5a625a3d22a3a0d9744ec75cab9225c914d2e15478f6bc5f8e2694c6e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 90, + 228, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3a2227634b79b47f81c7fe8b92d8118006ef75989a9db184213c1ccb0b1c2145.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 232, + 90, + 354, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6c00a34eaff5677c44d10ec0536358caa28c320f50f81da97bd6468e00a98f42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 101, + 478, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/93538b080502ab1a322105badc074aeae7795f08479e368552742f27761cd259.jpg", + "image_caption": [ + "Figure 2. Combination of Preservation- and Modification-Centric Metrics Deteriorates in Performance. The plot shows the human alignment score $s_{\\mathrm{align}}$ measured by a linear interpolation of {DINO, SC, CLIP-I} and CLIP-T. The results show that combining rather degrades the alignment with human judgment." + ], + "image_footnote": [], + "bbox": [ + 93, + 202, + 228, + 303 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/744d18e838725f65caa8433e102eaca6987b63a7313fd5eacf19d9ce13721c92.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 202, + 354, + 303 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8fa399fdc13a66b411439f291cd752df0581df85c4c6e870afbaab852d1187f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 210, + 478, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "preservation and modification aspects by evaluating directional alignment between the original and edited images concerning the source and target text.", + "bbox": [ + 89, + 428, + 482, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, these metrics employ a fixed evaluation standard, disregarding the context of each editing scenario, which leads to context blindness. As discussed in Sec. 3, combining preservation- and modification-centric metrics or using directional CLIP similarity fails to balance preservation and modification adequately, resulting in misalignment with human judgment.", + "bbox": [ + 89, + 473, + 482, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problems of Existing Metrics in Balancing Preservation and Modification Aspects", + "text_level": 1, + "bbox": [ + 89, + 590, + 482, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing evaluation metrics, that focus on either one of the preservation or modification aspects, face a challenge in assessing both aspects. Does combining these two metrics successfully balance the preservation and modification aspects? We systematically analyze how these metrics and their combinations still fail in balancing the two colliding objectives, suffering from context-blindness (Sec. 3.1). Moreover, we focus on directional CLIP similarity, the unique metric that accounts for both source image and target text, to reveal that it presents two significant problems that question its reliability (Sec. 3.2).", + "bbox": [ + 89, + 652, + 482, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Combination of Preservation- and Modification-Centric Metrics", + "text_level": 1, + "bbox": [ + 511, + 90, + 906, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We explore whether combining preservation- and modification-centric metrics can improve alignment with human judgments across two benchmark datasets: EditVal [1] and CelebA [20] (Results on the other three benchmark datasets are deferred to the Appendix). To do so, we combine CLIP-T, a modification-centric metric, and preservation-centric metrics (LPIPS, DINO similarity, CLIP-I) with varying interpolation values $\\gamma \\in [0,1]$ . Note that both metrics are scaled to the same range before interpolation, ensuring the interpolation value $\\gamma$ is properly reflected in the final combined score.", + "bbox": [ + 511, + 127, + 906, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, the combination of two powerful metrics in preservation and modification often leads to performance degradation. This manifests that a simple combination of the colliding metrics cannot be a reliable evaluation metric. This is due to the context-blindness of these metrics, failing to holistically consider source image and target text. Preservation-centric metrics compare only the source and edited images, ignoring the target context. Similarly, modification-centric metrics consider only the target text, overlooking the source context. This highlights the need for a tailored metric that is contextually aware of both preservation and modification, ensuring a reliable alignment with human evaluations across diverse datasets and tasks.", + "bbox": [ + 511, + 308, + 908, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Directional CLIP Similarity", + "text_level": 1, + "bbox": [ + 511, + 544, + 764, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Directional CLIP similarity $\\left(\\mathrm{CLIP}_{\\mathrm{dir}}\\right)$ is designed to assess both preservation and modification in text-guided image editing by measuring the similarity between image and text directions as follows:", + "bbox": [ + 511, + 566, + 905, + 627 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {C L I P} _ {\\text {d i r}} = \\operatorname {c s} (\\Delta I, \\Delta T) \\tag {1} \\\\ = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right), \\quad (2) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 638, + 903, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{cs}(\\mathbf{a},\\mathbf{b}) = \\frac{\\mathbf{a}\\cdot\\mathbf{b}}{\\|\\mathbf{a}\\|\\|\\mathbf{b}\\|}$ denotes cosine similarity and $E(\\cdot)$ is a CLIP encoder for either image or text. Here, $I_{\\mathrm{edit}}$ is the edited image to be evaluated, which is edited from the source image $I_{\\mathrm{src}}$ according to the target text $T_{\\mathrm{trg}}$ . For evaluation of directional CLIP similarity, $I_{\\mathrm{src}}$ , the corresponding text about the source image, is required. We analyze that $\\mathrm{CLIP}_{\\mathrm{dir}}$ has two major problems that hinder the balanced evaluation of preservation and modification.", + "bbox": [ + 511, + 696, + 906, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathrm{CLIP}_{\\mathrm{dir}}$ overly emphasizes modification. Directional CLIP similarity overly emphasizes the alignment with the target text while neglecting the preservation", + "bbox": [ + 511, + 852, + 906, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23476", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1b44e9ea270df7073b17db98998961ef898e5e6cd05e96607596615eb2b4f439.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 99, + 225, + 246 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b53cd2f5514d4b7404af639b680b2c7aedef8b4380f562690f7d3fc38badf4ff.jpg", + "image_caption": [], + "image_footnote": [ + "$\\Delta I =$ Ground truth $-I_{s r c}$ $\\Delta I =$ Excess. modif. $I_{s r c}$ $\\Delta T =$ \"A jumping dog\"-\"A standing dog" + ], + "bbox": [ + 233, + 102, + 359, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e8190263bcb328de08de33f9055b2a0c56cea6835b3cb68fcae68ace3e3e855c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 103, + 483, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/075e71b7abe87c38bf657e662f9dad1ee50a11302e0657687f56f753c991766b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 99, + 627, + 246 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f01aa218aa97bd91363b143788f29cccef0ec82a14846f147056ed6e33aab155.jpg", + "image_caption": [], + "image_footnote": [ + "$\\Delta I =$ Ground truth - $I_{s r c}$ $\\Delta I =$ Excess. modif. - $I_{s r c}$ $\\Delta T =$ \"Acheze pizza\"-\"Apepperoni pizza" + ], + "bbox": [ + 637, + 103, + 758, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4fa0ab85cff9b1a02c14cc2b57b4ff418607255ced43969c4ed097e0b86ff577.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 103, + 883, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/098dd07ac310cf24839e8ba4817157d4c13883224d8deea0b652c17db3a7087d.jpg", + "image_caption": [ + "(a) Problem1. Overemphasizing Modification over Preservation", + "Figure 3. Problems of Directional CLIP Similarity. (a) $\\mathrm{CLIP}_{\\mathrm{dir}}$ assigns higher scores to excessive modification, over well-edited ground truth images. (b) $\\mathrm{CLIP}_{\\mathrm{dir}}$ evaluates edited images by attending to irrelevant regions of the image. Adding visual annotations helps $\\mathrm{CLIP}_{\\mathrm{dir}}$ properly attend to edited regions." + ], + "image_footnote": [], + "bbox": [ + 99, + 303, + 888, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the source image. Despite attempting to incorporate preservation by subtracting $T_{\\mathrm{src}}$ from $T_{\\mathrm{trg}}$ , $\\mathrm{CLIP}_{\\mathrm{dir}}$ frequently favors excessively modified images over ground truth ideally edited images as shown in samples in Fig. 3(a). Specifically, $\\mathrm{CLIP}_{\\mathrm{dir}}$ metric fails on $63\\%$ of the 100 editing cases in TEdBench [12] and $35.1\\%$ of the 1053 cases in MagicBrush [28] (Details in Sec. 5). This problem happens since $\\mathrm{CLIP}_{\\mathrm{dir}}$ is designed to assume that a well-edited image should primarily adhere to the target text. Thus, it blindly favors the visual features of the target text, leading to unreliable results.", + "bbox": [ + 88, + 527, + 485, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathrm{CLIP}_{\\mathrm{dir}}$ overlooks edited regions. $\\mathrm{CLIP}_{\\mathrm{dir}}$ often focuses on peripheral or unmodified local areas of the edited image, overlooking the specific areas that are edited by the text. Using the relevancy map [4], $R(\\Delta I; \\Delta T)^1$ , to visualize attention on image regions corresponding to the text direction, we observe that $\\mathrm{CLIP}_{\\mathrm{dir}}$ frequently fails to concentrate on the image regions that are directly relevant to the target text as shown in Fig. 3(b). The figure also shows that", + "bbox": [ + 89, + 710, + 483, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "adding explicit visual details guides $\\mathrm{CLIP}_{\\mathrm{dir}}$ to attend to edited regions properly.", + "bbox": [ + 511, + 527, + 906, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. AugCLIP: A Context-Aware Evaluation Metric", + "text_level": 1, + "bbox": [ + 511, + 570, + 906, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce a novel evaluation metric, AugCLIP, for scoring the editing quality of the image in terms of preservation and modification. Given a target text $T_{\\mathrm{trg}}$ and a source image $I_{\\mathrm{src}}$ , AugCLIP measures the cosine similarity between the edited image $I_{\\mathrm{edit}}$ and the ideal editing. Since the ideal edited image is not given in most evaluation cases, we estimate the representation of an ideally edited image as a modification on the source image, $I_{\\mathrm{src}} + \\mathbf{v}$ , where $\\mathbf{v}$ is the modification vector. Then, the editing quality of the edited image $I_{\\mathrm{edit}}$ is evaluated as", + "bbox": [ + 509, + 613, + 906, + 779 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A u g C L I P} \\left(I _ {\\text {e d i t}}; I _ {\\text {s r c}}, T _ {\\text {t r g}}\\right) = \\mathbf {c s} \\left(E \\left(I _ {\\text {e d i t}}\\right), E \\left(I _ {\\text {s r c}}\\right) + \\mathbf {v}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 791, + 903, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $E(\\cdot)$ is a CLIP encoder.", + "bbox": [ + 511, + 823, + 735, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The evaluation score ranges between [0, 1], where the maximum value 1 indicates that the edited image is ideally modified by an editing model. We outline the framework of AugCLIP in Fig. 4. We extract the visual", + "bbox": [ + 511, + 838, + 906, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1The original relevancy map $\\pmb{R}$ utilizes an image-text pair. To adapt it to $\\mathrm{CLIP}_{\\mathrm{dir}}$ , we subtract two relevancy maps. Details are in the Appendix.", + "bbox": [ + 89, + 856, + 482, + 893 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23477", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/45eb7f797cf0782a3c775980250217466df33cde545f07f95042d268b2c43413.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 93, + 87, + 377, + 281 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/490b677c93ac8c32c507d7d2706bb918ff4d3acde950c427efd92b9e31f9ba30.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 383, + 88, + 666, + 281 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/426fc1f65916732dcde6805389ab9c50bbfdd7f3f0906d19f8fd7a77f386567c.jpg", + "image_caption": [ + "Figure 4. (a) Description Extraction Process. The source image describes a young child standing on the balance board. Target text guides the editing model to make the girl sit. The source and target attributes are extracted with MLLM. (b) Evaluation Process of AugCLIP. The two edited images demonstrate i) An older woman sitting down with legs crossed ( $I_{\\mathrm{edit}}^1$ ) and ii) A young girl sitting on the floor ( $I_{\\mathrm{edit}}^2$ ). AugCLIP derives the ideal image representation as a minimum modification $\\mathbf{v}$ on the source image to be classified as target. The second image that is closer to $I_{\\mathrm{src}} + \\mathbf{v}$ shows a higher score, while the first image that is excessively modified with lost source identity shows a lower score." + ], + "image_footnote": [], + "bbox": [ + 669, + 89, + 903, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "features of the source image and target text (Sec. 4.1), then derive the CLIP representation of an ideal modification that satisfies the two criteria: 'i) Does the edited image follow the target text?' and 'ii) Does the edited image preserve the source image?' (Sec. 4.2).", + "bbox": [ + 89, + 430, + 482, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Extracting and Processing Attributes", + "text_level": 1, + "bbox": [ + 89, + 513, + 411, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Source & Target Attribute Extraction As described in Fig. 4(a), we extract visual descriptions about attributes of the source image and target text using a state-of-the-art multi-modal large language model (MLLM), GPT-4V [22]. From the source image, we extract visual features that can be the object of preservation. Likewise, from the target text, we extract visual features that can be the object of modification. The extraction process is instructed by five annotated in-context examples, which are provided in the Appendix.", + "bbox": [ + 89, + 535, + 483, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Encoding into CLIP Space After attribute extraction from MLLM, each attribute is encoded into CLIP space. The source attributes are denoted as $\\mathcal{D}_S$ and target attributes as $\\mathcal{D}_T$ .", + "bbox": [ + 89, + 702, + 483, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relative Weighting on Attributes In editing scenarios, some of the attributes are more important than others. For instance, drawing stripes is more essential than a short mane to represent a zebra. To prioritize this, we emphasize the similarity between key attributes within the same class. Since multi-modal large-language models sample based on the empirical probability, frequently extracted attributes indicate higher", + "bbox": [ + 89, + 779, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "importance in representing the context. Formally, the importance of each visual attribute in $\\mathcal{D}_S$ and $\\mathcal{D}_T$ is represented as a cosine similarity between CLIP embeddings in the same set as", + "bbox": [ + 511, + 430, + 906, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI m p o r t a n c e (v _ {i}) = \\sum_ {j \\neq i} \\frac {u _ {i} \\cdot v _ {j}}{\\| u _ {i} \\| \\| v _ {j} \\|}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 496, + 903, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for all $u_{j}$ in the same attribute set, either $\\mathcal{D}_S$ or $\\mathcal{D}_T$ .", + "bbox": [ + 511, + 537, + 893, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additionally, the importance should be downweighted by how much the visual attribute hinders the preservation of the source image or modification of the target text. More specifically, a collision between source and target attributes is measured by averaged cosine distance to CLIP embeddings in the opposite set as", + "bbox": [ + 511, + 553, + 905, + 643 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC o l l i s i o n \\left(v _ {i}\\right) = - \\sum_ {l} \\frac {v _ {i} \\cdot w _ {l}}{\\| v _ {i} \\| \\| w _ {l} \\|}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 648, + 903, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for all $w_{l}$ in the opposite attribute set.", + "bbox": [ + 511, + 688, + 792, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adding these two measures, the weighting value for the attribute $v \\in \\mathcal{D}_S \\cup \\mathcal{D}_T$ is defined as", + "bbox": [ + 511, + 703, + 905, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha (v) = \\text {I m p o r t a n c e} (v) + \\text {C o l l i s i o n} (v). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 741, + 903, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This weighting value accounts for the relative significance of each attribute in the evaluation process and is integrated into Eq. (7).", + "bbox": [ + 511, + 763, + 905, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Deriving the Ideal Editing in CLIP Space", + "text_level": 1, + "bbox": [ + 511, + 816, + 867, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the extracted source and target attributes, we describe how to derive a modification vector that satisfies i) modification into the target text and ii) preservation of the source image.", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23478", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Criterion 1: Does the edited image follow the target text? To determine if the edited image faithfully follows the given target text, it is intuitive to employ a classifier that classifies the image into either source or target. Classification into source indicates the edited image is still closer to the source image, while classification into target means that the image is sufficiently modified. The classifier is derived by a hyperplane that separates the source $\\mathcal{D}_S$ and target $\\mathcal{D}_T$ .", + "bbox": [ + 89, + 90, + 480, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Formally, the classifier function $g(x) = \\mathbf{w}^T x + b$ assigns a CLIP embedding $x$ to the target class if $g(x) > 0$ , or to the source class if $g(x) < 0$ . Therefore, $E(I_{\\mathrm{edit}})$ should satisfy $\\mathbf{w}^T E(I_{\\mathrm{edit}}) + b > 0$ if the edited image faithfully follows the target text. Here, the optimization form of the classifier function $g(x)$ is", + "bbox": [ + 89, + 226, + 483, + 319 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w}, b} \\frac {1}{2} \\| \\mathbf {w} \\| ^ {2} + C \\sum_ {i = 1} ^ {N} \\alpha (v _ {i}) \\cdot \\max (0, 1 - y _ {i} (\\mathbf {w} \\cdot v _ {i} + b)), (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 329, + 483, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $y_{i} = +1$ for $v_{i}\\in \\mathcal{D}_{T}$ and $y_{i} = -1$ for $v_{i}\\in \\mathcal{D}_{S}$ . Here, the precomputed weighting values $\\alpha (\\cdot)$ in Eq. (6) are integrated into the optimization process.", + "bbox": [ + 89, + 378, + 483, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Criterion 2: Does the edited image preserve the source image? However, it is equally important to consider the second criterion, source image preservation. Therefore, the CLIP representation of modification should inflict minimum modification to the original embedding $E(I_{\\mathrm{src}})$ , while being classified as a target class. Formally, we derive the modification $\\mathbf{v}$ in CLIP space that satisfies", + "bbox": [ + 89, + 441, + 483, + 563 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {v}} \\| \\mathbf {v} \\| \\quad \\text {s u b j e c t t o} \\quad \\mathbf {w} ^ {T} \\left(E \\left(I _ {\\mathrm {s r c}}\\right) + \\mathbf {v}\\right) + b > 0. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 573, + 482, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Derivation of $\\mathbf{v}$ To minimize $\\| \\mathbf{v}\\|$ , $\\mathbf{v}$ should be in the direction that most efficiently increases the classifier output $g(\\cdot)$ . This direction is given by the gradient of the classifier function concerning $\\mathbf{x}$ , which is $\\mathbf{w} = \\nabla g(\\mathbf{x})$ . Therefore, the optimal $\\mathbf{v}$ is $c\\mathbf{w}$ where $c > 0$ is a scalar to be determined. Substituting $\\mathbf{v} = c\\mathbf{w}$ to Eq. (8), we derive the following equation", + "bbox": [ + 89, + 612, + 483, + 719 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nc > \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 728, + 482, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to solve for $c$ that minimizes $\\| \\mathbf{v}\\|$ , we derive the smallest $c$ satisfying the condition as $c_{\\mathrm{min}} = \\frac{-(\\mathbf{w}^\\top I_{\\mathrm{src}} + b)}{\\|\\mathbf{w}\\|^2}$ . Then the modification vector $\\mathbf{v}$ is derived as", + "bbox": [ + 89, + 772, + 483, + 833 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} = c _ {\\min } \\mathbf {w} = \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}} \\mathbf {w}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 833, + 482, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, AugCLIP is computed by substituting $\\mathbf{v}$ to Eq. (3).", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 90, + 666, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. For our experiments, we employ a pre-trained CLIP-ViT 16/B model for CLIP-based metrics. Source and target attributes are generated using GPT-4V [22]. Further details on prompting the source and target attributes are in the Appendix.", + "bbox": [ + 511, + 114, + 903, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline Metrics. We compare AugCLIP with DINO similarity, LPIPS, L2, Segmentation Consistency (SC), Directional CLIP similarity $(\\mathrm{CLIP}_{\\mathrm{dir}})$ , CLIP-I, and CLIP-T. The CLIP variants are summarized as follows:", + "bbox": [ + 511, + 207, + 903, + 282 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C L I P} _ {\\mathrm {d i r}} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 289, + 893, + 306 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C L I P - I} = \\mathbf {c s} \\left(E (I _ {\\mathrm {e d i t}}), E (I _ {\\mathrm {s r c}})\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 310, + 743, + 327 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {C L I P - T} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right)\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 329, + 761, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that FID measures the distance between two distributions of image features, this metric cannot be measured in a sample-wise manner. Therefore, FID cannot be tested in terms of alignment with human evaluation or preference test on ground truth samples.", + "bbox": [ + 511, + 354, + 903, + 430 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benchmark Datasets and Editing Models. We evaluate AugCLIP and existing metrics across several text-guided image editing benchmarks, including TEd-Bench [12], EditVal [1], MagicBrush [28], DreamBooth [26], and CelebA [20]. Each benchmark dataset represents varying editing scenarios as in Tab. 1. For each benchmark dataset, we employ multiple editing models [2, 5, 8, 9, 13, 14, 16-18, 23, 27] as specified in Tab. 1 for suitable type of benchmark dataset. Details on benchmark datasets are provided in the Appendix.", + "bbox": [ + 511, + 446, + 905, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Correlation with Human Judgment", + "text_level": 1, + "bbox": [ + 511, + 604, + 821, + 621 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "User Study To evaluate the effectiveness of AugCLIP compared to existing metrics, we conduct a Two-Alternative Forced Choice survey on human evaluators to collect preferences over diverse edited images. The alignment score $s_{2\\mathrm{AFC}}$ measures if each metric prefers the same option as human evaluators. The survey was conducted using Amazon Mechanical Turk (AMT), over three benchmark datasets, encompassing a total of 105 participants as detailed in Tab. 2. The survey questionnaire is structured as described in the Appendix, providing clear criteria to consider source image preservation and target text alignment.", + "bbox": [ + 511, + 627, + 906, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AugCLIP aligns better with human judgments. As shown in Tab. 3, AugCLIP, the context-aware metric that balances preservation and modification, is superior over all previous metrics across diverse benchmark datasets. A high level of alignment between", + "bbox": [ + 511, + 825, + 903, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23479", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/31291b9f4ad1862860f9c6550cba4452bd783225b822f87ddf07be6852b7c8cc.jpg", + "table_caption": [ + "Table 1. Benchmark Datasets and Editing Models Used for Evaluating the Performance of Metrics." + ], + "table_footnote": [], + "table_body": "
CelebAEditValTEdBenchMagicBrushDreamBooth
Dataset TypesFacial AttributeGeneral ObjectObject CentricLocal Region EditingPersonalized Generation
Editing Models[13, 14, 17, 23][2, 5, 8, 9, 12][2, 5, 8, 9, 12][2, 5, 8, 9, 12][16, 18, 27]
Dataset Size50648100105350
", + "bbox": [ + 96, + 109, + 898, + 180 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2530bfacd46e47e5004cf6ee8d1550481e60f74dfec5623bc5abf3d7ed2c6f59.jpg", + "table_caption": [ + "Table 2. User Study Statistics." + ], + "table_footnote": [], + "table_body": "
CelebAEditValDreamBooth
Survey questions393537
Participants453030
", + "bbox": [ + 96, + 224, + 478, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8d6f4faf50f0e7b17136c010d583f6cb3753b4a15e5a2e1ea55103b9c4d1025.jpg", + "table_caption": [ + "Table 3. Correlation with Human Judgment. Human alignment score $s_{2\\mathrm{AFC}} (\\uparrow)$ , scaled between 0 to 1." + ], + "table_footnote": [], + "table_body": "
MetricsPresv.Modif.CelebAEditValDreamBooth
L2✓✗0.6530.3480.464
LPIPS✓✗0.4650.3600.286
DINO✓✗0.5740.3480.286
SC✓✗0.7520.7640.571
CLIP-I✓✗0.8480.7300.857
CLIP-T✗✓0.4910.3990.321
CLIPdir▲✓0.6730.6970.357
AugCLIP✓✓0.8830.8310.857
", + "bbox": [ + 94, + 321, + 478, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "preservation-centric (L2, LPIPS, DINO, SC, CLIP-I) and human judgment is expected because these benchmarks do not significantly deviate from the source image.", + "bbox": [ + 89, + 468, + 482, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ground Truth Editing Selection Test", + "text_level": 1, + "bbox": [ + 89, + 537, + 406, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Creating Triplet Dataset We generate a triplet of images, each representing a well-edited, excessively preserved, and excessively modified image. Among the triplet of images, the well-edited image is provided in the benchmark datasets, TEdBench, and MagicBrush. Excessively modified images are generated with text-to-image models [25] instructed by the target text, completely ignoring the source image. Excessively preserved images are generated by applying a negligible transformation to the given source image, ignoring the target text. Then, we measure the accuracy where each metric correctly assigns the highest score to the well-edited image as AccBoth. Yielding high accuracy in this test means that the evaluation metric can balance both preservation and modification aspects, without being biased to either side.", + "bbox": [ + 88, + 560, + 482, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AugCLIP is superior in balancing preservation and modification. In Tab. 4, AugCLIP is on par with or even better than baseline metrics over all datasets. This emphasizes the balanced evaluation criteria of AugCLIP, which previous metrics fail to abide by. Seg-", + "bbox": [ + 89, + 820, + 483, + 895 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a1f74016f717102516915243a2bd598462ac55cc7407e494e3a47476c6162464.jpg", + "table_caption": [ + "Table 4. Ground Truth Selection Test. Accuracy, Accboth $(\\uparrow)$ of assigning higher scores to ground truth images over excessively preserved and modified images." + ], + "table_footnote": [], + "table_body": "
MetricsPresv. Modif.TEdBenchMagicBrush
L2✓X0.3100.002
LPIPS✓X0.0900.000
DINO✓X0.2800.008
SC✓X0.4200.936
CLIP-I✓X0.2810.810
CLIP-TX✓0.3120.260
CLIPdir▲✓0.3500.601
AugCLIP✓✓0.5700.889
", + "bbox": [ + 537, + 244, + 885, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ment Consistency (SC) excels in MagicBrush since the dataset requires editing a small local area of the image.", + "bbox": [ + 511, + 409, + 903, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Analysis", + "text_level": 1, + "bbox": [ + 511, + 454, + 625, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use $s_{2\\mathrm{AFC}}$ for CelebA, EditVal, and Dreambooth, and AccBoth for TEdBench and MagicBrush. We compare our metric, AugCLIP with $\\mathrm{CLIP}_{\\mathrm{dir}}$ , which is the only metric that considers both preservation and modification.", + "bbox": [ + 511, + 479, + 905, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AugCLIP generalizes to diverse editing scenarios. Text-guided image editing encompasses a wide range of tasks such as style editing, object replacement, local editing, partial alteration, and personalized generation. AugCLIP excels in the highly complex scenarios of local editing as conducted with the MagicBrush dataset. Moreover, AugCLIP highly aligns with human judgment in the personalized generation case of DreamBooth, which has been underexplored by previous metrics. We report how well AugCLIP aligns with human judgment with various editing cases provided in the EditVal dataset. Across all eight scenarios, except for the texture modification task, AugCLIP outperforms $\\mathrm{CLIP}_{\\mathrm{dir}}$ as shown in Tab. 5.", + "bbox": [ + 511, + 571, + 906, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Augmenting $\\mathrm{CLIP}_{\\mathrm{dir}}$ cannot provide reliable evaluation result. We demonstrate the impact of augmenting $\\mathrm{CLIP}_{\\mathrm{dir}}$ with attributes, extracted in Sec. 4.1. Specifically, we replace the source and target text embeddings with the average of their respective attribute embeddings, $\\mathcal{D}_S$ and $\\mathcal{D}_T$ . As shown in Tab. 6,", + "bbox": [ + 511, + 801, + 908, + 893 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23480", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3befeb3b719d2b96acc2c0e38a5c8f91562e1435bfe46b8d868c228386075c2f.jpg", + "table_caption": [ + "Table 5. Human Alignment Score $s_{2\\text{AFC}}$ on Various Text-guided Image Editing Scenarios." + ], + "table_footnote": [], + "table_body": "
Pos. AddObj. repl.Alter PartsBackground
CLIPdir0.6670.6880.7300.5
AugCLIP1.00.750.8381.0
TextureColorActionStyle
CLIPdir0.8061.01.00.529
AugCLIP0.7421.01.00.647
", + "bbox": [ + 93, + 119, + 480, + 213 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "this straightforward augmentation does not guarantee performance gain. AugCLIP consistently outperforms all description-augmented versions of $\\mathrm{CLIP}_{\\mathrm{dir}}$ . This improvement is due to AugCLIP's approach, which derives the ideal representation by a minimum modification vector. This is fundamentally different from the naive methodology of $\\mathrm{CLIP}_{\\mathrm{dir}}$ , which relies on a simple subtraction of the source from the target.", + "bbox": [ + 89, + 234, + 482, + 356 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ab1a3f68f0f6b543fd97f645549d1a27ba21bade7088525893c212ed2e737c44.jpg", + "table_caption": [ + "Table 6. Effect of Augmenting Attributes." + ], + "table_footnote": [], + "table_body": "
CelebAEditValDreamBoothTEDbenchMagicBrush
CLIPdir0.6730.6970.3570.3500.601
+DS0.8160.6290.3570.4000.429
+DT0.8190.7080.5360.4200.533
+DS∪DT0.8160.6070.5360.4400.402
AugCLIP0.8830.8310.8570.5700.889
", + "bbox": [ + 91, + 388, + 480, + 473 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weighting Strategy for Hyperplane We demonstrate the effectiveness of our weighting strategy, described in Eq. (6) in Tab. 7. Our weighting strategy enables AugCLIP to prioritize key features central to preservation and modification while estimating the representation of an ideally edited image, resulting in improvement in human alignment ( $s_{2\\mathrm{AFC}}$ ) and balancing preservation and modification ( $\\mathbf{Acc}_{\\mathrm{Both}}$ ).", + "bbox": [ + 89, + 503, + 482, + 626 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/303c8ceb15b6ef7e76616968006c82fb8aa3e71d7e21a6fac907f36a8135f0bd.jpg", + "table_caption": [ + "Table 7. Effect of Weighting Strategy." + ], + "table_footnote": [], + "table_body": "
CelebAEditValDreamBoothTEDBenchMagicBrush
Unweighted0.8490.7870.7860.4000.830
Weighted0.8830.8310.8570.5700.889
", + "bbox": [ + 91, + 659, + 480, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Length and Number of Attributes In Tab. 8, we compare short (under 5 words) and long (over 5 words), as well as cases with a fixed number (10, 20, or 30) of attributes. We observe that using short attributes tends to outperform using long ones, likely because they focus on a single visual aspect, avoiding the potential entanglement of multiple aspects in a single attribute. Moreover, the number of attributes impacts the performance depending on the scene complexity of the benchmark dataset, as complex scenarios require a higher number of attributes to fully capture the scene's", + "bbox": [ + 89, + 734, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "details. Therefore, allowing flexibility in the number of attributes, rather than imposing a strict limit, yields the best overall performance across all configurations.", + "bbox": [ + 511, + 90, + 906, + 137 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ab9e05ff9f2fa8260a741e691bd436ee3f78904a0bb52026fba91425e7b3936b.jpg", + "table_caption": [ + "Table 8. Effect of Length and Number of Attributes." + ], + "table_footnote": [], + "table_body": "
LengthNumberCelebAEditValDreamBoothTEDbenchMagicBrush
short100.8700.7190.8570.5400.889
short200.8290.8090.8210.5400.868
short300.8290.7640.7140.5700.863
long300.8430.6970.7500.5300.862
short-0.8830.8310.8570.5700.889
", + "bbox": [ + 514, + 170, + 903, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Description Randomness Using GPT-4V for description extraction introduces slight randomness across different seeds. Tests with five seeds show low variance (0.0197) in human alignment score ( $s_{2\\mathrm{AFC}}$ ), indicating that the description generation process does not affect the scoring. We also demonstrate in the Appendix that extracted attributes with different seeds do not vary.", + "bbox": [ + 511, + 277, + 906, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We provide analysis on the modification vector $\\mathbf{v}$ and choice of classifier function, discussion on limitations, description prompting, and extensive qualitative results in the Appendix.", + "bbox": [ + 511, + 398, + 905, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Discussions", + "text_level": 1, + "bbox": [ + 513, + 470, + 785, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method, AugCLIP, adds additional computation time compared to $\\mathrm{CLIP}_{\\mathrm{dir}}$ . It requires extracting attributes via MLLM, and then fitting a hyperplane to distinguish source and target attributes. This process takes around 12.3 seconds for attribute generation and 0.15 seconds for score computation. We will provide extracted attributes for all benchmark datasets to reduce this overhead, facilitating the evaluation process for future usage.", + "bbox": [ + 511, + 497, + 906, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion", + "text_level": 1, + "bbox": [ + 513, + 646, + 624, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present AugCLIP, a novel evaluation metric for text-guided image editing that balances source image preservation and target text modification. By leveraging a multi-modal language model to extract visual attributes and finding a separating hyperplane, AugCLIP estimates a representation of an ideal edited image that closely matches human preferences. Experiments on five benchmark datasets show that AugCLIP outperforms existing metrics, especially in challenging tasks, offering a more reliable tool for evaluating edits while preserving core attributes.", + "bbox": [ + 511, + 672, + 906, + 839 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23481", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 277, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the National Research Foundation of Korea (NRF) grants (RS-2023-00209060 A Study on Optimization and Network Interpretation Method for Large-Scale Machine Learning), Institute for Information & communications Technology Planning & Evaluation(IITP) grants (No.2022-0-00713 Meta-learning applicable to real-world problems, RS-2019-II190075 Artificial Intelligence Graduate School Program(KAIST)) funded by the Korea government(MSIT).", + "bbox": [ + 89, + 114, + 483, + 265 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 279, + 199, + 295 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samyadeep Basu, Mehrdad Saberi, Shweta Bhardwaj, Atoosa Malemir Chegini, Daniela Massiceti, Maziar Sanjabi, Shell Xu Hu, and Soheil Feizi. 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Gpt-4v (ision) as a generalist evaluator for vision-language tasks. arXiv preprint arXiv:2311.01361, 2023. 27" + ], + "bbox": [ + 91, + 90, + 480, + 667 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23483", + "bbox": [ + 478, + 943, + 517, + 954 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_model.json b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..609b7f8fc7fdbddc55c130064a597df2823bb17f --- /dev/null +++ b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_model.json @@ -0,0 +1,2420 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.725, + 0.031 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.032, + 0.756, + 0.047 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.13, + 0.859, + 0.177 + ], + "angle": 0, + "content": "Preserve or Modify? Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.202, + 0.49, + 0.222 + ], + "angle": 0, + "content": "Yoonjeon Kim\\(^{1,*}\\) Soohyun Ryu\\(^{1,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.222, + 0.478, + 0.24 + ], + "angle": 0, + "content": "Joowon Kim1 June Yong Yang1" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.204, + 0.793, + 0.221 + ], + "angle": 0, + "content": "Yeonsung Jung1 Hyunkoo Lee1" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.221, + 0.807, + 0.24 + ], + "angle": 0, + "content": "Jaeryong Hwang² Eunho Yang1,3,\\dagger" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.245, + 0.76, + 0.265 + ], + "angle": 0, + "content": "\\(^{1}\\) KAIST \\(^{2}\\) Republic of Korea Naval Academy \\(^{3}\\) AITRICS" + }, + { + "type": "text", + "bbox": [ + 0.381, + 0.274, + 0.611, + 0.29 + ], + "angle": 0, + "content": "https://augclip.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.243, + 0.324, + 0.333, + 0.34 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.355, + 0.486, + 0.794 + ], + "angle": 0, + "content": "The development of vision-language and generative models has significantly advanced text-guided image editing, which seeks the preservation of core elements in the source image while implementing modifications based on the target text. However, existing metrics have a context-blindness problem, indiscriminately applying the same evaluation criteria on completely different pairs of source image and target text, biasing towards either modification or preservation. Directional CLIP similarity, the only metric that considers both source image and target text, is also biased towards modification aspects and attends to irrelevant editing regions of the image. We propose AugCLIP, a context-aware metric that adaptively coordinates preservation and modification aspects, depending on the specific context of a given source image and target text. This is done by deriving the CLIP representation of an ideally edited image, that preserves the source image with necessary modifications to align with target text. More specifically, using a multi-modal large language model, AugCLIP augments the textual descriptions of the source and target, then calculates a modification vector through a hyperplane that separates source and target attributes in CLIP space. Extensive experiments on five benchmark datasets, encompassing a diverse range of editing scenarios, show that AugCLIP aligns remarkably well with human evaluation standards, outperforming existing metrics. The code is available at https://github.com/augclip/augclip_eval." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.822, + 0.245, + 0.837 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.847, + 0.485, + 0.88 + ], + "angle": 0, + "content": "Building on advancements in vision-language models [7, 19, 24], recent generative models [2, 8, 12] have" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.339, + 0.635, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.431, + 0.63, + 0.441 + ], + "angle": 0, + "content": "\"Turn into Ironman\"" + }, + { + "type": "text", + "bbox": [ + 0.64, + 0.344, + 0.721, + 0.357 + ], + "angle": 0, + "content": "Sitting down" + }, + { + "type": "text", + "bbox": [ + 0.644, + 0.367, + 0.72, + 0.378 + ], + "angle": 0, + "content": "Tree in behind" + }, + { + "type": "text", + "bbox": [ + 0.657, + 0.382, + 0.704, + 0.393 + ], + "angle": 0, + "content": "Preserve" + }, + { + "type": "text", + "bbox": [ + 0.644, + 0.398, + 0.721, + 0.417 + ], + "angle": 0, + "content": "Orange T-shirt Red armor suit" + }, + { + "type": "text", + "bbox": [ + 0.659, + 0.421, + 0.707, + 0.432 + ], + "angle": 0, + "content": "Blue cap" + }, + { + "type": "text", + "bbox": [ + 0.652, + 0.432, + 0.71, + 0.441 + ], + "angle": 0, + "content": "Ironman mask" + }, + { + "type": "text", + "bbox": [ + 0.66, + 0.441, + 0.701, + 0.452 + ], + "angle": 0, + "content": "Modify" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.47, + 0.621, + 0.482 + ], + "angle": 0, + "content": "(a) Given Context" + }, + { + "type": "text", + "bbox": [ + 0.641, + 0.47, + 0.705, + 0.482 + ], + "angle": 0, + "content": "(b) Guideline" + }, + { + "type": "text", + "bbox": [ + 0.746, + 0.327, + 0.884, + 0.34 + ], + "angle": 0, + "content": "Preserve or Modify ?" + }, + { + "type": "text", + "bbox": [ + 0.735, + 0.342, + 0.884, + 0.356 + ], + "angle": 0, + "content": "P√ M X m △ P" + }, + { + "type": "text", + "bbox": [ + 0.744, + 0.365, + 0.884, + 0.378 + ], + "angle": 0, + "content": "P√ M X m△ P√" + }, + { + "type": "text", + "bbox": [ + 0.744, + 0.399, + 0.884, + 0.411 + ], + "angle": 0, + "content": "P X M√ M√ M√" + }, + { + "type": "text", + "bbox": [ + 0.738, + 0.421, + 0.884, + 0.442 + ], + "angle": 0, + "content": "P×M√M" + }, + { + "type": "text", + "bbox": [ + 0.734, + 0.442, + 0.895, + 0.452 + ], + "angle": 0, + "content": "Presv.Modif. CLIP.. AugCLIP" + }, + { + "type": "text", + "bbox": [ + 0.734, + 0.452, + 0.802, + 0.461 + ], + "angle": 0, + "content": "Metric Metric" + }, + { + "type": "text", + "bbox": [ + 0.729, + 0.47, + 0.899, + 0.481 + ], + "angle": 0, + "content": "(c) Evaluation Standard of Metrics" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.498, + 0.907, + 0.61 + ], + "angle": 0, + "content": "Figure 1. Context Blindness Problem of Existing Evaluation Metrics. Evaluation metrics should consider the specific context of a given source image and target text. However, existing metrics exhibit context-blindness, applying the same criteria of either 'preserve' (P) or 'modify' (M) across the entire image. Our proposed metric, AugCLIP, is a context-aware metric that flexibly applies different criteria to local regions of the image." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.636, + 0.907, + 0.756 + ], + "angle": 0, + "content": "been widely utilized as creative tools for image editing via text instructions. Text-guided image editing models enable the modification of images in response to textual guidance, ensuring that changes are aligned with the provided instructions. The primary objective of these models is to apply the necessary modifications guided by the target text while preserving most of the source image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.757, + 0.909, + 0.894 + ], + "angle": 0, + "content": "Despite the remarkable advancements in editing models, there has been a lack of rigorous evaluation methods, tailored specifically for text-guided image editing. Consequently, most studies [1, 2, 6, 9, 13, 15, 26] have heavily relied on human evaluation, which provides balanced consideration of preservation and modification aspects. However, as it is costly and impractical for real-world applications, researchers have adapted automatic evaluation metrics [3, 10, 11, 29] originally" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.39, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution,† Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "23474" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.121 + ], + "angle": 0, + "content": "designed for other vision tasks, such as image generation or captioning." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.122, + 0.483, + 0.318 + ], + "angle": 0, + "content": "In text-guided editing scenarios, it is essential to assess which elements in the source to preserve and which in the target to modify into, based on the specific context of the given source image and target text (see Fig. 1(a)-(b) for example). Existing metrics, however, exhibit context blindness, meaning preservation-centric metrics completely ignore the target context while modification-centric metrics do not account for the source context. As shown in Fig. 1(c), preservation- and modification-centric metrics apply a fixed standard across the entire image, regardless of the true editing requirement of the given context. Even combining them fails to overcome the context blindness problem." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.319, + 0.485, + 0.529 + ], + "angle": 0, + "content": "Among existing metrics, directional CLIP similarity [6] is unique because it provides a method to consider both the source image and target text in the evaluation. Even this metric suffers from a context-blindness problem, using a fixed standard without considering the specific relationship between the source image and target text. We show that directional CLIP similarity tends to prioritize modification over preservation, and often focuses on peripheral parts rather than regions that are edited as guided by target text, in Sec. 3. These observations underscore the need for a context-aware metric to dynamically adjust the evaluation standard, balancing both aspects in response to diverse editing contexts." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.531, + 0.484, + 0.756 + ], + "angle": 0, + "content": "Based on our comprehensive analysis, we propose a novel context-aware metric, AugCLIP, which evaluates the quality of the edited image by comparing it with an estimated representation of a well-edited image. To balance preservation and modification, a well-edited image is represented by a minimum modification on the source image, while matching the target text. We use multi-modal large language models (MLLMs) to extract attributes that capture various visual aspects of the source image and target text. With these attributes, we derive a hyperplane that separates the source and target to derive the ideal modification as a projection to this hyperplane. AugCLIP evaluates how closely the edited image aligns with the estimated ideal image in CLIP space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.756, + 0.483, + 0.892 + ], + "angle": 0, + "content": "Our metric AugCLIP demonstrates remarkable improvement in alignment with human judgment on diverse editing scenarios such as object, attribute, and style alteration compared to all other existing metrics. Moreover, our metric is even applicable to personalized generation, the DreamBooth dataset, where the objective is to identify an object in the source image and edit it into a completely novel context. This shows the flexibility of AugCLIP, which seamlessly applies to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "a variety of editing directions. Notably, our metric excels in identifying minor differences between the source image and the edited image, showing superb ability in complex image editing scenarios such as MagicBrush." + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.153, + 0.904, + 0.167 + ], + "angle": 0, + "content": "The major contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.168, + 0.905, + 0.227 + ], + "angle": 0, + "content": "- We point out the unreliability of current evaluation metrics in text-guided image editing, noting their inability to balance preservation and modification effectively due to inherent context blindness." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.228, + 0.905, + 0.318 + ], + "angle": 0, + "content": "- We introduce AugCLIP, a context-aware metric for image editing by automatically augmenting descriptions via MLLM and estimating a balanced representation of preservation and modification, which takes into account the relative importance of each description." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.318, + 0.905, + 0.378 + ], + "angle": 0, + "content": "- AugCLIP demonstrates a significantly high correlation with human evaluations across various editing scenarios, even in complex applications where existing metrics struggle." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.168, + 0.905, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.392, + 0.856, + 0.41 + ], + "angle": 0, + "content": "2. Background on Existing Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.417, + 0.905, + 0.478 + ], + "angle": 0, + "content": "In the context of text-guided image editing, evaluation metrics should assess the quality of edited images in terms of both preservation of the source image and modification towards the target text." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.495, + 0.907, + 0.692 + ], + "angle": 0, + "content": "Preservation-Centric Metrics FID [11], LPIPS [29], and L2 distance measure feature-level distance between images. These metrics are primarily used in image generation tasks to compare the distributions of real and generated images. When applied to editing scenarios, they assess the distance between the source and edited images, completely ignoring the target text guiding the editing process. Segmentation consistency (SC) [13] measures the structural change. Additionally, DINO similarity (DINO) and CLIP-I evaluate the semantic similarity between the source and edited images within the DINO [3] and CLIP [24] embedding spaces, also focusing solely on preservation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.709, + 0.905, + 0.831 + ], + "angle": 0, + "content": "Modification-Centric Metrics To assess how well an edited image aligns with the target text, the primary approach involves using a pre-trained multimodal model [24]. CLIPScore (CLIP-T) [10] is the most widely adopted metric in this category, measuring the similarity between the edited image and the target text. This metric completely ignores the source image that should be considered for the preservation aspect." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.848, + 0.905, + 0.894 + ], + "angle": 0, + "content": "Holistic Evaluation of Preservation and Modification Directional CLIP similarity \\((\\mathrm{CLIP}_{\\mathrm{dir}})\\) [6] is unique among existing metrics as it assesses both" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "23475" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.092, + 0.23, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.233, + 0.092, + 0.356, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.102, + 0.48, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.203, + 0.23, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.203, + 0.355, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.212, + 0.48, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.318, + 0.483, + 0.402 + ], + "angle": 0, + "content": "Figure 2. Combination of Preservation- and Modification-Centric Metrics Deteriorates in Performance. The plot shows the human alignment score \\( s_{\\mathrm{align}} \\) measured by a linear interpolation of {DINO, SC, CLIP-I} and CLIP-T. The results show that combining rather degrades the alignment with human judgment." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.429, + 0.483, + 0.473 + ], + "angle": 0, + "content": "preservation and modification aspects by evaluating directional alignment between the original and edited images concerning the source and target text." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.474, + 0.483, + 0.581 + ], + "angle": 0, + "content": "However, these metrics employ a fixed evaluation standard, disregarding the context of each editing scenario, which leads to context blindness. As discussed in Sec. 3, combining preservation- and modification-centric metrics or using directional CLIP similarity fails to balance preservation and modification adequately, resulting in misalignment with human judgment." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.592, + 0.483, + 0.646 + ], + "angle": 0, + "content": "3. Problems of Existing Metrics in Balancing Preservation and Modification Aspects" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.653, + 0.483, + 0.835 + ], + "angle": 0, + "content": "Existing evaluation metrics, that focus on either one of the preservation or modification aspects, face a challenge in assessing both aspects. Does combining these two metrics successfully balance the preservation and modification aspects? We systematically analyze how these metrics and their combinations still fail in balancing the two colliding objectives, suffering from context-blindness (Sec. 3.1). Moreover, we focus on directional CLIP similarity, the unique metric that accounts for both source image and target text, to reveal that it presents two significant problems that question its reliability (Sec. 3.2)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.091, + 0.907, + 0.121 + ], + "angle": 0, + "content": "3.1. Combination of Preservation- and Modification-Centric Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.128, + 0.907, + 0.307 + ], + "angle": 0, + "content": "We explore whether combining preservation- and modification-centric metrics can improve alignment with human judgments across two benchmark datasets: EditVal [1] and CelebA [20] (Results on the other three benchmark datasets are deferred to the Appendix). To do so, we combine CLIP-T, a modification-centric metric, and preservation-centric metrics (LPIPS, DINO similarity, CLIP-I) with varying interpolation values \\(\\gamma \\in [0,1]\\). Note that both metrics are scaled to the same range before interpolation, ensuring the interpolation value \\(\\gamma\\) is properly reflected in the final combined score." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.309, + 0.909, + 0.535 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, the combination of two powerful metrics in preservation and modification often leads to performance degradation. This manifests that a simple combination of the colliding metrics cannot be a reliable evaluation metric. This is due to the context-blindness of these metrics, failing to holistically consider source image and target text. Preservation-centric metrics compare only the source and edited images, ignoring the target context. Similarly, modification-centric metrics consider only the target text, overlooking the source context. This highlights the need for a tailored metric that is contextually aware of both preservation and modification, ensuring a reliable alignment with human evaluations across diverse datasets and tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.545, + 0.766, + 0.562 + ], + "angle": 0, + "content": "3.2. Directional CLIP Similarity" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.906, + 0.628 + ], + "angle": 0, + "content": "Directional CLIP similarity \\(\\left(\\mathrm{CLIP}_{\\mathrm{dir}}\\right)\\) is designed to assess both preservation and modification in text-guided image editing by measuring the similarity between image and text directions as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.639, + 0.905, + 0.686 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {C L I P} _ {\\text {d i r}} = \\operatorname {c s} (\\Delta I, \\Delta T) \\tag {1} \\\\ = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right), \\quad (2) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.697, + 0.907, + 0.835 + ], + "angle": 0, + "content": "where \\(\\mathbf{cs}(\\mathbf{a},\\mathbf{b}) = \\frac{\\mathbf{a}\\cdot\\mathbf{b}}{\\|\\mathbf{a}\\|\\|\\mathbf{b}\\|}\\) denotes cosine similarity and \\(E(\\cdot)\\) is a CLIP encoder for either image or text. Here, \\(I_{\\mathrm{edit}}\\) is the edited image to be evaluated, which is edited from the source image \\(I_{\\mathrm{src}}\\) according to the target text \\(T_{\\mathrm{trg}}\\). For evaluation of directional CLIP similarity, \\(I_{\\mathrm{src}}\\), the corresponding text about the source image, is required. We analyze that \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) has two major problems that hinder the balanced evaluation of preservation and modification." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.853, + 0.907, + 0.899 + ], + "angle": 0, + "content": "\\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) overly emphasizes modification. Directional CLIP similarity overly emphasizes the alignment with the target text while neglecting the preservation" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "23476" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.101, + 0.226, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.234, + 0.103, + 0.36, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.104, + 0.485, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.244, + 0.242, + 0.482, + 0.269 + ], + "angle": 0, + "content": "\\(\\Delta I =\\) Ground truth \\(-I_{s r c}\\) \\(\\Delta I =\\) Excess. modif. \\(I_{s r c}\\) \\(\\Delta T =\\) \"A jumping dog\"-\"A standing dog" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.101, + 0.628, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.104, + 0.759, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.104, + 0.885, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.645, + 0.242, + 0.882, + 0.269 + ], + "angle": 0, + "content": "\\(\\Delta I =\\) Ground truth - \\(I_{s r c}\\) \\(\\Delta I =\\) Excess. modif. - \\(I_{s r c}\\) \\(\\Delta T =\\) \"Acheze pizza\"-\"Apepperoni pizza" + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.277, + 0.571, + 0.294 + ], + "angle": 0, + "content": "(a) Problem1. Overemphasizing Modification over Preservation" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.304, + 0.889, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.459, + 0.907, + 0.503 + ], + "angle": 0, + "content": "Figure 3. Problems of Directional CLIP Similarity. (a) \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) assigns higher scores to excessive modification, over well-edited ground truth images. (b) \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) evaluates edited images by attending to irrelevant regions of the image. Adding visual annotations helps \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) properly attend to edited regions." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.528, + 0.486, + 0.695 + ], + "angle": 0, + "content": "of the source image. Despite attempting to incorporate preservation by subtracting \\( T_{\\mathrm{src}} \\) from \\( T_{\\mathrm{trg}} \\), \\( \\mathrm{CLIP}_{\\mathrm{dir}} \\) frequently favors excessively modified images over ground truth ideally edited images as shown in samples in Fig. 3(a). Specifically, \\( \\mathrm{CLIP}_{\\mathrm{dir}} \\) metric fails on \\( 63\\% \\) of the 100 editing cases in TEdBench [12] and \\( 35.1\\% \\) of the 1053 cases in MagicBrush [28] (Details in Sec. 5). This problem happens since \\( \\mathrm{CLIP}_{\\mathrm{dir}} \\) is designed to assume that a well-edited image should primarily adhere to the target text. Thus, it blindly favors the visual features of the target text, leading to unreliable results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.711, + 0.484, + 0.849 + ], + "angle": 0, + "content": "\\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) overlooks edited regions. \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) often focuses on peripheral or unmodified local areas of the edited image, overlooking the specific areas that are edited by the text. Using the relevancy map [4], \\(R(\\Delta I; \\Delta T)^1\\), to visualize attention on image regions corresponding to the text direction, we observe that \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) frequently fails to concentrate on the image regions that are directly relevant to the target text as shown in Fig. 3(b). The figure also shows that" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.528, + 0.907, + 0.561 + ], + "angle": 0, + "content": "adding explicit visual details guides \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) to attend to edited regions properly." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.571, + 0.907, + 0.606 + ], + "angle": 0, + "content": "4. AugCLIP: A Context-Aware Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.614, + 0.907, + 0.78 + ], + "angle": 0, + "content": "We introduce a novel evaluation metric, AugCLIP, for scoring the editing quality of the image in terms of preservation and modification. Given a target text \\( T_{\\mathrm{trg}} \\) and a source image \\( I_{\\mathrm{src}} \\), AugCLIP measures the cosine similarity between the edited image \\( I_{\\mathrm{edit}} \\) and the ideal editing. Since the ideal edited image is not given in most evaluation cases, we estimate the representation of an ideally edited image as a modification on the source image, \\( I_{\\mathrm{src}} + \\mathbf{v} \\), where \\( \\mathbf{v} \\) is the modification vector. Then, the editing quality of the edited image \\( I_{\\mathrm{edit}} \\) is evaluated as" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.792, + 0.905, + 0.825 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A u g C L I P} \\left(I _ {\\text {e d i t}}; I _ {\\text {s r c}}, T _ {\\text {t r g}}\\right) = \\mathbf {c s} \\left(E \\left(I _ {\\text {e d i t}}\\right), E \\left(I _ {\\text {s r c}}\\right) + \\mathbf {v}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.824, + 0.736, + 0.838 + ], + "angle": 0, + "content": "where \\(E(\\cdot)\\) is a CLIP encoder." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.839, + 0.907, + 0.9 + ], + "angle": 0, + "content": "The evaluation score ranges between [0, 1], where the maximum value 1 indicates that the edited image is ideally modified by an editing model. We outline the framework of AugCLIP in Fig. 4. We extract the visual" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.857, + 0.483, + 0.895 + ], + "angle": 0, + "content": "1The original relevancy map \\( \\pmb{R} \\) utilizes an image-text pair. To adapt it to \\( \\mathrm{CLIP}_{\\mathrm{dir}} \\), we subtract two relevancy maps. Details are in the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "23477" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.379, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.23, + 0.285, + 0.255, + 0.3 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.089, + 0.667, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.09, + 0.905, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.283, + 0.667, + 0.3 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.321, + 0.907, + 0.404 + ], + "angle": 0, + "content": "Figure 4. (a) Description Extraction Process. The source image describes a young child standing on the balance board. Target text guides the editing model to make the girl sit. The source and target attributes are extracted with MLLM. (b) Evaluation Process of AugCLIP. The two edited images demonstrate i) An older woman sitting down with legs crossed (\\(I_{\\mathrm{edit}}^1\\)) and ii) A young girl sitting on the floor (\\(I_{\\mathrm{edit}}^2\\)). AugCLIP derives the ideal image representation as a minimum modification \\(\\mathbf{v}\\) on the source image to be classified as target. The second image that is closer to \\(I_{\\mathrm{src}} + \\mathbf{v}\\) shows a higher score, while the first image that is excessively modified with lost source identity shows a lower score." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.483, + 0.507 + ], + "angle": 0, + "content": "features of the source image and target text (Sec. 4.1), then derive the CLIP representation of an ideal modification that satisfies the two criteria: 'i) Does the edited image follow the target text?' and 'ii) Does the edited image preserve the source image?' (Sec. 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.514, + 0.413, + 0.53 + ], + "angle": 0, + "content": "4.1. Extracting and Processing Attributes" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.536, + 0.484, + 0.687 + ], + "angle": 0, + "content": "Source & Target Attribute Extraction As described in Fig. 4(a), we extract visual descriptions about attributes of the source image and target text using a state-of-the-art multi-modal large language model (MLLM), GPT-4V [22]. From the source image, we extract visual features that can be the object of preservation. Likewise, from the target text, we extract visual features that can be the object of modification. The extraction process is instructed by five annotated in-context examples, which are provided in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.703, + 0.484, + 0.764 + ], + "angle": 0, + "content": "Encoding into CLIP Space After attribute extraction from MLLM, each attribute is encoded into CLIP space. The source attributes are denoted as \\(\\mathcal{D}_S\\) and target attributes as \\(\\mathcal{D}_T\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Relative Weighting on Attributes In editing scenarios, some of the attributes are more important than others. For instance, drawing stripes is more essential than a short mane to represent a zebra. To prioritize this, we emphasize the similarity between key attributes within the same class. Since multi-modal large-language models sample based on the empirical probability, frequently extracted attributes indicate higher" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.907, + 0.492 + ], + "angle": 0, + "content": "importance in representing the context. Formally, the importance of each visual attribute in \\(\\mathcal{D}_S\\) and \\(\\mathcal{D}_T\\) is represented as a cosine similarity between CLIP embeddings in the same set as" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.497, + 0.905, + 0.533 + ], + "angle": 0, + "content": "\\[\nI m p o r t a n c e (v _ {i}) = \\sum_ {j \\neq i} \\frac {u _ {i} \\cdot v _ {j}}{\\| u _ {i} \\| \\| v _ {j} \\|}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.538, + 0.895, + 0.554 + ], + "angle": 0, + "content": "for all \\(u_{j}\\) in the same attribute set, either \\(\\mathcal{D}_S\\) or \\(\\mathcal{D}_T\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.906, + 0.645 + ], + "angle": 0, + "content": "Additionally, the importance should be downweighted by how much the visual attribute hinders the preservation of the source image or modification of the target text. More specifically, a collision between source and target attributes is measured by averaged cosine distance to CLIP embeddings in the opposite set as" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.649, + 0.905, + 0.682 + ], + "angle": 0, + "content": "\\[\nC o l l i s i o n \\left(v _ {i}\\right) = - \\sum_ {l} \\frac {v _ {i} \\cdot w _ {l}}{\\| v _ {i} \\| \\| w _ {l} \\|}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.689, + 0.794, + 0.704 + ], + "angle": 0, + "content": "for all \\(w_{l}\\) in the opposite attribute set." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.906, + 0.734 + ], + "angle": 0, + "content": "Adding these two measures, the weighting value for the attribute \\( v \\in \\mathcal{D}_S \\cup \\mathcal{D}_T \\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.742, + 0.905, + 0.759 + ], + "angle": 0, + "content": "\\[\n\\alpha (v) = \\text {I m p o r t a n c e} (v) + \\text {C o l l i s i o n} (v). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.813 + ], + "angle": 0, + "content": "This weighting value accounts for the relative significance of each attribute in the evaluation process and is integrated into Eq. (7)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.818, + 0.868, + 0.835 + ], + "angle": 0, + "content": "4.2. Deriving the Ideal Editing in CLIP Space" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Based on the extracted source and target attributes, we describe how to derive a modification vector that satisfies i) modification into the target text and ii) preservation of the source image." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "23478" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.227 + ], + "angle": 0, + "content": "Criterion 1: Does the edited image follow the target text? To determine if the edited image faithfully follows the given target text, it is intuitive to employ a classifier that classifies the image into either source or target. Classification into source indicates the edited image is still closer to the source image, while classification into target means that the image is sufficiently modified. The classifier is derived by a hyperplane that separates the source \\(\\mathcal{D}_S\\) and target \\(\\mathcal{D}_T\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.227, + 0.484, + 0.32 + ], + "angle": 0, + "content": "Formally, the classifier function \\( g(x) = \\mathbf{w}^T x + b \\) assigns a CLIP embedding \\( x \\) to the target class if \\( g(x) > 0 \\), or to the source class if \\( g(x) < 0 \\). Therefore, \\( E(I_{\\mathrm{edit}}) \\) should satisfy \\( \\mathbf{w}^T E(I_{\\mathrm{edit}}) + b > 0 \\) if the edited image faithfully follows the target text. Here, the optimization form of the classifier function \\( g(x) \\) is" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.33, + 0.484, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w}, b} \\frac {1}{2} \\| \\mathbf {w} \\| ^ {2} + C \\sum_ {i = 1} ^ {N} \\alpha (v _ {i}) \\cdot \\max (0, 1 - y _ {i} (\\mathbf {w} \\cdot v _ {i} + b)), (7)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.38, + 0.484, + 0.426 + ], + "angle": 0, + "content": "where \\(y_{i} = +1\\) for \\(v_{i}\\in \\mathcal{D}_{T}\\) and \\(y_{i} = -1\\) for \\(v_{i}\\in \\mathcal{D}_{S}\\). Here, the precomputed weighting values \\(\\alpha (\\cdot)\\) in Eq. (6) are integrated into the optimization process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.443, + 0.484, + 0.564 + ], + "angle": 0, + "content": "Criterion 2: Does the edited image preserve the source image? However, it is equally important to consider the second criterion, source image preservation. Therefore, the CLIP representation of modification should inflict minimum modification to the original embedding \\( E(I_{\\mathrm{src}}) \\), while being classified as a target class. Formally, we derive the modification \\( \\mathbf{v} \\) in CLIP space that satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.574, + 0.483, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {v}} \\| \\mathbf {v} \\| \\quad \\text {s u b j e c t t o} \\quad \\mathbf {w} ^ {T} \\left(E \\left(I _ {\\mathrm {s r c}}\\right) + \\mathbf {v}\\right) + b > 0. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.72 + ], + "angle": 0, + "content": "Derivation of \\(\\mathbf{v}\\) To minimize \\(\\| \\mathbf{v}\\|\\), \\(\\mathbf{v}\\) should be in the direction that most efficiently increases the classifier output \\(g(\\cdot)\\). This direction is given by the gradient of the classifier function concerning \\(\\mathbf{x}\\), which is \\(\\mathbf{w} = \\nabla g(\\mathbf{x})\\). Therefore, the optimal \\(\\mathbf{v}\\) is \\(c\\mathbf{w}\\) where \\(c > 0\\) is a scalar to be determined. Substituting \\(\\mathbf{v} = c\\mathbf{w}\\) to Eq. (8), we derive the following equation" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.729, + 0.483, + 0.765 + ], + "angle": 0, + "content": "\\[\nc > \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.773, + 0.484, + 0.834 + ], + "angle": 0, + "content": "In order to solve for \\(c\\) that minimizes \\(\\| \\mathbf{v}\\|\\), we derive the smallest \\(c\\) satisfying the condition as \\(c_{\\mathrm{min}} = \\frac{-(\\mathbf{w}^\\top I_{\\mathrm{src}} + b)}{\\|\\mathbf{w}\\|^2}\\). Then the modification vector \\(\\mathbf{v}\\) is derived as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.834, + 0.483, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} = c _ {\\min } \\mathbf {w} = \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}} \\mathbf {w}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Finally, AugCLIP is computed by substituting \\(\\mathbf{v}\\) to Eq. (3)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.667, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.905, + 0.192 + ], + "angle": 0, + "content": "Implementation Details. For our experiments, we employ a pre-trained CLIP-ViT 16/B model for CLIP-based metrics. Source and target attributes are generated using GPT-4V [22]. Further details on prompting the source and target attributes are in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.208, + 0.905, + 0.283 + ], + "angle": 0, + "content": "Baseline Metrics. We compare AugCLIP with DINO similarity, LPIPS, L2, Segmentation Consistency (SC), Directional CLIP similarity \\((\\mathrm{CLIP}_{\\mathrm{dir}})\\), CLIP-I, and CLIP-T. The CLIP variants are summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.29, + 0.895, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C L I P} _ {\\mathrm {d i r}} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.311, + 0.745, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C L I P - I} = \\mathbf {c s} \\left(E (I _ {\\mathrm {e d i t}}), E (I _ {\\mathrm {s r c}})\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.33, + 0.763, + 0.349 + ], + "angle": 0, + "content": "\\[\n\\mathrm {C L I P - T} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right)\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.355, + 0.905, + 0.431 + ], + "angle": 0, + "content": "Note that FID measures the distance between two distributions of image features, this metric cannot be measured in a sample-wise manner. Therefore, FID cannot be tested in terms of alignment with human evaluation or preference test on ground truth samples." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.447, + 0.906, + 0.599 + ], + "angle": 0, + "content": "Benchmark Datasets and Editing Models. We evaluate AugCLIP and existing metrics across several text-guided image editing benchmarks, including TEd-Bench [12], EditVal [1], MagicBrush [28], DreamBooth [26], and CelebA [20]. Each benchmark dataset represents varying editing scenarios as in Tab. 1. For each benchmark dataset, we employ multiple editing models [2, 5, 8, 9, 13, 14, 16-18, 23, 27] as specified in Tab. 1 for suitable type of benchmark dataset. Details on benchmark datasets are provided in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.606, + 0.822, + 0.622 + ], + "angle": 0, + "content": "5.1. Correlation with Human Judgment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.907, + 0.81 + ], + "angle": 0, + "content": "User Study To evaluate the effectiveness of AugCLIP compared to existing metrics, we conduct a Two-Alternative Forced Choice survey on human evaluators to collect preferences over diverse edited images. The alignment score \\( s_{2\\mathrm{AFC}} \\) measures if each metric prefers the same option as human evaluators. The survey was conducted using Amazon Mechanical Turk (AMT), over three benchmark datasets, encompassing a total of 105 participants as detailed in Tab. 2. The survey questionnaire is structured as described in the Appendix, providing clear criteria to consider source image preservation and target text alignment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.902 + ], + "angle": 0, + "content": "AugCLIP aligns better with human judgments. As shown in Tab. 3, AugCLIP, the context-aware metric that balances preservation and modification, is superior over all previous metrics across diverse benchmark datasets. A high level of alignment between" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "23479" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.175, + 0.088, + 0.822, + 0.101 + ], + "angle": 0, + "content": "Table 1. Benchmark Datasets and Editing Models Used for Evaluating the Performance of Metrics." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.111, + 0.9, + 0.181 + ], + "angle": 0, + "content": "
CelebAEditValTEdBenchMagicBrushDreamBooth
Dataset TypesFacial AttributeGeneral ObjectObject CentricLocal Region EditingPersonalized Generation
Editing Models[13, 14, 17, 23][2, 5, 8, 9, 12][2, 5, 8, 9, 12][2, 5, 8, 9, 12][16, 18, 27]
Dataset Size50648100105350
" + }, + { + "type": "table_caption", + "bbox": [ + 0.186, + 0.203, + 0.388, + 0.215 + ], + "angle": 0, + "content": "Table 2. User Study Statistics." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.226, + 0.479, + 0.279 + ], + "angle": 0, + "content": "
CelebAEditValDreamBooth
Survey questions393537
Participants453030
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.291, + 0.482, + 0.313 + ], + "angle": 0, + "content": "Table 3. Correlation with Human Judgment. Human alignment score \\( s_{2\\mathrm{AFC}} (\\uparrow) \\), scaled between 0 to 1." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.323, + 0.48, + 0.445 + ], + "angle": 0, + "content": "
MetricsPresv.Modif.CelebAEditValDreamBooth
L2✓✗0.6530.3480.464
LPIPS✓✗0.4650.3600.286
DINO✓✗0.5740.3480.286
SC✓✗0.7520.7640.571
CLIP-I✓✗0.8480.7300.857
CLIP-T✗✓0.4910.3990.321
CLIPdir▲✓0.6730.6970.357
AugCLIP✓✓0.8830.8310.857
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.469, + 0.483, + 0.53 + ], + "angle": 0, + "content": "preservation-centric (L2, LPIPS, DINO, SC, CLIP-I) and human judgment is expected because these benchmarks do not significantly deviate from the source image." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.539, + 0.408, + 0.556 + ], + "angle": 0, + "content": "5.2. Ground Truth Editing Selection Test" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.561, + 0.483, + 0.803 + ], + "angle": 0, + "content": "Creating Triplet Dataset We generate a triplet of images, each representing a well-edited, excessively preserved, and excessively modified image. Among the triplet of images, the well-edited image is provided in the benchmark datasets, TEdBench, and MagicBrush. Excessively modified images are generated with text-to-image models [25] instructed by the target text, completely ignoring the source image. Excessively preserved images are generated by applying a negligible transformation to the given source image, ignoring the target text. Then, we measure the accuracy where each metric correctly assigns the highest score to the well-edited image as AccBoth. Yielding high accuracy in this test means that the evaluation metric can balance both preservation and modification aspects, without being biased to either side." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.821, + 0.484, + 0.896 + ], + "angle": 0, + "content": "AugCLIP is superior in balancing preservation and modification. In Tab. 4, AugCLIP is on par with or even better than baseline metrics over all datasets. This emphasizes the balanced evaluation criteria of AugCLIP, which previous metrics fail to abide by. Seg-" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.203, + 0.905, + 0.235 + ], + "angle": 0, + "content": "Table 4. Ground Truth Selection Test. Accuracy, Accboth \\((\\uparrow)\\) of assigning higher scores to ground truth images over excessively preserved and modified images." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.246, + 0.886, + 0.387 + ], + "angle": 0, + "content": "
MetricsPresv. Modif.TEdBenchMagicBrush
L2✓X0.3100.002
LPIPS✓X0.0900.000
DINO✓X0.2800.008
SC✓X0.4200.936
CLIP-I✓X0.2810.810
CLIP-TX✓0.3120.260
CLIPdir▲✓0.3500.601
AugCLIP✓✓0.5700.889
" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.41, + 0.905, + 0.442 + ], + "angle": 0, + "content": "ment Consistency (SC) excels in MagicBrush since the dataset requires editing a small local area of the image." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.455, + 0.627, + 0.472 + ], + "angle": 0, + "content": "6. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.906, + 0.555 + ], + "angle": 0, + "content": "We use \\( s_{2\\mathrm{AFC}} \\) for CelebA, EditVal, and Dreambooth, and AccBoth for TEdBench and MagicBrush. We compare our metric, AugCLIP with \\( \\mathrm{CLIP}_{\\mathrm{dir}} \\), which is the only metric that considers both preservation and modification." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.573, + 0.907, + 0.785 + ], + "angle": 0, + "content": "AugCLIP generalizes to diverse editing scenarios. Text-guided image editing encompasses a wide range of tasks such as style editing, object replacement, local editing, partial alteration, and personalized generation. AugCLIP excels in the highly complex scenarios of local editing as conducted with the MagicBrush dataset. Moreover, AugCLIP highly aligns with human judgment in the personalized generation case of DreamBooth, which has been underexplored by previous metrics. We report how well AugCLIP aligns with human judgment with various editing cases provided in the EditVal dataset. Across all eight scenarios, except for the texture modification task, AugCLIP outperforms \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) as shown in Tab. 5." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.802, + 0.909, + 0.894 + ], + "angle": 0, + "content": "Augmenting \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) cannot provide reliable evaluation result. We demonstrate the impact of augmenting \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\) with attributes, extracted in Sec. 4.1. Specifically, we replace the source and target text embeddings with the average of their respective attribute embeddings, \\(\\mathcal{D}_S\\) and \\(\\mathcal{D}_T\\). As shown in Tab. 6," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "23480" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.089, + 0.483, + 0.111 + ], + "angle": 0, + "content": "Table 5. Human Alignment Score \\( s_{2\\text{AFC}} \\) on Various Text-guided Image Editing Scenarios." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.121, + 0.481, + 0.214 + ], + "angle": 0, + "content": "
Pos. AddObj. repl.Alter PartsBackground
CLIPdir0.6670.6880.7300.5
AugCLIP1.00.750.8381.0
TextureColorActionStyle
CLIPdir0.8061.01.00.529
AugCLIP0.7421.01.00.647
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.236, + 0.483, + 0.357 + ], + "angle": 0, + "content": "this straightforward augmentation does not guarantee performance gain. AugCLIP consistently outperforms all description-augmented versions of \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\). This improvement is due to AugCLIP's approach, which derives the ideal representation by a minimum modification vector. This is fundamentally different from the naive methodology of \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\), which relies on a simple subtraction of the source from the target." + }, + { + "type": "table_caption", + "bbox": [ + 0.15, + 0.368, + 0.424, + 0.38 + ], + "angle": 0, + "content": "Table 6. Effect of Augmenting Attributes." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.39, + 0.481, + 0.474 + ], + "angle": 0, + "content": "
CelebAEditValDreamBoothTEDbenchMagicBrush
CLIPdir0.6730.6970.3570.3500.601
+DS0.8160.6290.3570.4000.429
+DT0.8190.7080.5360.4200.533
+DS∪DT0.8160.6070.5360.4400.402
AugCLIP0.8830.8310.8570.5700.889
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.505, + 0.483, + 0.627 + ], + "angle": 0, + "content": "Weighting Strategy for Hyperplane We demonstrate the effectiveness of our weighting strategy, described in Eq. (6) in Tab. 7. Our weighting strategy enables AugCLIP to prioritize key features central to preservation and modification while estimating the representation of an ideally edited image, resulting in improvement in human alignment (\\(s_{2\\mathrm{AFC}}\\)) and balancing preservation and modification (\\(\\mathbf{Acc}_{\\mathrm{Both}}\\))." + }, + { + "type": "table_caption", + "bbox": [ + 0.163, + 0.638, + 0.411, + 0.651 + ], + "angle": 0, + "content": "Table 7. Effect of Weighting Strategy." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.66, + 0.481, + 0.706 + ], + "angle": 0, + "content": "
CelebAEditValDreamBoothTEDBenchMagicBrush
Unweighted0.8490.7870.7860.4000.830
Weighted0.8830.8310.8570.5700.889
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Length and Number of Attributes In Tab. 8, we compare short (under 5 words) and long (over 5 words), as well as cases with a fixed number (10, 20, or 30) of attributes. We observe that using short attributes tends to outperform using long ones, likely because they focus on a single visual aspect, avoiding the potential entanglement of multiple aspects in a single attribute. Moreover, the number of attributes impacts the performance depending on the scene complexity of the benchmark dataset, as complex scenarios require a higher number of attributes to fully capture the scene's" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.138 + ], + "angle": 0, + "content": "details. Therefore, allowing flexibility in the number of attributes, rather than imposing a strict limit, yields the best overall performance across all configurations." + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.149, + 0.882, + 0.161 + ], + "angle": 0, + "content": "Table 8. Effect of Length and Number of Attributes." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.171, + 0.905, + 0.246 + ], + "angle": 0, + "content": "
LengthNumberCelebAEditValDreamBoothTEDbenchMagicBrush
short100.8700.7190.8570.5400.889
short200.8290.8090.8210.5400.868
short300.8290.7640.7140.5700.863
long300.8430.6970.7500.5300.862
short-0.8830.8310.8570.5700.889
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.278, + 0.907, + 0.399 + ], + "angle": 0, + "content": "Description Randomness Using GPT-4V for description extraction introduces slight randomness across different seeds. Tests with five seeds show low variance (0.0197) in human alignment score (\\(s_{2\\mathrm{AFC}}\\)), indicating that the description generation process does not affect the scoring. We also demonstrate in the Appendix that extracted attributes with different seeds do not vary." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.399, + 0.906, + 0.459 + ], + "angle": 0, + "content": "We provide analysis on the modification vector \\(\\mathbf{v}\\) and choice of classifier function, discussion on limitations, description prompting, and extensive qualitative results in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.472, + 0.787, + 0.489 + ], + "angle": 0, + "content": "Limitations and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.907, + 0.634 + ], + "angle": 0, + "content": "Our method, AugCLIP, adds additional computation time compared to \\(\\mathrm{CLIP}_{\\mathrm{dir}}\\). It requires extracting attributes via MLLM, and then fitting a hyperplane to distinguish source and target attributes. This process takes around 12.3 seconds for attribute generation and 0.15 seconds for score computation. We will provide extracted attributes for all benchmark datasets to reduce this overhead, facilitating the evaluation process for future usage." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.647, + 0.625, + 0.663 + ], + "angle": 0, + "content": "Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.907, + 0.84 + ], + "angle": 0, + "content": "We present AugCLIP, a novel evaluation metric for text-guided image editing that balances source image preservation and target text modification. By leveraging a multi-modal language model to extract visual attributes and finding a separating hyperplane, AugCLIP estimates a representation of an ideal edited image that closely matches human preferences. Experiments on five benchmark datasets show that AugCLIP outperforms existing metrics, especially in challenging tasks, offering a more reliable tool for evaluating edits while preserving core attributes." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "23481" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.279, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.266 + ], + "angle": 0, + "content": "This work was supported by the National Research Foundation of Korea (NRF) grants (RS-2023-00209060 A Study on Optimization and Network Interpretation Method for Large-Scale Machine Learning), Institute for Information & communications Technology Planning & Evaluation(IITP) grants (No.2022-0-00713 Meta-learning applicable to real-world problems, RS-2019-II190075 Artificial Intelligence Graduate School Program(KAIST)) funded by the Korea government(MSIT)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.28, + 0.2, + 0.296 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.305, + 0.484, + 0.388 + ], + "angle": 0, + "content": "[1] Samyadeep Basu, Mehrdad Saberi, Shweta Bhardwaj, Atoosa Malemir Chegini, Daniela Massiceti, Maziar Sanjabi, Shell Xu Hu, and Soheil Feizi. 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Gpt-4v (ision) as a generalist evaluator for vision-language tasks. arXiv preprint arXiv:2311.01361, 2023. 27" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.482, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.518, + 0.955 + ], + "angle": 0, + "content": "23483" + } + ] +] \ No newline at end of file diff --git a/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_origin.pdf b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8fe5cf8e75e190e4bf899e0e6889f7fcb18cd243 --- /dev/null +++ b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/29ea49ed-c354-4bc9-af72-1f4bc52aa1a1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5149e1d91c912d14d74ae1ee4e7be35209b77fea07005968fdad64eff695f62a +size 3239154 diff --git a/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/full.md b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5ce792204e2e8d3f4423a9d5fdab417f8e22deae --- /dev/null +++ b/2025/Preserve or Modify_ Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing/full.md @@ -0,0 +1,380 @@ +# Preserve or Modify? Context-Aware Evaluation for Balancing Preservation and Modification in Text-Guided Image Editing + +Yoonjeon Kim $^{1,*}$ Soohyun Ryu $^{1,*}$ + +Joowon Kim1 June Yong Yang1 + +Yeonsung Jung1 Hyunkoo Lee1 + +Jaeryong Hwang² Eunho Yang1,3,\dagger + +$^{1}$ KAIST $^{2}$ Republic of Korea Naval Academy $^{3}$ AITRICS + +https://augclip.github.io/ + +# Abstract + +The development of vision-language and generative models has significantly advanced text-guided image editing, which seeks the preservation of core elements in the source image while implementing modifications based on the target text. However, existing metrics have a context-blindness problem, indiscriminately applying the same evaluation criteria on completely different pairs of source image and target text, biasing towards either modification or preservation. Directional CLIP similarity, the only metric that considers both source image and target text, is also biased towards modification aspects and attends to irrelevant editing regions of the image. We propose AugCLIP, a context-aware metric that adaptively coordinates preservation and modification aspects, depending on the specific context of a given source image and target text. This is done by deriving the CLIP representation of an ideally edited image, that preserves the source image with necessary modifications to align with target text. More specifically, using a multi-modal large language model, AugCLIP augments the textual descriptions of the source and target, then calculates a modification vector through a hyperplane that separates source and target attributes in CLIP space. Extensive experiments on five benchmark datasets, encompassing a diverse range of editing scenarios, show that AugCLIP aligns remarkably well with human evaluation standards, outperforming existing metrics. The code is available at https://github.com/augclip/augclip_eval. + +# 1. Introduction + +Building on advancements in vision-language models [7, 19, 24], recent generative models [2, 8, 12] have + +![](images/8c9eebbd2925c824938d973906dafb48c22165ddd0370f1de1e63043f81a15ac.jpg) +"Turn into Ironman" +Figure 1. Context Blindness Problem of Existing Evaluation Metrics. Evaluation metrics should consider the specific context of a given source image and target text. However, existing metrics exhibit context-blindness, applying the same criteria of either 'preserve' (P) or 'modify' (M) across the entire image. Our proposed metric, AugCLIP, is a context-aware metric that flexibly applies different criteria to local regions of the image. + +Sitting down + +Tree in behind + +Preserve + +Orange T-shirt Red armor suit + +Blue cap + +Ironman mask + +Modify + +(a) Given Context + +(b) Guideline + +Preserve or Modify ? + +P√ M X m △ P + +P√ M X m△ P√ + +P X M√ M√ M√ + +P×M√M + +Presv.Modif. CLIP.. AugCLIP + +Metric Metric + +(c) Evaluation Standard of Metrics + +been widely utilized as creative tools for image editing via text instructions. Text-guided image editing models enable the modification of images in response to textual guidance, ensuring that changes are aligned with the provided instructions. The primary objective of these models is to apply the necessary modifications guided by the target text while preserving most of the source image. + +Despite the remarkable advancements in editing models, there has been a lack of rigorous evaluation methods, tailored specifically for text-guided image editing. Consequently, most studies [1, 2, 6, 9, 13, 15, 26] have heavily relied on human evaluation, which provides balanced consideration of preservation and modification aspects. However, as it is costly and impractical for real-world applications, researchers have adapted automatic evaluation metrics [3, 10, 11, 29] originally + +designed for other vision tasks, such as image generation or captioning. + +In text-guided editing scenarios, it is essential to assess which elements in the source to preserve and which in the target to modify into, based on the specific context of the given source image and target text (see Fig. 1(a)-(b) for example). Existing metrics, however, exhibit context blindness, meaning preservation-centric metrics completely ignore the target context while modification-centric metrics do not account for the source context. As shown in Fig. 1(c), preservation- and modification-centric metrics apply a fixed standard across the entire image, regardless of the true editing requirement of the given context. Even combining them fails to overcome the context blindness problem. + +Among existing metrics, directional CLIP similarity [6] is unique because it provides a method to consider both the source image and target text in the evaluation. Even this metric suffers from a context-blindness problem, using a fixed standard without considering the specific relationship between the source image and target text. We show that directional CLIP similarity tends to prioritize modification over preservation, and often focuses on peripheral parts rather than regions that are edited as guided by target text, in Sec. 3. These observations underscore the need for a context-aware metric to dynamically adjust the evaluation standard, balancing both aspects in response to diverse editing contexts. + +Based on our comprehensive analysis, we propose a novel context-aware metric, AugCLIP, which evaluates the quality of the edited image by comparing it with an estimated representation of a well-edited image. To balance preservation and modification, a well-edited image is represented by a minimum modification on the source image, while matching the target text. We use multi-modal large language models (MLLMs) to extract attributes that capture various visual aspects of the source image and target text. With these attributes, we derive a hyperplane that separates the source and target to derive the ideal modification as a projection to this hyperplane. AugCLIP evaluates how closely the edited image aligns with the estimated ideal image in CLIP space. + +Our metric AugCLIP demonstrates remarkable improvement in alignment with human judgment on diverse editing scenarios such as object, attribute, and style alteration compared to all other existing metrics. Moreover, our metric is even applicable to personalized generation, the DreamBooth dataset, where the objective is to identify an object in the source image and edit it into a completely novel context. This shows the flexibility of AugCLIP, which seamlessly applies to + +a variety of editing directions. Notably, our metric excels in identifying minor differences between the source image and the edited image, showing superb ability in complex image editing scenarios such as MagicBrush. + +The major contributions are summarized as follows. + +- We point out the unreliability of current evaluation metrics in text-guided image editing, noting their inability to balance preservation and modification effectively due to inherent context blindness. +- We introduce AugCLIP, a context-aware metric for image editing by automatically augmenting descriptions via MLLM and estimating a balanced representation of preservation and modification, which takes into account the relative importance of each description. +- AugCLIP demonstrates a significantly high correlation with human evaluations across various editing scenarios, even in complex applications where existing metrics struggle. + +# 2. Background on Existing Metrics + +In the context of text-guided image editing, evaluation metrics should assess the quality of edited images in terms of both preservation of the source image and modification towards the target text. + +Preservation-Centric Metrics FID [11], LPIPS [29], and L2 distance measure feature-level distance between images. These metrics are primarily used in image generation tasks to compare the distributions of real and generated images. When applied to editing scenarios, they assess the distance between the source and edited images, completely ignoring the target text guiding the editing process. Segmentation consistency (SC) [13] measures the structural change. Additionally, DINO similarity (DINO) and CLIP-I evaluate the semantic similarity between the source and edited images within the DINO [3] and CLIP [24] embedding spaces, also focusing solely on preservation. + +Modification-Centric Metrics To assess how well an edited image aligns with the target text, the primary approach involves using a pre-trained multimodal model [24]. CLIPScore (CLIP-T) [10] is the most widely adopted metric in this category, measuring the similarity between the edited image and the target text. This metric completely ignores the source image that should be considered for the preservation aspect. + +Holistic Evaluation of Preservation and Modification Directional CLIP similarity $(\mathrm{CLIP}_{\mathrm{dir}})$ [6] is unique among existing metrics as it assesses both + +![](images/1c8ce8f5a625a3d22a3a0d9744ec75cab9225c914d2e15478f6bc5f8e2694c6e.jpg) + +![](images/3a2227634b79b47f81c7fe8b92d8118006ef75989a9db184213c1ccb0b1c2145.jpg) + +![](images/6c00a34eaff5677c44d10ec0536358caa28c320f50f81da97bd6468e00a98f42.jpg) + +![](images/93538b080502ab1a322105badc074aeae7795f08479e368552742f27761cd259.jpg) +Figure 2. Combination of Preservation- and Modification-Centric Metrics Deteriorates in Performance. The plot shows the human alignment score $s_{\mathrm{align}}$ measured by a linear interpolation of {DINO, SC, CLIP-I} and CLIP-T. The results show that combining rather degrades the alignment with human judgment. + +![](images/744d18e838725f65caa8433e102eaca6987b63a7313fd5eacf19d9ce13721c92.jpg) + +![](images/8fa399fdc13a66b411439f291cd752df0581df85c4c6e870afbaab852d1187f3.jpg) + +preservation and modification aspects by evaluating directional alignment between the original and edited images concerning the source and target text. + +However, these metrics employ a fixed evaluation standard, disregarding the context of each editing scenario, which leads to context blindness. As discussed in Sec. 3, combining preservation- and modification-centric metrics or using directional CLIP similarity fails to balance preservation and modification adequately, resulting in misalignment with human judgment. + +# 3. Problems of Existing Metrics in Balancing Preservation and Modification Aspects + +Existing evaluation metrics, that focus on either one of the preservation or modification aspects, face a challenge in assessing both aspects. Does combining these two metrics successfully balance the preservation and modification aspects? We systematically analyze how these metrics and their combinations still fail in balancing the two colliding objectives, suffering from context-blindness (Sec. 3.1). Moreover, we focus on directional CLIP similarity, the unique metric that accounts for both source image and target text, to reveal that it presents two significant problems that question its reliability (Sec. 3.2). + +# 3.1. Combination of Preservation- and Modification-Centric Metrics + +We explore whether combining preservation- and modification-centric metrics can improve alignment with human judgments across two benchmark datasets: EditVal [1] and CelebA [20] (Results on the other three benchmark datasets are deferred to the Appendix). To do so, we combine CLIP-T, a modification-centric metric, and preservation-centric metrics (LPIPS, DINO similarity, CLIP-I) with varying interpolation values $\gamma \in [0,1]$ . Note that both metrics are scaled to the same range before interpolation, ensuring the interpolation value $\gamma$ is properly reflected in the final combined score. + +As illustrated in Fig. 2, the combination of two powerful metrics in preservation and modification often leads to performance degradation. This manifests that a simple combination of the colliding metrics cannot be a reliable evaluation metric. This is due to the context-blindness of these metrics, failing to holistically consider source image and target text. Preservation-centric metrics compare only the source and edited images, ignoring the target context. Similarly, modification-centric metrics consider only the target text, overlooking the source context. This highlights the need for a tailored metric that is contextually aware of both preservation and modification, ensuring a reliable alignment with human evaluations across diverse datasets and tasks. + +# 3.2. Directional CLIP Similarity + +Directional CLIP similarity $\left(\mathrm{CLIP}_{\mathrm{dir}}\right)$ is designed to assess both preservation and modification in text-guided image editing by measuring the similarity between image and text directions as follows: + +$$ +\begin{array}{l} \operatorname {C L I P} _ {\text {d i r}} = \operatorname {c s} (\Delta I, \Delta T) \tag {1} \\ = \mathbf {c s} \left(E \left(I _ {\mathrm {e d i t}}\right) - E \left(I _ {\mathrm {s r c}}\right), E \left(T _ {\mathrm {t r g}}\right) - E \left(T _ {\mathrm {s r c}}\right)\right), \quad (2) \\ \end{array} +$$ + +where $\mathbf{cs}(\mathbf{a},\mathbf{b}) = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\|\mathbf{b}\|}$ denotes cosine similarity and $E(\cdot)$ is a CLIP encoder for either image or text. Here, $I_{\mathrm{edit}}$ is the edited image to be evaluated, which is edited from the source image $I_{\mathrm{src}}$ according to the target text $T_{\mathrm{trg}}$ . For evaluation of directional CLIP similarity, $I_{\mathrm{src}}$ , the corresponding text about the source image, is required. We analyze that $\mathrm{CLIP}_{\mathrm{dir}}$ has two major problems that hinder the balanced evaluation of preservation and modification. + +$\mathrm{CLIP}_{\mathrm{dir}}$ overly emphasizes modification. Directional CLIP similarity overly emphasizes the alignment with the target text while neglecting the preservation + +![](images/1b44e9ea270df7073b17db98998961ef898e5e6cd05e96607596615eb2b4f439.jpg) + +![](images/b53cd2f5514d4b7404af639b680b2c7aedef8b4380f562690f7d3fc38badf4ff.jpg) +$\Delta I =$ Ground truth $-I_{s r c}$ $\Delta I =$ Excess. modif. $I_{s r c}$ $\Delta T =$ "A jumping dog"-"A standing dog + +![](images/e8190263bcb328de08de33f9055b2a0c56cea6835b3cb68fcae68ace3e3e855c.jpg) + +![](images/075e71b7abe87c38bf657e662f9dad1ee50a11302e0657687f56f753c991766b.jpg) + +![](images/f01aa218aa97bd91363b143788f29cccef0ec82a14846f147056ed6e33aab155.jpg) +$\Delta I =$ Ground truth - $I_{s r c}$ $\Delta I =$ Excess. modif. - $I_{s r c}$ $\Delta T =$ "Acheze pizza"-"Apepperoni pizza + +![](images/4fa0ab85cff9b1a02c14cc2b57b4ff418607255ced43969c4ed097e0b86ff577.jpg) + +![](images/098dd07ac310cf24839e8ba4817157d4c13883224d8deea0b652c17db3a7087d.jpg) +(a) Problem1. Overemphasizing Modification over Preservation +Figure 3. Problems of Directional CLIP Similarity. (a) $\mathrm{CLIP}_{\mathrm{dir}}$ assigns higher scores to excessive modification, over well-edited ground truth images. (b) $\mathrm{CLIP}_{\mathrm{dir}}$ evaluates edited images by attending to irrelevant regions of the image. Adding visual annotations helps $\mathrm{CLIP}_{\mathrm{dir}}$ properly attend to edited regions. + +of the source image. Despite attempting to incorporate preservation by subtracting $T_{\mathrm{src}}$ from $T_{\mathrm{trg}}$ , $\mathrm{CLIP}_{\mathrm{dir}}$ frequently favors excessively modified images over ground truth ideally edited images as shown in samples in Fig. 3(a). Specifically, $\mathrm{CLIP}_{\mathrm{dir}}$ metric fails on $63\%$ of the 100 editing cases in TEdBench [12] and $35.1\%$ of the 1053 cases in MagicBrush [28] (Details in Sec. 5). This problem happens since $\mathrm{CLIP}_{\mathrm{dir}}$ is designed to assume that a well-edited image should primarily adhere to the target text. Thus, it blindly favors the visual features of the target text, leading to unreliable results. + +$\mathrm{CLIP}_{\mathrm{dir}}$ overlooks edited regions. $\mathrm{CLIP}_{\mathrm{dir}}$ often focuses on peripheral or unmodified local areas of the edited image, overlooking the specific areas that are edited by the text. Using the relevancy map [4], $R(\Delta I; \Delta T)^1$ , to visualize attention on image regions corresponding to the text direction, we observe that $\mathrm{CLIP}_{\mathrm{dir}}$ frequently fails to concentrate on the image regions that are directly relevant to the target text as shown in Fig. 3(b). The figure also shows that + +adding explicit visual details guides $\mathrm{CLIP}_{\mathrm{dir}}$ to attend to edited regions properly. + +# 4. AugCLIP: A Context-Aware Evaluation Metric + +We introduce a novel evaluation metric, AugCLIP, for scoring the editing quality of the image in terms of preservation and modification. Given a target text $T_{\mathrm{trg}}$ and a source image $I_{\mathrm{src}}$ , AugCLIP measures the cosine similarity between the edited image $I_{\mathrm{edit}}$ and the ideal editing. Since the ideal edited image is not given in most evaluation cases, we estimate the representation of an ideally edited image as a modification on the source image, $I_{\mathrm{src}} + \mathbf{v}$ , where $\mathbf{v}$ is the modification vector. Then, the editing quality of the edited image $I_{\mathrm{edit}}$ is evaluated as + +$$ +\operatorname {A u g C L I P} \left(I _ {\text {e d i t}}; I _ {\text {s r c}}, T _ {\text {t r g}}\right) = \mathbf {c s} \left(E \left(I _ {\text {e d i t}}\right), E \left(I _ {\text {s r c}}\right) + \mathbf {v}\right), \tag {3} +$$ + +where $E(\cdot)$ is a CLIP encoder. + +The evaluation score ranges between [0, 1], where the maximum value 1 indicates that the edited image is ideally modified by an editing model. We outline the framework of AugCLIP in Fig. 4. We extract the visual + +![](images/45eb7f797cf0782a3c775980250217466df33cde545f07f95042d268b2c43413.jpg) +(a) + +![](images/490b677c93ac8c32c507d7d2706bb918ff4d3acde950c427efd92b9e31f9ba30.jpg) +(b) + +![](images/426fc1f65916732dcde6805389ab9c50bbfdd7f3f0906d19f8fd7a77f386567c.jpg) +Figure 4. (a) Description Extraction Process. The source image describes a young child standing on the balance board. Target text guides the editing model to make the girl sit. The source and target attributes are extracted with MLLM. (b) Evaluation Process of AugCLIP. The two edited images demonstrate i) An older woman sitting down with legs crossed ( $I_{\mathrm{edit}}^1$ ) and ii) A young girl sitting on the floor ( $I_{\mathrm{edit}}^2$ ). AugCLIP derives the ideal image representation as a minimum modification $\mathbf{v}$ on the source image to be classified as target. The second image that is closer to $I_{\mathrm{src}} + \mathbf{v}$ shows a higher score, while the first image that is excessively modified with lost source identity shows a lower score. + +features of the source image and target text (Sec. 4.1), then derive the CLIP representation of an ideal modification that satisfies the two criteria: 'i) Does the edited image follow the target text?' and 'ii) Does the edited image preserve the source image?' (Sec. 4.2). + +# 4.1. Extracting and Processing Attributes + +Source & Target Attribute Extraction As described in Fig. 4(a), we extract visual descriptions about attributes of the source image and target text using a state-of-the-art multi-modal large language model (MLLM), GPT-4V [22]. From the source image, we extract visual features that can be the object of preservation. Likewise, from the target text, we extract visual features that can be the object of modification. The extraction process is instructed by five annotated in-context examples, which are provided in the Appendix. + +Encoding into CLIP Space After attribute extraction from MLLM, each attribute is encoded into CLIP space. The source attributes are denoted as $\mathcal{D}_S$ and target attributes as $\mathcal{D}_T$ . + +Relative Weighting on Attributes In editing scenarios, some of the attributes are more important than others. For instance, drawing stripes is more essential than a short mane to represent a zebra. To prioritize this, we emphasize the similarity between key attributes within the same class. Since multi-modal large-language models sample based on the empirical probability, frequently extracted attributes indicate higher + +importance in representing the context. Formally, the importance of each visual attribute in $\mathcal{D}_S$ and $\mathcal{D}_T$ is represented as a cosine similarity between CLIP embeddings in the same set as + +$$ +I m p o r t a n c e (v _ {i}) = \sum_ {j \neq i} \frac {u _ {i} \cdot v _ {j}}{\| u _ {i} \| \| v _ {j} \|}, \tag {4} +$$ + +for all $u_{j}$ in the same attribute set, either $\mathcal{D}_S$ or $\mathcal{D}_T$ . + +Additionally, the importance should be downweighted by how much the visual attribute hinders the preservation of the source image or modification of the target text. More specifically, a collision between source and target attributes is measured by averaged cosine distance to CLIP embeddings in the opposite set as + +$$ +C o l l i s i o n \left(v _ {i}\right) = - \sum_ {l} \frac {v _ {i} \cdot w _ {l}}{\| v _ {i} \| \| w _ {l} \|}, \tag {5} +$$ + +for all $w_{l}$ in the opposite attribute set. + +Adding these two measures, the weighting value for the attribute $v \in \mathcal{D}_S \cup \mathcal{D}_T$ is defined as + +$$ +\alpha (v) = \text {I m p o r t a n c e} (v) + \text {C o l l i s i o n} (v). \tag {6} +$$ + +This weighting value accounts for the relative significance of each attribute in the evaluation process and is integrated into Eq. (7). + +# 4.2. Deriving the Ideal Editing in CLIP Space + +Based on the extracted source and target attributes, we describe how to derive a modification vector that satisfies i) modification into the target text and ii) preservation of the source image. + +Criterion 1: Does the edited image follow the target text? To determine if the edited image faithfully follows the given target text, it is intuitive to employ a classifier that classifies the image into either source or target. Classification into source indicates the edited image is still closer to the source image, while classification into target means that the image is sufficiently modified. The classifier is derived by a hyperplane that separates the source $\mathcal{D}_S$ and target $\mathcal{D}_T$ . + +Formally, the classifier function $g(x) = \mathbf{w}^T x + b$ assigns a CLIP embedding $x$ to the target class if $g(x) > 0$ , or to the source class if $g(x) < 0$ . Therefore, $E(I_{\mathrm{edit}})$ should satisfy $\mathbf{w}^T E(I_{\mathrm{edit}}) + b > 0$ if the edited image faithfully follows the target text. Here, the optimization form of the classifier function $g(x)$ is + +$$ +\min _ {\mathbf {w}, b} \frac {1}{2} \| \mathbf {w} \| ^ {2} + C \sum_ {i = 1} ^ {N} \alpha (v _ {i}) \cdot \max (0, 1 - y _ {i} (\mathbf {w} \cdot v _ {i} + b)), (7) +$$ + +where $y_{i} = +1$ for $v_{i}\in \mathcal{D}_{T}$ and $y_{i} = -1$ for $v_{i}\in \mathcal{D}_{S}$ . Here, the precomputed weighting values $\alpha (\cdot)$ in Eq. (6) are integrated into the optimization process. + +Criterion 2: Does the edited image preserve the source image? However, it is equally important to consider the second criterion, source image preservation. Therefore, the CLIP representation of modification should inflict minimum modification to the original embedding $E(I_{\mathrm{src}})$ , while being classified as a target class. Formally, we derive the modification $\mathbf{v}$ in CLIP space that satisfies + +$$ +\min _ {\mathbf {v}} \| \mathbf {v} \| \quad \text {s u b j e c t t o} \quad \mathbf {w} ^ {T} \left(E \left(I _ {\mathrm {s r c}}\right) + \mathbf {v}\right) + b > 0. \tag {8} +$$ + +Derivation of $\mathbf{v}$ To minimize $\| \mathbf{v}\|$ , $\mathbf{v}$ should be in the direction that most efficiently increases the classifier output $g(\cdot)$ . This direction is given by the gradient of the classifier function concerning $\mathbf{x}$ , which is $\mathbf{w} = \nabla g(\mathbf{x})$ . Therefore, the optimal $\mathbf{v}$ is $c\mathbf{w}$ where $c > 0$ is a scalar to be determined. Substituting $\mathbf{v} = c\mathbf{w}$ to Eq. (8), we derive the following equation + +$$ +c > \frac {- \left(\mathbf {w} ^ {\top} I _ {\mathrm {s r c}} + b\right)}{\| \mathbf {w} \| ^ {2}}. \tag {9} +$$ + +In order to solve for $c$ that minimizes $\| \mathbf{v}\|$ , we derive the smallest $c$ satisfying the condition as $c_{\mathrm{min}} = \frac{-(\mathbf{w}^\top I_{\mathrm{src}} + b)}{\|\mathbf{w}\|^2}$ . Then the modification vector $\mathbf{v}$ is derived as + +$$ +\mathbf {v} = c _ {\min } \mathbf {w} = \frac {- \left(\mathbf {w} ^ {\top} I _ {\mathrm {s r c}} + b\right)}{\| \mathbf {w} \| ^ {2}} \mathbf {w}. \tag {10} +$$ + +Finally, AugCLIP is computed by substituting $\mathbf{v}$ to Eq. (3). + +# 5. Experiments + +Implementation Details. For our experiments, we employ a pre-trained CLIP-ViT 16/B model for CLIP-based metrics. Source and target attributes are generated using GPT-4V [22]. Further details on prompting the source and target attributes are in the Appendix. + +Baseline Metrics. We compare AugCLIP with DINO similarity, LPIPS, L2, Segmentation Consistency (SC), Directional CLIP similarity $(\mathrm{CLIP}_{\mathrm{dir}})$ , CLIP-I, and CLIP-T. The CLIP variants are summarized as follows: + +$$ +\operatorname {C L I P} _ {\mathrm {d i r}} = \mathbf {c s} \left(E \left(I _ {\mathrm {e d i t}}\right) - E \left(I _ {\mathrm {s r c}}\right), E \left(T _ {\mathrm {t r g}}\right) - E \left(T _ {\mathrm {s r c}}\right)\right) +$$ + +$$ +\operatorname {C L I P - I} = \mathbf {c s} \left(E (I _ {\mathrm {e d i t}}), E (I _ {\mathrm {s r c}})\right) +$$ + +$$ +\mathrm {C L I P - T} = \mathbf {c s} \left(E \left(I _ {\mathrm {e d i t}}\right), E \left(T _ {\mathrm {t r g}}\right)\right). +$$ + +Note that FID measures the distance between two distributions of image features, this metric cannot be measured in a sample-wise manner. Therefore, FID cannot be tested in terms of alignment with human evaluation or preference test on ground truth samples. + +Benchmark Datasets and Editing Models. We evaluate AugCLIP and existing metrics across several text-guided image editing benchmarks, including TEd-Bench [12], EditVal [1], MagicBrush [28], DreamBooth [26], and CelebA [20]. Each benchmark dataset represents varying editing scenarios as in Tab. 1. For each benchmark dataset, we employ multiple editing models [2, 5, 8, 9, 13, 14, 16-18, 23, 27] as specified in Tab. 1 for suitable type of benchmark dataset. Details on benchmark datasets are provided in the Appendix. + +# 5.1. Correlation with Human Judgment + +User Study To evaluate the effectiveness of AugCLIP compared to existing metrics, we conduct a Two-Alternative Forced Choice survey on human evaluators to collect preferences over diverse edited images. The alignment score $s_{2\mathrm{AFC}}$ measures if each metric prefers the same option as human evaluators. The survey was conducted using Amazon Mechanical Turk (AMT), over three benchmark datasets, encompassing a total of 105 participants as detailed in Tab. 2. The survey questionnaire is structured as described in the Appendix, providing clear criteria to consider source image preservation and target text alignment. + +AugCLIP aligns better with human judgments. As shown in Tab. 3, AugCLIP, the context-aware metric that balances preservation and modification, is superior over all previous metrics across diverse benchmark datasets. A high level of alignment between + +Table 1. Benchmark Datasets and Editing Models Used for Evaluating the Performance of Metrics. + +
CelebAEditValTEdBenchMagicBrushDreamBooth
Dataset TypesFacial AttributeGeneral ObjectObject CentricLocal Region EditingPersonalized Generation
Editing Models[13, 14, 17, 23][2, 5, 8, 9, 12][2, 5, 8, 9, 12][2, 5, 8, 9, 12][16, 18, 27]
Dataset Size50648100105350
+ +Table 2. User Study Statistics. + +
CelebAEditValDreamBooth
Survey questions393537
Participants453030
+ +Table 3. Correlation with Human Judgment. Human alignment score $s_{2\mathrm{AFC}} (\uparrow)$ , scaled between 0 to 1. + +
MetricsPresv.Modif.CelebAEditValDreamBooth
L2✓✗0.6530.3480.464
LPIPS✓✗0.4650.3600.286
DINO✓✗0.5740.3480.286
SC✓✗0.7520.7640.571
CLIP-I✓✗0.8480.7300.857
CLIP-T✗✓0.4910.3990.321
CLIPdir▲✓0.6730.6970.357
AugCLIP✓✓0.8830.8310.857
+ +preservation-centric (L2, LPIPS, DINO, SC, CLIP-I) and human judgment is expected because these benchmarks do not significantly deviate from the source image. + +# 5.2. Ground Truth Editing Selection Test + +Creating Triplet Dataset We generate a triplet of images, each representing a well-edited, excessively preserved, and excessively modified image. Among the triplet of images, the well-edited image is provided in the benchmark datasets, TEdBench, and MagicBrush. Excessively modified images are generated with text-to-image models [25] instructed by the target text, completely ignoring the source image. Excessively preserved images are generated by applying a negligible transformation to the given source image, ignoring the target text. Then, we measure the accuracy where each metric correctly assigns the highest score to the well-edited image as AccBoth. Yielding high accuracy in this test means that the evaluation metric can balance both preservation and modification aspects, without being biased to either side. + +AugCLIP is superior in balancing preservation and modification. In Tab. 4, AugCLIP is on par with or even better than baseline metrics over all datasets. This emphasizes the balanced evaluation criteria of AugCLIP, which previous metrics fail to abide by. Seg- + +Table 4. Ground Truth Selection Test. Accuracy, Accboth $(\uparrow)$ of assigning higher scores to ground truth images over excessively preserved and modified images. + +
MetricsPresv. Modif.TEdBenchMagicBrush
L2✓X0.3100.002
LPIPS✓X0.0900.000
DINO✓X0.2800.008
SC✓X0.4200.936
CLIP-I✓X0.2810.810
CLIP-TX✓0.3120.260
CLIPdir▲✓0.3500.601
AugCLIP✓✓0.5700.889
+ +ment Consistency (SC) excels in MagicBrush since the dataset requires editing a small local area of the image. + +# 6. Analysis + +We use $s_{2\mathrm{AFC}}$ for CelebA, EditVal, and Dreambooth, and AccBoth for TEdBench and MagicBrush. We compare our metric, AugCLIP with $\mathrm{CLIP}_{\mathrm{dir}}$ , which is the only metric that considers both preservation and modification. + +AugCLIP generalizes to diverse editing scenarios. Text-guided image editing encompasses a wide range of tasks such as style editing, object replacement, local editing, partial alteration, and personalized generation. AugCLIP excels in the highly complex scenarios of local editing as conducted with the MagicBrush dataset. Moreover, AugCLIP highly aligns with human judgment in the personalized generation case of DreamBooth, which has been underexplored by previous metrics. We report how well AugCLIP aligns with human judgment with various editing cases provided in the EditVal dataset. Across all eight scenarios, except for the texture modification task, AugCLIP outperforms $\mathrm{CLIP}_{\mathrm{dir}}$ as shown in Tab. 5. + +Augmenting $\mathrm{CLIP}_{\mathrm{dir}}$ cannot provide reliable evaluation result. We demonstrate the impact of augmenting $\mathrm{CLIP}_{\mathrm{dir}}$ with attributes, extracted in Sec. 4.1. Specifically, we replace the source and target text embeddings with the average of their respective attribute embeddings, $\mathcal{D}_S$ and $\mathcal{D}_T$ . As shown in Tab. 6, + +Table 5. Human Alignment Score $s_{2\text{AFC}}$ on Various Text-guided Image Editing Scenarios. + +
Pos. AddObj. repl.Alter PartsBackground
CLIPdir0.6670.6880.7300.5
AugCLIP1.00.750.8381.0
TextureColorActionStyle
CLIPdir0.8061.01.00.529
AugCLIP0.7421.01.00.647
+ +this straightforward augmentation does not guarantee performance gain. AugCLIP consistently outperforms all description-augmented versions of $\mathrm{CLIP}_{\mathrm{dir}}$ . This improvement is due to AugCLIP's approach, which derives the ideal representation by a minimum modification vector. This is fundamentally different from the naive methodology of $\mathrm{CLIP}_{\mathrm{dir}}$ , which relies on a simple subtraction of the source from the target. + +Table 6. Effect of Augmenting Attributes. + +
CelebAEditValDreamBoothTEDbenchMagicBrush
CLIPdir0.6730.6970.3570.3500.601
+DS0.8160.6290.3570.4000.429
+DT0.8190.7080.5360.4200.533
+DS∪DT0.8160.6070.5360.4400.402
AugCLIP0.8830.8310.8570.5700.889
+ +Weighting Strategy for Hyperplane We demonstrate the effectiveness of our weighting strategy, described in Eq. (6) in Tab. 7. Our weighting strategy enables AugCLIP to prioritize key features central to preservation and modification while estimating the representation of an ideally edited image, resulting in improvement in human alignment ( $s_{2\mathrm{AFC}}$ ) and balancing preservation and modification ( $\mathbf{Acc}_{\mathrm{Both}}$ ). + +Table 7. Effect of Weighting Strategy. + +
CelebAEditValDreamBoothTEDBenchMagicBrush
Unweighted0.8490.7870.7860.4000.830
Weighted0.8830.8310.8570.5700.889
+ +Length and Number of Attributes In Tab. 8, we compare short (under 5 words) and long (over 5 words), as well as cases with a fixed number (10, 20, or 30) of attributes. We observe that using short attributes tends to outperform using long ones, likely because they focus on a single visual aspect, avoiding the potential entanglement of multiple aspects in a single attribute. Moreover, the number of attributes impacts the performance depending on the scene complexity of the benchmark dataset, as complex scenarios require a higher number of attributes to fully capture the scene's + +details. Therefore, allowing flexibility in the number of attributes, rather than imposing a strict limit, yields the best overall performance across all configurations. + +Table 8. Effect of Length and Number of Attributes. + +
LengthNumberCelebAEditValDreamBoothTEDbenchMagicBrush
short100.8700.7190.8570.5400.889
short200.8290.8090.8210.5400.868
short300.8290.7640.7140.5700.863
long300.8430.6970.7500.5300.862
short-0.8830.8310.8570.5700.889
+ +Description Randomness Using GPT-4V for description extraction introduces slight randomness across different seeds. Tests with five seeds show low variance (0.0197) in human alignment score ( $s_{2\mathrm{AFC}}$ ), indicating that the description generation process does not affect the scoring. We also demonstrate in the Appendix that extracted attributes with different seeds do not vary. + +We provide analysis on the modification vector $\mathbf{v}$ and choice of classifier function, discussion on limitations, description prompting, and extensive qualitative results in the Appendix. + +# Limitations and Discussions + +Our method, AugCLIP, adds additional computation time compared to $\mathrm{CLIP}_{\mathrm{dir}}$ . It requires extracting attributes via MLLM, and then fitting a hyperplane to distinguish source and target attributes. This process takes around 12.3 seconds for attribute generation and 0.15 seconds for score computation. We will provide extracted attributes for all benchmark datasets to reduce this overhead, facilitating the evaluation process for future usage. + +# Conclusion + +We present AugCLIP, a novel evaluation metric for text-guided image editing that balances source image preservation and target text modification. By leveraging a multi-modal language model to extract visual attributes and finding a separating hyperplane, AugCLIP estimates a representation of an ideal edited image that closely matches human preferences. Experiments on five benchmark datasets show that AugCLIP outperforms existing metrics, especially in challenging tasks, offering a more reliable tool for evaluating edits while preserving core attributes. + +# Acknowledgements + +This work was supported by the National Research Foundation of Korea (NRF) grants (RS-2023-00209060 A Study on Optimization and Network Interpretation Method for Large-Scale Machine Learning), Institute for Information & communications Technology Planning & Evaluation(IITP) grants (No.2022-0-00713 Meta-learning applicable to real-world problems, RS-2019-II190075 Artificial Intelligence Graduate School Program(KAIST)) funded by the Korea government(MSIT). + +# References + +[1] Samyadeep Basu, Mehrdad Saberi, Shweta Bhardwaj, Atoosa Malemir Chegini, Daniela Massiceti, Maziar Sanjabi, Shell Xu Hu, and Soheil Feizi. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 1, 2, 21 +[30] Xinlu Zhang, Yujie Lu, Weizhi Wang, An Yan, Jun Yan, Lianke Qin, Heng Wang, Xifeng Yan, William Yang Wang, and Linda Ruth Petzold. 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Context Blindness Problem of Existing Evaluation Metrics. Evaluation metrics should consider the specific context of a given source image and target text. However, existing metrics exhibit context-blindness, applying the same criteria of either 'preserve' (P) or 'modify' (M) across the entire image. 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Text-guided image editing models enable the modification of images in response to textual guidance, ensuring that changes are aligned with the provided instructions. The primary objective of these models is to apply the necessary modifications guided by the target text while preserving most of the source image." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 313, + 599, + 556, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 556, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 556, + 708 + ], + "type": "text", + "content": "Despite the remarkable advancements in editing models, there has been a lack of rigorous evaluation methods, tailored specifically for text-guided image editing. Consequently, most studies [1, 2, 6, 9, 13, 15, 26] have heavily relied on human evaluation, which provides balanced consideration of preservation and modification aspects. However, as it is costly and impractical for real-world applications, researchers have adapted automatic evaluation metrics [3, 10, 11, 29] originally" + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "spans": [ + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "spans": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 702, + 238, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 238, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 238, + 713 + ], + "type": "text", + "content": "*Equal contribution,† Corresponding Author." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "23474" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "type": "text", + "content": "designed for other vision tasks, such as image generation or captioning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 96, + 295, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 96, + 295, + 251 + ], + "spans": [ + { + "bbox": [ + 54, + 96, + 295, + 251 + ], + "type": "text", + "content": "In text-guided editing scenarios, it is essential to assess which elements in the source to preserve and which in the target to modify into, based on the specific context of the given source image and target text (see Fig. 1(a)-(b) for example). Existing metrics, however, exhibit context blindness, meaning preservation-centric metrics completely ignore the target context while modification-centric metrics do not account for the source context. As shown in Fig. 1(c), preservation- and modification-centric metrics apply a fixed standard across the entire image, regardless of the true editing requirement of the given context. Even combining them fails to overcome the context blindness problem." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 252, + 296, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 252, + 296, + 418 + ], + "spans": [ + { + "bbox": [ + 56, + 252, + 296, + 418 + ], + "type": "text", + "content": "Among existing metrics, directional CLIP similarity [6] is unique because it provides a method to consider both the source image and target text in the evaluation. Even this metric suffers from a context-blindness problem, using a fixed standard without considering the specific relationship between the source image and target text. We show that directional CLIP similarity tends to prioritize modification over preservation, and often focuses on peripheral parts rather than regions that are edited as guided by target text, in Sec. 3. These observations underscore the need for a context-aware metric to dynamically adjust the evaluation standard, balancing both aspects in response to diverse editing contexts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 420, + 296, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 420, + 296, + 598 + ], + "spans": [ + { + "bbox": [ + 56, + 420, + 296, + 598 + ], + "type": "text", + "content": "Based on our comprehensive analysis, we propose a novel context-aware metric, AugCLIP, which evaluates the quality of the edited image by comparing it with an estimated representation of a well-edited image. To balance preservation and modification, a well-edited image is represented by a minimum modification on the source image, while matching the target text. We use multi-modal large language models (MLLMs) to extract attributes that capture various visual aspects of the source image and target text. With these attributes, we derive a hyperplane that separates the source and target to derive the ideal modification as a projection to this hyperplane. AugCLIP evaluates how closely the edited image aligns with the estimated ideal image in CLIP space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 598, + 295, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 295, + 706 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 295, + 706 + ], + "type": "text", + "content": "Our metric AugCLIP demonstrates remarkable improvement in alignment with human judgment on diverse editing scenarios such as object, attribute, and style alteration compared to all other existing metrics. Moreover, our metric is even applicable to personalized generation, the DreamBooth dataset, where the objective is to identify an object in the source image and edit it into a completely novel context. This shows the flexibility of AugCLIP, which seamlessly applies to" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "a variety of editing directions. Notably, our metric excels in identifying minor differences between the source image and the edited image, showing superb ability in complex image editing scenarios such as MagicBrush." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 328, + 121, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 121, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 328, + 121, + 553, + 132 + ], + "type": "text", + "content": "The major contributions are summarized as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 133, + 553, + 299 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 316, + 133, + 553, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 133, + 553, + 179 + ], + "spans": [ + { + "bbox": [ + 316, + 133, + 553, + 179 + ], + "type": "text", + "content": "- We point out the unreliability of current evaluation metrics in text-guided image editing, noting their inability to balance preservation and modification effectively due to inherent context blindness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 316, + 180, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 180, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 316, + 180, + 553, + 251 + ], + "type": "text", + "content": "- We introduce AugCLIP, a context-aware metric for image editing by automatically augmenting descriptions via MLLM and estimating a balanced representation of preservation and modification, which takes into account the relative importance of each description." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 251, + 553, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 251, + 553, + 299 + ], + "spans": [ + { + "bbox": [ + 316, + 251, + 553, + 299 + ], + "type": "text", + "content": "- AugCLIP demonstrates a significantly high correlation with human evaluations across various editing scenarios, even in complex applications where existing metrics struggle." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 310, + 523, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 523, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 523, + 324 + ], + "type": "text", + "content": "2. Background on Existing Metrics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 330, + 553, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 330, + 553, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 553, + 378 + ], + "type": "text", + "content": "In the context of text-guided image editing, evaluation metrics should assess the quality of edited images in terms of both preservation of the source image and modification towards the target text." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 392, + 555, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 548 + ], + "type": "text", + "content": "Preservation-Centric Metrics FID [11], LPIPS [29], and L2 distance measure feature-level distance between images. These metrics are primarily used in image generation tasks to compare the distributions of real and generated images. When applied to editing scenarios, they assess the distance between the source and edited images, completely ignoring the target text guiding the editing process. Segmentation consistency (SC) [13] measures the structural change. Additionally, DINO similarity (DINO) and CLIP-I evaluate the semantic similarity between the source and edited images within the DINO [3] and CLIP [24] embedding spaces, also focusing solely on preservation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 561, + 553, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 553, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 553, + 658 + ], + "type": "text", + "content": "Modification-Centric Metrics To assess how well an edited image aligns with the target text, the primary approach involves using a pre-trained multimodal model [24]. CLIPScore (CLIP-T) [10] is the most widely adopted metric in this category, measuring the similarity between the edited image and the target text. This metric completely ignores the source image that should be considered for the preservation aspect." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 671, + 553, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 671, + 553, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 671, + 553, + 708 + ], + "type": "text", + "content": "Holistic Evaluation of Preservation and Modification Directional CLIP similarity " + }, + { + "bbox": [ + 313, + 671, + 553, + 708 + ], + "type": "inline_equation", + "content": "(\\mathrm{CLIP}_{\\mathrm{dir}})" + }, + { + "bbox": [ + 313, + 671, + 553, + 708 + ], + "type": "text", + "content": " [6] is unique among existing metrics as it assesses both" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "23475" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 72, + 140, + 153 + ], + "blocks": [ + { + "bbox": [ + 58, + 72, + 140, + 153 + ], + "lines": [ + { + "bbox": [ + 58, + 72, + 140, + 153 + ], + "spans": [ + { + "bbox": [ + 58, + 72, + 140, + 153 + ], + "type": "image", + "image_path": "1c8ce8f5a625a3d22a3a0d9744ec75cab9225c914d2e15478f6bc5f8e2694c6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 142, + 72, + 217, + 153 + ], + "blocks": [ + { + "bbox": [ + 142, + 72, + 217, + 153 + ], + "lines": [ + { + "bbox": [ + 142, + 72, + 217, + 153 + ], + "spans": [ + { + "bbox": [ + 142, + 72, + 217, + 153 + ], + "type": "image", + "image_path": "3a2227634b79b47f81c7fe8b92d8118006ef75989a9db184213c1ccb0b1c2145.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 217, + 80, + 293, + 153 + ], + "blocks": [ + { + "bbox": [ + 217, + 80, + 293, + 153 + ], + "lines": [ + { + "bbox": [ + 217, + 80, + 293, + 153 + ], + "spans": [ + { + "bbox": [ + 217, + 80, + 293, + 153 + ], + "type": "image", + "image_path": "6c00a34eaff5677c44d10ec0536358caa28c320f50f81da97bd6468e00a98f42.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 57, + 160, + 140, + 240 + ], + "blocks": [ + { + "bbox": [ + 57, + 160, + 140, + 240 + ], + "lines": [ + { + "bbox": [ + 57, + 160, + 140, + 240 + ], + "spans": [ + { + "bbox": [ + 57, + 160, + 140, + 240 + ], + "type": "image", + "image_path": "93538b080502ab1a322105badc074aeae7795f08479e368552742f27761cd259.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 251, + 295, + 318 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 295, + 318 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 295, + 318 + ], + "type": "text", + "content": "Figure 2. Combination of Preservation- and Modification-Centric Metrics Deteriorates in Performance. The plot shows the human alignment score " + }, + { + "bbox": [ + 55, + 251, + 295, + 318 + ], + "type": "inline_equation", + "content": "s_{\\mathrm{align}}" + }, + { + "bbox": [ + 55, + 251, + 295, + 318 + ], + "type": "text", + "content": " measured by a linear interpolation of {DINO, SC, CLIP-I} and CLIP-T. The results show that combining rather degrades the alignment with human judgment." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 141, + 160, + 217, + 240 + ], + "blocks": [ + { + "bbox": [ + 141, + 160, + 217, + 240 + ], + "lines": [ + { + "bbox": [ + 141, + 160, + 217, + 240 + ], + "spans": [ + { + "bbox": [ + 141, + 160, + 217, + 240 + ], + "type": "image", + "image_path": "744d18e838725f65caa8433e102eaca6987b63a7313fd5eacf19d9ce13721c92.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 217, + 167, + 293, + 240 + ], + "blocks": [ + { + "bbox": [ + 217, + 167, + 293, + 240 + ], + "lines": [ + { + "bbox": [ + 217, + 167, + 293, + 240 + ], + "spans": [ + { + "bbox": [ + 217, + 167, + 293, + 240 + ], + "type": "image", + "image_path": "8fa399fdc13a66b411439f291cd752df0581df85c4c6e870afbaab852d1187f3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 339, + 295, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 295, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 295, + 374 + ], + "type": "text", + "content": "preservation and modification aspects by evaluating directional alignment between the original and edited images concerning the source and target text." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 375, + 295, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 375, + 295, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 375, + 295, + 460 + ], + "type": "text", + "content": "However, these metrics employ a fixed evaluation standard, disregarding the context of each editing scenario, which leads to context blindness. As discussed in Sec. 3, combining preservation- and modification-centric metrics or using directional CLIP similarity fails to balance preservation and modification adequately, resulting in misalignment with human judgment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 468, + 295, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 295, + 511 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 295, + 511 + ], + "type": "text", + "content": "3. Problems of Existing Metrics in Balancing Preservation and Modification Aspects" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 517, + 295, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 295, + 661 + ], + "type": "text", + "content": "Existing evaluation metrics, that focus on either one of the preservation or modification aspects, face a challenge in assessing both aspects. Does combining these two metrics successfully balance the preservation and modification aspects? We systematically analyze how these metrics and their combinations still fail in balancing the two colliding objectives, suffering from context-blindness (Sec. 3.1). Moreover, we focus on directional CLIP similarity, the unique metric that accounts for both source image and target text, to reveal that it presents two significant problems that question its reliability (Sec. 3.2)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": "3.1. Combination of Preservation- and Modification-Centric Metrics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "text", + "content": "We explore whether combining preservation- and modification-centric metrics can improve alignment with human judgments across two benchmark datasets: EditVal [1] and CelebA [20] (Results on the other three benchmark datasets are deferred to the Appendix). To do so, we combine CLIP-T, a modification-centric metric, and preservation-centric metrics (LPIPS, DINO similarity, CLIP-I) with varying interpolation values " + }, + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\gamma \\in [0,1]" + }, + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "text", + "content": ". Note that both metrics are scaled to the same range before interpolation, ensuring the interpolation value " + }, + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 101, + 555, + 243 + ], + "type": "text", + "content": " is properly reflected in the final combined score." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 244, + 556, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 244, + 556, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 244, + 556, + 423 + ], + "type": "text", + "content": "As illustrated in Fig. 2, the combination of two powerful metrics in preservation and modification often leads to performance degradation. This manifests that a simple combination of the colliding metrics cannot be a reliable evaluation metric. This is due to the context-blindness of these metrics, failing to holistically consider source image and target text. Preservation-centric metrics compare only the source and edited images, ignoring the target context. Similarly, modification-centric metrics consider only the target text, overlooking the source context. This highlights the need for a tailored metric that is contextually aware of both preservation and modification, ensuring a reliable alignment with human evaluations across diverse datasets and tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 431, + 468, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 468, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 468, + 445 + ], + "type": "text", + "content": "3.2. Directional CLIP Similarity" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 449, + 554, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 554, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 554, + 497 + ], + "type": "text", + "content": "Directional CLIP similarity " + }, + { + "bbox": [ + 313, + 449, + 554, + 497 + ], + "type": "inline_equation", + "content": "\\left(\\mathrm{CLIP}_{\\mathrm{dir}}\\right)" + }, + { + "bbox": [ + 313, + 449, + 554, + 497 + ], + "type": "text", + "content": " is designed to assess both preservation and modification in text-guided image editing by measuring the similarity between image and text directions as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 328, + 506, + 553, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 506, + 553, + 543 + ], + "spans": [ + { + "bbox": [ + 328, + 506, + 553, + 543 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {C L I P} _ {\\text {d i r}} = \\operatorname {c s} (\\Delta I, \\Delta T) \\tag {1} \\\\ = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right), \\quad (2) \\\\ \\end{array}", + "image_path": "d363517f5e450b4b3b3508a3f4d0fe59a922822a0965e60f8d1f62d69f26129c.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{cs}(\\mathbf{a},\\mathbf{b}) = \\frac{\\mathbf{a}\\cdot\\mathbf{b}}{\\|\\mathbf{a}\\|\\|\\mathbf{b}\\|}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " denotes cosine similarity and " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " is a CLIP encoder for either image or text. Here, " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{edit}}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " is the edited image to be evaluated, which is edited from the source image " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{src}}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " according to the target text " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{trg}}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": ". For evaluation of directional CLIP similarity, " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{src}}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": ", the corresponding text about the source image, is required. We analyze that " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " has two major problems that hinder the balanced evaluation of preservation and modification." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 675, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 675, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 675, + 555, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 675, + 555, + 712 + ], + "type": "text", + "content": " overly emphasizes modification. Directional CLIP similarity overly emphasizes the alignment with the target text while neglecting the preservation" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "23476" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 79, + 138, + 195 + ], + "blocks": [ + { + "bbox": [ + 61, + 79, + 138, + 195 + ], + "lines": [ + { + "bbox": [ + 61, + 79, + 138, + 195 + ], + "spans": [ + { + "bbox": [ + 61, + 79, + 138, + 195 + ], + "type": "image", + "image_path": "1b44e9ea270df7073b17db98998961ef898e5e6cd05e96607596615eb2b4f439.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 143, + 81, + 220, + 190 + ], + "blocks": [ + { + "bbox": [ + 143, + 81, + 220, + 190 + ], + "lines": [ + { + "bbox": [ + 143, + 81, + 220, + 190 + ], + "spans": [ + { + "bbox": [ + 143, + 81, + 220, + 190 + ], + "type": "image", + "image_path": "b53cd2f5514d4b7404af639b680b2c7aedef8b4380f562690f7d3fc38badf4ff.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "lines": [ + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "spans": [ + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "inline_equation", + "content": "\\Delta I =" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "text", + "content": " Ground truth " + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "inline_equation", + "content": "-I_{s r c}" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "inline_equation", + "content": "\\Delta I =" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "text", + "content": " Excess. modif. " + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "inline_equation", + "content": "I_{s r c}" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "inline_equation", + "content": "\\Delta T =" + }, + { + "bbox": [ + 149, + 191, + 294, + 213 + ], + "type": "text", + "content": " \"A jumping dog\"-\"A standing dog" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 221, + 82, + 296, + 190 + ], + "blocks": [ + { + "bbox": [ + 221, + 82, + 296, + 190 + ], + "lines": [ + { + "bbox": [ + 221, + 82, + 296, + 190 + ], + "spans": [ + { + "bbox": [ + 221, + 82, + 296, + 190 + ], + "type": "image", + "image_path": "e8190263bcb328de08de33f9055b2a0c56cea6835b3cb68fcae68ace3e3e855c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 309, + 79, + 384, + 195 + ], + "blocks": [ + { + "bbox": [ + 309, + 79, + 384, + 195 + ], + "lines": [ + { + "bbox": [ + 309, + 79, + 384, + 195 + ], + "spans": [ + { + "bbox": [ + 309, + 79, + 384, + 195 + ], + "type": "image", + "image_path": "075e71b7abe87c38bf657e662f9dad1ee50a11302e0657687f56f753c991766b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 390, + 82, + 464, + 190 + ], + "blocks": [ + { + "bbox": [ + 390, + 82, + 464, + 190 + ], + "lines": [ + { + "bbox": [ + 390, + 82, + 464, + 190 + ], + "spans": [ + { + "bbox": [ + 390, + 82, + 464, + 190 + ], + "type": "image", + "image_path": "f01aa218aa97bd91363b143788f29cccef0ec82a14846f147056ed6e33aab155.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "lines": [ + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "spans": [ + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "inline_equation", + "content": "\\Delta I =" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "text", + "content": " Ground truth - " + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "inline_equation", + "content": "I_{s r c}" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "inline_equation", + "content": "\\Delta I =" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "text", + "content": " Excess. modif. - " + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "inline_equation", + "content": "I_{s r c}" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "inline_equation", + "content": "\\Delta T =" + }, + { + "bbox": [ + 394, + 191, + 539, + 213 + ], + "type": "text", + "content": " \"Acheze pizza\"-\"Apepperoni pizza" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 466, + 82, + 541, + 190 + ], + "blocks": [ + { + "bbox": [ + 466, + 82, + 541, + 190 + ], + "lines": [ + { + "bbox": [ + 466, + 82, + 541, + 190 + ], + "spans": [ + { + "bbox": [ + 466, + 82, + 541, + 190 + ], + "type": "image", + "image_path": "4fa0ab85cff9b1a02c14cc2b57b4ff418607255ced43969c4ed097e0b86ff577.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 61, + 240, + 544, + 352 + ], + "blocks": [ + { + "bbox": [ + 62, + 219, + 349, + 232 + ], + "lines": [ + { + "bbox": [ + 62, + 219, + 349, + 232 + ], + "spans": [ + { + "bbox": [ + 62, + 219, + 349, + 232 + ], + "type": "text", + "content": "(a) Problem1. Overemphasizing Modification over Preservation" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 240, + 544, + 352 + ], + "lines": [ + { + "bbox": [ + 61, + 240, + 544, + 352 + ], + "spans": [ + { + "bbox": [ + 61, + 240, + 544, + 352 + ], + "type": "image", + "image_path": "098dd07ac310cf24839e8ba4817157d4c13883224d8deea0b652c17db3a7087d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "lines": [ + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "text", + "content": "Figure 3. Problems of Directional CLIP Similarity. (a) " + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "text", + "content": " assigns higher scores to excessive modification, over well-edited ground truth images. (b) " + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "text", + "content": " evaluates edited images by attending to irrelevant regions of the image. Adding visual annotations helps " + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 363, + 555, + 398 + ], + "type": "text", + "content": " properly attend to edited regions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "spans": [ + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": "of the source image. Despite attempting to incorporate preservation by subtracting " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{src}}" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{trg}}" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " frequently favors excessively modified images over ground truth ideally edited images as shown in samples in Fig. 3(a). Specifically, " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " metric fails on " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "63\\%" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " of the 100 editing cases in TEdBench [12] and " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "35.1\\%" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " of the 1053 cases in MagicBrush [28] (Details in Sec. 5). This problem happens since " + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 54, + 418, + 297, + 550 + ], + "type": "text", + "content": " is designed to assume that a well-edited image should primarily adhere to the target text. Thus, it blindly favors the visual features of the target text, leading to unreliable results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "text", + "content": " overlooks edited regions. " + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "text", + "content": " often focuses on peripheral or unmodified local areas of the edited image, overlooking the specific areas that are edited by the text. Using the relevancy map [4], " + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "inline_equation", + "content": "R(\\Delta I; \\Delta T)^1" + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "text", + "content": ", to visualize attention on image regions corresponding to the text direction, we observe that " + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 563, + 296, + 672 + ], + "type": "text", + "content": " frequently fails to concentrate on the image regions that are directly relevant to the target text as shown in Fig. 3(b). The figure also shows that" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 418, + 555, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 555, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 555, + 444 + ], + "type": "text", + "content": "adding explicit visual details guides " + }, + { + "bbox": [ + 313, + 418, + 555, + 444 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 418, + 555, + 444 + ], + "type": "text", + "content": " to attend to edited regions properly." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 452, + 555, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 452, + 555, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 452, + 555, + 479 + ], + "type": "text", + "content": "4. AugCLIP: A Context-Aware Evaluation Metric" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": "We introduce a novel evaluation metric, AugCLIP, for scoring the editing quality of the image in terms of preservation and modification. Given a target text " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{trg}}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": " and a source image " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{src}}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": ", AugCLIP measures the cosine similarity between the edited image " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{edit}}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": " and the ideal editing. Since the ideal edited image is not given in most evaluation cases, we estimate the representation of an ideally edited image as a modification on the source image, " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{src}} + \\mathbf{v}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": " is the modification vector. Then, the editing quality of the edited image " + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{edit}}" + }, + { + "bbox": [ + 312, + 486, + 555, + 617 + ], + "type": "text", + "content": " is evaluated as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 627, + 553, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 627, + 553, + 653 + ], + "spans": [ + { + "bbox": [ + 315, + 627, + 553, + 653 + ], + "type": "interline_equation", + "content": "\\operatorname {A u g C L I P} \\left(I _ {\\text {e d i t}}; I _ {\\text {s r c}}, T _ {\\text {t r g}}\\right) = \\mathbf {c s} \\left(E \\left(I _ {\\text {e d i t}}\\right), E \\left(I _ {\\text {s r c}}\\right) + \\mathbf {v}\\right), \\tag {3}", + "image_path": "fb1f374d69821ecaaa6175dd68147edda99113f11998cbe87cad3ded21a787c8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 652, + 450, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 450, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 450, + 663 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 652, + 450, + 663 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 313, + 652, + 450, + 663 + ], + "type": "text", + "content": " is a CLIP encoder." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 664, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 664, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 664, + 555, + 712 + ], + "type": "text", + "content": "The evaluation score ranges between [0, 1], where the maximum value 1 indicates that the edited image is ideally modified by an editing model. We outline the framework of AugCLIP in Fig. 4. We extract the visual" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "spans": [ + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "text", + "content": "1The original relevancy map " + }, + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "inline_equation", + "content": "\\pmb{R}" + }, + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "text", + "content": " utilizes an image-text pair. To adapt it to " + }, + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 55, + 678, + 295, + 708 + ], + "type": "text", + "content": ", we subtract two relevancy maps. Details are in the Appendix." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "23477" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 231, + 223 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 231, + 223 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 231, + 223 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 231, + 223 + ], + "type": "image", + "image_path": "45eb7f797cf0782a3c775980250217466df33cde545f07f95042d268b2c43413.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 140, + 225, + 156, + 237 + ], + "lines": [ + { + "bbox": [ + 140, + 225, + 156, + 237 + ], + "spans": [ + { + "bbox": [ + 140, + 225, + 156, + 237 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 235, + 70, + 408, + 223 + ], + "blocks": [ + { + "bbox": [ + 235, + 70, + 408, + 223 + ], + "lines": [ + { + "bbox": [ + 235, + 70, + 408, + 223 + ], + "spans": [ + { + "bbox": [ + 235, + 70, + 408, + 223 + ], + "type": "image", + "image_path": "490b677c93ac8c32c507d7d2706bb918ff4d3acde950c427efd92b9e31f9ba30.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 224, + 408, + 237 + ], + "lines": [ + { + "bbox": [ + 392, + 224, + 408, + 237 + ], + "spans": [ + { + "bbox": [ + 392, + 224, + 408, + 237 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 410, + 71, + 553, + 223 + ], + "blocks": [ + { + "bbox": [ + 410, + 71, + 553, + 223 + ], + "lines": [ + { + "bbox": [ + 410, + 71, + 553, + 223 + ], + "spans": [ + { + "bbox": [ + 410, + 71, + 553, + 223 + ], + "type": "image", + "image_path": "426fc1f65916732dcde6805389ab9c50bbfdd7f3f0906d19f8fd7a77f386567c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "lines": [ + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "text", + "content": "Figure 4. (a) Description Extraction Process. The source image describes a young child standing on the balance board. Target text guides the editing model to make the girl sit. The source and target attributes are extracted with MLLM. (b) Evaluation Process of AugCLIP. The two edited images demonstrate i) An older woman sitting down with legs crossed (" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{edit}}^1" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "text", + "content": ") and ii) A young girl sitting on the floor (" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{edit}}^2" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "text", + "content": "). AugCLIP derives the ideal image representation as a minimum modification " + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "text", + "content": " on the source image to be classified as target. The second image that is closer to " + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{src}} + \\mathbf{v}" + }, + { + "bbox": [ + 55, + 254, + 555, + 319 + ], + "type": "text", + "content": " shows a higher score, while the first image that is excessively modified with lost source identity shows a lower score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 341, + 295, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 295, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 295, + 401 + ], + "type": "text", + "content": "features of the source image and target text (Sec. 4.1), then derive the CLIP representation of an ideal modification that satisfies the two criteria: 'i) Does the edited image follow the target text?' and 'ii) Does the edited image preserve the source image?' (Sec. 4.2)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 407, + 252, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 252, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 252, + 419 + ], + "type": "text", + "content": "4.1. Extracting and Processing Attributes" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 424, + 296, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 424, + 296, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 424, + 296, + 544 + ], + "type": "text", + "content": "Source & Target Attribute Extraction As described in Fig. 4(a), we extract visual descriptions about attributes of the source image and target text using a state-of-the-art multi-modal large language model (MLLM), GPT-4V [22]. From the source image, we extract visual features that can be the object of preservation. Likewise, from the target text, we extract visual features that can be the object of modification. The extraction process is instructed by five annotated in-context examples, which are provided in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "text", + "content": "Encoding into CLIP Space After attribute extraction from MLLM, each attribute is encoded into CLIP space. The source attributes are denoted as " + }, + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "text", + "content": " and target attributes as " + }, + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 55, + 556, + 296, + 605 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": "Relative Weighting on Attributes In editing scenarios, some of the attributes are more important than others. For instance, drawing stripes is more essential than a short mane to represent a zebra. To prioritize this, we emphasize the similarity between key attributes within the same class. Since multi-modal large-language models sample based on the empirical probability, frequently extracted attributes indicate higher" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "text", + "content": "importance in representing the context. Formally, the importance of each visual attribute in " + }, + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 341, + 555, + 389 + ], + "type": "text", + "content": " is represented as a cosine similarity between CLIP embeddings in the same set as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 364, + 393, + 553, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 393, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 364, + 393, + 553, + 422 + ], + "type": "interline_equation", + "content": "I m p o r t a n c e (v _ {i}) = \\sum_ {j \\neq i} \\frac {u _ {i} \\cdot v _ {j}}{\\| u _ {i} \\| \\| v _ {j} \\|}, \\tag {4}", + "image_path": "863f1581c82b1e9c69347f4a4322f80c2589a736900b2cb0bce25b85e5db7e23.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "text", + "content": "for all " + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "inline_equation", + "content": "u_{j}" + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "text", + "content": " in the same attribute set, either " + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 426, + 547, + 438 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "type": "text", + "content": "Additionally, the importance should be downweighted by how much the visual attribute hinders the preservation of the source image or modification of the target text. More specifically, a collision between source and target attributes is measured by averaged cosine distance to CLIP embeddings in the opposite set as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 364, + 514, + 553, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 514, + 553, + 540 + ], + "spans": [ + { + "bbox": [ + 364, + 514, + 553, + 540 + ], + "type": "interline_equation", + "content": "C o l l i s i o n \\left(v _ {i}\\right) = - \\sum_ {l} \\frac {v _ {i} \\cdot w _ {l}}{\\| v _ {i} \\| \\| w _ {l} \\|}, \\tag {5}", + "image_path": "a5f1e4527b94d3d0318eeaacc5eaff05c594d24bf486dc802a65bff759a2761a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 545, + 485, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 485, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 485, + 557 + ], + "type": "text", + "content": "for all " + }, + { + "bbox": [ + 313, + 545, + 485, + 557 + ], + "type": "inline_equation", + "content": "w_{l}" + }, + { + "bbox": [ + 313, + 545, + 485, + 557 + ], + "type": "text", + "content": " in the opposite attribute set." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 557, + 554, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 554, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 554, + 581 + ], + "type": "text", + "content": "Adding these two measures, the weighting value for the attribute " + }, + { + "bbox": [ + 313, + 557, + 554, + 581 + ], + "type": "inline_equation", + "content": "v \\in \\mathcal{D}_S \\cup \\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 557, + 554, + 581 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 351, + 587, + 553, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 587, + 553, + 601 + ], + "spans": [ + { + "bbox": [ + 351, + 587, + 553, + 601 + ], + "type": "interline_equation", + "content": "\\alpha (v) = \\text {I m p o r t a n c e} (v) + \\text {C o l l i s i o n} (v). \\tag {6}", + "image_path": "f386084073b7269a2dca14a5c205a37ae8c90cce66d987cb25a2dbe5be9b954a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 605, + 554, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 643 + ], + "type": "text", + "content": "This weighting value accounts for the relative significance of each attribute in the evaluation process and is integrated into Eq. (7)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 647, + 531, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 531, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 531, + 661 + ], + "type": "text", + "content": "4.2. Deriving the Ideal Editing in CLIP Space" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Based on the extracted source and target attributes, we describe how to derive a modification vector that satisfies i) modification into the target text and ii) preservation of the source image." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "23478" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "content": "Criterion 1: Does the edited image follow the target text? To determine if the edited image faithfully follows the given target text, it is intuitive to employ a classifier that classifies the image into either source or target. Classification into source indicates the edited image is still closer to the source image, while classification into target means that the image is sufficiently modified. The classifier is derived by a hyperplane that separates the source " + }, + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "spans": [ + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": "Formally, the classifier function " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "g(x) = \\mathbf{w}^T x + b" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": " assigns a CLIP embedding " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": " to the target class if " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "g(x) > 0" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": ", or to the source class if " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "g(x) < 0" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": ". Therefore, " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "E(I_{\\mathrm{edit}})" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": " should satisfy " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^T E(I_{\\mathrm{edit}}) + b > 0" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": " if the edited image faithfully follows the target text. Here, the optimization form of the classifier function " + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 55, + 179, + 296, + 253 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 261, + 296, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 261, + 296, + 294 + ], + "spans": [ + { + "bbox": [ + 61, + 261, + 296, + 294 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w}, b} \\frac {1}{2} \\| \\mathbf {w} \\| ^ {2} + C \\sum_ {i = 1} ^ {N} \\alpha (v _ {i}) \\cdot \\max (0, 1 - y _ {i} (\\mathbf {w} \\cdot v _ {i} + b)), (7)", + "image_path": "a9b824b3c2d6a9e1cbf475b62f260d821b16bad7537f219571c31ea7a5f7760b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "y_{i} = +1" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "v_{i}\\in \\mathcal{D}_{T}" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "y_{i} = -1" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "v_{i}\\in \\mathcal{D}_{S}" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": ". Here, the precomputed weighting values " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "\\alpha (\\cdot)" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " in Eq. (6) are integrated into the optimization process." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "text", + "content": "Criterion 2: Does the edited image preserve the source image? However, it is equally important to consider the second criterion, source image preservation. Therefore, the CLIP representation of modification should inflict minimum modification to the original embedding " + }, + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "inline_equation", + "content": "E(I_{\\mathrm{src}})" + }, + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "text", + "content": ", while being classified as a target class. Formally, we derive the modification " + }, + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 350, + 296, + 446 + ], + "type": "text", + "content": " in CLIP space that satisfies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 63, + 454, + 295, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 454, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 63, + 454, + 295, + 472 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {v}} \\| \\mathbf {v} \\| \\quad \\text {s u b j e c t t o} \\quad \\mathbf {w} ^ {T} \\left(E \\left(I _ {\\mathrm {s r c}}\\right) + \\mathbf {v}\\right) + b > 0. \\tag {8}", + "image_path": "172ed283b76314f1da71888dfea4537b6dac6524ad6327705d9b5b50d5c00058.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": "Derivation of " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " To minimize " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{v}\\|" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " should be in the direction that most efficiently increases the classifier output " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": ". This direction is given by the gradient of the classifier function concerning " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": ", which is " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{w} = \\nabla g(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": ". Therefore, the optimal " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "c\\mathbf{w}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "c > 0" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " is a scalar to be determined. Substituting " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{v} = c\\mathbf{w}" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": " to Eq. (8), we derive the following equation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 132, + 577, + 295, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 577, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 132, + 577, + 295, + 605 + ], + "type": "interline_equation", + "content": "c > \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}}. \\tag {9}", + "image_path": "15619c1bcfdc51f8e074d93566f5a73f6b32177ad22f3e748505c7ed071ca7cb.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": "In order to solve for " + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": " that minimizes " + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{v}\\|" + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": ", we derive the smallest " + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": " satisfying the condition as " + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{min}} = \\frac{-(\\mathbf{w}^\\top I_{\\mathrm{src}} + b)}{\\|\\mathbf{w}\\|^2}" + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": ". Then the modification vector " + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 612, + 296, + 660 + ], + "type": "text", + "content": " is derived as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 660, + 295, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 660, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 107, + 660, + 295, + 687 + ], + "type": "interline_equation", + "content": "\\mathbf {v} = c _ {\\min } \\mathbf {w} = \\frac {- \\left(\\mathbf {w} ^ {\\top} I _ {\\mathrm {s r c}} + b\\right)}{\\| \\mathbf {w} \\| ^ {2}} \\mathbf {w}. \\tag {10}", + "image_path": "d151d063c63cd11b804b0dc7c17f3fa5a0b1037b50751c2472d200400a8de5eb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Finally, AugCLIP is computed by substituting " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " to Eq. (3)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 72, + 408, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 408, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 408, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 91, + 553, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 152 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 152 + ], + "type": "text", + "content": "Implementation Details. For our experiments, we employ a pre-trained CLIP-ViT 16/B model for CLIP-based metrics. Source and target attributes are generated using GPT-4V [22]. Further details on prompting the source and target attributes are in the Appendix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 164, + 553, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 164, + 553, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 553, + 224 + ], + "type": "text", + "content": "Baseline Metrics. We compare AugCLIP with DINO similarity, LPIPS, L2, Segmentation Consistency (SC), Directional CLIP similarity " + }, + { + "bbox": [ + 313, + 164, + 553, + 224 + ], + "type": "inline_equation", + "content": "(\\mathrm{CLIP}_{\\mathrm{dir}})" + }, + { + "bbox": [ + 313, + 164, + 553, + 224 + ], + "type": "text", + "content": ", CLIP-I, and CLIP-T. The CLIP variants are summarized as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 229, + 547, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 229, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 320, + 229, + 547, + 243 + ], + "type": "interline_equation", + "content": "\\operatorname {C L I P} _ {\\mathrm {d i r}} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right) - E \\left(I _ {\\mathrm {s r c}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right) - E \\left(T _ {\\mathrm {s r c}}\\right)\\right)", + "image_path": "6d8032e53682d933fa8352a4a8f43dcb767123851bb2e7b8de4b66adc1ac6082.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 321, + 246, + 455, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 246, + 455, + 259 + ], + "spans": [ + { + "bbox": [ + 321, + 246, + 455, + 259 + ], + "type": "interline_equation", + "content": "\\operatorname {C L I P - I} = \\mathbf {c s} \\left(E (I _ {\\mathrm {e d i t}}), E (I _ {\\mathrm {s r c}})\\right)", + "image_path": "c710633ab8b2bf6fc78629bce38f103a8e7ecc22303e41a70addf8de54845768.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 321, + 261, + 466, + 276 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 261, + 466, + 276 + ], + "spans": [ + { + "bbox": [ + 321, + 261, + 466, + 276 + ], + "type": "interline_equation", + "content": "\\mathrm {C L I P - T} = \\mathbf {c s} \\left(E \\left(I _ {\\mathrm {e d i t}}\\right), E \\left(T _ {\\mathrm {t r g}}\\right)\\right).", + "image_path": "67f700d00f17d1d15209aed18026910df864a32ecc20f5d2ef4a8cf50cc329bd.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 281, + 553, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 553, + 341 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 553, + 341 + ], + "type": "text", + "content": "Note that FID measures the distance between two distributions of image features, this metric cannot be measured in a sample-wise manner. Therefore, FID cannot be tested in terms of alignment with human evaluation or preference test on ground truth samples." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 354, + 554, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 474 + ], + "type": "text", + "content": "Benchmark Datasets and Editing Models. We evaluate AugCLIP and existing metrics across several text-guided image editing benchmarks, including TEd-Bench [12], EditVal [1], MagicBrush [28], DreamBooth [26], and CelebA [20]. Each benchmark dataset represents varying editing scenarios as in Tab. 1. For each benchmark dataset, we employ multiple editing models [2, 5, 8, 9, 13, 14, 16-18, 23, 27] as specified in Tab. 1 for suitable type of benchmark dataset. Details on benchmark datasets are provided in the Appendix." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 479, + 503, + 492 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 503, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 503, + 492 + ], + "type": "text", + "content": "5.1. Correlation with Human Judgment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 497, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 555, + 641 + ], + "type": "text", + "content": "User Study To evaluate the effectiveness of AugCLIP compared to existing metrics, we conduct a Two-Alternative Forced Choice survey on human evaluators to collect preferences over diverse edited images. The alignment score " + }, + { + "bbox": [ + 313, + 497, + 555, + 641 + ], + "type": "inline_equation", + "content": "s_{2\\mathrm{AFC}}" + }, + { + "bbox": [ + 313, + 497, + 555, + 641 + ], + "type": "text", + "content": " measures if each metric prefers the same option as human evaluators. The survey was conducted using Amazon Mechanical Turk (AMT), over three benchmark datasets, encompassing a total of 105 participants as detailed in Tab. 2. The survey questionnaire is structured as described in the Appendix, providing clear criteria to consider source image preservation and target text alignment." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "type": "text", + "content": "AugCLIP aligns better with human judgments. As shown in Tab. 3, AugCLIP, the context-aware metric that balances preservation and modification, is superior over all previous metrics across diverse benchmark datasets. A high level of alignment between" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "23479" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 87, + 550, + 143 + ], + "blocks": [ + { + "bbox": [ + 107, + 69, + 503, + 79 + ], + "lines": [ + { + "bbox": [ + 107, + 69, + 503, + 79 + ], + "spans": [ + { + "bbox": [ + 107, + 69, + 503, + 79 + ], + "type": "text", + "content": "Table 1. Benchmark Datasets and Editing Models Used for Evaluating the Performance of Metrics." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 87, + 550, + 143 + ], + "lines": [ + { + "bbox": [ + 59, + 87, + 550, + 143 + ], + "spans": [ + { + "bbox": [ + 59, + 87, + 550, + 143 + ], + "type": "table", + "html": "
CelebAEditValTEdBenchMagicBrushDreamBooth
Dataset TypesFacial AttributeGeneral ObjectObject CentricLocal Region EditingPersonalized Generation
Editing Models[13, 14, 17, 23][2, 5, 8, 9, 12][2, 5, 8, 9, 12][2, 5, 8, 9, 12][16, 18, 27]
Dataset Size50648100105350
", + "image_path": "31291b9f4ad1862860f9c6550cba4452bd783225b822f87ddf07be6852b7c8cc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 59, + 178, + 293, + 220 + ], + "blocks": [ + { + "bbox": [ + 113, + 160, + 237, + 170 + ], + "lines": [ + { + "bbox": [ + 113, + 160, + 237, + 170 + ], + "spans": [ + { + "bbox": [ + 113, + 160, + 237, + 170 + ], + "type": "text", + "content": "Table 2. User Study Statistics." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 178, + 293, + 220 + ], + "lines": [ + { + "bbox": [ + 59, + 178, + 293, + 220 + ], + "spans": [ + { + "bbox": [ + 59, + 178, + 293, + 220 + ], + "type": "table", + "html": "
CelebAEditValDreamBooth
Survey questions393537
Participants453030
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MetricsPresv.Modif.CelebAEditValDreamBooth
L2✓✗0.6530.3480.464
LPIPS✓✗0.4650.3600.286
DINO✓✗0.5740.3480.286
SC✓✗0.7520.7640.571
CLIP-I✓✗0.8480.7300.857
CLIP-T✗✓0.4910.3990.321
CLIPdir▲✓0.6730.6970.357
AugCLIP✓✓0.8830.8310.857
", + "image_path": "e8d6f4faf50f0e7b17136c010d583f6cb3753b4a15e5a2e1ea55103b9c4d1025.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 371, + 295, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 295, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 295, + 419 + ], + "type": "text", + "content": "preservation-centric (L2, LPIPS, DINO, SC, CLIP-I) and human judgment is expected because these benchmarks do not significantly deviate from the source image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 426, + 249, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 249, + 440 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 249, + 440 + ], + "type": "text", + "content": "5.2. Ground Truth Editing Selection Test" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 444, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 444, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 54, + 444, + 295, + 635 + ], + "type": "text", + "content": "Creating Triplet Dataset We generate a triplet of images, each representing a well-edited, excessively preserved, and excessively modified image. Among the triplet of images, the well-edited image is provided in the benchmark datasets, TEdBench, and MagicBrush. Excessively modified images are generated with text-to-image models [25] instructed by the target text, completely ignoring the source image. Excessively preserved images are generated by applying a negligible transformation to the given source image, ignoring the target text. Then, we measure the accuracy where each metric correctly assigns the highest score to the well-edited image as AccBoth. Yielding high accuracy in this test means that the evaluation metric can balance both preservation and modification aspects, without being biased to either side." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 650, + 296, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 650, + 296, + 709 + ], + "spans": [ + { + "bbox": [ + 55, + 650, + 296, + 709 + ], + "type": "text", + "content": "AugCLIP is superior in balancing preservation and modification. In Tab. 4, AugCLIP is on par with or even better than baseline metrics over all datasets. This emphasizes the balanced evaluation criteria of AugCLIP, which previous metrics fail to abide by. Seg-" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 329, + 194, + 542, + 306 + ], + "blocks": [ + { + "bbox": [ + 313, + 160, + 553, + 186 + ], + "lines": [ + { + "bbox": [ + 313, + 160, + 553, + 186 + ], + "spans": [ + { + "bbox": [ + 313, + 160, + 553, + 186 + ], + "type": "text", + "content": "Table 4. Ground Truth Selection Test. Accuracy, Accboth " + }, + { + "bbox": [ + 313, + 160, + 553, + 186 + ], + "type": "inline_equation", + "content": "(\\uparrow)" + }, + { + "bbox": [ + 313, + 160, + 553, + 186 + ], + "type": "text", + "content": " of assigning higher scores to ground truth images over excessively preserved and modified images." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 194, + 542, + 306 + ], + "lines": [ + { + "bbox": [ + 329, + 194, + 542, + 306 + ], + "spans": [ + { + "bbox": [ + 329, + 194, + 542, + 306 + ], + "type": "table", + "html": "
MetricsPresv. Modif.TEdBenchMagicBrush
L2✓X0.3100.002
LPIPS✓X0.0900.000
DINO✓X0.2800.008
SC✓X0.4200.936
CLIP-I✓X0.2810.810
CLIP-TX✓0.3120.260
CLIPdir▲✓0.3500.601
AugCLIP✓✓0.5700.889
", + "image_path": "a1f74016f717102516915243a2bd598462ac55cc7407e494e3a47476c6162464.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 324, + 553, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 553, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 553, + 350 + ], + "type": "text", + "content": "ment Consistency (SC) excels in MagicBrush since the dataset requires editing a small local area of the image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 360, + 383, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 383, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 383, + 373 + ], + "type": "text", + "content": "6. Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "text", + "content": "We use " + }, + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "inline_equation", + "content": "s_{2\\mathrm{AFC}}" + }, + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "text", + "content": " for CelebA, EditVal, and Dreambooth, and AccBoth for TEdBench and MagicBrush. We compare our metric, AugCLIP with " + }, + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 380, + 554, + 439 + ], + "type": "text", + "content": ", which is the only metric that considers both preservation and modification." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 453, + 555, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 621 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 621 + ], + "type": "text", + "content": "AugCLIP generalizes to diverse editing scenarios. Text-guided image editing encompasses a wide range of tasks such as style editing, object replacement, local editing, partial alteration, and personalized generation. AugCLIP excels in the highly complex scenarios of local editing as conducted with the MagicBrush dataset. Moreover, AugCLIP highly aligns with human judgment in the personalized generation case of DreamBooth, which has been underexplored by previous metrics. We report how well AugCLIP aligns with human judgment with various editing cases provided in the EditVal dataset. Across all eight scenarios, except for the texture modification task, AugCLIP outperforms " + }, + { + "bbox": [ + 313, + 453, + 555, + 621 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 453, + 555, + 621 + ], + "type": "text", + "content": " as shown in Tab. 5." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "content": "Augmenting " + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "content": " cannot provide reliable evaluation result. We demonstrate the impact of augmenting " + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "content": " with attributes, extracted in Sec. 4.1. Specifically, we replace the source and target text embeddings with the average of their respective attribute embeddings, " + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 635, + 556, + 708 + ], + "type": "text", + "content": ". As shown in Tab. 6," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "23480" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 95, + 294, + 169 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 295, + 87 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 295, + 87 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 295, + 87 + ], + "type": "text", + "content": "Table 5. Human Alignment Score " + }, + { + "bbox": [ + 56, + 70, + 295, + 87 + ], + "type": "inline_equation", + "content": "s_{2\\text{AFC}}" + }, + { + "bbox": [ + 56, + 70, + 295, + 87 + ], + "type": "text", + "content": " on Various Text-guided Image Editing Scenarios." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 95, + 294, + 169 + ], + "lines": [ + { + "bbox": [ + 57, + 95, + 294, + 169 + ], + "spans": [ + { + "bbox": [ + 57, + 95, + 294, + 169 + ], + "type": "table", + "html": "
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CelebAEditValDreamBoothTEDbenchMagicBrush
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", + "image_path": "ab1a3f68f0f6b543fd97f645549d1a27ba21bade7088525893c212ed2e737c44.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "text", + "content": "Weighting Strategy for Hyperplane We demonstrate the effectiveness of our weighting strategy, described in Eq. (6) in Tab. 7. Our weighting strategy enables AugCLIP to prioritize key features central to preservation and modification while estimating the representation of an ideally edited image, resulting in improvement in human alignment (" + }, + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "inline_equation", + "content": "s_{2\\mathrm{AFC}}" + }, + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "text", + "content": ") and balancing preservation and modification (" + }, + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{Acc}_{\\mathrm{Both}}" + }, + { + "bbox": [ + 55, + 399, + 295, + 496 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 56, + 522, + 294, + 559 + ], + "blocks": [ + { + "bbox": [ + 99, + 505, + 251, + 515 + ], + "lines": [ + { + "bbox": [ + 99, + 505, + 251, + 515 + ], + "spans": [ + { + "bbox": [ + 99, + 505, + 251, + 515 + ], + "type": "text", + "content": "Table 7. Effect of Weighting Strategy." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 522, + 294, + 559 + ], + "lines": [ + { + "bbox": [ + 56, + 522, + 294, + 559 + ], + "spans": [ + { + "bbox": [ + 56, + 522, + 294, + 559 + ], + "type": "table", + "html": "
CelebAEditValDreamBoothTEDBenchMagicBrush
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LengthNumberCelebAEditValDreamBoothTEDbenchMagicBrush
short100.8700.7190.8570.5400.889
short200.8290.8090.8210.5400.868
short300.8290.7640.7140.5700.863
long300.8430.6970.7500.5300.862
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", + "image_path": "ab9e05ff9f2fa8260a741e691bd436ee3f78904a0bb52026fba91425e7b3936b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 220, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 555, + 316 + ], + "type": "text", + "content": "Description Randomness Using GPT-4V for description extraction introduces slight randomness across different seeds. Tests with five seeds show low variance (0.0197) in human alignment score (" + }, + { + "bbox": [ + 313, + 220, + 555, + 316 + ], + "type": "inline_equation", + "content": "s_{2\\mathrm{AFC}}" + }, + { + "bbox": [ + 313, + 220, + 555, + 316 + ], + "type": "text", + "content": "), indicating that the description generation process does not affect the scoring. We also demonstrate in the Appendix that extracted attributes with different seeds do not vary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 316, + 554, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 554, + 363 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 554, + 363 + ], + "type": "text", + "content": "We provide analysis on the modification vector " + }, + { + "bbox": [ + 313, + 316, + 554, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 316, + 554, + 363 + ], + "type": "text", + "content": " and choice of classifier function, discussion on limitations, description prompting, and extensive qualitative results in the Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 373, + 481, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 373, + 481, + 387 + ], + "spans": [ + { + "bbox": [ + 314, + 373, + 481, + 387 + ], + "type": "text", + "content": "Limitations and Discussions" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 394, + 555, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 502 + ], + "type": "text", + "content": "Our method, AugCLIP, adds additional computation time compared to " + }, + { + "bbox": [ + 313, + 394, + 555, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP}_{\\mathrm{dir}}" + }, + { + "bbox": [ + 313, + 394, + 555, + 502 + ], + "type": "text", + "content": ". It requires extracting attributes via MLLM, and then fitting a hyperplane to distinguish source and target attributes. This process takes around 12.3 seconds for attribute generation and 0.15 seconds for score computation. We will provide extracted attributes for all benchmark datasets to reduce this overhead, facilitating the evaluation process for future usage." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 512, + 382, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 512, + 382, + 525 + ], + "spans": [ + { + "bbox": [ + 314, + 512, + 382, + 525 + ], + "type": "text", + "content": "Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "type": "text", + "content": "We present AugCLIP, a novel evaluation metric for text-guided image editing that balances source image preservation and target text modification. By leveraging a multi-modal language model to extract visual attributes and finding a separating hyperplane, AugCLIP estimates a representation of an ideal edited image that closely matches human preferences. Experiments on five benchmark datasets show that AugCLIP outperforms existing metrics, especially in challenging tasks, offering a more reliable tool for evaluating edits while preserving core attributes." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "23481" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 170, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 170, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 170, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "content": "This work was supported by the National Research Foundation of Korea (NRF) grants (RS-2023-00209060 A Study on Optimization and Network Interpretation Method for Large-Scale Machine Learning), Institute for Information & communications Technology Planning & Evaluation(IITP) grants (No.2022-0-00713 Meta-learning applicable to real-world problems, RS-2019-II190075 Artificial Intelligence Graduate School Program(KAIST)) funded by the Korea government(MSIT)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 221, + 122, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 221, + 122, + 234 + ], + "spans": [ + { + "bbox": [ + 56, + 221, + 122, + 234 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 241, + 296, + 699 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 62, + 241, + 296, + 307 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 241, + 296, + 307 + ], + "spans": [ + { + "bbox": [ + 62, + 241, + 296, + 307 + ], + "type": "text", + "content": "[1] Samyadeep Basu, Mehrdad Saberi, Shweta Bhardwaj, Atoosa Malemir Chegini, Daniela Massiceti, Maziar Sanjabi, Shell Xu Hu, and Soheil Feizi. 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While these methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. Thus, the training mechanism exhibits a key limitation wherein the visual embedding distribution in target domains can deviate from the visual embedding distribution in the pre-trained model, leading to misguided signals from class descriptions. This work introduces a fresh solution to reinforce these pseudo-labels and facilitate target-prompt learning, by exploiting the geometry of visual and text embeddings - an aspect that is overlooked by existing methods. We first propose to directly leverage the reference predictions (from source prompts) based on the relationship between source and target visual embeddings. We later show that there is a strong clustering behavior observed between visual and text embeddings in pre-trained multi-modal models. Building on optimal transport theory, we transform this insight into a novel strategy to enforce the clustering property in text embeddings, further enhancing the alignment in the target domain. Our experiments and ablation studies validate the effectiveness of the proposed approach, demonstrating superior performance and improved quality of target prompts in terms of representation.", + "bbox": [ + 91, + 316, + 483, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 784, + 220, + 800 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Significant advancements of deep learning have consistently enhanced performance on various tasks, albeit primarily within the confines of training data distributions. Therefore, deep models notoriously fail to maintain their performance when applied to new, unseen domains [19, 23, 36, 52]. Unsupervised domain adaptation (UDA) offers a promising solu", + "bbox": [ + 89, + 809, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion by utilizing labeled data from a source domain alongside unlabeled data from a target domain, thus circumventing the costly and labor-intensive process of annotating new domain data. In recent years, many domain adaptation methods have been proposed, typically focusing on learning invariant features across domains, as motivated by the theoretical analysis by Ben-David et al. [1, 2]. These methods generally (i) minimize the discrepancy between feature representations across domains [24, 25, 31, 40] or (ii) adversarially learn indistinguishable representations to fool a domain discriminator [10, 11, 26, 44]. However, focusing on aligning representations can inadvertently compromise model performance by diminishing discriminative features [12, 41].", + "bbox": [ + 511, + 287, + 906, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent developments have demonstrated the potential of leveraging pre-trained models such as CLIP [34] for the UDA problem, significantly bridging domain gaps and enhancing generalization. These benefits arise from the rich semantic and robust visual representations gained through extensive pre-training across diverse image-text datasets. Building on this approach, DAPL [12] innovatively introduces domain-specific and domain-agnostic prompts, enabling the efficient adaptation of pre-trained vision-language models without the need to fine-tune the entire model. Extending this training procedure to the multi-source domain adaptation scenario, MPA [4] employs an auto-encoder to align training and target prompts while PGA [32] frames the learning from a multi-domain problem as a multi-objective optimization problem and align per-objective gradients to promote consensus across objectives.", + "bbox": [ + 511, + 484, + 908, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contribution. While prior vision-language UDA methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from the use of base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. However, they do have limitations. First, the visual embedding distribution in the target domain may differ from the textual embedding distribution in the pre-trained models, resulting in misaligned class descriptions when relying on the \"over-generalized\" nature of pre-trained models (such as CLIP zero-shot predictions) without incorporating domain-", + "bbox": [ + 511, + 750, + 910, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19974", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "specific context. Secondly, previous methods primarily focus on aligning source-target prompts within the textual embedding space to refine target prompts, placing less emphasis on the representation perspective, specifically the alignment between visual and text embeddings. Moreover, we observe that source-target prompt alignment has a limited impact on target prompts (Table 1, Simple Alignment - Eq. (3): Even after alignment, the target prompt performs poorly. Further analysis is provided in Section 6.3.)", + "bbox": [ + 89, + 90, + 483, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we leverage reference predictions (from source prompts) based on the relationship between source and target visual embeddings. This helps enhance pseudo-labels and facilitates target-prompt learning. Additionally, drawing inspiration from the strong clustering behavior observed between visual and textual embeddings in pre-trained multi-modal models, we enforce clustering properties in text embeddings by minimizing the Wasserstein distance [47] between the distribution of text prompts and the distribution of visual embeddings in the target domains. Our experiments and ablation studies validate the effectiveness of this approach, showing superior performance and improved quality of target prompts in terms of representation.", + "bbox": [ + 89, + 227, + 483, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 89, + 436, + 227, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain Adaptation (DA) addresses the challenge of transferring knowledge learned from a source domain to a target domain, where both domains share the same label space but have different data distributions [2]. Deep domain adaptation has demonstrated impressive performance across various tasks through different approaches [55, 56]. The fundamental concept is to minimize the distributional gap between source and target domains in a shared feature space by reducing distribution divergence, commonly measured through Jensen-Shannon divergence [10, 39, 43], maximum mean discrepancy [14, 24], or Wasserstein distance [20, 38].", + "bbox": [ + 89, + 462, + 483, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation (UDA) presents additional challenges as the target domain is unlabeled. Early UDA methods focused on learning domain-invariant features by minimizing domain discrepancy [24, 25, 40]. For instance, DAN [24] aligns domains by minimizing maximum mean discrepancy on task-specific layers, while CORAL [40] aligns second-order statistics using linear projection. Inspired by GANs [13], adversarial learning emerged as another prominent approach. Methods like DANN [10] and CDAN [27] employ domain discriminators to distinguish source from target samples while training feature extractors to generate domain-invariant features. However, recent work has highlighted that while domain alignment can be successful, it may compromise class discrimination due to distorted semantic features [3, 41]. Several methods have attempted to address this challenge through approaches like entropy-based regularization [21] and batch nuclear-norm maximization [6].", + "bbox": [ + 89, + 628, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt Learning for Domain Adaptation. Prompt learning, initially introduced in NLP [30], has recently been adapted for vision-language models [18, 34]. Rather than fine-tuning entire networks, prompt learning enables efficient adaptation to downstream tasks by tuning prompt parameters. Such notable models as CLIP [34] have demonstrated strong visual representations through pre-training on large-scale image-text pairs. In the context of UDA, prompt learning offers a novel direction to address domain adaptation challenges [9, 33, 53]. DAPL [12] leverages CLIP's generalization capabilities to learn both domain-agnostic and domain-specific prompts, effectively balancing domain alignment and classification performance through contrastive learning. Building on this idea, MPA [4] extends prompt learning to multi-source UDA scenarios. MPA first learns from multiple source domains, then adapts the prompt learning strategy to each source-target domain pair. Prompts are aligned using a denoising auto-encoder with Euclidean distance. More recently, PGA [32] frames the multi-domain objective (including the target domain) as a multi-objective optimization problem, aligning per-objective gradients to promote consensus across objectives. PGA further incorporates gradient norm penalization to enhance prompt generalization.", + "bbox": [ + 511, + 90, + 906, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 513, + 463, + 640, + 479 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Unsupervised Domain Adaptation", + "text_level": 1, + "bbox": [ + 511, + 491, + 812, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a set of $N \\geq 1$ source domains $\\{D_{S_i}\\}_{i=1}^N$ each of which is a collection of data-label pairs of domain $i$ -th, i.e. $D_{S_i} = \\{\\pmb{x}_j, y_j\\}_{j=1}^{N_{S_i}}$ , $y_j \\in [K] := \\{1, \\dots, K\\}$ , and one unlabeled target domain $D_T = \\{\\pmb{x}_j\\}_{j=1}^{N_T}$ , where $N_{S_i}$ and $N_T$ are respectively the number of data points in source domain $D_{S_i}$ and target domain $D_T$ , the goal is to learn a model that can perform well on the unlabeled target domain. In this paper, we focus on classification problems and denote $K$ as the number of classes.", + "bbox": [ + 511, + 516, + 908, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.2. CLIP-based Zero-Shot Classification.", + "text_level": 1, + "bbox": [ + 511, + 678, + 834, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CLIP [34] is a vision-language model that consists of a visual encoder $f_{v}$ and a textual encoder $f_{t}$ , which are trained to align the visual embedding $f_{v}(\\boldsymbol{x})$ of an image $\\boldsymbol{x}$ with the textual embedding $f_{t}(y)$ of the corresponding label $y$ . The textual representation is derived from a manually crafted prompt $\\boldsymbol{p}_{k}$ in the form \"A photo of a $[\\mathrm{CLASS}_k]$ \", where $[\\mathrm{CLASS}_k]$ is the $k$ -th class's name.", + "bbox": [ + 511, + 704, + 906, + 810 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In zero-shot inference, $K$ class names are forwarded through the text encoder $f_{t}$ and one with the highest similarity with the visual embedding $f_{v}(x)$ is the predicted class:", + "bbox": [ + 511, + 813, + 908, + 859 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\operatorname {a r g m a x} _ {k} P (y | \\boldsymbol {x}, \\boldsymbol {p} _ {k}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 885, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19975", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where we have defined", + "bbox": [ + 89, + 90, + 243, + 104 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP (y \\mid \\boldsymbol {x}, \\boldsymbol {p} _ {k}) = \\frac {\\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k}\\right) \\right\\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k ^ {\\prime}}\\right) \\right\\rangle / \\gamma\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 114, + 483, + 152 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\langle ., \\cdot \\rangle$ measures cosine similarity and $\\gamma$ is the temperature.", + "bbox": [ + 89, + 162, + 467, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Domain Adaptation via Prompt Learning", + "text_level": 1, + "bbox": [ + 89, + 186, + 444, + 204 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt Design. A common assumption in domain adaptation literature is that each domain can be represented by domain-specific features - which are found/presented only in this particular domain and domain-invariant features - which are shared with others [4, 32].", + "bbox": [ + 89, + 210, + 483, + 285 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reflect this, prompt-learning-based approaches as [4, 32] utilize two sets of prompts for each domain $D_{S_i}$ : domain-invariant prompt $\\pmb{P}_{sh}$ shared among all domains and domain-specific prompt $\\pmb{P}_{S_i}$ specific to the domain $D_{S_i}$ . Similarly, the target domain $D_T$ will be represented by $\\pmb{P}_{sh}$ and $\\pmb{P}_T$ prompts. More specifically, following [4], we do not just use single but multiple domain-invariant prompts $\\{\\pmb{P}_{sh}^k\\}_{k=1}^K$ , where each $\\pmb{P}_{sh}^k = [\\pmb{v}_1^k | \\pmb{v}_2^k| \\dots | \\pmb{v}_{M_1}^k]$ is a shared prompt among all domains and specific to class $k$ -th. For domain-specific prompts $\\pmb{P}_{S_i}$ and $\\pmb{P}_T$ , which are not shared among domains, are represented by $M_2$ tokens, i.e., $\\pmb{P}_{S_i} = [\\pmb{u}_1^{S_i} | \\pmb{u}_2^{S_i} | \\dots | \\pmb{u}_{M_2}^{S_i}]$ , $\\pmb{P}_T = [\\pmb{u}_1^T | \\pmb{u}_2^T | \\dots | \\pmb{u}_{M_2}^T]$ . Based on this, a prompt $p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_{S_i}][\\mathrm{CLASS}_k]$ is to represent the predictive distribution of a sample of source domain $D_{S_i}$ belong to class $k$ , and similarly $p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]$ for that of a target sample.", + "bbox": [ + 89, + 286, + 483, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "UDA via Prompt Learning with CLIP-Pseudo-Label. To transfer knowledge from source domains to the target domain, [4] proposed to fine-tune these prompts $P_{sh}$ , $P_{S_i}$ , $P_T$ , simultaneously, where $P_{sh}$ captures the shared predictive features among domains while the prompts $P_{S_i}$ , $P_T$ capture unique characteristics of each domain, by optimizing the objective:", + "bbox": [ + 89, + 550, + 483, + 656 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) = \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) + \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 667, + 483, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where objectives for source domains are defined as:", + "bbox": [ + 89, + 720, + 431, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\operatorname {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}), \\text {a n d} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 747, + 447, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For target domain, since labels are not available in the target domain, previous approaches, such as DAPL [12], MPA [4], and PGA [32], use pre-trained CLIP models to generate pseudo-labels $\\hat{y}$ as in Eq. (1) for the target domain to train target classifiers and learn both domain-invariant and", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "domain-specific prompts. Therefore, the objective for the target domain is as follows:", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\alpha} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\mathbb {I} _ {\\left(P \\left(y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}\\right) \\geq \\alpha\\right)} \\log P (y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 147, + 901, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The target objective is applied to target samples for which the zero-shot prediction confidence from CLIP exceeds a threshold $\\alpha$ . It is evident that when there is a significant covariate shift between the target domain and the dataset used to train the CLIP models, the accuracy of the pseudo-labels decreases markedly. For instance, as shown in Table 1, the accuracy of CLIP's zero-shot predictions varies significantly across domains in the OfficeHome dataset. This limitation forms one of the motivations for our approach, as presented in the following sections.", + "bbox": [ + 511, + 220, + 906, + 371 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/23ca6bf0aa0833bca9b7356d25291a10bb91af0acb91c8ccc9465f9427be5bf7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingInferenceArClPrRw
Training on source data only
Zero-shot fromCLIP [34]71.250.481.482.6
Source-combinedSource prompt72.255.982.683.3
Multi-sourceAverage prompt74.357.484.584.7
Ar prompt-56.080.082.1
Cl prompt70.4-81.180.4
Pr prompt70.255.0-84.1
Wr prompt73.955.584.5-
Supervised training on target domain only
Target prompt99.691.699.398.6
Traininging both source-target domains as Eq. (3)
Target prompt47.629.053.563.5
Source prompt74.357.284.384.8
", + "bbox": [ + 514, + 383, + 903, + 627 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Analyses of prompts performance on OfficeHome dataset. Source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications.", + "bbox": [ + 511, + 638, + 906, + 693 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Motivations", + "text_level": 1, + "bbox": [ + 513, + 724, + 637, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Limitations of existing pseudo-label guidance. As described above, we design shared or domain-invariant prompts $P_{sh}$ to capture embeddings that are consistent across both source and target domains, while we use domain-specific prompts $P_{S_i}$ to capture unique characteristics of each source domain. The domain-invariant prompts $P_{sh}$ enable learning of shared knowledge across source domains, which can then be transferred to the target domain. Additionally, to train both domain-invariant prompts $P_{sh}$ and target-specific prompts $P_T$ with a focus on the target domain, most recent", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19976", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dfd3854966f17cdbaa4a795334c298c6ce86b749fa20c8d445214832d439d84a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 161, + 90, + 194, + 133 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pretrained Visual-embedding Distribution", + "bbox": [ + 199, + 95, + 413, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Domain Visual-embedding Distribution", + "bbox": [ + 200, + 109, + 401, + 122 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Refine Target Prompt Based on Pseudo-Label", + "bbox": [ + 199, + 125, + 431, + 137 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/959a13ca01eca6f45dd1539db64b5f48fdbc72e99557f0d564dce37e25dc4e36.jpg", + "image_caption": [ + "(a) Target prompt refinement.", + "(Same class from different domains)", + "Figure 1. (a) Target-domain prompt refinement. Pre-trained models are trained on large-scale datasets, which are assumed to fully or partially cover the data distribution of downstream tasks. For example, \"dog with style domain $S_{1,\\dots,3,T}$ \" can be viewed as subdomains of \"dog\". However, the visual embedding distribution in training may shift from that of the pretraining distribution, causing class descriptions without domain-specific context to become misaligned. This shift necessitates alignment using domain-specific contexts. While the source domain can leverage labeled data to refine its domain-specific context, the target domain lacks this advantage. A common approach to address this limitation is to incorporate domain-specific contexts and leverage zero-shot predictions from the CLIP model to guide alignment between domain-specific contexts and visual-representation in the target domain. (b) Effect of incorrect pseudo-label. Behavior of prompt learning with incorrect pseudo-labels in a supervised manner on the target domain. The flat regions in gray and orange represent areas in the embedding space corresponding to different classes, each centered on its optimal domain-specific prompt embedding (with class \"dog\" in orange and other classes in blue). Red points indicate samples from class \"dog\" with correct pseudo-labels, while black points represent samples from class \"dog\" that have been incorrectly pseudo-labeled. Additionally, some samples from regions belonging to other classes (gray areas) are mislabeled as class \"dog\", shown as black points with red borders. The text embeddings learned from these pseudo-labels fail to align well with the true target embeddings; instead, they form a cluster around a single point—the centroid of all samples labeled as class \"dog\" (both correctly and incorrectly labeled)—remaining distant from the actual target embeddings." + ], + "image_footnote": [], + "bbox": [ + 135, + 141, + 485, + 353 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ed933587a7fa1f08db98d7f92d9285b0552291e4f8302fb5f9fe234d151f7733.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 90, + 540, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Class description with based Prompts (A photo of a dog)", + "bbox": [ + 545, + 93, + 841, + 106 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/188ba586e08ec0d4354ef4c273aebe640a70b95fc14f4577f205b9469d838ef2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 107, + 540, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learnable Source-domain Prompts", + "bbox": [ + 545, + 108, + 720, + 122 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7006a8d06a9c0eb29348b28e0a09d386233c04316ff5b69c7107ba21138ea4df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 123, + 540, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learnable Target-domain Prompt", + "bbox": [ + 545, + 125, + 715, + 137 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/87d0cf5e9349f6128d26287a877a6604ec9a03597e23c6ff9fbd2b35ce09bf78.jpg", + "image_caption": [ + "(b) Effect of wrong Pseudo-label.", + "" + ], + "image_footnote": [], + "bbox": [ + 516, + 142, + 862, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "state-of-the-art approaches [12, 32] leverage pseudo-labels obtained through zero-shot inference using CLIP models. However, we argue that generating reliable and accurate pseudo-labels can be challenging when relying on zero-shot predictions from CLIP models, particularly if there is a significant covariate shift between the target domain and the dataset on which the CLIP models were trained. Furthermore, pseudo-labels are crucial for guiding the target text embeddings $\\tau_T^k$ for each class $k$ by aligning them with the visual embeddings from the corresponding target class. This raises the question: How can we enhance these critical pseudo-labels to improve the target target prompt?", + "bbox": [ + 88, + 613, + 485, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Enhancing pseudo-labels using source prompts. When training the source and target prompt, we use domain-invariant prompts $P_{sh}$ shared across both source and target domains to capture the domain-invariant embeddings common to data in both domains. As a result, the source", + "bbox": [ + 89, + 825, + 483, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "prompts can encapsulate domain-invariant embeddings of the target data. Additionally, the source and target data share certain common embeddings, making it reasonable to utilize source prompts to generate pseudo-labels for the target domain. To illustrate the advantage of using aggregated source prompts over standalone CLIP models in generating more accurate pseudo-labels, we conduct experiments on the Office-Home dataset. Table 1 (Training on source data only setting) presents the accuracies of the average aggregated source prompts (multi-source) and single source prompt (source combined) on the target domain, where only source prompts are used for predictions. The results indicate that aggregated source prompts produce more accurate pseudo-labels, hence further improving predictions. This observation aligns with our motivation and supports the proposed approach. Additionally, the transferability of different source domains to the target domain varies based on their similarity (Table 1: Training on source data only: Multi-source). This observation", + "bbox": [ + 511, + 613, + 908, + 886 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19977", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "motivates the design of a distance-aware transfer strategy to combine references from source prompts and base prompt for generating more accurate pseudo-labels, as detailed in Section 5.2.", + "bbox": [ + 89, + 90, + 483, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, we observe that while more accurate pseudo-labels help guide the text embeddings more effectively toward their class clusters, they still introduce inaccuracies. These inaccuracies cause the text embeddings to skew toward regions of correct pseudo-labels within their clusters, as illustrated in Figure 1, ultimately compromising performance on entire clusters. Thus, it is essential to introduce an additional component to correct this bias and maintain consistent predictions across clusters.", + "bbox": [ + 89, + 152, + 485, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Clustering preservation prediction. According to the clustering assumption, data tend to be organized into clusters. To verify this assumption for visual embeddings from CLIP models, we assume we have labels for the target domain and train a target prompt using only class-specific target prompts (i.e., $[P_T^k][CLASS_k]$ ) on the target domain. This setup implies that for each class $k$ , we rely on a single text embedding, $\\tau_T^k$ , to represent its visual embeddings. The high accuracies obtained, as shown in Table 1 (supervised training on target domain only), demonstrate that the visual embeddings for each class using CLIP models tend to form a single cluster in the embedding space.", + "bbox": [ + 89, + 311, + 483, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although using source prompts to generate pseudo-label guidance for the target prompt outperforms zero-shot predictions from CLIP models, incorrect pseudo-labels or the absence of pseudo-label guidance may still occur for lower-confidence predictions. Consequently, in the cluster for class $k$ in the target domain, there are visual embeddings with correct pseudo-labels and those with incorrect or missing pseudo-labels (shown in black in Figure 1b). As a result, the text embedding $\\tau_T^k$ for this class acts as a prototype or centroid for the red visual embeddings but may fail to represent the entire cluster for class $k$ . This limitation could lead to incorrect predictions for the black visual embeddings and potential confusion with visual embeddings from other classes. To obtain text embeddings $\\tau_T^k$ that effectively represent the entire cluster for each class $k$ and ensure clustering-preserving predictions, we adopt the clustering viewpoint of optimal transport [28, 48]. Specifically, our objective is to minimize the optimal transport (Wasserstein-WS) distance between the distribution of visual embeddings in the target domain and the distribution of the text embeddings $\\tau_T^k$ . As demonstrated in Lemma 1, the text embeddings $\\tau_T^k$ act as prototypes or centroids of the clusters, leading to an alignment correction for the text embeddings, as shown in Figure 2. Moreover, minimizing the WS distance adjusts the text embeddings $\\tau_T^k$ to serve as accurate cluster centroids, while the pseudo-label guidance aids in aligning these embeddings with their correct class- $k$ clusters.", + "bbox": [ + 89, + 493, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Proposed Method", + "text_level": 1, + "bbox": [ + 513, + 89, + 687, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Notation: Since our method focuses on analyzing the representations; for simplicity, we denote $\\pmb{\\tau}_{S_i}^k$ as the text embedding of the source domain-specific prompt, given by $\\pmb{\\tau}_{S_i}^k = f_t\\left([P_{sh}^k][P_{S_i}][\\mathrm{CLASS}_k]\\right)$ . Similarly, $\\pmb{\\tau}_T^k = f_t\\left([P_{sh}^k][P_T][\\mathrm{CLASS}_k]\\right)$ and $\\pmb{\\tau}_{base}^k = f_t\\left(\"A photo of a [CLASS_k]\"\\right)$ as the text embeddings of the target prompt and base prompt, respectively.", + "bbox": [ + 511, + 114, + 908, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Prompt Learning with Source Domains", + "text_level": 1, + "bbox": [ + 511, + 248, + 852, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Because labels are available in all source domains, we apply the cross-entropy loss to fine-tune these associated prompts $P_{sh}, P_{Si}$ with the source-domain objective loss:", + "bbox": [ + 511, + 270, + 906, + 316 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 329, + 906, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we have defined", + "bbox": [ + 511, + 378, + 666, + 391 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\mathrm {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}) \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 405, + 906, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Prompt Learning with Target Domain", + "text_level": 1, + "bbox": [ + 511, + 483, + 841, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pseudo-label Enhancement. Building on our motivation, we enhance the quality of pseudo-labels from zero-shot predictions on the target domain by incorporating predictions from the source domains. Specifically, we calculate the weighted average cosine distance from the visual embedding $\\mathbf{z} = f_v(\\mathbf{x})$ to the text embeddings of each class across all source domains. We then average this result with the text embedding from the base prompt as follows:", + "bbox": [ + 511, + 505, + 908, + 627 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} [ k ] = \\frac {\\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k} ((x)) \\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k ^ {\\prime}} (x) \\rangle / \\gamma\\right)} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 638, + 906, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we have defined", + "bbox": [ + 532, + 685, + 687, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\tau} _ {a v e} ^ {k} (x) = \\frac {1}{2} \\boldsymbol {\\tau} _ {b a s e} ^ {k} + \\frac {w _ {k , i} (x)}{2} \\sum_ {i = 1} ^ {N} \\boldsymbol {\\tau} _ {S _ {i}} ^ {k} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 713, + 906, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $w_{i,k}$ is the important weight for each domain-class.", + "bbox": [ + 532, + 762, + 900, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As discussed in Section 4, to compute $w_{k,i}(x)$ , we use the $l_2$ distance between the visual embedding $z^{pre}$ (the unnormalized visual embedding of $x$ , where $z = \\frac{z^{pre}}{\\|z^{pre}\\|_2}$ ) and the centroid of class $k$ in domain $i$ . Let $C^i = \\{c_k^i\\}_{k=1}^K$ represent the set of class centroids for the $i$ -th domain i.e., $c_k^i = \\frac{1}{\\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)}} \\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)} z_j^{pre,i}$ . The weight for class $k$ is then calculated by applying the softmax function:", + "bbox": [ + 511, + 777, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19978", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i, k} (z) = \\frac {\\exp \\left(\\left\\| z _ {p r e} - c _ {k} ^ {i} \\right\\| _ {2}\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(\\left\\| z - c _ {k} ^ {i ^ {\\prime}} \\right\\| _ {2}\\right)} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 99, + 483, + 142 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that the weights $w_{i,k}(z)$ are applied to compute the combined prompts $\\tau_{\\mathrm{ave}}^k$ , rather than being applied directly to the outputs of the softmax (i.e., the predictions from individual prompts). This design preserves semantic similarity, as the magnitude of cosine similarity between the visual embedding and the text embedding of each individual prompt is taken into account in the final pseudo-label. Meanwhile, the weights $w_{k,i}(x)$ represent the spatial relationship between the visual embedding and the text embedding.", + "bbox": [ + 89, + 147, + 483, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training target prompts with Pseudo-label Guidance. Given data sample $x_{j}$ and its corresponding enhanced pseudo-label $\\hat{y}_{j}$ , we minimize the following objective function to train the target prompts:", + "bbox": [ + 89, + 301, + 485, + 362 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\tau} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\sum_ {k = 1} ^ {K} \\hat {y} _ {j} [ k ] \\log P (y = k | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 375, + 482, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Clustering Refined by Optimal Transport", + "text_level": 1, + "bbox": [ + 89, + 446, + 444, + 463 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We propose minimizing the Wasserstein distance between the target prompts' text embeddings and the visual embeddings from the target domain. Specifically, denote $\\mathcal{T} = \\{\\pmb{\\tau}_T^k\\}_{k=1}^K$ where $\\pmb{\\tau}_T^k$ represents the text embeddings of the context prompt $[\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]$ for class $k$ . Let $\\mathbb{P}_{\\tau,\\pi} = \\sum_{k=1}^{K}\\pi_k\\delta_{\\tau_T^k}$ be the discrete distribution over the set of text embeddings $\\mathcal{T}$ for the target domain, where the category probabilities $\\pi \\in \\Delta_K = \\{\\alpha \\geq 0 : \\| \\alpha \\|_1 = 1\\}$ lie in the $K$ -simplex. Additionally, let $\\mathbb{P}^T = \\frac{1}{N_T}\\sum_{j=1}^{N_T}\\delta_{z_j}$", + "bbox": [ + 89, + 469, + 483, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "represent the visual embedding distribution of the target domain, where $\\delta$ is the Dirac delta function and $z = f_{v}(\\pmb{x})$ for the target image $\\pmb{x}$ . The clustering assumption is then enforced by the following objective:", + "bbox": [ + 89, + 611, + 483, + 669 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {W}} = \\mathcal {W} _ {d _ {z}} \\left(\\mathbb {P} _ {\\tau , \\pi}, \\mathbb {P} ^ {T}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 680, + 482, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $d_{z}$ represents a metric function. We use the cosine distance $d_{z}(a,b) = 1 - \\langle a,b\\rangle$ since the visual embeddings and text embeddings already lie in the unit hypersphere. The following lemma demonstrates the behavior of $\\pi$ and explains how the Wasserstein term helps target prompts enforce clustering properties.", + "bbox": [ + 89, + 709, + 485, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lemma 1 Let $\\mathcal{T}^{*} = \\left\\{\\pmb{\\tau}_{T}^{k,*}\\right\\}_{k=1}^{K}$ be the optimal solution of the OP in Eq. (10), then $\\mathcal{T}^{*}$ is also the optimal solution of the following OP:", + "bbox": [ + 89, + 808, + 485, + 864 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathcal {T}, \\pi} \\min _ {\\sigma \\in \\Sigma_ {\\pi}} \\mathbb {E} _ {z \\sim \\mathbb {P} ^ {T}} \\left[ d _ {z} \\left(z, \\tau_ {T} ^ {\\sigma (z)}\\right) \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 875, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\Sigma_{\\pi}$ is the set of assignment functions $\\sigma : \\mathcal{Z} \\to \\{1, \\dots, K\\}$ such that the cardinalities $|\\sigma^{-1}(k)|, k = 1, \\dots, K$ are proportional to $\\pi_k, k = 1, \\dots, K$ . Moreover, given the set of text embeddings $\\mathcal{T}$ , the optimal $\\sigma$ of the inner minimization is the nearest assignment: $\\sigma^{-1}(k) = \\{z \\mid k = \\operatorname{argmin}_m d_z(z, \\tau_T^m)\\}$ is set of visual embeddings which are quantized to $k^{th}$ text embedding $\\tau_T^k$ .", + "bbox": [ + 511, + 90, + 905, + 198 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lemma 1 indicates the aim of minimizing the Wasserstein term $\\mathcal{W}_{d_z}\\left(\\mathbb{P}_{\\tau,\\pi},\\mathbb{P}^T\\right)$ , by adjusting the text embeddings in $\\mathcal{T}$ to become the clustering centroids of the visual embeddings in the target domain, thereby minimizing the distortion between the text embeddings and target visual embeddings. Specifically, we can interpret the optimization problem in (11) as finding the optimal clustering assignment $\\sigma$ , which maps each target example $z$ to the text embedding $\\tau_T^{\\sigma(z)}$ to minimize distortion. Moreover, given the text embeddings in $\\mathcal{T}$ , the inner minimization in (11) specifies the nearest assignment by assigning each visual embedding $z$ to the closest text embedding. Furthermore, in the optimal solution, the optimal assignment $\\sigma^*$ , mapping target visual embeddings to clustering centroids (i.e., text embeddings), has a valuable property: the cardinalities $\\left|\\left(\\sigma^*\\right)^{-1}(k)\\right|, k = 1,\\dots,K$ are proportional to $\\pi_k, k = 1,\\dots,K$ . We set $\\pi_k = \\frac{1}{K}$ for $k = 1,\\dots,K$ , aiming to learn balanced clusters.", + "bbox": [ + 511, + 204, + 906, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is important to note that the Wasserstein distance alone can shift the text embeddings toward the cluster centroids of the visual embedding distribution in the target domain. However, this may inadvertently cause the text embedding for one class (e.g., class 1) to shift to the centroid of a different class's cluster (e.g., class 2). To prevent this, pseudo-label guidance is necessary to ensure that each text embedding moves toward its correct cluster.", + "bbox": [ + 511, + 463, + 908, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Final Objective. We combine the objective functions for source prompts, target prompts, and cluster enforcement, and perform joint training as follows:", + "bbox": [ + 511, + 601, + 906, + 646 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) := \\mathcal {L} _ {S} + \\lambda_ {T} \\mathcal {L} _ {T} + \\lambda_ {\\mathcal {W}} \\mathcal {L} _ {\\mathcal {W}} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 656, + 906, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_T$ and $\\lambda_{\\mathcal{W}}$ are hyper-parameters. Here we note that in our experiments, we simply set $\\lambda_T = \\lambda_{\\mathcal{W}} = 0.5$ .", + "bbox": [ + 511, + 681, + 906, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 511, + 724, + 645, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the efficacy of our proposed method on different UDA benchmarks, following the same protocol of recent prompt-based UDA studies [4, 12, 32]. Their detailed descriptions are available in Supplementary.", + "bbox": [ + 511, + 750, + 906, + 810 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Experimental setup", + "text_level": 1, + "bbox": [ + 511, + 818, + 700, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Following [32], we conduct experiments in two standard settings: a source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications.", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19979", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference. During inference, unlike previous baselines (MPA [4], DAPL [12], PGA [32]) that utilize both source and target domain prompts for predictions, we rely solely on the target prompt to evaluate whether we have effectively learned a meaningful textual description for the target domain. Further results, discussed in Section 6.3, reveal that previous methods fail to learn high-quality target prompts, as their performance heavily depends on the quality of source prompts. This dependency is obscured by the combined use of source and target prompts during prediction.", + "bbox": [ + 89, + 90, + 480, + 242 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Experimental results", + "text_level": 1, + "bbox": [ + 89, + 251, + 287, + 267 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the following results, our method is referred to as \"Clustering Reinforcement Prompt Learning\" (CRPL).", + "bbox": [ + 89, + 273, + 483, + 305 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/468f4715e6542112cd4360fa7c8cadb84dab3737e027337422b3f37f0cec9295.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ImageCLEFOffice-HomeAvg
→ C→ I→ PAvg→ Ar→ Cl→ Pr→ Rw
Zero-Shot
CLIP [34]87.988.278.788.171.250.481.482.671.4
Source Combined
DAN [10]93.392.277.687.768.559.479.082.572.4
DANN [11]93.791.877.987.868.459.179.582.772.4
D-CORAL [40]93.691.777.187.568.158.679.582.772.2
DAPL [12]96.089.276.087.172.851.982.683.772.8
Simple Prompt [4]93.690.680.988.470.752.982.983.972.4
PGA [32]94.292.178.588.274.153.984.485.674.5
CRPL (Ours)94.894.581.790.376.660.486.586.877.6
Multi-Source
DCTN [51]95.790.375.087.0N.A.N.A.N.A.N.A.N.A.
MDDA [57]N.A.N.A.N.A.N.A.66.762.379.579.671.0
SIMplDA [45]93.391.077.587.370.856.380.281.572.2
MFSAN [58]95.493.679.189.472.162.080.381.874.1
MPA [4]97.296.280.491.374.854.986.285.775.4
MPGA [32]93.895.782.890.874.856.085.286.075.5
M-CRPL (Ours)96.296.082.391.576.863.587.687.578.9
", + "bbox": [ + 89, + 316, + 486, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 presents the results for the ImageCLEF and OfficeHome datasets. Under the source-combined scenario, our method significantly outperforms all other baseline methods on both datasets and target domain settings. For instance, CRPL surpasses the second-best source combined method by $1.9\\%$ in average accuracy for ImageCLEF and $3.1\\%$ in average accuracy for Office-Home. In the multi-source setting, our method delivers the highest average performance across dataset, notably outperforming MPGAs, the state-of-the-art (SOTA) prompt-based method for multi-source UDA, by a substantial margin of $3.4\\%$ on Office-Home.", + "bbox": [ + 89, + 551, + 483, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On DomainNet, as shown in Table 3, we achieve superior average accuracy under both source-combined and multi-source settings, boosting the performance of pretrained CLIP by $\\approx 6\\%$ . We also consistently outperform other baselines on the ('Clp', 'Inf', and 'Pnt') domains across all settings, while showing competitive performance in the other three domains. This is because domains such as ('Clp', 'Inf', and 'Pnt') exhibit highly similar characteristics, whereas ('Qdr', 'Rel', and 'Skt') are significantly different, which impacts transferability from other domains. For more distinct domains, reference labels from the base prompts may be more appropriate. However, we do not have access to the", + "bbox": [ + 89, + 719, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68c12477955f888b9da045a6e734cec09693de53bb9955af7cd43ad60fd191a6.jpg", + "table_caption": [ + "Table 2. Accuracy (%) on ImageCLEF and Office-Home. We use bold to denote the best method overall." + ], + "table_footnote": [], + "table_body": "
DomainNet
→ Clp→ Inf→ Pnt→ Qdr→ Rel→ SktAvg
Zero-Shot
CLIP [34]61.342.056.110.379.354.150.5
Source Combined
DANN [11]45.513.137.013.248.931.832.6
MCD [37]54.322.145.77.658.443.538.5
DAPL [12]62.443.859.310.681.554.652.0
Simple Prompt [4]63.141.257.710.075.855.850.6
PGA [32]65.449.060.411.181.860.655.4
CRPL (Ours)65.650.866.710.680.061.155.8
Multi-Source
MPSDA-β [29]58.626.052.36.362.749.542.6
SImpAl101 [45]66.426.556.618.968.055.548.6
LtC-MSDA [49]63.128.756.116.366.153.847.4
T-SVDNet [22]66.125.054.316.565.454.647.0
PFSA [8]64.529.257.617.267.255.148.5
PTMDA [35]66.028.558.413.063.054.147.2
MPA [4]65.247.362.010.282.057.954.1
MPGA [32]67.247.863.111.681.761.055.4
M-CRPL (Ours)67.651.467.011.179.360.656.2
", + "bbox": [ + 516, + 89, + 903, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Accuracy (%) on DomainNet. We use **bold** to denote the best method overall.", + "bbox": [ + 511, + 327, + 903, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "data used to train the base prompts, which limits our ability to establish the relationship between the target domain and the base prompts. This makes it difficult to decide when to use the base prompts or the source-enhanced prompts. As a result, we apply an average combination of the base prompt and the source-enhanced prompt, as shown in Eq. (7), to balance their contributions.", + "bbox": [ + 511, + 383, + 906, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The effectiveness of our approach is further demonstrated through 12 pairwise source-target settings on Office-Home, as shown in Table 4. While prompt-based methods using pretrained CLIP outperform traditional UDA baselines, CRPL achieves the highest average score and consistently outperforms both DAPL and PGA across all 12 settings.", + "bbox": [ + 511, + 489, + 908, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Ablation study", + "text_level": 1, + "bbox": [ + 511, + 590, + 661, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct several ablation studies on the Office-Home dataset to evaluate the effectiveness of the two key components of our proposed approach: source-enhanced pseudo-labels and clustering reinforcement, denoted as $\\mathcal{L}_{\\mathcal{W}}$ . We also analyze the impact of the source-target prompt alignment strategy in previous approaches. In the following, CPL refers to using hard labels obtained from CLIP's zero-shot predictions to train the target prompt; SPL refers to using enhanced pseudo-labels derived from the source domains to train the target prompt; and with $\\mathcal{L}_{\\mathcal{W}}$ refers to adding the optimal transport (OT) clustering to enhance performance. Additionally, we consider different scenarios, including using only the target prompt $(\\tau_T)$ , averaging the source prompts $(\\tau_S)$ , and averaging all prompts $(\\tau_{avg})$ for inference.", + "bbox": [ + 511, + 612, + 906, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of SPL. Table 5 demonstrates that SPL significantly improves the performance of CPL. Moreover, when comparing performance across different inference scenarios $(\\tau_T, \\tau_S, \\tau_{avg})$ , it becomes evident that source-target prompt alignment in the simple baseline has a limited impact on the target", + "bbox": [ + 511, + 825, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19980", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/47f10088f1fddb4b61bd0f63bdd55397246433246838b98c96af236cf383222a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg
ResNet-50[16]34.950.058.037.441.946.238.531.260.453.941.259.946.1
DANN [10]45.659.370.147.058.560.946.143.768.563.251.876.857.6
JAN [25]45.961.268.950.459.761.045.843.470.363.952.476.858.3
CDAN+E [27]50.770.676.057.670.070.057.450.977.370.956.781.665.8
BSP+CDAN [5]52.068.676.158.070.370.258.650.277.672.259.381.966.3
SymNets [54]47.772.978.564.271.374.263.647.679.473.850.882.667.2
ETD [21]51.371.985.757.669.273.757.851.279.370.257.582.167.3
BNM [6]52.373.980.063.372.974.961.749.579.770.553.682.267.9
GSDA [17]61.376.179.465.473.374.365.053.280.072.260.683.170.3
GVB-GD [7]57.074.779.864.674.174.665.255.181.074.659.784.370.4
RSDA-MSTN [15]53.277.781.366.474.076.567.953.082.075.857.885.470.9
SPL [50]54.577.881.965.178.081.166.053.182.869.955.386.071.0
SRDC [41]52.376.381.069.576.278.068.753.881.776.357.185.071.3
DisClusterDA [42]58.877.080.867.074.677.165.956.381.474.260.583.671.4
CLIP [34]51.681.982.671.981.982.671.951.682.671.951.681.972.0
DAPL [12]52.782.284.173.982.083.873.654.684.073.353.482.573.3
PGA [32]53.783.985.073.283.984.673.253.884.173.553.185.373.9
CRPL (Ours)54.784.184.674.383.283.773.753.484.674.555.585.574.4
", + "bbox": [ + 93, + 88, + 903, + 325 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0397942e02bed4adc7a23f4c7118b32d3852365647216e5f7be1b2f5596f7920.jpg", + "table_caption": [ + "Table 4. Accuracy (%) on Office-Home[46] for unsupervised domain adaptation (ResNet-50[16]). The best accuracy is indicated in bold." + ], + "table_footnote": [], + "table_body": "
Inference PromptArClPrRw
CPLτT47.629.053.563.5
τS74.357.284.384.8
τavg61.240.373.377.8
SPLτT75.862.986.687.2
τS73.357.483.484.7
τavg75.858.183.685.3
CPL onlyτT47.629.053.563.5
CPL with LwτT7.94.780.482.3
SPL onlyτT75.862.986.687.2
SPL with LwτT76.863.587.587.6
", + "bbox": [ + 145, + 369, + 419, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prompt, as evidenced by the significantly lower accuracy in $\\tau_{T}$ compared to $\\tau_{S}$ . In contrast, SPL enables the target domain to learn text embeddings that effectively capture and represent the corresponding visual embeddings.", + "bbox": [ + 89, + 551, + 482, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of clustering reinforcement $\\mathcal{L}_{\\mathcal{W}}$ . Table 5 (last four rows) shows that clustering reinforcement $\\mathcal{L}_{\\mathcal{W}}$ further improves the performance of SPL. However, applying $\\mathcal{L}_{\\mathcal{W}}$ to the simple baseline reveals noticeable differences in CPL performance over target domains. Specifically, it seems that the effectiveness of $\\mathcal{L}_{\\mathcal{W}}$ strongly depends on the initial predictions, where weak initial predictions as observed in the CPL method on 'Ar' and 'Cl' domains with just $47.6\\%$ and $29.0\\%$ , leading to a collapse performance of accuracy less than $8\\%$ when combing with $\\mathcal{L}_{\\mathcal{W}}$ . However, with better initial predictions as observed in the CPL method on 'Pr' and 'Rw' domains, substantial improvement of $27\\%$ ( $53.5\\%$ to $80.4\\%$ ) and $19\\%$ ( $63.5\\%$ to $82.3\\%$ ) when combined with $\\mathcal{L}_{\\mathcal{W}}$ are observed. This indicates a mutual benefit between source-enhanced pseudo-labels and clustering reinforcement.", + "bbox": [ + 88, + 612, + 482, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Source-Target Prompts Alignment. We have shown that source-target prompt alignment has a limited impact on the target prompt. To further validate this, we analyze the performance of prompts from the most recent", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/94f71e8a3ae93a66db9359792af28f6804db246f19e49e2b75caa9625e6fc8c9.jpg", + "table_caption": [ + "Table 5. Effect of source-enhanced pseudo-labels and clustering reinforcement on the Office-Home dataset." + ], + "table_footnote": [], + "table_body": "
SettingInference PromptArClPrRw
PGAτT72.352.883.782.4
τS73.856.284.684.9
τavg75.657.086.086.6
M-CRPL (ours)τT76.863.587.587.6
τS75.358.083.984.7
τavg75.858.685.285.3
", + "bbox": [ + 570, + 369, + 844, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Analyses of prompts performance on OfficeHome dataset.", + "bbox": [ + 511, + 454, + 903, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SOTA method, PGA [32], which focuses on the source-target prompt strategy. As shown in Table 6, while PGA improves the performance of $\\tau_{T}$ , bringing it closer to the performance of the source prompts $\\tau_{S}$ , it does not surpass them. This result confirms the limitations of the alignment strategy. In contrast, for M-CRPL, $\\tau_{T}$ achieves the best performance for target prompts across all three scenarios, demonstrating the effectiveness of using enhanced pseudo-labels from source domains to refine target prompts in terms of representation.", + "bbox": [ + 511, + 489, + 906, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 646, + 633, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a framework for prompt learning UDA that begins by leveraging information from the source domains to enhance pseudo-labels for training target prompts. We demonstrate that while source-target prompt alignment has a limited effect on learning the target prompt, enhanced pseudo-labels result in significant improvements in both performance and the quality of target prompts in terms of representation. Additionally, inspired by the strong clustering behavior observed between visual and text embeddings in pre-trained models, we further refine target prompts by enforcing clustering properties. This is achieved by minimizing the Wasserstein distance between the distribution of text prompts and the distribution of visual embeddings in the target domains. Finally, our experiments and ablation studies validate the superior performance of our approach.", + "bbox": [ + 509, + 674, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19981", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 256, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by ARC DP23 grant DP230101176 and by the Air Force Office of Scientific Research under award number FA2386-23-1-4044.", + "bbox": [ + 89, + 114, + 485, + 160 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 176, + 187, + 191 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representations for domain adaptation. 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AAAI Press, 2019. 7" + ], + "bbox": [ + 91, + 90, + 483, + 369 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19984", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_model.json b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2539f00963f327d9f9f213cbd9ba4bb8d8c635a2 --- /dev/null +++ b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_model.json @@ -0,0 +1,2312 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.131, + 0.895, + 0.154 + ], + "angle": 0, + "content": "Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.18, + 0.88, + 0.218 + ], + "angle": 0, + "content": "Tung-Long Vuong\\(^{1}\\), Hoang Phan\\(^{2}\\), Vy Vo\\(^{1}\\), Anh Bui\\(^{1}\\), Thanh-Toan Do\\(^{1}\\), Trung Le\\(^{1}\\), Dinh Phung\\(^{1}\\) \n\\(^{1}\\)Monash University, \\(^{2}\\)New York University" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.22, + 0.816, + 0.252 + ], + "angle": 0, + "content": "{Tung-Long.Vuong,v.vo,tuananh.bui,toan.do,trunglm,dinh.phung}@monash.edu hvp2011@nyu.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.318, + 0.485, + 0.756 + ], + "angle": 0, + "content": "Recent approaches leveraging multi-modal pre-trained models like CLIP for Unsupervised Domain Adaptation (UDA) have shown significant promise in bridging domain gaps and improving generalization by utilizing rich semantic knowledge and robust visual representations learned through extensive pre-training on diverse image-text datasets. While these methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. Thus, the training mechanism exhibits a key limitation wherein the visual embedding distribution in target domains can deviate from the visual embedding distribution in the pre-trained model, leading to misguided signals from class descriptions. This work introduces a fresh solution to reinforce these pseudo-labels and facilitate target-prompt learning, by exploiting the geometry of visual and text embeddings - an aspect that is overlooked by existing methods. We first propose to directly leverage the reference predictions (from source prompts) based on the relationship between source and target visual embeddings. We later show that there is a strong clustering behavior observed between visual and text embeddings in pre-trained multi-modal models. Building on optimal transport theory, we transform this insight into a novel strategy to enforce the clustering property in text embeddings, further enhancing the alignment in the target domain. Our experiments and ablation studies validate the effectiveness of the proposed approach, demonstrating superior performance and improved quality of target prompts in terms of representation." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.785, + 0.222, + 0.801 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Significant advancements of deep learning have consistently enhanced performance on various tasks, albeit primarily within the confines of training data distributions. Therefore, deep models notoriously fail to maintain their performance when applied to new, unseen domains [19, 23, 36, 52]. Unsupervised domain adaptation (UDA) offers a promising solu" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.908, + 0.485 + ], + "angle": 0, + "content": "tion by utilizing labeled data from a source domain alongside unlabeled data from a target domain, thus circumventing the costly and labor-intensive process of annotating new domain data. In recent years, many domain adaptation methods have been proposed, typically focusing on learning invariant features across domains, as motivated by the theoretical analysis by Ben-David et al. [1, 2]. These methods generally (i) minimize the discrepancy between feature representations across domains [24, 25, 31, 40] or (ii) adversarially learn indistinguishable representations to fool a domain discriminator [10, 11, 26, 44]. However, focusing on aligning representations can inadvertently compromise model performance by diminishing discriminative features [12, 41]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.486, + 0.909, + 0.728 + ], + "angle": 0, + "content": "Recent developments have demonstrated the potential of leveraging pre-trained models such as CLIP [34] for the UDA problem, significantly bridging domain gaps and enhancing generalization. These benefits arise from the rich semantic and robust visual representations gained through extensive pre-training across diverse image-text datasets. Building on this approach, DAPL [12] innovatively introduces domain-specific and domain-agnostic prompts, enabling the efficient adaptation of pre-trained vision-language models without the need to fine-tune the entire model. Extending this training procedure to the multi-source domain adaptation scenario, MPA [4] employs an auto-encoder to align training and target prompts while PGA [32] frames the learning from a multi-domain problem as a multi-objective optimization problem and align per-objective gradients to promote consensus across objectives." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.911, + 0.902 + ], + "angle": 0, + "content": "Contribution. While prior vision-language UDA methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from the use of base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. However, they do have limitations. First, the visual embedding distribution in the target domain may differ from the textual embedding distribution in the pre-trained models, resulting in misaligned class descriptions when relying on the \"over-generalized\" nature of pre-trained models (such as CLIP zero-shot predictions) without incorporating domain-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19974" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.227 + ], + "angle": 0, + "content": "specific context. Secondly, previous methods primarily focus on aligning source-target prompts within the textual embedding space to refine target prompts, placing less emphasis on the representation perspective, specifically the alignment between visual and text embeddings. Moreover, we observe that source-target prompt alignment has a limited impact on target prompts (Table 1, Simple Alignment - Eq. (3): Even after alignment, the target prompt performs poorly. Further analysis is provided in Section 6.3.)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.228, + 0.484, + 0.424 + ], + "angle": 0, + "content": "To address these challenges, we leverage reference predictions (from source prompts) based on the relationship between source and target visual embeddings. This helps enhance pseudo-labels and facilitates target-prompt learning. Additionally, drawing inspiration from the strong clustering behavior observed between visual and textual embeddings in pre-trained multi-modal models, we enforce clustering properties in text embeddings by minimizing the Wasserstein distance [47] between the distribution of text prompts and the distribution of visual embeddings in the target domains. Our experiments and ablation studies validate the effectiveness of this approach, showing superior performance and improved quality of target prompts in terms of representation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.438, + 0.228, + 0.453 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.484, + 0.629 + ], + "angle": 0, + "content": "Domain Adaptation (DA) addresses the challenge of transferring knowledge learned from a source domain to a target domain, where both domains share the same label space but have different data distributions [2]. Deep domain adaptation has demonstrated impressive performance across various tasks through different approaches [55, 56]. The fundamental concept is to minimize the distributional gap between source and target domains in a shared feature space by reducing distribution divergence, commonly measured through Jensen-Shannon divergence [10, 39, 43], maximum mean discrepancy [14, 24], or Wasserstein distance [20, 38]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation (UDA) presents additional challenges as the target domain is unlabeled. Early UDA methods focused on learning domain-invariant features by minimizing domain discrepancy [24, 25, 40]. For instance, DAN [24] aligns domains by minimizing maximum mean discrepancy on task-specific layers, while CORAL [40] aligns second-order statistics using linear projection. Inspired by GANs [13], adversarial learning emerged as another prominent approach. Methods like DANN [10] and CDAN [27] employ domain discriminators to distinguish source from target samples while training feature extractors to generate domain-invariant features. However, recent work has highlighted that while domain alignment can be successful, it may compromise class discrimination due to distorted semantic features [3, 41]. Several methods have attempted to address this challenge through approaches like entropy-based regularization [21] and batch nuclear-norm maximization [6]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.44 + ], + "angle": 0, + "content": "Prompt Learning for Domain Adaptation. Prompt learning, initially introduced in NLP [30], has recently been adapted for vision-language models [18, 34]. Rather than fine-tuning entire networks, prompt learning enables efficient adaptation to downstream tasks by tuning prompt parameters. Such notable models as CLIP [34] have demonstrated strong visual representations through pre-training on large-scale image-text pairs. In the context of UDA, prompt learning offers a novel direction to address domain adaptation challenges [9, 33, 53]. DAPL [12] leverages CLIP's generalization capabilities to learn both domain-agnostic and domain-specific prompts, effectively balancing domain alignment and classification performance through contrastive learning. Building on this idea, MPA [4] extends prompt learning to multi-source UDA scenarios. MPA first learns from multiple source domains, then adapts the prompt learning strategy to each source-target domain pair. Prompts are aligned using a denoising auto-encoder with Euclidean distance. More recently, PGA [32] frames the multi-domain objective (including the target domain) as a multi-objective optimization problem, aligning per-objective gradients to promote consensus across objectives. PGA further incorporates gradient norm penalization to enhance prompt generalization." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.464, + 0.642, + 0.48 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.492, + 0.813, + 0.509 + ], + "angle": 0, + "content": "3.1. Unsupervised Domain Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.517, + 0.909, + 0.658 + ], + "angle": 0, + "content": "Given a set of \\(N \\geq 1\\) source domains \\(\\{D_{S_i}\\}_{i=1}^N\\) each of which is a collection of data-label pairs of domain \\(i\\)-th, i.e. \\(D_{S_i} = \\{\\pmb{x}_j, y_j\\}_{j=1}^{N_{S_i}}\\), \\(y_j \\in [K] := \\{1, \\dots, K\\}\\), and one unlabeled target domain \\(D_T = \\{\\pmb{x}_j\\}_{j=1}^{N_T}\\), where \\(N_{S_i}\\) and \\(N_T\\) are respectively the number of data points in source domain \\(D_{S_i}\\) and target domain \\(D_T\\), the goal is to learn a model that can perform well on the unlabeled target domain. In this paper, we focus on classification problems and denote \\(K\\) as the number of classes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.679, + 0.836, + 0.695 + ], + "angle": 0, + "content": "3.2. CLIP-based Zero-Shot Classification." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.811 + ], + "angle": 0, + "content": "CLIP [34] is a vision-language model that consists of a visual encoder \\( f_{v} \\) and a textual encoder \\( f_{t} \\), which are trained to align the visual embedding \\( f_{v}(\\boldsymbol{x}) \\) of an image \\( \\boldsymbol{x} \\) with the textual embedding \\( f_{t}(y) \\) of the corresponding label \\( y \\). The textual representation is derived from a manually crafted prompt \\( \\boldsymbol{p}_{k} \\) in the form \"A photo of a \\( [\\mathrm{CLASS}_k] \\)\", where \\( [\\mathrm{CLASS}_k] \\) is the \\( k \\)-th class's name." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.814, + 0.909, + 0.86 + ], + "angle": 0, + "content": "In zero-shot inference, \\(K\\) class names are forwarded through the text encoder \\(f_{t}\\) and one with the highest similarity with the visual embedding \\(f_{v}(x)\\) is the predicted class:" + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.886, + 0.908, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\operatorname {a r g m a x} _ {k} P (y | \\boldsymbol {x}, \\boldsymbol {p} _ {k}) \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19975" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.245, + 0.105 + ], + "angle": 0, + "content": "where we have defined" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.115, + 0.484, + 0.153 + ], + "angle": 0, + "content": "\\[\nP (y \\mid \\boldsymbol {x}, \\boldsymbol {p} _ {k}) = \\frac {\\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k}\\right) \\right\\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k ^ {\\prime}}\\right) \\right\\rangle / \\gamma\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.163, + 0.468, + 0.179 + ], + "angle": 0, + "content": "\\(\\langle ., \\cdot \\rangle\\) measures cosine similarity and \\(\\gamma\\) is the temperature." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.188, + 0.446, + 0.205 + ], + "angle": 0, + "content": "3.3. Domain Adaptation via Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.211, + 0.484, + 0.286 + ], + "angle": 0, + "content": "Prompt Design. A common assumption in domain adaptation literature is that each domain can be represented by domain-specific features - which are found/presented only in this particular domain and domain-invariant features - which are shared with others [4, 32]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.287, + 0.484, + 0.532 + ], + "angle": 0, + "content": "To reflect this, prompt-learning-based approaches as [4, 32] utilize two sets of prompts for each domain \\(D_{S_i}\\): domain-invariant prompt \\(\\pmb{P}_{sh}\\) shared among all domains and domain-specific prompt \\(\\pmb{P}_{S_i}\\) specific to the domain \\(D_{S_i}\\). Similarly, the target domain \\(D_T\\) will be represented by \\(\\pmb{P}_{sh}\\) and \\(\\pmb{P}_T\\) prompts. More specifically, following [4], we do not just use single but multiple domain-invariant prompts \\(\\{\\pmb{P}_{sh}^k\\}_{k=1}^K\\), where each \\(\\pmb{P}_{sh}^k = [\\pmb{v}_1^k | \\pmb{v}_2^k| \\dots | \\pmb{v}_{M_1}^k]\\) is a shared prompt among all domains and specific to class \\(k\\)-th. For domain-specific prompts \\(\\pmb{P}_{S_i}\\) and \\(\\pmb{P}_T\\), which are not shared among domains, are represented by \\(M_2\\) tokens, i.e., \\(\\pmb{P}_{S_i} = [\\pmb{u}_1^{S_i} | \\pmb{u}_2^{S_i} | \\dots | \\pmb{u}_{M_2}^{S_i}]\\), \\(\\pmb{P}_T = [\\pmb{u}_1^T | \\pmb{u}_2^T | \\dots | \\pmb{u}_{M_2}^T]\\). Based on this, a prompt \\(p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_{S_i}][\\mathrm{CLASS}_k]\\) is to represent the predictive distribution of a sample of source domain \\(D_{S_i}\\) belong to class \\(k\\), and similarly \\(p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]\\) for that of a target sample." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.551, + 0.485, + 0.657 + ], + "angle": 0, + "content": "UDA via Prompt Learning with CLIP-Pseudo-Label. To transfer knowledge from source domains to the target domain, [4] proposed to fine-tune these prompts \\( P_{sh} \\), \\( P_{S_i} \\), \\( P_T \\), simultaneously, where \\( P_{sh} \\) captures the shared predictive features among domains while the prompts \\( P_{S_i} \\), \\( P_T \\) capture unique characteristics of each domain, by optimizing the objective:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.669, + 0.484, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) = \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) + \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.722, + 0.432, + 0.736 + ], + "angle": 0, + "content": "where objectives for source domains are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.748, + 0.448, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\operatorname {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}), \\text {a n d} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "For target domain, since labels are not available in the target domain, previous approaches, such as DAPL [12], MPA [4], and PGA [32], use pre-trained CLIP models to generate pseudo-labels \\(\\hat{y}\\) as in Eq. (1) for the target domain to train target classifiers and learn both domain-invariant and" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "domain-specific prompts. Therefore, the objective for the target domain is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.148, + 0.903, + 0.211 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\alpha} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\mathbb {I} _ {\\left(P \\left(y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}\\right) \\geq \\alpha\\right)} \\log P (y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.221, + 0.907, + 0.372 + ], + "angle": 0, + "content": "The target objective is applied to target samples for which the zero-shot prediction confidence from CLIP exceeds a threshold \\(\\alpha\\). It is evident that when there is a significant covariate shift between the target domain and the dataset used to train the CLIP models, the accuracy of the pseudo-labels decreases markedly. For instance, as shown in Table 1, the accuracy of CLIP's zero-shot predictions varies significantly across domains in the OfficeHome dataset. This limitation forms one of the motivations for our approach, as presented in the following sections." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.385, + 0.905, + 0.628 + ], + "angle": 0, + "content": "
SettingInferenceArClPrRw
Training on source data only
Zero-shot fromCLIP [34]71.250.481.482.6
Source-combinedSource prompt72.255.982.683.3
Multi-sourceAverage prompt74.357.484.584.7
Ar prompt-56.080.082.1
Cl prompt70.4-81.180.4
Pr prompt70.255.0-84.1
Wr prompt73.955.584.5-
Supervised training on target domain only
Target prompt99.691.699.398.6
Traininging both source-target domains as Eq. (3)
Target prompt47.629.053.563.5
Source prompt74.357.284.384.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.639, + 0.907, + 0.694 + ], + "angle": 0, + "content": "Table 1. Analyses of prompts performance on OfficeHome dataset. Source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.725, + 0.638, + 0.74 + ], + "angle": 0, + "content": "4. Motivations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Limitations of existing pseudo-label guidance. As described above, we design shared or domain-invariant prompts \\( P_{sh} \\) to capture embeddings that are consistent across both source and target domains, while we use domain-specific prompts \\( P_{S_i} \\) to capture unique characteristics of each source domain. The domain-invariant prompts \\( P_{sh} \\) enable learning of shared knowledge across source domains, which can then be transferred to the target domain. Additionally, to train both domain-invariant prompts \\( P_{sh} \\) and target-specific prompts \\( P_T \\) with a focus on the target domain, most recent" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19976" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.162, + 0.092, + 0.195, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.096, + 0.414, + 0.11 + ], + "angle": 0, + "content": "Pretrained Visual-embedding Distribution" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.111, + 0.403, + 0.123 + ], + "angle": 0, + "content": "Domain Visual-embedding Distribution" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.125, + 0.432, + 0.138 + ], + "angle": 0, + "content": "Refine Target Prompt Based on Pseudo-Label" + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.142, + 0.486, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.208, + 0.355, + 0.386, + 0.368 + ], + "angle": 0, + "content": "(a) Target prompt refinement." + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.369, + 0.404, + 0.382 + ], + "angle": 0, + "content": "(Same class from different domains)" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.092, + 0.541, + 0.106 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.546, + 0.094, + 0.843, + 0.107 + ], + "angle": 0, + "content": "Class description with based Prompts (A photo of a dog)" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.108, + 0.541, + 0.122 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.546, + 0.109, + 0.722, + 0.123 + ], + "angle": 0, + "content": "Learnable Source-domain Prompts" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.124, + 0.541, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.546, + 0.125, + 0.716, + 0.138 + ], + "angle": 0, + "content": "Learnable Target-domain Prompt" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.143, + 0.864, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.611, + 0.355, + 0.805, + 0.368 + ], + "angle": 0, + "content": "(b) Effect of wrong Pseudo-label." + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.369, + 0.82, + 0.382 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.393, + 0.907, + 0.588 + ], + "angle": 0, + "content": "Figure 1. (a) Target-domain prompt refinement. Pre-trained models are trained on large-scale datasets, which are assumed to fully or partially cover the data distribution of downstream tasks. For example, \"dog with style domain \\(S_{1,\\dots,3,T}\\)\" can be viewed as subdomains of \"dog\". However, the visual embedding distribution in training may shift from that of the pretraining distribution, causing class descriptions without domain-specific context to become misaligned. This shift necessitates alignment using domain-specific contexts. While the source domain can leverage labeled data to refine its domain-specific context, the target domain lacks this advantage. A common approach to address this limitation is to incorporate domain-specific contexts and leverage zero-shot predictions from the CLIP model to guide alignment between domain-specific contexts and visual-representation in the target domain. (b) Effect of incorrect pseudo-label. Behavior of prompt learning with incorrect pseudo-labels in a supervised manner on the target domain. The flat regions in gray and orange represent areas in the embedding space corresponding to different classes, each centered on its optimal domain-specific prompt embedding (with class \"dog\" in orange and other classes in blue). Red points indicate samples from class \"dog\" with correct pseudo-labels, while black points represent samples from class \"dog\" that have been incorrectly pseudo-labeled. Additionally, some samples from regions belonging to other classes (gray areas) are mislabeled as class \"dog\", shown as black points with red borders. The text embeddings learned from these pseudo-labels fail to align well with the true target embeddings; instead, they form a cluster around a single point—the centroid of all samples labeled as class \"dog\" (both correctly and incorrectly labeled)—remaining distant from the actual target embeddings." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.614, + 0.486, + 0.796 + ], + "angle": 0, + "content": "state-of-the-art approaches [12, 32] leverage pseudo-labels obtained through zero-shot inference using CLIP models. However, we argue that generating reliable and accurate pseudo-labels can be challenging when relying on zero-shot predictions from CLIP models, particularly if there is a significant covariate shift between the target domain and the dataset on which the CLIP models were trained. Furthermore, pseudo-labels are crucial for guiding the target text embeddings \\(\\tau_T^k\\) for each class \\(k\\) by aligning them with the visual embeddings from the corresponding target class. This raises the question: How can we enhance these critical pseudo-labels to improve the target target prompt?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.485, + 0.9 + ], + "angle": 0, + "content": "Enhancing pseudo-labels using source prompts. When training the source and target prompt, we use domain-invariant prompts \\( P_{sh} \\) shared across both source and target domains to capture the domain-invariant embeddings common to data in both domains. As a result, the source" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.887 + ], + "angle": 0, + "content": "prompts can encapsulate domain-invariant embeddings of the target data. Additionally, the source and target data share certain common embeddings, making it reasonable to utilize source prompts to generate pseudo-labels for the target domain. To illustrate the advantage of using aggregated source prompts over standalone CLIP models in generating more accurate pseudo-labels, we conduct experiments on the Office-Home dataset. Table 1 (Training on source data only setting) presents the accuracies of the average aggregated source prompts (multi-source) and single source prompt (source combined) on the target domain, where only source prompts are used for predictions. The results indicate that aggregated source prompts produce more accurate pseudo-labels, hence further improving predictions. This observation aligns with our motivation and supports the proposed approach. Additionally, the transferability of different source domains to the target domain varies based on their similarity (Table 1: Training on source data only: Multi-source). This observation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19977" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.151 + ], + "angle": 0, + "content": "motivates the design of a distance-aware transfer strategy to combine references from source prompts and base prompt for generating more accurate pseudo-labels, as detailed in Section 5.2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.486, + 0.289 + ], + "angle": 0, + "content": "Furthermore, we observe that while more accurate pseudo-labels help guide the text embeddings more effectively toward their class clusters, they still introduce inaccuracies. These inaccuracies cause the text embeddings to skew toward regions of correct pseudo-labels within their clusters, as illustrated in Figure 1, ultimately compromising performance on entire clusters. Thus, it is essential to introduce an additional component to correct this bias and maintain consistent predictions across clusters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.312, + 0.484, + 0.493 + ], + "angle": 0, + "content": "Clustering preservation prediction. According to the clustering assumption, data tend to be organized into clusters. To verify this assumption for visual embeddings from CLIP models, we assume we have labels for the target domain and train a target prompt using only class-specific target prompts (i.e., \\([P_T^k][CLASS_k]\\)) on the target domain. This setup implies that for each class \\( k \\), we rely on a single text embedding, \\( \\tau_T^k \\), to represent its visual embeddings. The high accuracies obtained, as shown in Table 1 (supervised training on target domain only), demonstrate that the visual embeddings for each class using CLIP models tend to form a single cluster in the embedding space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.494, + 0.485, + 0.901 + ], + "angle": 0, + "content": "Although using source prompts to generate pseudo-label guidance for the target prompt outperforms zero-shot predictions from CLIP models, incorrect pseudo-labels or the absence of pseudo-label guidance may still occur for lower-confidence predictions. Consequently, in the cluster for class \\( k \\) in the target domain, there are visual embeddings with correct pseudo-labels and those with incorrect or missing pseudo-labels (shown in black in Figure 1b). As a result, the text embedding \\( \\tau_T^k \\) for this class acts as a prototype or centroid for the red visual embeddings but may fail to represent the entire cluster for class \\( k \\). This limitation could lead to incorrect predictions for the black visual embeddings and potential confusion with visual embeddings from other classes. To obtain text embeddings \\( \\tau_T^k \\) that effectively represent the entire cluster for each class \\( k \\) and ensure clustering-preserving predictions, we adopt the clustering viewpoint of optimal transport [28, 48]. Specifically, our objective is to minimize the optimal transport (Wasserstein-WS) distance between the distribution of visual embeddings in the target domain and the distribution of the text embeddings \\( \\tau_T^k \\). As demonstrated in Lemma 1, the text embeddings \\( \\tau_T^k \\) act as prototypes or centroids of the clusters, leading to an alignment correction for the text embeddings, as shown in Figure 2. Moreover, minimizing the WS distance adjusts the text embeddings \\( \\tau_T^k \\) to serve as accurate cluster centroids, while the pseudo-label guidance aids in aligning these embeddings with their correct class- \\( k \\) clusters." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.689, + 0.108 + ], + "angle": 0, + "content": "5. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.116, + 0.909, + 0.239 + ], + "angle": 0, + "content": "Notation: Since our method focuses on analyzing the representations; for simplicity, we denote \\(\\pmb{\\tau}_{S_i}^k\\) as the text embedding of the source domain-specific prompt, given by \\(\\pmb{\\tau}_{S_i}^k = f_t\\left([P_{sh}^k][P_{S_i}][\\mathrm{CLASS}_k]\\right)\\). Similarly, \\(\\pmb{\\tau}_T^k = f_t\\left([P_{sh}^k][P_T][\\mathrm{CLASS}_k]\\right)\\) and \\(\\pmb{\\tau}_{base}^k = f_t\\left(\"A photo of a [CLASS_k]\"\\right)\\) as the text embeddings of the target prompt and base prompt, respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.249, + 0.853, + 0.266 + ], + "angle": 0, + "content": "5.1. Prompt Learning with Source Domains" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.271, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Because labels are available in all source domains, we apply the cross-entropy loss to fine-tune these associated prompts \\( P_{sh}, P_{Si} \\) with the source-domain objective loss:" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.33, + 0.907, + 0.371 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.379, + 0.668, + 0.392 + ], + "angle": 0, + "content": "where we have defined" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.406, + 0.907, + 0.47 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\mathrm {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}) \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.484, + 0.843, + 0.501 + ], + "angle": 0, + "content": "5.2. Prompt Learning with Target Domain" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.506, + 0.909, + 0.628 + ], + "angle": 0, + "content": "Pseudo-label Enhancement. Building on our motivation, we enhance the quality of pseudo-labels from zero-shot predictions on the target domain by incorporating predictions from the source domains. Specifically, we calculate the weighted average cosine distance from the visual embedding \\( \\mathbf{z} = f_v(\\mathbf{x}) \\) to the text embeddings of each class across all source domains. We then average this result with the text embedding from the base prompt as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.64, + 0.907, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\hat {y} [ k ] = \\frac {\\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k} ((x)) \\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k ^ {\\prime}} (x) \\rangle / \\gamma\\right)} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.686, + 0.689, + 0.699 + ], + "angle": 0, + "content": "where we have defined" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.714, + 0.907, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\tau} _ {a v e} ^ {k} (x) = \\frac {1}{2} \\boldsymbol {\\tau} _ {b a s e} ^ {k} + \\frac {w _ {k , i} (x)}{2} \\sum_ {i = 1} ^ {N} \\boldsymbol {\\tau} _ {S _ {i}} ^ {k} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.763, + 0.901, + 0.777 + ], + "angle": 0, + "content": "and \\(w_{i,k}\\) is the important weight for each domain-class." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.778, + 0.909, + 0.902 + ], + "angle": 0, + "content": "As discussed in Section 4, to compute \\( w_{k,i}(x) \\), we use the \\( l_2 \\) distance between the visual embedding \\( z^{pre} \\) (the unnormalized visual embedding of \\( x \\), where \\( z = \\frac{z^{pre}}{\\|z^{pre}\\|_2} \\)) and the centroid of class \\( k \\) in domain \\( i \\). Let \\( C^i = \\{c_k^i\\}_{k=1}^K \\) represent the set of class centroids for the \\( i \\)-th domain i.e., \\( c_k^i = \\frac{1}{\\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)}} \\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)} z_j^{pre,i} \\). The weight for class \\( k \\) is then calculated by applying the softmax function:" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19978" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.168, + 0.101, + 0.484, + 0.143 + ], + "angle": 0, + "content": "\\[\nw _ {i, k} (z) = \\frac {\\exp \\left(\\left\\| z _ {p r e} - c _ {k} ^ {i} \\right\\| _ {2}\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(\\left\\| z - c _ {k} ^ {i ^ {\\prime}} \\right\\| _ {2}\\right)} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.148, + 0.485, + 0.284 + ], + "angle": 0, + "content": "Note that the weights \\( w_{i,k}(z) \\) are applied to compute the combined prompts \\( \\tau_{\\mathrm{ave}}^k \\), rather than being applied directly to the outputs of the softmax (i.e., the predictions from individual prompts). This design preserves semantic similarity, as the magnitude of cosine similarity between the visual embedding and the text embedding of each individual prompt is taken into account in the final pseudo-label. Meanwhile, the weights \\( w_{k,i}(x) \\) represent the spatial relationship between the visual embedding and the text embedding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.302, + 0.486, + 0.363 + ], + "angle": 0, + "content": "Training target prompts with Pseudo-label Guidance. Given data sample \\( x_{j} \\) and its corresponding enhanced pseudo-label \\( \\hat{y}_{j} \\), we minimize the following objective function to train the target prompts:" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.376, + 0.483, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\tau} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\sum_ {k = 1} ^ {K} \\hat {y} _ {j} [ k ] \\log P (y = k | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.448, + 0.445, + 0.464 + ], + "angle": 0, + "content": "5.3. Clustering Refined by Optimal Transport" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.47, + 0.484, + 0.611 + ], + "angle": 0, + "content": "We propose minimizing the Wasserstein distance between the target prompts' text embeddings and the visual embeddings from the target domain. Specifically, denote \\(\\mathcal{T} = \\{\\pmb{\\tau}_T^k\\}_{k=1}^K\\) where \\(\\pmb{\\tau}_T^k\\) represents the text embeddings of the context prompt \\([\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]\\) for class \\(k\\). Let \\(\\mathbb{P}_{\\tau,\\pi} = \\sum_{k=1}^{K}\\pi_k\\delta_{\\tau_T^k}\\) be the discrete distribution over the set of text embeddings \\(\\mathcal{T}\\) for the target domain, where the category probabilities \\(\\pi \\in \\Delta_K = \\{\\alpha \\geq 0 : \\| \\alpha \\|_1 = 1\\}\\) lie in the \\(K\\)-simplex. Additionally, let \\(\\mathbb{P}^T = \\frac{1}{N_T}\\sum_{j=1}^{N_T}\\delta_{z_j}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.484, + 0.67 + ], + "angle": 0, + "content": "represent the visual embedding distribution of the target domain, where \\(\\delta\\) is the Dirac delta function and \\(z = f_{v}(\\pmb{x})\\) for the target image \\(\\pmb{x}\\). The clustering assumption is then enforced by the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.681, + 0.483, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {W}} = \\mathcal {W} _ {d _ {z}} \\left(\\mathbb {P} _ {\\tau , \\pi}, \\mathbb {P} ^ {T}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.71, + 0.486, + 0.801 + ], + "angle": 0, + "content": "where \\( d_{z} \\) represents a metric function. We use the cosine distance \\( d_{z}(a,b) = 1 - \\langle a,b\\rangle \\) since the visual embeddings and text embeddings already lie in the unit hypersphere. The following lemma demonstrates the behavior of \\( \\pi \\) and explains how the Wasserstein term helps target prompts enforce clustering properties." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.809, + 0.486, + 0.866 + ], + "angle": 0, + "content": "Lemma 1 Let \\(\\mathcal{T}^{*} = \\left\\{\\pmb{\\tau}_{T}^{k,*}\\right\\}_{k=1}^{K}\\) be the optimal solution of the OP in Eq. (10), then \\(\\mathcal{T}^{*}\\) is also the optimal solution of the following OP:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.876, + 0.484, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathcal {T}, \\pi} \\min _ {\\sigma \\in \\Sigma_ {\\pi}} \\mathbb {E} _ {z \\sim \\mathbb {P} ^ {T}} \\left[ d _ {z} \\left(z, \\tau_ {T} ^ {\\sigma (z)}\\right) \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.199 + ], + "angle": 0, + "content": "where \\(\\Sigma_{\\pi}\\) is the set of assignment functions \\(\\sigma : \\mathcal{Z} \\to \\{1, \\dots, K\\}\\) such that the cardinalities \\(|\\sigma^{-1}(k)|, k = 1, \\dots, K\\) are proportional to \\(\\pi_k, k = 1, \\dots, K\\). Moreover, given the set of text embeddings \\(\\mathcal{T}\\), the optimal \\(\\sigma\\) of the inner minimization is the nearest assignment: \\(\\sigma^{-1}(k) = \\{z \\mid k = \\operatorname{argmin}_m d_z(z, \\tau_T^m)\\}\\) is set of visual embeddings which are quantized to \\(k^{th}\\) text embedding \\(\\tau_T^k\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.205, + 0.908, + 0.463 + ], + "angle": 0, + "content": "Lemma 1 indicates the aim of minimizing the Wasserstein term \\(\\mathcal{W}_{d_z}\\left(\\mathbb{P}_{\\tau,\\pi},\\mathbb{P}^T\\right)\\), by adjusting the text embeddings in \\(\\mathcal{T}\\) to become the clustering centroids of the visual embeddings in the target domain, thereby minimizing the distortion between the text embeddings and target visual embeddings. Specifically, we can interpret the optimization problem in (11) as finding the optimal clustering assignment \\(\\sigma\\), which maps each target example \\(z\\) to the text embedding \\(\\tau_T^{\\sigma(z)}\\) to minimize distortion. Moreover, given the text embeddings in \\(\\mathcal{T}\\), the inner minimization in (11) specifies the nearest assignment by assigning each visual embedding \\(z\\) to the closest text embedding. Furthermore, in the optimal solution, the optimal assignment \\(\\sigma^*\\), mapping target visual embeddings to clustering centroids (i.e., text embeddings), has a valuable property: the cardinalities \\(\\left|\\left(\\sigma^*\\right)^{-1}(k)\\right|, k = 1,\\dots,K\\) are proportional to \\(\\pi_k, k = 1,\\dots,K\\). We set \\(\\pi_k = \\frac{1}{K}\\) for \\(k = 1,\\dots,K\\), aiming to learn balanced clusters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.464, + 0.909, + 0.584 + ], + "angle": 0, + "content": "It is important to note that the Wasserstein distance alone can shift the text embeddings toward the cluster centroids of the visual embedding distribution in the target domain. However, this may inadvertently cause the text embedding for one class (e.g., class 1) to shift to the centroid of a different class's cluster (e.g., class 2). To prevent this, pseudo-label guidance is necessary to ensure that each text embedding moves toward its correct cluster." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.602, + 0.908, + 0.647 + ], + "angle": 0, + "content": "Final Objective. We combine the objective functions for source prompts, target prompts, and cluster enforcement, and perform joint training as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.657, + 0.907, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) := \\mathcal {L} _ {S} + \\lambda_ {T} \\mathcal {L} _ {T} + \\lambda_ {\\mathcal {W}} \\mathcal {L} _ {\\mathcal {W}} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.682, + 0.908, + 0.713 + ], + "angle": 0, + "content": "where \\(\\lambda_T\\) and \\(\\lambda_{\\mathcal{W}}\\) are hyper-parameters. Here we note that in our experiments, we simply set \\(\\lambda_T = \\lambda_{\\mathcal{W}} = 0.5\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.646, + 0.741 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.908, + 0.811 + ], + "angle": 0, + "content": "In this section, we evaluate the efficacy of our proposed method on different UDA benchmarks, following the same protocol of recent prompt-based UDA studies [4, 12, 32]. Their detailed descriptions are available in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.702, + 0.835 + ], + "angle": 0, + "content": "6.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Metrics. Following [32], we conduct experiments in two standard settings: a source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19979" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.243 + ], + "angle": 0, + "content": "Inference. During inference, unlike previous baselines (MPA [4], DAPL [12], PGA [32]) that utilize both source and target domain prompts for predictions, we rely solely on the target prompt to evaluate whether we have effectively learned a meaningful textual description for the target domain. Further results, discussed in Section 6.3, reveal that previous methods fail to learn high-quality target prompts, as their performance heavily depends on the quality of source prompts. This dependency is obscured by the combined use of source and target prompts during prediction." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.252, + 0.288, + 0.268 + ], + "angle": 0, + "content": "6.2. Experimental results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.275, + 0.485, + 0.306 + ], + "angle": 0, + "content": "In the following results, our method is referred to as \"Clustering Reinforcement Prompt Learning\" (CRPL)." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.317, + 0.487, + 0.515 + ], + "angle": 0, + "content": "
ImageCLEFOffice-HomeAvg
→ C→ I→ PAvg→ Ar→ Cl→ Pr→ Rw
Zero-Shot
CLIP [34]87.988.278.788.171.250.481.482.671.4
Source Combined
DAN [10]93.392.277.687.768.559.479.082.572.4
DANN [11]93.791.877.987.868.459.179.582.772.4
D-CORAL [40]93.691.777.187.568.158.679.582.772.2
DAPL [12]96.089.276.087.172.851.982.683.772.8
Simple Prompt [4]93.690.680.988.470.752.982.983.972.4
PGA [32]94.292.178.588.274.153.984.485.674.5
CRPL (Ours)94.894.581.790.376.660.486.586.877.6
Multi-Source
DCTN [51]95.790.375.087.0N.A.N.A.N.A.N.A.N.A.
MDDA [57]N.A.N.A.N.A.N.A.66.762.379.579.671.0
SIMplDA [45]93.391.077.587.370.856.380.281.572.2
MFSAN [58]95.493.679.189.472.162.080.381.874.1
MPA [4]97.296.280.491.374.854.986.285.775.4
MPGA [32]93.895.782.890.874.856.085.286.075.5
M-CRPL (Ours)96.296.082.391.576.863.587.687.578.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.52, + 0.483, + 0.547 + ], + "angle": 0, + "content": "Table 2. Accuracy (%) on ImageCLEF and Office-Home. We use bold to denote the best method overall." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.719 + ], + "angle": 0, + "content": "Table 2 presents the results for the ImageCLEF and OfficeHome datasets. Under the source-combined scenario, our method significantly outperforms all other baseline methods on both datasets and target domain settings. For instance, CRPL surpasses the second-best source combined method by \\(1.9\\%\\) in average accuracy for ImageCLEF and \\(3.1\\%\\) in average accuracy for Office-Home. In the multi-source setting, our method delivers the highest average performance across dataset, notably outperforming MPGAs, the state-of-the-art (SOTA) prompt-based method for multi-source UDA, by a substantial margin of \\(3.4\\%\\) on Office-Home." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.901 + ], + "angle": 0, + "content": "On DomainNet, as shown in Table 3, we achieve superior average accuracy under both source-combined and multi-source settings, boosting the performance of pretrained CLIP by \\(\\approx 6\\%\\). We also consistently outperform other baselines on the ('Clp', 'Inf', and 'Pnt') domains across all settings, while showing competitive performance in the other three domains. This is because domains such as ('Clp', 'Inf', and 'Pnt') exhibit highly similar characteristics, whereas ('Qdr', 'Rel', and 'Skt') are significantly different, which impacts transferability from other domains. For more distinct domains, reference labels from the base prompts may be more appropriate. However, we do not have access to the" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.09, + 0.905, + 0.324 + ], + "angle": 0, + "content": "
DomainNet
→ Clp→ Inf→ Pnt→ Qdr→ Rel→ SktAvg
Zero-Shot
CLIP [34]61.342.056.110.379.354.150.5
Source Combined
DANN [11]45.513.137.013.248.931.832.6
MCD [37]54.322.145.77.658.443.538.5
DAPL [12]62.443.859.310.681.554.652.0
Simple Prompt [4]63.141.257.710.075.855.850.6
PGA [32]65.449.060.411.181.860.655.4
CRPL (Ours)65.650.866.710.680.061.155.8
Multi-Source
MPSDA-β [29]58.626.052.36.362.749.542.6
SImpAl101 [45]66.426.556.618.968.055.548.6
LtC-MSDA [49]63.128.756.116.366.153.847.4
T-SVDNet [22]66.125.054.316.565.454.647.0
PFSA [8]64.529.257.617.267.255.148.5
PTMDA [35]66.028.558.413.063.054.147.2
MPA [4]65.247.362.010.282.057.954.1
MPGA [32]67.247.863.111.681.761.055.4
M-CRPL (Ours)67.651.467.011.179.360.656.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.328, + 0.905, + 0.356 + ], + "angle": 0, + "content": "Table 3. Accuracy (%) on DomainNet. We use **bold** to denote the best method overall." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.384, + 0.907, + 0.488 + ], + "angle": 0, + "content": "data used to train the base prompts, which limits our ability to establish the relationship between the target domain and the base prompts. This makes it difficult to decide when to use the base prompts or the source-enhanced prompts. As a result, we apply an average combination of the base prompt and the source-enhanced prompt, as shown in Eq. (7), to balance their contributions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.49, + 0.909, + 0.581 + ], + "angle": 0, + "content": "The effectiveness of our approach is further demonstrated through 12 pairwise source-target settings on Office-Home, as shown in Table 4. While prompt-based methods using pretrained CLIP outperform traditional UDA baselines, CRPL achieves the highest average score and consistently outperforms both DAPL and PGA across all 12 settings." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.591, + 0.663, + 0.607 + ], + "angle": 0, + "content": "6.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.908, + 0.825 + ], + "angle": 0, + "content": "In this section, we conduct several ablation studies on the Office-Home dataset to evaluate the effectiveness of the two key components of our proposed approach: source-enhanced pseudo-labels and clustering reinforcement, denoted as \\(\\mathcal{L}_{\\mathcal{W}}\\). We also analyze the impact of the source-target prompt alignment strategy in previous approaches. In the following, CPL refers to using hard labels obtained from CLIP's zero-shot predictions to train the target prompt; SPL refers to using enhanced pseudo-labels derived from the source domains to train the target prompt; and with \\(\\mathcal{L}_{\\mathcal{W}}\\) refers to adding the optimal transport (OT) clustering to enhance performance. Additionally, we consider different scenarios, including using only the target prompt \\((\\tau_T)\\), averaging the source prompts \\((\\tau_S)\\), and averaging all prompts \\((\\tau_{avg})\\) for inference." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Effect of SPL. Table 5 demonstrates that SPL significantly improves the performance of CPL. Moreover, when comparing performance across different inference scenarios \\((\\tau_T, \\tau_S, \\tau_{avg})\\), it becomes evident that source-target prompt alignment in the simple baseline has a limited impact on the target" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19980" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.326 + ], + "angle": 0, + "content": "
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg
ResNet-50[16]34.950.058.037.441.946.238.531.260.453.941.259.946.1
DANN [10]45.659.370.147.058.560.946.143.768.563.251.876.857.6
JAN [25]45.961.268.950.459.761.045.843.470.363.952.476.858.3
CDAN+E [27]50.770.676.057.670.070.057.450.977.370.956.781.665.8
BSP+CDAN [5]52.068.676.158.070.370.258.650.277.672.259.381.966.3
SymNets [54]47.772.978.564.271.374.263.647.679.473.850.882.667.2
ETD [21]51.371.985.757.669.273.757.851.279.370.257.582.167.3
BNM [6]52.373.980.063.372.974.961.749.579.770.553.682.267.9
GSDA [17]61.376.179.465.473.374.365.053.280.072.260.683.170.3
GVB-GD [7]57.074.779.864.674.174.665.255.181.074.659.784.370.4
RSDA-MSTN [15]53.277.781.366.474.076.567.953.082.075.857.885.470.9
SPL [50]54.577.881.965.178.081.166.053.182.869.955.386.071.0
SRDC [41]52.376.381.069.576.278.068.753.881.776.357.185.071.3
DisClusterDA [42]58.877.080.867.074.677.165.956.381.474.260.583.671.4
CLIP [34]51.681.982.671.981.982.671.951.682.671.951.681.972.0
DAPL [12]52.782.284.173.982.083.873.654.684.073.353.482.573.3
PGA [32]53.783.985.073.283.984.673.253.884.173.553.185.373.9
CRPL (Ours)54.784.184.674.383.283.773.753.484.674.555.585.574.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.332, + 0.903, + 0.346 + ], + "angle": 0, + "content": "Table 4. Accuracy (%) on Office-Home[46] for unsupervised domain adaptation (ResNet-50[16]). The best accuracy is indicated in bold." + }, + { + "type": "table", + "bbox": [ + 0.147, + 0.37, + 0.421, + 0.502 + ], + "angle": 0, + "content": "
Inference PromptArClPrRw
CPLτT47.629.053.563.5
τS74.357.284.384.8
τavg61.240.373.377.8
SPLτT75.862.986.687.2
τS73.357.483.484.7
τavg75.858.183.685.3
CPL onlyτT47.629.053.563.5
CPL with LwτT7.94.780.482.3
SPL onlyτT75.862.986.687.2
SPL with LwτT76.863.587.587.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.506, + 0.483, + 0.534 + ], + "angle": 0, + "content": "Table 5. Effect of source-enhanced pseudo-labels and clustering reinforcement on the Office-Home dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.483, + 0.612 + ], + "angle": 0, + "content": "prompt, as evidenced by the significantly lower accuracy in \\(\\tau_{T}\\) compared to \\(\\tau_{S}\\). In contrast, SPL enables the target domain to learn text embeddings that effectively capture and represent the corresponding visual embeddings." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.613, + 0.483, + 0.839 + ], + "angle": 0, + "content": "Effect of clustering reinforcement \\(\\mathcal{L}_{\\mathcal{W}}\\). Table 5 (last four rows) shows that clustering reinforcement \\(\\mathcal{L}_{\\mathcal{W}}\\) further improves the performance of SPL. However, applying \\(\\mathcal{L}_{\\mathcal{W}}\\) to the simple baseline reveals noticeable differences in CPL performance over target domains. Specifically, it seems that the effectiveness of \\(\\mathcal{L}_{\\mathcal{W}}\\) strongly depends on the initial predictions, where weak initial predictions as observed in the CPL method on 'Ar' and 'Cl' domains with just \\(47.6\\%\\) and \\(29.0\\%\\), leading to a collapse performance of accuracy less than \\(8\\%\\) when combing with \\(\\mathcal{L}_{\\mathcal{W}}\\). However, with better initial predictions as observed in the CPL method on 'Pr' and 'Rw' domains, substantial improvement of \\(27\\%\\) (\\(53.5\\%\\) to \\(80.4\\%\\)) and \\(19\\%\\) (\\(63.5\\%\\) to \\(82.3\\%\\)) when combined with \\(\\mathcal{L}_{\\mathcal{W}}\\) are observed. This indicates a mutual benefit between source-enhanced pseudo-labels and clustering reinforcement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Effect of Source-Target Prompts Alignment. We have shown that source-target prompt alignment has a limited impact on the target prompt. To further validate this, we analyze the performance of prompts from the most recent" + }, + { + "type": "table", + "bbox": [ + 0.571, + 0.37, + 0.845, + 0.452 + ], + "angle": 0, + "content": "
SettingInference PromptArClPrRw
PGAτT72.352.883.782.4
τS73.856.284.684.9
τavg75.657.086.086.6
M-CRPL (ours)τT76.863.587.587.6
τS75.358.083.984.7
τavg75.858.685.285.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.455, + 0.905, + 0.469 + ], + "angle": 0, + "content": "Table 6. Analyses of prompts performance on OfficeHome dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.49, + 0.907, + 0.627 + ], + "angle": 0, + "content": "SOTA method, PGA [32], which focuses on the source-target prompt strategy. As shown in Table 6, while PGA improves the performance of \\(\\tau_{T}\\), bringing it closer to the performance of the source prompts \\(\\tau_{S}\\), it does not surpass them. This result confirms the limitations of the alignment strategy. In contrast, for M-CRPL, \\(\\tau_{T}\\) achieves the best performance for target prompts across all three scenarios, demonstrating the effectiveness of using enhanced pseudo-labels from source domains to refine target prompts in terms of representation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.647, + 0.634, + 0.663 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.675, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We propose a framework for prompt learning UDA that begins by leveraging information from the source domains to enhance pseudo-labels for training target prompts. We demonstrate that while source-target prompt alignment has a limited effect on learning the target prompt, enhanced pseudo-labels result in significant improvements in both performance and the quality of target prompts in terms of representation. Additionally, inspired by the strong clustering behavior observed between visual and text embeddings in pre-trained models, we further refine target prompts by enforcing clustering properties. This is achieved by minimizing the Wasserstein distance between the distribution of text prompts and the distribution of visual embeddings in the target domains. Finally, our experiments and ablation studies validate the superior performance of our approach." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19981" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.258, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.486, + 0.161 + ], + "angle": 0, + "content": "This work was supported by ARC DP23 grant DP230101176 and by the Air Force Office of Scientific Research under award number FA2386-23-1-4044." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.177, + 0.188, + 0.192 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.201, + 0.486, + 0.256 + ], + "angle": 0, + "content": "[1] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representations for domain adaptation. 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AAAI Press, 2019. 7" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.484, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "19984" + } + ] +] \ No newline at end of file diff --git a/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_origin.pdf b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b99022324528374431eacf19722c0aec6b63d3b6 --- /dev/null +++ b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/c4c315b6-c9de-42ff-a0ca-93a857f517af_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:55299460e0507c32f9d6c37a8afba48ef39a26aaef6af5daa8d6e949ada3d6d9 +size 984862 diff --git a/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/full.md b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d7d34918a5c0627fbf664e1dd2bae1577f81e8bf --- /dev/null +++ b/2025/Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation/full.md @@ -0,0 +1,346 @@ +# Preserving Clusters in Prompt Learning for Unsupervised Domain Adaptation + +Tung-Long Vuong $^{1}$ , Hoang Phan $^{2}$ , Vy Vo $^{1}$ , Anh Bui $^{1}$ , Thanh-Toan Do $^{1}$ , Trung Le $^{1}$ , Dinh Phung $^{1}$ $^{1}$ Monash University, $^{2}$ New York University + +{Tung-Long.Vuong,v.vo,tuananh.bui,toan.do,trunglm,dinh.phung}@monash.edu hvp2011@nyu.edu + +# Abstract + +Recent approaches leveraging multi-modal pre-trained models like CLIP for Unsupervised Domain Adaptation (UDA) have shown significant promise in bridging domain gaps and improving generalization by utilizing rich semantic knowledge and robust visual representations learned through extensive pre-training on diverse image-text datasets. While these methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. Thus, the training mechanism exhibits a key limitation wherein the visual embedding distribution in target domains can deviate from the visual embedding distribution in the pre-trained model, leading to misguided signals from class descriptions. This work introduces a fresh solution to reinforce these pseudo-labels and facilitate target-prompt learning, by exploiting the geometry of visual and text embeddings - an aspect that is overlooked by existing methods. We first propose to directly leverage the reference predictions (from source prompts) based on the relationship between source and target visual embeddings. We later show that there is a strong clustering behavior observed between visual and text embeddings in pre-trained multi-modal models. Building on optimal transport theory, we transform this insight into a novel strategy to enforce the clustering property in text embeddings, further enhancing the alignment in the target domain. Our experiments and ablation studies validate the effectiveness of the proposed approach, demonstrating superior performance and improved quality of target prompts in terms of representation. + +# 1. Introduction + +Significant advancements of deep learning have consistently enhanced performance on various tasks, albeit primarily within the confines of training data distributions. Therefore, deep models notoriously fail to maintain their performance when applied to new, unseen domains [19, 23, 36, 52]. Unsupervised domain adaptation (UDA) offers a promising solu + +tion by utilizing labeled data from a source domain alongside unlabeled data from a target domain, thus circumventing the costly and labor-intensive process of annotating new domain data. In recent years, many domain adaptation methods have been proposed, typically focusing on learning invariant features across domains, as motivated by the theoretical analysis by Ben-David et al. [1, 2]. These methods generally (i) minimize the discrepancy between feature representations across domains [24, 25, 31, 40] or (ii) adversarially learn indistinguishable representations to fool a domain discriminator [10, 11, 26, 44]. However, focusing on aligning representations can inadvertently compromise model performance by diminishing discriminative features [12, 41]. + +Recent developments have demonstrated the potential of leveraging pre-trained models such as CLIP [34] for the UDA problem, significantly bridging domain gaps and enhancing generalization. These benefits arise from the rich semantic and robust visual representations gained through extensive pre-training across diverse image-text datasets. Building on this approach, DAPL [12] innovatively introduces domain-specific and domain-agnostic prompts, enabling the efficient adaptation of pre-trained vision-language models without the need to fine-tune the entire model. Extending this training procedure to the multi-source domain adaptation scenario, MPA [4] employs an auto-encoder to align training and target prompts while PGA [32] frames the learning from a multi-domain problem as a multi-objective optimization problem and align per-objective gradients to promote consensus across objectives. + +Contribution. While prior vision-language UDA methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from the use of base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. However, they do have limitations. First, the visual embedding distribution in the target domain may differ from the textual embedding distribution in the pre-trained models, resulting in misaligned class descriptions when relying on the "over-generalized" nature of pre-trained models (such as CLIP zero-shot predictions) without incorporating domain- + +specific context. Secondly, previous methods primarily focus on aligning source-target prompts within the textual embedding space to refine target prompts, placing less emphasis on the representation perspective, specifically the alignment between visual and text embeddings. Moreover, we observe that source-target prompt alignment has a limited impact on target prompts (Table 1, Simple Alignment - Eq. (3): Even after alignment, the target prompt performs poorly. Further analysis is provided in Section 6.3.) + +To address these challenges, we leverage reference predictions (from source prompts) based on the relationship between source and target visual embeddings. This helps enhance pseudo-labels and facilitates target-prompt learning. Additionally, drawing inspiration from the strong clustering behavior observed between visual and textual embeddings in pre-trained multi-modal models, we enforce clustering properties in text embeddings by minimizing the Wasserstein distance [47] between the distribution of text prompts and the distribution of visual embeddings in the target domains. Our experiments and ablation studies validate the effectiveness of this approach, showing superior performance and improved quality of target prompts in terms of representation. + +# 2. Related work + +Domain Adaptation (DA) addresses the challenge of transferring knowledge learned from a source domain to a target domain, where both domains share the same label space but have different data distributions [2]. Deep domain adaptation has demonstrated impressive performance across various tasks through different approaches [55, 56]. The fundamental concept is to minimize the distributional gap between source and target domains in a shared feature space by reducing distribution divergence, commonly measured through Jensen-Shannon divergence [10, 39, 43], maximum mean discrepancy [14, 24], or Wasserstein distance [20, 38]. + +Unsupervised Domain Adaptation (UDA) presents additional challenges as the target domain is unlabeled. Early UDA methods focused on learning domain-invariant features by minimizing domain discrepancy [24, 25, 40]. For instance, DAN [24] aligns domains by minimizing maximum mean discrepancy on task-specific layers, while CORAL [40] aligns second-order statistics using linear projection. Inspired by GANs [13], adversarial learning emerged as another prominent approach. Methods like DANN [10] and CDAN [27] employ domain discriminators to distinguish source from target samples while training feature extractors to generate domain-invariant features. However, recent work has highlighted that while domain alignment can be successful, it may compromise class discrimination due to distorted semantic features [3, 41]. Several methods have attempted to address this challenge through approaches like entropy-based regularization [21] and batch nuclear-norm maximization [6]. + +Prompt Learning for Domain Adaptation. Prompt learning, initially introduced in NLP [30], has recently been adapted for vision-language models [18, 34]. Rather than fine-tuning entire networks, prompt learning enables efficient adaptation to downstream tasks by tuning prompt parameters. Such notable models as CLIP [34] have demonstrated strong visual representations through pre-training on large-scale image-text pairs. In the context of UDA, prompt learning offers a novel direction to address domain adaptation challenges [9, 33, 53]. DAPL [12] leverages CLIP's generalization capabilities to learn both domain-agnostic and domain-specific prompts, effectively balancing domain alignment and classification performance through contrastive learning. Building on this idea, MPA [4] extends prompt learning to multi-source UDA scenarios. MPA first learns from multiple source domains, then adapts the prompt learning strategy to each source-target domain pair. Prompts are aligned using a denoising auto-encoder with Euclidean distance. More recently, PGA [32] frames the multi-domain objective (including the target domain) as a multi-objective optimization problem, aligning per-objective gradients to promote consensus across objectives. PGA further incorporates gradient norm penalization to enhance prompt generalization. + +# 3. Background + +# 3.1. Unsupervised Domain Adaptation + +Given a set of $N \geq 1$ source domains $\{D_{S_i}\}_{i=1}^N$ each of which is a collection of data-label pairs of domain $i$ -th, i.e. $D_{S_i} = \{\pmb{x}_j, y_j\}_{j=1}^{N_{S_i}}$ , $y_j \in [K] := \{1, \dots, K\}$ , and one unlabeled target domain $D_T = \{\pmb{x}_j\}_{j=1}^{N_T}$ , where $N_{S_i}$ and $N_T$ are respectively the number of data points in source domain $D_{S_i}$ and target domain $D_T$ , the goal is to learn a model that can perform well on the unlabeled target domain. In this paper, we focus on classification problems and denote $K$ as the number of classes. + +# 3.2. CLIP-based Zero-Shot Classification. + +CLIP [34] is a vision-language model that consists of a visual encoder $f_{v}$ and a textual encoder $f_{t}$ , which are trained to align the visual embedding $f_{v}(\boldsymbol{x})$ of an image $\boldsymbol{x}$ with the textual embedding $f_{t}(y)$ of the corresponding label $y$ . The textual representation is derived from a manually crafted prompt $\boldsymbol{p}_{k}$ in the form "A photo of a $[\mathrm{CLASS}_k]$ ", where $[\mathrm{CLASS}_k]$ is the $k$ -th class's name. + +In zero-shot inference, $K$ class names are forwarded through the text encoder $f_{t}$ and one with the highest similarity with the visual embedding $f_{v}(x)$ is the predicted class: + +$$ +\hat {y} = \operatorname {a r g m a x} _ {k} P (y | \boldsymbol {x}, \boldsymbol {p} _ {k}) \tag {1} +$$ + +where we have defined + +$$ +P (y \mid \boldsymbol {x}, \boldsymbol {p} _ {k}) = \frac {\exp \left(\left\langle f _ {v} (\boldsymbol {x}), f _ {t} \left(\boldsymbol {p} _ {k}\right) \right\rangle / \gamma\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \exp \left(\left\langle f _ {v} (\boldsymbol {x}), f _ {t} \left(\boldsymbol {p} _ {k ^ {\prime}}\right) \right\rangle / \gamma\right)}, \tag {2} +$$ + +$\langle ., \cdot \rangle$ measures cosine similarity and $\gamma$ is the temperature. + +# 3.3. Domain Adaptation via Prompt Learning + +Prompt Design. A common assumption in domain adaptation literature is that each domain can be represented by domain-specific features - which are found/presented only in this particular domain and domain-invariant features - which are shared with others [4, 32]. + +To reflect this, prompt-learning-based approaches as [4, 32] utilize two sets of prompts for each domain $D_{S_i}$ : domain-invariant prompt $\pmb{P}_{sh}$ shared among all domains and domain-specific prompt $\pmb{P}_{S_i}$ specific to the domain $D_{S_i}$ . Similarly, the target domain $D_T$ will be represented by $\pmb{P}_{sh}$ and $\pmb{P}_T$ prompts. More specifically, following [4], we do not just use single but multiple domain-invariant prompts $\{\pmb{P}_{sh}^k\}_{k=1}^K$ , where each $\pmb{P}_{sh}^k = [\pmb{v}_1^k | \pmb{v}_2^k| \dots | \pmb{v}_{M_1}^k]$ is a shared prompt among all domains and specific to class $k$ -th. For domain-specific prompts $\pmb{P}_{S_i}$ and $\pmb{P}_T$ , which are not shared among domains, are represented by $M_2$ tokens, i.e., $\pmb{P}_{S_i} = [\pmb{u}_1^{S_i} | \pmb{u}_2^{S_i} | \dots | \pmb{u}_{M_2}^{S_i}]$ , $\pmb{P}_T = [\pmb{u}_1^T | \pmb{u}_2^T | \dots | \pmb{u}_{M_2}^T]$ . Based on this, a prompt $p_k = [\pmb{P}_{sh}^k][\pmb{P}_{S_i}][\mathrm{CLASS}_k]$ is to represent the predictive distribution of a sample of source domain $D_{S_i}$ belong to class $k$ , and similarly $p_k = [\pmb{P}_{sh}^k][\pmb{P}_T][\mathrm{CLASS}_k]$ for that of a target sample. + +UDA via Prompt Learning with CLIP-Pseudo-Label. To transfer knowledge from source domains to the target domain, [4] proposed to fine-tune these prompts $P_{sh}$ , $P_{S_i}$ , $P_T$ , simultaneously, where $P_{sh}$ captures the shared predictive features among domains while the prompts $P_{S_i}$ , $P_T$ capture unique characteristics of each domain, by optimizing the objective: + +$$ +\mathcal {L} _ {\text {t o t a l}} (\boldsymbol {P}) = \sum_ {i = 1} ^ {N} \mathcal {L} _ {S _ {i}} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}\right) + \mathcal {L} _ {T} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}\right), \tag {3} +$$ + +where objectives for source domains are defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {S _ {i}} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}\right) = \operatorname {C E} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}; \boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\right) \\ = - \frac {1}{N _ {S _ {i}}} \sum_ {j = 1} ^ {N _ {S _ {i}}} \log P (y = y _ {j} | \boldsymbol {x} _ {j}, \boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}), \text {a n d} \\ \end{array} +$$ + +For target domain, since labels are not available in the target domain, previous approaches, such as DAPL [12], MPA [4], and PGA [32], use pre-trained CLIP models to generate pseudo-labels $\hat{y}$ as in Eq. (1) for the target domain to train target classifiers and learn both domain-invariant and + +domain-specific prompts. Therefore, the objective for the target domain is as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {T} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}\right) = \mathrm {C E} _ {\alpha} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}; \boldsymbol {X} _ {T}, Y _ {T}\right) \\ = - \frac {1}{N _ {T}} \sum_ {j = 1} ^ {N _ {T}} \mathbb {I} _ {\left(P \left(y = \hat {y} _ {j} \mid \boldsymbol {x} _ {j}\right) \geq \alpha\right)} \log P (y = \hat {y} _ {j} \mid \boldsymbol {x} _ {j}, \boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}) \\ \end{array} +$$ + +The target objective is applied to target samples for which the zero-shot prediction confidence from CLIP exceeds a threshold $\alpha$ . It is evident that when there is a significant covariate shift between the target domain and the dataset used to train the CLIP models, the accuracy of the pseudo-labels decreases markedly. For instance, as shown in Table 1, the accuracy of CLIP's zero-shot predictions varies significantly across domains in the OfficeHome dataset. This limitation forms one of the motivations for our approach, as presented in the following sections. + +
SettingInferenceArClPrRw
Training on source data only
Zero-shot fromCLIP [34]71.250.481.482.6
Source-combinedSource prompt72.255.982.683.3
Multi-sourceAverage prompt74.357.484.584.7
Ar prompt-56.080.082.1
Cl prompt70.4-81.180.4
Pr prompt70.255.0-84.1
Wr prompt73.955.584.5-
Supervised training on target domain only
Target prompt99.691.699.398.6
Traininging both source-target domains as Eq. (3)
Target prompt47.629.053.563.5
Source prompt74.357.284.384.8
+ +Table 1. Analyses of prompts performance on OfficeHome dataset. Source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications. + +# 4. Motivations + +Limitations of existing pseudo-label guidance. As described above, we design shared or domain-invariant prompts $P_{sh}$ to capture embeddings that are consistent across both source and target domains, while we use domain-specific prompts $P_{S_i}$ to capture unique characteristics of each source domain. The domain-invariant prompts $P_{sh}$ enable learning of shared knowledge across source domains, which can then be transferred to the target domain. Additionally, to train both domain-invariant prompts $P_{sh}$ and target-specific prompts $P_T$ with a focus on the target domain, most recent + +![](images/dfd3854966f17cdbaa4a795334c298c6ce86b749fa20c8d445214832d439d84a.jpg) + +Pretrained Visual-embedding Distribution + +Domain Visual-embedding Distribution + +Refine Target Prompt Based on Pseudo-Label + +![](images/959a13ca01eca6f45dd1539db64b5f48fdbc72e99557f0d564dce37e25dc4e36.jpg) +(a) Target prompt refinement. +(Same class from different domains) +Figure 1. (a) Target-domain prompt refinement. Pre-trained models are trained on large-scale datasets, which are assumed to fully or partially cover the data distribution of downstream tasks. For example, "dog with style domain $S_{1,\dots,3,T}$ " can be viewed as subdomains of "dog". However, the visual embedding distribution in training may shift from that of the pretraining distribution, causing class descriptions without domain-specific context to become misaligned. This shift necessitates alignment using domain-specific contexts. While the source domain can leverage labeled data to refine its domain-specific context, the target domain lacks this advantage. A common approach to address this limitation is to incorporate domain-specific contexts and leverage zero-shot predictions from the CLIP model to guide alignment between domain-specific contexts and visual-representation in the target domain. (b) Effect of incorrect pseudo-label. Behavior of prompt learning with incorrect pseudo-labels in a supervised manner on the target domain. The flat regions in gray and orange represent areas in the embedding space corresponding to different classes, each centered on its optimal domain-specific prompt embedding (with class "dog" in orange and other classes in blue). Red points indicate samples from class "dog" with correct pseudo-labels, while black points represent samples from class "dog" that have been incorrectly pseudo-labeled. Additionally, some samples from regions belonging to other classes (gray areas) are mislabeled as class "dog", shown as black points with red borders. The text embeddings learned from these pseudo-labels fail to align well with the true target embeddings; instead, they form a cluster around a single point—the centroid of all samples labeled as class "dog" (both correctly and incorrectly labeled)—remaining distant from the actual target embeddings. + +![](images/ed933587a7fa1f08db98d7f92d9285b0552291e4f8302fb5f9fe234d151f7733.jpg) + +Class description with based Prompts (A photo of a dog) + +![](images/188ba586e08ec0d4354ef4c273aebe640a70b95fc14f4577f205b9469d838ef2.jpg) + +Learnable Source-domain Prompts + +![](images/7006a8d06a9c0eb29348b28e0a09d386233c04316ff5b69c7107ba21138ea4df.jpg) + +Learnable Target-domain Prompt + +![](images/87d0cf5e9349f6128d26287a877a6604ec9a03597e23c6ff9fbd2b35ce09bf78.jpg) +(b) Effect of wrong Pseudo-label. + + +state-of-the-art approaches [12, 32] leverage pseudo-labels obtained through zero-shot inference using CLIP models. However, we argue that generating reliable and accurate pseudo-labels can be challenging when relying on zero-shot predictions from CLIP models, particularly if there is a significant covariate shift between the target domain and the dataset on which the CLIP models were trained. Furthermore, pseudo-labels are crucial for guiding the target text embeddings $\tau_T^k$ for each class $k$ by aligning them with the visual embeddings from the corresponding target class. This raises the question: How can we enhance these critical pseudo-labels to improve the target target prompt? + +Enhancing pseudo-labels using source prompts. When training the source and target prompt, we use domain-invariant prompts $P_{sh}$ shared across both source and target domains to capture the domain-invariant embeddings common to data in both domains. As a result, the source + +prompts can encapsulate domain-invariant embeddings of the target data. Additionally, the source and target data share certain common embeddings, making it reasonable to utilize source prompts to generate pseudo-labels for the target domain. To illustrate the advantage of using aggregated source prompts over standalone CLIP models in generating more accurate pseudo-labels, we conduct experiments on the Office-Home dataset. Table 1 (Training on source data only setting) presents the accuracies of the average aggregated source prompts (multi-source) and single source prompt (source combined) on the target domain, where only source prompts are used for predictions. The results indicate that aggregated source prompts produce more accurate pseudo-labels, hence further improving predictions. This observation aligns with our motivation and supports the proposed approach. Additionally, the transferability of different source domains to the target domain varies based on their similarity (Table 1: Training on source data only: Multi-source). This observation + +motivates the design of a distance-aware transfer strategy to combine references from source prompts and base prompt for generating more accurate pseudo-labels, as detailed in Section 5.2. + +Furthermore, we observe that while more accurate pseudo-labels help guide the text embeddings more effectively toward their class clusters, they still introduce inaccuracies. These inaccuracies cause the text embeddings to skew toward regions of correct pseudo-labels within their clusters, as illustrated in Figure 1, ultimately compromising performance on entire clusters. Thus, it is essential to introduce an additional component to correct this bias and maintain consistent predictions across clusters. + +Clustering preservation prediction. According to the clustering assumption, data tend to be organized into clusters. To verify this assumption for visual embeddings from CLIP models, we assume we have labels for the target domain and train a target prompt using only class-specific target prompts (i.e., $[P_T^k][CLASS_k]$ ) on the target domain. This setup implies that for each class $k$ , we rely on a single text embedding, $\tau_T^k$ , to represent its visual embeddings. The high accuracies obtained, as shown in Table 1 (supervised training on target domain only), demonstrate that the visual embeddings for each class using CLIP models tend to form a single cluster in the embedding space. + +Although using source prompts to generate pseudo-label guidance for the target prompt outperforms zero-shot predictions from CLIP models, incorrect pseudo-labels or the absence of pseudo-label guidance may still occur for lower-confidence predictions. Consequently, in the cluster for class $k$ in the target domain, there are visual embeddings with correct pseudo-labels and those with incorrect or missing pseudo-labels (shown in black in Figure 1b). As a result, the text embedding $\tau_T^k$ for this class acts as a prototype or centroid for the red visual embeddings but may fail to represent the entire cluster for class $k$ . This limitation could lead to incorrect predictions for the black visual embeddings and potential confusion with visual embeddings from other classes. To obtain text embeddings $\tau_T^k$ that effectively represent the entire cluster for each class $k$ and ensure clustering-preserving predictions, we adopt the clustering viewpoint of optimal transport [28, 48]. Specifically, our objective is to minimize the optimal transport (Wasserstein-WS) distance between the distribution of visual embeddings in the target domain and the distribution of the text embeddings $\tau_T^k$ . As demonstrated in Lemma 1, the text embeddings $\tau_T^k$ act as prototypes or centroids of the clusters, leading to an alignment correction for the text embeddings, as shown in Figure 2. Moreover, minimizing the WS distance adjusts the text embeddings $\tau_T^k$ to serve as accurate cluster centroids, while the pseudo-label guidance aids in aligning these embeddings with their correct class- $k$ clusters. + +# 5. Proposed Method + +Notation: Since our method focuses on analyzing the representations; for simplicity, we denote $\pmb{\tau}_{S_i}^k$ as the text embedding of the source domain-specific prompt, given by $\pmb{\tau}_{S_i}^k = f_t\left([P_{sh}^k][P_{S_i}][\mathrm{CLASS}_k]\right)$ . Similarly, $\pmb{\tau}_T^k = f_t\left([P_{sh}^k][P_T][\mathrm{CLASS}_k]\right)$ and $\pmb{\tau}_{base}^k = f_t\left("A photo of a [CLASS_k]"\right)$ as the text embeddings of the target prompt and base prompt, respectively. + +# 5.1. Prompt Learning with Source Domains + +Because labels are available in all source domains, we apply the cross-entropy loss to fine-tune these associated prompts $P_{sh}, P_{Si}$ with the source-domain objective loss: + +$$ +\mathcal {L} _ {S} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathcal {L} _ {S _ {i}} \tag {4} +$$ + +where we have defined + +$$ +\begin{array}{l} \mathcal {L} _ {S _ {i}} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}\right) = \mathrm {C E} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}; \boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\right) \\ = - \frac {1}{N _ {S _ {i}}} \sum_ {j = 1} ^ {N _ {S _ {i}}} \log P (y = y _ {j} | \boldsymbol {x} _ {j}, \boldsymbol {P} _ {s h}, \boldsymbol {P} _ {S _ {i}}) \tag {5} \\ \end{array} +$$ + +# 5.2. Prompt Learning with Target Domain + +Pseudo-label Enhancement. Building on our motivation, we enhance the quality of pseudo-labels from zero-shot predictions on the target domain by incorporating predictions from the source domains. Specifically, we calculate the weighted average cosine distance from the visual embedding $\mathbf{z} = f_v(\mathbf{x})$ to the text embeddings of each class across all source domains. We then average this result with the text embedding from the base prompt as follows: + +$$ +\hat {y} [ k ] = \frac {\exp \left(\langle \boldsymbol {z} , \boldsymbol {\tau} _ {a v e} ^ {k} ((x)) \rangle / \gamma\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \exp \left(\langle \boldsymbol {z} , \boldsymbol {\tau} _ {a v e} ^ {k ^ {\prime}} (x) \rangle / \gamma\right)} \tag {6} +$$ + +where we have defined + +$$ +\boldsymbol {\tau} _ {a v e} ^ {k} (x) = \frac {1}{2} \boldsymbol {\tau} _ {b a s e} ^ {k} + \frac {w _ {k , i} (x)}{2} \sum_ {i = 1} ^ {N} \boldsymbol {\tau} _ {S _ {i}} ^ {k} \tag {7} +$$ + +and $w_{i,k}$ is the important weight for each domain-class. + +As discussed in Section 4, to compute $w_{k,i}(x)$ , we use the $l_2$ distance between the visual embedding $z^{pre}$ (the unnormalized visual embedding of $x$ , where $z = \frac{z^{pre}}{\|z^{pre}\|_2}$ ) and the centroid of class $k$ in domain $i$ . Let $C^i = \{c_k^i\}_{k=1}^K$ represent the set of class centroids for the $i$ -th domain i.e., $c_k^i = \frac{1}{\sum_{j=1}^{N_{S_i}} \mathbb{I}_{(y_j^i = k)}} \sum_{j=1}^{N_{S_i}} \mathbb{I}_{(y_j^i = k)} z_j^{pre,i}$ . The weight for class $k$ is then calculated by applying the softmax function: + +$$ +w _ {i, k} (z) = \frac {\exp \left(\left\| z _ {p r e} - c _ {k} ^ {i} \right\| _ {2}\right)}{\sum_ {i ^ {\prime} = 1} ^ {N} \exp \left(\left\| z - c _ {k} ^ {i ^ {\prime}} \right\| _ {2}\right)} \tag {8} +$$ + +Note that the weights $w_{i,k}(z)$ are applied to compute the combined prompts $\tau_{\mathrm{ave}}^k$ , rather than being applied directly to the outputs of the softmax (i.e., the predictions from individual prompts). This design preserves semantic similarity, as the magnitude of cosine similarity between the visual embedding and the text embedding of each individual prompt is taken into account in the final pseudo-label. Meanwhile, the weights $w_{k,i}(x)$ represent the spatial relationship between the visual embedding and the text embedding. + +Training target prompts with Pseudo-label Guidance. Given data sample $x_{j}$ and its corresponding enhanced pseudo-label $\hat{y}_{j}$ , we minimize the following objective function to train the target prompts: + +$$ +\begin{array}{l} \mathcal {L} _ {T} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}\right) = \mathrm {C E} _ {\tau} \left(\boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}; \boldsymbol {X} _ {T}, Y _ {T}\right) \\ = - \frac {1}{N _ {T}} \sum_ {j = 1} ^ {N _ {T}} \sum_ {k = 1} ^ {K} \hat {y} _ {j} [ k ] \log P (y = k | \boldsymbol {x} _ {j}, \boldsymbol {P} _ {s h}, \boldsymbol {P} _ {T}) \tag {9} \\ \end{array} +$$ + +# 5.3. Clustering Refined by Optimal Transport + +We propose minimizing the Wasserstein distance between the target prompts' text embeddings and the visual embeddings from the target domain. Specifically, denote $\mathcal{T} = \{\pmb{\tau}_T^k\}_{k=1}^K$ where $\pmb{\tau}_T^k$ represents the text embeddings of the context prompt $[\pmb{P}_{sh}^k][\pmb{P}_T][\mathrm{CLASS}_k]$ for class $k$ . Let $\mathbb{P}_{\tau,\pi} = \sum_{k=1}^{K}\pi_k\delta_{\tau_T^k}$ be the discrete distribution over the set of text embeddings $\mathcal{T}$ for the target domain, where the category probabilities $\pi \in \Delta_K = \{\alpha \geq 0 : \| \alpha \|_1 = 1\}$ lie in the $K$ -simplex. Additionally, let $\mathbb{P}^T = \frac{1}{N_T}\sum_{j=1}^{N_T}\delta_{z_j}$ + +represent the visual embedding distribution of the target domain, where $\delta$ is the Dirac delta function and $z = f_{v}(\pmb{x})$ for the target image $\pmb{x}$ . The clustering assumption is then enforced by the following objective: + +$$ +\mathcal {L} _ {\mathcal {W}} = \mathcal {W} _ {d _ {z}} \left(\mathbb {P} _ {\tau , \pi}, \mathbb {P} ^ {T}\right) \tag {10} +$$ + +where $d_{z}$ represents a metric function. We use the cosine distance $d_{z}(a,b) = 1 - \langle a,b\rangle$ since the visual embeddings and text embeddings already lie in the unit hypersphere. The following lemma demonstrates the behavior of $\pi$ and explains how the Wasserstein term helps target prompts enforce clustering properties. + +Lemma 1 Let $\mathcal{T}^{*} = \left\{\pmb{\tau}_{T}^{k,*}\right\}_{k=1}^{K}$ be the optimal solution of the OP in Eq. (10), then $\mathcal{T}^{*}$ is also the optimal solution of the following OP: + +$$ +\min _ {\mathcal {T}, \pi} \min _ {\sigma \in \Sigma_ {\pi}} \mathbb {E} _ {z \sim \mathbb {P} ^ {T}} \left[ d _ {z} \left(z, \tau_ {T} ^ {\sigma (z)}\right) \right], \tag {11} +$$ + +where $\Sigma_{\pi}$ is the set of assignment functions $\sigma : \mathcal{Z} \to \{1, \dots, K\}$ such that the cardinalities $|\sigma^{-1}(k)|, k = 1, \dots, K$ are proportional to $\pi_k, k = 1, \dots, K$ . Moreover, given the set of text embeddings $\mathcal{T}$ , the optimal $\sigma$ of the inner minimization is the nearest assignment: $\sigma^{-1}(k) = \{z \mid k = \operatorname{argmin}_m d_z(z, \tau_T^m)\}$ is set of visual embeddings which are quantized to $k^{th}$ text embedding $\tau_T^k$ . + +Lemma 1 indicates the aim of minimizing the Wasserstein term $\mathcal{W}_{d_z}\left(\mathbb{P}_{\tau,\pi},\mathbb{P}^T\right)$ , by adjusting the text embeddings in $\mathcal{T}$ to become the clustering centroids of the visual embeddings in the target domain, thereby minimizing the distortion between the text embeddings and target visual embeddings. Specifically, we can interpret the optimization problem in (11) as finding the optimal clustering assignment $\sigma$ , which maps each target example $z$ to the text embedding $\tau_T^{\sigma(z)}$ to minimize distortion. Moreover, given the text embeddings in $\mathcal{T}$ , the inner minimization in (11) specifies the nearest assignment by assigning each visual embedding $z$ to the closest text embedding. Furthermore, in the optimal solution, the optimal assignment $\sigma^*$ , mapping target visual embeddings to clustering centroids (i.e., text embeddings), has a valuable property: the cardinalities $\left|\left(\sigma^*\right)^{-1}(k)\right|, k = 1,\dots,K$ are proportional to $\pi_k, k = 1,\dots,K$ . We set $\pi_k = \frac{1}{K}$ for $k = 1,\dots,K$ , aiming to learn balanced clusters. + +It is important to note that the Wasserstein distance alone can shift the text embeddings toward the cluster centroids of the visual embedding distribution in the target domain. However, this may inadvertently cause the text embedding for one class (e.g., class 1) to shift to the centroid of a different class's cluster (e.g., class 2). To prevent this, pseudo-label guidance is necessary to ensure that each text embedding moves toward its correct cluster. + +Final Objective. We combine the objective functions for source prompts, target prompts, and cluster enforcement, and perform joint training as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} (\boldsymbol {P}) := \mathcal {L} _ {S} + \lambda_ {T} \mathcal {L} _ {T} + \lambda_ {\mathcal {W}} \mathcal {L} _ {\mathcal {W}} \tag {12} +$$ + +where $\lambda_T$ and $\lambda_{\mathcal{W}}$ are hyper-parameters. Here we note that in our experiments, we simply set $\lambda_T = \lambda_{\mathcal{W}} = 0.5$ . + +# 6. Experiments + +In this section, we evaluate the efficacy of our proposed method on different UDA benchmarks, following the same protocol of recent prompt-based UDA studies [4, 12, 32]. Their detailed descriptions are available in Supplementary. + +# 6.1. Experimental setup + +Metrics. Following [32], we conduct experiments in two standard settings: a source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications. + +Inference. During inference, unlike previous baselines (MPA [4], DAPL [12], PGA [32]) that utilize both source and target domain prompts for predictions, we rely solely on the target prompt to evaluate whether we have effectively learned a meaningful textual description for the target domain. Further results, discussed in Section 6.3, reveal that previous methods fail to learn high-quality target prompts, as their performance heavily depends on the quality of source prompts. This dependency is obscured by the combined use of source and target prompts during prediction. + +# 6.2. Experimental results + +In the following results, our method is referred to as "Clustering Reinforcement Prompt Learning" (CRPL). + +
ImageCLEFOffice-HomeAvg
→ C→ I→ PAvg→ Ar→ Cl→ Pr→ Rw
Zero-Shot
CLIP [34]87.988.278.788.171.250.481.482.671.4
Source Combined
DAN [10]93.392.277.687.768.559.479.082.572.4
DANN [11]93.791.877.987.868.459.179.582.772.4
D-CORAL [40]93.691.777.187.568.158.679.582.772.2
DAPL [12]96.089.276.087.172.851.982.683.772.8
Simple Prompt [4]93.690.680.988.470.752.982.983.972.4
PGA [32]94.292.178.588.274.153.984.485.674.5
CRPL (Ours)94.894.581.790.376.660.486.586.877.6
Multi-Source
DCTN [51]95.790.375.087.0N.A.N.A.N.A.N.A.N.A.
MDDA [57]N.A.N.A.N.A.N.A.66.762.379.579.671.0
SIMplDA [45]93.391.077.587.370.856.380.281.572.2
MFSAN [58]95.493.679.189.472.162.080.381.874.1
MPA [4]97.296.280.491.374.854.986.285.775.4
MPGA [32]93.895.782.890.874.856.085.286.075.5
M-CRPL (Ours)96.296.082.391.576.863.587.687.578.9
+ +Table 2 presents the results for the ImageCLEF and OfficeHome datasets. Under the source-combined scenario, our method significantly outperforms all other baseline methods on both datasets and target domain settings. For instance, CRPL surpasses the second-best source combined method by $1.9\%$ in average accuracy for ImageCLEF and $3.1\%$ in average accuracy for Office-Home. In the multi-source setting, our method delivers the highest average performance across dataset, notably outperforming MPGAs, the state-of-the-art (SOTA) prompt-based method for multi-source UDA, by a substantial margin of $3.4\%$ on Office-Home. + +On DomainNet, as shown in Table 3, we achieve superior average accuracy under both source-combined and multi-source settings, boosting the performance of pretrained CLIP by $\approx 6\%$ . We also consistently outperform other baselines on the ('Clp', 'Inf', and 'Pnt') domains across all settings, while showing competitive performance in the other three domains. This is because domains such as ('Clp', 'Inf', and 'Pnt') exhibit highly similar characteristics, whereas ('Qdr', 'Rel', and 'Skt') are significantly different, which impacts transferability from other domains. For more distinct domains, reference labels from the base prompts may be more appropriate. However, we do not have access to the + +Table 2. Accuracy (%) on ImageCLEF and Office-Home. We use bold to denote the best method overall. + +
DomainNet
→ Clp→ Inf→ Pnt→ Qdr→ Rel→ SktAvg
Zero-Shot
CLIP [34]61.342.056.110.379.354.150.5
Source Combined
DANN [11]45.513.137.013.248.931.832.6
MCD [37]54.322.145.77.658.443.538.5
DAPL [12]62.443.859.310.681.554.652.0
Simple Prompt [4]63.141.257.710.075.855.850.6
PGA [32]65.449.060.411.181.860.655.4
CRPL (Ours)65.650.866.710.680.061.155.8
Multi-Source
MPSDA-β [29]58.626.052.36.362.749.542.6
SImpAl101 [45]66.426.556.618.968.055.548.6
LtC-MSDA [49]63.128.756.116.366.153.847.4
T-SVDNet [22]66.125.054.316.565.454.647.0
PFSA [8]64.529.257.617.267.255.148.5
PTMDA [35]66.028.558.413.063.054.147.2
MPA [4]65.247.362.010.282.057.954.1
MPGA [32]67.247.863.111.681.761.055.4
M-CRPL (Ours)67.651.467.011.179.360.656.2
+ +Table 3. Accuracy (%) on DomainNet. We use **bold** to denote the best method overall. + +data used to train the base prompts, which limits our ability to establish the relationship between the target domain and the base prompts. This makes it difficult to decide when to use the base prompts or the source-enhanced prompts. As a result, we apply an average combination of the base prompt and the source-enhanced prompt, as shown in Eq. (7), to balance their contributions. + +The effectiveness of our approach is further demonstrated through 12 pairwise source-target settings on Office-Home, as shown in Table 4. While prompt-based methods using pretrained CLIP outperform traditional UDA baselines, CRPL achieves the highest average score and consistently outperforms both DAPL and PGA across all 12 settings. + +# 6.3. Ablation study + +In this section, we conduct several ablation studies on the Office-Home dataset to evaluate the effectiveness of the two key components of our proposed approach: source-enhanced pseudo-labels and clustering reinforcement, denoted as $\mathcal{L}_{\mathcal{W}}$ . We also analyze the impact of the source-target prompt alignment strategy in previous approaches. In the following, CPL refers to using hard labels obtained from CLIP's zero-shot predictions to train the target prompt; SPL refers to using enhanced pseudo-labels derived from the source domains to train the target prompt; and with $\mathcal{L}_{\mathcal{W}}$ refers to adding the optimal transport (OT) clustering to enhance performance. Additionally, we consider different scenarios, including using only the target prompt $(\tau_T)$ , averaging the source prompts $(\tau_S)$ , and averaging all prompts $(\tau_{avg})$ for inference. + +Effect of SPL. Table 5 demonstrates that SPL significantly improves the performance of CPL. Moreover, when comparing performance across different inference scenarios $(\tau_T, \tau_S, \tau_{avg})$ , it becomes evident that source-target prompt alignment in the simple baseline has a limited impact on the target + +
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg
ResNet-50[16]34.950.058.037.441.946.238.531.260.453.941.259.946.1
DANN [10]45.659.370.147.058.560.946.143.768.563.251.876.857.6
JAN [25]45.961.268.950.459.761.045.843.470.363.952.476.858.3
CDAN+E [27]50.770.676.057.670.070.057.450.977.370.956.781.665.8
BSP+CDAN [5]52.068.676.158.070.370.258.650.277.672.259.381.966.3
SymNets [54]47.772.978.564.271.374.263.647.679.473.850.882.667.2
ETD [21]51.371.985.757.669.273.757.851.279.370.257.582.167.3
BNM [6]52.373.980.063.372.974.961.749.579.770.553.682.267.9
GSDA [17]61.376.179.465.473.374.365.053.280.072.260.683.170.3
GVB-GD [7]57.074.779.864.674.174.665.255.181.074.659.784.370.4
RSDA-MSTN [15]53.277.781.366.474.076.567.953.082.075.857.885.470.9
SPL [50]54.577.881.965.178.081.166.053.182.869.955.386.071.0
SRDC [41]52.376.381.069.576.278.068.753.881.776.357.185.071.3
DisClusterDA [42]58.877.080.867.074.677.165.956.381.474.260.583.671.4
CLIP [34]51.681.982.671.981.982.671.951.682.671.951.681.972.0
DAPL [12]52.782.284.173.982.083.873.654.684.073.353.482.573.3
PGA [32]53.783.985.073.283.984.673.253.884.173.553.185.373.9
CRPL (Ours)54.784.184.674.383.283.773.753.484.674.555.585.574.4
+ +Table 4. Accuracy (%) on Office-Home[46] for unsupervised domain adaptation (ResNet-50[16]). The best accuracy is indicated in bold. + +
Inference PromptArClPrRw
CPLτT47.629.053.563.5
τS74.357.284.384.8
τavg61.240.373.377.8
SPLτT75.862.986.687.2
τS73.357.483.484.7
τavg75.858.183.685.3
CPL onlyτT47.629.053.563.5
CPL with LwτT7.94.780.482.3
SPL onlyτT75.862.986.687.2
SPL with LwτT76.863.587.587.6
+ +prompt, as evidenced by the significantly lower accuracy in $\tau_{T}$ compared to $\tau_{S}$ . In contrast, SPL enables the target domain to learn text embeddings that effectively capture and represent the corresponding visual embeddings. + +Effect of clustering reinforcement $\mathcal{L}_{\mathcal{W}}$ . Table 5 (last four rows) shows that clustering reinforcement $\mathcal{L}_{\mathcal{W}}$ further improves the performance of SPL. However, applying $\mathcal{L}_{\mathcal{W}}$ to the simple baseline reveals noticeable differences in CPL performance over target domains. Specifically, it seems that the effectiveness of $\mathcal{L}_{\mathcal{W}}$ strongly depends on the initial predictions, where weak initial predictions as observed in the CPL method on 'Ar' and 'Cl' domains with just $47.6\%$ and $29.0\%$ , leading to a collapse performance of accuracy less than $8\%$ when combing with $\mathcal{L}_{\mathcal{W}}$ . However, with better initial predictions as observed in the CPL method on 'Pr' and 'Rw' domains, substantial improvement of $27\%$ ( $53.5\%$ to $80.4\%$ ) and $19\%$ ( $63.5\%$ to $82.3\%$ ) when combined with $\mathcal{L}_{\mathcal{W}}$ are observed. This indicates a mutual benefit between source-enhanced pseudo-labels and clustering reinforcement. + +Effect of Source-Target Prompts Alignment. We have shown that source-target prompt alignment has a limited impact on the target prompt. To further validate this, we analyze the performance of prompts from the most recent + +Table 5. Effect of source-enhanced pseudo-labels and clustering reinforcement on the Office-Home dataset. + +
SettingInference PromptArClPrRw
PGAτT72.352.883.782.4
τS73.856.284.684.9
τavg75.657.086.086.6
M-CRPL (ours)τT76.863.587.587.6
τS75.358.083.984.7
τavg75.858.685.285.3
+ +Table 6. Analyses of prompts performance on OfficeHome dataset. + +SOTA method, PGA [32], which focuses on the source-target prompt strategy. As shown in Table 6, while PGA improves the performance of $\tau_{T}$ , bringing it closer to the performance of the source prompts $\tau_{S}$ , it does not surpass them. This result confirms the limitations of the alignment strategy. In contrast, for M-CRPL, $\tau_{T}$ achieves the best performance for target prompts across all three scenarios, demonstrating the effectiveness of using enhanced pseudo-labels from source domains to refine target prompts in terms of representation. + +# 7. Conclusion + +We propose a framework for prompt learning UDA that begins by leveraging information from the source domains to enhance pseudo-labels for training target prompts. We demonstrate that while source-target prompt alignment has a limited effect on learning the target prompt, enhanced pseudo-labels result in significant improvements in both performance and the quality of target prompts in terms of representation. Additionally, inspired by the strong clustering behavior observed between visual and text embeddings in pre-trained models, we further refine target prompts by enforcing clustering properties. This is achieved by minimizing the Wasserstein distance between the distribution of text prompts and the distribution of visual embeddings in the target domains. Finally, our experiments and ablation studies validate the superior performance of our approach. + +# Acknowledgements + +This work was supported by ARC DP23 grant DP230101176 and by the Air Force Office of Scientific Research under award number FA2386-23-1-4044. + +# References + +[1] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. 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While these methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. Thus, the training mechanism exhibits a key limitation wherein the visual embedding distribution in target domains can deviate from the visual embedding distribution in the pre-trained model, leading to misguided signals from class descriptions. This work introduces a fresh solution to reinforce these pseudo-labels and facilitate target-prompt learning, by exploiting the geometry of visual and text embeddings - an aspect that is overlooked by existing methods. We first propose to directly leverage the reference predictions (from source prompts) based on the relationship between source and target visual embeddings. We later show that there is a strong clustering behavior observed between visual and text embeddings in pre-trained multi-modal models. Building on optimal transport theory, we transform this insight into a novel strategy to enforce the clustering property in text embeddings, further enhancing the alignment in the target domain. Our experiments and ablation studies validate the effectiveness of the proposed approach, demonstrating superior performance and improved quality of target prompts in terms of representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 621, + 135, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 621, + 135, + 634 + ], + "spans": [ + { + "bbox": [ + 56, + 621, + 135, + 634 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 641, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 297, + 715 + ], + "type": "text", + "content": "Significant advancements of deep learning have consistently enhanced performance on various tasks, albeit primarily within the confines of training data distributions. Therefore, deep models notoriously fail to maintain their performance when applied to new, unseen domains [19, 23, 36, 52]. Unsupervised domain adaptation (UDA) offers a promising solu" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 228, + 555, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 555, + 384 + ], + "type": "text", + "content": "tion by utilizing labeled data from a source domain alongside unlabeled data from a target domain, thus circumventing the costly and labor-intensive process of annotating new domain data. In recent years, many domain adaptation methods have been proposed, typically focusing on learning invariant features across domains, as motivated by the theoretical analysis by Ben-David et al. [1, 2]. These methods generally (i) minimize the discrepancy between feature representations across domains [24, 25, 31, 40] or (ii) adversarially learn indistinguishable representations to fool a domain discriminator [10, 11, 26, 44]. However, focusing on aligning representations can inadvertently compromise model performance by diminishing discriminative features [12, 41]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 384, + 556, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 556, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 556, + 576 + ], + "type": "text", + "content": "Recent developments have demonstrated the potential of leveraging pre-trained models such as CLIP [34] for the UDA problem, significantly bridging domain gaps and enhancing generalization. These benefits arise from the rich semantic and robust visual representations gained through extensive pre-training across diverse image-text datasets. Building on this approach, DAPL [12] innovatively introduces domain-specific and domain-agnostic prompts, enabling the efficient adaptation of pre-trained vision-language models without the need to fine-tune the entire model. Extending this training procedure to the multi-source domain adaptation scenario, MPA [4] employs an auto-encoder to align training and target prompts while PGA [32] frames the learning from a multi-domain problem as a multi-objective optimization problem and align per-objective gradients to promote consensus across objectives." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": "Contribution. While prior vision-language UDA methods achieve state-of-the-art performance across benchmarks, much of the improvement stems from the use of base pseudolabels (CLIP zero-shot predictions) and self-training mechanisms. However, they do have limitations. First, the visual embedding distribution in the target domain may differ from the textual embedding distribution in the pre-trained models, resulting in misaligned class descriptions when relying on the \"over-generalized\" nature of pre-trained models (such as CLIP zero-shot predictions) without incorporating domain-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19974" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 179 + ], + "type": "text", + "content": "specific context. Secondly, previous methods primarily focus on aligning source-target prompts within the textual embedding space to refine target prompts, placing less emphasis on the representation perspective, specifically the alignment between visual and text embeddings. Moreover, we observe that source-target prompt alignment has a limited impact on target prompts (Table 1, Simple Alignment - Eq. (3): Even after alignment, the target prompt performs poorly. Further analysis is provided in Section 6.3.)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 180, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 180, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 180, + 296, + 335 + ], + "type": "text", + "content": "To address these challenges, we leverage reference predictions (from source prompts) based on the relationship between source and target visual embeddings. This helps enhance pseudo-labels and facilitates target-prompt learning. Additionally, drawing inspiration from the strong clustering behavior observed between visual and textual embeddings in pre-trained multi-modal models, we enforce clustering properties in text embeddings by minimizing the Wasserstein distance [47] between the distribution of text prompts and the distribution of visual embeddings in the target domains. Our experiments and ablation studies validate the effectiveness of this approach, showing superior performance and improved quality of target prompts in terms of representation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 346, + 139, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 346, + 139, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 139, + 358 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 366, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 296, + 498 + ], + "type": "text", + "content": "Domain Adaptation (DA) addresses the challenge of transferring knowledge learned from a source domain to a target domain, where both domains share the same label space but have different data distributions [2]. Deep domain adaptation has demonstrated impressive performance across various tasks through different approaches [55, 56]. The fundamental concept is to minimize the distributional gap between source and target domains in a shared feature space by reducing distribution divergence, commonly measured through Jensen-Shannon divergence [10, 39, 43], maximum mean discrepancy [14, 24], or Wasserstein distance [20, 38]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 498, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 296, + 713 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation (UDA) presents additional challenges as the target domain is unlabeled. Early UDA methods focused on learning domain-invariant features by minimizing domain discrepancy [24, 25, 40]. For instance, DAN [24] aligns domains by minimizing maximum mean discrepancy on task-specific layers, while CORAL [40] aligns second-order statistics using linear projection. Inspired by GANs [13], adversarial learning emerged as another prominent approach. Methods like DANN [10] and CDAN [27] employ domain discriminators to distinguish source from target samples while training feature extractors to generate domain-invariant features. However, recent work has highlighted that while domain alignment can be successful, it may compromise class discrimination due to distorted semantic features [3, 41]. Several methods have attempted to address this challenge through approaches like entropy-based regularization [21] and batch nuclear-norm maximization [6]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 348 + ], + "type": "text", + "content": "Prompt Learning for Domain Adaptation. Prompt learning, initially introduced in NLP [30], has recently been adapted for vision-language models [18, 34]. Rather than fine-tuning entire networks, prompt learning enables efficient adaptation to downstream tasks by tuning prompt parameters. Such notable models as CLIP [34] have demonstrated strong visual representations through pre-training on large-scale image-text pairs. In the context of UDA, prompt learning offers a novel direction to address domain adaptation challenges [9, 33, 53]. DAPL [12] leverages CLIP's generalization capabilities to learn both domain-agnostic and domain-specific prompts, effectively balancing domain alignment and classification performance through contrastive learning. Building on this idea, MPA [4] extends prompt learning to multi-source UDA scenarios. MPA first learns from multiple source domains, then adapts the prompt learning strategy to each source-target domain pair. Prompts are aligned using a denoising auto-encoder with Euclidean distance. More recently, PGA [32] frames the multi-domain objective (including the target domain) as a multi-objective optimization problem, aligning per-objective gradients to promote consensus across objectives. PGA further incorporates gradient norm penalization to enhance prompt generalization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 367, + 392, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 367, + 392, + 380 + ], + "spans": [ + { + "bbox": [ + 314, + 367, + 392, + 380 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 389, + 497, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 497, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 497, + 403 + ], + "type": "text", + "content": "3.1. Unsupervised Domain Adaptation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": "Given a set of " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "N \\geq 1" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " source domains " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "\\{D_{S_i}\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " each of which is a collection of data-label pairs of domain " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": "-th, i.e. " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "D_{S_i} = \\{\\pmb{x}_j, y_j\\}_{j=1}^{N_{S_i}}" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "y_j \\in [K] := \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": ", and one unlabeled target domain " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "D_T = \\{\\pmb{x}_j\\}_{j=1}^{N_T}" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "N_{S_i}" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "N_T" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " are respectively the number of data points in source domain " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "D_{S_i}" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " and target domain " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "D_T" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": ", the goal is to learn a model that can perform well on the unlabeled target domain. In this paper, we focus on classification problems and denote " + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 409, + 556, + 521 + ], + "type": "text", + "content": " as the number of classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 537, + 511, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 537, + 511, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 537, + 511, + 550 + ], + "type": "text", + "content": "3.2. CLIP-based Zero-Shot Classification." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": "CLIP [34] is a vision-language model that consists of a visual encoder " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " and a textual encoder " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": ", which are trained to align the visual embedding " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "f_{v}(\\boldsymbol{x})" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " of an image " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " with the textual embedding " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "f_{t}(y)" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " of the corresponding label " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": ". The textual representation is derived from a manually crafted prompt " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "\\boldsymbol{p}_{k}" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " in the form \"A photo of a " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "[\\mathrm{CLASS}_k]" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": "\", where " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "[\\mathrm{CLASS}_k]" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 558, + 555, + 642 + ], + "type": "text", + "content": "-th class's name." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "text", + "content": "In zero-shot inference, " + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "text", + "content": " class names are forwarded through the text encoder " + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "text", + "content": " and one with the highest similarity with the visual embedding " + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "inline_equation", + "content": "f_{v}(x)" + }, + { + "bbox": [ + 313, + 644, + 556, + 681 + ], + "type": "text", + "content": " is the predicted class:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 383, + 701, + 555, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 701, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 383, + 701, + 555, + 715 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\operatorname {a r g m a x} _ {k} P (y | \\boldsymbol {x}, \\boldsymbol {p} _ {k}) \\tag {1}", + "image_path": "d8da294ff8b1ca68b64a1cb4dba15b8fd46f16261508dcf512022289c16c2b93.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19975" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "type": "text", + "content": "where we have defined" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 77, + 91, + 296, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 91, + 296, + 121 + ], + "spans": [ + { + "bbox": [ + 77, + 91, + 296, + 121 + ], + "type": "interline_equation", + "content": "P (y \\mid \\boldsymbol {x}, \\boldsymbol {p} _ {k}) = \\frac {\\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k}\\right) \\right\\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\left\\langle f _ {v} (\\boldsymbol {x}), f _ {t} \\left(\\boldsymbol {p} _ {k ^ {\\prime}}\\right) \\right\\rangle / \\gamma\\right)}, \\tag {2}", + "image_path": "be54c5b4a9229addefd632359916e9cbba1eabf9eebfe5005073304e9c73bfdd.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "type": "inline_equation", + "content": "\\langle ., \\cdot \\rangle" + }, + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "type": "text", + "content": " measures cosine similarity and " + }, + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 129, + 286, + 141 + ], + "type": "text", + "content": " is the temperature." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 148, + 272, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 148, + 272, + 162 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 272, + 162 + ], + "type": "text", + "content": "3.3. Domain Adaptation via Prompt Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 167, + 296, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 167, + 296, + 226 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 296, + 226 + ], + "type": "text", + "content": "Prompt Design. A common assumption in domain adaptation literature is that each domain can be represented by domain-specific features - which are found/presented only in this particular domain and domain-invariant features - which are shared with others [4, 32]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": "To reflect this, prompt-learning-based approaches as [4, 32] utilize two sets of prompts for each domain " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "D_{S_i}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ": domain-invariant prompt " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{sh}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " shared among all domains and domain-specific prompt " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{S_i}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " specific to the domain " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "D_{S_i}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ". Similarly, the target domain " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "D_T" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " will be represented by " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{sh}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_T" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " prompts. More specifically, following [4], we do not just use single but multiple domain-invariant prompts " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\{\\pmb{P}_{sh}^k\\}_{k=1}^K" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{sh}^k = [\\pmb{v}_1^k | \\pmb{v}_2^k| \\dots | \\pmb{v}_{M_1}^k]" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " is a shared prompt among all domains and specific to class " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": "-th. For domain-specific prompts " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{S_i}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_T" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ", which are not shared among domains, are represented by " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "M_2" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " tokens, i.e., " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{S_i} = [\\pmb{u}_1^{S_i} | \\pmb{u}_2^{S_i} | \\dots | \\pmb{u}_{M_2}^{S_i}]" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "\\pmb{P}_T = [\\pmb{u}_1^T | \\pmb{u}_2^T | \\dots | \\pmb{u}_{M_2}^T]" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ". Based on this, a prompt " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_{S_i}][\\mathrm{CLASS}_k]" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " is to represent the predictive distribution of a sample of source domain " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "D_{S_i}" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " belong to class " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": ", and similarly " + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "inline_equation", + "content": "p_k = [\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]" + }, + { + "bbox": [ + 55, + 227, + 296, + 421 + ], + "type": "text", + "content": " for that of a target sample." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": "UDA via Prompt Learning with CLIP-Pseudo-Label. To transfer knowledge from source domains to the target domain, [4] proposed to fine-tune these prompts " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_{S_i}" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_T" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": ", simultaneously, where " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": " captures the shared predictive features among domains while the prompts " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_{S_i}" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "inline_equation", + "content": "P_T" + }, + { + "bbox": [ + 55, + 436, + 296, + 520 + ], + "type": "text", + "content": " capture unique characteristics of each domain, by optimizing the objective:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 65, + 529, + 296, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 529, + 296, + 562 + ], + "spans": [ + { + "bbox": [ + 65, + 529, + 296, + 562 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) = \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) + \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right), \\tag {3}", + "image_path": "f0d85f665f8843a6fdc8306bd5a490ed57dc0b208ba9e825834e9ee1da01a748.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 571, + 264, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 571, + 264, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 571, + 264, + 582 + ], + "type": "text", + "content": "where objectives for source domains are defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 77, + 592, + 274, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 592, + 274, + 644 + ], + "spans": [ + { + "bbox": [ + 77, + 592, + 274, + 644 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\operatorname {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}), \\text {a n d} \\\\ \\end{array}", + "image_path": "e42f966b6b307d00ef55c174210dd1c8b6392afed34b51dbc5f12d5ac4d64064.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "For target domain, since labels are not available in the target domain, previous approaches, such as DAPL [12], MPA [4], and PGA [32], use pre-trained CLIP models to generate pseudo-labels " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": " as in Eq. (1) for the target domain to train target classifiers and learn both domain-invariant and" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "domain-specific prompts. Therefore, the objective for the target domain is as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 117, + 552, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 117, + 552, + 167 + ], + "spans": [ + { + "bbox": [ + 315, + 117, + 552, + 167 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\alpha} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\mathbb {I} _ {\\left(P \\left(y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}\\right) \\geq \\alpha\\right)} \\log P (y = \\hat {y} _ {j} \\mid \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\\\ \\end{array}", + "image_path": "0132869a3b4f195b2d2995e1f077bad509009c5ae3187f30a10102dca237f278.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 175, + 555, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 175, + 555, + 294 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 555, + 294 + ], + "type": "text", + "content": "The target objective is applied to target samples for which the zero-shot prediction confidence from CLIP exceeds a threshold " + }, + { + "bbox": [ + 313, + 175, + 555, + 294 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 175, + 555, + 294 + ], + "type": "text", + "content": ". It is evident that when there is a significant covariate shift between the target domain and the dataset used to train the CLIP models, the accuracy of the pseudo-labels decreases markedly. For instance, as shown in Table 1, the accuracy of CLIP's zero-shot predictions varies significantly across domains in the OfficeHome dataset. This limitation forms one of the motivations for our approach, as presented in the following sections." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 315, + 304, + 553, + 497 + ], + "blocks": [ + { + "bbox": [ + 315, + 304, + 553, + 497 + ], + "lines": [ + { + "bbox": [ + 315, + 304, + 553, + 497 + ], + "spans": [ + { + "bbox": [ + 315, + 304, + 553, + 497 + ], + "type": "table", + "html": "
SettingInferenceArClPrRw
Training on source data only
Zero-shot fromCLIP [34]71.250.481.482.6
Source-combinedSource prompt72.255.982.683.3
Multi-sourceAverage prompt74.357.484.584.7
Ar prompt-56.080.082.1
Cl prompt70.4-81.180.4
Pr prompt70.255.0-84.1
Wr prompt73.955.584.5-
Supervised training on target domain only
Target prompt99.691.699.398.6
Traininging both source-target domains as Eq. (3)
Target prompt47.629.053.563.5
Source prompt74.357.284.384.8
", + "image_path": "23ca6bf0aa0833bca9b7356d25291a10bb91af0acb91c8ccc9465f9427be5bf7.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 506, + 555, + 549 + ], + "lines": [ + { + "bbox": [ + 313, + 506, + 555, + 549 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 555, + 549 + ], + "type": "text", + "content": "Table 1. Analyses of prompts performance on OfficeHome dataset. Source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 314, + 574, + 390, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 574, + 390, + 586 + ], + "spans": [ + { + "bbox": [ + 314, + 574, + 390, + 586 + ], + "type": "text", + "content": "4. Motivations" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "Limitations of existing pseudo-label guidance. As described above, we design shared or domain-invariant prompts " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": " to capture embeddings that are consistent across both source and target domains, while we use domain-specific prompts " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "P_{S_i}" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": " to capture unique characteristics of each source domain. The domain-invariant prompts " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": " enable learning of shared knowledge across source domains, which can then be transferred to the target domain. Additionally, to train both domain-invariant prompts " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": " and target-specific prompts " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "P_T" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": " with a focus on the target domain, most recent" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19976" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 99, + 72, + 119, + 106 + ], + "blocks": [ + { + "bbox": [ + 99, + 72, + 119, + 106 + ], + "lines": [ + { + "bbox": [ + 99, + 72, + 119, + 106 + ], + "spans": [ + { + "bbox": [ + 99, + 72, + 119, + 106 + ], + "type": "image", + "image_path": "dfd3854966f17cdbaa4a795334c298c6ce86b749fa20c8d445214832d439d84a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 122, + 76, + 253, + 87 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 76, + 253, + 87 + ], + "spans": [ + { + "bbox": [ + 122, + 76, + 253, + 87 + ], + "type": "text", + "content": "Pretrained Visual-embedding Distribution" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 123, + 87, + 246, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 87, + 246, + 97 + ], + "spans": [ + { + "bbox": [ + 123, + 87, + 246, + 97 + ], + "type": "text", + "content": "Domain Visual-embedding Distribution" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 122, + 99, + 264, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 99, + 264, + 109 + ], + "spans": [ + { + "bbox": [ + 122, + 99, + 264, + 109 + ], + "type": "text", + "content": "Refine Target Prompt Based on Pseudo-Label" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 83, + 112, + 297, + 280 + ], + "blocks": [ + { + "bbox": [ + 83, + 112, + 297, + 280 + ], + "lines": [ + { + "bbox": [ + 83, + 112, + 297, + 280 + ], + "spans": [ + { + "bbox": [ + 83, + 112, + 297, + 280 + ], + "type": "image", + "image_path": "959a13ca01eca6f45dd1539db64b5f48fdbc72e99557f0d564dce37e25dc4e36.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 127, + 281, + 236, + 291 + ], + "lines": [ + { + "bbox": [ + 127, + 281, + 236, + 291 + ], + "spans": [ + { + "bbox": [ + 127, + 281, + 236, + 291 + ], + "type": "text", + "content": "(a) Target prompt refinement." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 119, + 292, + 247, + 302 + ], + "lines": [ + { + "bbox": [ + 119, + 292, + 247, + 302 + ], + "spans": [ + { + "bbox": [ + 119, + 292, + 247, + 302 + ], + "type": "text", + "content": "(Same class from different domains)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 311, + 555, + 465 + ], + "lines": [ + { + "bbox": [ + 54, + 311, + 555, + 465 + ], + "spans": [ + { + "bbox": [ + 54, + 311, + 555, + 465 + ], + "type": "text", + "content": "Figure 1. (a) Target-domain prompt refinement. Pre-trained models are trained on large-scale datasets, which are assumed to fully or partially cover the data distribution of downstream tasks. For example, \"dog with style domain " + }, + { + "bbox": [ + 54, + 311, + 555, + 465 + ], + "type": "inline_equation", + "content": "S_{1,\\dots,3,T}" + }, + { + "bbox": [ + 54, + 311, + 555, + 465 + ], + "type": "text", + "content": "\" can be viewed as subdomains of \"dog\". However, the visual embedding distribution in training may shift from that of the pretraining distribution, causing class descriptions without domain-specific context to become misaligned. This shift necessitates alignment using domain-specific contexts. While the source domain can leverage labeled data to refine its domain-specific context, the target domain lacks this advantage. A common approach to address this limitation is to incorporate domain-specific contexts and leverage zero-shot predictions from the CLIP model to guide alignment between domain-specific contexts and visual-representation in the target domain. (b) Effect of incorrect pseudo-label. Behavior of prompt learning with incorrect pseudo-labels in a supervised manner on the target domain. The flat regions in gray and orange represent areas in the embedding space corresponding to different classes, each centered on its optimal domain-specific prompt embedding (with class \"dog\" in orange and other classes in blue). Red points indicate samples from class \"dog\" with correct pseudo-labels, while black points represent samples from class \"dog\" that have been incorrectly pseudo-labeled. Additionally, some samples from regions belonging to other classes (gray areas) are mislabeled as class \"dog\", shown as black points with red borders. The text embeddings learned from these pseudo-labels fail to align well with the true target embeddings; instead, they form a cluster around a single point—the centroid of all samples labeled as class \"dog\" (both correctly and incorrectly labeled)—remaining distant from the actual target embeddings." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 319, + 72, + 331, + 83 + ], + "blocks": [ + { + "bbox": [ + 319, + 72, + 331, + 83 + ], + "lines": [ + { + "bbox": [ + 319, + 72, + 331, + 83 + ], + "spans": [ + { + "bbox": [ + 319, + 72, + 331, + 83 + ], + "type": "image", + "image_path": "ed933587a7fa1f08db98d7f92d9285b0552291e4f8302fb5f9fe234d151f7733.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 334, + 74, + 515, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 74, + 515, + 84 + ], + "spans": [ + { + "bbox": [ + 334, + 74, + 515, + 84 + ], + "type": "text", + "content": "Class description with based Prompts (A photo of a dog)" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 319, + 85, + 331, + 96 + ], + "blocks": [ + { + "bbox": [ + 319, + 85, + 331, + 96 + ], + "lines": [ + { + "bbox": [ + 319, + 85, + 331, + 96 + ], + "spans": [ + { + "bbox": [ + 319, + 85, + 331, + 96 + ], + "type": "image", + "image_path": "188ba586e08ec0d4354ef4c273aebe640a70b95fc14f4577f205b9469d838ef2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 334, + 86, + 441, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 86, + 441, + 97 + ], + "spans": [ + { + "bbox": [ + 334, + 86, + 441, + 97 + ], + "type": "text", + "content": "Learnable Source-domain Prompts" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 319, + 98, + 331, + 109 + ], + "blocks": [ + { + "bbox": [ + 319, + 98, + 331, + 109 + ], + "lines": [ + { + "bbox": [ + 319, + 98, + 331, + 109 + ], + "spans": [ + { + "bbox": [ + 319, + 98, + 331, + 109 + ], + "type": "image", + "image_path": "7006a8d06a9c0eb29348b28e0a09d386233c04316ff5b69c7107ba21138ea4df.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 334, + 99, + 438, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 99, + 438, + 109 + ], + "spans": [ + { + "bbox": [ + 334, + 99, + 438, + 109 + ], + "type": "text", + "content": "Learnable Target-domain Prompt" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 316, + 113, + 528, + 280 + ], + "blocks": [ + { + "bbox": [ + 316, + 113, + 528, + 280 + ], + "lines": [ + { + "bbox": [ + 316, + 113, + 528, + 280 + ], + "spans": [ + { + "bbox": [ + 316, + 113, + 528, + 280 + ], + "type": "image", + "image_path": "87d0cf5e9349f6128d26287a877a6604ec9a03597e23c6ff9fbd2b35ce09bf78.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 373, + 281, + 492, + 291 + ], + "lines": [ + { + "bbox": [ + 373, + 281, + 492, + 291 + ], + "spans": [ + { + "bbox": [ + 373, + 281, + 492, + 291 + ], + "type": "text", + "content": "(b) Effect of wrong Pseudo-label." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 365, + 292, + 501, + 302 + ], + "lines": [ + { + "bbox": [ + 365, + 292, + 501, + 302 + ], + "spans": [ + { + "bbox": [ + 365, + 292, + 501, + 302 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "spans": [ + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "text", + "content": "state-of-the-art approaches [12, 32] leverage pseudo-labels obtained through zero-shot inference using CLIP models. However, we argue that generating reliable and accurate pseudo-labels can be challenging when relying on zero-shot predictions from CLIP models, particularly if there is a significant covariate shift between the target domain and the dataset on which the CLIP models were trained. Furthermore, pseudo-labels are crucial for guiding the target text embeddings " + }, + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "text", + "content": " for each class " + }, + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 54, + 486, + 297, + 630 + ], + "type": "text", + "content": " by aligning them with the visual embeddings from the corresponding target class. This raises the question: How can we enhance these critical pseudo-labels to improve the target target prompt?" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 654, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 712 + ], + "type": "text", + "content": "Enhancing pseudo-labels using source prompts. When training the source and target prompt, we use domain-invariant prompts " + }, + { + "bbox": [ + 55, + 654, + 296, + 712 + ], + "type": "inline_equation", + "content": "P_{sh}" + }, + { + "bbox": [ + 55, + 654, + 296, + 712 + ], + "type": "text", + "content": " shared across both source and target domains to capture the domain-invariant embeddings common to data in both domains. As a result, the source" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 486, + 556, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 702 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 702 + ], + "type": "text", + "content": "prompts can encapsulate domain-invariant embeddings of the target data. Additionally, the source and target data share certain common embeddings, making it reasonable to utilize source prompts to generate pseudo-labels for the target domain. To illustrate the advantage of using aggregated source prompts over standalone CLIP models in generating more accurate pseudo-labels, we conduct experiments on the Office-Home dataset. Table 1 (Training on source data only setting) presents the accuracies of the average aggregated source prompts (multi-source) and single source prompt (source combined) on the target domain, where only source prompts are used for predictions. The results indicate that aggregated source prompts produce more accurate pseudo-labels, hence further improving predictions. This observation aligns with our motivation and supports the proposed approach. Additionally, the transferability of different source domains to the target domain varies based on their similarity (Table 1: Training on source data only: Multi-source). This observation" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19977" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 119 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 119 + ], + "type": "text", + "content": "motivates the design of a distance-aware transfer strategy to combine references from source prompts and base prompt for generating more accurate pseudo-labels, as detailed in Section 5.2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 297, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 297, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 297, + 228 + ], + "type": "text", + "content": "Furthermore, we observe that while more accurate pseudo-labels help guide the text embeddings more effectively toward their class clusters, they still introduce inaccuracies. These inaccuracies cause the text embeddings to skew toward regions of correct pseudo-labels within their clusters, as illustrated in Figure 1, ultimately compromising performance on entire clusters. Thus, it is essential to introduce an additional component to correct this bias and maintain consistent predictions across clusters." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "text", + "content": "Clustering preservation prediction. According to the clustering assumption, data tend to be organized into clusters. To verify this assumption for visual embeddings from CLIP models, we assume we have labels for the target domain and train a target prompt using only class-specific target prompts (i.e., " + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "inline_equation", + "content": "[P_T^k][CLASS_k]" + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "text", + "content": ") on the target domain. This setup implies that for each class " + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "text", + "content": ", we rely on a single text embedding, " + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 247, + 296, + 390 + ], + "type": "text", + "content": ", to represent its visual embeddings. The high accuracies obtained, as shown in Table 1 (supervised training on target domain only), demonstrate that the visual embeddings for each class using CLIP models tend to form a single cluster in the embedding space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": "Although using source prompts to generate pseudo-label guidance for the target prompt outperforms zero-shot predictions from CLIP models, incorrect pseudo-labels or the absence of pseudo-label guidance may still occur for lower-confidence predictions. Consequently, in the cluster for class " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " in the target domain, there are visual embeddings with correct pseudo-labels and those with incorrect or missing pseudo-labels (shown in black in Figure 1b). As a result, the text embedding " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " for this class acts as a prototype or centroid for the red visual embeddings but may fail to represent the entire cluster for class " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": ". This limitation could lead to incorrect predictions for the black visual embeddings and potential confusion with visual embeddings from other classes. To obtain text embeddings " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " that effectively represent the entire cluster for each class " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " and ensure clustering-preserving predictions, we adopt the clustering viewpoint of optimal transport [28, 48]. Specifically, our objective is to minimize the optimal transport (Wasserstein-WS) distance between the distribution of visual embeddings in the target domain and the distribution of the text embeddings " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": ". As demonstrated in Lemma 1, the text embeddings " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " act as prototypes or centroids of the clusters, leading to an alignment correction for the text embeddings, as shown in Figure 2. Moreover, minimizing the WS distance adjusts the text embeddings " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " to serve as accurate cluster centroids, while the pseudo-label guidance aids in aligning these embeddings with their correct class- " + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 391, + 296, + 713 + ], + "type": "text", + "content": " clusters." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 71, + 421, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 421, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 421, + 85 + ], + "type": "text", + "content": "5. Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "content": "Notation: Since our method focuses on analyzing the representations; for simplicity, we denote " + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}_{S_i}^k" + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "content": " as the text embedding of the source domain-specific prompt, given by " + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}_{S_i}^k = f_t\\left([P_{sh}^k][P_{S_i}][\\mathrm{CLASS}_k]\\right)" + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "content": ". Similarly, " + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}_T^k = f_t\\left([P_{sh}^k][P_T][\\mathrm{CLASS}_k]\\right)" + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}_{base}^k = f_t\\left(\"A photo of a [CLASS_k]\"\\right)" + }, + { + "bbox": [ + 313, + 91, + 556, + 189 + ], + "type": "text", + "content": " as the text embeddings of the target prompt and base prompt, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 197, + 522, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 522, + 210 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 522, + 210 + ], + "type": "text", + "content": "5.1. Prompt Learning with Source Domains" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": "Because labels are available in all source domains, we apply the cross-entropy loss to fine-tune these associated prompts " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "P_{sh}, P_{Si}" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": " with the source-domain objective loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 397, + 261, + 555, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 261, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 397, + 261, + 555, + 293 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {S _ {i}} \\tag {4}", + "image_path": "a73b63ed75164dd4c5d4c11b53a74e78a6c253bedfc3375966acb501845b3ecf.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 300, + 408, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 408, + 310 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 408, + 310 + ], + "type": "text", + "content": "where we have defined" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 343, + 321, + 555, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 321, + 555, + 372 + ], + "spans": [ + { + "bbox": [ + 343, + 321, + 555, + 372 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {S _ {i}} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}\\right) = \\mathrm {C E} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}; \\boldsymbol {X} _ {S _ {i}}, Y _ {S _ {i}}\\right) \\\\ = - \\frac {1}{N _ {S _ {i}}} \\sum_ {j = 1} ^ {N _ {S _ {i}}} \\log P (y = y _ {j} | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {S _ {i}}) \\tag {5} \\\\ \\end{array}", + "image_path": "b09d88726a98fcbf1b410a61685b48334e4e56cc125071224280b0e7e1093ee8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 383, + 515, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 515, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 515, + 396 + ], + "type": "text", + "content": "5.2. Prompt Learning with Target Domain" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 400, + 556, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 400, + 556, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 400, + 556, + 497 + ], + "type": "text", + "content": "Pseudo-label Enhancement. Building on our motivation, we enhance the quality of pseudo-labels from zero-shot predictions on the target domain by incorporating predictions from the source domains. Specifically, we calculate the weighted average cosine distance from the visual embedding " + }, + { + "bbox": [ + 313, + 400, + 556, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = f_v(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 400, + 556, + 497 + ], + "type": "text", + "content": " to the text embeddings of each class across all source domains. We then average this result with the text embedding from the base prompt as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 358, + 506, + 555, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 506, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 358, + 506, + 555, + 537 + ], + "type": "interline_equation", + "content": "\\hat {y} [ k ] = \\frac {\\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k} ((x)) \\rangle / \\gamma\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\langle \\boldsymbol {z} , \\boldsymbol {\\tau} _ {a v e} ^ {k ^ {\\prime}} (x) \\rangle / \\gamma\\right)} \\tag {6}", + "image_path": "0fcee1b3af9bc5081875071067fe501c6a98102893107c0caef7f2f4f0575d92.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 543, + 421, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 543, + 421, + 553 + ], + "spans": [ + { + "bbox": [ + 326, + 543, + 421, + 553 + ], + "type": "text", + "content": "where we have defined" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 355, + 565, + 555, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 565, + 555, + 597 + ], + "spans": [ + { + "bbox": [ + 355, + 565, + 555, + 597 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\tau} _ {a v e} ^ {k} (x) = \\frac {1}{2} \\boldsymbol {\\tau} _ {b a s e} ^ {k} + \\frac {w _ {k , i} (x)}{2} \\sum_ {i = 1} ^ {N} \\boldsymbol {\\tau} _ {S _ {i}} ^ {k} \\tag {7}", + "image_path": "946e7bc3f10ec5b46369304095f40d9f20b245fb69fed3f7c68561abad70cc79.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 604, + 551, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 604, + 551, + 615 + ], + "spans": [ + { + "bbox": [ + 326, + 604, + 551, + 615 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 326, + 604, + 551, + 615 + ], + "type": "inline_equation", + "content": "w_{i,k}" + }, + { + "bbox": [ + 326, + 604, + 551, + 615 + ], + "type": "text", + "content": " is the important weight for each domain-class." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": "As discussed in Section 4, to compute " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "w_{k,i}(x)" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": ", we use the " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "l_2" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": " distance between the visual embedding " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "z^{pre}" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": " (the unnormalized visual embedding of " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "z = \\frac{z^{pre}}{\\|z^{pre}\\|_2}" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": ") and the centroid of class " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": " in domain " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "C^i = \\{c_k^i\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": " represent the set of class centroids for the " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": "-th domain i.e., " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "c_k^i = \\frac{1}{\\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)}} \\sum_{j=1}^{N_{S_i}} \\mathbb{I}_{(y_j^i = k)} z_j^{pre,i}" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": ". The weight for class " + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 616, + 556, + 714 + ], + "type": "text", + "content": " is then calculated by applying the softmax function:" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19978" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 102, + 79, + 296, + 113 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 79, + 296, + 113 + ], + "spans": [ + { + "bbox": [ + 102, + 79, + 296, + 113 + ], + "type": "interline_equation", + "content": "w _ {i, k} (z) = \\frac {\\exp \\left(\\left\\| z _ {p r e} - c _ {k} ^ {i} \\right\\| _ {2}\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(\\left\\| z - c _ {k} ^ {i ^ {\\prime}} \\right\\| _ {2}\\right)} \\tag {8}", + "image_path": "a8909c2a34d2c713d9574a81d9ba09ca126aee7d619c3197458c206a94af1d07.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "text", + "content": "Note that the weights " + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "inline_equation", + "content": "w_{i,k}(z)" + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "text", + "content": " are applied to compute the combined prompts " + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{ave}}^k" + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "text", + "content": ", rather than being applied directly to the outputs of the softmax (i.e., the predictions from individual prompts). This design preserves semantic similarity, as the magnitude of cosine similarity between the visual embedding and the text embedding of each individual prompt is taken into account in the final pseudo-label. Meanwhile, the weights " + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "inline_equation", + "content": "w_{k,i}(x)" + }, + { + "bbox": [ + 55, + 117, + 296, + 224 + ], + "type": "text", + "content": " represent the spatial relationship between the visual embedding and the text embedding." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "text", + "content": "Training target prompts with Pseudo-label Guidance. Given data sample " + }, + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "text", + "content": " and its corresponding enhanced pseudo-label " + }, + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "inline_equation", + "content": "\\hat{y}_{j}" + }, + { + "bbox": [ + 55, + 239, + 297, + 287 + ], + "type": "text", + "content": ", we minimize the following objective function to train the target prompts:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 297, + 295, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 297, + 295, + 345 + ], + "spans": [ + { + "bbox": [ + 69, + 297, + 295, + 345 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {T} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}\\right) = \\mathrm {C E} _ {\\tau} \\left(\\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}; \\boldsymbol {X} _ {T}, Y _ {T}\\right) \\\\ = - \\frac {1}{N _ {T}} \\sum_ {j = 1} ^ {N _ {T}} \\sum_ {k = 1} ^ {K} \\hat {y} _ {j} [ k ] \\log P (y = k | \\boldsymbol {x} _ {j}, \\boldsymbol {P} _ {s h}, \\boldsymbol {P} _ {T}) \\tag {9} \\\\ \\end{array}", + "image_path": "ece84b1bdaac5486df5487fb3e11ff978eb04ca8b9d6b9be56c8642917874366.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 354, + 272, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 272, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 272, + 367 + ], + "type": "text", + "content": "5.3. Clustering Refined by Optimal Transport" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": "We propose minimizing the Wasserstein distance between the target prompts' text embeddings and the visual embeddings from the target domain. Specifically, denote " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\pmb{\\tau}_T^k\\}_{k=1}^K" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}_T^k" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " represents the text embeddings of the context prompt " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "[\\pmb{P}_{sh}^k][\\pmb{P}_T][\\mathrm{CLASS}_k]" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " for class " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_{\\tau,\\pi} = \\sum_{k=1}^{K}\\pi_k\\delta_{\\tau_T^k}" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " be the discrete distribution over the set of text embeddings " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " for the target domain, where the category probabilities " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\pi \\in \\Delta_K = \\{\\alpha \\geq 0 : \\| \\alpha \\|_1 = 1\\}" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": " lie in the " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "text", + "content": "-simplex. Additionally, let " + }, + { + "bbox": [ + 55, + 372, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{P}^T = \\frac{1}{N_T}\\sum_{j=1}^{N_T}\\delta_{z_j}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "text", + "content": "represent the visual embedding distribution of the target domain, where " + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "text", + "content": " is the Dirac delta function and " + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "inline_equation", + "content": "z = f_{v}(\\pmb{x})" + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "text", + "content": " for the target image " + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 484, + 296, + 530 + ], + "type": "text", + "content": ". The clustering assumption is then enforced by the following objective:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 127, + 539, + 295, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 539, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 127, + 539, + 295, + 554 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {W}} = \\mathcal {W} _ {d _ {z}} \\left(\\mathbb {P} _ {\\tau , \\pi}, \\mathbb {P} ^ {T}\\right) \\tag {10}", + "image_path": "62d79a37f5d3a8fc5e0a333cca0c743ea9d5e21cc923e65463a2b1b9ea3ae603.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "inline_equation", + "content": "d_{z}" + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "text", + "content": " represents a metric function. We use the cosine distance " + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "inline_equation", + "content": "d_{z}(a,b) = 1 - \\langle a,b\\rangle" + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "text", + "content": " since the visual embeddings and text embeddings already lie in the unit hypersphere. The following lemma demonstrates the behavior of " + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 55, + 562, + 297, + 634 + ], + "type": "text", + "content": " and explains how the Wasserstein term helps target prompts enforce clustering properties." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "text", + "content": "Lemma 1 Let " + }, + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^{*} = \\left\\{\\pmb{\\tau}_{T}^{k,*}\\right\\}_{k=1}^{K}" + }, + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "text", + "content": " be the optimal solution of the OP in Eq. (10), then " + }, + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^{*}" + }, + { + "bbox": [ + 55, + 640, + 297, + 685 + ], + "type": "text", + "content": " is also the optimal solution of the following OP:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 693, + 296, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 693, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 104, + 693, + 296, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathcal {T}, \\pi} \\min _ {\\sigma \\in \\Sigma_ {\\pi}} \\mathbb {E} _ {z \\sim \\mathbb {P} ^ {T}} \\left[ d _ {z} \\left(z, \\tau_ {T} ^ {\\sigma (z)}\\right) \\right], \\tag {11}", + "image_path": "1f79d595083a3ae2165087fde7762a5e803d8d1536dc2972f1ea4ca0c47f825a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\pi}" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " is the set of assignment functions " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\sigma : \\mathcal{Z} \\to \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " such that the cardinalities " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "|\\sigma^{-1}(k)|, k = 1, \\dots, K" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " are proportional to " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\pi_k, k = 1, \\dots, K" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": ". Moreover, given the set of text embeddings " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": ", the optimal " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " of the inner minimization is the nearest assignment: " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\sigma^{-1}(k) = \\{z \\mid k = \\operatorname{argmin}_m d_z(z, \\tau_T^m)\\}" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " is set of visual embeddings which are quantized to " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": " text embedding " + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "inline_equation", + "content": "\\tau_T^k" + }, + { + "bbox": [ + 313, + 72, + 554, + 157 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "spans": [ + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": "Lemma 1 indicates the aim of minimizing the Wasserstein term " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{d_z}\\left(\\mathbb{P}_{\\tau,\\pi},\\mathbb{P}^T\\right)" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ", by adjusting the text embeddings in " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " to become the clustering centroids of the visual embeddings in the target domain, thereby minimizing the distortion between the text embeddings and target visual embeddings. Specifically, we can interpret the optimization problem in (11) as finding the optimal clustering assignment " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ", which maps each target example " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " to the text embedding " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\tau_T^{\\sigma(z)}" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " to minimize distortion. Moreover, given the text embeddings in " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ", the inner minimization in (11) specifies the nearest assignment by assigning each visual embedding " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " to the closest text embedding. Furthermore, in the optimal solution, the optimal assignment " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\sigma^*" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ", mapping target visual embeddings to clustering centroids (i.e., text embeddings), has a valuable property: the cardinalities " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\left|\\left(\\sigma^*\\right)^{-1}(k)\\right|, k = 1,\\dots,K" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " are proportional to " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\pi_k, k = 1,\\dots,K" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\pi_k = \\frac{1}{K}" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "inline_equation", + "content": "k = 1,\\dots,K" + }, + { + "bbox": [ + 313, + 162, + 555, + 366 + ], + "type": "text", + "content": ", aiming to learn balanced clusters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 367, + 556, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 367, + 556, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 367, + 556, + 462 + ], + "type": "text", + "content": "It is important to note that the Wasserstein distance alone can shift the text embeddings toward the cluster centroids of the visual embedding distribution in the target domain. However, this may inadvertently cause the text embedding for one class (e.g., class 1) to shift to the centroid of a different class's cluster (e.g., class 2). To prevent this, pseudo-label guidance is necessary to ensure that each text embedding moves toward its correct cluster." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 476, + 555, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 476, + 555, + 512 + ], + "spans": [ + { + "bbox": [ + 313, + 476, + 555, + 512 + ], + "type": "text", + "content": "Final Objective. We combine the objective functions for source prompts, target prompts, and cluster enforcement, and perform joint training as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 520, + 555, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 520, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 358, + 520, + 555, + 533 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} (\\boldsymbol {P}) := \\mathcal {L} _ {S} + \\lambda_ {T} \\mathcal {L} _ {T} + \\lambda_ {\\mathcal {W}} \\mathcal {L} _ {\\mathcal {W}} \\tag {12}", + "image_path": "97e1e9c94212866bfb42c418af335faa429933efa84d2de0defb6671be851839.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_T" + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathcal{W}}" + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "text", + "content": " are hyper-parameters. Here we note that in our experiments, we simply set " + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_T = \\lambda_{\\mathcal{W}} = 0.5" + }, + { + "bbox": [ + 313, + 540, + 555, + 564 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 574, + 395, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 395, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 395, + 586 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 594, + 555, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 642 + ], + "type": "text", + "content": "In this section, we evaluate the efficacy of our proposed method on different UDA benchmarks, following the same protocol of recent prompt-based UDA studies [4, 12, 32]. Their detailed descriptions are available in Supplementary." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 648, + 429, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 429, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 429, + 661 + ], + "type": "text", + "content": "6.1. Experimental setup" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Metrics. Following [32], we conduct experiments in two standard settings: a source-combined setting, where data from all source domains are merged, and a multi-source setting, which utilizes individual domain identifications." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19979" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "type": "text", + "content": "Inference. During inference, unlike previous baselines (MPA [4], DAPL [12], PGA [32]) that utilize both source and target domain prompts for predictions, we rely solely on the target prompt to evaluate whether we have effectively learned a meaningful textual description for the target domain. Further results, discussed in Section 6.3, reveal that previous methods fail to learn high-quality target prompts, as their performance heavily depends on the quality of source prompts. This dependency is obscured by the combined use of source and target prompts during prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 199, + 176, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 199, + 176, + 212 + ], + "spans": [ + { + "bbox": [ + 55, + 199, + 176, + 212 + ], + "type": "text", + "content": "6.2. Experimental results" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 217, + 296, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 242 + ], + "type": "text", + "content": "In the following results, our method is referred to as \"Clustering Reinforcement Prompt Learning\" (CRPL)." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 55, + 251, + 298, + 407 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 298, + 407 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 298, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 298, + 407 + ], + "type": "table", + "html": "
ImageCLEFOffice-HomeAvg
→ C→ I→ PAvg→ Ar→ Cl→ Pr→ Rw
Zero-Shot
CLIP [34]87.988.278.788.171.250.481.482.671.4
Source Combined
DAN [10]93.392.277.687.768.559.479.082.572.4
DANN [11]93.791.877.987.868.459.179.582.772.4
D-CORAL [40]93.691.777.187.568.158.679.582.772.2
DAPL [12]96.089.276.087.172.851.982.683.772.8
Simple Prompt [4]93.690.680.988.470.752.982.983.972.4
PGA [32]94.292.178.588.274.153.984.485.674.5
CRPL (Ours)94.894.581.790.376.660.486.586.877.6
Multi-Source
DCTN [51]95.790.375.087.0N.A.N.A.N.A.N.A.N.A.
MDDA [57]N.A.N.A.N.A.N.A.66.762.379.579.671.0
SIMplDA [45]93.391.077.587.370.856.380.281.572.2
MFSAN [58]95.493.679.189.472.162.080.381.874.1
MPA [4]97.296.280.491.374.854.986.285.775.4
MPGA [32]93.895.782.890.874.856.085.286.075.5
M-CRPL (Ours)96.296.082.391.576.863.587.687.578.9
", + "image_path": "468f4715e6542112cd4360fa7c8cadb84dab3737e027337422b3f37f0cec9295.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "text", + "content": "Table 2 presents the results for the ImageCLEF and OfficeHome datasets. Under the source-combined scenario, our method significantly outperforms all other baseline methods on both datasets and target domain settings. For instance, CRPL surpasses the second-best source combined method by " + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "text", + "content": " in average accuracy for ImageCLEF and " + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "text", + "content": " in average accuracy for Office-Home. In the multi-source setting, our method delivers the highest average performance across dataset, notably outperforming MPGAs, the state-of-the-art (SOTA) prompt-based method for multi-source UDA, by a substantial margin of " + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 55, + 437, + 296, + 569 + ], + "type": "text", + "content": " on Office-Home." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": "On DomainNet, as shown in Table 3, we achieve superior average accuracy under both source-combined and multi-source settings, boosting the performance of pretrained CLIP by " + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\approx 6\\%" + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": ". We also consistently outperform other baselines on the ('Clp', 'Inf', and 'Pnt') domains across all settings, while showing competitive performance in the other three domains. This is because domains such as ('Clp', 'Inf', and 'Pnt') exhibit highly similar characteristics, whereas ('Qdr', 'Rel', and 'Skt') are significantly different, which impacts transferability from other domains. For more distinct domains, reference labels from the base prompts may be more appropriate. However, we do not have access to the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 316, + 71, + 553, + 256 + ], + "blocks": [ + { + "bbox": [ + 55, + 411, + 295, + 433 + ], + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 433 + ], + "type": "text", + "content": "Table 2. Accuracy (%) on ImageCLEF and Office-Home. We use bold to denote the best method overall." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 71, + 553, + 256 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 553, + 256 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 553, + 256 + ], + "type": "table", + "html": "
DomainNet
→ Clp→ Inf→ Pnt→ Qdr→ Rel→ SktAvg
Zero-Shot
CLIP [34]61.342.056.110.379.354.150.5
Source Combined
DANN [11]45.513.137.013.248.931.832.6
MCD [37]54.322.145.77.658.443.538.5
DAPL [12]62.443.859.310.681.554.652.0
Simple Prompt [4]63.141.257.710.075.855.850.6
PGA [32]65.449.060.411.181.860.655.4
CRPL (Ours)65.650.866.710.680.061.155.8
Multi-Source
MPSDA-β [29]58.626.052.36.362.749.542.6
SImpAl101 [45]66.426.556.618.968.055.548.6
LtC-MSDA [49]63.128.756.116.366.153.847.4
T-SVDNet [22]66.125.054.316.565.454.647.0
PFSA [8]64.529.257.617.267.255.148.5
PTMDA [35]66.028.558.413.063.054.147.2
MPA [4]65.247.362.010.282.057.954.1
MPGA [32]67.247.863.111.681.761.055.4
M-CRPL (Ours)67.651.467.011.179.360.656.2
", + "image_path": "68c12477955f888b9da045a6e734cec09693de53bb9955af7cd43ad60fd191a6.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 259, + 553, + 281 + ], + "lines": [ + { + "bbox": [ + 313, + 259, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 259, + 553, + 281 + ], + "type": "text", + "content": "Table 3. Accuracy (%) on DomainNet. We use **bold** to denote the best method overall." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 304, + 555, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 386 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 386 + ], + "type": "text", + "content": "data used to train the base prompts, which limits our ability to establish the relationship between the target domain and the base prompts. This makes it difficult to decide when to use the base prompts or the source-enhanced prompts. As a result, we apply an average combination of the base prompt and the source-enhanced prompt, as shown in Eq. (7), to balance their contributions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 388, + 556, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 556, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 556, + 460 + ], + "type": "text", + "content": "The effectiveness of our approach is further demonstrated through 12 pairwise source-target settings on Office-Home, as shown in Table 4. While prompt-based methods using pretrained CLIP outperform traditional UDA baselines, CRPL achieves the highest average score and consistently outperforms both DAPL and PGA across all 12 settings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 468, + 405, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 405, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 405, + 480 + ], + "type": "text", + "content": "6.3. Ablation study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": "In this section, we conduct several ablation studies on the Office-Home dataset to evaluate the effectiveness of the two key components of our proposed approach: source-enhanced pseudo-labels and clustering reinforcement, denoted as " + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": ". We also analyze the impact of the source-target prompt alignment strategy in previous approaches. In the following, CPL refers to using hard labels obtained from CLIP's zero-shot predictions to train the target prompt; SPL refers to using enhanced pseudo-labels derived from the source domains to train the target prompt; and with " + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": " refers to adding the optimal transport (OT) clustering to enhance performance. Additionally, we consider different scenarios, including using only the target prompt " + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "inline_equation", + "content": "(\\tau_T)" + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": ", averaging the source prompts " + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "inline_equation", + "content": "(\\tau_S)" + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": ", and averaging all prompts " + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "inline_equation", + "content": "(\\tau_{avg})" + }, + { + "bbox": [ + 313, + 485, + 555, + 653 + ], + "type": "text", + "content": " for inference." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "text", + "content": "Effect of SPL. Table 5 demonstrates that SPL significantly improves the performance of CPL. Moreover, when comparing performance across different inference scenarios " + }, + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "inline_equation", + "content": "(\\tau_T, \\tau_S, \\tau_{avg})" + }, + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "text", + "content": ", it becomes evident that source-target prompt alignment in the simple baseline has a limited impact on the target" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19980" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 553, + 258 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 258 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 258 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 258 + ], + "type": "table", + "html": "
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg
ResNet-50[16]34.950.058.037.441.946.238.531.260.453.941.259.946.1
DANN [10]45.659.370.147.058.560.946.143.768.563.251.876.857.6
JAN [25]45.961.268.950.459.761.045.843.470.363.952.476.858.3
CDAN+E [27]50.770.676.057.670.070.057.450.977.370.956.781.665.8
BSP+CDAN [5]52.068.676.158.070.370.258.650.277.672.259.381.966.3
SymNets [54]47.772.978.564.271.374.263.647.679.473.850.882.667.2
ETD [21]51.371.985.757.669.273.757.851.279.370.257.582.167.3
BNM [6]52.373.980.063.372.974.961.749.579.770.553.682.267.9
GSDA [17]61.376.179.465.473.374.365.053.280.072.260.683.170.3
GVB-GD [7]57.074.779.864.674.174.665.255.181.074.659.784.370.4
RSDA-MSTN [15]53.277.781.366.474.076.567.953.082.075.857.885.470.9
SPL [50]54.577.881.965.178.081.166.053.182.869.955.386.071.0
SRDC [41]52.376.381.069.576.278.068.753.881.776.357.185.071.3
DisClusterDA [42]58.877.080.867.074.677.165.956.381.474.260.583.671.4
CLIP [34]51.681.982.671.981.982.671.951.682.671.951.681.972.0
DAPL [12]52.782.284.173.982.083.873.654.684.073.353.482.573.3
PGA [32]53.783.985.073.283.984.673.253.884.173.553.185.373.9
CRPL (Ours)54.784.184.674.383.283.773.753.484.674.555.585.574.4
", + "image_path": "47f10088f1fddb4b61bd0f63bdd55397246433246838b98c96af236cf383222a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 89, + 293, + 257, + 397 + ], + "blocks": [ + { + "bbox": [ + 56, + 262, + 552, + 274 + ], + "lines": [ + { + "bbox": [ + 56, + 262, + 552, + 274 + ], + "spans": [ + { + "bbox": [ + 56, + 262, + 552, + 274 + ], + "type": "text", + "content": "Table 4. Accuracy (%) on Office-Home[46] for unsupervised domain adaptation (ResNet-50[16]). The best accuracy is indicated in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 89, + 293, + 257, + 397 + ], + "lines": [ + { + "bbox": [ + 89, + 293, + 257, + 397 + ], + "spans": [ + { + "bbox": [ + 89, + 293, + 257, + 397 + ], + "type": "table", + "html": "
Inference PromptArClPrRw
CPLτT47.629.053.563.5
τS74.357.284.384.8
τavg61.240.373.377.8
SPLτT75.862.986.687.2
τS73.357.483.484.7
τavg75.858.183.685.3
CPL onlyτT47.629.053.563.5
CPL with LwτT7.94.780.482.3
SPL onlyτT75.862.986.687.2
SPL with LwτT76.863.587.587.6
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In contrast, SPL enables the target domain to learn text embeddings that effectively capture and represent the corresponding visual embeddings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": "Effect of clustering reinforcement " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": ". Table 5 (last four rows) shows that clustering reinforcement " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " further improves the performance of SPL. However, applying " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " to the simple baseline reveals noticeable differences in CPL performance over target domains. Specifically, it seems that the effectiveness of " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " strongly depends on the initial predictions, where weak initial predictions as observed in the CPL method on 'Ar' and 'Cl' domains with just " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "47.6\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "29.0\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": ", leading to a collapse performance of accuracy less than " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " when combing with " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": ". However, with better initial predictions as observed in the CPL method on 'Pr' and 'Rw' domains, substantial improvement of " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "53.5\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "80.4\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "19\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "63.5\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "82.3\\%" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": ") when combined with " + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{W}}" + }, + { + "bbox": [ + 54, + 485, + 295, + 664 + ], + "type": "text", + "content": " are observed. This indicates a mutual benefit between source-enhanced pseudo-labels and clustering reinforcement." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "Effect of Source-Target Prompts Alignment. We have shown that source-target prompt alignment has a limited impact on the target prompt. To further validate this, we analyze the performance of prompts from the most recent" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 349, + 293, + 517, + 357 + ], + "blocks": [ + { + "bbox": [ + 55, + 400, + 295, + 422 + ], + "lines": [ + { + "bbox": [ + 55, + 400, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 295, + 422 + ], + "type": "text", + "content": "Table 5. Effect of source-enhanced pseudo-labels and clustering reinforcement on the Office-Home dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 349, + 293, + 517, + 357 + ], + "lines": [ + { + "bbox": [ + 349, + 293, + 517, + 357 + ], + "spans": [ + { + "bbox": [ + 349, + 293, + 517, + 357 + ], + "type": "table", + "html": "
SettingInference PromptArClPrRw
PGAτT72.352.883.782.4
τS73.856.284.684.9
τavg75.657.086.086.6
M-CRPL (ours)τT76.863.587.587.6
τS75.358.083.984.7
τavg75.858.685.285.3
", + "image_path": "94f71e8a3ae93a66db9359792af28f6804db246f19e49e2b75caa9625e6fc8c9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 360, + 553, + 371 + ], + "lines": [ + { + "bbox": [ + 313, + 360, + 553, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 553, + 371 + ], + "type": "text", + "content": "Table 6. Analyses of prompts performance on OfficeHome dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "text", + "content": "SOTA method, PGA [32], which focuses on the source-target prompt strategy. As shown in Table 6, while PGA improves the performance of " + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\tau_{T}" + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "text", + "content": ", bringing it closer to the performance of the source prompts " + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\tau_{S}" + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "text", + "content": ", it does not surpass them. This result confirms the limitations of the alignment strategy. In contrast, for M-CRPL, " + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\tau_{T}" + }, + { + "bbox": [ + 313, + 388, + 555, + 496 + ], + "type": "text", + "content": " achieves the best performance for target prompts across all three scenarios, demonstrating the effectiveness of using enhanced pseudo-labels from source domains to refine target prompts in terms of representation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "spans": [ + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 534, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 534, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 534, + 555, + 715 + ], + "type": "text", + "content": "We propose a framework for prompt learning UDA that begins by leveraging information from the source domains to enhance pseudo-labels for training target prompts. We demonstrate that while source-target prompt alignment has a limited effect on learning the target prompt, enhanced pseudo-labels result in significant improvements in both performance and the quality of target prompts in terms of representation. Additionally, inspired by the strong clustering behavior observed between visual and text embeddings in pre-trained models, we further refine target prompts by enforcing clustering properties. This is achieved by minimizing the Wasserstein distance between the distribution of text prompts and the distribution of visual embeddings in the target domains. Finally, our experiments and ablation studies validate the superior performance of our approach." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19981" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 127 + ], + "type": "text", + "content": "This work was supported by ARC DP23 grant DP230101176 and by the Air Force Office of Scientific Research under award number FA2386-23-1-4044." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 159, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 159, + 297, + 202 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 159, + 297, + 202 + ], + "spans": [ + { + "bbox": [ + 61, + 159, + 297, + 202 + ], + "type": "text", + "content": "[1] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. 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AAAI Press, 2019. 7" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19984" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_content_list.json b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e7696c0cb8bb8f80c217fdb458bd93af47265db8 --- /dev/null +++ b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_content_list.json @@ -0,0 +1,1701 @@ +[ + { + "type": "text", + "text": "Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Models", + "text_level": 1, + "bbox": [ + 111, + 130, + 883, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hao Ren $^{1}$ , Yiming Zeng $^{1}$ , Zetong Bi $^{1}$ , Zhaoliang Wan $^{1}$ , Junlong Huang $^{2}$ , Hui Cheng $^{1*}$ $^{1}$ School of Computer Science and Engineering, Sun Yat-sen University \n $^{2}$ School of Intelligent Systems Engineering, Sun Yat-sen University", + "bbox": [ + 160, + 179, + 841, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advancements in diffusion-based imitation learning, which shows impressive performance in modeling multimodal distributions and training stability, have led to substantial progress in various robot learning tasks. In visual navigation, previous diffusion-based policies typically generate action sequences by initiating from denoising Gaussian noise. However, the target action distribution often diverges significantly from Gaussian noise, leading to redundant denoising steps and increased learning complexity. Additionally, the sparsity of effective action distributions makes it challenging for the policy to generate accurate actions without guidance. To address these issues, we propose a novel, unified visual navigation framework leveraging the denoising diffusion bridge models named NaviBridger. This approach enables action generation by initiating from any informative prior actions, enhancing guidance and efficiency in the denoising process. We explore how diffusion bridges can enhance imitation learning in visual navigation tasks and further examine three source policies for generating prior actions. Extensive experiments in both simulated and real-world indoor and outdoor scenarios demonstrate that NaviBridger accelerates policy inference and outperforms the baselines in generating target action sequences. Code is available at https://github.com/hren20/NaviBridger.", + "bbox": [ + 89, + 301, + 483, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 710, + 220, + 726 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual navigation [5, 44, 58, 60] is vital for mobile robots, allowing them to reach targets like images or locations using visual observation. Previous methods typically consist of a global planner that provides high-level instructions or sub-goals, often leveraging large language models [10, 35, 43] or topological maps [50], to guide a local planner that generates feasible local paths in real time. Imitation learning from expert demonstrations for local path planning [45, 53] is emerging as a promising research direction, with advan", + "bbox": [ + 89, + 737, + 482, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/37155b73169d7bc77f2f9cd056e22fb25eac9de4f950a8d689a241fced1689ae.jpg", + "image_caption": [ + "Figure 1. Visual representation overview of the local path generation process. The top row shows the actions generated through vanilla diffusion models denoising from Gaussian noise. The bottom row illustrates actions generated using proposed NaviBridger, which leverage prior information to effectively guide the denoising bridge model towards the target action. This comparison demonstrates the importance of incorporating prior knowledge in achieving stable and accurate navigation." + ], + "image_footnote": [], + "bbox": [ + 522, + 271, + 897, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tages in modeling multimodal distributions and capturing sequence correlation.", + "bbox": [ + 511, + 672, + 906, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the significant progress of generative model-based local planners, this field faces two major issues due to the characteristics of generative models. First, substantial distributional discrepancies between the Gaussian noise, typically used in these models, and the robot's target action distribution lead to redundant denoising steps during inference. Second, the sparsity of desired actions makes it challenging for the policy to generate accurate actions, especially when denoising starts from chaotic random noise. Together, these issues increase computational costs and degrade overall performance.", + "bbox": [ + 509, + 704, + 906, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As Oscar Wilde stated, \"Without order, nothing can exist; without chaos, nothing can evolve,\" prompting an in-", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Hui Cheng (chengh9@mail.sysu.edu.cn).", + "bbox": [ + 107, + 886, + 457, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12100", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "triguing question: Could a structured, task-specific distribution serve as the starting point for denoising in diffusion models rather than relying on chaotic Gaussian noise? This idea aligns with optimal transport theory, which addresses translations between arbitrary distributions [12, 52], and has been successfully applied in diffusion models for paired-data tasks like image translation [28] and restoration [56]. However, diffusion bridge methods cannot be directly applied in robot learning tasks such as visual navigation, where no inherent source distribution exists to derive the target distribution. Therefore, the key challenge lies in constructing a suitable initial distribution and adapting the diffusion bridge techniques specifically for visual navigation.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this, we introduce NaviBridger, a novel, unified visual navigation framework that leverages Denoising Diffusion Bridge Models (DDBM) [59]. NaviBridger redefines action generation by initiating from informative prior actions rather than random Gaussian noise, enhancing guidance and efficiency in the denoising process. We analyze its application in imitation learning, presenting key computational formulas, and provide a theoretical analysis revealing a crucial insight: the quality of the target action distribution improves when derived from a more suitable source distribution. Based on this insight, We introduce various initialization methods tailored to different source distribution types, including uninformative noise priors, informative handcrafted priors, and learning-based priors, with a detailed discussion of the advantages and limitations. NaviBridger also unifies previous visual navigation methods that relied on traditional diffusion models, and maintains compatibility with Gaussian noise when no suitable source distribution prior is available. NaviBridger is, to our knowledge, the first work to explore diffusion bridge models for visual navigation. Our contributions are as follows:", + "bbox": [ + 91, + 289, + 483, + 607 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- General Framework for Visual Navigation: We introduce NaviBridger, a visual navigation framework based on the denoising diffusion bridge model, which uses prior actions instead of Gaussian noise as the initial input, achieving an effective balance between performance and computational efficiency. This framework can be easily adapted to a variety of imitation learning tasks.", + "- Theoretical Analysis of Source Distributions: We theoretically analyze the impact of source distributions on diffusion-based model performance, presenting tailored methods for generating prior source actions, including Gaussian, rule-based, and learning-based priors.", + "- Comprehensive Evaluation of NaviBridger: We conducted a comprehensive evaluation of our method across various scenarios and tasks, examining the effectiveness of the framework and the key design decisions of various source distributions and denoising steps. Experimental results show that NaviBridger exceeds baseline models across multiple scenarios." + ], + "bbox": [ + 88, + 613, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 89, + 653, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Models [22, 46] have rapidly advanced in areas such as conditional generation [15, 21], faster training [48], and theoretical refinements [26, 49]. Their strong generative capabilities are widely applied in image restoration [31], image translation [40], and text-to-image generation [38]. Recently, diffusion models have shown potential in decision-making fields like reinforcement learning [61] and imitation learning [1, 24].", + "bbox": [ + 511, + 114, + 903, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion bridges, initially a tool in probability theory, have evolved into a key approach in generative modeling [29, 47]. [41] laid the groundwork, and [17] explored diffusion bridges conditioned on fixed start and endpoints. Recent work extends these ideas by applying Doob's $h$ -transform for bridging arbitrary distributions [29]. [28] proposes reversing Brownian Bridges for distribution translation in discrete time, while [59] constructs bridge models using VP and VE diffusion processes in continuous time.", + "bbox": [ + 511, + 236, + 903, + 371 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Navigation. Traditional navigation approaches [6, 7, 33] typically divide the navigation task into three main components: mapping [8, 37], localization [9, 55], and path planning [54], with each element showing considerable advancements in recent studies. However, the modular design can lead to cumulative information loss and rely heavily on precise measurements. Since Zhu et al. [60] pioneered the training of agents in simulated environments, learning-based visual navigation has progressed rapidly [2, 4, 10, 16, 32]. [60] employed deep reinforcement learning to address visual navigation challenges for image-based target search in small indoor simulation scenarios. Subsequent research has focused on improving visual representation by incorporating supplementary information[23], auxiliary tasks[39], or optimized networks [57]. By contrast, recent works such as [19, 30, 44] emphasize navigation tasks in real-world robotic systems, aiming to achieve zero-shot or few-shot navigation. ViNT [45] introduced a foundational model based on topological mapping for long-range navigation tasks and implemented the generation of latent subgoal images using diffusion models.", + "bbox": [ + 511, + 372, + 903, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most recently, state-conditioned diffusion models for imitation learning in planning are particularly powerful[13, 24, 51]. NoMaD [50] incorporates diffusion models into visual navigation, enabling the direct generation of actions and achieving robust performance and enhanced multimodal representations. However, these approaches rely on standard diffusion models that denoise progressively from an initial Gaussian noise distribution. For more complex action spaces, this \"sampling from an initial Gaussian state\" approach often demands additional denoising steps [11]. Furthermore, since the Gaussian distribution differs significantly from the target action distribution, fitting the model to the target distribution becomes more challenging, potentially reducing the quality of generated actions [14, 34].", + "bbox": [ + 511, + 689, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12101", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4300746847bcc645c356748e655285fbf4a0c05521756aae747459a5115a1d50.jpg", + "image_caption": [ + "Figure 2. NaviBridger Overview. The policy takes RGB observations and a goal image, extracting features via a Transformer encoder. The FiLM condition module applies learned conditions to improve path accuracy, while the prior generation module ensures the policy outputs better aligns with target actions, starting from alternative prior actions generated using optional prior policies." + ], + "image_footnote": [], + "bbox": [ + 93, + 90, + 903, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 417, + 230, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Process: A diffusion process gradually adds noise to data, translating it from an initial distribution $p_0$ to a simpler, typically Gaussian distribution $p_T = \\mathcal{N}(0, I)$ . This forward process is modeled by the stochastic differential equation (SDE):", + "bbox": [ + 89, + 444, + 483, + 521 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd \\mathbf {x} _ {t} = f (\\mathbf {x} _ {t}, t) d t + g (t) d \\mathbf {w} _ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 539, + 482, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f$ is the drift function, $g(t)$ is the diffusion coefficient, and $\\mathbf{w}_t$ represents the Wiener process.", + "bbox": [ + 89, + 565, + 482, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reverse process, which removes noise to reconstruct data, is governed by the reverse-time SDE:", + "bbox": [ + 89, + 595, + 483, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd \\mathbf {x} _ {t} = \\left[ f \\left(\\mathbf {x} _ {t}, t\\right) - g (t) ^ {2} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) \\right] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 656, + 482, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)$ is the score function.", + "bbox": [ + 89, + 686, + 372, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models generate images by progressively adding noise to data and then training neural networks to reverse this process, removing noise to recreate the original image. However, diffusion models are limited because they can only transport complex data distributions to a standard Gaussian distribution. Building upon the study of stochastic differential equations, using a diffusion process to map data to a known fixed endpoint is achievable through Doob's $h$ -transform.", + "bbox": [ + 89, + 703, + 482, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Bridge: A diffusion bridge extends the diffusion process by interpolating between two fixed distributions, ensuring the generated data transitions from a starting distribution to a specified endpoint. The forward process", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which is expanded from Eq.(1) of diffusion bridge is expressed as:", + "bbox": [ + 511, + 419, + 906, + 450 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd \\mathbf {x} _ {t} = [ f (\\mathbf {x} _ {t}, t) + g (t) ^ {2} h (\\mathbf {x} _ {t}, t, y, T) ] d t + g (t) d \\mathbf {w} _ {t}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 470, + 906, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h(\\mathbf{x}_t, t, y, T) = \\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_T \\mid \\mathbf{x}_t) \\big|_{\\mathbf{x}_t = x, \\mathbf{x}_T = y}$ is the Doob's $h$ -transform ensures approximation to the target distribution $y$ at time $T$ .", + "bbox": [ + 511, + 494, + 905, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denoising Diffusion Bridge Models (DDBM): DDBMs generalize diffusion models by enabling transport between paired distributions, using reverse-time SDE or probability flow ODE. For the reverse diffusion bridge, the SDE is:", + "bbox": [ + 511, + 541, + 906, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} d \\mathbf {x} _ {t} = \\left[ f (\\mathbf {x} _ {t}, t) - g (t) ^ {2} \\left(s \\left(\\mathbf {x} _ {t}, t, y, T\\right) \\right. \\right. \\\\ \\left. - h \\left(\\mathbf {x} _ {t}, t, y, T\\right)\\right) ] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 619, + 836, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(4)", + "bbox": [ + 883, + 632, + 903, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{s}(\\mathbf{x}_t,t,y,T) = \\nabla_{\\mathbf{x}_t}\\log q(\\mathbf{x}_t\\mid \\mathbf{x}_T)\\big|_{\\mathbf{x}_t = x,\\mathbf{x}_T = y}$ is the score function, $h(\\mathbf{x}_t,t,y,T)$ ensures the transition to the target distribution. DDBM employs the sampling distribution $q(x_{t}\\mid x_{0},x_{T})$ as an approximation for the challenging-to-obtain distribution $q(\\mathbf{x}_t\\mid \\mathbf{x}_T)$ , offering a defined expression for $q(x_{t}\\mid x_{0},x_{T})$ and reparameterizing it to facilitate denoising (details provided in the Appendix). DDBMs use denoising score matching to learn the score function:", + "bbox": [ + 511, + 662, + 906, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\theta} = \\mathbb {E} _ {\\mathbf {x} _ {t}, \\mathbf {x} _ {0}, t} [ w (t) \\| s _ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {T}, t) - \\nabla_ {\\mathbf {x} _ {t}} \\log q (\\mathbf {x} _ {t} | \\mathbf {x} _ {0}, \\mathbf {x} _ {T}) \\| ^ {2} ] \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 792, + 903, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $w(t)$ indicates the weight scheduler of the loss.", + "bbox": [ + 511, + 825, + 870, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This method allows DDBMs to translate between distributions effectively, expanding the scope of diffusion models to a wide range of generative tasks. More details about DDBM refer to the Appendix.", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12102", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 89, + 89, + 225, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivated by the preceding discussion, we propose a novel approach, Navibridger. Instead of relying on sampling and denoising within a fixed Gaussian noise space, our method transforms this process into a denoising procedure that maps from an observation-based arbitrary source distribution policy $\\pi_s$ to a target distribution policy $\\pi$ . Navibridger consists of three core components: a feature extraction module, a prior action generation module, and a denoising diffusion bridge module. The architecture illustration is shown in Fig. 2.", + "bbox": [ + 89, + 114, + 483, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In visual navigation, the objective is to design a control policy $\\pi$ that allows a robot to execute target-oriented navigation effectively. The inputs to this policy consist of the robot's current and past visual observation sequence, denoted by $\\mathcal{O} = \\{I_t\\}_{t = T - p}^T$ , along with a future action sequence $\\mathbf{a} = \\{W_t\\}_{t = T}^{T + n}$ . Here, $p$ represents the past time window. The policy can also incorporate a goal image $I_{g}$ specifying the navigation target. Each observation $I_{i}$ is mapped to a feature vector $\\phi (I_i)$ , which is subsequently processed by a Transformer encoder to produce a contextual vector $c_{t}$ in the usual way. The context vector $c_{t}$ is input into the prior action generation module to produce the source action $\\mathbf{a}_s\\in \\pi_s$ associated with $I_{t}$ . The diffusion bridge model translates this source action into the desired target action $\\mathbf{a}\\in \\pi$ .", + "bbox": [ + 89, + 266, + 483, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Diffusion Bridge for Imitation Learning", + "text_level": 1, + "bbox": [ + 89, + 503, + 433, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the imitation learning framework based on DDBM, the model employs a reverse diffusion process to progressively adjust the initial action distribution continuously, resulting in an action trajectory that satisfies the target requirements. Specifically, the DDBM reverse diffusion process for imitation learning can be described as follows:", + "bbox": [ + 89, + 526, + 483, + 617 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} d \\mathbf {a} _ {t} = \\left[ f \\left(\\mathbf {a} _ {t}, t\\right) - g ^ {2} (t) \\left(s \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) \\right. \\right. \\tag {6} \\\\ \\left. - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) ] d t + g (t) d \\hat {w} _ {t}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 625, + 483, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f(\\mathbf{a}_t, t)$ denotes the drift term, $g(t)$ is the diffusion coefficient, $s(\\mathbf{a}_t, t, \\mathbf{a}_T, T)$ represents the score function that gives the conditional score at time $t$ for the current state $\\mathbf{a}_t$ relative to the target state $\\mathbf{a}_0$ , and $h(\\mathbf{a}_t, t, \\mathbf{a}_T, T)$ is the Doob's $h$ -transform, applied to adjust the diffusion path, thereby ensuring a controlled transition from $\\mathbf{a}_s$ to $\\mathbf{a}_T$ .", + "bbox": [ + 89, + 669, + 483, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$h(\\mathbf{a}_t,t,\\mathbf{a}_T,T)$ is a function of $\\nabla_{\\mathbf{a}_t}\\log p(\\mathbf{a}_T\\mid \\mathbf{a}_t)$ which is approximated by $q(\\mathbf{a}_t\\mid \\mathbf{a}_0,\\mathbf{a}_T)$", + "bbox": [ + 89, + 760, + 483, + 791 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {a} _ {t} \\mid \\mathbf {a} _ {0}, \\mathbf {a} _ {T}\\right) = \\mathcal {N} \\left(\\hat {\\mu} _ {t}, \\hat {\\sigma} _ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 797, + 482, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mu} _ {t} = \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} \\mathbf {a} _ {0} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (8) \\\\ \\hat {\\sigma} _ {t} ^ {2} = \\sigma_ {t} ^ {2} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (9) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 833, + 482, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ and $\\sigma_{t}$ denote predefined signal and noise schedules, with the signal-to-noise ratio at time $t$ given by $\\mathrm{SNR}_t = \\alpha_t^2 /\\sigma_t^2$ . With the reparametrization of Elucidating Diffusion Models, score function $\\mathbf{s}(\\mathbf{a},t,\\mathbf{a}_T,T)$ can be expressed as:", + "bbox": [ + 511, + 90, + 905, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\mathbf {a} _ {t}} \\log q (\\mathbf {a} _ {t} | \\mathbf {a} _ {T}) \\approx \\mathbf {s} (D _ {\\theta}, \\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T) \\\\ = \\frac {\\mathbf {a} _ {t} - \\left(\\frac {S N R _ {T}}{S N R _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} D _ {\\theta} (\\mathbf {a} _ {t} , t , \\mathbf {a} _ {T}) \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)\\right)}{\\sigma_ {t} ^ {2} \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)}, \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 191, + 903, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "here, $D_{\\theta}(\\mathbf{a}_t,t,\\mathbf{a}_T)$ denotes the output of the network.", + "bbox": [ + 511, + 263, + 870, + 279 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the above inferences, we developed a foundational imitation learning framework utilizing diffusion bridges. This approach theoretically enables action sampling by transferring samples $\\mathbf{a}_T$ from the source distribution $\\pi_s$ to the target distribution $\\pi$ , with neural networks employed to learn the reverse denoising process.", + "bbox": [ + 511, + 279, + 905, + 371 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Prior Policy Design", + "text_level": 1, + "bbox": [ + 511, + 381, + 697, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Previous research on diffusion bridge models has primarily focused on tasks like image translation and style transfer, which involve paired input-output tasks where the input corresponds to a source distribution sample. Compared to Gaussian noise, a well-defined source distribution offers an informative prior, often yielding more accurate outcomes.", + "bbox": [ + 511, + 404, + 905, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, in imitation learning tasks, such as visual navigation, the target action is not inherently paired with an initial action. In this section, we present the theoretical foundation for designing the source distribution and introduce three distinct strategies for generating the source distribution specifically for visual navigation tasks.", + "bbox": [ + 511, + 496, + 905, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Error Bound Analyzing: For a diffusion process to be effective, the initial source distribution must resemble the target distribution. If there is a significant discrepancy between the two, the diffusion process will require more extensive adjustments per step, amplifying drift, and score correction, thus increasing the probability of error in the likelihood flow ODE or SDE.", + "bbox": [ + 511, + 587, + 905, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Consider the error of the model denoising process. $\\mathbb{E}_{\\mathbf{a}_0}[\\| \\mathbf{a}_t - \\mathbf{a}_0\\|^2 ]$ . This error is driven by the difference between the target distribution $\\pi (\\mathbf{a}_0)$ and the source distribution $\\pi_s(\\mathbf{a}_T)$ , which can be represented using the KullbackLeibler (KL) divergence as:", + "bbox": [ + 511, + 693, + 905, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right) = \\int \\pi_ {s} (\\mathbf {a} _ {T}) \\log \\frac {\\pi_ {s} (\\mathbf {a} _ {T})}{\\pi (\\mathbf {a} _ {0})} d \\mathbf {a} _ {T}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 781, + 903, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This KL divergence measures how much information is \"lost\" if we approximate $\\pi (\\mathbf{a}_0)$ by $\\pi_s(\\mathbf{a}_T)$ . A more minor divergence indicates a smaller amount of drift, and noise adjustment will be necessary for the DDBM to match the target. A probability flow ODE controls the evolution of", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12103", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "samples in a DDBM:", + "bbox": [ + 89, + 90, + 233, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d \\mathbf {a} _ {t}}{d t} = f (\\mathbf {a} _ {t}, t) - g ^ {2} (t) \\left(\\frac {1}{2} \\mathbf {s} \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 119, + 486, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{s}(\\mathbf{a}_t,t,\\mathbf{a}_T,T) - h(\\mathbf{a}_t,t,\\mathbf{a}_T,T)$ represents the adjustment needed to shift $\\mathbf{a}_t$ closer to $\\mathbf{a}_0$ . The error bound for the model's convergence to $\\mathbf{a}_T$ can be formulated as:", + "bbox": [ + 89, + 167, + 482, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}} \\left[ \\left\\| \\mathbf {a} _ {t} - \\mathbf {a} _ {0} \\right\\| ^ {2} \\right] \\leq C \\cdot D _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 226, + 482, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C$ is a constant that depends on factors such as the noise schedule $g(t)$ and the time duration $T$ . Hence, the error bound shows that the closer the source distribution $q_{\\mathrm{source}}$ is to the target distribution $q_{\\mathrm{target}}$ , the lower the error bound for the DDBM, resulting in a more accurate diffusion process and improved model performance.", + "bbox": [ + 89, + 260, + 483, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prior Action Generation: As previously discussed, a source distribution that closely approximates the target distribution results in improved policy performance, underscoring the importance of an effective prior policy. A toy model is presented in Fig. 3. For the sake of comparison, we propose the following three methods for generating the prior action:", + "bbox": [ + 89, + 353, + 483, + 458 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Gaussian Prior: As an uninformative prior, we select Gaussian white noise, consistent with that used in standard diffusion, as the source distribution, serving as the initial state in the denoising process. This choice facilitates direct comparison with methods based on the original diffusion approach.", + "- Rule-based Prior: We employ a simple, fully connected layer to map the contextual vector $\\boldsymbol{c}_t$ to the action space, enabling the extraction of relevant low-dimensional features for action generation. The prior action is preset as a parabolic path passing through the current position, determined based on the predicted path length $d$ and movement behavior classification (straight, left turn, right turn, U-turn to the right, and U-turn to the left). Detailed information can be found in the Appendix.", + "- Learning-based Prior: This method involves generating prior actions by utilizing expert data and learning models. We use a lightweight conditional variational autoencoder (CVAE) as our learning model to achieve a lightweight design while maintaining effective generation. The observations $\\mathcal{O}$ are fed into the CVAE to produce corresponding actions. We aim for the model to effectively capture the significant correlations between observations and actions, thereby enabling a more efficient acquisition of the source distribution with reduced computational costs." + ], + "bbox": [ + 88, + 460, + 482, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These methods for prior action generation are readily adaptable to other tasks related to imitation learning. Through a comparative analysis of these methods, we seek to assess the potential advantages of the diffusion bridge.", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7f324dcdbffdfee2849c4fb0c1700d7c48d138a41d1a7bb9e40ec26abef2c28f.jpg", + "image_caption": [ + "Figure 3. DDBM trained on 2D synthetic data. The leftmost side represents the source distribution, and the rightmost side represents the target distribution. The distance between the source distribution and the target distribution increases from top to bottom. As the EMD increases, the required approximation steps increase while model performance progressively declines." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 903, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Traing Details", + "text_level": 1, + "bbox": [ + 511, + 364, + 660, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "**Denoising Network:** We utilize a 1-D temporal CNN, conditioned on the $c_t$ derived from observations, to iteratively denoise with the prior action $\\mathbf{a}_T$ serving as the initial input. The network is modulated by $c_t$ through Feature-wise Linear Modulation (FiLM) [36] and performs $k$ iterations of denoising, following an approach similar to that of [13].", + "bbox": [ + 511, + 387, + 903, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Function: The loss function in our architecture comprises the diffusion bridge loss $\\mathcal{L}_b$ , the prior action generation loss $\\mathcal{L}_p$ , and a temporal distance loss $\\mathcal{L}_d$ designed for high-level planning (following [50]).", + "bbox": [ + 511, + 479, + 903, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The diffusion bridge loss $\\mathcal{L}_b$ is calculated by a weighted Mean Square Error (MSE) loss function:", + "bbox": [ + 511, + 539, + 903, + 569 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} = \\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}, \\mathbf {a} _ {T}, t} [ w (t) \\| \\mathbf {a} _ {0} - D _ {\\theta} (\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}) \\| ^ {2} ], \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 577, + 903, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The prior action generation loss $\\mathcal{L}_p$ is categorized into rule-based and learning-based approaches. The rule-based approach uses a fully connected layer to generate a coarse action. It is accompanied by a classification task that classifies the action based on its movement direction (details in the Appendix). Thus, the loss function consists of an action prediction loss computed by Mean Squared Error (MSE) and a classification loss based on cross-entropy:", + "bbox": [ + 511, + 602, + 905, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} ^ {r u l e} = - \\lambda_ {c} \\sum p _ {c} \\log (\\hat {p} _ {c}) + \\lambda_ {a} \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 731, + 903, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_c$ represents the one-hot encoding of the ground truth class label, while $\\hat{p}_c$ denotes the predicted probability. Additionally, a signifies the expert action, and $\\hat{\\mathbf{a}}$ represents the predicted action by the FC layer. The terms $\\lambda_c$ and $\\lambda_a$ denote the respective weights for the loss functions.", + "bbox": [ + 511, + 780, + 905, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The learning-based approach employs the Conditional Variational Autoencoder (CVAE) model to efficiently generate actions in a lightweight manner, with the associated", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12104", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8ed51d5b96ae32c70580058ebe37ea4e954e896d1a2f29446831863e26f09ec8.jpg", + "table_caption": [ + "Table 1. Quantitative comparison between the proposed method with baselines in simulation environments" + ], + "table_footnote": [], + "table_body": "
SceneMethodBasic TaskAdaptation Task
Length (m)CollisionSuccessLength (m)CollisionSuccess
Indoor(2D-3D-S)ViNT [45]151.1 ± 31.5901.0268%19.9 ± 0.3141.5828%
NoMaD [50]147.9 ± 26.4750.7486%20.3 ± 0.2431.3232%
Gaussian Prior148.7 ± 28.5380.7282%19.8 ± 0.3170.9864%
Rule-based Prior163.57 ± 48.6582.5162%19.0 ± 1.390.8444%
Learning-based Prior143.7 ± 25.1750.6192%19.3 ± 0.340.4188%
Outdoor(Citysim)ViNT [45]254.8 ± 63.5970.7820%67.5 ± 26.3200.4138%
NoMaD [50]248.6 ± 67.6790.5822%68.3 ± 26.3150.3452%
Gaussian Prior244.8 ± 62.7490.6234%68.9 ± 24.6560.3550%
Rule-based Prior276.1 ± 83.7213.5914%71.8 ± 30.8560.5928%
Learning-based Prior237.7 ± 59.4760.5144%63.5 ± 20.6590.3064%
", + "bbox": [ + 94, + 112, + 898, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "loss function defined as follows:", + "bbox": [ + 89, + 321, + 307, + 335 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} ^ {c v a e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2} + \\operatorname {K L} (\\hat {\\pi} (z | \\mathcal {O}, \\mathbf {a}) \\| \\pi (z | \\mathcal {O})) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 345, + 480, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{\\pi} (\\cdot)$ represents the posterior distribution of actions, while $\\pi (\\cdot)$ represents the prior.", + "bbox": [ + 89, + 398, + 482, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The temporal distance loss $\\mathcal{L}_d$ quantifies the interval count between the target image and the current image within a discretized timeline:", + "bbox": [ + 89, + 429, + 483, + 474 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| f (\\boldsymbol {c} _ {t, i}) - d _ {i} \\| ^ {2}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 482, + 482, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $f(\\pmb{c}_{t,i})$ represents the prediction of temporal distance, and $d_{i}$ represents the ground truth.", + "bbox": [ + 89, + 534, + 482, + 565 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In summary, the loss function is defined as:", + "bbox": [ + 109, + 565, + 398, + 579 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {b} \\mathcal {L} _ {b} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {d} \\mathcal {L} _ {d}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 590, + 482, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{b},\\lambda_{p}$ and $\\lambda_{d}$ denote the respective weights for the loss functions.", + "bbox": [ + 89, + 618, + 483, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 661, + 223, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we comprehensively evaluate our method through simulated and real-world experiments in indoor and outdoor environments. The following sections provide an overview of the experimental setup, experiment results, and ablation studies.", + "bbox": [ + 89, + 686, + 483, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 771, + 281, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Our method and all baseline methods were trained on the same dataset to ensure a fair comparison. Following the approach in [50], the training data includes samples collected from diverse environments and various robotic platforms, incorporating data from RECON [42], SCAND [25], GoStanford [18], and SACSoN [20]. The dataset consists of sequences of consecutive image frames", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "along with their corresponding positional information, providing comprehensive scene diversity.", + "bbox": [ + 511, + 321, + 903, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We selected two state-of-the-art (SOTA) image-based visual navigation algorithms, NoMaD [50] and ViNT [45], for comparison. To examine the effect of integrating diffusion bridges on policy diffusion, we chose NoMaD, the first approach to apply policy diffusion to visual navigation tasks, which utilizes a standard diffusion policy model [13]. Additionally, we included ViNT, a regression-based model incorporating CNN and self-attention mechanisms, to compare the performance of generative and regression models in visual navigation tasks.", + "bbox": [ + 511, + 353, + 905, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We report three evaluation metrics in our experiments to comprehensively assess the performance of the diffusion bridge-based visual navigation method:", + "bbox": [ + 511, + 506, + 903, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Length: For paths that complete the task, we calculate the path lengths' mean and variance to assess the navigation paths' efficiency and consistency.", + "bbox": [ + 511, + 551, + 903, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Collision: The average number of collisions per trial, which serves as an indicator of navigation safety.", + "bbox": [ + 511, + 595, + 903, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Success Rate: The success rate under consistent conditions. A trial is considered a failure if the robot does not reach the target position, becomes stuck due to collisions, or exceeds the time limit.", + "bbox": [ + 511, + 626, + 903, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We trained the model for 30 epochs using a learning rate 0.0001 and a batch size 256 (224 for learning-based methods). The training process, conducted on a single NVIDIA RTX TITAN GPU, took approximately 30 hours. For DDBM, we employed a VE model with parameters $\\sigma_0 = \\sigma_T = 0.5$ and a default sampling step count of $k = 10$ .", + "bbox": [ + 511, + 688, + 905, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Settings. To validate the effectiveness of the proposed method, we conducted comparative experiments in a simulated environment, benchmarking against baseline methods and performing ablation studies. These experiments were conducted in both indoor and outdoor settings. Furthermore, we evaluated the models on a robotic platform to assess their practical performance. The model", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12105", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7a9c7a02128945c1916ada686ec10b2f3138cac1a46f557eafe6056be893c40a.jpg", + "image_caption": [ + "Figure 4. Comparison of navigation performance in simulation and real-world environments. NaviBridger with rule-based and model-based priors (DDBM) generates smoother, more stable paths compared to NoMaD (DDPM), demonstrating improved alignment with the target trajectory over denoising steps." + ], + "image_footnote": [], + "bbox": [ + 98, + 87, + 470, + 236 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d60e37aecfd9a780d715466ba39d6b6d339b68ade338e86b6881145806470be9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 88, + 905, + 236 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "operates on Nvidia Jetson Orin AGX deployed on the robot with RGB-only input.", + "bbox": [ + 89, + 297, + 482, + 328 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 89, + 342, + 184, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct simulated experiments in two types of scenarios(Visualized in appendix): $i$ ) Indoor (Stanford 2D-3D-S [3]) ii) Outdoor (Gazebo citysim [27]). In each scenario, we examine both basic and changed environments. The basic environment denotes a scenario where the test environment matches the configuration of the topological map, allowing us to evaluate long-distance navigation capabilities. The changed environment includes scenarios with obstacles in the test area that are not depicted in the topological map, aimed at testing the system's adaptability when the environment deviates from the mapped layout.", + "bbox": [ + 89, + 368, + 483, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 4 includes visualizations of the denoising process in both simulated indoor environments and real-world environments. For detailed configurations of the robot in both simulations and the physical setup, please refer to the Appendix. It can be observed that the DDPM-based method begins denoising from Gaussian noise, with most of the denoising process dedicated to constraining noise unsuitable for the action space into the action space, and only in the final few steps does it constrain the actions required by the task. In contrast, our method starts from a favorable initial state, achieving stable actions after only a few denoising steps, such as 2 to 4. Even when starting with Gaussian noise, our model reaches a stable action output in fewer denoising steps. This demonstrates that a rich prior significantly enhances the convergence of policy diffusion. Moreover, under the DDBM framework, even when using uninformed Gaussian noise as the source distribution, the denoising approximate rate is substantially faster than that of the DDPM-based method.", + "bbox": [ + 89, + 536, + 483, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The experimental results of the proposed method compared to the baseline in the simulation environment are presented in Table 1. The learning-based prior method demonstrates optimal performance across various tasks and scenarios. The Gaussian prior method performs similarly to", + "bbox": [ + 89, + 825, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the DDPM-based NoMaD method, outperforming the baseline in the basic task within the outdoor scenario and the adaptation task within the indoor scenario. The rule-based method, on the other hand, only exceeds the baseline in the indoor adaptation task. These findings suggest that well-designed prior information can significantly improve the effectiveness of diffusion models, whereas poorly designed priors may impair model performance in specific scenarios. The rule-based method requires careful design of prior rules, which can yield significant improvements in some particular scenarios but generally lacks strong generalization across diverse conditions. When appropriate prior actions are unavailable, Gaussian noise is an acceptable initial distribution. A practical approach involves obtaining learned prior actions from a lightweight model and then generating actions through a diffusion bridge, offering a more versatile and robust solution. The learning-based method shows notable improvements in adaptation tasks and outdoor scenarios, indicating a solid capacity for generalization in complex and dynamic environments. In contrast, the DDPM-based method demonstrates comparatively weaker performance.", + "bbox": [ + 511, + 297, + 906, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 647, + 679, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The impact of denoising steps on model learning. Table 2 shows the training results under different denoising step conditions, comparing the DDPM-based method and NaviBridger based on a Gaussian prior. We present the minimum mean squared error between the predicted action and the expert action on the training set and test sets of four datasets, along with the average ranking of each model across five items. Our method is closer to the expert trajectory in terms of overall data scale. Observing the trend, as the denoising steps decrease, the difference between the DDPM-based method's predicted trajectory and the expert trajectory increases significantly. In contrast, the difference between NaviBridger and a Gaussian prior remains relatively stable. This is also reflected in the average ranking; regardless of the number of denoising steps, Navibridger", + "bbox": [ + 511, + 674, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12106", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "consistently achieves a better ranking, with minimal variation in average ranking as the denoising steps change. Conversely, the DDPM-based method shows generally lower rankings with more considerable fluctuations.", + "bbox": [ + 89, + 90, + 482, + 151 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4c1246e026acf64c1d904eca5a066833cdab76d9daab9b62f9bac871a913b390.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NoMaD (DDPM)Gaussian Prior
k=1074110741
Train1.381.271.142.160.270.280.300.30
Recon1.191.100.971.430.880.910.890.98
Sacson1.741.731.653.131.651.431.611.52
SCAND0.720.760.711.170.590.690.630.61
Go Stanford4.123.473.463.893.473.443.223.32
Average Rank7.06.04.47.82.42.62.42.8
", + "bbox": [ + 91, + 157, + 480, + 308 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/755a50e3986b2e28279ec2f720314b1e025ffa7dc128240bb2fc87b5ede5e24b.jpg", + "table_caption": [ + "Table 2. Comparison of the mean square error between DDBM and vanilla diffusion model in predicting actions and expert actions in training sets and different test sets." + ], + "table_footnote": [], + "table_body": "
PriorMethodLength (m)Collision Success
GaussianSource-2.120%
Target19.8 ± 0.3170.9864%
Rule-basedSource28.1 ± 5.9421.778%
Target19.0 ± 1.3900.8444%
Learning-basedSource24.8 ± 1.351.4920%
Target19.3 ± 0.3400.4188%
", + "bbox": [ + 91, + 362, + 478, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Performance metrics of visual navigation tasks across different source priors: evaluation of policy effectiveness for source-target action mapping.", + "bbox": [ + 89, + 489, + 482, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effect of source distribution and the role of diffusion bridge. Table 3 compares the navigation performance of the proposed method in an indoor adaptation task by examining prior actions sampled from different source distributions and the target actions obtained through denoising. As the prior generation method transitions from random to ordered and from heuristic-based to expert data-driven approaches, the success rate of navigation using only the prior actions shows some improvement, although it remains pretty low. After bridge denoising, the navigation success rate improves markedly. The experiments indicate that more informative prior actions contribute to better performance. At the same time, the diffusion bridge effectively transforms less effective prior actions into higher-quality target actions, thereby enhancing overall performance.", + "bbox": [ + 88, + 537, + 482, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Less denoising steps and the same performance. The line chart as shown in Fig 5 illustrates the relationship between denoising steps, success rate, and inference time for visual navigation under different prior settings—Learning-based Prior DDBM, Gaussian Prior DDBM, and DDPM. Success rate, represented on the left vertical axis, generally increases as denoising steps progress, with the Learning-based Prior DDBM consistently achieving the highest success rates, peaking around $90\\%$ at 10 denoising steps. In", + "bbox": [ + 88, + 763, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/202e0faeeb213a2393d10f2b0d7306edd4a75eee94710c97711c457b6ca81b5b.jpg", + "image_caption": [ + "Figure 5. Success rate and inference time comparison across denoising steps. Learning-based and Gaussian priors in DDBM show higher success rates than DDPM, with learning-based priors achieving the best performance. DDBM also demonstrates faster inference times as denoising steps increase." + ], + "image_footnote": [], + "bbox": [ + 522, + 94, + 897, + 263 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "contrast, the Gaussian Prior DDBM shows a moderate success rate that fluctuates slightly, while DDPM achieves a lower success rate overall. The inference time indicated on the right vertical axis increases linearly with the denoising steps, and the time required by DDBM is longer than that of DDPM under the same denoising steps. Learning-based Prior DDBM demonstrates a more favorable balance between high success rate and moderate inference time, suggesting it is more efficient and reliable for visual navigation tasks than the Gaussian Prior DDBM and DDPM.", + "bbox": [ + 511, + 369, + 906, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 541, + 633, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a novel diffusion bridge-based framework for visual navigation. Our method advances policy generation by enabling translations across arbitrary distributions based on informative prior actions rather than the random Gaussian noise. Our theoretical analysis details fundamental principles, formulas, and the influence of source distributions on performance, along with an analysis of error lower bounds. Experimental results demonstrate a substantial increase in success rates and a reduction in collisions compared to baseline models in simulated environments. By exploring different strategies for source distribution generation and denoising steps, our method achieves greater robustness, more stability, and faster action generation than vanilla diffusion policy models, expanding the potential of policy diffusion in imitation learning.", + "bbox": [ + 511, + 568, + 906, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, although the results demonstrate a certain extent of generalization to dynamic scenarios, the scenario becomes more complex if high-speed moving objects are present, necessitating faster response or adaptive strategies.", + "bbox": [ + 511, + 797, + 906, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work is supported by the China National Key R&D Program (2022YFB3903804).", + "bbox": [ + 511, + 857, + 906, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12107", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua Tenenbaum, Tommi Jaakkola, and Pulkit Agrawal. Is conditional generative modeling all you need for decision-making? arXiv preprint arXiv:2211.15657, 2022. 2", + "[2] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. Zero experience required: Plug & play modular transfer learning for semantic visual navigation. 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Diffusion models for reinforcement learning: A survey. arXiv preprint arXiv:2311.01223, 2023. 2" + ], + "bbox": [ + 91, + 92, + 480, + 387 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12110", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_model.json b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2148727688787179a8df8970c349f3dd3722f17b --- /dev/null +++ b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/ee705ec4-0cf2-476b-b84e-1441c5f20d50_model.json @@ -0,0 +1,2389 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.131, + 0.885, + 0.154 + ], + "angle": 0, + "content": "Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Models" + }, + { + "type": "text", + "bbox": [ + 0.161, + 0.18, + 0.842, + 0.236 + ], + "angle": 0, + "content": "Hao Ren\\(^{1}\\), Yiming Zeng\\(^{1}\\), Zetong Bi\\(^{1}\\), Zhaoliang Wan\\(^{1}\\), Junlong Huang\\(^{2}\\), Hui Cheng\\(^{1*}\\) \n\\(^{1}\\)School of Computer Science and Engineering, Sun Yat-sen University \n\\(^{2}\\)School of Intelligent Systems Engineering, Sun Yat-sen University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.303, + 0.485, + 0.681 + ], + "angle": 0, + "content": "Recent advancements in diffusion-based imitation learning, which shows impressive performance in modeling multimodal distributions and training stability, have led to substantial progress in various robot learning tasks. In visual navigation, previous diffusion-based policies typically generate action sequences by initiating from denoising Gaussian noise. However, the target action distribution often diverges significantly from Gaussian noise, leading to redundant denoising steps and increased learning complexity. Additionally, the sparsity of effective action distributions makes it challenging for the policy to generate accurate actions without guidance. To address these issues, we propose a novel, unified visual navigation framework leveraging the denoising diffusion bridge models named NaviBridger. This approach enables action generation by initiating from any informative prior actions, enhancing guidance and efficiency in the denoising process. We explore how diffusion bridges can enhance imitation learning in visual navigation tasks and further examine three source policies for generating prior actions. Extensive experiments in both simulated and real-world indoor and outdoor scenarios demonstrate that NaviBridger accelerates policy inference and outperforms the baselines in generating target action sequences. Code is available at https://github.com/hren20/NaviBridger." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.712, + 0.222, + 0.727 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.738, + 0.483, + 0.875 + ], + "angle": 0, + "content": "Visual navigation [5, 44, 58, 60] is vital for mobile robots, allowing them to reach targets like images or locations using visual observation. Previous methods typically consist of a global planner that provides high-level instructions or sub-goals, often leveraging large language models [10, 35, 43] or topological maps [50], to guide a local planner that generates feasible local paths in real time. Imitation learning from expert demonstrations for local path planning [45, 53] is emerging as a promising research direction, with advan" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.272, + 0.898, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.556, + 0.907, + 0.669 + ], + "angle": 0, + "content": "Figure 1. Visual representation overview of the local path generation process. The top row shows the actions generated through vanilla diffusion models denoising from Gaussian noise. The bottom row illustrates actions generated using proposed NaviBridger, which leverage prior information to effectively guide the denoising bridge model towards the target action. This comparison demonstrates the importance of incorporating prior knowledge in achieving stable and accurate navigation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.907, + 0.703 + ], + "angle": 0, + "content": "tages in modeling multimodal distributions and capturing sequence correlation." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.705, + 0.907, + 0.87 + ], + "angle": 0, + "content": "Despite the significant progress of generative model-based local planners, this field faces two major issues due to the characteristics of generative models. First, substantial distributional discrepancies between the Gaussian noise, typically used in these models, and the robot's target action distribution lead to redundant denoising steps during inference. Second, the sparsity of desired actions makes it challenging for the policy to generate accurate actions, especially when denoising starts from chaotic random noise. Together, these issues increase computational costs and degrade overall performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "As Oscar Wilde stated, \"Without order, nothing can exist; without chaos, nothing can evolve,\" prompting an in-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.458, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: Hui Cheng (chengh9@mail.sysu.edu.cn)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12100" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "triguing question: Could a structured, task-specific distribution serve as the starting point for denoising in diffusion models rather than relying on chaotic Gaussian noise? This idea aligns with optimal transport theory, which addresses translations between arbitrary distributions [12, 52], and has been successfully applied in diffusion models for paired-data tasks like image translation [28] and restoration [56]. However, diffusion bridge methods cannot be directly applied in robot learning tasks such as visual navigation, where no inherent source distribution exists to derive the target distribution. Therefore, the key challenge lies in constructing a suitable initial distribution and adapting the diffusion bridge techniques specifically for visual navigation." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.29, + 0.485, + 0.608 + ], + "angle": 0, + "content": "To address this, we introduce NaviBridger, a novel, unified visual navigation framework that leverages Denoising Diffusion Bridge Models (DDBM) [59]. NaviBridger redefines action generation by initiating from informative prior actions rather than random Gaussian noise, enhancing guidance and efficiency in the denoising process. We analyze its application in imitation learning, presenting key computational formulas, and provide a theoretical analysis revealing a crucial insight: the quality of the target action distribution improves when derived from a more suitable source distribution. Based on this insight, We introduce various initialization methods tailored to different source distribution types, including uninformative noise priors, informative handcrafted priors, and learning-based priors, with a detailed discussion of the advantages and limitations. NaviBridger also unifies previous visual navigation methods that relied on traditional diffusion models, and maintains compatibility with Gaussian noise when no suitable source distribution prior is available. NaviBridger is, to our knowledge, the first work to explore diffusion bridge models for visual navigation. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.482, + 0.718 + ], + "angle": 0, + "content": "- General Framework for Visual Navigation: We introduce NaviBridger, a visual navigation framework based on the denoising diffusion bridge model, which uses prior actions instead of Gaussian noise as the initial input, achieving an effective balance between performance and computational efficiency. This framework can be easily adapted to a variety of imitation learning tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.482, + 0.794 + ], + "angle": 0, + "content": "- Theoretical Analysis of Source Distributions: We theoretically analyze the impact of source distributions on diffusion-based model performance, presenting tailored methods for generating prior source actions, including Gaussian, rule-based, and learning-based priors." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.796, + 0.482, + 0.9 + ], + "angle": 0, + "content": "- Comprehensive Evaluation of NaviBridger: We conducted a comprehensive evaluation of our method across various scenarios and tasks, examining the effectiveness of the framework and the key design decisions of various source distributions and denoising steps. Experimental results show that NaviBridger exceeds baseline models across multiple scenarios." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.614, + 0.482, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.655, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.905, + 0.236 + ], + "angle": 0, + "content": "Diffusion Models [22, 46] have rapidly advanced in areas such as conditional generation [15, 21], faster training [48], and theoretical refinements [26, 49]. Their strong generative capabilities are widely applied in image restoration [31], image translation [40], and text-to-image generation [38]. Recently, diffusion models have shown potential in decision-making fields like reinforcement learning [61] and imitation learning [1, 24]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.237, + 0.905, + 0.372 + ], + "angle": 0, + "content": "Diffusion bridges, initially a tool in probability theory, have evolved into a key approach in generative modeling [29, 47]. [41] laid the groundwork, and [17] explored diffusion bridges conditioned on fixed start and endpoints. Recent work extends these ideas by applying Doob's \\( h \\)-transform for bridging arbitrary distributions [29]. [28] proposes reversing Brownian Bridges for distribution translation in discrete time, while [59] constructs bridge models using VP and VE diffusion processes in continuous time." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.373, + 0.905, + 0.689 + ], + "angle": 0, + "content": "Visual Navigation. Traditional navigation approaches [6, 7, 33] typically divide the navigation task into three main components: mapping [8, 37], localization [9, 55], and path planning [54], with each element showing considerable advancements in recent studies. However, the modular design can lead to cumulative information loss and rely heavily on precise measurements. Since Zhu et al. [60] pioneered the training of agents in simulated environments, learning-based visual navigation has progressed rapidly [2, 4, 10, 16, 32]. [60] employed deep reinforcement learning to address visual navigation challenges for image-based target search in small indoor simulation scenarios. Subsequent research has focused on improving visual representation by incorporating supplementary information[23], auxiliary tasks[39], or optimized networks [57]. By contrast, recent works such as [19, 30, 44] emphasize navigation tasks in real-world robotic systems, aiming to achieve zero-shot or few-shot navigation. ViNT [45] introduced a foundational model based on topological mapping for long-range navigation tasks and implemented the generation of latent subgoal images using diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Most recently, state-conditioned diffusion models for imitation learning in planning are particularly powerful[13, 24, 51]. NoMaD [50] incorporates diffusion models into visual navigation, enabling the direct generation of actions and achieving robust performance and enhanced multimodal representations. However, these approaches rely on standard diffusion models that denoise progressively from an initial Gaussian noise distribution. For more complex action spaces, this \"sampling from an initial Gaussian state\" approach often demands additional denoising steps [11]. Furthermore, since the Gaussian distribution differs significantly from the target action distribution, fitting the model to the target distribution becomes more challenging, potentially reducing the quality of generated actions [14, 34]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12101" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.092, + 0.904, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.351, + 0.908, + 0.396 + ], + "angle": 0, + "content": "Figure 2. NaviBridger Overview. The policy takes RGB observations and a goal image, extracting features via a Transformer encoder. The FiLM condition module applies learned conditions to improve path accuracy, while the prior generation module ensures the policy outputs better aligns with target actions, starting from alternative prior actions generated using optional prior policies." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.419, + 0.232, + 0.435 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.445, + 0.484, + 0.522 + ], + "angle": 0, + "content": "Diffusion Process: A diffusion process gradually adds noise to data, translating it from an initial distribution \\( p_0 \\) to a simpler, typically Gaussian distribution \\( p_T = \\mathcal{N}(0, I) \\). This forward process is modeled by the stochastic differential equation (SDE):" + }, + { + "type": "equation", + "bbox": [ + 0.189, + 0.54, + 0.483, + 0.557 + ], + "angle": 0, + "content": "\\[\nd \\mathbf {x} _ {t} = f (\\mathbf {x} _ {t}, t) d t + g (t) d \\mathbf {w} _ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.566, + 0.483, + 0.597 + ], + "angle": 0, + "content": "where \\(f\\) is the drift function, \\(g(t)\\) is the diffusion coefficient, and \\(\\mathbf{w}_t\\) represents the Wiener process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.484, + 0.629 + ], + "angle": 0, + "content": "The reverse process, which removes noise to reconstruct data, is governed by the reverse-time SDE:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.657, + 0.483, + 0.675 + ], + "angle": 0, + "content": "\\[\nd \\mathbf {x} _ {t} = \\left[ f \\left(\\mathbf {x} _ {t}, t\\right) - g (t) ^ {2} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) \\right] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.688, + 0.373, + 0.703 + ], + "angle": 0, + "content": "where \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)\\) is the score function." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.483, + 0.838 + ], + "angle": 0, + "content": "Diffusion Models generate images by progressively adding noise to data and then training neural networks to reverse this process, removing noise to recreate the original image. However, diffusion models are limited because they can only transport complex data distributions to a standard Gaussian distribution. Building upon the study of stochastic differential equations, using a diffusion process to map data to a known fixed endpoint is achievable through Doob's \\( h \\)-transform." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Diffusion Bridge: A diffusion bridge extends the diffusion process by interpolating between two fixed distributions, ensuring the generated data transitions from a starting distribution to a specified endpoint. The forward process" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.42, + 0.907, + 0.451 + ], + "angle": 0, + "content": "which is expanded from Eq.(1) of diffusion bridge is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.472, + 0.907, + 0.49 + ], + "angle": 0, + "content": "\\[\nd \\mathbf {x} _ {t} = [ f (\\mathbf {x} _ {t}, t) + g (t) ^ {2} h (\\mathbf {x} _ {t}, t, y, T) ] d t + g (t) d \\mathbf {w} _ {t}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.495, + 0.906, + 0.542 + ], + "angle": 0, + "content": "where \\( h(\\mathbf{x}_t, t, y, T) = \\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_T \\mid \\mathbf{x}_t) \\big|_{\\mathbf{x}_t = x, \\mathbf{x}_T = y} \\) is the Doob's \\( h \\)-transform ensures approximation to the target distribution \\( y \\) at time \\( T \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.542, + 0.907, + 0.603 + ], + "angle": 0, + "content": "Denoising Diffusion Bridge Models (DDBM): DDBMs generalize diffusion models by enabling transport between paired distributions, using reverse-time SDE or probability flow ODE. For the reverse diffusion bridge, the SDE is:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.62, + 0.837, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} d \\mathbf {x} _ {t} = \\left[ f (\\mathbf {x} _ {t}, t) - g (t) ^ {2} \\left(s \\left(\\mathbf {x} _ {t}, t, y, T\\right) \\right. \\right. \\\\ \\left. - h \\left(\\mathbf {x} _ {t}, t, y, T\\right)\\right) ] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.884, + 0.633, + 0.905, + 0.646 + ], + "angle": 0, + "content": "(4)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.664, + 0.907, + 0.789 + ], + "angle": 0, + "content": "where \\(\\mathbf{s}(\\mathbf{x}_t,t,y,T) = \\nabla_{\\mathbf{x}_t}\\log q(\\mathbf{x}_t\\mid \\mathbf{x}_T)\\big|_{\\mathbf{x}_t = x,\\mathbf{x}_T = y}\\) is the score function, \\(h(\\mathbf{x}_t,t,y,T)\\) ensures the transition to the target distribution. DDBM employs the sampling distribution \\(q(x_{t}\\mid x_{0},x_{T})\\) as an approximation for the challenging-to-obtain distribution \\(q(\\mathbf{x}_t\\mid \\mathbf{x}_T)\\), offering a defined expression for \\(q(x_{t}\\mid x_{0},x_{T})\\) and reparameterizing it to facilitate denoising (details provided in the Appendix). DDBMs use denoising score matching to learn the score function:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.794, + 0.905, + 0.826 + ], + "angle": 0, + "content": "\\[\nL _ {\\theta} = \\mathbb {E} _ {\\mathbf {x} _ {t}, \\mathbf {x} _ {0}, t} [ w (t) \\| s _ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {T}, t) - \\nabla_ {\\mathbf {x} _ {t}} \\log q (\\mathbf {x} _ {t} | \\mathbf {x} _ {0}, \\mathbf {x} _ {T}) \\| ^ {2} ] \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.871, + 0.84 + ], + "angle": 0, + "content": "where \\( w(t) \\) indicates the weight scheduler of the loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "This method allows DDBMs to translate between distributions effectively, expanding the scope of diffusion models to a wide range of generative tasks. More details about DDBM refer to the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12102" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.226, + 0.108 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.266 + ], + "angle": 0, + "content": "Motivated by the preceding discussion, we propose a novel approach, Navibridger. Instead of relying on sampling and denoising within a fixed Gaussian noise space, our method transforms this process into a denoising procedure that maps from an observation-based arbitrary source distribution policy \\(\\pi_s\\) to a target distribution policy \\(\\pi\\). Navibridger consists of three core components: a feature extraction module, a prior action generation module, and a denoising diffusion bridge module. The architecture illustration is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.267, + 0.484, + 0.495 + ], + "angle": 0, + "content": "In visual navigation, the objective is to design a control policy \\(\\pi\\) that allows a robot to execute target-oriented navigation effectively. The inputs to this policy consist of the robot's current and past visual observation sequence, denoted by \\(\\mathcal{O} = \\{I_t\\}_{t = T - p}^T\\), along with a future action sequence \\(\\mathbf{a} = \\{W_t\\}_{t = T}^{T + n}\\). Here, \\(p\\) represents the past time window. The policy can also incorporate a goal image \\(I_{g}\\) specifying the navigation target. Each observation \\(I_{i}\\) is mapped to a feature vector \\(\\phi (I_i)\\), which is subsequently processed by a Transformer encoder to produce a contextual vector \\(c_{t}\\) in the usual way. The context vector \\(c_{t}\\) is input into the prior action generation module to produce the source action \\(\\mathbf{a}_s\\in \\pi_s\\) associated with \\(I_{t}\\). The diffusion bridge model translates this source action into the desired target action \\(\\mathbf{a}\\in \\pi\\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.504, + 0.434, + 0.52 + ], + "angle": 0, + "content": "4.1. Diffusion Bridge for Imitation Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.527, + 0.484, + 0.618 + ], + "angle": 0, + "content": "In the imitation learning framework based on DDBM, the model employs a reverse diffusion process to progressively adjust the initial action distribution continuously, resulting in an action trajectory that satisfies the target requirements. Specifically, the DDBM reverse diffusion process for imitation learning can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.625, + 0.484, + 0.661 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} d \\mathbf {a} _ {t} = \\left[ f \\left(\\mathbf {a} _ {t}, t\\right) - g ^ {2} (t) \\left(s \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) \\right. \\right. \\tag {6} \\\\ \\left. - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) ] d t + g (t) d \\hat {w} _ {t}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.484, + 0.761 + ], + "angle": 0, + "content": "where \\( f(\\mathbf{a}_t, t) \\) denotes the drift term, \\( g(t) \\) is the diffusion coefficient, \\( s(\\mathbf{a}_t, t, \\mathbf{a}_T, T) \\) represents the score function that gives the conditional score at time \\( t \\) for the current state \\( \\mathbf{a}_t \\) relative to the target state \\( \\mathbf{a}_0 \\), and \\( h(\\mathbf{a}_t, t, \\mathbf{a}_T, T) \\) is the Doob's \\( h \\)-transform, applied to adjust the diffusion path, thereby ensuring a controlled transition from \\( \\mathbf{a}_s \\) to \\( \\mathbf{a}_T \\)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.761, + 0.484, + 0.792 + ], + "angle": 0, + "content": "\\(h(\\mathbf{a}_t,t,\\mathbf{a}_T,T)\\) is a function of \\(\\nabla_{\\mathbf{a}_t}\\log p(\\mathbf{a}_T\\mid \\mathbf{a}_t)\\) which is approximated by \\(q(\\mathbf{a}_t\\mid \\mathbf{a}_0,\\mathbf{a}_T)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.798, + 0.483, + 0.817 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {a} _ {t} \\mid \\mathbf {a} _ {0}, \\mathbf {a} _ {T}\\right) = \\mathcal {N} \\left(\\hat {\\mu} _ {t}, \\hat {\\sigma} _ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.834, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mu} _ {t} = \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} \\mathbf {a} _ {0} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (8) \\\\ \\hat {\\sigma} _ {t} ^ {2} = \\sigma_ {t} ^ {2} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (9) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.168 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) and \\(\\sigma_{t}\\) denote predefined signal and noise schedules, with the signal-to-noise ratio at time \\(t\\) given by \\(\\mathrm{SNR}_t = \\alpha_t^2 /\\sigma_t^2\\). With the reparametrization of Elucidating Diffusion Models, score function \\(\\mathbf{s}(\\mathbf{a},t,\\mathbf{a}_T,T)\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.192, + 0.905, + 0.264 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\mathbf {a} _ {t}} \\log q (\\mathbf {a} _ {t} | \\mathbf {a} _ {T}) \\approx \\mathbf {s} (D _ {\\theta}, \\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T) \\\\ = \\frac {\\mathbf {a} _ {t} - \\left(\\frac {S N R _ {T}}{S N R _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} D _ {\\theta} (\\mathbf {a} _ {t} , t , \\mathbf {a} _ {T}) \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)\\right)}{\\sigma_ {t} ^ {2} \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)}, \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.265, + 0.871, + 0.28 + ], + "angle": 0, + "content": "here, \\(D_{\\theta}(\\mathbf{a}_t,t,\\mathbf{a}_T)\\) denotes the output of the network." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.28, + 0.906, + 0.372 + ], + "angle": 0, + "content": "Based on the above inferences, we developed a foundational imitation learning framework utilizing diffusion bridges. This approach theoretically enables action sampling by transferring samples \\(\\mathbf{a}_T\\) from the source distribution \\(\\pi_s\\) to the target distribution \\(\\pi\\), with neural networks employed to learn the reverse denoising process." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.382, + 0.699, + 0.398 + ], + "angle": 0, + "content": "4.2. Prior Policy Design" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.405, + 0.906, + 0.496 + ], + "angle": 0, + "content": "Previous research on diffusion bridge models has primarily focused on tasks like image translation and style transfer, which involve paired input-output tasks where the input corresponds to a source distribution sample. Compared to Gaussian noise, a well-defined source distribution offers an informative prior, often yielding more accurate outcomes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.497, + 0.906, + 0.587 + ], + "angle": 0, + "content": "However, in imitation learning tasks, such as visual navigation, the target action is not inherently paired with an initial action. In this section, we present the theoretical foundation for designing the source distribution and introduce three distinct strategies for generating the source distribution specifically for visual navigation tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.588, + 0.906, + 0.692 + ], + "angle": 0, + "content": "Error Bound Analyzing: For a diffusion process to be effective, the initial source distribution must resemble the target distribution. If there is a significant discrepancy between the two, the diffusion process will require more extensive adjustments per step, amplifying drift, and score correction, thus increasing the probability of error in the likelihood flow ODE or SDE." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.694, + 0.906, + 0.77 + ], + "angle": 0, + "content": "Consider the error of the model denoising process. \\(\\mathbb{E}_{\\mathbf{a}_0}[\\| \\mathbf{a}_t - \\mathbf{a}_0\\|^2 ]\\) . This error is driven by the difference between the target distribution \\(\\pi (\\mathbf{a}_0)\\) and the source distribution \\(\\pi_s(\\mathbf{a}_T)\\) , which can be represented using the KullbackLeibler (KL) divergence as:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.782, + 0.905, + 0.815 + ], + "angle": 0, + "content": "\\[\nD _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right) = \\int \\pi_ {s} (\\mathbf {a} _ {T}) \\log \\frac {\\pi_ {s} (\\mathbf {a} _ {T})}{\\pi (\\mathbf {a} _ {0})} d \\mathbf {a} _ {T}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "This KL divergence measures how much information is \"lost\" if we approximate \\(\\pi (\\mathbf{a}_0)\\) by \\(\\pi_s(\\mathbf{a}_T)\\). A more minor divergence indicates a smaller amount of drift, and noise adjustment will be necessary for the DDBM to match the target. A probability flow ODE controls the evolution of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12103" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.235, + 0.106 + ], + "angle": 0, + "content": "samples in a DDBM:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.121, + 0.487, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\frac {d \\mathbf {a} _ {t}}{d t} = f (\\mathbf {a} _ {t}, t) - g ^ {2} (t) \\left(\\frac {1}{2} \\mathbf {s} \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.168, + 0.483, + 0.213 + ], + "angle": 0, + "content": "where \\(\\mathbf{s}(\\mathbf{a}_t,t,\\mathbf{a}_T,T) - h(\\mathbf{a}_t,t,\\mathbf{a}_T,T)\\) represents the adjustment needed to shift \\(\\mathbf{a}_t\\) closer to \\(\\mathbf{a}_0\\). The error bound for the model's convergence to \\(\\mathbf{a}_T\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.227, + 0.483, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}} \\left[ \\left\\| \\mathbf {a} _ {t} - \\mathbf {a} _ {0} \\right\\| ^ {2} \\right] \\leq C \\cdot D _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.261, + 0.484, + 0.351 + ], + "angle": 0, + "content": "where \\( C \\) is a constant that depends on factors such as the noise schedule \\( g(t) \\) and the time duration \\( T \\). Hence, the error bound shows that the closer the source distribution \\( q_{\\mathrm{source}} \\) is to the target distribution \\( q_{\\mathrm{target}} \\), the lower the error bound for the DDBM, resulting in a more accurate diffusion process and improved model performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.354, + 0.484, + 0.459 + ], + "angle": 0, + "content": "Prior Action Generation: As previously discussed, a source distribution that closely approximates the target distribution results in improved policy performance, underscoring the importance of an effective prior policy. A toy model is presented in Fig. 3. For the sake of comparison, we propose the following three methods for generating the prior action:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.483, + 0.551 + ], + "angle": 0, + "content": "- Gaussian Prior: As an uninformative prior, we select Gaussian white noise, consistent with that used in standard diffusion, as the source distribution, serving as the initial state in the denoising process. This choice facilitates direct comparison with methods based on the original diffusion approach." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.552, + 0.483, + 0.688 + ], + "angle": 0, + "content": "- Rule-based Prior: We employ a simple, fully connected layer to map the contextual vector \\( \\boldsymbol{c}_t \\) to the action space, enabling the extraction of relevant low-dimensional features for action generation. The prior action is preset as a parabolic path passing through the current position, determined based on the predicted path length \\( d \\) and movement behavior classification (straight, left turn, right turn, U-turn to the right, and U-turn to the left). Detailed information can be found in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.688, + 0.483, + 0.839 + ], + "angle": 0, + "content": "- Learning-based Prior: This method involves generating prior actions by utilizing expert data and learning models. We use a lightweight conditional variational autoencoder (CVAE) as our learning model to achieve a lightweight design while maintaining effective generation. The observations \\(\\mathcal{O}\\) are fed into the CVAE to produce corresponding actions. We aim for the model to effectively capture the significant correlations between observations and actions, thereby enabling a more efficient acquisition of the source distribution with reduced computational costs." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.462, + 0.483, + 0.839 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "These methods for prior action generation are readily adaptable to other tasks related to imitation learning. Through a comparative analysis of these methods, we seek to assess the potential advantages of the diffusion bridge." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.905, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.258, + 0.907, + 0.343 + ], + "angle": 0, + "content": "Figure 3. DDBM trained on 2D synthetic data. The leftmost side represents the source distribution, and the rightmost side represents the target distribution. The distance between the source distribution and the target distribution increases from top to bottom. As the EMD increases, the required approximation steps increase while model performance progressively declines." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.365, + 0.661, + 0.381 + ], + "angle": 0, + "content": "4.3. Traing Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.388, + 0.905, + 0.479 + ], + "angle": 0, + "content": "**Denoising Network:** We utilize a 1-D temporal CNN, conditioned on the \\( c_t \\) derived from observations, to iteratively denoise with the prior action \\( \\mathbf{a}_T \\) serving as the initial input. The network is modulated by \\( c_t \\) through Feature-wise Linear Modulation (FiLM) [36] and performs \\( k \\) iterations of denoising, following an approach similar to that of [13]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.905, + 0.54 + ], + "angle": 0, + "content": "Loss Function: The loss function in our architecture comprises the diffusion bridge loss \\(\\mathcal{L}_b\\), the prior action generation loss \\(\\mathcal{L}_p\\), and a temporal distance loss \\(\\mathcal{L}_d\\) designed for high-level planning (following [50])." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.54, + 0.905, + 0.57 + ], + "angle": 0, + "content": "The diffusion bridge loss \\(\\mathcal{L}_b\\) is calculated by a weighted Mean Square Error (MSE) loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.578, + 0.905, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} = \\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}, \\mathbf {a} _ {T}, t} [ w (t) \\| \\mathbf {a} _ {0} - D _ {\\theta} (\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}) \\| ^ {2} ], \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.603, + 0.906, + 0.725 + ], + "angle": 0, + "content": "The prior action generation loss \\(\\mathcal{L}_p\\) is categorized into rule-based and learning-based approaches. The rule-based approach uses a fully connected layer to generate a coarse action. It is accompanied by a classification task that classifies the action based on its movement direction (details in the Appendix). Thus, the loss function consists of an action prediction loss computed by Mean Squared Error (MSE) and a classification loss based on cross-entropy:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.732, + 0.905, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} ^ {r u l e} = - \\lambda_ {c} \\sum p _ {c} \\log (\\hat {p} _ {c}) + \\lambda_ {a} \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.906, + 0.856 + ], + "angle": 0, + "content": "where \\( p_c \\) represents the one-hot encoding of the ground truth class label, while \\( \\hat{p}_c \\) denotes the predicted probability. Additionally, a signifies the expert action, and \\( \\hat{\\mathbf{a}} \\) represents the predicted action by the FC layer. The terms \\( \\lambda_c \\) and \\( \\lambda_a \\) denote the respective weights for the loss functions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "The learning-based approach employs the Conditional Variational Autoencoder (CVAE) model to efficiently generate actions in a lightweight manner, with the associated" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12104" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.183, + 0.09, + 0.816, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison between the proposed method with baselines in simulation environments" + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.113, + 0.9, + 0.303 + ], + "angle": 0, + "content": "
SceneMethodBasic TaskAdaptation Task
Length (m)CollisionSuccessLength (m)CollisionSuccess
Indoor(2D-3D-S)ViNT [45]151.1 ± 31.5901.0268%19.9 ± 0.3141.5828%
NoMaD [50]147.9 ± 26.4750.7486%20.3 ± 0.2431.3232%
Gaussian Prior148.7 ± 28.5380.7282%19.8 ± 0.3170.9864%
Rule-based Prior163.57 ± 48.6582.5162%19.0 ± 1.390.8444%
Learning-based Prior143.7 ± 25.1750.6192%19.3 ± 0.340.4188%
Outdoor(Citysim)ViNT [45]254.8 ± 63.5970.7820%67.5 ± 26.3200.4138%
NoMaD [50]248.6 ± 67.6790.5822%68.3 ± 26.3150.3452%
Gaussian Prior244.8 ± 62.7490.6234%68.9 ± 24.6560.3550%
Rule-based Prior276.1 ± 83.7213.5914%71.8 ± 30.8560.5928%
Learning-based Prior237.7 ± 59.4760.5144%63.5 ± 20.6590.3064%
" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.323, + 0.308, + 0.337 + ], + "angle": 0, + "content": "loss function defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.346, + 0.482, + 0.399 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} ^ {c v a e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2} + \\operatorname {K L} (\\hat {\\pi} (z | \\mathcal {O}, \\mathbf {a}) \\| \\pi (z | \\mathcal {O})) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.4, + 0.483, + 0.43 + ], + "angle": 0, + "content": "where \\(\\hat{\\pi} (\\cdot)\\) represents the posterior distribution of actions, while \\(\\pi (\\cdot)\\) represents the prior." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.43, + 0.484, + 0.475 + ], + "angle": 0, + "content": "The temporal distance loss \\(\\mathcal{L}_d\\) quantifies the interval count between the target image and the current image within a discretized timeline:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.483, + 0.483, + 0.525 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| f (\\boldsymbol {c} _ {t, i}) - d _ {i} \\| ^ {2}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.535, + 0.483, + 0.566 + ], + "angle": 0, + "content": "where \\( f(\\pmb{c}_{t,i}) \\) represents the prediction of temporal distance, and \\( d_{i} \\) represents the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.566, + 0.399, + 0.58 + ], + "angle": 0, + "content": "In summary, the loss function is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.592, + 0.483, + 0.609 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {b} \\mathcal {L} _ {b} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {d} \\mathcal {L} _ {d}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.619, + 0.484, + 0.648 + ], + "angle": 0, + "content": "where \\(\\lambda_{b},\\lambda_{p}\\) and \\(\\lambda_{d}\\) denote the respective weights for the loss functions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.662, + 0.224, + 0.68 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.484, + 0.763 + ], + "angle": 0, + "content": "In this section, we comprehensively evaluate our method through simulated and real-world experiments in indoor and outdoor environments. The following sections provide an overview of the experimental setup, experiment results, and ablation studies." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.772, + 0.282, + 0.789 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Datasets. Our method and all baseline methods were trained on the same dataset to ensure a fair comparison. Following the approach in [50], the training data includes samples collected from diverse environments and various robotic platforms, incorporating data from RECON [42], SCAND [25], GoStanford [18], and SACSoN [20]. The dataset consists of sequences of consecutive image frames" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.323, + 0.905, + 0.353 + ], + "angle": 0, + "content": "along with their corresponding positional information, providing comprehensive scene diversity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.354, + 0.906, + 0.505 + ], + "angle": 0, + "content": "Baselines. We selected two state-of-the-art (SOTA) image-based visual navigation algorithms, NoMaD [50] and ViNT [45], for comparison. To examine the effect of integrating diffusion bridges on policy diffusion, we chose NoMaD, the first approach to apply policy diffusion to visual navigation tasks, which utilizes a standard diffusion policy model [13]. Additionally, we included ViNT, a regression-based model incorporating CNN and self-attention mechanisms, to compare the performance of generative and regression models in visual navigation tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.507, + 0.905, + 0.551 + ], + "angle": 0, + "content": "Metrics. We report three evaluation metrics in our experiments to comprehensively assess the performance of the diffusion bridge-based visual navigation method:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.552, + 0.905, + 0.597 + ], + "angle": 0, + "content": "Length: For paths that complete the task, we calculate the path lengths' mean and variance to assess the navigation paths' efficiency and consistency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.597, + 0.905, + 0.627 + ], + "angle": 0, + "content": "Collision: The average number of collisions per trial, which serves as an indicator of navigation safety." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.905, + 0.687 + ], + "angle": 0, + "content": "Success Rate: The success rate under consistent conditions. A trial is considered a failure if the robot does not reach the target position, becomes stuck due to collisions, or exceeds the time limit." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.794 + ], + "angle": 0, + "content": "Implementation details. We trained the model for 30 epochs using a learning rate 0.0001 and a batch size 256 (224 for learning-based methods). The training process, conducted on a single NVIDIA RTX TITAN GPU, took approximately 30 hours. For DDBM, we employed a VE model with parameters \\(\\sigma_0 = \\sigma_T = 0.5\\) and a default sampling step count of \\(k = 10\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Evaluation Settings. To validate the effectiveness of the proposed method, we conducted comparative experiments in a simulated environment, benchmarking against baseline methods and performing ablation studies. These experiments were conducted in both indoor and outdoor settings. Furthermore, we evaluated the models on a robotic platform to assess their practical performance. The model" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12105" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.472, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.089, + 0.906, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.248, + 0.908, + 0.292 + ], + "angle": 0, + "content": "Figure 4. Comparison of navigation performance in simulation and real-world environments. NaviBridger with rule-based and model-based priors (DDBM) generates smoother, more stable paths compared to NoMaD (DDPM), demonstrating improved alignment with the target trajectory over denoising steps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.298, + 0.483, + 0.329 + ], + "angle": 0, + "content": "operates on Nvidia Jetson Orin AGX deployed on the robot with RGB-only input." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.343, + 0.185, + 0.358 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.369, + 0.484, + 0.534 + ], + "angle": 0, + "content": "We conduct simulated experiments in two types of scenarios(Visualized in appendix): \\(i\\) ) Indoor (Stanford 2D-3D-S [3]) ii) Outdoor (Gazebo citysim [27]). In each scenario, we examine both basic and changed environments. The basic environment denotes a scenario where the test environment matches the configuration of the topological map, allowing us to evaluate long-distance navigation capabilities. The changed environment includes scenarios with obstacles in the test area that are not depicted in the topological map, aimed at testing the system's adaptability when the environment deviates from the mapped layout." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.537, + 0.484, + 0.822 + ], + "angle": 0, + "content": "Fig. 4 includes visualizations of the denoising process in both simulated indoor environments and real-world environments. For detailed configurations of the robot in both simulations and the physical setup, please refer to the Appendix. It can be observed that the DDPM-based method begins denoising from Gaussian noise, with most of the denoising process dedicated to constraining noise unsuitable for the action space into the action space, and only in the final few steps does it constrain the actions required by the task. In contrast, our method starts from a favorable initial state, achieving stable actions after only a few denoising steps, such as 2 to 4. Even when starting with Gaussian noise, our model reaches a stable action output in fewer denoising steps. This demonstrates that a rich prior significantly enhances the convergence of policy diffusion. Moreover, under the DDBM framework, even when using uninformed Gaussian noise as the source distribution, the denoising approximate rate is substantially faster than that of the DDPM-based method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.903 + ], + "angle": 0, + "content": "The experimental results of the proposed method compared to the baseline in the simulation environment are presented in Table 1. The learning-based prior method demonstrates optimal performance across various tasks and scenarios. The Gaussian prior method performs similarly to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.298, + 0.908, + 0.63 + ], + "angle": 0, + "content": "the DDPM-based NoMaD method, outperforming the baseline in the basic task within the outdoor scenario and the adaptation task within the indoor scenario. The rule-based method, on the other hand, only exceeds the baseline in the indoor adaptation task. These findings suggest that well-designed prior information can significantly improve the effectiveness of diffusion models, whereas poorly designed priors may impair model performance in specific scenarios. The rule-based method requires careful design of prior rules, which can yield significant improvements in some particular scenarios but generally lacks strong generalization across diverse conditions. When appropriate prior actions are unavailable, Gaussian noise is an acceptable initial distribution. A practical approach involves obtaining learned prior actions from a lightweight model and then generating actions through a diffusion bridge, offering a more versatile and robust solution. The learning-based method shows notable improvements in adaptation tasks and outdoor scenarios, indicating a solid capacity for generalization in complex and dynamic environments. In contrast, the DDPM-based method demonstrates comparatively weaker performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.648, + 0.68, + 0.664 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The impact of denoising steps on model learning. Table 2 shows the training results under different denoising step conditions, comparing the DDPM-based method and NaviBridger based on a Gaussian prior. We present the minimum mean squared error between the predicted action and the expert action on the training set and test sets of four datasets, along with the average ranking of each model across five items. Our method is closer to the expert trajectory in terms of overall data scale. Observing the trend, as the denoising steps decrease, the difference between the DDPM-based method's predicted trajectory and the expert trajectory increases significantly. In contrast, the difference between NaviBridger and a Gaussian prior remains relatively stable. This is also reflected in the average ranking; regardless of the number of denoising steps, Navibridger" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12106" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.152 + ], + "angle": 0, + "content": "consistently achieves a better ranking, with minimal variation in average ranking as the denoising steps change. Conversely, the DDPM-based method shows generally lower rankings with more considerable fluctuations." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.159, + 0.482, + 0.309 + ], + "angle": 0, + "content": "
NoMaD (DDPM)Gaussian Prior
k=1074110741
Train1.381.271.142.160.270.280.300.30
Recon1.191.100.971.430.880.910.890.98
Sacson1.741.731.653.131.651.431.611.52
SCAND0.720.760.711.170.590.690.630.61
Go Stanford4.123.473.463.893.473.443.223.32
Average Rank7.06.04.47.82.42.62.42.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.315, + 0.483, + 0.358 + ], + "angle": 0, + "content": "Table 2. Comparison of the mean square error between DDBM and vanilla diffusion model in predicting actions and expert actions in training sets and different test sets." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.363, + 0.48, + 0.486 + ], + "angle": 0, + "content": "
PriorMethodLength (m)Collision Success
GaussianSource-2.120%
Target19.8 ± 0.3170.9864%
Rule-basedSource28.1 ± 5.9421.778%
Target19.0 ± 1.3900.8444%
Learning-basedSource24.8 ± 1.351.4920%
Target19.3 ± 0.3400.4188%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.49, + 0.483, + 0.533 + ], + "angle": 0, + "content": "Table 3. Performance metrics of visual navigation tasks across different source priors: evaluation of policy effectiveness for source-target action mapping." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.538, + 0.483, + 0.765 + ], + "angle": 0, + "content": "The effect of source distribution and the role of diffusion bridge. Table 3 compares the navigation performance of the proposed method in an indoor adaptation task by examining prior actions sampled from different source distributions and the target actions obtained through denoising. As the prior generation method transitions from random to ordered and from heuristic-based to expert data-driven approaches, the success rate of navigation using only the prior actions shows some improvement, although it remains pretty low. After bridge denoising, the navigation success rate improves markedly. The experiments indicate that more informative prior actions contribute to better performance. At the same time, the diffusion bridge effectively transforms less effective prior actions into higher-quality target actions, thereby enhancing overall performance." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Less denoising steps and the same performance. The line chart as shown in Fig 5 illustrates the relationship between denoising steps, success rate, and inference time for visual navigation under different prior settings—Learning-based Prior DDBM, Gaussian Prior DDBM, and DDPM. Success rate, represented on the left vertical axis, generally increases as denoising steps progress, with the Learning-based Prior DDBM consistently achieving the highest success rates, peaking around \\(90\\%\\) at 10 denoising steps. In" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.095, + 0.898, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.29, + 0.907, + 0.361 + ], + "angle": 0, + "content": "Figure 5. Success rate and inference time comparison across denoising steps. Learning-based and Gaussian priors in DDBM show higher success rates than DDPM, with learning-based priors achieving the best performance. DDBM also demonstrates faster inference times as denoising steps increase." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.371, + 0.907, + 0.522 + ], + "angle": 0, + "content": "contrast, the Gaussian Prior DDBM shows a moderate success rate that fluctuates slightly, while DDPM achieves a lower success rate overall. The inference time indicated on the right vertical axis increases linearly with the denoising steps, and the time required by DDBM is longer than that of DDPM under the same denoising steps. Learning-based Prior DDBM demonstrates a more favorable balance between high success rate and moderate inference time, suggesting it is more efficient and reliable for visual navigation tasks than the Gaussian Prior DDBM and DDPM." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.542, + 0.634, + 0.558 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.907, + 0.796 + ], + "angle": 0, + "content": "This paper proposes a novel diffusion bridge-based framework for visual navigation. Our method advances policy generation by enabling translations across arbitrary distributions based on informative prior actions rather than the random Gaussian noise. Our theoretical analysis details fundamental principles, formulas, and the influence of source distributions on performance, along with an analysis of error lower bounds. Experimental results demonstrate a substantial increase in success rates and a reduction in collisions compared to baseline models in simulated environments. By exploring different strategies for source distribution generation and denoising steps, our method achieves greater robustness, more stability, and faster action generation than vanilla diffusion policy models, expanding the potential of policy diffusion in imitation learning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.798, + 0.907, + 0.858 + ], + "angle": 0, + "content": "However, although the results demonstrate a certain extent of generalization to dynamic scenarios, the scenario becomes more complex if high-speed moving objects are present, necessitating faster response or adaptive strategies." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.858, + 0.907, + 0.888 + ], + "angle": 0, + "content": "Acknowledgment. This work is supported by the China National Key R&D Program (2022YFB3903804)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12107" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua Tenenbaum, Tommi Jaakkola, and Pulkit Agrawal. Is conditional generative modeling all you need for decision-making? arXiv preprint arXiv:2211.15657, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.172, + 0.484, + 0.242 + ], + "angle": 0, + "content": "[2] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. Zero experience required: Plug & play modular transfer learning for semantic visual navigation. 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In visual navigation, previous diffusion-based policies typically generate action sequences by initiating from denoising Gaussian noise. However, the target action distribution often diverges significantly from Gaussian noise, leading to redundant denoising steps and increased learning complexity. Additionally, the sparsity of effective action distributions makes it challenging for the policy to generate accurate actions without guidance. To address these issues, we propose a novel, unified visual navigation framework leveraging the denoising diffusion bridge models named NaviBridger. This approach enables action generation by initiating from any informative prior actions, enhancing guidance and efficiency in the denoising process. We explore how diffusion bridges can enhance imitation learning in visual navigation tasks and further examine three source policies for generating prior actions. Extensive experiments in both simulated and real-world indoor and outdoor scenarios demonstrate that NaviBridger accelerates policy inference and outperforms the baselines in generating target action sequences. Code is available at https://github.com/hren20/NaviBridger. + +# 1. Introduction + +Visual navigation [5, 44, 58, 60] is vital for mobile robots, allowing them to reach targets like images or locations using visual observation. Previous methods typically consist of a global planner that provides high-level instructions or sub-goals, often leveraging large language models [10, 35, 43] or topological maps [50], to guide a local planner that generates feasible local paths in real time. Imitation learning from expert demonstrations for local path planning [45, 53] is emerging as a promising research direction, with advan + +![](images/37155b73169d7bc77f2f9cd056e22fb25eac9de4f950a8d689a241fced1689ae.jpg) +Figure 1. Visual representation overview of the local path generation process. The top row shows the actions generated through vanilla diffusion models denoising from Gaussian noise. The bottom row illustrates actions generated using proposed NaviBridger, which leverage prior information to effectively guide the denoising bridge model towards the target action. This comparison demonstrates the importance of incorporating prior knowledge in achieving stable and accurate navigation. + +tages in modeling multimodal distributions and capturing sequence correlation. + +Despite the significant progress of generative model-based local planners, this field faces two major issues due to the characteristics of generative models. First, substantial distributional discrepancies between the Gaussian noise, typically used in these models, and the robot's target action distribution lead to redundant denoising steps during inference. Second, the sparsity of desired actions makes it challenging for the policy to generate accurate actions, especially when denoising starts from chaotic random noise. Together, these issues increase computational costs and degrade overall performance. + +As Oscar Wilde stated, "Without order, nothing can exist; without chaos, nothing can evolve," prompting an in- + +triguing question: Could a structured, task-specific distribution serve as the starting point for denoising in diffusion models rather than relying on chaotic Gaussian noise? This idea aligns with optimal transport theory, which addresses translations between arbitrary distributions [12, 52], and has been successfully applied in diffusion models for paired-data tasks like image translation [28] and restoration [56]. However, diffusion bridge methods cannot be directly applied in robot learning tasks such as visual navigation, where no inherent source distribution exists to derive the target distribution. Therefore, the key challenge lies in constructing a suitable initial distribution and adapting the diffusion bridge techniques specifically for visual navigation. + +To address this, we introduce NaviBridger, a novel, unified visual navigation framework that leverages Denoising Diffusion Bridge Models (DDBM) [59]. NaviBridger redefines action generation by initiating from informative prior actions rather than random Gaussian noise, enhancing guidance and efficiency in the denoising process. We analyze its application in imitation learning, presenting key computational formulas, and provide a theoretical analysis revealing a crucial insight: the quality of the target action distribution improves when derived from a more suitable source distribution. Based on this insight, We introduce various initialization methods tailored to different source distribution types, including uninformative noise priors, informative handcrafted priors, and learning-based priors, with a detailed discussion of the advantages and limitations. NaviBridger also unifies previous visual navigation methods that relied on traditional diffusion models, and maintains compatibility with Gaussian noise when no suitable source distribution prior is available. NaviBridger is, to our knowledge, the first work to explore diffusion bridge models for visual navigation. Our contributions are as follows: + +- General Framework for Visual Navigation: We introduce NaviBridger, a visual navigation framework based on the denoising diffusion bridge model, which uses prior actions instead of Gaussian noise as the initial input, achieving an effective balance between performance and computational efficiency. This framework can be easily adapted to a variety of imitation learning tasks. +- Theoretical Analysis of Source Distributions: We theoretically analyze the impact of source distributions on diffusion-based model performance, presenting tailored methods for generating prior source actions, including Gaussian, rule-based, and learning-based priors. +- Comprehensive Evaluation of NaviBridger: We conducted a comprehensive evaluation of our method across various scenarios and tasks, examining the effectiveness of the framework and the key design decisions of various source distributions and denoising steps. Experimental results show that NaviBridger exceeds baseline models across multiple scenarios. + +# 2. Related Work + +Diffusion Models [22, 46] have rapidly advanced in areas such as conditional generation [15, 21], faster training [48], and theoretical refinements [26, 49]. Their strong generative capabilities are widely applied in image restoration [31], image translation [40], and text-to-image generation [38]. Recently, diffusion models have shown potential in decision-making fields like reinforcement learning [61] and imitation learning [1, 24]. + +Diffusion bridges, initially a tool in probability theory, have evolved into a key approach in generative modeling [29, 47]. [41] laid the groundwork, and [17] explored diffusion bridges conditioned on fixed start and endpoints. Recent work extends these ideas by applying Doob's $h$ -transform for bridging arbitrary distributions [29]. [28] proposes reversing Brownian Bridges for distribution translation in discrete time, while [59] constructs bridge models using VP and VE diffusion processes in continuous time. + +Visual Navigation. Traditional navigation approaches [6, 7, 33] typically divide the navigation task into three main components: mapping [8, 37], localization [9, 55], and path planning [54], with each element showing considerable advancements in recent studies. However, the modular design can lead to cumulative information loss and rely heavily on precise measurements. Since Zhu et al. [60] pioneered the training of agents in simulated environments, learning-based visual navigation has progressed rapidly [2, 4, 10, 16, 32]. [60] employed deep reinforcement learning to address visual navigation challenges for image-based target search in small indoor simulation scenarios. Subsequent research has focused on improving visual representation by incorporating supplementary information[23], auxiliary tasks[39], or optimized networks [57]. By contrast, recent works such as [19, 30, 44] emphasize navigation tasks in real-world robotic systems, aiming to achieve zero-shot or few-shot navigation. ViNT [45] introduced a foundational model based on topological mapping for long-range navigation tasks and implemented the generation of latent subgoal images using diffusion models. + +Most recently, state-conditioned diffusion models for imitation learning in planning are particularly powerful[13, 24, 51]. NoMaD [50] incorporates diffusion models into visual navigation, enabling the direct generation of actions and achieving robust performance and enhanced multimodal representations. However, these approaches rely on standard diffusion models that denoise progressively from an initial Gaussian noise distribution. For more complex action spaces, this "sampling from an initial Gaussian state" approach often demands additional denoising steps [11]. Furthermore, since the Gaussian distribution differs significantly from the target action distribution, fitting the model to the target distribution becomes more challenging, potentially reducing the quality of generated actions [14, 34]. + +![](images/4300746847bcc645c356748e655285fbf4a0c05521756aae747459a5115a1d50.jpg) +Figure 2. NaviBridger Overview. The policy takes RGB observations and a goal image, extracting features via a Transformer encoder. The FiLM condition module applies learned conditions to improve path accuracy, while the prior generation module ensures the policy outputs better aligns with target actions, starting from alternative prior actions generated using optional prior policies. + +# 3. Preliminaries + +Diffusion Process: A diffusion process gradually adds noise to data, translating it from an initial distribution $p_0$ to a simpler, typically Gaussian distribution $p_T = \mathcal{N}(0, I)$ . This forward process is modeled by the stochastic differential equation (SDE): + +$$ +d \mathbf {x} _ {t} = f (\mathbf {x} _ {t}, t) d t + g (t) d \mathbf {w} _ {t}, \tag {1} +$$ + +where $f$ is the drift function, $g(t)$ is the diffusion coefficient, and $\mathbf{w}_t$ represents the Wiener process. + +The reverse process, which removes noise to reconstruct data, is governed by the reverse-time SDE: + +$$ +d \mathbf {x} _ {t} = \left[ f \left(\mathbf {x} _ {t}, t\right) - g (t) ^ {2} \nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {x} _ {t}) \right] d t + g (t) d \bar {\mathbf {w}} _ {t}, \tag {2} +$$ + +where $\nabla_{\mathbf{x}_t}\log p(\mathbf{x}_t)$ is the score function. + +Diffusion Models generate images by progressively adding noise to data and then training neural networks to reverse this process, removing noise to recreate the original image. However, diffusion models are limited because they can only transport complex data distributions to a standard Gaussian distribution. Building upon the study of stochastic differential equations, using a diffusion process to map data to a known fixed endpoint is achievable through Doob's $h$ -transform. + +Diffusion Bridge: A diffusion bridge extends the diffusion process by interpolating between two fixed distributions, ensuring the generated data transitions from a starting distribution to a specified endpoint. The forward process + +which is expanded from Eq.(1) of diffusion bridge is expressed as: + +$$ +d \mathbf {x} _ {t} = [ f (\mathbf {x} _ {t}, t) + g (t) ^ {2} h (\mathbf {x} _ {t}, t, y, T) ] d t + g (t) d \mathbf {w} _ {t}, \tag {3} +$$ + +where $h(\mathbf{x}_t, t, y, T) = \nabla_{\mathbf{x}_t} \log p(\mathbf{x}_T \mid \mathbf{x}_t) \big|_{\mathbf{x}_t = x, \mathbf{x}_T = y}$ is the Doob's $h$ -transform ensures approximation to the target distribution $y$ at time $T$ . + +Denoising Diffusion Bridge Models (DDBM): DDBMs generalize diffusion models by enabling transport between paired distributions, using reverse-time SDE or probability flow ODE. For the reverse diffusion bridge, the SDE is: + +$$ +\begin{array}{l} d \mathbf {x} _ {t} = \left[ f (\mathbf {x} _ {t}, t) - g (t) ^ {2} \left(s \left(\mathbf {x} _ {t}, t, y, T\right) \right. \right. \\ \left. - h \left(\mathbf {x} _ {t}, t, y, T\right)\right) ] d t + g (t) d \bar {\mathbf {w}} _ {t}, \\ \end{array} +$$ + +(4) + +where $\mathbf{s}(\mathbf{x}_t,t,y,T) = \nabla_{\mathbf{x}_t}\log q(\mathbf{x}_t\mid \mathbf{x}_T)\big|_{\mathbf{x}_t = x,\mathbf{x}_T = y}$ is the score function, $h(\mathbf{x}_t,t,y,T)$ ensures the transition to the target distribution. DDBM employs the sampling distribution $q(x_{t}\mid x_{0},x_{T})$ as an approximation for the challenging-to-obtain distribution $q(\mathbf{x}_t\mid \mathbf{x}_T)$ , offering a defined expression for $q(x_{t}\mid x_{0},x_{T})$ and reparameterizing it to facilitate denoising (details provided in the Appendix). DDBMs use denoising score matching to learn the score function: + +$$ +L _ {\theta} = \mathbb {E} _ {\mathbf {x} _ {t}, \mathbf {x} _ {0}, t} [ w (t) \| s _ {\theta} (\mathbf {x} _ {t}, \mathbf {x} _ {T}, t) - \nabla_ {\mathbf {x} _ {t}} \log q (\mathbf {x} _ {t} | \mathbf {x} _ {0}, \mathbf {x} _ {T}) \| ^ {2} ] \tag {5} +$$ + +where $w(t)$ indicates the weight scheduler of the loss. + +This method allows DDBMs to translate between distributions effectively, expanding the scope of diffusion models to a wide range of generative tasks. More details about DDBM refer to the Appendix. + +# 4. Methodology + +Motivated by the preceding discussion, we propose a novel approach, Navibridger. Instead of relying on sampling and denoising within a fixed Gaussian noise space, our method transforms this process into a denoising procedure that maps from an observation-based arbitrary source distribution policy $\pi_s$ to a target distribution policy $\pi$ . Navibridger consists of three core components: a feature extraction module, a prior action generation module, and a denoising diffusion bridge module. The architecture illustration is shown in Fig. 2. + +In visual navigation, the objective is to design a control policy $\pi$ that allows a robot to execute target-oriented navigation effectively. The inputs to this policy consist of the robot's current and past visual observation sequence, denoted by $\mathcal{O} = \{I_t\}_{t = T - p}^T$ , along with a future action sequence $\mathbf{a} = \{W_t\}_{t = T}^{T + n}$ . Here, $p$ represents the past time window. The policy can also incorporate a goal image $I_{g}$ specifying the navigation target. Each observation $I_{i}$ is mapped to a feature vector $\phi (I_i)$ , which is subsequently processed by a Transformer encoder to produce a contextual vector $c_{t}$ in the usual way. The context vector $c_{t}$ is input into the prior action generation module to produce the source action $\mathbf{a}_s\in \pi_s$ associated with $I_{t}$ . The diffusion bridge model translates this source action into the desired target action $\mathbf{a}\in \pi$ . + +# 4.1. Diffusion Bridge for Imitation Learning + +In the imitation learning framework based on DDBM, the model employs a reverse diffusion process to progressively adjust the initial action distribution continuously, resulting in an action trajectory that satisfies the target requirements. Specifically, the DDBM reverse diffusion process for imitation learning can be described as follows: + +$$ +\begin{array}{l} d \mathbf {a} _ {t} = \left[ f \left(\mathbf {a} _ {t}, t\right) - g ^ {2} (t) \left(s \left(\mathbf {a} _ {t}, t, \mathbf {a} _ {T}, T\right) \right. \right. \tag {6} \\ \left. - h \left(\mathbf {a} _ {t}, t, \mathbf {a} _ {T}, T\right)\right) ] d t + g (t) d \hat {w} _ {t}, \\ \end{array} +$$ + +where $f(\mathbf{a}_t, t)$ denotes the drift term, $g(t)$ is the diffusion coefficient, $s(\mathbf{a}_t, t, \mathbf{a}_T, T)$ represents the score function that gives the conditional score at time $t$ for the current state $\mathbf{a}_t$ relative to the target state $\mathbf{a}_0$ , and $h(\mathbf{a}_t, t, \mathbf{a}_T, T)$ is the Doob's $h$ -transform, applied to adjust the diffusion path, thereby ensuring a controlled transition from $\mathbf{a}_s$ to $\mathbf{a}_T$ . + +$h(\mathbf{a}_t,t,\mathbf{a}_T,T)$ is a function of $\nabla_{\mathbf{a}_t}\log p(\mathbf{a}_T\mid \mathbf{a}_t)$ which is approximated by $q(\mathbf{a}_t\mid \mathbf{a}_0,\mathbf{a}_T)$ + +$$ +q \left(\mathbf {a} _ {t} \mid \mathbf {a} _ {0}, \mathbf {a} _ {T}\right) = \mathcal {N} \left(\hat {\mu} _ {t}, \hat {\sigma} _ {t} ^ {2} \boldsymbol {I}\right), \tag {7} +$$ + +$$ +\begin{array}{l} \hat {\mu} _ {t} = \frac {\mathrm {S N R} _ {T}}{\mathrm {S N R} _ {t}} \frac {\alpha_ {t}}{\alpha_ {T}} \mathbf {a} _ {T} + \alpha_ {t} \mathbf {a} _ {0} \left(1 - \frac {\mathrm {S N R} _ {T}}{\mathrm {S N R} _ {t}}\right), (8) \\ \hat {\sigma} _ {t} ^ {2} = \sigma_ {t} ^ {2} \left(1 - \frac {\mathrm {S N R} _ {T}}{\mathrm {S N R} _ {t}}\right), (9) \\ \end{array} +$$ + +where $\alpha_{t}$ and $\sigma_{t}$ denote predefined signal and noise schedules, with the signal-to-noise ratio at time $t$ given by $\mathrm{SNR}_t = \alpha_t^2 /\sigma_t^2$ . With the reparametrization of Elucidating Diffusion Models, score function $\mathbf{s}(\mathbf{a},t,\mathbf{a}_T,T)$ can be expressed as: + +$$ +\begin{array}{l} \nabla_ {\mathbf {a} _ {t}} \log q (\mathbf {a} _ {t} | \mathbf {a} _ {T}) \approx \mathbf {s} (D _ {\theta}, \mathbf {a} _ {t}, t, \mathbf {a} _ {T}, T) \\ = \frac {\mathbf {a} _ {t} - \left(\frac {S N R _ {T}}{S N R _ {t}} \frac {\alpha_ {t}}{\alpha_ {T}} \mathbf {a} _ {T} + \alpha_ {t} D _ {\theta} (\mathbf {a} _ {t} , t , \mathbf {a} _ {T}) \left(1 - \frac {S N R _ {T}}{S N R _ {t}}\right)\right)}{\sigma_ {t} ^ {2} \left(1 - \frac {S N R _ {T}}{S N R _ {t}}\right)}, \tag {10} \\ \end{array} +$$ + +here, $D_{\theta}(\mathbf{a}_t,t,\mathbf{a}_T)$ denotes the output of the network. + +Based on the above inferences, we developed a foundational imitation learning framework utilizing diffusion bridges. This approach theoretically enables action sampling by transferring samples $\mathbf{a}_T$ from the source distribution $\pi_s$ to the target distribution $\pi$ , with neural networks employed to learn the reverse denoising process. + +# 4.2. Prior Policy Design + +Previous research on diffusion bridge models has primarily focused on tasks like image translation and style transfer, which involve paired input-output tasks where the input corresponds to a source distribution sample. Compared to Gaussian noise, a well-defined source distribution offers an informative prior, often yielding more accurate outcomes. + +However, in imitation learning tasks, such as visual navigation, the target action is not inherently paired with an initial action. In this section, we present the theoretical foundation for designing the source distribution and introduce three distinct strategies for generating the source distribution specifically for visual navigation tasks. + +Error Bound Analyzing: For a diffusion process to be effective, the initial source distribution must resemble the target distribution. If there is a significant discrepancy between the two, the diffusion process will require more extensive adjustments per step, amplifying drift, and score correction, thus increasing the probability of error in the likelihood flow ODE or SDE. + +Consider the error of the model denoising process. $\mathbb{E}_{\mathbf{a}_0}[\| \mathbf{a}_t - \mathbf{a}_0\|^2 ]$ . This error is driven by the difference between the target distribution $\pi (\mathbf{a}_0)$ and the source distribution $\pi_s(\mathbf{a}_T)$ , which can be represented using the KullbackLeibler (KL) divergence as: + +$$ +D _ {\mathrm {K L}} \left(\pi_ {s} (\mathbf {a} _ {T}) \| \pi (\mathbf {a} _ {0})\right) = \int \pi_ {s} (\mathbf {a} _ {T}) \log \frac {\pi_ {s} (\mathbf {a} _ {T})}{\pi (\mathbf {a} _ {0})} d \mathbf {a} _ {T}. \tag {11} +$$ + +This KL divergence measures how much information is "lost" if we approximate $\pi (\mathbf{a}_0)$ by $\pi_s(\mathbf{a}_T)$ . A more minor divergence indicates a smaller amount of drift, and noise adjustment will be necessary for the DDBM to match the target. A probability flow ODE controls the evolution of + +samples in a DDBM: + +$$ +\frac {d \mathbf {a} _ {t}}{d t} = f (\mathbf {a} _ {t}, t) - g ^ {2} (t) \left(\frac {1}{2} \mathbf {s} \left(\mathbf {a} _ {t}, t, \mathbf {a} _ {T}, T\right) - h \left(\mathbf {a} _ {t}, t, \mathbf {a} _ {T}, T\right)\right) \tag {12} +$$ + +where $\mathbf{s}(\mathbf{a}_t,t,\mathbf{a}_T,T) - h(\mathbf{a}_t,t,\mathbf{a}_T,T)$ represents the adjustment needed to shift $\mathbf{a}_t$ closer to $\mathbf{a}_0$ . The error bound for the model's convergence to $\mathbf{a}_T$ can be formulated as: + +$$ +\mathbb {E} _ {\mathbf {a} _ {t}, \mathbf {a} _ {0}} \left[ \left\| \mathbf {a} _ {t} - \mathbf {a} _ {0} \right\| ^ {2} \right] \leq C \cdot D _ {\mathrm {K L}} \left(\pi_ {s} (\mathbf {a} _ {T}) \| \pi (\mathbf {a} _ {0})\right), \tag {13} +$$ + +where $C$ is a constant that depends on factors such as the noise schedule $g(t)$ and the time duration $T$ . Hence, the error bound shows that the closer the source distribution $q_{\mathrm{source}}$ is to the target distribution $q_{\mathrm{target}}$ , the lower the error bound for the DDBM, resulting in a more accurate diffusion process and improved model performance. + +Prior Action Generation: As previously discussed, a source distribution that closely approximates the target distribution results in improved policy performance, underscoring the importance of an effective prior policy. A toy model is presented in Fig. 3. For the sake of comparison, we propose the following three methods for generating the prior action: + +- Gaussian Prior: As an uninformative prior, we select Gaussian white noise, consistent with that used in standard diffusion, as the source distribution, serving as the initial state in the denoising process. This choice facilitates direct comparison with methods based on the original diffusion approach. +- Rule-based Prior: We employ a simple, fully connected layer to map the contextual vector $\boldsymbol{c}_t$ to the action space, enabling the extraction of relevant low-dimensional features for action generation. The prior action is preset as a parabolic path passing through the current position, determined based on the predicted path length $d$ and movement behavior classification (straight, left turn, right turn, U-turn to the right, and U-turn to the left). Detailed information can be found in the Appendix. +- Learning-based Prior: This method involves generating prior actions by utilizing expert data and learning models. We use a lightweight conditional variational autoencoder (CVAE) as our learning model to achieve a lightweight design while maintaining effective generation. The observations $\mathcal{O}$ are fed into the CVAE to produce corresponding actions. We aim for the model to effectively capture the significant correlations between observations and actions, thereby enabling a more efficient acquisition of the source distribution with reduced computational costs. + +These methods for prior action generation are readily adaptable to other tasks related to imitation learning. Through a comparative analysis of these methods, we seek to assess the potential advantages of the diffusion bridge. + +![](images/7f324dcdbffdfee2849c4fb0c1700d7c48d138a41d1a7bb9e40ec26abef2c28f.jpg) +Figure 3. DDBM trained on 2D synthetic data. The leftmost side represents the source distribution, and the rightmost side represents the target distribution. The distance between the source distribution and the target distribution increases from top to bottom. As the EMD increases, the required approximation steps increase while model performance progressively declines. + +# 4.3. Traing Details + +**Denoising Network:** We utilize a 1-D temporal CNN, conditioned on the $c_t$ derived from observations, to iteratively denoise with the prior action $\mathbf{a}_T$ serving as the initial input. The network is modulated by $c_t$ through Feature-wise Linear Modulation (FiLM) [36] and performs $k$ iterations of denoising, following an approach similar to that of [13]. + +Loss Function: The loss function in our architecture comprises the diffusion bridge loss $\mathcal{L}_b$ , the prior action generation loss $\mathcal{L}_p$ , and a temporal distance loss $\mathcal{L}_d$ designed for high-level planning (following [50]). + +The diffusion bridge loss $\mathcal{L}_b$ is calculated by a weighted Mean Square Error (MSE) loss function: + +$$ +\mathcal {L} _ {b} = \mathbb {E} _ {\mathbf {a} _ {t}, \mathbf {a} _ {0}, \mathbf {a} _ {T}, t} [ w (t) \| \mathbf {a} _ {0} - D _ {\theta} (\mathbf {a} _ {t}, t, \mathbf {a} _ {T}) \| ^ {2} ], \tag {14} +$$ + +The prior action generation loss $\mathcal{L}_p$ is categorized into rule-based and learning-based approaches. The rule-based approach uses a fully connected layer to generate a coarse action. It is accompanied by a classification task that classifies the action based on its movement direction (details in the Appendix). Thus, the loss function consists of an action prediction loss computed by Mean Squared Error (MSE) and a classification loss based on cross-entropy: + +$$ +\mathcal {L} _ {p} ^ {r u l e} = - \lambda_ {c} \sum p _ {c} \log (\hat {p} _ {c}) + \lambda_ {a} \frac {1}{N} \sum_ {i = 1} ^ {N} \| \hat {\mathbf {a}} _ {i} - \mathbf {a} _ {i} \| ^ {2}, \tag {15} +$$ + +where $p_c$ represents the one-hot encoding of the ground truth class label, while $\hat{p}_c$ denotes the predicted probability. Additionally, a signifies the expert action, and $\hat{\mathbf{a}}$ represents the predicted action by the FC layer. The terms $\lambda_c$ and $\lambda_a$ denote the respective weights for the loss functions. + +The learning-based approach employs the Conditional Variational Autoencoder (CVAE) model to efficiently generate actions in a lightweight manner, with the associated + +Table 1. Quantitative comparison between the proposed method with baselines in simulation environments + +
SceneMethodBasic TaskAdaptation Task
Length (m)CollisionSuccessLength (m)CollisionSuccess
Indoor(2D-3D-S)ViNT [45]151.1 ± 31.5901.0268%19.9 ± 0.3141.5828%
NoMaD [50]147.9 ± 26.4750.7486%20.3 ± 0.2431.3232%
Gaussian Prior148.7 ± 28.5380.7282%19.8 ± 0.3170.9864%
Rule-based Prior163.57 ± 48.6582.5162%19.0 ± 1.390.8444%
Learning-based Prior143.7 ± 25.1750.6192%19.3 ± 0.340.4188%
Outdoor(Citysim)ViNT [45]254.8 ± 63.5970.7820%67.5 ± 26.3200.4138%
NoMaD [50]248.6 ± 67.6790.5822%68.3 ± 26.3150.3452%
Gaussian Prior244.8 ± 62.7490.6234%68.9 ± 24.6560.3550%
Rule-based Prior276.1 ± 83.7213.5914%71.8 ± 30.8560.5928%
Learning-based Prior237.7 ± 59.4760.5144%63.5 ± 20.6590.3064%
+ +loss function defined as follows: + +$$ +\mathcal {L} _ {p} ^ {c v a e} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| \hat {\mathbf {a}} _ {i} - \mathbf {a} _ {i} \| ^ {2} + \operatorname {K L} (\hat {\pi} (z | \mathcal {O}, \mathbf {a}) \| \pi (z | \mathcal {O})) \tag {16} +$$ + +where $\hat{\pi} (\cdot)$ represents the posterior distribution of actions, while $\pi (\cdot)$ represents the prior. + +The temporal distance loss $\mathcal{L}_d$ quantifies the interval count between the target image and the current image within a discretized timeline: + +$$ +\mathcal {L} _ {d} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| f (\boldsymbol {c} _ {t, i}) - d _ {i} \| ^ {2}, \tag {17} +$$ + +where $f(\pmb{c}_{t,i})$ represents the prediction of temporal distance, and $d_{i}$ represents the ground truth. + +In summary, the loss function is defined as: + +$$ +\mathcal {L} = \lambda_ {b} \mathcal {L} _ {b} + \lambda_ {p} \mathcal {L} _ {p} + \lambda_ {d} \mathcal {L} _ {d}, \tag {18} +$$ + +where $\lambda_{b},\lambda_{p}$ and $\lambda_{d}$ denote the respective weights for the loss functions. + +# 5. Experiments + +In this section, we comprehensively evaluate our method through simulated and real-world experiments in indoor and outdoor environments. The following sections provide an overview of the experimental setup, experiment results, and ablation studies. + +# 5.1. Experimental Setup + +Datasets. Our method and all baseline methods were trained on the same dataset to ensure a fair comparison. Following the approach in [50], the training data includes samples collected from diverse environments and various robotic platforms, incorporating data from RECON [42], SCAND [25], GoStanford [18], and SACSoN [20]. The dataset consists of sequences of consecutive image frames + +along with their corresponding positional information, providing comprehensive scene diversity. + +Baselines. We selected two state-of-the-art (SOTA) image-based visual navigation algorithms, NoMaD [50] and ViNT [45], for comparison. To examine the effect of integrating diffusion bridges on policy diffusion, we chose NoMaD, the first approach to apply policy diffusion to visual navigation tasks, which utilizes a standard diffusion policy model [13]. Additionally, we included ViNT, a regression-based model incorporating CNN and self-attention mechanisms, to compare the performance of generative and regression models in visual navigation tasks. + +Metrics. We report three evaluation metrics in our experiments to comprehensively assess the performance of the diffusion bridge-based visual navigation method: + +Length: For paths that complete the task, we calculate the path lengths' mean and variance to assess the navigation paths' efficiency and consistency. + +Collision: The average number of collisions per trial, which serves as an indicator of navigation safety. + +Success Rate: The success rate under consistent conditions. A trial is considered a failure if the robot does not reach the target position, becomes stuck due to collisions, or exceeds the time limit. + +Implementation details. We trained the model for 30 epochs using a learning rate 0.0001 and a batch size 256 (224 for learning-based methods). The training process, conducted on a single NVIDIA RTX TITAN GPU, took approximately 30 hours. For DDBM, we employed a VE model with parameters $\sigma_0 = \sigma_T = 0.5$ and a default sampling step count of $k = 10$ . + +Evaluation Settings. To validate the effectiveness of the proposed method, we conducted comparative experiments in a simulated environment, benchmarking against baseline methods and performing ablation studies. These experiments were conducted in both indoor and outdoor settings. Furthermore, we evaluated the models on a robotic platform to assess their practical performance. The model + +![](images/7a9c7a02128945c1916ada686ec10b2f3138cac1a46f557eafe6056be893c40a.jpg) +Figure 4. Comparison of navigation performance in simulation and real-world environments. NaviBridger with rule-based and model-based priors (DDBM) generates smoother, more stable paths compared to NoMaD (DDPM), demonstrating improved alignment with the target trajectory over denoising steps. + +![](images/d60e37aecfd9a780d715466ba39d6b6d339b68ade338e86b6881145806470be9.jpg) + +operates on Nvidia Jetson Orin AGX deployed on the robot with RGB-only input. + +# 5.2. Results + +We conduct simulated experiments in two types of scenarios(Visualized in appendix): $i$ ) Indoor (Stanford 2D-3D-S [3]) ii) Outdoor (Gazebo citysim [27]). In each scenario, we examine both basic and changed environments. The basic environment denotes a scenario where the test environment matches the configuration of the topological map, allowing us to evaluate long-distance navigation capabilities. The changed environment includes scenarios with obstacles in the test area that are not depicted in the topological map, aimed at testing the system's adaptability when the environment deviates from the mapped layout. + +Fig. 4 includes visualizations of the denoising process in both simulated indoor environments and real-world environments. For detailed configurations of the robot in both simulations and the physical setup, please refer to the Appendix. It can be observed that the DDPM-based method begins denoising from Gaussian noise, with most of the denoising process dedicated to constraining noise unsuitable for the action space into the action space, and only in the final few steps does it constrain the actions required by the task. In contrast, our method starts from a favorable initial state, achieving stable actions after only a few denoising steps, such as 2 to 4. Even when starting with Gaussian noise, our model reaches a stable action output in fewer denoising steps. This demonstrates that a rich prior significantly enhances the convergence of policy diffusion. Moreover, under the DDBM framework, even when using uninformed Gaussian noise as the source distribution, the denoising approximate rate is substantially faster than that of the DDPM-based method. + +The experimental results of the proposed method compared to the baseline in the simulation environment are presented in Table 1. The learning-based prior method demonstrates optimal performance across various tasks and scenarios. The Gaussian prior method performs similarly to + +the DDPM-based NoMaD method, outperforming the baseline in the basic task within the outdoor scenario and the adaptation task within the indoor scenario. The rule-based method, on the other hand, only exceeds the baseline in the indoor adaptation task. These findings suggest that well-designed prior information can significantly improve the effectiveness of diffusion models, whereas poorly designed priors may impair model performance in specific scenarios. The rule-based method requires careful design of prior rules, which can yield significant improvements in some particular scenarios but generally lacks strong generalization across diverse conditions. When appropriate prior actions are unavailable, Gaussian noise is an acceptable initial distribution. A practical approach involves obtaining learned prior actions from a lightweight model and then generating actions through a diffusion bridge, offering a more versatile and robust solution. The learning-based method shows notable improvements in adaptation tasks and outdoor scenarios, indicating a solid capacity for generalization in complex and dynamic environments. In contrast, the DDPM-based method demonstrates comparatively weaker performance. + +# 5.3. Ablation Studies + +The impact of denoising steps on model learning. Table 2 shows the training results under different denoising step conditions, comparing the DDPM-based method and NaviBridger based on a Gaussian prior. We present the minimum mean squared error between the predicted action and the expert action on the training set and test sets of four datasets, along with the average ranking of each model across five items. Our method is closer to the expert trajectory in terms of overall data scale. Observing the trend, as the denoising steps decrease, the difference between the DDPM-based method's predicted trajectory and the expert trajectory increases significantly. In contrast, the difference between NaviBridger and a Gaussian prior remains relatively stable. This is also reflected in the average ranking; regardless of the number of denoising steps, Navibridger + +consistently achieves a better ranking, with minimal variation in average ranking as the denoising steps change. Conversely, the DDPM-based method shows generally lower rankings with more considerable fluctuations. + +
NoMaD (DDPM)Gaussian Prior
k=1074110741
Train1.381.271.142.160.270.280.300.30
Recon1.191.100.971.430.880.910.890.98
Sacson1.741.731.653.131.651.431.611.52
SCAND0.720.760.711.170.590.690.630.61
Go Stanford4.123.473.463.893.473.443.223.32
Average Rank7.06.04.47.82.42.62.42.8
+ +Table 2. Comparison of the mean square error between DDBM and vanilla diffusion model in predicting actions and expert actions in training sets and different test sets. + +
PriorMethodLength (m)Collision Success
GaussianSource-2.120%
Target19.8 ± 0.3170.9864%
Rule-basedSource28.1 ± 5.9421.778%
Target19.0 ± 1.3900.8444%
Learning-basedSource24.8 ± 1.351.4920%
Target19.3 ± 0.3400.4188%
+ +Table 3. Performance metrics of visual navigation tasks across different source priors: evaluation of policy effectiveness for source-target action mapping. + +The effect of source distribution and the role of diffusion bridge. Table 3 compares the navigation performance of the proposed method in an indoor adaptation task by examining prior actions sampled from different source distributions and the target actions obtained through denoising. As the prior generation method transitions from random to ordered and from heuristic-based to expert data-driven approaches, the success rate of navigation using only the prior actions shows some improvement, although it remains pretty low. After bridge denoising, the navigation success rate improves markedly. The experiments indicate that more informative prior actions contribute to better performance. At the same time, the diffusion bridge effectively transforms less effective prior actions into higher-quality target actions, thereby enhancing overall performance. + +Less denoising steps and the same performance. The line chart as shown in Fig 5 illustrates the relationship between denoising steps, success rate, and inference time for visual navigation under different prior settings—Learning-based Prior DDBM, Gaussian Prior DDBM, and DDPM. Success rate, represented on the left vertical axis, generally increases as denoising steps progress, with the Learning-based Prior DDBM consistently achieving the highest success rates, peaking around $90\%$ at 10 denoising steps. In + +![](images/202e0faeeb213a2393d10f2b0d7306edd4a75eee94710c97711c457b6ca81b5b.jpg) +Figure 5. Success rate and inference time comparison across denoising steps. Learning-based and Gaussian priors in DDBM show higher success rates than DDPM, with learning-based priors achieving the best performance. DDBM also demonstrates faster inference times as denoising steps increase. + +contrast, the Gaussian Prior DDBM shows a moderate success rate that fluctuates slightly, while DDPM achieves a lower success rate overall. The inference time indicated on the right vertical axis increases linearly with the denoising steps, and the time required by DDBM is longer than that of DDPM under the same denoising steps. Learning-based Prior DDBM demonstrates a more favorable balance between high success rate and moderate inference time, suggesting it is more efficient and reliable for visual navigation tasks than the Gaussian Prior DDBM and DDPM. + +# 6. Conclusion + +This paper proposes a novel diffusion bridge-based framework for visual navigation. Our method advances policy generation by enabling translations across arbitrary distributions based on informative prior actions rather than the random Gaussian noise. Our theoretical analysis details fundamental principles, formulas, and the influence of source distributions on performance, along with an analysis of error lower bounds. Experimental results demonstrate a substantial increase in success rates and a reduction in collisions compared to baseline models in simulated environments. By exploring different strategies for source distribution generation and denoising steps, our method achieves greater robustness, more stability, and faster action generation than vanilla diffusion policy models, expanding the potential of policy diffusion in imitation learning. + +However, although the results demonstrate a certain extent of generalization to dynamic scenarios, the scenario becomes more complex if high-speed moving objects are present, necessitating faster response or adaptive strategies. + +Acknowledgment. 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Diffusion models for reinforcement learning: A survey. arXiv preprint arXiv:2311.01223, 2023. 2 \ No newline at end of file diff --git a/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/images.zip b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..da2f59502d3a571920f4697237b756dab256693f --- /dev/null +++ b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d630fed439f3a5f8c4cd51fcdeaf51be8efc75edeb11714db29bfa2d185c093e +size 629238 diff --git a/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/layout.json b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fb397731960ac8820a52722a9c1bd9c1ac951dda --- /dev/null +++ b/2025/Prior Does Matter_ Visual Navigation via Denoising Diffusion Bridge Models/layout.json @@ -0,0 +1,9267 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "spans": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "type": "text", + "content": "Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "spans": [ + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": "Hao Ren" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": ", Yiming Zeng" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": ", Zetong Bi" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": ", Zhaoliang Wan" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": ", Junlong Huang" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": ", Hui Cheng" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": "School of Computer Science and Engineering, Sun Yat-sen University \n" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 98, + 142, + 515, + 186 + ], + "type": "text", + "content": "School of Intelligent Systems Engineering, Sun Yat-sen University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "spans": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 239, + 296, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 239, + 296, + 539 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 296, + 539 + ], + "type": "text", + "content": "Recent advancements in diffusion-based imitation learning, which shows impressive performance in modeling multimodal distributions and training stability, have led to substantial progress in various robot learning tasks. In visual navigation, previous diffusion-based policies typically generate action sequences by initiating from denoising Gaussian noise. However, the target action distribution often diverges significantly from Gaussian noise, leading to redundant denoising steps and increased learning complexity. Additionally, the sparsity of effective action distributions makes it challenging for the policy to generate accurate actions without guidance. To address these issues, we propose a novel, unified visual navigation framework leveraging the denoising diffusion bridge models named NaviBridger. This approach enables action generation by initiating from any informative prior actions, enhancing guidance and efficiency in the denoising process. We explore how diffusion bridges can enhance imitation learning in visual navigation tasks and further examine three source policies for generating prior actions. Extensive experiments in both simulated and real-world indoor and outdoor scenarios demonstrate that NaviBridger accelerates policy inference and outperforms the baselines in generating target action sequences. Code is available at https://github.com/hren20/NaviBridger." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 563, + 135, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 563, + 135, + 575 + ], + "spans": [ + { + "bbox": [ + 56, + 563, + 135, + 575 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 584, + 295, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 584, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 584, + 295, + 693 + ], + "type": "text", + "content": "Visual navigation [5, 44, 58, 60] is vital for mobile robots, allowing them to reach targets like images or locations using visual observation. Previous methods typically consist of a global planner that provides high-level instructions or sub-goals, often leveraging large language models [10, 35, 43] or topological maps [50], to guide a local planner that generates feasible local paths in real time. Imitation learning from expert demonstrations for local path planning [45, 53] is emerging as a promising research direction, with advan" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 320, + 215, + 549, + 430 + ], + "blocks": [ + { + "bbox": [ + 320, + 215, + 549, + 430 + ], + "lines": [ + { + "bbox": [ + 320, + 215, + 549, + 430 + ], + "spans": [ + { + "bbox": [ + 320, + 215, + 549, + 430 + ], + "type": "image", + "image_path": "37155b73169d7bc77f2f9cd056e22fb25eac9de4f950a8d689a241fced1689ae.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 440, + 555, + 529 + ], + "lines": [ + { + "bbox": [ + 313, + 440, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 440, + 555, + 529 + ], + "type": "text", + "content": "Figure 1. Visual representation overview of the local path generation process. The top row shows the actions generated through vanilla diffusion models denoising from Gaussian noise. The bottom row illustrates actions generated using proposed NaviBridger, which leverage prior information to effectively guide the denoising bridge model towards the target action. This comparison demonstrates the importance of incorporating prior knowledge in achieving stable and accurate navigation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 533, + 555, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 556 + ], + "type": "text", + "content": "tages in modeling multimodal distributions and capturing sequence correlation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 558, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 558, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 312, + 558, + 555, + 689 + ], + "type": "text", + "content": "Despite the significant progress of generative model-based local planners, this field faces two major issues due to the characteristics of generative models. First, substantial distributional discrepancies between the Gaussian noise, typically used in these models, and the robot's target action distribution lead to redundant denoising steps during inference. Second, the sparsity of desired actions makes it challenging for the policy to generate accurate actions, especially when denoising starts from chaotic random noise. Together, these issues increase computational costs and degrade overall performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "As Oscar Wilde stated, \"Without order, nothing can exist; without chaos, nothing can evolve,\" prompting an in-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 280, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 280, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 280, + 713 + ], + "type": "text", + "content": "*Corresponding author: Hui Cheng (chengh9@mail.sysu.edu.cn)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12100" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": "triguing question: Could a structured, task-specific distribution serve as the starting point for denoising in diffusion models rather than relying on chaotic Gaussian noise? This idea aligns with optimal transport theory, which addresses translations between arbitrary distributions [12, 52], and has been successfully applied in diffusion models for paired-data tasks like image translation [28] and restoration [56]. However, diffusion bridge methods cannot be directly applied in robot learning tasks such as visual navigation, where no inherent source distribution exists to derive the target distribution. Therefore, the key challenge lies in constructing a suitable initial distribution and adapting the diffusion bridge techniques specifically for visual navigation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 229, + 296, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 229, + 296, + 481 + ], + "spans": [ + { + "bbox": [ + 56, + 229, + 296, + 481 + ], + "type": "text", + "content": "To address this, we introduce NaviBridger, a novel, unified visual navigation framework that leverages Denoising Diffusion Bridge Models (DDBM) [59]. NaviBridger redefines action generation by initiating from informative prior actions rather than random Gaussian noise, enhancing guidance and efficiency in the denoising process. We analyze its application in imitation learning, presenting key computational formulas, and provide a theoretical analysis revealing a crucial insight: the quality of the target action distribution improves when derived from a more suitable source distribution. Based on this insight, We introduce various initialization methods tailored to different source distribution types, including uninformative noise priors, informative handcrafted priors, and learning-based priors, with a detailed discussion of the advantages and limitations. NaviBridger also unifies previous visual navigation methods that relied on traditional diffusion models, and maintains compatibility with Gaussian noise when no suitable source distribution prior is available. NaviBridger is, to our knowledge, the first work to explore diffusion bridge models for visual navigation. Our contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 486, + 294, + 712 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 486, + 294, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 294, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 294, + 568 + ], + "type": "text", + "content": "- General Framework for Visual Navigation: We introduce NaviBridger, a visual navigation framework based on the denoising diffusion bridge model, which uses prior actions instead of Gaussian noise as the initial input, achieving an effective balance between performance and computational efficiency. This framework can be easily adapted to a variety of imitation learning tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 570, + 294, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 294, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 294, + 628 + ], + "type": "text", + "content": "- Theoretical Analysis of Source Distributions: We theoretically analyze the impact of source distributions on diffusion-based model performance, presenting tailored methods for generating prior source actions, including Gaussian, rule-based, and learning-based priors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 630, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 630, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 54, + 630, + 294, + 712 + ], + "type": "text", + "content": "- Comprehensive Evaluation of NaviBridger: We conducted a comprehensive evaluation of our method across various scenarios and tasks, examining the effectiveness of the framework and the key design decisions of various source distributions and denoising steps. Experimental results show that NaviBridger exceeds baseline models across multiple scenarios." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 91, + 553, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 186 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 186 + ], + "type": "text", + "content": "Diffusion Models [22, 46] have rapidly advanced in areas such as conditional generation [15, 21], faster training [48], and theoretical refinements [26, 49]. Their strong generative capabilities are widely applied in image restoration [31], image translation [40], and text-to-image generation [38]. Recently, diffusion models have shown potential in decision-making fields like reinforcement learning [61] and imitation learning [1, 24]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 187, + 553, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 187, + 553, + 294 + ], + "spans": [ + { + "bbox": [ + 313, + 187, + 553, + 294 + ], + "type": "text", + "content": "Diffusion bridges, initially a tool in probability theory, have evolved into a key approach in generative modeling [29, 47]. [41] laid the groundwork, and [17] explored diffusion bridges conditioned on fixed start and endpoints. Recent work extends these ideas by applying Doob's " + }, + { + "bbox": [ + 313, + 187, + 553, + 294 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 187, + 553, + 294 + ], + "type": "text", + "content": "-transform for bridging arbitrary distributions [29]. [28] proposes reversing Brownian Bridges for distribution translation in discrete time, while [59] constructs bridge models using VP and VE diffusion processes in continuous time." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 295, + 553, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 295, + 553, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 553, + 545 + ], + "type": "text", + "content": "Visual Navigation. Traditional navigation approaches [6, 7, 33] typically divide the navigation task into three main components: mapping [8, 37], localization [9, 55], and path planning [54], with each element showing considerable advancements in recent studies. However, the modular design can lead to cumulative information loss and rely heavily on precise measurements. Since Zhu et al. [60] pioneered the training of agents in simulated environments, learning-based visual navigation has progressed rapidly [2, 4, 10, 16, 32]. [60] employed deep reinforcement learning to address visual navigation challenges for image-based target search in small indoor simulation scenarios. Subsequent research has focused on improving visual representation by incorporating supplementary information[23], auxiliary tasks[39], or optimized networks [57]. By contrast, recent works such as [19, 30, 44] emphasize navigation tasks in real-world robotic systems, aiming to achieve zero-shot or few-shot navigation. ViNT [45] introduced a foundational model based on topological mapping for long-range navigation tasks and implemented the generation of latent subgoal images using diffusion models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": "Most recently, state-conditioned diffusion models for imitation learning in planning are particularly powerful[13, 24, 51]. NoMaD [50] incorporates diffusion models into visual navigation, enabling the direct generation of actions and achieving robust performance and enhanced multimodal representations. However, these approaches rely on standard diffusion models that denoise progressively from an initial Gaussian noise distribution. For more complex action spaces, this \"sampling from an initial Gaussian state\" approach often demands additional denoising steps [11]. Furthermore, since the Gaussian distribution differs significantly from the target action distribution, fitting the model to the target distribution becomes more challenging, potentially reducing the quality of generated actions [14, 34]." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12101" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 72, + 553, + 270 + ], + "blocks": [ + { + "bbox": [ + 57, + 72, + 553, + 270 + ], + "lines": [ + { + "bbox": [ + 57, + 72, + 553, + 270 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 553, + 270 + ], + "type": "image", + "image_path": "4300746847bcc645c356748e655285fbf4a0c05521756aae747459a5115a1d50.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 277, + 555, + 313 + ], + "lines": [ + { + "bbox": [ + 55, + 277, + 555, + 313 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 555, + 313 + ], + "type": "text", + "content": "Figure 2. NaviBridger Overview. The policy takes RGB observations and a goal image, extracting features via a Transformer encoder. The FiLM condition module applies learned conditions to improve path accuracy, while the prior generation module ensures the policy outputs better aligns with target actions, starting from alternative prior actions generated using optional prior policies." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 331, + 141, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 141, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 141, + 344 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "text", + "content": "Diffusion Process: A diffusion process gradually adds noise to data, translating it from an initial distribution " + }, + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "text", + "content": " to a simpler, typically Gaussian distribution " + }, + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "inline_equation", + "content": "p_T = \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 55, + 352, + 296, + 413 + ], + "type": "text", + "content": ". This forward process is modeled by the stochastic differential equation (SDE):" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 427, + 295, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 427, + 295, + 441 + ], + "spans": [ + { + "bbox": [ + 115, + 427, + 295, + 441 + ], + "type": "interline_equation", + "content": "d \\mathbf {x} _ {t} = f (\\mathbf {x} _ {t}, t) d t + g (t) d \\mathbf {w} _ {t}, \\tag {1}", + "image_path": "d779cdc1395e2d54a26bd047e1fc9625a7315f3add52e7b947b942935b5a86de.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "text", + "content": " is the drift function, " + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "text", + "content": " is the diffusion coefficient, and " + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_t" + }, + { + "bbox": [ + 55, + 448, + 295, + 472 + ], + "type": "text", + "content": " represents the Wiener process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 472, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 498 + ], + "type": "text", + "content": "The reverse process, which removes noise to reconstruct data, is governed by the reverse-time SDE:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 62, + 520, + 295, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 520, + 295, + 534 + ], + "spans": [ + { + "bbox": [ + 62, + 520, + 295, + 534 + ], + "type": "interline_equation", + "content": "d \\mathbf {x} _ {t} = \\left[ f \\left(\\mathbf {x} _ {t}, t\\right) - g (t) ^ {2} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) \\right] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\tag {2}", + "image_path": "852f3fa71b97d69f106d5f8472efb756b20cdfc3fdd7cec156b812d5543e9faf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 544, + 228, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 228, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 228, + 556 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 544, + 228, + 556 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)" + }, + { + "bbox": [ + 55, + 544, + 228, + 556 + ], + "type": "text", + "content": " is the score function." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 557, + 295, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 295, + 663 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 295, + 663 + ], + "type": "text", + "content": "Diffusion Models generate images by progressively adding noise to data and then training neural networks to reverse this process, removing noise to recreate the original image. However, diffusion models are limited because they can only transport complex data distributions to a standard Gaussian distribution. Building upon the study of stochastic differential equations, using a diffusion process to map data to a known fixed endpoint is achievable through Doob's " + }, + { + "bbox": [ + 55, + 557, + 295, + 663 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 55, + 557, + 295, + 663 + ], + "type": "text", + "content": "-transform." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Diffusion Bridge: A diffusion bridge extends the diffusion process by interpolating between two fixed distributions, ensuring the generated data transitions from a starting distribution to a specified endpoint. The forward process" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 332, + 555, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 332, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 332, + 555, + 357 + ], + "type": "text", + "content": "which is expanded from Eq.(1) of diffusion bridge is expressed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 322, + 373, + 555, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 373, + 555, + 388 + ], + "spans": [ + { + "bbox": [ + 322, + 373, + 555, + 388 + ], + "type": "interline_equation", + "content": "d \\mathbf {x} _ {t} = [ f (\\mathbf {x} _ {t}, t) + g (t) ^ {2} h (\\mathbf {x} _ {t}, t, y, T) ] d t + g (t) d \\mathbf {w} _ {t}, \\tag {3}", + "image_path": "8a0e929078c13ee82b70b60cdfbdc143445036618390a44dbfc6b2230fb8bd6c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x}_t, t, y, T) = \\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_T \\mid \\mathbf{x}_t) \\big|_{\\mathbf{x}_t = x, \\mathbf{x}_T = y}" + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "content": " is the Doob's " + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "content": "-transform ensures approximation to the target distribution " + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 392, + 554, + 429 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 429, + 555, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 429, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 555, + 477 + ], + "type": "text", + "content": "Denoising Diffusion Bridge Models (DDBM): DDBMs generalize diffusion models by enabling transport between paired distributions, using reverse-time SDE or probability flow ODE. For the reverse diffusion bridge, the SDE is:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 354, + 491, + 512, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 491, + 512, + 520 + ], + "spans": [ + { + "bbox": [ + 354, + 491, + 512, + 520 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} d \\mathbf {x} _ {t} = \\left[ f (\\mathbf {x} _ {t}, t) - g (t) ^ {2} \\left(s \\left(\\mathbf {x} _ {t}, t, y, T\\right) \\right. \\right. \\\\ \\left. - h \\left(\\mathbf {x} _ {t}, t, y, T\\right)\\right) ] d t + g (t) d \\bar {\\mathbf {w}} _ {t}, \\\\ \\end{array}", + "image_path": "203c303b5df4f99cb93899a9a52d887fed20943a00d655a7063d2aeeab0090bb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 541, + 501, + 553, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 541, + 501, + 553, + 511 + ], + "spans": [ + { + "bbox": [ + 541, + 501, + 553, + 511 + ], + "type": "text", + "content": "(4)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x}_t,t,y,T) = \\nabla_{\\mathbf{x}_t}\\log q(\\mathbf{x}_t\\mid \\mathbf{x}_T)\\big|_{\\mathbf{x}_t = x,\\mathbf{x}_T = y}" + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": " is the score function, " + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x}_t,t,y,T)" + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": " ensures the transition to the target distribution. DDBM employs the sampling distribution " + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "inline_equation", + "content": "q(x_{t}\\mid x_{0},x_{T})" + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": " as an approximation for the challenging-to-obtain distribution " + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t\\mid \\mathbf{x}_T)" + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": ", offering a defined expression for " + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "inline_equation", + "content": "q(x_{t}\\mid x_{0},x_{T})" + }, + { + "bbox": [ + 313, + 525, + 555, + 624 + ], + "type": "text", + "content": " and reparameterizing it to facilitate denoising (details provided in the Appendix). DDBMs use denoising score matching to learn the score function:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 628, + 553, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 628, + 553, + 654 + ], + "spans": [ + { + "bbox": [ + 315, + 628, + 553, + 654 + ], + "type": "interline_equation", + "content": "L _ {\\theta} = \\mathbb {E} _ {\\mathbf {x} _ {t}, \\mathbf {x} _ {0}, t} [ w (t) \\| s _ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {T}, t) - \\nabla_ {\\mathbf {x} _ {t}} \\log q (\\mathbf {x} _ {t} | \\mathbf {x} _ {0}, \\mathbf {x} _ {T}) \\| ^ {2} ] \\tag {5}", + "image_path": "9dee749186856c3265dbc48ad948817501a71a6b8a7ab782da83be66ba0b6689.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 654, + 533, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 533, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 533, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 654, + 533, + 665 + ], + "type": "inline_equation", + "content": "w(t)" + }, + { + "bbox": [ + 313, + 654, + 533, + 665 + ], + "type": "text", + "content": " indicates the weight scheduler of the loss." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "This method allows DDBMs to translate between distributions effectively, expanding the scope of diffusion models to a wide range of generative tasks. More details about DDBM refer to the Appendix." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12102" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 138, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 138, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 138, + 85 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "content": "Motivated by the preceding discussion, we propose a novel approach, Navibridger. Instead of relying on sampling and denoising within a fixed Gaussian noise space, our method transforms this process into a denoising procedure that maps from an observation-based arbitrary source distribution policy " + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "inline_equation", + "content": "\\pi_s" + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "content": " to a target distribution policy " + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 55, + 91, + 296, + 210 + ], + "type": "text", + "content": ". Navibridger consists of three core components: a feature extraction module, a prior action generation module, and a denoising diffusion bridge module. The architecture illustration is shown in Fig. 2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": "In visual navigation, the objective is to design a control policy " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " that allows a robot to execute target-oriented navigation effectively. The inputs to this policy consist of the robot's current and past visual observation sequence, denoted by " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = \\{I_t\\}_{t = T - p}^T" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": ", along with a future action sequence " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{a} = \\{W_t\\}_{t = T}^{T + n}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " represents the past time window. The policy can also incorporate a goal image " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "I_{g}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " specifying the navigation target. Each observation " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " is mapped to a feature vector " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\phi (I_i)" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": ", which is subsequently processed by a Transformer encoder to produce a contextual vector " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "c_{t}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " in the usual way. The context vector " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "c_{t}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " is input into the prior action generation module to produce the source action " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_s\\in \\pi_s" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": " associated with " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": ". The diffusion bridge model translates this source action into the desired target action " + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{a}\\in \\pi" + }, + { + "bbox": [ + 55, + 211, + 296, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 399, + 265, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 265, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 265, + 411 + ], + "type": "text", + "content": "4.1. Diffusion Bridge for Imitation Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 417, + 296, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 417, + 296, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 417, + 296, + 489 + ], + "type": "text", + "content": "In the imitation learning framework based on DDBM, the model employs a reverse diffusion process to progressively adjust the initial action distribution continuously, resulting in an action trajectory that satisfies the target requirements. Specifically, the DDBM reverse diffusion process for imitation learning can be described as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 94, + 495, + 296, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 495, + 296, + 523 + ], + "spans": [ + { + "bbox": [ + 94, + 495, + 296, + 523 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} d \\mathbf {a} _ {t} = \\left[ f \\left(\\mathbf {a} _ {t}, t\\right) - g ^ {2} (t) \\left(s \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) \\right. \\right. \\tag {6} \\\\ \\left. - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) ] d t + g (t) d \\hat {w} _ {t}, \\\\ \\end{array}", + "image_path": "c462efb0f037635cfea055d21d7b8314b3651739a74fa5d7b60e8c4c86cc4c00.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + 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"text", + "content": " for the current state " + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_t" + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "text", + "content": " relative to the target state " + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_0" + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "inline_equation", + "content": "h(\\mathbf{a}_t, t, \\mathbf{a}_T, T)" + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "text", + "content": " is the Doob's " + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 55, + 530, + 296, + 602 + ], + "type": "text", + "content": "-transform, applied to adjust the diffusion path, thereby ensuring a controlled transition from " + }, + { + 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296, + 627 + ], + "type": "text", + "content": " which is approximated by " + }, + { + "bbox": [ + 55, + 602, + 296, + 627 + ], + "type": "inline_equation", + "content": "q(\\mathbf{a}_t\\mid \\mathbf{a}_0,\\mathbf{a}_T)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 632, + 295, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 632, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 108, + 632, + 295, + 647 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {a} _ {t} \\mid \\mathbf {a} _ {0}, \\mathbf {a} _ {T}\\right) = \\mathcal {N} \\left(\\hat {\\mu} _ {t}, \\hat {\\sigma} _ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {7}", + "image_path": "f798d8d958555df4237b03d62826dc7280a5d80b7aabeacf2e07ee05c67f2468.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 90, + 660, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 660, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 90, + 660, + 295, + 717 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mu} _ {t} = \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} \\mathbf {a} _ {0} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (8) \\\\ \\hat {\\sigma} _ {t} ^ {2} = \\sigma_ {t} ^ {2} \\left(1 - \\frac {\\mathrm {S N R} _ {T}}{\\mathrm {S N R} _ {t}}\\right), (9) \\\\ \\end{array}", + "image_path": "edafedf0bff6726527c35948cfafe3f1641b8841e474de0c3e8b0f2a545f506f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 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With the reparametrization of Elucidating Diffusion Models, score function " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{a},t,\\mathbf{a}_T,T)" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 319, + 152, + 553, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 152, + 553, + 209 + ], + "spans": [ + { + "bbox": [ + 319, + 152, + 553, + 209 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\mathbf {a} _ {t}} \\log q (\\mathbf {a} _ {t} | \\mathbf {a} _ {T}) \\approx \\mathbf {s} (D _ {\\theta}, \\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T) \\\\ = \\frac {\\mathbf {a} _ {t} - \\left(\\frac {S N R _ {T}}{S N R _ {t}} \\frac {\\alpha_ {t}}{\\alpha_ {T}} \\mathbf {a} _ {T} + \\alpha_ {t} D _ {\\theta} (\\mathbf {a} _ {t} , t , \\mathbf {a} _ {T}) \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)\\right)}{\\sigma_ {t} ^ {2} \\left(1 - \\frac {S N R _ {T}}{S N R _ {t}}\\right)}, \\tag {10} \\\\ \\end{array}", + "image_path": "6a41f803296798dd87a681acc99a5b94331607d06c2e7268f1370c8ecfb8f113.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 209, + 533, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 533, + 221 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 533, + 221 + ], + "type": "text", + "content": "here, " + }, + { + "bbox": [ + 313, + 209, + 533, + 221 + ], + "type": "inline_equation", + "content": "D_{\\theta}(\\mathbf{a}_t,t,\\mathbf{a}_T)" + }, + { + "bbox": [ + 313, + 209, + 533, + 221 + ], + "type": "text", + "content": " denotes the output of the network." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "text", + "content": "Based on the above inferences, we developed a foundational imitation learning framework utilizing diffusion bridges. This approach theoretically enables action sampling by transferring samples " + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_T" + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "text", + "content": " from the source distribution " + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "inline_equation", + "content": "\\pi_s" + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "text", + "content": " to the target distribution " + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 221, + 554, + 294 + ], + "type": "text", + "content": ", with neural networks employed to learn the reverse denoising process." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 302, + 427, + 315 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 302, + 427, + 315 + ], + "spans": [ + { + "bbox": [ + 313, + 302, + 427, + 315 + ], + "type": "text", + "content": "4.2. Prior Policy Design" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 320, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 554, + 392 + ], + "type": "text", + "content": "Previous research on diffusion bridge models has primarily focused on tasks like image translation and style transfer, which involve paired input-output tasks where the input corresponds to a source distribution sample. Compared to Gaussian noise, a well-defined source distribution offers an informative prior, often yielding more accurate outcomes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 393, + 554, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 554, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 554, + 464 + ], + "type": "text", + "content": "However, in imitation learning tasks, such as visual navigation, the target action is not inherently paired with an initial action. In this section, we present the theoretical foundation for designing the source distribution and introduce three distinct strategies for generating the source distribution specifically for visual navigation tasks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 465, + 554, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 465, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 465, + 554, + 548 + ], + "type": "text", + "content": "Error Bound Analyzing: For a diffusion process to be effective, the initial source distribution must resemble the target distribution. If there is a significant discrepancy between the two, the diffusion process will require more extensive adjustments per step, amplifying drift, and score correction, thus increasing the probability of error in the likelihood flow ODE or SDE." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "spans": [ + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "text", + "content": "Consider the error of the model denoising process. " + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{\\mathbf{a}_0}[\\| \\mathbf{a}_t - \\mathbf{a}_0\\|^2 ]" + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "text", + "content": " . This error is driven by the difference between the target distribution " + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "inline_equation", + "content": "\\pi (\\mathbf{a}_0)" + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "text", + "content": " and the source distribution " + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "inline_equation", + "content": "\\pi_s(\\mathbf{a}_T)" + }, + { + "bbox": [ + 313, + 549, + 554, + 609 + ], + "type": "text", + "content": " , which can be represented using the KullbackLeibler (KL) divergence as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 320, + 619, + 553, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 619, + 553, + 645 + ], + "spans": [ + { + "bbox": [ + 320, + 619, + 553, + 645 + ], + "type": "interline_equation", + "content": "D _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right) = \\int \\pi_ {s} (\\mathbf {a} _ {T}) \\log \\frac {\\pi_ {s} (\\mathbf {a} _ {T})}{\\pi (\\mathbf {a} _ {0})} d \\mathbf {a} _ {T}. \\tag {11}", + "image_path": "84ecafef6bfea8174d69b87578538678a532a8d823fa35989079f66cbef06ae1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "This KL divergence measures how much information is \"lost\" if we approximate " + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\pi (\\mathbf{a}_0)" + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\pi_s(\\mathbf{a}_T)" + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": ". A more minor divergence indicates a smaller amount of drift, and noise adjustment will be necessary for the DDBM to match the target. A probability flow ODE controls the evolution of" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12103" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 143, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 143, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 143, + 83 + ], + "type": "text", + "content": "samples in a DDBM:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 95, + 298, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 95, + 298, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 95, + 298, + 131 + ], + "type": "interline_equation", + "content": "\\frac {d \\mathbf {a} _ {t}}{d t} = f (\\mathbf {a} _ {t}, t) - g ^ {2} (t) \\left(\\frac {1}{2} \\mathbf {s} \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right) - h \\left(\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}, T\\right)\\right) \\tag {12}", + "image_path": "d786b1c0c892a45ccb341a595d6dd8f3ecfacea7869ddbb35e1194f7d6875ed0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{a}_t,t,\\mathbf{a}_T,T) - h(\\mathbf{a}_t,t,\\mathbf{a}_T,T)" + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "content": " represents the adjustment needed to shift " + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_t" + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "content": " closer to " + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_0" + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "content": ". The error bound for the model's convergence to " + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_T" + }, + { + "bbox": [ + 55, + 133, + 295, + 168 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 65, + 179, + 295, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 179, + 295, + 196 + ], + "spans": [ + { + "bbox": [ + 65, + 179, + 295, + 196 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}} \\left[ \\left\\| \\mathbf {a} _ {t} - \\mathbf {a} _ {0} \\right\\| ^ {2} \\right] \\leq C \\cdot D _ {\\mathrm {K L}} \\left(\\pi_ {s} (\\mathbf {a} _ {T}) \\| \\pi (\\mathbf {a} _ {0})\\right), \\tag {13}", + "image_path": "4046d93c51e8a89fb4c4750c10636e48a3409b0530620f21117ef92bab6c00c8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": " is a constant that depends on factors such as the noise schedule " + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": " and the time duration " + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": ". Hence, the error bound shows that the closer the source distribution " + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{source}}" + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": " is to the target distribution " + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{target}}" + }, + { + "bbox": [ + 55, + 206, + 296, + 277 + ], + "type": "text", + "content": ", the lower the error bound for the DDBM, resulting in a more accurate diffusion process and improved model performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 280, + 296, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 280, + 296, + 363 + ], + "spans": [ + { + "bbox": [ + 55, + 280, + 296, + 363 + ], + "type": "text", + "content": "Prior Action Generation: As previously discussed, a source distribution that closely approximates the target distribution results in improved policy performance, underscoring the importance of an effective prior policy. A toy model is presented in Fig. 3. For the sake of comparison, we propose the following three methods for generating the prior action:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 365, + 295, + 664 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 55, + 365, + 295, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 436 + ], + "type": "text", + "content": "- Gaussian Prior: As an uninformative prior, we select Gaussian white noise, consistent with that used in standard diffusion, as the source distribution, serving as the initial state in the denoising process. This choice facilitates direct comparison with methods based on the original diffusion approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "content": "- Rule-based Prior: We employ a simple, fully connected layer to map the contextual vector " + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "inline_equation", + "content": "\\boldsymbol{c}_t" + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "content": " to the action space, enabling the extraction of relevant low-dimensional features for action generation. The prior action is preset as a parabolic path passing through the current position, determined based on the predicted path length " + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "content": " and movement behavior classification (straight, left turn, right turn, U-turn to the right, and U-turn to the left). Detailed information can be found in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 544, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 544, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 54, + 544, + 295, + 664 + ], + "type": "text", + "content": "- Learning-based Prior: This method involves generating prior actions by utilizing expert data and learning models. We use a lightweight conditional variational autoencoder (CVAE) as our learning model to achieve a lightweight design while maintaining effective generation. The observations " + }, + { + "bbox": [ + 54, + 544, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 54, + 544, + 295, + 664 + ], + "type": "text", + "content": " are fed into the CVAE to produce corresponding actions. We aim for the model to effectively capture the significant correlations between observations and actions, thereby enabling a more efficient acquisition of the source distribution with reduced computational costs." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "These methods for prior action generation are readily adaptable to other tasks related to imitation learning. Through a comparative analysis of these methods, we seek to assess the potential advantages of the diffusion bridge." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 553, + 196 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 196 + ], + "type": "image", + "image_path": "7f324dcdbffdfee2849c4fb0c1700d7c48d138a41d1a7bb9e40ec26abef2c28f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 204, + 555, + 271 + ], + "lines": [ + { + "bbox": [ + 313, + 204, + 555, + 271 + ], + "spans": [ + { + "bbox": [ + 313, + 204, + 555, + 271 + ], + "type": "text", + "content": "Figure 3. DDBM trained on 2D synthetic data. The leftmost side represents the source distribution, and the rightmost side represents the target distribution. The distance between the source distribution and the target distribution increases from top to bottom. As the EMD increases, the required approximation steps increase while model performance progressively declines." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 289, + 404, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 404, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 404, + 301 + ], + "type": "text", + "content": "4.3. Traing Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "content": "**Denoising Network:** We utilize a 1-D temporal CNN, conditioned on the " + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "content": " derived from observations, to iteratively denoise with the prior action " + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_T" + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "content": " serving as the initial input. The network is modulated by " + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "content": " through Feature-wise Linear Modulation (FiLM) [36] and performs " + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 307, + 553, + 379 + ], + "type": "text", + "content": " iterations of denoising, following an approach similar to that of [13]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "text", + "content": "Loss Function: The loss function in our architecture comprises the diffusion bridge loss " + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "text", + "content": ", the prior action generation loss " + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "text", + "content": ", and a temporal distance loss " + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 313, + 380, + 553, + 427 + ], + "type": "text", + "content": " designed for high-level planning (following [50])." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 427, + 553, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 553, + 451 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 553, + 451 + ], + "type": "text", + "content": "The diffusion bridge loss " + }, + { + "bbox": [ + 313, + 427, + 553, + 451 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 313, + 427, + 553, + 451 + ], + "type": "text", + "content": " is calculated by a weighted Mean Square Error (MSE) loss function:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 457, + 553, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 457, + 553, + 472 + ], + "spans": [ + { + "bbox": [ + 328, + 457, + 553, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b} = \\mathbb {E} _ {\\mathbf {a} _ {t}, \\mathbf {a} _ {0}, \\mathbf {a} _ {T}, t} [ w (t) \\| \\mathbf {a} _ {0} - D _ {\\theta} (\\mathbf {a} _ {t}, t, \\mathbf {a} _ {T}) \\| ^ {2} ], \\tag {14}", + "image_path": "2b8580375883009d2a0c8e10bb0c3d84745d885c24729510881d48135699f2fe.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 477, + 554, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 554, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 554, + 574 + ], + "type": "text", + "content": "The prior action generation loss " + }, + { + "bbox": [ + 313, + 477, + 554, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 313, + 477, + 554, + 574 + ], + "type": "text", + "content": " is categorized into rule-based and learning-based approaches. The rule-based approach uses a fully connected layer to generate a coarse action. It is accompanied by a classification task that classifies the action based on its movement direction (details in the Appendix). Thus, the loss function consists of an action prediction loss computed by Mean Squared Error (MSE) and a classification loss based on cross-entropy:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 318, + 579, + 553, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 579, + 553, + 612 + ], + "spans": [ + { + "bbox": [ + 318, + 579, + 553, + 612 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} ^ {r u l e} = - \\lambda_ {c} \\sum p _ {c} \\log (\\hat {p} _ {c}) + \\lambda_ {a} \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2}, \\tag {15}", + "image_path": "a2ad049f861f0755f2672dbe23fcc4eb777f8625c2c1f4182e4fcda817fd2ecc.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": " represents the one-hot encoding of the ground truth class label, while " + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "inline_equation", + "content": "\\hat{p}_c" + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": " denotes the predicted probability. Additionally, a signifies the expert action, and " + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{a}}" + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": " represents the predicted action by the FC layer. The terms " + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "inline_equation", + "content": "\\lambda_c" + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "inline_equation", + "content": "\\lambda_a" + }, + { + "bbox": [ + 313, + 618, + 554, + 677 + ], + "type": "text", + "content": " denote the respective weights for the loss functions." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "The learning-based approach employs the Conditional Variational Autoencoder (CVAE) model to efficiently generate actions in a lightweight manner, with the associated" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12104" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 89, + 550, + 239 + ], + "blocks": [ + { + "bbox": [ + 111, + 71, + 499, + 82 + ], + "lines": [ + { + "bbox": [ + 111, + 71, + 499, + 82 + ], + "spans": [ + { + "bbox": [ + 111, + 71, + 499, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative comparison between the proposed method with baselines in simulation environments" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 89, + 550, + 239 + ], + "lines": [ + { + "bbox": [ + 58, + 89, + 550, + 239 + ], + "spans": [ + { + "bbox": [ + 58, + 89, + 550, + 239 + ], + "type": "table", + "html": "
SceneMethodBasic TaskAdaptation Task
Length (m)CollisionSuccessLength (m)CollisionSuccess
Indoor(2D-3D-S)ViNT [45]151.1 ± 31.5901.0268%19.9 ± 0.3141.5828%
NoMaD [50]147.9 ± 26.4750.7486%20.3 ± 0.2431.3232%
Gaussian Prior148.7 ± 28.5380.7282%19.8 ± 0.3170.9864%
Rule-based Prior163.57 ± 48.6582.5162%19.0 ± 1.390.8444%
Learning-based Prior143.7 ± 25.1750.6192%19.3 ± 0.340.4188%
Outdoor(Citysim)ViNT [45]254.8 ± 63.5970.7820%67.5 ± 26.3200.4138%
NoMaD [50]248.6 ± 67.6790.5822%68.3 ± 26.3150.3452%
Gaussian Prior244.8 ± 62.7490.6234%68.9 ± 24.6560.3550%
Rule-based Prior276.1 ± 83.7213.5914%71.8 ± 30.8560.5928%
Learning-based Prior237.7 ± 59.4760.5144%63.5 ± 20.6590.3064%
", + "image_path": "8ed51d5b96ae32c70580058ebe37ea4e954e896d1a2f29446831863e26f09ec8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 255, + 188, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 188, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 188, + 266 + ], + "type": "text", + "content": "loss function defined as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 274, + 294, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 274, + 294, + 316 + ], + "spans": [ + { + "bbox": [ + 61, + 274, + 294, + 316 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} ^ {c v a e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\hat {\\mathbf {a}} _ {i} - \\mathbf {a} _ {i} \\| ^ {2} + \\operatorname {K L} (\\hat {\\pi} (z | \\mathcal {O}, \\mathbf {a}) \\| \\pi (z | \\mathcal {O})) \\tag {16}", + "image_path": "0f703ad25cc09d76d5f7eb2cc79a21374b6e8a420ba23f93999fab5fa2a28641.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "inline_equation", + "content": "\\hat{\\pi} (\\cdot)" + }, + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "text", + "content": " represents the posterior distribution of actions, while " + }, + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "inline_equation", + "content": "\\pi (\\cdot)" + }, + { + "bbox": [ + 55, + 316, + 295, + 340 + ], + "type": "text", + "content": " represents the prior." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 340, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 340, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 340, + 296, + 376 + ], + "type": "text", + "content": "The temporal distance loss " + }, + { + "bbox": [ + 55, + 340, + 296, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 55, + 340, + 296, + 376 + ], + "type": "text", + "content": " quantifies the interval count between the target image and the current image within a discretized timeline:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 382, + 295, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 382, + 295, + 415 + ], + "spans": [ + { + "bbox": [ + 113, + 382, + 295, + 415 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| f (\\boldsymbol {c} _ {t, i}) - d _ {i} \\| ^ {2}, \\tag {17}", + "image_path": "5287adf256df052f1c2b524f156eae0cb718f5d3ef35ccfe22a8202888c85329.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "inline_equation", + "content": "f(\\pmb{c}_{t,i})" + }, + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "text", + "content": " represents the prediction of temporal distance, and " + }, + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 55, + 423, + 295, + 448 + ], + "type": "text", + "content": " represents the ground truth." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 448, + 244, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 448, + 244, + 459 + ], + "spans": [ + { + "bbox": [ + 67, + 448, + 244, + 459 + ], + "type": "text", + "content": "In summary, the loss function is defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 117, + 468, + 295, + 482 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 468, + 295, + 482 + ], + "spans": [ + { + "bbox": [ + 117, + 468, + 295, + 482 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {b} \\mathcal {L} _ {b} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {d} \\mathcal {L} _ {d}, \\tag {18}", + "image_path": "171fd0be7ad59a87a3febb2dd7f1cf2986772c8422b30067a33cd39219caef1a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "inline_equation", + "content": "\\lambda_{b},\\lambda_{p}" + }, + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "inline_equation", + "content": "\\lambda_{d}" + }, + { + "bbox": [ + 55, + 490, + 296, + 513 + ], + "type": "text", + "content": " denote the respective weights for the loss functions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 524, + 137, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 524, + 137, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 524, + 137, + 538 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 544, + 296, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 296, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 296, + 604 + ], + "type": "text", + "content": "In this section, we comprehensively evaluate our method through simulated and real-world experiments in indoor and outdoor environments. The following sections provide an overview of the experimental setup, experiment results, and ablation studies." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 611, + 172, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 172, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 172, + 624 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "Datasets. Our method and all baseline methods were trained on the same dataset to ensure a fair comparison. Following the approach in [50], the training data includes samples collected from diverse environments and various robotic platforms, incorporating data from RECON [42], SCAND [25], GoStanford [18], and SACSoN [20]. The dataset consists of sequences of consecutive image frames" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 255, + 553, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 255, + 553, + 279 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 553, + 279 + ], + "type": "text", + "content": "along with their corresponding positional information, providing comprehensive scene diversity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 280, + 554, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 554, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 554, + 399 + ], + "type": "text", + "content": "Baselines. We selected two state-of-the-art (SOTA) image-based visual navigation algorithms, NoMaD [50] and ViNT [45], for comparison. To examine the effect of integrating diffusion bridges on policy diffusion, we chose NoMaD, the first approach to apply policy diffusion to visual navigation tasks, which utilizes a standard diffusion policy model [13]. Additionally, we included ViNT, a regression-based model incorporating CNN and self-attention mechanisms, to compare the performance of generative and regression models in visual navigation tasks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 401, + 553, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 401, + 553, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 401, + 553, + 436 + ], + "type": "text", + "content": "Metrics. We report three evaluation metrics in our experiments to comprehensively assess the performance of the diffusion bridge-based visual navigation method:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 437, + 553, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 553, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 553, + 472 + ], + "type": "text", + "content": "Length: For paths that complete the task, we calculate the path lengths' mean and variance to assess the navigation paths' efficiency and consistency." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 472, + 553, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 553, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 553, + 496 + ], + "type": "text", + "content": "Collision: The average number of collisions per trial, which serves as an indicator of navigation safety." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 496, + 553, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 553, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 553, + 544 + ], + "type": "text", + "content": "Success Rate: The success rate under consistent conditions. A trial is considered a failure if the robot does not reach the target position, becomes stuck due to collisions, or exceeds the time limit." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "text", + "content": "Implementation details. We trained the model for 30 epochs using a learning rate 0.0001 and a batch size 256 (224 for learning-based methods). The training process, conducted on a single NVIDIA RTX TITAN GPU, took approximately 30 hours. For DDBM, we employed a VE model with parameters " + }, + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\sigma_0 = \\sigma_T = 0.5" + }, + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "text", + "content": " and a default sampling step count of " + }, + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 313, + 545, + 554, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Evaluation Settings. To validate the effectiveness of the proposed method, we conducted comparative experiments in a simulated environment, benchmarking against baseline methods and performing ablation studies. These experiments were conducted in both indoor and outdoor settings. Furthermore, we evaluated the models on a robotic platform to assess their practical performance. The model" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12105" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 69, + 288, + 187 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 288, + 187 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 288, + 187 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 288, + 187 + ], + "type": "image", + "image_path": "7a9c7a02128945c1916ada686ec10b2f3138cac1a46f557eafe6056be893c40a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 196, + 555, + 231 + ], + "lines": [ + { + "bbox": [ + 54, + 196, + 555, + 231 + ], + "spans": [ + { + "bbox": [ + 54, + 196, + 555, + 231 + ], + "type": "text", + "content": "Figure 4. Comparison of navigation performance in simulation and real-world environments. NaviBridger with rule-based and model-based priors (DDBM) generates smoother, more stable paths compared to NoMaD (DDPM), demonstrating improved alignment with the target trajectory over denoising steps." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 291, + 70, + 554, + 187 + ], + "blocks": [ + { + "bbox": [ + 291, + 70, + 554, + 187 + ], + "lines": [ + { + "bbox": [ + 291, + 70, + 554, + 187 + ], + "spans": [ + { + "bbox": [ + 291, + 70, + 554, + 187 + ], + "type": "image", + "image_path": "d60e37aecfd9a780d715466ba39d6b6d339b68ade338e86b6881145806470be9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 236, + 295, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 295, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 295, + 260 + ], + "type": "text", + "content": "operates on Nvidia Jetson Orin AGX deployed on the robot with RGB-only input." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 271, + 113, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 271, + 113, + 283 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 113, + 283 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 292, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 292, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 292, + 296, + 422 + ], + "type": "text", + "content": "We conduct simulated experiments in two types of scenarios(Visualized in appendix): " + }, + { + "bbox": [ + 55, + 292, + 296, + 422 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 292, + 296, + 422 + ], + "type": "text", + "content": " ) Indoor (Stanford 2D-3D-S [3]) ii) Outdoor (Gazebo citysim [27]). In each scenario, we examine both basic and changed environments. The basic environment denotes a scenario where the test environment matches the configuration of the topological map, allowing us to evaluate long-distance navigation capabilities. The changed environment includes scenarios with obstacles in the test area that are not depicted in the topological map, aimed at testing the system's adaptability when the environment deviates from the mapped layout." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 425, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 425, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 425, + 296, + 651 + ], + "type": "text", + "content": "Fig. 4 includes visualizations of the denoising process in both simulated indoor environments and real-world environments. For detailed configurations of the robot in both simulations and the physical setup, please refer to the Appendix. It can be observed that the DDPM-based method begins denoising from Gaussian noise, with most of the denoising process dedicated to constraining noise unsuitable for the action space into the action space, and only in the final few steps does it constrain the actions required by the task. In contrast, our method starts from a favorable initial state, achieving stable actions after only a few denoising steps, such as 2 to 4. Even when starting with Gaussian noise, our model reaches a stable action output in fewer denoising steps. This demonstrates that a rich prior significantly enhances the convergence of policy diffusion. Moreover, under the DDBM framework, even when using uninformed Gaussian noise as the source distribution, the denoising approximate rate is substantially faster than that of the DDPM-based method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": "The experimental results of the proposed method compared to the baseline in the simulation environment are presented in Table 1. The learning-based prior method demonstrates optimal performance across various tasks and scenarios. The Gaussian prior method performs similarly to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 236, + 555, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 555, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 555, + 498 + ], + "type": "text", + "content": "the DDPM-based NoMaD method, outperforming the baseline in the basic task within the outdoor scenario and the adaptation task within the indoor scenario. The rule-based method, on the other hand, only exceeds the baseline in the indoor adaptation task. These findings suggest that well-designed prior information can significantly improve the effectiveness of diffusion models, whereas poorly designed priors may impair model performance in specific scenarios. The rule-based method requires careful design of prior rules, which can yield significant improvements in some particular scenarios but generally lacks strong generalization across diverse conditions. When appropriate prior actions are unavailable, Gaussian noise is an acceptable initial distribution. A practical approach involves obtaining learned prior actions from a lightweight model and then generating actions through a diffusion bridge, offering a more versatile and robust solution. The learning-based method shows notable improvements in adaptation tasks and outdoor scenarios, indicating a solid capacity for generalization in complex and dynamic environments. In contrast, the DDPM-based method demonstrates comparatively weaker performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 513, + 416, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 513, + 416, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 513, + 416, + 525 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": "The impact of denoising steps on model learning. Table 2 shows the training results under different denoising step conditions, comparing the DDPM-based method and NaviBridger based on a Gaussian prior. We present the minimum mean squared error between the predicted action and the expert action on the training set and test sets of four datasets, along with the average ranking of each model across five items. Our method is closer to the expert trajectory in terms of overall data scale. Observing the trend, as the denoising steps decrease, the difference between the DDPM-based method's predicted trajectory and the expert trajectory increases significantly. In contrast, the difference between NaviBridger and a Gaussian prior remains relatively stable. This is also reflected in the average ranking; regardless of the number of denoising steps, Navibridger" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12106" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": "consistently achieves a better ranking, with minimal variation in average ranking as the denoising steps change. Conversely, the DDPM-based method shows generally lower rankings with more considerable fluctuations." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 125, + 294, + 244 + ], + "blocks": [ + { + "bbox": [ + 56, + 125, + 294, + 244 + ], + "lines": [ + { + "bbox": [ + 56, + 125, + 294, + 244 + ], + "spans": [ + { + "bbox": [ + 56, + 125, + 294, + 244 + ], + "type": "table", + "html": "
NoMaD (DDPM)Gaussian Prior
k=1074110741
Train1.381.271.142.160.270.280.300.30
Recon1.191.100.971.430.880.910.890.98
Sacson1.741.731.653.131.651.431.611.52
SCAND0.720.760.711.170.590.690.630.61
Go Stanford4.123.473.463.893.473.443.223.32
Average Rank7.06.04.47.82.42.62.42.8
", + "image_path": "4c1246e026acf64c1d904eca5a066833cdab76d9daab9b62f9bac871a913b390.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 287, + 293, + 384 + ], + "blocks": [ + { + "bbox": [ + 55, + 249, + 295, + 283 + ], + "lines": [ + { + "bbox": [ + 55, + 249, + 295, + 283 + ], + "spans": [ + { + "bbox": [ + 55, + 249, + 295, + 283 + ], + "type": "text", + "content": "Table 2. Comparison of the mean square error between DDBM and vanilla diffusion model in predicting actions and expert actions in training sets and different test sets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 287, + 293, + 384 + ], + "lines": [ + { + "bbox": [ + 56, + 287, + 293, + 384 + ], + "spans": [ + { + "bbox": [ + 56, + 287, + 293, + 384 + ], + "type": "table", + "html": "
PriorMethodLength (m)Collision Success
GaussianSource-2.120%
Target19.8 ± 0.3170.9864%
Rule-basedSource28.1 ± 5.9421.778%
Target19.0 ± 1.3900.8444%
Learning-basedSource24.8 ± 1.351.4920%
Target19.3 ± 0.3400.4188%
", + "image_path": "755a50e3986b2e28279ec2f720314b1e025ffa7dc128240bb2fc87b5ede5e24b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 388, + 295, + 422 + ], + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 422 + ], + "type": "text", + "content": "Table 3. Performance metrics of visual navigation tasks across different source priors: evaluation of policy effectiveness for source-target action mapping." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 426, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 426, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 54, + 426, + 295, + 605 + ], + "type": "text", + "content": "The effect of source distribution and the role of diffusion bridge. Table 3 compares the navigation performance of the proposed method in an indoor adaptation task by examining prior actions sampled from different source distributions and the target actions obtained through denoising. As the prior generation method transitions from random to ordered and from heuristic-based to expert data-driven approaches, the success rate of navigation using only the prior actions shows some improvement, although it remains pretty low. After bridge denoising, the navigation success rate improves markedly. The experiments indicate that more informative prior actions contribute to better performance. At the same time, the diffusion bridge effectively transforms less effective prior actions into higher-quality target actions, thereby enhancing overall performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": "Less denoising steps and the same performance. The line chart as shown in Fig 5 illustrates the relationship between denoising steps, success rate, and inference time for visual navigation under different prior settings—Learning-based Prior DDBM, Gaussian Prior DDBM, and DDPM. Success rate, represented on the left vertical axis, generally increases as denoising steps progress, with the Learning-based Prior DDBM consistently achieving the highest success rates, peaking around " + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": " at 10 denoising steps. In" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 320, + 75, + 549, + 209 + ], + "blocks": [ + { + "bbox": [ + 320, + 75, + 549, + 209 + ], + "lines": [ + { + "bbox": [ + 320, + 75, + 549, + 209 + ], + "spans": [ + { + "bbox": [ + 320, + 75, + 549, + 209 + ], + "type": "image", + "image_path": "202e0faeeb213a2393d10f2b0d7306edd4a75eee94710c97711c457b6ca81b5b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 229, + 555, + 285 + ], + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 285 + ], + "type": "text", + "content": "Figure 5. Success rate and inference time comparison across denoising steps. Learning-based and Gaussian priors in DDBM show higher success rates than DDPM, with learning-based priors achieving the best performance. DDBM also demonstrates faster inference times as denoising steps increase." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 293, + 555, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 555, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 555, + 413 + ], + "type": "text", + "content": "contrast, the Gaussian Prior DDBM shows a moderate success rate that fluctuates slightly, while DDPM achieves a lower success rate overall. The inference time indicated on the right vertical axis increases linearly with the denoising steps, and the time required by DDBM is longer than that of DDPM under the same denoising steps. Learning-based Prior DDBM demonstrates a more favorable balance between high success rate and moderate inference time, suggesting it is more efficient and reliable for visual navigation tasks than the Gaussian Prior DDBM and DDPM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 429, + 388, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 429, + 388, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 388, + 441 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 450, + 555, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 630 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 630 + ], + "type": "text", + "content": "This paper proposes a novel diffusion bridge-based framework for visual navigation. Our method advances policy generation by enabling translations across arbitrary distributions based on informative prior actions rather than the random Gaussian noise. Our theoretical analysis details fundamental principles, formulas, and the influence of source distributions on performance, along with an analysis of error lower bounds. Experimental results demonstrate a substantial increase in success rates and a reduction in collisions compared to baseline models in simulated environments. By exploring different strategies for source distribution generation and denoising steps, our method achieves greater robustness, more stability, and faster action generation than vanilla diffusion policy models, expanding the potential of policy diffusion in imitation learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 632, + 555, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 555, + 679 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 555, + 679 + ], + "type": "text", + "content": "However, although the results demonstrate a certain extent of generalization to dynamic scenarios, the scenario becomes more complex if high-speed moving objects are present, necessitating faster response or adaptive strategies." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 679, + 555, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 679, + 555, + 703 + ], + "spans": [ + { + "bbox": [ + 313, + 679, + 555, + 703 + ], + "type": "text", + "content": "Acknowledgment. This work is supported by the China National Key R&D Program (2022YFB3903804)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12107" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua Tenenbaum, Tommi Jaakkola, and Pulkit Agrawal. 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Unlike existing methods that typically require pre-defined 3D models or specific training datasets as priors, which limit their applicability, our method is free from these constraints. Our method consists of a geometry generation module and a pose optimization module. Its core idea is to enable these two modules to automatically and iteratively enhance each other, thereby gradually building all the necessary information for the tracking task. We thus call the method as Bidirectional Iterative Tracking(BIT). The geometry generation module starts without priors and gradually generates high-precision mesh models for tracking, while the pose optimization module generates additional data during object tracking to further refine the generated models. Moreover, the generated 3D models can be stored and easily reused, allowing for seamless integration into various other tracking systems, not just our methods. Experimental results demonstrate that BIT outperforms many existing methods, even those that extensively utilize prior knowledge, while BIT does not rely on such information. Additionally, the generated 3D models deliver results comparable to actual 3D models, highlighting their superior and innovative qualities. The code is available at https://github.com/songxiuqiang/BIT.git.", + "bbox": [ + 89, + 444, + 483, + 824 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7644328fa7bae3244c8090e0f61eca659240d7c662e3e8f99351d02020a18ca9.jpg", + "image_caption": [ + "Figure 1. We propose a prior-free 3D object tracking method called BIT, which is both model-free and training-free. The pose optimization and geometry generation modules iteratively enhance each other to ultimately realize object tracking. The generated model can be reused, achieving excellent results." + ], + "image_footnote": [], + "bbox": [ + 535, + 390, + 880, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 691, + 645, + 707 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The advancement of embodied intelligence technology necessitates a deep understanding of the real world, and a crucial foundation for this understanding is the accurate and continuous real-time 6DoF pose estimation of objects in the real world, also known as 3D object tracking. Existing methods typically rely on predefined 3D model priors [4, 20, 22] or training priors [9, 30], or a combination of both [27], to achieve accurate tracking results. While the use of priors simplifies the tracking task, it also incurs high training costs and the need for precise model reconstruction, which significantly limits the flexibility and scalability of these methods across diverse environments and object", + "bbox": [ + 509, + 719, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Xueying Qin is the corresponding author.", + "bbox": [ + 107, + 886, + 334, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1200", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "types. In this paper, we explore, for the first time, a truly prior-free 3D object tracking paradigm that is both model-free and training-free, specifically without requiring given 3D models or pose-annotated training images.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce a Bidirectional Iterative Tracking (BIT) to tackle the challenging task of prior-free tracking. The key idea of BIT is to automatically generate the necessary information for tracking, rather than relying on pre-existing priors that serve a similar purpose. BIT relies solely on monocular RGB data as input. It comprises two key modules: the geometry generation module and the pose optimization module. The geometry generation module can automatically deform a sphere to match the target object's shape, while the pose optimization module tracks the pose and selects the appropriate information as a foundation for geometry generation. These modules work in cooperation, iteratively enhancing each other's functionality. Additionally, the information generated by BIT can be used immediately or stored for future reuse, allowing other tracking systems to seamlessly integrate it. The core components of BIT include a tracker SLOT [4], a segmenter SAM [6], and a differentiable renderer SoftRas [8].", + "bbox": [ + 89, + 152, + 482, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The BIT method improves upon previous methods by completely eliminating the reliance on model priors and training priors (the training of SAM is not specific to the tracked object, and in our method it also can be replaced with other segmentation method). Existing 3D object tracking methods typically depend on provided priors to reduce the difficulty of tracking, which can be classified into three main categories: Model-based methods, which rely on CAD models or reconstructed models as priors and cannot function without them. Training-based methods, which involve training on specific datasets and then generalizing to unseen objects. Model and training-based methods, which rely on both models and training data simultaneously. In practical scenarios, acquiring such models and training data incurs significant costs, which clearly limits the flexibility and applicability of these methods. BIT overcomes these limitations by functioning independently of such priors, making it more versatile and cost-effective. The key contributions of this paper are as follows:", + "bbox": [ + 89, + 426, + 482, + 714 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The BIT framework is proposed, which realizes prior-free tracking of 3D objects, encompassing both model-free and training-free.", + "- An effective bidirectional iterative tracking method is proposed, where the pose optimization module and the geometry generation module can iteratively enhance each other, achieving synchronized improvement in their effects and jointly completing the tracking task.", + "- The 3D models automatically generated by BIT can be easily reused and seamlessly integrated into many other tracking systems without additional processing, providing convenience for the utilization of other tracking methods." + ], + "bbox": [ + 89, + 719, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 89, + 663, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on our knowledge, there are currently no 3D object tracking methods that do not rely on either model priors or training priors. In this section, we will first provide an overview of 3D object tracking and methods for single-frame pose estimation relevant to our work, followed by an introduction to differentiable rendering. Single-frame pose estimation determines an object's pose from a single frame without relying on previous frames, leading to higher computational demands due to a larger search space. In contrast, 3D object tracking uses pose information from previous frames for a more efficient and accurate estimation, optimizing within a smaller search space.", + "bbox": [ + 511, + 114, + 903, + 297 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Model-based Methods", + "text_level": 1, + "bbox": [ + 511, + 305, + 720, + 320 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Precise 3D models can provide strong constraints for tracking, which is particularly important for textureless or weakly textured objects. In recent years, many model-based methods [4, 17, 19, 20, 22, 23] have achieved excellent tracking results by utilizing well-designed energy functions. These energy functions are typically constructed from interpretable features, such as the color distribution of pixels [4, 17, 19, 20, 23] or edges [3, 22, 24, 25] in the frame. These methods do not rely on deep networks, thereby avoiding issues related to training and generalization. They typically offer good tracking accuracy and real-time performance while having low hardware requirements. When precise CAD models are available, these methods are generally the best choice for object tracking. However, obtaining precise CAD models is not always feasible, which is the main limitation of these methods.", + "bbox": [ + 511, + 325, + 906, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Training-based Methods", + "text_level": 1, + "bbox": [ + 511, + 575, + 738, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some methods do not rely on explicit 3D models as priors but require training on specific datasets to acquire the necessary knowledge, subsequently using this learned information to predict poses. Additionally, some methods require a specific number of reference frames and corresponding camera poses to reconstruct an object's point cloud model via Structure-from-Motion (SfM), as seen in OnePose [21] and OnePose++ [2]. After reconstruction, the object's pose is estimated by matching the 2D image with the 3D point cloud. BundleSDF [29] utilizes RGB-D data for 3D reconstruction while tracking. Some methods, like Gen6D [9] and MFOS [7], estimate the pose directly from given reference frames. These techniques typically depend on a series of provided reference frames, thereby introducing certain constraints. FoundationPose [30] trains neural networks on large datasets to acquire as much knowledge as possible, enabling them to handle a wider range of scenarios. Overall, while these methods reduce dependence on model priors to some extent, their reliance on training can lead to generalization issues, and the collection of training data are costly.", + "bbox": [ + 511, + 598, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1201", + "bbox": [ + 483, + 944, + 513, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/abb3f4fa413882a4411450e8b4b96e79f9dba8d06ebe977d812d6b25c6ab476d.jpg", + "image_caption": [ + "Figure 2. Overview of our method BIT. Our method starts with the first frame, using a bounding box to identify the object to track, optionally incorporating available reference frames. The geometry generation module quickly inverse renders a mesh model for the pose optimization module, which in return supplies additional key frames as reference frames. This mutual enhancement between the modules transforms a model-free scene into a model-based scene, leading to improved results." + ], + "image_footnote": [], + "bbox": [ + 130, + 90, + 867, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Model and Training-based Methods", + "text_level": 1, + "bbox": [ + 89, + 402, + 403, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some methods rely on both model priors and training priors to achieve better tracking accuracy or address specific problems (such as category-level pose estimation [26, 28, 31]). DeepAC [27] combines deep networks with precise CAD models to achieve enhanced results. Additionally, some methods [26, 28, 31] can perform tracking with imprecise models. These methods estimate the poses of different instances within a category based on a shared category prior (which can be considered a model prior, typically 3D point clouds). However, these methods usually heavily rely on depth information and struggle to achieve ideal results when relying solely on RGB inputs. Another significant issue is that these methods require extensive training and are prone to generalization challenges.", + "bbox": [ + 89, + 426, + 485, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Differentiable Rendering", + "text_level": 1, + "bbox": [ + 89, + 650, + 320, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditional rendering pipelines are non-differentiable due to discrete sampling in rasterization. Differentiable rendering transforms this into a differentiable process, allowing gradients to flow from 2D images to 3D models, which provide a basis for generating 3D geometry from 2D data. Some methods [5, 10] use handcrafted functions for gradient approximation, while SoftRas [8] achieves full differentiability with an aggregation function. Differentiable rendering is applied in reconstruction, shape fitting, and technologies like NeRF [11]. It requires object poses and segmented contours or masks, often needing multiple views for better results. A method [15] combines 2D trackers with differentiable rendering to reconstruct the geometry, color, texture, and 6DoF pose of 3D objects. However, this method is time-consuming, requiring about 2 seconds per frame,", + "bbox": [ + 89, + 674, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "whereas we address a real-time, prior-free problem.", + "bbox": [ + 513, + 404, + 854, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 441, + 604, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of our method BIT is shown in Fig. 2. BIT takes RGB images as input, with the first frame utilizing a bounding box to indicate the target object for tracking. Additionally, if available, it can incorporate a limited number of reference frames. Our method is capable of simultaneously performing iterative real-time tracking and model generation. It primarily consists of two mutually enhancing components: the geometry generation module and the pose optimization module.", + "bbox": [ + 511, + 470, + 906, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After receiving the first frame and the reference frames (if available), the geometry generation module can quickly generate an initial model by inverse rendering using the given data and send the generated model to the pose optimization module. The pose optimization module then employs this generated model for continuous tracking, selecting key frames from the tracking results and feeding this data back to the geometry generation module. The geometry generation module, in turn, utilizes this feedback to further optimize the generated model. These two processes iterate continuously, simultaneously optimizing both the generated model and tracking performance. Once the generated model reaches a sufficient level of precision, only the pose optimization module needs to be executed.", + "bbox": [ + 511, + 609, + 908, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Throughout the entire process, the pose optimization module does not require any training. The reference for inverse rendering used by the geometry generation module is automatically generated during the tracking process, also eliminating the need for training.", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1202", + "bbox": [ + 483, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/19b2da3f0b15cff291726ee3f8fe5014201fa16d6ae766658d91f7a15e1691fe.jpg", + "image_caption": [ + "Figure 3. The geometry generation module. This module takes the first frame, along with a bounding box, an initial pose, and camera intrinsic $\\pmb{K}$ as input. It can also incorporate additional reference frames if available. A better mesh model can be obtained by inverse rendering a sphere or the previously generated model." + ], + "image_footnote": [], + "bbox": [ + 133, + 85, + 861, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Geometry Generation Module", + "text_level": 1, + "bbox": [ + 89, + 311, + 359, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The geometry generation module rapidly generates an object's mesh model by iteratively inverse rendering during the tracking process. The generated model is then supplied to the pose optimization module. Figure 3 illustrates the overview of the geometry generation module.", + "bbox": [ + 89, + 335, + 482, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The geometry generation module takes as input the first frame $\\mathcal{I}_0$ , an initial pose $\\pmb{T}_0 = [R_0|t_0]$ , and a bounding box $\\pmb{b}_0$ that specifies the target object. Here, $\\pmb{R}_0 \\in \\mathbb{R}^{3 \\times 3}$ represents the rotation matrix, and $\\pmb{t}_0 \\in \\mathbb{R}^3$ is the translation vector. Additionally, the camera intrinsic matrix $\\pmb{K} \\in \\mathbb{R}^{3 \\times 3}$ is also provided.", + "bbox": [ + 89, + 412, + 483, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, if available, the geometry generation module can incorporate reference frames $\\{\\mathcal{I}_i\\}$ , corresponding poses $\\{T_i\\}$ , and bounding boxes $\\{b_i\\}$ . Since the post-processing for the initial frame and reference frames is identical, we assume the presence of reference frames to streamline the description of our method. Furthermore, the pose optimization module can automatically generate these reference frames during the iterative process. For the sake of simplicity, we will use $\\{\\mathcal{I}_i\\}$ to refer to both $\\mathcal{I}_0$ and $\\{\\mathcal{I}_i\\}$ , and apply the same convention to $\\{T_i\\}$ and $\\{b_i\\}$ .", + "bbox": [ + 89, + 505, + 483, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The input frames $\\{\\mathcal{I}_i\\}$ are first fed to a segmenter SAM [6] to obtain the object's masks, with the bounding boxes $\\{b_i\\}$ serving as prompts. To ensure the object area defined by $\\{b_i\\}$ is not too small and to facilitate easier optimization during post-processing, we crop the object area and resize it to a fixed size, resulting in the resized masks $\\{\\mathcal{M}_i\\}$ . During this process, we adjust the camera intrinsics from $K$ to $K_{i}$ for each resized mask $\\mathcal{M}_i$ . This adjustment is necessary because $K$ influences the size and position of the image, ensuring that the input pose $\\{T_i\\}$ remains compatible with the modified masks $\\mathcal{M}_i$ . For further details on this process, please refer to our supplementary materials.", + "bbox": [ + 89, + 657, + 482, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Starting with a 3D sphere $G_{0}$ as the initial model and following the SoftRas [8] method, we iteratively deform this sphere $G_{0}$ into the target mesh model $G^{*}$ using the resized masks $\\{\\mathcal{M}_i\\}$ and poses $\\{T_i\\}$ . SoftRas is chosen due to its", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "rapid processing speed. Since the masks provide comprehensive cues and supervision for inverse rendering, there is no need to train the differentiable renderer. We simplified the loss function for mesh inverse rendering in SoftRas, resulting in a very concise loss function $\\mathcal{L}$ :", + "bbox": [ + 511, + 311, + 905, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {I o U} \\left(\\left\\{\\boldsymbol {G}, \\boldsymbol {T} _ {i}, \\boldsymbol {K} _ {i} \\right\\}, \\left\\{\\boldsymbol {\\mathcal {M}} _ {i} \\right\\}\\right) + \\mu \\mathcal {L} _ {l} (\\boldsymbol {G}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 395, + 903, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{IoU}$ represents the 2D IoU loss between the given masks $\\{\\mathcal{M}_i\\}$ and the projected masks of the model $G$ under poses $\\{\\pmb{T}_i\\}$ and intrinsics $\\{\\pmb{K}_i\\}$ , $G$ represents the intermediate 3D model transitioning from $G_0$ to $G^*$ . $\\mathcal{L}_l$ is the Laplacian regularization term used to control the smoothness of the geometry. The parameter $\\mu$ acts as a balancing factor. The loss function is intentionally kept simple to facilitate the rapid convergence of the input geometry to a specific shape suitable for tracking. Additionally, a straightforward loss function is crucial for generalization. For more details please see our supplementary materials.", + "bbox": [ + 511, + 417, + 905, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Throughout the process, the 3D model initially starts as a sphere, and each iteration generates a mesh model that can be utilized by the pose optimization module. Except for the first iteration, each subsequent iteration receives a fixed number of key frames generated by the pose optimization module as inputs. Additionally, in every iteration, the first frame and reference frames (if available) are consistently used as inputs. Since the contours of the masks segmented by SAM are not smooth and have minor pixel discrepancies, we found that the inverse-rendered model might appear slightly smaller than the actual object. To compensate for this, we scale the inverse-rendered model by a factor of 1.05, which is an empirically determined parameter.", + "bbox": [ + 511, + 584, + 906, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Pose Optimization Module", + "text_level": 1, + "bbox": [ + 511, + 787, + 754, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The pose optimization module is shown in Fig. 4, which has two main purposes: First, it receives the generated 3D mesh model and uses it to quickly estimate the object's pose in the frame. Second, it generates key frames and the object's bounding boxes, and sends these data along with their corresponding poses to the geometry generation module.", + "bbox": [ + 511, + 809, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1203", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/a5a0704bfce40e4fe2bbc48a6126189b6b2e8d5e1fb94ad27a1e7f0c5d491d76.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInputTrainingModelRefersblack_d Drillduplo_duderinse aidtoyPlanevim_mugAvg.↑
PoseRBPF [1]†RGB-D*✓✓×75.384.187.248.659.070.8
LatentFusion [13]†RGB-D✓×✓89.488.967.482.940.073.7
LatentFusion [13]‡RGB-D✓×✓74.175.463.055.038.361.1
PVNet [14]‡RGB✓✓×49.543.372.948.667.956.4
Gen6D [9]‡RGB✓×✓64.959.272.069.851.063.4
Ours(0)RGB×××63.169.780.576.281.474.2
Ours(3)RGB××✓82.989.988.381.788.486.2
", + "bbox": [ + 93, + 88, + 906, + 204 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6aae1249cde7f51cf6c6a02848ca16a22fbb1892ca2c679fd13e19d16e456af1.jpg", + "image_caption": [ + "Figure 4. The pose optimization module, which can track the object's pose and generate key frames for model generation module." + ], + "image_footnote": [], + "bbox": [ + 130, + 297, + 444, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilize the tracking method SLOT [4] as the baseline for tracking the object's pose. This method accepts the generated model as input and then optimizes the object's pose using the color features in the input RGB image around the projected mask of the model. Since it does not include any deep networks, it does not require training. For a detailed explanation of this method, please refer to our supplementary materials. Next, we will provide a detailed explanation of how to generate the key frames and bounding boxes required for the geometry generation module.", + "bbox": [ + 88, + 493, + 482, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The key frames should encompass as many viewpoints as possible to enhance the effectiveness of the geometry generation module. Concurrently, to reduce computational load, redundant viewpoints should be minimized. To achieve this, we construct a view group, denoted as $\\mathcal{V}$ , to store the viewpoints of frames calculated from the tracked poses:", + "bbox": [ + 89, + 645, + 482, + 736 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mathcal {V}} = \\left\\{\\boldsymbol {v} _ {0}, \\boldsymbol {v} _ {1}, \\boldsymbol {v} _ {2}, \\dots , \\boldsymbol {v} _ {n - 1} \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 742, + 480, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{v}_i\\in \\mathbb{R}^3$ is the $i$ -th view, which can be calculated from the corresponding pose $\\pmb{T}_i = [R_i|\\pmb {t}_i]$ :", + "bbox": [ + 89, + 763, + 482, + 796 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {i} = \\boldsymbol {R} _ {i} ^ {\\top} \\boldsymbol {t} _ {i} / | | \\boldsymbol {t} _ {i} | |. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 800, + 480, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When a new frame $\\mathcal{I}_n$ is tracked and the camera view $\\pmb{v}_n$ is established, we compute the angular differences between $\\pmb{v}_n$ and all the views in the set $\\pmb{\\nu}$ as follows:", + "bbox": [ + 89, + 825, + 482, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {a} _ {i} = a c o s \\left(\\frac {\\boldsymbol {v} _ {n} \\cdot \\boldsymbol {v} _ {i}}{| | \\boldsymbol {v} _ {n} | | | | \\boldsymbol {v} _ {i} | |\\right), f o r \\boldsymbol {v} _ {i} \\in \\boldsymbol {\\mathcal {V}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 875, + 482, + 905 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8a41287fa17e3d0242ff31530c7e6cdcd9c7de4746694e7ee1123671428ad8a8.jpg", + "table_caption": [ + "Table 1. Tracking results on the MOPED dataset under the ADD-AUC (0-10 cm). Ours(0) uses no reference frames, Ours(3) uses 3 reference frames. Bold indicates the best result, and underline indicates the second best. † denotes the data reported by LatentFusion, and ‡ denotes the results reported by Gen6D under its configuration. *According to the description in LatentFusion's experiments, we infer that this method uses RGB-D data." + ], + "table_footnote": [], + "table_body": "
MethodRefersKey FramesItersModel Acc. ↓
Ours(3)3330.035
Ours(6)61230.011
Ours(12)121230.010
", + "bbox": [ + 535, + 292, + 883, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Our generated models in different cases. Model accuracy is measured by the normalized Hausdorff distance.", + "bbox": [ + 511, + 364, + 905, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "If all the $\\Delta \\pmb{a}_i$ values exceed a certain threshold $\\pmb{a}_{\\mathrm{min}}$ , we consider the frame $\\mathcal{I}_n$ to be a key frame candidate.", + "bbox": [ + 511, + 424, + 903, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then project the 3D mesh model according to the tracked pose $\\pmb{T}_n$ to obtain a bounding box $\\pmb{b}_n$ . If $\\pmb{b}_n$ is more than 10 pixels away from the image border, we consider $\\pmb{b}_n$ to be valid and designate $\\mathcal{I}_n$ as a true key frame, subsequently adding $\\pmb{v}_n$ to $\\pmb{\\nu}$ . If a sufficient number of key frames are selected, these frames, along with their corresponding bounding boxes and poses, will be sent to the geometry generation module to perform inverse rendering.", + "bbox": [ + 511, + 455, + 905, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 598, + 645, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conducted experiments on both publicly available datasets and real-world scenarios, presenting both quantitative and qualitative results. The experimental setup consisted of a desktop computer equipped with an Intel 12700 CPU and a single NVIDIA GTX 3080 (10GB) GPU. In our experiments, we set $a_{\\mathrm{min}} = 3^{\\circ}$ . The masks were resized to $256 \\times 256$ resolutions during the inverse rendering process. We employed the Adam optimizer, configured with a learning rate of 0.01 and beta values of (0.50, 0.99), to optimize the model. The initial model is a 3D sphere with 1302 vertices. Additionally, $\\mu = 0.1$ was set in the loss function. Each inverse rendering iteration during the model generation process consisted of 200 optimization steps.", + "bbox": [ + 511, + 626, + 905, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In cases where we used reference frames on the dataset, we employed an algorithm that utilizes the golden ratio to evenly distribute a certain number of viewpoints on the surface of a sphere and then selected the frames closest to these generated viewpoints to serve as reference frames.", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1204", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4238df6d65d40da73cfec74118c26cda4c96b991d25bc285fd4f00252318c466.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 145, + 90, + 263, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b589fb2beb41c5b015e25eaa5f4aee7f84f640561a1e292ba4b0f8ec8342016c.jpg", + "image_caption": [ + "(a) Tracking results and generated models in iterations without reference frame" + ], + "image_footnote": [], + "bbox": [ + 264, + 90, + 380, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/17d390c0895a794906ec0f7c31f4a05f06d9ebe0b5d85b85e991f815d4f4f270.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 90, + 496, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c2a26f2a27b9a182f3f23e2d8c9b8f0793f0f3331a72e9cd1cb5e7812fc03b5b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 90, + 614, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/51ca4ddaa39b435a06719d7e2bfc628b17cb10c2156c2a3e675e7dd609a4409d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 90, + 730, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/27dff0902e88c6a51d22b6857377ec7010b1a9b63bf5c0e417bd052f2c3fcbd5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 90, + 849, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/145c5076038c949c2d193f06d698383998348a7f58eecbb21a7db2b6bce76b54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 145, + 174, + 263, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/59666ac528367ad54d9d6e0b54dfff5ded3049216b14fc61a87311b904fc9bc3.jpg", + "image_caption": [ + "(b) Tracking results and generated models in iterations with 3 reference frames" + ], + "image_footnote": [], + "bbox": [ + 264, + 174, + 379, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4d8915f9ed1ded9fca9293a65bb4bc4661f9ec2fd87af209e5c120795480d857.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 174, + 496, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5addd2ce10e46a4f9a293d413202088a2c14d659cbce0a6b8da7063732ce99a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 174, + 614, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ca37336470b50137bb422d580ef1c3fd31e373085215ee5141bb7bf1fd25370b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 174, + 730, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5b49e0fabc638feb5d976c1c96740f0b9431a9635157198c2ef562e30633870a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 174, + 849, + 242 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aa241454cc73db6a9fde639189c04d47e848183a04b4e9559cd8b0af6ef82eda.jpg", + "image_caption": [ + "Figure 5. Tracking results and generated models in 3 iterations on the MOPED dataset, displayed from left to right.", + "Figure 6. The accuracy of the generated models (solid lines) and tracking (dashed lines) across iterations (note the axis direction)." + ], + "image_footnote": [], + "bbox": [ + 125, + 309, + 450, + 424 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results on the MOPED Dataset", + "text_level": 1, + "bbox": [ + 89, + 493, + 369, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The MOPED dataset [13] is a real-world captured dataset containing 11 objects, each comprising several RGB-D video sequences divided into reference and evaluation sets, with a resolution of $640 \\times 480$ . The poses are obtained through a combination of multiple methods [12, 16, 32, 33]. Due to the annotation manner, the poses in some sequences may not be entirely accurate. Therefore, following the approach of Gen6D [9], we selected 5 relatively reliable objects for evaluation. For each object, there are 100-600 reference images and 100-300 query images.", + "bbox": [ + 88, + 517, + 482, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use the ADD-AUC $(0 - 10cm)$ metric to evaluate the tracking results. We test our method in two versions: Ours(0) uses no model or training priors and no reference frames, generating 3 key frames per iteration. Ours(3) also uses no model or training priors but employs 3 reference frames, generating 6 key frames per iteration. For each object, we perform model generation for up to 3 iterations.", + "bbox": [ + 88, + 671, + 482, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since the proposed method addresses a new problem, to the best of our knowledge, there are currently no directly comparable methods. Therefore, we selected the methods most similar to ours for comparison. We compare our results with PoseRBPF [1], LatentFusion [13], PVNet [14], and Gen6D [9]. The results are shown in the Tab. 1. We also present a part of tracking results, as well as the generated models, as shown in Fig. 5.", + "bbox": [ + 88, + 779, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6490ad5d385fa4eb21bc46af8a67f8ffa96d7ec34bfac4f7f1965420284411d.jpg", + "image_caption": [ + "Figure 7. The final generated models (3 iterations) in different reference frames and key frames on the RBOT dataset." + ], + "image_footnote": [], + "bbox": [ + 576, + 309, + 844, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Even without any priors and reference frames, our method (Ours(0)) outperforms all other methods in average. With 3 reference frames, our method (Ours(3)) significantly outperforms the others. Notably, our method requires no training and uses only RGB data, whereas other methods were trained on the tested or other objects. Additionally, compared to other methods, our method demonstrates more uniform accuracy across various objects, indicating that it is data-independent and a truly training-free approach.", + "bbox": [ + 511, + 575, + 906, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results on the RBOT Dataset", + "text_level": 1, + "bbox": [ + 511, + 724, + 774, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During tracking, our method can rapidly generate the 3D model of an object, by comparing the performance of various trackers using both precise ground truth CAD models and our generated models on the RBOT dataset [23], we explored the models' reusability.", + "bbox": [ + 511, + 748, + 905, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The RBOT dataset is a 3D object tracking dataset with 18 objects and 72 sequences, each containing 1000 test frames, with a resolution of $640\\times 512$ , covering a baseline regular scenario and dynamic light, noisy, and occlusion scenarios. It has been used to evaluate some advanced 3D track", + "bbox": [ + 511, + 824, + 905, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1205", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/718869fde34afd8479e38e171252a2b563f545af7976cbe7027d3678cae5ec71.jpg", + "image_caption": [ + "Figure 8. Generated models in the case of 6 reference frames and 12 key frames on the RBOT dataset, displayed from top to bottom in each iteration." + ], + "image_footnote": [], + "bbox": [ + 143, + 90, + 433, + 347 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/746bc6dd1a4635e88f9ee7e11155ba26f0e8db8d54b9457d010fddae1a434ade.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodModelReg.Dyn.NoisyOcc.Avg.↑
RBOT [23]GT79.981.256.673.372.8
Ours(3)38.137.525.932.433.5
Ours(6)63.262.942.356.156.1
Ours(12)67.867.044.960.260.0
SLOT [4]GT89.990.769.688.984.8
Ours(3)38.838.426.936.135.1
Ours(6)68.868.249.866.063.2
Ours(12)75.274.353.372.468.8
Song23 [17]GT95.494.986.293.292.4
Ours(3)52.750.944.848.349.2
Ours(6)81.579.870.977.777.5
Ours(12)85.783.874.681.981.5
RBGT [18]GT90.090.671.585.684.4
Ours(3)48.947.837.944.344.7
Ours(6)73.973.357.668.668.3
Ours(12)79.778.961.474.073.5
SRT3D [19]GT94.294.681.793.290.9
Ours(3)49.748.940.946.446.5
Ours(6)75.975.263.872.771.9
Ours(12)81.880.969.179.477.8
", + "bbox": [ + 102, + 416, + 472, + 714 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Tracking accuracy with GT models and the generated models by our method on the RBOT dataset. Bold indicates the best result except for the ground truth.", + "bbox": [ + 89, + 724, + 482, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing methods, such as SRT3D [19], RBGT [18], SLOT [4], Song23 [17] and the RBOT method [23].", + "bbox": [ + 89, + 792, + 482, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Due to the significant differences between frames in the RBOT dataset and the rapid movement of objects, we used 3-12 reference frames, and then tracked the first 100 frames in the regular scenario, and generate the objects' models during tracking. For each object, we performed up to 3 it", + "bbox": [ + 89, + 825, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d60d023bafaba966ec68c37d40557a386897af6636f566bc6e228ba39b746218.jpg", + "image_caption": [ + "Figure 9. Tracking accuracy of various trackers on the RBOT dataset using GT models and the our generated models." + ], + "image_footnote": [], + "bbox": [ + 573, + 90, + 851, + 345 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "erations. Then these generated models served as inputs for other model-based trackers for testing across all scenes of the entire dataset, allowing us to compare their performance against the ground truth CAD models.", + "bbox": [ + 511, + 415, + 906, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We employed the $5 \\, \\text{cm}/5^{\\circ}$ metric to measure the tracking accuracy, which indicates success in a frame if the translation error is less than $5 \\, \\text{cm}$ and the rotation error is less than $5^{\\circ}$ . Otherwise, it is considered a failure, and the pose is reset to the ground truth. The proportion of successful frames represents the tracking accuracy. We use the normalized Hausdorff distance between the generated models and ground truth models to measure the models accuracy.", + "bbox": [ + 511, + 476, + 905, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows the models' accuracy (in normalized Hausdorff distance) in the last iteration, and Fig. 6 shows the normalized Hausdorff distance in every iteration. It can be seen that the generated models have relatively high accuracy with 6 or more reference frames. Additionally, by the second iteration, the model is already close to the final one. This indicates the proposed method's rapid convergence. Figures 7 and 8 also display portions of the generated models, demonstrating the effectiveness of our method. Furthermore, Figure 6 illustrates the variation in tracking accuracy of the baseline tracker [4] across the entire dataset using the intermediate generated models. The results show that the tracking accuracy improves as the models become more accurate.", + "bbox": [ + 511, + 598, + 906, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The test results of the 5 tracking methods using the final generated models on the RBOT dataset are presented in Tab. 3 and Fig. 9. It is clear from these results that when given 6 or more reference frames, the generated models can achieve results very close to the ground truth CAD models. This proves the effectiveness of our method, as it can", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1206", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8bca42da9383f78b139cab67f0cf7cd92db3d1bc4de861fddd5dff601b51e87e.jpg", + "image_caption": [ + "(a) Tracking poses and the generated model without reference frame" + ], + "image_footnote": [], + "bbox": [ + 153, + 92, + 844, + 164 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e32ea592f4040d972a9f7cb13dba7a224d62f8a1efa465e1c1eea335ff40a31.jpg", + "image_caption": [ + "(b) Tracking poses and the generated model with 3 references frames" + ], + "image_footnote": [], + "bbox": [ + 153, + 178, + 843, + 248 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4676d7cb77a455b41329cf43274d7b5aab204f46822f716c9c81ad01237a91b5.jpg", + "image_caption": [ + "(c) Tracking poses and the generated model with 6 references frames", + "Figure 10. Qualitative results on the real world scenes. From left to right, the first frame, tracking results, and the generated models." + ], + "image_footnote": [], + "bbox": [ + 153, + 262, + 843, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "effectively transform a model-free tracking problem into a model-based tracking problem.", + "bbox": [ + 89, + 401, + 482, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 441, + 272, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We captured RGB images of real-world scenes to test the proposed method, with a resolution of $640 \\times 480$ . We evaluated our method under 3 conditions: (1) no reference and 3 key frames, (2) 3 reference frames and 3 key frames, and (3) 6 reference frames and 6 key frames. The reference frames are from the RBOT dataset. For each object, we performed up to 3 iterations. The tracking results are shown in Fig. 10. Under all 3 conditions, our method successfully achieved effective tracking and generated object models. Further experimental results can be found in our supplementary video.", + "bbox": [ + 89, + 464, + 483, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Time Analysis", + "text_level": 1, + "bbox": [ + 89, + 625, + 235, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With a resolution of $640 \\times 480$ , tracking a frame takes about $30~\\mathrm{ms}$ . When using 6 reference frames and 12 key frames for generating models, each iteration takes about 10 seconds. Therefore, a 3D model of an object can be obtained in about 30 seconds over 3 iterations. Notably, our method only utilizes a single NVIDIA 3080 (10GB) GPU. After completing the model generation, only tracking is required, allowing our method become real-time (30 FPS). Additionally, tracking can be run as a background thread to reduce time consumption.", + "bbox": [ + 89, + 648, + 482, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 89, + 814, + 212, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method has several limitations that need to be addressed. Firstly, it is incapable of generating recessed features on object surfaces and cannot accurately model specific topologies, such as ring-shaped or hollow structures.", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Secondly, in challenging scenarios, SAM's segmentation performance may be affected, particularly in cases involving occlusion, motion blur, or similar colors, and the object's complex geometry can also have a certain impact; errors in the mask may degrade the initially rendered model and tracking accuracy, further complicating iterative improvements. Lastly, tracking failures may occur in challenging scenes, particularly with fast-moving objects and when there is a lack of reference frames.", + "bbox": [ + 511, + 401, + 906, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 550, + 638, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a prior-free tracking method based on RGB data, capable of quickly generating 3D models of objects while tracking them. This approach transforms a model-free tracking problem into a model-based one without requiring pose-annotated training. The method operates when the target object is specified in the first frame and can incorporate reference frames if available. The generated models can be reused by other trackers and exhibit high accuracy. The method's consistent results across datasets demonstrate its independence from specific data, clearly distinguishing it from training-based methods. Extending 3D object tracking to non-rigid objects for broader applications and exploring tracking for objects with more complex topologies are future research directions in our work.", + "bbox": [ + 511, + 574, + 906, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 511, + 800, + 671, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is partially supported by the National Key R&D Program of China under grant (No. 2022YFB3303203), NSF of China (U23A20312, No. 62172260, 62202425), and Shandong Provincial Natural Science Foundation (No. ZR2022LZH007).", + "bbox": [ + 511, + 824, + 905, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1207", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Xinke Deng, Arsalan Mousavian, Yu Xiang, Fei Xia, Timothy Bretl, and Dieter Fox. 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Open3D: A modern library for 3D data processing. arXiv:1801.09847, 2018.6" + ], + "bbox": [ + 91, + 90, + 480, + 231 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1209", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_model.json b/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1f3c68896e80299ae286ed3d506248a8aa532db2 --- /dev/null +++ b/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_model.json @@ -0,0 +1,1925 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.344, + 0.131, + 0.654, + 0.154 + ], + "angle": 0, + "content": "Prior-free 3D Object Tracking" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.179, + 0.804, + 0.359 + ], + "angle": 0, + "content": "Xiuqiang Song\\(^{1,3}\\) Li Jin\\(^{1,3}\\) Zhengxian Zhang\\(^{1,3}\\) Jiachen Li\\(^{4}\\) \nFan Zhong\\(^{2,3}\\) Guofeng Zhang\\(^{5}\\) Xueying Qin\\(^{1,3*}\\) \n\\(^{1}\\)School of Software, Shandong University \n\\(^{2}\\)School of Computer Science and Technology, Shandong University \nering Research Center of Digital Media Technology, Ministry of Education, P. \noratory of Computing Power Network and Information Security, Ministry of E \nShandong Computer Science Center, Qilu University of Technology \n\\(^{5}\\)State Key Lab of CAD&CG, Zhejiang University \nsong_xq, jinli, zhangzhengxian@mail.sdu.edu.cn jcli@qlu.edu.cn \nzhongfan@sdu.edu.cn zhangguofeng@zju.edu.cn qxy@sdu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.392, + 0.327, + 0.409 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.445, + 0.485, + 0.825 + ], + "angle": 0, + "content": "In this paper, we introduce a novel, truly prior-free 3D object tracking method that operates without given any model or training priors. Unlike existing methods that typically require pre-defined 3D models or specific training datasets as priors, which limit their applicability, our method is free from these constraints. Our method consists of a geometry generation module and a pose optimization module. Its core idea is to enable these two modules to automatically and iteratively enhance each other, thereby gradually building all the necessary information for the tracking task. We thus call the method as Bidirectional Iterative Tracking(BIT). The geometry generation module starts without priors and gradually generates high-precision mesh models for tracking, while the pose optimization module generates additional data during object tracking to further refine the generated models. Moreover, the generated 3D models can be stored and easily reused, allowing for seamless integration into various other tracking systems, not just our methods. Experimental results demonstrate that BIT outperforms many existing methods, even those that extensively utilize prior knowledge, while BIT does not rely on such information. Additionally, the generated 3D models deliver results comparable to actual 3D models, highlighting their superior and innovative qualities. The code is available at https://github.com/songxiuqiang/BIT.git." + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.391, + 0.882, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.592, + 0.908, + 0.662 + ], + "angle": 0, + "content": "Figure 1. We propose a prior-free 3D object tracking method called BIT, which is both model-free and training-free. The pose optimization and geometry generation modules iteratively enhance each other to ultimately realize object tracking. The generated model can be reused, achieving excellent results." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.692, + 0.646, + 0.708 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.72, + 0.907, + 0.903 + ], + "angle": 0, + "content": "The advancement of embodied intelligence technology necessitates a deep understanding of the real world, and a crucial foundation for this understanding is the accurate and continuous real-time 6DoF pose estimation of objects in the real world, also known as 3D object tracking. Existing methods typically rely on predefined 3D model priors [4, 20, 22] or training priors [9, 30], or a combination of both [27], to achieve accurate tracking results. While the use of priors simplifies the tracking task, it also incurs high training costs and the need for precise model reconstruction, which significantly limits the flexibility and scalability of these methods across diverse environments and object" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.336, + 0.901 + ], + "angle": 0, + "content": "* Xueying Qin is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1200" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "types. In this paper, we explore, for the first time, a truly prior-free 3D object tracking paradigm that is both model-free and training-free, specifically without requiring given 3D models or pose-annotated training images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.426 + ], + "angle": 0, + "content": "We introduce a Bidirectional Iterative Tracking (BIT) to tackle the challenging task of prior-free tracking. The key idea of BIT is to automatically generate the necessary information for tracking, rather than relying on pre-existing priors that serve a similar purpose. BIT relies solely on monocular RGB data as input. It comprises two key modules: the geometry generation module and the pose optimization module. The geometry generation module can automatically deform a sphere to match the target object's shape, while the pose optimization module tracks the pose and selects the appropriate information as a foundation for geometry generation. These modules work in cooperation, iteratively enhancing each other's functionality. Additionally, the information generated by BIT can be used immediately or stored for future reuse, allowing other tracking systems to seamlessly integrate it. The core components of BIT include a tracker SLOT [4], a segmenter SAM [6], and a differentiable renderer SoftRas [8]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.483, + 0.715 + ], + "angle": 0, + "content": "The BIT method improves upon previous methods by completely eliminating the reliance on model priors and training priors (the training of SAM is not specific to the tracked object, and in our method it also can be replaced with other segmentation method). Existing 3D object tracking methods typically depend on provided priors to reduce the difficulty of tracking, which can be classified into three main categories: Model-based methods, which rely on CAD models or reconstructed models as priors and cannot function without them. Training-based methods, which involve training on specific datasets and then generalizing to unseen objects. Model and training-based methods, which rely on both models and training data simultaneously. In practical scenarios, acquiring such models and training data incurs significant costs, which clearly limits the flexibility and applicability of these methods. BIT overcomes these limitations by functioning independently of such priors, making it more versatile and cost-effective. The key contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.72, + 0.483, + 0.765 + ], + "angle": 0, + "content": "- The BIT framework is proposed, which realizes prior-free tracking of 3D objects, encompassing both model-free and training-free." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.765, + 0.483, + 0.841 + ], + "angle": 0, + "content": "- An effective bidirectional iterative tracking method is proposed, where the pose optimization module and the geometry generation module can iteratively enhance each other, achieving synchronized improvement in their effects and jointly completing the tracking task." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- The 3D models automatically generated by BIT can be easily reused and seamlessly integrated into many other tracking systems without additional processing, providing convenience for the utilization of other tracking methods." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.72, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.665, + 0.107 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.905, + 0.298 + ], + "angle": 0, + "content": "Based on our knowledge, there are currently no 3D object tracking methods that do not rely on either model priors or training priors. In this section, we will first provide an overview of 3D object tracking and methods for single-frame pose estimation relevant to our work, followed by an introduction to differentiable rendering. Single-frame pose estimation determines an object's pose from a single frame without relying on previous frames, leading to higher computational demands due to a larger search space. In contrast, 3D object tracking uses pose information from previous frames for a more efficient and accurate estimation, optimizing within a smaller search space." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.306, + 0.722, + 0.321 + ], + "angle": 0, + "content": "2.1. Model-based Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.327, + 0.908, + 0.569 + ], + "angle": 0, + "content": "Precise 3D models can provide strong constraints for tracking, which is particularly important for textureless or weakly textured objects. In recent years, many model-based methods [4, 17, 19, 20, 22, 23] have achieved excellent tracking results by utilizing well-designed energy functions. These energy functions are typically constructed from interpretable features, such as the color distribution of pixels [4, 17, 19, 20, 23] or edges [3, 22, 24, 25] in the frame. These methods do not rely on deep networks, thereby avoiding issues related to training and generalization. They typically offer good tracking accuracy and real-time performance while having low hardware requirements. When precise CAD models are available, these methods are generally the best choice for object tracking. However, obtaining precise CAD models is not always feasible, which is the main limitation of these methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.577, + 0.74, + 0.594 + ], + "angle": 0, + "content": "2.2. Training-based Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Some methods do not rely on explicit 3D models as priors but require training on specific datasets to acquire the necessary knowledge, subsequently using this learned information to predict poses. Additionally, some methods require a specific number of reference frames and corresponding camera poses to reconstruct an object's point cloud model via Structure-from-Motion (SfM), as seen in OnePose [21] and OnePose++ [2]. After reconstruction, the object's pose is estimated by matching the 2D image with the 3D point cloud. BundleSDF [29] utilizes RGB-D data for 3D reconstruction while tracking. Some methods, like Gen6D [9] and MFOS [7], estimate the pose directly from given reference frames. These techniques typically depend on a series of provided reference frames, thereby introducing certain constraints. FoundationPose [30] trains neural networks on large datasets to acquire as much knowledge as possible, enabling them to handle a wider range of scenarios. Overall, while these methods reduce dependence on model priors to some extent, their reliance on training can lead to generalization issues, and the collection of training data are costly." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "1201" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.092, + 0.868, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.322, + 0.908, + 0.381 + ], + "angle": 0, + "content": "Figure 2. Overview of our method BIT. Our method starts with the first frame, using a bounding box to identify the object to track, optionally incorporating available reference frames. The geometry generation module quickly inverse renders a mesh model for the pose optimization module, which in return supplies additional key frames as reference frames. This mutual enhancement between the modules transforms a model-free scene into a model-based scene, leading to improved results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.404, + 0.405, + 0.421 + ], + "angle": 0, + "content": "2.3. Model and Training-based Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.486, + 0.641 + ], + "angle": 0, + "content": "Some methods rely on both model priors and training priors to achieve better tracking accuracy or address specific problems (such as category-level pose estimation [26, 28, 31]). DeepAC [27] combines deep networks with precise CAD models to achieve enhanced results. Additionally, some methods [26, 28, 31] can perform tracking with imprecise models. These methods estimate the poses of different instances within a category based on a shared category prior (which can be considered a model prior, typically 3D point clouds). However, these methods usually heavily rely on depth information and struggle to achieve ideal results when relying solely on RGB inputs. Another significant issue is that these methods require extensive training and are prone to generalization challenges." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.651, + 0.321, + 0.668 + ], + "angle": 0, + "content": "2.4. Differentiable Rendering" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Traditional rendering pipelines are non-differentiable due to discrete sampling in rasterization. Differentiable rendering transforms this into a differentiable process, allowing gradients to flow from 2D images to 3D models, which provide a basis for generating 3D geometry from 2D data. Some methods [5, 10] use handcrafted functions for gradient approximation, while SoftRas [8] achieves full differentiability with an aggregation function. Differentiable rendering is applied in reconstruction, shape fitting, and technologies like NeRF [11]. It requires object poses and segmented contours or masks, often needing multiple views for better results. A method [15] combines 2D trackers with differentiable rendering to reconstruct the geometry, color, texture, and 6DoF pose of 3D objects. However, this method is time-consuming, requiring about 2 seconds per frame," + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.405, + 0.855, + 0.421 + ], + "angle": 0, + "content": "whereas we address a real-time, prior-free problem." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.443, + 0.606, + 0.459 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.472, + 0.907, + 0.608 + ], + "angle": 0, + "content": "The overview of our method BIT is shown in Fig. 2. BIT takes RGB images as input, with the first frame utilizing a bounding box to indicate the target object for tracking. Additionally, if available, it can incorporate a limited number of reference frames. Our method is capable of simultaneously performing iterative real-time tracking and model generation. It primarily consists of two mutually enhancing components: the geometry generation module and the pose optimization module." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.909, + 0.822 + ], + "angle": 0, + "content": "After receiving the first frame and the reference frames (if available), the geometry generation module can quickly generate an initial model by inverse rendering using the given data and send the generated model to the pose optimization module. The pose optimization module then employs this generated model for continuous tracking, selecting key frames from the tracking results and feeding this data back to the geometry generation module. The geometry generation module, in turn, utilizes this feedback to further optimize the generated model. These two processes iterate continuously, simultaneously optimizing both the generated model and tracking performance. Once the generated model reaches a sufficient level of precision, only the pose optimization module needs to be executed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Throughout the entire process, the pose optimization module does not require any training. The reference for inverse rendering used by the geometry generation module is automatically generated during the tracking process, also eliminating the need for training." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1202" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.087, + 0.862, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.245, + 0.908, + 0.288 + ], + "angle": 0, + "content": "Figure 3. The geometry generation module. This module takes the first frame, along with a bounding box, an initial pose, and camera intrinsic \\(\\pmb{K}\\) as input. It can also incorporate additional reference frames if available. A better mesh model can be obtained by inverse rendering a sphere or the previously generated model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.313, + 0.36, + 0.329 + ], + "angle": 0, + "content": "3.1. Geometry Generation Module" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.337, + 0.483, + 0.412 + ], + "angle": 0, + "content": "The geometry generation module rapidly generates an object's mesh model by iteratively inverse rendering during the tracking process. The generated model is then supplied to the pose optimization module. Figure 3 illustrates the overview of the geometry generation module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.414, + 0.484, + 0.504 + ], + "angle": 0, + "content": "The geometry generation module takes as input the first frame \\(\\mathcal{I}_0\\), an initial pose \\(\\pmb{T}_0 = [R_0|t_0]\\), and a bounding box \\(\\pmb{b}_0\\) that specifies the target object. Here, \\(\\pmb{R}_0 \\in \\mathbb{R}^{3 \\times 3}\\) represents the rotation matrix, and \\(\\pmb{t}_0 \\in \\mathbb{R}^3\\) is the translation vector. Additionally, the camera intrinsic matrix \\(\\pmb{K} \\in \\mathbb{R}^{3 \\times 3}\\) is also provided." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.506, + 0.484, + 0.657 + ], + "angle": 0, + "content": "Additionally, if available, the geometry generation module can incorporate reference frames \\(\\{\\mathcal{I}_i\\}\\), corresponding poses \\(\\{T_i\\}\\), and bounding boxes \\(\\{b_i\\}\\). Since the post-processing for the initial frame and reference frames is identical, we assume the presence of reference frames to streamline the description of our method. Furthermore, the pose optimization module can automatically generate these reference frames during the iterative process. For the sake of simplicity, we will use \\(\\{\\mathcal{I}_i\\}\\) to refer to both \\(\\mathcal{I}_0\\) and \\(\\{\\mathcal{I}_i\\}\\), and apply the same convention to \\(\\{T_i\\}\\) and \\(\\{b_i\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.658, + 0.483, + 0.839 + ], + "angle": 0, + "content": "The input frames \\(\\{\\mathcal{I}_i\\}\\) are first fed to a segmenter SAM [6] to obtain the object's masks, with the bounding boxes \\(\\{b_i\\}\\) serving as prompts. To ensure the object area defined by \\(\\{b_i\\}\\) is not too small and to facilitate easier optimization during post-processing, we crop the object area and resize it to a fixed size, resulting in the resized masks \\(\\{\\mathcal{M}_i\\}\\). During this process, we adjust the camera intrinsics from \\(K\\) to \\(K_{i}\\) for each resized mask \\(\\mathcal{M}_i\\). This adjustment is necessary because \\(K\\) influences the size and position of the image, ensuring that the input pose \\(\\{T_i\\}\\) remains compatible with the modified masks \\(\\mathcal{M}_i\\). For further details on this process, please refer to our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Starting with a 3D sphere \\( G_{0} \\) as the initial model and following the SoftRas [8] method, we iteratively deform this sphere \\( G_{0} \\) into the target mesh model \\( G^{*} \\) using the resized masks \\( \\{\\mathcal{M}_i\\} \\) and poses \\( \\{T_i\\} \\). SoftRas is chosen due to its" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.313, + 0.906, + 0.389 + ], + "angle": 0, + "content": "rapid processing speed. Since the masks provide comprehensive cues and supervision for inverse rendering, there is no need to train the differentiable renderer. We simplified the loss function for mesh inverse rendering in SoftRas, resulting in a very concise loss function \\(\\mathcal{L}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.396, + 0.905, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {I o U} \\left(\\left\\{\\boldsymbol {G}, \\boldsymbol {T} _ {i}, \\boldsymbol {K} _ {i} \\right\\}, \\left\\{\\boldsymbol {\\mathcal {M}} _ {i} \\right\\}\\right) + \\mu \\mathcal {L} _ {l} (\\boldsymbol {G}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.906, + 0.585 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{IoU}\\) represents the 2D IoU loss between the given masks \\(\\{\\mathcal{M}_i\\}\\) and the projected masks of the model \\(G\\) under poses \\(\\{\\pmb{T}_i\\}\\) and intrinsics \\(\\{\\pmb{K}_i\\}\\), \\(G\\) represents the intermediate 3D model transitioning from \\(G_0\\) to \\(G^*\\). \\(\\mathcal{L}_l\\) is the Laplacian regularization term used to control the smoothness of the geometry. The parameter \\(\\mu\\) acts as a balancing factor. The loss function is intentionally kept simple to facilitate the rapid convergence of the input geometry to a specific shape suitable for tracking. Additionally, a straightforward loss function is crucial for generalization. For more details please see our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.907, + 0.782 + ], + "angle": 0, + "content": "Throughout the process, the 3D model initially starts as a sphere, and each iteration generates a mesh model that can be utilized by the pose optimization module. Except for the first iteration, each subsequent iteration receives a fixed number of key frames generated by the pose optimization module as inputs. Additionally, in every iteration, the first frame and reference frames (if available) are consistently used as inputs. Since the contours of the masks segmented by SAM are not smooth and have minor pixel discrepancies, we found that the inverse-rendered model might appear slightly smaller than the actual object. To compensate for this, we scale the inverse-rendered model by a factor of 1.05, which is an empirically determined parameter." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.755, + 0.804 + ], + "angle": 0, + "content": "3.2. Pose Optimization Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.902 + ], + "angle": 0, + "content": "The pose optimization module is shown in Fig. 4, which has two main purposes: First, it receives the generated 3D mesh model and uses it to quickly estimate the object's pose in the frame. Second, it generates key frames and the object's bounding boxes, and sends these data along with their corresponding poses to the geometry generation module." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1203" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.908, + 0.205 + ], + "angle": 0, + "content": "
MethodInputTrainingModelRefersblack_d Drillduplo_duderinse aidtoyPlanevim_mugAvg.↑
PoseRBPF [1]†RGB-D*✓✓×75.384.187.248.659.070.8
LatentFusion [13]†RGB-D✓×✓89.488.967.482.940.073.7
LatentFusion [13]‡RGB-D✓×✓74.175.463.055.038.361.1
PVNet [14]‡RGB✓✓×49.543.372.948.667.956.4
Gen6D [9]‡RGB✓×✓64.959.272.069.851.063.4
Ours(0)RGB×××63.169.780.576.281.474.2
Ours(3)RGB××✓82.989.988.381.788.486.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.215, + 0.908, + 0.271 + ], + "angle": 0, + "content": "Table 1. Tracking results on the MOPED dataset under the ADD-AUC (0-10 cm). Ours(0) uses no reference frames, Ours(3) uses 3 reference frames. Bold indicates the best result, and underline indicates the second best. † denotes the data reported by LatentFusion, and ‡ denotes the results reported by Gen6D under its configuration. *According to the description in LatentFusion's experiments, we infer that this method uses RGB-D data." + }, + { + "type": "image", + "bbox": [ + 0.132, + 0.298, + 0.445, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.443, + 0.483, + 0.473 + ], + "angle": 0, + "content": "Figure 4. The pose optimization module, which can track the object's pose and generate key frames for model generation module." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.494, + 0.483, + 0.646 + ], + "angle": 0, + "content": "We utilize the tracking method SLOT [4] as the baseline for tracking the object's pose. This method accepts the generated model as input and then optimizes the object's pose using the color features in the input RGB image around the projected mask of the model. Since it does not include any deep networks, it does not require training. For a detailed explanation of this method, please refer to our supplementary materials. Next, we will provide a detailed explanation of how to generate the key frames and bounding boxes required for the geometry generation module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.646, + 0.483, + 0.737 + ], + "angle": 0, + "content": "The key frames should encompass as many viewpoints as possible to enhance the effectiveness of the geometry generation module. Concurrently, to reduce computational load, redundant viewpoints should be minimized. To achieve this, we construct a view group, denoted as \\(\\mathcal{V}\\), to store the viewpoints of frames calculated from the tracked poses:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.743, + 0.482, + 0.759 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mathcal {V}} = \\left\\{\\boldsymbol {v} _ {0}, \\boldsymbol {v} _ {1}, \\boldsymbol {v} _ {2}, \\dots , \\boldsymbol {v} _ {n - 1} \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.797 + ], + "angle": 0, + "content": "where \\(\\pmb{v}_i\\in \\mathbb{R}^3\\) is the \\(i\\)-th view, which can be calculated from the corresponding pose \\(\\pmb{T}_i = [R_i|\\pmb {t}_i]\\):" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.801, + 0.482, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {i} = \\boldsymbol {R} _ {i} ^ {\\top} \\boldsymbol {t} _ {i} / | | \\boldsymbol {t} _ {i} | |. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.871 + ], + "angle": 0, + "content": "When a new frame \\(\\mathcal{I}_n\\) is tracked and the camera view \\(\\pmb{v}_n\\) is established, we compute the angular differences between \\(\\pmb{v}_n\\) and all the views in the set \\(\\pmb{\\nu}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.875, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {a} _ {i} = a c o s \\left(\\frac {\\boldsymbol {v} _ {n} \\cdot \\boldsymbol {v} _ {i}}{| | \\boldsymbol {v} _ {n} | | | | \\boldsymbol {v} _ {i} | |\\right), f o r \\boldsymbol {v} _ {i} \\in \\boldsymbol {\\mathcal {V}}. \\tag {4}\n\\]" + }, + { + "type": "table", + "bbox": [ + 0.537, + 0.294, + 0.885, + 0.354 + ], + "angle": 0, + "content": "
MethodRefersKey FramesItersModel Acc. ↓
Ours(3)3330.035
Ours(6)61230.011
Ours(12)121230.010
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.365, + 0.906, + 0.393 + ], + "angle": 0, + "content": "Table 2. Our generated models in different cases. Model accuracy is measured by the normalized Hausdorff distance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.425, + 0.905, + 0.455 + ], + "angle": 0, + "content": "If all the \\(\\Delta \\pmb{a}_i\\) values exceed a certain threshold \\(\\pmb{a}_{\\mathrm{min}}\\), we consider the frame \\(\\mathcal{I}_n\\) to be a key frame candidate." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.906, + 0.579 + ], + "angle": 0, + "content": "We then project the 3D mesh model according to the tracked pose \\( \\pmb{T}_n \\) to obtain a bounding box \\( \\pmb{b}_n \\). If \\( \\pmb{b}_n \\) is more than 10 pixels away from the image border, we consider \\( \\pmb{b}_n \\) to be valid and designate \\( \\mathcal{I}_n \\) as a true key frame, subsequently adding \\( \\pmb{v}_n \\) to \\( \\pmb{\\nu} \\). If a sufficient number of key frames are selected, these frames, along with their corresponding bounding boxes and poses, will be sent to the geometry generation module to perform inverse rendering." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.599, + 0.646, + 0.617 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.906, + 0.824 + ], + "angle": 0, + "content": "We conducted experiments on both publicly available datasets and real-world scenarios, presenting both quantitative and qualitative results. The experimental setup consisted of a desktop computer equipped with an Intel 12700 CPU and a single NVIDIA GTX 3080 (10GB) GPU. In our experiments, we set \\(a_{\\mathrm{min}} = 3^{\\circ}\\). The masks were resized to \\(256 \\times 256\\) resolutions during the inverse rendering process. We employed the Adam optimizer, configured with a learning rate of 0.01 and beta values of (0.50, 0.99), to optimize the model. The initial model is a 3D sphere with 1302 vertices. Additionally, \\(\\mu = 0.1\\) was set in the loss function. Each inverse rendering iteration during the model generation process consisted of 200 optimization steps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In cases where we used reference frames on the dataset, we employed an algorithm that utilizes the golden ratio to evenly distribute a certain number of viewpoints on the surface of a sphere and then selected the frames closest to these generated viewpoints to serve as reference frames." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1204" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.146, + 0.091, + 0.264, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.092, + 0.381, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.092, + 0.498, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.092, + 0.615, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.092, + 0.732, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.092, + 0.85, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.291, + 0.162, + 0.706, + 0.174 + ], + "angle": 0, + "content": "(a) Tracking results and generated models in iterations without reference frame" + }, + { + "type": "image", + "bbox": [ + 0.146, + 0.175, + 0.264, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.175, + 0.38, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.175, + 0.498, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.175, + 0.615, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.175, + 0.732, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.175, + 0.85, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.291, + 0.245, + 0.705, + 0.258 + ], + "angle": 0, + "content": "(b) Tracking results and generated models in iterations with 3 reference frames" + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.271, + 0.838, + 0.285 + ], + "angle": 0, + "content": "Figure 5. Tracking results and generated models in 3 iterations on the MOPED dataset, displayed from left to right." + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.31, + 0.452, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.435, + 0.483, + 0.464 + ], + "angle": 0, + "content": "Figure 6. The accuracy of the generated models (solid lines) and tracking (dashed lines) across iterations (note the axis direction)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.494, + 0.37, + 0.509 + ], + "angle": 0, + "content": "4.1. Results on the MOPED Dataset" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.518, + 0.483, + 0.67 + ], + "angle": 0, + "content": "The MOPED dataset [13] is a real-world captured dataset containing 11 objects, each comprising several RGB-D video sequences divided into reference and evaluation sets, with a resolution of \\(640 \\times 480\\). The poses are obtained through a combination of multiple methods [12, 16, 32, 33]. Due to the annotation manner, the poses in some sequences may not be entirely accurate. Therefore, following the approach of Gen6D [9], we selected 5 relatively reliable objects for evaluation. For each object, there are 100-600 reference images and 100-300 query images." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.672, + 0.483, + 0.779 + ], + "angle": 0, + "content": "We use the ADD-AUC \\((0 - 10cm)\\) metric to evaluate the tracking results. We test our method in two versions: Ours(0) uses no model or training priors and no reference frames, generating 3 key frames per iteration. Ours(3) also uses no model or training priors but employs 3 reference frames, generating 6 key frames per iteration. For each object, we perform model generation for up to 3 iterations." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Since the proposed method addresses a new problem, to the best of our knowledge, there are currently no directly comparable methods. Therefore, we selected the methods most similar to ours for comparison. We compare our results with PoseRBPF [1], LatentFusion [13], PVNet [14], and Gen6D [9]. The results are shown in the Tab. 1. We also present a part of tracking results, as well as the generated models, as shown in Fig. 5." + }, + { + "type": "image", + "bbox": [ + 0.578, + 0.31, + 0.845, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.518, + 0.907, + 0.547 + ], + "angle": 0, + "content": "Figure 7. The final generated models (3 iterations) in different reference frames and key frames on the RBOT dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.576, + 0.907, + 0.713 + ], + "angle": 0, + "content": "Even without any priors and reference frames, our method (Ours(0)) outperforms all other methods in average. With 3 reference frames, our method (Ours(3)) significantly outperforms the others. Notably, our method requires no training and uses only RGB data, whereas other methods were trained on the tested or other objects. Additionally, compared to other methods, our method demonstrates more uniform accuracy across various objects, indicating that it is data-independent and a truly training-free approach." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.776, + 0.74 + ], + "angle": 0, + "content": "4.2. Results on the RBOT Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.906, + 0.825 + ], + "angle": 0, + "content": "During tracking, our method can rapidly generate the 3D model of an object, by comparing the performance of various trackers using both precise ground truth CAD models and our generated models on the RBOT dataset [23], we explored the models' reusability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.9 + ], + "angle": 0, + "content": "The RBOT dataset is a 3D object tracking dataset with 18 objects and 72 sequences, each containing 1000 test frames, with a resolution of \\(640\\times 512\\), covering a baseline regular scenario and dynamic light, noisy, and occlusion scenarios. It has been used to evaluate some advanced 3D track" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1205" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.144, + 0.091, + 0.434, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.36, + 0.486, + 0.403 + ], + "angle": 0, + "content": "Figure 8. Generated models in the case of 6 reference frames and 12 key frames on the RBOT dataset, displayed from top to bottom in each iteration." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.417, + 0.473, + 0.715 + ], + "angle": 0, + "content": "
MethodModelReg.Dyn.NoisyOcc.Avg.↑
RBOT [23]GT79.981.256.673.372.8
Ours(3)38.137.525.932.433.5
Ours(6)63.262.942.356.156.1
Ours(12)67.867.044.960.260.0
SLOT [4]GT89.990.769.688.984.8
Ours(3)38.838.426.936.135.1
Ours(6)68.868.249.866.063.2
Ours(12)75.274.353.372.468.8
Song23 [17]GT95.494.986.293.292.4
Ours(3)52.750.944.848.349.2
Ours(6)81.579.870.977.777.5
Ours(12)85.783.874.681.981.5
RBGT [18]GT90.090.671.585.684.4
Ours(3)48.947.837.944.344.7
Ours(6)73.973.357.668.668.3
Ours(12)79.778.961.474.073.5
SRT3D [19]GT94.294.681.793.290.9
Ours(3)49.748.940.946.446.5
Ours(6)75.975.263.872.771.9
Ours(12)81.880.969.179.477.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.725, + 0.483, + 0.768 + ], + "angle": 0, + "content": "Table 3. Tracking accuracy with GT models and the generated models by our method on the RBOT dataset. Bold indicates the best result except for the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.794, + 0.483, + 0.825 + ], + "angle": 0, + "content": "ing methods, such as SRT3D [19], RBGT [18], SLOT [4], Song23 [17] and the RBOT method [23]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Due to the significant differences between frames in the RBOT dataset and the rapid movement of objects, we used 3-12 reference frames, and then tracked the first 100 frames in the regular scenario, and generate the objects' models during tracking. For each object, we performed up to 3 it" + }, + { + "type": "image", + "bbox": [ + 0.575, + 0.091, + 0.852, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.36, + 0.907, + 0.389 + ], + "angle": 0, + "content": "Figure 9. Tracking accuracy of various trackers on the RBOT dataset using GT models and the our generated models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.416, + 0.907, + 0.476 + ], + "angle": 0, + "content": "erations. Then these generated models served as inputs for other model-based trackers for testing across all scenes of the entire dataset, allowing us to compare their performance against the ground truth CAD models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.906, + 0.597 + ], + "angle": 0, + "content": "We employed the \\(5 \\, \\text{cm}/5^{\\circ}\\) metric to measure the tracking accuracy, which indicates success in a frame if the translation error is less than \\(5 \\, \\text{cm}\\) and the rotation error is less than \\(5^{\\circ}\\). Otherwise, it is considered a failure, and the pose is reset to the ground truth. The proportion of successful frames represents the tracking accuracy. We use the normalized Hausdorff distance between the generated models and ground truth models to measure the models accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Table 2 shows the models' accuracy (in normalized Hausdorff distance) in the last iteration, and Fig. 6 shows the normalized Hausdorff distance in every iteration. It can be seen that the generated models have relatively high accuracy with 6 or more reference frames. Additionally, by the second iteration, the model is already close to the final one. This indicates the proposed method's rapid convergence. Figures 7 and 8 also display portions of the generated models, demonstrating the effectiveness of our method. Furthermore, Figure 6 illustrates the variation in tracking accuracy of the baseline tracker [4] across the entire dataset using the intermediate generated models. The results show that the tracking accuracy improves as the models become more accurate." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "The test results of the 5 tracking methods using the final generated models on the RBOT dataset are presented in Tab. 3 and Fig. 9. It is clear from these results that when given 6 or more reference frames, the generated models can achieve results very close to the ground truth CAD models. This proves the effectiveness of our method, as it can" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1206" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.155, + 0.093, + 0.846, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.167, + 0.679, + 0.178 + ], + "angle": 0, + "content": "(a) Tracking poses and the generated model without reference frame" + }, + { + "type": "image", + "bbox": [ + 0.155, + 0.179, + 0.844, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.319, + 0.251, + 0.68, + 0.262 + ], + "angle": 0, + "content": "(b) Tracking poses and the generated model with 3 references frames" + }, + { + "type": "image", + "bbox": [ + 0.155, + 0.263, + 0.844, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.336, + 0.681, + 0.347 + ], + "angle": 0, + "content": "(c) Tracking poses and the generated model with 6 references frames" + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.36, + 0.886, + 0.375 + ], + "angle": 0, + "content": "Figure 10. Qualitative results on the real world scenes. From left to right, the first frame, tracking results, and the generated models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.483, + 0.431 + ], + "angle": 0, + "content": "effectively transform a model-free tracking problem into a model-based tracking problem." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.442, + 0.274, + 0.457 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.465, + 0.484, + 0.616 + ], + "angle": 0, + "content": "We captured RGB images of real-world scenes to test the proposed method, with a resolution of \\(640 \\times 480\\). We evaluated our method under 3 conditions: (1) no reference and 3 key frames, (2) 3 reference frames and 3 key frames, and (3) 6 reference frames and 6 key frames. The reference frames are from the RBOT dataset. For each object, we performed up to 3 iterations. The tracking results are shown in Fig. 10. Under all 3 conditions, our method successfully achieved effective tracking and generated object models. Further experimental results can be found in our supplementary video." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.626, + 0.236, + 0.642 + ], + "angle": 0, + "content": "4.4. Time Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.649, + 0.483, + 0.8 + ], + "angle": 0, + "content": "With a resolution of \\(640 \\times 480\\), tracking a frame takes about \\(30~\\mathrm{ms}\\). When using 6 reference frames and 12 key frames for generating models, each iteration takes about 10 seconds. Therefore, a 3D model of an object can be obtained in about 30 seconds over 3 iterations. Notably, our method only utilizes a single NVIDIA 3080 (10GB) GPU. After completing the model generation, only tracking is required, allowing our method become real-time (30 FPS). Additionally, tracking can be run as a background thread to reduce time consumption." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.815, + 0.214, + 0.83 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Our method has several limitations that need to be addressed. Firstly, it is incapable of generating recessed features on object surfaces and cannot accurately model specific topologies, such as ring-shaped or hollow structures." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.402, + 0.907, + 0.537 + ], + "angle": 0, + "content": "Secondly, in challenging scenarios, SAM's segmentation performance may be affected, particularly in cases involving occlusion, motion blur, or similar colors, and the object's complex geometry can also have a certain impact; errors in the mask may degrade the initially rendered model and tracking accuracy, further complicating iterative improvements. Lastly, tracking failures may occur in challenging scenes, particularly with fast-moving objects and when there is a lack of reference frames." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.551, + 0.64, + 0.565 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.575, + 0.907, + 0.788 + ], + "angle": 0, + "content": "We have proposed a prior-free tracking method based on RGB data, capable of quickly generating 3D models of objects while tracking them. This approach transforms a model-free tracking problem into a model-based one without requiring pose-annotated training. The method operates when the target object is specified in the first frame and can incorporate reference frames if available. The generated models can be reused by other trackers and exhibit high accuracy. The method's consistent results across datasets demonstrate its independence from specific data, clearly distinguishing it from training-based methods. Extending 3D object tracking to non-rigid objects for broader applications and exploring tracking for objects with more complex topologies are future research directions in our work." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.801, + 0.673, + 0.817 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.9 + ], + "angle": 0, + "content": "This work is partially supported by the National Key R&D Program of China under grant (No. 2022YFB3303203), NSF of China (U23A20312, No. 62172260, 62202425), and Shandong Provincial Natural Science Foundation (No. ZR2022LZH007)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1207" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Xinke Deng, Arsalan Mousavian, Yu Xiang, Fei Xia, Timothy Bretl, and Dieter Fox. 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Open3D: A modern library for 3D data processing. arXiv:1801.09847, 2018.6" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.482, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1209" + } + ] +] \ No newline at end of file diff --git a/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_origin.pdf b/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b636031a33c7b2dd54293ac8600185726e7d806f --- /dev/null +++ b/2025/Prior-free 3D Object Tracking/56b7fc45-5f9f-43f7-bec3-8d552616dec5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e5a0eee671f4cd3deb7381bc8eb4902571f7dec029c826fb141cfc6a790df4e2 +size 4516877 diff --git a/2025/Prior-free 3D Object Tracking/full.md b/2025/Prior-free 3D Object Tracking/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a0d091a1e29e91499a6cc5544f15fbc3173b5623 --- /dev/null +++ b/2025/Prior-free 3D Object Tracking/full.md @@ -0,0 +1,279 @@ +# Prior-free 3D Object Tracking + +Xiuqiang Song $^{1,3}$ Li Jin $^{1,3}$ Zhengxian Zhang $^{1,3}$ Jiachen Li $^{4}$ +Fan Zhong $^{2,3}$ Guofeng Zhang $^{5}$ Xueying Qin $^{1,3*}$ $^{1}$ School of Software, Shandong University + $^{2}$ School of Computer Science and Technology, Shandong University +ering Research Center of Digital Media Technology, Ministry of Education, P. +oratory of Computing Power Network and Information Security, Ministry of E +Shandong Computer Science Center, Qilu University of Technology + $^{5}$ State Key Lab of CAD&CG, Zhejiang University +song_xq, jinli, zhangzhengxian@mail.sdu.edu.cn jcli@qlu.edu.cn +zhongfan@sdu.edu.cn zhangguofeng@zju.edu.cn qxy@sdu.edu.cn + +# Abstract + +In this paper, we introduce a novel, truly prior-free 3D object tracking method that operates without given any model or training priors. Unlike existing methods that typically require pre-defined 3D models or specific training datasets as priors, which limit their applicability, our method is free from these constraints. Our method consists of a geometry generation module and a pose optimization module. Its core idea is to enable these two modules to automatically and iteratively enhance each other, thereby gradually building all the necessary information for the tracking task. We thus call the method as Bidirectional Iterative Tracking(BIT). The geometry generation module starts without priors and gradually generates high-precision mesh models for tracking, while the pose optimization module generates additional data during object tracking to further refine the generated models. Moreover, the generated 3D models can be stored and easily reused, allowing for seamless integration into various other tracking systems, not just our methods. Experimental results demonstrate that BIT outperforms many existing methods, even those that extensively utilize prior knowledge, while BIT does not rely on such information. Additionally, the generated 3D models deliver results comparable to actual 3D models, highlighting their superior and innovative qualities. The code is available at https://github.com/songxiuqiang/BIT.git. + +![](images/7644328fa7bae3244c8090e0f61eca659240d7c662e3e8f99351d02020a18ca9.jpg) +Figure 1. We propose a prior-free 3D object tracking method called BIT, which is both model-free and training-free. The pose optimization and geometry generation modules iteratively enhance each other to ultimately realize object tracking. The generated model can be reused, achieving excellent results. + +# 1. Introduction + +The advancement of embodied intelligence technology necessitates a deep understanding of the real world, and a crucial foundation for this understanding is the accurate and continuous real-time 6DoF pose estimation of objects in the real world, also known as 3D object tracking. Existing methods typically rely on predefined 3D model priors [4, 20, 22] or training priors [9, 30], or a combination of both [27], to achieve accurate tracking results. While the use of priors simplifies the tracking task, it also incurs high training costs and the need for precise model reconstruction, which significantly limits the flexibility and scalability of these methods across diverse environments and object + +types. In this paper, we explore, for the first time, a truly prior-free 3D object tracking paradigm that is both model-free and training-free, specifically without requiring given 3D models or pose-annotated training images. + +We introduce a Bidirectional Iterative Tracking (BIT) to tackle the challenging task of prior-free tracking. The key idea of BIT is to automatically generate the necessary information for tracking, rather than relying on pre-existing priors that serve a similar purpose. BIT relies solely on monocular RGB data as input. It comprises two key modules: the geometry generation module and the pose optimization module. The geometry generation module can automatically deform a sphere to match the target object's shape, while the pose optimization module tracks the pose and selects the appropriate information as a foundation for geometry generation. These modules work in cooperation, iteratively enhancing each other's functionality. Additionally, the information generated by BIT can be used immediately or stored for future reuse, allowing other tracking systems to seamlessly integrate it. The core components of BIT include a tracker SLOT [4], a segmenter SAM [6], and a differentiable renderer SoftRas [8]. + +The BIT method improves upon previous methods by completely eliminating the reliance on model priors and training priors (the training of SAM is not specific to the tracked object, and in our method it also can be replaced with other segmentation method). Existing 3D object tracking methods typically depend on provided priors to reduce the difficulty of tracking, which can be classified into three main categories: Model-based methods, which rely on CAD models or reconstructed models as priors and cannot function without them. Training-based methods, which involve training on specific datasets and then generalizing to unseen objects. Model and training-based methods, which rely on both models and training data simultaneously. In practical scenarios, acquiring such models and training data incurs significant costs, which clearly limits the flexibility and applicability of these methods. BIT overcomes these limitations by functioning independently of such priors, making it more versatile and cost-effective. The key contributions of this paper are as follows: + +- The BIT framework is proposed, which realizes prior-free tracking of 3D objects, encompassing both model-free and training-free. +- An effective bidirectional iterative tracking method is proposed, where the pose optimization module and the geometry generation module can iteratively enhance each other, achieving synchronized improvement in their effects and jointly completing the tracking task. +- The 3D models automatically generated by BIT can be easily reused and seamlessly integrated into many other tracking systems without additional processing, providing convenience for the utilization of other tracking methods. + +# 2. Related Works + +Based on our knowledge, there are currently no 3D object tracking methods that do not rely on either model priors or training priors. In this section, we will first provide an overview of 3D object tracking and methods for single-frame pose estimation relevant to our work, followed by an introduction to differentiable rendering. Single-frame pose estimation determines an object's pose from a single frame without relying on previous frames, leading to higher computational demands due to a larger search space. In contrast, 3D object tracking uses pose information from previous frames for a more efficient and accurate estimation, optimizing within a smaller search space. + +# 2.1. Model-based Methods + +Precise 3D models can provide strong constraints for tracking, which is particularly important for textureless or weakly textured objects. In recent years, many model-based methods [4, 17, 19, 20, 22, 23] have achieved excellent tracking results by utilizing well-designed energy functions. These energy functions are typically constructed from interpretable features, such as the color distribution of pixels [4, 17, 19, 20, 23] or edges [3, 22, 24, 25] in the frame. These methods do not rely on deep networks, thereby avoiding issues related to training and generalization. They typically offer good tracking accuracy and real-time performance while having low hardware requirements. When precise CAD models are available, these methods are generally the best choice for object tracking. However, obtaining precise CAD models is not always feasible, which is the main limitation of these methods. + +# 2.2. Training-based Methods + +Some methods do not rely on explicit 3D models as priors but require training on specific datasets to acquire the necessary knowledge, subsequently using this learned information to predict poses. Additionally, some methods require a specific number of reference frames and corresponding camera poses to reconstruct an object's point cloud model via Structure-from-Motion (SfM), as seen in OnePose [21] and OnePose++ [2]. After reconstruction, the object's pose is estimated by matching the 2D image with the 3D point cloud. BundleSDF [29] utilizes RGB-D data for 3D reconstruction while tracking. Some methods, like Gen6D [9] and MFOS [7], estimate the pose directly from given reference frames. These techniques typically depend on a series of provided reference frames, thereby introducing certain constraints. FoundationPose [30] trains neural networks on large datasets to acquire as much knowledge as possible, enabling them to handle a wider range of scenarios. Overall, while these methods reduce dependence on model priors to some extent, their reliance on training can lead to generalization issues, and the collection of training data are costly. + +![](images/abb3f4fa413882a4411450e8b4b96e79f9dba8d06ebe977d812d6b25c6ab476d.jpg) +Figure 2. Overview of our method BIT. Our method starts with the first frame, using a bounding box to identify the object to track, optionally incorporating available reference frames. The geometry generation module quickly inverse renders a mesh model for the pose optimization module, which in return supplies additional key frames as reference frames. This mutual enhancement between the modules transforms a model-free scene into a model-based scene, leading to improved results. + +# 2.3. Model and Training-based Methods + +Some methods rely on both model priors and training priors to achieve better tracking accuracy or address specific problems (such as category-level pose estimation [26, 28, 31]). DeepAC [27] combines deep networks with precise CAD models to achieve enhanced results. Additionally, some methods [26, 28, 31] can perform tracking with imprecise models. These methods estimate the poses of different instances within a category based on a shared category prior (which can be considered a model prior, typically 3D point clouds). However, these methods usually heavily rely on depth information and struggle to achieve ideal results when relying solely on RGB inputs. Another significant issue is that these methods require extensive training and are prone to generalization challenges. + +# 2.4. Differentiable Rendering + +Traditional rendering pipelines are non-differentiable due to discrete sampling in rasterization. Differentiable rendering transforms this into a differentiable process, allowing gradients to flow from 2D images to 3D models, which provide a basis for generating 3D geometry from 2D data. Some methods [5, 10] use handcrafted functions for gradient approximation, while SoftRas [8] achieves full differentiability with an aggregation function. Differentiable rendering is applied in reconstruction, shape fitting, and technologies like NeRF [11]. It requires object poses and segmented contours or masks, often needing multiple views for better results. A method [15] combines 2D trackers with differentiable rendering to reconstruct the geometry, color, texture, and 6DoF pose of 3D objects. However, this method is time-consuming, requiring about 2 seconds per frame, + +whereas we address a real-time, prior-free problem. + +# 3. Method + +The overview of our method BIT is shown in Fig. 2. BIT takes RGB images as input, with the first frame utilizing a bounding box to indicate the target object for tracking. Additionally, if available, it can incorporate a limited number of reference frames. Our method is capable of simultaneously performing iterative real-time tracking and model generation. It primarily consists of two mutually enhancing components: the geometry generation module and the pose optimization module. + +After receiving the first frame and the reference frames (if available), the geometry generation module can quickly generate an initial model by inverse rendering using the given data and send the generated model to the pose optimization module. The pose optimization module then employs this generated model for continuous tracking, selecting key frames from the tracking results and feeding this data back to the geometry generation module. The geometry generation module, in turn, utilizes this feedback to further optimize the generated model. These two processes iterate continuously, simultaneously optimizing both the generated model and tracking performance. Once the generated model reaches a sufficient level of precision, only the pose optimization module needs to be executed. + +Throughout the entire process, the pose optimization module does not require any training. The reference for inverse rendering used by the geometry generation module is automatically generated during the tracking process, also eliminating the need for training. + +![](images/19b2da3f0b15cff291726ee3f8fe5014201fa16d6ae766658d91f7a15e1691fe.jpg) +Figure 3. The geometry generation module. This module takes the first frame, along with a bounding box, an initial pose, and camera intrinsic $\pmb{K}$ as input. It can also incorporate additional reference frames if available. A better mesh model can be obtained by inverse rendering a sphere or the previously generated model. + +# 3.1. Geometry Generation Module + +The geometry generation module rapidly generates an object's mesh model by iteratively inverse rendering during the tracking process. The generated model is then supplied to the pose optimization module. Figure 3 illustrates the overview of the geometry generation module. + +The geometry generation module takes as input the first frame $\mathcal{I}_0$ , an initial pose $\pmb{T}_0 = [R_0|t_0]$ , and a bounding box $\pmb{b}_0$ that specifies the target object. Here, $\pmb{R}_0 \in \mathbb{R}^{3 \times 3}$ represents the rotation matrix, and $\pmb{t}_0 \in \mathbb{R}^3$ is the translation vector. Additionally, the camera intrinsic matrix $\pmb{K} \in \mathbb{R}^{3 \times 3}$ is also provided. + +Additionally, if available, the geometry generation module can incorporate reference frames $\{\mathcal{I}_i\}$ , corresponding poses $\{T_i\}$ , and bounding boxes $\{b_i\}$ . Since the post-processing for the initial frame and reference frames is identical, we assume the presence of reference frames to streamline the description of our method. Furthermore, the pose optimization module can automatically generate these reference frames during the iterative process. For the sake of simplicity, we will use $\{\mathcal{I}_i\}$ to refer to both $\mathcal{I}_0$ and $\{\mathcal{I}_i\}$ , and apply the same convention to $\{T_i\}$ and $\{b_i\}$ . + +The input frames $\{\mathcal{I}_i\}$ are first fed to a segmenter SAM [6] to obtain the object's masks, with the bounding boxes $\{b_i\}$ serving as prompts. To ensure the object area defined by $\{b_i\}$ is not too small and to facilitate easier optimization during post-processing, we crop the object area and resize it to a fixed size, resulting in the resized masks $\{\mathcal{M}_i\}$ . During this process, we adjust the camera intrinsics from $K$ to $K_{i}$ for each resized mask $\mathcal{M}_i$ . This adjustment is necessary because $K$ influences the size and position of the image, ensuring that the input pose $\{T_i\}$ remains compatible with the modified masks $\mathcal{M}_i$ . For further details on this process, please refer to our supplementary materials. + +Starting with a 3D sphere $G_{0}$ as the initial model and following the SoftRas [8] method, we iteratively deform this sphere $G_{0}$ into the target mesh model $G^{*}$ using the resized masks $\{\mathcal{M}_i\}$ and poses $\{T_i\}$ . SoftRas is chosen due to its + +rapid processing speed. Since the masks provide comprehensive cues and supervision for inverse rendering, there is no need to train the differentiable renderer. We simplified the loss function for mesh inverse rendering in SoftRas, resulting in a very concise loss function $\mathcal{L}$ : + +$$ +\mathcal {L} = \mathcal {L} _ {I o U} \left(\left\{\boldsymbol {G}, \boldsymbol {T} _ {i}, \boldsymbol {K} _ {i} \right\}, \left\{\boldsymbol {\mathcal {M}} _ {i} \right\}\right) + \mu \mathcal {L} _ {l} (\boldsymbol {G}), \tag {1} +$$ + +where $\mathcal{L}_{IoU}$ represents the 2D IoU loss between the given masks $\{\mathcal{M}_i\}$ and the projected masks of the model $G$ under poses $\{\pmb{T}_i\}$ and intrinsics $\{\pmb{K}_i\}$ , $G$ represents the intermediate 3D model transitioning from $G_0$ to $G^*$ . $\mathcal{L}_l$ is the Laplacian regularization term used to control the smoothness of the geometry. The parameter $\mu$ acts as a balancing factor. The loss function is intentionally kept simple to facilitate the rapid convergence of the input geometry to a specific shape suitable for tracking. Additionally, a straightforward loss function is crucial for generalization. For more details please see our supplementary materials. + +Throughout the process, the 3D model initially starts as a sphere, and each iteration generates a mesh model that can be utilized by the pose optimization module. Except for the first iteration, each subsequent iteration receives a fixed number of key frames generated by the pose optimization module as inputs. Additionally, in every iteration, the first frame and reference frames (if available) are consistently used as inputs. Since the contours of the masks segmented by SAM are not smooth and have minor pixel discrepancies, we found that the inverse-rendered model might appear slightly smaller than the actual object. To compensate for this, we scale the inverse-rendered model by a factor of 1.05, which is an empirically determined parameter. + +# 3.2. Pose Optimization Module + +The pose optimization module is shown in Fig. 4, which has two main purposes: First, it receives the generated 3D mesh model and uses it to quickly estimate the object's pose in the frame. Second, it generates key frames and the object's bounding boxes, and sends these data along with their corresponding poses to the geometry generation module. + +
MethodInputTrainingModelRefersblack_d Drillduplo_duderinse aidtoyPlanevim_mugAvg.↑
PoseRBPF [1]†RGB-D*✓✓×75.384.187.248.659.070.8
LatentFusion [13]†RGB-D✓×✓89.488.967.482.940.073.7
LatentFusion [13]‡RGB-D✓×✓74.175.463.055.038.361.1
PVNet [14]‡RGB✓✓×49.543.372.948.667.956.4
Gen6D [9]‡RGB✓×✓64.959.272.069.851.063.4
Ours(0)RGB×××63.169.780.576.281.474.2
Ours(3)RGB××✓82.989.988.381.788.486.2
+ +![](images/6aae1249cde7f51cf6c6a02848ca16a22fbb1892ca2c679fd13e19d16e456af1.jpg) +Figure 4. The pose optimization module, which can track the object's pose and generate key frames for model generation module. + +We utilize the tracking method SLOT [4] as the baseline for tracking the object's pose. This method accepts the generated model as input and then optimizes the object's pose using the color features in the input RGB image around the projected mask of the model. Since it does not include any deep networks, it does not require training. For a detailed explanation of this method, please refer to our supplementary materials. Next, we will provide a detailed explanation of how to generate the key frames and bounding boxes required for the geometry generation module. + +The key frames should encompass as many viewpoints as possible to enhance the effectiveness of the geometry generation module. Concurrently, to reduce computational load, redundant viewpoints should be minimized. To achieve this, we construct a view group, denoted as $\mathcal{V}$ , to store the viewpoints of frames calculated from the tracked poses: + +$$ +\boldsymbol {\mathcal {V}} = \left\{\boldsymbol {v} _ {0}, \boldsymbol {v} _ {1}, \boldsymbol {v} _ {2}, \dots , \boldsymbol {v} _ {n - 1} \right\}, \tag {2} +$$ + +where $\pmb{v}_i\in \mathbb{R}^3$ is the $i$ -th view, which can be calculated from the corresponding pose $\pmb{T}_i = [R_i|\pmb {t}_i]$ : + +$$ +\boldsymbol {v} _ {i} = \boldsymbol {R} _ {i} ^ {\top} \boldsymbol {t} _ {i} / | | \boldsymbol {t} _ {i} | |. \tag {3} +$$ + +When a new frame $\mathcal{I}_n$ is tracked and the camera view $\pmb{v}_n$ is established, we compute the angular differences between $\pmb{v}_n$ and all the views in the set $\pmb{\nu}$ as follows: + +$$ +\Delta \boldsymbol {a} _ {i} = a c o s \left(\frac {\boldsymbol {v} _ {n} \cdot \boldsymbol {v} _ {i}}{| | \boldsymbol {v} _ {n} | | | | \boldsymbol {v} _ {i} | |\right), f o r \boldsymbol {v} _ {i} \in \boldsymbol {\mathcal {V}}. \tag {4} +$$ + +Table 1. Tracking results on the MOPED dataset under the ADD-AUC (0-10 cm). Ours(0) uses no reference frames, Ours(3) uses 3 reference frames. Bold indicates the best result, and underline indicates the second best. † denotes the data reported by LatentFusion, and ‡ denotes the results reported by Gen6D under its configuration. *According to the description in LatentFusion's experiments, we infer that this method uses RGB-D data. + +
MethodRefersKey FramesItersModel Acc. ↓
Ours(3)3330.035
Ours(6)61230.011
Ours(12)121230.010
+ +Table 2. Our generated models in different cases. Model accuracy is measured by the normalized Hausdorff distance. + +If all the $\Delta \pmb{a}_i$ values exceed a certain threshold $\pmb{a}_{\mathrm{min}}$ , we consider the frame $\mathcal{I}_n$ to be a key frame candidate. + +We then project the 3D mesh model according to the tracked pose $\pmb{T}_n$ to obtain a bounding box $\pmb{b}_n$ . If $\pmb{b}_n$ is more than 10 pixels away from the image border, we consider $\pmb{b}_n$ to be valid and designate $\mathcal{I}_n$ as a true key frame, subsequently adding $\pmb{v}_n$ to $\pmb{\nu}$ . If a sufficient number of key frames are selected, these frames, along with their corresponding bounding boxes and poses, will be sent to the geometry generation module to perform inverse rendering. + +# 4. Experiments + +We conducted experiments on both publicly available datasets and real-world scenarios, presenting both quantitative and qualitative results. The experimental setup consisted of a desktop computer equipped with an Intel 12700 CPU and a single NVIDIA GTX 3080 (10GB) GPU. In our experiments, we set $a_{\mathrm{min}} = 3^{\circ}$ . The masks were resized to $256 \times 256$ resolutions during the inverse rendering process. We employed the Adam optimizer, configured with a learning rate of 0.01 and beta values of (0.50, 0.99), to optimize the model. The initial model is a 3D sphere with 1302 vertices. Additionally, $\mu = 0.1$ was set in the loss function. Each inverse rendering iteration during the model generation process consisted of 200 optimization steps. + +In cases where we used reference frames on the dataset, we employed an algorithm that utilizes the golden ratio to evenly distribute a certain number of viewpoints on the surface of a sphere and then selected the frames closest to these generated viewpoints to serve as reference frames. + +![](images/4238df6d65d40da73cfec74118c26cda4c96b991d25bc285fd4f00252318c466.jpg) + +![](images/b589fb2beb41c5b015e25eaa5f4aee7f84f640561a1e292ba4b0f8ec8342016c.jpg) +(a) Tracking results and generated models in iterations without reference frame + +![](images/17d390c0895a794906ec0f7c31f4a05f06d9ebe0b5d85b85e991f815d4f4f270.jpg) + +![](images/c2a26f2a27b9a182f3f23e2d8c9b8f0793f0f3331a72e9cd1cb5e7812fc03b5b.jpg) + +![](images/51ca4ddaa39b435a06719d7e2bfc628b17cb10c2156c2a3e675e7dd609a4409d.jpg) + +![](images/27dff0902e88c6a51d22b6857377ec7010b1a9b63bf5c0e417bd052f2c3fcbd5.jpg) + +![](images/145c5076038c949c2d193f06d698383998348a7f58eecbb21a7db2b6bce76b54.jpg) + +![](images/59666ac528367ad54d9d6e0b54dfff5ded3049216b14fc61a87311b904fc9bc3.jpg) +(b) Tracking results and generated models in iterations with 3 reference frames + +![](images/4d8915f9ed1ded9fca9293a65bb4bc4661f9ec2fd87af209e5c120795480d857.jpg) + +![](images/5addd2ce10e46a4f9a293d413202088a2c14d659cbce0a6b8da7063732ce99a9.jpg) + +![](images/ca37336470b50137bb422d580ef1c3fd31e373085215ee5141bb7bf1fd25370b.jpg) + +![](images/5b49e0fabc638feb5d976c1c96740f0b9431a9635157198c2ef562e30633870a.jpg) + +![](images/aa241454cc73db6a9fde639189c04d47e848183a04b4e9559cd8b0af6ef82eda.jpg) +Figure 5. Tracking results and generated models in 3 iterations on the MOPED dataset, displayed from left to right. +Figure 6. The accuracy of the generated models (solid lines) and tracking (dashed lines) across iterations (note the axis direction). + +# 4.1. Results on the MOPED Dataset + +The MOPED dataset [13] is a real-world captured dataset containing 11 objects, each comprising several RGB-D video sequences divided into reference and evaluation sets, with a resolution of $640 \times 480$ . The poses are obtained through a combination of multiple methods [12, 16, 32, 33]. Due to the annotation manner, the poses in some sequences may not be entirely accurate. Therefore, following the approach of Gen6D [9], we selected 5 relatively reliable objects for evaluation. For each object, there are 100-600 reference images and 100-300 query images. + +We use the ADD-AUC $(0 - 10cm)$ metric to evaluate the tracking results. We test our method in two versions: Ours(0) uses no model or training priors and no reference frames, generating 3 key frames per iteration. Ours(3) also uses no model or training priors but employs 3 reference frames, generating 6 key frames per iteration. For each object, we perform model generation for up to 3 iterations. + +Since the proposed method addresses a new problem, to the best of our knowledge, there are currently no directly comparable methods. Therefore, we selected the methods most similar to ours for comparison. We compare our results with PoseRBPF [1], LatentFusion [13], PVNet [14], and Gen6D [9]. The results are shown in the Tab. 1. We also present a part of tracking results, as well as the generated models, as shown in Fig. 5. + +![](images/b6490ad5d385fa4eb21bc46af8a67f8ffa96d7ec34bfac4f7f1965420284411d.jpg) +Figure 7. The final generated models (3 iterations) in different reference frames and key frames on the RBOT dataset. + +Even without any priors and reference frames, our method (Ours(0)) outperforms all other methods in average. With 3 reference frames, our method (Ours(3)) significantly outperforms the others. Notably, our method requires no training and uses only RGB data, whereas other methods were trained on the tested or other objects. Additionally, compared to other methods, our method demonstrates more uniform accuracy across various objects, indicating that it is data-independent and a truly training-free approach. + +# 4.2. Results on the RBOT Dataset + +During tracking, our method can rapidly generate the 3D model of an object, by comparing the performance of various trackers using both precise ground truth CAD models and our generated models on the RBOT dataset [23], we explored the models' reusability. + +The RBOT dataset is a 3D object tracking dataset with 18 objects and 72 sequences, each containing 1000 test frames, with a resolution of $640\times 512$ , covering a baseline regular scenario and dynamic light, noisy, and occlusion scenarios. It has been used to evaluate some advanced 3D track + +![](images/718869fde34afd8479e38e171252a2b563f545af7976cbe7027d3678cae5ec71.jpg) +Figure 8. Generated models in the case of 6 reference frames and 12 key frames on the RBOT dataset, displayed from top to bottom in each iteration. + +
MethodModelReg.Dyn.NoisyOcc.Avg.↑
RBOT [23]GT79.981.256.673.372.8
Ours(3)38.137.525.932.433.5
Ours(6)63.262.942.356.156.1
Ours(12)67.867.044.960.260.0
SLOT [4]GT89.990.769.688.984.8
Ours(3)38.838.426.936.135.1
Ours(6)68.868.249.866.063.2
Ours(12)75.274.353.372.468.8
Song23 [17]GT95.494.986.293.292.4
Ours(3)52.750.944.848.349.2
Ours(6)81.579.870.977.777.5
Ours(12)85.783.874.681.981.5
RBGT [18]GT90.090.671.585.684.4
Ours(3)48.947.837.944.344.7
Ours(6)73.973.357.668.668.3
Ours(12)79.778.961.474.073.5
SRT3D [19]GT94.294.681.793.290.9
Ours(3)49.748.940.946.446.5
Ours(6)75.975.263.872.771.9
Ours(12)81.880.969.179.477.8
+ +Table 3. Tracking accuracy with GT models and the generated models by our method on the RBOT dataset. Bold indicates the best result except for the ground truth. + +ing methods, such as SRT3D [19], RBGT [18], SLOT [4], Song23 [17] and the RBOT method [23]. + +Due to the significant differences between frames in the RBOT dataset and the rapid movement of objects, we used 3-12 reference frames, and then tracked the first 100 frames in the regular scenario, and generate the objects' models during tracking. For each object, we performed up to 3 it + +![](images/d60d023bafaba966ec68c37d40557a386897af6636f566bc6e228ba39b746218.jpg) +Figure 9. Tracking accuracy of various trackers on the RBOT dataset using GT models and the our generated models. + +erations. Then these generated models served as inputs for other model-based trackers for testing across all scenes of the entire dataset, allowing us to compare their performance against the ground truth CAD models. + +We employed the $5 \, \text{cm}/5^{\circ}$ metric to measure the tracking accuracy, which indicates success in a frame if the translation error is less than $5 \, \text{cm}$ and the rotation error is less than $5^{\circ}$ . Otherwise, it is considered a failure, and the pose is reset to the ground truth. The proportion of successful frames represents the tracking accuracy. We use the normalized Hausdorff distance between the generated models and ground truth models to measure the models accuracy. + +Table 2 shows the models' accuracy (in normalized Hausdorff distance) in the last iteration, and Fig. 6 shows the normalized Hausdorff distance in every iteration. It can be seen that the generated models have relatively high accuracy with 6 or more reference frames. Additionally, by the second iteration, the model is already close to the final one. This indicates the proposed method's rapid convergence. Figures 7 and 8 also display portions of the generated models, demonstrating the effectiveness of our method. Furthermore, Figure 6 illustrates the variation in tracking accuracy of the baseline tracker [4] across the entire dataset using the intermediate generated models. The results show that the tracking accuracy improves as the models become more accurate. + +The test results of the 5 tracking methods using the final generated models on the RBOT dataset are presented in Tab. 3 and Fig. 9. It is clear from these results that when given 6 or more reference frames, the generated models can achieve results very close to the ground truth CAD models. This proves the effectiveness of our method, as it can + +![](images/8bca42da9383f78b139cab67f0cf7cd92db3d1bc4de861fddd5dff601b51e87e.jpg) +(a) Tracking poses and the generated model without reference frame + +![](images/8e32ea592f4040d972a9f7cb13dba7a224d62f8a1efa465e1c1eea335ff40a31.jpg) +(b) Tracking poses and the generated model with 3 references frames + +![](images/4676d7cb77a455b41329cf43274d7b5aab204f46822f716c9c81ad01237a91b5.jpg) +(c) Tracking poses and the generated model with 6 references frames +Figure 10. Qualitative results on the real world scenes. From left to right, the first frame, tracking results, and the generated models. + +effectively transform a model-free tracking problem into a model-based tracking problem. + +# 4.3. Qualitative Results + +We captured RGB images of real-world scenes to test the proposed method, with a resolution of $640 \times 480$ . We evaluated our method under 3 conditions: (1) no reference and 3 key frames, (2) 3 reference frames and 3 key frames, and (3) 6 reference frames and 6 key frames. The reference frames are from the RBOT dataset. For each object, we performed up to 3 iterations. The tracking results are shown in Fig. 10. Under all 3 conditions, our method successfully achieved effective tracking and generated object models. Further experimental results can be found in our supplementary video. + +# 4.4. Time Analysis + +With a resolution of $640 \times 480$ , tracking a frame takes about $30~\mathrm{ms}$ . When using 6 reference frames and 12 key frames for generating models, each iteration takes about 10 seconds. Therefore, a 3D model of an object can be obtained in about 30 seconds over 3 iterations. Notably, our method only utilizes a single NVIDIA 3080 (10GB) GPU. After completing the model generation, only tracking is required, allowing our method become real-time (30 FPS). Additionally, tracking can be run as a background thread to reduce time consumption. + +# 5. Limitations + +Our method has several limitations that need to be addressed. Firstly, it is incapable of generating recessed features on object surfaces and cannot accurately model specific topologies, such as ring-shaped or hollow structures. + +Secondly, in challenging scenarios, SAM's segmentation performance may be affected, particularly in cases involving occlusion, motion blur, or similar colors, and the object's complex geometry can also have a certain impact; errors in the mask may degrade the initially rendered model and tracking accuracy, further complicating iterative improvements. Lastly, tracking failures may occur in challenging scenes, particularly with fast-moving objects and when there is a lack of reference frames. + +# 6. Conclusions + +We have proposed a prior-free tracking method based on RGB data, capable of quickly generating 3D models of objects while tracking them. This approach transforms a model-free tracking problem into a model-based one without requiring pose-annotated training. The method operates when the target object is specified in the first frame and can incorporate reference frames if available. The generated models can be reused by other trackers and exhibit high accuracy. The method's consistent results across datasets demonstrate its independence from specific data, clearly distinguishing it from training-based methods. Extending 3D object tracking to non-rigid objects for broader applications and exploring tracking for objects with more complex topologies are future research directions in our work. + +# Acknowledgments + +This work is partially supported by the National Key R&D Program of China under grant (No. 2022YFB3303203), NSF of China (U23A20312, No. 62172260, 62202425), and Shandong Provincial Natural Science Foundation (No. ZR2022LZH007). + +# References + +[1] Xinke Deng, Arsalan Mousavian, Yu Xiang, Fei Xia, Timothy Bretl, and Dieter Fox. PoseRBPF: A rao-blackwellized particle filter for 6-D object pose tracking. IEEE Transactions on Robotics, 37(5):1328-1342, 2021. 5, 6 +[2] Xingyi He, Jiaming Sun, Yuang Wang, Di Huang, Hujun Bao, and Xiaowei Zhou. OnePose++: Keypoint-free one-shot object pose estimation without CAD models. In Advances in Neural Information Processing Systems, 2022. 2 +[3] Hong Huang, Fan Zhong, Yuqing Sun, and Xueying Qin. An occlusion-aware edge-based method for monocular 3D object tracking using edge confidence. Computer Graphics Forum, 39(7):399-409, 2020. 2 +[4] Hong Huang, Fan Zhong, and Xueying Qin. Pixel-wise weighted region-based 3D object tracking using contour constraints. TVCG, 28(12):4319-4331, 2022. 1, 2, 5, 7 +[5] Hiroharu Kato, Yoshitaka Ushiku, and Tatsuya Harada. Neural 3D mesh renderer. In CVPR, pages 3907-3916, 2018. 3 +[6] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C. Berg, Wan-Yen Lo, Piotr Dollar, and Ross B. Girshick. Segment anything. In ICCV, pages 3992-4003, 2023. 2, 4 +[7] JongMin Lee, Yohann Cabon, Romain Brégier, Sungjoo Yoo, and Jérôme Revaud. MFOS: Model-free & one-shot object pose estimation. In AAAI, pages 2911-2919, 2024. 2 +[8] Shichen Liu, Weikai Chen, Tianye Li, and Hao Li. Soft rasterizer: A differentiable renderer for image-based 3D reasoning. 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TPAMI, 41(8): 1797-1812, 2019. 2, 6, 7 +[24] Bin Wang, Fan Zhong, and Xueying Qin. Pose optimization in edge distance field for textureless 3D object tracking. In CGI, pages 32:1-32:6, 2017. 2 +[25] Bin Wang, Fan Zhong, and Xueying Qin. Robust edge-based 3D object tracking with direction-based pose validation. Multimedia Tools and Applications, 78(9):12307-12331, 2019. 2 +[26] Chen Wang, Roberto Martin-Martin, Danfei Xu, Jun Lv, Cewu Lu, Li Fei-Fei, Silvio Savarese, and Yuke Zhu. 6-PACK: Category-level 6D pose tracker with anchor-based keypoints. In ICRA, pages 10059-10066, 2020. 3 +[27] Long Wang, Shen Yan, Jianan Zhen, Yu Liu, Maojun Zhang, Guofeng Zhang, and Xiaowei Zhou. Deep active contours for real-time 6-DoF object tracking. In ICCV, pages 13988-13998, 2023. 1, 3 +[28] Bowen Wen and Kostas E. Bekris. BundleTrack: 6D pose tracking for novel objects without instance or category-level 3D models. 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Open3D: A modern library for 3D data processing. arXiv:1801.09847, 2018.6 \ No newline at end of file diff --git a/2025/Prior-free 3D Object Tracking/images.zip b/2025/Prior-free 3D Object Tracking/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e6ab148611440d3c38733f17db5394dc52e77a64 --- /dev/null +++ b/2025/Prior-free 3D Object Tracking/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3d235e44c70f3abff939055a94116582d9c0a909a3180b6175d18f9376c762a0 +size 680342 diff --git a/2025/Prior-free 3D Object Tracking/layout.json b/2025/Prior-free 3D Object Tracking/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..da71e8dcd3c005261f4c3069b47e03bd8bbd889a --- /dev/null +++ b/2025/Prior-free 3D Object Tracking/layout.json @@ -0,0 +1,7678 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 210, + 103, + 400, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 210, + 103, + 400, + 121 + ], + "spans": [ + { + "bbox": [ + 210, + 103, + 400, + 121 + ], + "type": "text", + "content": "Prior-free 3D Object Tracking" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "spans": [ + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": "Xiuqiang Song" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " Li Jin" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " Zhengxian Zhang" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " Jiachen Li" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " \nFan Zhong" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " Guofeng Zhang" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": " Xueying Qin" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{1,3*}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": "School of Software, Shandong University \n" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": "School of Computer Science and Technology, Shandong University \nering Research Center of Digital Media Technology, Ministry of Education, P. \noratory of Computing Power Network and Information Security, Ministry of E \nShandong Computer Science Center, Qilu University of Technology \n" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 118, + 141, + 492, + 284 + ], + "type": "text", + "content": "State Key Lab of CAD&CG, Zhejiang University \nsong_xq, jinli, zhangzhengxian@mail.sdu.edu.cn jcli@qlu.edu.cn \nzhongfan@sdu.edu.cn zhangguofeng@zju.edu.cn qxy@sdu.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 310, + 200, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 310, + 200, + 323 + ], + "spans": [ + { + "bbox": [ + 151, + 310, + 200, + 323 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 352, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 296, + 653 + ], + "type": "text", + "content": "In this paper, we introduce a novel, truly prior-free 3D object tracking method that operates without given any model or training priors. Unlike existing methods that typically require pre-defined 3D models or specific training datasets as priors, which limit their applicability, our method is free from these constraints. Our method consists of a geometry generation module and a pose optimization module. Its core idea is to enable these two modules to automatically and iteratively enhance each other, thereby gradually building all the necessary information for the tracking task. We thus call the method as Bidirectional Iterative Tracking(BIT). The geometry generation module starts without priors and gradually generates high-precision mesh models for tracking, while the pose optimization module generates additional data during object tracking to further refine the generated models. Moreover, the generated 3D models can be stored and easily reused, allowing for seamless integration into various other tracking systems, not just our methods. Experimental results demonstrate that BIT outperforms many existing methods, even those that extensively utilize prior knowledge, while BIT does not rely on such information. Additionally, the generated 3D models deliver results comparable to actual 3D models, highlighting their superior and innovative qualities. The code is available at https://github.com/songxiuqiang/BIT.git." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 328, + 309, + 539, + 460 + ], + "blocks": [ + { + "bbox": [ + 328, + 309, + 539, + 460 + ], + "lines": [ + { + "bbox": [ + 328, + 309, + 539, + 460 + ], + "spans": [ + { + "bbox": [ + 328, + 309, + 539, + 460 + ], + "type": "image", + "image_path": "7644328fa7bae3244c8090e0f61eca659240d7c662e3e8f99351d02020a18ca9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 468, + 555, + 524 + ], + "lines": [ + { + "bbox": [ + 313, + 468, + 555, + 524 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 555, + 524 + ], + "type": "text", + "content": "Figure 1. We propose a prior-free 3D object tracking method called BIT, which is both model-free and training-free. The pose optimization and geometry generation modules iteratively enhance each other to ultimately realize object tracking. The generated model can be reused, achieving excellent results." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 548, + 395, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 548, + 395, + 560 + ], + "spans": [ + { + "bbox": [ + 314, + 548, + 395, + 560 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 570, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 570, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 570, + 555, + 715 + ], + "type": "text", + "content": "The advancement of embodied intelligence technology necessitates a deep understanding of the real world, and a crucial foundation for this understanding is the accurate and continuous real-time 6DoF pose estimation of objects in the real world, also known as 3D object tracking. Existing methods typically rely on predefined 3D model priors [4, 20, 22] or training priors [9, 30], or a combination of both [27], to achieve accurate tracking results. While the use of priors simplifies the tracking task, it also incurs high training costs and the need for precise model reconstruction, which significantly limits the flexibility and scalability of these methods across diverse environments and object" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 205, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 205, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 205, + 713 + ], + "type": "text", + "content": "* Xueying Qin is the corresponding author." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1200" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "types. In this paper, we explore, for the first time, a truly prior-free 3D object tracking paradigm that is both model-free and training-free, specifically without requiring given 3D models or pose-annotated training images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 337 + ], + "type": "text", + "content": "We introduce a Bidirectional Iterative Tracking (BIT) to tackle the challenging task of prior-free tracking. The key idea of BIT is to automatically generate the necessary information for tracking, rather than relying on pre-existing priors that serve a similar purpose. BIT relies solely on monocular RGB data as input. It comprises two key modules: the geometry generation module and the pose optimization module. The geometry generation module can automatically deform a sphere to match the target object's shape, while the pose optimization module tracks the pose and selects the appropriate information as a foundation for geometry generation. These modules work in cooperation, iteratively enhancing each other's functionality. Additionally, the information generated by BIT can be used immediately or stored for future reuse, allowing other tracking systems to seamlessly integrate it. The core components of BIT include a tracker SLOT [4], a segmenter SAM [6], and a differentiable renderer SoftRas [8]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 338, + 295, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 295, + 566 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 295, + 566 + ], + "type": "text", + "content": "The BIT method improves upon previous methods by completely eliminating the reliance on model priors and training priors (the training of SAM is not specific to the tracked object, and in our method it also can be replaced with other segmentation method). Existing 3D object tracking methods typically depend on provided priors to reduce the difficulty of tracking, which can be classified into three main categories: Model-based methods, which rely on CAD models or reconstructed models as priors and cannot function without them. Training-based methods, which involve training on specific datasets and then generalizing to unseen objects. Model and training-based methods, which rely on both models and training data simultaneously. In practical scenarios, acquiring such models and training data incurs significant costs, which clearly limits the flexibility and applicability of these methods. BIT overcomes these limitations by functioning independently of such priors, making it more versatile and cost-effective. The key contributions of this paper are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "type": "text", + "content": "- The BIT framework is proposed, which realizes prior-free tracking of 3D objects, encompassing both model-free and training-free." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": "- An effective bidirectional iterative tracking method is proposed, where the pose optimization module and the geometry generation module can iteratively enhance each other, achieving synchronized improvement in their effects and jointly completing the tracking task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "- The 3D models automatically generated by BIT can be easily reused and seamlessly integrated into many other tracking systems without additional processing, providing convenience for the utilization of other tracking methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 406, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 406, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 406, + 84 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 91, + 553, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 236 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 236 + ], + "type": "text", + "content": "Based on our knowledge, there are currently no 3D object tracking methods that do not rely on either model priors or training priors. In this section, we will first provide an overview of 3D object tracking and methods for single-frame pose estimation relevant to our work, followed by an introduction to differentiable rendering. Single-frame pose estimation determines an object's pose from a single frame without relying on previous frames, leading to higher computational demands due to a larger search space. In contrast, 3D object tracking uses pose information from previous frames for a more efficient and accurate estimation, optimizing within a smaller search space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 242, + 441, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 242, + 441, + 254 + ], + "spans": [ + { + "bbox": [ + 313, + 242, + 441, + 254 + ], + "type": "text", + "content": "2.1. Model-based Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 258, + 555, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 555, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 555, + 450 + ], + "type": "text", + "content": "Precise 3D models can provide strong constraints for tracking, which is particularly important for textureless or weakly textured objects. In recent years, many model-based methods [4, 17, 19, 20, 22, 23] have achieved excellent tracking results by utilizing well-designed energy functions. These energy functions are typically constructed from interpretable features, such as the color distribution of pixels [4, 17, 19, 20, 23] or edges [3, 22, 24, 25] in the frame. These methods do not rely on deep networks, thereby avoiding issues related to training and generalization. They typically offer good tracking accuracy and real-time performance while having low hardware requirements. When precise CAD models are available, these methods are generally the best choice for object tracking. However, obtaining precise CAD models is not always feasible, which is the main limitation of these methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 456, + 452, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 452, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 452, + 470 + ], + "type": "text", + "content": "2.2. Training-based Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "text", + "content": "Some methods do not rely on explicit 3D models as priors but require training on specific datasets to acquire the necessary knowledge, subsequently using this learned information to predict poses. Additionally, some methods require a specific number of reference frames and corresponding camera poses to reconstruct an object's point cloud model via Structure-from-Motion (SfM), as seen in OnePose [21] and OnePose++ [2]. After reconstruction, the object's pose is estimated by matching the 2D image with the 3D point cloud. BundleSDF [29] utilizes RGB-D data for 3D reconstruction while tracking. Some methods, like Gen6D [9] and MFOS [7], estimate the pose directly from given reference frames. These techniques typically depend on a series of provided reference frames, thereby introducing certain constraints. FoundationPose [30] trains neural networks on large datasets to acquire as much knowledge as possible, enabling them to handle a wider range of scenarios. Overall, while these methods reduce dependence on model priors to some extent, their reliance on training can lead to generalization issues, and the collection of training data are costly." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "type": "text", + "content": "1201" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 72, + 531, + 244 + ], + "blocks": [ + { + "bbox": [ + 80, + 72, + 531, + 244 + ], + "lines": [ + { + "bbox": [ + 80, + 72, + 531, + 244 + ], + "spans": [ + { + "bbox": [ + 80, + 72, + 531, + 244 + ], + "type": "image", + "image_path": "abb3f4fa413882a4411450e8b4b96e79f9dba8d06ebe977d812d6b25c6ab476d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "lines": [ + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": "Figure 2. Overview of our method BIT. Our method starts with the first frame, using a bounding box to identify the object to track, optionally incorporating available reference frames. The geometry generation module quickly inverse renders a mesh model for the pose optimization module, which in return supplies additional key frames as reference frames. This mutual enhancement between the modules transforms a model-free scene into a model-based scene, leading to improved results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 319, + 247, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 247, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 247, + 333 + ], + "type": "text", + "content": "2.3. Model and Training-based Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 338, + 297, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 297, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 297, + 507 + ], + "type": "text", + "content": "Some methods rely on both model priors and training priors to achieve better tracking accuracy or address specific problems (such as category-level pose estimation [26, 28, 31]). DeepAC [27] combines deep networks with precise CAD models to achieve enhanced results. Additionally, some methods [26, 28, 31] can perform tracking with imprecise models. These methods estimate the poses of different instances within a category based on a shared category prior (which can be considered a model prior, typically 3D point clouds). However, these methods usually heavily rely on depth information and struggle to achieve ideal results when relying solely on RGB inputs. Another significant issue is that these methods require extensive training and are prone to generalization challenges." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 515, + 196, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 196, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 196, + 529 + ], + "type": "text", + "content": "2.4. Differentiable Rendering" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": "Traditional rendering pipelines are non-differentiable due to discrete sampling in rasterization. Differentiable rendering transforms this into a differentiable process, allowing gradients to flow from 2D images to 3D models, which provide a basis for generating 3D geometry from 2D data. Some methods [5, 10] use handcrafted functions for gradient approximation, while SoftRas [8] achieves full differentiability with an aggregation function. Differentiable rendering is applied in reconstruction, shape fitting, and technologies like NeRF [11]. It requires object poses and segmented contours or masks, often needing multiple views for better results. A method [15] combines 2D trackers with differentiable rendering to reconstruct the geometry, color, texture, and 6DoF pose of 3D objects. However, this method is time-consuming, requiring about 2 seconds per frame," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 320, + 523, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 320, + 523, + 333 + ], + "spans": [ + { + "bbox": [ + 314, + 320, + 523, + 333 + ], + "type": "text", + "content": "whereas we address a real-time, prior-free problem." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 350, + 370, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 350, + 370, + 363 + ], + "spans": [ + { + "bbox": [ + 314, + 350, + 370, + 363 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 373, + 555, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 555, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 555, + 481 + ], + "type": "text", + "content": "The overview of our method BIT is shown in Fig. 2. BIT takes RGB images as input, with the first frame utilizing a bounding box to indicate the target object for tracking. Additionally, if available, it can incorporate a limited number of reference frames. Our method is capable of simultaneously performing iterative real-time tracking and model generation. It primarily consists of two mutually enhancing components: the geometry generation module and the pose optimization module." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 483, + 556, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 556, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 556, + 651 + ], + "type": "text", + "content": "After receiving the first frame and the reference frames (if available), the geometry generation module can quickly generate an initial model by inverse rendering using the given data and send the generated model to the pose optimization module. The pose optimization module then employs this generated model for continuous tracking, selecting key frames from the tracking results and feeding this data back to the geometry generation module. The geometry generation module, in turn, utilizes this feedback to further optimize the generated model. These two processes iterate continuously, simultaneously optimizing both the generated model and tracking performance. Once the generated model reaches a sufficient level of precision, only the pose optimization module needs to be executed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "Throughout the entire process, the pose optimization module does not require any training. The reference for inverse rendering used by the geometry generation module is automatically generated during the tracking process, also eliminating the need for training." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "text", + "content": "1202" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 68, + 527, + 186 + ], + "blocks": [ + { + "bbox": [ + 82, + 68, + 527, + 186 + ], + "lines": [ + { + "bbox": [ + 82, + 68, + 527, + 186 + ], + "spans": [ + { + "bbox": [ + 82, + 68, + 527, + 186 + ], + "type": "image", + "image_path": "19b2da3f0b15cff291726ee3f8fe5014201fa16d6ae766658d91f7a15e1691fe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 194, + 555, + 228 + ], + "lines": [ + { + "bbox": [ + 54, + 194, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 54, + 194, + 555, + 228 + ], + "type": "text", + "content": "Figure 3. The geometry generation module. This module takes the first frame, along with a bounding box, an initial pose, and camera intrinsic " + }, + { + "bbox": [ + 54, + 194, + 555, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{K}" + }, + { + "bbox": [ + 54, + 194, + 555, + 228 + ], + "type": "text", + "content": " as input. It can also incorporate additional reference frames if available. A better mesh model can be obtained by inverse rendering a sphere or the previously generated model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 247, + 220, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 220, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 220, + 260 + ], + "type": "text", + "content": "3.1. Geometry Generation Module" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 266, + 295, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 295, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 295, + 326 + ], + "type": "text", + "content": "The geometry generation module rapidly generates an object's mesh model by iteratively inverse rendering during the tracking process. The generated model is then supplied to the pose optimization module. Figure 3 illustrates the overview of the geometry generation module." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": "The geometry generation module takes as input the first frame " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": ", an initial pose " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{T}_0 = [R_0|t_0]" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": ", and a bounding box " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{b}_0" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": " that specifies the target object. Here, " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{R}_0 \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": " represents the rotation matrix, and " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{t}_0 \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": " is the translation vector. Additionally, the camera intrinsic matrix " + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{K} \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 55, + 327, + 296, + 399 + ], + "type": "text", + "content": " is also provided." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": "Additionally, if available, the geometry generation module can incorporate reference frames " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{I}_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": ", corresponding poses " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{T_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": ", and bounding boxes " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{b_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": ". Since the post-processing for the initial frame and reference frames is identical, we assume the presence of reference frames to streamline the description of our method. Furthermore, the pose optimization module can automatically generate these reference frames during the iterative process. For the sake of simplicity, we will use " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{I}_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": " to refer to both " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{I}_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": ", and apply the same convention to " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{T_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\{b_i\\}" + }, + { + "bbox": [ + 55, + 400, + 296, + 520 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": "The input frames " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{I}_i\\}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " are first fed to a segmenter SAM [6] to obtain the object's masks, with the bounding boxes " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\{b_i\\}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " serving as prompts. To ensure the object area defined by " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\{b_i\\}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " is not too small and to facilitate easier optimization during post-processing, we crop the object area and resize it to a fixed size, resulting in the resized masks " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{M}_i\\}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": ". During this process, we adjust the camera intrinsics from " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "K_{i}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " for each resized mask " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_i" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": ". This adjustment is necessary because " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " influences the size and position of the image, ensuring that the input pose " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\{T_i\\}" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": " remains compatible with the modified masks " + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_i" + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": ". For further details on this process, please refer to our supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Starting with a 3D sphere " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "G_{0}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " as the initial model and following the SoftRas [8] method, we iteratively deform this sphere " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "G_{0}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " into the target mesh model " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "G^{*}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " using the resized masks " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{M}_i\\}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " and poses " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\{T_i\\}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ". SoftRas is chosen due to its" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 247, + 554, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 247, + 554, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 554, + 308 + ], + "type": "text", + "content": "rapid processing speed. Since the masks provide comprehensive cues and supervision for inverse rendering, there is no need to train the differentiable renderer. We simplified the loss function for mesh inverse rendering in SoftRas, resulting in a very concise loss function " + }, + { + "bbox": [ + 313, + 247, + 554, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 247, + 554, + 308 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 342, + 313, + 553, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 313, + 553, + 327 + ], + "spans": [ + { + "bbox": [ + 342, + 313, + 553, + 327 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {I o U} \\left(\\left\\{\\boldsymbol {G}, \\boldsymbol {T} _ {i}, \\boldsymbol {K} _ {i} \\right\\}, \\left\\{\\boldsymbol {\\mathcal {M}} _ {i} \\right\\}\\right) + \\mu \\mathcal {L} _ {l} (\\boldsymbol {G}), \\tag {1}", + "image_path": "1d816f60d82ea02b3d116d21800cca9c0241942f0573734497a0c378dfca9396.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{IoU}" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " represents the 2D IoU loss between the given masks " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{M}_i\\}" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " and the projected masks of the model " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " under poses " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\{\\pmb{T}_i\\}" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " and intrinsics " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\{\\pmb{K}_i\\}" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " represents the intermediate 3D model transitioning from " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "G^*" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_l" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " is the Laplacian regularization term used to control the smoothness of the geometry. The parameter " + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 331, + 554, + 463 + ], + "type": "text", + "content": " acts as a balancing factor. The loss function is intentionally kept simple to facilitate the rapid convergence of the input geometry to a specific shape suitable for tracking. Additionally, a straightforward loss function is crucial for generalization. For more details please see our supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 463, + 555, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 555, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 555, + 619 + ], + "type": "text", + "content": "Throughout the process, the 3D model initially starts as a sphere, and each iteration generates a mesh model that can be utilized by the pose optimization module. Except for the first iteration, each subsequent iteration receives a fixed number of key frames generated by the pose optimization module as inputs. Additionally, in every iteration, the first frame and reference frames (if available) are consistently used as inputs. Since the contours of the masks segmented by SAM are not smooth and have minor pixel discrepancies, we found that the inverse-rendered model might appear slightly smaller than the actual object. To compensate for this, we scale the inverse-rendered model by a factor of 1.05, which is an empirically determined parameter." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 624, + 462, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 462, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 462, + 636 + ], + "type": "text", + "content": "3.2. Pose Optimization Module" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "content": "The pose optimization module is shown in Fig. 4, which has two main purposes: First, it receives the generated 3D mesh model and uses it to quickly estimate the object's pose in the frame. Second, it generates key frames and the object's bounding boxes, and sends these data along with their corresponding poses to the geometry generation module." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1203" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 555, + 162 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 555, + 162 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 555, + 162 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 555, + 162 + ], + "type": "table", + "html": "
MethodInputTrainingModelRefersblack_d Drillduplo_duderinse aidtoyPlanevim_mugAvg.↑
PoseRBPF [1]†RGB-D*✓✓×75.384.187.248.659.070.8
LatentFusion [13]†RGB-D✓×✓89.488.967.482.940.073.7
LatentFusion [13]‡RGB-D✓×✓74.175.463.055.038.361.1
PVNet [14]‡RGB✓✓×49.543.372.948.667.956.4
Gen6D [9]‡RGB✓×✓64.959.272.069.851.063.4
Ours(0)RGB×××63.169.780.576.281.474.2
Ours(3)RGB××✓82.989.988.381.788.486.2
", + "image_path": "a5a0704bfce40e4fe2bbc48a6126189b6b2e8d5e1fb94ad27a1e7f0c5d491d76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 80, + 236, + 272, + 342 + ], + "blocks": [ + { + "bbox": [ + 80, + 236, + 272, + 342 + ], + "lines": [ + { + "bbox": [ + 80, + 236, + 272, + 342 + ], + "spans": [ + { + "bbox": [ + 80, + 236, + 272, + 342 + ], + "type": "image", + "image_path": "6aae1249cde7f51cf6c6a02848ca16a22fbb1892ca2c679fd13e19d16e456af1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 350, + 295, + 374 + ], + "lines": [ + { + "bbox": [ + 55, + 350, + 295, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 295, + 374 + ], + "type": "text", + "content": "Figure 4. The pose optimization module, which can track the object's pose and generate key frames for model generation module." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 391, + 295, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 391, + 295, + 511 + ], + "spans": [ + { + "bbox": [ + 54, + 391, + 295, + 511 + ], + "type": "text", + "content": "We utilize the tracking method SLOT [4] as the baseline for tracking the object's pose. This method accepts the generated model as input and then optimizes the object's pose using the color features in the input RGB image around the projected mask of the model. Since it does not include any deep networks, it does not require training. For a detailed explanation of this method, please refer to our supplementary materials. Next, we will provide a detailed explanation of how to generate the key frames and bounding boxes required for the geometry generation module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 511, + 295, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 511, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 55, + 511, + 295, + 583 + ], + "type": "text", + "content": "The key frames should encompass as many viewpoints as possible to enhance the effectiveness of the geometry generation module. Concurrently, to reduce computational load, redundant viewpoints should be minimized. To achieve this, we construct a view group, denoted as " + }, + { + "bbox": [ + 55, + 511, + 295, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 511, + 295, + 583 + ], + "type": "text", + "content": ", to store the viewpoints of frames calculated from the tracked poses:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 588, + 294, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 588, + 294, + 601 + ], + "spans": [ + { + "bbox": [ + 117, + 588, + 294, + 601 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mathcal {V}} = \\left\\{\\boldsymbol {v} _ {0}, \\boldsymbol {v} _ {1}, \\boldsymbol {v} _ {2}, \\dots , \\boldsymbol {v} _ {n - 1} \\right\\}, \\tag {2}", + "image_path": "d666588434a0d9c30915c9990a58eb2a3c1f883bb975894ed2c8a5244f5e31b9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "inline_equation", + "content": "\\pmb{v}_i\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "text", + "content": "-th view, which can be calculated from the corresponding pose " + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "inline_equation", + "content": "\\pmb{T}_i = [R_i|\\pmb {t}_i]" + }, + { + "bbox": [ + 55, + 605, + 295, + 631 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 138, + 634, + 294, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 634, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 138, + 634, + 294, + 649 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {i} = \\boldsymbol {R} _ {i} ^ {\\top} \\boldsymbol {t} _ {i} / | | \\boldsymbol {t} _ {i} | |. \\tag {3}", + "image_path": "ad83f97584d92a7a8fb3910c885f944eb3b91ed39acdffeab6edb414bdca5398.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": "When a new frame " + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_n" + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": " is tracked and the camera view " + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{v}_n" + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": " is established, we compute the angular differences between " + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{v}_n" + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": " and all the views in the set " + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu}" + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 693, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 693, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 93, + 693, + 295, + 717 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {a} _ {i} = a c o s \\left(\\frac {\\boldsymbol {v} _ {n} \\cdot \\boldsymbol {v} _ {i}}{| | \\boldsymbol {v} _ {n} | | | | \\boldsymbol {v} _ {i} | |\\right), f o r \\boldsymbol {v} _ {i} \\in \\boldsymbol {\\mathcal {V}}. \\tag {4}", + "image_path": "3aa6eb652127f55178e55b7cef29721627831e3c810e96add77d088696895cea.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 328, + 232, + 541, + 280 + ], + "blocks": [ + { + "bbox": [ + 55, + 170, + 555, + 214 + ], + "lines": [ + { + "bbox": [ + 55, + 170, + 555, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 170, + 555, + 214 + ], + "type": "text", + "content": "Table 1. Tracking results on the MOPED dataset under the ADD-AUC (0-10 cm). Ours(0) uses no reference frames, Ours(3) uses 3 reference frames. Bold indicates the best result, and underline indicates the second best. † denotes the data reported by LatentFusion, and ‡ denotes the results reported by Gen6D under its configuration. *According to the description in LatentFusion's experiments, we infer that this method uses RGB-D data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 232, + 541, + 280 + ], + "lines": [ + { + "bbox": [ + 328, + 232, + 541, + 280 + ], + "spans": [ + { + "bbox": [ + 328, + 232, + 541, + 280 + ], + "type": "table", + "html": "
MethodRefersKey FramesItersModel Acc. ↓
Ours(3)3330.035
Ours(6)61230.011
Ours(12)121230.010
", + "image_path": "8a41287fa17e3d0242ff31530c7e6cdcd9c7de4746694e7ee1123671428ad8a8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 289, + 554, + 311 + ], + "lines": [ + { + "bbox": [ + 313, + 289, + 554, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 554, + 311 + ], + "type": "text", + "content": "Table 2. Our generated models in different cases. Model accuracy is measured by the normalized Hausdorff distance." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "text", + "content": "If all the " + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "inline_equation", + "content": "\\Delta \\pmb{a}_i" + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "text", + "content": " values exceed a certain threshold " + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "inline_equation", + "content": "\\pmb{a}_{\\mathrm{min}}" + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "text", + "content": ", we consider the frame " + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_n" + }, + { + "bbox": [ + 313, + 336, + 553, + 360 + ], + "type": "text", + "content": " to be a key frame candidate." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": "We then project the 3D mesh model according to the tracked pose " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{T}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": " to obtain a bounding box " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{b}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{b}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": " is more than 10 pixels away from the image border, we consider " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{b}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": " to be valid and designate " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": " as a true key frame, subsequently adding " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{v}_n" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu}" + }, + { + "bbox": [ + 313, + 361, + 554, + 458 + ], + "type": "text", + "content": ". If a sufficient number of key frames are selected, these frames, along with their corresponding bounding boxes and poses, will be sent to the geometry generation module to perform inverse rendering." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 474, + 395, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 395, + 488 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 395, + 488 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "text", + "content": "We conducted experiments on both publicly available datasets and real-world scenarios, presenting both quantitative and qualitative results. The experimental setup consisted of a desktop computer equipped with an Intel 12700 CPU and a single NVIDIA GTX 3080 (10GB) GPU. In our experiments, we set " + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "inline_equation", + "content": "a_{\\mathrm{min}} = 3^{\\circ}" + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "text", + "content": ". The masks were resized to " + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "text", + "content": " resolutions during the inverse rendering process. We employed the Adam optimizer, configured with a learning rate of 0.01 and beta values of (0.50, 0.99), to optimize the model. The initial model is a 3D sphere with 1302 vertices. Additionally, " + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\mu = 0.1" + }, + { + "bbox": [ + 313, + 496, + 554, + 652 + ], + "type": "text", + "content": " was set in the loss function. Each inverse rendering iteration during the model generation process consisted of 200 optimization steps." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "In cases where we used reference frames on the dataset, we employed an algorithm that utilizes the golden ratio to evenly distribute a certain number of viewpoints on the surface of a sphere and then selected the frames closest to these generated viewpoints to serve as reference frames." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1204" + } + ] + } + ], + 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Tracking results and generated models in 3 iterations on the MOPED dataset, displayed from left to right." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 77, + 245, + 276, + 336 + ], + "lines": [ + { + "bbox": [ + 77, + 245, + 276, + 336 + ], + "spans": [ + { + "bbox": [ + 77, + 245, + 276, + 336 + ], + "type": "image", + "image_path": "aa241454cc73db6a9fde639189c04d47e848183a04b4e9559cd8b0af6ef82eda.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 344, + 295, + 367 + ], + "lines": [ + { + "bbox": [ + 55, + 344, + 295, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 295, + 367 + ], + "type": "text", + "content": "Figure 6. The accuracy of the generated models (solid lines) and tracking (dashed lines) across iterations (note the axis direction)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 391, + 226, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 226, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 226, + 403 + ], + "type": "text", + "content": "4.1. Results on the MOPED Dataset" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 54, + 410, + 295, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 410, + 295, + 530 + ], + "spans": [ + { + "bbox": [ + 54, + 410, + 295, + 530 + ], + "type": "text", + "content": "The MOPED dataset [13] is a real-world captured dataset containing 11 objects, each comprising several RGB-D video sequences divided into reference and evaluation sets, with a resolution of " + }, + { + "bbox": [ + 54, + 410, + 295, + 530 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 54, + 410, + 295, + 530 + ], + "type": "text", + "content": ". The poses are obtained through a combination of multiple methods [12, 16, 32, 33]. Due to the annotation manner, the poses in some sequences may not be entirely accurate. Therefore, following the approach of Gen6D [9], we selected 5 relatively reliable objects for evaluation. For each object, there are 100-600 reference images and 100-300 query images." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 54, + 532, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 532, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 54, + 532, + 295, + 616 + ], + "type": "text", + "content": "We use the ADD-AUC " + }, + { + "bbox": [ + 54, + 532, + 295, + 616 + ], + "type": "inline_equation", + "content": "(0 - 10cm)" + }, + { + "bbox": [ + 54, + 532, + 295, + 616 + ], + "type": "text", + "content": " metric to evaluate the tracking results. We test our method in two versions: Ours(0) uses no model or training priors and no reference frames, generating 3 key frames per iteration. Ours(3) also uses no model or training priors but employs 3 reference frames, generating 6 key frames per iteration. For each object, we perform model generation for up to 3 iterations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "content": "Since the proposed method addresses a new problem, to the best of our knowledge, there are currently no directly comparable methods. Therefore, we selected the methods most similar to ours for comparison. We compare our results with PoseRBPF [1], LatentFusion [13], PVNet [14], and Gen6D [9]. The results are shown in the Tab. 1. We also present a part of tracking results, as well as the generated models, as shown in Fig. 5." + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 353, + 245, + 517, + 401 + ], + "blocks": [ + { + "bbox": [ + 353, + 245, + 517, + 401 + ], + "lines": [ + { + "bbox": [ + 353, + 245, + 517, + 401 + ], + "spans": [ + { + "bbox": [ + 353, + 245, + 517, + 401 + ], + "type": "image", + "image_path": "b6490ad5d385fa4eb21bc46af8a67f8ffa96d7ec34bfac4f7f1965420284411d.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 410, + 555, + 433 + ], + "lines": [ + { + "bbox": [ + 313, + 410, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 555, + 433 + ], + "type": "text", + "content": "Figure 7. The final generated models (3 iterations) in different reference frames and key frames on the RBOT dataset." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 456, + 555, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 555, + 564 + ], + "type": "text", + "content": "Even without any priors and reference frames, our method (Ours(0)) outperforms all other methods in average. With 3 reference frames, our method (Ours(3)) significantly outperforms the others. Notably, our method requires no training and uses only RGB data, whereas other methods were trained on the tested or other objects. Additionally, compared to other methods, our method demonstrates more uniform accuracy across various objects, indicating that it is data-independent and a truly training-free approach." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 574, + 474, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 474, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 474, + 586 + ], + "type": "text", + "content": "4.2. Results on the RBOT Dataset" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 593, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 554, + 653 + ], + "type": "text", + "content": "During tracking, our method can rapidly generate the 3D model of an object, by comparing the performance of various trackers using both precise ground truth CAD models and our generated models on the RBOT dataset [23], we explored the models' reusability." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "content": "The RBOT dataset is a 3D object tracking dataset with 18 objects and 72 sequences, each containing 1000 test frames, with a resolution of " + }, + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "inline_equation", + "content": "640\\times 512" + }, + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "content": ", covering a baseline regular scenario and dynamic light, noisy, and occlusion scenarios. It has been used to evaluate some advanced 3D track" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1205" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 88, + 72, + 265, + 275 + ], + "blocks": [ + { + "bbox": [ + 88, + 72, + 265, + 275 + ], + "lines": [ + { + "bbox": [ + 88, + 72, + 265, + 275 + ], + "spans": [ + { + "bbox": [ + 88, + 72, + 265, + 275 + ], + "type": "image", + "image_path": "718869fde34afd8479e38e171252a2b563f545af7976cbe7027d3678cae5ec71.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 285, + 297, + 319 + ], + "lines": [ + { + "bbox": [ + 55, + 285, + 297, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 297, + 319 + ], + "type": "text", + "content": "Figure 8. Generated models in the case of 6 reference frames and 12 key frames on the RBOT dataset, displayed from top to bottom in each iteration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 63, + 330, + 289, + 566 + ], + "blocks": [ + { + "bbox": [ + 63, + 330, + 289, + 566 + ], + "lines": [ + { + "bbox": [ + 63, + 330, + 289, + 566 + ], + "spans": [ + { + "bbox": [ + 63, + 330, + 289, + 566 + ], + "type": "table", + "html": "
MethodModelReg.Dyn.NoisyOcc.Avg.↑
RBOT [23]GT79.981.256.673.372.8
Ours(3)38.137.525.932.433.5
Ours(6)63.262.942.356.156.1
Ours(12)67.867.044.960.260.0
SLOT [4]GT89.990.769.688.984.8
Ours(3)38.838.426.936.135.1
Ours(6)68.868.249.866.063.2
Ours(12)75.274.353.372.468.8
Song23 [17]GT95.494.986.293.292.4
Ours(3)52.750.944.848.349.2
Ours(6)81.579.870.977.777.5
Ours(12)85.783.874.681.981.5
RBGT [18]GT90.090.671.585.684.4
Ours(3)48.947.837.944.344.7
Ours(6)73.973.357.668.668.3
Ours(12)79.778.961.474.073.5
SRT3D [19]GT94.294.681.793.290.9
Ours(3)49.748.940.946.446.5
Ours(6)75.975.263.872.771.9
Ours(12)81.880.969.179.477.8
", + "image_path": "746bc6dd1a4635e88f9ee7e11155ba26f0e8db8d54b9457d010fddae1a434ade.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 574, + 295, + 608 + ], + "lines": [ + { + "bbox": [ + 55, + 574, + 295, + 608 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 295, + 608 + ], + "type": "text", + "content": "Table 3. Tracking accuracy with GT models and the generated models by our method on the RBOT dataset. Bold indicates the best result except for the ground truth." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 628, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 295, + 653 + ], + "type": "text", + "content": "ing methods, such as SRT3D [19], RBGT [18], SLOT [4], Song23 [17] and the RBOT method [23]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": "Due to the significant differences between frames in the RBOT dataset and the rapid movement of objects, we used 3-12 reference frames, and then tracked the first 100 frames in the regular scenario, and generate the objects' models during tracking. For each object, we performed up to 3 it" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 351, + 72, + 521, + 274 + ], + "blocks": [ + { + "bbox": [ + 351, + 72, + 521, + 274 + ], + "lines": [ + { + "bbox": [ + 351, + 72, + 521, + 274 + ], + "spans": [ + { + "bbox": [ + 351, + 72, + 521, + 274 + ], + "type": "image", + "image_path": "d60d023bafaba966ec68c37d40557a386897af6636f566bc6e228ba39b746218.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 285, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 313, + 285, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 555, + 308 + ], + "type": "text", + "content": "Figure 9. Tracking accuracy of various trackers on the RBOT dataset using GT models and the our generated models." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 329, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 329, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 329, + 555, + 376 + ], + "type": "text", + "content": "erations. Then these generated models served as inputs for other model-based trackers for testing across all scenes of the entire dataset, allowing us to compare their performance against the ground truth CAD models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "text", + "content": "We employed the " + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "inline_equation", + "content": "5 \\, \\text{cm}/5^{\\circ}" + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "text", + "content": " metric to measure the tracking accuracy, which indicates success in a frame if the translation error is less than " + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "inline_equation", + "content": "5 \\, \\text{cm}" + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "text", + "content": " and the rotation error is less than " + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "inline_equation", + "content": "5^{\\circ}" + }, + { + "bbox": [ + 313, + 377, + 554, + 472 + ], + "type": "text", + "content": ". Otherwise, it is considered a failure, and the pose is reset to the ground truth. The proportion of successful frames represents the tracking accuracy. We use the normalized Hausdorff distance between the generated models and ground truth models to measure the models accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 474, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 640 + ], + "type": "text", + "content": "Table 2 shows the models' accuracy (in normalized Hausdorff distance) in the last iteration, and Fig. 6 shows the normalized Hausdorff distance in every iteration. It can be seen that the generated models have relatively high accuracy with 6 or more reference frames. Additionally, by the second iteration, the model is already close to the final one. This indicates the proposed method's rapid convergence. Figures 7 and 8 also display portions of the generated models, demonstrating the effectiveness of our method. Furthermore, Figure 6 illustrates the variation in tracking accuracy of the baseline tracker [4] across the entire dataset using the intermediate generated models. The results show that the tracking accuracy improves as the models become more accurate." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "The test results of the 5 tracking methods using the final generated models on the RBOT dataset are presented in Tab. 3 and Fig. 9. It is clear from these results that when given 6 or more reference frames, the generated models can achieve results very close to the ground truth CAD models. This proves the effectiveness of our method, as it can" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1206" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 94, + 73, + 517, + 130 + ], + "blocks": [ + { + "bbox": [ + 94, + 73, + 517, + 130 + ], + "lines": [ + { + "bbox": [ + 94, + 73, + 517, + 130 + ], + "spans": [ + { + "bbox": [ + 94, + 73, + 517, + 130 + ], + "type": "image", + "image_path": "8bca42da9383f78b139cab67f0cf7cd92db3d1bc4de861fddd5dff601b51e87e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 132, + 415, + 140 + ], + "lines": [ + { + "bbox": [ + 195, + 132, + 415, + 140 + ], + "spans": [ + { + "bbox": [ + 195, + 132, + 415, + 140 + ], + "type": "text", + "content": "(a) Tracking poses and the generated model without reference frame" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 94, + 141, + 516, + 197 + ], + "blocks": [ + { + "bbox": [ + 94, + 141, + 516, + 197 + ], + "lines": [ + { + "bbox": [ + 94, + 141, + 516, + 197 + ], + "spans": [ + { + "bbox": [ + 94, + 141, + 516, + 197 + ], + "type": "image", + "image_path": "8e32ea592f4040d972a9f7cb13dba7a224d62f8a1efa465e1c1eea335ff40a31.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 198, + 416, + 207 + ], + "lines": [ + { + "bbox": [ + 195, + 198, + 416, + 207 + ], + "spans": [ + { + "bbox": [ + 195, + 198, + 416, + 207 + ], + "type": "text", + "content": "(b) Tracking poses and the generated model with 3 references frames" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 94, + 208, + 516, + 264 + ], + "blocks": [ + { + "bbox": [ + 94, + 208, + 516, + 264 + ], + "lines": [ + { + "bbox": [ + 94, + 208, + 516, + 264 + ], + "spans": [ + { + "bbox": [ + 94, + 208, + 516, + 264 + ], + "type": "image", + "image_path": "4676d7cb77a455b41329cf43274d7b5aab204f46822f716c9c81ad01237a91b5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 266, + 416, + 274 + ], + "lines": [ + { + "bbox": [ + 195, + 266, + 416, + 274 + ], + "spans": [ + { + "bbox": [ + 195, + 266, + 416, + 274 + ], + "type": "text", + "content": "(c) Tracking poses and the generated model with 6 references frames" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 66, + 285, + 542, + 297 + ], + "lines": [ + { + "bbox": [ + 66, + 285, + 542, + 297 + ], + "spans": [ + { + "bbox": [ + 66, + 285, + 542, + 297 + ], + "type": "text", + "content": "Figure 10. Qualitative results on the real world scenes. From left to right, the first frame, tracking results, and the generated models." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 318, + 295, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 295, + 341 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 295, + 341 + ], + "type": "text", + "content": "effectively transform a model-free tracking problem into a model-based tracking problem." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 350, + 167, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 167, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 167, + 361 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 368, + 296, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 368, + 296, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 368, + 296, + 487 + ], + "type": "text", + "content": "We captured RGB images of real-world scenes to test the proposed method, with a resolution of " + }, + { + "bbox": [ + 55, + 368, + 296, + 487 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 55, + 368, + 296, + 487 + ], + "type": "text", + "content": ". We evaluated our method under 3 conditions: (1) no reference and 3 key frames, (2) 3 reference frames and 3 key frames, and (3) 6 reference frames and 6 key frames. The reference frames are from the RBOT dataset. For each object, we performed up to 3 iterations. The tracking results are shown in Fig. 10. Under all 3 conditions, our method successfully achieved effective tracking and generated object models. Further experimental results can be found in our supplementary video." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 495, + 144, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 144, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 144, + 508 + ], + "type": "text", + "content": "4.4. Time Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "text", + "content": "With a resolution of " + }, + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "text", + "content": ", tracking a frame takes about " + }, + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "inline_equation", + "content": "30~\\mathrm{ms}" + }, + { + "bbox": [ + 55, + 514, + 295, + 633 + ], + "type": "text", + "content": ". When using 6 reference frames and 12 key frames for generating models, each iteration takes about 10 seconds. Therefore, a 3D model of an object can be obtained in about 30 seconds over 3 iterations. Notably, our method only utilizes a single NVIDIA 3080 (10GB) GPU. After completing the model generation, only tracking is required, allowing our method become real-time (30 FPS). Additionally, tracking can be run as a background thread to reduce time consumption." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 645, + 130, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 645, + 130, + 657 + ], + "spans": [ + { + "bbox": [ + 55, + 645, + 130, + 657 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Our method has several limitations that need to be addressed. Firstly, it is incapable of generating recessed features on object surfaces and cannot accurately model specific topologies, such as ring-shaped or hollow structures." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 318, + 555, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 318, + 555, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 555, + 425 + ], + "type": "text", + "content": "Secondly, in challenging scenarios, SAM's segmentation performance may be affected, particularly in cases involving occlusion, motion blur, or similar colors, and the object's complex geometry can also have a certain impact; errors in the mask may degrade the initially rendered model and tracking accuracy, further complicating iterative improvements. Lastly, tracking failures may occur in challenging scenes, particularly with fast-moving objects and when there is a lack of reference frames." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 436, + 391, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 391, + 447 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 391, + 447 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 455, + 555, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 555, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 555, + 624 + ], + "type": "text", + "content": "We have proposed a prior-free tracking method based on RGB data, capable of quickly generating 3D models of objects while tracking them. This approach transforms a model-free tracking problem into a model-based one without requiring pose-annotated training. The method operates when the target object is specified in the first frame and can incorporate reference frames if available. The generated models can be reused by other trackers and exhibit high accuracy. The method's consistent results across datasets demonstrate its independence from specific data, clearly distinguishing it from training-based methods. Extending 3D object tracking to non-rigid objects for broader applications and exploring tracking for objects with more complex topologies are future research directions in our work." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 634, + 411, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 411, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 411, + 647 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "content": "This work is partially supported by the National Key R&D Program of China under grant (No. 2022YFB3303203), NSF of China (U23A20312, No. 62172260, 62202425), and Shandong Provincial Natural Science Foundation (No. ZR2022LZH007)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1207" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Xinke Deng, Arsalan Mousavian, Yu Xiang, Fei Xia, Timothy Bretl, and Dieter Fox. 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Open3D: A modern library for 3D data processing. arXiv:1801.09847, 2018.6" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1209" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_content_list.json b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a59d143f96ca20588079d759ece0bc55ee4993c1 --- /dev/null +++ b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_content_list.json @@ -0,0 +1,1721 @@ +[ + { + "type": "text", + "text": "ProAPO: Progressively Automatic Prompt Optimization for Visual Classification", + "text_level": 1, + "bbox": [ + 102, + 140, + 893, + 161 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiangyan $\\mathbf{Q}\\mathbf{u}^{12}$ Gaopeng $\\mathrm{Gou}^{12\\dagger}$ Jiamin Zhuang $^{12}$ Jing Yu $^{3}$ Kun Song $^{4}$ Qihao Wang $^{12}$ Yili Li $^{12}$ Gang Xiong $^{12}$", + "bbox": [ + 243, + 186, + 750, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences $^{2}$ School of Cyber Security, Chinese Academy of Sciences $^{3}$ School of Information Engineering, Minzu University of China $^{4}$ University of Science and Technology Beijing {quxiangyan, gougaopeng, zhuangjiamin}@iie.ac.cn, jing.yu@muc.edu.cn songkun@xs.ustb.edu.cn, wangqihao22@mails.ucas.ac.cn, {liyili, xionggang}@iie.ac.cn", + "bbox": [ + 125, + 224, + 870, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 254, + 311, + 330, + 327 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-language models (VLMs) have made significant progress in image classification by training with large-scale paired image-text data. Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones. Our code is available at here.", + "bbox": [ + 99, + 343, + 485, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 102, + 782, + 230, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, vision-language models (VLMs) [1, 27, 33, 43, 55, 64, 72, 73] pre-trained on large-scale paired imagedtext data, such as CLIP [55], have shown strong generalization on various image classification tasks. These mod", + "bbox": [ + 99, + 806, + 483, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "els classify images by computing the similarity between the image and the prompt (a human-readable natural language) associated with a category. The prediction is the category with the highest similarity to the query image. Their performance highly relies on prompt quality, especially in fine-grained categories. Finding the optimal prompts for the downstream task becomes an urgent challenge [36, 52, 77].", + "bbox": [ + 511, + 313, + 893, + 416 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works have made efforts to improve prompt quality [4, 16, 55]. Manual prompt engineering [8, 55, 71] is a standard approach, writing several templates to include task-specific information, e.g., \"a photo of a {class}, a type of bird.\" for bird recognition. However, designing templates requires domain expertise, making it costly and challenging to scale [36, 39, 40, 52, 77]. Moreover, the template may lack details to recognize fine-grained categories as only the class name provides the distinct information in prompts [39, 52, 77]. Prompt tuning methods [6, 76, 77, 79] introduce a set of learnable tokens in the prompt to represent task-specific context, optimizing through gradient updates. While improving the performance of VLMs, they require additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39, 40, 52, 57, 68, 81] leverage the implicit knowledge of large language models (LLMs) [4, 48] to generate descriptions with class-specific details, enhancing generalization ability of VLMs. However, due to the hallucination in LLMs [25, 56], generated descriptions are suboptimal due to inaccurate, e.g., \"feet\" for the food Peking Duck, or lack discrimination for fine-grained recognition, e.g., the same descriptions \"hooked bill\" and \"webbed feet\" appear in Laysan Albatross and Sooty Albatross (see Fig. 1(a)), or exhibit non-visual descriptions, e.g., \"strong smell\" for Jackfruit. To this end, we propose the following key questions:", + "bbox": [ + 511, + 417, + 895, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How can we find the optimal class-specific prompts that are visually discriminative for fine-grained categories with minimal supervision and no human intervention?", + "bbox": [ + 511, + 815, + 893, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by recent automatic prompt optimization (APO) methods [18, 53, 60, 78] in language tasks, we aim to opti", + "bbox": [ + 511, + 859, + 893, + 888 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 116, + 16, + 189, + 55 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 243, + 13, + 799, + 56 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 119, + 875, + 241, + 888 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25145", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e63f097a767799822fae67a3f7a636d04eef95c7b2cd9ff77e191be1357e864b.jpg", + "image_caption": [ + "Laysan Albatross" + ], + "image_footnote": [], + "bbox": [ + 168, + 103, + 238, + 157 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "white with black wings", + "a seabird", + "- long, webbed feet", + "a long hooked bill", + "- flight over the ocean" + ], + "bbox": [ + 246, + 116, + 349, + 154 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dbe349e7ec28f885c1e4bc7752aa5cff0ecac6499344b041851dca58b7392d00.jpg", + "image_caption": [ + "Sooty Albatross", + "(a) Issues in generated descriptions." + ], + "image_footnote": [], + "bbox": [ + 169, + 162, + 238, + 217 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "large, dark-colored bird", + "white band around its neck", + "- webbed feet", + "- long, hooked bill", + "a species of albatross" + ], + "bbox": [ + 246, + 175, + 364, + 214 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/049a3c7aa48209e08d15461fce46f480bd79e53b91cccb9e82bc8e1e648c80e6.jpg", + "image_caption": [ + "Natural Language Prompt Search Space", + "Figure 1. Issues of optimizing class-specific prompts. (a) Due to the hallucination in LLMs, generated descriptions may be inaccurate and lack discrimination between fine-grained categories (see red words). (b) Compared to task-specific templates, we see an explosion in the number of class-specific prompts (see red rectangle). This leads to higher generation costs, iteration times, and the overfitting problem. (c) Overfitting problem: Multiple candidate prompts have the same best training accuracy but variable and low test results (see red circle)." + ], + "image_footnote": [], + "bbox": [ + 403, + 116, + 598, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b83463002562daf6374f429ecf87595bec2f86d3769b12fc80cec7d47281c33.jpg", + "image_caption": [ + "(c) Overfitting in evaluation metric." + ], + "image_footnote": [], + "bbox": [ + 604, + 103, + 833, + 217 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mize class-specific prompts by an evolution-based process, removing confused prompts while retaining discriminative ones. We consider an approximate zero-shot setting, i.e., one-shot classification, where minimal supervision is introduced to evaluate the prompt quality. However, previous APO methods focus solely on task-specific template optimization. In contrast, except for templates, a class-specific prompt also contains a description associated with visual details in a category, as shown in Fig. 1(b). Compared with templates, class-specific optimization introduces new challenges due to the expanded search space (see Fig. 1(b)), which leads to: (1) High generation costs. As the search space grows, it is costly and time-consuming to generate class-specific prompts exclusively with LLMs at each iteration. (2) Long iteration times. Evaluating each candidate prompt in the search space may exponentially increase the iteration time, which is impractical in this scenario. (3) Overfitting problem. As shown in Fig. 1(c), multiple candidate prompts achieve variable and low test results (from $63.6\\%$ to $64.3\\%$ ) at the best training accuracy.", + "bbox": [ + 99, + 299, + 483, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we propose a Progressively Automatic Prompt Optimization (ProAPO) algorithm to iteratively optimize prompts from task-specific to class-specific levels. In each iteration, we use several edited-based (i.e., add, remove, and replace) and evolution-based operators (i.e., crossover, and mutation) to generate diverse candidate prompts from a prompt library. We query LLMs to generate this library in the initialization stage. Compared to querying LLMs at each iteration, these simple operations can effectively save generation costs. Then, we introduce a novel fitness score to evaluate generated candidate prompts and retain several top-scoring ones for the next iteration generation. An entropy constraint is added to the score to increase the soft prediction score and reduce overfitting. After several iterations, we return the best prompt for classification. To reduce iteration times in class-specific descriptions, we propose a prompt sampling strategy to find a better initial point in the search space and a group sampling strategy to explore a few salient classes instead of all for optimization. Our key contributions are:", + "bbox": [ + 99, + 595, + 483, + 890 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose an evolution-based algorithm to progressively optimize prompts from task-specific to class-specific levels with one-shot supervision and no human intervention. It solves issues of inaccuracy and lack of discrimination in LLM-generated descriptions.", + "- We address challenges in class-specific prompt optimization by an offline generation algorithm to reduce LLM querying costs, an entropy-constrained fitness score to prevent overfitting, and two sampling strategies to find an optimal initial point and reduce iteration times.", + "- Extensive experiments on thirteen datasets show that our proposed ProAPO consistently outperforms SOTA textual prompt-based methods and improves description-based methods in a challenging one-shot supervision. Moreover, our optimal prompts improve adapter-based methods and transfer effectively across different backbones." + ], + "bbox": [ + 511, + 300, + 893, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 551, + 651, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adaptation of VLMs for image classification tasks. Inspired by successes in VLMs, recent works aim to adapt them for image classification tasks. Some works utilize lightweight linear layers [26, 35, 49, 55, 62, 65, 82], adapters [15, 39], visual prompting [2, 28, 47], or cache models [66, 74, 80] to enhance visual features. Other works aim to improve the quality of prompts. Manual prompt engineering [8, 34, 55] applies task-specific information in prompt templates to enhance performance. However, templates need to be hand-written and lack fine-grained details [36, 39, 40, 52, 77]. Prompt tuning methods [6, 11, 22, 29, 30, 32, 37, 61, 76, 77, 79] learn task-specific context by a set of learnable tokens. However, they need additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39-41, 44, 52, 54, 57, 59, 68, 81] exploit implicit knowledge in LLMs to generate visual descriptions for each category. They enrich semantics in prompts and offer interpretable predictions. In this work, we aim to further improve description quality through an evolution process.", + "bbox": [ + 509, + 579, + 895, + 873 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LLM-generated description methods apply class-specific", + "bbox": [ + 511, + 875, + 893, + 890 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25146", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "descriptions to language prompts to adapt VLMs for classification. DCLIP [40] and CuPL [52] design prompts such as \"What does a {class} look like?\" to instruct LLMs to generate category descriptions. GPT4Vis [68] and VDT [39] use GPT-4 [48] for rich and diverse descriptions. Some work utilizes LLM-generated hierarchy labels [46] or descriptions [57] to recognize images from coarse to fine-grained levels. However, due to the hallucination in LLMs, generated descriptions might be inaccurate, non-visual, and lack discrimination [40, 57, 58]. To this end, we propose ProAPO to iteratively remove ambiguous and retain discriminative prompts. Moreover, category names, ignored in previous methods, are equally crucial for improving accuracy and are introduced in our optimization.", + "bbox": [ + 99, + 102, + 483, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Automatic prompt optimization aims to automatically find optimal prompts for language tasks, overcoming the time-consuming issue in manual prompt methods [5]. Early methods [10, 51, 60] generate discrete prompts by filling templates with trigger tokens, iteratively refining prompts by mining, generation, or paraphrasing. Recently, chat-based LLMs have been applied as prompt engineers [14, 17, 18, 53, 70, 78], using a meta-prompt with task information to find optimal prompt design. PN [36] is the first to instruct LLMs to optimize templates on multimodal tasks, which feeds visual feedback of the best and worst templates to guide. However, these methods only optimize task-specific templates. iCM [19] is somewhat similar to ours, optimizing class-specific prompts with chat-based LLMs. However, it uses the whole validation set as supervision. In contrast, we optimize prompts with one-shot supervision and propose solutions to solve high generation costs, long iteration times, and overfitting in class-specific optimization.", + "bbox": [ + 99, + 306, + 486, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 101, + 585, + 191, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our ProAPO algorithm is shown in Fig. 2 and summarized in Alg. 1. We first describe iterative optimization in templates (Sec. 3.1). For each iteration, candidates are generated by several operators (Sec. 3.2) and then evaluated by a fitness score (Sec. 3.3). Afterward, similar iterative optimization is applied in descriptions, where we introduce two sampling strategies to save iteration costs (Sec. 3.4).", + "bbox": [ + 99, + 609, + 483, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminaries. Given an image, CLIP [55] predicts by selecting the highest similarity between the image and category prompt. The category prompt is a human-readable natural language associated with a category, which contains a template, e.g., \"a photo of a bird: {class}. {description} \"., and class-specific descriptions, e.g., class name \"Laysan Albatross\" and its descriptions \"It has white with black wings\". Some categories may use multiple prompts with varied templates or descriptions, i.e., prompt ensembling. We denote the prompt set that includes all categories in the task as a candidate prompt $P$ . A score function $F: \\mathcal{D} \\times P \\to \\mathbb{R}$ is", + "bbox": [ + 99, + 712, + 485, + 891 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1 Our Progressively Automatic Prompt Optimization (ProAPO) for visual classification, which iteratively refines prompts from task-specific to class-specific.", + "bbox": [ + 511, + 102, + 895, + 146 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Require: $\\mathcal{D}\\gets \\{(x,y)\\}_{n}$ training samples, $F:\\mathcal{D}\\times P\\to$ R: score function 1: Initialize Template: $\\mathcal{U}_t\\gets \\{P_0\\}$ 2: Build Template Library: $B_{t}\\gets \\{d_{1},\\dots ,d_{n}\\}$ 3: Iterative Optimization: $\\mathcal{U}_t\\gets \\mathrm{APO}(\\mathcal{D},F,\\mathcal{U}_t,B_t)$ 4: $P_{t}^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{t}}F(\\mathcal{D},P)$ 5: Initialize Description: $\\mathcal{U}_c\\gets \\{\\hat{P}_0\\}$ , initializing with $P_{t}^{*}$ and prompt sampling strategy 6: Group Sampling: Sample $S$ groups by class salience 7: for $s = 1$ to $S$ do 8: Build Description Library: $B_{s}\\gets \\{\\hat{d}_{1},\\dots ,\\hat{d}_{q}\\}$ 9: Iterative Optimization: $\\mathcal{U}_c\\gets \\mathrm{APO}(D,F,\\mathcal{U}_c,B_s)$ 10: end for 11: $P^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{c}}F(\\mathcal{D},P)$ 12: return candidate prompt with the highest score $P^{*}$", + "bbox": [ + 514, + 151, + 893, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 2 Automatic Prompt Optimization (APO) algorithm for VLMs - Lines 3 and 9 of Alg. 1, APO(D,F,U,B).", + "bbox": [ + 513, + 396, + 893, + 426 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Require: $\\mathcal{D}\\gets \\{(x,y)\\}_{n}$ : training samples, $F:\\mathcal{D}\\times P\\to$ $\\mathbb{R}$ : score function, $\\mathcal{U}$ : candidate prompt set, $B$ : tem- plate or description library \n1: Initialize Evaluation Score: $S\\gets \\{F(\\mathcal{D},P)\\}_{P\\in \\mathcal{U}}$ \n2: for $t = 1$ to $T$ do \n3: $\\mathcal{U}_g\\gets \\emptyset$ \n4: for all $P\\in \\mathcal{U}$ do \n5: Edit-based Generate: $\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\mathrm{GEN}(P,B)$ \n6: end for \n7: Evaluate: $S_{g}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{g}}$ \n8: Update: $\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_g\\}$ and $S\\gets \\{S,S_g\\}$ , retaining the top- $k$ of candidate prompts with high scores \n9: Evolution-based Generate: $\\mathcal{U}_e\\gets \\mathrm{EVO}(\\mathcal{U},B)$ \n10: Evaluate: $S_{e}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{e}}$ \n11: Update: $\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_e\\}$ and $S\\gets \\{S,S_e\\}$ , retaining the top- $k$ of candidate prompts with high scores \n12: end for \n13: return the latest candidate prompt set $\\mathcal{U}$", + "bbox": [ + 514, + 430, + 893, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "introduced in Sec. 3.3 to evaluate the candidate prompt $P$ on a limited training set $\\mathcal{D} = \\{(x,y)\\}_{n}$ with one-shot supervision, where $x$ is an image and $y$ is its label. Finally, we use a test set to evaluate optimized prompts. Our goal is to refine prompts in the natural language space to achieve superior performance in per training sample $(x,y)$ :", + "bbox": [ + 511, + 712, + 895, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {P} {\\arg \\max } F (\\mathcal {D}, P) = \\underset {P} {\\arg \\max } \\mathbb {E} _ {(x, y)} [ F (\\{(x, y) \\}, P) ]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 803, + 893, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Automatic Template Optimization", + "text_level": 1, + "bbox": [ + 511, + 835, + 803, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To mitigate issues of semantic ambiguity caused by class names, we first iteratively optimize the template to provide", + "bbox": [ + 511, + 859, + 895, + 890 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25147", + "bbox": [ + 478, + 926, + 517, + 939 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5ea67a56e1e271ca509f8d492e96a947fc7cfa3f6577256c477f177abc6f9f9c.jpg", + "image_caption": [ + "Figure 2. Overview of our ProAPO algorithm. We progressively refine prompts from task-specific (green lines) to class-specific (brown lines) levels. Specifically, we first explore the best template by an iterative optimization process (Sec. 3.1). For each iteration, ProAPO generates a set of candidate templates by several operators (Sec. 3.2) and filters/refines templates by a fitness score (Sec. 3.3). After several iterations, we choose the top-scoring template for description initialization. Subsequently, we introduce two sampling strategies to find a better initial point and reduce traversed categories (Sec. 3.4). Similar iterative optimization is then applied to class-specific descriptions." + ], + "image_footnote": [], + "bbox": [ + 153, + 98, + 844, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "better task-specific contextual information.", + "bbox": [ + 99, + 301, + 377, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Template initialization offers a candidate prompt $P_0$ as a starting point in the language search space (Line 1 of Alg. 1). Similar to PN [36], we use \"a photo of a {class}.\" filling with class names in the dataset as $P_0$ .", + "bbox": [ + 99, + 315, + 483, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Building template library aims to provide a set of templates (Line 2 of Alg. 1) for subsequent prompt generation. We denote template library as $B_{t} = \\{d_{1},\\dots ,d_{n}\\}$ , where $d$ is a single template. Similar to PN [36], we can instruct LLMs with a one-time query to generate a set of templates as the library. Pre-defined templates, e.g., Template80 provided in CLIP [55], can also be used. Inspired by description-based methods [39, 58], we also supplement templates with dataset domain information generated by LLMs, such as \"flower\" for FLO and \"bird\" for CUB.", + "bbox": [ + 99, + 375, + 483, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Iterative optimization. Automatic prompt optimization (APO) algorithm is introduced to refine template set $\\mathcal{U}_t$ by an evolution-based process (Line 3 of Alg. 1). As summarized in Alg. 2, each iteration of APO contains the process of: (1) Generate new candidate prompts $\\mathcal{U}_g$ and $\\mathcal{U}_e$ by several edit-based (Lines 4-6) and evolution-based (Line 9) operations based on the set $\\mathcal{U}$ and library $B$ . (2) Evaluate each new candidate prompt (Lines 7 and 10) by a score function. We regard this score as an implied \"gradient\". (3) Update the prompt set $\\mathcal{U}$ based on score (Lines 8 and 11). This process retains the top- $k$ of prompts with high scores to explore the search space around the current best candidates. Finally, we return the latest candidate set $\\mathcal{U}$ .", + "bbox": [ + 99, + 521, + 483, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Prompt Generation by Several Operators", + "text_level": 1, + "bbox": [ + 101, + 720, + 447, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the explosion of class-specific prompts, it is costly and time-intensive to generate new prompts exclusively with LLMs like previous methods [19, 36]. To this end, we introduce edit-based and evolution-based operators to generate diverse candidate prompts from the library.", + "bbox": [ + 99, + 742, + 482, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Edit-based generation is introduced to create a set of new candidate prompts by several simple arithmetic operators. As shown in Alg. 3, we iteratively operate a candidate prompt $P$ with the library $B$ , where $\\hat{d}$ in $P$ and $d$ in $B$ denotes a single template or description. The Select(·) op", + "bbox": [ + 99, + 816, + 483, + 890 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 3 Edit-based prompt generation algorithm - Line 5 of Alg. 2, GEN(P,B)." + ], + "code_body": "Require: $P\\gets \\{\\hat{d}_1,\\dots ,\\hat{d}_i\\}$ : a candidate prompt, $B\\gets$ $\\{d_1,\\dots ,d_j\\}$ : template or description library \n1: $\\mathcal{U}_g\\gets \\emptyset$ \n2: for $m = 1$ to $M$ do \n3: $d_{add}\\gets \\mathrm{Select}(B)$ \n4: $P_{add}\\gets P\\cup \\{d_{add}\\}$ Add \n5: $d_{del}\\gets \\mathrm{Select}(P)$ \n6: $P_{del}\\gets P\\setminus \\{d_{del}\\}$ $\\triangleright$ Delete \n7: $d_{in}\\gets \\mathrm{Select}(B)$ \n8: $d_{out}\\gets \\mathrm{Select}(P)$ \n9: $P_{rep}\\gets (P\\cup \\{d_{in}\\})\\setminus \\{d_{out}\\}$ Replace \n10: $\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\{P_{add},P_{del},P_{rep}\\}$ \n11: end for \n12: return the generated candidate prompt set $\\mathcal{U}_g$", + "bbox": [ + 514, + 335, + 893, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "erator samples an element from a given prompt set. Three operations are then applied to $P$ in each iteration: (1) Add a new element $d_{add}$ to $P$ . (2) Remove an existing element $d_{del}$ from $P$ . (3) Replace an element $d_{out}$ in $P$ with a new element $d_{in}$ in $B$ . These new candidates are ensembled around the current high-score candidate $P$ , which makes them more likely to succeed. Moreover, selecting elements from the library ensures differences between generated candidates. After $M$ -times steps, we return the latest set $\\mathcal{U}_g$ .", + "bbox": [ + 509, + 561, + 895, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Evolution-based generation is introduced to improve search efficiency over random steps, as shown in Alg. 4. Inspired by widely used Generic Algorithm [20, 24, 42], we introduce crossover and mutation operators to enhance candidate generation. Crossover operator aims to find the optimal direction quickly by combining high-scoring candidate prompts. We randomly take the concatenation of two candidates $P_{c1}$ and $P_{c2}$ sampled from the current optimal set $\\mathcal{U}$ , yielding a new candidate $P_{c}$ . Mutation operator aims to prevent convergence to local optima by introducing variations. We randomly add new elements selected from library $B$ into the candidate $P_{c}$ , yielding mutation candidate $P_{m}$ . After $N$ -times steps, we return the generated set $\\mathcal{U}_{e}$ .", + "bbox": [ + 511, + 698, + 895, + 890 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25148", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 4 Evolution-based generation algorithm - Line 9 of Alg. 2, EVO(U, B)." + ], + "code_body": "Require: $\\mathcal{U}\\gets \\{P_1,\\dots ,P_n\\}$ : candidate prompt set, $B\\gets$ $\\{d_1,\\dots ,d_j\\}$ : template or description library \n1: $\\mathcal{U}_e\\gets \\emptyset$ \n2: for $n = 1$ to $N$ do \n3: $P_{c1}\\gets \\mathrm{Select}(\\mathcal{U})$ \n4: $P_{c2}\\gets \\mathrm{Select}(\\mathcal{U})$ \n5: $P_{c}\\gets P_{c1}\\cup P_{c2}$ $\\triangleright$ Crossover \n6: $P_{all}\\gets B\\cup P_c$ \n7: $P_{m}\\gets \\mathrm{RANDOMSELECT}(P_{all},\\mathrm{len}(P_{c}))\\triangleright$ Mutation \n8: $\\mathcal{U}_e\\gets \\mathcal{U}_e\\cup \\{P_c,P_m\\}$ \n9: end for \n10: return the generated candidate prompt set $\\mathcal{U}_e$", + "bbox": [ + 102, + 135, + 483, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Score Functions", + "text_level": 1, + "bbox": [ + 101, + 329, + 256, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To measure candidate prompts, we introduce a fitness score to approximately obtain the \"gradient\" used for optimization. It contains the accuracy and an entropy constraint.", + "bbox": [ + 99, + 352, + 483, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Accuracy. Given an image $x$ , we obtain a prediction $\\operatorname{pred}(x)$ that yields the highest cosine similarity:", + "bbox": [ + 99, + 397, + 483, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns (x, c) = \\frac {1}{| D (c) |} \\sum_ {d \\in D (c)} \\cos (I (x), T (d)). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 428, + 482, + 464 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {p r e d} (x) = \\underset {c \\in C} {\\arg \\max } s (x, c), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 469, + 482, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D(c) \\in P$ is a set with all prompts describing the category $c$ in candidate prompt $P$ , and $C$ is the entire category in the dataset. $I$ and $T$ are image encoder and text encoder, respectively. The accuracy is formulated as follows:", + "bbox": [ + 99, + 494, + 483, + 554 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A c c} = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ \\mathbb {I} (\\operatorname {p r e d} (x) = y) ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 558, + 482, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{D}$ is the training set and $\\mathbb{I}(\\cdot)$ is an indicator function.", + "bbox": [ + 101, + 575, + 482, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Entropy constrain. Previous methods [19, 36] only use accuracy as the evaluation metric. However, the overfitting problem appears as shown in Fig. 1(c). To this end, we include a simple entropy constrain, which penalizes the model to predict a higher probabilistic score in the true label $y$ :", + "bbox": [ + 99, + 592, + 483, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ - \\log (s (x, y)) ]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 667, + 482, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final score is formulated as follows:", + "bbox": [ + 101, + 686, + 362, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF (\\mathcal {D}, P) = \\operatorname {A c c} + \\alpha H. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 705, + 482, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is a scalar to balance them. In Sec. 4.4, we empirically show that this score effectively reduces overfitting.", + "bbox": [ + 99, + 723, + 483, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Sampling Strategy for Initialization", + "text_level": 1, + "bbox": [ + 101, + 763, + 401, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After exploring the best template, we continue to optimize the class-specific descriptions. To save iteration costs, we introduce a prompt sampling strategy to find a better start point and a grouping sampling strategy to select some salient categories instead of all for iterative optimization.", + "bbox": [ + 99, + 785, + 483, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prompt sampling strategy aims to initialize the class-specific candidate prompt $\\hat{P}_0$ with the optimized template", + "bbox": [ + 101, + 859, + 483, + 890 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$P_{t}^{*}$ and high-score descriptions (Line 5 of Alg. 1). Similar to description-based methods [40, 52], we instruct LLM to generate a set of visual descriptions for each class. Besides, we replace the class name with its synonyms generated by LLMs to increase the number of descriptions. To obtain a better initial point, we randomly sample descriptions of each category to obtain multiple candidate prompts and select the one with the highest score as $\\hat{P}_0$ . It ensures that subsequent optimization is around candidates with relatively high scores. More details are shown in Supp.B.", + "bbox": [ + 511, + 102, + 893, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Group sampling strategy aims to explore several salient categories into groups for optimization (Line 6 of Alg. 1). We consider two ways to sample categories. First, we select the groups with the lowest top- $n_{wst}$ accuracy and its misclassified categories. Moreover, we also choose salient groups by the category with the top- $n_{sln}$ result gains after adding descriptions and its misclassified categories. In the end, We use $S = n_{wst} + n_{sln}$ groups for optimization. More details are shown in Supp.C. In Sec. 4.4, experiments show that optimizing these selected categories can effectively improve performance and save costs.", + "bbox": [ + 511, + 250, + 893, + 410 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Building Library and Iterative Optimization for Descriptions. In Lines 7-10 of Alg. 1, we iteratively optimize the class-specific description in selected groups. Similar to template optimization, we first build the description library, which contains visual descriptions for categories in the specific group. Then, we apply APO algorithm to refine descriptions automatically. After several iterations, we use the candidate $P^{*}$ with the highest score as the final prompt.", + "bbox": [ + 511, + 410, + 893, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 541, + 640, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Following prompt tuning [76, 77] and LLM-generated description works [40], we evaluate our ProAPO on thirteen downstream tasks, including ImageNet-1K (IN1K) [9], Caltech101 [13] (object recognition), StandfordCars [31], CUB200-2011 [67] (bird classification), DTD [7] (Textures), EuroSAT (ESAT) [23] (satellite images), FGVCAircraft [38], Flowers102 [45], Food101 [3], OxfordPets [50], Places365 [75], SUN397 [69] (scene recognition), UCF101 [63] (human action).", + "bbox": [ + 511, + 566, + 893, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. In the default setting, we use template-80 pre-defined in CLIP [55] as the template library and CuPL [52] as the description library for searching the hyperparameters in a fixed language space. Dataset domain and synonym labels are generated by LLMs. This setting ensures a one-time query of LLMs, and no human intervention is required. If not explicitly stated, we set iteration times $T = 4$ in both template and description optimization, generated number $M = N = 8$ , $\\alpha = 1e3$ , $n_{wst} = n_{sln} = \\log(|C|)$ for all datasets, where $|C|$ is the number of classes. All results are average with four seeds. Besides, our ProAPO is implemented in PyTorch and runs with an RTX 3090 GPU. More details are shown in Supp.D.", + "bbox": [ + 511, + 699, + 895, + 890 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25149", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/745e43a5286c8ed0ec898df686aca54bc5a42a91ab05b6a99a2130ad403db35c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModuleTFIN-1KCaltechCarsCUBDTDESATFGVCFLOFoodPetsPlacesSUNUCFAvg (11)Avg (13)
ResNet-50 Backbone
CLIP (a photo of a {} )✓57.984.553.944.738.828.615.960.274.083.238.258.056.955.653.4
prompt tuning methods
CoOp [77]X57.287.555.6-44.450.69.668.174.385.9-60.361.959.6-
PLOT [6]X59.589.856.6-46.654.117.971.777.787.5-62.564.562.6-
ProGrad [79]X57.888.758.4-46.156.318.873.276.088.4-60.565.662.7-
automatic prompt optimization methods
PN [36]✓59.689.156.2-44.849.018.167.278.388.1-61.060.261.1-
ProAPO (ours)✓61.590.358.050.752.351.721.175.181.888.741.863.766.064.661.8
ViT-B/32 Backbone
CLIP (a photo of a {} )✓62.191.260.451.742.943.920.266.083.286.839.962.160.961.859.3
hand-engineered methods
Template-80 [55]✓63.591.660.451.242.852.619.566.184.287.441.663.562.963.160.6
FILIP-8 [71]✓63.891.460.752.743.454.318.967.084.687.541.263.965.063.761.1
DEFILIP-6 [8]✓62.591.059.951.141.346.418.866.584.387.540.262.363.662.259.6
description-based methods
DCLIP [40]✓63.392.759.452.744.138.419.466.183.988.141.265.065.862.460.0
Waffle [58]✓63.392.159.352.943.251.619.666.384.987.741.565.064.563.460.9
CuPL [52]✓64.492.960.753.350.650.520.969.584.287.043.166.366.464.962.3
GPT4Vis [68]✓63.593.161.452.748.547.021.469.884.388.142.764.265.764.361.7
AdaptCLIP [59]✓63.392.759.753.647.451.320.867.284.287.641.966.166.564.261.7
ProAPO w/ DCLIP✓64.193.260.653.648.259.422.671.584.288.742.766.068.066.063.3
ProAPO (ours)✓64.794.461.755.453.563.023.074.385.391.043.366.669.067.965.0
", + "bbox": [ + 160, + 99, + 836, + 433 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison of our ProAPO with SOTA textual prompt-based methods. We report the top-1 accuracy (%) on the test set. The best and second best results of the same backbone for each dataset are bolded and underlined, respectively. Avg (11) and Avg (13) denote average results across 11 datasets (excluding CUB [67] and Places [75]) and all 13 datasets. TF denotes training-free approaches.", + "bbox": [ + 99, + 436, + 895, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparison with SOTA Methods", + "text_level": 1, + "bbox": [ + 101, + 489, + 387, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. We compare our results with state-of-the-art (SOTA) textual prompt-based methods, including vanilla CLIP with \"a photo of a {}\" template, prompt tuning methods [6, 77, 79], hand-engineered methods (i.e., best templates released by [8, 55, 71]), LLM-generated description methods [40, 52, 58, 59, 68], and automatic prompt optimization methods [36]. We test our ProAPO on two popular backbones (ResNet50 [21] and ViT-B/32 [12]). Prompt tuning and automatic prompt optimization methods are evaluated under one-shot supervision.", + "bbox": [ + 99, + 517, + 483, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. In Tab. 1, we see that our ProAPO consistently outperforms previous prompt-based methods across diverse datasets on ResNet50 and ViT-B/32 backbones. Our optimized prompts improve vanilla CLIP by an average of $8.4\\%$ (from $53.4\\%$ to $61.8\\%$ ) on ResNet50 and $5.7\\%$ (from $59.3\\%$ to $65.0\\%$ ) on ViT-B/32. Moreover, our training-free ProAPO surpasses gradient-based prompting methods (CoOp, PLOT, ProGrad) by at least $1.9\\%$ average accuracy in eleven datasets. It shows optimizing prompts in a natural language space is more effective in low-shot tasks. Compared to template-optimized methods (i.e., PN and hand-engineered methods), our ProAPO achieves remarkable performance on fine-grained datasets, e.g., CUB, FLO, ESAT, and UCF. This is because class-specific descriptions provide fine-grained discriminative de", + "bbox": [ + 99, + 669, + 483, + 890 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tails. Our ProAPO also outperforms description-based methods, even with DCLIP as initialization. We improve performances of DCLIP and CuPL by $3.3\\%$ and $2.7\\%$ on average across thirteen datasets. Notably, it improves DCLIP and CuPL by $5.4\\%$ and $4.8\\%$ on FLO and by $21\\%$ and $12.5\\%$ on ESAT, confirming that iterative optimization of class-specific prompts enhances fine-grained recognition.", + "bbox": [ + 509, + 489, + 893, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Critical analysis. On datasets like ImageNet [9], Caltech [13], Places [75], and SUN [69], performance gains are relatively small. We attribute this to two reasons: First, datasets like ImageNet and Caltech contain coarse-grained categories. The differences between categories have become clearer with LLM-generated descriptions, eliminating the need for our method. Second, fine-grained datasets, such as Places and SUN for scene recognition, are easily confusing between different images, limiting performance from only textual side optimization. In Sec. 4.2, we show that adapter-based methods with our optimized prompt improve performance again after addressing issues of image confusion. Moreover, we observe that the language search space impacts performance. Since CuPL has better descriptions than DCLIP, our ProAPO with CuPL performs well.", + "bbox": [ + 509, + 594, + 895, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. More Benefits by Optimal Prompts", + "text_level": 1, + "bbox": [ + 511, + 823, + 808, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Transfer to adapter-based methods. In Fig. 3, we show the results of popular adapter-based methods [15, 66, 74, 80] with different prompt initialization, i.e., SOTA method", + "bbox": [ + 511, + 845, + 893, + 890 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25150", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0b20e8bec51d3b3e92b796bc2aca4bed61ef01b6cf4a41275a8a1a5583357b99.jpg", + "image_caption": [ + "(a) Training-free methods." + ], + "image_footnote": [], + "bbox": [ + 109, + 99, + 290, + 213 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/160af41786585830ee9b282e8dd10218ced495ead64dbc88d6ec3bebcb54a58c.jpg", + "image_caption": [ + "(b) Fine-tuning methods.", + "Figure 3. Results of adapter-based methods with different initial prompts. Solid and dotted lines denote prompt initialization with ProAPO and CuPL, respectively." + ], + "image_footnote": [], + "bbox": [ + 295, + 99, + 475, + 214 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0f4e811bf4ffbe5db5f48d3f97cb98b1742cef0e9ebfc396f80e64ff4cacc3d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModuleShotsSourceTarget
RN50RN101ViT-B/32ViT-B/16
CLIP [55]057.960.661.966.6
CoOp [77]1663.020.631.739.5
PN [36]159.960.762.267.0
ProAPO161.562.164.669.9
", + "bbox": [ + 138, + 290, + 442, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Results of prompt transfer from ResNet-50 to other architectures. We report the top-1 accuracy in ImageNet-1K.", + "bbox": [ + 101, + 380, + 482, + 407 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/93056dc3a886e4a4fdecd3874dffc0f3c47fe843ed9d70f8b56d900f17e3eb55.jpg", + "image_caption": [ + "Figure 4. Results of prompt transfer to different backbones. The value denotes performance gains compared to vanilla VLMs. Our optimized prompts of ResNet50 and ViT-B/32 are reported." + ], + "image_footnote": [], + "bbox": [ + 133, + 420, + 444, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CuPL [52] and our ProAPO. Adapter-based methods with ProAPO (solid lines) consistently surpass those with CuPL (dotted lines). It reveals that high-quality prompts make adapters perform better. Even in low shots, training with ProAPO achieves notable performance gains, which verifies its effectiveness. As the number of shots increases, adapters further improve results by enhancing image features.", + "bbox": [ + 99, + 590, + 482, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transfer to different backbones. In Tab. 2, we report accuracy in ImageNet across different backbones, with prompts optimized on a source backbone (ResNet50) adapted to target backbones (ResNet101, ViT-B/32, ViT-B/16). We observe that CoOp [77] obtains a significant drop in accuracy on target backbones while our ProAPO maintains performance. It verifies that discrete prompts searched in natural language spaces transfer better than continuous prompts. ProAPO also outperforms PN, which reveals the effectiveness of class-specific optimization. Moreover, we achieve stable performance gains compared to CuPL [52] from source to target models in Fig. 4. It further verifies that ProAPO transfers easily across different backbones.", + "bbox": [ + 99, + 698, + 482, + 890 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e83c5891091559a7b1a3c86809e7b3510c3abc596436993d5797a8ab0ac0d63c.jpg", + "image_caption": [ + "(a)", + "Figure 5. Performance improvement analysis. (a) Analysis of the effect of single vs. ensemble prompts. * denotes results evaluated in the test set. ATO is our automatic template optimization algorithm. (b) Results of previous description-based methods with prompt optimization by our ATO and ProAPO algorithms." + ], + "image_footnote": [], + "bbox": [ + 521, + 99, + 718, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f119cfcc2312fe6d6ff623f993d2f0f75e83404177272ffc57a7dd65a7df80df.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 723, + 99, + 887, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/387ecd78d9b29ec6a4469cd8a025d23610f105fc2fe3daaf9ad8f9b4f6289449.jpg", + "image_caption": [ + "Figure 6. Qualitative analysis of class-specific prompt optimization by ProAPO. Shaded red and blue words denote common and discriminative descriptions in two confused categories." + ], + "image_footnote": [], + "bbox": [ + 517, + 297, + 890, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Performance Improvement Analysis", + "text_level": 1, + "bbox": [ + 511, + 474, + 816, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we analyze the key reasons for the performance improvement of our ProAPO.", + "bbox": [ + 511, + 500, + 892, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Prompt ensembling is better than a single prompt. Compared to PN [36], we utilize prompt ensembling instead of a single prompt to optimize the template and description. To evaluate the effectiveness of prompt ensembling, we use Template-80 [55] as the template library and denote the prompts searched by the test set as the upper bound. As shown in Fig. 5(a), we observe that ensemble templates have a higher upper bound than the single template, consistent with prior work [8, 40, 71]. Similarly, we observe that our optimized templates achieve higher performance than PN [36], even better than the best single template, further verifying the effectiveness of our method.", + "bbox": [ + 509, + 532, + 893, + 708 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Iterative optimization improves prompt quality. In Fig. 6, we show the changes in descriptions with our ProAPO. After iterative optimization, common descriptions such as \"flight over ocean\" and \"long wings and hooked bill\" are removed. Discriminative descriptions are also retained in candidate prompts, e.g., \"white body\" for Laysan Albatross, and \"black underpants\" for Sooty Albatross. As such, we see a notable improvement in description-based methods [40, 52, 59, 68] with our ATO and ProAPO in Fig. 5(b) by at least $2.7\\%$ average in thirteen datasets. It further verifies the effectiveness of our progressive optimization.", + "bbox": [ + 511, + 713, + 893, + 890 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25151", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5cf8c081385bf42e147d70beb22fe7545d7a87e7a5279f56352c850a44be7af8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ComponentIN-1KAvg (11)Avg (13)
AddDelRepCrossMut
CLIP (Baseline)62.161.859.3
edit-based generation
a)✓63.866.063.3
b)✓✓64.666.463.8
c)✓✓64.466.563.8
d)✓✓✓64.666.764.0
evolution-based generation
e)✓✓✓✓64.667.364.5
f)✓✓✓✓64.767.164.3
g)✓✓✓✓✓64.767.965.0
", + "bbox": [ + 122, + 99, + 460, + 239 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2779c1b1d548226d80bc742a2fec2643687499fe38b2cd55ce165fdc73ecdeca.jpg", + "table_caption": [ + "Table 3. Ablation of edit- and evolution-based operators." + ], + "table_footnote": [], + "table_body": "
Module (ViT-B/32)IN-1KAvg (11)Avg (13)Times
a) w/o prompt sampling64.467.364.512 min
b) w/o group sampling64.868.165.2306 min
c) w/o sampling strategies64.567.264.4302 min
ProAPO (full model)64.767.965.015 min
", + "bbox": [ + 125, + 263, + 455, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation of two sampling strategies.", + "bbox": [ + 155, + 333, + 429, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 101, + 351, + 250, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Are both GEN and EVO algorithms necessary? In Tab. 3, we ablate edit- and evolution-based operators. For edit-based operators, we observe that the model with add, delete, and replace operations achieves a higher result in row d). After introducing evolution-based operators, i.e., crossover operator to combine advantages of high-scoring candidates, and mutation operator to avoid locally optimal solutions, we see an increase in performance in rows e)-g). It confirms that evolution-based operators make the model search the optimal prompt faster with limited iterations.", + "bbox": [ + 99, + 372, + 483, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Does sample strategies degrade performance? In Tab. 4, we ablate two sampling strategies for description optimization. Without the prompt sampling, we see a slight decrease in times while results drop in row a). It verifies the effectiveness of the prompt sampling in finding a better initial point. Without the group sampling to select salient categories for optimization, we observe a notable increase in time costs (from $15\\mathrm{min}$ to $300+\\mathrm{min}$ , 20 times) yet similar results in row b) and the full model. It reveals that group sampling simultaneously improves performance and efficiency.", + "bbox": [ + 99, + 518, + 483, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Which score function is better? In Fig. 7, we compare the different score functions, i.e., accuracy (used in PN [36]) and our fitness score, to evaluate the quality of the candidate prompt. PCCs (Pearson Correlation Coefficients) are introduced to evaluate the linear relationship between training metrics and test performance. The high PCC values mean a strong correlation. We see that the model with our fitness score achieves stable and high test results compared to previous score functions when achieving the best score. Besides, a higher PPC value further verifies that our fitness score effectively alleviates the overfitting problem.", + "bbox": [ + 99, + 666, + 483, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Hyperparameter Sensitivity", + "text_level": 1, + "bbox": [ + 101, + 838, + 344, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How many iterations of Alg. 2 to use? In Fig. 8(a), we show the effect of iteration times $T$ in APO algorithm. As", + "bbox": [ + 101, + 859, + 483, + 890 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1422cb4fb01e0a9cb11c85fac5589417c144bd685c96d5d672770770d36c250f.jpg", + "image_caption": [ + "(a) Previous score function." + ], + "image_footnote": [], + "bbox": [ + 521, + 101, + 702, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad36d704a88f07408ad69e596b499ce60ae8b37c4b85be1b47aa0646b325fb6e.jpg", + "image_caption": [ + "(b) Our fitness score" + ], + "image_footnote": [], + "bbox": [ + 707, + 99, + 888, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eef2cb9cc956e7eddca66ec30699427c29e702c465f6d010e58839b7a315ba1c.jpg", + "image_caption": [ + "Figure 7. Effect of different score functions. Higher PCC values mean stronger correlations between training metrics and test results. Best Acc is the test result when achieving the best score." + ], + "image_footnote": [], + "bbox": [ + 517, + 262, + 638, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13d6a353a7ef56021b8d88d9fdcb78b124fd4353bed05ed36edd3585e097eca8.jpg", + "image_caption": [ + "(a) Iteration times $T$", + "(b) Generated numbers" + ], + "image_footnote": [], + "bbox": [ + 643, + 262, + 763, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f78abbc69d70a57e5e144db4dc10066f153170207e6aca9950616559306a268f.jpg", + "image_caption": [ + "(c) Sampling groups $S$", + "Figure 8. The effect of hyperparameter analysis. The hyperparameter value set to 0 denotes the result of CuPL [52]." + ], + "image_footnote": [], + "bbox": [ + 767, + 262, + 887, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the number of iterations increases, we see a consistent performance improvement compared to the baseline CuPL. It demonstrates that iterative optimization improves prompt quality. Stable results are achieved when $T \\geq 4$ .", + "bbox": [ + 511, + 397, + 893, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How many generated prompts to use? In Fig. 8(b), we show the effect of generated numbers in GEN and EVO algorithm, where we set $M = N$ . Similarly, progressive improvements are seen as generated numbers increase. We see a reliable result when $M = N \\geq 8$ . It reveals the effectiveness of generating diverse candidates by our algorithm.", + "bbox": [ + 511, + 455, + 893, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Are more sampling groups better? In Fig. 8(c), we show the effect of the number of salient groups $S$ in the group sampling strategy. We see a notable improvement when $S = 2$ . As the number of groups $S$ increases, it achieves stable results when $S \\geq 8$ . It verifies that optimizing several salient categories can achieve comparable performances with all categories and save iteration costs.", + "bbox": [ + 511, + 544, + 893, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 659, + 627, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose an evolution-based algorithm for VLMs to progressively refine prompts from task-specific to class-specific levels. To save generation costs, ProAPO uses several edit- and evolution-based operators to create candidate prompts with a prompt library. Results show that our fitness score mitigates overfitting in class-specific prompts. We empirically verify that two sampling strategies improve performance and save iteration times. Extensive experiments on thirteen datasets reveal that ProAPO consistently outperforms SOTA textual prompt-based methods on low-shot tasks. Moreover, our method effectively improves adapter-based and description-based methods and easily transfers across different backbones. We hope ProAPO could provide new insight into adapting VLMs from the textual side.", + "bbox": [ + 509, + 683, + 893, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25152", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 102, + 101, + 266, + 118 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the Central Guidance for Local Special Project (Grant No. Z231100005923044).", + "bbox": [ + 101, + 126, + 483, + 156 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 102, + 170, + 196, + 186 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, and Pauline Luc et al. Flamingo: a visual language model for few-shot learning. 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AWT: transferring vision-language models via augmentation, weighting, and transportation. In NeurIPS, 2024. 1, 2", + "[82] Jiamin Zhuang, Jing Yu, Yang Ding, Xiangyan Qu, and Yue Hu. Towards fast and accurate image-text retrieval with self-supervised fine-grained alignment. IEEE TMM, 26:1361-1372, 2024. 2" + ], + "bbox": [ + 514, + 103, + 893, + 404 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "25155", + "bbox": [ + 478, + 926, + 517, + 938 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_model.json b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_model.json new file mode 100644 index 0000000000000000000000000000000000000000..00d3978b0e55247e83b8c69882d639ac5e4dd1fd --- /dev/null +++ b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_model.json @@ -0,0 +1,2840 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.117, + 0.017, + 0.191, + 0.056 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.244, + 0.015, + 0.8, + 0.058 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.104, + 0.141, + 0.895, + 0.162 + ], + "angle": 0, + "content": "ProAPO: Progressively Automatic Prompt Optimization for Visual Classification" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.188, + 0.751, + 0.224 + ], + "angle": 0, + "content": "Xiangyan \\(\\mathbf{Q}\\mathbf{u}^{12}\\) Gaopeng \\(\\mathrm{Gou}^{12\\dagger}\\) Jiamin Zhuang\\(^{12}\\) Jing Yu\\(^{3}\\) Kun Song\\(^{4}\\) Qihao Wang\\(^{12}\\) Yili Li\\(^{12}\\) Gang Xiong\\(^{12}\\)" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.226, + 0.871, + 0.293 + ], + "angle": 0, + "content": "\\(^{1}\\)Institute of Information Engineering, Chinese Academy of Sciences \\(^{2}\\)School of Cyber Security, Chinese Academy of Sciences \\(^{3}\\)School of Information Engineering, Minzu University of China \\(^{4}\\)University of Science and Technology Beijing {quxiangyan, gougaopeng, zhuangjiamin}@iie.ac.cn, jing.yu@muc.edu.cn songkun@xs.ustb.edu.cn, wangqihao22@mails.ucas.ac.cn, {liyili, xionggang}@iie.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.256, + 0.313, + 0.331, + 0.328 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.344, + 0.486, + 0.771 + ], + "angle": 0, + "content": "Vision-language models (VLMs) have made significant progress in image classification by training with large-scale paired image-text data. Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones. Our code is available at here." + }, + { + "type": "title", + "bbox": [ + 0.103, + 0.784, + 0.231, + 0.799 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.808, + 0.485, + 0.868 + ], + "angle": 0, + "content": "In recent years, vision-language models (VLMs) [1, 27, 33, 43, 55, 64, 72, 73] pre-trained on large-scale paired imagedtext data, such as CLIP [55], have shown strong generalization on various image classification tasks. These mod" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.314, + 0.895, + 0.417 + ], + "angle": 0, + "content": "els classify images by computing the similarity between the image and the prompt (a human-readable natural language) associated with a category. The prediction is the category with the highest similarity to the query image. Their performance highly relies on prompt quality, especially in fine-grained categories. Finding the optimal prompts for the downstream task becomes an urgent challenge [36, 52, 77]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.419, + 0.897, + 0.815 + ], + "angle": 0, + "content": "Recent works have made efforts to improve prompt quality [4, 16, 55]. Manual prompt engineering [8, 55, 71] is a standard approach, writing several templates to include task-specific information, e.g., \"a photo of a {class}, a type of bird.\" for bird recognition. However, designing templates requires domain expertise, making it costly and challenging to scale [36, 39, 40, 52, 77]. Moreover, the template may lack details to recognize fine-grained categories as only the class name provides the distinct information in prompts [39, 52, 77]. Prompt tuning methods [6, 76, 77, 79] introduce a set of learnable tokens in the prompt to represent task-specific context, optimizing through gradient updates. While improving the performance of VLMs, they require additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39, 40, 52, 57, 68, 81] leverage the implicit knowledge of large language models (LLMs) [4, 48] to generate descriptions with class-specific details, enhancing generalization ability of VLMs. However, due to the hallucination in LLMs [25, 56], generated descriptions are suboptimal due to inaccurate, e.g., \"feet\" for the food Peking Duck, or lack discrimination for fine-grained recognition, e.g., the same descriptions \"hooked bill\" and \"webbed feet\" appear in Laysan Albatross and Sooty Albatross (see Fig. 1(a)), or exhibit non-visual descriptions, e.g., \"strong smell\" for Jackfruit. To this end, we propose the following key questions:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.816, + 0.895, + 0.859 + ], + "angle": 0, + "content": "How can we find the optimal class-specific prompts that are visually discriminative for fine-grained categories with minimal supervision and no human intervention?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.86, + 0.895, + 0.89 + ], + "angle": 0, + "content": "Inspired by recent automatic prompt optimization (APO) methods [18, 53, 60, 78] in language tasks, we aim to opti" + }, + { + "type": "page_footnote", + "bbox": [ + 0.12, + 0.876, + 0.242, + 0.89 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.518, + 0.939 + ], + "angle": 0, + "content": "25145" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.169, + 0.104, + 0.24, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.247, + 0.107, + 0.327, + 0.116 + ], + "angle": 0, + "content": "Laysan Albatross" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.117, + 0.35, + 0.125 + ], + "angle": 0, + "content": "white with black wings" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.125, + 0.3, + 0.131 + ], + "angle": 0, + "content": "a seabird" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.132, + 0.335, + 0.139 + ], + "angle": 0, + "content": "- long, webbed feet" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.14, + 0.335, + 0.147 + ], + "angle": 0, + "content": "a long hooked bill" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.148, + 0.343, + 0.155 + ], + "angle": 0, + "content": "- flight over the ocean" + }, + { + "type": "list", + "bbox": [ + 0.247, + 0.117, + 0.35, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.17, + 0.163, + 0.24, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.247, + 0.166, + 0.322, + 0.175 + ], + "angle": 0, + "content": "Sooty Albatross" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.176, + 0.353, + 0.183 + ], + "angle": 0, + "content": "large, dark-colored bird" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.184, + 0.365, + 0.19 + ], + "angle": 0, + "content": "white band around its neck" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.191, + 0.312, + 0.198 + ], + "angle": 0, + "content": "- webbed feet" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.199, + 0.327, + 0.206 + ], + "angle": 0, + "content": "- long, hooked bill" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.207, + 0.353, + 0.215 + ], + "angle": 0, + "content": "a species of albatross" + }, + { + "type": "list", + "bbox": [ + 0.247, + 0.176, + 0.365, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.22, + 0.355, + 0.23 + ], + "angle": 0, + "content": "(a) Issues in generated descriptions." + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.104, + 0.584, + 0.114 + ], + "angle": 0, + "content": "Natural Language Prompt Search Space" + }, + { + "type": "image", + "bbox": [ + 0.404, + 0.117, + 0.599, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.104, + 0.834, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.22, + 0.819, + 0.23 + ], + "angle": 0, + "content": "(c) Overfitting in evaluation metric." + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.234, + 0.895, + 0.289 + ], + "angle": 0, + "content": "Figure 1. Issues of optimizing class-specific prompts. (a) Due to the hallucination in LLMs, generated descriptions may be inaccurate and lack discrimination between fine-grained categories (see red words). (b) Compared to task-specific templates, we see an explosion in the number of class-specific prompts (see red rectangle). This leads to higher generation costs, iteration times, and the overfitting problem. (c) Overfitting problem: Multiple candidate prompts have the same best training accuracy but variable and low test results (see red circle)." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.3, + 0.485, + 0.594 + ], + "angle": 0, + "content": "mize class-specific prompts by an evolution-based process, removing confused prompts while retaining discriminative ones. We consider an approximate zero-shot setting, i.e., one-shot classification, where minimal supervision is introduced to evaluate the prompt quality. However, previous APO methods focus solely on task-specific template optimization. In contrast, except for templates, a class-specific prompt also contains a description associated with visual details in a category, as shown in Fig. 1(b). Compared with templates, class-specific optimization introduces new challenges due to the expanded search space (see Fig. 1(b)), which leads to: (1) High generation costs. As the search space grows, it is costly and time-consuming to generate class-specific prompts exclusively with LLMs at each iteration. (2) Long iteration times. Evaluating each candidate prompt in the search space may exponentially increase the iteration time, which is impractical in this scenario. (3) Overfitting problem. As shown in Fig. 1(c), multiple candidate prompts achieve variable and low test results (from \\(63.6\\%\\) to \\(64.3\\%\\)) at the best training accuracy." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.596, + 0.484, + 0.891 + ], + "angle": 0, + "content": "To address these issues, we propose a Progressively Automatic Prompt Optimization (ProAPO) algorithm to iteratively optimize prompts from task-specific to class-specific levels. In each iteration, we use several edited-based (i.e., add, remove, and replace) and evolution-based operators (i.e., crossover, and mutation) to generate diverse candidate prompts from a prompt library. We query LLMs to generate this library in the initialization stage. Compared to querying LLMs at each iteration, these simple operations can effectively save generation costs. Then, we introduce a novel fitness score to evaluate generated candidate prompts and retain several top-scoring ones for the next iteration generation. An entropy constraint is added to the score to increase the soft prediction score and reduce overfitting. After several iterations, we return the best prompt for classification. To reduce iteration times in class-specific descriptions, we propose a prompt sampling strategy to find a better initial point in the search space and a group sampling strategy to explore a few salient classes instead of all for optimization. Our key contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.301, + 0.895, + 0.373 + ], + "angle": 0, + "content": "- We propose an evolution-based algorithm to progressively optimize prompts from task-specific to class-specific levels with one-shot supervision and no human intervention. It solves issues of inaccuracy and lack of discrimination in LLM-generated descriptions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.373, + 0.895, + 0.446 + ], + "angle": 0, + "content": "- We address challenges in class-specific prompt optimization by an offline generation algorithm to reduce LLM querying costs, an entropy-constrained fitness score to prevent overfitting, and two sampling strategies to find an optimal initial point and reduce iteration times." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.448, + 0.895, + 0.535 + ], + "angle": 0, + "content": "- Extensive experiments on thirteen datasets show that our proposed ProAPO consistently outperforms SOTA textual prompt-based methods and improves description-based methods in a challenging one-shot supervision. Moreover, our optimal prompts improve adapter-based methods and transfer effectively across different backbones." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.301, + 0.895, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.553, + 0.652, + 0.569 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.58, + 0.896, + 0.874 + ], + "angle": 0, + "content": "Adaptation of VLMs for image classification tasks. Inspired by successes in VLMs, recent works aim to adapt them for image classification tasks. Some works utilize lightweight linear layers [26, 35, 49, 55, 62, 65, 82], adapters [15, 39], visual prompting [2, 28, 47], or cache models [66, 74, 80] to enhance visual features. Other works aim to improve the quality of prompts. Manual prompt engineering [8, 34, 55] applies task-specific information in prompt templates to enhance performance. However, templates need to be hand-written and lack fine-grained details [36, 39, 40, 52, 77]. Prompt tuning methods [6, 11, 22, 29, 30, 32, 37, 61, 76, 77, 79] learn task-specific context by a set of learnable tokens. However, they need additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39-41, 44, 52, 54, 57, 59, 68, 81] exploit implicit knowledge in LLMs to generate visual descriptions for each category. They enrich semantics in prompts and offer interpretable predictions. In this work, we aim to further improve description quality through an evolution process." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.875, + 0.895, + 0.891 + ], + "angle": 0, + "content": "LLM-generated description methods apply class-specific" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.519, + 0.939 + ], + "angle": 0, + "content": "25146" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.101, + 0.103, + 0.485, + 0.307 + ], + "angle": 0, + "content": "descriptions to language prompts to adapt VLMs for classification. DCLIP [40] and CuPL [52] design prompts such as \"What does a {class} look like?\" to instruct LLMs to generate category descriptions. GPT4Vis [68] and VDT [39] use GPT-4 [48] for rich and diverse descriptions. Some work utilizes LLM-generated hierarchy labels [46] or descriptions [57] to recognize images from coarse to fine-grained levels. However, due to the hallucination in LLMs, generated descriptions might be inaccurate, non-visual, and lack discrimination [40, 57, 58]. To this end, we propose ProAPO to iteratively remove ambiguous and retain discriminative prompts. Moreover, category names, ignored in previous methods, are equally crucial for improving accuracy and are introduced in our optimization." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.308, + 0.487, + 0.574 + ], + "angle": 0, + "content": "Automatic prompt optimization aims to automatically find optimal prompts for language tasks, overcoming the time-consuming issue in manual prompt methods [5]. Early methods [10, 51, 60] generate discrete prompts by filling templates with trigger tokens, iteratively refining prompts by mining, generation, or paraphrasing. Recently, chat-based LLMs have been applied as prompt engineers [14, 17, 18, 53, 70, 78], using a meta-prompt with task information to find optimal prompt design. PN [36] is the first to instruct LLMs to optimize templates on multimodal tasks, which feeds visual feedback of the best and worst templates to guide. However, these methods only optimize task-specific templates. iCM [19] is somewhat similar to ours, optimizing class-specific prompts with chat-based LLMs. However, it uses the whole validation set as supervision. In contrast, we optimize prompts with one-shot supervision and propose solutions to solve high generation costs, long iteration times, and overfitting in class-specific optimization." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.586, + 0.192, + 0.601 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.61, + 0.485, + 0.713 + ], + "angle": 0, + "content": "Our ProAPO algorithm is shown in Fig. 2 and summarized in Alg. 1. We first describe iterative optimization in templates (Sec. 3.1). For each iteration, candidates are generated by several operators (Sec. 3.2) and then evaluated by a fitness score (Sec. 3.3). Afterward, similar iterative optimization is applied in descriptions, where we introduce two sampling strategies to save iteration costs (Sec. 3.4)." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.713, + 0.486, + 0.892 + ], + "angle": 0, + "content": "Preliminaries. Given an image, CLIP [55] predicts by selecting the highest similarity between the image and category prompt. The category prompt is a human-readable natural language associated with a category, which contains a template, e.g., \"a photo of a bird: {class}. {description} \"., and class-specific descriptions, e.g., class name \"Laysan Albatross\" and its descriptions \"It has white with black wings\". Some categories may use multiple prompts with varied templates or descriptions, i.e., prompt ensembling. We denote the prompt set that includes all categories in the task as a candidate prompt \\( P \\). A score function \\( F: \\mathcal{D} \\times P \\to \\mathbb{R} \\) is" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.103, + 0.896, + 0.147 + ], + "angle": 0, + "content": "Algorithm 1 Our Progressively Automatic Prompt Optimization (ProAPO) for visual classification, which iteratively refines prompts from task-specific to class-specific." + }, + { + "type": "algorithm", + "bbox": [ + 0.516, + 0.152, + 0.895, + 0.374 + ], + "angle": 0, + "content": "Require: \\(\\mathcal{D}\\gets \\{(x,y)\\}_{n}\\) training samples, \\(F:\\mathcal{D}\\times P\\to\\) R: score function 1: Initialize Template: \\(\\mathcal{U}_t\\gets \\{P_0\\}\\) 2: Build Template Library: \\(B_{t}\\gets \\{d_{1},\\dots ,d_{n}\\}\\) 3: Iterative Optimization: \\(\\mathcal{U}_t\\gets \\mathrm{APO}(\\mathcal{D},F,\\mathcal{U}_t,B_t)\\) 4: \\(P_{t}^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{t}}F(\\mathcal{D},P)\\) 5: Initialize Description: \\(\\mathcal{U}_c\\gets \\{\\hat{P}_0\\}\\) , initializing with \\(P_{t}^{*}\\) and prompt sampling strategy 6: Group Sampling: Sample \\(S\\) groups by class salience 7: for \\(s = 1\\) to \\(S\\) do 8: Build Description Library: \\(B_{s}\\gets \\{\\hat{d}_{1},\\dots ,\\hat{d}_{q}\\}\\) 9: Iterative Optimization: \\(\\mathcal{U}_c\\gets \\mathrm{APO}(D,F,\\mathcal{U}_c,B_s)\\) 10: end for 11: \\(P^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{c}}F(\\mathcal{D},P)\\) 12: return candidate prompt with the highest score \\(P^{*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.397, + 0.895, + 0.427 + ], + "angle": 0, + "content": "Algorithm 2 Automatic Prompt Optimization (APO) algorithm for VLMs - Lines 3 and 9 of Alg. 1, APO(D,F,U,B)." + }, + { + "type": "algorithm", + "bbox": [ + 0.516, + 0.431, + 0.895, + 0.697 + ], + "angle": 0, + "content": "Require: \\(\\mathcal{D}\\gets \\{(x,y)\\}_{n}\\) : training samples, \\(F:\\mathcal{D}\\times P\\to\\) \\(\\mathbb{R}\\) : score function, \\(\\mathcal{U}\\) : candidate prompt set, \\(B\\) : tem- plate or description library \n1: Initialize Evaluation Score: \\(S\\gets \\{F(\\mathcal{D},P)\\}_{P\\in \\mathcal{U}}\\) \n2: for \\(t = 1\\) to \\(T\\) do \n3: \\(\\mathcal{U}_g\\gets \\emptyset\\) \n4: for all \\(P\\in \\mathcal{U}\\) do \n5: Edit-based Generate: \\(\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\mathrm{GEN}(P,B)\\) \n6: end for \n7: Evaluate: \\(S_{g}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{g}}\\) \n8: Update: \\(\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_g\\}\\) and \\(S\\gets \\{S,S_g\\}\\) , retaining the top- \\(k\\) of candidate prompts with high scores \n9: Evolution-based Generate: \\(\\mathcal{U}_e\\gets \\mathrm{EVO}(\\mathcal{U},B)\\) \n10: Evaluate: \\(S_{e}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{e}}\\) \n11: Update: \\(\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_e\\}\\) and \\(S\\gets \\{S,S_e\\}\\) , retaining the top- \\(k\\) of candidate prompts with high scores \n12: end for \n13: return the latest candidate prompt set \\(\\mathcal{U}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.713, + 0.896, + 0.802 + ], + "angle": 0, + "content": "introduced in Sec. 3.3 to evaluate the candidate prompt \\( P \\) on a limited training set \\( \\mathcal{D} = \\{(x,y)\\}_{n} \\) with one-shot supervision, where \\( x \\) is an image and \\( y \\) is its label. Finally, we use a test set to evaluate optimized prompts. Our goal is to refine prompts in the natural language space to achieve superior performance in per training sample \\( (x,y) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.804, + 0.895, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\underset {P} {\\arg \\max } F (\\mathcal {D}, P) = \\underset {P} {\\arg \\max } \\mathbb {E} _ {(x, y)} [ F (\\{(x, y) \\}, P) ]. \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.836, + 0.805, + 0.853 + ], + "angle": 0, + "content": "3.1. Automatic Template Optimization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.86, + 0.896, + 0.891 + ], + "angle": 0, + "content": "To mitigate issues of semantic ambiguity caused by class names, we first iteratively optimize the template to provide" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.519, + 0.94 + ], + "angle": 0, + "content": "25147" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.154, + 0.099, + 0.845, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.22, + 0.897, + 0.29 + ], + "angle": 0, + "content": "Figure 2. Overview of our ProAPO algorithm. We progressively refine prompts from task-specific (green lines) to class-specific (brown lines) levels. Specifically, we first explore the best template by an iterative optimization process (Sec. 3.1). For each iteration, ProAPO generates a set of candidate templates by several operators (Sec. 3.2) and filters/refines templates by a fitness score (Sec. 3.3). After several iterations, we choose the top-scoring template for description initialization. Subsequently, we introduce two sampling strategies to find a better initial point and reduce traversed categories (Sec. 3.4). Similar iterative optimization is then applied to class-specific descriptions." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.302, + 0.379, + 0.316 + ], + "angle": 0, + "content": "better task-specific contextual information." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.316, + 0.484, + 0.375 + ], + "angle": 0, + "content": "Template initialization offers a candidate prompt \\( P_0 \\) as a starting point in the language search space (Line 1 of Alg. 1). Similar to PN [36], we use \"a photo of a {class}.\" filling with class names in the dataset as \\( P_0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.376, + 0.484, + 0.521 + ], + "angle": 0, + "content": "Building template library aims to provide a set of templates (Line 2 of Alg. 1) for subsequent prompt generation. We denote template library as \\( B_{t} = \\{d_{1},\\dots ,d_{n}\\} \\), where \\( d \\) is a single template. Similar to PN [36], we can instruct LLMs with a one-time query to generate a set of templates as the library. Pre-defined templates, e.g., Template80 provided in CLIP [55], can also be used. Inspired by description-based methods [39, 58], we also supplement templates with dataset domain information generated by LLMs, such as \"flower\" for FLO and \"bird\" for CUB." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.522, + 0.484, + 0.713 + ], + "angle": 0, + "content": "Iterative optimization. Automatic prompt optimization (APO) algorithm is introduced to refine template set \\(\\mathcal{U}_t\\) by an evolution-based process (Line 3 of Alg. 1). As summarized in Alg. 2, each iteration of APO contains the process of: (1) Generate new candidate prompts \\(\\mathcal{U}_g\\) and \\(\\mathcal{U}_e\\) by several edit-based (Lines 4-6) and evolution-based (Line 9) operations based on the set \\(\\mathcal{U}\\) and library \\(B\\). (2) Evaluate each new candidate prompt (Lines 7 and 10) by a score function. We regard this score as an implied \"gradient\". (3) Update the prompt set \\(\\mathcal{U}\\) based on score (Lines 8 and 11). This process retains the top-\\(k\\) of prompts with high scores to explore the search space around the current best candidates. Finally, we return the latest candidate set \\(\\mathcal{U}\\)." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.721, + 0.449, + 0.737 + ], + "angle": 0, + "content": "3.2. Prompt Generation by Several Operators" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.743, + 0.483, + 0.816 + ], + "angle": 0, + "content": "Due to the explosion of class-specific prompts, it is costly and time-intensive to generate new prompts exclusively with LLMs like previous methods [19, 36]. To this end, we introduce edit-based and evolution-based operators to generate diverse candidate prompts from the library." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.817, + 0.484, + 0.891 + ], + "angle": 0, + "content": "Edit-based generation is introduced to create a set of new candidate prompts by several simple arithmetic operators. As shown in Alg. 3, we iteratively operate a candidate prompt \\( P \\) with the library \\( B \\), where \\( \\hat{d} \\) in \\( P \\) and \\( d \\) in \\( B \\) denotes a single template or description. The Select(·) op" + }, + { + "type": "code_caption", + "bbox": [ + 0.513, + 0.301, + 0.894, + 0.331 + ], + "angle": 0, + "content": "Algorithm 3 Edit-based prompt generation algorithm - Line 5 of Alg. 2, GEN(P,B)." + }, + { + "type": "algorithm", + "bbox": [ + 0.516, + 0.337, + 0.895, + 0.548 + ], + "angle": 0, + "content": "Require: \\(P\\gets \\{\\hat{d}_1,\\dots ,\\hat{d}_i\\}\\) : a candidate prompt, \\(B\\gets\\) \\(\\{d_1,\\dots ,d_j\\}\\) : template or description library \n1: \\(\\mathcal{U}_g\\gets \\emptyset\\) \n2: for \\(m = 1\\) to \\(M\\) do \n3: \\(d_{add}\\gets \\mathrm{Select}(B)\\) \n4: \\(P_{add}\\gets P\\cup \\{d_{add}\\}\\) Add \n5: \\(d_{del}\\gets \\mathrm{Select}(P)\\) \n6: \\(P_{del}\\gets P\\setminus \\{d_{del}\\}\\) \\(\\triangleright\\) Delete \n7: \\(d_{in}\\gets \\mathrm{Select}(B)\\) \n8: \\(d_{out}\\gets \\mathrm{Select}(P)\\) \n9: \\(P_{rep}\\gets (P\\cup \\{d_{in}\\})\\setminus \\{d_{out}\\}\\) Replace \n10: \\(\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\{P_{add},P_{del},P_{rep}\\}\\) \n11: end for \n12: return the generated candidate prompt set \\(\\mathcal{U}_g\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.563, + 0.896, + 0.696 + ], + "angle": 0, + "content": "erator samples an element from a given prompt set. Three operations are then applied to \\( P \\) in each iteration: (1) Add a new element \\( d_{add} \\) to \\( P \\). (2) Remove an existing element \\( d_{del} \\) from \\( P \\). (3) Replace an element \\( d_{out} \\) in \\( P \\) with a new element \\( d_{in} \\) in \\( B \\). These new candidates are ensembled around the current high-score candidate \\( P \\), which makes them more likely to succeed. Moreover, selecting elements from the library ensures differences between generated candidates. After \\( M \\)-times steps, we return the latest set \\( \\mathcal{U}_g \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.699, + 0.897, + 0.891 + ], + "angle": 0, + "content": "Evolution-based generation is introduced to improve search efficiency over random steps, as shown in Alg. 4. Inspired by widely used Generic Algorithm [20, 24, 42], we introduce crossover and mutation operators to enhance candidate generation. Crossover operator aims to find the optimal direction quickly by combining high-scoring candidate prompts. We randomly take the concatenation of two candidates \\( P_{c1} \\) and \\( P_{c2} \\) sampled from the current optimal set \\( \\mathcal{U} \\), yielding a new candidate \\( P_{c} \\). Mutation operator aims to prevent convergence to local optima by introducing variations. We randomly add new elements selected from library \\( B \\) into the candidate \\( P_{c} \\), yielding mutation candidate \\( P_{m} \\). After \\( N \\)-times steps, we return the generated set \\( \\mathcal{U}_{e} \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.519, + 0.939 + ], + "angle": 0, + "content": "25148" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.102, + 0.103, + 0.484, + 0.132 + ], + "angle": 0, + "content": "Algorithm 4 Evolution-based generation algorithm - Line 9 of Alg. 2, EVO(U, B)." + }, + { + "type": "algorithm", + "bbox": [ + 0.103, + 0.136, + 0.484, + 0.316 + ], + "angle": 0, + "content": "Require: \\(\\mathcal{U}\\gets \\{P_1,\\dots ,P_n\\}\\) : candidate prompt set, \\(B\\gets\\) \\(\\{d_1,\\dots ,d_j\\}\\) : template or description library \n1: \\(\\mathcal{U}_e\\gets \\emptyset\\) \n2: for \\(n = 1\\) to \\(N\\) do \n3: \\(P_{c1}\\gets \\mathrm{Select}(\\mathcal{U})\\) \n4: \\(P_{c2}\\gets \\mathrm{Select}(\\mathcal{U})\\) \n5: \\(P_{c}\\gets P_{c1}\\cup P_{c2}\\) \\(\\triangleright\\) Crossover \n6: \\(P_{all}\\gets B\\cup P_c\\) \n7: \\(P_{m}\\gets \\mathrm{RANDOMSELECT}(P_{all},\\mathrm{len}(P_{c}))\\triangleright\\) Mutation \n8: \\(\\mathcal{U}_e\\gets \\mathcal{U}_e\\cup \\{P_c,P_m\\}\\) \n9: end for \n10: return the generated candidate prompt set \\(\\mathcal{U}_e\\)" + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.33, + 0.258, + 0.345 + ], + "angle": 0, + "content": "3.3. Score Functions" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.353, + 0.484, + 0.397 + ], + "angle": 0, + "content": "To measure candidate prompts, we introduce a fitness score to approximately obtain the \"gradient\" used for optimization. It contains the accuracy and an entropy constraint." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.398, + 0.484, + 0.427 + ], + "angle": 0, + "content": "Accuracy. Given an image \\( x \\), we obtain a prediction \\( \\operatorname{pred}(x) \\) that yields the highest cosine similarity:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.429, + 0.483, + 0.465 + ], + "angle": 0, + "content": "\\[\ns (x, c) = \\frac {1}{| D (c) |} \\sum_ {d \\in D (c)} \\cos (I (x), T (d)). \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.47, + 0.483, + 0.493 + ], + "angle": 0, + "content": "\\[\n\\operatorname {p r e d} (x) = \\underset {c \\in C} {\\arg \\max } s (x, c), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.496, + 0.484, + 0.555 + ], + "angle": 0, + "content": "where \\( D(c) \\in P \\) is a set with all prompts describing the category \\( c \\) in candidate prompt \\( P \\), and \\( C \\) is the entire category in the dataset. \\( I \\) and \\( T \\) are image encoder and text encoder, respectively. The accuracy is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.559, + 0.483, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A c c} = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ \\mathbb {I} (\\operatorname {p r e d} (x) = y) ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.577, + 0.483, + 0.591 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}\\) is the training set and \\(\\mathbb{I}(\\cdot)\\) is an indicator function." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.593, + 0.484, + 0.665 + ], + "angle": 0, + "content": "Entropy constrain. Previous methods [19, 36] only use accuracy as the evaluation metric. However, the overfitting problem appears as shown in Fig. 1(c). To this end, we include a simple entropy constrain, which penalizes the model to predict a higher probabilistic score in the true label \\( y \\):" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.668, + 0.483, + 0.686 + ], + "angle": 0, + "content": "\\[\nH = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ - \\log (s (x, y)) ]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.687, + 0.364, + 0.701 + ], + "angle": 0, + "content": "The final score is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.706, + 0.483, + 0.721 + ], + "angle": 0, + "content": "\\[\nF (\\mathcal {D}, P) = \\operatorname {A c c} + \\alpha H. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.724, + 0.484, + 0.754 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a scalar to balance them. In Sec. 4.4, we empirically show that this score effectively reduces overfitting." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.764, + 0.403, + 0.78 + ], + "angle": 0, + "content": "3.4. Sampling Strategy for Initialization" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.786, + 0.484, + 0.86 + ], + "angle": 0, + "content": "After exploring the best template, we continue to optimize the class-specific descriptions. To save iteration costs, we introduce a prompt sampling strategy to find a better start point and a grouping sampling strategy to select some salient categories instead of all for iterative optimization." + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.861, + 0.484, + 0.891 + ], + "angle": 0, + "content": "Prompt sampling strategy aims to initialize the class-specific candidate prompt \\(\\hat{P}_0\\) with the optimized template" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.103, + 0.895, + 0.249 + ], + "angle": 0, + "content": "\\(P_{t}^{*}\\) and high-score descriptions (Line 5 of Alg. 1). Similar to description-based methods [40, 52], we instruct LLM to generate a set of visual descriptions for each class. Besides, we replace the class name with its synonyms generated by LLMs to increase the number of descriptions. To obtain a better initial point, we randomly sample descriptions of each category to obtain multiple candidate prompts and select the one with the highest score as \\(\\hat{P}_0\\). It ensures that subsequent optimization is around candidates with relatively high scores. More details are shown in Supp.B." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.25, + 0.895, + 0.411 + ], + "angle": 0, + "content": "Group sampling strategy aims to explore several salient categories into groups for optimization (Line 6 of Alg. 1). We consider two ways to sample categories. First, we select the groups with the lowest top-\\( n_{wst} \\) accuracy and its misclassified categories. Moreover, we also choose salient groups by the category with the top-\\( n_{sln} \\) result gains after adding descriptions and its misclassified categories. In the end, We use \\( S = n_{wst} + n_{sln} \\) groups for optimization. More details are shown in Supp.C. In Sec. 4.4, experiments show that optimizing these selected categories can effectively improve performance and save costs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.411, + 0.894, + 0.53 + ], + "angle": 0, + "content": "Building Library and Iterative Optimization for Descriptions. In Lines 7-10 of Alg. 1, we iteratively optimize the class-specific description in selected groups. Similar to template optimization, we first build the description library, which contains visual descriptions for categories in the specific group. Then, we apply APO algorithm to refine descriptions automatically. After several iterations, we use the candidate \\( P^{*} \\) with the highest score as the final prompt." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.542, + 0.642, + 0.559 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.895, + 0.699 + ], + "angle": 0, + "content": "Datasets. Following prompt tuning [76, 77] and LLM-generated description works [40], we evaluate our ProAPO on thirteen downstream tasks, including ImageNet-1K (IN1K) [9], Caltech101 [13] (object recognition), StandfordCars [31], CUB200-2011 [67] (bird classification), DTD [7] (Textures), EuroSAT (ESAT) [23] (satellite images), FGVCAircraft [38], Flowers102 [45], Food101 [3], OxfordPets [50], Places365 [75], SUN397 [69] (scene recognition), UCF101 [63] (human action)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.7, + 0.896, + 0.891 + ], + "angle": 0, + "content": "Implementation details. In the default setting, we use template-80 pre-defined in CLIP [55] as the template library and CuPL [52] as the description library for searching the hyperparameters in a fixed language space. Dataset domain and synonym labels are generated by LLMs. This setting ensures a one-time query of LLMs, and no human intervention is required. If not explicitly stated, we set iteration times \\( T = 4 \\) in both template and description optimization, generated number \\( M = N = 8 \\), \\( \\alpha = 1e3 \\), \\( n_{wst} = n_{sln} = \\log(|C|) \\) for all datasets, where \\( |C| \\) is the number of classes. All results are average with four seeds. Besides, our ProAPO is implemented in PyTorch and runs with an RTX 3090 GPU. More details are shown in Supp.D." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.519, + 0.939 + ], + "angle": 0, + "content": "25149" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.161, + 0.1, + 0.837, + 0.434 + ], + "angle": 0, + "content": "
ModuleTFIN-1KCaltechCarsCUBDTDESATFGVCFLOFoodPetsPlacesSUNUCFAvg (11)Avg (13)
ResNet-50 Backbone
CLIP (a photo of a {} )✓57.984.553.944.738.828.615.960.274.083.238.258.056.955.653.4
prompt tuning methods
CoOp [77]X57.287.555.6-44.450.69.668.174.385.9-60.361.959.6-
PLOT [6]X59.589.856.6-46.654.117.971.777.787.5-62.564.562.6-
ProGrad [79]X57.888.758.4-46.156.318.873.276.088.4-60.565.662.7-
automatic prompt optimization methods
PN [36]✓59.689.156.2-44.849.018.167.278.388.1-61.060.261.1-
ProAPO (ours)✓61.590.358.050.752.351.721.175.181.888.741.863.766.064.661.8
ViT-B/32 Backbone
CLIP (a photo of a {} )✓62.191.260.451.742.943.920.266.083.286.839.962.160.961.859.3
hand-engineered methods
Template-80 [55]✓63.591.660.451.242.852.619.566.184.287.441.663.562.963.160.6
FILIP-8 [71]✓63.891.460.752.743.454.318.967.084.687.541.263.965.063.761.1
DEFILIP-6 [8]✓62.591.059.951.141.346.418.866.584.387.540.262.363.662.259.6
description-based methods
DCLIP [40]✓63.392.759.452.744.138.419.466.183.988.141.265.065.862.460.0
Waffle [58]✓63.392.159.352.943.251.619.666.384.987.741.565.064.563.460.9
CuPL [52]✓64.492.960.753.350.650.520.969.584.287.043.166.366.464.962.3
GPT4Vis [68]✓63.593.161.452.748.547.021.469.884.388.142.764.265.764.361.7
AdaptCLIP [59]✓63.392.759.753.647.451.320.867.284.287.641.966.166.564.261.7
ProAPO w/ DCLIP✓64.193.260.653.648.259.422.671.584.288.742.766.068.066.063.3
ProAPO (ours)✓64.794.461.755.453.563.023.074.385.391.043.366.669.067.965.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.438, + 0.896, + 0.482 + ], + "angle": 0, + "content": "Table 1. Comparison of our ProAPO with SOTA textual prompt-based methods. We report the top-1 accuracy (%) on the test set. The best and second best results of the same backbone for each dataset are bolded and underlined, respectively. Avg (11) and Avg (13) denote average results across 11 datasets (excluding CUB [67] and Places [75]) and all 13 datasets. TF denotes training-free approaches." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.491, + 0.388, + 0.506 + ], + "angle": 0, + "content": "4.1. Comparison with SOTA Methods" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.518, + 0.484, + 0.665 + ], + "angle": 0, + "content": "Compared methods. We compare our results with state-of-the-art (SOTA) textual prompt-based methods, including vanilla CLIP with \"a photo of a {}\" template, prompt tuning methods [6, 77, 79], hand-engineered methods (i.e., best templates released by [8, 55, 71]), LLM-generated description methods [40, 52, 58, 59, 68], and automatic prompt optimization methods [36]. We test our ProAPO on two popular backbones (ResNet50 [21] and ViT-B/32 [12]). Prompt tuning and automatic prompt optimization methods are evaluated under one-shot supervision." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.67, + 0.484, + 0.891 + ], + "angle": 0, + "content": "Results. In Tab. 1, we see that our ProAPO consistently outperforms previous prompt-based methods across diverse datasets on ResNet50 and ViT-B/32 backbones. Our optimized prompts improve vanilla CLIP by an average of \\(8.4\\%\\) (from \\(53.4\\%\\) to \\(61.8\\%\\)) on ResNet50 and \\(5.7\\%\\) (from \\(59.3\\%\\) to \\(65.0\\%\\)) on ViT-B/32. Moreover, our training-free ProAPO surpasses gradient-based prompting methods (CoOp, PLOT, ProGrad) by at least \\(1.9\\%\\) average accuracy in eleven datasets. It shows optimizing prompts in a natural language space is more effective in low-shot tasks. Compared to template-optimized methods (i.e., PN and hand-engineered methods), our ProAPO achieves remarkable performance on fine-grained datasets, e.g., CUB, FLO, ESAT, and UCF. This is because class-specific descriptions provide fine-grained discriminative de" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.491, + 0.895, + 0.594 + ], + "angle": 0, + "content": "tails. Our ProAPO also outperforms description-based methods, even with DCLIP as initialization. We improve performances of DCLIP and CuPL by \\(3.3\\%\\) and \\(2.7\\%\\) on average across thirteen datasets. Notably, it improves DCLIP and CuPL by \\(5.4\\%\\) and \\(4.8\\%\\) on FLO and by \\(21\\%\\) and \\(12.5\\%\\) on ESAT, confirming that iterative optimization of class-specific prompts enhances fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.595, + 0.896, + 0.816 + ], + "angle": 0, + "content": "Critical analysis. On datasets like ImageNet [9], Caltech [13], Places [75], and SUN [69], performance gains are relatively small. We attribute this to two reasons: First, datasets like ImageNet and Caltech contain coarse-grained categories. The differences between categories have become clearer with LLM-generated descriptions, eliminating the need for our method. Second, fine-grained datasets, such as Places and SUN for scene recognition, are easily confusing between different images, limiting performance from only textual side optimization. In Sec. 4.2, we show that adapter-based methods with our optimized prompt improve performance again after addressing issues of image confusion. Moreover, we observe that the language search space impacts performance. Since CuPL has better descriptions than DCLIP, our ProAPO with CuPL performs well." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.824, + 0.81, + 0.84 + ], + "angle": 0, + "content": "4.2. More Benefits by Optimal Prompts" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.846, + 0.895, + 0.891 + ], + "angle": 0, + "content": "Transfer to adapter-based methods. In Fig. 3, we show the results of popular adapter-based methods [15, 66, 74, 80] with different prompt initialization, i.e., SOTA method" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.519, + 0.939 + ], + "angle": 0, + "content": "25150" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.101, + 0.291, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.22, + 0.268, + 0.232 + ], + "angle": 0, + "content": "(a) Training-free methods." + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.101, + 0.476, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.322, + 0.22, + 0.451, + 0.232 + ], + "angle": 0, + "content": "(b) Fine-tuning methods." + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.235, + 0.483, + 0.276 + ], + "angle": 0, + "content": "Figure 3. Results of adapter-based methods with different initial prompts. Solid and dotted lines denote prompt initialization with ProAPO and CuPL, respectively." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.291, + 0.443, + 0.376 + ], + "angle": 0, + "content": "
ModuleShotsSourceTarget
RN50RN101ViT-B/32ViT-B/16
CLIP [55]057.960.661.966.6
CoOp [77]1663.020.631.739.5
PN [36]159.960.762.267.0
ProAPO161.562.164.669.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.381, + 0.483, + 0.409 + ], + "angle": 0, + "content": "Table 2. Results of prompt transfer from ResNet-50 to other architectures. We report the top-1 accuracy in ImageNet-1K." + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.421, + 0.446, + 0.542 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.545, + 0.483, + 0.587 + ], + "angle": 0, + "content": "Figure 4. Results of prompt transfer to different backbones. The value denotes performance gains compared to vanilla VLMs. Our optimized prompts of ResNet50 and ViT-B/32 are reported." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.592, + 0.483, + 0.696 + ], + "angle": 0, + "content": "CuPL [52] and our ProAPO. Adapter-based methods with ProAPO (solid lines) consistently surpass those with CuPL (dotted lines). It reveals that high-quality prompts make adapters perform better. Even in low shots, training with ProAPO achieves notable performance gains, which verifies its effectiveness. As the number of shots increases, adapters further improve results by enhancing image features." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.699, + 0.483, + 0.891 + ], + "angle": 0, + "content": "Transfer to different backbones. In Tab. 2, we report accuracy in ImageNet across different backbones, with prompts optimized on a source backbone (ResNet50) adapted to target backbones (ResNet101, ViT-B/32, ViT-B/16). We observe that CoOp [77] obtains a significant drop in accuracy on target backbones while our ProAPO maintains performance. It verifies that discrete prompts searched in natural language spaces transfer better than continuous prompts. ProAPO also outperforms PN, which reveals the effectiveness of class-specific optimization. Moreover, we achieve stable performance gains compared to CuPL [52] from source to target models in Fig. 4. It further verifies that ProAPO transfers easily across different backbones." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.1, + 0.72, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.611, + 0.202, + 0.627, + 0.213 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.101, + 0.888, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.202, + 0.813, + 0.213 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.214, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 5. Performance improvement analysis. (a) Analysis of the effect of single vs. ensemble prompts. * denotes results evaluated in the test set. ATO is our automatic template optimization algorithm. (b) Results of previous description-based methods with prompt optimization by our ATO and ProAPO algorithms." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.298, + 0.892, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.429, + 0.894, + 0.469 + ], + "angle": 0, + "content": "Figure 6. Qualitative analysis of class-specific prompt optimization by ProAPO. Shaded red and blue words denote common and discriminative descriptions in two confused categories." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.475, + 0.818, + 0.491 + ], + "angle": 0, + "content": "4.3. Performance Improvement Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.893, + 0.53 + ], + "angle": 0, + "content": "In this section, we analyze the key reasons for the performance improvement of our ProAPO." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.534, + 0.895, + 0.709 + ], + "angle": 0, + "content": "Prompt ensembling is better than a single prompt. Compared to PN [36], we utilize prompt ensembling instead of a single prompt to optimize the template and description. To evaluate the effectiveness of prompt ensembling, we use Template-80 [55] as the template library and denote the prompts searched by the test set as the upper bound. As shown in Fig. 5(a), we observe that ensemble templates have a higher upper bound than the single template, consistent with prior work [8, 40, 71]. Similarly, we observe that our optimized templates achieve higher performance than PN [36], even better than the best single template, further verifying the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.714, + 0.895, + 0.891 + ], + "angle": 0, + "content": "Iterative optimization improves prompt quality. In Fig. 6, we show the changes in descriptions with our ProAPO. After iterative optimization, common descriptions such as \"flight over ocean\" and \"long wings and hooked bill\" are removed. Discriminative descriptions are also retained in candidate prompts, e.g., \"white body\" for Laysan Albatross, and \"black underpants\" for Sooty Albatross. As such, we see a notable improvement in description-based methods [40, 52, 59, 68] with our ATO and ProAPO in Fig. 5(b) by at least \\(2.7\\%\\) average in thirteen datasets. It further verifies the effectiveness of our progressive optimization." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.518, + 0.939 + ], + "angle": 0, + "content": "25151" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.1, + 0.462, + 0.24 + ], + "angle": 0, + "content": "
ComponentIN-1KAvg (11)Avg (13)
AddDelRepCrossMut
CLIP (Baseline)62.161.859.3
edit-based generation
a)✓63.866.063.3
b)✓✓64.666.463.8
c)✓✓64.466.563.8
d)✓✓✓64.666.764.0
evolution-based generation
e)✓✓✓✓64.667.364.5
f)✓✓✓✓64.767.164.3
g)✓✓✓✓✓64.767.965.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.242, + 0.466, + 0.256 + ], + "angle": 0, + "content": "Table 3. Ablation of edit- and evolution-based operators." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.264, + 0.457, + 0.332 + ], + "angle": 0, + "content": "
Module (ViT-B/32)IN-1KAvg (11)Avg (13)Times
a) w/o prompt sampling64.467.364.512 min
b) w/o group sampling64.868.165.2306 min
c) w/o sampling strategies64.567.264.4302 min
ProAPO (full model)64.767.965.015 min
" + }, + { + "type": "table_caption", + "bbox": [ + 0.156, + 0.334, + 0.43, + 0.348 + ], + "angle": 0, + "content": "Table 4. Ablation of two sampling strategies." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.352, + 0.251, + 0.367 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.373, + 0.484, + 0.519 + ], + "angle": 0, + "content": "Are both GEN and EVO algorithms necessary? In Tab. 3, we ablate edit- and evolution-based operators. For edit-based operators, we observe that the model with add, delete, and replace operations achieves a higher result in row d). After introducing evolution-based operators, i.e., crossover operator to combine advantages of high-scoring candidates, and mutation operator to avoid locally optimal solutions, we see an increase in performance in rows e)-g). It confirms that evolution-based operators make the model search the optimal prompt faster with limited iterations." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.52, + 0.484, + 0.667 + ], + "angle": 0, + "content": "Does sample strategies degrade performance? In Tab. 4, we ablate two sampling strategies for description optimization. Without the prompt sampling, we see a slight decrease in times while results drop in row a). It verifies the effectiveness of the prompt sampling in finding a better initial point. Without the group sampling to select salient categories for optimization, we observe a notable increase in time costs (from \\(15\\mathrm{min}\\) to \\(300+\\mathrm{min}\\), 20 times) yet similar results in row b) and the full model. It reveals that group sampling simultaneously improves performance and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.667, + 0.484, + 0.83 + ], + "angle": 0, + "content": "Which score function is better? In Fig. 7, we compare the different score functions, i.e., accuracy (used in PN [36]) and our fitness score, to evaluate the quality of the candidate prompt. PCCs (Pearson Correlation Coefficients) are introduced to evaluate the linear relationship between training metrics and test performance. The high PCC values mean a strong correlation. We see that the model with our fitness score achieves stable and high test results compared to previous score functions when achieving the best score. Besides, a higher PPC value further verifies that our fitness score effectively alleviates the overfitting problem." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.839, + 0.345, + 0.855 + ], + "angle": 0, + "content": "4.5. Hyperparameter Sensitivity" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.86, + 0.484, + 0.891 + ], + "angle": 0, + "content": "How many iterations of Alg. 2 to use? In Fig. 8(a), we show the effect of iteration times \\( T \\) in APO algorithm. As" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.102, + 0.703, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.2, + 0.683, + 0.211 + ], + "angle": 0, + "content": "(a) Previous score function." + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.101, + 0.889, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.2, + 0.851, + 0.211 + ], + "angle": 0, + "content": "(b) Our fitness score" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.215, + 0.895, + 0.256 + ], + "angle": 0, + "content": "Figure 7. Effect of different score functions. Higher PCC values mean stronger correlations between training metrics and test results. Best Acc is the test result when achieving the best score." + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.263, + 0.64, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.348, + 0.636, + 0.359 + ], + "angle": 0, + "content": "(a) Iteration times \\(T\\)" + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.263, + 0.764, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.347, + 0.764, + 0.359 + ], + "angle": 0, + "content": "(b) Generated numbers" + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.263, + 0.888, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.347, + 0.887, + 0.359 + ], + "angle": 0, + "content": "(c) Sampling groups \\(S\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.363, + 0.894, + 0.39 + ], + "angle": 0, + "content": "Figure 8. The effect of hyperparameter analysis. The hyperparameter value set to 0 denotes the result of CuPL [52]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.895, + 0.456 + ], + "angle": 0, + "content": "the number of iterations increases, we see a consistent performance improvement compared to the baseline CuPL. It demonstrates that iterative optimization improves prompt quality. Stable results are achieved when \\( T \\geq 4 \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.894, + 0.544 + ], + "angle": 0, + "content": "How many generated prompts to use? In Fig. 8(b), we show the effect of generated numbers in GEN and EVO algorithm, where we set \\( M = N \\). Similarly, progressive improvements are seen as generated numbers increase. We see a reliable result when \\( M = N \\geq 8 \\). It reveals the effectiveness of generating diverse candidates by our algorithm." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.894, + 0.648 + ], + "angle": 0, + "content": "Are more sampling groups better? In Fig. 8(c), we show the effect of the number of salient groups \\( S \\) in the group sampling strategy. We see a notable improvement when \\( S = 2 \\). As the number of groups \\( S \\) increases, it achieves stable results when \\( S \\geq 8 \\). It verifies that optimizing several salient categories can achieve comparable performances with all categories and save iteration costs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.66, + 0.629, + 0.675 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.684, + 0.895, + 0.891 + ], + "angle": 0, + "content": "We propose an evolution-based algorithm for VLMs to progressively refine prompts from task-specific to class-specific levels. To save generation costs, ProAPO uses several edit- and evolution-based operators to create candidate prompts with a prompt library. Results show that our fitness score mitigates overfitting in class-specific prompts. We empirically verify that two sampling strategies improve performance and save iteration times. Extensive experiments on thirteen datasets reveal that ProAPO consistently outperforms SOTA textual prompt-based methods on low-shot tasks. Moreover, our method effectively improves adapter-based and description-based methods and easily transfers across different backbones. We hope ProAPO could provide new insight into adapting VLMs from the textual side." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.518, + 0.939 + ], + "angle": 0, + "content": "25152" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.103, + 0.102, + 0.267, + 0.119 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.127, + 0.484, + 0.157 + ], + "angle": 0, + "content": "This work was supported by the Central Guidance for Local Special Project (Grant No. Z231100005923044)." + }, + { + "type": "title", + "bbox": [ + 0.104, + 0.171, + 0.197, + 0.187 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.112, + 0.195, + 0.484, + 0.235 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, and Pauline Luc et al. Flamingo: a visual language model for few-shot learning. 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IEEE TMM, 26:1361-1372, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.104, + 0.894, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.928, + 0.518, + 0.939 + ], + "angle": 0, + "content": "25155" + } + ] +] \ No newline at end of file diff --git a/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_origin.pdf b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..abe56cee71dcaf163edaebc9746beaf38a8fc46f --- /dev/null +++ b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/a3c1ad48-aaba-47a6-aeeb-2ef7d80a2260_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3d4dcec4f766b7df7a2a659e79aa5da8b1e5e729ee244f24a1da230937166e6e +size 635315 diff --git a/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/full.md b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..eb23fce251b4c440fbdd88d94ea1658615520bea --- /dev/null +++ b/2025/ProAPO_ Progressively Automatic Prompt Optimization for Visual Classification/full.md @@ -0,0 +1,401 @@ +# ProAPO: Progressively Automatic Prompt Optimization for Visual Classification + +Xiangyan $\mathbf{Q}\mathbf{u}^{12}$ Gaopeng $\mathrm{Gou}^{12\dagger}$ Jiamin Zhuang $^{12}$ Jing Yu $^{3}$ Kun Song $^{4}$ Qihao Wang $^{12}$ Yili Li $^{12}$ Gang Xiong $^{12}$ + +$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences $^{2}$ School of Cyber Security, Chinese Academy of Sciences $^{3}$ School of Information Engineering, Minzu University of China $^{4}$ University of Science and Technology Beijing {quxiangyan, gougaopeng, zhuangjiamin}@iie.ac.cn, jing.yu@muc.edu.cn songkun@xs.ustb.edu.cn, wangqihao22@mails.ucas.ac.cn, {liyili, xionggang}@iie.ac.cn + +# Abstract + +Vision-language models (VLMs) have made significant progress in image classification by training with large-scale paired image-text data. Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones. Our code is available at here. + +# 1. Introduction + +In recent years, vision-language models (VLMs) [1, 27, 33, 43, 55, 64, 72, 73] pre-trained on large-scale paired imagedtext data, such as CLIP [55], have shown strong generalization on various image classification tasks. These mod + +els classify images by computing the similarity between the image and the prompt (a human-readable natural language) associated with a category. The prediction is the category with the highest similarity to the query image. Their performance highly relies on prompt quality, especially in fine-grained categories. Finding the optimal prompts for the downstream task becomes an urgent challenge [36, 52, 77]. + +Recent works have made efforts to improve prompt quality [4, 16, 55]. Manual prompt engineering [8, 55, 71] is a standard approach, writing several templates to include task-specific information, e.g., "a photo of a {class}, a type of bird." for bird recognition. However, designing templates requires domain expertise, making it costly and challenging to scale [36, 39, 40, 52, 77]. Moreover, the template may lack details to recognize fine-grained categories as only the class name provides the distinct information in prompts [39, 52, 77]. Prompt tuning methods [6, 76, 77, 79] introduce a set of learnable tokens in the prompt to represent task-specific context, optimizing through gradient updates. While improving the performance of VLMs, they require additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39, 40, 52, 57, 68, 81] leverage the implicit knowledge of large language models (LLMs) [4, 48] to generate descriptions with class-specific details, enhancing generalization ability of VLMs. However, due to the hallucination in LLMs [25, 56], generated descriptions are suboptimal due to inaccurate, e.g., "feet" for the food Peking Duck, or lack discrimination for fine-grained recognition, e.g., the same descriptions "hooked bill" and "webbed feet" appear in Laysan Albatross and Sooty Albatross (see Fig. 1(a)), or exhibit non-visual descriptions, e.g., "strong smell" for Jackfruit. To this end, we propose the following key questions: + +How can we find the optimal class-specific prompts that are visually discriminative for fine-grained categories with minimal supervision and no human intervention? + +Inspired by recent automatic prompt optimization (APO) methods [18, 53, 60, 78] in language tasks, we aim to opti + +![](images/e63f097a767799822fae67a3f7a636d04eef95c7b2cd9ff77e191be1357e864b.jpg) +Laysan Albatross + +white with black wings +a seabird +- long, webbed feet +a long hooked bill +- flight over the ocean + +![](images/dbe349e7ec28f885c1e4bc7752aa5cff0ecac6499344b041851dca58b7392d00.jpg) +Sooty Albatross +(a) Issues in generated descriptions. + +large, dark-colored bird +white band around its neck +- webbed feet +- long, hooked bill +a species of albatross + +![](images/049a3c7aa48209e08d15461fce46f480bd79e53b91cccb9e82bc8e1e648c80e6.jpg) +Natural Language Prompt Search Space +Figure 1. Issues of optimizing class-specific prompts. (a) Due to the hallucination in LLMs, generated descriptions may be inaccurate and lack discrimination between fine-grained categories (see red words). (b) Compared to task-specific templates, we see an explosion in the number of class-specific prompts (see red rectangle). This leads to higher generation costs, iteration times, and the overfitting problem. (c) Overfitting problem: Multiple candidate prompts have the same best training accuracy but variable and low test results (see red circle). + +![](images/3b83463002562daf6374f429ecf87595bec2f86d3769b12fc80cec7d47281c33.jpg) +(c) Overfitting in evaluation metric. + +mize class-specific prompts by an evolution-based process, removing confused prompts while retaining discriminative ones. We consider an approximate zero-shot setting, i.e., one-shot classification, where minimal supervision is introduced to evaluate the prompt quality. However, previous APO methods focus solely on task-specific template optimization. In contrast, except for templates, a class-specific prompt also contains a description associated with visual details in a category, as shown in Fig. 1(b). Compared with templates, class-specific optimization introduces new challenges due to the expanded search space (see Fig. 1(b)), which leads to: (1) High generation costs. As the search space grows, it is costly and time-consuming to generate class-specific prompts exclusively with LLMs at each iteration. (2) Long iteration times. Evaluating each candidate prompt in the search space may exponentially increase the iteration time, which is impractical in this scenario. (3) Overfitting problem. As shown in Fig. 1(c), multiple candidate prompts achieve variable and low test results (from $63.6\%$ to $64.3\%$ ) at the best training accuracy. + +To address these issues, we propose a Progressively Automatic Prompt Optimization (ProAPO) algorithm to iteratively optimize prompts from task-specific to class-specific levels. In each iteration, we use several edited-based (i.e., add, remove, and replace) and evolution-based operators (i.e., crossover, and mutation) to generate diverse candidate prompts from a prompt library. We query LLMs to generate this library in the initialization stage. Compared to querying LLMs at each iteration, these simple operations can effectively save generation costs. Then, we introduce a novel fitness score to evaluate generated candidate prompts and retain several top-scoring ones for the next iteration generation. An entropy constraint is added to the score to increase the soft prediction score and reduce overfitting. After several iterations, we return the best prompt for classification. To reduce iteration times in class-specific descriptions, we propose a prompt sampling strategy to find a better initial point in the search space and a group sampling strategy to explore a few salient classes instead of all for optimization. Our key contributions are: + +- We propose an evolution-based algorithm to progressively optimize prompts from task-specific to class-specific levels with one-shot supervision and no human intervention. It solves issues of inaccuracy and lack of discrimination in LLM-generated descriptions. +- We address challenges in class-specific prompt optimization by an offline generation algorithm to reduce LLM querying costs, an entropy-constrained fitness score to prevent overfitting, and two sampling strategies to find an optimal initial point and reduce iteration times. +- Extensive experiments on thirteen datasets show that our proposed ProAPO consistently outperforms SOTA textual prompt-based methods and improves description-based methods in a challenging one-shot supervision. Moreover, our optimal prompts improve adapter-based methods and transfer effectively across different backbones. + +# 2. Related Work + +Adaptation of VLMs for image classification tasks. Inspired by successes in VLMs, recent works aim to adapt them for image classification tasks. Some works utilize lightweight linear layers [26, 35, 49, 55, 62, 65, 82], adapters [15, 39], visual prompting [2, 28, 47], or cache models [66, 74, 80] to enhance visual features. Other works aim to improve the quality of prompts. Manual prompt engineering [8, 34, 55] applies task-specific information in prompt templates to enhance performance. However, templates need to be hand-written and lack fine-grained details [36, 39, 40, 52, 77]. Prompt tuning methods [6, 11, 22, 29, 30, 32, 37, 61, 76, 77, 79] learn task-specific context by a set of learnable tokens. However, they need additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39-41, 44, 52, 54, 57, 59, 68, 81] exploit implicit knowledge in LLMs to generate visual descriptions for each category. They enrich semantics in prompts and offer interpretable predictions. In this work, we aim to further improve description quality through an evolution process. + +LLM-generated description methods apply class-specific + +descriptions to language prompts to adapt VLMs for classification. DCLIP [40] and CuPL [52] design prompts such as "What does a {class} look like?" to instruct LLMs to generate category descriptions. GPT4Vis [68] and VDT [39] use GPT-4 [48] for rich and diverse descriptions. Some work utilizes LLM-generated hierarchy labels [46] or descriptions [57] to recognize images from coarse to fine-grained levels. However, due to the hallucination in LLMs, generated descriptions might be inaccurate, non-visual, and lack discrimination [40, 57, 58]. To this end, we propose ProAPO to iteratively remove ambiguous and retain discriminative prompts. Moreover, category names, ignored in previous methods, are equally crucial for improving accuracy and are introduced in our optimization. + +Automatic prompt optimization aims to automatically find optimal prompts for language tasks, overcoming the time-consuming issue in manual prompt methods [5]. Early methods [10, 51, 60] generate discrete prompts by filling templates with trigger tokens, iteratively refining prompts by mining, generation, or paraphrasing. Recently, chat-based LLMs have been applied as prompt engineers [14, 17, 18, 53, 70, 78], using a meta-prompt with task information to find optimal prompt design. PN [36] is the first to instruct LLMs to optimize templates on multimodal tasks, which feeds visual feedback of the best and worst templates to guide. However, these methods only optimize task-specific templates. iCM [19] is somewhat similar to ours, optimizing class-specific prompts with chat-based LLMs. However, it uses the whole validation set as supervision. In contrast, we optimize prompts with one-shot supervision and propose solutions to solve high generation costs, long iteration times, and overfitting in class-specific optimization. + +# 3. Method + +Our ProAPO algorithm is shown in Fig. 2 and summarized in Alg. 1. We first describe iterative optimization in templates (Sec. 3.1). For each iteration, candidates are generated by several operators (Sec. 3.2) and then evaluated by a fitness score (Sec. 3.3). Afterward, similar iterative optimization is applied in descriptions, where we introduce two sampling strategies to save iteration costs (Sec. 3.4). + +Preliminaries. Given an image, CLIP [55] predicts by selecting the highest similarity between the image and category prompt. The category prompt is a human-readable natural language associated with a category, which contains a template, e.g., "a photo of a bird: {class}. {description} "., and class-specific descriptions, e.g., class name "Laysan Albatross" and its descriptions "It has white with black wings". Some categories may use multiple prompts with varied templates or descriptions, i.e., prompt ensembling. We denote the prompt set that includes all categories in the task as a candidate prompt $P$ . A score function $F: \mathcal{D} \times P \to \mathbb{R}$ is + +Algorithm 1 Our Progressively Automatic Prompt Optimization (ProAPO) for visual classification, which iteratively refines prompts from task-specific to class-specific. + +Require: $\mathcal{D}\gets \{(x,y)\}_{n}$ training samples, $F:\mathcal{D}\times P\to$ R: score function 1: Initialize Template: $\mathcal{U}_t\gets \{P_0\}$ 2: Build Template Library: $B_{t}\gets \{d_{1},\dots ,d_{n}\}$ 3: Iterative Optimization: $\mathcal{U}_t\gets \mathrm{APO}(\mathcal{D},F,\mathcal{U}_t,B_t)$ 4: $P_{t}^{*}\gets \arg \max_{P\in \mathcal{U}_{t}}F(\mathcal{D},P)$ 5: Initialize Description: $\mathcal{U}_c\gets \{\hat{P}_0\}$ , initializing with $P_{t}^{*}$ and prompt sampling strategy 6: Group Sampling: Sample $S$ groups by class salience 7: for $s = 1$ to $S$ do 8: Build Description Library: $B_{s}\gets \{\hat{d}_{1},\dots ,\hat{d}_{q}\}$ 9: Iterative Optimization: $\mathcal{U}_c\gets \mathrm{APO}(D,F,\mathcal{U}_c,B_s)$ 10: end for 11: $P^{*}\gets \arg \max_{P\in \mathcal{U}_{c}}F(\mathcal{D},P)$ 12: return candidate prompt with the highest score $P^{*}$ + +Algorithm 2 Automatic Prompt Optimization (APO) algorithm for VLMs - Lines 3 and 9 of Alg. 1, APO(D,F,U,B). + +Require: $\mathcal{D}\gets \{(x,y)\}_{n}$ : training samples, $F:\mathcal{D}\times P\to$ $\mathbb{R}$ : score function, $\mathcal{U}$ : candidate prompt set, $B$ : tem- plate or description library +1: Initialize Evaluation Score: $S\gets \{F(\mathcal{D},P)\}_{P\in \mathcal{U}}$ +2: for $t = 1$ to $T$ do +3: $\mathcal{U}_g\gets \emptyset$ +4: for all $P\in \mathcal{U}$ do +5: Edit-based Generate: $\mathcal{U}_g\gets \mathcal{U}_g\cup \mathrm{GEN}(P,B)$ +6: end for +7: Evaluate: $S_{g}\gets \{F(\mathcal{D},P^{\prime})\}_{P^{\prime}\in \mathcal{U}_{g}}$ +8: Update: $\mathcal{U}\gets \{\mathcal{U},\mathcal{U}_g\}$ and $S\gets \{S,S_g\}$ , retaining the top- $k$ of candidate prompts with high scores +9: Evolution-based Generate: $\mathcal{U}_e\gets \mathrm{EVO}(\mathcal{U},B)$ +10: Evaluate: $S_{e}\gets \{F(\mathcal{D},P^{\prime})\}_{P^{\prime}\in \mathcal{U}_{e}}$ +11: Update: $\mathcal{U}\gets \{\mathcal{U},\mathcal{U}_e\}$ and $S\gets \{S,S_e\}$ , retaining the top- $k$ of candidate prompts with high scores +12: end for +13: return the latest candidate prompt set $\mathcal{U}$ + +introduced in Sec. 3.3 to evaluate the candidate prompt $P$ on a limited training set $\mathcal{D} = \{(x,y)\}_{n}$ with one-shot supervision, where $x$ is an image and $y$ is its label. Finally, we use a test set to evaluate optimized prompts. Our goal is to refine prompts in the natural language space to achieve superior performance in per training sample $(x,y)$ : + +$$ +\underset {P} {\arg \max } F (\mathcal {D}, P) = \underset {P} {\arg \max } \mathbb {E} _ {(x, y)} [ F (\{(x, y) \}, P) ]. \tag {1} +$$ + +# 3.1. Automatic Template Optimization + +To mitigate issues of semantic ambiguity caused by class names, we first iteratively optimize the template to provide + +![](images/5ea67a56e1e271ca509f8d492e96a947fc7cfa3f6577256c477f177abc6f9f9c.jpg) +Figure 2. Overview of our ProAPO algorithm. We progressively refine prompts from task-specific (green lines) to class-specific (brown lines) levels. Specifically, we first explore the best template by an iterative optimization process (Sec. 3.1). For each iteration, ProAPO generates a set of candidate templates by several operators (Sec. 3.2) and filters/refines templates by a fitness score (Sec. 3.3). After several iterations, we choose the top-scoring template for description initialization. Subsequently, we introduce two sampling strategies to find a better initial point and reduce traversed categories (Sec. 3.4). Similar iterative optimization is then applied to class-specific descriptions. + +better task-specific contextual information. + +Template initialization offers a candidate prompt $P_0$ as a starting point in the language search space (Line 1 of Alg. 1). Similar to PN [36], we use "a photo of a {class}." filling with class names in the dataset as $P_0$ . + +Building template library aims to provide a set of templates (Line 2 of Alg. 1) for subsequent prompt generation. We denote template library as $B_{t} = \{d_{1},\dots ,d_{n}\}$ , where $d$ is a single template. Similar to PN [36], we can instruct LLMs with a one-time query to generate a set of templates as the library. Pre-defined templates, e.g., Template80 provided in CLIP [55], can also be used. Inspired by description-based methods [39, 58], we also supplement templates with dataset domain information generated by LLMs, such as "flower" for FLO and "bird" for CUB. + +Iterative optimization. Automatic prompt optimization (APO) algorithm is introduced to refine template set $\mathcal{U}_t$ by an evolution-based process (Line 3 of Alg. 1). As summarized in Alg. 2, each iteration of APO contains the process of: (1) Generate new candidate prompts $\mathcal{U}_g$ and $\mathcal{U}_e$ by several edit-based (Lines 4-6) and evolution-based (Line 9) operations based on the set $\mathcal{U}$ and library $B$ . (2) Evaluate each new candidate prompt (Lines 7 and 10) by a score function. We regard this score as an implied "gradient". (3) Update the prompt set $\mathcal{U}$ based on score (Lines 8 and 11). This process retains the top- $k$ of prompts with high scores to explore the search space around the current best candidates. Finally, we return the latest candidate set $\mathcal{U}$ . + +# 3.2. Prompt Generation by Several Operators + +Due to the explosion of class-specific prompts, it is costly and time-intensive to generate new prompts exclusively with LLMs like previous methods [19, 36]. To this end, we introduce edit-based and evolution-based operators to generate diverse candidate prompts from the library. + +Edit-based generation is introduced to create a set of new candidate prompts by several simple arithmetic operators. As shown in Alg. 3, we iteratively operate a candidate prompt $P$ with the library $B$ , where $\hat{d}$ in $P$ and $d$ in $B$ denotes a single template or description. The Select(·) op + +Algorithm 3 Edit-based prompt generation algorithm - Line 5 of Alg. 2, GEN(P,B). +Require: $P\gets \{\hat{d}_1,\dots ,\hat{d}_i\}$ : a candidate prompt, $B\gets$ $\{d_1,\dots ,d_j\}$ : template or description library +1: $\mathcal{U}_g\gets \emptyset$ +2: for $m = 1$ to $M$ do +3: $d_{add}\gets \mathrm{Select}(B)$ +4: $P_{add}\gets P\cup \{d_{add}\}$ Add +5: $d_{del}\gets \mathrm{Select}(P)$ +6: $P_{del}\gets P\setminus \{d_{del}\}$ $\triangleright$ Delete +7: $d_{in}\gets \mathrm{Select}(B)$ +8: $d_{out}\gets \mathrm{Select}(P)$ +9: $P_{rep}\gets (P\cup \{d_{in}\})\setminus \{d_{out}\}$ Replace +10: $\mathcal{U}_g\gets \mathcal{U}_g\cup \{P_{add},P_{del},P_{rep}\}$ +11: end for +12: return the generated candidate prompt set $\mathcal{U}_g$ + +erator samples an element from a given prompt set. Three operations are then applied to $P$ in each iteration: (1) Add a new element $d_{add}$ to $P$ . (2) Remove an existing element $d_{del}$ from $P$ . (3) Replace an element $d_{out}$ in $P$ with a new element $d_{in}$ in $B$ . These new candidates are ensembled around the current high-score candidate $P$ , which makes them more likely to succeed. Moreover, selecting elements from the library ensures differences between generated candidates. After $M$ -times steps, we return the latest set $\mathcal{U}_g$ . + +Evolution-based generation is introduced to improve search efficiency over random steps, as shown in Alg. 4. Inspired by widely used Generic Algorithm [20, 24, 42], we introduce crossover and mutation operators to enhance candidate generation. Crossover operator aims to find the optimal direction quickly by combining high-scoring candidate prompts. We randomly take the concatenation of two candidates $P_{c1}$ and $P_{c2}$ sampled from the current optimal set $\mathcal{U}$ , yielding a new candidate $P_{c}$ . Mutation operator aims to prevent convergence to local optima by introducing variations. We randomly add new elements selected from library $B$ into the candidate $P_{c}$ , yielding mutation candidate $P_{m}$ . After $N$ -times steps, we return the generated set $\mathcal{U}_{e}$ . + +Algorithm 4 Evolution-based generation algorithm - Line 9 of Alg. 2, EVO(U, B). +Require: $\mathcal{U}\gets \{P_1,\dots ,P_n\}$ : candidate prompt set, $B\gets$ $\{d_1,\dots ,d_j\}$ : template or description library +1: $\mathcal{U}_e\gets \emptyset$ +2: for $n = 1$ to $N$ do +3: $P_{c1}\gets \mathrm{Select}(\mathcal{U})$ +4: $P_{c2}\gets \mathrm{Select}(\mathcal{U})$ +5: $P_{c}\gets P_{c1}\cup P_{c2}$ $\triangleright$ Crossover +6: $P_{all}\gets B\cup P_c$ +7: $P_{m}\gets \mathrm{RANDOMSELECT}(P_{all},\mathrm{len}(P_{c}))\triangleright$ Mutation +8: $\mathcal{U}_e\gets \mathcal{U}_e\cup \{P_c,P_m\}$ +9: end for +10: return the generated candidate prompt set $\mathcal{U}_e$ + +# 3.3. Score Functions + +To measure candidate prompts, we introduce a fitness score to approximately obtain the "gradient" used for optimization. It contains the accuracy and an entropy constraint. + +Accuracy. Given an image $x$ , we obtain a prediction $\operatorname{pred}(x)$ that yields the highest cosine similarity: + +$$ +s (x, c) = \frac {1}{| D (c) |} \sum_ {d \in D (c)} \cos (I (x), T (d)). \tag {2} +$$ + +$$ +\operatorname {p r e d} (x) = \underset {c \in C} {\arg \max } s (x, c), \tag {3} +$$ + +where $D(c) \in P$ is a set with all prompts describing the category $c$ in candidate prompt $P$ , and $C$ is the entire category in the dataset. $I$ and $T$ are image encoder and text encoder, respectively. The accuracy is formulated as follows: + +$$ +\operatorname {A c c} = \mathbb {E} _ {(x, y) \in \mathcal {D}} [ \mathbb {I} (\operatorname {p r e d} (x) = y) ], \tag {4} +$$ + +where $\mathcal{D}$ is the training set and $\mathbb{I}(\cdot)$ is an indicator function. + +Entropy constrain. Previous methods [19, 36] only use accuracy as the evaluation metric. However, the overfitting problem appears as shown in Fig. 1(c). To this end, we include a simple entropy constrain, which penalizes the model to predict a higher probabilistic score in the true label $y$ : + +$$ +H = \mathbb {E} _ {(x, y) \in \mathcal {D}} [ - \log (s (x, y)) ]. \tag {5} +$$ + +The final score is formulated as follows: + +$$ +F (\mathcal {D}, P) = \operatorname {A c c} + \alpha H. \tag {6} +$$ + +where $\alpha$ is a scalar to balance them. In Sec. 4.4, we empirically show that this score effectively reduces overfitting. + +# 3.4. Sampling Strategy for Initialization + +After exploring the best template, we continue to optimize the class-specific descriptions. To save iteration costs, we introduce a prompt sampling strategy to find a better start point and a grouping sampling strategy to select some salient categories instead of all for iterative optimization. + +Prompt sampling strategy aims to initialize the class-specific candidate prompt $\hat{P}_0$ with the optimized template + +$P_{t}^{*}$ and high-score descriptions (Line 5 of Alg. 1). Similar to description-based methods [40, 52], we instruct LLM to generate a set of visual descriptions for each class. Besides, we replace the class name with its synonyms generated by LLMs to increase the number of descriptions. To obtain a better initial point, we randomly sample descriptions of each category to obtain multiple candidate prompts and select the one with the highest score as $\hat{P}_0$ . It ensures that subsequent optimization is around candidates with relatively high scores. More details are shown in Supp.B. + +Group sampling strategy aims to explore several salient categories into groups for optimization (Line 6 of Alg. 1). We consider two ways to sample categories. First, we select the groups with the lowest top- $n_{wst}$ accuracy and its misclassified categories. Moreover, we also choose salient groups by the category with the top- $n_{sln}$ result gains after adding descriptions and its misclassified categories. In the end, We use $S = n_{wst} + n_{sln}$ groups for optimization. More details are shown in Supp.C. In Sec. 4.4, experiments show that optimizing these selected categories can effectively improve performance and save costs. + +Building Library and Iterative Optimization for Descriptions. In Lines 7-10 of Alg. 1, we iteratively optimize the class-specific description in selected groups. Similar to template optimization, we first build the description library, which contains visual descriptions for categories in the specific group. Then, we apply APO algorithm to refine descriptions automatically. After several iterations, we use the candidate $P^{*}$ with the highest score as the final prompt. + +# 4. Experiments + +Datasets. Following prompt tuning [76, 77] and LLM-generated description works [40], we evaluate our ProAPO on thirteen downstream tasks, including ImageNet-1K (IN1K) [9], Caltech101 [13] (object recognition), StandfordCars [31], CUB200-2011 [67] (bird classification), DTD [7] (Textures), EuroSAT (ESAT) [23] (satellite images), FGVCAircraft [38], Flowers102 [45], Food101 [3], OxfordPets [50], Places365 [75], SUN397 [69] (scene recognition), UCF101 [63] (human action). + +Implementation details. In the default setting, we use template-80 pre-defined in CLIP [55] as the template library and CuPL [52] as the description library for searching the hyperparameters in a fixed language space. Dataset domain and synonym labels are generated by LLMs. This setting ensures a one-time query of LLMs, and no human intervention is required. If not explicitly stated, we set iteration times $T = 4$ in both template and description optimization, generated number $M = N = 8$ , $\alpha = 1e3$ , $n_{wst} = n_{sln} = \log(|C|)$ for all datasets, where $|C|$ is the number of classes. All results are average with four seeds. Besides, our ProAPO is implemented in PyTorch and runs with an RTX 3090 GPU. More details are shown in Supp.D. + +
ModuleTFIN-1KCaltechCarsCUBDTDESATFGVCFLOFoodPetsPlacesSUNUCFAvg (11)Avg (13)
ResNet-50 Backbone
CLIP (a photo of a {} )✓57.984.553.944.738.828.615.960.274.083.238.258.056.955.653.4
prompt tuning methods
CoOp [77]X57.287.555.6-44.450.69.668.174.385.9-60.361.959.6-
PLOT [6]X59.589.856.6-46.654.117.971.777.787.5-62.564.562.6-
ProGrad [79]X57.888.758.4-46.156.318.873.276.088.4-60.565.662.7-
automatic prompt optimization methods
PN [36]✓59.689.156.2-44.849.018.167.278.388.1-61.060.261.1-
ProAPO (ours)✓61.590.358.050.752.351.721.175.181.888.741.863.766.064.661.8
ViT-B/32 Backbone
CLIP (a photo of a {} )✓62.191.260.451.742.943.920.266.083.286.839.962.160.961.859.3
hand-engineered methods
Template-80 [55]✓63.591.660.451.242.852.619.566.184.287.441.663.562.963.160.6
FILIP-8 [71]✓63.891.460.752.743.454.318.967.084.687.541.263.965.063.761.1
DEFILIP-6 [8]✓62.591.059.951.141.346.418.866.584.387.540.262.363.662.259.6
description-based methods
DCLIP [40]✓63.392.759.452.744.138.419.466.183.988.141.265.065.862.460.0
Waffle [58]✓63.392.159.352.943.251.619.666.384.987.741.565.064.563.460.9
CuPL [52]✓64.492.960.753.350.650.520.969.584.287.043.166.366.464.962.3
GPT4Vis [68]✓63.593.161.452.748.547.021.469.884.388.142.764.265.764.361.7
AdaptCLIP [59]✓63.392.759.753.647.451.320.867.284.287.641.966.166.564.261.7
ProAPO w/ DCLIP✓64.193.260.653.648.259.422.671.584.288.742.766.068.066.063.3
ProAPO (ours)✓64.794.461.755.453.563.023.074.385.391.043.366.669.067.965.0
+ +Table 1. Comparison of our ProAPO with SOTA textual prompt-based methods. We report the top-1 accuracy (%) on the test set. The best and second best results of the same backbone for each dataset are bolded and underlined, respectively. Avg (11) and Avg (13) denote average results across 11 datasets (excluding CUB [67] and Places [75]) and all 13 datasets. TF denotes training-free approaches. + +# 4.1. Comparison with SOTA Methods + +Compared methods. We compare our results with state-of-the-art (SOTA) textual prompt-based methods, including vanilla CLIP with "a photo of a {}" template, prompt tuning methods [6, 77, 79], hand-engineered methods (i.e., best templates released by [8, 55, 71]), LLM-generated description methods [40, 52, 58, 59, 68], and automatic prompt optimization methods [36]. We test our ProAPO on two popular backbones (ResNet50 [21] and ViT-B/32 [12]). Prompt tuning and automatic prompt optimization methods are evaluated under one-shot supervision. + +Results. In Tab. 1, we see that our ProAPO consistently outperforms previous prompt-based methods across diverse datasets on ResNet50 and ViT-B/32 backbones. Our optimized prompts improve vanilla CLIP by an average of $8.4\%$ (from $53.4\%$ to $61.8\%$ ) on ResNet50 and $5.7\%$ (from $59.3\%$ to $65.0\%$ ) on ViT-B/32. Moreover, our training-free ProAPO surpasses gradient-based prompting methods (CoOp, PLOT, ProGrad) by at least $1.9\%$ average accuracy in eleven datasets. It shows optimizing prompts in a natural language space is more effective in low-shot tasks. Compared to template-optimized methods (i.e., PN and hand-engineered methods), our ProAPO achieves remarkable performance on fine-grained datasets, e.g., CUB, FLO, ESAT, and UCF. This is because class-specific descriptions provide fine-grained discriminative de + +tails. Our ProAPO also outperforms description-based methods, even with DCLIP as initialization. We improve performances of DCLIP and CuPL by $3.3\%$ and $2.7\%$ on average across thirteen datasets. Notably, it improves DCLIP and CuPL by $5.4\%$ and $4.8\%$ on FLO and by $21\%$ and $12.5\%$ on ESAT, confirming that iterative optimization of class-specific prompts enhances fine-grained recognition. + +Critical analysis. On datasets like ImageNet [9], Caltech [13], Places [75], and SUN [69], performance gains are relatively small. We attribute this to two reasons: First, datasets like ImageNet and Caltech contain coarse-grained categories. The differences between categories have become clearer with LLM-generated descriptions, eliminating the need for our method. Second, fine-grained datasets, such as Places and SUN for scene recognition, are easily confusing between different images, limiting performance from only textual side optimization. In Sec. 4.2, we show that adapter-based methods with our optimized prompt improve performance again after addressing issues of image confusion. Moreover, we observe that the language search space impacts performance. Since CuPL has better descriptions than DCLIP, our ProAPO with CuPL performs well. + +# 4.2. More Benefits by Optimal Prompts + +Transfer to adapter-based methods. In Fig. 3, we show the results of popular adapter-based methods [15, 66, 74, 80] with different prompt initialization, i.e., SOTA method + +![](images/0b20e8bec51d3b3e92b796bc2aca4bed61ef01b6cf4a41275a8a1a5583357b99.jpg) +(a) Training-free methods. + +![](images/160af41786585830ee9b282e8dd10218ced495ead64dbc88d6ec3bebcb54a58c.jpg) +(b) Fine-tuning methods. +Figure 3. Results of adapter-based methods with different initial prompts. Solid and dotted lines denote prompt initialization with ProAPO and CuPL, respectively. + +
ModuleShotsSourceTarget
RN50RN101ViT-B/32ViT-B/16
CLIP [55]057.960.661.966.6
CoOp [77]1663.020.631.739.5
PN [36]159.960.762.267.0
ProAPO161.562.164.669.9
+ +Table 2. Results of prompt transfer from ResNet-50 to other architectures. We report the top-1 accuracy in ImageNet-1K. + +![](images/93056dc3a886e4a4fdecd3874dffc0f3c47fe843ed9d70f8b56d900f17e3eb55.jpg) +Figure 4. Results of prompt transfer to different backbones. The value denotes performance gains compared to vanilla VLMs. Our optimized prompts of ResNet50 and ViT-B/32 are reported. + +CuPL [52] and our ProAPO. Adapter-based methods with ProAPO (solid lines) consistently surpass those with CuPL (dotted lines). It reveals that high-quality prompts make adapters perform better. Even in low shots, training with ProAPO achieves notable performance gains, which verifies its effectiveness. As the number of shots increases, adapters further improve results by enhancing image features. + +Transfer to different backbones. In Tab. 2, we report accuracy in ImageNet across different backbones, with prompts optimized on a source backbone (ResNet50) adapted to target backbones (ResNet101, ViT-B/32, ViT-B/16). We observe that CoOp [77] obtains a significant drop in accuracy on target backbones while our ProAPO maintains performance. It verifies that discrete prompts searched in natural language spaces transfer better than continuous prompts. ProAPO also outperforms PN, which reveals the effectiveness of class-specific optimization. Moreover, we achieve stable performance gains compared to CuPL [52] from source to target models in Fig. 4. It further verifies that ProAPO transfers easily across different backbones. + +![](images/e83c5891091559a7b1a3c86809e7b3510c3abc596436993d5797a8ab0ac0d63c.jpg) +(a) +Figure 5. Performance improvement analysis. (a) Analysis of the effect of single vs. ensemble prompts. * denotes results evaluated in the test set. ATO is our automatic template optimization algorithm. (b) Results of previous description-based methods with prompt optimization by our ATO and ProAPO algorithms. + +![](images/f119cfcc2312fe6d6ff623f993d2f0f75e83404177272ffc57a7dd65a7df80df.jpg) +(b) + +![](images/387ecd78d9b29ec6a4469cd8a025d23610f105fc2fe3daaf9ad8f9b4f6289449.jpg) +Figure 6. Qualitative analysis of class-specific prompt optimization by ProAPO. Shaded red and blue words denote common and discriminative descriptions in two confused categories. + +# 4.3. Performance Improvement Analysis + +In this section, we analyze the key reasons for the performance improvement of our ProAPO. + +Prompt ensembling is better than a single prompt. Compared to PN [36], we utilize prompt ensembling instead of a single prompt to optimize the template and description. To evaluate the effectiveness of prompt ensembling, we use Template-80 [55] as the template library and denote the prompts searched by the test set as the upper bound. As shown in Fig. 5(a), we observe that ensemble templates have a higher upper bound than the single template, consistent with prior work [8, 40, 71]. Similarly, we observe that our optimized templates achieve higher performance than PN [36], even better than the best single template, further verifying the effectiveness of our method. + +Iterative optimization improves prompt quality. In Fig. 6, we show the changes in descriptions with our ProAPO. After iterative optimization, common descriptions such as "flight over ocean" and "long wings and hooked bill" are removed. Discriminative descriptions are also retained in candidate prompts, e.g., "white body" for Laysan Albatross, and "black underpants" for Sooty Albatross. As such, we see a notable improvement in description-based methods [40, 52, 59, 68] with our ATO and ProAPO in Fig. 5(b) by at least $2.7\%$ average in thirteen datasets. It further verifies the effectiveness of our progressive optimization. + +
ComponentIN-1KAvg (11)Avg (13)
AddDelRepCrossMut
CLIP (Baseline)62.161.859.3
edit-based generation
a)✓63.866.063.3
b)✓✓64.666.463.8
c)✓✓64.466.563.8
d)✓✓✓64.666.764.0
evolution-based generation
e)✓✓✓✓64.667.364.5
f)✓✓✓✓64.767.164.3
g)✓✓✓✓✓64.767.965.0
+ +Table 3. Ablation of edit- and evolution-based operators. + +
Module (ViT-B/32)IN-1KAvg (11)Avg (13)Times
a) w/o prompt sampling64.467.364.512 min
b) w/o group sampling64.868.165.2306 min
c) w/o sampling strategies64.567.264.4302 min
ProAPO (full model)64.767.965.015 min
+ +Table 4. Ablation of two sampling strategies. + +# 4.4. Ablation Study + +Are both GEN and EVO algorithms necessary? In Tab. 3, we ablate edit- and evolution-based operators. For edit-based operators, we observe that the model with add, delete, and replace operations achieves a higher result in row d). After introducing evolution-based operators, i.e., crossover operator to combine advantages of high-scoring candidates, and mutation operator to avoid locally optimal solutions, we see an increase in performance in rows e)-g). It confirms that evolution-based operators make the model search the optimal prompt faster with limited iterations. + +Does sample strategies degrade performance? In Tab. 4, we ablate two sampling strategies for description optimization. Without the prompt sampling, we see a slight decrease in times while results drop in row a). It verifies the effectiveness of the prompt sampling in finding a better initial point. Without the group sampling to select salient categories for optimization, we observe a notable increase in time costs (from $15\mathrm{min}$ to $300+\mathrm{min}$ , 20 times) yet similar results in row b) and the full model. It reveals that group sampling simultaneously improves performance and efficiency. + +Which score function is better? In Fig. 7, we compare the different score functions, i.e., accuracy (used in PN [36]) and our fitness score, to evaluate the quality of the candidate prompt. PCCs (Pearson Correlation Coefficients) are introduced to evaluate the linear relationship between training metrics and test performance. The high PCC values mean a strong correlation. We see that the model with our fitness score achieves stable and high test results compared to previous score functions when achieving the best score. Besides, a higher PPC value further verifies that our fitness score effectively alleviates the overfitting problem. + +# 4.5. Hyperparameter Sensitivity + +How many iterations of Alg. 2 to use? In Fig. 8(a), we show the effect of iteration times $T$ in APO algorithm. As + +![](images/1422cb4fb01e0a9cb11c85fac5589417c144bd685c96d5d672770770d36c250f.jpg) +(a) Previous score function. + +![](images/ad36d704a88f07408ad69e596b499ce60ae8b37c4b85be1b47aa0646b325fb6e.jpg) +(b) Our fitness score + +![](images/eef2cb9cc956e7eddca66ec30699427c29e702c465f6d010e58839b7a315ba1c.jpg) +Figure 7. Effect of different score functions. Higher PCC values mean stronger correlations between training metrics and test results. Best Acc is the test result when achieving the best score. + +![](images/13d6a353a7ef56021b8d88d9fdcb78b124fd4353bed05ed36edd3585e097eca8.jpg) +(a) Iteration times $T$ +(b) Generated numbers + +![](images/f78abbc69d70a57e5e144db4dc10066f153170207e6aca9950616559306a268f.jpg) +(c) Sampling groups $S$ +Figure 8. The effect of hyperparameter analysis. The hyperparameter value set to 0 denotes the result of CuPL [52]. + +the number of iterations increases, we see a consistent performance improvement compared to the baseline CuPL. It demonstrates that iterative optimization improves prompt quality. Stable results are achieved when $T \geq 4$ . + +How many generated prompts to use? In Fig. 8(b), we show the effect of generated numbers in GEN and EVO algorithm, where we set $M = N$ . Similarly, progressive improvements are seen as generated numbers increase. We see a reliable result when $M = N \geq 8$ . It reveals the effectiveness of generating diverse candidates by our algorithm. + +Are more sampling groups better? In Fig. 8(c), we show the effect of the number of salient groups $S$ in the group sampling strategy. We see a notable improvement when $S = 2$ . As the number of groups $S$ increases, it achieves stable results when $S \geq 8$ . It verifies that optimizing several salient categories can achieve comparable performances with all categories and save iteration costs. + +# 5. Conclusion + +We propose an evolution-based algorithm for VLMs to progressively refine prompts from task-specific to class-specific levels. To save generation costs, ProAPO uses several edit- and evolution-based operators to create candidate prompts with a prompt library. Results show that our fitness score mitigates overfitting in class-specific prompts. We empirically verify that two sampling strategies improve performance and save iteration times. Extensive experiments on thirteen datasets reveal that ProAPO consistently outperforms SOTA textual prompt-based methods on low-shot tasks. Moreover, our method effectively improves adapter-based and description-based methods and easily transfers across different backbones. 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Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones. Our code is available at here." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 620, + 141, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 620, + 141, + 632 + ], + "spans": [ + { + "bbox": [ + 63, + 620, + 141, + 632 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 639, + 296, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 639, + 296, + 687 + ], + "spans": [ + { + "bbox": [ + 61, + 639, + 296, + 687 + ], + "type": "text", + "content": "In recent years, vision-language models (VLMs) [1, 27, 33, 43, 55, 64, 72, 73] pre-trained on large-scale paired imagedtext data, such as CLIP [55], have shown strong generalization on various image classification tasks. These mod" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 248, + 547, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 248, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 313, + 248, + 547, + 330 + ], + "type": "text", + "content": "els classify images by computing the similarity between the image and the prompt (a human-readable natural language) associated with a category. The prediction is the category with the highest similarity to the query image. Their performance highly relies on prompt quality, especially in fine-grained categories. Finding the optimal prompts for the downstream task becomes an urgent challenge [36, 52, 77]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 331, + 548, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 548, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 548, + 645 + ], + "type": "text", + "content": "Recent works have made efforts to improve prompt quality [4, 16, 55]. Manual prompt engineering [8, 55, 71] is a standard approach, writing several templates to include task-specific information, e.g., \"a photo of a {class}, a type of bird.\" for bird recognition. However, designing templates requires domain expertise, making it costly and challenging to scale [36, 39, 40, 52, 77]. Moreover, the template may lack details to recognize fine-grained categories as only the class name provides the distinct information in prompts [39, 52, 77]. Prompt tuning methods [6, 76, 77, 79] introduce a set of learnable tokens in the prompt to represent task-specific context, optimizing through gradient updates. While improving the performance of VLMs, they require additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39, 40, 52, 57, 68, 81] leverage the implicit knowledge of large language models (LLMs) [4, 48] to generate descriptions with class-specific details, enhancing generalization ability of VLMs. However, due to the hallucination in LLMs [25, 56], generated descriptions are suboptimal due to inaccurate, e.g., \"feet\" for the food Peking Duck, or lack discrimination for fine-grained recognition, e.g., the same descriptions \"hooked bill\" and \"webbed feet\" appear in Laysan Albatross and Sooty Albatross (see Fig. 1(a)), or exhibit non-visual descriptions, e.g., \"strong smell\" for Jackfruit. To this end, we propose the following key questions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 646, + 547, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 646, + 547, + 680 + ], + "spans": [ + { + "bbox": [ + 313, + 646, + 547, + 680 + ], + "type": "text", + "content": "How can we find the optimal class-specific prompts that are visually discriminative for fine-grained categories with minimal supervision and no human intervention?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 681, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 681, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 681, + 547, + 704 + ], + "type": "text", + "content": "Inspired by recent automatic prompt optimization (APO) methods [18, 53, 60, 78] in language tasks, we aim to opti" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "spans": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "spans": [ + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 73, + 693, + 148, + 704 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 693, + 148, + 704 + ], + "spans": [ + { + "bbox": [ + 73, + 693, + 148, + 704 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25145" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 103, + 82, + 146, + 125 + ], + "blocks": [ + { + "bbox": [ + 103, + 82, + 146, + 125 + ], + "lines": [ + { + "bbox": 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[ + 151, + 117, + 209, + 122 + ], + "type": "text", + "content": "- flight over the ocean" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 104, + 129, + 146, + 172 + ], + "blocks": [ + { + "bbox": [ + 104, + 129, + 146, + 172 + ], + "lines": [ + { + "bbox": [ + 104, + 129, + 146, + 172 + ], + "spans": [ + { + "bbox": [ + 104, + 129, + 146, + 172 + ], + "type": "image", + "image_path": "dbe349e7ec28f885c1e4bc7752aa5cff0ecac6499344b041851dca58b7392d00.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 151, + 131, + 197, + 138 + ], + "lines": [ + { + "bbox": [ + 151, + 131, + 197, + 138 + ], + "spans": [ + { + "bbox": [ + 151, + 131, + 197, + 138 + ], + "type": "text", + "content": "Sooty Albatross" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 116, + 174, + 217, + 182 + ], + "lines": [ + { + "bbox": [ + 116, + 174, + 217, + 182 + ], + "spans": [ + { + "bbox": [ + 116, + 174, + 217, + 182 + ], + "type": "text", + "content": "(a) Issues in generated descriptions." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 151, + 139, + 223, + 170 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 151, + 139, + 216, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 139, + 216, + 144 + ], + "spans": [ + { + "bbox": [ + 151, + 139, + 216, + 144 + ], + "type": "text", + "content": "large, dark-colored bird" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 151, + 145, + 223, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 145, + 223, + 150 + ], + "spans": [ + { + "bbox": [ + 151, + 145, + 223, + 150 + ], + "type": "text", + "content": "white band around its neck" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 151, + 151, + 190, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 151, + 190, + 156 + ], + "spans": [ + { + "bbox": [ + 151, + 151, + 190, + 156 + ], + "type": "text", + "content": "- webbed feet" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 151, + 157, + 200, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 157, + 200, + 163 + ], + "spans": [ + { + "bbox": [ + 151, + 157, + 200, + 163 + ], + "type": "text", + "content": "- long, hooked bill" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 151, + 163, + 216, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 163, + 216, + 170 + ], + "spans": [ + { + "bbox": [ + 151, + 163, + 216, + 170 + ], + "type": "text", + "content": "a species of albatross" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 247, + 92, + 366, + 182 + ], + "blocks": [ + { + "bbox": [ + 247, + 82, + 357, + 90 + ], + "lines": [ + { + "bbox": [ + 247, + 82, + 357, + 90 + ], + "spans": [ + { + "bbox": [ + 247, + 82, + 357, + 90 + ], + "type": "text", + "content": "Natural Language Prompt Search Space" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 247, + 92, + 366, + 182 + ], + "lines": [ + { + "bbox": [ + 247, + 92, + 366, + 182 + ], + "spans": [ + { + "bbox": [ + 247, + 92, + 366, + 182 + ], + "type": "image", + "image_path": "049a3c7aa48209e08d15461fce46f480bd79e53b91cccb9e82bc8e1e648c80e6.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 185, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 61, + 185, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 185, + 547, + 228 + ], + "type": "text", + "content": "Figure 1. Issues of optimizing class-specific prompts. (a) Due to the hallucination in LLMs, generated descriptions may be inaccurate and lack discrimination between fine-grained categories (see red words). (b) Compared to task-specific templates, we see an explosion in the number of class-specific prompts (see red rectangle). This leads to higher generation costs, iteration times, and the overfitting problem. (c) Overfitting problem: Multiple candidate prompts have the same best training accuracy but variable and low test results (see red circle)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 370, + 82, + 510, + 172 + ], + "blocks": [ + { + "bbox": [ + 370, + 82, + 510, + 172 + ], + "lines": [ + { + "bbox": [ + 370, + 82, + 510, + 172 + ], + "spans": [ + { + "bbox": [ + 370, + 82, + 510, + 172 + ], + "type": "image", + "image_path": "3b83463002562daf6374f429ecf87595bec2f86d3769b12fc80cec7d47281c33.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 399, + 174, + 501, + 182 + ], + "lines": [ + { + "bbox": [ + 399, + 174, + 501, + 182 + ], + "spans": [ + { + "bbox": [ + 399, + 174, + 501, + 182 + ], + "type": "text", + "content": "(c) Overfitting in evaluation metric." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "spans": [ + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "text", + "content": "mize class-specific prompts by an evolution-based process, removing confused prompts while retaining discriminative ones. We consider an approximate zero-shot setting, i.e., one-shot classification, where minimal supervision is introduced to evaluate the prompt quality. However, previous APO methods focus solely on task-specific template optimization. In contrast, except for templates, a class-specific prompt also contains a description associated with visual details in a category, as shown in Fig. 1(b). Compared with templates, class-specific optimization introduces new challenges due to the expanded search space (see Fig. 1(b)), which leads to: (1) High generation costs. As the search space grows, it is costly and time-consuming to generate class-specific prompts exclusively with LLMs at each iteration. (2) Long iteration times. Evaluating each candidate prompt in the search space may exponentially increase the iteration time, which is impractical in this scenario. (3) Overfitting problem. As shown in Fig. 1(c), multiple candidate prompts achieve variable and low test results (from " + }, + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "inline_equation", + "content": "63.6\\%" + }, + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "inline_equation", + "content": "64.3\\%" + }, + { + "bbox": [ + 61, + 237, + 296, + 470 + ], + "type": "text", + "content": ") at the best training accuracy." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 61, + 472, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 472, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 472, + 296, + 705 + ], + "type": "text", + "content": "To address these issues, we propose a Progressively Automatic Prompt Optimization (ProAPO) algorithm to iteratively optimize prompts from task-specific to class-specific levels. In each iteration, we use several edited-based (i.e., add, remove, and replace) and evolution-based operators (i.e., crossover, and mutation) to generate diverse candidate prompts from a prompt library. We query LLMs to generate this library in the initialization stage. Compared to querying LLMs at each iteration, these simple operations can effectively save generation costs. Then, we introduce a novel fitness score to evaluate generated candidate prompts and retain several top-scoring ones for the next iteration generation. An entropy constraint is added to the score to increase the soft prediction score and reduce overfitting. After several iterations, we return the best prompt for classification. To reduce iteration times in class-specific descriptions, we propose a prompt sampling strategy to find a better initial point in the search space and a group sampling strategy to explore a few salient classes instead of all for optimization. Our key contributions are:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 238, + 547, + 423 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 313, + 238, + 547, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 238, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 547, + 295 + ], + "type": "text", + "content": "- We propose an evolution-based algorithm to progressively optimize prompts from task-specific to class-specific levels with one-shot supervision and no human intervention. It solves issues of inaccuracy and lack of discrimination in LLM-generated descriptions." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 295, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 295, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 547, + 353 + ], + "type": "text", + "content": "- We address challenges in class-specific prompt optimization by an offline generation algorithm to reduce LLM querying costs, an entropy-constrained fitness score to prevent overfitting, and two sampling strategies to find an optimal initial point and reduce iteration times." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 354, + 547, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 547, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 547, + 423 + ], + "type": "text", + "content": "- Extensive experiments on thirteen datasets show that our proposed ProAPO consistently outperforms SOTA textual prompt-based methods and improves description-based methods in a challenging one-shot supervision. Moreover, our optimal prompts improve adapter-based methods and transfer effectively across different backbones." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 437, + 399, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 399, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 399, + 450 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 312, + 459, + 548, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 459, + 548, + 692 + ], + "spans": [ + { + "bbox": [ + 312, + 459, + 548, + 692 + ], + "type": "text", + "content": "Adaptation of VLMs for image classification tasks. Inspired by successes in VLMs, recent works aim to adapt them for image classification tasks. Some works utilize lightweight linear layers [26, 35, 49, 55, 62, 65, 82], adapters [15, 39], visual prompting [2, 28, 47], or cache models [66, 74, 80] to enhance visual features. Other works aim to improve the quality of prompts. Manual prompt engineering [8, 34, 55] applies task-specific information in prompt templates to enhance performance. However, templates need to be hand-written and lack fine-grained details [36, 39, 40, 52, 77]. Prompt tuning methods [6, 11, 22, 29, 30, 32, 37, 61, 76, 77, 79] learn task-specific context by a set of learnable tokens. However, they need additional training and lack interpretability [36, 40, 58]. In contrast, LLM-generated description methods [39-41, 44, 52, 54, 57, 59, 68, 81] exploit implicit knowledge in LLMs to generate visual descriptions for each category. They enrich semantics in prompts and offer interpretable predictions. In this work, we aim to further improve description quality through an evolution process." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 693, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 547, + 705 + ], + "type": "text", + "content": "LLM-generated description methods apply class-specific" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25146" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 61, + 81, + 296, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 81, + 296, + 243 + ], + "spans": [ + { + "bbox": [ + 61, + 81, + 296, + 243 + ], + "type": "text", + "content": "descriptions to language prompts to adapt VLMs for classification. DCLIP [40] and CuPL [52] design prompts such as \"What does a {class} look like?\" to instruct LLMs to generate category descriptions. GPT4Vis [68] and VDT [39] use GPT-4 [48] for rich and diverse descriptions. Some work utilizes LLM-generated hierarchy labels [46] or descriptions [57] to recognize images from coarse to fine-grained levels. However, due to the hallucination in LLMs, generated descriptions might be inaccurate, non-visual, and lack discrimination [40, 57, 58]. To this end, we propose ProAPO to iteratively remove ambiguous and retain discriminative prompts. Moreover, category names, ignored in previous methods, are equally crucial for improving accuracy and are introduced in our optimization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 243, + 298, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 243, + 298, + 454 + ], + "spans": [ + { + "bbox": [ + 61, + 243, + 298, + 454 + ], + "type": "text", + "content": "Automatic prompt optimization aims to automatically find optimal prompts for language tasks, overcoming the time-consuming issue in manual prompt methods [5]. Early methods [10, 51, 60] generate discrete prompts by filling templates with trigger tokens, iteratively refining prompts by mining, generation, or paraphrasing. Recently, chat-based LLMs have been applied as prompt engineers [14, 17, 18, 53, 70, 78], using a meta-prompt with task information to find optimal prompt design. PN [36] is the first to instruct LLMs to optimize templates on multimodal tasks, which feeds visual feedback of the best and worst templates to guide. However, these methods only optimize task-specific templates. iCM [19] is somewhat similar to ours, optimizing class-specific prompts with chat-based LLMs. However, it uses the whole validation set as supervision. In contrast, we optimize prompts with one-shot supervision and propose solutions to solve high generation costs, long iteration times, and overfitting in class-specific optimization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 464, + 117, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 464, + 117, + 475 + ], + "spans": [ + { + "bbox": [ + 62, + 464, + 117, + 475 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 483, + 296, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 483, + 296, + 564 + ], + "spans": [ + { + "bbox": [ + 61, + 483, + 296, + 564 + ], + "type": "text", + "content": "Our ProAPO algorithm is shown in Fig. 2 and summarized in Alg. 1. We first describe iterative optimization in templates (Sec. 3.1). For each iteration, candidates are generated by several operators (Sec. 3.2) and then evaluated by a fitness score (Sec. 3.3). Afterward, similar iterative optimization is applied in descriptions, where we introduce two sampling strategies to save iteration costs (Sec. 3.4)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "spans": [ + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "text", + "content": "Preliminaries. Given an image, CLIP [55] predicts by selecting the highest similarity between the image and category prompt. The category prompt is a human-readable natural language associated with a category, which contains a template, e.g., \"a photo of a bird: {class}. {description} \"., and class-specific descriptions, e.g., class name \"Laysan Albatross\" and its descriptions \"It has white with black wings\". Some categories may use multiple prompts with varied templates or descriptions, i.e., prompt ensembling. We denote the prompt set that includes all categories in the task as a candidate prompt " + }, + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "text", + "content": ". A score function " + }, + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "inline_equation", + "content": "F: \\mathcal{D} \\times P \\to \\mathbb{R}" + }, + { + "bbox": [ + 61, + 564, + 297, + 706 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 81, + 548, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 81, + 548, + 116 + ], + "spans": [ + { + "bbox": [ + 313, + 81, + 548, + 116 + ], + "type": "text", + "content": "Algorithm 1 Our Progressively Automatic Prompt Optimization (ProAPO) for visual classification, which iteratively refines prompts from task-specific to class-specific." + } + ] + } + ], + "index": 5 + }, + { + "type": "code", + "bbox": [ + 315, + 120, + 547, + 296 + ], + "blocks": [ + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "lines": [ + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "spans": [ + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{D}\\gets \\{(x,y)\\}_{n}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " training samples, " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "F:\\mathcal{D}\\times P\\to" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " R: score function 1: Initialize Template: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_t\\gets \\{P_0\\}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 2: Build Template Library: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "B_{t}\\gets \\{d_{1},\\dots ,d_{n}\\}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 3: Iterative Optimization: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_t\\gets \\mathrm{APO}(\\mathcal{D},F,\\mathcal{U}_t,B_t)" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 4: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "P_{t}^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{t}}F(\\mathcal{D},P)" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 5: Initialize Description: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_c\\gets \\{\\hat{P}_0\\}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " , initializing with " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "P_{t}^{*}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " and prompt sampling strategy 6: Group Sampling: Sample " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " groups by class salience 7: for " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "s = 1" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " do 8: Build Description Library: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "B_{s}\\gets \\{\\hat{d}_{1},\\dots ,\\hat{d}_{q}\\}" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 9: Iterative Optimization: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_c\\gets \\mathrm{APO}(D,F,\\mathcal{U}_c,B_s)" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 10: end for 11: " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "P^{*}\\gets \\arg \\max_{P\\in \\mathcal{U}_{c}}F(\\mathcal{D},P)" + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "text", + "content": " 12: return candidate prompt with the highest score " + }, + { + "bbox": [ + 315, + 120, + 547, + 296 + ], + "type": "inline_equation", + "content": "P^{*}" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_body" + } + ], + "index": 6, + "sub_type": "algorithm" + }, + { + "bbox": [ + 314, + 314, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 314, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 314, + 314, + 547, + 338 + ], + "type": "text", + "content": "Algorithm 2 Automatic Prompt Optimization (APO) algorithm for VLMs - Lines 3 and 9 of Alg. 1, APO(D,F,U,B)." + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 315, + 341, + 547, + 552 + ], + "blocks": [ + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "lines": [ + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{D}\\gets \\{(x,y)\\}_{n}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " : training samples, " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "F:\\mathcal{D}\\times P\\to" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathbb{R}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " : score function, " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " : candidate prompt set, " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " : tem- plate or description library \n1: Initialize Evaluation Score: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "S\\gets \\{F(\\mathcal{D},P)\\}_{P\\in \\mathcal{U}}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n2: for " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " do \n3: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g\\gets \\emptyset" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n4: for all " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "P\\in \\mathcal{U}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " do \n5: Edit-based Generate: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\mathrm{GEN}(P,B)" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n6: end for \n7: Evaluate: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "S_{g}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{g}}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n8: Update: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_g\\}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "S\\gets \\{S,S_g\\}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " , retaining the top- " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " of candidate prompts with high scores \n9: Evolution-based Generate: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_e\\gets \\mathrm{EVO}(\\mathcal{U},B)" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n10: Evaluate: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "S_{e}\\gets \\{F(\\mathcal{D},P^{\\prime})\\}_{P^{\\prime}\\in \\mathcal{U}_{e}}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " \n11: Update: " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}\\gets \\{\\mathcal{U},\\mathcal{U}_e\\}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "S\\gets \\{S,S_e\\}" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " , retaining the top- " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "text", + "content": " of candidate prompts with high scores \n12: end for \n13: return the latest candidate prompt set " + }, + { + "bbox": [ + 315, + 341, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_body" + } + ], + "index": 8, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": "introduced in Sec. 3.3 to evaluate the candidate prompt " + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": " on a limited training set " + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x,y)\\}_{n}" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": " with one-shot supervision, where " + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": " is an image and " + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": " is its label. Finally, we use a test set to evaluate optimized prompts. Our goal is to refine prompts in the natural language space to achieve superior performance in per training sample " + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 313, + 564, + 548, + 635 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 636, + 547, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 636, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 318, + 636, + 547, + 656 + ], + "type": "interline_equation", + "content": "\\underset {P} {\\arg \\max } F (\\mathcal {D}, P) = \\underset {P} {\\arg \\max } \\mathbb {E} _ {(x, y)} [ F (\\{(x, y) \\}, P) ]. \\tag {1}", + "image_path": "09ad272f01863931d6208d968b73987852d094eb265bca4de47614f6646a2cc0.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 662, + 492, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 662, + 492, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 662, + 492, + 675 + ], + "type": "text", + "content": "3.1. Automatic Template Optimization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 681, + 548, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 681, + 548, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 681, + 548, + 705 + ], + "type": "text", + "content": "To mitigate issues of semantic ambiguity caused by class names, we first iteratively optimize the template to provide" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 744 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 744 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 744 + ], + "type": "text", + "content": "25147" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 94, + 78, + 517, + 170 + ], + "blocks": [ + { + "bbox": [ + 94, + 78, + 517, + 170 + ], + "lines": [ + { + "bbox": [ + 94, + 78, + 517, + 170 + ], + "spans": [ + { + "bbox": [ + 94, + 78, + 517, + 170 + ], + "type": "image", + "image_path": "5ea67a56e1e271ca509f8d492e96a947fc7cfa3f6577256c477f177abc6f9f9c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 174, + 548, + 229 + ], + "lines": [ + { + "bbox": [ + 61, + 174, + 548, + 229 + ], + "spans": [ + { + "bbox": [ + 61, + 174, + 548, + 229 + ], + "type": "text", + "content": "Figure 2. Overview of our ProAPO algorithm. We progressively refine prompts from task-specific (green lines) to class-specific (brown lines) levels. Specifically, we first explore the best template by an iterative optimization process (Sec. 3.1). For each iteration, ProAPO generates a set of candidate templates by several operators (Sec. 3.2) and filters/refines templates by a fitness score (Sec. 3.3). After several iterations, we choose the top-scoring template for description initialization. Subsequently, we introduce two sampling strategies to find a better initial point and reduce traversed categories (Sec. 3.4). Similar iterative optimization is then applied to class-specific descriptions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 239, + 231, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 239, + 231, + 250 + ], + "spans": [ + { + "bbox": [ + 61, + 239, + 231, + 250 + ], + "type": "text", + "content": "better task-specific contextual information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "spans": [ + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "text", + "content": "Template initialization offers a candidate prompt " + }, + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "inline_equation", + "content": "P_0" + }, + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "text", + "content": " as a starting point in the language search space (Line 1 of Alg. 1). Similar to PN [36], we use \"a photo of a {class}.\" filling with class names in the dataset as " + }, + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "inline_equation", + "content": "P_0" + }, + { + "bbox": [ + 61, + 250, + 296, + 297 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "spans": [ + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "text", + "content": "Building template library aims to provide a set of templates (Line 2 of Alg. 1) for subsequent prompt generation. We denote template library as " + }, + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "inline_equation", + "content": "B_{t} = \\{d_{1},\\dots ,d_{n}\\}" + }, + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 61, + 297, + 296, + 412 + ], + "type": "text", + "content": " is a single template. Similar to PN [36], we can instruct LLMs with a one-time query to generate a set of templates as the library. Pre-defined templates, e.g., Template80 provided in CLIP [55], can also be used. Inspired by description-based methods [39, 58], we also supplement templates with dataset domain information generated by LLMs, such as \"flower\" for FLO and \"bird\" for CUB." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "spans": [ + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": "Iterative optimization. Automatic prompt optimization (APO) algorithm is introduced to refine template set " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_t" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " by an evolution-based process (Line 3 of Alg. 1). As summarized in Alg. 2, each iteration of APO contains the process of: (1) Generate new candidate prompts " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_e" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " by several edit-based (Lines 4-6) and evolution-based (Line 9) operations based on the set " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " and library " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": ". (2) Evaluate each new candidate prompt (Lines 7 and 10) by a score function. We regard this score as an implied \"gradient\". (3) Update the prompt set " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " based on score (Lines 8 and 11). This process retains the top-" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": " of prompts with high scores to explore the search space around the current best candidates. Finally, we return the latest candidate set " + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 61, + 413, + 296, + 564 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 571, + 274, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 571, + 274, + 583 + ], + "spans": [ + { + "bbox": [ + 62, + 571, + 274, + 583 + ], + "type": "text", + "content": "3.2. Prompt Generation by Several Operators" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 588, + 295, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 588, + 295, + 646 + ], + "spans": [ + { + "bbox": [ + 61, + 588, + 295, + 646 + ], + "type": "text", + "content": "Due to the explosion of class-specific prompts, it is costly and time-intensive to generate new prompts exclusively with LLMs like previous methods [19, 36]. To this end, we introduce edit-based and evolution-based operators to generate diverse candidate prompts from the library." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": "Edit-based generation is introduced to create a set of new candidate prompts by several simple arithmetic operators. As shown in Alg. 3, we iteratively operate a candidate prompt " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": " with the library " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "\\hat{d}" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 61, + 647, + 296, + 705 + ], + "type": "text", + "content": " denotes a single template or description. The Select(·) op" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 315, + 266, + 547, + 434 + ], + "blocks": [ + { + "bbox": [ + 313, + 238, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 313, + 238, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 547, + 262 + ], + "type": "text", + "content": "Algorithm 3 Edit-based prompt generation algorithm - Line 5 of Alg. 2, GEN(P,B)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "lines": [ + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "P\\gets \\{\\hat{d}_1,\\dots ,\\hat{d}_i\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " : a candidate prompt, " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "B\\gets" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\{d_1,\\dots ,d_j\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " : template or description library \n1: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g\\gets \\emptyset" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n2: for " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "m = 1" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " do \n3: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "d_{add}\\gets \\mathrm{Select}(B)" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "P_{add}\\gets P\\cup \\{d_{add}\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " Add \n5: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "d_{del}\\gets \\mathrm{Select}(P)" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "P_{del}\\gets P\\setminus \\{d_{del}\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " Delete \n7: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "d_{in}\\gets \\mathrm{Select}(B)" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "d_{out}\\gets \\mathrm{Select}(P)" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n9: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "P_{rep}\\gets (P\\cup \\{d_{in}\\})\\setminus \\{d_{out}\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " Replace \n10: " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g\\gets \\mathcal{U}_g\\cup \\{P_{add},P_{del},P_{rep}\\}" + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "text", + "content": " \n11: end for \n12: return the generated candidate prompt set " + }, + { + "bbox": [ + 315, + 266, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "spans": [ + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": "erator samples an element from a given prompt set. Three operations are then applied to " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " in each iteration: (1) Add a new element " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "d_{add}" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": ". (2) Remove an existing element " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "d_{del}" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": ". (3) Replace an element " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "d_{out}" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " with a new element " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "d_{in}" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": ". These new candidates are ensembled around the current high-score candidate " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": ", which makes them more likely to succeed. Moreover, selecting elements from the library ensures differences between generated candidates. After " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": "-times steps, we return the latest set " + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_g" + }, + { + "bbox": [ + 312, + 445, + 548, + 551 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": "Evolution-based generation is introduced to improve search efficiency over random steps, as shown in Alg. 4. Inspired by widely used Generic Algorithm [20, 24, 42], we introduce crossover and mutation operators to enhance candidate generation. Crossover operator aims to find the optimal direction quickly by combining high-scoring candidate prompts. We randomly take the concatenation of two candidates " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "P_{c1}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "P_{c2}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": " sampled from the current optimal set " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": ", yielding a new candidate " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "P_{c}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": ". Mutation operator aims to prevent convergence to local optima by introducing variations. We randomly add new elements selected from library " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": " into the candidate " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "P_{c}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": ", yielding mutation candidate " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "P_{m}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": ". After " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": "-times steps, we return the generated set " + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{e}" + }, + { + "bbox": [ + 313, + 553, + 548, + 705 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25148" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 63, + 107, + 296, + 250 + ], + "blocks": [ + { + "bbox": [ + 62, + 81, + 296, + 104 + ], + "lines": [ + { + "bbox": [ + 62, + 81, + 296, + 104 + ], + "spans": [ + { + "bbox": [ + 62, + 81, + 296, + 104 + ], + "type": "text", + "content": "Algorithm 4 Evolution-based generation algorithm - Line 9 of Alg. 2, EVO(U, B)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "lines": [ + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "spans": [ + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\mathcal{U}\\gets \\{P_1,\\dots ,P_n\\}" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " : candidate prompt set, " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "B\\gets" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\{d_1,\\dots ,d_j\\}" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " : template or description library \n1: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_e\\gets \\emptyset" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " \n2: for " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " do \n3: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "P_{c1}\\gets \\mathrm{Select}(\\mathcal{U})" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "P_{c2}\\gets \\mathrm{Select}(\\mathcal{U})" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "P_{c}\\gets P_{c1}\\cup P_{c2}" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " Crossover \n6: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "P_{all}\\gets B\\cup P_c" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "P_{m}\\gets \\mathrm{RANDOMSELECT}(P_{all},\\mathrm{len}(P_{c}))\\triangleright" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " Mutation \n8: " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_e\\gets \\mathcal{U}_e\\cup \\{P_c,P_m\\}" + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "text", + "content": " \n9: end for \n10: return the generated candidate prompt set " + }, + { + "bbox": [ + 63, + 107, + 296, + 250 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_e" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 62, + 261, + 157, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 261, + 157, + 273 + ], + "spans": [ + { + "bbox": [ + 62, + 261, + 157, + 273 + ], + "type": "text", + "content": "3.3. Score Functions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 279, + 296, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 279, + 296, + 314 + ], + "spans": [ + { + "bbox": [ + 61, + 279, + 296, + 314 + ], + "type": "text", + "content": "To measure candidate prompts, we introduce a fitness score to approximately obtain the \"gradient\" used for optimization. It contains the accuracy and an entropy constraint." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "spans": [ + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "text", + "content": "Accuracy. Given an image " + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "text", + "content": ", we obtain a prediction " + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "inline_equation", + "content": "\\operatorname{pred}(x)" + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "text", + "content": " that yields the highest cosine similarity:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 339, + 295, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 339, + 295, + 368 + ], + "spans": [ + { + "bbox": [ + 99, + 339, + 295, + 368 + ], + "type": "interline_equation", + "content": "s (x, c) = \\frac {1}{| D (c) |} \\sum_ {d \\in D (c)} \\cos (I (x), T (d)). \\tag {2}", + "image_path": "cae54346fd145d7be5f99ec39648c7d0ee580f5e0e5e3b1f7db30c0593b0dc45.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 372, + 295, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 372, + 295, + 390 + ], + "spans": [ + { + "bbox": [ + 94, + 372, + 295, + 390 + ], + "type": "interline_equation", + "content": "\\operatorname {p r e d} (x) = \\underset {c \\in C} {\\arg \\max } s (x, c), \\tag {3}", + "image_path": "8153193728c171395dc041d74117470c5dacc0692b899a2efea23c736b6e9447.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "spans": [ + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "D(c) \\in P" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": " is a set with all prompts describing the category " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": " in candidate prompt " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": " is the entire category in the dataset. " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 61, + 392, + 296, + 439 + ], + "type": "text", + "content": " are image encoder and text encoder, respectively. The accuracy is formulated as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 442, + 295, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 442, + 295, + 455 + ], + "spans": [ + { + "bbox": [ + 111, + 442, + 295, + 455 + ], + "type": "interline_equation", + "content": "\\operatorname {A c c} = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ \\mathbb {I} (\\operatorname {p r e d} (x) = y) ], \\tag {4}", + "image_path": "33bb8bdef159ba0335917b40cd17467c5ba334f75101195e80a8fd0fb2c65bde.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "text", + "content": " is the training set and " + }, + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "inline_equation", + "content": "\\mathbb{I}(\\cdot)" + }, + { + "bbox": [ + 62, + 456, + 295, + 468 + ], + "type": "text", + "content": " is an indicator function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 469, + 296, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 469, + 296, + 526 + ], + "spans": [ + { + "bbox": [ + 61, + 469, + 296, + 526 + ], + "type": "text", + "content": "Entropy constrain. Previous methods [19, 36] only use accuracy as the evaluation metric. However, the overfitting problem appears as shown in Fig. 1(c). To this end, we include a simple entropy constrain, which penalizes the model to predict a higher probabilistic score in the true label " + }, + { + "bbox": [ + 61, + 469, + 296, + 526 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 61, + 469, + 296, + 526 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 116, + 529, + 295, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 529, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 116, + 529, + 295, + 543 + ], + "type": "interline_equation", + "content": "H = \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} [ - \\log (s (x, y)) ]. \\tag {5}", + "image_path": "37378554ffd9b76ebedcdb313784008ed3bb90a1b63b0994285ae05ab84f6ad2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 62, + 544, + 222, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 544, + 222, + 555 + ], + "spans": [ + { + "bbox": [ + 62, + 544, + 222, + 555 + ], + "type": "text", + "content": "The final score is formulated as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 131, + 559, + 295, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 559, + 295, + 571 + ], + "spans": [ + { + "bbox": [ + 131, + 559, + 295, + 571 + ], + "type": "interline_equation", + "content": "F (\\mathcal {D}, P) = \\operatorname {A c c} + \\alpha H. \\tag {6}", + "image_path": "96e0b0eff804ff14fe570e6ab1723067792efd79019732e41fd1be3ce0d45c3b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 61, + 573, + 296, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 573, + 296, + 597 + ], + "spans": [ + { + "bbox": [ + 61, + 573, + 296, + 597 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 61, + 573, + 296, + 597 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 61, + 573, + 296, + 597 + ], + "type": "text", + "content": " is a scalar to balance them. In Sec. 4.4, we empirically show that this score effectively reduces overfitting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 62, + 605, + 246, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 605, + 246, + 617 + ], + "spans": [ + { + "bbox": [ + 62, + 605, + 246, + 617 + ], + "type": "text", + "content": "3.4. Sampling Strategy for Initialization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 61, + 622, + 296, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 622, + 296, + 681 + ], + "spans": [ + { + "bbox": [ + 61, + 622, + 296, + 681 + ], + "type": "text", + "content": "After exploring the best template, we continue to optimize the class-specific descriptions. To save iteration costs, we introduce a prompt sampling strategy to find a better start point and a grouping sampling strategy to select some salient categories instead of all for iterative optimization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "content": "Prompt sampling strategy aims to initialize the class-specific candidate prompt " + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "inline_equation", + "content": "\\hat{P}_0" + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "content": " with the optimized template" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "spans": [ + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "type": "inline_equation", + "content": "P_{t}^{*}" + }, + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "type": "text", + "content": " and high-score descriptions (Line 5 of Alg. 1). Similar to description-based methods [40, 52], we instruct LLM to generate a set of visual descriptions for each class. Besides, we replace the class name with its synonyms generated by LLMs to increase the number of descriptions. To obtain a better initial point, we randomly sample descriptions of each category to obtain multiple candidate prompts and select the one with the highest score as " + }, + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "type": "inline_equation", + "content": "\\hat{P}_0" + }, + { + "bbox": [ + 313, + 81, + 547, + 197 + ], + "type": "text", + "content": ". It ensures that subsequent optimization is around candidates with relatively high scores. More details are shown in Supp.B." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "text", + "content": "Group sampling strategy aims to explore several salient categories into groups for optimization (Line 6 of Alg. 1). We consider two ways to sample categories. First, we select the groups with the lowest top-" + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "inline_equation", + "content": "n_{wst}" + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "text", + "content": " accuracy and its misclassified categories. Moreover, we also choose salient groups by the category with the top-" + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "inline_equation", + "content": "n_{sln}" + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "text", + "content": " result gains after adding descriptions and its misclassified categories. In the end, We use " + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "inline_equation", + "content": "S = n_{wst} + n_{sln}" + }, + { + "bbox": [ + 313, + 198, + 547, + 325 + ], + "type": "text", + "content": " groups for optimization. More details are shown in Supp.C. In Sec. 4.4, experiments show that optimizing these selected categories can effectively improve performance and save costs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 325, + 547, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 325, + 547, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 325, + 547, + 419 + ], + "type": "text", + "content": "Building Library and Iterative Optimization for Descriptions. In Lines 7-10 of Alg. 1, we iteratively optimize the class-specific description in selected groups. Similar to template optimization, we first build the description library, which contains visual descriptions for categories in the specific group. Then, we apply APO algorithm to refine descriptions automatically. After several iterations, we use the candidate " + }, + { + "bbox": [ + 313, + 325, + 547, + 419 + ], + "type": "inline_equation", + "content": "P^{*}" + }, + { + "bbox": [ + 313, + 325, + 547, + 419 + ], + "type": "text", + "content": " with the highest score as the final prompt." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 429, + 392, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 429, + 392, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 392, + 442 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 449, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 547, + 553 + ], + "type": "text", + "content": "Datasets. Following prompt tuning [76, 77] and LLM-generated description works [40], we evaluate our ProAPO on thirteen downstream tasks, including ImageNet-1K (IN1K) [9], Caltech101 [13] (object recognition), StandfordCars [31], CUB200-2011 [67] (bird classification), DTD [7] (Textures), EuroSAT (ESAT) [23] (satellite images), FGVCAircraft [38], Flowers102 [45], Food101 [3], OxfordPets [50], Places365 [75], SUN397 [69] (scene recognition), UCF101 [63] (human action)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": "Implementation details. In the default setting, we use template-80 pre-defined in CLIP [55] as the template library and CuPL [52] as the description library for searching the hyperparameters in a fixed language space. Dataset domain and synonym labels are generated by LLMs. This setting ensures a one-time query of LLMs, and no human intervention is required. If not explicitly stated, we set iteration times " + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "inline_equation", + "content": "T = 4" + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": " in both template and description optimization, generated number " + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "inline_equation", + "content": "M = N = 8" + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "inline_equation", + "content": "\\alpha = 1e3" + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "inline_equation", + "content": "n_{wst} = n_{sln} = \\log(|C|)" + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": " for all datasets, where " + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "inline_equation", + "content": "|C|" + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": " is the number of classes. All results are average with four seeds. Besides, our ProAPO is implemented in PyTorch and runs with an RTX 3090 GPU. More details are shown in Supp.D." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25149" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 98, + 79, + 512, + 343 + ], + "blocks": [ + { + "bbox": [ + 98, + 79, + 512, + 343 + ], + "lines": [ + { + "bbox": [ + 98, + 79, + 512, + 343 + ], + "spans": [ + { + "bbox": [ + 98, + 79, + 512, + 343 + ], + "type": "table", + "html": "
ModuleTFIN-1KCaltechCarsCUBDTDESATFGVCFLOFoodPetsPlacesSUNUCFAvg (11)Avg (13)
ResNet-50 Backbone
CLIP (a photo of a {} )✓57.984.553.944.738.828.615.960.274.083.238.258.056.955.653.4
prompt tuning methods
CoOp [77]X57.287.555.6-44.450.69.668.174.385.9-60.361.959.6-
PLOT [6]X59.589.856.6-46.654.117.971.777.787.5-62.564.562.6-
ProGrad [79]X57.888.758.4-46.156.318.873.276.088.4-60.565.662.7-
automatic prompt optimization methods
PN [36]✓59.689.156.2-44.849.018.167.278.388.1-61.060.261.1-
ProAPO (ours)✓61.590.358.050.752.351.721.175.181.888.741.863.766.064.661.8
ViT-B/32 Backbone
CLIP (a photo of a {} )✓62.191.260.451.742.943.920.266.083.286.839.962.160.961.859.3
hand-engineered methods
Template-80 [55]✓63.591.660.451.242.852.619.566.184.287.441.663.562.963.160.6
FILIP-8 [71]✓63.891.460.752.743.454.318.967.084.687.541.263.965.063.761.1
DEFILIP-6 [8]✓62.591.059.951.141.346.418.866.584.387.540.262.363.662.259.6
description-based methods
DCLIP [40]✓63.392.759.452.744.138.419.466.183.988.141.265.065.862.460.0
Waffle [58]✓63.392.159.352.943.251.619.666.384.987.741.565.064.563.460.9
CuPL [52]✓64.492.960.753.350.650.520.969.584.287.043.166.366.464.962.3
GPT4Vis [68]✓63.593.161.452.748.547.021.469.884.388.142.764.265.764.361.7
AdaptCLIP [59]✓63.392.759.753.647.451.320.867.284.287.641.966.166.564.261.7
ProAPO w/ DCLIP✓64.193.260.653.648.259.422.671.584.288.742.766.068.066.063.3
ProAPO (ours)✓64.794.461.755.453.563.023.074.385.391.043.366.669.067.965.0
", + "image_path": "745e43a5286c8ed0ec898df686aca54bc5a42a91ab05b6a99a2130ad403db35c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 346, + 548, + 381 + ], + "lines": [ + { + "bbox": [ + 61, + 346, + 548, + 381 + ], + "spans": [ + { + "bbox": [ + 61, + 346, + 548, + 381 + ], + "type": "text", + "content": "Table 1. Comparison of our ProAPO with SOTA textual prompt-based methods. We report the top-1 accuracy (%) on the test set. The best and second best results of the same backbone for each dataset are bolded and underlined, respectively. Avg (11) and Avg (13) denote average results across 11 datasets (excluding CUB [67] and Places [75]) and all 13 datasets. TF denotes training-free approaches." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 62, + 388, + 237, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 388, + 237, + 400 + ], + "spans": [ + { + "bbox": [ + 62, + 388, + 237, + 400 + ], + "type": "text", + "content": "4.1. Comparison with SOTA Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 410, + 296, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 410, + 296, + 526 + ], + "spans": [ + { + "bbox": [ + 61, + 410, + 296, + 526 + ], + "type": "text", + "content": "Compared methods. We compare our results with state-of-the-art (SOTA) textual prompt-based methods, including vanilla CLIP with \"a photo of a {}\" template, prompt tuning methods [6, 77, 79], hand-engineered methods (i.e., best templates released by [8, 55, 71]), LLM-generated description methods [40, 52, 58, 59, 68], and automatic prompt optimization methods [36]. We test our ProAPO on two popular backbones (ResNet50 [21] and ViT-B/32 [12]). Prompt tuning and automatic prompt optimization methods are evaluated under one-shot supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": "Results. In Tab. 1, we see that our ProAPO consistently outperforms previous prompt-based methods across diverse datasets on ResNet50 and ViT-B/32 backbones. Our optimized prompts improve vanilla CLIP by an average of " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "8.4\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "53.4\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "61.8\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": ") on ResNet50 and " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "59.3\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "65.0\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": ") on ViT-B/32. Moreover, our training-free ProAPO surpasses gradient-based prompting methods (CoOp, PLOT, ProGrad) by at least " + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 61, + 530, + 296, + 705 + ], + "type": "text", + "content": " average accuracy in eleven datasets. It shows optimizing prompts in a natural language space is more effective in low-shot tasks. Compared to template-optimized methods (i.e., PN and hand-engineered methods), our ProAPO achieves remarkable performance on fine-grained datasets, e.g., CUB, FLO, ESAT, and UCF. This is because class-specific descriptions provide fine-grained discriminative de" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "spans": [ + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": "tails. Our ProAPO also outperforms description-based methods, even with DCLIP as initialization. We improve performances of DCLIP and CuPL by " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " on average across thirteen datasets. Notably, it improves DCLIP and CuPL by " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " on FLO and by " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "21\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 312, + 388, + 547, + 470 + ], + "type": "text", + "content": " on ESAT, confirming that iterative optimization of class-specific prompts enhances fine-grained recognition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 312, + 471, + 548, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 471, + 548, + 646 + ], + "spans": [ + { + "bbox": [ + 312, + 471, + 548, + 646 + ], + "type": "text", + "content": "Critical analysis. On datasets like ImageNet [9], Caltech [13], Places [75], and SUN [69], performance gains are relatively small. We attribute this to two reasons: First, datasets like ImageNet and Caltech contain coarse-grained categories. The differences between categories have become clearer with LLM-generated descriptions, eliminating the need for our method. Second, fine-grained datasets, such as Places and SUN for scene recognition, are easily confusing between different images, limiting performance from only textual side optimization. In Sec. 4.2, we show that adapter-based methods with our optimized prompt improve performance again after addressing issues of image confusion. Moreover, we observe that the language search space impacts performance. Since CuPL has better descriptions than DCLIP, our ProAPO with CuPL performs well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 652, + 495, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 495, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 495, + 665 + ], + "type": "text", + "content": "4.2. More Benefits by Optimal Prompts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 670, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 547, + 705 + ], + "type": "text", + "content": "Transfer to adapter-based methods. In Fig. 3, we show the results of popular adapter-based methods [15, 66, 74, 80] with different prompt initialization, i.e., SOTA method" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25150" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 79, + 178, + 169 + ], + "blocks": [ + { + "bbox": [ + 67, + 79, + 178, + 169 + ], + "lines": [ + { + "bbox": [ + 67, + 79, + 178, + 169 + ], + "spans": [ + { + "bbox": [ + 67, + 79, + 178, + 169 + ], + "type": "image", + "image_path": "0b20e8bec51d3b3e92b796bc2aca4bed61ef01b6cf4a41275a8a1a5583357b99.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 174, + 164, + 183 + ], + "lines": [ + { + "bbox": [ + 80, + 174, + 164, + 183 + ], + "spans": [ + { + "bbox": [ + 80, + 174, + 164, + 183 + ], + "type": "text", + "content": "(a) Training-free methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 181, + 79, + 291, + 170 + ], + "blocks": [ + { + "bbox": [ + 181, + 79, + 291, + 170 + ], + "lines": [ + { + "bbox": [ + 181, + 79, + 291, + 170 + ], + "spans": [ + { + "bbox": [ + 181, + 79, + 291, + 170 + ], + "type": "image", + "image_path": "160af41786585830ee9b282e8dd10218ced495ead64dbc88d6ec3bebcb54a58c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 197, + 174, + 276, + 183 + ], + "lines": [ + { + "bbox": [ + 197, + 174, + 276, + 183 + ], + "spans": [ + { + "bbox": [ + 197, + 174, + 276, + 183 + ], + "type": "text", + "content": "(b) Fine-tuning methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 186, + 295, + 218 + ], + "lines": [ + { + "bbox": [ + 62, + 186, + 295, + 218 + ], + "spans": [ + { + "bbox": [ + 62, + 186, + 295, + 218 + ], + "type": "text", + "content": "Figure 3. Results of adapter-based methods with different initial prompts. Solid and dotted lines denote prompt initialization with ProAPO and CuPL, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 85, + 230, + 271, + 297 + ], + "blocks": [ + { + "bbox": [ + 85, + 230, + 271, + 297 + ], + "lines": [ + { + "bbox": [ + 85, + 230, + 271, + 297 + ], + "spans": [ + { + "bbox": [ + 85, + 230, + 271, + 297 + ], + "type": "table", + "html": "
ModuleShotsSourceTarget
RN50RN101ViT-B/32ViT-B/16
CLIP [55]057.960.661.966.6
CoOp [77]1663.020.631.739.5
PN [36]159.960.762.267.0
ProAPO161.562.164.669.9
", + "image_path": "e0f4e811bf4ffbe5db5f48d3f97cb98b1742cef0e9ebfc396f80e64ff4cacc3d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 301, + 295, + 323 + ], + "lines": [ + { + "bbox": [ + 62, + 301, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 62, + 301, + 295, + 323 + ], + "type": "text", + "content": "Table 2. Results of prompt transfer from ResNet-50 to other architectures. We report the top-1 accuracy in ImageNet-1K." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 82, + 333, + 272, + 429 + ], + "blocks": [ + { + "bbox": [ + 82, + 333, + 272, + 429 + ], + "lines": [ + { + "bbox": [ + 82, + 333, + 272, + 429 + ], + "spans": [ + { + "bbox": [ + 82, + 333, + 272, + 429 + ], + "type": "image", + "image_path": "93056dc3a886e4a4fdecd3874dffc0f3c47fe843ed9d70f8b56d900f17e3eb55.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 431, + 295, + 464 + ], + "lines": [ + { + "bbox": [ + 62, + 431, + 295, + 464 + ], + "spans": [ + { + "bbox": [ + 62, + 431, + 295, + 464 + ], + "type": "text", + "content": "Figure 4. Results of prompt transfer to different backbones. The value denotes performance gains compared to vanilla VLMs. Our optimized prompts of ResNet50 and ViT-B/32 are reported." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 468, + 295, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 468, + 295, + 551 + ], + "spans": [ + { + "bbox": [ + 61, + 468, + 295, + 551 + ], + "type": "text", + "content": "CuPL [52] and our ProAPO. Adapter-based methods with ProAPO (solid lines) consistently surpass those with CuPL (dotted lines). It reveals that high-quality prompts make adapters perform better. Even in low shots, training with ProAPO achieves notable performance gains, which verifies its effectiveness. As the number of shots increases, adapters further improve results by enhancing image features." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 553, + 295, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 553, + 295, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 553, + 295, + 705 + ], + "type": "text", + "content": "Transfer to different backbones. In Tab. 2, we report accuracy in ImageNet across different backbones, with prompts optimized on a source backbone (ResNet50) adapted to target backbones (ResNet101, ViT-B/32, ViT-B/16). We observe that CoOp [77] obtains a significant drop in accuracy on target backbones while our ProAPO maintains performance. It verifies that discrete prompts searched in natural language spaces transfer better than continuous prompts. ProAPO also outperforms PN, which reveals the effectiveness of class-specific optimization. Moreover, we achieve stable performance gains compared to CuPL [52] from source to target models in Fig. 4. It further verifies that ProAPO transfers easily across different backbones." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 319, + 79, + 440, + 156 + ], + "blocks": [ + { + "bbox": [ + 319, + 79, + 440, + 156 + ], + "lines": [ + { + "bbox": [ + 319, + 79, + 440, + 156 + ], + "spans": [ + { + "bbox": [ + 319, + 79, + 440, + 156 + ], + "type": "image", + "image_path": "e83c5891091559a7b1a3c86809e7b3510c3abc596436993d5797a8ab0ac0d63c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 373, + 159, + 383, + 168 + ], + "lines": [ + { + "bbox": [ + 373, + 159, + 383, + 168 + ], + "spans": [ + { + "bbox": [ + 373, + 159, + 383, + 168 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 169, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 313, + 169, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 169, + 547, + 222 + ], + "type": "text", + "content": "Figure 5. Performance improvement analysis. (a) Analysis of the effect of single vs. ensemble prompts. * denotes results evaluated in the test set. ATO is our automatic template optimization algorithm. (b) Results of previous description-based methods with prompt optimization by our ATO and ProAPO algorithms." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 443, + 79, + 543, + 156 + ], + "blocks": [ + { + "bbox": [ + 443, + 79, + 543, + 156 + ], + "lines": [ + { + "bbox": [ + 443, + 79, + 543, + 156 + ], + "spans": [ + { + "bbox": [ + 443, + 79, + 543, + 156 + ], + "type": "image", + "image_path": "f119cfcc2312fe6d6ff623f993d2f0f75e83404177272ffc57a7dd65a7df80df.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 487, + 159, + 497, + 168 + ], + "lines": [ + { + "bbox": [ + 487, + 159, + 497, + 168 + ], + "spans": [ + { + "bbox": [ + 487, + 159, + 497, + 168 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 236, + 545, + 324 + ], + "blocks": [ + { + "bbox": [ + 317, + 236, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 317, + 236, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 317, + 236, + 545, + 324 + ], + "type": "image", + "image_path": "387ecd78d9b29ec6a4469cd8a025d23610f105fc2fe3daaf9ad8f9b4f6289449.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 339, + 547, + 371 + ], + "lines": [ + { + "bbox": [ + 313, + 339, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 547, + 371 + ], + "type": "text", + "content": "Figure 6. Qualitative analysis of class-specific prompt optimization by ProAPO. Shaded red and blue words denote common and discriminative descriptions in two confused categories." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 376, + 500, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 500, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 500, + 388 + ], + "type": "text", + "content": "4.3. Performance Improvement Analysis" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 396, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 546, + 419 + ], + "type": "text", + "content": "In this section, we analyze the key reasons for the performance improvement of our ProAPO." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 422, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 422, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 312, + 422, + 547, + 561 + ], + "type": "text", + "content": "Prompt ensembling is better than a single prompt. Compared to PN [36], we utilize prompt ensembling instead of a single prompt to optimize the template and description. To evaluate the effectiveness of prompt ensembling, we use Template-80 [55] as the template library and denote the prompts searched by the test set as the upper bound. As shown in Fig. 5(a), we observe that ensemble templates have a higher upper bound than the single template, consistent with prior work [8, 40, 71]. Similarly, we observe that our optimized templates achieve higher performance than PN [36], even better than the best single template, further verifying the effectiveness of our method." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 565, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 565, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 565, + 547, + 705 + ], + "type": "text", + "content": "Iterative optimization improves prompt quality. In Fig. 6, we show the changes in descriptions with our ProAPO. After iterative optimization, common descriptions such as \"flight over ocean\" and \"long wings and hooked bill\" are removed. Discriminative descriptions are also retained in candidate prompts, e.g., \"white body\" for Laysan Albatross, and \"black underpants\" for Sooty Albatross. As such, we see a notable improvement in description-based methods [40, 52, 59, 68] with our ATO and ProAPO in Fig. 5(b) by at least " + }, + { + "bbox": [ + 313, + 565, + 547, + 705 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 313, + 565, + 547, + 705 + ], + "type": "text", + "content": " average in thirteen datasets. It further verifies the effectiveness of our progressive optimization." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25151" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 79, + 282, + 190 + ], + "blocks": [ + { + "bbox": [ + 75, + 79, + 282, + 190 + ], + "lines": [ + { + "bbox": [ + 75, + 79, + 282, + 190 + ], + "spans": [ + { + "bbox": [ + 75, + 79, + 282, + 190 + ], + "type": "table", + "html": "
ComponentIN-1KAvg (11)Avg (13)
AddDelRepCrossMut
CLIP (Baseline)62.161.859.3
edit-based generation
a)✓63.866.063.3
b)✓✓64.666.463.8
c)✓✓64.466.563.8
d)✓✓✓64.666.764.0
evolution-based generation
e)✓✓✓✓64.667.364.5
f)✓✓✓✓64.767.164.3
g)✓✓✓✓✓64.767.965.0
", + "image_path": "5cf8c081385bf42e147d70beb22fe7545d7a87e7a5279f56352c850a44be7af8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 77, + 209, + 279, + 262 + ], + "blocks": [ + { + "bbox": [ + 73, + 191, + 285, + 202 + ], + "lines": [ + { + "bbox": [ + 73, + 191, + 285, + 202 + ], + "spans": [ + { + "bbox": [ + 73, + 191, + 285, + 202 + ], + "type": "text", + "content": "Table 3. Ablation of edit- and evolution-based operators." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 209, + 279, + 262 + ], + "lines": [ + { + "bbox": [ + 77, + 209, + 279, + 262 + ], + "spans": [ + { + "bbox": [ + 77, + 209, + 279, + 262 + ], + "type": "table", + "html": "
Module (ViT-B/32)IN-1KAvg (11)Avg (13)Times
a) w/o prompt sampling64.467.364.512 min
b) w/o group sampling64.868.165.2306 min
c) w/o sampling strategies64.567.264.4302 min
ProAPO (full model)64.767.965.015 min
", + "image_path": "2779c1b1d548226d80bc742a2fec2643687499fe38b2cd55ce165fdc73ecdeca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 95, + 264, + 263, + 275 + ], + "lines": [ + { + "bbox": [ + 95, + 264, + 263, + 275 + ], + "spans": [ + { + "bbox": [ + 95, + 264, + 263, + 275 + ], + "type": "text", + "content": "Table 4. Ablation of two sampling strategies." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 62, + 278, + 153, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 278, + 153, + 290 + ], + "spans": [ + { + "bbox": [ + 62, + 278, + 153, + 290 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 295, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 295, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 61, + 295, + 296, + 411 + ], + "type": "text", + "content": "Are both GEN and EVO algorithms necessary? In Tab. 3, we ablate edit- and evolution-based operators. For edit-based operators, we observe that the model with add, delete, and replace operations achieves a higher result in row d). After introducing evolution-based operators, i.e., crossover operator to combine advantages of high-scoring candidates, and mutation operator to avoid locally optimal solutions, we see an increase in performance in rows e)-g). It confirms that evolution-based operators make the model search the optimal prompt faster with limited iterations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "spans": [ + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "text", + "content": "Does sample strategies degrade performance? In Tab. 4, we ablate two sampling strategies for description optimization. Without the prompt sampling, we see a slight decrease in times while results drop in row a). It verifies the effectiveness of the prompt sampling in finding a better initial point. Without the group sampling to select salient categories for optimization, we observe a notable increase in time costs (from " + }, + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "inline_equation", + "content": "15\\mathrm{min}" + }, + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "inline_equation", + "content": "300+\\mathrm{min}" + }, + { + "bbox": [ + 61, + 411, + 296, + 528 + ], + "type": "text", + "content": ", 20 times) yet similar results in row b) and the full model. It reveals that group sampling simultaneously improves performance and efficiency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 528, + 296, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 528, + 296, + 657 + ], + "spans": [ + { + "bbox": [ + 61, + 528, + 296, + 657 + ], + "type": "text", + "content": "Which score function is better? In Fig. 7, we compare the different score functions, i.e., accuracy (used in PN [36]) and our fitness score, to evaluate the quality of the candidate prompt. PCCs (Pearson Correlation Coefficients) are introduced to evaluate the linear relationship between training metrics and test performance. The high PCC values mean a strong correlation. We see that the model with our fitness score achieves stable and high test results compared to previous score functions when achieving the best score. Besides, a higher PPC value further verifies that our fitness score effectively alleviates the overfitting problem." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 664, + 211, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 664, + 211, + 677 + ], + "spans": [ + { + "bbox": [ + 62, + 664, + 211, + 677 + ], + "type": "text", + "content": "4.5. Hyperparameter Sensitivity" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "content": "How many iterations of Alg. 2 to use? In Fig. 8(a), we show the effect of iteration times " + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 62, + 681, + 296, + 705 + ], + "type": "text", + "content": " in APO algorithm. As" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 319, + 80, + 430, + 155 + ], + "blocks": [ + { + "bbox": [ + 319, + 80, + 430, + 155 + ], + "lines": [ + { + "bbox": [ + 319, + 80, + 430, + 155 + ], + "spans": [ + { + "bbox": [ + 319, + 80, + 430, + 155 + ], + "type": "image", + "image_path": "1422cb4fb01e0a9cb11c85fac5589417c144bd685c96d5d672770770d36c250f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 158, + 417, + 167 + ], + "lines": [ + { + "bbox": [ + 331, + 158, + 417, + 167 + ], + "spans": [ + { + "bbox": [ + 331, + 158, + 417, + 167 + ], + "type": "text", + "content": "(a) Previous score function." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 433, + 79, + 544, + 155 + ], + "blocks": [ + { + "bbox": [ + 433, + 79, + 544, + 155 + ], + "lines": [ + { + "bbox": [ + 433, + 79, + 544, + 155 + ], + "spans": [ + { + "bbox": [ + 433, + 79, + 544, + 155 + ], + "type": "image", + "image_path": "ad36d704a88f07408ad69e596b499ce60ae8b37c4b85be1b47aa0646b325fb6e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 158, + 520, + 167 + ], + "lines": [ + { + "bbox": [ + 456, + 158, + 520, + 167 + ], + "spans": [ + { + "bbox": [ + 456, + 158, + 520, + 167 + ], + "type": "text", + "content": "(b) Our fitness score" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 208, + 391, + 272 + ], + "blocks": [ + { + "bbox": [ + 313, + 170, + 547, + 202 + ], + "lines": [ + { + "bbox": [ + 313, + 170, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 170, + 547, + 202 + ], + "type": "text", + "content": "Figure 7. Effect of different score functions. Higher PCC values mean stronger correlations between training metrics and test results. Best Acc is the test result when achieving the best score." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 208, + 391, + 272 + ], + "lines": [ + { + "bbox": [ + 317, + 208, + 391, + 272 + ], + "spans": [ + { + "bbox": [ + 317, + 208, + 391, + 272 + ], + "type": "image", + "image_path": "eef2cb9cc956e7eddca66ec30699427c29e702c465f6d010e58839b7a315ba1c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 394, + 208, + 467, + 272 + ], + "blocks": [ + { + "bbox": [ + 321, + 275, + 389, + 284 + ], + "lines": [ + { + "bbox": [ + 321, + 275, + 389, + 284 + ], + "spans": [ + { + "bbox": [ + 321, + 275, + 389, + 284 + ], + "type": "text", + "content": "(a) Iteration times " + }, + { + "bbox": [ + 321, + 275, + 389, + 284 + ], + "type": "inline_equation", + "content": "T" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 394, + 208, + 467, + 272 + ], + "lines": [ + { + "bbox": [ + 394, + 208, + 467, + 272 + ], + "spans": [ + { + "bbox": [ + 394, + 208, + 467, + 272 + ], + "type": "image", + "image_path": "13d6a353a7ef56021b8d88d9fdcb78b124fd4353bed05ed36edd3585e097eca8.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 394, + 274, + 467, + 284 + ], + "lines": [ + { + "bbox": [ + 394, + 274, + 467, + 284 + ], + "spans": [ + { + "bbox": [ + 394, + 274, + 467, + 284 + ], + "type": "text", + "content": "(b) Generated numbers" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 470, + 208, + 543, + 272 + ], + "blocks": [ + { + "bbox": [ + 470, + 208, + 543, + 272 + ], + "lines": [ + { + "bbox": [ + 470, + 208, + 543, + 272 + ], + "spans": [ + { + "bbox": [ + 470, + 208, + 543, + 272 + ], + "type": "image", + "image_path": "f78abbc69d70a57e5e144db4dc10066f153170207e6aca9950616559306a268f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 274, + 542, + 284 + ], + "lines": [ + { + "bbox": [ + 470, + 274, + 542, + 284 + ], + "spans": [ + { + "bbox": [ + 470, + 274, + 542, + 284 + ], + "type": "text", + "content": "(c) Sampling groups " + }, + { + "bbox": [ + 470, + 274, + 542, + 284 + ], + "type": "inline_equation", + "content": "S" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 287, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 313, + 287, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 287, + 547, + 308 + ], + "type": "text", + "content": "Figure 8. The effect of hyperparameter analysis. The hyperparameter value set to 0 denotes the result of CuPL [52]." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 315, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 547, + 361 + ], + "type": "text", + "content": "the number of iterations increases, we see a consistent performance improvement compared to the baseline CuPL. It demonstrates that iterative optimization improves prompt quality. Stable results are achieved when " + }, + { + "bbox": [ + 313, + 315, + 547, + 361 + ], + "type": "inline_equation", + "content": "T \\geq 4" + }, + { + "bbox": [ + 313, + 315, + 547, + 361 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "text", + "content": "How many generated prompts to use? In Fig. 8(b), we show the effect of generated numbers in GEN and EVO algorithm, where we set " + }, + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "inline_equation", + "content": "M = N" + }, + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "text", + "content": ". Similarly, progressive improvements are seen as generated numbers increase. We see a reliable result when " + }, + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "inline_equation", + "content": "M = N \\geq 8" + }, + { + "bbox": [ + 313, + 361, + 547, + 430 + ], + "type": "text", + "content": ". It reveals the effectiveness of generating diverse candidates by our algorithm." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "content": "Are more sampling groups better? In Fig. 8(c), we show the effect of the number of salient groups " + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "content": " in the group sampling strategy. We see a notable improvement when " + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "inline_equation", + "content": "S = 2" + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "content": ". As the number of groups " + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "content": " increases, it achieves stable results when " + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "inline_equation", + "content": "S \\geq 8" + }, + { + "bbox": [ + 313, + 431, + 547, + 513 + ], + "type": "text", + "content": ". It verifies that optimizing several salient categories can achieve comparable performances with all categories and save iteration costs." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 522, + 384, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 384, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 384, + 534 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 312, + 541, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 541, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 312, + 541, + 547, + 705 + ], + "type": "text", + "content": "We propose an evolution-based algorithm for VLMs to progressively refine prompts from task-specific to class-specific levels. To save generation costs, ProAPO uses several edit- and evolution-based operators to create candidate prompts with a prompt library. Results show that our fitness score mitigates overfitting in class-specific prompts. We empirically verify that two sampling strategies improve performance and save iteration times. Extensive experiments on thirteen datasets reveal that ProAPO consistently outperforms SOTA textual prompt-based methods on low-shot tasks. Moreover, our method effectively improves adapter-based and description-based methods and easily transfers across different backbones. We hope ProAPO could provide new insight into adapting VLMs from the textual side." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 743 + ], + "type": "text", + "content": "25152" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 63, + 80, + 163, + 94 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 80, + 163, + 94 + ], + "spans": [ + { + "bbox": [ + 63, + 80, + 163, + 94 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 100, + 296, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 100, + 296, + 124 + ], + "spans": [ + { + "bbox": [ + 62, + 100, + 296, + 124 + ], + "type": "text", + "content": "This work was supported by the Central Guidance for Local Special Project (Grant No. Z231100005923044)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 135, + 120, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 135, + 120, + 148 + ], + "spans": [ + { + "bbox": [ + 63, + 135, + 120, + 148 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 154, + 296, + 704 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 68, + 154, + 296, + 186 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 154, + 296, + 186 + ], + "spans": [ + { + "bbox": [ + 68, + 154, + 296, + 186 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, and Pauline Luc et al. 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We propose a framework for detecting and classifying OOD samples in a given class hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the class hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the class hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined class hierarchies and show the effectiveness of our method. Our code is available at https://github.com/walline/prohoc.", + "bbox": [ + 89, + 324, + 483, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 614, + 220, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Effectively handling out-of-distribution samples is important for deep-learning applications. Data outside the training domain often yield unpredictable results when fed through deep neural networks [7], making it essential to account for previously unseen data when deploying these models in real-world settings to ensure robust performance and avoid unexpected outcomes. Previous literature [31] has focused on binary out-of-distribution detection, predicting data either as ID (in-distribution) or OOD (out-of-distribution), without differentiating between OOD samples that are semantically close or far from ID. For example, with ID classes consisting of dog breeds, this binary paradigm would treat an image of an unknown dog the same as an image of an airplane, overlooking the varying degrees of semantic similarity these samples have to the known classes.", + "bbox": [ + 89, + 641, + 482, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We explore a new setting of OOD detection, utilizing class hierarchies to predict semantically close OOD sam", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/38109b5948ff6e1a05eb42a085ab871465e8c992573b245b45441e181a33e5c9.jpg", + "image_caption": [ + "Figure 1. Out-of-distribution detection in class hierarchies. Instead of simply predicting the unseen dog and cat types as OOD, we aim to classify them as the high-level categories dog and cat." + ], + "image_footnote": [], + "bbox": [ + 516, + 289, + 898, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plies as their correct nodes in the class hierarchy. Hierarchical models for organizing and classifying objects are widespread, from foundational examples like Linnaeus' taxonomy in Systema Naturae [17] to modern structures like WordNet [21] for semantic relations. While the deep learning community has shown a growing interest in utilizing class hierarchies [4, 9], their application for OOD detection remains largely unexplored. However, such hierarchies can provide a foundation for enabling more informative OOD predictions. For instance, in the hierarchy shown in Figure 1, the binary paradigm of OOD detection treats the unseen cat and dog as simply OOD. In contrast, with knowledge of the hierarchy, we can classify the unseen dog as the broader dog category (while recognizing it as distinct from previously seen breeds).", + "bbox": [ + 511, + 595, + 906, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of many motivating examples arises in the context of an autonomous driving system. A sensor model might be trained to classify objects such as bicycles, electric scooters, and mopeds (among other classes). However, many system components treat these objects similarly, grouping them as", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20612", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "slow-moving vehicles. When encountering an obscure object not present in the training data, such as a unicycle or a penny-farthing, the ideal response would be to recognize it as a slow-moving vehicle, rather than misclassifying it as a known class or simply marking it as OOD, which would provide limited actionable information.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach addresses this problem by leveraging the class hierarchy to factorize the probability distribution of predictions in the tree. This probability model includes conditional probabilities at each parent node, at which the possible predictions are either one of its child nodes or OOD at that specific node. Our key challenge lies in modeling these conditionals, as we assume no OOD data are available for training. To approximate these conditionals, we train classification networks at each depth of the hierarchy. We find that networks trained to classify classes higher in the hierarchy better recognize features associated with broad categories, making them better at predicting OOD samples to the correct high-level category. Similarly, the more fine-grained models may display larger uncertainty for these OOD samples because they contain low-level features that are not recognized by these models.", + "bbox": [ + 89, + 183, + 482, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We explore several methods for leveraging these multi-depth networks to approximate the conditionals in our probabilistic framework based on standard OOD scores. We evaluate our proposed model, ProHOC, on three datasets with predefined class hierarchies that we split into ID and OOD and show that our method outperforms previous attempts. Moreover, our framework has the benefit of introducing no new hyperparameters and uses standard methods for training the underlying multi-depth networks, making it straightforward to extend and build upon. We believe that our model can serve as a strong foundation for further research in this relatively unexplored area.", + "bbox": [ + 89, + 425, + 482, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are as follows:", + "bbox": [ + 109, + 607, + 367, + 621 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We formulate a probabilistic framework for classifying data, both ID and OOD, as nodes in a class hierarchy.", + "- We explore and enable the implementation of this framework by utilizing multi-depth networks to approximate the conditionals in the probabilistic model.", + "- We experimentally evaluate our framework and baselines on several datasets, showing the effectiveness of our method." + ], + "bbox": [ + 89, + 623, + 482, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 89, + 760, + 227, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Hierarchy-aware ID classification", + "text_level": 1, + "bbox": [ + 89, + 785, + 383, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several works incorporate class hierarchies in training models for ID classification, focusing on minimizing the hierarchical distance between predictions and ground truth rather than only optimizing for classification accuracy [4, 5, 9, 10, 15]. This approach prioritizes models that make errors close to the correct class in the hierarchy, which often can be", + "bbox": [ + 89, + 810, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "preferable to models that make more distant mistakes. This aspect of performance is typically disregarded in works on standard flat classification.", + "bbox": [ + 511, + 90, + 903, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The existing approaches to this problem vary. In [4], they propose adjustments to the standard cross-entropy loss to account for higher-level decisions in the hierarchy. The works [5, 15] introduce hierarchy-aware feature spaces to obtain the desired model properties. In [10], they suggest a post-hoc method that rescales flat prediction probabilities by hierarchical distances to produce predictions minimizing the expected hierarchical distance.", + "bbox": [ + 511, + 137, + 903, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most similar to our approach is [9], which proposes training separate coarse and fine-grained classifiers to improve both classification accuracy and hierarchical distance. However, their method is restricted to classifiers at two levels (one coarse and one fine), whereas we train classifiers at all levels of the hierarchy.", + "bbox": [ + 511, + 258, + 903, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This overall line of research is similar to our setting in that we consider class hierarchies to minimize the hierarchical distance between ground truth and predictions. However, a key difference is that these works only consider ID data and therefore restrict the predictions to leaf nodes only. In contrast, we need a framework able to predict internal nodes as OOD predictions.", + "bbox": [ + 511, + 349, + 903, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Out-of-distribution detection", + "text_level": 1, + "bbox": [ + 513, + 467, + 769, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Out-of-distribution is an active field of research [2, 7, 12, 14, 27]. The goal is to detect whether a data sample belongs to the training distribution or not, motivated by the need to handle real-world, uncurated settings. The common approach in this field is to design a score based on neural network outputs, which takes high values for OOD data and low values for ID data (or vice versa). The score can be derived from, e.g., predicted distributions [7, 19, 24], logits [18, 29], or feature representations [1, 12, 30].", + "bbox": [ + 511, + 491, + 903, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our setting introduces some new challenges compared to the standard binary paradigm of OOD detection. First, instead of only detecting OOD as a binary prediction, we aim to classify OOD samples as specific nodes within the class hierarchy. Second, we ultimately need to make hard decisions about which node to predict, so unnormalized scores that lack probabilistic interpretations or easily inferrable thresholds are of limited use. Lastly, many works on OOD detection use comparably simple problem settings, using one dataset as ID and an unrelated dataset as OOD [12, 18]. In contrast, our setting naturally involves complex, fine-grained detection tasks, as OOD samples can appear at any depth within the class hierarchy.", + "bbox": [ + 511, + 628, + 905, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As a final note, a few works exist that consider class hierarchies and OOD detection simultaneously [8, 11, 29]. In [11, 29], they use class hierarchies to construct OOD sets of varying difficulty by selecting the OOD sets from different depths of the class hierarchy. The work [8] proposes a score", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20613", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that signals high OOD-ness if two classifiers predict distinct classes separated by a large hierarchical distance. However, these works still consider only binary OOD predictions.", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Hierarchical out-of-distribution detection", + "text_level": 1, + "bbox": [ + 89, + 143, + 444, + 159 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To the best of our knowledge, the only work that considers detection and classification of OOD in class hierarchies similarly to us is [16]. Their method involves separate model heads for each internal node in the hierarchy. For data that are descendants of a specific node, the corresponding head is trained to predict the correct child using a standard cross-entropy loss. For non-descendant data points, the head is trained to produce a uniform distribution.", + "bbox": [ + 89, + 167, + 482, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are key distinctions between [16] and our work. First, our method introduces no additional hyperparameters, whereas [16] requires balancing multiple loss terms during training. Second, their approach performs hierarchical inference in a top-down manner, with thresholds at each node to decide where to stop. These thresholds need to be assigned using ID data and it is not clear how to select these to ensure performance on both ID and OOD data while generalizing to multiple datasets. In contrast, our fully probabilistic approach provides a predictive distribution over all nodes in the hierarchy, eliminating the need for threshold-based top-down inference.", + "bbox": [ + 89, + 287, + 483, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. A probabilistic hierarchy-framework", + "text_level": 1, + "bbox": [ + 89, + 481, + 424, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach for detecting and classifying OOD in class hierarchies is based on creating a probabilistic model from the class hierarchy. We assume that this hierarchy $\\mathcal{H}$ is given and that it is structured as a directed rooted tree [3] (e.g., the green nodes of Figure 1). We denote the nodes of this tree as $\\mathcal{C}$ with the leaf nodes being $\\mathcal{C}^{\\mathrm{id}}\\subset \\mathcal{C}$ . We assume a distribution of ID data with classes corresponding to leaves in this hierarchy: $p^{\\mathrm{id}}(x,y)$ , with $y\\in \\mathcal{C}^{\\mathrm{id}}$ . These data are observed during training. Furthermore, we have a distribution of OOD data, not observable during training, $p^{\\mathrm{odd}}(x,y)$ , with $y\\in \\mathcal{C}\\setminus \\mathcal{C}^{\\mathrm{id}}$ . In other words, the OOD data do not match any ID leaf classes but correspond to groups of ID classes higher in the hierarchy.", + "bbox": [ + 89, + 506, + 483, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to learn a model $f(x)$ that predicts samples from the balanced mix of ID and OOD, defined as $p^{\\mathrm{mix}}(x,y) = 0.5(p^{\\mathrm{id}}(x,y) + p^{\\mathrm{odd}}(x,y))$ , to their correct nodes in $\\mathcal{H}$ . If misclassified, the predictions should be hierarchically close to the ground truth. Formally, we aim to minimize the expected hierarchical distance between the prediction and the ground truth:", + "bbox": [ + 89, + 703, + 483, + 809 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min \\mathbb {E} _ {p ^ {\\operatorname {m i x}} (x, y)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} (f (x), y) \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 816, + 482, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)$ is the number of edges in the shortest path between two nodes in the undirected equivalent of $\\mathcal{H}$ .", + "bbox": [ + 89, + 839, + 482, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To model $f(\\cdot)$ , we construct a probabilistic model from the class hierarchy $\\mathcal{H}$ . Specifically, we append a child node", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to each internal node of $\\mathcal{H}$ to represent OOD predictions at that node (e.g., the red nodes of Figure 1), creating the new tree $\\mathcal{G}$ . We denote the set of these OOD nodes as", + "bbox": [ + 511, + 90, + 906, + 136 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} ^ {\\mathrm {o o d}} = \\left\\{\\operatorname {o o d} (c) | c \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 147, + 906, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These nodes represent a sample belonging to class $c$ but not to any of $c$ 's known descendants. The model $\\mathcal{G}$ describes the semantic classes of a sample as random binary variables at each node. We denote the probability of the set of nodes $\\mathcal{C}'$ being active for a given sample $x$ as $p(\\mathcal{C}'|x)$ . We assume that all samples belong to a leaf node $c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}}$ but that the leaf nodes are mutually exclusive, i.e., a sample belongs to only one leaf node. Moreover, the internal nodes of $\\mathcal{G}$ describe unions of these leaf nodes such that internal node $c$ is active if any of its descendant leaf nodes are active. This implies $p(c|x) = p(\\operatorname{Anc}_{\\mathcal{G}}^{+}(c)|x)$ , where $\\operatorname{Anc}_{\\mathcal{G}}^{+}(c)$ is the set of $c$ and all $c$ 's ancestors. From this follows the conditional independences $p(c|\\operatorname{Anc}_{\\mathcal{G}}^{+}(\\operatorname{Par}_{\\mathcal{G}}(c))) = p(c|\\operatorname{Par}_{\\mathcal{G}}(c))$ where $\\operatorname{Par}_{\\mathcal{G}}(c)$ is the parent node of $c$ .", + "bbox": [ + 511, + 176, + 906, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We can now factorize the probability of paths in $\\mathcal{G}$ using the chain rule of probability and the induced conditional independences as", + "bbox": [ + 511, + 388, + 905, + 434 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (c | x) = p \\left(\\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) | x\\right) = \\prod_ {c ^ {\\prime} \\in \\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) \\backslash R} p \\left(c ^ {\\prime} \\mid \\operatorname {P a r} _ {\\mathcal {G}} \\left(c ^ {\\prime}\\right), x\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 445, + 906, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the root node $R$ is excluded in the product because $p(R|x) = 1$ . For example, in the hierarchy of Figure 1, the probability for Lynx becomes $p(\\mathrm{Lynx}|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x)$ whereas the probability for an OOD Cat is $p(\\mathrm{odd}(\\mathrm{Cat})|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x)$ .", + "bbox": [ + 511, + 493, + 905, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By applying (3) with $c \\in \\mathcal{C}^{\\mathrm{id}} \\cup C^{\\mathrm{odd}}$ , we obtain the predictive distribution over all ID classes and OOD predictions at each internal node of $\\mathcal{H}$ . Note that for evaluation purposes, predictions of $\\mathrm{odd}(c)$ are mapped to the corresponding node $c$ in $\\mathcal{H}$ to compute hierarchical distances.", + "bbox": [ + 511, + 568, + 905, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use this distribution to obtain our final prediction. A standard approach is to use the argmax of $p(c|x)$ with $c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}}$ . However, to better align with our objective in (1), we instead utilize the uncertainties of the predictive distribution to minimize the expected hierarchical distance between the predicted node for sample $x$ and its ground truth:", + "bbox": [ + 511, + 643, + 905, + 736 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (x) = \\underset {c \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 746, + 906, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the expectation is obtained by", + "bbox": [ + 513, + 782, + 756, + 797 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] = \\sum_ {c ^ {\\prime} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) p \\left(c ^ {\\prime} \\mid x\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 809, + 906, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that $\\mathrm{odd}(c)$ is mapped to $c$ in $\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)$ . In Sec. 7.2, we experimentally show the benefit of using (4) compared to the standard argmax approach.", + "bbox": [ + 511, + 854, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20614", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Leveraging multi-depth networks", + "text_level": 1, + "bbox": [ + 89, + 89, + 395, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The predictive distribution of (3) requires the conditional distributions at each internal node of the class hierarchy:", + "bbox": [ + 89, + 114, + 482, + 145 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (y | c, x), \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\cup \\{\\operatorname {o o d} (c) \\} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 152, + 482, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for $c \\in \\mathcal{C} \\setminus \\mathcal{C}^{\\mathrm{id}}$ , where $\\mathrm{Ch}_{\\mathcal{H}}(c)$ is the set of children of $c$ according to the original tree $\\mathcal{H}$ . However, as no OOD data are available during training, we cannot train a model to directly predict $p(\\mathrm{odd}(c)|c,x)$ . Instead, as common for binary OOD detection [12, 30], we resort to hand-crafted models for the OOD predictions.", + "bbox": [ + 89, + 174, + 482, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our idea for approaching these conditionals is to design classifiers from ID data that, given a sample belonging to $\\mathrm{odd}(c)$ , confidently predict class $c$ while expressing uncertainty for the known child classes $\\mathrm{Ch}_{\\mathcal{H}}(c)$ . With such a model, the uncertainty of the sample's membership in $\\mathrm{Ch}_{\\mathcal{H}}(c)$ can be used as a proxy for $p(\\mathrm{odd}(c)|c,x)$ .", + "bbox": [ + 89, + 266, + 482, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following this reasoning, we propose training separate classification networks for the different depths of the hierarchy, with each network responsible for classifying data into nodes at a particular depth (see Figure 2). The intuition behind this approach is that the networks for high levels will emphasize the features associated with broad categories, which may not be helpful for more fine-grained classification. For instance, in the dogs-and-cats hierarchy of Figure 1, the network trained for the level above the leaves, responsible for classifying dog or cat, may focus on features like ear and tail shape, useful for distinguishing between any dog and any cat. Conversely, the leaf-level network might focus on fur patterns or facial features, important for distinguishing specific breeds. Consequently, an unseen cat breed might lack the features the leaf model recognizes, causing it to show uncertainty. However, the high-level network could still identify the features common to all cats and confidently classify the unseen cat breed as a cat.", + "bbox": [ + 89, + 357, + 482, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we train these multi-depth networks using an ID dataset of samples and labels", + "bbox": [ + 89, + 628, + 482, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 662, + 482, + 685 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train high-level models, we map these leaf-level labels to their corresponding ancestors at specific depths. For this purpose, we define the function $\\lambda(y, d)$ which maps the label $y$ to its corresponding ancestor at depth $d$ , or if $\\mathrm{Depth}_{\\mathcal{H}}(y) \\leq d$ , maps $y$ to itself (this handles the case of all leaves not having equal depth). Consequently, we train the network for depth $d$ , denoted $f_{\\theta_d}$ , using standard cross-entropy training, with the dataset", + "bbox": [ + 89, + 689, + 482, + 809 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {d} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, \\lambda \\left(y _ {i}, d\\right)\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 814, + 482, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and obtain the multi-depth networks $f_{\\theta_1}, \\ldots, f_{\\theta_D}$ with the parameters $\\theta_1, \\ldots, \\theta_D$ , where $D = \\max_{c \\in \\mathcal{C}} \\mathrm{Depth}_{\\mathcal{H}}(c)$ .", + "bbox": [ + 89, + 839, + 482, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Sec. 5.2, we present results showing that our multi-depth networks effectively classify OOD data.", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b342aa40f4ec27d88cf8c55bf12d588e45b71c9cd330d0d2b0fba19ee440d880.jpg", + "image_caption": [ + "Figure 2. For a hierarchy of depth 3, we train separate neural networks, parameterized by $\\theta_{1}$ , $\\theta_{2}$ , and $\\theta_{3}$ , to classify data into nodes within that depth level." + ], + "image_footnote": [], + "bbox": [ + 527, + 87, + 898, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Modeling the conditionals of the hierarchy", + "text_level": 1, + "bbox": [ + 511, + 334, + 874, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To model the conditionals $p(y|c, x)$ based on the multi-depth networks, $f_{\\theta_1}, \\ldots, f_{\\theta_D}$ , we are looking for ways to quantify the uncertainty of $x$ belonging to $\\mathrm{Ch}_{\\mathcal{H}}(c)$ and use this to estimate $p(\\mathrm{odd}(c)|c, x)$ . There are a variety of ways one could approach this. We have evaluated several alternatives based on standard OOD scores in Sec. 7.1. An intuitive and simple approach is to use", + "bbox": [ + 511, + 358, + 905, + 464 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (y | c, x) = p (y | x; \\theta_ {d}) \\quad \\text {f o r} \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 473, + 903, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 513, + 500, + 542, + 512 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathbf {o o d} (c) | c, x) = 1 - \\sum_ {y \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 511, + 903, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1$ . This formulation uses the probability of a sample belonging to a class outside the children of $c$ as a proxy for the OOD probability while keeping the conditional probabilities for the children as predicted by $p(y|x;\\theta_d)$ . However, we find that this approach alone tends to assign too low probabilities for OOD and fails to account for the uncertainty among the child nodes. To address this, we also consider the entropy of the normalized distribution over the children:", + "bbox": [ + 511, + 549, + 905, + 685 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH (c) = - \\sum_ {c ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right) \\log \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 691, + 903, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 513, + 734, + 558, + 748 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {p} \\left(c ^ {\\prime} \\mid x; \\theta_ {d}\\right) = \\frac {p \\left(c ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}{\\sum_ {\\tilde {c} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (\\tilde {c} \\mid x ; \\theta_ {d})}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 744, + 903, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "High entropies indicate uncertainty among the children, i.e., when multiple children are assigned similar probabilities.", + "bbox": [ + 511, + 785, + 903, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the entropy and the complementary probability (10) are independent and account for different aspects of uncertainty, we combine these in a sum as", + "bbox": [ + 511, + 815, + 903, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns (c) = H (c) + 1 - \\sum_ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 869, + 903, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20615", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, this score no longer forms a probability distribution when combined with $p(y|x;\\theta_d)$ for $y \\in \\mathrm{Ch}_{\\mathcal{H}}(c)$ . To resolve this, we normalize to obtain the valid distribution as", + "bbox": [ + 89, + 90, + 483, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (y | c, x) = \\frac {p (y | x ; \\theta_ {d})}{s (c) + \\sum_ {y ^ {\\prime} \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} | x ; \\theta_ {d}\\right)} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 143, + 482, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $y\\in \\mathrm{Ch}_{\\mathcal{H}}(c)$ and", + "bbox": [ + 89, + 186, + 227, + 203 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\operatorname {o o d} (c) \\mid c, x\\right) = \\frac {s (c)}{s (c) + \\sum_ {y ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 209, + 482, + 246 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which gives us the final model for the conditional distributions in our hierarchical framework.", + "bbox": [ + 89, + 251, + 483, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments and results", + "text_level": 1, + "bbox": [ + 89, + 294, + 318, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 319, + 192, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "There are no established datasets for OOD detection in class hierarchies. We construct our benchmarks using three datasets with predefined hierarchies commonly used in work for hierarchy-aware ID classification. We generate ID and OOD subsets by selecting OOD nodes from various depths within these hierarchies. Our experiments are conducted on the following datasets:", + "bbox": [ + 89, + 340, + 483, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FGVC-Aircraft [20]: This dataset contains aircraft images with a three-level hierarchy: at the highest level are manufacturers (e.g., Boeing), the second level groups aircraft by family (e.g., Boeing 747), and the most specific level contains variants (e.g., Boeing 747-200). FGVC-Aircraft has the most shallow hierarchy and the fewest classes among the considered datasets, but it poses challenging classification tasks, such as distinguishing between separate Boeing 747 types.", + "bbox": [ + 89, + 446, + 483, + 584 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "iNaturalist19 [28]: A dataset of biological species organized in a hierarchy according to taxonomic ranks such as kingdom, phylum, and genus. It includes a large number of classes with fine-grained relationships and has a deeper hierarchy than FGVC-Aircraft.", + "bbox": [ + 89, + 584, + 483, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SimpleHierImageNet: This dataset is based on tieredImageNet [25], which is a subset of ImageNet using a hierarchy based on the WordNet graph [21]. However, the hierarchy of tieredImageNet has many nodes representing conceptual rather than visual similarities. For example, it has the high-level class timepiece with the subclasses analog clock and digital clock, or the leaf class laptop computer under the high-level class portable computer, while computer keyboard is nine edges away under electronic equipment. To address this, we introduce SimpleHierImageNet by reorganizing parts of the tieredImageNet hierarchy to reflect visual similarities. Despite these adjustments, SimpleHierImageNet remains a challenging problem with a wide range of categories and a deep hierarchy with many internal nodes. More details on SimpleHierImageNet are available in the supplementary material.", + "bbox": [ + 89, + 659, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b457cfa30b7d43b03a37436986513173bc45586e04c3850266814d8500e54582.jpg", + "table_caption": [ + "Table 1. Dataset details (after being split into ID and OOD)." + ], + "table_footnote": [], + "table_body": "
Max depthNr. ID leavesNr. internal nodesNr. OOD classes
FGVC-Aircraft3802820
SimpleHierImageNet115186380
iNaturalist19672177289
", + "bbox": [ + 524, + 104, + 893, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The considered datasets lack established ID/OOD splits. Therefore, we construct the OOD set by selecting nodes from various depths of the hierarchy. For each selected OOD node, we remove it and all its descendants from the hierarchy, leaving the remaining nodes to form our ID hierarchy $\\mathcal{H}$ . After defining the ID hierarchy $\\mathcal{H}$ and the set of OOD classes, we map the labels of the OOD data (which are leaf nodes in the full original hierarchy) to their closest ancestor present in the ID hierarchy $\\mathcal{H}$ . These mapped labels are then used in the experimental evaluation.", + "bbox": [ + 511, + 203, + 903, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Details of the datasets, after defining the ID and OOD sets are described in Tab. 1. Additional information on the datasets and the selection of OOD sets is available in the supplementary material.", + "bbox": [ + 511, + 354, + 903, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Evaluating multi-depth networks for OOD", + "text_level": 1, + "bbox": [ + 511, + 422, + 877, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate our hypothesis that multi-depth networks are effective for OOD classification, we compare the accuracy obtained from our high-level models $f_{\\theta_1}, \\ldots, f_{\\theta_{D-1}}$ to the accuracy obtained by marginalizing the leaf-level model $f_{\\theta_D}$ , when evaluated on OOD data.", + "bbox": [ + 511, + 446, + 903, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we have a dataset of OOD data associated with different depths of the hierarchy:", + "bbox": [ + 511, + 521, + 903, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {o o d}}}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 558, + 903, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We define subsets of $S^{\\mathrm{odd}}$ associated with specific depths as", + "bbox": [ + 511, + 587, + 903, + 603 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {d} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\in \\mathcal {S} ^ {\\mathrm {o o d}} \\mid \\operatorname {D e p t h} _ {\\mathcal {H}} \\left(y _ {i}\\right) = d \\right\\}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 609, + 903, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $d\\in \\{1,\\dots ,D - 1\\}$ . Now we can compute the classification accuracies obtained by the network $f_{\\theta_d}$ on the dataset $S_{d}^{\\mathrm{odd}}$ . We compare this with the predictions obtained by marginalizing the predictions of the ID leaf model $f_{\\theta_D}$ as", + "bbox": [ + 511, + 637, + 903, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {d} ^ {\\text {m a r g i n}} (c | x) = \\sum_ {c ^ {\\prime} \\in \\text {L e a v e s} _ {\\mathcal {H}} (c)} p \\left(c ^ {\\prime} | x; \\theta_ {D}\\right) \\quad \\text {f o r} c \\in \\mathcal {C} ^ {d}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 705, + 903, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{Leaves}_{\\mathcal{H}}(c)$ are the descendant leaves of $c$", + "bbox": [ + 511, + 750, + 841, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2 shows the results of this comparison across our three considered datasets. The multi-depth model obtains higher accuracies than the marginalized model for all datasets, indicating that the high-level models are better at classifying OOD samples as the correct class. Moreover, this implies that while a high-level model correctly predicts an OOD sample as class $c$ , the lower-level model leans towards predicting classes not in $\\mathrm{Ch}_{\\mathcal{H}}(c)$ , which is the behavior we are looking for.", + "bbox": [ + 511, + 765, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20616", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ff97c8c51d27e9093d36247298ce394a79e9e6e5332ef406036f095d94026999.jpg", + "table_caption": [ + "Table 2. Classification accuracies on OOD data at ground-truth depths. We compare models trained with high-level labels with models trained using the leaf labels." + ], + "table_footnote": [], + "table_body": "
DatasetAccuracy (%) ↑Δ ↑
Multi-depth p(c|x; θd)Marginalized pdmargin(c|x)
SimpleHierImageNet70.168.5+1.6
iNaturalist1976.573.6+2.9
FGVC-Aircraft67.350.3+17.0
", + "bbox": [ + 107, + 132, + 464, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Evaluation metrics", + "text_level": 1, + "bbox": [ + 89, + 252, + 272, + 266 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How to evaluate a framework for OOD detection in class hierarchies is not established. In alignment with works on ID classification with class hierarchies [10, 15], we focus primarily on hierarchical distances between predictions and ground truth. However, given that our OOD nodes are selected at varying depths in the hierarchy, the resulting OOD sets have highly imbalanced class distributions. Therefore we propose to use a balanced mean hierarchical distance (BMHD), defined as", + "bbox": [ + 89, + 275, + 483, + 411 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {B M H D} \\left(\\mathcal {C} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {C} ^ {\\prime} |} \\sum_ {c \\in \\mathcal {C} ^ {\\prime}} \\frac {1}{n _ {c}} \\sum_ {i = 1} ^ {n _ {c}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(f \\left(x _ {i} ^ {c}\\right), c\\right), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 421, + 480, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{C}'$ is the set of classes being considered, $n_c$ is the number of samples in the test set with ground truth label $c$ , $x_i^c$ is the $i$ -th sample out of those, and $|\\mathcal{C}'|$ is the cardinality of $\\mathcal{C}'$ . In BMHD( $\\mathcal{C}'$ ), the mean distances for nodes in $\\mathcal{C}'$ are weighted equally, regardless of how many samples are associated with a specific node.", + "bbox": [ + 89, + 472, + 482, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we want to evaluate the performance on a combined set of ID and OOD data. To this end, we define the mixed BMHD as", + "bbox": [ + 89, + 564, + 483, + 607 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M i x B M H D} = 0. 5 \\left(\\mathrm {B M H D} _ {\\text {i d}} + \\mathrm {B M H D} _ {\\text {o o d}}\\right), \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 619, + 480, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{BMHD_{id}}$ and $\\mathrm{BMHD_{ood}}$ are evaluated with (19) on the set of ID and OOD classes with test data available, respectively. Similarly, we evaluate classification accuracies as the proportion of predictions that match the ground truth labels. Because of the class imbalance, we consider a balanced accuracy score [22]:", + "bbox": [ + 89, + 647, + 483, + 738 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M i x B A c c} = 0. 5 \\left(\\mathrm {B A c c} _ {\\mathrm {i d}} + \\mathrm {B A c c} _ {\\mathrm {o o d}}\\right), \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 750, + 480, + 766 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{BAcc_{id}}$ and $\\mathrm{BAcc_{ood}}$ denote the balanced accuracies for ID and OOD classes, respectively.", + "bbox": [ + 89, + 777, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Results", + "text_level": 1, + "bbox": [ + 89, + 816, + 184, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our framework to the following baselines:", + "bbox": [ + 89, + 840, + 454, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Depth oracle: We make predictions using the ground-truth depth with the corresponding $p(c|x;\\theta_d)$ for all data, i.e., $p(c|x;\\theta_D)$ for ID data and $p(c|x;\\theta_d), d < D$ for OOD", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "data. Given the accuracies of the multi-depth networks, we consider this an upper performance bound.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Leaf model: We predict all data using $p(c|x;\\theta_D)$ , i.e., all data are predicted as leaves, including OOD.", + "bbox": [ + 511, + 122, + 903, + 152 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HSC: We train and evaluate the model proposed in [16] using the authors' code. We present results using the synset-based stopping-criterion because that gives the best results. We set thresholds for stopping criteria based on TPR rates to minimize MixBMHD on the test sets. However, in real-world settings, we cannot optimize these thresholds based on test performance.", + "bbox": [ + 511, + 152, + 905, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our framework, denoted ProHOC (for probabilistic hierarchical OOD classification), is evaluated using the two different models for the conditionals described in Sec. 4.1. The first, denoted CompProb, uses the complementary probabilities to model the OOD probabilities, as defined in (10). The second, EntCompProb, uses the sum of the entropy and the complementary probability, as defined in (13).", + "bbox": [ + 511, + 258, + 905, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results are presented in Tab. 3. Excluding the oracle model, ProHOC with EntCompProb yields the best MixBMHD and MixBAcc across all three datasets, with CompProb consistently ranking second. Looking at the numbers for ID and OOD separately, we note the tradeoff between ID and OOD performance, where the CompProb model favors ID performance by making deeper predictions. In contrast, the EntCompProb model has a more balanced performance across ID and OOD.", + "bbox": [ + 511, + 366, + 905, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ProHOC outperforms HSC [16], the existing method for OOD detection in hierarchies. This is despite optimizing the inference thresholds in HSC using OOD test data. We can see that HSC tends to make overly deep predictions, keeping an ID performance close to the leaf model but showing poor OOD performance. More detailed analyses of the results are available in the supplementary material.", + "bbox": [ + 511, + 502, + 905, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.5. Evaluating out-of-hierarchy data", + "text_level": 1, + "bbox": [ + 511, + 619, + 803, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Section 5.4 focuses on evaluating within-hierarchy OOD data, as these samples are the most challenging and distinguish our hierarchical approach from the binary OOD setting. However, ProHOC supports out-of-hierarchy OOD by classifying such samples as OOD at the root node. The OOD probability at the root is computed via (15) with $s(\\mathrm{root})$ being a positive score from any suitable binary OOD method. For simplicity, we use the entropy of the deepest network for $s(\\mathrm{root})$ which is a common baseline for binary OOD detection [24] that aligns well with our EntComp-Prob model. Table 4 shows ProHOC for FGVC-Aircraft with root predictions on three out-of-hierarchy datasets. MixBAcc is the (balanced) accuracy on the mix of within-hierarchy ID and OOD. Acc for out-of-hierarchy datasets is the percentage of samples correctly classified as root. We get high accuracies on out-of-hierarchy OOD while keeping most within-hierarchy performance.", + "bbox": [ + 511, + 643, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20617", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ea09c351f7a28775cb84243cf52e4dd691d7b6712dbf7a54984e114f4ca672d4.jpg", + "table_caption": [ + "Table 3. Mean hierarchical distances and accuracies on ID, OOD, and the mix of ID and OOD for ProHOC and baselines. The oracle model serves as an upper performance bound. Excluding the oracle model, the best results are boldfaced. Evaluations use test sets." + ], + "table_footnote": [], + "table_body": "
BAccid↑BAccood↑MixBAcc↑BMHDid↓BMHDood↓MixBMHD↓
SIMPLEHIERIMAGENET
Depth oracle79.772.576.10.821.050.93
Leaf model79.70.039.80.822.121.47
HSC [16]76.87.842.30.771.781.28
ProHOC (CompProb)67.819.243.50.921.611.27
ProHOC (EntCompProb)62.530.346.40.961.451.21
INATURALIST19
Depth oracle72.475.974.20.850.820.83
Leaf model72.40.036.20.852.231.54
HSC [16]68.18.438.20.801.761.28
ProHOC (CompProb)66.118.042.00.771.341.06
ProHOC (EntCompProb)57.735.646.70.781.100.94
FGVC-AIRCRAFT
Depth oracle84.767.676.10.490.670.58
Leaf model84.70.042.30.492.001.25
HSC [16]77.914.446.10.401.480.94
ProHOC (CompProb)80.117.148.60.411.250.83
ProHOC (EntCompProb)78.022.750.30.411.210.81
", + "bbox": [ + 181, + 119, + 812, + 411 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d88922283b8ca92dd2221a47c7ba38186fb6d1d1c5d3ee43559850bdbd66cb3a.jpg", + "table_caption": [ + "Table 4. Evaluating ProHOC on out-of-hierarchy data." + ], + "table_footnote": [], + "table_body": "
MixBAcc ↑ (FGVC-Air.)Acc ↑ Office31 [26]Acc ↑ iNat19Acc ↑ PACS [13]
ProHOC w/ root47.178.283.994.4
ProHOC w/o root50.3---
", + "bbox": [ + 106, + 449, + 465, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.6. Training details", + "text_level": 1, + "bbox": [ + 89, + 536, + 248, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We train our multi-depth networks with standard supervised NLL training using the remapped labels from (8). We use the ResNet50 architecture [6] for all experiments. For FGVC-Aircraft and iNaturalist19, the network is initialized with pre-trained weights from ImageNet, whereas for SimpleHierImageNet, we train the network from scratch. We train for 90 epochs on FGVC-Aircraft and iNaturalist19, and 250 epochs on SimpleHierImageNet. We use stochastic gradient descent with an initial learning rate of 0.05, decayed to zero by the end of training using a cosine schedule. A batch size of 128 is used throughout. During training, images are randomly cropped and resized to $224 \\times 224$ .", + "bbox": [ + 89, + 559, + 483, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 89, + 753, + 212, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This work focuses on establishing the key building blocks of our framework for hierarchical OOD detection, with little attention given to optimizing the performance of the underlying multi-depth networks. Further work could explore stronger architectures and advanced training techniques to improve the performance of ProHOC. Finally, a fundamental limitation of our problem formulation is the assumption that the class hierarchy reflects observable visual similarities", + "bbox": [ + 89, + 779, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ties. If ID and OOD siblings do not share common visual features, we can not expect this type of framework to accurately predict OOD.", + "bbox": [ + 511, + 435, + 906, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "7. Ablation studies", + "text_level": 1, + "bbox": [ + 513, + 493, + 674, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "7.1. Evaluating different scores for the conditionals", + "text_level": 1, + "bbox": [ + 511, + 517, + 906, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Sec. 4.1 we described how we use the multi-depth networks to model the conditionals $p(y|c, x)$ for $y \\in \\mathrm{Ch}_{\\mathcal{H}}(c) \\cup \\{\\mathrm{odd}(c)\\}$ . The primary challenge in modeling $p(y|c, x)$ lies in assigning the OOD probability. Here, we explore several approaches to modeling this OOD probability, or an unnormalized OOD score, based on the predictions from our multi-depth networks. We consider the following models:", + "bbox": [ + 511, + 541, + 905, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CompProb: The complementary probability, as defined in (10). It uses the sum of probabilities for classes outside of $\\mathrm{Ch}_{\\mathcal{H}}(c)$ as a proxy for the OOD probability.", + "bbox": [ + 511, + 646, + 905, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Entropy: As defined in (11), indicates the uncertainty of predictions among the children. The entropy is widely used as an OOD score in the literature [24].", + "bbox": [ + 511, + 691, + 905, + 737 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "MaxProb: The (negated) maximum probability among the children, defined as", + "bbox": [ + 511, + 737, + 905, + 767 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\ns ^ {\\operatorname {M a x P r o b}} (c) = 1 - \\max _ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}) \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 773, + 906, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with $d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1$ . This alternative is similar to the widely used MSP score [7] for binary OOD detection.", + "bbox": [ + 511, + 809, + 905, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "EntCompProb: Since the entropy and the complementary probability are independent and signal different aspects of uncertainty, we find it intuitive to combine scores in a sum, as defined in (13).", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20618", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CompLogits: We sum the unnormalized logits for classes outside $\\mathrm{Ch}_{\\mathcal{H}}(c)$ and use the sum in the softmax function alongside the logits for the child nodes. This method resembles CompProb, although it differs in the scaling of the OOD probability due to summing before applying the exponential function in the softmax.", + "bbox": [ + 89, + 90, + 482, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The methods denoted CompProb and CompLogits form valid probability distributions directly by design. For the other alternatives, we obtain the conditional distribution by normalization following (14) and (15).", + "bbox": [ + 89, + 181, + 482, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A well-performing model for the conditionals should display certain qualities. The probability for OOD in the conditional distribution should be the maximum when the sample is OOD. Moreover, if the network misclassifies an ID sample (predicting it as an incorrect ID child), we want our model to predict the OOD node instead of an incorrect ID prediction, which would increase the hierarchical distance from the ground truth. To assess these aspects of the performance, we use several metrics that are evaluated locally for a specific internal node:", + "bbox": [ + 89, + 243, + 483, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "F1: The F1 score for binary classification where OOD is considered the positive label. A prediction is OOD if $p(\\mathrm{odd}(c)|c,x)$ is the largest element of $p(y|c,x)$ , otherwise ID. We also report the corresponding FPR and TPR.", + "bbox": [ + 89, + 395, + 483, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Purity: The fraction of predicted ID samples, predicted as the correct child node.", + "bbox": [ + 89, + 455, + 482, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dirty F1: Our variant of the F1 score where ID data that are misclassified as an incorrect child are labeled as OOD when computing the F1 score.", + "bbox": [ + 89, + 486, + 482, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluate these metrics for all parent nodes $c$ for which OOD data with ground truth at $c$ are available. As ID data, we use all data that belong to descendants of $c$ . We report the mean metrics over all evaluated nodes.", + "bbox": [ + 89, + 532, + 482, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 shows results from FGVC-Aircraft. EntCompProb achieves the highest F1 score. It has the largest FPR but this is compensated by its high purity, indicating that many false positives would have been classified as incorrect ID children if they were predicted as ID. For Dirty F1, EntCompProb again outperforms other methods, by an even larger margin. This suggests that the entropy-based uncertainty and the complementary probability interact effectively to create a model with the desired properties. In contrast, CompLogits performs poorly due to being underconfident on OOD (a low TPR). This implies that summation at the logit level leads to smaller OOD probabilities than summation at the probability level (as with CompProb).", + "bbox": [ + 89, + 593, + 482, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7.2. Minimizing the expected hierarchical distance", + "text_level": 1, + "bbox": [ + 89, + 801, + 480, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ProHOC provides a predictive distribution over all nodes in the hierarchy, allowing us to incorporate uncertainty into our final prediction. Given our objective to produce predictions that are hierarchically close to the ground truth (1), we can use the predicted distribution $p(c|x)$ to minimize the", + "bbox": [ + 89, + 824, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/492300802d4bb17534ae9a976de88f6368fa2e68582d484a9ff5d39e8740b6b0.jpg", + "table_caption": [ + "Table 5. Analyzing the performance of different methods for modeling $p(\\mathrm{odd}(c)|c,x)$ . Results are from FGVC-Aircraft." + ], + "table_footnote": [], + "table_body": "
F1 ↑FPR ↓TPR ↑Purity ↑Dirty F1 ↑
CompProb0.470.090.420.880.49
Entropy0.510.120.450.900.55
MaxProb0.500.100.450.890.52
EntCompProb0.560.150.520.900.59
CompLogits0.170.010.140.870.18
", + "bbox": [ + 532, + 117, + 879, + 205 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d55765fc275953687f01f535d2140ed58151d1f0c6171ab85cae5284c95f3cd3.jpg", + "table_caption": [ + "Table 6. Comparing predictions from minimizing the expected hierarchical distance to predictions using the most probable class." + ], + "table_footnote": [], + "table_body": "
argmin E[distH]argmax p(c|x)
MixBAcc ↑ MixBMHD ↓MixBAcc ↑ MixBMHD ↓
SIMPLEHIERIMAGENET
EntCompProb46.41.2145.81.25
CompProb43.51.2739.71.37
INATURALIST19
EntCompProb46.70.9445.60.98
CompProb42.01.0638.41.17
FGVC-AIRCRAFT
EntCompProb50.30.8150.20.88
CompProb48.60.8347.40.90
", + "bbox": [ + 524, + 250, + 887, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "expected hierarchical distance of the prediction", + "bbox": [ + 511, + 449, + 826, + 464 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nf (x) = \\underset {c} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right], \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 479, + 903, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "as presented in Sec. 3. This is similar to the post-hoc correction proposed in [10], although they restrict the predictions to leaves. We compute the expected hierarchical distance over all nodes in the hierarchy.", + "bbox": [ + 511, + 518, + 903, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare the predictions from (23) with the standard $\\mathrm{argmax}_c p(c|x)$ in Tab. 6, using ProHOC with both CompProb and EntCompProb. As expected, (23) achieves lower hierarchical distances since it optimizes for that specifically. However, we also see improvements in accuracy as an additional benefit of using (23).", + "bbox": [ + 511, + 580, + 905, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 691, + 633, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The deep-learning community has made substantial progress in the binary setting of OOD detection. In this paper, we raise the bar for OOD detection by aiming for more informative predictions: predicting OOD as internal nodes in a class hierarchy. Our framework shows promising results. We also believe its simplicity in introducing no new hyperparameters and using underlying networks trained with standard methods makes it accessible and adaptable for further development. We hope this work will inspire continued exploration of OOD classification in class hierarchies and that ProHOC can serve as a foundation for even more effective methods.", + "bbox": [ + 511, + 719, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20619", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by Saab AB and Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agreement no. 2022-06725.", + "bbox": [ + 89, + 113, + 483, + 224 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 237, + 187, + 252 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. Neo: Neural collapse based out-of-distribution detection. In International Conference on Learning Representations, 2024. 2", + "[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. In IEEE conference on computer vision and pattern recognition, 2016. 2", + "[3] Edward A Bender and S Gill Williamson. Lists, decisions and graphs. S. 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Openood v1.5: Enhanced benchmark for out-of-distribution detection. arXiv preprint arXiv:2306.09301, 2023. 1" + ], + "bbox": [ + 89, + 92, + 482, + 444 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20621", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_model.json b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_model.json new file mode 100644 index 0000000000000000000000000000000000000000..38880556e45f493eb707c4c9a1abdbeb35081ce4 --- /dev/null +++ b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.127, + 0.13, + 0.872, + 0.177 + ], + "angle": 0, + "content": "ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.203, + 0.7, + 0.24 + ], + "angle": 0, + "content": "Erik Wallin\\(^{1,2}\\), Fredrik Kahl\\(^{2}\\), Lars Hammarstrand\\(^{2}\\), Saab AB,\\(^{2}\\)Chalmers University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.27, + 0.242, + 0.728, + 0.256 + ], + "angle": 0, + "content": "{wallline, fredrik. kahl, lars.hammarstrand}@chalmers.se" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.485, + 0.581 + ], + "angle": 0, + "content": "Out-of-distribution (OOD) detection in deep learning has traditionally been framed as a binary task, where samples are either classified as belonging to the known classes or marked as OOD, with little attention given to the semantic relationships between OOD samples and the indistribution (ID) classes. We propose a framework for detecting and classifying OOD samples in a given class hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the class hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the class hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined class hierarchies and show the effectiveness of our method. Our code is available at https://github.com/walline/prohoc." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.616, + 0.222, + 0.631 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.642, + 0.483, + 0.868 + ], + "angle": 0, + "content": "Effectively handling out-of-distribution samples is important for deep-learning applications. Data outside the training domain often yield unpredictable results when fed through deep neural networks [7], making it essential to account for previously unseen data when deploying these models in real-world settings to ensure robust performance and avoid unexpected outcomes. Previous literature [31] has focused on binary out-of-distribution detection, predicting data either as ID (in-distribution) or OOD (out-of-distribution), without differentiating between OOD samples that are semantically close or far from ID. For example, with ID classes consisting of dog breeds, this binary paradigm would treat an image of an unknown dog the same as an image of an airplane, overlooking the varying degrees of semantic similarity these samples have to the known classes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We explore a new setting of OOD detection, utilizing class hierarchies to predict semantically close OOD sam" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.29, + 0.9, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.52, + 0.907, + 0.563 + ], + "angle": 0, + "content": "Figure 1. Out-of-distribution detection in class hierarchies. Instead of simply predicting the unseen dog and cat types as OOD, we aim to classify them as the high-level categories dog and cat." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.596, + 0.907, + 0.822 + ], + "angle": 0, + "content": "plies as their correct nodes in the class hierarchy. Hierarchical models for organizing and classifying objects are widespread, from foundational examples like Linnaeus' taxonomy in Systema Naturae [17] to modern structures like WordNet [21] for semantic relations. While the deep learning community has shown a growing interest in utilizing class hierarchies [4, 9], their application for OOD detection remains largely unexplored. However, such hierarchies can provide a foundation for enabling more informative OOD predictions. For instance, in the hierarchy shown in Figure 1, the binary paradigm of OOD detection treats the unseen cat and dog as simply OOD. In contrast, with knowledge of the hierarchy, we can classify the unseen dog as the broader dog category (while recognizing it as distinct from previously seen breeds)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "One of many motivating examples arises in the context of an autonomous driving system. A sensor model might be trained to classify objects such as bicycles, electric scooters, and mopeds (among other classes). However, many system components treat these objects similarly, grouping them as" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20612" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "slow-moving vehicles. When encountering an obscure object not present in the training data, such as a unicycle or a penny-farthing, the ideal response would be to recognize it as a slow-moving vehicle, rather than misclassifying it as a known class or simply marking it as OOD, which would provide limited actionable information." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.184, + 0.483, + 0.424 + ], + "angle": 0, + "content": "Our approach addresses this problem by leveraging the class hierarchy to factorize the probability distribution of predictions in the tree. This probability model includes conditional probabilities at each parent node, at which the possible predictions are either one of its child nodes or OOD at that specific node. Our key challenge lies in modeling these conditionals, as we assume no OOD data are available for training. To approximate these conditionals, we train classification networks at each depth of the hierarchy. We find that networks trained to classify classes higher in the hierarchy better recognize features associated with broad categories, making them better at predicting OOD samples to the correct high-level category. Similarly, the more fine-grained models may display larger uncertainty for these OOD samples because they contain low-level features that are not recognized by these models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.426, + 0.483, + 0.606 + ], + "angle": 0, + "content": "We explore several methods for leveraging these multi-depth networks to approximate the conditionals in our probabilistic framework based on standard OOD scores. We evaluate our proposed model, ProHOC, on three datasets with predefined class hierarchies that we split into ID and OOD and show that our method outperforms previous attempts. Moreover, our framework has the benefit of introducing no new hyperparameters and uses standard methods for training the underlying multi-depth networks, making it straightforward to extend and build upon. We believe that our model can serve as a strong foundation for further research in this relatively unexplored area." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.608, + 0.368, + 0.622 + ], + "angle": 0, + "content": "Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.624, + 0.483, + 0.653 + ], + "angle": 0, + "content": "- We formulate a probabilistic framework for classifying data, both ID and OOD, as nodes in a class hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.654, + 0.483, + 0.699 + ], + "angle": 0, + "content": "- We explore and enable the implementation of this framework by utilizing multi-depth networks to approximate the conditionals in the probabilistic model." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.7, + 0.483, + 0.743 + ], + "angle": 0, + "content": "- We experimentally evaluate our framework and baselines on several datasets, showing the effectiveness of our method." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.624, + 0.483, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.761, + 0.228, + 0.777 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.786, + 0.385, + 0.802 + ], + "angle": 0, + "content": "2.1. Hierarchy-aware ID classification" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Several works incorporate class hierarchies in training models for ID classification, focusing on minimizing the hierarchical distance between predictions and ground truth rather than only optimizing for classification accuracy [4, 5, 9, 10, 15]. This approach prioritizes models that make errors close to the correct class in the hierarchy, which often can be" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.136 + ], + "angle": 0, + "content": "preferable to models that make more distant mistakes. This aspect of performance is typically disregarded in works on standard flat classification." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.138, + 0.905, + 0.257 + ], + "angle": 0, + "content": "The existing approaches to this problem vary. In [4], they propose adjustments to the standard cross-entropy loss to account for higher-level decisions in the hierarchy. The works [5, 15] introduce hierarchy-aware feature spaces to obtain the desired model properties. In [10], they suggest a post-hoc method that rescales flat prediction probabilities by hierarchical distances to produce predictions minimizing the expected hierarchical distance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.259, + 0.905, + 0.349 + ], + "angle": 0, + "content": "Most similar to our approach is [9], which proposes training separate coarse and fine-grained classifiers to improve both classification accuracy and hierarchical distance. However, their method is restricted to classifiers at two levels (one coarse and one fine), whereas we train classifiers at all levels of the hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.905, + 0.456 + ], + "angle": 0, + "content": "This overall line of research is similar to our setting in that we consider class hierarchies to minimize the hierarchical distance between ground truth and predictions. However, a key difference is that these works only consider ID data and therefore restrict the predictions to leaf nodes only. In contrast, we need a framework able to predict internal nodes as OOD predictions." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.468, + 0.771, + 0.483 + ], + "angle": 0, + "content": "2.2. Out-of-distribution detection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.905, + 0.628 + ], + "angle": 0, + "content": "Out-of-distribution is an active field of research [2, 7, 12, 14, 27]. The goal is to detect whether a data sample belongs to the training distribution or not, motivated by the need to handle real-world, uncurated settings. The common approach in this field is to design a score based on neural network outputs, which takes high values for OOD data and low values for ID data (or vice versa). The score can be derived from, e.g., predicted distributions [7, 19, 24], logits [18, 29], or feature representations [1, 12, 30]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.906, + 0.824 + ], + "angle": 0, + "content": "Our setting introduces some new challenges compared to the standard binary paradigm of OOD detection. First, instead of only detecting OOD as a binary prediction, we aim to classify OOD samples as specific nodes within the class hierarchy. Second, we ultimately need to make hard decisions about which node to predict, so unnormalized scores that lack probabilistic interpretations or easily inferrable thresholds are of limited use. Lastly, many works on OOD detection use comparably simple problem settings, using one dataset as ID and an unrelated dataset as OOD [12, 18]. In contrast, our setting naturally involves complex, fine-grained detection tasks, as OOD samples can appear at any depth within the class hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "As a final note, a few works exist that consider class hierarchies and OOD detection simultaneously [8, 11, 29]. In [11, 29], they use class hierarchies to construct OOD sets of varying difficulty by selecting the OOD sets from different depths of the class hierarchy. The work [8] proposes a score" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20613" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "that signals high OOD-ness if two classifiers predict distinct classes separated by a large hierarchical distance. However, these works still consider only binary OOD predictions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.145, + 0.445, + 0.16 + ], + "angle": 0, + "content": "2.3. Hierarchical out-of-distribution detection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.168, + 0.483, + 0.288 + ], + "angle": 0, + "content": "To the best of our knowledge, the only work that considers detection and classification of OOD in class hierarchies similarly to us is [16]. Their method involves separate model heads for each internal node in the hierarchy. For data that are descendants of a specific node, the corresponding head is trained to predict the correct child using a standard cross-entropy loss. For non-descendant data points, the head is trained to produce a uniform distribution." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.484, + 0.471 + ], + "angle": 0, + "content": "There are key distinctions between [16] and our work. First, our method introduces no additional hyperparameters, whereas [16] requires balancing multiple loss terms during training. Second, their approach performs hierarchical inference in a top-down manner, with thresholds at each node to decide where to stop. These thresholds need to be assigned using ID data and it is not clear how to select these to ensure performance on both ID and OOD data while generalizing to multiple datasets. In contrast, our fully probabilistic approach provides a predictive distribution over all nodes in the hierarchy, eliminating the need for threshold-based top-down inference." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.482, + 0.426, + 0.5 + ], + "angle": 0, + "content": "3. A probabilistic hierarchy-framework" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.507, + 0.484, + 0.703 + ], + "angle": 0, + "content": "Our approach for detecting and classifying OOD in class hierarchies is based on creating a probabilistic model from the class hierarchy. We assume that this hierarchy \\(\\mathcal{H}\\) is given and that it is structured as a directed rooted tree [3] (e.g., the green nodes of Figure 1). We denote the nodes of this tree as \\(\\mathcal{C}\\) with the leaf nodes being \\(\\mathcal{C}^{\\mathrm{id}}\\subset \\mathcal{C}\\). We assume a distribution of ID data with classes corresponding to leaves in this hierarchy: \\(p^{\\mathrm{id}}(x,y)\\), with \\(y\\in \\mathcal{C}^{\\mathrm{id}}\\). These data are observed during training. Furthermore, we have a distribution of OOD data, not observable during training, \\(p^{\\mathrm{odd}}(x,y)\\), with \\(y\\in \\mathcal{C}\\setminus \\mathcal{C}^{\\mathrm{id}}\\). In other words, the OOD data do not match any ID leaf classes but correspond to groups of ID classes higher in the hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.81 + ], + "angle": 0, + "content": "Our goal is to learn a model \\( f(x) \\) that predicts samples from the balanced mix of ID and OOD, defined as \\( p^{\\mathrm{mix}}(x,y) = 0.5(p^{\\mathrm{id}}(x,y) + p^{\\mathrm{odd}}(x,y)) \\), to their correct nodes in \\( \\mathcal{H} \\). If misclassified, the predictions should be hierarchically close to the ground truth. Formally, we aim to minimize the expected hierarchical distance between the prediction and the ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.817, + 0.483, + 0.835 + ], + "angle": 0, + "content": "\\[\n\\min \\mathbb {E} _ {p ^ {\\operatorname {m i x}} (x, y)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} (f (x), y) \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.871 + ], + "angle": 0, + "content": "where \\(\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)\\) is the number of edges in the shortest path between two nodes in the undirected equivalent of \\(\\mathcal{H}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To model \\( f(\\cdot) \\), we construct a probabilistic model from the class hierarchy \\( \\mathcal{H} \\). Specifically, we append a child node" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.137 + ], + "angle": 0, + "content": "to each internal node of \\(\\mathcal{H}\\) to represent OOD predictions at that node (e.g., the red nodes of Figure 1), creating the new tree \\(\\mathcal{G}\\). We denote the set of these OOD nodes as" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.148, + 0.907, + 0.169 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} ^ {\\mathrm {o o d}} = \\left\\{\\operatorname {o o d} (c) | c \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.177, + 0.907, + 0.389 + ], + "angle": 0, + "content": "These nodes represent a sample belonging to class \\( c \\) but not to any of \\( c \\)'s known descendants. The model \\( \\mathcal{G} \\) describes the semantic classes of a sample as random binary variables at each node. We denote the probability of the set of nodes \\( \\mathcal{C}' \\) being active for a given sample \\( x \\) as \\( p(\\mathcal{C}'|x) \\). We assume that all samples belong to a leaf node \\( c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}} \\) but that the leaf nodes are mutually exclusive, i.e., a sample belongs to only one leaf node. Moreover, the internal nodes of \\( \\mathcal{G} \\) describe unions of these leaf nodes such that internal node \\( c \\) is active if any of its descendant leaf nodes are active. This implies \\( p(c|x) = p(\\operatorname{Anc}_{\\mathcal{G}}^{+}(c)|x) \\), where \\( \\operatorname{Anc}_{\\mathcal{G}}^{+}(c) \\) is the set of \\( c \\) and all \\( c \\)'s ancestors. From this follows the conditional independences \\( p(c|\\operatorname{Anc}_{\\mathcal{G}}^{+}(\\operatorname{Par}_{\\mathcal{G}}(c))) = p(c|\\operatorname{Par}_{\\mathcal{G}}(c)) \\) where \\( \\operatorname{Par}_{\\mathcal{G}}(c) \\) is the parent node of \\( c \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.906, + 0.435 + ], + "angle": 0, + "content": "We can now factorize the probability of paths in \\(\\mathcal{G}\\) using the chain rule of probability and the induced conditional independences as" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.446, + 0.907, + 0.483 + ], + "angle": 0, + "content": "\\[\np (c | x) = p \\left(\\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) | x\\right) = \\prod_ {c ^ {\\prime} \\in \\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) \\backslash R} p \\left(c ^ {\\prime} \\mid \\operatorname {P a r} _ {\\mathcal {G}} \\left(c ^ {\\prime}\\right), x\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.906, + 0.569 + ], + "angle": 0, + "content": "where the root node \\( R \\) is excluded in the product because \\( p(R|x) = 1 \\). For example, in the hierarchy of Figure 1, the probability for Lynx becomes \\( p(\\mathrm{Lynx}|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x) \\) whereas the probability for an OOD Cat is \\( p(\\mathrm{odd}(\\mathrm{Cat})|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x) \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.906, + 0.645 + ], + "angle": 0, + "content": "By applying (3) with \\( c \\in \\mathcal{C}^{\\mathrm{id}} \\cup C^{\\mathrm{odd}} \\), we obtain the predictive distribution over all ID classes and OOD predictions at each internal node of \\( \\mathcal{H} \\). Note that for evaluation purposes, predictions of \\( \\mathrm{odd}(c) \\) are mapped to the corresponding node \\( c \\) in \\( \\mathcal{H} \\) to compute hierarchical distances." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.645, + 0.906, + 0.737 + ], + "angle": 0, + "content": "We use this distribution to obtain our final prediction. A standard approach is to use the argmax of \\( p(c|x) \\) with \\( c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}} \\). However, to better align with our objective in (1), we instead utilize the uncertainties of the predictive distribution to minimize the expected hierarchical distance between the predicted node for sample \\( x \\) and its ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.747, + 0.907, + 0.773 + ], + "angle": 0, + "content": "\\[\nf (x) = \\underset {c \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.784, + 0.757, + 0.799 + ], + "angle": 0, + "content": "where the expectation is obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.81, + 0.907, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] = \\sum_ {c ^ {\\prime} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) p \\left(c ^ {\\prime} \\mid x\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Note that \\(\\mathrm{odd}(c)\\) is mapped to \\(c\\) in \\(\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)\\). In Sec. 7.2, we experimentally show the benefit of using (4) compared to the standard argmax approach." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20614" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.396, + 0.108 + ], + "angle": 0, + "content": "4. Leveraging multi-depth networks" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.483, + 0.146 + ], + "angle": 0, + "content": "The predictive distribution of (3) requires the conditional distributions at each internal node of the class hierarchy:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.153, + 0.483, + 0.171 + ], + "angle": 0, + "content": "\\[\np (y | c, x), \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\cup \\{\\operatorname {o o d} (c) \\} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.175, + 0.483, + 0.266 + ], + "angle": 0, + "content": "for \\( c \\in \\mathcal{C} \\setminus \\mathcal{C}^{\\mathrm{id}} \\), where \\( \\mathrm{Ch}_{\\mathcal{H}}(c) \\) is the set of children of \\( c \\) according to the original tree \\( \\mathcal{H} \\). However, as no OOD data are available during training, we cannot train a model to directly predict \\( p(\\mathrm{odd}(c)|c,x) \\). Instead, as common for binary OOD detection [12, 30], we resort to hand-crafted models for the OOD predictions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.267, + 0.483, + 0.357 + ], + "angle": 0, + "content": "Our idea for approaching these conditionals is to design classifiers from ID data that, given a sample belonging to \\(\\mathrm{odd}(c)\\), confidently predict class \\(c\\) while expressing uncertainty for the known child classes \\(\\mathrm{Ch}_{\\mathcal{H}}(c)\\). With such a model, the uncertainty of the sample's membership in \\(\\mathrm{Ch}_{\\mathcal{H}}(c)\\) can be used as a proxy for \\(p(\\mathrm{odd}(c)|c,x)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.629 + ], + "angle": 0, + "content": "Following this reasoning, we propose training separate classification networks for the different depths of the hierarchy, with each network responsible for classifying data into nodes at a particular depth (see Figure 2). The intuition behind this approach is that the networks for high levels will emphasize the features associated with broad categories, which may not be helpful for more fine-grained classification. For instance, in the dogs-and-cats hierarchy of Figure 1, the network trained for the level above the leaves, responsible for classifying dog or cat, may focus on features like ear and tail shape, useful for distinguishing between any dog and any cat. Conversely, the leaf-level network might focus on fur patterns or facial features, important for distinguishing specific breeds. Consequently, an unseen cat breed might lack the features the leaf model recognizes, causing it to show uncertainty. However, the high-level network could still identify the features common to all cats and confidently classify the unseen cat breed as a cat." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.483, + 0.659 + ], + "angle": 0, + "content": "Specifically, we train these multi-depth networks using an ID dataset of samples and labels" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.664, + 0.483, + 0.686 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.81 + ], + "angle": 0, + "content": "To train high-level models, we map these leaf-level labels to their corresponding ancestors at specific depths. For this purpose, we define the function \\(\\lambda(y, d)\\) which maps the label \\(y\\) to its corresponding ancestor at depth \\(d\\), or if \\(\\mathrm{Depth}_{\\mathcal{H}}(y) \\leq d\\), maps \\(y\\) to itself (this handles the case of all leaves not having equal depth). Consequently, we train the network for depth \\(d\\), denoted \\(f_{\\theta_d}\\), using standard cross-entropy training, with the dataset" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.815, + 0.483, + 0.837 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {d} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, \\lambda \\left(y _ {i}, d\\right)\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.871 + ], + "angle": 0, + "content": "and obtain the multi-depth networks \\(f_{\\theta_1}, \\ldots, f_{\\theta_D}\\) with the parameters \\(\\theta_1, \\ldots, \\theta_D\\), where \\(D = \\max_{c \\in \\mathcal{C}} \\mathrm{Depth}_{\\mathcal{H}}(c)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "In Sec. 5.2, we present results showing that our multi-depth networks effectively classify OOD data." + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.088, + 0.9, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.269, + 0.906, + 0.312 + ], + "angle": 0, + "content": "Figure 2. For a hierarchy of depth 3, we train separate neural networks, parameterized by \\(\\theta_{1}\\), \\(\\theta_{2}\\), and \\(\\theta_{3}\\), to classify data into nodes within that depth level." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.335, + 0.875, + 0.352 + ], + "angle": 0, + "content": "4.1. Modeling the conditionals of the hierarchy" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.359, + 0.906, + 0.465 + ], + "angle": 0, + "content": "To model the conditionals \\( p(y|c, x) \\) based on the multi-depth networks, \\( f_{\\theta_1}, \\ldots, f_{\\theta_D} \\), we are looking for ways to quantify the uncertainty of \\( x \\) belonging to \\( \\mathrm{Ch}_{\\mathcal{H}}(c) \\) and use this to estimate \\( p(\\mathrm{odd}(c)|c, x) \\). There are a variety of ways one could approach this. We have evaluated several alternatives based on standard OOD scores in Sec. 7.1. An intuitive and simple approach is to use" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.474, + 0.905, + 0.491 + ], + "angle": 0, + "content": "\\[\np (y | c, x) = p (y | x; \\theta_ {d}) \\quad \\text {f o r} \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.5, + 0.543, + 0.513 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.512, + 0.905, + 0.546 + ], + "angle": 0, + "content": "\\[\np (\\mathbf {o o d} (c) | c, x) = 1 - \\sum_ {y \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.55, + 0.906, + 0.686 + ], + "angle": 0, + "content": "where \\( d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1 \\). This formulation uses the probability of a sample belonging to a class outside the children of \\( c \\) as a proxy for the OOD probability while keeping the conditional probabilities for the children as predicted by \\( p(y|x;\\theta_d) \\). However, we find that this approach alone tends to assign too low probabilities for OOD and fails to account for the uncertainty among the child nodes. To address this, we also consider the entropy of the normalized distribution over the children:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.693, + 0.905, + 0.728 + ], + "angle": 0, + "content": "\\[\nH (c) = - \\sum_ {c ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right) \\log \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.736, + 0.559, + 0.749 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.746, + 0.905, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\tilde {p} \\left(c ^ {\\prime} \\mid x; \\theta_ {d}\\right) = \\frac {p \\left(c ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}{\\sum_ {\\tilde {c} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (\\tilde {c} \\mid x ; \\theta_ {d})}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.786, + 0.904, + 0.815 + ], + "angle": 0, + "content": "High entropies indicate uncertainty among the children, i.e., when multiple children are assigned similar probabilities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.816, + 0.905, + 0.86 + ], + "angle": 0, + "content": "Since the entropy and the complementary probability (10) are independent and account for different aspects of uncertainty, we combine these in a sum as" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.87, + 0.905, + 0.904 + ], + "angle": 0, + "content": "\\[\ns (c) = H (c) + 1 - \\sum_ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}). \\tag {13}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20615" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.138 + ], + "angle": 0, + "content": "However, this score no longer forms a probability distribution when combined with \\( p(y|x;\\theta_d) \\) for \\( y \\in \\mathrm{Ch}_{\\mathcal{H}}(c) \\). To resolve this, we normalize to obtain the valid distribution as" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.144, + 0.483, + 0.18 + ], + "angle": 0, + "content": "\\[\np (y | c, x) = \\frac {p (y | x ; \\theta_ {d})}{s (c) + \\sum_ {y ^ {\\prime} \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} | x ; \\theta_ {d}\\right)} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.187, + 0.228, + 0.204 + ], + "angle": 0, + "content": "for \\(y\\in \\mathrm{Ch}_{\\mathcal{H}}(c)\\) and" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.21, + 0.483, + 0.247 + ], + "angle": 0, + "content": "\\[\np \\left(\\operatorname {o o d} (c) \\mid c, x\\right) = \\frac {s (c)}{s (c) + \\sum_ {y ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.252, + 0.484, + 0.282 + ], + "angle": 0, + "content": "which gives us the final model for the conditional distributions in our hierarchical framework." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.295, + 0.32, + 0.312 + ], + "angle": 0, + "content": "5. Experiments and results" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.32, + 0.194, + 0.334 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.342, + 0.484, + 0.448 + ], + "angle": 0, + "content": "There are no established datasets for OOD detection in class hierarchies. We construct our benchmarks using three datasets with predefined hierarchies commonly used in work for hierarchy-aware ID classification. We generate ID and OOD subsets by selecting OOD nodes from various depths within these hierarchies. Our experiments are conducted on the following datasets:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.484, + 0.585 + ], + "angle": 0, + "content": "FGVC-Aircraft [20]: This dataset contains aircraft images with a three-level hierarchy: at the highest level are manufacturers (e.g., Boeing), the second level groups aircraft by family (e.g., Boeing 747), and the most specific level contains variants (e.g., Boeing 747-200). FGVC-Aircraft has the most shallow hierarchy and the fewest classes among the considered datasets, but it poses challenging classification tasks, such as distinguishing between separate Boeing 747 types." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.659 + ], + "angle": 0, + "content": "iNaturalist19 [28]: A dataset of biological species organized in a hierarchy according to taxonomic ranks such as kingdom, phylum, and genus. It includes a large number of classes with fine-grained relationships and has a deeper hierarchy than FGVC-Aircraft." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.902 + ], + "angle": 0, + "content": "SimpleHierImageNet: This dataset is based on tieredImageNet [25], which is a subset of ImageNet using a hierarchy based on the WordNet graph [21]. However, the hierarchy of tieredImageNet has many nodes representing conceptual rather than visual similarities. For example, it has the high-level class timepiece with the subclasses analog clock and digital clock, or the leaf class laptop computer under the high-level class portable computer, while computer keyboard is nine edges away under electronic equipment. To address this, we introduce SimpleHierImageNet by reorganizing parts of the tieredImageNet hierarchy to reflect visual similarities. Despite these adjustments, SimpleHierImageNet remains a challenging problem with a wide range of categories and a deep hierarchy with many internal nodes. More details on SimpleHierImageNet are available in the supplementary material." + }, + { + "type": "table_caption", + "bbox": [ + 0.531, + 0.09, + 0.888, + 0.104 + ], + "angle": 0, + "content": "Table 1. Dataset details (after being split into ID and OOD)." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.105, + 0.894, + 0.182 + ], + "angle": 0, + "content": "
Max depthNr. ID leavesNr. internal nodesNr. OOD classes
FGVC-Aircraft3802820
SimpleHierImageNet115186380
iNaturalist19672177289
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.204, + 0.905, + 0.354 + ], + "angle": 0, + "content": "The considered datasets lack established ID/OOD splits. Therefore, we construct the OOD set by selecting nodes from various depths of the hierarchy. For each selected OOD node, we remove it and all its descendants from the hierarchy, leaving the remaining nodes to form our ID hierarchy \\(\\mathcal{H}\\). After defining the ID hierarchy \\(\\mathcal{H}\\) and the set of OOD classes, we map the labels of the OOD data (which are leaf nodes in the full original hierarchy) to their closest ancestor present in the ID hierarchy \\(\\mathcal{H}\\). These mapped labels are then used in the experimental evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.355, + 0.905, + 0.416 + ], + "angle": 0, + "content": "Details of the datasets, after defining the ID and OOD sets are described in Tab. 1. Additional information on the datasets and the selection of OOD sets is available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.424, + 0.878, + 0.44 + ], + "angle": 0, + "content": "5.2. Evaluating multi-depth networks for OOD" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.447, + 0.905, + 0.522 + ], + "angle": 0, + "content": "To evaluate our hypothesis that multi-depth networks are effective for OOD classification, we compare the accuracy obtained from our high-level models \\( f_{\\theta_1}, \\ldots, f_{\\theta_{D-1}} \\) to the accuracy obtained by marginalizing the leaf-level model \\( f_{\\theta_D} \\), when evaluated on OOD data." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.522, + 0.905, + 0.553 + ], + "angle": 0, + "content": "Specifically, we have a dataset of OOD data associated with different depths of the hierarchy:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.559, + 0.905, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {o o d}}}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.588, + 0.905, + 0.604 + ], + "angle": 0, + "content": "We define subsets of \\(S^{\\mathrm{odd}}\\) associated with specific depths as" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.611, + 0.905, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {d} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\in \\mathcal {S} ^ {\\mathrm {o o d}} \\mid \\operatorname {D e p t h} _ {\\mathcal {H}} \\left(y _ {i}\\right) = d \\right\\}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.638, + 0.905, + 0.699 + ], + "angle": 0, + "content": "for \\(d\\in \\{1,\\dots ,D - 1\\}\\) . Now we can compute the classification accuracies obtained by the network \\(f_{\\theta_d}\\) on the dataset \\(S_{d}^{\\mathrm{odd}}\\) . We compare this with the predictions obtained by marginalizing the predictions of the ID leaf model \\(f_{\\theta_D}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.707, + 0.905, + 0.742 + ], + "angle": 0, + "content": "\\[\np _ {d} ^ {\\text {m a r g i n}} (c | x) = \\sum_ {c ^ {\\prime} \\in \\text {L e a v e s} _ {\\mathcal {H}} (c)} p \\left(c ^ {\\prime} | x; \\theta_ {D}\\right) \\quad \\text {f o r} c \\in \\mathcal {C} ^ {d}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.75, + 0.842, + 0.765 + ], + "angle": 0, + "content": "where \\(\\mathrm{Leaves}_{\\mathcal{H}}(c)\\) are the descendant leaves of \\(c\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Table 2 shows the results of this comparison across our three considered datasets. The multi-depth model obtains higher accuracies than the marginalized model for all datasets, indicating that the high-level models are better at classifying OOD samples as the correct class. Moreover, this implies that while a high-level model correctly predicts an OOD sample as class \\( c \\), the lower-level model leans towards predicting classes not in \\( \\mathrm{Ch}_{\\mathcal{H}}(c) \\), which is the behavior we are looking for." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20616" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.09, + 0.483, + 0.131 + ], + "angle": 0, + "content": "Table 2. Classification accuracies on OOD data at ground-truth depths. We compare models trained with high-level labels with models trained using the leaf labels." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.133, + 0.465, + 0.228 + ], + "angle": 0, + "content": "
DatasetAccuracy (%) ↑Δ ↑
Multi-depth p(c|x; θd)Marginalized pdmargin(c|x)
SimpleHierImageNet70.168.5+1.6
iNaturalist1976.573.6+2.9
FGVC-Aircraft67.350.3+17.0
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.253, + 0.273, + 0.267 + ], + "angle": 0, + "content": "5.3. Evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.276, + 0.484, + 0.412 + ], + "angle": 0, + "content": "How to evaluate a framework for OOD detection in class hierarchies is not established. In alignment with works on ID classification with class hierarchies [10, 15], we focus primarily on hierarchical distances between predictions and ground truth. However, given that our OOD nodes are selected at varying depths in the hierarchy, the resulting OOD sets have highly imbalanced class distributions. Therefore we propose to use a balanced mean hierarchical distance (BMHD), defined as" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.422, + 0.482, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\operatorname {B M H D} \\left(\\mathcal {C} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {C} ^ {\\prime} |} \\sum_ {c \\in \\mathcal {C} ^ {\\prime}} \\frac {1}{n _ {c}} \\sum_ {i = 1} ^ {n _ {c}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(f \\left(x _ {i} ^ {c}\\right), c\\right), \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.473, + 0.483, + 0.564 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}'\\) is the set of classes being considered, \\(n_c\\) is the number of samples in the test set with ground truth label \\(c\\), \\(x_i^c\\) is the \\(i\\)-th sample out of those, and \\(|\\mathcal{C}'|\\) is the cardinality of \\(\\mathcal{C}'\\). In BMHD(\\(\\mathcal{C}'\\)), the mean distances for nodes in \\(\\mathcal{C}'\\) are weighted equally, regardless of how many samples are associated with a specific node." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.484, + 0.608 + ], + "angle": 0, + "content": "Furthermore, we want to evaluate the performance on a combined set of ID and OOD data. To this end, we define the mixed BMHD as" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.621, + 0.482, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M i x B M H D} = 0. 5 \\left(\\mathrm {B M H D} _ {\\text {i d}} + \\mathrm {B M H D} _ {\\text {o o d}}\\right), \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.648, + 0.484, + 0.739 + ], + "angle": 0, + "content": "where \\(\\mathrm{BMHD_{id}}\\) and \\(\\mathrm{BMHD_{ood}}\\) are evaluated with (19) on the set of ID and OOD classes with test data available, respectively. Similarly, we evaluate classification accuracies as the proportion of predictions that match the ground truth labels. Because of the class imbalance, we consider a balanced accuracy score [22]:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.751, + 0.482, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M i x B A c c} = 0. 5 \\left(\\mathrm {B A c c} _ {\\mathrm {i d}} + \\mathrm {B A c c} _ {\\mathrm {o o d}}\\right), \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.778, + 0.483, + 0.809 + ], + "angle": 0, + "content": "where \\(\\mathrm{BAcc_{id}}\\) and \\(\\mathrm{BAcc_{ood}}\\) denote the balanced accuracies for ID and OOD classes, respectively." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.185, + 0.832 + ], + "angle": 0, + "content": "5.4. Results" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.841, + 0.455, + 0.856 + ], + "angle": 0, + "content": "We compare our framework to the following baselines:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Depth oracle: We make predictions using the ground-truth depth with the corresponding \\( p(c|x;\\theta_d) \\) for all data, i.e., \\( p(c|x;\\theta_D) \\) for ID data and \\( p(c|x;\\theta_d), d < D \\) for OOD" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "data. Given the accuracies of the multi-depth networks, we consider this an upper performance bound." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.123, + 0.905, + 0.153 + ], + "angle": 0, + "content": "Leaf model: We predict all data using \\( p(c|x;\\theta_D) \\), i.e., all data are predicted as leaves, including OOD." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.154, + 0.906, + 0.259 + ], + "angle": 0, + "content": "HSC: We train and evaluate the model proposed in [16] using the authors' code. We present results using the synset-based stopping-criterion because that gives the best results. We set thresholds for stopping criteria based on TPR rates to minimize MixBMHD on the test sets. However, in real-world settings, we cannot optimize these thresholds based on test performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.26, + 0.906, + 0.366 + ], + "angle": 0, + "content": "Our framework, denoted ProHOC (for probabilistic hierarchical OOD classification), is evaluated using the two different models for the conditionals described in Sec. 4.1. The first, denoted CompProb, uses the complementary probabilities to model the OOD probabilities, as defined in (10). The second, EntCompProb, uses the sum of the entropy and the complementary probability, as defined in (13)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.367, + 0.906, + 0.502 + ], + "angle": 0, + "content": "The results are presented in Tab. 3. Excluding the oracle model, ProHOC with EntCompProb yields the best MixBMHD and MixBAcc across all three datasets, with CompProb consistently ranking second. Looking at the numbers for ID and OOD separately, we note the tradeoff between ID and OOD performance, where the CompProb model favors ID performance by making deeper predictions. In contrast, the EntCompProb model has a more balanced performance across ID and OOD." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.906, + 0.609 + ], + "angle": 0, + "content": "ProHOC outperforms HSC [16], the existing method for OOD detection in hierarchies. This is despite optimizing the inference thresholds in HSC using OOD test data. We can see that HSC tends to make overly deep predictions, keeping an ID performance close to the leaf model but showing poor OOD performance. More detailed analyses of the results are available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.62, + 0.804, + 0.637 + ], + "angle": 0, + "content": "5.5. Evaluating out-of-hierarchy data" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Section 5.4 focuses on evaluating within-hierarchy OOD data, as these samples are the most challenging and distinguish our hierarchical approach from the binary OOD setting. However, ProHOC supports out-of-hierarchy OOD by classifying such samples as OOD at the root node. The OOD probability at the root is computed via (15) with \\( s(\\mathrm{root}) \\) being a positive score from any suitable binary OOD method. For simplicity, we use the entropy of the deepest network for \\( s(\\mathrm{root}) \\) which is a common baseline for binary OOD detection [24] that aligns well with our EntComp-Prob model. Table 4 shows ProHOC for FGVC-Aircraft with root predictions on three out-of-hierarchy datasets. MixBAcc is the (balanced) accuracy on the mix of within-hierarchy ID and OOD. Acc for out-of-hierarchy datasets is the percentage of samples correctly classified as root. We get high accuracies on out-of-hierarchy OOD while keeping most within-hierarchy performance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20617" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.118 + ], + "angle": 0, + "content": "Table 3. Mean hierarchical distances and accuracies on ID, OOD, and the mix of ID and OOD for ProHOC and baselines. The oracle model serves as an upper performance bound. Excluding the oracle model, the best results are boldfaced. Evaluations use test sets." + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.12, + 0.813, + 0.412 + ], + "angle": 0, + "content": "
BAccid↑BAccood↑MixBAcc↑BMHDid↓BMHDood↓MixBMHD↓
SIMPLEHIERIMAGENET
Depth oracle79.772.576.10.821.050.93
Leaf model79.70.039.80.822.121.47
HSC [16]76.87.842.30.771.781.28
ProHOC (CompProb)67.819.243.50.921.611.27
ProHOC (EntCompProb)62.530.346.40.961.451.21
INATURALIST19
Depth oracle72.475.974.20.850.820.83
Leaf model72.40.036.20.852.231.54
HSC [16]68.18.438.20.801.761.28
ProHOC (CompProb)66.118.042.00.771.341.06
ProHOC (EntCompProb)57.735.646.70.781.100.94
FGVC-AIRCRAFT
Depth oracle84.767.676.10.490.670.58
Leaf model84.70.042.30.492.001.25
HSC [16]77.914.446.10.401.480.94
ProHOC (CompProb)80.117.148.60.411.250.83
ProHOC (EntCompProb)78.022.750.30.411.210.81
" + }, + { + "type": "table_caption", + "bbox": [ + 0.125, + 0.434, + 0.449, + 0.448 + ], + "angle": 0, + "content": "Table 4. Evaluating ProHOC on out-of-hierarchy data." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.45, + 0.466, + 0.514 + ], + "angle": 0, + "content": "
MixBAcc ↑ (FGVC-Air.)Acc ↑ Office31 [26]Acc ↑ iNat19Acc ↑ PACS [13]
ProHOC w/ root47.178.283.994.4
ProHOC w/o root50.3---
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.537, + 0.249, + 0.553 + ], + "angle": 0, + "content": "5.6. Training details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.56, + 0.484, + 0.742 + ], + "angle": 0, + "content": "We train our multi-depth networks with standard supervised NLL training using the remapped labels from (8). We use the ResNet50 architecture [6] for all experiments. For FGVC-Aircraft and iNaturalist19, the network is initialized with pre-trained weights from ImageNet, whereas for SimpleHierImageNet, we train the network from scratch. We train for 90 epochs on FGVC-Aircraft and iNaturalist19, and 250 epochs on SimpleHierImageNet. We use stochastic gradient descent with an initial learning rate of 0.05, decayed to zero by the end of training using a cosine schedule. A batch size of 128 is used throughout. During training, images are randomly cropped and resized to \\(224 \\times 224\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.755, + 0.214, + 0.77 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.901 + ], + "angle": 0, + "content": "This work focuses on establishing the key building blocks of our framework for hierarchical OOD detection, with little attention given to optimizing the performance of the underlying multi-depth networks. Further work could explore stronger architectures and advanced training techniques to improve the performance of ProHOC. Finally, a fundamental limitation of our problem formulation is the assumption that the class hierarchy reflects observable visual similarities" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.436, + 0.907, + 0.482 + ], + "angle": 0, + "content": "ties. If ID and OOD siblings do not share common visual features, we can not expect this type of framework to accurately predict OOD." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.494, + 0.676, + 0.51 + ], + "angle": 0, + "content": "7. Ablation studies" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.518, + 0.907, + 0.535 + ], + "angle": 0, + "content": "7.1. Evaluating different scores for the conditionals" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.542, + 0.906, + 0.648 + ], + "angle": 0, + "content": "In Sec. 4.1 we described how we use the multi-depth networks to model the conditionals \\( p(y|c, x) \\) for \\( y \\in \\mathrm{Ch}_{\\mathcal{H}}(c) \\cup \\{\\mathrm{odd}(c)\\} \\). The primary challenge in modeling \\( p(y|c, x) \\) lies in assigning the OOD probability. Here, we explore several approaches to modeling this OOD probability, or an unnormalized OOD score, based on the predictions from our multi-depth networks. We consider the following models:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.906, + 0.693 + ], + "angle": 0, + "content": "CompProb: The complementary probability, as defined in (10). It uses the sum of probabilities for classes outside of \\(\\mathrm{Ch}_{\\mathcal{H}}(c)\\) as a proxy for the OOD probability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.693, + 0.906, + 0.738 + ], + "angle": 0, + "content": "Entropy: As defined in (11), indicates the uncertainty of predictions among the children. The entropy is widely used as an OOD score in the literature [24]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.738, + 0.906, + 0.768 + ], + "angle": 0, + "content": "MaxProb: The (negated) maximum probability among the children, defined as" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.775, + 0.907, + 0.802 + ], + "angle": 0, + "content": "\\[\ns ^ {\\operatorname {M a x P r o b}} (c) = 1 - \\max _ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}) \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.841 + ], + "angle": 0, + "content": "with \\(d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1\\). This alternative is similar to the widely used MSP score [7] for binary OOD detection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "EntCompProb: Since the entropy and the complementary probability are independent and signal different aspects of uncertainty, we find it intuitive to combine scores in a sum, as defined in (13)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20618" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.182 + ], + "angle": 0, + "content": "CompLogits: We sum the unnormalized logits for classes outside \\(\\mathrm{Ch}_{\\mathcal{H}}(c)\\) and use the sum in the softmax function alongside the logits for the child nodes. This method resembles CompProb, although it differs in the scaling of the OOD probability due to summing before applying the exponential function in the softmax." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.183, + 0.483, + 0.243 + ], + "angle": 0, + "content": "The methods denoted CompProb and CompLogits form valid probability distributions directly by design. For the other alternatives, we obtain the conditional distribution by normalization following (14) and (15)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.244, + 0.484, + 0.394 + ], + "angle": 0, + "content": "A well-performing model for the conditionals should display certain qualities. The probability for OOD in the conditional distribution should be the maximum when the sample is OOD. Moreover, if the network misclassifies an ID sample (predicting it as an incorrect ID child), we want our model to predict the OOD node instead of an incorrect ID prediction, which would increase the hierarchical distance from the ground truth. To assess these aspects of the performance, we use several metrics that are evaluated locally for a specific internal node:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.396, + 0.484, + 0.456 + ], + "angle": 0, + "content": "F1: The F1 score for binary classification where OOD is considered the positive label. A prediction is OOD if \\( p(\\mathrm{odd}(c)|c,x) \\) is the largest element of \\( p(y|c,x) \\), otherwise ID. We also report the corresponding FPR and TPR." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.483, + 0.485 + ], + "angle": 0, + "content": "Purity: The fraction of predicted ID samples, predicted as the correct child node." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.532 + ], + "angle": 0, + "content": "Dirty F1: Our variant of the F1 score where ID data that are misclassified as an incorrect child are labeled as OOD when computing the F1 score." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.483, + 0.593 + ], + "angle": 0, + "content": "We evaluate these metrics for all parent nodes \\( c \\) for which OOD data with ground truth at \\( c \\) are available. As ID data, we use all data that belong to descendants of \\( c \\). We report the mean metrics over all evaluated nodes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.594, + 0.483, + 0.791 + ], + "angle": 0, + "content": "Table 5 shows results from FGVC-Aircraft. EntCompProb achieves the highest F1 score. It has the largest FPR but this is compensated by its high purity, indicating that many false positives would have been classified as incorrect ID children if they were predicted as ID. For Dirty F1, EntCompProb again outperforms other methods, by an even larger margin. This suggests that the entropy-based uncertainty and the complementary probability interact effectively to create a model with the desired properties. In contrast, CompLogits performs poorly due to being underconfident on OOD (a low TPR). This implies that summation at the logit level leads to smaller OOD probabilities than summation at the probability level (as with CompProb)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.802, + 0.481, + 0.818 + ], + "angle": 0, + "content": "7.2. Minimizing the expected hierarchical distance" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.901 + ], + "angle": 0, + "content": "ProHOC provides a predictive distribution over all nodes in the hierarchy, allowing us to incorporate uncertainty into our final prediction. Given our objective to produce predictions that are hierarchically close to the ground truth (1), we can use the predicted distribution \\( p(c|x) \\) to minimize the" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.905, + 0.117 + ], + "angle": 0, + "content": "Table 5. Analyzing the performance of different methods for modeling \\( p(\\mathrm{odd}(c)|c,x) \\). Results are from FGVC-Aircraft." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.118, + 0.88, + 0.207 + ], + "angle": 0, + "content": "
F1 ↑FPR ↓TPR ↑Purity ↑Dirty F1 ↑
CompProb0.470.090.420.880.49
Entropy0.510.120.450.900.55
MaxProb0.500.100.450.890.52
EntCompProb0.560.150.520.900.59
CompLogits0.170.010.140.870.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.221, + 0.905, + 0.248 + ], + "angle": 0, + "content": "Table 6. Comparing predictions from minimizing the expected hierarchical distance to predictions using the most probable class." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.25, + 0.888, + 0.435 + ], + "angle": 0, + "content": "
argmin E[distH]argmax p(c|x)
MixBAcc ↑ MixBMHD ↓MixBAcc ↑ MixBMHD ↓
SIMPLEHIERIMAGENET
EntCompProb46.41.2145.81.25
CompProb43.51.2739.71.37
INATURALIST19
EntCompProb46.70.9445.60.98
CompProb42.01.0638.41.17
FGVC-AIRCRAFT
EntCompProb50.30.8150.20.88
CompProb48.60.8347.40.90
" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.45, + 0.827, + 0.465 + ], + "angle": 0, + "content": "expected hierarchical distance of the prediction" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.481, + 0.905, + 0.505 + ], + "angle": 0, + "content": "\\[\nf (x) = \\underset {c} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right], \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.905, + 0.58 + ], + "angle": 0, + "content": "as presented in Sec. 3. This is similar to the post-hoc correction proposed in [10], although they restrict the predictions to leaves. We compute the expected hierarchical distance over all nodes in the hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.906, + 0.673 + ], + "angle": 0, + "content": "We compare the predictions from (23) with the standard \\(\\mathrm{argmax}_c p(c|x)\\) in Tab. 6, using ProHOC with both CompProb and EntCompProb. As expected, (23) achieves lower hierarchical distances since it optimizes for that specifically. However, we also see improvements in accuracy as an additional benefit of using (23)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.693, + 0.634, + 0.708 + ], + "angle": 0, + "content": "8. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.9 + ], + "angle": 0, + "content": "The deep-learning community has made substantial progress in the binary setting of OOD detection. In this paper, we raise the bar for OOD detection by aiming for more informative predictions: predicting OOD as internal nodes in a class hierarchy. Our framework shows promising results. We also believe its simplicity in introducing no new hyperparameters and using underlying networks trained with standard methods makes it accessible and adaptable for further development. We hope this work will inspire continued exploration of OOD classification in class hierarchies and that ProHOC can serve as a foundation for even more effective methods." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20619" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.114, + 0.484, + 0.226 + ], + "angle": 0, + "content": "This work was supported by Saab AB and Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agreement no. 2022-06725." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.238, + 0.188, + 0.253 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.263, + 0.484, + 0.318 + ], + "angle": 0, + "content": "[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. Neo: Neural collapse based out-of-distribution detection. In International Conference on Learning Representations, 2024. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.319, + 0.484, + 0.36 + ], + "angle": 0, + "content": "[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. 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Openood v1.5: Enhanced benchmark for out-of-distribution detection. arXiv preprint arXiv:2306.09301, 2023. 1" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.093, + 0.483, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20621" + } + ] +] \ No newline at end of file diff --git a/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_origin.pdf b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..50fc3665b68c4f34dce5c263d6ab7d5b1c31b495 --- /dev/null +++ b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/ea6afc41-0a54-4fa5-8ade-1924337e5c45_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:deefa7fb0b78436888227972ae13d72104909f0afcc3a197f79493bfcedfa205 +size 857721 diff --git a/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/full.md b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..66a14090881eb5590dfbdbb7b072aecb4523de93 --- /dev/null +++ b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/full.md @@ -0,0 +1,407 @@ +# ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks + +Erik Wallin $^{1,2}$ , Fredrik Kahl $^{2}$ , Lars Hammarstrand $^{2}$ , Saab AB, $^{2}$ Chalmers University of Technology + +{wallline, fredrik. kahl, lars.hammarstrand}@chalmers.se + +# Abstract + +Out-of-distribution (OOD) detection in deep learning has traditionally been framed as a binary task, where samples are either classified as belonging to the known classes or marked as OOD, with little attention given to the semantic relationships between OOD samples and the indistribution (ID) classes. We propose a framework for detecting and classifying OOD samples in a given class hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the class hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the class hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined class hierarchies and show the effectiveness of our method. Our code is available at https://github.com/walline/prohoc. + +# 1. Introduction + +Effectively handling out-of-distribution samples is important for deep-learning applications. Data outside the training domain often yield unpredictable results when fed through deep neural networks [7], making it essential to account for previously unseen data when deploying these models in real-world settings to ensure robust performance and avoid unexpected outcomes. Previous literature [31] has focused on binary out-of-distribution detection, predicting data either as ID (in-distribution) or OOD (out-of-distribution), without differentiating between OOD samples that are semantically close or far from ID. For example, with ID classes consisting of dog breeds, this binary paradigm would treat an image of an unknown dog the same as an image of an airplane, overlooking the varying degrees of semantic similarity these samples have to the known classes. + +We explore a new setting of OOD detection, utilizing class hierarchies to predict semantically close OOD sam + +![](images/38109b5948ff6e1a05eb42a085ab871465e8c992573b245b45441e181a33e5c9.jpg) +Figure 1. Out-of-distribution detection in class hierarchies. Instead of simply predicting the unseen dog and cat types as OOD, we aim to classify them as the high-level categories dog and cat. + +plies as their correct nodes in the class hierarchy. Hierarchical models for organizing and classifying objects are widespread, from foundational examples like Linnaeus' taxonomy in Systema Naturae [17] to modern structures like WordNet [21] for semantic relations. While the deep learning community has shown a growing interest in utilizing class hierarchies [4, 9], their application for OOD detection remains largely unexplored. However, such hierarchies can provide a foundation for enabling more informative OOD predictions. For instance, in the hierarchy shown in Figure 1, the binary paradigm of OOD detection treats the unseen cat and dog as simply OOD. In contrast, with knowledge of the hierarchy, we can classify the unseen dog as the broader dog category (while recognizing it as distinct from previously seen breeds). + +One of many motivating examples arises in the context of an autonomous driving system. A sensor model might be trained to classify objects such as bicycles, electric scooters, and mopeds (among other classes). However, many system components treat these objects similarly, grouping them as + +slow-moving vehicles. When encountering an obscure object not present in the training data, such as a unicycle or a penny-farthing, the ideal response would be to recognize it as a slow-moving vehicle, rather than misclassifying it as a known class or simply marking it as OOD, which would provide limited actionable information. + +Our approach addresses this problem by leveraging the class hierarchy to factorize the probability distribution of predictions in the tree. This probability model includes conditional probabilities at each parent node, at which the possible predictions are either one of its child nodes or OOD at that specific node. Our key challenge lies in modeling these conditionals, as we assume no OOD data are available for training. To approximate these conditionals, we train classification networks at each depth of the hierarchy. We find that networks trained to classify classes higher in the hierarchy better recognize features associated with broad categories, making them better at predicting OOD samples to the correct high-level category. Similarly, the more fine-grained models may display larger uncertainty for these OOD samples because they contain low-level features that are not recognized by these models. + +We explore several methods for leveraging these multi-depth networks to approximate the conditionals in our probabilistic framework based on standard OOD scores. We evaluate our proposed model, ProHOC, on three datasets with predefined class hierarchies that we split into ID and OOD and show that our method outperforms previous attempts. Moreover, our framework has the benefit of introducing no new hyperparameters and uses standard methods for training the underlying multi-depth networks, making it straightforward to extend and build upon. We believe that our model can serve as a strong foundation for further research in this relatively unexplored area. + +Our main contributions are as follows: + +- We formulate a probabilistic framework for classifying data, both ID and OOD, as nodes in a class hierarchy. +- We explore and enable the implementation of this framework by utilizing multi-depth networks to approximate the conditionals in the probabilistic model. +- We experimentally evaluate our framework and baselines on several datasets, showing the effectiveness of our method. + +# 2. Related work + +# 2.1. Hierarchy-aware ID classification + +Several works incorporate class hierarchies in training models for ID classification, focusing on minimizing the hierarchical distance between predictions and ground truth rather than only optimizing for classification accuracy [4, 5, 9, 10, 15]. This approach prioritizes models that make errors close to the correct class in the hierarchy, which often can be + +preferable to models that make more distant mistakes. This aspect of performance is typically disregarded in works on standard flat classification. + +The existing approaches to this problem vary. In [4], they propose adjustments to the standard cross-entropy loss to account for higher-level decisions in the hierarchy. The works [5, 15] introduce hierarchy-aware feature spaces to obtain the desired model properties. In [10], they suggest a post-hoc method that rescales flat prediction probabilities by hierarchical distances to produce predictions minimizing the expected hierarchical distance. + +Most similar to our approach is [9], which proposes training separate coarse and fine-grained classifiers to improve both classification accuracy and hierarchical distance. However, their method is restricted to classifiers at two levels (one coarse and one fine), whereas we train classifiers at all levels of the hierarchy. + +This overall line of research is similar to our setting in that we consider class hierarchies to minimize the hierarchical distance between ground truth and predictions. However, a key difference is that these works only consider ID data and therefore restrict the predictions to leaf nodes only. In contrast, we need a framework able to predict internal nodes as OOD predictions. + +# 2.2. Out-of-distribution detection + +Out-of-distribution is an active field of research [2, 7, 12, 14, 27]. The goal is to detect whether a data sample belongs to the training distribution or not, motivated by the need to handle real-world, uncurated settings. The common approach in this field is to design a score based on neural network outputs, which takes high values for OOD data and low values for ID data (or vice versa). The score can be derived from, e.g., predicted distributions [7, 19, 24], logits [18, 29], or feature representations [1, 12, 30]. + +Our setting introduces some new challenges compared to the standard binary paradigm of OOD detection. First, instead of only detecting OOD as a binary prediction, we aim to classify OOD samples as specific nodes within the class hierarchy. Second, we ultimately need to make hard decisions about which node to predict, so unnormalized scores that lack probabilistic interpretations or easily inferrable thresholds are of limited use. Lastly, many works on OOD detection use comparably simple problem settings, using one dataset as ID and an unrelated dataset as OOD [12, 18]. In contrast, our setting naturally involves complex, fine-grained detection tasks, as OOD samples can appear at any depth within the class hierarchy. + +As a final note, a few works exist that consider class hierarchies and OOD detection simultaneously [8, 11, 29]. In [11, 29], they use class hierarchies to construct OOD sets of varying difficulty by selecting the OOD sets from different depths of the class hierarchy. The work [8] proposes a score + +that signals high OOD-ness if two classifiers predict distinct classes separated by a large hierarchical distance. However, these works still consider only binary OOD predictions. + +# 2.3. Hierarchical out-of-distribution detection + +To the best of our knowledge, the only work that considers detection and classification of OOD in class hierarchies similarly to us is [16]. Their method involves separate model heads for each internal node in the hierarchy. For data that are descendants of a specific node, the corresponding head is trained to predict the correct child using a standard cross-entropy loss. For non-descendant data points, the head is trained to produce a uniform distribution. + +There are key distinctions between [16] and our work. First, our method introduces no additional hyperparameters, whereas [16] requires balancing multiple loss terms during training. Second, their approach performs hierarchical inference in a top-down manner, with thresholds at each node to decide where to stop. These thresholds need to be assigned using ID data and it is not clear how to select these to ensure performance on both ID and OOD data while generalizing to multiple datasets. In contrast, our fully probabilistic approach provides a predictive distribution over all nodes in the hierarchy, eliminating the need for threshold-based top-down inference. + +# 3. A probabilistic hierarchy-framework + +Our approach for detecting and classifying OOD in class hierarchies is based on creating a probabilistic model from the class hierarchy. We assume that this hierarchy $\mathcal{H}$ is given and that it is structured as a directed rooted tree [3] (e.g., the green nodes of Figure 1). We denote the nodes of this tree as $\mathcal{C}$ with the leaf nodes being $\mathcal{C}^{\mathrm{id}}\subset \mathcal{C}$ . We assume a distribution of ID data with classes corresponding to leaves in this hierarchy: $p^{\mathrm{id}}(x,y)$ , with $y\in \mathcal{C}^{\mathrm{id}}$ . These data are observed during training. Furthermore, we have a distribution of OOD data, not observable during training, $p^{\mathrm{odd}}(x,y)$ , with $y\in \mathcal{C}\setminus \mathcal{C}^{\mathrm{id}}$ . In other words, the OOD data do not match any ID leaf classes but correspond to groups of ID classes higher in the hierarchy. + +Our goal is to learn a model $f(x)$ that predicts samples from the balanced mix of ID and OOD, defined as $p^{\mathrm{mix}}(x,y) = 0.5(p^{\mathrm{id}}(x,y) + p^{\mathrm{odd}}(x,y))$ , to their correct nodes in $\mathcal{H}$ . If misclassified, the predictions should be hierarchically close to the ground truth. Formally, we aim to minimize the expected hierarchical distance between the prediction and the ground truth: + +$$ +\min \mathbb {E} _ {p ^ {\operatorname {m i x}} (x, y)} \left[ \operatorname {d i s t} _ {\mathcal {H}} (f (x), y) \right], \tag {1} +$$ + +where $\mathrm{dist}_{\mathcal{H}}(\cdot, \cdot)$ is the number of edges in the shortest path between two nodes in the undirected equivalent of $\mathcal{H}$ . + +To model $f(\cdot)$ , we construct a probabilistic model from the class hierarchy $\mathcal{H}$ . Specifically, we append a child node + +to each internal node of $\mathcal{H}$ to represent OOD predictions at that node (e.g., the red nodes of Figure 1), creating the new tree $\mathcal{G}$ . We denote the set of these OOD nodes as + +$$ +\mathcal {C} ^ {\mathrm {o o d}} = \left\{\operatorname {o o d} (c) | c \in \mathcal {C} \backslash \mathcal {C} ^ {\mathrm {i d}} \right\}. \tag {2} +$$ + +These nodes represent a sample belonging to class $c$ but not to any of $c$ 's known descendants. The model $\mathcal{G}$ describes the semantic classes of a sample as random binary variables at each node. We denote the probability of the set of nodes $\mathcal{C}'$ being active for a given sample $x$ as $p(\mathcal{C}'|x)$ . We assume that all samples belong to a leaf node $c \in \mathcal{C}^{\mathrm{id}} \cup \mathcal{C}^{\mathrm{odd}}$ but that the leaf nodes are mutually exclusive, i.e., a sample belongs to only one leaf node. Moreover, the internal nodes of $\mathcal{G}$ describe unions of these leaf nodes such that internal node $c$ is active if any of its descendant leaf nodes are active. This implies $p(c|x) = p(\operatorname{Anc}_{\mathcal{G}}^{+}(c)|x)$ , where $\operatorname{Anc}_{\mathcal{G}}^{+}(c)$ is the set of $c$ and all $c$ 's ancestors. From this follows the conditional independences $p(c|\operatorname{Anc}_{\mathcal{G}}^{+}(\operatorname{Par}_{\mathcal{G}}(c))) = p(c|\operatorname{Par}_{\mathcal{G}}(c))$ where $\operatorname{Par}_{\mathcal{G}}(c)$ is the parent node of $c$ . + +We can now factorize the probability of paths in $\mathcal{G}$ using the chain rule of probability and the induced conditional independences as + +$$ +p (c | x) = p \left(\operatorname {A n c} _ {\mathcal {G}} ^ {+} (c) | x\right) = \prod_ {c ^ {\prime} \in \operatorname {A n c} _ {\mathcal {G}} ^ {+} (c) \backslash R} p \left(c ^ {\prime} \mid \operatorname {P a r} _ {\mathcal {G}} \left(c ^ {\prime}\right), x\right), \tag {3} +$$ + +where the root node $R$ is excluded in the product because $p(R|x) = 1$ . For example, in the hierarchy of Figure 1, the probability for Lynx becomes $p(\mathrm{Lynx}|\mathrm{Cat}, x)p(\mathrm{Cat}|R, x)$ whereas the probability for an OOD Cat is $p(\mathrm{odd}(\mathrm{Cat})|\mathrm{Cat}, x)p(\mathrm{Cat}|R, x)$ . + +By applying (3) with $c \in \mathcal{C}^{\mathrm{id}} \cup C^{\mathrm{odd}}$ , we obtain the predictive distribution over all ID classes and OOD predictions at each internal node of $\mathcal{H}$ . Note that for evaluation purposes, predictions of $\mathrm{odd}(c)$ are mapped to the corresponding node $c$ in $\mathcal{H}$ to compute hierarchical distances. + +We use this distribution to obtain our final prediction. A standard approach is to use the argmax of $p(c|x)$ with $c \in \mathcal{C}^{\mathrm{id}} \cup \mathcal{C}^{\mathrm{odd}}$ . However, to better align with our objective in (1), we instead utilize the uncertainties of the predictive distribution to minimize the expected hierarchical distance between the predicted node for sample $x$ and its ground truth: + +$$ +f (x) = \underset {c \in \mathcal {C} ^ {\mathrm {i d}} \cup \mathcal {C} ^ {\mathrm {o o d}}} {\operatorname {a r g m i n}} \mathbb {E} _ {p \left(c ^ {\prime} \mid x\right)} \left[ \operatorname {d i s t} _ {\mathcal {H}} \left(c, c ^ {\prime}\right) \right] \tag {4} +$$ + +where the expectation is obtained by + +$$ +\mathbb {E} _ {p \left(c ^ {\prime} \mid x\right)} \left[ \operatorname {d i s t} _ {\mathcal {H}} \left(c, c ^ {\prime}\right) \right] = \sum_ {c ^ {\prime} \in \mathcal {C} ^ {\mathrm {i d}} \cup \mathcal {C} ^ {\mathrm {o o d}}} \operatorname {d i s t} _ {\mathcal {H}} \left(c, c ^ {\prime}\right) p \left(c ^ {\prime} \mid x\right). \tag {5} +$$ + +Note that $\mathrm{odd}(c)$ is mapped to $c$ in $\mathrm{dist}_{\mathcal{H}}(\cdot, \cdot)$ . In Sec. 7.2, we experimentally show the benefit of using (4) compared to the standard argmax approach. + +# 4. Leveraging multi-depth networks + +The predictive distribution of (3) requires the conditional distributions at each internal node of the class hierarchy: + +$$ +p (y | c, x), \quad y \in \operatorname {C h} _ {\mathcal {H}} (c) \cup \{\operatorname {o o d} (c) \} \tag {6} +$$ + +for $c \in \mathcal{C} \setminus \mathcal{C}^{\mathrm{id}}$ , where $\mathrm{Ch}_{\mathcal{H}}(c)$ is the set of children of $c$ according to the original tree $\mathcal{H}$ . However, as no OOD data are available during training, we cannot train a model to directly predict $p(\mathrm{odd}(c)|c,x)$ . Instead, as common for binary OOD detection [12, 30], we resort to hand-crafted models for the OOD predictions. + +Our idea for approaching these conditionals is to design classifiers from ID data that, given a sample belonging to $\mathrm{odd}(c)$ , confidently predict class $c$ while expressing uncertainty for the known child classes $\mathrm{Ch}_{\mathcal{H}}(c)$ . With such a model, the uncertainty of the sample's membership in $\mathrm{Ch}_{\mathcal{H}}(c)$ can be used as a proxy for $p(\mathrm{odd}(c)|c,x)$ . + +Following this reasoning, we propose training separate classification networks for the different depths of the hierarchy, with each network responsible for classifying data into nodes at a particular depth (see Figure 2). The intuition behind this approach is that the networks for high levels will emphasize the features associated with broad categories, which may not be helpful for more fine-grained classification. For instance, in the dogs-and-cats hierarchy of Figure 1, the network trained for the level above the leaves, responsible for classifying dog or cat, may focus on features like ear and tail shape, useful for distinguishing between any dog and any cat. Conversely, the leaf-level network might focus on fur patterns or facial features, important for distinguishing specific breeds. Consequently, an unseen cat breed might lack the features the leaf model recognizes, causing it to show uncertainty. However, the high-level network could still identify the features common to all cats and confidently classify the unseen cat breed as a cat. + +Specifically, we train these multi-depth networks using an ID dataset of samples and labels + +$$ +\mathcal {S} ^ {\mathrm {i d}} = \left\{\left(x _ {i}, y _ {i}\right) \mid y _ {i} \in \mathcal {C} ^ {\mathrm {i d}} \right\} _ {i = 1} ^ {n _ {\mathrm {i d}}}. \tag {7} +$$ + +To train high-level models, we map these leaf-level labels to their corresponding ancestors at specific depths. For this purpose, we define the function $\lambda(y, d)$ which maps the label $y$ to its corresponding ancestor at depth $d$ , or if $\mathrm{Depth}_{\mathcal{H}}(y) \leq d$ , maps $y$ to itself (this handles the case of all leaves not having equal depth). Consequently, we train the network for depth $d$ , denoted $f_{\theta_d}$ , using standard cross-entropy training, with the dataset + +$$ +\mathcal {S} _ {d} ^ {\mathrm {i d}} = \left\{\left(x _ {i}, \lambda \left(y _ {i}, d\right)\right) \mid y _ {i} \in \mathcal {C} ^ {\mathrm {i d}} \right\} _ {i = 1} ^ {n _ {\mathrm {i d}}}, \tag {8} +$$ + +and obtain the multi-depth networks $f_{\theta_1}, \ldots, f_{\theta_D}$ with the parameters $\theta_1, \ldots, \theta_D$ , where $D = \max_{c \in \mathcal{C}} \mathrm{Depth}_{\mathcal{H}}(c)$ . + +In Sec. 5.2, we present results showing that our multi-depth networks effectively classify OOD data. + +![](images/b342aa40f4ec27d88cf8c55bf12d588e45b71c9cd330d0d2b0fba19ee440d880.jpg) +Figure 2. For a hierarchy of depth 3, we train separate neural networks, parameterized by $\theta_{1}$ , $\theta_{2}$ , and $\theta_{3}$ , to classify data into nodes within that depth level. + +# 4.1. Modeling the conditionals of the hierarchy + +To model the conditionals $p(y|c, x)$ based on the multi-depth networks, $f_{\theta_1}, \ldots, f_{\theta_D}$ , we are looking for ways to quantify the uncertainty of $x$ belonging to $\mathrm{Ch}_{\mathcal{H}}(c)$ and use this to estimate $p(\mathrm{odd}(c)|c, x)$ . There are a variety of ways one could approach this. We have evaluated several alternatives based on standard OOD scores in Sec. 7.1. An intuitive and simple approach is to use + +$$ +p (y | c, x) = p (y | x; \theta_ {d}) \quad \text {f o r} \quad y \in \operatorname {C h} _ {\mathcal {H}} (c) \tag {9} +$$ + +and + +$$ +p (\mathbf {o o d} (c) | c, x) = 1 - \sum_ {y \in \mathrm {C h} _ {\mathcal {H}} (c)} p (y | x; \theta_ {d}), \tag {10} +$$ + +where $d = \mathrm{Depth}_{\mathcal{H}}(c) + 1$ . This formulation uses the probability of a sample belonging to a class outside the children of $c$ as a proxy for the OOD probability while keeping the conditional probabilities for the children as predicted by $p(y|x;\theta_d)$ . However, we find that this approach alone tends to assign too low probabilities for OOD and fails to account for the uncertainty among the child nodes. To address this, we also consider the entropy of the normalized distribution over the children: + +$$ +H (c) = - \sum_ {c ^ {\prime} \in \operatorname {C h} _ {\mathcal {H}} (c)} \tilde {p} \left(c ^ {\prime} | x; \theta_ {d}\right) \log \tilde {p} \left(c ^ {\prime} | x; \theta_ {d}\right), \tag {11} +$$ + +where + +$$ +\tilde {p} \left(c ^ {\prime} \mid x; \theta_ {d}\right) = \frac {p \left(c ^ {\prime} \mid x ; \theta_ {d}\right)}{\sum_ {\tilde {c} \in \operatorname {C h} _ {\mathcal {H}} (c)} p (\tilde {c} \mid x ; \theta_ {d})}. \tag {12} +$$ + +High entropies indicate uncertainty among the children, i.e., when multiple children are assigned similar probabilities. + +Since the entropy and the complementary probability (10) are independent and account for different aspects of uncertainty, we combine these in a sum as + +$$ +s (c) = H (c) + 1 - \sum_ {y \in \operatorname {C h} _ {\mathcal {H}} (c)} p (y | x; \theta_ {d}). \tag {13} +$$ + +However, this score no longer forms a probability distribution when combined with $p(y|x;\theta_d)$ for $y \in \mathrm{Ch}_{\mathcal{H}}(c)$ . To resolve this, we normalize to obtain the valid distribution as + +$$ +p (y | c, x) = \frac {p (y | x ; \theta_ {d})}{s (c) + \sum_ {y ^ {\prime} \in \mathrm {C h} _ {\mathcal {H}} (c)} p \left(y ^ {\prime} | x ; \theta_ {d}\right)} \tag {14} +$$ + +for $y\in \mathrm{Ch}_{\mathcal{H}}(c)$ and + +$$ +p \left(\operatorname {o o d} (c) \mid c, x\right) = \frac {s (c)}{s (c) + \sum_ {y ^ {\prime} \in \operatorname {C h} _ {\mathcal {H}} (c)} p \left(y ^ {\prime} \mid x ; \theta_ {d}\right)}, \tag {15} +$$ + +which gives us the final model for the conditional distributions in our hierarchical framework. + +# 5. Experiments and results + +# 5.1. Datasets + +There are no established datasets for OOD detection in class hierarchies. We construct our benchmarks using three datasets with predefined hierarchies commonly used in work for hierarchy-aware ID classification. We generate ID and OOD subsets by selecting OOD nodes from various depths within these hierarchies. Our experiments are conducted on the following datasets: + +FGVC-Aircraft [20]: This dataset contains aircraft images with a three-level hierarchy: at the highest level are manufacturers (e.g., Boeing), the second level groups aircraft by family (e.g., Boeing 747), and the most specific level contains variants (e.g., Boeing 747-200). FGVC-Aircraft has the most shallow hierarchy and the fewest classes among the considered datasets, but it poses challenging classification tasks, such as distinguishing between separate Boeing 747 types. + +iNaturalist19 [28]: A dataset of biological species organized in a hierarchy according to taxonomic ranks such as kingdom, phylum, and genus. It includes a large number of classes with fine-grained relationships and has a deeper hierarchy than FGVC-Aircraft. + +SimpleHierImageNet: This dataset is based on tieredImageNet [25], which is a subset of ImageNet using a hierarchy based on the WordNet graph [21]. However, the hierarchy of tieredImageNet has many nodes representing conceptual rather than visual similarities. For example, it has the high-level class timepiece with the subclasses analog clock and digital clock, or the leaf class laptop computer under the high-level class portable computer, while computer keyboard is nine edges away under electronic equipment. To address this, we introduce SimpleHierImageNet by reorganizing parts of the tieredImageNet hierarchy to reflect visual similarities. Despite these adjustments, SimpleHierImageNet remains a challenging problem with a wide range of categories and a deep hierarchy with many internal nodes. More details on SimpleHierImageNet are available in the supplementary material. + +Table 1. Dataset details (after being split into ID and OOD). + +
Max depthNr. ID leavesNr. internal nodesNr. OOD classes
FGVC-Aircraft3802820
SimpleHierImageNet115186380
iNaturalist19672177289
+ +The considered datasets lack established ID/OOD splits. Therefore, we construct the OOD set by selecting nodes from various depths of the hierarchy. For each selected OOD node, we remove it and all its descendants from the hierarchy, leaving the remaining nodes to form our ID hierarchy $\mathcal{H}$ . After defining the ID hierarchy $\mathcal{H}$ and the set of OOD classes, we map the labels of the OOD data (which are leaf nodes in the full original hierarchy) to their closest ancestor present in the ID hierarchy $\mathcal{H}$ . These mapped labels are then used in the experimental evaluation. + +Details of the datasets, after defining the ID and OOD sets are described in Tab. 1. Additional information on the datasets and the selection of OOD sets is available in the supplementary material. + +# 5.2. Evaluating multi-depth networks for OOD + +To evaluate our hypothesis that multi-depth networks are effective for OOD classification, we compare the accuracy obtained from our high-level models $f_{\theta_1}, \ldots, f_{\theta_{D-1}}$ to the accuracy obtained by marginalizing the leaf-level model $f_{\theta_D}$ , when evaluated on OOD data. + +Specifically, we have a dataset of OOD data associated with different depths of the hierarchy: + +$$ +\mathcal {S} ^ {\mathrm {o o d}} = \left\{\left(x _ {i}, y _ {i}\right) \mid y _ {i} \in \mathcal {C} \backslash \mathcal {C} ^ {\mathrm {i d}} \right\} _ {i = 1} ^ {n _ {\mathrm {o o d}}}. \tag {16} +$$ + +We define subsets of $S^{\mathrm{odd}}$ associated with specific depths as + +$$ +\mathcal {S} _ {d} ^ {\mathrm {o o d}} = \left\{\left(x _ {i}, y _ {i}\right) \in \mathcal {S} ^ {\mathrm {o o d}} \mid \operatorname {D e p t h} _ {\mathcal {H}} \left(y _ {i}\right) = d \right\}, \tag {17} +$$ + +for $d\in \{1,\dots ,D - 1\}$ . Now we can compute the classification accuracies obtained by the network $f_{\theta_d}$ on the dataset $S_{d}^{\mathrm{odd}}$ . We compare this with the predictions obtained by marginalizing the predictions of the ID leaf model $f_{\theta_D}$ as + +$$ +p _ {d} ^ {\text {m a r g i n}} (c | x) = \sum_ {c ^ {\prime} \in \text {L e a v e s} _ {\mathcal {H}} (c)} p \left(c ^ {\prime} | x; \theta_ {D}\right) \quad \text {f o r} c \in \mathcal {C} ^ {d}, \tag {18} +$$ + +where $\mathrm{Leaves}_{\mathcal{H}}(c)$ are the descendant leaves of $c$ + +Table 2 shows the results of this comparison across our three considered datasets. The multi-depth model obtains higher accuracies than the marginalized model for all datasets, indicating that the high-level models are better at classifying OOD samples as the correct class. Moreover, this implies that while a high-level model correctly predicts an OOD sample as class $c$ , the lower-level model leans towards predicting classes not in $\mathrm{Ch}_{\mathcal{H}}(c)$ , which is the behavior we are looking for. + +Table 2. Classification accuracies on OOD data at ground-truth depths. We compare models trained with high-level labels with models trained using the leaf labels. + +
DatasetAccuracy (%) ↑Δ ↑
Multi-depth p(c|x; θd)Marginalized pdmargin(c|x)
SimpleHierImageNet70.168.5+1.6
iNaturalist1976.573.6+2.9
FGVC-Aircraft67.350.3+17.0
+ +# 5.3. Evaluation metrics + +How to evaluate a framework for OOD detection in class hierarchies is not established. In alignment with works on ID classification with class hierarchies [10, 15], we focus primarily on hierarchical distances between predictions and ground truth. However, given that our OOD nodes are selected at varying depths in the hierarchy, the resulting OOD sets have highly imbalanced class distributions. Therefore we propose to use a balanced mean hierarchical distance (BMHD), defined as + +$$ +\operatorname {B M H D} \left(\mathcal {C} ^ {\prime}\right) = \frac {1}{| \mathcal {C} ^ {\prime} |} \sum_ {c \in \mathcal {C} ^ {\prime}} \frac {1}{n _ {c}} \sum_ {i = 1} ^ {n _ {c}} \operatorname {d i s t} _ {\mathcal {H}} \left(f \left(x _ {i} ^ {c}\right), c\right), \tag {19} +$$ + +where $\mathcal{C}'$ is the set of classes being considered, $n_c$ is the number of samples in the test set with ground truth label $c$ , $x_i^c$ is the $i$ -th sample out of those, and $|\mathcal{C}'|$ is the cardinality of $\mathcal{C}'$ . In BMHD( $\mathcal{C}'$ ), the mean distances for nodes in $\mathcal{C}'$ are weighted equally, regardless of how many samples are associated with a specific node. + +Furthermore, we want to evaluate the performance on a combined set of ID and OOD data. To this end, we define the mixed BMHD as + +$$ +\operatorname {M i x B M H D} = 0. 5 \left(\mathrm {B M H D} _ {\text {i d}} + \mathrm {B M H D} _ {\text {o o d}}\right), \tag {20} +$$ + +where $\mathrm{BMHD_{id}}$ and $\mathrm{BMHD_{ood}}$ are evaluated with (19) on the set of ID and OOD classes with test data available, respectively. Similarly, we evaluate classification accuracies as the proportion of predictions that match the ground truth labels. Because of the class imbalance, we consider a balanced accuracy score [22]: + +$$ +\operatorname {M i x B A c c} = 0. 5 \left(\mathrm {B A c c} _ {\mathrm {i d}} + \mathrm {B A c c} _ {\mathrm {o o d}}\right), \tag {21} +$$ + +where $\mathrm{BAcc_{id}}$ and $\mathrm{BAcc_{ood}}$ denote the balanced accuracies for ID and OOD classes, respectively. + +# 5.4. Results + +We compare our framework to the following baselines: + +Depth oracle: We make predictions using the ground-truth depth with the corresponding $p(c|x;\theta_d)$ for all data, i.e., $p(c|x;\theta_D)$ for ID data and $p(c|x;\theta_d), d < D$ for OOD + +data. Given the accuracies of the multi-depth networks, we consider this an upper performance bound. + +Leaf model: We predict all data using $p(c|x;\theta_D)$ , i.e., all data are predicted as leaves, including OOD. + +HSC: We train and evaluate the model proposed in [16] using the authors' code. We present results using the synset-based stopping-criterion because that gives the best results. We set thresholds for stopping criteria based on TPR rates to minimize MixBMHD on the test sets. However, in real-world settings, we cannot optimize these thresholds based on test performance. + +Our framework, denoted ProHOC (for probabilistic hierarchical OOD classification), is evaluated using the two different models for the conditionals described in Sec. 4.1. The first, denoted CompProb, uses the complementary probabilities to model the OOD probabilities, as defined in (10). The second, EntCompProb, uses the sum of the entropy and the complementary probability, as defined in (13). + +The results are presented in Tab. 3. Excluding the oracle model, ProHOC with EntCompProb yields the best MixBMHD and MixBAcc across all three datasets, with CompProb consistently ranking second. Looking at the numbers for ID and OOD separately, we note the tradeoff between ID and OOD performance, where the CompProb model favors ID performance by making deeper predictions. In contrast, the EntCompProb model has a more balanced performance across ID and OOD. + +ProHOC outperforms HSC [16], the existing method for OOD detection in hierarchies. This is despite optimizing the inference thresholds in HSC using OOD test data. We can see that HSC tends to make overly deep predictions, keeping an ID performance close to the leaf model but showing poor OOD performance. More detailed analyses of the results are available in the supplementary material. + +# 5.5. Evaluating out-of-hierarchy data + +Section 5.4 focuses on evaluating within-hierarchy OOD data, as these samples are the most challenging and distinguish our hierarchical approach from the binary OOD setting. However, ProHOC supports out-of-hierarchy OOD by classifying such samples as OOD at the root node. The OOD probability at the root is computed via (15) with $s(\mathrm{root})$ being a positive score from any suitable binary OOD method. For simplicity, we use the entropy of the deepest network for $s(\mathrm{root})$ which is a common baseline for binary OOD detection [24] that aligns well with our EntComp-Prob model. Table 4 shows ProHOC for FGVC-Aircraft with root predictions on three out-of-hierarchy datasets. MixBAcc is the (balanced) accuracy on the mix of within-hierarchy ID and OOD. Acc for out-of-hierarchy datasets is the percentage of samples correctly classified as root. We get high accuracies on out-of-hierarchy OOD while keeping most within-hierarchy performance. + +Table 3. Mean hierarchical distances and accuracies on ID, OOD, and the mix of ID and OOD for ProHOC and baselines. The oracle model serves as an upper performance bound. Excluding the oracle model, the best results are boldfaced. Evaluations use test sets. + +
BAccid↑BAccood↑MixBAcc↑BMHDid↓BMHDood↓MixBMHD↓
SIMPLEHIERIMAGENET
Depth oracle79.772.576.10.821.050.93
Leaf model79.70.039.80.822.121.47
HSC [16]76.87.842.30.771.781.28
ProHOC (CompProb)67.819.243.50.921.611.27
ProHOC (EntCompProb)62.530.346.40.961.451.21
INATURALIST19
Depth oracle72.475.974.20.850.820.83
Leaf model72.40.036.20.852.231.54
HSC [16]68.18.438.20.801.761.28
ProHOC (CompProb)66.118.042.00.771.341.06
ProHOC (EntCompProb)57.735.646.70.781.100.94
FGVC-AIRCRAFT
Depth oracle84.767.676.10.490.670.58
Leaf model84.70.042.30.492.001.25
HSC [16]77.914.446.10.401.480.94
ProHOC (CompProb)80.117.148.60.411.250.83
ProHOC (EntCompProb)78.022.750.30.411.210.81
+ +Table 4. Evaluating ProHOC on out-of-hierarchy data. + +
MixBAcc ↑ (FGVC-Air.)Acc ↑ Office31 [26]Acc ↑ iNat19Acc ↑ PACS [13]
ProHOC w/ root47.178.283.994.4
ProHOC w/o root50.3---
+ +# 5.6. Training details + +We train our multi-depth networks with standard supervised NLL training using the remapped labels from (8). We use the ResNet50 architecture [6] for all experiments. For FGVC-Aircraft and iNaturalist19, the network is initialized with pre-trained weights from ImageNet, whereas for SimpleHierImageNet, we train the network from scratch. We train for 90 epochs on FGVC-Aircraft and iNaturalist19, and 250 epochs on SimpleHierImageNet. We use stochastic gradient descent with an initial learning rate of 0.05, decayed to zero by the end of training using a cosine schedule. A batch size of 128 is used throughout. During training, images are randomly cropped and resized to $224 \times 224$ . + +# 6. Limitations + +This work focuses on establishing the key building blocks of our framework for hierarchical OOD detection, with little attention given to optimizing the performance of the underlying multi-depth networks. Further work could explore stronger architectures and advanced training techniques to improve the performance of ProHOC. Finally, a fundamental limitation of our problem formulation is the assumption that the class hierarchy reflects observable visual similarities + +ties. If ID and OOD siblings do not share common visual features, we can not expect this type of framework to accurately predict OOD. + +# 7. Ablation studies + +# 7.1. Evaluating different scores for the conditionals + +In Sec. 4.1 we described how we use the multi-depth networks to model the conditionals $p(y|c, x)$ for $y \in \mathrm{Ch}_{\mathcal{H}}(c) \cup \{\mathrm{odd}(c)\}$ . The primary challenge in modeling $p(y|c, x)$ lies in assigning the OOD probability. Here, we explore several approaches to modeling this OOD probability, or an unnormalized OOD score, based on the predictions from our multi-depth networks. We consider the following models: + +CompProb: The complementary probability, as defined in (10). It uses the sum of probabilities for classes outside of $\mathrm{Ch}_{\mathcal{H}}(c)$ as a proxy for the OOD probability. + +Entropy: As defined in (11), indicates the uncertainty of predictions among the children. The entropy is widely used as an OOD score in the literature [24]. + +MaxProb: The (negated) maximum probability among the children, defined as + +$$ +s ^ {\operatorname {M a x P r o b}} (c) = 1 - \max _ {y \in \operatorname {C h} _ {\mathcal {H}} (c)} p (y | x; \theta_ {d}) \tag {22} +$$ + +with $d = \mathrm{Depth}_{\mathcal{H}}(c) + 1$ . This alternative is similar to the widely used MSP score [7] for binary OOD detection. + +EntCompProb: Since the entropy and the complementary probability are independent and signal different aspects of uncertainty, we find it intuitive to combine scores in a sum, as defined in (13). + +CompLogits: We sum the unnormalized logits for classes outside $\mathrm{Ch}_{\mathcal{H}}(c)$ and use the sum in the softmax function alongside the logits for the child nodes. This method resembles CompProb, although it differs in the scaling of the OOD probability due to summing before applying the exponential function in the softmax. + +The methods denoted CompProb and CompLogits form valid probability distributions directly by design. For the other alternatives, we obtain the conditional distribution by normalization following (14) and (15). + +A well-performing model for the conditionals should display certain qualities. The probability for OOD in the conditional distribution should be the maximum when the sample is OOD. Moreover, if the network misclassifies an ID sample (predicting it as an incorrect ID child), we want our model to predict the OOD node instead of an incorrect ID prediction, which would increase the hierarchical distance from the ground truth. To assess these aspects of the performance, we use several metrics that are evaluated locally for a specific internal node: + +F1: The F1 score for binary classification where OOD is considered the positive label. A prediction is OOD if $p(\mathrm{odd}(c)|c,x)$ is the largest element of $p(y|c,x)$ , otherwise ID. We also report the corresponding FPR and TPR. + +Purity: The fraction of predicted ID samples, predicted as the correct child node. + +Dirty F1: Our variant of the F1 score where ID data that are misclassified as an incorrect child are labeled as OOD when computing the F1 score. + +We evaluate these metrics for all parent nodes $c$ for which OOD data with ground truth at $c$ are available. As ID data, we use all data that belong to descendants of $c$ . We report the mean metrics over all evaluated nodes. + +Table 5 shows results from FGVC-Aircraft. EntCompProb achieves the highest F1 score. It has the largest FPR but this is compensated by its high purity, indicating that many false positives would have been classified as incorrect ID children if they were predicted as ID. For Dirty F1, EntCompProb again outperforms other methods, by an even larger margin. This suggests that the entropy-based uncertainty and the complementary probability interact effectively to create a model with the desired properties. In contrast, CompLogits performs poorly due to being underconfident on OOD (a low TPR). This implies that summation at the logit level leads to smaller OOD probabilities than summation at the probability level (as with CompProb). + +# 7.2. Minimizing the expected hierarchical distance + +ProHOC provides a predictive distribution over all nodes in the hierarchy, allowing us to incorporate uncertainty into our final prediction. Given our objective to produce predictions that are hierarchically close to the ground truth (1), we can use the predicted distribution $p(c|x)$ to minimize the + +Table 5. Analyzing the performance of different methods for modeling $p(\mathrm{odd}(c)|c,x)$ . Results are from FGVC-Aircraft. + +
F1 ↑FPR ↓TPR ↑Purity ↑Dirty F1 ↑
CompProb0.470.090.420.880.49
Entropy0.510.120.450.900.55
MaxProb0.500.100.450.890.52
EntCompProb0.560.150.520.900.59
CompLogits0.170.010.140.870.18
+ +Table 6. Comparing predictions from minimizing the expected hierarchical distance to predictions using the most probable class. + +
argmin E[distH]argmax p(c|x)
MixBAcc ↑ MixBMHD ↓MixBAcc ↑ MixBMHD ↓
SIMPLEHIERIMAGENET
EntCompProb46.41.2145.81.25
CompProb43.51.2739.71.37
INATURALIST19
EntCompProb46.70.9445.60.98
CompProb42.01.0638.41.17
FGVC-AIRCRAFT
EntCompProb50.30.8150.20.88
CompProb48.60.8347.40.90
+ +expected hierarchical distance of the prediction + +$$ +f (x) = \underset {c} {\operatorname {a r g m i n}} \mathbb {E} _ {p \left(c ^ {\prime} \mid x\right)} \left[ \operatorname {d i s t} _ {\mathcal {H}} \left(c, c ^ {\prime}\right) \right], \tag {23} +$$ + +as presented in Sec. 3. This is similar to the post-hoc correction proposed in [10], although they restrict the predictions to leaves. We compute the expected hierarchical distance over all nodes in the hierarchy. + +We compare the predictions from (23) with the standard $\mathrm{argmax}_c p(c|x)$ in Tab. 6, using ProHOC with both CompProb and EntCompProb. As expected, (23) achieves lower hierarchical distances since it optimizes for that specifically. However, we also see improvements in accuracy as an additional benefit of using (23). + +# 8. Conclusion + +The deep-learning community has made substantial progress in the binary setting of OOD detection. In this paper, we raise the bar for OOD detection by aiming for more informative predictions: predicting OOD as internal nodes in a class hierarchy. Our framework shows promising results. We also believe its simplicity in introducing no new hyperparameters and using underlying networks trained with standard methods makes it accessible and adaptable for further development. We hope this work will inspire continued exploration of OOD classification in class hierarchies and that ProHOC can serve as a foundation for even more effective methods. + +# Acknowledgement + +This work was supported by Saab AB and Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agreement no. 2022-06725. + +# References + +[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. Neo: Neural collapse based out-of-distribution detection. In International Conference on Learning Representations, 2024. 2 +[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. In IEEE conference on computer vision and pattern recognition, 2016. 2 +[3] Edward A Bender and S Gill Williamson. Lists, decisions and graphs. S. Gill Williamson, 2010. 3 +[4] Luca Bertinetto, Romain Mueller, Konstantinos Tertikas, Sina Samangooei, and Nicholas A Lord. Making better mistakes: Leveraging class hierarchies with deep networks. 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Vim: Out-of-distribution with virtual-logit matching. In IEEE/CVF conference on computer vision and pattern recognition, 2022. 2, 4 +[31] Jingyang Zhang, Jingkang Yang, Pengyun Wang, Haoqi Wang, Yueqian Lin, Haoran Zhang, Yiyou Sun, Xuefeng Du, Kaiyang Zhou, Wayne Zhang, et al. Openood v1.5: Enhanced benchmark for out-of-distribution detection. arXiv preprint arXiv:2306.09301, 2023. 1 \ No newline at end of file diff --git a/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/images.zip b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..01a456d248d449ad432901f308d46665cc840f1c --- /dev/null +++ b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fc5e302bf48c21841017b202abcb1d88ea9e9c01d9a2bc7a163ceaf958cd14ff +size 378899 diff --git a/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/layout.json b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ae016906a45e4ebb0b6a008a43145ab31190784d --- /dev/null +++ b/2025/ProHOC_ Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks/layout.json @@ -0,0 +1,9864 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "type": "text", + "content": "ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "spans": [ + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "content": "Erik Wallin" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "content": ", Fredrik Kahl" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "content": ", Lars Hammarstrand" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "content": ", Saab AB," + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 181, + 160, + 428, + 190 + ], + "type": "text", + "content": "Chalmers University of Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 165, + 191, + 445, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 165, + 191, + 445, + 202 + ], + "spans": [ + { + "bbox": [ + 165, + 191, + 445, + 202 + ], + "type": "text", + "content": "{wallline, fredrik. kahl, lars.hammarstrand}@chalmers.se" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 257, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 296, + 460 + ], + "type": "text", + "content": "Out-of-distribution (OOD) detection in deep learning has traditionally been framed as a binary task, where samples are either classified as belonging to the known classes or marked as OOD, with little attention given to the semantic relationships between OOD samples and the indistribution (ID) classes. We propose a framework for detecting and classifying OOD samples in a given class hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the class hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the class hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined class hierarchies and show the effectiveness of our method. Our code is available at https://github.com/walline/prohoc." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 508, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 295, + 687 + ], + "type": "text", + "content": "Effectively handling out-of-distribution samples is important for deep-learning applications. Data outside the training domain often yield unpredictable results when fed through deep neural networks [7], making it essential to account for previously unseen data when deploying these models in real-world settings to ensure robust performance and avoid unexpected outcomes. Previous literature [31] has focused on binary out-of-distribution detection, predicting data either as ID (in-distribution) or OOD (out-of-distribution), without differentiating between OOD samples that are semantically close or far from ID. For example, with ID classes consisting of dog breeds, this binary paradigm would treat an image of an unknown dog the same as an image of an airplane, overlooking the varying degrees of semantic similarity these samples have to the known classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "We explore a new setting of OOD detection, utilizing class hierarchies to predict semantically close OOD sam" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 229, + 550, + 407 + ], + "blocks": [ + { + "bbox": [ + 316, + 229, + 550, + 407 + ], + "lines": [ + { + "bbox": [ + 316, + 229, + 550, + 407 + ], + "spans": [ + { + "bbox": [ + 316, + 229, + 550, + 407 + ], + "type": "image", + "image_path": "38109b5948ff6e1a05eb42a085ab871465e8c992573b245b45441e181a33e5c9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 411, + 555, + 445 + ], + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 445 + ], + "type": "text", + "content": "Figure 1. Out-of-distribution detection in class hierarchies. Instead of simply predicting the unseen dog and cat types as OOD, we aim to classify them as the high-level categories dog and cat." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "type": "text", + "content": "plies as their correct nodes in the class hierarchy. Hierarchical models for organizing and classifying objects are widespread, from foundational examples like Linnaeus' taxonomy in Systema Naturae [17] to modern structures like WordNet [21] for semantic relations. While the deep learning community has shown a growing interest in utilizing class hierarchies [4, 9], their application for OOD detection remains largely unexplored. However, such hierarchies can provide a foundation for enabling more informative OOD predictions. For instance, in the hierarchy shown in Figure 1, the binary paradigm of OOD detection treats the unseen cat and dog as simply OOD. In contrast, with knowledge of the hierarchy, we can classify the unseen dog as the broader dog category (while recognizing it as distinct from previously seen breeds)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "One of many motivating examples arises in the context of an autonomous driving system. A sensor model might be trained to classify objects such as bicycles, electric scooters, and mopeds (among other classes). However, many system components treat these objects similarly, grouping them as" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20612" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "slow-moving vehicles. When encountering an obscure object not present in the training data, such as a unicycle or a penny-farthing, the ideal response would be to recognize it as a slow-moving vehicle, rather than misclassifying it as a known class or simply marking it as OOD, which would provide limited actionable information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 145, + 295, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 145, + 295, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 145, + 295, + 335 + ], + "type": "text", + "content": "Our approach addresses this problem by leveraging the class hierarchy to factorize the probability distribution of predictions in the tree. This probability model includes conditional probabilities at each parent node, at which the possible predictions are either one of its child nodes or OOD at that specific node. Our key challenge lies in modeling these conditionals, as we assume no OOD data are available for training. To approximate these conditionals, we train classification networks at each depth of the hierarchy. We find that networks trained to classify classes higher in the hierarchy better recognize features associated with broad categories, making them better at predicting OOD samples to the correct high-level category. Similarly, the more fine-grained models may display larger uncertainty for these OOD samples because they contain low-level features that are not recognized by these models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 337, + 295, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 295, + 479 + ], + "type": "text", + "content": "We explore several methods for leveraging these multi-depth networks to approximate the conditionals in our probabilistic framework based on standard OOD scores. We evaluate our proposed model, ProHOC, on three datasets with predefined class hierarchies that we split into ID and OOD and show that our method outperforms previous attempts. Moreover, our framework has the benefit of introducing no new hyperparameters and uses standard methods for training the underlying multi-depth networks, making it straightforward to extend and build upon. We believe that our model can serve as a strong foundation for further research in this relatively unexplored area." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 481, + 225, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 481, + 225, + 492 + ], + "spans": [ + { + "bbox": [ + 67, + 481, + 225, + 492 + ], + "type": "text", + "content": "Our main contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 494, + 295, + 588 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "type": "text", + "content": "- We formulate a probabilistic framework for classifying data, both ID and OOD, as nodes in a class hierarchy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": "- We explore and enable the implementation of this framework by utilizing multi-depth networks to approximate the conditionals in the probabilistic model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 554, + 295, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 554, + 295, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 554, + 295, + 588 + ], + "type": "text", + "content": "- We experimentally evaluate our framework and baselines on several datasets, showing the effectiveness of our method." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 602, + 139, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 602, + 139, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 602, + 139, + 615 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 622, + 235, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 622, + 235, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 622, + 235, + 635 + ], + "type": "text", + "content": "2.1. Hierarchy-aware ID classification" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "content": "Several works incorporate class hierarchies in training models for ID classification, focusing on minimizing the hierarchical distance between predictions and ground truth rather than only optimizing for classification accuracy [4, 5, 9, 10, 15]. This approach prioritizes models that make errors close to the correct class in the hierarchy, which often can be" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 107 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 107 + ], + "type": "text", + "content": "preferable to models that make more distant mistakes. This aspect of performance is typically disregarded in works on standard flat classification." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 109, + 553, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 553, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 553, + 203 + ], + "type": "text", + "content": "The existing approaches to this problem vary. In [4], they propose adjustments to the standard cross-entropy loss to account for higher-level decisions in the hierarchy. The works [5, 15] introduce hierarchy-aware feature spaces to obtain the desired model properties. In [10], they suggest a post-hoc method that rescales flat prediction probabilities by hierarchical distances to produce predictions minimizing the expected hierarchical distance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 205, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 553, + 276 + ], + "type": "text", + "content": "Most similar to our approach is [9], which proposes training separate coarse and fine-grained classifiers to improve both classification accuracy and hierarchical distance. However, their method is restricted to classifiers at two levels (one coarse and one fine), whereas we train classifiers at all levels of the hierarchy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 277, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 553, + 361 + ], + "type": "text", + "content": "This overall line of research is similar to our setting in that we consider class hierarchies to minimize the hierarchical distance between ground truth and predictions. However, a key difference is that these works only consider ID data and therefore restrict the predictions to leaf nodes only. In contrast, we need a framework able to predict internal nodes as OOD predictions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 370, + 471, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 370, + 471, + 382 + ], + "spans": [ + { + "bbox": [ + 314, + 370, + 471, + 382 + ], + "type": "text", + "content": "2.2. Out-of-distribution detection" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 389, + 553, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 553, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 553, + 497 + ], + "type": "text", + "content": "Out-of-distribution is an active field of research [2, 7, 12, 14, 27]. The goal is to detect whether a data sample belongs to the training distribution or not, motivated by the need to handle real-world, uncurated settings. The common approach in this field is to design a score based on neural network outputs, which takes high values for OOD data and low values for ID data (or vice versa). The score can be derived from, e.g., predicted distributions [7, 19, 24], logits [18, 29], or feature representations [1, 12, 30]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 498, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 652 + ], + "type": "text", + "content": "Our setting introduces some new challenges compared to the standard binary paradigm of OOD detection. First, instead of only detecting OOD as a binary prediction, we aim to classify OOD samples as specific nodes within the class hierarchy. Second, we ultimately need to make hard decisions about which node to predict, so unnormalized scores that lack probabilistic interpretations or easily inferrable thresholds are of limited use. Lastly, many works on OOD detection use comparably simple problem settings, using one dataset as ID and an unrelated dataset as OOD [12, 18]. In contrast, our setting naturally involves complex, fine-grained detection tasks, as OOD samples can appear at any depth within the class hierarchy." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "As a final note, a few works exist that consider class hierarchies and OOD detection simultaneously [8, 11, 29]. In [11, 29], they use class hierarchies to construct OOD sets of varying difficulty by selecting the OOD sets from different depths of the class hierarchy. The work [8] proposes a score" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20613" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "that signals high OOD-ness if two classifiers predict distinct classes separated by a large hierarchical distance. However, these works still consider only binary OOD predictions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 114, + 272, + 126 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 114, + 272, + 126 + ], + "spans": [ + { + "bbox": [ + 55, + 114, + 272, + 126 + ], + "type": "text", + "content": "2.3. Hierarchical out-of-distribution detection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "type": "text", + "content": "To the best of our knowledge, the only work that considers detection and classification of OOD in class hierarchies similarly to us is [16]. Their method involves separate model heads for each internal node in the hierarchy. For data that are descendants of a specific node, the corresponding head is trained to predict the correct child using a standard cross-entropy loss. For non-descendant data points, the head is trained to produce a uniform distribution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 228, + 296, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 296, + 373 + ], + "type": "text", + "content": "There are key distinctions between [16] and our work. First, our method introduces no additional hyperparameters, whereas [16] requires balancing multiple loss terms during training. Second, their approach performs hierarchical inference in a top-down manner, with thresholds at each node to decide where to stop. These thresholds need to be assigned using ID data and it is not clear how to select these to ensure performance on both ID and OOD data while generalizing to multiple datasets. In contrast, our fully probabilistic approach provides a predictive distribution over all nodes in the hierarchy, eliminating the need for threshold-based top-down inference." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 381, + 260, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 260, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 260, + 396 + ], + "type": "text", + "content": "3. A probabilistic hierarchy-framework" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": "Our approach for detecting and classifying OOD in class hierarchies is based on creating a probabilistic model from the class hierarchy. We assume that this hierarchy " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": " is given and that it is structured as a directed rooted tree [3] (e.g., the green nodes of Figure 1). We denote the nodes of this tree as " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": " with the leaf nodes being " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{\\mathrm{id}}\\subset \\mathcal{C}" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": ". We assume a distribution of ID data with classes corresponding to leaves in this hierarchy: " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "p^{\\mathrm{id}}(x,y)" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{C}^{\\mathrm{id}}" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": ". These data are observed during training. Furthermore, we have a distribution of OOD data, not observable during training, " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "p^{\\mathrm{odd}}(x,y)" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{C}\\setminus \\mathcal{C}^{\\mathrm{id}}" + }, + { + "bbox": [ + 55, + 401, + 296, + 556 + ], + "type": "text", + "content": ". In other words, the OOD data do not match any ID leaf classes but correspond to groups of ID classes higher in the hierarchy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "text", + "content": "Our goal is to learn a model " + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "text", + "content": " that predicts samples from the balanced mix of ID and OOD, defined as " + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "inline_equation", + "content": "p^{\\mathrm{mix}}(x,y) = 0.5(p^{\\mathrm{id}}(x,y) + p^{\\mathrm{odd}}(x,y))" + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "text", + "content": ", to their correct nodes in " + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 557, + 296, + 641 + ], + "type": "text", + "content": ". If misclassified, the predictions should be hierarchically close to the ground truth. Formally, we aim to minimize the expected hierarchical distance between the prediction and the ground truth:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 111, + 647, + 295, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 647, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 111, + 647, + 295, + 661 + ], + "type": "interline_equation", + "content": "\\min \\mathbb {E} _ {p ^ {\\operatorname {m i x}} (x, y)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} (f (x), y) \\right], \\tag {1}", + "image_path": "1050e9632fe9a2e5c66ab3288f317e3dfd268f9af2774cb559f12c1e29a48917.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": " is the number of edges in the shortest path between two nodes in the undirected equivalent of " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "To model " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ", we construct a probabilistic model from the class hierarchy " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ". Specifically, we append a child node" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": "to each internal node of " + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": " to represent OOD predictions at that node (e.g., the red nodes of Figure 1), creating the new tree " + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": ". We denote the set of these OOD nodes as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 372, + 117, + 555, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 117, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 372, + 117, + 555, + 133 + ], + "type": "interline_equation", + "content": "\\mathcal {C} ^ {\\mathrm {o o d}} = \\left\\{\\operatorname {o o d} (c) | c \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\}. \\tag {2}", + "image_path": "8c45c1420e707580fbe71cd07eba931cda4c8ff3f959716f62d0ddd40b6a8cc2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": "These nodes represent a sample belonging to class " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " but not to any of " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": "'s known descendants. The model " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " describes the semantic classes of a sample as random binary variables at each node. We denote the probability of the set of nodes " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " being active for a given sample " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "p(\\mathcal{C}'|x)" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": ". We assume that all samples belong to a leaf node " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}}" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " but that the leaf nodes are mutually exclusive, i.e., a sample belongs to only one leaf node. Moreover, the internal nodes of " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " describe unions of these leaf nodes such that internal node " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " is active if any of its descendant leaf nodes are active. This implies " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "p(c|x) = p(\\operatorname{Anc}_{\\mathcal{G}}^{+}(c)|x)" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\operatorname{Anc}_{\\mathcal{G}}^{+}(c)" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " is the set of " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " and all " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": "'s ancestors. From this follows the conditional independences " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "p(c|\\operatorname{Anc}_{\\mathcal{G}}^{+}(\\operatorname{Par}_{\\mathcal{G}}(c))) = p(c|\\operatorname{Par}_{\\mathcal{G}}(c))" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\operatorname{Par}_{\\mathcal{G}}(c)" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": " is the parent node of " + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 140, + 555, + 308 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 308, + 554, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 554, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 554, + 344 + ], + "type": "text", + "content": "We can now factorize the probability of paths in " + }, + { + "bbox": [ + 313, + 308, + 554, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 308, + 554, + 344 + ], + "type": "text", + "content": " using the chain rule of probability and the induced conditional independences as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 353, + 555, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 353, + 555, + 382 + ], + "spans": [ + { + "bbox": [ + 329, + 353, + 555, + 382 + ], + "type": "interline_equation", + "content": "p (c | x) = p \\left(\\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) | x\\right) = \\prod_ {c ^ {\\prime} \\in \\operatorname {A n c} _ {\\mathcal {G}} ^ {+} (c) \\backslash R} p \\left(c ^ {\\prime} \\mid \\operatorname {P a r} _ {\\mathcal {G}} \\left(c ^ {\\prime}\\right), x\\right), \\tag {3}", + "image_path": "d3600aa6e7aac5364691d4e48c540feb873161c7316c3bf77b1b6819b7995808.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "content": "where the root node " + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "content": " is excluded in the product because " + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "inline_equation", + "content": "p(R|x) = 1" + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "content": ". For example, in the hierarchy of Figure 1, the probability for Lynx becomes " + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "inline_equation", + "content": "p(\\mathrm{Lynx}|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x)" + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "content": " whereas the probability for an OOD Cat is " + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(\\mathrm{Cat})|\\mathrm{Cat}, x)p(\\mathrm{Cat}|R, x)" + }, + { + "bbox": [ + 313, + 391, + 554, + 450 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": "By applying (3) with " + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}^{\\mathrm{id}} \\cup C^{\\mathrm{odd}}" + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": ", we obtain the predictive distribution over all ID classes and OOD predictions at each internal node of " + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": ". Note that for evaluation purposes, predictions of " + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{odd}(c)" + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": " are mapped to the corresponding node " + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 450, + 554, + 510 + ], + "type": "text", + "content": " to compute hierarchical distances." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "text", + "content": "We use this distribution to obtain our final prediction. A standard approach is to use the argmax of " + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "inline_equation", + "content": "p(c|x)" + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}^{\\mathrm{id}} \\cup \\mathcal{C}^{\\mathrm{odd}}" + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "text", + "content": ". However, to better align with our objective in (1), we instead utilize the uncertainties of the predictive distribution to minimize the expected hierarchical distance between the predicted node for sample " + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 510, + 554, + 583 + ], + "type": "text", + "content": " and its ground truth:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 355, + 591, + 555, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 591, + 555, + 612 + ], + "spans": [ + { + "bbox": [ + 355, + 591, + 555, + 612 + ], + "type": "interline_equation", + "content": "f (x) = \\underset {c \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] \\tag {4}", + "image_path": "bbdc25d9552c51df00c86d7fc1ff343f18e6e24c0f2210f891d8dceda94ec9e4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 620, + 463, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 620, + 463, + 632 + ], + "spans": [ + { + "bbox": [ + 314, + 620, + 463, + 632 + ], + "type": "text", + "content": "where the expectation is obtained by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 337, + 641, + 555, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 641, + 555, + 669 + ], + "spans": [ + { + "bbox": [ + 337, + 641, + 555, + 669 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right] = \\sum_ {c ^ {\\prime} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\cup \\mathcal {C} ^ {\\mathrm {o o d}}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) p \\left(c ^ {\\prime} \\mid x\\right). \\tag {5}", + "image_path": "d02411221b1d3f9ab7d85c13663e5f21e08e55b28fb803910b79903be689d43e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{odd}(c)" + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": " is mapped to " + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{dist}_{\\mathcal{H}}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": ". In Sec. 7.2, we experimentally show the benefit of using (4) compared to the standard argmax approach." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20614" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 242, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 242, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 242, + 85 + ], + "type": "text", + "content": "4. Leveraging multi-depth networks" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 295, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 295, + 115 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 295, + 115 + ], + "type": "text", + "content": "The predictive distribution of (3) requires the conditional distributions at each internal node of the class hierarchy:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 100, + 121, + 295, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 121, + 295, + 135 + ], + "spans": [ + { + "bbox": [ + 100, + 121, + 295, + 135 + ], + "type": "interline_equation", + "content": "p (y | c, x), \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\cup \\{\\operatorname {o o d} (c) \\} \\tag {6}", + "image_path": "398f6c3b07aa85cd602122c57daa3d2f292159707518eeeda5f0ec8d08cb0a3f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "spans": [ + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C} \\setminus \\mathcal{C}^{\\mathrm{id}}" + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": " is the set of children of " + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": " according to the original tree " + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": ". However, as no OOD data are available during training, we cannot train a model to directly predict " + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(c)|c,x)" + }, + { + "bbox": [ + 55, + 138, + 295, + 210 + ], + "type": "text", + "content": ". Instead, as common for binary OOD detection [12, 30], we resort to hand-crafted models for the OOD predictions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": "Our idea for approaching these conditionals is to design classifiers from ID data that, given a sample belonging to " + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "inline_equation", + "content": "\\mathrm{odd}(c)" + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": ", confidently predict class " + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": " while expressing uncertainty for the known child classes " + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": ". With such a model, the uncertainty of the sample's membership in " + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": " can be used as a proxy for " + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(c)|c,x)" + }, + { + "bbox": [ + 55, + 211, + 295, + 282 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 283, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 498 + ], + "type": "text", + "content": "Following this reasoning, we propose training separate classification networks for the different depths of the hierarchy, with each network responsible for classifying data into nodes at a particular depth (see Figure 2). The intuition behind this approach is that the networks for high levels will emphasize the features associated with broad categories, which may not be helpful for more fine-grained classification. For instance, in the dogs-and-cats hierarchy of Figure 1, the network trained for the level above the leaves, responsible for classifying dog or cat, may focus on features like ear and tail shape, useful for distinguishing between any dog and any cat. Conversely, the leaf-level network might focus on fur patterns or facial features, important for distinguishing specific breeds. Consequently, an unseen cat breed might lack the features the leaf model recognizes, causing it to show uncertainty. However, the high-level network could still identify the features common to all cats and confidently classify the unseen cat breed as a cat." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 498, + 295, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 521 + ], + "type": "text", + "content": "Specifically, we train these multi-depth networks using an ID dataset of samples and labels" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 525, + 295, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 525, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 113, + 525, + 295, + 543 + ], + "type": "interline_equation", + "content": "\\mathcal {S} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}. \\tag {7}", + "image_path": "bd4f5690c7a77f539dc2a1def8ca5595cb1cef75e2cb7aee3c32fc5558fea845.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": "To train high-level models, we map these leaf-level labels to their corresponding ancestors at specific depths. For this purpose, we define the function " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "\\lambda(y, d)" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": " which maps the label " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": " to its corresponding ancestor at depth " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": ", or if " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{Depth}_{\\mathcal{H}}(y) \\leq d" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": ", maps " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": " to itself (this handles the case of all leaves not having equal depth). Consequently, we train the network for depth " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": ", denoted " + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "inline_equation", + "content": "f_{\\theta_d}" + }, + { + "bbox": [ + 55, + 546, + 295, + 641 + ], + "type": "text", + "content": ", using standard cross-entropy training, with the dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 102, + 645, + 295, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 645, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 102, + 645, + 295, + 662 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {d} ^ {\\mathrm {i d}} = \\left\\{\\left(x _ {i}, \\lambda \\left(y _ {i}, d\\right)\\right) \\mid y _ {i} \\in \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {i d}}}, \\tag {8}", + "image_path": "beb2cd1be3eb16996b336f2a92599da2d3e3eab164873731b19f3549e336afc5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": "and obtain the multi-depth networks " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "f_{\\theta_1}, \\ldots, f_{\\theta_D}" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": " with the parameters " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\theta_1, \\ldots, \\theta_D" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "D = \\max_{c \\in \\mathcal{C}} \\mathrm{Depth}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "In Sec. 5.2, we present results showing that our multi-depth networks effectively classify OOD data." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 323, + 69, + 550, + 211 + ], + "blocks": [ + { + "bbox": [ + 323, + 69, + 550, + 211 + ], + "lines": [ + { + "bbox": [ + 323, + 69, + 550, + 211 + ], + "spans": [ + { + "bbox": [ + 323, + 69, + 550, + 211 + ], + "type": "image", + "image_path": "b342aa40f4ec27d88cf8c55bf12d588e45b71c9cd330d0d2b0fba19ee440d880.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "lines": [ + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "text", + "content": "Figure 2. For a hierarchy of depth 3, we train separate neural networks, parameterized by " + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\theta_{1}" + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\theta_{2}" + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\theta_{3}" + }, + { + "bbox": [ + 313, + 213, + 554, + 247 + ], + "type": "text", + "content": ", to classify data into nodes within that depth level." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 265, + 535, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 265, + 535, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 265, + 535, + 278 + ], + "type": "text", + "content": "4.1. Modeling the conditionals of the hierarchy" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": "To model the conditionals " + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "inline_equation", + "content": "p(y|c, x)" + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": " based on the multi-depth networks, " + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "inline_equation", + "content": "f_{\\theta_1}, \\ldots, f_{\\theta_D}" + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": ", we are looking for ways to quantify the uncertainty of " + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": " belonging to " + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": " and use this to estimate " + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(c)|c, x)" + }, + { + "bbox": [ + 313, + 284, + 554, + 368 + ], + "type": "text", + "content": ". There are a variety of ways one could approach this. We have evaluated several alternatives based on standard OOD scores in Sec. 7.1. An intuitive and simple approach is to use" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 347, + 375, + 553, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 375, + 553, + 388 + ], + "spans": [ + { + "bbox": [ + 347, + 375, + 553, + 388 + ], + "type": "interline_equation", + "content": "p (y | c, x) = p (y | x; \\theta_ {d}) \\quad \\text {f o r} \\quad y \\in \\operatorname {C h} _ {\\mathcal {H}} (c) \\tag {9}", + "image_path": "e5ab3997e0acb62cf3433a80b481ce2076204cc51fb79d974704e8b46bb9b746.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 396, + 332, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 396, + 332, + 406 + ], + "spans": [ + { + "bbox": [ + 314, + 396, + 332, + 406 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 358, + 405, + 553, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 405, + 553, + 432 + ], + "spans": [ + { + "bbox": [ + 358, + 405, + 553, + 432 + ], + "type": "interline_equation", + "content": "p (\\mathbf {o o d} (c) | c, x) = 1 - \\sum_ {y \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}), \\tag {10}", + "image_path": "d963298abc6318f02659d955e6b65b6e3476cfd0a37779765b007b63a0b5333b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "inline_equation", + "content": "d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1" + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "text", + "content": ". This formulation uses the probability of a sample belonging to a class outside the children of " + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "text", + "content": " as a proxy for the OOD probability while keeping the conditional probabilities for the children as predicted by " + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "inline_equation", + "content": "p(y|x;\\theta_d)" + }, + { + "bbox": [ + 313, + 435, + 554, + 543 + ], + "type": "text", + "content": ". However, we find that this approach alone tends to assign too low probabilities for OOD and fails to account for the uncertainty among the child nodes. To address this, we also consider the entropy of the normalized distribution over the children:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 548, + 553, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 548, + 553, + 576 + ], + "spans": [ + { + "bbox": [ + 351, + 548, + 553, + 576 + ], + "type": "interline_equation", + "content": "H (c) = - \\sum_ {c ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right) \\log \\tilde {p} \\left(c ^ {\\prime} | x; \\theta_ {d}\\right), \\tag {11}", + "image_path": "9ea57057194b0f6b668d50578fff2919e20dabedfaa44a061c7a757639a6f16d.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 582, + 342, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 582, + 342, + 593 + ], + "spans": [ + { + "bbox": [ + 314, + 582, + 342, + 593 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 359, + 590, + 553, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 590, + 553, + 619 + ], + "spans": [ + { + "bbox": [ + 359, + 590, + 553, + 619 + ], + "type": "interline_equation", + "content": "\\tilde {p} \\left(c ^ {\\prime} \\mid x; \\theta_ {d}\\right) = \\frac {p \\left(c ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}{\\sum_ {\\tilde {c} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (\\tilde {c} \\mid x ; \\theta_ {d})}. \\tag {12}", + "image_path": "e2bc02fc9fa06588e1df3b580b4f7d357acbe46ba0e1f58aa4e39b40213119bb.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 622, + 553, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 622, + 553, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 622, + 553, + 645 + ], + "type": "text", + "content": "High entropies indicate uncertainty among the children, i.e., when multiple children are assigned similar probabilities." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 646, + 553, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 646, + 553, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 646, + 553, + 681 + ], + "type": "text", + "content": "Since the entropy and the complementary probability (10) are independent and account for different aspects of uncertainty, we combine these in a sum as" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 362, + 689, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 689, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 362, + 689, + 553, + 715 + ], + "type": "interline_equation", + "content": "s (c) = H (c) + 1 - \\sum_ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}). \\tag {13}", + "image_path": "b1fb32b9c3a62625b52a9b27b592574e38a8e2961623a94679e58d7f1b36b3d0.jpg" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20615" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": "However, this score no longer forms a probability distribution when combined with " + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "inline_equation", + "content": "p(y|x;\\theta_d)" + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "inline_equation", + "content": "y \\in \\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": ". To resolve this, we normalize to obtain the valid distribution as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 114, + 295, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 114, + 295, + 142 + ], + "spans": [ + { + "bbox": [ + 78, + 114, + 295, + 142 + ], + "type": "interline_equation", + "content": "p (y | c, x) = \\frac {p (y | x ; \\theta_ {d})}{s (c) + \\sum_ {y ^ {\\prime} \\in \\mathrm {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} | x ; \\theta_ {d}\\right)} \\tag {14}", + "image_path": "0d9e0938cfc316f2148bbf15f8226a39b327e25a3cd635e45d7071a93661d94d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 148, + 139, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 148, + 139, + 161 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 139, + 161 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 55, + 148, + 139, + 161 + ], + "type": "inline_equation", + "content": "y\\in \\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 148, + 139, + 161 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 166, + 295, + 195 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 166, + 295, + 195 + ], + "spans": [ + { + "bbox": [ + 66, + 166, + 295, + 195 + ], + "type": "interline_equation", + "content": "p \\left(\\operatorname {o o d} (c) \\mid c, x\\right) = \\frac {s (c)}{s (c) + \\sum_ {y ^ {\\prime} \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p \\left(y ^ {\\prime} \\mid x ; \\theta_ {d}\\right)}, \\tag {15}", + "image_path": "1a377aa3aea886f88d6018ec1c87c3e9f74c6efe5326b55cd84009b2ac00871a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 199, + 296, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 199, + 296, + 223 + ], + "spans": [ + { + "bbox": [ + 55, + 199, + 296, + 223 + ], + "type": "text", + "content": "which gives us the final model for the conditional distributions in our hierarchical framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 233, + 195, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 233, + 195, + 247 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 195, + 247 + ], + "type": "text", + "content": "5. Experiments and results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 253, + 118, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 118, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 118, + 264 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 270, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 296, + 354 + ], + "type": "text", + "content": "There are no established datasets for OOD detection in class hierarchies. We construct our benchmarks using three datasets with predefined hierarchies commonly used in work for hierarchy-aware ID classification. We generate ID and OOD subsets by selecting OOD nodes from various depths within these hierarchies. Our experiments are conducted on the following datasets:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 354, + 296, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 463 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 463 + ], + "type": "text", + "content": "FGVC-Aircraft [20]: This dataset contains aircraft images with a three-level hierarchy: at the highest level are manufacturers (e.g., Boeing), the second level groups aircraft by family (e.g., Boeing 747), and the most specific level contains variants (e.g., Boeing 747-200). FGVC-Aircraft has the most shallow hierarchy and the fewest classes among the considered datasets, but it poses challenging classification tasks, such as distinguishing between separate Boeing 747 types." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 463, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 521 + ], + "type": "text", + "content": "iNaturalist19 [28]: A dataset of biological species organized in a hierarchy according to taxonomic ranks such as kingdom, phylum, and genus. It includes a large number of classes with fine-grained relationships and has a deeper hierarchy than FGVC-Aircraft." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": "SimpleHierImageNet: This dataset is based on tieredImageNet [25], which is a subset of ImageNet using a hierarchy based on the WordNet graph [21]. However, the hierarchy of tieredImageNet has many nodes representing conceptual rather than visual similarities. For example, it has the high-level class timepiece with the subclasses analog clock and digital clock, or the leaf class laptop computer under the high-level class portable computer, while computer keyboard is nine edges away under electronic equipment. To address this, we introduce SimpleHierImageNet by reorganizing parts of the tieredImageNet hierarchy to reflect visual similarities. Despite these adjustments, SimpleHierImageNet remains a challenging problem with a wide range of categories and a deep hierarchy with many internal nodes. More details on SimpleHierImageNet are available in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 321, + 83, + 547, + 144 + ], + "blocks": [ + { + "bbox": [ + 324, + 71, + 543, + 82 + ], + "lines": [ + { + "bbox": [ + 324, + 71, + 543, + 82 + ], + "spans": [ + { + "bbox": [ + 324, + 71, + 543, + 82 + ], + "type": "text", + "content": "Table 1. Dataset details (after being split into ID and OOD)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 83, + 547, + 144 + ], + "lines": [ + { + "bbox": [ + 321, + 83, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 321, + 83, + 547, + 144 + ], + "type": "table", + "html": "
Max depthNr. ID leavesNr. internal nodesNr. OOD classes
FGVC-Aircraft3802820
SimpleHierImageNet115186380
iNaturalist19672177289
", + "image_path": "b457cfa30b7d43b03a37436986513173bc45586e04c3850266814d8500e54582.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "text", + "content": "The considered datasets lack established ID/OOD splits. Therefore, we construct the OOD set by selecting nodes from various depths of the hierarchy. For each selected OOD node, we remove it and all its descendants from the hierarchy, leaving the remaining nodes to form our ID hierarchy " + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "text", + "content": ". After defining the ID hierarchy " + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "text", + "content": " and the set of OOD classes, we map the labels of the OOD data (which are leaf nodes in the full original hierarchy) to their closest ancestor present in the ID hierarchy " + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 161, + 553, + 280 + ], + "type": "text", + "content": ". These mapped labels are then used in the experimental evaluation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 281, + 553, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 553, + 329 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 553, + 329 + ], + "type": "text", + "content": "Details of the datasets, after defining the ID and OOD sets are described in Tab. 1. Additional information on the datasets and the selection of OOD sets is available in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 335, + 537, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 537, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 537, + 348 + ], + "type": "text", + "content": "5.2. Evaluating multi-depth networks for OOD" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "text", + "content": "To evaluate our hypothesis that multi-depth networks are effective for OOD classification, we compare the accuracy obtained from our high-level models " + }, + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "inline_equation", + "content": "f_{\\theta_1}, \\ldots, f_{\\theta_{D-1}}" + }, + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "text", + "content": " to the accuracy obtained by marginalizing the leaf-level model " + }, + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "inline_equation", + "content": "f_{\\theta_D}" + }, + { + "bbox": [ + 313, + 354, + 553, + 413 + ], + "type": "text", + "content": ", when evaluated on OOD data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 413, + 553, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 553, + 437 + ], + "type": "text", + "content": "Specifically, we have a dataset of OOD data associated with different depths of the hierarchy:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 361, + 442, + 553, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 442, + 553, + 460 + ], + "spans": [ + { + "bbox": [ + 361, + 442, + 553, + 460 + ], + "type": "interline_equation", + "content": "\\mathcal {S} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\mid y _ {i} \\in \\mathcal {C} \\backslash \\mathcal {C} ^ {\\mathrm {i d}} \\right\\} _ {i = 1} ^ {n _ {\\mathrm {o o d}}}. \\tag {16}", + "image_path": "e9b2e8c4a22a74c1a208b8eb18b090155730dc0e602e67c756225546e3bbfd33.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 465, + 553, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 465, + 553, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 465, + 553, + 478 + ], + "type": "text", + "content": "We define subsets of " + }, + { + "bbox": [ + 313, + 465, + 553, + 478 + ], + "type": "inline_equation", + "content": "S^{\\mathrm{odd}}" + }, + { + "bbox": [ + 313, + 465, + 553, + 478 + ], + "type": "text", + "content": " associated with specific depths as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 336, + 483, + 553, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 483, + 553, + 499 + ], + "spans": [ + { + "bbox": [ + 336, + 483, + 553, + 499 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {d} ^ {\\mathrm {o o d}} = \\left\\{\\left(x _ {i}, y _ {i}\\right) \\in \\mathcal {S} ^ {\\mathrm {o o d}} \\mid \\operatorname {D e p t h} _ {\\mathcal {H}} \\left(y _ {i}\\right) = d \\right\\}, \\tag {17}", + "image_path": "801f197bf1ee9c9cf449c6bf5e50fc9d60649e3d50e53ad69ebf4b60bbb18bf6.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "inline_equation", + "content": "d\\in \\{1,\\dots ,D - 1\\}" + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "content": " . Now we can compute the classification accuracies obtained by the network " + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "inline_equation", + "content": "f_{\\theta_d}" + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "content": " on the dataset " + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "inline_equation", + "content": "S_{d}^{\\mathrm{odd}}" + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "content": " . We compare this with the predictions obtained by marginalizing the predictions of the ID leaf model " + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "inline_equation", + "content": "f_{\\theta_D}" + }, + { + "bbox": [ + 313, + 505, + 553, + 553 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 336, + 559, + 553, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 559, + 553, + 587 + ], + "spans": [ + { + "bbox": [ + 336, + 559, + 553, + 587 + ], + "type": "interline_equation", + "content": "p _ {d} ^ {\\text {m a r g i n}} (c | x) = \\sum_ {c ^ {\\prime} \\in \\text {L e a v e s} _ {\\mathcal {H}} (c)} p \\left(c ^ {\\prime} | x; \\theta_ {D}\\right) \\quad \\text {f o r} c \\in \\mathcal {C} ^ {d}, \\tag {18}", + "image_path": "70b25a41c0e62319ed5da6d060cc2c7f2308e870fb90e486385eaf35462f2902.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "type": "inline_equation", + "content": "\\mathrm{Leaves}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "type": "text", + "content": " are the descendant leaves of " + }, + { + "bbox": [ + 313, + 594, + 515, + 605 + ], + "type": "inline_equation", + "content": "c" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "text", + "content": "Table 2 shows the results of this comparison across our three considered datasets. The multi-depth model obtains higher accuracies than the marginalized model for all datasets, indicating that the high-level models are better at classifying OOD samples as the correct class. Moreover, this implies that while a high-level model correctly predicts an OOD sample as class " + }, + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "text", + "content": ", the lower-level model leans towards predicting classes not in " + }, + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 313, + 606, + 555, + 714 + ], + "type": "text", + "content": ", which is the behavior we are looking for." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20616" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 105, + 284, + 180 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 103 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 103 + ], + "type": "text", + "content": "Table 2. Classification accuracies on OOD data at ground-truth depths. We compare models trained with high-level labels with models trained using the leaf labels." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 105, + 284, + 180 + ], + "lines": [ + { + "bbox": [ + 66, + 105, + 284, + 180 + ], + "spans": [ + { + "bbox": [ + 66, + 105, + 284, + 180 + ], + "type": "table", + "html": "
DatasetAccuracy (%) ↑Δ ↑
Multi-depth p(c|x; θd)Marginalized pdmargin(c|x)
SimpleHierImageNet70.168.5+1.6
iNaturalist1976.573.6+2.9
FGVC-Aircraft67.350.3+17.0
", + "image_path": "ff97c8c51d27e9093d36247298ce394a79e9e6e5332ef406036f095d94026999.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 200, + 167, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 200, + 167, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 200, + 167, + 211 + ], + "type": "text", + "content": "5.3. Evaluation metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 218, + 296, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 218, + 296, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 296, + 326 + ], + "type": "text", + "content": "How to evaluate a framework for OOD detection in class hierarchies is not established. In alignment with works on ID classification with class hierarchies [10, 15], we focus primarily on hierarchical distances between predictions and ground truth. However, given that our OOD nodes are selected at varying depths in the hierarchy, the resulting OOD sets have highly imbalanced class distributions. Therefore we propose to use a balanced mean hierarchical distance (BMHD), defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 334, + 294, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 334, + 294, + 365 + ], + "spans": [ + { + "bbox": [ + 70, + 334, + 294, + 365 + ], + "type": "interline_equation", + "content": "\\operatorname {B M H D} \\left(\\mathcal {C} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {C} ^ {\\prime} |} \\sum_ {c \\in \\mathcal {C} ^ {\\prime}} \\frac {1}{n _ {c}} \\sum_ {i = 1} ^ {n _ {c}} \\operatorname {d i s t} _ {\\mathcal {H}} \\left(f \\left(x _ {i} ^ {c}\\right), c\\right), \\tag {19}", + "image_path": "735f5a4c786eaeab7d7ddb191393fe979ca7cb03410cbf6859033ec56d05fe58.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": " is the set of classes being considered, " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "n_c" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": " is the number of samples in the test set with ground truth label " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "x_i^c" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": "-th sample out of those, and " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}'|" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": " is the cardinality of " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": ". In BMHD(" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": "), the mean distances for nodes in " + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 55, + 374, + 295, + 446 + ], + "type": "text", + "content": " are weighted equally, regardless of how many samples are associated with a specific node." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 447, + 296, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 481 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 481 + ], + "type": "text", + "content": "Furthermore, we want to evaluate the performance on a combined set of ID and OOD data. To this end, we define the mixed BMHD as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 77, + 491, + 294, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 491, + 294, + 504 + ], + "spans": [ + { + "bbox": [ + 77, + 491, + 294, + 504 + ], + "type": "interline_equation", + "content": "\\operatorname {M i x B M H D} = 0. 5 \\left(\\mathrm {B M H D} _ {\\text {i d}} + \\mathrm {B M H D} _ {\\text {o o d}}\\right), \\tag {20}", + "image_path": "9d6433f58aad6a50c312d6bc569150c7846b7db7f6fcb0377f4c39582e60457a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "spans": [ + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "inline_equation", + "content": "\\mathrm{BMHD_{id}}" + }, + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "inline_equation", + "content": "\\mathrm{BMHD_{ood}}" + }, + { + "bbox": [ + 55, + 513, + 296, + 585 + ], + "type": "text", + "content": " are evaluated with (19) on the set of ID and OOD classes with test data available, respectively. Similarly, we evaluate classification accuracies as the proportion of predictions that match the ground truth labels. Because of the class imbalance, we consider a balanced accuracy score [22]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 97, + 594, + 294, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 594, + 294, + 607 + ], + "spans": [ + { + "bbox": [ + 97, + 594, + 294, + 607 + ], + "type": "interline_equation", + "content": "\\operatorname {M i x B A c c} = 0. 5 \\left(\\mathrm {B A c c} _ {\\mathrm {i d}} + \\mathrm {B A c c} _ {\\mathrm {o o d}}\\right), \\tag {21}", + "image_path": "68892be9843c4ed219dca2c89ffcd704005e0e5b6bcea445c0cc6b0834dcfc38.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{BAcc_{id}}" + }, + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{BAcc_{ood}}" + }, + { + "bbox": [ + 55, + 616, + 295, + 640 + ], + "type": "text", + "content": " denote the balanced accuracies for ID and OOD classes, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 647, + 113, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 113, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 113, + 658 + ], + "type": "text", + "content": "5.4. Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 666, + 278, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 278, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 278, + 677 + ], + "type": "text", + "content": "We compare our framework to the following baselines:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "Depth oracle: We make predictions using the ground-truth depth with the corresponding " + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "inline_equation", + "content": "p(c|x;\\theta_d)" + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": " for all data, i.e., " + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "inline_equation", + "content": "p(c|x;\\theta_D)" + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": " for ID data and " + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "inline_equation", + "content": "p(c|x;\\theta_d), d < D" + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": " for OOD" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "data. Given the accuracies of the multi-depth networks, we consider this an upper performance bound." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 97, + 553, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 97, + 553, + 121 + ], + "spans": [ + { + "bbox": [ + 313, + 97, + 553, + 121 + ], + "type": "text", + "content": "Leaf model: We predict all data using " + }, + { + "bbox": [ + 313, + 97, + 553, + 121 + ], + "type": "inline_equation", + "content": "p(c|x;\\theta_D)" + }, + { + "bbox": [ + 313, + 97, + 553, + 121 + ], + "type": "text", + "content": ", i.e., all data are predicted as leaves, including OOD." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 121, + 554, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 554, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 554, + 205 + ], + "type": "text", + "content": "HSC: We train and evaluate the model proposed in [16] using the authors' code. We present results using the synset-based stopping-criterion because that gives the best results. We set thresholds for stopping criteria based on TPR rates to minimize MixBMHD on the test sets. However, in real-world settings, we cannot optimize these thresholds based on test performance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 205, + 554, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 554, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 554, + 289 + ], + "type": "text", + "content": "Our framework, denoted ProHOC (for probabilistic hierarchical OOD classification), is evaluated using the two different models for the conditionals described in Sec. 4.1. The first, denoted CompProb, uses the complementary probabilities to model the OOD probabilities, as defined in (10). The second, EntCompProb, uses the sum of the entropy and the complementary probability, as defined in (13)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 290, + 554, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 290, + 554, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 290, + 554, + 397 + ], + "type": "text", + "content": "The results are presented in Tab. 3. Excluding the oracle model, ProHOC with EntCompProb yields the best MixBMHD and MixBAcc across all three datasets, with CompProb consistently ranking second. Looking at the numbers for ID and OOD separately, we note the tradeoff between ID and OOD performance, where the CompProb model favors ID performance by making deeper predictions. In contrast, the EntCompProb model has a more balanced performance across ID and OOD." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 398, + 554, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 554, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 554, + 482 + ], + "type": "text", + "content": "ProHOC outperforms HSC [16], the existing method for OOD detection in hierarchies. This is despite optimizing the inference thresholds in HSC using OOD test data. We can see that HSC tends to make overly deep predictions, keeping an ID performance close to the leaf model but showing poor OOD performance. More detailed analyses of the results are available in the supplementary material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 491, + 492, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 492, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 492, + 504 + ], + "type": "text", + "content": "5.5. Evaluating out-of-hierarchy data" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "content": "Section 5.4 focuses on evaluating within-hierarchy OOD data, as these samples are the most challenging and distinguish our hierarchical approach from the binary OOD setting. However, ProHOC supports out-of-hierarchy OOD by classifying such samples as OOD at the root node. The OOD probability at the root is computed via (15) with " + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "inline_equation", + "content": "s(\\mathrm{root})" + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "content": " being a positive score from any suitable binary OOD method. For simplicity, we use the entropy of the deepest network for " + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "inline_equation", + "content": "s(\\mathrm{root})" + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "content": " which is a common baseline for binary OOD detection [24] that aligns well with our EntComp-Prob model. Table 4 shows ProHOC for FGVC-Aircraft with root predictions on three out-of-hierarchy datasets. MixBAcc is the (balanced) accuracy on the mix of within-hierarchy ID and OOD. Acc for out-of-hierarchy datasets is the percentage of samples correctly classified as root. We get high accuracies on out-of-hierarchy OOD while keeping most within-hierarchy performance." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20617" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 95, + 497, + 326 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": "Table 3. Mean hierarchical distances and accuracies on ID, OOD, and the mix of ID and OOD for ProHOC and baselines. The oracle model serves as an upper performance bound. Excluding the oracle model, the best results are boldfaced. Evaluations use test sets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 111, + 95, + 497, + 326 + ], + "lines": [ + { + "bbox": [ + 111, + 95, + 497, + 326 + ], + "spans": [ + { + "bbox": [ + 111, + 95, + 497, + 326 + ], + "type": "table", + "html": "
BAccid↑BAccood↑MixBAcc↑BMHDid↓BMHDood↓MixBMHD↓
SIMPLEHIERIMAGENET
Depth oracle79.772.576.10.821.050.93
Leaf model79.70.039.80.822.121.47
HSC [16]76.87.842.30.771.781.28
ProHOC (CompProb)67.819.243.50.921.611.27
ProHOC (EntCompProb)62.530.346.40.961.451.21
INATURALIST19
Depth oracle72.475.974.20.850.820.83
Leaf model72.40.036.20.852.231.54
HSC [16]68.18.438.20.801.761.28
ProHOC (CompProb)66.118.042.00.771.341.06
ProHOC (EntCompProb)57.735.646.70.781.100.94
FGVC-AIRCRAFT
Depth oracle84.767.676.10.490.670.58
Leaf model84.70.042.30.492.001.25
HSC [16]77.914.446.10.401.480.94
ProHOC (CompProb)80.117.148.60.411.250.83
ProHOC (EntCompProb)78.022.750.30.411.210.81
", + "image_path": "ea09c351f7a28775cb84243cf52e4dd691d7b6712dbf7a54984e114f4ca672d4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 65, + 356, + 285, + 407 + ], + "blocks": [ + { + "bbox": [ + 76, + 343, + 274, + 354 + ], + "lines": [ + { + "bbox": [ + 76, + 343, + 274, + 354 + ], + "spans": [ + { + "bbox": [ + 76, + 343, + 274, + 354 + ], + "type": "text", + "content": "Table 4. Evaluating ProHOC on out-of-hierarchy data." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 356, + 285, + 407 + ], + "lines": [ + { + "bbox": [ + 65, + 356, + 285, + 407 + ], + "spans": [ + { + "bbox": [ + 65, + 356, + 285, + 407 + ], + "type": "table", + "html": "
MixBAcc ↑ (FGVC-Air.)Acc ↑ Office31 [26]Acc ↑ iNat19Acc ↑ PACS [13]
ProHOC w/ root47.178.283.994.4
ProHOC w/o root50.3---
", + "image_path": "d88922283b8ca92dd2221a47c7ba38186fb6d1d1c5d3ee43559850bdbd66cb3a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 425, + 152, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 425, + 152, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 425, + 152, + 437 + ], + "type": "text", + "content": "5.6. Training details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 443, + 296, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 296, + 587 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 296, + 587 + ], + "type": "text", + "content": "We train our multi-depth networks with standard supervised NLL training using the remapped labels from (8). We use the ResNet50 architecture [6] for all experiments. For FGVC-Aircraft and iNaturalist19, the network is initialized with pre-trained weights from ImageNet, whereas for SimpleHierImageNet, we train the network from scratch. We train for 90 epochs on FGVC-Aircraft and iNaturalist19, and 250 epochs on SimpleHierImageNet. We use stochastic gradient descent with an initial learning rate of 0.05, decayed to zero by the end of training using a cosine schedule. A batch size of 128 is used throughout. During training, images are randomly cropped and resized to " + }, + { + "bbox": [ + 55, + 443, + 296, + 587 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 55, + 443, + 296, + 587 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 597, + 130, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 130, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 130, + 609 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "content": "This work focuses on establishing the key building blocks of our framework for hierarchical OOD detection, with little attention given to optimizing the performance of the underlying multi-depth networks. Further work could explore stronger architectures and advanced training techniques to improve the performance of ProHOC. Finally, a fundamental limitation of our problem formulation is the assumption that the class hierarchy reflects observable visual similarities" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 345, + 555, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 555, + 381 + ], + "type": "text", + "content": "ties. If ID and OOD siblings do not share common visual features, we can not expect this type of framework to accurately predict OOD." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 391, + 413, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 391, + 413, + 403 + ], + "spans": [ + { + "bbox": [ + 314, + 391, + 413, + 403 + ], + "type": "text", + "content": "7. Ablation studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 410, + 555, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 555, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 555, + 423 + ], + "type": "text", + "content": "7.1. Evaluating different scores for the conditionals" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "text", + "content": "In Sec. 4.1 we described how we use the multi-depth networks to model the conditionals " + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "inline_equation", + "content": "p(y|c, x)" + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "inline_equation", + "content": "y \\in \\mathrm{Ch}_{\\mathcal{H}}(c) \\cup \\{\\mathrm{odd}(c)\\}" + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "text", + "content": ". The primary challenge in modeling " + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "inline_equation", + "content": "p(y|c, x)" + }, + { + "bbox": [ + 313, + 429, + 554, + 513 + ], + "type": "text", + "content": " lies in assigning the OOD probability. Here, we explore several approaches to modeling this OOD probability, or an unnormalized OOD score, based on the predictions from our multi-depth networks. We consider the following models:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 512, + 554, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 554, + 548 + ], + "type": "text", + "content": "CompProb: The complementary probability, as defined in (10). It uses the sum of probabilities for classes outside of " + }, + { + "bbox": [ + 313, + 512, + 554, + 548 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 313, + 512, + 554, + 548 + ], + "type": "text", + "content": " as a proxy for the OOD probability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 548, + 554, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 554, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 554, + 584 + ], + "type": "text", + "content": "Entropy: As defined in (11), indicates the uncertainty of predictions among the children. The entropy is widely used as an OOD score in the literature [24]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 584, + 554, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 584, + 554, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 584, + 554, + 608 + ], + "type": "text", + "content": "MaxProb: The (negated) maximum probability among the children, defined as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 613, + 555, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 613, + 555, + 635 + ], + "spans": [ + { + "bbox": [ + 358, + 613, + 555, + 635 + ], + "type": "interline_equation", + "content": "s ^ {\\operatorname {M a x P r o b}} (c) = 1 - \\max _ {y \\in \\operatorname {C h} _ {\\mathcal {H}} (c)} p (y | x; \\theta_ {d}) \\tag {22}", + "image_path": "a43971729b85d92d63292f1bdb59bfca3b67930bba04f15e11a985403f2a1b76.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 641, + 554, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 666 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 313, + 641, + 554, + 666 + ], + "type": "inline_equation", + "content": "d = \\mathrm{Depth}_{\\mathcal{H}}(c) + 1" + }, + { + "bbox": [ + 313, + 641, + 554, + 666 + ], + "type": "text", + "content": ". This alternative is similar to the widely used MSP score [7] for binary OOD detection." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "EntCompProb: Since the entropy and the complementary probability are independent and signal different aspects of uncertainty, we find it intuitive to combine scores in a sum, as defined in (13)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20618" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 144 + ], + "type": "text", + "content": "CompLogits: We sum the unnormalized logits for classes outside " + }, + { + "bbox": [ + 55, + 72, + 295, + 144 + ], + "type": "inline_equation", + "content": "\\mathrm{Ch}_{\\mathcal{H}}(c)" + }, + { + "bbox": [ + 55, + 72, + 295, + 144 + ], + "type": "text", + "content": " and use the sum in the softmax function alongside the logits for the child nodes. This method resembles CompProb, although it differs in the scaling of the OOD probability due to summing before applying the exponential function in the softmax." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 295, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 192 + ], + "type": "text", + "content": "The methods denoted CompProb and CompLogits form valid probability distributions directly by design. For the other alternatives, we obtain the conditional distribution by normalization following (14) and (15)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 193, + 296, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 193, + 296, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 193, + 296, + 312 + ], + "type": "text", + "content": "A well-performing model for the conditionals should display certain qualities. The probability for OOD in the conditional distribution should be the maximum when the sample is OOD. Moreover, if the network misclassifies an ID sample (predicting it as an incorrect ID child), we want our model to predict the OOD node instead of an incorrect ID prediction, which would increase the hierarchical distance from the ground truth. To assess these aspects of the performance, we use several metrics that are evaluated locally for a specific internal node:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "text", + "content": "F1: The F1 score for binary classification where OOD is considered the positive label. A prediction is OOD if " + }, + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(c)|c,x)" + }, + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "text", + "content": " is the largest element of " + }, + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "inline_equation", + "content": "p(y|c,x)" + }, + { + "bbox": [ + 55, + 313, + 296, + 361 + ], + "type": "text", + "content": ", otherwise ID. We also report the corresponding FPR and TPR." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 361, + 295, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 295, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 295, + 384 + ], + "type": "text", + "content": "Purity: The fraction of predicted ID samples, predicted as the correct child node." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": "Dirty F1: Our variant of the F1 score where ID data that are misclassified as an incorrect child are labeled as OOD when computing the F1 score." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "text", + "content": "We evaluate these metrics for all parent nodes " + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "text", + "content": " for which OOD data with ground truth at " + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "text", + "content": " are available. As ID data, we use all data that belong to descendants of " + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 422, + 295, + 469 + ], + "type": "text", + "content": ". We report the mean metrics over all evaluated nodes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 470, + 295, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 470, + 295, + 626 + ], + "spans": [ + { + "bbox": [ + 55, + 470, + 295, + 626 + ], + "type": "text", + "content": "Table 5 shows results from FGVC-Aircraft. EntCompProb achieves the highest F1 score. It has the largest FPR but this is compensated by its high purity, indicating that many false positives would have been classified as incorrect ID children if they were predicted as ID. For Dirty F1, EntCompProb again outperforms other methods, by an even larger margin. This suggests that the entropy-based uncertainty and the complementary probability interact effectively to create a model with the desired properties. In contrast, CompLogits performs poorly due to being underconfident on OOD (a low TPR). This implies that summation at the logit level leads to smaller OOD probabilities than summation at the probability level (as with CompProb)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 635, + 294, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 294, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 294, + 647 + ], + "type": "text", + "content": "7.2. Minimizing the expected hierarchical distance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": "ProHOC provides a predictive distribution over all nodes in the hierarchy, allowing us to incorporate uncertainty into our final prediction. Given our objective to produce predictions that are hierarchically close to the ground truth (1), we can use the predicted distribution " + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "inline_equation", + "content": "p(c|x)" + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": " to minimize the" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 326, + 93, + 538, + 163 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 553, + 92 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 553, + 92 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 553, + 92 + ], + "type": "text", + "content": "Table 5. Analyzing the performance of different methods for modeling " + }, + { + "bbox": [ + 313, + 71, + 553, + 92 + ], + "type": "inline_equation", + "content": "p(\\mathrm{odd}(c)|c,x)" + }, + { + "bbox": [ + 313, + 71, + 553, + 92 + ], + "type": "text", + "content": ". Results are from FGVC-Aircraft." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 93, + 538, + 163 + ], + "lines": [ + { + "bbox": [ + 326, + 93, + 538, + 163 + ], + "spans": [ + { + "bbox": [ + 326, + 93, + 538, + 163 + ], + "type": "table", + "html": "
F1 ↑FPR ↓TPR ↑Purity ↑Dirty F1 ↑
CompProb0.470.090.420.880.49
Entropy0.510.120.450.900.55
MaxProb0.500.100.450.890.52
EntCompProb0.560.150.520.900.59
CompLogits0.170.010.140.870.18
", + "image_path": "492300802d4bb17534ae9a976de88f6368fa2e68582d484a9ff5d39e8740b6b0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 321, + 198, + 543, + 344 + ], + "blocks": [ + { + "bbox": [ + 313, + 175, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 313, + 175, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 553, + 196 + ], + "type": "text", + "content": "Table 6. Comparing predictions from minimizing the expected hierarchical distance to predictions using the most probable class." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 198, + 543, + 344 + ], + "lines": [ + { + "bbox": [ + 321, + 198, + 543, + 344 + ], + "spans": [ + { + "bbox": [ + 321, + 198, + 543, + 344 + ], + "type": "table", + "html": "
argmin E[distH]argmax p(c|x)
MixBAcc ↑ MixBMHD ↓MixBAcc ↑ MixBMHD ↓
SIMPLEHIERIMAGENET
EntCompProb46.41.2145.81.25
CompProb43.51.2739.71.37
INATURALIST19
EntCompProb46.70.9445.60.98
CompProb42.01.0638.41.17
FGVC-AIRCRAFT
EntCompProb50.30.8150.20.88
CompProb48.60.8347.40.90
", + "image_path": "d55765fc275953687f01f535d2140ed58151d1f0c6171ab85cae5284c95f3cd3.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 356, + 506, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 506, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 506, + 368 + ], + "type": "text", + "content": "expected hierarchical distance of the prediction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 380, + 553, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 380, + 553, + 399 + ], + "spans": [ + { + "bbox": [ + 356, + 380, + 553, + 399 + ], + "type": "interline_equation", + "content": "f (x) = \\underset {c} {\\operatorname {a r g m i n}} \\mathbb {E} _ {p \\left(c ^ {\\prime} \\mid x\\right)} \\left[ \\operatorname {d i s t} _ {\\mathcal {H}} \\left(c, c ^ {\\prime}\\right) \\right], \\tag {23}", + "image_path": "2f83f5fd169440fd46cea198fedba83211ec8581c39052cf86826bbc584e3513.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 411, + 553, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 553, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 553, + 459 + ], + "type": "text", + "content": "as presented in Sec. 3. This is similar to the post-hoc correction proposed in [10], although they restrict the predictions to leaves. We compute the expected hierarchical distance over all nodes in the hierarchy." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 460, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 533 + ], + "type": "text", + "content": "We compare the predictions from (23) with the standard " + }, + { + "bbox": [ + 313, + 460, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\mathrm{argmax}_c p(c|x)" + }, + { + "bbox": [ + 313, + 460, + 554, + 533 + ], + "type": "text", + "content": " in Tab. 6, using ProHOC with both CompProb and EntCompProb. As expected, (23) achieves lower hierarchical distances since it optimizes for that specifically. However, we also see improvements in accuracy as an additional benefit of using (23)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 548, + 388, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 388, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 388, + 560 + ], + "type": "text", + "content": "8. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "type": "text", + "content": "The deep-learning community has made substantial progress in the binary setting of OOD detection. In this paper, we raise the bar for OOD detection by aiming for more informative predictions: predicting OOD as internal nodes in a class hierarchy. Our framework shows promising results. We also believe its simplicity in introducing no new hyperparameters and using underlying networks trained with standard methods makes it accessible and adaptable for further development. We hope this work will inspire continued exploration of OOD classification in class hierarchies and that ProHOC can serve as a foundation for even more effective methods." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20619" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 296, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 296, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 296, + 178 + ], + "type": "text", + "content": "This work was supported by Saab AB and Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. 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To enhance CLIP's effectiveness and versatility, efficient few-shot adaptation techniques have been widely adopted. Among these approaches, training-free methods, particularly caching methods exemplified by Tip-Adapter, have gained attention for their lightweight adaptation without the need for additional fine-tuning. In this paper, we revisit Tip-Adapter from a kernel perspective, showing that caching methods function as local adapters and are connected to a well-established kernel literature. Drawing on this insight, we offer a theoretical understanding of how these methods operate and suggest multiple avenues for enhancing the Tip-Adapter baseline. Notably, our analysis shows the importance of incorporating global information in local adapters. Therefore, we subsequently propose a global method that learns a proximal regularizer in a reproducing kernel Hilbert space (RKHS) using CLIP as a base learner. Our method, which we call ProKeR (Proximal Kernel ridge Regression), has a closed form solution and achieves state-of-the-art performances across 11 datasets in the standard few-shot adaptation benchmark. Code is available at https://ybendou.github.io/ProKeR/", + "bbox": [ + 88, + 323, + 485, + 670 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 699, + 220, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large scale vision-language models (VLMs) trained with contrastive learning have gained an increasing attraction in recent years [21, 41]. These models have shown outstanding performances across a wide range of tasks such as classification [41], segmentation [30] and video understanding [28]. CLIP [41] is one of the most established VLMs offering remarkable zero-shot capabilities in various downstream tasks. It operates using only the class label within a textual prompt such as \"A photo of a {CLASS}\" where {CLASS} is the groundtruth text label for each class. However, it is well-", + "bbox": [ + 89, + 724, + 485, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d679260231af9ba232857873b7293663576f9664ad670c973d786bc24e1cccc.jpg", + "image_caption": [ + "Figure 1. Fitting comparison between different methods on synthetically generated data, illustrating Nadaraya-Watson (Tip-Adapter) bias mitigation via our proposed Local Linear Regression (LLR, Sec. 3.3) and our final method ProKeR." + ], + "image_footnote": [], + "bbox": [ + 513, + 287, + 901, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "known that the zero-shot performance of CLIP is limited in scenarios with large domain shift from the pre-training distribution [10, 34]. To further improve CLIP's generalization, multiple follow-up works proposed to include few-shot data [12, 62, 67] which has shown substantial performance gains compared to zero-shot CLIP.", + "bbox": [ + 509, + 628, + 906, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Few-shot adaptation of CLIP can be categorized into two types of methods based on whether they require fine-tuning on the few-shot samples or not. Among fine-tuning based methods, prompt learning consists of learning continuous tokens instead of hand-crafted templates in CLIP as proposed by CoOp [67] and CoCoOp [66]. In addition, adapter-based fine-tuning methods operate in the feature space to train their classifiers [12, 29]. Despite their promising performance on downstream tasks, fine-tuning methods require additional training costs to learn the new set of parameters. Furthermore, Tip-Adapter proposed a training-free few-shot adaptation alternative [62]. Using a caching mechanism,", + "bbox": [ + 509, + 719, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work", + "bbox": [ + 109, + 886, + 362, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25092", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "it captures knowledge from the few-shot samples without additional fine-tuning and ensembles it with zero-shot CLIP. This cache model has shown a significant improvement over the zero-shot performance, which has led to follow-up work such as APE [68] and Tip-X [53].", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to understand caching effectiveness and limitations, we undertake a theoretical analysis to explore the nature of Tip-Adapter. We begin by demonstrating that the Tip-Adapter adaptation term is a modified version of the well-known Nadaraya-Watson (NW) estimator [33], a local nonparametric regression method that allows Tip-Adapter to effectively capture various distributions. However, the NW estimator is also known to be strongly biased [25, 36] (e.g. Fig. 1). To mitigate this bias, we leverage existing tools from the literature of kernel methods. An effective extension to NW estimator is locally linear regression [46]. Initially, by fitting a local linear regression around each test point using a closed-form solution, we significantly improve the performance of Tip-Adapter. However, the parameters are estimated locally, which is prone to overfitting in high-dimensional problems [16, 36].", + "bbox": [ + 89, + 169, + 482, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our analysis shows that caching methods can be understood as local nonparametric regression methods regularised through CLIP pointwise zero-shot predictions. However, this regularization only acts locally and does not provide any global information about the few-shot task. Conversely, recent training-based methods rely on global regularizers to incorporate global information [50]. Hence, we ask ourselves the question: how can we leverage global regularizers for few-shot adapters while conserving the benefits of training-free methods? In order to design such global regularizer, we devise two important design choices: - Firstly, we restrain the hypothesis space of the learned function to be a reproducing kernel Hilbert space (RKHS). - Second, using the RKHS norm, we introduce a proximal regularization term to ensure that the obtained solution is close to the base predictor i.e. $f_{\\mathrm{clip}}$ . Thanks to the properties of the RKHS, minimizing the difference between two functions using the RKHS norm ensures that they are close pointwise. Our method ProKeR provides a more effective way to preserve prior knowledge from the zero-shot predictor and maintains the expressive capacity of the learned functions. Through extensive experiments, we show the effectiveness of our method ProKeR which achieves consistent gains over state-of-the-art training-free methods on standard few-shot classification benchmarks [62] and can be successfully combined with existing training-based methods. In addition, we highlight the robustness and generalizability of the proposed method across different architectures and on out-of-distribution datasets.", + "bbox": [ + 89, + 412, + 485, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Summary of contributions:", + "text_level": 1, + "bbox": [ + 89, + 853, + 284, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. We frame the cache model of Tip-Adapter [62] as a Nadaraya-Watson estimator, a classical kernel regression", + "bbox": [ + 91, + 869, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "method, and provide a theoretical understanding of how Tip-Adapter functions.", + "bbox": [ + 532, + 90, + 903, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2. Under this new perspective, we propose multiple improvements on Tip-Adapter either through a closed-form local linear regression fit or by incorporating global information.", + "3. Our analysis leads to our new proposed method ProKeR, a training-free method that leverages global regularization in a reproducing kernel Hilbert space. Through extensive experiments, ProKeR outperforms existing methods and sets a new state-of-the-art on standard few-shot classification benchmarks." + ], + "bbox": [ + 511, + 121, + 908, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 287, + 653, + 304 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Vision-Language Pre-trained Models", + "text_level": 1, + "bbox": [ + 511, + 313, + 831, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual-language models (VLMs) have gained an increasing popularity lately. These methods, exemplified by CLIP [41], DeCLIP [27] and ALIGN [21], employ a contrastive learning framework to learn a vision encoder and a language encoder with a shared representation space between text and images. Trained on large-scale datasets of image-text pairs, VLMs have shown remarkable zero-shot capabilities on downstream tasks without additional fine-tuning, paving the way for open vocabulary recognition [14]. VLMs have been extended to few-shot classification [67] as well as other tasks beyond image classification such as video understanding [28, 54], image segmentation [30, 52], image generation [43] and 3D reconstruction [7, 63].", + "bbox": [ + 511, + 335, + 906, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Few-shot Adaptation", + "text_level": 1, + "bbox": [ + 511, + 544, + 710, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-shot adaptation methods in the context of classification can be categorized into prompt learning and adapter based approaches. Inspired by the recent advances in natural language processing [26], prompt learning aims to learn effective global text or visual prompts for the downstream tasks [2, 6, 23, 45, 47, 49, 58, 61, 66, 67]. Although prompt learning methods have brought significant improvements over the zero-shot baseline, they require back-propagating through the entire text encoder and require having access to the text encoder [38]. On the other hand, adapter-based approaches operate in the feature space and do not require having access to the pre-trained model weights. We distinguish two families of adapter-based approaches. The first one is training-based methods [12, 29, 60] which either train a linear layer [29, 60] or a two-layer MLP such as CLIP-Adapter [12] to perform residual feature blending of the zero-shot classifier.", + "bbox": [ + 511, + 566, + 908, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While fine-tuning adapters have achieved a good level of performance, they still require additional training time which is impractical under limited resources and might suffer from the caveats of gradient optimization. To alleviate these issues, Tip-Adapter [62] emerges as a training-free solution", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25093", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c05d6151d3311f7b2b9f10def3df6a98ab4b807f5d1a9d79b9542fc5b697cf6e.jpg", + "image_caption": [ + "Figure 2. Overview of our training-free method ProKeR. While Tip-Adapter builds a key-value cache model using the few-shot samples, ProKeR incorporates a proximal global regularization based on the zero-shot predictor in a reproducing kernel Hilbert space (RKHS). This allows the use of a richer model without overfitting on the few-shot data." + ], + "image_footnote": [], + "bbox": [ + 89, + 90, + 908, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "based on a key-value cache model. Building on Tip-Adapter, multiple caching methods have been proposed. APE [68] includes a feature selection step to the cache model. CaFo [64] uses an ensemble of foundation models for the cache model and augments text prompts using a Large Language model. SuS-X and its module Tip-X [53] first generates the few-shot set using Stable Diffusion then uses the inter-modal similarities between the test images and the few-shot set. In a transductive setting, DMN [65] proposes a dynamic memory mechanism to cache historical test data. More recently, GDA proposes to use a Linear Discriminant Analysis to set a strong baseline for training-free methods [55]. Despite the good level of performance, there is currently no theoretical framework for understanding the motivation behind caching models.", + "bbox": [ + 88, + 431, + 485, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 674, + 181, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We expose in this section the details of the proposed method. Our starting point consists in framing Tip-Adapter as a kernel method. Thanks to this new perspective, we develop multiple improvements tailored for it. Conclusively, we propose ProKeR, a method that introduces a global proximal regularization in a reproducing kernel Hilbert space (RKHS).", + "bbox": [ + 89, + 700, + 485, + 791 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Tip-Adapter as a Nadaraya-Watson estimator", + "text_level": 1, + "bbox": [ + 89, + 801, + 478, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, let $\\mathbf{x} \\in \\mathbb{R}^D$ be the features of an input query image extracted using the visual encoder of CLIP, $\\mathbf{S} \\in \\mathbb{R}^{NK \\times D}$ the visual features of the training set and $\\mathbf{L} \\in \\mathbb{R}^{NK \\times N}$ the associated matrix of one-hot labels where $N$ is the number of classes and $K$ is the number of shots per class.", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbf{W}_{\\mathrm{clip}} \\in \\mathbb{R}^{D \\times N}$ be the text prototypes of the classes extracted with the text encoder using the standard handcrafted templates in the form of \"a photo of a {CLASS}\" [29, 62, 67]. The zero-shot predictor from CLIP is defined as $f_{\\mathrm{clip}}: \\mathbf{x} \\mapsto \\mathbf{x} \\mathbf{W}_{\\mathrm{clip}}$ .", + "bbox": [ + 511, + 431, + 906, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To alleviate $f_{\\mathrm{clip}}$ prediction errors due to lack of generalization, Tip-Adapter [62] utilizes a cache model to learn knowledge from the few-shot samples. The predicted logits can be formulated as:", + "bbox": [ + 511, + 508, + 906, + 566 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\exp \\left(- \\beta (1 - \\mathbf {x} \\mathbf {S} ^ {\\top})\\right) \\mathbf {L}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 578, + 906, + 597 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta$ is a smoothing scalar and $\\alpha$ controls the balance between textual features and few-shot images. Note that since the features in CLIP are normalized (i.e. $||\\mathbf{x}||_2 = 1$ ), we can rewrite Eq. (1) as:", + "bbox": [ + 511, + 607, + 906, + 667 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\sum_ {i = 1} ^ {N K} \\exp \\left(- \\frac {\\beta}{2} | | \\mathbf {S} _ {i} - \\mathbf {x} | | _ {2} ^ {2}\\right) \\mathbf {L} _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 678, + 906, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{S}_i$ is the $i$ -th few-shot sample. Interestingly, the right term of Tip-Adapter can be seen as a modified version of the well-known Nadaraya-Watson (NW) estimator [33] with a Radial Basis Function (RBF) kernel [37]:", + "bbox": [ + 511, + 746, + 906, + 808 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i})) \\mathbf {L} _ {i}}{\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i}))}, \\\\ \\text {w h e r e} k _ {\\beta} (u) = \\left(\\frac {\\beta}{2}\\right) ^ {D} \\exp \\left(- \\frac {\\beta}{2} u\\right), \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 820, + 906, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25094", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d$ is the distance between the query image and the shots in the feature space. In essence, when $d$ is the Euclidean distance, as in Eq. (2), the adaptation term of TipAdapter is a nonparametric regression, obtained by performing a smooth and locally weighted average of the one-hot labels of the few-shot samples using a kernel function, which quantifies the similarity between the query image and the shots.", + "bbox": [ + 89, + 90, + 483, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Training-free few-shot adapters as a Bayes optimal mapping", + "text_level": 1, + "bbox": [ + 89, + 229, + 483, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We formulate the few-shot visual-language adaptation as a Bayes optimal mapping [17] associated to the following pointwise risk:", + "bbox": [ + 89, + 268, + 483, + 316 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR (\\mathbf {x}, \\phi (\\mathbf {x})) = \\mathbb {E} _ {Y \\mid X} [ s (Y, \\phi (X)) + \\mathcal {R} _ {\\mathrm {c l i p}} | X = \\mathbf {x} ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 332, + 483, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s$ is a cost function and $\\mathcal{R}_{\\mathrm{clip}}$ is a regularization term using CLIP prediction independent of $Y$ . Here, $X$ and $Y$ are random variables representing the image features and the labels respectively.", + "bbox": [ + 89, + 366, + 483, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The pointwise Bayes optimal mapping is defined as [17]:", + "bbox": [ + 109, + 429, + 483, + 445 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\underset {\\mathbf {q} \\in M} {\\arg \\min } R (\\mathbf {x}, \\mathbf {q}) (5) \\\\ = \\arg \\min _ {\\mathbf {q} \\in M} \\int_ {M} s (\\mathbf {y}, \\mathbf {q}) d \\mu_ {\\mathbf {x}} (\\mathbf {y}) + \\mathcal {R} _ {\\mathrm {c l i p}}, (6) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 477, + 483, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d\\mu_{\\mathbf{x}}$ is the conditional probability of $Y$ conditioned on $X = \\mathbf{x}$ and $M$ is the output space. Following [17], we leverage kernel estimators to rewrite the adaptation problem as:", + "bbox": [ + 89, + 550, + 483, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\mathbf {x}) = \\arg \\min _ {\\mathbf {q}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) s (\\mathbf {q}, \\mathbf {L} _ {i}) + \\mathcal {R} _ {\\mathrm {c l i p}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 625, + 483, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This formulation offers a new perspective on the adaptation, where for each test point the cost function is minimized over the output space, with a weighting from each training sample. The regularization term guarantees that the obtained predictions are not far from zero-shot CLIP.", + "bbox": [ + 89, + 700, + 483, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Interestingly, this formulation paves the way for considering different choices of cost functions $s$ , regularization terms $\\mathcal{R}_{\\mathrm{clip}}$ and kernels $k_{\\beta}$ . The consistency of the obtained estimator is discussed in [17] where the solution of Eq. (7) is obtained using a gradient descent algorithm. While this optimisation can be time consuming, there are cases where a closed form solution can be derived. For instance, when $s$ is the squared Euclidean distance and $\\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\mathbf{q} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2$ ,", + "bbox": [ + 89, + 779, + 485, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we can derive the following solution:", + "bbox": [ + 511, + 90, + 759, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\lambda N K}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} f _ {\\mathrm {c l i p}} (\\mathbf {x}) \\\\ + \\frac {1}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) \\mathbf {L} _ {i}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 119, + 839, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\mathcal {Z} (\\mathbf {x}) = \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 200, + 906, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a regularization term that balances the predictions of zero-shot CLIP and the local fit. The obtained closed form of the estimator in Eq. (7) is equivalent to Tip-Adapter up to a scaling factor which depends on each input $\\mathbf{x}$ . The main difference between the two formulations in Eq. (2) and Eq. (8) is that the second term in Eq. (8) is agnostic to the training size and is query dependent.", + "bbox": [ + 511, + 251, + 906, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the Nadaraya-Watson estimator is a nonparametric model that allows to capture any type of distribution, it is well known to suffer from poor bias at the boundaries of the training samples [36]. In the following, we propose two methods to alleviate this bias.", + "bbox": [ + 511, + 357, + 906, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Local Linear Regression", + "text_level": 1, + "bbox": [ + 513, + 441, + 736, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A standard way to alleviate the boundary bias of the NW estimator is by moving from a local constant fit to a local linear fit around each test point. Instead of using the estimate from Eq. (7), local linear regression (LLR) forms the local estimate $\\phi (\\mathbf{x}) = \\tilde{\\mathbf{x}}\\mathbf{A}$ , where $\\tilde{\\mathbf{x}} = [1\\quad \\mathbf{x}]$ , and $\\mathbf{A}\\in \\mathbb{R}^{(d + 1)c}$ minimizes the following problem:", + "bbox": [ + 511, + 464, + 906, + 555 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {A}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right) s \\left(\\tilde {\\mathbf {S}} _ {i} \\mathbf {A}, \\mathbf {L} _ {i}\\right) + \\mathcal {R} _ {\\mathrm {c l i p}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 566, + 906, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is a weighted ordinary least square problem around each test point weighted by the kernel values $k_{\\beta}(d(\\mathbf{x}, \\mathbf{S}_i))$ . Using the same cost function as for Eq. (8) and using the regularization term $\\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\tilde{\\mathbf{x}} \\mathbf{A} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2$ , we derive a closed form solution for Eq. (9) as follows:", + "bbox": [ + 511, + 617, + 908, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {\\phi} (\\mathbf {x}) = \\tilde {\\mathbf {x}} \\mathbf {A} ^ {- 1} \\mathbf {B}, \\\\ w h e r e \\quad \\mathbf {A} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\tilde {\\mathbf {S}} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} \\tilde {\\mathbf {x}}, \\\\ \\text {a n d} \\quad \\mathbf {B} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\mathbf {L} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} f _ {\\operatorname {c l i p}} (\\mathbf {x}), \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 708, + 906, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Omega$ is the $NK\\times NK$ matrix with ith diagonal element as $k_{\\beta}(d(\\mathbf{x},\\mathbf{S}_i))$", + "bbox": [ + 511, + 779, + 905, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This method, that we dub henceforth LLR, boils down to fitting a local linear regression while enforcing the obtained fit to be close to the text predictions locally around the query input sample. While LLR usually improves performance, it is time consuming as one needs to fit a linear regression for each input sample. Furthermore, the parameters of LLR", + "bbox": [ + 511, + 810, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25095", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are solely estimated locally, which is prone to overfitting in high-dimensional problems [36]. Alternatively, one possible way to eliminate the bias of NW estimator due to the bandwidth selection without significantly increasing the time complexity is by equipping the kernel with a better distance function $d$ [36].", + "bbox": [ + 89, + 90, + 483, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Local methods with a global metric", + "text_level": 1, + "bbox": [ + 89, + 190, + 397, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While there exists multiple strategies to construct a good metric [36, 56], using the Mahalanobis distance with the covariance matrix estimated from the training data is a simple yet well-performing one [3]:", + "bbox": [ + 89, + 212, + 485, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd (\\mathbf {x}, \\mathbf {S} _ {i}) = \\| \\mathbf {x} - \\mathbf {S} _ {i} \\| _ {\\hat {\\mathbf {A}}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 282, + 483, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\Lambda}$ is the estimated precision matrix from the few-shot samples. This metric effectively incorporates global information and captures the geometry of the space which allows to construct a better kernel function tailored to the downstream task. The classical RBF kernel corresponds to using an isotropic covariance matrix. While still being a local method, adapting the metric to the downstream task allows to incorporate global information about the underlying distribution and improves over Tip-Adapter as shown in Fig. 3.", + "bbox": [ + 89, + 311, + 483, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Proximal Kernel Ridge Regression", + "text_level": 1, + "bbox": [ + 89, + 470, + 390, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As can be seen in Fig. 3, incorporating global information about the task through a global metric effectively outperforms both Tip-Adapter and LLR. However, the choice of the global metric for NW estimator beyond the Mahalanobis distance remains challenging [56], especially in the few-shot setting. Furthermore, despite being equipped with a global metric, the NW estimator remains in essence a local method and still lacks a global regularization. Whilst the use of a global regularization has been recently addressed in training-based methods [50], using a truly global regularization in a training-free manner remains challenging and unexplored.", + "bbox": [ + 89, + 493, + 483, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These limitations highlight the necessity for regularization in this adaptation process. The main idea is to balance the need to maintain the expressive capacity of the learned functions while ensuring stability and robustness. To this end we introduce two key design choices: (1) we constrain the hypothesis space of the learned function to a reproducing kernel Hilbert space (RKHS), and (2) we incorporate a proximal regularization term, based on the RKHS norm, to ensure the solution remains close to the base predictor $(f_{\\mathrm{clip}})$ . The RKHS norm's properties guarantee that minimizing the difference between two functions in this space results in pointwise closeness. Consequently, this proximal term serves as a global regularization that preserves prior knowledge from the zero-shot predictor, resulting in more robust solutions that are less prone to overfitting on the few-shot data.", + "bbox": [ + 89, + 659, + 485, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the multi-output nature of the problem, the employed reproducing kernel $\\mathbf{K}_{\\beta}$ is a reproducing kernel for vector valued functions. The main difference is that the kernel is matrix valued. Several instances of multi-output kernels have been proposed in the literature [1, 5], with separable kernels being among the most widely used for learning vector-valued functions due to their simplicity and computational efficiency. These kernels are formulated as a product of a kernel function for the input space alone and a matrix that encodes the interactions among the outputs. Let us consider $\\mathbf{K}_{\\beta}:\\mathbb{R}^{D}\\times \\mathbb{R}^{D}\\mapsto \\mathbb{R}^{N\\times N}$ as a separable kernel of the form:", + "bbox": [ + 511, + 90, + 906, + 271 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {K} _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right)\\right) _ {j, j ^ {\\prime}} = k _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) \\mathbf {B}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 280, + 906, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{B}$ is a $N\\times N$ symmetric and positive semi-definite matrix which captures the correlations between the outputs. A simple yet effective choice for $\\mathbf{B}$ is the identity matrix where all outputs are treated as being unrelated.", + "bbox": [ + 511, + 304, + 906, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our goal is to learn a multi-output predictor $\\phi$ using the following objective:", + "bbox": [ + 511, + 364, + 905, + 395 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\phi \\in \\mathcal {H}} \\sum_ {i = 1} ^ {N K} \\| \\phi (\\mathbf {S} _ {\\mathbf {i}}) - \\mathbf {L} _ {i} \\| _ {2} ^ {2} + \\lambda \\| \\phi - f _ {\\mathrm {c l i p}} \\| _ {\\mathcal {H}} ^ {2}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 402, + 906, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By the representative theorem [22, 32], the unique minimizer of problem in Eq. (13) emerges naturally as the solution of a Kernel Ridge Regression (KRR) problem:", + "bbox": [ + 511, + 450, + 906, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi = f _ {\\mathrm {c l i p}} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}},.) \\gamma_ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 506, + 723, + 547 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\gamma = \\left(\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})\\right) ^ {- 1} \\left(\\mathbf {L} - f _ {\\mathrm {c l i p}} (\\mathbf {S})\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 550, + 906, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $(k_{\\beta}(\\mathbf{S},\\mathbf{S}))_{i,j} = k_{\\beta}(\\mathbf{S}_i,\\mathbf{S}_j)$ and $\\gamma_{i}\\in \\mathbb{R}^{N}$ . This approach allows to map data to an infinite dimensional space. Furthermore, the regularization term allows the use of a richer model that captures the complex structure of the data while preserving its smoothness, avoiding overfitting on the few-shot data.", + "bbox": [ + 511, + 585, + 906, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Mercer decomposition of kernel methods", + "text_level": 1, + "bbox": [ + 511, + 685, + 864, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One additional benefit of this perspective on caching methods is memory reduction which allows to overcome the necessity of storing training data. For positive definite kernel, we can leverage Mercer theorem [13] to write the kernel function as follow:", + "bbox": [ + 511, + 707, + 906, + 781 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nk _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) = \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {x} ^ {\\top}\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 789, + 906, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This allows us to write:", + "bbox": [ + 532, + 815, + 691, + 829 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}\\right) \\gamma_ {i} = \\sum_ {i = 1} ^ {N K} \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}\\right) \\gamma_ {i} (16) \\\\ = \\psi_ {\\beta} (\\mathbf {x}) [ \\boldsymbol {\\Psi} _ {\\beta} ^ {1}, \\dots , \\boldsymbol {\\Psi} _ {\\beta} ^ {N} ]. (17) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 835, + 906, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25096", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hence, we compute prototypes per class without the need to store additional samples. However, the feature map $\\psi$ may not be available in closed form and may be infinite dimensional. For shift invariant kernels like the Gaussian kernel, we leverage the Bochner's theorem following [42] to write:", + "bbox": [ + 89, + 90, + 483, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nk _ {\\beta} (\\mathbf {x}, \\mathbf {x} ^ {\\prime}) = k (\\mathbf {x} - \\mathbf {x} ^ {\\prime}) = \\mathbb {E} _ {\\mathbf {w} \\sim p (\\mathbf {w})} \\left(\\psi_ {\\mathbf {w}} (\\mathbf {x}) \\psi_ {\\mathbf {w}} \\left(\\mathbf {x} ^ {\\prime}\\right) ^ {\\top}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 195, + 464, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\psi (\\mathbf{x}) = \\exp (i\\mathbf{x}\\mathbf{w})$ (18)", + "bbox": [ + 253, + 215, + 482, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $p(\\mathbf{w})$ is the Fourier transform of the kernel $k$ . This formulation allows to approximate the RBF kernel with Random Fourier features (RFF). In practice, to lower the variance of the kernel estimate, and thus keep a good balance between performance and the number of RFFs, we use Orthogonal Fourier Features [59].", + "bbox": [ + 89, + 242, + 483, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.7. Training-based ProKeR", + "text_level": 1, + "bbox": [ + 89, + 340, + 310, + 358 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to our training-free method, we propose a trained version of ProKeR. The optimization problem in Eq. 13 allows for the use of any base learner and is not limited to the zero-shot CLIP. In this training-based version, instead of using the zero-shot CLIP as the base learner to regularize our method in the RKHS, we iteratively optimize for a regularizer and the obtained solution from ProKeR. Our method consists of training a linear classifier using the same loss $\\mathcal{L}_{\\mathrm{CLAP}}$ proposed in CLAP [50] while solving the linear system of ProKeR at each iteration as follows:", + "bbox": [ + 89, + 363, + 483, + 515 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {W}} \\mathcal {L} _ {\\mathrm {C L A P}} (\\phi_ {\\mathbf {W}}, \\mathbf {S}, \\mathbf {L}),\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 529, + 264, + 551 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\phi_ {\\mathbf {W}} (\\mathbf {x}) = \\mathbf {x} \\mathbf {W} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}) \\gamma_ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 555, + 434, + 595 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\text {a n d} \\quad \\gamma = (\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})) ^ {- 1} (\\mathbf {L} - \\mathbf {S W}). \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 598, + 483, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By jointly optimizing the base learner and the solution of the Kernel Ridge Regression problem, our method (ProKeR + CLAP) allows to learn a regularizer specific to the few-shot task which takes into account the latter problem.", + "bbox": [ + 89, + 635, + 485, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 709, + 223, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate our method on multiple image classification benchmarks. We compare our results to existing training-free methods, notably Tip-Adapter [62], which is the baseline of our work. For a fair comparison, we use the same text inputs for all reported methods. We also compare to other state-of-the-art conventional methods, such as APE [68], Tip-X [53], GDA [55], CLIP [41] and CALIP [15] which proposes a parameter-free attention mechanism to improve CLIP in a zero-shot manner. We run APE with the same text templates as Tip-Adapter using their official implementation. Finally, we report the average running times", + "bbox": [ + 89, + 734, + 485, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on ImageNet [9] for each method using an NVIDIA RTX A6000 GPU. For completeness, we additionally provide a comparison of our method with existing state-of-the-art training-based methods.", + "bbox": [ + 511, + 90, + 905, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Protocol", + "text_level": 1, + "bbox": [ + 511, + 161, + 805, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For comprehensive evaluation, we adopt 11 image classification benchmarks: ImageNet [9], Caltech101 [11], DTD [8], EuroSAT [18], FGVCAircraft [31], Flowers102 [35], Food101 [4], OxfordPets [40], StanfordCars [24], SUN397 [57], and UCF101 [51]. For testing the generalization ability of our method, we further test on ImageNet-Sketch [48] and ImageNet-V2 [44].", + "bbox": [ + 511, + 183, + 906, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a fair comparison with previous work, we use ResNet-50 for the visual encoder of CLIP unless mentioned otherwise. We follow two settings for our experiments. The first setting, initially introduced by [50] for training-based methods, consists of selecting the best hyperparameters of each method on ImageNet and transfer them to the other datasets and report the average performance. This setting reflects real-life scenarios where a validation set may not be available especially in a few-shot regime. The second setting follows CoOp's benchmark [67] where validation shots are used to select the hyperparameters and evaluate the results on the full test set.", + "bbox": [ + 511, + 289, + 908, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiment Results and Analysis", + "text_level": 1, + "bbox": [ + 511, + 479, + 803, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1. Comparison with alternatives to Tip-Adapter", + "text_level": 1, + "bbox": [ + 511, + 501, + 874, + 517 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/15a885ba4228ca9f7ba0776fc60bd0a0d2f1465cfe8a909eae575bc00a2f8be8.jpg", + "image_caption": [ + "Figure 3. Average performance for different methods on 11 image classification datasets." + ], + "image_footnote": [], + "bbox": [ + 517, + 536, + 903, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare in Fig. 3 our result when improving Tip-Adapter using kernel based approaches across 11 datasets. Our reformulation in Eq. (8) outperforms Tip-Adapter for 8", + "bbox": [ + 511, + 854, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25097", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and 16 shots and maintains the same level of performance in the lower shot setting. We argue that this is due to the fact that our reformulation is agnostic to the training size. Debiasing the NW estimator using our regularized LLR in Eq. (9) significantly improves the performance as a first order polynomial fit compared to the constant fit of the NW estimator. Additionally, the use of the Mahalanobis distance as global metric for NW estimator further increases the performance especially with more shots as the estimation of the precision matrix from the training set becomes more accurate. Furthermore, by introducing a proximal regularization in the RKHS, our method ProKeR significantly outperforms Tip-Adapter as well as all the proposed alternatives especially with more shots.", + "bbox": [ + 89, + 90, + 485, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2. Comparison with training-free methods", + "text_level": 1, + "bbox": [ + 89, + 316, + 413, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report in Tab. 1 the performance of different methods in a realistic and practical validation-free experimental setting. First, our method ProKeR outperforms existing alternatives on average by a large margin (2.04% compared to the second best), especially in the low shot regimes (1, 2 and 4) and is only outperformed in the 8 shot setting. Furthermore, when using a Polynomial kernel (as defined in Tab. 5), our method sets a new standard in the 16 shots regime.", + "bbox": [ + 89, + 337, + 483, + 459 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2cb4f2ee1a73cecd550a7c44c62b021a5ca4e4e37c68ba5ed18962636a5b5139.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Shots124816Average
Tip-Adapter [62]58.8660.3361.4963.1564.6161.68
APE [68]60.0962.3365.3667.9569.8965.12
GDA [55]57.4963.4366.6872.4675.1267.03
ProKeR (Polynomial) (ours)62.3965.5968.0571.8175.8268.72
ProKeR (RBF) (ours)63.1366.3168.6472.1575.1269.07
", + "bbox": [ + 93, + 474, + 480, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the CoOp's benchmark where hyperparameters are tailored for each dataset, our method ProKeR surpasses existing training-free methods as shown in Tab. 2. These superior results fully validate the significance of using the global regularization in the RKHS. However, as noted by [50], this setting may not be practical since the hyperparameters are tuned on the test set.", + "bbox": [ + 89, + 609, + 483, + 715 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f174b8fa6ab717abb788c0e473225b63d19c7ad391d7694a98b6c4525aee8b0c.jpg", + "table_caption": [ + "Table 1. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet." + ], + "table_footnote": [], + "table_body": "
Shots124816Average
GDA [55]62.1966.1969.7773.3076.0469.49
Tip-Adapter [62]62.8364.8466.5068.6470.0266.56
Tip-Adapter [62] with RFF62.7764.5866.2968.1569.6066.27
APE [68]64.4366.4868.6670.7572.8168.62
APE [68] with RFF64.1666.1168.7670.3772.0268.28
ProKeR (ours)64.0167.3170.4273.8576.7570.46
ProKeR with RFF (ours)64.0167.1270.2873.6176.4470.29
", + "bbox": [ + 93, + 729, + 480, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3. Generalization Ability", + "text_level": 1, + "bbox": [ + 511, + 90, + 714, + 106 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Tab. 3, we test the generalization ability of the different methods on out-of-distribution datasets. Notably, the shots are drawn from ImageNet and the test set is drawn from either ImageNet-V2 or ImageNet-Sketch. ProKeR achieves state-of-the-art performance for training-free methods on both in-distribution and out-of-distribution datasets.", + "bbox": [ + 511, + 109, + 905, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8e4857f61c817e9ebd34477c2bde8459a8b8239feffe75e8996c9517f1c7a615.jpg", + "table_caption": [ + "Table 2. Performance on 11 different classification datasets (CoOp's benchmark)." + ], + "table_footnote": [], + "table_body": "
DatasetsSourceTarget
ImageNet [9]-V2 [44]-Sketch [48]-A [20]-R [19]Average
Zero-Shot CLIP [41]60.3353.2735.4423.6160.4246.61
Tip-Adapter [62]61.4354.1335.7123.6360.4147.06
APE [68]62.6054.9335.4122.9559.9047.15
GDA [55]63.8255.3534.3219.5355.5645.71
ProKeR (Polynomial) (Ours)64.6656.1136.0823.2760.5548.13
ProKeR (Ours)64.4556.0236.0823.3760.5948.10
", + "bbox": [ + 514, + 210, + 903, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.4. Comparison with training-based methods", + "text_level": 1, + "bbox": [ + 511, + 378, + 849, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report in Tab. 4 the comparison of our method with training-based methods. While being training-free, our method ProKeR outperforms existing training-based methods on 8 out of 11 datasets. This emphasizes the effectiveness of incorporating a global regularization using the zero-shot predictor in a reproducing kernel Hilbert space (RKHS).", + "bbox": [ + 511, + 397, + 908, + 502 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/65e7c382036ce13878b3a9cd5a019cc7bd9d8fb9a362f4294e140c55a9dd2c82.jpg", + "table_caption": [ + "Table 3. Robustness to distribution shift of different methods for 16 shots." + ], + "table_footnote": [], + "table_body": "
Shots124816Average
Tip-Adapter-F [62]60.2962.2665.3268.3571.4065.52
CrossModalLP [29]62.2464.4866.6770.3673.6567.48
TaskRes [60]61.4465.2668.3571.6674.4268.22
APE-T [68]62.7263.9366.5768.9672.1566.86
CLAP [50]62.7966.0769.1372.0874.5768.92
ProKeR (ours)63.1366.3168.6472.1575.1269.07
ProKeR + CLAP (ours)64.1667.6070.9774.1276.8470.73
", + "bbox": [ + 517, + 515, + 903, + 616 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet.", + "bbox": [ + 511, + 626, + 906, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The jointly trained version of ProKeR with CLAP achieves significantly better results compared to existing training-based methods and increases the average performance of the ProKeR by $1.73\\%$ accuracy. This shows the importance of using a strong base learner. Furthermore, the joint training allows to leverage both the expressive power of the RKHS and the flexibility of the linear classifier.", + "bbox": [ + 511, + 671, + 908, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Kernel ablation", + "text_level": 1, + "bbox": [ + 511, + 787, + 674, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "So far, we have performed our analysis using the RBF kernel, a commonly used kernel in the kernel literature and in cache-based methods. Nevertheless, through the lens of our kernel perspective on cache-based methods, different kernels can be considered ranging from a linear kernels to more elaborate ones. We perform in Tab. 5 an ablation study where", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25098", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we discuss different kernel choices. Besides RBF, we consider three commonly used kernels: the Linear kernel, the Epanechnikov kernel and the Polynomial kernel. The RBF kernel outperforms the linear, Epanechnikov and the polynomial kernels. Using the RBF kernel allows us to project data into an infinite dimensional space which captures more complex relationships.", + "bbox": [ + 89, + 90, + 483, + 196 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/decabc604ebf22445c9d60be75ede839deef4d5519c442f7118fdc7bc906f645.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Kernelk(x, x')Accuracy
Linearxx'^T72.34
Epanechnikov3/4 (1 - ||x - y'||2)74.43
Polynomial(xy'^T)^276.61
RBFexp(-β/2||(x - y'||2))76.75
", + "bbox": [ + 106, + 209, + 468, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation on CLIP architectures", + "text_level": 1, + "bbox": [ + 89, + 372, + 369, + 387 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 6, we report the performance of training-free methods using different backbones on ImageNet for 16 shots. Our method consistently outperforms the alternatives across all architectures. While all methods improve with more capable architectures, the gap between our method and the second best one (APE) remains stable.", + "bbox": [ + 89, + 393, + 483, + 484 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0c69d7efcbc97123f10a81bae3a2e4a0b36177caa531c27be3b42edee14fb723.jpg", + "table_caption": [ + "Table 5. Kernel Ablation for 16 shots on 11 datasets on CoOp's benchmark." + ], + "table_footnote": [], + "table_body": "
ModelsResNet-50ResNet-101ViT-B/32ViT-B/16
Zero-shot CLIP [41]60.3362.5363.8068.73
Tip-Adapter [62]61.4364.0865.1870.25
APE [68]62.6065.6166.3171.37
ProKeR (Ours)64.4567.3968.1273.25
", + "bbox": [ + 93, + 497, + 478, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Adressing memory limitations of cache-based methods", + "text_level": 1, + "bbox": [ + 89, + 633, + 482, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 2, we report the performance when using Random Fourier features to alleviate the memory limitations of cache-based methods. Using RFFs, we are able to drastically reduce the memory footprint of caching methods while maintaining almost the same performance across different shots. Our method when combined with RFFs still maintains state-of-the-art performance.", + "bbox": [ + 89, + 671, + 483, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Running times and memory requirements", + "text_level": 1, + "bbox": [ + 89, + 787, + 447, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Next, we report running time (train and test) for different methods as well as the memory requirements for each method (Tab.7). Our method is on par with Tip-Adapter and GDA in term of speed. Note that APE runs a feature selection step which takes additional time to run, making it slower than the previously mentioned competition. On the", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "other hand, training-based methods are orders of magnitude slower. Regarding the memory complexity, ProKeR stores the training shots similarly to APE and Tip-Adapter. However, when using Random Fourier features, our method does need to store additional training samples.", + "bbox": [ + 511, + 90, + 906, + 167 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f481ad0a60050538f3e90f9a527eb97d45eb61e46881dae89a5b480ee597625e.jpg", + "table_caption": [ + "Table 6. Average performance on 16-shot ImageNet with different backbones." + ], + "table_footnote": [], + "table_body": "
MethodsOverall TimeTrainMemory requirements
CoOp[67]~ 17h✓N × T × D
Clip-Adapter[12]~ 40min✓(2N + D1) × D
CrossModal-LP[29]~ 3min✓N × D
Standard LP[41]~ 3min✓N × D
Tip-adapter-F[62]~ 7min✓N × K + N × (K + 1) × D
Tip-Adapter[62]2.1s✗N × K + N × (K + 1) × D
APE [68]24.6s✗N × K + N × (K + 1) × D
GDA [55]1.6 s✗2 × N × D
ProKeR (Ours)4.7s✗N × K + N × (K + 1) × D
ProKeR with RFF (Ours)4.2s✗N × (D + R)
", + "bbox": [ + 519, + 183, + 903, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Running times on ImageNet for 16 shots. All experiments are performed on a RTX A6000 GPU. For each method we report the memory requirements. $D_{1}$ is the inner dimension of the MLP used in Clip-Adapter [12] and $T$ is the number of text tokens in CoOp [67]. $R$ is the number of Fourier features used to approximate the RBF kernel.", + "bbox": [ + 511, + 325, + 906, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations & Future Work", + "text_level": 1, + "bbox": [ + 511, + 446, + 769, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Based on our analysis, caching methods can be understood as local non-parametric regressors. These methods lack a global regularization from zero-shot CLIP which limits their generalization ability when performing adaptation. On the other hand, global methods may lack the flexibility when dealing with complex data. As part of future work, we will explore how both local and global methods can be combined to benefit from the best of both worlds. Furthermore, our formulation of caching methods as a Nadaraya-Watson estimator offers multiple options for the choice the regularization term, the metric used in the kernel, as well as the bandwidth selection [39]. These choices constitute different ways to reduce the bias-variance trade-off inherent to these methods [16].", + "bbox": [ + 511, + 474, + 908, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 705, + 633, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a new theoretical understanding of Tip-Adapter, a prominent training-free caching-based approach for LVM few-shot adaptation. Our analysis suggests that Tip-Adapter is a local nonparametric regression that has well-known bias limitations. We proposed multiple angles of improvement that have shown significant increase over the Tip-Adapter baseline. Subsequently, we demonstrate that incorporating global information in a training-free method can be achieved using a global regularization in a reproducing kernel Hilbert space (RKHS), which conclusively further improves the state-of-the-art for training-free methods.", + "bbox": [ + 511, + 734, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25099", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Maurizio A Alvarez, Lorenzo Rosasco, Neil D Lawrence, et al. Kernels for vector-valued functions: A review. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2605-2615, 2023. 2, 3, 6, 7, 8" + ], + "bbox": [ + 514, + 90, + 906, + 219 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "25102", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_model.json b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..496a4f8195a8048d8fc71d6c51fecda80e4e99c3 --- /dev/null +++ b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_model.json @@ -0,0 +1,2576 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.13, + 0.908, + 0.175 + ], + "angle": 0, + "content": "ProKeR: A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.203, + 0.79, + 0.257 + ], + "angle": 0, + "content": "Yassir Bendou\\(^{1*}\\), Amine Ouasfi\\(^{2*}\\), Vincent Gripon\\(^{1}\\), Adnane Boukhayma\\(^{2}\\) \n\\(^{1}\\)IMT Atlantique, Brest, France \n\\(^{2}\\)Inria, University Rennes, IRISA, CNRS" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.291, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.324, + 0.486, + 0.671 + ], + "angle": 0, + "content": "The growing popularity of Contrastive Language-Image Pretraining (CLIP) has led to its widespread application in various visual downstream tasks. To enhance CLIP's effectiveness and versatility, efficient few-shot adaptation techniques have been widely adopted. Among these approaches, training-free methods, particularly caching methods exemplified by Tip-Adapter, have gained attention for their lightweight adaptation without the need for additional fine-tuning. In this paper, we revisit Tip-Adapter from a kernel perspective, showing that caching methods function as local adapters and are connected to a well-established kernel literature. Drawing on this insight, we offer a theoretical understanding of how these methods operate and suggest multiple avenues for enhancing the Tip-Adapter baseline. Notably, our analysis shows the importance of incorporating global information in local adapters. Therefore, we subsequently propose a global method that learns a proximal regularizer in a reproducing kernel Hilbert space (RKHS) using CLIP as a base learner. Our method, which we call ProKeR (Proximal Kernel ridge Regression), has a closed form solution and achieves state-of-the-art performances across 11 datasets in the standard few-shot adaptation benchmark. Code is available at https://ybendou.github.io/ProKeR/" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.7, + 0.222, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.726, + 0.486, + 0.877 + ], + "angle": 0, + "content": "Large scale vision-language models (VLMs) trained with contrastive learning have gained an increasing attraction in recent years [21, 41]. These models have shown outstanding performances across a wide range of tasks such as classification [41], segmentation [30] and video understanding [28]. CLIP [41] is one of the most established VLMs offering remarkable zero-shot capabilities in various downstream tasks. It operates using only the class label within a textual prompt such as \"A photo of a {CLASS}\" where {CLASS} is the groundtruth text label for each class. However, it is well-" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.289, + 0.903, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.545, + 0.908, + 0.603 + ], + "angle": 0, + "content": "Figure 1. Fitting comparison between different methods on synthetically generated data, illustrating Nadaraya-Watson (Tip-Adapter) bias mitigation via our proposed Local Linear Regression (LLR, Sec. 3.3) and our final method ProKeR." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.629, + 0.907, + 0.719 + ], + "angle": 0, + "content": "known that the zero-shot performance of CLIP is limited in scenarios with large domain shift from the pre-training distribution [10, 34]. To further improve CLIP's generalization, multiple follow-up works proposed to include few-shot data [12, 62, 67] which has shown substantial performance gains compared to zero-shot CLIP." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.72, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Few-shot adaptation of CLIP can be categorized into two types of methods based on whether they require fine-tuning on the few-shot samples or not. Among fine-tuning based methods, prompt learning consists of learning continuous tokens instead of hand-crafted templates in CLIP as proposed by CoOp [67] and CoCoOp [66]. In addition, adapter-based fine-tuning methods operate in the feature space to train their classifiers [12, 29]. Despite their promising performance on downstream tasks, fine-tuning methods require additional training costs to learn the new set of parameters. Furthermore, Tip-Adapter proposed a training-free few-shot adaptation alternative [62]. Using a caching mechanism," + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.363, + 0.9 + ], + "angle": 0, + "content": "*These authors contributed equally to this work" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25092" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "it captures knowledge from the few-shot samples without additional fine-tuning and ensembles it with zero-shot CLIP. This cache model has shown a significant improvement over the zero-shot performance, which has led to follow-up work such as APE [68] and Tip-X [53]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.17, + 0.483, + 0.412 + ], + "angle": 0, + "content": "In order to understand caching effectiveness and limitations, we undertake a theoretical analysis to explore the nature of Tip-Adapter. We begin by demonstrating that the Tip-Adapter adaptation term is a modified version of the well-known Nadaraya-Watson (NW) estimator [33], a local nonparametric regression method that allows Tip-Adapter to effectively capture various distributions. However, the NW estimator is also known to be strongly biased [25, 36] (e.g. Fig. 1). To mitigate this bias, we leverage existing tools from the literature of kernel methods. An effective extension to NW estimator is locally linear regression [46]. Initially, by fitting a local linear regression around each test point using a closed-form solution, we significantly improve the performance of Tip-Adapter. However, the parameters are estimated locally, which is prone to overfitting in high-dimensional problems [16, 36]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.413, + 0.486, + 0.851 + ], + "angle": 0, + "content": "Our analysis shows that caching methods can be understood as local nonparametric regression methods regularised through CLIP pointwise zero-shot predictions. However, this regularization only acts locally and does not provide any global information about the few-shot task. Conversely, recent training-based methods rely on global regularizers to incorporate global information [50]. Hence, we ask ourselves the question: how can we leverage global regularizers for few-shot adapters while conserving the benefits of training-free methods? In order to design such global regularizer, we devise two important design choices: - Firstly, we restrain the hypothesis space of the learned function to be a reproducing kernel Hilbert space (RKHS). - Second, using the RKHS norm, we introduce a proximal regularization term to ensure that the obtained solution is close to the base predictor i.e. \\( f_{\\mathrm{clip}} \\). Thanks to the properties of the RKHS, minimizing the difference between two functions using the RKHS norm ensures that they are close pointwise. Our method ProKeR provides a more effective way to preserve prior knowledge from the zero-shot predictor and maintains the expressive capacity of the learned functions. Through extensive experiments, we show the effectiveness of our method ProKeR which achieves consistent gains over state-of-the-art training-free methods on standard few-shot classification benchmarks [62] and can be successfully combined with existing training-based methods. In addition, we highlight the robustness and generalizability of the proposed method across different architectures and on out-of-distribution datasets." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.854, + 0.285, + 0.868 + ], + "angle": 0, + "content": "Summary of contributions:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "1. We frame the cache model of Tip-Adapter [62] as a Nadaraya-Watson estimator, a classical kernel regression" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "method, and provide a theoretical understanding of how Tip-Adapter functions." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.122, + 0.908, + 0.18 + ], + "angle": 0, + "content": "2. Under this new perspective, we propose multiple improvements on Tip-Adapter either through a closed-form local linear regression fit or by incorporating global information." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.182, + 0.909, + 0.272 + ], + "angle": 0, + "content": "3. Our analysis leads to our new proposed method ProKeR, a training-free method that leverages global regularization in a reproducing kernel Hilbert space. Through extensive experiments, ProKeR outperforms existing methods and sets a new state-of-the-art on standard few-shot classification benchmarks." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.122, + 0.909, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.289, + 0.655, + 0.305 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.314, + 0.833, + 0.331 + ], + "angle": 0, + "content": "2.1. Vision-Language Pre-trained Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.337, + 0.908, + 0.534 + ], + "angle": 0, + "content": "Visual-language models (VLMs) have gained an increasing popularity lately. These methods, exemplified by CLIP [41], DeCLIP [27] and ALIGN [21], employ a contrastive learning framework to learn a vision encoder and a language encoder with a shared representation space between text and images. Trained on large-scale datasets of image-text pairs, VLMs have shown remarkable zero-shot capabilities on downstream tasks without additional fine-tuning, paving the way for open vocabulary recognition [14]. VLMs have been extended to few-shot classification [67] as well as other tasks beyond image classification such as video understanding [28, 54], image segmentation [30, 52], image generation [43] and 3D reconstruction [7, 63]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.545, + 0.712, + 0.561 + ], + "angle": 0, + "content": "2.2. Few-shot Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.909, + 0.824 + ], + "angle": 0, + "content": "Few-shot adaptation methods in the context of classification can be categorized into prompt learning and adapter based approaches. Inspired by the recent advances in natural language processing [26], prompt learning aims to learn effective global text or visual prompts for the downstream tasks [2, 6, 23, 45, 47, 49, 58, 61, 66, 67]. Although prompt learning methods have brought significant improvements over the zero-shot baseline, they require back-propagating through the entire text encoder and require having access to the text encoder [38]. On the other hand, adapter-based approaches operate in the feature space and do not require having access to the pre-trained model weights. We distinguish two families of adapter-based approaches. The first one is training-based methods [12, 29, 60] which either train a linear layer [29, 60] or a two-layer MLP such as CLIP-Adapter [12] to perform residual feature blending of the zero-shot classifier." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.908, + 0.903 + ], + "angle": 0, + "content": "While fine-tuning adapters have achieved a good level of performance, they still require additional training time which is impractical under limited resources and might suffer from the caveats of gradient optimization. To alleviate these issues, Tip-Adapter [62] emerges as a training-free solution" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25093" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.092, + 0.91, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.364, + 0.908, + 0.407 + ], + "angle": 0, + "content": "Figure 2. Overview of our training-free method ProKeR. While Tip-Adapter builds a key-value cache model using the few-shot samples, ProKeR incorporates a proximal global regularization based on the zero-shot predictor in a reproducing kernel Hilbert space (RKHS). This allows the use of a richer model without overfitting on the few-shot data." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.433, + 0.486, + 0.658 + ], + "angle": 0, + "content": "based on a key-value cache model. Building on Tip-Adapter, multiple caching methods have been proposed. APE [68] includes a feature selection step to the cache model. CaFo [64] uses an ensemble of foundation models for the cache model and augments text prompts using a Large Language model. SuS-X and its module Tip-X [53] first generates the few-shot set using Stable Diffusion then uses the inter-modal similarities between the test images and the few-shot set. In a transductive setting, DMN [65] proposes a dynamic memory mechanism to cache historical test data. More recently, GDA proposes to use a Linear Discriminant Analysis to set a strong baseline for training-free methods [55]. Despite the good level of performance, there is currently no theoretical framework for understanding the motivation behind caching models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.675, + 0.182, + 0.691 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.701, + 0.486, + 0.792 + ], + "angle": 0, + "content": "We expose in this section the details of the proposed method. Our starting point consists in framing Tip-Adapter as a kernel method. Thanks to this new perspective, we develop multiple improvements tailored for it. Conclusively, we propose ProKeR, a method that introduces a global proximal regularization in a reproducing kernel Hilbert space (RKHS)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.803, + 0.48, + 0.82 + ], + "angle": 0, + "content": "3.1. Tip-Adapter as a Nadaraya-Watson estimator" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.485, + 0.902 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, let \\(\\mathbf{x} \\in \\mathbb{R}^D\\) be the features of an input query image extracted using the visual encoder of CLIP, \\(\\mathbf{S} \\in \\mathbb{R}^{NK \\times D}\\) the visual features of the training set and \\(\\mathbf{L} \\in \\mathbb{R}^{NK \\times N}\\) the associated matrix of one-hot labels where \\(N\\) is the number of classes and \\(K\\) is the number of shots per class." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.432, + 0.907, + 0.509 + ], + "angle": 0, + "content": "Let \\(\\mathbf{W}_{\\mathrm{clip}} \\in \\mathbb{R}^{D \\times N}\\) be the text prototypes of the classes extracted with the text encoder using the standard handcrafted templates in the form of \"a photo of a {CLASS}\" [29, 62, 67]. The zero-shot predictor from CLIP is defined as \\(f_{\\mathrm{clip}}: \\mathbf{x} \\mapsto \\mathbf{x} \\mathbf{W}_{\\mathrm{clip}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.907, + 0.568 + ], + "angle": 0, + "content": "To alleviate \\( f_{\\mathrm{clip}} \\) prediction errors due to lack of generalization, Tip-Adapter [62] utilizes a cache model to learn knowledge from the few-shot samples. The predicted logits can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.579, + 0.907, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\exp \\left(- \\beta (1 - \\mathbf {x} \\mathbf {S} ^ {\\top})\\right) \\mathbf {L}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.907, + 0.669 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a smoothing scalar and \\(\\alpha\\) controls the balance between textual features and few-shot images. Note that since the features in CLIP are normalized (i.e. \\(||\\mathbf{x}||_2 = 1\\)), we can rewrite Eq. (1) as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.679, + 0.907, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\sum_ {i = 1} ^ {N K} \\exp \\left(- \\frac {\\beta}{2} | | \\mathbf {S} _ {i} - \\mathbf {x} | | _ {2} ^ {2}\\right) \\mathbf {L} _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.908, + 0.809 + ], + "angle": 0, + "content": "where \\(\\mathbf{S}_i\\) is the \\(i\\)-th few-shot sample. Interestingly, the right term of Tip-Adapter can be seen as a modified version of the well-known Nadaraya-Watson (NW) estimator [33] with a Radial Basis Function (RBF) kernel [37]:" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.821, + 0.907, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i})) \\mathbf {L} _ {i}}{\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i}))}, \\\\ \\text {w h e r e} k _ {\\beta} (u) = \\left(\\frac {\\beta}{2}\\right) ^ {D} \\exp \\left(- \\frac {\\beta}{2} u\\right), \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25094" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.211 + ], + "angle": 0, + "content": "where \\(d\\) is the distance between the query image and the shots in the feature space. In essence, when \\(d\\) is the Euclidean distance, as in Eq. (2), the adaptation term of TipAdapter is a nonparametric regression, obtained by performing a smooth and locally weighted average of the one-hot labels of the few-shot samples using a kernel function, which quantifies the similarity between the query image and the shots." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.231, + 0.484, + 0.263 + ], + "angle": 0, + "content": "3.2. Training-free few-shot adapters as a Bayes optimal mapping" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.27, + 0.484, + 0.318 + ], + "angle": 0, + "content": "We formulate the few-shot visual-language adaptation as a Bayes optimal mapping [17] associated to the following pointwise risk:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.333, + 0.484, + 0.351 + ], + "angle": 0, + "content": "\\[\nR (\\mathbf {x}, \\phi (\\mathbf {x})) = \\mathbb {E} _ {Y \\mid X} [ s (Y, \\phi (X)) + \\mathcal {R} _ {\\mathrm {c l i p}} | X = \\mathbf {x} ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.367, + 0.484, + 0.427 + ], + "angle": 0, + "content": "where \\( s \\) is a cost function and \\( \\mathcal{R}_{\\mathrm{clip}} \\) is a regularization term using CLIP prediction independent of \\( Y \\). Here, \\( X \\) and \\( Y \\) are random variables representing the image features and the labels respectively." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.43, + 0.484, + 0.446 + ], + "angle": 0, + "content": "The pointwise Bayes optimal mapping is defined as [17]:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.478, + 0.484, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\underset {\\mathbf {q} \\in M} {\\arg \\min } R (\\mathbf {x}, \\mathbf {q}) (5) \\\\ = \\arg \\min _ {\\mathbf {q} \\in M} \\int_ {M} s (\\mathbf {y}, \\mathbf {q}) d \\mu_ {\\mathbf {x}} (\\mathbf {y}) + \\mathcal {R} _ {\\mathrm {c l i p}}, (6) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.551, + 0.484, + 0.61 + ], + "angle": 0, + "content": "where \\(d\\mu_{\\mathbf{x}}\\) is the conditional probability of \\(Y\\) conditioned on \\(X = \\mathbf{x}\\) and \\(M\\) is the output space. Following [17], we leverage kernel estimators to rewrite the adaptation problem as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.626, + 0.484, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\phi (\\mathbf {x}) = \\arg \\min _ {\\mathbf {q}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) s (\\mathbf {q}, \\mathbf {L} _ {i}) + \\mathcal {R} _ {\\mathrm {c l i p}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.484, + 0.778 + ], + "angle": 0, + "content": "This formulation offers a new perspective on the adaptation, where for each test point the cost function is minimized over the output space, with a weighting from each training sample. The regularization term guarantees that the obtained predictions are not far from zero-shot CLIP." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.486, + 0.904 + ], + "angle": 0, + "content": "Interestingly, this formulation paves the way for considering different choices of cost functions \\( s \\), regularization terms \\( \\mathcal{R}_{\\mathrm{clip}} \\) and kernels \\( k_{\\beta} \\). The consistency of the obtained estimator is discussed in [17] where the solution of Eq. (7) is obtained using a gradient descent algorithm. While this optimisation can be time consuming, there are cases where a closed form solution can be derived. For instance, when \\( s \\) is the squared Euclidean distance and \\( \\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\mathbf{q} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2 \\)," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.761, + 0.107 + ], + "angle": 0, + "content": "we can derive the following solution:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.12, + 0.84, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\lambda N K}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} f _ {\\mathrm {c l i p}} (\\mathbf {x}) \\\\ + \\frac {1}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) \\mathbf {L} _ {i}, \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.639, + 0.201, + 0.907, + 0.242 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\mathcal {Z} (\\mathbf {x}) = \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.252, + 0.907, + 0.357 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a regularization term that balances the predictions of zero-shot CLIP and the local fit. The obtained closed form of the estimator in Eq. (7) is equivalent to Tip-Adapter up to a scaling factor which depends on each input \\(\\mathbf{x}\\). The main difference between the two formulations in Eq. (2) and Eq. (8) is that the second term in Eq. (8) is agnostic to the training size and is query dependent." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.358, + 0.908, + 0.433 + ], + "angle": 0, + "content": "Although the Nadaraya-Watson estimator is a nonparametric model that allows to capture any type of distribution, it is well known to suffer from poor bias at the boundaries of the training samples [36]. In the following, we propose two methods to alleviate this bias." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.443, + 0.738, + 0.459 + ], + "angle": 0, + "content": "3.3. Local Linear Regression" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.465, + 0.907, + 0.556 + ], + "angle": 0, + "content": "A standard way to alleviate the boundary bias of the NW estimator is by moving from a local constant fit to a local linear fit around each test point. Instead of using the estimate from Eq. (7), local linear regression (LLR) forms the local estimate \\(\\phi (\\mathbf{x}) = \\tilde{\\mathbf{x}}\\mathbf{A}\\), where \\(\\tilde{\\mathbf{x}} = [1\\quad \\mathbf{x}]\\), and \\(\\mathbf{A}\\in \\mathbb{R}^{(d + 1)c}\\) minimizes the following problem:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.567, + 0.907, + 0.609 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {A}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right) s \\left(\\tilde {\\mathbf {S}} _ {i} \\mathbf {A}, \\mathbf {L} _ {i}\\right) + \\mathcal {R} _ {\\mathrm {c l i p}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.618, + 0.909, + 0.695 + ], + "angle": 0, + "content": "which is a weighted ordinary least square problem around each test point weighted by the kernel values \\(k_{\\beta}(d(\\mathbf{x}, \\mathbf{S}_i))\\). Using the same cost function as for Eq. (8) and using the regularization term \\(\\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\tilde{\\mathbf{x}} \\mathbf{A} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2\\), we derive a closed form solution for Eq. (9) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.709, + 0.907, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {\\phi} (\\mathbf {x}) = \\tilde {\\mathbf {x}} \\mathbf {A} ^ {- 1} \\mathbf {B}, \\\\ w h e r e \\quad \\mathbf {A} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\tilde {\\mathbf {S}} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} \\tilde {\\mathbf {x}}, \\\\ \\text {a n d} \\quad \\mathbf {B} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\mathbf {L} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} f _ {\\operatorname {c l i p}} (\\mathbf {x}), \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.906, + 0.811 + ], + "angle": 0, + "content": "where \\(\\Omega\\) is the \\(NK\\times NK\\) matrix with ith diagonal element as \\(k_{\\beta}(d(\\mathbf{x},\\mathbf{S}_i))\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.901 + ], + "angle": 0, + "content": "This method, that we dub henceforth LLR, boils down to fitting a local linear regression while enforcing the obtained fit to be close to the text predictions locally around the query input sample. While LLR usually improves performance, it is time consuming as one needs to fit a linear regression for each input sample. Furthermore, the parameters of LLR" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25095" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.182 + ], + "angle": 0, + "content": "are solely estimated locally, which is prone to overfitting in high-dimensional problems [36]. Alternatively, one possible way to eliminate the bias of NW estimator due to the bandwidth selection without significantly increasing the time complexity is by equipping the kernel with a better distance function \\(d\\) [36]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.191, + 0.398, + 0.208 + ], + "angle": 0, + "content": "3.4. Local methods with a global metric" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.213, + 0.486, + 0.274 + ], + "angle": 0, + "content": "While there exists multiple strategies to construct a good metric [36, 56], using the Mahalanobis distance with the covariance matrix estimated from the training data is a simple yet well-performing one [3]:" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.283, + 0.484, + 0.301 + ], + "angle": 0, + "content": "\\[\nd (\\mathbf {x}, \\mathbf {S} _ {i}) = \\| \\mathbf {x} - \\mathbf {S} _ {i} \\| _ {\\hat {\\mathbf {A}}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.312, + 0.485, + 0.463 + ], + "angle": 0, + "content": "where \\(\\hat{\\Lambda}\\) is the estimated precision matrix from the few-shot samples. This metric effectively incorporates global information and captures the geometry of the space which allows to construct a better kernel function tailored to the downstream task. The classical RBF kernel corresponds to using an isotropic covariance matrix. While still being a local method, adapting the metric to the downstream task allows to incorporate global information about the underlying distribution and improves over Tip-Adapter as shown in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.472, + 0.392, + 0.488 + ], + "angle": 0, + "content": "3.5. Proximal Kernel Ridge Regression" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.494, + 0.484, + 0.659 + ], + "angle": 0, + "content": "As can be seen in Fig. 3, incorporating global information about the task through a global metric effectively outperforms both Tip-Adapter and LLR. However, the choice of the global metric for NW estimator beyond the Mahalanobis distance remains challenging [56], especially in the few-shot setting. Furthermore, despite being equipped with a global metric, the NW estimator remains in essence a local method and still lacks a global regularization. Whilst the use of a global regularization has been recently addressed in training-based methods [50], using a truly global regularization in a training-free manner remains challenging and unexplored." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.486, + 0.901 + ], + "angle": 0, + "content": "These limitations highlight the necessity for regularization in this adaptation process. The main idea is to balance the need to maintain the expressive capacity of the learned functions while ensuring stability and robustness. To this end we introduce two key design choices: (1) we constrain the hypothesis space of the learned function to a reproducing kernel Hilbert space (RKHS), and (2) we incorporate a proximal regularization term, based on the RKHS norm, to ensure the solution remains close to the base predictor \\((f_{\\mathrm{clip}})\\). The RKHS norm's properties guarantee that minimizing the difference between two functions in this space results in pointwise closeness. Consequently, this proximal term serves as a global regularization that preserves prior knowledge from the zero-shot predictor, resulting in more robust solutions that are less prone to overfitting on the few-shot data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.272 + ], + "angle": 0, + "content": "Given the multi-output nature of the problem, the employed reproducing kernel \\(\\mathbf{K}_{\\beta}\\) is a reproducing kernel for vector valued functions. The main difference is that the kernel is matrix valued. Several instances of multi-output kernels have been proposed in the literature [1, 5], with separable kernels being among the most widely used for learning vector-valued functions due to their simplicity and computational efficiency. These kernels are formulated as a product of a kernel function for the input space alone and a matrix that encodes the interactions among the outputs. Let us consider \\(\\mathbf{K}_{\\beta}:\\mathbb{R}^{D}\\times \\mathbb{R}^{D}\\mapsto \\mathbb{R}^{N\\times N}\\) as a separable kernel of the form:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.281, + 0.907, + 0.298 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {K} _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right)\\right) _ {j, j ^ {\\prime}} = k _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) \\mathbf {B}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.305, + 0.907, + 0.366 + ], + "angle": 0, + "content": "where \\(\\mathbf{B}\\) is a \\(N\\times N\\) symmetric and positive semi-definite matrix which captures the correlations between the outputs. A simple yet effective choice for \\(\\mathbf{B}\\) is the identity matrix where all outputs are treated as being unrelated." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.366, + 0.906, + 0.396 + ], + "angle": 0, + "content": "Our goal is to learn a multi-output predictor \\(\\phi\\) using the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.403, + 0.907, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\phi \\in \\mathcal {H}} \\sum_ {i = 1} ^ {N K} \\| \\phi (\\mathbf {S} _ {\\mathbf {i}}) - \\mathbf {L} _ {i} \\| _ {2} ^ {2} + \\lambda \\| \\phi - f _ {\\mathrm {c l i p}} \\| _ {\\mathcal {H}} ^ {2}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.451, + 0.908, + 0.497 + ], + "angle": 0, + "content": "By the representative theorem [22, 32], the unique minimizer of problem in Eq. (13) emerges naturally as the solution of a Kernel Ridge Regression (KRR) problem:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.507, + 0.725, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\phi = f _ {\\mathrm {c l i p}} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}},.) \\gamma_ {i},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.551, + 0.907, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\gamma = \\left(\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})\\right) ^ {- 1} \\left(\\mathbf {L} - f _ {\\mathrm {c l i p}} (\\mathbf {S})\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.908, + 0.677 + ], + "angle": 0, + "content": "Here, \\((k_{\\beta}(\\mathbf{S},\\mathbf{S}))_{i,j} = k_{\\beta}(\\mathbf{S}_i,\\mathbf{S}_j)\\) and \\(\\gamma_{i}\\in \\mathbb{R}^{N}\\). This approach allows to map data to an infinite dimensional space. Furthermore, the regularization term allows the use of a richer model that captures the complex structure of the data while preserving its smoothness, avoiding overfitting on the few-shot data." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.686, + 0.866, + 0.702 + ], + "angle": 0, + "content": "3.6. Mercer decomposition of kernel methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.908, + 0.782 + ], + "angle": 0, + "content": "One additional benefit of this perspective on caching methods is memory reduction which allows to overcome the necessity of storing training data. For positive definite kernel, we can leverage Mercer theorem [13] to write the kernel function as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.79, + 0.907, + 0.809 + ], + "angle": 0, + "content": "\\[\nk _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) = \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {x} ^ {\\top}\\right). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.816, + 0.692, + 0.83 + ], + "angle": 0, + "content": "This allows us to write:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.836, + 0.907, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}\\right) \\gamma_ {i} = \\sum_ {i = 1} ^ {N K} \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}\\right) \\gamma_ {i} (16) \\\\ = \\psi_ {\\beta} (\\mathbf {x}) [ \\boldsymbol {\\Psi} _ {\\beta} ^ {1}, \\dots , \\boldsymbol {\\Psi} _ {\\beta} ^ {N} ]. (17) \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "25096" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.182 + ], + "angle": 0, + "content": "Hence, we compute prototypes per class without the need to store additional samples. However, the feature map \\(\\psi\\) may not be available in closed form and may be infinite dimensional. For shift invariant kernels like the Gaussian kernel, we leverage the Bochner's theorem following [42] to write:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.196, + 0.465, + 0.214 + ], + "angle": 0, + "content": "\\[\nk _ {\\beta} (\\mathbf {x}, \\mathbf {x} ^ {\\prime}) = k (\\mathbf {x} - \\mathbf {x} ^ {\\prime}) = \\mathbb {E} _ {\\mathbf {w} \\sim p (\\mathbf {w})} \\left(\\psi_ {\\mathbf {w}} (\\mathbf {x}) \\psi_ {\\mathbf {w}} \\left(\\mathbf {x} ^ {\\prime}\\right) ^ {\\top}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.217, + 0.483, + 0.232 + ], + "angle": 0, + "content": "where \\(\\psi (\\mathbf{x}) = \\exp (i\\mathbf{x}\\mathbf{w})\\) (18)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.243, + 0.485, + 0.334 + ], + "angle": 0, + "content": "where \\( p(\\mathbf{w}) \\) is the Fourier transform of the kernel \\( k \\). This formulation allows to approximate the RBF kernel with Random Fourier features (RFF). In practice, to lower the variance of the kernel estimate, and thus keep a good balance between performance and the number of RFFs, we use Orthogonal Fourier Features [59]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.342, + 0.312, + 0.359 + ], + "angle": 0, + "content": "3.7. Training-based ProKeR" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.364, + 0.484, + 0.516 + ], + "angle": 0, + "content": "In addition to our training-free method, we propose a trained version of ProKeR. The optimization problem in Eq. 13 allows for the use of any base learner and is not limited to the zero-shot CLIP. In this training-based version, instead of using the zero-shot CLIP as the base learner to regularize our method in the RKHS, we iteratively optimize for a regularizer and the obtained solution from ProKeR. Our method consists of training a linear classifier using the same loss \\(\\mathcal{L}_{\\mathrm{CLAP}}\\) proposed in CLAP [50] while solving the linear system of ProKeR at each iteration as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.53, + 0.265, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {W}} \\mathcal {L} _ {\\mathrm {C L A P}} (\\phi_ {\\mathbf {W}}, \\mathbf {S}, \\mathbf {L}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.556, + 0.435, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\phi_ {\\mathbf {W}} (\\mathbf {x}) = \\mathbf {x} \\mathbf {W} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}) \\gamma_ {i},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.599, + 0.484, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\text {a n d} \\quad \\gamma = (\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})) ^ {- 1} (\\mathbf {L} - \\mathbf {S W}). \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.636, + 0.486, + 0.698 + ], + "angle": 0, + "content": "By jointly optimizing the base learner and the solution of the Kernel Ridge Regression problem, our method (ProKeR + CLAP) allows to learn a regularizer specific to the few-shot task which takes into account the latter problem." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.224, + 0.727 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.486, + 0.902 + ], + "angle": 0, + "content": "In this section, we evaluate our method on multiple image classification benchmarks. We compare our results to existing training-free methods, notably Tip-Adapter [62], which is the baseline of our work. For a fair comparison, we use the same text inputs for all reported methods. We also compare to other state-of-the-art conventional methods, such as APE [68], Tip-X [53], GDA [55], CLIP [41] and CALIP [15] which proposes a parameter-free attention mechanism to improve CLIP in a zero-shot manner. We run APE with the same text templates as Tip-Adapter using their official implementation. Finally, we report the average running times" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.152 + ], + "angle": 0, + "content": "on ImageNet [9] for each method using an NVIDIA RTX A6000 GPU. For completeness, we additionally provide a comparison of our method with existing state-of-the-art training-based methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.162, + 0.807, + 0.177 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.184, + 0.908, + 0.289 + ], + "angle": 0, + "content": "For comprehensive evaluation, we adopt 11 image classification benchmarks: ImageNet [9], Caltech101 [11], DTD [8], EuroSAT [18], FGVCAircraft [31], Flowers102 [35], Food101 [4], OxfordPets [40], StanfordCars [24], SUN397 [57], and UCF101 [51]. For testing the generalization ability of our method, we further test on ImageNet-Sketch [48] and ImageNet-V2 [44]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.909, + 0.47 + ], + "angle": 0, + "content": "For a fair comparison with previous work, we use ResNet-50 for the visual encoder of CLIP unless mentioned otherwise. We follow two settings for our experiments. The first setting, initially introduced by [50] for training-based methods, consists of selecting the best hyperparameters of each method on ImageNet and transfer them to the other datasets and report the average performance. This setting reflects real-life scenarios where a validation set may not be available especially in a few-shot regime. The second setting follows CoOp's benchmark [67] where validation shots are used to select the hyperparameters and evaluate the results on the full test set." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.48, + 0.805, + 0.496 + ], + "angle": 0, + "content": "4.2. Experiment Results and Analysis" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.502, + 0.875, + 0.518 + ], + "angle": 0, + "content": "4.2.1. Comparison with alternatives to Tip-Adapter" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.537, + 0.905, + 0.798 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.811, + 0.908, + 0.838 + ], + "angle": 0, + "content": "Figure 3. Average performance for different methods on 11 image classification datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.91, + 0.902 + ], + "angle": 0, + "content": "We compare in Fig. 3 our result when improving Tip-Adapter using kernel based approaches across 11 datasets. Our reformulation in Eq. (8) outperforms Tip-Adapter for 8" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25097" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.302 + ], + "angle": 0, + "content": "and 16 shots and maintains the same level of performance in the lower shot setting. We argue that this is due to the fact that our reformulation is agnostic to the training size. Debiasing the NW estimator using our regularized LLR in Eq. (9) significantly improves the performance as a first order polynomial fit compared to the constant fit of the NW estimator. Additionally, the use of the Mahalanobis distance as global metric for NW estimator further increases the performance especially with more shots as the estimation of the precision matrix from the training set becomes more accurate. Furthermore, by introducing a proximal regularization in the RKHS, our method ProKeR significantly outperforms Tip-Adapter as well as all the proposed alternatives especially with more shots." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.318, + 0.414, + 0.334 + ], + "angle": 0, + "content": "4.2.2. Comparison with training-free methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.338, + 0.485, + 0.46 + ], + "angle": 0, + "content": "We report in Tab. 1 the performance of different methods in a realistic and practical validation-free experimental setting. First, our method ProKeR outperforms existing alternatives on average by a large margin (2.04% compared to the second best), especially in the low shot regimes (1, 2 and 4) and is only outperformed in the 8 shot setting. Furthermore, when using a Polynomial kernel (as defined in Tab. 5), our method sets a new standard in the 16 shots regime." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.476, + 0.482, + 0.551 + ], + "angle": 0, + "content": "
Shots124816Average
Tip-Adapter [62]58.8660.3361.4963.1564.6161.68
APE [68]60.0962.3365.3667.9569.8965.12
GDA [55]57.4963.4366.6872.4675.1267.03
ProKeR (Polynomial) (ours)62.3965.5968.0571.8175.8268.72
ProKeR (RBF) (ours)63.1366.3168.6472.1575.1269.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.561, + 0.483, + 0.591 + ], + "angle": 0, + "content": "Table 1. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.485, + 0.716 + ], + "angle": 0, + "content": "In the CoOp's benchmark where hyperparameters are tailored for each dataset, our method ProKeR surpasses existing training-free methods as shown in Tab. 2. These superior results fully validate the significance of using the global regularization in the RKHS. However, as noted by [50], this setting may not be practical since the hyperparameters are tuned on the test set." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.73, + 0.482, + 0.842 + ], + "angle": 0, + "content": "
Shots124816Average
GDA [55]62.1966.1969.7773.3076.0469.49
Tip-Adapter [62]62.8364.8466.5068.6470.0266.56
Tip-Adapter [62] with RFF62.7764.5866.2968.1569.6066.27
APE [68]64.4366.4868.6670.7572.8168.62
APE [68] with RFF64.1666.1168.7670.3772.0268.28
ProKeR (ours)64.0167.3170.4273.8576.7570.46
ProKeR with RFF (ours)64.0167.1270.2873.6176.4470.29
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.851, + 0.483, + 0.88 + ], + "angle": 0, + "content": "Table 2. Performance on 11 different classification datasets (CoOp's benchmark)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.092, + 0.715, + 0.107 + ], + "angle": 0, + "content": "4.2.3. Generalization Ability" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.11, + 0.906, + 0.201 + ], + "angle": 0, + "content": "In Tab. 3, we test the generalization ability of the different methods on out-of-distribution datasets. Notably, the shots are drawn from ImageNet and the test set is drawn from either ImageNet-V2 or ImageNet-Sketch. ProKeR achieves state-of-the-art performance for training-free methods on both in-distribution and out-of-distribution datasets." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.211, + 0.905, + 0.315 + ], + "angle": 0, + "content": "
DatasetsSourceTarget
ImageNet [9]-V2 [44]-Sketch [48]-A [20]-R [19]Average
Zero-Shot CLIP [41]60.3353.2735.4423.6160.4246.61
Tip-Adapter [62]61.4354.1335.7123.6360.4147.06
APE [68]62.6054.9335.4122.9559.9047.15
GDA [55]63.8255.3534.3219.5355.5645.71
ProKeR (Polynomial) (Ours)64.6656.1136.0823.2760.5548.13
ProKeR (Ours)64.4556.0236.0823.3760.5948.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.324, + 0.907, + 0.351 + ], + "angle": 0, + "content": "Table 3. Robustness to distribution shift of different methods for 16 shots." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.379, + 0.85, + 0.394 + ], + "angle": 0, + "content": "4.2.4. Comparison with training-based methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.909, + 0.503 + ], + "angle": 0, + "content": "We report in Tab. 4 the comparison of our method with training-based methods. While being training-free, our method ProKeR outperforms existing training-based methods on 8 out of 11 datasets. This emphasizes the effectiveness of incorporating a global regularization using the zero-shot predictor in a reproducing kernel Hilbert space (RKHS)." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.516, + 0.905, + 0.617 + ], + "angle": 0, + "content": "
Shots124816Average
Tip-Adapter-F [62]60.2962.2665.3268.3571.4065.52
CrossModalLP [29]62.2464.4866.6770.3673.6567.48
TaskRes [60]61.4465.2668.3571.6674.4268.22
APE-T [68]62.7263.9366.5768.9672.1566.86
CLAP [50]62.7966.0769.1372.0874.5768.92
ProKeR (ours)63.1366.3168.6472.1575.1269.07
ProKeR + CLAP (ours)64.1667.6070.9774.1276.8470.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.627, + 0.907, + 0.656 + ], + "angle": 0, + "content": "Table 4. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.672, + 0.909, + 0.779 + ], + "angle": 0, + "content": "The jointly trained version of ProKeR with CLAP achieves significantly better results compared to existing training-based methods and increases the average performance of the ProKeR by \\(1.73\\%\\) accuracy. This shows the importance of using a strong base learner. Furthermore, the joint training allows to leverage both the expressive power of the RKHS and the flexibility of the linear classifier." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.789, + 0.676, + 0.803 + ], + "angle": 0, + "content": "4.3. Kernel ablation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "So far, we have performed our analysis using the RBF kernel, a commonly used kernel in the kernel literature and in cache-based methods. Nevertheless, through the lens of our kernel perspective on cache-based methods, different kernels can be considered ranging from a linear kernels to more elaborate ones. We perform in Tab. 5 an ablation study where" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25098" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.198 + ], + "angle": 0, + "content": "we discuss different kernel choices. Besides RBF, we consider three commonly used kernels: the Linear kernel, the Epanechnikov kernel and the Polynomial kernel. The RBF kernel outperforms the linear, Epanechnikov and the polynomial kernels. Using the RBF kernel allows us to project data into an infinite dimensional space which captures more complex relationships." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.21, + 0.47, + 0.307 + ], + "angle": 0, + "content": "
Kernelk(x, x')Accuracy
Linearxx'^T72.34
Epanechnikov3/4 (1 - ||x - y'||2)74.43
Polynomial(xy'^T)^276.61
RBFexp(-β/2||(x - y'||2))76.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.318, + 0.483, + 0.345 + ], + "angle": 0, + "content": "Table 5. Kernel Ablation for 16 shots on 11 datasets on CoOp's benchmark." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.373, + 0.37, + 0.388 + ], + "angle": 0, + "content": "4.4. Ablation on CLIP architectures" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.395, + 0.484, + 0.485 + ], + "angle": 0, + "content": "In Tab. 6, we report the performance of training-free methods using different backbones on ImageNet for 16 shots. Our method consistently outperforms the alternatives across all architectures. While all methods improve with more capable architectures, the gap between our method and the second best one (APE) remains stable." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.498, + 0.48, + 0.568 + ], + "angle": 0, + "content": "
ModelsResNet-50ResNet-101ViT-B/32ViT-B/16
Zero-shot CLIP [41]60.3362.5363.8068.73
Tip-Adapter [62]61.4364.0865.1870.25
APE [68]62.6065.6166.3171.37
ProKeR (Ours)64.4567.3968.1273.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.578, + 0.483, + 0.606 + ], + "angle": 0, + "content": "Table 6. Average performance on 16-shot ImageNet with different backbones." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.634, + 0.483, + 0.665 + ], + "angle": 0, + "content": "4.5. Adressing memory limitations of cache-based methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.485, + 0.779 + ], + "angle": 0, + "content": "In Tab. 2, we report the performance when using Random Fourier features to alleviate the memory limitations of cache-based methods. Using RFFs, we are able to drastically reduce the memory footprint of caching methods while maintaining almost the same performance across different shots. Our method when combined with RFFs still maintains state-of-the-art performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.449, + 0.805 + ], + "angle": 0, + "content": "4.6. Running times and memory requirements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Next, we report running time (train and test) for different methods as well as the memory requirements for each method (Tab.7). Our method is on par with Tip-Adapter and GDA in term of speed. Note that APE runs a feature selection step which takes additional time to run, making it slower than the previously mentioned competition. On the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.168 + ], + "angle": 0, + "content": "other hand, training-based methods are orders of magnitude slower. Regarding the memory complexity, ProKeR stores the training shots similarly to APE and Tip-Adapter. However, when using Random Fourier features, our method does need to store additional training samples." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.184, + 0.905, + 0.316 + ], + "angle": 0, + "content": "
MethodsOverall TimeTrainMemory requirements
CoOp[67]~ 17h✓N × T × D
Clip-Adapter[12]~ 40min✓(2N + D1) × D
CrossModal-LP[29]~ 3min✓N × D
Standard LP[41]~ 3min✓N × D
Tip-adapter-F[62]~ 7min✓N × K + N × (K + 1) × D
Tip-Adapter[62]2.1s✗N × K + N × (K + 1) × D
APE [68]24.6s✗N × K + N × (K + 1) × D
GDA [55]1.6 s✗2 × N × D
ProKeR (Ours)4.7s✗N × K + N × (K + 1) × D
ProKeR with RFF (Ours)4.2s✗N × (D + R)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.326, + 0.908, + 0.41 + ], + "angle": 0, + "content": "Table 7. Running times on ImageNet for 16 shots. All experiments are performed on a RTX A6000 GPU. For each method we report the memory requirements. \\( D_{1} \\) is the inner dimension of the MLP used in Clip-Adapter [12] and \\( T \\) is the number of text tokens in CoOp [67]. \\( R \\) is the number of Fourier features used to approximate the RBF kernel." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.448, + 0.771, + 0.464 + ], + "angle": 0, + "content": "5. Limitations & Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.476, + 0.909, + 0.687 + ], + "angle": 0, + "content": "Based on our analysis, caching methods can be understood as local non-parametric regressors. These methods lack a global regularization from zero-shot CLIP which limits their generalization ability when performing adaptation. On the other hand, global methods may lack the flexibility when dealing with complex data. As part of future work, we will explore how both local and global methods can be combined to benefit from the best of both worlds. Furthermore, our formulation of caching methods as a Nadaraya-Watson estimator offers multiple options for the choice the regularization term, the metric used in the kernel, as well as the bandwidth selection [39]. These choices constitute different ways to reduce the bias-variance trade-off inherent to these methods [16]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.707, + 0.634, + 0.723 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.901 + ], + "angle": 0, + "content": "In this paper, we proposed a new theoretical understanding of Tip-Adapter, a prominent training-free caching-based approach for LVM few-shot adaptation. Our analysis suggests that Tip-Adapter is a local nonparametric regression that has well-known bias limitations. We proposed multiple angles of improvement that have shown significant increase over the Tip-Adapter baseline. Subsequently, we demonstrate that incorporating global information in a training-free method can be achieved using a global regularization in a reproducing kernel Hilbert space (RKHS), which conclusively further improves the state-of-the-art for training-free methods." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25099" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.157 + ], + "angle": 0, + "content": "[1] Maurizio A Alvarez, Lorenzo Rosasco, Neil D Lawrence, et al. Kernels for vector-valued functions: A review. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2605-2615, 2023. 2, 3, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.092, + 0.908, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "25102" + } + ] +] \ No newline at end of file diff --git a/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_origin.pdf b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..48fe5466f0f976cea349953537bb0dd1f6838487 --- /dev/null +++ b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/db02e676-2ec5-438d-b07d-f0e3ebad98e1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f7a85a035bd9098eaa30d6698c6fda47d3669ef23d56cfb3a41e4553553b71f6 +size 1318159 diff --git a/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/full.md b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..06e6f19c9bec5283f011f17a475d4e976e74da66 --- /dev/null +++ b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/full.md @@ -0,0 +1,397 @@ +# ProKeR: A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models + +Yassir Bendou $^{1*}$ , Amine Ouasfi $^{2*}$ , Vincent Gripon $^{1}$ , Adnane Boukhayma $^{2}$ $^{1}$ IMT Atlantique, Brest, France + $^{2}$ Inria, University Rennes, IRISA, CNRS + +# Abstract + +The growing popularity of Contrastive Language-Image Pretraining (CLIP) has led to its widespread application in various visual downstream tasks. To enhance CLIP's effectiveness and versatility, efficient few-shot adaptation techniques have been widely adopted. Among these approaches, training-free methods, particularly caching methods exemplified by Tip-Adapter, have gained attention for their lightweight adaptation without the need for additional fine-tuning. In this paper, we revisit Tip-Adapter from a kernel perspective, showing that caching methods function as local adapters and are connected to a well-established kernel literature. Drawing on this insight, we offer a theoretical understanding of how these methods operate and suggest multiple avenues for enhancing the Tip-Adapter baseline. Notably, our analysis shows the importance of incorporating global information in local adapters. Therefore, we subsequently propose a global method that learns a proximal regularizer in a reproducing kernel Hilbert space (RKHS) using CLIP as a base learner. Our method, which we call ProKeR (Proximal Kernel ridge Regression), has a closed form solution and achieves state-of-the-art performances across 11 datasets in the standard few-shot adaptation benchmark. Code is available at https://ybendou.github.io/ProKeR/ + +# 1. Introduction + +Large scale vision-language models (VLMs) trained with contrastive learning have gained an increasing attraction in recent years [21, 41]. These models have shown outstanding performances across a wide range of tasks such as classification [41], segmentation [30] and video understanding [28]. CLIP [41] is one of the most established VLMs offering remarkable zero-shot capabilities in various downstream tasks. It operates using only the class label within a textual prompt such as "A photo of a {CLASS}" where {CLASS} is the groundtruth text label for each class. However, it is well- + +![](images/8d679260231af9ba232857873b7293663576f9664ad670c973d786bc24e1cccc.jpg) +Figure 1. Fitting comparison between different methods on synthetically generated data, illustrating Nadaraya-Watson (Tip-Adapter) bias mitigation via our proposed Local Linear Regression (LLR, Sec. 3.3) and our final method ProKeR. + +known that the zero-shot performance of CLIP is limited in scenarios with large domain shift from the pre-training distribution [10, 34]. To further improve CLIP's generalization, multiple follow-up works proposed to include few-shot data [12, 62, 67] which has shown substantial performance gains compared to zero-shot CLIP. + +Few-shot adaptation of CLIP can be categorized into two types of methods based on whether they require fine-tuning on the few-shot samples or not. Among fine-tuning based methods, prompt learning consists of learning continuous tokens instead of hand-crafted templates in CLIP as proposed by CoOp [67] and CoCoOp [66]. In addition, adapter-based fine-tuning methods operate in the feature space to train their classifiers [12, 29]. Despite their promising performance on downstream tasks, fine-tuning methods require additional training costs to learn the new set of parameters. Furthermore, Tip-Adapter proposed a training-free few-shot adaptation alternative [62]. Using a caching mechanism, + +it captures knowledge from the few-shot samples without additional fine-tuning and ensembles it with zero-shot CLIP. This cache model has shown a significant improvement over the zero-shot performance, which has led to follow-up work such as APE [68] and Tip-X [53]. + +In order to understand caching effectiveness and limitations, we undertake a theoretical analysis to explore the nature of Tip-Adapter. We begin by demonstrating that the Tip-Adapter adaptation term is a modified version of the well-known Nadaraya-Watson (NW) estimator [33], a local nonparametric regression method that allows Tip-Adapter to effectively capture various distributions. However, the NW estimator is also known to be strongly biased [25, 36] (e.g. Fig. 1). To mitigate this bias, we leverage existing tools from the literature of kernel methods. An effective extension to NW estimator is locally linear regression [46]. Initially, by fitting a local linear regression around each test point using a closed-form solution, we significantly improve the performance of Tip-Adapter. However, the parameters are estimated locally, which is prone to overfitting in high-dimensional problems [16, 36]. + +Our analysis shows that caching methods can be understood as local nonparametric regression methods regularised through CLIP pointwise zero-shot predictions. However, this regularization only acts locally and does not provide any global information about the few-shot task. Conversely, recent training-based methods rely on global regularizers to incorporate global information [50]. Hence, we ask ourselves the question: how can we leverage global regularizers for few-shot adapters while conserving the benefits of training-free methods? In order to design such global regularizer, we devise two important design choices: - Firstly, we restrain the hypothesis space of the learned function to be a reproducing kernel Hilbert space (RKHS). - Second, using the RKHS norm, we introduce a proximal regularization term to ensure that the obtained solution is close to the base predictor i.e. $f_{\mathrm{clip}}$ . Thanks to the properties of the RKHS, minimizing the difference between two functions using the RKHS norm ensures that they are close pointwise. Our method ProKeR provides a more effective way to preserve prior knowledge from the zero-shot predictor and maintains the expressive capacity of the learned functions. Through extensive experiments, we show the effectiveness of our method ProKeR which achieves consistent gains over state-of-the-art training-free methods on standard few-shot classification benchmarks [62] and can be successfully combined with existing training-based methods. In addition, we highlight the robustness and generalizability of the proposed method across different architectures and on out-of-distribution datasets. + +# Summary of contributions: + +1. We frame the cache model of Tip-Adapter [62] as a Nadaraya-Watson estimator, a classical kernel regression + +method, and provide a theoretical understanding of how Tip-Adapter functions. + +2. Under this new perspective, we propose multiple improvements on Tip-Adapter either through a closed-form local linear regression fit or by incorporating global information. +3. Our analysis leads to our new proposed method ProKeR, a training-free method that leverages global regularization in a reproducing kernel Hilbert space. Through extensive experiments, ProKeR outperforms existing methods and sets a new state-of-the-art on standard few-shot classification benchmarks. + +# 2. Related Work + +# 2.1. Vision-Language Pre-trained Models + +Visual-language models (VLMs) have gained an increasing popularity lately. These methods, exemplified by CLIP [41], DeCLIP [27] and ALIGN [21], employ a contrastive learning framework to learn a vision encoder and a language encoder with a shared representation space between text and images. Trained on large-scale datasets of image-text pairs, VLMs have shown remarkable zero-shot capabilities on downstream tasks without additional fine-tuning, paving the way for open vocabulary recognition [14]. VLMs have been extended to few-shot classification [67] as well as other tasks beyond image classification such as video understanding [28, 54], image segmentation [30, 52], image generation [43] and 3D reconstruction [7, 63]. + +# 2.2. Few-shot Adaptation + +Few-shot adaptation methods in the context of classification can be categorized into prompt learning and adapter based approaches. Inspired by the recent advances in natural language processing [26], prompt learning aims to learn effective global text or visual prompts for the downstream tasks [2, 6, 23, 45, 47, 49, 58, 61, 66, 67]. Although prompt learning methods have brought significant improvements over the zero-shot baseline, they require back-propagating through the entire text encoder and require having access to the text encoder [38]. On the other hand, adapter-based approaches operate in the feature space and do not require having access to the pre-trained model weights. We distinguish two families of adapter-based approaches. The first one is training-based methods [12, 29, 60] which either train a linear layer [29, 60] or a two-layer MLP such as CLIP-Adapter [12] to perform residual feature blending of the zero-shot classifier. + +While fine-tuning adapters have achieved a good level of performance, they still require additional training time which is impractical under limited resources and might suffer from the caveats of gradient optimization. To alleviate these issues, Tip-Adapter [62] emerges as a training-free solution + +![](images/c05d6151d3311f7b2b9f10def3df6a98ab4b807f5d1a9d79b9542fc5b697cf6e.jpg) +Figure 2. Overview of our training-free method ProKeR. While Tip-Adapter builds a key-value cache model using the few-shot samples, ProKeR incorporates a proximal global regularization based on the zero-shot predictor in a reproducing kernel Hilbert space (RKHS). This allows the use of a richer model without overfitting on the few-shot data. + +based on a key-value cache model. Building on Tip-Adapter, multiple caching methods have been proposed. APE [68] includes a feature selection step to the cache model. CaFo [64] uses an ensemble of foundation models for the cache model and augments text prompts using a Large Language model. SuS-X and its module Tip-X [53] first generates the few-shot set using Stable Diffusion then uses the inter-modal similarities between the test images and the few-shot set. In a transductive setting, DMN [65] proposes a dynamic memory mechanism to cache historical test data. More recently, GDA proposes to use a Linear Discriminant Analysis to set a strong baseline for training-free methods [55]. Despite the good level of performance, there is currently no theoretical framework for understanding the motivation behind caching models. + +# 3. Method + +We expose in this section the details of the proposed method. Our starting point consists in framing Tip-Adapter as a kernel method. Thanks to this new perspective, we develop multiple improvements tailored for it. Conclusively, we propose ProKeR, a method that introduces a global proximal regularization in a reproducing kernel Hilbert space (RKHS). + +# 3.1. Tip-Adapter as a Nadaraya-Watson estimator + +As illustrated in Fig. 2, let $\mathbf{x} \in \mathbb{R}^D$ be the features of an input query image extracted using the visual encoder of CLIP, $\mathbf{S} \in \mathbb{R}^{NK \times D}$ the visual features of the training set and $\mathbf{L} \in \mathbb{R}^{NK \times N}$ the associated matrix of one-hot labels where $N$ is the number of classes and $K$ is the number of shots per class. + +Let $\mathbf{W}_{\mathrm{clip}} \in \mathbb{R}^{D \times N}$ be the text prototypes of the classes extracted with the text encoder using the standard handcrafted templates in the form of "a photo of a {CLASS}" [29, 62, 67]. The zero-shot predictor from CLIP is defined as $f_{\mathrm{clip}}: \mathbf{x} \mapsto \mathbf{x} \mathbf{W}_{\mathrm{clip}}$ . + +To alleviate $f_{\mathrm{clip}}$ prediction errors due to lack of generalization, Tip-Adapter [62] utilizes a cache model to learn knowledge from the few-shot samples. The predicted logits can be formulated as: + +$$ +\phi_ {\mathrm {T i p}} (\mathbf {x}) = f _ {\mathrm {c l i p}} (\mathbf {x}) + \alpha \exp \left(- \beta (1 - \mathbf {x} \mathbf {S} ^ {\top})\right) \mathbf {L}, \tag {1} +$$ + +where $\beta$ is a smoothing scalar and $\alpha$ controls the balance between textual features and few-shot images. Note that since the features in CLIP are normalized (i.e. $||\mathbf{x}||_2 = 1$ ), we can rewrite Eq. (1) as: + +$$ +\phi_ {\mathrm {T i p}} (\mathbf {x}) = f _ {\mathrm {c l i p}} (\mathbf {x}) + \alpha \sum_ {i = 1} ^ {N K} \exp \left(- \frac {\beta}{2} | | \mathbf {S} _ {i} - \mathbf {x} | | _ {2} ^ {2}\right) \mathbf {L} _ {i}, \tag {2} +$$ + +where $\mathbf{S}_i$ is the $i$ -th few-shot sample. Interestingly, the right term of Tip-Adapter can be seen as a modified version of the well-known Nadaraya-Watson (NW) estimator [33] with a Radial Basis Function (RBF) kernel [37]: + +$$ +\begin{array}{l} \phi (\mathbf {x}) = \frac {\sum_ {i = 1} ^ {N K} k _ {\beta} (d (\mathbf {x} , \mathbf {S} _ {i})) \mathbf {L} _ {i}}{\sum_ {i = 1} ^ {N K} k _ {\beta} (d (\mathbf {x} , \mathbf {S} _ {i}))}, \\ \text {w h e r e} k _ {\beta} (u) = \left(\frac {\beta}{2}\right) ^ {D} \exp \left(- \frac {\beta}{2} u\right), \tag {3} \\ \end{array} +$$ + +where $d$ is the distance between the query image and the shots in the feature space. In essence, when $d$ is the Euclidean distance, as in Eq. (2), the adaptation term of TipAdapter is a nonparametric regression, obtained by performing a smooth and locally weighted average of the one-hot labels of the few-shot samples using a kernel function, which quantifies the similarity between the query image and the shots. + +# 3.2. Training-free few-shot adapters as a Bayes optimal mapping + +We formulate the few-shot visual-language adaptation as a Bayes optimal mapping [17] associated to the following pointwise risk: + +$$ +R (\mathbf {x}, \phi (\mathbf {x})) = \mathbb {E} _ {Y \mid X} [ s (Y, \phi (X)) + \mathcal {R} _ {\mathrm {c l i p}} | X = \mathbf {x} ], \tag {4} +$$ + +where $s$ is a cost function and $\mathcal{R}_{\mathrm{clip}}$ is a regularization term using CLIP prediction independent of $Y$ . Here, $X$ and $Y$ are random variables representing the image features and the labels respectively. + +The pointwise Bayes optimal mapping is defined as [17]: + +$$ +\begin{array}{l} \phi (\mathbf {x}) = \underset {\mathbf {q} \in M} {\arg \min } R (\mathbf {x}, \mathbf {q}) (5) \\ = \arg \min _ {\mathbf {q} \in M} \int_ {M} s (\mathbf {y}, \mathbf {q}) d \mu_ {\mathbf {x}} (\mathbf {y}) + \mathcal {R} _ {\mathrm {c l i p}}, (6) \\ \end{array} +$$ + +where $d\mu_{\mathbf{x}}$ is the conditional probability of $Y$ conditioned on $X = \mathbf{x}$ and $M$ is the output space. Following [17], we leverage kernel estimators to rewrite the adaptation problem as: + +$$ +\phi (\mathbf {x}) = \arg \min _ {\mathbf {q}} \frac {1}{N K} \sum_ {i = 1} ^ {N K} k _ {\beta} (d (\mathbf {x}, \mathbf {S} _ {i})) s (\mathbf {q}, \mathbf {L} _ {i}) + \mathcal {R} _ {\mathrm {c l i p}}. \tag {7} +$$ + +This formulation offers a new perspective on the adaptation, where for each test point the cost function is minimized over the output space, with a weighting from each training sample. The regularization term guarantees that the obtained predictions are not far from zero-shot CLIP. + +Interestingly, this formulation paves the way for considering different choices of cost functions $s$ , regularization terms $\mathcal{R}_{\mathrm{clip}}$ and kernels $k_{\beta}$ . The consistency of the obtained estimator is discussed in [17] where the solution of Eq. (7) is obtained using a gradient descent algorithm. While this optimisation can be time consuming, there are cases where a closed form solution can be derived. For instance, when $s$ is the squared Euclidean distance and $\mathcal{R}_{\mathrm{clip}} = \lambda \| \mathbf{q} - f_{\mathrm{clip}}(\mathbf{x})\|_2^2$ , + +we can derive the following solution: + +$$ +\begin{array}{l} \phi (\mathbf {x}) = \frac {\lambda N K}{\lambda N K + \mathcal {Z} (\mathbf {x})} f _ {\mathrm {c l i p}} (\mathbf {x}) \\ + \frac {1}{\lambda N K + \mathcal {Z} (\mathbf {x})} \sum_ {i = 1} ^ {N K} k _ {\beta} (d (\mathbf {x}, \mathbf {S} _ {i})) \mathbf {L} _ {i}, \\ \end{array} +$$ + +$$ +\text {w h e r e} \quad \mathcal {Z} (\mathbf {x}) = \sum_ {i = 1} ^ {N K} k _ {\beta} \left(d \left(\mathbf {x}, \mathbf {S} _ {i}\right)\right), \tag {8} +$$ + +where $\lambda$ is a regularization term that balances the predictions of zero-shot CLIP and the local fit. The obtained closed form of the estimator in Eq. (7) is equivalent to Tip-Adapter up to a scaling factor which depends on each input $\mathbf{x}$ . The main difference between the two formulations in Eq. (2) and Eq. (8) is that the second term in Eq. (8) is agnostic to the training size and is query dependent. + +Although the Nadaraya-Watson estimator is a nonparametric model that allows to capture any type of distribution, it is well known to suffer from poor bias at the boundaries of the training samples [36]. In the following, we propose two methods to alleviate this bias. + +# 3.3. Local Linear Regression + +A standard way to alleviate the boundary bias of the NW estimator is by moving from a local constant fit to a local linear fit around each test point. Instead of using the estimate from Eq. (7), local linear regression (LLR) forms the local estimate $\phi (\mathbf{x}) = \tilde{\mathbf{x}}\mathbf{A}$ , where $\tilde{\mathbf{x}} = [1\quad \mathbf{x}]$ , and $\mathbf{A}\in \mathbb{R}^{(d + 1)c}$ minimizes the following problem: + +$$ +\min _ {\mathbf {A}} \frac {1}{N K} \sum_ {i = 1} ^ {N K} k _ {\beta} \left(d \left(\mathbf {x}, \mathbf {S} _ {i}\right)\right) s \left(\tilde {\mathbf {S}} _ {i} \mathbf {A}, \mathbf {L} _ {i}\right) + \mathcal {R} _ {\mathrm {c l i p}}, \tag {9} +$$ + +which is a weighted ordinary least square problem around each test point weighted by the kernel values $k_{\beta}(d(\mathbf{x}, \mathbf{S}_i))$ . Using the same cost function as for Eq. (8) and using the regularization term $\mathcal{R}_{\mathrm{clip}} = \lambda \| \tilde{\mathbf{x}} \mathbf{A} - f_{\mathrm{clip}}(\mathbf{x})\|_2^2$ , we derive a closed form solution for Eq. (9) as follows: + +$$ +\begin{array}{l} \boldsymbol {\phi} (\mathbf {x}) = \tilde {\mathbf {x}} \mathbf {A} ^ {- 1} \mathbf {B}, \\ w h e r e \quad \mathbf {A} = \tilde {\mathbf {S}} ^ {\top} \boldsymbol {\Omega} \tilde {\mathbf {S}} + \lambda N K \tilde {\mathbf {x}} ^ {\top} \tilde {\mathbf {x}}, \\ \text {a n d} \quad \mathbf {B} = \tilde {\mathbf {S}} ^ {\top} \boldsymbol {\Omega} \mathbf {L} + \lambda N K \tilde {\mathbf {x}} ^ {\top} f _ {\operatorname {c l i p}} (\mathbf {x}), \tag {10} \\ \end{array} +$$ + +where $\Omega$ is the $NK\times NK$ matrix with ith diagonal element as $k_{\beta}(d(\mathbf{x},\mathbf{S}_i))$ + +This method, that we dub henceforth LLR, boils down to fitting a local linear regression while enforcing the obtained fit to be close to the text predictions locally around the query input sample. While LLR usually improves performance, it is time consuming as one needs to fit a linear regression for each input sample. Furthermore, the parameters of LLR + +are solely estimated locally, which is prone to overfitting in high-dimensional problems [36]. Alternatively, one possible way to eliminate the bias of NW estimator due to the bandwidth selection without significantly increasing the time complexity is by equipping the kernel with a better distance function $d$ [36]. + +# 3.4. Local methods with a global metric + +While there exists multiple strategies to construct a good metric [36, 56], using the Mahalanobis distance with the covariance matrix estimated from the training data is a simple yet well-performing one [3]: + +$$ +d (\mathbf {x}, \mathbf {S} _ {i}) = \| \mathbf {x} - \mathbf {S} _ {i} \| _ {\hat {\mathbf {A}}}, \tag {11} +$$ + +where $\hat{\Lambda}$ is the estimated precision matrix from the few-shot samples. This metric effectively incorporates global information and captures the geometry of the space which allows to construct a better kernel function tailored to the downstream task. The classical RBF kernel corresponds to using an isotropic covariance matrix. While still being a local method, adapting the metric to the downstream task allows to incorporate global information about the underlying distribution and improves over Tip-Adapter as shown in Fig. 3. + +# 3.5. Proximal Kernel Ridge Regression + +As can be seen in Fig. 3, incorporating global information about the task through a global metric effectively outperforms both Tip-Adapter and LLR. However, the choice of the global metric for NW estimator beyond the Mahalanobis distance remains challenging [56], especially in the few-shot setting. Furthermore, despite being equipped with a global metric, the NW estimator remains in essence a local method and still lacks a global regularization. Whilst the use of a global regularization has been recently addressed in training-based methods [50], using a truly global regularization in a training-free manner remains challenging and unexplored. + +These limitations highlight the necessity for regularization in this adaptation process. The main idea is to balance the need to maintain the expressive capacity of the learned functions while ensuring stability and robustness. To this end we introduce two key design choices: (1) we constrain the hypothesis space of the learned function to a reproducing kernel Hilbert space (RKHS), and (2) we incorporate a proximal regularization term, based on the RKHS norm, to ensure the solution remains close to the base predictor $(f_{\mathrm{clip}})$ . The RKHS norm's properties guarantee that minimizing the difference between two functions in this space results in pointwise closeness. Consequently, this proximal term serves as a global regularization that preserves prior knowledge from the zero-shot predictor, resulting in more robust solutions that are less prone to overfitting on the few-shot data. + +Given the multi-output nature of the problem, the employed reproducing kernel $\mathbf{K}_{\beta}$ is a reproducing kernel for vector valued functions. The main difference is that the kernel is matrix valued. Several instances of multi-output kernels have been proposed in the literature [1, 5], with separable kernels being among the most widely used for learning vector-valued functions due to their simplicity and computational efficiency. These kernels are formulated as a product of a kernel function for the input space alone and a matrix that encodes the interactions among the outputs. Let us consider $\mathbf{K}_{\beta}:\mathbb{R}^{D}\times \mathbb{R}^{D}\mapsto \mathbb{R}^{N\times N}$ as a separable kernel of the form: + +$$ +\left(\mathbf {K} _ {\beta} \left(\mathbf {x}, \mathbf {x} ^ {\prime}\right)\right) _ {j, j ^ {\prime}} = k _ {\beta} \left(\mathbf {x}, \mathbf {x} ^ {\prime}\right) \mathbf {B}, \tag {12} +$$ + +where $\mathbf{B}$ is a $N\times N$ symmetric and positive semi-definite matrix which captures the correlations between the outputs. A simple yet effective choice for $\mathbf{B}$ is the identity matrix where all outputs are treated as being unrelated. + +Our goal is to learn a multi-output predictor $\phi$ using the following objective: + +$$ +\min _ {\phi \in \mathcal {H}} \sum_ {i = 1} ^ {N K} \| \phi (\mathbf {S} _ {\mathbf {i}}) - \mathbf {L} _ {i} \| _ {2} ^ {2} + \lambda \| \phi - f _ {\mathrm {c l i p}} \| _ {\mathcal {H}} ^ {2}. \tag {13} +$$ + +By the representative theorem [22, 32], the unique minimizer of problem in Eq. (13) emerges naturally as the solution of a Kernel Ridge Regression (KRR) problem: + +$$ +\phi = f _ {\mathrm {c l i p}} + \sum_ {i = 1} ^ {N K} k _ {\beta} (\mathbf {S} _ {\mathbf {i}},.) \gamma_ {i}, +$$ + +$$ +\text {w h e r e} \quad \gamma = \left(\mathbf {I} + \frac {1}{\lambda} k _ {\beta} (\mathbf {S}, \mathbf {S})\right) ^ {- 1} \left(\mathbf {L} - f _ {\mathrm {c l i p}} (\mathbf {S})\right). \tag {14} +$$ + +Here, $(k_{\beta}(\mathbf{S},\mathbf{S}))_{i,j} = k_{\beta}(\mathbf{S}_i,\mathbf{S}_j)$ and $\gamma_{i}\in \mathbb{R}^{N}$ . This approach allows to map data to an infinite dimensional space. Furthermore, the regularization term allows the use of a richer model that captures the complex structure of the data while preserving its smoothness, avoiding overfitting on the few-shot data. + +# 3.6. Mercer decomposition of kernel methods + +One additional benefit of this perspective on caching methods is memory reduction which allows to overcome the necessity of storing training data. For positive definite kernel, we can leverage Mercer theorem [13] to write the kernel function as follow: + +$$ +k _ {\beta} \left(\mathbf {x}, \mathbf {x} ^ {\prime}\right) = \psi_ {\beta} (\mathbf {x}) \psi_ {\beta} \left(\mathbf {x} ^ {\top}\right). \tag {15} +$$ + +This allows us to write: + +$$ +\begin{array}{l} \sum_ {i = 1} ^ {N K} k _ {\beta} \left(\mathbf {S} _ {\mathbf {i}}, \mathbf {x}\right) \gamma_ {i} = \sum_ {i = 1} ^ {N K} \psi_ {\beta} (\mathbf {x}) \psi_ {\beta} \left(\mathbf {S} _ {\mathbf {i}}\right) \gamma_ {i} (16) \\ = \psi_ {\beta} (\mathbf {x}) [ \boldsymbol {\Psi} _ {\beta} ^ {1}, \dots , \boldsymbol {\Psi} _ {\beta} ^ {N} ]. (17) \\ \end{array} +$$ + +Hence, we compute prototypes per class without the need to store additional samples. However, the feature map $\psi$ may not be available in closed form and may be infinite dimensional. For shift invariant kernels like the Gaussian kernel, we leverage the Bochner's theorem following [42] to write: + +$$ +k _ {\beta} (\mathbf {x}, \mathbf {x} ^ {\prime}) = k (\mathbf {x} - \mathbf {x} ^ {\prime}) = \mathbb {E} _ {\mathbf {w} \sim p (\mathbf {w})} \left(\psi_ {\mathbf {w}} (\mathbf {x}) \psi_ {\mathbf {w}} \left(\mathbf {x} ^ {\prime}\right) ^ {\top}\right), +$$ + +where $\psi (\mathbf{x}) = \exp (i\mathbf{x}\mathbf{w})$ (18) + +where $p(\mathbf{w})$ is the Fourier transform of the kernel $k$ . This formulation allows to approximate the RBF kernel with Random Fourier features (RFF). In practice, to lower the variance of the kernel estimate, and thus keep a good balance between performance and the number of RFFs, we use Orthogonal Fourier Features [59]. + +# 3.7. Training-based ProKeR + +In addition to our training-free method, we propose a trained version of ProKeR. The optimization problem in Eq. 13 allows for the use of any base learner and is not limited to the zero-shot CLIP. In this training-based version, instead of using the zero-shot CLIP as the base learner to regularize our method in the RKHS, we iteratively optimize for a regularizer and the obtained solution from ProKeR. Our method consists of training a linear classifier using the same loss $\mathcal{L}_{\mathrm{CLAP}}$ proposed in CLAP [50] while solving the linear system of ProKeR at each iteration as follows: + +$$ +\min _ {\mathbf {W}} \mathcal {L} _ {\mathrm {C L A P}} (\phi_ {\mathbf {W}}, \mathbf {S}, \mathbf {L}), +$$ + +$$ +\text {w h e r e} \quad \phi_ {\mathbf {W}} (\mathbf {x}) = \mathbf {x} \mathbf {W} + \sum_ {i = 1} ^ {N K} k _ {\beta} (\mathbf {S} _ {\mathbf {i}}, \mathbf {x}) \gamma_ {i}, +$$ + +$$ +\text {a n d} \quad \gamma = (\mathbf {I} + \frac {1}{\lambda} k _ {\beta} (\mathbf {S}, \mathbf {S})) ^ {- 1} (\mathbf {L} - \mathbf {S W}). \tag {19} +$$ + +By jointly optimizing the base learner and the solution of the Kernel Ridge Regression problem, our method (ProKeR + CLAP) allows to learn a regularizer specific to the few-shot task which takes into account the latter problem. + +# 4. Experiments + +In this section, we evaluate our method on multiple image classification benchmarks. We compare our results to existing training-free methods, notably Tip-Adapter [62], which is the baseline of our work. For a fair comparison, we use the same text inputs for all reported methods. We also compare to other state-of-the-art conventional methods, such as APE [68], Tip-X [53], GDA [55], CLIP [41] and CALIP [15] which proposes a parameter-free attention mechanism to improve CLIP in a zero-shot manner. We run APE with the same text templates as Tip-Adapter using their official implementation. Finally, we report the average running times + +on ImageNet [9] for each method using an NVIDIA RTX A6000 GPU. For completeness, we additionally provide a comparison of our method with existing state-of-the-art training-based methods. + +# 4.1. Datasets and Evaluation Protocol + +For comprehensive evaluation, we adopt 11 image classification benchmarks: ImageNet [9], Caltech101 [11], DTD [8], EuroSAT [18], FGVCAircraft [31], Flowers102 [35], Food101 [4], OxfordPets [40], StanfordCars [24], SUN397 [57], and UCF101 [51]. For testing the generalization ability of our method, we further test on ImageNet-Sketch [48] and ImageNet-V2 [44]. + +For a fair comparison with previous work, we use ResNet-50 for the visual encoder of CLIP unless mentioned otherwise. We follow two settings for our experiments. The first setting, initially introduced by [50] for training-based methods, consists of selecting the best hyperparameters of each method on ImageNet and transfer them to the other datasets and report the average performance. This setting reflects real-life scenarios where a validation set may not be available especially in a few-shot regime. The second setting follows CoOp's benchmark [67] where validation shots are used to select the hyperparameters and evaluate the results on the full test set. + +# 4.2. Experiment Results and Analysis + +# 4.2.1. Comparison with alternatives to Tip-Adapter + +![](images/15a885ba4228ca9f7ba0776fc60bd0a0d2f1465cfe8a909eae575bc00a2f8be8.jpg) +Figure 3. Average performance for different methods on 11 image classification datasets. + +We compare in Fig. 3 our result when improving Tip-Adapter using kernel based approaches across 11 datasets. Our reformulation in Eq. (8) outperforms Tip-Adapter for 8 + +and 16 shots and maintains the same level of performance in the lower shot setting. We argue that this is due to the fact that our reformulation is agnostic to the training size. Debiasing the NW estimator using our regularized LLR in Eq. (9) significantly improves the performance as a first order polynomial fit compared to the constant fit of the NW estimator. Additionally, the use of the Mahalanobis distance as global metric for NW estimator further increases the performance especially with more shots as the estimation of the precision matrix from the training set becomes more accurate. Furthermore, by introducing a proximal regularization in the RKHS, our method ProKeR significantly outperforms Tip-Adapter as well as all the proposed alternatives especially with more shots. + +# 4.2.2. Comparison with training-free methods + +We report in Tab. 1 the performance of different methods in a realistic and practical validation-free experimental setting. First, our method ProKeR outperforms existing alternatives on average by a large margin (2.04% compared to the second best), especially in the low shot regimes (1, 2 and 4) and is only outperformed in the 8 shot setting. Furthermore, when using a Polynomial kernel (as defined in Tab. 5), our method sets a new standard in the 16 shots regime. + +
Shots124816Average
Tip-Adapter [62]58.8660.3361.4963.1564.6161.68
APE [68]60.0962.3365.3667.9569.8965.12
GDA [55]57.4963.4366.6872.4675.1267.03
ProKeR (Polynomial) (ours)62.3965.5968.0571.8175.8268.72
ProKeR (RBF) (ours)63.1366.3168.6472.1575.1269.07
+ +In the CoOp's benchmark where hyperparameters are tailored for each dataset, our method ProKeR surpasses existing training-free methods as shown in Tab. 2. These superior results fully validate the significance of using the global regularization in the RKHS. However, as noted by [50], this setting may not be practical since the hyperparameters are tuned on the test set. + +Table 1. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet. + +
Shots124816Average
GDA [55]62.1966.1969.7773.3076.0469.49
Tip-Adapter [62]62.8364.8466.5068.6470.0266.56
Tip-Adapter [62] with RFF62.7764.5866.2968.1569.6066.27
APE [68]64.4366.4868.6670.7572.8168.62
APE [68] with RFF64.1666.1168.7670.3772.0268.28
ProKeR (ours)64.0167.3170.4273.8576.7570.46
ProKeR with RFF (ours)64.0167.1270.2873.6176.4470.29
+ +# 4.2.3. Generalization Ability + +In Tab. 3, we test the generalization ability of the different methods on out-of-distribution datasets. Notably, the shots are drawn from ImageNet and the test set is drawn from either ImageNet-V2 or ImageNet-Sketch. ProKeR achieves state-of-the-art performance for training-free methods on both in-distribution and out-of-distribution datasets. + +Table 2. Performance on 11 different classification datasets (CoOp's benchmark). + +
DatasetsSourceTarget
ImageNet [9]-V2 [44]-Sketch [48]-A [20]-R [19]Average
Zero-Shot CLIP [41]60.3353.2735.4423.6160.4246.61
Tip-Adapter [62]61.4354.1335.7123.6360.4147.06
APE [68]62.6054.9335.4122.9559.9047.15
GDA [55]63.8255.3534.3219.5355.5645.71
ProKeR (Polynomial) (Ours)64.6656.1136.0823.2760.5548.13
ProKeR (Ours)64.4556.0236.0823.3760.5948.10
+ +# 4.2.4. Comparison with training-based methods + +We report in Tab. 4 the comparison of our method with training-based methods. While being training-free, our method ProKeR outperforms existing training-based methods on 8 out of 11 datasets. This emphasizes the effectiveness of incorporating a global regularization using the zero-shot predictor in a reproducing kernel Hilbert space (RKHS). + +Table 3. Robustness to distribution shift of different methods for 16 shots. + +
Shots124816Average
Tip-Adapter-F [62]60.2962.2665.3268.3571.4065.52
CrossModalLP [29]62.2464.4866.6770.3673.6567.48
TaskRes [60]61.4465.2668.3571.6674.4268.22
APE-T [68]62.7263.9366.5768.9672.1566.86
CLAP [50]62.7966.0769.1372.0874.5768.92
ProKeR (ours)63.1366.3168.6472.1575.1269.07
ProKeR + CLAP (ours)64.1667.6070.9774.1276.8470.73
+ +Table 4. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet. + +The jointly trained version of ProKeR with CLAP achieves significantly better results compared to existing training-based methods and increases the average performance of the ProKeR by $1.73\%$ accuracy. This shows the importance of using a strong base learner. Furthermore, the joint training allows to leverage both the expressive power of the RKHS and the flexibility of the linear classifier. + +# 4.3. Kernel ablation + +So far, we have performed our analysis using the RBF kernel, a commonly used kernel in the kernel literature and in cache-based methods. Nevertheless, through the lens of our kernel perspective on cache-based methods, different kernels can be considered ranging from a linear kernels to more elaborate ones. We perform in Tab. 5 an ablation study where + +we discuss different kernel choices. Besides RBF, we consider three commonly used kernels: the Linear kernel, the Epanechnikov kernel and the Polynomial kernel. The RBF kernel outperforms the linear, Epanechnikov and the polynomial kernels. Using the RBF kernel allows us to project data into an infinite dimensional space which captures more complex relationships. + +
Kernelk(x, x')Accuracy
Linearxx'^T72.34
Epanechnikov3/4 (1 - ||x - y'||2)74.43
Polynomial(xy'^T)^276.61
RBFexp(-β/2||(x - y'||2))76.75
+ +# 4.4. Ablation on CLIP architectures + +In Tab. 6, we report the performance of training-free methods using different backbones on ImageNet for 16 shots. Our method consistently outperforms the alternatives across all architectures. While all methods improve with more capable architectures, the gap between our method and the second best one (APE) remains stable. + +Table 5. Kernel Ablation for 16 shots on 11 datasets on CoOp's benchmark. + +
ModelsResNet-50ResNet-101ViT-B/32ViT-B/16
Zero-shot CLIP [41]60.3362.5363.8068.73
Tip-Adapter [62]61.4364.0865.1870.25
APE [68]62.6065.6166.3171.37
ProKeR (Ours)64.4567.3968.1273.25
+ +# 4.5. Adressing memory limitations of cache-based methods + +In Tab. 2, we report the performance when using Random Fourier features to alleviate the memory limitations of cache-based methods. Using RFFs, we are able to drastically reduce the memory footprint of caching methods while maintaining almost the same performance across different shots. Our method when combined with RFFs still maintains state-of-the-art performance. + +# 4.6. Running times and memory requirements + +Next, we report running time (train and test) for different methods as well as the memory requirements for each method (Tab.7). Our method is on par with Tip-Adapter and GDA in term of speed. Note that APE runs a feature selection step which takes additional time to run, making it slower than the previously mentioned competition. On the + +other hand, training-based methods are orders of magnitude slower. Regarding the memory complexity, ProKeR stores the training shots similarly to APE and Tip-Adapter. However, when using Random Fourier features, our method does need to store additional training samples. + +Table 6. Average performance on 16-shot ImageNet with different backbones. + +
MethodsOverall TimeTrainMemory requirements
CoOp[67]~ 17h✓N × T × D
Clip-Adapter[12]~ 40min✓(2N + D1) × D
CrossModal-LP[29]~ 3min✓N × D
Standard LP[41]~ 3min✓N × D
Tip-adapter-F[62]~ 7min✓N × K + N × (K + 1) × D
Tip-Adapter[62]2.1s✗N × K + N × (K + 1) × D
APE [68]24.6s✗N × K + N × (K + 1) × D
GDA [55]1.6 s✗2 × N × D
ProKeR (Ours)4.7s✗N × K + N × (K + 1) × D
ProKeR with RFF (Ours)4.2s✗N × (D + R)
+ +Table 7. Running times on ImageNet for 16 shots. All experiments are performed on a RTX A6000 GPU. For each method we report the memory requirements. $D_{1}$ is the inner dimension of the MLP used in Clip-Adapter [12] and $T$ is the number of text tokens in CoOp [67]. $R$ is the number of Fourier features used to approximate the RBF kernel. + +# 5. Limitations & Future Work + +Based on our analysis, caching methods can be understood as local non-parametric regressors. These methods lack a global regularization from zero-shot CLIP which limits their generalization ability when performing adaptation. On the other hand, global methods may lack the flexibility when dealing with complex data. As part of future work, we will explore how both local and global methods can be combined to benefit from the best of both worlds. Furthermore, our formulation of caching methods as a Nadaraya-Watson estimator offers multiple options for the choice the regularization term, the metric used in the kernel, as well as the bandwidth selection [39]. These choices constitute different ways to reduce the bias-variance trade-off inherent to these methods [16]. + +# 6. Conclusion + +In this paper, we proposed a new theoretical understanding of Tip-Adapter, a prominent training-free caching-based approach for LVM few-shot adaptation. Our analysis suggests that Tip-Adapter is a local nonparametric regression that has well-known bias limitations. We proposed multiple angles of improvement that have shown significant increase over the Tip-Adapter baseline. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2605-2615, 2023. 2, 3, 6, 7, 8 \ No newline at end of file diff --git a/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/images.zip b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6f97fc1fe53098c563117e76c53f5dcb6b2b3b5a --- /dev/null +++ b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f1d2c03d40fe9cce4393f9c0bc4d37696ab172649c5337ebc1ee42d43930a143 +size 474714 diff --git a/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/layout.json b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b005d19164b373f0a3b6a3da79a4faffa763237f --- /dev/null +++ b/2025/ProKeR_ A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models/layout.json @@ -0,0 +1,9098 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 102, + 555, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 102, + 555, + 138 + ], + "spans": [ + { + "bbox": [ + 56, + 102, + 555, + 138 + ], + "type": "text", + "content": "ProKeR: A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "spans": [ + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": "Yassir Bendou" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": ", Amine Ouasfi" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": ", Vincent Gripon" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": ", Adnane Boukhayma" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": "IMT Atlantique, Brest, France \n" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 127, + 160, + 483, + 203 + ], + "type": "text", + "content": "Inria, University Rennes, IRISA, CNRS" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 230, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 230, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 230, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 256, + 297, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 256, + 297, + 531 + ], + "spans": [ + { + "bbox": [ + 54, + 256, + 297, + 531 + ], + "type": "text", + "content": "The growing popularity of Contrastive Language-Image Pretraining (CLIP) has led to its widespread application in various visual downstream tasks. To enhance CLIP's effectiveness and versatility, efficient few-shot adaptation techniques have been widely adopted. Among these approaches, training-free methods, particularly caching methods exemplified by Tip-Adapter, have gained attention for their lightweight adaptation without the need for additional fine-tuning. In this paper, we revisit Tip-Adapter from a kernel perspective, showing that caching methods function as local adapters and are connected to a well-established kernel literature. Drawing on this insight, we offer a theoretical understanding of how these methods operate and suggest multiple avenues for enhancing the Tip-Adapter baseline. Notably, our analysis shows the importance of incorporating global information in local adapters. Therefore, we subsequently propose a global method that learns a proximal regularizer in a reproducing kernel Hilbert space (RKHS) using CLIP as a base learner. Our method, which we call ProKeR (Proximal Kernel ridge Regression), has a closed form solution and achieves state-of-the-art performances across 11 datasets in the standard few-shot adaptation benchmark. Code is available at https://ybendou.github.io/ProKeR/" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 554, + 135, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 554, + 135, + 566 + ], + "spans": [ + { + "bbox": [ + 55, + 554, + 135, + 566 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 574, + 297, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 297, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 297, + 694 + ], + "type": "text", + "content": "Large scale vision-language models (VLMs) trained with contrastive learning have gained an increasing attraction in recent years [21, 41]. These models have shown outstanding performances across a wide range of tasks such as classification [41], segmentation [30] and video understanding [28]. CLIP [41] is one of the most established VLMs offering remarkable zero-shot capabilities in various downstream tasks. It operates using only the class label within a textual prompt such as \"A photo of a {CLASS}\" where {CLASS} is the groundtruth text label for each class. However, it is well-" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 314, + 228, + 552, + 423 + ], + "blocks": [ + { + "bbox": [ + 314, + 228, + 552, + 423 + ], + "lines": [ + { + "bbox": [ + 314, + 228, + 552, + 423 + ], + "spans": [ + { + "bbox": [ + 314, + 228, + 552, + 423 + ], + "type": "image", + "image_path": "8d679260231af9ba232857873b7293663576f9664ad670c973d786bc24e1cccc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 431, + 555, + 477 + ], + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 477 + ], + "type": "text", + "content": "Figure 1. Fitting comparison between different methods on synthetically generated data, illustrating Nadaraya-Watson (Tip-Adapter) bias mitigation via our proposed Local Linear Regression (LLR, Sec. 3.3) and our final method ProKeR." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 498, + 555, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 498, + 555, + 569 + ], + "spans": [ + { + "bbox": [ + 312, + 498, + 555, + 569 + ], + "type": "text", + "content": "known that the zero-shot performance of CLIP is limited in scenarios with large domain shift from the pre-training distribution [10, 34]. To further improve CLIP's generalization, multiple follow-up works proposed to include few-shot data [12, 62, 67] which has shown substantial performance gains compared to zero-shot CLIP." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 570, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 570, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 312, + 570, + 556, + 714 + ], + "type": "text", + "content": "Few-shot adaptation of CLIP can be categorized into two types of methods based on whether they require fine-tuning on the few-shot samples or not. Among fine-tuning based methods, prompt learning consists of learning continuous tokens instead of hand-crafted templates in CLIP as proposed by CoOp [67] and CoCoOp [66]. In addition, adapter-based fine-tuning methods operate in the feature space to train their classifiers [12, 29]. Despite their promising performance on downstream tasks, fine-tuning methods require additional training costs to learn the new set of parameters. Furthermore, Tip-Adapter proposed a training-free few-shot adaptation alternative [62]. Using a caching mechanism," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 222, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 222, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 222, + 712 + ], + "type": "text", + "content": "*These authors contributed equally to this work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25092" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "it captures knowledge from the few-shot samples without additional fine-tuning and ensembles it with zero-shot CLIP. This cache model has shown a significant improvement over the zero-shot performance, which has led to follow-up work such as APE [68] and Tip-X [53]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 134, + 295, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 134, + 295, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 134, + 295, + 326 + ], + "type": "text", + "content": "In order to understand caching effectiveness and limitations, we undertake a theoretical analysis to explore the nature of Tip-Adapter. We begin by demonstrating that the Tip-Adapter adaptation term is a modified version of the well-known Nadaraya-Watson (NW) estimator [33], a local nonparametric regression method that allows Tip-Adapter to effectively capture various distributions. However, the NW estimator is also known to be strongly biased [25, 36] (e.g. Fig. 1). To mitigate this bias, we leverage existing tools from the literature of kernel methods. An effective extension to NW estimator is locally linear regression [46]. Initially, by fitting a local linear regression around each test point using a closed-form solution, we significantly improve the performance of Tip-Adapter. However, the parameters are estimated locally, which is prone to overfitting in high-dimensional problems [16, 36]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 327, + 297, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 297, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 297, + 673 + ], + "type": "text", + "content": "Our analysis shows that caching methods can be understood as local nonparametric regression methods regularised through CLIP pointwise zero-shot predictions. However, this regularization only acts locally and does not provide any global information about the few-shot task. Conversely, recent training-based methods rely on global regularizers to incorporate global information [50]. Hence, we ask ourselves the question: how can we leverage global regularizers for few-shot adapters while conserving the benefits of training-free methods? In order to design such global regularizer, we devise two important design choices: - Firstly, we restrain the hypothesis space of the learned function to be a reproducing kernel Hilbert space (RKHS). - Second, using the RKHS norm, we introduce a proximal regularization term to ensure that the obtained solution is close to the base predictor i.e. " + }, + { + "bbox": [ + 55, + 327, + 297, + 673 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{clip}}" + }, + { + "bbox": [ + 55, + 327, + 297, + 673 + ], + "type": "text", + "content": ". Thanks to the properties of the RKHS, minimizing the difference between two functions using the RKHS norm ensures that they are close pointwise. Our method ProKeR provides a more effective way to preserve prior knowledge from the zero-shot predictor and maintains the expressive capacity of the learned functions. Through extensive experiments, we show the effectiveness of our method ProKeR which achieves consistent gains over state-of-the-art training-free methods on standard few-shot classification benchmarks [62] and can be successfully combined with existing training-based methods. In addition, we highlight the robustness and generalizability of the proposed method across different architectures and on out-of-distribution datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 676, + 174, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 676, + 174, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 676, + 174, + 687 + ], + "type": "text", + "content": "Summary of contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 689, + 295, + 714 + ], + "type": "text", + "content": "1. We frame the cache model of Tip-Adapter [62] as a Nadaraya-Watson estimator, a classical kernel regression" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 326, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 326, + 72, + 553, + 95 + ], + "type": "text", + "content": "method, and provide a theoretical understanding of how Tip-Adapter functions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 96, + 556, + 215 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 96, + 555, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 96, + 555, + 142 + ], + "spans": [ + { + "bbox": [ + 314, + 96, + 555, + 142 + ], + "type": "text", + "content": "2. Under this new perspective, we propose multiple improvements on Tip-Adapter either through a closed-form local linear regression fit or by incorporating global information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 144, + 556, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 556, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 556, + 215 + ], + "type": "text", + "content": "3. Our analysis leads to our new proposed method ProKeR, a training-free method that leverages global regularization in a reproducing kernel Hilbert space. Through extensive experiments, ProKeR outperforms existing methods and sets a new state-of-the-art on standard few-shot classification benchmarks." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 228, + 400, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 400, + 241 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 400, + 241 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 248, + 509, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 248, + 509, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 248, + 509, + 262 + ], + "type": "text", + "content": "2.1. Vision-Language Pre-trained Models" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 266, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 555, + 422 + ], + "type": "text", + "content": "Visual-language models (VLMs) have gained an increasing popularity lately. These methods, exemplified by CLIP [41], DeCLIP [27] and ALIGN [21], employ a contrastive learning framework to learn a vision encoder and a language encoder with a shared representation space between text and images. Trained on large-scale datasets of image-text pairs, VLMs have shown remarkable zero-shot capabilities on downstream tasks without additional fine-tuning, paving the way for open vocabulary recognition [14]. VLMs have been extended to few-shot classification [67] as well as other tasks beyond image classification such as video understanding [28, 54], image segmentation [30, 52], image generation [43] and 3D reconstruction [7, 63]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 431, + 435, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 435, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 435, + 444 + ], + "type": "text", + "content": "2.2. Few-shot Adaptation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 449, + 556, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 556, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 556, + 652 + ], + "type": "text", + "content": "Few-shot adaptation methods in the context of classification can be categorized into prompt learning and adapter based approaches. Inspired by the recent advances in natural language processing [26], prompt learning aims to learn effective global text or visual prompts for the downstream tasks [2, 6, 23, 45, 47, 49, 58, 61, 66, 67]. Although prompt learning methods have brought significant improvements over the zero-shot baseline, they require back-propagating through the entire text encoder and require having access to the text encoder [38]. On the other hand, adapter-based approaches operate in the feature space and do not require having access to the pre-trained model weights. We distinguish two families of adapter-based approaches. The first one is training-based methods [12, 29, 60] which either train a linear layer [29, 60] or a two-layer MLP such as CLIP-Adapter [12] to perform residual feature blending of the zero-shot classifier." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "While fine-tuning adapters have achieved a good level of performance, they still require additional training time which is impractical under limited resources and might suffer from the caveats of gradient optimization. To alleviate these issues, Tip-Adapter [62] emerges as a training-free solution" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25093" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 72, + 556, + 281 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 556, + 281 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 556, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 556, + 281 + ], + "type": "image", + "image_path": "c05d6151d3311f7b2b9f10def3df6a98ab4b807f5d1a9d79b9542fc5b697cf6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 288, + 555, + 322 + ], + "lines": [ + { + "bbox": [ + 54, + 288, + 555, + 322 + ], + "spans": [ + { + "bbox": [ + 54, + 288, + 555, + 322 + ], + "type": "text", + "content": "Figure 2. Overview of our training-free method ProKeR. While Tip-Adapter builds a key-value cache model using the few-shot samples, ProKeR incorporates a proximal global regularization based on the zero-shot predictor in a reproducing kernel Hilbert space (RKHS). This allows the use of a richer model without overfitting on the few-shot data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 342, + 297, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 342, + 297, + 521 + ], + "spans": [ + { + "bbox": [ + 54, + 342, + 297, + 521 + ], + "type": "text", + "content": "based on a key-value cache model. Building on Tip-Adapter, multiple caching methods have been proposed. APE [68] includes a feature selection step to the cache model. CaFo [64] uses an ensemble of foundation models for the cache model and augments text prompts using a Large Language model. SuS-X and its module Tip-X [53] first generates the few-shot set using Stable Diffusion then uses the inter-modal similarities between the test images and the few-shot set. In a transductive setting, DMN [65] proposes a dynamic memory mechanism to cache historical test data. More recently, GDA proposes to use a Linear Discriminant Analysis to set a strong baseline for training-free methods [55]. Despite the good level of performance, there is currently no theoretical framework for understanding the motivation behind caching models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 534, + 111, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 111, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 111, + 547 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 555, + 297, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 297, + 627 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 297, + 627 + ], + "type": "text", + "content": "We expose in this section the details of the proposed method. Our starting point consists in framing Tip-Adapter as a kernel method. Thanks to this new perspective, we develop multiple improvements tailored for it. Conclusively, we propose ProKeR, a method that introduces a global proximal regularization in a reproducing kernel Hilbert space (RKHS)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 635, + 293, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 293, + 649 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 293, + 649 + ], + "type": "text", + "content": "3.1. Tip-Adapter as a Nadaraya-Watson estimator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "As illustrated in Fig. 2, let " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " be the features of an input query image extracted using the visual encoder of CLIP, " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{NK \\times D}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " the visual features of the training set and " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{L} \\in \\mathbb{R}^{NK \\times N}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " the associated matrix of one-hot labels where " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " is the number of classes and " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " is the number of shots per class." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{clip}} \\in \\mathbb{R}^{D \\times N}" + }, + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "text", + "content": " be the text prototypes of the classes extracted with the text encoder using the standard handcrafted templates in the form of \"a photo of a {CLASS}\" [29, 62, 67]. The zero-shot predictor from CLIP is defined as " + }, + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{clip}}: \\mathbf{x} \\mapsto \\mathbf{x} \\mathbf{W}_{\\mathrm{clip}}" + }, + { + "bbox": [ + 313, + 342, + 555, + 403 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 403, + 555, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 449 + ], + "type": "text", + "content": "To alleviate " + }, + { + "bbox": [ + 313, + 403, + 555, + 449 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{clip}}" + }, + { + "bbox": [ + 313, + 403, + 555, + 449 + ], + "type": "text", + "content": " prediction errors due to lack of generalization, Tip-Adapter [62] utilizes a cache model to learn knowledge from the few-shot samples. The predicted logits can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 328, + 458, + 555, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 458, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 328, + 458, + 555, + 473 + ], + "type": "interline_equation", + "content": "\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\exp \\left(- \\beta (1 - \\mathbf {x} \\mathbf {S} ^ {\\top})\\right) \\mathbf {L}, \\tag {1}", + "image_path": "d0bdc5c52e3f382f420fd152c2e34dc31910f20301c5fbb48c33c14f51b50979.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "text", + "content": " is a smoothing scalar and " + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "text", + "content": " controls the balance between textual features and few-shot images. Note that since the features in CLIP are normalized (i.e. " + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "inline_equation", + "content": "||\\mathbf{x}||_2 = 1" + }, + { + "bbox": [ + 313, + 481, + 555, + 529 + ], + "type": "text", + "content": "), we can rewrite Eq. (1) as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 537, + 555, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 537, + 555, + 582 + ], + "spans": [ + { + "bbox": [ + 321, + 537, + 555, + 582 + ], + "type": "interline_equation", + "content": "\\phi_ {\\mathrm {T i p}} (\\mathbf {x}) = f _ {\\mathrm {c l i p}} (\\mathbf {x}) + \\alpha \\sum_ {i = 1} ^ {N K} \\exp \\left(- \\frac {\\beta}{2} | | \\mathbf {S} _ {i} - \\mathbf {x} | | _ {2} ^ {2}\\right) \\mathbf {L} _ {i}, \\tag {2}", + "image_path": "7350d3f1f2e5b5fcd6ae60ad89b295156f49bd22b517465fb35128954dd485fe.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_i" + }, + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 591, + 555, + 640 + ], + "type": "text", + "content": "-th few-shot sample. Interestingly, the right term of Tip-Adapter can be seen as a modified version of the well-known Nadaraya-Watson (NW) estimator [33] with a Radial Basis Function (RBF) kernel [37]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 323, + 650, + 555, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 650, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 323, + 650, + 555, + 712 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i})) \\mathbf {L} _ {i}}{\\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x} , \\mathbf {S} _ {i}))}, \\\\ \\text {w h e r e} k _ {\\beta} (u) = \\left(\\frac {\\beta}{2}\\right) ^ {D} \\exp \\left(- \\frac {\\beta}{2} u\\right), \\tag {3} \\\\ \\end{array}", + "image_path": "84cc6209b8e21be53491d032708ba7a0a876b7b26ed9a1e5730ecbeea0df2a5c.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25094" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "text", + "content": " is the distance between the query image and the shots in the feature space. In essence, when " + }, + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 72, + 296, + 167 + ], + "type": "text", + "content": " is the Euclidean distance, as in Eq. (2), the adaptation term of TipAdapter is a nonparametric regression, obtained by performing a smooth and locally weighted average of the one-hot labels of the few-shot samples using a kernel function, which quantifies the similarity between the query image and the shots." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 182, + 296, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 182, + 296, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 296, + 208 + ], + "type": "text", + "content": "3.2. Training-free few-shot adapters as a Bayes optimal mapping" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 213, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 296, + 251 + ], + "type": "text", + "content": "We formulate the few-shot visual-language adaptation as a Bayes optimal mapping [17] associated to the following pointwise risk:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 263, + 296, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 263, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 67, + 263, + 296, + 277 + ], + "type": "interline_equation", + "content": "R (\\mathbf {x}, \\phi (\\mathbf {x})) = \\mathbb {E} _ {Y \\mid X} [ s (Y, \\phi (X)) + \\mathcal {R} _ {\\mathrm {c l i p}} | X = \\mathbf {x} ], \\tag {4}", + "image_path": "16b55afd2d9e8afd3cf911ff0bc0b8fa105c2829f978df207c15a72aa208b3e7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": " is a cost function and " + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\mathrm{clip}}" + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": " is a regularization term using CLIP prediction independent of " + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 290, + 296, + 338 + ], + "type": "text", + "content": " are random variables representing the image features and the labels respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 340, + 296, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 340, + 296, + 353 + ], + "spans": [ + { + "bbox": [ + 67, + 340, + 296, + 353 + ], + "type": "text", + "content": "The pointwise Bayes optimal mapping is defined as [17]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 378, + 296, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 378, + 296, + 425 + ], + "spans": [ + { + "bbox": [ + 84, + 378, + 296, + 425 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\phi (\\mathbf {x}) = \\underset {\\mathbf {q} \\in M} {\\arg \\min } R (\\mathbf {x}, \\mathbf {q}) (5) \\\\ = \\arg \\min _ {\\mathbf {q} \\in M} \\int_ {M} s (\\mathbf {y}, \\mathbf {q}) d \\mu_ {\\mathbf {x}} (\\mathbf {y}) + \\mathcal {R} _ {\\mathrm {c l i p}}, (6) \\\\ \\end{array}", + "image_path": "de124303ae0590393ffb9f63b57808154d6798c0b520dc32b428ae35685b9358.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "inline_equation", + "content": "d\\mu_{\\mathbf{x}}" + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": " is the conditional probability of " + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": " conditioned on " + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "inline_equation", + "content": "X = \\mathbf{x}" + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": " is the output space. Following [17], we leverage kernel estimators to rewrite the adaptation problem as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 495, + 296, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 495, + 296, + 540 + ], + "spans": [ + { + "bbox": [ + 59, + 495, + 296, + 540 + ], + "type": "interline_equation", + "content": "\\phi (\\mathbf {x}) = \\arg \\min _ {\\mathbf {q}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) s (\\mathbf {q}, \\mathbf {L} _ {i}) + \\mathcal {R} _ {\\mathrm {c l i p}}. \\tag {7}", + "image_path": "5113d817a083b88c0eba1b9984e713130e1c07bcc345481c4c806cf0abe54ed9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 555, + 296, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 296, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 296, + 616 + ], + "type": "text", + "content": "This formulation offers a new perspective on the adaptation, where for each test point the cost function is minimized over the output space, with a weighting from each training sample. The regularization term guarantees that the obtained predictions are not far from zero-shot CLIP." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": "Interestingly, this formulation paves the way for considering different choices of cost functions " + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": ", regularization terms " + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\mathrm{clip}}" + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": " and kernels " + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "k_{\\beta}" + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": ". The consistency of the obtained estimator is discussed in [17] where the solution of Eq. (7) is obtained using a gradient descent algorithm. While this optimisation can be time consuming, there are cases where a closed form solution can be derived. For instance, when " + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": " is the squared Euclidean distance and " + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\mathbf{q} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2" + }, + { + "bbox": [ + 55, + 617, + 297, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "type": "text", + "content": "we can derive the following solution:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 95, + 514, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 95, + 514, + 156 + ], + "spans": [ + { + "bbox": [ + 324, + 95, + 514, + 156 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\phi (\\mathbf {x}) = \\frac {\\lambda N K}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} f _ {\\mathrm {c l i p}} (\\mathbf {x}) \\\\ + \\frac {1}{\\lambda N K + \\mathcal {Z} (\\mathbf {x})} \\sum_ {i = 1} ^ {N K} k _ {\\beta} (d (\\mathbf {x}, \\mathbf {S} _ {i})) \\mathbf {L} _ {i}, \\\\ \\end{array}", + "image_path": "8ef752806b2483bcf4fa72cf933239f1bd94e17a296edfaafd5ffb4786cf7ec3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 391, + 159, + 555, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 159, + 555, + 191 + ], + "spans": [ + { + "bbox": [ + 391, + 159, + 555, + 191 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\mathcal {Z} (\\mathbf {x}) = \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right), \\tag {8}", + "image_path": "59603e5024a9bb239d02922bc22ca9c166a08eb8c2a4326d9d84fe2dba80e0b1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "spans": [ + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "text", + "content": " is a regularization term that balances the predictions of zero-shot CLIP and the local fit. The obtained closed form of the estimator in Eq. (7) is equivalent to Tip-Adapter up to a scaling factor which depends on each input " + }, + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 199, + 555, + 282 + ], + "type": "text", + "content": ". The main difference between the two formulations in Eq. (2) and Eq. (8) is that the second term in Eq. (8) is agnostic to the training size and is query dependent." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 283, + 555, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 283, + 555, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 555, + 342 + ], + "type": "text", + "content": "Although the Nadaraya-Watson estimator is a nonparametric model that allows to capture any type of distribution, it is well known to suffer from poor bias at the boundaries of the training samples [36]. In the following, we propose two methods to alleviate this bias." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 350, + 451, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 350, + 451, + 363 + ], + "spans": [ + { + "bbox": [ + 314, + 350, + 451, + 363 + ], + "type": "text", + "content": "3.3. Local Linear Regression" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "spans": [ + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "text", + "content": "A standard way to alleviate the boundary bias of the NW estimator is by moving from a local constant fit to a local linear fit around each test point. Instead of using the estimate from Eq. (7), local linear regression (LLR) forms the local estimate " + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "inline_equation", + "content": "\\phi (\\mathbf{x}) = \\tilde{\\mathbf{x}}\\mathbf{A}" + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}} = [1\\quad \\mathbf{x}]" + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\in \\mathbb{R}^{(d + 1)c}" + }, + { + "bbox": [ + 313, + 368, + 555, + 440 + ], + "type": "text", + "content": " minimizes the following problem:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 338, + 449, + 555, + 482 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 449, + 555, + 482 + ], + "spans": [ + { + "bbox": [ + 338, + 449, + 555, + 482 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {A}} \\frac {1}{N K} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(d \\left(\\mathbf {x}, \\mathbf {S} _ {i}\\right)\\right) s \\left(\\tilde {\\mathbf {S}} _ {i} \\mathbf {A}, \\mathbf {L} _ {i}\\right) + \\mathcal {R} _ {\\mathrm {c l i p}}, \\tag {9}", + "image_path": "552c7cb7a663d152d8ca7dce2b2660e16a4380b22d9c3a681584c632438646bd.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "text", + "content": "which is a weighted ordinary least square problem around each test point weighted by the kernel values " + }, + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "inline_equation", + "content": "k_{\\beta}(d(\\mathbf{x}, \\mathbf{S}_i))" + }, + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "text", + "content": ". Using the same cost function as for Eq. (8) and using the regularization term " + }, + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\mathrm{clip}} = \\lambda \\| \\tilde{\\mathbf{x}} \\mathbf{A} - f_{\\mathrm{clip}}(\\mathbf{x})\\|_2^2" + }, + { + "bbox": [ + 313, + 489, + 556, + 550 + ], + "type": "text", + "content": ", we derive a closed form solution for Eq. (9) as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 324, + 561, + 555, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 561, + 555, + 609 + ], + "spans": [ + { + "bbox": [ + 324, + 561, + 555, + 609 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {\\phi} (\\mathbf {x}) = \\tilde {\\mathbf {x}} \\mathbf {A} ^ {- 1} \\mathbf {B}, \\\\ w h e r e \\quad \\mathbf {A} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\tilde {\\mathbf {S}} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} \\tilde {\\mathbf {x}}, \\\\ \\text {a n d} \\quad \\mathbf {B} = \\tilde {\\mathbf {S}} ^ {\\top} \\boldsymbol {\\Omega} \\mathbf {L} + \\lambda N K \\tilde {\\mathbf {x}} ^ {\\top} f _ {\\operatorname {c l i p}} (\\mathbf {x}), \\tag {10} \\\\ \\end{array}", + "image_path": "8ecbfe3095b444441fc5b2fd7a02b5b63fdf7c03fd54dc2b0db4c2237d7a879f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "inline_equation", + "content": "NK\\times NK" + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "text", + "content": " matrix with ith diagonal element as " + }, + { + "bbox": [ + 313, + 617, + 554, + 642 + ], + "type": "inline_equation", + "content": "k_{\\beta}(d(\\mathbf{x},\\mathbf{S}_i))" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "content": "This method, that we dub henceforth LLR, boils down to fitting a local linear regression while enforcing the obtained fit to be close to the text predictions locally around the query input sample. While LLR usually improves performance, it is time consuming as one needs to fit a linear regression for each input sample. Furthermore, the parameters of LLR" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25095" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": "are solely estimated locally, which is prone to overfitting in high-dimensional problems [36]. Alternatively, one possible way to eliminate the bias of NW estimator due to the bandwidth selection without significantly increasing the time complexity is by equipping the kernel with a better distance function " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " [36]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 151, + 243, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 151, + 243, + 164 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 243, + 164 + ], + "type": "text", + "content": "3.4. Local methods with a global metric" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 168, + 297, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 168, + 297, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 168, + 297, + 217 + ], + "type": "text", + "content": "While there exists multiple strategies to construct a good metric [36, 56], using the Mahalanobis distance with the covariance matrix estimated from the training data is a simple yet well-performing one [3]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 124, + 224, + 296, + 238 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 224, + 296, + 238 + ], + "spans": [ + { + "bbox": [ + 124, + 224, + 296, + 238 + ], + "type": "interline_equation", + "content": "d (\\mathbf {x}, \\mathbf {S} _ {i}) = \\| \\mathbf {x} - \\mathbf {S} _ {i} \\| _ {\\hat {\\mathbf {A}}}, \\tag {11}", + "image_path": "206cb95512274be874d3afc3e952abd3a4c6e160357317bac8fb00efb06770ed.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 296, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 296, + 366 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 296, + 366 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 247, + 296, + 366 + ], + "type": "inline_equation", + "content": "\\hat{\\Lambda}" + }, + { + "bbox": [ + 55, + 247, + 296, + 366 + ], + "type": "text", + "content": " is the estimated precision matrix from the few-shot samples. This metric effectively incorporates global information and captures the geometry of the space which allows to construct a better kernel function tailored to the downstream task. The classical RBF kernel corresponds to using an isotropic covariance matrix. While still being a local method, adapting the metric to the downstream task allows to incorporate global information about the underlying distribution and improves over Tip-Adapter as shown in Fig. 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 373, + 239, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 239, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 239, + 386 + ], + "type": "text", + "content": "3.5. Proximal Kernel Ridge Regression" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 391, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 296, + 521 + ], + "type": "text", + "content": "As can be seen in Fig. 3, incorporating global information about the task through a global metric effectively outperforms both Tip-Adapter and LLR. However, the choice of the global metric for NW estimator beyond the Mahalanobis distance remains challenging [56], especially in the few-shot setting. Furthermore, despite being equipped with a global metric, the NW estimator remains in essence a local method and still lacks a global regularization. Whilst the use of a global regularization has been recently addressed in training-based methods [50], using a truly global regularization in a training-free manner remains challenging and unexplored." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 522, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 297, + 713 + ], + "type": "text", + "content": "These limitations highlight the necessity for regularization in this adaptation process. The main idea is to balance the need to maintain the expressive capacity of the learned functions while ensuring stability and robustness. To this end we introduce two key design choices: (1) we constrain the hypothesis space of the learned function to a reproducing kernel Hilbert space (RKHS), and (2) we incorporate a proximal regularization term, based on the RKHS norm, to ensure the solution remains close to the base predictor " + }, + { + "bbox": [ + 55, + 522, + 297, + 713 + ], + "type": "inline_equation", + "content": "(f_{\\mathrm{clip}})" + }, + { + "bbox": [ + 55, + 522, + 297, + 713 + ], + "type": "text", + "content": ". The RKHS norm's properties guarantee that minimizing the difference between two functions in this space results in pointwise closeness. Consequently, this proximal term serves as a global regularization that preserves prior knowledge from the zero-shot predictor, resulting in more robust solutions that are less prone to overfitting on the few-shot data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "text", + "content": "Given the multi-output nature of the problem, the employed reproducing kernel " + }, + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\beta}" + }, + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "text", + "content": " is a reproducing kernel for vector valued functions. The main difference is that the kernel is matrix valued. Several instances of multi-output kernels have been proposed in the literature [1, 5], with separable kernels being among the most widely used for learning vector-valued functions due to their simplicity and computational efficiency. These kernels are formulated as a product of a kernel function for the input space alone and a matrix that encodes the interactions among the outputs. Let us consider " + }, + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\beta}:\\mathbb{R}^{D}\\times \\mathbb{R}^{D}\\mapsto \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 313, + 72, + 555, + 215 + ], + "type": "text", + "content": " as a separable kernel of the form:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 371, + 222, + 555, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 222, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 371, + 222, + 555, + 236 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {K} _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right)\\right) _ {j, j ^ {\\prime}} = k _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) \\mathbf {B}, \\tag {12}", + "image_path": "6c8a8aae4320cab86a28200ae579c7023ca653c0b8b684c933e4f28e6650c278.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "text", + "content": " symmetric and positive semi-definite matrix which captures the correlations between the outputs. A simple yet effective choice for " + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 313, + 241, + 555, + 289 + ], + "type": "text", + "content": " is the identity matrix where all outputs are treated as being unrelated." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 289, + 554, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 554, + 313 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 554, + 313 + ], + "type": "text", + "content": "Our goal is to learn a multi-output predictor " + }, + { + "bbox": [ + 313, + 289, + 554, + 313 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 289, + 554, + 313 + ], + "type": "text", + "content": " using the following objective:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 319, + 555, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 319, + 555, + 352 + ], + "spans": [ + { + "bbox": [ + 347, + 319, + 555, + 352 + ], + "type": "interline_equation", + "content": "\\min _ {\\phi \\in \\mathcal {H}} \\sum_ {i = 1} ^ {N K} \\| \\phi (\\mathbf {S} _ {\\mathbf {i}}) - \\mathbf {L} _ {i} \\| _ {2} ^ {2} + \\lambda \\| \\phi - f _ {\\mathrm {c l i p}} \\| _ {\\mathcal {H}} ^ {2}. \\tag {13}", + "image_path": "ef504a17ee79c8d78cdf6766dd148a23d32af43f84ffb517c2e56f53bdb981f3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 357, + 555, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 555, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 555, + 393 + ], + "type": "text", + "content": "By the representative theorem [22, 32], the unique minimizer of problem in Eq. (13) emerges naturally as the solution of a Kernel Ridge Regression (KRR) problem:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 324, + 401, + 443, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 401, + 443, + 434 + ], + "spans": [ + { + "bbox": [ + 324, + 401, + 443, + 434 + ], + "type": "interline_equation", + "content": "\\phi = f _ {\\mathrm {c l i p}} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}},.) \\gamma_ {i},", + "image_path": "6639752cda0fd726b3323f67b1b99ce1c212536f31b0880214a101079cc115ad.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 328, + 436, + 555, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 436, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 328, + 436, + 555, + 460 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\gamma = \\left(\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})\\right) ^ {- 1} \\left(\\mathbf {L} - f _ {\\mathrm {c l i p}} (\\mathbf {S})\\right). \\tag {14}", + "image_path": "72857d5f887734ec0c7d8798a37b732e310c42a97b6aa1f7e89855eb782c408e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "inline_equation", + "content": "(k_{\\beta}(\\mathbf{S},\\mathbf{S}))_{i,j} = k_{\\beta}(\\mathbf{S}_i,\\mathbf{S}_j)" + }, + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "inline_equation", + "content": "\\gamma_{i}\\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 313, + 464, + 555, + 536 + ], + "type": "text", + "content": ". This approach allows to map data to an infinite dimensional space. Furthermore, the regularization term allows the use of a richer model that captures the complex structure of the data while preserving its smoothness, avoiding overfitting on the few-shot data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 543, + 529, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 529, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 529, + 555 + ], + "type": "text", + "content": "3.6. Mercer decomposition of kernel methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 560, + 555, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 555, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 555, + 619 + ], + "type": "text", + "content": "One additional benefit of this perspective on caching methods is memory reduction which allows to overcome the necessity of storing training data. For positive definite kernel, we can leverage Mercer theorem [13] to write the kernel function as follow:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 376, + 625, + 555, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 625, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 376, + 625, + 555, + 640 + ], + "type": "interline_equation", + "content": "k _ {\\beta} \\left(\\mathbf {x}, \\mathbf {x} ^ {\\prime}\\right) = \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {x} ^ {\\top}\\right). \\tag {15}", + "image_path": "dfe0428f38beb997a0a47f3f435526add9db7ed3845a0a7175b86cb8f83314e3.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 326, + 646, + 423, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 646, + 423, + 657 + ], + "spans": [ + { + "bbox": [ + 326, + 646, + 423, + 657 + ], + "type": "text", + "content": "This allows us to write:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 350, + 662, + 555, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 662, + 555, + 711 + ], + "spans": [ + { + "bbox": [ + 350, + 662, + 555, + 711 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\sum_ {i = 1} ^ {N K} k _ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}\\right) \\gamma_ {i} = \\sum_ {i = 1} ^ {N K} \\psi_ {\\beta} (\\mathbf {x}) \\psi_ {\\beta} \\left(\\mathbf {S} _ {\\mathbf {i}}\\right) \\gamma_ {i} (16) \\\\ = \\psi_ {\\beta} (\\mathbf {x}) [ \\boldsymbol {\\Psi} _ {\\beta} ^ {1}, \\dots , \\boldsymbol {\\Psi} _ {\\beta} ^ {N} ]. (17) \\\\ \\end{array}", + "image_path": "dfb92ea9f4ee4249221e6ce05134de222bd96323c26f66f1ea4e93368224d702.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25096" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": "Hence, we compute prototypes per class without the need to store additional samples. However, the feature map " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " may not be available in closed form and may be infinite dimensional. For shift invariant kernels like the Gaussian kernel, we leverage the Bochner's theorem following [42] to write:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 64, + 155, + 284, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 155, + 284, + 169 + ], + "spans": [ + { + "bbox": [ + 64, + 155, + 284, + 169 + ], + "type": "interline_equation", + "content": "k _ {\\beta} (\\mathbf {x}, \\mathbf {x} ^ {\\prime}) = k (\\mathbf {x} - \\mathbf {x} ^ {\\prime}) = \\mathbb {E} _ {\\mathbf {w} \\sim p (\\mathbf {w})} \\left(\\psi_ {\\mathbf {w}} (\\mathbf {x}) \\psi_ {\\mathbf {w}} \\left(\\mathbf {x} ^ {\\prime}\\right) ^ {\\top}\\right),", + "image_path": "3c521e003273a3e163091666cae1d35d96b50f02aa3f664dc1ad7889ffa8ee07.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 155, + 171, + 295, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 155, + 171, + 295, + 183 + ], + "spans": [ + { + "bbox": [ + 155, + 171, + 295, + 183 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 155, + 171, + 295, + 183 + ], + "type": "inline_equation", + "content": "\\psi (\\mathbf{x}) = \\exp (i\\mathbf{x}\\mathbf{w})" + }, + { + "bbox": [ + 155, + 171, + 295, + 183 + ], + "type": "text", + "content": " (18)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "inline_equation", + "content": "p(\\mathbf{w})" + }, + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "text", + "content": " is the Fourier transform of the kernel " + }, + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 192, + 296, + 264 + ], + "type": "text", + "content": ". This formulation allows to approximate the RBF kernel with Random Fourier features (RFF). In practice, to lower the variance of the kernel estimate, and thus keep a good balance between performance and the number of RFFs, we use Orthogonal Fourier Features [59]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 270, + 190, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 190, + 284 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 190, + 284 + ], + "type": "text", + "content": "3.7. Training-based ProKeR" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 288, + 296, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 288, + 296, + 408 + ], + "spans": [ + { + "bbox": [ + 55, + 288, + 296, + 408 + ], + "type": "text", + "content": "In addition to our training-free method, we propose a trained version of ProKeR. The optimization problem in Eq. 13 allows for the use of any base learner and is not limited to the zero-shot CLIP. In this training-based version, instead of using the zero-shot CLIP as the base learner to regularize our method in the RKHS, we iteratively optimize for a regularizer and the obtained solution from ProKeR. Our method consists of training a linear classifier using the same loss " + }, + { + "bbox": [ + 55, + 288, + 296, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CLAP}}" + }, + { + "bbox": [ + 55, + 288, + 296, + 408 + ], + "type": "text", + "content": " proposed in CLAP [50] while solving the linear system of ProKeR at each iteration as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 419, + 162, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 419, + 162, + 437 + ], + "spans": [ + { + "bbox": [ + 67, + 419, + 162, + 437 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {W}} \\mathcal {L} _ {\\mathrm {C L A P}} (\\phi_ {\\mathbf {W}}, \\mathbf {S}, \\mathbf {L}),", + "image_path": "7876786cf5cbb3a80528e67772db990e7cf0612fcd5d6e3f56ffa70529ceda70.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 440, + 266, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 440, + 266, + 472 + ], + "spans": [ + { + "bbox": [ + 85, + 440, + 266, + 472 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\phi_ {\\mathbf {W}} (\\mathbf {x}) = \\mathbf {x} \\mathbf {W} + \\sum_ {i = 1} ^ {N K} k _ {\\beta} (\\mathbf {S} _ {\\mathbf {i}}, \\mathbf {x}) \\gamma_ {i},", + "image_path": "0570ce66a8aebd41574709efb79202d6473cc3fb1e5f5508f970a4393af0d657.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 474, + 296, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 474, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 91, + 474, + 296, + 498 + ], + "type": "interline_equation", + "content": "\\text {a n d} \\quad \\gamma = (\\mathbf {I} + \\frac {1}{\\lambda} k _ {\\beta} (\\mathbf {S}, \\mathbf {S})) ^ {- 1} (\\mathbf {L} - \\mathbf {S W}). \\tag {19}", + "image_path": "118fd50eaac90066df54d967ba0102e723ddfc1b0d1c67cafe02740003764c36.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 503, + 297, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 297, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 297, + 552 + ], + "type": "text", + "content": "By jointly optimizing the base learner and the solution of the Kernel Ridge Regression problem, our method (ProKeR + CLAP) allows to learn a regularizer specific to the few-shot task which takes into account the latter problem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 562, + 137, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 137, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 137, + 575 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 582, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 297, + 714 + ], + "type": "text", + "content": "In this section, we evaluate our method on multiple image classification benchmarks. We compare our results to existing training-free methods, notably Tip-Adapter [62], which is the baseline of our work. For a fair comparison, we use the same text inputs for all reported methods. We also compare to other state-of-the-art conventional methods, such as APE [68], Tip-X [53], GDA [55], CLIP [41] and CALIP [15] which proposes a parameter-free attention mechanism to improve CLIP in a zero-shot manner. We run APE with the same text templates as Tip-Adapter using their official implementation. Finally, we report the average running times" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": "on ImageNet [9] for each method using an NVIDIA RTX A6000 GPU. For completeness, we additionally provide a comparison of our method with existing state-of-the-art training-based methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 128, + 493, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 128, + 493, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 128, + 493, + 140 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Protocol" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 145, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 145, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 145, + 555, + 228 + ], + "type": "text", + "content": "For comprehensive evaluation, we adopt 11 image classification benchmarks: ImageNet [9], Caltech101 [11], DTD [8], EuroSAT [18], FGVCAircraft [31], Flowers102 [35], Food101 [4], OxfordPets [40], StanfordCars [24], SUN397 [57], and UCF101 [51]. For testing the generalization ability of our method, we further test on ImageNet-Sketch [48] and ImageNet-V2 [44]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 229, + 556, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 556, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 556, + 372 + ], + "type": "text", + "content": "For a fair comparison with previous work, we use ResNet-50 for the visual encoder of CLIP unless mentioned otherwise. We follow two settings for our experiments. The first setting, initially introduced by [50] for training-based methods, consists of selecting the best hyperparameters of each method on ImageNet and transfer them to the other datasets and report the average performance. This setting reflects real-life scenarios where a validation set may not be available especially in a few-shot regime. The second setting follows CoOp's benchmark [67] where validation shots are used to select the hyperparameters and evaluate the results on the full test set." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 380, + 492, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 492, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 492, + 392 + ], + "type": "text", + "content": "4.2. Experiment Results and Analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 397, + 535, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 397, + 535, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 397, + 535, + 410 + ], + "type": "text", + "content": "4.2.1. Comparison with alternatives to Tip-Adapter" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 317, + 425, + 553, + 632 + ], + "blocks": [ + { + "bbox": [ + 317, + 425, + 553, + 632 + ], + "lines": [ + { + "bbox": [ + 317, + 425, + 553, + 632 + ], + "spans": [ + { + "bbox": [ + 317, + 425, + 553, + 632 + ], + "type": "image", + "image_path": "15a885ba4228ca9f7ba0776fc60bd0a0d2f1465cfe8a909eae575bc00a2f8be8.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 642, + 555, + 663 + ], + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 663 + ], + "type": "text", + "content": "Figure 3. Average performance for different methods on 11 image classification datasets." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "type": "text", + "content": "We compare in Fig. 3 our result when improving Tip-Adapter using kernel based approaches across 11 datasets. Our reformulation in Eq. (8) outperforms Tip-Adapter for 8" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25097" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 239 + ], + "type": "text", + "content": "and 16 shots and maintains the same level of performance in the lower shot setting. We argue that this is due to the fact that our reformulation is agnostic to the training size. Debiasing the NW estimator using our regularized LLR in Eq. (9) significantly improves the performance as a first order polynomial fit compared to the constant fit of the NW estimator. Additionally, the use of the Mahalanobis distance as global metric for NW estimator further increases the performance especially with more shots as the estimation of the precision matrix from the training set becomes more accurate. Furthermore, by introducing a proximal regularization in the RKHS, our method ProKeR significantly outperforms Tip-Adapter as well as all the proposed alternatives especially with more shots." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 251, + 253, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 253, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 253, + 264 + ], + "type": "text", + "content": "4.2.2. Comparison with training-free methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 267, + 296, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 267, + 296, + 364 + ], + "spans": [ + { + "bbox": [ + 55, + 267, + 296, + 364 + ], + "type": "text", + "content": "We report in Tab. 1 the performance of different methods in a realistic and practical validation-free experimental setting. First, our method ProKeR outperforms existing alternatives on average by a large margin (2.04% compared to the second best), especially in the low shot regimes (1, 2 and 4) and is only outperformed in the 8 shot setting. Furthermore, when using a Polynomial kernel (as defined in Tab. 5), our method sets a new standard in the 16 shots regime." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 57, + 376, + 294, + 436 + ], + "blocks": [ + { + "bbox": [ + 57, + 376, + 294, + 436 + ], + "lines": [ + { + "bbox": [ + 57, + 376, + 294, + 436 + ], + "spans": [ + { + "bbox": [ + 57, + 376, + 294, + 436 + ], + "type": "table", + "html": "
Shots124816Average
Tip-Adapter [62]58.8660.3361.4963.1564.6161.68
APE [68]60.0962.3365.3667.9569.8965.12
GDA [55]57.4963.4366.6872.4675.1267.03
ProKeR (Polynomial) (ours)62.3965.5968.0571.8175.8268.72
ProKeR (RBF) (ours)63.1366.3168.6472.1575.1269.07
", + "image_path": "2cb4f2ee1a73cecd550a7c44c62b021a5ca4e4e37c68ba5ed18962636a5b5139.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 483, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 296, + 567 + ], + "type": "text", + "content": "In the CoOp's benchmark where hyperparameters are tailored for each dataset, our method ProKeR surpasses existing training-free methods as shown in Tab. 2. These superior results fully validate the significance of using the global regularization in the RKHS. However, as noted by [50], this setting may not be practical since the hyperparameters are tuned on the test set." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 57, + 578, + 294, + 666 + ], + "blocks": [ + { + "bbox": [ + 55, + 444, + 295, + 468 + ], + "lines": [ + { + "bbox": [ + 55, + 444, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 295, + 468 + ], + "type": "text", + "content": "Table 1. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 578, + 294, + 666 + ], + "lines": [ + { + "bbox": [ + 57, + 578, + 294, + 666 + ], + "spans": [ + { + "bbox": [ + 57, + 578, + 294, + 666 + ], + "type": "table", + "html": "
Shots124816Average
GDA [55]62.1966.1969.7773.3076.0469.49
Tip-Adapter [62]62.8364.8466.5068.6470.0266.56
Tip-Adapter [62] with RFF62.7764.5866.2968.1569.6066.27
APE [68]64.4366.4868.6670.7572.8168.62
APE [68] with RFF64.1666.1168.7670.3772.0268.28
ProKeR (ours)64.0167.3170.4273.8576.7570.46
ProKeR with RFF (ours)64.0167.1270.2873.6176.4470.29
", + "image_path": "f174b8fa6ab717abb788c0e473225b63d19c7ad391d7694a98b6c4525aee8b0c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 437, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 437, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 437, + 84 + ], + "type": "text", + "content": "4.2.3. Generalization Ability" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 87, + 554, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 87, + 554, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 87, + 554, + 159 + ], + "type": "text", + "content": "In Tab. 3, we test the generalization ability of the different methods on out-of-distribution datasets. Notably, the shots are drawn from ImageNet and the test set is drawn from either ImageNet-V2 or ImageNet-Sketch. ProKeR achieves state-of-the-art performance for training-free methods on both in-distribution and out-of-distribution datasets." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 315, + 167, + 553, + 249 + ], + "blocks": [ + { + "bbox": [ + 55, + 673, + 295, + 696 + ], + "lines": [ + { + "bbox": [ + 55, + 673, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 295, + 696 + ], + "type": "text", + "content": "Table 2. Performance on 11 different classification datasets (CoOp's benchmark)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 167, + 553, + 249 + ], + "lines": [ + { + "bbox": [ + 315, + 167, + 553, + 249 + ], + "spans": [ + { + "bbox": [ + 315, + 167, + 553, + 249 + ], + "type": "table", + "html": "
DatasetsSourceTarget
ImageNet [9]-V2 [44]-Sketch [48]-A [20]-R [19]Average
Zero-Shot CLIP [41]60.3353.2735.4423.6160.4246.61
Tip-Adapter [62]61.4354.1335.7123.6360.4147.06
APE [68]62.6054.9335.4122.9559.9047.15
GDA [55]63.8255.3534.3219.5355.5645.71
ProKeR (Polynomial) (Ours)64.6656.1136.0823.2760.5548.13
ProKeR (Ours)64.4556.0236.0823.3760.5948.10
", + "image_path": "8e4857f61c817e9ebd34477c2bde8459a8b8239feffe75e8996c9517f1c7a615.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 300, + 520, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 520, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 520, + 312 + ], + "type": "text", + "content": "4.2.4. Comparison with training-based methods" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 315, + 556, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 556, + 398 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 556, + 398 + ], + "type": "text", + "content": "We report in Tab. 4 the comparison of our method with training-based methods. While being training-free, our method ProKeR outperforms existing training-based methods on 8 out of 11 datasets. This emphasizes the effectiveness of incorporating a global regularization using the zero-shot predictor in a reproducing kernel Hilbert space (RKHS)." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 317, + 408, + 553, + 488 + ], + "blocks": [ + { + "bbox": [ + 313, + 256, + 555, + 277 + ], + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 277 + ], + "type": "text", + "content": "Table 3. Robustness to distribution shift of different methods for 16 shots." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 408, + 553, + 488 + ], + "lines": [ + { + "bbox": [ + 317, + 408, + 553, + 488 + ], + "spans": [ + { + "bbox": [ + 317, + 408, + 553, + 488 + ], + "type": "table", + "html": "
Shots124816Average
Tip-Adapter-F [62]60.2962.2665.3268.3571.4065.52
CrossModalLP [29]62.2464.4866.6770.3673.6567.48
TaskRes [60]61.4465.2668.3571.6674.4268.22
APE-T [68]62.7263.9366.5768.9672.1566.86
CLAP [50]62.7966.0769.1372.0874.5768.92
ProKeR (ours)63.1366.3168.6472.1575.1269.07
ProKeR + CLAP (ours)64.1667.6070.9774.1276.8470.73
", + "image_path": "65e7c382036ce13878b3a9cd5a019cc7bd9d8fb9a362f4294e140c55a9dd2c82.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 496, + 555, + 519 + ], + "lines": [ + { + "bbox": [ + 313, + 496, + 555, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 555, + 519 + ], + "type": "text", + "content": "Table 4. Average performance on 11 classification datasets for different shots. Hyperparameters are transferred from ImageNet." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 532, + 556, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 556, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 556, + 616 + ], + "type": "text", + "content": "The jointly trained version of ProKeR with CLAP achieves significantly better results compared to existing training-based methods and increases the average performance of the ProKeR by " + }, + { + "bbox": [ + 313, + 532, + 556, + 616 + ], + "type": "inline_equation", + "content": "1.73\\%" + }, + { + "bbox": [ + 313, + 532, + 556, + 616 + ], + "type": "text", + "content": " accuracy. This shows the importance of using a strong base learner. Furthermore, the joint training allows to leverage both the expressive power of the RKHS and the flexibility of the linear classifier." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 624, + 413, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 413, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 413, + 635 + ], + "type": "text", + "content": "4.3. Kernel ablation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": "So far, we have performed our analysis using the RBF kernel, a commonly used kernel in the kernel literature and in cache-based methods. Nevertheless, through the lens of our kernel perspective on cache-based methods, different kernels can be considered ranging from a linear kernels to more elaborate ones. We perform in Tab. 5 an ablation study where" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25098" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": "we discuss different kernel choices. Besides RBF, we consider three commonly used kernels: the Linear kernel, the Epanechnikov kernel and the Polynomial kernel. The RBF kernel outperforms the linear, Epanechnikov and the polynomial kernels. Using the RBF kernel allows us to project data into an infinite dimensional space which captures more complex relationships." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 166, + 287, + 243 + ], + "blocks": [ + { + "bbox": [ + 65, + 166, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 65, + 166, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 65, + 166, + 287, + 243 + ], + "type": "table", + "html": "
Kernelk(x, x')Accuracy
Linearxx'^T72.34
Epanechnikov3/4 (1 - ||x - y'||2)74.43
Polynomial(xy'^T)^276.61
RBFexp(-β/2||(x - y'||2))76.75
", + "image_path": "decabc604ebf22445c9d60be75ede839deef4d5519c442f7118fdc7bc906f645.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 295, + 226, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 226, + 307 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 226, + 307 + ], + "type": "text", + "content": "4.4. Ablation on CLIP architectures" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 312, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 296, + 384 + ], + "type": "text", + "content": "In Tab. 6, we report the performance of training-free methods using different backbones on ImageNet for 16 shots. Our method consistently outperforms the alternatives across all architectures. While all methods improve with more capable architectures, the gap between our method and the second best one (APE) remains stable." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 57, + 394, + 293, + 449 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 295, + 273 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 295, + 273 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 295, + 273 + ], + "type": "text", + "content": "Table 5. Kernel Ablation for 16 shots on 11 datasets on CoOp's benchmark." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 394, + 293, + 449 + ], + "lines": [ + { + "bbox": [ + 57, + 394, + 293, + 449 + ], + "spans": [ + { + "bbox": [ + 57, + 394, + 293, + 449 + ], + "type": "table", + "html": "
ModelsResNet-50ResNet-101ViT-B/32ViT-B/16
Zero-shot CLIP [41]60.3362.5363.8068.73
Tip-Adapter [62]61.4364.0865.1870.25
APE [68]62.6065.6166.3171.37
ProKeR (Ours)64.4567.3968.1273.25
", + "image_path": "0c69d7efcbc97123f10a81bae3a2e4a0b36177caa531c27be3b42edee14fb723.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 502, + 295, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 295, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 295, + 526 + ], + "type": "text", + "content": "4.5. Adressing memory limitations of cache-based methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 532, + 296, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 296, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 296, + 616 + ], + "type": "text", + "content": "In Tab. 2, we report the performance when using Random Fourier features to alleviate the memory limitations of cache-based methods. Using RFFs, we are able to drastically reduce the memory footprint of caching methods while maintaining almost the same performance across different shots. Our method when combined with RFFs still maintains state-of-the-art performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 624, + 274, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 274, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 274, + 637 + ], + "type": "text", + "content": "4.6. Running times and memory requirements" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "Next, we report running time (train and test) for different methods as well as the memory requirements for each method (Tab.7). Our method is on par with Tip-Adapter and GDA in term of speed. Note that APE runs a feature selection step which takes additional time to run, making it slower than the previously mentioned competition. On the" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "type": "text", + "content": "other hand, training-based methods are orders of magnitude slower. Regarding the memory complexity, ProKeR stores the training shots similarly to APE and Tip-Adapter. However, when using Random Fourier features, our method does need to store additional training samples." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 318, + 145, + 553, + 250 + ], + "blocks": [ + { + "bbox": [ + 55, + 457, + 295, + 479 + ], + "lines": [ + { + "bbox": [ + 55, + 457, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 457, + 295, + 479 + ], + "type": "text", + "content": "Table 6. Average performance on 16-shot ImageNet with different backbones." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 145, + 553, + 250 + ], + "lines": [ + { + "bbox": [ + 318, + 145, + 553, + 250 + ], + "spans": [ + { + "bbox": [ + 318, + 145, + 553, + 250 + ], + "type": "table", + "html": "
MethodsOverall TimeTrainMemory requirements
CoOp[67]~ 17h✓N × T × D
Clip-Adapter[12]~ 40min✓(2N + D1) × D
CrossModal-LP[29]~ 3min✓N × D
Standard LP[41]~ 3min✓N × D
Tip-adapter-F[62]~ 7min✓N × K + N × (K + 1) × D
Tip-Adapter[62]2.1s✗N × K + N × (K + 1) × D
APE [68]24.6s✗N × K + N × (K + 1) × D
GDA [55]1.6 s✗2 × N × D
ProKeR (Ours)4.7s✗N × K + N × (K + 1) × D
ProKeR with RFF (Ours)4.2s✗N × (D + R)
", + "image_path": "f481ad0a60050538f3e90f9a527eb97d45eb61e46881dae89a5b480ee597625e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "lines": [ + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "text", + "content": "Table 7. Running times on ImageNet for 16 shots. All experiments are performed on a RTX A6000 GPU. For each method we report the memory requirements. " + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "text", + "content": " is the inner dimension of the MLP used in Clip-Adapter [12] and " + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "text", + "content": " is the number of text tokens in CoOp [67]. " + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 258, + 555, + 324 + ], + "type": "text", + "content": " is the number of Fourier features used to approximate the RBF kernel." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 354, + 471, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 471, + 367 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 471, + 367 + ], + "type": "text", + "content": "5. Limitations & Future Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 376, + 556, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 556, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 556, + 544 + ], + "type": "text", + "content": "Based on our analysis, caching methods can be understood as local non-parametric regressors. These methods lack a global regularization from zero-shot CLIP which limits their generalization ability when performing adaptation. On the other hand, global methods may lack the flexibility when dealing with complex data. As part of future work, we will explore how both local and global methods can be combined to benefit from the best of both worlds. Furthermore, our formulation of caching methods as a Nadaraya-Watson estimator offers multiple options for the choice the regularization term, the metric used in the kernel, as well as the bandwidth selection [39]. These choices constitute different ways to reduce the bias-variance trade-off inherent to these methods [16]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 559, + 388, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 388, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 388, + 572 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": "In this paper, we proposed a new theoretical understanding of Tip-Adapter, a prominent training-free caching-based approach for LVM few-shot adaptation. Our analysis suggests that Tip-Adapter is a local nonparametric regression that has well-known bias limitations. We proposed multiple angles of improvement that have shown significant increase over the Tip-Adapter baseline. Subsequently, we demonstrate that incorporating global information in a training-free method can be achieved using a global regularization in a reproducing kernel Hilbert space (RKHS), which conclusively further improves the state-of-the-art for training-free methods." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25099" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 124 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 124 + ], + "type": "text", + "content": "[1] Maurizio A Alvarez, Lorenzo Rosasco, Neil D Lawrence, et al. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2605-2615, 2023. 2, 3, 6, 7, 8" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25102" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_content_list.json b/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6e0543c33a4bfc86698c95ed323a09829d3b61 --- /dev/null +++ b/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_content_list.json @@ -0,0 +1,1790 @@ +[ + { + "type": "text", + "text": "ProReflow: Progressive Reflow with Decomposed Velocity", + "text_level": 1, + "bbox": [ + 207, + 130, + 789, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lei Ke $^{1}$ Haohang Xu $^{3}$ Xuefei Ning $^{1}$ Yu Li $^{1}$ \nJiajun Li $^{4}$ Haoling Li $^{1}$ Yuxuan Lin $^{1}$ Dongsheng Jiang $^{3}$ Yujiu Yang $^{1\\dagger}$ Linfeng Zhang $^{2\\dagger}$ $^{1}$ Tsinghua University $^{2}$ Shanghai Jiao Tong University \nuawei Inc. $^{4}$ University of Electronic Science and Technology of", + "bbox": [ + 233, + 179, + 733, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "k123@mails.tsinghua.edu.cn, yang.yujiu@sz.tsinghua.edu.cn, zhanglinfeng@sjtu.edu.cn", + "bbox": [ + 178, + 273, + 815, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 321, + 326, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, rectified flow aims to rectify the diffusion process of diffusion models into a straight line for few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of reflow is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned $\\nu$ -prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, $FID = 10.05$ ). Our codes will be released at Github.", + "bbox": [ + 88, + 353, + 485, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 670, + 220, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have achieved significant breakthroughs in image and video generation, boosting various downstream applications such as text-to-image generation [27, 32] and image editing [2, 3, 10]. However, compared with traditional generation models such as GANs [9], the sampling process of diffusion models is formulated to include multiple timesteps, which severely harms its computation efficiency, hindering its application in edge devices and real-time applications. To solve this problem, abundant methods have been proposed to reduce the number of sampling steps such as step distillation [24, 34], consistency models [23, 38] and flow matching [16, 17].", + "bbox": [ + 89, + 695, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57188b1f7afcfdd67069ad8bd01fc7d5da751dab21d630de4511cefc082022b4.jpg", + "image_caption": [ + "(a) Velocity differences across timesteps in diffusion model." + ], + "image_footnote": [], + "bbox": [ + 540, + 323, + 705, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/91b5267d3e030913dd5e387d49662107209451281c8d7892165944db8405f30c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 714, + 321, + 893, + 445 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f41952a6a6a173f887293faac108717d152212902c98df343f3fc2c7bb3e3a9d.jpg", + "image_caption": [ + "(b) Flow model's performance degrades with increased noise.", + "Figure 1. (a) L2 distance and Cosine similarity across velocities at different timesteps, the velocity discrepancy between timesteps increases with their distance in timesteps. (b) The consistently larger FID degradation under directional noise demonstrates that velocity direction is more critical for generation quality." + ], + "image_footnote": [], + "bbox": [ + 524, + 469, + 893, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among them, flow matching has gained popularity due to its simplicity and effectiveness. By re-flowing the pretrained diffusion models into a line, few steps and even 1-step generation can be achieved with tolerant loss in generation quality. The training process of reflow usually contains two steps. Firstly, the pretrained diffusion model generates abundant (noise, image) pairs. Then, the diffusion model is trained to make the velocity at different timesteps to be identical, indicating that the trajectory is rectified. However, in this paper, we suggest that such a training strategy has not fully unleashed the potential of rectified flow and introduced two training techniques referred to as progressive reflow and aligned $\\nu$ -prediction to further improve it.", + "bbox": [ + 511, + 704, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author.", + "bbox": [ + 114, + 887, + 241, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28029", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Progressive Reflow: Traditional Reflow usually starts from a pretrained diffusion model and directly trains it to have a consistent prediction of velocity in all timesteps, which is theoretically correct but introduces difficulty in the optimization process. As shown in Figure 1 (a), the pretrained diffusion model has significantly different velocities at different timesteps, and directly eliminating these differences raises challenges in the training process.", + "bbox": [ + 89, + 90, + 480, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fortunately, Figure 1 (a) also shows that the pretrained diffusion model exhibits similar velocity in the adjacent timesteps, which provides the possibility to first reflow the model in a local window, and then reflow it in the whole training process. Such a progressive reflow pipeline allows the model to first learn to solve an easy problem and then extend to a difficult problem, which implies curriculum learning in generative models and thus facilitates the training process. Based on this observation, we propose progressive reflow, which firstly divides the whole diffusion process into $N$ windows, and then progressive reflow $N$ windows into $N/2$ , $N/4$ , $N/2$ , $N/8$ until very few and even one window.", + "bbox": [ + 89, + 220, + 480, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Aligned V-Prediction: Flow matching aims to match the velocity in different timesteps to achieve the target that the whole diffusion process is a straight line. However, we suggest that such a velocity matching is not optimal for the target of a \"straight line\" as the velocity can be further decomposed into its direction and magnitude, where the direction is more crucial for straightness. In other words, matching the direction of the velocity should have a higher priority than matching the magnitude, which has been ignored in previous works. Based on this observation, we propose to modify the original training loss of flow matching by introducing direction matching to solve this problem.", + "bbox": [ + 89, + 410, + 480, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our experiments have validated the effectiveness of the two improved training techniques. For instance, on MSCOCO-2017, 10.94 and 21.73 FID reduction can be observed with our ProReflow-II compared to rectified flow (2-ReFlow [18]) at 4 steps and 2 steps respectively, demonstrating improvements in generation quality", + "bbox": [ + 89, + 599, + 480, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows.", + "bbox": [ + 109, + 700, + 410, + 714 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose progressive reflow, which progressive reflow the diffusion model in local timesteps until the whole diffusion process. Progressive reflow implies the curriculum learning in flow matching and facilitates model training.", + "- Based on the observation that the direction of velocity is more crucial than the magnitude for straightness, we introduce velocity direction matching as an additional target for flow matching to facilitate model training.", + "- Extensive experiments demonstrate that both components are effective individually, and their combination achieves state-of-the-art performance with only 4 sampling steps." + ], + "bbox": [ + 89, + 734, + 478, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 89, + 653, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Text-to-Image Generation", + "text_level": 1, + "bbox": [ + 513, + 114, + 748, + 130 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models(DMs) learn the mapping from noise to images by fitting marginal probability distributions at each timestep [8, 37]. It works well because the forward diffusion process, which progressively adds noise to images, maintains the same marginal distributions as the sampling process [22]. Combined with some technologies like classifier-free guidance and text encoder [7, 26, 33], DMs have surpassed GANs [4, 31] and VAEs [12, 29] not only in generation quality but also in training stability. Besides applied in pixel space, DMs can be effectively applied in latent space as well, which significantly reduces computational complexity [32]. Despite achieving impressive generation quality, the iterative nature of DMs impacts its generation efficiency. Consequently, accelerating inference of diffusion models has emerged as an avtive research topic.", + "bbox": [ + 511, + 137, + 903, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Efficient Diffusion", + "text_level": 1, + "bbox": [ + 513, + 375, + 689, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing approaches for accelerating DMs can be predominantly classified into two categories: efficient diffusion samplers and step distillation [45].", + "bbox": [ + 511, + 397, + 903, + 443 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The former category incorporates differential equation solvers into inference without requiring additional training. DDIM [36] enables step skipping in the reverse process by introducing a non-Markovian sampling strategy. DPM-Solver [21] reformulates the reverse diffusion process into an ODE system and solves it with high-order numerical methods, achieving superior sampling efficiency. Sampler-based methods enable diffusion models to maintain satisfactory generation quality with 20 steps; however, performance deteriorates significantly when further reducing the step count (such as below 10).", + "bbox": [ + 511, + 443, + 903, + 608 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second category methods enhance few-step inference performance through another step distillation process. Progressive Distillation(PD) [34] adopts a staged approach, iteratively halving the student model's sampling steps. Adversarial Diffusion Distillation(ADD) [35] leverages adversarial training for improved supervision, while Consistency Distillation (CD) [38] enforces output convergence toward the target image across the sampling trajectory.", + "bbox": [ + 511, + 609, + 903, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Rectified Flow", + "text_level": 1, + "bbox": [ + 513, + 741, + 660, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Flow matching has emerged as a kind of advanced diffusion model [16, 17]. It reformulates the forward process as a linear interpolation between noise and images, thereby proposing to predict a consistent velocity $v$ across the entire sampling trajectory. Thus, the sampling process is simplified to a temporal integration of the velocity field $v$ .", + "bbox": [ + 511, + 763, + 903, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Similarly, ReFlow was proposed as a technique applying flow matching to pretrained diffusion models, enabling the adaptation of existing architectures without retraining from", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28030", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c1922ae9a0c28c05c01b41aa8188bf7634b207da617a4a740e51cbf17d09c221.jpg", + "image_caption": [ + "(a) Diffusion Model" + ], + "image_footnote": [], + "bbox": [ + 112, + 85, + 277, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/65ebad54b2ffd369364dc27a601ab7ad3b461528aebd10d750e20573bd9c9fb5.jpg", + "image_caption": [ + "(b) Consistency Model" + ], + "image_footnote": [], + "bbox": [ + 315, + 87, + 480, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/32c04b8c3714608d1c35870ca28a98c5983ce41065309dace7384826dea09c5d.jpg", + "image_caption": [ + "(c) Rectified Flow" + ], + "image_footnote": [], + "bbox": [ + 519, + 87, + 684, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/357ac8930d7b9b812c668f22b837df2b5be09b87cec856db150a9c997bd82ae1.jpg", + "image_caption": [ + "(d) Piecewise ReFlow" + ], + "image_footnote": [], + "bbox": [ + 722, + 87, + 885, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/42fe5ffd883a90f4ab4be602f5a74a5ea6d8d299270e26dcb7f61e6dd7e90fbf.jpg", + "image_caption": [ + "(e) Progressive Reflow: windows num 4-2-1" + ], + "image_footnote": [], + "bbox": [ + 109, + 210, + 274, + 314 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e1cd8d087c90f967fab4cf831a847a18969c2327a96a7e45bedcee6e6182a759.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 241, + 316, + 268 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b82debd4ea1552aea74eb8d9d6c01c749e7c2ffeebb3f44c9fd0b3e6200d7afe.jpg", + "image_caption": [ + "sample trajectory" + ], + "image_footnote": [], + "bbox": [ + 318, + 212, + 519, + 313 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/82f97e2f8d2033c5ce9e33f1c0f6f1b54fba238f7d7c697ec6dcc4c3c0a20b56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 212, + 681, + 313 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c4fde4337de53cbdda273a87fb034cc479e7e1f9bebff87c28e2bd4174777173.jpg", + "image_caption": [ + "(f) Direction Alignment" + ], + "image_footnote": [], + "bbox": [ + 717, + 210, + 885, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9155448c15b635ece3ec0e95421e4f190eb4194390a88aa08c69632c41da14ef.jpg", + "image_caption": [ + "original trajectory" + ], + "image_footnote": [], + "bbox": [ + 112, + 335, + 189, + 347 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/314e0cd06abe2dbd051ab6c523cc1711aed4d395ad41c24e274ac0aeee88222c.jpg", + "image_caption": [ + "Figure 2. Conceptual illustration of different methods. (a)-(e) compare training objectives and sampling trajectories across different methods. Arrows show optimization targets, and red dashed lines represent actual sampling trajectories, which are curved due to the optimization not achieving the theoretical optimum. (e) shows our progressive reflow method achieves better approximation. (f) presents how our proposed aligned v-prediction works between timesteps $[t, t + 1]$ , it reduces prediction deviation with velocity direction correction." + ], + "image_footnote": [], + "bbox": [ + 303, + 338, + 383, + 348 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f4ff1e156a8e63069d7297e34a2c5f3e3023548aa177d966d28ee1fd52013d80.jpg", + "image_caption": [ + "optimation goal" + ], + "image_footnote": [], + "bbox": [ + 504, + 338, + 576, + 348 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/53d422977a58b690b46f23f008e94fc4e95cfa030cb087615b0c70a1479f869c.jpg", + "image_caption": [ + "optimization goal (ours)" + ], + "image_footnote": [], + "bbox": [ + 681, + 337, + 753, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "scratch [17]. InstaFlow [18] first extended ReFlow to large-scale text-to-image models through consecutive ReFlow to straighten the ODE trajectory, followed by distillation to achieve single-step sampling. Subsequently, some works explored improving ReFlow's effectiveness or simplifying its training[13, 14, 42, 43]. While ReFlow showed promise for single-step generation, its few-step sampling performance lagged behind state-of-the-art methods [30, 34, 39]. To address this limitation, PeRFlow [44] proposed trajectory partitioning into time windows, achieving competitive few-step sampling through localized straightening within each temporal segment.", + "bbox": [ + 88, + 450, + 483, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Privileged Information in Distillation", + "text_level": 1, + "bbox": [ + 89, + 647, + 410, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although knowledge distillation has been proven effective as a model compression technique and further extended successfully to diffusion model acceleration, the theoretical explanation for its efficacy has remained elusive. How 'dark knowledge' is effectively captured from teacher models and utilized to guide student learning remains a fundamental theoretical question [6].", + "bbox": [ + 89, + 671, + 482, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lopez-Paz et al. [19] presented a unified theoretical framework that connects distillation with privileged information, establishing a generalized framework for understanding machine-to-machine knowledge transfer. Viewing distillation as a transfer of privileged information, TAKD [25] showed that an assistant model of intermediate capacity could more effectively mediate the knowledge flow between teacher and student models.", + "bbox": [ + 89, + 779, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 513, + 449, + 611, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present ProReflow, a more robust flow model training method. Our approach is motivated by the observation that training efficient few-step flow models faces two main challenges: (1) the significant trajectory approximation gap between teacher and student models, and (2) the difficulty in achieving accurate velocity prediction across large time intervals. To address these challenges, we propose progressive reflow for stable optimization of sample trajectory and aligned v-prediction for achieving precise velocity prediction, respectively, shown in Fig. 2.", + "bbox": [ + 511, + 474, + 906, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Temporal Segmentation for ReFlow", + "text_level": 1, + "bbox": [ + 511, + 635, + 823, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rectified Flow ReFlow aims to achieve temporally consistent velocity predictions across all timesteps. Given initial Gaussian distribution $\\pi_0$ and target image distribution $\\pi_1$ , where $X_1 \\sim \\pi_1$ and $X_0 \\sim \\pi_0$ . Reflow defines a linear process from $\\pi_0$ to $\\pi_1$ , where the corresponding sampling process follows the ODE:", + "bbox": [ + 511, + 657, + 905, + 748 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd X _ {t} = v \\left(X _ {t}, t\\right) d t, \\quad t \\in [ 0, 1 ], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 758, + 903, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, it formulates a least-squares optimization problem to ensure the predictions consistency:", + "bbox": [ + 511, + 786, + 906, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\int_ {0} ^ {1} \\mathbb {E} [ \\| X _ {1} - X _ {0} - v _ {\\theta} (X _ {t}, t) \\| ^ {2} ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 825, + 903, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $X_{t} = tX_{1} + (1 - t)X_{0}$ .", + "bbox": [ + 511, + 869, + 720, + 886 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28031", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/565469283a4a3a8ce982993175ded6899658c0c2eceecf05324112c060eb11d9.jpg", + "image_caption": [ + "Figure 3. Performance of our models under different factors of classifier-free guidance (CFG) on COCO-2017. CFG scale ranges from 2 to 7. I and II stands for ProReflow-I with 4 steps and ProReflow-II with 2 steps, respectively." + ], + "image_footnote": [], + "bbox": [ + 140, + 99, + 428, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Piecewise ReFlow Aimed at improving the few-step generation, PeRFlow divides the sampling trajectory into multiple time windows, defined by endpoints $1 = t_{K} > \\dots > t_{k} > t_{k - 1} > \\dots > t_{0} = 0$ . Within each time window $[t_k, t_{k - 1})$ formed by adjacent endpoints, PeRFlow assumes a linear process to straighten the trajectory, thus eq.(2) can be reformulated as:", + "bbox": [ + 89, + 330, + 483, + 436 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\sum_ {k = 1} ^ {K} \\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\left[ \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 443, + 480, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{t} = \\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}$ . Finally, PeRFlow results in a piecewise linear trajectory composed of multiple segments.", + "bbox": [ + 89, + 496, + 482, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Progressive ReFlow", + "text_level": 1, + "bbox": [ + 89, + 551, + 277, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "PeRFlow originally sets the number of time windows to 4. Despite achieving improvement in few-step inference, PeRFlow faces a significant optimization challenge: it attempts to approximate the teacher model's irregular trajectory using four linear intervals within a single training stage.", + "bbox": [ + 89, + 574, + 482, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a multi-stage progressive training scheme to tackle this challenge. Rather than directly mapping the original trajectory to four time windows, our method first obtains an eight-window approximation from the original trajectory, and subsequently apply Cross-windows ReFlow to refine this eight-window representation into the target four-window configuration.", + "bbox": [ + 89, + 651, + 482, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-windows ReFlow Consider three consecutive time points $t_{k-1}, t_k, t_{k+1}$ . The optimization objectives in first training stage can be formulated as:", + "bbox": [ + 89, + 756, + 483, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\theta} \\left(\\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t + \\right. \\\\ \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k}} - z _ {t _ {k + 1}}}{t _ {k} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\Bigg), \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 809, + 480, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7a18179b322256a4976e13096526107d177f46629151ec9b90fa760336dd0672.jpg", + "image_caption": [ + "Figure 4. FID on COCO-30K. The yellow curve shows results trained with 4 windows and evaluated using 4 inference steps, while the blue curve represents the model trained with 8 windows and evaluated using 8 inference steps. Both configurations are compared against their baselines where $\\alpha = 0$ (MSE loss only). Each model is trained for 10,000 iterations with batch size 32." + ], + "image_footnote": [], + "bbox": [ + 571, + 112, + 846, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{t} = \\left\\{ \\begin{array}{ll}\\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}}, & t\\in [t_{k - 1},t_{k})\\\\ \\beta_{t}z_{t_{k + 1}} + (1 - \\beta_{t})z_{t_{k}}, & t\\in [t_{k},t_{k + 1}) \\end{array} \\right.$ with $\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}$ and $\\beta_{t} = \\frac{t - t_{k}}{t_{k + 1} - t_{k}}$ . In adjacent time windows, trajectories evolve from $z_{t_{k - 1}}$ to $z_{t_k}$ in $[t_{k - 1},t_k]$ , and from $z_{t_k}$ to $z_{t_{k + 1}}$ in $[t_k,t_{k + 1}]$ .", + "bbox": [ + 511, + 329, + 903, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-windows ReFlow aligns the optimization direction by guiding trajectories in both intervals to progress from $z_{t_{k-1}}$ towards $z_{t_{k+1}}$ , thus eq.(4) can be reformulated as:", + "bbox": [ + 511, + 422, + 903, + 468 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k - 1}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k + 1}}}{t _ {k - 1} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 491, + 903, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{t} = \\alpha_{t}z_{t_{k + 1}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k + 1} - t_{k - 1}}.$", + "bbox": [ + 513, + 537, + 874, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theoretical Explanation Based on the theoretical framework of knowledge distillation [19], we can explain the effectiveness of Progressive ReFlow. Consider three key functions: the teacher function $f_{t} \\in \\mathcal{F}_{t}$ representing the original diffusion trajectory, an intermediate function $f_{a} \\in \\mathcal{F}_{a}$ for the 8-segment approximation, and the student function $f_{s} \\in \\mathcal{F}_{s}$ for the target 4-segment representation. According to the VC theory [41], when the student learns directly from the teacher, the learning rate is bounded by:", + "bbox": [ + 511, + 561, + 906, + 699 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {t}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {l}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 718, + 903, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta \\in [\\frac{1}{2}, 1]$ denotes the learning rate associated with task difficulty, $\\varepsilon_{l}$ represents the approximation error, $\\mathcal{R}$ represents the error, $\\mathcal{O}(\\cdot)$ and $\\epsilon$ represent the estimation error and approximation error, respectively.. The challenge lies in the significant capacity gap between the complex trajectory and the 4-segment approximation, resulting in a small $\\beta$ that indicates difficult learning.", + "bbox": [ + 511, + 773, + 906, + 880 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Progressive ReFlow decomposes this challenging pro", + "bbox": [ + 531, + 885, + 903, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28032", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cess into two stages:", + "bbox": [ + 89, + 92, + 230, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {S t a g e} 1: \\mathcal {R} (f _ {a}) - \\mathcal {R} (f _ {t}) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}}\\right) + \\varepsilon_ {a t}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 114, + 483, + 148 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {S t a g e} 2: \\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {a}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {s a}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 151, + 483, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The effectiveness is theoretically guaranteed when:", + "bbox": [ + 89, + 194, + 429, + 209 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {a t} + \\varepsilon_ {s a} \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {s}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 218, + 483, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "this inequality is satisfied in practice due to two key principles: (1) 8-segment allows for better fitting of the teacher's complex sampling trajectory, leading to smaller combined approximation error $(\\varepsilon_{at} + \\varepsilon_{sa} < \\varepsilon_l)$ , (2) Enhanced optimization efficiency through the progressive process, where each stage solves a simpler problem compared to direct optimization, resulting in $\\beta_1, \\beta_2 > \\beta$ .", + "bbox": [ + 89, + 261, + 483, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Aligned V-prediction", + "text_level": 1, + "bbox": [ + 89, + 376, + 289, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We analyzed approximate error in the optimization process and found that directional errors lead to more significant performance degradation compared to magnitude errors, shown in Fig.1 (b). We then propose aligned $\\nu$ -prediction, which emphasizes direction alignment in training.", + "bbox": [ + 89, + 398, + 483, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Direction Matters Consider two arbitrary points $z_{t_{i-1}}$ and $z_{t_i}$ along the trajectory. Given the target vector $v = z_{t_i} - z_{t_{i-1}}$ and the model prediction $p$ . According to the law of cosines, the error between $v$ and $p$ can be expressed as:", + "bbox": [ + 89, + 474, + 483, + 534 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr = | p | ^ {2} + | v | ^ {2} - 2 | p | | v | \\cos \\theta , \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 544, + 482, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\theta$ denotes the angle between $p$ and $v$ . We analyze two extreme cases:", + "bbox": [ + 89, + 573, + 482, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Misaligned, accurate magnitude $(|p| = |v|, \\theta = \\epsilon)$ :", + "bbox": [ + 89, + 603, + 439, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {1} = 2 | v | ^ {2} (1 - \\cos \\epsilon); \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 628, + 482, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Aligned, inaccurate magnitude $(\\theta = 0, |p| = |v| + \\epsilon)$ :", + "bbox": [ + 89, + 657, + 459, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {2} = \\left(| v | + \\epsilon\\right) ^ {2} + | v | ^ {2} - 2 | v | \\left(| v | + \\epsilon\\right) = \\epsilon^ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 681, + 482, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $y = r_{1} - r_{2}$ . Using Taylor expansion for small $\\epsilon$ :", + "bbox": [ + 89, + 710, + 442, + 726 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny = \\left(| v | ^ {2} - 1\\right) \\epsilon^ {2}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 736, + 482, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our empirical measurements using real image-noise pairs during training show that $|v|$ typically ranges from 70 to 120, yielding $y > 0$ with a substantial margin. This indicates that directional errors lead to significantly larger performance degradation than magnitude errors.", + "bbox": [ + 89, + 763, + 482, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Directional Alignment Our analysis reveals that directional components of $v$ play a more crucial role in generation quality than magnitude. Based on this, we proposed aligned v-prediction in flow matching, which incorporates", + "bbox": [ + 89, + 840, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "directional alignment through cosine similarity measurements. Specifically, we propose a novel flow matching loss function that places greater emphasis on directional alignment:", + "bbox": [ + 511, + 90, + 905, + 148 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = (1 - \\alpha) \\cdot \\operatorname {M S E} (v, p r e d) + \\alpha \\cdot (1 - \\cos (v, p r e d)), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 157, + 905, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first term provides basic magnitude consistency, the second term enforces explicit directional alignment via cosine similarity. The hyperparameter $\\alpha$ balances the relative importance between magnitude and direction.", + "bbox": [ + 511, + 180, + 905, + 239 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: ProReflow Algorithm" + ], + "code_body": "Input: $\\mathcal{D}$ dataset, $f_{\\phi}$ teacher model, $K$ : list of window numbers (e.g., [8,4,2]), $\\alpha$ : loss weight (default=0.1) 1 Initialize student model $f_{\\theta}\\gets f_{\\phi}$ . \n2 for k in K do \n3 Split time [0, 1] into k windows; \n4 while not converged do \n5 Sample $x$ from dataset D; \n6 Sample $\\epsilon \\sim N(0,1)$ . \n7 Sample timestep t and locate window $[t_1,t_2]$ s.t. $t\\in [t_1,t_2]$ .. \n8 $z_{t_2} = t_2*x + (1 - t_2)\\epsilon$ . \n9 Compute $z_{t_1}$ using $f_{\\phi}$ .. \n10 $z_{t} = t*x + (1 - t)\\epsilon$ . \n11 Compute target velocity $v = x - \\epsilon$ . \n12 Predict $v_{\\theta} = f_{\\theta}(z_t,t)$ .. \n13 $\\mathcal{L} = (1 - \\alpha)\\mathrm{MSE}(v,v_{\\theta}) + \\alpha \\mathrm{Dir}(v,v_{\\theta})$ . \n14 Update parameters $\\theta$ . \nend \nend \nOutput: Trained model $f_{\\theta}$", + "bbox": [ + 516, + 273, + 903, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hyperparameter Configuration Increasing the value of $\\alpha$ enhances the directional supervision in the optimization objective. When $\\alpha = 0$ , the loss function degenerates to the conventional MSE loss. To determine the optimal hyperparameter configuration, we systematically evaluated different settings: We randomly sampled 0.8M images from LAION-art as our training set and fine-tuned SDv1.5 with different $\\alpha$ values while maintaining the same number of windows. We computed FID on coco-30k to evaluate these models.", + "bbox": [ + 511, + 613, + 905, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4, the choice of $\\alpha$ significantly impacts the model performance. Among the evaluated $\\alpha$ values, more positive gains were observed with windows $= 4$ compared to windows $= 8$ , which may be attributed to the increased importance of directional consistency at larger window spans. Our experiment results show that $\\alpha = 0.1$ works well in all experiment settings, thus we maintained $\\alpha = 0.1$ for subsequent experiments.", + "bbox": [ + 511, + 750, + 905, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Combining progressive reflow and aligned $\\nu$ -prediction, we present ProReflow, as shown in Algorithm 1.", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28033", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/276c923c89404481677cb5e0e946e37051ac63929f6bcd1fd383de0a999be01b.jpg", + "table_caption": [ + "Table 1. Performance comparison on COCO-2017 validation set, following the evaluation setup in [40]. Our method outperforms existing flow-based approaches." + ], + "table_footnote": [], + "table_body": "
MethodStepFID (↓)CLIP Score(↑)
2-Reflow [18]249.3227.36
2-Reflow [18]432.9728.93
Instaflow-0.9B [18]271.5426.07
Instaflow-0.9B [18]4102.4124.39
PeRFlow [44]423.8130.24
ProReflow-I (ours)422.9730.29
ProReflow-II (ours)227.5927.79
ProReflow-II (ours)422.0329.95
", + "bbox": [ + 91, + 142, + 483, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 333, + 225, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Configuration", + "text_level": 1, + "bbox": [ + 89, + 366, + 331, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model and Dataset We evaluate our proposed method primarily on Stable Diffusion v1.5 and Stable Diffusion XL. During training, we freeze all modules except the UNet and employ BF16 mixed precision training. For SDv1.5, we initialize our training process with windows numbers=8 and progressively apply our method to derive ProReflow-I (4 windows), which subsequently serves as the basis for developing ProReflow-II. For SDXL, we adopt training configurations established in ProReflow-I on SDXL to develop ProReflow-SDXL, achieving four-steps sampling.", + "bbox": [ + 89, + 395, + 483, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As for multi-stage training, we maintain consistency in the teacher model's sampling trajectory across different training stages by fixing the total DDIM steps to 32. Specifically, when windows $= 8$ , we use 4 DDIM steps within each window to derive the endpoint from the starting point. For windows $= 4$ , we use 8 DDIM steps per window. This ensures that the teacher's sampling trajectory remains identical across different training stages, allowing for fair comparisons and stable optimization.", + "bbox": [ + 89, + 554, + 483, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SDv1.5 is trained on the LAION-Art dataset, with all images center-cropped to $512 \\times 512$ resolution following its default setup. For SDXL, we fine-tune the model using a combination of LAION-Art and 1.5 million samples from the laion2B-en-aesthetic dataset, with all images center-cropped to $1024 \\times 1024$ resolution. All experiments were conducted on 8 NVIDIA H20 GPUs.", + "bbox": [ + 89, + 696, + 483, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Setting Following common practice in text-to-image generation, we adopt two widely-used quantitative metrics: Fréchet Inception Distance (FID) [5] and clip score [28]. The evaluation is mainly conducted on two standard benchmarks: MS COCO 2014 validation dataset [15] and MS COCO 2017 validation dataset [15].", + "bbox": [ + 89, + 809, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/61226bf598b91abc7daddb47aaefb098174ff52b600e43803e11baeb9abe6598.jpg", + "table_caption": [ + "Table 2. Performance comparison on COCO-2014 validation set, following the evaluation setup in [11]." + ], + "table_footnote": [], + "table_body": "
MethodTime (↓)StepFID (↓)
ODE-solver based methods
DPMSolver [21]0.88s259.78
DPMSolver [21]0.34s822.44
DPMSolver++ [20]0.26s422.36
DDIM(our teacher) [36]-3210.05
Distillation-based methods
LCM-LoRA [23]0.12s224.28
LCM-LoRA [23]0.19s423.62
UniPC [46]0.19s423.30
Flash Diffusion [1]0.19s412.41
PCM [39]0.19s411.70
Flow-based methods
Instaflow-0.9B [18]0.13s224.61
Instaflow-0.9B [18]0.21s444.01
2-ReFlow [18]0.13s220.17
2-ReFlow [18]0.21s415.32
PeRFlow [44]0.21s412.01
ProReflow-I (ours)0.21s411.16
ProReflow-II (ours)0.13s215.44
ProReflow-II (ours)0.21s410.70
", + "bbox": [ + 511, + 128, + 906, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 511, + 500, + 707, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first compare our method with other flow-based acceleration approaches on COCO-2017 validation set, as shown in Table 1. With 4 inference steps, ProReflow-II achieves an FID of 22.03 and a CLIP score of 29.95, showing significant improvements over 2-ReFlow, Instaflow and PeRFlow. Even with only 2 steps, ProReflow-II maintains competitive performance. ProReflow-I also demonstrates strong performance with an FID of 22.97 and the highest CLIP score of 30.29. Table 2 summarizes the comprehensive evaluation results Result on COCO-2014 validation dataset with other diffusion acceleration methods. With 32-step DDIM serving as our teacher model, ProReflow-II achieves a competitive FID of 10.70 using only 4 steps.", + "bbox": [ + 509, + 522, + 906, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3 presents a comprehensive comparison of our method with advanced acceleration approaches on SDXL. Our method achieves state-of-the-art performance while maintaining the same inference cost.", + "bbox": [ + 511, + 718, + 906, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Comparison", + "text_level": 1, + "bbox": [ + 511, + 787, + 735, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared our method against leading flow-based approaches (Rectified Flow, InstaFlow, and PerFlow) as shown in Figure 5. Our method demonstrates superior performance across multiple aspects: it achieves more faithful detail preservation, renders more coherent global structures, and produces sharper textures with fewer artifacts.", + "bbox": [ + 511, + 809, + 905, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28034", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/32f9e593ef686388968f01f578e7cfa64f1e349182fb30a2144f50174c38da54.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of image generation results. Our method demonstrates superior performance in detail rendering compared to other flow-based approaches at both 2-steps and 4-steps sampling." + ], + "image_footnote": [], + "bbox": [ + 93, + 89, + 906, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, while baseline methods often struggle with detail preservation and suffer from blurry regions or structural distortions, our approach consistently maintains both fine-grained details and global coherence across various scenarios. This comprehensive improvement in generation quality validates the effectiveness of our method.", + "bbox": [ + 89, + 804, + 480, + 893 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Training Cost", + "text_level": 1, + "bbox": [ + 513, + 803, + 656, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method, though multi-staged, is computationally cheaper compared to traditional approaches. ProReflow-II involves three distinct training stages, starting with windows=8, where each stage is trained for 10,000 iterations at", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28035", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/948beccb16d435d1c0c39889da65f4fbf42fbd9c172390324166ec2d68410a7d.jpg", + "table_caption": [ + "Table 3. Comparison results on SDXL on COCO2017 validation set and COCO2014-10k validation set with 4 steps, following the evaluation setup in [40]." + ], + "table_footnote": [], + "table_body": "
MethodRes.StepsFID (↓)
COCO2017
Perflow1024427.06
Rectified Diffusion1024425.81
ProReflow-SDXL (Ours)1024425.36
COCO2014-10k
SDXL-Lightning1024424.56
SDXL-Turbo1024423.19
LCM1024422.16
PCM1024421.04
Perflow1024420.99
Rectified Diffusion1024419.71
DMDv21024419.32
ProReflow-SDXL (Ours)1024419.10
", + "bbox": [ + 91, + 142, + 480, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a batch size of 256. Although the number of samples remains consistent across stages, the training time varies due to differences in computational complexity. Following the approach outlined in [44], we randomly sample timesteps per batch, with windows defining the velocity prediction targets: the starting points are derived from noisy real images, while the endpoints are generated by the teacher model. With 32 teacher inference steps uniformly applied across all stages, windows $= 4$ requires double the number of steps compared to windows $= 8$ , which directly aligns with their training time ratio. Specifically, ProReflow-I completes its training in 6.5 H20 days, while ProReflow-II extends this by an additional 8.7 days, resulting in a total training duration of 15.2 H20 days.", + "bbox": [ + 93, + 402, + 480, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 94, + 627, + 202, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1. Ablation Study", + "text_level": 1, + "bbox": [ + 94, + 651, + 240, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation studies to examine our two core designs: aligned $\\nu$ -prediction and progressive reflow. Table 4 presents results on COCO-2017 validation set. Both components contribute to model performance, with their combination yielding the best result.", + "bbox": [ + 94, + 674, + 480, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. CFG Influence", + "text_level": 1, + "bbox": [ + 94, + 757, + 238, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It is well-established that the classifier-free guidance scale $w$ is a crucial factor affecting the performance of Stable Diffusion. During training, we set $w = 1$ (i.e., without classifier-free guidance) throughout all the stages. To thoroughly understand the model's behavior under different guidance settings, we conducted extensive evaluations across a broad range of $w$ values from 2 to 7, measuring both FID and CLIP score, results are shown in Figure 3.", + "bbox": [ + 94, + 780, + 480, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/62116561d66abca3076d00a0d565e8be7a8f580699a12e65ac1bf6212e3c461c.jpg", + "table_caption": [ + "Table 4. Ablation studies on COCO-2017 validation set. We first show the results of gradually removing progressive reflow, aligned v-prediction, and both components, followed by our full model. We use a guidance scale of 4 for all the models." + ], + "table_footnote": [], + "table_body": "
MethodStepsFID (↓)CLIP (↑)
w/o progressive reflow423.4630.21
w/o aligned v-prediction423.0930.25
w/o both423.8130.24
ProReflow-I422.9730.29
", + "bbox": [ + 514, + 156, + 903, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Step scalability", + "text_level": 1, + "bbox": [ + 516, + 276, + 663, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Intuitively, for diffusion models, higher sampling steps should lead to better performance. However, this assumption does not always hold in practice, as certain models exhibit counterintuitive behavior. For instance, PeRFlow demonstrates an unexpected increase in FID when increasing sampling steps from 4 to 8 on COCO-2014 [44], which significantly limits its practical applications. We find that our progressive training scheme effectively addresses this limitation by optimizing the model's ability to generalize across varying sampling steps. Although ProReflow-II is trained with fewer window numbers $(= 2)$ , it achieves lower FID score with 4-steps sampling compared to ProReflow-I, as shown in Table 1 and Table 2, demonstrating its superior performance.", + "bbox": [ + 516, + 299, + 903, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 516, + 526, + 630, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose an efficient training framework for flow-based diffusion acceleration. If viewing the optimization process from temporal and spatial dimensions, our method naturally leads to two complementary techniques that correspond to these two dimensions respectively. Temporally, progressive reflow bridges the trajectory approximation gap through curriculum learning, enabling gradual adaptation from more windows to fewer windows. Spatially, our velocity decomposition strategy emphasizes directional alignment over magnitude accuracy in velocity prediction. This principled design not only yields superior sampling quality but also brings advantages in optimization stability, training efficiency, and computational costs.", + "bbox": [ + 516, + 553, + 903, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Given promising few-step sampling performance, our method shows potential for one-step generation. However, due to computational constraints, we were unable to train the model with single window to full convergence. Nevertheless, we have validated the effectiveness of velocity decomposition in this challenging setting with the same training cost, only-one-window model equipped with aligned v-prediction demonstrate superior performance compared to the vanilla counterpart. We plan to move to one-step generation when resources allow.", + "bbox": [ + 516, + 750, + 903, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28036", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was partly supported by the National Key Research and Development Program of China(No.2024YFB2808903), the Shenzhen Science and Technology Program(JCYJ20220818101014030) and the research grant No.CT20240905126002 of the Doubao Large Model Fund.", + "bbox": [ + 89, + 90, + 485, + 189 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 204, + 187, + 220 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Clement Chadebec, Onur Tasar, Eyal Benaroche, and Benjamin Aubin. 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Advances in Neural Information Processing Systems, 36, 2024. 6" + ], + "bbox": [ + 516, + 92, + 903, + 571 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28038", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_model.json b/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..14fc23ba9b662ccc408851f3a35db7ba99d5f26e --- /dev/null +++ b/2025/ProReflow_ Progressive Reflow with Decomposed Velocity/ab413bbc-dea1-4ace-8805-5da24de9f86f_model.json @@ -0,0 +1,2420 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.208, + 0.131, + 0.79, + 0.154 + ], + "angle": 0, + "content": "ProReflow: Progressive Reflow with Decomposed Velocity" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.18, + 0.734, + 0.27 + ], + "angle": 0, + "content": "Lei Ke\\(^{1}\\) Haohang Xu\\(^{3}\\) Xuefei Ning\\(^{1}\\) Yu Li\\(^{1}\\) \nJiajun Li\\(^{4}\\) Haoling Li\\(^{1}\\) Yuxuan Lin\\(^{1}\\) Dongsheng Jiang\\(^{3}\\) Yujiu Yang\\(^{1\\dagger}\\) Linfeng Zhang\\(^{2\\dagger}\\) \n\\(^{1}\\)Tsinghua University \\(^{2}\\)Shanghai Jiao Tong University \nuawei Inc. \\(^{4}\\)University of Electronic Science and Technology of" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.274, + 0.816, + 0.287 + ], + "angle": 0, + "content": "k123@mails.tsinghua.edu.cn, yang.yujiu@sz.tsinghua.edu.cn, zhanglinfeng@sjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.322, + 0.327, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.354, + 0.486, + 0.641 + ], + "angle": 0, + "content": "Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, rectified flow aims to rectify the diffusion process of diffusion models into a straight line for few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of reflow is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned \\( \\nu \\)-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, \\( FID = 10.05 \\)). Our codes will be released at Github." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.671, + 0.222, + 0.687 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.696, + 0.484, + 0.879 + ], + "angle": 0, + "content": "Diffusion models have achieved significant breakthroughs in image and video generation, boosting various downstream applications such as text-to-image generation [27, 32] and image editing [2, 3, 10]. However, compared with traditional generation models such as GANs [9], the sampling process of diffusion models is formulated to include multiple timesteps, which severely harms its computation efficiency, hindering its application in edge devices and real-time applications. To solve this problem, abundant methods have been proposed to reduce the number of sampling steps such as step distillation [24, 34], consistency models [23, 38] and flow matching [16, 17]." + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.324, + 0.707, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.715, + 0.323, + 0.895, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.454, + 0.851, + 0.467 + ], + "angle": 0, + "content": "(a) Velocity differences across timesteps in diffusion model." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.47, + 0.895, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.611, + 0.86, + 0.624 + ], + "angle": 0, + "content": "(b) Flow model's performance degrades with increased noise." + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.627, + 0.906, + 0.698 + ], + "angle": 0, + "content": "Figure 1. (a) L2 distance and Cosine similarity across velocities at different timesteps, the velocity discrepancy between timesteps increases with their distance in timesteps. (b) The consistently larger FID degradation under directional noise demonstrates that velocity direction is more critical for generation quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Among them, flow matching has gained popularity due to its simplicity and effectiveness. By re-flowing the pretrained diffusion models into a line, few steps and even 1-step generation can be achieved with tolerant loss in generation quality. The training process of reflow usually contains two steps. Firstly, the pretrained diffusion model generates abundant (noise, image) pairs. Then, the diffusion model is trained to make the velocity at different timesteps to be identical, indicating that the trajectory is rectified. However, in this paper, we suggest that such a training strategy has not fully unleashed the potential of rectified flow and introduced two training techniques referred to as progressive reflow and aligned \\( \\nu \\)-prediction to further improve it." + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.888, + 0.242, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28029" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.213 + ], + "angle": 0, + "content": "Progressive Reflow: Traditional Reflow usually starts from a pretrained diffusion model and directly trains it to have a consistent prediction of velocity in all timesteps, which is theoretically correct but introduces difficulty in the optimization process. As shown in Figure 1 (a), the pretrained diffusion model has significantly different velocities at different timesteps, and directly eliminating these differences raises challenges in the training process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.221, + 0.482, + 0.403 + ], + "angle": 0, + "content": "Fortunately, Figure 1 (a) also shows that the pretrained diffusion model exhibits similar velocity in the adjacent timesteps, which provides the possibility to first reflow the model in a local window, and then reflow it in the whole training process. Such a progressive reflow pipeline allows the model to first learn to solve an easy problem and then extend to a difficult problem, which implies curriculum learning in generative models and thus facilitates the training process. Based on this observation, we propose progressive reflow, which firstly divides the whole diffusion process into \\( N \\) windows, and then progressive reflow \\( N \\) windows into \\( N/2 \\), \\( N/4 \\), \\( N/2 \\), \\( N/8 \\) until very few and even one window." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.411, + 0.482, + 0.593 + ], + "angle": 0, + "content": "Aligned V-Prediction: Flow matching aims to match the velocity in different timesteps to achieve the target that the whole diffusion process is a straight line. However, we suggest that such a velocity matching is not optimal for the target of a \"straight line\" as the velocity can be further decomposed into its direction and magnitude, where the direction is more crucial for straightness. In other words, matching the direction of the velocity should have a higher priority than matching the magnitude, which has been ignored in previous works. Based on this observation, we propose to modify the original training loss of flow matching by introducing direction matching to solve this problem." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.601, + 0.482, + 0.692 + ], + "angle": 0, + "content": "Our experiments have validated the effectiveness of the two improved training techniques. For instance, on MSCOCO-2017, 10.94 and 21.73 FID reduction can be observed with our ProReflow-II compared to rectified flow (2-ReFlow [18]) at 4 steps and 2 steps respectively, demonstrating improvements in generation quality" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.701, + 0.411, + 0.715 + ], + "angle": 0, + "content": "In summary, our contributions are as follows." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.735, + 0.48, + 0.794 + ], + "angle": 0, + "content": "- We propose progressive reflow, which progressive reflow the diffusion model in local timesteps until the whole diffusion process. Progressive reflow implies the curriculum learning in flow matching and facilitates model training." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.796, + 0.48, + 0.853 + ], + "angle": 0, + "content": "- Based on the observation that the direction of velocity is more crucial than the magnitude for straightness, we introduce velocity direction matching as an additional target for flow matching to facilitate model training." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.856, + 0.48, + 0.899 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that both components are effective individually, and their combination achieves state-of-the-art performance with only 4 sampling steps." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.735, + 0.48, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.655, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.115, + 0.749, + 0.131 + ], + "angle": 0, + "content": "2.1. Text-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.138, + 0.905, + 0.365 + ], + "angle": 0, + "content": "Diffusion models(DMs) learn the mapping from noise to images by fitting marginal probability distributions at each timestep [8, 37]. It works well because the forward diffusion process, which progressively adds noise to images, maintains the same marginal distributions as the sampling process [22]. Combined with some technologies like classifier-free guidance and text encoder [7, 26, 33], DMs have surpassed GANs [4, 31] and VAEs [12, 29] not only in generation quality but also in training stability. Besides applied in pixel space, DMs can be effectively applied in latent space as well, which significantly reduces computational complexity [32]. Despite achieving impressive generation quality, the iterative nature of DMs impacts its generation efficiency. Consequently, accelerating inference of diffusion models has emerged as an avtive research topic." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.375, + 0.691, + 0.39 + ], + "angle": 0, + "content": "2.2. Efficient Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.905, + 0.444 + ], + "angle": 0, + "content": "Existing approaches for accelerating DMs can be predominantly classified into two categories: efficient diffusion samplers and step distillation [45]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.444, + 0.905, + 0.609 + ], + "angle": 0, + "content": "The former category incorporates differential equation solvers into inference without requiring additional training. DDIM [36] enables step skipping in the reverse process by introducing a non-Markovian sampling strategy. DPM-Solver [21] reformulates the reverse diffusion process into an ODE system and solves it with high-order numerical methods, achieving superior sampling efficiency. Sampler-based methods enable diffusion models to maintain satisfactory generation quality with 20 steps; however, performance deteriorates significantly when further reducing the step count (such as below 10)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.905, + 0.732 + ], + "angle": 0, + "content": "The second category methods enhance few-step inference performance through another step distillation process. Progressive Distillation(PD) [34] adopts a staged approach, iteratively halving the student model's sampling steps. Adversarial Diffusion Distillation(ADD) [35] leverages adversarial training for improved supervision, while Consistency Distillation (CD) [38] enforces output convergence toward the target image across the sampling trajectory." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.742, + 0.661, + 0.756 + ], + "angle": 0, + "content": "2.3. Rectified Flow" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.905, + 0.855 + ], + "angle": 0, + "content": "Flow matching has emerged as a kind of advanced diffusion model [16, 17]. It reformulates the forward process as a linear interpolation between noise and images, thereby proposing to predict a consistent velocity \\( v \\) across the entire sampling trajectory. Thus, the sampling process is simplified to a temporal integration of the velocity field \\( v \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Similarly, ReFlow was proposed as a technique applying flow matching to pretrained diffusion models, enabling the adaptation of existing architectures without retraining from" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28030" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.087, + 0.278, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.139, + 0.192, + 0.243, + 0.204 + ], + "angle": 0, + "content": "(a) Diffusion Model" + }, + { + "type": "image", + "bbox": [ + 0.316, + 0.088, + 0.481, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.192, + 0.454, + 0.205 + ], + "angle": 0, + "content": "(b) Consistency Model" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.088, + 0.685, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.192, + 0.648, + 0.204 + ], + "angle": 0, + "content": "(c) Rectified Flow" + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.088, + 0.887, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.749, + 0.192, + 0.862, + 0.204 + ], + "angle": 0, + "content": "(d) Piecewise ReFlow" + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.212, + 0.276, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.242, + 0.318, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.319, + 0.213, + 0.52, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.213, + 0.683, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.212, + 0.886, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.289, + 0.317, + 0.513, + 0.327 + ], + "angle": 0, + "content": "(e) Progressive Reflow: windows num 4-2-1" + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.317, + 0.871, + 0.329 + ], + "angle": 0, + "content": "(f) Direction Alignment" + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.337, + 0.19, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.337, + 0.297, + 0.349 + ], + "angle": 0, + "content": "original trajectory" + }, + { + "type": "image", + "bbox": [ + 0.304, + 0.339, + 0.385, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.397, + 0.338, + 0.487, + 0.349 + ], + "angle": 0, + "content": "sample trajectory" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.339, + 0.578, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.338, + 0.675, + 0.349 + ], + "angle": 0, + "content": "optimation goal" + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.338, + 0.754, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.338, + 0.884, + 0.349 + ], + "angle": 0, + "content": "optimization goal (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.369, + 0.907, + 0.426 + ], + "angle": 0, + "content": "Figure 2. Conceptual illustration of different methods. (a)-(e) compare training objectives and sampling trajectories across different methods. Arrows show optimization targets, and red dashed lines represent actual sampling trajectories, which are curved due to the optimization not achieving the theoretical optimum. (e) shows our progressive reflow method achieves better approximation. (f) presents how our proposed aligned v-prediction works between timesteps \\([t, t + 1]\\), it reduces prediction deviation with velocity direction correction." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.451, + 0.484, + 0.633 + ], + "angle": 0, + "content": "scratch [17]. InstaFlow [18] first extended ReFlow to large-scale text-to-image models through consecutive ReFlow to straighten the ODE trajectory, followed by distillation to achieve single-step sampling. Subsequently, some works explored improving ReFlow's effectiveness or simplifying its training[13, 14, 42, 43]. While ReFlow showed promise for single-step generation, its few-step sampling performance lagged behind state-of-the-art methods [30, 34, 39]. To address this limitation, PeRFlow [44] proposed trajectory partitioning into time windows, achieving competitive few-step sampling through localized straightening within each temporal segment." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.648, + 0.411, + 0.665 + ], + "angle": 0, + "content": "2.4. Privileged Information in Distillation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Although knowledge distillation has been proven effective as a model compression technique and further extended successfully to diffusion model acceleration, the theoretical explanation for its efficacy has remained elusive. How 'dark knowledge' is effectively captured from teacher models and utilized to guide student learning remains a fundamental theoretical question [6]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Lopez-Paz et al. [19] presented a unified theoretical framework that connects distillation with privileged information, establishing a generalized framework for understanding machine-to-machine knowledge transfer. Viewing distillation as a transfer of privileged information, TAKD [25] showed that an assistant model of intermediate capacity could more effectively mediate the knowledge flow between teacher and student models." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.45, + 0.612, + 0.466 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.907, + 0.627 + ], + "angle": 0, + "content": "We present ProReflow, a more robust flow model training method. Our approach is motivated by the observation that training efficient few-step flow models faces two main challenges: (1) the significant trajectory approximation gap between teacher and student models, and (2) the difficulty in achieving accurate velocity prediction across large time intervals. To address these challenges, we propose progressive reflow for stable optimization of sample trajectory and aligned v-prediction for achieving precise velocity prediction, respectively, shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.636, + 0.824, + 0.652 + ], + "angle": 0, + "content": "3.1. Temporal Segmentation for ReFlow" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.658, + 0.906, + 0.749 + ], + "angle": 0, + "content": "Rectified Flow ReFlow aims to achieve temporally consistent velocity predictions across all timesteps. Given initial Gaussian distribution \\(\\pi_0\\) and target image distribution \\(\\pi_1\\), where \\(X_1 \\sim \\pi_1\\) and \\(X_0 \\sim \\pi_0\\). Reflow defines a linear process from \\(\\pi_0\\) to \\(\\pi_1\\), where the corresponding sampling process follows the ODE:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.759, + 0.905, + 0.777 + ], + "angle": 0, + "content": "\\[\nd X _ {t} = v \\left(X _ {t}, t\\right) d t, \\quad t \\in [ 0, 1 ], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.787, + 0.907, + 0.817 + ], + "angle": 0, + "content": "Then, it formulates a least-squares optimization problem to ensure the predictions consistency:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.827, + 0.905, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\int_ {0} ^ {1} \\mathbb {E} [ \\| X _ {1} - X _ {0} - v _ {\\theta} (X _ {t}, t) \\| ^ {2} ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.722, + 0.887 + ], + "angle": 0, + "content": "where \\(X_{t} = tX_{1} + (1 - t)X_{0}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28031" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.101, + 0.429, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.25, + 0.48, + 0.306 + ], + "angle": 0, + "content": "Figure 3. Performance of our models under different factors of classifier-free guidance (CFG) on COCO-2017. CFG scale ranges from 2 to 7. I and II stands for ProReflow-I with 4 steps and ProReflow-II with 2 steps, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.332, + 0.484, + 0.437 + ], + "angle": 0, + "content": "Piecewise ReFlow Aimed at improving the few-step generation, PeRFlow divides the sampling trajectory into multiple time windows, defined by endpoints \\(1 = t_{K} > \\dots > t_{k} > t_{k - 1} > \\dots > t_{0} = 0\\). Within each time window \\([t_k, t_{k - 1})\\) formed by adjacent endpoints, PeRFlow assumes a linear process to straighten the trajectory, thus eq.(2) can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.444, + 0.482, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\sum_ {k = 1} ^ {K} \\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\left[ \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.497, + 0.483, + 0.546 + ], + "angle": 0, + "content": "where \\( z_{t} = \\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}} \\). Finally, PeRFlow results in a piecewise linear trajectory composed of multiple segments." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.553, + 0.279, + 0.57 + ], + "angle": 0, + "content": "3.2. Progressive ReFlow" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.483, + 0.651 + ], + "angle": 0, + "content": "PeRFlow originally sets the number of time windows to 4. Despite achieving improvement in few-step inference, PeRFlow faces a significant optimization challenge: it attempts to approximate the teacher model's irregular trajectory using four linear intervals within a single training stage." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.652, + 0.483, + 0.756 + ], + "angle": 0, + "content": "We propose a multi-stage progressive training scheme to tackle this challenge. Rather than directly mapping the original trajectory to four time windows, our method first obtains an eight-window approximation from the original trajectory, and subsequently apply Cross-windows ReFlow to refine this eight-window representation into the target four-window configuration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.757, + 0.484, + 0.802 + ], + "angle": 0, + "content": "Cross-windows ReFlow Consider three consecutive time points \\( t_{k-1}, t_k, t_{k+1} \\). The optimization objectives in first training stage can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.81, + 0.482, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\theta} \\left(\\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t + \\right. \\\\ \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k}} - z _ {t _ {k + 1}}}{t _ {k} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\Bigg), \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.113, + 0.847, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.22, + 0.905, + 0.304 + ], + "angle": 0, + "content": "Figure 4. FID on COCO-30K. The yellow curve shows results trained with 4 windows and evaluated using 4 inference steps, while the blue curve represents the model trained with 8 windows and evaluated using 8 inference steps. Both configurations are compared against their baselines where \\(\\alpha = 0\\) (MSE loss only). Each model is trained for 10,000 iterations with batch size 32." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.33, + 0.905, + 0.42 + ], + "angle": 0, + "content": "where \\( z_{t} = \\left\\{ \\begin{array}{ll}\\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}}, & t\\in [t_{k - 1},t_{k})\\\\ \\beta_{t}z_{t_{k + 1}} + (1 - \\beta_{t})z_{t_{k}}, & t\\in [t_{k},t_{k + 1}) \\end{array} \\right. \\) with \\( \\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}} \\) and \\( \\beta_{t} = \\frac{t - t_{k}}{t_{k + 1} - t_{k}} \\). In adjacent time windows, trajectories evolve from \\( z_{t_{k - 1}} \\) to \\( z_{t_k} \\) in \\( [t_{k - 1},t_k] \\), and from \\( z_{t_k} \\) to \\( z_{t_{k + 1}} \\) in \\( [t_k,t_{k + 1}] \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.423, + 0.905, + 0.469 + ], + "angle": 0, + "content": "Cross-windows ReFlow aligns the optimization direction by guiding trajectories in both intervals to progress from \\( z_{t_{k-1}} \\) towards \\( z_{t_{k+1}} \\), thus eq.(4) can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.492, + 0.905, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k - 1}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k + 1}}}{t _ {k - 1} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.538, + 0.875, + 0.56 + ], + "angle": 0, + "content": "where \\(z_{t} = \\alpha_{t}z_{t_{k + 1}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k + 1} - t_{k - 1}}.\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.562, + 0.907, + 0.7 + ], + "angle": 0, + "content": "Theoretical Explanation Based on the theoretical framework of knowledge distillation [19], we can explain the effectiveness of Progressive ReFlow. Consider three key functions: the teacher function \\( f_{t} \\in \\mathcal{F}_{t} \\) representing the original diffusion trajectory, an intermediate function \\( f_{a} \\in \\mathcal{F}_{a} \\) for the 8-segment approximation, and the student function \\( f_{s} \\in \\mathcal{F}_{s} \\) for the target 4-segment representation. According to the VC theory [41], when the student learns directly from the teacher, the learning rate is bounded by:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.719, + 0.905, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {t}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {l}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.907, + 0.881 + ], + "angle": 0, + "content": "where \\(\\beta \\in [\\frac{1}{2}, 1]\\) denotes the learning rate associated with task difficulty, \\(\\varepsilon_{l}\\) represents the approximation error, \\(\\mathcal{R}\\) represents the error, \\(\\mathcal{O}(\\cdot)\\) and \\(\\epsilon\\) represent the estimation error and approximation error, respectively.. The challenge lies in the significant capacity gap between the complex trajectory and the 4-segment approximation, resulting in a small \\(\\beta\\) that indicates difficult learning." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Progressive ReFlow decomposes this challenging pro" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28032" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.093, + 0.232, + 0.107 + ], + "angle": 0, + "content": "cess into two stages:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.116, + 0.484, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\text {S t a g e} 1: \\mathcal {R} (f _ {a}) - \\mathcal {R} (f _ {t}) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}}\\right) + \\varepsilon_ {a t}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.152, + 0.484, + 0.186 + ], + "angle": 0, + "content": "\\[\n\\text {S t a g e} 2: \\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {a}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {s a}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.195, + 0.431, + 0.21 + ], + "angle": 0, + "content": "The effectiveness is theoretically guaranteed when:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.219, + 0.484, + 0.254 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {a t} + \\varepsilon_ {s a} \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {s}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.262, + 0.484, + 0.368 + ], + "angle": 0, + "content": "this inequality is satisfied in practice due to two key principles: (1) 8-segment allows for better fitting of the teacher's complex sampling trajectory, leading to smaller combined approximation error \\((\\varepsilon_{at} + \\varepsilon_{sa} < \\varepsilon_l)\\), (2) Enhanced optimization efficiency through the progressive process, where each stage solves a simpler problem compared to direct optimization, resulting in \\(\\beta_1, \\beta_2 > \\beta\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.377, + 0.29, + 0.394 + ], + "angle": 0, + "content": "3.3. Aligned V-prediction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.484, + 0.475 + ], + "angle": 0, + "content": "We analyzed approximate error in the optimization process and found that directional errors lead to more significant performance degradation compared to magnitude errors, shown in Fig.1 (b). We then propose aligned \\(\\nu\\)-prediction, which emphasizes direction alignment in training." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.476, + 0.484, + 0.535 + ], + "angle": 0, + "content": "Direction Matters Consider two arbitrary points \\( z_{t_{i-1}} \\) and \\( z_{t_i} \\) along the trajectory. Given the target vector \\( v = z_{t_i} - z_{t_{i-1}} \\) and the model prediction \\( p \\). According to the law of cosines, the error between \\( v \\) and \\( p \\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.545, + 0.483, + 0.563 + ], + "angle": 0, + "content": "\\[\nr = | p | ^ {2} + | v | ^ {2} - 2 | p | | v | \\cos \\theta , \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.574, + 0.483, + 0.602 + ], + "angle": 0, + "content": "where \\(\\theta\\) denotes the angle between \\(p\\) and \\(v\\). We analyze two extreme cases:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.604, + 0.44, + 0.62 + ], + "angle": 0, + "content": "- Misaligned, accurate magnitude \\((|p| = |v|, \\theta = \\epsilon)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.63, + 0.483, + 0.647 + ], + "angle": 0, + "content": "\\[\nr _ {1} = 2 | v | ^ {2} (1 - \\cos \\epsilon); \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.658, + 0.46, + 0.674 + ], + "angle": 0, + "content": "- Aligned, inaccurate magnitude \\((\\theta = 0, |p| = |v| + \\epsilon)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.683, + 0.483, + 0.701 + ], + "angle": 0, + "content": "\\[\nr _ {2} = \\left(| v | + \\epsilon\\right) ^ {2} + | v | ^ {2} - 2 | v | \\left(| v | + \\epsilon\\right) = \\epsilon^ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.712, + 0.444, + 0.727 + ], + "angle": 0, + "content": "Let \\(y = r_{1} - r_{2}\\). Using Taylor expansion for small \\(\\epsilon\\):" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.737, + 0.483, + 0.754 + ], + "angle": 0, + "content": "\\[\ny = \\left(| v | ^ {2} - 1\\right) \\epsilon^ {2}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Our empirical measurements using real image-noise pairs during training show that \\( |v| \\) typically ranges from 70 to 120, yielding \\( y > 0 \\) with a substantial margin. This indicates that directional errors lead to significantly larger performance degradation than magnitude errors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Directional Alignment Our analysis reveals that directional components of \\( v \\) play a more crucial role in generation quality than magnitude. Based on this, we proposed aligned v-prediction in flow matching, which incorporates" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.15 + ], + "angle": 0, + "content": "directional alignment through cosine similarity measurements. Specifically, we propose a novel flow matching loss function that places greater emphasis on directional alignment:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.158, + 0.906, + 0.175 + ], + "angle": 0, + "content": "\\[\nL = (1 - \\alpha) \\cdot \\operatorname {M S E} (v, p r e d) + \\alpha \\cdot (1 - \\cos (v, p r e d)), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.181, + 0.906, + 0.241 + ], + "angle": 0, + "content": "where the first term provides basic magnitude consistency, the second term enforces explicit directional alignment via cosine similarity. The hyperparameter \\(\\alpha\\) balances the relative importance between magnitude and direction." + }, + { + "type": "code_caption", + "bbox": [ + 0.523, + 0.257, + 0.766, + 0.272 + ], + "angle": 0, + "content": "Algorithm 1: ProReflow Algorithm" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.274, + 0.905, + 0.596 + ], + "angle": 0, + "content": "Input: \\(\\mathcal{D}\\) dataset, \\(f_{\\phi}\\) teacher model, \\(K\\) : list of window numbers (e.g., [8,4,2]), \\(\\alpha\\) : loss weight (default=0.1) 1 Initialize student model \\(f_{\\theta}\\gets f_{\\phi}\\) . \n2 for k in K do \n3 Split time [0, 1] into k windows; \n4 while not converged do \n5 Sample \\(x\\) from dataset D; \n6 Sample \\(\\epsilon \\sim N(0,1)\\) . \n7 Sample timestep t and locate window \\([t_1,t_2]\\) s.t. \\(t\\in [t_1,t_2]\\) .. \n8 \\(z_{t_2} = t_2*x + (1 - t_2)\\epsilon\\) . \n9 Compute \\(z_{t_1}\\) using \\(f_{\\phi}\\) .. \n10 \\(z_{t} = t*x + (1 - t)\\epsilon\\) . \n11 Compute target velocity \\(v = x - \\epsilon\\) . \n12 Predict \\(v_{\\theta} = f_{\\theta}(z_t,t)\\) .. \n13 \\(\\mathcal{L} = (1 - \\alpha)\\mathrm{MSE}(v,v_{\\theta}) + \\alpha \\mathrm{Dir}(v,v_{\\theta})\\) . \n14 Update parameters \\(\\theta\\) . \nend \nend \nOutput: Trained model \\(f_{\\theta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.749 + ], + "angle": 0, + "content": "Hyperparameter Configuration Increasing the value of \\(\\alpha\\) enhances the directional supervision in the optimization objective. When \\(\\alpha = 0\\), the loss function degenerates to the conventional MSE loss. To determine the optimal hyperparameter configuration, we systematically evaluated different settings: We randomly sampled 0.8M images from LAION-art as our training set and fine-tuned SDv1.5 with different \\(\\alpha\\) values while maintaining the same number of windows. We computed FID on coco-30k to evaluate these models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.871 + ], + "angle": 0, + "content": "As shown in Fig. 4, the choice of \\(\\alpha\\) significantly impacts the model performance. Among the evaluated \\(\\alpha\\) values, more positive gains were observed with windows \\(= 4\\) compared to windows \\(= 8\\), which may be attributed to the increased importance of directional consistency at larger window spans. Our experiment results show that \\(\\alpha = 0.1\\) works well in all experiment settings, thus we maintained \\(\\alpha = 0.1\\) for subsequent experiments." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Combining progressive reflow and aligned \\( \\nu \\)-prediction, we present ProReflow, as shown in Algorithm 1." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28033" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.486, + 0.133 + ], + "angle": 0, + "content": "Table 1. Performance comparison on COCO-2017 validation set, following the evaluation setup in [40]. Our method outperforms existing flow-based approaches." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.143, + 0.485, + 0.297 + ], + "angle": 0, + "content": "
MethodStepFID (↓)CLIP Score(↑)
2-Reflow [18]249.3227.36
2-Reflow [18]432.9728.93
Instaflow-0.9B [18]271.5426.07
Instaflow-0.9B [18]4102.4124.39
PeRFlow [44]423.8130.24
ProReflow-I (ours)422.9730.29
ProReflow-II (ours)227.5927.79
ProReflow-II (ours)422.0329.95
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.334, + 0.226, + 0.353 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.367, + 0.332, + 0.385 + ], + "angle": 0, + "content": "4.1. Experiment Configuration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.396, + 0.485, + 0.548 + ], + "angle": 0, + "content": "Model and Dataset We evaluate our proposed method primarily on Stable Diffusion v1.5 and Stable Diffusion XL. During training, we freeze all modules except the UNet and employ BF16 mixed precision training. For SDv1.5, we initialize our training process with windows numbers=8 and progressively apply our method to derive ProReflow-I (4 windows), which subsequently serves as the basis for developing ProReflow-II. For SDXL, we adopt training configurations established in ProReflow-I on SDXL to develop ProReflow-SDXL, achieving four-steps sampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.555, + 0.484, + 0.691 + ], + "angle": 0, + "content": "As for multi-stage training, we maintain consistency in the teacher model's sampling trajectory across different training stages by fixing the total DDIM steps to 32. Specifically, when windows \\(= 8\\), we use 4 DDIM steps within each window to derive the endpoint from the starting point. For windows \\(= 4\\), we use 8 DDIM steps per window. This ensures that the teacher's sampling trajectory remains identical across different training stages, allowing for fair comparisons and stable optimization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.484, + 0.803 + ], + "angle": 0, + "content": "SDv1.5 is trained on the LAION-Art dataset, with all images center-cropped to \\( 512 \\times 512 \\) resolution following its default setup. For SDXL, we fine-tune the model using a combination of LAION-Art and 1.5 million samples from the laion2B-en-aesthetic dataset, with all images center-cropped to \\( 1024 \\times 1024 \\) resolution. All experiments were conducted on 8 NVIDIA H20 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Evaluation Setting Following common practice in text-to-image generation, we adopt two widely-used quantitative metrics: Fréchet Inception Distance (FID) [5] and clip score [28]. The evaluation is mainly conducted on two standard benchmarks: MS COCO 2014 validation dataset [15] and MS COCO 2017 validation dataset [15]." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.12 + ], + "angle": 0, + "content": "Table 2. Performance comparison on COCO-2014 validation set, following the evaluation setup in [11]." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.129, + 0.907, + 0.476 + ], + "angle": 0, + "content": "
MethodTime (↓)StepFID (↓)
ODE-solver based methods
DPMSolver [21]0.88s259.78
DPMSolver [21]0.34s822.44
DPMSolver++ [20]0.26s422.36
DDIM(our teacher) [36]-3210.05
Distillation-based methods
LCM-LoRA [23]0.12s224.28
LCM-LoRA [23]0.19s423.62
UniPC [46]0.19s423.30
Flash Diffusion [1]0.19s412.41
PCM [39]0.19s411.70
Flow-based methods
Instaflow-0.9B [18]0.13s224.61
Instaflow-0.9B [18]0.21s444.01
2-ReFlow [18]0.13s220.17
2-ReFlow [18]0.21s415.32
PeRFlow [44]0.21s412.01
ProReflow-I (ours)0.21s411.16
ProReflow-II (ours)0.13s215.44
ProReflow-II (ours)0.21s410.70
" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.501, + 0.709, + 0.517 + ], + "angle": 0, + "content": "4.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.523, + 0.907, + 0.719 + ], + "angle": 0, + "content": "We first compare our method with other flow-based acceleration approaches on COCO-2017 validation set, as shown in Table 1. With 4 inference steps, ProReflow-II achieves an FID of 22.03 and a CLIP score of 29.95, showing significant improvements over 2-ReFlow, Instaflow and PeRFlow. Even with only 2 steps, ProReflow-II maintains competitive performance. ProReflow-I also demonstrates strong performance with an FID of 22.97 and the highest CLIP score of 30.29. Table 2 summarizes the comprehensive evaluation results Result on COCO-2014 validation dataset with other diffusion acceleration methods. With 32-step DDIM serving as our teacher model, ProReflow-II achieves a competitive FID of 10.70 using only 4 steps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.719, + 0.907, + 0.78 + ], + "angle": 0, + "content": "Table 3 presents a comprehensive comparison of our method with advanced acceleration approaches on SDXL. Our method achieves state-of-the-art performance while maintaining the same inference cost." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.789, + 0.736, + 0.805 + ], + "angle": 0, + "content": "4.3. Qualitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.903 + ], + "angle": 0, + "content": "We compared our method against leading flow-based approaches (Rectified Flow, InstaFlow, and PerFlow) as shown in Figure 5. Our method demonstrates superior performance across multiple aspects: it achieves more faithful detail preservation, renders more coherent global structures, and produces sharper textures with fewer artifacts." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28034" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.09, + 0.907, + 0.74 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.749, + 0.908, + 0.78 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of image generation results. Our method demonstrates superior performance in detail rendering compared to other flow-based approaches at both 2-steps and 4-steps sampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.805, + 0.482, + 0.895 + ], + "angle": 0, + "content": "Specifically, while baseline methods often struggle with detail preservation and suffer from blurry regions or structural distortions, our approach consistently maintains both fine-grained details and global coherence across various scenarios. This comprehensive improvement in generation quality validates the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.804, + 0.658, + 0.82 + ], + "angle": 0, + "content": "4.4. Training Cost" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Our method, though multi-staged, is computationally cheaper compared to traditional approaches. ProReflow-II involves three distinct training stages, starting with windows=8, where each stage is trained for 10,000 iterations at" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28035" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.09, + 0.482, + 0.131 + ], + "angle": 0, + "content": "Table 3. Comparison results on SDXL on COCO2017 validation set and COCO2014-10k validation set with 4 steps, following the evaluation setup in [40]." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.143, + 0.482, + 0.377 + ], + "angle": 0, + "content": "
MethodRes.StepsFID (↓)
COCO2017
Perflow1024427.06
Rectified Diffusion1024425.81
ProReflow-SDXL (Ours)1024425.36
COCO2014-10k
SDXL-Lightning1024424.56
SDXL-Turbo1024423.19
LCM1024422.16
PCM1024421.04
Perflow1024420.99
Rectified Diffusion1024419.71
DMDv21024419.32
ProReflow-SDXL (Ours)1024419.10
" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.403, + 0.482, + 0.614 + ], + "angle": 0, + "content": "a batch size of 256. Although the number of samples remains consistent across stages, the training time varies due to differences in computational complexity. Following the approach outlined in [44], we randomly sample timesteps per batch, with windows defining the velocity prediction targets: the starting points are derived from noisy real images, while the endpoints are generated by the teacher model. With 32 teacher inference steps uniformly applied across all stages, windows \\(= 4\\) requires double the number of steps compared to windows \\(= 8\\), which directly aligns with their training time ratio. Specifically, ProReflow-I completes its training in 6.5 H20 days, while ProReflow-II extends this by an additional 8.7 days, resulting in a total training duration of 15.2 H20 days." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.628, + 0.203, + 0.643 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.652, + 0.241, + 0.668 + ], + "angle": 0, + "content": "5.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.675, + 0.482, + 0.748 + ], + "angle": 0, + "content": "We conduct ablation studies to examine our two core designs: aligned \\( \\nu \\)-prediction and progressive reflow. Table 4 presents results on COCO-2017 validation set. Both components contribute to model performance, with their combination yielding the best result." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.758, + 0.24, + 0.773 + ], + "angle": 0, + "content": "5.2. CFG Influence" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.781, + 0.482, + 0.9 + ], + "angle": 0, + "content": "It is well-established that the classifier-free guidance scale \\( w \\) is a crucial factor affecting the performance of Stable Diffusion. During training, we set \\( w = 1 \\) (i.e., without classifier-free guidance) throughout all the stages. To thoroughly understand the model's behavior under different guidance settings, we conducted extensive evaluations across a broad range of \\( w \\) values from 2 to 7, measuring both FID and CLIP score, results are shown in Figure 3." + }, + { + "type": "table_caption", + "bbox": [ + 0.517, + 0.09, + 0.905, + 0.145 + ], + "angle": 0, + "content": "Table 4. Ablation studies on COCO-2017 validation set. We first show the results of gradually removing progressive reflow, aligned v-prediction, and both components, followed by our full model. We use a guidance scale of 4 for all the models." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.157, + 0.905, + 0.248 + ], + "angle": 0, + "content": "
MethodStepsFID (↓)CLIP (↑)
w/o progressive reflow423.4630.21
w/o aligned v-prediction423.0930.25
w/o both423.8130.24
ProReflow-I422.9730.29
" + }, + { + "type": "title", + "bbox": [ + 0.517, + 0.277, + 0.665, + 0.293 + ], + "angle": 0, + "content": "5.3. Step scalability" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.3, + 0.905, + 0.51 + ], + "angle": 0, + "content": "Intuitively, for diffusion models, higher sampling steps should lead to better performance. However, this assumption does not always hold in practice, as certain models exhibit counterintuitive behavior. For instance, PeRFlow demonstrates an unexpected increase in FID when increasing sampling steps from 4 to 8 on COCO-2014 [44], which significantly limits its practical applications. We find that our progressive training scheme effectively addresses this limitation by optimizing the model's ability to generalize across varying sampling steps. Although ProReflow-II is trained with fewer window numbers \\((= 2)\\), it achieves lower FID score with 4-steps sampling compared to ProReflow-I, as shown in Table 1 and Table 2, demonstrating its superior performance." + }, + { + "type": "title", + "bbox": [ + 0.517, + 0.527, + 0.631, + 0.542 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.554, + 0.905, + 0.748 + ], + "angle": 0, + "content": "In this paper, we propose an efficient training framework for flow-based diffusion acceleration. If viewing the optimization process from temporal and spatial dimensions, our method naturally leads to two complementary techniques that correspond to these two dimensions respectively. Temporally, progressive reflow bridges the trajectory approximation gap through curriculum learning, enabling gradual adaptation from more windows to fewer windows. Spatially, our velocity decomposition strategy emphasizes directional alignment over magnitude accuracy in velocity prediction. This principled design not only yields superior sampling quality but also brings advantages in optimization stability, training efficiency, and computational costs." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.75, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Limitations Given promising few-step sampling performance, our method shows potential for one-step generation. However, due to computational constraints, we were unable to train the model with single window to full convergence. Nevertheless, we have validated the effectiveness of velocity decomposition in this challenging setting with the same training cost, only-one-window model equipped with aligned v-prediction demonstrate superior performance compared to the vanilla counterpart. We plan to move to one-step generation when resources allow." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28036" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.19 + ], + "angle": 0, + "content": "Acknowledgments This work was partly supported by the National Key Research and Development Program of China(No.2024YFB2808903), the Shenzhen Science and Technology Program(JCYJ20220818101014030) and the research grant No.CT20240905126002 of the Doubao Large Model Fund." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.205, + 0.188, + 0.221 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.23, + 0.482, + 0.286 + ], + "angle": 0, + "content": "[1] Clement Chadebec, Onur Tasar, Eyal Benaroche, and Benjamin Aubin. 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As an effective solution, rectified flow aims to rectify the diffusion process of diffusion models into a straight line for few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of reflow is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned $\nu$ -prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, $FID = 10.05$ ). Our codes will be released at Github. + +# 1. Introduction + +Diffusion models have achieved significant breakthroughs in image and video generation, boosting various downstream applications such as text-to-image generation [27, 32] and image editing [2, 3, 10]. However, compared with traditional generation models such as GANs [9], the sampling process of diffusion models is formulated to include multiple timesteps, which severely harms its computation efficiency, hindering its application in edge devices and real-time applications. To solve this problem, abundant methods have been proposed to reduce the number of sampling steps such as step distillation [24, 34], consistency models [23, 38] and flow matching [16, 17]. + +![](images/57188b1f7afcfdd67069ad8bd01fc7d5da751dab21d630de4511cefc082022b4.jpg) +(a) Velocity differences across timesteps in diffusion model. + +![](images/91b5267d3e030913dd5e387d49662107209451281c8d7892165944db8405f30c.jpg) + +![](images/f41952a6a6a173f887293faac108717d152212902c98df343f3fc2c7bb3e3a9d.jpg) +(b) Flow model's performance degrades with increased noise. +Figure 1. (a) L2 distance and Cosine similarity across velocities at different timesteps, the velocity discrepancy between timesteps increases with their distance in timesteps. (b) The consistently larger FID degradation under directional noise demonstrates that velocity direction is more critical for generation quality. + +Among them, flow matching has gained popularity due to its simplicity and effectiveness. By re-flowing the pretrained diffusion models into a line, few steps and even 1-step generation can be achieved with tolerant loss in generation quality. The training process of reflow usually contains two steps. Firstly, the pretrained diffusion model generates abundant (noise, image) pairs. Then, the diffusion model is trained to make the velocity at different timesteps to be identical, indicating that the trajectory is rectified. However, in this paper, we suggest that such a training strategy has not fully unleashed the potential of rectified flow and introduced two training techniques referred to as progressive reflow and aligned $\nu$ -prediction to further improve it. + +Progressive Reflow: Traditional Reflow usually starts from a pretrained diffusion model and directly trains it to have a consistent prediction of velocity in all timesteps, which is theoretically correct but introduces difficulty in the optimization process. As shown in Figure 1 (a), the pretrained diffusion model has significantly different velocities at different timesteps, and directly eliminating these differences raises challenges in the training process. + +Fortunately, Figure 1 (a) also shows that the pretrained diffusion model exhibits similar velocity in the adjacent timesteps, which provides the possibility to first reflow the model in a local window, and then reflow it in the whole training process. Such a progressive reflow pipeline allows the model to first learn to solve an easy problem and then extend to a difficult problem, which implies curriculum learning in generative models and thus facilitates the training process. Based on this observation, we propose progressive reflow, which firstly divides the whole diffusion process into $N$ windows, and then progressive reflow $N$ windows into $N/2$ , $N/4$ , $N/2$ , $N/8$ until very few and even one window. + +Aligned V-Prediction: Flow matching aims to match the velocity in different timesteps to achieve the target that the whole diffusion process is a straight line. However, we suggest that such a velocity matching is not optimal for the target of a "straight line" as the velocity can be further decomposed into its direction and magnitude, where the direction is more crucial for straightness. In other words, matching the direction of the velocity should have a higher priority than matching the magnitude, which has been ignored in previous works. Based on this observation, we propose to modify the original training loss of flow matching by introducing direction matching to solve this problem. + +Our experiments have validated the effectiveness of the two improved training techniques. For instance, on MSCOCO-2017, 10.94 and 21.73 FID reduction can be observed with our ProReflow-II compared to rectified flow (2-ReFlow [18]) at 4 steps and 2 steps respectively, demonstrating improvements in generation quality + +In summary, our contributions are as follows. + +- We propose progressive reflow, which progressive reflow the diffusion model in local timesteps until the whole diffusion process. Progressive reflow implies the curriculum learning in flow matching and facilitates model training. +- Based on the observation that the direction of velocity is more crucial than the magnitude for straightness, we introduce velocity direction matching as an additional target for flow matching to facilitate model training. +- Extensive experiments demonstrate that both components are effective individually, and their combination achieves state-of-the-art performance with only 4 sampling steps. + +# 2. Related Work + +# 2.1. Text-to-Image Generation + +Diffusion models(DMs) learn the mapping from noise to images by fitting marginal probability distributions at each timestep [8, 37]. It works well because the forward diffusion process, which progressively adds noise to images, maintains the same marginal distributions as the sampling process [22]. Combined with some technologies like classifier-free guidance and text encoder [7, 26, 33], DMs have surpassed GANs [4, 31] and VAEs [12, 29] not only in generation quality but also in training stability. Besides applied in pixel space, DMs can be effectively applied in latent space as well, which significantly reduces computational complexity [32]. Despite achieving impressive generation quality, the iterative nature of DMs impacts its generation efficiency. Consequently, accelerating inference of diffusion models has emerged as an avtive research topic. + +# 2.2. Efficient Diffusion + +Existing approaches for accelerating DMs can be predominantly classified into two categories: efficient diffusion samplers and step distillation [45]. + +The former category incorporates differential equation solvers into inference without requiring additional training. DDIM [36] enables step skipping in the reverse process by introducing a non-Markovian sampling strategy. DPM-Solver [21] reformulates the reverse diffusion process into an ODE system and solves it with high-order numerical methods, achieving superior sampling efficiency. Sampler-based methods enable diffusion models to maintain satisfactory generation quality with 20 steps; however, performance deteriorates significantly when further reducing the step count (such as below 10). + +The second category methods enhance few-step inference performance through another step distillation process. Progressive Distillation(PD) [34] adopts a staged approach, iteratively halving the student model's sampling steps. Adversarial Diffusion Distillation(ADD) [35] leverages adversarial training for improved supervision, while Consistency Distillation (CD) [38] enforces output convergence toward the target image across the sampling trajectory. + +# 2.3. Rectified Flow + +Flow matching has emerged as a kind of advanced diffusion model [16, 17]. It reformulates the forward process as a linear interpolation between noise and images, thereby proposing to predict a consistent velocity $v$ across the entire sampling trajectory. Thus, the sampling process is simplified to a temporal integration of the velocity field $v$ . + +Similarly, ReFlow was proposed as a technique applying flow matching to pretrained diffusion models, enabling the adaptation of existing architectures without retraining from + +![](images/c1922ae9a0c28c05c01b41aa8188bf7634b207da617a4a740e51cbf17d09c221.jpg) +(a) Diffusion Model + +![](images/65ebad54b2ffd369364dc27a601ab7ad3b461528aebd10d750e20573bd9c9fb5.jpg) +(b) Consistency Model + +![](images/32c04b8c3714608d1c35870ca28a98c5983ce41065309dace7384826dea09c5d.jpg) +(c) Rectified Flow + +![](images/357ac8930d7b9b812c668f22b837df2b5be09b87cec856db150a9c997bd82ae1.jpg) +(d) Piecewise ReFlow + +![](images/42fe5ffd883a90f4ab4be602f5a74a5ea6d8d299270e26dcb7f61e6dd7e90fbf.jpg) +(e) Progressive Reflow: windows num 4-2-1 + +![](images/e1cd8d087c90f967fab4cf831a847a18969c2327a96a7e45bedcee6e6182a759.jpg) + +![](images/b82debd4ea1552aea74eb8d9d6c01c749e7c2ffeebb3f44c9fd0b3e6200d7afe.jpg) +sample trajectory + +![](images/82f97e2f8d2033c5ce9e33f1c0f6f1b54fba238f7d7c697ec6dcc4c3c0a20b56.jpg) + +![](images/c4fde4337de53cbdda273a87fb034cc479e7e1f9bebff87c28e2bd4174777173.jpg) +(f) Direction Alignment + +![](images/9155448c15b635ece3ec0e95421e4f190eb4194390a88aa08c69632c41da14ef.jpg) +original trajectory + +![](images/314e0cd06abe2dbd051ab6c523cc1711aed4d395ad41c24e274ac0aeee88222c.jpg) +Figure 2. Conceptual illustration of different methods. (a)-(e) compare training objectives and sampling trajectories across different methods. Arrows show optimization targets, and red dashed lines represent actual sampling trajectories, which are curved due to the optimization not achieving the theoretical optimum. (e) shows our progressive reflow method achieves better approximation. (f) presents how our proposed aligned v-prediction works between timesteps $[t, t + 1]$ , it reduces prediction deviation with velocity direction correction. + +![](images/f4ff1e156a8e63069d7297e34a2c5f3e3023548aa177d966d28ee1fd52013d80.jpg) +optimation goal + +![](images/53d422977a58b690b46f23f008e94fc4e95cfa030cb087615b0c70a1479f869c.jpg) +optimization goal (ours) + +scratch [17]. InstaFlow [18] first extended ReFlow to large-scale text-to-image models through consecutive ReFlow to straighten the ODE trajectory, followed by distillation to achieve single-step sampling. Subsequently, some works explored improving ReFlow's effectiveness or simplifying its training[13, 14, 42, 43]. While ReFlow showed promise for single-step generation, its few-step sampling performance lagged behind state-of-the-art methods [30, 34, 39]. To address this limitation, PeRFlow [44] proposed trajectory partitioning into time windows, achieving competitive few-step sampling through localized straightening within each temporal segment. + +# 2.4. Privileged Information in Distillation + +Although knowledge distillation has been proven effective as a model compression technique and further extended successfully to diffusion model acceleration, the theoretical explanation for its efficacy has remained elusive. How 'dark knowledge' is effectively captured from teacher models and utilized to guide student learning remains a fundamental theoretical question [6]. + +Lopez-Paz et al. [19] presented a unified theoretical framework that connects distillation with privileged information, establishing a generalized framework for understanding machine-to-machine knowledge transfer. Viewing distillation as a transfer of privileged information, TAKD [25] showed that an assistant model of intermediate capacity could more effectively mediate the knowledge flow between teacher and student models. + +# 3. Methods + +We present ProReflow, a more robust flow model training method. Our approach is motivated by the observation that training efficient few-step flow models faces two main challenges: (1) the significant trajectory approximation gap between teacher and student models, and (2) the difficulty in achieving accurate velocity prediction across large time intervals. To address these challenges, we propose progressive reflow for stable optimization of sample trajectory and aligned v-prediction for achieving precise velocity prediction, respectively, shown in Fig. 2. + +# 3.1. Temporal Segmentation for ReFlow + +Rectified Flow ReFlow aims to achieve temporally consistent velocity predictions across all timesteps. Given initial Gaussian distribution $\pi_0$ and target image distribution $\pi_1$ , where $X_1 \sim \pi_1$ and $X_0 \sim \pi_0$ . Reflow defines a linear process from $\pi_0$ to $\pi_1$ , where the corresponding sampling process follows the ODE: + +$$ +d X _ {t} = v \left(X _ {t}, t\right) d t, \quad t \in [ 0, 1 ], \tag {1} +$$ + +Then, it formulates a least-squares optimization problem to ensure the predictions consistency: + +$$ +\min _ {\theta} \int_ {0} ^ {1} \mathbb {E} [ \| X _ {1} - X _ {0} - v _ {\theta} (X _ {t}, t) \| ^ {2} ], \tag {2} +$$ + +where $X_{t} = tX_{1} + (1 - t)X_{0}$ . + +![](images/565469283a4a3a8ce982993175ded6899658c0c2eceecf05324112c060eb11d9.jpg) +Figure 3. Performance of our models under different factors of classifier-free guidance (CFG) on COCO-2017. CFG scale ranges from 2 to 7. I and II stands for ProReflow-I with 4 steps and ProReflow-II with 2 steps, respectively. + +Piecewise ReFlow Aimed at improving the few-step generation, PeRFlow divides the sampling trajectory into multiple time windows, defined by endpoints $1 = t_{K} > \dots > t_{k} > t_{k - 1} > \dots > t_{0} = 0$ . Within each time window $[t_k, t_{k - 1})$ formed by adjacent endpoints, PeRFlow assumes a linear process to straighten the trajectory, thus eq.(2) can be reformulated as: + +$$ +\min _ {\theta} \sum_ {k = 1} ^ {K} \mathbb {E} _ {z _ {t _ {k}} \sim \pi_ {k}} \left[ \int_ {t _ {k - 1}} ^ {t _ {k}} \| \frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\theta} (z _ {t}, t) \| ^ {2} d t \right], \tag {3} +$$ + +where $z_{t} = \alpha_{t}z_{t_{k}} + (1 - \alpha_{t})z_{t_{k - 1}},\alpha_{t} = \frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}$ . Finally, PeRFlow results in a piecewise linear trajectory composed of multiple segments. + +# 3.2. Progressive ReFlow + +PeRFlow originally sets the number of time windows to 4. Despite achieving improvement in few-step inference, PeRFlow faces a significant optimization challenge: it attempts to approximate the teacher model's irregular trajectory using four linear intervals within a single training stage. + +We propose a multi-stage progressive training scheme to tackle this challenge. Rather than directly mapping the original trajectory to four time windows, our method first obtains an eight-window approximation from the original trajectory, and subsequently apply Cross-windows ReFlow to refine this eight-window representation into the target four-window configuration. + +Cross-windows ReFlow Consider three consecutive time points $t_{k-1}, t_k, t_{k+1}$ . The optimization objectives in first training stage can be formulated as: + +$$ +\begin{array}{l} \min _ {\theta} \left(\mathbb {E} _ {z _ {t _ {k}} \sim \pi_ {k}} \int_ {t _ {k - 1}} ^ {t _ {k}} \| \frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\theta} (z _ {t}, t) \| ^ {2} d t + \right. \\ \mathbb {E} _ {z _ {t _ {k + 1}} \sim \pi_ {k + 1}} \int_ {t _ {k}} ^ {t _ {k + 1}} \| \frac {z _ {t _ {k}} - z _ {t _ {k + 1}}}{t _ {k} - t _ {k + 1}} - v _ {\theta} (z _ {t}, t) \| ^ {2} d t \Bigg), \tag {4} \\ \end{array} +$$ + +![](images/7a18179b322256a4976e13096526107d177f46629151ec9b90fa760336dd0672.jpg) +Figure 4. FID on COCO-30K. The yellow curve shows results trained with 4 windows and evaluated using 4 inference steps, while the blue curve represents the model trained with 8 windows and evaluated using 8 inference steps. Both configurations are compared against their baselines where $\alpha = 0$ (MSE loss only). Each model is trained for 10,000 iterations with batch size 32. + +where $z_{t} = \left\{ \begin{array}{ll}\alpha_{t}z_{t_{k}} + (1 - \alpha_{t})z_{t_{k - 1}}, & t\in [t_{k - 1},t_{k})\\ \beta_{t}z_{t_{k + 1}} + (1 - \beta_{t})z_{t_{k}}, & t\in [t_{k},t_{k + 1}) \end{array} \right.$ with $\alpha_{t} = \frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}$ and $\beta_{t} = \frac{t - t_{k}}{t_{k + 1} - t_{k}}$ . In adjacent time windows, trajectories evolve from $z_{t_{k - 1}}$ to $z_{t_k}$ in $[t_{k - 1},t_k]$ , and from $z_{t_k}$ to $z_{t_{k + 1}}$ in $[t_k,t_{k + 1}]$ . + +Cross-windows ReFlow aligns the optimization direction by guiding trajectories in both intervals to progress from $z_{t_{k-1}}$ towards $z_{t_{k+1}}$ , thus eq.(4) can be reformulated as: + +$$ +\min _ {\theta} \mathbb {E} _ {z _ {t _ {k + 1}} \sim \pi_ {k + 1}} \int_ {t _ {k - 1}} ^ {t _ {k + 1}} \| \frac {z _ {t _ {k - 1}} - z _ {t _ {k + 1}}}{t _ {k - 1} - t _ {k + 1}} - v _ {\theta} (z _ {t}, t) \| ^ {2} d t, \tag {5} +$$ + +where $z_{t} = \alpha_{t}z_{t_{k + 1}} + (1 - \alpha_{t})z_{t_{k - 1}},\alpha_{t} = \frac{t - t_{k - 1}}{t_{k + 1} - t_{k - 1}}.$ + +Theoretical Explanation Based on the theoretical framework of knowledge distillation [19], we can explain the effectiveness of Progressive ReFlow. Consider three key functions: the teacher function $f_{t} \in \mathcal{F}_{t}$ representing the original diffusion trajectory, an intermediate function $f_{a} \in \mathcal{F}_{a}$ for the 8-segment approximation, and the student function $f_{s} \in \mathcal{F}_{s}$ for the target 4-segment representation. According to the VC theory [41], when the student learns directly from the teacher, the learning rate is bounded by: + +$$ +\mathcal {R} \left(f _ {s}\right) - \mathcal {R} \left(f _ {t}\right) \leq \mathcal {O} \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\beta}}\right) + \varepsilon_ {l}, \tag {6} +$$ + +where $\beta \in [\frac{1}{2}, 1]$ denotes the learning rate associated with task difficulty, $\varepsilon_{l}$ represents the approximation error, $\mathcal{R}$ represents the error, $\mathcal{O}(\cdot)$ and $\epsilon$ represent the estimation error and approximation error, respectively.. The challenge lies in the significant capacity gap between the complex trajectory and the 4-segment approximation, resulting in a small $\beta$ that indicates difficult learning. + +Progressive ReFlow decomposes this challenging pro + +cess into two stages: + +$$ +\text {S t a g e} 1: \mathcal {R} (f _ {a}) - \mathcal {R} (f _ {t}) \leq \mathcal {O} \left(\frac {\left| \mathcal {F} _ {a} \right| _ {C}}{n ^ {\beta_ {1}}}\right) + \varepsilon_ {a t}, \tag {7} +$$ + +$$ +\text {S t a g e} 2: \mathcal {R} \left(f _ {s}\right) - \mathcal {R} \left(f _ {a}\right) \leq \mathcal {O} \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\beta_ {2}}}\right) + \varepsilon_ {s a}. \tag {8} +$$ + +The effectiveness is theoretically guaranteed when: + +$$ +\mathcal {O} \left(\frac {\left| \mathcal {F} _ {a} \right| _ {C}}{n ^ {\beta_ {1}}} + \frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\beta_ {2}}}\right) + \varepsilon_ {a t} + \varepsilon_ {s a} \leq \mathcal {O} \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\beta}}\right) + \varepsilon_ {s}, \tag {9} +$$ + +this inequality is satisfied in practice due to two key principles: (1) 8-segment allows for better fitting of the teacher's complex sampling trajectory, leading to smaller combined approximation error $(\varepsilon_{at} + \varepsilon_{sa} < \varepsilon_l)$ , (2) Enhanced optimization efficiency through the progressive process, where each stage solves a simpler problem compared to direct optimization, resulting in $\beta_1, \beta_2 > \beta$ . + +# 3.3. Aligned V-prediction + +We analyzed approximate error in the optimization process and found that directional errors lead to more significant performance degradation compared to magnitude errors, shown in Fig.1 (b). We then propose aligned $\nu$ -prediction, which emphasizes direction alignment in training. + +Direction Matters Consider two arbitrary points $z_{t_{i-1}}$ and $z_{t_i}$ along the trajectory. Given the target vector $v = z_{t_i} - z_{t_{i-1}}$ and the model prediction $p$ . According to the law of cosines, the error between $v$ and $p$ can be expressed as: + +$$ +r = | p | ^ {2} + | v | ^ {2} - 2 | p | | v | \cos \theta , \tag {10} +$$ + +where $\theta$ denotes the angle between $p$ and $v$ . We analyze two extreme cases: + +- Misaligned, accurate magnitude $(|p| = |v|, \theta = \epsilon)$ : + +$$ +r _ {1} = 2 | v | ^ {2} (1 - \cos \epsilon); \tag {11} +$$ + +- Aligned, inaccurate magnitude $(\theta = 0, |p| = |v| + \epsilon)$ : + +$$ +r _ {2} = \left(| v | + \epsilon\right) ^ {2} + | v | ^ {2} - 2 | v | \left(| v | + \epsilon\right) = \epsilon^ {2}. \tag {12} +$$ + +Let $y = r_{1} - r_{2}$ . Using Taylor expansion for small $\epsilon$ : + +$$ +y = \left(| v | ^ {2} - 1\right) \epsilon^ {2}. \tag {13} +$$ + +Our empirical measurements using real image-noise pairs during training show that $|v|$ typically ranges from 70 to 120, yielding $y > 0$ with a substantial margin. This indicates that directional errors lead to significantly larger performance degradation than magnitude errors. + +Directional Alignment Our analysis reveals that directional components of $v$ play a more crucial role in generation quality than magnitude. Based on this, we proposed aligned v-prediction in flow matching, which incorporates + +directional alignment through cosine similarity measurements. Specifically, we propose a novel flow matching loss function that places greater emphasis on directional alignment: + +$$ +L = (1 - \alpha) \cdot \operatorname {M S E} (v, p r e d) + \alpha \cdot (1 - \cos (v, p r e d)), \tag {14} +$$ + +where the first term provides basic magnitude consistency, the second term enforces explicit directional alignment via cosine similarity. The hyperparameter $\alpha$ balances the relative importance between magnitude and direction. + +Algorithm 1: ProReflow Algorithm +Input: $\mathcal{D}$ dataset, $f_{\phi}$ teacher model, $K$ : list of window numbers (e.g., [8,4,2]), $\alpha$ : loss weight (default=0.1) 1 Initialize student model $f_{\theta}\gets f_{\phi}$ . +2 for k in K do +3 Split time [0, 1] into k windows; +4 while not converged do +5 Sample $x$ from dataset D; +6 Sample $\epsilon \sim N(0,1)$ . +7 Sample timestep t and locate window $[t_1,t_2]$ s.t. $t\in [t_1,t_2]$ .. +8 $z_{t_2} = t_2*x + (1 - t_2)\epsilon$ . +9 Compute $z_{t_1}$ using $f_{\phi}$ .. +10 $z_{t} = t*x + (1 - t)\epsilon$ . +11 Compute target velocity $v = x - \epsilon$ . +12 Predict $v_{\theta} = f_{\theta}(z_t,t)$ .. +13 $\mathcal{L} = (1 - \alpha)\mathrm{MSE}(v,v_{\theta}) + \alpha \mathrm{Dir}(v,v_{\theta})$ . +14 Update parameters $\theta$ . +end +end +Output: Trained model $f_{\theta}$ + +Hyperparameter Configuration Increasing the value of $\alpha$ enhances the directional supervision in the optimization objective. When $\alpha = 0$ , the loss function degenerates to the conventional MSE loss. To determine the optimal hyperparameter configuration, we systematically evaluated different settings: We randomly sampled 0.8M images from LAION-art as our training set and fine-tuned SDv1.5 with different $\alpha$ values while maintaining the same number of windows. We computed FID on coco-30k to evaluate these models. + +As shown in Fig. 4, the choice of $\alpha$ significantly impacts the model performance. Among the evaluated $\alpha$ values, more positive gains were observed with windows $= 4$ compared to windows $= 8$ , which may be attributed to the increased importance of directional consistency at larger window spans. Our experiment results show that $\alpha = 0.1$ works well in all experiment settings, thus we maintained $\alpha = 0.1$ for subsequent experiments. + +Combining progressive reflow and aligned $\nu$ -prediction, we present ProReflow, as shown in Algorithm 1. + +Table 1. Performance comparison on COCO-2017 validation set, following the evaluation setup in [40]. Our method outperforms existing flow-based approaches. + +
MethodStepFID (↓)CLIP Score(↑)
2-Reflow [18]249.3227.36
2-Reflow [18]432.9728.93
Instaflow-0.9B [18]271.5426.07
Instaflow-0.9B [18]4102.4124.39
PeRFlow [44]423.8130.24
ProReflow-I (ours)422.9730.29
ProReflow-II (ours)227.5927.79
ProReflow-II (ours)422.0329.95
+ +# 4. Experiments + +# 4.1. Experiment Configuration + +Model and Dataset We evaluate our proposed method primarily on Stable Diffusion v1.5 and Stable Diffusion XL. During training, we freeze all modules except the UNet and employ BF16 mixed precision training. For SDv1.5, we initialize our training process with windows numbers=8 and progressively apply our method to derive ProReflow-I (4 windows), which subsequently serves as the basis for developing ProReflow-II. For SDXL, we adopt training configurations established in ProReflow-I on SDXL to develop ProReflow-SDXL, achieving four-steps sampling. + +As for multi-stage training, we maintain consistency in the teacher model's sampling trajectory across different training stages by fixing the total DDIM steps to 32. Specifically, when windows $= 8$ , we use 4 DDIM steps within each window to derive the endpoint from the starting point. For windows $= 4$ , we use 8 DDIM steps per window. This ensures that the teacher's sampling trajectory remains identical across different training stages, allowing for fair comparisons and stable optimization. + +SDv1.5 is trained on the LAION-Art dataset, with all images center-cropped to $512 \times 512$ resolution following its default setup. For SDXL, we fine-tune the model using a combination of LAION-Art and 1.5 million samples from the laion2B-en-aesthetic dataset, with all images center-cropped to $1024 \times 1024$ resolution. All experiments were conducted on 8 NVIDIA H20 GPUs. + +Evaluation Setting Following common practice in text-to-image generation, we adopt two widely-used quantitative metrics: Fréchet Inception Distance (FID) [5] and clip score [28]. The evaluation is mainly conducted on two standard benchmarks: MS COCO 2014 validation dataset [15] and MS COCO 2017 validation dataset [15]. + +Table 2. Performance comparison on COCO-2014 validation set, following the evaluation setup in [11]. + +
MethodTime (↓)StepFID (↓)
ODE-solver based methods
DPMSolver [21]0.88s259.78
DPMSolver [21]0.34s822.44
DPMSolver++ [20]0.26s422.36
DDIM(our teacher) [36]-3210.05
Distillation-based methods
LCM-LoRA [23]0.12s224.28
LCM-LoRA [23]0.19s423.62
UniPC [46]0.19s423.30
Flash Diffusion [1]0.19s412.41
PCM [39]0.19s411.70
Flow-based methods
Instaflow-0.9B [18]0.13s224.61
Instaflow-0.9B [18]0.21s444.01
2-ReFlow [18]0.13s220.17
2-ReFlow [18]0.21s415.32
PeRFlow [44]0.21s412.01
ProReflow-I (ours)0.21s411.16
ProReflow-II (ours)0.13s215.44
ProReflow-II (ours)0.21s410.70
+ +# 4.2. Quantitative Results + +We first compare our method with other flow-based acceleration approaches on COCO-2017 validation set, as shown in Table 1. With 4 inference steps, ProReflow-II achieves an FID of 22.03 and a CLIP score of 29.95, showing significant improvements over 2-ReFlow, Instaflow and PeRFlow. Even with only 2 steps, ProReflow-II maintains competitive performance. ProReflow-I also demonstrates strong performance with an FID of 22.97 and the highest CLIP score of 30.29. Table 2 summarizes the comprehensive evaluation results Result on COCO-2014 validation dataset with other diffusion acceleration methods. With 32-step DDIM serving as our teacher model, ProReflow-II achieves a competitive FID of 10.70 using only 4 steps. + +Table 3 presents a comprehensive comparison of our method with advanced acceleration approaches on SDXL. Our method achieves state-of-the-art performance while maintaining the same inference cost. + +# 4.3. Qualitative Comparison + +We compared our method against leading flow-based approaches (Rectified Flow, InstaFlow, and PerFlow) as shown in Figure 5. Our method demonstrates superior performance across multiple aspects: it achieves more faithful detail preservation, renders more coherent global structures, and produces sharper textures with fewer artifacts. + +![](images/32f9e593ef686388968f01f578e7cfa64f1e349182fb30a2144f50174c38da54.jpg) +Figure 5. Qualitative comparison of image generation results. Our method demonstrates superior performance in detail rendering compared to other flow-based approaches at both 2-steps and 4-steps sampling. + +Specifically, while baseline methods often struggle with detail preservation and suffer from blurry regions or structural distortions, our approach consistently maintains both fine-grained details and global coherence across various scenarios. This comprehensive improvement in generation quality validates the effectiveness of our method. + +# 4.4. Training Cost + +Our method, though multi-staged, is computationally cheaper compared to traditional approaches. ProReflow-II involves three distinct training stages, starting with windows=8, where each stage is trained for 10,000 iterations at + +Table 3. Comparison results on SDXL on COCO2017 validation set and COCO2014-10k validation set with 4 steps, following the evaluation setup in [40]. + +
MethodRes.StepsFID (↓)
COCO2017
Perflow1024427.06
Rectified Diffusion1024425.81
ProReflow-SDXL (Ours)1024425.36
COCO2014-10k
SDXL-Lightning1024424.56
SDXL-Turbo1024423.19
LCM1024422.16
PCM1024421.04
Perflow1024420.99
Rectified Diffusion1024419.71
DMDv21024419.32
ProReflow-SDXL (Ours)1024419.10
+ +a batch size of 256. Although the number of samples remains consistent across stages, the training time varies due to differences in computational complexity. Following the approach outlined in [44], we randomly sample timesteps per batch, with windows defining the velocity prediction targets: the starting points are derived from noisy real images, while the endpoints are generated by the teacher model. With 32 teacher inference steps uniformly applied across all stages, windows $= 4$ requires double the number of steps compared to windows $= 8$ , which directly aligns with their training time ratio. Specifically, ProReflow-I completes its training in 6.5 H20 days, while ProReflow-II extends this by an additional 8.7 days, resulting in a total training duration of 15.2 H20 days. + +# 5. Discussion + +# 5.1. Ablation Study + +We conduct ablation studies to examine our two core designs: aligned $\nu$ -prediction and progressive reflow. Table 4 presents results on COCO-2017 validation set. Both components contribute to model performance, with their combination yielding the best result. + +# 5.2. CFG Influence + +It is well-established that the classifier-free guidance scale $w$ is a crucial factor affecting the performance of Stable Diffusion. During training, we set $w = 1$ (i.e., without classifier-free guidance) throughout all the stages. To thoroughly understand the model's behavior under different guidance settings, we conducted extensive evaluations across a broad range of $w$ values from 2 to 7, measuring both FID and CLIP score, results are shown in Figure 3. + +Table 4. Ablation studies on COCO-2017 validation set. We first show the results of gradually removing progressive reflow, aligned v-prediction, and both components, followed by our full model. We use a guidance scale of 4 for all the models. + +
MethodStepsFID (↓)CLIP (↑)
w/o progressive reflow423.4630.21
w/o aligned v-prediction423.0930.25
w/o both423.8130.24
ProReflow-I422.9730.29
+ +# 5.3. Step scalability + +Intuitively, for diffusion models, higher sampling steps should lead to better performance. However, this assumption does not always hold in practice, as certain models exhibit counterintuitive behavior. For instance, PeRFlow demonstrates an unexpected increase in FID when increasing sampling steps from 4 to 8 on COCO-2014 [44], which significantly limits its practical applications. We find that our progressive training scheme effectively addresses this limitation by optimizing the model's ability to generalize across varying sampling steps. Although ProReflow-II is trained with fewer window numbers $(= 2)$ , it achieves lower FID score with 4-steps sampling compared to ProReflow-I, as shown in Table 1 and Table 2, demonstrating its superior performance. + +# 6. Conclusion + +In this paper, we propose an efficient training framework for flow-based diffusion acceleration. If viewing the optimization process from temporal and spatial dimensions, our method naturally leads to two complementary techniques that correspond to these two dimensions respectively. Temporally, progressive reflow bridges the trajectory approximation gap through curriculum learning, enabling gradual adaptation from more windows to fewer windows. Spatially, our velocity decomposition strategy emphasizes directional alignment over magnitude accuracy in velocity prediction. This principled design not only yields superior sampling quality but also brings advantages in optimization stability, training efficiency, and computational costs. + +Limitations Given promising few-step sampling performance, our method shows potential for one-step generation. However, due to computational constraints, we were unable to train the model with single window to full convergence. Nevertheless, we have validated the effectiveness of velocity decomposition in this challenging setting with the same training cost, only-one-window model equipped with aligned v-prediction demonstrate superior performance compared to the vanilla counterpart. We plan to move to one-step generation when resources allow. + +Acknowledgments This work was partly supported by the National Key Research and Development Program of China(No.2024YFB2808903), the Shenzhen Science and Technology Program(JCYJ20220818101014030) and the research grant No.CT20240905126002 of the Doubao Large Model Fund. + +# References + +[1] Clement Chadebec, Onur Tasar, Eyal Benaroche, and Benjamin Aubin. Flash diffusion: Accelerating any conditional diffusion model for few steps image generation. arXiv preprint arXiv:2406.02347, 2024. 6 +[2] Guillaume Couairon, Jakob Verbeek, Holger Schwenk, and Matthieu Cord. Diffedit: Diffusion-based semantic image editing with mask guidance. 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(a) L2 distance and Cosine similarity across velocities at different timesteps, the velocity discrepancy between timesteps increases with their distance in timesteps. (b) The consistently larger FID degradation under directional noise demonstrates that velocity direction is more critical for generation quality." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": "Among them, flow matching has gained popularity due to its simplicity and effectiveness. By re-flowing the pretrained diffusion models into a line, few steps and even 1-step generation can be achieved with tolerant loss in generation quality. The training process of reflow usually contains two steps. 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However, in this paper, we suggest that such a training strategy has not fully unleashed the potential of rectified flow and introduced two training techniques referred to as progressive reflow and aligned " + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": "-prediction to further improve it." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 703, + 148, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 703, + 148, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 703, + 148, + 713 + ], + "type": "text", + "content": "†Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28029" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "type": "text", + "content": "Progressive Reflow: Traditional Reflow usually starts from a pretrained diffusion model and directly trains it to have a consistent prediction of velocity in all timesteps, which is theoretically correct but introduces difficulty in the optimization process. As shown in Figure 1 (a), the pretrained diffusion model has significantly different velocities at different timesteps, and directly eliminating these differences raises challenges in the training process." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": "Fortunately, Figure 1 (a) also shows that the pretrained diffusion model exhibits similar velocity in the adjacent timesteps, which provides the possibility to first reflow the model in a local window, and then reflow it in the whole training process. Such a progressive reflow pipeline allows the model to first learn to solve an easy problem and then extend to a difficult problem, which implies curriculum learning in generative models and thus facilitates the training process. Based on this observation, we propose progressive reflow, which firstly divides the whole diffusion process into " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": " windows, and then progressive reflow " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": " windows into " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N/4" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "inline_equation", + "content": "N/8" + }, + { + "bbox": [ + 55, + 175, + 294, + 319 + ], + "type": "text", + "content": " until very few and even one window." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 325, + 294, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 325, + 294, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 294, + 469 + ], + "type": "text", + "content": "Aligned V-Prediction: Flow matching aims to match the velocity in different timesteps to achieve the target that the whole diffusion process is a straight line. However, we suggest that such a velocity matching is not optimal for the target of a \"straight line\" as the velocity can be further decomposed into its direction and magnitude, where the direction is more crucial for straightness. In other words, matching the direction of the velocity should have a higher priority than matching the magnitude, which has been ignored in previous works. Based on this observation, we propose to modify the original training loss of flow matching by introducing direction matching to solve this problem." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 475, + 294, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 294, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 294, + 548 + ], + "type": "text", + "content": "Our experiments have validated the effectiveness of the two improved training techniques. For instance, on MSCOCO-2017, 10.94 and 21.73 FID reduction can be observed with our ProReflow-II compared to rectified flow (2-ReFlow [18]) at 4 steps and 2 steps respectively, demonstrating improvements in generation quality" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 555, + 251, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 555, + 251, + 566 + ], + "spans": [ + { + "bbox": [ + 67, + 555, + 251, + 566 + ], + "type": "text", + "content": "In summary, our contributions are as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 582, + 293, + 712 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 55, + 582, + 293, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 293, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 293, + 628 + ], + "type": "text", + "content": "- We propose progressive reflow, which progressive reflow the diffusion model in local timesteps until the whole diffusion process. Progressive reflow implies the curriculum learning in flow matching and facilitates model training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 293, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 293, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 293, + 675 + ], + "type": "text", + "content": "- Based on the observation that the direction of velocity is more crucial than the magnitude for straightness, we introduce velocity direction matching as an additional target for flow matching to facilitate model training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 293, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 293, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 293, + 712 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that both components are effective individually, and their combination achieves state-of-the-art performance with only 4 sampling steps." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 91, + 458, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 91, + 458, + 103 + ], + "spans": [ + { + "bbox": [ + 314, + 91, + 458, + 103 + ], + "type": "text", + "content": "2.1. Text-to-Image Generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 109, + 553, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 553, + 289 + ], + "type": "text", + "content": "Diffusion models(DMs) learn the mapping from noise to images by fitting marginal probability distributions at each timestep [8, 37]. It works well because the forward diffusion process, which progressively adds noise to images, maintains the same marginal distributions as the sampling process [22]. Combined with some technologies like classifier-free guidance and text encoder [7, 26, 33], DMs have surpassed GANs [4, 31] and VAEs [12, 29] not only in generation quality but also in training stability. Besides applied in pixel space, DMs can be effectively applied in latent space as well, which significantly reduces computational complexity [32]. Despite achieving impressive generation quality, the iterative nature of DMs impacts its generation efficiency. Consequently, accelerating inference of diffusion models has emerged as an avtive research topic." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 297, + 422, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 297, + 422, + 308 + ], + "spans": [ + { + "bbox": [ + 314, + 297, + 422, + 308 + ], + "type": "text", + "content": "2.2. Efficient Diffusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 315, + 553, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 553, + 351 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 553, + 351 + ], + "type": "text", + "content": "Existing approaches for accelerating DMs can be predominantly classified into two categories: efficient diffusion samplers and step distillation [45]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 351, + 553, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 351, + 553, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 351, + 553, + 482 + ], + "type": "text", + "content": "The former category incorporates differential equation solvers into inference without requiring additional training. DDIM [36] enables step skipping in the reverse process by introducing a non-Markovian sampling strategy. DPM-Solver [21] reformulates the reverse diffusion process into an ODE system and solves it with high-order numerical methods, achieving superior sampling efficiency. Sampler-based methods enable diffusion models to maintain satisfactory generation quality with 20 steps; however, performance deteriorates significantly when further reducing the step count (such as below 10)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 483, + 553, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 553, + 579 + ], + "type": "text", + "content": "The second category methods enhance few-step inference performance through another step distillation process. Progressive Distillation(PD) [34] adopts a staged approach, iteratively halving the student model's sampling steps. 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"index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 186, + 268, + 235, + 276 + ], + "blocks": [ + { + "bbox": [ + 186, + 268, + 235, + 276 + ], + "lines": [ + { + "bbox": [ + 186, + 268, + 235, + 276 + ], + "spans": [ + { + "bbox": [ + 186, + 268, + 235, + 276 + ], + "type": "image", + "image_path": "314e0cd06abe2dbd051ab6c523cc1711aed4d395ad41c24e274ac0aeee88222c.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 292, + 555, + 337 + ], + "lines": [ + { + "bbox": [ + 54, + 292, + 555, + 337 + ], + "spans": [ + { + "bbox": [ + 54, + 292, + 555, + 337 + ], + "type": "text", + "content": "Figure 2. Conceptual illustration of different methods. (a)-(e) compare training objectives and sampling trajectories across different methods. Arrows show optimization targets, and red dashed lines represent actual sampling trajectories, which are curved due to the optimization not achieving the theoretical optimum. (e) shows our progressive reflow method achieves better approximation. (f) presents how our proposed aligned v-prediction works between timesteps " + }, + { + "bbox": [ + 54, + 292, + 555, + 337 + ], + "type": "inline_equation", + "content": "[t, t + 1]" + }, + { + "bbox": [ + 54, + 292, + 555, + 337 + ], + "type": "text", + "content": ", it reduces prediction deviation with velocity direction correction." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 309, + 268, + 353, + 276 + ], + "blocks": [ + { + "bbox": [ + 309, + 268, + 353, + 276 + ], + "lines": [ + { + "bbox": [ + 309, + 268, + 353, + 276 + ], + "spans": [ + { + "bbox": [ + 309, + 268, + 353, + 276 + ], + "type": "image", + "image_path": "f4ff1e156a8e63069d7297e34a2c5f3e3023548aa177d966d28ee1fd52013d80.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 362, + 267, + 413, + 276 + ], + "lines": [ + { + "bbox": [ + 362, + 267, + 413, + 276 + ], + "spans": [ + { + "bbox": [ + 362, + 267, + 413, + 276 + ], + "type": "text", + "content": "optimation goal" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 417, + 267, + 461, + 276 + ], + "blocks": [ + { + "bbox": [ + 417, + 267, + 461, + 276 + ], + "lines": [ + { + "bbox": [ + 417, + 267, + 461, + 276 + ], + "spans": [ + { + "bbox": [ + 417, + 267, + 461, + 276 + ], + "type": "image", + "image_path": "53d422977a58b690b46f23f008e94fc4e95cfa030cb087615b0c70a1479f869c.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 267, + 541, + 276 + ], + "lines": [ + { + "bbox": [ + 470, + 267, + 541, + 276 + ], + "spans": [ + { + "bbox": [ + 470, + 267, + 541, + 276 + ], + "type": "text", + "content": "optimization goal (ours)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 54, + 357, + 296, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 357, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 54, + 357, + 296, + 501 + ], + "type": "text", + "content": "scratch [17]. InstaFlow [18] first extended ReFlow to large-scale text-to-image models through consecutive ReFlow to straighten the ODE trajectory, followed by distillation to achieve single-step sampling. Subsequently, some works explored improving ReFlow's effectiveness or simplifying its training[13, 14, 42, 43]. While ReFlow showed promise for single-step generation, its few-step sampling performance lagged behind state-of-the-art methods [30, 34, 39]. To address this limitation, PeRFlow [44] proposed trajectory partitioning into time windows, achieving competitive few-step sampling through localized straightening within each temporal segment." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 55, + 513, + 251, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 513, + 251, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 513, + 251, + 526 + ], + "type": "text", + "content": "2.4. Privileged Information in Distillation" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 55, + 532, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 616 + ], + "type": "text", + "content": "Although knowledge distillation has been proven effective as a model compression technique and further extended successfully to diffusion model acceleration, the theoretical explanation for its efficacy has remained elusive. How 'dark knowledge' is effectively captured from teacher models and utilized to guide student learning remains a fundamental theoretical question [6]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": "Lopez-Paz et al. [19] presented a unified theoretical framework that connects distillation with privileged information, establishing a generalized framework for understanding machine-to-machine knowledge transfer. Viewing distillation as a transfer of privileged information, TAKD [25] showed that an assistant model of intermediate capacity could more effectively mediate the knowledge flow between teacher and student models." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 314, + 356, + 374, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 356, + 374, + 369 + ], + "spans": [ + { + "bbox": [ + 314, + 356, + 374, + 369 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 376, + 555, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 496 + ], + "type": "text", + "content": "We present ProReflow, a more robust flow model training method. Our approach is motivated by the observation that training efficient few-step flow models faces two main challenges: (1) the significant trajectory approximation gap between teacher and student models, and (2) the difficulty in achieving accurate velocity prediction across large time intervals. To address these challenges, we propose progressive reflow for stable optimization of sample trajectory and aligned v-prediction for achieving precise velocity prediction, respectively, shown in Fig. 2." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 503, + 504, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 503, + 504, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 504, + 516 + ], + "type": "text", + "content": "3.1. Temporal Segmentation for ReFlow" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": "Rectified Flow ReFlow aims to achieve temporally consistent velocity predictions across all timesteps. Given initial Gaussian distribution " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\pi_0" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": " and target image distribution " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\pi_1" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "X_1 \\sim \\pi_1" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "X_0 \\sim \\pi_0" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": ". Reflow defines a linear process from " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\pi_0" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\pi_1" + }, + { + "bbox": [ + 313, + 521, + 554, + 593 + ], + "type": "text", + "content": ", where the corresponding sampling process follows the ODE:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 369, + 601, + 553, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 601, + 553, + 615 + ], + "spans": [ + { + "bbox": [ + 369, + 601, + 553, + 615 + ], + "type": "interline_equation", + "content": "d X _ {t} = v \\left(X _ {t}, t\\right) d t, \\quad t \\in [ 0, 1 ], \\tag {1}", + "image_path": "bbe63cafac76b6229e4012a34dc8479bad8fee7bc2c0afdcbe9e59d74362ab64.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 623, + 555, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 623, + 555, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 623, + 555, + 647 + ], + "type": "text", + "content": "Then, it formulates a least-squares optimization problem to ensure the predictions consistency:" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 356, + 654, + 553, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 654, + 553, + 682 + ], + "spans": [ + { + "bbox": [ + 356, + 654, + 553, + 682 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\int_ {0} ^ {1} \\mathbb {E} [ \\| X _ {1} - X _ {0} - v _ {\\theta} (X _ {t}, t) \\| ^ {2} ], \\tag {2}", + "image_path": "03fa478dfde0c38254a3222b534b92e30e5f4280fdccce7a57bc3721f9513361.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 313, + 689, + 441, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 441, + 702 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 441, + 702 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 441, + 702 + ], + "type": "inline_equation", + "content": "X_{t} = tX_{1} + (1 - t)X_{0}" + }, + { + "bbox": [ + 313, + 689, + 441, + 702 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28031" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 79, + 262, + 186 + ], + "blocks": [ + { + "bbox": [ + 86, + 79, + 262, + 186 + ], + "lines": [ + { + "bbox": [ + 86, + 79, + 262, + 186 + ], + "spans": [ + { + "bbox": [ + 86, + 79, + 262, + 186 + ], + "type": "image", + "image_path": "565469283a4a3a8ce982993175ded6899658c0c2eceecf05324112c060eb11d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 198, + 293, + 242 + ], + "lines": [ + { + "bbox": [ + 55, + 198, + 293, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 293, + 242 + ], + "type": "text", + "content": "Figure 3. Performance of our models under different factors of classifier-free guidance (CFG) on COCO-2017. CFG scale ranges from 2 to 7. I and II stands for ProReflow-I with 4 steps and ProReflow-II with 2 steps, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "text", + "content": "Piecewise ReFlow Aimed at improving the few-step generation, PeRFlow divides the sampling trajectory into multiple time windows, defined by endpoints " + }, + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "inline_equation", + "content": "1 = t_{K} > \\dots > t_{k} > t_{k - 1} > \\dots > t_{0} = 0" + }, + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "text", + "content": ". Within each time window " + }, + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "inline_equation", + "content": "[t_k, t_{k - 1})" + }, + { + "bbox": [ + 55, + 262, + 296, + 346 + ], + "type": "text", + "content": " formed by adjacent endpoints, PeRFlow assumes a linear process to straighten the trajectory, thus eq.(2) can be reformulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 351, + 294, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 351, + 294, + 393 + ], + "spans": [ + { + "bbox": [ + 59, + 351, + 294, + 393 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\sum_ {k = 1} ^ {K} \\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\left[ \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\right], \\tag {3}", + "image_path": "dbc2b00e35acc0544f7f3dd72094f30d3fbd676aa291487c80894a7eca5cbfea.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 393, + 295, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 295, + 432 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 295, + 432 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 393, + 295, + 432 + ], + "type": "inline_equation", + "content": "z_{t} = \\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}" + }, + { + "bbox": [ + 55, + 393, + 295, + 432 + ], + "type": "text", + "content": ". Finally, PeRFlow results in a piecewise linear trajectory composed of multiple segments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 437, + 170, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 170, + 451 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 170, + 451 + ], + "type": "text", + "content": "3.2. Progressive ReFlow" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 455, + 295, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 295, + 515 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 295, + 515 + ], + "type": "text", + "content": "PeRFlow originally sets the number of time windows to 4. Despite achieving improvement in few-step inference, PeRFlow faces a significant optimization challenge: it attempts to approximate the teacher model's irregular trajectory using four linear intervals within a single training stage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 516, + 295, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 516, + 295, + 598 + ], + "spans": [ + { + "bbox": [ + 55, + 516, + 295, + 598 + ], + "type": "text", + "content": "We propose a multi-stage progressive training scheme to tackle this challenge. Rather than directly mapping the original trajectory to four time windows, our method first obtains an eight-window approximation from the original trajectory, and subsequently apply Cross-windows ReFlow to refine this eight-window representation into the target four-window configuration." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 599, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 599, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 599, + 296, + 635 + ], + "type": "text", + "content": "Cross-windows ReFlow Consider three consecutive time points " + }, + { + "bbox": [ + 55, + 599, + 296, + 635 + ], + "type": "inline_equation", + "content": "t_{k-1}, t_k, t_{k+1}" + }, + { + "bbox": [ + 55, + 599, + 296, + 635 + ], + "type": "text", + "content": ". The optimization objectives in first training stage can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 641, + 294, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 641, + 294, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 641, + 294, + 714 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\theta} \\left(\\mathbb {E} _ {z _ {t _ {k}} \\sim \\pi_ {k}} \\int_ {t _ {k - 1}} ^ {t _ {k}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k}}}{t _ {k - 1} - t _ {k}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t + \\right. \\\\ \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k}} - z _ {t _ {k + 1}}}{t _ {k} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t \\Bigg), \\tag {4} \\\\ \\end{array}", + "image_path": "b9221c1bb813f53f26c9fc02e90d42a011af53e64ea87ca082c64a442e2b3e47.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 350, + 89, + 518, + 163 + ], + "blocks": [ + { + "bbox": [ + 350, + 89, + 518, + 163 + ], + "lines": [ + { + "bbox": [ + 350, + 89, + 518, + 163 + ], + "spans": [ + { + "bbox": [ + 350, + 89, + 518, + 163 + ], + "type": "image", + "image_path": "7a18179b322256a4976e13096526107d177f46629151ec9b90fa760336dd0672.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 314, + 174, + 553, + 240 + ], + "lines": [ + { + "bbox": [ + 314, + 174, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 314, + 174, + 553, + 240 + ], + "type": "text", + "content": "Figure 4. FID on COCO-30K. The yellow curve shows results trained with 4 windows and evaluated using 4 inference steps, while the blue curve represents the model trained with 8 windows and evaluated using 8 inference steps. Both configurations are compared against their baselines where " + }, + { + "bbox": [ + 314, + 174, + 553, + 240 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 314, + 174, + 553, + 240 + ], + "type": "text", + "content": " (MSE loss only). Each model is trained for 10,000 iterations with batch size 32." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "z_{t} = \\left\\{ \\begin{array}{ll}\\alpha_{t}z_{t_{k}} + (1 - \\alpha_{t})z_{t_{k - 1}}, & t\\in [t_{k - 1},t_{k})\\\\ \\beta_{t}z_{t_{k + 1}} + (1 - \\beta_{t})z_{t_{k}}, & t\\in [t_{k},t_{k + 1}) \\end{array} \\right." + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k} - t_{k - 1}}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "\\beta_{t} = \\frac{t - t_{k}}{t_{k + 1} - t_{k}}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": ". In adjacent time windows, trajectories evolve from " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "z_{t_{k - 1}}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "z_{t_k}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "[t_{k - 1},t_k]" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": ", and from " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "z_{t_k}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "z_{t_{k + 1}}" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "inline_equation", + "content": "[t_k,t_{k + 1}]" + }, + { + "bbox": [ + 313, + 261, + 553, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "text", + "content": "Cross-windows ReFlow aligns the optimization direction by guiding trajectories in both intervals to progress from " + }, + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "inline_equation", + "content": "z_{t_{k-1}}" + }, + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "inline_equation", + "content": "z_{t_{k+1}}" + }, + { + "bbox": [ + 313, + 335, + 553, + 371 + ], + "type": "text", + "content": ", thus eq.(4) can be reformulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 389, + 553, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 389, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 318, + 389, + 553, + 427 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {z _ {t _ {k + 1}} \\sim \\pi_ {k + 1}} \\int_ {t _ {k - 1}} ^ {t _ {k + 1}} \\| \\frac {z _ {t _ {k - 1}} - z _ {t _ {k + 1}}}{t _ {k - 1} - t _ {k + 1}} - v _ {\\theta} (z _ {t}, t) \\| ^ {2} d t, \\tag {5}", + "image_path": "bfc12ea474e56a0a346441cc4a522ab47b8d0071f6626d19ae17e7e1c955c271.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 426, + 535, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 426, + 535, + 443 + ], + "spans": [ + { + "bbox": [ + 314, + 426, + 535, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 314, + 426, + 535, + 443 + ], + "type": "inline_equation", + "content": "z_{t} = \\alpha_{t}z_{t_{k + 1}} + (1 - \\alpha_{t})z_{t_{k - 1}},\\alpha_{t} = \\frac{t - t_{k - 1}}{t_{k + 1} - t_{k - 1}}." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "text", + "content": "Theoretical Explanation Based on the theoretical framework of knowledge distillation [19], we can explain the effectiveness of Progressive ReFlow. Consider three key functions: the teacher function " + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "inline_equation", + "content": "f_{t} \\in \\mathcal{F}_{t}" + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "text", + "content": " representing the original diffusion trajectory, an intermediate function " + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "inline_equation", + "content": "f_{a} \\in \\mathcal{F}_{a}" + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "text", + "content": " for the 8-segment approximation, and the student function " + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "inline_equation", + "content": "f_{s} \\in \\mathcal{F}_{s}" + }, + { + "bbox": [ + 313, + 445, + 555, + 554 + ], + "type": "text", + "content": " for the target 4-segment representation. According to the VC theory [41], when the student learns directly from the teacher, the learning rate is bounded by:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 358, + 569, + 553, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 569, + 553, + 596 + ], + "spans": [ + { + "bbox": [ + 358, + 569, + 553, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {t}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {l}, \\tag {6}", + "image_path": "6ae41b39de7196fe473d7d071e0a295a4b97d940fd6e553b8be567cc53230d7a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\beta \\in [\\frac{1}{2}, 1]" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " denotes the learning rate associated with task difficulty, " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\varepsilon_{l}" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " represents the approximation error, " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " represents the error, " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\cdot)" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " represent the estimation error and approximation error, respectively.. The challenge lies in the significant capacity gap between the complex trajectory and the 4-segment approximation, resulting in a small " + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 613, + 555, + 697 + ], + "type": "text", + "content": " that indicates difficult learning." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "type": "text", + "content": "Progressive ReFlow decomposes this challenging pro" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28032" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 73, + 141, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 73, + 141, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 141, + 84 + ], + "type": "text", + "content": "cess into two stages:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 72, + 91, + 296, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 91, + 296, + 118 + ], + "spans": [ + { + "bbox": [ + 72, + 91, + 296, + 118 + ], + "type": "interline_equation", + "content": "\\text {S t a g e} 1: \\mathcal {R} (f _ {a}) - \\mathcal {R} (f _ {t}) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}}\\right) + \\varepsilon_ {a t}, \\tag {7}", + "image_path": "d81b0a75257d5b92baaa8e2decbaf347729a6884d07c1278043a3534a7697913.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 72, + 120, + 296, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 120, + 296, + 147 + ], + "spans": [ + { + "bbox": [ + 72, + 120, + 296, + 147 + ], + "type": "interline_equation", + "content": "\\text {S t a g e} 2: \\mathcal {R} \\left(f _ {s}\\right) - \\mathcal {R} \\left(f _ {a}\\right) \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {s a}. \\tag {8}", + "image_path": "26eea36ee556b333fe7216f8baf293035060a85a5a0c27bef45e50fdb2f52e3f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 154, + 263, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 154, + 263, + 166 + ], + "spans": [ + { + "bbox": [ + 55, + 154, + 263, + 166 + ], + "type": "text", + "content": "The effectiveness is theoretically guaranteed when:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 60, + 173, + 296, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 173, + 296, + 201 + ], + "spans": [ + { + "bbox": [ + 60, + 173, + 296, + 201 + ], + "type": "interline_equation", + "content": "\\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {a} \\right| _ {C}}{n ^ {\\beta_ {1}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta_ {2}}}\\right) + \\varepsilon_ {a t} + \\varepsilon_ {s a} \\leq \\mathcal {O} \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\beta}}\\right) + \\varepsilon_ {s}, \\tag {9}", + "image_path": "2c252d60e01d7fbb45dd0934cc5bf66bc59e86fa2bd8632e35f7752518477d5d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "text", + "content": "this inequality is satisfied in practice due to two key principles: (1) 8-segment allows for better fitting of the teacher's complex sampling trajectory, leading to smaller combined approximation error " + }, + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "inline_equation", + "content": "(\\varepsilon_{at} + \\varepsilon_{sa} < \\varepsilon_l)" + }, + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "text", + "content": ", (2) Enhanced optimization efficiency through the progressive process, where each stage solves a simpler problem compared to direct optimization, resulting in " + }, + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "inline_equation", + "content": "\\beta_1, \\beta_2 > \\beta" + }, + { + "bbox": [ + 55, + 207, + 296, + 291 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 298, + 177, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 298, + 177, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 298, + 177, + 312 + ], + "type": "text", + "content": "3.3. Aligned V-prediction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 316, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 296, + 376 + ], + "type": "text", + "content": "We analyzed approximate error in the optimization process and found that directional errors lead to more significant performance degradation compared to magnitude errors, shown in Fig.1 (b). We then propose aligned " + }, + { + "bbox": [ + 55, + 316, + 296, + 376 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 55, + 316, + 296, + 376 + ], + "type": "text", + "content": "-prediction, which emphasizes direction alignment in training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": "Direction Matters Consider two arbitrary points " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "z_{t_{i-1}}" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "z_{t_i}" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": " along the trajectory. Given the target vector " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "v = z_{t_i} - z_{t_{i-1}}" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": " and the model prediction " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": ". According to the law of cosines, the error between " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 376, + 296, + 423 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 431, + 295, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 431, + 295, + 445 + ], + "spans": [ + { + "bbox": [ + 111, + 431, + 295, + 445 + ], + "type": "interline_equation", + "content": "r = | p | ^ {2} + | v | ^ {2} - 2 | p | | v | \\cos \\theta , \\tag {10}", + "image_path": "749d4666959653f932c6f557867389a05271148a232324cf188db14bd599317d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "spans": [ + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "text", + "content": " denotes the angle between " + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 454, + 295, + 476 + ], + "type": "text", + "content": ". We analyze two extreme cases:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 478, + 269, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 478, + 269, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 478, + 269, + 491 + ], + "type": "text", + "content": "- Misaligned, accurate magnitude " + }, + { + "bbox": [ + 55, + 478, + 269, + 491 + ], + "type": "inline_equation", + "content": "(|p| = |v|, \\theta = \\epsilon)" + }, + { + "bbox": [ + 55, + 478, + 269, + 491 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 129, + 498, + 295, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 498, + 295, + 512 + ], + "spans": [ + { + "bbox": [ + 129, + 498, + 295, + 512 + ], + "type": "interline_equation", + "content": "r _ {1} = 2 | v | ^ {2} (1 - \\cos \\epsilon); \\tag {11}", + "image_path": "0558357706fe06f2d47879512369ac94de1b7286fc36fe44f414d3f27b69e6d8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 521, + 281, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 281, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 281, + 533 + ], + "type": "text", + "content": "- Aligned, inaccurate magnitude " + }, + { + "bbox": [ + 55, + 521, + 281, + 533 + ], + "type": "inline_equation", + "content": "(\\theta = 0, |p| = |v| + \\epsilon)" + }, + { + "bbox": [ + 55, + 521, + 281, + 533 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 77, + 540, + 295, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 540, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 77, + 540, + 295, + 555 + ], + "type": "interline_equation", + "content": "r _ {2} = \\left(| v | + \\epsilon\\right) ^ {2} + | v | ^ {2} - 2 | v | \\left(| v | + \\epsilon\\right) = \\epsilon^ {2}. \\tag {12}", + "image_path": "52aa7259d2fa42f7e6a7c37be10d2b0b8722e2f31f420873c581941073c8f2ee.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "inline_equation", + "content": "y = r_{1} - r_{2}" + }, + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "text", + "content": ". Using Taylor expansion for small " + }, + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 563, + 271, + 575 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 138, + 583, + 295, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 583, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 138, + 583, + 295, + 597 + ], + "type": "interline_equation", + "content": "y = \\left(| v | ^ {2} - 1\\right) \\epsilon^ {2}. \\tag {13}", + "image_path": "334f1c83257cd2aa8d2d4ee8b3cf78f9c19f43d4094019a426f941f82098a272.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "text", + "content": "Our empirical measurements using real image-noise pairs during training show that " + }, + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "inline_equation", + "content": "|v|" + }, + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "text", + "content": " typically ranges from 70 to 120, yielding " + }, + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "inline_equation", + "content": "y > 0" + }, + { + "bbox": [ + 55, + 605, + 295, + 665 + ], + "type": "text", + "content": " with a substantial margin. This indicates that directional errors lead to significantly larger performance degradation than magnitude errors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "text", + "content": "Directional Alignment Our analysis reveals that directional components of " + }, + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "text", + "content": " play a more crucial role in generation quality than magnitude. Based on this, we proposed aligned v-prediction in flow matching, which incorporates" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 72, + 554, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 118 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 118 + ], + "type": "text", + "content": "directional alignment through cosine similarity measurements. Specifically, we propose a novel flow matching loss function that places greater emphasis on directional alignment:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 125, + 554, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 125, + 554, + 138 + ], + "spans": [ + { + "bbox": [ + 319, + 125, + 554, + 138 + ], + "type": "interline_equation", + "content": "L = (1 - \\alpha) \\cdot \\operatorname {M S E} (v, p r e d) + \\alpha \\cdot (1 - \\cos (v, p r e d)), \\tag {14}", + "image_path": "fa9b0d4bcb4f46fe6925418c1e739ce9c25a3fd509ccae684f3e4f870a8d129b.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 143, + 554, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 143, + 554, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 143, + 554, + 190 + ], + "type": "text", + "content": "where the first term provides basic magnitude consistency, the second term enforces explicit directional alignment via cosine similarity. The hyperparameter " + }, + { + "bbox": [ + 313, + 143, + 554, + 190 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 143, + 554, + 190 + ], + "type": "text", + "content": " balances the relative importance between magnitude and direction." + } + ] + } + ], + "index": 21 + }, + { + "type": "code", + "bbox": [ + 316, + 217, + 553, + 472 + ], + "blocks": [ + { + "bbox": [ + 320, + 203, + 468, + 215 + ], + "lines": [ + { + "bbox": [ + 320, + 203, + 468, + 215 + ], + "spans": [ + { + "bbox": [ + 320, + 203, + 468, + 215 + ], + "type": "text", + "content": "Algorithm 1: ProReflow Algorithm" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "lines": [ + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "spans": [ + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " dataset, " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "f_{\\phi}" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " teacher model, " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " : list of window numbers (e.g., [8,4,2]), " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " : loss weight (default=0.1) 1 Initialize student model " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "f_{\\theta}\\gets f_{\\phi}" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n2 for k in K do \n3 Split time [0, 1] into k windows; \n4 while not converged do \n5 Sample " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " from dataset D; \n6 Sample " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim N(0,1)" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n7 Sample timestep t and locate window " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "[t_1,t_2]" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "t\\in [t_1,t_2]" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " .. \n8 " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "z_{t_2} = t_2*x + (1 - t_2)\\epsilon" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n9 Compute " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "z_{t_1}" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "f_{\\phi}" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " .. \n10 " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "z_{t} = t*x + (1 - t)\\epsilon" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n11 Compute target velocity " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "v = x - \\epsilon" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n12 Predict " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "v_{\\theta} = f_{\\theta}(z_t,t)" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " .. \n13 " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = (1 - \\alpha)\\mathrm{MSE}(v,v_{\\theta}) + \\alpha \\mathrm{Dir}(v,v_{\\theta})" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \n14 Update parameters " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "text", + "content": " . \nend \nend \nOutput: Trained model " + }, + { + "bbox": [ + 316, + 217, + 553, + 472 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "code_body" + } + ], + "index": 23, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "text", + "content": "Hyperparameter Configuration Increasing the value of " + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "text", + "content": " enhances the directional supervision in the optimization objective. When " + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "text", + "content": ", the loss function degenerates to the conventional MSE loss. To determine the optimal hyperparameter configuration, we systematically evaluated different settings: We randomly sampled 0.8M images from LAION-art as our training set and fine-tuned SDv1.5 with different " + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 486, + 554, + 593 + ], + "type": "text", + "content": " values while maintaining the same number of windows. We computed FID on coco-30k to evaluate these models." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": "As shown in Fig. 4, the choice of " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": " significantly impacts the model performance. Among the evaluated " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": " values, more positive gains were observed with windows " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "= 4" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": " compared to windows " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "= 8" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": ", which may be attributed to the increased importance of directional consistency at larger window spans. Our experiment results show that " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": " works well in all experiment settings, thus we maintained " + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 313, + 594, + 554, + 689 + ], + "type": "text", + "content": " for subsequent experiments." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "Combining progressive reflow and aligned " + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "-prediction, we present ProReflow, as shown in Algorithm 1." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28033" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 113, + 296, + 235 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "type": "text", + "content": "Table 1. Performance comparison on COCO-2017 validation set, following the evaluation setup in [40]. Our method outperforms existing flow-based approaches." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 113, + 296, + 235 + ], + "lines": [ + { + "bbox": [ + 56, + 113, + 296, + 235 + ], + "spans": [ + { + "bbox": [ + 56, + 113, + 296, + 235 + ], + "type": "table", + "html": "
MethodStepFID (↓)CLIP Score(↑)
2-Reflow [18]249.3227.36
2-Reflow [18]432.9728.93
Instaflow-0.9B [18]271.5426.07
Instaflow-0.9B [18]4102.4124.39
PeRFlow [44]423.8130.24
ProReflow-I (ours)422.9730.29
ProReflow-II (ours)227.5927.79
ProReflow-II (ours)422.0329.95
", + "image_path": "276c923c89404481677cb5e0e946e37051ac63929f6bcd1fd383de0a999be01b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 264, + 138, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 138, + 279 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 138, + 279 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 290, + 203, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 290, + 203, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 290, + 203, + 304 + ], + "type": "text", + "content": "4.1. Experiment Configuration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 313, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 296, + 434 + ], + "type": "text", + "content": "Model and Dataset We evaluate our proposed method primarily on Stable Diffusion v1.5 and Stable Diffusion XL. During training, we freeze all modules except the UNet and employ BF16 mixed precision training. For SDv1.5, we initialize our training process with windows numbers=8 and progressively apply our method to derive ProReflow-I (4 windows), which subsequently serves as the basis for developing ProReflow-II. For SDXL, we adopt training configurations established in ProReflow-I on SDXL to develop ProReflow-SDXL, achieving four-steps sampling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "text", + "content": "As for multi-stage training, we maintain consistency in the teacher model's sampling trajectory across different training stages by fixing the total DDIM steps to 32. Specifically, when windows " + }, + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "inline_equation", + "content": "= 8" + }, + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "text", + "content": ", we use 4 DDIM steps within each window to derive the endpoint from the starting point. For windows " + }, + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "inline_equation", + "content": "= 4" + }, + { + "bbox": [ + 55, + 439, + 296, + 547 + ], + "type": "text", + "content": ", we use 8 DDIM steps per window. This ensures that the teacher's sampling trajectory remains identical across different training stages, allowing for fair comparisons and stable optimization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "text", + "content": "SDv1.5 is trained on the LAION-Art dataset, with all images center-cropped to " + }, + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "text", + "content": " resolution following its default setup. For SDXL, we fine-tune the model using a combination of LAION-Art and 1.5 million samples from the laion2B-en-aesthetic dataset, with all images center-cropped to " + }, + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 55, + 552, + 296, + 635 + ], + "type": "text", + "content": " resolution. All experiments were conducted on 8 NVIDIA H20 GPUs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "content": "Evaluation Setting Following common practice in text-to-image generation, we adopt two widely-used quantitative metrics: Fréchet Inception Distance (FID) [5] and clip score [28]. The evaluation is mainly conducted on two standard benchmarks: MS COCO 2014 validation dataset [15] and MS COCO 2017 validation dataset [15]." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 102, + 555, + 376 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "type": "text", + "content": "Table 2. Performance comparison on COCO-2014 validation set, following the evaluation setup in [11]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 102, + 555, + 376 + ], + "lines": [ + { + "bbox": [ + 313, + 102, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 555, + 376 + ], + "type": "table", + "html": "
MethodTime (↓)StepFID (↓)
ODE-solver based methods
DPMSolver [21]0.88s259.78
DPMSolver [21]0.34s822.44
DPMSolver++ [20]0.26s422.36
DDIM(our teacher) [36]-3210.05
Distillation-based methods
LCM-LoRA [23]0.12s224.28
LCM-LoRA [23]0.19s423.62
UniPC [46]0.19s423.30
Flash Diffusion [1]0.19s412.41
PCM [39]0.19s411.70
Flow-based methods
Instaflow-0.9B [18]0.13s224.61
Instaflow-0.9B [18]0.21s444.01
2-ReFlow [18]0.13s220.17
2-ReFlow [18]0.21s415.32
PeRFlow [44]0.21s412.01
ProReflow-I (ours)0.21s411.16
ProReflow-II (ours)0.13s215.44
ProReflow-II (ours)0.21s410.70
", + "image_path": "61226bf598b91abc7daddb47aaefb098174ff52b600e43803e11baeb9abe6598.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 396, + 433, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 433, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 433, + 409 + ], + "type": "text", + "content": "4.2. Quantitative Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 414, + 555, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 414, + 555, + 569 + ], + "spans": [ + { + "bbox": [ + 312, + 414, + 555, + 569 + ], + "type": "text", + "content": "We first compare our method with other flow-based acceleration approaches on COCO-2017 validation set, as shown in Table 1. With 4 inference steps, ProReflow-II achieves an FID of 22.03 and a CLIP score of 29.95, showing significant improvements over 2-ReFlow, Instaflow and PeRFlow. Even with only 2 steps, ProReflow-II maintains competitive performance. ProReflow-I also demonstrates strong performance with an FID of 22.97 and the highest CLIP score of 30.29. Table 2 summarizes the comprehensive evaluation results Result on COCO-2014 validation dataset with other diffusion acceleration methods. With 32-step DDIM serving as our teacher model, ProReflow-II achieves a competitive FID of 10.70 using only 4 steps." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 569, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 569, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 569, + 555, + 617 + ], + "type": "text", + "content": "Table 3 presents a comprehensive comparison of our method with advanced acceleration approaches on SDXL. Our method achieves state-of-the-art performance while maintaining the same inference cost." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 624, + 450, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 450, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 450, + 637 + ], + "type": "text", + "content": "4.3. Qualitative Comparison" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "content": "We compared our method against leading flow-based approaches (Rectified Flow, InstaFlow, and PerFlow) as shown in Figure 5. Our method demonstrates superior performance across multiple aspects: it achieves more faithful detail preservation, renders more coherent global structures, and produces sharper textures with fewer artifacts." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28034" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 71, + 555, + 586 + ], + "blocks": [ + { + "bbox": [ + 57, + 71, + 555, + 586 + ], + "lines": [ + { + "bbox": [ + 57, + 71, + 555, + 586 + ], + "spans": [ + { + "bbox": [ + 57, + 71, + 555, + 586 + ], + "type": "image", + "image_path": "32f9e593ef686388968f01f578e7cfa64f1e349182fb30a2144f50174c38da54.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 593, + 555, + 617 + ], + "lines": [ + { + "bbox": [ + 55, + 593, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 593, + 555, + 617 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of image generation results. Our method demonstrates superior performance in detail rendering compared to other flow-based approaches at both 2-steps and 4-steps sampling." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 637, + 294, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 637, + 294, + 708 + ], + "spans": [ + { + "bbox": [ + 55, + 637, + 294, + 708 + ], + "type": "text", + "content": "Specifically, while baseline methods often struggle with detail preservation and suffer from blurry regions or structural distortions, our approach consistently maintains both fine-grained details and global coherence across various scenarios. This comprehensive improvement in generation quality validates the effectiveness of our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 314, + 636, + 402, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 636, + 402, + 649 + ], + "spans": [ + { + "bbox": [ + 314, + 636, + 402, + 649 + ], + "type": "text", + "content": "4.4. Training Cost" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "Our method, though multi-staged, is computationally cheaper compared to traditional approaches. ProReflow-II involves three distinct training stages, starting with windows=8, where each stage is trained for 10,000 iterations at" + } + ] + } + ], + "index": 4 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28035" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 113, + 294, + 298 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 294, + 103 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 294, + 103 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 294, + 103 + ], + "type": "text", + "content": "Table 3. Comparison results on SDXL on COCO2017 validation set and COCO2014-10k validation set with 4 steps, following the evaluation setup in [40]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 113, + 294, + 298 + ], + "lines": [ + { + "bbox": [ + 56, + 113, + 294, + 298 + ], + "spans": [ + { + "bbox": [ + 56, + 113, + 294, + 298 + ], + "type": "table", + "html": "
MethodRes.StepsFID (↓)
COCO2017
Perflow1024427.06
Rectified Diffusion1024425.81
ProReflow-SDXL (Ours)1024425.36
COCO2014-10k
SDXL-Lightning1024424.56
SDXL-Turbo1024423.19
LCM1024422.16
PCM1024421.04
Perflow1024420.99
Rectified Diffusion1024419.71
DMDv21024419.32
ProReflow-SDXL (Ours)1024419.10
", + "image_path": "948beccb16d435d1c0c39889da65f4fbf42fbd9c172390324166ec2d68410a7d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "spans": [ + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "text", + "content": "a batch size of 256. Although the number of samples remains consistent across stages, the training time varies due to differences in computational complexity. Following the approach outlined in [44], we randomly sample timesteps per batch, with windows defining the velocity prediction targets: the starting points are derived from noisy real images, while the endpoints are generated by the teacher model. With 32 teacher inference steps uniformly applied across all stages, windows " + }, + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "inline_equation", + "content": "= 4" + }, + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "text", + "content": " requires double the number of steps compared to windows " + }, + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "inline_equation", + "content": "= 8" + }, + { + "bbox": [ + 57, + 319, + 294, + 486 + ], + "type": "text", + "content": ", which directly aligns with their training time ratio. Specifically, ProReflow-I completes its training in 6.5 H20 days, while ProReflow-II extends this by an additional 8.7 days, resulting in a total training duration of 15.2 H20 days." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 497, + 124, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 497, + 124, + 509 + ], + "spans": [ + { + "bbox": [ + 58, + 497, + 124, + 509 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 516, + 147, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 516, + 147, + 529 + ], + "spans": [ + { + "bbox": [ + 58, + 516, + 147, + 529 + ], + "type": "text", + "content": "5.1. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 534, + 294, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 534, + 294, + 592 + ], + "spans": [ + { + "bbox": [ + 58, + 534, + 294, + 592 + ], + "type": "text", + "content": "We conduct ablation studies to examine our two core designs: aligned " + }, + { + "bbox": [ + 58, + 534, + 294, + 592 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 58, + 534, + 294, + 592 + ], + "type": "text", + "content": "-prediction and progressive reflow. Table 4 presents results on COCO-2017 validation set. Both components contribute to model performance, with their combination yielding the best result." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 600, + 146, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 600, + 146, + 612 + ], + "spans": [ + { + "bbox": [ + 58, + 600, + 146, + 612 + ], + "type": "text", + "content": "5.2. CFG Influence" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "text", + "content": "It is well-established that the classifier-free guidance scale " + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "text", + "content": " is a crucial factor affecting the performance of Stable Diffusion. During training, we set " + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "inline_equation", + "content": "w = 1" + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "text", + "content": " (i.e., without classifier-free guidance) throughout all the stages. To thoroughly understand the model's behavior under different guidance settings, we conducted extensive evaluations across a broad range of " + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 58, + 618, + 294, + 712 + ], + "type": "text", + "content": " values from 2 to 7, measuring both FID and CLIP score, results are shown in Figure 3." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 124, + 553, + 196 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 553, + 114 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 553, + 114 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 553, + 114 + ], + "type": "text", + "content": "Table 4. Ablation studies on COCO-2017 validation set. We first show the results of gradually removing progressive reflow, aligned v-prediction, and both components, followed by our full model. We use a guidance scale of 4 for all the models." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 124, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 315, + 124, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 315, + 124, + 553, + 196 + ], + "type": "table", + "html": "
MethodStepsFID (↓)CLIP (↑)
w/o progressive reflow423.4630.21
w/o aligned v-prediction423.0930.25
w/o both423.8130.24
ProReflow-I422.9730.29
", + "image_path": "62116561d66abca3076d00a0d565e8be7a8f580699a12e65ac1bf6212e3c461c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 219, + 406, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 219, + 406, + 232 + ], + "spans": [ + { + "bbox": [ + 316, + 219, + 406, + 232 + ], + "type": "text", + "content": "5.3. Step scalability" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 316, + 237, + 553, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 237, + 553, + 403 + ], + "spans": [ + { + "bbox": [ + 316, + 237, + 553, + 403 + ], + "type": "text", + "content": "Intuitively, for diffusion models, higher sampling steps should lead to better performance. However, this assumption does not always hold in practice, as certain models exhibit counterintuitive behavior. For instance, PeRFlow demonstrates an unexpected increase in FID when increasing sampling steps from 4 to 8 on COCO-2014 [44], which significantly limits its practical applications. We find that our progressive training scheme effectively addresses this limitation by optimizing the model's ability to generalize across varying sampling steps. Although ProReflow-II is trained with fewer window numbers " + }, + { + "bbox": [ + 316, + 237, + 553, + 403 + ], + "type": "inline_equation", + "content": "(= 2)" + }, + { + "bbox": [ + 316, + 237, + 553, + 403 + ], + "type": "text", + "content": ", it achieves lower FID score with 4-steps sampling compared to ProReflow-I, as shown in Table 1 and Table 2, demonstrating its superior performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 316, + 417, + 386, + 429 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 417, + 386, + 429 + ], + "spans": [ + { + "bbox": [ + 316, + 417, + 386, + 429 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 316, + 438, + 553, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 438, + 553, + 592 + ], + "spans": [ + { + "bbox": [ + 316, + 438, + 553, + 592 + ], + "type": "text", + "content": "In this paper, we propose an efficient training framework for flow-based diffusion acceleration. If viewing the optimization process from temporal and spatial dimensions, our method naturally leads to two complementary techniques that correspond to these two dimensions respectively. Temporally, progressive reflow bridges the trajectory approximation gap through curriculum learning, enabling gradual adaptation from more windows to fewer windows. Spatially, our velocity decomposition strategy emphasizes directional alignment over magnitude accuracy in velocity prediction. This principled design not only yields superior sampling quality but also brings advantages in optimization stability, training efficiency, and computational costs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 594, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 594, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 316, + 594, + 553, + 712 + ], + "type": "text", + "content": "Limitations Given promising few-step sampling performance, our method shows potential for one-step generation. However, due to computational constraints, we were unable to train the model with single window to full convergence. Nevertheless, we have validated the effectiveness of velocity decomposition in this challenging setting with the same training cost, only-one-window model equipped with aligned v-prediction demonstrate superior performance compared to the vanilla counterpart. We plan to move to one-step generation when resources allow." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "28036" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 150 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 150 + ], + "type": "text", + "content": "Acknowledgments This work was partly supported by the National Key Research and Development Program of China(No.2024YFB2808903), the Shenzhen Science and Technology Program(JCYJ20220818101014030) and the research grant No.CT20240905126002 of the Doubao Large Model Fund." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 162, + 115, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 162, + 115, + 175 + ], + "spans": [ + { + "bbox": [ + 56, + 162, + 115, + 175 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 182, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 182, + 294, + 226 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 182, + 294, + 226 + ], + "spans": [ + { + "bbox": [ + 61, + 182, + 294, + 226 + ], + "type": "text", + "content": "[1] Clement Chadebec, Onur Tasar, Eyal Benaroche, and Benjamin Aubin. 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Advances in Neural Information Processing Systems, 36, 2024. 6" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28038" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_content_list.json b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..358084b2d92cbeddef2fad311d102195d25a4d1d --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_content_list.json @@ -0,0 +1,1700 @@ +[ + { + "type": "text", + "text": "ProbPose: A Probabilistic Approach to 2D Human Pose Estimation", + "text_level": 1, + "bbox": [ + 158, + 130, + 836, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Miroslav Purkrabek and Jiri Matas Visual Recognition Group Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague purkrmir@fel(cvut.cz", + "bbox": [ + 349, + 181, + 643, + 290 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 325, + 326, + 340 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current state-of-the-art Human Pose Estimation methods ignore out-of-image keypoints in both training and evaluation and use uncalibrated heatmaps as keypoint location representations. We propose ProbPose, which predicts for each keypoint: a calibrated probability of keypoint presence at each location in the activation window, the probability of being outside of it, and its predicted visibility. To address the lack of evaluation protocols for out-of-image keypoints, we introduce the CropCOCO dataset and the Extended OKS (Ex-OKS) metric, which extends OKS to out-of-image points. Tested on COCO, CropCOCO, and OCHuman, ProbPose shows significant gains in out-of-image keypoint localization while also improving in-image localization through data augmentation. Additionally, the model improves robustness along the edges of the bounding box and offers better flexibility in keypoint evaluation. The code and weights are available on the project website1.", + "bbox": [ + 89, + 359, + 483, + 617 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 648, + 220, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human pose estimation (HPE) has seen significant progress, achieving robust performance on standard datasets. The most successful models like ViTPose [32] typically use a top-down, heatmap-based approach, where heatmaps serve as dense representations of keypoint locations across an image.", + "bbox": [ + 89, + 674, + 482, + 765 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we address two limitations of top-down HPE methods: (1) all previous methods overlook out-of-image keypoints during training and, more importantly, ignore them in evaluation, and (2) heatmaps restrict their use to simple point estimates. While seemingly separate, these issues are interrelated and can be addressed through an appropriate choice of representation and loss function.", + "bbox": [ + 89, + 766, + 482, + 873 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9264fed1fb088b7d1b4601da40a0699c37b18ccc5799f5e06beca7f9b78bd56a.jpg", + "image_caption": [ + "Figure 1. ProbPose (left) vs. ViTPose [32] (right) output on a cropped image with the dark part removed. The bounding box, on which the pose estimators operate, is detected by YOLOX-x [5]. ProbPose estimates keypoints outside of the image better, e.g. the right leg which is wrongly aligned with the left leg by ViTPose, for which out-of-image keypoints represent a domain shift." + ], + "image_footnote": [], + "bbox": [ + 516, + 323, + 709, + 487 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/063bdb24d5745424cd9d52d13f5e87e0d9596f500f9996f875865dda6f4f735a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 324, + 903, + 487 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Top-down methods localize keypoints within a specific region called the activation window. This activation window is the part of the image mapped to the predicted heatmap. The activation window often matches the model input and it may exceed image boundaries due to preprocessing steps, such as maintaining aspect ratios or enlarging bounding boxes.", + "bbox": [ + 511, + 611, + 906, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Under challenging conditions, such as heavy occlusion or cropped images, keypoints may fall outside the activation window. Current methods do not address this issue and simply ignore out-of-window keypoints during training. Even more concerning, evaluation metrics such as OKS (Object Keypoint Similarity) and PCK (Percentage of Correct Keypoints) assess only in-image keypoints. This lack of accountability often leads models to predict keypoints inaccurately on other joints when the actual keypoint is not visible in the image. For example, as shown in Fig. 1, the left leg is mistakenly assigned to the same joints as the right leg. Furthermore, current top-down models do not provide any", + "bbox": [ + 511, + 719, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1MiraPurkrabek.github.io/ProbPose/", + "bbox": [ + 107, + 886, + 377, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27124", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "indication of whether a keypoint is inside or outside the activation window, and models are not penalized for attempting to localize every keypoint.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A second challenge in existing HPE methods lies in the reliance on heatmaps as the keypoint representation. Heatmaps provide dense representation of keypoint locations. However, the standard approach of generating target heatmaps with a fixed Gaussian sigma and training with mean square error (MSE) forces the model to output heatmaps with fixed sigmas as well, limiting the accuracy of these estimates.", + "bbox": [ + 89, + 138, + 480, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Decoding heatmaps to obtain a point estimate typically involves taking the argmax, often refined with UDP decoding [9]. While this approach is effective for identifying the most likely pixel, it is optimal only when the goal is to classify a single correct pixel for each keypoint. However, practical applications demand more flexible interpretations of keypoint locations. For example, an application might require an estimate of the smallest area where a keypoint is located with at least $95\\%$ probability, or, as in humanrobot interaction, identify areas where the model has high uncertainty to ensure safe interactions. Heatmaps, which are prone to overconfidence, are not designed to indicate uncertainty or convey \"don't know\" outcomes, even when Bayes risk is high, an essential factor in safety-critical applications.", + "bbox": [ + 89, + 261, + 482, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these limitations, we propose ProbPose, a model with multiple outputs that fully describe each keypoint. ProbPose predicts (1) calibrated presence probabilities indicating whether the keypoint lies within the activation window, (2) keypoint's location within the activation window, (3) quality estimate of the localization and (4) visibility. Moreover, instead of using traditional heatmaps, we employ probability maps.", + "bbox": [ + 89, + 489, + 480, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probability maps differ from heatmaps in several ways: they contain values between 0 and 1 and are normalized to sum to 1, providing calibrated probabilities. Unlike heatmaps, which assume a fixed Gaussian shape, probability maps adapt their shape based on the data, without forcing any assumptions. Additionally, instead of decoding using a simple argmax, we compute the expected OKS for each pixel and select the location that maximizes this score, an approach we term expected OKS maximization. Probability maps are trained using an OKS-based loss modified for dense predictions, formulated as an expected risk minimization problem. Probability maps do not outperform heatmaps on keypoints in the image but have comparable localization ability. Their biggest advantage is in their versatility and better modeling of the underlying distribution. Calibrated probability maps allow for more complex reasoning than point estimates and have a direct interpretation.", + "bbox": [ + 89, + 612, + 482, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since current datasets and metrics lack evaluation protocols for out-of-image keypoints, we introduce a new dataset,", + "bbox": [ + 89, + 869, + 480, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CropCOCO, comprising cropped images from COCO, and the Extended OKS (Ex-OKS) metric, which builds on OKS to evaluate out-of-image keypoints and presence probability.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are:", + "bbox": [ + 535, + 152, + 799, + 165 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. A concept of presence probability that keypoints is in the activation window, distinct from confidence, which measures the model's trust in its own estimate.", + "2. Model for out-of-image keypoints that can localize keypoints within the activation window, even beyond the image boundaries, or predict presence probability for out-of-window keypoints.", + "3. OKSLoss adapted for dense predictions in risk minimization formulation", + "4. We show that cropping-based data augmentation improves out-of-image keypoint localization, supports presence probability estimation, and enhances in-image localization, similar to Hide&Seek [10]", + "5. New CropCOCO dataset and Ex-OKS evaluation metric for more realistic assessment of real-world performance" + ], + "bbox": [ + 511, + 167, + 903, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 513, + 422, + 650, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There are three main approaches to 2D human pose estimation: top-down, bottom-up, and single-stage. Single-stage [22, 23, 28, 31] methods directly predict individuals and their skeletons in an image. Bottom-up methods [3, 6] detect all keypoints first and then group them into individual skeletons. The top-down methods [16, 24, 29, 32, 33], despite their challenges, remain the most successful. They use human detectors to process each bounding box independently, providing the best performance on most datasets.", + "bbox": [ + 511, + 446, + 903, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among top-down methods, heatmap-based approaches are the most popular. Unlike regression-based methods [25, 27], which directly predict 2D coordinates, heatmap-based methods [16, 24, 32] predict a heatmap with the same aspect ratio as the input. The keypoints are then estimated as the maximum of the heatmap. Heatmaps are more robust and easier to train than regression-based methods, although efforts have been made to narrow the gap between the two approaches [18, 26].", + "bbox": [ + 511, + 584, + 903, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key development in heatmap-based methods is UDP (unbiased data processing) [9], which improves coordinate encoding and decoding. Heatmaps are typically defined as 2D Gaussians with a fixed sigma centered on the keypoint. Subpixel decoding allows for smaller heatmaps, reducing computational costs. The maximum value of the heatmap, called the \"confidence,\" is often used for three tasks: visibility estimation, quality estimation, and in/out-of-image decisions. Visibility is sometimes outsourced to specialized heads, quality prediction could be improved by OKS prediction, as shown in [7]. In/out decisions (later defined as presence probability in this paper) are not explicit, as they", + "bbox": [ + 511, + 719, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27125", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/35b997d928c0d097b15e4240a2ec850dce80eab75496bf4c97b4de1ac2f90fde.jpg", + "image_caption": [ + "Figure 2. ProbPose-s (left), compared with ViTPose-s (right), improves localization outside the image and handles occlusion better on COCO (first row) and the proposed CropCOCO (second row). ProbPose estimates points well outside of the image." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 480, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are not needed for OKS evaluation, but are important for visualization and real-world applications.", + "bbox": [ + 89, + 578, + 482, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most heatmap-based methods are trained with MSE loss, which encourages the output heatmap to match the target Gaussian heatmap. All keypoints are treated equally, with the same Gaussian and sigma. The training focuses only on keypoints within the activation window, meaning the model never encounters an empty heatmap. Since the input of the model often extends beyond the bounding box to capture more context, the activation window can include areas outside the image. This enables a limited prediction of keypoints outside the image, although the models are not specifically trained for this task. For more details, see Appendix A in the supplementary.", + "bbox": [ + 89, + 609, + 482, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Heatmap-based approaches can predict keypoints outside of the image to some degree. Regression methods like RLE [13] go even further and predict keypoints further from the image. Our goal is not to localize out-of-image keypoints per se but emphasize their importance in training and evaluation.", + "bbox": [ + 89, + 792, + 482, + 882 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Alternative loss functions have also been proposed.", + "bbox": [ + 109, + 885, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adaptive Wing Loss [30] improves on original Wing Loss [4]. CornerNet [11] introduces a modified Focal Loss (originally in [15]) for object detection. RTMO [17] treats pose estimation as coordinate classification, assuming a normal distribution with varying sigmas for different keypoints, and trains with a negative log likelihood loss. Distribution-based losses such as [21] or Kullback-Leibler divergence have also been used for heatmap-based pose estimation. Most importantly, [19] introduce a new OKSLoss, that is directly tied to the evaluation metric. Their OKSLoss is computed on the predicted keypoints. We modify it to use pixel-wise to optimize probability maps without any shape assumptions.", + "bbox": [ + 511, + 90, + 903, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This paper also applies a cropping data augmentation technique. Similarly to information-dropping methods [10] like Hide&Seek or random bounding box masking, this technique introduces the domain shift by creating more invisible keypoints during training, encouraging the model to leverage the structure of the human body.", + "bbox": [ + 511, + 287, + 903, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The most widely used dataset for 2D human pose estimation is COCO [14], with MPII [1] being a less common alternative. Datasets like OCHuman [34] and CrowdPose [12] focus on multibody problems such as occlusion and self-occlusion. For COCO and related datasets, the evaluation metric is Object Keypoint Similarity (OKS), while Percentage of Correct Keypoints (PCKh) is used for MPII.", + "bbox": [ + 511, + 378, + 903, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However OKS ignores unannotated keypoints, as COCO is not fully annotated – many individuals have missing keypoints. Missing annotations can occur either because the keypoint is outside the image or because of occlusion. All annotated keypoints in current datasets are within the image, as annotating keypoints outside the image would be too costly and imprecise. Additionally, OKS does not penalize guessing, and if a model predicts a keypoint inside the image when it is not present, there is no penalty. Evaluating the presence probability of keypoints (whether they are in the activation window) is crucial for real-world applications and requires out-of-image annotations.", + "bbox": [ + 511, + 483, + 903, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We address these issues by introducing a new dataset, CropCOCO, created by cropping COCO images, along with a new evaluation metric, Extended OKS (Ex-OKS), which accounts for keypoints outside the image.", + "bbox": [ + 511, + 665, + 903, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 737, + 604, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ProbPose introduces several key innovations:", + "bbox": [ + 511, + 762, + 812, + 777 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. A novel approach to keypoint localization using probability maps.", + "2. A different application of OKSLoss [19] corresponding to expected risk minimization.", + "3. A new attribute for each keypoint, termed presence probability.", + "4. A data augmentation technique to handle keypoints outside the image." + ], + "bbox": [ + 511, + 779, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27126", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "5. A double-probmap approach that expands the field of view, enabling localization of keypoints positioned far outside the image.", + "bbox": [ + 89, + 90, + 485, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In combination with visibility and quality estimation, these elements provide a complete description of each keypoint's state in ProbPose - indicating whether it is within the image, visible, and the confidence level of the estimate. The probability map offers calibrated localization estimates. Each component is explained in detail in the following sections.", + "bbox": [ + 89, + 138, + 483, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Probability maps and loss function", + "text_level": 1, + "bbox": [ + 89, + 252, + 393, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In conventional methods, heatmaps are trained with Gaussian targets and MSE loss, resulting in fast convergence, but a Gaussian-shaped bias in output. However, there is no theoretical basis for assuming that the posterior localization probability follows a Gaussian distribution. The normal distribution in OKS metric reflects human-induced error in the annotation process, but we assume the underlaying distribution is not Gaussian but reflects the body shape. During inference, heatmaps typically use the argmax for point localization and the peak value as a combined measure of localization quality and visibility.", + "bbox": [ + 89, + 273, + 483, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our approach, we require the model to output probability maps rather than traditional heatmaps. Unlike heatmaps, probability maps always sum to 1, achieved through Sparsemax [20] as the final activation function.", + "bbox": [ + 89, + 440, + 483, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each pixel in the probability map represents the posterior probability", + "bbox": [ + 89, + 500, + 483, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {L} \\left(x _ {i}\\right) = p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 539, + 480, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{i}$ is pixel coordinate, $k_{j}$ is the j-th keypoint and $AW$ stands for activation window. With Sparsemax, each probability map sums to 1 for each keypoint:", + "bbox": [ + 89, + 563, + 483, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF \\sum_ {x _ {i} \\in A W} p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right) = 1 \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 617, + 480, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We refer to this as the localization probability $p_L(x_i)$ .", + "bbox": [ + 89, + 657, + 457, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1. Loss function", + "text_level": 1, + "bbox": [ + 89, + 678, + 230, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train the probability maps using a modified version of OKSLoss [19], aligned with the evaluation function. The loss is formulated as an expected risk minimization problem.", + "bbox": [ + 89, + 696, + 483, + 756 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {e x p} \\left(x _ {i}\\right) = \\left(1 - O K S \\left(x _ {i}\\right)\\right) \\cdot p _ {L} \\left(x _ {i}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 765, + 482, + 782 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {O K S} \\left(x _ {i}\\right) = (1 - \\alpha) R _ {e x p} \\left(x _ {i}\\right) + \\alpha g \\left(x _ {i}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 785, + 482, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (4), $R_{exp}(x_i)$ represents expected risk and $\\mathcal{L}_{OKS}(x_i)$ is the loss function for pixel $x_i$ . In contrast to [19], we apply OKSLoss on each pixel of probability map instead of on predicted keypoints. This loss encourages pixels with low OKS to have low localization probability and those with high OKS to have higher localization probability.", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c6f8b771598d29a1dac86d426fc4d5af159e75969dd0da2ac51da2b14860d261.jpg", + "image_caption": [ + "(a) Predicted probability map $p_L$", + "Figure 3. UDP [9] decoding of $p_L$ vs. expected OKS maximization. On the left, the white cross marks the maximum value and the light purple one is the point refined by UDP. In the right image, the dark purple cross is maximum expected OKS. The probability map contains a small, one-pixel-wide peak marked by the white cross. Maximizing expected OKS is robust to sharp local peaks and prefers areas with big mass compared to simple maxima." + ], + "image_footnote": [], + "bbox": [ + 517, + 88, + 709, + 287 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c7115537a05bef544aea5dd7c83be680c3544843df1ae100b5fcbfc238ea38d6.jpg", + "image_caption": [ + "(b) Expected OKS map $\\mathbb{E}_{OKS}$" + ], + "image_footnote": [], + "bbox": [ + 709, + 88, + 903, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The term $g(x_{i})$ is the heatmap gradient, computed with the Sobel operator, and serves as a regularizer controlled by the hyperparameter $\\alpha$ . Without regularization, the probability map quickly forms a sharp peak and overfits to training data. Smoothing regularization minimizes differences between neighboring pixels, promoting a smooth distribution without assuming a specific shape, as Gaussian regularization does for MSE-trained heatmaps.", + "bbox": [ + 511, + 450, + 905, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For localization, instead of directly using argmax, we compute the expected OKS (Eq. (5)) for each pixel and take its argmax, refining it with quadratic interpolation for subpixel precision. This approach, based on expected OKS rather than UDP decoding, slightly enhances localization, especially in cases of bimodal heatmaps such as in Fig. 3.", + "bbox": [ + 511, + 578, + 905, + 669 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {O K S} \\left(x _ {i}\\right) = \\sum_ {x _ {j} \\in P M} p _ {L} \\left(x _ {j}\\right) \\cdot O K S \\left(x _ {i}, x _ {j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 691, + 906, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Probability maps offer improved versatility. They allow point estimates, as required by the COCO evaluation protocol, and enable probabilistic queries, such as defining the smallest area containing a keypoint with at least $90\\%$ probability. However, the peak of the probability map can no longer reliably indicate the quality of the localization or the presence of keypoints in the activation window. The former is addressed by predicting the OKS for each keypoint as in [7], and the latter is addressed by directly predicting the keypoint's presence probability.", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27127", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Presence probability", + "text_level": 1, + "bbox": [ + 89, + 90, + 284, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Previous models and evaluation protocols have overlooked the question of whether a keypoint is within the activation window. Top-down approaches assume that the bounding boxes fully enclose all keypoints, but this is not always the case due to factors such as occlusion or crop (see Appendix A in the supplementary for further discussion). Thus, it is essential for the model to assess whether a keypoint is actually present in the activation window. This is usually addressed by thresholding confidence (the maximum heatmap value) with an arbitrary cut-off. However, evaluation protocols have ignored keypoint presence, with models predicting a location regardless.", + "bbox": [ + 89, + 112, + 483, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Presence probability $p(k_{j} \\in AW|img)$ complements probability maps, which inherently assume that keypoints are within the activation window. If the keypoint is outside, the presence probability reflects this; if inside, the probability map provides the location. The visual explanation is in Fig. 4. We abbreviate the presence probability to $p_{p}(k_{j})$ and train it with Binary Cross Entropy loss.", + "bbox": [ + 89, + 294, + 483, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train the presence probability, we need keypoints that are certainly outside the activation window. These samples are generated through various data augmentation techniques, such as scaling and rotation, with random cropping as the primary source.", + "bbox": [ + 89, + 400, + 483, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Calibration", + "text_level": 1, + "bbox": [ + 89, + 484, + 217, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Both the probability maps and presence probability are calibrated. Probability maps are calibrated so that the top $5\\%$ of the map contains $5\\%$ of the GT keypoints, the top $10\\%$ contains $10\\%$ of the GT keypoints, and so on. We achieve this calibration through temperature scaling [8] on CropCOCO. As a result, the calibrated probabilities align with the true underlying distribution, enabling more versatile evaluations beyond simple point estimates. Details and calibration curves are in Appendix B in the supplementary.", + "bbox": [ + 89, + 506, + 483, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Crop image augmentation", + "text_level": 1, + "bbox": [ + 89, + 652, + 323, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As discussed in Appendix A, we consider the image border as a type of occlusion. To train the model to correctly identify keypoints outside the image, we need suitable training samples. Manual annotation of such keypoints is both costly and imprecise, so we generate these samples by cropping existing annotated keypoints out of the image.", + "bbox": [ + 89, + 674, + 482, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depending on the crop strength, the in-the-image keypoint may end up within the activation window but outside the image, or entirely outside the activation window. Keypoints within the activation window but outside the image are used to train probability maps, while those outside the activation window train the presence probability.", + "bbox": [ + 89, + 765, + 482, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The cropping not only provides data for presence probability training but also enhances the model's ability to localize keypoints near the image boundary, extending even", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/126fe217dbd29214f3aa08c1aba97e67739b28137afbb39145793f130e8700cb.jpg", + "image_caption": [ + "(a) Traditional method", + "Figure 4. Key regions in top-down pose estimation. Rectangles represent the bounding box, the model input and the activation window. Right: the double-probmap approach with a larger activation window. The probability map is responsible for localization of keypoints in activation windows (A, B, C) and the presence probability predicts whether the keypoint is outside (D, E). Note that double-probmap has a larger field-of-view. For detailed discussion about keypoint location, see Appendix A." + ], + "image_footnote": [], + "bbox": [ + 516, + 89, + 709, + 227 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0a0514b3c3a8a242de83bebfac39b889dbc7bad7295c8d9ecdac7186e22bc730.jpg", + "image_caption": [ + "(b) Double-probmap approach" + ], + "image_footnote": [], + "bbox": [ + 710, + 89, + 903, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to areas beyond the visible border. This is especially useful for cases where the subject is partially cropped by the image border or in close-up pose estimation, where keypoints may lie far from the visible body. Examples of crops and result visualizations are in the Figs. 1 and 2.", + "bbox": [ + 511, + 404, + 906, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Enlarging activation window size", + "text_level": 1, + "bbox": [ + 513, + 510, + 803, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When predicting keypoints outside the image, a key question is how far from the image we aim to localize them. In applications where out-of-image keypoints localization is essential, it might be helpful to enlarge the activation window. However, simply increasing the input size or activation window typically reduces performance.", + "bbox": [ + 511, + 539, + 905, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this, we propose a double-probmap approach (illustrated in Fig. 4b). In this method, an expert heatmap precisely localizes keypoints within a smaller activation window that matches the model input, while a larger activation window captures keypoints further from the image. The larger probability map has the same resolution but a wider field of view, resulting in a lower effective resolution. Both maps are trained on keypoints within their respective activation areas. If the larger map predicts a keypoint within the smaller activation area, the expert map refines the localization for greater accuracy.", + "bbox": [ + 511, + 637, + 906, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This approach balances the trade-off between field-of-view and precision. The larger map offers a broader field of view, but with lower accuracy, while the expert map maintains precision within a smaller activation window. This method is particularly suitable for applications like close-up pose estimation, where a wide field of view is essential.", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27128", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Data", + "text_level": 1, + "bbox": [ + 89, + 90, + 156, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate ProbPose, we introduce a new evaluation protocol based on OKS and mAP, along with a new dataset specifically designed for out-of-image keypoint localization and presence probability classification.", + "bbox": [ + 89, + 114, + 483, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation metrics", + "text_level": 1, + "bbox": [ + 89, + 186, + 272, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Current metrics, such as OKS and PCK, evaluate only in-image keypoints, overlooking false positives. As a result, models overestimate confidence, guess keypoint locations, and are not penalized for predicting absent keypoints.", + "bbox": [ + 89, + 209, + 482, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We propose a new evaluation approach that checks whether a keypoint is within the activation window and, if so, assesses its precise localization. This approach better reflects real-world scenarios, like human-machine interaction, where knowing if a keypoint cannot be localized is critical. To address this, we introduce Extended OKS (Ex-OKS), an extension of OKS that accommodates keypoints outside the activation window. For bottom-up and single-stage methods, where the activation window spans the entire image, Ex-OKS can be adapted accordingly.", + "bbox": [ + 89, + 270, + 483, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In its localization-only form, Ex-OKS functions identically to the original OKS. However, Ex-OKS extends OKS by accounting for keypoints outside the activation window. The essential goal is for the model to indicate if a keypoint is absent, rather than attempting a guess.", + "bbox": [ + 89, + 421, + 483, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ex-OKS evaluates two variables for each keypoint: location $x_{i}$ and presence probability $p_{p}$ . Although the model outputs a continuous value for $p_{p}$ , a binary decision (0 or 1) is often required in real-world applications, so we optimally threshold it for each model.", + "bbox": [ + 89, + 497, + 483, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Formally, we define Ex-OKS as:", + "bbox": [ + 109, + 573, + 331, + 587 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} = \\left\\{ \\begin{array}{l l} d _ {e} \\left(x _ {i} ^ {*}, x _ {i} ^ {\\prime}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} (\\mathrm {A W}, x _ {i} ^ {\\prime}) & \\text {i f} p _ {p} ^ {*} = 0 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} \\left(x _ {i} ^ {*}, \\mathrm {A W}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 0 \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 602, + 482, + 672 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E x} - \\mathrm {O K S} = \\exp \\left(\\frac {- d _ {i} ^ {2}}{2 k ^ {2} \\sigma^ {2}}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 676, + 482, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": ", where $AW$ stands for activation window, $d_{e}$ is Euclidean distance and $\\cdot^{*}$ and $\\cdot^{\\prime}$ are ground truth and predicted variables, respectively.", + "bbox": [ + 89, + 718, + 482, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "If both the ground truth and the model agree that $p_{p} = 1$ , Ex-OKS defaults to the standard OKS evaluation.", + "bbox": [ + 89, + 763, + 482, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When the ground truth $p_{p}^{*} = 0$ and the model predicts $p_{p}^{\\prime} = 1$ , the penalty depends on the predicted location $x_{i}^{\\prime}$ and its distance from the edge of the activation window, with lower penalties for points near the boundary. Similarly, if $p_{p}^{*} = 1$ but the model predicts $p_{p}^{\\prime} = 0$ , the penalty is based on the ground truth location $x_{i}^{*}$ , with smaller penalties for errors near the border of the activation window.", + "bbox": [ + 89, + 795, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When both $p_{p}^{*} = 0$ and $p_{p}^{\\prime} = 0$ , there is no penalty and the similarity score is 1.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ex-mAP, built on Ex-OKS, extends mAP by incorporating both keypoint localization and presence probability, making it suitable for evaluating models with keypoints outside the activation window.", + "bbox": [ + 511, + 121, + 903, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets", + "text_level": 1, + "bbox": [ + 513, + 191, + 614, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated our model on the COCO dataset to ensure a fair comparison with existing models. All training was conducted on COCO, with crop image augmentation applied in specified experiments.", + "bbox": [ + 511, + 212, + 903, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To assess performance on out-of-image keypoints, we introduce a new dataset, CropCOCO. CropCOCO consists of randomly cropped COCO validation images, with some keypoints positioned outside the activation window. Bounding boxes are recomputed for the cropped images to evaluate the model appropriately. While other researchers can create their own cropped dataset, we release CropCOCO to support reproducibility.", + "bbox": [ + 511, + 273, + 905, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During COCO evaluation, we observed that keypoints near the image boundary are often annotated further inside the image, likely due to annotators avoiding placements near the edge. This causes our model to be penalized for accurately localizing keypoints outside the image. When keypoints near the border are excluded from evaluation, Prob-Pos demonstrates even stronger performance compared to other state-of-the-art methods. Although this issue is minor (causing about a $0.2\\%$ performance difference) and difficult to correct, we highlight it to raise awareness of its potential impact. For further details, see Appendix D.", + "bbox": [ + 511, + 393, + 905, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we evaluated our model on the OCHuman dataset to demonstrate its generalizability across different domains.", + "bbox": [ + 511, + 560, + 905, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 618, + 645, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results in Tab. 1 compare our method with other SOTA approaches on COCO, CropCOCO, and OCHuman datasets using mAP and Ex-mAP metrics. For fair comparison, we evaluate models of similar size. All experiments use ground truth bounding boxes.", + "bbox": [ + 511, + 643, + 905, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ProbPose improves on its baseline model, ViTpose, by approximately $1\\%$ in localization, a gain comparable to that achieved by other information-dropping augmentations like [10]. Importantly, ProbPose demonstrates stronger performance in Ex-OKS, showing improved detection of keypoints outside the activation window due to its direct presence probability prediction, as discussed in Sec. 5.1. Since COCO lacks out-of-image keypoints, Ex-OKS improvement here reflects enhanced presence probability classification. Localization metrics could be slightly higher if not for incorrect annotations near the bounding box borders, discussed further in Appendix D.", + "bbox": [ + 511, + 719, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27129", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1c555994fb691ef72fc2a4689fcde968e59eade72bcb418492344923e305bfb7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelCOCOMAPEx-mAPCropCOCOMAPEx-mAPOCHumanmAPEx-mAP
HRFormer-s [33]75.274.670.964.360.360.0
PVTv2 [29]72.071.570.763.158.558.1
SWIN-t [16]73.572.971.365.058.157.9
ViTPose-s [32]75.975.372.766.560.360.1
ProbPose-s76.676.481.773.960.460.2
ProbPose-s-DP76.275.480.971.461.461.2
", + "bbox": [ + 241, + 88, + 756, + 224 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Keypoint localization accuracy in terms of the standard mAP and the novel Ex-mAP metrics. ProbPose is compared with SOTA models of similar size on the COCO, CropCOCO, and OCHuman datasets. All evaluation is done using GT bounding boxes. DH stands for the double-probmap approach with a wider field of view. To compute Ex-mAP, we select the optimal threshold for each model. The best model is in bold, the second-best is underlined. ProbPose brings significant improvement for out-of-image keypoints and minor improvement on standard COCO.", + "bbox": [ + 89, + 236, + 906, + 305 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The most significant improvement is unsurprisingly observed on CropCOCO, where ProbPose excels at detecting out-of-image keypoints, primarily due to crop data augmentation. Again, the localization metrics could be higher without annotation errors along the bounding box borders.", + "bbox": [ + 89, + 332, + 480, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ProbPose-DP, the double-probmap variant, shows a slight performance decrease on COCO and CropCOCO, reflecting the trade-off between a broader field of view and in-image precision (see Sec. 3.5). In this variant, each heatmap is predicted by one head from shared features, and the larger heatmap decides when to defer to the more precise heatmap. If the larger heatmap estimates the wrong localization, the specialized heatmap cannot correct it.", + "bbox": [ + 89, + 409, + 482, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ProbPose-DP has worse Ex-mAP as it solves a more difficult task. Ex-mAP evaluates keypoint presence in the AW so the larger AW in ProbPose-DP makes presence classification harder as the AW border is further from the image.", + "bbox": [ + 89, + 531, + 482, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ProbPose-DP remains competitive with other SOTA methods, providing a better alternative to simply enlarging the input size or activation window. Interestingly, ProbPose-DP shows a notable improvement in OCHuman, likely due to its extended field of view, which enhances individual differentiation in multi-body scenes.", + "bbox": [ + 89, + 592, + 482, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ProbPose variants perform well on OCHuman (unseen during the training), highlighting their strong generalization across domains.", + "bbox": [ + 89, + 684, + 482, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Presence probability vs. confidence", + "text_level": 1, + "bbox": [ + 89, + 741, + 397, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 1 highlights the advantages of using presence probability over confidence, reflected in the increase in Ex-mAP. For clarity, Fig. 5 shows an additional classification accuracy for CropCOCO and its balanced subset. The task is to classify whether keypoints are inside or outside the activation window, indicating if they should be drawn or used in other applications. CropCOCO is unbalanced as there is much more in-AW than out-of-AW keypoints. To get a balanced subset, we randomly selected keypoints from both", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/011b11334c14357429c08ca6e3ef7561afa0967ff4a04f9899c1cbfe307d6be6.jpg", + "image_caption": [ + "Figure 5. Keypoint presence in the activation window. Accuracy, inside and outside of the AW, of the classification based on thresholding of the ProbPose's presence probability and ViTPose's confidence. The accuracy is measured for CropCOCO dataset (full line) and its balanced subset (dotted line). The proposed presence probability outperforms ViTPose's confidence in both cases, reducing the error by $30\\%$ and $45\\%$ respectively." + ], + "image_footnote": [], + "bbox": [ + 529, + 354, + 867, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "classes to have the same amount of each.", + "bbox": [ + 511, + 686, + 784, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In both balanced and unbalanced datasets, the presence probability outperforms the confidence score from the ViT-Pose model. This improvement is due to confidence not being trained to reflect presence probability, and the standard COCO dataset, without crop data augmentation, lacks sufficient training samples for this purpose.", + "bbox": [ + 511, + 703, + 905, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 also provides insights into confidence thresholding. Current models often use an arbitrary threshold of 0.3 to decide whether to trust predictions without theoretical justification. The evaluation on CropCOCO reveals that the optimal confidence threshold is between 0.15 (for unbalanced datasets) and 0.4 (for balanced datasets). Thus, the commonly used threshold of 0.3 is close to the optimum,", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27130", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cfb353ea2fe5057495fedd2c07f7630a270cb7380e16ffca3f1896546b44f35a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
cropp-mapsCOCOCropCOCO
XX76.073.7
X✓76.472.4
✓X76.681.7
✓✓76.681.7
", + "bbox": [ + 151, + 88, + 421, + 179 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. ProbPose ablation; mAP on COCO and CropCOCO for versions without the probability maps and crop data augmentation. Crop augmentation clearly helps for cropped images. Probability maps bring negligible performance improvement as their main strength is in versatility.", + "bbox": [ + 89, + 190, + 480, + 261 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "which aligns with its generally good results. This study offers guidance on setting an appropriate threshold based on the characteristics of a specific dataset.", + "bbox": [ + 89, + 279, + 482, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Ablation study", + "text_level": 1, + "bbox": [ + 89, + 335, + 241, + 351 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 2 evaluates the core components of our approach, probability maps and crop data augmentation. The analysis is conducted on the ProbPose-s model using ground truth bounding boxes on the COCO and CropCOCO datasets.", + "bbox": [ + 89, + 357, + 482, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using probability maps without crop data augmentation yields the lowest performance. This setup slightly improves localization on COCO but reduces the accuracy of out-of-image keypoints in CropCOCO. Without crop data augmentation, ProbPose encounters few out-of-image training samples, and probability map normalization forces predictions within the activation window, making probability maps less effective than heatmaps for out-of-image keypoints.", + "bbox": [ + 89, + 417, + 482, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Adding crop data augmentation improves localization accuracy on both COCO and CropCOCO. Training with out-of-image keypoints also improves in-image localization, as the model relies more on the structure of the human body, similar to [10]. Compared to Hide&Seek, crop augmentation brings the same in-image performance improvement, but also improve out-of-image localization and generate samples for training presence probability.", + "bbox": [ + 89, + 537, + 482, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Combining crop augmentation and probmaps achieves the same localization accuracy as using crop data augmentation alone. However, as discussed in Tab. 1, the probabilistic approach is more important for presence classification. While COCO-like evaluation protocols focus on point estimates, probability maps are more versatile and provide a direct mathematical interpretation. Heatmaps are optimized for point estimates, but probmaps support broader applications without compromising point-estimate accuracy.", + "bbox": [ + 89, + 659, + 482, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computational complexity. ViTPose-s (ViT-s backbone + HeatmapHead) performs 24M FLOPs. The full ProbPose-s (visibility, OKS, and $p_p$ estimation) used for all experiments performs 35M FLOPs. The minimal version shrinks to 27M FLOPs (16% more than ViTPose-s). The difference in runtime is smaller than our measurement precision and both models run a $\\sim 50$ fps.", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 513, + 89, + 638, + 104 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present ProbPose, a novel approach to 2D human pose estimation that uses probability maps instead of heatmaps and introduces presence within-the-activation-map probability prediction. Unlike previous methods, we do not assume a Gaussian distribution for the localization probability and employ the expected OKS for both training and decoding, thus aligning the training loss and the evaluation metric. The key findings are:", + "bbox": [ + 511, + 123, + 903, + 243 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Probability maps with OKSLoss improve versatility without sacrificing performance, offering more flexibility than point estimates.", + "2. Modified OKSLoss adapts to each keypoint type, enforcing sharper distributions for high-precision keypoints like eyes or nose, while broader distributions are used for less precise keypoints like hips. These distributions are more reflective of the image and are not constrained by a Gaussian assumption.", + "3. Predicting presence probability is more effective than thresholding confidence, reducing error by $45\\%$ . Presence probability is a better indicator for in/out decisions than the peak of a predicted Gaussian.", + "4. Cropping images during training improves both out-of-image localization and in-image performance by increasing data variability, similar to other information-dropping augmentations. Unlike Hide&Seek [10], crop augmentation also enables out-of-image localization.", + "5. Increasing the activation window size comes with some performance trade-offs, but the impact can be minimized. Our double-probmap model can localize keypoints up to $25\\%$ outside the bounding box with only an $0.4\\%$ decrease in AP performance." + ], + "bbox": [ + 514, + 262, + 903, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future work could explore the behavior of probability maps in multibody scenarios. Decoding with expected OKS maximization has proven especially useful for bimodal heatmaps, which are common in multibody images.", + "bbox": [ + 511, + 628, + 903, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The issue of COCO keypoints near the edge of the bounding box remains unresolved. Ignoring these keypoints during training reduces performance as valuable data is lost. However, training with them teaches the model to place keypoints further inside the image. Cropping as a data augmentation strategy helps mitigate this issue during training but not during evaluation. Re-annotating the dataset would be too costly and likely imprecise, as it is difficult for humans to accurately place keypoints outside the image.", + "bbox": [ + 511, + 696, + 903, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the Ministry of the Interior of the Czech Republic project No. VJ02010041 and the Czech Technical University student grant SGS23/173/OHK3/3T/13.", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27131", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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Pose2seg: Detection free human instance segmentation, 2019. 3, 16" + ], + "bbox": [ + 91, + 92, + 480, + 500 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "27133", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_model.json b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1192be5c8036b0248e748f875e1446965a45d39f --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_model.json @@ -0,0 +1,2233 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.16, + 0.131, + 0.838, + 0.153 + ], + "angle": 0, + "content": "ProbPose: A Probabilistic Approach to 2D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.35, + 0.182, + 0.644, + 0.291 + ], + "angle": 0, + "content": "Miroslav Purkrabek and Jiri Matas Visual Recognition Group Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague purkrmir@fel(cvut.cz" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.326, + 0.327, + 0.341 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.36, + 0.484, + 0.618 + ], + "angle": 0, + "content": "Current state-of-the-art Human Pose Estimation methods ignore out-of-image keypoints in both training and evaluation and use uncalibrated heatmaps as keypoint location representations. We propose ProbPose, which predicts for each keypoint: a calibrated probability of keypoint presence at each location in the activation window, the probability of being outside of it, and its predicted visibility. To address the lack of evaluation protocols for out-of-image keypoints, we introduce the CropCOCO dataset and the Extended OKS (Ex-OKS) metric, which extends OKS to out-of-image points. Tested on COCO, CropCOCO, and OCHuman, ProbPose shows significant gains in out-of-image keypoint localization while also improving in-image localization through data augmentation. Additionally, the model improves robustness along the edges of the bounding box and offers better flexibility in keypoint evaluation. The code and weights are available on the project website1." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.649, + 0.222, + 0.665 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.766 + ], + "angle": 0, + "content": "Human pose estimation (HPE) has seen significant progress, achieving robust performance on standard datasets. The most successful models like ViTPose [32] typically use a top-down, heatmap-based approach, where heatmaps serve as dense representations of keypoint locations across an image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.483, + 0.874 + ], + "angle": 0, + "content": "In this paper, we address two limitations of top-down HPE methods: (1) all previous methods overlook out-of-image keypoints during training and, more importantly, ignore them in evaluation, and (2) heatmaps restrict their use to simple point estimates. While seemingly separate, these issues are interrelated and can be addressed through an appropriate choice of representation and loss function." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.324, + 0.71, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.325, + 0.905, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.498, + 0.907, + 0.583 + ], + "angle": 0, + "content": "Figure 1. ProbPose (left) vs. ViTPose [32] (right) output on a cropped image with the dark part removed. The bounding box, on which the pose estimators operate, is detected by YOLOX-x [5]. ProbPose estimates keypoints outside of the image better, e.g. the right leg which is wrongly aligned with the left leg by ViTPose, for which out-of-image keypoints represent a domain shift." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.907, + 0.718 + ], + "angle": 0, + "content": "Top-down methods localize keypoints within a specific region called the activation window. This activation window is the part of the image mapped to the predicted heatmap. The activation window often matches the model input and it may exceed image boundaries due to preprocessing steps, such as maintaining aspect ratios or enlarging bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Under challenging conditions, such as heavy occlusion or cropped images, keypoints may fall outside the activation window. Current methods do not address this issue and simply ignore out-of-window keypoints during training. Even more concerning, evaluation metrics such as OKS (Object Keypoint Similarity) and PCK (Percentage of Correct Keypoints) assess only in-image keypoints. This lack of accountability often leads models to predict keypoints inaccurately on other joints when the actual keypoint is not visible in the image. For example, as shown in Fig. 1, the left leg is mistakenly assigned to the same joints as the right leg. Furthermore, current top-down models do not provide any" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.378, + 0.9 + ], + "angle": 0, + "content": "1MiraPurkrabek.github.io/ProbPose/" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27124" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "indication of whether a keypoint is inside or outside the activation window, and models are not penalized for attempting to localize every keypoint." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.139, + 0.482, + 0.258 + ], + "angle": 0, + "content": "A second challenge in existing HPE methods lies in the reliance on heatmaps as the keypoint representation. Heatmaps provide dense representation of keypoint locations. However, the standard approach of generating target heatmaps with a fixed Gaussian sigma and training with mean square error (MSE) forces the model to output heatmaps with fixed sigmas as well, limiting the accuracy of these estimates." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.262, + 0.483, + 0.488 + ], + "angle": 0, + "content": "Decoding heatmaps to obtain a point estimate typically involves taking the argmax, often refined with UDP decoding [9]. While this approach is effective for identifying the most likely pixel, it is optimal only when the goal is to classify a single correct pixel for each keypoint. However, practical applications demand more flexible interpretations of keypoint locations. For example, an application might require an estimate of the smallest area where a keypoint is located with at least \\(95\\%\\) probability, or, as in humanrobot interaction, identify areas where the model has high uncertainty to ensure safe interactions. Heatmaps, which are prone to overconfidence, are not designed to indicate uncertainty or convey \"don't know\" outcomes, even when Bayes risk is high, an essential factor in safety-critical applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.49, + 0.482, + 0.61 + ], + "angle": 0, + "content": "To address these limitations, we propose ProbPose, a model with multiple outputs that fully describe each keypoint. ProbPose predicts (1) calibrated presence probabilities indicating whether the keypoint lies within the activation window, (2) keypoint's location within the activation window, (3) quality estimate of the localization and (4) visibility. Moreover, instead of using traditional heatmaps, we employ probability maps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.483, + 0.868 + ], + "angle": 0, + "content": "Probability maps differ from heatmaps in several ways: they contain values between 0 and 1 and are normalized to sum to 1, providing calibrated probabilities. Unlike heatmaps, which assume a fixed Gaussian shape, probability maps adapt their shape based on the data, without forcing any assumptions. Additionally, instead of decoding using a simple argmax, we compute the expected OKS for each pixel and select the location that maximizes this score, an approach we term expected OKS maximization. Probability maps are trained using an OKS-based loss modified for dense predictions, formulated as an expected risk minimization problem. Probability maps do not outperform heatmaps on keypoints in the image but have comparable localization ability. Their biggest advantage is in their versatility and better modeling of the underlying distribution. Calibrated probability maps allow for more complex reasoning than point estimates and have a direct interpretation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Since current datasets and metrics lack evaluation protocols for out-of-image keypoints, we introduce a new dataset," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "CropCOCO, comprising cropped images from COCO, and the Extended OKS (Ex-OKS) metric, which builds on OKS to evaluate out-of-image keypoints and presence probability." + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.153, + 0.8, + 0.166 + ], + "angle": 0, + "content": "In summary, our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.168, + 0.905, + 0.211 + ], + "angle": 0, + "content": "1. A concept of presence probability that keypoints is in the activation window, distinct from confidence, which measures the model's trust in its own estimate." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.213, + 0.905, + 0.272 + ], + "angle": 0, + "content": "2. Model for out-of-image keypoints that can localize keypoints within the activation window, even beyond the image boundaries, or predict presence probability for out-of-window keypoints." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.273, + 0.904, + 0.301 + ], + "angle": 0, + "content": "3. OKSLoss adapted for dense predictions in risk minimization formulation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.304, + 0.905, + 0.362 + ], + "angle": 0, + "content": "4. We show that cropping-based data augmentation improves out-of-image keypoint localization, supports presence probability estimation, and enhances in-image localization, similar to Hide&Seek [10]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.364, + 0.904, + 0.407 + ], + "angle": 0, + "content": "5. New CropCOCO dataset and Ex-OKS evaluation metric for more realistic assessment of real-world performance" + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.168, + 0.905, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.423, + 0.651, + 0.438 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.905, + 0.583 + ], + "angle": 0, + "content": "There are three main approaches to 2D human pose estimation: top-down, bottom-up, and single-stage. Single-stage [22, 23, 28, 31] methods directly predict individuals and their skeletons in an image. Bottom-up methods [3, 6] detect all keypoints first and then group them into individual skeletons. The top-down methods [16, 24, 29, 32, 33], despite their challenges, remain the most successful. They use human detectors to process each bounding box independently, providing the best performance on most datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.905, + 0.719 + ], + "angle": 0, + "content": "Among top-down methods, heatmap-based approaches are the most popular. Unlike regression-based methods [25, 27], which directly predict 2D coordinates, heatmap-based methods [16, 24, 32] predict a heatmap with the same aspect ratio as the input. The keypoints are then estimated as the maximum of the heatmap. Heatmaps are more robust and easier to train than regression-based methods, although efforts have been made to narrow the gap between the two approaches [18, 26]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.905, + 0.901 + ], + "angle": 0, + "content": "A key development in heatmap-based methods is UDP (unbiased data processing) [9], which improves coordinate encoding and decoding. Heatmaps are typically defined as 2D Gaussians with a fixed sigma centered on the keypoint. Subpixel decoding allows for smaller heatmaps, reducing computational costs. The maximum value of the heatmap, called the \"confidence,\" is often used for three tasks: visibility estimation, quality estimation, and in/out-of-image decisions. Visibility is sometimes outsourced to specialized heads, quality prediction could be improved by OKS prediction, as shown in [7]. In/out decisions (later defined as presence probability in this paper) are not explicit, as they" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27125" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.482, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.5, + 0.483, + 0.556 + ], + "angle": 0, + "content": "Figure 2. ProbPose-s (left), compared with ViTPose-s (right), improves localization outside the image and handles occlusion better on COCO (first row) and the proposed CropCOCO (second row). ProbPose estimates points well outside of the image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.579, + 0.483, + 0.609 + ], + "angle": 0, + "content": "are not needed for OKS evaluation, but are important for visualization and real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.611, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Most heatmap-based methods are trained with MSE loss, which encourages the output heatmap to match the target Gaussian heatmap. All keypoints are treated equally, with the same Gaussian and sigma. The training focuses only on keypoints within the activation window, meaning the model never encounters an empty heatmap. Since the input of the model often extends beyond the bounding box to capture more context, the activation window can include areas outside the image. This enables a limited prediction of keypoints outside the image, although the models are not specifically trained for this task. For more details, see Appendix A in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.794, + 0.483, + 0.883 + ], + "angle": 0, + "content": "Heatmap-based approaches can predict keypoints outside of the image to some degree. Regression methods like RLE [13] go even further and predict keypoints further from the image. Our goal is not to localize out-of-image keypoints per se but emphasize their importance in training and evaluation." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Alternative loss functions have also been proposed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.287 + ], + "angle": 0, + "content": "Adaptive Wing Loss [30] improves on original Wing Loss [4]. CornerNet [11] introduces a modified Focal Loss (originally in [15]) for object detection. RTMO [17] treats pose estimation as coordinate classification, assuming a normal distribution with varying sigmas for different keypoints, and trains with a negative log likelihood loss. Distribution-based losses such as [21] or Kullback-Leibler divergence have also been used for heatmap-based pose estimation. Most importantly, [19] introduce a new OKSLoss, that is directly tied to the evaluation metric. Their OKSLoss is computed on the predicted keypoints. We modify it to use pixel-wise to optimize probability maps without any shape assumptions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.378 + ], + "angle": 0, + "content": "This paper also applies a cropping data augmentation technique. Similarly to information-dropping methods [10] like Hide&Seek or random bounding box masking, this technique introduces the domain shift by creating more invisible keypoints during training, encouraging the model to leverage the structure of the human body." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.379, + 0.905, + 0.483 + ], + "angle": 0, + "content": "The most widely used dataset for 2D human pose estimation is COCO [14], with MPII [1] being a less common alternative. Datasets like OCHuman [34] and CrowdPose [12] focus on multibody problems such as occlusion and self-occlusion. For COCO and related datasets, the evaluation metric is Object Keypoint Similarity (OKS), while Percentage of Correct Keypoints (PCKh) is used for MPII." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.484, + 0.905, + 0.665 + ], + "angle": 0, + "content": "However OKS ignores unannotated keypoints, as COCO is not fully annotated – many individuals have missing keypoints. Missing annotations can occur either because the keypoint is outside the image or because of occlusion. All annotated keypoints in current datasets are within the image, as annotating keypoints outside the image would be too costly and imprecise. Additionally, OKS does not penalize guessing, and if a model predicts a keypoint inside the image when it is not present, there is no penalty. Evaluating the presence probability of keypoints (whether they are in the activation window) is crucial for real-world applications and requires out-of-image annotations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.666, + 0.905, + 0.726 + ], + "angle": 0, + "content": "We address these issues by introducing a new dataset, CropCOCO, created by cropping COCO images, along with a new evaluation metric, Extended OKS (Ex-OKS), which accounts for keypoints outside the image." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.738, + 0.605, + 0.753 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.763, + 0.813, + 0.778 + ], + "angle": 0, + "content": "ProbPose introduces several key innovations:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.78, + 0.905, + 0.81 + ], + "angle": 0, + "content": "1. A novel approach to keypoint localization using probability maps." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.811, + 0.905, + 0.84 + ], + "angle": 0, + "content": "2. A different application of OKSLoss [19] corresponding to expected risk minimization." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.841, + 0.905, + 0.87 + ], + "angle": 0, + "content": "3. A new attribute for each keypoint, termed presence probability." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "4. A data augmentation technique to handle keypoints outside the image." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.78, + 0.905, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "27126" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.486, + 0.137 + ], + "angle": 0, + "content": "5. A double-probmap approach that expands the field of view, enabling localization of keypoints positioned far outside the image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.139, + 0.485, + 0.244 + ], + "angle": 0, + "content": "In combination with visibility and quality estimation, these elements provide a complete description of each keypoint's state in ProbPose - indicating whether it is within the image, visible, and the confidence level of the estimate. The probability map offers calibrated localization estimates. Each component is explained in detail in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.253, + 0.395, + 0.269 + ], + "angle": 0, + "content": "3.1. Probability maps and loss function" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.275, + 0.485, + 0.44 + ], + "angle": 0, + "content": "In conventional methods, heatmaps are trained with Gaussian targets and MSE loss, resulting in fast convergence, but a Gaussian-shaped bias in output. However, there is no theoretical basis for assuming that the posterior localization probability follows a Gaussian distribution. The normal distribution in OKS metric reflects human-induced error in the annotation process, but we assume the underlaying distribution is not Gaussian but reflects the body shape. During inference, heatmaps typically use the argmax for point localization and the peak value as a combined measure of localization quality and visibility." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.441, + 0.484, + 0.501 + ], + "angle": 0, + "content": "In our approach, we require the model to output probability maps rather than traditional heatmaps. Unlike heatmaps, probability maps always sum to 1, achieved through Sparsemax [20] as the final activation function." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.484, + 0.532 + ], + "angle": 0, + "content": "Each pixel in the probability map represents the posterior probability" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.54, + 0.482, + 0.557 + ], + "angle": 0, + "content": "\\[\np _ {L} \\left(x _ {i}\\right) = p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.564, + 0.485, + 0.61 + ], + "angle": 0, + "content": "where \\( x_{i} \\) is pixel coordinate, \\( k_{j} \\) is the j-th keypoint and \\( AW \\) stands for activation window. With Sparsemax, each probability map sums to 1 for each keypoint:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.618, + 0.482, + 0.65 + ], + "angle": 0, + "content": "\\[\nF \\sum_ {x _ {i} \\in A W} p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right) = 1 \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.658, + 0.458, + 0.674 + ], + "angle": 0, + "content": "We refer to this as the localization probability \\( p_L(x_i) \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.679, + 0.232, + 0.693 + ], + "angle": 0, + "content": "3.1.1. Loss function" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.485, + 0.757 + ], + "angle": 0, + "content": "We train the probability maps using a modified version of OKSLoss [19], aligned with the evaluation function. The loss is formulated as an expected risk minimization problem." + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.766, + 0.483, + 0.784 + ], + "angle": 0, + "content": "\\[\nR _ {e x p} \\left(x _ {i}\\right) = \\left(1 - O K S \\left(x _ {i}\\right)\\right) \\cdot p _ {L} \\left(x _ {i}\\right) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.786, + 0.483, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {O K S} \\left(x _ {i}\\right) = (1 - \\alpha) R _ {e x p} \\left(x _ {i}\\right) + \\alpha g \\left(x _ {i}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.485, + 0.902 + ], + "angle": 0, + "content": "In Eq. (4), \\( R_{exp}(x_i) \\) represents expected risk and \\( \\mathcal{L}_{OKS}(x_i) \\) is the loss function for pixel \\( x_i \\). In contrast to [19], we apply OKSLoss on each pixel of probability map instead of on predicted keypoints. This loss encourages pixels with low OKS to have low localization probability and those with high OKS to have higher localization probability." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.089, + 0.71, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.29, + 0.7, + 0.305 + ], + "angle": 0, + "content": "(a) Predicted probability map \\(p_L\\)" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.089, + 0.905, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.726, + 0.29, + 0.888, + 0.304 + ], + "angle": 0, + "content": "(b) Expected OKS map \\(\\mathbb{E}_{OKS}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.315, + 0.906, + 0.413 + ], + "angle": 0, + "content": "Figure 3. UDP [9] decoding of \\( p_L \\) vs. expected OKS maximization. On the left, the white cross marks the maximum value and the light purple one is the point refined by UDP. In the right image, the dark purple cross is maximum expected OKS. The probability map contains a small, one-pixel-wide peak marked by the white cross. Maximizing expected OKS is robust to sharp local peaks and prefers areas with big mass compared to simple maxima." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.452, + 0.906, + 0.572 + ], + "angle": 0, + "content": "The term \\( g(x_{i}) \\) is the heatmap gradient, computed with the Sobel operator, and serves as a regularizer controlled by the hyperparameter \\( \\alpha \\). Without regularization, the probability map quickly forms a sharp peak and overfits to training data. Smoothing regularization minimizes differences between neighboring pixels, promoting a smooth distribution without assuming a specific shape, as Gaussian regularization does for MSE-trained heatmaps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.579, + 0.906, + 0.67 + ], + "angle": 0, + "content": "For localization, instead of directly using argmax, we compute the expected OKS (Eq. (5)) for each pixel and take its argmax, refining it with quadratic interpolation for subpixel precision. This approach, based on expected OKS rather than UDP decoding, slightly enhances localization, especially in cases of bimodal heatmaps such as in Fig. 3." + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.693, + 0.907, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {O K S} \\left(x _ {i}\\right) = \\sum_ {x _ {j} \\in P M} p _ {L} \\left(x _ {j}\\right) \\cdot O K S \\left(x _ {i}, x _ {j}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Probability maps offer improved versatility. They allow point estimates, as required by the COCO evaluation protocol, and enable probabilistic queries, such as defining the smallest area containing a keypoint with at least \\(90\\%\\) probability. However, the peak of the probability map can no longer reliably indicate the quality of the localization or the presence of keypoints in the activation window. The former is addressed by predicting the OKS for each keypoint as in [7], and the latter is addressed by directly predicting the keypoint's presence probability." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27127" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.285, + 0.108 + ], + "angle": 0, + "content": "3.2. Presence probability" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.295 + ], + "angle": 0, + "content": "Previous models and evaluation protocols have overlooked the question of whether a keypoint is within the activation window. Top-down approaches assume that the bounding boxes fully enclose all keypoints, but this is not always the case due to factors such as occlusion or crop (see Appendix A in the supplementary for further discussion). Thus, it is essential for the model to assess whether a keypoint is actually present in the activation window. This is usually addressed by thresholding confidence (the maximum heatmap value) with an arbitrary cut-off. However, evaluation protocols have ignored keypoint presence, with models predicting a location regardless." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.295, + 0.484, + 0.4 + ], + "angle": 0, + "content": "Presence probability \\( p(k_{j} \\in AW|img) \\) complements probability maps, which inherently assume that keypoints are within the activation window. If the keypoint is outside, the presence probability reflects this; if inside, the probability map provides the location. The visual explanation is in Fig. 4. We abbreviate the presence probability to \\( p_{p}(k_{j}) \\) and train it with Binary Cross Entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.401, + 0.484, + 0.476 + ], + "angle": 0, + "content": "To train the presence probability, we need keypoints that are certainly outside the activation window. These samples are generated through various data augmentation techniques, such as scaling and rotation, with random cropping as the primary source." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.485, + 0.218, + 0.499 + ], + "angle": 0, + "content": "3.3. Calibration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.507, + 0.484, + 0.645 + ], + "angle": 0, + "content": "Both the probability maps and presence probability are calibrated. Probability maps are calibrated so that the top \\(5\\%\\) of the map contains \\(5\\%\\) of the GT keypoints, the top \\(10\\%\\) contains \\(10\\%\\) of the GT keypoints, and so on. We achieve this calibration through temperature scaling [8] on CropCOCO. As a result, the calibrated probabilities align with the true underlying distribution, enabling more versatile evaluations beyond simple point estimates. Details and calibration curves are in Appendix B in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.653, + 0.324, + 0.669 + ], + "angle": 0, + "content": "3.4. Crop image augmentation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.765 + ], + "angle": 0, + "content": "As discussed in Appendix A, we consider the image border as a type of occlusion. To train the model to correctly identify keypoints outside the image, we need suitable training samples. Manual annotation of such keypoints is both costly and imprecise, so we generate these samples by cropping existing annotated keypoints out of the image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.766, + 0.483, + 0.856 + ], + "angle": 0, + "content": "Depending on the crop strength, the in-the-image keypoint may end up within the activation window but outside the image, or entirely outside the activation window. Keypoints within the activation window but outside the image are used to train probability maps, while those outside the activation window train the presence probability." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The cropping not only provides data for presence probability training but also enhances the model's ability to localize keypoints near the image boundary, extending even" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.09, + 0.71, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.231, + 0.674, + 0.243 + ], + "angle": 0, + "content": "(a) Traditional method" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.09, + 0.905, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.231, + 0.888, + 0.243 + ], + "angle": 0, + "content": "(b) Double-probmap approach" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.255, + 0.907, + 0.378 + ], + "angle": 0, + "content": "Figure 4. Key regions in top-down pose estimation. Rectangles represent the bounding box, the model input and the activation window. Right: the double-probmap approach with a larger activation window. The probability map is responsible for localization of keypoints in activation windows (A, B, C) and the presence probability predicts whether the keypoint is outside (D, E). Note that double-probmap has a larger field-of-view. For detailed discussion about keypoint location, see Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.405, + 0.907, + 0.482 + ], + "angle": 0, + "content": "to areas beyond the visible border. This is especially useful for cases where the subject is partially cropped by the image border or in close-up pose estimation, where keypoints may lie far from the visible body. Examples of crops and result visualizations are in the Figs. 1 and 2." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.511, + 0.805, + 0.527 + ], + "angle": 0, + "content": "3.5. Enlarging activation window size" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.54, + 0.906, + 0.631 + ], + "angle": 0, + "content": "When predicting keypoints outside the image, a key question is how far from the image we aim to localize them. In applications where out-of-image keypoints localization is essential, it might be helpful to enlarge the activation window. However, simply increasing the input size or activation window typically reduces performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.638, + 0.907, + 0.804 + ], + "angle": 0, + "content": "To address this, we propose a double-probmap approach (illustrated in Fig. 4b). In this method, an expert heatmap precisely localizes keypoints within a smaller activation window that matches the model input, while a larger activation window captures keypoints further from the image. The larger probability map has the same resolution but a wider field of view, resulting in a lower effective resolution. Both maps are trained on keypoints within their respective activation areas. If the larger map predicts a keypoint within the smaller activation area, the expert map refines the localization for greater accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "This approach balances the trade-off between field-of-view and precision. The larger map offers a broader field of view, but with lower accuracy, while the expert map maintains precision within a smaller activation window. This method is particularly suitable for applications like close-up pose estimation, where a wide field of view is essential." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27128" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.158, + 0.105 + ], + "angle": 0, + "content": "4. Data" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.485, + 0.178 + ], + "angle": 0, + "content": "To evaluate ProbPose, we introduce a new evaluation protocol based on OKS and mAP, along with a new dataset specifically designed for out-of-image keypoint localization and presence probability classification." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.187, + 0.274, + 0.202 + ], + "angle": 0, + "content": "4.1. Evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.21, + 0.483, + 0.27 + ], + "angle": 0, + "content": "Current metrics, such as OKS and PCK, evaluate only in-image keypoints, overlooking false positives. As a result, models overestimate confidence, guess keypoint locations, and are not penalized for predicting absent keypoints." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.271, + 0.484, + 0.42 + ], + "angle": 0, + "content": "We propose a new evaluation approach that checks whether a keypoint is within the activation window and, if so, assesses its precise localization. This approach better reflects real-world scenarios, like human-machine interaction, where knowing if a keypoint cannot be localized is critical. To address this, we introduce Extended OKS (Ex-OKS), an extension of OKS that accommodates keypoints outside the activation window. For bottom-up and single-stage methods, where the activation window spans the entire image, Ex-OKS can be adapted accordingly." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.422, + 0.484, + 0.497 + ], + "angle": 0, + "content": "In its localization-only form, Ex-OKS functions identically to the original OKS. However, Ex-OKS extends OKS by accounting for keypoints outside the activation window. The essential goal is for the model to indicate if a keypoint is absent, rather than attempting a guess." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.498, + 0.484, + 0.572 + ], + "angle": 0, + "content": "Ex-OKS evaluates two variables for each keypoint: location \\( x_{i} \\) and presence probability \\( p_{p} \\). Although the model outputs a continuous value for \\( p_{p} \\), a binary decision (0 or 1) is often required in real-world applications, so we optimally threshold it for each model." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.574, + 0.332, + 0.588 + ], + "angle": 0, + "content": "Formally, we define Ex-OKS as:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.603, + 0.483, + 0.673 + ], + "angle": 0, + "content": "\\[\nd _ {i} = \\left\\{ \\begin{array}{l l} d _ {e} \\left(x _ {i} ^ {*}, x _ {i} ^ {\\prime}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} (\\mathrm {A W}, x _ {i} ^ {\\prime}) & \\text {i f} p _ {p} ^ {*} = 0 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} \\left(x _ {i} ^ {*}, \\mathrm {A W}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 0 \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.678, + 0.483, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E x} - \\mathrm {O K S} = \\exp \\left(\\frac {- d _ {i} ^ {2}}{2 k ^ {2} \\sigma^ {2}}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.483, + 0.764 + ], + "angle": 0, + "content": ", where \\( AW \\) stands for activation window, \\( d_{e} \\) is Euclidean distance and \\( \\cdot^{*} \\) and \\( \\cdot^{\\prime} \\) are ground truth and predicted variables, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.794 + ], + "angle": 0, + "content": "If both the ground truth and the model agree that \\( p_{p} = 1 \\), Ex-OKS defaults to the standard OKS evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.901 + ], + "angle": 0, + "content": "When the ground truth \\( p_{p}^{*} = 0 \\) and the model predicts \\( p_{p}^{\\prime} = 1 \\), the penalty depends on the predicted location \\( x_{i}^{\\prime} \\) and its distance from the edge of the activation window, with lower penalties for points near the boundary. Similarly, if \\( p_{p}^{*} = 1 \\) but the model predicts \\( p_{p}^{\\prime} = 0 \\), the penalty is based on the ground truth location \\( x_{i}^{*} \\), with smaller penalties for errors near the border of the activation window." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "When both \\( p_{p}^{*} = 0 \\) and \\( p_{p}^{\\prime} = 0 \\), there is no penalty and the similarity score is 1." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.122, + 0.905, + 0.182 + ], + "angle": 0, + "content": "Ex-mAP, built on Ex-OKS, extends mAP by incorporating both keypoint localization and presence probability, making it suitable for evaluating models with keypoints outside the activation window." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.192, + 0.616, + 0.206 + ], + "angle": 0, + "content": "4.2. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.213, + 0.905, + 0.273 + ], + "angle": 0, + "content": "We evaluated our model on the COCO dataset to ensure a fair comparison with existing models. All training was conducted on COCO, with crop image augmentation applied in specified experiments." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.274, + 0.906, + 0.394 + ], + "angle": 0, + "content": "To assess performance on out-of-image keypoints, we introduce a new dataset, CropCOCO. CropCOCO consists of randomly cropped COCO validation images, with some keypoints positioned outside the activation window. Bounding boxes are recomputed for the cropped images to evaluate the model appropriately. While other researchers can create their own cropped dataset, we release CropCOCO to support reproducibility." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.395, + 0.906, + 0.56 + ], + "angle": 0, + "content": "During COCO evaluation, we observed that keypoints near the image boundary are often annotated further inside the image, likely due to annotators avoiding placements near the edge. This causes our model to be penalized for accurately localizing keypoints outside the image. When keypoints near the border are excluded from evaluation, Prob-Pos demonstrates even stronger performance compared to other state-of-the-art methods. Although this issue is minor (causing about a \\(0.2\\%\\) performance difference) and difficult to correct, we highlight it to raise awareness of its potential impact. For further details, see Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.561, + 0.906, + 0.604 + ], + "angle": 0, + "content": "Additionally, we evaluated our model on the OCHuman dataset to demonstrate its generalizability across different domains." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.619, + 0.646, + 0.635 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.645, + 0.906, + 0.719 + ], + "angle": 0, + "content": "The results in Tab. 1 compare our method with other SOTA approaches on COCO, CropCOCO, and OCHuman datasets using mAP and Ex-mAP metrics. For fair comparison, we evaluate models of similar size. All experiments use ground truth bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.901 + ], + "angle": 0, + "content": "ProbPose improves on its baseline model, ViTpose, by approximately \\(1\\%\\) in localization, a gain comparable to that achieved by other information-dropping augmentations like [10]. Importantly, ProbPose demonstrates stronger performance in Ex-OKS, showing improved detection of keypoints outside the activation window due to its direct presence probability prediction, as discussed in Sec. 5.1. Since COCO lacks out-of-image keypoints, Ex-OKS improvement here reflects enhanced presence probability classification. Localization metrics could be slightly higher if not for incorrect annotations near the bounding box borders, discussed further in Appendix D." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27129" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.242, + 0.089, + 0.758, + 0.226 + ], + "angle": 0, + "content": "
ModelCOCOMAPEx-mAPCropCOCOMAPEx-mAPOCHumanmAPEx-mAP
HRFormer-s [33]75.274.670.964.360.360.0
PVTv2 [29]72.071.570.763.158.558.1
SWIN-t [16]73.572.971.365.058.157.9
ViTPose-s [32]75.975.372.766.560.360.1
ProbPose-s76.676.481.773.960.460.2
ProbPose-s-DP76.275.480.971.461.461.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.237, + 0.907, + 0.306 + ], + "angle": 0, + "content": "Table 1. Keypoint localization accuracy in terms of the standard mAP and the novel Ex-mAP metrics. ProbPose is compared with SOTA models of similar size on the COCO, CropCOCO, and OCHuman datasets. All evaluation is done using GT bounding boxes. DH stands for the double-probmap approach with a wider field of view. To compute Ex-mAP, we select the optimal threshold for each model. The best model is in bold, the second-best is underlined. ProbPose brings significant improvement for out-of-image keypoints and minor improvement on standard COCO." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.333, + 0.482, + 0.409 + ], + "angle": 0, + "content": "The most significant improvement is unsurprisingly observed on CropCOCO, where ProbPose excels at detecting out-of-image keypoints, primarily due to crop data augmentation. Again, the localization metrics could be higher without annotation errors along the bounding box borders." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.483, + 0.53 + ], + "angle": 0, + "content": "ProbPose-DP, the double-probmap variant, shows a slight performance decrease on COCO and CropCOCO, reflecting the trade-off between a broader field of view and in-image precision (see Sec. 3.5). In this variant, each heatmap is predicted by one head from shared features, and the larger heatmap decides when to defer to the more precise heatmap. If the larger heatmap estimates the wrong localization, the specialized heatmap cannot correct it." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.532, + 0.483, + 0.592 + ], + "angle": 0, + "content": "ProbPose-DP has worse Ex-mAP as it solves a more difficult task. Ex-mAP evaluates keypoint presence in the AW so the larger AW in ProbPose-DP makes presence classification harder as the AW border is further from the image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.593, + 0.483, + 0.683 + ], + "angle": 0, + "content": "ProbPose-DP remains competitive with other SOTA methods, providing a better alternative to simply enlarging the input size or activation window. Interestingly, ProbPose-DP shows a notable improvement in OCHuman, likely due to its extended field of view, which enhances individual differentiation in multi-body scenes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.685, + 0.483, + 0.729 + ], + "angle": 0, + "content": "ProbPose variants perform well on OCHuman (unseen during the training), highlighting their strong generalization across domains." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.398, + 0.759 + ], + "angle": 0, + "content": "5.1. Presence probability vs. confidence" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 highlights the advantages of using presence probability over confidence, reflected in the increase in Ex-mAP. For clarity, Fig. 5 shows an additional classification accuracy for CropCOCO and its balanced subset. The task is to classify whether keypoints are inside or outside the activation window, indicating if they should be drawn or used in other applications. CropCOCO is unbalanced as there is much more in-AW than out-of-AW keypoints. To get a balanced subset, we randomly selected keypoints from both" + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.356, + 0.868, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.667 + ], + "angle": 0, + "content": "Figure 5. Keypoint presence in the activation window. Accuracy, inside and outside of the AW, of the classification based on thresholding of the ProbPose's presence probability and ViTPose's confidence. The accuracy is measured for CropCOCO dataset (full line) and its balanced subset (dotted line). The proposed presence probability outperforms ViTPose's confidence in both cases, reducing the error by \\(30\\%\\) and \\(45\\%\\) respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.688, + 0.785, + 0.701 + ], + "angle": 0, + "content": "classes to have the same amount of each." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.906, + 0.795 + ], + "angle": 0, + "content": "In both balanced and unbalanced datasets, the presence probability outperforms the confidence score from the ViT-Pose model. This improvement is due to confidence not being trained to reflect presence probability, and the standard COCO dataset, without crop data augmentation, lacks sufficient training samples for this purpose." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Fig. 5 also provides insights into confidence thresholding. Current models often use an arbitrary threshold of 0.3 to decide whether to trust predictions without theoretical justification. The evaluation on CropCOCO reveals that the optimal confidence threshold is between 0.15 (for unbalanced datasets) and 0.4 (for balanced datasets). Thus, the commonly used threshold of 0.3 is close to the optimum," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27130" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.153, + 0.089, + 0.422, + 0.18 + ], + "angle": 0, + "content": "
cropp-mapsCOCOCropCOCO
XX76.073.7
X✓76.472.4
✓X76.681.7
✓✓76.681.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.191, + 0.482, + 0.262 + ], + "angle": 0, + "content": "Table 2. ProbPose ablation; mAP on COCO and CropCOCO for versions without the probability maps and crop data augmentation. Crop augmentation clearly helps for cropped images. Probability maps bring negligible performance improvement as their main strength is in versatility." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.483, + 0.327 + ], + "angle": 0, + "content": "which aligns with its generally good results. This study offers guidance on setting an appropriate threshold based on the characteristics of a specific dataset." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.336, + 0.242, + 0.352 + ], + "angle": 0, + "content": "5.2. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.418 + ], + "angle": 0, + "content": "Tab. 2 evaluates the core components of our approach, probability maps and crop data augmentation. The analysis is conducted on the ProbPose-s model using ground truth bounding boxes on the COCO and CropCOCO datasets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.419, + 0.483, + 0.538 + ], + "angle": 0, + "content": "Using probability maps without crop data augmentation yields the lowest performance. This setup slightly improves localization on COCO but reduces the accuracy of out-of-image keypoints in CropCOCO. Without crop data augmentation, ProbPose encounters few out-of-image training samples, and probability map normalization forces predictions within the activation window, making probability maps less effective than heatmaps for out-of-image keypoints." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.483, + 0.659 + ], + "angle": 0, + "content": "Adding crop data augmentation improves localization accuracy on both COCO and CropCOCO. Training with out-of-image keypoints also improves in-image localization, as the model relies more on the structure of the human body, similar to [10]. Compared to Hide&Seek, crop augmentation brings the same in-image performance improvement, but also improve out-of-image localization and generate samples for training presence probability." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.795 + ], + "angle": 0, + "content": "Combining crop augmentation and probmaps achieves the same localization accuracy as using crop data augmentation alone. However, as discussed in Tab. 1, the probabilistic approach is more important for presence classification. While COCO-like evaluation protocols focus on point estimates, probability maps are more versatile and provide a direct mathematical interpretation. Heatmaps are optimized for point estimates, but probmaps support broader applications without compromising point-estimate accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Computational complexity. ViTPose-s (ViT-s backbone + HeatmapHead) performs 24M FLOPs. The full ProbPose-s (visibility, OKS, and \\( p_p \\) estimation) used for all experiments performs 35M FLOPs. The minimal version shrinks to 27M FLOPs (16% more than ViTPose-s). The difference in runtime is smaller than our measurement precision and both models run a \\(\\sim 50\\) fps." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.64, + 0.106 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.124, + 0.905, + 0.244 + ], + "angle": 0, + "content": "We present ProbPose, a novel approach to 2D human pose estimation that uses probability maps instead of heatmaps and introduces presence within-the-activation-map probability prediction. Unlike previous methods, we do not assume a Gaussian distribution for the localization probability and employ the expected OKS for both training and decoding, thus aligning the training loss and the evaluation metric. The key findings are:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.263, + 0.905, + 0.308 + ], + "angle": 0, + "content": "1. Probability maps with OKSLoss improve versatility without sacrificing performance, offering more flexibility than point estimates." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.308, + 0.905, + 0.398 + ], + "angle": 0, + "content": "2. Modified OKSLoss adapts to each keypoint type, enforcing sharper distributions for high-precision keypoints like eyes or nose, while broader distributions are used for less precise keypoints like hips. These distributions are more reflective of the image and are not constrained by a Gaussian assumption." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.399, + 0.905, + 0.459 + ], + "angle": 0, + "content": "3. Predicting presence probability is more effective than thresholding confidence, reducing error by \\(45\\%\\). Presence probability is a better indicator for in/out decisions than the peak of a predicted Gaussian." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.46, + 0.905, + 0.534 + ], + "angle": 0, + "content": "4. Cropping images during training improves both out-of-image localization and in-image performance by increasing data variability, similar to other information-dropping augmentations. Unlike Hide&Seek [10], crop augmentation also enables out-of-image localization." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.535, + 0.905, + 0.61 + ], + "angle": 0, + "content": "5. Increasing the activation window size comes with some performance trade-offs, but the impact can be minimized. Our double-probmap model can localize keypoints up to \\(25\\%\\) outside the bounding box with only an \\(0.4\\%\\) decrease in AP performance." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.263, + 0.905, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.629, + 0.905, + 0.689 + ], + "angle": 0, + "content": "Future work could explore the behavior of probability maps in multibody scenarios. Decoding with expected OKS maximization has proven especially useful for bimodal heatmaps, which are common in multibody images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.697, + 0.905, + 0.833 + ], + "angle": 0, + "content": "The issue of COCO keypoints near the edge of the bounding box remains unresolved. Ignoring these keypoints during training reduces performance as valuable data is lost. However, training with them teaches the model to place keypoints further inside the image. Cropping as a data augmentation strategy helps mitigate this issue during training but not during evaluation. Re-annotating the dataset would be too costly and likely imprecise, as it is difficult for humans to accurately place keypoints outside the image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the Ministry of the Interior of the Czech Republic project No. VJ02010041 and the Czech Technical University student grant SGS23/173/OHK3/3T/13." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27131" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.172, + 0.484, + 0.24 + ], + "angle": 0, + "content": "[2] Yanrui Bin, Xuan Cao, Xinya Chen, Yanhao Ge, Ying Tai, Chengjie Wang, Jilin Li, Feiyue Huang, Changxin Gao, and Nong Sang. 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Pose2seg: Detection free human instance segmentation, 2019. 3, 16" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27133" + } + ] +] \ No newline at end of file diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_origin.pdf b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3144758c0754e8419f094bbbb30b01f7dd428374 --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/8ccd2594-9394-4eab-a971-5f2753ccb58b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:85ad6670de0b50e1b63ff83e174d3eef17651f50b47d979f44c79410c47c3bf4 +size 7018808 diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/full.md b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1fcdc8a1403cb1ff873990ecda7da2635e470abb --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/full.md @@ -0,0 +1,325 @@ +# ProbPose: A Probabilistic Approach to 2D Human Pose Estimation + +Miroslav Purkrabek and Jiri Matas Visual Recognition Group Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague purkrmir@fel(cvut.cz + +# Abstract + +Current state-of-the-art Human Pose Estimation methods ignore out-of-image keypoints in both training and evaluation and use uncalibrated heatmaps as keypoint location representations. We propose ProbPose, which predicts for each keypoint: a calibrated probability of keypoint presence at each location in the activation window, the probability of being outside of it, and its predicted visibility. To address the lack of evaluation protocols for out-of-image keypoints, we introduce the CropCOCO dataset and the Extended OKS (Ex-OKS) metric, which extends OKS to out-of-image points. Tested on COCO, CropCOCO, and OCHuman, ProbPose shows significant gains in out-of-image keypoint localization while also improving in-image localization through data augmentation. Additionally, the model improves robustness along the edges of the bounding box and offers better flexibility in keypoint evaluation. The code and weights are available on the project website1. + +# 1. Introduction + +Human pose estimation (HPE) has seen significant progress, achieving robust performance on standard datasets. The most successful models like ViTPose [32] typically use a top-down, heatmap-based approach, where heatmaps serve as dense representations of keypoint locations across an image. + +In this paper, we address two limitations of top-down HPE methods: (1) all previous methods overlook out-of-image keypoints during training and, more importantly, ignore them in evaluation, and (2) heatmaps restrict their use to simple point estimates. While seemingly separate, these issues are interrelated and can be addressed through an appropriate choice of representation and loss function. + +![](images/9264fed1fb088b7d1b4601da40a0699c37b18ccc5799f5e06beca7f9b78bd56a.jpg) +Figure 1. ProbPose (left) vs. ViTPose [32] (right) output on a cropped image with the dark part removed. The bounding box, on which the pose estimators operate, is detected by YOLOX-x [5]. ProbPose estimates keypoints outside of the image better, e.g. the right leg which is wrongly aligned with the left leg by ViTPose, for which out-of-image keypoints represent a domain shift. + +![](images/063bdb24d5745424cd9d52d13f5e87e0d9596f500f9996f875865dda6f4f735a.jpg) + +Top-down methods localize keypoints within a specific region called the activation window. This activation window is the part of the image mapped to the predicted heatmap. The activation window often matches the model input and it may exceed image boundaries due to preprocessing steps, such as maintaining aspect ratios or enlarging bounding boxes. + +Under challenging conditions, such as heavy occlusion or cropped images, keypoints may fall outside the activation window. Current methods do not address this issue and simply ignore out-of-window keypoints during training. Even more concerning, evaluation metrics such as OKS (Object Keypoint Similarity) and PCK (Percentage of Correct Keypoints) assess only in-image keypoints. This lack of accountability often leads models to predict keypoints inaccurately on other joints when the actual keypoint is not visible in the image. For example, as shown in Fig. 1, the left leg is mistakenly assigned to the same joints as the right leg. Furthermore, current top-down models do not provide any + +indication of whether a keypoint is inside or outside the activation window, and models are not penalized for attempting to localize every keypoint. + +A second challenge in existing HPE methods lies in the reliance on heatmaps as the keypoint representation. Heatmaps provide dense representation of keypoint locations. However, the standard approach of generating target heatmaps with a fixed Gaussian sigma and training with mean square error (MSE) forces the model to output heatmaps with fixed sigmas as well, limiting the accuracy of these estimates. + +Decoding heatmaps to obtain a point estimate typically involves taking the argmax, often refined with UDP decoding [9]. While this approach is effective for identifying the most likely pixel, it is optimal only when the goal is to classify a single correct pixel for each keypoint. However, practical applications demand more flexible interpretations of keypoint locations. For example, an application might require an estimate of the smallest area where a keypoint is located with at least $95\%$ probability, or, as in humanrobot interaction, identify areas where the model has high uncertainty to ensure safe interactions. Heatmaps, which are prone to overconfidence, are not designed to indicate uncertainty or convey "don't know" outcomes, even when Bayes risk is high, an essential factor in safety-critical applications. + +To address these limitations, we propose ProbPose, a model with multiple outputs that fully describe each keypoint. ProbPose predicts (1) calibrated presence probabilities indicating whether the keypoint lies within the activation window, (2) keypoint's location within the activation window, (3) quality estimate of the localization and (4) visibility. Moreover, instead of using traditional heatmaps, we employ probability maps. + +Probability maps differ from heatmaps in several ways: they contain values between 0 and 1 and are normalized to sum to 1, providing calibrated probabilities. Unlike heatmaps, which assume a fixed Gaussian shape, probability maps adapt their shape based on the data, without forcing any assumptions. Additionally, instead of decoding using a simple argmax, we compute the expected OKS for each pixel and select the location that maximizes this score, an approach we term expected OKS maximization. Probability maps are trained using an OKS-based loss modified for dense predictions, formulated as an expected risk minimization problem. Probability maps do not outperform heatmaps on keypoints in the image but have comparable localization ability. Their biggest advantage is in their versatility and better modeling of the underlying distribution. Calibrated probability maps allow for more complex reasoning than point estimates and have a direct interpretation. + +Since current datasets and metrics lack evaluation protocols for out-of-image keypoints, we introduce a new dataset, + +CropCOCO, comprising cropped images from COCO, and the Extended OKS (Ex-OKS) metric, which builds on OKS to evaluate out-of-image keypoints and presence probability. + +In summary, our main contributions are: + +1. A concept of presence probability that keypoints is in the activation window, distinct from confidence, which measures the model's trust in its own estimate. +2. Model for out-of-image keypoints that can localize keypoints within the activation window, even beyond the image boundaries, or predict presence probability for out-of-window keypoints. +3. OKSLoss adapted for dense predictions in risk minimization formulation +4. We show that cropping-based data augmentation improves out-of-image keypoint localization, supports presence probability estimation, and enhances in-image localization, similar to Hide&Seek [10] +5. New CropCOCO dataset and Ex-OKS evaluation metric for more realistic assessment of real-world performance + +# 2. Related work + +There are three main approaches to 2D human pose estimation: top-down, bottom-up, and single-stage. Single-stage [22, 23, 28, 31] methods directly predict individuals and their skeletons in an image. Bottom-up methods [3, 6] detect all keypoints first and then group them into individual skeletons. The top-down methods [16, 24, 29, 32, 33], despite their challenges, remain the most successful. They use human detectors to process each bounding box independently, providing the best performance on most datasets. + +Among top-down methods, heatmap-based approaches are the most popular. Unlike regression-based methods [25, 27], which directly predict 2D coordinates, heatmap-based methods [16, 24, 32] predict a heatmap with the same aspect ratio as the input. The keypoints are then estimated as the maximum of the heatmap. Heatmaps are more robust and easier to train than regression-based methods, although efforts have been made to narrow the gap between the two approaches [18, 26]. + +A key development in heatmap-based methods is UDP (unbiased data processing) [9], which improves coordinate encoding and decoding. Heatmaps are typically defined as 2D Gaussians with a fixed sigma centered on the keypoint. Subpixel decoding allows for smaller heatmaps, reducing computational costs. The maximum value of the heatmap, called the "confidence," is often used for three tasks: visibility estimation, quality estimation, and in/out-of-image decisions. Visibility is sometimes outsourced to specialized heads, quality prediction could be improved by OKS prediction, as shown in [7]. In/out decisions (later defined as presence probability in this paper) are not explicit, as they + +![](images/35b997d928c0d097b15e4240a2ec850dce80eab75496bf4c97b4de1ac2f90fde.jpg) +Figure 2. ProbPose-s (left), compared with ViTPose-s (right), improves localization outside the image and handles occlusion better on COCO (first row) and the proposed CropCOCO (second row). ProbPose estimates points well outside of the image. + +are not needed for OKS evaluation, but are important for visualization and real-world applications. + +Most heatmap-based methods are trained with MSE loss, which encourages the output heatmap to match the target Gaussian heatmap. All keypoints are treated equally, with the same Gaussian and sigma. The training focuses only on keypoints within the activation window, meaning the model never encounters an empty heatmap. Since the input of the model often extends beyond the bounding box to capture more context, the activation window can include areas outside the image. This enables a limited prediction of keypoints outside the image, although the models are not specifically trained for this task. For more details, see Appendix A in the supplementary. + +Heatmap-based approaches can predict keypoints outside of the image to some degree. Regression methods like RLE [13] go even further and predict keypoints further from the image. Our goal is not to localize out-of-image keypoints per se but emphasize their importance in training and evaluation. + +Alternative loss functions have also been proposed. + +Adaptive Wing Loss [30] improves on original Wing Loss [4]. CornerNet [11] introduces a modified Focal Loss (originally in [15]) for object detection. RTMO [17] treats pose estimation as coordinate classification, assuming a normal distribution with varying sigmas for different keypoints, and trains with a negative log likelihood loss. Distribution-based losses such as [21] or Kullback-Leibler divergence have also been used for heatmap-based pose estimation. Most importantly, [19] introduce a new OKSLoss, that is directly tied to the evaluation metric. Their OKSLoss is computed on the predicted keypoints. We modify it to use pixel-wise to optimize probability maps without any shape assumptions. + +This paper also applies a cropping data augmentation technique. Similarly to information-dropping methods [10] like Hide&Seek or random bounding box masking, this technique introduces the domain shift by creating more invisible keypoints during training, encouraging the model to leverage the structure of the human body. + +The most widely used dataset for 2D human pose estimation is COCO [14], with MPII [1] being a less common alternative. Datasets like OCHuman [34] and CrowdPose [12] focus on multibody problems such as occlusion and self-occlusion. For COCO and related datasets, the evaluation metric is Object Keypoint Similarity (OKS), while Percentage of Correct Keypoints (PCKh) is used for MPII. + +However OKS ignores unannotated keypoints, as COCO is not fully annotated – many individuals have missing keypoints. Missing annotations can occur either because the keypoint is outside the image or because of occlusion. All annotated keypoints in current datasets are within the image, as annotating keypoints outside the image would be too costly and imprecise. Additionally, OKS does not penalize guessing, and if a model predicts a keypoint inside the image when it is not present, there is no penalty. Evaluating the presence probability of keypoints (whether they are in the activation window) is crucial for real-world applications and requires out-of-image annotations. + +We address these issues by introducing a new dataset, CropCOCO, created by cropping COCO images, along with a new evaluation metric, Extended OKS (Ex-OKS), which accounts for keypoints outside the image. + +# 3. Method + +ProbPose introduces several key innovations: + +1. A novel approach to keypoint localization using probability maps. +2. A different application of OKSLoss [19] corresponding to expected risk minimization. +3. A new attribute for each keypoint, termed presence probability. +4. A data augmentation technique to handle keypoints outside the image. + +5. A double-probmap approach that expands the field of view, enabling localization of keypoints positioned far outside the image. + +In combination with visibility and quality estimation, these elements provide a complete description of each keypoint's state in ProbPose - indicating whether it is within the image, visible, and the confidence level of the estimate. The probability map offers calibrated localization estimates. Each component is explained in detail in the following sections. + +# 3.1. Probability maps and loss function + +In conventional methods, heatmaps are trained with Gaussian targets and MSE loss, resulting in fast convergence, but a Gaussian-shaped bias in output. However, there is no theoretical basis for assuming that the posterior localization probability follows a Gaussian distribution. The normal distribution in OKS metric reflects human-induced error in the annotation process, but we assume the underlaying distribution is not Gaussian but reflects the body shape. During inference, heatmaps typically use the argmax for point localization and the peak value as a combined measure of localization quality and visibility. + +In our approach, we require the model to output probability maps rather than traditional heatmaps. Unlike heatmaps, probability maps always sum to 1, achieved through Sparsemax [20] as the final activation function. + +Each pixel in the probability map represents the posterior probability + +$$ +p _ {L} \left(x _ {i}\right) = p \left(x _ {i} \mid k _ {j} \in A W, i m g\right), \tag {1} +$$ + +where $x_{i}$ is pixel coordinate, $k_{j}$ is the j-th keypoint and $AW$ stands for activation window. With Sparsemax, each probability map sums to 1 for each keypoint: + +$$ +F \sum_ {x _ {i} \in A W} p \left(x _ {i} \mid k _ {j} \in A W, i m g\right) = 1 \tag {2} +$$ + +We refer to this as the localization probability $p_L(x_i)$ . + +# 3.1.1. Loss function + +We train the probability maps using a modified version of OKSLoss [19], aligned with the evaluation function. The loss is formulated as an expected risk minimization problem. + +$$ +R _ {e x p} \left(x _ {i}\right) = \left(1 - O K S \left(x _ {i}\right)\right) \cdot p _ {L} \left(x _ {i}\right) \tag {3} +$$ + +$$ +\mathcal {L} _ {O K S} \left(x _ {i}\right) = (1 - \alpha) R _ {e x p} \left(x _ {i}\right) + \alpha g \left(x _ {i}\right) \tag {4} +$$ + +In Eq. (4), $R_{exp}(x_i)$ represents expected risk and $\mathcal{L}_{OKS}(x_i)$ is the loss function for pixel $x_i$ . In contrast to [19], we apply OKSLoss on each pixel of probability map instead of on predicted keypoints. This loss encourages pixels with low OKS to have low localization probability and those with high OKS to have higher localization probability. + +![](images/c6f8b771598d29a1dac86d426fc4d5af159e75969dd0da2ac51da2b14860d261.jpg) +(a) Predicted probability map $p_L$ +Figure 3. UDP [9] decoding of $p_L$ vs. expected OKS maximization. On the left, the white cross marks the maximum value and the light purple one is the point refined by UDP. In the right image, the dark purple cross is maximum expected OKS. The probability map contains a small, one-pixel-wide peak marked by the white cross. Maximizing expected OKS is robust to sharp local peaks and prefers areas with big mass compared to simple maxima. + +![](images/c7115537a05bef544aea5dd7c83be680c3544843df1ae100b5fcbfc238ea38d6.jpg) +(b) Expected OKS map $\mathbb{E}_{OKS}$ + +The term $g(x_{i})$ is the heatmap gradient, computed with the Sobel operator, and serves as a regularizer controlled by the hyperparameter $\alpha$ . Without regularization, the probability map quickly forms a sharp peak and overfits to training data. Smoothing regularization minimizes differences between neighboring pixels, promoting a smooth distribution without assuming a specific shape, as Gaussian regularization does for MSE-trained heatmaps. + +For localization, instead of directly using argmax, we compute the expected OKS (Eq. (5)) for each pixel and take its argmax, refining it with quadratic interpolation for subpixel precision. This approach, based on expected OKS rather than UDP decoding, slightly enhances localization, especially in cases of bimodal heatmaps such as in Fig. 3. + +$$ +\mathbb {E} _ {O K S} \left(x _ {i}\right) = \sum_ {x _ {j} \in P M} p _ {L} \left(x _ {j}\right) \cdot O K S \left(x _ {i}, x _ {j}\right) \tag {5} +$$ + +Probability maps offer improved versatility. They allow point estimates, as required by the COCO evaluation protocol, and enable probabilistic queries, such as defining the smallest area containing a keypoint with at least $90\%$ probability. However, the peak of the probability map can no longer reliably indicate the quality of the localization or the presence of keypoints in the activation window. The former is addressed by predicting the OKS for each keypoint as in [7], and the latter is addressed by directly predicting the keypoint's presence probability. + +# 3.2. Presence probability + +Previous models and evaluation protocols have overlooked the question of whether a keypoint is within the activation window. Top-down approaches assume that the bounding boxes fully enclose all keypoints, but this is not always the case due to factors such as occlusion or crop (see Appendix A in the supplementary for further discussion). Thus, it is essential for the model to assess whether a keypoint is actually present in the activation window. This is usually addressed by thresholding confidence (the maximum heatmap value) with an arbitrary cut-off. However, evaluation protocols have ignored keypoint presence, with models predicting a location regardless. + +Presence probability $p(k_{j} \in AW|img)$ complements probability maps, which inherently assume that keypoints are within the activation window. If the keypoint is outside, the presence probability reflects this; if inside, the probability map provides the location. The visual explanation is in Fig. 4. We abbreviate the presence probability to $p_{p}(k_{j})$ and train it with Binary Cross Entropy loss. + +To train the presence probability, we need keypoints that are certainly outside the activation window. These samples are generated through various data augmentation techniques, such as scaling and rotation, with random cropping as the primary source. + +# 3.3. Calibration + +Both the probability maps and presence probability are calibrated. Probability maps are calibrated so that the top $5\%$ of the map contains $5\%$ of the GT keypoints, the top $10\%$ contains $10\%$ of the GT keypoints, and so on. We achieve this calibration through temperature scaling [8] on CropCOCO. As a result, the calibrated probabilities align with the true underlying distribution, enabling more versatile evaluations beyond simple point estimates. Details and calibration curves are in Appendix B in the supplementary. + +# 3.4. Crop image augmentation + +As discussed in Appendix A, we consider the image border as a type of occlusion. To train the model to correctly identify keypoints outside the image, we need suitable training samples. Manual annotation of such keypoints is both costly and imprecise, so we generate these samples by cropping existing annotated keypoints out of the image. + +Depending on the crop strength, the in-the-image keypoint may end up within the activation window but outside the image, or entirely outside the activation window. Keypoints within the activation window but outside the image are used to train probability maps, while those outside the activation window train the presence probability. + +The cropping not only provides data for presence probability training but also enhances the model's ability to localize keypoints near the image boundary, extending even + +![](images/126fe217dbd29214f3aa08c1aba97e67739b28137afbb39145793f130e8700cb.jpg) +(a) Traditional method +Figure 4. Key regions in top-down pose estimation. Rectangles represent the bounding box, the model input and the activation window. Right: the double-probmap approach with a larger activation window. The probability map is responsible for localization of keypoints in activation windows (A, B, C) and the presence probability predicts whether the keypoint is outside (D, E). Note that double-probmap has a larger field-of-view. For detailed discussion about keypoint location, see Appendix A. + +![](images/0a0514b3c3a8a242de83bebfac39b889dbc7bad7295c8d9ecdac7186e22bc730.jpg) +(b) Double-probmap approach + +to areas beyond the visible border. This is especially useful for cases where the subject is partially cropped by the image border or in close-up pose estimation, where keypoints may lie far from the visible body. Examples of crops and result visualizations are in the Figs. 1 and 2. + +# 3.5. Enlarging activation window size + +When predicting keypoints outside the image, a key question is how far from the image we aim to localize them. In applications where out-of-image keypoints localization is essential, it might be helpful to enlarge the activation window. However, simply increasing the input size or activation window typically reduces performance. + +To address this, we propose a double-probmap approach (illustrated in Fig. 4b). In this method, an expert heatmap precisely localizes keypoints within a smaller activation window that matches the model input, while a larger activation window captures keypoints further from the image. The larger probability map has the same resolution but a wider field of view, resulting in a lower effective resolution. Both maps are trained on keypoints within their respective activation areas. If the larger map predicts a keypoint within the smaller activation area, the expert map refines the localization for greater accuracy. + +This approach balances the trade-off between field-of-view and precision. The larger map offers a broader field of view, but with lower accuracy, while the expert map maintains precision within a smaller activation window. This method is particularly suitable for applications like close-up pose estimation, where a wide field of view is essential. + +# 4. Data + +To evaluate ProbPose, we introduce a new evaluation protocol based on OKS and mAP, along with a new dataset specifically designed for out-of-image keypoint localization and presence probability classification. + +# 4.1. Evaluation metrics + +Current metrics, such as OKS and PCK, evaluate only in-image keypoints, overlooking false positives. As a result, models overestimate confidence, guess keypoint locations, and are not penalized for predicting absent keypoints. + +We propose a new evaluation approach that checks whether a keypoint is within the activation window and, if so, assesses its precise localization. This approach better reflects real-world scenarios, like human-machine interaction, where knowing if a keypoint cannot be localized is critical. To address this, we introduce Extended OKS (Ex-OKS), an extension of OKS that accommodates keypoints outside the activation window. For bottom-up and single-stage methods, where the activation window spans the entire image, Ex-OKS can be adapted accordingly. + +In its localization-only form, Ex-OKS functions identically to the original OKS. However, Ex-OKS extends OKS by accounting for keypoints outside the activation window. The essential goal is for the model to indicate if a keypoint is absent, rather than attempting a guess. + +Ex-OKS evaluates two variables for each keypoint: location $x_{i}$ and presence probability $p_{p}$ . Although the model outputs a continuous value for $p_{p}$ , a binary decision (0 or 1) is often required in real-world applications, so we optimally threshold it for each model. + +Formally, we define Ex-OKS as: + +$$ +d _ {i} = \left\{ \begin{array}{l l} d _ {e} \left(x _ {i} ^ {*}, x _ {i} ^ {\prime}\right) & \text {i f} p _ {p} ^ {*} = 1 \text {a n d} p _ {p} ^ {\prime} = 1 \\ d _ {e} (\mathrm {A W}, x _ {i} ^ {\prime}) & \text {i f} p _ {p} ^ {*} = 0 \text {a n d} p _ {p} ^ {\prime} = 1 \\ d _ {e} \left(x _ {i} ^ {*}, \mathrm {A W}\right) & \text {i f} p _ {p} ^ {*} = 1 \text {a n d} p _ {p} ^ {\prime} = 0 \\ 0 & \text {e l s e} \end{array} \right. \tag {6} +$$ + +$$ +\operatorname {E x} - \mathrm {O K S} = \exp \left(\frac {- d _ {i} ^ {2}}{2 k ^ {2} \sigma^ {2}}\right) \tag {7} +$$ + +, where $AW$ stands for activation window, $d_{e}$ is Euclidean distance and $\cdot^{*}$ and $\cdot^{\prime}$ are ground truth and predicted variables, respectively. + +If both the ground truth and the model agree that $p_{p} = 1$ , Ex-OKS defaults to the standard OKS evaluation. + +When the ground truth $p_{p}^{*} = 0$ and the model predicts $p_{p}^{\prime} = 1$ , the penalty depends on the predicted location $x_{i}^{\prime}$ and its distance from the edge of the activation window, with lower penalties for points near the boundary. Similarly, if $p_{p}^{*} = 1$ but the model predicts $p_{p}^{\prime} = 0$ , the penalty is based on the ground truth location $x_{i}^{*}$ , with smaller penalties for errors near the border of the activation window. + +When both $p_{p}^{*} = 0$ and $p_{p}^{\prime} = 0$ , there is no penalty and the similarity score is 1. + +Ex-mAP, built on Ex-OKS, extends mAP by incorporating both keypoint localization and presence probability, making it suitable for evaluating models with keypoints outside the activation window. + +# 4.2. Datasets + +We evaluated our model on the COCO dataset to ensure a fair comparison with existing models. All training was conducted on COCO, with crop image augmentation applied in specified experiments. + +To assess performance on out-of-image keypoints, we introduce a new dataset, CropCOCO. CropCOCO consists of randomly cropped COCO validation images, with some keypoints positioned outside the activation window. Bounding boxes are recomputed for the cropped images to evaluate the model appropriately. While other researchers can create their own cropped dataset, we release CropCOCO to support reproducibility. + +During COCO evaluation, we observed that keypoints near the image boundary are often annotated further inside the image, likely due to annotators avoiding placements near the edge. This causes our model to be penalized for accurately localizing keypoints outside the image. When keypoints near the border are excluded from evaluation, Prob-Pos demonstrates even stronger performance compared to other state-of-the-art methods. Although this issue is minor (causing about a $0.2\%$ performance difference) and difficult to correct, we highlight it to raise awareness of its potential impact. For further details, see Appendix D. + +Additionally, we evaluated our model on the OCHuman dataset to demonstrate its generalizability across different domains. + +# 5. Experiments + +The results in Tab. 1 compare our method with other SOTA approaches on COCO, CropCOCO, and OCHuman datasets using mAP and Ex-mAP metrics. For fair comparison, we evaluate models of similar size. All experiments use ground truth bounding boxes. + +ProbPose improves on its baseline model, ViTpose, by approximately $1\%$ in localization, a gain comparable to that achieved by other information-dropping augmentations like [10]. Importantly, ProbPose demonstrates stronger performance in Ex-OKS, showing improved detection of keypoints outside the activation window due to its direct presence probability prediction, as discussed in Sec. 5.1. Since COCO lacks out-of-image keypoints, Ex-OKS improvement here reflects enhanced presence probability classification. Localization metrics could be slightly higher if not for incorrect annotations near the bounding box borders, discussed further in Appendix D. + +
ModelCOCOMAPEx-mAPCropCOCOMAPEx-mAPOCHumanmAPEx-mAP
HRFormer-s [33]75.274.670.964.360.360.0
PVTv2 [29]72.071.570.763.158.558.1
SWIN-t [16]73.572.971.365.058.157.9
ViTPose-s [32]75.975.372.766.560.360.1
ProbPose-s76.676.481.773.960.460.2
ProbPose-s-DP76.275.480.971.461.461.2
+ +Table 1. Keypoint localization accuracy in terms of the standard mAP and the novel Ex-mAP metrics. ProbPose is compared with SOTA models of similar size on the COCO, CropCOCO, and OCHuman datasets. All evaluation is done using GT bounding boxes. DH stands for the double-probmap approach with a wider field of view. To compute Ex-mAP, we select the optimal threshold for each model. The best model is in bold, the second-best is underlined. ProbPose brings significant improvement for out-of-image keypoints and minor improvement on standard COCO. + +The most significant improvement is unsurprisingly observed on CropCOCO, where ProbPose excels at detecting out-of-image keypoints, primarily due to crop data augmentation. Again, the localization metrics could be higher without annotation errors along the bounding box borders. + +ProbPose-DP, the double-probmap variant, shows a slight performance decrease on COCO and CropCOCO, reflecting the trade-off between a broader field of view and in-image precision (see Sec. 3.5). In this variant, each heatmap is predicted by one head from shared features, and the larger heatmap decides when to defer to the more precise heatmap. If the larger heatmap estimates the wrong localization, the specialized heatmap cannot correct it. + +ProbPose-DP has worse Ex-mAP as it solves a more difficult task. Ex-mAP evaluates keypoint presence in the AW so the larger AW in ProbPose-DP makes presence classification harder as the AW border is further from the image. + +ProbPose-DP remains competitive with other SOTA methods, providing a better alternative to simply enlarging the input size or activation window. Interestingly, ProbPose-DP shows a notable improvement in OCHuman, likely due to its extended field of view, which enhances individual differentiation in multi-body scenes. + +ProbPose variants perform well on OCHuman (unseen during the training), highlighting their strong generalization across domains. + +# 5.1. Presence probability vs. confidence + +Tab. 1 highlights the advantages of using presence probability over confidence, reflected in the increase in Ex-mAP. For clarity, Fig. 5 shows an additional classification accuracy for CropCOCO and its balanced subset. The task is to classify whether keypoints are inside or outside the activation window, indicating if they should be drawn or used in other applications. CropCOCO is unbalanced as there is much more in-AW than out-of-AW keypoints. To get a balanced subset, we randomly selected keypoints from both + +![](images/011b11334c14357429c08ca6e3ef7561afa0967ff4a04f9899c1cbfe307d6be6.jpg) +Figure 5. Keypoint presence in the activation window. Accuracy, inside and outside of the AW, of the classification based on thresholding of the ProbPose's presence probability and ViTPose's confidence. The accuracy is measured for CropCOCO dataset (full line) and its balanced subset (dotted line). The proposed presence probability outperforms ViTPose's confidence in both cases, reducing the error by $30\%$ and $45\%$ respectively. + +classes to have the same amount of each. + +In both balanced and unbalanced datasets, the presence probability outperforms the confidence score from the ViT-Pose model. This improvement is due to confidence not being trained to reflect presence probability, and the standard COCO dataset, without crop data augmentation, lacks sufficient training samples for this purpose. + +Fig. 5 also provides insights into confidence thresholding. Current models often use an arbitrary threshold of 0.3 to decide whether to trust predictions without theoretical justification. The evaluation on CropCOCO reveals that the optimal confidence threshold is between 0.15 (for unbalanced datasets) and 0.4 (for balanced datasets). Thus, the commonly used threshold of 0.3 is close to the optimum, + +
cropp-mapsCOCOCropCOCO
XX76.073.7
X✓76.472.4
✓X76.681.7
✓✓76.681.7
+ +Table 2. ProbPose ablation; mAP on COCO and CropCOCO for versions without the probability maps and crop data augmentation. Crop augmentation clearly helps for cropped images. Probability maps bring negligible performance improvement as their main strength is in versatility. + +which aligns with its generally good results. This study offers guidance on setting an appropriate threshold based on the characteristics of a specific dataset. + +# 5.2. Ablation study + +Tab. 2 evaluates the core components of our approach, probability maps and crop data augmentation. The analysis is conducted on the ProbPose-s model using ground truth bounding boxes on the COCO and CropCOCO datasets. + +Using probability maps without crop data augmentation yields the lowest performance. This setup slightly improves localization on COCO but reduces the accuracy of out-of-image keypoints in CropCOCO. Without crop data augmentation, ProbPose encounters few out-of-image training samples, and probability map normalization forces predictions within the activation window, making probability maps less effective than heatmaps for out-of-image keypoints. + +Adding crop data augmentation improves localization accuracy on both COCO and CropCOCO. Training with out-of-image keypoints also improves in-image localization, as the model relies more on the structure of the human body, similar to [10]. Compared to Hide&Seek, crop augmentation brings the same in-image performance improvement, but also improve out-of-image localization and generate samples for training presence probability. + +Combining crop augmentation and probmaps achieves the same localization accuracy as using crop data augmentation alone. However, as discussed in Tab. 1, the probabilistic approach is more important for presence classification. While COCO-like evaluation protocols focus on point estimates, probability maps are more versatile and provide a direct mathematical interpretation. Heatmaps are optimized for point estimates, but probmaps support broader applications without compromising point-estimate accuracy. + +Computational complexity. ViTPose-s (ViT-s backbone + HeatmapHead) performs 24M FLOPs. The full ProbPose-s (visibility, OKS, and $p_p$ estimation) used for all experiments performs 35M FLOPs. The minimal version shrinks to 27M FLOPs (16% more than ViTPose-s). The difference in runtime is smaller than our measurement precision and both models run a $\sim 50$ fps. + +# 6. Conclusions + +We present ProbPose, a novel approach to 2D human pose estimation that uses probability maps instead of heatmaps and introduces presence within-the-activation-map probability prediction. Unlike previous methods, we do not assume a Gaussian distribution for the localization probability and employ the expected OKS for both training and decoding, thus aligning the training loss and the evaluation metric. The key findings are: + +1. Probability maps with OKSLoss improve versatility without sacrificing performance, offering more flexibility than point estimates. +2. Modified OKSLoss adapts to each keypoint type, enforcing sharper distributions for high-precision keypoints like eyes or nose, while broader distributions are used for less precise keypoints like hips. These distributions are more reflective of the image and are not constrained by a Gaussian assumption. +3. Predicting presence probability is more effective than thresholding confidence, reducing error by $45\%$ . Presence probability is a better indicator for in/out decisions than the peak of a predicted Gaussian. +4. Cropping images during training improves both out-of-image localization and in-image performance by increasing data variability, similar to other information-dropping augmentations. Unlike Hide&Seek [10], crop augmentation also enables out-of-image localization. +5. Increasing the activation window size comes with some performance trade-offs, but the impact can be minimized. Our double-probmap model can localize keypoints up to $25\%$ outside the bounding box with only an $0.4\%$ decrease in AP performance. + +Future work could explore the behavior of probability maps in multibody scenarios. Decoding with expected OKS maximization has proven especially useful for bimodal heatmaps, which are common in multibody images. + +The issue of COCO keypoints near the edge of the bounding box remains unresolved. Ignoring these keypoints during training reduces performance as valuable data is lost. However, training with them teaches the model to place keypoints further inside the image. 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Pose2seg: Detection free human instance segmentation, 2019. 3, 16 \ No newline at end of file diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/images.zip b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1e5698e58315178542b914b89aa914ab20b413ef --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6f1b3ffcd069a3e850986a9f086a2676328772ad43b2048df4dc77f830de33e4 +size 291779 diff --git a/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/layout.json b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..9920b54a1988b8e61e80f78e999434864bc41fd9 --- /dev/null +++ b/2025/ProbPose_ A Probabilistic Approach to 2D Human Pose Estimation/layout.json @@ -0,0 +1,7644 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 97, + 103, + 512, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 103, + 512, + 121 + ], + "spans": [ + { + "bbox": [ + 97, + 103, + 512, + 121 + ], + "type": "text", + "content": "ProbPose: A Probabilistic Approach to 2D Human Pose Estimation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 214, + 144, + 394, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 214, + 144, + 394, + 230 + ], + "spans": [ + { + "bbox": [ + 214, + 144, + 394, + 230 + ], + "type": "text", + "content": "Miroslav Purkrabek and Jiri Matas Visual Recognition Group Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague purkrmir@fel(cvut.cz" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 258, + 200, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 258, + 200, + 270 + ], + "spans": [ + { + "bbox": [ + 152, + 258, + 200, + 270 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 285, + 296, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 296, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 296, + 489 + ], + "type": "text", + "content": "Current state-of-the-art Human Pose Estimation methods ignore out-of-image keypoints in both training and evaluation and use uncalibrated heatmaps as keypoint location representations. We propose ProbPose, which predicts for each keypoint: a calibrated probability of keypoint presence at each location in the activation window, the probability of being outside of it, and its predicted visibility. To address the lack of evaluation protocols for out-of-image keypoints, we introduce the CropCOCO dataset and the Extended OKS (Ex-OKS) metric, which extends OKS to out-of-image points. Tested on COCO, CropCOCO, and OCHuman, ProbPose shows significant gains in out-of-image keypoint localization while also improving in-image localization through data augmentation. Additionally, the model improves robustness along the edges of the bounding box and offers better flexibility in keypoint evaluation. The code and weights are available on the project website1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 514, + 135, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 514, + 135, + 526 + ], + "spans": [ + { + "bbox": [ + 56, + 514, + 135, + 526 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 534, + 295, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 606 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 606 + ], + "type": "text", + "content": "Human pose estimation (HPE) has seen significant progress, achieving robust performance on standard datasets. The most successful models like ViTPose [32] typically use a top-down, heatmap-based approach, where heatmaps serve as dense representations of keypoint locations across an image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 607, + 295, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 295, + 692 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 295, + 692 + ], + "type": "text", + "content": "In this paper, we address two limitations of top-down HPE methods: (1) all previous methods overlook out-of-image keypoints during training and, more importantly, ignore them in evaluation, and (2) heatmaps restrict their use to simple point estimates. While seemingly separate, these issues are interrelated and can be addressed through an appropriate choice of representation and loss function." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 256, + 434, + 386 + ], + "blocks": [ + { + "bbox": [ + 316, + 256, + 434, + 386 + ], + "lines": [ + { + "bbox": [ + 316, + 256, + 434, + 386 + ], + "spans": [ + { + "bbox": [ + 316, + 256, + 434, + 386 + ], + "type": "image", + "image_path": "9264fed1fb088b7d1b4601da40a0699c37b18ccc5799f5e06beca7f9b78bd56a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 394, + 555, + 461 + ], + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 461 + ], + "type": "text", + "content": "Figure 1. ProbPose (left) vs. ViTPose [32] (right) output on a cropped image with the dark part removed. The bounding box, on which the pose estimators operate, is detected by YOLOX-x [5]. ProbPose estimates keypoints outside of the image better, e.g. the right leg which is wrongly aligned with the left leg by ViTPose, for which out-of-image keypoints represent a domain shift." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 435, + 257, + 553, + 386 + ], + "blocks": [ + { + "bbox": [ + 435, + 257, + 553, + 386 + ], + "lines": [ + { + "bbox": [ + 435, + 257, + 553, + 386 + ], + "spans": [ + { + "bbox": [ + 435, + 257, + 553, + 386 + ], + "type": "image", + "image_path": "063bdb24d5745424cd9d52d13f5e87e0d9596f500f9996f875865dda6f4f735a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "content": "Top-down methods localize keypoints within a specific region called the activation window. This activation window is the part of the image mapped to the predicted heatmap. The activation window often matches the model input and it may exceed image boundaries due to preprocessing steps, such as maintaining aspect ratios or enlarging bounding boxes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "content": "Under challenging conditions, such as heavy occlusion or cropped images, keypoints may fall outside the activation window. Current methods do not address this issue and simply ignore out-of-window keypoints during training. Even more concerning, evaluation metrics such as OKS (Object Keypoint Similarity) and PCK (Percentage of Correct Keypoints) assess only in-image keypoints. This lack of accountability often leads models to predict keypoints inaccurately on other joints when the actual keypoint is not visible in the image. For example, as shown in Fig. 1, the left leg is mistakenly assigned to the same joints as the right leg. Furthermore, current top-down models do not provide any" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 231, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 231, + 712 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 231, + 712 + ], + "type": "text", + "content": "1MiraPurkrabek.github.io/ProbPose/" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27124" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "indication of whether a keypoint is inside or outside the activation window, and models are not penalized for attempting to localize every keypoint." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 110, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 110, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 294, + 204 + ], + "type": "text", + "content": "A second challenge in existing HPE methods lies in the reliance on heatmaps as the keypoint representation. Heatmaps provide dense representation of keypoint locations. However, the standard approach of generating target heatmaps with a fixed Gaussian sigma and training with mean square error (MSE) forces the model to output heatmaps with fixed sigmas as well, limiting the accuracy of these estimates." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 207, + 295, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 207, + 295, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 207, + 295, + 386 + ], + "type": "text", + "content": "Decoding heatmaps to obtain a point estimate typically involves taking the argmax, often refined with UDP decoding [9]. While this approach is effective for identifying the most likely pixel, it is optimal only when the goal is to classify a single correct pixel for each keypoint. However, practical applications demand more flexible interpretations of keypoint locations. For example, an application might require an estimate of the smallest area where a keypoint is located with at least " + }, + { + "bbox": [ + 55, + 207, + 295, + 386 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 207, + 295, + 386 + ], + "type": "text", + "content": " probability, or, as in humanrobot interaction, identify areas where the model has high uncertainty to ensure safe interactions. Heatmaps, which are prone to overconfidence, are not designed to indicate uncertainty or convey \"don't know\" outcomes, even when Bayes risk is high, an essential factor in safety-critical applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 388, + 294, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 294, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 294, + 483 + ], + "type": "text", + "content": "To address these limitations, we propose ProbPose, a model with multiple outputs that fully describe each keypoint. ProbPose predicts (1) calibrated presence probabilities indicating whether the keypoint lies within the activation window, (2) keypoint's location within the activation window, (3) quality estimate of the localization and (4) visibility. Moreover, instead of using traditional heatmaps, we employ probability maps." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 485, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 295, + 687 + ], + "type": "text", + "content": "Probability maps differ from heatmaps in several ways: they contain values between 0 and 1 and are normalized to sum to 1, providing calibrated probabilities. Unlike heatmaps, which assume a fixed Gaussian shape, probability maps adapt their shape based on the data, without forcing any assumptions. Additionally, instead of decoding using a simple argmax, we compute the expected OKS for each pixel and select the location that maximizes this score, an approach we term expected OKS maximization. Probability maps are trained using an OKS-based loss modified for dense predictions, formulated as an expected risk minimization problem. Probability maps do not outperform heatmaps on keypoints in the image but have comparable localization ability. Their biggest advantage is in their versatility and better modeling of the underlying distribution. Calibrated probability maps allow for more complex reasoning than point estimates and have a direct interpretation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "content": "Since current datasets and metrics lack evaluation protocols for out-of-image keypoints, we introduce a new dataset," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "CropCOCO, comprising cropped images from COCO, and the Extended OKS (Ex-OKS) metric, which builds on OKS to evaluate out-of-image keypoints and presence probability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 328, + 121, + 489, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 121, + 489, + 131 + ], + "spans": [ + { + "bbox": [ + 328, + 121, + 489, + 131 + ], + "type": "text", + "content": "In summary, our main contributions are:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 133, + 553, + 322 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 314, + 133, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 133, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 314, + 133, + 553, + 167 + ], + "type": "text", + "content": "1. A concept of presence probability that keypoints is in the activation window, distinct from confidence, which measures the model's trust in its own estimate." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 168, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 215 + ], + "type": "text", + "content": "2. Model for out-of-image keypoints that can localize keypoints within the activation window, even beyond the image boundaries, or predict presence probability for out-of-window keypoints." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 216, + 553, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 216, + 553, + 238 + ], + "spans": [ + { + "bbox": [ + 313, + 216, + 553, + 238 + ], + "type": "text", + "content": "3. OKSLoss adapted for dense predictions in risk minimization formulation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 240, + 553, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 553, + 286 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 553, + 286 + ], + "type": "text", + "content": "4. We show that cropping-based data augmentation improves out-of-image keypoint localization, supports presence probability estimation, and enhances in-image localization, similar to Hide&Seek [10]" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 288, + 553, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 288, + 553, + 322 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 553, + 322 + ], + "type": "text", + "content": "5. New CropCOCO dataset and Ex-OKS evaluation metric for more realistic assessment of real-world performance" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "spans": [ + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 354, + 553, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 553, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 553, + 461 + ], + "type": "text", + "content": "There are three main approaches to 2D human pose estimation: top-down, bottom-up, and single-stage. Single-stage [22, 23, 28, 31] methods directly predict individuals and their skeletons in an image. Bottom-up methods [3, 6] detect all keypoints first and then group them into individual skeletons. The top-down methods [16, 24, 29, 32, 33], despite their challenges, remain the most successful. They use human detectors to process each bounding box independently, providing the best performance on most datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 463, + 553, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 553, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 553, + 569 + ], + "type": "text", + "content": "Among top-down methods, heatmap-based approaches are the most popular. Unlike regression-based methods [25, 27], which directly predict 2D coordinates, heatmap-based methods [16, 24, 32] predict a heatmap with the same aspect ratio as the input. The keypoints are then estimated as the maximum of the heatmap. Heatmaps are more robust and easier to train than regression-based methods, although efforts have been made to narrow the gap between the two approaches [18, 26]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "content": "A key development in heatmap-based methods is UDP (unbiased data processing) [9], which improves coordinate encoding and decoding. Heatmaps are typically defined as 2D Gaussians with a fixed sigma centered on the keypoint. Subpixel decoding allows for smaller heatmaps, reducing computational costs. The maximum value of the heatmap, called the \"confidence,\" is often used for three tasks: visibility estimation, quality estimation, and in/out-of-image decisions. Visibility is sometimes outsourced to specialized heads, quality prediction could be improved by OKS prediction, as shown in [7]. In/out decisions (later defined as presence probability in this paper) are not explicit, as they" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27125" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 294, + 388 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 294, + 388 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 294, + 388 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 294, + 388 + ], + "type": "image", + "image_path": "35b997d928c0d097b15e4240a2ec850dce80eab75496bf4c97b4de1ac2f90fde.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 396, + 295, + 440 + ], + "lines": [ + { + "bbox": [ + 55, + 396, + 295, + 440 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 295, + 440 + ], + "type": "text", + "content": "Figure 2. ProbPose-s (left), compared with ViTPose-s (right), improves localization outside the image and handles occlusion better on COCO (first row) and the proposed CropCOCO (second row). ProbPose estimates points well outside of the image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 458, + 295, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 295, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 295, + 482 + ], + "type": "text", + "content": "are not needed for OKS evaluation, but are important for visualization and real-world applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 483, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 628 + ], + "type": "text", + "content": "Most heatmap-based methods are trained with MSE loss, which encourages the output heatmap to match the target Gaussian heatmap. All keypoints are treated equally, with the same Gaussian and sigma. The training focuses only on keypoints within the activation window, meaning the model never encounters an empty heatmap. Since the input of the model often extends beyond the bounding box to capture more context, the activation window can include areas outside the image. This enables a limited prediction of keypoints outside the image, although the models are not specifically trained for this task. For more details, see Appendix A in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 628, + 295, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 295, + 699 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 295, + 699 + ], + "type": "text", + "content": "Heatmap-based approaches can predict keypoints outside of the image to some degree. Regression methods like RLE [13] go even further and predict keypoints further from the image. Our goal is not to localize out-of-image keypoints per se but emphasize their importance in training and evaluation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "content": "Alternative loss functions have also been proposed." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": "Adaptive Wing Loss [30] improves on original Wing Loss [4]. CornerNet [11] introduces a modified Focal Loss (originally in [15]) for object detection. RTMO [17] treats pose estimation as coordinate classification, assuming a normal distribution with varying sigmas for different keypoints, and trains with a negative log likelihood loss. Distribution-based losses such as [21] or Kullback-Leibler divergence have also been used for heatmap-based pose estimation. Most importantly, [19] introduce a new OKSLoss, that is directly tied to the evaluation metric. Their OKSLoss is computed on the predicted keypoints. We modify it to use pixel-wise to optimize probability maps without any shape assumptions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 228, + 553, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 299 + ], + "type": "text", + "content": "This paper also applies a cropping data augmentation technique. Similarly to information-dropping methods [10] like Hide&Seek or random bounding box masking, this technique introduces the domain shift by creating more invisible keypoints during training, encouraging the model to leverage the structure of the human body." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 300, + 553, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 553, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 553, + 382 + ], + "type": "text", + "content": "The most widely used dataset for 2D human pose estimation is COCO [14], with MPII [1] being a less common alternative. Datasets like OCHuman [34] and CrowdPose [12] focus on multibody problems such as occlusion and self-occlusion. For COCO and related datasets, the evaluation metric is Object Keypoint Similarity (OKS), while Percentage of Correct Keypoints (PCKh) is used for MPII." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 383, + 553, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 553, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 553, + 526 + ], + "type": "text", + "content": "However OKS ignores unannotated keypoints, as COCO is not fully annotated – many individuals have missing keypoints. Missing annotations can occur either because the keypoint is outside the image or because of occlusion. All annotated keypoints in current datasets are within the image, as annotating keypoints outside the image would be too costly and imprecise. Additionally, OKS does not penalize guessing, and if a model predicts a keypoint inside the image when it is not present, there is no penalty. Evaluating the presence probability of keypoints (whether they are in the activation window) is crucial for real-world applications and requires out-of-image annotations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 527, + 553, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 527, + 553, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 527, + 553, + 574 + ], + "type": "text", + "content": "We address these issues by introducing a new dataset, CropCOCO, created by cropping COCO images, along with a new evaluation metric, Extended OKS (Ex-OKS), which accounts for keypoints outside the image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 584, + 370, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 584, + 370, + 596 + ], + "spans": [ + { + "bbox": [ + 314, + 584, + 370, + 596 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 604, + 497, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 497, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 497, + 616 + ], + "type": "text", + "content": "ProbPose introduces several key innovations:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 314, + 617, + 553, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 617, + 553, + 641 + ], + "spans": [ + { + "bbox": [ + 314, + 617, + 553, + 641 + ], + "type": "text", + "content": "1. A novel approach to keypoint localization using probability maps." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 642, + 553, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 642, + 553, + 665 + ], + "spans": [ + { + "bbox": [ + 314, + 642, + 553, + 665 + ], + "type": "text", + "content": "2. A different application of OKSLoss [19] corresponding to expected risk minimization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 666, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 666, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 314, + 666, + 553, + 689 + ], + "type": "text", + "content": "3. A new attribute for each keypoint, termed presence probability." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "4. A data augmentation technique to handle keypoints outside the image." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "27126" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 108 + ], + "type": "text", + "content": "5. A double-probmap approach that expands the field of view, enabling localization of keypoints positioned far outside the image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 110, + 296, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 110, + 296, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 296, + 193 + ], + "type": "text", + "content": "In combination with visibility and quality estimation, these elements provide a complete description of each keypoint's state in ProbPose - indicating whether it is within the image, visible, and the confidence level of the estimate. The probability map offers calibrated localization estimates. Each component is explained in detail in the following sections." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 200, + 241, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 200, + 241, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 200, + 241, + 213 + ], + "type": "text", + "content": "3.1. Probability maps and loss function" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 217, + 296, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 348 + ], + "type": "text", + "content": "In conventional methods, heatmaps are trained with Gaussian targets and MSE loss, resulting in fast convergence, but a Gaussian-shaped bias in output. However, there is no theoretical basis for assuming that the posterior localization probability follows a Gaussian distribution. The normal distribution in OKS metric reflects human-induced error in the annotation process, but we assume the underlaying distribution is not Gaussian but reflects the body shape. During inference, heatmaps typically use the argmax for point localization and the peak value as a combined measure of localization quality and visibility." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 349, + 296, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 296, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 296, + 396 + ], + "type": "text", + "content": "In our approach, we require the model to output probability maps rather than traditional heatmaps. Unlike heatmaps, probability maps always sum to 1, achieved through Sparsemax [20] as the final activation function." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 396, + 296, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 421 + ], + "type": "text", + "content": "Each pixel in the probability map represents the posterior probability" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 427, + 294, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 427, + 294, + 441 + ], + "spans": [ + { + "bbox": [ + 108, + 427, + 294, + 441 + ], + "type": "interline_equation", + "content": "p _ {L} \\left(x _ {i}\\right) = p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right), \\tag {1}", + "image_path": "bc10b4395cb4ccb3dac4cc9bbf6aaf87ffe5595e321074b590bc731afd659970.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "text", + "content": " is pixel coordinate, " + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "k_{j}" + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "text", + "content": " is the j-th keypoint and " + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "AW" + }, + { + "bbox": [ + 55, + 446, + 296, + 483 + ], + "type": "text", + "content": " stands for activation window. With Sparsemax, each probability map sums to 1 for each keypoint:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 102, + 489, + 294, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 489, + 294, + 514 + ], + "spans": [ + { + "bbox": [ + 102, + 489, + 294, + 514 + ], + "type": "interline_equation", + "content": "F \\sum_ {x _ {i} \\in A W} p \\left(x _ {i} \\mid k _ {j} \\in A W, i m g\\right) = 1 \\tag {2}", + "image_path": "7c2426639d36e987033b34b2493b98d893340cd03eca3d5db2efb7acbb23d27f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 521, + 280, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 280, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 280, + 533 + ], + "type": "text", + "content": "We refer to this as the localization probability " + }, + { + "bbox": [ + 55, + 521, + 280, + 533 + ], + "type": "inline_equation", + "content": "p_L(x_i)" + }, + { + "bbox": [ + 55, + 521, + 280, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 537, + 141, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 537, + 141, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 537, + 141, + 548 + ], + "type": "text", + "content": "3.1.1. Loss function" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 552, + 296, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 599 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 599 + ], + "type": "text", + "content": "We train the probability maps using a modified version of OKSLoss [19], aligned with the evaluation function. The loss is formulated as an expected risk minimization problem." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 96, + 606, + 295, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 606, + 295, + 620 + ], + "spans": [ + { + "bbox": [ + 96, + 606, + 295, + 620 + ], + "type": "interline_equation", + "content": "R _ {e x p} \\left(x _ {i}\\right) = \\left(1 - O K S \\left(x _ {i}\\right)\\right) \\cdot p _ {L} \\left(x _ {i}\\right) \\tag {3}", + "image_path": "7ed2010bf53779ec47cdd791ce1f8aac0fdc5f4d001c07665e1300504e773c20.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 622, + 295, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 622, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 91, + 622, + 295, + 635 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {O K S} \\left(x _ {i}\\right) = (1 - \\alpha) R _ {e x p} \\left(x _ {i}\\right) + \\alpha g \\left(x _ {i}\\right) \\tag {4}", + "image_path": "b72ef9684f68e92618176f2dbce5fbc82acc7140090fe5272955124e129d4200.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "In Eq. (4), " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "R_{exp}(x_i)" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " represents expected risk and " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{OKS}(x_i)" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " is the loss function for pixel " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": ". In contrast to [19], we apply OKSLoss on each pixel of probability map instead of on predicted keypoints. This loss encourages pixels with low OKS to have low localization probability and those with high OKS to have higher localization probability." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 317, + 70, + 434, + 228 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 434, + 228 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 434, + 228 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 434, + 228 + ], + "type": "image", + "image_path": "c6f8b771598d29a1dac86d426fc4d5af159e75969dd0da2ac51da2b14860d261.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 229, + 428, + 241 + ], + "lines": [ + { + "bbox": [ + 321, + 229, + 428, + 241 + ], + "spans": [ + { + "bbox": [ + 321, + 229, + 428, + 241 + ], + "type": "text", + "content": "(a) Predicted probability map " + }, + { + "bbox": [ + 321, + 229, + 428, + 241 + ], + "type": "inline_equation", + "content": "p_L" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 249, + 554, + 327 + ], + "lines": [ + { + "bbox": [ + 313, + 249, + 554, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 249, + 554, + 327 + ], + "type": "text", + "content": "Figure 3. UDP [9] decoding of " + }, + { + "bbox": [ + 313, + 249, + 554, + 327 + ], + "type": "inline_equation", + "content": "p_L" + }, + { + "bbox": [ + 313, + 249, + 554, + 327 + ], + "type": "text", + "content": " vs. expected OKS maximization. On the left, the white cross marks the maximum value and the light purple one is the point refined by UDP. In the right image, the dark purple cross is maximum expected OKS. The probability map contains a small, one-pixel-wide peak marked by the white cross. Maximizing expected OKS is robust to sharp local peaks and prefers areas with big mass compared to simple maxima." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 434, + 70, + 553, + 228 + ], + "blocks": [ + { + "bbox": [ + 434, + 70, + 553, + 228 + ], + "lines": [ + { + "bbox": [ + 434, + 70, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 434, + 70, + 553, + 228 + ], + "type": "image", + "image_path": "c7115537a05bef544aea5dd7c83be680c3544843df1ae100b5fcbfc238ea38d6.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 444, + 229, + 543, + 240 + ], + "lines": [ + { + "bbox": [ + 444, + 229, + 543, + 240 + ], + "spans": [ + { + "bbox": [ + 444, + 229, + 543, + 240 + ], + "type": "text", + "content": "(b) Expected OKS map " + }, + { + "bbox": [ + 444, + 229, + 543, + 240 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{OKS}" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "content": "The term " + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "inline_equation", + "content": "g(x_{i})" + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "content": " is the heatmap gradient, computed with the Sobel operator, and serves as a regularizer controlled by the hyperparameter " + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "content": ". Without regularization, the probability map quickly forms a sharp peak and overfits to training data. Smoothing regularization minimizes differences between neighboring pixels, promoting a smooth distribution without assuming a specific shape, as Gaussian regularization does for MSE-trained heatmaps." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 458, + 554, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 458, + 554, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 458, + 554, + 530 + ], + "type": "text", + "content": "For localization, instead of directly using argmax, we compute the expected OKS (Eq. (5)) for each pixel and take its argmax, refining it with quadratic interpolation for subpixel precision. This approach, based on expected OKS rather than UDP decoding, slightly enhances localization, especially in cases of bimodal heatmaps such as in Fig. 3." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 345, + 548, + 555, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 548, + 555, + 575 + ], + "spans": [ + { + "bbox": [ + 345, + 548, + 555, + 575 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {O K S} \\left(x _ {i}\\right) = \\sum_ {x _ {j} \\in P M} p _ {L} \\left(x _ {j}\\right) \\cdot O K S \\left(x _ {i}, x _ {j}\\right) \\tag {5}", + "image_path": "297cd7e2fe7f6b496bcfca067bc527e525f83b40da60574fe9589ea1a068b006.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "Probability maps offer improved versatility. They allow point estimates, as required by the COCO evaluation protocol, and enable probabilistic queries, such as defining the smallest area containing a keypoint with at least " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": " probability. However, the peak of the probability map can no longer reliably indicate the quality of the localization or the presence of keypoints in the activation window. The former is addressed by predicting the OKS for each keypoint as in [7], and the latter is addressed by directly predicting the keypoint's presence probability." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27127" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 174, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 174, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 174, + 85 + ], + "type": "text", + "content": "3.2. Presence probability" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 233 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 233 + ], + "type": "text", + "content": "Previous models and evaluation protocols have overlooked the question of whether a keypoint is within the activation window. Top-down approaches assume that the bounding boxes fully enclose all keypoints, but this is not always the case due to factors such as occlusion or crop (see Appendix A in the supplementary for further discussion). Thus, it is essential for the model to assess whether a keypoint is actually present in the activation window. This is usually addressed by thresholding confidence (the maximum heatmap value) with an arbitrary cut-off. However, evaluation protocols have ignored keypoint presence, with models predicting a location regardless." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "text", + "content": "Presence probability " + }, + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "inline_equation", + "content": "p(k_{j} \\in AW|img)" + }, + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "text", + "content": " complements probability maps, which inherently assume that keypoints are within the activation window. If the keypoint is outside, the presence probability reflects this; if inside, the probability map provides the location. The visual explanation is in Fig. 4. We abbreviate the presence probability to " + }, + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "inline_equation", + "content": "p_{p}(k_{j})" + }, + { + "bbox": [ + 55, + 233, + 296, + 316 + ], + "type": "text", + "content": " and train it with Binary Cross Entropy loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 317, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 317, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 296, + 376 + ], + "type": "text", + "content": "To train the presence probability, we need keypoints that are certainly outside the activation window. These samples are generated through various data augmentation techniques, such as scaling and rotation, with random cropping as the primary source." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 384, + 133, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 133, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 133, + 395 + ], + "type": "text", + "content": "3.3. Calibration" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "content": "Both the probability maps and presence probability are calibrated. Probability maps are calibrated so that the top " + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "content": " of the map contains " + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "content": " of the GT keypoints, the top " + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 401, + 296, + 510 + ], + "type": "text", + "content": " of the GT keypoints, and so on. We achieve this calibration through temperature scaling [8] on CropCOCO. As a result, the calibrated probabilities align with the true underlying distribution, enabling more versatile evaluations beyond simple point estimates. Details and calibration curves are in Appendix B in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 517, + 198, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 198, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 198, + 529 + ], + "type": "text", + "content": "3.4. Crop image augmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 534, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 605 + ], + "type": "text", + "content": "As discussed in Appendix A, we consider the image border as a type of occlusion. To train the model to correctly identify keypoints outside the image, we need suitable training samples. Manual annotation of such keypoints is both costly and imprecise, so we generate these samples by cropping existing annotated keypoints out of the image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 606, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 606, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 606, + 295, + 677 + ], + "type": "text", + "content": "Depending on the crop strength, the in-the-image keypoint may end up within the activation window but outside the image, or entirely outside the activation window. Keypoints within the activation window but outside the image are used to train probability maps, while those outside the activation window train the presence probability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "The cropping not only provides data for presence probability training but also enhances the model's ability to localize keypoints near the image boundary, extending even" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 71, + 434, + 180 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 434, + 180 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 434, + 180 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 434, + 180 + ], + "type": "image", + "image_path": "126fe217dbd29214f3aa08c1aba97e67739b28137afbb39145793f130e8700cb.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 338, + 182, + 412, + 192 + ], + "lines": [ + { + "bbox": [ + 338, + 182, + 412, + 192 + ], + "spans": [ + { + "bbox": [ + 338, + 182, + 412, + 192 + ], + "type": "text", + "content": "(a) Traditional method" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 201, + 555, + 299 + ], + "lines": [ + { + "bbox": [ + 313, + 201, + 555, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 555, + 299 + ], + "type": "text", + "content": "Figure 4. Key regions in top-down pose estimation. Rectangles represent the bounding box, the model input and the activation window. Right: the double-probmap approach with a larger activation window. The probability map is responsible for localization of keypoints in activation windows (A, B, C) and the presence probability predicts whether the keypoint is outside (D, E). Note that double-probmap has a larger field-of-view. For detailed discussion about keypoint location, see Appendix A." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 435, + 71, + 553, + 180 + ], + "blocks": [ + { + "bbox": [ + 435, + 71, + 553, + 180 + ], + "lines": [ + { + "bbox": [ + 435, + 71, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 435, + 71, + 553, + 180 + ], + "type": "image", + "image_path": "0a0514b3c3a8a242de83bebfac39b889dbc7bad7295c8d9ecdac7186e22bc730.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 445, + 182, + 543, + 192 + ], + "lines": [ + { + "bbox": [ + 445, + 182, + 543, + 192 + ], + "spans": [ + { + "bbox": [ + 445, + 182, + 543, + 192 + ], + "type": "text", + "content": "(b) Double-probmap approach" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 320, + 555, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 555, + 381 + ], + "type": "text", + "content": "to areas beyond the visible border. This is especially useful for cases where the subject is partially cropped by the image border or in close-up pose estimation, where keypoints may lie far from the visible body. Examples of crops and result visualizations are in the Figs. 1 and 2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 404, + 492, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 404, + 492, + 417 + ], + "spans": [ + { + "bbox": [ + 314, + 404, + 492, + 417 + ], + "type": "text", + "content": "3.5. Enlarging activation window size" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 427, + 554, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 554, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 554, + 499 + ], + "type": "text", + "content": "When predicting keypoints outside the image, a key question is how far from the image we aim to localize them. In applications where out-of-image keypoints localization is essential, it might be helpful to enlarge the activation window. However, simply increasing the input size or activation window typically reduces performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 505, + 555, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 505, + 555, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 505, + 555, + 636 + ], + "type": "text", + "content": "To address this, we propose a double-probmap approach (illustrated in Fig. 4b). In this method, an expert heatmap precisely localizes keypoints within a smaller activation window that matches the model input, while a larger activation window captures keypoints further from the image. The larger probability map has the same resolution but a wider field of view, resulting in a lower effective resolution. Both maps are trained on keypoints within their respective activation areas. If the larger map predicts a keypoint within the smaller activation area, the expert map refines the localization for greater accuracy." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": "This approach balances the trade-off between field-of-view and precision. The larger map offers a broader field of view, but with lower accuracy, while the expert map maintains precision within a smaller activation window. This method is particularly suitable for applications like close-up pose estimation, where a wide field of view is essential." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27128" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 96, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 96, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 96, + 83 + ], + "type": "text", + "content": "4. Data" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "content": "To evaluate ProbPose, we introduce a new evaluation protocol based on OKS and mAP, along with a new dataset specifically designed for out-of-image keypoint localization and presence probability classification." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 148, + 167, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 148, + 167, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 167, + 159 + ], + "type": "text", + "content": "4.1. Evaluation metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 166, + 295, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 166, + 295, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 166, + 295, + 213 + ], + "type": "text", + "content": "Current metrics, such as OKS and PCK, evaluate only in-image keypoints, overlooking false positives. As a result, models overestimate confidence, guess keypoint locations, and are not penalized for predicting absent keypoints." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 214, + 296, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 214, + 296, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 214, + 296, + 332 + ], + "type": "text", + "content": "We propose a new evaluation approach that checks whether a keypoint is within the activation window and, if so, assesses its precise localization. This approach better reflects real-world scenarios, like human-machine interaction, where knowing if a keypoint cannot be localized is critical. To address this, we introduce Extended OKS (Ex-OKS), an extension of OKS that accommodates keypoints outside the activation window. For bottom-up and single-stage methods, where the activation window spans the entire image, Ex-OKS can be adapted accordingly." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 334, + 296, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 296, + 393 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 296, + 393 + ], + "type": "text", + "content": "In its localization-only form, Ex-OKS functions identically to the original OKS. However, Ex-OKS extends OKS by accounting for keypoints outside the activation window. The essential goal is for the model to indicate if a keypoint is absent, rather than attempting a guess." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "text", + "content": "Ex-OKS evaluates two variables for each keypoint: location " + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "text", + "content": " and presence probability " + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "inline_equation", + "content": "p_{p}" + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "text", + "content": ". Although the model outputs a continuous value for " + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "inline_equation", + "content": "p_{p}" + }, + { + "bbox": [ + 55, + 394, + 296, + 453 + ], + "type": "text", + "content": ", a binary decision (0 or 1) is often required in real-world applications, so we optimally threshold it for each model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 454, + 203, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 454, + 203, + 465 + ], + "spans": [ + { + "bbox": [ + 67, + 454, + 203, + 465 + ], + "type": "text", + "content": "Formally, we define Ex-OKS as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 477, + 295, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 477, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 86, + 477, + 295, + 533 + ], + "type": "interline_equation", + "content": "d _ {i} = \\left\\{ \\begin{array}{l l} d _ {e} \\left(x _ {i} ^ {*}, x _ {i} ^ {\\prime}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} (\\mathrm {A W}, x _ {i} ^ {\\prime}) & \\text {i f} p _ {p} ^ {*} = 0 \\text {a n d} p _ {p} ^ {\\prime} = 1 \\\\ d _ {e} \\left(x _ {i} ^ {*}, \\mathrm {A W}\\right) & \\text {i f} p _ {p} ^ {*} = 1 \\text {a n d} p _ {p} ^ {\\prime} = 0 \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {6}", + "image_path": "cb846a40a8a8a712014d66a438baea7fb9638819f52ed92376d41506c672b7ea.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 87, + 536, + 295, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 536, + 295, + 562 + ], + "spans": [ + { + "bbox": [ + 87, + 536, + 295, + 562 + ], + "type": "interline_equation", + "content": "\\operatorname {E x} - \\mathrm {O K S} = \\exp \\left(\\frac {- d _ {i} ^ {2}}{2 k ^ {2} \\sigma^ {2}}\\right) \\tag {7}", + "image_path": "4c1d70e9df0a8f748810351ce7f97d9089d1769add67a72c099d10e93adf7724.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "inline_equation", + "content": "AW" + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "content": " stands for activation window, " + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "inline_equation", + "content": "d_{e}" + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "content": " is Euclidean distance and " + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\cdot^{*}" + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\cdot^{\\prime}" + }, + { + "bbox": [ + 55, + 569, + 295, + 605 + ], + "type": "text", + "content": " are ground truth and predicted variables, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "content": "If both the ground truth and the model agree that " + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "inline_equation", + "content": "p_{p} = 1" + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "content": ", Ex-OKS defaults to the standard OKS evaluation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": "When the ground truth " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{p}^{*} = 0" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": " and the model predicts " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{p}^{\\prime} = 1" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": ", the penalty depends on the predicted location " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "x_{i}^{\\prime}" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": " and its distance from the edge of the activation window, with lower penalties for points near the boundary. Similarly, if " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{p}^{*} = 1" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": " but the model predicts " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{p}^{\\prime} = 0" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": ", the penalty is based on the ground truth location " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "x_{i}^{*}" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": ", with smaller penalties for errors near the border of the activation window." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "When both " + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "inline_equation", + "content": "p_{p}^{*} = 0" + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "inline_equation", + "content": "p_{p}^{\\prime} = 0" + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": ", there is no penalty and the similarity score is 1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": "Ex-mAP, built on Ex-OKS, extends mAP by incorporating both keypoint localization and presence probability, making it suitable for evaluating models with keypoints outside the activation window." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 152, + 376, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 152, + 376, + 163 + ], + "spans": [ + { + "bbox": [ + 314, + 152, + 376, + 163 + ], + "type": "text", + "content": "4.2. Datasets" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 168, + 553, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 216 + ], + "type": "text", + "content": "We evaluated our model on the COCO dataset to ensure a fair comparison with existing models. All training was conducted on COCO, with crop image augmentation applied in specified experiments." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 217, + 554, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 554, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 554, + 312 + ], + "type": "text", + "content": "To assess performance on out-of-image keypoints, we introduce a new dataset, CropCOCO. CropCOCO consists of randomly cropped COCO validation images, with some keypoints positioned outside the activation window. Bounding boxes are recomputed for the cropped images to evaluate the model appropriately. While other researchers can create their own cropped dataset, we release CropCOCO to support reproducibility." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 312, + 554, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 554, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 554, + 443 + ], + "type": "text", + "content": "During COCO evaluation, we observed that keypoints near the image boundary are often annotated further inside the image, likely due to annotators avoiding placements near the edge. This causes our model to be penalized for accurately localizing keypoints outside the image. When keypoints near the border are excluded from evaluation, Prob-Pos demonstrates even stronger performance compared to other state-of-the-art methods. Although this issue is minor (causing about a " + }, + { + "bbox": [ + 313, + 312, + 554, + 443 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 313, + 312, + 554, + 443 + ], + "type": "text", + "content": " performance difference) and difficult to correct, we highlight it to raise awareness of its potential impact. For further details, see Appendix D." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 444, + 554, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 554, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 554, + 478 + ], + "type": "text", + "content": "Additionally, we evaluated our model on the OCHuman dataset to demonstrate its generalizability across different domains." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 490, + 395, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 490, + 395, + 502 + ], + "spans": [ + { + "bbox": [ + 314, + 490, + 395, + 502 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 510, + 554, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 569 + ], + "type": "text", + "content": "The results in Tab. 1 compare our method with other SOTA approaches on COCO, CropCOCO, and OCHuman datasets using mAP and Ex-mAP metrics. For fair comparison, we evaluate models of similar size. All experiments use ground truth bounding boxes." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "content": "ProbPose improves on its baseline model, ViTpose, by approximately " + }, + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "content": " in localization, a gain comparable to that achieved by other information-dropping augmentations like [10]. Importantly, ProbPose demonstrates stronger performance in Ex-OKS, showing improved detection of keypoints outside the activation window due to its direct presence probability prediction, as discussed in Sec. 5.1. Since COCO lacks out-of-image keypoints, Ex-OKS improvement here reflects enhanced presence probability classification. Localization metrics could be slightly higher if not for incorrect annotations near the bounding box borders, discussed further in Appendix D." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27129" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 148, + 70, + 463, + 178 + ], + "blocks": [ + { + "bbox": [ + 148, + 70, + 463, + 178 + ], + "lines": [ + { + "bbox": [ + 148, + 70, + 463, + 178 + ], + "spans": [ + { + "bbox": [ + 148, + 70, + 463, + 178 + ], + "type": "table", + "html": "
ModelCOCOMAPEx-mAPCropCOCOMAPEx-mAPOCHumanmAPEx-mAP
HRFormer-s [33]75.274.670.964.360.360.0
PVTv2 [29]72.071.570.763.158.558.1
SWIN-t [16]73.572.971.365.058.157.9
ViTPose-s [32]75.975.372.766.560.360.1
ProbPose-s76.676.481.773.960.460.2
ProbPose-s-DP76.275.480.971.461.461.2
", + "image_path": "1c555994fb691ef72fc2a4689fcde968e59eade72bcb418492344923e305bfb7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 187, + 555, + 242 + ], + "lines": [ + { + "bbox": [ + 55, + 187, + 555, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 187, + 555, + 242 + ], + "type": "text", + "content": "Table 1. Keypoint localization accuracy in terms of the standard mAP and the novel Ex-mAP metrics. ProbPose is compared with SOTA models of similar size on the COCO, CropCOCO, and OCHuman datasets. All evaluation is done using GT bounding boxes. DH stands for the double-probmap approach with a wider field of view. To compute Ex-mAP, we select the optimal threshold for each model. The best model is in bold, the second-best is underlined. ProbPose brings significant improvement for out-of-image keypoints and minor improvement on standard COCO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 263, + 294, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 263, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 263, + 294, + 323 + ], + "type": "text", + "content": "The most significant improvement is unsurprisingly observed on CropCOCO, where ProbPose excels at detecting out-of-image keypoints, primarily due to crop data augmentation. Again, the localization metrics could be higher without annotation errors along the bounding box borders." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 324, + 295, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 295, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 295, + 419 + ], + "type": "text", + "content": "ProbPose-DP, the double-probmap variant, shows a slight performance decrease on COCO and CropCOCO, reflecting the trade-off between a broader field of view and in-image precision (see Sec. 3.5). In this variant, each heatmap is predicted by one head from shared features, and the larger heatmap decides when to defer to the more precise heatmap. If the larger heatmap estimates the wrong localization, the specialized heatmap cannot correct it." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 421, + 295, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 421, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 421, + 295, + 468 + ], + "type": "text", + "content": "ProbPose-DP has worse Ex-mAP as it solves a more difficult task. Ex-mAP evaluates keypoint presence in the AW so the larger AW in ProbPose-DP makes presence classification harder as the AW border is further from the image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 469, + 295, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 295, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 295, + 540 + ], + "type": "text", + "content": "ProbPose-DP remains competitive with other SOTA methods, providing a better alternative to simply enlarging the input size or activation window. Interestingly, ProbPose-DP shows a notable improvement in OCHuman, likely due to its extended field of view, which enhances individual differentiation in multi-body scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 542, + 295, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 542, + 295, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 542, + 295, + 577 + ], + "type": "text", + "content": "ProbPose variants perform well on OCHuman (unseen during the training), highlighting their strong generalization across domains." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 587, + 243, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 243, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 243, + 601 + ], + "type": "text", + "content": "5.1. Presence probability vs. confidence" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Tab. 1 highlights the advantages of using presence probability over confidence, reflected in the increase in Ex-mAP. For clarity, Fig. 5 shows an additional classification accuracy for CropCOCO and its balanced subset. The task is to classify whether keypoints are inside or outside the activation window, indicating if they should be drawn or used in other applications. CropCOCO is unbalanced as there is much more in-AW than out-of-AW keypoints. To get a balanced subset, we randomly selected keypoints from both" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 324, + 281, + 531, + 437 + ], + "blocks": [ + { + "bbox": [ + 324, + 281, + 531, + 437 + ], + "lines": [ + { + "bbox": [ + 324, + 281, + 531, + 437 + ], + "spans": [ + { + "bbox": [ + 324, + 281, + 531, + 437 + ], + "type": "image", + "image_path": "011b11334c14357429c08ca6e3ef7561afa0967ff4a04f9899c1cbfe307d6be6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "type": "text", + "content": "Figure 5. Keypoint presence in the activation window. Accuracy, inside and outside of the AW, of the classification based on thresholding of the ProbPose's presence probability and ViTPose's confidence. The accuracy is measured for CropCOCO dataset (full line) and its balanced subset (dotted line). The proposed presence probability outperforms ViTPose's confidence in both cases, reducing the error by " + }, + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 313, + 449, + 555, + 528 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 544, + 480, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 480, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 480, + 555 + ], + "type": "text", + "content": "classes to have the same amount of each." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 557, + 554, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 554, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 554, + 629 + ], + "type": "text", + "content": "In both balanced and unbalanced datasets, the presence probability outperforms the confidence score from the ViT-Pose model. This improvement is due to confidence not being trained to reflect presence probability, and the standard COCO dataset, without crop data augmentation, lacks sufficient training samples for this purpose." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Fig. 5 also provides insights into confidence thresholding. Current models often use an arbitrary threshold of 0.3 to decide whether to trust predictions without theoretical justification. The evaluation on CropCOCO reveals that the optimal confidence threshold is between 0.15 (for unbalanced datasets) and 0.4 (for balanced datasets). Thus, the commonly used threshold of 0.3 is close to the optimum," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27130" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 70, + 258, + 142 + ], + "blocks": [ + { + "bbox": [ + 93, + 70, + 258, + 142 + ], + "lines": [ + { + "bbox": [ + 93, + 70, + 258, + 142 + ], + "spans": [ + { + "bbox": [ + 93, + 70, + 258, + 142 + ], + "type": "table", + "html": "
cropp-mapsCOCOCropCOCO
XX76.073.7
X✓76.472.4
✓X76.681.7
✓✓76.681.7
", + "image_path": "cfb353ea2fe5057495fedd2c07f7630a270cb7380e16ffca3f1896546b44f35a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 151, + 294, + 207 + ], + "lines": [ + { + "bbox": [ + 55, + 151, + 294, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 294, + 207 + ], + "type": "text", + "content": "Table 2. ProbPose ablation; mAP on COCO and CropCOCO for versions without the probability maps and crop data augmentation. Crop augmentation clearly helps for cropped images. Probability maps bring negligible performance improvement as their main strength is in versatility." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 221, + 295, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 295, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 295, + 258 + ], + "type": "text", + "content": "which aligns with its generally good results. This study offers guidance on setting an appropriate threshold based on the characteristics of a specific dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 266, + 148, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 148, + 278 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 148, + 278 + ], + "type": "text", + "content": "5.2. Ablation study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 283, + 295, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 331 + ], + "type": "text", + "content": "Tab. 2 evaluates the core components of our approach, probability maps and crop data augmentation. The analysis is conducted on the ProbPose-s model using ground truth bounding boxes on the COCO and CropCOCO datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 331, + 295, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 295, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 295, + 426 + ], + "type": "text", + "content": "Using probability maps without crop data augmentation yields the lowest performance. This setup slightly improves localization on COCO but reduces the accuracy of out-of-image keypoints in CropCOCO. Without crop data augmentation, ProbPose encounters few out-of-image training samples, and probability map normalization forces predictions within the activation window, making probability maps less effective than heatmaps for out-of-image keypoints." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 426, + 295, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 521 + ], + "type": "text", + "content": "Adding crop data augmentation improves localization accuracy on both COCO and CropCOCO. Training with out-of-image keypoints also improves in-image localization, as the model relies more on the structure of the human body, similar to [10]. Compared to Hide&Seek, crop augmentation brings the same in-image performance improvement, but also improve out-of-image localization and generate samples for training presence probability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "type": "text", + "content": "Combining crop augmentation and probmaps achieves the same localization accuracy as using crop data augmentation alone. However, as discussed in Tab. 1, the probabilistic approach is more important for presence classification. While COCO-like evaluation protocols focus on point estimates, probability maps are more versatile and provide a direct mathematical interpretation. Heatmaps are optimized for point estimates, but probmaps support broader applications without compromising point-estimate accuracy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Computational complexity. ViTPose-s (ViT-s backbone + HeatmapHead) performs 24M FLOPs. The full ProbPose-s (visibility, OKS, and " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "p_p" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " estimation) used for all experiments performs 35M FLOPs. The minimal version shrinks to 27M FLOPs (16% more than ViTPose-s). The difference in runtime is smaller than our measurement precision and both models run a " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\sim 50" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " fps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 71, + 391, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 391, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 391, + 83 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 98, + 553, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 98, + 553, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 98, + 553, + 193 + ], + "type": "text", + "content": "We present ProbPose, a novel approach to 2D human pose estimation that uses probability maps instead of heatmaps and introduces presence within-the-activation-map probability prediction. Unlike previous methods, we do not assume a Gaussian distribution for the localization probability and employ the expected OKS for both training and decoding, thus aligning the training loss and the evaluation metric. The key findings are:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 208, + 553, + 483 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 315, + 208, + 553, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 208, + 553, + 243 + ], + "spans": [ + { + "bbox": [ + 315, + 208, + 553, + 243 + ], + "type": "text", + "content": "1. Probability maps with OKSLoss improve versatility without sacrificing performance, offering more flexibility than point estimates." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 243, + 553, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 243, + 553, + 315 + ], + "spans": [ + { + "bbox": [ + 315, + 243, + 553, + 315 + ], + "type": "text", + "content": "2. Modified OKSLoss adapts to each keypoint type, enforcing sharper distributions for high-precision keypoints like eyes or nose, while broader distributions are used for less precise keypoints like hips. These distributions are more reflective of the image and are not constrained by a Gaussian assumption." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 316, + 553, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 316, + 553, + 363 + ], + "spans": [ + { + "bbox": [ + 315, + 316, + 553, + 363 + ], + "type": "text", + "content": "3. Predicting presence probability is more effective than thresholding confidence, reducing error by " + }, + { + "bbox": [ + 315, + 316, + 553, + 363 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 315, + 316, + 553, + 363 + ], + "type": "text", + "content": ". Presence probability is a better indicator for in/out decisions than the peak of a predicted Gaussian." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 364, + 553, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 364, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 315, + 364, + 553, + 422 + ], + "type": "text", + "content": "4. Cropping images during training improves both out-of-image localization and in-image performance by increasing data variability, similar to other information-dropping augmentations. Unlike Hide&Seek [10], crop augmentation also enables out-of-image localization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "text", + "content": "5. Increasing the activation window size comes with some performance trade-offs, but the impact can be minimized. Our double-probmap model can localize keypoints up to " + }, + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "text", + "content": " outside the bounding box with only an " + }, + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 315, + 423, + 553, + 483 + ], + "type": "text", + "content": " decrease in AP performance." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 498, + 553, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 553, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 553, + 545 + ], + "type": "text", + "content": "Future work could explore the behavior of probability maps in multibody scenarios. Decoding with expected OKS maximization has proven especially useful for bimodal heatmaps, which are common in multibody images." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 552, + 553, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 553, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 553, + 659 + ], + "type": "text", + "content": "The issue of COCO keypoints near the edge of the bounding box remains unresolved. Ignoring these keypoints during training reduces performance as valuable data is lost. However, training with them teaches the model to place keypoints further inside the image. Cropping as a data augmentation strategy helps mitigate this issue during training but not during evaluation. Re-annotating the dataset would be too costly and likely imprecise, as it is difficult for humans to accurately place keypoints outside the image." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the Ministry of the Interior of the Czech Republic project No. VJ02010041 and the Czech Technical University student grant SGS23/173/OHK3/3T/13." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27131" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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Pose2seg: Detection free human instance segmentation, 2019. 3, 16" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27133" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_content_list.json b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..65e11041570f3740e7b9367ab27937a784db3a36 --- /dev/null +++ b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_content_list.json @@ -0,0 +1,1492 @@ +[ + { + "type": "text", + "text": "Probabilistic Prompt Distribution Learning for Animal Pose Estimation", + "text_level": 1, + "bbox": [ + 137, + 130, + 859, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiyong Rao $^{1}$ Brian Nlong Zhao $^{2\\dagger}$ Yu Wang $^{1*}$ $^{1}$ School of Computer Science and Technology, Tongji University $^{2}$ Stanford University jiyongrao@tongji.edu.cn, brianlz@stanford.edu, yuwangtj@yeah.net", + "bbox": [ + 145, + 179, + 849, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multi-species animal pose estimation has emerged as a challenging yet critical task, hindered by substantial visual diversity and uncertainty. This paper challenges the problem by efficient prompt learning for Vision-Language Pretrained (VLP) models, e.g. CLIP, aiming to resolve the cross-species generalization problem. At the core of the solution lies in the prompt designing, probabilistic prompt modeling and cross-modal adaptation, thereby enabling prompts to compensate for cross-modal information and effectively overcome large data variances under unbalanced data distribution. To this end, we propose a novel probabilistic prompting approach to fully explore textual descriptions, which could alleviate the diversity issues caused by long-tail property and increase the adaptability of prompts on unseen category instance. Specifically, we first introduce a set of learnable prompts and propose a diversity loss to maintain distinctiveness among prompts, thus representing diverse image attributes. Diverse textual probabilistic representations are sampled and used as the guidance for the pose estimation. Subsequently, we explore three different cross-modal fusion strategies at spatial level to alleviate the adverse impacts of visual uncertainty. Extensive experiments on multi-species animal pose benchmarks show that our method achieves the state-of-the-art performance under both supervised and zero-shot settings. The code is available at https://github.com/Raojiyong/PPAP.", + "bbox": [ + 88, + 300, + 485, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 734, + 220, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Animal Pose Estimation (APE) [1, 16, 20, 21, 37] represents a fundamental vision task, the objective of which is to identify a series of keypoint locations in an animal skeleton. The skeleton (i.e. a set of connected coordinates), serves as a minimal yet informative unit for encoding both static structure and motion cues, thereby providing critical support for understanding animal behaviour. Consequently, APE plays", + "bbox": [ + 89, + 760, + 483, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a76d73037140fcdae575fb26810646565a3371e329c65949f91eacf34eba2997.jpg", + "image_caption": [ + "Figure 1. The motivation that one key point can be complementarily described in different views (An example of left shoulder)." + ], + "image_footnote": [], + "bbox": [ + 517, + 268, + 903, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a significant role in various research fields, such as neuroscience [16, 20], ecology [3, 4], zoology study [9, 21] and biotechnological quests [18, 28].", + "bbox": [ + 511, + 534, + 906, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In numerous instances [16, 18, 38], researchers have opted to directly apply Human Pose Estimation (HPE) methodologies to animals. However, it is evident that many animal species exhibit pose distributions that deviate significantly from human-specific models, leading to substantial domain shifts. To address the multi-species Animal Pose Estimation (APE) challenge, Category-Agnostic Pose Estimation (CAPE) methods [25, 30] have been investigated. These methods frame keypoint prediction as a keypoint matching problem, necessitating supplementary support sets that belong to the same category as the test image. While promising, this approach introduces additional computational overhead and necessitates prior knowledge of the animal category, thereby limiting its practicality. Moreover, given the substantial data variances observed across species [18, 38], vision-only APE methods falter when confronted with cross-species challenges that rely solely on visual cues.", + "bbox": [ + 509, + 580, + 908, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, the multimodal system proposed in [22] has garnered substantial research attention due to its ability to combine complementary data to enhance visual recognition. Despite the distinct visual characteristics of various", + "bbox": [ + 511, + 839, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 107, + 875, + 235, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Equal contribution.", + "bbox": [ + 109, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "29438", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "animal species, they share common textual descriptions, as noted in [42]. Consequently, the straightforward approach of setting the keypoint name as the class token, known as deterministic prompt learning, has become prevalent in the current literature [34, 42]. For instance, X-Pose [34] utilizes a fixed text template like \"A [Image Style] photo of a [Keypoint]\", while CLAMP [42] employs a continuous prompt template of \"[Learnable Tokens] + [Keypoint)\". However, existing multimodal APE methods fall short in terms of rich text prompt design. Moreover, manually crafting keypoint-specific prompts is a cumbersome task. As depicted in Figure 1, a solitary textual description often fails to encapsulate all the nuances of a specific keypoint, such as its color, position, and shape. For example, the \"left shoulder\" keypoint can be described from both spatial and color perspectives as \"Left shoulder is near the right shoulder\" and \"The color of the left shoulder is light salmon\", respectively. From a textual standpoint, multiple descriptions provide diverse perspectives, enabling pose estimation to grasp high-level semantics and pinpoint keypoints accurately based on one or more of these cues. On the visual front, the intricacies of wild scenes and the presence of multiple species introduce uncertain statistical shifts compared to the training domain [4, 14, 27]. Given this \"uncertainty\" in potential data variations, synthesizing novel feature statistics variants to model diverse representations can bolster the network's robustness against unseen categories. To address these challenges, this paper introduces a novel probabilistic method that enhances network generalization to handle unseen categories by adeptly modeling keypoint-adaptive prompts.", + "bbox": [ + 93, + 90, + 480, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach leverages multiple learnable text prompts to enhance flexibility and robustness in text prompt initialization, moving beyond a single template. By strategically inserting keypoint names within templates, we enable flexible sentence construction akin to natural language. We hypothesize that prompt statistics, incorporating uncertainties, follow a multivariate Gaussian distribution, with the center defined by the original prompt statistic and the range indicating data variation across animal categories. We estimate this range using mini-batch statistics in a parametric learning framework and randomly sample variants from the estimated distribution to model diverse textual descriptions, as illustrated in Figure 2. To capture diverse and informative keypoint attributes, we introduce a novel diversity loss function that ensures distinctiveness across prompt distributions. In summary, our contributions are as follows:", + "bbox": [ + 93, + 549, + 480, + 787 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel Probabilistic Prompt Distribution Learning framework for APE to learn the probabilistic representation of specific keypoint descriptions.", + "- We introduce multiple prompt attributes and design a diversity loss to prevent the learned attributes from being identical. Additionally, we explore three different cross-modal fusion strategies to achieve spatial adaptation." + ], + "bbox": [ + 89, + 794, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We demonstrate the effectiveness of the proposed probabilistic-based approach through extensive experiments on multi-species animal pose estimation.", + "bbox": [ + 513, + 90, + 903, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 152, + 661, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Animal Pose Estimation", + "text_level": 1, + "bbox": [ + 513, + 178, + 733, + 193 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Typical vision-only APE methods [1, 16, 18, 23, 31, 38], with most directly adapting human pose estimation methods [13, 26, 29, 32, 36, 39], such as DeepLabCut [9, 16], AP-10K [26, 38] and ViTPose [32, 33] to animal counterpart. These methods leverage powerful visual backbones for feature extraction but fail to handle rare or even unseen categories explicitly. The relatively limited animal data volume compared to its human counterpart increases the risk of overfitting in complex networks [4]. To cope with the limited labelled animal data volume, direct attempts [10, 17] learn prior-aware knowledge from synthetic animal datasets, and generate pseudo labels for unlabelled data. In terms of refining the pseudo labels, ScarceNet [11] and FreeNet[40] propose the novel semi-supervised learning methods that improves the reliability of pseudo label generation, effectively mitigating the data scarcity problem. Following the principles of few-shot learning, Xu et al. [30] proposed a novel Category-Agnostic Pose Estimation (CAPE) paradigm, which treats keypoint prediction as the keypoint matching problem, enabling the prediction of poses on unseen categories. This is accomplished by offering a few support sets from the same category as the test image to guide the learning process. CAPE [19, 25, 30] introduces an additional computational burden and necessitates prior animal categories, making the methods less practical. To eliminate the reliance on category-specific prior, pretrained VLMs have been applied in the APE. CLAMP [42] is the first text-guided APE method, aligning text-visual features at both the feature and spatial levels, thereby enabling the textual prompt to effectively align the visual representation. X-Pose [34] proposes an end-to-end pose estimation framework that leverages both visual and textual prompts to support keypoint prediction for arbitrary targets. In view of this, we focus on designing keypoint prompts that offer enriched keypoint representations, facilitating accurate pose estimation.", + "bbox": [ + 511, + 200, + 903, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Deterministic Prompt Learning", + "text_level": 1, + "bbox": [ + 513, + 757, + 790, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt learning [5, 6, 24, 43, 44] aims to adapt foundation models to downstream tasks by efficiently optimizing prompts. CoOp [44] represents a seminal application of prompt learning in VLMs, transforming hard-coded discrete prompt templates into learnable continuous prompts. CoCoOp [43], as its variants, integrates image-conditioned knowledge into text prompts to enhance generalization to unseen classes. Similarly, DenseCLIP [24] employs a", + "bbox": [ + 511, + 779, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "29439", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5834ab97d8f33e2a02ff383be4f75318361d081ef9418fbd95b0f6571e7ff655.jpg", + "image_caption": [ + "Figure 2. Overall framework of PPAP. Firstly, we create $N_{p}$ keypoint attribute templates and generate distinctive embeddings for these attributes using a text encoder. Each keypoint prompt embedding is represented probabilistically as a multivariate Gaussian distribution, with its mean derived from the text decoder and variance from the visual-text decoder. Subsequently, we sample these keypoint prompt representations from the distribution and perform cross-modal fusion during the spatial adaptation stage to capture the spatial relationship between textual and visual content." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 903, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer to facilitate interaction between visual context and textual prompts, producing context-aware prompts for improved performance. Building upon this, PromptSRC [6] uses a set of hand-crafted prompts and introduces several regularization losses to prompt learning. To further improve diversity, we specialize different keypoint prompts to guide spatial adaptation for different animal categories, thus aligning them with different attribute sets for each keypoint.", + "bbox": [ + 88, + 393, + 480, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Probabilistic Prompt Learning", + "text_level": 1, + "bbox": [ + 89, + 523, + 362, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared to deterministic prompt learning, probabilistic prompt learning [2, 8, 15] is not tied to specific classes, making it more adaptable to cross-species challenges with prompt adjustments. APP [2] proposes a Bayesian-based prompt learning framework to enhance the flexibility and adaptability of input embeddings. However, various descriptions are dispersed in the input space, resulting in difficulty in representing their distribution. Several studies focus on probabilistic learning within the output embedding space. ProDA [15] is the first probabilistic prompt model, allowing for straightforward modeling by a multivariate Gaussian distribution. PPL [8] introduces attribute prompts to represent shared attributes across different categories by constructing a mixture of Gaussian distribution to address dense prediction problems. Conversely, we prioritize probabilistic modeling for each individual prompt rather than constructing a single overarching distribution, as it provides us with nuanced contextual information better and shows greater generalization to unseen data.", + "bbox": [ + 91, + 544, + 483, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 844, + 181, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To enhance the generalization capabilities for multi-species animal data, we propose a probabilistic prompt learn", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing technique. This technique is grounded in the Contrastive Learning for Connecting Language and Animal Pose (CLAMP) framework [42]. We begin by providing a concise overview of CLAMP's fundamental principles before presenting our probabilistic prompt learning method.", + "bbox": [ + 511, + 393, + 906, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 511, + 478, + 653, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CLAMP is proposed based on the powerful model CLIP [22]. Given an image and its corresponding textual description, CLIP extracts textual and visual embeddings by processing the input through a text encoder and an image encoder, respectively. To effectively leverage the textual description for APE, CLAMP uses a pose-specific template $p_n = \\{T_l\\}_{l=1}^L[KeyPoint]_n$ to represent $n$ -th keypoint prompt, where $\\{T_l\\}_{l=1}^L$ is $L$ learnable prefix tokens, and $[Keypoint]_n$ denotes the $n$ -th keypoint name token. Then prompt embedding $E_{prompt} \\in \\mathbb{R}^{K \\times C_{emb}}$ is obtained by the prompt encoder. To establish spatial connections between textual description and image features, CLAMP performs cross-modal adaptation at both spatial and feature levels. In the spatial adaptation stage, the extracted prompt representations and image features are used to generate score map $S \\in \\mathbb{R}^{K \\times H \\times W}$ , where $H, W$ and $K$ represent the height, width and the number of keypoints, respectively. This $S$ is utilized to indicate the probability of keypoint occurrence at specific locations. Besides, the spatial objective $\\mathcal{L}_{spatial}$ is calculated as follows:", + "bbox": [ + 511, + 500, + 908, + 800 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s p a t i a l}} = M S E (U p s a m p l e (S), H _ {\\text {t a r g e t}}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 813, + 906, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $MSE$ denotes mean squared error, Upsample is the upsample operation, and $H_{target}$ is the target heatmap. Meanwhile, in the feature adaptation stage, ground truths are performed to grid-sample local keypoint", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "29440", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "features $F_{keypoint} \\in \\mathbb{R}^{K \\times C_{emb}}$ from image embeddings. The pairwise similarity $M = F_{keypoint} \\cdot E_{prompt}^T$ is utilized to facilitate feature alignment:", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t u r e}} = \\frac {1}{2} \\left(C E (M, M _ {\\text {l a b e l}}) + C E \\left(M ^ {T}, M _ {\\text {l a b e l}}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 143, + 482, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $CE$ denotes cross-entropy loss and $M_{label}$ is the diagonal matrix, used as matching target. Building on these two adaptations, we introduce a set of learnable keypoint-agnostic prompts, modeling each prompt distribution with a Gaussian. Finally, we explore three fusion strategies for spatial adaptation and design a novel pose estimation paradigm to handle the multi-species APE.", + "bbox": [ + 89, + 180, + 483, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Diverse Prompt Construction", + "text_level": 1, + "bbox": [ + 89, + 294, + 354, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relying solely on visual features and the keypoint name prompt proves to be insufficient to address the long-tail problem present in animal datasets [18, 38]. As previous literature [8, 15] indicated, multiple diverse prompts could offer enriched semantics to aid multi-modal models in recognizing visual patterns, thereby alleviating the adverse impact of long-tail challenge. However, it is hard to explicitly identify \"what constitutes useful keypoint visual attributes for locating keypoints?\". To this end, we introduce multiple learnable textual attribute prompts for each keypoint to constitute the prompt templates. Formally, as illustrated in Figure 2, for the $i$ -th keypoint token $k_{i}$ , we create $N_{p}$ keypoint attribute templates for each keypoint by combining learnable attribute description tokens.", + "bbox": [ + 89, + 316, + 483, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} ^ {t} = \\left\\{a _ {1} ^ {t}, a _ {2} ^ {t}, \\dots , a _ {L} ^ {t} \\mid k _ {i} \\right\\}, \\quad t = 1, \\dots , N _ {p}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 537, + 482, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\{a_1^t, a_2^t, \\ldots, a_L^t\\}$ comprises $L$ learnable attribute tokens, initialized randomly with \"X X ... X\". As shown in Figure 1, we aim to simulate the locations of keypoint in natural language descriptions. To this end, we introduce the Generalized Keypoint Placement (GKP) strategy, enabling flexible placement of keypoint names within the prompt template for enhanced naturalness and diversity. Unlike the insertion strategy used in ProDA [15], which restricts keypoint placement to specific positions (i.e. beginning, middle, or end), our approach permits random placement throughout the template, offering greater positional flexibility. During training, these tokens are optimized to better suit APE tasks, offering increased contextual flexibility. By inputting the textual attribute prompts into the text encoder $\\theta(\\cdot)$ , we can obtain the encoded diverse prompt representations:", + "bbox": [ + 89, + 561, + 483, + 804 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {i} = \\{\\theta (\\boldsymbol {p} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\quad \\tilde {\\boldsymbol {P}} _ {i} = \\{\\theta (\\tilde {\\boldsymbol {p}} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 811, + 482, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{i}$ denotes the complete embedding for the $i$ -th keypoint prompt. Meanwhile, $\\tilde{p}_i^t$ represents attribute tokens excluding keypoint names, and $\\tilde{P}_{i}$ signifies the keypoint-agnostic attribute embedding.", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multiple Attributes Diversity Loss. To make the keypoint-agnostic attribute representations capture distinct content, we introduce diversity among representations, and design a novel diversity loss to keep differentiation between them. The specific formulation is as follows:", + "bbox": [ + 511, + 90, + 905, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i v} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {\\boldsymbol {P}} _ {i} \\tilde {\\boldsymbol {P}} _ {i} ^ {T} - \\mathbb {I} \\| _ {2} ^ {2}, \\quad \\mathbb {I} = \\operatorname {d i a g} (\\underbrace {1 , 1 , \\dots , 1} _ {N _ {p}}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 176, + 905, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The diversity loss applies a squared $\\ell_2$ -norm penalty on attribute representations to foster greater dissimilarity among them, thereby amplifying attribute diversity. Subsequently, the resultant prompt representations encapsulate the abundant and varied textual semantics, providing enhanced contextual support for subsequent visual localization.", + "bbox": [ + 511, + 229, + 905, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Probabilistic Prompt Modeling", + "text_level": 1, + "bbox": [ + 511, + 332, + 790, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the observation [15]: the output embedding of the descriptions within a category are close to each other, allowing them to be modeled with a sample distribution, i.e. Gaussian. We propose a probabilistic prompt learning strategy to reformulate the prompt distribution. As subsection 3.2 discussed, we strive to maintain orthogonality among the attribute embeddings. Thus, these embeddings are better represented as independent Gaussian distributions, each characterized by distinct means and variances. For each $p_i$ , we define a probabilistic distribution $\\mathcal{G}(z_i^t | p_i^t)$ as a factorized Gaussian with its center vector $\\mu_i^t$ and variance matrix $\\sigma_i^t$ , where $t$ is the $t$ -th attribute for the $i$ -th keypoint. This distribution is formulated as:", + "bbox": [ + 511, + 353, + 906, + 551 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} \\left(z _ {i} \\mid p _ {i}\\right) \\sim \\left\\{\\mathcal {N} \\left(\\boldsymbol {\\mu} _ {i} ^ {t}, \\boldsymbol {\\sigma} _ {i} ^ {t} \\mathbf {I}\\right) \\right\\} _ {t = 1} ^ {N _ {p}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 561, + 903, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we introduce a text decoder to obtain the mean of Gaussian distribution $\\pmb{\\mu}_i^t$ and a visual-text decoder for the variances $\\sigma_i^t$ , as illustrated in Figure 2. In the text decoder, we facilitate interaction among prompt embeddings by self-attention (SA) module, as well as a form of self-augmentation. The default number of the layer is set to 1.", + "bbox": [ + 511, + 593, + 905, + 684 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + S A \\left(L N \\left(q _ {i} ^ {t}, k _ {i} ^ {t}, v _ {i} ^ {t}\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 698, + 903, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the query $q_{i}^{t}$ , key $k_{i}^{t}$ , and value $v_{i}^{t}$ are all derived from prompt embedding $P_{i}$ . $LN$ and $MLP$ denote layer norm and multilayer perceptron layer, respectively. Meanwhile, in the visual-text decoder Here, the key $v_{k}$ and value $v_{\\mathrm{v}}$ vectors are both obtained from the $F$ . The variance matrix of each attribute representation is computed as:", + "bbox": [ + 511, + 722, + 905, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\sigma} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + C A \\left(L N \\left(q _ {i} ^ {t}, v _ {k}, v _ {\\mathrm {v}}\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 825, + 903, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where CA stands for cross-attention module. Once the statistics of each keypoint description are obtained, the Gaussian distribution for probabilistic prompt statistics can", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "29441", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be established. By exploiting the Gaussian distribution, random sampling can generate various new feature statistics information with different means and variances. Therefore, we adopt random sampling to further exploit the probabilistic representations. $N_{s}$ prompt representations are sampled for $i$ -th keypoint with $t$ -th attribute $z_{i}^{t} = \\{z_{i}^{1},\\ldots ,z_{i}^{N_{s}}\\} \\stackrel {i.i.d.}{\\sim}\\mathcal{G}(z_{i}^{t}|p_{i}^{t})$ , and we interpret $z_{i}^{t}$ as independently enriched contextual description. Here we use the re-parameterization trick [7] to make the sampling operation differentiable.", + "bbox": [ + 89, + 90, + 483, + 244 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} _ {i} ^ {t} = \\mu \\left(p _ {i} ^ {t}\\right) + \\epsilon \\cdot \\sigma \\left(p _ {i} ^ {t}\\right), \\quad \\epsilon \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 251, + 482, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu(p_i^t)$ , $\\sigma(p_i^t)$ are mean and standard deviation of distribution $\\mathcal{G}(z_i^t | p_i^t)$ , and $\\epsilon$ follows the standard normal distribution. Finally, we obtain a set of diverse prompt representations $\\hat{z}_i^t$ for each keypoint. To prevent learned variances from collapsing to zero, we employ an additional KL divergence regularizer between prompt distributions and the Gaussian prior, forming the keypoint prompt loss:", + "bbox": [ + 89, + 273, + 483, + 381 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {d i v}} + \\frac {1}{N _ {p}} \\sum_ {t} ^ {N _ {p}} K L \\left(\\mathcal {G} \\left(\\hat {z} _ {i} ^ {t} \\mid p _ {i} ^ {t}\\right) \\| \\mathcal {N} (\\mathbf {0}, I)\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 385, + 482, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Cross-Modal Fusion", + "text_level": 1, + "bbox": [ + 89, + 426, + 284, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once various prompt embeddings have been obtained, the problem of \"how to align them with the visual features?\" inevitably arises. Given these prompt representations, we explore three strategies for multi-modal information fusion: 1) heuristic selection; 2) ensemble selection; 3) attention-based selection. Specifically, the heuristic selection strategy computes the similarity between the $N_{s}$ sampled score maps $S' \\in \\mathbb{R}^{N_s \\times K \\times H \\times W}$ and the keypoints target $H_{target} \\in \\mathbb{R}^{K \\times H \\times W}$ , assigning the most similar ones as the final score map $S$ . Thus, the score map for the $i$ -th keypoint is voted from all the sampling turns. The ensemble selection strategy considers all the representations to contain informative context. To prevent the loss of textual cues, we concat score maps and apply convolution operation (Conv) for signal modulation, ultimately generating the final score map.", + "bbox": [ + 89, + 449, + 483, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(S ^ {\\prime}\\right)\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 696, + 482, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the attention-based selection, we introduce an additional learnable query to leverage the attention module for capturing relationships between the query embedding and the prompt representations. We predefine the query embedding, i.e. $q_{i} \\in \\mathbb{R}^{K \\times (HW)}$ for learning the suitable prompt representation. Meanwhile, the attention module takes the sampled prompts as key and value, which is formulated as:", + "bbox": [ + 89, + 720, + 483, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} S _ {i} = \\text {F l a t t e n} \\left(S ^ {\\prime}\\right), \\\\ Q _ {i} = q _ {i} W _ {q}, K _ {i} = S _ {i} W _ {k}, V _ {i} = S _ {i} W _ {v}, \\tag {12} \\\\ S _ {i} = Q _ {i} + W _ {a} (\\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {H W}}\\right) V _ {i}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 832, + 480, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{q}, W_{k}, W_{v}$ are learnable linear projections, and $S_{i}$ represents $i$ -th keypoint score map. Subsequently, $S_{i}$ is reshaped back to 2D with the final score map $S = \\{S_{i}\\}_{i=1}^{K}$ . Unless otherwise specified, we choose two attention layers in our experiments as default.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training", + "text_level": 1, + "bbox": [ + 513, + 175, + 617, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Total objective. For the pose estimation task, we employ the commonly used MSE loss $\\mathcal{L}_{pred}$ , and the total objective $\\mathcal{L}_{total}$ is formulated as follows:", + "bbox": [ + 511, + 196, + 903, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l l} \\mathcal {L} _ {p r e d} = M S E (F _ {o}, H _ {t a r g e t}), & F _ {o} = H E A D (F _ {v i s} \\oplus S), \\\\ f _ {o} = f _ {o + 1} + f _ {o + 2} + \\dots + f _ {o + n} + \\dots + f _ {o + n - 1} \\end{array} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 247, + 903, + 268 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {p r e d}} + \\mathcal {L} _ {\\text {s p a t i a l}} + \\gamma \\cdot \\mathcal {L} _ {\\text {f e a t u r e}} + \\beta \\cdot \\mathcal {L} _ {\\text {p r o m p t}},\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 265, + 866, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{vis}$ denotes the visual features output by image encoder, and HEAD is the common keypoint prediction head [29], which consists of multiple deconvolution and MLP layers. The coefficient $\\gamma$ and $\\beta$ are hyper-parameters, which are discussed in detail in the ablation study section.", + "bbox": [ + 511, + 282, + 905, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 369, + 645, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 511, + 395, + 594, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and evaluation metrics. (1) AP-10K [38] is a large-scale benchmark for multi-species animal pose estimation and contains over 10K images collected and filtered from 23 animal families and 54 species with 17 key points. We employ the mean average precision (AP) as the primary evaluation metric. Average recall (AR) and APs at different OKS (Object Keypoint Similarity) thresholds are also reported, i.e. AR, AP.5 and AP.75, as well as APs for different instance sizes, i.e. $\\mathrm{AP^M}$ and $\\mathrm{AP^L}$ . (2) AnimalKingdom [18] is a more challenging dataset, which includes over 33K samples with 23 keypoints across 850 species in 6 classes. Unlike AP-10K, AnimalKingdom contains a larger number of categories with more imbalanced and diverse data distribution, enhancing its difficulty. Besides, AnimalKingdom define three protocols (P1, P2, P3) for different tasks. P1-All involves training on the whole dataset for supervised learning. P2-LeaveKOut selects k sub-classes for training and performs few-shot learning on the remaining subclasses. P3-Amphibians/Birds/Fishes/Mammals/Reptiles specifies training within each distinct animal class, enabling zero-shot learning on unseen classes. We report the Percentage of Correct Keypoint $(\\mathrm{PCK}@\\alpha)$ score for evaluation, which computes the percentage of correct keypoints whose distance to ground truth is within $\\alpha$ times the longest bounding box side. Besides, we adhere to the evaluation protocol in [18], and set $\\alpha = 0.05$ .", + "bbox": [ + 511, + 417, + 906, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We follow the widely-used two-stage pose estimation paradigm in our experiments. The ground-truth bounding box annotations are utilized to crop the instance target, which is subsequently resized to a uniform shape. We select the representative CNN-based model ResNet alongside the transformer-based model ViT", + "bbox": [ + 511, + 810, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "29442", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bd839f0bcb3bb76834ac5959711a1165292fbcc82a756c027f800662c103e294.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDatasetBackboneAPAP·50AP·75APMAPLAR
Foundation Models
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Base74.594.982.246.875.070.0
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Large80.497.688.552.780.8-
SuperAnimal [37]Quadruped-80KHRNet-W3280.1-----
X-Pose-V [34]UniKPT(226K)Swin-Tiny73.691.980.647.274.2-
X-Pose-V [34]UniKPT(226K)Swin-Large79.095.786.857.079.6-
Expert Models
SimpleBaseline [29]AP-10KResNet-5070.294.276.045.570.473.5
HRNet [26]AP-10KHRNet-W3273.895.880.352.374.276.9
HRNet [26]AP-10KHRNet-W4874.495.980.758.974.8-
TokenPose [12]AP-10KHRNet-W4872.794.379.260.672.775.7
TransPose [35]AP-10KHRNet-W4874.295.780.856.274.677.0
HRFormer [39]AP-10KHRFormer-B74.595.981.655.874.977.6
Prompt-based Models
CLAMP [42]AP-10KCLIP / ResNet-5072.995.479.443.273.276.3
PPAP (Ours)AP-10KCLIP / ResNet-5073.494.179.957.173.876.5
CLAMP [42]AP-10KCLIP / ViT-Base74.395.881.447.674.977.5
PPAP (Ours)AP-10KCLIP / ViT-Base75.495.883.053.475.978.7
CLAMP [42]AP-10KCLIP / ViT-Large77.896.885.058.778.181.0
PPAP (Ours)AP-10KCLIP / ViT-Large78.697.186.159.378.981.7
", + "bbox": [ + 98, + 88, + 903, + 373 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/87f39062cf3ce60ec0d3f0fb3202155949affb415f1bc3959c45b7d6903dddca.jpg", + "table_caption": [ + "Table 1. Performance comparisons on AP-10K val set. The image resolution is $256 \\times 256$ , with an exception for ViTPose++, which utilizes a resolution of $256 \\times 192$ . Notably, the foundation models, such as ViTPose++, are trained on mixed datasets with extra corpora, which can be regarded as an upper bound for model performance." + ], + "table_footnote": [ + "(a) Comparisons across various protocols on AnimalKingdom." + ], + "table_body": "
MethodsBackboneP3-Amph.P3-BirdsP3-FishesP3-Mam.P3-Rep.P1-All
CLAMP [29]CLIP / ResNet-5051.876.162.454.043.560.5
PPAP (Ours)CLIP / ResNet-5051.976.562.455.548.260.9
CLAMP [29]CLIP / ViT-Base58.976.965.359.255.762.8
PPAP (Ours)CLIP / ViT-Base60.978.066.161.256.664.5
", + "bbox": [ + 91, + 431, + 643, + 503 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5eec807cd9fed048360676857220880c7a628b6a766ac6c60dfe26c9ffb75174.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Comparisons with the SOTA methods." + ], + "table_body": "
MethodsBackboneP1-All
HRNet [26]HRNet-W3266.1
DARK [41]HRNet-W3266.6
CLAMP [42]ViT-Large65.6
PPAP (Ours)ViT-Large68.4
", + "bbox": [ + 655, + 431, + 883, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Performance comparisons on the AnimalKingdom test set (PCK@0.05). The input resolution of all methods is ${256} \\times {256}$ .", + "bbox": [ + 98, + 518, + 893, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as backbones, serving as feature extractors in our framework. The text encoder after CLIP pre-training is adopted as our language models and initialized with the corresponding CLIP pre-trained weights. For prompt learning, we configure the length of the learnable context tokens to match CLAMP, setting $L = 8$ for fair comparisons.", + "bbox": [ + 88, + 547, + 482, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During training, we use $256 \\times 256$ input images and applied data augmentation including random rotation, scaling, flipping, and half-body transformation. All models are trained for 210 epochs with a step-wise learning rate scheduler that decreases by a factor of 10 at the 170th and 200th epochs. We used the AdamW optimizer with a weight decay of $2.5e - 5$ and froze the text encoder to preserve pretrained language knowledge. Supervised learning experiments were conducted to evaluate performance on both AP-10K and AnimalKingdom, with a batch size of 64, an initial learning rate of $3e - 4$ , and $N_{p} = N_{s} = 2$ for attribute embeddings and sampling turns, respectively.", + "bbox": [ + 88, + 638, + 482, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results and Analysis", + "text_level": 1, + "bbox": [ + 89, + 829, + 285, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1. Supervised Learning.", + "text_level": 1, + "bbox": [ + 89, + 851, + 285, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 presents the results under the supervised learning setting on AP-10K [38], comparing our method with repre", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sentative expert models for pose estimation. It can be observed that probabilistic prompt learning contributes to improved performance in multi-species APE under the prompt learning paradigm. With the basic ResNet-50 as the feature extractor, PPAP achieves a modest AP improvement of 0.5, which we attribute to the limited capacity of the feature extractor in capturing sufficient image features. When switching to the more powerful ViT-Base backbone, PPAP achieves 75.4 AP and outperforms CLAMP by 1.1 points. These observations indicate that our prompt learning approach offers a more effective solution to the challenges posed by significant data variance in multi-species Animal Pose Estimation (APE), as opposed to merely relying on the keypoint name prompt.", + "bbox": [ + 511, + 547, + 906, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we conduct comparisons against expert pose estimation models, validating our approach's effectiveness. On the AP-10K validation set, our PPAP method significantly outperforms the SimpleBaseline by 3.2 AP when using the ResNet-50 backbone, compared to the state-of-the-art CNN-based expert models. Additionally, when equipped with the ViT-Base backbone, our approach achieves 1.6 and 1.0 AP gains over the highly representative pose estimation model HRNet, respectively. In par", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "29443", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/301c5f3161bb59d6c106a007e04cb0251f4d77d49ba822f065f762982ab8e548.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrainTestPCK@0.05
ResNet-50CLAMP PPAPFishesBirds9.5
FishesBirds9.8 (↑ 0.3)
CLAMP PPAPMammalsAmphibians6.8
MammalsAmphibians9.8 (↑ 3.0)
CLAMP PPAPReptilesAmphibians19.2
ReptilesAmphibians19.3
ViT-BaseCLAMP PPAPFishesBirds0.1
FishesBirds12.0 (↑ 11.9)
CLAMP PPAPMammalsAmphibians12.3
MammalsAmphibians16.5 (↑ 4.2)
CLAMP PPAPReptilesAmphibians20.8
ReptilesAmphibians21.8 (↑ 1.0)
", + "bbox": [ + 99, + 88, + 475, + 286 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a12f4bc0d413465af795a48bb285375ae182db9c483c8bc064591caf68440f94.jpg", + "table_caption": [ + "Table 3. Zero-shot performance comparison on AnimalKingdom." + ], + "table_footnote": [], + "table_body": "
LdivKLGKPAPΔ
74.30
✓74.9+0.6
✓74.9+0.6
✓✓75.2+0.9
✓✓✓75.4+1.1
", + "bbox": [ + 112, + 330, + 460, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ticular, PPAP also demonstrates notable performance improvements of 2.7 and 1.2 AP, respectively, when compared to hybrid architectures such as TokenPose and TransPose. We also observe that these methods underperform on multi-species animal datasets compared to human ones, all falling below HRNet. This is due to their inability to manage large data variances, highlighting our approach's effectiveness in overcoming this challenge. Besides, PPAP surpasses HRFformer by 0.9 AP when compared to a plain transformer-based architecture.", + "bbox": [ + 89, + 457, + 482, + 607 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It's worth mentioning that foundation models are trained across multiple datasets like Quadruped-80K [37] and UniKPT-226K [34], allowing them to gain broader knowledge, richer pose priors, and generally enhanced performance. Despite this, our PPAP, trained exclusively on AP10K, matches foundation models with a score of 78.6 vs. 79.0. This indicates that our method's robustness stems not from extensive pose data but from its effective utilization of textual knowledge to tackle multi-species variability.", + "bbox": [ + 89, + 611, + 482, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to AP-10K, we further evaluate the effectiveness of PPAP on the more challenging dataset, AnimalKingdom [18]. The training setting is the same as the previous section. Table 2 reports the performance of prompt-based methods across various protocols on the AnimalKingdom dataset. We observe that the PPAP method consistently achieves superior performance across all protocols. By constructing diverse prompts and employing probabilistic modeling, our PPAP gets gains of 0.4 and 1.7 PCK values with ResNet-50 and ViT-Base, respectively. Notably,", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0cc596071179f8cd9a2eed9588d1e242249f97a9bf62cd718969ff6bd993e754.jpg", + "table_caption": [ + "Table 4. Ablation studies on components." + ], + "table_footnote": [], + "table_body": "
Number of attributes (γ = 5e-4, β = 1e-5, Ns = Np)
Parameter Np1234
AP74.875.475.175.0
Objective hyper-parameter (Ns = Np = 2)
Parameter β (γ=5e-4)1e-45e-51e-51e-6
AP74.574.875.474.9
Parameter γ (β=1e-5)5e-35e-45e-55e-6
AP73.575.474.775.1
Number of sampled turns (γ = 5e-4, β = 1e-5, Np = 2)
Parameter Ns2468
AP75.474.774.574.6
", + "bbox": [ + 517, + 88, + 905, + 268 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/edc94ab5526c331233e4fa007bd9b96ae455742ca1fd434ec9fb93cd75400f0b.jpg", + "table_caption": [ + "Table 5. Ablation studies on hyper-parameters. The number of attributes $N_{p}$ , objective hyper-parameters $\\gamma, \\beta$ , and the number of sampled representations $N_{s}$ ." + ], + "table_footnote": [], + "table_body": "
StrategyAPAP.50AP.75
heuristic selection75.195.682.1
ensemble selection75.495.883.0
attention-based selection74.695.782.3
", + "bbox": [ + 555, + 321, + 864, + 390 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation studies on cross-modal fusion strategies.", + "bbox": [ + 532, + 393, + 885, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the considerable performance gains on specific classes underscore the adaptability of our method. For example, PPAP with ResNet-50 achieves a 4.7 PCK improvement in reptiles, while PPAP with ViT-Base yields a 3.0 PCK increase in mammals. Compared to the existing SOTA methods, our PPAP with ViT-Large outperforms them by 2.0 AP gains. Furthermore, we argue that incorporating the plug-and-play DARK [41] leads to an additional boost in performance. Therefore, by training exclusively on the single pose data, our method achieves a new state-of-the-art performance with the ViT-Large backbone on both multispecies animal pose benchmarks.", + "bbox": [ + 511, + 417, + 906, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, to intuitively highlight the superiority of our approach, we present qualitative comparisons with CLAMP in Figure 3. Since AP-10K consists of mammals, we specifically select fishes and birds from AnimalKingdom for diversity. Differences in predicted locations are highlighted in red circles, clearly illustrating that our method consistently achieves more precise localization across these three animal classes.", + "bbox": [ + 511, + 599, + 905, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2. Zero-Shot Learning.", + "text_level": 1, + "bbox": [ + 511, + 729, + 702, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given that the AnimalKingdom dataset includes a broader range of classes and presents a more challenging benchmark, we further conduct zero-shot learning experiments on it to evaluate the model's generalization ability on unseen animal species. Since the AnimalKingdom is sourced from wildlife data, it inevitably exhibits a long-tail distribution across various animal species [18]. We select three types of zero-shot settings to compare with the prompt-based method CLAMP [42]. The experiment settings include similar classes (\"Reptiles vs. Amphibians\"), typical", + "bbox": [ + 511, + 750, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "29444", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "classes (\"Mammals vs. Amphibians\"), and highly divergent classes (\"Fishes vs. Birds\"), thereby covering a range of taxonomic variations to fully reflect the generalization of the PPAP for dealing with unseen species. The results are shown in Table 3, which reflects that our PPAP achieves better performance for all three settings. While PPAP achieves only a modest performance gain with ResNet-50, it demonstrates a significantly greater improvement when paired with the more powerful ViT-Base backbone. Interestingly, when trained on Fish and tested on Birds, CLAMP fails to perform pose estimation across such extreme inter-classes variations, resulting in nearly zero PCK value, while PPAP achieves a substantial improvement of 11.9 gains. Furthermore, our method demonstrates additional performance gains of 4.2 and 1.0 in the other two settings, respectively. Such observation clearly illustrates the generalization capability of our probability-based modeling approach on multispecies APE, effectively mitigating challenges associated with large data variance and imbalanced data distribution.", + "bbox": [ + 89, + 90, + 483, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 391, + 243, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we conduct a comprehensive ablation study of our proposed method on the AP-10K dataset using ViT-Base backbone. We analyze the impact of various components and hyper-parameters, and also investigate different cross-modal fusion strategies for generating the score map.", + "bbox": [ + 89, + 414, + 483, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of Different Components. We conducted experiments to evaluate the impact of various loss functions and the Generalized Keypoint Placement (GKP) strategy. Table 4 summarizes the results. By constructing diverse prompts and applying the constraint $\\mathcal{L}_{\\mathrm{div}}$ , the model achieved a 74.9 AP score, outperforming the baseline by 0.6 points. Similarly, applying the constraint $\\mathcal{L}_{\\mathrm{KL}}$ with Gaussian distribution reformulation also improved the AP score by 0.6 points. Combining both constraints, the model reached 75.2 AP, significantly surpassing the baseline. Additionally, using the GKP strategy generated more generalized prompts, leading to further improvements.", + "bbox": [ + 89, + 491, + 483, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of Hyper-parameter. The hyper-parameters of the number of attributes $N_{p}$ , objective function coefficient $\\gamma, \\beta$ in Eq. 13 and the sampling turns $N_{s}$ are to trade off the model performance. Firstly, we compare performance with respect to different attribute numbers $N_{p}$ . As shown in the first block of Table 5, two prompt templates are sufficient to represent different image attributes and achieve optimal performance. As the number of prompt templates increases, however, performance declines, suggesting that excessive template quantity can lead to information redundancy, thereby impairing model efficacy. Then, we adjust the weighting ratio of the $\\mathcal{L}_{\\text {feature }}$ and $\\mathcal{L}_{\\text {prompt }}$ , and observe that $\\gamma = 5e - 4$ , $\\beta = 1e - 5$ are more suitable. It suggests excessive weighting leads each prompt representation to converge toward a standard normal distribution, thereby", + "bbox": [ + 89, + 674, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d28b589b27137de56f71b255a881eae18abe85f2271a9efbfb47bee03a59b29.jpg", + "image_caption": [ + "Figure 3. Qualitative visualization of several examples with CLAMP and our proposed PPAP." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 903, + 218 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "diminishing their distinctiveness. Conversely, overly small weights result in excessive variance in the distribution of each embedding, which increases uncertainty. To achieve a balance, we choose $\\beta = 1e - 5$ to get the optimal result. In our approach, we employ reparameterization techniques to ensure differentiability, while also utilizing sampling to enhance the diversity of the text prompts. As we can see in the last block of Table 5, the results are not sensitive to the sampling turns and the accuracy reaches the best performance when setting $N_{s}$ and $N_{p}$ to be equal.", + "bbox": [ + 511, + 277, + 906, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Choices of Cross-modal Fusion. In our experiments, we explore three different fusion strategies, with results summarized in Table 6. As we can see, no matter which strategy is employed, the performances are consistently higher than the baseline method. Selecting the representation most similar to the target can achieve competitive performance. However, as similarity computation relies on labeled data unavailable during testing, we instead average the sampled representations. This discrepancy between training and testing leads to suboptimal performance. Directly ensembling all representations followed by the conv modulation yields the best performance by avoiding information loss. Besides, the results show that the attention-based strategy has worse performances, which may be attributed to the randomly initialized queries to effectively learn the suitable prompt representations.", + "bbox": [ + 511, + 433, + 908, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 704, + 633, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a probabilistic prompt distribution learning method to adapt pre-trained vision-language models for the multi-species APE task. With the diverse key-point prompt construction, probabilistic prompt modeling and cross-modal fusion strategies, PPAP uses text guidance in a more comprehensive and effective manner, presenting a novel solution to the multi-species problem, i.e. large data variance and imbalanced data distribution. PPAP reflects superiority and generalization for multi-species APE on the representative multi-species animal pose benchmarks including AP-10K and AnimalKingdom.", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "29445", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the National Key Research and Development Project under Grant 2023YFC3806000, in part by the National Natural Science Foundation of China under Grant 62406226 and 61936014, in part sponsored by Shanghai Sailing Program under Grant 24YF2748700, and in part sponsored by Tongji University Independent Original Cultivation Project under Grant 20230106.", + "bbox": [ + 89, + 114, + 483, + 227 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 256, + 187, + 272 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jinkun Cao, Hongyang Tang, Hao-Shu Fang, Xiaoyong Shen, Cewu Lu, and Yu-Wing Tai. 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IJCV, 130(9):2337-2348, 2022. 2" + ], + "bbox": [ + 514, + 90, + 903, + 232 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "29447", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_model.json b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e3df8f81b3d5a6034f65f7200b454b2119e92588 --- /dev/null +++ b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_model.json @@ -0,0 +1,1991 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.138, + 0.131, + 0.86, + 0.152 + ], + "angle": 0, + "content": "Probabilistic Prompt Distribution Learning for Animal Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.147, + 0.18, + 0.851, + 0.235 + ], + "angle": 0, + "content": "Jiyong Rao\\(^{1}\\) Brian Nlong Zhao\\(^{2\\dagger}\\) Yu Wang\\(^{1*}\\) \n\\(^{1}\\) School of Computer Science and Technology, Tongji University \\(^{2}\\) Stanford University jiyongrao@tongji.edu.cn, brianlz@stanford.edu, yuwangtj@yeah.net" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.301, + 0.486, + 0.694 + ], + "angle": 0, + "content": "Multi-species animal pose estimation has emerged as a challenging yet critical task, hindered by substantial visual diversity and uncertainty. This paper challenges the problem by efficient prompt learning for Vision-Language Pretrained (VLP) models, e.g. CLIP, aiming to resolve the cross-species generalization problem. At the core of the solution lies in the prompt designing, probabilistic prompt modeling and cross-modal adaptation, thereby enabling prompts to compensate for cross-modal information and effectively overcome large data variances under unbalanced data distribution. To this end, we propose a novel probabilistic prompting approach to fully explore textual descriptions, which could alleviate the diversity issues caused by long-tail property and increase the adaptability of prompts on unseen category instance. Specifically, we first introduce a set of learnable prompts and propose a diversity loss to maintain distinctiveness among prompts, thus representing diverse image attributes. Diverse textual probabilistic representations are sampled and used as the guidance for the pose estimation. Subsequently, we explore three different cross-modal fusion strategies at spatial level to alleviate the adverse impacts of visual uncertainty. Extensive experiments on multi-species animal pose benchmarks show that our method achieves the state-of-the-art performance under both supervised and zero-shot settings. The code is available at https://github.com/Raojiyong/PPAP." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.736, + 0.222, + 0.751 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.761, + 0.484, + 0.868 + ], + "angle": 0, + "content": "Animal Pose Estimation (APE) [1, 16, 20, 21, 37] represents a fundamental vision task, the objective of which is to identify a series of keypoint locations in an animal skeleton. The skeleton (i.e. a set of connected coordinates), serves as a minimal yet informative unit for encoding both static structure and motion cues, thereby providing critical support for understanding animal behaviour. Consequently, APE plays" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.269, + 0.905, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.496, + 0.907, + 0.525 + ], + "angle": 0, + "content": "Figure 1. The motivation that one key point can be complementarily described in different views (An example of left shoulder)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.535, + 0.907, + 0.581 + ], + "angle": 0, + "content": "a significant role in various research fields, such as neuroscience [16, 20], ecology [3, 4], zoology study [9, 21] and biotechnological quests [18, 28]." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.582, + 0.909, + 0.839 + ], + "angle": 0, + "content": "In numerous instances [16, 18, 38], researchers have opted to directly apply Human Pose Estimation (HPE) methodologies to animals. However, it is evident that many animal species exhibit pose distributions that deviate significantly from human-specific models, leading to substantial domain shifts. To address the multi-species Animal Pose Estimation (APE) challenge, Category-Agnostic Pose Estimation (CAPE) methods [25, 30] have been investigated. These methods frame keypoint prediction as a keypoint matching problem, necessitating supplementary support sets that belong to the same category as the test image. While promising, this approach introduces additional computational overhead and necessitates prior knowledge of the animal category, thereby limiting its practicality. Moreover, given the substantial data variances observed across species [18, 38], vision-only APE methods falter when confronted with cross-species challenges that rely solely on visual cues." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Recently, the multimodal system proposed in [22] has garnered substantial research attention due to its ability to combine complementary data to enhance visual recognition. Despite the distinct visual characteristics of various" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.236, + 0.888 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "Equal contribution." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.236, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "29438" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.544 + ], + "angle": 0, + "content": "animal species, they share common textual descriptions, as noted in [42]. Consequently, the straightforward approach of setting the keypoint name as the class token, known as deterministic prompt learning, has become prevalent in the current literature [34, 42]. For instance, X-Pose [34] utilizes a fixed text template like \"A [Image Style] photo of a [Keypoint]\", while CLAMP [42] employs a continuous prompt template of \"[Learnable Tokens] + [Keypoint)\". However, existing multimodal APE methods fall short in terms of rich text prompt design. Moreover, manually crafting keypoint-specific prompts is a cumbersome task. As depicted in Figure 1, a solitary textual description often fails to encapsulate all the nuances of a specific keypoint, such as its color, position, and shape. For example, the \"left shoulder\" keypoint can be described from both spatial and color perspectives as \"Left shoulder is near the right shoulder\" and \"The color of the left shoulder is light salmon\", respectively. From a textual standpoint, multiple descriptions provide diverse perspectives, enabling pose estimation to grasp high-level semantics and pinpoint keypoints accurately based on one or more of these cues. On the visual front, the intricacies of wild scenes and the presence of multiple species introduce uncertain statistical shifts compared to the training domain [4, 14, 27]. Given this \"uncertainty\" in potential data variations, synthesizing novel feature statistics variants to model diverse representations can bolster the network's robustness against unseen categories. To address these challenges, this paper introduces a novel probabilistic method that enhances network generalization to handle unseen categories by adeptly modeling keypoint-adaptive prompts." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.55, + 0.482, + 0.789 + ], + "angle": 0, + "content": "Our approach leverages multiple learnable text prompts to enhance flexibility and robustness in text prompt initialization, moving beyond a single template. By strategically inserting keypoint names within templates, we enable flexible sentence construction akin to natural language. We hypothesize that prompt statistics, incorporating uncertainties, follow a multivariate Gaussian distribution, with the center defined by the original prompt statistic and the range indicating data variation across animal categories. We estimate this range using mini-batch statistics in a parametric learning framework and randomly sample variants from the estimated distribution to model diverse textual descriptions, as illustrated in Figure 2. To capture diverse and informative keypoint attributes, we introduce a novel diversity loss function that ensures distinctiveness across prompt distributions. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.795, + 0.481, + 0.839 + ], + "angle": 0, + "content": "- We propose a novel Probabilistic Prompt Distribution Learning framework for APE to learn the probabilistic representation of specific keypoint descriptions." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.841, + 0.482, + 0.9 + ], + "angle": 0, + "content": "- We introduce multiple prompt attributes and design a diversity loss to prevent the learned attributes from being identical. Additionally, we explore three different cross-modal fusion strategies to achieve spatial adaptation." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.795, + 0.482, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.136 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of the proposed probabilistic-based approach through extensive experiments on multi-species animal pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.153, + 0.663, + 0.168 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.179, + 0.734, + 0.194 + ], + "angle": 0, + "content": "2.1. Animal Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.201, + 0.905, + 0.744 + ], + "angle": 0, + "content": "Typical vision-only APE methods [1, 16, 18, 23, 31, 38], with most directly adapting human pose estimation methods [13, 26, 29, 32, 36, 39], such as DeepLabCut [9, 16], AP-10K [26, 38] and ViTPose [32, 33] to animal counterpart. These methods leverage powerful visual backbones for feature extraction but fail to handle rare or even unseen categories explicitly. The relatively limited animal data volume compared to its human counterpart increases the risk of overfitting in complex networks [4]. To cope with the limited labelled animal data volume, direct attempts [10, 17] learn prior-aware knowledge from synthetic animal datasets, and generate pseudo labels for unlabelled data. In terms of refining the pseudo labels, ScarceNet [11] and FreeNet[40] propose the novel semi-supervised learning methods that improves the reliability of pseudo label generation, effectively mitigating the data scarcity problem. Following the principles of few-shot learning, Xu et al. [30] proposed a novel Category-Agnostic Pose Estimation (CAPE) paradigm, which treats keypoint prediction as the keypoint matching problem, enabling the prediction of poses on unseen categories. This is accomplished by offering a few support sets from the same category as the test image to guide the learning process. CAPE [19, 25, 30] introduces an additional computational burden and necessitates prior animal categories, making the methods less practical. To eliminate the reliance on category-specific prior, pretrained VLMs have been applied in the APE. CLAMP [42] is the first text-guided APE method, aligning text-visual features at both the feature and spatial levels, thereby enabling the textual prompt to effectively align the visual representation. X-Pose [34] proposes an end-to-end pose estimation framework that leverages both visual and textual prompts to support keypoint prediction for arbitrary targets. In view of this, we focus on designing keypoint prompts that offer enriched keypoint representations, facilitating accurate pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.758, + 0.792, + 0.773 + ], + "angle": 0, + "content": "2.2. Deterministic Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.78, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Prompt learning [5, 6, 24, 43, 44] aims to adapt foundation models to downstream tasks by efficiently optimizing prompts. CoOp [44] represents a seminal application of prompt learning in VLMs, transforming hard-coded discrete prompt templates into learnable continuous prompts. CoCoOp [43], as its variants, integrates image-conditioned knowledge into text prompts to enhance generalization to unseen classes. Similarly, DenseCLIP [24] employs a" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29439" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.904, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.317, + 0.908, + 0.386 + ], + "angle": 0, + "content": "Figure 2. Overall framework of PPAP. Firstly, we create \\( N_{p} \\) keypoint attribute templates and generate distinctive embeddings for these attributes using a text encoder. Each keypoint prompt embedding is represented probabilistically as a multivariate Gaussian distribution, with its mean derived from the text decoder and variance from the visual-text decoder. Subsequently, we sample these keypoint prompt representations from the distribution and perform cross-modal fusion during the spatial adaptation stage to capture the spatial relationship between textual and visual content." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.394, + 0.482, + 0.515 + ], + "angle": 0, + "content": "Transformer to facilitate interaction between visual context and textual prompts, producing context-aware prompts for improved performance. Building upon this, PromptSRC [6] uses a set of hand-crafted prompts and introduces several regularization losses to prompt learning. To further improve diversity, we specialize different keypoint prompts to guide spatial adaptation for different animal categories, thus aligning them with different attribute sets for each keypoint." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.524, + 0.363, + 0.54 + ], + "angle": 0, + "content": "2.3. Probabilistic Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.545, + 0.485, + 0.833 + ], + "angle": 0, + "content": "Compared to deterministic prompt learning, probabilistic prompt learning [2, 8, 15] is not tied to specific classes, making it more adaptable to cross-species challenges with prompt adjustments. APP [2] proposes a Bayesian-based prompt learning framework to enhance the flexibility and adaptability of input embeddings. However, various descriptions are dispersed in the input space, resulting in difficulty in representing their distribution. Several studies focus on probabilistic learning within the output embedding space. ProDA [15] is the first probabilistic prompt model, allowing for straightforward modeling by a multivariate Gaussian distribution. PPL [8] introduces attribute prompts to represent shared attributes across different categories by constructing a mixture of Gaussian distribution to address dense prediction problems. Conversely, we prioritize probabilistic modeling for each individual prompt rather than constructing a single overarching distribution, as it provides us with nuanced contextual information better and shows greater generalization to unseen data." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.182, + 0.86 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "To enhance the generalization capabilities for multi-species animal data, we propose a probabilistic prompt learn" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.394, + 0.907, + 0.471 + ], + "angle": 0, + "content": "ing technique. This technique is grounded in the Contrastive Learning for Connecting Language and Animal Pose (CLAMP) framework [42]. We begin by providing a concise overview of CLAMP's fundamental principles before presenting our probabilistic prompt learning method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.479, + 0.655, + 0.493 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.5, + 0.909, + 0.801 + ], + "angle": 0, + "content": "CLAMP is proposed based on the powerful model CLIP [22]. Given an image and its corresponding textual description, CLIP extracts textual and visual embeddings by processing the input through a text encoder and an image encoder, respectively. To effectively leverage the textual description for APE, CLAMP uses a pose-specific template \\( p_n = \\{T_l\\}_{l=1}^L[KeyPoint]_n \\) to represent \\( n \\)-th keypoint prompt, where \\( \\{T_l\\}_{l=1}^L \\) is \\( L \\) learnable prefix tokens, and \\( [Keypoint]_n \\) denotes the \\( n \\)-th keypoint name token. Then prompt embedding \\( E_{prompt} \\in \\mathbb{R}^{K \\times C_{emb}} \\) is obtained by the prompt encoder. To establish spatial connections between textual description and image features, CLAMP performs cross-modal adaptation at both spatial and feature levels. In the spatial adaptation stage, the extracted prompt representations and image features are used to generate score map \\( S \\in \\mathbb{R}^{K \\times H \\times W} \\), where \\( H, W \\) and \\( K \\) represent the height, width and the number of keypoints, respectively. This \\( S \\) is utilized to indicate the probability of keypoint occurrence at specific locations. Besides, the spatial objective \\( \\mathcal{L}_{spatial} \\) is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.814, + 0.907, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s p a t i a l}} = M S E (U p s a m p l e (S), H _ {\\text {t a r g e t}}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "where \\( MSE \\) denotes mean squared error, Upsample is the upsample operation, and \\( H_{target} \\) is the target heatmap. Meanwhile, in the feature adaptation stage, ground truths are performed to grid-sample local keypoint" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "29440" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.137 + ], + "angle": 0, + "content": "features \\(F_{keypoint} \\in \\mathbb{R}^{K \\times C_{emb}}\\) from image embeddings. The pairwise similarity \\(M = F_{keypoint} \\cdot E_{prompt}^T\\) is utilized to facilitate feature alignment:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.145, + 0.483, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t u r e}} = \\frac {1}{2} \\left(C E (M, M _ {\\text {l a b e l}}) + C E \\left(M ^ {T}, M _ {\\text {l a b e l}}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.181, + 0.484, + 0.288 + ], + "angle": 0, + "content": "where \\( CE \\) denotes cross-entropy loss and \\( M_{label} \\) is the diagonal matrix, used as matching target. Building on these two adaptations, we introduce a set of learnable keypoint-agnostic prompts, modeling each prompt distribution with a Gaussian. Finally, we explore three fusion strategies for spatial adaptation and design a novel pose estimation paradigm to handle the multi-species APE." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.295, + 0.355, + 0.311 + ], + "angle": 0, + "content": "3.2. Diverse Prompt Construction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.317, + 0.484, + 0.529 + ], + "angle": 0, + "content": "Relying solely on visual features and the keypoint name prompt proves to be insufficient to address the long-tail problem present in animal datasets [18, 38]. As previous literature [8, 15] indicated, multiple diverse prompts could offer enriched semantics to aid multi-modal models in recognizing visual patterns, thereby alleviating the adverse impact of long-tail challenge. However, it is hard to explicitly identify \"what constitutes useful keypoint visual attributes for locating keypoints?\". To this end, we introduce multiple learnable textual attribute prompts for each keypoint to constitute the prompt templates. Formally, as illustrated in Figure 2, for the \\(i\\)-th keypoint token \\(k_{i}\\), we create \\(N_{p}\\) keypoint attribute templates for each keypoint by combining learnable attribute description tokens." + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.538, + 0.483, + 0.556 + ], + "angle": 0, + "content": "\\[\np _ {i} ^ {t} = \\left\\{a _ {1} ^ {t}, a _ {2} ^ {t}, \\dots , a _ {L} ^ {t} \\mid k _ {i} \\right\\}, \\quad t = 1, \\dots , N _ {p}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.563, + 0.484, + 0.805 + ], + "angle": 0, + "content": "where \\(\\{a_1^t, a_2^t, \\ldots, a_L^t\\}\\) comprises \\(L\\) learnable attribute tokens, initialized randomly with \"X X ... X\". As shown in Figure 1, we aim to simulate the locations of keypoint in natural language descriptions. To this end, we introduce the Generalized Keypoint Placement (GKP) strategy, enabling flexible placement of keypoint names within the prompt template for enhanced naturalness and diversity. Unlike the insertion strategy used in ProDA [15], which restricts keypoint placement to specific positions (i.e. beginning, middle, or end), our approach permits random placement throughout the template, offering greater positional flexibility. During training, these tokens are optimized to better suit APE tasks, offering increased contextual flexibility. By inputting the textual attribute prompts into the text encoder \\(\\theta(\\cdot)\\), we can obtain the encoded diverse prompt representations:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.812, + 0.483, + 0.833 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {i} = \\{\\theta (\\boldsymbol {p} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\quad \\tilde {\\boldsymbol {P}} _ {i} = \\{\\theta (\\tilde {\\boldsymbol {p}} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\( P_{i} \\) denotes the complete embedding for the \\( i \\)-th keypoint prompt. Meanwhile, \\( \\tilde{p}_i^t \\) represents attribute tokens excluding keypoint names, and \\( \\tilde{P}_{i} \\) signifies the keypoint-agnostic attribute embedding." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.168 + ], + "angle": 0, + "content": "Multiple Attributes Diversity Loss. To make the keypoint-agnostic attribute representations capture distinct content, we introduce diversity among representations, and design a novel diversity loss to keep differentiation between them. The specific formulation is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.177, + 0.906, + 0.222 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i v} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {\\boldsymbol {P}} _ {i} \\tilde {\\boldsymbol {P}} _ {i} ^ {T} - \\mathbb {I} \\| _ {2} ^ {2}, \\quad \\mathbb {I} = \\operatorname {d i a g} (\\underbrace {1 , 1 , \\dots , 1} _ {N _ {p}}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.231, + 0.906, + 0.322 + ], + "angle": 0, + "content": "The diversity loss applies a squared \\(\\ell_2\\)-norm penalty on attribute representations to foster greater dissimilarity among them, thereby amplifying attribute diversity. Subsequently, the resultant prompt representations encapsulate the abundant and varied textual semantics, providing enhanced contextual support for subsequent visual localization." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.333, + 0.792, + 0.349 + ], + "angle": 0, + "content": "3.3. Probabilistic Prompt Modeling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.354, + 0.907, + 0.552 + ], + "angle": 0, + "content": "Based on the observation [15]: the output embedding of the descriptions within a category are close to each other, allowing them to be modeled with a sample distribution, i.e. Gaussian. We propose a probabilistic prompt learning strategy to reformulate the prompt distribution. As subsection 3.2 discussed, we strive to maintain orthogonality among the attribute embeddings. Thus, these embeddings are better represented as independent Gaussian distributions, each characterized by distinct means and variances. For each \\( p_i \\), we define a probabilistic distribution \\( \\mathcal{G}(z_i^t | p_i^t) \\) as a factorized Gaussian with its center vector \\( \\mu_i^t \\) and variance matrix \\( \\sigma_i^t \\), where \\( t \\) is the \\( t \\)-th attribute for the \\( i \\)-th keypoint. This distribution is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.562, + 0.905, + 0.583 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} \\left(z _ {i} \\mid p _ {i}\\right) \\sim \\left\\{\\mathcal {N} \\left(\\boldsymbol {\\mu} _ {i} ^ {t}, \\boldsymbol {\\sigma} _ {i} ^ {t} \\mathbf {I}\\right) \\right\\} _ {t = 1} ^ {N _ {p}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.594, + 0.906, + 0.685 + ], + "angle": 0, + "content": "Specifically, we introduce a text decoder to obtain the mean of Gaussian distribution \\(\\pmb{\\mu}_i^t\\) and a visual-text decoder for the variances \\(\\sigma_i^t\\), as illustrated in Figure 2. In the text decoder, we facilitate interaction among prompt embeddings by self-attention (SA) module, as well as a form of self-augmentation. The default number of the layer is set to 1." + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.699, + 0.905, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + S A \\left(L N \\left(q _ {i} ^ {t}, k _ {i} ^ {t}, v _ {i} ^ {t}\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.723, + 0.906, + 0.814 + ], + "angle": 0, + "content": "where the query \\( q_{i}^{t} \\), key \\( k_{i}^{t} \\), and value \\( v_{i}^{t} \\) are all derived from prompt embedding \\( P_{i} \\). \\( LN \\) and \\( MLP \\) denote layer norm and multilayer perceptron layer, respectively. Meanwhile, in the visual-text decoder Here, the key \\( v_{k} \\) and value \\( v_{\\mathrm{v}} \\) vectors are both obtained from the \\( F \\). The variance matrix of each attribute representation is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.826, + 0.905, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\sigma} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + C A \\left(L N \\left(q _ {i} ^ {t}, v _ {k}, v _ {\\mathrm {v}}\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "where CA stands for cross-attention module. Once the statistics of each keypoint description are obtained, the Gaussian distribution for probabilistic prompt statistics can" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29441" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.246 + ], + "angle": 0, + "content": "be established. By exploiting the Gaussian distribution, random sampling can generate various new feature statistics information with different means and variances. Therefore, we adopt random sampling to further exploit the probabilistic representations. \\(N_{s}\\) prompt representations are sampled for \\(i\\)-th keypoint with \\(t\\)-th attribute \\(z_{i}^{t} = \\{z_{i}^{1},\\ldots ,z_{i}^{N_{s}}\\} \\stackrel {i.i.d.}{\\sim}\\mathcal{G}(z_{i}^{t}|p_{i}^{t})\\), and we interpret \\(z_{i}^{t}\\) as independently enriched contextual description. Here we use the re-parameterization trick [7] to make the sampling operation differentiable." + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.252, + 0.483, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\hat {z} _ {i} ^ {t} = \\mu \\left(p _ {i} ^ {t}\\right) + \\epsilon \\cdot \\sigma \\left(p _ {i} ^ {t}\\right), \\quad \\epsilon \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.275, + 0.484, + 0.382 + ], + "angle": 0, + "content": "where \\(\\mu(p_i^t)\\), \\(\\sigma(p_i^t)\\) are mean and standard deviation of distribution \\(\\mathcal{G}(z_i^t | p_i^t)\\), and \\(\\epsilon\\) follows the standard normal distribution. Finally, we obtain a set of diverse prompt representations \\(\\hat{z}_i^t\\) for each keypoint. To prevent learned variances from collapsing to zero, we employ an additional KL divergence regularizer between prompt distributions and the Gaussian prior, forming the keypoint prompt loss:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.386, + 0.483, + 0.424 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {d i v}} + \\frac {1}{N _ {p}} \\sum_ {t} ^ {N _ {p}} K L \\left(\\mathcal {G} \\left(\\hat {z} _ {i} ^ {t} \\mid p _ {i} ^ {t}\\right) \\| \\mathcal {N} (\\mathbf {0}, I)\\right). \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.428, + 0.285, + 0.443 + ], + "angle": 0, + "content": "3.4. Cross-Modal Fusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.45, + 0.484, + 0.693 + ], + "angle": 0, + "content": "Once various prompt embeddings have been obtained, the problem of \"how to align them with the visual features?\" inevitably arises. Given these prompt representations, we explore three strategies for multi-modal information fusion: 1) heuristic selection; 2) ensemble selection; 3) attention-based selection. Specifically, the heuristic selection strategy computes the similarity between the \\( N_{s} \\) sampled score maps \\( S' \\in \\mathbb{R}^{N_s \\times K \\times H \\times W} \\) and the keypoints target \\( H_{target} \\in \\mathbb{R}^{K \\times H \\times W} \\), assigning the most similar ones as the final score map \\( S \\). Thus, the score map for the \\( i \\)-th keypoint is voted from all the sampling turns. The ensemble selection strategy considers all the representations to contain informative context. To prevent the loss of textual cues, we concat score maps and apply convolution operation (Conv) for signal modulation, ultimately generating the final score map." + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.698, + 0.483, + 0.716 + ], + "angle": 0, + "content": "\\[\nS = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(S ^ {\\prime}\\right)\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.721, + 0.484, + 0.827 + ], + "angle": 0, + "content": "For the attention-based selection, we introduce an additional learnable query to leverage the attention module for capturing relationships between the query embedding and the prompt representations. We predefine the query embedding, i.e. \\( q_{i} \\in \\mathbb{R}^{K \\times (HW)} \\) for learning the suitable prompt representation. Meanwhile, the attention module takes the sampled prompts as key and value, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.833, + 0.482, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} S _ {i} = \\text {F l a t t e n} \\left(S ^ {\\prime}\\right), \\\\ Q _ {i} = q _ {i} W _ {q}, K _ {i} = S _ {i} W _ {k}, V _ {i} = S _ {i} W _ {v}, \\tag {12} \\\\ S _ {i} = Q _ {i} + W _ {a} (\\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {H W}}\\right) V _ {i}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "where \\( W_{q}, W_{k}, W_{v} \\) are learnable linear projections, and \\( S_{i} \\) represents \\( i \\)-th keypoint score map. Subsequently, \\( S_{i} \\) is reshaped back to 2D with the final score map \\( S = \\{S_{i}\\}_{i=1}^{K} \\). Unless otherwise specified, we choose two attention layers in our experiments as default." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.176, + 0.619, + 0.192 + ], + "angle": 0, + "content": "3.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.198, + 0.905, + 0.243 + ], + "angle": 0, + "content": "Total objective. For the pose estimation task, we employ the commonly used MSE loss \\(\\mathcal{L}_{pred}\\), and the total objective \\(\\mathcal{L}_{total}\\) is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.248, + 0.905, + 0.269 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l l} \\mathcal {L} _ {p r e d} = M S E (F _ {o}, H _ {t a r g e t}), & F _ {o} = H E A D (F _ {v i s} \\oplus S), \\\\ f _ {o} = f _ {o + 1} + f _ {o + 2} + \\dots + f _ {o + n} + \\dots + f _ {o + n - 1} \\end{array} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.266, + 0.867, + 0.278 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {p r e d}} + \\mathcal {L} _ {\\text {s p a t i a l}} + \\gamma \\cdot \\mathcal {L} _ {\\text {f e a t u r e}} + \\beta \\cdot \\mathcal {L} _ {\\text {p r o m p t}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.283, + 0.906, + 0.358 + ], + "angle": 0, + "content": "where \\(F_{vis}\\) denotes the visual features output by image encoder, and HEAD is the common keypoint prediction head [29], which consists of multiple deconvolution and MLP layers. The coefficient \\(\\gamma\\) and \\(\\beta\\) are hyper-parameters, which are discussed in detail in the ablation study section." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.371, + 0.646, + 0.388 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.396, + 0.596, + 0.412 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.907, + 0.81 + ], + "angle": 0, + "content": "Datasets and evaluation metrics. (1) AP-10K [38] is a large-scale benchmark for multi-species animal pose estimation and contains over 10K images collected and filtered from 23 animal families and 54 species with 17 key points. We employ the mean average precision (AP) as the primary evaluation metric. Average recall (AR) and APs at different OKS (Object Keypoint Similarity) thresholds are also reported, i.e. AR, AP.5 and AP.75, as well as APs for different instance sizes, i.e. \\(\\mathrm{AP^M}\\) and \\(\\mathrm{AP^L}\\). (2) AnimalKingdom [18] is a more challenging dataset, which includes over 33K samples with 23 keypoints across 850 species in 6 classes. Unlike AP-10K, AnimalKingdom contains a larger number of categories with more imbalanced and diverse data distribution, enhancing its difficulty. Besides, AnimalKingdom define three protocols (P1, P2, P3) for different tasks. P1-All involves training on the whole dataset for supervised learning. P2-LeaveKOut selects k sub-classes for training and performs few-shot learning on the remaining subclasses. P3-Amphibians/Birds/Fishes/Mammals/Reptiles specifies training within each distinct animal class, enabling zero-shot learning on unseen classes. We report the Percentage of Correct Keypoint \\((\\mathrm{PCK}@\\alpha)\\) score for evaluation, which computes the percentage of correct keypoints whose distance to ground truth is within \\(\\alpha\\) times the longest bounding box side. Besides, we adhere to the evaluation protocol in [18], and set \\(\\alpha = 0.05\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We follow the widely-used two-stage pose estimation paradigm in our experiments. The ground-truth bounding box annotations are utilized to crop the instance target, which is subsequently resized to a uniform shape. We select the representative CNN-based model ResNet alongside the transformer-based model ViT" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "29442" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.089, + 0.904, + 0.374 + ], + "angle": 0, + "content": "
MethodsDatasetBackboneAPAP·50AP·75APMAPLAR
Foundation Models
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Base74.594.982.246.875.070.0
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Large80.497.688.552.780.8-
SuperAnimal [37]Quadruped-80KHRNet-W3280.1-----
X-Pose-V [34]UniKPT(226K)Swin-Tiny73.691.980.647.274.2-
X-Pose-V [34]UniKPT(226K)Swin-Large79.095.786.857.079.6-
Expert Models
SimpleBaseline [29]AP-10KResNet-5070.294.276.045.570.473.5
HRNet [26]AP-10KHRNet-W3273.895.880.352.374.276.9
HRNet [26]AP-10KHRNet-W4874.495.980.758.974.8-
TokenPose [12]AP-10KHRNet-W4872.794.379.260.672.775.7
TransPose [35]AP-10KHRNet-W4874.295.780.856.274.677.0
HRFormer [39]AP-10KHRFormer-B74.595.981.655.874.977.6
Prompt-based Models
CLAMP [42]AP-10KCLIP / ResNet-5072.995.479.443.273.276.3
PPAP (Ours)AP-10KCLIP / ResNet-5073.494.179.957.173.876.5
CLAMP [42]AP-10KCLIP / ViT-Base74.395.881.447.674.977.5
PPAP (Ours)AP-10KCLIP / ViT-Base75.495.883.053.475.978.7
CLAMP [42]AP-10KCLIP / ViT-Large77.896.885.058.778.181.0
PPAP (Ours)AP-10KCLIP / ViT-Large78.697.186.159.378.981.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.383, + 0.907, + 0.425 + ], + "angle": 0, + "content": "Table 1. Performance comparisons on AP-10K val set. The image resolution is \\(256 \\times 256\\), with an exception for ViTPose++, which utilizes a resolution of \\(256 \\times 192\\). Notably, the foundation models, such as ViTPose++, are trained on mixed datasets with extra corpora, which can be regarded as an upper bound for model performance." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.432, + 0.645, + 0.504 + ], + "angle": 0, + "content": "
MethodsBackboneP3-Amph.P3-BirdsP3-FishesP3-Mam.P3-Rep.P1-All
CLAMP [29]CLIP / ResNet-5051.876.162.454.043.560.5
PPAP (Ours)CLIP / ResNet-5051.976.562.455.548.260.9
CLAMP [29]CLIP / ViT-Base58.976.965.359.255.762.8
PPAP (Ours)CLIP / ViT-Base60.978.066.161.256.664.5
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.191, + 0.506, + 0.521, + 0.518 + ], + "angle": 0, + "content": "(a) Comparisons across various protocols on AnimalKingdom." + }, + { + "type": "table", + "bbox": [ + 0.656, + 0.432, + 0.884, + 0.503 + ], + "angle": 0, + "content": "
MethodsBackboneP1-All
HRNet [26]HRNet-W3266.1
DARK [41]HRNet-W3266.6
CLAMP [42]ViT-Large65.6
PPAP (Ours)ViT-Large68.4
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.665, + 0.505, + 0.888, + 0.517 + ], + "angle": 0, + "content": "(b) Comparisons with the SOTA methods." + }, + { + "type": "table_caption", + "bbox": [ + 0.099, + 0.52, + 0.895, + 0.535 + ], + "angle": 0, + "content": "Table 2. Performance comparisons on the AnimalKingdom test set (PCK@0.05). The input resolution of all methods is \\( {256} \\times {256} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.549, + 0.483, + 0.639 + ], + "angle": 0, + "content": "as backbones, serving as feature extractors in our framework. The text encoder after CLIP pre-training is adopted as our language models and initialized with the corresponding CLIP pre-trained weights. For prompt learning, we configure the length of the learnable context tokens to match CLAMP, setting \\( L = 8 \\) for fair comparisons." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.64, + 0.483, + 0.821 + ], + "angle": 0, + "content": "During training, we use \\(256 \\times 256\\) input images and applied data augmentation including random rotation, scaling, flipping, and half-body transformation. All models are trained for 210 epochs with a step-wise learning rate scheduler that decreases by a factor of 10 at the 170th and 200th epochs. We used the AdamW optimizer with a weight decay of \\(2.5e - 5\\) and froze the text encoder to preserve pretrained language knowledge. Supervised learning experiments were conducted to evaluate performance on both AP-10K and AnimalKingdom, with a batch size of 64, an initial learning rate of \\(3e - 4\\), and \\(N_{p} = N_{s} = 2\\) for attribute embeddings and sampling turns, respectively." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.83, + 0.287, + 0.846 + ], + "angle": 0, + "content": "4.2. Results and Analysis" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.852, + 0.286, + 0.867 + ], + "angle": 0, + "content": "4.2.1. Supervised Learning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Table 1 presents the results under the supervised learning setting on AP-10K [38], comparing our method with repre" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.549, + 0.907, + 0.761 + ], + "angle": 0, + "content": "sentative expert models for pose estimation. It can be observed that probabilistic prompt learning contributes to improved performance in multi-species APE under the prompt learning paradigm. With the basic ResNet-50 as the feature extractor, PPAP achieves a modest AP improvement of 0.5, which we attribute to the limited capacity of the feature extractor in capturing sufficient image features. When switching to the more powerful ViT-Base backbone, PPAP achieves 75.4 AP and outperforms CLAMP by 1.1 points. These observations indicate that our prompt learning approach offers a more effective solution to the challenges posed by significant data variance in multi-species Animal Pose Estimation (APE), as opposed to merely relying on the keypoint name prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Furthermore, we conduct comparisons against expert pose estimation models, validating our approach's effectiveness. On the AP-10K validation set, our PPAP method significantly outperforms the SimpleBaseline by 3.2 AP when using the ResNet-50 backbone, compared to the state-of-the-art CNN-based expert models. Additionally, when equipped with the ViT-Base backbone, our approach achieves 1.6 and 1.0 AP gains over the highly representative pose estimation model HRNet, respectively. In par" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29443" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.477, + 0.287 + ], + "angle": 0, + "content": "
MethodTrainTestPCK@0.05
ResNet-50CLAMP PPAPFishesBirds9.5
FishesBirds9.8 (↑ 0.3)
CLAMP PPAPMammalsAmphibians6.8
MammalsAmphibians9.8 (↑ 3.0)
CLAMP PPAPReptilesAmphibians19.2
ReptilesAmphibians19.3
ViT-BaseCLAMP PPAPFishesBirds0.1
FishesBirds12.0 (↑ 11.9)
CLAMP PPAPMammalsAmphibians12.3
MammalsAmphibians16.5 (↑ 4.2)
CLAMP PPAPReptilesAmphibians20.8
ReptilesAmphibians21.8 (↑ 1.0)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.291, + 0.483, + 0.318 + ], + "angle": 0, + "content": "Table 3. Zero-shot performance comparison on AnimalKingdom." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.331, + 0.462, + 0.428 + ], + "angle": 0, + "content": "
LdivKLGKPAPΔ
74.30
✓74.9+0.6
✓74.9+0.6
✓✓75.2+0.9
✓✓✓75.4+1.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.16, + 0.431, + 0.414, + 0.446 + ], + "angle": 0, + "content": "Table 4. Ablation studies on components." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.483, + 0.608 + ], + "angle": 0, + "content": "ticular, PPAP also demonstrates notable performance improvements of 2.7 and 1.2 AP, respectively, when compared to hybrid architectures such as TokenPose and TransPose. We also observe that these methods underperform on multi-species animal datasets compared to human ones, all falling below HRNet. This is due to their inability to manage large data variances, highlighting our approach's effectiveness in overcoming this challenge. Besides, PPAP surpasses HRFformer by 0.9 AP when compared to a plain transformer-based architecture." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.748 + ], + "angle": 0, + "content": "It's worth mentioning that foundation models are trained across multiple datasets like Quadruped-80K [37] and UniKPT-226K [34], allowing them to gain broader knowledge, richer pose priors, and generally enhanced performance. Despite this, our PPAP, trained exclusively on AP10K, matches foundation models with a score of 78.6 vs. 79.0. This indicates that our method's robustness stems not from extensive pose data but from its effective utilization of textual knowledge to tackle multi-species variability." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "In addition to AP-10K, we further evaluate the effectiveness of PPAP on the more challenging dataset, AnimalKingdom [18]. The training setting is the same as the previous section. Table 2 reports the performance of prompt-based methods across various protocols on the AnimalKingdom dataset. We observe that the PPAP method consistently achieves superior performance across all protocols. By constructing diverse prompts and employing probabilistic modeling, our PPAP gets gains of 0.4 and 1.7 PCK values with ResNet-50 and ViT-Base, respectively. Notably," + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.906, + 0.27 + ], + "angle": 0, + "content": "
Number of attributes (γ = 5e-4, β = 1e-5, Ns = Np)
Parameter Np1234
AP74.875.475.175.0
Objective hyper-parameter (Ns = Np = 2)
Parameter β (γ=5e-4)1e-45e-51e-51e-6
AP74.574.875.474.9
Parameter γ (β=1e-5)5e-35e-45e-55e-6
AP73.575.474.775.1
Number of sampled turns (γ = 5e-4, β = 1e-5, Np = 2)
Parameter Ns2468
AP75.474.774.574.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.275, + 0.908, + 0.317 + ], + "angle": 0, + "content": "Table 5. Ablation studies on hyper-parameters. The number of attributes \\(N_{p}\\), objective hyper-parameters \\(\\gamma, \\beta\\), and the number of sampled representations \\(N_{s}\\)." + }, + { + "type": "table", + "bbox": [ + 0.556, + 0.322, + 0.866, + 0.391 + ], + "angle": 0, + "content": "
StrategyAPAP.50AP.75
heuristic selection75.195.682.1
ensemble selection75.495.883.0
attention-based selection74.695.782.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.533, + 0.395, + 0.886, + 0.409 + ], + "angle": 0, + "content": "Table 6. Ablation studies on cross-modal fusion strategies." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.907, + 0.599 + ], + "angle": 0, + "content": "the considerable performance gains on specific classes underscore the adaptability of our method. For example, PPAP with ResNet-50 achieves a 4.7 PCK improvement in reptiles, while PPAP with ViT-Base yields a 3.0 PCK increase in mammals. Compared to the existing SOTA methods, our PPAP with ViT-Large outperforms them by 2.0 AP gains. Furthermore, we argue that incorporating the plug-and-play DARK [41] leads to an additional boost in performance. Therefore, by training exclusively on the single pose data, our method achieves a new state-of-the-art performance with the ViT-Large backbone on both multispecies animal pose benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.6, + 0.906, + 0.72 + ], + "angle": 0, + "content": "Besides, to intuitively highlight the superiority of our approach, we present qualitative comparisons with CLAMP in Figure 3. Since AP-10K consists of mammals, we specifically select fishes and birds from AnimalKingdom for diversity. Differences in predicted locations are highlighted in red circles, clearly illustrating that our method consistently achieves more precise localization across these three animal classes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.731, + 0.704, + 0.745 + ], + "angle": 0, + "content": "4.2.2. Zero-Shot Learning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Given that the AnimalKingdom dataset includes a broader range of classes and presents a more challenging benchmark, we further conduct zero-shot learning experiments on it to evaluate the model's generalization ability on unseen animal species. Since the AnimalKingdom is sourced from wildlife data, it inevitably exhibits a long-tail distribution across various animal species [18]. We select three types of zero-shot settings to compare with the prompt-based method CLAMP [42]. The experiment settings include similar classes (\"Reptiles vs. Amphibians\"), typical" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "29444" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.381 + ], + "angle": 0, + "content": "classes (\"Mammals vs. Amphibians\"), and highly divergent classes (\"Fishes vs. Birds\"), thereby covering a range of taxonomic variations to fully reflect the generalization of the PPAP for dealing with unseen species. The results are shown in Table 3, which reflects that our PPAP achieves better performance for all three settings. While PPAP achieves only a modest performance gain with ResNet-50, it demonstrates a significantly greater improvement when paired with the more powerful ViT-Base backbone. Interestingly, when trained on Fish and tested on Birds, CLAMP fails to perform pose estimation across such extreme inter-classes variations, resulting in nearly zero PCK value, while PPAP achieves a substantial improvement of 11.9 gains. Furthermore, our method demonstrates additional performance gains of 4.2 and 1.0 in the other two settings, respectively. Such observation clearly illustrates the generalization capability of our probability-based modeling approach on multispecies APE, effectively mitigating challenges associated with large data variance and imbalanced data distribution." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.392, + 0.245, + 0.409 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.415, + 0.484, + 0.492 + ], + "angle": 0, + "content": "In this section, we conduct a comprehensive ablation study of our proposed method on the AP-10K dataset using ViT-Base backbone. We analyze the impact of various components and hyper-parameters, and also investigate different cross-modal fusion strategies for generating the score map." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.484, + 0.674 + ], + "angle": 0, + "content": "Effects of Different Components. We conducted experiments to evaluate the impact of various loss functions and the Generalized Keypoint Placement (GKP) strategy. Table 4 summarizes the results. By constructing diverse prompts and applying the constraint \\(\\mathcal{L}_{\\mathrm{div}}\\), the model achieved a 74.9 AP score, outperforming the baseline by 0.6 points. Similarly, applying the constraint \\(\\mathcal{L}_{\\mathrm{KL}}\\) with Gaussian distribution reformulation also improved the AP score by 0.6 points. Combining both constraints, the model reached 75.2 AP, significantly surpassing the baseline. Additionally, using the GKP strategy generated more generalized prompts, leading to further improvements." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Effects of Hyper-parameter. The hyper-parameters of the number of attributes \\(N_{p}\\), objective function coefficient \\(\\gamma, \\beta\\) in Eq. 13 and the sampling turns \\(N_{s}\\) are to trade off the model performance. Firstly, we compare performance with respect to different attribute numbers \\(N_{p}\\). As shown in the first block of Table 5, two prompt templates are sufficient to represent different image attributes and achieve optimal performance. As the number of prompt templates increases, however, performance declines, suggesting that excessive template quantity can lead to information redundancy, thereby impairing model efficacy. Then, we adjust the weighting ratio of the \\(\\mathcal{L}_{\\text {feature }}\\) and \\(\\mathcal{L}_{\\text {prompt }}\\), and observe that \\(\\gamma = 5e - 4\\), \\(\\beta = 1e - 5\\) are more suitable. It suggests excessive weighting leads each prompt representation to converge toward a standard normal distribution, thereby" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.905, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.232, + 0.907, + 0.261 + ], + "angle": 0, + "content": "Figure 3. Qualitative visualization of several examples with CLAMP and our proposed PPAP." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.278, + 0.907, + 0.43 + ], + "angle": 0, + "content": "diminishing their distinctiveness. Conversely, overly small weights result in excessive variance in the distribution of each embedding, which increases uncertainty. To achieve a balance, we choose \\(\\beta = 1e - 5\\) to get the optimal result. In our approach, we employ reparameterization techniques to ensure differentiability, while also utilizing sampling to enhance the diversity of the text prompts. As we can see in the last block of Table 5, the results are not sensitive to the sampling turns and the accuracy reaches the best performance when setting \\(N_{s}\\) and \\(N_{p}\\) to be equal." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.434, + 0.909, + 0.678 + ], + "angle": 0, + "content": "Choices of Cross-modal Fusion. In our experiments, we explore three different fusion strategies, with results summarized in Table 6. As we can see, no matter which strategy is employed, the performances are consistently higher than the baseline method. Selecting the representation most similar to the target can achieve competitive performance. However, as similarity computation relies on labeled data unavailable during testing, we instead average the sampled representations. This discrepancy between training and testing leads to suboptimal performance. Directly ensembling all representations followed by the conv modulation yields the best performance by avoiding information loss. Besides, the results show that the attention-based strategy has worse performances, which may be attributed to the randomly initialized queries to effectively learn the suitable prompt representations." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.705, + 0.634, + 0.721 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a probabilistic prompt distribution learning method to adapt pre-trained vision-language models for the multi-species APE task. With the diverse key-point prompt construction, probabilistic prompt modeling and cross-modal fusion strategies, PPAP uses text guidance in a more comprehensive and effective manner, presenting a novel solution to the multi-species problem, i.e. large data variance and imbalanced data distribution. PPAP reflects superiority and generalization for multi-species APE on the representative multi-species animal pose benchmarks including AP-10K and AnimalKingdom." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29445" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.228 + ], + "angle": 0, + "content": "This work was supported in part by the National Key Research and Development Project under Grant 2023YFC3806000, in part by the National Natural Science Foundation of China under Grant 62406226 and 61936014, in part sponsored by Shanghai Sailing Program under Grant 24YF2748700, and in part sponsored by Tongji University Independent Original Cultivation Project under Grant 20230106." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.257, + 0.188, + 0.273 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.283, + 0.484, + 0.338 + ], + "angle": 0, + "content": "[1] Jinkun Cao, Hongyang Tang, Hao-Shu Fang, Xiaoyong Shen, Cewu Lu, and Yu-Wing Tai. 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IJCV, 130(9):2337-2348, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.092, + 0.905, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29447" + } + ] +] \ No newline at end of file diff --git a/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_origin.pdf b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9c56a0495d69fe14ee4496c688bc10fafc162b66 --- /dev/null +++ b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/1be3cde5-60cb-4a57-a201-7a6dd25687f0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4b8b6aac1f0f3a22882b5b70071e9cf4d47858947c6764141455ab9e3f64a9a3 +size 825993 diff --git a/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/full.md b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f52c562738763e46a7cdad9eb100d4bb703bf73b --- /dev/null +++ b/2025/Probabilistic Prompt Distribution Learning for Animal Pose Estimation/full.md @@ -0,0 +1,301 @@ +# Probabilistic Prompt Distribution Learning for Animal Pose Estimation + +Jiyong Rao $^{1}$ Brian Nlong Zhao $^{2\dagger}$ Yu Wang $^{1*}$ $^{1}$ School of Computer Science and Technology, Tongji University $^{2}$ Stanford University jiyongrao@tongji.edu.cn, brianlz@stanford.edu, yuwangtj@yeah.net + +# Abstract + +Multi-species animal pose estimation has emerged as a challenging yet critical task, hindered by substantial visual diversity and uncertainty. This paper challenges the problem by efficient prompt learning for Vision-Language Pretrained (VLP) models, e.g. CLIP, aiming to resolve the cross-species generalization problem. At the core of the solution lies in the prompt designing, probabilistic prompt modeling and cross-modal adaptation, thereby enabling prompts to compensate for cross-modal information and effectively overcome large data variances under unbalanced data distribution. To this end, we propose a novel probabilistic prompting approach to fully explore textual descriptions, which could alleviate the diversity issues caused by long-tail property and increase the adaptability of prompts on unseen category instance. Specifically, we first introduce a set of learnable prompts and propose a diversity loss to maintain distinctiveness among prompts, thus representing diverse image attributes. Diverse textual probabilistic representations are sampled and used as the guidance for the pose estimation. Subsequently, we explore three different cross-modal fusion strategies at spatial level to alleviate the adverse impacts of visual uncertainty. Extensive experiments on multi-species animal pose benchmarks show that our method achieves the state-of-the-art performance under both supervised and zero-shot settings. The code is available at https://github.com/Raojiyong/PPAP. + +# 1. Introduction + +Animal Pose Estimation (APE) [1, 16, 20, 21, 37] represents a fundamental vision task, the objective of which is to identify a series of keypoint locations in an animal skeleton. The skeleton (i.e. a set of connected coordinates), serves as a minimal yet informative unit for encoding both static structure and motion cues, thereby providing critical support for understanding animal behaviour. Consequently, APE plays + +![](images/a76d73037140fcdae575fb26810646565a3371e329c65949f91eacf34eba2997.jpg) +Figure 1. The motivation that one key point can be complementarily described in different views (An example of left shoulder). + +a significant role in various research fields, such as neuroscience [16, 20], ecology [3, 4], zoology study [9, 21] and biotechnological quests [18, 28]. + +In numerous instances [16, 18, 38], researchers have opted to directly apply Human Pose Estimation (HPE) methodologies to animals. However, it is evident that many animal species exhibit pose distributions that deviate significantly from human-specific models, leading to substantial domain shifts. To address the multi-species Animal Pose Estimation (APE) challenge, Category-Agnostic Pose Estimation (CAPE) methods [25, 30] have been investigated. These methods frame keypoint prediction as a keypoint matching problem, necessitating supplementary support sets that belong to the same category as the test image. While promising, this approach introduces additional computational overhead and necessitates prior knowledge of the animal category, thereby limiting its practicality. Moreover, given the substantial data variances observed across species [18, 38], vision-only APE methods falter when confronted with cross-species challenges that rely solely on visual cues. + +Recently, the multimodal system proposed in [22] has garnered substantial research attention due to its ability to combine complementary data to enhance visual recognition. Despite the distinct visual characteristics of various + +animal species, they share common textual descriptions, as noted in [42]. Consequently, the straightforward approach of setting the keypoint name as the class token, known as deterministic prompt learning, has become prevalent in the current literature [34, 42]. For instance, X-Pose [34] utilizes a fixed text template like "A [Image Style] photo of a [Keypoint]", while CLAMP [42] employs a continuous prompt template of "[Learnable Tokens] + [Keypoint)". However, existing multimodal APE methods fall short in terms of rich text prompt design. Moreover, manually crafting keypoint-specific prompts is a cumbersome task. As depicted in Figure 1, a solitary textual description often fails to encapsulate all the nuances of a specific keypoint, such as its color, position, and shape. For example, the "left shoulder" keypoint can be described from both spatial and color perspectives as "Left shoulder is near the right shoulder" and "The color of the left shoulder is light salmon", respectively. From a textual standpoint, multiple descriptions provide diverse perspectives, enabling pose estimation to grasp high-level semantics and pinpoint keypoints accurately based on one or more of these cues. On the visual front, the intricacies of wild scenes and the presence of multiple species introduce uncertain statistical shifts compared to the training domain [4, 14, 27]. Given this "uncertainty" in potential data variations, synthesizing novel feature statistics variants to model diverse representations can bolster the network's robustness against unseen categories. To address these challenges, this paper introduces a novel probabilistic method that enhances network generalization to handle unseen categories by adeptly modeling keypoint-adaptive prompts. + +Our approach leverages multiple learnable text prompts to enhance flexibility and robustness in text prompt initialization, moving beyond a single template. By strategically inserting keypoint names within templates, we enable flexible sentence construction akin to natural language. We hypothesize that prompt statistics, incorporating uncertainties, follow a multivariate Gaussian distribution, with the center defined by the original prompt statistic and the range indicating data variation across animal categories. We estimate this range using mini-batch statistics in a parametric learning framework and randomly sample variants from the estimated distribution to model diverse textual descriptions, as illustrated in Figure 2. To capture diverse and informative keypoint attributes, we introduce a novel diversity loss function that ensures distinctiveness across prompt distributions. In summary, our contributions are as follows: + +- We propose a novel Probabilistic Prompt Distribution Learning framework for APE to learn the probabilistic representation of specific keypoint descriptions. +- We introduce multiple prompt attributes and design a diversity loss to prevent the learned attributes from being identical. Additionally, we explore three different cross-modal fusion strategies to achieve spatial adaptation. + +- We demonstrate the effectiveness of the proposed probabilistic-based approach through extensive experiments on multi-species animal pose estimation. + +# 2. Related Works + +# 2.1. Animal Pose Estimation + +Typical vision-only APE methods [1, 16, 18, 23, 31, 38], with most directly adapting human pose estimation methods [13, 26, 29, 32, 36, 39], such as DeepLabCut [9, 16], AP-10K [26, 38] and ViTPose [32, 33] to animal counterpart. These methods leverage powerful visual backbones for feature extraction but fail to handle rare or even unseen categories explicitly. The relatively limited animal data volume compared to its human counterpart increases the risk of overfitting in complex networks [4]. To cope with the limited labelled animal data volume, direct attempts [10, 17] learn prior-aware knowledge from synthetic animal datasets, and generate pseudo labels for unlabelled data. In terms of refining the pseudo labels, ScarceNet [11] and FreeNet[40] propose the novel semi-supervised learning methods that improves the reliability of pseudo label generation, effectively mitigating the data scarcity problem. Following the principles of few-shot learning, Xu et al. [30] proposed a novel Category-Agnostic Pose Estimation (CAPE) paradigm, which treats keypoint prediction as the keypoint matching problem, enabling the prediction of poses on unseen categories. This is accomplished by offering a few support sets from the same category as the test image to guide the learning process. CAPE [19, 25, 30] introduces an additional computational burden and necessitates prior animal categories, making the methods less practical. To eliminate the reliance on category-specific prior, pretrained VLMs have been applied in the APE. CLAMP [42] is the first text-guided APE method, aligning text-visual features at both the feature and spatial levels, thereby enabling the textual prompt to effectively align the visual representation. X-Pose [34] proposes an end-to-end pose estimation framework that leverages both visual and textual prompts to support keypoint prediction for arbitrary targets. In view of this, we focus on designing keypoint prompts that offer enriched keypoint representations, facilitating accurate pose estimation. + +# 2.2. Deterministic Prompt Learning + +Prompt learning [5, 6, 24, 43, 44] aims to adapt foundation models to downstream tasks by efficiently optimizing prompts. CoOp [44] represents a seminal application of prompt learning in VLMs, transforming hard-coded discrete prompt templates into learnable continuous prompts. CoCoOp [43], as its variants, integrates image-conditioned knowledge into text prompts to enhance generalization to unseen classes. Similarly, DenseCLIP [24] employs a + +![](images/5834ab97d8f33e2a02ff383be4f75318361d081ef9418fbd95b0f6571e7ff655.jpg) +Figure 2. Overall framework of PPAP. Firstly, we create $N_{p}$ keypoint attribute templates and generate distinctive embeddings for these attributes using a text encoder. Each keypoint prompt embedding is represented probabilistically as a multivariate Gaussian distribution, with its mean derived from the text decoder and variance from the visual-text decoder. Subsequently, we sample these keypoint prompt representations from the distribution and perform cross-modal fusion during the spatial adaptation stage to capture the spatial relationship between textual and visual content. + +Transformer to facilitate interaction between visual context and textual prompts, producing context-aware prompts for improved performance. Building upon this, PromptSRC [6] uses a set of hand-crafted prompts and introduces several regularization losses to prompt learning. To further improve diversity, we specialize different keypoint prompts to guide spatial adaptation for different animal categories, thus aligning them with different attribute sets for each keypoint. + +# 2.3. Probabilistic Prompt Learning + +Compared to deterministic prompt learning, probabilistic prompt learning [2, 8, 15] is not tied to specific classes, making it more adaptable to cross-species challenges with prompt adjustments. APP [2] proposes a Bayesian-based prompt learning framework to enhance the flexibility and adaptability of input embeddings. However, various descriptions are dispersed in the input space, resulting in difficulty in representing their distribution. Several studies focus on probabilistic learning within the output embedding space. ProDA [15] is the first probabilistic prompt model, allowing for straightforward modeling by a multivariate Gaussian distribution. PPL [8] introduces attribute prompts to represent shared attributes across different categories by constructing a mixture of Gaussian distribution to address dense prediction problems. Conversely, we prioritize probabilistic modeling for each individual prompt rather than constructing a single overarching distribution, as it provides us with nuanced contextual information better and shows greater generalization to unseen data. + +# 3. Method + +To enhance the generalization capabilities for multi-species animal data, we propose a probabilistic prompt learn + +ing technique. This technique is grounded in the Contrastive Learning for Connecting Language and Animal Pose (CLAMP) framework [42]. We begin by providing a concise overview of CLAMP's fundamental principles before presenting our probabilistic prompt learning method. + +# 3.1. Preliminaries + +CLAMP is proposed based on the powerful model CLIP [22]. Given an image and its corresponding textual description, CLIP extracts textual and visual embeddings by processing the input through a text encoder and an image encoder, respectively. To effectively leverage the textual description for APE, CLAMP uses a pose-specific template $p_n = \{T_l\}_{l=1}^L[KeyPoint]_n$ to represent $n$ -th keypoint prompt, where $\{T_l\}_{l=1}^L$ is $L$ learnable prefix tokens, and $[Keypoint]_n$ denotes the $n$ -th keypoint name token. Then prompt embedding $E_{prompt} \in \mathbb{R}^{K \times C_{emb}}$ is obtained by the prompt encoder. To establish spatial connections between textual description and image features, CLAMP performs cross-modal adaptation at both spatial and feature levels. In the spatial adaptation stage, the extracted prompt representations and image features are used to generate score map $S \in \mathbb{R}^{K \times H \times W}$ , where $H, W$ and $K$ represent the height, width and the number of keypoints, respectively. This $S$ is utilized to indicate the probability of keypoint occurrence at specific locations. Besides, the spatial objective $\mathcal{L}_{spatial}$ is calculated as follows: + +$$ +\mathcal {L} _ {\text {s p a t i a l}} = M S E (U p s a m p l e (S), H _ {\text {t a r g e t}}), \tag {1} +$$ + +where $MSE$ denotes mean squared error, Upsample is the upsample operation, and $H_{target}$ is the target heatmap. Meanwhile, in the feature adaptation stage, ground truths are performed to grid-sample local keypoint + +features $F_{keypoint} \in \mathbb{R}^{K \times C_{emb}}$ from image embeddings. The pairwise similarity $M = F_{keypoint} \cdot E_{prompt}^T$ is utilized to facilitate feature alignment: + +$$ +\mathcal {L} _ {\text {f e a t u r e}} = \frac {1}{2} \left(C E (M, M _ {\text {l a b e l}}) + C E \left(M ^ {T}, M _ {\text {l a b e l}}\right)\right), \tag {2} +$$ + +where $CE$ denotes cross-entropy loss and $M_{label}$ is the diagonal matrix, used as matching target. Building on these two adaptations, we introduce a set of learnable keypoint-agnostic prompts, modeling each prompt distribution with a Gaussian. Finally, we explore three fusion strategies for spatial adaptation and design a novel pose estimation paradigm to handle the multi-species APE. + +# 3.2. Diverse Prompt Construction + +Relying solely on visual features and the keypoint name prompt proves to be insufficient to address the long-tail problem present in animal datasets [18, 38]. As previous literature [8, 15] indicated, multiple diverse prompts could offer enriched semantics to aid multi-modal models in recognizing visual patterns, thereby alleviating the adverse impact of long-tail challenge. However, it is hard to explicitly identify "what constitutes useful keypoint visual attributes for locating keypoints?". To this end, we introduce multiple learnable textual attribute prompts for each keypoint to constitute the prompt templates. Formally, as illustrated in Figure 2, for the $i$ -th keypoint token $k_{i}$ , we create $N_{p}$ keypoint attribute templates for each keypoint by combining learnable attribute description tokens. + +$$ +p _ {i} ^ {t} = \left\{a _ {1} ^ {t}, a _ {2} ^ {t}, \dots , a _ {L} ^ {t} \mid k _ {i} \right\}, \quad t = 1, \dots , N _ {p}, \tag {3} +$$ + +where $\{a_1^t, a_2^t, \ldots, a_L^t\}$ comprises $L$ learnable attribute tokens, initialized randomly with "X X ... X". As shown in Figure 1, we aim to simulate the locations of keypoint in natural language descriptions. To this end, we introduce the Generalized Keypoint Placement (GKP) strategy, enabling flexible placement of keypoint names within the prompt template for enhanced naturalness and diversity. Unlike the insertion strategy used in ProDA [15], which restricts keypoint placement to specific positions (i.e. beginning, middle, or end), our approach permits random placement throughout the template, offering greater positional flexibility. During training, these tokens are optimized to better suit APE tasks, offering increased contextual flexibility. By inputting the textual attribute prompts into the text encoder $\theta(\cdot)$ , we can obtain the encoded diverse prompt representations: + +$$ +\boldsymbol {P} _ {i} = \{\theta (\boldsymbol {p} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \}, \quad \tilde {\boldsymbol {P}} _ {i} = \{\theta (\tilde {\boldsymbol {p}} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \}, \qquad (4) +$$ + +where $P_{i}$ denotes the complete embedding for the $i$ -th keypoint prompt. Meanwhile, $\tilde{p}_i^t$ represents attribute tokens excluding keypoint names, and $\tilde{P}_{i}$ signifies the keypoint-agnostic attribute embedding. + +Multiple Attributes Diversity Loss. To make the keypoint-agnostic attribute representations capture distinct content, we introduce diversity among representations, and design a novel diversity loss to keep differentiation between them. The specific formulation is as follows: + +$$ +\mathcal {L} _ {d i v} = \frac {1}{K} \sum_ {i = 1} ^ {K} \| \tilde {\boldsymbol {P}} _ {i} \tilde {\boldsymbol {P}} _ {i} ^ {T} - \mathbb {I} \| _ {2} ^ {2}, \quad \mathbb {I} = \operatorname {d i a g} (\underbrace {1 , 1 , \dots , 1} _ {N _ {p}}). \tag {5} +$$ + +The diversity loss applies a squared $\ell_2$ -norm penalty on attribute representations to foster greater dissimilarity among them, thereby amplifying attribute diversity. Subsequently, the resultant prompt representations encapsulate the abundant and varied textual semantics, providing enhanced contextual support for subsequent visual localization. + +# 3.3. Probabilistic Prompt Modeling + +Based on the observation [15]: the output embedding of the descriptions within a category are close to each other, allowing them to be modeled with a sample distribution, i.e. Gaussian. We propose a probabilistic prompt learning strategy to reformulate the prompt distribution. As subsection 3.2 discussed, we strive to maintain orthogonality among the attribute embeddings. Thus, these embeddings are better represented as independent Gaussian distributions, each characterized by distinct means and variances. For each $p_i$ , we define a probabilistic distribution $\mathcal{G}(z_i^t | p_i^t)$ as a factorized Gaussian with its center vector $\mu_i^t$ and variance matrix $\sigma_i^t$ , where $t$ is the $t$ -th attribute for the $i$ -th keypoint. This distribution is formulated as: + +$$ +\mathcal {G} \left(z _ {i} \mid p _ {i}\right) \sim \left\{\mathcal {N} \left(\boldsymbol {\mu} _ {i} ^ {t}, \boldsymbol {\sigma} _ {i} ^ {t} \mathbf {I}\right) \right\} _ {t = 1} ^ {N _ {p}}. \tag {6} +$$ + +Specifically, we introduce a text decoder to obtain the mean of Gaussian distribution $\pmb{\mu}_i^t$ and a visual-text decoder for the variances $\sigma_i^t$ , as illustrated in Figure 2. In the text decoder, we facilitate interaction among prompt embeddings by self-attention (SA) module, as well as a form of self-augmentation. The default number of the layer is set to 1. + +$$ +\boldsymbol {\mu} _ {i} ^ {t} = M L P \left(L N \left(q _ {i} ^ {t}\right)\right) + S A \left(L N \left(q _ {i} ^ {t}, k _ {i} ^ {t}, v _ {i} ^ {t}\right)\right), \tag {7} +$$ + +where the query $q_{i}^{t}$ , key $k_{i}^{t}$ , and value $v_{i}^{t}$ are all derived from prompt embedding $P_{i}$ . $LN$ and $MLP$ denote layer norm and multilayer perceptron layer, respectively. Meanwhile, in the visual-text decoder Here, the key $v_{k}$ and value $v_{\mathrm{v}}$ vectors are both obtained from the $F$ . The variance matrix of each attribute representation is computed as: + +$$ +\boldsymbol {\sigma} _ {i} ^ {t} = M L P \left(L N \left(q _ {i} ^ {t}\right)\right) + C A \left(L N \left(q _ {i} ^ {t}, v _ {k}, v _ {\mathrm {v}}\right)\right), \tag {8} +$$ + +where CA stands for cross-attention module. Once the statistics of each keypoint description are obtained, the Gaussian distribution for probabilistic prompt statistics can + +be established. By exploiting the Gaussian distribution, random sampling can generate various new feature statistics information with different means and variances. Therefore, we adopt random sampling to further exploit the probabilistic representations. $N_{s}$ prompt representations are sampled for $i$ -th keypoint with $t$ -th attribute $z_{i}^{t} = \{z_{i}^{1},\ldots ,z_{i}^{N_{s}}\} \stackrel {i.i.d.}{\sim}\mathcal{G}(z_{i}^{t}|p_{i}^{t})$ , and we interpret $z_{i}^{t}$ as independently enriched contextual description. Here we use the re-parameterization trick [7] to make the sampling operation differentiable. + +$$ +\hat {z} _ {i} ^ {t} = \mu \left(p _ {i} ^ {t}\right) + \epsilon \cdot \sigma \left(p _ {i} ^ {t}\right), \quad \epsilon \sim \mathcal {N} (\boldsymbol {0}, \boldsymbol {I}), \tag {9} +$$ + +where $\mu(p_i^t)$ , $\sigma(p_i^t)$ are mean and standard deviation of distribution $\mathcal{G}(z_i^t | p_i^t)$ , and $\epsilon$ follows the standard normal distribution. Finally, we obtain a set of diverse prompt representations $\hat{z}_i^t$ for each keypoint. To prevent learned variances from collapsing to zero, we employ an additional KL divergence regularizer between prompt distributions and the Gaussian prior, forming the keypoint prompt loss: + +$$ +\mathcal {L} _ {\text {p r o m p t}} = \mathcal {L} _ {\text {d i v}} + \frac {1}{N _ {p}} \sum_ {t} ^ {N _ {p}} K L \left(\mathcal {G} \left(\hat {z} _ {i} ^ {t} \mid p _ {i} ^ {t}\right) \| \mathcal {N} (\mathbf {0}, I)\right). \tag {10} +$$ + +# 3.4. Cross-Modal Fusion + +Once various prompt embeddings have been obtained, the problem of "how to align them with the visual features?" inevitably arises. Given these prompt representations, we explore three strategies for multi-modal information fusion: 1) heuristic selection; 2) ensemble selection; 3) attention-based selection. Specifically, the heuristic selection strategy computes the similarity between the $N_{s}$ sampled score maps $S' \in \mathbb{R}^{N_s \times K \times H \times W}$ and the keypoints target $H_{target} \in \mathbb{R}^{K \times H \times W}$ , assigning the most similar ones as the final score map $S$ . Thus, the score map for the $i$ -th keypoint is voted from all the sampling turns. The ensemble selection strategy considers all the representations to contain informative context. To prevent the loss of textual cues, we concat score maps and apply convolution operation (Conv) for signal modulation, ultimately generating the final score map. + +$$ +S = \operatorname {C o n v} \left(\operatorname {C o n c a t} \left(S ^ {\prime}\right)\right). \tag {11} +$$ + +For the attention-based selection, we introduce an additional learnable query to leverage the attention module for capturing relationships between the query embedding and the prompt representations. We predefine the query embedding, i.e. $q_{i} \in \mathbb{R}^{K \times (HW)}$ for learning the suitable prompt representation. Meanwhile, the attention module takes the sampled prompts as key and value, which is formulated as: + +$$ +\begin{array}{l} S _ {i} = \text {F l a t t e n} \left(S ^ {\prime}\right), \\ Q _ {i} = q _ {i} W _ {q}, K _ {i} = S _ {i} W _ {k}, V _ {i} = S _ {i} W _ {v}, \tag {12} \\ S _ {i} = Q _ {i} + W _ {a} (\operatorname {s o f t m a x} \left(\frac {Q _ {i} K _ {i} ^ {T}}{\sqrt {H W}}\right) V _ {i}), \\ \end{array} +$$ + +where $W_{q}, W_{k}, W_{v}$ are learnable linear projections, and $S_{i}$ represents $i$ -th keypoint score map. Subsequently, $S_{i}$ is reshaped back to 2D with the final score map $S = \{S_{i}\}_{i=1}^{K}$ . Unless otherwise specified, we choose two attention layers in our experiments as default. + +# 3.5. Training + +Total objective. For the pose estimation task, we employ the commonly used MSE loss $\mathcal{L}_{pred}$ , and the total objective $\mathcal{L}_{total}$ is formulated as follows: + +$$ +\begin{array}{l l} \mathcal {L} _ {p r e d} = M S E (F _ {o}, H _ {t a r g e t}), & F _ {o} = H E A D (F _ {v i s} \oplus S), \\ f _ {o} = f _ {o + 1} + f _ {o + 2} + \dots + f _ {o + n} + \dots + f _ {o + n - 1} \end{array} \tag {13} +$$ + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {p r e d}} + \mathcal {L} _ {\text {s p a t i a l}} + \gamma \cdot \mathcal {L} _ {\text {f e a t u r e}} + \beta \cdot \mathcal {L} _ {\text {p r o m p t}}, +$$ + +where $F_{vis}$ denotes the visual features output by image encoder, and HEAD is the common keypoint prediction head [29], which consists of multiple deconvolution and MLP layers. The coefficient $\gamma$ and $\beta$ are hyper-parameters, which are discussed in detail in the ablation study section. + +# 4. Experiments + +# 4.1. Setup + +Datasets and evaluation metrics. (1) AP-10K [38] is a large-scale benchmark for multi-species animal pose estimation and contains over 10K images collected and filtered from 23 animal families and 54 species with 17 key points. We employ the mean average precision (AP) as the primary evaluation metric. Average recall (AR) and APs at different OKS (Object Keypoint Similarity) thresholds are also reported, i.e. AR, AP.5 and AP.75, as well as APs for different instance sizes, i.e. $\mathrm{AP^M}$ and $\mathrm{AP^L}$ . (2) AnimalKingdom [18] is a more challenging dataset, which includes over 33K samples with 23 keypoints across 850 species in 6 classes. Unlike AP-10K, AnimalKingdom contains a larger number of categories with more imbalanced and diverse data distribution, enhancing its difficulty. Besides, AnimalKingdom define three protocols (P1, P2, P3) for different tasks. P1-All involves training on the whole dataset for supervised learning. P2-LeaveKOut selects k sub-classes for training and performs few-shot learning on the remaining subclasses. P3-Amphibians/Birds/Fishes/Mammals/Reptiles specifies training within each distinct animal class, enabling zero-shot learning on unseen classes. We report the Percentage of Correct Keypoint $(\mathrm{PCK}@\alpha)$ score for evaluation, which computes the percentage of correct keypoints whose distance to ground truth is within $\alpha$ times the longest bounding box side. Besides, we adhere to the evaluation protocol in [18], and set $\alpha = 0.05$ . + +Implementation details. We follow the widely-used two-stage pose estimation paradigm in our experiments. The ground-truth bounding box annotations are utilized to crop the instance target, which is subsequently resized to a uniform shape. We select the representative CNN-based model ResNet alongside the transformer-based model ViT + +
MethodsDatasetBackboneAPAP·50AP·75APMAPLAR
Foundation Models
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Base74.594.982.246.875.070.0
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Large80.497.688.552.780.8-
SuperAnimal [37]Quadruped-80KHRNet-W3280.1-----
X-Pose-V [34]UniKPT(226K)Swin-Tiny73.691.980.647.274.2-
X-Pose-V [34]UniKPT(226K)Swin-Large79.095.786.857.079.6-
Expert Models
SimpleBaseline [29]AP-10KResNet-5070.294.276.045.570.473.5
HRNet [26]AP-10KHRNet-W3273.895.880.352.374.276.9
HRNet [26]AP-10KHRNet-W4874.495.980.758.974.8-
TokenPose [12]AP-10KHRNet-W4872.794.379.260.672.775.7
TransPose [35]AP-10KHRNet-W4874.295.780.856.274.677.0
HRFormer [39]AP-10KHRFormer-B74.595.981.655.874.977.6
Prompt-based Models
CLAMP [42]AP-10KCLIP / ResNet-5072.995.479.443.273.276.3
PPAP (Ours)AP-10KCLIP / ResNet-5073.494.179.957.173.876.5
CLAMP [42]AP-10KCLIP / ViT-Base74.395.881.447.674.977.5
PPAP (Ours)AP-10KCLIP / ViT-Base75.495.883.053.475.978.7
CLAMP [42]AP-10KCLIP / ViT-Large77.896.885.058.778.181.0
PPAP (Ours)AP-10KCLIP / ViT-Large78.697.186.159.378.981.7
+ +Table 1. Performance comparisons on AP-10K val set. The image resolution is $256 \times 256$ , with an exception for ViTPose++, which utilizes a resolution of $256 \times 192$ . Notably, the foundation models, such as ViTPose++, are trained on mixed datasets with extra corpora, which can be regarded as an upper bound for model performance. + +
MethodsBackboneP3-Amph.P3-BirdsP3-FishesP3-Mam.P3-Rep.P1-All
CLAMP [29]CLIP / ResNet-5051.876.162.454.043.560.5
PPAP (Ours)CLIP / ResNet-5051.976.562.455.548.260.9
CLAMP [29]CLIP / ViT-Base58.976.965.359.255.762.8
PPAP (Ours)CLIP / ViT-Base60.978.066.161.256.664.5
+ +(a) Comparisons across various protocols on AnimalKingdom. + +
MethodsBackboneP1-All
HRNet [26]HRNet-W3266.1
DARK [41]HRNet-W3266.6
CLAMP [42]ViT-Large65.6
PPAP (Ours)ViT-Large68.4
+ +(b) Comparisons with the SOTA methods. + +Table 2. Performance comparisons on the AnimalKingdom test set (PCK@0.05). The input resolution of all methods is ${256} \times {256}$ . + +as backbones, serving as feature extractors in our framework. The text encoder after CLIP pre-training is adopted as our language models and initialized with the corresponding CLIP pre-trained weights. For prompt learning, we configure the length of the learnable context tokens to match CLAMP, setting $L = 8$ for fair comparisons. + +During training, we use $256 \times 256$ input images and applied data augmentation including random rotation, scaling, flipping, and half-body transformation. All models are trained for 210 epochs with a step-wise learning rate scheduler that decreases by a factor of 10 at the 170th and 200th epochs. We used the AdamW optimizer with a weight decay of $2.5e - 5$ and froze the text encoder to preserve pretrained language knowledge. Supervised learning experiments were conducted to evaluate performance on both AP-10K and AnimalKingdom, with a batch size of 64, an initial learning rate of $3e - 4$ , and $N_{p} = N_{s} = 2$ for attribute embeddings and sampling turns, respectively. + +# 4.2. Results and Analysis + +# 4.2.1. Supervised Learning. + +Table 1 presents the results under the supervised learning setting on AP-10K [38], comparing our method with repre + +sentative expert models for pose estimation. It can be observed that probabilistic prompt learning contributes to improved performance in multi-species APE under the prompt learning paradigm. With the basic ResNet-50 as the feature extractor, PPAP achieves a modest AP improvement of 0.5, which we attribute to the limited capacity of the feature extractor in capturing sufficient image features. When switching to the more powerful ViT-Base backbone, PPAP achieves 75.4 AP and outperforms CLAMP by 1.1 points. These observations indicate that our prompt learning approach offers a more effective solution to the challenges posed by significant data variance in multi-species Animal Pose Estimation (APE), as opposed to merely relying on the keypoint name prompt. + +Furthermore, we conduct comparisons against expert pose estimation models, validating our approach's effectiveness. On the AP-10K validation set, our PPAP method significantly outperforms the SimpleBaseline by 3.2 AP when using the ResNet-50 backbone, compared to the state-of-the-art CNN-based expert models. Additionally, when equipped with the ViT-Base backbone, our approach achieves 1.6 and 1.0 AP gains over the highly representative pose estimation model HRNet, respectively. In par + +
MethodTrainTestPCK@0.05
ResNet-50CLAMP PPAPFishesBirds9.5
FishesBirds9.8 (↑ 0.3)
CLAMP PPAPMammalsAmphibians6.8
MammalsAmphibians9.8 (↑ 3.0)
CLAMP PPAPReptilesAmphibians19.2
ReptilesAmphibians19.3
ViT-BaseCLAMP PPAPFishesBirds0.1
FishesBirds12.0 (↑ 11.9)
CLAMP PPAPMammalsAmphibians12.3
MammalsAmphibians16.5 (↑ 4.2)
CLAMP PPAPReptilesAmphibians20.8
ReptilesAmphibians21.8 (↑ 1.0)
+ +Table 3. Zero-shot performance comparison on AnimalKingdom. + +
LdivKLGKPAPΔ
74.30
✓74.9+0.6
✓74.9+0.6
✓✓75.2+0.9
✓✓✓75.4+1.1
+ +ticular, PPAP also demonstrates notable performance improvements of 2.7 and 1.2 AP, respectively, when compared to hybrid architectures such as TokenPose and TransPose. We also observe that these methods underperform on multi-species animal datasets compared to human ones, all falling below HRNet. This is due to their inability to manage large data variances, highlighting our approach's effectiveness in overcoming this challenge. Besides, PPAP surpasses HRFformer by 0.9 AP when compared to a plain transformer-based architecture. + +It's worth mentioning that foundation models are trained across multiple datasets like Quadruped-80K [37] and UniKPT-226K [34], allowing them to gain broader knowledge, richer pose priors, and generally enhanced performance. Despite this, our PPAP, trained exclusively on AP10K, matches foundation models with a score of 78.6 vs. 79.0. This indicates that our method's robustness stems not from extensive pose data but from its effective utilization of textual knowledge to tackle multi-species variability. + +In addition to AP-10K, we further evaluate the effectiveness of PPAP on the more challenging dataset, AnimalKingdom [18]. The training setting is the same as the previous section. Table 2 reports the performance of prompt-based methods across various protocols on the AnimalKingdom dataset. We observe that the PPAP method consistently achieves superior performance across all protocols. By constructing diverse prompts and employing probabilistic modeling, our PPAP gets gains of 0.4 and 1.7 PCK values with ResNet-50 and ViT-Base, respectively. Notably, + +Table 4. Ablation studies on components. + +
Number of attributes (γ = 5e-4, β = 1e-5, Ns = Np)
Parameter Np1234
AP74.875.475.175.0
Objective hyper-parameter (Ns = Np = 2)
Parameter β (γ=5e-4)1e-45e-51e-51e-6
AP74.574.875.474.9
Parameter γ (β=1e-5)5e-35e-45e-55e-6
AP73.575.474.775.1
Number of sampled turns (γ = 5e-4, β = 1e-5, Np = 2)
Parameter Ns2468
AP75.474.774.574.6
+ +Table 5. Ablation studies on hyper-parameters. The number of attributes $N_{p}$ , objective hyper-parameters $\gamma, \beta$ , and the number of sampled representations $N_{s}$ . + +
StrategyAPAP.50AP.75
heuristic selection75.195.682.1
ensemble selection75.495.883.0
attention-based selection74.695.782.3
+ +Table 6. Ablation studies on cross-modal fusion strategies. + +the considerable performance gains on specific classes underscore the adaptability of our method. For example, PPAP with ResNet-50 achieves a 4.7 PCK improvement in reptiles, while PPAP with ViT-Base yields a 3.0 PCK increase in mammals. Compared to the existing SOTA methods, our PPAP with ViT-Large outperforms them by 2.0 AP gains. Furthermore, we argue that incorporating the plug-and-play DARK [41] leads to an additional boost in performance. Therefore, by training exclusively on the single pose data, our method achieves a new state-of-the-art performance with the ViT-Large backbone on both multispecies animal pose benchmarks. + +Besides, to intuitively highlight the superiority of our approach, we present qualitative comparisons with CLAMP in Figure 3. Since AP-10K consists of mammals, we specifically select fishes and birds from AnimalKingdom for diversity. Differences in predicted locations are highlighted in red circles, clearly illustrating that our method consistently achieves more precise localization across these three animal classes. + +# 4.2.2. Zero-Shot Learning. + +Given that the AnimalKingdom dataset includes a broader range of classes and presents a more challenging benchmark, we further conduct zero-shot learning experiments on it to evaluate the model's generalization ability on unseen animal species. Since the AnimalKingdom is sourced from wildlife data, it inevitably exhibits a long-tail distribution across various animal species [18]. We select three types of zero-shot settings to compare with the prompt-based method CLAMP [42]. The experiment settings include similar classes ("Reptiles vs. Amphibians"), typical + +classes ("Mammals vs. Amphibians"), and highly divergent classes ("Fishes vs. Birds"), thereby covering a range of taxonomic variations to fully reflect the generalization of the PPAP for dealing with unseen species. The results are shown in Table 3, which reflects that our PPAP achieves better performance for all three settings. While PPAP achieves only a modest performance gain with ResNet-50, it demonstrates a significantly greater improvement when paired with the more powerful ViT-Base backbone. Interestingly, when trained on Fish and tested on Birds, CLAMP fails to perform pose estimation across such extreme inter-classes variations, resulting in nearly zero PCK value, while PPAP achieves a substantial improvement of 11.9 gains. Furthermore, our method demonstrates additional performance gains of 4.2 and 1.0 in the other two settings, respectively. Such observation clearly illustrates the generalization capability of our probability-based modeling approach on multispecies APE, effectively mitigating challenges associated with large data variance and imbalanced data distribution. + +# 4.3. Ablation Study + +In this section, we conduct a comprehensive ablation study of our proposed method on the AP-10K dataset using ViT-Base backbone. We analyze the impact of various components and hyper-parameters, and also investigate different cross-modal fusion strategies for generating the score map. + +Effects of Different Components. We conducted experiments to evaluate the impact of various loss functions and the Generalized Keypoint Placement (GKP) strategy. Table 4 summarizes the results. By constructing diverse prompts and applying the constraint $\mathcal{L}_{\mathrm{div}}$ , the model achieved a 74.9 AP score, outperforming the baseline by 0.6 points. Similarly, applying the constraint $\mathcal{L}_{\mathrm{KL}}$ with Gaussian distribution reformulation also improved the AP score by 0.6 points. Combining both constraints, the model reached 75.2 AP, significantly surpassing the baseline. Additionally, using the GKP strategy generated more generalized prompts, leading to further improvements. + +Effects of Hyper-parameter. The hyper-parameters of the number of attributes $N_{p}$ , objective function coefficient $\gamma, \beta$ in Eq. 13 and the sampling turns $N_{s}$ are to trade off the model performance. Firstly, we compare performance with respect to different attribute numbers $N_{p}$ . As shown in the first block of Table 5, two prompt templates are sufficient to represent different image attributes and achieve optimal performance. As the number of prompt templates increases, however, performance declines, suggesting that excessive template quantity can lead to information redundancy, thereby impairing model efficacy. Then, we adjust the weighting ratio of the $\mathcal{L}_{\text {feature }}$ and $\mathcal{L}_{\text {prompt }}$ , and observe that $\gamma = 5e - 4$ , $\beta = 1e - 5$ are more suitable. It suggests excessive weighting leads each prompt representation to converge toward a standard normal distribution, thereby + +![](images/0d28b589b27137de56f71b255a881eae18abe85f2271a9efbfb47bee03a59b29.jpg) +Figure 3. Qualitative visualization of several examples with CLAMP and our proposed PPAP. + +diminishing their distinctiveness. Conversely, overly small weights result in excessive variance in the distribution of each embedding, which increases uncertainty. To achieve a balance, we choose $\beta = 1e - 5$ to get the optimal result. In our approach, we employ reparameterization techniques to ensure differentiability, while also utilizing sampling to enhance the diversity of the text prompts. As we can see in the last block of Table 5, the results are not sensitive to the sampling turns and the accuracy reaches the best performance when setting $N_{s}$ and $N_{p}$ to be equal. + +Choices of Cross-modal Fusion. In our experiments, we explore three different fusion strategies, with results summarized in Table 6. As we can see, no matter which strategy is employed, the performances are consistently higher than the baseline method. Selecting the representation most similar to the target can achieve competitive performance. However, as similarity computation relies on labeled data unavailable during testing, we instead average the sampled representations. This discrepancy between training and testing leads to suboptimal performance. Directly ensembling all representations followed by the conv modulation yields the best performance by avoiding information loss. Besides, the results show that the attention-based strategy has worse performances, which may be attributed to the randomly initialized queries to effectively learn the suitable prompt representations. + +# 5. Conclusion + +In this paper, we propose a probabilistic prompt distribution learning method to adapt pre-trained vision-language models for the multi-species APE task. With the diverse key-point prompt construction, probabilistic prompt modeling and cross-modal fusion strategies, PPAP uses text guidance in a more comprehensive and effective manner, presenting a novel solution to the multi-species problem, i.e. large data variance and imbalanced data distribution. PPAP reflects superiority and generalization for multi-species APE on the representative multi-species animal pose benchmarks including AP-10K and AnimalKingdom. + +# Acknowledgements + +This work was supported in part by the National Key Research and Development Project under Grant 2023YFC3806000, in part by the National Natural Science Foundation of China under Grant 62406226 and 61936014, in part sponsored by Shanghai Sailing Program under Grant 24YF2748700, and in part sponsored by Tongji University Independent Original Cultivation Project under Grant 20230106. + +# References + +[1] Jinkun Cao, Hongyang Tang, Hao-Shu Fang, Xiaoyong Shen, Cewu Lu, and Yu-Wing Tai. Cross-domain adaptation for animal pose estimation. In ICCV, pages 9498-9507, 2019. 1, 2 +[2] Youngjae Cho, HeeSun Bae, Seungjae Shin, Yeo Dong Youn, Weonyoung Joo, and Il-Chul Moon. Make prompts adaptable: Bayesian modeling for vision-language prompt learning with data-dependent prior. 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This paper challenges the problem by efficient prompt learning for Vision-Language Pretrained (VLP) models, e.g. CLIP, aiming to resolve the cross-species generalization problem. At the core of the solution lies in the prompt designing, probabilistic prompt modeling and cross-modal adaptation, thereby enabling prompts to compensate for cross-modal information and effectively overcome large data variances under unbalanced data distribution. To this end, we propose a novel probabilistic prompting approach to fully explore textual descriptions, which could alleviate the diversity issues caused by long-tail property and increase the adaptability of prompts on unseen category instance. Specifically, we first introduce a set of learnable prompts and propose a diversity loss to maintain distinctiveness among prompts, thus representing diverse image attributes. Diverse textual probabilistic representations are sampled and used as the guidance for the pose estimation. Subsequently, we explore three different cross-modal fusion strategies at spatial level to alleviate the adverse impacts of visual uncertainty. Extensive experiments on multi-species animal pose benchmarks show that our method achieves the state-of-the-art performance under both supervised and zero-shot settings. The code is available at https://github.com/Raojiyong/PPAP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 135, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 135, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 135, + 594 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 602, + 296, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 602, + 296, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 602, + 296, + 687 + ], + "type": "text", + "content": "Animal Pose Estimation (APE) [1, 16, 20, 21, 37] represents a fundamental vision task, the objective of which is to identify a series of keypoint locations in an animal skeleton. The skeleton (i.e. a set of connected coordinates), serves as a minimal yet informative unit for encoding both static structure and motion cues, thereby providing critical support for understanding animal behaviour. Consequently, APE plays" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 213, + 553, + 380 + ], + "blocks": [ + { + "bbox": [ + 317, + 213, + 553, + 380 + ], + "lines": [ + { + "bbox": [ + 317, + 213, + 553, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 213, + 553, + 380 + ], + "type": "image", + "image_path": "a76d73037140fcdae575fb26810646565a3371e329c65949f91eacf34eba2997.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 392, + 555, + 415 + ], + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 415 + ], + "type": "text", + "content": "Figure 1. The motivation that one key point can be complementarily described in different views (An example of left shoulder)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 423, + 555, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 555, + 460 + ], + "type": "text", + "content": "a significant role in various research fields, such as neuroscience [16, 20], ecology [3, 4], zoology study [9, 21] and biotechnological quests [18, 28]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 460, + 556, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 460, + 556, + 664 + ], + "spans": [ + { + "bbox": [ + 312, + 460, + 556, + 664 + ], + "type": "text", + "content": "In numerous instances [16, 18, 38], researchers have opted to directly apply Human Pose Estimation (HPE) methodologies to animals. However, it is evident that many animal species exhibit pose distributions that deviate significantly from human-specific models, leading to substantial domain shifts. To address the multi-species Animal Pose Estimation (APE) challenge, Category-Agnostic Pose Estimation (CAPE) methods [25, 30] have been investigated. These methods frame keypoint prediction as a keypoint matching problem, necessitating supplementary support sets that belong to the same category as the test image. While promising, this approach introduces additional computational overhead and necessitates prior knowledge of the animal category, thereby limiting its practicality. Moreover, given the substantial data variances observed across species [18, 38], vision-only APE methods falter when confronted with cross-species challenges that rely solely on visual cues." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "type": "text", + "content": "Recently, the multimodal system proposed in [22] has garnered substantial research attention due to its ability to combine complementary data to enhance visual recognition. Despite the distinct visual characteristics of various" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 144, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 144, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 144, + 703 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 67, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 134, + 712 + ], + "type": "text", + "content": "Equal contribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "29438" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "content": "animal species, they share common textual descriptions, as noted in [42]. Consequently, the straightforward approach of setting the keypoint name as the class token, known as deterministic prompt learning, has become prevalent in the current literature [34, 42]. For instance, X-Pose [34] utilizes a fixed text template like \"A [Image Style] photo of a [Keypoint]\", while CLAMP [42] employs a continuous prompt template of \"[Learnable Tokens] + [Keypoint)\". However, existing multimodal APE methods fall short in terms of rich text prompt design. Moreover, manually crafting keypoint-specific prompts is a cumbersome task. As depicted in Figure 1, a solitary textual description often fails to encapsulate all the nuances of a specific keypoint, such as its color, position, and shape. For example, the \"left shoulder\" keypoint can be described from both spatial and color perspectives as \"Left shoulder is near the right shoulder\" and \"The color of the left shoulder is light salmon\", respectively. From a textual standpoint, multiple descriptions provide diverse perspectives, enabling pose estimation to grasp high-level semantics and pinpoint keypoints accurately based on one or more of these cues. On the visual front, the intricacies of wild scenes and the presence of multiple species introduce uncertain statistical shifts compared to the training domain [4, 14, 27]. Given this \"uncertainty\" in potential data variations, synthesizing novel feature statistics variants to model diverse representations can bolster the network's robustness against unseen categories. To address these challenges, this paper introduces a novel probabilistic method that enhances network generalization to handle unseen categories by adeptly modeling keypoint-adaptive prompts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 435, + 294, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 435, + 294, + 624 + ], + "spans": [ + { + "bbox": [ + 57, + 435, + 294, + 624 + ], + "type": "text", + "content": "Our approach leverages multiple learnable text prompts to enhance flexibility and robustness in text prompt initialization, moving beyond a single template. By strategically inserting keypoint names within templates, we enable flexible sentence construction akin to natural language. We hypothesize that prompt statistics, incorporating uncertainties, follow a multivariate Gaussian distribution, with the center defined by the original prompt statistic and the range indicating data variation across animal categories. We estimate this range using mini-batch statistics in a parametric learning framework and randomly sample variants from the estimated distribution to model diverse textual descriptions, as illustrated in Figure 2. To capture diverse and informative keypoint attributes, we introduce a novel diversity loss function that ensures distinctiveness across prompt distributions. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 629, + 294, + 712 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 55, + 629, + 294, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 294, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 294, + 664 + ], + "type": "text", + "content": "- We propose a novel Probabilistic Prompt Distribution Learning framework for APE to learn the probabilistic representation of specific keypoint descriptions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 666, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 666, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 56, + 666, + 294, + 712 + ], + "type": "text", + "content": "- We introduce multiple prompt attributes and design a diversity loss to prevent the learned attributes from being identical. Additionally, we explore three different cross-modal fusion strategies to achieve spatial adaptation." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 72, + 553, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 107 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 107 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of the proposed probabilistic-based approach through extensive experiments on multi-species animal pose estimation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 121, + 405, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 405, + 133 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 405, + 133 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 141, + 449, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 141, + 449, + 153 + ], + "spans": [ + { + "bbox": [ + 314, + 141, + 449, + 153 + ], + "type": "text", + "content": "2.1. Animal Pose Estimation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 159, + 553, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 553, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 553, + 589 + ], + "type": "text", + "content": "Typical vision-only APE methods [1, 16, 18, 23, 31, 38], with most directly adapting human pose estimation methods [13, 26, 29, 32, 36, 39], such as DeepLabCut [9, 16], AP-10K [26, 38] and ViTPose [32, 33] to animal counterpart. These methods leverage powerful visual backbones for feature extraction but fail to handle rare or even unseen categories explicitly. The relatively limited animal data volume compared to its human counterpart increases the risk of overfitting in complex networks [4]. To cope with the limited labelled animal data volume, direct attempts [10, 17] learn prior-aware knowledge from synthetic animal datasets, and generate pseudo labels for unlabelled data. In terms of refining the pseudo labels, ScarceNet [11] and FreeNet[40] propose the novel semi-supervised learning methods that improves the reliability of pseudo label generation, effectively mitigating the data scarcity problem. Following the principles of few-shot learning, Xu et al. [30] proposed a novel Category-Agnostic Pose Estimation (CAPE) paradigm, which treats keypoint prediction as the keypoint matching problem, enabling the prediction of poses on unseen categories. This is accomplished by offering a few support sets from the same category as the test image to guide the learning process. CAPE [19, 25, 30] introduces an additional computational burden and necessitates prior animal categories, making the methods less practical. To eliminate the reliance on category-specific prior, pretrained VLMs have been applied in the APE. CLAMP [42] is the first text-guided APE method, aligning text-visual features at both the feature and spatial levels, thereby enabling the textual prompt to effectively align the visual representation. X-Pose [34] proposes an end-to-end pose estimation framework that leverages both visual and textual prompts to support keypoint prediction for arbitrary targets. In view of this, we focus on designing keypoint prompts that offer enriched keypoint representations, facilitating accurate pose estimation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 600, + 484, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 600, + 484, + 612 + ], + "spans": [ + { + "bbox": [ + 314, + 600, + 484, + 612 + ], + "type": "text", + "content": "2.2. Deterministic Prompt Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "type": "text", + "content": "Prompt learning [5, 6, 24, 43, 44] aims to adapt foundation models to downstream tasks by efficiently optimizing prompts. CoOp [44] represents a seminal application of prompt learning in VLMs, transforming hard-coded discrete prompt templates into learnable continuous prompts. CoCoOp [43], as its variants, integrates image-conditioned knowledge into text prompts to enhance generalization to unseen classes. Similarly, DenseCLIP [24] employs a" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "29439" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 553, + 238 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 553, + 238 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 553, + 238 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 553, + 238 + ], + "type": "image", + "image_path": "5834ab97d8f33e2a02ff383be4f75318361d081ef9418fbd95b0f6571e7ff655.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 251, + 555, + 305 + ], + "lines": [ + { + "bbox": [ + 54, + 251, + 555, + 305 + ], + "spans": [ + { + "bbox": [ + 54, + 251, + 555, + 305 + ], + "type": "text", + "content": "Figure 2. Overall framework of PPAP. Firstly, we create " + }, + { + "bbox": [ + 54, + 251, + 555, + 305 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 54, + 251, + 555, + 305 + ], + "type": "text", + "content": " keypoint attribute templates and generate distinctive embeddings for these attributes using a text encoder. Each keypoint prompt embedding is represented probabilistically as a multivariate Gaussian distribution, with its mean derived from the text decoder and variance from the visual-text decoder. Subsequently, we sample these keypoint prompt representations from the distribution and perform cross-modal fusion during the spatial adaptation stage to capture the spatial relationship between textual and visual content." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 312, + 294, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 312, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 54, + 312, + 294, + 407 + ], + "type": "text", + "content": "Transformer to facilitate interaction between visual context and textual prompts, producing context-aware prompts for improved performance. Building upon this, PromptSRC [6] uses a set of hand-crafted prompts and introduces several regularization losses to prompt learning. To further improve diversity, we specialize different keypoint prompts to guide spatial adaptation for different animal categories, thus aligning them with different attribute sets for each keypoint." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 415, + 222, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 222, + 427 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 222, + 427 + ], + "type": "text", + "content": "2.3. Probabilistic Prompt Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 431, + 296, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 431, + 296, + 659 + ], + "spans": [ + { + "bbox": [ + 56, + 431, + 296, + 659 + ], + "type": "text", + "content": "Compared to deterministic prompt learning, probabilistic prompt learning [2, 8, 15] is not tied to specific classes, making it more adaptable to cross-species challenges with prompt adjustments. APP [2] proposes a Bayesian-based prompt learning framework to enhance the flexibility and adaptability of input embeddings. However, various descriptions are dispersed in the input space, resulting in difficulty in representing their distribution. Several studies focus on probabilistic learning within the output embedding space. ProDA [15] is the first probabilistic prompt model, allowing for straightforward modeling by a multivariate Gaussian distribution. PPL [8] introduces attribute prompts to represent shared attributes across different categories by constructing a mixture of Gaussian distribution to address dense prediction problems. Conversely, we prioritize probabilistic modeling for each individual prompt rather than constructing a single overarching distribution, as it provides us with nuanced contextual information better and shows greater generalization to unseen data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 669, + 111, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 111, + 681 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 111, + 681 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "To enhance the generalization capabilities for multi-species animal data, we propose a probabilistic prompt learn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 312, + 555, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 373 + ], + "type": "text", + "content": "ing technique. This technique is grounded in the Contrastive Learning for Connecting Language and Animal Pose (CLAMP) framework [42]. We begin by providing a concise overview of CLAMP's fundamental principles before presenting our probabilistic prompt learning method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 379, + 400, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 379, + 400, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 379, + 400, + 390 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": "CLAMP is proposed based on the powerful model CLIP [22]. Given an image and its corresponding textual description, CLIP extracts textual and visual embeddings by processing the input through a text encoder and an image encoder, respectively. To effectively leverage the textual description for APE, CLAMP uses a pose-specific template " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "p_n = \\{T_l\\}_{l=1}^L[KeyPoint]_n" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " to represent " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": "-th keypoint prompt, where " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "\\{T_l\\}_{l=1}^L" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " learnable prefix tokens, and " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "[Keypoint]_n" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": "-th keypoint name token. Then prompt embedding " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "E_{prompt} \\in \\mathbb{R}^{K \\times C_{emb}}" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " is obtained by the prompt encoder. To establish spatial connections between textual description and image features, CLAMP performs cross-modal adaptation at both spatial and feature levels. In the spatial adaptation stage, the extracted prompt representations and image features are used to generate score map " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{K \\times H \\times W}" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " represent the height, width and the number of keypoints, respectively. This " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " is utilized to indicate the probability of keypoint occurrence at specific locations. Besides, the spatial objective " + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{spatial}" + }, + { + "bbox": [ + 313, + 396, + 556, + 634 + ], + "type": "text", + "content": " is calculated as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 344, + 644, + 555, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 644, + 555, + 658 + ], + "spans": [ + { + "bbox": [ + 344, + 644, + 555, + 658 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s p a t i a l}} = M S E (U p s a m p l e (S), H _ {\\text {t a r g e t}}), \\tag {1}", + "image_path": "61c7279b4b68b3d1d10aac69018965a8cce21b497bfefb8068b79812094294b1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "MSE" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": " denotes mean squared error, Upsample is the upsample operation, and " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "H_{target}" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": " is the target heatmap. Meanwhile, in the feature adaptation stage, ground truths are performed to grid-sample local keypoint" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29440" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "features " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "F_{keypoint} \\in \\mathbb{R}^{K \\times C_{emb}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": " from image embeddings. The pairwise similarity " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "M = F_{keypoint} \\cdot E_{prompt}^T" + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": " is utilized to facilitate feature alignment:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 114, + 295, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 114, + 295, + 137 + ], + "spans": [ + { + "bbox": [ + 61, + 114, + 295, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t u r e}} = \\frac {1}{2} \\left(C E (M, M _ {\\text {l a b e l}}) + C E \\left(M ^ {T}, M _ {\\text {l a b e l}}\\right)\\right), \\tag {2}", + "image_path": "25e66300e63f1af8b2d23ca1a31bdf4206c5e8f5d115e67202661865a9ce9a86.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "text", + "content": " denotes cross-entropy loss and " + }, + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "inline_equation", + "content": "M_{label}" + }, + { + "bbox": [ + 55, + 143, + 296, + 228 + ], + "type": "text", + "content": " is the diagonal matrix, used as matching target. Building on these two adaptations, we introduce a set of learnable keypoint-agnostic prompts, modeling each prompt distribution with a Gaussian. Finally, we explore three fusion strategies for spatial adaptation and design a novel pose estimation paradigm to handle the multi-species APE." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 233, + 217, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 233, + 217, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 217, + 246 + ], + "type": "text", + "content": "3.2. Diverse Prompt Construction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "text", + "content": "Relying solely on visual features and the keypoint name prompt proves to be insufficient to address the long-tail problem present in animal datasets [18, 38]. As previous literature [8, 15] indicated, multiple diverse prompts could offer enriched semantics to aid multi-modal models in recognizing visual patterns, thereby alleviating the adverse impact of long-tail challenge. However, it is hard to explicitly identify \"what constitutes useful keypoint visual attributes for locating keypoints?\". To this end, we introduce multiple learnable textual attribute prompts for each keypoint to constitute the prompt templates. Formally, as illustrated in Figure 2, for the " + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "text", + "content": "-th keypoint token " + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "text", + "content": ", we create " + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 55, + 251, + 296, + 418 + ], + "type": "text", + "content": " keypoint attribute templates for each keypoint by combining learnable attribute description tokens." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 426, + 295, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 426, + 295, + 440 + ], + "spans": [ + { + "bbox": [ + 83, + 426, + 295, + 440 + ], + "type": "interline_equation", + "content": "p _ {i} ^ {t} = \\left\\{a _ {1} ^ {t}, a _ {2} ^ {t}, \\dots , a _ {L} ^ {t} \\mid k _ {i} \\right\\}, \\quad t = 1, \\dots , N _ {p}, \\tag {3}", + "image_path": "d40c5036af3bd3c3288216ef3616a3975651bd38116d7955708ffbd85732840c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "inline_equation", + "content": "\\{a_1^t, a_2^t, \\ldots, a_L^t\\}" + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "text", + "content": " comprises " + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "text", + "content": " learnable attribute tokens, initialized randomly with \"X X ... X\". As shown in Figure 1, we aim to simulate the locations of keypoint in natural language descriptions. To this end, we introduce the Generalized Keypoint Placement (GKP) strategy, enabling flexible placement of keypoint names within the prompt template for enhanced naturalness and diversity. Unlike the insertion strategy used in ProDA [15], which restricts keypoint placement to specific positions (i.e. beginning, middle, or end), our approach permits random placement throughout the template, offering greater positional flexibility. During training, these tokens are optimized to better suit APE tasks, offering increased contextual flexibility. By inputting the textual attribute prompts into the text encoder " + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "inline_equation", + "content": "\\theta(\\cdot)" + }, + { + "bbox": [ + 55, + 445, + 296, + 637 + ], + "type": "text", + "content": ", we can obtain the encoded diverse prompt representations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 92, + 643, + 295, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 643, + 295, + 659 + ], + "spans": [ + { + "bbox": [ + 92, + 643, + 295, + 659 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {i} = \\{\\theta (\\boldsymbol {p} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\quad \\tilde {\\boldsymbol {P}} _ {i} = \\{\\theta (\\tilde {\\boldsymbol {p}} _ {i} ^ {t}) | _ {t = 1} ^ {N _ {p}} \\}, \\qquad (4)", + "image_path": "78da32ebcf3c1616e6b2f2c0226f11cf25e6ae3e5f1fc1161aeced1b6e67a109.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " denotes the complete embedding for the " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "-th keypoint prompt. Meanwhile, " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{p}_i^t" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " represents attribute tokens excluding keypoint names, and " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{P}_{i}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " signifies the keypoint-agnostic attribute embedding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": "Multiple Attributes Diversity Loss. To make the keypoint-agnostic attribute representations capture distinct content, we introduce diversity among representations, and design a novel diversity loss to keep differentiation between them. The specific formulation is as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 322, + 140, + 554, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 140, + 554, + 175 + ], + "spans": [ + { + "bbox": [ + 322, + 140, + 554, + 175 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i v} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {\\boldsymbol {P}} _ {i} \\tilde {\\boldsymbol {P}} _ {i} ^ {T} - \\mathbb {I} \\| _ {2} ^ {2}, \\quad \\mathbb {I} = \\operatorname {d i a g} (\\underbrace {1 , 1 , \\dots , 1} _ {N _ {p}}). \\tag {5}", + "image_path": "68025db2b52a85a96d4ac7023f50283d67e501540438f2c1f4d9bbd2e18310ad.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 182, + 554, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 554, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 554, + 255 + ], + "type": "text", + "content": "The diversity loss applies a squared " + }, + { + "bbox": [ + 313, + 182, + 554, + 255 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 313, + 182, + 554, + 255 + ], + "type": "text", + "content": "-norm penalty on attribute representations to foster greater dissimilarity among them, thereby amplifying attribute diversity. Subsequently, the resultant prompt representations encapsulate the abundant and varied textual semantics, providing enhanced contextual support for subsequent visual localization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 263, + 484, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 484, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 484, + 276 + ], + "type": "text", + "content": "3.3. Probabilistic Prompt Modeling" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": "Based on the observation [15]: the output embedding of the descriptions within a category are close to each other, allowing them to be modeled with a sample distribution, i.e. Gaussian. We propose a probabilistic prompt learning strategy to reformulate the prompt distribution. As subsection 3.2 discussed, we strive to maintain orthogonality among the attribute embeddings. Thus, these embeddings are better represented as independent Gaussian distributions, each characterized by distinct means and variances. For each " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": ", we define a probabilistic distribution " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(z_i^t | p_i^t)" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": " as a factorized Gaussian with its center vector " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\mu_i^t" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": " and variance matrix " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\sigma_i^t" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": "-th attribute for the " + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 280, + 555, + 437 + ], + "type": "text", + "content": "-th keypoint. This distribution is formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 372, + 445, + 553, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 445, + 553, + 461 + ], + "spans": [ + { + "bbox": [ + 372, + 445, + 553, + 461 + ], + "type": "interline_equation", + "content": "\\mathcal {G} \\left(z _ {i} \\mid p _ {i}\\right) \\sim \\left\\{\\mathcal {N} \\left(\\boldsymbol {\\mu} _ {i} ^ {t}, \\boldsymbol {\\sigma} _ {i} ^ {t} \\mathbf {I}\\right) \\right\\} _ {t = 1} ^ {N _ {p}}. \\tag {6}", + "image_path": "443127adfe26bb9b4ba20bf8ba423506fb8b35cbf99e59f8d297052b4abaf682.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "text", + "content": "Specifically, we introduce a text decoder to obtain the mean of Gaussian distribution " + }, + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_i^t" + }, + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "text", + "content": " and a visual-text decoder for the variances " + }, + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "inline_equation", + "content": "\\sigma_i^t" + }, + { + "bbox": [ + 313, + 470, + 554, + 542 + ], + "type": "text", + "content": ", as illustrated in Figure 2. In the text decoder, we facilitate interaction among prompt embeddings by self-attention (SA) module, as well as a form of self-augmentation. The default number of the layer is set to 1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 340, + 553, + 553, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 553, + 553, + 569 + ], + "spans": [ + { + "bbox": [ + 340, + 553, + 553, + 569 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + S A \\left(L N \\left(q _ {i} ^ {t}, k _ {i} ^ {t}, v _ {i} ^ {t}\\right)\\right), \\tag {7}", + "image_path": "c352201b28b7aae672fb09cf9b281b51a302a70c88bb8e9a251bbc098f794780.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "spans": [ + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": "where the query " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "q_{i}^{t}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "k_{i}^{t}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "v_{i}^{t}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": " are all derived from prompt embedding " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "LN" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "MLP" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": " denote layer norm and multilayer perceptron layer, respectively. Meanwhile, in the visual-text decoder Here, the key " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "v_{k}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "v_{\\mathrm{v}}" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": " vectors are both obtained from the " + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 572, + 554, + 644 + ], + "type": "text", + "content": ". The variance matrix of each attribute representation is computed as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 339, + 654, + 553, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 654, + 553, + 669 + ], + "spans": [ + { + "bbox": [ + 339, + 654, + 553, + 669 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\sigma} _ {i} ^ {t} = M L P \\left(L N \\left(q _ {i} ^ {t}\\right)\\right) + C A \\left(L N \\left(q _ {i} ^ {t}, v _ {k}, v _ {\\mathrm {v}}\\right)\\right), \\tag {8}", + "image_path": "eff6d488d1ab1b45760bdaf72eb5c0d51961bcef997a2b83e6d441778cb75cb2.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "where CA stands for cross-attention module. Once the statistics of each keypoint description are obtained, the Gaussian distribution for probabilistic prompt statistics can" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29441" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": "be established. By exploiting the Gaussian distribution, random sampling can generate various new feature statistics information with different means and variances. Therefore, we adopt random sampling to further exploit the probabilistic representations. " + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": " prompt representations are sampled for " + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": "-th keypoint with " + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": "-th attribute " + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "inline_equation", + "content": "z_{i}^{t} = \\{z_{i}^{1},\\ldots ,z_{i}^{N_{s}}\\} \\stackrel {i.i.d.}{\\sim}\\mathcal{G}(z_{i}^{t}|p_{i}^{t})" + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": ", and we interpret " + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "inline_equation", + "content": "z_{i}^{t}" + }, + { + "bbox": [ + 55, + 72, + 296, + 194 + ], + "type": "text", + "content": " as independently enriched contextual description. Here we use the re-parameterization trick [7] to make the sampling operation differentiable." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 199, + 295, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 199, + 295, + 214 + ], + "spans": [ + { + "bbox": [ + 94, + 199, + 295, + 214 + ], + "type": "interline_equation", + "content": "\\hat {z} _ {i} ^ {t} = \\mu \\left(p _ {i} ^ {t}\\right) + \\epsilon \\cdot \\sigma \\left(p _ {i} ^ {t}\\right), \\quad \\epsilon \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}), \\tag {9}", + "image_path": "fcb7b22df39847263238ce9aa85ca209d8290f9526d83c6d9ef187129a627b10.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "inline_equation", + "content": "\\mu(p_i^t)" + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "inline_equation", + "content": "\\sigma(p_i^t)" + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": " are mean and standard deviation of distribution " + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(z_i^t | p_i^t)" + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": " follows the standard normal distribution. Finally, we obtain a set of diverse prompt representations " + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "inline_equation", + "content": "\\hat{z}_i^t" + }, + { + "bbox": [ + 55, + 217, + 296, + 302 + ], + "type": "text", + "content": " for each keypoint. To prevent learned variances from collapsing to zero, we employ an additional KL divergence regularizer between prompt distributions and the Gaussian prior, forming the keypoint prompt loss:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 305, + 295, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 305, + 295, + 335 + ], + "spans": [ + { + "bbox": [ + 67, + 305, + 295, + 335 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {d i v}} + \\frac {1}{N _ {p}} \\sum_ {t} ^ {N _ {p}} K L \\left(\\mathcal {G} \\left(\\hat {z} _ {i} ^ {t} \\mid p _ {i} ^ {t}\\right) \\| \\mathcal {N} (\\mathbf {0}, I)\\right). \\tag {10}", + "image_path": "a3e3a6dc750a146f3ec550f666c8b38e6d031d8c17bd77810460b8db7410a306.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 338, + 174, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 174, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 174, + 350 + ], + "type": "text", + "content": "3.4. Cross-Modal Fusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": "Once various prompt embeddings have been obtained, the problem of \"how to align them with the visual features?\" inevitably arises. Given these prompt representations, we explore three strategies for multi-modal information fusion: 1) heuristic selection; 2) ensemble selection; 3) attention-based selection. Specifically, the heuristic selection strategy computes the similarity between the " + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": " sampled score maps " + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "inline_equation", + "content": "S' \\in \\mathbb{R}^{N_s \\times K \\times H \\times W}" + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": " and the keypoints target " + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "inline_equation", + "content": "H_{target} \\in \\mathbb{R}^{K \\times H \\times W}" + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": ", assigning the most similar ones as the final score map " + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": ". Thus, the score map for the " + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 356, + 296, + 548 + ], + "type": "text", + "content": "-th keypoint is voted from all the sampling turns. The ensemble selection strategy considers all the representations to contain informative context. To prevent the loss of textual cues, we concat score maps and apply convolution operation (Conv) for signal modulation, ultimately generating the final score map." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 122, + 552, + 295, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 552, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 122, + 552, + 295, + 567 + ], + "type": "interline_equation", + "content": "S = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(S ^ {\\prime}\\right)\\right). \\tag {11}", + "image_path": "add7d5c21bd3f0649c905191be2cdbc76343f414f1b2d6399a7d5d62cf69f77f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 571, + 296, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 571, + 296, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 571, + 296, + 654 + ], + "type": "text", + "content": "For the attention-based selection, we introduce an additional learnable query to leverage the attention module for capturing relationships between the query embedding and the prompt representations. We predefine the query embedding, i.e. " + }, + { + "bbox": [ + 55, + 571, + 296, + 654 + ], + "type": "inline_equation", + "content": "q_{i} \\in \\mathbb{R}^{K \\times (HW)}" + }, + { + "bbox": [ + 55, + 571, + 296, + 654 + ], + "type": "text", + "content": " for learning the suitable prompt representation. Meanwhile, the attention module takes the sampled prompts as key and value, which is formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 96, + 659, + 294, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 659, + 294, + 716 + ], + "spans": [ + { + "bbox": [ + 96, + 659, + 294, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} S _ {i} = \\text {F l a t t e n} \\left(S ^ {\\prime}\\right), \\\\ Q _ {i} = q _ {i} W _ {q}, K _ {i} = S _ {i} W _ {k}, V _ {i} = S _ {i} W _ {v}, \\tag {12} \\\\ S _ {i} = Q _ {i} + W _ {a} (\\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {H W}}\\right) V _ {i}), \\\\ \\end{array}", + "image_path": "d3660c1f14bf995399ffa3128910b354fd5b90c63155465e4bc2afa492333818.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "W_{q}, W_{k}, W_{v}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " are learnable linear projections, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "-th keypoint score map. Subsequently, " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " is reshaped back to 2D with the final score map " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "S = \\{S_{i}\\}_{i=1}^{K}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": ". Unless otherwise specified, we choose two attention layers in our experiments as default." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 139, + 378, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 139, + 378, + 152 + ], + "spans": [ + { + "bbox": [ + 314, + 139, + 378, + 152 + ], + "type": "text", + "content": "3.5. Training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "text", + "content": "Total objective. For the pose estimation task, we employ the commonly used MSE loss " + }, + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pred}" + }, + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "text", + "content": ", and the total objective " + }, + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 313, + 156, + 553, + 192 + ], + "type": "text", + "content": " is formulated as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 196, + 553, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 196, + 553, + 213 + ], + "spans": [ + { + "bbox": [ + 324, + 196, + 553, + 213 + ], + "type": "interline_equation", + "content": "\\begin{array}{l l} \\mathcal {L} _ {p r e d} = M S E (F _ {o}, H _ {t a r g e t}), & F _ {o} = H E A D (F _ {v i s} \\oplus S), \\\\ f _ {o} = f _ {o + 1} + f _ {o + 2} + \\dots + f _ {o + n} + \\dots + f _ {o + n - 1} \\end{array} \\tag {13}", + "image_path": "c3ffb32e182e90134603250c2e99989b25efa08bda435833ea17a7564131439c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 326, + 210, + 530, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 210, + 530, + 220 + ], + "spans": [ + { + "bbox": [ + 326, + 210, + 530, + 220 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {p r e d}} + \\mathcal {L} _ {\\text {s p a t i a l}} + \\gamma \\cdot \\mathcal {L} _ {\\text {f e a t u r e}} + \\beta \\cdot \\mathcal {L} _ {\\text {p r o m p t}},", + "image_path": "76f9cb7f5d978fcc441416099ee0c3f0f9d8ae3d9cafa62f89eb3d092f0bc1b5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "spans": [ + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "inline_equation", + "content": "F_{vis}" + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "text", + "content": " denotes the visual features output by image encoder, and HEAD is the common keypoint prediction head [29], which consists of multiple deconvolution and MLP layers. The coefficient " + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 224, + 554, + 283 + ], + "type": "text", + "content": " are hyper-parameters, which are discussed in detail in the ablation study section." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 293, + 395, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 395, + 307 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 395, + 307 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 313, + 364, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 313, + 364, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 313, + 364, + 326 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": "Datasets and evaluation metrics. (1) AP-10K [38] is a large-scale benchmark for multi-species animal pose estimation and contains over 10K images collected and filtered from 23 animal families and 54 species with 17 key points. We employ the mean average precision (AP) as the primary evaluation metric. Average recall (AR) and APs at different OKS (Object Keypoint Similarity) thresholds are also reported, i.e. AR, AP.5 and AP.75, as well as APs for different instance sizes, i.e. " + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^M}" + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^L}" + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": ". (2) AnimalKingdom [18] is a more challenging dataset, which includes over 33K samples with 23 keypoints across 850 species in 6 classes. Unlike AP-10K, AnimalKingdom contains a larger number of categories with more imbalanced and diverse data distribution, enhancing its difficulty. Besides, AnimalKingdom define three protocols (P1, P2, P3) for different tasks. P1-All involves training on the whole dataset for supervised learning. P2-LeaveKOut selects k sub-classes for training and performs few-shot learning on the remaining subclasses. P3-Amphibians/Birds/Fishes/Mammals/Reptiles specifies training within each distinct animal class, enabling zero-shot learning on unseen classes. We report the Percentage of Correct Keypoint " + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "inline_equation", + "content": "(\\mathrm{PCK}@\\alpha)" + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": " score for evaluation, which computes the percentage of correct keypoints whose distance to ground truth is within " + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": " times the longest bounding box side. Besides, we adhere to the evaluation protocol in [18], and set " + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "inline_equation", + "content": "\\alpha = 0.05" + }, + { + "bbox": [ + 313, + 331, + 555, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "content": "Implementation details. We follow the widely-used two-stage pose estimation paradigm in our experiments. The ground-truth bounding box annotations are utilized to crop the instance target, which is subsequently resized to a uniform shape. We select the representative CNN-based model ResNet alongside the transformer-based model ViT" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29442" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 70, + 553, + 296 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 553, + 296 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 553, + 296 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 553, + 296 + ], + "type": "table", + "html": "
MethodsDatasetBackboneAPAP·50AP·75APMAPLAR
Foundation Models
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Base74.594.982.246.875.070.0
ViTPose++ [33]Mixed Datasets(387K)MAE / ViT-Large80.497.688.552.780.8-
SuperAnimal [37]Quadruped-80KHRNet-W3280.1-----
X-Pose-V [34]UniKPT(226K)Swin-Tiny73.691.980.647.274.2-
X-Pose-V [34]UniKPT(226K)Swin-Large79.095.786.857.079.6-
Expert Models
SimpleBaseline [29]AP-10KResNet-5070.294.276.045.570.473.5
HRNet [26]AP-10KHRNet-W3273.895.880.352.374.276.9
HRNet [26]AP-10KHRNet-W4874.495.980.758.974.8-
TokenPose [12]AP-10KHRNet-W4872.794.379.260.672.775.7
TransPose [35]AP-10KHRNet-W4874.295.780.856.274.677.0
HRFormer [39]AP-10KHRFormer-B74.595.981.655.874.977.6
Prompt-based Models
CLAMP [42]AP-10KCLIP / ResNet-5072.995.479.443.273.276.3
PPAP (Ours)AP-10KCLIP / ResNet-5073.494.179.957.173.876.5
CLAMP [42]AP-10KCLIP / ViT-Base74.395.881.447.674.977.5
PPAP (Ours)AP-10KCLIP / ViT-Base75.495.883.053.475.978.7
CLAMP [42]AP-10KCLIP / ViT-Large77.896.885.058.778.181.0
PPAP (Ours)AP-10KCLIP / ViT-Large78.697.186.159.378.981.7
", + "image_path": "bd839f0bcb3bb76834ac5959711a1165292fbcc82a756c027f800662c103e294.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 342, + 394, + 399 + ], + "blocks": [ + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "lines": [ + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "spans": [ + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "type": "text", + "content": "Table 1. Performance comparisons on AP-10K val set. The image resolution is " + }, + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "type": "text", + "content": ", with an exception for ViTPose++, which utilizes a resolution of " + }, + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "type": "inline_equation", + "content": "256 \\times 192" + }, + { + "bbox": [ + 55, + 303, + 555, + 336 + ], + "type": "text", + "content": ". Notably, the foundation models, such as ViTPose++, are trained on mixed datasets with extra corpora, which can be regarded as an upper bound for model performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 342, + 394, + 399 + ], + "lines": [ + { + "bbox": [ + 56, + 342, + 394, + 399 + ], + "spans": [ + { + "bbox": [ + 56, + 342, + 394, + 399 + ], + "type": "table", + "html": "
MethodsBackboneP3-Amph.P3-BirdsP3-FishesP3-Mam.P3-Rep.P1-All
CLAMP [29]CLIP / ResNet-5051.876.162.454.043.560.5
PPAP (Ours)CLIP / ResNet-5051.976.562.455.548.260.9
CLAMP [29]CLIP / ViT-Base58.976.965.359.255.762.8
PPAP (Ours)CLIP / ViT-Base60.978.066.161.256.664.5
", + "image_path": "87f39062cf3ce60ec0d3f0fb3202155949affb415f1bc3959c45b7d6903dddca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 116, + 400, + 318, + 410 + ], + "lines": [ + { + "bbox": [ + 116, + 400, + 318, + 410 + ], + "spans": [ + { + "bbox": [ + 116, + 400, + 318, + 410 + ], + "type": "text", + "content": "(a) Comparisons across various protocols on AnimalKingdom." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 401, + 342, + 541, + 398 + ], + "blocks": [ + { + "bbox": [ + 401, + 342, + 541, + 398 + ], + "lines": [ + { + "bbox": [ + 401, + 342, + 541, + 398 + ], + "spans": [ + { + "bbox": [ + 401, + 342, + 541, + 398 + ], + "type": "table", + "html": "
MethodsBackboneP1-All
HRNet [26]HRNet-W3266.1
DARK [41]HRNet-W3266.6
CLAMP [42]ViT-Large65.6
PPAP (Ours)ViT-Large68.4
", + "image_path": "5eec807cd9fed048360676857220880c7a628b6a766ac6c60dfe26c9ffb75174.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 406, + 399, + 543, + 409 + ], + "lines": [ + { + "bbox": [ + 406, + 399, + 543, + 409 + ], + "spans": [ + { + "bbox": [ + 406, + 399, + 543, + 409 + ], + "type": "text", + "content": "(b) Comparisons with the SOTA methods." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 60, + 411, + 547, + 423 + ], + "lines": [ + { + "bbox": [ + 60, + 411, + 547, + 423 + ], + "spans": [ + { + "bbox": [ + 60, + 411, + 547, + 423 + ], + "type": "text", + "content": "Table 2. Performance comparisons on the AnimalKingdom test set (PCK@0.05). The input resolution of all methods is " + }, + { + "bbox": [ + 60, + 411, + 547, + 423 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 60, + 411, + 547, + 423 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 434, + 295, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 434, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 54, + 434, + 295, + 506 + ], + "type": "text", + "content": "as backbones, serving as feature extractors in our framework. The text encoder after CLIP pre-training is adopted as our language models and initialized with the corresponding CLIP pre-trained weights. For prompt learning, we configure the length of the learnable context tokens to match CLAMP, setting " + }, + { + "bbox": [ + 54, + 434, + 295, + 506 + ], + "type": "inline_equation", + "content": "L = 8" + }, + { + "bbox": [ + 54, + 434, + 295, + 506 + ], + "type": "text", + "content": " for fair comparisons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "spans": [ + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "content": "During training, we use " + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "content": " input images and applied data augmentation including random rotation, scaling, flipping, and half-body transformation. All models are trained for 210 epochs with a step-wise learning rate scheduler that decreases by a factor of 10 at the 170th and 200th epochs. We used the AdamW optimizer with a weight decay of " + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "inline_equation", + "content": "2.5e - 5" + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "content": " and froze the text encoder to preserve pretrained language knowledge. Supervised learning experiments were conducted to evaluate performance on both AP-10K and AnimalKingdom, with a batch size of 64, an initial learning rate of " + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "inline_equation", + "content": "3e - 4" + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "inline_equation", + "content": "N_{p} = N_{s} = 2" + }, + { + "bbox": [ + 54, + 506, + 295, + 650 + ], + "type": "text", + "content": " for attribute embeddings and sampling turns, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 657, + 175, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 175, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 175, + 670 + ], + "type": "text", + "content": "4.2. Results and Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 674, + 175, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 175, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 175, + 686 + ], + "type": "text", + "content": "4.2.1. Supervised Learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "Table 1 presents the results under the supervised learning setting on AP-10K [38], comparing our method with repre" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 434, + 555, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 555, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 555, + 602 + ], + "type": "text", + "content": "sentative expert models for pose estimation. It can be observed that probabilistic prompt learning contributes to improved performance in multi-species APE under the prompt learning paradigm. With the basic ResNet-50 as the feature extractor, PPAP achieves a modest AP improvement of 0.5, which we attribute to the limited capacity of the feature extractor in capturing sufficient image features. When switching to the more powerful ViT-Base backbone, PPAP achieves 75.4 AP and outperforms CLAMP by 1.1 points. These observations indicate that our prompt learning approach offers a more effective solution to the challenges posed by significant data variance in multi-species Animal Pose Estimation (APE), as opposed to merely relying on the keypoint name prompt." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Furthermore, we conduct comparisons against expert pose estimation models, validating our approach's effectiveness. On the AP-10K validation set, our PPAP method significantly outperforms the SimpleBaseline by 3.2 AP when using the ResNet-50 backbone, compared to the state-of-the-art CNN-based expert models. Additionally, when equipped with the ViT-Base backbone, our approach achieves 1.6 and 1.0 AP gains over the highly representative pose estimation model HRNet, respectively. In par" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29443" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 291, + 227 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 291, + 227 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 291, + 227 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 291, + 227 + ], + "type": "table", + "html": "
MethodTrainTestPCK@0.05
ResNet-50CLAMP PPAPFishesBirds9.5
FishesBirds9.8 (↑ 0.3)
CLAMP PPAPMammalsAmphibians6.8
MammalsAmphibians9.8 (↑ 3.0)
CLAMP PPAPReptilesAmphibians19.2
ReptilesAmphibians19.3
ViT-BaseCLAMP PPAPFishesBirds0.1
FishesBirds12.0 (↑ 11.9)
CLAMP PPAPMammalsAmphibians12.3
MammalsAmphibians16.5 (↑ 4.2)
CLAMP PPAPReptilesAmphibians20.8
ReptilesAmphibians21.8 (↑ 1.0)
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LdivKLGKPAPΔ
74.30
✓74.9+0.6
✓74.9+0.6
✓✓75.2+0.9
✓✓✓75.4+1.1
", + "image_path": "a12f4bc0d413465af795a48bb285375ae182db9c483c8bc064591caf68440f94.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 362, + 295, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 295, + 481 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 295, + 481 + ], + "type": "text", + "content": "ticular, PPAP also demonstrates notable performance improvements of 2.7 and 1.2 AP, respectively, when compared to hybrid architectures such as TokenPose and TransPose. We also observe that these methods underperform on multi-species animal datasets compared to human ones, all falling below HRNet. This is due to their inability to manage large data variances, highlighting our approach's effectiveness in overcoming this challenge. Besides, PPAP surpasses HRFformer by 0.9 AP when compared to a plain transformer-based architecture." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 484, + 295, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 592 + ], + "type": "text", + "content": "It's worth mentioning that foundation models are trained across multiple datasets like Quadruped-80K [37] and UniKPT-226K [34], allowing them to gain broader knowledge, richer pose priors, and generally enhanced performance. Despite this, our PPAP, trained exclusively on AP10K, matches foundation models with a score of 78.6 vs. 79.0. This indicates that our method's robustness stems not from extensive pose data but from its effective utilization of textual knowledge to tackle multi-species variability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "In addition to AP-10K, we further evaluate the effectiveness of PPAP on the more challenging dataset, AnimalKingdom [18]. The training setting is the same as the previous section. Table 2 reports the performance of prompt-based methods across various protocols on the AnimalKingdom dataset. We observe that the PPAP method consistently achieves superior performance across all protocols. By constructing diverse prompts and employing probabilistic modeling, our PPAP gets gains of 0.4 and 1.7 PCK values with ResNet-50 and ViT-Base, respectively. Notably," + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 554, + 213 + ], + "blocks": [ + { + "bbox": [ + 97, + 341, + 253, + 353 + ], + "lines": [ + { + "bbox": [ + 97, + 341, + 253, + 353 + ], + "spans": [ + { + "bbox": [ + 97, + 341, + 253, + 353 + ], + "type": "text", + "content": "Table 4. Ablation studies on components." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 70, + 554, + 213 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 554, + 213 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 554, + 213 + ], + "type": "table", + "html": "
Number of attributes (γ = 5e-4, β = 1e-5, Ns = Np)
Parameter Np1234
AP74.875.475.175.0
Objective hyper-parameter (Ns = Np = 2)
Parameter β (γ=5e-4)1e-45e-51e-51e-6
AP74.574.875.474.9
Parameter γ (β=1e-5)5e-35e-45e-55e-6
AP73.575.474.775.1
Number of sampled turns (γ = 5e-4, β = 1e-5, Np = 2)
Parameter Ns2468
AP75.474.774.574.6
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StrategyAPAP.50AP.75
heuristic selection75.195.682.1
ensemble selection75.495.883.0
attention-based selection74.695.782.3
", + "image_path": "edc94ab5526c331233e4fa007bd9b96ae455742ca1fd434ec9fb93cd75400f0b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 326, + 312, + 542, + 323 + ], + "lines": [ + { + "bbox": [ + 326, + 312, + 542, + 323 + ], + "spans": [ + { + "bbox": [ + 326, + 312, + 542, + 323 + ], + "type": "text", + "content": "Table 6. Ablation studies on cross-modal fusion strategies." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 331, + 555, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 555, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 555, + 474 + ], + "type": "text", + "content": "the considerable performance gains on specific classes underscore the adaptability of our method. For example, PPAP with ResNet-50 achieves a 4.7 PCK improvement in reptiles, while PPAP with ViT-Base yields a 3.0 PCK increase in mammals. Compared to the existing SOTA methods, our PPAP with ViT-Large outperforms them by 2.0 AP gains. Furthermore, we argue that incorporating the plug-and-play DARK [41] leads to an additional boost in performance. Therefore, by training exclusively on the single pose data, our method achieves a new state-of-the-art performance with the ViT-Large backbone on both multispecies animal pose benchmarks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "type": "text", + "content": "Besides, to intuitively highlight the superiority of our approach, we present qualitative comparisons with CLAMP in Figure 3. Since AP-10K consists of mammals, we specifically select fishes and birds from AnimalKingdom for diversity. Differences in predicted locations are highlighted in red circles, clearly illustrating that our method consistently achieves more precise localization across these three animal classes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 578, + 430, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 430, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 430, + 590 + ], + "type": "text", + "content": "4.2.2. Zero-Shot Learning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": "Given that the AnimalKingdom dataset includes a broader range of classes and presents a more challenging benchmark, we further conduct zero-shot learning experiments on it to evaluate the model's generalization ability on unseen animal species. Since the AnimalKingdom is sourced from wildlife data, it inevitably exhibits a long-tail distribution across various animal species [18]. We select three types of zero-shot settings to compare with the prompt-based method CLAMP [42]. The experiment settings include similar classes (\"Reptiles vs. Amphibians\"), typical" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29444" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 301 + ], + "type": "text", + "content": "classes (\"Mammals vs. Amphibians\"), and highly divergent classes (\"Fishes vs. Birds\"), thereby covering a range of taxonomic variations to fully reflect the generalization of the PPAP for dealing with unseen species. The results are shown in Table 3, which reflects that our PPAP achieves better performance for all three settings. While PPAP achieves only a modest performance gain with ResNet-50, it demonstrates a significantly greater improvement when paired with the more powerful ViT-Base backbone. Interestingly, when trained on Fish and tested on Birds, CLAMP fails to perform pose estimation across such extreme inter-classes variations, resulting in nearly zero PCK value, while PPAP achieves a substantial improvement of 11.9 gains. Furthermore, our method demonstrates additional performance gains of 4.2 and 1.0 in the other two settings, respectively. Such observation clearly illustrates the generalization capability of our probability-based modeling approach on multispecies APE, effectively mitigating challenges associated with large data variance and imbalanced data distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 310, + 149, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 310, + 149, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 310, + 149, + 323 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 328, + 296, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 328, + 296, + 389 + ], + "spans": [ + { + "bbox": [ + 55, + 328, + 296, + 389 + ], + "type": "text", + "content": "In this section, we conduct a comprehensive ablation study of our proposed method on the AP-10K dataset using ViT-Base backbone. We analyze the impact of various components and hyper-parameters, and also investigate different cross-modal fusion strategies for generating the score map." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "text", + "content": "Effects of Different Components. We conducted experiments to evaluate the impact of various loss functions and the Generalized Keypoint Placement (GKP) strategy. Table 4 summarizes the results. By constructing diverse prompts and applying the constraint " + }, + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{div}}" + }, + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "text", + "content": ", the model achieved a 74.9 AP score, outperforming the baseline by 0.6 points. Similarly, applying the constraint " + }, + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + }, + { + "bbox": [ + 55, + 389, + 296, + 533 + ], + "type": "text", + "content": " with Gaussian distribution reformulation also improved the AP score by 0.6 points. Combining both constraints, the model reached 75.2 AP, significantly surpassing the baseline. Additionally, using the GKP strategy generated more generalized prompts, leading to further improvements." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": "Effects of Hyper-parameter. The hyper-parameters of the number of attributes " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": ", objective function coefficient " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\gamma, \\beta" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": " in Eq. 13 and the sampling turns " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": " are to trade off the model performance. Firstly, we compare performance with respect to different attribute numbers " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": ". As shown in the first block of Table 5, two prompt templates are sufficient to represent different image attributes and achieve optimal performance. As the number of prompt templates increases, however, performance declines, suggesting that excessive template quantity can lead to information redundancy, thereby impairing model efficacy. Then, we adjust the weighting ratio of the " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {feature }}" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {prompt }}" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": ", and observe that " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\gamma = 5e - 4" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\beta = 1e - 5" + }, + { + "bbox": [ + 55, + 534, + 296, + 715 + ], + "type": "text", + "content": " are more suitable. It suggests excessive weighting leads each prompt representation to converge toward a standard normal distribution, thereby" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 553, + 173 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 173 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 173 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 173 + ], + "type": "image", + "image_path": "0d28b589b27137de56f71b255a881eae18abe85f2271a9efbfb47bee03a59b29.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 183, + 555, + 206 + ], + "lines": [ + { + "bbox": [ + 313, + 183, + 555, + 206 + ], + "spans": [ + { + "bbox": [ + 313, + 183, + 555, + 206 + ], + "type": "text", + "content": "Figure 3. Qualitative visualization of several examples with CLAMP and our proposed PPAP." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": "diminishing their distinctiveness. Conversely, overly small weights result in excessive variance in the distribution of each embedding, which increases uncertainty. To achieve a balance, we choose " + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "inline_equation", + "content": "\\beta = 1e - 5" + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": " to get the optimal result. In our approach, we employ reparameterization techniques to ensure differentiability, while also utilizing sampling to enhance the diversity of the text prompts. As we can see in the last block of Table 5, the results are not sensitive to the sampling turns and the accuracy reaches the best performance when setting " + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": " to be equal." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 343, + 556, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 343, + 556, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 343, + 556, + 536 + ], + "type": "text", + "content": "Choices of Cross-modal Fusion. In our experiments, we explore three different fusion strategies, with results summarized in Table 6. As we can see, no matter which strategy is employed, the performances are consistently higher than the baseline method. Selecting the representation most similar to the target can achieve competitive performance. However, as similarity computation relies on labeled data unavailable during testing, we instead average the sampled representations. This discrepancy between training and testing leads to suboptimal performance. Directly ensembling all representations followed by the conv modulation yields the best performance by avoiding information loss. Besides, the results show that the attention-based strategy has worse performances, which may be attributed to the randomly initialized queries to effectively learn the suitable prompt representations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 558, + 388, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 558, + 388, + 571 + ], + "spans": [ + { + "bbox": [ + 314, + 558, + 388, + 571 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "In this paper, we propose a probabilistic prompt distribution learning method to adapt pre-trained vision-language models for the multi-species APE task. With the diverse key-point prompt construction, probabilistic prompt modeling and cross-modal fusion strategies, PPAP uses text guidance in a more comprehensive and effective manner, presenting a novel solution to the multi-species problem, i.e. large data variance and imbalanced data distribution. PPAP reflects superiority and generalization for multi-species APE on the representative multi-species animal pose benchmarks including AP-10K and AnimalKingdom." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29445" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 180 + ], + "type": "text", + "content": "This work was supported in part by the National Key Research and Development Project under Grant 2023YFC3806000, in part by the National Natural Science Foundation of China under Grant 62406226 and 61936014, in part sponsored by Shanghai Sailing Program under Grant 24YF2748700, and in part sponsored by Tongji University Independent Original Cultivation Project under Grant 20230106." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 203, + 115, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 203, + 115, + 216 + ], + "spans": [ + { + "bbox": [ + 56, + 203, + 115, + 216 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 224, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 224, + 296, + 267 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 224, + 296, + 267 + ], + "spans": [ + { + "bbox": [ + 61, + 224, + 296, + 267 + ], + "type": "text", + "content": "[1] Jinkun Cao, Hongyang Tang, Hao-Shu Fang, Xiaoyong Shen, Cewu Lu, and Yu-Wing Tai. 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In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the spatially-varying inner product is inversely proportional to the probability density. In this formulation, a path that traverses a high density (that is, probable) region of image latent space is shorter than the equivalent path through a low density region. We present algorithms for solving the associated initial and boundary value problems and show how to compute the probability density along the path and the geodesic distance between two points. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. Finally, we demonstrate how these techniques can be applied to training-free image sequence interpolation and extrapolation, given a pre-trained image diffusion model.", + "bbox": [ + 89, + 335, + 483, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 618, + 220, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When trained over a data space, a diffusion model [43-46] can tell us the direction in which a data point of that space should move in order to increase its likelihood. That is, it learns a vector field corresponding to the gradient of the log-probability of the data (the Stein score function [47]). This is sufficient information to define a Riemannian manifold in this space, where the norm induced by a spatially-varying inner product is chosen to be inversely proportional to the probability density. This has the effect that geodesics—loosely, shortest paths—on this manifold 'prefer' to traverse high-density regions, which can be thought of as shortcuts in the space. In the context of image latent diffusion models [37], these regions correspond to the latent vectors of probable images, while low-density regions correspond to unrealistic image latents. By computing geodesics in this space, we can find shortest paths between images and study the structure of the learned space.", + "bbox": [ + 89, + 643, + 483, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b76ed9a0321ed1d8f794ca3afbcdb7d98f525448fad997a5e1ba8858297f6269.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 516, + 303, + 671, + 424 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85750950bd3dabbffca514585fc02b2e470692307d49abbbb9e087f2ab51f52a.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 676, + 303, + 903, + 425 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4817e1493a4a219a56f4e0bf3b3b12f94c45392bc83ffa310cbfeed992ec5288.jpg", + "image_caption": [ + "Figure 1. Given a probability density and initial or boundary conditions (here, the position of two points A and B), geodesics can be computed in this space. If the norm is chosen to be inversely proportional to the probability density, these geodesics preferentially traverse high density regions of the space. For an image data space, these correspond to plausible, realistic images according to the probability density, such as that learned by an image diffusion model. Here, we show the outputs of our boundary value problem (BVP) solver that computes a geodesic between endpoints A and B on a toy 2D example. (a) The geodesic and straight-line trajectories between A and B, given the underlying visualized probability density field (contours) and its gradient (arrows). (b) Probability density curves for both trajectories, showing that the straight-line path drops to zero probability very rapidly whereas the geodesic remains in higher probability regions. (c) Images corresponding to points along a geodesic in Stable Diffusion [37] latent space, given the left and right endpoints, computed using our BVP solver." + ], + "image_footnote": [], + "bbox": [ + 517, + 439, + 562, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/712bcb5a2d2c53ca9948c06a0c92b9cc9f5736eaf805bca6bbd6f56c4df43afb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 565, + 439, + 611, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d2e3360ae48276359215761191cc1c5cf979e134b193f12c5f6f90e46e3bf8cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 439, + 658, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c589e5472a96ece391fc441db2bd28ecff572d17afda3cdfbbb280594f8a16d1.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 661, + 439, + 707, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81bfbc6b2980be51a1778fe359cbf139d7ec43f4f6b674e5fc67f0edbeef41f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 439, + 756, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dc27b4cef213587df36c9132ca475bc645147307bd08a750b5eee06957ae055c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 439, + 805, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/23d23c705011c30b46a558a50ec4f08a86cd6567066f461d7da2c6cf3a5f1a35.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 439, + 854, + 478 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d47f8244cae9f30736e16ceca8788717344093ed20e7e6feb9aa7701670c19c5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 857, + 439, + 903, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we outline the relevant theory needed for computing probability density geodesics in diffusion latent space and present algorithms for solving the associated initial and boundary value problems. A 2D toy example of the boundary value problem (BVP) is presented in Fig. 1, alongside image outputs from the BVP solved in the 16384-D latent space of Stable Diffusion [37]. We address several challenges associated with computing", + "bbox": [ + 511, + 779, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27989", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "geodesics in this space: (i) accurately estimating the score function, especially in low-density regions; (ii) handling (potentially spatially-varying) conditional probability densities; and (iii) solving initial and boundary value problems efficiently in an extremely high-dimensional space.", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also describe how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. This work is part exploratory (e.g., what image sequences correspond to geodesics?) and part applied (e.g., how can these techniques be used to solve image sequence-based tasks?). For the latter, we evaluate the performance of these techniques on training-free image sequence interpolation and extrapolation tasks, given a pre-trained image diffusion model. Our contributions are:", + "bbox": [ + 89, + 167, + 482, + 362 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. characterizing probability density geodesics in diffusion latent space;", + "2. algorithms for solving initial and boundary value problems that address challenges specific to conditional diffusion models; and", + "3. an application to image sequence interpolation and extrapolation tasks." + ], + "bbox": [ + 89, + 364, + 482, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our training-free approach on five datasets with respect to other interpolation methods, including those that fine-tune the underlying diffusion model, achieving state-of-the-art results.", + "bbox": [ + 89, + 470, + 482, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 547, + 232, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-image diffusion models. Recently, diffusion models [8, 19] have gained significant attention in deep generative modeling. Given specific input conditions, these models generate realistic data by progressively denoising Gaussian noise through a noise prediction network, resulting in outputs that closely resemble real data distributions based on the provided conditions. With the availability of large-scale image-text pairs for training, diffusion models have achieved remarkable performance in the text-to-image generation task [34, 37, 40]. Due to the flexibility of textual prompting, text-to-image diffusion models have been widely applied to image editing [2, 14, 15, 26], personalization [9, 12, 29, 38], stylization [16, 48, 49], etc. In this work, we use a pretrained Stable Diffusion [37] model with which to explore probability density geodesics for video analysis, image interpolation and extrapolation.", + "bbox": [ + 89, + 574, + 482, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image interpolation. Image interpolation, also known as image morphing, refers to the process of generating a smooth transition between two images by creating intermediate images [51, 56]. Traditional methods rely on pixel-based transformations, such as mesh morphing or defining", + "bbox": [ + 89, + 825, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a blending function [30, 41, 55]. However, these methods typically require pre-labeled corresponding points and human involvement. Some attempts have been made to automate this process [21, 32], but they generally work only on image pairs generated in controlled environments. With advances in generative models, Generative Adversarial Networks (GANs) [10] have been applied to the image interpolation task [28, 33, 42] and achieve moderate success. However, GAN-based image interpolation frameworks do not perform well in open-world settings. Specifically, input image pairs are required to be in-distribution with the training data of GAN models, which limits the application scenarios for image interpolation. With recent progress in text-to-image diffusion models, several works [11, 13, 50, 52, 53] have shown that these models achieve impressive results in image interpolation. Given any image pair, through textual embedding inversion and embedding interpolation, relatively smooth intermediate images can be obtained. In this work, we also employ a diffusion model; however, compared with prior works [11, 52, 53], our method is training-free and can be applied to image extrapolation. Furthermore, our approach offers a theoretical framework with which to understand these tasks.", + "bbox": [ + 511, + 90, + 903, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Probability Density Geodesics", + "text_level": 1, + "bbox": [ + 511, + 450, + 785, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we will outline the theory of probability density geodesics, followed by the algorithmic development. The following section will apply the theory to a diffusion latent space and address some design decisions particular to that context. We aim to show that the structure of a data space can be studied by computing geodesics with respect to the probability distribution of the data, which can be obtained by training a diffusion model in that space.", + "bbox": [ + 511, + 477, + 903, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A geodesic is the (locally) shortest path between two points on a Riemannian manifold with a constant speed parameterization and can be obtained by minimizing the length of a curve between them using the calculus of variations. In the following, time derivatives are denoted $\\dot{x}$ and second derivatives as $\\ddot{x}$ .", + "bbox": [ + 511, + 598, + 903, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Equation for path length. Let $\\gamma :[0,1]\\to \\mathbb{R}^n$ be a path such that $\\gamma (0) = x_0$ and $\\gamma (1) = x_{1}$ , and $S:\\{\\gamma_i\\} \\rightarrow \\mathbb{R}$ be the action functional on the set of such paths, defined by", + "bbox": [ + 511, + 694, + 903, + 739 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nS [ \\gamma ] = \\int_ {a} ^ {b} L (t, \\gamma (t), \\dot {\\gamma} (t)) d t, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 750, + 903, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $L$ is the Lagrangian given by", + "bbox": [ + 511, + 792, + 750, + 809 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nL (t, \\gamma , \\dot {\\gamma}) = \\sqrt {\\langle \\dot {\\gamma} , \\dot {\\gamma} \\rangle_ {K (\\gamma)}} \\text {w i t h} K (\\gamma) = p (\\gamma) ^ {- 2} I. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 819, + 903, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Then $S[\\gamma]$ is the path length for path $\\gamma$ . The norm $\\| x \\| = \\sqrt{\\langle x, x \\rangle_M}$ induced by the inner product $\\langle x, y \\rangle_M = x^\\top M y$ is inversely proportional to the probability density with", + "bbox": [ + 511, + 854, + 903, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27990", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "function $p: \\mathbb{R}^n \\to \\mathbb{R}_+$ . The interpretation here is that paths that pass through high density regions are 'shorter' than paths through low density regions. Note that this reduces to the standard formulation for the path length of a curve when the probability distribution is uniform.", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Euler-Lagrange equations. Given this definition, a path $\\gamma$ is a stationary point of $S$ if and only if it satisfies the Euler-Lagrange equations, viz.,", + "bbox": [ + 89, + 172, + 483, + 217 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial}{\\partial \\gamma} L (t, \\gamma (t), \\dot {\\gamma} (t)) - \\frac {\\mathrm {d}}{\\mathrm {d} t} \\frac {\\partial}{\\partial \\dot {\\gamma}} L (t, \\gamma (t), \\dot {\\gamma} (t)) = 0. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 226, + 482, + 260 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using $\\nabla \\log p(\\gamma) = \\frac{1}{p}\\frac{\\mathrm{d}p}{\\mathrm{d}\\gamma}^{\\mathsf{T}}$ and a constant speed parameterization of the path, for our Lagrangian we obtain", + "bbox": [ + 89, + 268, + 482, + 306 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ddot {\\gamma} + \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) = 0, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 316, + 482, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the unit velocity is given by $\\hat{\\gamma} = \\dot{\\gamma} / \\| \\dot{\\gamma}\\|$ . That is, we obtain a nonlinear second-order ordinary differential equation (ODE) that expresses the relationship between the scaled acceleration and the gradient of the log probability. It is important to observe here that $\\nabla \\log p(\\gamma)$ is the Stein score function [20, 47], the exact quantity that is estimated by a score-based diffusion model. The full derivation is presented in the appendix.", + "bbox": [ + 89, + 353, + 483, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Functional derivative. This second-order ODE expresses the relationship at optimality, i.e., given an initial position and velocity we can obtain the associated optimal path. However, we can also derive the functional derivative $\\frac{\\delta S}{\\delta \\gamma}$ of the path length functional $S$ by approximating the curve by a polygonal line with $n$ segments, as $n$ grows arbitrarily large. We obtain, for any $\\gamma$ with a constant speed parameterization,", + "bbox": [ + 89, + 479, + 483, + 599 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\delta S}{\\delta \\gamma} = \\frac {- 1}{p (\\gamma) \\| \\dot {\\gamma} \\|} \\left(\\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) + \\frac {\\ddot {\\gamma}}{\\| \\dot {\\gamma} \\| ^ {2}}\\right). (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 609, + 482, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Probability density along the path. While estimating the absolute probability of any data point is challenging, the probability relative to the starting point is convenient to compute. For a conservative vector field $\\nabla \\log p$ (the gradient of a scalar field), line integrals are path independent. Therefore, the relative log-probability between two points $\\gamma(a)$ and $\\gamma(t)$ , along any path $\\gamma$ connecting them, is", + "bbox": [ + 89, + 652, + 483, + 760 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\log \\tilde {p} _ {0} (\\gamma (t)) := \\log p (\\gamma (t)) - \\log p (\\gamma (0)) (6) \\\\ = \\int_ {0} ^ {t} \\dot {\\gamma} (\\tau) ^ {\\top} \\nabla \\log p (\\gamma (\\tau)) d \\tau . (7) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 770, + 482, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $f(x) = \\dot{\\gamma}(x)^{\\mathsf{T}}\\nabla \\log p(\\gamma(x))$ and let $t_i = i/n$ for $0 \\leq i \\leq n$ be $n + 1$ equally spaced samples along the path.", + "bbox": [ + 89, + 834, + 483, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then by the trapezoidal rule, the relative probability at these points along the path can be approximated as", + "bbox": [ + 511, + 90, + 906, + 122 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\log \\tilde {p} _ {0} (\\gamma (t _ {i})) \\approx \\frac {1}{n} \\left(\\frac {f (t _ {0})}{2} + \\sum_ {k = 1} ^ {i - 1} f (t _ {k}) + \\frac {f (t _ {i})}{2}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 132, + 906, + 174 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Higher-order approaches, such as Simpson's rule, may also be used for this approximation. From this, we may compute the relative probability $\\tilde{p}_0(\\gamma(t)) = p(\\gamma(t_i)) / p(\\gamma(0))$ at every point $\\gamma(t_i)$ along the curve.", + "bbox": [ + 511, + 184, + 906, + 246 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Geodesic distance. Given the probabilities computed in the previous section, it is trivial to estimate the geodesic distance. Let $t_i = i / n$ for $0 \\leq i \\leq n$ be $n + 1$ equally spaced samples along the geodesic $\\gamma$ , then the relative geodesic distance is given by", + "bbox": [ + 511, + 251, + 906, + 327 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {d} _ {a} (b) = \\int_ {a} ^ {b} \\frac {\\left\\| \\dot {\\gamma} (t) \\right\\|}{\\tilde {p} _ {a} (\\gamma (t))} d t \\tag {9} \\\\ \\approx \\frac {1}{n} \\left(\\frac {\\| \\dot {\\gamma} (a) \\|}{2} + \\sum_ {i = 1} ^ {n - 1} \\frac {\\| \\dot {\\gamma} (t _ {i}) \\|}{\\tilde {p} _ {a} (\\gamma (t _ {i}))} + \\frac {\\| \\dot {\\gamma} (b) \\|}{2 \\tilde {p} _ {a} (\\gamma (t _ {n}))}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 337, + 906, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and the absolute geodesic distance is given by $d(a, b) = \\tilde{d}_a(b) / p(\\gamma(a))$ .", + "bbox": [ + 511, + 426, + 905, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Geodesics in Diffusion Latent Space", + "text_level": 1, + "bbox": [ + 511, + 470, + 839, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we show how to compute geodesics in the latent space of a pre-trained Stable Diffusion [37] model. An element $x \\in \\mathbb{R}^{64 \\times 64 \\times 4}$ of this latent space can be obtained from an image $\\mathcal{I}$ via an encoder $\\mathcal{E}(\\mathcal{I})$ ; a decoder $\\mathcal{D}(x)$ performs the inverse mapping. A forward process incrementally corrupts these elements with Gaussian noise, up to timestep $\\tau = T$ , resulting in a noise element $x_{T} \\sim \\mathcal{N}(0, I)$ . To distinguish between the time dependence of the diffusion process and that of the path formulation in Sec. 3, we use $\\tau$ instead of $t$ to denote the diffusion time-step throughout the rest of the paper. The diffusion model is trained on a very large dataset of images to denoise elements of this latent space at all timesteps. It is parameterized by a neural network $\\epsilon_{\\theta}(x_{\\tau}; z)$ that predicts the noise $\\epsilon$ that was used to produce noisy sample $x_{\\tau}$ from clean sample $x_{0}$ [19]. This is proportional to the score function $\\nabla_{x_{\\tau}} \\log p_{\\tau}(x_{\\tau})$ of the smoothed (noised) density $p_{\\tau}$ [19]. Finally, our method makes use of the deterministic DDIM forward and backward processes (DDIM-F, DDIM-B) with noise schedule parameter $\\overline{\\alpha}_{\\tau}$ , known as inversion [44], defined by", + "bbox": [ + 511, + 497, + 906, + 799 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\frac {x _ {\\tau}}{\\sqrt {\\bar {\\alpha} _ {\\tau}}}\\right) = \\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\sqrt {\\frac {1 - \\bar {\\alpha} _ {\\tau}}{\\bar {\\alpha} _ {\\tau}}}\\right) \\epsilon_ {\\theta} (x _ {\\tau}; z). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 810, + 905, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Working with diffusion models introduces several challenges, which we address in this section. In particular, (i) how to handle (potentially varying) conditional probability", + "bbox": [ + 511, + 854, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1This assumption is not strictly true for standard diffusion models, but is a good approximation [3].", + "bbox": [ + 89, + 875, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27991", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "densities; (ii) how to accurately estimate the score function $\\nabla \\log p(x)$ , especially in low density regions; and (iii) how to solve the initial and boundary value problems efficiently in an extremely high-dimensional space (e.g., $\\mathbb{R}^{16384}$ ).", + "bbox": [ + 89, + 90, + 482, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Conditional probability density geodesics", + "text_level": 1, + "bbox": [ + 89, + 162, + 444, + 180 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most image diffusion models are conditional models, trained to denoise an image conditioned on a signal $z$ such as a CLIP-encoded text prompt [36, 37, 40]. Hence, we extend the formulation from Sec. 3 to consider the conditional probability density function $p(\\gamma(t) \\mid \\zeta(t, \\gamma(t))$ . Here, $\\zeta: \\mathbb{R} \\times \\mathbb{R}^n \\to \\mathbb{R}^d$ is a function over the path parameter and latent space that obtains the values of the conditioning vectors $z_a$ and $z_b$ at the endpoints, such that $\\zeta(0, \\gamma(0)) = z_0$ and $\\zeta(1, \\gamma(1)) = z_1$ for $(a, b) = (0, 1)$ . In our experiments, we primarily consider the case where $\\zeta$ is linear in time and constant in the latent space: $\\zeta(t) = (1 - t)z_0 + tz_1$ .", + "bbox": [ + 89, + 186, + 483, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Score estimation", + "text_level": 1, + "bbox": [ + 89, + 363, + 254, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The score function is likely to be poorly estimated in low-density regions [45]. This occurs since the diffusion model does not have enough evidence during training to estimate the score accurately in regions of the latent space where data is scarce. However, estimating accurate directions in these regions is critical for solving boundary value problems, since the initial path to be optimized is likely to traverse low-density regions. Diffusion models apply multiple levels of noise to data elements in order to alleviate this problem. By doing so, low-density regions of the space can be populated by noised data, improving the quality of the estimated gradients at those locations. As a result, we choose to compute geodesics (and query the diffusion model) at a particular non-zero noise level, with the associated diffusion timestep $\\tau$ . A side benefit of this is that the probability density becomes increasingly Gaussian as the timestep increases, which provides a useful inductive bias, as explained in the next section.", + "bbox": [ + 89, + 385, + 483, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, there is an additional complexity. For a noised training sample $x_{\\tau}$ , the unconditional model $\\epsilon_{\\theta}(x_{\\tau};z = \\varnothing ,\\tau)$ is expected to predict the noise $\\epsilon$ that was used to produce this sample from clean sample $x_0$ . Unfortunately, in our case, we obtain vectors $x_{\\tau}$ from an optimization procedure, initialized along a great circle between endpoints $x_{a,\\tau}$ and $x_{b,\\tau}$ . These points are (at least initially) out-of-distribution (OOD) for the model, and we should not expect it to predict the noise well. Instead, Katzir et al. [25] observe that the prediction consists of a domain correction term $\\delta_{\\mathrm{D}}$ and a denoising term $\\delta_{\\mathrm{N}}$ . The residual $\\delta_{\\mathrm{N}} - \\epsilon$ , as used in score distillation sampling [35], is generally non-zero and noisy, leading to an averaging (over-smoothing) effect in the optimized latents. In our optimization procedure, we are not aiming to denoise the samples, so neglect the denoising direction $\\delta_{\\mathrm{N}}$ and instead use noise-free score distillation [25]", + "bbox": [ + 89, + 659, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b10bcac0e23f1561c1de13bda2da6048800f843756e192db64b363369cc676ba.jpg", + "image_caption": [ + "(a) The pipeline for image interpolation." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 903, + 170 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/77a2c9220bebbd8d64c0948ee28f3022eda76bb244b7feb9f22c994fc454afe6.jpg", + "image_caption": [ + "(b) The pipeline for image extrapolation.", + "Figure 2. Pipelines for the image interpolation and extrapolation tasks, addressed by solving boundary and initial value problems in diffusion latent space." + ], + "image_footnote": [], + "bbox": [ + 517, + 191, + 901, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "direction $\\phi (x\\mid z,\\tau)$ to approximate the gradient direction,", + "bbox": [ + 511, + 368, + 901, + 383 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla \\log p (x \\mid z, \\tau) \\approx \\beta \\phi (x \\mid z, \\tau) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 396, + 903, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (x \\mid z, \\tau) = \\mathbb {E} _ {\\tau^ {\\prime} \\in \\mathcal {R} _ {\\tau}} w \\left(\\tau^ {\\prime}\\right) \\left(\\sigma d \\left(x _ {\\tau^ {\\prime}} \\mid z\\right) - d \\left(x _ {\\tau^ {\\prime}} \\mid z _ {\\text {n e g}}\\right)\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 415, + 903, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is a scalar hyperparameter, $w(\\tau)$ is a weighting function, $\\sigma$ is the classifier-free guidance parameter (0 if unconditional) [18], $z_{\\mathrm{neg}}$ is a negative prompt embedding that says something about the specific OOD latent vector (see Appendix B), $d(x_{\\tau}|z) = \\epsilon_{\\theta}(x_{\\tau}|\\varnothing) - \\epsilon_{\\theta}(x_{\\tau}|z)$ is the direction function, and the expectation is taken over a range of timesteps $\\mathcal{R}_{\\tau} = [\\tau -\\Delta \\tau ,\\tau +\\Delta \\tau ]$", + "bbox": [ + 511, + 444, + 906, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Efficient IVP and BVP solvers", + "text_level": 1, + "bbox": [ + 511, + 560, + 782, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Solving the initial and boundary value problems efficiently with respect to time and memory becomes challenging in the extremely high-dimensional latent space $\\mathbb{R}^{4\\times 64\\times 64}$ of Stable Diffusion [37]. For this dimensionality, standard techniques, such as collocation algorithms for solving BVPs [27], become prohibitive in time and memory. We also aim to minimize calls to the diffusion model, since this is expensive to compute. In view of these aims, we use a simple low-memory parametrization and optimization strategy.", + "bbox": [ + 511, + 583, + 905, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Before outlining the algorithms, we first observe that the probability distribution becomes more Gaussian as the diffusion timestep increases [5] and that the Gaussian Annulus Theorem [1] states that a point chosen at random from a unit variance $d$ -dimensional Gaussian distribution will be located in a small annulus around a sphere of radius $\\sqrt{d}$ with high probability. However, for finite-sized gradient descent steps, the optimizer may take the curve away from the sphere, moving into low-density regions where probability density gradients are poorly estimated. To mitigate this, we reproject the curve back onto the sphere, ensuring that optimization remains within the high-density region where gra", + "bbox": [ + 511, + 719, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27992", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: BVP solver for image interpolation." + ], + "code_body": "Input: start/end image $\\mathcal{I}_0 / \\mathcal{I}_1$ ; text prompts $p_0 / p_1$ diffusion timestep $\\tau$ ; learning rate $\\eta$ optimizer steps $n$ hyperparameter $\\beta$ ; VAE encoder $\\mathcal{E}$ ; CLIP text encoder $\\mathcal{C}$ Output: geodesic $\\gamma$ \n1 $\\{z_0,z_1\\} \\gets \\{\\mathcal{C}(p_0),\\mathcal{C}(p_1)\\}$ \n2 $\\{x_0,x_1\\} \\gets \\{\\mathrm{DDIM - F}(\\mathcal{E}(\\mathcal{I}_i),\\tau ,z_i)\\}_{i = \\{0,1\\}}$ \n3 $\\gamma \\leftarrow$ Interpolate((0,xo),(1,x1)) \n4 for $i = 1$ to n do \n5 T $\\leftarrow$ TimeSampler(i) \n6 S $\\leftarrow$ {(0,xo),(1,x1)} \n7 forall $t\\in \\mathcal{T}$ do \n8 x $\\leftarrow$ y(t); \n9 z $\\leftarrow$ (1-t)z0+tz1 \n10 s $\\leftarrow$ Score(x,z,τ,β); %Eq. (11) \n11 g $\\leftarrow$ FuncDeriv(s,x, $\\dot{x},\\ddot{x})$ %Eq. (13) \n12 x $\\leftarrow$ ||x||(x-ηg)/||x-ηg|| \n13 S $\\leftarrow$ SU{(t,x)} \n14 $\\gamma \\leftarrow$ Interpolate(S)", + "bbox": [ + 94, + 111, + 455, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dient estimates are more reliable, and we project the functional derivative to the tangent space of the sphere,", + "bbox": [ + 89, + 434, + 482, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng = \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\frac {\\delta S}{\\delta \\gamma}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 222, + 473, + 482, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BVP. Given a start position $x^{(0)}$ and an end position $x^{(k + 1)}$ , we parameterize the path $\\gamma$ with a set of control points $\\{x_{\\tau}^{(i)}\\}_{i = 1}^{k}$ connected by a spherical piecewise linear function (great circle arcs). For clarity, we note points on this curve as $x_{t}$ with the curve parameter $t \\in [0,1]$ , dropping $\\tau$ and the ordinal superscript. Algorithm 1 initializes the path as a great circle. It then computes the projected gradient descent update for the control points using Eq. (13), where the associated velocities $\\dot{\\gamma}$ and accelerations $\\ddot{\\gamma}$ are obtained from a natural cubic spline fit to the control points and end points, and projects the updated control points back onto the sphere. To save computation, the algorithm uses a coarse-to-fine discretization, where the number of control points $k \\in [1,3,7,15]$ varies as optimization progresses, using a bisection strategy.", + "bbox": [ + 88, + 515, + 482, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "IVP. Algorithm 2 takes an image $\\mathcal{I}_0$ and its corresponding text description $p_0$ , and extrapolates how the geodesic evolves given an initial velocity formulated from the target prompt $p_1$ . As with Eq. (13), the updates are projected to the tangent space, resulting in the ODE given by", + "bbox": [ + 89, + 750, + 482, + 828 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ddot {\\gamma} = - \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 835, + 482, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which can be solved by applying the Runge-Kutta (RK4) method to the first-order system of equations.", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2: IVP solver for image extrapolation." + ], + "code_body": "Input: image $\\mathcal{I}_0$ ; source text prompt $p_0$ ; target text prompt $p_1$ ; diffusion timestep $\\tau$ ; optimizer steps $n$ ; VAE encoder $\\mathcal{E}$ ; CLIP text encoder $\\mathcal{C}$ ; hyperparameter $\\beta$ \nOutput: image sequence $\\mathcal{I}$ ; geodesic $\\gamma$ \n1 $\\{z_0, z_1\\} \\gets \\{\\mathcal{C}(p_0), \\mathcal{C}(p_1)\\}$ \n2 $x \\gets \\text{DDIM-F}(\\mathcal{E}(\\mathcal{I}_0), \\tau, z_0)$ \n3 $\\dot{x} \\gets \\text{GetInitVelocity}(x, z_0, z_1)$ \n4 $\\mathcal{S} \\gets \\{(0, x)\\}$ \n5 $\\mathcal{I} \\gets \\{\\mathcal{I}_0\\}$ \n6 for $i = 1$ to $n$ do \n7 $z \\gets (1 - i/n)z_0 + (i/n)z_1$ \n8 $s \\gets \\text{Score}(x, z, \\tau, \\beta)$ ; % Eq. (11) \n9 $\\ddot{x} \\gets \\text{ODE}(s, x, \\dot{x})$ ; % Eq. (14) \n10 $\\dot{x} \\gets \\text{RK4}(\\dot{x}, \\ddot{x}, 1/n)$ \n11 $x \\gets \\|x\\| \\text{RK4}(x, \\dot{x}, 1/n)/\\|\\text{RK4}(x, \\dot{x}, 1/n)\\|$ \n12 $\\mathcal{S} \\gets \\mathcal{S} \\cup \\{(i/n, x)\\}$ \n13 $\\mathcal{I} \\gets \\mathcal{I} \\cup \\{\\mathcal{D}(\\text{DDIM-B}(x, \\tau, z))\\}$ \n14 $\\gamma \\gets \\text{Interpolate}(\\mathcal{S})$", + "bbox": [ + 516, + 111, + 903, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 431, + 643, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first analyze whether short video sequences are geodesics in diffusion latent space. Second, we evaluate applications of the theory, focusing on the image interpolation task framed as solving a boundary value problem. For all experiments, we use a pre-trained Stable Diffusion v2.1-base model [37].", + "bbox": [ + 511, + 458, + 906, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Geodesic analysis of videos", + "text_level": 1, + "bbox": [ + 511, + 559, + 756, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The objective of this experiment is to assess how close video clips are to geodesics.", + "bbox": [ + 511, + 580, + 905, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We use the CLEVR framework [22] to render 40 synthetic videos with Blender. Each 100-frame sequence contains one of the three CLEVR objects (cube, sphere, cylinder) and has a single varying attribute, including camera rotation and translation, light source location, and the size, color and motion of the object.", + "bbox": [ + 511, + 616, + 905, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. The path $\\gamma_v$ corresponding to the original video clip is compared to the path after geodesic optimization $\\gamma_o$ , the path after a sinuoidal perturbation $\\gamma_{\\delta} = \\gamma_v + \\delta \\sin (\\pi \\gamma)$ , and the path after smoothing $\\gamma_s$ , by fitting a smoothed cubic spline [7] with smoothing factor 0.9999.", + "bbox": [ + 511, + 713, + 905, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results. In Fig. 3a, we report the $l_{2}$ norm of the functional derivative in Eq. (5) as it varies along the path, for a single video clip (translating red cube). For a geodesic, this is zero everywhere along the path. In Fig. 3b, we report the average of this norm across the path and the dataset. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm along the path $\\gamma_v$ to be near zero, (ii)", + "bbox": [ + 511, + 794, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27993", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/28ce7a8a02ed09744a6a23095798dcfa2e55c44259d4eacf7d70856f62e86fa0.jpg", + "image_caption": [ + "(a) Geodesic gradient norm along the path, for the translating red cube." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 473, + 243 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6b5ba3c5ac95f794d76c568d844e8eea69c2cd2c4f22b96832f23af59c5ddc91.jpg", + "image_caption": [ + "(b) Geodesic gradient norm, averaged across the path and dataset." + ], + "image_footnote": [], + "bbox": [ + 102, + 265, + 473, + 361 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the norm to be close to that of the optimized path $\\gamma_{o}$ , and (iii) the norm of the perturbed $\\gamma_{\\delta}$ or smoothed $\\gamma_{s}$ paths to be larger. We observe these trends in the results, and conclude that many of the videos are approximately geodesic.", + "bbox": [ + 89, + 516, + 483, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Applications", + "text_level": 1, + "bbox": [ + 89, + 589, + 225, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, we assess the performance of the geodesic solvers for the image interpolation and extrapolation tasks.", + "bbox": [ + 89, + 611, + 482, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We compile a union of datasets from prior works [50, 52, 53]. This includes MorphBench [53], which contains 90 image pairs of object animations and object metamorphoses; Animals and Humans [52], which contains 50 animal image pairs from AFHQ [6] with an LPIPS below 0.7 and 50 human face image pairs from CelebA-HQ [23] with an LPIPS below 0.6; and Web, which contains 20 image pairs sourced from publicly accessible websites, some of which have been used in other related studies [50].", + "bbox": [ + 89, + 650, + 482, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Quantitatively evaluating image interpolation and extrapolation is extremely challenging and subjective. Following previous work [52, 53], we report (1) the Fréchet inception distance (FID) [17] between the set of input images and the set of generated images to measure how close the distributions are; (2) the perceptual path length (PPL) [24] as the sum of LPIPS between adjacent images to assess the", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bde90908e57ae11e25ea923cf2ec9b2fcf70061e61bd912ed6ae0fdbce5ae003.jpg", + "image_caption": [ + "Figure 3. Analysis of simple videos generated using CLEVR [22]. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm of the geodesic gradient along the path $\\gamma_v$ to be near zero, (ii) the norm to be close to that of the optimized path $\\gamma_o$ , and (iii) the norm of the perturbed $\\gamma_{\\delta}$ or smoothed $\\gamma_s$ paths to be larger. From the evidence, we conclude that many of the videos are approximately geodesic.", + "Figure 4. Qualitative comparison of image interpolation results." + ], + "image_footnote": [], + "bbox": [ + 511, + 88, + 903, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "directness of the generated image sequence; (3) perceptual distance variance (PDV) as the standard deviation of LPIPS between consecutive images to assess the consistency of transition rates across the sequence; and (4) the TOPIQ [4] score, an image quality metric that evaluates the perceptual quality of each generated image in alignment with human perception. To focus on the quality of interior frames, we compute a weighted TOPIQ score, detailed in Appendix C. We report all metrics on 17-frame sequences by sampling 15 intermediate images between the input pairs.", + "bbox": [ + 511, + 487, + 906, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We use BLIP [31] to generate short text prompts $p$ for each input image. For text inversion, we finetune the CLIP [36] encoded text embedding $z$ , using 500 steps with a learning rate of 0.005 and the AdamW optimizer. For BVP optimization, we perform 400 steps of gradient descent with an initial learning rate of 0.1, following a linear learning rate schedule. The hyperparameters are set as $\\tau = 600$ , $\\Delta \\tau = 100$ , $\\beta = 0.002$ , and $\\sigma = 1$ . As detailed in Sec. 4.3, we adopt a bisection strategy to add additional sample points every 100 steps. For IVP optimization, we set the iteration number to 200. To obtain a diverse set of initial velocities, we apply text inversion to the target text embedding using several generated images from random initial noise $\\mathcal{N}(0, I)$ , conditioned on the target prompt [39]. All methods use the same pre-trained diffusion model (Stable Diffusion v2.1-base) and text prompts, and default settings otherwise. Further details are in Appendix B.", + "bbox": [ + 511, + 643, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27994", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/aa461b590f3ee978e55376cd71333cc7e568bdaeb4f0ac28b82e08e190a196c7.jpg", + "table_caption": [ + "Table 1. Image interpolation results. We report the performance on three datasets: MorphBench (MB), Animals and Humans (AH), and Web data (Web). TF denotes \"training-free\", which also prohibits fine-tuning; best results are in bold; second best ones are underlined. \"Ours\" represents the optimized geodesic path and \"Ours w/o opt.\" represents the unoptimized path as the great circle initialization." + ], + "table_footnote": [], + "table_body": "
MethodTFFID ↓PPL↓PDV↓TOPIQ ↑
AHMBWebAHMBWebAHMBWebAHMBWeb
NoiseDiffusion [54]✓71.85100.87201.082.5072.7183.7380.1170.1110.0990.7000.6660.650
AID [13]✓86.30124.11242.342.7092.6483.8130.1810.1880.2080.6990.6750.665
IMPUS [52]✗25.7536.3389.731.8611.7182.5540.0650.0660.1150.6220.5870.539
DiffMorpher [53]✗32.8942.39160.691.1951.0111.9340.0180.0160.0240.6860.6510.592
SmoothDiffusion [11]✗30.8052.19135.780.9030.8791.3710.0270.0330.0450.5710.5150.389
Ours w/o opt.✓24.7137.85112.810.8740.8411.4730.0320.0350.0530.5840.5460.466
Ours✓33.8746.51134.680.9600.9211.5650.0160.0220.0260.6070.5590.479
", + "bbox": [ + 91, + 133, + 906, + 301 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4bd2214034ddb32ada9fb0d06d17db5a16ecd20c7c9709372d50419a1af3782d.jpg", + "table_caption": [ + "Table 2. We ablate the impact of different text conditioning strategies for BVP solver, including text inversion, positive $(\\oplus)$ prompts, and negative $(\\ominus)$ prompts, on the validation dataset." + ], + "table_footnote": [], + "table_body": "
Text inv. ⊕ prompt ⊘ promptFID↓PPL↓PDV↓TOPIQ↑
✓70.561.060.0170.518
69.061.0460.0170.529
✓✓65.051.0450.0180.562
✓64.721.0370.0190.564
✓✓63.281.0000.0170.553
", + "bbox": [ + 91, + 369, + 483, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We compare our method for the image interpolation task with several state-of-the-art diffusion-based methods, including NoiseDiffusion [54], DiffMorpher [53], IMPUS [52], AID [13], SmoothDiffusion [11] and report the result of a baseline ('Ours w/o opt.'), which returns the initial path before geodesic optimization. This corresponds to the great circle trajectory, the most direct path between the endpoints on the sphere. The quantitative and qualitative results are presented in Tab. 1 and Figs. 4 and 6. We observe that methods involving finetuning the diffusion model on input images, like DiffMorpher and IMPUS, tend to score better with respect to most of the metrics. While AID and NoiseDiffusion generate high-quality images, they have a weaker connection to the input images. SmoothDiffusion [11], trained on the large LAION dataset, performs well with respect to perceptual path length, but has high variance and weaker image quality scores, especially on the partially OOD Web dataset. In contrast, our method has high directness (low PPL), high fidelity to the input distribution (low FID), and very high perceptual smoothness (low PDV), but has slightly lower image quality (low TOPIQ). Overall, our approach is on-par with the best methods without requiring any training. Finally, we show qualitative results for the image extrapolation task in Fig. 7, where we visualize two trajectories for each prompt.", + "bbox": [ + 88, + 523, + 485, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7cebf3d09a35509fab795b2c5898550cf77237f8c9651eb6c21d5ea8f5e5bebc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 321, + 901, + 436 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13ea20c75c86ec6a2ca6af7acc857a465d65dbd5fc42da323fa524580438e7a4.jpg", + "image_caption": [ + "(a) Relative log-probability along the path as optimization progresses, where iteration 0 is the lightest curve and iteration 400 is the darkest.", + "(b) Path length with respect to optimization step.", + "Figure 5. Example of the evolution of the probability density along the path and the path length during BVP optimization." + ], + "image_footnote": [], + "bbox": [ + 517, + 467, + 903, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis. We constructed a validation dataset for ablation and analysis by randomly selecting 25 image pairs from the three datasets (Sec. 5.2). In Fig. 5, we show that optimization correctly increases the log probability of samples along the path and decreases the path length. This indicates that the curve smoothly approaches a geodesic during optimization. We also present an ablation study in Tab. 2, where we show how the text conditioning formulation (text inversion, positive prompt, and negative prompt) contributes to the performance of the method. In Appendix D, we compare the time-linear conditioning signal with the constant one. In Appendix E, we analyze the trade-off between the different choices of hyperparameter settings.", + "bbox": [ + 511, + 641, + 908, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Limitations", + "text_level": 1, + "bbox": [ + 511, + 847, + 640, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This work has several limitations. First, the metrics used for evaluating image interpolation struggle to capture inter", + "bbox": [ + 511, + 869, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27995", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bcf5418d0216f5f1c0292fd158702ab39263e83ce081b9f7ebff49ee6a4d500c.jpg", + "image_caption": [ + "Figure 6. Qualitative image interpolation results using our geodesic BVP solver." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 906, + 378 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0284ee75145d6d6e5565e3d64f9692d5efad83163d206b393173c72b02c006b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 428, + 480, + 513 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e34cb4778b5e0bea73147eebf27571ccb52879b29fafedddbc5e842b12ed830f.jpg", + "image_caption": [ + "(a) Target prompt: \"Volcano eruption\"." + ], + "image_footnote": [], + "bbox": [ + 94, + 529, + 480, + 616 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3dc590cc7147462962cd7525bd021f125d6c1f96c6dbef5177c91f618bcfd50a.jpg", + "image_caption": [ + "(b) Target prompt: \"An expensive cake worth $1,000, adorned with fancy decorations and looking incredibly delicious\".", + "(c) Target prompt: \"A real photo of a cute but scary monstrous creature with sharp teeth and bulging eyes\".", + "Figure 7. Qualitative image extrapolation results using our geodesic IVP solver. For each image, we plot two extrapolated paths, each with different initial velocities but the same prompt." + ], + "image_footnote": [], + "bbox": [ + 94, + 643, + 480, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "polation quality (smoothness, directness, and realism). In particular, FID, which measures fidelity to the input distribution, is unreliable when applied to small image sets like these, and the other metrics only capture individual aspects", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of interpolation quality. Second, the method performs well for image morphing (local changes) but struggles with large camera motions or domain gaps, as illustrated in Figs. 15 and 16. We hypothesize that by initializing with a great circle, which also performs poorly in such cases, our optimizer gets stuck in nearby local optima rather than finding more optimal solutions. A global search strategy is indicated. Third, we approximate the log-probability gradient with a score distillation gradient, which is not necessarily well-aligned. Fourth, the path representation is inelegant: a spherical piecewise linear function (great circle arcs) for which the velocities and accelerations are approximated by fitting a cubic spline. Finally, the image extrapolation performance is unreliable, as determining a good initial velocity is challenging; a more robust approach is called for.", + "bbox": [ + 511, + 430, + 906, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 670, + 633, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented the theory required for computing probability density geodesics in diffusion latent space and algorithms for solving the associated initial and boundary value problems. We also described how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Finally, we presented applications to image interpolation and extrapolation and evaluated the performance of these training-free approaches. We show that they perform comparably or better than existing state-of-the-art. We expect these techniques to be useful for tasks involving generative modeling, as well as for studying the distribution of image space.", + "bbox": [ + 511, + 696, + 906, + 893 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27996", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank all reviewers and ACs for their constructive comments. This research was, in part, funded by the U.S. Government—DARPA TIAMAT HR00112490421. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government.", + "bbox": [ + 89, + 114, + 483, + 220 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 234, + 187, + 250 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Avrim Blum, John Hopcroft, and Ravindran Kannan. Foundations of Data Science. Cambridge University Press, 2020. 4", + "[2] Tim Brooks, Aleksander Holynski, and Alexei A. Efros. Instructpix2pix: Learning to follow image editing instructions. In CVPR, pages 18392-18402, 2023. 2", + "[3] Chen-Hao Chao, Wei-Fang Sun, Bo-Wun Cheng, and Chun-Yi Lee. On investigating the conservative property of score-based generative models. 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International Journal of Advanced Engineering, Management and Science, 3(2):239773, 2017. 2" + ], + "bbox": [ + 516, + 92, + 903, + 573 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "27998", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Probability Density Geodesics in Image Diffusion Latent Space/ae7d5292-3106-44ab-bc09-b7c04df42c2c_model.json b/2025/Probability Density Geodesics in Image Diffusion Latent Space/ae7d5292-3106-44ab-bc09-b7c04df42c2c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5a503816f311e4625ce08eab009c4dbea9aff4 --- /dev/null +++ b/2025/Probability Density Geodesics in Image Diffusion Latent Space/ae7d5292-3106-44ab-bc09-b7c04df42c2c_model.json @@ -0,0 +1,2376 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.182, + 0.131, + 0.819, + 0.154 + ], + "angle": 0, + "content": "Probability Density Geodesics in Image Diffusion Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.18, + 0.8, + 0.234 + ], + "angle": 0, + "content": "Qingtao Yu\\(^{1}\\), Jaskirat Singh\\(^{1}\\), Zhaoyuan Yang\\(^{2}\\), Peter Henry Tu\\(^{2}\\), Jing Zhang\\(^{1}\\), Hongdong Li\\(^{1}\\), Richard Hartley\\(^{1}\\), Dylan Campbell\\(^{1}\\), Australian National University \\({}^{2}\\)GE Research" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.237, + 0.896, + 0.27 + ], + "angle": 0, + "content": "{terry.yu, jaskirat.singh, jing.zhang, hongdong.li, richard.hartley, dylan.campbell}@anu.edu.au {peter.tu, zhaoyuan.yang}@ge.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.304, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.336, + 0.484, + 0.593 + ], + "angle": 0, + "content": "Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the spatially-varying inner product is inversely proportional to the probability density. In this formulation, a path that traverses a high density (that is, probable) region of image latent space is shorter than the equivalent path through a low density region. We present algorithms for solving the associated initial and boundary value problems and show how to compute the probability density along the path and the geodesic distance between two points. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. Finally, we demonstrate how these techniques can be applied to training-free image sequence interpolation and extrapolation, given a pre-trained image diffusion model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.619, + 0.222, + 0.634 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.484, + 0.901 + ], + "angle": 0, + "content": "When trained over a data space, a diffusion model [43-46] can tell us the direction in which a data point of that space should move in order to increase its likelihood. That is, it learns a vector field corresponding to the gradient of the log-probability of the data (the Stein score function [47]). This is sufficient information to define a Riemannian manifold in this space, where the norm induced by a spatially-varying inner product is chosen to be inversely proportional to the probability density. This has the effect that geodesics—loosely, shortest paths—on this manifold 'prefer' to traverse high-density regions, which can be thought of as shortcuts in the space. In the context of image latent diffusion models [37], these regions correspond to the latent vectors of probable images, while low-density regions correspond to unrealistic image latents. By computing geodesics in this space, we can find shortest paths between images and study the structure of the learned space." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.304, + 0.673, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.428, + 0.603, + 0.439 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.304, + 0.905, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.428, + 0.801, + 0.439 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.44, + 0.563, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.566, + 0.44, + 0.612, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.44, + 0.659, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.663, + 0.44, + 0.708, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.44, + 0.758, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.44, + 0.806, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.44, + 0.856, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.858, + 0.44, + 0.905, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.702, + 0.483, + 0.72, + 0.495 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.506, + 0.907, + 0.743 + ], + "angle": 0, + "content": "Figure 1. Given a probability density and initial or boundary conditions (here, the position of two points A and B), geodesics can be computed in this space. If the norm is chosen to be inversely proportional to the probability density, these geodesics preferentially traverse high density regions of the space. For an image data space, these correspond to plausible, realistic images according to the probability density, such as that learned by an image diffusion model. Here, we show the outputs of our boundary value problem (BVP) solver that computes a geodesic between endpoints A and B on a toy 2D example. (a) The geodesic and straight-line trajectories between A and B, given the underlying visualized probability density field (contours) and its gradient (arrows). (b) Probability density curves for both trajectories, showing that the straight-line path drops to zero probability very rapidly whereas the geodesic remains in higher probability regions. (c) Images corresponding to points along a geodesic in Stable Diffusion [37] latent space, given the left and right endpoints, computed using our BVP solver." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this work, we outline the relevant theory needed for computing probability density geodesics in diffusion latent space and present algorithms for solving the associated initial and boundary value problems. A 2D toy example of the boundary value problem (BVP) is presented in Fig. 1, alongside image outputs from the BVP solved in the 16384-D latent space of Stable Diffusion [37]. We address several challenges associated with computing" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "27989" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "geodesics in this space: (i) accurately estimating the score function, especially in low-density regions; (ii) handling (potentially spatially-varying) conditional probability densities; and (iii) solving initial and boundary value problems efficiently in an extremely high-dimensional space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.169, + 0.483, + 0.363 + ], + "angle": 0, + "content": "We also describe how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. This work is part exploratory (e.g., what image sequences correspond to geodesics?) and part applied (e.g., how can these techniques be used to solve image sequence-based tasks?). For the latter, we evaluate the performance of these techniques on training-free image sequence interpolation and extrapolation tasks, given a pre-trained image diffusion model. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.366, + 0.483, + 0.395 + ], + "angle": 0, + "content": "1. characterizing probability density geodesics in diffusion latent space;" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.396, + 0.482, + 0.44 + ], + "angle": 0, + "content": "2. algorithms for solving initial and boundary value problems that address challenges specific to conditional diffusion models; and" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.441, + 0.482, + 0.47 + ], + "angle": 0, + "content": "3. an application to image sequence interpolation and extrapolation tasks." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.366, + 0.483, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.472, + 0.483, + 0.532 + ], + "angle": 0, + "content": "We evaluate our training-free approach on five datasets with respect to other interpolation methods, including those that fine-tune the underlying diffusion model, achieving state-of-the-art results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.549, + 0.233, + 0.565 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.483, + 0.818 + ], + "angle": 0, + "content": "Text-to-image diffusion models. Recently, diffusion models [8, 19] have gained significant attention in deep generative modeling. Given specific input conditions, these models generate realistic data by progressively denoising Gaussian noise through a noise prediction network, resulting in outputs that closely resemble real data distributions based on the provided conditions. With the availability of large-scale image-text pairs for training, diffusion models have achieved remarkable performance in the text-to-image generation task [34, 37, 40]. Due to the flexibility of textual prompting, text-to-image diffusion models have been widely applied to image editing [2, 14, 15, 26], personalization [9, 12, 29, 38], stylization [16, 48, 49], etc. In this work, we use a pretrained Stable Diffusion [37] model with which to explore probability density geodesics for video analysis, image interpolation and extrapolation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Image interpolation. Image interpolation, also known as image morphing, refers to the process of generating a smooth transition between two images by creating intermediate images [51, 56]. Traditional methods rely on pixel-based transformations, such as mesh morphing or defining" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.438 + ], + "angle": 0, + "content": "a blending function [30, 41, 55]. However, these methods typically require pre-labeled corresponding points and human involvement. Some attempts have been made to automate this process [21, 32], but they generally work only on image pairs generated in controlled environments. With advances in generative models, Generative Adversarial Networks (GANs) [10] have been applied to the image interpolation task [28, 33, 42] and achieve moderate success. However, GAN-based image interpolation frameworks do not perform well in open-world settings. Specifically, input image pairs are required to be in-distribution with the training data of GAN models, which limits the application scenarios for image interpolation. With recent progress in text-to-image diffusion models, several works [11, 13, 50, 52, 53] have shown that these models achieve impressive results in image interpolation. Given any image pair, through textual embedding inversion and embedding interpolation, relatively smooth intermediate images can be obtained. In this work, we also employ a diffusion model; however, compared with prior works [11, 52, 53], our method is training-free and can be applied to image extrapolation. Furthermore, our approach offers a theoretical framework with which to understand these tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.452, + 0.787, + 0.469 + ], + "angle": 0, + "content": "3. Probability Density Geodesics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.905, + 0.598 + ], + "angle": 0, + "content": "In this section, we will outline the theory of probability density geodesics, followed by the algorithmic development. The following section will apply the theory to a diffusion latent space and address some design decisions particular to that context. We aim to show that the structure of a data space can be studied by computing geodesics with respect to the probability distribution of the data, which can be obtained by training a diffusion model in that space." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.905, + 0.688 + ], + "angle": 0, + "content": "A geodesic is the (locally) shortest path between two points on a Riemannian manifold with a constant speed parameterization and can be obtained by minimizing the length of a curve between them using the calculus of variations. In the following, time derivatives are denoted \\(\\dot{x}\\) and second derivatives as \\(\\ddot{x}\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.695, + 0.905, + 0.741 + ], + "angle": 0, + "content": "Equation for path length. Let \\(\\gamma :[0,1]\\to \\mathbb{R}^n\\) be a path such that \\(\\gamma (0) = x_0\\) and \\(\\gamma (1) = x_{1}\\), and \\(S:\\{\\gamma_i\\} \\rightarrow \\mathbb{R}\\) be the action functional on the set of such paths, defined by" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.75, + 0.905, + 0.786 + ], + "angle": 0, + "content": "\\[\nS [ \\gamma ] = \\int_ {a} ^ {b} L (t, \\gamma (t), \\dot {\\gamma} (t)) d t, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.794, + 0.75, + 0.81 + ], + "angle": 0, + "content": "where \\(L\\) is the Lagrangian given by" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.82, + 0.905, + 0.845 + ], + "angle": 0, + "content": "\\[\nL (t, \\gamma , \\dot {\\gamma}) = \\sqrt {\\langle \\dot {\\gamma} , \\dot {\\gamma} \\rangle_ {K (\\gamma)}} \\text {w i t h} K (\\gamma) = p (\\gamma) ^ {- 2} I. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.855, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Then \\( S[\\gamma] \\) is the path length for path \\( \\gamma \\). The norm \\( \\| x \\| = \\sqrt{\\langle x, x \\rangle_M} \\) induced by the inner product \\( \\langle x, y \\rangle_M = x^\\top M y \\) is inversely proportional to the probability density with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27990" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "function \\(p: \\mathbb{R}^n \\to \\mathbb{R}_+\\). The interpretation here is that paths that pass through high density regions are 'shorter' than paths through low density regions. Note that this reduces to the standard formulation for the path length of a curve when the probability distribution is uniform." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.173, + 0.485, + 0.218 + ], + "angle": 0, + "content": "Euler-Lagrange equations. Given this definition, a path \\(\\gamma\\) is a stationary point of \\(S\\) if and only if it satisfies the Euler-Lagrange equations, viz.," + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.227, + 0.483, + 0.261 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial}{\\partial \\gamma} L (t, \\gamma (t), \\dot {\\gamma} (t)) - \\frac {\\mathrm {d}}{\\mathrm {d} t} \\frac {\\partial}{\\partial \\dot {\\gamma}} L (t, \\gamma (t), \\dot {\\gamma} (t)) = 0. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.27, + 0.483, + 0.307 + ], + "angle": 0, + "content": "Using \\(\\nabla \\log p(\\gamma) = \\frac{1}{p}\\frac{\\mathrm{d}p}{\\mathrm{d}\\gamma}^{\\mathsf{T}}\\) and a constant speed parameterization of the path, for our Lagrangian we obtain" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.317, + 0.483, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\ddot {\\gamma} + \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) = 0, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.354, + 0.484, + 0.476 + ], + "angle": 0, + "content": "where the unit velocity is given by \\(\\hat{\\gamma} = \\dot{\\gamma} / \\| \\dot{\\gamma}\\|\\). That is, we obtain a nonlinear second-order ordinary differential equation (ODE) that expresses the relationship between the scaled acceleration and the gradient of the log probability. It is important to observe here that \\(\\nabla \\log p(\\gamma)\\) is the Stein score function [20, 47], the exact quantity that is estimated by a score-based diffusion model. The full derivation is presented in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.481, + 0.484, + 0.601 + ], + "angle": 0, + "content": "Functional derivative. This second-order ODE expresses the relationship at optimality, i.e., given an initial position and velocity we can obtain the associated optimal path. However, we can also derive the functional derivative \\(\\frac{\\delta S}{\\delta \\gamma}\\) of the path length functional \\(S\\) by approximating the curve by a polygonal line with \\(n\\) segments, as \\(n\\) grows arbitrarily large. We obtain, for any \\(\\gamma\\) with a constant speed parameterization," + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.611, + 0.483, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\frac {\\delta S}{\\delta \\gamma} = \\frac {- 1}{p (\\gamma) \\| \\dot {\\gamma} \\|} \\left(\\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) + \\frac {\\ddot {\\gamma}}{\\| \\dot {\\gamma} \\| ^ {2}}\\right). (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.654, + 0.484, + 0.761 + ], + "angle": 0, + "content": "Probability density along the path. While estimating the absolute probability of any data point is challenging, the probability relative to the starting point is convenient to compute. For a conservative vector field \\(\\nabla \\log p\\) (the gradient of a scalar field), line integrals are path independent. Therefore, the relative log-probability between two points \\(\\gamma(a)\\) and \\(\\gamma(t)\\), along any path \\(\\gamma\\) connecting them, is" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.771, + 0.483, + 0.826 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\log \\tilde {p} _ {0} (\\gamma (t)) := \\log p (\\gamma (t)) - \\log p (\\gamma (0)) (6) \\\\ = \\int_ {0} ^ {t} \\dot {\\gamma} (\\tau) ^ {\\top} \\nabla \\log p (\\gamma (\\tau)) d \\tau . (7) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.835, + 0.484, + 0.868 + ], + "angle": 0, + "content": "Let \\( f(x) = \\dot{\\gamma}(x)^{\\mathsf{T}}\\nabla \\log p(\\gamma(x)) \\) and let \\( t_i = i/n \\) for \\( 0 \\leq i \\leq n \\) be \\( n + 1 \\) equally spaced samples along the path." + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.875, + 0.484, + 0.901 + ], + "angle": 0, + "content": "1This assumption is not strictly true for standard diffusion models, but is a good approximation [3]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.123 + ], + "angle": 0, + "content": "Then by the trapezoidal rule, the relative probability at these points along the path can be approximated as" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.133, + 0.907, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\log \\tilde {p} _ {0} (\\gamma (t _ {i})) \\approx \\frac {1}{n} \\left(\\frac {f (t _ {0})}{2} + \\sum_ {k = 1} ^ {i - 1} f (t _ {k}) + \\frac {f (t _ {i})}{2}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.185, + 0.907, + 0.247 + ], + "angle": 0, + "content": "Higher-order approaches, such as Simpson's rule, may also be used for this approximation. From this, we may compute the relative probability \\(\\tilde{p}_0(\\gamma(t)) = p(\\gamma(t_i)) / p(\\gamma(0))\\) at every point \\(\\gamma(t_i)\\) along the curve." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.252, + 0.907, + 0.328 + ], + "angle": 0, + "content": "Geodesic distance. Given the probabilities computed in the previous section, it is trivial to estimate the geodesic distance. Let \\( t_i = i / n \\) for \\( 0 \\leq i \\leq n \\) be \\( n + 1 \\) equally spaced samples along the geodesic \\( \\gamma \\), then the relative geodesic distance is given by" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.338, + 0.907, + 0.418 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {d} _ {a} (b) = \\int_ {a} ^ {b} \\frac {\\left\\| \\dot {\\gamma} (t) \\right\\|}{\\tilde {p} _ {a} (\\gamma (t))} d t \\tag {9} \\\\ \\approx \\frac {1}{n} \\left(\\frac {\\| \\dot {\\gamma} (a) \\|}{2} + \\sum_ {i = 1} ^ {n - 1} \\frac {\\| \\dot {\\gamma} (t _ {i}) \\|}{\\tilde {p} _ {a} (\\gamma (t _ {i}))} + \\frac {\\| \\dot {\\gamma} (b) \\|}{2 \\tilde {p} _ {a} (\\gamma (t _ {n}))}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.428, + 0.906, + 0.46 + ], + "angle": 0, + "content": "and the absolute geodesic distance is given by \\( d(a, b) = \\tilde{d}_a(b) / p(\\gamma(a)) \\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.472, + 0.84, + 0.49 + ], + "angle": 0, + "content": "4. Geodesics in Diffusion Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.907, + 0.8 + ], + "angle": 0, + "content": "In this section, we show how to compute geodesics in the latent space of a pre-trained Stable Diffusion [37] model. An element \\(x \\in \\mathbb{R}^{64 \\times 64 \\times 4}\\) of this latent space can be obtained from an image \\(\\mathcal{I}\\) via an encoder \\(\\mathcal{E}(\\mathcal{I})\\); a decoder \\(\\mathcal{D}(x)\\) performs the inverse mapping. A forward process incrementally corrupts these elements with Gaussian noise, up to timestep \\(\\tau = T\\), resulting in a noise element \\(x_{T} \\sim \\mathcal{N}(0, I)\\). To distinguish between the time dependence of the diffusion process and that of the path formulation in Sec. 3, we use \\(\\tau\\) instead of \\(t\\) to denote the diffusion time-step throughout the rest of the paper. The diffusion model is trained on a very large dataset of images to denoise elements of this latent space at all timesteps. It is parameterized by a neural network \\(\\epsilon_{\\theta}(x_{\\tau}; z)\\) that predicts the noise \\(\\epsilon\\) that was used to produce noisy sample \\(x_{\\tau}\\) from clean sample \\(x_{0}\\) [19]. This is proportional to the score function \\(\\nabla_{x_{\\tau}} \\log p_{\\tau}(x_{\\tau})\\) of the smoothed (noised) density \\(p_{\\tau}\\) [19]. Finally, our method makes use of the deterministic DDIM forward and backward processes (DDIM-F, DDIM-B) with noise schedule parameter \\(\\overline{\\alpha}_{\\tau}\\), known as inversion [44], defined by" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.811, + 0.906, + 0.846 + ], + "angle": 0, + "content": "\\[\n\\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\frac {x _ {\\tau}}{\\sqrt {\\bar {\\alpha} _ {\\tau}}}\\right) = \\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\sqrt {\\frac {1 - \\bar {\\alpha} _ {\\tau}}{\\bar {\\alpha} _ {\\tau}}}\\right) \\epsilon_ {\\theta} (x _ {\\tau}; z). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Working with diffusion models introduces several challenges, which we address in this section. In particular, (i) how to handle (potentially varying) conditional probability" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27991" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.155 + ], + "angle": 0, + "content": "densities; (ii) how to accurately estimate the score function \\(\\nabla \\log p(x)\\), especially in low density regions; and (iii) how to solve the initial and boundary value problems efficiently in an extremely high-dimensional space (e.g., \\(\\mathbb{R}^{16384}\\))." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.164, + 0.445, + 0.181 + ], + "angle": 0, + "content": "4.1. Conditional probability density geodesics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.187, + 0.485, + 0.354 + ], + "angle": 0, + "content": "Most image diffusion models are conditional models, trained to denoise an image conditioned on a signal \\(z\\) such as a CLIP-encoded text prompt [36, 37, 40]. Hence, we extend the formulation from Sec. 3 to consider the conditional probability density function \\(p(\\gamma(t) \\mid \\zeta(t, \\gamma(t))\\). Here, \\(\\zeta: \\mathbb{R} \\times \\mathbb{R}^n \\to \\mathbb{R}^d\\) is a function over the path parameter and latent space that obtains the values of the conditioning vectors \\(z_a\\) and \\(z_b\\) at the endpoints, such that \\(\\zeta(0, \\gamma(0)) = z_0\\) and \\(\\zeta(1, \\gamma(1)) = z_1\\) for \\((a, b) = (0, 1)\\). In our experiments, we primarily consider the case where \\(\\zeta\\) is linear in time and constant in the latent space: \\(\\zeta(t) = (1 - t)z_0 + tz_1\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.364, + 0.255, + 0.379 + ], + "angle": 0, + "content": "4.2. Score estimation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.386, + 0.484, + 0.657 + ], + "angle": 0, + "content": "The score function is likely to be poorly estimated in low-density regions [45]. This occurs since the diffusion model does not have enough evidence during training to estimate the score accurately in regions of the latent space where data is scarce. However, estimating accurate directions in these regions is critical for solving boundary value problems, since the initial path to be optimized is likely to traverse low-density regions. Diffusion models apply multiple levels of noise to data elements in order to alleviate this problem. By doing so, low-density regions of the space can be populated by noised data, improving the quality of the estimated gradients at those locations. As a result, we choose to compute geodesics (and query the diffusion model) at a particular non-zero noise level, with the associated diffusion timestep \\(\\tau\\). A side benefit of this is that the probability density becomes increasingly Gaussian as the timestep increases, which provides a useful inductive bias, as explained in the next section." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.902 + ], + "angle": 0, + "content": "However, there is an additional complexity. For a noised training sample \\( x_{\\tau} \\), the unconditional model \\( \\epsilon_{\\theta}(x_{\\tau};z = \\varnothing ,\\tau) \\) is expected to predict the noise \\( \\epsilon \\) that was used to produce this sample from clean sample \\( x_0 \\). Unfortunately, in our case, we obtain vectors \\( x_{\\tau} \\) from an optimization procedure, initialized along a great circle between endpoints \\( x_{a,\\tau} \\) and \\( x_{b,\\tau} \\). These points are (at least initially) out-of-distribution (OOD) for the model, and we should not expect it to predict the noise well. Instead, Katzir et al. [25] observe that the prediction consists of a domain correction term \\( \\delta_{\\mathrm{D}} \\) and a denoising term \\( \\delta_{\\mathrm{N}} \\). The residual \\( \\delta_{\\mathrm{N}} - \\epsilon \\), as used in score distillation sampling [35], is generally non-zero and noisy, leading to an averaging (over-smoothing) effect in the optimized latents. In our optimization procedure, we are not aiming to denoise the samples, so neglect the denoising direction \\( \\delta_{\\mathrm{N}} \\) and instead use noise-free score distillation [25]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.092, + 0.905, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.176, + 0.818, + 0.189 + ], + "angle": 0, + "content": "(a) The pipeline for image interpolation." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.192, + 0.903, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.603, + 0.275, + 0.819, + 0.288 + ], + "angle": 0, + "content": "(b) The pipeline for image extrapolation." + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.299, + 0.908, + 0.342 + ], + "angle": 0, + "content": "Figure 2. Pipelines for the image interpolation and extrapolation tasks, addressed by solving boundary and initial value problems in diffusion latent space." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.369, + 0.902, + 0.385 + ], + "angle": 0, + "content": "direction \\(\\phi (x\\mid z,\\tau)\\) to approximate the gradient direction," + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.397, + 0.905, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\nabla \\log p (x \\mid z, \\tau) \\approx \\beta \\phi (x \\mid z, \\tau) \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.416, + 0.905, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\phi (x \\mid z, \\tau) = \\mathbb {E} _ {\\tau^ {\\prime} \\in \\mathcal {R} _ {\\tau}} w \\left(\\tau^ {\\prime}\\right) \\left(\\sigma d \\left(x _ {\\tau^ {\\prime}} \\mid z\\right) - d \\left(x _ {\\tau^ {\\prime}} \\mid z _ {\\text {n e g}}\\right)\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.445, + 0.907, + 0.552 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a scalar hyperparameter, \\(w(\\tau)\\) is a weighting function, \\(\\sigma\\) is the classifier-free guidance parameter (0 if unconditional) [18], \\(z_{\\mathrm{neg}}\\) is a negative prompt embedding that says something about the specific OOD latent vector (see Appendix B), \\(d(x_{\\tau}|z) = \\epsilon_{\\theta}(x_{\\tau}|\\varnothing) - \\epsilon_{\\theta}(x_{\\tau}|z)\\) is the direction function, and the expectation is taken over a range of timesteps \\(\\mathcal{R}_{\\tau} = [\\tau -\\Delta \\tau ,\\tau +\\Delta \\tau ]\\)" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.561, + 0.783, + 0.576 + ], + "angle": 0, + "content": "4.3. Efficient IVP and BVP solvers" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.906, + 0.719 + ], + "angle": 0, + "content": "Solving the initial and boundary value problems efficiently with respect to time and memory becomes challenging in the extremely high-dimensional latent space \\(\\mathbb{R}^{4\\times 64\\times 64}\\) of Stable Diffusion [37]. For this dimensionality, standard techniques, such as collocation algorithms for solving BVPs [27], become prohibitive in time and memory. We also aim to minimize calls to the diffusion model, since this is expensive to compute. In view of these aims, we use a simple low-memory parametrization and optimization strategy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Before outlining the algorithms, we first observe that the probability distribution becomes more Gaussian as the diffusion timestep increases [5] and that the Gaussian Annulus Theorem [1] states that a point chosen at random from a unit variance \\(d\\)-dimensional Gaussian distribution will be located in a small annulus around a sphere of radius \\(\\sqrt{d}\\) with high probability. However, for finite-sized gradient descent steps, the optimizer may take the curve away from the sphere, moving into low-density regions where probability density gradients are poorly estimated. To mitigate this, we reproject the curve back onto the sphere, ensuring that optimization remains within the high-density region where gra" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27992" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.102, + 0.095, + 0.434, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: BVP solver for image interpolation." + }, + { + "type": "algorithm", + "bbox": [ + 0.095, + 0.112, + 0.457, + 0.407 + ], + "angle": 0, + "content": "Input: start/end image \\(\\mathcal{I}_0 / \\mathcal{I}_1\\) ; text prompts \\(p_0 / p_1\\) diffusion timestep \\(\\tau\\) ; learning rate \\(\\eta\\) optimizer steps \\(n\\) hyperparameter \\(\\beta\\) ; VAE encoder \\(\\mathcal{E}\\) ; CLIP text encoder \\(\\mathcal{C}\\) Output: geodesic \\(\\gamma\\) \n1 \\(\\{z_0,z_1\\} \\gets \\{\\mathcal{C}(p_0),\\mathcal{C}(p_1)\\}\\) \n2 \\(\\{x_0,x_1\\} \\gets \\{\\mathrm{DDIM - F}(\\mathcal{E}(\\mathcal{I}_i),\\tau ,z_i)\\}_{i = \\{0,1\\}}\\) \n3 \\(\\gamma \\leftarrow\\) Interpolate((0,xo),(1,x1)) \n4 for \\(i = 1\\) to n do \n5 T \\(\\leftarrow\\) TimeSampler(i) \n6 S \\(\\leftarrow\\) {(0,xo),(1,x1)} \n7 forall \\(t\\in \\mathcal{T}\\) do \n8 x \\(\\leftarrow\\) y(t); \n9 z \\(\\leftarrow\\) (1-t)z0+tz1 \n10 s \\(\\leftarrow\\) Score(x,z,τ,β); %Eq. (11) \n11 g \\(\\leftarrow\\) FuncDeriv(s,x, \\(\\dot{x},\\ddot{x})\\) %Eq. (13) \n12 x \\(\\leftarrow\\) ||x||(x-ηg)/||x-ηg|| \n13 S \\(\\leftarrow\\) SU{(t,x)} \n14 \\(\\gamma \\leftarrow\\) Interpolate(S)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.435, + 0.483, + 0.466 + ], + "angle": 0, + "content": "dient estimates are more reliable, and we project the functional derivative to the tangent space of the sphere," + }, + { + "type": "equation", + "bbox": [ + 0.223, + 0.474, + 0.483, + 0.507 + ], + "angle": 0, + "content": "\\[\ng = \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\frac {\\delta S}{\\delta \\gamma}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.516, + 0.483, + 0.746 + ], + "angle": 0, + "content": "BVP. Given a start position \\( x^{(0)} \\) and an end position \\( x^{(k + 1)} \\), we parameterize the path \\( \\gamma \\) with a set of control points \\( \\{x_{\\tau}^{(i)}\\}_{i = 1}^{k} \\) connected by a spherical piecewise linear function (great circle arcs). For clarity, we note points on this curve as \\( x_{t} \\) with the curve parameter \\( t \\in [0,1] \\), dropping \\( \\tau \\) and the ordinal superscript. Algorithm 1 initializes the path as a great circle. It then computes the projected gradient descent update for the control points using Eq. (13), where the associated velocities \\( \\dot{\\gamma} \\) and accelerations \\( \\ddot{\\gamma} \\) are obtained from a natural cubic spline fit to the control points and end points, and projects the updated control points back onto the sphere. To save computation, the algorithm uses a coarse-to-fine discretization, where the number of control points \\( k \\in [1,3,7,15] \\) varies as optimization progresses, using a bisection strategy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.751, + 0.483, + 0.829 + ], + "angle": 0, + "content": "IVP. Algorithm 2 takes an image \\(\\mathcal{I}_0\\) and its corresponding text description \\(p_0\\), and extrapolates how the geodesic evolves given an initial velocity formulated from the target prompt \\(p_1\\). As with Eq. (13), the updates are projected to the tangent space, resulting in the ODE given by" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.837, + 0.483, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\ddot {\\gamma} = - \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "which can be solved by applying the Runge-Kutta (RK4) method to the first-order system of equations." + }, + { + "type": "code_caption", + "bbox": [ + 0.525, + 0.095, + 0.854, + 0.11 + ], + "angle": 0, + "content": "Algorithm 2: IVP solver for image extrapolation." + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.905, + 0.405 + ], + "angle": 0, + "content": "Input: image \\(\\mathcal{I}_0\\); source text prompt \\(p_0\\); target text prompt \\(p_1\\); diffusion timestep \\(\\tau\\); optimizer steps \\(n\\); VAE encoder \\(\\mathcal{E}\\); CLIP text encoder \\(\\mathcal{C}\\); hyperparameter \\(\\beta\\) \nOutput: image sequence \\(\\mathcal{I}\\); geodesic \\(\\gamma\\) \n1 \\(\\{z_0, z_1\\} \\gets \\{\\mathcal{C}(p_0), \\mathcal{C}(p_1)\\}\\) \n2 \\(x \\gets \\text{DDIM-F}(\\mathcal{E}(\\mathcal{I}_0), \\tau, z_0)\\) \n3 \\(\\dot{x} \\gets \\text{GetInitVelocity}(x, z_0, z_1)\\) \n4 \\(\\mathcal{S} \\gets \\{(0, x)\\}\\) \n5 \\(\\mathcal{I} \\gets \\{\\mathcal{I}_0\\}\\) \n6 for \\(i = 1\\) to \\(n\\) do \n7 \\(z \\gets (1 - i/n)z_0 + (i/n)z_1\\) \n8 \\(s \\gets \\text{Score}(x, z, \\tau, \\beta)\\); % Eq. (11) \n9 \\(\\ddot{x} \\gets \\text{ODE}(s, x, \\dot{x})\\); % Eq. (14) \n10 \\(\\dot{x} \\gets \\text{RK4}(\\dot{x}, \\ddot{x}, 1/n)\\) \n11 \\(x \\gets \\|x\\| \\text{RK4}(x, \\dot{x}, 1/n)/\\|\\text{RK4}(x, \\dot{x}, 1/n)\\|\\) \n12 \\(\\mathcal{S} \\gets \\mathcal{S} \\cup \\{(i/n, x)\\}\\) \n13 \\(\\mathcal{I} \\gets \\mathcal{I} \\cup \\{\\mathcal{D}(\\text{DDIM-B}(x, \\tau, z))\\}\\) \n14 \\(\\gamma \\gets \\text{Interpolate}(\\mathcal{S})\\)" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.433, + 0.645, + 0.451 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.907, + 0.55 + ], + "angle": 0, + "content": "In this section, we first analyze whether short video sequences are geodesics in diffusion latent space. Second, we evaluate applications of the theory, focusing on the image interpolation task framed as solving a boundary value problem. For all experiments, we use a pre-trained Stable Diffusion v2.1-base model [37]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.56, + 0.757, + 0.575 + ], + "angle": 0, + "content": "5.1. Geodesic analysis of videos" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.906, + 0.612 + ], + "angle": 0, + "content": "The objective of this experiment is to assess how close video clips are to geodesics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.617, + 0.906, + 0.709 + ], + "angle": 0, + "content": "Dataset. We use the CLEVR framework [22] to render 40 synthetic videos with Blender. Each 100-frame sequence contains one of the three CLEVR objects (cube, sphere, cylinder) and has a single varying attribute, including camera rotation and translation, light source location, and the size, color and motion of the object." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.714, + 0.906, + 0.79 + ], + "angle": 0, + "content": "Baselines. The path \\(\\gamma_v\\) corresponding to the original video clip is compared to the path after geodesic optimization \\(\\gamma_o\\), the path after a sinuoidal perturbation \\(\\gamma_{\\delta} = \\gamma_v + \\delta \\sin (\\pi \\gamma)\\), and the path after smoothing \\(\\gamma_s\\), by fitting a smoothed cubic spline [7] with smoothing factor 0.9999." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Results. In Fig. 3a, we report the \\(l_{2}\\) norm of the functional derivative in Eq. (5) as it varies along the path, for a single video clip (translating red cube). For a geodesic, this is zero everywhere along the path. In Fig. 3b, we report the average of this norm across the path and the dataset. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm along the path \\(\\gamma_v\\) to be near zero, (ii)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27993" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.474, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.249, + 0.474, + 0.263 + ], + "angle": 0, + "content": "(a) Geodesic gradient norm along the path, for the translating red cube." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.266, + 0.474, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.366, + 0.46, + 0.38 + ], + "angle": 0, + "content": "(b) Geodesic gradient norm, averaged across the path and dataset." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.391, + 0.484, + 0.489 + ], + "angle": 0, + "content": "Figure 3. Analysis of simple videos generated using CLEVR [22]. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm of the geodesic gradient along the path \\(\\gamma_v\\) to be near zero, (ii) the norm to be close to that of the optimized path \\(\\gamma_o\\), and (iii) the norm of the perturbed \\(\\gamma_{\\delta}\\) or smoothed \\(\\gamma_s\\) paths to be larger. From the evidence, we conclude that many of the videos are approximately geodesic." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.517, + 0.484, + 0.579 + ], + "angle": 0, + "content": "the norm to be close to that of the optimized path \\(\\gamma_{o}\\), and (iii) the norm of the perturbed \\(\\gamma_{\\delta}\\) or smoothed \\(\\gamma_{s}\\) paths to be larger. We observe these trends in the results, and conclude that many of the videos are approximately geodesic." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.59, + 0.226, + 0.607 + ], + "angle": 0, + "content": "5.2. Applications" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.644 + ], + "angle": 0, + "content": "Here, we assess the performance of the geodesic solvers for the image interpolation and extrapolation tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.651, + 0.483, + 0.788 + ], + "angle": 0, + "content": "Datasets. We compile a union of datasets from prior works [50, 52, 53]. This includes MorphBench [53], which contains 90 image pairs of object animations and object metamorphoses; Animals and Humans [52], which contains 50 animal image pairs from AFHQ [6] with an LPIPS below 0.7 and 50 human face image pairs from CelebA-HQ [23] with an LPIPS below 0.6; and Web, which contains 20 image pairs sourced from publicly accessible websites, some of which have been used in other related studies [50]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Metrics. Quantitatively evaluating image interpolation and extrapolation is extremely challenging and subjective. Following previous work [52, 53], we report (1) the Fréchet inception distance (FID) [17] between the set of input images and the set of generated images to measure how close the distributions are; (2) the perceptual path length (PPL) [24] as the sum of LPIPS between adjacent images to assess the" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.089, + 0.905, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.447, + 0.899, + 0.462 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of image interpolation results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.907, + 0.64 + ], + "angle": 0, + "content": "directness of the generated image sequence; (3) perceptual distance variance (PDV) as the standard deviation of LPIPS between consecutive images to assess the consistency of transition rates across the sequence; and (4) the TOPIQ [4] score, an image quality metric that evaluates the perceptual quality of each generated image in alignment with human perception. To focus on the quality of interior frames, we compute a weighted TOPIQ score, detailed in Appendix C. We report all metrics on 17-frame sequences by sampling 15 intermediate images between the input pairs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Implementation details. We use BLIP [31] to generate short text prompts \\( p \\) for each input image. For text inversion, we finetune the CLIP [36] encoded text embedding \\( z \\), using 500 steps with a learning rate of 0.005 and the AdamW optimizer. For BVP optimization, we perform 400 steps of gradient descent with an initial learning rate of 0.1, following a linear learning rate schedule. The hyperparameters are set as \\( \\tau = 600 \\), \\( \\Delta \\tau = 100 \\), \\( \\beta = 0.002 \\), and \\( \\sigma = 1 \\). As detailed in Sec. 4.3, we adopt a bisection strategy to add additional sample points every 100 steps. For IVP optimization, we set the iteration number to 200. To obtain a diverse set of initial velocities, we apply text inversion to the target text embedding using several generated images from random initial noise \\( \\mathcal{N}(0, I) \\), conditioned on the target prompt [39]. All methods use the same pre-trained diffusion model (Stable Diffusion v2.1-base) and text prompts, and default settings otherwise. Further details are in Appendix B." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "27994" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.133 + ], + "angle": 0, + "content": "Table 1. Image interpolation results. We report the performance on three datasets: MorphBench (MB), Animals and Humans (AH), and Web data (Web). TF denotes \"training-free\", which also prohibits fine-tuning; best results are in bold; second best ones are underlined. \"Ours\" represents the optimized geodesic path and \"Ours w/o opt.\" represents the unoptimized path as the great circle initialization." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.135, + 0.907, + 0.303 + ], + "angle": 0, + "content": "
MethodTFFID ↓PPL↓PDV↓TOPIQ ↑
AHMBWebAHMBWebAHMBWebAHMBWeb
NoiseDiffusion [54]✓71.85100.87201.082.5072.7183.7380.1170.1110.0990.7000.6660.650
AID [13]✓86.30124.11242.342.7092.6483.8130.1810.1880.2080.6990.6750.665
IMPUS [52]✗25.7536.3389.731.8611.7182.5540.0650.0660.1150.6220.5870.539
DiffMorpher [53]✗32.8942.39160.691.1951.0111.9340.0180.0160.0240.6860.6510.592
SmoothDiffusion [11]✗30.8052.19135.780.9030.8791.3710.0270.0330.0450.5710.5150.389
Ours w/o opt.✓24.7137.85112.810.8740.8411.4730.0320.0350.0530.5840.5460.466
Ours✓33.8746.51134.680.9600.9211.5650.0160.0220.0260.6070.5590.479
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.324, + 0.483, + 0.368 + ], + "angle": 0, + "content": "Table 2. We ablate the impact of different text conditioning strategies for BVP solver, including text inversion, positive \\((\\oplus)\\) prompts, and negative \\((\\ominus)\\) prompts, on the validation dataset." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.37, + 0.485, + 0.48 + ], + "angle": 0, + "content": "
Text inv. ⊕ prompt ⊘ promptFID↓PPL↓PDV↓TOPIQ↑
✓70.561.060.0170.518
69.061.0460.0170.529
✓✓65.051.0450.0180.562
✓64.721.0370.0190.564
✓✓63.281.0000.0170.553
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.524, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Results. We compare our method for the image interpolation task with several state-of-the-art diffusion-based methods, including NoiseDiffusion [54], DiffMorpher [53], IMPUS [52], AID [13], SmoothDiffusion [11] and report the result of a baseline ('Ours w/o opt.'), which returns the initial path before geodesic optimization. This corresponds to the great circle trajectory, the most direct path between the endpoints on the sphere. The quantitative and qualitative results are presented in Tab. 1 and Figs. 4 and 6. We observe that methods involving finetuning the diffusion model on input images, like DiffMorpher and IMPUS, tend to score better with respect to most of the metrics. While AID and NoiseDiffusion generate high-quality images, they have a weaker connection to the input images. SmoothDiffusion [11], trained on the large LAION dataset, performs well with respect to perceptual path length, but has high variance and weaker image quality scores, especially on the partially OOD Web dataset. In contrast, our method has high directness (low PPL), high fidelity to the input distribution (low FID), and very high perceptual smoothness (low PDV), but has slightly lower image quality (low TOPIQ). Overall, our approach is on-par with the best methods without requiring any training. Finally, we show qualitative results for the image extrapolation task in Fig. 7, where we visualize two trajectories for each prompt." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.323, + 0.902, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.441, + 0.907, + 0.466 + ], + "angle": 0, + "content": "(a) Relative log-probability along the path as optimization progresses, where iteration 0 is the lightest curve and iteration 400 is the darkest." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.468, + 0.905, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.563, + 0.839, + 0.576 + ], + "angle": 0, + "content": "(b) Path length with respect to optimization step." + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.587, + 0.907, + 0.618 + ], + "angle": 0, + "content": "Figure 5. Example of the evolution of the probability density along the path and the path length during BVP optimization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.642, + 0.909, + 0.84 + ], + "angle": 0, + "content": "Analysis. We constructed a validation dataset for ablation and analysis by randomly selecting 25 image pairs from the three datasets (Sec. 5.2). In Fig. 5, we show that optimization correctly increases the log probability of samples along the path and decreases the path length. This indicates that the curve smoothly approaches a geodesic during optimization. We also present an ablation study in Tab. 2, where we show how the text conditioning formulation (text inversion, positive prompt, and negative prompt) contributes to the performance of the method. In Appendix D, we compare the time-linear conditioning signal with the constant one. In Appendix E, we analyze the trade-off between the different choices of hyperparameter settings." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.848, + 0.642, + 0.864 + ], + "angle": 0, + "content": "5.3. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.909, + 0.903 + ], + "angle": 0, + "content": "This work has several limitations. First, the metrics used for evaluating image interpolation struggle to capture inter" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27995" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.907, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.258, + 0.39, + 0.735, + 0.406 + ], + "angle": 0, + "content": "Figure 6. Qualitative image interpolation results using our geodesic BVP solver." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.429, + 0.482, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.517, + 0.39, + 0.53 + ], + "angle": 0, + "content": "(a) Target prompt: \"Volcano eruption\"." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.53, + 0.482, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.619, + 0.483, + 0.643 + ], + "angle": 0, + "content": "(b) Target prompt: \"An expensive cake worth $1,000, adorned with fancy decorations and looking incredibly delicious\"." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.645, + 0.482, + 0.731 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.734, + 0.483, + 0.759 + ], + "angle": 0, + "content": "(c) Target prompt: \"A real photo of a cute but scary monstrous creature with sharp teeth and bulging eyes\"." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.77, + 0.483, + 0.813 + ], + "angle": 0, + "content": "Figure 7. Qualitative image extrapolation results using our geodesic IVP solver. For each image, we plot two extrapolated paths, each with different initial velocities but the same prompt." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "polation quality (smoothness, directness, and realism). In particular, FID, which measures fidelity to the input distribution, is unreliable when applied to small image sets like these, and the other metrics only capture individual aspects" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.907, + 0.658 + ], + "angle": 0, + "content": "of interpolation quality. Second, the method performs well for image morphing (local changes) but struggles with large camera motions or domain gaps, as illustrated in Figs. 15 and 16. We hypothesize that by initializing with a great circle, which also performs poorly in such cases, our optimizer gets stuck in nearby local optima rather than finding more optimal solutions. A global search strategy is indicated. Third, we approximate the log-probability gradient with a score distillation gradient, which is not necessarily well-aligned. Fourth, the path representation is inelegant: a spherical piecewise linear function (great circle arcs) for which the velocities and accelerations are approximated by fitting a cubic spline. Finally, the image extrapolation performance is unreliable, as determining a good initial velocity is challenging; a more robust approach is called for." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.671, + 0.634, + 0.687 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.697, + 0.907, + 0.895 + ], + "angle": 0, + "content": "In this paper, we have presented the theory required for computing probability density geodesics in diffusion latent space and algorithms for solving the associated initial and boundary value problems. We also described how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Finally, we presented applications to image interpolation and extrapolation and evaluated the performance of these training-free approaches. We show that they perform comparably or better than existing state-of-the-art. We expect these techniques to be useful for tasks involving generative modeling, as well as for studying the distribution of image space." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "27996" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.484, + 0.221 + ], + "angle": 0, + "content": "We thank all reviewers and ACs for their constructive comments. This research was, in part, funded by the U.S. Government—DARPA TIAMAT HR00112490421. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.236, + 0.188, + 0.251 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.26, + 0.484, + 0.302 + ], + "angle": 0, + "content": "[1] Avrim Blum, John Hopcroft, and Ravindran Kannan. Foundations of Data Science. Cambridge University Press, 2020. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.1, + 0.304, + 0.484, + 0.345 + ], + "angle": 0, + "content": "[2] Tim Brooks, Aleksander Holynski, and Alexei A. Efros. Instructpix2pix: Learning to follow image editing instructions. In CVPR, pages 18392-18402, 2023. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.347, + 0.484, + 0.4 + ], + "angle": 0, + "content": "[3] Chen-Hao Chao, Wei-Fang Sun, Bo-Wun Cheng, and Chun-Yi Lee. 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In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the spatially-varying inner product is inversely proportional to the probability density. In this formulation, a path that traverses a high density (that is, probable) region of image latent space is shorter than the equivalent path through a low density region. We present algorithms for solving the associated initial and boundary value problems and show how to compute the probability density along the path and the geodesic distance between two points. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. Finally, we demonstrate how these techniques can be applied to training-free image sequence interpolation and extrapolation, given a pre-trained image diffusion model. + +# 1. Introduction + +When trained over a data space, a diffusion model [43-46] can tell us the direction in which a data point of that space should move in order to increase its likelihood. That is, it learns a vector field corresponding to the gradient of the log-probability of the data (the Stein score function [47]). This is sufficient information to define a Riemannian manifold in this space, where the norm induced by a spatially-varying inner product is chosen to be inversely proportional to the probability density. This has the effect that geodesics—loosely, shortest paths—on this manifold 'prefer' to traverse high-density regions, which can be thought of as shortcuts in the space. In the context of image latent diffusion models [37], these regions correspond to the latent vectors of probable images, while low-density regions correspond to unrealistic image latents. By computing geodesics in this space, we can find shortest paths between images and study the structure of the learned space. + +![](images/b76ed9a0321ed1d8f794ca3afbcdb7d98f525448fad997a5e1ba8858297f6269.jpg) +(a) + +![](images/85750950bd3dabbffca514585fc02b2e470692307d49abbbb9e087f2ab51f52a.jpg) +(b) + +![](images/4817e1493a4a219a56f4e0bf3b3b12f94c45392bc83ffa310cbfeed992ec5288.jpg) +Figure 1. Given a probability density and initial or boundary conditions (here, the position of two points A and B), geodesics can be computed in this space. If the norm is chosen to be inversely proportional to the probability density, these geodesics preferentially traverse high density regions of the space. For an image data space, these correspond to plausible, realistic images according to the probability density, such as that learned by an image diffusion model. Here, we show the outputs of our boundary value problem (BVP) solver that computes a geodesic between endpoints A and B on a toy 2D example. (a) The geodesic and straight-line trajectories between A and B, given the underlying visualized probability density field (contours) and its gradient (arrows). (b) Probability density curves for both trajectories, showing that the straight-line path drops to zero probability very rapidly whereas the geodesic remains in higher probability regions. (c) Images corresponding to points along a geodesic in Stable Diffusion [37] latent space, given the left and right endpoints, computed using our BVP solver. + +![](images/712bcb5a2d2c53ca9948c06a0c92b9cc9f5736eaf805bca6bbd6f56c4df43afb.jpg) + +![](images/d2e3360ae48276359215761191cc1c5cf979e134b193f12c5f6f90e46e3bf8cb.jpg) + +![](images/c589e5472a96ece391fc441db2bd28ecff572d17afda3cdfbbb280594f8a16d1.jpg) +(c) + +![](images/81bfbc6b2980be51a1778fe359cbf139d7ec43f4f6b674e5fc67f0edbeef41f6.jpg) + +![](images/dc27b4cef213587df36c9132ca475bc645147307bd08a750b5eee06957ae055c.jpg) + +![](images/23d23c705011c30b46a558a50ec4f08a86cd6567066f461d7da2c6cf3a5f1a35.jpg) + +![](images/d47f8244cae9f30736e16ceca8788717344093ed20e7e6feb9aa7701670c19c5.jpg) + +In this work, we outline the relevant theory needed for computing probability density geodesics in diffusion latent space and present algorithms for solving the associated initial and boundary value problems. A 2D toy example of the boundary value problem (BVP) is presented in Fig. 1, alongside image outputs from the BVP solved in the 16384-D latent space of Stable Diffusion [37]. We address several challenges associated with computing + +geodesics in this space: (i) accurately estimating the score function, especially in low-density regions; (ii) handling (potentially spatially-varying) conditional probability densities; and (iii) solving initial and boundary value problems efficiently in an extremely high-dimensional space. + +We also describe how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. This work is part exploratory (e.g., what image sequences correspond to geodesics?) and part applied (e.g., how can these techniques be used to solve image sequence-based tasks?). For the latter, we evaluate the performance of these techniques on training-free image sequence interpolation and extrapolation tasks, given a pre-trained image diffusion model. Our contributions are: + +1. characterizing probability density geodesics in diffusion latent space; +2. algorithms for solving initial and boundary value problems that address challenges specific to conditional diffusion models; and +3. an application to image sequence interpolation and extrapolation tasks. + +We evaluate our training-free approach on five datasets with respect to other interpolation methods, including those that fine-tune the underlying diffusion model, achieving state-of-the-art results. + +# 2. Related Work + +Text-to-image diffusion models. Recently, diffusion models [8, 19] have gained significant attention in deep generative modeling. Given specific input conditions, these models generate realistic data by progressively denoising Gaussian noise through a noise prediction network, resulting in outputs that closely resemble real data distributions based on the provided conditions. With the availability of large-scale image-text pairs for training, diffusion models have achieved remarkable performance in the text-to-image generation task [34, 37, 40]. Due to the flexibility of textual prompting, text-to-image diffusion models have been widely applied to image editing [2, 14, 15, 26], personalization [9, 12, 29, 38], stylization [16, 48, 49], etc. In this work, we use a pretrained Stable Diffusion [37] model with which to explore probability density geodesics for video analysis, image interpolation and extrapolation. + +Image interpolation. Image interpolation, also known as image morphing, refers to the process of generating a smooth transition between two images by creating intermediate images [51, 56]. Traditional methods rely on pixel-based transformations, such as mesh morphing or defining + +a blending function [30, 41, 55]. However, these methods typically require pre-labeled corresponding points and human involvement. Some attempts have been made to automate this process [21, 32], but they generally work only on image pairs generated in controlled environments. With advances in generative models, Generative Adversarial Networks (GANs) [10] have been applied to the image interpolation task [28, 33, 42] and achieve moderate success. However, GAN-based image interpolation frameworks do not perform well in open-world settings. Specifically, input image pairs are required to be in-distribution with the training data of GAN models, which limits the application scenarios for image interpolation. With recent progress in text-to-image diffusion models, several works [11, 13, 50, 52, 53] have shown that these models achieve impressive results in image interpolation. Given any image pair, through textual embedding inversion and embedding interpolation, relatively smooth intermediate images can be obtained. In this work, we also employ a diffusion model; however, compared with prior works [11, 52, 53], our method is training-free and can be applied to image extrapolation. Furthermore, our approach offers a theoretical framework with which to understand these tasks. + +# 3. Probability Density Geodesics + +In this section, we will outline the theory of probability density geodesics, followed by the algorithmic development. The following section will apply the theory to a diffusion latent space and address some design decisions particular to that context. We aim to show that the structure of a data space can be studied by computing geodesics with respect to the probability distribution of the data, which can be obtained by training a diffusion model in that space. + +A geodesic is the (locally) shortest path between two points on a Riemannian manifold with a constant speed parameterization and can be obtained by minimizing the length of a curve between them using the calculus of variations. In the following, time derivatives are denoted $\dot{x}$ and second derivatives as $\ddot{x}$ . + +Equation for path length. Let $\gamma :[0,1]\to \mathbb{R}^n$ be a path such that $\gamma (0) = x_0$ and $\gamma (1) = x_{1}$ , and $S:\{\gamma_i\} \rightarrow \mathbb{R}$ be the action functional on the set of such paths, defined by + +$$ +S [ \gamma ] = \int_ {a} ^ {b} L (t, \gamma (t), \dot {\gamma} (t)) d t, \tag {1} +$$ + +where $L$ is the Lagrangian given by + +$$ +L (t, \gamma , \dot {\gamma}) = \sqrt {\langle \dot {\gamma} , \dot {\gamma} \rangle_ {K (\gamma)}} \text {w i t h} K (\gamma) = p (\gamma) ^ {- 2} I. \tag {2} +$$ + +Then $S[\gamma]$ is the path length for path $\gamma$ . The norm $\| x \| = \sqrt{\langle x, x \rangle_M}$ induced by the inner product $\langle x, y \rangle_M = x^\top M y$ is inversely proportional to the probability density with + +function $p: \mathbb{R}^n \to \mathbb{R}_+$ . The interpretation here is that paths that pass through high density regions are 'shorter' than paths through low density regions. Note that this reduces to the standard formulation for the path length of a curve when the probability distribution is uniform. + +Euler-Lagrange equations. Given this definition, a path $\gamma$ is a stationary point of $S$ if and only if it satisfies the Euler-Lagrange equations, viz., + +$$ +\frac {\partial}{\partial \gamma} L (t, \gamma (t), \dot {\gamma} (t)) - \frac {\mathrm {d}}{\mathrm {d} t} \frac {\partial}{\partial \dot {\gamma}} L (t, \gamma (t), \dot {\gamma} (t)) = 0. \tag {3} +$$ + +Using $\nabla \log p(\gamma) = \frac{1}{p}\frac{\mathrm{d}p}{\mathrm{d}\gamma}^{\mathsf{T}}$ and a constant speed parameterization of the path, for our Lagrangian we obtain + +$$ +\ddot {\gamma} + \left\| \dot {\gamma} \right\| ^ {2} \left(I - \hat {\dot {\gamma}} \hat {\gamma} ^ {\mathsf {T}}\right) \nabla \log p (\gamma) = 0, \tag {4} +$$ + +where the unit velocity is given by $\hat{\gamma} = \dot{\gamma} / \| \dot{\gamma}\|$ . That is, we obtain a nonlinear second-order ordinary differential equation (ODE) that expresses the relationship between the scaled acceleration and the gradient of the log probability. It is important to observe here that $\nabla \log p(\gamma)$ is the Stein score function [20, 47], the exact quantity that is estimated by a score-based diffusion model. The full derivation is presented in the appendix. + +Functional derivative. This second-order ODE expresses the relationship at optimality, i.e., given an initial position and velocity we can obtain the associated optimal path. However, we can also derive the functional derivative $\frac{\delta S}{\delta \gamma}$ of the path length functional $S$ by approximating the curve by a polygonal line with $n$ segments, as $n$ grows arbitrarily large. We obtain, for any $\gamma$ with a constant speed parameterization, + +$$ +\frac {\delta S}{\delta \gamma} = \frac {- 1}{p (\gamma) \| \dot {\gamma} \|} \left(\left(I - \hat {\dot {\gamma}} \hat {\dot {\gamma}} ^ {\mathsf {T}}\right) \nabla \log p (\gamma) + \frac {\ddot {\gamma}}{\| \dot {\gamma} \| ^ {2}}\right). (5) +$$ + +Probability density along the path. While estimating the absolute probability of any data point is challenging, the probability relative to the starting point is convenient to compute. For a conservative vector field $\nabla \log p$ (the gradient of a scalar field), line integrals are path independent. Therefore, the relative log-probability between two points $\gamma(a)$ and $\gamma(t)$ , along any path $\gamma$ connecting them, is + +$$ +\begin{array}{l} \log \tilde {p} _ {0} (\gamma (t)) := \log p (\gamma (t)) - \log p (\gamma (0)) (6) \\ = \int_ {0} ^ {t} \dot {\gamma} (\tau) ^ {\top} \nabla \log p (\gamma (\tau)) d \tau . (7) \\ \end{array} +$$ + +Let $f(x) = \dot{\gamma}(x)^{\mathsf{T}}\nabla \log p(\gamma(x))$ and let $t_i = i/n$ for $0 \leq i \leq n$ be $n + 1$ equally spaced samples along the path. + +Then by the trapezoidal rule, the relative probability at these points along the path can be approximated as + +$$ +\log \tilde {p} _ {0} (\gamma (t _ {i})) \approx \frac {1}{n} \left(\frac {f (t _ {0})}{2} + \sum_ {k = 1} ^ {i - 1} f (t _ {k}) + \frac {f (t _ {i})}{2}\right). \tag {8} +$$ + +Higher-order approaches, such as Simpson's rule, may also be used for this approximation. From this, we may compute the relative probability $\tilde{p}_0(\gamma(t)) = p(\gamma(t_i)) / p(\gamma(0))$ at every point $\gamma(t_i)$ along the curve. + +Geodesic distance. Given the probabilities computed in the previous section, it is trivial to estimate the geodesic distance. Let $t_i = i / n$ for $0 \leq i \leq n$ be $n + 1$ equally spaced samples along the geodesic $\gamma$ , then the relative geodesic distance is given by + +$$ +\begin{array}{l} \tilde {d} _ {a} (b) = \int_ {a} ^ {b} \frac {\left\| \dot {\gamma} (t) \right\|}{\tilde {p} _ {a} (\gamma (t))} d t \tag {9} \\ \approx \frac {1}{n} \left(\frac {\| \dot {\gamma} (a) \|}{2} + \sum_ {i = 1} ^ {n - 1} \frac {\| \dot {\gamma} (t _ {i}) \|}{\tilde {p} _ {a} (\gamma (t _ {i}))} + \frac {\| \dot {\gamma} (b) \|}{2 \tilde {p} _ {a} (\gamma (t _ {n}))}\right) \\ \end{array} +$$ + +and the absolute geodesic distance is given by $d(a, b) = \tilde{d}_a(b) / p(\gamma(a))$ . + +# 4. Geodesics in Diffusion Latent Space + +In this section, we show how to compute geodesics in the latent space of a pre-trained Stable Diffusion [37] model. An element $x \in \mathbb{R}^{64 \times 64 \times 4}$ of this latent space can be obtained from an image $\mathcal{I}$ via an encoder $\mathcal{E}(\mathcal{I})$ ; a decoder $\mathcal{D}(x)$ performs the inverse mapping. A forward process incrementally corrupts these elements with Gaussian noise, up to timestep $\tau = T$ , resulting in a noise element $x_{T} \sim \mathcal{N}(0, I)$ . To distinguish between the time dependence of the diffusion process and that of the path formulation in Sec. 3, we use $\tau$ instead of $t$ to denote the diffusion time-step throughout the rest of the paper. The diffusion model is trained on a very large dataset of images to denoise elements of this latent space at all timesteps. It is parameterized by a neural network $\epsilon_{\theta}(x_{\tau}; z)$ that predicts the noise $\epsilon$ that was used to produce noisy sample $x_{\tau}$ from clean sample $x_{0}$ [19]. This is proportional to the score function $\nabla_{x_{\tau}} \log p_{\tau}(x_{\tau})$ of the smoothed (noised) density $p_{\tau}$ [19]. Finally, our method makes use of the deterministic DDIM forward and backward processes (DDIM-F, DDIM-B) with noise schedule parameter $\overline{\alpha}_{\tau}$ , known as inversion [44], defined by + +$$ +\frac {\mathrm {d}}{\mathrm {d} \tau} \left(\frac {x _ {\tau}}{\sqrt {\bar {\alpha} _ {\tau}}}\right) = \frac {\mathrm {d}}{\mathrm {d} \tau} \left(\sqrt {\frac {1 - \bar {\alpha} _ {\tau}}{\bar {\alpha} _ {\tau}}}\right) \epsilon_ {\theta} (x _ {\tau}; z). \tag {10} +$$ + +Working with diffusion models introduces several challenges, which we address in this section. In particular, (i) how to handle (potentially varying) conditional probability + +densities; (ii) how to accurately estimate the score function $\nabla \log p(x)$ , especially in low density regions; and (iii) how to solve the initial and boundary value problems efficiently in an extremely high-dimensional space (e.g., $\mathbb{R}^{16384}$ ). + +# 4.1. Conditional probability density geodesics + +Most image diffusion models are conditional models, trained to denoise an image conditioned on a signal $z$ such as a CLIP-encoded text prompt [36, 37, 40]. Hence, we extend the formulation from Sec. 3 to consider the conditional probability density function $p(\gamma(t) \mid \zeta(t, \gamma(t))$ . Here, $\zeta: \mathbb{R} \times \mathbb{R}^n \to \mathbb{R}^d$ is a function over the path parameter and latent space that obtains the values of the conditioning vectors $z_a$ and $z_b$ at the endpoints, such that $\zeta(0, \gamma(0)) = z_0$ and $\zeta(1, \gamma(1)) = z_1$ for $(a, b) = (0, 1)$ . In our experiments, we primarily consider the case where $\zeta$ is linear in time and constant in the latent space: $\zeta(t) = (1 - t)z_0 + tz_1$ . + +# 4.2. Score estimation + +The score function is likely to be poorly estimated in low-density regions [45]. This occurs since the diffusion model does not have enough evidence during training to estimate the score accurately in regions of the latent space where data is scarce. However, estimating accurate directions in these regions is critical for solving boundary value problems, since the initial path to be optimized is likely to traverse low-density regions. Diffusion models apply multiple levels of noise to data elements in order to alleviate this problem. By doing so, low-density regions of the space can be populated by noised data, improving the quality of the estimated gradients at those locations. As a result, we choose to compute geodesics (and query the diffusion model) at a particular non-zero noise level, with the associated diffusion timestep $\tau$ . A side benefit of this is that the probability density becomes increasingly Gaussian as the timestep increases, which provides a useful inductive bias, as explained in the next section. + +However, there is an additional complexity. For a noised training sample $x_{\tau}$ , the unconditional model $\epsilon_{\theta}(x_{\tau};z = \varnothing ,\tau)$ is expected to predict the noise $\epsilon$ that was used to produce this sample from clean sample $x_0$ . Unfortunately, in our case, we obtain vectors $x_{\tau}$ from an optimization procedure, initialized along a great circle between endpoints $x_{a,\tau}$ and $x_{b,\tau}$ . These points are (at least initially) out-of-distribution (OOD) for the model, and we should not expect it to predict the noise well. Instead, Katzir et al. [25] observe that the prediction consists of a domain correction term $\delta_{\mathrm{D}}$ and a denoising term $\delta_{\mathrm{N}}$ . The residual $\delta_{\mathrm{N}} - \epsilon$ , as used in score distillation sampling [35], is generally non-zero and noisy, leading to an averaging (over-smoothing) effect in the optimized latents. In our optimization procedure, we are not aiming to denoise the samples, so neglect the denoising direction $\delta_{\mathrm{N}}$ and instead use noise-free score distillation [25] + +![](images/b10bcac0e23f1561c1de13bda2da6048800f843756e192db64b363369cc676ba.jpg) +(a) The pipeline for image interpolation. + +![](images/77a2c9220bebbd8d64c0948ee28f3022eda76bb244b7feb9f22c994fc454afe6.jpg) +(b) The pipeline for image extrapolation. +Figure 2. Pipelines for the image interpolation and extrapolation tasks, addressed by solving boundary and initial value problems in diffusion latent space. + +direction $\phi (x\mid z,\tau)$ to approximate the gradient direction, + +$$ +\nabla \log p (x \mid z, \tau) \approx \beta \phi (x \mid z, \tau) \tag {11} +$$ + +$$ +\phi (x \mid z, \tau) = \mathbb {E} _ {\tau^ {\prime} \in \mathcal {R} _ {\tau}} w \left(\tau^ {\prime}\right) \left(\sigma d \left(x _ {\tau^ {\prime}} \mid z\right) - d \left(x _ {\tau^ {\prime}} \mid z _ {\text {n e g}}\right)\right), \tag {12} +$$ + +where $\beta$ is a scalar hyperparameter, $w(\tau)$ is a weighting function, $\sigma$ is the classifier-free guidance parameter (0 if unconditional) [18], $z_{\mathrm{neg}}$ is a negative prompt embedding that says something about the specific OOD latent vector (see Appendix B), $d(x_{\tau}|z) = \epsilon_{\theta}(x_{\tau}|\varnothing) - \epsilon_{\theta}(x_{\tau}|z)$ is the direction function, and the expectation is taken over a range of timesteps $\mathcal{R}_{\tau} = [\tau -\Delta \tau ,\tau +\Delta \tau ]$ + +# 4.3. Efficient IVP and BVP solvers + +Solving the initial and boundary value problems efficiently with respect to time and memory becomes challenging in the extremely high-dimensional latent space $\mathbb{R}^{4\times 64\times 64}$ of Stable Diffusion [37]. For this dimensionality, standard techniques, such as collocation algorithms for solving BVPs [27], become prohibitive in time and memory. We also aim to minimize calls to the diffusion model, since this is expensive to compute. In view of these aims, we use a simple low-memory parametrization and optimization strategy. + +Before outlining the algorithms, we first observe that the probability distribution becomes more Gaussian as the diffusion timestep increases [5] and that the Gaussian Annulus Theorem [1] states that a point chosen at random from a unit variance $d$ -dimensional Gaussian distribution will be located in a small annulus around a sphere of radius $\sqrt{d}$ with high probability. However, for finite-sized gradient descent steps, the optimizer may take the curve away from the sphere, moving into low-density regions where probability density gradients are poorly estimated. To mitigate this, we reproject the curve back onto the sphere, ensuring that optimization remains within the high-density region where gra + +Algorithm 1: BVP solver for image interpolation. +Input: start/end image $\mathcal{I}_0 / \mathcal{I}_1$ ; text prompts $p_0 / p_1$ diffusion timestep $\tau$ ; learning rate $\eta$ optimizer steps $n$ hyperparameter $\beta$ ; VAE encoder $\mathcal{E}$ ; CLIP text encoder $\mathcal{C}$ Output: geodesic $\gamma$ +1 $\{z_0,z_1\} \gets \{\mathcal{C}(p_0),\mathcal{C}(p_1)\}$ +2 $\{x_0,x_1\} \gets \{\mathrm{DDIM - F}(\mathcal{E}(\mathcal{I}_i),\tau ,z_i)\}_{i = \{0,1\}}$ +3 $\gamma \leftarrow$ Interpolate((0,xo),(1,x1)) +4 for $i = 1$ to n do +5 T $\leftarrow$ TimeSampler(i) +6 S $\leftarrow$ {(0,xo),(1,x1)} +7 forall $t\in \mathcal{T}$ do +8 x $\leftarrow$ y(t); +9 z $\leftarrow$ (1-t)z0+tz1 +10 s $\leftarrow$ Score(x,z,τ,β); %Eq. (11) +11 g $\leftarrow$ FuncDeriv(s,x, $\dot{x},\ddot{x})$ %Eq. (13) +12 x $\leftarrow$ ||x||(x-ηg)/||x-ηg|| +13 S $\leftarrow$ SU{(t,x)} +14 $\gamma \leftarrow$ Interpolate(S) + +dient estimates are more reliable, and we project the functional derivative to the tangent space of the sphere, + +$$ +g = \left(I - \hat {\gamma} \hat {\gamma} ^ {\mathsf {T}}\right) \frac {\delta S}{\delta \gamma}. \tag {13} +$$ + +BVP. Given a start position $x^{(0)}$ and an end position $x^{(k + 1)}$ , we parameterize the path $\gamma$ with a set of control points $\{x_{\tau}^{(i)}\}_{i = 1}^{k}$ connected by a spherical piecewise linear function (great circle arcs). For clarity, we note points on this curve as $x_{t}$ with the curve parameter $t \in [0,1]$ , dropping $\tau$ and the ordinal superscript. Algorithm 1 initializes the path as a great circle. It then computes the projected gradient descent update for the control points using Eq. (13), where the associated velocities $\dot{\gamma}$ and accelerations $\ddot{\gamma}$ are obtained from a natural cubic spline fit to the control points and end points, and projects the updated control points back onto the sphere. To save computation, the algorithm uses a coarse-to-fine discretization, where the number of control points $k \in [1,3,7,15]$ varies as optimization progresses, using a bisection strategy. + +IVP. Algorithm 2 takes an image $\mathcal{I}_0$ and its corresponding text description $p_0$ , and extrapolates how the geodesic evolves given an initial velocity formulated from the target prompt $p_1$ . As with Eq. (13), the updates are projected to the tangent space, resulting in the ODE given by + +$$ +\ddot {\gamma} = - \left\| \dot {\gamma} \right\| ^ {2} \left(I - \hat {\gamma} \hat {\gamma} ^ {\mathsf {T}}\right) \left(I - \hat {\dot {\gamma}} \hat {\dot {\gamma}} ^ {\mathsf {T}}\right) \nabla \log p (\gamma), \tag {14} +$$ + +which can be solved by applying the Runge-Kutta (RK4) method to the first-order system of equations. + +Algorithm 2: IVP solver for image extrapolation. +Input: image $\mathcal{I}_0$ ; source text prompt $p_0$ ; target text prompt $p_1$ ; diffusion timestep $\tau$ ; optimizer steps $n$ ; VAE encoder $\mathcal{E}$ ; CLIP text encoder $\mathcal{C}$ ; hyperparameter $\beta$ +Output: image sequence $\mathcal{I}$ ; geodesic $\gamma$ +1 $\{z_0, z_1\} \gets \{\mathcal{C}(p_0), \mathcal{C}(p_1)\}$ +2 $x \gets \text{DDIM-F}(\mathcal{E}(\mathcal{I}_0), \tau, z_0)$ +3 $\dot{x} \gets \text{GetInitVelocity}(x, z_0, z_1)$ +4 $\mathcal{S} \gets \{(0, x)\}$ +5 $\mathcal{I} \gets \{\mathcal{I}_0\}$ +6 for $i = 1$ to $n$ do +7 $z \gets (1 - i/n)z_0 + (i/n)z_1$ +8 $s \gets \text{Score}(x, z, \tau, \beta)$ ; % Eq. (11) +9 $\ddot{x} \gets \text{ODE}(s, x, \dot{x})$ ; % Eq. (14) +10 $\dot{x} \gets \text{RK4}(\dot{x}, \ddot{x}, 1/n)$ +11 $x \gets \|x\| \text{RK4}(x, \dot{x}, 1/n)/\|\text{RK4}(x, \dot{x}, 1/n)\|$ +12 $\mathcal{S} \gets \mathcal{S} \cup \{(i/n, x)\}$ +13 $\mathcal{I} \gets \mathcal{I} \cup \{\mathcal{D}(\text{DDIM-B}(x, \tau, z))\}$ +14 $\gamma \gets \text{Interpolate}(\mathcal{S})$ + +# 5. Experiments + +In this section, we first analyze whether short video sequences are geodesics in diffusion latent space. Second, we evaluate applications of the theory, focusing on the image interpolation task framed as solving a boundary value problem. For all experiments, we use a pre-trained Stable Diffusion v2.1-base model [37]. + +# 5.1. Geodesic analysis of videos + +The objective of this experiment is to assess how close video clips are to geodesics. + +Dataset. We use the CLEVR framework [22] to render 40 synthetic videos with Blender. Each 100-frame sequence contains one of the three CLEVR objects (cube, sphere, cylinder) and has a single varying attribute, including camera rotation and translation, light source location, and the size, color and motion of the object. + +Baselines. The path $\gamma_v$ corresponding to the original video clip is compared to the path after geodesic optimization $\gamma_o$ , the path after a sinuoidal perturbation $\gamma_{\delta} = \gamma_v + \delta \sin (\pi \gamma)$ , and the path after smoothing $\gamma_s$ , by fitting a smoothed cubic spline [7] with smoothing factor 0.9999. + +Results. In Fig. 3a, we report the $l_{2}$ norm of the functional derivative in Eq. (5) as it varies along the path, for a single video clip (translating red cube). For a geodesic, this is zero everywhere along the path. In Fig. 3b, we report the average of this norm across the path and the dataset. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm along the path $\gamma_v$ to be near zero, (ii) + +![](images/28ce7a8a02ed09744a6a23095798dcfa2e55c44259d4eacf7d70856f62e86fa0.jpg) +(a) Geodesic gradient norm along the path, for the translating red cube. + +![](images/6b5ba3c5ac95f794d76c568d844e8eea69c2cd2c4f22b96832f23af59c5ddc91.jpg) +(b) Geodesic gradient norm, averaged across the path and dataset. + +the norm to be close to that of the optimized path $\gamma_{o}$ , and (iii) the norm of the perturbed $\gamma_{\delta}$ or smoothed $\gamma_{s}$ paths to be larger. We observe these trends in the results, and conclude that many of the videos are approximately geodesic. + +# 5.2. Applications + +Here, we assess the performance of the geodesic solvers for the image interpolation and extrapolation tasks. + +Datasets. We compile a union of datasets from prior works [50, 52, 53]. This includes MorphBench [53], which contains 90 image pairs of object animations and object metamorphoses; Animals and Humans [52], which contains 50 animal image pairs from AFHQ [6] with an LPIPS below 0.7 and 50 human face image pairs from CelebA-HQ [23] with an LPIPS below 0.6; and Web, which contains 20 image pairs sourced from publicly accessible websites, some of which have been used in other related studies [50]. + +Metrics. Quantitatively evaluating image interpolation and extrapolation is extremely challenging and subjective. Following previous work [52, 53], we report (1) the Fréchet inception distance (FID) [17] between the set of input images and the set of generated images to measure how close the distributions are; (2) the perceptual path length (PPL) [24] as the sum of LPIPS between adjacent images to assess the + +![](images/bde90908e57ae11e25ea923cf2ec9b2fcf70061e61bd912ed6ae0fdbce5ae003.jpg) +Figure 3. Analysis of simple videos generated using CLEVR [22]. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm of the geodesic gradient along the path $\gamma_v$ to be near zero, (ii) the norm to be close to that of the optimized path $\gamma_o$ , and (iii) the norm of the perturbed $\gamma_{\delta}$ or smoothed $\gamma_s$ paths to be larger. From the evidence, we conclude that many of the videos are approximately geodesic. +Figure 4. Qualitative comparison of image interpolation results. + +directness of the generated image sequence; (3) perceptual distance variance (PDV) as the standard deviation of LPIPS between consecutive images to assess the consistency of transition rates across the sequence; and (4) the TOPIQ [4] score, an image quality metric that evaluates the perceptual quality of each generated image in alignment with human perception. To focus on the quality of interior frames, we compute a weighted TOPIQ score, detailed in Appendix C. We report all metrics on 17-frame sequences by sampling 15 intermediate images between the input pairs. + +Implementation details. We use BLIP [31] to generate short text prompts $p$ for each input image. For text inversion, we finetune the CLIP [36] encoded text embedding $z$ , using 500 steps with a learning rate of 0.005 and the AdamW optimizer. For BVP optimization, we perform 400 steps of gradient descent with an initial learning rate of 0.1, following a linear learning rate schedule. The hyperparameters are set as $\tau = 600$ , $\Delta \tau = 100$ , $\beta = 0.002$ , and $\sigma = 1$ . As detailed in Sec. 4.3, we adopt a bisection strategy to add additional sample points every 100 steps. For IVP optimization, we set the iteration number to 200. To obtain a diverse set of initial velocities, we apply text inversion to the target text embedding using several generated images from random initial noise $\mathcal{N}(0, I)$ , conditioned on the target prompt [39]. All methods use the same pre-trained diffusion model (Stable Diffusion v2.1-base) and text prompts, and default settings otherwise. Further details are in Appendix B. + +Table 1. Image interpolation results. We report the performance on three datasets: MorphBench (MB), Animals and Humans (AH), and Web data (Web). TF denotes "training-free", which also prohibits fine-tuning; best results are in bold; second best ones are underlined. "Ours" represents the optimized geodesic path and "Ours w/o opt." represents the unoptimized path as the great circle initialization. + +
MethodTFFID ↓PPL↓PDV↓TOPIQ ↑
AHMBWebAHMBWebAHMBWebAHMBWeb
NoiseDiffusion [54]✓71.85100.87201.082.5072.7183.7380.1170.1110.0990.7000.6660.650
AID [13]✓86.30124.11242.342.7092.6483.8130.1810.1880.2080.6990.6750.665
IMPUS [52]✗25.7536.3389.731.8611.7182.5540.0650.0660.1150.6220.5870.539
DiffMorpher [53]✗32.8942.39160.691.1951.0111.9340.0180.0160.0240.6860.6510.592
SmoothDiffusion [11]✗30.8052.19135.780.9030.8791.3710.0270.0330.0450.5710.5150.389
Ours w/o opt.✓24.7137.85112.810.8740.8411.4730.0320.0350.0530.5840.5460.466
Ours✓33.8746.51134.680.9600.9211.5650.0160.0220.0260.6070.5590.479
+ +Table 2. We ablate the impact of different text conditioning strategies for BVP solver, including text inversion, positive $(\oplus)$ prompts, and negative $(\ominus)$ prompts, on the validation dataset. + +
Text inv. ⊕ prompt ⊘ promptFID↓PPL↓PDV↓TOPIQ↑
✓70.561.060.0170.518
69.061.0460.0170.529
✓✓65.051.0450.0180.562
✓64.721.0370.0190.564
✓✓63.281.0000.0170.553
+ +Results. We compare our method for the image interpolation task with several state-of-the-art diffusion-based methods, including NoiseDiffusion [54], DiffMorpher [53], IMPUS [52], AID [13], SmoothDiffusion [11] and report the result of a baseline ('Ours w/o opt.'), which returns the initial path before geodesic optimization. This corresponds to the great circle trajectory, the most direct path between the endpoints on the sphere. The quantitative and qualitative results are presented in Tab. 1 and Figs. 4 and 6. We observe that methods involving finetuning the diffusion model on input images, like DiffMorpher and IMPUS, tend to score better with respect to most of the metrics. While AID and NoiseDiffusion generate high-quality images, they have a weaker connection to the input images. SmoothDiffusion [11], trained on the large LAION dataset, performs well with respect to perceptual path length, but has high variance and weaker image quality scores, especially on the partially OOD Web dataset. In contrast, our method has high directness (low PPL), high fidelity to the input distribution (low FID), and very high perceptual smoothness (low PDV), but has slightly lower image quality (low TOPIQ). Overall, our approach is on-par with the best methods without requiring any training. Finally, we show qualitative results for the image extrapolation task in Fig. 7, where we visualize two trajectories for each prompt. + +![](images/7cebf3d09a35509fab795b2c5898550cf77237f8c9651eb6c21d5ea8f5e5bebc.jpg) + +![](images/13ea20c75c86ec6a2ca6af7acc857a465d65dbd5fc42da323fa524580438e7a4.jpg) +(a) Relative log-probability along the path as optimization progresses, where iteration 0 is the lightest curve and iteration 400 is the darkest. +(b) Path length with respect to optimization step. +Figure 5. Example of the evolution of the probability density along the path and the path length during BVP optimization. + +Analysis. We constructed a validation dataset for ablation and analysis by randomly selecting 25 image pairs from the three datasets (Sec. 5.2). In Fig. 5, we show that optimization correctly increases the log probability of samples along the path and decreases the path length. This indicates that the curve smoothly approaches a geodesic during optimization. We also present an ablation study in Tab. 2, where we show how the text conditioning formulation (text inversion, positive prompt, and negative prompt) contributes to the performance of the method. In Appendix D, we compare the time-linear conditioning signal with the constant one. In Appendix E, we analyze the trade-off between the different choices of hyperparameter settings. + +# 5.3. Limitations + +This work has several limitations. First, the metrics used for evaluating image interpolation struggle to capture inter + +![](images/bcf5418d0216f5f1c0292fd158702ab39263e83ce081b9f7ebff49ee6a4d500c.jpg) +Figure 6. Qualitative image interpolation results using our geodesic BVP solver. + +![](images/0284ee75145d6d6e5565e3d64f9692d5efad83163d206b393173c72b02c006b1.jpg) + +![](images/e34cb4778b5e0bea73147eebf27571ccb52879b29fafedddbc5e842b12ed830f.jpg) +(a) Target prompt: "Volcano eruption". + +![](images/3dc590cc7147462962cd7525bd021f125d6c1f96c6dbef5177c91f618bcfd50a.jpg) +(b) Target prompt: "An expensive cake worth $1,000, adorned with fancy decorations and looking incredibly delicious". +(c) Target prompt: "A real photo of a cute but scary monstrous creature with sharp teeth and bulging eyes". +Figure 7. Qualitative image extrapolation results using our geodesic IVP solver. For each image, we plot two extrapolated paths, each with different initial velocities but the same prompt. + +polation quality (smoothness, directness, and realism). In particular, FID, which measures fidelity to the input distribution, is unreliable when applied to small image sets like these, and the other metrics only capture individual aspects + +of interpolation quality. Second, the method performs well for image morphing (local changes) but struggles with large camera motions or domain gaps, as illustrated in Figs. 15 and 16. We hypothesize that by initializing with a great circle, which also performs poorly in such cases, our optimizer gets stuck in nearby local optima rather than finding more optimal solutions. A global search strategy is indicated. Third, we approximate the log-probability gradient with a score distillation gradient, which is not necessarily well-aligned. Fourth, the path representation is inelegant: a spherical piecewise linear function (great circle arcs) for which the velocities and accelerations are approximated by fitting a cubic spline. Finally, the image extrapolation performance is unreliable, as determining a good initial velocity is challenging; a more robust approach is called for. + +# 6. Conclusion + +In this paper, we have presented the theory required for computing probability density geodesics in diffusion latent space and algorithms for solving the associated initial and boundary value problems. We also described how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Finally, we presented applications to image interpolation and extrapolation and evaluated the performance of these training-free approaches. We show that they perform comparably or better than existing state-of-the-art. We expect these techniques to be useful for tasks involving generative modeling, as well as for studying the distribution of image space. + +# Acknowledgments + +We thank all reviewers and ACs for their constructive comments. This research was, in part, funded by the U.S. Government—DARPA TIAMAT HR00112490421. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government. + +# References + +[1] Avrim Blum, John Hopcroft, and Ravindran Kannan. Foundations of Data Science. Cambridge University Press, 2020. 4 +[2] Tim Brooks, Aleksander Holynski, and Alexei A. Efros. Instructpix2pix: Learning to follow image editing instructions. In CVPR, pages 18392-18402, 2023. 2 +[3] Chen-Hao Chao, Wei-Fang Sun, Bo-Wun Cheng, and Chun-Yi Lee. On investigating the conservative property of score-based generative models. 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In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the spatially-varying inner product is inversely proportional to the probability density. In this formulation, a path that traverses a high density (that is, probable) region of image latent space is shorter than the equivalent path through a low density region. We present algorithms for solving the associated initial and boundary value problems and show how to compute the probability density along the path and the geodesic distance between two points. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. Finally, we demonstrate how these techniques can be applied to training-free image sequence interpolation and extrapolation, given a pre-trained image diffusion model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 510, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 713 + ], + "type": "text", + "content": "When trained over a data space, a diffusion model [43-46] can tell us the direction in which a data point of that space should move in order to increase its likelihood. That is, it learns a vector field corresponding to the gradient of the log-probability of the data (the Stein score function [47]). This is sufficient information to define a Riemannian manifold in this space, where the norm induced by a spatially-varying inner product is chosen to be inversely proportional to the probability density. This has the effect that geodesics—loosely, shortest paths—on this manifold 'prefer' to traverse high-density regions, which can be thought of as shortcuts in the space. In the context of image latent diffusion models [37], these regions correspond to the latent vectors of probable images, while low-density regions correspond to unrealistic image latents. By computing geodesics in this space, we can find shortest paths between images and study the structure of the learned space." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 240, + 411, + 336 + ], + "blocks": [ + { + "bbox": [ + 316, + 240, + 411, + 336 + ], + "lines": [ + { + "bbox": [ + 316, + 240, + 411, + 336 + ], + "spans": [ + { + "bbox": [ + 316, + 240, + 411, + 336 + ], + "type": "image", + "image_path": "b76ed9a0321ed1d8f794ca3afbcdb7d98f525448fad997a5e1ba8858297f6269.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 359, + 338, + 369, + 347 + ], + "lines": [ + { + "bbox": [ + 359, + 338, + 369, + 347 + ], + "spans": [ + { + "bbox": [ + 359, + 338, + 369, + 347 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 414, + 240, + 553, + 337 + ], + "blocks": [ + { + "bbox": [ + 414, + 240, + 553, + 337 + ], + "lines": [ + { + "bbox": [ + 414, + 240, + 553, + 337 + ], + "spans": [ + { + "bbox": [ + 414, + 240, + 553, + 337 + ], + "type": "image", + "image_path": "85750950bd3dabbffca514585fc02b2e470692307d49abbbb9e087f2ab51f52a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 338, + 490, + 347 + ], + "lines": [ + { + "bbox": [ + 479, + 338, + 490, + 347 + ], + "spans": [ + { + "bbox": [ + 479, + 338, + 490, + 347 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 317, + 348, + 344, + 380 + ], + "blocks": [ + { + "bbox": [ + 317, + 348, + 344, + 380 + ], + "lines": [ + { + "bbox": [ + 317, + 348, + 344, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 348, + 344, + 380 + ], + "type": "image", + "image_path": "4817e1493a4a219a56f4e0bf3b3b12f94c45392bc83ffa310cbfeed992ec5288.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 400, + 555, + 588 + ], + "lines": [ + { + "bbox": [ + 313, + 400, + 555, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 400, + 555, + 588 + ], + "type": "text", + "content": "Figure 1. Given a probability density and initial or boundary conditions (here, the position of two points A and B), geodesics can be computed in this space. If the norm is chosen to be inversely proportional to the probability density, these geodesics preferentially traverse high density regions of the space. For an image data space, these correspond to plausible, realistic images according to the probability density, such as that learned by an image diffusion model. Here, we show the outputs of our boundary value problem (BVP) solver that computes a geodesic between endpoints A and B on a toy 2D example. (a) The geodesic and straight-line trajectories between A and B, given the underlying visualized probability density field (contours) and its gradient (arrows). (b) Probability density curves for both trajectories, showing that the straight-line path drops to zero probability very rapidly whereas the geodesic remains in higher probability regions. (c) Images corresponding to points along a geodesic in Stable Diffusion [37] latent space, given the left and right endpoints, computed using our BVP solver." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 346, + 348, + 374, + 379 + ], + "blocks": [ + { + "bbox": [ + 346, + 348, + 374, + 379 + ], + "lines": [ + { + "bbox": [ + 346, + 348, + 374, + 379 + ], + "spans": [ + { + "bbox": [ + 346, + 348, + 374, + 379 + ], + "type": "image", + "image_path": "712bcb5a2d2c53ca9948c06a0c92b9cc9f5736eaf805bca6bbd6f56c4df43afb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 375, + 348, + 403, + 379 + ], + "blocks": [ + { + "bbox": [ + 375, + 348, + 403, + 379 + ], + "lines": [ + { + "bbox": [ + 375, + 348, + 403, + 379 + ], + "spans": [ + { + "bbox": [ + 375, + 348, + 403, + 379 + ], + "type": "image", + "image_path": "d2e3360ae48276359215761191cc1c5cf979e134b193f12c5f6f90e46e3bf8cb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 405, + 348, + 433, + 379 + ], + "blocks": [ + { + "bbox": [ + 405, + 348, + 433, + 379 + ], + "lines": [ + { + "bbox": [ + 405, + 348, + 433, + 379 + ], + "spans": [ + { + "bbox": [ + 405, + 348, + 433, + 379 + ], + "type": "image", + "image_path": "c589e5472a96ece391fc441db2bd28ecff572d17afda3cdfbbb280594f8a16d1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 382, + 440, + 392 + ], + "lines": [ + { + "bbox": [ + 429, + 382, + 440, + 392 + ], + "spans": [ + { + "bbox": [ + 429, + 382, + 440, + 392 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 434, + 348, + 463, + 379 + ], + "blocks": [ + { + "bbox": [ + 434, + 348, + 463, + 379 + ], + "lines": [ + { + "bbox": [ + 434, + 348, + 463, + 379 + ], + "spans": [ + { + "bbox": [ + 434, + 348, + 463, + 379 + ], + "type": "image", + "image_path": "81bfbc6b2980be51a1778fe359cbf139d7ec43f4f6b674e5fc67f0edbeef41f6.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 465, + 348, + 493, + 379 + ], + "blocks": [ + { + "bbox": [ + 465, + 348, + 493, + 379 + ], + "lines": [ + { + "bbox": [ + 465, + 348, + 493, + 379 + ], + "spans": [ + { + "bbox": [ + 465, + 348, + 493, + 379 + ], + "type": "image", + "image_path": "dc27b4cef213587df36c9132ca475bc645147307bd08a750b5eee06957ae055c.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 493, + 348, + 523, + 379 + ], + "blocks": [ + { + "bbox": [ + 493, + 348, + 523, + 379 + ], + "lines": [ + { + "bbox": [ + 493, + 348, + 523, + 379 + ], + "spans": [ + { + "bbox": [ + 493, + 348, + 523, + 379 + ], + "type": "image", + "image_path": "23d23c705011c30b46a558a50ec4f08a86cd6567066f461d7da2c6cf3a5f1a35.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 525, + 348, + 553, + 379 + ], + "blocks": [ + { + "bbox": [ + 525, + 348, + 553, + 379 + ], + "lines": [ + { + "bbox": [ + 525, + 348, + 553, + 379 + ], + "spans": [ + { + "bbox": [ + 525, + 348, + 553, + 379 + ], + "type": "image", + "image_path": "d47f8244cae9f30736e16ceca8788717344093ed20e7e6feb9aa7701670c19c5.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "content": "In this work, we outline the relevant theory needed for computing probability density geodesics in diffusion latent space and present algorithms for solving the associated initial and boundary value problems. A 2D toy example of the boundary value problem (BVP) is presented in Fig. 1, alongside image outputs from the BVP solved in the 16384-D latent space of Stable Diffusion [37]. We address several challenges associated with computing" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "27989" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "geodesics in this space: (i) accurately estimating the score function, especially in low-density regions; (ii) handling (potentially spatially-varying) conditional probability densities; and (iii) solving initial and boundary value problems efficiently in an extremely high-dimensional space." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 133, + 295, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 287 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 287 + ], + "type": "text", + "content": "We also describe how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. This work is part exploratory (e.g., what image sequences correspond to geodesics?) and part applied (e.g., how can these techniques be used to solve image sequence-based tasks?). For the latter, we evaluate the performance of these techniques on training-free image sequence interpolation and extrapolation tasks, given a pre-trained image diffusion model. Our contributions are:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 289, + 295, + 372 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 56, + 289, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 289, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 289, + 295, + 312 + ], + "type": "text", + "content": "1. characterizing probability density geodesics in diffusion latent space;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 313, + 294, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 294, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 294, + 348 + ], + "type": "text", + "content": "2. algorithms for solving initial and boundary value problems that address challenges specific to conditional diffusion models; and" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 349, + 294, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 294, + 372 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 294, + 372 + ], + "type": "text", + "content": "3. an application to image sequence interpolation and extrapolation tasks." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 373, + 295, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 295, + 421 + ], + "type": "text", + "content": "We evaluate our training-free approach on five datasets with respect to other interpolation methods, including those that fine-tune the underlying diffusion model, achieving state-of-the-art results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 434, + 142, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 142, + 447 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 142, + 447 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 455, + 295, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 295, + 647 + ], + "type": "text", + "content": "Text-to-image diffusion models. Recently, diffusion models [8, 19] have gained significant attention in deep generative modeling. Given specific input conditions, these models generate realistic data by progressively denoising Gaussian noise through a noise prediction network, resulting in outputs that closely resemble real data distributions based on the provided conditions. With the availability of large-scale image-text pairs for training, diffusion models have achieved remarkable performance in the text-to-image generation task [34, 37, 40]. Due to the flexibility of textual prompting, text-to-image diffusion models have been widely applied to image editing [2, 14, 15, 26], personalization [9, 12, 29, 38], stylization [16, 48, 49], etc. In this work, we use a pretrained Stable Diffusion [37] model with which to explore probability density geodesics for video analysis, image interpolation and extrapolation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "content": "Image interpolation. Image interpolation, also known as image morphing, refers to the process of generating a smooth transition between two images by creating intermediate images [51, 56]. Traditional methods rely on pixel-based transformations, such as mesh morphing or defining" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 346 + ], + "type": "text", + "content": "a blending function [30, 41, 55]. However, these methods typically require pre-labeled corresponding points and human involvement. Some attempts have been made to automate this process [21, 32], but they generally work only on image pairs generated in controlled environments. With advances in generative models, Generative Adversarial Networks (GANs) [10] have been applied to the image interpolation task [28, 33, 42] and achieve moderate success. However, GAN-based image interpolation frameworks do not perform well in open-world settings. Specifically, input image pairs are required to be in-distribution with the training data of GAN models, which limits the application scenarios for image interpolation. With recent progress in text-to-image diffusion models, several works [11, 13, 50, 52, 53] have shown that these models achieve impressive results in image interpolation. Given any image pair, through textual embedding inversion and embedding interpolation, relatively smooth intermediate images can be obtained. In this work, we also employ a diffusion model; however, compared with prior works [11, 52, 53], our method is training-free and can be applied to image extrapolation. Furthermore, our approach offers a theoretical framework with which to understand these tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 357, + 481, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 481, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 481, + 371 + ], + "type": "text", + "content": "3. Probability Density Geodesics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 378, + 553, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 553, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 553, + 473 + ], + "type": "text", + "content": "In this section, we will outline the theory of probability density geodesics, followed by the algorithmic development. The following section will apply the theory to a diffusion latent space and address some design decisions particular to that context. We aim to show that the structure of a data space can be studied by computing geodesics with respect to the probability distribution of the data, which can be obtained by training a diffusion model in that space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 474, + 553, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 553, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 553, + 544 + ], + "type": "text", + "content": "A geodesic is the (locally) shortest path between two points on a Riemannian manifold with a constant speed parameterization and can be obtained by minimizing the length of a curve between them using the calculus of variations. 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Let " + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "inline_equation", + "content": "\\gamma :[0,1]\\to \\mathbb{R}^n" + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "text", + "content": " be a path such that " + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "inline_equation", + "content": "\\gamma (0) = x_0" + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "inline_equation", + "content": "\\gamma (1) = x_{1}" + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "inline_equation", + "content": "S:\\{\\gamma_i\\} \\rightarrow \\mathbb{R}" + }, + { + "bbox": [ + 313, + 550, + 553, + 586 + ], + "type": "text", + "content": " be the action functional on the set of such paths, defined by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 371, + 594, + 553, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 594, + 553, + 622 + ], + "spans": [ + { + "bbox": [ + 371, + 594, + 553, + 622 + ], + "type": "interline_equation", + "content": "S [ \\gamma ] = \\int_ {a} ^ {b} L (t, \\gamma (t), \\dot {\\gamma} (t)) d t, \\tag {1}", + "image_path": "48e51dbf52573378864722d0f9e45284f1fc12e11c9b10612390e07b61c9cfd6.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 628, + 459, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 628, + 459, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 628, + 459, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 628, + 459, + 641 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 628, + 459, + 641 + ], + "type": "text", + "content": " is the Lagrangian given by" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 649, + 553, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 649, + 553, + 669 + ], + "spans": [ + { + "bbox": [ + 328, + 649, + 553, + 669 + ], + "type": "interline_equation", + "content": "L (t, \\gamma , \\dot {\\gamma}) = \\sqrt {\\langle \\dot {\\gamma} , \\dot {\\gamma} \\rangle_ {K (\\gamma)}} \\text {w i t h} K (\\gamma) = p (\\gamma) ^ {- 2} I. \\tag {2}", + "image_path": "974f262e8100711a07496bb91545cd32d9a1ef5b8cd9a865ef8975040fc3133e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "content": "Then " + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "inline_equation", + "content": "S[\\gamma]" + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "content": " is the path length for path " + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "content": ". The norm " + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "inline_equation", + "content": "\\| x \\| = \\sqrt{\\langle x, x \\rangle_M}" + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "content": " induced by the inner product " + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "inline_equation", + "content": "\\langle x, y \\rangle_M = x^\\top M y" + }, + { + "bbox": [ + 313, + 677, + 553, + 714 + ], + "type": "text", + "content": " is inversely proportional to the probability density with" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27990" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "function " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "p: \\mathbb{R}^n \\to \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": ". The interpretation here is that paths that pass through high density regions are 'shorter' than paths through low density regions. Note that this reduces to the standard formulation for the path length of a curve when the probability distribution is uniform." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "spans": [ + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "text", + "content": "Euler-Lagrange equations. Given this definition, a path " + }, + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "text", + "content": " is a stationary point of " + }, + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 137, + 296, + 172 + ], + "type": "text", + "content": " if and only if it satisfies the Euler-Lagrange equations, viz.," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 71, + 179, + 295, + 206 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 179, + 295, + 206 + ], + "spans": [ + { + "bbox": [ + 71, + 179, + 295, + 206 + ], + "type": "interline_equation", + "content": "\\frac {\\partial}{\\partial \\gamma} L (t, \\gamma (t), \\dot {\\gamma} (t)) - \\frac {\\mathrm {d}}{\\mathrm {d} t} \\frac {\\partial}{\\partial \\dot {\\gamma}} L (t, \\gamma (t), \\dot {\\gamma} (t)) = 0. \\tag {3}", + "image_path": "e4dd09dec0a78223341cc86250b02f12e1f6edae1823ed95af2a4857c864c9ad.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 213, + 295, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 295, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 295, + 243 + ], + "type": "text", + "content": "Using " + }, + { + "bbox": [ + 55, + 213, + 295, + 243 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\gamma) = \\frac{1}{p}\\frac{\\mathrm{d}p}{\\mathrm{d}\\gamma}^{\\mathsf{T}}" + }, + { + "bbox": [ + 55, + 213, + 295, + 243 + ], + "type": "text", + "content": " and a constant speed parameterization of the path, for our Lagrangian we obtain" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 97, + 251, + 295, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 251, + 295, + 270 + ], + "spans": [ + { + "bbox": [ + 97, + 251, + 295, + 270 + ], + "type": "interline_equation", + "content": "\\ddot {\\gamma} + \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) = 0, \\tag {4}", + "image_path": "26e67a277919a043ff71fd19beb7c093f51f75a79d1bd25ad411dafa01546467.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "text", + "content": "where the unit velocity is given by " + }, + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "inline_equation", + "content": "\\hat{\\gamma} = \\dot{\\gamma} / \\| \\dot{\\gamma}\\|" + }, + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "text", + "content": ". That is, we obtain a nonlinear second-order ordinary differential equation (ODE) that expresses the relationship between the scaled acceleration and the gradient of the log probability. It is important to observe here that " + }, + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\gamma)" + }, + { + "bbox": [ + 55, + 280, + 296, + 376 + ], + "type": "text", + "content": " is the Stein score function [20, 47], the exact quantity that is estimated by a score-based diffusion model. The full derivation is presented in the appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": "Functional derivative. This second-order ODE expresses the relationship at optimality, i.e., given an initial position and velocity we can obtain the associated optimal path. However, we can also derive the functional derivative " + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\frac{\\delta S}{\\delta \\gamma}" + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": " of the path length functional " + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": " by approximating the curve by a polygonal line with " + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": " segments, as " + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": " grows arbitrarily large. We obtain, for any " + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 380, + 296, + 475 + ], + "type": "text", + "content": " with a constant speed parameterization," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 483, + 295, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 483, + 295, + 512 + ], + "spans": [ + { + "bbox": [ + 63, + 483, + 295, + 512 + ], + "type": "interline_equation", + "content": "\\frac {\\delta S}{\\delta \\gamma} = \\frac {- 1}{p (\\gamma) \\| \\dot {\\gamma} \\|} \\left(\\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma) + \\frac {\\ddot {\\gamma}}{\\| \\dot {\\gamma} \\| ^ {2}}\\right). (5)", + "image_path": "5b2a227b63677b9a8103d9418fb953886f56a7d8a592ecb4a5ad5c4b404d1f83.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "content": "Probability density along the path. While estimating the absolute probability of any data point is challenging, the probability relative to the starting point is convenient to compute. For a conservative vector field " + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\nabla \\log p" + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "content": " (the gradient of a scalar field), line integrals are path independent. Therefore, the relative log-probability between two points " + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\gamma(a)" + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\gamma(t)" + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "content": ", along any path " + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 517, + 296, + 602 + ], + "type": "text", + "content": " connecting them, is" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 610, + 295, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 610, + 295, + 654 + ], + "spans": [ + { + "bbox": [ + 86, + 610, + 295, + 654 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\log \\tilde {p} _ {0} (\\gamma (t)) := \\log p (\\gamma (t)) - \\log p (\\gamma (0)) (6) \\\\ = \\int_ {0} ^ {t} \\dot {\\gamma} (\\tau) ^ {\\top} \\nabla \\log p (\\gamma (\\tau)) d \\tau . (7) \\\\ \\end{array}", + "image_path": "2f77d5e57b56528458f0a276e6eb3387fc482e7d0f9d56beef6877c4226bd3b0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "inline_equation", + "content": "f(x) = \\dot{\\gamma}(x)^{\\mathsf{T}}\\nabla \\log p(\\gamma(x))" + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "content": " and let " + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "inline_equation", + "content": "t_i = i/n" + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "inline_equation", + "content": "0 \\leq i \\leq n" + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "inline_equation", + "content": "n + 1" + }, + { + "bbox": [ + 55, + 661, + 296, + 687 + ], + "type": "text", + "content": " equally spaced samples along the path." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "content": "Then by the trapezoidal rule, the relative probability at these points along the path can be approximated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 105, + 555, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 105, + 555, + 138 + ], + "spans": [ + { + "bbox": [ + 329, + 105, + 555, + 138 + ], + "type": "interline_equation", + "content": "\\log \\tilde {p} _ {0} (\\gamma (t _ {i})) \\approx \\frac {1}{n} \\left(\\frac {f (t _ {0})}{2} + \\sum_ {k = 1} ^ {i - 1} f (t _ {k}) + \\frac {f (t _ {i})}{2}\\right). \\tag {8}", + "image_path": "94df5460d425b59f64df9d3cf72753db99f3c5a3df563dc5e1e6e2d2e753f29b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "spans": [ + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "text", + "content": "Higher-order approaches, such as Simpson's rule, may also be used for this approximation. From this, we may compute the relative probability " + }, + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "inline_equation", + "content": "\\tilde{p}_0(\\gamma(t)) = p(\\gamma(t_i)) / p(\\gamma(0))" + }, + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "text", + "content": " at every point " + }, + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "inline_equation", + "content": "\\gamma(t_i)" + }, + { + "bbox": [ + 313, + 146, + 555, + 195 + ], + "type": "text", + "content": " along the curve." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "spans": [ + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "content": "Geodesic distance. Given the probabilities computed in the previous section, it is trivial to estimate the geodesic distance. Let " + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "inline_equation", + "content": "t_i = i / n" + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "inline_equation", + "content": "0 \\leq i \\leq n" + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "inline_equation", + "content": "n + 1" + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "content": " equally spaced samples along the geodesic " + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 199, + 555, + 259 + ], + "type": "text", + "content": ", then the relative geodesic distance is given by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 329, + 267, + 555, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 267, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 329, + 267, + 555, + 331 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {d} _ {a} (b) = \\int_ {a} ^ {b} \\frac {\\left\\| \\dot {\\gamma} (t) \\right\\|}{\\tilde {p} _ {a} (\\gamma (t))} d t \\tag {9} \\\\ \\approx \\frac {1}{n} \\left(\\frac {\\| \\dot {\\gamma} (a) \\|}{2} + \\sum_ {i = 1} ^ {n - 1} \\frac {\\| \\dot {\\gamma} (t _ {i}) \\|}{\\tilde {p} _ {a} (\\gamma (t _ {i}))} + \\frac {\\| \\dot {\\gamma} (b) \\|}{2 \\tilde {p} _ {a} (\\gamma (t _ {n}))}\\right) \\\\ \\end{array}", + "image_path": "ce81018af1ba694a00e00019f12b46b357c0aa1bbc0a33f25016e6361e18f9ea.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 338, + 554, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 554, + 364 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 554, + 364 + ], + "type": "text", + "content": "and the absolute geodesic distance is given by " + }, + { + "bbox": [ + 313, + 338, + 554, + 364 + ], + "type": "inline_equation", + "content": "d(a, b) = \\tilde{d}_a(b) / p(\\gamma(a))" + }, + { + "bbox": [ + 313, + 338, + 554, + 364 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 373, + 514, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 514, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 514, + 388 + ], + "type": "text", + "content": "4. Geodesics in Diffusion Latent Space" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": "In this section, we show how to compute geodesics in the latent space of a pre-trained Stable Diffusion [37] model. An element " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{64 \\times 64 \\times 4}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " of this latent space can be obtained from an image " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " via an encoder " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\mathcal{I})" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": "; a decoder " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(x)" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " performs the inverse mapping. A forward process incrementally corrupts these elements with Gaussian noise, up to timestep " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\tau = T" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": ", resulting in a noise element " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "x_{T} \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": ". To distinguish between the time dependence of the diffusion process and that of the path formulation in Sec. 3, we use " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " to denote the diffusion time-step throughout the rest of the paper. The diffusion model is trained on a very large dataset of images to denoise elements of this latent space at all timesteps. It is parameterized by a neural network " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_{\\tau}; z)" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " that predicts the noise " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " that was used to produce noisy sample " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "x_{\\tau}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " from clean sample " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "x_{0}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " [19]. This is proportional to the score function " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\nabla_{x_{\\tau}} \\log p_{\\tau}(x_{\\tau})" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " of the smoothed (noised) density " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "p_{\\tau}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": " [19]. Finally, our method makes use of the deterministic DDIM forward and backward processes (DDIM-F, DDIM-B) with noise schedule parameter " + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_{\\tau}" + }, + { + "bbox": [ + 313, + 394, + 555, + 633 + ], + "type": "text", + "content": ", known as inversion [44], defined by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 335, + 642, + 554, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 642, + 554, + 670 + ], + "spans": [ + { + "bbox": [ + 335, + 642, + 554, + 670 + ], + "type": "interline_equation", + "content": "\\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\frac {x _ {\\tau}}{\\sqrt {\\bar {\\alpha} _ {\\tau}}}\\right) = \\frac {\\mathrm {d}}{\\mathrm {d} \\tau} \\left(\\sqrt {\\frac {1 - \\bar {\\alpha} _ {\\tau}}{\\bar {\\alpha} _ {\\tau}}}\\right) \\epsilon_ {\\theta} (x _ {\\tau}; z). \\tag {10}", + "image_path": "e79cbd8feb5027a908ff0ac1e1562a05c26394c7d5dc947ac63817b5f5bbb0bd.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": "Working with diffusion models introduces several challenges, which we address in this section. In particular, (i) how to handle (potentially varying) conditional probability" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 693, + 296, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 296, + 713 + ], + "type": "text", + "content": "1This assumption is not strictly true for standard diffusion models, but is a good approximation [3]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27991" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "text", + "content": "densities; (ii) how to accurately estimate the score function " + }, + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(x)" + }, + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "text", + "content": ", especially in low density regions; and (iii) how to solve the initial and boundary value problems efficiently in an extremely high-dimensional space (e.g., " + }, + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{16384}" + }, + { + "bbox": [ + 55, + 72, + 295, + 122 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 129, + 272, + 143 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 272, + 143 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 272, + 143 + ], + "type": "text", + "content": "4.1. Conditional probability density geodesics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": "Most image diffusion models are conditional models, trained to denoise an image conditioned on a signal " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " such as a CLIP-encoded text prompt [36, 37, 40]. Hence, we extend the formulation from Sec. 3 to consider the conditional probability density function " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "p(\\gamma(t) \\mid \\zeta(t, \\gamma(t))" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\zeta: \\mathbb{R} \\times \\mathbb{R}^n \\to \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " is a function over the path parameter and latent space that obtains the values of the conditioning vectors " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "z_a" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "z_b" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " at the endpoints, such that " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\zeta(0, \\gamma(0)) = z_0" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\zeta(1, \\gamma(1)) = z_1" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "(a, b) = (0, 1)" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": ". In our experiments, we primarily consider the case where " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": " is linear in time and constant in the latent space: " + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\zeta(t) = (1 - t)z_0 + tz_1" + }, + { + "bbox": [ + 55, + 148, + 296, + 280 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 288, + 156, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 288, + 156, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 288, + 156, + 300 + ], + "type": "text", + "content": "4.2. Score estimation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 305, + 296, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 305, + 296, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 305, + 296, + 520 + ], + "type": "text", + "content": "The score function is likely to be poorly estimated in low-density regions [45]. This occurs since the diffusion model does not have enough evidence during training to estimate the score accurately in regions of the latent space where data is scarce. However, estimating accurate directions in these regions is critical for solving boundary value problems, since the initial path to be optimized is likely to traverse low-density regions. Diffusion models apply multiple levels of noise to data elements in order to alleviate this problem. By doing so, low-density regions of the space can be populated by noised data, improving the quality of the estimated gradients at those locations. As a result, we choose to compute geodesics (and query the diffusion model) at a particular non-zero noise level, with the associated diffusion timestep " + }, + { + "bbox": [ + 55, + 305, + 296, + 520 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 305, + 296, + 520 + ], + "type": "text", + "content": ". A side benefit of this is that the probability density becomes increasingly Gaussian as the timestep increases, which provides a useful inductive bias, as explained in the next section." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": "However, there is an additional complexity. For a noised training sample " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_{\\tau}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": ", the unconditional model " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_{\\tau};z = \\varnothing ,\\tau)" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " is expected to predict the noise " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " that was used to produce this sample from clean sample " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": ". Unfortunately, in our case, we obtain vectors " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_{\\tau}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " from an optimization procedure, initialized along a great circle between endpoints " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_{a,\\tau}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_{b,\\tau}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": ". These points are (at least initially) out-of-distribution (OOD) for the model, and we should not expect it to predict the noise well. Instead, Katzir et al. [25] observe that the prediction consists of a domain correction term " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{D}}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " and a denoising term " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{N}}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": ". The residual " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{N}} - \\epsilon" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": ", as used in score distillation sampling [35], is generally non-zero and noisy, leading to an averaging (over-smoothing) effect in the optimized latents. In our optimization procedure, we are not aiming to denoise the samples, so neglect the denoising direction " + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{N}}" + }, + { + "bbox": [ + 55, + 522, + 296, + 714 + ], + "type": "text", + "content": " and instead use noise-free score distillation [25]" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 553, + 135 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 135 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 135 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 135 + ], + "type": "image", + "image_path": "b10bcac0e23f1561c1de13bda2da6048800f843756e192db64b363369cc676ba.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 369, + 139, + 500, + 149 + ], + "lines": [ + { + "bbox": [ + 369, + 139, + 500, + 149 + ], + "spans": [ + { + "bbox": [ + 369, + 139, + 500, + 149 + ], + "type": "text", + "content": "(a) The pipeline for image interpolation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 152, + 552, + 213 + ], + "blocks": [ + { + "bbox": [ + 317, + 152, + 552, + 213 + ], + "lines": [ + { + "bbox": [ + 317, + 152, + 552, + 213 + ], + "spans": [ + { + "bbox": [ + 317, + 152, + 552, + 213 + ], + "type": "image", + "image_path": "77a2c9220bebbd8d64c0948ee28f3022eda76bb244b7feb9f22c994fc454afe6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 369, + 217, + 501, + 228 + ], + "lines": [ + { + "bbox": [ + 369, + 217, + 501, + 228 + ], + "spans": [ + { + "bbox": [ + 369, + 217, + 501, + 228 + ], + "type": "text", + "content": "(b) The pipeline for image extrapolation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 236, + 555, + 270 + ], + "lines": [ + { + "bbox": [ + 313, + 236, + 555, + 270 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 555, + 270 + ], + "type": "text", + "content": "Figure 2. Pipelines for the image interpolation and extrapolation tasks, addressed by solving boundary and initial value problems in diffusion latent space." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 292, + 552, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 292, + 552, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 552, + 304 + ], + "type": "text", + "content": "direction " + }, + { + "bbox": [ + 313, + 292, + 552, + 304 + ], + "type": "inline_equation", + "content": "\\phi (x\\mid z,\\tau)" + }, + { + "bbox": [ + 313, + 292, + 552, + 304 + ], + "type": "text", + "content": " to approximate the gradient direction," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 319, + 314, + 553, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 314, + 553, + 327 + ], + "spans": [ + { + "bbox": [ + 319, + 314, + 553, + 327 + ], + "type": "interline_equation", + "content": "\\nabla \\log p (x \\mid z, \\tau) \\approx \\beta \\phi (x \\mid z, \\tau) \\tag {11}", + "image_path": "560db4f1146db02e9831eac847fd4cc6a2ae9c2d445a72d6bc458e7051f6b819.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 329, + 553, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 329, + 553, + 342 + ], + "spans": [ + { + "bbox": [ + 319, + 329, + 553, + 342 + ], + "type": "interline_equation", + "content": "\\phi (x \\mid z, \\tau) = \\mathbb {E} _ {\\tau^ {\\prime} \\in \\mathcal {R} _ {\\tau}} w \\left(\\tau^ {\\prime}\\right) \\left(\\sigma d \\left(x _ {\\tau^ {\\prime}} \\mid z\\right) - d \\left(x _ {\\tau^ {\\prime}} \\mid z _ {\\text {n e g}}\\right)\\right), \\tag {12}", + "image_path": "f40f6cf543dcd2a0081ea4d841fd359d4c177e694fbd32ceee675aedf9d3f0fa.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": " is a scalar hyperparameter, " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "w(\\tau)" + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": " is a weighting function, " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": " is the classifier-free guidance parameter (0 if unconditional) [18], " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{neg}}" + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": " is a negative prompt embedding that says something about the specific OOD latent vector (see Appendix B), " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "d(x_{\\tau}|z) = \\epsilon_{\\theta}(x_{\\tau}|\\varnothing) - \\epsilon_{\\theta}(x_{\\tau}|z)" + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "text", + "content": " is the direction function, and the expectation is taken over a range of timesteps " + }, + { + "bbox": [ + 313, + 352, + 555, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\tau} = [\\tau -\\Delta \\tau ,\\tau +\\Delta \\tau ]" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 444, + 479, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 479, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 479, + 456 + ], + "type": "text", + "content": "4.3. Efficient IVP and BVP solvers" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 462, + 554, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 554, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 554, + 569 + ], + "type": "text", + "content": "Solving the initial and boundary value problems efficiently with respect to time and memory becomes challenging in the extremely high-dimensional latent space " + }, + { + "bbox": [ + 313, + 462, + 554, + 569 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{4\\times 64\\times 64}" + }, + { + "bbox": [ + 313, + 462, + 554, + 569 + ], + "type": "text", + "content": " of Stable Diffusion [37]. For this dimensionality, standard techniques, such as collocation algorithms for solving BVPs [27], become prohibitive in time and memory. We also aim to minimize calls to the diffusion model, since this is expensive to compute. In view of these aims, we use a simple low-memory parametrization and optimization strategy." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "text", + "content": "Before outlining the algorithms, we first observe that the probability distribution becomes more Gaussian as the diffusion timestep increases [5] and that the Gaussian Annulus Theorem [1] states that a point chosen at random from a unit variance " + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "text", + "content": "-dimensional Gaussian distribution will be located in a small annulus around a sphere of radius " + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\sqrt{d}" + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "text", + "content": " with high probability. However, for finite-sized gradient descent steps, the optimizer may take the curve away from the sphere, moving into low-density regions where probability density gradients are poorly estimated. To mitigate this, we reproject the curve back onto the sphere, ensuring that optimization remains within the high-density region where gra" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27992" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 58, + 88, + 279, + 322 + ], + "blocks": [ + { + "bbox": [ + 62, + 75, + 265, + 87 + ], + "lines": [ + { + "bbox": [ + 62, + 75, + 265, + 87 + ], + "spans": [ + { + "bbox": [ + 62, + 75, + 265, + 87 + ], + "type": "text", + "content": "Algorithm 1: BVP solver for image interpolation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "lines": [ + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "spans": [ + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": "Input: start/end image " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0 / \\mathcal{I}_1" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " ; text prompts " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "p_0 / p_1" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " diffusion timestep " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " ; learning rate " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " optimizer steps " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " hyperparameter " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " ; 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(11) \n11 g " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " FuncDeriv(s,x, " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\dot{x},\\ddot{x})" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " %Eq. (13) \n12 x " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " ||x||(x-ηg)/||x-ηg|| \n13 S " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " SU{(t,x)} \n14 " + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "inline_equation", + "content": "\\gamma \\leftarrow" + }, + { + "bbox": [ + 58, + 88, + 279, + 322 + ], + "type": "text", + "content": " Interpolate(S)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 55, + 344, + 295, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 344, + 295, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 295, + 369 + ], + "type": "text", + "content": "dient estimates are more reliable, and we project the functional derivative to the tangent space of the sphere," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 136, + 375, + 295, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 375, + 295, + 401 + ], + "spans": [ + { + "bbox": [ + 136, + 375, + 295, + 401 + ], + "type": "interline_equation", + "content": "g = \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\frac {\\delta S}{\\delta \\gamma}. \\tag {13}", + "image_path": "20e3ff09d1626d151fb64d9422426c7708bc3d9c1f52b32f4cf0c7fd8ffea875.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": "BVP. Given a start position " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "x^{(0)}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " and an end position " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "x^{(k + 1)}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": ", we parameterize the path " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " with a set of control points " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\{x_{\\tau}^{(i)}\\}_{i = 1}^{k}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " connected by a spherical piecewise linear function (great circle arcs). For clarity, we note points on this curve as " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " with the curve parameter " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": ", dropping " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " and the ordinal superscript. Algorithm 1 initializes the path as a great circle. It then computes the projected gradient descent update for the control points using Eq. (13), where the associated velocities " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\dot{\\gamma}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " and accelerations " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\ddot{\\gamma}" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " are obtained from a natural cubic spline fit to the control points and end points, and projects the updated control points back onto the sphere. To save computation, the algorithm uses a coarse-to-fine discretization, where the number of control points " + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "inline_equation", + "content": "k \\in [1,3,7,15]" + }, + { + "bbox": [ + 54, + 408, + 295, + 590 + ], + "type": "text", + "content": " varies as optimization progresses, using a bisection strategy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "text", + "content": "IVP. Algorithm 2 takes an image " + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "text", + "content": " and its corresponding text description " + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "text", + "content": ", and extrapolates how the geodesic evolves given an initial velocity formulated from the target prompt " + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 55, + 594, + 295, + 656 + ], + "type": "text", + "content": ". As with Eq. (13), the updates are projected to the tangent space, resulting in the ODE given by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 71, + 662, + 295, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 662, + 295, + 682 + ], + "spans": [ + { + "bbox": [ + 71, + 662, + 295, + 682 + ], + "type": "interline_equation", + "content": "\\ddot {\\gamma} = - \\left\\| \\dot {\\gamma} \\right\\| ^ {2} \\left(I - \\hat {\\gamma} \\hat {\\gamma} ^ {\\mathsf {T}}\\right) \\left(I - \\hat {\\dot {\\gamma}} \\hat {\\dot {\\gamma}} ^ {\\mathsf {T}}\\right) \\nabla \\log p (\\gamma), \\tag {14}", + "image_path": "74a8d5e17f66e71e5e8e7e4c4b3a81e35b92795bf9a98f9af0cb4e57cf7a4c61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "which can be solved by applying the Runge-Kutta (RK4) method to the first-order system of equations." + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 553, + 320 + ], + "blocks": [ + { + "bbox": [ + 321, + 75, + 522, + 87 + ], + "lines": [ + { + "bbox": [ + 321, + 75, + 522, + 87 + ], + "spans": [ + { + "bbox": [ + 321, + 75, + 522, + 87 + ], + "type": "text", + "content": "Algorithm 2: IVP solver for image extrapolation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "Input: image " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; source text prompt " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; target text prompt " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; diffusion timestep " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; optimizer steps " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; VAE encoder " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; CLIP text encoder " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; hyperparameter " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \nOutput: image sequence " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; geodesic " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n1 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\{z_0, z_1\\} \\gets \\{\\mathcal{C}(p_0), \\mathcal{C}(p_1)\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n2 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "x \\gets \\text{DDIM-F}(\\mathcal{E}(\\mathcal{I}_0), \\tau, z_0)" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n3 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\dot{x} \\gets \\text{GetInitVelocity}(x, z_0, z_1)" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n4 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{S} \\gets \\{(0, x)\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n5 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{I} \\gets \\{\\mathcal{I}_0\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n6 for " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " do \n7 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "z \\gets (1 - i/n)z_0 + (i/n)z_1" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n8 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "s \\gets \\text{Score}(x, z, \\tau, \\beta)" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; % Eq. (11) \n9 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\ddot{x} \\gets \\text{ODE}(s, x, \\dot{x})" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": "; % Eq. (14) \n10 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\dot{x} \\gets \\text{RK4}(\\dot{x}, \\ddot{x}, 1/n)" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n11 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "x \\gets \\|x\\| \\text{RK4}(x, \\dot{x}, 1/n)/\\|\\text{RK4}(x, \\dot{x}, 1/n)\\|" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n12 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{S} \\gets \\mathcal{S} \\cup \\{(i/n, x)\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n13 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\mathcal{I} \\gets \\mathcal{I} \\cup \\{\\mathcal{D}(\\text{DDIM-B}(x, \\tau, z))\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "text", + "content": " \n14 " + }, + { + "bbox": [ + 316, + 88, + 553, + 320 + ], + "type": "inline_equation", + "content": "\\gamma \\gets \\text{Interpolate}(\\mathcal{S})" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_body" + } + ], + "index": 9, + "sub_type": "algorithm" + }, + { + "bbox": [ + 314, + 342, + 394, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 342, + 394, + 357 + ], + "spans": [ + { + "bbox": [ + 314, + 342, + 394, + 357 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 363, + 555, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 435 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 435 + ], + "type": "text", + "content": "In this section, we first analyze whether short video sequences are geodesics in diffusion latent space. Second, we evaluate applications of the theory, focusing on the image interpolation task framed as solving a boundary value problem. For all experiments, we use a pre-trained Stable Diffusion v2.1-base model [37]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 443, + 463, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 463, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 463, + 455 + ], + "type": "text", + "content": "5.1. Geodesic analysis of videos" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 460, + 554, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 484 + ], + "type": "text", + "content": "The objective of this experiment is to assess how close video clips are to geodesics." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 488, + 554, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 488, + 554, + 561 + ], + "spans": [ + { + "bbox": [ + 313, + 488, + 554, + 561 + ], + "type": "text", + "content": "Dataset. We use the CLEVR framework [22] to render 40 synthetic videos with Blender. Each 100-frame sequence contains one of the three CLEVR objects (cube, sphere, cylinder) and has a single varying attribute, including camera rotation and translation, light source location, and the size, color and motion of the object." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "content": "Baselines. The path " + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "inline_equation", + "content": "\\gamma_v" + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "content": " corresponding to the original video clip is compared to the path after geodesic optimization " + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "inline_equation", + "content": "\\gamma_o" + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "content": ", the path after a sinuoidal perturbation " + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "inline_equation", + "content": "\\gamma_{\\delta} = \\gamma_v + \\delta \\sin (\\pi \\gamma)" + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "content": ", and the path after smoothing " + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "inline_equation", + "content": "\\gamma_s" + }, + { + "bbox": [ + 313, + 565, + 554, + 625 + ], + "type": "text", + "content": ", by fitting a smoothed cubic spline [7] with smoothing factor 0.9999." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": "Results. In Fig. 3a, we report the " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " norm of the functional derivative in Eq. (5) as it varies along the path, for a single video clip (translating red cube). For a geodesic, this is zero everywhere along the path. In Fig. 3b, we report the average of this norm across the path and the dataset. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm along the path " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\gamma_v" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " to be near zero, (ii)" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27993" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 290, + 193 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 290, + 193 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 290, + 193 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 290, + 193 + ], + "type": "image", + "image_path": "28ce7a8a02ed09744a6a23095798dcfa2e55c44259d4eacf7d70856f62e86fa0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 197, + 290, + 208 + ], + "lines": [ + { + "bbox": [ + 61, + 197, + 290, + 208 + ], + "spans": [ + { + "bbox": [ + 61, + 197, + 290, + 208 + ], + "type": "text", + "content": "(a) Geodesic gradient norm along the path, for the translating red cube." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 210, + 290, + 286 + ], + "blocks": [ + { + "bbox": [ + 63, + 210, + 290, + 286 + ], + "lines": [ + { + "bbox": [ + 63, + 210, + 290, + 286 + ], + "spans": [ + { + "bbox": [ + 63, + 210, + 290, + 286 + ], + "type": "image", + "image_path": "6b5ba3c5ac95f794d76c568d844e8eea69c2cd2c4f22b96832f23af59c5ddc91.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 289, + 281, + 300 + ], + "lines": [ + { + "bbox": [ + 70, + 289, + 281, + 300 + ], + "spans": [ + { + "bbox": [ + 70, + 289, + 281, + 300 + ], + "type": "text", + "content": "(b) Geodesic gradient norm, averaged across the path and dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "text", + "content": "the norm to be close to that of the optimized path " + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "inline_equation", + "content": "\\gamma_{o}" + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "text", + "content": ", and (iii) the norm of the perturbed " + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "inline_equation", + "content": "\\gamma_{\\delta}" + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "text", + "content": " or smoothed " + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "inline_equation", + "content": "\\gamma_{s}" + }, + { + "bbox": [ + 55, + 409, + 296, + 458 + ], + "type": "text", + "content": " paths to be larger. We observe these trends in the results, and conclude that many of the videos are approximately geodesic." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 467, + 138, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 467, + 138, + 480 + ], + "spans": [ + { + "bbox": [ + 55, + 467, + 138, + 480 + ], + "type": "text", + "content": "5.2. Applications" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 484, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 510 + ], + "type": "text", + "content": "Here, we assess the performance of the geodesic solvers for the image interpolation and extrapolation tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 515, + 295, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 295, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 295, + 624 + ], + "type": "text", + "content": "Datasets. We compile a union of datasets from prior works [50, 52, 53]. This includes MorphBench [53], which contains 90 image pairs of object animations and object metamorphoses; Animals and Humans [52], which contains 50 animal image pairs from AFHQ [6] with an LPIPS below 0.7 and 50 human face image pairs from CelebA-HQ [23] with an LPIPS below 0.6; and Web, which contains 20 image pairs sourced from publicly accessible websites, some of which have been used in other related studies [50]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "Metrics. Quantitatively evaluating image interpolation and extrapolation is extremely challenging and subjective. Following previous work [52, 53], we report (1) the Fréchet inception distance (FID) [17] between the set of input images and the set of generated images to measure how close the distributions are; (2) the perceptual path length (PPL) [24] as the sum of LPIPS between adjacent images to assess the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 553, + 346 + ], + "blocks": [ + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "lines": [ + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "text", + "content": "Figure 3. Analysis of simple videos generated using CLEVR [22]. If a video path was a geodesic in the diffusion latent space, we would expect (i) the norm of the geodesic gradient along the path " + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\gamma_v" + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "text", + "content": " to be near zero, (ii) the norm to be close to that of the optimized path " + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\gamma_o" + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "text", + "content": ", and (iii) the norm of the perturbed " + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\gamma_{\\delta}" + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "text", + "content": " or smoothed " + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\gamma_s" + }, + { + "bbox": [ + 55, + 309, + 296, + 387 + ], + "type": "text", + "content": " paths to be larger. From the evidence, we conclude that many of the videos are approximately geodesic." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 70, + 553, + 346 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 553, + 346 + ], + "type": "image", + "image_path": "bde90908e57ae11e25ea923cf2ec9b2fcf70061e61bd912ed6ae0fdbce5ae003.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 354, + 550, + 365 + ], + "lines": [ + { + "bbox": [ + 318, + 354, + 550, + 365 + ], + "spans": [ + { + "bbox": [ + 318, + 354, + 550, + 365 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of image interpolation results." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 386, + 555, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 555, + 506 + ], + "type": "text", + "content": "directness of the generated image sequence; (3) perceptual distance variance (PDV) as the standard deviation of LPIPS between consecutive images to assess the consistency of transition rates across the sequence; and (4) the TOPIQ [4] score, an image quality metric that evaluates the perceptual quality of each generated image in alignment with human perception. To focus on the quality of interior frames, we compute a weighted TOPIQ score, detailed in Appendix C. We report all metrics on 17-frame sequences by sampling 15 intermediate images between the input pairs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": "Implementation details. We use BLIP [31] to generate short text prompts " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": " for each input image. For text inversion, we finetune the CLIP [36] encoded text embedding " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ", using 500 steps with a learning rate of 0.005 and the AdamW optimizer. For BVP optimization, we perform 400 steps of gradient descent with an initial learning rate of 0.1, following a linear learning rate schedule. The hyperparameters are set as " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\tau = 600" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\Delta \\tau = 100" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\beta = 0.002" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\sigma = 1" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ". As detailed in Sec. 4.3, we adopt a bisection strategy to add additional sample points every 100 steps. For IVP optimization, we set the iteration number to 200. To obtain a diverse set of initial velocities, we apply text inversion to the target text embedding using several generated images from random initial noise " + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0, I)" + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": ", conditioned on the target prompt [39]. All methods use the same pre-trained diffusion model (Stable Diffusion v2.1-base) and text prompts, and default settings otherwise. Further details are in Appendix B." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27994" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 106, + 555, + 239 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "type": "text", + "content": "Table 1. Image interpolation results. We report the performance on three datasets: MorphBench (MB), Animals and Humans (AH), and Web data (Web). TF denotes \"training-free\", which also prohibits fine-tuning; best results are in bold; second best ones are underlined. \"Ours\" represents the optimized geodesic path and \"Ours w/o opt.\" represents the unoptimized path as the great circle initialization." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 106, + 555, + 239 + ], + "lines": [ + { + "bbox": [ + 56, + 106, + 555, + 239 + ], + "spans": [ + { + "bbox": [ + 56, + 106, + 555, + 239 + ], + "type": "table", + "html": "
MethodTFFID ↓PPL↓PDV↓TOPIQ ↑
AHMBWebAHMBWebAHMBWebAHMBWeb
NoiseDiffusion [54]✓71.85100.87201.082.5072.7183.7380.1170.1110.0990.7000.6660.650
AID [13]✓86.30124.11242.342.7092.6483.8130.1810.1880.2080.6990.6750.665
IMPUS [52]✗25.7536.3389.731.8611.7182.5540.0650.0660.1150.6220.5870.539
DiffMorpher [53]✗32.8942.39160.691.1951.0111.9340.0180.0160.0240.6860.6510.592
SmoothDiffusion [11]✗30.8052.19135.780.9030.8791.3710.0270.0330.0450.5710.5150.389
Ours w/o opt.✓24.7137.85112.810.8740.8411.4730.0320.0350.0530.5840.5460.466
Ours✓33.8746.51134.680.9600.9211.5650.0160.0220.0260.6070.5590.479
", + "image_path": "aa461b590f3ee978e55376cd71333cc7e568bdaeb4f0ac28b82e08e190a196c7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 293, + 296, + 380 + ], + "blocks": [ + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "lines": [ + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "type": "text", + "content": "Table 2. We ablate the impact of different text conditioning strategies for BVP solver, including text inversion, positive " + }, + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "type": "inline_equation", + "content": "(\\oplus)" + }, + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "type": "text", + "content": " prompts, and negative " + }, + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "type": "inline_equation", + "content": "(\\ominus)" + }, + { + "bbox": [ + 55, + 256, + 295, + 291 + ], + "type": "text", + "content": " prompts, on the validation dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 293, + 296, + 380 + ], + "lines": [ + { + "bbox": [ + 56, + 293, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 56, + 293, + 296, + 380 + ], + "type": "table", + "html": "
Text inv. ⊕ prompt ⊘ promptFID↓PPL↓PDV↓TOPIQ↑
✓70.561.060.0170.518
69.061.0460.0170.529
✓✓65.051.0450.0180.562
✓64.721.0370.0190.564
✓✓63.281.0000.0170.553
", + "image_path": "4bd2214034ddb32ada9fb0d06d17db5a16ecd20c7c9709372d50419a1af3782d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 415, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 415, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 415, + 297, + 715 + ], + "type": "text", + "content": "Results. We compare our method for the image interpolation task with several state-of-the-art diffusion-based methods, including NoiseDiffusion [54], DiffMorpher [53], IMPUS [52], AID [13], SmoothDiffusion [11] and report the result of a baseline ('Ours w/o opt.'), which returns the initial path before geodesic optimization. This corresponds to the great circle trajectory, the most direct path between the endpoints on the sphere. The quantitative and qualitative results are presented in Tab. 1 and Figs. 4 and 6. We observe that methods involving finetuning the diffusion model on input images, like DiffMorpher and IMPUS, tend to score better with respect to most of the metrics. While AID and NoiseDiffusion generate high-quality images, they have a weaker connection to the input images. SmoothDiffusion [11], trained on the large LAION dataset, performs well with respect to perceptual path length, but has high variance and weaker image quality scores, especially on the partially OOD Web dataset. In contrast, our method has high directness (low PPL), high fidelity to the input distribution (low FID), and very high perceptual smoothness (low PDV), but has slightly lower image quality (low TOPIQ). Overall, our approach is on-par with the best methods without requiring any training. Finally, we show qualitative results for the image extrapolation task in Fig. 7, where we visualize two trajectories for each prompt." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 255, + 552, + 346 + ], + "blocks": [ + { + "bbox": [ + 317, + 255, + 552, + 346 + ], + "lines": [ + { + "bbox": [ + 317, + 255, + 552, + 346 + ], + "spans": [ + { + "bbox": [ + 317, + 255, + 552, + 346 + ], + "type": "image", + "image_path": "7cebf3d09a35509fab795b2c5898550cf77237f8c9651eb6c21d5ea8f5e5bebc.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 370, + 553, + 443 + ], + "blocks": [ + { + "bbox": [ + 314, + 349, + 555, + 369 + ], + "lines": [ + { + "bbox": [ + 314, + 349, + 555, + 369 + ], + "spans": [ + { + "bbox": [ + 314, + 349, + 555, + 369 + ], + "type": "text", + "content": "(a) Relative log-probability along the path as optimization progresses, where iteration 0 is the lightest curve and iteration 400 is the darkest." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 370, + 553, + 443 + ], + "lines": [ + { + "bbox": [ + 317, + 370, + 553, + 443 + ], + "spans": [ + { + "bbox": [ + 317, + 370, + 553, + 443 + ], + "type": "image", + "image_path": "13ea20c75c86ec6a2ca6af7acc857a465d65dbd5fc42da323fa524580438e7a4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 355, + 445, + 513, + 456 + ], + "lines": [ + { + "bbox": [ + 355, + 445, + 513, + 456 + ], + "spans": [ + { + "bbox": [ + 355, + 445, + 513, + 456 + ], + "type": "text", + "content": "(b) Path length with respect to optimization step." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 464, + 555, + 489 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 489 + ], + "type": "text", + "content": "Figure 5. Example of the evolution of the probability density along the path and the path length during BVP optimization." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 508, + 556, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 508, + 556, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 508, + 556, + 665 + ], + "type": "text", + "content": "Analysis. We constructed a validation dataset for ablation and analysis by randomly selecting 25 image pairs from the three datasets (Sec. 5.2). In Fig. 5, we show that optimization correctly increases the log probability of samples along the path and decreases the path length. This indicates that the curve smoothly approaches a geodesic during optimization. We also present an ablation study in Tab. 2, where we show how the text conditioning formulation (text inversion, positive prompt, and negative prompt) contributes to the performance of the method. In Appendix D, we compare the time-linear conditioning signal with the constant one. In Appendix E, we analyze the trade-off between the different choices of hyperparameter settings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 671, + 392, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 671, + 392, + 684 + ], + "spans": [ + { + "bbox": [ + 313, + 671, + 392, + 684 + ], + "type": "text", + "content": "5.3. Limitations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "content": "This work has several limitations. First, the metrics used for evaluating image interpolation struggle to capture inter" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27995" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 555, + 300 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 555, + 300 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 555, + 300 + ], + "type": "image", + "image_path": "bcf5418d0216f5f1c0292fd158702ab39263e83ce081b9f7ebff49ee6a4d500c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 157, + 308, + 449, + 321 + ], + "lines": [ + { + "bbox": [ + 157, + 308, + 449, + 321 + ], + "spans": [ + { + "bbox": [ + 157, + 308, + 449, + 321 + ], + "type": "text", + "content": "Figure 6. Qualitative image interpolation results using our geodesic BVP solver." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 339, + 294, + 407 + ], + "blocks": [ + { + "bbox": [ + 58, + 339, + 294, + 407 + ], + "lines": [ + { + "bbox": [ + 58, + 339, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 58, + 339, + 294, + 407 + ], + "type": "image", + "image_path": "0284ee75145d6d6e5565e3d64f9692d5efad83163d206b393173c72b02c006b1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 58, + 419, + 294, + 488 + ], + "blocks": [ + { + "bbox": [ + 113, + 409, + 238, + 419 + ], + "lines": [ + { + "bbox": [ + 113, + 409, + 238, + 419 + ], + "spans": [ + { + "bbox": [ + 113, + 409, + 238, + 419 + ], + "type": "text", + "content": "(a) Target prompt: \"Volcano eruption\"." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 419, + 294, + 488 + ], + "lines": [ + { + "bbox": [ + 58, + 419, + 294, + 488 + ], + "spans": [ + { + "bbox": [ + 58, + 419, + 294, + 488 + ], + "type": "image", + "image_path": "e34cb4778b5e0bea73147eebf27571ccb52879b29fafedddbc5e842b12ed830f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 58, + 510, + 294, + 578 + ], + "blocks": [ + { + "bbox": [ + 56, + 490, + 295, + 509 + ], + "lines": [ + { + "bbox": [ + 56, + 490, + 295, + 509 + ], + "spans": [ + { + "bbox": [ + 56, + 490, + 295, + 509 + ], + "type": "text", + "content": "(b) Target prompt: \"An expensive cake worth $1,000, adorned with fancy decorations and looking incredibly delicious\"." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 510, + 294, + 578 + ], + "lines": [ + { + "bbox": [ + 58, + 510, + 294, + 578 + ], + "spans": [ + { + "bbox": [ + 58, + 510, + 294, + 578 + ], + "type": "image", + "image_path": "3dc590cc7147462962cd7525bd021f125d6c1f96c6dbef5177c91f618bcfd50a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 581, + 295, + 601 + ], + "lines": [ + { + "bbox": [ + 56, + 581, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 56, + 581, + 295, + 601 + ], + "type": "text", + "content": "(c) Target prompt: \"A real photo of a cute but scary monstrous creature with sharp teeth and bulging eyes\"." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 609, + 295, + 643 + ], + "lines": [ + { + "bbox": [ + 55, + 609, + 295, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 295, + 643 + ], + "type": "text", + "content": "Figure 7. Qualitative image extrapolation results using our geodesic IVP solver. For each image, we plot two extrapolated paths, each with different initial velocities but the same prompt." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "polation quality (smoothness, directness, and realism). In particular, FID, which measures fidelity to the input distribution, is unreliable when applied to small image sets like these, and the other metrics only capture individual aspects" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 341, + 555, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 555, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 555, + 521 + ], + "type": "text", + "content": "of interpolation quality. Second, the method performs well for image morphing (local changes) but struggles with large camera motions or domain gaps, as illustrated in Figs. 15 and 16. We hypothesize that by initializing with a great circle, which also performs poorly in such cases, our optimizer gets stuck in nearby local optima rather than finding more optimal solutions. A global search strategy is indicated. Third, we approximate the log-probability gradient with a score distillation gradient, which is not necessarily well-aligned. Fourth, the path representation is inelegant: a spherical piecewise linear function (great circle arcs) for which the velocities and accelerations are approximated by fitting a cubic spline. Finally, the image extrapolation performance is unreliable, as determining a good initial velocity is challenging; a more robust approach is called for." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 531, + 388, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 388, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 388, + 544 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "type": "text", + "content": "In this paper, we have presented the theory required for computing probability density geodesics in diffusion latent space and algorithms for solving the associated initial and boundary value problems. We also described how to compute several useful quantities for analysis: the relative probability density along the path, the geodesic distance between two points, and the geodesic gradient norm. Finally, we presented applications to image interpolation and extrapolation and evaluated the performance of these training-free approaches. We show that they perform comparably or better than existing state-of-the-art. We expect these techniques to be useful for tasks involving generative modeling, as well as for studying the distribution of image space." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "27996" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "content": "We thank all reviewers and ACs for their constructive comments. 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International Journal of Advanced Engineering, Management and Science, 3(2):239773, 2017. 2" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "27998" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_content_list.json b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..58289c2157aa5614062a2bb2bf6b90a41cd084e7 --- /dev/null +++ b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_content_list.json @@ -0,0 +1,1453 @@ +[ + { + "type": "text", + "text": "ProbeSDF: Light Field Probes For Neural Surface Reconstruction", + "text_level": 1, + "bbox": [ + 165, + 130, + 831, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Briac Toussaint", + "bbox": [ + 289, + 180, + 421, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "briac.toussaint@inria.fr", + "bbox": [ + 246, + 202, + 464, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diego Thomas", + "bbox": [ + 571, + 180, + 699, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thomas@ait.kyushu-u.ac.jp", + "bbox": [ + 524, + 202, + 746, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jean-Sébastien Franco1", + "bbox": [ + 403, + 223, + 589, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jean-sebastien.franco@inria.fr", + "bbox": [ + 366, + 244, + 630, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, France", + "bbox": [ + 241, + 258, + 754, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Kyushu University, Japan", + "bbox": [ + 393, + 277, + 602, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 329, + 326, + 344 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SDF-based differential rendering frameworks have achieved state-of-the-art multiview 3D shape reconstruction. In this work, we re-examine this family of approaches by minimally reformulating its core appearance model in a way that simultaneously yields faster computation and increased performance. To this goal, we exhibit a physically-inspired minimal radiance parametrization decoupling angular and spatial contributions, by encoding them with a small number of features stored in two respective volumetric grids of different resolutions. Requiring as little as four parameters per voxel, and a tiny MLP call inside a single fully fused kernel, our approach allows to enhance performance with both surface and image (PSNR) metrics, while providing a significant training speedup and real-time rendering. We show this performance to be consistently achieved on real data over two widely different and popular application fields, generic object and human subject shape reconstruction, using four representative and challenging datasets.", + "bbox": [ + 88, + 359, + 483, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 675, + 220, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural radiance fields have established a new milestone for the task of novel view synthesis and have led to a plethora of variants of broad applicability. We here take particular interest in SDF surface-based radiance fields, which have proven to be a highly performing variant for the tasks of 3D modeling from images [30, 33], with wide reaching applications ranging from object and performance capture, to immersive and 3D content production.", + "bbox": [ + 89, + 700, + 482, + 820 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "At the heart of such methods usually lies a parametrization of the light field, in the form of a 5-dimensional function. This function maps the spatial coordinates of a point", + "bbox": [ + 89, + 821, + 482, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in space and the observed direction to a color and a signed distance to the reconstructed surface. On one hand, the mapping can be global and use a complex scene-wide MLP as implicit 5D decoder, as is the case for most seminal approaches [18, 30]. On the other hand, recent popular variants that target higher speed and memory efficiency use explicit representations. Global representations are based on a grid encoding [4, 31, 33] where interpolated spatial and angular features are run through a global shallow MLP. Local representations use the sparse 3D Gaussian Splatting [13] sample-based encoding approach, where each separate Gaussian comes with its own opacity and adjoining set of angular color features. While grids or local approaches use a single deep MLP to densely encode the complete light field function, they almost always co-locate storage and decoding of color and angular features.", + "bbox": [ + 511, + 329, + 906, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "But is this really a necessary or even desirable feature of any light field encoding? We question these assertions by postulating that, contrary to the spatial components of the light field that mainly encode intrinsic surface texture, the angular components encode phenomena that are predominantly extrinsic to the surface, i.e. lighting and environment, and as such can be encoded at a lower spatial resolution as they are locally almost invariant to parallax. This hypothesis is in fact exploited by the rendering community, where angular and environment components contributing to the radiance equation used to compute rendered colors, are typically precomputed at sparse 3D locations coined light field probes [24], and interpolated in-between.", + "bbox": [ + 511, + 577, + 908, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Leveraging this intuition, our approach borrows the spherical harmonic parametrization popular with explicit methods e.g. [4, 13] to represent angular components, but instead decorrelates high density spatial variation from lower density angular variation using a mid-resolution probe grid of angular features. Each of the components encode abstract features that are fed to a tiny MLP, which acts as a minimal BRDF decoder of spatial and angular", + "bbox": [ + 511, + 780, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Source code is available at https://gitlab.inria.fr/projects-morpheo/ProbeSDF", + "bbox": [ + 89, + 875, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11026", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d262540ec2d12070175fdbb9071174bc9e7fc9b3cbbd71efc5a97a9ae50fa147.jpg", + "image_caption": [ + "Figure 1. We design a new appearance model for neural surface approaches, which combines high resolution spatial features and lower resolution angular features for improved reconstruction quality, training and inference speed. We plot the chamfer distance as a function of training speed for several baselines on MVMannequins (top) and DTU (bottom)." + ], + "image_footnote": [], + "bbox": [ + 133, + 85, + 869, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "varying components, while we explicitly store SDF values. This scheme advantageously replaces the core appearance and decoding model of SDF approaches [15, 30, 31, 33] to predict ray colors. We are careful to also include power terms of the cosine angle between the view direction and the estimated surface normal, allowing our lightweight model to effectively account for increased surface reflectivity at grazing angles. This yields an unprecedented performance combination, superseding both 3D and image metric performances with four popular benchmarks for general object reconstruction [9, 34] and human reconstruction [8, 27] while simultaneously achieving a significant training and rendering performance boost. In summary, our contributions are:", + "bbox": [ + 91, + 359, + 482, + 554 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An explicit embedding of the angular dependency that is simultaneously local, smooth and efficient.", + "- A simpler color prediction MLP that is agnostic to the surface position and orientation." + ], + "bbox": [ + 89, + 556, + 483, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 89, + 631, + 240, + 647 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work we leverage disentangled spatial and angular parameterization of radiance towards high quality appearance and surface modeling. Here we consequently review closely related works on surface-based 3D scene representations and existing parametrizations of color.", + "bbox": [ + 89, + 657, + 482, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Surface Reconstruction. Through the use of implicit surface representations, neural implicit fields have demonstrated increasing capabilities to generate high-quality 3D models [23, 35, 36]. In NeuS [30], Wang et al. proposed to parametrize the surface with a signed distance function that is modeled with a multi layer perceptron (MLP). The approach opened new frontiers in the generation of accurate 3D scenes from images but at the cost of prohibitive training times (several hours). Follow-up works have thus focused on boosting both accuracy and computation time by employing explicit grids of features", + "bbox": [ + 89, + 734, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and smaller MLPs. Notably, Wu et al. proposed in Vox-urf [33] to use a dense grid of voxels, and Neus2 was also proposed using hash grids [31]. Recently, Millimetric humans [27] have demonstrated remarkably fast and accurate reconstructions in the case of human datasets by using sparse and dynamic grids. Other reparametrizations target performance improvement, e.g. point-based with Fast Dipole Sums [3] and PGSR [2] both leveraging multi-view stereo priors, or by seeking mutual advantage of a hybrid volume/mesh representation [7]. All the methods discussed above rely on co-located encodings of position and view direction to parametrize the appearance. As a consequence, these approaches either fail to model local radiance effects like inter-reflections, or require larger MLPs and training times, and may thus benefit from our refactored appearance model as drop-in replacement.", + "bbox": [ + 511, + 359, + 906, + 601 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Angular parametrization Deep MLPs have become ubiquitous to model view-dependent colors, taking as input the view direction [18], the view and normal [30, 31, 33, 35] or the reflected direction [27, 28]. Non-neural approaches such as plenoxels [4] or the Gaussian splatting methods [6, 13] favor a straightforward spherical harmonics decomposition in color space. The main advantage compared to a deep MLP is the computational efficiency, at the cost of a large number of appearance parameters: 27 per voxel for [4] and 48 per Gaussian for [13]. Note that some neural architectures [27, 28, 31] use spherical harmonics as a positional encoding of the directional vectors, but this is completely distinct from encoding the signal into spherical harmonic coefficients. In this work we propose a lighter yet efficient parametrization of color by using two decorrelated voxel structures to encode different components of the observed color, and spherical harmonics encoding of pre-MLP features for more parsimonious and expressive color decoding.", + "bbox": [ + 511, + 607, + 908, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the field of real-time rendering, where lighting and", + "bbox": [ + 532, + 885, + 906, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11027", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "BRDF are known in advance, the idea of caching the incoming light at discrete locations, known as light field probes, has become standard [16, 17, 24]. We draw inspiration from this technique for our proposed approach to multi-view 3D reconstruction, with the difference in our case that the probe parameters are optimized along with the voxel parameters.", + "bbox": [ + 89, + 90, + 480, + 183 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "High Frequency Reflections. A number of approaches specifically deal with high frequency reflections, which requires dedicated representations and algorithms. Guo et al. [5] train an additional NeRF that is composited with the main image. This approach is under-constrained and thus requires strong priors such as the reflective surfaces being flat. Verbin et al. [28] model lighting as a neural envmap, modulated by a per-point roughness. The roughness and base color of the object can be edited afterwards but a long training time is required due to the large MLP.", + "bbox": [ + 89, + 195, + 482, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent works [29, 32] recover detailed reflections using cone tracing, which inherently solves the problem posed by self-reflections. Both approaches give impressive results even when confronted with curved, mirror-like objects but at a large training cost exceeding 10 GPU-hours per scene. In contrast, we target objects with mild specularities, and show that both fast training and real-time rendering can be achieved. More specifically, our neural light field probes can learn information about the surroundings whereas cone tracing gathers it at a greater cost. This assumption proves to be valid for standard acquisition scenes, with the four datasets tested.", + "bbox": [ + 89, + 359, + 482, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Minimal Parametrization. Explicitly disentangling the material parameters from the lighting is particularly challenging but also rewarding because it can yield a minimal parametrization of the appearance. Munkberg et al. [22] show that the approximate rendering equation developed in [12] is sufficiently accurate to recover the geometry using a differentiable rasterizer, along with an approximate material decomposition. Jiang et al. [10] applies a similar strategy but with the 3D gaussian splatting volume rendering. The NeRFactor pipeline [37] starts from a pre-trained NeRF that is distilled into lighting, albedo and neural BRDF parameters. Jin et al. proposed TensoIR [11], which achieves a more accurate decomposition by evaluating the rendering equation with importance sampling. An efficient tensor representation helps to accelerate the rendering of the secondary rays, but the complete training still takes five hours on a single GPU, with decent results available after half an hour of training. Our proposed method converges in just a few minutes and we find that only 4 coefficients per voxel are sufficient in most cases. The dimensionality is equivalent to the albedo and roughness values of a physically-based material parametrization, but without the cost associated with the inversion of the rendering equation.", + "bbox": [ + 89, + 553, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 89, + 604, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use an SDF grid as the implicit representation of the 3D shape. SDF values in the grid are optimized via our newly proposed differentiable appearance model and the derived surface normal vectors $\\mathbf{n}$ .", + "bbox": [ + 511, + 114, + 906, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Decoupled Parametrization of Radiance", + "text_level": 1, + "bbox": [ + 511, + 184, + 856, + 200 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Volumetric neural rendering, as proposed in the seminal work NeRF, computes the color at a given pixel by integrating radiances along camera-pixel rays weighted by local opacity values. Follow-up papers condition the opacity on the distance to the surface to improve the reconstruction quality [20, 30, 36]. The radiance $C$ represents the amount of energy that is emitted by a point in space. In physics it is expressed as the integral over the hemisphere $\\Omega$ of the spatially varying bidirectional reflectance distribution function (SVBRDF) $f_{r}$ multiplied by the incoming radiance $L$ and by the cosine between the incoming direction $\\omega$ and the surface normal $\\mathbf{n}$ :", + "bbox": [ + 511, + 205, + 906, + 388 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC = \\int_ {\\Omega} f _ {r} (\\mathbf {v}, \\omega , \\mathbf {x}) L (\\omega , \\mathbf {x}) (\\omega \\cdot \\mathbf {n}) d \\omega . \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 396, + 906, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The (spatially varying) BRDF depends on the point's position $\\mathbf{x}$ , direction of incoming light $\\omega$ and viewing direction $\\mathbf{v}$ . $L(\\omega, \\mathbf{x})$ is the intensity of light at point $\\mathbf{x}$ that comes from the direction $\\omega$ and $\\mathbf{n}$ is the normal vector of the surface at position $\\mathbf{x}$ . In equation 1, both $f_{r}$ and $L$ are unknown and disentangling these two functions during optimization is extremely difficult. As a consequence, a current research trend is to use an MLP to directly approximate the result of this integral and obtain the outgoing radiance with the following equation:", + "bbox": [ + 511, + 436, + 908, + 589 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC = M L P (\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {v}, \\mathbf {n}, \\mathbf {r}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 601, + 906, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{F}_s(\\mathbf{x})$ represents spatial features encoded at a point position $\\mathbf{x}$ , and $\\mathbf{r}$ is the reflected vector at point $\\mathbf{x}$ for the viewing direction $\\mathbf{v}$ . This approximation works well if the incoming light is positionally invariant, but its accuracy degrades in the presence of local lighting effects such as close point lights, inter-reflections and self-shadows. In such cases, the spatial features must additionally encode some information about the local lighting and thus require a larger dimensionality than one would expect. A large and deep MLP is also necessary to decode this compressed information, which lowers the computational efficiency.", + "bbox": [ + 511, + 628, + 906, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose to decouple the radiance model into spatial and angular features. We model a 3D scene with a combination of a high resolution sparse voxel grid that models the SDF field and a coarser grid that models the angular features as shown in fig. 2. For each point in space, the spatial features are obtained with a planar factorization in the coarse resolution tile with $\\mathbf{F}_s = \\mathbf{F}_x\\otimes \\mathbf{F}_y\\otimes \\mathbf{F}_z$ for", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11028", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4bd17308d7cfc01a73e605af7e0509cfefe748fb35fcf24f97a0ea5b5423673e.jpg", + "image_caption": [ + "Figure 2. Overview of the color prediction for a single voxel inside a $16^{3}$ tile. The angular features $F_{a}$ are computed by interpolating and evaluating the spherical harmonics from the 8 corner probes with the reflected vector $\\mathbf{r}$ . The spatial features $F_{s}$ are computed as the outer product of three orthogonal planes of resolution $16\\times 16$ , specific to the tile. A small neural network decodes these inputs into a color." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 908, + 260 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dimensionality reduction [1]. The angular features $\\mathbf{F}_a$ are obtained by tri-linearly interpolating light field probes as explained in sec. 3.2. In addition, a dependency on the angle of incidence must be added to account for differences in reflectivity, as shown in fig. 3.", + "bbox": [ + 88, + 340, + 486, + 417 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1a0b693822b42540b2584761c40aed93b62ede012c30c78729214334f5055e03.jpg", + "image_caption": [ + "Figure 3. The reflectivity cannot be encoded in $\\mathbf{F}_a$ alone because different incident vectors can map to the same reflected vector (in red). In that case, similar angular features will be obtained for the two viewpoints due to the spatial and angular proximity of the lookups. The angle of incidence disambiguates the two situations." + ], + "image_footnote": [], + "bbox": [ + 107, + 428, + 465, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The reflectivity, also called the Fresnel term, is commonly approximated as follows for rendering purposes [25]:", + "bbox": [ + 89, + 640, + 483, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR (\\theta) = R _ {0} + (1 - R _ {0}) (1 - \\cos \\theta) ^ {5}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 695, + 482, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$R_0$ is the reflectivity at normal incidence and $\\theta$ is the angle between the view direction and the half-way vector to the light source. In our case, $R_0$ is unknown and there is no explicit light source which means that we cannot use this formula directly. Instead, we approximate $\\cos \\theta$ by $\\mathbf{n} \\cdot \\mathbf{v}$ and let the first layer of the neural network learn a polynomial approximation of the Fresnel term. Our revised parametrization is given by eq. 4:", + "bbox": [ + 89, + 723, + 483, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} C = M L P \\left(\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {F} _ {a} (\\mathbf {x}, \\mathbf {r})\\right), \\\\ (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {0}, \\dots , (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {5}). \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 859, + 480, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We denote the dimensionality of the features by $n_s$ and $n_a$ such that $\\mathbf{F}_s \\in \\mathbb{R}^{n_s}$ and $\\mathbf{F}_a \\in \\mathbb{R}^{n_a}$ . Most materials reflect the light in a cone around the reflected vector which is why we condition $\\mathbf{F}_a$ on $\\mathbf{r}$ , but some materials have retroreflective properties that break this assumption. In that case, conditioning on the view direction would be more appropriate. Lastly, eq. 4 assumes isotropic materials since the reflectivity depends only on $\\mathbf{n} \\cdot \\mathbf{v}$ . Anisotropic materials could be handled by adding a dependency on the azimuthal angle.", + "bbox": [ + 511, + 340, + 906, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Light Field Probes on a Coarse Grid", + "text_level": 1, + "bbox": [ + 511, + 487, + 830, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we replace the generic angular inputs $\\mathbf{v}$ , $\\mathbf{n}$ , $\\mathbf{r}$ with new angular inputs encoding the local illumination (the light field probes), with the goal to achieve a more efficient parametrization of the appearance in terms of parameter count, training and inference speed. Similarly to previous works [4, 13], we use a spherical harmonics decomposition to model this dependency, but with several important differences: first, we encode abstract features on the sphere rather than the outgoing radiance which lets a neural network handle the non-linearities. Second, our directional embedding has a low spatial resolution which takes advantage of the smooth spatial variations of the lighting. Third, we sample this embedding with the reflected vector instead of the view vector to link the local surface orientation with the shading function, which has been showed to be beneficial for improved surface quality [28]. The angular features encoded into a single neural probe are given by eq. 5:", + "bbox": [ + 511, + 508, + 906, + 767 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {a} = \\mathcal {S H} (\\mathbf {r}) = \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {j} Y _ {j} (\\mathbf {r}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 777, + 906, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The polynomials of the SH basis are denoted with $Y_{j}$ . There are $l^2$ coefficients $\\mathbf{b}_j \\in \\mathbb{R}^{n_a}$ . Increasing values of $l$ unlock", + "bbox": [ + 511, + 833, + 906, + 864 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2We use a one-indexed notation for the SH order $l$ instead of the traditional zero-indexing so that we have $l^2$ coefficients.", + "bbox": [ + 511, + 875, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11029", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "signals of increasing angular frequency which gives an explicit control on the representable amount of specularities. We observe two guiding principles: (1) The shinier the material, the higher the frequency of $\\mathbf{F}_a$ should be in the angular domain. (2) The closer the light source, the higher the frequency $\\mathbf{F}_a$ should be in the spatial domain. See fig. 4 for an illustration.", + "bbox": [ + 89, + 90, + 483, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8f15472fede64b66507349dce8821e329eae4d23f383990d0c58bc8945702423.jpg", + "image_caption": [ + "Figure 4. Left and center: The lighting direction changes at a lower rate on the surface for distant light sources. Right: Self shadows impose variations in lighting even with directional illumination." + ], + "image_footnote": [], + "bbox": [ + 91, + 205, + 478, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the case of common scenes such as humans or everyday objects, assuming materials with high to medium roughness so that $\\mathbf{F}_a$ does not need to be of very high angular frequency is generally sufficient. We also assume that the lights are far enough, so that probes at a low spatial frequency can explain the parallax. The probes are stored at 1/16th the resolution of the main voxel grid, as shown in fig. 2. The voxels tri-linearly interpolate the 8 nearest probes according to eq. 6 and 7, with $w_i$ the interpolation weight of the i-th corner.", + "bbox": [ + 89, + 364, + 483, + 516 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {F} _ {a} = \\sum_ {i = 1} ^ {8} \\mathcal {S H} _ {i} (\\mathbf {r}) w _ {i} = \\sum_ {i = 1} ^ {8} \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {i j} Y _ {j} (\\mathbf {r}) w _ {i} (6) \\\\ = \\sum_ {j = 1} ^ {l ^ {2}} \\hat {\\mathbf {b}} _ {j} Y _ {j} (\\mathbf {r}) \\quad \\text {w i t h} \\hat {\\mathbf {b}} _ {j} = \\sum_ {i = 1} ^ {8} \\mathbf {b} _ {i j} w _ {i} (7) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 523, + 482, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. SDF Estimation Approach", + "text_level": 1, + "bbox": [ + 89, + 621, + 331, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We here discuss how to embed the new proposed color decoder in an implicit surface reconstruction pipeline. During the forward pass, for a pixel $(u,v)$ in a given viewpoint, the color is computed by a transmittance $T_{i}$ -weighted average of the colors $C_i$ of $N$ points sampled from the current scene volume estimate along the pixel aligned ray, where $T_{i}$ is the product of obstructing opacities $\\alpha_{j}$ . We use the NeuS equation to relate volumetric opacities to the SDF $s_i$ at each sample point [30]:", + "bbox": [ + 89, + 643, + 483, + 780 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} c (u, v) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} C _ {i}, \\quad T _ {i} = \\prod_ {j < i} (1 - \\alpha_ {j}), (8) \\\\ \\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {\\tau} (s _ {i}) - \\Phi_ {\\tau} (s _ {i + 1})}{\\Phi_ {\\tau} (s _ {i})}, 0\\right), (9) \\\\ \\Phi_ {\\tau} \\left(s _ {i}\\right) = \\frac {1}{1 + \\exp^ {- \\tau s _ {i}}}. (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 786, + 482, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a scale factor that increases during optimization. The SDF field can then be optimized by backpropagating updates from the observed color loss through the rendering equation, and from the set of regularization losses.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our losses and regularizations are detailed in equations 11 to 16. The raw SDF $\\hat{s}$ is convolved by a $5^{3}$ gaussian kernel $G$ into a smoother SDF $s$ to stabilize training [33]. Note that $s$ is used for all subsequent operations such as normal computation and rendering. Eq. 11 maintains $s$ and $\\hat{s}$ close to each other to promote smoothness. The Eikonal regularization 12 ensures that $s$ is a signed distance. Equations 13, 14, 15 promote spatial smoothness for the normals, for the factorized spatial features and for the probe coefficients respectively. In eq. 15, $\\mathcal{V}_i$ is the set of neighboring probes adjacent to the i-th one and $N$ is the total number of probes. The regularizations are applied on each voxel, factorized feature, probe or image pixel when appropriate.", + "bbox": [ + 511, + 152, + 906, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s d f}} = \\sum_ {\\text {v o x e l}} | s - \\hat {s} | ^ {2}, \\quad s = G (\\hat {s}) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 369, + 906, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {E i k}} = \\sum_ {\\text {v o x e l}} \\left(\\left| \\left| \\nabla s \\right| \\right| - 1\\right) ^ {2} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 404, + 903, + 436 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {\\text {v o x e l}} | | \\nabla \\mathbf {n} | | ^ {2}, \\quad \\mathbf {n} = \\nabla s / | | \\nabla s | | \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 440, + 903, + 470 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t u r e s}} = \\sum_ {\\text {t e x e l}} | | \\nabla \\mathbf {F} _ {x} | | ^ {2} + | | \\nabla \\mathbf {F} _ {y} | | ^ {2} + | | \\nabla \\mathbf {F} _ {z} | | ^ {2} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 473, + 903, + 506 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r o b e s}} = \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {l ^ {2}} \\sum_ {k \\in \\mathcal {V} _ {i}} \\left| \\left| \\mathbf {b} _ {i j} - \\mathbf {b} _ {k j} \\right| \\right| ^ {2} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 508, + 903, + 554 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {u, v} | | c (u, v) - c _ {\\mathrm {g t}} (u, v) | | ^ {2} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 556, + 903, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In eq. 16, $c$ is the rendered image and $c_{\\mathrm{gt}}$ is the ground truth image. We apply a weight of $(\\max(c, c_{\\mathrm{gt}}) + \\epsilon)^{-1}$ on the photometric gradient of each pixel in eq. 16 to penalize relative differences rather than absolute differences [19]. A similar strategy is used on $\\mathcal{L}_{\\mathrm{sdf}}$ and $\\mathcal{L}_{\\mathrm{features}}$ . We apply an empirical factor of $(1 + |s| * 5)^{-1}$ on the gradients of the per-voxel regularizations to lower their importance when the distance to the zero-crossing increases. The idea is to keep the regularizations and the data term balanced for regions near and far from the surface alike.", + "bbox": [ + 511, + 598, + 906, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training", + "text_level": 1, + "bbox": [ + 513, + 757, + 617, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our complete loss is a weighted sum of eq. 11 to 16 that we minimize with the Adam optimizer [14], please refer to the supplementary document for more details. In summary, the trained parameters are the raw SDF values $\\hat{s}$ , the factorized features $\\mathbf{F}_x, \\mathbf{F}_y, \\mathbf{F}_z$ , the probes coefficients $\\mathbf{b}$ and the MLP weights. We follow a coarse-to-fine learning strategy, both in the spatial and angular domains. We start with coarse voxels and $l = 2$ , under the supervision of low resolution", + "bbox": [ + 511, + 779, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11030", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "images. We iteratively subdivide the voxels and switch to higher resolution images, and introduce higher angular frequencies by increasing $l$ . Starting the optimization with too many degrees of freedom for the appearance parametrization can lead to local minima, as noted by [13].", + "bbox": [ + 89, + 90, + 482, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 181, + 312, + 199 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use a 2 hidden layer MLP with 32 neurons and ReLU activations with a sigmoid for the last layer. The probes at the shared corners of adjacent tiles are duplicated in memory (but keep shared values) to benefit from hardware-accelerated interpolation. We support up to 16 spherical harmonic coefficients $(l = 4)$ per probe. The computation of $\\mathbf{F}_a$ , $\\mathbf{F}_s$ and the MLP call are fused into a single CUDA kernel for efficiency, following [21] and [27]. Each $16^3$ tile contains $3 \\times 16 \\times 16 \\times n_s$ spatial coefficients and $8 \\times l^2 \\times n_a$ spherical harmonic features. Assuming $l = 4$ and $n_s = n_a$ , the probes only require $(8 \\times 16) / (3 \\times 16 \\times 16) = 1/6$ th of the memory taken by the spatial features. The sparse voxel grid is based on the code of [27], with targeted modifications to implement our probes.", + "bbox": [ + 89, + 208, + 483, + 420 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 435, + 222, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Protocol We evaluate our method on 4 datasets: MVMannequins [27], ActorsHQ [8], DTU [9] and BlendedMVS [34]. Due to the various evaluation settings employed in the community, we chose to re-train and re-evaluate all the baselines using the same experimental protocol for fairness. Following [6], all available images were given as input and used for evaluation. Timings are measured on a workstation equipped with an RTX A6000 GPU (Ampere series). PSNR values are computed inside the silhouette region of objects of interest and chamfer error is computed using official scripts. We use the following grid resolutions: DTU $(1000^{3})$ , BMVS $(666^{3})$ , MVMannequins $(2500 \\times 1250 \\times 2500$ , $2\\mathrm{mm} / \\mathrm{voxel}$ ), ActorsHQ $(3000 \\times 4000 \\times 3000$ , $0.6\\mathrm{mm} / \\mathrm{voxel}$ ). Some datasets may contain inconsistent shadows or large exposure changes (DTU and BMVS) that are hard to model by our representation so we optionally train per-camera bias vectors in the MLP.", + "bbox": [ + 89, + 460, + 482, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MVMannequins is a dataset of 14 dressed mannequins for multi-view reconstruction benchmarking with 68 cameras at $2048^{2}$ resolution. We use the official evaluation code and report the metrics in table 1. We outperform all the baselines while taking only about a minute of training time, almost 3x faster than [27], with 5GB of VRAM, a rendering speed of $300\\mathrm{Hz}$ to $400\\mathrm{Hz}$ and a model size of 30MB.", + "bbox": [ + 89, + 719, + 482, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ActorsHQ is a multiview dataset of humans in motion with 160 cameras at a high resolution of $4088 \\times 2990$ . We evaluate on the 1000th temporal frame of 13 sequences. We compare against Voxurf [33] and NeuS2 [31], which we trained with half resolution images since we ran into issues", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with full resolution images. We report the PSNR in table 2 and show qualitative results in fig. 5. Voxurf takes about one hour to fully converge (with $3 \\times$ the training iterations of the DTU configuration). NeuS2 converges fast but with a lower PSNR. In comparison, our method only takes $\\sim 4$ minutes to converge on the full resolution images, and we also outperform both when training at the same resolution. This benchmark highlights the capability of our method to gracefully scale to high-resolution scenes.", + "bbox": [ + 511, + 90, + 906, + 227 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/39cf5a02c63ca7ce393954b0baf9ba2cb9f9b84ff86abf51ea396ade50531227.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 239, + 903, + 468 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ee07766ddd3cf39740b317b7b0fb4153a46d381674e2e6aa2f2b04c8c4aa83c.jpg", + "image_caption": [ + "Figure 5. High-resolution reconstructions for ActorsHQ." + ], + "image_footnote": [], + "bbox": [ + 516, + 469, + 903, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DTU provides 49 to 64 images of various objects at $1600 \\times 1200$ resolution, along with evaluation point clouds. We use the foreground masks provided by IDR [35] for training and testing. 2DGS [6] does not support masks for training so it uses complete images instead, cropped and at half resolution according to its evaluation protocol. We compare against Voxurf [33], Neus2 [31] and 2DGS [6] on DTU in table 3, using the official python script for geometric evaluation. We outperform all three in terms of chamfer distance and PSNR, twice as fast as NeuS2 on the same hardware. Rendering speed ranges from $200\\mathrm{Hz}$ to $300\\mathrm{Hz}$ .", + "bbox": [ + 511, + 703, + 906, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BlendedMVS. Finally, we test our method on 8 scenes of the BlendedMVS dataset [34] and report the metrics in", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11031", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/777b401cf67313819f22c84be26af1b9dfd7b2138f9ce6c3f3ddba4a211519b2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Metrics(4,4,4)X(8,8,4)XMMH [27]Voxurf [33]Neus2 [31]Colmap [26]2DGS [6]
Chamfer (mm)1.041.031.141.592.133.523.35
PSNR36.8136.9036.3335.5134.22-34.89
Training1min1min2-3min15min5min>1h>1h
", + "bbox": [ + 158, + 88, + 836, + 148 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7dff7dde10247f985c12f468ad6dc9c92691718022c5bef6c46fb4c10137f2ab.jpg", + "table_caption": [ + "Table 1. Evaluation on MVMannequins with two configurations for $\\left( {{n}_{s},{n}_{a},l}\\right)$ . Per-camera bias vectors are not used (X-symbol)." + ], + "table_footnote": [], + "table_body": "
(ns,na,l) = (4,4,4)XVoxurfNeuS2
Resolutionr/1r/2r/4r/2r/2
PSNR37.4836.6234.7436.5634.53
Training250s110s53s1h250s
Model size232MB57MB15MB500MB25MB
", + "bbox": [ + 91, + 210, + 488, + 289 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1a8e96d54512e620c59cafeaa9eaaf90fceb5e8064684cd206ad3d8c906f3228.jpg", + "table_caption": [ + "Table 2. Evaluation for ActorsHQ. Per-camera bias vectors are not used ( $\\times$ -symbol). Full, half and quarter-resolution input images are denoted as $r/1$ , $r/2$ , $r/4$ respectively. Renderings are up-scaled before comparison with the full resolution images $(4088 \\times 2990)$ ." + ], + "table_footnote": [], + "table_body": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus22DGS
Chamfer0.680.710.730.800.76
PSNR37.0337.7437.083636.03
Training150s160s15min5min12min
Model size56MB88MB500MB25MB49MB
", + "bbox": [ + 91, + 378, + 501, + 455 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cbbd618c1b628d21a1871f2a43dff9d2c95218567c8be35ff1a2e6be309da69b.jpg", + "table_caption": [ + "Table 3. DTU evaluation with two configurations for $\\left( {{n}_{s},{n}_{a},l}\\right)$ . Per-camera bias vectors are used (✓-symbol)." + ], + "table_footnote": [], + "table_body": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus2
Chamfer2.372.222.642.93
PSNR35.1935.8935.1133.62
Training110s120s15min5min
", + "bbox": [ + 119, + 507, + 454, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "table 4. The BlendedMVS is a semi-synthetic dataset were objects have been first reconstructed then reprojected in the images in order to produce reliable ground truth geometry and masks. There is no official script for geometric evaluation so we measure two-ways point to mesh distances in the reference frame used for training in [30], scaled by $1000\\mathrm{x}$ .", + "bbox": [ + 89, + 665, + 482, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations. We ablate the probes smoothing and the polynomial approximation of the Fresnel term in tab. 5 on the MVMannequins dataset by imposing $\\mathbf{n} \\cdot \\mathbf{v} = 1$ in eq. 4 during training, with noticeable incidence on Chamfer error. A visual ablation of the components of our parametrization is presented in fig. 8 on the kino/jea mannequin, clearly showing the role of each parameter group. Figure 9 contains more examples. Various choices of configurations are compared in table 6 on the BlendedMVS dataset.", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f5a3a2455dff7b84bc9cad531116ba4f215606ea8b5c69cb14384b2831714bc.jpg", + "image_caption": [ + "Figure 6. Reconstructions on challenging examples of DTU." + ], + "image_footnote": [], + "bbox": [ + 511, + 208, + 905, + 558 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d50d312a18dd8425b22968db20d0ed86e633ea977559d155646ab1d371fe641c.jpg", + "table_caption": [ + "Table 4. BMVS evaluation with two configurations for $\\left( {{n}_{s},{n}_{a},l}\\right)$ . Per-camera bias vectors are used (✓-symbol)." + ], + "table_footnote": [], + "table_body": "
(4,4,4)Xw/o probes smoothingw/o Fresnel
Chamfer (mm)1.041.091.18
PSNR36.8136.9136.79
", + "bbox": [ + 537, + 601, + 882, + 635 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/879e9b99b175d1f9115a9fd752c2010c20d9de22fed231cd5115e71bf74cacc5.jpg", + "table_caption": [ + "Table 5. Ablation on MVMannequins" + ], + "table_footnote": [], + "table_body": "
Metrics(4,4,4)X(4,4,4)Y(8,8,4)√(12,12,4)√(4,4,1)√(4,4,2)√(4,4,3)√
Chamfer2.472.372.222.312.582.342.37
PSNR34.7635.1935.8936.1734.4434.8635.05
", + "bbox": [ + 514, + 672, + 903, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. We ablate the number of spatial features $n_s$ , angular features $n_a$ and spherical harmonics order $l$ on BlendedMVS. Each triplet denotes a configuration $(n_s, n_a, l)$ . The $\\checkmark$ -symbol indicates when per-camera bias vectors are trained.", + "bbox": [ + 511, + 714, + 905, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 511, + 811, + 635, + 828 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We identify several limitations to our approach. First, the fact that the lighting is encoded locally can degrade the extrapolation capabilities compared to modeling the environment with a global representation. This becomes appar", + "bbox": [ + 511, + 839, + 905, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11032", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/640b930eea7e84d7a965f5dd7d665765845086cc30a160cc6e305ef8a106e75e.jpg", + "image_caption": [ + "Figure 7. Reconstructed examples on BlendedMVS." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 480, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75e4fbe567e4be83399a9de27bcb214dfebe374a4a40ba4f1b1c5d634ee04587.jpg", + "image_caption": [ + "Figure 8. Our model can be intuitively explained. We disable some components of a pre-trained example from the MVMannequins dataset [27] (left). From left to right, we remove the spatial features (set $\\mathbf{F}_s = 0$ ), only keep the constant coefficient of the SH basis ( $l = 1$ ), disable the incidence angle embedding (set $\\mathbf{n} \\cdot \\mathbf{v} = 1$ in eq. 4). The learned Fresnel term encodes grazing reflections (red circles), the angular features provide the shading (green squares) and the spatial features contain the high frequency details." + ], + "image_footnote": [], + "bbox": [ + 93, + 411, + 480, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ent on the ActorsHQ dataset where there is a good overlap of the cameras field of views along the longitude, but very little overlap along the latitude on the legs. This creates shadows artifacts when looking from above or below rather that at a level angle. Second, although our decomposition is physically-inspired, we do not explicitly simulate light transport which can result in local minima due to shape-radiance ambiguities. Relighting and/or material editing is not supported but fine-tuning the probes to new lighting seems possible and worthy of future investigations.", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c2bb73b2cd549ee7a4ad3cb3cd923b38fdf80d6d9db6affb6c2da389a389577.jpg", + "image_caption": [ + "Figure 9. Effect of the learned Fresnel term on three examples from MVMannequins, DTU and ActorsHQ. Left to right: input image, volume rendering (A), volume rendering w/o the Fresnel term (B) (we set $\\mathbf{n}\\cdot \\mathbf{v} = 1$ in eq. 4), difference image $(4\\times |A - B|)$ ." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 903, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 511, + 436, + 782, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel approach to model the view dependent appearance, enabling both fast reconstruction and real-time rendering of humans and objects. Notably, our model does not compromise on geometric and photometric quality, even surpassing the previous approaches in many instances. It can easily scale to high resolution inputs while maintaining high performance. We have reached a parsimonious parametrization of the surface properties thanks to a simple formulation. Disentangling the spatial and angular components with high efficiency also offers promising future avenues of research toward temporal reconstruction. Other future research can build on this work, e.g. handling high frequency reflections at a lower cost than current dedicated approaches and unifying neural rendering and physically-based rendering. Other embeddings of the angular dependency representations can be investigated, such as cubemaps or mixtures of spherical gaussians.", + "bbox": [ + 511, + 464, + 906, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgments", + "text_level": 1, + "bbox": [ + 511, + 738, + 691, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) grant ANR-21-ESRE-0030 (CONTINUUM). Research conducted at Kyushu University was supported by JSPS/KAKENHI JP23H03439 and AMED JP24wm0625404. We thank Laurence Boissieux for her valuable help generating 3D renderings, and Edmond Boyer for insightful discussions and comments.", + "bbox": [ + 511, + 763, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11033", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In European Conference on Computer Vision (ECCV), 2022. 4", + "[2] Danpeng Chen, Hai Li, Weicai Ye, Yifan Wang, Weijian Xie, Shangjin Zhai, Nan Wang, Haomin Liu, Hujun Bao, and Guofeng Zhang. 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ACM Transactions on Graphics (TOG), 40(6), 2021. 3" + ], + "bbox": [ + 91, + 90, + 483, + 852 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11035", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_model.json b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..906bf738353e5376d96da32ac4787ab452ff402c --- /dev/null +++ b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_model.json @@ -0,0 +1,1925 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.131, + 0.833, + 0.152 + ], + "angle": 0, + "content": "ProbeSDF: Light Field Probes For Neural Surface Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.181, + 0.422, + 0.198 + ], + "angle": 0, + "content": "Briac Toussaint" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.203, + 0.465, + 0.216 + ], + "angle": 0, + "content": "briac.toussaint@inria.fr" + }, + { + "type": "text", + "bbox": [ + 0.573, + 0.181, + 0.7, + 0.199 + ], + "angle": 0, + "content": "Diego Thomas" + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.203, + 0.748, + 0.217 + ], + "angle": 0, + "content": "thomas@ait.kyushu-u.ac.jp" + }, + { + "type": "text", + "bbox": [ + 0.405, + 0.224, + 0.591, + 0.24 + ], + "angle": 0, + "content": "Jean-Sébastien Franco1" + }, + { + "type": "text", + "bbox": [ + 0.367, + 0.246, + 0.632, + 0.259 + ], + "angle": 0, + "content": "jean-sebastien.franco@inria.fr" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.26, + 0.756, + 0.277 + ], + "angle": 0, + "content": "1Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, France" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.278, + 0.604, + 0.295 + ], + "angle": 0, + "content": "\\(^{2}\\)Kyushu University, Japan" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.33, + 0.327, + 0.345 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.361, + 0.485, + 0.633 + ], + "angle": 0, + "content": "SDF-based differential rendering frameworks have achieved state-of-the-art multiview 3D shape reconstruction. In this work, we re-examine this family of approaches by minimally reformulating its core appearance model in a way that simultaneously yields faster computation and increased performance. To this goal, we exhibit a physically-inspired minimal radiance parametrization decoupling angular and spatial contributions, by encoding them with a small number of features stored in two respective volumetric grids of different resolutions. Requiring as little as four parameters per voxel, and a tiny MLP call inside a single fully fused kernel, our approach allows to enhance performance with both surface and image (PSNR) metrics, while providing a significant training speedup and real-time rendering. We show this performance to be consistently achieved on real data over two widely different and popular application fields, generic object and human subject shape reconstruction, using four representative and challenging datasets." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.676, + 0.222, + 0.691 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.701, + 0.483, + 0.821 + ], + "angle": 0, + "content": "Neural radiance fields have established a new milestone for the task of novel view synthesis and have led to a plethora of variants of broad applicability. We here take particular interest in SDF surface-based radiance fields, which have proven to be a highly performing variant for the tasks of 3D modeling from images [30, 33], with wide reaching applications ranging from object and performance capture, to immersive and 3D content production." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.822, + 0.483, + 0.868 + ], + "angle": 0, + "content": "At the heart of such methods usually lies a parametrization of the light field, in the form of a 5-dimensional function. This function maps the spatial coordinates of a point" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.33, + 0.908, + 0.572 + ], + "angle": 0, + "content": "in space and the observed direction to a color and a signed distance to the reconstructed surface. On one hand, the mapping can be global and use a complex scene-wide MLP as implicit 5D decoder, as is the case for most seminal approaches [18, 30]. On the other hand, recent popular variants that target higher speed and memory efficiency use explicit representations. Global representations are based on a grid encoding [4, 31, 33] where interpolated spatial and angular features are run through a global shallow MLP. Local representations use the sparse 3D Gaussian Splatting [13] sample-based encoding approach, where each separate Gaussian comes with its own opacity and adjoining set of angular color features. While grids or local approaches use a single deep MLP to densely encode the complete light field function, they almost always co-locate storage and decoding of color and angular features." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.578, + 0.909, + 0.775 + ], + "angle": 0, + "content": "But is this really a necessary or even desirable feature of any light field encoding? We question these assertions by postulating that, contrary to the spatial components of the light field that mainly encode intrinsic surface texture, the angular components encode phenomena that are predominantly extrinsic to the surface, i.e. lighting and environment, and as such can be encoded at a lower spatial resolution as they are locally almost invariant to parallax. This hypothesis is in fact exploited by the rendering community, where angular and environment components contributing to the radiance equation used to compute rendered colors, are typically precomputed at sparse 3D locations coined light field probes [24], and interpolated in-between." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Leveraging this intuition, our approach borrows the spherical harmonic parametrization popular with explicit methods e.g. [4, 13] to represent angular components, but instead decorrelates high density spatial variation from lower density angular variation using a mid-resolution probe grid of angular features. Each of the components encode abstract features that are fed to a tiny MLP, which acts as a minimal BRDF decoder of spatial and angular" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.875, + 0.483, + 0.901 + ], + "angle": 0, + "content": "1Source code is available at https://gitlab.inria.fr/projects-morpheo/ProbeSDF" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11026" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.087, + 0.87, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.291, + 0.908, + 0.335 + ], + "angle": 0, + "content": "Figure 1. We design a new appearance model for neural surface approaches, which combines high resolution spatial features and lower resolution angular features for improved reconstruction quality, training and inference speed. We plot the chamfer distance as a function of training speed for several baselines on MVMannequins (top) and DTU (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.36, + 0.483, + 0.555 + ], + "angle": 0, + "content": "varying components, while we explicitly store SDF values. This scheme advantageously replaces the core appearance and decoding model of SDF approaches [15, 30, 31, 33] to predict ray colors. We are careful to also include power terms of the cosine angle between the view direction and the estimated surface normal, allowing our lightweight model to effectively account for increased surface reflectivity at grazing angles. This yields an unprecedented performance combination, superseding both 3D and image metric performances with four popular benchmarks for general object reconstruction [9, 34] and human reconstruction [8, 27] while simultaneously achieving a significant training and rendering performance boost. In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.557, + 0.483, + 0.587 + ], + "angle": 0, + "content": "- An explicit embedding of the angular dependency that is simultaneously local, smooth and efficient." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.587, + 0.484, + 0.618 + ], + "angle": 0, + "content": "- A simpler color prediction MLP that is agnostic to the surface position and orientation." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.557, + 0.484, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.632, + 0.241, + 0.648 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.735 + ], + "angle": 0, + "content": "In this work we leverage disentangled spatial and angular parameterization of radiance towards high quality appearance and surface modeling. Here we consequently review closely related works on surface-based 3D scene representations and existing parametrizations of color." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Neural Surface Reconstruction. Through the use of implicit surface representations, neural implicit fields have demonstrated increasing capabilities to generate high-quality 3D models [23, 35, 36]. In NeuS [30], Wang et al. proposed to parametrize the surface with a signed distance function that is modeled with a multi layer perceptron (MLP). The approach opened new frontiers in the generation of accurate 3D scenes from images but at the cost of prohibitive training times (several hours). Follow-up works have thus focused on boosting both accuracy and computation time by employing explicit grids of features" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.36, + 0.907, + 0.602 + ], + "angle": 0, + "content": "and smaller MLPs. Notably, Wu et al. proposed in Vox-urf [33] to use a dense grid of voxels, and Neus2 was also proposed using hash grids [31]. Recently, Millimetric humans [27] have demonstrated remarkably fast and accurate reconstructions in the case of human datasets by using sparse and dynamic grids. Other reparametrizations target performance improvement, e.g. point-based with Fast Dipole Sums [3] and PGSR [2] both leveraging multi-view stereo priors, or by seeking mutual advantage of a hybrid volume/mesh representation [7]. All the methods discussed above rely on co-located encodings of position and view direction to parametrize the appearance. As a consequence, these approaches either fail to model local radiance effects like inter-reflections, or require larger MLPs and training times, and may thus benefit from our refactored appearance model as drop-in replacement." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.909, + 0.88 + ], + "angle": 0, + "content": "Angular parametrization Deep MLPs have become ubiquitous to model view-dependent colors, taking as input the view direction [18], the view and normal [30, 31, 33, 35] or the reflected direction [27, 28]. Non-neural approaches such as plenoxels [4] or the Gaussian splatting methods [6, 13] favor a straightforward spherical harmonics decomposition in color space. The main advantage compared to a deep MLP is the computational efficiency, at the cost of a large number of appearance parameters: 27 per voxel for [4] and 48 per Gaussian for [13]. Note that some neural architectures [27, 28, 31] use spherical harmonics as a positional encoding of the directional vectors, but this is completely distinct from encoding the signal into spherical harmonic coefficients. In this work we propose a lighter yet efficient parametrization of color by using two decorrelated voxel structures to encode different components of the observed color, and spherical harmonics encoding of pre-MLP features for more parsimonious and expressive color decoding." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In the field of real-time rendering, where lighting and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11027" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.184 + ], + "angle": 0, + "content": "BRDF are known in advance, the idea of caching the incoming light at discrete locations, known as light field probes, has become standard [16, 17, 24]. We draw inspiration from this technique for our proposed approach to multi-view 3D reconstruction, with the difference in our case that the probe parameters are optimized along with the voxel parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.196, + 0.483, + 0.348 + ], + "angle": 0, + "content": "High Frequency Reflections. A number of approaches specifically deal with high frequency reflections, which requires dedicated representations and algorithms. Guo et al. [5] train an additional NeRF that is composited with the main image. This approach is under-constrained and thus requires strong priors such as the reflective surfaces being flat. Verbin et al. [28] model lighting as a neural envmap, modulated by a per-point roughness. The roughness and base color of the object can be edited afterwards but a long training time is required due to the large MLP." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.36, + 0.483, + 0.541 + ], + "angle": 0, + "content": "Recent works [29, 32] recover detailed reflections using cone tracing, which inherently solves the problem posed by self-reflections. Both approaches give impressive results even when confronted with curved, mirror-like objects but at a large training cost exceeding 10 GPU-hours per scene. In contrast, we target objects with mild specularities, and show that both fast training and real-time rendering can be achieved. More specifically, our neural light field probes can learn information about the surroundings whereas cone tracing gathers it at a greater cost. This assumption proves to be valid for standard acquisition scenes, with the four datasets tested." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.554, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Minimal Parametrization. Explicitly disentangling the material parameters from the lighting is particularly challenging but also rewarding because it can yield a minimal parametrization of the appearance. Munkberg et al. [22] show that the approximate rendering equation developed in [12] is sufficiently accurate to recover the geometry using a differentiable rasterizer, along with an approximate material decomposition. Jiang et al. [10] applies a similar strategy but with the 3D gaussian splatting volume rendering. The NeRFactor pipeline [37] starts from a pre-trained NeRF that is distilled into lighting, albedo and neural BRDF parameters. Jin et al. proposed TensoIR [11], which achieves a more accurate decomposition by evaluating the rendering equation with importance sampling. An efficient tensor representation helps to accelerate the rendering of the secondary rays, but the complete training still takes five hours on a single GPU, with decent results available after half an hour of training. Our proposed method converges in just a few minutes and we find that only 4 coefficients per voxel are sufficient in most cases. The dimensionality is equivalent to the albedo and roughness values of a physically-based material parametrization, but without the cost associated with the inversion of the rendering equation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.605, + 0.107 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.907, + 0.177 + ], + "angle": 0, + "content": "We use an SDF grid as the implicit representation of the 3D shape. SDF values in the grid are optimized via our newly proposed differentiable appearance model and the derived surface normal vectors \\(\\mathbf{n}\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.185, + 0.857, + 0.202 + ], + "angle": 0, + "content": "3.1. Decoupled Parametrization of Radiance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.207, + 0.907, + 0.389 + ], + "angle": 0, + "content": "Volumetric neural rendering, as proposed in the seminal work NeRF, computes the color at a given pixel by integrating radiances along camera-pixel rays weighted by local opacity values. Follow-up papers condition the opacity on the distance to the surface to improve the reconstruction quality [20, 30, 36]. The radiance \\(C\\) represents the amount of energy that is emitted by a point in space. In physics it is expressed as the integral over the hemisphere \\(\\Omega\\) of the spatially varying bidirectional reflectance distribution function (SVBRDF) \\(f_{r}\\) multiplied by the incoming radiance \\(L\\) and by the cosine between the incoming direction \\(\\omega\\) and the surface normal \\(\\mathbf{n}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.397, + 0.907, + 0.43 + ], + "angle": 0, + "content": "\\[\nC = \\int_ {\\Omega} f _ {r} (\\mathbf {v}, \\omega , \\mathbf {x}) L (\\omega , \\mathbf {x}) (\\omega \\cdot \\mathbf {n}) d \\omega . \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.438, + 0.909, + 0.59 + ], + "angle": 0, + "content": "The (spatially varying) BRDF depends on the point's position \\(\\mathbf{x}\\), direction of incoming light \\(\\omega\\) and viewing direction \\(\\mathbf{v}\\). \\(L(\\omega, \\mathbf{x})\\) is the intensity of light at point \\(\\mathbf{x}\\) that comes from the direction \\(\\omega\\) and \\(\\mathbf{n}\\) is the normal vector of the surface at position \\(\\mathbf{x}\\). In equation 1, both \\(f_{r}\\) and \\(L\\) are unknown and disentangling these two functions during optimization is extremely difficult. As a consequence, a current research trend is to use an MLP to directly approximate the result of this integral and obtain the outgoing radiance with the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.602, + 0.907, + 0.619 + ], + "angle": 0, + "content": "\\[\nC = M L P (\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {v}, \\mathbf {n}, \\mathbf {r}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.795 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}_s(\\mathbf{x})\\) represents spatial features encoded at a point position \\(\\mathbf{x}\\), and \\(\\mathbf{r}\\) is the reflected vector at point \\(\\mathbf{x}\\) for the viewing direction \\(\\mathbf{v}\\). This approximation works well if the incoming light is positionally invariant, but its accuracy degrades in the presence of local lighting effects such as close point lights, inter-reflections and self-shadows. In such cases, the spatial features must additionally encode some information about the local lighting and thus require a larger dimensionality than one would expect. A large and deep MLP is also necessary to decode this compressed information, which lowers the computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We propose to decouple the radiance model into spatial and angular features. We model a 3D scene with a combination of a high resolution sparse voxel grid that models the SDF field and a coarser grid that models the angular features as shown in fig. 2. For each point in space, the spatial features are obtained with a planar factorization in the coarse resolution tile with \\(\\mathbf{F}_s = \\mathbf{F}_x\\otimes \\mathbf{F}_y\\otimes \\mathbf{F}_z\\) for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11028" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.91, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.272, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Figure 2. Overview of the color prediction for a single voxel inside a \\(16^{3}\\) tile. The angular features \\(F_{a}\\) are computed by interpolating and evaluating the spherical harmonics from the 8 corner probes with the reflected vector \\(\\mathbf{r}\\). The spatial features \\(F_{s}\\) are computed as the outer product of three orthogonal planes of resolution \\(16\\times 16\\), specific to the tile. A small neural network decodes these inputs into a color." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.341, + 0.487, + 0.419 + ], + "angle": 0, + "content": "dimensionality reduction [1]. The angular features \\(\\mathbf{F}_a\\) are obtained by tri-linearly interpolating light field probes as explained in sec. 3.2. In addition, a dependency on the angle of incidence must be added to account for differences in reflectivity, as shown in fig. 3." + }, + { + "type": "image", + "bbox": [ + 0.109, + 0.429, + 0.466, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.555, + 0.484, + 0.626 + ], + "angle": 0, + "content": "Figure 3. The reflectivity cannot be encoded in \\(\\mathbf{F}_a\\) alone because different incident vectors can map to the same reflected vector (in red). In that case, similar angular features will be obtained for the two viewpoints due to the spatial and angular proximity of the lookups. The angle of incidence disambiguates the two situations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.641, + 0.484, + 0.673 + ], + "angle": 0, + "content": "The reflectivity, also called the Fresnel term, is commonly approximated as follows for rendering purposes [25]:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.696, + 0.483, + 0.715 + ], + "angle": 0, + "content": "\\[\nR (\\theta) = R _ {0} + (1 - R _ {0}) (1 - \\cos \\theta) ^ {5}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.724, + 0.484, + 0.846 + ], + "angle": 0, + "content": "\\(R_0\\) is the reflectivity at normal incidence and \\(\\theta\\) is the angle between the view direction and the half-way vector to the light source. In our case, \\(R_0\\) is unknown and there is no explicit light source which means that we cannot use this formula directly. Instead, we approximate \\(\\cos \\theta\\) by \\(\\mathbf{n} \\cdot \\mathbf{v}\\) and let the first layer of the neural network learn a polynomial approximation of the Fresnel term. Our revised parametrization is given by eq. 4:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.86, + 0.482, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} C = M L P \\left(\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {F} _ {a} (\\mathbf {x}, \\mathbf {r})\\right), \\\\ (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {0}, \\dots , (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {5}). \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.341, + 0.907, + 0.478 + ], + "angle": 0, + "content": "We denote the dimensionality of the features by \\( n_s \\) and \\( n_a \\) such that \\( \\mathbf{F}_s \\in \\mathbb{R}^{n_s} \\) and \\( \\mathbf{F}_a \\in \\mathbb{R}^{n_a} \\). Most materials reflect the light in a cone around the reflected vector which is why we condition \\( \\mathbf{F}_a \\) on \\( \\mathbf{r} \\), but some materials have retroreflective properties that break this assumption. In that case, conditioning on the view direction would be more appropriate. Lastly, eq. 4 assumes isotropic materials since the reflectivity depends only on \\( \\mathbf{n} \\cdot \\mathbf{v} \\). Anisotropic materials could be handled by adding a dependency on the azimuthal angle." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.488, + 0.831, + 0.504 + ], + "angle": 0, + "content": "3.2. Light Field Probes on a Coarse Grid" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.51, + 0.907, + 0.768 + ], + "angle": 0, + "content": "In this work, we replace the generic angular inputs \\(\\mathbf{v}\\), \\(\\mathbf{n}\\), \\(\\mathbf{r}\\) with new angular inputs encoding the local illumination (the light field probes), with the goal to achieve a more efficient parametrization of the appearance in terms of parameter count, training and inference speed. Similarly to previous works [4, 13], we use a spherical harmonics decomposition to model this dependency, but with several important differences: first, we encode abstract features on the sphere rather than the outgoing radiance which lets a neural network handle the non-linearities. Second, our directional embedding has a low spatial resolution which takes advantage of the smooth spatial variations of the lighting. Third, we sample this embedding with the reflected vector instead of the view vector to link the local surface orientation with the shading function, which has been showed to be beneficial for improved surface quality [28]. The angular features encoded into a single neural probe are given by eq. 5:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.778, + 0.907, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {a} = \\mathcal {S H} (\\mathbf {r}) = \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {j} Y _ {j} (\\mathbf {r}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.834, + 0.907, + 0.866 + ], + "angle": 0, + "content": "The polynomials of the SH basis are denoted with \\( Y_{j} \\). There are \\( l^2 \\) coefficients \\( \\mathbf{b}_j \\in \\mathbb{R}^{n_a} \\). Increasing values of \\( l \\) unlock" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.907, + 0.901 + ], + "angle": 0, + "content": "2We use a one-indexed notation for the SH order \\(l\\) instead of the traditional zero-indexing so that we have \\(l^2\\) coefficients." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11029" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.198 + ], + "angle": 0, + "content": "signals of increasing angular frequency which gives an explicit control on the representable amount of specularities. We observe two guiding principles: (1) The shinier the material, the higher the frequency of \\(\\mathbf{F}_a\\) should be in the angular domain. (2) The closer the light source, the higher the frequency \\(\\mathbf{F}_a\\) should be in the spatial domain. See fig. 4 for an illustration." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.206, + 0.48, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.306, + 0.485, + 0.35 + ], + "angle": 0, + "content": "Figure 4. Left and center: The lighting direction changes at a lower rate on the surface for distant light sources. Right: Self shadows impose variations in lighting even with directional illumination." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.366, + 0.484, + 0.517 + ], + "angle": 0, + "content": "For the case of common scenes such as humans or everyday objects, assuming materials with high to medium roughness so that \\(\\mathbf{F}_a\\) does not need to be of very high angular frequency is generally sufficient. We also assume that the lights are far enough, so that probes at a low spatial frequency can explain the parallax. The probes are stored at 1/16th the resolution of the main voxel grid, as shown in fig. 2. The voxels tri-linearly interpolate the 8 nearest probes according to eq. 6 and 7, with \\(w_i\\) the interpolation weight of the i-th corner." + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.524, + 0.483, + 0.616 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {F} _ {a} = \\sum_ {i = 1} ^ {8} \\mathcal {S H} _ {i} (\\mathbf {r}) w _ {i} = \\sum_ {i = 1} ^ {8} \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {i j} Y _ {j} (\\mathbf {r}) w _ {i} (6) \\\\ = \\sum_ {j = 1} ^ {l ^ {2}} \\hat {\\mathbf {b}} _ {j} Y _ {j} (\\mathbf {r}) \\quad \\text {w i t h} \\hat {\\mathbf {b}} _ {j} = \\sum_ {i = 1} ^ {8} \\mathbf {b} _ {i j} w _ {i} (7) \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.622, + 0.332, + 0.639 + ], + "angle": 0, + "content": "3.3. SDF Estimation Approach" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.484, + 0.781 + ], + "angle": 0, + "content": "We here discuss how to embed the new proposed color decoder in an implicit surface reconstruction pipeline. During the forward pass, for a pixel \\((u,v)\\) in a given viewpoint, the color is computed by a transmittance \\(T_{i}\\)-weighted average of the colors \\(C_i\\) of \\(N\\) points sampled from the current scene volume estimate along the pixel aligned ray, where \\(T_{i}\\) is the product of obstructing opacities \\(\\alpha_{j}\\). We use the NeuS equation to relate volumetric opacities to the SDF \\(s_i\\) at each sample point [30]:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.787, + 0.483, + 0.9 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} c (u, v) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} C _ {i}, \\quad T _ {i} = \\prod_ {j < i} (1 - \\alpha_ {j}), (8) \\\\ \\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {\\tau} (s _ {i}) - \\Phi_ {\\tau} (s _ {i + 1})}{\\Phi_ {\\tau} (s _ {i})}, 0\\right), (9) \\\\ \\Phi_ {\\tau} \\left(s _ {i}\\right) = \\frac {1}{1 + \\exp^ {- \\tau s _ {i}}}. (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a scale factor that increases during optimization. The SDF field can then be optimized by backpropagating updates from the observed color loss through the rendering equation, and from the set of regularization losses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.153, + 0.907, + 0.35 + ], + "angle": 0, + "content": "Our losses and regularizations are detailed in equations 11 to 16. The raw SDF \\(\\hat{s}\\) is convolved by a \\(5^{3}\\) gaussian kernel \\(G\\) into a smoother SDF \\(s\\) to stabilize training [33]. Note that \\(s\\) is used for all subsequent operations such as normal computation and rendering. Eq. 11 maintains \\(s\\) and \\(\\hat{s}\\) close to each other to promote smoothness. The Eikonal regularization 12 ensures that \\(s\\) is a signed distance. Equations 13, 14, 15 promote spatial smoothness for the normals, for the factorized spatial features and for the probe coefficients respectively. In eq. 15, \\(\\mathcal{V}_i\\) is the set of neighboring probes adjacent to the i-th one and \\(N\\) is the total number of probes. The regularizations are applied on each voxel, factorized feature, probe or image pixel when appropriate." + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.37, + 0.907, + 0.403 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s d f}} = \\sum_ {\\text {v o x e l}} | s - \\hat {s} | ^ {2}, \\quad s = G (\\hat {s}) \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.405, + 0.905, + 0.437 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {E i k}} = \\sum_ {\\text {v o x e l}} \\left(\\left| \\left| \\nabla s \\right| \\right| - 1\\right) ^ {2} \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.441, + 0.905, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {\\text {v o x e l}} | | \\nabla \\mathbf {n} | | ^ {2}, \\quad \\mathbf {n} = \\nabla s / | | \\nabla s | | \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.474, + 0.905, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t u r e s}} = \\sum_ {\\text {t e x e l}} | | \\nabla \\mathbf {F} _ {x} | | ^ {2} + | | \\nabla \\mathbf {F} _ {y} | | ^ {2} + | | \\nabla \\mathbf {F} _ {z} | | ^ {2} \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.51, + 0.905, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r o b e s}} = \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {l ^ {2}} \\sum_ {k \\in \\mathcal {V} _ {i}} \\left| \\left| \\mathbf {b} _ {i j} - \\mathbf {b} _ {k j} \\right| \\right| ^ {2} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.557, + 0.905, + 0.589 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {u, v} | | c (u, v) - c _ {\\mathrm {g t}} (u, v) | | ^ {2} \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.75 + ], + "angle": 0, + "content": "In eq. 16, \\( c \\) is the rendered image and \\( c_{\\mathrm{gt}} \\) is the ground truth image. We apply a weight of \\( (\\max(c, c_{\\mathrm{gt}}) + \\epsilon)^{-1} \\) on the photometric gradient of each pixel in eq. 16 to penalize relative differences rather than absolute differences [19]. A similar strategy is used on \\( \\mathcal{L}_{\\mathrm{sdf}} \\) and \\( \\mathcal{L}_{\\mathrm{features}} \\). We apply an empirical factor of \\( (1 + |s| * 5)^{-1} \\) on the gradients of the per-voxel regularizations to lower their importance when the distance to the zero-crossing increases. The idea is to keep the regularizations and the data term balanced for regions near and far from the surface alike." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.758, + 0.619, + 0.774 + ], + "angle": 0, + "content": "3.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Our complete loss is a weighted sum of eq. 11 to 16 that we minimize with the Adam optimizer [14], please refer to the supplementary document for more details. In summary, the trained parameters are the raw SDF values \\(\\hat{s}\\), the factorized features \\(\\mathbf{F}_x, \\mathbf{F}_y, \\mathbf{F}_z\\), the probes coefficients \\(\\mathbf{b}\\) and the MLP weights. We follow a coarse-to-fine learning strategy, both in the spatial and angular domains. We start with coarse voxels and \\(l = 2\\), under the supervision of low resolution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11030" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.168 + ], + "angle": 0, + "content": "images. We iteratively subdivide the voxels and switch to higher resolution images, and introduce higher angular frequencies by increasing \\( l \\). Starting the optimization with too many degrees of freedom for the appearance parametrization can lead to local minima, as noted by [13]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.183, + 0.313, + 0.2 + ], + "angle": 0, + "content": "4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.209, + 0.484, + 0.421 + ], + "angle": 0, + "content": "We use a 2 hidden layer MLP with 32 neurons and ReLU activations with a sigmoid for the last layer. The probes at the shared corners of adjacent tiles are duplicated in memory (but keep shared values) to benefit from hardware-accelerated interpolation. We support up to 16 spherical harmonic coefficients \\((l = 4)\\) per probe. The computation of \\(\\mathbf{F}_a\\), \\(\\mathbf{F}_s\\) and the MLP call are fused into a single CUDA kernel for efficiency, following [21] and [27]. Each \\(16^3\\) tile contains \\(3 \\times 16 \\times 16 \\times n_s\\) spatial coefficients and \\(8 \\times l^2 \\times n_a\\) spherical harmonic features. Assuming \\(l = 4\\) and \\(n_s = n_a\\), the probes only require \\((8 \\times 16) / (3 \\times 16 \\times 16) = 1/6\\)th of the memory taken by the spatial features. The sparse voxel grid is based on the code of [27], with targeted modifications to implement our probes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.436, + 0.223, + 0.453 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.483, + 0.718 + ], + "angle": 0, + "content": "Protocol We evaluate our method on 4 datasets: MVMannequins [27], ActorsHQ [8], DTU [9] and BlendedMVS [34]. Due to the various evaluation settings employed in the community, we chose to re-train and re-evaluate all the baselines using the same experimental protocol for fairness. Following [6], all available images were given as input and used for evaluation. Timings are measured on a workstation equipped with an RTX A6000 GPU (Ampere series). PSNR values are computed inside the silhouette region of objects of interest and chamfer error is computed using official scripts. We use the following grid resolutions: DTU \\((1000^{3})\\), BMVS \\((666^{3})\\), MVMannequins \\((2500 \\times 1250 \\times 2500\\), \\(2\\mathrm{mm} / \\mathrm{voxel}\\)), ActorsHQ \\((3000 \\times 4000 \\times 3000\\), \\(0.6\\mathrm{mm} / \\mathrm{voxel}\\)). Some datasets may contain inconsistent shadows or large exposure changes (DTU and BMVS) that are hard to model by our representation so we optionally train per-camera bias vectors in the MLP." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.824 + ], + "angle": 0, + "content": "MVMannequins is a dataset of 14 dressed mannequins for multi-view reconstruction benchmarking with 68 cameras at \\(2048^{2}\\) resolution. We use the official evaluation code and report the metrics in table 1. We outperform all the baselines while taking only about a minute of training time, almost 3x faster than [27], with 5GB of VRAM, a rendering speed of \\(300\\mathrm{Hz}\\) to \\(400\\mathrm{Hz}\\) and a model size of 30MB." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "ActorsHQ is a multiview dataset of humans in motion with 160 cameras at a high resolution of \\(4088 \\times 2990\\). We evaluate on the 1000th temporal frame of 13 sequences. We compare against Voxurf [33] and NeuS2 [31], which we trained with half resolution images since we ran into issues" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.228 + ], + "angle": 0, + "content": "with full resolution images. We report the PSNR in table 2 and show qualitative results in fig. 5. Voxurf takes about one hour to fully converge (with \\(3 \\times\\) the training iterations of the DTU configuration). NeuS2 converges fast but with a lower PSNR. In comparison, our method only takes \\(\\sim 4\\) minutes to converge on the full resolution images, and we also outperform both when training at the same resolution. This benchmark highlights the capability of our method to gracefully scale to high-resolution scenes." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.241, + 0.905, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.47, + 0.905, + 0.659 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.67, + 0.878, + 0.685 + ], + "angle": 0, + "content": "Figure 5. High-resolution reconstructions for ActorsHQ." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.87 + ], + "angle": 0, + "content": "DTU provides 49 to 64 images of various objects at \\(1600 \\times 1200\\) resolution, along with evaluation point clouds. We use the foreground masks provided by IDR [35] for training and testing. 2DGS [6] does not support masks for training so it uses complete images instead, cropped and at half resolution according to its evaluation protocol. We compare against Voxurf [33], Neus2 [31] and 2DGS [6] on DTU in table 3, using the official python script for geometric evaluation. We outperform all three in terms of chamfer distance and PSNR, twice as fast as NeuS2 on the same hardware. Rendering speed ranges from \\(200\\mathrm{Hz}\\) to \\(300\\mathrm{Hz}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "BlendedMVS. Finally, we test our method on 8 scenes of the BlendedMVS dataset [34] and report the metrics in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11031" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.16, + 0.089, + 0.838, + 0.15 + ], + "angle": 0, + "content": "
Metrics(4,4,4)X(8,8,4)XMMH [27]Voxurf [33]Neus2 [31]Colmap [26]2DGS [6]
Chamfer (mm)1.041.031.141.592.133.523.35
PSNR36.8136.9036.3335.5134.22-34.89
Training1min1min2-3min15min5min>1h>1h
" + }, + { + "type": "table_caption", + "bbox": [ + 0.116, + 0.16, + 0.878, + 0.174 + ], + "angle": 0, + "content": "Table 1. Evaluation on MVMannequins with two configurations for \\( \\left( {{n}_{s},{n}_{a},l}\\right) \\) . Per-camera bias vectors are not used (X-symbol)." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.212, + 0.49, + 0.29 + ], + "angle": 0, + "content": "
(ns,na,l) = (4,4,4)XVoxurfNeuS2
Resolutionr/1r/2r/4r/2r/2
PSNR37.4836.6234.7436.5634.53
Training250s110s53s1h250s
Model size232MB57MB15MB500MB25MB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.301, + 0.484, + 0.357 + ], + "angle": 0, + "content": "Table 2. Evaluation for ActorsHQ. Per-camera bias vectors are not used (\\(\\times\\)-symbol). Full, half and quarter-resolution input images are denoted as \\(r/1\\), \\(r/2\\), \\(r/4\\) respectively. Renderings are up-scaled before comparison with the full resolution images \\((4088 \\times 2990)\\)." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.379, + 0.502, + 0.457 + ], + "angle": 0, + "content": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus22DGS
Chamfer0.680.710.730.800.76
PSNR37.0337.7437.083636.03
Training150s160s15min5min12min
Model size56MB88MB500MB25MB49MB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.467, + 0.482, + 0.496 + ], + "angle": 0, + "content": "Table 3. DTU evaluation with two configurations for \\( \\left( {{n}_{s},{n}_{a},l}\\right) \\) . Per-camera bias vectors are used (✓-symbol)." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.508, + 0.455, + 0.572 + ], + "angle": 0, + "content": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus2
Chamfer2.372.222.642.93
PSNR35.1935.8935.1133.62
Training110s120s15min5min
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.582, + 0.482, + 0.611 + ], + "angle": 0, + "content": "Table 4. BMVS evaluation with two configurations for \\( \\left( {{n}_{s},{n}_{a},l}\\right) \\) . Per-camera bias vectors are used (✓-symbol)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.666, + 0.483, + 0.757 + ], + "angle": 0, + "content": "table 4. The BlendedMVS is a semi-synthetic dataset were objects have been first reconstructed then reprojected in the images in order to produce reliable ground truth geometry and masks. There is no official script for geometric evaluation so we measure two-ways point to mesh distances in the reference frame used for training in [30], scaled by \\(1000\\mathrm{x}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Ablations. We ablate the probes smoothing and the polynomial approximation of the Fresnel term in tab. 5 on the MVMannequins dataset by imposing \\(\\mathbf{n} \\cdot \\mathbf{v} = 1\\) in eq. 4 during training, with noticeable incidence on Chamfer error. A visual ablation of the components of our parametrization is presented in fig. 8 on the kino/jea mannequin, clearly showing the role of each parameter group. Figure 9 contains more examples. Various choices of configurations are compared in table 6 on the BlendedMVS dataset." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.209, + 0.906, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.569, + 0.889, + 0.584 + ], + "angle": 0, + "content": "Figure 6. Reconstructions on challenging examples of DTU." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.602, + 0.883, + 0.636 + ], + "angle": 0, + "content": "
(4,4,4)Xw/o probes smoothingw/o Fresnel
Chamfer (mm)1.041.091.18
PSNR36.8136.9136.79
" + }, + { + "type": "table_caption", + "bbox": [ + 0.606, + 0.647, + 0.813, + 0.661 + ], + "angle": 0, + "content": "Table 5. Ablation on MVMannequins" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.673, + 0.905, + 0.706 + ], + "angle": 0, + "content": "
Metrics(4,4,4)X(4,4,4)Y(8,8,4)√(12,12,4)√(4,4,1)√(4,4,2)√(4,4,3)√
Chamfer2.472.372.222.312.582.342.37
PSNR34.7635.1935.8936.1734.4434.8635.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.715, + 0.906, + 0.772 + ], + "angle": 0, + "content": "Table 6. We ablate the number of spatial features \\( n_s \\), angular features \\( n_a \\) and spherical harmonics order \\( l \\) on BlendedMVS. Each triplet denotes a configuration \\( (n_s, n_a, l) \\). The \\( \\checkmark \\)-symbol indicates when per-camera bias vectors are trained." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.813, + 0.636, + 0.829 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.903 + ], + "angle": 0, + "content": "We identify several limitations to our approach. First, the fact that the lighting is encoded locally can degrade the extrapolation capabilities compared to modeling the environment with a global representation. This becomes appar" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11032" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.086, + 0.482, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.381, + 0.447, + 0.395 + ], + "angle": 0, + "content": "Figure 7. Reconstructed examples on BlendedMVS." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.412, + 0.481, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.609, + 0.484, + 0.722 + ], + "angle": 0, + "content": "Figure 8. Our model can be intuitively explained. We disable some components of a pre-trained example from the MVMannequins dataset [27] (left). From left to right, we remove the spatial features (set \\(\\mathbf{F}_s = 0\\)), only keep the constant coefficient of the SH basis (\\(l = 1\\)), disable the incidence angle embedding (set \\(\\mathbf{n} \\cdot \\mathbf{v} = 1\\) in eq. 4). The learned Fresnel term encodes grazing reflections (red circles), the angular features provide the shading (green squares) and the spatial features contain the high frequency details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "ent on the ActorsHQ dataset where there is a good overlap of the cameras field of views along the longitude, but very little overlap along the latitude on the legs. This creates shadows artifacts when looking from above or below rather that at a level angle. Second, although our decomposition is physically-inspired, we do not explicitly simulate light transport which can result in local minima due to shape-radiance ambiguities. Relighting and/or material editing is not supported but fine-tuning the probes to new lighting seems possible and worthy of future investigations." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.905, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.355, + 0.907, + 0.412 + ], + "angle": 0, + "content": "Figure 9. Effect of the learned Fresnel term on three examples from MVMannequins, DTU and ActorsHQ. Left to right: input image, volume rendering (A), volume rendering w/o the Fresnel term (B) (we set \\(\\mathbf{n}\\cdot \\mathbf{v} = 1\\) in eq. 4), difference image \\((4\\times |A - B|)\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.438, + 0.783, + 0.454 + ], + "angle": 0, + "content": "7. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.465, + 0.907, + 0.722 + ], + "angle": 0, + "content": "We have presented a novel approach to model the view dependent appearance, enabling both fast reconstruction and real-time rendering of humans and objects. Notably, our model does not compromise on geometric and photometric quality, even surpassing the previous approaches in many instances. It can easily scale to high resolution inputs while maintaining high performance. We have reached a parsimonious parametrization of the surface properties thanks to a simple formulation. Disentangling the spatial and angular components with high efficiency also offers promising future avenues of research toward temporal reconstruction. Other future research can build on this work, e.g. handling high frequency reflections at a lower cost than current dedicated approaches and unifying neural rendering and physically-based rendering. Other embeddings of the angular dependency representations can be investigated, such as cubemaps or mixtures of spherical gaussians." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.739, + 0.692, + 0.756 + ], + "angle": 0, + "content": "8. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.9 + ], + "angle": 0, + "content": "This work was supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) grant ANR-21-ESRE-0030 (CONTINUUM). Research conducted at Kyushu University was supported by JSPS/KAKENHI JP23H03439 and AMED JP24wm0625404. We thank Laurence Boissieux for her valuable help generating 3D renderings, and Edmond Boyer for insightful discussions and comments." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11033" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.156 + ], + "angle": 0, + "content": "[1] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In European Conference on Computer Vision (ECCV), 2022. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.159, + 0.483, + 0.226 + ], + "angle": 0, + "content": "[2] Danpeng Chen, Hai Li, Weicai Ye, Yifan Wang, Weijian Xie, Shangjin Zhai, Nan Wang, Haomin Liu, Hujun Bao, and Guofeng Zhang. 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ACM Transactions on Graphics (TOG), 40(6), 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.484, + 0.853 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11035" + } + ] +] \ No newline at end of file diff --git a/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_origin.pdf b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1323535a1609bfc9405aacc41c3a2099400a73a7 --- /dev/null +++ b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/c8ccc978-962a-4a2e-a885-9ef25eda0c9f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c775fefc51b3feac2ad1bf5bcce52f4b87298c25319dae571fc65ca91d67d6ab +size 4746467 diff --git a/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/full.md b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f0069418c42779b240e517f1a6c79766d2893ce4 --- /dev/null +++ b/2025/ProbeSDF_ Light Field Probes For Neural Surface Reconstruction/full.md @@ -0,0 +1,290 @@ +# ProbeSDF: Light Field Probes For Neural Surface Reconstruction + +Briac Toussaint + +briac.toussaint@inria.fr + +Diego Thomas + +thomas@ait.kyushu-u.ac.jp + +Jean-Sébastien Franco1 + +jean-sebastien.franco@inria.fr + +1Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, France + +$^{2}$ Kyushu University, Japan + +# Abstract + +SDF-based differential rendering frameworks have achieved state-of-the-art multiview 3D shape reconstruction. In this work, we re-examine this family of approaches by minimally reformulating its core appearance model in a way that simultaneously yields faster computation and increased performance. To this goal, we exhibit a physically-inspired minimal radiance parametrization decoupling angular and spatial contributions, by encoding them with a small number of features stored in two respective volumetric grids of different resolutions. Requiring as little as four parameters per voxel, and a tiny MLP call inside a single fully fused kernel, our approach allows to enhance performance with both surface and image (PSNR) metrics, while providing a significant training speedup and real-time rendering. We show this performance to be consistently achieved on real data over two widely different and popular application fields, generic object and human subject shape reconstruction, using four representative and challenging datasets. + +# 1. Introduction + +Neural radiance fields have established a new milestone for the task of novel view synthesis and have led to a plethora of variants of broad applicability. We here take particular interest in SDF surface-based radiance fields, which have proven to be a highly performing variant for the tasks of 3D modeling from images [30, 33], with wide reaching applications ranging from object and performance capture, to immersive and 3D content production. + +At the heart of such methods usually lies a parametrization of the light field, in the form of a 5-dimensional function. This function maps the spatial coordinates of a point + +in space and the observed direction to a color and a signed distance to the reconstructed surface. On one hand, the mapping can be global and use a complex scene-wide MLP as implicit 5D decoder, as is the case for most seminal approaches [18, 30]. On the other hand, recent popular variants that target higher speed and memory efficiency use explicit representations. Global representations are based on a grid encoding [4, 31, 33] where interpolated spatial and angular features are run through a global shallow MLP. Local representations use the sparse 3D Gaussian Splatting [13] sample-based encoding approach, where each separate Gaussian comes with its own opacity and adjoining set of angular color features. While grids or local approaches use a single deep MLP to densely encode the complete light field function, they almost always co-locate storage and decoding of color and angular features. + +But is this really a necessary or even desirable feature of any light field encoding? We question these assertions by postulating that, contrary to the spatial components of the light field that mainly encode intrinsic surface texture, the angular components encode phenomena that are predominantly extrinsic to the surface, i.e. lighting and environment, and as such can be encoded at a lower spatial resolution as they are locally almost invariant to parallax. This hypothesis is in fact exploited by the rendering community, where angular and environment components contributing to the radiance equation used to compute rendered colors, are typically precomputed at sparse 3D locations coined light field probes [24], and interpolated in-between. + +Leveraging this intuition, our approach borrows the spherical harmonic parametrization popular with explicit methods e.g. [4, 13] to represent angular components, but instead decorrelates high density spatial variation from lower density angular variation using a mid-resolution probe grid of angular features. Each of the components encode abstract features that are fed to a tiny MLP, which acts as a minimal BRDF decoder of spatial and angular + +![](images/d262540ec2d12070175fdbb9071174bc9e7fc9b3cbbd71efc5a97a9ae50fa147.jpg) +Figure 1. We design a new appearance model for neural surface approaches, which combines high resolution spatial features and lower resolution angular features for improved reconstruction quality, training and inference speed. We plot the chamfer distance as a function of training speed for several baselines on MVMannequins (top) and DTU (bottom). + +varying components, while we explicitly store SDF values. This scheme advantageously replaces the core appearance and decoding model of SDF approaches [15, 30, 31, 33] to predict ray colors. We are careful to also include power terms of the cosine angle between the view direction and the estimated surface normal, allowing our lightweight model to effectively account for increased surface reflectivity at grazing angles. This yields an unprecedented performance combination, superseding both 3D and image metric performances with four popular benchmarks for general object reconstruction [9, 34] and human reconstruction [8, 27] while simultaneously achieving a significant training and rendering performance boost. In summary, our contributions are: + +- An explicit embedding of the angular dependency that is simultaneously local, smooth and efficient. +- A simpler color prediction MLP that is agnostic to the surface position and orientation. + +# 2. Related Works + +In this work we leverage disentangled spatial and angular parameterization of radiance towards high quality appearance and surface modeling. Here we consequently review closely related works on surface-based 3D scene representations and existing parametrizations of color. + +Neural Surface Reconstruction. Through the use of implicit surface representations, neural implicit fields have demonstrated increasing capabilities to generate high-quality 3D models [23, 35, 36]. In NeuS [30], Wang et al. proposed to parametrize the surface with a signed distance function that is modeled with a multi layer perceptron (MLP). The approach opened new frontiers in the generation of accurate 3D scenes from images but at the cost of prohibitive training times (several hours). Follow-up works have thus focused on boosting both accuracy and computation time by employing explicit grids of features + +and smaller MLPs. Notably, Wu et al. proposed in Vox-urf [33] to use a dense grid of voxels, and Neus2 was also proposed using hash grids [31]. Recently, Millimetric humans [27] have demonstrated remarkably fast and accurate reconstructions in the case of human datasets by using sparse and dynamic grids. Other reparametrizations target performance improvement, e.g. point-based with Fast Dipole Sums [3] and PGSR [2] both leveraging multi-view stereo priors, or by seeking mutual advantage of a hybrid volume/mesh representation [7]. All the methods discussed above rely on co-located encodings of position and view direction to parametrize the appearance. As a consequence, these approaches either fail to model local radiance effects like inter-reflections, or require larger MLPs and training times, and may thus benefit from our refactored appearance model as drop-in replacement. + +Angular parametrization Deep MLPs have become ubiquitous to model view-dependent colors, taking as input the view direction [18], the view and normal [30, 31, 33, 35] or the reflected direction [27, 28]. Non-neural approaches such as plenoxels [4] or the Gaussian splatting methods [6, 13] favor a straightforward spherical harmonics decomposition in color space. The main advantage compared to a deep MLP is the computational efficiency, at the cost of a large number of appearance parameters: 27 per voxel for [4] and 48 per Gaussian for [13]. Note that some neural architectures [27, 28, 31] use spherical harmonics as a positional encoding of the directional vectors, but this is completely distinct from encoding the signal into spherical harmonic coefficients. In this work we propose a lighter yet efficient parametrization of color by using two decorrelated voxel structures to encode different components of the observed color, and spherical harmonics encoding of pre-MLP features for more parsimonious and expressive color decoding. + +In the field of real-time rendering, where lighting and + +BRDF are known in advance, the idea of caching the incoming light at discrete locations, known as light field probes, has become standard [16, 17, 24]. We draw inspiration from this technique for our proposed approach to multi-view 3D reconstruction, with the difference in our case that the probe parameters are optimized along with the voxel parameters. + +High Frequency Reflections. A number of approaches specifically deal with high frequency reflections, which requires dedicated representations and algorithms. Guo et al. [5] train an additional NeRF that is composited with the main image. This approach is under-constrained and thus requires strong priors such as the reflective surfaces being flat. Verbin et al. [28] model lighting as a neural envmap, modulated by a per-point roughness. The roughness and base color of the object can be edited afterwards but a long training time is required due to the large MLP. + +Recent works [29, 32] recover detailed reflections using cone tracing, which inherently solves the problem posed by self-reflections. Both approaches give impressive results even when confronted with curved, mirror-like objects but at a large training cost exceeding 10 GPU-hours per scene. In contrast, we target objects with mild specularities, and show that both fast training and real-time rendering can be achieved. More specifically, our neural light field probes can learn information about the surroundings whereas cone tracing gathers it at a greater cost. This assumption proves to be valid for standard acquisition scenes, with the four datasets tested. + +Minimal Parametrization. Explicitly disentangling the material parameters from the lighting is particularly challenging but also rewarding because it can yield a minimal parametrization of the appearance. Munkberg et al. [22] show that the approximate rendering equation developed in [12] is sufficiently accurate to recover the geometry using a differentiable rasterizer, along with an approximate material decomposition. Jiang et al. [10] applies a similar strategy but with the 3D gaussian splatting volume rendering. The NeRFactor pipeline [37] starts from a pre-trained NeRF that is distilled into lighting, albedo and neural BRDF parameters. Jin et al. proposed TensoIR [11], which achieves a more accurate decomposition by evaluating the rendering equation with importance sampling. An efficient tensor representation helps to accelerate the rendering of the secondary rays, but the complete training still takes five hours on a single GPU, with decent results available after half an hour of training. Our proposed method converges in just a few minutes and we find that only 4 coefficients per voxel are sufficient in most cases. The dimensionality is equivalent to the albedo and roughness values of a physically-based material parametrization, but without the cost associated with the inversion of the rendering equation. + +# 3. Method + +We use an SDF grid as the implicit representation of the 3D shape. SDF values in the grid are optimized via our newly proposed differentiable appearance model and the derived surface normal vectors $\mathbf{n}$ . + +# 3.1. Decoupled Parametrization of Radiance + +Volumetric neural rendering, as proposed in the seminal work NeRF, computes the color at a given pixel by integrating radiances along camera-pixel rays weighted by local opacity values. Follow-up papers condition the opacity on the distance to the surface to improve the reconstruction quality [20, 30, 36]. The radiance $C$ represents the amount of energy that is emitted by a point in space. In physics it is expressed as the integral over the hemisphere $\Omega$ of the spatially varying bidirectional reflectance distribution function (SVBRDF) $f_{r}$ multiplied by the incoming radiance $L$ and by the cosine between the incoming direction $\omega$ and the surface normal $\mathbf{n}$ : + +$$ +C = \int_ {\Omega} f _ {r} (\mathbf {v}, \omega , \mathbf {x}) L (\omega , \mathbf {x}) (\omega \cdot \mathbf {n}) d \omega . \tag {1} +$$ + +The (spatially varying) BRDF depends on the point's position $\mathbf{x}$ , direction of incoming light $\omega$ and viewing direction $\mathbf{v}$ . $L(\omega, \mathbf{x})$ is the intensity of light at point $\mathbf{x}$ that comes from the direction $\omega$ and $\mathbf{n}$ is the normal vector of the surface at position $\mathbf{x}$ . In equation 1, both $f_{r}$ and $L$ are unknown and disentangling these two functions during optimization is extremely difficult. As a consequence, a current research trend is to use an MLP to directly approximate the result of this integral and obtain the outgoing radiance with the following equation: + +$$ +C = M L P (\mathbf {F} _ {s} (\mathbf {x}), \mathbf {v}, \mathbf {n}, \mathbf {r}). \tag {2} +$$ + +where $\mathbf{F}_s(\mathbf{x})$ represents spatial features encoded at a point position $\mathbf{x}$ , and $\mathbf{r}$ is the reflected vector at point $\mathbf{x}$ for the viewing direction $\mathbf{v}$ . This approximation works well if the incoming light is positionally invariant, but its accuracy degrades in the presence of local lighting effects such as close point lights, inter-reflections and self-shadows. In such cases, the spatial features must additionally encode some information about the local lighting and thus require a larger dimensionality than one would expect. A large and deep MLP is also necessary to decode this compressed information, which lowers the computational efficiency. + +We propose to decouple the radiance model into spatial and angular features. We model a 3D scene with a combination of a high resolution sparse voxel grid that models the SDF field and a coarser grid that models the angular features as shown in fig. 2. For each point in space, the spatial features are obtained with a planar factorization in the coarse resolution tile with $\mathbf{F}_s = \mathbf{F}_x\otimes \mathbf{F}_y\otimes \mathbf{F}_z$ for + +![](images/4bd17308d7cfc01a73e605af7e0509cfefe748fb35fcf24f97a0ea5b5423673e.jpg) +Figure 2. Overview of the color prediction for a single voxel inside a $16^{3}$ tile. The angular features $F_{a}$ are computed by interpolating and evaluating the spherical harmonics from the 8 corner probes with the reflected vector $\mathbf{r}$ . The spatial features $F_{s}$ are computed as the outer product of three orthogonal planes of resolution $16\times 16$ , specific to the tile. A small neural network decodes these inputs into a color. + +dimensionality reduction [1]. The angular features $\mathbf{F}_a$ are obtained by tri-linearly interpolating light field probes as explained in sec. 3.2. In addition, a dependency on the angle of incidence must be added to account for differences in reflectivity, as shown in fig. 3. + +![](images/1a0b693822b42540b2584761c40aed93b62ede012c30c78729214334f5055e03.jpg) +Figure 3. The reflectivity cannot be encoded in $\mathbf{F}_a$ alone because different incident vectors can map to the same reflected vector (in red). In that case, similar angular features will be obtained for the two viewpoints due to the spatial and angular proximity of the lookups. The angle of incidence disambiguates the two situations. + +The reflectivity, also called the Fresnel term, is commonly approximated as follows for rendering purposes [25]: + +$$ +R (\theta) = R _ {0} + (1 - R _ {0}) (1 - \cos \theta) ^ {5}. \tag {3} +$$ + +$R_0$ is the reflectivity at normal incidence and $\theta$ is the angle between the view direction and the half-way vector to the light source. In our case, $R_0$ is unknown and there is no explicit light source which means that we cannot use this formula directly. Instead, we approximate $\cos \theta$ by $\mathbf{n} \cdot \mathbf{v}$ and let the first layer of the neural network learn a polynomial approximation of the Fresnel term. Our revised parametrization is given by eq. 4: + +$$ +\begin{array}{l} C = M L P \left(\mathbf {F} _ {s} (\mathbf {x}), \mathbf {F} _ {a} (\mathbf {x}, \mathbf {r})\right), \\ (1 - \mathbf {n} \cdot \mathbf {v}) ^ {0}, \dots , (1 - \mathbf {n} \cdot \mathbf {v}) ^ {5}). \tag {4} \\ \end{array} +$$ + +We denote the dimensionality of the features by $n_s$ and $n_a$ such that $\mathbf{F}_s \in \mathbb{R}^{n_s}$ and $\mathbf{F}_a \in \mathbb{R}^{n_a}$ . Most materials reflect the light in a cone around the reflected vector which is why we condition $\mathbf{F}_a$ on $\mathbf{r}$ , but some materials have retroreflective properties that break this assumption. In that case, conditioning on the view direction would be more appropriate. Lastly, eq. 4 assumes isotropic materials since the reflectivity depends only on $\mathbf{n} \cdot \mathbf{v}$ . Anisotropic materials could be handled by adding a dependency on the azimuthal angle. + +# 3.2. Light Field Probes on a Coarse Grid + +In this work, we replace the generic angular inputs $\mathbf{v}$ , $\mathbf{n}$ , $\mathbf{r}$ with new angular inputs encoding the local illumination (the light field probes), with the goal to achieve a more efficient parametrization of the appearance in terms of parameter count, training and inference speed. Similarly to previous works [4, 13], we use a spherical harmonics decomposition to model this dependency, but with several important differences: first, we encode abstract features on the sphere rather than the outgoing radiance which lets a neural network handle the non-linearities. Second, our directional embedding has a low spatial resolution which takes advantage of the smooth spatial variations of the lighting. Third, we sample this embedding with the reflected vector instead of the view vector to link the local surface orientation with the shading function, which has been showed to be beneficial for improved surface quality [28]. The angular features encoded into a single neural probe are given by eq. 5: + +$$ +\mathbf {F} _ {a} = \mathcal {S H} (\mathbf {r}) = \sum_ {j = 1} ^ {l ^ {2}} \mathbf {b} _ {j} Y _ {j} (\mathbf {r}). \tag {5} +$$ + +The polynomials of the SH basis are denoted with $Y_{j}$ . There are $l^2$ coefficients $\mathbf{b}_j \in \mathbb{R}^{n_a}$ . Increasing values of $l$ unlock + +signals of increasing angular frequency which gives an explicit control on the representable amount of specularities. We observe two guiding principles: (1) The shinier the material, the higher the frequency of $\mathbf{F}_a$ should be in the angular domain. (2) The closer the light source, the higher the frequency $\mathbf{F}_a$ should be in the spatial domain. See fig. 4 for an illustration. + +![](images/8f15472fede64b66507349dce8821e329eae4d23f383990d0c58bc8945702423.jpg) +Figure 4. Left and center: The lighting direction changes at a lower rate on the surface for distant light sources. Right: Self shadows impose variations in lighting even with directional illumination. + +For the case of common scenes such as humans or everyday objects, assuming materials with high to medium roughness so that $\mathbf{F}_a$ does not need to be of very high angular frequency is generally sufficient. We also assume that the lights are far enough, so that probes at a low spatial frequency can explain the parallax. The probes are stored at 1/16th the resolution of the main voxel grid, as shown in fig. 2. The voxels tri-linearly interpolate the 8 nearest probes according to eq. 6 and 7, with $w_i$ the interpolation weight of the i-th corner. + +$$ +\begin{array}{l} \mathbf {F} _ {a} = \sum_ {i = 1} ^ {8} \mathcal {S H} _ {i} (\mathbf {r}) w _ {i} = \sum_ {i = 1} ^ {8} \sum_ {j = 1} ^ {l ^ {2}} \mathbf {b} _ {i j} Y _ {j} (\mathbf {r}) w _ {i} (6) \\ = \sum_ {j = 1} ^ {l ^ {2}} \hat {\mathbf {b}} _ {j} Y _ {j} (\mathbf {r}) \quad \text {w i t h} \hat {\mathbf {b}} _ {j} = \sum_ {i = 1} ^ {8} \mathbf {b} _ {i j} w _ {i} (7) \\ \end{array} +$$ + +# 3.3. SDF Estimation Approach + +We here discuss how to embed the new proposed color decoder in an implicit surface reconstruction pipeline. During the forward pass, for a pixel $(u,v)$ in a given viewpoint, the color is computed by a transmittance $T_{i}$ -weighted average of the colors $C_i$ of $N$ points sampled from the current scene volume estimate along the pixel aligned ray, where $T_{i}$ is the product of obstructing opacities $\alpha_{j}$ . We use the NeuS equation to relate volumetric opacities to the SDF $s_i$ at each sample point [30]: + +$$ +\begin{array}{l} c (u, v) = \sum_ {i = 1} ^ {N} T _ {i} \alpha_ {i} C _ {i}, \quad T _ {i} = \prod_ {j < i} (1 - \alpha_ {j}), (8) \\ \alpha_ {i} = \max \left(\frac {\Phi_ {\tau} (s _ {i}) - \Phi_ {\tau} (s _ {i + 1})}{\Phi_ {\tau} (s _ {i})}, 0\right), (9) \\ \Phi_ {\tau} \left(s _ {i}\right) = \frac {1}{1 + \exp^ {- \tau s _ {i}}}. (10) \\ \end{array} +$$ + +where $\tau$ is a scale factor that increases during optimization. The SDF field can then be optimized by backpropagating updates from the observed color loss through the rendering equation, and from the set of regularization losses. + +Our losses and regularizations are detailed in equations 11 to 16. The raw SDF $\hat{s}$ is convolved by a $5^{3}$ gaussian kernel $G$ into a smoother SDF $s$ to stabilize training [33]. Note that $s$ is used for all subsequent operations such as normal computation and rendering. Eq. 11 maintains $s$ and $\hat{s}$ close to each other to promote smoothness. The Eikonal regularization 12 ensures that $s$ is a signed distance. Equations 13, 14, 15 promote spatial smoothness for the normals, for the factorized spatial features and for the probe coefficients respectively. In eq. 15, $\mathcal{V}_i$ is the set of neighboring probes adjacent to the i-th one and $N$ is the total number of probes. The regularizations are applied on each voxel, factorized feature, probe or image pixel when appropriate. + +$$ +\mathcal {L} _ {\mathrm {s d f}} = \sum_ {\text {v o x e l}} | s - \hat {s} | ^ {2}, \quad s = G (\hat {s}) \tag {11} +$$ + +$$ +\mathcal {L} _ {\mathrm {E i k}} = \sum_ {\text {v o x e l}} \left(\left| \left| \nabla s \right| \right| - 1\right) ^ {2} \tag {12} +$$ + +$$ +\mathcal {L} _ {\text {n o r m a l}} = \sum_ {\text {v o x e l}} | | \nabla \mathbf {n} | | ^ {2}, \quad \mathbf {n} = \nabla s / | | \nabla s | | \tag {13} +$$ + +$$ +\mathcal {L} _ {\text {f e a t u r e s}} = \sum_ {\text {t e x e l}} | | \nabla \mathbf {F} _ {x} | | ^ {2} + | | \nabla \mathbf {F} _ {y} | | ^ {2} + | | \nabla \mathbf {F} _ {z} | | ^ {2} \tag {14} +$$ + +$$ +\mathcal {L} _ {\text {p r o b e s}} = \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {l ^ {2}} \sum_ {k \in \mathcal {V} _ {i}} \left| \left| \mathbf {b} _ {i j} - \mathbf {b} _ {k j} \right| \right| ^ {2} \tag {15} +$$ + +$$ +\mathcal {L} _ {\text {p h o t o}} = \sum_ {u, v} | | c (u, v) - c _ {\mathrm {g t}} (u, v) | | ^ {2} \tag {16} +$$ + +In eq. 16, $c$ is the rendered image and $c_{\mathrm{gt}}$ is the ground truth image. We apply a weight of $(\max(c, c_{\mathrm{gt}}) + \epsilon)^{-1}$ on the photometric gradient of each pixel in eq. 16 to penalize relative differences rather than absolute differences [19]. A similar strategy is used on $\mathcal{L}_{\mathrm{sdf}}$ and $\mathcal{L}_{\mathrm{features}}$ . We apply an empirical factor of $(1 + |s| * 5)^{-1}$ on the gradients of the per-voxel regularizations to lower their importance when the distance to the zero-crossing increases. The idea is to keep the regularizations and the data term balanced for regions near and far from the surface alike. + +# 3.4. Training + +Our complete loss is a weighted sum of eq. 11 to 16 that we minimize with the Adam optimizer [14], please refer to the supplementary document for more details. In summary, the trained parameters are the raw SDF values $\hat{s}$ , the factorized features $\mathbf{F}_x, \mathbf{F}_y, \mathbf{F}_z$ , the probes coefficients $\mathbf{b}$ and the MLP weights. We follow a coarse-to-fine learning strategy, both in the spatial and angular domains. We start with coarse voxels and $l = 2$ , under the supervision of low resolution + +images. We iteratively subdivide the voxels and switch to higher resolution images, and introduce higher angular frequencies by increasing $l$ . Starting the optimization with too many degrees of freedom for the appearance parametrization can lead to local minima, as noted by [13]. + +# 4. Implementation Details + +We use a 2 hidden layer MLP with 32 neurons and ReLU activations with a sigmoid for the last layer. The probes at the shared corners of adjacent tiles are duplicated in memory (but keep shared values) to benefit from hardware-accelerated interpolation. We support up to 16 spherical harmonic coefficients $(l = 4)$ per probe. The computation of $\mathbf{F}_a$ , $\mathbf{F}_s$ and the MLP call are fused into a single CUDA kernel for efficiency, following [21] and [27]. Each $16^3$ tile contains $3 \times 16 \times 16 \times n_s$ spatial coefficients and $8 \times l^2 \times n_a$ spherical harmonic features. Assuming $l = 4$ and $n_s = n_a$ , the probes only require $(8 \times 16) / (3 \times 16 \times 16) = 1/6$ th of the memory taken by the spatial features. The sparse voxel grid is based on the code of [27], with targeted modifications to implement our probes. + +# 5. Experiments + +Protocol We evaluate our method on 4 datasets: MVMannequins [27], ActorsHQ [8], DTU [9] and BlendedMVS [34]. Due to the various evaluation settings employed in the community, we chose to re-train and re-evaluate all the baselines using the same experimental protocol for fairness. Following [6], all available images were given as input and used for evaluation. Timings are measured on a workstation equipped with an RTX A6000 GPU (Ampere series). PSNR values are computed inside the silhouette region of objects of interest and chamfer error is computed using official scripts. We use the following grid resolutions: DTU $(1000^{3})$ , BMVS $(666^{3})$ , MVMannequins $(2500 \times 1250 \times 2500$ , $2\mathrm{mm} / \mathrm{voxel}$ ), ActorsHQ $(3000 \times 4000 \times 3000$ , $0.6\mathrm{mm} / \mathrm{voxel}$ ). Some datasets may contain inconsistent shadows or large exposure changes (DTU and BMVS) that are hard to model by our representation so we optionally train per-camera bias vectors in the MLP. + +MVMannequins is a dataset of 14 dressed mannequins for multi-view reconstruction benchmarking with 68 cameras at $2048^{2}$ resolution. We use the official evaluation code and report the metrics in table 1. We outperform all the baselines while taking only about a minute of training time, almost 3x faster than [27], with 5GB of VRAM, a rendering speed of $300\mathrm{Hz}$ to $400\mathrm{Hz}$ and a model size of 30MB. + +ActorsHQ is a multiview dataset of humans in motion with 160 cameras at a high resolution of $4088 \times 2990$ . We evaluate on the 1000th temporal frame of 13 sequences. We compare against Voxurf [33] and NeuS2 [31], which we trained with half resolution images since we ran into issues + +with full resolution images. We report the PSNR in table 2 and show qualitative results in fig. 5. Voxurf takes about one hour to fully converge (with $3 \times$ the training iterations of the DTU configuration). NeuS2 converges fast but with a lower PSNR. In comparison, our method only takes $\sim 4$ minutes to converge on the full resolution images, and we also outperform both when training at the same resolution. This benchmark highlights the capability of our method to gracefully scale to high-resolution scenes. + +![](images/39cf5a02c63ca7ce393954b0baf9ba2cb9f9b84ff86abf51ea396ade50531227.jpg) + +![](images/3ee07766ddd3cf39740b317b7b0fb4153a46d381674e2e6aa2f2b04c8c4aa83c.jpg) +Figure 5. High-resolution reconstructions for ActorsHQ. + +DTU provides 49 to 64 images of various objects at $1600 \times 1200$ resolution, along with evaluation point clouds. We use the foreground masks provided by IDR [35] for training and testing. 2DGS [6] does not support masks for training so it uses complete images instead, cropped and at half resolution according to its evaluation protocol. We compare against Voxurf [33], Neus2 [31] and 2DGS [6] on DTU in table 3, using the official python script for geometric evaluation. We outperform all three in terms of chamfer distance and PSNR, twice as fast as NeuS2 on the same hardware. Rendering speed ranges from $200\mathrm{Hz}$ to $300\mathrm{Hz}$ . + +BlendedMVS. Finally, we test our method on 8 scenes of the BlendedMVS dataset [34] and report the metrics in + +
Metrics(4,4,4)X(8,8,4)XMMH [27]Voxurf [33]Neus2 [31]Colmap [26]2DGS [6]
Chamfer (mm)1.041.031.141.592.133.523.35
PSNR36.8136.9036.3335.5134.22-34.89
Training1min1min2-3min15min5min>1h>1h
+ +Table 1. Evaluation on MVMannequins with two configurations for $\left( {{n}_{s},{n}_{a},l}\right)$ . Per-camera bias vectors are not used (X-symbol). + +
(ns,na,l) = (4,4,4)XVoxurfNeuS2
Resolutionr/1r/2r/4r/2r/2
PSNR37.4836.6234.7436.5634.53
Training250s110s53s1h250s
Model size232MB57MB15MB500MB25MB
+ +Table 2. Evaluation for ActorsHQ. Per-camera bias vectors are not used ( $\times$ -symbol). Full, half and quarter-resolution input images are denoted as $r/1$ , $r/2$ , $r/4$ respectively. Renderings are up-scaled before comparison with the full resolution images $(4088 \times 2990)$ . + +
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus22DGS
Chamfer0.680.710.730.800.76
PSNR37.0337.7437.083636.03
Training150s160s15min5min12min
Model size56MB88MB500MB25MB49MB
+ +Table 3. DTU evaluation with two configurations for $\left( {{n}_{s},{n}_{a},l}\right)$ . Per-camera bias vectors are used (✓-symbol). + +
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus2
Chamfer2.372.222.642.93
PSNR35.1935.8935.1133.62
Training110s120s15min5min
+ +table 4. The BlendedMVS is a semi-synthetic dataset were objects have been first reconstructed then reprojected in the images in order to produce reliable ground truth geometry and masks. There is no official script for geometric evaluation so we measure two-ways point to mesh distances in the reference frame used for training in [30], scaled by $1000\mathrm{x}$ . + +Ablations. We ablate the probes smoothing and the polynomial approximation of the Fresnel term in tab. 5 on the MVMannequins dataset by imposing $\mathbf{n} \cdot \mathbf{v} = 1$ in eq. 4 during training, with noticeable incidence on Chamfer error. A visual ablation of the components of our parametrization is presented in fig. 8 on the kino/jea mannequin, clearly showing the role of each parameter group. Figure 9 contains more examples. Various choices of configurations are compared in table 6 on the BlendedMVS dataset. + +![](images/4f5a3a2455dff7b84bc9cad531116ba4f215606ea8b5c69cb14384b2831714bc.jpg) +Figure 6. Reconstructions on challenging examples of DTU. + +Table 4. BMVS evaluation with two configurations for $\left( {{n}_{s},{n}_{a},l}\right)$ . Per-camera bias vectors are used (✓-symbol). + +
(4,4,4)Xw/o probes smoothingw/o Fresnel
Chamfer (mm)1.041.091.18
PSNR36.8136.9136.79
+ +Table 5. Ablation on MVMannequins + +
Metrics(4,4,4)X(4,4,4)Y(8,8,4)√(12,12,4)√(4,4,1)√(4,4,2)√(4,4,3)√
Chamfer2.472.372.222.312.582.342.37
PSNR34.7635.1935.8936.1734.4434.8635.05
+ +Table 6. We ablate the number of spatial features $n_s$ , angular features $n_a$ and spherical harmonics order $l$ on BlendedMVS. Each triplet denotes a configuration $(n_s, n_a, l)$ . The $\checkmark$ -symbol indicates when per-camera bias vectors are trained. + +# 6. Limitations + +We identify several limitations to our approach. First, the fact that the lighting is encoded locally can degrade the extrapolation capabilities compared to modeling the environment with a global representation. This becomes appar + +![](images/640b930eea7e84d7a965f5dd7d665765845086cc30a160cc6e305ef8a106e75e.jpg) +Figure 7. Reconstructed examples on BlendedMVS. + +![](images/75e4fbe567e4be83399a9de27bcb214dfebe374a4a40ba4f1b1c5d634ee04587.jpg) +Figure 8. Our model can be intuitively explained. We disable some components of a pre-trained example from the MVMannequins dataset [27] (left). From left to right, we remove the spatial features (set $\mathbf{F}_s = 0$ ), only keep the constant coefficient of the SH basis ( $l = 1$ ), disable the incidence angle embedding (set $\mathbf{n} \cdot \mathbf{v} = 1$ in eq. 4). The learned Fresnel term encodes grazing reflections (red circles), the angular features provide the shading (green squares) and the spatial features contain the high frequency details. + +ent on the ActorsHQ dataset where there is a good overlap of the cameras field of views along the longitude, but very little overlap along the latitude on the legs. This creates shadows artifacts when looking from above or below rather that at a level angle. Second, although our decomposition is physically-inspired, we do not explicitly simulate light transport which can result in local minima due to shape-radiance ambiguities. Relighting and/or material editing is not supported but fine-tuning the probes to new lighting seems possible and worthy of future investigations. + +![](images/6c2bb73b2cd549ee7a4ad3cb3cd923b38fdf80d6d9db6affb6c2da389a389577.jpg) +Figure 9. Effect of the learned Fresnel term on three examples from MVMannequins, DTU and ActorsHQ. Left to right: input image, volume rendering (A), volume rendering w/o the Fresnel term (B) (we set $\mathbf{n}\cdot \mathbf{v} = 1$ in eq. 4), difference image $(4\times |A - B|)$ . + +# 7. Conclusion and Future Work + +We have presented a novel approach to model the view dependent appearance, enabling both fast reconstruction and real-time rendering of humans and objects. Notably, our model does not compromise on geometric and photometric quality, even surpassing the previous approaches in many instances. It can easily scale to high resolution inputs while maintaining high performance. We have reached a parsimonious parametrization of the surface properties thanks to a simple formulation. Disentangling the spatial and angular components with high efficiency also offers promising future avenues of research toward temporal reconstruction. Other future research can build on this work, e.g. handling high frequency reflections at a lower cost than current dedicated approaches and unifying neural rendering and physically-based rendering. Other embeddings of the angular dependency representations can be investigated, such as cubemaps or mixtures of spherical gaussians. + +# 8. Acknowledgments + +This work was supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) grant ANR-21-ESRE-0030 (CONTINUUM). Research conducted at Kyushu University was supported by JSPS/KAKENHI JP23H03439 and AMED JP24wm0625404. 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Neural directional encoding for efficient and accurate view-dependent appearance modeling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 3 +[33] Tong Wu, Jiaqi Wang, Xingang Pan, Xudong Xu, Christian Theobalt, Ziwei Liu, and Dahua Lin. Voxurf: Voxel-based efficient and accurate neural surface reconstruction. In International Conference on Learning Representations (ICLR), 2022. 1, 2, 5, 6, 7 +[34] Yao Yao, Zixin Luo, Shiwei Li, Jingyang Zhang, Yufan Ren, Lei Zhou, Tian Fang, and Long Quan. Blendedmvs: A large-scale dataset for generalized multi-view stereo networks. Computer Vision and Pattern Recognition (CVPR), 2020. 2, 6 +[35] Lior Yariv, Yoni Kasten, Dror Moran, Meirav Galun, Matan Atzmon, Basri Ronen, and Yaron Lipman. Multiview neural surface reconstruction by disentangling geometry and appearance. Advances in Neural Information Processing Systems, 33, 2020. 2, 6 +[36] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021. 2, 3 +[37] Xiuming Zhang, Pratul P. Srinivasan, Boyang Deng, Paul Debevec, William T. Freeman, and Jonathan T. Barron. Ner-factor: neural factorization of shape and reflectance under an unknown illumination. 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Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, France" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 241, + 220, + 369, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 241, + 220, + 369, + 233 + ], + "spans": [ + { + "bbox": [ + 241, + 220, + 369, + 233 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 241, + 220, + 369, + 233 + ], + "type": "text", + "content": "Kyushu University, Japan" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 151, + 261, + 200, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 261, + 200, + 273 + ], + "spans": [ + { + "bbox": [ + 151, + 261, + 200, + 273 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 54, + 285, + 296, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 285, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 296, + 501 + ], + "type": "text", + "content": "SDF-based differential rendering frameworks have achieved state-of-the-art multiview 3D shape reconstruction. In this work, we re-examine this family of approaches by minimally reformulating its core appearance model in a way that simultaneously yields faster computation and increased performance. To this goal, we exhibit a physically-inspired minimal radiance parametrization decoupling angular and spatial contributions, by encoding them with a small number of features stored in two respective volumetric grids of different resolutions. Requiring as little as four parameters per voxel, and a tiny MLP call inside a single fully fused kernel, our approach allows to enhance performance with both surface and image (PSNR) metrics, while providing a significant training speedup and real-time rendering. We show this performance to be consistently achieved on real data over two widely different and popular application fields, generic object and human subject shape reconstruction, using four representative and challenging datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 535, + 135, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 535, + 135, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 535, + 135, + 547 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 555, + 295, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 295, + 650 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 295, + 650 + ], + "type": "text", + "content": "Neural radiance fields have established a new milestone for the task of novel view synthesis and have led to a plethora of variants of broad applicability. We here take particular interest in SDF surface-based radiance fields, which have proven to be a highly performing variant for the tasks of 3D modeling from images [30, 33], with wide reaching applications ranging from object and performance capture, to immersive and 3D content production." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 651, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 295, + 687 + ], + "type": "text", + "content": "At the heart of such methods usually lies a parametrization of the light field, in the form of a 5-dimensional function. This function maps the spatial coordinates of a point" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 261, + 555, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 555, + 453 + ], + "type": "text", + "content": "in space and the observed direction to a color and a signed distance to the reconstructed surface. On one hand, the mapping can be global and use a complex scene-wide MLP as implicit 5D decoder, as is the case for most seminal approaches [18, 30]. On the other hand, recent popular variants that target higher speed and memory efficiency use explicit representations. Global representations are based on a grid encoding [4, 31, 33] where interpolated spatial and angular features are run through a global shallow MLP. Local representations use the sparse 3D Gaussian Splatting [13] sample-based encoding approach, where each separate Gaussian comes with its own opacity and adjoining set of angular color features. While grids or local approaches use a single deep MLP to densely encode the complete light field function, they almost always co-locate storage and decoding of color and angular features." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 457, + 556, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 556, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 556, + 613 + ], + "type": "text", + "content": "But is this really a necessary or even desirable feature of any light field encoding? We question these assertions by postulating that, contrary to the spatial components of the light field that mainly encode intrinsic surface texture, the angular components encode phenomena that are predominantly extrinsic to the surface, i.e. lighting and environment, and as such can be encoded at a lower spatial resolution as they are locally almost invariant to parallax. This hypothesis is in fact exploited by the rendering community, where angular and environment components contributing to the radiance equation used to compute rendered colors, are typically precomputed at sparse 3D locations coined light field probes [24], and interpolated in-between." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": "Leveraging this intuition, our approach borrows the spherical harmonic parametrization popular with explicit methods e.g. [4, 13] to represent angular components, but instead decorrelates high density spatial variation from lower density angular variation using a mid-resolution probe grid of angular features. Each of the components encode abstract features that are fed to a tiny MLP, which acts as a minimal BRDF decoder of spatial and angular" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "text", + "content": "1Source code is available at https://gitlab.inria.fr/projects-morpheo/ProbeSDF" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11026" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 68, + 532, + 223 + ], + "blocks": [ + { + "bbox": [ + 82, + 68, + 532, + 223 + ], + "lines": [ + { + "bbox": [ + 82, + 68, + 532, + 223 + ], + "spans": [ + { + "bbox": [ + 82, + 68, + 532, + 223 + ], + "type": "image", + "image_path": "d262540ec2d12070175fdbb9071174bc9e7fc9b3cbbd71efc5a97a9ae50fa147.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 230, + 555, + 265 + ], + "lines": [ + { + "bbox": [ + 54, + 230, + 555, + 265 + ], + "spans": [ + { + "bbox": [ + 54, + 230, + 555, + 265 + ], + "type": "text", + "content": "Figure 1. We design a new appearance model for neural surface approaches, which combines high resolution spatial features and lower resolution angular features for improved reconstruction quality, training and inference speed. We plot the chamfer distance as a function of training speed for several baselines on MVMannequins (top) and DTU (bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 285, + 295, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 285, + 295, + 439 + ], + "spans": [ + { + "bbox": [ + 56, + 285, + 295, + 439 + ], + "type": "text", + "content": "varying components, while we explicitly store SDF values. This scheme advantageously replaces the core appearance and decoding model of SDF approaches [15, 30, 31, 33] to predict ray colors. We are careful to also include power terms of the cosine angle between the view direction and the estimated surface normal, allowing our lightweight model to effectively account for increased surface reflectivity at grazing angles. This yields an unprecedented performance combination, superseding both 3D and image metric performances with four popular benchmarks for general object reconstruction [9, 34] and human reconstruction [8, 27] while simultaneously achieving a significant training and rendering performance boost. In summary, our contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 441, + 296, + 489 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 441, + 295, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 295, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 295, + 464 + ], + "type": "text", + "content": "- An explicit embedding of the angular dependency that is simultaneously local, smooth and efficient." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 464, + 296, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 296, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 296, + 489 + ], + "type": "text", + "content": "- A simpler color prediction MLP that is agnostic to the surface position and orientation." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 500, + 147, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 500, + 147, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 500, + 147, + 513 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 521, + 295, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 582 + ], + "type": "text", + "content": "In this work we leverage disentangled spatial and angular parameterization of radiance towards high quality appearance and surface modeling. Here we consequently review closely related works on surface-based 3D scene representations and existing parametrizations of color." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": "Neural Surface Reconstruction. Through the use of implicit surface representations, neural implicit fields have demonstrated increasing capabilities to generate high-quality 3D models [23, 35, 36]. In NeuS [30], Wang et al. proposed to parametrize the surface with a signed distance function that is modeled with a multi layer perceptron (MLP). The approach opened new frontiers in the generation of accurate 3D scenes from images but at the cost of prohibitive training times (several hours). Follow-up works have thus focused on boosting both accuracy and computation time by employing explicit grids of features" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 285, + 555, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 555, + 476 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 555, + 476 + ], + "type": "text", + "content": "and smaller MLPs. Notably, Wu et al. proposed in Vox-urf [33] to use a dense grid of voxels, and Neus2 was also proposed using hash grids [31]. Recently, Millimetric humans [27] have demonstrated remarkably fast and accurate reconstructions in the case of human datasets by using sparse and dynamic grids. Other reparametrizations target performance improvement, e.g. point-based with Fast Dipole Sums [3] and PGSR [2] both leveraging multi-view stereo priors, or by seeking mutual advantage of a hybrid volume/mesh representation [7]. All the methods discussed above rely on co-located encodings of position and view direction to parametrize the appearance. As a consequence, these approaches either fail to model local radiance effects like inter-reflections, or require larger MLPs and training times, and may thus benefit from our refactored appearance model as drop-in replacement." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 481, + 556, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 556, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 556, + 696 + ], + "type": "text", + "content": "Angular parametrization Deep MLPs have become ubiquitous to model view-dependent colors, taking as input the view direction [18], the view and normal [30, 31, 33, 35] or the reflected direction [27, 28]. Non-neural approaches such as plenoxels [4] or the Gaussian splatting methods [6, 13] favor a straightforward spherical harmonics decomposition in color space. The main advantage compared to a deep MLP is the computational efficiency, at the cost of a large number of appearance parameters: 27 per voxel for [4] and 48 per Gaussian for [13]. Note that some neural architectures [27, 28, 31] use spherical harmonics as a positional encoding of the directional vectors, but this is completely distinct from encoding the signal into spherical harmonic coefficients. In this work we propose a lighter yet efficient parametrization of color by using two decorrelated voxel structures to encode different components of the observed color, and spherical harmonics encoding of pre-MLP features for more parsimonious and expressive color decoding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "In the field of real-time rendering, where lighting and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11027" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 145 + ], + "type": "text", + "content": "BRDF are known in advance, the idea of caching the incoming light at discrete locations, known as light field probes, has become standard [16, 17, 24]. We draw inspiration from this technique for our proposed approach to multi-view 3D reconstruction, with the difference in our case that the probe parameters are optimized along with the voxel parameters." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 155, + 295, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 155, + 295, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 155, + 295, + 275 + ], + "type": "text", + "content": "High Frequency Reflections. A number of approaches specifically deal with high frequency reflections, which requires dedicated representations and algorithms. Guo et al. [5] train an additional NeRF that is composited with the main image. This approach is under-constrained and thus requires strong priors such as the reflective surfaces being flat. Verbin et al. [28] model lighting as a neural envmap, modulated by a per-point roughness. The roughness and base color of the object can be edited afterwards but a long training time is required due to the large MLP." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 285, + 295, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 295, + 428 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 295, + 428 + ], + "type": "text", + "content": "Recent works [29, 32] recover detailed reflections using cone tracing, which inherently solves the problem posed by self-reflections. Both approaches give impressive results even when confronted with curved, mirror-like objects but at a large training cost exceeding 10 GPU-hours per scene. In contrast, we target objects with mild specularities, and show that both fast training and real-time rendering can be achieved. More specifically, our neural light field probes can learn information about the surroundings whereas cone tracing gathers it at a greater cost. This assumption proves to be valid for standard acquisition scenes, with the four datasets tested." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 438, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 438, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 438, + 295, + 715 + ], + "type": "text", + "content": "Minimal Parametrization. Explicitly disentangling the material parameters from the lighting is particularly challenging but also rewarding because it can yield a minimal parametrization of the appearance. Munkberg et al. [22] show that the approximate rendering equation developed in [12] is sufficiently accurate to recover the geometry using a differentiable rasterizer, along with an approximate material decomposition. Jiang et al. [10] applies a similar strategy but with the 3D gaussian splatting volume rendering. The NeRFactor pipeline [37] starts from a pre-trained NeRF that is distilled into lighting, albedo and neural BRDF parameters. Jin et al. proposed TensoIR [11], which achieves a more accurate decomposition by evaluating the rendering equation with importance sampling. An efficient tensor representation helps to accelerate the rendering of the secondary rays, but the complete training still takes five hours on a single GPU, with decent results available after half an hour of training. Our proposed method converges in just a few minutes and we find that only 4 coefficients per voxel are sufficient in most cases. The dimensionality is equivalent to the albedo and roughness values of a physically-based material parametrization, but without the cost associated with the inversion of the rendering equation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 71, + 370, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 370, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 370, + 84 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 91, + 555, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 140 + ], + "type": "text", + "content": "We use an SDF grid as the implicit representation of the 3D shape. SDF values in the grid are optimized via our newly proposed differentiable appearance model and the derived surface normal vectors " + }, + { + "bbox": [ + 313, + 91, + 555, + 140 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 313, + 91, + 555, + 140 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 146, + 524, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 146, + 524, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 146, + 524, + 159 + ], + "type": "text", + "content": "3.1. Decoupled Parametrization of Radiance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": "Volumetric neural rendering, as proposed in the seminal work NeRF, computes the color at a given pixel by integrating radiances along camera-pixel rays weighted by local opacity values. Follow-up papers condition the opacity on the distance to the surface to improve the reconstruction quality [20, 30, 36]. The radiance " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": " represents the amount of energy that is emitted by a point in space. In physics it is expressed as the integral over the hemisphere " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": " of the spatially varying bidirectional reflectance distribution function (SVBRDF) " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": " multiplied by the incoming radiance " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": " and by the cosine between the incoming direction " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": " and the surface normal " + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 313, + 163, + 555, + 308 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 355, + 314, + 555, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 314, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 355, + 314, + 555, + 340 + ], + "type": "interline_equation", + "content": "C = \\int_ {\\Omega} f _ {r} (\\mathbf {v}, \\omega , \\mathbf {x}) L (\\omega , \\mathbf {x}) (\\omega \\cdot \\mathbf {n}) d \\omega . \\tag {1}", + "image_path": "6cced1f62f65fa5db4225c76e41cf5e02affd2a2687c924891f82f1e5c19efdb.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": "The (spatially varying) BRDF depends on the point's position " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": ", direction of incoming light " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " and viewing direction " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "L(\\omega, \\mathbf{x})" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " is the intensity of light at point " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " that comes from the direction " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " is the normal vector of the surface at position " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": ". In equation 1, both " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 346, + 556, + 467 + ], + "type": "text", + "content": " are unknown and disentangling these two functions during optimization is extremely difficult. As a consequence, a current research trend is to use an MLP to directly approximate the result of this integral and obtain the outgoing radiance with the following equation:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 376, + 476, + 555, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 476, + 555, + 490 + ], + "spans": [ + { + "bbox": [ + 376, + 476, + 555, + 490 + ], + "type": "interline_equation", + "content": "C = M L P (\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {v}, \\mathbf {n}, \\mathbf {r}). \\tag {2}", + "image_path": "68a0c451c549b288fd4631607dbef2bb21406d6104f11e41a8b900e30ab8b99a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": " represents spatial features encoded at a point position " + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": " is the reflected vector at point " + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": " for the viewing direction " + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": ". This approximation works well if the incoming light is positionally invariant, but its accuracy degrades in the presence of local lighting effects such as close point lights, inter-reflections and self-shadows. In such cases, the spatial features must additionally encode some information about the local lighting and thus require a larger dimensionality than one would expect. A large and deep MLP is also necessary to decode this compressed information, which lowers the computational efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "We propose to decouple the radiance model into spatial and angular features. We model a 3D scene with a combination of a high resolution sparse voxel grid that models the SDF field and a coarser grid that models the angular features as shown in fig. 2. For each point in space, the spatial features are obtained with a planar factorization in the coarse resolution tile with " + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s = \\mathbf{F}_x\\otimes \\mathbf{F}_y\\otimes \\mathbf{F}_z" + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": " for" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11028" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 556, + 206 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 556, + 206 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 556, + 206 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 556, + 206 + ], + "type": "image", + "image_path": "4bd17308d7cfc01a73e605af7e0509cfefe748fb35fcf24f97a0ea5b5423673e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": "Figure 2. Overview of the color prediction for a single voxel inside a " + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "inline_equation", + "content": "16^{3}" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": " tile. The angular features " + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "inline_equation", + "content": "F_{a}" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": " are computed by interpolating and evaluating the spherical harmonics from the 8 corner probes with the reflected vector " + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": ". The spatial features " + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": " are computed as the outer product of three orthogonal planes of resolution " + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "inline_equation", + "content": "16\\times 16" + }, + { + "bbox": [ + 54, + 215, + 555, + 251 + ], + "type": "text", + "content": ", specific to the tile. A small neural network decodes these inputs into a color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 270, + 298, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 270, + 298, + 331 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 298, + 331 + ], + "type": "text", + "content": "dimensionality reduction [1]. The angular features " + }, + { + "bbox": [ + 54, + 270, + 298, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 54, + 270, + 298, + 331 + ], + "type": "text", + "content": " are obtained by tri-linearly interpolating light field probes as explained in sec. 3.2. In addition, a dependency on the angle of incidence must be added to account for differences in reflectivity, as shown in fig. 3." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 66, + 339, + 285, + 432 + ], + "blocks": [ + { + "bbox": [ + 66, + 339, + 285, + 432 + ], + "lines": [ + { + "bbox": [ + 66, + 339, + 285, + 432 + ], + "spans": [ + { + "bbox": [ + 66, + 339, + 285, + 432 + ], + "type": "image", + "image_path": "1a0b693822b42540b2584761c40aed93b62ede012c30c78729214334f5055e03.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 439, + 296, + 495 + ], + "lines": [ + { + "bbox": [ + 55, + 439, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 439, + 296, + 495 + ], + "type": "text", + "content": "Figure 3. The reflectivity cannot be encoded in " + }, + { + "bbox": [ + 55, + 439, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 55, + 439, + 296, + 495 + ], + "type": "text", + "content": " alone because different incident vectors can map to the same reflected vector (in red). In that case, similar angular features will be obtained for the two viewpoints due to the spatial and angular proximity of the lookups. The angle of incidence disambiguates the two situations." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 507, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 507, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 296, + 533 + ], + "type": "text", + "content": "The reflectivity, also called the Fresnel term, is commonly approximated as follows for rendering purposes [25]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 100, + 551, + 295, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 551, + 295, + 566 + ], + "spans": [ + { + "bbox": [ + 100, + 551, + 295, + 566 + ], + "type": "interline_equation", + "content": "R (\\theta) = R _ {0} + (1 - R _ {0}) (1 - \\cos \\theta) ^ {5}. \\tag {3}", + "image_path": "41c37bd4c2cf619846a991678c3205ffcba6569c8b160fe46b0514a591955a47.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "inline_equation", + "content": "R_0" + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "content": " is the reflectivity at normal incidence and " + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "content": " is the angle between the view direction and the half-way vector to the light source. In our case, " + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "inline_equation", + "content": "R_0" + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "content": " is unknown and there is no explicit light source which means that we cannot use this formula directly. Instead, we approximate " + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\cos \\theta" + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\cdot \\mathbf{v}" + }, + { + "bbox": [ + 55, + 573, + 296, + 670 + ], + "type": "text", + "content": " and let the first layer of the neural network learn a polynomial approximation of the Fresnel term. Our revised parametrization is given by eq. 4:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 64, + 681, + 294, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 681, + 294, + 711 + ], + "spans": [ + { + "bbox": [ + 64, + 681, + 294, + 711 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} C = M L P \\left(\\mathbf {F} _ {s} (\\mathbf {x}), \\mathbf {F} _ {a} (\\mathbf {x}, \\mathbf {r})\\right), \\\\ (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {0}, \\dots , (1 - \\mathbf {n} \\cdot \\mathbf {v}) ^ {5}). \\tag {4} \\\\ \\end{array}", + "image_path": "f96c3150c3160b2047c2df544db0fcfd982e1a50e02b8108211227f553c61e94.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": "We denote the dimensionality of the features by " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "n_s" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "n_a" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s \\in \\mathbb{R}^{n_s}" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a \\in \\mathbb{R}^{n_a}" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": ". Most materials reflect the light in a cone around the reflected vector which is why we condition " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": ", but some materials have retroreflective properties that break this assumption. In that case, conditioning on the view direction would be more appropriate. Lastly, eq. 4 assumes isotropic materials since the reflectivity depends only on " + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\cdot \\mathbf{v}" + }, + { + "bbox": [ + 313, + 270, + 555, + 378 + ], + "type": "text", + "content": ". Anisotropic materials could be handled by adding a dependency on the azimuthal angle." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 386, + 508, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 508, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 508, + 399 + ], + "type": "text", + "content": "3.2. Light Field Probes on a Coarse Grid" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "text", + "content": "In this work, we replace the generic angular inputs " + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 313, + 403, + 555, + 608 + ], + "type": "text", + "content": " with new angular inputs encoding the local illumination (the light field probes), with the goal to achieve a more efficient parametrization of the appearance in terms of parameter count, training and inference speed. Similarly to previous works [4, 13], we use a spherical harmonics decomposition to model this dependency, but with several important differences: first, we encode abstract features on the sphere rather than the outgoing radiance which lets a neural network handle the non-linearities. Second, our directional embedding has a low spatial resolution which takes advantage of the smooth spatial variations of the lighting. Third, we sample this embedding with the reflected vector instead of the view vector to link the local surface orientation with the shading function, which has been showed to be beneficial for improved surface quality [28]. The angular features encoded into a single neural probe are given by eq. 5:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 371, + 616, + 555, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 616, + 555, + 651 + ], + "spans": [ + { + "bbox": [ + 371, + 616, + 555, + 651 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {a} = \\mathcal {S H} (\\mathbf {r}) = \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {j} Y _ {j} (\\mathbf {r}). \\tag {5}", + "image_path": "4263fbeabd3fc9221fdaabd00f969d74d51e7359e646e6e7e5a02d2c1893476e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "content": "The polynomials of the SH basis are denoted with " + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "inline_equation", + "content": "Y_{j}" + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "content": ". There are " + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "inline_equation", + "content": "l^2" + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "content": " coefficients " + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_j \\in \\mathbb{R}^{n_a}" + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "content": ". Increasing values of " + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 660, + 555, + 685 + ], + "type": "text", + "content": " unlock" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": "2We use a one-indexed notation for the SH order " + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": " instead of the traditional zero-indexing so that we have " + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "inline_equation", + "content": "l^2" + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": " coefficients." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11029" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": "signals of increasing angular frequency which gives an explicit control on the representable amount of specularities. We observe two guiding principles: (1) The shinier the material, the higher the frequency of " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " should be in the angular domain. (2) The closer the light source, the higher the frequency " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " should be in the spatial domain. See fig. 4 for an illustration." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 163, + 293, + 232 + ], + "blocks": [ + { + "bbox": [ + 56, + 163, + 293, + 232 + ], + "lines": [ + { + "bbox": [ + 56, + 163, + 293, + 232 + ], + "spans": [ + { + "bbox": [ + 56, + 163, + 293, + 232 + ], + "type": "image", + "image_path": "8f15472fede64b66507349dce8821e329eae4d23f383990d0c58bc8945702423.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 242, + 296, + 277 + ], + "lines": [ + { + "bbox": [ + 55, + 242, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 242, + 296, + 277 + ], + "type": "text", + "content": "Figure 4. Left and center: The lighting direction changes at a lower rate on the surface for distant light sources. Right: Self shadows impose variations in lighting even with directional illumination." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "text", + "content": "For the case of common scenes such as humans or everyday objects, assuming materials with high to medium roughness so that " + }, + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "text", + "content": " does not need to be of very high angular frequency is generally sufficient. We also assume that the lights are far enough, so that probes at a low spatial frequency can explain the parallax. The probes are stored at 1/16th the resolution of the main voxel grid, as shown in fig. 2. The voxels tri-linearly interpolate the 8 nearest probes according to eq. 6 and 7, with " + }, + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 55, + 289, + 296, + 409 + ], + "type": "text", + "content": " the interpolation weight of the i-th corner." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 415, + 295, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 415, + 295, + 487 + ], + "spans": [ + { + "bbox": [ + 85, + 415, + 295, + 487 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {F} _ {a} = \\sum_ {i = 1} ^ {8} \\mathcal {S H} _ {i} (\\mathbf {r}) w _ {i} = \\sum_ {i = 1} ^ {8} \\sum_ {j = 1} ^ {l ^ {2}} \\mathbf {b} _ {i j} Y _ {j} (\\mathbf {r}) w _ {i} (6) \\\\ = \\sum_ {j = 1} ^ {l ^ {2}} \\hat {\\mathbf {b}} _ {j} Y _ {j} (\\mathbf {r}) \\quad \\text {w i t h} \\hat {\\mathbf {b}} _ {j} = \\sum_ {i = 1} ^ {8} \\mathbf {b} _ {i j} w _ {i} (7) \\\\ \\end{array}", + "image_path": "2b4535d279716d08bf4980e2829412f75d03c1b4e59d59eeb8e7835266ee14ea.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 492, + 203, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 492, + 203, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 492, + 203, + 506 + ], + "type": "text", + "content": "3.3. SDF Estimation Approach" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": "We here discuss how to embed the new proposed color decoder in an implicit surface reconstruction pipeline. During the forward pass, for a pixel " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": " in a given viewpoint, the color is computed by a transmittance " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": "-weighted average of the colors " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": " points sampled from the current scene volume estimate along the pixel aligned ray, where " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": " is the product of obstructing opacities " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "\\alpha_{j}" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": ". We use the NeuS equation to relate volumetric opacities to the SDF " + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 55, + 510, + 296, + 618 + ], + "type": "text", + "content": " at each sample point [30]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 81, + 623, + 295, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 623, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 81, + 623, + 295, + 712 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} c (u, v) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} C _ {i}, \\quad T _ {i} = \\prod_ {j < i} (1 - \\alpha_ {j}), (8) \\\\ \\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {\\tau} (s _ {i}) - \\Phi_ {\\tau} (s _ {i + 1})}{\\Phi_ {\\tau} (s _ {i})}, 0\\right), (9) \\\\ \\Phi_ {\\tau} \\left(s _ {i}\\right) = \\frac {1}{1 + \\exp^ {- \\tau s _ {i}}}. (10) \\\\ \\end{array}", + "image_path": "807004bc21ea7ba70b585d1ce28510e1195fdf9b84ee7507ad544537badc0cae.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": " is a scale factor that increases during optimization. The SDF field can then be optimized by backpropagating updates from the observed color loss through the rendering equation, and from the set of regularization losses." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": "Our losses and regularizations are detailed in equations 11 to 16. The raw SDF " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " is convolved by a " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "5^{3}" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " gaussian kernel " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " into a smoother SDF " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " to stabilize training [33]. Note that " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " is used for all subsequent operations such as normal computation and rendering. Eq. 11 maintains " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " close to each other to promote smoothness. The Eikonal regularization 12 ensures that " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " is a signed distance. Equations 13, 14, 15 promote spatial smoothness for the normals, for the factorized spatial features and for the probe coefficients respectively. In eq. 15, " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " is the set of neighboring probes adjacent to the i-th one and " + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 121, + 555, + 277 + ], + "type": "text", + "content": " is the total number of probes. The regularizations are applied on each voxel, factorized feature, probe or image pixel when appropriate." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 342, + 293, + 555, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 293, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 342, + 293, + 555, + 319 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s d f}} = \\sum_ {\\text {v o x e l}} | s - \\hat {s} | ^ {2}, \\quad s = G (\\hat {s}) \\tag {11}", + "image_path": "668866049d1448a3c1564caf5e03cea5d25bc48f8922bc8b156ff53eec0b5ad5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 342, + 320, + 553, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 320, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 342, + 320, + 553, + 346 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {E i k}} = \\sum_ {\\text {v o x e l}} \\left(\\left| \\left| \\nabla s \\right| \\right| - 1\\right) ^ {2} \\tag {12}", + "image_path": "b16b3c0824923aa09b837621ac0cc0c89198ebd929d05f4bada980177812cea2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 349, + 553, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 349, + 553, + 373 + ], + "spans": [ + { + "bbox": [ + 331, + 349, + 553, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {\\text {v o x e l}} | | \\nabla \\mathbf {n} | | ^ {2}, \\quad \\mathbf {n} = \\nabla s / | | \\nabla s | | \\tag {13}", + "image_path": "830504251da5221c4cc4a7f78753e40ad6eb78be05e014b20128492a678a3350.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 375, + 553, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 375, + 553, + 401 + ], + "spans": [ + { + "bbox": [ + 329, + 375, + 553, + 401 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t u r e s}} = \\sum_ {\\text {t e x e l}} | | \\nabla \\mathbf {F} _ {x} | | ^ {2} + | | \\nabla \\mathbf {F} _ {y} | | ^ {2} + | | \\nabla \\mathbf {F} _ {z} | | ^ {2} \\tag {14}", + "image_path": "496e8ccb7e4216e378eb425dc577e27021ec983fc7a746c30e2b328c5396a071.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 332, + 403, + 553, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 403, + 553, + 439 + ], + "spans": [ + { + "bbox": [ + 332, + 403, + 553, + 439 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r o b e s}} = \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {l ^ {2}} \\sum_ {k \\in \\mathcal {V} _ {i}} \\left| \\left| \\mathbf {b} _ {i j} - \\mathbf {b} _ {k j} \\right| \\right| ^ {2} \\tag {15}", + "image_path": "0e4f6298bd812ea1ea87fe5475d5a8b439b4c6263dde20734c2627809be1be6d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 441, + 553, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 441, + 553, + 466 + ], + "spans": [ + { + "bbox": [ + 335, + 441, + 553, + 466 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {u, v} | | c (u, v) - c _ {\\mathrm {g t}} (u, v) | | ^ {2} \\tag {16}", + "image_path": "96a9026b8e0b1c8c1aa7694d1b5a092b70a2f2ff9cab1381e40a3959dd57e52f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": "In eq. 16, " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": " is the rendered image and " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{gt}}" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": " is the ground truth image. We apply a weight of " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "(\\max(c, c_{\\mathrm{gt}}) + \\epsilon)^{-1}" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": " on the photometric gradient of each pixel in eq. 16 to penalize relative differences rather than absolute differences [19]. A similar strategy is used on " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sdf}}" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{features}}" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": ". We apply an empirical factor of " + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "inline_equation", + "content": "(1 + |s| * 5)^{-1}" + }, + { + "bbox": [ + 313, + 474, + 555, + 594 + ], + "type": "text", + "content": " on the gradients of the per-voxel regularizations to lower their importance when the distance to the zero-crossing increases. The idea is to keep the regularizations and the data term balanced for regions near and far from the surface alike." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 600, + 378, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 600, + 378, + 613 + ], + "spans": [ + { + "bbox": [ + 314, + 600, + 378, + 613 + ], + "type": "text", + "content": "3.4. Training" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": "Our complete loss is a weighted sum of eq. 11 to 16 that we minimize with the Adam optimizer [14], please refer to the supplementary document for more details. In summary, the trained parameters are the raw SDF values " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": ", the factorized features " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_x, \\mathbf{F}_y, \\mathbf{F}_z" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": ", the probes coefficients " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{b}" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": " and the MLP weights. We follow a coarse-to-fine learning strategy, both in the spatial and angular domains. We start with coarse voxels and " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "l = 2" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": ", under the supervision of low resolution" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11030" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 133 + ], + "type": "text", + "content": "images. We iteratively subdivide the voxels and switch to higher resolution images, and introduce higher angular frequencies by increasing " + }, + { + "bbox": [ + 55, + 72, + 295, + 133 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 72, + 295, + 133 + ], + "type": "text", + "content": ". Starting the optimization with too many degrees of freedom for the appearance parametrization can lead to local minima, as noted by [13]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 191, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 191, + 158 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 191, + 158 + ], + "type": "text", + "content": "4. Implementation Details" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": "We use a 2 hidden layer MLP with 32 neurons and ReLU activations with a sigmoid for the last layer. The probes at the shared corners of adjacent tiles are duplicated in memory (but keep shared values) to benefit from hardware-accelerated interpolation. We support up to 16 spherical harmonic coefficients " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "(l = 4)" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " per probe. The computation of " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " and the MLP call are fused into a single CUDA kernel for efficiency, following [21] and [27]. Each " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "16^3" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " tile contains " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "3 \\times 16 \\times 16 \\times n_s" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " spatial coefficients and " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "8 \\times l^2 \\times n_a" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " spherical harmonic features. Assuming " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "l = 4" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "n_s = n_a" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": ", the probes only require " + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "inline_equation", + "content": "(8 \\times 16) / (3 \\times 16 \\times 16) = 1/6" + }, + { + "bbox": [ + 55, + 165, + 296, + 333 + ], + "type": "text", + "content": "th of the memory taken by the spatial features. The sparse voxel grid is based on the code of [27], with targeted modifications to implement our probes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 345, + 136, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 345, + 136, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 136, + 358 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": "Protocol We evaluate our method on 4 datasets: MVMannequins [27], ActorsHQ [8], DTU [9] and BlendedMVS [34]. Due to the various evaluation settings employed in the community, we chose to re-train and re-evaluate all the baselines using the same experimental protocol for fairness. Following [6], all available images were given as input and used for evaluation. Timings are measured on a workstation equipped with an RTX A6000 GPU (Ampere series). PSNR values are computed inside the silhouette region of objects of interest and chamfer error is computed using official scripts. We use the following grid resolutions: DTU " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "(1000^{3})" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": ", BMVS " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "(666^{3})" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": ", MVMannequins " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "(2500 \\times 1250 \\times 2500" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "2\\mathrm{mm} / \\mathrm{voxel}" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": "), ActorsHQ " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "(3000 \\times 4000 \\times 3000" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "inline_equation", + "content": "0.6\\mathrm{mm} / \\mathrm{voxel}" + }, + { + "bbox": [ + 55, + 365, + 295, + 568 + ], + "type": "text", + "content": "). Some datasets may contain inconsistent shadows or large exposure changes (DTU and BMVS) that are hard to model by our representation so we optionally train per-camera bias vectors in the MLP." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "text", + "content": "MVMannequins is a dataset of 14 dressed mannequins for multi-view reconstruction benchmarking with 68 cameras at " + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "inline_equation", + "content": "2048^{2}" + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "text", + "content": " resolution. We use the official evaluation code and report the metrics in table 1. We outperform all the baselines while taking only about a minute of training time, almost 3x faster than [27], with 5GB of VRAM, a rendering speed of " + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "inline_equation", + "content": "300\\mathrm{Hz}" + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "inline_equation", + "content": "400\\mathrm{Hz}" + }, + { + "bbox": [ + 55, + 570, + 295, + 652 + ], + "type": "text", + "content": " and a model size of 30MB." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "ActorsHQ is a multiview dataset of humans in motion with 160 cameras at a high resolution of " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "4088 \\times 2990" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": ". We evaluate on the 1000th temporal frame of 13 sequences. We compare against Voxurf [33] and NeuS2 [31], which we trained with half resolution images since we ran into issues" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": "with full resolution images. We report the PSNR in table 2 and show qualitative results in fig. 5. Voxurf takes about one hour to fully converge (with " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " the training iterations of the DTU configuration). NeuS2 converges fast but with a lower PSNR. In comparison, our method only takes " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "\\sim 4" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " minutes to converge on the full resolution images, and we also outperform both when training at the same resolution. This benchmark highlights the capability of our method to gracefully scale to high-resolution scenes." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 190, + 553, + 371 + ], + "blocks": [ + { + "bbox": [ + 316, + 190, + 553, + 371 + ], + "lines": [ + { + "bbox": [ + 316, + 190, + 553, + 371 + ], + "spans": [ + { + "bbox": [ + 316, + 190, + 553, + 371 + ], + "type": "image", + "image_path": "39cf5a02c63ca7ce393954b0baf9ba2cb9f9b84ff86abf51ea396ade50531227.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 372, + 553, + 521 + ], + "blocks": [ + { + "bbox": [ + 316, + 372, + 553, + 521 + ], + "lines": [ + { + "bbox": [ + 316, + 372, + 553, + 521 + ], + "spans": [ + { + "bbox": [ + 316, + 372, + 553, + 521 + ], + "type": "image", + "image_path": "3ee07766ddd3cf39740b317b7b0fb4153a46d381674e2e6aa2f2b04c8c4aa83c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 530, + 537, + 542 + ], + "lines": [ + { + "bbox": [ + 331, + 530, + 537, + 542 + ], + "spans": [ + { + "bbox": [ + 331, + 530, + 537, + 542 + ], + "type": "text", + "content": "Figure 5. High-resolution reconstructions for ActorsHQ." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "text", + "content": "DTU provides 49 to 64 images of various objects at " + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "inline_equation", + "content": "1600 \\times 1200" + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "text", + "content": " resolution, along with evaluation point clouds. We use the foreground masks provided by IDR [35] for training and testing. 2DGS [6] does not support masks for training so it uses complete images instead, cropped and at half resolution according to its evaluation protocol. We compare against Voxurf [33], Neus2 [31] and 2DGS [6] on DTU in table 3, using the official python script for geometric evaluation. We outperform all three in terms of chamfer distance and PSNR, twice as fast as NeuS2 on the same hardware. Rendering speed ranges from " + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "inline_equation", + "content": "200\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "inline_equation", + "content": "300\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 557, + 555, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "BlendedMVS. Finally, we test our method on 8 scenes of the BlendedMVS dataset [34] and report the metrics in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11031" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 97, + 70, + 512, + 118 + ], + "blocks": [ + { + "bbox": [ + 97, + 70, + 512, + 118 + ], + "lines": [ + { + "bbox": [ + 97, + 70, + 512, + 118 + ], + "spans": [ + { + "bbox": [ + 97, + 70, + 512, + 118 + ], + "type": "table", + "html": "
Metrics(4,4,4)X(8,8,4)XMMH [27]Voxurf [33]Neus2 [31]Colmap [26]2DGS [6]
Chamfer (mm)1.041.031.141.592.133.523.35
PSNR36.8136.9036.3335.5134.22-34.89
Training1min1min2-3min15min5min>1h>1h
", + "image_path": "777b401cf67313819f22c84be26af1b9dfd7b2138f9ce6c3f3ddba4a211519b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 167, + 299, + 229 + ], + "blocks": [ + { + "bbox": [ + 70, + 126, + 537, + 137 + ], + "lines": [ + { + "bbox": [ + 70, + 126, + 537, + 137 + ], + "spans": [ + { + "bbox": [ + 70, + 126, + 537, + 137 + ], + "type": "text", + "content": "Table 1. Evaluation on MVMannequins with two configurations for " + }, + { + "bbox": [ + 70, + 126, + 537, + 137 + ], + "type": "inline_equation", + "content": "\\left( {{n}_{s},{n}_{a},l}\\right)" + }, + { + "bbox": [ + 70, + 126, + 537, + 137 + ], + "type": "text", + "content": " . Per-camera bias vectors are not used (X-symbol)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 167, + 299, + 229 + ], + "lines": [ + { + "bbox": [ + 56, + 167, + 299, + 229 + ], + "spans": [ + { + "bbox": [ + 56, + 167, + 299, + 229 + ], + "type": "table", + "html": "
(ns,na,l) = (4,4,4)XVoxurfNeuS2
Resolutionr/1r/2r/4r/2r/2
PSNR37.4836.6234.7436.5634.53
Training250s110s53s1h250s
Model size232MB57MB15MB500MB25MB
", + "image_path": "7dff7dde10247f985c12f468ad6dc9c92691718022c5bef6c46fb4c10137f2ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 56, + 300, + 307, + 361 + ], + "blocks": [ + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "lines": [ + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": "Table 2. Evaluation for ActorsHQ. Per-camera bias vectors are not used (" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": "-symbol). Full, half and quarter-resolution input images are denoted as " + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "inline_equation", + "content": "r/1" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "inline_equation", + "content": "r/2" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "inline_equation", + "content": "r/4" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": " respectively. Renderings are up-scaled before comparison with the full resolution images " + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "inline_equation", + "content": "(4088 \\times 2990)" + }, + { + "bbox": [ + 55, + 238, + 296, + 282 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 300, + 307, + 361 + ], + "lines": [ + { + "bbox": [ + 56, + 300, + 307, + 361 + ], + "spans": [ + { + "bbox": [ + 56, + 300, + 307, + 361 + ], + "type": "table", + "html": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus22DGS
Chamfer0.680.710.730.800.76
PSNR37.0337.7437.083636.03
Training150s160s15min5min12min
Model size56MB88MB500MB25MB49MB
", + "image_path": "1a8e96d54512e620c59cafeaa9eaaf90fceb5e8064684cd206ad3d8c906f3228.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 73, + 402, + 278, + 453 + ], + "blocks": [ + { + "bbox": [ + 55, + 369, + 294, + 392 + ], + "lines": [ + { + "bbox": [ + 55, + 369, + 294, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 294, + 392 + ], + "type": "text", + "content": "Table 3. DTU evaluation with two configurations for " + }, + { + "bbox": [ + 55, + 369, + 294, + 392 + ], + "type": "inline_equation", + "content": "\\left( {{n}_{s},{n}_{a},l}\\right)" + }, + { + "bbox": [ + 55, + 369, + 294, + 392 + ], + "type": "text", + "content": " . Per-camera bias vectors are used (✓-symbol)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 402, + 278, + 453 + ], + "lines": [ + { + "bbox": [ + 73, + 402, + 278, + 453 + ], + "spans": [ + { + "bbox": [ + 73, + 402, + 278, + 453 + ], + "type": "table", + "html": "
Metrics(4,4,4)✓(8,8,4)✓VoxurfNeus2
Chamfer2.372.222.642.93
PSNR35.1935.8935.1133.62
Training110s120s15min5min
", + "image_path": "cbbd618c1b628d21a1871f2a43dff9d2c95218567c8be35ff1a2e6be309da69b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 527, + 295, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 527, + 295, + 599 + ], + "spans": [ + { + "bbox": [ + 55, + 527, + 295, + 599 + ], + "type": "text", + "content": "table 4. The BlendedMVS is a semi-synthetic dataset were objects have been first reconstructed then reprojected in the images in order to produce reliable ground truth geometry and masks. There is no official script for geometric evaluation so we measure two-ways point to mesh distances in the reference frame used for training in [30], scaled by " + }, + { + "bbox": [ + 55, + 527, + 295, + 599 + ], + "type": "inline_equation", + "content": "1000\\mathrm{x}" + }, + { + "bbox": [ + 55, + 527, + 295, + 599 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "Ablations. We ablate the probes smoothing and the polynomial approximation of the Fresnel term in tab. 5 on the MVMannequins dataset by imposing " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\cdot \\mathbf{v} = 1" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " in eq. 4 during training, with noticeable incidence on Chamfer error. A visual ablation of the components of our parametrization is presented in fig. 8 on the kino/jea mannequin, clearly showing the role of each parameter group. Figure 9 contains more examples. Various choices of configurations are compared in table 6 on the BlendedMVS dataset." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 165, + 554, + 442 + ], + "blocks": [ + { + "bbox": [ + 313, + 165, + 554, + 442 + ], + "lines": [ + { + "bbox": [ + 313, + 165, + 554, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 165, + 554, + 442 + ], + "type": "image", + "image_path": "4f5a3a2455dff7b84bc9cad531116ba4f215606ea8b5c69cb14384b2831714bc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 450, + 544, + 462 + ], + "lines": [ + { + "bbox": [ + 324, + 450, + 544, + 462 + ], + "spans": [ + { + "bbox": [ + 324, + 450, + 544, + 462 + ], + "type": "text", + "content": "Figure 6. Reconstructions on challenging examples of DTU." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 329, + 476, + 540, + 503 + ], + "blocks": [ + { + "bbox": [ + 55, + 460, + 294, + 483 + ], + "lines": [ + { + "bbox": [ + 55, + 460, + 294, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 294, + 483 + ], + "type": "text", + "content": "Table 4. BMVS evaluation with two configurations for " + }, + { + "bbox": [ + 55, + 460, + 294, + 483 + ], + "type": "inline_equation", + "content": "\\left( {{n}_{s},{n}_{a},l}\\right)" + }, + { + "bbox": [ + 55, + 460, + 294, + 483 + ], + "type": "text", + "content": " . Per-camera bias vectors are used (✓-symbol)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 476, + 540, + 503 + ], + "lines": [ + { + "bbox": [ + 329, + 476, + 540, + 503 + ], + "spans": [ + { + "bbox": [ + 329, + 476, + 540, + 503 + ], + "type": "table", + "html": "
(4,4,4)Xw/o probes smoothingw/o Fresnel
Chamfer (mm)1.041.091.18
PSNR36.8136.9136.79
", + "image_path": "d50d312a18dd8425b22968db20d0ed86e633ea977559d155646ab1d371fe641c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 315, + 533, + 553, + 559 + ], + "blocks": [ + { + "bbox": [ + 370, + 512, + 497, + 523 + ], + "lines": [ + { + "bbox": [ + 370, + 512, + 497, + 523 + ], + "spans": [ + { + "bbox": [ + 370, + 512, + 497, + 523 + ], + "type": "text", + "content": "Table 5. Ablation on MVMannequins" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 533, + 553, + 559 + ], + "lines": [ + { + "bbox": [ + 315, + 533, + 553, + 559 + ], + "spans": [ + { + "bbox": [ + 315, + 533, + 553, + 559 + ], + "type": "table", + "html": "
Metrics(4,4,4)X(4,4,4)Y(8,8,4)√(12,12,4)√(4,4,1)√(4,4,2)√(4,4,3)√
Chamfer2.472.372.222.312.582.342.37
PSNR34.7635.1935.8936.1734.4434.8635.05
", + "image_path": "879e9b99b175d1f9115a9fd752c2010c20d9de22fed231cd5115e71bf74cacc5.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "lines": [ + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": "Table 6. We ablate the number of spatial features " + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "inline_equation", + "content": "n_s" + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": ", angular features " + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "inline_equation", + "content": "n_a" + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": " and spherical harmonics order " + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": " on BlendedMVS. Each triplet denotes a configuration " + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "inline_equation", + "content": "(n_s, n_a, l)" + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 313, + 566, + 554, + 611 + ], + "type": "text", + "content": "-symbol indicates when per-camera bias vectors are trained." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 643, + 389, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 643, + 389, + 656 + ], + "spans": [ + { + "bbox": [ + 313, + 643, + 389, + 656 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "content": "We identify several limitations to our approach. First, the fact that the lighting is encoded locally can degrade the extrapolation capabilities compared to modeling the environment with a global representation. This becomes appar" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11032" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 294, + 293 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 294, + 293 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 294, + 293 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 294, + 293 + ], + "type": "image", + "image_path": "640b930eea7e84d7a965f5dd7d665765845086cc30a160cc6e305ef8a106e75e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 301, + 273, + 312 + ], + "lines": [ + { + "bbox": [ + 77, + 301, + 273, + 312 + ], + "spans": [ + { + "bbox": [ + 77, + 301, + 273, + 312 + ], + "type": "text", + "content": "Figure 7. Reconstructed examples on BlendedMVS." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 57, + 326, + 294, + 472 + ], + "blocks": [ + { + "bbox": [ + 57, + 326, + 294, + 472 + ], + "lines": [ + { + "bbox": [ + 57, + 326, + 294, + 472 + ], + "spans": [ + { + "bbox": [ + 57, + 326, + 294, + 472 + ], + "type": "image", + "image_path": "75e4fbe567e4be83399a9de27bcb214dfebe374a4a40ba4f1b1c5d634ee04587.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "lines": [ + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "text", + "content": "Figure 8. Our model can be intuitively explained. We disable some components of a pre-trained example from the MVMannequins dataset [27] (left). From left to right, we remove the spatial features (set " + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s = 0" + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "text", + "content": "), only keep the constant coefficient of the SH basis (" + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "text", + "content": "), disable the incidence angle embedding (set " + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\cdot \\mathbf{v} = 1" + }, + { + "bbox": [ + 55, + 482, + 296, + 571 + ], + "type": "text", + "content": " in eq. 4). The learned Fresnel term encodes grazing reflections (red circles), the angular features provide the shading (green squares) and the spatial features contain the high frequency details." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "ent on the ActorsHQ dataset where there is a good overlap of the cameras field of views along the longitude, but very little overlap along the latitude on the legs. This creates shadows artifacts when looking from above or below rather that at a level angle. Second, although our decomposition is physically-inspired, we do not explicitly simulate light transport which can result in local minima due to shape-radiance ambiguities. Relighting and/or material editing is not supported but fine-tuning the probes to new lighting seems possible and worthy of future investigations." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 553, + 273 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 553, + 273 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 553, + 273 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 553, + 273 + ], + "type": "image", + "image_path": "6c2bb73b2cd549ee7a4ad3cb3cd923b38fdf80d6d9db6affb6c2da389a389577.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "type": "text", + "content": "Figure 9. Effect of the learned Fresnel term on three examples from MVMannequins, DTU and ActorsHQ. Left to right: input image, volume rendering (A), volume rendering w/o the Fresnel term (B) (we set " + }, + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{n}\\cdot \\mathbf{v} = 1" + }, + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "type": "text", + "content": " in eq. 4), difference image " + }, + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "type": "inline_equation", + "content": "(4\\times |A - B|)" + }, + { + "bbox": [ + 313, + 281, + 555, + 326 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 346, + 479, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 479, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 479, + 359 + ], + "type": "text", + "content": "7. Conclusion and Future Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 368, + 555, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 368, + 555, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 368, + 555, + 571 + ], + "type": "text", + "content": "We have presented a novel approach to model the view dependent appearance, enabling both fast reconstruction and real-time rendering of humans and objects. Notably, our model does not compromise on geometric and photometric quality, even surpassing the previous approaches in many instances. It can easily scale to high resolution inputs while maintaining high performance. We have reached a parsimonious parametrization of the surface properties thanks to a simple formulation. Disentangling the spatial and angular components with high efficiency also offers promising future avenues of research toward temporal reconstruction. Other future research can build on this work, e.g. handling high frequency reflections at a lower cost than current dedicated approaches and unifying neural rendering and physically-based rendering. Other embeddings of the angular dependency representations can be investigated, such as cubemaps or mixtures of spherical gaussians." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 585, + 423, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 585, + 423, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 585, + 423, + 598 + ], + "type": "text", + "content": "8. Acknowledgments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 712 + ], + "type": "text", + "content": "This work was supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) grant ANR-21-ESRE-0030 (CONTINUUM). Research conducted at Kyushu University was supported by JSPS/KAKENHI JP23H03439 and AMED JP24wm0625404. We thank Laurence Boissieux for her valuable help generating 3D renderings, and Edmond Boyer for insightful discussions and comments." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11033" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "text", + "content": "[1] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. 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These abilities emerge with minimal supervision during the early stages of human visual development. Despite their significance, current self-supervised learning (SSL) approaches are primarily designed and evaluated for high-level recognition tasks, leaving their mid-level vision capabilities largely unexamined.", + "bbox": [ + 88, + 282, + 482, + 434 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this study, we introduce a suite of benchmark protocols to systematically assess mid-level vision capabilities and present a comprehensive, controlled evaluation of 22 prominent SSL models across 8 mid-level vision tasks. Our experiments reveal a weak correlation between mid-level and high-level task performance. We also identify several SSL methods with highly imbalanced performance across mid-level and high-level capabilities, as well as some that excel in both. Additionally, we investigate key factors contributing to mid-level vision performance, such as pretraining objectives and network architectures. Our study provides a holistic and timely view of what SSL models have learned, complementing existing research that primarily focuses on high-level vision tasks. We hope our findings guide future SSL research to benchmark models not only on high-level vision tasks but on mid-level as well.", + "bbox": [ + 89, + 435, + 483, + 675 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 693, + 220, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mid-level vision capabilities [41] (Fig. 1a) play a vital role in human visual development and daily life activities. By the age of one, children can re-organize retinal images into objects (i.e., perceptual grouping), construct the visual world in three dimensions (i.e., 3D geometric understanding), track moving objects (i.e., cross-view correspondence), grasp and bite these objects without knowing their semantics, and purposefully navigate through the 3D world. Importantly, such mid-level perception is developed without supervision [32].", + "bbox": [ + 89, + 718, + 482, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the other hand, self-supervised learning (SSL) in computer vision has made significant strides [5-8, 25, 42,", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/36b0239bc536d9193363ae202a6a5bed217c8fa32f4e4a726e8cdc34c897266a.jpg", + "image_caption": [ + "Generic Object Seg" + ], + "image_footnote": [], + "bbox": [ + 516, + 250, + 589, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0e65aa87559799e2fbe1b31116aac1ac6474d43c10898cd8377d7e5e3adb43b.jpg", + "image_caption": [ + "Depth Estimation" + ], + "image_footnote": [], + "bbox": [ + 589, + 250, + 661, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb89f0418692726bd48b18967bb3e68c060579b275ba8de791a063b0faca8e2b.jpg", + "image_caption": [ + "Surface Normal" + ], + "image_footnote": [], + "bbox": [ + 661, + 250, + 733, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f4f2cdd33e93fcab5b70cb4cb6ccfb1b1087881fac970b2252c7e8fd6380bea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 250, + 808, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/874bcc34c2dc3b15983927414c6af19892a600d7fd556ce5637c72647ed5c7f1.jpg", + "image_caption": [ + "Input", + "3D Geometric Correspondence" + ], + "image_footnote": [], + "bbox": [ + 516, + 321, + 589, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a8df851d534fdf5a4bec1f6c72b6a7d935fa4e7352b6426a38141c9b09fb7c7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 589, + 321, + 661, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Correspondence:", + "bbox": [ + 596, + 378, + 645, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/985f8b1aeef683dc67e621fd25218555d16967c6e3f2a82a720e830c890e0129.jpg", + "image_caption": [ + "Image Similarity" + ], + "image_footnote": [], + "bbox": [ + 661, + 321, + 733, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a13317ebe94ead3099e5af3e2af93ea2a0bd3bdfef3c676aecd1d46053e1ed0d.jpg", + "image_caption": [ + "Classification & Detection" + ], + "image_footnote": [], + "bbox": [ + 735, + 321, + 808, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 516, + 402, + 705, + 522 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ec78c3116e3b97d45120eb785a6e831bcece59cee47d7097aa7af6ce201c9724.jpg", + "image_caption": [ + "RotNet", + "NPID", + "SeLa-v", + "NPID+", + "PIRL", + "(c) SSLs for mid-level and high-level vision w.r.t. ImageNet classification", + "Figure 1. Mid-Level Vision vs. High-Level Vision Tasks. We provide a comprehensive evaluation of prominent self-supervised learning methods (SSLs) across a wide range of mid-level vision tasks (a), complementing the standard evaluation in high-level vision tasks (b). Although SSL performance in mid-level vision tasks (e.g., depth estimation) is positively correlated with ImageNet linear probing, this correlation is much weaker than that observed among high-level vision tasks, as shown in (c) by the $R^2$ statistics." + ], + "image_footnote": [], + "bbox": [ + 527, + 525, + 576, + 534 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48b112a3ffd212baa75a8f271b9056fc9783f1368c69d92134291bdce59f426c.jpg", + "image_caption": [ + "DeepCI", + "SwAV", + "SimCLR", + "MoCo v2", + "SimSiam" + ], + "image_footnote": [], + "bbox": [ + 598, + 525, + 653, + 534 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f5d6985b26ce70ae242e2dd6210dabe697c97aeb810e90371e9b281923aabe0.jpg", + "image_caption": [ + "r-v2 Barlo", + "DenseCL", + "DINO", + "MoCo v3 (RN-50)", + "Barlow Twins", + "DenseCL", + "DINO (RN-50)" + ], + "image_footnote": [], + "bbox": [ + 661, + 525, + 733, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 790, + 525, + 872, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "iBOT", + "bbox": [ + 790, + 535, + 834, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MoCo v3 (ViT-B/16)", + "bbox": [ + 790, + 542, + 883, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MAE", + "bbox": [ + 790, + 553, + 833, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "45, 46, 66, 71]. The goal of SSL is to learn visual representations from unlabeled data so that these pretrained representations can be applied to a wide range of downstream tasks, reducing the need for human annotations and enhancing learning efficiency and performance. However, SSL is predominantly evaluated based on performance in high-level visual recognition tasks, such as image classification, object detection, and semantic segmentation (Fig. 1b). At the same time, the mid-level vision capabilities of SSL models are largely under-explored. To fill this gap, this pa", + "bbox": [ + 511, + 750, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c6d97088c3e6e069e8e9fd43caef709bc988aa989971af63e70713b05bc5d6f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 820, + 251, + 895, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7abcecf034b59ae93fbb2608e677635f8630cb79ead35c805463707508bc5e7f.jpg", + "image_caption": [ + "Semantic Seg." + ], + "image_footnote": [], + "bbox": [ + 820, + 321, + 895, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Classification & Detection", + "bbox": [ + 799, + 380, + 898, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eabe40bb5032ca094bb21a57911d3d6815f002322675453d914e566940174070.jpg", + "image_caption": [ + "(a) Mid-level vision" + ], + "image_footnote": [], + "bbox": [ + 516, + 402, + 707, + 522 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/369ffc6d86d23ca3c462ab0cb014d191f8b877d581e09837096fc8ef77955c4d.jpg", + "image_caption": [ + "- - MaskFeat", + "(b) High-level vision" + ], + "image_footnote": [], + "bbox": [ + 712, + 402, + 903, + 522 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c77d81b7ede8ef2e7bb46609554f362cee3c42bfd21b83d28c810395f19f1516.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 523, + 735, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MoCo v3 (RN-50)", + "bbox": [ + 712, + 561, + 774, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 790, + 525, + 872, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "iBOT", + "bbox": [ + 790, + 535, + 834, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MoCo v3 (ViT-B/16)", + "bbox": [ + 790, + 542, + 883, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MAE", + "bbox": [ + 790, + 553, + 833, + 561 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "30095", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "per addresses the following questions:", + "bbox": [ + 89, + 90, + 344, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Does strong high-level vision performance of SSLs indicate strong mid-level vision capabilities?", + "- What makes an SSL model effective for mid-level vision tasks?" + ], + "bbox": [ + 89, + 108, + 482, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To answer these questions, we comprehensively evaluate SSLs in a wide range of mid-level vision tasks, including generic object segmentation, monocular depth and surface normal estimation, geometric correspondence, and mid-level image similarity (Fig. 1a and Tab. 2). We then relate the mid-level vision performance of these SSLs to their high-level vision performance. Our evaluations covers 22 seminar SSL approaches (Tab. 1) from diverse categories developed in the past decades (e.g. pretext tasks [25, 45], contrastive learning [6, 7, 9, 27, 66], self-distillation [5], and generative modeling [30, 62]). To make a controlled study and fair comparisons across different SSLs, our study primarily focuses on SSLs with publicly available checkpoints pretrained on ImageNet1K [12]. This allows us to gain insights into what factors may contribute to the mid-level vision capabilities in SSL (e.g., training objectives, network architectures, etc.).", + "bbox": [ + 89, + 170, + 482, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our observations are as follows:", + "bbox": [ + 109, + 428, + 325, + 441 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The mid-level vision capabilities of SSLs are positively correlated with high-level vision. However, that correlation is generally weaker than that among high-level vision tasks (Fig. 1c and Fig. 2).", + "- Some SSLs have highly imbalanced mid-level and high-level vision capabilities. For instance, MAE [31] underperforms most SSLs in the mid-level vision tasks while having competitive high-level vision performance; MaskFeat [62] has better mid-level performance than most SSLs with similar high-level vision (Fig. 5).", + "- Network architectures, model capacity, and pretraining strategies impact mid-level vision capabilities. In general, ViT [14] outperforms ResNet [28]; Increasing the network capacity is beneficial (Tab. 3); The leading methods are generally based on generative modeling (Fig. 5)." + ], + "bbox": [ + 89, + 444, + 482, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our study is built upon Probe3D [17], a recent work that evaluates the 3D awareness of visual models. In this work, we explore a broader range of mid-level vision tasks. Furthermore, our study primarily focuses on SSLs pretrained exclusively on ImageNet1K, while Probe3D probes visual foundation models that are trained from very diverse training configurations such as varying supervision signals (e.g. CLIP [50]) and dataset sizes. Our controlled settings allow us to gain insights into the factors contributing to model performance. Our exploration is also closely related to prior works that benchmark SSLs in various vision tasks [18, 26, 44, 55], such as out-of-domain classification [40] and fine-grained recognition [54, 57]. Unlike these works, our evaluation includes more recent SSLs, providing a timely study on this topic.", + "bbox": [ + 89, + 674, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our study offers a comprehensive view of the representations learned by SSL models. We hope these findings inspire practical approaches that perform well across both mid-level and high-level vision tasks. We will release our benchmark suite to support future SSL benchmarking in the research community.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 196, + 653, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-Supervised Learning (SSL). The goal of self-supervised learning (SSL) in computer vision is to pretrain image representations using unlabeled data, enabling these representations to be transferred effectively to various downstream tasks. Early SSL methods leveraged a range of pretext tasks, such as colorization [70], rotation prediction [25], jigsaw puzzle solving [45], and inpainting [47]. Recent advances have focused on contrastive learning [6, 7, 27, 29, 66, 69] and generative modeling [13, 31, 37, 48, 62]. Despite extensive research, SSL performance is primarily evaluated on high-level vision tasks (e.g., ImageNet classification, object detection), overlooking the practical relevance of mid-level vision tasks. In this work, we focus on evaluating SSL methods on mid-level vision tasks.", + "bbox": [ + 511, + 220, + 906, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-Supervised Pretraining for 3D Vision. Unlike most SSL methods focusing on 2D visual recognition tasks, a few recent works explore SSLs for 3D vision. For example, CroCo [63] adopts masked image modeling to learn 3D representations from image pairs showing the same scene from different viewpoints. Despite the improvement in downstream 3D vision tasks, CroCo compromises high-level recognition performance. As a followup, CroCo-v2 [64] extends the training data of CroCo to a large dataset of natural images and demonstrates improved performance in downstream optical flow and stereo vision tasks. However, learning representations for 3D vision tasks remains under-explored.", + "bbox": [ + 511, + 440, + 908, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Benchmarking Self-Supervised Learning. Numerous studies underscore the growing importance of empirically evaluating general-purpose representation learning. For example, Goyal et al. [26] provide extensive benchmarking of SSLs across multiple downstream tasks, including classification, navigation, object detection, and surface normal estimation. Newell et al. [44] examine the effectiveness of SSLs under various configurations (e.g., annotation quantities) in downstream tasks such as pose estimation and depth estimation. Ericsson et al. [18] evaluate 13 SSLs across 40 downstream vision tasks, demonstrating a weak correlation between SSL performance on ImageNet classification and tasks like few-shot learning, object detection, and dense prediction. More recently, Marks et al. [40] studied how classification-based SSL evaluation protocols correlate with and predict downstream performance on out-of-domain datasets. In line with these works, we comprehen", + "bbox": [ + 511, + 643, + 908, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "30096", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sively evaluate existing SSLs across various downstream tasks. We focus on mid-level vision performance and how it relates to high-level vision.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Benchmarking Visual Foundation Models. More recently, several studies have evaluated large visual foundation models (VFMs) that are not exclusively trained by self-supervised learning methods (e.g., CLIP [50]). For example, Probe3D [17] examines the 3D awareness of VFMs [5, 34], while Cambrian-1 [55] utilizes large language models (LLMs) and visual instruction tuning to assess visual representations across various 2D and 3D vision tasks. Since VFMs are typically trained with diverse approaches (e.g., different supervision signals, datasets, and architectures), isolating the factors contributing to the performance of the representations they learn is challenging. In contrast, we conduct a controlled evaluation of SSL models that provide publicly available checkpoints pretrained on ImageNet1K. This approach enables fair comparisons across SSLs and offers deeper insights into their methodologies.", + "bbox": [ + 91, + 161, + 482, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background: Vision Task Taxonomy", + "text_level": 1, + "bbox": [ + 89, + 436, + 419, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There exist numerous computer vision tasks [68] which can be categorized from different perspectives. We briefly introduce two popular frameworks in this section:", + "bbox": [ + 89, + 462, + 482, + 508 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Bottom-up Hierarchical Vision. David Marr [41] proposes to break up the vision system into low-level, mid-level, and high-level stages. Low-level vision tasks aim to extract edges, contours, and blobs from raw pixels, while high-level vision concerns the semantics, functionality, and holistic 3D shape of objects. Mid-level vision, lying in-between the low-level and high-level vision, addresses the view-centric geometric properties of surfaces (e.g., depth and surface normal), generic object segmentation and localization without semantics, cross-view image correspondences, and so on. This framework favors a feed-forward and bottom-up vision process.", + "- Three R's of Vision. Malik et al. [39] categorize vision tasks into recognition, reconstruction, and reorganization. Recognition refers to the task of assigning semantic categories to images. Reconstruction concerns the estimation of 3D structures. Reorganization addresses the grouping and segmentation of images on spatial or perceptual similarity. Instead of a bottom-up process, 3R's emphasizes the mutual benefits and relationship across these three visual capabilities." + ], + "bbox": [ + 89, + 513, + 482, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Both frameworks highlight the importance of the nonsemantic vision tasks — mid-level vision in Marr's framework, reconstruction and reorganization in 3R's. We adopt the term \"mid-level\" for the convenience of differentiating", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from high-level recognition tasks. However, the underlying vision mechanism remains under debate.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Experimental Setup", + "text_level": 1, + "bbox": [ + 511, + 140, + 705, + 159 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce the SSLs considered in this work (Tab. 1) and our generic evaluation protocols for probing these SSLs. We then present the mid-level vision tasks in detail, including their definitions, datasets, and evaluation approaches (Sec. 4.1- 4.3 and Tab. 2).", + "bbox": [ + 511, + 167, + 903, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our probing approaches are largely inspired by Probe3D [17], the recent work that evaluates the 3D awareness of visual foundation models (VFMs). The VFMs are usually trained under distinct settings (e.g. supervision signals, dataset sizes, network architectures and capacity), while we aim at probing self-supervised visual models that are trained with similar configurations. Therefore, our work provides a complementary study, specifically a more controlled setting, compared to Probe3D [17].", + "bbox": [ + 511, + 246, + 906, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Supervised Models. Tab. 1 presents an overview of the SSL models considered in our study. We primarily focus on SSLs that have publicly available checkpoints pretrained on ImageNet1K [12], with standard neural network architectures (e.g. ResNet50 [28] or Vision Transformers (ViT) [14]) as the image feature extractor. These SSLs cover a wide range of pretraining strategies, including clustering, contrastive learning, generative modeling, or a mixture of different training objectives. Targeting a comprehensive benchmark, we track the SSL literature back to classic methods that learn image representations from pre-text tasks such as Jigsaw [45] and RotNet [25]. Our selection of SSLs is inspired by Marks et al. [40], which provides a detailed study of the evaluation protocols of SSLs.", + "bbox": [ + 511, + 398, + 906, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generic Evaluation Protocols. Many mid-level vision tasks can be formulated as dense prediction (e.g., depth estimation). Unlike image classification, dense prediction requires local pixel or patch representations as input, and the main design choice is to decide which network layers (e.g., ResNet layers or ViT blocks) to extract the dense features from. Following Probe3D, we use the DPT decoder [52], a non-linear dense multi-scale network. For ResNet [28], we use the outputs of the last four ResNet blocks as the input to the DPT head, following the architecture of the feature pyramid network [36]; For ViT [14], following Probe3D, the network is split into four blocks evenly, and the features are extracted after each block — for ViT-B, we extract features after layers 3, 6, 9, and 12. Like Probe3D, we probe the frozen representations to evaluate the capabilities of learned representations instead of their transferability. We provide task-specific evaluation protocols in the following sections and hyperparameter settings in the supplementary material.", + "bbox": [ + 511, + 628, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "30097", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/9d6607b2ec83e4c8d4216055a2e543f9bb6ab863c836505b75d5f11b29780c1a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IDSSLArchitectureCategory
1Jigsaw [45]ResNet50Pre-text
2RotNet [25]ResNet50Pre-text
3NPID [66]ResNet50Contrastive
4NPID++ [42]ResNet50Contrastive
5PIRL [42]ResNet50Contrastive
6ClusterFit [67]ResNet50Clustering
7SwAV [4]ResNet50Clustering
8SeLa-v2 [4]ResNet50Clustering
9DeepCluster-v2 [4]ResNet50Clustering
10SimCLR [6]ResNet50Contrastive
11MoCo-v2 [8]ResNet50Contrastive
12SimSiam [7]ResNet50Contrastive
13DenseCL [58]ResNet50Contrastive
14BYOL [27]ResNet50Contrastive
15Barlow Twins [69]ResNet50Contrastive
16MoCo-v3 [9]ResNet50Contrastive
17DINO [5]ResNet50Self-distillation
18MoCo-v3 [9]ViT-B/16Contrastive
19DINO [5]ViT-B/16Self-distillation
20MAE [31]ViT-B/16Generative
21iBOT [71]ViT-B/16Mixture
22MaskFeat [62]ViT-B/16Generative
", + "bbox": [ + 99, + 88, + 475, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Evaluated Self-Supervised Learning Methods (SSLs). We provide a comprehensive evaluation of SSLs that provide publicly available checkpoints trained from the ImageNet1K dataset [12]. We categorize SSLs based on their training objectives and network backbones. Mixture denotes the combination of different SSLs (e.g., iBOT [71]). The SSLs are listed in order of their publication year.", + "bbox": [ + 89, + 440, + 483, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Generic Object Segmentation", + "text_level": 1, + "bbox": [ + 89, + 566, + 354, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generic object segmentation (or figure-ground segmentation) refers to the task of separating objects (figure) from the surrounding background without any semantics. This mid-level vision task is different from semantic segmentation (i.e., assigning each pixel to a semantic category) which is commonly used for evaluating the high-level visual capabilities of SSLs.", + "bbox": [ + 89, + 590, + 482, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the VOC07 and VOC12 datasets [19, 20] as our benchmarks, following prior research on unsupervised object segmentation [56, 59, 61]. Given a pretrained feature extractor, we freeze the backbone and train a DPT decoder [51] with a simple binary cross-entropy loss (BCE). We use standard segmentation metrics (e.g., mean IoU) to measure the performance of SSLs in this task.", + "bbox": [ + 89, + 696, + 482, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Monocular Surface Reconstruction", + "text_level": 1, + "bbox": [ + 89, + 816, + 397, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate SSLs in two tasks related to monocular 2.5D surface reconstruction: depth and surface normal estimation from Probe3D [17]. Even though these two tasks are closely related, they rely on different visual cues and cap", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ture distinct geometric properties.", + "bbox": [ + 511, + 92, + 740, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate depth estimation and surface normal prediction at both scene and object levels. For scene-level performance, we employ the NYUv2 dataset [43], a widely used benchmark for indoor environments. Object-level depth is assessed using the NAVI dataset [33], which provides diverse object instances across scenes and orientations.", + "bbox": [ + 511, + 106, + 903, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present the task-specific configurations as follows.", + "bbox": [ + 532, + 196, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Monocular Depth Estimation The task aims at predicting pixel-wise depth from monocular images. We adopt the formulation of binned depth estimation from AdaBins [21], instead of the classical regression approaches [15]. We estimate the scale-invariant depth for object-centric images (e.g., NAVI) while predict metric depths on scene-centric datasets (e.g., NYUv2). We report root-mean-squared error (RMSE) and recall at various threshold ratios.", + "bbox": [ + 511, + 217, + 905, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Surface Normal Estimation. This task is to predict per-pixel surface direction. We train the DPT head with the uncertainty-aware angular loss [2]. As for depth estimation, we report RMSE and percentage recall at various angular thresholds.", + "bbox": [ + 511, + 344, + 905, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Multiview Correspondence", + "text_level": 1, + "bbox": [ + 513, + 429, + 756, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we consider the tasks of estimating correspondences across multiple views that involve mid-level variations, such as changes in camera perspective and object motion. These mid-level variations differ from low-level variations in image properties (e.g., color and texture) and high-level variations in semantic attributes (e.g., object categories). Specifically, we probe SSLs in two tasks: geometric correspondence and mid-level image similarity. Following Probe3D [17], we extract image or pixel representations from pretrained SSLs model without additional training.", + "bbox": [ + 511, + 450, + 906, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Geometric Correspondence This task aims to build pixel correspondences across two views that depict the same 3D scene. Our evaluation follows Probe3D [17]. Specifically, we estimate the pixel correspondences using the dense feature maps extracted from pretrained SSL models. We use the Paired ScanNet [10] to evaluate scene-centric images and the NAVI dataset [33] for object-centric images. We sample views with a maximum rotation of 120 degrees to ensure that a mutually visible surface exists without a large viewpoint change. We report the correspondence recall — the percentage of correspondence that falls within some defined distance.", + "bbox": [ + 511, + 607, + 905, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mid-Level Image Similarity The task aims at measuring the similarity of two images with mid-level variations (e.g., viewpoint). We evaluate the SSLs on the NIGHTS dataset collected by DreamSim [23]. Specifically, for each triplets $(x, \\tilde{x}_0, \\tilde{x}_1)$ from the NIGHTS dataset, we predict whether $\\tilde{x}_0$ or $\\tilde{x}_1$ is more similar to the reference image $x$ . We denote a distance between two images as $D(x, \\tilde{x}; f_\\theta) =$", + "bbox": [ + 511, + 794, + 905, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "30098", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/61f9fbbbd85b31a6b872b54d3c2d280ba54bf754dcaf488c7e9ee5632740bd09.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
HierarchyTasksTypeBenchmarksLossesMetrics
High-levelImage Classification2DImageNet1K [53]CEAccuracy
Object Detection2DVOC07 [19], COCO [35]CE+L2AP
Semantic Segmentation2DCOCO [35]CEmIOU
Mid-levelGeneric Object Segmentation2DVOC07 [19], VOC12 [20]BCEF1, mIoU, Acc
Depth Prediction3DNAVI [33], NYU [43]AdaBinRMSE, ε1, ε2, ε3
Surface Normal Estimation3DNAVI [33], NYU [43]AngularRMSE, ε1, ε2, ε3
Geometric Correspondence3DNAVI [33], ScanNet [11]Training-free2D, 3D Recall
Mid-level Image Similarity2DNIGHTS [24]Training-freeRetrieval Score (F1-Score)
", + "bbox": [ + 109, + 88, + 890, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Probing Tasks. In comparison with the standard SSL evaluation protocols that primarily focus on high-level vision tasks (top), we provide a comprehensive, systematic, and controlled evaluation of SSL in mid-level vision tasks (bottom). Our evaluations cover 2D and 3D vision with a wide range of benchmarks. The $\\epsilon_{1}$ , $\\epsilon_{2}$ and $\\epsilon_{3}$ in depth and surface normal estimation represents recall at different threshold rations [16, 22]. Detailed descriptions of each metric can be found in the supplementary.", + "bbox": [ + 89, + 246, + 906, + 303 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4d68657de68262b76a2a508915e0f61aefd2c44e04777c7bddfd4f125df5276d.jpg", + "image_caption": [ + "Figure 2. Mid-Level Vision v.s. ImageNet Linear Probing. We report the performance of self-supervised learning methods on mid-level vision tasks (y-axis) against their ImageNet 1K linear classification accuracy. Metrics are detailed in Tab. 2. Linear regression shows correlation with $R^2$ in each plot's top-left corner, and the red shaded area marks the $95\\%$ confidence interval." + ], + "image_footnote": [], + "bbox": [ + 94, + 314, + 906, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$1 - \\cos \\bigl (f_{\\theta}(x),f_{\\theta}(\\tilde{x})\\bigr)$ where $f_{\\theta}$ is the image representations from pretrained SSLs. For ViT, we use the CLS tokens taken from the last layer; For ResNet, we use the global image representation in the output layer. The model's vote is calculated as follows: if $d_1 < d_0$ , then $\\hat{y} = 1$ ; otherwise, if $d_0 < d_1$ , then $\\hat{y} = 0$ , where $d_0 = D(x,\\tilde{x}_0;f_\\theta)$ and $d_{1} = D(x,\\tilde{x}_{1};f_{\\theta})$ . We use voting accuracy as our evaluation metric.", + "bbox": [ + 89, + 675, + 482, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Analysis", + "text_level": 1, + "bbox": [ + 89, + 808, + 187, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Does strong high-level performance imply strong mid-level performance?", + "text_level": 1, + "bbox": [ + 89, + 833, + 482, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Yes, to some extent. As ImageNet (IN1k) probing results improve, we generally observe a corresponding enhance-", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ment in mid-level vision tasks, as depicted in Fig. 2. This positive trend indicates that SSL models capable of high-level visual recognition tend to provide better representations for mid-level vision tasks as well, benefiting tasks that leverage spatial and structural information.", + "bbox": [ + 511, + 675, + 906, + 751 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Some mid-level tasks are highly correlated with high-level. A per-task closer examination, however, reveals nuances in this relationship. For example, generic object segmentation shows the highest correlation with high-level tasks, achieving a coefficient of determination $(R^2 = 0.70)$ . This suggests that high-level features indeed capture spatial structures that enhance segmentation accuracy. Mid-level and high-level vision also correlate highly in the task", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "30099", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ce8e65d923a5b56d8e2fa40490a2c5765b8cfc204a5de46df2509149689efe43.jpg", + "image_caption": [ + "Figure 3. Cross-task performance correlation. We present Pearson coefficients across mid-level and high-level vision tasks. We use the same set of metrics we used in Fig. 2." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 486, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of mid-level image similarity. This indicates that the high-level image representations are invariant to mid-level variations to some extent (e.g., viewpoint variations).", + "bbox": [ + 89, + 409, + 483, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3D geometric understanding is weakly correlated with high-level vision. For tasks like scene surface normal estimating, we observe notably weaker correlations. These tasks often require intricate, fine-grained geometric and surface features that high-level SSL objectives alone do not sufficiently capture. This gap implies that mid-level vision depends on specialized cues not fully addressed by high-level feature extraction.", + "bbox": [ + 89, + 477, + 483, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Correlation across mid-level vision tasks. Fig. 3 shows the Pearson correlations across tasks. We find a strong correlation between object segmentation and mid-level image similarity (coefficients above 0.76). Object segmentation further correlates well with depth estimation and object-level multi-view geometric correspondence, indicating that spatial understanding aids segmentation and underscores the importance of 3D awareness in image understanding. In contrast, scene geometry correspondence correlates weaker with other mid-level and high-level tasks. Mid-level image similarity aligns with object segmentation and correspondence but correlates less with 3D tasks.", + "bbox": [ + 89, + 619, + 483, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ranking in mid-level vision. In Fig. 5, we present a comparative ranking of SSL models based on their performance across mid-level vision tasks and ImageNet probing. Each model received a task-specific rank, and we computed an average score, with higher scores indicating stronger performance in both mid-level and high-level vision tasks. Our", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f9816ee3b028d715802190d47802c78d414f86304f5da9f8b87a4d3609fd8c00.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 87, + 903, + 186 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3f281907399737c7b57adf6ab5fba359553ffc886f27f0411a89dc8b40c6e06d.jpg", + "image_caption": [ + "Figure 4. Mid-Level Vision v.s. ImageNet Linear Probing with Contrastive Learning Methods. We examine several contrastive learning methods [6-9, 27, 58, 69] and observe a negative correlation between ImageNet linear probing accuracy and task performance. Depth estimation results are shown at the top, with surface normal estimation results at the bottom. The y-axis represents prediction accuracy, where higher values indicate better performance." + ], + "image_footnote": [], + "bbox": [ + 522, + 191, + 900, + 328 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "analysis suggests an imbalance in model performance, with some models excelling in high-level tasks but showing comparatively modest capabilities in mid-level vision tasks. Notably, MaskFeat stands out as an exception, demonstrating a significant advantage in mid-level vision tasks over high-level performance.", + "bbox": [ + 511, + 467, + 906, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Conversely, MAE ranks lower on mid-level tasks, demonstrating limited proficiency in capturing finer visual details. In the following sections, we will discuss the specifics of MAE and MaskFeat.", + "bbox": [ + 511, + 559, + 905, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Notably, iBOT [71] and DINO [4] rank among the top performers, exhibiting strong capabilities in both mid-level and high-level vision tasks. In contrast, pretext pre-trained models like RotNet [25] and Jigsaw [45] fall behind other SSL methods.", + "bbox": [ + 511, + 619, + 905, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. What makes a strong mid-level vision model?", + "text_level": 1, + "bbox": [ + 511, + 709, + 897, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training objective. We observe that the top-performing SSL models in mid-level vision tasks are typically generative-based, such as iBOT [71] and MaskFeat [62]. In contrast, recent contrastive self-supervised learning (SSL) models [6-9, 27, 58, 69] show an inverse relationship between mid-level vision performance and ImageNet linear probing accuracy, as illustrated in Fig. 4.", + "bbox": [ + 511, + 732, + 905, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although these methods have improved ImageNet linear probing accuracy by over $10\\%$ , they exhibit notable declines in mid-level vision tasks. We illustrate this trend with model performance on depth and surface normal estimation and", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "30100", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/44f36bb5c9845416877d7d1b35e2cb1f5641444144b0231c877949de93f2cb36.jpg", + "image_caption": [ + "Figure 5. Ranking SSLs based on Overall Score. Comparative ranking of SSL models based on performance in mid-level vision tasks and ImageNet probing. Models are ranked per task, and average scores reflect overall performance across mid-level and high-level vision tasks, with higher scores indicating stronger results." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 908, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "provide a broader analysis across six additional tasks in the supplementary materials. Notably, SSL models pre-trained on pretext tasks show the lowest performance on mid-level vision tasks.", + "bbox": [ + 89, + 255, + 480, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network architecture. We further compare ViT-B (ViT Base) and ViT-L (ViT Large) backbones with the same SSL method in Tab. 3. Our findings show that ViT-L models tend to perform better than ViT-B across mid-level vision tasks. In particular, we evaluate two popular SSL models, iBOT and MAE, on both ViT-B and ViT-L backbones. This pattern suggests that larger backbones like ViT-L may capture mid-level vision features better.", + "bbox": [ + 89, + 323, + 483, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network capability. We also compare ViT-B and ViT-L backbones using the same SSL method in Tab. 3. Our results indicate that ViT-Large models generally achieve higher scores across various mid-level vision tasks. Specifically, we examine two popular SSL models, iBOT and MAE, with ViT-B and ViT-L backbones. This trend suggests that larger models are better at capturing mid-level vision features.", + "bbox": [ + 89, + 450, + 483, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Which SSL works the best per task?", + "text_level": 1, + "bbox": [ + 89, + 582, + 405, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Tab. 4, we highlight the best-performing models for each task. iBOT [71] consistently leads in most mid-level vision tasks while MaskFeat performs even better on scene correspondence and scene surface normal. DINO works the best on object correspondence and achieves quite competitive results compared to other SSLs.", + "bbox": [ + 89, + 604, + 480, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Analysis of specific SSL", + "text_level": 1, + "bbox": [ + 89, + 705, + 307, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "MAE. MAE [30] stands out as a clear outlier, as illustrated in Fig. 2 and Fig. 5. MAE consistently performs poorly on mid-level vision tasks compared to other ViT-based SSLs such as iBOT [71] and MaskFeat [62].", + "bbox": [ + 89, + 726, + 480, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "MaskFeat. In Fig. 2 and Fig. 5, we observe that MaskFeat [62] demonstrates surprisingly strong mid-level vision capabilities despite showing relatively modest performance in high-level vision tasks. Since the MaskFeat checkpoint we used was trained exclusively on the ImageNet-1K dataset and followed a training process similar to MAE, we attribute its mid-level vision strength to its choice of target", + "bbox": [ + 89, + 794, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "features. Unlike models trained on raw pixels, tokens, or high-level features, MaskFeat is optimized on HOG (Histograms of Oriented Gradients) features, which are widely used for keypoint detection in methods such as SIFT [38]. Importantly, HOG does not rely on any external models, making it a robust feature for capturing mid-level vision attributes. This finding suggests that incorporating mid-level vision-relevant features, like HOG, into SSL training may enhance model performance on mid-level vision tasks.", + "bbox": [ + 511, + 255, + 903, + 392 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SSLs based on pre-text tasks. RotNet and Jigsaw are the two lowest-performing SSLs on mid- and high-level vision. Given that they are the early design of SSLs, it revalidate our claim that ImageNet (IN1k) probing results improve, we generally observe a corresponding enhancement in mid-level vision task performance.", + "bbox": [ + 511, + 397, + 905, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. How do visual foundation models (VFMs) perform?", + "text_level": 1, + "bbox": [ + 511, + 497, + 903, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Even though our study aims to conduct a controlled benchmarking of SSLs in the mid-level vision tasks, we put VFMs into our context in this section to understand the comparison between the latest visual foundation models and the set of SSLs we analyzed. We observed that CLIP is much worse than most of the SSLs. DINO-v2 is the winner. We include a comparison in Fig. 6 focusing on depth estimation.", + "bbox": [ + 511, + 534, + 905, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DINO-V2 [46]. Our findings, consistent with Probe3D and Cambrian-1 [55], show DINO-V2 as the best-performing model across both ImageNet linear probing and mid-level vision tasks, making it a standout choice for comprehensive vision capabilities.", + "bbox": [ + 511, + 646, + 905, + 723 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CLIP [50]. CLIP's overall performance is notably lower across mid-level tasks, as reported in Probe3D [17] and Cambrian-1 [55]. This suggests that, while generalizable for 2D understanding, CLIP may be less suited for tasks requiring 3D spatial understanding.", + "bbox": [ + 511, + 728, + 905, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CroCo [65]. Using depth estimation as a representative task, we observe that CroCo performs competitively in mid-level vision tasks despite lagging in high-level vision tasks. Pretrained on synthetic multi-view image datasets, CroCo learns strong 3D-aware image representations. This distinction underscores its potential for 3D-specific applications,", + "bbox": [ + 511, + 809, + 905, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "30101", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/54a2dcdc880c40378ce4e673986347491ae5778cb7ea01abf7d950c65e389ed3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SSLsBackboneObject Seg.Object SNorm.Scene SNorm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
MoCo-v3 [9]RN-5071.4827.2243.0345.9375.561.715.2384.37
MoCo-v3 [9]ViT-B/1672.4531.7249.6451.0780.143.1225.0386.90
DINO [5]RN-5071.9531.4347.6447.6377.683.1626.6383.31
DINO [5]ViT-B/1674.0031.0648.4247.7579.382.6124.3889.36
SSLsModel SizeObject Seg.Object Norm.Scene Norm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
iBOTB/1675.7432.7552.0250.0281.323.1220.0489.27
iBOTL/1675.3235.6554.5352.5685.143.1614.7982.37
MAEB/1665.7722.6743.8926.7866.172.746.6482.91
MAEL/1666.5826.6045.6026.8170.222.9310.0584.26
", + "bbox": [ + 94, + 88, + 903, + 244 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/445f8a584230319e20d0f93bf49187885ed200d8a7e783e0b1d6495881f6a165.jpg", + "table_caption": [ + "Table 3. Impact of Network Architecture and Model Size on Mid-Level Vision Performance. The top table demonstrates that the Vision Transformer (ViT) [14] generally outperforms ResNet-50 (RN-50) [28] across most mid-level vision tasks when using MoCo-v3 or DINO as the self-supervised pretraining method. The bottom table shows that larger model sizes tend to enhance mid-level vision capabilities. Detailed numerical comparisons are provided in the supplementary material." + ], + "table_footnote": [ + "Table 4. Top SSL Methods in Mid-Level Vision Tasks. iBOT outperformed all other SSL methods (listed in Tab. 1) in multiple mid-level vision tasks. Surprisingly, despite the low performance on ImageNet linear classification, MaskFeat achieved leading results in depth and surface normal estimation." + ], + "table_body": "
ModelImage Sim.Object Corres.Object DepthObject SNorm.
DINO (RN-50)83.313.1647.6331.43
MaskFeat [62]75.702.0849.5032.40
MoCo v384.371.7045.9327.22
iBOT [71]89.273.1250.0232.75
ModelObject Seg.Scene Corres.Scene DepthScene SNorm.
DINO (RN-50)71.9526.6377.6847.64
MaskFeat [62]70.2827.9480.3953.63
MoCo v371.4815.2375.5643.03
iBOT [71]75.7420.0481.3252.02
", + "bbox": [ + 91, + 316, + 480, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where spatial understanding is prioritized over high-level visual semantics because of its design choice.", + "bbox": [ + 89, + 539, + 482, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SAM [34]. Although SAM excels at image segmentation, it exhibits moderate performance on mid-level vision tasks and notably weaker performance on image classification, in comparison with ImageNet-pretrained SSLs. This reveals the imbalanced performance of SAM among reorganization, reconstruction and recognition.", + "bbox": [ + 89, + 575, + 482, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 89, + 672, + 204, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, this study introduces a suite of benchmark protocols to systematically evaluate mid-level vision capabilities, offering a comprehensive and controlled assessment of 22 SSL models across mid-level vision tasks. Our findings indicate a positive correlation between SSL performance in mid-level and high-level vision tasks, though this correlation is generally weaker than that observed within high-level tasks.", + "bbox": [ + 89, + 696, + 482, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Some SSL models exhibit imbalanced performance across these task levels. For instance, MAE [31] underperforms in mid-level tasks despite competitive high-level performance, while MaskFeat [62] excels in mid-level tasks", + "bbox": [ + 89, + 818, + 482, + 878 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1bc9099a0e4ce2d4b52db42d7c490e9ab78f998e0d6a09cf37f49257be5dca67.jpg", + "image_caption": [ + "Figure 6. Comparison of ImageNet1K-Pretrained SSLs with models trained with larger datasets (e.g., DINO-v2 [46]) or different training supervisions (e.g., CLIP [50] ${}^{1}$ ) in the scene depth estimation task." + ], + "image_footnote": [], + "bbox": [ + 514, + 316, + 906, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "relative to its high-level results (Fig. 5). Mid-level vision capabilities are influenced by factors such as network architecture, dataset size, and pretraining strategy. Overall, ViT [14] outperforms ResNet [28], increasing model capacity proves beneficial (Tab. 3), and generative modeling approaches often lead in performance (Fig. 5). Additionally, we compare SSL models with VFMs, finding that DINOv2 [46] leads in both mid-level and high-level vision tasks and language objectives (e.g., CLIP) do not help on mid-level tasks.", + "bbox": [ + 511, + 578, + 906, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since SSL's overall goal is to produce a very general feature representation that works well for a wide range of downstream tasks, we encourage the community to evaluate new SSL methods on both high- and mid-level tasks.", + "bbox": [ + 511, + 732, + 906, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is limited by resources, which prevents us from scaling up our experiments to more tasks and models, and we did not include ending tasks such as navigation and robotic manipulation to emphasize mid-level vision's role further. We provide details of our probing hyper-parameters and include visualizations for each task in the supplementary materials.", + "bbox": [ + 511, + 795, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "1We evaluated CLIP with the ViT-B/16 checkpoint released by OpenAI.", + "bbox": [ + 107, + 886, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "30102", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 269, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The authors gratefully acknowledge Research Computing at the University of Virginia for providing the computational resources and technical support that made the results in this work possible. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.148, + 0.131, + 0.851, + 0.154 + ], + "angle": 0, + "content": "Probing the Mid-level Vision Capabilities of Self-Supervised Learning" + }, + { + "type": "text", + "bbox": [ + 0.256, + 0.18, + 0.737, + 0.218 + ], + "angle": 0, + "content": "Xuweiyi Chen1 Markus Marks2 Zezhou Cheng1 \n1University of Virginia 2California Institute of Technology" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.252, + 0.326, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.284, + 0.483, + 0.435 + ], + "angle": 0, + "content": "Mid-level vision capabilities — such as generic object localization and 3D geometric understanding — are not only fundamental to human vision but are also crucial for many real-world applications of computer vision. These abilities emerge with minimal supervision during the early stages of human visual development. Despite their significance, current self-supervised learning (SSL) approaches are primarily designed and evaluated for high-level recognition tasks, leaving their mid-level vision capabilities largely unexamined." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.436, + 0.484, + 0.676 + ], + "angle": 0, + "content": "In this study, we introduce a suite of benchmark protocols to systematically assess mid-level vision capabilities and present a comprehensive, controlled evaluation of 22 prominent SSL models across 8 mid-level vision tasks. Our experiments reveal a weak correlation between mid-level and high-level task performance. We also identify several SSL methods with highly imbalanced performance across mid-level and high-level capabilities, as well as some that excel in both. Additionally, we investigate key factors contributing to mid-level vision performance, such as pretraining objectives and network architectures. Our study provides a holistic and timely view of what SSL models have learned, complementing existing research that primarily focuses on high-level vision tasks. We hope our findings guide future SSL research to benchmark models not only on high-level vision tasks but on mid-level as well." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.694, + 0.222, + 0.709 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Mid-level vision capabilities [41] (Fig. 1a) play a vital role in human visual development and daily life activities. By the age of one, children can re-organize retinal images into objects (i.e., perceptual grouping), construct the visual world in three dimensions (i.e., 3D geometric understanding), track moving objects (i.e., cross-view correspondence), grasp and bite these objects without knowing their semantics, and purposefully navigate through the 3D world. Importantly, such mid-level perception is developed without supervision [32]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "On the other hand, self-supervised learning (SSL) in computer vision has made significant strides [5-8, 25, 42," + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.25, + 0.59, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.312, + 0.565, + 0.32 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.59, + 0.251, + 0.662, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.311, + 0.662, + 0.32 + ], + "angle": 0, + "content": "Generic Object Seg" + }, + { + "type": "image", + "bbox": [ + 0.663, + 0.251, + 0.735, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.311, + 0.734, + 0.32 + ], + "angle": 0, + "content": "Depth Estimation" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.251, + 0.81, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.311, + 0.802, + 0.32 + ], + "angle": 0, + "content": "Surface Normal" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.322, + 0.59, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.38, + 0.647, + 0.389 + ], + "angle": 0, + "content": "3D Geometric Correspondence" + }, + { + "type": "image", + "bbox": [ + 0.59, + 0.322, + 0.662, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.597, + 0.38, + 0.647, + 0.389 + ], + "angle": 0, + "content": "Correspondence:" + }, + { + "type": "image", + "bbox": [ + 0.663, + 0.322, + 0.735, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.38, + 0.767, + 0.39 + ], + "angle": 0, + "content": "Image Similarity" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.322, + 0.81, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.38, + 0.899, + 0.39 + ], + "angle": 0, + "content": "Classification & Detection" + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.392, + 0.701, + 0.4 + ], + "angle": 0, + "content": "(a) Mid-level vision" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.403, + 0.707, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.526, + 0.578, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.536, + 0.578, + 0.544 + ], + "angle": 0, + "content": "RotNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.545, + 0.574, + 0.553 + ], + "angle": 0, + "content": "NPID" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.554, + 0.579, + 0.562 + ], + "angle": 0, + "content": "SeLa-v" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.563, + 0.579, + 0.571 + ], + "angle": 0, + "content": "NPID+" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.572, + 0.572, + 0.579 + ], + "angle": 0, + "content": "PIRL" + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.526, + 0.654, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.536, + 0.648, + 0.544 + ], + "angle": 0, + "content": "DeepCI" + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.545, + 0.643, + 0.553 + ], + "angle": 0, + "content": "SwAV" + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.554, + 0.653, + 0.562 + ], + "angle": 0, + "content": "SimCLR" + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.563, + 0.653, + 0.57 + ], + "angle": 0, + "content": "MoCo v2" + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.571, + 0.653, + 0.579 + ], + "angle": 0, + "content": "SimSiam" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.526, + 0.735, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.536, + 0.733, + 0.544 + ], + "angle": 0, + "content": "r-v2 Barlo" + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.545, + 0.745, + 0.553 + ], + "angle": 0, + "content": "DenseCL" + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.554, + 0.737, + 0.562 + ], + "angle": 0, + "content": "DINO" + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.563, + 0.775, + 0.57 + ], + "angle": 0, + "content": "MoCo v3 (RN-50)" + }, + { + "type": "image", + "bbox": [ + 0.791, + 0.526, + 0.874, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.536, + 0.835, + 0.544 + ], + "angle": 0, + "content": "iBOT" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.544, + 0.885, + 0.553 + ], + "angle": 0, + "content": "MoCo v3 (ViT-B/16)" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.554, + 0.834, + 0.562 + ], + "angle": 0, + "content": "MAE" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.563, + 0.848, + 0.569 + ], + "angle": 0, + "content": "- - MaskFeat" + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.58, + 0.874, + 0.59 + ], + "angle": 0, + "content": "(c) SSLs for mid-level and high-level vision w.r.t. ImageNet classification" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.596, + 0.907, + 0.719 + ], + "angle": 0, + "content": "Figure 1. Mid-Level Vision vs. High-Level Vision Tasks. We provide a comprehensive evaluation of prominent self-supervised learning methods (SSLs) across a wide range of mid-level vision tasks (a), complementing the standard evaluation in high-level vision tasks (b). Although SSL performance in mid-level vision tasks (e.g., depth estimation) is positively correlated with ImageNet linear probing, this correlation is much weaker than that observed among high-level vision tasks, as shown in (c) by the \\( R^2 \\) statistics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.903 + ], + "angle": 0, + "content": "45, 46, 66, 71]. The goal of SSL is to learn visual representations from unlabeled data so that these pretrained representations can be applied to a wide range of downstream tasks, reducing the need for human annotations and enhancing learning efficiency and performance. However, SSL is predominantly evaluated based on performance in high-level visual recognition tasks, such as image classification, object detection, and semantic segmentation (Fig. 1b). At the same time, the mid-level vision capabilities of SSL models are largely under-explored. To fill this gap, this pa" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30095" + }, + { + "type": "image", + "bbox": [ + 0.821, + 0.252, + 0.896, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.311, + 0.886, + 0.32 + ], + "angle": 0, + "content": "Semantic Seg." + }, + { + "type": "image", + "bbox": [ + 0.821, + 0.323, + 0.896, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.381, + 0.899, + 0.389 + ], + "angle": 0, + "content": "Classification & Detection" + }, + { + "type": "image_caption", + "bbox": [ + 0.816, + 0.391, + 0.897, + 0.4 + ], + "angle": 0, + "content": "(b) High-level vision" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.403, + 0.708, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.403, + 0.904, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.525, + 0.736, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.535, + 0.761, + 0.543 + ], + "angle": 0, + "content": "Barlow Twins" + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.544, + 0.745, + 0.552 + ], + "angle": 0, + "content": "DenseCL" + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.553, + 0.766, + 0.561 + ], + "angle": 0, + "content": "DINO (RN-50)" + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.562, + 0.775, + 0.569 + ], + "angle": 0, + "content": "MoCo v3 (RN-50)" + }, + { + "type": "image", + "bbox": [ + 0.791, + 0.526, + 0.874, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.536, + 0.835, + 0.544 + ], + "angle": 0, + "content": "iBOT" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.544, + 0.885, + 0.553 + ], + "angle": 0, + "content": "MoCo v3 (ViT-B/16)" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.554, + 0.834, + 0.562 + ], + "angle": 0, + "content": "MAE" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.345, + 0.106 + ], + "angle": 0, + "content": "per addresses the following questions:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.109, + 0.482, + 0.139 + ], + "angle": 0, + "content": "- Does strong high-level vision performance of SSLs indicate strong mid-level vision capabilities?" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.14, + 0.483, + 0.168 + ], + "angle": 0, + "content": "- What makes an SSL model effective for mid-level vision tasks?" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.109, + 0.483, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.171, + 0.483, + 0.427 + ], + "angle": 0, + "content": "To answer these questions, we comprehensively evaluate SSLs in a wide range of mid-level vision tasks, including generic object segmentation, monocular depth and surface normal estimation, geometric correspondence, and mid-level image similarity (Fig. 1a and Tab. 2). We then relate the mid-level vision performance of these SSLs to their high-level vision performance. Our evaluations covers 22 seminar SSL approaches (Tab. 1) from diverse categories developed in the past decades (e.g. pretext tasks [25, 45], contrastive learning [6, 7, 9, 27, 66], self-distillation [5], and generative modeling [30, 62]). To make a controlled study and fair comparisons across different SSLs, our study primarily focuses on SSLs with publicly available checkpoints pretrained on ImageNet1K [12]. This allows us to gain insights into what factors may contribute to the mid-level vision capabilities in SSL (e.g., training objectives, network architectures, etc.)." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.429, + 0.326, + 0.442 + ], + "angle": 0, + "content": "Our observations are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.445, + 0.483, + 0.505 + ], + "angle": 0, + "content": "- The mid-level vision capabilities of SSLs are positively correlated with high-level vision. However, that correlation is generally weaker than that among high-level vision tasks (Fig. 1c and Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.506, + 0.483, + 0.597 + ], + "angle": 0, + "content": "- Some SSLs have highly imbalanced mid-level and high-level vision capabilities. For instance, MAE [31] underperforms most SSLs in the mid-level vision tasks while having competitive high-level vision performance; MaskFeat [62] has better mid-level performance than most SSLs with similar high-level vision (Fig. 5)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.598, + 0.483, + 0.674 + ], + "angle": 0, + "content": "- Network architectures, model capacity, and pretraining strategies impact mid-level vision capabilities. In general, ViT [14] outperforms ResNet [28]; Increasing the network capacity is beneficial (Tab. 3); The leading methods are generally based on generative modeling (Fig. 5)." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.445, + 0.483, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Our study is built upon Probe3D [17], a recent work that evaluates the 3D awareness of visual models. In this work, we explore a broader range of mid-level vision tasks. Furthermore, our study primarily focuses on SSLs pretrained exclusively on ImageNet1K, while Probe3D probes visual foundation models that are trained from very diverse training configurations such as varying supervision signals (e.g. CLIP [50]) and dataset sizes. Our controlled settings allow us to gain insights into the factors contributing to model performance. Our exploration is also closely related to prior works that benchmark SSLs in various vision tasks [18, 26, 44, 55], such as out-of-domain classification [40] and fine-grained recognition [54, 57]. Unlike these works, our evaluation includes more recent SSLs, providing a timely study on this topic." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.183 + ], + "angle": 0, + "content": "In summary, our study offers a comprehensive view of the representations learned by SSL models. We hope these findings inspire practical approaches that perform well across both mid-level and high-level vision tasks. We will release our benchmark suite to support future SSL benchmarking in the research community." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.197, + 0.655, + 0.212 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.222, + 0.907, + 0.435 + ], + "angle": 0, + "content": "Self-Supervised Learning (SSL). The goal of self-supervised learning (SSL) in computer vision is to pretrain image representations using unlabeled data, enabling these representations to be transferred effectively to various downstream tasks. Early SSL methods leveraged a range of pretext tasks, such as colorization [70], rotation prediction [25], jigsaw puzzle solving [45], and inpainting [47]. Recent advances have focused on contrastive learning [6, 7, 27, 29, 66, 69] and generative modeling [13, 31, 37, 48, 62]. Despite extensive research, SSL performance is primarily evaluated on high-level vision tasks (e.g., ImageNet classification, object detection), overlooking the practical relevance of mid-level vision tasks. In this work, we focus on evaluating SSL methods on mid-level vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.441, + 0.909, + 0.637 + ], + "angle": 0, + "content": "Self-Supervised Pretraining for 3D Vision. Unlike most SSL methods focusing on 2D visual recognition tasks, a few recent works explore SSLs for 3D vision. For example, CroCo [63] adopts masked image modeling to learn 3D representations from image pairs showing the same scene from different viewpoints. Despite the improvement in downstream 3D vision tasks, CroCo compromises high-level recognition performance. As a followup, CroCo-v2 [64] extends the training data of CroCo to a large dataset of natural images and demonstrates improved performance in downstream optical flow and stereo vision tasks. However, learning representations for 3D vision tasks remains under-explored." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Benchmarking Self-Supervised Learning. Numerous studies underscore the growing importance of empirically evaluating general-purpose representation learning. For example, Goyal et al. [26] provide extensive benchmarking of SSLs across multiple downstream tasks, including classification, navigation, object detection, and surface normal estimation. Newell et al. [44] examine the effectiveness of SSLs under various configurations (e.g., annotation quantities) in downstream tasks such as pose estimation and depth estimation. Ericsson et al. [18] evaluate 13 SSLs across 40 downstream vision tasks, demonstrating a weak correlation between SSL performance on ImageNet classification and tasks like few-shot learning, object detection, and dense prediction. More recently, Marks et al. [40] studied how classification-based SSL evaluation protocols correlate with and predict downstream performance on out-of-domain datasets. In line with these works, we comprehen" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30096" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "sively evaluate existing SSLs across various downstream tasks. We focus on mid-level vision performance and how it relates to high-level vision." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.162, + 0.483, + 0.42 + ], + "angle": 0, + "content": "Benchmarking Visual Foundation Models. More recently, several studies have evaluated large visual foundation models (VFMs) that are not exclusively trained by self-supervised learning methods (e.g., CLIP [50]). For example, Probe3D [17] examines the 3D awareness of VFMs [5, 34], while Cambrian-1 [55] utilizes large language models (LLMs) and visual instruction tuning to assess visual representations across various 2D and 3D vision tasks. Since VFMs are typically trained with diverse approaches (e.g., different supervision signals, datasets, and architectures), isolating the factors contributing to the performance of the representations they learn is challenging. In contrast, we conduct a controlled evaluation of SSL models that provide publicly available checkpoints pretrained on ImageNet1K. This approach enables fair comparisons across SSLs and offers deeper insights into their methodologies." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.437, + 0.421, + 0.453 + ], + "angle": 0, + "content": "3. Background: Vision Task Taxonomy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.509 + ], + "angle": 0, + "content": "There exist numerous computer vision tasks [68] which can be categorized from different perspectives. We briefly introduce two popular frameworks in this section:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.515, + 0.483, + 0.697 + ], + "angle": 0, + "content": "- Bottom-up Hierarchical Vision. David Marr [41] proposes to break up the vision system into low-level, mid-level, and high-level stages. Low-level vision tasks aim to extract edges, contours, and blobs from raw pixels, while high-level vision concerns the semantics, functionality, and holistic 3D shape of objects. Mid-level vision, lying in-between the low-level and high-level vision, addresses the view-centric geometric properties of surfaces (e.g., depth and surface normal), generic object segmentation and localization without semantics, cross-view image correspondences, and so on. This framework favors a feed-forward and bottom-up vision process." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.698, + 0.483, + 0.835 + ], + "angle": 0, + "content": "- Three R's of Vision. Malik et al. [39] categorize vision tasks into recognition, reconstruction, and reorganization. Recognition refers to the task of assigning semantic categories to images. Reconstruction concerns the estimation of 3D structures. Reorganization addresses the grouping and segmentation of images on spatial or perceptual similarity. Instead of a bottom-up process, 3R's emphasizes the mutual benefits and relationship across these three visual capabilities." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.515, + 0.483, + 0.835 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Both frameworks highlight the importance of the nonsemantic vision tasks — mid-level vision in Marr's framework, reconstruction and reorganization in 3R's. We adopt the term \"mid-level\" for the convenience of differentiating" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "from high-level recognition tasks. However, the underlying vision mechanism remains under debate." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.141, + 0.707, + 0.16 + ], + "angle": 0, + "content": "4. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.169, + 0.905, + 0.244 + ], + "angle": 0, + "content": "In this section, we first introduce the SSLs considered in this work (Tab. 1) and our generic evaluation protocols for probing these SSLs. We then present the mid-level vision tasks in detail, including their definitions, datasets, and evaluation approaches (Sec. 4.1- 4.3 and Tab. 2)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.247, + 0.907, + 0.385 + ], + "angle": 0, + "content": "Our probing approaches are largely inspired by Probe3D [17], the recent work that evaluates the 3D awareness of visual foundation models (VFMs). The VFMs are usually trained under distinct settings (e.g. supervision signals, dataset sizes, network architectures and capacity), while we aim at probing self-supervised visual models that are trained with similar configurations. Therefore, our work provides a complementary study, specifically a more controlled setting, compared to Probe3D [17]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.4, + 0.908, + 0.613 + ], + "angle": 0, + "content": "Self-Supervised Models. Tab. 1 presents an overview of the SSL models considered in our study. We primarily focus on SSLs that have publicly available checkpoints pretrained on ImageNet1K [12], with standard neural network architectures (e.g. ResNet50 [28] or Vision Transformers (ViT) [14]) as the image feature extractor. These SSLs cover a wide range of pretraining strategies, including clustering, contrastive learning, generative modeling, or a mixture of different training objectives. Targeting a comprehensive benchmark, we track the SSL literature back to classic methods that learn image representations from pre-text tasks such as Jigsaw [45] and RotNet [25]. Our selection of SSLs is inspired by Marks et al. [40], which provides a detailed study of the evaluation protocols of SSLs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Generic Evaluation Protocols. Many mid-level vision tasks can be formulated as dense prediction (e.g., depth estimation). Unlike image classification, dense prediction requires local pixel or patch representations as input, and the main design choice is to decide which network layers (e.g., ResNet layers or ViT blocks) to extract the dense features from. Following Probe3D, we use the DPT decoder [52], a non-linear dense multi-scale network. For ResNet [28], we use the outputs of the last four ResNet blocks as the input to the DPT head, following the architecture of the feature pyramid network [36]; For ViT [14], following Probe3D, the network is split into four blocks evenly, and the features are extracted after each block — for ViT-B, we extract features after layers 3, 6, 9, and 12. Like Probe3D, we probe the frozen representations to evaluate the capabilities of learned representations instead of their transferability. We provide task-specific evaluation protocols in the following sections and hyperparameter settings in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30097" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.477, + 0.43 + ], + "angle": 0, + "content": "
IDSSLArchitectureCategory
1Jigsaw [45]ResNet50Pre-text
2RotNet [25]ResNet50Pre-text
3NPID [66]ResNet50Contrastive
4NPID++ [42]ResNet50Contrastive
5PIRL [42]ResNet50Contrastive
6ClusterFit [67]ResNet50Clustering
7SwAV [4]ResNet50Clustering
8SeLa-v2 [4]ResNet50Clustering
9DeepCluster-v2 [4]ResNet50Clustering
10SimCLR [6]ResNet50Contrastive
11MoCo-v2 [8]ResNet50Contrastive
12SimSiam [7]ResNet50Contrastive
13DenseCL [58]ResNet50Contrastive
14BYOL [27]ResNet50Contrastive
15Barlow Twins [69]ResNet50Contrastive
16MoCo-v3 [9]ResNet50Contrastive
17DINO [5]ResNet50Self-distillation
18MoCo-v3 [9]ViT-B/16Contrastive
19DINO [5]ViT-B/16Self-distillation
20MAE [31]ViT-B/16Generative
21iBOT [71]ViT-B/16Mixture
22MaskFeat [62]ViT-B/16Generative
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.441, + 0.484, + 0.54 + ], + "angle": 0, + "content": "Table 1. Evaluated Self-Supervised Learning Methods (SSLs). We provide a comprehensive evaluation of SSLs that provide publicly available checkpoints trained from the ImageNet1K dataset [12]. We categorize SSLs based on their training objectives and network backbones. Mixture denotes the combination of different SSLs (e.g., iBOT [71]). The SSLs are listed in order of their publication year." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.567, + 0.355, + 0.584 + ], + "angle": 0, + "content": "4.1. Generic Object Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.591, + 0.483, + 0.696 + ], + "angle": 0, + "content": "Generic object segmentation (or figure-ground segmentation) refers to the task of separating objects (figure) from the surrounding background without any semantics. This mid-level vision task is different from semantic segmentation (i.e., assigning each pixel to a semantic category) which is commonly used for evaluating the high-level visual capabilities of SSLs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.483, + 0.804 + ], + "angle": 0, + "content": "We use the VOC07 and VOC12 datasets [19, 20] as our benchmarks, following prior research on unsupervised object segmentation [56, 59, 61]. Given a pretrained feature extractor, we freeze the backbone and train a DPT decoder [51] with a simple binary cross-entropy loss (BCE). We use standard segmentation metrics (e.g., mean IoU) to measure the performance of SSLs in this task." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.817, + 0.398, + 0.833 + ], + "angle": 0, + "content": "4.2. Monocular Surface Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We evaluate SSLs in two tasks related to monocular 2.5D surface reconstruction: depth and surface normal estimation from Probe3D [17]. Even though these two tasks are closely related, they rely on different visual cues and cap" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.093, + 0.741, + 0.107 + ], + "angle": 0, + "content": "ture distinct geometric properties." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.107, + 0.905, + 0.197 + ], + "angle": 0, + "content": "We evaluate depth estimation and surface normal prediction at both scene and object levels. For scene-level performance, we employ the NYUv2 dataset [43], a widely used benchmark for indoor environments. Object-level depth is assessed using the NAVI dataset [33], which provides diverse object instances across scenes and orientations." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.198, + 0.892, + 0.213 + ], + "angle": 0, + "content": "We present the task-specific configurations as follows." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.218, + 0.906, + 0.339 + ], + "angle": 0, + "content": "Monocular Depth Estimation The task aims at predicting pixel-wise depth from monocular images. We adopt the formulation of binned depth estimation from AdaBins [21], instead of the classical regression approaches [15]. We estimate the scale-invariant depth for object-centric images (e.g., NAVI) while predict metric depths on scene-centric datasets (e.g., NYUv2). We report root-mean-squared error (RMSE) and recall at various threshold ratios." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.345, + 0.906, + 0.419 + ], + "angle": 0, + "content": "Surface Normal Estimation. This task is to predict per-pixel surface direction. We train the DPT head with the uncertainty-aware angular loss [2]. As for depth estimation, we report RMSE and percentage recall at various angular thresholds." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.43, + 0.757, + 0.446 + ], + "angle": 0, + "content": "4.3. Multiview Correspondence" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.452, + 0.907, + 0.604 + ], + "angle": 0, + "content": "In this section, we consider the tasks of estimating correspondences across multiple views that involve mid-level variations, such as changes in camera perspective and object motion. These mid-level variations differ from low-level variations in image properties (e.g., color and texture) and high-level variations in semantic attributes (e.g., object categories). Specifically, we probe SSLs in two tasks: geometric correspondence and mid-level image similarity. Following Probe3D [17], we extract image or pixel representations from pretrained SSLs model without additional training." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.608, + 0.906, + 0.789 + ], + "angle": 0, + "content": "Geometric Correspondence This task aims to build pixel correspondences across two views that depict the same 3D scene. Our evaluation follows Probe3D [17]. Specifically, we estimate the pixel correspondences using the dense feature maps extracted from pretrained SSL models. We use the Paired ScanNet [10] to evaluate scene-centric images and the NAVI dataset [33] for object-centric images. We sample views with a maximum rotation of 120 degrees to ensure that a mutually visible surface exists without a large viewpoint change. We report the correspondence recall — the percentage of correspondence that falls within some defined distance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.795, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Mid-Level Image Similarity The task aims at measuring the similarity of two images with mid-level variations (e.g., viewpoint). We evaluate the SSLs on the NIGHTS dataset collected by DreamSim [23]. Specifically, for each triplets \\((x, \\tilde{x}_0, \\tilde{x}_1)\\) from the NIGHTS dataset, we predict whether \\(\\tilde{x}_0\\) or \\(\\tilde{x}_1\\) is more similar to the reference image \\(x\\). We denote a distance between two images as \\(D(x, \\tilde{x}; f_\\theta) =\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30098" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.891, + 0.238 + ], + "angle": 0, + "content": "
HierarchyTasksTypeBenchmarksLossesMetrics
High-levelImage Classification2DImageNet1K [53]CEAccuracy
Object Detection2DVOC07 [19], COCO [35]CE+L2AP
Semantic Segmentation2DCOCO [35]CEmIOU
Mid-levelGeneric Object Segmentation2DVOC07 [19], VOC12 [20]BCEF1, mIoU, Acc
Depth Prediction3DNAVI [33], NYU [43]AdaBinRMSE, ε1, ε2, ε3
Surface Normal Estimation3DNAVI [33], NYU [43]AngularRMSE, ε1, ε2, ε3
Geometric Correspondence3DNAVI [33], ScanNet [11]Training-free2D, 3D Recall
Mid-level Image Similarity2DNIGHTS [24]Training-freeRetrieval Score (F1-Score)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.247, + 0.907, + 0.304 + ], + "angle": 0, + "content": "Table 2. Probing Tasks. In comparison with the standard SSL evaluation protocols that primarily focus on high-level vision tasks (top), we provide a comprehensive, systematic, and controlled evaluation of SSL in mid-level vision tasks (bottom). Our evaluations cover 2D and 3D vision with a wide range of benchmarks. The \\(\\epsilon_{1}\\), \\(\\epsilon_{2}\\) and \\(\\epsilon_{3}\\) in depth and surface normal estimation represents recall at different threshold rations [16, 22]. Detailed descriptions of each metric can be found in the supplementary." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.315, + 0.907, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.607, + 0.908, + 0.651 + ], + "angle": 0, + "content": "Figure 2. Mid-Level Vision v.s. ImageNet Linear Probing. We report the performance of self-supervised learning methods on mid-level vision tasks (y-axis) against their ImageNet 1K linear classification accuracy. Metrics are detailed in Tab. 2. Linear regression shows correlation with \\( R^2 \\) in each plot's top-left corner, and the red shaded area marks the \\( 95\\% \\) confidence interval." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.676, + 0.483, + 0.797 + ], + "angle": 0, + "content": "\\(1 - \\cos \\bigl (f_{\\theta}(x),f_{\\theta}(\\tilde{x})\\bigr)\\) where \\(f_{\\theta}\\) is the image representations from pretrained SSLs. For ViT, we use the CLS tokens taken from the last layer; For ResNet, we use the global image representation in the output layer. The model's vote is calculated as follows: if \\(d_1 < d_0\\) , then \\(\\hat{y} = 1\\) ; otherwise, if \\(d_0 < d_1\\) , then \\(\\hat{y} = 0\\) , where \\(d_0 = D(x,\\tilde{x}_0;f_\\theta)\\) and \\(d_{1} = D(x,\\tilde{x}_{1};f_{\\theta})\\) . We use voting accuracy as our evaluation metric." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.809, + 0.188, + 0.827 + ], + "angle": 0, + "content": "5. Analysis" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.834, + 0.483, + 0.866 + ], + "angle": 0, + "content": "5.1. Does strong high-level performance imply strong mid-level performance?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Yes, to some extent. As ImageNet (IN1k) probing results improve, we generally observe a corresponding enhance-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.676, + 0.907, + 0.752 + ], + "angle": 0, + "content": "ment in mid-level vision tasks, as depicted in Fig. 2. This positive trend indicates that SSL models capable of high-level visual recognition tend to provide better representations for mid-level vision tasks as well, benefiting tasks that leverage spatial and structural information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Some mid-level tasks are highly correlated with high-level. A per-task closer examination, however, reveals nuances in this relationship. For example, generic object segmentation shows the highest correlation with high-level tasks, achieving a coefficient of determination \\((R^2 = 0.70)\\). This suggests that high-level features indeed capture spatial structures that enhance segmentation accuracy. Mid-level and high-level vision also correlate highly in the task" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "30099" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.488, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.341, + 0.484, + 0.385 + ], + "angle": 0, + "content": "Figure 3. Cross-task performance correlation. We present Pearson coefficients across mid-level and high-level vision tasks. We use the same set of metrics we used in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.456 + ], + "angle": 0, + "content": "of mid-level image similarity. This indicates that the high-level image representations are invariant to mid-level variations to some extent (e.g., viewpoint variations)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.478, + 0.484, + 0.598 + ], + "angle": 0, + "content": "3D geometric understanding is weakly correlated with high-level vision. For tasks like scene surface normal estimating, we observe notably weaker correlations. These tasks often require intricate, fine-grained geometric and surface features that high-level SSL objectives alone do not sufficiently capture. This gap implies that mid-level vision depends on specialized cues not fully addressed by high-level feature extraction." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.62, + 0.484, + 0.801 + ], + "angle": 0, + "content": "Correlation across mid-level vision tasks. Fig. 3 shows the Pearson correlations across tasks. We find a strong correlation between object segmentation and mid-level image similarity (coefficients above 0.76). Object segmentation further correlates well with depth estimation and object-level multi-view geometric correspondence, indicating that spatial understanding aids segmentation and underscores the importance of 3D awareness in image understanding. In contrast, scene geometry correspondence correlates weaker with other mid-level and high-level tasks. Mid-level image similarity aligns with object segmentation and correspondence but correlates less with 3D tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Ranking in mid-level vision. In Fig. 5, we present a comparative ranking of SSL models based on their performance across mid-level vision tasks and ImageNet probing. Each model received a task-specific rank, and we computed an average score, with higher scores indicating stronger performance in both mid-level and high-level vision tasks. Our" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.088, + 0.905, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.192, + 0.901, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.341, + 0.907, + 0.44 + ], + "angle": 0, + "content": "Figure 4. Mid-Level Vision v.s. ImageNet Linear Probing with Contrastive Learning Methods. We examine several contrastive learning methods [6-9, 27, 58, 69] and observe a negative correlation between ImageNet linear probing accuracy and task performance. Depth estimation results are shown at the top, with surface normal estimation results at the bottom. The y-axis represents prediction accuracy, where higher values indicate better performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.468, + 0.907, + 0.558 + ], + "angle": 0, + "content": "analysis suggests an imbalance in model performance, with some models excelling in high-level tasks but showing comparatively modest capabilities in mid-level vision tasks. Notably, MaskFeat stands out as an exception, demonstrating a significant advantage in mid-level vision tasks over high-level performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.56, + 0.906, + 0.62 + ], + "angle": 0, + "content": "Conversely, MAE ranks lower on mid-level tasks, demonstrating limited proficiency in capturing finer visual details. In the following sections, we will discuss the specifics of MAE and MaskFeat." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.906, + 0.696 + ], + "angle": 0, + "content": "Notably, iBOT [71] and DINO [4] rank among the top performers, exhibiting strong capabilities in both mid-level and high-level vision tasks. In contrast, pretext pre-trained models like RotNet [25] and Jigsaw [45] fall behind other SSL methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.71, + 0.898, + 0.727 + ], + "angle": 0, + "content": "5.2. What makes a strong mid-level vision model?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Training objective. We observe that the top-performing SSL models in mid-level vision tasks are typically generative-based, such as iBOT [71] and MaskFeat [62]. In contrast, recent contrastive self-supervised learning (SSL) models [6-9, 27, 58, 69] show an inverse relationship between mid-level vision performance and ImageNet linear probing accuracy, as illustrated in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Although these methods have improved ImageNet linear probing accuracy by over \\(10\\%\\), they exhibit notable declines in mid-level vision tasks. We illustrate this trend with model performance on depth and surface normal estimation and" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30100" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.91, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.207, + 0.908, + 0.248 + ], + "angle": 0, + "content": "Figure 5. Ranking SSLs based on Overall Score. Comparative ranking of SSL models based on performance in mid-level vision tasks and ImageNet probing. Models are ranked per task, and average scores reflect overall performance across mid-level and high-level vision tasks, with higher scores indicating stronger results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.256, + 0.482, + 0.318 + ], + "angle": 0, + "content": "provide a broader analysis across six additional tasks in the supplementary materials. Notably, SSL models pre-trained on pretext tasks show the lowest performance on mid-level vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.324, + 0.484, + 0.445 + ], + "angle": 0, + "content": "Network architecture. We further compare ViT-B (ViT Base) and ViT-L (ViT Large) backbones with the same SSL method in Tab. 3. Our findings show that ViT-L models tend to perform better than ViT-B across mid-level vision tasks. In particular, we evaluate two popular SSL models, iBOT and MAE, on both ViT-B and ViT-L backbones. This pattern suggests that larger backbones like ViT-L may capture mid-level vision features better." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.572 + ], + "angle": 0, + "content": "Network capability. We also compare ViT-B and ViT-L backbones using the same SSL method in Tab. 3. Our results indicate that ViT-Large models generally achieve higher scores across various mid-level vision tasks. Specifically, we examine two popular SSL models, iBOT and MAE, with ViT-B and ViT-L backbones. This trend suggests that larger models are better at capturing mid-level vision features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.583, + 0.406, + 0.599 + ], + "angle": 0, + "content": "5.3. Which SSL works the best per task?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.605, + 0.482, + 0.696 + ], + "angle": 0, + "content": "In Tab. 4, we highlight the best-performing models for each task. iBOT [71] consistently leads in most mid-level vision tasks while MaskFeat performs even better on scene correspondence and scene surface normal. DINO works the best on object correspondence and achieves quite competitive results compared to other SSLs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.706, + 0.308, + 0.722 + ], + "angle": 0, + "content": "5.4. Analysis of specific SSL" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.482, + 0.789 + ], + "angle": 0, + "content": "MAE. MAE [30] stands out as a clear outlier, as illustrated in Fig. 2 and Fig. 5. MAE consistently performs poorly on mid-level vision tasks compared to other ViT-based SSLs such as iBOT [71] and MaskFeat [62]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.902 + ], + "angle": 0, + "content": "MaskFeat. In Fig. 2 and Fig. 5, we observe that MaskFeat [62] demonstrates surprisingly strong mid-level vision capabilities despite showing relatively modest performance in high-level vision tasks. Since the MaskFeat checkpoint we used was trained exclusively on the ImageNet-1K dataset and followed a training process similar to MAE, we attribute its mid-level vision strength to its choice of target" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.256, + 0.905, + 0.393 + ], + "angle": 0, + "content": "features. Unlike models trained on raw pixels, tokens, or high-level features, MaskFeat is optimized on HOG (Histograms of Oriented Gradients) features, which are widely used for keypoint detection in methods such as SIFT [38]. Importantly, HOG does not rely on any external models, making it a robust feature for capturing mid-level vision attributes. This finding suggests that incorporating mid-level vision-relevant features, like HOG, into SSL training may enhance model performance on mid-level vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.906, + 0.489 + ], + "angle": 0, + "content": "SSLs based on pre-text tasks. RotNet and Jigsaw are the two lowest-performing SSLs on mid- and high-level vision. Given that they are the early design of SSLs, it revalidate our claim that ImageNet (IN1k) probing results improve, we generally observe a corresponding enhancement in mid-level vision task performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.498, + 0.905, + 0.529 + ], + "angle": 0, + "content": "5.5. How do visual foundation models (VFMs) perform?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.535, + 0.906, + 0.643 + ], + "angle": 0, + "content": "Even though our study aims to conduct a controlled benchmarking of SSLs in the mid-level vision tasks, we put VFMs into our context in this section to understand the comparison between the latest visual foundation models and the set of SSLs we analyzed. We observed that CLIP is much worse than most of the SSLs. DINO-v2 is the winner. We include a comparison in Fig. 6 focusing on depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.906, + 0.724 + ], + "angle": 0, + "content": "DINO-V2 [46]. Our findings, consistent with Probe3D and Cambrian-1 [55], show DINO-V2 as the best-performing model across both ImageNet linear probing and mid-level vision tasks, making it a standout choice for comprehensive vision capabilities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.729, + 0.906, + 0.805 + ], + "angle": 0, + "content": "CLIP [50]. CLIP's overall performance is notably lower across mid-level tasks, as reported in Probe3D [17] and Cambrian-1 [55]. This suggests that, while generalizable for 2D understanding, CLIP may be less suited for tasks requiring 3D spatial understanding." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.903 + ], + "angle": 0, + "content": "CroCo [65]. Using depth estimation as a representative task, we observe that CroCo performs competitively in mid-level vision tasks despite lagging in high-level vision tasks. Pretrained on synthetic multi-view image datasets, CroCo learns strong 3D-aware image representations. This distinction underscores its potential for 3D-specific applications," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30101" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.904, + 0.246 + ], + "angle": 0, + "content": "
SSLsBackboneObject Seg.Object SNorm.Scene SNorm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
MoCo-v3 [9]RN-5071.4827.2243.0345.9375.561.715.2384.37
MoCo-v3 [9]ViT-B/1672.4531.7249.6451.0780.143.1225.0386.90
DINO [5]RN-5071.9531.4347.6447.6377.683.1626.6383.31
DINO [5]ViT-B/1674.0031.0648.4247.7579.382.6124.3889.36
SSLsModel SizeObject Seg.Object Norm.Scene Norm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
iBOTB/1675.7432.7552.0250.0281.323.1220.0489.27
iBOTL/1675.3235.6554.5352.5685.143.1614.7982.37
MAEB/1665.7722.6743.8926.7866.172.746.6482.91
MAEL/1666.5826.6045.6026.8170.222.9310.0584.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.257, + 0.907, + 0.313 + ], + "angle": 0, + "content": "Table 3. Impact of Network Architecture and Model Size on Mid-Level Vision Performance. The top table demonstrates that the Vision Transformer (ViT) [14] generally outperforms ResNet-50 (RN-50) [28] across most mid-level vision tasks when using MoCo-v3 or DINO as the self-supervised pretraining method. The bottom table shows that larger model sizes tend to enhance mid-level vision capabilities. Detailed numerical comparisons are provided in the supplementary material." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.318, + 0.482, + 0.452 + ], + "angle": 0, + "content": "
ModelImage Sim.Object Corres.Object DepthObject SNorm.
DINO (RN-50)83.313.1647.6331.43
MaskFeat [62]75.702.0849.5032.40
MoCo v384.371.7045.9327.22
iBOT [71]89.273.1250.0232.75
ModelObject Seg.Scene Corres.Scene DepthScene SNorm.
DINO (RN-50)71.9526.6377.6847.64
MaskFeat [62]70.2827.9480.3953.63
MoCo v371.4815.2375.5643.03
iBOT [71]75.7420.0481.3252.02
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.532 + ], + "angle": 0, + "content": "Table 4. Top SSL Methods in Mid-Level Vision Tasks. iBOT outperformed all other SSL methods (listed in Tab. 1) in multiple mid-level vision tasks. Surprisingly, despite the low performance on ImageNet linear classification, MaskFeat achieved leading results in depth and surface normal estimation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.483, + 0.571 + ], + "angle": 0, + "content": "where spatial understanding is prioritized over high-level visual semantics because of its design choice." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.576, + 0.483, + 0.667 + ], + "angle": 0, + "content": "SAM [34]. Although SAM excels at image segmentation, it exhibits moderate performance on mid-level vision tasks and notably weaker performance on image classification, in comparison with ImageNet-pretrained SSLs. This reveals the imbalanced performance of SAM among reorganization, reconstruction and recognition." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.673, + 0.205, + 0.688 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.483, + 0.818 + ], + "angle": 0, + "content": "In conclusion, this study introduces a suite of benchmark protocols to systematically evaluate mid-level vision capabilities, offering a comprehensive and controlled assessment of 22 SSL models across mid-level vision tasks. Our findings indicate a positive correlation between SSL performance in mid-level and high-level vision tasks, though this correlation is generally weaker than that observed within high-level tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.819, + 0.483, + 0.879 + ], + "angle": 0, + "content": "Some SSL models exhibit imbalanced performance across these task levels. For instance, MAE [31] underperforms in mid-level tasks despite competitive high-level performance, while MaskFeat [62] excels in mid-level tasks" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.318, + 0.907, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.517, + 0.907, + 0.572 + ], + "angle": 0, + "content": "Figure 6. Comparison of ImageNet1K-Pretrained SSLs with models trained with larger datasets (e.g., DINO-v2 [46]) or different training supervisions (e.g., CLIP [50] \\({}^{1}\\)) in the scene depth estimation task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.579, + 0.907, + 0.73 + ], + "angle": 0, + "content": "relative to its high-level results (Fig. 5). Mid-level vision capabilities are influenced by factors such as network architecture, dataset size, and pretraining strategy. Overall, ViT [14] outperforms ResNet [28], increasing model capacity proves beneficial (Tab. 3), and generative modeling approaches often lead in performance (Fig. 5). Additionally, we compare SSL models with VFMs, finding that DINOv2 [46] leads in both mid-level and high-level vision tasks and language objectives (e.g., CLIP) do not help on mid-level tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.907, + 0.793 + ], + "angle": 0, + "content": "Since SSL's overall goal is to produce a very general feature representation that works well for a wide range of downstream tasks, we encourage the community to evaluate new SSL methods on both high- and mid-level tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.907, + 0.901 + ], + "angle": 0, + "content": "This work is limited by resources, which prevents us from scaling up our experiments to more tasks and models, and we did not include ending tasks such as navigation and robotic manipulation to emphasize mid-level vision's role further. We provide details of our probing hyper-parameters and include visualizations for each task in the supplementary materials." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.483, + 0.901 + ], + "angle": 0, + "content": "1We evaluated CLIP with the ViT-B/16 checkpoint released by OpenAI." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30102" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.271, + 0.108 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.117, + 0.484, + 0.178 + ], + "angle": 0, + "content": "The authors gratefully acknowledge Research Computing at the University of Virginia for providing the computational resources and technical support that made the results in this work possible. 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These abilities emerge with minimal supervision during the early stages of human visual development. Despite their significance, current self-supervised learning (SSL) approaches are primarily designed and evaluated for high-level recognition tasks, leaving their mid-level vision capabilities largely unexamined. + +In this study, we introduce a suite of benchmark protocols to systematically assess mid-level vision capabilities and present a comprehensive, controlled evaluation of 22 prominent SSL models across 8 mid-level vision tasks. Our experiments reveal a weak correlation between mid-level and high-level task performance. We also identify several SSL methods with highly imbalanced performance across mid-level and high-level capabilities, as well as some that excel in both. Additionally, we investigate key factors contributing to mid-level vision performance, such as pretraining objectives and network architectures. Our study provides a holistic and timely view of what SSL models have learned, complementing existing research that primarily focuses on high-level vision tasks. We hope our findings guide future SSL research to benchmark models not only on high-level vision tasks but on mid-level as well. + +# 1. Introduction + +Mid-level vision capabilities [41] (Fig. 1a) play a vital role in human visual development and daily life activities. By the age of one, children can re-organize retinal images into objects (i.e., perceptual grouping), construct the visual world in three dimensions (i.e., 3D geometric understanding), track moving objects (i.e., cross-view correspondence), grasp and bite these objects without knowing their semantics, and purposefully navigate through the 3D world. Importantly, such mid-level perception is developed without supervision [32]. + +On the other hand, self-supervised learning (SSL) in computer vision has made significant strides [5-8, 25, 42, + +![](images/36b0239bc536d9193363ae202a6a5bed217c8fa32f4e4a726e8cdc34c897266a.jpg) +Generic Object Seg + +![](images/c0e65aa87559799e2fbe1b31116aac1ac6474d43c10898cd8377d7e5e3adb43b.jpg) +Depth Estimation + +![](images/bb89f0418692726bd48b18967bb3e68c060579b275ba8de791a063b0faca8e2b.jpg) +Surface Normal + +![](images/9f4f2cdd33e93fcab5b70cb4cb6ccfb1b1087881fac970b2252c7e8fd6380bea.jpg) + +![](images/874bcc34c2dc3b15983927414c6af19892a600d7fd556ce5637c72647ed5c7f1.jpg) +Input +3D Geometric Correspondence + +![](images/a8df851d534fdf5a4bec1f6c72b6a7d935fa4e7352b6426a38141c9b09fb7c7d.jpg) + +Correspondence: + +![](images/985f8b1aeef683dc67e621fd25218555d16967c6e3f2a82a720e830c890e0129.jpg) +Image Similarity + +![](images/a13317ebe94ead3099e5af3e2af93ea2a0bd3bdfef3c676aecd1d46053e1ed0d.jpg) +Classification & Detection + +![](images/ec78c3116e3b97d45120eb785a6e831bcece59cee47d7097aa7af6ce201c9724.jpg) +RotNet +NPID +SeLa-v +NPID+ +PIRL +(c) SSLs for mid-level and high-level vision w.r.t. ImageNet classification +Figure 1. Mid-Level Vision vs. High-Level Vision Tasks. We provide a comprehensive evaluation of prominent self-supervised learning methods (SSLs) across a wide range of mid-level vision tasks (a), complementing the standard evaluation in high-level vision tasks (b). Although SSL performance in mid-level vision tasks (e.g., depth estimation) is positively correlated with ImageNet linear probing, this correlation is much weaker than that observed among high-level vision tasks, as shown in (c) by the $R^2$ statistics. + +![](images/48b112a3ffd212baa75a8f271b9056fc9783f1368c69d92134291bdce59f426c.jpg) +DeepCI +SwAV +SimCLR +MoCo v2 +SimSiam + +![](images/4f5d6985b26ce70ae242e2dd6210dabe697c97aeb810e90371e9b281923aabe0.jpg) +r-v2 Barlo +DenseCL +DINO +MoCo v3 (RN-50) +Barlow Twins +DenseCL +DINO (RN-50) + +iBOT + +MoCo v3 (ViT-B/16) + +MAE + +45, 46, 66, 71]. The goal of SSL is to learn visual representations from unlabeled data so that these pretrained representations can be applied to a wide range of downstream tasks, reducing the need for human annotations and enhancing learning efficiency and performance. However, SSL is predominantly evaluated based on performance in high-level visual recognition tasks, such as image classification, object detection, and semantic segmentation (Fig. 1b). At the same time, the mid-level vision capabilities of SSL models are largely under-explored. To fill this gap, this pa + +![](images/c6d97088c3e6e069e8e9fd43caef709bc988aa989971af63e70713b05bc5d6f8.jpg) + +![](images/7abcecf034b59ae93fbb2608e677635f8630cb79ead35c805463707508bc5e7f.jpg) +Semantic Seg. + +Classification & Detection + +![](images/eabe40bb5032ca094bb21a57911d3d6815f002322675453d914e566940174070.jpg) +(a) Mid-level vision + +![](images/369ffc6d86d23ca3c462ab0cb014d191f8b877d581e09837096fc8ef77955c4d.jpg) +- - MaskFeat +(b) High-level vision + +![](images/c77d81b7ede8ef2e7bb46609554f362cee3c42bfd21b83d28c810395f19f1516.jpg) + +MoCo v3 (RN-50) + +iBOT + +MoCo v3 (ViT-B/16) + +MAE + +per addresses the following questions: + +- Does strong high-level vision performance of SSLs indicate strong mid-level vision capabilities? +- What makes an SSL model effective for mid-level vision tasks? + +To answer these questions, we comprehensively evaluate SSLs in a wide range of mid-level vision tasks, including generic object segmentation, monocular depth and surface normal estimation, geometric correspondence, and mid-level image similarity (Fig. 1a and Tab. 2). We then relate the mid-level vision performance of these SSLs to their high-level vision performance. Our evaluations covers 22 seminar SSL approaches (Tab. 1) from diverse categories developed in the past decades (e.g. pretext tasks [25, 45], contrastive learning [6, 7, 9, 27, 66], self-distillation [5], and generative modeling [30, 62]). To make a controlled study and fair comparisons across different SSLs, our study primarily focuses on SSLs with publicly available checkpoints pretrained on ImageNet1K [12]. This allows us to gain insights into what factors may contribute to the mid-level vision capabilities in SSL (e.g., training objectives, network architectures, etc.). + +Our observations are as follows: + +- The mid-level vision capabilities of SSLs are positively correlated with high-level vision. However, that correlation is generally weaker than that among high-level vision tasks (Fig. 1c and Fig. 2). +- Some SSLs have highly imbalanced mid-level and high-level vision capabilities. For instance, MAE [31] underperforms most SSLs in the mid-level vision tasks while having competitive high-level vision performance; MaskFeat [62] has better mid-level performance than most SSLs with similar high-level vision (Fig. 5). +- Network architectures, model capacity, and pretraining strategies impact mid-level vision capabilities. In general, ViT [14] outperforms ResNet [28]; Increasing the network capacity is beneficial (Tab. 3); The leading methods are generally based on generative modeling (Fig. 5). + +Our study is built upon Probe3D [17], a recent work that evaluates the 3D awareness of visual models. In this work, we explore a broader range of mid-level vision tasks. Furthermore, our study primarily focuses on SSLs pretrained exclusively on ImageNet1K, while Probe3D probes visual foundation models that are trained from very diverse training configurations such as varying supervision signals (e.g. CLIP [50]) and dataset sizes. Our controlled settings allow us to gain insights into the factors contributing to model performance. Our exploration is also closely related to prior works that benchmark SSLs in various vision tasks [18, 26, 44, 55], such as out-of-domain classification [40] and fine-grained recognition [54, 57]. Unlike these works, our evaluation includes more recent SSLs, providing a timely study on this topic. + +In summary, our study offers a comprehensive view of the representations learned by SSL models. We hope these findings inspire practical approaches that perform well across both mid-level and high-level vision tasks. We will release our benchmark suite to support future SSL benchmarking in the research community. + +# 2. Related Work + +Self-Supervised Learning (SSL). The goal of self-supervised learning (SSL) in computer vision is to pretrain image representations using unlabeled data, enabling these representations to be transferred effectively to various downstream tasks. Early SSL methods leveraged a range of pretext tasks, such as colorization [70], rotation prediction [25], jigsaw puzzle solving [45], and inpainting [47]. Recent advances have focused on contrastive learning [6, 7, 27, 29, 66, 69] and generative modeling [13, 31, 37, 48, 62]. Despite extensive research, SSL performance is primarily evaluated on high-level vision tasks (e.g., ImageNet classification, object detection), overlooking the practical relevance of mid-level vision tasks. In this work, we focus on evaluating SSL methods on mid-level vision tasks. + +Self-Supervised Pretraining for 3D Vision. Unlike most SSL methods focusing on 2D visual recognition tasks, a few recent works explore SSLs for 3D vision. For example, CroCo [63] adopts masked image modeling to learn 3D representations from image pairs showing the same scene from different viewpoints. Despite the improvement in downstream 3D vision tasks, CroCo compromises high-level recognition performance. As a followup, CroCo-v2 [64] extends the training data of CroCo to a large dataset of natural images and demonstrates improved performance in downstream optical flow and stereo vision tasks. However, learning representations for 3D vision tasks remains under-explored. + +Benchmarking Self-Supervised Learning. Numerous studies underscore the growing importance of empirically evaluating general-purpose representation learning. For example, Goyal et al. [26] provide extensive benchmarking of SSLs across multiple downstream tasks, including classification, navigation, object detection, and surface normal estimation. Newell et al. [44] examine the effectiveness of SSLs under various configurations (e.g., annotation quantities) in downstream tasks such as pose estimation and depth estimation. Ericsson et al. [18] evaluate 13 SSLs across 40 downstream vision tasks, demonstrating a weak correlation between SSL performance on ImageNet classification and tasks like few-shot learning, object detection, and dense prediction. More recently, Marks et al. [40] studied how classification-based SSL evaluation protocols correlate with and predict downstream performance on out-of-domain datasets. In line with these works, we comprehen + +sively evaluate existing SSLs across various downstream tasks. We focus on mid-level vision performance and how it relates to high-level vision. + +Benchmarking Visual Foundation Models. More recently, several studies have evaluated large visual foundation models (VFMs) that are not exclusively trained by self-supervised learning methods (e.g., CLIP [50]). For example, Probe3D [17] examines the 3D awareness of VFMs [5, 34], while Cambrian-1 [55] utilizes large language models (LLMs) and visual instruction tuning to assess visual representations across various 2D and 3D vision tasks. Since VFMs are typically trained with diverse approaches (e.g., different supervision signals, datasets, and architectures), isolating the factors contributing to the performance of the representations they learn is challenging. In contrast, we conduct a controlled evaluation of SSL models that provide publicly available checkpoints pretrained on ImageNet1K. This approach enables fair comparisons across SSLs and offers deeper insights into their methodologies. + +# 3. Background: Vision Task Taxonomy + +There exist numerous computer vision tasks [68] which can be categorized from different perspectives. We briefly introduce two popular frameworks in this section: + +- Bottom-up Hierarchical Vision. David Marr [41] proposes to break up the vision system into low-level, mid-level, and high-level stages. Low-level vision tasks aim to extract edges, contours, and blobs from raw pixels, while high-level vision concerns the semantics, functionality, and holistic 3D shape of objects. Mid-level vision, lying in-between the low-level and high-level vision, addresses the view-centric geometric properties of surfaces (e.g., depth and surface normal), generic object segmentation and localization without semantics, cross-view image correspondences, and so on. This framework favors a feed-forward and bottom-up vision process. +- Three R's of Vision. Malik et al. [39] categorize vision tasks into recognition, reconstruction, and reorganization. Recognition refers to the task of assigning semantic categories to images. Reconstruction concerns the estimation of 3D structures. Reorganization addresses the grouping and segmentation of images on spatial or perceptual similarity. Instead of a bottom-up process, 3R's emphasizes the mutual benefits and relationship across these three visual capabilities. + +Both frameworks highlight the importance of the nonsemantic vision tasks — mid-level vision in Marr's framework, reconstruction and reorganization in 3R's. We adopt the term "mid-level" for the convenience of differentiating + +from high-level recognition tasks. However, the underlying vision mechanism remains under debate. + +# 4. Experimental Setup + +In this section, we first introduce the SSLs considered in this work (Tab. 1) and our generic evaluation protocols for probing these SSLs. We then present the mid-level vision tasks in detail, including their definitions, datasets, and evaluation approaches (Sec. 4.1- 4.3 and Tab. 2). + +Our probing approaches are largely inspired by Probe3D [17], the recent work that evaluates the 3D awareness of visual foundation models (VFMs). The VFMs are usually trained under distinct settings (e.g. supervision signals, dataset sizes, network architectures and capacity), while we aim at probing self-supervised visual models that are trained with similar configurations. Therefore, our work provides a complementary study, specifically a more controlled setting, compared to Probe3D [17]. + +Self-Supervised Models. Tab. 1 presents an overview of the SSL models considered in our study. We primarily focus on SSLs that have publicly available checkpoints pretrained on ImageNet1K [12], with standard neural network architectures (e.g. ResNet50 [28] or Vision Transformers (ViT) [14]) as the image feature extractor. These SSLs cover a wide range of pretraining strategies, including clustering, contrastive learning, generative modeling, or a mixture of different training objectives. Targeting a comprehensive benchmark, we track the SSL literature back to classic methods that learn image representations from pre-text tasks such as Jigsaw [45] and RotNet [25]. Our selection of SSLs is inspired by Marks et al. [40], which provides a detailed study of the evaluation protocols of SSLs. + +Generic Evaluation Protocols. Many mid-level vision tasks can be formulated as dense prediction (e.g., depth estimation). Unlike image classification, dense prediction requires local pixel or patch representations as input, and the main design choice is to decide which network layers (e.g., ResNet layers or ViT blocks) to extract the dense features from. Following Probe3D, we use the DPT decoder [52], a non-linear dense multi-scale network. For ResNet [28], we use the outputs of the last four ResNet blocks as the input to the DPT head, following the architecture of the feature pyramid network [36]; For ViT [14], following Probe3D, the network is split into four blocks evenly, and the features are extracted after each block — for ViT-B, we extract features after layers 3, 6, 9, and 12. Like Probe3D, we probe the frozen representations to evaluate the capabilities of learned representations instead of their transferability. We provide task-specific evaluation protocols in the following sections and hyperparameter settings in the supplementary material. + +
IDSSLArchitectureCategory
1Jigsaw [45]ResNet50Pre-text
2RotNet [25]ResNet50Pre-text
3NPID [66]ResNet50Contrastive
4NPID++ [42]ResNet50Contrastive
5PIRL [42]ResNet50Contrastive
6ClusterFit [67]ResNet50Clustering
7SwAV [4]ResNet50Clustering
8SeLa-v2 [4]ResNet50Clustering
9DeepCluster-v2 [4]ResNet50Clustering
10SimCLR [6]ResNet50Contrastive
11MoCo-v2 [8]ResNet50Contrastive
12SimSiam [7]ResNet50Contrastive
13DenseCL [58]ResNet50Contrastive
14BYOL [27]ResNet50Contrastive
15Barlow Twins [69]ResNet50Contrastive
16MoCo-v3 [9]ResNet50Contrastive
17DINO [5]ResNet50Self-distillation
18MoCo-v3 [9]ViT-B/16Contrastive
19DINO [5]ViT-B/16Self-distillation
20MAE [31]ViT-B/16Generative
21iBOT [71]ViT-B/16Mixture
22MaskFeat [62]ViT-B/16Generative
+ +Table 1. Evaluated Self-Supervised Learning Methods (SSLs). We provide a comprehensive evaluation of SSLs that provide publicly available checkpoints trained from the ImageNet1K dataset [12]. We categorize SSLs based on their training objectives and network backbones. Mixture denotes the combination of different SSLs (e.g., iBOT [71]). The SSLs are listed in order of their publication year. + +# 4.1. Generic Object Segmentation + +Generic object segmentation (or figure-ground segmentation) refers to the task of separating objects (figure) from the surrounding background without any semantics. This mid-level vision task is different from semantic segmentation (i.e., assigning each pixel to a semantic category) which is commonly used for evaluating the high-level visual capabilities of SSLs. + +We use the VOC07 and VOC12 datasets [19, 20] as our benchmarks, following prior research on unsupervised object segmentation [56, 59, 61]. Given a pretrained feature extractor, we freeze the backbone and train a DPT decoder [51] with a simple binary cross-entropy loss (BCE). We use standard segmentation metrics (e.g., mean IoU) to measure the performance of SSLs in this task. + +# 4.2. Monocular Surface Reconstruction + +We evaluate SSLs in two tasks related to monocular 2.5D surface reconstruction: depth and surface normal estimation from Probe3D [17]. Even though these two tasks are closely related, they rely on different visual cues and cap + +ture distinct geometric properties. + +We evaluate depth estimation and surface normal prediction at both scene and object levels. For scene-level performance, we employ the NYUv2 dataset [43], a widely used benchmark for indoor environments. Object-level depth is assessed using the NAVI dataset [33], which provides diverse object instances across scenes and orientations. + +We present the task-specific configurations as follows. + +Monocular Depth Estimation The task aims at predicting pixel-wise depth from monocular images. We adopt the formulation of binned depth estimation from AdaBins [21], instead of the classical regression approaches [15]. We estimate the scale-invariant depth for object-centric images (e.g., NAVI) while predict metric depths on scene-centric datasets (e.g., NYUv2). We report root-mean-squared error (RMSE) and recall at various threshold ratios. + +Surface Normal Estimation. This task is to predict per-pixel surface direction. We train the DPT head with the uncertainty-aware angular loss [2]. As for depth estimation, we report RMSE and percentage recall at various angular thresholds. + +# 4.3. Multiview Correspondence + +In this section, we consider the tasks of estimating correspondences across multiple views that involve mid-level variations, such as changes in camera perspective and object motion. These mid-level variations differ from low-level variations in image properties (e.g., color and texture) and high-level variations in semantic attributes (e.g., object categories). Specifically, we probe SSLs in two tasks: geometric correspondence and mid-level image similarity. Following Probe3D [17], we extract image or pixel representations from pretrained SSLs model without additional training. + +Geometric Correspondence This task aims to build pixel correspondences across two views that depict the same 3D scene. Our evaluation follows Probe3D [17]. Specifically, we estimate the pixel correspondences using the dense feature maps extracted from pretrained SSL models. We use the Paired ScanNet [10] to evaluate scene-centric images and the NAVI dataset [33] for object-centric images. We sample views with a maximum rotation of 120 degrees to ensure that a mutually visible surface exists without a large viewpoint change. We report the correspondence recall — the percentage of correspondence that falls within some defined distance. + +Mid-Level Image Similarity The task aims at measuring the similarity of two images with mid-level variations (e.g., viewpoint). We evaluate the SSLs on the NIGHTS dataset collected by DreamSim [23]. Specifically, for each triplets $(x, \tilde{x}_0, \tilde{x}_1)$ from the NIGHTS dataset, we predict whether $\tilde{x}_0$ or $\tilde{x}_1$ is more similar to the reference image $x$ . We denote a distance between two images as $D(x, \tilde{x}; f_\theta) =$ + +
HierarchyTasksTypeBenchmarksLossesMetrics
High-levelImage Classification2DImageNet1K [53]CEAccuracy
Object Detection2DVOC07 [19], COCO [35]CE+L2AP
Semantic Segmentation2DCOCO [35]CEmIOU
Mid-levelGeneric Object Segmentation2DVOC07 [19], VOC12 [20]BCEF1, mIoU, Acc
Depth Prediction3DNAVI [33], NYU [43]AdaBinRMSE, ε1, ε2, ε3
Surface Normal Estimation3DNAVI [33], NYU [43]AngularRMSE, ε1, ε2, ε3
Geometric Correspondence3DNAVI [33], ScanNet [11]Training-free2D, 3D Recall
Mid-level Image Similarity2DNIGHTS [24]Training-freeRetrieval Score (F1-Score)
+ +Table 2. Probing Tasks. In comparison with the standard SSL evaluation protocols that primarily focus on high-level vision tasks (top), we provide a comprehensive, systematic, and controlled evaluation of SSL in mid-level vision tasks (bottom). Our evaluations cover 2D and 3D vision with a wide range of benchmarks. The $\epsilon_{1}$ , $\epsilon_{2}$ and $\epsilon_{3}$ in depth and surface normal estimation represents recall at different threshold rations [16, 22]. Detailed descriptions of each metric can be found in the supplementary. + +![](images/4d68657de68262b76a2a508915e0f61aefd2c44e04777c7bddfd4f125df5276d.jpg) +Figure 2. Mid-Level Vision v.s. ImageNet Linear Probing. We report the performance of self-supervised learning methods on mid-level vision tasks (y-axis) against their ImageNet 1K linear classification accuracy. Metrics are detailed in Tab. 2. Linear regression shows correlation with $R^2$ in each plot's top-left corner, and the red shaded area marks the $95\%$ confidence interval. + +$1 - \cos \bigl (f_{\theta}(x),f_{\theta}(\tilde{x})\bigr)$ where $f_{\theta}$ is the image representations from pretrained SSLs. For ViT, we use the CLS tokens taken from the last layer; For ResNet, we use the global image representation in the output layer. The model's vote is calculated as follows: if $d_1 < d_0$ , then $\hat{y} = 1$ ; otherwise, if $d_0 < d_1$ , then $\hat{y} = 0$ , where $d_0 = D(x,\tilde{x}_0;f_\theta)$ and $d_{1} = D(x,\tilde{x}_{1};f_{\theta})$ . We use voting accuracy as our evaluation metric. + +# 5. Analysis + +# 5.1. Does strong high-level performance imply strong mid-level performance? + +Yes, to some extent. As ImageNet (IN1k) probing results improve, we generally observe a corresponding enhance- + +ment in mid-level vision tasks, as depicted in Fig. 2. This positive trend indicates that SSL models capable of high-level visual recognition tend to provide better representations for mid-level vision tasks as well, benefiting tasks that leverage spatial and structural information. + +Some mid-level tasks are highly correlated with high-level. A per-task closer examination, however, reveals nuances in this relationship. For example, generic object segmentation shows the highest correlation with high-level tasks, achieving a coefficient of determination $(R^2 = 0.70)$ . This suggests that high-level features indeed capture spatial structures that enhance segmentation accuracy. Mid-level and high-level vision also correlate highly in the task + +![](images/ce8e65d923a5b56d8e2fa40490a2c5765b8cfc204a5de46df2509149689efe43.jpg) +Figure 3. Cross-task performance correlation. We present Pearson coefficients across mid-level and high-level vision tasks. We use the same set of metrics we used in Fig. 2. + +of mid-level image similarity. This indicates that the high-level image representations are invariant to mid-level variations to some extent (e.g., viewpoint variations). + +3D geometric understanding is weakly correlated with high-level vision. For tasks like scene surface normal estimating, we observe notably weaker correlations. These tasks often require intricate, fine-grained geometric and surface features that high-level SSL objectives alone do not sufficiently capture. This gap implies that mid-level vision depends on specialized cues not fully addressed by high-level feature extraction. + +Correlation across mid-level vision tasks. Fig. 3 shows the Pearson correlations across tasks. We find a strong correlation between object segmentation and mid-level image similarity (coefficients above 0.76). Object segmentation further correlates well with depth estimation and object-level multi-view geometric correspondence, indicating that spatial understanding aids segmentation and underscores the importance of 3D awareness in image understanding. In contrast, scene geometry correspondence correlates weaker with other mid-level and high-level tasks. Mid-level image similarity aligns with object segmentation and correspondence but correlates less with 3D tasks. + +Ranking in mid-level vision. In Fig. 5, we present a comparative ranking of SSL models based on their performance across mid-level vision tasks and ImageNet probing. Each model received a task-specific rank, and we computed an average score, with higher scores indicating stronger performance in both mid-level and high-level vision tasks. Our + +![](images/f9816ee3b028d715802190d47802c78d414f86304f5da9f8b87a4d3609fd8c00.jpg) + +![](images/3f281907399737c7b57adf6ab5fba359553ffc886f27f0411a89dc8b40c6e06d.jpg) +Figure 4. Mid-Level Vision v.s. ImageNet Linear Probing with Contrastive Learning Methods. We examine several contrastive learning methods [6-9, 27, 58, 69] and observe a negative correlation between ImageNet linear probing accuracy and task performance. Depth estimation results are shown at the top, with surface normal estimation results at the bottom. The y-axis represents prediction accuracy, where higher values indicate better performance. + +analysis suggests an imbalance in model performance, with some models excelling in high-level tasks but showing comparatively modest capabilities in mid-level vision tasks. Notably, MaskFeat stands out as an exception, demonstrating a significant advantage in mid-level vision tasks over high-level performance. + +Conversely, MAE ranks lower on mid-level tasks, demonstrating limited proficiency in capturing finer visual details. In the following sections, we will discuss the specifics of MAE and MaskFeat. + +Notably, iBOT [71] and DINO [4] rank among the top performers, exhibiting strong capabilities in both mid-level and high-level vision tasks. In contrast, pretext pre-trained models like RotNet [25] and Jigsaw [45] fall behind other SSL methods. + +# 5.2. What makes a strong mid-level vision model? + +Training objective. We observe that the top-performing SSL models in mid-level vision tasks are typically generative-based, such as iBOT [71] and MaskFeat [62]. In contrast, recent contrastive self-supervised learning (SSL) models [6-9, 27, 58, 69] show an inverse relationship between mid-level vision performance and ImageNet linear probing accuracy, as illustrated in Fig. 4. + +Although these methods have improved ImageNet linear probing accuracy by over $10\%$ , they exhibit notable declines in mid-level vision tasks. We illustrate this trend with model performance on depth and surface normal estimation and + +![](images/44f36bb5c9845416877d7d1b35e2cb1f5641444144b0231c877949de93f2cb36.jpg) +Figure 5. Ranking SSLs based on Overall Score. Comparative ranking of SSL models based on performance in mid-level vision tasks and ImageNet probing. Models are ranked per task, and average scores reflect overall performance across mid-level and high-level vision tasks, with higher scores indicating stronger results. + +provide a broader analysis across six additional tasks in the supplementary materials. Notably, SSL models pre-trained on pretext tasks show the lowest performance on mid-level vision tasks. + +Network architecture. We further compare ViT-B (ViT Base) and ViT-L (ViT Large) backbones with the same SSL method in Tab. 3. Our findings show that ViT-L models tend to perform better than ViT-B across mid-level vision tasks. In particular, we evaluate two popular SSL models, iBOT and MAE, on both ViT-B and ViT-L backbones. This pattern suggests that larger backbones like ViT-L may capture mid-level vision features better. + +Network capability. We also compare ViT-B and ViT-L backbones using the same SSL method in Tab. 3. Our results indicate that ViT-Large models generally achieve higher scores across various mid-level vision tasks. Specifically, we examine two popular SSL models, iBOT and MAE, with ViT-B and ViT-L backbones. This trend suggests that larger models are better at capturing mid-level vision features. + +# 5.3. Which SSL works the best per task? + +In Tab. 4, we highlight the best-performing models for each task. iBOT [71] consistently leads in most mid-level vision tasks while MaskFeat performs even better on scene correspondence and scene surface normal. DINO works the best on object correspondence and achieves quite competitive results compared to other SSLs. + +# 5.4. Analysis of specific SSL + +MAE. MAE [30] stands out as a clear outlier, as illustrated in Fig. 2 and Fig. 5. MAE consistently performs poorly on mid-level vision tasks compared to other ViT-based SSLs such as iBOT [71] and MaskFeat [62]. + +MaskFeat. In Fig. 2 and Fig. 5, we observe that MaskFeat [62] demonstrates surprisingly strong mid-level vision capabilities despite showing relatively modest performance in high-level vision tasks. Since the MaskFeat checkpoint we used was trained exclusively on the ImageNet-1K dataset and followed a training process similar to MAE, we attribute its mid-level vision strength to its choice of target + +features. Unlike models trained on raw pixels, tokens, or high-level features, MaskFeat is optimized on HOG (Histograms of Oriented Gradients) features, which are widely used for keypoint detection in methods such as SIFT [38]. Importantly, HOG does not rely on any external models, making it a robust feature for capturing mid-level vision attributes. This finding suggests that incorporating mid-level vision-relevant features, like HOG, into SSL training may enhance model performance on mid-level vision tasks. + +SSLs based on pre-text tasks. RotNet and Jigsaw are the two lowest-performing SSLs on mid- and high-level vision. Given that they are the early design of SSLs, it revalidate our claim that ImageNet (IN1k) probing results improve, we generally observe a corresponding enhancement in mid-level vision task performance. + +# 5.5. How do visual foundation models (VFMs) perform? + +Even though our study aims to conduct a controlled benchmarking of SSLs in the mid-level vision tasks, we put VFMs into our context in this section to understand the comparison between the latest visual foundation models and the set of SSLs we analyzed. We observed that CLIP is much worse than most of the SSLs. DINO-v2 is the winner. We include a comparison in Fig. 6 focusing on depth estimation. + +DINO-V2 [46]. Our findings, consistent with Probe3D and Cambrian-1 [55], show DINO-V2 as the best-performing model across both ImageNet linear probing and mid-level vision tasks, making it a standout choice for comprehensive vision capabilities. + +CLIP [50]. CLIP's overall performance is notably lower across mid-level tasks, as reported in Probe3D [17] and Cambrian-1 [55]. This suggests that, while generalizable for 2D understanding, CLIP may be less suited for tasks requiring 3D spatial understanding. + +CroCo [65]. Using depth estimation as a representative task, we observe that CroCo performs competitively in mid-level vision tasks despite lagging in high-level vision tasks. Pretrained on synthetic multi-view image datasets, CroCo learns strong 3D-aware image representations. This distinction underscores its potential for 3D-specific applications, + +
SSLsBackboneObject Seg.Object SNorm.Scene SNorm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
MoCo-v3 [9]RN-5071.4827.2243.0345.9375.561.715.2384.37
MoCo-v3 [9]ViT-B/1672.4531.7249.6451.0780.143.1225.0386.90
DINO [5]RN-5071.9531.4347.6447.6377.683.1626.6383.31
DINO [5]ViT-B/1674.0031.0648.4247.7579.382.6124.3889.36
SSLsModel SizeObject Seg.Object Norm.Scene Norm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
iBOTB/1675.7432.7552.0250.0281.323.1220.0489.27
iBOTL/1675.3235.6554.5352.5685.143.1614.7982.37
MAEB/1665.7722.6743.8926.7866.172.746.6482.91
MAEL/1666.5826.6045.6026.8170.222.9310.0584.26
+ +Table 3. Impact of Network Architecture and Model Size on Mid-Level Vision Performance. The top table demonstrates that the Vision Transformer (ViT) [14] generally outperforms ResNet-50 (RN-50) [28] across most mid-level vision tasks when using MoCo-v3 or DINO as the self-supervised pretraining method. The bottom table shows that larger model sizes tend to enhance mid-level vision capabilities. Detailed numerical comparisons are provided in the supplementary material. + +
ModelImage Sim.Object Corres.Object DepthObject SNorm.
DINO (RN-50)83.313.1647.6331.43
MaskFeat [62]75.702.0849.5032.40
MoCo v384.371.7045.9327.22
iBOT [71]89.273.1250.0232.75
ModelObject Seg.Scene Corres.Scene DepthScene SNorm.
DINO (RN-50)71.9526.6377.6847.64
MaskFeat [62]70.2827.9480.3953.63
MoCo v371.4815.2375.5643.03
iBOT [71]75.7420.0481.3252.02
+ +Table 4. Top SSL Methods in Mid-Level Vision Tasks. iBOT outperformed all other SSL methods (listed in Tab. 1) in multiple mid-level vision tasks. Surprisingly, despite the low performance on ImageNet linear classification, MaskFeat achieved leading results in depth and surface normal estimation. + +where spatial understanding is prioritized over high-level visual semantics because of its design choice. + +SAM [34]. Although SAM excels at image segmentation, it exhibits moderate performance on mid-level vision tasks and notably weaker performance on image classification, in comparison with ImageNet-pretrained SSLs. This reveals the imbalanced performance of SAM among reorganization, reconstruction and recognition. + +# 6. Discussion + +In conclusion, this study introduces a suite of benchmark protocols to systematically evaluate mid-level vision capabilities, offering a comprehensive and controlled assessment of 22 SSL models across mid-level vision tasks. Our findings indicate a positive correlation between SSL performance in mid-level and high-level vision tasks, though this correlation is generally weaker than that observed within high-level tasks. + +Some SSL models exhibit imbalanced performance across these task levels. For instance, MAE [31] underperforms in mid-level tasks despite competitive high-level performance, while MaskFeat [62] excels in mid-level tasks + +![](images/1bc9099a0e4ce2d4b52db42d7c490e9ab78f998e0d6a09cf37f49257be5dca67.jpg) +Figure 6. Comparison of ImageNet1K-Pretrained SSLs with models trained with larger datasets (e.g., DINO-v2 [46]) or different training supervisions (e.g., CLIP [50] ${}^{1}$ ) in the scene depth estimation task. + +relative to its high-level results (Fig. 5). Mid-level vision capabilities are influenced by factors such as network architecture, dataset size, and pretraining strategy. Overall, ViT [14] outperforms ResNet [28], increasing model capacity proves beneficial (Tab. 3), and generative modeling approaches often lead in performance (Fig. 5). Additionally, we compare SSL models with VFMs, finding that DINOv2 [46] leads in both mid-level and high-level vision tasks and language objectives (e.g., CLIP) do not help on mid-level tasks. + +Since SSL's overall goal is to produce a very general feature representation that works well for a wide range of downstream tasks, we encourage the community to evaluate new SSL methods on both high- and mid-level tasks. + +This work is limited by resources, which prevents us from scaling up our experiments to more tasks and models, and we did not include ending tasks such as navigation and robotic manipulation to emphasize mid-level vision's role further. We provide details of our probing hyper-parameters and include visualizations for each task in the supplementary materials. + +# 7. 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In ECCV, 2016. 2 +[71] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. ibot: Image bert pre-training + +with online tokenizer. arXiv preprint arXiv:2111.07832, 2021. 1, 4, 6, 7, 8, 2, 9, 10 \ No newline at end of file diff --git a/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/images.zip b/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d7f7f4e0c4c6b97c10c13ea17253e260e957856c --- /dev/null +++ b/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2e33a7b1c59ec71ea0f320b7821e706005f2893f91eb924a311a2639de589b1c +size 609539 diff --git a/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/layout.json b/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..8263e19d84195e226ec2a1910341e00a8220426f --- /dev/null +++ b/2025/Probing the Mid-level Vision Capabilities of Self-Supervised Learning/layout.json @@ -0,0 +1,9390 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 90, + 103, + 520, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 103, + 520, + 121 + ], + "spans": [ + { + "bbox": [ + 90, + 103, + 520, + 121 + ], + "type": "text", + "content": "Probing the Mid-level Vision Capabilities of Self-Supervised Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 156, + 142, + 451, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 142, + 451, + 172 + ], + "spans": [ + { + "bbox": [ + 156, + 142, + 451, + 172 + ], + "type": "text", + "content": "Xuweiyi Chen1 Markus Marks2 Zezhou Cheng1 \n1University of Virginia 2California Institute of Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 199, + 199, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 199, + 199, + 211 + ], + "spans": [ + { + "bbox": [ + 152, + 199, + 199, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 224, + 295, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 224, + 295, + 344 + ], + "spans": [ + { + "bbox": [ + 54, + 224, + 295, + 344 + ], + "type": "text", + "content": "Mid-level vision capabilities — such as generic object localization and 3D geometric understanding — are not only fundamental to human vision but are also crucial for many real-world applications of computer vision. These abilities emerge with minimal supervision during the early stages of human visual development. Despite their significance, current self-supervised learning (SSL) approaches are primarily designed and evaluated for high-level recognition tasks, leaving their mid-level vision capabilities largely unexamined." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 345, + 296, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 345, + 296, + 535 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 296, + 535 + ], + "type": "text", + "content": "In this study, we introduce a suite of benchmark protocols to systematically assess mid-level vision capabilities and present a comprehensive, controlled evaluation of 22 prominent SSL models across 8 mid-level vision tasks. Our experiments reveal a weak correlation between mid-level and high-level task performance. We also identify several SSL methods with highly imbalanced performance across mid-level and high-level capabilities, as well as some that excel in both. Additionally, we investigate key factors contributing to mid-level vision performance, such as pretraining objectives and network architectures. Our study provides a holistic and timely view of what SSL models have learned, complementing existing research that primarily focuses on high-level vision tasks. We hope our findings guide future SSL research to benchmark models not only on high-level vision tasks but on mid-level as well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 549, + 135, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 549, + 135, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 549, + 135, + 561 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 569, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 689 + ], + "type": "text", + "content": "Mid-level vision capabilities [41] (Fig. 1a) play a vital role in human visual development and daily life activities. By the age of one, children can re-organize retinal images into objects (i.e., perceptual grouping), construct the visual world in three dimensions (i.e., 3D geometric understanding), track moving objects (i.e., cross-view correspondence), grasp and bite these objects without knowing their semantics, and purposefully navigate through the 3D world. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30095" + } + ] + } + ], + "index": 53 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 211, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 211, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 211, + 83 + ], + "type": "text", + "content": "per addresses the following questions:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 86, + 295, + 133 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 55, + 86, + 294, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 86, + 294, + 110 + ], + "spans": [ + { + "bbox": [ + 55, + 86, + 294, + 110 + ], + "type": "text", + "content": "- Does strong high-level vision performance of SSLs indicate strong mid-level vision capabilities?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 110, + 295, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 110, + 295, + 133 + ], + "spans": [ + { + "bbox": [ + 56, + 110, + 295, + 133 + ], + "type": "text", + "content": "- What makes an SSL model effective for mid-level vision tasks?" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 135, + 295, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 135, + 295, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 135, + 295, + 338 + ], + "type": "text", + "content": "To answer these questions, we comprehensively evaluate SSLs in a wide range of mid-level vision tasks, including generic object segmentation, monocular depth and surface normal estimation, geometric correspondence, and mid-level image similarity (Fig. 1a and Tab. 2). We then relate the mid-level vision performance of these SSLs to their high-level vision performance. Our evaluations covers 22 seminar SSL approaches (Tab. 1) from diverse categories developed in the past decades (e.g. pretext tasks [25, 45], contrastive learning [6, 7, 9, 27, 66], self-distillation [5], and generative modeling [30, 62]). To make a controlled study and fair comparisons across different SSLs, our study primarily focuses on SSLs with publicly available checkpoints pretrained on ImageNet1K [12]. This allows us to gain insights into what factors may contribute to the mid-level vision capabilities in SSL (e.g., training objectives, network architectures, etc.)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 339, + 199, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 339, + 199, + 350 + ], + "spans": [ + { + "bbox": [ + 67, + 339, + 199, + 350 + ], + "type": "text", + "content": "Our observations are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 352, + 295, + 533 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 55, + 352, + 295, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 295, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 295, + 399 + ], + "type": "text", + "content": "- The mid-level vision capabilities of SSLs are positively correlated with high-level vision. However, that correlation is generally weaker than that among high-level vision tasks (Fig. 1c and Fig. 2)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 400, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 400, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 295, + 472 + ], + "type": "text", + "content": "- Some SSLs have highly imbalanced mid-level and high-level vision capabilities. For instance, MAE [31] underperforms most SSLs in the mid-level vision tasks while having competitive high-level vision performance; MaskFeat [62] has better mid-level performance than most SSLs with similar high-level vision (Fig. 5)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "text", + "content": "- Network architectures, model capacity, and pretraining strategies impact mid-level vision capabilities. In general, ViT [14] outperforms ResNet [28]; Increasing the network capacity is beneficial (Tab. 3); The leading methods are generally based on generative modeling (Fig. 5)." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "content": "Our study is built upon Probe3D [17], a recent work that evaluates the 3D awareness of visual models. In this work, we explore a broader range of mid-level vision tasks. Furthermore, our study primarily focuses on SSLs pretrained exclusively on ImageNet1K, while Probe3D probes visual foundation models that are trained from very diverse training configurations such as varying supervision signals (e.g. CLIP [50]) and dataset sizes. Our controlled settings allow us to gain insights into the factors contributing to model performance. Our exploration is also closely related to prior works that benchmark SSLs in various vision tasks [18, 26, 44, 55], such as out-of-domain classification [40] and fine-grained recognition [54, 57]. Unlike these works, our evaluation includes more recent SSLs, providing a timely study on this topic." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "In summary, our study offers a comprehensive view of the representations learned by SSL models. We hope these findings inspire practical approaches that perform well across both mid-level and high-level vision tasks. We will release our benchmark suite to support future SSL benchmarking in the research community." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 156, + 400, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 156, + 400, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 400, + 167 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 175, + 555, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 175, + 555, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 555, + 344 + ], + "type": "text", + "content": "Self-Supervised Learning (SSL). The goal of self-supervised learning (SSL) in computer vision is to pretrain image representations using unlabeled data, enabling these representations to be transferred effectively to various downstream tasks. Early SSL methods leveraged a range of pretext tasks, such as colorization [70], rotation prediction [25], jigsaw puzzle solving [45], and inpainting [47]. Recent advances have focused on contrastive learning [6, 7, 27, 29, 66, 69] and generative modeling [13, 31, 37, 48, 62]. Despite extensive research, SSL performance is primarily evaluated on high-level vision tasks (e.g., ImageNet classification, object detection), overlooking the practical relevance of mid-level vision tasks. In this work, we focus on evaluating SSL methods on mid-level vision tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 349, + 556, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 349, + 556, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 349, + 556, + 504 + ], + "type": "text", + "content": "Self-Supervised Pretraining for 3D Vision. Unlike most SSL methods focusing on 2D visual recognition tasks, a few recent works explore SSLs for 3D vision. For example, CroCo [63] adopts masked image modeling to learn 3D representations from image pairs showing the same scene from different viewpoints. Despite the improvement in downstream 3D vision tasks, CroCo compromises high-level recognition performance. As a followup, CroCo-v2 [64] extends the training data of CroCo to a large dataset of natural images and demonstrates improved performance in downstream optical flow and stereo vision tasks. However, learning representations for 3D vision tasks remains under-explored." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 510, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 714 + ], + "type": "text", + "content": "Benchmarking Self-Supervised Learning. Numerous studies underscore the growing importance of empirically evaluating general-purpose representation learning. For example, Goyal et al. [26] provide extensive benchmarking of SSLs across multiple downstream tasks, including classification, navigation, object detection, and surface normal estimation. Newell et al. [44] examine the effectiveness of SSLs under various configurations (e.g., annotation quantities) in downstream tasks such as pose estimation and depth estimation. Ericsson et al. [18] evaluate 13 SSLs across 40 downstream vision tasks, demonstrating a weak correlation between SSL performance on ImageNet classification and tasks like few-shot learning, object detection, and dense prediction. More recently, Marks et al. [40] studied how classification-based SSL evaluation protocols correlate with and predict downstream performance on out-of-domain datasets. In line with these works, we comprehen" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30096" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "sively evaluate existing SSLs across various downstream tasks. We focus on mid-level vision performance and how it relates to high-level vision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 128, + 295, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 128, + 295, + 332 + ], + "spans": [ + { + "bbox": [ + 56, + 128, + 295, + 332 + ], + "type": "text", + "content": "Benchmarking Visual Foundation Models. More recently, several studies have evaluated large visual foundation models (VFMs) that are not exclusively trained by self-supervised learning methods (e.g., CLIP [50]). For example, Probe3D [17] examines the 3D awareness of VFMs [5, 34], while Cambrian-1 [55] utilizes large language models (LLMs) and visual instruction tuning to assess visual representations across various 2D and 3D vision tasks. Since VFMs are typically trained with diverse approaches (e.g., different supervision signals, datasets, and architectures), isolating the factors contributing to the performance of the representations they learn is challenging. In contrast, we conduct a controlled evaluation of SSL models that provide publicly available checkpoints pretrained on ImageNet1K. This approach enables fair comparisons across SSLs and offers deeper insights into their methodologies." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 346, + 257, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 346, + 257, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 257, + 358 + ], + "type": "text", + "content": "3. Background: Vision Task Taxonomy" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 366, + 295, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 403 + ], + "type": "text", + "content": "There exist numerous computer vision tasks [68] which can be categorized from different perspectives. We briefly introduce two popular frameworks in this section:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 407, + 295, + 661 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 407, + 295, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 295, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 295, + 552 + ], + "type": "text", + "content": "- Bottom-up Hierarchical Vision. David Marr [41] proposes to break up the vision system into low-level, mid-level, and high-level stages. Low-level vision tasks aim to extract edges, contours, and blobs from raw pixels, while high-level vision concerns the semantics, functionality, and holistic 3D shape of objects. Mid-level vision, lying in-between the low-level and high-level vision, addresses the view-centric geometric properties of surfaces (e.g., depth and surface normal), generic object segmentation and localization without semantics, cross-view image correspondences, and so on. This framework favors a feed-forward and bottom-up vision process." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "content": "- Three R's of Vision. Malik et al. [39] categorize vision tasks into recognition, reconstruction, and reorganization. Recognition refers to the task of assigning semantic categories to images. Reconstruction concerns the estimation of 3D structures. Reorganization addresses the grouping and segmentation of images on spatial or perceptual similarity. Instead of a bottom-up process, 3R's emphasizes the mutual benefits and relationship across these three visual capabilities." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Both frameworks highlight the importance of the nonsemantic vision tasks — mid-level vision in Marr's framework, reconstruction and reorganization in 3R's. We adopt the term \"mid-level\" for the convenience of differentiating" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "from high-level recognition tasks. However, the underlying vision mechanism remains under debate." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 111, + 432, + 126 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 111, + 432, + 126 + ], + "spans": [ + { + "bbox": [ + 313, + 111, + 432, + 126 + ], + "type": "text", + "content": "4. Experimental Setup" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 133, + 553, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 553, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 553, + 193 + ], + "type": "text", + "content": "In this section, we first introduce the SSLs considered in this work (Tab. 1) and our generic evaluation protocols for probing these SSLs. We then present the mid-level vision tasks in detail, including their definitions, datasets, and evaluation approaches (Sec. 4.1- 4.3 and Tab. 2)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 195, + 555, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 195, + 555, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 195, + 555, + 304 + ], + "type": "text", + "content": "Our probing approaches are largely inspired by Probe3D [17], the recent work that evaluates the 3D awareness of visual foundation models (VFMs). The VFMs are usually trained under distinct settings (e.g. supervision signals, dataset sizes, network architectures and capacity), while we aim at probing self-supervised visual models that are trained with similar configurations. Therefore, our work provides a complementary study, specifically a more controlled setting, compared to Probe3D [17]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 316, + 555, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 485 + ], + "type": "text", + "content": "Self-Supervised Models. Tab. 1 presents an overview of the SSL models considered in our study. We primarily focus on SSLs that have publicly available checkpoints pretrained on ImageNet1K [12], with standard neural network architectures (e.g. ResNet50 [28] or Vision Transformers (ViT) [14]) as the image feature extractor. These SSLs cover a wide range of pretraining strategies, including clustering, contrastive learning, generative modeling, or a mixture of different training objectives. Targeting a comprehensive benchmark, we track the SSL literature back to classic methods that learn image representations from pre-text tasks such as Jigsaw [45] and RotNet [25]. Our selection of SSLs is inspired by Marks et al. [40], which provides a detailed study of the evaluation protocols of SSLs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "content": "Generic Evaluation Protocols. Many mid-level vision tasks can be formulated as dense prediction (e.g., depth estimation). Unlike image classification, dense prediction requires local pixel or patch representations as input, and the main design choice is to decide which network layers (e.g., ResNet layers or ViT blocks) to extract the dense features from. Following Probe3D, we use the DPT decoder [52], a non-linear dense multi-scale network. For ResNet [28], we use the outputs of the last four ResNet blocks as the input to the DPT head, following the architecture of the feature pyramid network [36]; For ViT [14], following Probe3D, the network is split into four blocks evenly, and the features are extracted after each block — for ViT-B, we extract features after layers 3, 6, 9, and 12. Like Probe3D, we probe the frozen representations to evaluate the capabilities of learned representations instead of their transferability. We provide task-specific evaluation protocols in the following sections and hyperparameter settings in the supplementary material." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30097" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 291, + 340 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 291, + 340 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 291, + 340 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 291, + 340 + ], + "type": "table", + "html": "
IDSSLArchitectureCategory
1Jigsaw [45]ResNet50Pre-text
2RotNet [25]ResNet50Pre-text
3NPID [66]ResNet50Contrastive
4NPID++ [42]ResNet50Contrastive
5PIRL [42]ResNet50Contrastive
6ClusterFit [67]ResNet50Clustering
7SwAV [4]ResNet50Clustering
8SeLa-v2 [4]ResNet50Clustering
9DeepCluster-v2 [4]ResNet50Clustering
10SimCLR [6]ResNet50Contrastive
11MoCo-v2 [8]ResNet50Contrastive
12SimSiam [7]ResNet50Contrastive
13DenseCL [58]ResNet50Contrastive
14BYOL [27]ResNet50Contrastive
15Barlow Twins [69]ResNet50Contrastive
16MoCo-v3 [9]ResNet50Contrastive
17DINO [5]ResNet50Self-distillation
18MoCo-v3 [9]ViT-B/16Contrastive
19DINO [5]ViT-B/16Self-distillation
20MAE [31]ViT-B/16Generative
21iBOT [71]ViT-B/16Mixture
22MaskFeat [62]ViT-B/16Generative
", + "image_path": "9d6607b2ec83e4c8d4216055a2e543f9bb6ab863c836505b75d5f11b29780c1a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 349, + 296, + 427 + ], + "lines": [ + { + "bbox": [ + 55, + 349, + 296, + 427 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 296, + 427 + ], + "type": "text", + "content": "Table 1. Evaluated Self-Supervised Learning Methods (SSLs). We provide a comprehensive evaluation of SSLs that provide publicly available checkpoints trained from the ImageNet1K dataset [12]. We categorize SSLs based on their training objectives and network backbones. Mixture denotes the combination of different SSLs (e.g., iBOT [71]). The SSLs are listed in order of their publication year." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 449, + 217, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 217, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 217, + 462 + ], + "type": "text", + "content": "4.1. Generic Object Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 468, + 295, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 295, + 551 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 295, + 551 + ], + "type": "text", + "content": "Generic object segmentation (or figure-ground segmentation) refers to the task of separating objects (figure) from the surrounding background without any semantics. This mid-level vision task is different from semantic segmentation (i.e., assigning each pixel to a semantic category) which is commonly used for evaluating the high-level visual capabilities of SSLs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "text", + "content": "We use the VOC07 and VOC12 datasets [19, 20] as our benchmarks, following prior research on unsupervised object segmentation [56, 59, 61]. Given a pretrained feature extractor, we freeze the backbone and train a DPT decoder [51] with a simple binary cross-entropy loss (BCE). We use standard segmentation metrics (e.g., mean IoU) to measure the performance of SSLs in this task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 647, + 243, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 243, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 243, + 659 + ], + "type": "text", + "content": "4.2. Monocular Surface Reconstruction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "We evaluate SSLs in two tasks related to monocular 2.5D surface reconstruction: depth and surface normal estimation from Probe3D [17]. Even though these two tasks are closely related, they rely on different visual cues and cap" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 73, + 453, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 73, + 453, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 73, + 453, + 84 + ], + "type": "text", + "content": "ture distinct geometric properties." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "type": "text", + "content": "We evaluate depth estimation and surface normal prediction at both scene and object levels. For scene-level performance, we employ the NYUv2 dataset [43], a widely used benchmark for indoor environments. Object-level depth is assessed using the NAVI dataset [33], which provides diverse object instances across scenes and orientations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 326, + 156, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 156, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 326, + 156, + 545, + 168 + ], + "type": "text", + "content": "We present the task-specific configurations as follows." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 172, + 554, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 172, + 554, + 268 + ], + "spans": [ + { + "bbox": [ + 313, + 172, + 554, + 268 + ], + "type": "text", + "content": "Monocular Depth Estimation The task aims at predicting pixel-wise depth from monocular images. We adopt the formulation of binned depth estimation from AdaBins [21], instead of the classical regression approaches [15]. We estimate the scale-invariant depth for object-centric images (e.g., NAVI) while predict metric depths on scene-centric datasets (e.g., NYUv2). We report root-mean-squared error (RMSE) and recall at various threshold ratios." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 273, + 554, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 273, + 554, + 331 + ], + "spans": [ + { + "bbox": [ + 313, + 273, + 554, + 331 + ], + "type": "text", + "content": "Surface Normal Estimation. This task is to predict per-pixel surface direction. We train the DPT head with the uncertainty-aware angular loss [2]. As for depth estimation, we report RMSE and percentage recall at various angular thresholds." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 340, + 463, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 340, + 463, + 353 + ], + "spans": [ + { + "bbox": [ + 314, + 340, + 463, + 353 + ], + "type": "text", + "content": "4.3. Multiview Correspondence" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 357, + 555, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 555, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 555, + 478 + ], + "type": "text", + "content": "In this section, we consider the tasks of estimating correspondences across multiple views that involve mid-level variations, such as changes in camera perspective and object motion. These mid-level variations differ from low-level variations in image properties (e.g., color and texture) and high-level variations in semantic attributes (e.g., object categories). Specifically, we probe SSLs in two tasks: geometric correspondence and mid-level image similarity. Following Probe3D [17], we extract image or pixel representations from pretrained SSLs model without additional training." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 481, + 554, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 554, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 554, + 624 + ], + "type": "text", + "content": "Geometric Correspondence This task aims to build pixel correspondences across two views that depict the same 3D scene. Our evaluation follows Probe3D [17]. Specifically, we estimate the pixel correspondences using the dense feature maps extracted from pretrained SSL models. We use the Paired ScanNet [10] to evaluate scene-centric images and the NAVI dataset [33] for object-centric images. We sample views with a maximum rotation of 120 degrees to ensure that a mutually visible surface exists without a large viewpoint change. We report the correspondence recall — the percentage of correspondence that falls within some defined distance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": "Mid-Level Image Similarity The task aims at measuring the similarity of two images with mid-level variations (e.g., viewpoint). We evaluate the SSLs on the NIGHTS dataset collected by DreamSim [23]. Specifically, for each triplets " + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "inline_equation", + "content": "(x, \\tilde{x}_0, \\tilde{x}_1)" + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": " from the NIGHTS dataset, we predict whether " + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_0" + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_1" + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": " is more similar to the reference image " + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": ". We denote a distance between two images as " + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "inline_equation", + "content": "D(x, \\tilde{x}; f_\\theta) =" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30098" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 545, + 188 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 545, + 188 + ], + "type": "table", + "html": "
HierarchyTasksTypeBenchmarksLossesMetrics
High-levelImage Classification2DImageNet1K [53]CEAccuracy
Object Detection2DVOC07 [19], COCO [35]CE+L2AP
Semantic Segmentation2DCOCO [35]CEmIOU
Mid-levelGeneric Object Segmentation2DVOC07 [19], VOC12 [20]BCEF1, mIoU, Acc
Depth Prediction3DNAVI [33], NYU [43]AdaBinRMSE, ε1, ε2, ε3
Surface Normal Estimation3DNAVI [33], NYU [43]AngularRMSE, ε1, ε2, ε3
Geometric Correspondence3DNAVI [33], ScanNet [11]Training-free2D, 3D Recall
Mid-level Image Similarity2DNIGHTS [24]Training-freeRetrieval Score (F1-Score)
", + "image_path": "61f9fbbbd85b31a6b872b54d3c2d280ba54bf754dcaf488c7e9ee5632740bd09.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "text", + "content": "Table 2. Probing Tasks. In comparison with the standard SSL evaluation protocols that primarily focus on high-level vision tasks (top), we provide a comprehensive, systematic, and controlled evaluation of SSL in mid-level vision tasks (bottom). Our evaluations cover 2D and 3D vision with a wide range of benchmarks. The " + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon_{1}" + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon_{2}" + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon_{3}" + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "text", + "content": " in depth and surface normal estimation represents recall at different threshold rations [16, 22]. Detailed descriptions of each metric can be found in the supplementary." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 58, + 249, + 555, + 467 + ], + "blocks": [ + { + "bbox": [ + 58, + 249, + 555, + 467 + ], + "lines": [ + { + "bbox": [ + 58, + 249, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 58, + 249, + 555, + 467 + ], + "type": "image", + "image_path": "4d68657de68262b76a2a508915e0f61aefd2c44e04777c7bddfd4f125df5276d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "lines": [ + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "type": "text", + "content": "Figure 2. Mid-Level Vision v.s. ImageNet Linear Probing. We report the performance of self-supervised learning methods on mid-level vision tasks (y-axis) against their ImageNet 1K linear classification accuracy. Metrics are detailed in Tab. 2. Linear regression shows correlation with " + }, + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "type": "text", + "content": " in each plot's top-left corner, and the red shaded area marks the " + }, + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 480, + 555, + 515 + ], + "type": "text", + "content": " confidence interval." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "spans": [ + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "1 - \\cos \\bigl (f_{\\theta}(x),f_{\\theta}(\\tilde{x})\\bigr)" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " is the image representations from pretrained SSLs. For ViT, we use the CLS tokens taken from the last layer; For ResNet, we use the global image representation in the output layer. The model's vote is calculated as follows: if " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "d_1 < d_0" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " , then " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "\\hat{y} = 1" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " ; otherwise, if " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "d_0 < d_1" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " , then " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "\\hat{y} = 0" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "d_0 = D(x,\\tilde{x}_0;f_\\theta)" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "inline_equation", + "content": "d_{1} = D(x,\\tilde{x}_{1};f_{\\theta})" + }, + { + "bbox": [ + 55, + 535, + 295, + 631 + ], + "type": "text", + "content": " . We use voting accuracy as our evaluation metric." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 640, + 115, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 640, + 115, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 640, + 115, + 654 + ], + "type": "text", + "content": "5. Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 660, + 295, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 660, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 660, + 295, + 685 + ], + "type": "text", + "content": "5.1. Does strong high-level performance imply strong mid-level performance?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Yes, to some extent. As ImageNet (IN1k) probing results improve, we generally observe a corresponding enhance-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 535, + 555, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 535, + 555, + 595 + ], + "spans": [ + { + "bbox": [ + 313, + 535, + 555, + 595 + ], + "type": "text", + "content": "ment in mid-level vision tasks, as depicted in Fig. 2. This positive trend indicates that SSL models capable of high-level visual recognition tend to provide better representations for mid-level vision tasks as well, benefiting tasks that leverage spatial and structural information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "Some mid-level tasks are highly correlated with high-level. A per-task closer examination, however, reveals nuances in this relationship. For example, generic object segmentation shows the highest correlation with high-level tasks, achieving a coefficient of determination " + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "inline_equation", + "content": "(R^2 = 0.70)" + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": ". This suggests that high-level features indeed capture spatial structures that enhance segmentation accuracy. Mid-level and high-level vision also correlate highly in the task" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30099" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 298, + 269 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 298, + 269 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 298, + 269 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 298, + 269 + ], + "type": "image", + "image_path": "ce8e65d923a5b56d8e2fa40490a2c5765b8cfc204a5de46df2509149689efe43.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 270, + 296, + 304 + ], + "lines": [ + { + "bbox": [ + 55, + 270, + 296, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 296, + 304 + ], + "type": "text", + "content": "Figure 3. Cross-task performance correlation. We present Pearson coefficients across mid-level and high-level vision tasks. We use the same set of metrics we used in Fig. 2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 324, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 361 + ], + "type": "text", + "content": "of mid-level image similarity. This indicates that the high-level image representations are invariant to mid-level variations to some extent (e.g., viewpoint variations)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 378, + 296, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 296, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 296, + 473 + ], + "type": "text", + "content": "3D geometric understanding is weakly correlated with high-level vision. For tasks like scene surface normal estimating, we observe notably weaker correlations. These tasks often require intricate, fine-grained geometric and surface features that high-level SSL objectives alone do not sufficiently capture. This gap implies that mid-level vision depends on specialized cues not fully addressed by high-level feature extraction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 491, + 296, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 296, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 296, + 634 + ], + "type": "text", + "content": "Correlation across mid-level vision tasks. Fig. 3 shows the Pearson correlations across tasks. We find a strong correlation between object segmentation and mid-level image similarity (coefficients above 0.76). Object segmentation further correlates well with depth estimation and object-level multi-view geometric correspondence, indicating that spatial understanding aids segmentation and underscores the importance of 3D awareness in image understanding. In contrast, scene geometry correspondence correlates weaker with other mid-level and high-level tasks. Mid-level image similarity aligns with object segmentation and correspondence but correlates less with 3D tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "Ranking in mid-level vision. In Fig. 5, we present a comparative ranking of SSL models based on their performance across mid-level vision tasks and ImageNet probing. Each model received a task-specific rank, and we computed an average score, with higher scores indicating stronger performance in both mid-level and high-level vision tasks. Our" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 319, + 69, + 553, + 148 + ], + "blocks": [ + { + "bbox": [ + 319, + 69, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 319, + 69, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 319, + 69, + 553, + 148 + ], + "type": "image", + "image_path": "f9816ee3b028d715802190d47802c78d414f86304f5da9f8b87a4d3609fd8c00.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 320, + 152, + 551, + 260 + ], + "blocks": [ + { + "bbox": [ + 320, + 152, + 551, + 260 + ], + "lines": [ + { + "bbox": [ + 320, + 152, + 551, + 260 + ], + "spans": [ + { + "bbox": [ + 320, + 152, + 551, + 260 + ], + "type": "image", + "image_path": "3f281907399737c7b57adf6ab5fba359553ffc886f27f0411a89dc8b40c6e06d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 270, + 555, + 348 + ], + "lines": [ + { + "bbox": [ + 313, + 270, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 555, + 348 + ], + "type": "text", + "content": "Figure 4. Mid-Level Vision v.s. ImageNet Linear Probing with Contrastive Learning Methods. We examine several contrastive learning methods [6-9, 27, 58, 69] and observe a negative correlation between ImageNet linear probing accuracy and task performance. Depth estimation results are shown at the top, with surface normal estimation results at the bottom. The y-axis represents prediction accuracy, where higher values indicate better performance." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 370, + 555, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 555, + 441 + ], + "type": "text", + "content": "analysis suggests an imbalance in model performance, with some models excelling in high-level tasks but showing comparatively modest capabilities in mid-level vision tasks. Notably, MaskFeat stands out as an exception, demonstrating a significant advantage in mid-level vision tasks over high-level performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 443, + 554, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 554, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 554, + 491 + ], + "type": "text", + "content": "Conversely, MAE ranks lower on mid-level tasks, demonstrating limited proficiency in capturing finer visual details. In the following sections, we will discuss the specifics of MAE and MaskFeat." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 491, + 554, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 554, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 554, + 551 + ], + "type": "text", + "content": "Notably, iBOT [71] and DINO [4] rank among the top performers, exhibiting strong capabilities in both mid-level and high-level vision tasks. In contrast, pretext pre-trained models like RotNet [25] and Jigsaw [45] fall behind other SSL methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 562, + 549, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 562, + 549, + 575 + ], + "spans": [ + { + "bbox": [ + 313, + 562, + 549, + 575 + ], + "type": "text", + "content": "5.2. What makes a strong mid-level vision model?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 580, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 554, + 665 + ], + "type": "text", + "content": "Training objective. We observe that the top-performing SSL models in mid-level vision tasks are typically generative-based, such as iBOT [71] and MaskFeat [62]. In contrast, recent contrastive self-supervised learning (SSL) models [6-9, 27, 58, 69] show an inverse relationship between mid-level vision performance and ImageNet linear probing accuracy, as illustrated in Fig. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "Although these methods have improved ImageNet linear probing accuracy by over " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": ", they exhibit notable declines in mid-level vision tasks. We illustrate this trend with model performance on depth and surface normal estimation and" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30100" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 556, + 159 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 556, + 159 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 556, + 159 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 556, + 159 + ], + "type": "image", + "image_path": "44f36bb5c9845416877d7d1b35e2cb1f5641444144b0231c877949de93f2cb36.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "type": "text", + "content": "Figure 5. Ranking SSLs based on Overall Score. Comparative ranking of SSL models based on performance in mid-level vision tasks and ImageNet probing. Models are ranked per task, and average scores reflect overall performance across mid-level and high-level vision tasks, with higher scores indicating stronger results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 202, + 294, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 202, + 294, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 202, + 294, + 251 + ], + "type": "text", + "content": "provide a broader analysis across six additional tasks in the supplementary materials. Notably, SSL models pre-trained on pretext tasks show the lowest performance on mid-level vision tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 256, + 296, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 256, + 296, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 256, + 296, + 352 + ], + "type": "text", + "content": "Network architecture. We further compare ViT-B (ViT Base) and ViT-L (ViT Large) backbones with the same SSL method in Tab. 3. Our findings show that ViT-L models tend to perform better than ViT-B across mid-level vision tasks. In particular, we evaluate two popular SSL models, iBOT and MAE, on both ViT-B and ViT-L backbones. This pattern suggests that larger backbones like ViT-L may capture mid-level vision features better." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "text", + "content": "Network capability. We also compare ViT-B and ViT-L backbones using the same SSL method in Tab. 3. Our results indicate that ViT-Large models generally achieve higher scores across various mid-level vision tasks. Specifically, we examine two popular SSL models, iBOT and MAE, with ViT-B and ViT-L backbones. This trend suggests that larger models are better at capturing mid-level vision features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 461, + 248, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 248, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 248, + 474 + ], + "type": "text", + "content": "5.3. Which SSL works the best per task?" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 479, + 294, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 294, + 551 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 294, + 551 + ], + "type": "text", + "content": "In Tab. 4, we highlight the best-performing models for each task. iBOT [71] consistently leads in most mid-level vision tasks while MaskFeat performs even better on scene correspondence and scene surface normal. DINO works the best on object correspondence and achieves quite competitive results compared to other SSLs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 559, + 188, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 559, + 188, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 188, + 571 + ], + "type": "text", + "content": "5.4. Analysis of specific SSL" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 575, + 294, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 294, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 294, + 624 + ], + "type": "text", + "content": "MAE. MAE [30] stands out as a clear outlier, as illustrated in Fig. 2 and Fig. 5. MAE consistently performs poorly on mid-level vision tasks compared to other ViT-based SSLs such as iBOT [71] and MaskFeat [62]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 629, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 714 + ], + "type": "text", + "content": "MaskFeat. In Fig. 2 and Fig. 5, we observe that MaskFeat [62] demonstrates surprisingly strong mid-level vision capabilities despite showing relatively modest performance in high-level vision tasks. Since the MaskFeat checkpoint we used was trained exclusively on the ImageNet-1K dataset and followed a training process similar to MAE, we attribute its mid-level vision strength to its choice of target" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 202, + 553, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 202, + 553, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 202, + 553, + 311 + ], + "type": "text", + "content": "features. Unlike models trained on raw pixels, tokens, or high-level features, MaskFeat is optimized on HOG (Histograms of Oriented Gradients) features, which are widely used for keypoint detection in methods such as SIFT [38]. Importantly, HOG does not rely on any external models, making it a robust feature for capturing mid-level vision attributes. This finding suggests that incorporating mid-level vision-relevant features, like HOG, into SSL training may enhance model performance on mid-level vision tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 315, + 554, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 554, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 554, + 387 + ], + "type": "text", + "content": "SSLs based on pre-text tasks. RotNet and Jigsaw are the two lowest-performing SSLs on mid- and high-level vision. Given that they are the early design of SSLs, it revalidate our claim that ImageNet (IN1k) probing results improve, we generally observe a corresponding enhancement in mid-level vision task performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 394, + 553, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 553, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 553, + 418 + ], + "type": "text", + "content": "5.5. How do visual foundation models (VFMs) perform?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 423, + 554, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 554, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 554, + 509 + ], + "type": "text", + "content": "Even though our study aims to conduct a controlled benchmarking of SSLs in the mid-level vision tasks, we put VFMs into our context in this section to understand the comparison between the latest visual foundation models and the set of SSLs we analyzed. We observed that CLIP is much worse than most of the SSLs. DINO-v2 is the winner. We include a comparison in Fig. 6 focusing on depth estimation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 512, + 554, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 554, + 573 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 554, + 573 + ], + "type": "text", + "content": "DINO-V2 [46]. Our findings, consistent with Probe3D and Cambrian-1 [55], show DINO-V2 as the best-performing model across both ImageNet linear probing and mid-level vision tasks, making it a standout choice for comprehensive vision capabilities." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 577, + 554, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 577, + 554, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 577, + 554, + 637 + ], + "type": "text", + "content": "CLIP [50]. CLIP's overall performance is notably lower across mid-level tasks, as reported in Probe3D [17] and Cambrian-1 [55]. This suggests that, while generalizable for 2D understanding, CLIP may be less suited for tasks requiring 3D spatial understanding." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "content": "CroCo [65]. Using depth estimation as a representative task, we observe that CroCo performs competitively in mid-level vision tasks despite lagging in high-level vision tasks. Pretrained on synthetic multi-view image datasets, CroCo learns strong 3D-aware image representations. This distinction underscores its potential for 3D-specific applications," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30101" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 553, + 194 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 194 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 194 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 194 + ], + "type": "table", + "html": "
SSLsBackboneObject Seg.Object SNorm.Scene SNorm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
MoCo-v3 [9]RN-5071.4827.2243.0345.9375.561.715.2384.37
MoCo-v3 [9]ViT-B/1672.4531.7249.6451.0780.143.1225.0386.90
DINO [5]RN-5071.9531.4347.6447.6377.683.1626.6383.31
DINO [5]ViT-B/1674.0031.0648.4247.7579.382.6124.3889.36
SSLsModel SizeObject Seg.Object Norm.Scene Norm.Object DepthScene DepthObject Corres.Scene Corres.Image Sim.
iBOTB/1675.7432.7552.0250.0281.323.1220.0489.27
iBOTL/1675.3235.6554.5352.5685.143.1614.7982.37
MAEB/1665.7722.6743.8926.7866.172.746.6482.91
MAEL/1666.5826.6045.6026.8170.222.9310.0584.26
", + "image_path": "54a2dcdc880c40378ce4e673986347491ae5778cb7ea01abf7d950c65e389ed3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 251, + 294, + 357 + ], + "blocks": [ + { + "bbox": [ + 55, + 203, + 555, + 247 + ], + "lines": [ + { + "bbox": [ + 55, + 203, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 55, + 203, + 555, + 247 + ], + "type": "text", + "content": "Table 3. Impact of Network Architecture and Model Size on Mid-Level Vision Performance. The top table demonstrates that the Vision Transformer (ViT) [14] generally outperforms ResNet-50 (RN-50) [28] across most mid-level vision tasks when using MoCo-v3 or DINO as the self-supervised pretraining method. The bottom table shows that larger model sizes tend to enhance mid-level vision capabilities. Detailed numerical comparisons are provided in the supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 251, + 294, + 357 + ], + "lines": [ + { + "bbox": [ + 56, + 251, + 294, + 357 + ], + "spans": [ + { + "bbox": [ + 56, + 251, + 294, + 357 + ], + "type": "table", + "html": "
ModelImage Sim.Object Corres.Object DepthObject SNorm.
DINO (RN-50)83.313.1647.6331.43
MaskFeat [62]75.702.0849.5032.40
MoCo v384.371.7045.9327.22
iBOT [71]89.273.1250.0232.75
ModelObject Seg.Scene Corres.Scene DepthScene SNorm.
DINO (RN-50)71.9526.6377.6847.64
MaskFeat [62]70.2827.9480.3953.63
MoCo v371.4815.2375.5643.03
iBOT [71]75.7420.0481.3252.02
", + "image_path": "445f8a584230319e20d0f93bf49187885ed200d8a7e783e0b1d6495881f6a165.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 366, + 295, + 421 + ], + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 421 + ], + "type": "text", + "content": "Table 4. Top SSL Methods in Mid-Level Vision Tasks. iBOT outperformed all other SSL methods (listed in Tab. 1) in multiple mid-level vision tasks. Surprisingly, despite the low performance on ImageNet linear classification, MaskFeat achieved leading results in depth and surface normal estimation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 427, + 295, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 295, + 452 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 295, + 452 + ], + "type": "text", + "content": "where spatial understanding is prioritized over high-level visual semantics because of its design choice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 456, + 295, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 295, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 295, + 528 + ], + "type": "text", + "content": "SAM [34]. Although SAM excels at image segmentation, it exhibits moderate performance on mid-level vision tasks and notably weaker performance on image classification, in comparison with ImageNet-pretrained SSLs. This reveals the imbalanced performance of SAM among reorganization, reconstruction and recognition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 533, + 125, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 125, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 125, + 544 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "type": "text", + "content": "In conclusion, this study introduces a suite of benchmark protocols to systematically evaluate mid-level vision capabilities, offering a comprehensive and controlled assessment of 22 SSL models across mid-level vision tasks. Our findings indicate a positive correlation between SSL performance in mid-level and high-level vision tasks, though this correlation is generally weaker than that observed within high-level tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 648, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 648, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 648, + 295, + 696 + ], + "type": "text", + "content": "Some SSL models exhibit imbalanced performance across these task levels. For instance, MAE [31] underperforms in mid-level tasks despite competitive high-level performance, while MaskFeat [62] excels in mid-level tasks" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 251, + 555, + 406 + ], + "blocks": [ + { + "bbox": [ + 315, + 251, + 555, + 406 + ], + "lines": [ + { + "bbox": [ + 315, + 251, + 555, + 406 + ], + "spans": [ + { + "bbox": [ + 315, + 251, + 555, + 406 + ], + "type": "image", + "image_path": "1bc9099a0e4ce2d4b52db42d7c490e9ab78f998e0d6a09cf37f49257be5dca67.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 409, + 555, + 453 + ], + "lines": [ + { + "bbox": [ + 313, + 409, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 555, + 453 + ], + "type": "text", + "content": "Figure 6. Comparison of ImageNet1K-Pretrained SSLs with models trained with larger datasets (e.g., DINO-v2 [46]) or different training supervisions (e.g., CLIP [50] " + }, + { + "bbox": [ + 313, + 409, + 555, + 453 + ], + "type": "inline_equation", + "content": "{}^{1}" + }, + { + "bbox": [ + 313, + 409, + 555, + 453 + ], + "type": "text", + "content": ") in the scene depth estimation task." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 458, + 555, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 458, + 555, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 458, + 555, + 578 + ], + "type": "text", + "content": "relative to its high-level results (Fig. 5). Mid-level vision capabilities are influenced by factors such as network architecture, dataset size, and pretraining strategy. Overall, ViT [14] outperforms ResNet [28], increasing model capacity proves beneficial (Tab. 3), and generative modeling approaches often lead in performance (Fig. 5). Additionally, we compare SSL models with VFMs, finding that DINOv2 [46] leads in both mid-level and high-level vision tasks and language objectives (e.g., CLIP) do not help on mid-level tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 580, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 555, + 628 + ], + "type": "text", + "content": "Since SSL's overall goal is to produce a very general feature representation that works well for a wide range of downstream tasks, we encourage the community to evaluate new SSL methods on both high- and mid-level tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "type": "text", + "content": "This work is limited by resources, which prevents us from scaling up our experiments to more tasks and models, and we did not include ending tasks such as navigation and robotic manipulation to emphasize mid-level vision's role further. We provide details of our probing hyper-parameters and include visualizations for each task in the supplementary materials." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 702, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 295, + 713 + ], + "type": "text", + "content": "1We evaluated CLIP with the ViT-B/16 checkpoint released by OpenAI." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30102" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "type": "text", + "content": "The authors gratefully acknowledge Research Computing at the University of Virginia for providing the computational resources and technical support that made the results in this work possible. 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ROBOT" + ], + "image_footnote": [], + "bbox": [ + 94, + 287, + 294, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/22dbfa581d84d95479313a6149f61ff888917a7a8acacef85daec2daf585ee3e.jpg", + "image_caption": [ + "STATIC COLLISION", + "PROF. ROBOT (OURS)" + ], + "image_footnote": [], + "bbox": [ + 295, + 287, + 495, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f9636415819062b10688396cfcf53c78c3ecae972a13824c2492d20cfcaf6d0b.jpg", + "image_caption": [ + "SELF COLLISION", + "DR. ROBOT", + "Figure 1. Our method improves upon Dr.Robot [32] by additionally enabling differentiable avoidance of static and self-collisions. By learning and integrating a gradient-consistent pose classifier into a differentiable rendering pipeline, the generated pose trajectories are free from physical collisions. The objective is to penalize high collision probabilities during optimization. On the left, our method can push robotic arms away from intersecting objects. On the right, it can also avoid self-collisions. Images are rendered using Blender with meshes." + ], + "image_footnote": [], + "bbox": [ + 501, + 287, + 700, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/009d0bfb7c4e8d93bb4932b7eadaccec09ae2dba1896fcfce43e167335e24350.jpg", + "image_caption": [ + "PROF. ROBOT (OURS)" + ], + "image_footnote": [], + "bbox": [ + 702, + 289, + 901, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 526, + 326, + 541 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Differentiable rendering has gained significant attention in the field of robotics, with differentiable robot rendering emerging as an effective paradigm for learning robotic actions from image-space supervision. However, the lack of physical world perception in this approach may lead to potential collisions during action optimization. In this work, we introduce a novel improvement on previous efforts by incorporating physical awareness of collisions through the learning of a neural robotic collision classifier. This enables the optimization of actions that avoid collisions with static, non-interactable environments as well as the robot itself. To facilitate effective gradient optimization with the classifier, we identify the underlying issue and propose leveraging Eikonal regularization to ensure consistent gradients for optimization. Our solution can be seamlessly integrated into existing differentiable robot rendering frameworks, utilizing gradients for optimization and providing a foundation for future applications of differentiable rendering in robotics with improved reliability of interactions with the", + "bbox": [ + 88, + 559, + 485, + 847 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "physical world. Both qualitative and quantitative experiments demonstrate the necessity and effectiveness of our method compared to previous solutions.", + "bbox": [ + 511, + 530, + 906, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 603, + 643, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conventional methods for representing a robot involve partitioning it into many rigid body parts and then articulating them according to structural kinematic constraints. However, they only model the robots geometrically and do not possess a realistic appearance for rendering; therefore, they are less applicable for integration into a differentiable pipeline involving images, which is currently a popular approach in computer vision. A recent approach [32] has been proposed to model robots' appearance in a differentiable manner, facilitating the integration of robots into a differentiable rendering solution. It allows for backpropagating the appearance supervision from images to the control space, thereby enabling the learning of plausible robot movements. Their method is straightforward. They leverage Gaussian splatting [24] for efficient differentiable rendering, where each Gaussian point is associated with the robotic arms using implicit LBS [32, 34], and the arms are generated by the control parameters through forward kinematics.", + "bbox": [ + 509, + 628, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal contribution.", + "bbox": [ + 112, + 862, + 228, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding authors.", + "bbox": [ + 112, + 875, + 250, + 888 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Project: https://qrcat.github.io/prof-robot/", + "bbox": [ + 122, + 888, + 444, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22562", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While promising, their method clearly lacks awareness of how to avoid physical collisions with a static environment that does not dynamically interact with the robot, as well as collisions with the robot itself. When optimized using gradient information, it is likely to produce invalid robotic parameters that lead to intersections. This problem is particularly severe in real scenarios, where minor collisions damage the robot's mechanical structure. Due to the typically high cost of robots, which can result in significant financial losses. To address this issue and ensure that the differentiable rendering pipeline produces valid robotic parameters that prevent collisions, we need to guide the robot to evade collision scenarios during gradient-guided optimization. Intuitively, we employ a similar approach to that in [55] to achieve collision-free optimization, with some critical adaptations and improvements.", + "bbox": [ + 89, + 90, + 480, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our idea is simple. We observe that some robotic poses are free from collisions, while others are not. Therefore, we can classify these poses based on whether they lead to a collision. We can leverage a discriminative model to classify these poses. The classifier $f$ is a mapping $\\mathrm{SO}(2)^K \\to [0,1]$ that maps a pose $\\pmb{\\theta} \\in \\mathrm{SO}(2)^K$ to a decision $c \\in [0,1]$ , where a value of $c > 0.5$ indicates a collision. A rotation occurs in $\\mathrm{SO}(2)$ because the motor of a robotic joint typically possesses only one degree of freedom for rotation. Finally, we need to integrate the model into a differentiable pipeline. During optimization, to ensure that the robotic pose remains in the collision-free zone, we must push the pose $\\pmb{\\theta}$ toward the collision-free regions $\\{\\pmb{\\theta} \\in \\mathrm{SO}(2)^K \\mid f(\\pmb{\\theta}) \\leq 0.5\\}$ that correspond to a classification result of $c \\leq 0.5$ . Compared to [55], we should note that the biggest benefit of using classification rather than fitting a distance field is that classification does not require computing manifold distances and only needs to provide classification labels, corresponding to either \"collided\" or \"not collided.\" Computing labels is expensive and may lack accuracy, as the normally generated samples are often too sparse to accurately compute the manifold distances in such a high-dimensional space due to the curse of dimensionality.", + "bbox": [ + 91, + 337, + 483, + 685 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unfortunately, the direct application of the above idea does not yield the desired results due to the variability of the gradients obtained after sheer classification learning. The update direction of the gradients may not be consistent, and a later update may offset the previous one. We will mathematically analyze the reasons for this phenomenon in Section 3.2. To address this issue, we introduce a regularization term to enforce the consistency of gradients by imposing that the gradient's norm be one, as expressed by $\\mathcal{L}_{\\mathrm{ek}} = (\\|\\nabla_{\\theta}g(\\pmb{\\theta})\\| - 1)^2$ . We immediately notice that this is a requirement for being a Signed Distance Field (SDF). To integrate the regularization term into the optimization, we take the function $g$ as the value before the Sigmoid function $\\sigma$ , as given by $f = (\\sigma \\circ \\omega \\circ g)(\\pmb{\\theta})$ . The function $g$ is im", + "bbox": [ + 89, + 689, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pleted as a multi-layer perceptron (MLP), $\\omega$ is a scalar multiplication function, and $\\sigma$ is the sigmoid function. We notice that although we leverage the SDF, it does not require fitting any manifold distance; the SDF property is ensured by the regularization term. Interestingly, the method of imposing the Eikonal constraint is similar to the work of [16, 63]; instead of regularizing in three-dimensional space, we regularize the field $g$ in a high-dimensional pose space.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lastly, we verify in our extensive ablation studies and comparative experiments that our method of learning a high-dimensional pose classifier $f$ can avoid physical collisions with the static environment and the robot itself, making the robotic pose produced by a differentiable pipeline physically reliable.", + "bbox": [ + 511, + 213, + 903, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our technical contributions as follows:", + "bbox": [ + 531, + 304, + 887, + 318 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We address the issue of efficient differentiable robot rendering with potential collisions involving a static, non-interactive environment and self-collisions. This is achieved by learning a multi-layer perceptron (MLP), denoted as $f$ , to classify the control pose $\\theta$ and determine whether it corresponds to a collision. Classification eliminates the need for accurate manifold distance.", + "2. To address the issue of poor reliability of gradients from the classifier and to integrate $f$ into a gradient-based optimization pipeline, we introduce the Eikonal regularization term $\\mathcal{L}_{\\mathrm{ek}}$ to enforce consistency among gradients, effectively transforming the value before the Sigmoid, $g$ , into a signed distance function (SDF). This regularization enhances the reliability of the gradients and leverages the beneficial properties of the SDF without the need for explicit computation of manifold distance.", + "3. To model the dependency of adjacent robotic joints efficiently, we introduce hierarchical joint encoding that conditions a joint angle on an ancestor's rotation, thereby better capturing the hierarchical dependency of robotic arms." + ], + "bbox": [ + 514, + 323, + 903, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 656, + 663, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Differentiable Rendering and Simulation", + "text_level": 1, + "bbox": [ + 511, + 681, + 862, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differentiable rendering and simulation play a pivotal role in computer vision and graphics. In differentiable rendering, gradients are propagated from primitives to image, while differentiable simulators compute gradients of physical processes similarly, which facilitates seamless integration with gradient-based optimization techniques. The integration of neural fields into robotics has attracted considerable attention. Researchers have employed diverse representations to bridge the digital and physical realms [20, 23, 24, 33, 38, 40, 44, 47, 67, 70]. Innovative approaches, such as Gaussian splatting for the precise reconstruction of robots and their environments, exemplify this trend [35, 50]. Moreover, techniques such as neural radi", + "bbox": [ + 511, + 703, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22563", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ance fields for teleoperation [45] and future scene prediction [36] have significantly advanced robotic manipulation capabilities. Feature distillation has further empowered robots to perform complex tasks by translating language embeddings into corresponding 3D actions [49, 51, 52, 71, 73]. Additional advancements include comprehensive physical world modeling, future state prediction [1], and learning continuous manifolds of valid grasps using signed distance functions (SDF) [25, 64]. Significant progress has also been made in perceptual scene understanding and grasp planning [4-6]. One of the primary challenges in developing these simulators is accurately modeling contact interactions—a difficulty that arises from the inherently binary, discontinuous nature of contacts, where objects are either in contact or not [42]. According to [42], contact models can be broadly categorized into four classes: complementarity problems, compliant models, position-based models, and material point method (MPM) frameworks. Complementarity problems emphasize maintaining strict zero-penetration contact between objects [7-9, 12, 13, 19, 21, 28, 29, 46, 48, 60-62, 65, 74]. Compliant models relax the complementarity problem's constraint by replacing the sharp, step-like contact functions with smooth approximations that have large but finite gradients[9, 13, 15, 18, 19, 27, 41, 54, 57, 58]. The position-based method directly constrains object positions to prevent penetration [11, 37]. Meanwhile, the MPM handles contact interactions between both rigid- and soft-body objects[22, 53]. Despite these impressive advances, the effectiveness of differentiable systems for robotic manipulation remains under active validation, marking a promising yet nascent stage of development.", + "bbox": [ + 89, + 90, + 483, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Signed Distance Fields in Robotics", + "text_level": 1, + "bbox": [ + 89, + 568, + 392, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the realm of robotics and computer graphics, the construction of SDF has been an important technique for various applications, particularly in motion planning and collision avoidance. Some researchers pioneered a method to construct SDF on grid maps [10]. Afterwards, some others introduced incremental SDF construction techniques [17, 43], significantly enhancing the adaptability of SDF in dynamic environments. A novel implicit SDF method is proposed to leverage swept volumes for construction [72]. This method allows for efficient evaluation of the SDF at specific obstacle points with known coordinates, simplifying the process and reducing computational overhead. Another work [69] made a significant stride with the introduction of RobotSDF, an implicit morphology modeling technique. Furthermore, the application of SDF in obstacle avoidance has been extensively explored by [30, 59, 66].", + "bbox": [ + 89, + 590, + 483, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 845, + 181, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will detail our method for achieving collision avoidance in robotic operations in combination", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with Gaussian splattering-based differentiable robotic rendering [32]. The types of collisions we consider in this paper include static collisions, which occur when the robot collides with a static and non-interactive environment, as well as self-collisions, which involve collisions with the robot itself. Section 3.1 will model the problem of collision detection as a robotic pose classification problem. In Section 3.2, we will address some challenges that arose in formulating collision detection and propose the introduction of a signed distance field (SDF) as an underlying field for the classifier to tackle the gradient inconsistency problem during optimization. Section 3.3 will explain how we hierarchically encode the robotic pose while respecting the robotic kinematic dependencies. Finally, we will present our loss functions and training schemes in Section 3.4.", + "bbox": [ + 511, + 90, + 906, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Collision Detection by Pose Classification", + "text_level": 1, + "bbox": [ + 511, + 327, + 864, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make the model aware of physical collisions during optimization, we need a collision detector to determine whether the robotic pose has caused intersections with other environmental objects or with the robot itself. The collision detector is essentially a function $f: \\theta \\mapsto c$ with $c \\in [0,1]$ that classifies each pose $\\theta$ into two categories: either collided ( $c > 0.5$ ) or not ( $c \\leq 0.5$ ).", + "bbox": [ + 511, + 349, + 906, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The robots we consider in this paper have $K$ joints, and each joint has exactly one degree of freedom for rotation; thus, the pose parameter is within the space $\\theta \\in \\mathrm{SO}(2)^K$ . The classifier network $f$ will partition the space into many regions, and ideally, the regions corresponding to valid poses (non-collided poses) will form a manifold as given by", + "bbox": [ + 511, + 455, + 908, + 561 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} = \\left\\{\\boldsymbol {\\theta} \\in \\operatorname {S O} (2) ^ {K} \\mid f (\\boldsymbol {\\theta}) \\leq 0. 5 \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 575, + 906, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure that the output value falls within the range [0, 1], we follow convention and apply a Sigmoid function $\\sigma$ to the last output, meaning that the function $f$ is effectively defined by $f = \\sigma \\circ g$ , where $g$ is another scalar-valued function that we will detail later in Section 3.2.", + "bbox": [ + 511, + 601, + 905, + 675 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To effectively learn the classifier $f$ , we follow tradition and use binary cross-entropy loss to supervise $f$ , as expressed by", + "bbox": [ + 511, + 676, + 905, + 722 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {B C E}} = \\operatorname {B C E} (f (\\boldsymbol {\\theta}), c ^ {\\mathrm {g t}}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 723, + 906, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c^{\\mathrm{gt}} \\in \\{0,1\\}$ is the ground truth label indicating whether it is valid ( $c^{\\mathrm{gt}} = 1$ ) or not ( $c^{\\mathrm{gt}} = 0$ ).", + "bbox": [ + 511, + 746, + 905, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Eikonal Regularizer for Consistent Gradients", + "text_level": 1, + "bbox": [ + 511, + 787, + 897, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, directly applying $f$ to gradient optimization is problematic. The function is nearly binary, and the gradients near the values of 0 and 1 are almost zero, leading to noisy and unreliable supervision signals.", + "bbox": [ + 511, + 809, + 905, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We visualize a possible function $f$ with a two-dimensional input space in Figure 3. We notice that, since", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22564", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ab7c31edc7a2d990abb1f45d5ccac67340e44698344a502c532166b000346e19.jpg", + "image_caption": [ + "Figure 2. Our Pipeline. We predict whether a collision has occurred based on pose input, using Eikonal loss $(\\mathcal{L}_{\\mathrm{ek}})$ and binary cross-entropy loss $(\\mathcal{L}_{\\mathrm{BCE}})$ to ensure this. It can then be seamlessly integrated with Dr. Robot [32] to create a fully differentiable pipeline for optimization." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 632, + 261 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cea4236373b47a470d2754153e5bc0b6ba3e10ac1bfba32aa6dbef8a5e46e993.jpg", + "image_caption": [ + "Figure 3. An illustration of the potential fluctuation of the classification loss landscape." + ], + "image_footnote": [], + "bbox": [ + 691, + 102, + 905, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the values at both far sides fluctuate, the gradients also fluctuate, leading to inconsistent gradients. When we aim to optimize a pose from the exterior (collided region) toward the interior (collision-free region), this may not be the case because the gradient directions are inconsistent (see the two red points) due to fluctuations in the loss landscape. Small fluctuations do not significantly influence the loss value, but they can lead to noisy and inconsistent gradients, which are harmful to optimization.", + "bbox": [ + 88, + 352, + 482, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the issue, we need to consider the function $g$ before the Sigmoid function $\\sigma$ , as $\\sigma$ will restrict the gradient and render it too small for updating poses. Specifically, for two consecutive gradient updates with poses $\\pmb{\\theta}_t$ and $\\pmb{\\theta}_{t + 1}$ , the update at $t + 1$ is likely to offset the previous update at $t$ , as expressed by", + "bbox": [ + 89, + 488, + 483, + 580 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\leq 0, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 583, + 482, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "especially in regions with high confidence levels close to 0 or 1. This is visualized in Figure 3, where two red dots are plotted; their gradient directions may not be consistent (or correlated) as they point in opposite directions.", + "bbox": [ + 89, + 622, + 483, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also note that gradient updates are typically small. Assuming the updates $\\theta_{t + 1}$ and $\\theta_t$ are close enough and correlated, we have", + "bbox": [ + 89, + 683, + 483, + 727 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\approx \\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\rangle = \\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\| ^ {2} \\geq 0. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 732, + 482, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This analysis indicates that to enforce gradient consistency, we only need to manipulate the norm of the gradients. To make the correlation of the gradients as uniform as possible (which is desirable for gradient updates), we enforce the above term to be a positive constant $a > 0$ . This motivates us to adopt the following regularization term", + "bbox": [ + 89, + 772, + 483, + 863 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {e k}} = \\left(\\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta}} \\right\\| - a\\right) ^ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 867, + 482, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to ensure gradient consistency between the two adjacent updates. We immediately notice that when $a = 1$ , it becomes an Eikonal regularizer that is widely employed by the signed distance function [16, 44]. Interestingly, this term can be viewed as generalizing the implicit geometric regularization [16] to high-dimensional pose space by learning a function $g$ . To simplify implementation, we use $a = 1$ throughout the paper.", + "bbox": [ + 511, + 352, + 905, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The function $g$ is practically implemented as a multilayer perceptron that receives robotic poses $\\pmb{\\theta}$ as input and produces a scalar; the final classifier is therefore", + "bbox": [ + 511, + 473, + 905, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf (\\boldsymbol {\\theta}) = (\\sigma \\circ \\omega \\circ g) (\\boldsymbol {\\theta}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 527, + 903, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\omega : x \\mapsto sx$ denotes a function that multiplies the input $x$ by an estimable positive constant $s$ , which will be further discussed in Section 4.2.3. Our current pipeline is illustrated in Figure 2.", + "bbox": [ + 511, + 553, + 905, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Hierarchical Robotic Pose Encoding", + "text_level": 1, + "bbox": [ + 511, + 622, + 826, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We represent the robotic pose using rotation angles, each describing the relative rotation between two arms. The pose parameters are defined in local coordinate frames, such that continuous modifications of a single joint result in realistic motion. However, since angles only describe relative rotations, they may not respect the kinematic structure and cannot effectively handle the structural dependency relationships between the arms. We observe that each individual joint needs to be conditioned on the parent rotations and thus must be influenced by them. To incorporate this notion of kinematic dependency into the function $g$ , we implement the function as a hierarchical network that encodes the dependency within the network structure [2, 14, 39, 55].", + "bbox": [ + 511, + 643, + 906, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is similar to the method described in [55]. Specifically, for a given robotic pose $\\pmb{\\theta} = [\\theta_{1};\\dots;\\theta_{K}]$ , where $\\theta_{k}$ (with $k\\in \\{1,\\ldots ,K\\}$ ) is the rotation angle for joint $k$ , and a function $\\tau (k)$ maps the index of each joint to its parent joint", + "bbox": [ + 511, + 840, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22565", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "index, we encode each pose using a multi-layer perceptron (MLP) as follows:", + "bbox": [ + 89, + 90, + 485, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng _ {1}: \\theta_ {1} \\mapsto \\boldsymbol {\\nu} _ {1} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 133, + 480, + 157 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng _ {k}: \\left(\\theta_ {k}, \\boldsymbol {\\nu} _ {\\tau (k)}\\right) \\mapsto \\boldsymbol {\\nu} _ {k}, \\quad k \\in \\{2, \\dots , K \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 152, + 421, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This process takes the joint angle and the encoded feature $\\pmb{\\nu}_{\\tau (k)}\\in \\mathbb{R}^{\\ell}$ of its parent joint as input and produces an output feature $\\pmb{\\nu}_k\\in \\mathbb{R}^\\ell$ , where $\\ell = 8$ is the feature dimension. We then concatenate the encoded features of every joint to obtain a combined pose embedding $\\pmb {\\nu} = [\\pmb {\\nu}_1;\\dots ;\\pmb {\\nu}_K]$ This embedding is further transformed by a linear mapping $\\mathbb{R}^{\\ell ,K}\\to \\mathbb{R}$ to yield a scalar value that serves as the output of the function $g$", + "bbox": [ + 89, + 179, + 483, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Data and Objectives", + "text_level": 1, + "bbox": [ + 89, + 311, + 354, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training dataset comprises $N$ poses and their corresponding decisions, represented by $\\mathcal{D} = \\{(\\pmb{\\theta}_i, c_i^{\\mathrm{gt}})\\}_{i=1}^N$ . It is constructed as follows: the robotic pose $\\pmb{\\theta}_i$ is randomly sampled, and a (non-differentiable) collision detector is then applied to produce the decision $c_i^{\\mathrm{gt}} \\in \\{0, 1\\}$ , indicating whether a collision has occurred ( $c_i^{\\mathrm{gt}} = 1$ ).", + "bbox": [ + 89, + 334, + 483, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The model is trained using batched samples; we omit the summation-over-samples notation here for simplicity. The objective is simply the weighted combination of $\\mathcal{L}_{\\mathrm{BCE}}$ and $\\mathcal{L}_{\\mathrm{ek}}$ . With $\\alpha = 0.1$ , it is expressed as", + "bbox": [ + 89, + 425, + 483, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {B C E}} + \\alpha \\mathcal {L} _ {\\mathrm {e k}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 498, + 480, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depending on how it is learned, we may additionally have, for example, $\\mathcal{L}_{\\mathrm{RGB}}$ for image-space supervision, which we omit here for simplicity.", + "bbox": [ + 89, + 526, + 483, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 89, + 585, + 326, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct ablation studies on Prof. Robot (section 4.2), experiments on collision resolution (section 4.3), integration with Dr. Robot (section 4.4), and sim-to-real deployment (section 4.5). Comparison with the differentiable simulator, training with alternative regularizers, and manipulation with Dr. Robot are detailed in the supplementary materials.", + "bbox": [ + 89, + 611, + 483, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 727, + 281, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Preparation. We adopt a data-driven approach, leveraging the Mujoco [56] configurations provided by [32] with some modifications. Specifically, we selected six scenes and randomly sampled poses from the robot's joint limits, used Mujoco (which is non-differentiable) to check for collisions, and employed a resampling technique to balance the ratio of collision to non-collision data at approximately the same amount.", + "bbox": [ + 89, + 750, + 483, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We primarily evaluate the network's ability to distinguish between collision and non-collision", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/29c38e3f1ddf1daf2cd021fe3acb1b7052330c533c32c0f0001217c62c80b33a.jpg", + "table_caption": [ + "Table 1. Ablation study on hierarchical and flattened encoding." + ], + "table_footnote": [], + "table_body": "
HierarchicalFlatten
Classification Accuracy97.70%97.51%
", + "bbox": [ + 547, + 114, + 870, + 160 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "states, as well as its performance in optimizing the gradients. The former metric (accuracy) assesses the network's ability to detect collisions, while the latter $(\\mathcal{L}_{\\mathrm{ek}})$ measures its capacity to avoid collisions through optimization. Furthermore, for a given robot pose denoted as $\\theta$ , we are able to determine the collision points of the mesh within the simulator and subsequently calculate the collision rate for all possible poses.", + "bbox": [ + 511, + 176, + 905, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experimental Details. We leverage the joint connection relationships defined in the URDF, where each joint is encoded using a tiny MLP. The encoded features from all joints are then concatenated and passed through an MLP with four hidden layers, each containing 512 units, followed by a final output layer with a single unit. LeakyReLU is used as the activation function for all layers. We introduce a learnable scale factor $s$ , which, after being multiplied by the MLP output, is passed through a Sigmoid function to produce a probability. We conduct experiments within a simulation environment, where the network's ability determines the success rate of collision resolution. Finally, we integrate our method into a differentiable robot rendering pipeline and perform control experiments. The experiments are conducted on a single NVIDIA RTX 4090 GPU.", + "bbox": [ + 511, + 297, + 906, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Learning Robotic Signed Distance Fields", + "text_level": 1, + "bbox": [ + 511, + 532, + 862, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1. Ablation: Hierarchical Encoding", + "text_level": 1, + "bbox": [ + 511, + 554, + 790, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To assess the impact of hierarchical encoding, we replaced it with a simple linear layer for encoding the input joint data while keeping the rest of the components unchanged. As shown in Table 1, after 10,000 iterations, the use of the hierarchical MLP results in higher accuracy. This shows that the hierarchical encoding strategy better captures the kinematic structure and increases performance.", + "bbox": [ + 511, + 571, + 905, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.2. Ablation: Eikonal Regularizer", + "text_level": 1, + "bbox": [ + 511, + 685, + 772, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To investigate the effect of the Eikonal regularizer, we trained an MLP under two conditions: one without the Eikonal regularizer and one with it, and compared both the classification accuracy and the numerical value of the Eikonal loss. We then tested whether the models could resolve collisions (as described in Section 4.3). The models were trained for 10,000 iterations. During pose optimization, for the model trained without the Eikonal regularizer, we stopped the iteration if the collision probability dropped below 0.5. For the model trained with the Eikonal regularizer, we halted the iteration if the SDF value, which is negative in non-collision regions, fell below the threshold $l_{\\mathrm{thres}} = -0.1$ .", + "bbox": [ + 511, + 704, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22566", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8e70c00682eae285a7f506fe911fd121b1b28a74ee205c99925f1ef6b113dbd0.jpg", + "table_caption": [ + "Table 2. Ablation study on the Eikonal loss." + ], + "table_footnote": [], + "table_body": "
w. Eikonal lossw/o. Eikonal loss
Classification97.70%98.39%
Accuracy
Iteration Nums ↓119.991000
Iteration Time ↓0.97 s10.64 s
Move Angle ↓0.604.49
Collision Point ↓0.6711.52
Collision Rate ↓17%99%
Gradient Norm8.53 × 10-11.89 × 10-6
", + "bbox": [ + 107, + 114, + 460, + 256 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4c18781d13b5e6d3dd777372ef4cb5e6ecc926baac1e6c3733de60404098e8ee.jpg", + "table_caption": [ + "Table 3. Ablation study on the scaling factor $s$ ." + ], + "table_footnote": [], + "table_body": "
AccuracyEikonal Loss ↓
w. s97.70%0.0850
w/o. s85.37%0.2568
", + "bbox": [ + 163, + 287, + 408, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results were compared, as shown in Table 2. Without the Eikonal regularizer, the optimizer struggled to generate a collision-free pose from a collision state, with iterations exceeding 1,000, and the propagated gradients were too small to facilitate further optimization.", + "bbox": [ + 89, + 364, + 482, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.3. Ablation: Scaling Factor", + "text_level": 1, + "bbox": [ + 89, + 446, + 310, + 463 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The cross-entropy loss and Eikonal loss may require gradients of different magnitudes, potentially interfering with each other and hindering the model's ability to learn useful information. To address this, a scaling factor $s$ for the SDF is introduced to allow for large gradients in classification and limited gradients in the SDF. We removed the scaling factor $s$ (setting $s = 1$ ) and directly passed the SDF value to the Sigmoid function to produce $f$ .", + "bbox": [ + 89, + 465, + 482, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The numerical results, as shown in Table 3, demonstrate that the scaling factor effectively achieves good classification results while preserving the uniform gradient property.", + "bbox": [ + 89, + 587, + 483, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.4. Comparison Between NDF and SDF", + "text_level": 1, + "bbox": [ + 89, + 638, + 390, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In contrast to [55], which models collision-free poses as a high-dimensional submanifold using a Neural Distance Field (NDF), we represent collision-free poses as a set of discontinuous regions in high-dimensional space that can be modeled using an SDF. To explore the differences between these two approaches, we also conducted experiments with an NDF. Learning an NDF requires accurate manifold distances; unlike [55], our method does not require this because it can be implicitly learned through $\\mathcal{L}_{\\mathrm{ek}}$ . To provide distance labels for [55], we followed their convention and employed Faiss to compute the L2 distance of each pose as an approximate ground truth distance.", + "bbox": [ + 89, + 657, + 482, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After 10,000 iterations of optimization, the results are presented in Table 4. As shown in the table, our modeling approach outperforms the NDF. By learning a region (rather than a submanifold) and implicitly learning through", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/63ff3eb97ebb6ebdab5a0695115f4439fa1b1d321360db3dfe431c98bb94c8b5.jpg", + "table_caption": [ + "Table 4. Comparison between SDF and NDF." + ], + "table_footnote": [], + "table_body": "
AccuracyEikonal Loss ↓
SDF97.70%0.0850
NDF54.33%0.1916
", + "bbox": [ + 589, + 114, + 826, + 172 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{\\mathrm{ek}}$ , our method achieves better results.", + "bbox": [ + 513, + 190, + 774, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Collision Resolution by Pose Optimization", + "text_level": 1, + "bbox": [ + 511, + 214, + 870, + 231 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/38ece8f977fde81d82a31c583a2f06f4c7488a0d6a5139b4af1d4d4a96cbd896.jpg", + "image_caption": [ + "Figure 4. An illustration of how collision resolution optimizes a collided robot towards a collision-free state. The figure shown visualizes the SDF, where red points (representing collisions) are optimized to green points (representing non-collisions) along the gradient update trajectories." + ], + "image_footnote": [], + "bbox": [ + 555, + 250, + 864, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Given a collision pose, our neural network can optimize the collision pose to the nearest non-colliding pose, as shown in Figure 4. After training the network, we sample 1,000 collision poses and use our $g$ to predict their SDF values. We then apply gradient optimization, fixing the trained model's weights, and minimize the predicted SDF until it falls below a threshold value $l_{\\mathrm{thres}}$ .", + "bbox": [ + 511, + 491, + 905, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specifically, we use the Adam optimizer [26] with a learning rate of 0.01, keeping all other parameters unchanged. The results are presented in Table 5. As the SDF values decrease, both the likelihood and severity of collisions reduce, demonstrating that our method effectively predicts and avoids collisions.", + "bbox": [ + 511, + 598, + 905, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To assess the robustness of our model, we perform optimization with varying learning rates, anticipating consistent performance across these rates. To examine the effect of the learning rate, we replicate the experimental setup as described previously, setting $l_{\\mathrm{thres}} = -0.1$ . We then compare the number of collision points and analyze the overall trends. The results demonstrate that the model performs comparably across different learning rates, further validating the robustness of our approach. A summary of these results is presented in Table 6.", + "bbox": [ + 511, + 688, + 905, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Integration with Dr. Robot", + "text_level": 1, + "bbox": [ + 511, + 848, + 756, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Differentiable robot rendering (Dr. Robot) enables us to obtain a differentiable pose from the rendered view. From", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22567", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bdb385fbb910359ccac80f2078ec4b763a8b4f7c5e103dc2dfd1d6ad1719380b.jpg", + "table_caption": [ + "Table 5. Effect of different threshold $(l_{\\mathrm{thres}})$ . $\\overline{\\mathrm{Iter}}$ represents the average number of iterations, while $\\Delta \\theta$ denotes the change in angle. The last two columns display the collision points in the scenario prior to optimization and after optimization, respectively." + ], + "table_footnote": [], + "table_body": "
l_thresIter.↓Time (s) ↓Δθ↓BeforeAfter ↓
-0.00019.0170.1550.1625.5570.399
-0.00119.3920.1560.1655.6330.375
-0.00518.8740.1530.1595.5080.312
-0.01020.1240.1540.1735.6170.187
-0.02020.0900.1620.1735.4710.080
-0.03020.2360.1600.1725.3430.019
-0.04021.2560.1710.1815.6260.016
-0.05022.6270.1740.1905.7570.006
-0.10024.4500.1920.2035.1970.001
", + "bbox": [ + 96, + 156, + 475, + 311 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d4bf0438311b8e2d160eebad6d4906f8f9b7e2c7c54309994739f504ecff524a.jpg", + "table_caption": [ + "Table 6. Impact of different learning rate. The content of the last two columns is identical to that of Table 5." + ], + "table_footnote": [], + "table_body": "
LRIter.↓Time(s)↓Δθ↓BeforeAfter↓
0.001241.3631.8410.2035.4600.003
0.01024.4500.1920.2035.1970.001
0.02012.8260.1040.2155.4950.000
0.0505.6340.0490.2365.6220.000
0.1003.0260.0280.2565.5690.000
0.2001.7850.0180.3155.6350.001
0.5001.1270.0130.5275.3260.000
1.0001.1040.0131.0405.5530.000
", + "bbox": [ + 96, + 356, + 473, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "this pose, our method can infer prior knowledge about potential collisions with the external environment or self-intersections. This prior knowledge can be seamlessly integrated into the differentiable rendering process.", + "bbox": [ + 89, + 515, + 483, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.1. Inverse Action from Collision Image", + "text_level": 1, + "bbox": [ + 89, + 583, + 393, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We leverage Dr. Robot to optimize the robot's pose from images. However, we observe that the optimized poses are not always reasonable; in some cases, they result in collisions, limiting the practical application of Dr. Robot in real-world scenarios. To address this, we combine our SDF $g$ with Dr. Robot, enabling us to optimize reasonable poses that minimize collisions while maintaining image consistency.", + "bbox": [ + 89, + 601, + 483, + 707 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Striving for an efficient evaluation, we introduce immovable rigid blocks next to the robot. This way, if the robot's pose is unreasonable, it will collide with these blocks or self-collision. In each scene, we set up four cameras from different viewpoints and capture rendered images, instance segmentations, and depth maps from the simulation engine. This setting closely aligns with the real-world scenarios using monocular depth estimation models, such as Depth Pro[3]. To optimize the robot's pose, we use the following loss functions:", + "bbox": [ + 89, + 707, + 483, + 858 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R G B}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {r} - \\boldsymbol {r} _ {\\mathrm {g t}} \\| \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 864, + 483, + 904 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3f003de504a726cb0fb822556697a4cfa785797ed6e690a14c72bfee46420370.jpg", + "table_caption": [ + "Table 7. The number of collision points (averaged) and collision rate of the pose inverse from images. We control the collision point from simulator and generate images for Dr. Robot optimization." + ], + "table_footnote": [], + "table_body": "
Original collision point in dataCollision Point ↓Collision Rate ↓
Dr. RobotOursDr. RobotOurs
10.969.170.8378%9%
2.002.330.0486%2%
1.001.180.0278%2%
0.000.050.002%0%
", + "bbox": [ + 517, + 148, + 898, + 250 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {d} - \\boldsymbol {d} _ {\\mathrm {g t}} \\| \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 262, + 906, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Where $\\operatorname{seg}[i,j]$ is the robot's mask, with 0 indicating the robot is not present at that position in the image and 1 indicating it is present. Here, $\\boldsymbol{r}$ represents the rendered image from Dr. Robot, and $r_{\\mathrm{gt}}$ represents the rendered image from the simulation engine; $\\boldsymbol{d}$ represents the rendered depth from Dr. Robot, and $d_{\\mathrm{gt}}$ represents the rendered depth from the simulation engine. The baseline loss function is the sum of the image and depth losses:", + "bbox": [ + 511, + 306, + 906, + 429 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 439, + 906, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To address collisions, we use our trained SDF model. The data burden is manageable as we can obtain sufficient data from the simulation engine for training. During the optimization process, we introduce an additional term to the loss function:", + "bbox": [ + 511, + 465, + 905, + 541 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S D F}} = \\operatorname {R e L U} (g (\\boldsymbol {\\theta}) - l _ {\\text {t h r e s}}) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 551, + 906, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Thus, our loss function is", + "bbox": [ + 532, + 579, + 705, + 593 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S D F}} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 606, + 906, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\beta$ is a weight scalar. The optimization stops when $g(\\pmb{\\theta}) \\leq l_{\\mathrm{thres}}$ , with $l_{\\mathrm{thres}} = -0.1$ . We sampled 100 instances for testing, and the results are shown in Table 7. The quantitative results demonstrate that, after optimization, Dr. Robot effectively avoids collisions and achieves the closest possible pose without collision.", + "bbox": [ + 511, + 633, + 905, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.2. Inverse Trajectory from Optimization", + "text_level": 1, + "bbox": [ + 511, + 731, + 823, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we aim to explore the feasibility of using Dr. Robot for trajectory generation. Given the starting posture $\\theta_{\\mathrm{start}}$ and the end posture $\\theta_{\\mathrm{end}}$ , we employ gradient optimization with Dr. Robot to generate the intermediate trajectory for robot control.", + "bbox": [ + 511, + 750, + 905, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As mentioned in Section 4.4.1, we randomly sample two collision-free poses and obtain their respective rendering results. Dr. Robot uses $\\theta_{\\mathrm{start}}$ as the initial configuration and utilizes the image, mask, depth, and pose information of $\\theta_{\\mathrm{end}}$ from the simulator as supervisory signals. In addition,", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22568", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f658d563706f4fb18db5a55223684fbacb4b0125ef3e24d6fd8bb4e40affa26b.jpg", + "table_caption": [ + "Table 8. Optimize Trajectory by Dr. Robot and SDF." + ], + "table_footnote": [], + "table_body": "
Collision Point ↓Collision Rate ↓
Dr. Robot4.0710.64%
Ours (-0.00)3.5010.00%
Ours (-0.01)0.000.00%
Ours (-0.05)0.000.00%
Ours (-0.10)0.000.00%
", + "bbox": [ + 119, + 114, + 452, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we incorporate our SDF model and add $\\mathcal{L}_{\\mathrm{SDF}}$ (Equation 12) to the loss function.", + "bbox": [ + 89, + 232, + 482, + 261 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, during the optimization process, the value of the SDF fluctuates around $l_{\\mathrm{thres}}$ , which causes some data points to violate the SDF constraints. To address this, we perform post-processing on the intermediate trajectory:", + "bbox": [ + 89, + 263, + 483, + 324 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {S D F}} (\\hat {\\boldsymbol {\\theta}} _ {i}) + \\frac {1}{N - 1} \\sum_ {i = 1} ^ {N - 1} \\| \\hat {\\boldsymbol {\\theta}} _ {i + 1} - \\hat {\\boldsymbol {\\theta}} _ {i} \\| \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 334, + 482, + 377 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\hat{\\theta}_i, i = 1\\ldots N$ is the middle trajectory generate from optimization. Here, we combine the SDF loss and the total variation loss. The results, as shown in Table 8, demonstrate that our approach effectively generates intermediate trajectories suitable for robot control.", + "bbox": [ + 89, + 388, + 483, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4.3. Inverse Action from VLM", + "text_level": 1, + "bbox": [ + 89, + 472, + 318, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have observed that directly extracting data from the Vision-Language Model (VLM) using Dr. Robot can lead to unconstrained optimization, potentially resulting in implausible poses. Conversely, employing a simulator to refine these poses is problematic due to the absence of gradient information, which hinders seamless integration with Dr. Robot. Our novel approach successfully circumvents the optimization of collision-prone poses, thereby maintaining the plausibility of the outcomes.", + "bbox": [ + 89, + 491, + 482, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In alignment with Dr. Robot's methodology, we utilized CLIP to extract action data from the VLM. Our experiments use shadow hand and leveraged the openai/clip-vit-base-patch32 model from HuggingFace. We aimed to maximize the dot product between the language and image embeddings generated by their respective processing towers. We computed the optimized collision points and associated collision probabilities. To substantiate that our method does not compromise the efficacy of action distillation from the VLM, we conducted a comparative analysis of the optimized dot products. The findings, presented in Table 9, demonstrate that our technique effectively precludes the optimization of implausible poses without impeding the extraction of actions from the VLM.", + "bbox": [ + 89, + 628, + 482, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Sim-to-Real Deployment", + "text_level": 1, + "bbox": [ + 89, + 848, + 316, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the performance of our method, we conducted several sim-to-real experiments. In an illustrative scenario,", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. The metrics of collision and optimization while optimizing robotic pose by CLIP. We indicate the collision point(Point) and collision rate(Rate) for average, and report the mean and std of dot product metrics.", + "bbox": [ + 511, + 88, + 906, + 145 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0e57e4a026938f567c192575c5495b4c4d4a99565df29aa80412739b04143e43.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Point ↓Rate ↓meanstd ↓
Dr. Robot1.3042.50%33.861.53
Ours (-0.00)0.4030.00%34.421.58
Ours (-0.01)0.8040.00%34.131.20
Ours (-0.05)0.3020.00%34.221.60
Ours (-0.10)0.1010.00%34.021.23
", + "bbox": [ + 544, + 156, + 870, + 256 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e753e663bd5df8d664d4a1428366b6d328084fca485ff009dcfb0a17088da637.jpg", + "image_caption": [ + "Figure 5. Sim2Real Experiment: Obstacle Avoidance with Prof. Robot. The first row illustrates that, in the simulator, the robot arm collides with the red box due to its inability to perceive obstacles. The second row shows that after integrating Prof. Robot, the robot successfully avoids the red obstacle. The red box represents an obstacle, and without Prof. Robot, the robot fails to circumvent it. The final row demonstrates that, with Prof. Robot, the robot smoothly navigates around the obstacle, confirming the effectiveness of our method for real-world applications." + ], + "image_footnote": [], + "bbox": [ + 514, + 262, + 906, + 444 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a robot navigates around obstacles – including a wall and a box – while moving from an initial pose to a target pose. We interpolate 100 poses between the initial and target positions using SO(2) interpolation and optimize the trajectory with our Prof. Robot algorithm. The results, shown in Figure 5, demonstrate that our approach effectively guides the robot arm around obstacles while preventing collisions in simulation and reality.", + "bbox": [ + 511, + 602, + 906, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations and Future Work", + "text_level": 1, + "bbox": [ + 511, + 736, + 785, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method tackles the problem of cross-environment generalization. To address this, a new mechanism could be proposed that enhances Prof. Robot's scene perception by modeling dynamic objects. The dynamic environment could be represented by supplementary joints $\\delta$ , which constrain the robotic system's joint space. By training with a collision-aware discriminator $p(\\cdot|\\delta)$ , our joint learning framework could practical effectiveness despite environmental perturbations from ideal conditions. In practical scenarios, this is achieved by estimating the poses of dynamic objects.", + "bbox": [ + 511, + 761, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22569", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 119, + 187, + 136 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jad Abou-Chakra, Krishan Rana, Feras Dayoub, and Niko Sünderhauf. Physically embodied gaussian splatting: A real-time correctable world model for robotics. arXiv preprint arXiv:2406.10788, 2024. 3", + "[2] Emre Aksan, Manuel Kaufmann, and Otmar Hilliges. Structured prediction helps 3d human motion modelling. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7144-7153, 2019. 4", + "[3] Aleksei Bochkovskii, Amaël Delaunoy, Hugo Germain, Marcel Santos, Yichao Zhou, Stephan R. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.9, + 0.152 + ], + "angle": 0, + "content": "Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisions" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.179, + 0.279, + 0.2 + ], + "angle": 0, + "content": "Quanyuan Ruan\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.311, + 0.18, + 0.411, + 0.198 + ], + "angle": 0, + "content": "Jiabao Lei\\(^{2\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.445, + 0.181, + 0.563, + 0.198 + ], + "angle": 0, + "content": "Wenhao Yuan" + }, + { + "type": "text", + "bbox": [ + 0.607, + 0.181, + 0.732, + 0.199 + ], + "angle": 0, + "content": "Yanglin Zhang" + }, + { + "type": "text", + "bbox": [ + 0.774, + 0.181, + 0.862, + 0.198 + ], + "angle": 0, + "content": "Dekun Lu" + }, + { + "type": "text", + "bbox": [ + 0.369, + 0.2, + 0.488, + 0.216 + ], + "angle": 0, + "content": "Guiliang Liu\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.562, + 0.2, + 0.635, + 0.215 + ], + "angle": 0, + "content": "Kui Jia*" + }, + { + "type": "text", + "bbox": [ + 0.342, + 0.217, + 0.656, + 0.235 + ], + "angle": 0, + "content": "\\(^{1}\\)South China University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.235, + 0.795, + 0.252 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Data Science, The Chinese University of Hong Kong, Shenzhen" + }, + { + "type": "image_caption", + "bbox": [ + 0.208, + 0.271, + 0.38, + 0.286 + ], + "angle": 0, + "content": "STATIC COLLISION" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.289, + 0.295, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.42, + 0.246, + 0.435 + ], + "angle": 0, + "content": "DR. ROBOT" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.289, + 0.496, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.42, + 0.488, + 0.437 + ], + "angle": 0, + "content": "PROF. ROBOT (OURS)" + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.271, + 0.778, + 0.286 + ], + "angle": 0, + "content": "SELF COLLISION" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.289, + 0.702, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.42, + 0.654, + 0.435 + ], + "angle": 0, + "content": "DR. ROBOT" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.29, + 0.903, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.42, + 0.895, + 0.437 + ], + "angle": 0, + "content": "PROF. ROBOT (OURS)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.447, + 0.907, + 0.516 + ], + "angle": 0, + "content": "Figure 1. Our method improves upon Dr.Robot [32] by additionally enabling differentiable avoidance of static and self-collisions. By learning and integrating a gradient-consistent pose classifier into a differentiable rendering pipeline, the generated pose trajectories are free from physical collisions. The objective is to penalize high collision probabilities during optimization. On the left, our method can push robotic arms away from intersecting objects. On the right, it can also avoid self-collisions. Images are rendered using Blender with meshes." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.527, + 0.327, + 0.542 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.56, + 0.486, + 0.848 + ], + "angle": 0, + "content": "Differentiable rendering has gained significant attention in the field of robotics, with differentiable robot rendering emerging as an effective paradigm for learning robotic actions from image-space supervision. However, the lack of physical world perception in this approach may lead to potential collisions during action optimization. In this work, we introduce a novel improvement on previous efforts by incorporating physical awareness of collisions through the learning of a neural robotic collision classifier. This enables the optimization of actions that avoid collisions with static, non-interactable environments as well as the robot itself. To facilitate effective gradient optimization with the classifier, we identify the underlying issue and propose leveraging Eikonal regularization to ensure consistent gradients for optimization. Our solution can be seamlessly integrated into existing differentiable robot rendering frameworks, utilizing gradients for optimization and providing a foundation for future applications of differentiable rendering in robotics with improved reliability of interactions with the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.531, + 0.907, + 0.577 + ], + "angle": 0, + "content": "physical world. Both qualitative and quantitative experiments demonstrate the necessity and effectiveness of our method compared to previous solutions." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.604, + 0.645, + 0.619 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Conventional methods for representing a robot involve partitioning it into many rigid body parts and then articulating them according to structural kinematic constraints. However, they only model the robots geometrically and do not possess a realistic appearance for rendering; therefore, they are less applicable for integration into a differentiable pipeline involving images, which is currently a popular approach in computer vision. A recent approach [32] has been proposed to model robots' appearance in a differentiable manner, facilitating the integration of robots into a differentiable rendering solution. It allows for backpropagating the appearance supervision from images to the control space, thereby enabling the learning of plausible robot movements. Their method is straightforward. They leverage Gaussian splatting [24] for efficient differentiable rendering, where each Gaussian point is associated with the robotic arms using implicit LBS [32, 34], and the arms are generated by the control parameters through forward kinematics." + }, + { + "type": "page_footnote", + "bbox": [ + 0.114, + 0.863, + 0.229, + 0.876 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.114, + 0.876, + 0.251, + 0.889 + ], + "angle": 0, + "content": "* Corresponding authors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.124, + 0.889, + 0.446, + 0.9 + ], + "angle": 0, + "content": "Project: https://qrcat.github.io/prof-robot/" + }, + { + "type": "list", + "bbox": [ + 0.114, + 0.863, + 0.446, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "22562" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.333 + ], + "angle": 0, + "content": "While promising, their method clearly lacks awareness of how to avoid physical collisions with a static environment that does not dynamically interact with the robot, as well as collisions with the robot itself. When optimized using gradient information, it is likely to produce invalid robotic parameters that lead to intersections. This problem is particularly severe in real scenarios, where minor collisions damage the robot's mechanical structure. Due to the typically high cost of robots, which can result in significant financial losses. To address this issue and ensure that the differentiable rendering pipeline produces valid robotic parameters that prevent collisions, we need to guide the robot to evade collision scenarios during gradient-guided optimization. Intuitively, we employ a similar approach to that in [55] to achieve collision-free optimization, with some critical adaptations and improvements." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.338, + 0.485, + 0.686 + ], + "angle": 0, + "content": "Our idea is simple. We observe that some robotic poses are free from collisions, while others are not. Therefore, we can classify these poses based on whether they lead to a collision. We can leverage a discriminative model to classify these poses. The classifier \\( f \\) is a mapping \\( \\mathrm{SO}(2)^K \\to [0,1] \\) that maps a pose \\( \\pmb{\\theta} \\in \\mathrm{SO}(2)^K \\) to a decision \\( c \\in [0,1] \\), where a value of \\( c > 0.5 \\) indicates a collision. A rotation occurs in \\( \\mathrm{SO}(2) \\) because the motor of a robotic joint typically possesses only one degree of freedom for rotation. Finally, we need to integrate the model into a differentiable pipeline. During optimization, to ensure that the robotic pose remains in the collision-free zone, we must push the pose \\( \\pmb{\\theta} \\) toward the collision-free regions \\( \\{\\pmb{\\theta} \\in \\mathrm{SO}(2)^K \\mid f(\\pmb{\\theta}) \\leq 0.5\\} \\) that correspond to a classification result of \\( c \\leq 0.5 \\). Compared to [55], we should note that the biggest benefit of using classification rather than fitting a distance field is that classification does not require computing manifold distances and only needs to provide classification labels, corresponding to either \"collided\" or \"not collided.\" Computing labels is expensive and may lack accuracy, as the normally generated samples are often too sparse to accurately compute the manifold distances in such a high-dimensional space due to the curse of dimensionality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Unfortunately, the direct application of the above idea does not yield the desired results due to the variability of the gradients obtained after sheer classification learning. The update direction of the gradients may not be consistent, and a later update may offset the previous one. We will mathematically analyze the reasons for this phenomenon in Section 3.2. To address this issue, we introduce a regularization term to enforce the consistency of gradients by imposing that the gradient's norm be one, as expressed by \\(\\mathcal{L}_{\\mathrm{ek}} = (\\|\\nabla_{\\theta}g(\\pmb{\\theta})\\| - 1)^2\\). We immediately notice that this is a requirement for being a Signed Distance Field (SDF). To integrate the regularization term into the optimization, we take the function \\(g\\) as the value before the Sigmoid function \\(\\sigma\\), as given by \\(f = (\\sigma \\circ \\omega \\circ g)(\\pmb{\\theta})\\). The function \\(g\\) is im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "pleted as a multi-layer perceptron (MLP), \\(\\omega\\) is a scalar multiplication function, and \\(\\sigma\\) is the sigmoid function. We notice that although we leverage the SDF, it does not require fitting any manifold distance; the SDF property is ensured by the regularization term. Interestingly, the method of imposing the Eikonal constraint is similar to the work of [16, 63]; instead of regularizing in three-dimensional space, we regularize the field \\(g\\) in a high-dimensional pose space." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.214, + 0.905, + 0.304 + ], + "angle": 0, + "content": "Lastly, we verify in our extensive ablation studies and comparative experiments that our method of learning a high-dimensional pose classifier \\( f \\) can avoid physical collisions with the static environment and the robot itself, making the robotic pose produced by a differentiable pipeline physically reliable." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.305, + 0.888, + 0.319 + ], + "angle": 0, + "content": "We summarize our technical contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.324, + 0.905, + 0.429 + ], + "angle": 0, + "content": "1. We address the issue of efficient differentiable robot rendering with potential collisions involving a static, non-interactive environment and self-collisions. This is achieved by learning a multi-layer perceptron (MLP), denoted as \\( f \\), to classify the control pose \\( \\theta \\) and determine whether it corresponds to a collision. Classification eliminates the need for accurate manifold distance." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.43, + 0.905, + 0.564 + ], + "angle": 0, + "content": "2. To address the issue of poor reliability of gradients from the classifier and to integrate \\( f \\) into a gradient-based optimization pipeline, we introduce the Eikonal regularization term \\( \\mathcal{L}_{\\mathrm{ek}} \\) to enforce consistency among gradients, effectively transforming the value before the Sigmoid, \\( g \\), into a signed distance function (SDF). This regularization enhances the reliability of the gradients and leverages the beneficial properties of the SDF without the need for explicit computation of manifold distance." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.565, + 0.905, + 0.639 + ], + "angle": 0, + "content": "3. To model the dependency of adjacent robotic joints efficiently, we introduce hierarchical joint encoding that conditions a joint angle on an ancestor's rotation, thereby better capturing the hierarchical dependency of robotic arms." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.324, + 0.905, + 0.639 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.657, + 0.664, + 0.672 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.682, + 0.864, + 0.698 + ], + "angle": 0, + "content": "2.1. Differentiable Rendering and Simulation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Differentiable rendering and simulation play a pivotal role in computer vision and graphics. In differentiable rendering, gradients are propagated from primitives to image, while differentiable simulators compute gradients of physical processes similarly, which facilitates seamless integration with gradient-based optimization techniques. The integration of neural fields into robotics has attracted considerable attention. Researchers have employed diverse representations to bridge the digital and physical realms [20, 23, 24, 33, 38, 40, 44, 47, 67, 70]. Innovative approaches, such as Gaussian splatting for the precise reconstruction of robots and their environments, exemplify this trend [35, 50]. Moreover, techniques such as neural radi" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22563" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.562 + ], + "angle": 0, + "content": "ance fields for teleoperation [45] and future scene prediction [36] have significantly advanced robotic manipulation capabilities. Feature distillation has further empowered robots to perform complex tasks by translating language embeddings into corresponding 3D actions [49, 51, 52, 71, 73]. Additional advancements include comprehensive physical world modeling, future state prediction [1], and learning continuous manifolds of valid grasps using signed distance functions (SDF) [25, 64]. Significant progress has also been made in perceptual scene understanding and grasp planning [4-6]. One of the primary challenges in developing these simulators is accurately modeling contact interactions—a difficulty that arises from the inherently binary, discontinuous nature of contacts, where objects are either in contact or not [42]. According to [42], contact models can be broadly categorized into four classes: complementarity problems, compliant models, position-based models, and material point method (MPM) frameworks. Complementarity problems emphasize maintaining strict zero-penetration contact between objects [7-9, 12, 13, 19, 21, 28, 29, 46, 48, 60-62, 65, 74]. Compliant models relax the complementarity problem's constraint by replacing the sharp, step-like contact functions with smooth approximations that have large but finite gradients[9, 13, 15, 18, 19, 27, 41, 54, 57, 58]. The position-based method directly constrains object positions to prevent penetration [11, 37]. Meanwhile, the MPM handles contact interactions between both rigid- and soft-body objects[22, 53]. Despite these impressive advances, the effectiveness of differentiable systems for robotic manipulation remains under active validation, marking a promising yet nascent stage of development." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.569, + 0.393, + 0.584 + ], + "angle": 0, + "content": "2.2. Signed Distance Fields in Robotics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.591, + 0.484, + 0.834 + ], + "angle": 0, + "content": "In the realm of robotics and computer graphics, the construction of SDF has been an important technique for various applications, particularly in motion planning and collision avoidance. Some researchers pioneered a method to construct SDF on grid maps [10]. Afterwards, some others introduced incremental SDF construction techniques [17, 43], significantly enhancing the adaptability of SDF in dynamic environments. A novel implicit SDF method is proposed to leverage swept volumes for construction [72]. This method allows for efficient evaluation of the SDF at specific obstacle points with known coordinates, simplifying the process and reducing computational overhead. Another work [69] made a significant stride with the introduction of RobotSDF, an implicit morphology modeling technique. Furthermore, the application of SDF in obstacle avoidance has been extensively explored by [30, 59, 66]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.846, + 0.182, + 0.86 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In this section, we will detail our method for achieving collision avoidance in robotic operations in combination" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.319 + ], + "angle": 0, + "content": "with Gaussian splattering-based differentiable robotic rendering [32]. The types of collisions we consider in this paper include static collisions, which occur when the robot collides with a static and non-interactive environment, as well as self-collisions, which involve collisions with the robot itself. Section 3.1 will model the problem of collision detection as a robotic pose classification problem. In Section 3.2, we will address some challenges that arose in formulating collision detection and propose the introduction of a signed distance field (SDF) as an underlying field for the classifier to tackle the gradient inconsistency problem during optimization. Section 3.3 will explain how we hierarchically encode the robotic pose while respecting the robotic kinematic dependencies. Finally, we will present our loss functions and training schemes in Section 3.4." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.328, + 0.866, + 0.344 + ], + "angle": 0, + "content": "3.1. Collision Detection by Pose Classification" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.907, + 0.457 + ], + "angle": 0, + "content": "To make the model aware of physical collisions during optimization, we need a collision detector to determine whether the robotic pose has caused intersections with other environmental objects or with the robot itself. The collision detector is essentially a function \\( f: \\theta \\mapsto c \\) with \\( c \\in [0,1] \\) that classifies each pose \\( \\theta \\) into two categories: either collided (\\( c > 0.5 \\)) or not (\\( c \\leq 0.5 \\))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.909, + 0.563 + ], + "angle": 0, + "content": "The robots we consider in this paper have \\(K\\) joints, and each joint has exactly one degree of freedom for rotation; thus, the pose parameter is within the space \\(\\theta \\in \\mathrm{SO}(2)^K\\). The classifier network \\(f\\) will partition the space into many regions, and ideally, the regions corresponding to valid poses (non-collided poses) will form a manifold as given by" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.577, + 0.907, + 0.596 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} = \\left\\{\\boldsymbol {\\theta} \\in \\operatorname {S O} (2) ^ {K} \\mid f (\\boldsymbol {\\theta}) \\leq 0. 5 \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.602, + 0.906, + 0.676 + ], + "angle": 0, + "content": "To ensure that the output value falls within the range [0, 1], we follow convention and apply a Sigmoid function \\(\\sigma\\) to the last output, meaning that the function \\(f\\) is effectively defined by \\(f = \\sigma \\circ g\\), where \\(g\\) is another scalar-valued function that we will detail later in Section 3.2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.678, + 0.906, + 0.723 + ], + "angle": 0, + "content": "To effectively learn the classifier \\( f \\), we follow tradition and use binary cross-entropy loss to supervise \\( f \\), as expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.724, + 0.907, + 0.74 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {B C E}} = \\operatorname {B C E} (f (\\boldsymbol {\\theta}), c ^ {\\mathrm {g t}}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.906, + 0.779 + ], + "angle": 0, + "content": "where \\( c^{\\mathrm{gt}} \\in \\{0,1\\} \\) is the ground truth label indicating whether it is valid (\\( c^{\\mathrm{gt}} = 1 \\)) or not (\\( c^{\\mathrm{gt}} = 0 \\))." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.898, + 0.804 + ], + "angle": 0, + "content": "3.2. Eikonal Regularizer for Consistent Gradients" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.87 + ], + "angle": 0, + "content": "However, directly applying \\( f \\) to gradient optimization is problematic. The function is nearly binary, and the gradients near the values of 0 and 1 are almost zero, leading to noisy and unreliable supervision signals." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "We visualize a possible function \\( f \\) with a two-dimensional input space in Figure 3. We notice that, since" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22564" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.633, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.27, + 0.633, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Our Pipeline. We predict whether a collision has occurred based on pose input, using Eikonal loss \\((\\mathcal{L}_{\\mathrm{ek}})\\) and binary cross-entropy loss \\((\\mathcal{L}_{\\mathrm{BCE}})\\) to ensure this. It can then be seamlessly integrated with Dr. Robot [32] to create a fully differentiable pipeline for optimization." + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.103, + 0.906, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.689, + 0.269, + 0.908, + 0.312 + ], + "angle": 0, + "content": "Figure 3. An illustration of the potential fluctuation of the classification loss landscape." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.353, + 0.483, + 0.488 + ], + "angle": 0, + "content": "the values at both far sides fluctuate, the gradients also fluctuate, leading to inconsistent gradients. When we aim to optimize a pose from the exterior (collided region) toward the interior (collision-free region), this may not be the case because the gradient directions are inconsistent (see the two red points) due to fluctuations in the loss landscape. Small fluctuations do not significantly influence the loss value, but they can lead to noisy and inconsistent gradients, which are harmful to optimization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.581 + ], + "angle": 0, + "content": "To address the issue, we need to consider the function \\( g \\) before the Sigmoid function \\( \\sigma \\), as \\( \\sigma \\) will restrict the gradient and render it too small for updating poses. Specifically, for two consecutive gradient updates with poses \\( \\pmb{\\theta}_t \\) and \\( \\pmb{\\theta}_{t + 1} \\), the update at \\( t + 1 \\) is likely to offset the previous update at \\( t \\), as expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.584, + 0.483, + 0.619 + ], + "angle": 0, + "content": "\\[\n\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\leq 0, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.623, + 0.484, + 0.683 + ], + "angle": 0, + "content": "especially in regions with high confidence levels close to 0 or 1. This is visualized in Figure 3, where two red dots are plotted; their gradient directions may not be consistent (or correlated) as they point in opposite directions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.684, + 0.484, + 0.728 + ], + "angle": 0, + "content": "We also note that gradient updates are typically small. Assuming the updates \\(\\theta_{t + 1}\\) and \\(\\theta_t\\) are close enough and correlated, we have" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.733, + 0.483, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\approx \\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\rangle = \\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\| ^ {2} \\geq 0. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.773, + 0.484, + 0.864 + ], + "angle": 0, + "content": "This analysis indicates that to enforce gradient consistency, we only need to manipulate the norm of the gradients. To make the correlation of the gradients as uniform as possible (which is desirable for gradient updates), we enforce the above term to be a positive constant \\(a > 0\\). This motivates us to adopt the following regularization term" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.868, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {e k}} = \\left(\\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta}} \\right\\| - a\\right) ^ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.906, + 0.474 + ], + "angle": 0, + "content": "to ensure gradient consistency between the two adjacent updates. We immediately notice that when \\( a = 1 \\), it becomes an Eikonal regularizer that is widely employed by the signed distance function [16, 44]. Interestingly, this term can be viewed as generalizing the implicit geometric regularization [16] to high-dimensional pose space by learning a function \\( g \\). To simplify implementation, we use \\( a = 1 \\) throughout the paper." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.474, + 0.906, + 0.52 + ], + "angle": 0, + "content": "The function \\( g \\) is practically implemented as a multilayer perceptron that receives robotic poses \\( \\pmb{\\theta} \\) as input and produces a scalar; the final classifier is therefore" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.529, + 0.905, + 0.546 + ], + "angle": 0, + "content": "\\[\nf (\\boldsymbol {\\theta}) = (\\sigma \\circ \\omega \\circ g) (\\boldsymbol {\\theta}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.906, + 0.614 + ], + "angle": 0, + "content": "where \\(\\omega : x \\mapsto sx\\) denotes a function that multiplies the input \\(x\\) by an estimable positive constant \\(s\\), which will be further discussed in Section 4.2.3. Our current pipeline is illustrated in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.623, + 0.828, + 0.64 + ], + "angle": 0, + "content": "3.3. Hierarchical Robotic Pose Encoding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.907, + 0.84 + ], + "angle": 0, + "content": "We represent the robotic pose using rotation angles, each describing the relative rotation between two arms. The pose parameters are defined in local coordinate frames, such that continuous modifications of a single joint result in realistic motion. However, since angles only describe relative rotations, they may not respect the kinematic structure and cannot effectively handle the structural dependency relationships between the arms. We observe that each individual joint needs to be conditioned on the parent rotations and thus must be influenced by them. To incorporate this notion of kinematic dependency into the function \\( g \\), we implement the function as a hierarchical network that encodes the dependency within the network structure [2, 14, 39, 55]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.902 + ], + "angle": 0, + "content": "This is similar to the method described in [55]. Specifically, for a given robotic pose \\(\\pmb{\\theta} = [\\theta_{1};\\dots;\\theta_{K}]\\), where \\(\\theta_{k}\\) (with \\(k\\in \\{1,\\ldots ,K\\}\\)) is the rotation angle for joint \\(k\\), and a function \\(\\tau (k)\\) maps the index of each joint to its parent joint" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22565" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.123 + ], + "angle": 0, + "content": "index, we encode each pose using a multi-layer perceptron (MLP) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.134, + 0.482, + 0.159 + ], + "angle": 0, + "content": "\\[\ng _ {1}: \\theta_ {1} \\mapsto \\boldsymbol {\\nu} _ {1} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.153, + 0.423, + 0.169 + ], + "angle": 0, + "content": "\\[\ng _ {k}: \\left(\\theta_ {k}, \\boldsymbol {\\nu} _ {\\tau (k)}\\right) \\mapsto \\boldsymbol {\\nu} _ {k}, \\quad k \\in \\{2, \\dots , K \\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.485, + 0.304 + ], + "angle": 0, + "content": "This process takes the joint angle and the encoded feature \\(\\pmb{\\nu}_{\\tau (k)}\\in \\mathbb{R}^{\\ell}\\) of its parent joint as input and produces an output feature \\(\\pmb{\\nu}_k\\in \\mathbb{R}^\\ell\\) , where \\(\\ell = 8\\) is the feature dimension. We then concatenate the encoded features of every joint to obtain a combined pose embedding \\(\\pmb {\\nu} = [\\pmb {\\nu}_1;\\dots ;\\pmb {\\nu}_K]\\) This embedding is further transformed by a linear mapping \\(\\mathbb{R}^{\\ell ,K}\\to \\mathbb{R}\\) to yield a scalar value that serves as the output of the function \\(g\\)" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.312, + 0.355, + 0.329 + ], + "angle": 0, + "content": "3.4. Training Data and Objectives" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.335, + 0.484, + 0.426 + ], + "angle": 0, + "content": "The training dataset comprises \\(N\\) poses and their corresponding decisions, represented by \\(\\mathcal{D} = \\{(\\pmb{\\theta}_i, c_i^{\\mathrm{gt}})\\}_{i=1}^N\\). It is constructed as follows: the robotic pose \\(\\pmb{\\theta}_i\\) is randomly sampled, and a (non-differentiable) collision detector is then applied to produce the decision \\(c_i^{\\mathrm{gt}} \\in \\{0, 1\\}\\), indicating whether a collision has occurred (\\(c_i^{\\mathrm{gt}} = 1\\))." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.426, + 0.484, + 0.486 + ], + "angle": 0, + "content": "The model is trained using batched samples; we omit the summation-over-samples notation here for simplicity. The objective is simply the weighted combination of \\(\\mathcal{L}_{\\mathrm{BCE}}\\) and \\(\\mathcal{L}_{\\mathrm{ek}}\\). With \\(\\alpha = 0.1\\), it is expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.499, + 0.482, + 0.515 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {B C E}} + \\alpha \\mathcal {L} _ {\\mathrm {e k}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.527, + 0.484, + 0.573 + ], + "angle": 0, + "content": "Depending on how it is learned, we may additionally have, for example, \\(\\mathcal{L}_{\\mathrm{RGB}}\\) for image-space supervision, which we omit here for simplicity." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.587, + 0.327, + 0.604 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.484, + 0.717 + ], + "angle": 0, + "content": "We conduct ablation studies on Prof. Robot (section 4.2), experiments on collision resolution (section 4.3), integration with Dr. Robot (section 4.4), and sim-to-real deployment (section 4.5). Comparison with the differentiable simulator, training with alternative regularizers, and manipulation with Dr. Robot are detailed in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.728, + 0.282, + 0.744 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.869 + ], + "angle": 0, + "content": "Data Preparation. We adopt a data-driven approach, leveraging the Mujoco [56] configurations provided by [32] with some modifications. Specifically, we selected six scenes and randomly sampled poses from the robot's joint limits, used Mujoco (which is non-differentiable) to check for collisions, and employed a resampling technique to balance the ratio of collision to non-collision data at approximately the same amount." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. We primarily evaluate the network's ability to distinguish between collision and non-collision" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.09, + 0.905, + 0.104 + ], + "angle": 0, + "content": "Table 1. Ablation study on hierarchical and flattened encoding." + }, + { + "type": "table", + "bbox": [ + 0.548, + 0.116, + 0.871, + 0.161 + ], + "angle": 0, + "content": "
HierarchicalFlatten
Classification Accuracy97.70%97.51%
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.177, + 0.906, + 0.297 + ], + "angle": 0, + "content": "states, as well as its performance in optimizing the gradients. The former metric (accuracy) assesses the network's ability to detect collisions, while the latter \\((\\mathcal{L}_{\\mathrm{ek}})\\) measures its capacity to avoid collisions through optimization. Furthermore, for a given robot pose denoted as \\(\\theta\\), we are able to determine the collision points of the mesh within the simulator and subsequently calculate the collision rate for all possible poses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.298, + 0.907, + 0.525 + ], + "angle": 0, + "content": "Experimental Details. We leverage the joint connection relationships defined in the URDF, where each joint is encoded using a tiny MLP. The encoded features from all joints are then concatenated and passed through an MLP with four hidden layers, each containing 512 units, followed by a final output layer with a single unit. LeakyReLU is used as the activation function for all layers. We introduce a learnable scale factor \\( s \\), which, after being multiplied by the MLP output, is passed through a Sigmoid function to produce a probability. We conduct experiments within a simulation environment, where the network's ability determines the success rate of collision resolution. Finally, we integrate our method into a differentiable robot rendering pipeline and perform control experiments. The experiments are conducted on a single NVIDIA RTX 4090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.533, + 0.863, + 0.549 + ], + "angle": 0, + "content": "4.2. Learning Robotic Signed Distance Fields" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.555, + 0.791, + 0.57 + ], + "angle": 0, + "content": "4.2.1. Ablation: Hierarchical Encoding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.573, + 0.906, + 0.68 + ], + "angle": 0, + "content": "To assess the impact of hierarchical encoding, we replaced it with a simple linear layer for encoding the input joint data while keeping the rest of the components unchanged. As shown in Table 1, after 10,000 iterations, the use of the hierarchical MLP results in higher accuracy. This shows that the hierarchical encoding strategy better captures the kinematic structure and increases performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.686, + 0.774, + 0.701 + ], + "angle": 0, + "content": "4.2.2. Ablation: Eikonal Regularizer" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.901 + ], + "angle": 0, + "content": "To investigate the effect of the Eikonal regularizer, we trained an MLP under two conditions: one without the Eikonal regularizer and one with it, and compared both the classification accuracy and the numerical value of the Eikonal loss. We then tested whether the models could resolve collisions (as described in Section 4.3). The models were trained for 10,000 iterations. During pose optimization, for the model trained without the Eikonal regularizer, we stopped the iteration if the collision probability dropped below 0.5. For the model trained with the Eikonal regularizer, we halted the iteration if the SDF value, which is negative in non-collision regions, fell below the threshold \\( l_{\\mathrm{thres}} = -0.1 \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22566" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.151, + 0.09, + 0.424, + 0.103 + ], + "angle": 0, + "content": "Table 2. Ablation study on the Eikonal loss." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.115, + 0.462, + 0.257 + ], + "angle": 0, + "content": "
w. Eikonal lossw/o. Eikonal loss
Classification97.70%98.39%
Accuracy
Iteration Nums ↓119.991000
Iteration Time ↓0.97 s10.64 s
Move Angle ↓0.604.49
Collision Point ↓0.6711.52
Collision Rate ↓17%99%
Gradient Norm8.53 × 10-11.89 × 10-6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.263, + 0.434, + 0.277 + ], + "angle": 0, + "content": "Table 3. Ablation study on the scaling factor \\( s \\) ." + }, + { + "type": "table", + "bbox": [ + 0.164, + 0.289, + 0.409, + 0.348 + ], + "angle": 0, + "content": "
AccuracyEikonal Loss ↓
w. s97.70%0.0850
w/o. s85.37%0.2568
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.365, + 0.483, + 0.442 + ], + "angle": 0, + "content": "The results were compared, as shown in Table 2. Without the Eikonal regularizer, the optimizer struggled to generate a collision-free pose from a collision state, with iterations exceeding 1,000, and the propagated gradients were too small to facilitate further optimization." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.448, + 0.312, + 0.464 + ], + "angle": 0, + "content": "4.2.3. Ablation: Scaling Factor" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.467, + 0.483, + 0.588 + ], + "angle": 0, + "content": "The cross-entropy loss and Eikonal loss may require gradients of different magnitudes, potentially interfering with each other and hindering the model's ability to learn useful information. To address this, a scaling factor \\( s \\) for the SDF is introduced to allow for large gradients in classification and limited gradients in the SDF. We removed the scaling factor \\( s \\) (setting \\( s = 1 \\)) and directly passed the SDF value to the Sigmoid function to produce \\( f \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.588, + 0.484, + 0.635 + ], + "angle": 0, + "content": "The numerical results, as shown in Table 3, demonstrate that the scaling factor effectively achieves good classification results while preserving the uniform gradient property." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.64, + 0.391, + 0.655 + ], + "angle": 0, + "content": "4.2.4. Comparison Between NDF and SDF" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.84 + ], + "angle": 0, + "content": "In contrast to [55], which models collision-free poses as a high-dimensional submanifold using a Neural Distance Field (NDF), we represent collision-free poses as a set of discontinuous regions in high-dimensional space that can be modeled using an SDF. To explore the differences between these two approaches, we also conducted experiments with an NDF. Learning an NDF requires accurate manifold distances; unlike [55], our method does not require this because it can be implicitly learned through \\(\\mathcal{L}_{\\mathrm{ek}}\\). To provide distance labels for [55], we followed their convention and employed Faiss to compute the L2 distance of each pose as an approximate ground truth distance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "After 10,000 iterations of optimization, the results are presented in Table 4. As shown in the table, our modeling approach outperforms the NDF. By learning a region (rather than a submanifold) and implicitly learning through" + }, + { + "type": "table_caption", + "bbox": [ + 0.569, + 0.09, + 0.852, + 0.103 + ], + "angle": 0, + "content": "Table 4. Comparison between SDF and NDF." + }, + { + "type": "table", + "bbox": [ + 0.59, + 0.116, + 0.828, + 0.174 + ], + "angle": 0, + "content": "
AccuracyEikonal Loss ↓
SDF97.70%0.0850
NDF54.33%0.1916
" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.191, + 0.775, + 0.206 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{\\mathrm{ek}}\\) , our method achieves better results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.215, + 0.872, + 0.232 + ], + "angle": 0, + "content": "4.3. Collision Resolution by Pose Optimization" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.251, + 0.866, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.407, + 0.906, + 0.477 + ], + "angle": 0, + "content": "Figure 4. An illustration of how collision resolution optimizes a collided robot towards a collision-free state. The figure shown visualizes the SDF, where red points (representing collisions) are optimized to green points (representing non-collisions) along the gradient update trajectories." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.906, + 0.599 + ], + "angle": 0, + "content": "Given a collision pose, our neural network can optimize the collision pose to the nearest non-colliding pose, as shown in Figure 4. After training the network, we sample 1,000 collision poses and use our \\( g \\) to predict their SDF values. We then apply gradient optimization, fixing the trained model's weights, and minimize the predicted SDF until it falls below a threshold value \\( l_{\\mathrm{thres}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.906, + 0.688 + ], + "angle": 0, + "content": "Specifically, we use the Adam optimizer [26] with a learning rate of 0.01, keeping all other parameters unchanged. The results are presented in Table 5. As the SDF values decrease, both the likelihood and severity of collisions reduce, demonstrating that our method effectively predicts and avoids collisions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.84 + ], + "angle": 0, + "content": "To assess the robustness of our model, we perform optimization with varying learning rates, anticipating consistent performance across these rates. To examine the effect of the learning rate, we replicate the experimental setup as described previously, setting \\( l_{\\mathrm{thres}} = -0.1 \\). We then compare the number of collision points and analyze the overall trends. The results demonstrate that the model performs comparably across different learning rates, further validating the robustness of our approach. A summary of these results is presented in Table 6." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.849, + 0.757, + 0.865 + ], + "angle": 0, + "content": "4.4. Integration with Dr. Robot" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Differentiable robot rendering (Dr. Robot) enables us to obtain a differentiable pose from the rendered view. From" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22567" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.486, + 0.148 + ], + "angle": 0, + "content": "Table 5. Effect of different threshold \\( (l_{\\mathrm{thres}}) \\). \\( \\overline{\\mathrm{Iter}} \\) represents the average number of iterations, while \\( \\Delta \\theta \\) denotes the change in angle. The last two columns display the collision points in the scenario prior to optimization and after optimization, respectively." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.157, + 0.477, + 0.312 + ], + "angle": 0, + "content": "
l_thresIter.↓Time (s) ↓Δθ↓BeforeAfter ↓
-0.00019.0170.1550.1625.5570.399
-0.00119.3920.1560.1655.6330.375
-0.00518.8740.1530.1595.5080.312
-0.01020.1240.1540.1735.6170.187
-0.02020.0900.1620.1735.4710.080
-0.03020.2360.1600.1725.3430.019
-0.04021.2560.1710.1815.6260.016
-0.05022.6270.1740.1905.7570.006
-0.10024.4500.1920.2035.1970.001
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.318, + 0.485, + 0.348 + ], + "angle": 0, + "content": "Table 6. Impact of different learning rate. The content of the last two columns is identical to that of Table 5." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.357, + 0.475, + 0.501 + ], + "angle": 0, + "content": "
LRIter.↓Time(s)↓Δθ↓BeforeAfter↓
0.001241.3631.8410.2035.4600.003
0.01024.4500.1920.2035.1970.001
0.02012.8260.1040.2155.4950.000
0.0505.6340.0490.2365.6220.000
0.1003.0260.0280.2565.5690.000
0.2001.7850.0180.3155.6350.001
0.5001.1270.0130.5275.3260.000
1.0001.1040.0131.0405.5530.000
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.516, + 0.485, + 0.579 + ], + "angle": 0, + "content": "this pose, our method can infer prior knowledge about potential collisions with the external environment or self-intersections. This prior knowledge can be seamlessly integrated into the differentiable rendering process." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.584, + 0.394, + 0.599 + ], + "angle": 0, + "content": "4.4.1. Inverse Action from Collision Image" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.602, + 0.484, + 0.708 + ], + "angle": 0, + "content": "We leverage Dr. Robot to optimize the robot's pose from images. However, we observe that the optimized poses are not always reasonable; in some cases, they result in collisions, limiting the practical application of Dr. Robot in real-world scenarios. To address this, we combine our SDF \\( g \\) with Dr. Robot, enabling us to optimize reasonable poses that minimize collisions while maintaining image consistency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.708, + 0.484, + 0.859 + ], + "angle": 0, + "content": "Striving for an efficient evaluation, we introduce immovable rigid blocks next to the robot. This way, if the robot's pose is unreasonable, it will collide with these blocks or self-collision. In each scene, we set up four cameras from different viewpoints and capture rendered images, instance segmentations, and depth maps from the simulation engine. This setting closely aligns with the real-world scenarios using monocular depth estimation models, such as Depth Pro[3]. To optimize the robot's pose, we use the following loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.865, + 0.484, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R G B}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {r} - \\boldsymbol {r} _ {\\mathrm {g t}} \\| \\tag {9}\n\\]" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.145 + ], + "angle": 0, + "content": "Table 7. The number of collision points (averaged) and collision rate of the pose inverse from images. We control the collision point from simulator and generate images for Dr. Robot optimization." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.15, + 0.9, + 0.25 + ], + "angle": 0, + "content": "
Original collision point in dataCollision Point ↓Collision Rate ↓
Dr. RobotOursDr. RobotOurs
10.969.170.8378%9%
2.002.330.0486%2%
1.001.180.0278%2%
0.000.050.002%0%
" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.263, + 0.907, + 0.302 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {D}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {d} - \\boldsymbol {d} _ {\\mathrm {g t}} \\| \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.307, + 0.907, + 0.43 + ], + "angle": 0, + "content": "Where \\(\\operatorname{seg}[i,j]\\) is the robot's mask, with 0 indicating the robot is not present at that position in the image and 1 indicating it is present. Here, \\(\\boldsymbol{r}\\) represents the rendered image from Dr. Robot, and \\(r_{\\mathrm{gt}}\\) represents the rendered image from the simulation engine; \\(\\boldsymbol{d}\\) represents the rendered depth from Dr. Robot, and \\(d_{\\mathrm{gt}}\\) represents the rendered depth from the simulation engine. The baseline loss function is the sum of the image and depth losses:" + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.44, + 0.907, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.906, + 0.542 + ], + "angle": 0, + "content": "To address collisions, we use our trained SDF model. The data burden is manageable as we can obtain sufficient data from the simulation engine for training. During the optimization process, we introduce an additional term to the loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.553, + 0.907, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {S D F}} = \\operatorname {R e L U} (g (\\boldsymbol {\\theta}) - l _ {\\text {t h r e s}}) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.58, + 0.706, + 0.594 + ], + "angle": 0, + "content": "Thus, our loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.607, + 0.907, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S D F}} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.634, + 0.906, + 0.725 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a weight scalar. The optimization stops when \\(g(\\pmb{\\theta}) \\leq l_{\\mathrm{thres}}\\), with \\(l_{\\mathrm{thres}} = -0.1\\). We sampled 100 instances for testing, and the results are shown in Table 7. The quantitative results demonstrate that, after optimization, Dr. Robot effectively avoids collisions and achieves the closest possible pose without collision." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.732, + 0.825, + 0.747 + ], + "angle": 0, + "content": "4.4.2. Inverse Trajectory from Optimization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.825 + ], + "angle": 0, + "content": "Furthermore, we aim to explore the feasibility of using Dr. Robot for trajectory generation. Given the starting posture \\(\\theta_{\\mathrm{start}}\\) and the end posture \\(\\theta_{\\mathrm{end}}\\), we employ gradient optimization with Dr. Robot to generate the intermediate trajectory for robot control." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.903 + ], + "angle": 0, + "content": "As mentioned in Section 4.4.1, we randomly sample two collision-free poses and obtain their respective rendering results. Dr. Robot uses \\(\\theta_{\\mathrm{start}}\\) as the initial configuration and utilizes the image, mask, depth, and pose information of \\(\\theta_{\\mathrm{end}}\\) from the simulator as supervisory signals. In addition," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22568" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.089, + 0.454, + 0.105 + ], + "angle": 0, + "content": "Table 8. Optimize Trajectory by Dr. Robot and SDF." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.115, + 0.454, + 0.216 + ], + "angle": 0, + "content": "
Collision Point ↓Collision Rate ↓
Dr. Robot4.0710.64%
Ours (-0.00)3.5010.00%
Ours (-0.01)0.000.00%
Ours (-0.05)0.000.00%
Ours (-0.10)0.000.00%
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.233, + 0.483, + 0.262 + ], + "angle": 0, + "content": "we incorporate our SDF model and add \\(\\mathcal{L}_{\\mathrm{SDF}}\\) (Equation 12) to the loss function." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.264, + 0.484, + 0.325 + ], + "angle": 0, + "content": "However, during the optimization process, the value of the SDF fluctuates around \\( l_{\\mathrm{thres}} \\), which causes some data points to violate the SDF constraints. To address this, we perform post-processing on the intermediate trajectory:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.335, + 0.483, + 0.378 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {S D F}} (\\hat {\\boldsymbol {\\theta}} _ {i}) + \\frac {1}{N - 1} \\sum_ {i = 1} ^ {N - 1} \\| \\hat {\\boldsymbol {\\theta}} _ {i + 1} - \\hat {\\boldsymbol {\\theta}} _ {i} \\| \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.389, + 0.484, + 0.466 + ], + "angle": 0, + "content": "where \\(\\hat{\\theta}_i, i = 1\\ldots N\\) is the middle trajectory generate from optimization. Here, we combine the SDF loss and the total variation loss. The results, as shown in Table 8, demonstrate that our approach effectively generates intermediate trajectories suitable for robot control." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.473, + 0.32, + 0.487 + ], + "angle": 0, + "content": "4.4.3. Inverse Action from VLM" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.483, + 0.627 + ], + "angle": 0, + "content": "We have observed that directly extracting data from the Vision-Language Model (VLM) using Dr. Robot can lead to unconstrained optimization, potentially resulting in implausible poses. Conversely, employing a simulator to refine these poses is problematic due to the absence of gradient information, which hinders seamless integration with Dr. Robot. Our novel approach successfully circumvents the optimization of collision-prone poses, thereby maintaining the plausibility of the outcomes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.839 + ], + "angle": 0, + "content": "In alignment with Dr. Robot's methodology, we utilized CLIP to extract action data from the VLM. Our experiments use shadow hand and leveraged the openai/clip-vit-base-patch32 model from HuggingFace. We aimed to maximize the dot product between the language and image embeddings generated by their respective processing towers. We computed the optimized collision points and associated collision probabilities. To substantiate that our method does not compromise the efficacy of action distillation from the VLM, we conducted a comparative analysis of the optimized dot products. The findings, presented in Table 9, demonstrate that our technique effectively precludes the optimization of implausible poses without impeding the extraction of actions from the VLM." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.318, + 0.866 + ], + "angle": 0, + "content": "4.5. Sim-to-Real Deployment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To validate the performance of our method, we conducted several sim-to-real experiments. In an illustrative scenario," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.146 + ], + "angle": 0, + "content": "Table 9. The metrics of collision and optimization while optimizing robotic pose by CLIP. We indicate the collision point(Point) and collision rate(Rate) for average, and report the mean and std of dot product metrics." + }, + { + "type": "table", + "bbox": [ + 0.545, + 0.157, + 0.872, + 0.257 + ], + "angle": 0, + "content": "
Point ↓Rate ↓meanstd ↓
Dr. Robot1.3042.50%33.861.53
Ours (-0.00)0.4030.00%34.421.58
Ours (-0.01)0.8040.00%34.131.20
Ours (-0.05)0.3020.00%34.221.60
Ours (-0.10)0.1010.00%34.021.23
" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.263, + 0.907, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.453, + 0.907, + 0.593 + ], + "angle": 0, + "content": "Figure 5. Sim2Real Experiment: Obstacle Avoidance with Prof. Robot. The first row illustrates that, in the simulator, the robot arm collides with the red box due to its inability to perceive obstacles. The second row shows that after integrating Prof. Robot, the robot successfully avoids the red obstacle. The red box represents an obstacle, and without Prof. Robot, the robot fails to circumvent it. The final row demonstrates that, with Prof. Robot, the robot smoothly navigates around the obstacle, confirming the effectiveness of our method for real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.603, + 0.907, + 0.725 + ], + "angle": 0, + "content": "a robot navigates around obstacles – including a wall and a box – while moving from an initial pose to a target pose. We interpolate 100 poses between the initial and target positions using SO(2) interpolation and optimize the trajectory with our Prof. Robot algorithm. The results, shown in Figure 5, demonstrate that our approach effectively guides the robot arm around obstacles while preventing collisions in simulation and reality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.737, + 0.787, + 0.753 + ], + "angle": 0, + "content": "5. Limitations and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Our method tackles the problem of cross-environment generalization. To address this, a new mechanism could be proposed that enhances Prof. Robot's scene perception by modeling dynamic objects. The dynamic environment could be represented by supplementary joints \\(\\delta\\), which constrain the robotic system's joint space. By training with a collision-aware discriminator \\(p(\\cdot|\\delta)\\), our joint learning framework could practical effectiveness despite environmental perturbations from ideal conditions. 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Advances in Neural Information Processing Systems, 34:21910-21922, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22572" + } + ] +] \ No newline at end of file diff --git a/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/f5b2ba36-3dfc-406e-a34c-8757ef9ca5cd_origin.pdf b/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/f5b2ba36-3dfc-406e-a34c-8757ef9ca5cd_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8c298a0a7c7e06ee7228c9bdebce9b05e7137e41 --- /dev/null +++ b/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/f5b2ba36-3dfc-406e-a34c-8757ef9ca5cd_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:608c4485a01b105ea2c33353b54b9f8eba83ae648e77f8239e0770087f10136e +size 8679080 diff --git a/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/full.md b/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7bd99085a737a3a9290c31910e6a4f3d73143a44 --- /dev/null +++ b/2025/Prof. Robot_ Differentiable Robot Rendering Without Static and Self-Collisions/full.md @@ -0,0 +1,419 @@ +# Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisions + +Quanyuan Ruan $^{1\dagger}$ + +Jiabao Lei $^{2\dagger}$ + +Wenhao Yuan + +Yanglin Zhang + +Dekun Lu + +Guiliang Liu $^{2*}$ + +Kui Jia* + +$^{1}$ South China University of Technology + +$^{2}$ School of Data Science, The Chinese University of Hong Kong, Shenzhen + +![](images/b8c9384acbd61b1839e5df24c8fcc3f1880b200e64e9cb7849e6f9b0fdbda67c.jpg) +DR. ROBOT + +![](images/22dbfa581d84d95479313a6149f61ff888917a7a8acacef85daec2daf585ee3e.jpg) +STATIC COLLISION +PROF. ROBOT (OURS) + +![](images/f9636415819062b10688396cfcf53c78c3ecae972a13824c2492d20cfcaf6d0b.jpg) +SELF COLLISION +DR. ROBOT +Figure 1. Our method improves upon Dr.Robot [32] by additionally enabling differentiable avoidance of static and self-collisions. By learning and integrating a gradient-consistent pose classifier into a differentiable rendering pipeline, the generated pose trajectories are free from physical collisions. The objective is to penalize high collision probabilities during optimization. On the left, our method can push robotic arms away from intersecting objects. On the right, it can also avoid self-collisions. Images are rendered using Blender with meshes. + +![](images/009d0bfb7c4e8d93bb4932b7eadaccec09ae2dba1896fcfce43e167335e24350.jpg) +PROF. ROBOT (OURS) + +# Abstract + +Differentiable rendering has gained significant attention in the field of robotics, with differentiable robot rendering emerging as an effective paradigm for learning robotic actions from image-space supervision. However, the lack of physical world perception in this approach may lead to potential collisions during action optimization. In this work, we introduce a novel improvement on previous efforts by incorporating physical awareness of collisions through the learning of a neural robotic collision classifier. This enables the optimization of actions that avoid collisions with static, non-interactable environments as well as the robot itself. To facilitate effective gradient optimization with the classifier, we identify the underlying issue and propose leveraging Eikonal regularization to ensure consistent gradients for optimization. Our solution can be seamlessly integrated into existing differentiable robot rendering frameworks, utilizing gradients for optimization and providing a foundation for future applications of differentiable rendering in robotics with improved reliability of interactions with the + +physical world. Both qualitative and quantitative experiments demonstrate the necessity and effectiveness of our method compared to previous solutions. + +# 1. Introduction + +Conventional methods for representing a robot involve partitioning it into many rigid body parts and then articulating them according to structural kinematic constraints. However, they only model the robots geometrically and do not possess a realistic appearance for rendering; therefore, they are less applicable for integration into a differentiable pipeline involving images, which is currently a popular approach in computer vision. A recent approach [32] has been proposed to model robots' appearance in a differentiable manner, facilitating the integration of robots into a differentiable rendering solution. It allows for backpropagating the appearance supervision from images to the control space, thereby enabling the learning of plausible robot movements. Their method is straightforward. They leverage Gaussian splatting [24] for efficient differentiable rendering, where each Gaussian point is associated with the robotic arms using implicit LBS [32, 34], and the arms are generated by the control parameters through forward kinematics. + +While promising, their method clearly lacks awareness of how to avoid physical collisions with a static environment that does not dynamically interact with the robot, as well as collisions with the robot itself. When optimized using gradient information, it is likely to produce invalid robotic parameters that lead to intersections. This problem is particularly severe in real scenarios, where minor collisions damage the robot's mechanical structure. Due to the typically high cost of robots, which can result in significant financial losses. To address this issue and ensure that the differentiable rendering pipeline produces valid robotic parameters that prevent collisions, we need to guide the robot to evade collision scenarios during gradient-guided optimization. Intuitively, we employ a similar approach to that in [55] to achieve collision-free optimization, with some critical adaptations and improvements. + +Our idea is simple. We observe that some robotic poses are free from collisions, while others are not. Therefore, we can classify these poses based on whether they lead to a collision. We can leverage a discriminative model to classify these poses. The classifier $f$ is a mapping $\mathrm{SO}(2)^K \to [0,1]$ that maps a pose $\pmb{\theta} \in \mathrm{SO}(2)^K$ to a decision $c \in [0,1]$ , where a value of $c > 0.5$ indicates a collision. A rotation occurs in $\mathrm{SO}(2)$ because the motor of a robotic joint typically possesses only one degree of freedom for rotation. Finally, we need to integrate the model into a differentiable pipeline. During optimization, to ensure that the robotic pose remains in the collision-free zone, we must push the pose $\pmb{\theta}$ toward the collision-free regions $\{\pmb{\theta} \in \mathrm{SO}(2)^K \mid f(\pmb{\theta}) \leq 0.5\}$ that correspond to a classification result of $c \leq 0.5$ . Compared to [55], we should note that the biggest benefit of using classification rather than fitting a distance field is that classification does not require computing manifold distances and only needs to provide classification labels, corresponding to either "collided" or "not collided." Computing labels is expensive and may lack accuracy, as the normally generated samples are often too sparse to accurately compute the manifold distances in such a high-dimensional space due to the curse of dimensionality. + +Unfortunately, the direct application of the above idea does not yield the desired results due to the variability of the gradients obtained after sheer classification learning. The update direction of the gradients may not be consistent, and a later update may offset the previous one. We will mathematically analyze the reasons for this phenomenon in Section 3.2. To address this issue, we introduce a regularization term to enforce the consistency of gradients by imposing that the gradient's norm be one, as expressed by $\mathcal{L}_{\mathrm{ek}} = (\|\nabla_{\theta}g(\pmb{\theta})\| - 1)^2$ . We immediately notice that this is a requirement for being a Signed Distance Field (SDF). To integrate the regularization term into the optimization, we take the function $g$ as the value before the Sigmoid function $\sigma$ , as given by $f = (\sigma \circ \omega \circ g)(\pmb{\theta})$ . The function $g$ is im + +pleted as a multi-layer perceptron (MLP), $\omega$ is a scalar multiplication function, and $\sigma$ is the sigmoid function. We notice that although we leverage the SDF, it does not require fitting any manifold distance; the SDF property is ensured by the regularization term. Interestingly, the method of imposing the Eikonal constraint is similar to the work of [16, 63]; instead of regularizing in three-dimensional space, we regularize the field $g$ in a high-dimensional pose space. + +Lastly, we verify in our extensive ablation studies and comparative experiments that our method of learning a high-dimensional pose classifier $f$ can avoid physical collisions with the static environment and the robot itself, making the robotic pose produced by a differentiable pipeline physically reliable. + +We summarize our technical contributions as follows: + +1. We address the issue of efficient differentiable robot rendering with potential collisions involving a static, non-interactive environment and self-collisions. This is achieved by learning a multi-layer perceptron (MLP), denoted as $f$ , to classify the control pose $\theta$ and determine whether it corresponds to a collision. Classification eliminates the need for accurate manifold distance. +2. To address the issue of poor reliability of gradients from the classifier and to integrate $f$ into a gradient-based optimization pipeline, we introduce the Eikonal regularization term $\mathcal{L}_{\mathrm{ek}}$ to enforce consistency among gradients, effectively transforming the value before the Sigmoid, $g$ , into a signed distance function (SDF). This regularization enhances the reliability of the gradients and leverages the beneficial properties of the SDF without the need for explicit computation of manifold distance. +3. To model the dependency of adjacent robotic joints efficiently, we introduce hierarchical joint encoding that conditions a joint angle on an ancestor's rotation, thereby better capturing the hierarchical dependency of robotic arms. + +# 2. Related Works + +# 2.1. Differentiable Rendering and Simulation + +Differentiable rendering and simulation play a pivotal role in computer vision and graphics. In differentiable rendering, gradients are propagated from primitives to image, while differentiable simulators compute gradients of physical processes similarly, which facilitates seamless integration with gradient-based optimization techniques. The integration of neural fields into robotics has attracted considerable attention. Researchers have employed diverse representations to bridge the digital and physical realms [20, 23, 24, 33, 38, 40, 44, 47, 67, 70]. Innovative approaches, such as Gaussian splatting for the precise reconstruction of robots and their environments, exemplify this trend [35, 50]. Moreover, techniques such as neural radi + +ance fields for teleoperation [45] and future scene prediction [36] have significantly advanced robotic manipulation capabilities. Feature distillation has further empowered robots to perform complex tasks by translating language embeddings into corresponding 3D actions [49, 51, 52, 71, 73]. Additional advancements include comprehensive physical world modeling, future state prediction [1], and learning continuous manifolds of valid grasps using signed distance functions (SDF) [25, 64]. Significant progress has also been made in perceptual scene understanding and grasp planning [4-6]. One of the primary challenges in developing these simulators is accurately modeling contact interactions—a difficulty that arises from the inherently binary, discontinuous nature of contacts, where objects are either in contact or not [42]. According to [42], contact models can be broadly categorized into four classes: complementarity problems, compliant models, position-based models, and material point method (MPM) frameworks. Complementarity problems emphasize maintaining strict zero-penetration contact between objects [7-9, 12, 13, 19, 21, 28, 29, 46, 48, 60-62, 65, 74]. Compliant models relax the complementarity problem's constraint by replacing the sharp, step-like contact functions with smooth approximations that have large but finite gradients[9, 13, 15, 18, 19, 27, 41, 54, 57, 58]. The position-based method directly constrains object positions to prevent penetration [11, 37]. Meanwhile, the MPM handles contact interactions between both rigid- and soft-body objects[22, 53]. Despite these impressive advances, the effectiveness of differentiable systems for robotic manipulation remains under active validation, marking a promising yet nascent stage of development. + +# 2.2. Signed Distance Fields in Robotics + +In the realm of robotics and computer graphics, the construction of SDF has been an important technique for various applications, particularly in motion planning and collision avoidance. Some researchers pioneered a method to construct SDF on grid maps [10]. Afterwards, some others introduced incremental SDF construction techniques [17, 43], significantly enhancing the adaptability of SDF in dynamic environments. A novel implicit SDF method is proposed to leverage swept volumes for construction [72]. This method allows for efficient evaluation of the SDF at specific obstacle points with known coordinates, simplifying the process and reducing computational overhead. Another work [69] made a significant stride with the introduction of RobotSDF, an implicit morphology modeling technique. Furthermore, the application of SDF in obstacle avoidance has been extensively explored by [30, 59, 66]. + +# 3. Method + +In this section, we will detail our method for achieving collision avoidance in robotic operations in combination + +with Gaussian splattering-based differentiable robotic rendering [32]. The types of collisions we consider in this paper include static collisions, which occur when the robot collides with a static and non-interactive environment, as well as self-collisions, which involve collisions with the robot itself. Section 3.1 will model the problem of collision detection as a robotic pose classification problem. In Section 3.2, we will address some challenges that arose in formulating collision detection and propose the introduction of a signed distance field (SDF) as an underlying field for the classifier to tackle the gradient inconsistency problem during optimization. Section 3.3 will explain how we hierarchically encode the robotic pose while respecting the robotic kinematic dependencies. Finally, we will present our loss functions and training schemes in Section 3.4. + +# 3.1. Collision Detection by Pose Classification + +To make the model aware of physical collisions during optimization, we need a collision detector to determine whether the robotic pose has caused intersections with other environmental objects or with the robot itself. The collision detector is essentially a function $f: \theta \mapsto c$ with $c \in [0,1]$ that classifies each pose $\theta$ into two categories: either collided ( $c > 0.5$ ) or not ( $c \leq 0.5$ ). + +The robots we consider in this paper have $K$ joints, and each joint has exactly one degree of freedom for rotation; thus, the pose parameter is within the space $\theta \in \mathrm{SO}(2)^K$ . The classifier network $f$ will partition the space into many regions, and ideally, the regions corresponding to valid poses (non-collided poses) will form a manifold as given by + +$$ +\mathcal {V} = \left\{\boldsymbol {\theta} \in \operatorname {S O} (2) ^ {K} \mid f (\boldsymbol {\theta}) \leq 0. 5 \right\}. \tag {1} +$$ + +To ensure that the output value falls within the range [0, 1], we follow convention and apply a Sigmoid function $\sigma$ to the last output, meaning that the function $f$ is effectively defined by $f = \sigma \circ g$ , where $g$ is another scalar-valued function that we will detail later in Section 3.2. + +To effectively learn the classifier $f$ , we follow tradition and use binary cross-entropy loss to supervise $f$ , as expressed by + +$$ +\mathcal {L} _ {\mathrm {B C E}} = \operatorname {B C E} (f (\boldsymbol {\theta}), c ^ {\mathrm {g t}}), \tag {2} +$$ + +where $c^{\mathrm{gt}} \in \{0,1\}$ is the ground truth label indicating whether it is valid ( $c^{\mathrm{gt}} = 1$ ) or not ( $c^{\mathrm{gt}} = 0$ ). + +# 3.2. Eikonal Regularizer for Consistent Gradients + +However, directly applying $f$ to gradient optimization is problematic. The function is nearly binary, and the gradients near the values of 0 and 1 are almost zero, leading to noisy and unreliable supervision signals. + +We visualize a possible function $f$ with a two-dimensional input space in Figure 3. We notice that, since + +![](images/ab7c31edc7a2d990abb1f45d5ccac67340e44698344a502c532166b000346e19.jpg) +Figure 2. Our Pipeline. We predict whether a collision has occurred based on pose input, using Eikonal loss $(\mathcal{L}_{\mathrm{ek}})$ and binary cross-entropy loss $(\mathcal{L}_{\mathrm{BCE}})$ to ensure this. It can then be seamlessly integrated with Dr. Robot [32] to create a fully differentiable pipeline for optimization. + +![](images/cea4236373b47a470d2754153e5bc0b6ba3e10ac1bfba32aa6dbef8a5e46e993.jpg) +Figure 3. An illustration of the potential fluctuation of the classification loss landscape. + +the values at both far sides fluctuate, the gradients also fluctuate, leading to inconsistent gradients. When we aim to optimize a pose from the exterior (collided region) toward the interior (collision-free region), this may not be the case because the gradient directions are inconsistent (see the two red points) due to fluctuations in the loss landscape. Small fluctuations do not significantly influence the loss value, but they can lead to noisy and inconsistent gradients, which are harmful to optimization. + +To address the issue, we need to consider the function $g$ before the Sigmoid function $\sigma$ , as $\sigma$ will restrict the gradient and render it too small for updating poses. Specifically, for two consecutive gradient updates with poses $\pmb{\theta}_t$ and $\pmb{\theta}_{t + 1}$ , the update at $t + 1$ is likely to offset the previous update at $t$ , as expressed by + +$$ +\left\langle \frac {\partial g}{\partial \boldsymbol {\theta} _ {t}}, \frac {\partial g}{\partial \boldsymbol {\theta} _ {t + 1}} \right\rangle \leq 0, \tag {3} +$$ + +especially in regions with high confidence levels close to 0 or 1. This is visualized in Figure 3, where two red dots are plotted; their gradient directions may not be consistent (or correlated) as they point in opposite directions. + +We also note that gradient updates are typically small. Assuming the updates $\theta_{t + 1}$ and $\theta_t$ are close enough and correlated, we have + +$$ +\left\langle \frac {\partial g}{\partial \boldsymbol {\theta} _ {t}}, \frac {\partial g}{\partial \boldsymbol {\theta} _ {t + 1}} \right\rangle \approx \left\langle \frac {\partial g}{\partial \boldsymbol {\theta} _ {t}}, \frac {\partial g}{\partial \boldsymbol {\theta} _ {t}} \right\rangle = \left\| \frac {\partial g}{\partial \boldsymbol {\theta} _ {t}} \right\| ^ {2} \geq 0. \tag {4} +$$ + +This analysis indicates that to enforce gradient consistency, we only need to manipulate the norm of the gradients. To make the correlation of the gradients as uniform as possible (which is desirable for gradient updates), we enforce the above term to be a positive constant $a > 0$ . This motivates us to adopt the following regularization term + +$$ +\mathcal {L} _ {\mathrm {e k}} = \left(\left\| \frac {\partial g}{\partial \boldsymbol {\theta}} \right\| - a\right) ^ {2} \tag {5} +$$ + +to ensure gradient consistency between the two adjacent updates. We immediately notice that when $a = 1$ , it becomes an Eikonal regularizer that is widely employed by the signed distance function [16, 44]. Interestingly, this term can be viewed as generalizing the implicit geometric regularization [16] to high-dimensional pose space by learning a function $g$ . To simplify implementation, we use $a = 1$ throughout the paper. + +The function $g$ is practically implemented as a multilayer perceptron that receives robotic poses $\pmb{\theta}$ as input and produces a scalar; the final classifier is therefore + +$$ +f (\boldsymbol {\theta}) = (\sigma \circ \omega \circ g) (\boldsymbol {\theta}), \tag {6} +$$ + +where $\omega : x \mapsto sx$ denotes a function that multiplies the input $x$ by an estimable positive constant $s$ , which will be further discussed in Section 4.2.3. Our current pipeline is illustrated in Figure 2. + +# 3.3. Hierarchical Robotic Pose Encoding + +We represent the robotic pose using rotation angles, each describing the relative rotation between two arms. The pose parameters are defined in local coordinate frames, such that continuous modifications of a single joint result in realistic motion. However, since angles only describe relative rotations, they may not respect the kinematic structure and cannot effectively handle the structural dependency relationships between the arms. We observe that each individual joint needs to be conditioned on the parent rotations and thus must be influenced by them. To incorporate this notion of kinematic dependency into the function $g$ , we implement the function as a hierarchical network that encodes the dependency within the network structure [2, 14, 39, 55]. + +This is similar to the method described in [55]. Specifically, for a given robotic pose $\pmb{\theta} = [\theta_{1};\dots;\theta_{K}]$ , where $\theta_{k}$ (with $k\in \{1,\ldots ,K\}$ ) is the rotation angle for joint $k$ , and a function $\tau (k)$ maps the index of each joint to its parent joint + +index, we encode each pose using a multi-layer perceptron (MLP) as follows: + +$$ +g _ {1}: \theta_ {1} \mapsto \boldsymbol {\nu} _ {1} \tag {7} +$$ + +$$ +g _ {k}: \left(\theta_ {k}, \boldsymbol {\nu} _ {\tau (k)}\right) \mapsto \boldsymbol {\nu} _ {k}, \quad k \in \{2, \dots , K \} +$$ + +This process takes the joint angle and the encoded feature $\pmb{\nu}_{\tau (k)}\in \mathbb{R}^{\ell}$ of its parent joint as input and produces an output feature $\pmb{\nu}_k\in \mathbb{R}^\ell$ , where $\ell = 8$ is the feature dimension. We then concatenate the encoded features of every joint to obtain a combined pose embedding $\pmb {\nu} = [\pmb {\nu}_1;\dots ;\pmb {\nu}_K]$ This embedding is further transformed by a linear mapping $\mathbb{R}^{\ell ,K}\to \mathbb{R}$ to yield a scalar value that serves as the output of the function $g$ + +# 3.4. Training Data and Objectives + +The training dataset comprises $N$ poses and their corresponding decisions, represented by $\mathcal{D} = \{(\pmb{\theta}_i, c_i^{\mathrm{gt}})\}_{i=1}^N$ . It is constructed as follows: the robotic pose $\pmb{\theta}_i$ is randomly sampled, and a (non-differentiable) collision detector is then applied to produce the decision $c_i^{\mathrm{gt}} \in \{0, 1\}$ , indicating whether a collision has occurred ( $c_i^{\mathrm{gt}} = 1$ ). + +The model is trained using batched samples; we omit the summation-over-samples notation here for simplicity. The objective is simply the weighted combination of $\mathcal{L}_{\mathrm{BCE}}$ and $\mathcal{L}_{\mathrm{ek}}$ . With $\alpha = 0.1$ , it is expressed as + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {B C E}} + \alpha \mathcal {L} _ {\mathrm {e k}}. \tag {8} +$$ + +Depending on how it is learned, we may additionally have, for example, $\mathcal{L}_{\mathrm{RGB}}$ for image-space supervision, which we omit here for simplicity. + +# 4. Experiments and Results + +We conduct ablation studies on Prof. Robot (section 4.2), experiments on collision resolution (section 4.3), integration with Dr. Robot (section 4.4), and sim-to-real deployment (section 4.5). Comparison with the differentiable simulator, training with alternative regularizers, and manipulation with Dr. Robot are detailed in the supplementary materials. + +# 4.1. Experimental Setup + +Data Preparation. We adopt a data-driven approach, leveraging the Mujoco [56] configurations provided by [32] with some modifications. Specifically, we selected six scenes and randomly sampled poses from the robot's joint limits, used Mujoco (which is non-differentiable) to check for collisions, and employed a resampling technique to balance the ratio of collision to non-collision data at approximately the same amount. + +Evaluation Metrics. We primarily evaluate the network's ability to distinguish between collision and non-collision + +Table 1. Ablation study on hierarchical and flattened encoding. + +
HierarchicalFlatten
Classification Accuracy97.70%97.51%
+ +states, as well as its performance in optimizing the gradients. The former metric (accuracy) assesses the network's ability to detect collisions, while the latter $(\mathcal{L}_{\mathrm{ek}})$ measures its capacity to avoid collisions through optimization. Furthermore, for a given robot pose denoted as $\theta$ , we are able to determine the collision points of the mesh within the simulator and subsequently calculate the collision rate for all possible poses. + +Experimental Details. We leverage the joint connection relationships defined in the URDF, where each joint is encoded using a tiny MLP. The encoded features from all joints are then concatenated and passed through an MLP with four hidden layers, each containing 512 units, followed by a final output layer with a single unit. LeakyReLU is used as the activation function for all layers. We introduce a learnable scale factor $s$ , which, after being multiplied by the MLP output, is passed through a Sigmoid function to produce a probability. We conduct experiments within a simulation environment, where the network's ability determines the success rate of collision resolution. Finally, we integrate our method into a differentiable robot rendering pipeline and perform control experiments. The experiments are conducted on a single NVIDIA RTX 4090 GPU. + +# 4.2. Learning Robotic Signed Distance Fields + +# 4.2.1. Ablation: Hierarchical Encoding + +To assess the impact of hierarchical encoding, we replaced it with a simple linear layer for encoding the input joint data while keeping the rest of the components unchanged. As shown in Table 1, after 10,000 iterations, the use of the hierarchical MLP results in higher accuracy. This shows that the hierarchical encoding strategy better captures the kinematic structure and increases performance. + +# 4.2.2. Ablation: Eikonal Regularizer + +To investigate the effect of the Eikonal regularizer, we trained an MLP under two conditions: one without the Eikonal regularizer and one with it, and compared both the classification accuracy and the numerical value of the Eikonal loss. We then tested whether the models could resolve collisions (as described in Section 4.3). The models were trained for 10,000 iterations. During pose optimization, for the model trained without the Eikonal regularizer, we stopped the iteration if the collision probability dropped below 0.5. For the model trained with the Eikonal regularizer, we halted the iteration if the SDF value, which is negative in non-collision regions, fell below the threshold $l_{\mathrm{thres}} = -0.1$ . + +Table 2. Ablation study on the Eikonal loss. + +
w. Eikonal lossw/o. Eikonal loss
Classification97.70%98.39%
Accuracy
Iteration Nums ↓119.991000
Iteration Time ↓0.97 s10.64 s
Move Angle ↓0.604.49
Collision Point ↓0.6711.52
Collision Rate ↓17%99%
Gradient Norm8.53 × 10-11.89 × 10-6
+ +Table 3. Ablation study on the scaling factor $s$ . + +
AccuracyEikonal Loss ↓
w. s97.70%0.0850
w/o. s85.37%0.2568
+ +The results were compared, as shown in Table 2. Without the Eikonal regularizer, the optimizer struggled to generate a collision-free pose from a collision state, with iterations exceeding 1,000, and the propagated gradients were too small to facilitate further optimization. + +# 4.2.3. Ablation: Scaling Factor + +The cross-entropy loss and Eikonal loss may require gradients of different magnitudes, potentially interfering with each other and hindering the model's ability to learn useful information. To address this, a scaling factor $s$ for the SDF is introduced to allow for large gradients in classification and limited gradients in the SDF. We removed the scaling factor $s$ (setting $s = 1$ ) and directly passed the SDF value to the Sigmoid function to produce $f$ . + +The numerical results, as shown in Table 3, demonstrate that the scaling factor effectively achieves good classification results while preserving the uniform gradient property. + +# 4.2.4. Comparison Between NDF and SDF + +In contrast to [55], which models collision-free poses as a high-dimensional submanifold using a Neural Distance Field (NDF), we represent collision-free poses as a set of discontinuous regions in high-dimensional space that can be modeled using an SDF. To explore the differences between these two approaches, we also conducted experiments with an NDF. Learning an NDF requires accurate manifold distances; unlike [55], our method does not require this because it can be implicitly learned through $\mathcal{L}_{\mathrm{ek}}$ . To provide distance labels for [55], we followed their convention and employed Faiss to compute the L2 distance of each pose as an approximate ground truth distance. + +After 10,000 iterations of optimization, the results are presented in Table 4. As shown in the table, our modeling approach outperforms the NDF. By learning a region (rather than a submanifold) and implicitly learning through + +Table 4. Comparison between SDF and NDF. + +
AccuracyEikonal Loss ↓
SDF97.70%0.0850
NDF54.33%0.1916
+ +$\mathcal{L}_{\mathrm{ek}}$ , our method achieves better results. + +# 4.3. Collision Resolution by Pose Optimization + +![](images/38ece8f977fde81d82a31c583a2f06f4c7488a0d6a5139b4af1d4d4a96cbd896.jpg) +Figure 4. An illustration of how collision resolution optimizes a collided robot towards a collision-free state. The figure shown visualizes the SDF, where red points (representing collisions) are optimized to green points (representing non-collisions) along the gradient update trajectories. + +Given a collision pose, our neural network can optimize the collision pose to the nearest non-colliding pose, as shown in Figure 4. After training the network, we sample 1,000 collision poses and use our $g$ to predict their SDF values. We then apply gradient optimization, fixing the trained model's weights, and minimize the predicted SDF until it falls below a threshold value $l_{\mathrm{thres}}$ . + +Specifically, we use the Adam optimizer [26] with a learning rate of 0.01, keeping all other parameters unchanged. The results are presented in Table 5. As the SDF values decrease, both the likelihood and severity of collisions reduce, demonstrating that our method effectively predicts and avoids collisions. + +To assess the robustness of our model, we perform optimization with varying learning rates, anticipating consistent performance across these rates. To examine the effect of the learning rate, we replicate the experimental setup as described previously, setting $l_{\mathrm{thres}} = -0.1$ . We then compare the number of collision points and analyze the overall trends. The results demonstrate that the model performs comparably across different learning rates, further validating the robustness of our approach. A summary of these results is presented in Table 6. + +# 4.4. Integration with Dr. Robot + +Differentiable robot rendering (Dr. Robot) enables us to obtain a differentiable pose from the rendered view. From + +Table 5. Effect of different threshold $(l_{\mathrm{thres}})$ . $\overline{\mathrm{Iter}}$ represents the average number of iterations, while $\Delta \theta$ denotes the change in angle. The last two columns display the collision points in the scenario prior to optimization and after optimization, respectively. + +
l_thresIter.↓Time (s) ↓Δθ↓BeforeAfter ↓
-0.00019.0170.1550.1625.5570.399
-0.00119.3920.1560.1655.6330.375
-0.00518.8740.1530.1595.5080.312
-0.01020.1240.1540.1735.6170.187
-0.02020.0900.1620.1735.4710.080
-0.03020.2360.1600.1725.3430.019
-0.04021.2560.1710.1815.6260.016
-0.05022.6270.1740.1905.7570.006
-0.10024.4500.1920.2035.1970.001
+ +Table 6. Impact of different learning rate. The content of the last two columns is identical to that of Table 5. + +
LRIter.↓Time(s)↓Δθ↓BeforeAfter↓
0.001241.3631.8410.2035.4600.003
0.01024.4500.1920.2035.1970.001
0.02012.8260.1040.2155.4950.000
0.0505.6340.0490.2365.6220.000
0.1003.0260.0280.2565.5690.000
0.2001.7850.0180.3155.6350.001
0.5001.1270.0130.5275.3260.000
1.0001.1040.0131.0405.5530.000
+ +this pose, our method can infer prior knowledge about potential collisions with the external environment or self-intersections. This prior knowledge can be seamlessly integrated into the differentiable rendering process. + +# 4.4.1. Inverse Action from Collision Image + +We leverage Dr. Robot to optimize the robot's pose from images. However, we observe that the optimized poses are not always reasonable; in some cases, they result in collisions, limiting the practical application of Dr. Robot in real-world scenarios. To address this, we combine our SDF $g$ with Dr. Robot, enabling us to optimize reasonable poses that minimize collisions while maintaining image consistency. + +Striving for an efficient evaluation, we introduce immovable rigid blocks next to the robot. This way, if the robot's pose is unreasonable, it will collide with these blocks or self-collision. In each scene, we set up four cameras from different viewpoints and capture rendered images, instance segmentations, and depth maps from the simulation engine. This setting closely aligns with the real-world scenarios using monocular depth estimation models, such as Depth Pro[3]. To optimize the robot's pose, we use the following loss functions: + +$$ +\mathcal {L} _ {\mathrm {R G B}} = \frac {1}{N} \sum_ {\operatorname {s e g} [ i, j ] = 1} \| \boldsymbol {r} - \boldsymbol {r} _ {\mathrm {g t}} \| \tag {9} +$$ + +Table 7. The number of collision points (averaged) and collision rate of the pose inverse from images. We control the collision point from simulator and generate images for Dr. Robot optimization. + +
Original collision point in dataCollision Point ↓Collision Rate ↓
Dr. RobotOursDr. RobotOurs
10.969.170.8378%9%
2.002.330.0486%2%
1.001.180.0278%2%
0.000.050.002%0%
+ +$$ +\mathcal {L} _ {\mathrm {D}} = \frac {1}{N} \sum_ {\operatorname {s e g} [ i, j ] = 1} \| \boldsymbol {d} - \boldsymbol {d} _ {\mathrm {g t}} \| \tag {10} +$$ + +Where $\operatorname{seg}[i,j]$ is the robot's mask, with 0 indicating the robot is not present at that position in the image and 1 indicating it is present. Here, $\boldsymbol{r}$ represents the rendered image from Dr. Robot, and $r_{\mathrm{gt}}$ represents the rendered image from the simulation engine; $\boldsymbol{d}$ represents the rendered depth from Dr. Robot, and $d_{\mathrm{gt}}$ represents the rendered depth from the simulation engine. The baseline loss function is the sum of the image and depth losses: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {R G B}} + \mathcal {L} _ {\mathrm {D}} \tag {11} +$$ + +To address collisions, we use our trained SDF model. The data burden is manageable as we can obtain sufficient data from the simulation engine for training. During the optimization process, we introduce an additional term to the loss function: + +$$ +\mathcal {L} _ {\mathrm {S D F}} = \operatorname {R e L U} (g (\boldsymbol {\theta}) - l _ {\text {t h r e s}}) \tag {12} +$$ + +Thus, our loss function is + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {R G B}} + \mathcal {L} _ {\mathrm {D}} + \beta \cdot \mathcal {L} _ {\mathrm {S D F}} \tag {13} +$$ + +where $\beta$ is a weight scalar. The optimization stops when $g(\pmb{\theta}) \leq l_{\mathrm{thres}}$ , with $l_{\mathrm{thres}} = -0.1$ . We sampled 100 instances for testing, and the results are shown in Table 7. The quantitative results demonstrate that, after optimization, Dr. Robot effectively avoids collisions and achieves the closest possible pose without collision. + +# 4.4.2. Inverse Trajectory from Optimization + +Furthermore, we aim to explore the feasibility of using Dr. Robot for trajectory generation. Given the starting posture $\theta_{\mathrm{start}}$ and the end posture $\theta_{\mathrm{end}}$ , we employ gradient optimization with Dr. Robot to generate the intermediate trajectory for robot control. + +As mentioned in Section 4.4.1, we randomly sample two collision-free poses and obtain their respective rendering results. Dr. Robot uses $\theta_{\mathrm{start}}$ as the initial configuration and utilizes the image, mask, depth, and pose information of $\theta_{\mathrm{end}}$ from the simulator as supervisory signals. In addition, + +Table 8. Optimize Trajectory by Dr. Robot and SDF. + +
Collision Point ↓Collision Rate ↓
Dr. Robot4.0710.64%
Ours (-0.00)3.5010.00%
Ours (-0.01)0.000.00%
Ours (-0.05)0.000.00%
Ours (-0.10)0.000.00%
+ +we incorporate our SDF model and add $\mathcal{L}_{\mathrm{SDF}}$ (Equation 12) to the loss function. + +However, during the optimization process, the value of the SDF fluctuates around $l_{\mathrm{thres}}$ , which causes some data points to violate the SDF constraints. To address this, we perform post-processing on the intermediate trajectory: + +$$ +\mathcal {L} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathcal {L} _ {\mathrm {S D F}} (\hat {\boldsymbol {\theta}} _ {i}) + \frac {1}{N - 1} \sum_ {i = 1} ^ {N - 1} \| \hat {\boldsymbol {\theta}} _ {i + 1} - \hat {\boldsymbol {\theta}} _ {i} \| \tag {14} +$$ + +where $\hat{\theta}_i, i = 1\ldots N$ is the middle trajectory generate from optimization. Here, we combine the SDF loss and the total variation loss. The results, as shown in Table 8, demonstrate that our approach effectively generates intermediate trajectories suitable for robot control. + +# 4.4.3. Inverse Action from VLM + +We have observed that directly extracting data from the Vision-Language Model (VLM) using Dr. Robot can lead to unconstrained optimization, potentially resulting in implausible poses. Conversely, employing a simulator to refine these poses is problematic due to the absence of gradient information, which hinders seamless integration with Dr. Robot. Our novel approach successfully circumvents the optimization of collision-prone poses, thereby maintaining the plausibility of the outcomes. + +In alignment with Dr. Robot's methodology, we utilized CLIP to extract action data from the VLM. Our experiments use shadow hand and leveraged the openai/clip-vit-base-patch32 model from HuggingFace. We aimed to maximize the dot product between the language and image embeddings generated by their respective processing towers. We computed the optimized collision points and associated collision probabilities. To substantiate that our method does not compromise the efficacy of action distillation from the VLM, we conducted a comparative analysis of the optimized dot products. The findings, presented in Table 9, demonstrate that our technique effectively precludes the optimization of implausible poses without impeding the extraction of actions from the VLM. + +# 4.5. Sim-to-Real Deployment + +To validate the performance of our method, we conducted several sim-to-real experiments. In an illustrative scenario, + +Table 9. The metrics of collision and optimization while optimizing robotic pose by CLIP. We indicate the collision point(Point) and collision rate(Rate) for average, and report the mean and std of dot product metrics. + +
Point ↓Rate ↓meanstd ↓
Dr. Robot1.3042.50%33.861.53
Ours (-0.00)0.4030.00%34.421.58
Ours (-0.01)0.8040.00%34.131.20
Ours (-0.05)0.3020.00%34.221.60
Ours (-0.10)0.1010.00%34.021.23
+ +![](images/e753e663bd5df8d664d4a1428366b6d328084fca485ff009dcfb0a17088da637.jpg) +Figure 5. Sim2Real Experiment: Obstacle Avoidance with Prof. Robot. The first row illustrates that, in the simulator, the robot arm collides with the red box due to its inability to perceive obstacles. The second row shows that after integrating Prof. Robot, the robot successfully avoids the red obstacle. The red box represents an obstacle, and without Prof. Robot, the robot fails to circumvent it. The final row demonstrates that, with Prof. Robot, the robot smoothly navigates around the obstacle, confirming the effectiveness of our method for real-world applications. + +a robot navigates around obstacles – including a wall and a box – while moving from an initial pose to a target pose. We interpolate 100 poses between the initial and target positions using SO(2) interpolation and optimize the trajectory with our Prof. Robot algorithm. 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Our solution can be seamlessly integrated into existing differentiable robot rendering frameworks, utilizing gradients for optimization and providing a foundation for future applications of differentiable rendering in robotics with improved reliability of interactions with the" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 420, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 555, + 456 + ], + "type": "text", + "content": "physical world. Both qualitative and quantitative experiments demonstrate the necessity and effectiveness of our method compared to previous solutions." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 478, + 394, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 478, + 394, + 490 + ], + "spans": [ + { + "bbox": [ + 314, + 478, + 394, + 490 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 312, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 498, + 555, + 713 + ], + "type": "text", + "content": "Conventional methods for representing a robot involve partitioning it into many rigid body parts and then articulating them according to structural kinematic constraints. However, they only model the robots geometrically and do not possess a realistic appearance for rendering; therefore, they are less applicable for integration into a differentiable pipeline involving images, which is currently a popular approach in computer vision. A recent approach [32] has been proposed to model robots' appearance in a differentiable manner, facilitating the integration of robots into a differentiable rendering solution. It allows for backpropagating the appearance supervision from images to the control space, thereby enabling the learning of plausible robot movements. Their method is straightforward. They leverage Gaussian splatting [24] for efficient differentiable rendering, where each Gaussian point is associated with the robotic arms using implicit LBS [32, 34], and the arms are generated by the control parameters through forward kinematics." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 683, + 140, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 683, + 140, + 693 + ], + "spans": [ + { + "bbox": [ + 69, + 683, + 140, + 693 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 69, + 683, + 140, + 693 + ], + "type": "text", + "content": " Equal contribution." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 69, + 693, + 153, + 704 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 693, + 153, + 704 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 153, + 704 + ], + "type": "text", + "content": "* Corresponding authors." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 75, + 704, + 272, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 704, + 272, + 712 + ], + "spans": [ + { + "bbox": [ + 75, + 704, + 272, + 712 + ], + "type": "text", + "content": "Project: https://qrcat.github.io/prof-robot/" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22562" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "content": "While promising, their method clearly lacks awareness of how to avoid physical collisions with a static environment that does not dynamically interact with the robot, as well as collisions with the robot itself. When optimized using gradient information, it is likely to produce invalid robotic parameters that lead to intersections. This problem is particularly severe in real scenarios, where minor collisions damage the robot's mechanical structure. Due to the typically high cost of robots, which can result in significant financial losses. To address this issue and ensure that the differentiable rendering pipeline produces valid robotic parameters that prevent collisions, we need to guide the robot to evade collision scenarios during gradient-guided optimization. Intuitively, we employ a similar approach to that in [55] to achieve collision-free optimization, with some critical adaptations and improvements." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "spans": [ + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": "Our idea is simple. We observe that some robotic poses are free from collisions, while others are not. Therefore, we can classify these poses based on whether they lead to a collision. We can leverage a discriminative model to classify these poses. The classifier " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " is a mapping " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)^K \\to [0,1]" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " that maps a pose " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} \\in \\mathrm{SO}(2)^K" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " to a decision " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "c \\in [0,1]" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": ", where a value of " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "c > 0.5" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " indicates a collision. A rotation occurs in " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " because the motor of a robotic joint typically possesses only one degree of freedom for rotation. Finally, we need to integrate the model into a differentiable pipeline. During optimization, to ensure that the robotic pose remains in the collision-free zone, we must push the pose " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " toward the collision-free regions " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "\\{\\pmb{\\theta} \\in \\mathrm{SO}(2)^K \\mid f(\\pmb{\\theta}) \\leq 0.5\\}" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": " that correspond to a classification result of " + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "inline_equation", + "content": "c \\leq 0.5" + }, + { + "bbox": [ + 56, + 267, + 296, + 543 + ], + "type": "text", + "content": ". Compared to [55], we should note that the biggest benefit of using classification rather than fitting a distance field is that classification does not require computing manifold distances and only needs to provide classification labels, corresponding to either \"collided\" or \"not collided.\" Computing labels is expensive and may lack accuracy, as the normally generated samples are often too sparse to accurately compute the manifold distances in such a high-dimensional space due to the curse of dimensionality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": "Unfortunately, the direct application of the above idea does not yield the desired results due to the variability of the gradients obtained after sheer classification learning. The update direction of the gradients may not be consistent, and a later update may offset the previous one. We will mathematically analyze the reasons for this phenomenon in Section 3.2. To address this issue, we introduce a regularization term to enforce the consistency of gradients by imposing that the gradient's norm be one, as expressed by " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ek}} = (\\|\\nabla_{\\theta}g(\\pmb{\\theta})\\| - 1)^2" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": ". We immediately notice that this is a requirement for being a Signed Distance Field (SDF). To integrate the regularization term into the optimization, we take the function " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": " as the value before the Sigmoid function " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": ", as given by " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "f = (\\sigma \\circ \\omega \\circ g)(\\pmb{\\theta})" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": ". The function " + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 546, + 295, + 714 + ], + "type": "text", + "content": " is im" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "pleted as a multi-layer perceptron (MLP), " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " is a scalar multiplication function, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " is the sigmoid function. We notice that although we leverage the SDF, it does not require fitting any manifold distance; the SDF property is ensured by the regularization term. Interestingly, the method of imposing the Eikonal constraint is similar to the work of [16, 63]; instead of regularizing in three-dimensional space, we regularize the field " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " in a high-dimensional pose space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 169, + 553, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 169, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 169, + 553, + 240 + ], + "type": "text", + "content": "Lastly, we verify in our extensive ablation studies and comparative experiments that our method of learning a high-dimensional pose classifier " + }, + { + "bbox": [ + 313, + 169, + 553, + 240 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 169, + 553, + 240 + ], + "type": "text", + "content": " can avoid physical collisions with the static environment and the robot itself, making the robotic pose produced by a differentiable pipeline physically reliable." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 325, + 241, + 543, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 241, + 543, + 252 + ], + "spans": [ + { + "bbox": [ + 325, + 241, + 543, + 252 + ], + "type": "text", + "content": "We summarize our technical contributions as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 256, + 553, + 506 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "spans": [ + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "text", + "content": "1. We address the issue of efficient differentiable robot rendering with potential collisions involving a static, non-interactive environment and self-collisions. This is achieved by learning a multi-layer perceptron (MLP), denoted as " + }, + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "text", + "content": ", to classify the control pose " + }, + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 315, + 256, + 553, + 339 + ], + "type": "text", + "content": " and determine whether it corresponds to a collision. Classification eliminates the need for accurate manifold distance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "spans": [ + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "text", + "content": "2. To address the issue of poor reliability of gradients from the classifier and to integrate " + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "text", + "content": " into a gradient-based optimization pipeline, we introduce the Eikonal regularization term " + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ek}}" + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "text", + "content": " to enforce consistency among gradients, effectively transforming the value before the Sigmoid, " + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 315, + 340, + 553, + 446 + ], + "type": "text", + "content": ", into a signed distance function (SDF). This regularization enhances the reliability of the gradients and leverages the beneficial properties of the SDF without the need for explicit computation of manifold distance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 447, + 553, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 447, + 553, + 506 + ], + "spans": [ + { + "bbox": [ + 315, + 447, + 553, + 506 + ], + "type": "text", + "content": "3. To model the dependency of adjacent robotic joints efficiently, we introduce hierarchical joint encoding that conditions a joint angle on an ancestor's rotation, thereby better capturing the hierarchical dependency of robotic arms." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 520, + 406, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 520, + 406, + 532 + ], + "spans": [ + { + "bbox": [ + 314, + 520, + 406, + 532 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 540, + 528, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 528, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 528, + 552 + ], + "type": "text", + "content": "2.1. Differentiable Rendering and Simulation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 557, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 553, + 713 + ], + "type": "text", + "content": "Differentiable rendering and simulation play a pivotal role in computer vision and graphics. In differentiable rendering, gradients are propagated from primitives to image, while differentiable simulators compute gradients of physical processes similarly, which facilitates seamless integration with gradient-based optimization techniques. The integration of neural fields into robotics has attracted considerable attention. Researchers have employed diverse representations to bridge the digital and physical realms [20, 23, 24, 33, 38, 40, 44, 47, 67, 70]. Innovative approaches, such as Gaussian splatting for the precise reconstruction of robots and their environments, exemplify this trend [35, 50]. Moreover, techniques such as neural radi" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22563" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 445 + ], + "type": "text", + "content": "ance fields for teleoperation [45] and future scene prediction [36] have significantly advanced robotic manipulation capabilities. Feature distillation has further empowered robots to perform complex tasks by translating language embeddings into corresponding 3D actions [49, 51, 52, 71, 73]. Additional advancements include comprehensive physical world modeling, future state prediction [1], and learning continuous manifolds of valid grasps using signed distance functions (SDF) [25, 64]. Significant progress has also been made in perceptual scene understanding and grasp planning [4-6]. One of the primary challenges in developing these simulators is accurately modeling contact interactions—a difficulty that arises from the inherently binary, discontinuous nature of contacts, where objects are either in contact or not [42]. According to [42], contact models can be broadly categorized into four classes: complementarity problems, compliant models, position-based models, and material point method (MPM) frameworks. Complementarity problems emphasize maintaining strict zero-penetration contact between objects [7-9, 12, 13, 19, 21, 28, 29, 46, 48, 60-62, 65, 74]. Compliant models relax the complementarity problem's constraint by replacing the sharp, step-like contact functions with smooth approximations that have large but finite gradients[9, 13, 15, 18, 19, 27, 41, 54, 57, 58]. The position-based method directly constrains object positions to prevent penetration [11, 37]. Meanwhile, the MPM handles contact interactions between both rigid- and soft-body objects[22, 53]. Despite these impressive advances, the effectiveness of differentiable systems for robotic manipulation remains under active validation, marking a promising yet nascent stage of development." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 450, + 240, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 240, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 240, + 462 + ], + "type": "text", + "content": "2.2. Signed Distance Fields in Robotics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 468, + 296, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 296, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 296, + 660 + ], + "type": "text", + "content": "In the realm of robotics and computer graphics, the construction of SDF has been an important technique for various applications, particularly in motion planning and collision avoidance. Some researchers pioneered a method to construct SDF on grid maps [10]. Afterwards, some others introduced incremental SDF construction techniques [17, 43], significantly enhancing the adaptability of SDF in dynamic environments. A novel implicit SDF method is proposed to leverage swept volumes for construction [72]. This method allows for efficient evaluation of the SDF at specific obstacle points with known coordinates, simplifying the process and reducing computational overhead. Another work [69] made a significant stride with the introduction of RobotSDF, an implicit morphology modeling technique. Furthermore, the application of SDF in obstacle avoidance has been extensively explored by [30, 59, 66]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 670, + 111, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 670, + 111, + 681 + ], + "spans": [ + { + "bbox": [ + 55, + 670, + 111, + 681 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "In this section, we will detail our method for achieving collision avoidance in robotic operations in combination" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": "with Gaussian splattering-based differentiable robotic rendering [32]. The types of collisions we consider in this paper include static collisions, which occur when the robot collides with a static and non-interactive environment, as well as self-collisions, which involve collisions with the robot itself. Section 3.1 will model the problem of collision detection as a robotic pose classification problem. In Section 3.2, we will address some challenges that arose in formulating collision detection and propose the introduction of a signed distance field (SDF) as an underlying field for the classifier to tackle the gradient inconsistency problem during optimization. Section 3.3 will explain how we hierarchically encode the robotic pose while respecting the robotic kinematic dependencies. Finally, we will present our loss functions and training schemes in Section 3.4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 259, + 529, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 259, + 529, + 272 + ], + "spans": [ + { + "bbox": [ + 313, + 259, + 529, + 272 + ], + "type": "text", + "content": "3.1. Collision Detection by Pose Classification" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": "To make the model aware of physical collisions during optimization, we need a collision detector to determine whether the robotic pose has caused intersections with other environmental objects or with the robot itself. The collision detector is essentially a function " + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "inline_equation", + "content": "f: \\theta \\mapsto c" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "inline_equation", + "content": "c \\in [0,1]" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": " that classifies each pose " + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": " into two categories: either collided (" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "inline_equation", + "content": "c > 0.5" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": ") or not (" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "inline_equation", + "content": "c \\leq 0.5" + }, + { + "bbox": [ + 313, + 277, + 555, + 361 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "text", + "content": "The robots we consider in this paper have " + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "text", + "content": " joints, and each joint has exactly one degree of freedom for rotation; thus, the pose parameter is within the space " + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathrm{SO}(2)^K" + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "text", + "content": ". The classifier network " + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 361, + 556, + 445 + ], + "type": "text", + "content": " will partition the space into many regions, and ideally, the regions corresponding to valid poses (non-collided poses) will form a manifold as given by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 361, + 456, + 555, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 456, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 361, + 456, + 555, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {V} = \\left\\{\\boldsymbol {\\theta} \\in \\operatorname {S O} (2) ^ {K} \\mid f (\\boldsymbol {\\theta}) \\leq 0. 5 \\right\\}. \\tag {1}", + "image_path": "b4f4d499ed562206fba1a25544608815e4088af89bf99eff8cbcfb892742d19b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "spans": [ + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "content": "To ensure that the output value falls within the range [0, 1], we follow convention and apply a Sigmoid function " + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "content": " to the last output, meaning that the function " + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "content": " is effectively defined by " + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "inline_equation", + "content": "f = \\sigma \\circ g" + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 476, + 554, + 535 + ], + "type": "text", + "content": " is another scalar-valued function that we will detail later in Section 3.2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": "To effectively learn the classifier " + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": ", we follow tradition and use binary cross-entropy loss to supervise " + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": ", as expressed by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 383, + 573, + 555, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 573, + 555, + 586 + ], + "spans": [ + { + "bbox": [ + 383, + 573, + 555, + 586 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {B C E}} = \\operatorname {B C E} (f (\\boldsymbol {\\theta}), c ^ {\\mathrm {g t}}), \\tag {2}", + "image_path": "e59499b73c4f5cb7451c1788c984b79a631b84c9ed53783eff99aa8bbd4c6f66.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "inline_equation", + "content": "c^{\\mathrm{gt}} \\in \\{0,1\\}" + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "text", + "content": " is the ground truth label indicating whether it is valid (" + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "inline_equation", + "content": "c^{\\mathrm{gt}} = 1" + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "text", + "content": ") or not (" + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "inline_equation", + "content": "c^{\\mathrm{gt}} = 0" + }, + { + "bbox": [ + 313, + 591, + 554, + 616 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 624, + 549, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 549, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 549, + 636 + ], + "type": "text", + "content": "3.2. Eikonal Regularizer for Consistent Gradients" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 641, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 689 + ], + "type": "text", + "content": "However, directly applying " + }, + { + "bbox": [ + 313, + 641, + 554, + 689 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 641, + 554, + 689 + ], + "type": "text", + "content": " to gradient optimization is problematic. The function is nearly binary, and the gradients near the values of 0 and 1 are almost zero, leading to noisy and unreliable supervision signals." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "We visualize a possible function " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " with a two-dimensional input space in Figure 3. We notice that, since" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22564" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 387, + 207 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 387, + 207 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 387, + 207 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 387, + 207 + ], + "type": "image", + "image_path": "ab7c31edc7a2d990abb1f45d5ccac67340e44698344a502c532166b000346e19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "lines": [ + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "spans": [ + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "type": "text", + "content": "Figure 2. Our Pipeline. We predict whether a collision has occurred based on pose input, using Eikonal loss " + }, + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{ek}})" + }, + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "type": "text", + "content": " and binary cross-entropy loss " + }, + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{BCE}})" + }, + { + "bbox": [ + 54, + 213, + 387, + 258 + ], + "type": "text", + "content": " to ensure this. It can then be seamlessly integrated with Dr. Robot [32] to create a fully differentiable pipeline for optimization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 423, + 81, + 554, + 205 + ], + "blocks": [ + { + "bbox": [ + 423, + 81, + 554, + 205 + ], + "lines": [ + { + "bbox": [ + 423, + 81, + 554, + 205 + ], + "spans": [ + { + "bbox": [ + 423, + 81, + 554, + 205 + ], + "type": "image", + "image_path": "cea4236373b47a470d2754153e5bc0b6ba3e10ac1bfba32aa6dbef8a5e46e993.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 213, + 555, + 247 + ], + "lines": [ + { + "bbox": [ + 421, + 213, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 421, + 213, + 555, + 247 + ], + "type": "text", + "content": "Figure 3. An illustration of the potential fluctuation of the classification loss landscape." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 279, + 295, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 279, + 295, + 386 + ], + "spans": [ + { + "bbox": [ + 54, + 279, + 295, + 386 + ], + "type": "text", + "content": "the values at both far sides fluctuate, the gradients also fluctuate, leading to inconsistent gradients. When we aim to optimize a pose from the exterior (collided region) toward the interior (collision-free region), this may not be the case because the gradient directions are inconsistent (see the two red points) due to fluctuations in the loss landscape. Small fluctuations do not significantly influence the loss value, but they can lead to noisy and inconsistent gradients, which are harmful to optimization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": "To address the issue, we need to consider the function " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": " before the Sigmoid function " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": " will restrict the gradient and render it too small for updating poses. Specifically, for two consecutive gradient updates with poses " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_t" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_{t + 1}" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": ", the update at " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": " is likely to offset the previous update at " + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 387, + 296, + 460 + ], + "type": "text", + "content": ", as expressed by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 131, + 462, + 295, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 462, + 295, + 490 + ], + "spans": [ + { + "bbox": [ + 131, + 462, + 295, + 490 + ], + "type": "interline_equation", + "content": "\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\leq 0, \\tag {3}", + "image_path": "21aa3e83550e1f1ef481a88c0bf13eec573d45bbd0f53e31006ff4d64ab73838.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 493, + 296, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 493, + 296, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 493, + 296, + 540 + ], + "type": "text", + "content": "especially in regions with high confidence levels close to 0 or 1. This is visualized in Figure 3, where two red dots are plotted; their gradient directions may not be consistent (or correlated) as they point in opposite directions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "spans": [ + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "text", + "content": "We also note that gradient updates are typically small. Assuming the updates " + }, + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "inline_equation", + "content": "\\theta_{t + 1}" + }, + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 55, + 541, + 296, + 576 + ], + "type": "text", + "content": " are close enough and correlated, we have" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 580, + 295, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 580, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 69, + 580, + 295, + 609 + ], + "type": "interline_equation", + "content": "\\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t + 1}} \\right\\rangle \\approx \\left\\langle \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}}, \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\rangle = \\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta} _ {t}} \\right\\| ^ {2} \\geq 0. \\tag {4}", + "image_path": "46cb9f708735f9e460fcd148e61240a1c472acc79f33da190c9e850f37f0a661.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 612, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 296, + 684 + ], + "type": "text", + "content": "This analysis indicates that to enforce gradient consistency, we only need to manipulate the norm of the gradients. To make the correlation of the gradients as uniform as possible (which is desirable for gradient updates), we enforce the above term to be a positive constant " + }, + { + "bbox": [ + 55, + 612, + 296, + 684 + ], + "type": "inline_equation", + "content": "a > 0" + }, + { + "bbox": [ + 55, + 612, + 296, + 684 + ], + "type": "text", + "content": ". This motivates us to adopt the following regularization term" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 129, + 687, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 687, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 129, + 687, + 295, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {e k}} = \\left(\\left\\| \\frac {\\partial g}{\\partial \\boldsymbol {\\theta}} \\right\\| - a\\right) ^ {2} \\tag {5}", + "image_path": "9b02ef86ae5f4fb37ada10b9f3ce3022919fd638e3c8057b74513263756d3cf6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "text", + "content": "to ensure gradient consistency between the two adjacent updates. We immediately notice that when " + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "inline_equation", + "content": "a = 1" + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "text", + "content": ", it becomes an Eikonal regularizer that is widely employed by the signed distance function [16, 44]. Interestingly, this term can be viewed as generalizing the implicit geometric regularization [16] to high-dimensional pose space by learning a function " + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "text", + "content": ". To simplify implementation, we use " + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "inline_equation", + "content": "a = 1" + }, + { + "bbox": [ + 313, + 279, + 554, + 375 + ], + "type": "text", + "content": " throughout the paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "text", + "content": "The function " + }, + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "text", + "content": " is practically implemented as a multilayer perceptron that receives robotic poses " + }, + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 313, + 375, + 554, + 411 + ], + "type": "text", + "content": " as input and produces a scalar; the final classifier is therefore" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 386, + 418, + 553, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 418, + 553, + 432 + ], + "spans": [ + { + "bbox": [ + 386, + 418, + 553, + 432 + ], + "type": "interline_equation", + "content": "f (\\boldsymbol {\\theta}) = (\\sigma \\circ \\omega \\circ g) (\\boldsymbol {\\theta}), \\tag {6}", + "image_path": "9eecb51678cbeea0fcdd01a6325593bff31984d6c955eaa66032b7caad604e8a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "inline_equation", + "content": "\\omega : x \\mapsto sx" + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "text", + "content": " denotes a function that multiplies the input " + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "text", + "content": " by an estimable positive constant " + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 438, + 554, + 486 + ], + "type": "text", + "content": ", which will be further discussed in Section 4.2.3. Our current pipeline is illustrated in Figure 2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 493, + 506, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 493, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 493, + 506, + 506 + ], + "type": "text", + "content": "3.3. Hierarchical Robotic Pose Encoding" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 510, + 555, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 665 + ], + "type": "text", + "content": "We represent the robotic pose using rotation angles, each describing the relative rotation between two arms. The pose parameters are defined in local coordinate frames, such that continuous modifications of a single joint result in realistic motion. However, since angles only describe relative rotations, they may not respect the kinematic structure and cannot effectively handle the structural dependency relationships between the arms. We observe that each individual joint needs to be conditioned on the parent rotations and thus must be influenced by them. To incorporate this notion of kinematic dependency into the function " + }, + { + "bbox": [ + 313, + 510, + 555, + 665 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 510, + 555, + 665 + ], + "type": "text", + "content": ", we implement the function as a hierarchical network that encodes the dependency within the network structure [2, 14, 39, 55]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": "This is similar to the method described in [55]. Specifically, for a given robotic pose " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} = [\\theta_{1};\\dots;\\theta_{K}]" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": " (with " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "k\\in \\{1,\\ldots ,K\\}" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": ") is the rotation angle for joint " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": ", and a function " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\tau (k)" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": " maps the index of each joint to its parent joint" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22565" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": "index, we encode each pose using a multi-layer perceptron (MLP) as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 90, + 106, + 294, + 125 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 106, + 294, + 125 + ], + "spans": [ + { + "bbox": [ + 90, + 106, + 294, + 125 + ], + "type": "interline_equation", + "content": "g _ {1}: \\theta_ {1} \\mapsto \\boldsymbol {\\nu} _ {1} \\tag {7}", + "image_path": "0ff0e326499508b23cda14696711daaa3aed8b024b9f7818b2fa4ce47616a09a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 91, + 121, + 258, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 121, + 258, + 133 + ], + "spans": [ + { + "bbox": [ + 91, + 121, + 258, + 133 + ], + "type": "interline_equation", + "content": "g _ {k}: \\left(\\theta_ {k}, \\boldsymbol {\\nu} _ {\\tau (k)}\\right) \\mapsto \\boldsymbol {\\nu} _ {k}, \\quad k \\in \\{2, \\dots , K \\}", + "image_path": "38a62c5e0d16f217c4aeeedf8272be677c8346b1fd0bd55ed944b3fb0cdba52e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": "This process takes the joint angle and the encoded feature " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu}_{\\tau (k)}\\in \\mathbb{R}^{\\ell}" + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": " of its parent joint as input and produces an output feature " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu}_k\\in \\mathbb{R}^\\ell" + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\ell = 8" + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": " is the feature dimension. We then concatenate the encoded features of every joint to obtain a combined pose embedding " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\pmb {\\nu} = [\\pmb {\\nu}_1;\\dots ;\\pmb {\\nu}_K]" + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": " This embedding is further transformed by a linear mapping " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\ell ,K}\\to \\mathbb{R}" + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "text", + "content": " to yield a scalar value that serves as the output of the function " + }, + { + "bbox": [ + 55, + 142, + 296, + 240 + ], + "type": "inline_equation", + "content": "g" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 217, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 217, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 217, + 260 + ], + "type": "text", + "content": "3.4. Training Data and Objectives" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": "The training dataset comprises " + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": " poses and their corresponding decisions, represented by " + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\pmb{\\theta}_i, c_i^{\\mathrm{gt}})\\}_{i=1}^N" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": ". It is constructed as follows: the robotic pose " + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_i" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": " is randomly sampled, and a (non-differentiable) collision detector is then applied to produce the decision " + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "inline_equation", + "content": "c_i^{\\mathrm{gt}} \\in \\{0, 1\\}" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": ", indicating whether a collision has occurred (" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "inline_equation", + "content": "c_i^{\\mathrm{gt}} = 1" + }, + { + "bbox": [ + 55, + 265, + 296, + 337 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "text", + "content": "The model is trained using batched samples; we omit the summation-over-samples notation here for simplicity. The objective is simply the weighted combination of " + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BCE}}" + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ek}}" + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "text", + "content": ". With " + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 55, + 337, + 296, + 384 + ], + "type": "text", + "content": ", it is expressed as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 135, + 395, + 294, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 395, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 135, + 395, + 294, + 407 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {B C E}} + \\alpha \\mathcal {L} _ {\\mathrm {e k}}. \\tag {8}", + "image_path": "6267470bef1dabf0c340bee8aea1767757f9ccd87728136d1099a61d9ea742b5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 417, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 417, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 417, + 296, + 453 + ], + "type": "text", + "content": "Depending on how it is learned, we may additionally have, for example, " + }, + { + "bbox": [ + 55, + 417, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RGB}}" + }, + { + "bbox": [ + 55, + 417, + 296, + 453 + ], + "type": "text", + "content": " for image-space supervision, which we omit here for simplicity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 464, + 200, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 200, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 200, + 478 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 484, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 296, + 567 + ], + "type": "text", + "content": "We conduct ablation studies on Prof. Robot (section 4.2), experiments on collision resolution (section 4.3), integration with Dr. Robot (section 4.4), and sim-to-real deployment (section 4.5). Comparison with the differentiable simulator, training with alternative regularizers, and manipulation with Dr. Robot are detailed in the supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 576, + 172, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 172, + 589 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 172, + 589 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 594, + 296, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 688 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 688 + ], + "type": "text", + "content": "Data Preparation. We adopt a data-driven approach, leveraging the Mujoco [56] configurations provided by [32] with some modifications. Specifically, we selected six scenes and randomly sampled poses from the robot's joint limits, used Mujoco (which is non-differentiable) to check for collisions, and employed a resampling technique to balance the ratio of collision to non-collision data at approximately the same amount." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. We primarily evaluate the network's ability to distinguish between collision and non-collision" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 335, + 91, + 533, + 127 + ], + "blocks": [ + { + "bbox": [ + 314, + 71, + 553, + 82 + ], + "lines": [ + { + "bbox": [ + 314, + 71, + 553, + 82 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 553, + 82 + ], + "type": "text", + "content": "Table 1. Ablation study on hierarchical and flattened encoding." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 335, + 91, + 533, + 127 + ], + "lines": [ + { + "bbox": [ + 335, + 91, + 533, + 127 + ], + "spans": [ + { + "bbox": [ + 335, + 91, + 533, + 127 + ], + "type": "table", + "html": "
HierarchicalFlatten
Classification Accuracy97.70%97.51%
", + "image_path": "29c38e3f1ddf1daf2cd021fe3acb1b7052330c533c32c0f0001217c62c80b33a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "text", + "content": "states, as well as its performance in optimizing the gradients. The former metric (accuracy) assesses the network's ability to detect collisions, while the latter " + }, + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{ek}})" + }, + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "text", + "content": " measures its capacity to avoid collisions through optimization. Furthermore, for a given robot pose denoted as " + }, + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 140, + 554, + 235 + ], + "type": "text", + "content": ", we are able to determine the collision points of the mesh within the simulator and subsequently calculate the collision rate for all possible poses." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 236, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 555, + 415 + ], + "type": "text", + "content": "Experimental Details. We leverage the joint connection relationships defined in the URDF, where each joint is encoded using a tiny MLP. The encoded features from all joints are then concatenated and passed through an MLP with four hidden layers, each containing 512 units, followed by a final output layer with a single unit. LeakyReLU is used as the activation function for all layers. We introduce a learnable scale factor " + }, + { + "bbox": [ + 313, + 236, + 555, + 415 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 236, + 555, + 415 + ], + "type": "text", + "content": ", which, after being multiplied by the MLP output, is passed through a Sigmoid function to produce a probability. We conduct experiments within a simulation environment, where the network's ability determines the success rate of collision resolution. Finally, we integrate our method into a differentiable robot rendering pipeline and perform control experiments. The experiments are conducted on a single NVIDIA RTX 4090 GPU." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 422, + 528, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 528, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 528, + 434 + ], + "type": "text", + "content": "4.2. Learning Robotic Signed Distance Fields" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 439, + 484, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 439, + 484, + 451 + ], + "spans": [ + { + "bbox": [ + 313, + 439, + 484, + 451 + ], + "type": "text", + "content": "4.2.1. Ablation: Hierarchical Encoding" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 453, + 554, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 554, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 554, + 538 + ], + "type": "text", + "content": "To assess the impact of hierarchical encoding, we replaced it with a simple linear layer for encoding the input joint data while keeping the rest of the components unchanged. As shown in Table 1, after 10,000 iterations, the use of the hierarchical MLP results in higher accuracy. This shows that the hierarchical encoding strategy better captures the kinematic structure and increases performance." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 543, + 473, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 473, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 473, + 555 + ], + "type": "text", + "content": "4.2.2. Ablation: Eikonal Regularizer" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "content": "To investigate the effect of the Eikonal regularizer, we trained an MLP under two conditions: one without the Eikonal regularizer and one with it, and compared both the classification accuracy and the numerical value of the Eikonal loss. We then tested whether the models could resolve collisions (as described in Section 4.3). The models were trained for 10,000 iterations. During pose optimization, for the model trained without the Eikonal regularizer, we stopped the iteration if the collision probability dropped below 0.5. For the model trained with the Eikonal regularizer, we halted the iteration if the SDF value, which is negative in non-collision regions, fell below the threshold " + }, + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{thres}} = -0.1" + }, + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22566" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 91, + 282, + 203 + ], + "blocks": [ + { + "bbox": [ + 92, + 71, + 259, + 81 + ], + "lines": [ + { + "bbox": [ + 92, + 71, + 259, + 81 + ], + "spans": [ + { + "bbox": [ + 92, + 71, + 259, + 81 + ], + "type": "text", + "content": "Table 2. Ablation study on the Eikonal loss." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 91, + 282, + 203 + ], + "lines": [ + { + "bbox": [ + 66, + 91, + 282, + 203 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 282, + 203 + ], + "type": "table", + "html": "
w. Eikonal lossw/o. Eikonal loss
Classification97.70%98.39%
Accuracy
Iteration Nums ↓119.991000
Iteration Time ↓0.97 s10.64 s
Move Angle ↓0.604.49
Collision Point ↓0.6711.52
Collision Rate ↓17%99%
Gradient Norm8.53 × 10-11.89 × 10-6
", + "image_path": "8e70c00682eae285a7f506fe911fd121b1b28a74ee205c99925f1ef6b113dbd0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 100, + 228, + 250, + 275 + ], + "blocks": [ + { + "bbox": [ + 85, + 208, + 265, + 219 + ], + "lines": [ + { + "bbox": [ + 85, + 208, + 265, + 219 + ], + "spans": [ + { + "bbox": [ + 85, + 208, + 265, + 219 + ], + "type": "text", + "content": "Table 3. Ablation study on the scaling factor " + }, + { + "bbox": [ + 85, + 208, + 265, + 219 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 85, + 208, + 265, + 219 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 100, + 228, + 250, + 275 + ], + "lines": [ + { + "bbox": [ + 100, + 228, + 250, + 275 + ], + "spans": [ + { + "bbox": [ + 100, + 228, + 250, + 275 + ], + "type": "table", + "html": "
AccuracyEikonal Loss ↓
w. s97.70%0.0850
w/o. s85.37%0.2568
", + "image_path": "4c18781d13b5e6d3dd777372ef4cb5e6ecc926baac1e6c3733de60404098e8ee.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 289, + 295, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 295, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 295, + 350 + ], + "type": "text", + "content": "The results were compared, as shown in Table 2. Without the Eikonal regularizer, the optimizer struggled to generate a collision-free pose from a collision state, with iterations exceeding 1,000, and the propagated gradients were too small to facilitate further optimization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 354, + 190, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 190, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 190, + 367 + ], + "type": "text", + "content": "4.2.3. Ablation: Scaling Factor" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "content": "The cross-entropy loss and Eikonal loss may require gradients of different magnitudes, potentially interfering with each other and hindering the model's ability to learn useful information. To address this, a scaling factor " + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "content": " for the SDF is introduced to allow for large gradients in classification and limited gradients in the SDF. We removed the scaling factor " + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "content": " (setting " + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "inline_equation", + "content": "s = 1" + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "content": ") and directly passed the SDF value to the Sigmoid function to produce " + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 369, + 295, + 465 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 465, + 296, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 296, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 296, + 502 + ], + "type": "text", + "content": "The numerical results, as shown in Table 3, demonstrate that the scaling factor effectively achieves good classification results while preserving the uniform gradient property." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 506, + 239, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 239, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 239, + 518 + ], + "type": "text", + "content": "4.2.4. Comparison Between NDF and SDF" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "text", + "content": "In contrast to [55], which models collision-free poses as a high-dimensional submanifold using a Neural Distance Field (NDF), we represent collision-free poses as a set of discontinuous regions in high-dimensional space that can be modeled using an SDF. To explore the differences between these two approaches, we also conducted experiments with an NDF. Learning an NDF requires accurate manifold distances; unlike [55], our method does not require this because it can be implicitly learned through " + }, + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ek}}" + }, + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "text", + "content": ". To provide distance labels for [55], we followed their convention and employed Faiss to compute the L2 distance of each pose as an approximate ground truth distance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "After 10,000 iterations of optimization, the results are presented in Table 4. As shown in the table, our modeling approach outperforms the NDF. By learning a region (rather than a submanifold) and implicitly learning through" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 361, + 91, + 506, + 137 + ], + "blocks": [ + { + "bbox": [ + 348, + 71, + 521, + 81 + ], + "lines": [ + { + "bbox": [ + 348, + 71, + 521, + 81 + ], + "spans": [ + { + "bbox": [ + 348, + 71, + 521, + 81 + ], + "type": "text", + "content": "Table 4. Comparison between SDF and NDF." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 361, + 91, + 506, + 137 + ], + "lines": [ + { + "bbox": [ + 361, + 91, + 506, + 137 + ], + "spans": [ + { + "bbox": [ + 361, + 91, + 506, + 137 + ], + "type": "table", + "html": "
AccuracyEikonal Loss ↓
SDF97.70%0.0850
NDF54.33%0.1916
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Collision Resolution by Pose Optimization" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 340, + 198, + 529, + 312 + ], + "blocks": [ + { + "bbox": [ + 340, + 198, + 529, + 312 + ], + "lines": [ + { + "bbox": [ + 340, + 198, + 529, + 312 + ], + "spans": [ + { + "bbox": [ + 340, + 198, + 529, + 312 + ], + "type": "image", + "image_path": "38ece8f977fde81d82a31c583a2f06f4c7488a0d6a5139b4af1d4d4a96cbd896.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 322, + 554, + 377 + ], + "lines": [ + { + "bbox": [ + 313, + 322, + 554, + 377 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 554, + 377 + ], + "type": "text", + "content": "Figure 4. An illustration of how collision resolution optimizes a collided robot towards a collision-free state. The figure shown visualizes the SDF, where red points (representing collisions) are optimized to green points (representing non-collisions) along the gradient update trajectories." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "text", + "content": "Given a collision pose, our neural network can optimize the collision pose to the nearest non-colliding pose, as shown in Figure 4. After training the network, we sample 1,000 collision poses and use our " + }, + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "text", + "content": " to predict their SDF values. We then apply gradient optimization, fixing the trained model's weights, and minimize the predicted SDF until it falls below a threshold value " + }, + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{thres}}" + }, + { + "bbox": [ + 313, + 389, + 554, + 474 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 474, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 554, + 544 + ], + "type": "text", + "content": "Specifically, we use the Adam optimizer [26] with a learning rate of 0.01, keeping all other parameters unchanged. The results are presented in Table 5. As the SDF values decrease, both the likelihood and severity of collisions reduce, demonstrating that our method effectively predicts and avoids collisions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "content": "To assess the robustness of our model, we perform optimization with varying learning rates, anticipating consistent performance across these rates. To examine the effect of the learning rate, we replicate the experimental setup as described previously, setting " + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{thres}} = -0.1" + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "content": ". We then compare the number of collision points and analyze the overall trends. The results demonstrate that the model performs comparably across different learning rates, further validating the robustness of our approach. A summary of these results is presented in Table 6." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 672, + 463, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 672, + 463, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 672, + 463, + 685 + ], + "type": "text", + "content": "4.4. Integration with Dr. Robot" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "Differentiable robot rendering (Dr. Robot) enables us to obtain a differentiable pose from the rendered view. From" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22567" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 124, + 291, + 247 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": "Table 5. Effect of different threshold " + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "inline_equation", + "content": "(l_{\\mathrm{thres}})" + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "inline_equation", + "content": "\\overline{\\mathrm{Iter}}" + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": " represents the average number of iterations, while " + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "inline_equation", + "content": "\\Delta \\theta" + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": " denotes the change in angle. The last two columns display the collision points in the scenario prior to optimization and after optimization, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 124, + 291, + 247 + ], + "lines": [ + { + "bbox": [ + 59, + 124, + 291, + 247 + ], + "spans": [ + { + "bbox": [ + 59, + 124, + 291, + 247 + ], + "type": "table", + "html": "
l_thresIter.↓Time (s) ↓Δθ↓BeforeAfter ↓
-0.00019.0170.1550.1625.5570.399
-0.00119.3920.1560.1655.6330.375
-0.00518.8740.1530.1595.5080.312
-0.01020.1240.1540.1735.6170.187
-0.02020.0900.1620.1735.4710.080
-0.03020.2360.1600.1725.3430.019
-0.04021.2560.1710.1815.6260.016
-0.05022.6270.1740.1905.7570.006
-0.10024.4500.1920.2035.1970.001
", + "image_path": "bdb385fbb910359ccac80f2078ec4b763a8b4f7c5e103dc2dfd1d6ad1719380b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 59, + 282, + 290, + 396 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "text", + "content": "Table 6. Impact of different learning rate. The content of the last two columns is identical to that of Table 5." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 282, + 290, + 396 + ], + "lines": [ + { + "bbox": [ + 59, + 282, + 290, + 396 + ], + "spans": [ + { + "bbox": [ + 59, + 282, + 290, + 396 + ], + "type": "table", + "html": "
LRIter.↓Time(s)↓Δθ↓BeforeAfter↓
0.001241.3631.8410.2035.4600.003
0.01024.4500.1920.2035.1970.001
0.02012.8260.1040.2155.4950.000
0.0505.6340.0490.2365.6220.000
0.1003.0260.0280.2565.5690.000
0.2001.7850.0180.3155.6350.001
0.5001.1270.0130.5275.3260.000
1.0001.1040.0131.0405.5530.000
", + "image_path": "d4bf0438311b8e2d160eebad6d4906f8f9b7e2c7c54309994739f504ecff524a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 408, + 296, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 296, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 296, + 458 + ], + "type": "text", + "content": "this pose, our method can infer prior knowledge about potential collisions with the external environment or self-intersections. This prior knowledge can be seamlessly integrated into the differentiable rendering process." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 462, + 241, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 241, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 241, + 474 + ], + "type": "text", + "content": "4.4.1. Inverse Action from Collision Image" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 476, + 296, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 476, + 296, + 560 + ], + "spans": [ + { + "bbox": [ + 55, + 476, + 296, + 560 + ], + "type": "text", + "content": "We leverage Dr. Robot to optimize the robot's pose from images. However, we observe that the optimized poses are not always reasonable; in some cases, they result in collisions, limiting the practical application of Dr. Robot in real-world scenarios. To address this, we combine our SDF " + }, + { + "bbox": [ + 55, + 476, + 296, + 560 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 476, + 296, + 560 + ], + "type": "text", + "content": " with Dr. Robot, enabling us to optimize reasonable poses that minimize collisions while maintaining image consistency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 560, + 296, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 560, + 296, + 680 + ], + "spans": [ + { + "bbox": [ + 55, + 560, + 296, + 680 + ], + "type": "text", + "content": "Striving for an efficient evaluation, we introduce immovable rigid blocks next to the robot. This way, if the robot's pose is unreasonable, it will collide with these blocks or self-collision. In each scene, we set up four cameras from different viewpoints and capture rendered images, instance segmentations, and depth maps from the simulation engine. This setting closely aligns with the real-world scenarios using monocular depth estimation models, such as Depth Pro[3]. To optimize the robot's pose, we use the following loss functions:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 685, + 296, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 685, + 296, + 716 + ], + "spans": [ + { + "bbox": [ + 113, + 685, + 296, + 716 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R G B}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {r} - \\boldsymbol {r} _ {\\mathrm {g t}} \\| \\tag {9}", + "image_path": "cf971d704b3d5b863718a37663a10428c154cc87cbf34a6af5889a44efdceffb.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 118, + 550, + 198 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "type": "text", + "content": "Table 7. The number of collision points (averaged) and collision rate of the pose inverse from images. We control the collision point from simulator and generate images for Dr. Robot optimization." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 118, + 550, + 198 + ], + "lines": [ + { + "bbox": [ + 317, + 118, + 550, + 198 + ], + "spans": [ + { + "bbox": [ + 317, + 118, + 550, + 198 + ], + "type": "table", + "html": "
Original collision point in dataCollision Point ↓Collision Rate ↓
Dr. RobotOursDr. RobotOurs
10.969.170.8378%9%
2.002.330.0486%2%
1.001.180.0278%2%
0.000.050.002%0%
", + "image_path": "3f003de504a726cb0fb822556697a4cfa785797ed6e690a14c72bfee46420370.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 208, + 555, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 208, + 555, + 239 + ], + "spans": [ + { + "bbox": [ + 375, + 208, + 555, + 239 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {D}} = \\frac {1}{N} \\sum_ {\\operatorname {s e g} [ i, j ] = 1} \\| \\boldsymbol {d} - \\boldsymbol {d} _ {\\mathrm {g t}} \\| \\tag {10}", + "image_path": "9bee2b19cdf0100c497e6e9978dc30ff6d8e1bb47ceac4641c56e3f475cd8fde.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "inline_equation", + "content": "\\operatorname{seg}[i,j]" + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": " is the robot's mask, with 0 indicating the robot is not present at that position in the image and 1 indicating it is present. Here, " + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}" + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": " represents the rendered image from Dr. Robot, and " + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{gt}}" + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": " represents the rendered image from the simulation engine; " + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "inline_equation", + "content": "\\boldsymbol{d}" + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": " represents the rendered depth from Dr. Robot, and " + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{gt}}" + }, + { + "bbox": [ + 313, + 243, + 555, + 340 + ], + "type": "text", + "content": " represents the rendered depth from the simulation engine. The baseline loss function is the sum of the image and depth losses:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 399, + 348, + 555, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 348, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 399, + 348, + 555, + 361 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} \\tag {11}", + "image_path": "67c0006de2ab33c53b4a08d1ab4e995114c27b7d5a3c4dc74941d28e327bdbd1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 369, + 554, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 554, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 554, + 429 + ], + "type": "text", + "content": "To address collisions, we use our trained SDF model. The data burden is manageable as we can obtain sufficient data from the simulation engine for training. During the optimization process, we introduce an additional term to the loss function:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 374, + 437, + 555, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 437, + 555, + 452 + ], + "spans": [ + { + "bbox": [ + 374, + 437, + 555, + 452 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {S D F}} = \\operatorname {R e L U} (g (\\boldsymbol {\\theta}) - l _ {\\text {t h r e s}}) \\tag {12}", + "image_path": "ed94e176d36c555456f8a943251e95d2af0505f4b169e532991b9bab1c10bb37.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 459, + 432, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 459, + 432, + 470 + ], + "spans": [ + { + "bbox": [ + 326, + 459, + 432, + 470 + ], + "type": "text", + "content": "Thus, our loss function is" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 376, + 480, + 555, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 480, + 555, + 493 + ], + "spans": [ + { + "bbox": [ + 376, + 480, + 555, + 493 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\mathcal {L} _ {\\mathrm {D}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S D F}} \\tag {13}", + "image_path": "84f18df8a51b4d8e78d795b4af895190c18af38f3722802e5d03d4e4c20669e2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "text", + "content": " is a weight scalar. The optimization stops when " + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "inline_equation", + "content": "g(\\pmb{\\theta}) \\leq l_{\\mathrm{thres}}" + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{thres}} = -0.1" + }, + { + "bbox": [ + 313, + 502, + 554, + 574 + ], + "type": "text", + "content": ". We sampled 100 instances for testing, and the results are shown in Table 7. The quantitative results demonstrate that, after optimization, Dr. Robot effectively avoids collisions and achieves the closest possible pose without collision." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 579, + 504, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 579, + 504, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 579, + 504, + 591 + ], + "type": "text", + "content": "4.4.2. Inverse Trajectory from Optimization" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "text", + "content": "Furthermore, we aim to explore the feasibility of using Dr. Robot for trajectory generation. Given the starting posture " + }, + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{start}}" + }, + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "text", + "content": " and the end posture " + }, + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{end}}" + }, + { + "bbox": [ + 313, + 594, + 554, + 653 + ], + "type": "text", + "content": ", we employ gradient optimization with Dr. Robot to generate the intermediate trajectory for robot control." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "As mentioned in Section 4.4.1, we randomly sample two collision-free poses and obtain their respective rendering results. Dr. Robot uses " + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{start}}" + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": " as the initial configuration and utilizes the image, mask, depth, and pose information of " + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{end}}" + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": " from the simulator as supervisory signals. In addition," + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22568" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 91, + 277, + 171 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 277, + 83 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 277, + 83 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 277, + 83 + ], + "type": "text", + "content": "Table 8. Optimize Trajectory by Dr. Robot and SDF." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 91, + 277, + 171 + ], + "lines": [ + { + "bbox": [ + 73, + 91, + 277, + 171 + ], + "spans": [ + { + "bbox": [ + 73, + 91, + 277, + 171 + ], + "type": "table", + "html": "
Collision Point ↓Collision Rate ↓
Dr. Robot4.0710.64%
Ours (-0.00)3.5010.00%
Ours (-0.01)0.000.00%
Ours (-0.05)0.000.00%
Ours (-0.10)0.000.00%
", + "image_path": "f658d563706f4fb18db5a55223684fbacb4b0125ef3e24d6fd8bb4e40affa26b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 184, + 295, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 184, + 295, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 184, + 295, + 207 + ], + "type": "text", + "content": "we incorporate our SDF model and add " + }, + { + "bbox": [ + 55, + 184, + 295, + 207 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SDF}}" + }, + { + "bbox": [ + 55, + 184, + 295, + 207 + ], + "type": "text", + "content": " (Equation 12) to the loss function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 209, + 296, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 296, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 296, + 257 + ], + "type": "text", + "content": "However, during the optimization process, the value of the SDF fluctuates around " + }, + { + "bbox": [ + 55, + 209, + 296, + 257 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{thres}}" + }, + { + "bbox": [ + 55, + 209, + 296, + 257 + ], + "type": "text", + "content": ", which causes some data points to violate the SDF constraints. To address this, we perform post-processing on the intermediate trajectory:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 265, + 295, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 265, + 295, + 299 + ], + "spans": [ + { + "bbox": [ + 63, + 265, + 295, + 299 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {S D F}} (\\hat {\\boldsymbol {\\theta}} _ {i}) + \\frac {1}{N - 1} \\sum_ {i = 1} ^ {N - 1} \\| \\hat {\\boldsymbol {\\theta}} _ {i + 1} - \\hat {\\boldsymbol {\\theta}} _ {i} \\| \\tag {14}", + "image_path": "f97e5eef1a19830aaf42ae76fc268f26f95a38363ac7fe90d7306f0cd40342c0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 308, + 296, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 308, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 296, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 308, + 296, + 369 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_i, i = 1\\ldots N" + }, + { + "bbox": [ + 55, + 308, + 296, + 369 + ], + "type": "text", + "content": " is the middle trajectory generate from optimization. Here, we combine the SDF loss and the total variation loss. The results, as shown in Table 8, demonstrate that our approach effectively generates intermediate trajectories suitable for robot control." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 374, + 195, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 374, + 195, + 385 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 195, + 385 + ], + "type": "text", + "content": "4.4.3. Inverse Action from VLM" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 389, + 295, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 295, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 295, + 496 + ], + "type": "text", + "content": "We have observed that directly extracting data from the Vision-Language Model (VLM) using Dr. Robot can lead to unconstrained optimization, potentially resulting in implausible poses. Conversely, employing a simulator to refine these poses is problematic due to the absence of gradient information, which hinders seamless integration with Dr. Robot. Our novel approach successfully circumvents the optimization of collision-prone poses, thereby maintaining the plausibility of the outcomes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 498, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 664 + ], + "type": "text", + "content": "In alignment with Dr. Robot's methodology, we utilized CLIP to extract action data from the VLM. Our experiments use shadow hand and leveraged the openai/clip-vit-base-patch32 model from HuggingFace. We aimed to maximize the dot product between the language and image embeddings generated by their respective processing towers. We computed the optimized collision points and associated collision probabilities. To substantiate that our method does not compromise the efficacy of action distillation from the VLM, we conducted a comparative analysis of the optimized dot products. The findings, presented in Table 9, demonstrate that our technique effectively precludes the optimization of implausible poses without impeding the extraction of actions from the VLM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 672, + 194, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 194, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 194, + 685 + ], + "type": "text", + "content": "4.5. Sim-to-Real Deployment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "To validate the performance of our method, we conducted several sim-to-real experiments. In an illustrative scenario," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 70, + 555, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 115 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 115 + ], + "type": "text", + "content": "Table 9. The metrics of collision and optimization while optimizing robotic pose by CLIP. We indicate the collision point(Point) and collision rate(Rate) for average, and report the mean and std of dot product metrics." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 333, + 124, + 533, + 203 + ], + "blocks": [ + { + "bbox": [ + 333, + 124, + 533, + 203 + ], + "lines": [ + { + "bbox": [ + 333, + 124, + 533, + 203 + ], + "spans": [ + { + "bbox": [ + 333, + 124, + 533, + 203 + ], + "type": "table", + "html": "
Point ↓Rate ↓meanstd ↓
Dr. Robot1.3042.50%33.861.53
Ours (-0.00)0.4030.00%34.421.58
Ours (-0.01)0.8040.00%34.131.20
Ours (-0.05)0.3020.00%34.221.60
Ours (-0.10)0.1010.00%34.021.23
", + "image_path": "0e57e4a026938f567c192575c5495b4c4d4a99565df29aa80412739b04143e43.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 315, + 208, + 555, + 352 + ], + "blocks": [ + { + "bbox": [ + 315, + 208, + 555, + 352 + ], + "lines": [ + { + "bbox": [ + 315, + 208, + 555, + 352 + ], + "spans": [ + { + "bbox": [ + 315, + 208, + 555, + 352 + ], + "type": "image", + "image_path": "e753e663bd5df8d664d4a1428366b6d328084fca485ff009dcfb0a17088da637.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 358, + 555, + 469 + ], + "lines": [ + { + "bbox": [ + 313, + 358, + 555, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 555, + 469 + ], + "type": "text", + "content": "Figure 5. Sim2Real Experiment: Obstacle Avoidance with Prof. Robot. The first row illustrates that, in the simulator, the robot arm collides with the red box due to its inability to perceive obstacles. The second row shows that after integrating Prof. Robot, the robot successfully avoids the red obstacle. The red box represents an obstacle, and without Prof. Robot, the robot fails to circumvent it. The final row demonstrates that, with Prof. Robot, the robot smoothly navigates around the obstacle, confirming the effectiveness of our method for real-world applications." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 477, + 555, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 555, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 555, + 574 + ], + "type": "text", + "content": "a robot navigates around obstacles – including a wall and a box – while moving from an initial pose to a target pose. We interpolate 100 poses between the initial and target positions using SO(2) interpolation and optimize the trajectory with our Prof. Robot algorithm. The results, shown in Figure 5, demonstrate that our approach effectively guides the robot arm around obstacles while preventing collisions in simulation and reality." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 583, + 481, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 583, + 481, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 583, + 481, + 596 + ], + "type": "text", + "content": "5. Limitations and Future Work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "text", + "content": "Our method tackles the problem of cross-environment generalization. To address this, a new mechanism could be proposed that enhances Prof. Robot's scene perception by modeling dynamic objects. The dynamic environment could be represented by supplementary joints " + }, + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "text", + "content": ", which constrain the robotic system's joint space. By training with a collision-aware discriminator " + }, + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "inline_equation", + "content": "p(\\cdot|\\delta)" + }, + { + "bbox": [ + 313, + 603, + 555, + 715 + ], + "type": "text", + "content": ", our joint learning framework could practical effectiveness despite environmental perturbations from ideal conditions. 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Advances in Neural Information Processing Systems, 34:21910-21922, 2021. 3" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22572" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_content_list.json b/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f82b8efec15fb957b60810aba7d208001ae2d4c8 --- /dev/null +++ b/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_content_list.json @@ -0,0 +1,1734 @@ +[ + { + "type": "text", + "text": "Progress-Aware Video Frame Captioning", + "text_level": 1, + "bbox": [ + 289, + 130, + 707, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zihui Xue $^{1}$ , Joungbin An $^{1}$ , Xitong Yang $^{\\dagger}$ , Kristen Grauman $^{1}$ $^{1}$ University of Texas at Austin", + "bbox": [ + 253, + 179, + 740, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 251, + 326, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While image captioning provides isolated descriptions for individual images, and video captioning offers one single narrative for an entire video clip, our work explores an important middle ground: progress-aware video captioning at the frame level. This novel task aims to generate temporally fine-grained captions that not only accurately describe each frame but also capture the subtle progression of actions throughout a video sequence. Despite the strong capabilities of existing leading vision language models, they often struggle to discern the nuances of frame-wise differences. To address this, we propose ProgressCaptioner, a captioning model designed to capture the fine-grained temporal dynamics within an action sequence. Alongside, we develop the FrameCap dataset to support training and the FrameCapEval benchmark to assess caption quality. The results demonstrate that ProgressCaptioner significantly surpasses leading captioning models, producing precise captions that accurately capture action progression and set a new standard for temporal precision in video captioning. Finally, we showcase practical applications of our approach, specifically in aiding keyframe selection and advancing video understanding, highlighting its broad utility.", + "bbox": [ + 86, + 282, + 483, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 643, + 220, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual captioning [38]—the task of generating textual descriptions of visual content—is a fundamental problem in computer vision with extensive practical applications. Existing captioning paradigms are broadly divided into two categories: image captioning and video captioning, with a clear distinction between them. Image captioning [23] generates a single, isolated description for each image, with no contextual linkage among different images. In contrast, video captioning [1] assigns a single caption for the entire video clip, aggregating information across frames without addressing the specifics of individual frames.", + "bbox": [ + 89, + 670, + 482, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1 illustrates this dichotomy. Employing an im", + "bbox": [ + 109, + 837, + 480, + 852 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e6d9ab00d3afc8d6656a1ed3461dd509bcf58765d513a50ec52fb2900cd4026f.jpg", + "image_caption": [ + "a close up of a wok with a lot of oil in it" + ], + "image_footnote": [], + "bbox": [ + 516, + 250, + 612, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/91abd2e9679717edf60d2c052865a1c41330ea35bc253ba98fc41e3e4ed98920.jpg", + "image_caption": [ + "Eggs are fried in a wok on a stove top" + ], + "image_footnote": [], + "bbox": [ + 614, + 250, + 707, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7d9aaa54505f12e24ae223828985754f5bba2962d947218934f87dfaba8b35e7.jpg", + "image_caption": [ + "cooking eggs in a wok on the stove", + "Progress-aware video frame captioning" + ], + "image_footnote": [], + "bbox": [ + 710, + 250, + 803, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0c28d214b88c17575d88b673cea6832519b2bc8f6ddedb19745f8db974c8d65.jpg", + "image_caption": [ + "cooking food in a wok on the stove", + "Image captioning", + "Scramble the eggs in the wok", + "Video captioning" + ], + "image_footnote": [], + "bbox": [ + 807, + 250, + 901, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The frame shows a large, worn-out wok with a dark interior. There is a small amount of oil visible at the bottom of the wok, indicating that it is ready for cooking.", + "bbox": [ + 522, + 357, + 604, + 439 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Three eggs are being added into the wok. The eggs are still intact and have bright yellow yolks. The wok remains in the same position as in the first frame.", + "bbox": [ + 620, + 357, + 699, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A metal spatula is used to stir the eggs. The eggs are starting to cook, with some white parts becoming more solid while others remain runny.", + "bbox": [ + 715, + 357, + 792, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The scene transitions to show the same wok, now containing scrambled eggs. The yolks are fully mixed into the whites.", + "bbox": [ + 813, + 358, + 890, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. We propose progress-aware video frame captioning (bottom), which aims to generate a sequence of captions that capture the temporal dynamics within a video. Unlike traditional image and video captioning (top) that focus on broad event-level descriptions, our task delves into the detailed, progressive dynamics of an action, necessitating precise, temporally fine-grained capabilities. Blue text highlights how the progress-aware captions build successively on the earlier content to highlight what is changing.", + "bbox": [ + 511, + 465, + 906, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "age captioning model like BLIP [37] to describe each frame of the video results in captions that are local, not temporally context-aware, and may exhibit little variation across the sequence. Conversely, video captioning provides a global, not temporally fine-grained overview of the event, as exemplified by the YouCook2 [85] ground truth label \"scramble the eggs in the wok\". In both scenarios, the nuances of how the action unfolds over time are missed. This raises the question: Can we develop temporally fine-grained captions that capture the subtle, progressive nature of action sequences? Figure 1 (bottom) illustrates what we seek.", + "bbox": [ + 511, + 594, + 906, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Having such progress-aware captions could benefit a great variety of downstream tasks, bringing improved video understanding [73, 79], more precise video retrieval [66-68], and enriched video generation [50, 58]. Moreover, such a capability could open up new AR/VR and robotics applications. For instance, in AI coaching, a captioning system could meticulously analyze an expert's tennis forehand, simplifying the learning process for users. Similarly, for how-to video creation, it could elicit and describe the", + "bbox": [ + 511, + 763, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13639", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{\\dagger}$ Work conducted as an independent researcher \n $^{1}$ Project webpage: https://vision.cs.utexas.edu/projects/ProgressCaptioner.", + "bbox": [ + 89, + 862, + 480, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c058b9e88e2098a77521a3979eb43f8e0da6845a3366e4720de495cde682a4a5.jpg", + "image_caption": [ + "Figure 2. Use cases of video frame captioning: finer-grained captions enable detailed, step-by-step guidance for daily tasks." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 482, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "key object state changes at each stage (e.g., \"how to make whipped cream\")—useful for both content creators as well as visually-impaired users learning a new skill. See Fig. 2.", + "bbox": [ + 89, + 204, + 482, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Towards this end, we introduce a novel captioning task—progress-aware video captioning at the frame level. This task involves generating captions that not only coherently depict action progression but also tailor each description specifically to its corresponding frame.2 Our task is uniquely characterized by its demand for fine-grained temporal sensitivity. By \"fine-grained\", we refer to generating detailed descriptions that elucidate the stages or procedural steps of the action, effectively conveying how the action is performed throughout the video sequence.", + "bbox": [ + 88, + 250, + 482, + 400 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As discussed, traditional video captioning [9, 63, 70, 86] settles for broad event-level descriptions, where a description like scrambling eggs for the video in Figure 1 would be considered entirely accurate. In contrast, we seek progress-aware captions that detail each stage of the action, such as \"eggs still intact\", \"starting to cook\" and \"fully mixed\". While recent works [6, 8, 11, 12, 61, 83] enhance the overall descriptiveness of video captions, they continue to produce a single video-level description without distinguishing the nuances across time. Our task delves deeper, exploring how each frame contributes to the narrative of the action's progression, thereby setting a new standard for fine-grained temporal precision in video captioning.", + "bbox": [ + 89, + 402, + 482, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite great advancements of vision language models (VLMs) [2, 33, 37, 40-42, 62, 75, 81, 83] that have markedly improved visual captioning, we observe that these models still struggle with this nuanced task. Two main issues persist: first, the lack of temporally fine-grained captions; when shown adjacent frames that depict subtle variations in action progression (such as frames 2 and 3 in Figure 3), the generated captions can be overly coarse, failing to differentiate between the frames (see row 2, Gemini1.5-Pro's captions). Second, we identify and term a notable issue of \"temporal hallucination\", where the captions suggest temporal progression in disagreement with what the visual frames exhibit. See frame 2 of Figure 3, where GPT-4o's generated captions (row 1) incorrectly advance the action sequence. The prevalence of such errors can", + "bbox": [ + 89, + 599, + 482, + 825 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a475753a870a3e9e824c7bc301a9bed437a5862d538e247a9c59cead97161916.jpg", + "image_caption": [ + "Figure 3. Issues of existing VLMs in video frame captioning: (1) Lack of temporal granularity. See captions for frames 2 and 3, produced by Gemini-1.5-Pro (row 2), which fail to distinguish subtle differences between the frames. (2) Temporal hallucination. See frame 2's caption produced by GPT-4o (row 1), which inaccurately suggests progression that is not visible." + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 903, + 304 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "be attributed to models' reliance on the common statistics of activity sequences, which mistakenly override matching specific statements to specific frames. Meanwhile, image captioners—even if trained with fine-grained annotations—treat frames in isolation and hence lack the temporal context to say what is progressing versus what is present.", + "bbox": [ + 511, + 406, + 905, + 497 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce ProgressCaptioner, a model for generating progress-aware frame-level video captions. Our approach uniquely interleaves pseudo labeling with two learning stages. Stage I develops a frame pair captioning model, and stage II extends this to full frame sequences. This process also creates the FrameCap training dataset, comprising action videos along with high-quality frame-wise captions, which are initially generated by an ensemble of VLMs and then filtered using our proposed evaluation methods.", + "bbox": [ + 511, + 497, + 905, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To assess the quality of frame-wise captions and benchmark ProgressCaptioner against leading VLMs, we introduce the FrameCapEval benchmark comprised of videos from four public video action datasets. ProgressCaptioner consistently outperforms leading open-source VLMs with a $1.8 \\times$ to $2.7 \\times$ improvement in caption quality and also achieves the highest selection rate in user studies, even surpassing the much larger proprietary models GPT-4o [2] and Gemini-1.5-Pro [53]. Finally, we highlight potential applications enabled by our advanced captions: keyframe selection and enhanced video understanding. We hope that our task, model, and benchmark can inspire future development in temporally fine-grained video captioning.", + "bbox": [ + 511, + 633, + 905, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 842, + 653, + 858 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Captioning Image captioning has been extensively studied in recent years [3, 13, 60, 76]. A related line of", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2Without loss of generality, we obtain the input frame sequence by uniformly sampling from the action clips at a fixed rate (1FPS). These frames may or may not demonstrate visual action progression from one to the next, demanding that the model discern the difference when generating progress-aware captions.", + "bbox": [ + 89, + 838, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13640", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "work is image difference captioning, where the task is to describe differences between two images [27, 48, 56] or sets of images [15]. Building on the success of generative models, recent benchmarks [4, 28, 77] challenge models to distinguish between two visually similar images, advancing fine-grained image understanding. However, all the above models are restricted to static (typically synthesized) image pairs and address coarse-grained differences like object presence or absence. Temporal intricacies—accurately describing how an action progresses—remain unexplored.", + "bbox": [ + 89, + 90, + 483, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Captioning Video captioning [1] aims to produce a single description that encapsulates a video clip. While traditional benchmarks [9, 63, 70, 86] offer a brief onesentence caption for each video, recent efforts expand this scope, extending captioning to hours-long videos [26], enriching the granularity of details [8, 11, 61], enhancing caption uniqueness [49], integrating a causal temporal narrative [46], or introducing LLM summarization [34].", + "bbox": [ + 89, + 244, + 483, + 366 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adjacent to traditional video captioning are the tasks of visual storytelling [25, 36] (creating a coherent story for a sequence of snapshots), dense video captioning [30, 74, 87] (temporal localization and captioning of all events in an untrimmed video), audio description [20-22] (detailed narrations of visual events in videos (e.g., movies) for visually impaired audiences), and video paragraph captioning [78] (producing a multi-sentence paragraph describing the video). However, all these works still address \"what is happening\" at a coarse-grained event level, e.g., noting that someone is making aSouffle within a specific time range. The ability to break down frame-level details—such as whisking egg whites, folding ingredients, and observing the souffle rising—is still lacking.", + "bbox": [ + 89, + 367, + 483, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Language Models Recent advancements in VLMs [2, 33, 37, 40-42, 62, 75, 81, 83] have greatly enhanced the capabilities of both image and video captioning. Despite their strong performance, VLMs often exhibit \"hallucination\" [19, 65], and preference learning [52, 84] has proven effective in mitigating this issue.", + "bbox": [ + 89, + 582, + 483, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared to image-LMs, video-LMs crucially require the integration of temporal dynamics understanding, spurring a series of work on evaluating temporal perception [18, 39, 43, 69]. While these assessments ensure that a model can generate an accurate overall video summary or answer general questions, they entail neither temporal localization nor discernment of fine-grained differences between frames. The OSCaR benchmark [47] focuses on object state change (OSC) captioning, yet it is limited to just three frames and specifically OSC videos, with models and captions not publicly released yet preventing direct comparison. Additionally, their approach relies on human annotation and a single advanced GPT model. In contrast, our approach features a scalable data collection pipeline that reduces reliance on these labor-intensive resources, employs", + "bbox": [ + 89, + 674, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/aa1341d9a86938e2680af0038c9c60327dbfe4c95497c53234fa5d70a87a6217.jpg", + "image_caption": [ + "Figure 4. Captioning outcomes using Gemini-1.5-Pro [53]." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 901, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "novel automatic evaluation tasks, and broadens the scope beyond OSC videos. Finally, unlike methods for long-form video and event localization with VLMs [10, 44, 54], our focus is distinctly more temporally fine-grained, concentrating on how individual frames evolve within a single event.", + "bbox": [ + 511, + 292, + 906, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 513, + 382, + 622, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We delve into the specific challenges of our progress-aware video frame captioning problem in Sec. 3.1 and outline ProgressCaptioner's development in Sec. 3.2.", + "bbox": [ + 511, + 407, + 906, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Progress-aware Video Frame Captioning", + "text_level": 1, + "bbox": [ + 511, + 464, + 862, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Formulation Our objective is to develop a captioning model that, given a video, produces accurate temporally fine-grained captions. Formally, for a sequence of $T$ frames, denoted as $\\mathcal{V} = \\{v_i\\}_{i=1}^T$ , the captioning model generates a corresponding sequence of captions $\\mathcal{C} = \\{c_i\\}_{c=1}^T$ , where each $c_i$ describes the $i$ -th frame $v_i$ (recall we sample at 1FPS). This captioning process has three key requirements: (1) Accuracy, where each caption $c_i$ must faithfully represent what is visually occurring in frame $v_i$ , without hallucinating from the context of other frames; (2) Temporal Specificity, where each caption $c_i$ specifically attends to $v_i$ , without being overly generic to be applicable to multiple frames in the sequence; (3) Progressive Coherence: The sequence of captions $\\{c_i\\}_{i=1}^T$ should build upon each other to reflect the essential changes in the action over time.", + "bbox": [ + 511, + 489, + 906, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FrameCap Dataset To train our captioning model, we require a dataset that pairs frame sequences $(\\mathcal{V})$ with corresponding captions $(\\mathcal{C})$ . Existing datasets [9, 63, 70, 86] provide only a single, generic caption for an entire video clip, lacking the frame-wise caption format we need. To address this gap and train our model, we develop the FrameCap dataset. Given the prohibitive expense of collecting human-labeled caption sequences as our ground truth $(\\mathcal{C})$ , especially at scale, we leverage leading VLMs as powerful tools to create a pseudo caption sequence $\\hat{\\mathcal{C}}$ from $\\mathcal{V}$ . For video sources, we refer to two large-scale datasets that focus on fine-grained human activities: HowToChange [72]", + "bbox": [ + 511, + 719, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13641", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ef23e90098191fdb05907c04b2c94526641d5fc51cfdbf298f8951d116133dc9.jpg", + "image_caption": [ + "Figure 5. Framework of ProgressCaptioner, designed in two stages. In Stage-I, we prepare frame pairs and generate corresponding caption pairs using multiple VLMs. Each pair undergoes our designed progression detection and caption matching evaluations, to decide if they are selected for model supervised fine-tuning or rejected, with the latter contributing to preference data to aid in model preference learning. The Stage-I model training then proceeds using this collected data. In Stage-II, the trained stage-I model labels frame sequences with a two-frame sliding window, in conjunction with other VLMs. These sequences are again assessed through progression detection and caption matching to classify them as selected or rejected. All collected data from both stages contribute to the final training of ProgressCaptioner." + ], + "image_footnote": [], + "bbox": [ + 148, + 90, + 836, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(featuring object state change videos from YouTube) and COIN [59] (featuring daily activities from YouTube).", + "bbox": [ + 89, + 395, + 482, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Caption Sequence Construction Prompting VLMs for our desired caption sequence is nontrivial. We identify two key problems: (1) Input considerations: how many context frames from $\\{v_i\\}_i^T$ should be provided? (2) Output assessment: what issues arise in VLM-generated captions, and how can we filter to retain only high-quality ones? To explore these questions, we conduct preliminary experiments by prompting leading VLMs to perform the frame-wise captioning task. We share our findings below.", + "bbox": [ + 89, + 431, + 483, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation I Intuitively, inputting all $T$ frames would seem best. However, current VLM capabilities do not support this extensive context. Specifically, providing too many frames at once often leads to descriptions that lack detail and exhibit temporal inaccuracies, with VLMs also risking memory overload, as similarly observed in [11]. Conversely, providing a single frame at a time reduces the task to image captioning, which is not optimal either, resulting in captions that lack temporal context and coherence.", + "bbox": [ + 89, + 573, + 482, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 4 shows a representative trial with Gemini-1.5-Pro [53]. Inputting the full sequence (case (a)) yields brief per-frame descriptions with temporal misalignment (i.e., the second caption erroneously describes what is visually occurring in the third frame). On the other hand, captioning frames in isolation (case (b)) removes essential temporal context, where the model mistakes the initial stage of a tennis serve for the follow-through of a forehand swing. These findings underscore the importance of finding a balanced approach and motivate us to adopt a frame pair as the stepping stone of our captioning model.", + "bbox": [ + 89, + 712, + 482, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation II Next, building upon the use of a frame", + "bbox": [ + 89, + 885, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pair $(v_{1}, v_{2})$ , is the caption pair $(\\hat{c}_{1}, \\hat{c}_{2})$ produced by existing VLMs of sufficient quality to be directly adopted? Our preliminary experiments reveal two main issues: (a) lack of temporal granularity, and (b) temporal hallucination, as showcased in Figure 3. To dissect these issues, we analyze the captions in relation to the visual progression between frames $v_{1}$ and $v_{2}$ . Specifically, if there is a visible progression from $v_{1}$ to $v_{2}$ (e.g., the slight peeling of a shrimp's shell from frame 2 to frame 3 in Figure 3), the captions should adequately reflect this change. Overly similar captions in such a scenario signify a failure in temporal granularity. Conversely, when there is no change between frames (e.g. frames 1 and 2 in Figure 3), the captions should remain consistent. We deem it a temporal hallucination when captions erroneously indicate progression in disagreement with the visuals. This deficiency in existing VLMs motivates our development of a new captioning model and specialized evaluations for high-quality caption selection.", + "bbox": [ + 511, + 395, + 906, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. ProgressCaptioner", + "text_level": 1, + "bbox": [ + 513, + 678, + 692, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The observations above drive the design of our model, ProgressCaptioner, which unfolds in two stages. Based on our findings that current VLMs have trouble maintaining caption quality when handling extensive $T$ -frame inputs, our approach begins with frame pair captioning. In the first stage, we develop a ProgressCaptioner to excel at describing the nuances between adjacent frames. The second stage then leverages the first-stage model to pseudo label the full $T$ -frame sequence with a two-frame sliding window. This staged approach refines caption quality along with model development, enhancing the captioning process iteratively with more precise pseudo labels.", + "bbox": [ + 511, + 700, + 906, + 882 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Frame Pair Data Preparation Starting with a frame pair", + "bbox": [ + 511, + 885, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13642", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{v} = (v_{1}, v_{2})$ , we employ $K$ captioning models to generate an initial set of caption pairs $\\{(\\hat{c}_{1}, \\hat{c}_{2})\\}_{1}^{K}$ . Acknowledging the potential inaccuracies in these captions, as per observation II, we design two automatic evaluation tasks to assess caption quality. The first task, progression detection, examines progress awareness: it checks whether the captions appropriately reflect visual changes between $v_{1}$ and $v_{2}$ . Specifically, an LLM assesses each caption pair $(\\hat{c}_{1}, \\hat{c}_{2})_{k}$ to determine if they suggest a visible physical change. We utilize majority voting across multiple LLMs' assessments for all $K$ caption pairs to establish a consensus visual-change label. Caption pairs that align with this consensus are marked as passing; others are marked as failing.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For pairs passing progression detection, we proceed to our second evaluation task—caption matching—to assess how precisely $\\hat{c}_1$ and $\\hat{c}_2$ describe $v_1$ and $v_2$ , respectively. The task is designed as a multi-choice question format, where a VLM is given $\\hat{c}_1$ , $\\hat{c}_2$ , and an \"unsure\" option, and tasked with matching the correct caption to each frame. A caption pair is considered good if the evaluation VLM correctly identifies $\\hat{c}_1$ for $v_1$ and $\\hat{c}_2$ for $v_2$ . Because the captions will all be topically related, this is essentially a matching task with \"hard negatives\" that lets us automatically gauge the precision of the proposed captions for the target images.", + "bbox": [ + 89, + 287, + 480, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This automatic pipeline distinguishes between high-quality caption pairs, denoted by $\\hat{\\mathbf{c}}^{+} = (\\hat{c}_{1}^{+},\\hat{c}_{2}^{+})$ , and those that exhibit inaccuracies or hallucinations, denoted by $\\hat{\\mathbf{c}}^{-} = (\\hat{c}_{1}^{-},\\hat{c}_{2}^{-})$ , forming training data for Stage I.3", + "bbox": [ + 89, + 455, + 480, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage I Training Following the success of versatile VLMs in captioning tasks [34, 42, 61, 71], we initialize Progress-Captioner with the LLAVA-OV-7B [33] checkpoint to inherit its pretrained capabilities. Stage-I training utilizes frame and caption pair data collected on HowToChange and COIN YouTube videos $\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle$ through two principal methods: supervised fine-tuning (SFT) and direct preference optimization (DPO). The SFT process is straightforward given our dataset; we perform instructional tuning to tailor the general capabilities of the original VLM to our specific frame-wise captioning requirements using $\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+}\\rangle$ . The subsequent DPO step targets the prevalent issue of hallucination in VLMs and is innovatively driven by our proposed automatic evaluation critics. Preference optimization [52] in LLM training typically requires human-provided preference data to steer LLM responses towards more desirable outputs. Here, we employ progression detection and caption matching to automatically construct preference data $\\hat{\\mathbf{c}}^{+}$ and $\\hat{\\mathbf{c}}^{-}$ , eliminating the reliance on manual labeling. This preference data $\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle$ is adopted in DPO training to further enhance model performance with feedback from LLM and VLM evaluations.", + "bbox": [ + 89, + 518, + 482, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frame Sequence Data Preparation The second stage expands our pseudo labeling scheme from 2 to $T$ frames, where our Stage-I ProgressCaptioner first generates captions using a two-frame sliding window. To increase data diversity and volume, we also incorporate captions produced by other VLMs, with both two-frame and full $T$ -frame contexts, since captions of low-quality are also useful (after undergoing our evaluation tasks, those that are rejected enrich the preference data). Once the initial set of caption sequences is generated, we conduct progression detection to identify $M$ visually distinct frames from the original $T$ -frame sequence, denoted as $\\mathcal{V}_M = \\{v_i\\}_{i=1}^M$ , using majority voting; $M$ varies based on the distinctiveness of each frame sequence's content. The caption matching task is then employed to encompass $M$ frames, with a selection pool of all $M$ captions, $\\hat{\\mathcal{C}}_M = \\{\\hat{c}_i\\}_{i=1}^M$ , plus an \"unsure\" option. A high-quality caption sequence $\\hat{\\mathcal{C}}^+$ is identified when the evaluation VLM correctly selects $\\hat{c}_i$ for $v_i$ across all frames. Conversely, a caption sequence is deemed problematic, $\\hat{\\mathcal{C}}^-$ , if the VLM incorrectly answers more than half of the caption selections. This process forms our Stage-II data.", + "bbox": [ + 511, + 90, + 903, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage II Training Following the same pipeline as stage I, ProgressCaptioner is first trained through SFT using data prepared during both stages, which includes frame-caption pairs $<\\mathbf{v}, \\hat{\\mathbf{c}}^{+}>$ and frame-caption sequences $<\\mathcal{V}, \\hat{\\mathcal{C}}^{+}>$ . Subsequently, we conduct DPO with preference data collected from both stages $<\\mathbf{v}, \\hat{\\mathbf{c}}^{+}, \\hat{\\mathbf{c}}^{-}>$ and $<\\mathcal{V}, \\hat{\\mathcal{C}}^{+}, \\hat{\\mathcal{C}}^{-}>$ to further refine performance and mitigate hallucination. This sequential approach results in our final captioning model, that accepts inputs ranging from 2 to $T$ frames. This flexibility allows users to control the temporal context, balancing the need for local frame-wise changes (smaller window) and global event progressions (larger window). The framework is illustrated in Figure 5.", + "bbox": [ + 511, + 411, + 903, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 623, + 643, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We tackle two questions below: (1) How to evaluate frameworkwise caption quality of existing models? And how does ProgressCaptioner perform? (Sec. 4.1); (2) What applications are enabled by precise progress-aware captions? (Sec. 4.2)", + "bbox": [ + 511, + 648, + 903, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Benchmarking Video Frame Captioning", + "text_level": 1, + "bbox": [ + 511, + 720, + 857, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benchmark Data Curation We establish the FrameCapEval benchmark, featuring videos from four action understanding datasets: HowToChange [72] and COIN [59] (on which ProgressCaptioner was trained), along with Penn Action [82] and Kinetics [7], which are unseen in training and serve to assess generalization capabilities. We are mindful of the single frame bias [32] and manually verify all videos to exclude sequences lacking fine-grained action progression. This process yields a final set of 684 videos.", + "bbox": [ + 511, + 746, + 903, + 881 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics We employ the automatic evalua", + "bbox": [ + 511, + 885, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3We encourage readers to view data examples provided in Supp. for a better understanding of our data refinement process, as well as details on pseudo labeling, prompts used, and the $K$ VLMs we employ.", + "bbox": [ + 89, + 862, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13643", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/193aa68adc4dcafa38d05082683920438b914a82c705930db9324fe4fd367842.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 143, + 90, + 250, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ec0f3016a56e9e5ae2e5bbdbbef1ea4c7a70791ac6834f72ca833d5626fa6244.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 90, + 357, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d97e58c1f897e399fe8d5441d46f38e2911e44a424711b7382ca9e76da973e6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 90, + 468, + 138 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[VILA] A person is using a tool to press down on a blue strip of material on the floor.", + "bbox": [ + 147, + 146, + 276, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[LLAVA-OV] Using a hammer, the person is tapping the plank into place, aligning it with the baseboard and securing it in position.", + "bbox": [ + 148, + 185, + 281, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[ProgressCaptioner] The person continues to work on the floor installation, adjusting the wooden plank near the base of the door.", + "bbox": [ + 148, + 244, + 277, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "They use their hands to press down on the plank.", + "bbox": [ + 148, + 292, + 279, + 311 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5a9930787c07b50f37b479b5b92ea8086efaf8aa367189b51c1d6ebef07decc8.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 140, + 337, + 251, + 398 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5cf44e48812041aab7f4989b9d70f73889899c75284ad03e802fb7f1ccced43a.jpg", + "image_caption": [ + "Figure 6. Qualitative comparisons of ProgressCaptioner with SOTA VLMs on three action sequences. For sequences (a) and (b), only the middle frame predictions are displayed. See Supp. for all models' predictions on full sequences and more examples. Inaccuracies in descriptions are highlighted in red. Even top VLMs often produce descriptions that misalign with the corresponding frames, while ProgressCaptioner delivers hallucination-free and temporally fine-grained captions, including phrases explicitly calling out progress (blue)." + ], + "image_footnote": [], + "bbox": [ + 253, + 337, + 357, + 398 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b103bfb9153ab78ca927d7d03b978ce94cc4ab800695daa57faff6710f3bb832.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 337, + 467, + 398 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f500e5bb089d20ee3417ec3170d2a04f4eed89610368fa953d91b7abfa26b738.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 513, + 90, + 617, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/622274eac135f4e64a400f4562630e4b3ea1c9f71eb66993d26560cc07f2eec1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 90, + 743, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/33396d83b80c54a1d97d35e82ccecaca6e31c83dd768994e7e74f23dd68106bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 90, + 867, + 138 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[LLAVA-OV] The tofu cubes are now being cooked in the pan. They have started to brown slightly on the edges, indicating they are being seared.", + "bbox": [ + 511, + 148, + 612, + 217 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[Gemini-1.5-Pro] The tofu cubes are being added to the pan, some are already sizzling in the oil.", + "bbox": [ + 511, + 227, + 611, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[ProgressCaptioner] In this frame, a hand is seen placing tofu cubes into a black frying pan. The pan is on a stove, and the tofu is being added to it, indicating the start of the cooking process.", + "bbox": [ + 511, + 286, + 614, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[GPT-4o] The tofu cubes are now visibly sizzling in the pan, beginning to develop a light golden hue on their surfaces.", + "bbox": [ + 642, + 148, + 746, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[LLAVA-Video] The tofu cubes are shown browning in the pan, with some pieces already turning golden brown while others are still pale.", + "bbox": [ + 642, + 217, + 746, + 285 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[ProgressCaptioner] This frame displays a close-up view of the same black frying pan filled with cubed tofu. The tofu pieces are evenly distributed throughout the pan, and there is no visible action taking place.", + "bbox": [ + 642, + 295, + 743, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[Idefics2] The tofu cubes are still browned, but they have a darker color.", + "bbox": [ + 772, + 148, + 861, + 186 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[Qwen2-VL] The tofu is being cooked in the pan.", + "bbox": [ + 772, + 198, + 864, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[ProgressCaptioner] The frame displays the same black frying pan filled with cubed tofu, but now the tofu has a golden-brown color, indicating that it has been cooked and is likely being fried. The tofu pieces appear crispy and well-cooked, suggesting that they have been in the pan for sometime.", + "bbox": [ + 772, + 237, + 870, + 393 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c4508c176cff0dc0d9d881e2af33913713e80192f573f89e02d3c8e733109bc5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelSizeHTCCOINPenn&K
CapProgCapProgCapProg
Proprietary models
Gemini-1.5-Pro [53] (img)-28.459.724.358.615.351.2
Gemini-1.5-Pro [53]-31.463.825.063.817.660.3
GPT-4o [2]-32.464.221.358.418.263.2
Open-source models
Idefics2 [31]8B2.054.42.952.212.550.9
VILA [40]8B6.953.65.148.215.951.4
Qwen2-VL [62]7B13.769.611.070.88.558.8
LLAVA-Video [83]7B3.959.38.853.09.751.8
LLAVA-OV [33] (img)7B5.956.317.655.411.955.5
LLAVA-OV [33]7B7.859.05.957.35.150.8
PL (VLM ensemble)-18.662.517.660.119.352.4
ProgressCaptioner (ours)7B37.373.632.366.131.363.7
", + "bbox": [ + 91, + 486, + 480, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Results on the FrameCapEval Benchmark, composed of video from four public datasets. Cap and Prog denote caption matching and progression detection accuracy, respectively. PL denotes the pseudo labeling baseline adopting filtered captions from multiple VLMs. ProgressCaptioner greatly outperforms SOTA open-source VLMs and even the leading proprietary models, despite being a 7B model. The best results are bolded and underlined, the second best are bolded, and the third best are italicized. The results confirm our model's generalizability from in-domain datasets (HTC for HowToChange and COIN) to external datasets not seen during training (Penn&K for Penn Action and Kinetics).", + "bbox": [ + 88, + 700, + 482, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion tasks of progression detection and caption matching (Sec. 3.2), reporting accuracy with Llama-3.1-70B", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fa5f53838a540ba5e032d2ab3323713ea0246ca621b54ffb2dc3568cdfe9b1d8.jpg", + "image_caption": [ + "Figure 7. User study results comparing ProgressCaptioner with top competitors show it as the most preferred model (see text)." + ], + "image_footnote": [], + "bbox": [ + 558, + 493, + 856, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Instruct [14] as the evaluation LLM and Gemini-1.5-Pro [53] as the evaluation VLM. Additionally, we enhance our evaluation with a user study of 15 participants, reporting the average selection rate. See Supp. for experiments on evaluation metric reliability and full user study details.", + "bbox": [ + 511, + 667, + 905, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines We evaluate an array of state-of-the-art VLMs, including two proprietary models, GPT-4o [2] and Gemini1.5-Pro [53], and five open-source models—Idefics2 [31], VILA [40], Qwen2-VL [62], LLAVA-Video [83], and LLAVA-OV [33]. We also include a pseudo labeling baseline using filtered captions produced by an ensemble of VLMs (Sec. 3), and image captioning baselines using Gemini-1.5-Pro and LLAVA-OV. We select open-source VLM variants with fewer than 10B parameters for computational efficiency and a fair comparison with our Progress", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13644", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2912ea9319633ffe89f419cb930ad89e2b0993fabc2014fd9f3f32f57b358da8.jpg", + "image_caption": [ + "Figure 8. ProgressCaptioner facilitates keyframe selection and enriches the selected keyframes with progress-aware descriptions." + ], + "image_footnote": [], + "bbox": [ + 194, + 88, + 803, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Captioner, which is an 7B model. The closed proprietary models are much larger and trained with much more extensive data; we include them as a useful reference point, but stress that they do not constitute an apples-to-apples comparison, to the disadvantage of our ProgressCaptioner.", + "bbox": [ + 89, + 308, + 483, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation ProgressCaptioner is constructed with SigLIP [80] as the vision encoder and Qwen2 [62] as the language model, linked through a projector, and initialized from the LLAVA-OV-7B checkpoint [33]. For benchmark evaluations in Sec. 4.1, ProgressCaptioner operates on the full $T$ -frame sequence for a comprehensive temporal context. For applications presented in Sec. 4.2, where fine-grained analysis of local frame changes is crucial, a sliding window approach is used, with the model processing frame pairs. To ensure a fair comparison, all video baseline models are provided with the same temporal context as ProgressCaptioner across all evaluations.", + "bbox": [ + 89, + 391, + 483, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results As shown in Table 1, on the FrameCapEval benchmark, ProgressCaptioner greatly outperforms existing open-source VLMs of similar capacity and even the (much larger) latest Gemini-1.5-Pro and GPT-4o. We observe that strong language-backed VLMs like GPT-4o show high caption matching accuracy, whereas Qwen2-VL excels in progression detection, reducing hallucination. However, it tends to produce less detailed captions, leading to lower caption matching accuracy. In contrast, ProgressCaptioner effectively balances precision and detail in frame-wise captioning, consistently leading the benchmark across both indomain and out-of-domain datasets.", + "bbox": [ + 89, + 579, + 483, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 6 provides qualitative comparisons on three action sequences. Consider the (a) bowling sequence for instance: baseline models erroneously suggest progression in frame 2, like \"arm forward\", exemplifying the common issue of temporal hallucination in current VLMs. This issue recurs in the other two sequences. Conversely, ProgressCaptioner delivers high-quality captions that precisely characterize action progress in each frame. See Supp. for more qualitative examples and an ablation of ProgressCaptioner.", + "bbox": [ + 89, + 763, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study Figure 7 presents the user study results, where ProgressCaptioner is compared against four of the strongest competitors: LLAVA-OV, Qwen2-VL, Gemini-1.5-Pro and GPT-4o. Each participant is presented with five captions produced by these models and is tasked with selecting the top-2, with an additional \"none\" option if the captions are deemed inadequate. ProgressCaptioner emerges as the most preferred model, with an average best caption selection rate of $31.6\\% - 2 \\times$ to $3.6 \\times$ better than the comparably sized best models from the literature [33, 62], and even surpassing top-tier proprietary models that enjoy significant scaling advantages. While our model outperforms all open-source and proprietary models for top-1 preference, the more forgiving top-2 metric brings the proprietary closed models back in the game, though our model remains competitive even there (50.3% for GPT-4o vs. 47.3% for ours). These findings underscore our model's strong ability to produce accurate, temporally fine-grained captions.", + "bbox": [ + 511, + 308, + 906, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Applications of Video Frame Captioning", + "text_level": 1, + "bbox": [ + 511, + 595, + 862, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ProgressCaptioner offers progress-aware frame-wise captions, which hold great potential for many real-world applications. We explore several practical use-cases below.", + "bbox": [ + 511, + 619, + 906, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Keyframe Selection Our first use-case leverages ProgressCaptioner's temporally precise captions as an intermediate representation to identify keyframes within a densely sampled sequence, aided by an LLM (see Supp. for details). Figure 8 provides two examples, showcasing how ProgressCaptioner's produced captions allow selecting distinct frames that effectively capture different stages of the welding and squeezing grapefruit action. While recent video summarization work [24] explores using VLMs and LLMs for keyframe selection, it aims to identify coarse-grained events within long videos, which is not adequate for our problem scenario. See Supp. for a side-to-side comparison and more qualitatives that underscore this distinction.", + "bbox": [ + 511, + 670, + 908, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Keyframes for Action Recognition Not only is keyframe selection useful for human viewers to quickly preview a", + "bbox": [ + 511, + 869, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13645", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6138d919ae380b527566d5e0792f46ba974184174eacd80aa2d9057af94d8b23.jpg", + "image_caption": [ + "Figure 9. On Kinetics test videos, ProgressCaptioner selects four frames that are more informative of the action than uniform sampling, resulting in improved action recognition accuracy." + ], + "image_footnote": [], + "bbox": [ + 112, + 89, + 460, + 202 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "longer video, but it can also extract the most informative portions of a video to benefit activity recognition [29]. To illustrate, we next apply our keyframe selection mechanism to Kinetics [7] Temporal [57] subset that necessitates multi-frame reasoning. Given that the original video clips are short (sampled at 1FPS, resulting in sequences of 10 frames), we employ two models that take four frames as input: Slow backbone from SlowFast [17] and X3D-XS [16]. We prompt GPT-4o to select four representative frames from frame-wise captions produced by ProgressCaptioner. We take the two model checkpoints that have been trained on the Kinetics training set and replace uniformly sampled frames with our selected keyframes during inference. Figure 9 presents a qualitative comparison, highlighting performance gains such as a $+1.7\\%$ increase in top-1 accuracy for both SlowFast and X3D models. Even among just 10 candidate frames, our method's fine-grained ability to identify the 4 most informative ones translates into better recognition.", + "bbox": [ + 91, + 261, + 483, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Advancing Video Understanding The precise, framewise captions generated by ProgressCaptioner enhance our understanding of videos. To demonstrate this, we consider two video tasks that demand temporally fine-grained understanding: (1) frame-wise classification on HowToChange [72] and Penn Action [82], and (2) video question answering (QA) on NExT-QA [69] (ATP-Hard [5]). These tasks are chosen because they challenge the model to comprehend not just the overarching content of a video, but also the more fine-grained event progression within a video. The HowToChange and Penn Action test sets provide frame-wise labels detailing object state changes or action phases, requiring frame-level understanding. Similarly, NexTQA (ATP-Hard) poses temporally challenging questions that demand multi-frame reasoning, such as determining event order, emphasizing the need for precise temporal comprehension. For baseline comparisons, we evaluate against the LLAVA-OV-7B [33] model, from which ProgressCaptioner is initialized, to highlight the enhancements that our specialized training on FrameCap brings to video understanding tasks. For the first task, as we pioneer a zero-shot, language-guided approach to this traditionally vision-centric problem (details below), no other zero-shot baselines exist. For the second task, we compare ProgressCap", + "bbox": [ + 91, + 537, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e59679fe7f106c6012fe5b6bdbfcb03513eb02f1820bbcf995ec58f4006edc65.jpg", + "image_caption": [ + "Figure 10. ProgressCaptioner delivers precise and detailed per-frame descriptions, leading to enhanced zero-shot frame-wise classification performance when compared with LLAVA-OV." + ], + "image_footnote": [], + "bbox": [ + 535, + 92, + 879, + 210 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0505d52028a89b773e8676ad703e6bc5bbd454f76e11989b2b5596dc1775b252.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelAcc@CAcc@TAcc@All
VFC [45]32.230.031.4
VideoAgent [64]57.858.858.4
LLAVA-OV [33] + GPT-4o62.653.458.8
ProgressCaptioner + GPT-4o (ours)64.458.161.8
", + "bbox": [ + 527, + 263, + 890, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Video QA results on NExT-QA (ATP-Hard). C and T denote causal and temporal subsets, respectively.", + "bbox": [ + 511, + 338, + 906, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "titioner against two existing zero-shot approaches [45, 64].", + "bbox": [ + 511, + 375, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) Zero-shot Frame Classification We repurpose zero-shot frame-wise classification task into a multi-choice QA format, using frame-wise captions to guide an LLM in identifying the correct label per frame, evaluating caption accuracy and granularity (Figure 10 left). Results (Figure 10 right) show that ProgressCaptioner consistently outperforms LLAVA-OV across both datasets. Notably, our training involves no signals related to these frame-wise labels, underscoring its generalizability and effectiveness in enhancing video frame-level understanding.", + "bbox": [ + 511, + 391, + 905, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(b) Video QA Finally, we report results using frame-wise descriptions for video QA, where an LLM (we use GPT-4o) is employed to answer questions on NExT-QA (ATP-Hard) set. As shown in Table 2, ProgressCaptioner achieves the best results on this benchmark, outperforming the previous leader VideoAgent [64] by $+3.4\\%$ . Compared with a similar setup using LLAVA-OV, ProgressCaptioner achieves a $+4.7\\%$ gain in the temporal subset, highlighting its superior ability to produce fine-grained, temporally precise descriptions and bring enhanced video understanding.", + "bbox": [ + 511, + 544, + 906, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 709, + 633, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce progress-aware video frame captioning, which necessitates a significant enhancement in current captioning models' capability to describe temporal action dynamics. Towards this end, we develop ProgressCaptioner and show its effectiveness in enhancing the temporal precision and alignment of captions with corresponding frames. Furthermore, we demonstrate its practical applications: keyframe selection and enhanced video understanding. By setting a new standard for temporal precision in video captioning, we hope our work inspires further development in this domain.", + "bbox": [ + 511, + 734, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13646", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 256, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Research supported in part by the IFML NSF AI Institute.", + "bbox": [ + 91, + 114, + 473, + 130 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 143, + 187, + 157 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Moloud Abdar, Meenakshi Kollati, Swaraja Kuraparthi, Farhad Pourpanah, Daniel McDuff, Mohammad Ghavamzadeh, Shuicheng Yan, Abduallah Mohamed, Abbas Khosravi, Erik Cambria, et al. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 18243-18252, 2024. 3", + "bbox": [ + 545, + 90, + 906, + 133 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "13650", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_model.json b/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_model.json new file mode 100644 index 0000000000000000000000000000000000000000..48b266bab4bc4d4d30529cff57f8e9396700352c --- /dev/null +++ b/2025/Progress-Aware Video Frame Captioning/1ef336dd-a39c-4288-9c6c-56f22b842b12_model.json @@ -0,0 +1,2787 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.29, + 0.131, + 0.709, + 0.154 + ], + "angle": 0, + "content": "Progress-Aware Video Frame Captioning" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.18, + 0.741, + 0.217 + ], + "angle": 0, + "content": "Zihui Xue\\(^{1}\\), Joungbin An\\(^{1}\\), Xitong Yang\\(^{\\dagger}\\), Kristen Grauman\\(^{1}\\) \n\\(^{1}\\)University of Texas at Austin" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.252, + 0.327, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.284, + 0.485, + 0.617 + ], + "angle": 0, + "content": "While image captioning provides isolated descriptions for individual images, and video captioning offers one single narrative for an entire video clip, our work explores an important middle ground: progress-aware video captioning at the frame level. This novel task aims to generate temporally fine-grained captions that not only accurately describe each frame but also capture the subtle progression of actions throughout a video sequence. Despite the strong capabilities of existing leading vision language models, they often struggle to discern the nuances of frame-wise differences. To address this, we propose ProgressCaptioner, a captioning model designed to capture the fine-grained temporal dynamics within an action sequence. Alongside, we develop the FrameCap dataset to support training and the FrameCapEval benchmark to assess caption quality. The results demonstrate that ProgressCaptioner significantly surpasses leading captioning models, producing precise captions that accurately capture action progression and set a new standard for temporal precision in video captioning. Finally, we showcase practical applications of our approach, specifically in aiding keyframe selection and advancing video understanding, highlighting its broad utility." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.645, + 0.222, + 0.66 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.671, + 0.483, + 0.837 + ], + "angle": 0, + "content": "Visual captioning [38]—the task of generating textual descriptions of visual content—is a fundamental problem in computer vision with extensive practical applications. Existing captioning paradigms are broadly divided into two categories: image captioning and video captioning, with a clear distinction between them. Image captioning [23] generates a single, isolated description for each image, with no contextual linkage among different images. In contrast, video captioning [1] assigns a single caption for the entire video clip, aggregating information across frames without addressing the specifics of individual frames." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.838, + 0.482, + 0.853 + ], + "angle": 0, + "content": "Figure 1 illustrates this dichotomy. Employing an im" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.25, + 0.613, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.298, + 0.605, + 0.315 + ], + "angle": 0, + "content": "a close up of a wok with a lot of oil in it" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.25, + 0.709, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.298, + 0.7, + 0.315 + ], + "angle": 0, + "content": "Eggs are fried in a wok on a stove top" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.25, + 0.805, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.298, + 0.794, + 0.315 + ], + "angle": 0, + "content": "cooking eggs in a wok on the stove" + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.25, + 0.902, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.298, + 0.89, + 0.315 + ], + "angle": 0, + "content": "cooking food in a wok on the stove" + }, + { + "type": "image_caption", + "bbox": [ + 0.818, + 0.319, + 0.899, + 0.33 + ], + "angle": 0, + "content": "Image captioning" + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.333, + 0.769, + 0.342 + ], + "angle": 0, + "content": "Scramble the eggs in the wok" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.358, + 0.605, + 0.44 + ], + "angle": 0, + "content": "The frame shows a large, worn-out wok with a dark interior. There is a small amount of oil visible at the bottom of the wok, indicating that it is ready for cooking." + }, + { + "type": "text", + "bbox": [ + 0.621, + 0.358, + 0.7, + 0.439 + ], + "angle": 0, + "content": "Three eggs are being added into the wok. The eggs are still intact and have bright yellow yolks. The wok remains in the same position as in the first frame." + }, + { + "type": "text", + "bbox": [ + 0.717, + 0.358, + 0.793, + 0.439 + ], + "angle": 0, + "content": "A metal spatula is used to stir the eggs. The eggs are starting to cook, with some white parts becoming more solid while others remain runny." + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.344, + 0.899, + 0.353 + ], + "angle": 0, + "content": "Video captioning" + }, + { + "type": "text", + "bbox": [ + 0.814, + 0.359, + 0.891, + 0.439 + ], + "angle": 0, + "content": "The scene transitions to show the same wok, now containing scrambled eggs. The yolks are fully mixed into the whites." + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.443, + 0.898, + 0.453 + ], + "angle": 0, + "content": "Progress-aware video frame captioning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.907, + 0.577 + ], + "angle": 0, + "content": "Figure 1. We propose progress-aware video frame captioning (bottom), which aims to generate a sequence of captions that capture the temporal dynamics within a video. Unlike traditional image and video captioning (top) that focus on broad event-level descriptions, our task delves into the detailed, progressive dynamics of an action, necessitating precise, temporally fine-grained capabilities. Blue text highlights how the progress-aware captions build successively on the earlier content to highlight what is changing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.907, + 0.761 + ], + "angle": 0, + "content": "age captioning model like BLIP [37] to describe each frame of the video results in captions that are local, not temporally context-aware, and may exhibit little variation across the sequence. Conversely, video captioning provides a global, not temporally fine-grained overview of the event, as exemplified by the YouCook2 [85] ground truth label \"scramble the eggs in the wok\". In both scenarios, the nuances of how the action unfolds over time are missed. This raises the question: Can we develop temporally fine-grained captions that capture the subtle, progressive nature of action sequences? Figure 1 (bottom) illustrates what we seek." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Having such progress-aware captions could benefit a great variety of downstream tasks, bringing improved video understanding [73, 79], more precise video retrieval [66-68], and enriched video generation [50, 58]. Moreover, such a capability could open up new AR/VR and robotics applications. For instance, in AI coaching, a captioning system could meticulously analyze an expert's tennis forehand, simplifying the learning process for users. Similarly, for how-to video creation, it could elicit and describe the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13639" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.863, + 0.482, + 0.901 + ], + "angle": 0, + "content": "\\(^{\\dagger}\\)Work conducted as an independent researcher \n\\(^{1}\\)Project webpage: https://vision.cs.utexas.edu/projects/ProgressCaptioner." + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.483, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.166, + 0.483, + 0.195 + ], + "angle": 0, + "content": "Figure 2. Use cases of video frame captioning: finer-grained captions enable detailed, step-by-step guidance for daily tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.205, + 0.483, + 0.25 + ], + "angle": 0, + "content": "key object state changes at each stage (e.g., \"how to make whipped cream\")—useful for both content creators as well as visually-impaired users learning a new skill. See Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.251, + 0.483, + 0.401 + ], + "angle": 0, + "content": "Towards this end, we introduce a novel captioning task—progress-aware video captioning at the frame level. This task involves generating captions that not only coherently depict action progression but also tailor each description specifically to its corresponding frame.2 Our task is uniquely characterized by its demand for fine-grained temporal sensitivity. By \"fine-grained\", we refer to generating detailed descriptions that elucidate the stages or procedural steps of the action, effectively conveying how the action is performed throughout the video sequence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.403, + 0.483, + 0.599 + ], + "angle": 0, + "content": "As discussed, traditional video captioning [9, 63, 70, 86] settles for broad event-level descriptions, where a description like scrambling eggs for the video in Figure 1 would be considered entirely accurate. In contrast, we seek progress-aware captions that detail each stage of the action, such as \"eggs still intact\", \"starting to cook\" and \"fully mixed\". While recent works [6, 8, 11, 12, 61, 83] enhance the overall descriptiveness of video captions, they continue to produce a single video-level description without distinguishing the nuances across time. Our task delves deeper, exploring how each frame contributes to the narrative of the action's progression, thereby setting a new standard for fine-grained temporal precision in video captioning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.601, + 0.483, + 0.827 + ], + "angle": 0, + "content": "Despite great advancements of vision language models (VLMs) [2, 33, 37, 40-42, 62, 75, 81, 83] that have markedly improved visual captioning, we observe that these models still struggle with this nuanced task. Two main issues persist: first, the lack of temporally fine-grained captions; when shown adjacent frames that depict subtle variations in action progression (such as frames 2 and 3 in Figure 3), the generated captions can be overly coarse, failing to differentiate between the frames (see row 2, Gemini1.5-Pro's captions). Second, we identify and term a notable issue of \"temporal hallucination\", where the captions suggest temporal progression in disagreement with what the visual frames exhibit. See frame 2 of Figure 3, where GPT-4o's generated captions (row 1) incorrectly advance the action sequence. The prevalence of such errors can" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.091, + 0.905, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.317, + 0.907, + 0.402 + ], + "angle": 0, + "content": "Figure 3. Issues of existing VLMs in video frame captioning: (1) Lack of temporal granularity. See captions for frames 2 and 3, produced by Gemini-1.5-Pro (row 2), which fail to distinguish subtle differences between the frames. (2) Temporal hallucination. See frame 2's caption produced by GPT-4o (row 1), which inaccurately suggests progression that is not visible." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.407, + 0.906, + 0.498 + ], + "angle": 0, + "content": "be attributed to models' reliance on the common statistics of activity sequences, which mistakenly override matching specific statements to specific frames. Meanwhile, image captioners—even if trained with fine-grained annotations—treat frames in isolation and hence lack the temporal context to say what is progressing versus what is present." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.906, + 0.634 + ], + "angle": 0, + "content": "We introduce ProgressCaptioner, a model for generating progress-aware frame-level video captions. Our approach uniquely interleaves pseudo labeling with two learning stages. Stage I develops a frame pair captioning model, and stage II extends this to full frame sequences. This process also creates the FrameCap training dataset, comprising action videos along with high-quality frame-wise captions, which are initially generated by an ensemble of VLMs and then filtered using our proposed evaluation methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.634, + 0.906, + 0.831 + ], + "angle": 0, + "content": "To assess the quality of frame-wise captions and benchmark ProgressCaptioner against leading VLMs, we introduce the FrameCapEval benchmark comprised of videos from four public video action datasets. ProgressCaptioner consistently outperforms leading open-source VLMs with a \\(1.8 \\times\\) to \\(2.7 \\times\\) improvement in caption quality and also achieves the highest selection rate in user studies, even surpassing the much larger proprietary models GPT-4o [2] and Gemini-1.5-Pro [53]. Finally, we highlight potential applications enabled by our advanced captions: keyframe selection and enhanced video understanding. We hope that our task, model, and benchmark can inspire future development in temporally fine-grained video captioning." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.843, + 0.655, + 0.859 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Image Captioning Image captioning has been extensively studied in recent years [3, 13, 60, 76]. A related line of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.839, + 0.483, + 0.902 + ], + "angle": 0, + "content": "2Without loss of generality, we obtain the input frame sequence by uniformly sampling from the action clips at a fixed rate (1FPS). These frames may or may not demonstrate visual action progression from one to the next, demanding that the model discern the difference when generating progress-aware captions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13640" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.243 + ], + "angle": 0, + "content": "work is image difference captioning, where the task is to describe differences between two images [27, 48, 56] or sets of images [15]. Building on the success of generative models, recent benchmarks [4, 28, 77] challenge models to distinguish between two visually similar images, advancing fine-grained image understanding. However, all the above models are restricted to static (typically synthesized) image pairs and address coarse-grained differences like object presence or absence. Temporal intricacies—accurately describing how an action progresses—remain unexplored." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.246, + 0.484, + 0.367 + ], + "angle": 0, + "content": "Video Captioning Video captioning [1] aims to produce a single description that encapsulates a video clip. While traditional benchmarks [9, 63, 70, 86] offer a brief onesentence caption for each video, recent efforts expand this scope, extending captioning to hours-long videos [26], enriching the granularity of details [8, 11, 61], enhancing caption uniqueness [49], integrating a causal temporal narrative [46], or introducing LLM summarization [34]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.368, + 0.484, + 0.58 + ], + "angle": 0, + "content": "Adjacent to traditional video captioning are the tasks of visual storytelling [25, 36] (creating a coherent story for a sequence of snapshots), dense video captioning [30, 74, 87] (temporal localization and captioning of all events in an untrimmed video), audio description [20-22] (detailed narrations of visual events in videos (e.g., movies) for visually impaired audiences), and video paragraph captioning [78] (producing a multi-sentence paragraph describing the video). However, all these works still address \"what is happening\" at a coarse-grained event level, e.g., noting that someone is making aSouffle within a specific time range. The ability to break down frame-level details—such as whisking egg whites, folding ingredients, and observing the souffle rising—is still lacking." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.484, + 0.674 + ], + "angle": 0, + "content": "Vision Language Models Recent advancements in VLMs [2, 33, 37, 40-42, 62, 75, 81, 83] have greatly enhanced the capabilities of both image and video captioning. Despite their strong performance, VLMs often exhibit \"hallucination\" [19, 65], and preference learning [52, 84] has proven effective in mitigating this issue." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Compared to image-LMs, video-LMs crucially require the integration of temporal dynamics understanding, spurring a series of work on evaluating temporal perception [18, 39, 43, 69]. While these assessments ensure that a model can generate an accurate overall video summary or answer general questions, they entail neither temporal localization nor discernment of fine-grained differences between frames. The OSCaR benchmark [47] focuses on object state change (OSC) captioning, yet it is limited to just three frames and specifically OSC videos, with models and captions not publicly released yet preventing direct comparison. Additionally, their approach relies on human annotation and a single advanced GPT model. In contrast, our approach features a scalable data collection pipeline that reduces reliance on these labor-intensive resources, employs" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.903, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.269, + 0.885, + 0.283 + ], + "angle": 0, + "content": "Figure 4. Captioning outcomes using Gemini-1.5-Pro [53]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.293, + 0.907, + 0.368 + ], + "angle": 0, + "content": "novel automatic evaluation tasks, and broadens the scope beyond OSC videos. Finally, unlike methods for long-form video and event localization with VLMs [10, 44, 54], our focus is distinctly more temporally fine-grained, concentrating on how individual frames evolve within a single event." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.383, + 0.623, + 0.4 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.408, + 0.907, + 0.454 + ], + "angle": 0, + "content": "We delve into the specific challenges of our progress-aware video frame captioning problem in Sec. 3.1 and outline ProgressCaptioner's development in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.465, + 0.864, + 0.481 + ], + "angle": 0, + "content": "3.1. Progress-aware Video Frame Captioning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.49, + 0.907, + 0.717 + ], + "angle": 0, + "content": "Problem Formulation Our objective is to develop a captioning model that, given a video, produces accurate temporally fine-grained captions. Formally, for a sequence of \\( T \\) frames, denoted as \\( \\mathcal{V} = \\{v_i\\}_{i=1}^T \\), the captioning model generates a corresponding sequence of captions \\( \\mathcal{C} = \\{c_i\\}_{c=1}^T \\), where each \\( c_i \\) describes the \\( i \\)-th frame \\( v_i \\) (recall we sample at 1FPS). This captioning process has three key requirements: (1) Accuracy, where each caption \\( c_i \\) must faithfully represent what is visually occurring in frame \\( v_i \\), without hallucinating from the context of other frames; (2) Temporal Specificity, where each caption \\( c_i \\) specifically attends to \\( v_i \\), without being overly generic to be applicable to multiple frames in the sequence; (3) Progressive Coherence: The sequence of captions \\( \\{c_i\\}_{i=1}^T \\) should build upon each other to reflect the essential changes in the action over time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.902 + ], + "angle": 0, + "content": "FrameCap Dataset To train our captioning model, we require a dataset that pairs frame sequences \\((\\mathcal{V})\\) with corresponding captions \\((\\mathcal{C})\\). Existing datasets [9, 63, 70, 86] provide only a single, generic caption for an entire video clip, lacking the frame-wise caption format we need. To address this gap and train our model, we develop the FrameCap dataset. Given the prohibitive expense of collecting human-labeled caption sequences as our ground truth \\((\\mathcal{C})\\), especially at scale, we leverage leading VLMs as powerful tools to create a pseudo caption sequence \\(\\hat{\\mathcal{C}}\\) from \\(\\mathcal{V}\\). For video sources, we refer to two large-scale datasets that focus on fine-grained human activities: HowToChange [72]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13641" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.15, + 0.092, + 0.837, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.3, + 0.907, + 0.386 + ], + "angle": 0, + "content": "Figure 5. Framework of ProgressCaptioner, designed in two stages. In Stage-I, we prepare frame pairs and generate corresponding caption pairs using multiple VLMs. Each pair undergoes our designed progression detection and caption matching evaluations, to decide if they are selected for model supervised fine-tuning or rejected, with the latter contributing to preference data to aid in model preference learning. The Stage-I model training then proceeds using this collected data. In Stage-II, the trained stage-I model labels frame sequences with a two-frame sliding window, in conjunction with other VLMs. These sequences are again assessed through progression detection and caption matching to classify them as selected or rejected. All collected data from both stages contribute to the final training of ProgressCaptioner." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.396, + 0.483, + 0.426 + ], + "angle": 0, + "content": "(featuring object state change videos from YouTube) and COIN [59] (featuring daily activities from YouTube)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.432, + 0.484, + 0.569 + ], + "angle": 0, + "content": "Caption Sequence Construction Prompting VLMs for our desired caption sequence is nontrivial. We identify two key problems: (1) Input considerations: how many context frames from \\(\\{v_i\\}_i^T\\) should be provided? (2) Output assessment: what issues arise in VLM-generated captions, and how can we filter to retain only high-quality ones? To explore these questions, we conduct preliminary experiments by prompting leading VLMs to perform the frame-wise captioning task. We share our findings below." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.574, + 0.483, + 0.71 + ], + "angle": 0, + "content": "Observation I Intuitively, inputting all \\( T \\) frames would seem best. However, current VLM capabilities do not support this extensive context. Specifically, providing too many frames at once often leads to descriptions that lack detail and exhibit temporal inaccuracies, with VLMs also risking memory overload, as similarly observed in [11]. Conversely, providing a single frame at a time reduces the task to image captioning, which is not optimal either, resulting in captions that lack temporal context and coherence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.713, + 0.483, + 0.88 + ], + "angle": 0, + "content": "Figure 4 shows a representative trial with Gemini-1.5-Pro [53]. Inputting the full sequence (case (a)) yields brief per-frame descriptions with temporal misalignment (i.e., the second caption erroneously describes what is visually occurring in the third frame). On the other hand, captioning frames in isolation (case (b)) removes essential temporal context, where the model mistakes the initial stage of a tennis serve for the follow-through of a forehand swing. These findings underscore the importance of finding a balanced approach and motivate us to adopt a frame pair as the stepping stone of our captioning model." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Observation II Next, building upon the use of a frame" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.396, + 0.907, + 0.669 + ], + "angle": 0, + "content": "pair \\((v_{1}, v_{2})\\), is the caption pair \\((\\hat{c}_{1}, \\hat{c}_{2})\\) produced by existing VLMs of sufficient quality to be directly adopted? Our preliminary experiments reveal two main issues: (a) lack of temporal granularity, and (b) temporal hallucination, as showcased in Figure 3. To dissect these issues, we analyze the captions in relation to the visual progression between frames \\(v_{1}\\) and \\(v_{2}\\). Specifically, if there is a visible progression from \\(v_{1}\\) to \\(v_{2}\\) (e.g., the slight peeling of a shrimp's shell from frame 2 to frame 3 in Figure 3), the captions should adequately reflect this change. Overly similar captions in such a scenario signify a failure in temporal granularity. Conversely, when there is no change between frames (e.g. frames 1 and 2 in Figure 3), the captions should remain consistent. We deem it a temporal hallucination when captions erroneously indicate progression in disagreement with the visuals. This deficiency in existing VLMs motivates our development of a new captioning model and specialized evaluations for high-quality caption selection." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.679, + 0.694, + 0.695 + ], + "angle": 0, + "content": "3.2. ProgressCaptioner" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.702, + 0.907, + 0.883 + ], + "angle": 0, + "content": "The observations above drive the design of our model, ProgressCaptioner, which unfolds in two stages. Based on our findings that current VLMs have trouble maintaining caption quality when handling extensive \\( T \\)-frame inputs, our approach begins with frame pair captioning. In the first stage, we develop a ProgressCaptioner to excel at describing the nuances between adjacent frames. The second stage then leverages the first-stage model to pseudo label the full \\( T \\)-frame sequence with a two-frame sliding window. This staged approach refines caption quality along with model development, enhancing the captioning process iteratively with more precise pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Frame Pair Data Preparation Starting with a frame pair" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13642" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "\\(\\mathbf{v} = (v_{1}, v_{2})\\), we employ \\(K\\) captioning models to generate an initial set of caption pairs \\(\\{(\\hat{c}_{1}, \\hat{c}_{2})\\}_{1}^{K}\\). Acknowledging the potential inaccuracies in these captions, as per observation II, we design two automatic evaluation tasks to assess caption quality. The first task, progression detection, examines progress awareness: it checks whether the captions appropriately reflect visual changes between \\(v_{1}\\) and \\(v_{2}\\). Specifically, an LLM assesses each caption pair \\((\\hat{c}_{1}, \\hat{c}_{2})_{k}\\) to determine if they suggest a visible physical change. We utilize majority voting across multiple LLMs' assessments for all \\(K\\) caption pairs to establish a consensus visual-change label. Caption pairs that align with this consensus are marked as passing; others are marked as failing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.482, + 0.456 + ], + "angle": 0, + "content": "For pairs passing progression detection, we proceed to our second evaluation task—caption matching—to assess how precisely \\(\\hat{c}_1\\) and \\(\\hat{c}_2\\) describe \\(v_1\\) and \\(v_2\\), respectively. The task is designed as a multi-choice question format, where a VLM is given \\(\\hat{c}_1\\), \\(\\hat{c}_2\\), and an \"unsure\" option, and tasked with matching the correct caption to each frame. A caption pair is considered good if the evaluation VLM correctly identifies \\(\\hat{c}_1\\) for \\(v_1\\) and \\(\\hat{c}_2\\) for \\(v_2\\). Because the captions will all be topically related, this is essentially a matching task with \"hard negatives\" that lets us automatically gauge the precision of the proposed captions for the target images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.482, + 0.517 + ], + "angle": 0, + "content": "This automatic pipeline distinguishes between high-quality caption pairs, denoted by \\(\\hat{\\mathbf{c}}^{+} = (\\hat{c}_{1}^{+},\\hat{c}_{2}^{+})\\) , and those that exhibit inaccuracies or hallucinations, denoted by \\(\\hat{\\mathbf{c}}^{-} = (\\hat{c}_{1}^{-},\\hat{c}_{2}^{-})\\) , forming training data for Stage I.3" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.483, + 0.852 + ], + "angle": 0, + "content": "Stage I Training Following the success of versatile VLMs in captioning tasks [34, 42, 61, 71], we initialize Progress-Captioner with the LLAVA-OV-7B [33] checkpoint to inherit its pretrained capabilities. Stage-I training utilizes frame and caption pair data collected on HowToChange and COIN YouTube videos \\(\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle\\) through two principal methods: supervised fine-tuning (SFT) and direct preference optimization (DPO). The SFT process is straightforward given our dataset; we perform instructional tuning to tailor the general capabilities of the original VLM to our specific frame-wise captioning requirements using \\(\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+}\\rangle\\). The subsequent DPO step targets the prevalent issue of hallucination in VLMs and is innovatively driven by our proposed automatic evaluation critics. Preference optimization [52] in LLM training typically requires human-provided preference data to steer LLM responses towards more desirable outputs. Here, we employ progression detection and caption matching to automatically construct preference data \\(\\hat{\\mathbf{c}}^{+}\\) and \\(\\hat{\\mathbf{c}}^{-}\\), eliminating the reliance on manual labeling. This preference data \\(\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle\\) is adopted in DPO training to further enhance model performance with feedback from LLM and VLM evaluations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.41 + ], + "angle": 0, + "content": "Frame Sequence Data Preparation The second stage expands our pseudo labeling scheme from 2 to \\(T\\) frames, where our Stage-I ProgressCaptioner first generates captions using a two-frame sliding window. To increase data diversity and volume, we also incorporate captions produced by other VLMs, with both two-frame and full \\(T\\)-frame contexts, since captions of low-quality are also useful (after undergoing our evaluation tasks, those that are rejected enrich the preference data). Once the initial set of caption sequences is generated, we conduct progression detection to identify \\(M\\) visually distinct frames from the original \\(T\\)-frame sequence, denoted as \\(\\mathcal{V}_M = \\{v_i\\}_{i=1}^M\\), using majority voting; \\(M\\) varies based on the distinctiveness of each frame sequence's content. The caption matching task is then employed to encompass \\(M\\) frames, with a selection pool of all \\(M\\) captions, \\(\\hat{\\mathcal{C}}_M = \\{\\hat{c}_i\\}_{i=1}^M\\), plus an \"unsure\" option. A high-quality caption sequence \\(\\hat{\\mathcal{C}}^+\\) is identified when the evaluation VLM correctly selects \\(\\hat{c}_i\\) for \\(v_i\\) across all frames. Conversely, a caption sequence is deemed problematic, \\(\\hat{\\mathcal{C}}^-\\), if the VLM incorrectly answers more than half of the caption selections. This process forms our Stage-II data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.412, + 0.905, + 0.61 + ], + "angle": 0, + "content": "Stage II Training Following the same pipeline as stage I, ProgressCaptioner is first trained through SFT using data prepared during both stages, which includes frame-caption pairs \\( <\\mathbf{v}, \\hat{\\mathbf{c}}^{+}> \\) and frame-caption sequences \\( <\\mathcal{V}, \\hat{\\mathcal{C}}^{+}> \\). Subsequently, we conduct DPO with preference data collected from both stages \\( <\\mathbf{v}, \\hat{\\mathbf{c}}^{+}, \\hat{\\mathbf{c}}^{-}> \\) and \\( <\\mathcal{V}, \\hat{\\mathcal{C}}^{+}, \\hat{\\mathcal{C}}^{-}> \\) to further refine performance and mitigate hallucination. This sequential approach results in our final captioning model, that accepts inputs ranging from 2 to \\( T \\) frames. This flexibility allows users to control the temporal context, balancing the need for local frame-wise changes (smaller window) and global event progressions (larger window). The framework is illustrated in Figure 5." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.624, + 0.645, + 0.641 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.65, + 0.905, + 0.711 + ], + "angle": 0, + "content": "We tackle two questions below: (1) How to evaluate frameworkwise caption quality of existing models? And how does ProgressCaptioner perform? (Sec. 4.1); (2) What applications are enabled by precise progress-aware captions? (Sec. 4.2)" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.721, + 0.858, + 0.737 + ], + "angle": 0, + "content": "4.1. Benchmarking Video Frame Captioning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.905, + 0.882 + ], + "angle": 0, + "content": "Benchmark Data Curation We establish the FrameCapEval benchmark, featuring videos from four action understanding datasets: HowToChange [72] and COIN [59] (on which ProgressCaptioner was trained), along with Penn Action [82] and Kinetics [7], which are unseen in training and serve to assess generalization capabilities. We are mindful of the single frame bias [32] and manually verify all videos to exclude sequences lacking fine-grained action progression. This process yields a final set of 684 videos." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics We employ the automatic evalua" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.863, + 0.483, + 0.901 + ], + "angle": 0, + "content": "3We encourage readers to view data examples provided in Supp. for a better understanding of our data refinement process, as well as details on pseudo labeling, prompts used, and the \\(K\\) VLMs we employ." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13643" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.122, + 0.108, + 0.139, + 0.12 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.092, + 0.251, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.092, + 0.358, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.092, + 0.469, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.147, + 0.277, + 0.177 + ], + "angle": 0, + "content": "[VILA] A person is using a tool to press down on a blue strip of material on the floor." + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.186, + 0.282, + 0.235 + ], + "angle": 0, + "content": "[LLAVA-OV] Using a hammer, the person is tapping the plank into place, aligning it with the baseboard and securing it in position." + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.245, + 0.278, + 0.293 + ], + "angle": 0, + "content": "[ProgressCaptioner] The person continues to work on the floor installation, adjusting the wooden plank near the base of the door." + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.294, + 0.28, + 0.313 + ], + "angle": 0, + "content": "They use their hands to press down on the plank." + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.363, + 0.139, + 0.374 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.142, + 0.338, + 0.253, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.338, + 0.358, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.338, + 0.468, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.495, + 0.108, + 0.512, + 0.12 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.092, + 0.619, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.092, + 0.744, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.092, + 0.869, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.149, + 0.614, + 0.218 + ], + "angle": 0, + "content": "[LLAVA-OV] The tofu cubes are now being cooked in the pan. They have started to brown slightly on the edges, indicating they are being seared." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.228, + 0.612, + 0.277 + ], + "angle": 0, + "content": "[Gemini-1.5-Pro] The tofu cubes are being added to the pan, some are already sizzling in the oil." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.287, + 0.616, + 0.385 + ], + "angle": 0, + "content": "[ProgressCaptioner] In this frame, a hand is seen placing tofu cubes into a black frying pan. The pan is on a stove, and the tofu is being added to it, indicating the start of the cooking process." + }, + { + "type": "text", + "bbox": [ + 0.643, + 0.149, + 0.747, + 0.207 + ], + "angle": 0, + "content": "[GPT-4o] The tofu cubes are now visibly sizzling in the pan, beginning to develop a light golden hue on their surfaces." + }, + { + "type": "text", + "bbox": [ + 0.643, + 0.218, + 0.747, + 0.286 + ], + "angle": 0, + "content": "[LLAVA-Video] The tofu cubes are shown browning in the pan, with some pieces already turning golden brown while others are still pale." + }, + { + "type": "text", + "bbox": [ + 0.643, + 0.296, + 0.744, + 0.395 + ], + "angle": 0, + "content": "[ProgressCaptioner] This frame displays a close-up view of the same black frying pan filled with cubed tofu. The tofu pieces are evenly distributed throughout the pan, and there is no visible action taking place." + }, + { + "type": "text", + "bbox": [ + 0.774, + 0.149, + 0.862, + 0.187 + ], + "angle": 0, + "content": "[Idefics2] The tofu cubes are still browned, but they have a darker color." + }, + { + "type": "text", + "bbox": [ + 0.774, + 0.199, + 0.866, + 0.228 + ], + "angle": 0, + "content": "[Qwen2-VL] The tofu is being cooked in the pan." + }, + { + "type": "text", + "bbox": [ + 0.774, + 0.238, + 0.871, + 0.395 + ], + "angle": 0, + "content": "[ProgressCaptioner] The frame displays the same black frying pan filled with cubed tofu, but now the tofu has a golden-brown color, indicating that it has been cooked and is likely being fried. The tofu pieces appear crispy and well-cooked, suggesting that they have been in the pan for sometime." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.408, + 0.907, + 0.465 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons of ProgressCaptioner with SOTA VLMs on three action sequences. For sequences (a) and (b), only the middle frame predictions are displayed. See Supp. for all models' predictions on full sequences and more examples. Inaccuracies in descriptions are highlighted in red. Even top VLMs often produce descriptions that misalign with the corresponding frames, while ProgressCaptioner delivers hallucination-free and temporally fine-grained captions, including phrases explicitly calling out progress (blue)." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.487, + 0.481, + 0.691 + ], + "angle": 0, + "content": "
ModelSizeHTCCOINPenn&K
CapProgCapProgCapProg
Proprietary models
Gemini-1.5-Pro [53] (img)-28.459.724.358.615.351.2
Gemini-1.5-Pro [53]-31.463.825.063.817.660.3
GPT-4o [2]-32.464.221.358.418.263.2
Open-source models
Idefics2 [31]8B2.054.42.952.212.550.9
VILA [40]8B6.953.65.148.215.951.4
Qwen2-VL [62]7B13.769.611.070.88.558.8
LLAVA-Video [83]7B3.959.38.853.09.751.8
LLAVA-OV [33] (img)7B5.956.317.655.411.955.5
LLAVA-OV [33]7B7.859.05.957.35.150.8
PL (VLM ensemble)-18.662.517.660.119.352.4
ProgressCaptioner (ours)7B37.373.632.366.131.363.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.089, + 0.702, + 0.483, + 0.855 + ], + "angle": 0, + "content": "Table 1. Results on the FrameCapEval Benchmark, composed of video from four public datasets. Cap and Prog denote caption matching and progression detection accuracy, respectively. PL denotes the pseudo labeling baseline adopting filtered captions from multiple VLMs. ProgressCaptioner greatly outperforms SOTA open-source VLMs and even the leading proprietary models, despite being a 7B model. The best results are bolded and underlined, the second best are bolded, and the third best are italicized. The results confirm our model's generalizability from in-domain datasets (HTC for HowToChange and COIN) to external datasets not seen during training (Penn&K for Penn Action and Kinetics)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "tion tasks of progression detection and caption matching (Sec. 3.2), reporting accuracy with Llama-3.1-70B" + }, + { + "type": "image", + "bbox": [ + 0.56, + 0.494, + 0.857, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.627, + 0.906, + 0.656 + ], + "angle": 0, + "content": "Figure 7. User study results comparing ProgressCaptioner with top competitors show it as the most preferred model (see text)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.669, + 0.906, + 0.746 + ], + "angle": 0, + "content": "Instruct [14] as the evaluation LLM and Gemini-1.5-Pro [53] as the evaluation VLM. Additionally, we enhance our evaluation with a user study of 15 participants, reporting the average selection rate. See Supp. for experiments on evaluation metric reliability and full user study details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Baselines We evaluate an array of state-of-the-art VLMs, including two proprietary models, GPT-4o [2] and Gemini1.5-Pro [53], and five open-source models—Idefics2 [31], VILA [40], Qwen2-VL [62], LLAVA-Video [83], and LLAVA-OV [33]. We also include a pseudo labeling baseline using filtered captions produced by an ensemble of VLMs (Sec. 3), and image captioning baselines using Gemini-1.5-Pro and LLAVA-OV. We select open-source VLM variants with fewer than 10B parameters for computational efficiency and a fair comparison with our Progress" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13644" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.195, + 0.089, + 0.805, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.283, + 0.877, + 0.298 + ], + "angle": 0, + "content": "Figure 8. ProgressCaptioner facilitates keyframe selection and enriches the selected keyframes with progress-aware descriptions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.309, + 0.484, + 0.386 + ], + "angle": 0, + "content": "Captioner, which is an 7B model. The closed proprietary models are much larger and trained with much more extensive data; we include them as a useful reference point, but stress that they do not constitute an apples-to-apples comparison, to the disadvantage of our ProgressCaptioner." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.392, + 0.484, + 0.573 + ], + "angle": 0, + "content": "Implementation ProgressCaptioner is constructed with SigLIP [80] as the vision encoder and Qwen2 [62] as the language model, linked through a projector, and initialized from the LLAVA-OV-7B checkpoint [33]. For benchmark evaluations in Sec. 4.1, ProgressCaptioner operates on the full \\( T \\)-frame sequence for a comprehensive temporal context. For applications presented in Sec. 4.2, where fine-grained analysis of local frame changes is crucial, a sliding window approach is used, with the model processing frame pairs. To ensure a fair comparison, all video baseline models are provided with the same temporal context as ProgressCaptioner across all evaluations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.484, + 0.761 + ], + "angle": 0, + "content": "Results As shown in Table 1, on the FrameCapEval benchmark, ProgressCaptioner greatly outperforms existing open-source VLMs of similar capacity and even the (much larger) latest Gemini-1.5-Pro and GPT-4o. We observe that strong language-backed VLMs like GPT-4o show high caption matching accuracy, whereas Qwen2-VL excels in progression detection, reducing hallucination. However, it tends to produce less detailed captions, leading to lower caption matching accuracy. In contrast, ProgressCaptioner effectively balances precision and detail in frame-wise captioning, consistently leading the benchmark across both indomain and out-of-domain datasets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Figure 6 provides qualitative comparisons on three action sequences. Consider the (a) bowling sequence for instance: baseline models erroneously suggest progression in frame 2, like \"arm forward\", exemplifying the common issue of temporal hallucination in current VLMs. This issue recurs in the other two sequences. Conversely, ProgressCaptioner delivers high-quality captions that precisely characterize action progress in each frame. See Supp. for more qualitative examples and an ablation of ProgressCaptioner." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.309, + 0.908, + 0.583 + ], + "angle": 0, + "content": "User Study Figure 7 presents the user study results, where ProgressCaptioner is compared against four of the strongest competitors: LLAVA-OV, Qwen2-VL, Gemini-1.5-Pro and GPT-4o. Each participant is presented with five captions produced by these models and is tasked with selecting the top-2, with an additional \"none\" option if the captions are deemed inadequate. ProgressCaptioner emerges as the most preferred model, with an average best caption selection rate of \\(31.6\\% - 2 \\times\\) to \\(3.6 \\times\\) better than the comparably sized best models from the literature [33, 62], and even surpassing top-tier proprietary models that enjoy significant scaling advantages. While our model outperforms all open-source and proprietary models for top-1 preference, the more forgiving top-2 metric brings the proprietary closed models back in the game, though our model remains competitive even there (50.3% for GPT-4o vs. 47.3% for ours). These findings underscore our model's strong ability to produce accurate, temporally fine-grained captions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.596, + 0.864, + 0.613 + ], + "angle": 0, + "content": "4.2. Applications of Video Frame Captioning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.907, + 0.667 + ], + "angle": 0, + "content": "ProgressCaptioner offers progress-aware frame-wise captions, which hold great potential for many real-world applications. We explore several practical use-cases below." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.909, + 0.867 + ], + "angle": 0, + "content": "Keyframe Selection Our first use-case leverages ProgressCaptioner's temporally precise captions as an intermediate representation to identify keyframes within a densely sampled sequence, aided by an LLM (see Supp. for details). Figure 8 provides two examples, showcasing how ProgressCaptioner's produced captions allow selecting distinct frames that effectively capture different stages of the welding and squeezing grapefruit action. While recent video summarization work [24] explores using VLMs and LLMs for keyframe selection, it aims to identify coarse-grained events within long videos, which is not adequate for our problem scenario. See Supp. for a side-to-side comparison and more qualitatives that underscore this distinction." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Keyframes for Action Recognition Not only is keyframe selection useful for human viewers to quickly preview a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13645" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.09, + 0.462, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.211, + 0.484, + 0.255 + ], + "angle": 0, + "content": "Figure 9. On Kinetics test videos, ProgressCaptioner selects four frames that are more informative of the action than uniform sampling, resulting in improved action recognition accuracy." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.262, + 0.485, + 0.534 + ], + "angle": 0, + "content": "longer video, but it can also extract the most informative portions of a video to benefit activity recognition [29]. To illustrate, we next apply our keyframe selection mechanism to Kinetics [7] Temporal [57] subset that necessitates multi-frame reasoning. Given that the original video clips are short (sampled at 1FPS, resulting in sequences of 10 frames), we employ two models that take four frames as input: Slow backbone from SlowFast [17] and X3D-XS [16]. We prompt GPT-4o to select four representative frames from frame-wise captions produced by ProgressCaptioner. We take the two model checkpoints that have been trained on the Kinetics training set and replace uniformly sampled frames with our selected keyframes during inference. Figure 9 presents a qualitative comparison, highlighting performance gains such as a \\(+1.7\\%\\) increase in top-1 accuracy for both SlowFast and X3D models. Even among just 10 candidate frames, our method's fine-grained ability to identify the 4 most informative ones translates into better recognition." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.539, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Advancing Video Understanding The precise, framewise captions generated by ProgressCaptioner enhance our understanding of videos. To demonstrate this, we consider two video tasks that demand temporally fine-grained understanding: (1) frame-wise classification on HowToChange [72] and Penn Action [82], and (2) video question answering (QA) on NExT-QA [69] (ATP-Hard [5]). These tasks are chosen because they challenge the model to comprehend not just the overarching content of a video, but also the more fine-grained event progression within a video. The HowToChange and Penn Action test sets provide frame-wise labels detailing object state changes or action phases, requiring frame-level understanding. Similarly, NexTQA (ATP-Hard) poses temporally challenging questions that demand multi-frame reasoning, such as determining event order, emphasizing the need for precise temporal comprehension. For baseline comparisons, we evaluate against the LLAVA-OV-7B [33] model, from which ProgressCaptioner is initialized, to highlight the enhancements that our specialized training on FrameCap brings to video understanding tasks. For the first task, as we pioneer a zero-shot, language-guided approach to this traditionally vision-centric problem (details below), no other zero-shot baselines exist. For the second task, we compare ProgressCap" + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.093, + 0.88, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.219, + 0.907, + 0.261 + ], + "angle": 0, + "content": "Figure 10. ProgressCaptioner delivers precise and detailed per-frame descriptions, leading to enhanced zero-shot frame-wise classification performance when compared with LLAVA-OV." + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.264, + 0.892, + 0.336 + ], + "angle": 0, + "content": "
ModelAcc@CAcc@TAcc@All
VFC [45]32.230.031.4
VideoAgent [64]57.858.858.4
LLAVA-OV [33] + GPT-4o62.653.458.8
ProgressCaptioner + GPT-4o (ours)64.458.161.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.339, + 0.907, + 0.368 + ], + "angle": 0, + "content": "Table 2. Video QA results on NExT-QA (ATP-Hard). C and T denote causal and temporal subsets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.375, + 0.892, + 0.39 + ], + "angle": 0, + "content": "titioner against two existing zero-shot approaches [45, 64]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.392, + 0.906, + 0.543 + ], + "angle": 0, + "content": "(a) Zero-shot Frame Classification We repurpose zero-shot frame-wise classification task into a multi-choice QA format, using frame-wise captions to guide an LLM in identifying the correct label per frame, evaluating caption accuracy and granularity (Figure 10 left). Results (Figure 10 right) show that ProgressCaptioner consistently outperforms LLAVA-OV across both datasets. Notably, our training involves no signals related to these frame-wise labels, underscoring its generalizability and effectiveness in enhancing video frame-level understanding." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.907, + 0.697 + ], + "angle": 0, + "content": "(b) Video QA Finally, we report results using frame-wise descriptions for video QA, where an LLM (we use GPT-4o) is employed to answer questions on NExT-QA (ATP-Hard) set. As shown in Table 2, ProgressCaptioner achieves the best results on this benchmark, outperforming the previous leader VideoAgent [64] by \\(+3.4\\%\\). Compared with a similar setup using LLAVA-OV, ProgressCaptioner achieves a \\(+4.7\\%\\) gain in the temporal subset, highlighting its superior ability to produce fine-grained, temporally precise descriptions and bring enhanced video understanding." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.71, + 0.634, + 0.725 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We introduce progress-aware video frame captioning, which necessitates a significant enhancement in current captioning models' capability to describe temporal action dynamics. Towards this end, we develop ProgressCaptioner and show its effectiveness in enhancing the temporal precision and alignment of captions with corresponding frames. Furthermore, we demonstrate its practical applications: keyframe selection and enhanced video understanding. By setting a new standard for temporal precision in video captioning, we hope our work inspires further development in this domain." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13646" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.258, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.115, + 0.474, + 0.131 + ], + "angle": 0, + "content": "Research supported in part by the IFML NSF AI Institute." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.144, + 0.188, + 0.159 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.169, + 0.483, + 0.25 + ], + "angle": 0, + "content": "[1] Moloud Abdar, Meenakshi Kollati, Swaraja Kuraparthi, Farhad Pourpanah, Daniel McDuff, Mohammad Ghavamzadeh, Shuicheng Yan, Abduallah Mohamed, Abbas Khosravi, Erik Cambria, et al. 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This novel task aims to generate temporally fine-grained captions that not only accurately describe each frame but also capture the subtle progression of actions throughout a video sequence. Despite the strong capabilities of existing leading vision language models, they often struggle to discern the nuances of frame-wise differences. To address this, we propose ProgressCaptioner, a captioning model designed to capture the fine-grained temporal dynamics within an action sequence. Alongside, we develop the FrameCap dataset to support training and the FrameCapEval benchmark to assess caption quality. The results demonstrate that ProgressCaptioner significantly surpasses leading captioning models, producing precise captions that accurately capture action progression and set a new standard for temporal precision in video captioning. Finally, we showcase practical applications of our approach, specifically in aiding keyframe selection and advancing video understanding, highlighting its broad utility. + +# 1. Introduction + +Visual captioning [38]—the task of generating textual descriptions of visual content—is a fundamental problem in computer vision with extensive practical applications. Existing captioning paradigms are broadly divided into two categories: image captioning and video captioning, with a clear distinction between them. Image captioning [23] generates a single, isolated description for each image, with no contextual linkage among different images. In contrast, video captioning [1] assigns a single caption for the entire video clip, aggregating information across frames without addressing the specifics of individual frames. + +Figure 1 illustrates this dichotomy. Employing an im + +![](images/e6d9ab00d3afc8d6656a1ed3461dd509bcf58765d513a50ec52fb2900cd4026f.jpg) +a close up of a wok with a lot of oil in it + +![](images/91abd2e9679717edf60d2c052865a1c41330ea35bc253ba98fc41e3e4ed98920.jpg) +Eggs are fried in a wok on a stove top + +![](images/7d9aaa54505f12e24ae223828985754f5bba2962d947218934f87dfaba8b35e7.jpg) +cooking eggs in a wok on the stove +Progress-aware video frame captioning + +![](images/a0c28d214b88c17575d88b673cea6832519b2bc8f6ddedb19745f8db974c8d65.jpg) +cooking food in a wok on the stove +Image captioning +Scramble the eggs in the wok +Video captioning + +The frame shows a large, worn-out wok with a dark interior. There is a small amount of oil visible at the bottom of the wok, indicating that it is ready for cooking. + +Three eggs are being added into the wok. The eggs are still intact and have bright yellow yolks. The wok remains in the same position as in the first frame. + +A metal spatula is used to stir the eggs. The eggs are starting to cook, with some white parts becoming more solid while others remain runny. + +The scene transitions to show the same wok, now containing scrambled eggs. The yolks are fully mixed into the whites. + +Figure 1. We propose progress-aware video frame captioning (bottom), which aims to generate a sequence of captions that capture the temporal dynamics within a video. Unlike traditional image and video captioning (top) that focus on broad event-level descriptions, our task delves into the detailed, progressive dynamics of an action, necessitating precise, temporally fine-grained capabilities. Blue text highlights how the progress-aware captions build successively on the earlier content to highlight what is changing. + +age captioning model like BLIP [37] to describe each frame of the video results in captions that are local, not temporally context-aware, and may exhibit little variation across the sequence. Conversely, video captioning provides a global, not temporally fine-grained overview of the event, as exemplified by the YouCook2 [85] ground truth label "scramble the eggs in the wok". In both scenarios, the nuances of how the action unfolds over time are missed. This raises the question: Can we develop temporally fine-grained captions that capture the subtle, progressive nature of action sequences? Figure 1 (bottom) illustrates what we seek. + +Having such progress-aware captions could benefit a great variety of downstream tasks, bringing improved video understanding [73, 79], more precise video retrieval [66-68], and enriched video generation [50, 58]. Moreover, such a capability could open up new AR/VR and robotics applications. For instance, in AI coaching, a captioning system could meticulously analyze an expert's tennis forehand, simplifying the learning process for users. Similarly, for how-to video creation, it could elicit and describe the + +![](images/c058b9e88e2098a77521a3979eb43f8e0da6845a3366e4720de495cde682a4a5.jpg) +Figure 2. Use cases of video frame captioning: finer-grained captions enable detailed, step-by-step guidance for daily tasks. + +key object state changes at each stage (e.g., "how to make whipped cream")—useful for both content creators as well as visually-impaired users learning a new skill. See Fig. 2. + +Towards this end, we introduce a novel captioning task—progress-aware video captioning at the frame level. This task involves generating captions that not only coherently depict action progression but also tailor each description specifically to its corresponding frame.2 Our task is uniquely characterized by its demand for fine-grained temporal sensitivity. By "fine-grained", we refer to generating detailed descriptions that elucidate the stages or procedural steps of the action, effectively conveying how the action is performed throughout the video sequence. + +As discussed, traditional video captioning [9, 63, 70, 86] settles for broad event-level descriptions, where a description like scrambling eggs for the video in Figure 1 would be considered entirely accurate. In contrast, we seek progress-aware captions that detail each stage of the action, such as "eggs still intact", "starting to cook" and "fully mixed". While recent works [6, 8, 11, 12, 61, 83] enhance the overall descriptiveness of video captions, they continue to produce a single video-level description without distinguishing the nuances across time. Our task delves deeper, exploring how each frame contributes to the narrative of the action's progression, thereby setting a new standard for fine-grained temporal precision in video captioning. + +Despite great advancements of vision language models (VLMs) [2, 33, 37, 40-42, 62, 75, 81, 83] that have markedly improved visual captioning, we observe that these models still struggle with this nuanced task. Two main issues persist: first, the lack of temporally fine-grained captions; when shown adjacent frames that depict subtle variations in action progression (such as frames 2 and 3 in Figure 3), the generated captions can be overly coarse, failing to differentiate between the frames (see row 2, Gemini1.5-Pro's captions). Second, we identify and term a notable issue of "temporal hallucination", where the captions suggest temporal progression in disagreement with what the visual frames exhibit. See frame 2 of Figure 3, where GPT-4o's generated captions (row 1) incorrectly advance the action sequence. The prevalence of such errors can + +![](images/a475753a870a3e9e824c7bc301a9bed437a5862d538e247a9c59cead97161916.jpg) +Figure 3. Issues of existing VLMs in video frame captioning: (1) Lack of temporal granularity. See captions for frames 2 and 3, produced by Gemini-1.5-Pro (row 2), which fail to distinguish subtle differences between the frames. (2) Temporal hallucination. See frame 2's caption produced by GPT-4o (row 1), which inaccurately suggests progression that is not visible. + +be attributed to models' reliance on the common statistics of activity sequences, which mistakenly override matching specific statements to specific frames. Meanwhile, image captioners—even if trained with fine-grained annotations—treat frames in isolation and hence lack the temporal context to say what is progressing versus what is present. + +We introduce ProgressCaptioner, a model for generating progress-aware frame-level video captions. Our approach uniquely interleaves pseudo labeling with two learning stages. Stage I develops a frame pair captioning model, and stage II extends this to full frame sequences. This process also creates the FrameCap training dataset, comprising action videos along with high-quality frame-wise captions, which are initially generated by an ensemble of VLMs and then filtered using our proposed evaluation methods. + +To assess the quality of frame-wise captions and benchmark ProgressCaptioner against leading VLMs, we introduce the FrameCapEval benchmark comprised of videos from four public video action datasets. ProgressCaptioner consistently outperforms leading open-source VLMs with a $1.8 \times$ to $2.7 \times$ improvement in caption quality and also achieves the highest selection rate in user studies, even surpassing the much larger proprietary models GPT-4o [2] and Gemini-1.5-Pro [53]. Finally, we highlight potential applications enabled by our advanced captions: keyframe selection and enhanced video understanding. We hope that our task, model, and benchmark can inspire future development in temporally fine-grained video captioning. + +# 2. Related Work + +Image Captioning Image captioning has been extensively studied in recent years [3, 13, 60, 76]. A related line of + +work is image difference captioning, where the task is to describe differences between two images [27, 48, 56] or sets of images [15]. Building on the success of generative models, recent benchmarks [4, 28, 77] challenge models to distinguish between two visually similar images, advancing fine-grained image understanding. However, all the above models are restricted to static (typically synthesized) image pairs and address coarse-grained differences like object presence or absence. Temporal intricacies—accurately describing how an action progresses—remain unexplored. + +Video Captioning Video captioning [1] aims to produce a single description that encapsulates a video clip. While traditional benchmarks [9, 63, 70, 86] offer a brief onesentence caption for each video, recent efforts expand this scope, extending captioning to hours-long videos [26], enriching the granularity of details [8, 11, 61], enhancing caption uniqueness [49], integrating a causal temporal narrative [46], or introducing LLM summarization [34]. + +Adjacent to traditional video captioning are the tasks of visual storytelling [25, 36] (creating a coherent story for a sequence of snapshots), dense video captioning [30, 74, 87] (temporal localization and captioning of all events in an untrimmed video), audio description [20-22] (detailed narrations of visual events in videos (e.g., movies) for visually impaired audiences), and video paragraph captioning [78] (producing a multi-sentence paragraph describing the video). However, all these works still address "what is happening" at a coarse-grained event level, e.g., noting that someone is making aSouffle within a specific time range. The ability to break down frame-level details—such as whisking egg whites, folding ingredients, and observing the souffle rising—is still lacking. + +Vision Language Models Recent advancements in VLMs [2, 33, 37, 40-42, 62, 75, 81, 83] have greatly enhanced the capabilities of both image and video captioning. Despite their strong performance, VLMs often exhibit "hallucination" [19, 65], and preference learning [52, 84] has proven effective in mitigating this issue. + +Compared to image-LMs, video-LMs crucially require the integration of temporal dynamics understanding, spurring a series of work on evaluating temporal perception [18, 39, 43, 69]. While these assessments ensure that a model can generate an accurate overall video summary or answer general questions, they entail neither temporal localization nor discernment of fine-grained differences between frames. The OSCaR benchmark [47] focuses on object state change (OSC) captioning, yet it is limited to just three frames and specifically OSC videos, with models and captions not publicly released yet preventing direct comparison. Additionally, their approach relies on human annotation and a single advanced GPT model. In contrast, our approach features a scalable data collection pipeline that reduces reliance on these labor-intensive resources, employs + +![](images/aa1341d9a86938e2680af0038c9c60327dbfe4c95497c53234fa5d70a87a6217.jpg) +Figure 4. Captioning outcomes using Gemini-1.5-Pro [53]. + +novel automatic evaluation tasks, and broadens the scope beyond OSC videos. Finally, unlike methods for long-form video and event localization with VLMs [10, 44, 54], our focus is distinctly more temporally fine-grained, concentrating on how individual frames evolve within a single event. + +# 3. Approach + +We delve into the specific challenges of our progress-aware video frame captioning problem in Sec. 3.1 and outline ProgressCaptioner's development in Sec. 3.2. + +# 3.1. Progress-aware Video Frame Captioning + +Problem Formulation Our objective is to develop a captioning model that, given a video, produces accurate temporally fine-grained captions. Formally, for a sequence of $T$ frames, denoted as $\mathcal{V} = \{v_i\}_{i=1}^T$ , the captioning model generates a corresponding sequence of captions $\mathcal{C} = \{c_i\}_{c=1}^T$ , where each $c_i$ describes the $i$ -th frame $v_i$ (recall we sample at 1FPS). This captioning process has three key requirements: (1) Accuracy, where each caption $c_i$ must faithfully represent what is visually occurring in frame $v_i$ , without hallucinating from the context of other frames; (2) Temporal Specificity, where each caption $c_i$ specifically attends to $v_i$ , without being overly generic to be applicable to multiple frames in the sequence; (3) Progressive Coherence: The sequence of captions $\{c_i\}_{i=1}^T$ should build upon each other to reflect the essential changes in the action over time. + +FrameCap Dataset To train our captioning model, we require a dataset that pairs frame sequences $(\mathcal{V})$ with corresponding captions $(\mathcal{C})$ . Existing datasets [9, 63, 70, 86] provide only a single, generic caption for an entire video clip, lacking the frame-wise caption format we need. To address this gap and train our model, we develop the FrameCap dataset. Given the prohibitive expense of collecting human-labeled caption sequences as our ground truth $(\mathcal{C})$ , especially at scale, we leverage leading VLMs as powerful tools to create a pseudo caption sequence $\hat{\mathcal{C}}$ from $\mathcal{V}$ . For video sources, we refer to two large-scale datasets that focus on fine-grained human activities: HowToChange [72] + +![](images/ef23e90098191fdb05907c04b2c94526641d5fc51cfdbf298f8951d116133dc9.jpg) +Figure 5. Framework of ProgressCaptioner, designed in two stages. In Stage-I, we prepare frame pairs and generate corresponding caption pairs using multiple VLMs. Each pair undergoes our designed progression detection and caption matching evaluations, to decide if they are selected for model supervised fine-tuning or rejected, with the latter contributing to preference data to aid in model preference learning. The Stage-I model training then proceeds using this collected data. In Stage-II, the trained stage-I model labels frame sequences with a two-frame sliding window, in conjunction with other VLMs. These sequences are again assessed through progression detection and caption matching to classify them as selected or rejected. All collected data from both stages contribute to the final training of ProgressCaptioner. + +(featuring object state change videos from YouTube) and COIN [59] (featuring daily activities from YouTube). + +Caption Sequence Construction Prompting VLMs for our desired caption sequence is nontrivial. We identify two key problems: (1) Input considerations: how many context frames from $\{v_i\}_i^T$ should be provided? (2) Output assessment: what issues arise in VLM-generated captions, and how can we filter to retain only high-quality ones? To explore these questions, we conduct preliminary experiments by prompting leading VLMs to perform the frame-wise captioning task. We share our findings below. + +Observation I Intuitively, inputting all $T$ frames would seem best. However, current VLM capabilities do not support this extensive context. Specifically, providing too many frames at once often leads to descriptions that lack detail and exhibit temporal inaccuracies, with VLMs also risking memory overload, as similarly observed in [11]. Conversely, providing a single frame at a time reduces the task to image captioning, which is not optimal either, resulting in captions that lack temporal context and coherence. + +Figure 4 shows a representative trial with Gemini-1.5-Pro [53]. Inputting the full sequence (case (a)) yields brief per-frame descriptions with temporal misalignment (i.e., the second caption erroneously describes what is visually occurring in the third frame). On the other hand, captioning frames in isolation (case (b)) removes essential temporal context, where the model mistakes the initial stage of a tennis serve for the follow-through of a forehand swing. These findings underscore the importance of finding a balanced approach and motivate us to adopt a frame pair as the stepping stone of our captioning model. + +Observation II Next, building upon the use of a frame + +pair $(v_{1}, v_{2})$ , is the caption pair $(\hat{c}_{1}, \hat{c}_{2})$ produced by existing VLMs of sufficient quality to be directly adopted? Our preliminary experiments reveal two main issues: (a) lack of temporal granularity, and (b) temporal hallucination, as showcased in Figure 3. To dissect these issues, we analyze the captions in relation to the visual progression between frames $v_{1}$ and $v_{2}$ . Specifically, if there is a visible progression from $v_{1}$ to $v_{2}$ (e.g., the slight peeling of a shrimp's shell from frame 2 to frame 3 in Figure 3), the captions should adequately reflect this change. Overly similar captions in such a scenario signify a failure in temporal granularity. Conversely, when there is no change between frames (e.g. frames 1 and 2 in Figure 3), the captions should remain consistent. We deem it a temporal hallucination when captions erroneously indicate progression in disagreement with the visuals. This deficiency in existing VLMs motivates our development of a new captioning model and specialized evaluations for high-quality caption selection. + +# 3.2. ProgressCaptioner + +The observations above drive the design of our model, ProgressCaptioner, which unfolds in two stages. Based on our findings that current VLMs have trouble maintaining caption quality when handling extensive $T$ -frame inputs, our approach begins with frame pair captioning. In the first stage, we develop a ProgressCaptioner to excel at describing the nuances between adjacent frames. The second stage then leverages the first-stage model to pseudo label the full $T$ -frame sequence with a two-frame sliding window. This staged approach refines caption quality along with model development, enhancing the captioning process iteratively with more precise pseudo labels. + +Frame Pair Data Preparation Starting with a frame pair + +$\mathbf{v} = (v_{1}, v_{2})$ , we employ $K$ captioning models to generate an initial set of caption pairs $\{(\hat{c}_{1}, \hat{c}_{2})\}_{1}^{K}$ . Acknowledging the potential inaccuracies in these captions, as per observation II, we design two automatic evaluation tasks to assess caption quality. The first task, progression detection, examines progress awareness: it checks whether the captions appropriately reflect visual changes between $v_{1}$ and $v_{2}$ . Specifically, an LLM assesses each caption pair $(\hat{c}_{1}, \hat{c}_{2})_{k}$ to determine if they suggest a visible physical change. We utilize majority voting across multiple LLMs' assessments for all $K$ caption pairs to establish a consensus visual-change label. Caption pairs that align with this consensus are marked as passing; others are marked as failing. + +For pairs passing progression detection, we proceed to our second evaluation task—caption matching—to assess how precisely $\hat{c}_1$ and $\hat{c}_2$ describe $v_1$ and $v_2$ , respectively. The task is designed as a multi-choice question format, where a VLM is given $\hat{c}_1$ , $\hat{c}_2$ , and an "unsure" option, and tasked with matching the correct caption to each frame. A caption pair is considered good if the evaluation VLM correctly identifies $\hat{c}_1$ for $v_1$ and $\hat{c}_2$ for $v_2$ . Because the captions will all be topically related, this is essentially a matching task with "hard negatives" that lets us automatically gauge the precision of the proposed captions for the target images. + +This automatic pipeline distinguishes between high-quality caption pairs, denoted by $\hat{\mathbf{c}}^{+} = (\hat{c}_{1}^{+},\hat{c}_{2}^{+})$ , and those that exhibit inaccuracies or hallucinations, denoted by $\hat{\mathbf{c}}^{-} = (\hat{c}_{1}^{-},\hat{c}_{2}^{-})$ , forming training data for Stage I.3 + +Stage I Training Following the success of versatile VLMs in captioning tasks [34, 42, 61, 71], we initialize Progress-Captioner with the LLAVA-OV-7B [33] checkpoint to inherit its pretrained capabilities. Stage-I training utilizes frame and caption pair data collected on HowToChange and COIN YouTube videos $\langle \mathbf{v},\hat{\mathbf{c}}^{+},\hat{\mathbf{c}}^{-}\rangle$ through two principal methods: supervised fine-tuning (SFT) and direct preference optimization (DPO). The SFT process is straightforward given our dataset; we perform instructional tuning to tailor the general capabilities of the original VLM to our specific frame-wise captioning requirements using $\langle \mathbf{v},\hat{\mathbf{c}}^{+}\rangle$ . The subsequent DPO step targets the prevalent issue of hallucination in VLMs and is innovatively driven by our proposed automatic evaluation critics. Preference optimization [52] in LLM training typically requires human-provided preference data to steer LLM responses towards more desirable outputs. Here, we employ progression detection and caption matching to automatically construct preference data $\hat{\mathbf{c}}^{+}$ and $\hat{\mathbf{c}}^{-}$ , eliminating the reliance on manual labeling. This preference data $\langle \mathbf{v},\hat{\mathbf{c}}^{+},\hat{\mathbf{c}}^{-}\rangle$ is adopted in DPO training to further enhance model performance with feedback from LLM and VLM evaluations. + +Frame Sequence Data Preparation The second stage expands our pseudo labeling scheme from 2 to $T$ frames, where our Stage-I ProgressCaptioner first generates captions using a two-frame sliding window. To increase data diversity and volume, we also incorporate captions produced by other VLMs, with both two-frame and full $T$ -frame contexts, since captions of low-quality are also useful (after undergoing our evaluation tasks, those that are rejected enrich the preference data). Once the initial set of caption sequences is generated, we conduct progression detection to identify $M$ visually distinct frames from the original $T$ -frame sequence, denoted as $\mathcal{V}_M = \{v_i\}_{i=1}^M$ , using majority voting; $M$ varies based on the distinctiveness of each frame sequence's content. The caption matching task is then employed to encompass $M$ frames, with a selection pool of all $M$ captions, $\hat{\mathcal{C}}_M = \{\hat{c}_i\}_{i=1}^M$ , plus an "unsure" option. A high-quality caption sequence $\hat{\mathcal{C}}^+$ is identified when the evaluation VLM correctly selects $\hat{c}_i$ for $v_i$ across all frames. Conversely, a caption sequence is deemed problematic, $\hat{\mathcal{C}}^-$ , if the VLM incorrectly answers more than half of the caption selections. This process forms our Stage-II data. + +Stage II Training Following the same pipeline as stage I, ProgressCaptioner is first trained through SFT using data prepared during both stages, which includes frame-caption pairs $<\mathbf{v}, \hat{\mathbf{c}}^{+}>$ and frame-caption sequences $<\mathcal{V}, \hat{\mathcal{C}}^{+}>$ . Subsequently, we conduct DPO with preference data collected from both stages $<\mathbf{v}, \hat{\mathbf{c}}^{+}, \hat{\mathbf{c}}^{-}>$ and $<\mathcal{V}, \hat{\mathcal{C}}^{+}, \hat{\mathcal{C}}^{-}>$ to further refine performance and mitigate hallucination. This sequential approach results in our final captioning model, that accepts inputs ranging from 2 to $T$ frames. This flexibility allows users to control the temporal context, balancing the need for local frame-wise changes (smaller window) and global event progressions (larger window). The framework is illustrated in Figure 5. + +# 4. Experiments + +We tackle two questions below: (1) How to evaluate frameworkwise caption quality of existing models? And how does ProgressCaptioner perform? (Sec. 4.1); (2) What applications are enabled by precise progress-aware captions? (Sec. 4.2) + +# 4.1. Benchmarking Video Frame Captioning + +Benchmark Data Curation We establish the FrameCapEval benchmark, featuring videos from four action understanding datasets: HowToChange [72] and COIN [59] (on which ProgressCaptioner was trained), along with Penn Action [82] and Kinetics [7], which are unseen in training and serve to assess generalization capabilities. We are mindful of the single frame bias [32] and manually verify all videos to exclude sequences lacking fine-grained action progression. This process yields a final set of 684 videos. + +Evaluation Metrics We employ the automatic evalua + +![](images/193aa68adc4dcafa38d05082683920438b914a82c705930db9324fe4fd367842.jpg) +(a) + +![](images/ec0f3016a56e9e5ae2e5bbdbbef1ea4c7a70791ac6834f72ca833d5626fa6244.jpg) + +![](images/d97e58c1f897e399fe8d5441d46f38e2911e44a424711b7382ca9e76da973e6f.jpg) + +[VILA] A person is using a tool to press down on a blue strip of material on the floor. + +[LLAVA-OV] Using a hammer, the person is tapping the plank into place, aligning it with the baseboard and securing it in position. + +[ProgressCaptioner] The person continues to work on the floor installation, adjusting the wooden plank near the base of the door. + +They use their hands to press down on the plank. + +![](images/5a9930787c07b50f37b479b5b92ea8086efaf8aa367189b51c1d6ebef07decc8.jpg) +(b) + +![](images/5cf44e48812041aab7f4989b9d70f73889899c75284ad03e802fb7f1ccced43a.jpg) +Figure 6. Qualitative comparisons of ProgressCaptioner with SOTA VLMs on three action sequences. For sequences (a) and (b), only the middle frame predictions are displayed. See Supp. for all models' predictions on full sequences and more examples. Inaccuracies in descriptions are highlighted in red. Even top VLMs often produce descriptions that misalign with the corresponding frames, while ProgressCaptioner delivers hallucination-free and temporally fine-grained captions, including phrases explicitly calling out progress (blue). + +![](images/b103bfb9153ab78ca927d7d03b978ce94cc4ab800695daa57faff6710f3bb832.jpg) + +![](images/f500e5bb089d20ee3417ec3170d2a04f4eed89610368fa953d91b7abfa26b738.jpg) +(c) + +![](images/622274eac135f4e64a400f4562630e4b3ea1c9f71eb66993d26560cc07f2eec1.jpg) + +![](images/33396d83b80c54a1d97d35e82ccecaca6e31c83dd768994e7e74f23dd68106bd.jpg) + +[LLAVA-OV] The tofu cubes are now being cooked in the pan. They have started to brown slightly on the edges, indicating they are being seared. + +[Gemini-1.5-Pro] The tofu cubes are being added to the pan, some are already sizzling in the oil. + +[ProgressCaptioner] In this frame, a hand is seen placing tofu cubes into a black frying pan. The pan is on a stove, and the tofu is being added to it, indicating the start of the cooking process. + +[GPT-4o] The tofu cubes are now visibly sizzling in the pan, beginning to develop a light golden hue on their surfaces. + +[LLAVA-Video] The tofu cubes are shown browning in the pan, with some pieces already turning golden brown while others are still pale. + +[ProgressCaptioner] This frame displays a close-up view of the same black frying pan filled with cubed tofu. The tofu pieces are evenly distributed throughout the pan, and there is no visible action taking place. + +[Idefics2] The tofu cubes are still browned, but they have a darker color. + +[Qwen2-VL] The tofu is being cooked in the pan. + +[ProgressCaptioner] The frame displays the same black frying pan filled with cubed tofu, but now the tofu has a golden-brown color, indicating that it has been cooked and is likely being fried. The tofu pieces appear crispy and well-cooked, suggesting that they have been in the pan for sometime. + +
ModelSizeHTCCOINPenn&K
CapProgCapProgCapProg
Proprietary models
Gemini-1.5-Pro [53] (img)-28.459.724.358.615.351.2
Gemini-1.5-Pro [53]-31.463.825.063.817.660.3
GPT-4o [2]-32.464.221.358.418.263.2
Open-source models
Idefics2 [31]8B2.054.42.952.212.550.9
VILA [40]8B6.953.65.148.215.951.4
Qwen2-VL [62]7B13.769.611.070.88.558.8
LLAVA-Video [83]7B3.959.38.853.09.751.8
LLAVA-OV [33] (img)7B5.956.317.655.411.955.5
LLAVA-OV [33]7B7.859.05.957.35.150.8
PL (VLM ensemble)-18.662.517.660.119.352.4
ProgressCaptioner (ours)7B37.373.632.366.131.363.7
+ +Table 1. Results on the FrameCapEval Benchmark, composed of video from four public datasets. Cap and Prog denote caption matching and progression detection accuracy, respectively. PL denotes the pseudo labeling baseline adopting filtered captions from multiple VLMs. ProgressCaptioner greatly outperforms SOTA open-source VLMs and even the leading proprietary models, despite being a 7B model. The best results are bolded and underlined, the second best are bolded, and the third best are italicized. The results confirm our model's generalizability from in-domain datasets (HTC for HowToChange and COIN) to external datasets not seen during training (Penn&K for Penn Action and Kinetics). + +tion tasks of progression detection and caption matching (Sec. 3.2), reporting accuracy with Llama-3.1-70B + +![](images/fa5f53838a540ba5e032d2ab3323713ea0246ca621b54ffb2dc3568cdfe9b1d8.jpg) +Figure 7. User study results comparing ProgressCaptioner with top competitors show it as the most preferred model (see text). + +Instruct [14] as the evaluation LLM and Gemini-1.5-Pro [53] as the evaluation VLM. Additionally, we enhance our evaluation with a user study of 15 participants, reporting the average selection rate. See Supp. for experiments on evaluation metric reliability and full user study details. + +Baselines We evaluate an array of state-of-the-art VLMs, including two proprietary models, GPT-4o [2] and Gemini1.5-Pro [53], and five open-source models—Idefics2 [31], VILA [40], Qwen2-VL [62], LLAVA-Video [83], and LLAVA-OV [33]. We also include a pseudo labeling baseline using filtered captions produced by an ensemble of VLMs (Sec. 3), and image captioning baselines using Gemini-1.5-Pro and LLAVA-OV. We select open-source VLM variants with fewer than 10B parameters for computational efficiency and a fair comparison with our Progress + +![](images/2912ea9319633ffe89f419cb930ad89e2b0993fabc2014fd9f3f32f57b358da8.jpg) +Figure 8. ProgressCaptioner facilitates keyframe selection and enriches the selected keyframes with progress-aware descriptions. + +Captioner, which is an 7B model. The closed proprietary models are much larger and trained with much more extensive data; we include them as a useful reference point, but stress that they do not constitute an apples-to-apples comparison, to the disadvantage of our ProgressCaptioner. + +Implementation ProgressCaptioner is constructed with SigLIP [80] as the vision encoder and Qwen2 [62] as the language model, linked through a projector, and initialized from the LLAVA-OV-7B checkpoint [33]. For benchmark evaluations in Sec. 4.1, ProgressCaptioner operates on the full $T$ -frame sequence for a comprehensive temporal context. For applications presented in Sec. 4.2, where fine-grained analysis of local frame changes is crucial, a sliding window approach is used, with the model processing frame pairs. To ensure a fair comparison, all video baseline models are provided with the same temporal context as ProgressCaptioner across all evaluations. + +Results As shown in Table 1, on the FrameCapEval benchmark, ProgressCaptioner greatly outperforms existing open-source VLMs of similar capacity and even the (much larger) latest Gemini-1.5-Pro and GPT-4o. We observe that strong language-backed VLMs like GPT-4o show high caption matching accuracy, whereas Qwen2-VL excels in progression detection, reducing hallucination. However, it tends to produce less detailed captions, leading to lower caption matching accuracy. In contrast, ProgressCaptioner effectively balances precision and detail in frame-wise captioning, consistently leading the benchmark across both indomain and out-of-domain datasets. + +Figure 6 provides qualitative comparisons on three action sequences. Consider the (a) bowling sequence for instance: baseline models erroneously suggest progression in frame 2, like "arm forward", exemplifying the common issue of temporal hallucination in current VLMs. This issue recurs in the other two sequences. Conversely, ProgressCaptioner delivers high-quality captions that precisely characterize action progress in each frame. See Supp. for more qualitative examples and an ablation of ProgressCaptioner. + +User Study Figure 7 presents the user study results, where ProgressCaptioner is compared against four of the strongest competitors: LLAVA-OV, Qwen2-VL, Gemini-1.5-Pro and GPT-4o. Each participant is presented with five captions produced by these models and is tasked with selecting the top-2, with an additional "none" option if the captions are deemed inadequate. ProgressCaptioner emerges as the most preferred model, with an average best caption selection rate of $31.6\% - 2 \times$ to $3.6 \times$ better than the comparably sized best models from the literature [33, 62], and even surpassing top-tier proprietary models that enjoy significant scaling advantages. While our model outperforms all open-source and proprietary models for top-1 preference, the more forgiving top-2 metric brings the proprietary closed models back in the game, though our model remains competitive even there (50.3% for GPT-4o vs. 47.3% for ours). These findings underscore our model's strong ability to produce accurate, temporally fine-grained captions. + +# 4.2. Applications of Video Frame Captioning + +ProgressCaptioner offers progress-aware frame-wise captions, which hold great potential for many real-world applications. We explore several practical use-cases below. + +Keyframe Selection Our first use-case leverages ProgressCaptioner's temporally precise captions as an intermediate representation to identify keyframes within a densely sampled sequence, aided by an LLM (see Supp. for details). Figure 8 provides two examples, showcasing how ProgressCaptioner's produced captions allow selecting distinct frames that effectively capture different stages of the welding and squeezing grapefruit action. While recent video summarization work [24] explores using VLMs and LLMs for keyframe selection, it aims to identify coarse-grained events within long videos, which is not adequate for our problem scenario. See Supp. for a side-to-side comparison and more qualitatives that underscore this distinction. + +Keyframes for Action Recognition Not only is keyframe selection useful for human viewers to quickly preview a + +![](images/6138d919ae380b527566d5e0792f46ba974184174eacd80aa2d9057af94d8b23.jpg) +Figure 9. On Kinetics test videos, ProgressCaptioner selects four frames that are more informative of the action than uniform sampling, resulting in improved action recognition accuracy. + +longer video, but it can also extract the most informative portions of a video to benefit activity recognition [29]. To illustrate, we next apply our keyframe selection mechanism to Kinetics [7] Temporal [57] subset that necessitates multi-frame reasoning. Given that the original video clips are short (sampled at 1FPS, resulting in sequences of 10 frames), we employ two models that take four frames as input: Slow backbone from SlowFast [17] and X3D-XS [16]. We prompt GPT-4o to select four representative frames from frame-wise captions produced by ProgressCaptioner. We take the two model checkpoints that have been trained on the Kinetics training set and replace uniformly sampled frames with our selected keyframes during inference. Figure 9 presents a qualitative comparison, highlighting performance gains such as a $+1.7\%$ increase in top-1 accuracy for both SlowFast and X3D models. Even among just 10 candidate frames, our method's fine-grained ability to identify the 4 most informative ones translates into better recognition. + +Advancing Video Understanding The precise, framewise captions generated by ProgressCaptioner enhance our understanding of videos. To demonstrate this, we consider two video tasks that demand temporally fine-grained understanding: (1) frame-wise classification on HowToChange [72] and Penn Action [82], and (2) video question answering (QA) on NExT-QA [69] (ATP-Hard [5]). These tasks are chosen because they challenge the model to comprehend not just the overarching content of a video, but also the more fine-grained event progression within a video. The HowToChange and Penn Action test sets provide frame-wise labels detailing object state changes or action phases, requiring frame-level understanding. Similarly, NexTQA (ATP-Hard) poses temporally challenging questions that demand multi-frame reasoning, such as determining event order, emphasizing the need for precise temporal comprehension. For baseline comparisons, we evaluate against the LLAVA-OV-7B [33] model, from which ProgressCaptioner is initialized, to highlight the enhancements that our specialized training on FrameCap brings to video understanding tasks. For the first task, as we pioneer a zero-shot, language-guided approach to this traditionally vision-centric problem (details below), no other zero-shot baselines exist. For the second task, we compare ProgressCap + +![](images/e59679fe7f106c6012fe5b6bdbfcb03513eb02f1820bbcf995ec58f4006edc65.jpg) +Figure 10. ProgressCaptioner delivers precise and detailed per-frame descriptions, leading to enhanced zero-shot frame-wise classification performance when compared with LLAVA-OV. + +
ModelAcc@CAcc@TAcc@All
VFC [45]32.230.031.4
VideoAgent [64]57.858.858.4
LLAVA-OV [33] + GPT-4o62.653.458.8
ProgressCaptioner + GPT-4o (ours)64.458.161.8
+ +Table 2. Video QA results on NExT-QA (ATP-Hard). C and T denote causal and temporal subsets, respectively. + +titioner against two existing zero-shot approaches [45, 64]. + +(a) Zero-shot Frame Classification We repurpose zero-shot frame-wise classification task into a multi-choice QA format, using frame-wise captions to guide an LLM in identifying the correct label per frame, evaluating caption accuracy and granularity (Figure 10 left). Results (Figure 10 right) show that ProgressCaptioner consistently outperforms LLAVA-OV across both datasets. Notably, our training involves no signals related to these frame-wise labels, underscoring its generalizability and effectiveness in enhancing video frame-level understanding. + +(b) Video QA Finally, we report results using frame-wise descriptions for video QA, where an LLM (we use GPT-4o) is employed to answer questions on NExT-QA (ATP-Hard) set. As shown in Table 2, ProgressCaptioner achieves the best results on this benchmark, outperforming the previous leader VideoAgent [64] by $+3.4\%$ . Compared with a similar setup using LLAVA-OV, ProgressCaptioner achieves a $+4.7\%$ gain in the temporal subset, highlighting its superior ability to produce fine-grained, temporally precise descriptions and bring enhanced video understanding. + +# 5. Conclusion + +We introduce progress-aware video frame captioning, which necessitates a significant enhancement in current captioning models' capability to describe temporal action dynamics. Towards this end, we develop ProgressCaptioner and show its effectiveness in enhancing the temporal precision and alignment of captions with corresponding frames. Furthermore, we demonstrate its practical applications: keyframe selection and enhanced video understanding. 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In IEEE/CVF International Conference on Computer Vision (ICCV), pages 2248-2255, 2013. 5, 8, 1, 2 +[83] Yuanhan Zhang, Jinming Wu, Wei Li, Bo Li, Zejun Ma, Ziwei Liu, and Chunyuan Li. Video instruction tuning with synthetic data. arXiv preprint arXiv:2410.02713, 2024. 2, 3, 6, 1 +[84] Zhiyuan Zhao, Bin Wang, Linke Ouyang, Xiaoyi Dong, Ji-aqi Wang, and Conghui He. Beyond hallucinations: Enhancing lvlms through hallucination-aware direct preference optimization. arXiv preprint arXiv:2311.16839, 2023. 3 +[85] Luowei Zhou, Chenliang Xu, and Jason Corso. Towards automatic learning of procedures from web instructional videos. In Association for the Advancement of Artificial Intelligence (AAAI), 2018. 1 +[86] Luowei Zhou, Chenliang Xu, and Jason Corso. Towards automatic learning of procedures from web instructional videos. In Association for the Advancement of Artificial Intelligence (AAAI), 2018. 2, 3 +[87] Xingyi Zhou, Anurag Arnab, Shyamal Buch, Shen Yan, Austin Myers, Xuehan Xiong, Arsha Nagrani, and Cordelia + +Schmid. Streaming dense video captioning. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 18243-18252, 2024. 3 \ No newline at end of file diff --git a/2025/Progress-Aware Video Frame Captioning/images.zip b/2025/Progress-Aware Video Frame Captioning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bd76cf4a6d0081f6291522938df38c240700571d --- /dev/null +++ b/2025/Progress-Aware Video Frame Captioning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:00d86825b37408b3b323f4a16f50630ef268612379bc4778a8372cab882dff26 +size 491349 diff --git a/2025/Progress-Aware Video Frame Captioning/layout.json b/2025/Progress-Aware Video Frame Captioning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a2bbeeae3ab6c851fe1c22de2623c0a281aa300e --- /dev/null +++ b/2025/Progress-Aware Video Frame Captioning/layout.json @@ -0,0 +1,10216 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 177, + 103, + 433, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 177, + 103, + 433, + 121 + ], + "spans": [ + { + "bbox": [ + 177, + 103, + 433, + 121 + ], + "type": "text", + "content": "Progress-Aware Video Frame Captioning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "spans": [ + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "content": "Zihui Xue" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "content": ", Joungbin An" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "content": ", Xitong Yang" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "content": ", Kristen Grauman" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 155, + 142, + 453, + 171 + ], + "type": "text", + "content": "University of Texas at Austin" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 199, + 200, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 199, + 200, + 211 + ], + "spans": [ + { + "bbox": [ + 152, + 199, + 200, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 224, + 296, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 224, + 296, + 488 + ], + "spans": [ + { + "bbox": [ + 53, + 224, + 296, + 488 + ], + "type": "text", + "content": "While image captioning provides isolated descriptions for individual images, and video captioning offers one single narrative for an entire video clip, our work explores an important middle ground: progress-aware video captioning at the frame level. This novel task aims to generate temporally fine-grained captions that not only accurately describe each frame but also capture the subtle progression of actions throughout a video sequence. Despite the strong capabilities of existing leading vision language models, they often struggle to discern the nuances of frame-wise differences. To address this, we propose ProgressCaptioner, a captioning model designed to capture the fine-grained temporal dynamics within an action sequence. Alongside, we develop the FrameCap dataset to support training and the FrameCapEval benchmark to assess caption quality. The results demonstrate that ProgressCaptioner significantly surpasses leading captioning models, producing precise captions that accurately capture action progression and set a new standard for temporal precision in video captioning. Finally, we showcase practical applications of our approach, specifically in aiding keyframe selection and advancing video understanding, highlighting its broad utility." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 510, + 135, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 510, + 135, + 522 + ], + "spans": [ + { + "bbox": [ + 56, + 510, + 135, + 522 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 531, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 531, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 531, + 295, + 662 + ], + "type": "text", + "content": "Visual captioning [38]—the task of generating textual descriptions of visual content—is a fundamental problem in computer vision with extensive practical applications. Existing captioning paradigms are broadly divided into two categories: image captioning and video captioning, with a clear distinction between them. Image captioning [23] generates a single, isolated description for each image, with no contextual linkage among different images. In contrast, video captioning [1] assigns a single caption for the entire video clip, aggregating information across frames without addressing the specifics of individual frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 663, + 294, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 663, + 294, + 675 + ], + "spans": [ + { + "bbox": [ + 67, + 663, + 294, + 675 + ], + "type": "text", + "content": "Figure 1 illustrates this dichotomy. 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There is a small amount of oil visible at the bottom of the wok, indicating that it is ready for cooking." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 380, + 283, + 428, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 283, + 428, + 347 + ], + "spans": [ + { + "bbox": [ + 380, + 283, + 428, + 347 + ], + "type": "text", + "content": "Three eggs are being added into the wok. The eggs are still intact and have bright yellow yolks. The wok remains in the same position as in the first frame." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 438, + 283, + 485, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 438, + 283, + 485, + 347 + ], + "spans": [ + { + "bbox": [ + 438, + 283, + 485, + 347 + ], + "type": "text", + "content": "A metal spatula is used to stir the eggs. The eggs are starting to cook, with some white parts becoming more solid while others remain runny." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 498, + 284, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 498, + 284, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 498, + 284, + 545, + 347 + ], + "type": "text", + "content": "The scene transitions to show the same wok, now containing scrambled eggs. The yolks are fully mixed into the whites." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 369, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 456 + ], + "type": "text", + "content": "Figure 1. We propose progress-aware video frame captioning (bottom), which aims to generate a sequence of captions that capture the temporal dynamics within a video. Unlike traditional image and video captioning (top) that focus on broad event-level descriptions, our task delves into the detailed, progressive dynamics of an action, necessitating precise, temporally fine-grained capabilities. Blue text highlights how the progress-aware captions build successively on the earlier content to highlight what is changing." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 471, + 555, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 555, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 555, + 602 + ], + "type": "text", + "content": "age captioning model like BLIP [37] to describe each frame of the video results in captions that are local, not temporally context-aware, and may exhibit little variation across the sequence. Conversely, video captioning provides a global, not temporally fine-grained overview of the event, as exemplified by the YouCook2 [85] ground truth label \"scramble the eggs in the wok\". In both scenarios, the nuances of how the action unfolds over time are missed. This raises the question: Can we develop temporally fine-grained captions that capture the subtle, progressive nature of action sequences? Figure 1 (bottom) illustrates what we seek." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": "Having such progress-aware captions could benefit a great variety of downstream tasks, bringing improved video understanding [73, 79], more precise video retrieval [66-68], and enriched video generation [50, 58]. Moreover, such a capability could open up new AR/VR and robotics applications. For instance, in AI coaching, a captioning system could meticulously analyze an expert's tennis forehand, simplifying the learning process for users. Similarly, for how-to video creation, it could elicit and describe the" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13639" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "type": "text", + "content": "Work conducted as an independent researcher \n" + }, + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 55, + 683, + 294, + 713 + ], + "type": "text", + "content": "Project webpage: https://vision.cs.utexas.edu/projects/ProgressCaptioner." + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 295, + 121 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 295, + 121 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 295, + 121 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 295, + 121 + ], + "type": "image", + "image_path": "c058b9e88e2098a77521a3979eb43f8e0da6845a3366e4720de495cde682a4a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 131, + 295, + 154 + ], + "lines": [ + { + "bbox": [ + 55, + 131, + 295, + 154 + ], + "spans": [ + { + "bbox": [ + 55, + 131, + 295, + 154 + ], + "type": "text", + "content": "Figure 2. Use cases of video frame captioning: finer-grained captions enable detailed, step-by-step guidance for daily tasks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 162, + 295, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 295, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 295, + 198 + ], + "type": "text", + "content": "key object state changes at each stage (e.g., \"how to make whipped cream\")—useful for both content creators as well as visually-impaired users learning a new skill. See Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 198, + 295, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 198, + 295, + 317 + ], + "spans": [ + { + "bbox": [ + 54, + 198, + 295, + 317 + ], + "type": "text", + "content": "Towards this end, we introduce a novel captioning task—progress-aware video captioning at the frame level. This task involves generating captions that not only coherently depict action progression but also tailor each description specifically to its corresponding frame.2 Our task is uniquely characterized by its demand for fine-grained temporal sensitivity. By \"fine-grained\", we refer to generating detailed descriptions that elucidate the stages or procedural steps of the action, effectively conveying how the action is performed throughout the video sequence." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 319, + 295, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 295, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 295, + 474 + ], + "type": "text", + "content": "As discussed, traditional video captioning [9, 63, 70, 86] settles for broad event-level descriptions, where a description like scrambling eggs for the video in Figure 1 would be considered entirely accurate. In contrast, we seek progress-aware captions that detail each stage of the action, such as \"eggs still intact\", \"starting to cook\" and \"fully mixed\". While recent works [6, 8, 11, 12, 61, 83] enhance the overall descriptiveness of video captions, they continue to produce a single video-level description without distinguishing the nuances across time. Our task delves deeper, exploring how each frame contributes to the narrative of the action's progression, thereby setting a new standard for fine-grained temporal precision in video captioning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 475, + 295, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 295, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 295, + 654 + ], + "type": "text", + "content": "Despite great advancements of vision language models (VLMs) [2, 33, 37, 40-42, 62, 75, 81, 83] that have markedly improved visual captioning, we observe that these models still struggle with this nuanced task. Two main issues persist: first, the lack of temporally fine-grained captions; when shown adjacent frames that depict subtle variations in action progression (such as frames 2 and 3 in Figure 3), the generated captions can be overly coarse, failing to differentiate between the frames (see row 2, Gemini1.5-Pro's captions). Second, we identify and term a notable issue of \"temporal hallucination\", where the captions suggest temporal progression in disagreement with what the visual frames exhibit. See frame 2 of Figure 3, where GPT-4o's generated captions (row 1) incorrectly advance the action sequence. The prevalence of such errors can" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 553, + 241 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 553, + 241 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 553, + 241 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 553, + 241 + ], + "type": "image", + "image_path": "a475753a870a3e9e824c7bc301a9bed437a5862d538e247a9c59cead97161916.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 251, + 555, + 318 + ], + "lines": [ + { + "bbox": [ + 313, + 251, + 555, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 555, + 318 + ], + "type": "text", + "content": "Figure 3. Issues of existing VLMs in video frame captioning: (1) Lack of temporal granularity. See captions for frames 2 and 3, produced by Gemini-1.5-Pro (row 2), which fail to distinguish subtle differences between the frames. (2) Temporal hallucination. See frame 2's caption produced by GPT-4o (row 1), which inaccurately suggests progression that is not visible." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 322, + 554, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 322, + 554, + 394 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 554, + 394 + ], + "type": "text", + "content": "be attributed to models' reliance on the common statistics of activity sequences, which mistakenly override matching specific statements to specific frames. Meanwhile, image captioners—even if trained with fine-grained annotations—treat frames in isolation and hence lack the temporal context to say what is progressing versus what is present." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": "We introduce ProgressCaptioner, a model for generating progress-aware frame-level video captions. Our approach uniquely interleaves pseudo labeling with two learning stages. Stage I develops a frame pair captioning model, and stage II extends this to full frame sequences. This process also creates the FrameCap training dataset, comprising action videos along with high-quality frame-wise captions, which are initially generated by an ensemble of VLMs and then filtered using our proposed evaluation methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "text", + "content": "To assess the quality of frame-wise captions and benchmark ProgressCaptioner against leading VLMs, we introduce the FrameCapEval benchmark comprised of videos from four public video action datasets. ProgressCaptioner consistently outperforms leading open-source VLMs with a " + }, + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "inline_equation", + "content": "2.7 \\times" + }, + { + "bbox": [ + 313, + 502, + 554, + 658 + ], + "type": "text", + "content": " improvement in caption quality and also achieves the highest selection rate in user studies, even surpassing the much larger proprietary models GPT-4o [2] and Gemini-1.5-Pro [53]. Finally, we highlight potential applications enabled by our advanced captions: keyframe selection and enhanced video understanding. We hope that our task, model, and benchmark can inspire future development in temporally fine-grained video captioning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 667, + 400, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 667, + 400, + 680 + ], + "spans": [ + { + "bbox": [ + 313, + 667, + 400, + 680 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Image Captioning Image captioning has been extensively studied in recent years [3, 13, 60, 76]. A related line of" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 664, + 295, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 664, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 664, + 295, + 714 + ], + "type": "text", + "content": "2Without loss of generality, we obtain the input frame sequence by uniformly sampling from the action clips at a fixed rate (1FPS). These frames may or may not demonstrate visual action progression from one to the next, demanding that the model discern the difference when generating progress-aware captions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13640" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": "work is image difference captioning, where the task is to describe differences between two images [27, 48, 56] or sets of images [15]. Building on the success of generative models, recent benchmarks [4, 28, 77] challenge models to distinguish between two visually similar images, advancing fine-grained image understanding. However, all the above models are restricted to static (typically synthesized) image pairs and address coarse-grained differences like object presence or absence. Temporal intricacies—accurately describing how an action progresses—remain unexplored." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "type": "text", + "content": "Video Captioning Video captioning [1] aims to produce a single description that encapsulates a video clip. While traditional benchmarks [9, 63, 70, 86] offer a brief onesentence caption for each video, recent efforts expand this scope, extending captioning to hours-long videos [26], enriching the granularity of details [8, 11, 61], enhancing caption uniqueness [49], integrating a causal temporal narrative [46], or introducing LLM summarization [34]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 291, + 296, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 291, + 296, + 459 + ], + "spans": [ + { + "bbox": [ + 55, + 291, + 296, + 459 + ], + "type": "text", + "content": "Adjacent to traditional video captioning are the tasks of visual storytelling [25, 36] (creating a coherent story for a sequence of snapshots), dense video captioning [30, 74, 87] (temporal localization and captioning of all events in an untrimmed video), audio description [20-22] (detailed narrations of visual events in videos (e.g., movies) for visually impaired audiences), and video paragraph captioning [78] (producing a multi-sentence paragraph describing the video). However, all these works still address \"what is happening\" at a coarse-grained event level, e.g., noting that someone is making aSouffle within a specific time range. The ability to break down frame-level details—such as whisking egg whites, folding ingredients, and observing the souffle rising—is still lacking." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 461, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 296, + 533 + ], + "type": "text", + "content": "Vision Language Models Recent advancements in VLMs [2, 33, 37, 40-42, 62, 75, 81, 83] have greatly enhanced the capabilities of both image and video captioning. Despite their strong performance, VLMs often exhibit \"hallucination\" [19, 65], and preference learning [52, 84] has proven effective in mitigating this issue." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 534, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 714 + ], + "type": "text", + "content": "Compared to image-LMs, video-LMs crucially require the integration of temporal dynamics understanding, spurring a series of work on evaluating temporal perception [18, 39, 43, 69]. While these assessments ensure that a model can generate an accurate overall video summary or answer general questions, they entail neither temporal localization nor discernment of fine-grained differences between frames. The OSCaR benchmark [47] focuses on object state change (OSC) captioning, yet it is limited to just three frames and specifically OSC videos, with models and captions not publicly released yet preventing direct comparison. Additionally, their approach relies on human annotation and a single advanced GPT model. In contrast, our approach features a scalable data collection pipeline that reduces reliance on these labor-intensive resources, employs" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 552, + 208 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 552, + 208 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 552, + 208 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 552, + 208 + ], + "type": "image", + "image_path": "aa1341d9a86938e2680af0038c9c60327dbfe4c95497c53234fa5d70a87a6217.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 213, + 541, + 224 + ], + "lines": [ + { + "bbox": [ + 326, + 213, + 541, + 224 + ], + "spans": [ + { + "bbox": [ + 326, + 213, + 541, + 224 + ], + "type": "text", + "content": "Figure 4. Captioning outcomes using Gemini-1.5-Pro [53]." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 232, + 555, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 555, + 291 + ], + "type": "text", + "content": "novel automatic evaluation tasks, and broadens the scope beyond OSC videos. Finally, unlike methods for long-form video and event localization with VLMs [10, 44, 54], our focus is distinctly more temporally fine-grained, concentrating on how individual frames evolve within a single event." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 303, + 381, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 303, + 381, + 316 + ], + "spans": [ + { + "bbox": [ + 314, + 303, + 381, + 316 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 323, + 555, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 555, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 555, + 359 + ], + "type": "text", + "content": "We delve into the specific challenges of our progress-aware video frame captioning problem in Sec. 3.1 and outline ProgressCaptioner's development in Sec. 3.2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 368, + 528, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 368, + 528, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 368, + 528, + 380 + ], + "type": "text", + "content": "3.1. Progress-aware Video Frame Captioning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": "Problem Formulation Our objective is to develop a captioning model that, given a video, produces accurate temporally fine-grained captions. Formally, for a sequence of " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " frames, denoted as " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_i\\}_{i=1}^T" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": ", the captioning model generates a corresponding sequence of captions " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\{c_i\\}_{c=1}^T" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " describes the " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": "-th frame " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " (recall we sample at 1FPS). This captioning process has three key requirements: (1) Accuracy, where each caption " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " must faithfully represent what is visually occurring in frame " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": ", without hallucinating from the context of other frames; (2) Temporal Specificity, where each caption " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " specifically attends to " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": ", without being overly generic to be applicable to multiple frames in the sequence; (3) Progressive Coherence: The sequence of captions " + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i=1}^T" + }, + { + "bbox": [ + 313, + 388, + 555, + 567 + ], + "type": "text", + "content": " should build upon each other to reflect the essential changes in the action over time." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": "FrameCap Dataset To train our captioning model, we require a dataset that pairs frame sequences " + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{V})" + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": " with corresponding captions " + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{C})" + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": ". Existing datasets [9, 63, 70, 86] provide only a single, generic caption for an entire video clip, lacking the frame-wise caption format we need. To address this gap and train our model, we develop the FrameCap dataset. Given the prohibitive expense of collecting human-labeled caption sequences as our ground truth " + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{C})" + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": ", especially at scale, we leverage leading VLMs as powerful tools to create a pseudo caption sequence " + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}" + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": ". For video sources, we refer to two large-scale datasets that focus on fine-grained human activities: HowToChange [72]" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13641" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 91, + 72, + 512, + 235 + ], + "blocks": [ + { + "bbox": [ + 91, + 72, + 512, + 235 + ], + "lines": [ + { + "bbox": [ + 91, + 72, + 512, + 235 + ], + "spans": [ + { + "bbox": [ + 91, + 72, + 512, + 235 + ], + "type": "image", + "image_path": "ef23e90098191fdb05907c04b2c94526641d5fc51cfdbf298f8951d116133dc9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 237, + 555, + 305 + ], + "lines": [ + { + "bbox": [ + 54, + 237, + 555, + 305 + ], + "spans": [ + { + "bbox": [ + 54, + 237, + 555, + 305 + ], + "type": "text", + "content": "Figure 5. Framework of ProgressCaptioner, designed in two stages. In Stage-I, we prepare frame pairs and generate corresponding caption pairs using multiple VLMs. Each pair undergoes our designed progression detection and caption matching evaluations, to decide if they are selected for model supervised fine-tuning or rejected, with the latter contributing to preference data to aid in model preference learning. The Stage-I model training then proceeds using this collected data. In Stage-II, the trained stage-I model labels frame sequences with a two-frame sliding window, in conjunction with other VLMs. These sequences are again assessed through progression detection and caption matching to classify them as selected or rejected. All collected data from both stages contribute to the final training of ProgressCaptioner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 313, + 295, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 295, + 337 + ], + "type": "text", + "content": "(featuring object state change videos from YouTube) and COIN [59] (featuring daily activities from YouTube)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 342, + 296, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 296, + 450 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 296, + 450 + ], + "type": "text", + "content": "Caption Sequence Construction Prompting VLMs for our desired caption sequence is nontrivial. We identify two key problems: (1) Input considerations: how many context frames from " + }, + { + "bbox": [ + 55, + 342, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\{v_i\\}_i^T" + }, + { + "bbox": [ + 55, + 342, + 296, + 450 + ], + "type": "text", + "content": " should be provided? (2) Output assessment: what issues arise in VLM-generated captions, and how can we filter to retain only high-quality ones? To explore these questions, we conduct preliminary experiments by prompting leading VLMs to perform the frame-wise captioning task. We share our findings below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 454, + 295, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 454, + 295, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 454, + 295, + 562 + ], + "type": "text", + "content": "Observation I Intuitively, inputting all " + }, + { + "bbox": [ + 55, + 454, + 295, + 562 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 454, + 295, + 562 + ], + "type": "text", + "content": " frames would seem best. However, current VLM capabilities do not support this extensive context. Specifically, providing too many frames at once often leads to descriptions that lack detail and exhibit temporal inaccuracies, with VLMs also risking memory overload, as similarly observed in [11]. Conversely, providing a single frame at a time reduces the task to image captioning, which is not optimal either, resulting in captions that lack temporal context and coherence." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 564, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 564, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 564, + 295, + 696 + ], + "type": "text", + "content": "Figure 4 shows a representative trial with Gemini-1.5-Pro [53]. Inputting the full sequence (case (a)) yields brief per-frame descriptions with temporal misalignment (i.e., the second caption erroneously describes what is visually occurring in the third frame). On the other hand, captioning frames in isolation (case (b)) removes essential temporal context, where the model mistakes the initial stage of a tennis serve for the follow-through of a forehand swing. These findings underscore the importance of finding a balanced approach and motivate us to adopt a frame pair as the stepping stone of our captioning model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "Observation II Next, building upon the use of a frame" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": "pair " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "(v_{1}, v_{2})" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": ", is the caption pair " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "(\\hat{c}_{1}, \\hat{c}_{2})" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": " produced by existing VLMs of sufficient quality to be directly adopted? Our preliminary experiments reveal two main issues: (a) lack of temporal granularity, and (b) temporal hallucination, as showcased in Figure 3. To dissect these issues, we analyze the captions in relation to the visual progression between frames " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "v_{2}" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": ". Specifically, if there is a visible progression from " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "inline_equation", + "content": "v_{2}" + }, + { + "bbox": [ + 313, + 313, + 555, + 529 + ], + "type": "text", + "content": " (e.g., the slight peeling of a shrimp's shell from frame 2 to frame 3 in Figure 3), the captions should adequately reflect this change. Overly similar captions in such a scenario signify a failure in temporal granularity. Conversely, when there is no change between frames (e.g. frames 1 and 2 in Figure 3), the captions should remain consistent. We deem it a temporal hallucination when captions erroneously indicate progression in disagreement with the visuals. This deficiency in existing VLMs motivates our development of a new captioning model and specialized evaluations for high-quality caption selection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 537, + 424, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 537, + 424, + 550 + ], + "spans": [ + { + "bbox": [ + 314, + 537, + 424, + 550 + ], + "type": "text", + "content": "3.2. ProgressCaptioner" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "text", + "content": "The observations above drive the design of our model, ProgressCaptioner, which unfolds in two stages. Based on our findings that current VLMs have trouble maintaining caption quality when handling extensive " + }, + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "text", + "content": "-frame inputs, our approach begins with frame pair captioning. In the first stage, we develop a ProgressCaptioner to excel at describing the nuances between adjacent frames. The second stage then leverages the first-stage model to pseudo label the full " + }, + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 555, + 555, + 699 + ], + "type": "text", + "content": "-frame sequence with a two-frame sliding window. This staged approach refines caption quality along with model development, enhancing the captioning process iteratively with more precise pseudo labels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "type": "text", + "content": "Frame Pair Data Preparation Starting with a frame pair" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13642" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{v} = (v_{1}, v_{2})" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": ", we employ " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " captioning models to generate an initial set of caption pairs " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "\\{(\\hat{c}_{1}, \\hat{c}_{2})\\}_{1}^{K}" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": ". Acknowledging the potential inaccuracies in these captions, as per observation II, we design two automatic evaluation tasks to assess caption quality. The first task, progression detection, examines progress awareness: it checks whether the captions appropriately reflect visual changes between " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "v_{2}" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": ". Specifically, an LLM assesses each caption pair " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "(\\hat{c}_{1}, \\hat{c}_{2})_{k}" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " to determine if they suggest a visible physical change. We utilize majority voting across multiple LLMs' assessments for all " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " caption pairs to establish a consensus visual-change label. Caption pairs that align with this consensus are marked as passing; others are marked as failing." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": "For pairs passing progression detection, we proceed to our second evaluation task—caption matching—to assess how precisely " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_1" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_2" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " describe " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "v_1" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "v_2" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": ", respectively. The task is designed as a multi-choice question format, where a VLM is given " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_1" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_2" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": ", and an \"unsure\" option, and tasked with matching the correct caption to each frame. A caption pair is considered good if the evaluation VLM correctly identifies " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_1" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "v_1" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "\\hat{c}_2" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "inline_equation", + "content": "v_2" + }, + { + "bbox": [ + 55, + 228, + 294, + 361 + ], + "type": "text", + "content": ". Because the captions will all be topically related, this is essentially a matching task with \"hard negatives\" that lets us automatically gauge the precision of the proposed captions for the target images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "text", + "content": "This automatic pipeline distinguishes between high-quality caption pairs, denoted by " + }, + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}^{+} = (\\hat{c}_{1}^{+},\\hat{c}_{2}^{+})" + }, + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "text", + "content": " , and those that exhibit inaccuracies or hallucinations, denoted by " + }, + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}^{-} = (\\hat{c}_{1}^{-},\\hat{c}_{2}^{-})" + }, + { + "bbox": [ + 55, + 361, + 294, + 409 + ], + "type": "text", + "content": " , forming training data for Stage I.3" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": "Stage I Training Following the success of versatile VLMs in captioning tasks [34, 42, 61, 71], we initialize Progress-Captioner with the LLAVA-OV-7B [33] checkpoint to inherit its pretrained capabilities. Stage-I training utilizes frame and caption pair data collected on HowToChange and COIN YouTube videos " + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle" + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": " through two principal methods: supervised fine-tuning (SFT) and direct preference optimization (DPO). The SFT process is straightforward given our dataset; we perform instructional tuning to tailor the general capabilities of the original VLM to our specific frame-wise captioning requirements using " + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+}\\rangle" + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": ". The subsequent DPO step targets the prevalent issue of hallucination in VLMs and is innovatively driven by our proposed automatic evaluation critics. Preference optimization [52] in LLM training typically requires human-provided preference data to steer LLM responses towards more desirable outputs. Here, we employ progression detection and caption matching to automatically construct preference data " + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}^{+}" + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}^{-}" + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": ", eliminating the reliance on manual labeling. This preference data " + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{v},\\hat{\\mathbf{c}}^{+},\\hat{\\mathbf{c}}^{-}\\rangle" + }, + { + "bbox": [ + 55, + 411, + 295, + 674 + ], + "type": "text", + "content": " is adopted in DPO training to further enhance model performance with feedback from LLM and VLM evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "Frame Sequence Data Preparation The second stage expands our pseudo labeling scheme from 2 to " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " frames, where our Stage-I ProgressCaptioner first generates captions using a two-frame sliding window. To increase data diversity and volume, we also incorporate captions produced by other VLMs, with both two-frame and full " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "-frame contexts, since captions of low-quality are also useful (after undergoing our evaluation tasks, those that are rejected enrich the preference data). Once the initial set of caption sequences is generated, we conduct progression detection to identify " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " visually distinct frames from the original " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "-frame sequence, denoted as " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_M = \\{v_i\\}_{i=1}^M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": ", using majority voting; " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " varies based on the distinctiveness of each frame sequence's content. The caption matching task is then employed to encompass " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " frames, with a selection pool of all " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " captions, " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}_M = \\{\\hat{c}_i\\}_{i=1}^M" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": ", plus an \"unsure\" option. A high-quality caption sequence " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}^+" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " is identified when the evaluation VLM correctly selects " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\hat{c}_i" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": " across all frames. Conversely, a caption sequence is deemed problematic, " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}^-" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": ", if the VLM incorrectly answers more than half of the caption selections. This process forms our Stage-II data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": "Stage II Training Following the same pipeline as stage I, ProgressCaptioner is first trained through SFT using data prepared during both stages, which includes frame-caption pairs " + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "inline_equation", + "content": "<\\mathbf{v}, \\hat{\\mathbf{c}}^{+}>" + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": " and frame-caption sequences " + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "inline_equation", + "content": "<\\mathcal{V}, \\hat{\\mathcal{C}}^{+}>" + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": ". Subsequently, we conduct DPO with preference data collected from both stages " + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "inline_equation", + "content": "<\\mathbf{v}, \\hat{\\mathbf{c}}^{+}, \\hat{\\mathbf{c}}^{-}>" + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "inline_equation", + "content": "<\\mathcal{V}, \\hat{\\mathcal{C}}^{+}, \\hat{\\mathcal{C}}^{-}>" + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": " to further refine performance and mitigate hallucination. This sequential approach results in our final captioning model, that accepts inputs ranging from 2 to " + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 326, + 553, + 483 + ], + "type": "text", + "content": " frames. This flexibility allows users to control the temporal context, balancing the need for local frame-wise changes (smaller window) and global event progressions (larger window). The framework is illustrated in Figure 5." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 494, + 394, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 394, + 507 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 394, + 507 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 514, + 553, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 553, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 553, + 563 + ], + "type": "text", + "content": "We tackle two questions below: (1) How to evaluate frameworkwise caption quality of existing models? And how does ProgressCaptioner perform? (Sec. 4.1); (2) What applications are enabled by precise progress-aware captions? (Sec. 4.2)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 571, + 525, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 571, + 525, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 571, + 525, + 583 + ], + "type": "text", + "content": "4.1. Benchmarking Video Frame Captioning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 591, + 553, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 553, + 698 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 553, + 698 + ], + "type": "text", + "content": "Benchmark Data Curation We establish the FrameCapEval benchmark, featuring videos from four action understanding datasets: HowToChange [72] and COIN [59] (on which ProgressCaptioner was trained), along with Penn Action [82] and Kinetics [7], which are unseen in training and serve to assess generalization capabilities. We are mindful of the single frame bias [32] and manually verify all videos to exclude sequences lacking fine-grained action progression. This process yields a final set of 684 videos." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "content": "Evaluation Metrics We employ the automatic evalua" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": "3We encourage readers to view data examples provided in Supp. for a better understanding of our data refinement process, as well as details on pseudo labeling, prompts used, and the " + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": " VLMs we employ." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13643" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 88, + 72, + 153, + 110 + ], + "blocks": [ + { + "bbox": [ + 74, + 85, + 85, + 95 + ], + "lines": [ + { + "bbox": [ + 74, + 85, + 85, + 95 + ], + "spans": [ + { + "bbox": [ + 74, + 85, + 85, + 95 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 88, + 72, + 153, + 110 + ], + "lines": [ + { + "bbox": [ + 88, + 72, + 153, + 110 + ], + "spans": [ + { + "bbox": [ + 88, + 72, + 153, + 110 + ], + "type": "image", + 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Qualitative comparisons of ProgressCaptioner with SOTA VLMs on three action sequences. For sequences (a) and (b), only the middle frame predictions are displayed. See Supp. for all models' predictions on full sequences and more examples. Inaccuracies in descriptions are highlighted in red. Even top VLMs often produce descriptions that misalign with the corresponding frames, while ProgressCaptioner delivers hallucination-free and temporally fine-grained captions, including phrases explicitly calling out progress (blue)." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 220, + 267, + 286, + 316 + ], + "blocks": [ + { + "bbox": [ + 220, + 267, + 286, + 316 + ], + "lines": [ + { + "bbox": [ + 220, + 267, + 286, + 316 + ], + "spans": [ + { + "bbox": [ + 220, + 267, + 286, + 316 + ], + "type": "image", + "image_path": "b103bfb9153ab78ca927d7d03b978ce94cc4ab800695daa57faff6710f3bb832.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 314, + 72, + 378, + 110 + ], + "blocks": [ + { + "bbox": [ + 302, + 85, + 313, + 95 + ], + "lines": [ + { + "bbox": [ + 302, + 85, + 313, + 95 + ], + "spans": [ + { + "bbox": [ + 302, + 85, + 313, + 95 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 314, + 72, + 378, + 110 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 378, + 110 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 378, + 110 + ], + "type": "image", + "image_path": "f500e5bb089d20ee3417ec3170d2a04f4eed89610368fa953d91b7abfa26b738.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 390, + 72, + 455, + 110 + ], + "blocks": [ + { + "bbox": [ + 390, + 72, + 455, + 110 + ], + "lines": [ + { + "bbox": [ + 390, + 72, + 455, + 110 + ], + "spans": [ + { + "bbox": [ + 390, + 72, + 455, + 110 + ], + "type": "image", + "image_path": "622274eac135f4e64a400f4562630e4b3ea1c9f71eb66993d26560cc07f2eec1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 467, + 72, + 531, + 110 + ], + "blocks": [ + { + "bbox": [ + 467, + 72, + 531, + 110 + ], + "lines": [ + { + "bbox": [ + 467, + 72, + 531, + 110 + ], + "spans": [ + { + "bbox": [ + 467, + 72, + 531, + 110 + ], + "type": "image", + "image_path": "33396d83b80c54a1d97d35e82ccecaca6e31c83dd768994e7e74f23dd68106bd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 118, + 375, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 118, + 375, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 118, + 375, + 172 + ], + "type": "text", + "content": "[LLAVA-OV] The tofu cubes are now being cooked in the pan. They have started to brown slightly on the edges, indicating they are being seared." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 180, + 374, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 374, + 219 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 374, + 219 + ], + "type": "text", + "content": "[Gemini-1.5-Pro] The tofu cubes are being added to the pan, some are already sizzling in the oil." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 227, + 376, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 376, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 376, + 304 + ], + "type": "text", + "content": "[ProgressCaptioner] In this frame, a hand is seen placing tofu cubes into a black frying pan. The pan is on a stove, and the tofu is being added to it, indicating the start of the cooking process." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 393, + 118, + 457, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 118, + 457, + 163 + ], + "spans": [ + { + "bbox": [ + 393, + 118, + 457, + 163 + ], + "type": "text", + "content": "[GPT-4o] The tofu cubes are now visibly sizzling in the pan, beginning to develop a light golden hue on their surfaces." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 393, + 172, + 457, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 172, + 457, + 226 + ], + "spans": [ + { + "bbox": [ + 393, + 172, + 457, + 226 + ], + "type": "text", + "content": "[LLAVA-Video] The tofu cubes are shown browning in the pan, with some pieces already turning golden brown while others are still pale." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 393, + 234, + 455, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 234, + 455, + 312 + ], + "spans": [ + { + "bbox": [ + 393, + 234, + 455, + 312 + ], + "type": "text", + "content": "[ProgressCaptioner] This frame displays a close-up view of the same black frying pan filled with cubed tofu. The tofu pieces are evenly distributed throughout the pan, and there is no visible action taking place." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 473, + 118, + 527, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 473, + 118, + 527, + 148 + ], + "spans": [ + { + "bbox": [ + 473, + 118, + 527, + 148 + ], + "type": "text", + "content": "[Idefics2] The tofu cubes are still browned, but they have a darker color." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 473, + 157, + 529, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 473, + 157, + 529, + 180 + ], + "spans": [ + { + "bbox": [ + 473, + 157, + 529, + 180 + ], + "type": "text", + "content": "[Qwen2-VL] The tofu is being cooked in the pan." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 473, + 188, + 533, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 473, + 188, + 533, + 312 + ], + "spans": [ + { + "bbox": [ + 473, + 188, + 533, + 312 + ], + "type": "text", + "content": "[ProgressCaptioner] The frame displays the same black frying pan filled with cubed tofu, but now the tofu has a golden-brown color, indicating that it has been cooked and is likely being fried. The tofu pieces appear crispy and well-cooked, suggesting that they have been in the pan for sometime." + } + ] + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 56, + 385, + 294, + 547 + ], + "blocks": [ + { + "bbox": [ + 56, + 385, + 294, + 547 + ], + "lines": [ + { + "bbox": [ + 56, + 385, + 294, + 547 + ], + "spans": [ + { + "bbox": [ + 56, + 385, + 294, + 547 + ], + "type": "table", + "html": "
ModelSizeHTCCOINPenn&K
CapProgCapProgCapProg
Proprietary models
Gemini-1.5-Pro [53] (img)-28.459.724.358.615.351.2
Gemini-1.5-Pro [53]-31.463.825.063.817.660.3
GPT-4o [2]-32.464.221.358.418.263.2
Open-source models
Idefics2 [31]8B2.054.42.952.212.550.9
VILA [40]8B6.953.65.148.215.951.4
Qwen2-VL [62]7B13.769.611.070.88.558.8
LLAVA-Video [83]7B3.959.38.853.09.751.8
LLAVA-OV [33] (img)7B5.956.317.655.411.955.5
LLAVA-OV [33]7B7.859.05.957.35.150.8
PL (VLM ensemble)-18.662.517.660.119.352.4
ProgressCaptioner (ours)7B37.373.632.366.131.363.7
", + "image_path": "c4508c176cff0dc0d9d881e2af33913713e80192f573f89e02d3c8e733109bc5.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_body" + } + ], + "index": 26 + }, + { + "bbox": [ + 54, + 555, + 295, + 677 + ], + "lines": [ + { + "bbox": [ + 54, + 555, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 54, + 555, + 295, + 677 + ], + "type": "text", + "content": "Table 1. Results on the FrameCapEval Benchmark, composed of video from four public datasets. Cap and Prog denote caption matching and progression detection accuracy, respectively. PL denotes the pseudo labeling baseline adopting filtered captions from multiple VLMs. ProgressCaptioner greatly outperforms SOTA open-source VLMs and even the leading proprietary models, despite being a 7B model. The best results are bolded and underlined, the second best are bolded, and the third best are italicized. The results confirm our model's generalizability from in-domain datasets (HTC for HowToChange and COIN) to external datasets not seen during training (Penn&K for Penn Action and Kinetics)." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "tion tasks of progression detection and caption matching (Sec. 3.2), reporting accuracy with Llama-3.1-70B" + } + ] + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 342, + 391, + 524, + 495 + ], + "blocks": [ + { + "bbox": [ + 342, + 391, + 524, + 495 + ], + "lines": [ + { + "bbox": [ + 342, + 391, + 524, + 495 + ], + "spans": [ + { + "bbox": [ + 342, + 391, + 524, + 495 + ], + "type": "image", + "image_path": "fa5f53838a540ba5e032d2ab3323713ea0246ca621b54ffb2dc3568cdfe9b1d8.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 496, + 554, + 519 + ], + "lines": [ + { + "bbox": [ + 313, + 496, + 554, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 554, + 519 + ], + "type": "text", + "content": "Figure 7. User study results comparing ProgressCaptioner with top competitors show it as the most preferred model (see text)." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 529, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 554, + 590 + ], + "type": "text", + "content": "Instruct [14] as the evaluation LLM and Gemini-1.5-Pro [53] as the evaluation VLM. Additionally, we enhance our evaluation with a user study of 15 participants, reporting the average selection rate. See Supp. for experiments on evaluation metric reliability and full user study details." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "Baselines We evaluate an array of state-of-the-art VLMs, including two proprietary models, GPT-4o [2] and Gemini1.5-Pro [53], and five open-source models—Idefics2 [31], VILA [40], Qwen2-VL [62], LLAVA-Video [83], and LLAVA-OV [33]. We also include a pseudo labeling baseline using filtered captions produced by an ensemble of VLMs (Sec. 3), and image captioning baselines using Gemini-1.5-Pro and LLAVA-OV. We select open-source VLM variants with fewer than 10B parameters for computational efficiency and a fair comparison with our Progress" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "13644" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 119, + 70, + 492, + 216 + ], + "blocks": [ + { + "bbox": [ + 119, + 70, + 492, + 216 + ], + "lines": [ + { + "bbox": [ + 119, + 70, + 492, + 216 + ], + "spans": [ + { + "bbox": [ + 119, + 70, + 492, + 216 + ], + "type": "image", + "image_path": "2912ea9319633ffe89f419cb930ad89e2b0993fabc2014fd9f3f32f57b358da8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 224, + 536, + 236 + ], + "lines": [ + { + "bbox": [ + 70, + 224, + 536, + 236 + ], + "spans": [ + { + "bbox": [ + 70, + 224, + 536, + 236 + ], + "type": "text", + "content": "Figure 8. ProgressCaptioner facilitates keyframe selection and enriches the selected keyframes with progress-aware descriptions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 244, + 296, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 244, + 296, + 305 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 296, + 305 + ], + "type": "text", + "content": "Captioner, which is an 7B model. The closed proprietary models are much larger and trained with much more extensive data; we include them as a useful reference point, but stress that they do not constitute an apples-to-apples comparison, to the disadvantage of our ProgressCaptioner." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 310, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 310, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 310, + 296, + 453 + ], + "type": "text", + "content": "Implementation ProgressCaptioner is constructed with SigLIP [80] as the vision encoder and Qwen2 [62] as the language model, linked through a projector, and initialized from the LLAVA-OV-7B checkpoint [33]. For benchmark evaluations in Sec. 4.1, ProgressCaptioner operates on the full " + }, + { + "bbox": [ + 55, + 310, + 296, + 453 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 310, + 296, + 453 + ], + "type": "text", + "content": "-frame sequence for a comprehensive temporal context. For applications presented in Sec. 4.2, where fine-grained analysis of local frame changes is crucial, a sliding window approach is used, with the model processing frame pairs. To ensure a fair comparison, all video baseline models are provided with the same temporal context as ProgressCaptioner across all evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 459, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 296, + 602 + ], + "type": "text", + "content": "Results As shown in Table 1, on the FrameCapEval benchmark, ProgressCaptioner greatly outperforms existing open-source VLMs of similar capacity and even the (much larger) latest Gemini-1.5-Pro and GPT-4o. We observe that strong language-backed VLMs like GPT-4o show high caption matching accuracy, whereas Qwen2-VL excels in progression detection, reducing hallucination. However, it tends to produce less detailed captions, leading to lower caption matching accuracy. In contrast, ProgressCaptioner effectively balances precision and detail in frame-wise captioning, consistently leading the benchmark across both indomain and out-of-domain datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": "Figure 6 provides qualitative comparisons on three action sequences. Consider the (a) bowling sequence for instance: baseline models erroneously suggest progression in frame 2, like \"arm forward\", exemplifying the common issue of temporal hallucination in current VLMs. This issue recurs in the other two sequences. Conversely, ProgressCaptioner delivers high-quality captions that precisely characterize action progress in each frame. See Supp. for more qualitative examples and an ablation of ProgressCaptioner." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "text", + "content": "User Study Figure 7 presents the user study results, where ProgressCaptioner is compared against four of the strongest competitors: LLAVA-OV, Qwen2-VL, Gemini-1.5-Pro and GPT-4o. Each participant is presented with five captions produced by these models and is tasked with selecting the top-2, with an additional \"none\" option if the captions are deemed inadequate. ProgressCaptioner emerges as the most preferred model, with an average best caption selection rate of " + }, + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "inline_equation", + "content": "31.6\\% - 2 \\times" + }, + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "inline_equation", + "content": "3.6 \\times" + }, + { + "bbox": [ + 313, + 244, + 555, + 461 + ], + "type": "text", + "content": " better than the comparably sized best models from the literature [33, 62], and even surpassing top-tier proprietary models that enjoy significant scaling advantages. While our model outperforms all open-source and proprietary models for top-1 preference, the more forgiving top-2 metric brings the proprietary closed models back in the game, though our model remains competitive even there (50.3% for GPT-4o vs. 47.3% for ours). These findings underscore our model's strong ability to produce accurate, temporally fine-grained captions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 472, + 528, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 528, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 528, + 485 + ], + "type": "text", + "content": "4.2. Applications of Video Frame Captioning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "type": "text", + "content": "ProgressCaptioner offers progress-aware frame-wise captions, which hold great potential for many real-world applications. We explore several practical use-cases below." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 531, + 556, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 556, + 686 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 556, + 686 + ], + "type": "text", + "content": "Keyframe Selection Our first use-case leverages ProgressCaptioner's temporally precise captions as an intermediate representation to identify keyframes within a densely sampled sequence, aided by an LLM (see Supp. for details). Figure 8 provides two examples, showcasing how ProgressCaptioner's produced captions allow selecting distinct frames that effectively capture different stages of the welding and squeezing grapefruit action. While recent video summarization work [24] explores using VLMs and LLMs for keyframe selection, it aims to identify coarse-grained events within long videos, which is not adequate for our problem scenario. See Supp. for a side-to-side comparison and more qualitatives that underscore this distinction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "content": "Keyframes for Action Recognition Not only is keyframe selection useful for human viewers to quickly preview a" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13645" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 71, + 282, + 160 + ], + "blocks": [ + { + "bbox": [ + 69, + 71, + 282, + 160 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 282, + 160 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 282, + 160 + ], + "type": "image", + "image_path": "6138d919ae380b527566d5e0792f46ba974184174eacd80aa2d9057af94d8b23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 167, + 296, + 201 + ], + "lines": [ + { + "bbox": [ + 55, + 167, + 296, + 201 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 296, + 201 + ], + "type": "text", + "content": "Figure 9. On Kinetics test videos, ProgressCaptioner selects four frames that are more informative of the action than uniform sampling, resulting in improved action recognition accuracy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 207, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 207, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 56, + 207, + 296, + 422 + ], + "type": "text", + "content": "longer video, but it can also extract the most informative portions of a video to benefit activity recognition [29]. To illustrate, we next apply our keyframe selection mechanism to Kinetics [7] Temporal [57] subset that necessitates multi-frame reasoning. Given that the original video clips are short (sampled at 1FPS, resulting in sequences of 10 frames), we employ two models that take four frames as input: Slow backbone from SlowFast [17] and X3D-XS [16]. We prompt GPT-4o to select four representative frames from frame-wise captions produced by ProgressCaptioner. We take the two model checkpoints that have been trained on the Kinetics training set and replace uniformly sampled frames with our selected keyframes during inference. Figure 9 presents a qualitative comparison, highlighting performance gains such as a " + }, + { + "bbox": [ + 56, + 207, + 296, + 422 + ], + "type": "inline_equation", + "content": "+1.7\\%" + }, + { + "bbox": [ + 56, + 207, + 296, + 422 + ], + "type": "text", + "content": " increase in top-1 accuracy for both SlowFast and X3D models. Even among just 10 candidate frames, our method's fine-grained ability to identify the 4 most informative ones translates into better recognition." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 426, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 426, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 426, + 296, + 714 + ], + "type": "text", + "content": "Advancing Video Understanding The precise, framewise captions generated by ProgressCaptioner enhance our understanding of videos. To demonstrate this, we consider two video tasks that demand temporally fine-grained understanding: (1) frame-wise classification on HowToChange [72] and Penn Action [82], and (2) video question answering (QA) on NExT-QA [69] (ATP-Hard [5]). These tasks are chosen because they challenge the model to comprehend not just the overarching content of a video, but also the more fine-grained event progression within a video. The HowToChange and Penn Action test sets provide frame-wise labels detailing object state changes or action phases, requiring frame-level understanding. Similarly, NexTQA (ATP-Hard) poses temporally challenging questions that demand multi-frame reasoning, such as determining event order, emphasizing the need for precise temporal comprehension. For baseline comparisons, we evaluate against the LLAVA-OV-7B [33] model, from which ProgressCaptioner is initialized, to highlight the enhancements that our specialized training on FrameCap brings to video understanding tasks. For the first task, as we pioneer a zero-shot, language-guided approach to this traditionally vision-centric problem (details below), no other zero-shot baselines exist. For the second task, we compare ProgressCap" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 328, + 73, + 538, + 167 + ], + "blocks": [ + { + "bbox": [ + 328, + 73, + 538, + 167 + ], + "lines": [ + { + "bbox": [ + 328, + 73, + 538, + 167 + ], + "spans": [ + { + "bbox": [ + 328, + 73, + 538, + 167 + ], + "type": "image", + "image_path": "e59679fe7f106c6012fe5b6bdbfcb03513eb02f1820bbcf995ec58f4006edc65.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 173, + 555, + 206 + ], + "lines": [ + { + "bbox": [ + 313, + 173, + 555, + 206 + ], + "spans": [ + { + "bbox": [ + 313, + 173, + 555, + 206 + ], + "type": "text", + "content": "Figure 10. ProgressCaptioner delivers precise and detailed per-frame descriptions, leading to enhanced zero-shot frame-wise classification performance when compared with LLAVA-OV." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 323, + 209, + 545, + 266 + ], + "blocks": [ + { + "bbox": [ + 323, + 209, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 323, + 209, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 323, + 209, + 545, + 266 + ], + "type": "table", + "html": "
ModelAcc@CAcc@TAcc@All
VFC [45]32.230.031.4
VideoAgent [64]57.858.858.4
LLAVA-OV [33] + GPT-4o62.653.458.8
ProgressCaptioner + GPT-4o (ours)64.458.161.8
", + "image_path": "0505d52028a89b773e8676ad703e6bc5bbd454f76e11989b2b5596dc1775b252.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 268, + 555, + 291 + ], + "lines": [ + { + "bbox": [ + 313, + 268, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 555, + 291 + ], + "type": "text", + "content": "Table 2. Video QA results on NExT-QA (ATP-Hard). C and T denote causal and temporal subsets, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 297, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 297, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 297, + 545, + 308 + ], + "type": "text", + "content": "titioner against two existing zero-shot approaches [45, 64]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 310, + 554, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 554, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 554, + 430 + ], + "type": "text", + "content": "(a) Zero-shot Frame Classification We repurpose zero-shot frame-wise classification task into a multi-choice QA format, using frame-wise captions to guide an LLM in identifying the correct label per frame, evaluating caption accuracy and granularity (Figure 10 left). Results (Figure 10 right) show that ProgressCaptioner consistently outperforms LLAVA-OV across both datasets. Notably, our training involves no signals related to these frame-wise labels, underscoring its generalizability and effectiveness in enhancing video frame-level understanding." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": "(b) Video QA Finally, we report results using frame-wise descriptions for video QA, where an LLM (we use GPT-4o) is employed to answer questions on NExT-QA (ATP-Hard) set. As shown in Table 2, ProgressCaptioner achieves the best results on this benchmark, outperforming the previous leader VideoAgent [64] by " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "+3.4\\%" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": ". Compared with a similar setup using LLAVA-OV, ProgressCaptioner achieves a " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "+4.7\\%" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": " gain in the temporal subset, highlighting its superior ability to produce fine-grained, temporally precise descriptions and bring enhanced video understanding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "content": "We introduce progress-aware video frame captioning, which necessitates a significant enhancement in current captioning models' capability to describe temporal action dynamics. Towards this end, we develop ProgressCaptioner and show its effectiveness in enhancing the temporal precision and alignment of captions with corresponding frames. Furthermore, we demonstrate its practical applications: keyframe selection and enhanced video understanding. By setting a new standard for temporal precision in video captioning, we hope our work inspires further development in this domain." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "13646" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 91, + 290, + 103 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 91, + 290, + 103 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 290, + 103 + ], + "type": "text", + "content": "Research supported in part by the IFML NSF AI Institute." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "spans": [ + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 133, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 133, + 295, + 198 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 133, + 295, + 198 + ], + "spans": [ + { + "bbox": [ + 61, + 133, + 295, + 198 + ], + "type": "text", + "content": "[1] Moloud Abdar, Meenakshi Kollati, Swaraja Kuraparthi, Farhad Pourpanah, Daniel McDuff, Mohammad Ghavamzadeh, Shuicheng Yan, Abduallah Mohamed, Abbas Khosravi, Erik Cambria, et al. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 18243-18252, 2024. 3" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "13650" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_content_list.json b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..97ac23ad791f172d402459389a9127173f5ffb9b --- /dev/null +++ b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_content_list.json @@ -0,0 +1,1653 @@ +[ + { + "type": "text", + "text": "Progressive Correspondence Regenerator for Robust 3D Registration", + "text_level": 1, + "bbox": [ + 150, + 130, + 848, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guiyu Zhao $^{1,2,4}$ , Sheng Ao $^{1,2,3}$ , Ye Zhang $^{3\\dagger}$ , Kai Xu $^{5}$ , Yulan Guo $^{3}$", + "bbox": [ + 240, + 179, + 754, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University", + "bbox": [ + 153, + 199, + 843, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China 3Sun Yat-sen University", + "bbox": [ + 169, + 215, + 826, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ Beijing Institute of Technology $^{5}$ National University of Defense Technology", + "bbox": [ + 191, + 251, + 799, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 304, + 326, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Obtaining enough high-quality correspondences is crucial for robust registration. Existing correspondence refinement methods mostly follow the paradigm of outlier removal, which either fails to correctly identify the accurate correspondences under extreme outlier ratios, or select too few correct correspondences to support robust registration. To address this challenge, we propose a novel approach named Regor, which is a progressive correspondence generator that generates higher-quality matches whilst sufficiently robust for numerous outliers. In each iteration, we first apply prior-guided local grouping and generalized mutual matching to generate the local region correspondences. A powerful center-aware three-point consistency is then presented to achieve local correspondence correction, instead of removal. Further, we employ global correspondence refinement to obtain accurate correspondences from a global perspective. Through progressive iterations, this process yields a large number of high-quality correspondences. Extensive experiments on both indoor and outdoor datasets demonstrate that the proposed Regor significantly outperforms existing outlier removal techniques. More critically, our approach obtains 10 times more correct correspondences than outlier removal methods. As a result, our method is able to achieve robust registration even with weak features. The code is available at [Regor].", + "bbox": [ + 86, + 337, + 483, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 744, + 220, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Point cloud registration [8, 21] is a fundamental and critical task in 3D computer vision, with widespread applications across various domains such as robotic localization [36, 42] and remote sensing [21, 35]. Point cloud registration aims to estimate a rigid transformation to align two point clouds scanned from different perspectives. With the advancement", + "bbox": [ + 89, + 771, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5e3d55d3854d2fb91c7087265aad59ffaf4edddf5ee683c386f3e2091bc343bc.jpg", + "image_caption": [ + "(a) Existing Methods", + "Figure 1. Difference between our method and existing outlier removal techniques. Outlier removal methods perform top-down pruning, producing an optimized set of correspondences that is a subset of the initial correspondences. When the initial inliers are few, this approach can obtain only a limited number of inliers, which is insufficient for robust pose estimation. In contrast, our method takes a bottom-up approach, using a regeneration strategy to generate more inliers, thereby effectively addressing this issue." + ], + "image_footnote": [], + "bbox": [ + 517, + 305, + 696, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/875f1fa3c092e798725c207e9675f40e2c4ed381a6e08fd12e33425f3acee42b.jpg", + "image_caption": [ + "(b) Our Method" + ], + "image_footnote": [], + "bbox": [ + 723, + 305, + 903, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of feature metric learning, feature-based point cloud registration methods [1, 20, 30, 43] have garnered significant attention and achieved promising results. However, in scenarios characterized by low overlap and high noise, direct feature matching often leads to a large number of outliers, which poses a great challenge for point cloud registration.", + "bbox": [ + 511, + 684, + 906, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Currently, the mainstream approach to address the issue of numerous outliers in point cloud registration is to filter wrong correspondences. Existing outlier removal methods [3, 6, 22, 27, 47] can be categorized into two types: geometry-based methods and learning-based methods. Geometry-based methods [6, 14, 28, 47] typically remove outliers according to whether point correspondences satisfy geometric consistency. Learning-based methods [3,", + "bbox": [ + 511, + 779, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally.", + "bbox": [ + 107, + 875, + 297, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding Author.", + "bbox": [ + 111, + 887, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1210", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "22, 27] treat this task as a classification problem to distinguish between outliers and inliers. However, in challenging scenarios, these correspondence filtering methods all suffer from a common problem: when initial correspondences only contains few inliers, estimating the correct rigid transformation between two point clouds is extremely difficult even if all inliers are identified.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to design a new 3D registration architecture, which is robust to few inliers and is able to estimate precise 6DoF pose. As shown in Figure 1, different from existing outlier removal methods [3, 6, 7, 47] that focus on pruning correspondences, our approach clearly regenerate more high-quality correspondences to achieve robust registration. The key insight is to progressively generate correspondences and leverage the positional priors of correspondences from the previous iteration to guide more refined local regeneration, thereby obtaining more high-quality point correspondences.", + "bbox": [ + 88, + 198, + 480, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method, named Regor, follows a progressive iterative framework composed of three main modules: Local Grouping and Rematching, Local Correspondence Refinement and Global Correspondence Refinement. In each iteration, Local Grouping and Rematching leverages prior-guided local grouping to gradually reduce the matching space and generalized mutual matching to perform reliable local matching. The Local Correspondence Refinement introduces an effective center-aware three-point consistency to mine inliers and update local correspondences. The Global Correspondence Refinement is employed to perform further optimization from a global perspective. Note that, each iteration gradually increases the number of inliers, instead of only removing outliers. Our method achieves state-of-the-art performance on both the 3DMatch [46] and KITTI [16] datasets. Notably, the proposed Regor demonstrates a strong ability to generate correspondences, yielding up to 10 times more correct matches than existing outlier removal methods [6, 7, 47]. The main contributions of this paper are as follows:", + "bbox": [ + 91, + 364, + 482, + 667 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel registration approach named Regor to obtain massive high-quality point correspondences, overcoming the challenge of scarce inliers by progressively generating correspondences.", + "- Our method achieves state-of-the-art performance. In particular, the number of correct correspondences is 10 times higher than that of outlier removal methods.", + "- Benefiting from the proposed regenerator, our approach achieves robust registration even with weak features." + ], + "bbox": [ + 89, + 667, + 482, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 821, + 232, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 3D Feature Matching", + "text_level": 1, + "bbox": [ + 89, + 847, + 290, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Feature matching is a crucial step in correspondence-based point cloud registration [1, 20, 30, 32, 43, 45, 46]. Accord", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing to the approach of feature extraction, feature matching methods can be categorized into two types: traditional descriptor-based methods [31-33] and learning-based methods [1, 20, 30, 43, 45]. Before the widespread adoption of deep learning, features were manually designed descriptors tailored to represent local information. They are classified into LRF-based methods [18, 33] and LRF-free methods [31, 32] based on whether a local reference frame (LRF) is needed. With the advancements in deep learning, numerous learning-based methods have emerged. Based on the representation strategy, they can be further divided into patch-based methods [1, 17, 49] and fragment-based methods [9, 15, 20, 43]. SpinNet [1] and BUFFER [2] have achieved excellent generalization ability through 3D cylindrical convolution. Additionally, CoFiNet [43] and GeoTransformer [30] propose a coarse-to-fine matching strategy and a Transformer-based framework, which has garnered widespread attention. Subsequent methods [23, 37, 44, 45] have further improved performance by incorporating position encoding and prior information into this framework. ODIN [23] achieves the best performance through diffusion strategy and global optimization.", + "bbox": [ + 511, + 90, + 903, + 424 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Geometry-based Outlier Removal", + "text_level": 1, + "bbox": [ + 511, + 435, + 808, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geometry-based outlier removal involves fitting models from noisy correspondences using the geometric properties of 3D scenes to estimate poses. The most classic method is random sampling consensus (RANSAC) [14], which samples correspondences multiple times and validates to obtain the best pose, thus mitigating the impact of noisy correspondences. Subsequently, numerous variants of RANSAC [4, 5, 12, 34] have been proposed to address issues of time consumption and instability. TEASER [38] introduces the truncated least squares (TLS) cost to solve for pose and employ rotation invariant measurements to handle outliers. Then, $\\mathrm{SC^2}$ -PCR [6, 7] propose second-order consistency for robust outlier removal. In recent years, methods [39, 47] based on geometric consistency have been widely applied in point cloud registration, leveraging graph-theoretic approaches [13] and geometric consistency to remove outliers, thereby achieving robust registration.", + "bbox": [ + 511, + 458, + 906, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Learning-based Outlier Removal", + "text_level": 1, + "bbox": [ + 511, + 726, + 802, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent researches [3, 22, 29] have integrated deep learning into outlier removal and pose estimation, showcasing promising performance through training. Inspired by image matching [41], 3DRegNet [29] adapts CN-Net [41] to remove outliers in point cloud registration. Subsequently, PointDSC [3] embeds the spatial consistency into feature maps and employs neural spectral matching to estimate confidence of correspondences, achieving robust registration. VBReg [22] utilizes variational Bayesian inference to achieve better outlier removal. Hunter [40] addresses severe", + "bbox": [ + 511, + 750, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1211", + "bbox": [ + 483, + 945, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a1b3ba4747a198ac85ef57a190ff03c990f5ba0c887bd6a1656fd7b26c914e91.jpg", + "image_caption": [ + "Figure 2. Overall framework of our method. We extract features from the original point cloud, obtaining features $\\mathbf{F}^{\\mathcal{P}}$ and $\\mathbf{F}^{\\mathcal{Q}}$ as input for our method. Subsequently, a progressive process is applied to iteratively regenerate more accurate and denser correspondences $\\mathcal{G}^t$ . At each iteration, the output correspondences $\\mathcal{G}^{t-1}$ from the previous iteration serve as input. Firstly, prior-guided local grouping is employed to sample seed corresponding points and form local correspondence regions $\\mathbf{P}_i^t$ and $\\mathbf{Q}_i^t$ . Then, for each pair of local correspondence regions, generalized mutual matching is performed to get new correspondences. Next, these correspondences are refined locally and globally using our center-aware three-point consistency, followed by a merging operation $\\oplus$ of local correspondences $\\mathcal{G}_i^t$ using a hash table. Finally, using these refined correspondences, we achieve robust and accurate transformation estimation $\\mathbf{T}\\{\\mathbf{R}, \\mathbf{t}\\}$ only with SVD." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 897, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "outlier issues by introducing higher-order consistency using hypergraphs. However, while both geometry-based and learning-based methods have shown effectiveness in outlier removal, they inherently rely on the initial correspondences and only trim down on them, which poses challenges when initial inliers are scarce.", + "bbox": [ + 88, + 438, + 480, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 545, + 181, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 89, + 571, + 294, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Point cloud registration is aligning two point clouds $\\mathbf{P}$ and $\\mathbf{Q}$ , captured from different perspectives, by estimating a pose transformation $\\mathbf{T} \\{\\mathbf{R}, \\mathbf{t}\\}$ where $\\mathbf{R}$ is a rotation matrix and $\\mathbf{t}$ is a translation vector. Feature-based point cloud registration estimates correspondences through feature extraction and matching, then minimizes the average Euclidean distance between these correspondences, as shown in Eq. 1:", + "bbox": [ + 89, + 594, + 482, + 700 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {R} \\in S O (3), \\mathbf {t} \\in \\mathbb {R} ^ {3}} {\\arg \\min } \\sum_ {\\left(\\mathbf {p} _ {x _ {i}}, \\mathbf {q} _ {y _ {i}}\\right) \\in \\mathcal {I}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {x _ {i}} + \\mathbf {t} - \\mathbf {q} _ {y _ {i}} \\| _ {2} ^ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 713, + 482, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this study, unlike outlier removal methods that perform \"subtraction\" filtering on initial correspondences, resulting in a subset of initial correspondences highly dependent on them, our aim is to generate more higher-quality correspondences $\\mathcal{G}^t$ where $t = 1,2,\\dots,m$ represents the current iterative stage. We define the regeneration process as $\\mathcal{G}^t = \\Theta (\\mathcal{G}^{t - 1};\\mathbf{P},\\mathbf{Q},\\varphi^t)$ where $\\Theta$ is the operation of the correspondence regeneration, and $\\varphi^t$ represents the parameter used in the regeneration of the $t$ th stage.", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Progressive Regeneration: Key Insight", + "text_level": 1, + "bbox": [ + 511, + 436, + 846, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing methods focus on pruning the initial correspondences to remove outliers and retain inliers. Due to common problems such as weak feature representation and low overlap, the proportion of correct initial correspondences is typically very small. Even all correct correspondences are identified, achieving accurate registration remains challenging. To this end, we design a novel progressive correspondence regeneration strategy to address the scarcity of initial inliers and the frequent failures of correspondence filtering under extreme outlier ratios.", + "bbox": [ + 511, + 459, + 903, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key idea of our method is to progressively regenerate better correspondences in a radius-variable local sphere. We use the positional priors of correspondences generated in the previous stage to guide the creation of the local sphere. In each local sphere, we regenerate more correspondences with higher quality. Compared to direct global matching, re-matching and refining within these local spheres significantly reduce the problem's scale and search space, resulting in more precise matches and reduced computational time. As the quality of the correspondence gets higher, we progressively reduce the size of the local spheres to achieve exact convergence of the correspondences. This approach not only generates a large number of new dense correspondences but also incrementally enhances their accuracy.", + "bbox": [ + 511, + 611, + 905, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Local Grouping and Rematching", + "text_level": 1, + "bbox": [ + 511, + 832, + 803, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this module, we implement the core of each iteration: local correspondence generation. First, we introduce prior-guided local grouping to leverage priors from the previous", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1212", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d4ee624d3ce7db74bdf52e25eade2d97a5647c9a57f226ebb813712085498a97.jpg", + "image_caption": [ + "Figure 3. Illustration of GMM. The orange, blue, green, and red lines are the MNN correspondences, NN correspondences, correct correspondences, and wrong correspondences, respectively." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 480, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "iteration. Then, we propose a generalized mutual matching technique to ensure the generation of a sufficient number of inliers even under high outlier rates.", + "bbox": [ + 89, + 369, + 483, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prior-guided Local Grouping. The input to our method is the correspondence $\\mathcal{G}^{t - 1}$ of the previous stage. Efficiency is crucial for our method due to the need for iterative processing. Therefore, we sample $\\mathcal{G}^{t - 1}$ using efficient random sampling [19] to derive seed correspondences $\\widetilde{\\mathcal{G}}^{t - 1}$ . We then utilize the positional priors of each seed correspondence to guide the construction of local regions. Specifically, we conduct a radius $r^t$ nearest neighbor search centered on each seed correspondence $\\widetilde{g}_i^{t - 1}\\in \\widetilde{\\mathcal{G}}^{t - 1}$ to obtain local point clouds $\\mathbf{P}_i^t$ and $\\mathbf{Q}_i^t$ , $i = 1,2,\\dots,n$ :", + "bbox": [ + 89, + 415, + 483, + 568 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {p} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\mathbf {Q} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {q} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 578, + 480, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{RNN}(\\mathbf{p};r,\\mathcal{G})$ is a radius nearest neighbor search on $\\mathcal{G}$ with $\\mathbf{p}$ as the center and $r$ as the radius. $\\mathbf{p}_i^{t - 1}$ and $\\mathbf{q}_i^{t - 1}$ satisfy $\\widetilde{g}_i^{t - 1} = (\\mathbf{p}_i^{t - 1},\\mathbf{q}_i^{t - 1})$ . We perform the above grouping operation for each pair of seed corresponding points and obtain $n$ pairs of local region $(\\mathbf{P}_i^t,\\mathbf{Q}_i^t)$ .", + "bbox": [ + 89, + 612, + 483, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generalized Mutual Matching. The next step is to generate new point correspondences from each pair of local regions by feature matching. However, the features in small local regions are usually similar, which results in traditional nearest-neighbor (NN) matching [11] producing a large number of false correspondences. Unfortunately, mutual NN matching [24, 26] may even fail to find any correspondence at all. To address this issue, we propose a generalized mutual matching to relax the strict mutual constraint, thereby improving the robustness of the local correspondences.", + "bbox": [ + 89, + 688, + 483, + 852 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given point cloud $\\mathbf{Q}_i^t$ as the query, the NN matching matrix $\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}$ and multi-nearest-neighbor (MNN) matching matrix $\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}$ are obtained by performing a k-nearest", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "neighbor (KNN) search in feature space, respectively:", + "bbox": [ + 511, + 90, + 870, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\mathrm {N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 116, + 833, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\operatorname {M N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 138, + 846, + 156 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\forall \\mathbf{p}_m\\in \\mathbf{P}_i^t,\\mathbf{q}_n\\in \\mathbf{Q}_i^t$ and $\\mathbf{F}(\\cdot)$ represents the mapping from points to features. $\\mathrm{NN}(\\cdot)$ and MNN(·) represent the indicator functions for NN and MNN matching, respectively. If the matching condition is satisfied, the value is set to 1. Then, we conduct mutual matching from $\\mathbf{P}_i^t$ to $\\mathbf{Q}_i^t$ and from $\\mathbf{Q}_i^t$ to $\\mathbf{P}_i^t$ , resulting in four matching matrices $\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}$ , $\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}$ , $\\mathbf{M}_1^{\\mathcal{Q}\\to \\mathcal{P}}$ , and $\\mathbf{M}_2^{\\mathcal{Q}\\to \\mathcal{P}}$ .", + "bbox": [ + 511, + 167, + 906, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By computing the Hadamard product between the NN and MNN matching matrices, we obtain the mutual matching matrices $\\mathbf{M}_*^{\\mathcal{P} \\to \\mathcal{Q}}$ , $\\mathbf{M}_*^{\\mathcal{Q} \\to \\mathcal{P}}$ . Further, we perform an element-wise logical OR operation to relax the constraint and get the generalized mutual matching matrix:", + "bbox": [ + 511, + 273, + 906, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {*} = \\left(\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}}\\right) \\otimes \\left(\\mathbf {M} _ {1} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 359, + 906, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where operation $\\odot$ and $\\otimes$ denote Hadamard product and element-wise logical OR, respectively. It is important to note that, to avoid a large number of outliers, we discard the strategy of directly applying mutual matching only based on MNN. Finally, using the matching matrix $\\mathbf{M}^*$ , we establish $n$ sets of local correspondences $\\mathcal{G}_i^t$ .", + "bbox": [ + 511, + 390, + 905, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Local Correspondence Refinement", + "text_level": 1, + "bbox": [ + 511, + 491, + 815, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because some corresponding local regions may not overlap exactly, the rematching in local regions still introduces some erroneous correspondences. Therefore, we further enhance the quality of the regenerated correspondences through local correspondence refinement.", + "bbox": [ + 511, + 513, + 906, + 589 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/afc4c3e1f37e88da1c2b88fb033d76797d6fb68cd212e1ff9c4f781a81389dc6.jpg", + "image_caption": [ + "Figure 4. Illustration of the local correspondence correction. Yellow and blue areas represent a pair of local point clouds. The purple line indicates the correct correspondence after correction." + ], + "image_footnote": [], + "bbox": [ + 519, + 604, + 903, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Center-aware Three-point Consistency. Note that, our seed correspondences $g_{i}^{t - 1} = (\\mathbf{p}_{i}^{t - 1},\\mathbf{q}_{i}^{t - 1})$ (central points) are derived from the previous stage and exhibit high accuracy. Therefore, they can serve as prior information to", + "bbox": [ + 511, + 839, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1213", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "guide the optimization of local correspondence refinement. Based on this, we propose an efficient center-aware three-point consistency (CTC) to search inliers.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first utilize efficient translation and rotation invariants [38] to describe the consistency $s_{\\sigma}(g_i, g_j)$ between two point pairs $g_i = (\\mathbf{p}_i, \\mathbf{q}_i)$ and $g_j = (\\mathbf{p}_j, \\mathbf{q}_j)$ :", + "bbox": [ + 89, + 136, + 482, + 184 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {\\sigma} \\left(g _ {i}, g _ {j}\\right) = \\mathbb {1} \\left(\\left| | \\left| \\mathbf {p} _ {i} - \\mathbf {p} _ {j} \\right| | _ {2} - | | \\mathbf {q} _ {i} - \\mathbf {q} _ {j} | | _ {2} \\right| \\leqslant \\sigma\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 189, + 482, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we leverage the prior information of accurate center points to compute the center-aware consistency between $g_{j}$ and $g_{k}$ , denoted as $s_{\\sigma}(g_j,g_i^{t - 1})\\cdot s_{\\sigma}(g_i^{t - 1},g_k)$ . Additionally, we account for the possibility that seed correspondences may not always be correct. Relying solely on the aforementioned criterion could allow errors in the seed correspondences to negatively impact the optimization of the entire region. To mitigate this, we introduce a strict point-pair constraint $s_{\\frac{\\sigma}{2}}(g_j,g_k)$ . CTC is computed as:", + "bbox": [ + 89, + 222, + 483, + 359 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {\\Delta} \\left(g _ {j}, g _ {k}\\right) = \\left(s _ {\\sigma} \\left(g _ {j}, g _ {i} ^ {t - 1}\\right) \\cdot s _ {\\sigma} \\left(g _ {i} ^ {t - 1}, g _ {k}\\right)\\right) \\mid | s _ {\\frac {\\sigma}{2}} \\left(g _ {j}, g _ {k}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 367, + 482, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $||$ represents operator OR and it means if either condition is satisfied, the correspondence is considered correct. Therefore, we get the score matrix $\\mathbf{S}_i^t = [s_\\Delta (g_j,g_k)]_{jk}\\in$ $\\mathbb{R}^{N\\times N}$ of the local correspondences $\\mathcal{G}_i^t\\in \\mathbb{R}^{N\\times 2}$ . To evaluate the overall quality of the local region, we define a local overall score:", + "bbox": [ + 89, + 400, + 483, + 488 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S c o r e} \\left(\\mathcal {G} _ {i} ^ {t}\\right) = \\frac {\\left| \\left| \\mathbf {S} _ {i} ^ {t} \\right| \\right| _ {1}}{a \\cdot N}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 487, + 480, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $||\\cdot ||_1$ represents the $L_{1}$ -norm of a matrix and $a \\in (0,1)$ denotes the threshold for the proportion of correct correspondences. Essentially, we consider regions where the proportion of correct correspondences exceeds $a$ as correct correspondence regions. It is proved in the Appendix.", + "bbox": [ + 89, + 520, + 483, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Local Correspondence Correction. Within each correct corresponding region, we identify a set of precise correspondences $\\widehat{\\mathcal{G}}_i^t$ to guide the refinement of correspondences across the entire local region. Specifically, based on the CTC score, we identify precise correspondences $\\widehat{\\mathcal{G}}_i^t$ with high scores. Subsequently, using these correspondences, we estimate the local transformation $\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}$ :", + "bbox": [ + 89, + 595, + 483, + 704 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} _ {i} ^ {t}, \\mathbf {t} _ {i} ^ {t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {j}, \\mathbf {q} _ {j}\\right) \\in \\widehat {\\mathcal {G}} _ {i} ^ {t}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {j} + \\mathbf {t} - \\mathbf {q} _ {j} \\| _ {2} ^ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 710, + 482, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Leveraging this local pose $\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}$ , we search for the nearest points $\\mathbf{q}'$ in the target local point cloud $\\mathbf{Q}_i^t$ for each point $\\mathbf{p}$ in the source local point cloud $\\mathbf{P}_i^t$ :", + "bbox": [ + 89, + 744, + 482, + 792 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {q} ^ {\\prime} = \\underset {\\mathbf {q} _ {j} \\in \\mathbf {Q} _ {i} ^ {t}} {\\arg \\min } \\left\\| \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} _ {j} \\right\\| _ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 797, + 482, + 830 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns. t. | | \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} ^ {\\prime} | | _ {2} \\leqslant \\sigma_ {d}, \\forall (\\mathbf {p}, \\mathbf {q}) \\in \\mathcal {G} _ {i} ^ {t}.\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 830, + 429, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through the one-way refinement of $\\mathbf{Q}$ , we update our local correspondences $\\mathcal{G}_i^t\\gets \\Omega_l(\\mathcal{G}_i^t) = \\{(\\mathbf{p},\\mathbf{q}^{\\prime})\\}$ where $\\Omega_{l}$ represents the operation of local correspondence correction.", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Global Correspondence Refinement", + "text_level": 1, + "bbox": [ + 513, + 90, + 823, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through local refinement, we obtain $n$ sets of refined local correspondences. However, consistency across sets is not fully aligned. Therefore, we need a global merging and refinement step to complete the global correspondence optimization. Since there is no seed correspondence at the global scale, we use second-order consistency [6].", + "bbox": [ + 511, + 113, + 903, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Correspondence Merging. After correcting the local correspondences, we merge them into global correspondences $\\mathcal{G}^t$ . It is worth noting that some local regions overlap with each other. Therefore, we utilize a hash table $\\mathbb{H}$ to implement correspondence merging. By using point indices as hash table keys, we efficiently merge local correspondences and remove duplicates to obtain the global correspondences $\\mathcal{G}^t = \\bigcup_{i=1}^{n} \\mathcal{G}_i^t$ . With this strategy, we further enhance the efficiency of our method and save memory overhead.", + "bbox": [ + 511, + 205, + 903, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Global Correspondence Correction. Although we achieve the correspondence correction in local regions, if the seed correspondences $\\widetilde{\\mathcal{G}}^{t - 1}$ are significantly incorrect, it may still result in wrong refinement for the entire local region. Therefore, similar to local correction, we refine global correspondences $\\mathcal{G}^t\\gets \\Omega_g(\\mathcal{G}^t)$ , where $\\Omega_{g}$ represents the operation of global correspondence correction. The key difference is that, in the global stage, we use second-order consistency [6] to identify correct correspondences. By leveraging correspondences that satisfy maximum consistency, we rectify anomalous correspondences globally, completing one iteration of correspondence regeneration $\\Theta (\\cdot)$ .", + "bbox": [ + 511, + 342, + 906, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 513, + 540, + 637, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our algorithm using the indoor 3DMatch dataset [46] and the outdoor KITTI dataset [16], demonstrating its superior performance. Furthermore, we introduce the 3DMatch-EOR benchmark and conduct experiments to demonstrate the effectiveness of our method in scenarios with very few correct initial correspondences. Additionally, we also conduct robustness test experiments to verify that our algorithm can achieve robust registration using only weak features, thereby demonstrating its robustness across different descriptors. Finally, we conduct ablation studies to validate the effectiveness of each module.", + "bbox": [ + 511, + 566, + 906, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metric. Following [6, 47], we use registration recall (RR), rotation error (RE), and translation error (TE) to evaluate registration performance. For outdoor scenes, we consider a registration successful if the error is within $(5^{\\circ}, 60\\mathrm{cm})$ , and for indoor scenes, within $(15^{\\circ}, 30\\mathrm{cm})$ . Additionally, we assess the quality of correspondences using feature matching recall (FMR) and inlier precision (IP) which represents the proportion of inliers to the total correspondences. To further demonstrate our method's ability to generate a higher number of accurate correspondences, we define two new metrics: inlier number ratio (INR) and inlier", + "bbox": [ + 511, + 734, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1214", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/03aa71c29822c2d107641537c654569efba574dd633fbcb20f65c9fca4143a39.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFPFH (Traditional Descriptor)FCGF (Learning-based Descriptor)
RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)
PointDSC [3]76.962.256.7666.6470.16290.2392.612.106.4878.3785.881174.62
VBReg [22]78.012.287.3467.2370.93166.5692.772.246.8279.9286.30690.38
Hunter [40]84.701.806.4674.3979.27309.2894.051.866.5482.5588.011203.88
SM [25]55.882.948.1547.9670.69230.0386.572.297.0781.4438.36405.10
TEASER [38]75.482.487.3173.0178.60270.9885.772.738.6682.4387.901182.44
RANSAC-1M [14]64.204.0511.3563.9669.03264.0988.423.059.4277.9683.08672.22
SC2-PCR [6]83.242.216.7073.6478.78289.1793.162.116.4480.1787.241140.85
MAC [47]83.902.116.80---93.722.076.52---
FastMAC [48]82.872.156.73---92.672.006.47---
Regor (ours)88.481.705.9482.681253.742532.4093.961.756.1487.48263.812620.30
", + "bbox": [ + 94, + 88, + 903, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1f879f51ce93e1e8805f8365bd8ac4d6afab4d183ab1225bf758dbeeef074412.jpg", + "image_caption": [ + "Figure 5. Correspondences before and after processing." + ], + "image_footnote": [], + "bbox": [ + 91, + 290, + 279, + 366 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4563e242a96dfbc0c674b267ed4cd3d30db7dca26126e06836921839d284b3ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 290, + 480, + 366 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ae4c7659b95b16411042579a7a769b57ce1f298946dc55e6ad9dff0589b29249.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on the 3DMatch dataset with descriptors FPFH [32] and FCGF [9]." + ], + "table_footnote": [], + "table_body": "
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
FPFH
PointDSC [3]27.914.2710.4523.8025.7646.52
VBReg [22]30.834.3810.9226.6129.7048.41
Hunter [40]36.903.8910.0531.5536.1756.01
RANSAC [14]19.834.6710.3230.8221.2037.02
SC2-PCR [6]35.934.2610.8630.1135.6555.23
MAC [47]40.883.669.45---
FastMAC [48]38.464.0410.47---
PCRegen (ours)43.962.898.9337.73778.35643.24
Predator
PointDSC [3]68.303.459.4456.3566.70863.40
VBReg [22]69.823.8710.0756.9067.09872.05
Hunter [40]71.103.589.7258.9069.06892.07
RANSAC [14]64.854.2811.0456.4466.81869.21
SC2-PCR [6]69.463.489.6358.0768.63883.59
MAC [47]70.913.699.81---
FastMAC [48]68.773.9010.32---
PCRegen (ours)72.043.179.4663.95220.462138.47
", + "bbox": [ + 94, + 407, + 483, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison on the 3DLoMatch Dataset.", + "bbox": [ + 102, + 637, + 470, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "numbers (IN). INR represents the ratio of the final number of inliers $\\mathrm{IN}_{\\text {final }}$ to the initial number of inliers $\\mathrm{IN}_{\\text {initial }}$ , defined explicitly in Appendix.", + "bbox": [ + 89, + 680, + 482, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation on Indoor Scenes", + "text_level": 1, + "bbox": [ + 89, + 739, + 346, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Setup. For indoor scenes, we utilize the 3DMatch dataset. Our method is validated on both 3DMatch [46] and 3DLoMatch benchmarks [20]. Following [3, 6], we perform voxel downsampling on the raw point clouds, and use two descriptors, FPFH [32] and FCGF [10], to extract features as inputs for each method.", + "bbox": [ + 89, + 762, + 482, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Result on 3DMatch. We compare our method against several baselines on the 3DMatch dataset, including PointDSC [3], VBReg [22], Hunter [40], SM [25]", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TEASER [38], RANSAC [14], $\\mathrm{SC^2}$ -PCR [6], MAC [47], and FastMAC [48]. The first three baselines are learning-based methods, while others are geometry-based approaches. The results are summarized in Table 1. Our method outperforms the previous state-of-the-art [6, 47]. Using the FPFH [9], our method outperforms all others across all metrics. Notably, our method achieves $88.48\\%$ RR, surpassing $\\mathrm{SC^2}$ -PCR [6] by 5.2 percentage points (pp). It also achieves more accurate registration with the lowest RE and TE. One significant advantage of our method is obtaining more high-quality correspondences, as reflected in the INR and IN. Our Regor achieves a $1253.74\\%$ INR, which is much better than $78.78\\%$ of SC2-PCR. Previous methods [6, 47, 48] only perform top-down filtering, which inevitably limits the INR to below $100\\%$ . In contrast, our Regor regenerates more high-quality correspondences, producing around 10 times the original amount. This advantage allows our method to achieve robust registration even when there are few initial correct correspondences. Moreover, despite employing multiple iterations, it still maintains a comparable speed to the baselines [22, 40] due to its simple sampling strategy and efficient consistency computation.", + "bbox": [ + 511, + 290, + 906, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Result on 3DLoMatch. Since Predator [20] is specifically designed for scenarios with low overlap, we use Predator [20] and FPFH [32] to extract features on 3DLoMatch. The comparative results are presented in Table 2. Our approach achieves the highest RR and RE on 3DLoMatch, regardless of the descriptors used. Due to the inherent weakness of FPFH, nearly all baselines perform poorly on 3DLoMatch. In contrast, our method shows significant performance improvement, surpassing MAC [47] by 3.08 pp.", + "bbox": [ + 511, + 626, + 908, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Result on 3DMatch-EOR. The key to the effectiveness of our method lies in its ability to generate more accurate correspondences, particularly in scenarios with extremely high outlier ratios. To validate this, we select extreme outlier ratio cases from the 3DMatch/3DLoMatch datasets and propose the 3DMatch-EOR benchmark which is described in Appendix. We establish two benchmarks with outlier rates exceeding $99\\%$ and $90\\%$ , respectively. Our method is compared to SC2-PCR [6] and PointDSC [3], with results", + "bbox": [ + 511, + 763, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1215", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/78e51931f438f30dbfa78ec5a2b3c2270e542dd72b583d1469eae076888d831e.jpg", + "image_caption": [ + "(a) Initial", + "(b) 1st stage", + "Figure 6. Correspondences visualization in different stages." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 415, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d914672291d03fd9d8456ab6c0dff514f4c009e0d0fa764c8f06ba6ae662b946.jpg", + "image_caption": [ + "(c) 2nd stage" + ], + "image_footnote": [], + "bbox": [ + 424, + 95, + 571, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d150a068e3af489695fe8c918c6251d41fc79ee7793e65b300c2408e87746ea7.jpg", + "image_caption": [ + "(d) 3rd stage" + ], + "image_footnote": [], + "bbox": [ + 586, + 95, + 728, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5b51c73e037bc0050138ebae523d9146a062a35f6d2cdb506c63c372b28fb9b.jpg", + "image_caption": [ + "(c) 4th stage" + ], + "image_footnote": [], + "bbox": [ + 738, + 92, + 897, + 276 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bb061b9ca613d14448788a7bec0242829066601e5dcf1a29e58c6f0a4c0726dc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)
Outlier ratio above 90%
3DMatch3DLoMatch
PointDSC [3]71.122.527.7977.7660.0563.55129.1223.274.8412.9439.7818.1626.5731.18
SC2-PCR [6]78.582.497.7384.0251.9173.73138.9835.394.2910.9642.5829.635.1449.73
PCRegen (ours)84.881.866.6786.3878.141457.542334.3643.502.959.2446.3436.96780.05632.62
Outlier ratio above 99%
3DMatch3DLoMatch
PointDSC [3]2.565.1215.2810.903.074.880.170.754.9329.340.750.081.460.02
SC2-PCR [6]9.154.9412.2116.206.089.610.343.285.9419.447.882.474.960.89
PCRegen (ours)26.762.178.6028.8721.541545.12666.949.273.3612.3911.846.30291.40118.45
", + "bbox": [ + 94, + 334, + 906, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shown in Table 3. In cases with such high outlier rates, achieving robust registration is exceptionally challenging, as the number of initial correct correspondences is minimal. When the outlier rate exceeded $99\\%$ , the average inlier count of SC2-PCR is less than 1, leading to registration failure and achieving only $9.15\\% / 3.28\\%$ in RR. In contrast, our method achieves an average of 667 inliers, an improvement of nearly 2000 times compared to SC2-PCR [6], resulting in a $26.76\\%$ RR. Our Regor enables success in scenarios where failure would otherwise be inevitable, allowing for relatively robust registration even with few initial inliers.", + "bbox": [ + 88, + 531, + 483, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation on Outdoor Scenes", + "text_level": 1, + "bbox": [ + 89, + 710, + 362, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental Setup. Following [7, 47], we validate our method's performance on the outdoor KITTI dataset. We select sequences 8 to 10 for testing. Consistent with the settings [6], we perform downsampling using a $30\\mathrm{cm}$ voxel grid and extract features using FPFH descriptors.", + "bbox": [ + 89, + 733, + 483, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Result on KITTI. We conduct comparative experiments between our method and PointDSC [3], VBReg [22], Hunter [40], RANSAC [14], $\\mathrm{SC^2}$ -PCR [6], MAC [47], and FastMAC [48] on the KITTI dataset. The results are presented in Table 4. Our Regor achieves the best performance with the highest RR, outperforming RANSAC [14] by 25.41", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0d83016a8ac802ae103d7de39dc777ef709fa7d9346aded6098fcceb9bf7fd94.jpg", + "table_caption": [ + "Table 3. Results on the 3DMatch-EOR benchmark with extreme outlier ratios." + ], + "table_footnote": [], + "table_body": "
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
PointDSC [3]99.460.577.2291.3993.05247.11
VBReg [22]98.928.398.4190.8292.13246.09
Hunter [40]99.820.556.2992.1194.58247.50
RANSAC [14]74.411.5530.2085.2987.20189.70
SC2-PCR [6]99.820.618.1693.5995.94248.46
MAC [47]99.460.598.70---
FastMAC [48]98.020.558.24---
Regor (ours)99.820.505.3679.572486.825353.22
", + "bbox": [ + 517, + 529, + 901, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Quantitative comparison on the KITTI Dataset.", + "bbox": [ + 540, + 643, + 877, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pp. It also demonstrates lower RE and TE, achieving the most accurate registration. Furthermore, our method shows superior performance in generating new correspondences, with INR over 25 times higher than those of other baselines [6, 40]. Despite IP is lower compared to SOTA [6], our method achieves more accurate pose estimation due to a larger number of high-quality inliers.", + "bbox": [ + 511, + 686, + 906, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Robustness to Different Features", + "text_level": 1, + "bbox": [ + 511, + 801, + 802, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further assess the robustness of various descriptors, we also test with traditional descriptors such as FPFH [32], SHOT [33], PFH [31], and PoRS [18], as well as learning-based descriptors like SpinNet [1], FCGF [9], Predator [20], and GeoTrans [30]. As shown in Table 5, our Regor con", + "bbox": [ + 511, + 825, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1216", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1f2736c3bf2f772d13aaadbb717bfb5ff4999d39810c0e62066262a30c6485f.jpg", + "image_caption": [ + "Figure 7. RR under different features." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 480, + 217 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/176656bedbbf0a2e452bbe520a9358d3d7f74cd61c0cf71dacdaa9888978b1ee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRR(%)↑IP(%)↑IN(/)↑
FPFH [32]54.3445.74228.71
FPFH [32] + Regor88.48 (+34.14)82.68 (+36.94)1253.74 (×5.48)
PFH [31]69.3857.28286.38
PFH [31] + Regor89.28 (+19.90)81.72 (+24.44)2477.39 (×8.65)
RoPS [18]54.1642.49212.46
RoPS [18] + Regor91.37 (+37.21)84.29 (+41.80)2542.32 (×11.96)
SHOT [33]55.3346.01229.50
SHOT [33] + Regor71.90 (+16.57)66.41 (+20.40)1981.10 (×8.63)
FCGF [9]86.3256.85405.27
FCGF [9] + Regor93.96 (+7.64)87.48 (+30.63)2620.30 (×6.46)
SpinNet [1]88.6047.53444.84
SpinNet [1] + Regor96.30 (+7.70)88.24 (+40.71)2799.74 (×6.29)
Predator [20]89.0058.01444.38
Predator [20] + Regor91.44 (+2.44)86.84 (+28.83)4608.34 (×10.37)
GeoTrans [30]91.8075.20449.85
GeoTrans [30] + Regor97.10 (+5.30)91.01 (+15.81)2649.30 (×5.88)
", + "bbox": [ + 94, + 257, + 478, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sistently improves performance across all features, which demonstrates it is robust to different features. Notably, GeoTrans [30] + Regor achieves a SOTA RR of $97.10\\%$ .", + "bbox": [ + 89, + 530, + 482, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Good Performance with Weak Features. Moreover, our method significantly enhance the performance of the weak descriptors, increasing the RR from $54.16\\%$ to $91.37\\%$ with RoPS [18]. As can be seen in Figure 7, with our Regor, the traditional descriptors [18, 31, 32] achieves $88\\% + \\mathrm{RR}$ , surpassing the learning-based baseline [9]. When combined with our Regor, RoPS [18] exhibits performance that exceeds the learning-based methods [1, 9, 20], only second to GeoTrans [30]. This demonstrates that our method can achieve robust registration even with weak features.", + "bbox": [ + 89, + 577, + 482, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 739, + 243, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation experiments on the 3DMatch and 3DMatch-EOR benchmarks using FPFH descriptor.", + "bbox": [ + 89, + 763, + 482, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Progressive or One-stage. We verify the effectiveness of our progressive strategy by only using the one-stage process. The results are shown in Table 6 (1) and (2). Our strategy improves RR by $1.65 / 2.82$ pp compared to the one-stage approach. It is attributed to the heuristic setting: starting with a larger radius ensures global optimality and robustness, and gradually reducing the radius with each iter-", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b6110e177a63bc8d30fc51b9bfe6f948623afbf6727b1677aac8ba8cf6667a55.jpg", + "table_caption": [ + "Table 5. Enhancement of feature-based methods." + ], + "table_footnote": [], + "table_body": "
No.Methods3DMatch3DMatch-EOR
RRIPINRRIPIN
1)One-stage86.8176.34290.3223.9415.889.13
2)Progressive*88.4882.682532.4026.7621.54666.94
3)NNM87.3580.902487.2325.0619.82643.45
4)MM86.8181.032392.5323.9420.80600.09
5)GMM*88.4882.682532.4026.7621.54666.94
6)Only Local87.3578.402526.6323.0617.32668.08
7)Only Global76.3780.482502.2124.6516.57641.42
8)Local & Global*88.4882.682532.4026.7621.54666.94
9)SC86.8881.092491.5422.5418.18574.74
10)CTC*88.4882.682532.4026.7621.54666.94
", + "bbox": [ + 517, + 89, + 903, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study on 3DMatch and 3DMatch-EOR.", + "bbox": [ + 537, + 253, + 879, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ation enhances accuracy. More importantly, IN drops by $1\\sim 2$ orders of magnitude, suggesting that our progressive strategy is key to generating more correspondences.", + "bbox": [ + 511, + 296, + 903, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Matching Strategy. We replace our GMM with mutual matching (MM) and nearest neighbor matching (NNM). Results are shown in Table 6 (3), (4) and (5). The model with GMM achieves the highest RR, IP, and IN. Compared with MM, using GMM results in a significant improvement in IN, which indicates our GMM is helpful to generate more inliers and addresses the issue of few initial inliers.", + "bbox": [ + 511, + 343, + 903, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Local-Global Refinement. To demonstrate the importance of our correspondence refinement, we compare the complete model with two ablation models. The results, shown in Rows 6, 7, and 8 of Table 6, indicate a significant performance drop when either local or global refinement is removed, with RR falling to $87\\%$ and $86\\%$ . In addition, the IP of the ablation model decreases by over 4 pp, which underscores the substantial contribution of the local-global refinement to the quality of the correspondences.", + "bbox": [ + 511, + 449, + 905, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Spatial Compatibility. We compared the SOTA second-order consistency (SC) [6, 7] with our CTC, and the results are shown at the bottom of Table 6. Our method with CTC obtains higher IP and IN, which indicates that CTC is more suitable for local refinement and achieves higher-quality correspondences. In addition, our CTC has less computational complexity than SC. Through it, we can implement an efficient iterative process.", + "bbox": [ + 511, + 585, + 905, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 723, + 633, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a new idea for optimizing correspondences. Unlike previous methods that focus solely on outlier removal, our Regor effectively addresses the challenge of limited correct initial correspondences. By generating more high-quality correspondences, our method enables more robust and accurate registration, achieving state-of-the-art performance across all datasets. Notably, it demonstrates significant improvements even under extreme outlier conditions. When combined with our Regor, using traditional descriptors can also achieve robust registration.", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1217", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. Spinnet: Learning a general surface descriptor for 3d point cloud registration. In CVPR, pages 11753-11762, 2021. 1, 2, 7, 8", + "[2] Sheng Ao, Qingyong Hu, Hanyun Wang, Kai Xu, and Yulan Guo. 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IEEE TGRS, 62:1-16, 2024. 2" + ], + "bbox": [ + 91, + 90, + 482, + 815 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1219", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_model.json b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_model.json new file mode 100644 index 0000000000000000000000000000000000000000..675d60958970977dab8c92d7574e7e9536f01b34 --- /dev/null +++ b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_model.json @@ -0,0 +1,2299 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.151, + 0.131, + 0.849, + 0.155 + ], + "angle": 0, + "content": "Progressive Correspondence Regenerator for Robust 3D Registration" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.18, + 0.756, + 0.199 + ], + "angle": 0, + "content": "Guiyu Zhao\\(^{1,2,4}\\), Sheng Ao\\(^{1,2,3}\\), Ye Zhang\\(^{3\\dagger}\\), Kai Xu\\(^{5}\\), Yulan Guo\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.2, + 0.844, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.217, + 0.827, + 0.252 + ], + "angle": 0, + "content": "2Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China 3Sun Yat-sen University" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.252, + 0.8, + 0.271 + ], + "angle": 0, + "content": "\\(^{4}\\)Beijing Institute of Technology \\(^{5}\\)National University of Defense Technology" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.305, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.338, + 0.485, + 0.716 + ], + "angle": 0, + "content": "Obtaining enough high-quality correspondences is crucial for robust registration. Existing correspondence refinement methods mostly follow the paradigm of outlier removal, which either fails to correctly identify the accurate correspondences under extreme outlier ratios, or select too few correct correspondences to support robust registration. To address this challenge, we propose a novel approach named Regor, which is a progressive correspondence generator that generates higher-quality matches whilst sufficiently robust for numerous outliers. In each iteration, we first apply prior-guided local grouping and generalized mutual matching to generate the local region correspondences. A powerful center-aware three-point consistency is then presented to achieve local correspondence correction, instead of removal. Further, we employ global correspondence refinement to obtain accurate correspondences from a global perspective. Through progressive iterations, this process yields a large number of high-quality correspondences. Extensive experiments on both indoor and outdoor datasets demonstrate that the proposed Regor significantly outperforms existing outlier removal techniques. More critically, our approach obtains 10 times more correct correspondences than outlier removal methods. As a result, our method is able to achieve robust registration even with weak features. The code is available at [Regor]." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.746, + 0.222, + 0.761 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.772, + 0.484, + 0.864 + ], + "angle": 0, + "content": "Point cloud registration [8, 21] is a fundamental and critical task in 3D computer vision, with widespread applications across various domains such as robotic localization [36, 42] and remote sensing [21, 35]. Point cloud registration aims to estimate a rigid transformation to align two point clouds scanned from different perspectives. With the advancement" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.306, + 0.697, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.521, + 0.659, + 0.531 + ], + "angle": 0, + "content": "(a) Existing Methods" + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.306, + 0.904, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.521, + 0.852, + 0.531 + ], + "angle": 0, + "content": "(b) Our Method" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.545, + 0.907, + 0.657 + ], + "angle": 0, + "content": "Figure 1. Difference between our method and existing outlier removal techniques. Outlier removal methods perform top-down pruning, producing an optimized set of correspondences that is a subset of the initial correspondences. When the initial inliers are few, this approach can obtain only a limited number of inliers, which is insufficient for robust pose estimation. In contrast, our method takes a bottom-up approach, using a regeneration strategy to generate more inliers, thereby effectively addressing this issue." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.685, + 0.907, + 0.777 + ], + "angle": 0, + "content": "of feature metric learning, feature-based point cloud registration methods [1, 20, 30, 43] have garnered significant attention and achieved promising results. However, in scenarios characterized by low overlap and high noise, direct feature matching often leads to a large number of outliers, which poses a great challenge for point cloud registration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Currently, the mainstream approach to address the issue of numerous outliers in point cloud registration is to filter wrong correspondences. Existing outlier removal methods [3, 6, 22, 27, 47] can be categorized into two types: geometry-based methods and learning-based methods. Geometry-based methods [6, 14, 28, 47] typically remove outliers according to whether point correspondences satisfy geometric consistency. Learning-based methods [3," + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.298, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.112, + 0.888, + 0.24, + 0.9 + ], + "angle": 0, + "content": "† Corresponding Author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.298, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1210" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "22, 27] treat this task as a classification problem to distinguish between outliers and inliers. However, in challenging scenarios, these correspondence filtering methods all suffer from a common problem: when initial correspondences only contains few inliers, estimating the correct rigid transformation between two point clouds is extremely difficult even if all inliers are identified." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.199, + 0.482, + 0.365 + ], + "angle": 0, + "content": "In this paper, we aim to design a new 3D registration architecture, which is robust to few inliers and is able to estimate precise 6DoF pose. As shown in Figure 1, different from existing outlier removal methods [3, 6, 7, 47] that focus on pruning correspondences, our approach clearly regenerate more high-quality correspondences to achieve robust registration. The key insight is to progressively generate correspondences and leverage the positional priors of correspondences from the previous iteration to guide more refined local regeneration, thereby obtaining more high-quality point correspondences." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.366, + 0.483, + 0.668 + ], + "angle": 0, + "content": "Our method, named Regor, follows a progressive iterative framework composed of three main modules: Local Grouping and Rematching, Local Correspondence Refinement and Global Correspondence Refinement. In each iteration, Local Grouping and Rematching leverages prior-guided local grouping to gradually reduce the matching space and generalized mutual matching to perform reliable local matching. The Local Correspondence Refinement introduces an effective center-aware three-point consistency to mine inliers and update local correspondences. The Global Correspondence Refinement is employed to perform further optimization from a global perspective. Note that, each iteration gradually increases the number of inliers, instead of only removing outliers. Our method achieves state-of-the-art performance on both the 3DMatch [46] and KITTI [16] datasets. Notably, the proposed Regor demonstrates a strong ability to generate correspondences, yielding up to 10 times more correct matches than existing outlier removal methods [6, 7, 47]. The main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.669, + 0.483, + 0.729 + ], + "angle": 0, + "content": "- We propose a novel registration approach named Regor to obtain massive high-quality point correspondences, overcoming the challenge of scarce inliers by progressively generating correspondences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.73, + 0.483, + 0.773 + ], + "angle": 0, + "content": "- Our method achieves state-of-the-art performance. In particular, the number of correct correspondences is 10 times higher than that of outlier removal methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.775, + 0.483, + 0.805 + ], + "angle": 0, + "content": "- Benefiting from the proposed regenerator, our approach achieves robust registration even with weak features." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.669, + 0.483, + 0.805 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.822, + 0.233, + 0.837 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.292, + 0.864 + ], + "angle": 0, + "content": "2.1. 3D Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Feature matching is a crucial step in correspondence-based point cloud registration [1, 20, 30, 32, 43, 45, 46]. Accord" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.425 + ], + "angle": 0, + "content": "ing to the approach of feature extraction, feature matching methods can be categorized into two types: traditional descriptor-based methods [31-33] and learning-based methods [1, 20, 30, 43, 45]. Before the widespread adoption of deep learning, features were manually designed descriptors tailored to represent local information. They are classified into LRF-based methods [18, 33] and LRF-free methods [31, 32] based on whether a local reference frame (LRF) is needed. With the advancements in deep learning, numerous learning-based methods have emerged. Based on the representation strategy, they can be further divided into patch-based methods [1, 17, 49] and fragment-based methods [9, 15, 20, 43]. SpinNet [1] and BUFFER [2] have achieved excellent generalization ability through 3D cylindrical convolution. Additionally, CoFiNet [43] and GeoTransformer [30] propose a coarse-to-fine matching strategy and a Transformer-based framework, which has garnered widespread attention. Subsequent methods [23, 37, 44, 45] have further improved performance by incorporating position encoding and prior information into this framework. ODIN [23] achieves the best performance through diffusion strategy and global optimization." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.436, + 0.809, + 0.451 + ], + "angle": 0, + "content": "2.2. Geometry-based Outlier Removal" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.907, + 0.716 + ], + "angle": 0, + "content": "Geometry-based outlier removal involves fitting models from noisy correspondences using the geometric properties of 3D scenes to estimate poses. The most classic method is random sampling consensus (RANSAC) [14], which samples correspondences multiple times and validates to obtain the best pose, thus mitigating the impact of noisy correspondences. Subsequently, numerous variants of RANSAC [4, 5, 12, 34] have been proposed to address issues of time consumption and instability. TEASER [38] introduces the truncated least squares (TLS) cost to solve for pose and employ rotation invariant measurements to handle outliers. Then, \\(\\mathrm{SC^2}\\)-PCR [6, 7] propose second-order consistency for robust outlier removal. In recent years, methods [39, 47] based on geometric consistency have been widely applied in point cloud registration, leveraging graph-theoretic approaches [13] and geometric consistency to remove outliers, thereby achieving robust registration." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.803, + 0.743 + ], + "angle": 0, + "content": "2.3. Learning-based Outlier Removal" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Recent researches [3, 22, 29] have integrated deep learning into outlier removal and pose estimation, showcasing promising performance through training. Inspired by image matching [41], 3DRegNet [29] adapts CN-Net [41] to remove outliers in point cloud registration. Subsequently, PointDSC [3] embeds the spatial consistency into feature maps and employs neural spectral matching to estimate confidence of correspondences, achieving robust registration. VBReg [22] utilizes variational Bayesian inference to achieve better outlier removal. Hunter [40] addresses severe" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1211" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.898, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.314, + 0.908, + 0.412 + ], + "angle": 0, + "content": "Figure 2. Overall framework of our method. We extract features from the original point cloud, obtaining features \\(\\mathbf{F}^{\\mathcal{P}}\\) and \\(\\mathbf{F}^{\\mathcal{Q}}\\) as input for our method. Subsequently, a progressive process is applied to iteratively regenerate more accurate and denser correspondences \\(\\mathcal{G}^t\\). At each iteration, the output correspondences \\(\\mathcal{G}^{t-1}\\) from the previous iteration serve as input. Firstly, prior-guided local grouping is employed to sample seed corresponding points and form local correspondence regions \\(\\mathbf{P}_i^t\\) and \\(\\mathbf{Q}_i^t\\). Then, for each pair of local correspondence regions, generalized mutual matching is performed to get new correspondences. Next, these correspondences are refined locally and globally using our center-aware three-point consistency, followed by a merging operation \\(\\oplus\\) of local correspondences \\(\\mathcal{G}_i^t\\) using a hash table. Finally, using these refined correspondences, we achieve robust and accurate transformation estimation \\(\\mathbf{T}\\{\\mathbf{R}, \\mathbf{t}\\}\\) only with SVD." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.439, + 0.482, + 0.528 + ], + "angle": 0, + "content": "outlier issues by introducing higher-order consistency using hypergraphs. However, while both geometry-based and learning-based methods have shown effectiveness in outlier removal, they inherently rely on the initial correspondences and only trim down on them, which poses challenges when initial inliers are scarce." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.546, + 0.182, + 0.561 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.572, + 0.295, + 0.587 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.595, + 0.483, + 0.701 + ], + "angle": 0, + "content": "Point cloud registration is aligning two point clouds \\(\\mathbf{P}\\) and \\(\\mathbf{Q}\\), captured from different perspectives, by estimating a pose transformation \\(\\mathbf{T} \\{\\mathbf{R}, \\mathbf{t}\\}\\) where \\(\\mathbf{R}\\) is a rotation matrix and \\(\\mathbf{t}\\) is a translation vector. Feature-based point cloud registration estimates correspondences through feature extraction and matching, then minimizes the average Euclidean distance between these correspondences, as shown in Eq. 1:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.714, + 0.483, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {R} \\in S O (3), \\mathbf {t} \\in \\mathbb {R} ^ {3}} {\\arg \\min } \\sum_ {\\left(\\mathbf {p} _ {x _ {i}}, \\mathbf {q} _ {y _ {i}}\\right) \\in \\mathcal {I}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {x _ {i}} + \\mathbf {t} - \\mathbf {q} _ {y _ {i}} \\| _ {2} ^ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this study, unlike outlier removal methods that perform \"subtraction\" filtering on initial correspondences, resulting in a subset of initial correspondences highly dependent on them, our aim is to generate more higher-quality correspondences \\(\\mathcal{G}^t\\) where \\(t = 1,2,\\dots,m\\) represents the current iterative stage. We define the regeneration process as \\(\\mathcal{G}^t = \\Theta (\\mathcal{G}^{t - 1};\\mathbf{P},\\mathbf{Q},\\varphi^t)\\) where \\(\\Theta\\) is the operation of the correspondence regeneration, and \\(\\varphi^t\\) represents the parameter used in the regeneration of the \\(t\\)th stage." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.438, + 0.847, + 0.455 + ], + "angle": 0, + "content": "3.2. Progressive Regeneration: Key Insight" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.905, + 0.61 + ], + "angle": 0, + "content": "Existing methods focus on pruning the initial correspondences to remove outliers and retain inliers. Due to common problems such as weak feature representation and low overlap, the proportion of correct initial correspondences is typically very small. Even all correct correspondences are identified, achieving accurate registration remains challenging. To this end, we design a novel progressive correspondence regeneration strategy to address the scarcity of initial inliers and the frequent failures of correspondence filtering under extreme outlier ratios." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.906, + 0.823 + ], + "angle": 0, + "content": "The key idea of our method is to progressively regenerate better correspondences in a radius-variable local sphere. We use the positional priors of correspondences generated in the previous stage to guide the creation of the local sphere. In each local sphere, we regenerate more correspondences with higher quality. Compared to direct global matching, re-matching and refining within these local spheres significantly reduce the problem's scale and search space, resulting in more precise matches and reduced computational time. As the quality of the correspondence gets higher, we progressively reduce the size of the local spheres to achieve exact convergence of the correspondences. This approach not only generates a large number of new dense correspondences but also incrementally enhances their accuracy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.805, + 0.851 + ], + "angle": 0, + "content": "3.3. Local Grouping and Rematching" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In this module, we implement the core of each iteration: local correspondence generation. First, we introduce prior-guided local grouping to leverage priors from the previous" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1212" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.482, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.3, + 0.485, + 0.343 + ], + "angle": 0, + "content": "Figure 3. Illustration of GMM. The orange, blue, green, and red lines are the MNN correspondences, NN correspondences, correct correspondences, and wrong correspondences, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.37, + 0.484, + 0.415 + ], + "angle": 0, + "content": "iteration. Then, we propose a generalized mutual matching technique to ensure the generation of a sufficient number of inliers even under high outlier rates." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.416, + 0.484, + 0.569 + ], + "angle": 0, + "content": "Prior-guided Local Grouping. The input to our method is the correspondence \\(\\mathcal{G}^{t - 1}\\) of the previous stage. Efficiency is crucial for our method due to the need for iterative processing. Therefore, we sample \\(\\mathcal{G}^{t - 1}\\) using efficient random sampling [19] to derive seed correspondences \\(\\widetilde{\\mathcal{G}}^{t - 1}\\). We then utilize the positional priors of each seed correspondence to guide the construction of local regions. Specifically, we conduct a radius \\(r^t\\) nearest neighbor search centered on each seed correspondence \\(\\widetilde{g}_i^{t - 1}\\in \\widetilde{\\mathcal{G}}^{t - 1}\\) to obtain local point clouds \\(\\mathbf{P}_i^t\\) and \\(\\mathbf{Q}_i^t\\), \\(i = 1,2,\\dots,n\\):" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.579, + 0.482, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {p} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\mathbf {Q} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {q} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.689 + ], + "angle": 0, + "content": "where \\(\\mathrm{RNN}(\\mathbf{p};r,\\mathcal{G})\\) is a radius nearest neighbor search on \\(\\mathcal{G}\\) with \\(\\mathbf{p}\\) as the center and \\(r\\) as the radius. \\(\\mathbf{p}_i^{t - 1}\\) and \\(\\mathbf{q}_i^{t - 1}\\) satisfy \\(\\widetilde{g}_i^{t - 1} = (\\mathbf{p}_i^{t - 1},\\mathbf{q}_i^{t - 1})\\). We perform the above grouping operation for each pair of seed corresponding points and obtain \\(n\\) pairs of local region \\((\\mathbf{P}_i^t,\\mathbf{Q}_i^t)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.853 + ], + "angle": 0, + "content": "Generalized Mutual Matching. The next step is to generate new point correspondences from each pair of local regions by feature matching. However, the features in small local regions are usually similar, which results in traditional nearest-neighbor (NN) matching [11] producing a large number of false correspondences. Unfortunately, mutual NN matching [24, 26] may even fail to find any correspondence at all. To address this issue, we propose a generalized mutual matching to relax the strict mutual constraint, thereby improving the robustness of the local correspondences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Given point cloud \\(\\mathbf{Q}_i^t\\) as the query, the NN matching matrix \\(\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}\\) and multi-nearest-neighbor (MNN) matching matrix \\(\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}\\) are obtained by performing a k-nearest" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.871, + 0.107 + ], + "angle": 0, + "content": "neighbor (KNN) search in feature space, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.117, + 0.834, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\mathrm {N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.139, + 0.848, + 0.157 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\operatorname {M N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.907, + 0.275 + ], + "angle": 0, + "content": "where \\(\\forall \\mathbf{p}_m\\in \\mathbf{P}_i^t,\\mathbf{q}_n\\in \\mathbf{Q}_i^t\\) and \\(\\mathbf{F}(\\cdot)\\) represents the mapping from points to features. \\(\\mathrm{NN}(\\cdot)\\) and MNN(·) represent the indicator functions for NN and MNN matching, respectively. If the matching condition is satisfied, the value is set to 1. Then, we conduct mutual matching from \\(\\mathbf{P}_i^t\\) to \\(\\mathbf{Q}_i^t\\) and from \\(\\mathbf{Q}_i^t\\) to \\(\\mathbf{P}_i^t\\), resulting in four matching matrices \\(\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}\\), \\(\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}\\), \\(\\mathbf{M}_1^{\\mathcal{Q}\\to \\mathcal{P}}\\), and \\(\\mathbf{M}_2^{\\mathcal{Q}\\to \\mathcal{P}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.275, + 0.907, + 0.351 + ], + "angle": 0, + "content": "By computing the Hadamard product between the NN and MNN matching matrices, we obtain the mutual matching matrices \\(\\mathbf{M}_*^{\\mathcal{P} \\to \\mathcal{Q}}\\), \\(\\mathbf{M}_*^{\\mathcal{Q} \\to \\mathcal{P}}\\). Further, we perform an element-wise logical OR operation to relax the constraint and get the generalized mutual matching matrix:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.361, + 0.907, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {*} = \\left(\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}}\\right) \\otimes \\left(\\mathbf {M} _ {1} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.391, + 0.906, + 0.483 + ], + "angle": 0, + "content": "where operation \\(\\odot\\) and \\(\\otimes\\) denote Hadamard product and element-wise logical OR, respectively. It is important to note that, to avoid a large number of outliers, we discard the strategy of directly applying mutual matching only based on MNN. Finally, using the matching matrix \\(\\mathbf{M}^*\\), we establish \\(n\\) sets of local correspondences \\(\\mathcal{G}_i^t\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.492, + 0.816, + 0.508 + ], + "angle": 0, + "content": "3.4. Local Correspondence Refinement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.514, + 0.907, + 0.59 + ], + "angle": 0, + "content": "Because some corresponding local regions may not overlap exactly, the rematching in local regions still introduces some erroneous correspondences. Therefore, we further enhance the quality of the regenerated correspondences through local correspondence refinement." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.605, + 0.905, + 0.771 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.782, + 0.907, + 0.825 + ], + "angle": 0, + "content": "Figure 4. Illustration of the local correspondence correction. Yellow and blue areas represent a pair of local point clouds. The purple line indicates the correct correspondence after correction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Center-aware Three-point Consistency. Note that, our seed correspondences \\( g_{i}^{t - 1} = (\\mathbf{p}_{i}^{t - 1},\\mathbf{q}_{i}^{t - 1}) \\) (central points) are derived from the previous stage and exhibit high accuracy. Therefore, they can serve as prior information to" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1213" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "guide the optimization of local correspondence refinement. Based on this, we propose an efficient center-aware three-point consistency (CTC) to search inliers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.137, + 0.483, + 0.185 + ], + "angle": 0, + "content": "We first utilize efficient translation and rotation invariants [38] to describe the consistency \\( s_{\\sigma}(g_i, g_j) \\) between two point pairs \\( g_i = (\\mathbf{p}_i, \\mathbf{q}_i) \\) and \\( g_j = (\\mathbf{p}_j, \\mathbf{q}_j) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.19, + 0.483, + 0.217 + ], + "angle": 0, + "content": "\\[\ns _ {\\sigma} \\left(g _ {i}, g _ {j}\\right) = \\mathbb {1} \\left(\\left| | \\left| \\mathbf {p} _ {i} - \\mathbf {p} _ {j} \\right| | _ {2} - | | \\mathbf {q} _ {i} - \\mathbf {q} _ {j} | | _ {2} \\right| \\leqslant \\sigma\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.223, + 0.484, + 0.36 + ], + "angle": 0, + "content": "Next, we leverage the prior information of accurate center points to compute the center-aware consistency between \\( g_{j} \\) and \\( g_{k} \\), denoted as \\( s_{\\sigma}(g_j,g_i^{t - 1})\\cdot s_{\\sigma}(g_i^{t - 1},g_k) \\). Additionally, we account for the possibility that seed correspondences may not always be correct. Relying solely on the aforementioned criterion could allow errors in the seed correspondences to negatively impact the optimization of the entire region. To mitigate this, we introduce a strict point-pair constraint \\( s_{\\frac{\\sigma}{2}}(g_j,g_k) \\). CTC is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.368, + 0.483, + 0.4 + ], + "angle": 0, + "content": "\\[\ns _ {\\Delta} \\left(g _ {j}, g _ {k}\\right) = \\left(s _ {\\sigma} \\left(g _ {j}, g _ {i} ^ {t - 1}\\right) \\cdot s _ {\\sigma} \\left(g _ {i} ^ {t - 1}, g _ {k}\\right)\\right) \\mid | s _ {\\frac {\\sigma}{2}} \\left(g _ {j}, g _ {k}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.401, + 0.484, + 0.489 + ], + "angle": 0, + "content": "where \\(||\\) represents operator OR and it means if either condition is satisfied, the correspondence is considered correct. Therefore, we get the score matrix \\(\\mathbf{S}_i^t = [s_\\Delta (g_j,g_k)]_{jk}\\in\\) \\(\\mathbb{R}^{N\\times N}\\) of the local correspondences \\(\\mathcal{G}_i^t\\in \\mathbb{R}^{N\\times 2}\\). To evaluate the overall quality of the local region, we define a local overall score:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.488, + 0.482, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S c o r e} \\left(\\mathcal {G} _ {i} ^ {t}\\right) = \\frac {\\left| \\left| \\mathbf {S} _ {i} ^ {t} \\right| \\right| _ {1}}{a \\cdot N}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.521, + 0.484, + 0.596 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_1\\) represents the \\(L_{1}\\)-norm of a matrix and \\(a \\in (0,1)\\) denotes the threshold for the proportion of correct correspondences. Essentially, we consider regions where the proportion of correct correspondences exceeds \\(a\\) as correct correspondence regions. It is proved in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.484, + 0.705 + ], + "angle": 0, + "content": "Local Correspondence Correction. Within each correct corresponding region, we identify a set of precise correspondences \\(\\widehat{\\mathcal{G}}_i^t\\) to guide the refinement of correspondences across the entire local region. Specifically, based on the CTC score, we identify precise correspondences \\(\\widehat{\\mathcal{G}}_i^t\\) with high scores. Subsequently, using these correspondences, we estimate the local transformation \\(\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.711, + 0.483, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} _ {i} ^ {t}, \\mathbf {t} _ {i} ^ {t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {j}, \\mathbf {q} _ {j}\\right) \\in \\widehat {\\mathcal {G}} _ {i} ^ {t}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {j} + \\mathbf {t} - \\mathbf {q} _ {j} \\| _ {2} ^ {2}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.746, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Leveraging this local pose \\(\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}\\), we search for the nearest points \\(\\mathbf{q}'\\) in the target local point cloud \\(\\mathbf{Q}_i^t\\) for each point \\(\\mathbf{p}\\) in the source local point cloud \\(\\mathbf{P}_i^t\\):" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.799, + 0.483, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\mathbf {q} ^ {\\prime} = \\underset {\\mathbf {q} _ {j} \\in \\mathbf {Q} _ {i} ^ {t}} {\\arg \\min } \\left\\| \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} _ {j} \\right\\| _ {2}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.832, + 0.43, + 0.849 + ], + "angle": 0, + "content": "\\[\ns. t. | | \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} ^ {\\prime} | | _ {2} \\leqslant \\sigma_ {d}, \\forall (\\mathbf {p}, \\mathbf {q}) \\in \\mathcal {G} _ {i} ^ {t}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Through the one-way refinement of \\(\\mathbf{Q}\\), we update our local correspondences \\(\\mathcal{G}_i^t\\gets \\Omega_l(\\mathcal{G}_i^t) = \\{(\\mathbf{p},\\mathbf{q}^{\\prime})\\}\\) where \\(\\Omega_{l}\\) represents the operation of local correspondence correction." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.825, + 0.107 + ], + "angle": 0, + "content": "3.5. Global Correspondence Refinement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.114, + 0.905, + 0.205 + ], + "angle": 0, + "content": "Through local refinement, we obtain \\( n \\) sets of refined local correspondences. However, consistency across sets is not fully aligned. Therefore, we need a global merging and refinement step to complete the global correspondence optimization. Since there is no seed correspondence at the global scale, we use second-order consistency [6]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.206, + 0.905, + 0.342 + ], + "angle": 0, + "content": "Correspondence Merging. After correcting the local correspondences, we merge them into global correspondences \\(\\mathcal{G}^t\\). It is worth noting that some local regions overlap with each other. Therefore, we utilize a hash table \\(\\mathbb{H}\\) to implement correspondence merging. By using point indices as hash table keys, we efficiently merge local correspondences and remove duplicates to obtain the global correspondences \\(\\mathcal{G}^t = \\bigcup_{i=1}^{n} \\mathcal{G}_i^t\\). With this strategy, we further enhance the efficiency of our method and save memory overhead." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.343, + 0.907, + 0.526 + ], + "angle": 0, + "content": "Global Correspondence Correction. Although we achieve the correspondence correction in local regions, if the seed correspondences \\(\\widetilde{\\mathcal{G}}^{t - 1}\\) are significantly incorrect, it may still result in wrong refinement for the entire local region. Therefore, similar to local correction, we refine global correspondences \\(\\mathcal{G}^t\\gets \\Omega_g(\\mathcal{G}^t)\\), where \\(\\Omega_{g}\\) represents the operation of global correspondence correction. The key difference is that, in the global stage, we use second-order consistency [6] to identify correct correspondences. By leveraging correspondences that satisfy maximum consistency, we rectify anomalous correspondences globally, completing one iteration of correspondence regeneration \\(\\Theta (\\cdot)\\)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.541, + 0.638, + 0.558 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.734 + ], + "angle": 0, + "content": "We evaluate our algorithm using the indoor 3DMatch dataset [46] and the outdoor KITTI dataset [16], demonstrating its superior performance. Furthermore, we introduce the 3DMatch-EOR benchmark and conduct experiments to demonstrate the effectiveness of our method in scenarios with very few correct initial correspondences. Additionally, we also conduct robustness test experiments to verify that our algorithm can achieve robust registration using only weak features, thereby demonstrating its robustness across different descriptors. Finally, we conduct ablation studies to validate the effectiveness of each module." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.735, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metric. Following [6, 47], we use registration recall (RR), rotation error (RE), and translation error (TE) to evaluate registration performance. For outdoor scenes, we consider a registration successful if the error is within \\((5^{\\circ}, 60\\mathrm{cm})\\), and for indoor scenes, within \\((15^{\\circ}, 30\\mathrm{cm})\\). Additionally, we assess the quality of correspondences using feature matching recall (FMR) and inlier precision (IP) which represents the proportion of inliers to the total correspondences. To further demonstrate our method's ability to generate a higher number of accurate correspondences, we define two new metrics: inlier number ratio (INR) and inlier" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1214" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.905, + 0.241 + ], + "angle": 0, + "content": "
MethodFPFH (Traditional Descriptor)FCGF (Learning-based Descriptor)
RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)
PointDSC [3]76.962.256.7666.6470.16290.2392.612.106.4878.3785.881174.62
VBReg [22]78.012.287.3467.2370.93166.5692.772.246.8279.9286.30690.38
Hunter [40]84.701.806.4674.3979.27309.2894.051.866.5482.5588.011203.88
SM [25]55.882.948.1547.9670.69230.0386.572.297.0781.4438.36405.10
TEASER [38]75.482.487.3173.0178.60270.9885.772.738.6682.4387.901182.44
RANSAC-1M [14]64.204.0511.3563.9669.03264.0988.423.059.4277.9683.08672.22
SC2-PCR [6]83.242.216.7073.6478.78289.1793.162.116.4480.1787.241140.85
MAC [47]83.902.116.80---93.722.076.52---
FastMAC [48]82.872.156.73---92.672.006.47---
Regor (ours)88.481.705.9482.681253.742532.4093.961.756.1487.48263.812620.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.199, + 0.251, + 0.798, + 0.266 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on the 3DMatch dataset with descriptors FPFH [32] and FCGF [9]." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.291, + 0.28, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.291, + 0.482, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.379, + 0.452, + 0.394 + ], + "angle": 0, + "content": "Figure 5. Correspondences before and after processing." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.409, + 0.485, + 0.628 + ], + "angle": 0, + "content": "
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
FPFH
PointDSC [3]27.914.2710.4523.8025.7646.52
VBReg [22]30.834.3810.9226.6129.7048.41
Hunter [40]36.903.8910.0531.5536.1756.01
RANSAC [14]19.834.6710.3230.8221.2037.02
SC2-PCR [6]35.934.2610.8630.1135.6555.23
MAC [47]40.883.669.45---
FastMAC [48]38.464.0410.47---
PCRegen (ours)43.962.898.9337.73778.35643.24
Predator
PointDSC [3]68.303.459.4456.3566.70863.40
VBReg [22]69.823.8710.0756.9067.09872.05
Hunter [40]71.103.589.7258.9069.06892.07
RANSAC [14]64.854.2811.0456.4466.81869.21
SC2-PCR [6]69.463.489.6358.0768.63883.59
MAC [47]70.913.699.81---
FastMAC [48]68.773.9010.32---
PCRegen (ours)72.043.179.4663.95220.462138.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.638, + 0.471, + 0.652 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on the 3DLoMatch Dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.681, + 0.483, + 0.728 + ], + "angle": 0, + "content": "numbers (IN). INR represents the ratio of the final number of inliers \\(\\mathrm{IN}_{\\text {final }}\\) to the initial number of inliers \\(\\mathrm{IN}_{\\text {initial }}\\), defined explicitly in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.74, + 0.348, + 0.755 + ], + "angle": 0, + "content": "4.1. Evaluation on Indoor Scenes" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.763, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Experimental Setup. For indoor scenes, we utilize the 3DMatch dataset. Our method is validated on both 3DMatch [46] and 3DLoMatch benchmarks [20]. Following [3, 6], we perform voxel downsampling on the raw point clouds, and use two descriptors, FPFH [32] and FCGF [10], to extract features as inputs for each method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Result on 3DMatch. We compare our method against several baselines on the 3DMatch dataset, including PointDSC [3], VBReg [22], Hunter [40], SM [25]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.291, + 0.908, + 0.626 + ], + "angle": 0, + "content": "TEASER [38], RANSAC [14], \\(\\mathrm{SC^2}\\)-PCR [6], MAC [47], and FastMAC [48]. The first three baselines are learning-based methods, while others are geometry-based approaches. The results are summarized in Table 1. Our method outperforms the previous state-of-the-art [6, 47]. Using the FPFH [9], our method outperforms all others across all metrics. Notably, our method achieves \\(88.48\\%\\) RR, surpassing \\(\\mathrm{SC^2}\\)-PCR [6] by 5.2 percentage points (pp). It also achieves more accurate registration with the lowest RE and TE. One significant advantage of our method is obtaining more high-quality correspondences, as reflected in the INR and IN. Our Regor achieves a \\(1253.74\\%\\) INR, which is much better than \\(78.78\\%\\) of SC2-PCR. Previous methods [6, 47, 48] only perform top-down filtering, which inevitably limits the INR to below \\(100\\%\\). In contrast, our Regor regenerates more high-quality correspondences, producing around 10 times the original amount. This advantage allows our method to achieve robust registration even when there are few initial correct correspondences. Moreover, despite employing multiple iterations, it still maintains a comparable speed to the baselines [22, 40] due to its simple sampling strategy and efficient consistency computation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.909, + 0.763 + ], + "angle": 0, + "content": "Result on 3DLoMatch. Since Predator [20] is specifically designed for scenarios with low overlap, we use Predator [20] and FPFH [32] to extract features on 3DLoMatch. The comparative results are presented in Table 2. Our approach achieves the highest RR and RE on 3DLoMatch, regardless of the descriptors used. Due to the inherent weakness of FPFH, nearly all baselines perform poorly on 3DLoMatch. In contrast, our method shows significant performance improvement, surpassing MAC [47] by 3.08 pp." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Result on 3DMatch-EOR. The key to the effectiveness of our method lies in its ability to generate more accurate correspondences, particularly in scenarios with extremely high outlier ratios. To validate this, we select extreme outlier ratio cases from the 3DMatch/3DLoMatch datasets and propose the 3DMatch-EOR benchmark which is described in Appendix. We establish two benchmarks with outlier rates exceeding \\(99\\%\\) and \\(90\\%\\), respectively. Our method is compared to SC2-PCR [6] and PointDSC [3], with results" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1215" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.092, + 0.416, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.28, + 0.204, + 0.292 + ], + "angle": 0, + "content": "(a) Initial" + }, + { + "type": "image_caption", + "bbox": [ + 0.304, + 0.279, + 0.372, + 0.292 + ], + "angle": 0, + "content": "(b) 1st stage" + }, + { + "type": "image", + "bbox": [ + 0.426, + 0.097, + 0.573, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.468, + 0.279, + 0.54, + 0.292 + ], + "angle": 0, + "content": "(c) 2nd stage" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.097, + 0.73, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.279, + 0.702, + 0.292 + ], + "angle": 0, + "content": "(d) 3rd stage" + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.093, + 0.898, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.28, + 0.866, + 0.292 + ], + "angle": 0, + "content": "(c) 4th stage" + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.308, + 0.677, + 0.323 + ], + "angle": 0, + "content": "Figure 6. Correspondences visualization in different stages." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.335, + 0.907, + 0.482 + ], + "angle": 0, + "content": "
RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)
Outlier ratio above 90%
3DMatch3DLoMatch
PointDSC [3]71.122.527.7977.7660.0563.55129.1223.274.8412.9439.7818.1626.5731.18
SC2-PCR [6]78.582.497.7384.0251.9173.73138.9835.394.2910.9642.5829.635.1449.73
PCRegen (ours)84.881.866.6786.3878.141457.542334.3643.502.959.2446.3436.96780.05632.62
Outlier ratio above 99%
3DMatch3DLoMatch
PointDSC [3]2.565.1215.2810.903.074.880.170.754.9329.340.750.081.460.02
SC2-PCR [6]9.154.9412.2116.206.089.610.343.285.9419.447.882.474.960.89
PCRegen (ours)26.762.178.6028.8721.541545.12666.949.273.3612.3911.846.30291.40118.45
" + }, + { + "type": "table_caption", + "bbox": [ + 0.266, + 0.492, + 0.731, + 0.506 + ], + "angle": 0, + "content": "Table 3. Results on the 3DMatch-EOR benchmark with extreme outlier ratios." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.532, + 0.484, + 0.699 + ], + "angle": 0, + "content": "shown in Table 3. In cases with such high outlier rates, achieving robust registration is exceptionally challenging, as the number of initial correct correspondences is minimal. When the outlier rate exceeded \\(99\\%\\), the average inlier count of SC2-PCR is less than 1, leading to registration failure and achieving only \\(9.15\\% / 3.28\\%\\) in RR. In contrast, our method achieves an average of 667 inliers, an improvement of nearly 2000 times compared to SC2-PCR [6], resulting in a \\(26.76\\%\\) RR. Our Regor enables success in scenarios where failure would otherwise be inevitable, allowing for relatively robust registration even with few initial inliers." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.711, + 0.363, + 0.727 + ], + "angle": 0, + "content": "4.2. Evaluation on Outdoor Scenes" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.484, + 0.81 + ], + "angle": 0, + "content": "Experimental Setup. Following [7, 47], we validate our method's performance on the outdoor KITTI dataset. We select sequences 8 to 10 for testing. Consistent with the settings [6], we perform downsampling using a \\(30\\mathrm{cm}\\) voxel grid and extract features using FPFH descriptors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Result on KITTI. We conduct comparative experiments between our method and PointDSC [3], VBReg [22], Hunter [40], RANSAC [14], \\(\\mathrm{SC^2}\\)-PCR [6], MAC [47], and FastMAC [48] on the KITTI dataset. The results are presented in Table 4. Our Regor achieves the best performance with the highest RR, outperforming RANSAC [14] by 25.41" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.53, + 0.903, + 0.635 + ], + "angle": 0, + "content": "
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
PointDSC [3]99.460.577.2291.3993.05247.11
VBReg [22]98.928.398.4190.8292.13246.09
Hunter [40]99.820.556.2992.1194.58247.50
RANSAC [14]74.411.5530.2085.2987.20189.70
SC2-PCR [6]99.820.618.1693.5995.94248.46
MAC [47]99.460.598.70---
FastMAC [48]98.020.558.24---
Regor (ours)99.820.505.3679.572486.825353.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.542, + 0.645, + 0.878, + 0.658 + ], + "angle": 0, + "content": "Table 4. Quantitative comparison on the KITTI Dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.907, + 0.793 + ], + "angle": 0, + "content": "pp. It also demonstrates lower RE and TE, achieving the most accurate registration. Furthermore, our method shows superior performance in generating new correspondences, with INR over 25 times higher than those of other baselines [6, 40]. Despite IP is lower compared to SOTA [6], our method achieves more accurate pose estimation due to a larger number of high-quality inliers." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.803, + 0.818 + ], + "angle": 0, + "content": "4.3. Robustness to Different Features" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.902 + ], + "angle": 0, + "content": "To further assess the robustness of various descriptors, we also test with traditional descriptors such as FPFH [32], SHOT [33], PFH [31], and PoRS [18], as well as learning-based descriptors like SpinNet [1], FCGF [9], Predator [20], and GeoTrans [30]. As shown in Table 5, our Regor con" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1216" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.482, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.228, + 0.4, + 0.243 + ], + "angle": 0, + "content": "Figure 7. RR under different features." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.258, + 0.48, + 0.477 + ], + "angle": 0, + "content": "
MethodRR(%)↑IP(%)↑IN(/)↑
FPFH [32]54.3445.74228.71
FPFH [32] + Regor88.48 (+34.14)82.68 (+36.94)1253.74 (×5.48)
PFH [31]69.3857.28286.38
PFH [31] + Regor89.28 (+19.90)81.72 (+24.44)2477.39 (×8.65)
RoPS [18]54.1642.49212.46
RoPS [18] + Regor91.37 (+37.21)84.29 (+41.80)2542.32 (×11.96)
SHOT [33]55.3346.01229.50
SHOT [33] + Regor71.90 (+16.57)66.41 (+20.40)1981.10 (×8.63)
FCGF [9]86.3256.85405.27
FCGF [9] + Regor93.96 (+7.64)87.48 (+30.63)2620.30 (×6.46)
SpinNet [1]88.6047.53444.84
SpinNet [1] + Regor96.30 (+7.70)88.24 (+40.71)2799.74 (×6.29)
Predator [20]89.0058.01444.38
Predator [20] + Regor91.44 (+2.44)86.84 (+28.83)4608.34 (×10.37)
GeoTrans [30]91.8075.20449.85
GeoTrans [30] + Regor97.10 (+5.30)91.01 (+15.81)2649.30 (×5.88)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.141, + 0.488, + 0.432, + 0.501 + ], + "angle": 0, + "content": "Table 5. Enhancement of feature-based methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.531, + 0.483, + 0.576 + ], + "angle": 0, + "content": "sistently improves performance across all features, which demonstrates it is robust to different features. Notably, GeoTrans [30] + Regor achieves a SOTA RR of \\(97.10\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.578, + 0.483, + 0.729 + ], + "angle": 0, + "content": "Good Performance with Weak Features. Moreover, our method significantly enhance the performance of the weak descriptors, increasing the RR from \\(54.16\\%\\) to \\(91.37\\%\\) with RoPS [18]. As can be seen in Figure 7, with our Regor, the traditional descriptors [18, 31, 32] achieves \\(88\\% + \\mathrm{RR}\\), surpassing the learning-based baseline [9]. When combined with our Regor, RoPS [18] exhibits performance that exceeds the learning-based methods [1, 9, 20], only second to GeoTrans [30]. This demonstrates that our method can achieve robust registration even with weak features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.741, + 0.245, + 0.758 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.794 + ], + "angle": 0, + "content": "We conduct ablation experiments on the 3DMatch and 3DMatch-EOR benchmarks using FPFH descriptor." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Progressive or One-stage. We verify the effectiveness of our progressive strategy by only using the one-stage process. The results are shown in Table 6 (1) and (2). Our strategy improves RR by \\(1.65 / 2.82\\) pp compared to the one-stage approach. It is attributed to the heuristic setting: starting with a larger radius ensures global optimality and robustness, and gradually reducing the radius with each iter-" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.09, + 0.905, + 0.245 + ], + "angle": 0, + "content": "
No.Methods3DMatch3DMatch-EOR
RRIPINRRIPIN
1)One-stage86.8176.34290.3223.9415.889.13
2)Progressive*88.4882.682532.4026.7621.54666.94
3)NNM87.3580.902487.2325.0619.82643.45
4)MM86.8181.032392.5323.9420.80600.09
5)GMM*88.4882.682532.4026.7621.54666.94
6)Only Local87.3578.402526.6323.0617.32668.08
7)Only Global76.3780.482502.2124.6516.57641.42
8)Local & Global*88.4882.682532.4026.7621.54666.94
9)SC86.8881.092491.5422.5418.18574.74
10)CTC*88.4882.682532.4026.7621.54666.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.255, + 0.88, + 0.269 + ], + "angle": 0, + "content": "Table 6. Ablation study on 3DMatch and 3DMatch-EOR." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.297, + 0.905, + 0.342 + ], + "angle": 0, + "content": "ation enhances accuracy. More importantly, IN drops by \\(1\\sim 2\\) orders of magnitude, suggesting that our progressive strategy is key to generating more correspondences." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.344, + 0.905, + 0.448 + ], + "angle": 0, + "content": "Matching Strategy. We replace our GMM with mutual matching (MM) and nearest neighbor matching (NNM). Results are shown in Table 6 (3), (4) and (5). The model with GMM achieves the highest RR, IP, and IN. Compared with MM, using GMM results in a significant improvement in IN, which indicates our GMM is helpful to generate more inliers and addresses the issue of few initial inliers." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.45, + 0.906, + 0.586 + ], + "angle": 0, + "content": "Local-Global Refinement. To demonstrate the importance of our correspondence refinement, we compare the complete model with two ablation models. The results, shown in Rows 6, 7, and 8 of Table 6, indicate a significant performance drop when either local or global refinement is removed, with RR falling to \\(87\\%\\) and \\(86\\%\\). In addition, the IP of the ablation model decreases by over 4 pp, which underscores the substantial contribution of the local-global refinement to the quality of the correspondences." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.906, + 0.708 + ], + "angle": 0, + "content": "Spatial Compatibility. We compared the SOTA second-order consistency (SC) [6, 7] with our CTC, and the results are shown at the bottom of Table 6. Our method with CTC obtains higher IP and IN, which indicates that CTC is more suitable for local refinement and achieves higher-quality correspondences. In addition, our CTC has less computational complexity than SC. Through it, we can implement an efficient iterative process." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.724, + 0.634, + 0.74 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In this paper, we introduce a new idea for optimizing correspondences. Unlike previous methods that focus solely on outlier removal, our Regor effectively addresses the challenge of limited correct initial correspondences. By generating more high-quality correspondences, our method enables more robust and accurate registration, achieving state-of-the-art performance across all datasets. Notably, it demonstrates significant improvements even under extreme outlier conditions. When combined with our Regor, using traditional descriptors can also achieve robust registration." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1217" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. Spinnet: Learning a general surface descriptor for 3d point cloud registration. 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IEEE TGRS, 62:1-16, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.483, + 0.816 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1219" + } + ] +] \ No newline at end of file diff --git a/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_origin.pdf b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..49e19377a76647ebc8dc92bef9b28fbb487b0cec --- /dev/null +++ b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/efc41f9b-f851-485a-97ce-67b61ab26c11_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b4eacb21d2adfe301df6f049823f848da9944121a7809fcf287a7ccc705630a0 +size 4614549 diff --git a/2025/Progressive Correspondence Regenerator for Robust 3D Registration/full.md b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3b4652903e5cf209dbf7f213beafc379fb740c1e --- /dev/null +++ b/2025/Progressive Correspondence Regenerator for Robust 3D Registration/full.md @@ -0,0 +1,333 @@ +# Progressive Correspondence Regenerator for Robust 3D Registration + +Guiyu Zhao $^{1,2,4}$ , Sheng Ao $^{1,2,3}$ , Ye Zhang $^{3\dagger}$ , Kai Xu $^{5}$ , Yulan Guo $^{3}$ + +$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University + +2Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China 3Sun Yat-sen University + +$^{4}$ Beijing Institute of Technology $^{5}$ National University of Defense Technology + +# Abstract + +Obtaining enough high-quality correspondences is crucial for robust registration. Existing correspondence refinement methods mostly follow the paradigm of outlier removal, which either fails to correctly identify the accurate correspondences under extreme outlier ratios, or select too few correct correspondences to support robust registration. To address this challenge, we propose a novel approach named Regor, which is a progressive correspondence generator that generates higher-quality matches whilst sufficiently robust for numerous outliers. In each iteration, we first apply prior-guided local grouping and generalized mutual matching to generate the local region correspondences. A powerful center-aware three-point consistency is then presented to achieve local correspondence correction, instead of removal. Further, we employ global correspondence refinement to obtain accurate correspondences from a global perspective. Through progressive iterations, this process yields a large number of high-quality correspondences. Extensive experiments on both indoor and outdoor datasets demonstrate that the proposed Regor significantly outperforms existing outlier removal techniques. More critically, our approach obtains 10 times more correct correspondences than outlier removal methods. As a result, our method is able to achieve robust registration even with weak features. The code is available at [Regor]. + +# 1. Introduction + +Point cloud registration [8, 21] is a fundamental and critical task in 3D computer vision, with widespread applications across various domains such as robotic localization [36, 42] and remote sensing [21, 35]. Point cloud registration aims to estimate a rigid transformation to align two point clouds scanned from different perspectives. With the advancement + +![](images/5e3d55d3854d2fb91c7087265aad59ffaf4edddf5ee683c386f3e2091bc343bc.jpg) +(a) Existing Methods +Figure 1. Difference between our method and existing outlier removal techniques. Outlier removal methods perform top-down pruning, producing an optimized set of correspondences that is a subset of the initial correspondences. When the initial inliers are few, this approach can obtain only a limited number of inliers, which is insufficient for robust pose estimation. In contrast, our method takes a bottom-up approach, using a regeneration strategy to generate more inliers, thereby effectively addressing this issue. + +![](images/875f1fa3c092e798725c207e9675f40e2c4ed381a6e08fd12e33425f3acee42b.jpg) +(b) Our Method + +of feature metric learning, feature-based point cloud registration methods [1, 20, 30, 43] have garnered significant attention and achieved promising results. However, in scenarios characterized by low overlap and high noise, direct feature matching often leads to a large number of outliers, which poses a great challenge for point cloud registration. + +Currently, the mainstream approach to address the issue of numerous outliers in point cloud registration is to filter wrong correspondences. Existing outlier removal methods [3, 6, 22, 27, 47] can be categorized into two types: geometry-based methods and learning-based methods. Geometry-based methods [6, 14, 28, 47] typically remove outliers according to whether point correspondences satisfy geometric consistency. Learning-based methods [3, + +22, 27] treat this task as a classification problem to distinguish between outliers and inliers. However, in challenging scenarios, these correspondence filtering methods all suffer from a common problem: when initial correspondences only contains few inliers, estimating the correct rigid transformation between two point clouds is extremely difficult even if all inliers are identified. + +In this paper, we aim to design a new 3D registration architecture, which is robust to few inliers and is able to estimate precise 6DoF pose. As shown in Figure 1, different from existing outlier removal methods [3, 6, 7, 47] that focus on pruning correspondences, our approach clearly regenerate more high-quality correspondences to achieve robust registration. The key insight is to progressively generate correspondences and leverage the positional priors of correspondences from the previous iteration to guide more refined local regeneration, thereby obtaining more high-quality point correspondences. + +Our method, named Regor, follows a progressive iterative framework composed of three main modules: Local Grouping and Rematching, Local Correspondence Refinement and Global Correspondence Refinement. In each iteration, Local Grouping and Rematching leverages prior-guided local grouping to gradually reduce the matching space and generalized mutual matching to perform reliable local matching. The Local Correspondence Refinement introduces an effective center-aware three-point consistency to mine inliers and update local correspondences. The Global Correspondence Refinement is employed to perform further optimization from a global perspective. Note that, each iteration gradually increases the number of inliers, instead of only removing outliers. Our method achieves state-of-the-art performance on both the 3DMatch [46] and KITTI [16] datasets. Notably, the proposed Regor demonstrates a strong ability to generate correspondences, yielding up to 10 times more correct matches than existing outlier removal methods [6, 7, 47]. The main contributions of this paper are as follows: + +- We propose a novel registration approach named Regor to obtain massive high-quality point correspondences, overcoming the challenge of scarce inliers by progressively generating correspondences. +- Our method achieves state-of-the-art performance. In particular, the number of correct correspondences is 10 times higher than that of outlier removal methods. +- Benefiting from the proposed regenerator, our approach achieves robust registration even with weak features. + +# 2. Related Work + +# 2.1. 3D Feature Matching + +Feature matching is a crucial step in correspondence-based point cloud registration [1, 20, 30, 32, 43, 45, 46]. Accord + +ing to the approach of feature extraction, feature matching methods can be categorized into two types: traditional descriptor-based methods [31-33] and learning-based methods [1, 20, 30, 43, 45]. Before the widespread adoption of deep learning, features were manually designed descriptors tailored to represent local information. They are classified into LRF-based methods [18, 33] and LRF-free methods [31, 32] based on whether a local reference frame (LRF) is needed. With the advancements in deep learning, numerous learning-based methods have emerged. Based on the representation strategy, they can be further divided into patch-based methods [1, 17, 49] and fragment-based methods [9, 15, 20, 43]. SpinNet [1] and BUFFER [2] have achieved excellent generalization ability through 3D cylindrical convolution. Additionally, CoFiNet [43] and GeoTransformer [30] propose a coarse-to-fine matching strategy and a Transformer-based framework, which has garnered widespread attention. Subsequent methods [23, 37, 44, 45] have further improved performance by incorporating position encoding and prior information into this framework. ODIN [23] achieves the best performance through diffusion strategy and global optimization. + +# 2.2. Geometry-based Outlier Removal + +Geometry-based outlier removal involves fitting models from noisy correspondences using the geometric properties of 3D scenes to estimate poses. The most classic method is random sampling consensus (RANSAC) [14], which samples correspondences multiple times and validates to obtain the best pose, thus mitigating the impact of noisy correspondences. Subsequently, numerous variants of RANSAC [4, 5, 12, 34] have been proposed to address issues of time consumption and instability. TEASER [38] introduces the truncated least squares (TLS) cost to solve for pose and employ rotation invariant measurements to handle outliers. Then, $\mathrm{SC^2}$ -PCR [6, 7] propose second-order consistency for robust outlier removal. In recent years, methods [39, 47] based on geometric consistency have been widely applied in point cloud registration, leveraging graph-theoretic approaches [13] and geometric consistency to remove outliers, thereby achieving robust registration. + +# 2.3. Learning-based Outlier Removal + +Recent researches [3, 22, 29] have integrated deep learning into outlier removal and pose estimation, showcasing promising performance through training. Inspired by image matching [41], 3DRegNet [29] adapts CN-Net [41] to remove outliers in point cloud registration. Subsequently, PointDSC [3] embeds the spatial consistency into feature maps and employs neural spectral matching to estimate confidence of correspondences, achieving robust registration. VBReg [22] utilizes variational Bayesian inference to achieve better outlier removal. Hunter [40] addresses severe + +![](images/a1b3ba4747a198ac85ef57a190ff03c990f5ba0c887bd6a1656fd7b26c914e91.jpg) +Figure 2. Overall framework of our method. We extract features from the original point cloud, obtaining features $\mathbf{F}^{\mathcal{P}}$ and $\mathbf{F}^{\mathcal{Q}}$ as input for our method. Subsequently, a progressive process is applied to iteratively regenerate more accurate and denser correspondences $\mathcal{G}^t$ . At each iteration, the output correspondences $\mathcal{G}^{t-1}$ from the previous iteration serve as input. Firstly, prior-guided local grouping is employed to sample seed corresponding points and form local correspondence regions $\mathbf{P}_i^t$ and $\mathbf{Q}_i^t$ . Then, for each pair of local correspondence regions, generalized mutual matching is performed to get new correspondences. Next, these correspondences are refined locally and globally using our center-aware three-point consistency, followed by a merging operation $\oplus$ of local correspondences $\mathcal{G}_i^t$ using a hash table. Finally, using these refined correspondences, we achieve robust and accurate transformation estimation $\mathbf{T}\{\mathbf{R}, \mathbf{t}\}$ only with SVD. + +outlier issues by introducing higher-order consistency using hypergraphs. However, while both geometry-based and learning-based methods have shown effectiveness in outlier removal, they inherently rely on the initial correspondences and only trim down on them, which poses challenges when initial inliers are scarce. + +# 3. Method + +# 3.1. Problem Formulation + +Point cloud registration is aligning two point clouds $\mathbf{P}$ and $\mathbf{Q}$ , captured from different perspectives, by estimating a pose transformation $\mathbf{T} \{\mathbf{R}, \mathbf{t}\}$ where $\mathbf{R}$ is a rotation matrix and $\mathbf{t}$ is a translation vector. Feature-based point cloud registration estimates correspondences through feature extraction and matching, then minimizes the average Euclidean distance between these correspondences, as shown in Eq. 1: + +$$ +\underset {\mathbf {R} \in S O (3), \mathbf {t} \in \mathbb {R} ^ {3}} {\arg \min } \sum_ {\left(\mathbf {p} _ {x _ {i}}, \mathbf {q} _ {y _ {i}}\right) \in \mathcal {I}} \| \mathbf {R} \cdot \mathbf {p} _ {x _ {i}} + \mathbf {t} - \mathbf {q} _ {y _ {i}} \| _ {2} ^ {2}. \tag {1} +$$ + +In this study, unlike outlier removal methods that perform "subtraction" filtering on initial correspondences, resulting in a subset of initial correspondences highly dependent on them, our aim is to generate more higher-quality correspondences $\mathcal{G}^t$ where $t = 1,2,\dots,m$ represents the current iterative stage. We define the regeneration process as $\mathcal{G}^t = \Theta (\mathcal{G}^{t - 1};\mathbf{P},\mathbf{Q},\varphi^t)$ where $\Theta$ is the operation of the correspondence regeneration, and $\varphi^t$ represents the parameter used in the regeneration of the $t$ th stage. + +# 3.2. Progressive Regeneration: Key Insight + +Existing methods focus on pruning the initial correspondences to remove outliers and retain inliers. Due to common problems such as weak feature representation and low overlap, the proportion of correct initial correspondences is typically very small. Even all correct correspondences are identified, achieving accurate registration remains challenging. To this end, we design a novel progressive correspondence regeneration strategy to address the scarcity of initial inliers and the frequent failures of correspondence filtering under extreme outlier ratios. + +The key idea of our method is to progressively regenerate better correspondences in a radius-variable local sphere. We use the positional priors of correspondences generated in the previous stage to guide the creation of the local sphere. In each local sphere, we regenerate more correspondences with higher quality. Compared to direct global matching, re-matching and refining within these local spheres significantly reduce the problem's scale and search space, resulting in more precise matches and reduced computational time. As the quality of the correspondence gets higher, we progressively reduce the size of the local spheres to achieve exact convergence of the correspondences. This approach not only generates a large number of new dense correspondences but also incrementally enhances their accuracy. + +# 3.3. Local Grouping and Rematching + +In this module, we implement the core of each iteration: local correspondence generation. First, we introduce prior-guided local grouping to leverage priors from the previous + +![](images/d4ee624d3ce7db74bdf52e25eade2d97a5647c9a57f226ebb813712085498a97.jpg) +Figure 3. Illustration of GMM. The orange, blue, green, and red lines are the MNN correspondences, NN correspondences, correct correspondences, and wrong correspondences, respectively. + +iteration. Then, we propose a generalized mutual matching technique to ensure the generation of a sufficient number of inliers even under high outlier rates. + +Prior-guided Local Grouping. The input to our method is the correspondence $\mathcal{G}^{t - 1}$ of the previous stage. Efficiency is crucial for our method due to the need for iterative processing. Therefore, we sample $\mathcal{G}^{t - 1}$ using efficient random sampling [19] to derive seed correspondences $\widetilde{\mathcal{G}}^{t - 1}$ . We then utilize the positional priors of each seed correspondence to guide the construction of local regions. Specifically, we conduct a radius $r^t$ nearest neighbor search centered on each seed correspondence $\widetilde{g}_i^{t - 1}\in \widetilde{\mathcal{G}}^{t - 1}$ to obtain local point clouds $\mathbf{P}_i^t$ and $\mathbf{Q}_i^t$ , $i = 1,2,\dots,n$ : + +$$ +\mathbf {P} _ {i} ^ {t} = \operatorname {R N N} \left(\mathbf {p} _ {i} ^ {t - 1}; r ^ {t}, \widetilde {\mathcal {G}} ^ {t - 1}\right), \mathbf {Q} _ {i} ^ {t} = \operatorname {R N N} \left(\mathbf {q} _ {i} ^ {t - 1}; r ^ {t}, \widetilde {\mathcal {G}} ^ {t - 1}\right), \tag {2} +$$ + +where $\mathrm{RNN}(\mathbf{p};r,\mathcal{G})$ is a radius nearest neighbor search on $\mathcal{G}$ with $\mathbf{p}$ as the center and $r$ as the radius. $\mathbf{p}_i^{t - 1}$ and $\mathbf{q}_i^{t - 1}$ satisfy $\widetilde{g}_i^{t - 1} = (\mathbf{p}_i^{t - 1},\mathbf{q}_i^{t - 1})$ . We perform the above grouping operation for each pair of seed corresponding points and obtain $n$ pairs of local region $(\mathbf{P}_i^t,\mathbf{Q}_i^t)$ . + +Generalized Mutual Matching. The next step is to generate new point correspondences from each pair of local regions by feature matching. However, the features in small local regions are usually similar, which results in traditional nearest-neighbor (NN) matching [11] producing a large number of false correspondences. Unfortunately, mutual NN matching [24, 26] may even fail to find any correspondence at all. To address this issue, we propose a generalized mutual matching to relax the strict mutual constraint, thereby improving the robustness of the local correspondences. + +Given point cloud $\mathbf{Q}_i^t$ as the query, the NN matching matrix $\mathbf{M}_1^{\mathcal{P}\to \mathcal{Q}}$ and multi-nearest-neighbor (MNN) matching matrix $\mathbf{M}_2^{\mathcal{P}\to \mathcal{Q}}$ are obtained by performing a k-nearest + +neighbor (KNN) search in feature space, respectively: + +$$ +\mathbf {M} _ {1} ^ {\mathcal {P} \rightarrow \mathcal {Q}} (m, n) = \mathrm {N N} (\mathbf {F} (\mathbf {p} _ {m}), \mathbf {F} (\mathbf {q} _ {n})), +$$ + +$$ +\mathbf {M} _ {2} ^ {\mathcal {P} \rightarrow \mathcal {Q}} (m, n) = \operatorname {M N N} (\mathbf {F} (\mathbf {p} _ {m}), \mathbf {F} (\mathbf {q} _ {n})), +$$ + +where $\forall \mathbf{p}_m\in \mathbf{P}_i^t,\mathbf{q}_n\in \mathbf{Q}_i^t$ and $\mathbf{F}(\cdot)$ represents the mapping from points to features. $\mathrm{NN}(\cdot)$ and MNN(·) represent the indicator functions for NN and MNN matching, respectively. If the matching condition is satisfied, the value is set to 1. Then, we conduct mutual matching from $\mathbf{P}_i^t$ to $\mathbf{Q}_i^t$ and from $\mathbf{Q}_i^t$ to $\mathbf{P}_i^t$ , resulting in four matching matrices $\mathbf{M}_1^{\mathcal{P}\to \mathcal{Q}}$ , $\mathbf{M}_2^{\mathcal{P}\to \mathcal{Q}}$ , $\mathbf{M}_1^{\mathcal{Q}\to \mathcal{P}}$ , and $\mathbf{M}_2^{\mathcal{Q}\to \mathcal{P}}$ . + +By computing the Hadamard product between the NN and MNN matching matrices, we obtain the mutual matching matrices $\mathbf{M}_*^{\mathcal{P} \to \mathcal{Q}}$ , $\mathbf{M}_*^{\mathcal{Q} \to \mathcal{P}}$ . Further, we perform an element-wise logical OR operation to relax the constraint and get the generalized mutual matching matrix: + +$$ +\mathbf {M} ^ {*} = \left(\mathbf {M} _ {1} ^ {\mathcal {P} \rightarrow \mathcal {Q}} \odot \mathbf {M} _ {2} ^ {\mathcal {Q} \rightarrow \mathcal {P}}\right) \otimes \left(\mathbf {M} _ {1} ^ {\mathcal {Q} \rightarrow \mathcal {P}} \odot \mathbf {M} _ {2} ^ {\mathcal {P} \rightarrow \mathcal {Q}}\right), \tag {4} +$$ + +where operation $\odot$ and $\otimes$ denote Hadamard product and element-wise logical OR, respectively. It is important to note that, to avoid a large number of outliers, we discard the strategy of directly applying mutual matching only based on MNN. Finally, using the matching matrix $\mathbf{M}^*$ , we establish $n$ sets of local correspondences $\mathcal{G}_i^t$ . + +# 3.4. Local Correspondence Refinement + +Because some corresponding local regions may not overlap exactly, the rematching in local regions still introduces some erroneous correspondences. Therefore, we further enhance the quality of the regenerated correspondences through local correspondence refinement. + +![](images/afc4c3e1f37e88da1c2b88fb033d76797d6fb68cd212e1ff9c4f781a81389dc6.jpg) +Figure 4. Illustration of the local correspondence correction. Yellow and blue areas represent a pair of local point clouds. The purple line indicates the correct correspondence after correction. + +Center-aware Three-point Consistency. Note that, our seed correspondences $g_{i}^{t - 1} = (\mathbf{p}_{i}^{t - 1},\mathbf{q}_{i}^{t - 1})$ (central points) are derived from the previous stage and exhibit high accuracy. Therefore, they can serve as prior information to + +guide the optimization of local correspondence refinement. Based on this, we propose an efficient center-aware three-point consistency (CTC) to search inliers. + +We first utilize efficient translation and rotation invariants [38] to describe the consistency $s_{\sigma}(g_i, g_j)$ between two point pairs $g_i = (\mathbf{p}_i, \mathbf{q}_i)$ and $g_j = (\mathbf{p}_j, \mathbf{q}_j)$ : + +$$ +s _ {\sigma} \left(g _ {i}, g _ {j}\right) = \mathbb {1} \left(\left| | \left| \mathbf {p} _ {i} - \mathbf {p} _ {j} \right| | _ {2} - | | \mathbf {q} _ {i} - \mathbf {q} _ {j} | | _ {2} \right| \leqslant \sigma\right). \tag {5} +$$ + +Next, we leverage the prior information of accurate center points to compute the center-aware consistency between $g_{j}$ and $g_{k}$ , denoted as $s_{\sigma}(g_j,g_i^{t - 1})\cdot s_{\sigma}(g_i^{t - 1},g_k)$ . Additionally, we account for the possibility that seed correspondences may not always be correct. Relying solely on the aforementioned criterion could allow errors in the seed correspondences to negatively impact the optimization of the entire region. To mitigate this, we introduce a strict point-pair constraint $s_{\frac{\sigma}{2}}(g_j,g_k)$ . CTC is computed as: + +$$ +s _ {\Delta} \left(g _ {j}, g _ {k}\right) = \left(s _ {\sigma} \left(g _ {j}, g _ {i} ^ {t - 1}\right) \cdot s _ {\sigma} \left(g _ {i} ^ {t - 1}, g _ {k}\right)\right) \mid | s _ {\frac {\sigma}{2}} \left(g _ {j}, g _ {k}\right), \tag {6} +$$ + +where $||$ represents operator OR and it means if either condition is satisfied, the correspondence is considered correct. Therefore, we get the score matrix $\mathbf{S}_i^t = [s_\Delta (g_j,g_k)]_{jk}\in$ $\mathbb{R}^{N\times N}$ of the local correspondences $\mathcal{G}_i^t\in \mathbb{R}^{N\times 2}$ . To evaluate the overall quality of the local region, we define a local overall score: + +$$ +\operatorname {S c o r e} \left(\mathcal {G} _ {i} ^ {t}\right) = \frac {\left| \left| \mathbf {S} _ {i} ^ {t} \right| \right| _ {1}}{a \cdot N}, \tag {7} +$$ + +where $||\cdot ||_1$ represents the $L_{1}$ -norm of a matrix and $a \in (0,1)$ denotes the threshold for the proportion of correct correspondences. Essentially, we consider regions where the proportion of correct correspondences exceeds $a$ as correct correspondence regions. It is proved in the Appendix. + +Local Correspondence Correction. Within each correct corresponding region, we identify a set of precise correspondences $\widehat{\mathcal{G}}_i^t$ to guide the refinement of correspondences across the entire local region. Specifically, based on the CTC score, we identify precise correspondences $\widehat{\mathcal{G}}_i^t$ with high scores. Subsequently, using these correspondences, we estimate the local transformation $\mathbf{T}_i^t\{\mathbf{R}_i^t,\mathbf{t}_i^t\}$ : + +$$ +\mathbf {R} _ {i} ^ {t}, \mathbf {t} _ {i} ^ {t} = \min _ {\mathbf {R}, \mathbf {t}} \sum_ {\left(\mathbf {p} _ {j}, \mathbf {q} _ {j}\right) \in \widehat {\mathcal {G}} _ {i} ^ {t}} \| \mathbf {R} \cdot \mathbf {p} _ {j} + \mathbf {t} - \mathbf {q} _ {j} \| _ {2} ^ {2}. \tag {8} +$$ + +Leveraging this local pose $\mathbf{T}_i^t\{\mathbf{R}_i^t,\mathbf{t}_i^t\}$ , we search for the nearest points $\mathbf{q}'$ in the target local point cloud $\mathbf{Q}_i^t$ for each point $\mathbf{p}$ in the source local point cloud $\mathbf{P}_i^t$ : + +$$ +\mathbf {q} ^ {\prime} = \underset {\mathbf {q} _ {j} \in \mathbf {Q} _ {i} ^ {t}} {\arg \min } \left\| \mathbf {R} _ {i} ^ {t} \mathbf {p} + \mathbf {t} _ {i} ^ {t} - \mathbf {q} _ {j} \right\| _ {2}, \tag {9} +$$ + +$$ +s. t. | | \mathbf {R} _ {i} ^ {t} \mathbf {p} + \mathbf {t} _ {i} ^ {t} - \mathbf {q} ^ {\prime} | | _ {2} \leqslant \sigma_ {d}, \forall (\mathbf {p}, \mathbf {q}) \in \mathcal {G} _ {i} ^ {t}. +$$ + +Through the one-way refinement of $\mathbf{Q}$ , we update our local correspondences $\mathcal{G}_i^t\gets \Omega_l(\mathcal{G}_i^t) = \{(\mathbf{p},\mathbf{q}^{\prime})\}$ where $\Omega_{l}$ represents the operation of local correspondence correction. + +# 3.5. Global Correspondence Refinement + +Through local refinement, we obtain $n$ sets of refined local correspondences. However, consistency across sets is not fully aligned. Therefore, we need a global merging and refinement step to complete the global correspondence optimization. Since there is no seed correspondence at the global scale, we use second-order consistency [6]. + +Correspondence Merging. After correcting the local correspondences, we merge them into global correspondences $\mathcal{G}^t$ . It is worth noting that some local regions overlap with each other. Therefore, we utilize a hash table $\mathbb{H}$ to implement correspondence merging. By using point indices as hash table keys, we efficiently merge local correspondences and remove duplicates to obtain the global correspondences $\mathcal{G}^t = \bigcup_{i=1}^{n} \mathcal{G}_i^t$ . With this strategy, we further enhance the efficiency of our method and save memory overhead. + +Global Correspondence Correction. Although we achieve the correspondence correction in local regions, if the seed correspondences $\widetilde{\mathcal{G}}^{t - 1}$ are significantly incorrect, it may still result in wrong refinement for the entire local region. Therefore, similar to local correction, we refine global correspondences $\mathcal{G}^t\gets \Omega_g(\mathcal{G}^t)$ , where $\Omega_{g}$ represents the operation of global correspondence correction. The key difference is that, in the global stage, we use second-order consistency [6] to identify correct correspondences. By leveraging correspondences that satisfy maximum consistency, we rectify anomalous correspondences globally, completing one iteration of correspondence regeneration $\Theta (\cdot)$ . + +# 4. Experiment + +We evaluate our algorithm using the indoor 3DMatch dataset [46] and the outdoor KITTI dataset [16], demonstrating its superior performance. Furthermore, we introduce the 3DMatch-EOR benchmark and conduct experiments to demonstrate the effectiveness of our method in scenarios with very few correct initial correspondences. Additionally, we also conduct robustness test experiments to verify that our algorithm can achieve robust registration using only weak features, thereby demonstrating its robustness across different descriptors. Finally, we conduct ablation studies to validate the effectiveness of each module. + +Evaluation Metric. Following [6, 47], we use registration recall (RR), rotation error (RE), and translation error (TE) to evaluate registration performance. For outdoor scenes, we consider a registration successful if the error is within $(5^{\circ}, 60\mathrm{cm})$ , and for indoor scenes, within $(15^{\circ}, 30\mathrm{cm})$ . Additionally, we assess the quality of correspondences using feature matching recall (FMR) and inlier precision (IP) which represents the proportion of inliers to the total correspondences. To further demonstrate our method's ability to generate a higher number of accurate correspondences, we define two new metrics: inlier number ratio (INR) and inlier + +
MethodFPFH (Traditional Descriptor)FCGF (Learning-based Descriptor)
RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)
PointDSC [3]76.962.256.7666.6470.16290.2392.612.106.4878.3785.881174.62
VBReg [22]78.012.287.3467.2370.93166.5692.772.246.8279.9286.30690.38
Hunter [40]84.701.806.4674.3979.27309.2894.051.866.5482.5588.011203.88
SM [25]55.882.948.1547.9670.69230.0386.572.297.0781.4438.36405.10
TEASER [38]75.482.487.3173.0178.60270.9885.772.738.6682.4387.901182.44
RANSAC-1M [14]64.204.0511.3563.9669.03264.0988.423.059.4277.9683.08672.22
SC2-PCR [6]83.242.216.7073.6478.78289.1793.162.116.4480.1787.241140.85
MAC [47]83.902.116.80---93.722.076.52---
FastMAC [48]82.872.156.73---92.672.006.47---
Regor (ours)88.481.705.9482.681253.742532.4093.961.756.1487.48263.812620.30
+ +![](images/1f879f51ce93e1e8805f8365bd8ac4d6afab4d183ab1225bf758dbeeef074412.jpg) +Figure 5. Correspondences before and after processing. + +![](images/4563e242a96dfbc0c674b267ed4cd3d30db7dca26126e06836921839d284b3ed.jpg) + +Table 1. Quantitative comparison on the 3DMatch dataset with descriptors FPFH [32] and FCGF [9]. + +
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
FPFH
PointDSC [3]27.914.2710.4523.8025.7646.52
VBReg [22]30.834.3810.9226.6129.7048.41
Hunter [40]36.903.8910.0531.5536.1756.01
RANSAC [14]19.834.6710.3230.8221.2037.02
SC2-PCR [6]35.934.2610.8630.1135.6555.23
MAC [47]40.883.669.45---
FastMAC [48]38.464.0410.47---
PCRegen (ours)43.962.898.9337.73778.35643.24
Predator
PointDSC [3]68.303.459.4456.3566.70863.40
VBReg [22]69.823.8710.0756.9067.09872.05
Hunter [40]71.103.589.7258.9069.06892.07
RANSAC [14]64.854.2811.0456.4466.81869.21
SC2-PCR [6]69.463.489.6358.0768.63883.59
MAC [47]70.913.699.81---
FastMAC [48]68.773.9010.32---
PCRegen (ours)72.043.179.4663.95220.462138.47
+ +Table 2. Quantitative comparison on the 3DLoMatch Dataset. + +numbers (IN). INR represents the ratio of the final number of inliers $\mathrm{IN}_{\text {final }}$ to the initial number of inliers $\mathrm{IN}_{\text {initial }}$ , defined explicitly in Appendix. + +# 4.1. Evaluation on Indoor Scenes + +Experimental Setup. For indoor scenes, we utilize the 3DMatch dataset. Our method is validated on both 3DMatch [46] and 3DLoMatch benchmarks [20]. Following [3, 6], we perform voxel downsampling on the raw point clouds, and use two descriptors, FPFH [32] and FCGF [10], to extract features as inputs for each method. + +Result on 3DMatch. We compare our method against several baselines on the 3DMatch dataset, including PointDSC [3], VBReg [22], Hunter [40], SM [25] + +TEASER [38], RANSAC [14], $\mathrm{SC^2}$ -PCR [6], MAC [47], and FastMAC [48]. The first three baselines are learning-based methods, while others are geometry-based approaches. The results are summarized in Table 1. Our method outperforms the previous state-of-the-art [6, 47]. Using the FPFH [9], our method outperforms all others across all metrics. Notably, our method achieves $88.48\%$ RR, surpassing $\mathrm{SC^2}$ -PCR [6] by 5.2 percentage points (pp). It also achieves more accurate registration with the lowest RE and TE. One significant advantage of our method is obtaining more high-quality correspondences, as reflected in the INR and IN. Our Regor achieves a $1253.74\%$ INR, which is much better than $78.78\%$ of SC2-PCR. Previous methods [6, 47, 48] only perform top-down filtering, which inevitably limits the INR to below $100\%$ . In contrast, our Regor regenerates more high-quality correspondences, producing around 10 times the original amount. This advantage allows our method to achieve robust registration even when there are few initial correct correspondences. Moreover, despite employing multiple iterations, it still maintains a comparable speed to the baselines [22, 40] due to its simple sampling strategy and efficient consistency computation. + +Result on 3DLoMatch. Since Predator [20] is specifically designed for scenarios with low overlap, we use Predator [20] and FPFH [32] to extract features on 3DLoMatch. The comparative results are presented in Table 2. Our approach achieves the highest RR and RE on 3DLoMatch, regardless of the descriptors used. Due to the inherent weakness of FPFH, nearly all baselines perform poorly on 3DLoMatch. In contrast, our method shows significant performance improvement, surpassing MAC [47] by 3.08 pp. + +Result on 3DMatch-EOR. The key to the effectiveness of our method lies in its ability to generate more accurate correspondences, particularly in scenarios with extremely high outlier ratios. To validate this, we select extreme outlier ratio cases from the 3DMatch/3DLoMatch datasets and propose the 3DMatch-EOR benchmark which is described in Appendix. We establish two benchmarks with outlier rates exceeding $99\%$ and $90\%$ , respectively. Our method is compared to SC2-PCR [6] and PointDSC [3], with results + +![](images/78e51931f438f30dbfa78ec5a2b3c2270e542dd72b583d1469eae076888d831e.jpg) +(a) Initial +(b) 1st stage +Figure 6. Correspondences visualization in different stages. + +![](images/d914672291d03fd9d8456ab6c0dff514f4c009e0d0fa764c8f06ba6ae662b946.jpg) +(c) 2nd stage + +![](images/d150a068e3af489695fe8c918c6251d41fc79ee7793e65b300c2408e87746ea7.jpg) +(d) 3rd stage + +![](images/f5b51c73e037bc0050138ebae523d9146a062a35f6d2cdb506c63c372b28fb9b.jpg) +(c) 4th stage + +
RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)
Outlier ratio above 90%
3DMatch3DLoMatch
PointDSC [3]71.122.527.7977.7660.0563.55129.1223.274.8412.9439.7818.1626.5731.18
SC2-PCR [6]78.582.497.7384.0251.9173.73138.9835.394.2910.9642.5829.635.1449.73
PCRegen (ours)84.881.866.6786.3878.141457.542334.3643.502.959.2446.3436.96780.05632.62
Outlier ratio above 99%
3DMatch3DLoMatch
PointDSC [3]2.565.1215.2810.903.074.880.170.754.9329.340.750.081.460.02
SC2-PCR [6]9.154.9412.2116.206.089.610.343.285.9419.447.882.474.960.89
PCRegen (ours)26.762.178.6028.8721.541545.12666.949.273.3612.3911.846.30291.40118.45
+ +shown in Table 3. In cases with such high outlier rates, achieving robust registration is exceptionally challenging, as the number of initial correct correspondences is minimal. When the outlier rate exceeded $99\%$ , the average inlier count of SC2-PCR is less than 1, leading to registration failure and achieving only $9.15\% / 3.28\%$ in RR. In contrast, our method achieves an average of 667 inliers, an improvement of nearly 2000 times compared to SC2-PCR [6], resulting in a $26.76\%$ RR. Our Regor enables success in scenarios where failure would otherwise be inevitable, allowing for relatively robust registration even with few initial inliers. + +# 4.2. Evaluation on Outdoor Scenes + +Experimental Setup. Following [7, 47], we validate our method's performance on the outdoor KITTI dataset. We select sequences 8 to 10 for testing. Consistent with the settings [6], we perform downsampling using a $30\mathrm{cm}$ voxel grid and extract features using FPFH descriptors. + +Result on KITTI. We conduct comparative experiments between our method and PointDSC [3], VBReg [22], Hunter [40], RANSAC [14], $\mathrm{SC^2}$ -PCR [6], MAC [47], and FastMAC [48] on the KITTI dataset. The results are presented in Table 4. Our Regor achieves the best performance with the highest RR, outperforming RANSAC [14] by 25.41 + +Table 3. Results on the 3DMatch-EOR benchmark with extreme outlier ratios. + +
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
PointDSC [3]99.460.577.2291.3993.05247.11
VBReg [22]98.928.398.4190.8292.13246.09
Hunter [40]99.820.556.2992.1194.58247.50
RANSAC [14]74.411.5530.2085.2987.20189.70
SC2-PCR [6]99.820.618.1693.5995.94248.46
MAC [47]99.460.598.70---
FastMAC [48]98.020.558.24---
Regor (ours)99.820.505.3679.572486.825353.22
+ +Table 4. Quantitative comparison on the KITTI Dataset. + +pp. It also demonstrates lower RE and TE, achieving the most accurate registration. Furthermore, our method shows superior performance in generating new correspondences, with INR over 25 times higher than those of other baselines [6, 40]. Despite IP is lower compared to SOTA [6], our method achieves more accurate pose estimation due to a larger number of high-quality inliers. + +# 4.3. Robustness to Different Features + +To further assess the robustness of various descriptors, we also test with traditional descriptors such as FPFH [32], SHOT [33], PFH [31], and PoRS [18], as well as learning-based descriptors like SpinNet [1], FCGF [9], Predator [20], and GeoTrans [30]. As shown in Table 5, our Regor con + +![](images/e1f2736c3bf2f772d13aaadbb717bfb5ff4999d39810c0e62066262a30c6485f.jpg) +Figure 7. RR under different features. + +
MethodRR(%)↑IP(%)↑IN(/)↑
FPFH [32]54.3445.74228.71
FPFH [32] + Regor88.48 (+34.14)82.68 (+36.94)1253.74 (×5.48)
PFH [31]69.3857.28286.38
PFH [31] + Regor89.28 (+19.90)81.72 (+24.44)2477.39 (×8.65)
RoPS [18]54.1642.49212.46
RoPS [18] + Regor91.37 (+37.21)84.29 (+41.80)2542.32 (×11.96)
SHOT [33]55.3346.01229.50
SHOT [33] + Regor71.90 (+16.57)66.41 (+20.40)1981.10 (×8.63)
FCGF [9]86.3256.85405.27
FCGF [9] + Regor93.96 (+7.64)87.48 (+30.63)2620.30 (×6.46)
SpinNet [1]88.6047.53444.84
SpinNet [1] + Regor96.30 (+7.70)88.24 (+40.71)2799.74 (×6.29)
Predator [20]89.0058.01444.38
Predator [20] + Regor91.44 (+2.44)86.84 (+28.83)4608.34 (×10.37)
GeoTrans [30]91.8075.20449.85
GeoTrans [30] + Regor97.10 (+5.30)91.01 (+15.81)2649.30 (×5.88)
+ +sistently improves performance across all features, which demonstrates it is robust to different features. Notably, GeoTrans [30] + Regor achieves a SOTA RR of $97.10\%$ . + +Good Performance with Weak Features. Moreover, our method significantly enhance the performance of the weak descriptors, increasing the RR from $54.16\%$ to $91.37\%$ with RoPS [18]. As can be seen in Figure 7, with our Regor, the traditional descriptors [18, 31, 32] achieves $88\% + \mathrm{RR}$ , surpassing the learning-based baseline [9]. When combined with our Regor, RoPS [18] exhibits performance that exceeds the learning-based methods [1, 9, 20], only second to GeoTrans [30]. This demonstrates that our method can achieve robust registration even with weak features. + +# 4.4. Ablation Study + +We conduct ablation experiments on the 3DMatch and 3DMatch-EOR benchmarks using FPFH descriptor. + +Progressive or One-stage. We verify the effectiveness of our progressive strategy by only using the one-stage process. The results are shown in Table 6 (1) and (2). Our strategy improves RR by $1.65 / 2.82$ pp compared to the one-stage approach. It is attributed to the heuristic setting: starting with a larger radius ensures global optimality and robustness, and gradually reducing the radius with each iter- + +Table 5. Enhancement of feature-based methods. + +
No.Methods3DMatch3DMatch-EOR
RRIPINRRIPIN
1)One-stage86.8176.34290.3223.9415.889.13
2)Progressive*88.4882.682532.4026.7621.54666.94
3)NNM87.3580.902487.2325.0619.82643.45
4)MM86.8181.032392.5323.9420.80600.09
5)GMM*88.4882.682532.4026.7621.54666.94
6)Only Local87.3578.402526.6323.0617.32668.08
7)Only Global76.3780.482502.2124.6516.57641.42
8)Local & Global*88.4882.682532.4026.7621.54666.94
9)SC86.8881.092491.5422.5418.18574.74
10)CTC*88.4882.682532.4026.7621.54666.94
+ +Table 6. Ablation study on 3DMatch and 3DMatch-EOR. + +ation enhances accuracy. More importantly, IN drops by $1\sim 2$ orders of magnitude, suggesting that our progressive strategy is key to generating more correspondences. + +Matching Strategy. We replace our GMM with mutual matching (MM) and nearest neighbor matching (NNM). Results are shown in Table 6 (3), (4) and (5). The model with GMM achieves the highest RR, IP, and IN. Compared with MM, using GMM results in a significant improvement in IN, which indicates our GMM is helpful to generate more inliers and addresses the issue of few initial inliers. + +Local-Global Refinement. To demonstrate the importance of our correspondence refinement, we compare the complete model with two ablation models. The results, shown in Rows 6, 7, and 8 of Table 6, indicate a significant performance drop when either local or global refinement is removed, with RR falling to $87\%$ and $86\%$ . In addition, the IP of the ablation model decreases by over 4 pp, which underscores the substantial contribution of the local-global refinement to the quality of the correspondences. + +Spatial Compatibility. We compared the SOTA second-order consistency (SC) [6, 7] with our CTC, and the results are shown at the bottom of Table 6. Our method with CTC obtains higher IP and IN, which indicates that CTC is more suitable for local refinement and achieves higher-quality correspondences. In addition, our CTC has less computational complexity than SC. Through it, we can implement an efficient iterative process. + +# 5. Conclusion + +In this paper, we introduce a new idea for optimizing correspondences. Unlike previous methods that focus solely on outlier removal, our Regor effectively addresses the challenge of limited correct initial correspondences. 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NeurIPS, 34:23872-23884, 2021. 1, 2 +[44] Hao Yu, Zheng Qin, Ji Hou, Mahdi Saleh, Dongsheng Li, Benjamin Busam, and Slobodan Ilic. Rotation-invariant transformer for point cloud matching. In CVPR, pages 5384-5393, 2023. 2 +[45] Junle Yu, Luwei Ren, Yu Zhang, Wenhui Zhou, Lili Lin, and Guojun Dai. Peal: Prior-embedded explicit attention learning for low-overlap point cloud registration. In CVPR, pages 17702–17711, 2023. 2 +[46] Andy Zeng, Shuran Song, Matthias Nießner, Matthew Fisher, Jianxiong Xiao, and Thomas Funkhouser. 3dmatch: Learning local geometric descriptors from rgb-d reconstructions. In CVPR, pages 1802-1811, 2017. 2, 5, 6 +[47] Xiyu Zhang, Jiaqi Yang, Shikun Zhang, and Yanning Zhang. 3d registration with maximal cliques. In CVPR, pages 17745-17754, 2023. 1, 2, 5, 6, 7 +[48] Yifei Zhang, Hao Zhao, Hongyang Li, and Siheng Chen. Fastmac: Stochastic spectral sampling of correspondence graph. In CVPR, pages 17857-17867, 2024. 6, 7 +[49] Guiyu Zhao, Zhentao Guo, Xin Wang, and Hongbin Ma. Spherenet: Learning a noise-robust and general descriptor for point cloud registration. 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Existing correspondence refinement methods mostly follow the paradigm of outlier removal, which either fails to correctly identify the accurate correspondences under extreme outlier ratios, or select too few correct correspondences to support robust registration. To address this challenge, we propose a novel approach named Regor, which is a progressive correspondence generator that generates higher-quality matches whilst sufficiently robust for numerous outliers. In each iteration, we first apply prior-guided local grouping and generalized mutual matching to generate the local region correspondences. A powerful center-aware three-point consistency is then presented to achieve local correspondence correction, instead of removal. Further, we employ global correspondence refinement to obtain accurate correspondences from a global perspective. Through progressive iterations, this process yields a large number of high-quality correspondences. Extensive experiments on both indoor and outdoor datasets demonstrate that the proposed Regor significantly outperforms existing outlier removal techniques. More critically, our approach obtains 10 times more correct correspondences than outlier removal methods. As a result, our method is able to achieve robust registration even with weak features. The code is available at [Regor]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 590, + 135, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 590, + 135, + 602 + ], + "spans": [ + { + "bbox": [ + 56, + 590, + 135, + 602 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "type": "text", + "content": "Point cloud registration [8, 21] is a fundamental and critical task in 3D computer vision, with widespread applications across various domains such as robotic localization [36, 42] and remote sensing [21, 35]. Point cloud registration aims to estimate a rigid transformation to align two point clouds scanned from different perspectives. With the advancement" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 242, + 426, + 407 + ], + "blocks": [ + { + "bbox": [ + 317, + 242, + 426, + 407 + ], + "lines": [ + { + "bbox": [ + 317, + 242, + 426, + 407 + ], + "spans": [ + { + "bbox": [ + 317, + 242, + 426, + 407 + ], + "type": "image", + "image_path": "5e3d55d3854d2fb91c7087265aad59ffaf4edddf5ee683c386f3e2091bc343bc.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 412, + 403, + 420 + ], + "lines": [ + { + "bbox": [ + 339, + 412, + 403, + 420 + ], + "spans": [ + { + "bbox": [ + 339, + 412, + 403, + 420 + ], + "type": "text", + "content": "(a) Existing Methods" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 431, + 555, + 520 + ], + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 520 + ], + "type": "text", + "content": "Figure 1. Difference between our method and existing outlier removal techniques. Outlier removal methods perform top-down pruning, producing an optimized set of correspondences that is a subset of the initial correspondences. When the initial inliers are few, this approach can obtain only a limited number of inliers, which is insufficient for robust pose estimation. In contrast, our method takes a bottom-up approach, using a regeneration strategy to generate more inliers, thereby effectively addressing this issue." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 443, + 242, + 553, + 407 + ], + "blocks": [ + { + "bbox": [ + 443, + 242, + 553, + 407 + ], + "lines": [ + { + "bbox": [ + 443, + 242, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 443, + 242, + 553, + 407 + ], + "type": "image", + "image_path": "875f1fa3c092e798725c207e9675f40e2c4ed381a6e08fd12e33425f3acee42b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 412, + 521, + 420 + ], + "lines": [ + { + "bbox": [ + 473, + 412, + 521, + 420 + ], + "spans": [ + { + "bbox": [ + 473, + 412, + 521, + 420 + ], + "type": "text", + "content": "(b) Our Method" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 542, + 555, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 555, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 555, + 615 + ], + "type": "text", + "content": "of feature metric learning, feature-based point cloud registration methods [1, 20, 30, 43] have garnered significant attention and achieved promising results. However, in scenarios characterized by low overlap and high noise, direct feature matching often leads to a large number of outliers, which poses a great challenge for point cloud registration." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "content": "Currently, the mainstream approach to address the issue of numerous outliers in point cloud registration is to filter wrong correspondences. Existing outlier removal methods [3, 6, 22, 27, 47] can be categorized into two types: geometry-based methods and learning-based methods. Geometry-based methods [6, 14, 28, 47] typically remove outliers according to whether point correspondences satisfy geometric consistency. Learning-based methods [3," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "type": "text", + "content": "*These authors contributed equally." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 68, + 703, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 703, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 68, + 703, + 146, + 712 + ], + "type": "text", + "content": "† Corresponding Author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1210" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "22, 27] treat this task as a classification problem to distinguish between outliers and inliers. However, in challenging scenarios, these correspondence filtering methods all suffer from a common problem: when initial correspondences only contains few inliers, estimating the correct rigid transformation between two point clouds is extremely difficult even if all inliers are identified." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 157, + 294, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 157, + 294, + 289 + ], + "spans": [ + { + "bbox": [ + 54, + 157, + 294, + 289 + ], + "type": "text", + "content": "In this paper, we aim to design a new 3D registration architecture, which is robust to few inliers and is able to estimate precise 6DoF pose. As shown in Figure 1, different from existing outlier removal methods [3, 6, 7, 47] that focus on pruning correspondences, our approach clearly regenerate more high-quality correspondences to achieve robust registration. The key insight is to progressively generate correspondences and leverage the positional priors of correspondences from the previous iteration to guide more refined local regeneration, thereby obtaining more high-quality point correspondences." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 289, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 289, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 56, + 289, + 295, + 529 + ], + "type": "text", + "content": "Our method, named Regor, follows a progressive iterative framework composed of three main modules: Local Grouping and Rematching, Local Correspondence Refinement and Global Correspondence Refinement. In each iteration, Local Grouping and Rematching leverages prior-guided local grouping to gradually reduce the matching space and generalized mutual matching to perform reliable local matching. The Local Correspondence Refinement introduces an effective center-aware three-point consistency to mine inliers and update local correspondences. The Global Correspondence Refinement is employed to perform further optimization from a global perspective. Note that, each iteration gradually increases the number of inliers, instead of only removing outliers. Our method achieves state-of-the-art performance on both the 3DMatch [46] and KITTI [16] datasets. Notably, the proposed Regor demonstrates a strong ability to generate correspondences, yielding up to 10 times more correct matches than existing outlier removal methods [6, 7, 47]. The main contributions of this paper are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 529, + 295, + 637 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 529, + 295, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 295, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 295, + 577 + ], + "type": "text", + "content": "- We propose a novel registration approach named Regor to obtain massive high-quality point correspondences, overcoming the challenge of scarce inliers by progressively generating correspondences." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 578, + 295, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 612 + ], + "type": "text", + "content": "- Our method achieves state-of-the-art performance. In particular, the number of correct correspondences is 10 times higher than that of outlier removal methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 613, + 295, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 613, + 295, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 613, + 295, + 637 + ], + "type": "text", + "content": "- Benefiting from the proposed regenerator, our approach achieves robust registration even with weak features." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 671, + 178, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 178, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 178, + 684 + ], + "type": "text", + "content": "2.1. 3D Feature Matching" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Feature matching is a crucial step in correspondence-based point cloud registration [1, 20, 30, 32, 43, 45, 46]. Accord" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 336 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 336 + ], + "type": "text", + "content": "ing to the approach of feature extraction, feature matching methods can be categorized into two types: traditional descriptor-based methods [31-33] and learning-based methods [1, 20, 30, 43, 45]. Before the widespread adoption of deep learning, features were manually designed descriptors tailored to represent local information. They are classified into LRF-based methods [18, 33] and LRF-free methods [31, 32] based on whether a local reference frame (LRF) is needed. With the advancements in deep learning, numerous learning-based methods have emerged. Based on the representation strategy, they can be further divided into patch-based methods [1, 17, 49] and fragment-based methods [9, 15, 20, 43]. SpinNet [1] and BUFFER [2] have achieved excellent generalization ability through 3D cylindrical convolution. Additionally, CoFiNet [43] and GeoTransformer [30] propose a coarse-to-fine matching strategy and a Transformer-based framework, which has garnered widespread attention. Subsequent methods [23, 37, 44, 45] have further improved performance by incorporating position encoding and prior information into this framework. ODIN [23] achieves the best performance through diffusion strategy and global optimization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 345, + 495, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 495, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 495, + 357 + ], + "type": "text", + "content": "2.2. Geometry-based Outlier Removal" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 363, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 567 + ], + "type": "text", + "content": "Geometry-based outlier removal involves fitting models from noisy correspondences using the geometric properties of 3D scenes to estimate poses. The most classic method is random sampling consensus (RANSAC) [14], which samples correspondences multiple times and validates to obtain the best pose, thus mitigating the impact of noisy correspondences. Subsequently, numerous variants of RANSAC [4, 5, 12, 34] have been proposed to address issues of time consumption and instability. TEASER [38] introduces the truncated least squares (TLS) cost to solve for pose and employ rotation invariant measurements to handle outliers. Then, " + }, + { + "bbox": [ + 313, + 363, + 555, + 567 + ], + "type": "inline_equation", + "content": "\\mathrm{SC^2}" + }, + { + "bbox": [ + 313, + 363, + 555, + 567 + ], + "type": "text", + "content": "-PCR [6, 7] propose second-order consistency for robust outlier removal. In recent years, methods [39, 47] based on geometric consistency have been widely applied in point cloud registration, leveraging graph-theoretic approaches [13] and geometric consistency to remove outliers, thereby achieving robust registration." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 575, + 491, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 491, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 491, + 588 + ], + "type": "text", + "content": "2.3. Learning-based Outlier Removal" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "type": "text", + "content": "Recent researches [3, 22, 29] have integrated deep learning into outlier removal and pose estimation, showcasing promising performance through training. Inspired by image matching [41], 3DRegNet [29] adapts CN-Net [41] to remove outliers in point cloud registration. Subsequently, PointDSC [3] embeds the spatial consistency into feature maps and employs neural spectral matching to estimate confidence of correspondences, achieving robust registration. VBReg [22] utilizes variational Bayesian inference to achieve better outlier removal. Hunter [40] addresses severe" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "text", + "content": "1211" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 549, + 238 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 549, + 238 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 549, + 238 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 549, + 238 + ], + "type": "image", + "image_path": "a1b3ba4747a198ac85ef57a190ff03c990f5ba0c887bd6a1656fd7b26c914e91.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "lines": [ + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": "Figure 2. Overall framework of our method. We extract features from the original point cloud, obtaining features " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{\\mathcal{P}}" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{\\mathcal{Q}}" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " as input for our method. Subsequently, a progressive process is applied to iteratively regenerate more accurate and denser correspondences " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": ". At each iteration, the output correspondences " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{t-1}" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " from the previous iteration serve as input. Firstly, prior-guided local grouping is employed to sample seed corresponding points and form local correspondence regions " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i^t" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": ". Then, for each pair of local correspondence regions, generalized mutual matching is performed to get new correspondences. Next, these correspondences are refined locally and globally using our center-aware three-point consistency, followed by a merging operation " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " of local correspondences " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^t" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " using a hash table. Finally, using these refined correspondences, we achieve robust and accurate transformation estimation " + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{T}\\{\\mathbf{R}, \\mathbf{t}\\}" + }, + { + "bbox": [ + 54, + 248, + 555, + 326 + ], + "type": "text", + "content": " only with SVD." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 347, + 294, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 347, + 294, + 418 + ], + "spans": [ + { + "bbox": [ + 54, + 347, + 294, + 418 + ], + "type": "text", + "content": "outlier issues by introducing higher-order consistency using hypergraphs. However, while both geometry-based and learning-based methods have shown effectiveness in outlier removal, they inherently rely on the initial correspondences and only trim down on them, which poses challenges when initial inliers are scarce." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 432, + 111, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 432, + 111, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 432, + 111, + 444 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 453, + 180, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 180, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 180, + 464 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": "Point cloud registration is aligning two point clouds " + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": ", captured from different perspectives, by estimating a pose transformation " + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{T} \\{\\mathbf{R}, \\mathbf{t}\\}" + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": " is a rotation matrix and " + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 55, + 471, + 295, + 555 + ], + "type": "text", + "content": " is a translation vector. Feature-based point cloud registration estimates correspondences through feature extraction and matching, then minimizes the average Euclidean distance between these correspondences, as shown in Eq. 1:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 70, + 565, + 295, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 565, + 295, + 595 + ], + "spans": [ + { + "bbox": [ + 70, + 565, + 295, + 595 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {R} \\in S O (3), \\mathbf {t} \\in \\mathbb {R} ^ {3}} {\\arg \\min } \\sum_ {\\left(\\mathbf {p} _ {x _ {i}}, \\mathbf {q} _ {y _ {i}}\\right) \\in \\mathcal {I}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {x _ {i}} + \\mathbf {t} - \\mathbf {q} _ {y _ {i}} \\| _ {2} ^ {2}. \\tag {1}", + "image_path": "f82681229cbff8aedb26406d2f661ffe9f3e16f075c5c55bac9b3798dd69f71c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "In this study, unlike outlier removal methods that perform \"subtraction\" filtering on initial correspondences, resulting in a subset of initial correspondences highly dependent on them, our aim is to generate more higher-quality correspondences " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "t = 1,2,\\dots,m" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " represents the current iterative stage. We define the regeneration process as " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t = \\Theta (\\mathcal{G}^{t - 1};\\mathbf{P},\\mathbf{Q},\\varphi^t)" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " is the operation of the correspondence regeneration, and " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\varphi^t" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " represents the parameter used in the regeneration of the " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "th stage." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 346, + 518, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 518, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 518, + 360 + ], + "type": "text", + "content": "3.2. Progressive Regeneration: Key Insight" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 364, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 553, + 483 + ], + "type": "text", + "content": "Existing methods focus on pruning the initial correspondences to remove outliers and retain inliers. Due to common problems such as weak feature representation and low overlap, the proportion of correct initial correspondences is typically very small. Even all correct correspondences are identified, achieving accurate registration remains challenging. To this end, we design a novel progressive correspondence regeneration strategy to address the scarcity of initial inliers and the frequent failures of correspondence filtering under extreme outlier ratios." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 484, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 554, + 651 + ], + "type": "text", + "content": "The key idea of our method is to progressively regenerate better correspondences in a radius-variable local sphere. We use the positional priors of correspondences generated in the previous stage to guide the creation of the local sphere. In each local sphere, we regenerate more correspondences with higher quality. Compared to direct global matching, re-matching and refining within these local spheres significantly reduce the problem's scale and search space, resulting in more precise matches and reduced computational time. As the quality of the correspondence gets higher, we progressively reduce the size of the local spheres to achieve exact convergence of the correspondences. This approach not only generates a large number of new dense correspondences but also incrementally enhances their accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 659, + 492, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 492, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 492, + 673 + ], + "type": "text", + "content": "3.3. Local Grouping and Rematching" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "In this module, we implement the core of each iteration: local correspondence generation. First, we introduce prior-guided local grouping to leverage priors from the previous" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1212" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 294, + 228 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 294, + 228 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 294, + 228 + ], + "type": "image", + "image_path": "d4ee624d3ce7db74bdf52e25eade2d97a5647c9a57f226ebb813712085498a97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 237, + 296, + 271 + ], + "lines": [ + { + "bbox": [ + 55, + 237, + 296, + 271 + ], + "spans": [ + { + "bbox": [ + 55, + 237, + 296, + 271 + ], + "type": "text", + "content": "Figure 3. Illustration of GMM. The orange, blue, green, and red lines are the MNN correspondences, NN correspondences, correct correspondences, and wrong correspondences, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 293, + 296, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 296, + 328 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 296, + 328 + ], + "type": "text", + "content": "iteration. Then, we propose a generalized mutual matching technique to ensure the generation of a sufficient number of inliers even under high outlier rates." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": "Prior-guided Local Grouping. The input to our method is the correspondence " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{t - 1}" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": " of the previous stage. Efficiency is crucial for our method due to the need for iterative processing. Therefore, we sample " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{t - 1}" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": " using efficient random sampling [19] to derive seed correspondences " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{G}}^{t - 1}" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": ". We then utilize the positional priors of each seed correspondence to guide the construction of local regions. Specifically, we conduct a radius " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "r^t" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": " nearest neighbor search centered on each seed correspondence " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\widetilde{g}_i^{t - 1}\\in \\widetilde{\\mathcal{G}}^{t - 1}" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": " to obtain local point clouds " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i^t" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "inline_equation", + "content": "i = 1,2,\\dots,n" + }, + { + "bbox": [ + 55, + 329, + 296, + 450 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 458, + 294, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 458, + 294, + 485 + ], + "spans": [ + { + "bbox": [ + 58, + 458, + 294, + 485 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {p} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\mathbf {Q} _ {i} ^ {t} = \\operatorname {R N N} \\left(\\mathbf {q} _ {i} ^ {t - 1}; r ^ {t}, \\widetilde {\\mathcal {G}} ^ {t - 1}\\right), \\tag {2}", + "image_path": "814cd8f5e22fbba9d1057a67d4fd5ffdc9a6b4afd9606cc9ea187cc22d079ff1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\mathrm{RNN}(\\mathbf{p};r,\\mathcal{G})" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " is a radius nearest neighbor search on " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " as the center and " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " as the radius. " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^{t - 1}" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i^{t - 1}" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " satisfy " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\widetilde{g}_i^{t - 1} = (\\mathbf{p}_i^{t - 1},\\mathbf{q}_i^{t - 1})" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": ". We perform the above grouping operation for each pair of seed corresponding points and obtain " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": " pairs of local region " + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "inline_equation", + "content": "(\\mathbf{P}_i^t,\\mathbf{Q}_i^t)" + }, + { + "bbox": [ + 55, + 485, + 296, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 545, + 296, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 675 + ], + "type": "text", + "content": "Generalized Mutual Matching. The next step is to generate new point correspondences from each pair of local regions by feature matching. However, the features in small local regions are usually similar, which results in traditional nearest-neighbor (NN) matching [11] producing a large number of false correspondences. Unfortunately, mutual NN matching [24, 26] may even fail to find any correspondence at all. To address this issue, we propose a generalized mutual matching to relax the strict mutual constraint, thereby improving the robustness of the local correspondences." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Given point cloud " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " as the query, the NN matching matrix " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " and multi-nearest-neighbor (MNN) matching matrix " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " are obtained by performing a k-nearest" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 533, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 533, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 533, + 84 + ], + "type": "text", + "content": "neighbor (KNN) search in feature space, respectively:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 348, + 92, + 510, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 92, + 510, + 107 + ], + "spans": [ + { + "bbox": [ + 348, + 92, + 510, + 107 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\mathrm {N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),", + "image_path": "e3ec94257589836308c92d1f57c29ce621e2dbe55a3e06449d46688f0714b411.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 350, + 110, + 518, + 124 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 110, + 518, + 124 + ], + "spans": [ + { + "bbox": [ + 350, + 110, + 518, + 124 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} (m, n) = \\operatorname {M N N} (\\mathbf {F} (\\mathbf {p} _ {m}), \\mathbf {F} (\\mathbf {q} _ {n})),", + "image_path": "ad0ad94de3f71e63efbd871a0d8c2afd88eaab700137caee00a9fe0958fd70f5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\forall \\mathbf{p}_m\\in \\mathbf{P}_i^t,\\mathbf{q}_n\\in \\mathbf{Q}_i^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{F}(\\cdot)" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " represents the mapping from points to features. " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{NN}(\\cdot)" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " and MNN(·) represent the indicator functions for NN and MNN matching, respectively. If the matching condition is satisfied, the value is set to 1. Then, we conduct mutual matching from " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " and from " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": ", resulting in four matching matrices " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_1^{\\mathcal{P}\\to \\mathcal{Q}}" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_2^{\\mathcal{P}\\to \\mathcal{Q}}" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_1^{\\mathcal{Q}\\to \\mathcal{P}}" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_2^{\\mathcal{Q}\\to \\mathcal{P}}" + }, + { + "bbox": [ + 313, + 133, + 555, + 217 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "text", + "content": "By computing the Hadamard product between the NN and MNN matching matrices, we obtain the mutual matching matrices " + }, + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_*^{\\mathcal{P} \\to \\mathcal{Q}}" + }, + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_*^{\\mathcal{Q} \\to \\mathcal{P}}" + }, + { + "bbox": [ + 313, + 217, + 555, + 277 + ], + "type": "text", + "content": ". Further, we perform an element-wise logical OR operation to relax the constraint and get the generalized mutual matching matrix:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 285, + 555, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 285, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 318, + 285, + 555, + 301 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {*} = \\left(\\mathbf {M} _ {1} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}}\\right) \\otimes \\left(\\mathbf {M} _ {1} ^ {\\mathcal {Q} \\rightarrow \\mathcal {P}} \\odot \\mathbf {M} _ {2} ^ {\\mathcal {P} \\rightarrow \\mathcal {Q}}\\right), \\tag {4}", + "image_path": "ac80fa95d0fce1d3c9aabcbb72996602bc0b9ba28db4a769878cc9e756eaae29.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": "where operation " + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": " denote Hadamard product and element-wise logical OR, respectively. It is important to note that, to avoid a large number of outliers, we discard the strategy of directly applying mutual matching only based on MNN. Finally, using the matching matrix " + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^*" + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": ", we establish " + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": " sets of local correspondences " + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^t" + }, + { + "bbox": [ + 313, + 309, + 554, + 382 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 389, + 499, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 499, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 499, + 402 + ], + "type": "text", + "content": "3.4. Local Correspondence Refinement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "content": "Because some corresponding local regions may not overlap exactly, the rematching in local regions still introduces some erroneous correspondences. Therefore, we further enhance the quality of the regenerated correspondences through local correspondence refinement." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 318, + 479, + 553, + 610 + ], + "blocks": [ + { + "bbox": [ + 318, + 479, + 553, + 610 + ], + "lines": [ + { + "bbox": [ + 318, + 479, + 553, + 610 + ], + "spans": [ + { + "bbox": [ + 318, + 479, + 553, + 610 + ], + "type": "image", + "image_path": "afc4c3e1f37e88da1c2b88fb033d76797d6fb68cd212e1ff9c4f781a81389dc6.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 619, + 555, + 653 + ], + "lines": [ + { + "bbox": [ + 313, + 619, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 619, + 555, + 653 + ], + "type": "text", + "content": "Figure 4. Illustration of the local correspondence correction. Yellow and blue areas represent a pair of local point clouds. The purple line indicates the correct correspondence after correction." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": "Center-aware Three-point Consistency. Note that, our seed correspondences " + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "inline_equation", + "content": "g_{i}^{t - 1} = (\\mathbf{p}_{i}^{t - 1},\\mathbf{q}_{i}^{t - 1})" + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": " (central points) are derived from the previous stage and exhibit high accuracy. Therefore, they can serve as prior information to" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1213" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "guide the optimization of local correspondence refinement. Based on this, we propose an efficient center-aware three-point consistency (CTC) to search inliers." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "spans": [ + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "text", + "content": "We first utilize efficient translation and rotation invariants [38] to describe the consistency " + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "inline_equation", + "content": "s_{\\sigma}(g_i, g_j)" + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "text", + "content": " between two point pairs " + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "inline_equation", + "content": "g_i = (\\mathbf{p}_i, \\mathbf{q}_i)" + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "inline_equation", + "content": "g_j = (\\mathbf{p}_j, \\mathbf{q}_j)" + }, + { + "bbox": [ + 55, + 108, + 295, + 146 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 150, + 295, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 150, + 295, + 171 + ], + "spans": [ + { + "bbox": [ + 63, + 150, + 295, + 171 + ], + "type": "interline_equation", + "content": "s _ {\\sigma} \\left(g _ {i}, g _ {j}\\right) = \\mathbb {1} \\left(\\left| | \\left| \\mathbf {p} _ {i} - \\mathbf {p} _ {j} \\right| | _ {2} - | | \\mathbf {q} _ {i} - \\mathbf {q} _ {j} | | _ {2} \\right| \\leqslant \\sigma\\right). \\tag {5}", + "image_path": "1cde1e2035b728b43b9fe9e52a489c9455b3656e34cbba0af2e48703cad043f4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "content": "Next, we leverage the prior information of accurate center points to compute the center-aware consistency between " + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "inline_equation", + "content": "g_{j}" + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "inline_equation", + "content": "g_{k}" + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "inline_equation", + "content": "s_{\\sigma}(g_j,g_i^{t - 1})\\cdot s_{\\sigma}(g_i^{t - 1},g_k)" + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "content": ". Additionally, we account for the possibility that seed correspondences may not always be correct. Relying solely on the aforementioned criterion could allow errors in the seed correspondences to negatively impact the optimization of the entire region. To mitigate this, we introduce a strict point-pair constraint " + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "inline_equation", + "content": "s_{\\frac{\\sigma}{2}}(g_j,g_k)" + }, + { + "bbox": [ + 55, + 176, + 296, + 285 + ], + "type": "text", + "content": ". CTC is computed as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 291, + 295, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 291, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 61, + 291, + 295, + 316 + ], + "type": "interline_equation", + "content": "s _ {\\Delta} \\left(g _ {j}, g _ {k}\\right) = \\left(s _ {\\sigma} \\left(g _ {j}, g _ {i} ^ {t - 1}\\right) \\cdot s _ {\\sigma} \\left(g _ {i} ^ {t - 1}, g _ {k}\\right)\\right) \\mid | s _ {\\frac {\\sigma}{2}} \\left(g _ {j}, g _ {k}\\right), \\tag {6}", + "image_path": "9fa893fdbbbffc5210cdd75d13448a82872fe4afffc5d56334042c3d9ad26439.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "inline_equation", + "content": "||" + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "text", + "content": " represents operator OR and it means if either condition is satisfied, the correspondence is considered correct. Therefore, we get the score matrix " + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_i^t = [s_\\Delta (g_j,g_k)]_{jk}\\in" + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "text", + "content": " of the local correspondences " + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^t\\in \\mathbb{R}^{N\\times 2}" + }, + { + "bbox": [ + 55, + 317, + 296, + 387 + ], + "type": "text", + "content": ". To evaluate the overall quality of the local region, we define a local overall score:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 130, + 386, + 294, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 386, + 294, + 410 + ], + "spans": [ + { + "bbox": [ + 130, + 386, + 294, + 410 + ], + "type": "interline_equation", + "content": "\\operatorname {S c o r e} \\left(\\mathcal {G} _ {i} ^ {t}\\right) = \\frac {\\left| \\left| \\mathbf {S} _ {i} ^ {t} \\right| \\right| _ {1}}{a \\cdot N}, \\tag {7}", + "image_path": "4ea824021d9a515cae9e474a38f00bf111c4eea00b852497d40e1e4e5c340806.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "||\\cdot ||_1" + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "content": "-norm of a matrix and " + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "a \\in (0,1)" + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "content": " denotes the threshold for the proportion of correct correspondences. Essentially, we consider regions where the proportion of correct correspondences exceeds " + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 55, + 412, + 296, + 472 + ], + "type": "text", + "content": " as correct correspondence regions. It is proved in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "text", + "content": "Local Correspondence Correction. Within each correct corresponding region, we identify a set of precise correspondences " + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{G}}_i^t" + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "text", + "content": " to guide the refinement of correspondences across the entire local region. Specifically, based on the CTC score, we identify precise correspondences " + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{G}}_i^t" + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "text", + "content": " with high scores. Subsequently, using these correspondences, we estimate the local transformation " + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}" + }, + { + "bbox": [ + 55, + 472, + 296, + 558 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 563, + 295, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 563, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 69, + 563, + 295, + 583 + ], + "type": "interline_equation", + "content": "\\mathbf {R} _ {i} ^ {t}, \\mathbf {t} _ {i} ^ {t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {j}, \\mathbf {q} _ {j}\\right) \\in \\widehat {\\mathcal {G}} _ {i} ^ {t}} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {j} + \\mathbf {t} - \\mathbf {q} _ {j} \\| _ {2} ^ {2}. \\tag {8}", + "image_path": "a8b15056f88a8955067ac1044c18cd5b879f63470e6ebc9e5785bb80f179928f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": "Leveraging this local pose " + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i^t\\{\\mathbf{R}_i^t,\\mathbf{t}_i^t\\}" + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": ", we search for the nearest points " + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{q}'" + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": " in the target local point cloud " + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i^t" + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": " for each point " + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": " in the source local point cloud " + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i^t" + }, + { + "bbox": [ + 55, + 590, + 295, + 628 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 101, + 632, + 295, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 632, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 101, + 632, + 295, + 658 + ], + "type": "interline_equation", + "content": "\\mathbf {q} ^ {\\prime} = \\underset {\\mathbf {q} _ {j} \\in \\mathbf {Q} _ {i} ^ {t}} {\\arg \\min } \\left\\| \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} _ {j} \\right\\| _ {2}, \\tag {9}", + "image_path": "96faba5659f0c30c14a9a33d30b63f73f93d3359694419ece6dec8d5b6b69690.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 88, + 658, + 263, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 658, + 263, + 672 + ], + "spans": [ + { + "bbox": [ + 88, + 658, + 263, + 672 + ], + "type": "interline_equation", + "content": "s. t. | | \\mathbf {R} _ {i} ^ {t} \\mathbf {p} + \\mathbf {t} _ {i} ^ {t} - \\mathbf {q} ^ {\\prime} | | _ {2} \\leqslant \\sigma_ {d}, \\forall (\\mathbf {p}, \\mathbf {q}) \\in \\mathcal {G} _ {i} ^ {t}.", + "image_path": "e35fc2a2b35242aa7509c6d2524ae556999369a0440f375c40208c01d82a0fbd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Through the one-way refinement of " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": ", we update our local correspondences " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^t\\gets \\Omega_l(\\mathcal{G}_i^t) = \\{(\\mathbf{p},\\mathbf{q}^{\\prime})\\}" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\Omega_{l}" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": " represents the operation of local correspondence correction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 72, + 504, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 504, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 504, + 84 + ], + "type": "text", + "content": "3.5. Global Correspondence Refinement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 90, + 553, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 90, + 553, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 90, + 553, + 162 + ], + "type": "text", + "content": "Through local refinement, we obtain " + }, + { + "bbox": [ + 313, + 90, + 553, + 162 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 90, + 553, + 162 + ], + "type": "text", + "content": " sets of refined local correspondences. However, consistency across sets is not fully aligned. Therefore, we need a global merging and refinement step to complete the global correspondence optimization. Since there is no seed correspondence at the global scale, we use second-order consistency [6]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "text", + "content": "Correspondence Merging. After correcting the local correspondences, we merge them into global correspondences " + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t" + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "text", + "content": ". It is worth noting that some local regions overlap with each other. Therefore, we utilize a hash table " + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "inline_equation", + "content": "\\mathbb{H}" + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "text", + "content": " to implement correspondence merging. By using point indices as hash table keys, we efficiently merge local correspondences and remove duplicates to obtain the global correspondences " + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t = \\bigcup_{i=1}^{n} \\mathcal{G}_i^t" + }, + { + "bbox": [ + 313, + 163, + 553, + 270 + ], + "type": "text", + "content": ". With this strategy, we further enhance the efficiency of our method and save memory overhead." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "spans": [ + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "content": "Global Correspondence Correction. Although we achieve the correspondence correction in local regions, if the seed correspondences " + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{G}}^{t - 1}" + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "content": " are significantly incorrect, it may still result in wrong refinement for the entire local region. Therefore, similar to local correction, we refine global correspondences " + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t\\gets \\Omega_g(\\mathcal{G}^t)" + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "inline_equation", + "content": "\\Omega_{g}" + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "content": " represents the operation of global correspondence correction. The key difference is that, in the global stage, we use second-order consistency [6] to identify correct correspondences. By leveraging correspondences that satisfy maximum consistency, we rectify anomalous correspondences globally, completing one iteration of correspondence regeneration " + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "inline_equation", + "content": "\\Theta (\\cdot)" + }, + { + "bbox": [ + 313, + 271, + 555, + 416 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 428, + 390, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 428, + 390, + 441 + ], + "spans": [ + { + "bbox": [ + 314, + 428, + 390, + 441 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 449, + 555, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 581 + ], + "type": "text", + "content": "We evaluate our algorithm using the indoor 3DMatch dataset [46] and the outdoor KITTI dataset [16], demonstrating its superior performance. Furthermore, we introduce the 3DMatch-EOR benchmark and conduct experiments to demonstrate the effectiveness of our method in scenarios with very few correct initial correspondences. Additionally, we also conduct robustness test experiments to verify that our algorithm can achieve robust registration using only weak features, thereby demonstrating its robustness across different descriptors. Finally, we conduct ablation studies to validate the effectiveness of each module." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": "Evaluation Metric. Following [6, 47], we use registration recall (RR), rotation error (RE), and translation error (TE) to evaluate registration performance. For outdoor scenes, we consider a registration successful if the error is within " + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "inline_equation", + "content": "(5^{\\circ}, 60\\mathrm{cm})" + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": ", and for indoor scenes, within " + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "inline_equation", + "content": "(15^{\\circ}, 30\\mathrm{cm})" + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": ". Additionally, we assess the quality of correspondences using feature matching recall (FMR) and inlier precision (IP) which represents the proportion of inliers to the total correspondences. To further demonstrate our method's ability to generate a higher number of accurate correspondences, we define two new metrics: inlier number ratio (INR) and inlier" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1214" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 553, + 190 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 190 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 190 + ], + "type": "table", + "html": "
MethodFPFH (Traditional Descriptor)FCGF (Learning-based Descriptor)
RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)RR(↑)RE(↓)TE(↓)IP(↑)INR(↑)IN(↑)
PointDSC [3]76.962.256.7666.6470.16290.2392.612.106.4878.3785.881174.62
VBReg [22]78.012.287.3467.2370.93166.5692.772.246.8279.9286.30690.38
Hunter [40]84.701.806.4674.3979.27309.2894.051.866.5482.5588.011203.88
SM [25]55.882.948.1547.9670.69230.0386.572.297.0781.4438.36405.10
TEASER [38]75.482.487.3173.0178.60270.9885.772.738.6682.4387.901182.44
RANSAC-1M [14]64.204.0511.3563.9669.03264.0988.423.059.4277.9683.08672.22
SC2-PCR [6]83.242.216.7073.6478.78289.1793.162.116.4480.1787.241140.85
MAC [47]83.902.116.80---93.722.076.52---
FastMAC [48]82.872.156.73---92.672.006.47---
Regor (ours)88.481.705.9482.681253.742532.4093.961.756.1487.48263.812620.30
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RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
FPFH
PointDSC [3]27.914.2710.4523.8025.7646.52
VBReg [22]30.834.3810.9226.6129.7048.41
Hunter [40]36.903.8910.0531.5536.1756.01
RANSAC [14]19.834.6710.3230.8221.2037.02
SC2-PCR [6]35.934.2610.8630.1135.6555.23
MAC [47]40.883.669.45---
FastMAC [48]38.464.0410.47---
PCRegen (ours)43.962.898.9337.73778.35643.24
Predator
PointDSC [3]68.303.459.4456.3566.70863.40
VBReg [22]69.823.8710.0756.9067.09872.05
Hunter [40]71.103.589.7258.9069.06892.07
RANSAC [14]64.854.2811.0456.4466.81869.21
SC2-PCR [6]69.463.489.6358.0768.63883.59
MAC [47]70.913.699.81---
FastMAC [48]68.773.9010.32---
PCRegen (ours)72.043.179.4663.95220.462138.47
", + "image_path": "ae4c7659b95b16411042579a7a769b57ce1f298946dc55e6ad9dff0589b29249.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 505, + 288, + 516 + ], + "lines": [ + { + "bbox": [ + 63, + 505, + 288, + 516 + ], + "spans": [ + { + "bbox": [ + 63, + 505, + 288, + 516 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on the 3DLoMatch Dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "text", + "content": "numbers (IN). INR represents the ratio of the final number of inliers " + }, + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "inline_equation", + "content": "\\mathrm{IN}_{\\text {final }}" + }, + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "text", + "content": " to the initial number of inliers " + }, + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "inline_equation", + "content": "\\mathrm{IN}_{\\text {initial }}" + }, + { + "bbox": [ + 55, + 539, + 295, + 576 + ], + "type": "text", + "content": ", defined explicitly in Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 586, + 212, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 212, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 212, + 597 + ], + "type": "text", + "content": "4.1. Evaluation on Indoor Scenes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 604, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 295, + 676 + ], + "type": "text", + "content": "Experimental Setup. For indoor scenes, we utilize the 3DMatch dataset. Our method is validated on both 3DMatch [46] and 3DLoMatch benchmarks [20]. Following [3, 6], we perform voxel downsampling on the raw point clouds, and use two descriptors, FPFH [32] and FCGF [10], to extract features as inputs for each method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Result on 3DMatch. We compare our method against several baselines on the 3DMatch dataset, including PointDSC [3], VBReg [22], Hunter [40], SM [25]" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": "TEASER [38], RANSAC [14], " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "\\mathrm{SC^2}" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": "-PCR [6], MAC [47], and FastMAC [48]. The first three baselines are learning-based methods, while others are geometry-based approaches. The results are summarized in Table 1. Our method outperforms the previous state-of-the-art [6, 47]. Using the FPFH [9], our method outperforms all others across all metrics. Notably, our method achieves " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "88.48\\%" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": " RR, surpassing " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "\\mathrm{SC^2}" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": "-PCR [6] by 5.2 percentage points (pp). It also achieves more accurate registration with the lowest RE and TE. One significant advantage of our method is obtaining more high-quality correspondences, as reflected in the INR and IN. Our Regor achieves a " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "1253.74\\%" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": " INR, which is much better than " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "78.78\\%" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": " of SC2-PCR. Previous methods [6, 47, 48] only perform top-down filtering, which inevitably limits the INR to below " + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 230, + 555, + 495 + ], + "type": "text", + "content": ". In contrast, our Regor regenerates more high-quality correspondences, producing around 10 times the original amount. This advantage allows our method to achieve robust registration even when there are few initial correct correspondences. Moreover, despite employing multiple iterations, it still maintains a comparable speed to the baselines [22, 40] due to its simple sampling strategy and efficient consistency computation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 496, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 556, + 604 + ], + "type": "text", + "content": "Result on 3DLoMatch. Since Predator [20] is specifically designed for scenarios with low overlap, we use Predator [20] and FPFH [32] to extract features on 3DLoMatch. The comparative results are presented in Table 2. Our approach achieves the highest RR and RE on 3DLoMatch, regardless of the descriptors used. Due to the inherent weakness of FPFH, nearly all baselines perform poorly on 3DLoMatch. In contrast, our method shows significant performance improvement, surpassing MAC [47] by 3.08 pp." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "text", + "content": "Result on 3DMatch-EOR. The key to the effectiveness of our method lies in its ability to generate more accurate correspondences, particularly in scenarios with extremely high outlier ratios. To validate this, we select extreme outlier ratio cases from the 3DMatch/3DLoMatch datasets and propose the 3DMatch-EOR benchmark which is described in Appendix. We establish two benchmarks with outlier rates exceeding " + }, + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 313, + 605, + 556, + 714 + ], + "type": "text", + "content": ", respectively. Our method is compared to SC2-PCR [6] and PointDSC [3], with results" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1215" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 254, + 220 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 254, + 220 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 254, + 220 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 254, + 220 + ], + "type": "image", + "image_path": "78e51931f438f30dbfa78ec5a2b3c2270e542dd72b583d1469eae076888d831e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 92, + 221, + 124, + 231 + ], + "lines": [ + { + "bbox": [ + 92, + 221, + 124, + 231 + ], + "spans": [ + { + "bbox": [ + 92, + 221, + 124, + 231 + ], + "type": "text", + "content": "(a) Initial" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 186, + 220, + 227, + 231 + ], + "lines": [ + { + "bbox": [ + 186, + 220, + 227, + 231 + ], + "spans": [ + { + "bbox": [ + 186, + 220, + 227, + 231 + ], + "type": "text", + "content": "(b) 1st stage" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 196, + 243, + 414, + 255 + ], + "lines": [ + { + "bbox": [ + 196, + 243, + 414, + 255 + ], + "spans": [ + { + "bbox": [ + 196, + 243, + 414, + 255 + ], + "type": "text", + "content": "Figure 6. 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RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)RR(%)RE(°)TE(cm)FMR(%)IP(%)INR(%)IN(/)
Outlier ratio above 90%
3DMatch3DLoMatch
PointDSC [3]71.122.527.7977.7660.0563.55129.1223.274.8412.9439.7818.1626.5731.18
SC2-PCR [6]78.582.497.7384.0251.9173.73138.9835.394.2910.9642.5829.635.1449.73
PCRegen (ours)84.881.866.6786.3878.141457.542334.3643.502.959.2446.3436.96780.05632.62
Outlier ratio above 99%
3DMatch3DLoMatch
PointDSC [3]2.565.1215.2810.903.074.880.170.754.9329.340.750.081.460.02
SC2-PCR [6]9.154.9412.2116.206.089.610.343.285.9419.447.882.474.960.89
PCRegen (ours)26.762.178.6028.8721.541545.12666.949.273.3612.3911.846.30291.40118.45
", + "image_path": "bb061b9ca613d14448788a7bec0242829066601e5dcf1a29e58c6f0a4c0726dc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "text", + "content": "shown in Table 3. In cases with such high outlier rates, achieving robust registration is exceptionally challenging, as the number of initial correct correspondences is minimal. When the outlier rate exceeded " + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "text", + "content": ", the average inlier count of SC2-PCR is less than 1, leading to registration failure and achieving only " + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "inline_equation", + "content": "9.15\\% / 3.28\\%" + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "text", + "content": " in RR. In contrast, our method achieves an average of 667 inliers, an improvement of nearly 2000 times compared to SC2-PCR [6], resulting in a " + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "inline_equation", + "content": "26.76\\%" + }, + { + "bbox": [ + 54, + 421, + 296, + 553 + ], + "type": "text", + "content": " RR. Our Regor enables success in scenarios where failure would otherwise be inevitable, allowing for relatively robust registration even with few initial inliers." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 563, + 222, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 222, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 222, + 575 + ], + "type": "text", + "content": "4.2. Evaluation on Outdoor Scenes" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": "Experimental Setup. Following [7, 47], we validate our method's performance on the outdoor KITTI dataset. We select sequences 8 to 10 for testing. Consistent with the settings [6], we perform downsampling using a " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "30\\mathrm{cm}" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": " voxel grid and extract features using FPFH descriptors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Result on KITTI. We conduct comparative experiments between our method and PointDSC [3], VBReg [22], Hunter [40], RANSAC [14], " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{SC^2}" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "-PCR [6], MAC [47], and FastMAC [48] on the KITTI dataset. The results are presented in Table 4. Our Regor achieves the best performance with the highest RR, outperforming RANSAC [14] by 25.41" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 317, + 419, + 552, + 502 + ], + "blocks": [ + { + "bbox": [ + 162, + 389, + 447, + 400 + ], + "lines": [ + { + "bbox": [ + 162, + 389, + 447, + 400 + ], + "spans": [ + { + "bbox": [ + 162, + 389, + 447, + 400 + ], + "type": "text", + "content": "Table 3. Results on the 3DMatch-EOR benchmark with extreme outlier ratios." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 419, + 552, + 502 + ], + "lines": [ + { + "bbox": [ + 317, + 419, + 552, + 502 + ], + "spans": [ + { + "bbox": [ + 317, + 419, + 552, + 502 + ], + "type": "table", + "html": "
RR(%)RE(°)TE(cm)IP(%)INR(%)IN(/)
PointDSC [3]99.460.577.2291.3993.05247.11
VBReg [22]98.928.398.4190.8292.13246.09
Hunter [40]99.820.556.2992.1194.58247.50
RANSAC [14]74.411.5530.2085.2987.20189.70
SC2-PCR [6]99.820.618.1693.5995.94248.46
MAC [47]99.460.598.70---
FastMAC [48]98.020.558.24---
Regor (ours)99.820.505.3679.572486.825353.22
", + "image_path": "0d83016a8ac802ae103d7de39dc777ef709fa7d9346aded6098fcceb9bf7fd94.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 331, + 510, + 537, + 521 + ], + "lines": [ + { + "bbox": [ + 331, + 510, + 537, + 521 + ], + "spans": [ + { + "bbox": [ + 331, + 510, + 537, + 521 + ], + "type": "text", + "content": "Table 4. Quantitative comparison on the KITTI Dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 544, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 555, + 628 + ], + "type": "text", + "content": "pp. It also demonstrates lower RE and TE, achieving the most accurate registration. Furthermore, our method shows superior performance in generating new correspondences, with INR over 25 times higher than those of other baselines [6, 40]. Despite IP is lower compared to SOTA [6], our method achieves more accurate pose estimation due to a larger number of high-quality inliers." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 635, + 491, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 491, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 491, + 647 + ], + "type": "text", + "content": "4.3. Robustness to Different Features" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 654, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 714 + ], + "type": "text", + "content": "To further assess the robustness of various descriptors, we also test with traditional descriptors such as FPFH [32], SHOT [33], PFH [31], and PoRS [18], as well as learning-based descriptors like SpinNet [1], FCGF [9], Predator [20], and GeoTrans [30]. As shown in Table 5, our Regor con" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1216" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 294, + 172 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 294, + 172 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 294, + 172 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 294, + 172 + ], + "type": "image", + "image_path": "e1f2736c3bf2f772d13aaadbb717bfb5ff4999d39810c0e62066262a30c6485f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 106, + 180, + 244, + 192 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 244, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 244, + 192 + ], + "type": "text", + "content": "Figure 7. RR under different features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 204, + 293, + 377 + ], + "blocks": [ + { + "bbox": [ + 58, + 204, + 293, + 377 + ], + "lines": [ + { + "bbox": [ + 58, + 204, + 293, + 377 + ], + "spans": [ + { + "bbox": [ + 58, + 204, + 293, + 377 + ], + "type": "table", + "html": "
MethodRR(%)↑IP(%)↑IN(/)↑
FPFH [32]54.3445.74228.71
FPFH [32] + Regor88.48 (+34.14)82.68 (+36.94)1253.74 (×5.48)
PFH [31]69.3857.28286.38
PFH [31] + Regor89.28 (+19.90)81.72 (+24.44)2477.39 (×8.65)
RoPS [18]54.1642.49212.46
RoPS [18] + Regor91.37 (+37.21)84.29 (+41.80)2542.32 (×11.96)
SHOT [33]55.3346.01229.50
SHOT [33] + Regor71.90 (+16.57)66.41 (+20.40)1981.10 (×8.63)
FCGF [9]86.3256.85405.27
FCGF [9] + Regor93.96 (+7.64)87.48 (+30.63)2620.30 (×6.46)
SpinNet [1]88.6047.53444.84
SpinNet [1] + Regor96.30 (+7.70)88.24 (+40.71)2799.74 (×6.29)
Predator [20]89.0058.01444.38
Predator [20] + Regor91.44 (+2.44)86.84 (+28.83)4608.34 (×10.37)
GeoTrans [30]91.8075.20449.85
GeoTrans [30] + Regor97.10 (+5.30)91.01 (+15.81)2649.30 (×5.88)
", + "image_path": "176656bedbbf0a2e452bbe520a9358d3d7f74cd61c0cf71dacdaa9888978b1ee.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "content": "sistently improves performance across all features, which demonstrates it is robust to different features. Notably, GeoTrans [30] + Regor achieves a SOTA RR of " + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "inline_equation", + "content": "97.10\\%" + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "text", + "content": "Good Performance with Weak Features. Moreover, our method significantly enhance the performance of the weak descriptors, increasing the RR from " + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "inline_equation", + "content": "54.16\\%" + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "inline_equation", + "content": "91.37\\%" + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "text", + "content": " with RoPS [18]. As can be seen in Figure 7, with our Regor, the traditional descriptors [18, 31, 32] achieves " + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "inline_equation", + "content": "88\\% + \\mathrm{RR}" + }, + { + "bbox": [ + 55, + 457, + 295, + 577 + ], + "type": "text", + "content": ", surpassing the learning-based baseline [9]. When combined with our Regor, RoPS [18] exhibits performance that exceeds the learning-based methods [1, 9, 20], only second to GeoTrans [30]. This demonstrates that our method can achieve robust registration even with weak features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 586, + 149, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 149, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 149, + 600 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "content": "We conduct ablation experiments on the 3DMatch and 3DMatch-EOR benchmarks using FPFH descriptor." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Progressive or One-stage. We verify the effectiveness of our progressive strategy by only using the one-stage process. The results are shown in Table 6 (1) and (2). Our strategy improves RR by " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "1.65 / 2.82" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " pp compared to the one-stage approach. It is attributed to the heuristic setting: starting with a larger radius ensures global optimality and robustness, and gradually reducing the radius with each iter-" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 71, + 553, + 194 + ], + "blocks": [ + { + "bbox": [ + 86, + 386, + 264, + 396 + ], + "lines": [ + { + "bbox": [ + 86, + 386, + 264, + 396 + ], + "spans": [ + { + "bbox": [ + 86, + 386, + 264, + 396 + ], + "type": "text", + "content": "Table 5. Enhancement of feature-based methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 71, + 553, + 194 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 553, + 194 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 553, + 194 + ], + "type": "table", + "html": "
No.Methods3DMatch3DMatch-EOR
RRIPINRRIPIN
1)One-stage86.8176.34290.3223.9415.889.13
2)Progressive*88.4882.682532.4026.7621.54666.94
3)NNM87.3580.902487.2325.0619.82643.45
4)MM86.8181.032392.5323.9420.80600.09
5)GMM*88.4882.682532.4026.7621.54666.94
6)Only Local87.3578.402526.6323.0617.32668.08
7)Only Global76.3780.482502.2124.6516.57641.42
8)Local & Global*88.4882.682532.4026.7621.54666.94
9)SC86.8881.092491.5422.5418.18574.74
10)CTC*88.4882.682532.4026.7621.54666.94
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More importantly, IN drops by " + }, + { + "bbox": [ + 313, + 235, + 553, + 270 + ], + "type": "inline_equation", + "content": "1\\sim 2" + }, + { + "bbox": [ + 313, + 235, + 553, + 270 + ], + "type": "text", + "content": " orders of magnitude, suggesting that our progressive strategy is key to generating more correspondences." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 272, + 553, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 272, + 553, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 272, + 553, + 354 + ], + "type": "text", + "content": "Matching Strategy. We replace our GMM with mutual matching (MM) and nearest neighbor matching (NNM). Results are shown in Table 6 (3), (4) and (5). The model with GMM achieves the highest RR, IP, and IN. Compared with MM, using GMM results in a significant improvement in IN, which indicates our GMM is helpful to generate more inliers and addresses the issue of few initial inliers." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "text", + "content": "Local-Global Refinement. To demonstrate the importance of our correspondence refinement, we compare the complete model with two ablation models. The results, shown in Rows 6, 7, and 8 of Table 6, indicate a significant performance drop when either local or global refinement is removed, with RR falling to " + }, + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "inline_equation", + "content": "87\\%" + }, + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "inline_equation", + "content": "86\\%" + }, + { + "bbox": [ + 313, + 356, + 554, + 464 + ], + "type": "text", + "content": ". In addition, the IP of the ablation model decreases by over 4 pp, which underscores the substantial contribution of the local-global refinement to the quality of the correspondences." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 464, + 554, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 560 + ], + "type": "text", + "content": "Spatial Compatibility. We compared the SOTA second-order consistency (SC) [6, 7] with our CTC, and the results are shown at the bottom of Table 6. Our method with CTC obtains higher IP and IN, which indicates that CTC is more suitable for local refinement and achieves higher-quality correspondences. In addition, our CTC has less computational complexity than SC. Through it, we can implement an efficient iterative process." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "spans": [ + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "In this paper, we introduce a new idea for optimizing correspondences. Unlike previous methods that focus solely on outlier removal, our Regor effectively addresses the challenge of limited correct initial correspondences. By generating more high-quality correspondences, our method enables more robust and accurate registration, achieving state-of-the-art performance across all datasets. Notably, it demonstrates significant improvements even under extreme outlier conditions. When combined with our Regor, using traditional descriptors can also achieve robust registration." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1217" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. 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IEEE TGRS, 62:1-16, 2024. 2" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1219" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_content_list.json b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..767d5e9cfa94e5254492a6c5a4a22d1f9f8e4905 --- /dev/null +++ b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_content_list.json @@ -0,0 +1,1297 @@ +[ + { + "type": "text", + "text": "Progressive Focused Transformer for Single Image Super-Resolution", + "text_level": 1, + "bbox": [ + 153, + 130, + 844, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei Long $^{1}$ , Xingyu Zhou $^{1}$ , Leheng Zhang $^{1}$ , Shuhang Gu $^{1*}$ $^{1}$ University of Electronic Science and Technology of China", + "bbox": [ + 264, + 179, + 733, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "weilong@std.uestc.edu.cn, shuhanggu@gmail.com", + "bbox": [ + 297, + 219, + 699, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/LabShuHangGU/PFT-SR", + "bbox": [ + 323, + 237, + 663, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformer-based methods have achieved remarkable results in image super-resolution tasks because they can capture non-local dependencies in low-quality input images. However, this feature-intensive modeling approach is computationally expensive because it calculates the similarities between numerous features that are irrelevant to the query features when obtaining attention weights. These unnecessary similarity calculations not only degrade the reconstruction performance but also introduce significant computational overhead. How to accurately identify the features that are important to the current query features and avoid similarity calculations between irrelevant features remains an urgent problem. To address this issue, we propose a novel and effective Progressive Focused Transformer (PFT) that links all isolated attention maps in the network through Progressive Focused Attention (PFA) to focus attention on the most important tokens. PFA not only enables the network to capture more critical similar features, but also significantly reduces the computational cost of the overall network by filtering out irrelevant features before calculating similarities. Extensive experiments demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance on various single image superresolution benchmarks.", + "bbox": [ + 86, + 318, + 483, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 712, + 220, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image Super-Resolution (SR) aims to reconstruct high-resolution details and textures from Low-Resolution (LR) images. Effective SR techniques not only enhance visual quality but also enable more meaningful information extraction from high-resolution outputs. It has critical applications in fields such as medical imaging, satellite remote sensing, and video surveillance.", + "bbox": [ + 89, + 737, + 482, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several classical Convolutional Neural Networks (CNNs) [10, 11, 15, 23] designed for SR have achieved", + "bbox": [ + 89, + 844, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/36bb171c828feb9e4a8afd5a8e36ded71d1a3dad601c8af9ec6fb1a55be78341.jpg", + "image_caption": [ + "(a) Self-Attention" + ], + "image_footnote": [], + "bbox": [ + 519, + 287, + 705, + 385 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1be1190e67514fdd1c155d4d4e4ba527619724909decb741136239f3fe66762b.jpg", + "image_caption": [ + "(b) Sparse Attention" + ], + "image_footnote": [], + "bbox": [ + 714, + 287, + 897, + 385 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be95d238a86e6dc13ee1fd1cab6d4ca0d5beee74c0cb09377569463cf2170fe4.jpg", + "image_caption": [ + "(c) Progressive Focused Attention (ours)", + "Figure 1. Comparison of different attention mechanisms. (a) Vanilla self-attention calculates attention weights in the whole window and generates non-zero weights for both highly relevant and less relevant tokens. (b) Sparse Attention is able to filter out the impact of less relevant tokens with small weights, but still requires the calculation of attention weights for all tokens. (c) Progressive Focused Attention connects isolated attention maps, leveraging attention weights to skip unnecessary computations and better aggregate relevant tokens." + ], + "image_footnote": [ + "★Query patch Attention calculation region Attention weight" + ], + "bbox": [ + 521, + 414, + 898, + 511 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "promising reconstruction results. Due to the limitations of convolution operations, these methods can capture only local feature information. Many studies have focused on enabling networks to achieve broader feature interaction to improve image restoration. Recently, Transformer-based methods [6, 22, 42, 46] have been increasingly applied to image reconstruction, owing to their ability to effectively leverage long-range dependencies, thereby enhancing the recovery of detailed information in images.", + "bbox": [ + 511, + 714, + 906, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformer-based super-resolution methods utilize cascaded self-attention blocks to recover the missing High-Resolution (HR) details. At the core of the self-attention", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author", + "bbox": [ + 109, + 886, + 233, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2279", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "block is the attention map, which determines how the input features are aggregated to generate output features. Due to the quadratic computational complexity of the self-attention mechanism, most of the existing methods confine attention computation within local windows and only aggregate a limited number of tokens to update image features. Therefore, how to exploit information of relevant tokens while alleviating the disruption from irrelevant tokens is critical in Transformer-based SR models. For the pursuit of high-quality SR results, one category of research tries to enrich the information source by enlarging the window size [6, 46], leveraging cross-window information [7], and introducing an external token dictionary [41]. Since more information can be incorporated into the weighted feature updating process, these methods have shown promising capability in delivering superior SR results. However, calculating similarities between more tokens inevitably leads to extra computational footprint. These methods still need to compromise on model overhead and introduce limited extra information. Another category of studies investigates sophisticated weighting strategies to make better use of input information [5, 28]. Instead of combining all the tokens according to the normalized productive similarities, as in a vanilla self-attention block, various elaborately designed weighting mechanisms have been exploited to make better use of highly relevant tokens while at the same time filtering out less relevant tokens. While the overall concept of seeking more rational weights is highly appealing, the challenge of obtaining enhanced attention weights remains an open problem in the literature.", + "bbox": [ + 93, + 90, + 480, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we link the attention maps between adjacent layers and propose a Progressive Focused Attention (PFA) block to better leverage input tokens across a wider range. Instead of combining input features merely according to the calculated attention map $\\mathbf{A}_{cal}^{l}$ , we inherit attention information from the previous block in a productive manner $\\mathbf{A}^{l} = \\text{Norm}(\\mathbf{A}^{l-1} \\odot \\mathbf{A}_{cal}^{l})$ , where $\\text{Norm}(\\cdot)$ is the row-wise normalization operation. Such an attention inheritance mechanism enables our method to make a comprehensive measurement of token similarity: tokens that are consistently similar to each other are empowered with larger weights to help each other while the weights of irrelevant tokens are suppressed during the cascaded multiplications. Furthermore, in addition to boosting weights for important tokens and suppressing weights for less relevant tokens, another advantage of our PFA lies in its calculation pre-filtering capability. Specifically, since the final attention map $\\mathbf{A}^{l}$ will be multiplied by the previous attention map $\\mathbf{A}^{l-1}$ , small weights in $\\mathbf{A}^{l-1}$ are a sign of unimportant tokens, for which the weight calculation process can be skipped. As shown in Fig.1, the previous attention map not only helps our PFA block to generate better weights which emphasize highly relevant tokens, but also enables", + "bbox": [ + 93, + 554, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "it to skip unnecessary similarity calculations so that we are able to afford the computational overhead of large window. Therefore, with comparable computational resources, our SR model could employ a larger window size to leverage input tokens from a broader range.", + "bbox": [ + 517, + 92, + 903, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper are as follows:", + "bbox": [ + 535, + 167, + 872, + 181 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the idea of Progressive Focused Attention (PFA) which inherits attention weights from previous layers in a productive manner. PFA not only avoids unnecessary similarity computation with less relevant tokens but also endows highly relevant tokens with larger weights to better enhance the input feature.", + "- We instantiate a Progressive Focused Transformer (PFT) for image super-resolution, which takes the progressive focusing benefits of PFA and systematically arranges computational resources for different layers. This property enables the PFT to leverage the merit of large window while maintaining model efficiency.", + "- We conduct extensive experiments on super-resolution benchmarks. Our superior experimental results over recent state-of-the-art methods as well as our detailed ablation studies demonstrate the effectiveness of our method." + ], + "bbox": [ + 516, + 184, + 903, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 517, + 438, + 653, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformer-based SR. Transformer models were initially used for natural language processing [9, 33]. Subsequently, they have attracted extensive research interest in the field of computer vision [3, 13, 14, 24, 36]. Due to its excellent feature extraction capabilities, Transformers have also been introduced to low-level visual tasks, including single image super-resolution [21, 37, 43]. Classical SR models [18, 19, 30, 40] based on CNN architectures were limited by narrow receptive fields and limited feature interaction capabilities, and their effectiveness was gradually surpassed by Transformer-based approaches. For example, IPT [4] implements a pre-trained Transformer-based model for better super-resolution. SwinIR [22] improves image quality by using shifted window attention and residual blocks, effectively capturing a broad range of features for restoration. Subsequently, CAT [7] improves image restoration by using rectangle-window self-attention and axial shifting to enhance cross-window interaction. To address the perceptual limitations of window-based methods, several approaches have been proposed. HAT [6] combines channel and window-based attention to overcome these limitations and enhance cross-window interactions for superior image reconstruction. Another approach is ATD [41], which addresses the limitations of local windows by using an Adaptive-Token Dictionary and category-based self-attention to incorporate global information and enhance features. In addition, IPG [31] improves SR by prioritizing detail-rich pixels and using flexible local and global graphs to enhance reconstruction. Unlike existing methods, we", + "bbox": [ + 514, + 463, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2280", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "propose a PFT method that can better focus on key tokens and filter out irrelevant features through PFA, thereby reducing the impact of irrelevant features on SR results and the computational effort.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer with Sparse Attention. The dense attention maps in Transformers may introduce features from irrelevant locations, which interferes with the effectiveness of feature extraction. To address this, many approaches explore how to leverage sparse attention calculations to better utilize relevant information. For example, NLSA [28] combines non-local operations with sparse representations, using dynamic sparse attention to focus on pertinent features, thereby improving efficiency and robustness while reducing computational costs. ART [39] enhances image restoration by combining both dense and sparse attention mechanisms, expanding the receptive field to enable more effective interactions and better feature representation. Additionally, a class of methods [35, 45] explicitly selects the most relevant positions in the attention map for retention, filtering out irrelevant information that might interfere with feature aggregation. Building on this, DRSformer [5] further develops the idea of sparse selection by introducing a learnable top- $k$ -selection operator, that adaptively retains the most relevant self-attention values, thus improving image restoration. We propose the PFT method, which connects isolated attention maps across the entire network to efficiently identify the positions each attention map collectively focuses on. PFA performs a Hadamard product on adjacent attention maps to pinpoint the most relevant attention locations, thereby enhancing the filtering of irrelevant information.", + "bbox": [ + 91, + 154, + 483, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Progressive Focused Transformer", + "text_level": 1, + "bbox": [ + 89, + 561, + 395, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 587, + 230, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Attention. The self-attention mechanism [33] is a fundamental part of Transformer, which computes the similarity between tokens and aggregates features based on the corresponding attention weights.", + "bbox": [ + 89, + 609, + 482, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the query matrix $\\mathbf{Q} \\in \\mathbb{R}^{N \\times d}$ , key matrix $\\mathbf{K} \\in \\mathbb{R}^{N \\times d}$ , the attention weights are calculated as follows:", + "bbox": [ + 89, + 669, + 482, + 700 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {s a} = \\operatorname {S o f t m a x} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 712, + 482, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the $i$ -th row in $\\mathbf{A}_{sa}$ represents normalized weights to aggregate value tokens $\\mathbf{V} \\in \\mathbb{R}^{N \\times d}$ and the output of self-attention module is obtained by $\\mathbf{O}_{SA} = \\mathbf{A}_{sa}\\mathbf{K}$ . Although the exponential function in Softmax could suppress irrelevant tokens to some extent, the above vanilla self-attention still apply dense weights which utilize all the input tokens in the window to generate the final output. Moreover, another feature of the above self-attention lies in its computational overhead. The complexity of Eq. (1) grows quadratically with the number of tokens $N$ . Therefore, most existing", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods need to perform self-attention calculations in small windows to manage this computational burden.", + "bbox": [ + 511, + 90, + 906, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sparse Attention. To mitigate the negative impact of irrelevant features in the dense attention map, numerous sparse attention methods have been proposed. Generally speaking, the overall idea of sparse attention is to introduce a selection operation to sparsify the attention weights:", + "bbox": [ + 511, + 128, + 906, + 204 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {s s a} = \\operatorname {S o f t m a x} \\left(\\mathcal {S} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 209, + 906, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S(\\cdot)$ is a sparsification operation which removes the weights for less relevant tokens. The most commonly adopted sparsify operation is the top- $k$ selection, which only allows $K$ non-zero values in each row. Despite its strong capability of irrelevant token suppression, top- $k$ selection only adjusts aggregation weights according to a single step of similarity calculation and has limited ability to make effective use of highly relevant tokens.", + "bbox": [ + 511, + 241, + 906, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Progressive Focused Attention", + "text_level": 1, + "bbox": [ + 511, + 376, + 782, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As reviewed in the previous section, although sparse attention methods are able to improve the vanilla self-attention by alleviating the negative impact of irrelevant tokens, they still have limited capability in further distinguishing highly relevant tokens from mildly relevant tokens. Moreover, both the vanilla and sparse attention methods fail to identify the relevant feature regions prior to similarity calculation, resulting in a significant amount of unnecessary calculations, which impedes the incorporation of additional input tokens.", + "bbox": [ + 511, + 398, + 905, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we propose Progressive Focused Attention, which links the attention maps between adjacent layers to better aggregate relevant features. Generally, the proposed PFA advances the existing methods in two aspects. Firstly, PFA makes use of attention maps from previous layers to better weight input features. The weights of highly relevant tokens that are consistently similar to each other across layers will be enhanced during the cascade multiplication process. Secondly, PFA leverages the attention map of previous layers to identify irrelevant features for saving computational overhead. This selective calculation mechanism enables us to conduct self-attention within a larger window. In the remaining part of this section, we first introduce the basic idea of our PFA, which inherits the attention map from the previous layers through a Hadamard product. Then, we introduce how we could further leverage previous attention maps to reduce computational overhead.", + "bbox": [ + 511, + 535, + 906, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Progressive Attention Across Layers. As introduced in Eq. (1) and (2), the previous methods obtain attention weights merely according to the calculated similarities between tokens from the current layer. The standard similarity calculation has limited discriminative capability in boosting highly relevant tokens while suppressing less relevant tokens. To address this issue, we propose to inherit attention", + "bbox": [ + 511, + 795, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2281", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/89f3984760226f1a873b496ba83a32f8c367515bebc76c2e808fb4747ee198da.jpg", + "image_caption": [ + "Figure 2. The overall architecture of PFT. PFA Block consists of $M$ Progressive Focused Attention Layers (PFAL). Each PFA takes both image features and aggregated PFA maps from previous layers as input. Sparse Matrix Multiplication (SMM) ensures each row of $Q$ interacts only with sparse columns of $K^T$ , producing calculated attention maps. After applying the Hadamard product and sparse focusing, PFA maps of the current layer are obtained and used with the $V$ matrix in an SMM operation to generate attention-aggregated features." + ], + "image_footnote": [], + "bbox": [ + 117, + 98, + 867, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "weights from previous layers in a productive manner:", + "bbox": [ + 89, + 460, + 444, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} ^ {l} = \\operatorname {N o r m} \\left(\\mathbf {A} ^ {l - 1} \\odot \\mathbf {A} _ {\\text {c a l}} ^ {l}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 487, + 482, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{A}_{cal}^{l}$ is the calculated attention map for the $l$ -th layer according to the vanilla self-attention mechanism as in Eq. (1); $\\mathbf{A}^{l - 1}$ is the attention map of the previous layer; Norm(\\cdot) represents the row-wise normalization operation, which ensures the summation of each row to be 1. As indicated in Eq. (3), the final attention map in the $l$ -th layer is obtained by multiplying the calculated similarities with the attention map from the previous layer. Such a mechanism enables us to make a comprehensive assessment of token similarity: the weights for less relevant tokens will be wiped out during the successive multiplication process, while important tokens with high similarity values across layers will be assigned with larger weights after normalization. As will be validated in our ablation studies, with improved feature aggregation weights, such a Progressive Attention mechanism could deliver better SR results over the top- $k$ sparse attention as well as the standard self-attention block.", + "bbox": [ + 88, + 521, + 482, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Progressive Focused Attention. Since all the normalized similarities are less than 1, the above strategy of multiplicative attention inheritance could gradually filter out the impact of irrelevant tokens and obtain sparse weights as the network depth increases. Actually, based on the previous attention map $\\mathbf{A}^{l - 1}$ , we are able to identify unimportant positions before calculation. Therefore, we can avoid unnecessary computations with a Sparse Matrix Multiplica", + "bbox": [ + 88, + 779, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion (SMM) operation:", + "bbox": [ + 511, + 460, + 666, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {s c} ^ {l} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {\\Psi} \\left(\\mathbf {Q} ^ {l}, \\left(\\mathbf {K} ^ {l}\\right) ^ {\\top}, \\mathbf {I} ^ {l - 1}\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 484, + 906, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Psi$ denotes the SMM operation; $\\mathbf{I}^{l - 1}\\in \\mathbb{R}^{N\\times N}$ is a sparse index matrix; we calculate $\\mathbf{A}_{sc}^l (i,j)$ with $\\mathbf{Q}^l (i,:)$ and $\\mathbf{K}^l (j,:)^T$ only if $\\mathbf{I}^{l - 1}(i,j) = 1$ , otherwise we set $\\mathbf{A}_{sc}^l (i,j) = 0$ . Note that after the SMM operation we still need to normalize each row of the calculation results using the Softmax function. For an all-ones indexing matrix, the SMM operation in Eq. (4) is equivalent to the standard attention calculation process as in Eq. (1); However, if we are able to obtain a sparse $\\mathbf{I}^{l - 1}$ prior to the calculation process, a significant portion of computations can be skipped. Due to our progressive attention mechanism, we utilize $\\mathbf{A}^{l - 1}$ to indicate skippable positions. Specifically, inspired by the success of top- $k$ sparse attention, we only keep $K^l$ non-zero attention weights for each layer and generate the indexing matrix $\\mathbf{I}^l$ according to the non-zero positions in $\\mathbf{A}^l$ . To sum up, the attention map of our progressive focused attention is achieved through the following formula:", + "bbox": [ + 511, + 515, + 906, + 776 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\mathbf {A} _ {s c} ^ {l} = S o f t m a x (\\boldsymbol {\\Psi} (\\mathbf {Q} ^ {l}, (\\mathbf {K} ^ {l}) ^ {\\top}, \\mathbf {I} ^ {l - 1})), \\\\ \\mathbf {A} ^ {l} = \\mathcal {S} _ {K ^ {l}} (N o r m (\\mathbf {A} _ {s c} ^ {l} \\odot \\mathbf {A} ^ {l - 1})), \\\\ \\mathbf {I} ^ {l} = \\operatorname {S i g n} (\\mathbf {A} ^ {l}), \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 787, + 906, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $S_{K^l}(\\cdot)$ is the sparsification operation that selects the top $K^l$ values in each row and $\\mathrm{Sign}(\\cdot)$ generates a binary index matrix according to the sign of input matrix. Then,", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2282", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we can also use the SMM operation to calculate the output matrix of the $l$ -th layer:", + "bbox": [ + 89, + 90, + 485, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {O} ^ {l} = \\Psi (\\mathbf {A} ^ {l}, \\mathbf {V} ^ {l}, \\mathbf {I} ^ {l}). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 130, + 482, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the first attention block, in which we do not have previous attention map, we simply set $\\mathbf{A}^0$ and $\\mathbf{I}^0$ as allones matrix and calculate $\\mathbf{A}^1$ as standard self-attention in Eq. (1) to aggregate input features. For subsequent layers, we exploit the attention map from previous layer to generate better weights and filter out unnecessary computations as in Eq. (5). Since tokens which have been determined as irrelevant tokens to a specific query token in previous layers will not be considered in the following layers at all, to avoid filtering-out important tokens at early stages, we set $K^1 = N$ and gradually reduce the nonzero values with a focus ratio: $K^l = \\alpha K^{l - 1}$ , where $K$ represents the number of retained attention values within the window. With $0 < \\alpha < 1$ , our cascade PFA layers gradually focus on important candidates and reduce the number of key-tokens to be considered for each input query-token, resulting in significant reduction in computational burden for each window. Notably, using standard matrix multiplication to implement the SMM operation is highly inefficient. Therefore, we developed efficient CUDA kernels for SMM. This implementation significantly enhances the efficiency of our model, enabling PFT to achieve inference speeds comparable to those of existing methods.", + "bbox": [ + 89, + 159, + 483, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. The Overall Network Architecture", + "text_level": 1, + "bbox": [ + 89, + 516, + 393, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, the overall architecture of PFT follows the structure adopted in recent state-of-the-art Transformer-based SR models [6, 22, 41]. While, we replace the standard self-attention blocks with our proposed PFA block for the pursuit of better SR results. Notably, we also incorporate the shifted window approach from the Swin Transformer, though it is omitted in the illustration for simplicity. Thus, the attention map in PFA is passed from the first layer to the last through two pathways, divided by the shift operation into even and odd layers for focused processing. Additionally, we incorporate LePE positional encoding [12] during attention computation. For classical SR, the PFT network consists of 6 blocks, with the number of attention layers in each block being [4, 4, 4, 6, 6, 6]. The model utilizes multi-head attention with 6 attention heads, and the total number of channels is 240. The window size is $32 \\times 32$ , and the number of retained attention values in each block is [1024, 256, 128, 64, 32, 16], respectively. For lightweight SR, the PFT-light network is composed of five blocks, with the number of attention layers in each block being [2, 4, 6, 6, 6]. It employs 4 attention heads, with a total of 52 channels. The window size is $32 \\times 32$ , and the number of retained attention values in each block follows the pattern [1024, 256, 128, 64, 32].", + "bbox": [ + 89, + 537, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Analysis of Computational Complexity. Self-Attention and sparse attention have the same computational cost, as both measure similarity with neighboring positions by interacting with tokens within non-overlapping windows. When the input feature map size is $h \\times w \\times C$ and the window size is $W \\times W$ , the feature map is divided into $\\frac{h}{W} \\times \\frac{w}{W}$ windows, each with $W \\times W$ tokens. Assuming that the network has a total of $L$ attention layers, the computational complexity of the attention component for the entire network is:", + "bbox": [ + 511, + 90, + 906, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Omega (S A) = 4 h w L C ^ {2} + 2 W ^ {2} h w L C. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 233, + 906, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PFA can control the proportion of key tokens that are most relevant to the query features by adjusting the retention ratio $\\alpha$ . The index matrix $\\mathbf{I}$ allows shallow attention aggregation information to be carried into deeper layers for further focusing, resulting in a gradually decreasing $K$ . For a network with $L$ attention layers, we assume that the number of retained attention values within the window decreases, as expressed by the following formula: $K^{l} = \\alpha K^{l - 1}$ , where $0 < \\alpha < 1$ and $K^{-1}$ is generally set to $W^2$ . It can be represented as $K^{l} = W^{2}\\alpha^{l - 1}$ . The overall computational complexity of the model is:", + "bbox": [ + 511, + 258, + 908, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Omega (P F A) = \\sum_ {l = 1} ^ {L} \\left(4 h w C ^ {2} + 2 \\alpha^ {(l - 1)} W ^ {2} h w C\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 441, + 906, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha^{(l-1)}$ controls the decay of the focus ratio across layers, with $0 < \\alpha < 1$ . As $l$ increases, the focus ratio progressively decreases. The first term, $4hwC^2$ , represents the computational complexity of the projection layers. The second term, $2\\alpha^{(l-1)}W^2hwC$ , accounts for the complexity of computing the similarity between the query and the selected key tokens, as well as redistributing the corresponding value information at the focused positions. Obviously, since $\\alpha$ is less than 1, the complexity of this term decreases exponentially with depth. For example, with $\\alpha = 0.5$ , the computational complexity is reduced to just $6.25\\%$ of the original after four decay steps.", + "bbox": [ + 511, + 491, + 908, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 686, + 648, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setting", + "text_level": 1, + "bbox": [ + 511, + 712, + 700, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the DF2K dataset, which combines DIV2K [32] and Flickr2K [23], as our training set. To ensure fair comparisons, we adopt the same training configuration as utilized in recent SR studies [6, 31, 41]. Our model is trained for 500K iterations using the AdamW optimizer and an initial learning rate of $2 \\times 10^{-4}$ . The input patch size for training is fixed at $64 \\times 64$ , and we employ a MultistepLR scheduler, which reduces the learning rate by half at specified iterations [250000, 400000, 450000, 475000]. The batch size is set to 32. We evaluate our method on five standard benchmark datasets: Set5 [2], Set14 [38], BSD100 [26],", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2283", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a004fc6841d016abb23d427db65ad3bba33de8256dac09259f9695001aca7805.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
EDSR [23]×242.6M22.14T38.110.960233.920.919532.320.901332.930.935139.100.9773
RCAN [44]×215.4M7.02T38.270.961434.120.921632.410.902733.340.938439.440.9786
HAN [29]×263.6M7.24T38.270.961434.160.921732.410.902733.350.938539.460.9785
IPT [4]×2115M7.38T38.37-34.43-32.48-33.76---
SwinIR [22]×211.8M3.04T38.420.962334.460.925032.530.904133.810.943339.920.9797
CAT-A [7]×216.5M5.08T38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [39]×216.4M7.04T38.560.962934.590.926732.580.904834.300.945240.240.9808
HAT [6]×220.6M5.81T38.630.963034.860.927432.620.905334.450.946640.260.9809
IPG [31]×218.1M5.35T38.610.963234.730.927032.600.905234.480.946440.240.9810
ATD [41]×220.1M6.07T38.610.962934.950.927632.650.905634.700.947640.370.9810
PFT (Ours)×219.6M5.03T38.680.963535.000.928032.670.905834.900.949040.490.9815
EDSR [23]×343.0M9.82T34.650.928030.520.846229.250.809328.800.865334.170.9476
RCAN [44]×315.6M3.12T34.740.929930.650.848229.320.811129.090.870234.440.9499
HAN [29]×364.2M3.21T34.750.929930.670.848329.320.811029.100.870534.480.9500
IPT [4]×3116M3.28T34.81-30.85-29.38-29.49---
SwinIR [22]×311.9M1.35T34.970.931830.930.853429.460.814529.750.882635.120.9537
CAT-A [7]×316.6M2.26T35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [39]×316.6M3.12T35.070.932531.020.854129.510.815930.100.887135.390.9548
HAT [6]×320.8M2.58T35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG [31]×318.3M2.39T35.100.933231.100.855429.530.816830.360.890135.530.9554
ATD [41]×320.3M2.69T35.110.933031.130.855629.570.817630.460.891735.630.9558
PFT (Ours)×319.8M2.23T35.150.933331.160.856129.580.817830.560.893135.670.9560
EDSR [23]×443.0M5.54T32.460.896828.800.787627.710.742026.640.803331.020.9148
RCAN [44]×415.6M1.76T32.630.900228.870.788927.770.743626.820.808731.220.9173
HAN [29]×464.2M1.81T32.640.900228.900.789027.800.744226.850.809431.420.9177
IPT [4]×4116M1.85T32.64-29.01-27.82-27.26---
SwinIR [22]×411.9M0.76T32.920.904429.090.795027.920.748927.450.825432.030.9260
CAT-A [7]×416.6M1.27T33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [39]×416.6M1.76T33.040.905129.160.795827.970.751027.770.832132.310.9283
HAT [6]×420.8M1.45T33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG [31]×417.0M1.30T33.150.906229.240.797327.990.751928.130.839232.530.9300
ATD [41]×420.3M1.52T33.100.905829.240.797428.010.752628.170.840432.620.9306
PFT (Ours)×419.8M1.26T33.150.906529.290.797828.020.752728.200.841232.630.9306
", + "bbox": [ + 114, + 80, + 883, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on classical SR task. The best and second best results are colored with red and blue.", + "bbox": [ + 89, + 455, + 906, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Urban100 [16], and Manga109 [27]. In addition, the computational costs of all models in this paper are measured at an output resolution of $1280 \\times 640$ .", + "bbox": [ + 89, + 497, + 483, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 89, + 558, + 459, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the performance of our model with various SR baselines on widely used benchmark datasets, including Set5 [2], Set14 [38], BSD100 [26], Urban100 [16], and Manga109 [27]. These SR methods include both classical and state-of-the-art approaches, such as EDSR [23], RCAN [44], HAN [29], IPT [4], SwinIR [8], CAT [7], ART [39], HAT [6], IPG [31], and ATD [41]. We use PSNR and SSIM metrics to assess the performance of SR models at $\\times 2$ , $\\times 3$ , and $\\times 4$ upscaling factors. All computational costs are calculated at the output resolution of $1280\\times 640$ , and PFT uses a window size of $32\\times 32$ .", + "bbox": [ + 88, + 580, + 482, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results, shown in Tab. 1, indicate that the proposed PFT model achieves superior performance over ATD, with significantly reduced computational costs. Notably, PFT reduces computational load by $17.1\\%$ compared to ATD, while attaining the highest PSNR in most datasets. For lightweight SR tasks, we further compare our model with other efficient SR methods, including CARN [1], IMDN [17], LAPAR [20], LatticeNet [25], SwinIR [8], SwinIR-NG [8], ELAN [42], and OmniSR [34]. As shown in Tab. 2, the proposed PFT-light outperforms the", + "bbox": [ + 89, + 750, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "recently introduced ATD-light [41] on nearly all benchmark datasets, while reducing computational complexity by $20.1\\%$ . On the $\\times 2$ Urban100 benchmark, PFT-light outperforms ATD-light by 0.40dB and IPG-Tiny by 0.63dB. For the $\\times 4$ SR experiments, PFT-light also outperforms IPG Tiny by 0.42dB and ATD-light by 0.23dB on the Urban100 test set. The superior performance of PFT can be attributed to its use of Progressive Focused Attention, which connects otherwise isolated attention maps across the network. This enables the model to focus on essential features, filter out irrelevant patches, substantially reduce computational costs, and support the use of larger window sizes.", + "bbox": [ + 511, + 497, + 906, + 679 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0ad7c72860c53ecd930625860b0371c1de4310305ccbb9a39d26f2d098faa37c.jpg", + "image_caption": [ + "Figure 3. Visual comparison of attention distributions in the 18th layer. SA and top- $k$ Attention distribute attention broadly, failing to focus on the most relevant areas. In contrast, PFA filters out irrelevant tokens and concentrates attention on key regions. By reducing computational costs, it enables the use of a larger $32 \\times 32$ window for more extensive feature interactions." + ], + "image_footnote": [], + "bbox": [ + 517, + 683, + 901, + 816 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2284", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/08111f7aa3313af65db2476a14a511a0997f90daf9ca3f5bf17977768ea36e5c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
CARN [1]×21,592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [17]×2694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [20]×2548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [25]×2756K169.5G38.150.961033.780.919332.250.900532.430.9302--
SwinIR-light [22]×2910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [42]×2582K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [8]×21181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
OmniSR [34]×2772K194.5G38.220.961333.980.921032.360.902033.050.936339.280.9784
IPG-Tiny [31]×2872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
ATD-light [41]×2753K348.6G38.280.961634.110.921732.390.902333.270.937639.510.9789
PFT-light (Ours)×2776K278.3G38.360.962034.190.923232.430.903033.670.941139.550.9792
CARN [1]×31,592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [17]×3703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [20]×3544K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [25]×3765K76.3G34.530.928130.390.842429.150.805928.330.8538--
SwinIR-light [22]×3918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [42]×3590K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [8]×31190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
OmniSR [34]×3780K88.4G34.700.929430.570.846929.280.809428.840.865634.220.9487
IPG-Tiny [31]×2878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
ATD-light [41]×3760K154.7G34.700.930030.680.848529.320.810929.160.871034.600.9505
PFT-light (ours)×3783K123.5G34.810.930530.750.849329.330.811629.430.875934.600.9510
CARN [1]×41,592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [17]×4715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [20]×4659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [25]×4777K43.6G32.300.896228.680.783027.620.736726.250.7873--
SwinIR-light [22]×4930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [42]×4582K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [8]×41201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
OmniSR [34]×4792K50.9G32.490.898828.780.785927.710.741526.650.801831.020.9151
IPG-Tiny [31]×4887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
ATD-light [41]×4769K87.1G32.620.899728.870.788427.770.743926.970.810731.470.9198
PFT-light (Ours)×4792K69.6G32.630.900528.920.789127.790.744527.200.817131.510.9204
", + "bbox": [ + 106, + 80, + 893, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual comparison of attention distribution. The attention distribution visualizations are shown in Fig. 3. The attention distributions of the Vanilla Self-Attention and top-k Attention methods are relatively scattered, failing to allocate attention to the regions most relevant to the current query. In contrast, our PFA method filters out irrelevant tokens and focuses on most important positions. It also lowers computation costs, enabling larger $32 \\times 32$ windows for broader feature interactions.", + "bbox": [ + 88, + 493, + 480, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual comparison of SR reconstruction results. To evaluate the quality of different super-resolution methods, we show visual examples in Fig. 4. These comparisons demonstrate the strength of our PFT approach in restoring sharp edges and fine textures from low-resolution images. For example, in img_001 and img_095, most methods struggle to reconstruct textures accurately, leading to noticeable distortions. Similarly, in the zebra and barbara images, many methods fail to recover details, resulting in blurry or incorrect textures. In contrast, our PFT effectively captures fine textures by focusing on the most relevant features. This ability to selectively attend helps restore clean edges and reduce artifacts, producing more accurate reconstructions.", + "bbox": [ + 88, + 628, + 482, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 833, + 243, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies on the proposed PFT-light model, with all models trained for 250k iterations on the DIV2K dataset at $\\times 4$ scale. Except for the experiments on", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "window size, all other experiments use a window size of $16 \\times 16$ . In top- $k$ Attention, the value of $k$ is set to half the number of window elements, which is 128.", + "bbox": [ + 511, + 493, + 906, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Progressive Focused Attention. We conducted experiments to demonstrate the effectiveness of the proposed Progressive Attention and Progressive Focused Attention, with results presented in Tab. 3. These experiments compare the quantitative performance of $\\times 4$ super-resolution on the Set5, Urban100, and Manga109 datasets. Progressive Attention applies a straightforward Hadamard product connection of the attention maps. As shown, even the Progressive Attention provides notable performance improvements over Self-Attention and top- $k$ Attention. Progressive Focused Attention achieved the best results with a $27.69\\%$ reduction in computation, and notably increasing PSNR by 0.36dB on the Urban100 dataset. The effectiveness of PFA lies in its ability to link adjacent attention maps across the network via the Hadamard product, allowing the model to reduce redundant computations and focus on the most relevant tokens.", + "bbox": [ + 511, + 542, + 908, + 800 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0c7277d048727fa824dc1ea45d0ddb15b3324ec19ad6fe67de01d0707063652f.jpg", + "table_caption": [ + "Table 2. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on lightweight SR task. The best and second best results are colored with red and blue." + ], + "table_footnote": [], + "table_body": "
MethodFLOPsSet5Urban100Manga109
Vanilla Self-Attention70.4G32.2826.2630.62
Top-k Attention70.4G32.3026.2930.67
Progressive Attention70.4G32.3526.4130.78
Progressive Focused Attention50.9G32.4126.6230.85
", + "bbox": [ + 517, + 813, + 906, + 885 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study on the proposed focused attention.", + "bbox": [ + 534, + 888, + 883, + 904 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2285", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dfd4ad0d0122ada1d7b87ecbcee880e5c6bfc2312408fad0c788fd0b09653ce7.jpg", + "image_caption": [ + "Figure 4. Visual comparison of SR reconstruction results." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 903, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of focus ratio. As discussed in Sec. 3.2, the parameter $\\alpha$ controls the focus degree of Progressive Focused Attention as network depth increases. A smaller $\\alpha$ retains fewer attention positions, accelerating the focusing process. However, $\\alpha$ is generally kept above 0.1, as a rapid reduction in attention retention may cause the network to make premature choices. As shown in Tab. 4, model performance is optimal when $\\alpha$ is around 0.5. Experimental results indicate that both excessively large and small values of $\\alpha$ can hinder effective attention focusing. A very small $\\alpha$ may cause the network to overlook important tokens, leading to incomplete representations. On the other hand, a large $\\alpha$ keeps too many irrelevant tokens, weakening the focus and limiting the network's ability to reduce noise.", + "bbox": [ + 89, + 383, + 483, + 595 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2ab3bf3f27f3cd0ae00fa48db01f48887149dfdf5c3683d3bec27f0228cecbe7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Focus ratio0.10.30.50.70.9
PSNR26.4826.5826.6226.6126.56
", + "bbox": [ + 101, + 604, + 478, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of different window sizes. The window size determines the model's scope of correlation extraction and significant impact on reconstruction performance. Previous studies have shown that larger windows yield better reconstruction results for image super-resolution tasks. However, due to the quadratic complexity of self-attention, previous methods find it challenging to use large windows effectively. Our PFA dynamically filters out patches irrelevant to the current query patch. This allows us to select the interaction scope before computing similarity. As a result, the overall computational load is greatly reduced. This enables us to use large windows while maintaining a low computational cost. As shown in Tab. 5, reconstruction performance", + "bbox": [ + 89, + 703, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "improves as the window size increases. We ultimately select a window size of $32 \\times 32$ to balance performance, model parameters, and computational cost.", + "bbox": [ + 511, + 383, + 906, + 429 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d89a875ab6679881dead4fe0ad78a5876bb5c7484580d6a670916869b57b0dc0.jpg", + "table_caption": [ + "Table 4. Ablation study on focus ratio for $\\times 4$ SR,evaluated on Urban100." + ], + "table_footnote": [], + "table_body": "
Window sizeSet5Urban100Manga109
8 × 832.3326.4030.71
16 × 1632.4126.6230.85
32 × 3232.4926.8130.93
", + "bbox": [ + 517, + 435, + 906, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation study on window sizes for $\\times 4$ SR,evaluated on the Urban100 dataset, with PSNR as the evaluation metric.", + "bbox": [ + 511, + 517, + 906, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 554, + 633, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose the PFT, which introduces a novel approach to linking attention maps across layers through the key innovation of the PFA mechanism, progressively refining the focus on relevant features. By inheriting and modifying attention maps from previous layers, the PFA mechanism reduces unnecessary similarity calculations, improving attention efficiency. This enables the model to prioritize the most relevant tokens while effectively suppressing the influence of irrelevant ones. Experiments show that PFT and PFT-light achieves leading performance in single-image super-resolution with lower computation. As a key component of the Progressive Focused Transformer, PFA has proven to be both effective and efficient for super-resolution tasks. We look forward to exploring its potential in other high-level vision tasks, as well as in natural language processing.", + "bbox": [ + 509, + 579, + 906, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 511, + 820, + 671, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (No. 62476051) and the Sichuan Natural Science Foundation (No. 2024NSFTD0041).", + "bbox": [ + 511, + 844, + 906, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2286", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12780–12791, 2023. 1, 2" + ], + "bbox": [ + 516, + 92, + 906, + 739 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2288", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_model.json b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f5e9876be589b371f91a57a33748619649bd710f --- /dev/null +++ b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_model.json @@ -0,0 +1,1848 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.131, + 0.845, + 0.154 + ], + "angle": 0, + "content": "Progressive Focused Transformer for Single Image Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.265, + 0.18, + 0.734, + 0.218 + ], + "angle": 0, + "content": "Wei Long\\(^{1}\\), Xingyu Zhou\\(^{1}\\), Leheng Zhang\\(^{1}\\), Shuhang Gu\\(^{1*}\\) \n\\(^{1}\\)University of Electronic Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.22, + 0.7, + 0.234 + ], + "angle": 0, + "content": "weilong@std.uestc.edu.cn, shuhanggu@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.325, + 0.238, + 0.665, + 0.251 + ], + "angle": 0, + "content": "https://github.com/LabShuHangGU/PFT-SR" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.319, + 0.485, + 0.681 + ], + "angle": 0, + "content": "Transformer-based methods have achieved remarkable results in image super-resolution tasks because they can capture non-local dependencies in low-quality input images. However, this feature-intensive modeling approach is computationally expensive because it calculates the similarities between numerous features that are irrelevant to the query features when obtaining attention weights. These unnecessary similarity calculations not only degrade the reconstruction performance but also introduce significant computational overhead. How to accurately identify the features that are important to the current query features and avoid similarity calculations between irrelevant features remains an urgent problem. To address this issue, we propose a novel and effective Progressive Focused Transformer (PFT) that links all isolated attention maps in the network through Progressive Focused Attention (PFA) to focus attention on the most important tokens. PFA not only enables the network to capture more critical similar features, but also significantly reduces the computational cost of the overall network by filtering out irrelevant features before calculating similarities. Extensive experiments demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance on various single image superresolution benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.713, + 0.222, + 0.728 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.738, + 0.483, + 0.844 + ], + "angle": 0, + "content": "Image Super-Resolution (SR) aims to reconstruct high-resolution details and textures from Low-Resolution (LR) images. Effective SR techniques not only enhance visual quality but also enable more meaningful information extraction from high-resolution outputs. It has critical applications in fields such as medical imaging, satellite remote sensing, and video surveillance." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.845, + 0.484, + 0.875 + ], + "angle": 0, + "content": "Several classical Convolutional Neural Networks (CNNs) [10, 11, 15, 23] designed for SR have achieved" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.288, + 0.707, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.391, + 0.662, + 0.403 + ], + "angle": 0, + "content": "(a) Self-Attention" + }, + { + "type": "image", + "bbox": [ + 0.715, + 0.289, + 0.898, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.391, + 0.864, + 0.404 + ], + "angle": 0, + "content": "(b) Sparse Attention" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.415, + 0.899, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.516, + 0.822, + 0.529 + ], + "angle": 0, + "content": "(c) Progressive Focused Attention (ours)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.532, + 0.534, + 0.89, + 0.547 + ], + "angle": 0, + "content": "★Query patch Attention calculation region Attention weight" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.565, + 0.907, + 0.69 + ], + "angle": 0, + "content": "Figure 1. Comparison of different attention mechanisms. (a) Vanilla self-attention calculates attention weights in the whole window and generates non-zero weights for both highly relevant and less relevant tokens. (b) Sparse Attention is able to filter out the impact of less relevant tokens with small weights, but still requires the calculation of attention weights for all tokens. (c) Progressive Focused Attention connects isolated attention maps, leveraging attention weights to skip unnecessary computations and better aggregate relevant tokens." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.907, + 0.852 + ], + "angle": 0, + "content": "promising reconstruction results. Due to the limitations of convolution operations, these methods can capture only local feature information. Many studies have focused on enabling networks to achieve broader feature interaction to improve image restoration. Recently, Transformer-based methods [6, 22, 42, 46] have been increasingly applied to image reconstruction, owing to their ability to effectively leverage long-range dependencies, thereby enhancing the recovery of detailed information in images." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Transformer-based super-resolution methods utilize cascaded self-attention blocks to recover the missing High-Resolution (HR) details. At the core of the self-attention" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.235, + 0.9 + ], + "angle": 0, + "content": "* Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2279" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.543 + ], + "angle": 0, + "content": "block is the attention map, which determines how the input features are aggregated to generate output features. Due to the quadratic computational complexity of the self-attention mechanism, most of the existing methods confine attention computation within local windows and only aggregate a limited number of tokens to update image features. Therefore, how to exploit information of relevant tokens while alleviating the disruption from irrelevant tokens is critical in Transformer-based SR models. For the pursuit of high-quality SR results, one category of research tries to enrich the information source by enlarging the window size [6, 46], leveraging cross-window information [7], and introducing an external token dictionary [41]. Since more information can be incorporated into the weighted feature updating process, these methods have shown promising capability in delivering superior SR results. However, calculating similarities between more tokens inevitably leads to extra computational footprint. These methods still need to compromise on model overhead and introduce limited extra information. Another category of studies investigates sophisticated weighting strategies to make better use of input information [5, 28]. Instead of combining all the tokens according to the normalized productive similarities, as in a vanilla self-attention block, various elaborately designed weighting mechanisms have been exploited to make better use of highly relevant tokens while at the same time filtering out less relevant tokens. While the overall concept of seeking more rational weights is highly appealing, the challenge of obtaining enhanced attention weights remains an open problem in the literature." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.555, + 0.482, + 0.9 + ], + "angle": 0, + "content": "In this paper, we link the attention maps between adjacent layers and propose a Progressive Focused Attention (PFA) block to better leverage input tokens across a wider range. Instead of combining input features merely according to the calculated attention map \\(\\mathbf{A}_{cal}^{l}\\), we inherit attention information from the previous block in a productive manner \\(\\mathbf{A}^{l} = \\text{Norm}(\\mathbf{A}^{l-1} \\odot \\mathbf{A}_{cal}^{l})\\), where \\(\\text{Norm}(\\cdot)\\) is the row-wise normalization operation. Such an attention inheritance mechanism enables our method to make a comprehensive measurement of token similarity: tokens that are consistently similar to each other are empowered with larger weights to help each other while the weights of irrelevant tokens are suppressed during the cascaded multiplications. Furthermore, in addition to boosting weights for important tokens and suppressing weights for less relevant tokens, another advantage of our PFA lies in its calculation pre-filtering capability. Specifically, since the final attention map \\(\\mathbf{A}^{l}\\) will be multiplied by the previous attention map \\(\\mathbf{A}^{l-1}\\), small weights in \\(\\mathbf{A}^{l-1}\\) are a sign of unimportant tokens, for which the weight calculation process can be skipped. As shown in Fig.1, the previous attention map not only helps our PFA block to generate better weights which emphasize highly relevant tokens, but also enables" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.093, + 0.905, + 0.167 + ], + "angle": 0, + "content": "it to skip unnecessary similarity calculations so that we are able to afford the computational overhead of large window. Therefore, with comparable computational resources, our SR model could employ a larger window size to leverage input tokens from a broader range." + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.168, + 0.874, + 0.182 + ], + "angle": 0, + "content": "The main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.185, + 0.905, + 0.274 + ], + "angle": 0, + "content": "- We propose the idea of Progressive Focused Attention (PFA) which inherits attention weights from previous layers in a productive manner. PFA not only avoids unnecessary similarity computation with less relevant tokens but also endows highly relevant tokens with larger weights to better enhance the input feature." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.275, + 0.905, + 0.364 + ], + "angle": 0, + "content": "- We instantiate a Progressive Focused Transformer (PFT) for image super-resolution, which takes the progressive focusing benefits of PFA and systematically arranges computational resources for different layers. This property enables the PFT to leverage the merit of large window while maintaining model efficiency." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.366, + 0.905, + 0.424 + ], + "angle": 0, + "content": "- We conduct extensive experiments on super-resolution benchmarks. Our superior experimental results over recent state-of-the-art methods as well as our detailed ablation studies demonstrate the effectiveness of our method." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.185, + 0.905, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.439, + 0.654, + 0.453 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.464, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Transformer-based SR. Transformer models were initially used for natural language processing [9, 33]. Subsequently, they have attracted extensive research interest in the field of computer vision [3, 13, 14, 24, 36]. Due to its excellent feature extraction capabilities, Transformers have also been introduced to low-level visual tasks, including single image super-resolution [21, 37, 43]. Classical SR models [18, 19, 30, 40] based on CNN architectures were limited by narrow receptive fields and limited feature interaction capabilities, and their effectiveness was gradually surpassed by Transformer-based approaches. For example, IPT [4] implements a pre-trained Transformer-based model for better super-resolution. SwinIR [22] improves image quality by using shifted window attention and residual blocks, effectively capturing a broad range of features for restoration. Subsequently, CAT [7] improves image restoration by using rectangle-window self-attention and axial shifting to enhance cross-window interaction. To address the perceptual limitations of window-based methods, several approaches have been proposed. HAT [6] combines channel and window-based attention to overcome these limitations and enhance cross-window interactions for superior image reconstruction. Another approach is ATD [41], which addresses the limitations of local windows by using an Adaptive-Token Dictionary and category-based self-attention to incorporate global information and enhance features. In addition, IPG [31] improves SR by prioritizing detail-rich pixels and using flexible local and global graphs to enhance reconstruction. Unlike existing methods, we" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "2280" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "propose a PFT method that can better focus on key tokens and filter out irrelevant features through PFA, thereby reducing the impact of irrelevant features on SR results and the computational effort." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.155, + 0.485, + 0.548 + ], + "angle": 0, + "content": "Transformer with Sparse Attention. The dense attention maps in Transformers may introduce features from irrelevant locations, which interferes with the effectiveness of feature extraction. To address this, many approaches explore how to leverage sparse attention calculations to better utilize relevant information. For example, NLSA [28] combines non-local operations with sparse representations, using dynamic sparse attention to focus on pertinent features, thereby improving efficiency and robustness while reducing computational costs. ART [39] enhances image restoration by combining both dense and sparse attention mechanisms, expanding the receptive field to enable more effective interactions and better feature representation. Additionally, a class of methods [35, 45] explicitly selects the most relevant positions in the attention map for retention, filtering out irrelevant information that might interfere with feature aggregation. Building on this, DRSformer [5] further develops the idea of sparse selection by introducing a learnable top-\\(k\\)-selection operator, that adaptively retains the most relevant self-attention values, thus improving image restoration. We propose the PFT method, which connects isolated attention maps across the entire network to efficiently identify the positions each attention map collectively focuses on. PFA performs a Hadamard product on adjacent attention maps to pinpoint the most relevant attention locations, thereby enhancing the filtering of irrelevant information." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.563, + 0.396, + 0.579 + ], + "angle": 0, + "content": "3. Progressive Focused Transformer" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.588, + 0.232, + 0.603 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.483, + 0.67 + ], + "angle": 0, + "content": "Self-Attention. The self-attention mechanism [33] is a fundamental part of Transformer, which computes the similarity between tokens and aggregates features based on the corresponding attention weights." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.67, + 0.483, + 0.702 + ], + "angle": 0, + "content": "Given the query matrix \\(\\mathbf{Q} \\in \\mathbb{R}^{N \\times d}\\), key matrix \\(\\mathbf{K} \\in \\mathbb{R}^{N \\times d}\\), the attention weights are calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.713, + 0.483, + 0.74 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {s a} = \\operatorname {S o f t m a x} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "where the \\(i\\)-th row in \\(\\mathbf{A}_{sa}\\) represents normalized weights to aggregate value tokens \\(\\mathbf{V} \\in \\mathbb{R}^{N \\times d}\\) and the output of self-attention module is obtained by \\(\\mathbf{O}_{SA} = \\mathbf{A}_{sa}\\mathbf{K}\\). Although the exponential function in Softmax could suppress irrelevant tokens to some extent, the above vanilla self-attention still apply dense weights which utilize all the input tokens in the window to generate the final output. Moreover, another feature of the above self-attention lies in its computational overhead. The complexity of Eq. (1) grows quadratically with the number of tokens \\(N\\). Therefore, most existing" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.122 + ], + "angle": 0, + "content": "methods need to perform self-attention calculations in small windows to manage this computational burden." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.129, + 0.907, + 0.205 + ], + "angle": 0, + "content": "Sparse Attention. To mitigate the negative impact of irrelevant features in the dense attention map, numerous sparse attention methods have been proposed. Generally speaking, the overall idea of sparse attention is to introduce a selection operation to sparsify the attention weights:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.21, + 0.907, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {s s a} = \\operatorname {S o f t m a x} \\left(\\mathcal {S} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.242, + 0.907, + 0.363 + ], + "angle": 0, + "content": "where \\( S(\\cdot) \\) is a sparsification operation which removes the weights for less relevant tokens. The most commonly adopted sparsify operation is the top-\\( k \\) selection, which only allows \\( K \\) non-zero values in each row. Despite its strong capability of irrelevant token suppression, top-\\( k \\) selection only adjusts aggregation weights according to a single step of similarity calculation and has limited ability to make effective use of highly relevant tokens." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.377, + 0.783, + 0.393 + ], + "angle": 0, + "content": "3.2. Progressive Focused Attention" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.399, + 0.906, + 0.534 + ], + "angle": 0, + "content": "As reviewed in the previous section, although sparse attention methods are able to improve the vanilla self-attention by alleviating the negative impact of irrelevant tokens, they still have limited capability in further distinguishing highly relevant tokens from mildly relevant tokens. Moreover, both the vanilla and sparse attention methods fail to identify the relevant feature regions prior to similarity calculation, resulting in a significant amount of unnecessary calculations, which impedes the incorporation of additional input tokens." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.536, + 0.907, + 0.793 + ], + "angle": 0, + "content": "In this paper, we propose Progressive Focused Attention, which links the attention maps between adjacent layers to better aggregate relevant features. Generally, the proposed PFA advances the existing methods in two aspects. Firstly, PFA makes use of attention maps from previous layers to better weight input features. The weights of highly relevant tokens that are consistently similar to each other across layers will be enhanced during the cascade multiplication process. Secondly, PFA leverages the attention map of previous layers to identify irrelevant features for saving computational overhead. This selective calculation mechanism enables us to conduct self-attention within a larger window. In the remaining part of this section, we first introduce the basic idea of our PFA, which inherits the attention map from the previous layers through a Hadamard product. Then, we introduce how we could further leverage previous attention maps to reduce computational overhead." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Progressive Attention Across Layers. As introduced in Eq. (1) and (2), the previous methods obtain attention weights merely according to the calculated similarities between tokens from the current layer. The standard similarity calculation has limited discriminative capability in boosting highly relevant tokens while suppressing less relevant tokens. To address this issue, we propose to inherit attention" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2281" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.099, + 0.868, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.389, + 0.908, + 0.446 + ], + "angle": 0, + "content": "Figure 2. The overall architecture of PFT. PFA Block consists of \\(M\\) Progressive Focused Attention Layers (PFAL). Each PFA takes both image features and aggregated PFA maps from previous layers as input. Sparse Matrix Multiplication (SMM) ensures each row of \\(Q\\) interacts only with sparse columns of \\(K^T\\), producing calculated attention maps. After applying the Hadamard product and sparse focusing, PFA maps of the current layer are obtained and used with the \\(V\\) matrix in an SMM operation to generate attention-aggregated features." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.461, + 0.445, + 0.476 + ], + "angle": 0, + "content": "weights from previous layers in a productive manner:" + }, + { + "type": "equation", + "bbox": [ + 0.189, + 0.488, + 0.483, + 0.508 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} ^ {l} = \\operatorname {N o r m} \\left(\\mathbf {A} ^ {l - 1} \\odot \\mathbf {A} _ {\\text {c a l}} ^ {l}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.522, + 0.483, + 0.779 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}_{cal}^{l}\\) is the calculated attention map for the \\(l\\)-th layer according to the vanilla self-attention mechanism as in Eq. (1); \\(\\mathbf{A}^{l - 1}\\) is the attention map of the previous layer; Norm(\\cdot) represents the row-wise normalization operation, which ensures the summation of each row to be 1. As indicated in Eq. (3), the final attention map in the \\(l\\)-th layer is obtained by multiplying the calculated similarities with the attention map from the previous layer. Such a mechanism enables us to make a comprehensive assessment of token similarity: the weights for less relevant tokens will be wiped out during the successive multiplication process, while important tokens with high similarity values across layers will be assigned with larger weights after normalization. As will be validated in our ablation studies, with improved feature aggregation weights, such a Progressive Attention mechanism could deliver better SR results over the top-\\(k\\) sparse attention as well as the standard self-attention block." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Progressive Focused Attention. Since all the normalized similarities are less than 1, the above strategy of multiplicative attention inheritance could gradually filter out the impact of irrelevant tokens and obtain sparse weights as the network depth increases. Actually, based on the previous attention map \\(\\mathbf{A}^{l - 1}\\), we are able to identify unimportant positions before calculation. Therefore, we can avoid unnecessary computations with a Sparse Matrix Multiplica" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.461, + 0.668, + 0.476 + ], + "angle": 0, + "content": "tion (SMM) operation:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.486, + 0.907, + 0.505 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {s c} ^ {l} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {\\Psi} \\left(\\mathbf {Q} ^ {l}, \\left(\\mathbf {K} ^ {l}\\right) ^ {\\top}, \\mathbf {I} ^ {l - 1}\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.907, + 0.777 + ], + "angle": 0, + "content": "where \\(\\Psi\\) denotes the SMM operation; \\(\\mathbf{I}^{l - 1}\\in \\mathbb{R}^{N\\times N}\\) is a sparse index matrix; we calculate \\(\\mathbf{A}_{sc}^l (i,j)\\) with \\(\\mathbf{Q}^l (i,:)\\) and \\(\\mathbf{K}^l (j,:)^T\\) only if \\(\\mathbf{I}^{l - 1}(i,j) = 1\\), otherwise we set \\(\\mathbf{A}_{sc}^l (i,j) = 0\\). Note that after the SMM operation we still need to normalize each row of the calculation results using the Softmax function. For an all-ones indexing matrix, the SMM operation in Eq. (4) is equivalent to the standard attention calculation process as in Eq. (1); However, if we are able to obtain a sparse \\(\\mathbf{I}^{l - 1}\\) prior to the calculation process, a significant portion of computations can be skipped. Due to our progressive attention mechanism, we utilize \\(\\mathbf{A}^{l - 1}\\) to indicate skippable positions. Specifically, inspired by the success of top-\\(k\\) sparse attention, we only keep \\(K^l\\) non-zero attention weights for each layer and generate the indexing matrix \\(\\mathbf{I}^l\\) according to the non-zero positions in \\(\\mathbf{A}^l\\). To sum up, the attention map of our progressive focused attention is achieved through the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.788, + 0.907, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l l} \\mathbf {A} _ {s c} ^ {l} = S o f t m a x (\\boldsymbol {\\Psi} (\\mathbf {Q} ^ {l}, (\\mathbf {K} ^ {l}) ^ {\\top}, \\mathbf {I} ^ {l - 1})), \\\\ \\mathbf {A} ^ {l} = \\mathcal {S} _ {K ^ {l}} (N o r m (\\mathbf {A} _ {s c} ^ {l} \\odot \\mathbf {A} ^ {l - 1})), \\\\ \\mathbf {I} ^ {l} = \\operatorname {S i g n} (\\mathbf {A} ^ {l}), \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Where \\(S_{K^l}(\\cdot)\\) is the sparsification operation that selects the top \\(K^l\\) values in each row and \\(\\mathrm{Sign}(\\cdot)\\) generates a binary index matrix according to the sign of input matrix. Then," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2282" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.486, + 0.123 + ], + "angle": 0, + "content": "we can also use the SMM operation to calculate the output matrix of the \\(l\\)-th layer:" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.131, + 0.483, + 0.151 + ], + "angle": 0, + "content": "\\[\n\\mathbf {O} ^ {l} = \\Psi (\\mathbf {A} ^ {l}, \\mathbf {V} ^ {l}, \\mathbf {I} ^ {l}). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.16, + 0.485, + 0.509 + ], + "angle": 0, + "content": "For the first attention block, in which we do not have previous attention map, we simply set \\(\\mathbf{A}^0\\) and \\(\\mathbf{I}^0\\) as allones matrix and calculate \\(\\mathbf{A}^1\\) as standard self-attention in Eq. (1) to aggregate input features. For subsequent layers, we exploit the attention map from previous layer to generate better weights and filter out unnecessary computations as in Eq. (5). Since tokens which have been determined as irrelevant tokens to a specific query token in previous layers will not be considered in the following layers at all, to avoid filtering-out important tokens at early stages, we set \\(K^1 = N\\) and gradually reduce the nonzero values with a focus ratio: \\(K^l = \\alpha K^{l - 1}\\), where \\(K\\) represents the number of retained attention values within the window. With \\(0 < \\alpha < 1\\), our cascade PFA layers gradually focus on important candidates and reduce the number of key-tokens to be considered for each input query-token, resulting in significant reduction in computational burden for each window. Notably, using standard matrix multiplication to implement the SMM operation is highly inefficient. Therefore, we developed efficient CUDA kernels for SMM. This implementation significantly enhances the efficiency of our model, enabling PFT to achieve inference speeds comparable to those of existing methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.517, + 0.395, + 0.532 + ], + "angle": 0, + "content": "3.3. The Overall Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.484, + 0.902 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, the overall architecture of PFT follows the structure adopted in recent state-of-the-art Transformer-based SR models [6, 22, 41]. While, we replace the standard self-attention blocks with our proposed PFA block for the pursuit of better SR results. Notably, we also incorporate the shifted window approach from the Swin Transformer, though it is omitted in the illustration for simplicity. Thus, the attention map in PFA is passed from the first layer to the last through two pathways, divided by the shift operation into even and odd layers for focused processing. Additionally, we incorporate LePE positional encoding [12] during attention computation. For classical SR, the PFT network consists of 6 blocks, with the number of attention layers in each block being [4, 4, 4, 6, 6, 6]. The model utilizes multi-head attention with 6 attention heads, and the total number of channels is 240. The window size is \\(32 \\times 32\\), and the number of retained attention values in each block is [1024, 256, 128, 64, 32, 16], respectively. For lightweight SR, the PFT-light network is composed of five blocks, with the number of attention layers in each block being [2, 4, 6, 6, 6]. It employs 4 attention heads, with a total of 52 channels. The window size is \\(32 \\times 32\\), and the number of retained attention values in each block follows the pattern [1024, 256, 128, 64, 32]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.228 + ], + "angle": 0, + "content": "Analysis of Computational Complexity. Self-Attention and sparse attention have the same computational cost, as both measure similarity with neighboring positions by interacting with tokens within non-overlapping windows. When the input feature map size is \\( h \\times w \\times C \\) and the window size is \\( W \\times W \\), the feature map is divided into \\( \\frac{h}{W} \\times \\frac{w}{W} \\) windows, each with \\( W \\times W \\) tokens. Assuming that the network has a total of \\( L \\) attention layers, the computational complexity of the attention component for the entire network is:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.234, + 0.907, + 0.253 + ], + "angle": 0, + "content": "\\[\n\\Omega (S A) = 4 h w L C ^ {2} + 2 W ^ {2} h w L C. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.259, + 0.909, + 0.427 + ], + "angle": 0, + "content": "PFA can control the proportion of key tokens that are most relevant to the query features by adjusting the retention ratio \\(\\alpha\\). The index matrix \\(\\mathbf{I}\\) allows shallow attention aggregation information to be carried into deeper layers for further focusing, resulting in a gradually decreasing \\(K\\). For a network with \\(L\\) attention layers, we assume that the number of retained attention values within the window decreases, as expressed by the following formula: \\(K^{l} = \\alpha K^{l - 1}\\), where \\(0 < \\alpha < 1\\) and \\(K^{-1}\\) is generally set to \\(W^2\\). It can be represented as \\(K^{l} = W^{2}\\alpha^{l - 1}\\). The overall computational complexity of the model is:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.442, + 0.907, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\Omega (P F A) = \\sum_ {l = 1} ^ {L} \\left(4 h w C ^ {2} + 2 \\alpha^ {(l - 1)} W ^ {2} h w C\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.909, + 0.676 + ], + "angle": 0, + "content": "where \\(\\alpha^{(l-1)}\\) controls the decay of the focus ratio across layers, with \\(0 < \\alpha < 1\\). As \\(l\\) increases, the focus ratio progressively decreases. The first term, \\(4hwC^2\\), represents the computational complexity of the projection layers. The second term, \\(2\\alpha^{(l-1)}W^2hwC\\), accounts for the complexity of computing the similarity between the query and the selected key tokens, as well as redistributing the corresponding value information at the focused positions. Obviously, since \\(\\alpha\\) is less than 1, the complexity of this term decreases exponentially with depth. For example, with \\(\\alpha = 0.5\\), the computational complexity is reduced to just \\(6.25\\%\\) of the original after four decay steps." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.688, + 0.649, + 0.705 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.702, + 0.73 + ], + "angle": 0, + "content": "4.1. Experiment Setting" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We use the DF2K dataset, which combines DIV2K [32] and Flickr2K [23], as our training set. To ensure fair comparisons, we adopt the same training configuration as utilized in recent SR studies [6, 31, 41]. Our model is trained for 500K iterations using the AdamW optimizer and an initial learning rate of \\(2 \\times 10^{-4}\\). The input patch size for training is fixed at \\(64 \\times 64\\), and we employ a MultistepLR scheduler, which reduces the learning rate by half at specified iterations [250000, 400000, 450000, 475000]. The batch size is set to 32. We evaluate our method on five standard benchmark datasets: Set5 [2], Set14 [38], BSD100 [26]," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2283" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.116, + 0.082, + 0.885, + 0.446 + ], + "angle": 0, + "content": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
EDSR [23]×242.6M22.14T38.110.960233.920.919532.320.901332.930.935139.100.9773
RCAN [44]×215.4M7.02T38.270.961434.120.921632.410.902733.340.938439.440.9786
HAN [29]×263.6M7.24T38.270.961434.160.921732.410.902733.350.938539.460.9785
IPT [4]×2115M7.38T38.37-34.43-32.48-33.76---
SwinIR [22]×211.8M3.04T38.420.962334.460.925032.530.904133.810.943339.920.9797
CAT-A [7]×216.5M5.08T38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [39]×216.4M7.04T38.560.962934.590.926732.580.904834.300.945240.240.9808
HAT [6]×220.6M5.81T38.630.963034.860.927432.620.905334.450.946640.260.9809
IPG [31]×218.1M5.35T38.610.963234.730.927032.600.905234.480.946440.240.9810
ATD [41]×220.1M6.07T38.610.962934.950.927632.650.905634.700.947640.370.9810
PFT (Ours)×219.6M5.03T38.680.963535.000.928032.670.905834.900.949040.490.9815
EDSR [23]×343.0M9.82T34.650.928030.520.846229.250.809328.800.865334.170.9476
RCAN [44]×315.6M3.12T34.740.929930.650.848229.320.811129.090.870234.440.9499
HAN [29]×364.2M3.21T34.750.929930.670.848329.320.811029.100.870534.480.9500
IPT [4]×3116M3.28T34.81-30.85-29.38-29.49---
SwinIR [22]×311.9M1.35T34.970.931830.930.853429.460.814529.750.882635.120.9537
CAT-A [7]×316.6M2.26T35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [39]×316.6M3.12T35.070.932531.020.854129.510.815930.100.887135.390.9548
HAT [6]×320.8M2.58T35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG [31]×318.3M2.39T35.100.933231.100.855429.530.816830.360.890135.530.9554
ATD [41]×320.3M2.69T35.110.933031.130.855629.570.817630.460.891735.630.9558
PFT (Ours)×319.8M2.23T35.150.933331.160.856129.580.817830.560.893135.670.9560
EDSR [23]×443.0M5.54T32.460.896828.800.787627.710.742026.640.803331.020.9148
RCAN [44]×415.6M1.76T32.630.900228.870.788927.770.743626.820.808731.220.9173
HAN [29]×464.2M1.81T32.640.900228.900.789027.800.744226.850.809431.420.9177
IPT [4]×4116M1.85T32.64-29.01-27.82-27.26---
SwinIR [22]×411.9M0.76T32.920.904429.090.795027.920.748927.450.825432.030.9260
CAT-A [7]×416.6M1.27T33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [39]×416.6M1.76T33.040.905129.160.795827.970.751027.770.832132.310.9283
HAT [6]×420.8M1.45T33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG [31]×417.0M1.30T33.150.906229.240.797327.990.751928.130.839232.530.9300
ATD [41]×420.3M1.52T33.100.905829.240.797428.010.752628.170.840432.620.9306
PFT (Ours)×419.8M1.26T33.150.906529.290.797828.020.752728.200.841232.630.9306
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.457, + 0.908, + 0.485 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on classical SR task. The best and second best results are colored with red and blue." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.498, + 0.484, + 0.543 + ], + "angle": 0, + "content": "Urban100 [16], and Manga109 [27]. In addition, the computational costs of all models in this paper are measured at an output resolution of \\( 1280 \\times 640 \\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.559, + 0.46, + 0.575 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.582, + 0.483, + 0.748 + ], + "angle": 0, + "content": "We compare the performance of our model with various SR baselines on widely used benchmark datasets, including Set5 [2], Set14 [38], BSD100 [26], Urban100 [16], and Manga109 [27]. These SR methods include both classical and state-of-the-art approaches, such as EDSR [23], RCAN [44], HAN [29], IPT [4], SwinIR [8], CAT [7], ART [39], HAT [6], IPG [31], and ATD [41]. We use PSNR and SSIM metrics to assess the performance of SR models at \\(\\times 2\\), \\(\\times 3\\), and \\(\\times 4\\) upscaling factors. All computational costs are calculated at the output resolution of \\(1280\\times 640\\), and PFT uses a window size of \\(32\\times 32\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The results, shown in Tab. 1, indicate that the proposed PFT model achieves superior performance over ATD, with significantly reduced computational costs. Notably, PFT reduces computational load by \\(17.1\\%\\) compared to ATD, while attaining the highest PSNR in most datasets. For lightweight SR tasks, we further compare our model with other efficient SR methods, including CARN [1], IMDN [17], LAPAR [20], LatticeNet [25], SwinIR [8], SwinIR-NG [8], ELAN [42], and OmniSR [34]. As shown in Tab. 2, the proposed PFT-light outperforms the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.907, + 0.68 + ], + "angle": 0, + "content": "recently introduced ATD-light [41] on nearly all benchmark datasets, while reducing computational complexity by \\(20.1\\%\\). On the \\(\\times 2\\) Urban100 benchmark, PFT-light outperforms ATD-light by 0.40dB and IPG-Tiny by 0.63dB. For the \\(\\times 4\\) SR experiments, PFT-light also outperforms IPG Tiny by 0.42dB and ATD-light by 0.23dB on the Urban100 test set. The superior performance of PFT can be attributed to its use of Progressive Focused Attention, which connects otherwise isolated attention maps across the network. This enables the model to focus on essential features, filter out irrelevant patches, substantially reduce computational costs, and support the use of larger window sizes." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.684, + 0.903, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.818, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Figure 3. Visual comparison of attention distributions in the 18th layer. SA and top-\\(k\\) Attention distribute attention broadly, failing to focus on the most relevant areas. In contrast, PFA filters out irrelevant tokens and concentrates attention on key regions. By reducing computational costs, it enables the use of a larger \\(32 \\times 32\\) window for more extensive feature interactions." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2284" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.082, + 0.894, + 0.449 + ], + "angle": 0, + "content": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
CARN [1]×21,592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [17]×2694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [20]×2548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [25]×2756K169.5G38.150.961033.780.919332.250.900532.430.9302--
SwinIR-light [22]×2910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [42]×2582K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [8]×21181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
OmniSR [34]×2772K194.5G38.220.961333.980.921032.360.902033.050.936339.280.9784
IPG-Tiny [31]×2872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
ATD-light [41]×2753K348.6G38.280.961634.110.921732.390.902333.270.937639.510.9789
PFT-light (Ours)×2776K278.3G38.360.962034.190.923232.430.903033.670.941139.550.9792
CARN [1]×31,592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [17]×3703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [20]×3544K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [25]×3765K76.3G34.530.928130.390.842429.150.805928.330.8538--
SwinIR-light [22]×3918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [42]×3590K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [8]×31190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
OmniSR [34]×3780K88.4G34.700.929430.570.846929.280.809428.840.865634.220.9487
IPG-Tiny [31]×2878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
ATD-light [41]×3760K154.7G34.700.930030.680.848529.320.810929.160.871034.600.9505
PFT-light (ours)×3783K123.5G34.810.930530.750.849329.330.811629.430.875934.600.9510
CARN [1]×41,592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [17]×4715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [20]×4659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [25]×4777K43.6G32.300.896228.680.783027.620.736726.250.7873--
SwinIR-light [22]×4930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [42]×4582K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [8]×41201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
OmniSR [34]×4792K50.9G32.490.898828.780.785927.710.741526.650.801831.020.9151
IPG-Tiny [31]×4887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
ATD-light [41]×4769K87.1G32.620.899728.870.788427.770.743926.970.810731.470.9198
PFT-light (Ours)×4792K69.6G32.630.900528.920.789127.790.744527.200.817131.510.9204
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.453, + 0.908, + 0.482 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on lightweight SR task. The best and second best results are colored with red and blue." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.494, + 0.482, + 0.629 + ], + "angle": 0, + "content": "Visual comparison of attention distribution. The attention distribution visualizations are shown in Fig. 3. The attention distributions of the Vanilla Self-Attention and top-k Attention methods are relatively scattered, failing to allocate attention to the regions most relevant to the current query. In contrast, our PFA method filters out irrelevant tokens and focuses on most important positions. It also lowers computation costs, enabling larger \\(32 \\times 32\\) windows for broader feature interactions." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.63, + 0.483, + 0.827 + ], + "angle": 0, + "content": "Visual comparison of SR reconstruction results. To evaluate the quality of different super-resolution methods, we show visual examples in Fig. 4. These comparisons demonstrate the strength of our PFT approach in restoring sharp edges and fine textures from low-resolution images. For example, in img_001 and img_095, most methods struggle to reconstruct textures accurately, leading to noticeable distortions. Similarly, in the zebra and barbara images, many methods fail to recover details, resulting in blurry or incorrect textures. In contrast, our PFT effectively captures fine textures by focusing on the most relevant features. This ability to selectively attend helps restore clean edges and reduce artifacts, producing more accurate reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.834, + 0.245, + 0.851 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.903 + ], + "angle": 0, + "content": "We conduct ablation studies on the proposed PFT-light model, with all models trained for 250k iterations on the DIV2K dataset at \\(\\times 4\\) scale. Except for the experiments on" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.494, + 0.907, + 0.539 + ], + "angle": 0, + "content": "window size, all other experiments use a window size of \\(16 \\times 16\\). In top-\\(k\\) Attention, the value of \\(k\\) is set to half the number of window elements, which is 128." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.544, + 0.909, + 0.801 + ], + "angle": 0, + "content": "Effectiveness of Progressive Focused Attention. We conducted experiments to demonstrate the effectiveness of the proposed Progressive Attention and Progressive Focused Attention, with results presented in Tab. 3. These experiments compare the quantitative performance of \\(\\times 4\\) super-resolution on the Set5, Urban100, and Manga109 datasets. Progressive Attention applies a straightforward Hadamard product connection of the attention maps. As shown, even the Progressive Attention provides notable performance improvements over Self-Attention and top-\\(k\\) Attention. Progressive Focused Attention achieved the best results with a \\(27.69\\%\\) reduction in computation, and notably increasing PSNR by 0.36dB on the Urban100 dataset. The effectiveness of PFA lies in its ability to link adjacent attention maps across the network via the Hadamard product, allowing the model to reduce redundant computations and focus on the most relevant tokens." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.814, + 0.907, + 0.886 + ], + "angle": 0, + "content": "
MethodFLOPsSet5Urban100Manga109
Vanilla Self-Attention70.4G32.2826.2630.62
Top-k Attention70.4G32.3026.2930.67
Progressive Attention70.4G32.3526.4130.78
Progressive Focused Attention50.9G32.4126.6230.85
" + }, + { + "type": "table_caption", + "bbox": [ + 0.535, + 0.89, + 0.884, + 0.905 + ], + "angle": 0, + "content": "Table 3. Ablation study on the proposed focused attention." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "2285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.905, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.327, + 0.343, + 0.672, + 0.358 + ], + "angle": 0, + "content": "Figure 4. Visual comparison of SR reconstruction results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.384, + 0.484, + 0.596 + ], + "angle": 0, + "content": "Effects of focus ratio. As discussed in Sec. 3.2, the parameter \\(\\alpha\\) controls the focus degree of Progressive Focused Attention as network depth increases. A smaller \\(\\alpha\\) retains fewer attention positions, accelerating the focusing process. However, \\(\\alpha\\) is generally kept above 0.1, as a rapid reduction in attention retention may cause the network to make premature choices. As shown in Tab. 4, model performance is optimal when \\(\\alpha\\) is around 0.5. Experimental results indicate that both excessively large and small values of \\(\\alpha\\) can hinder effective attention focusing. A very small \\(\\alpha\\) may cause the network to overlook important tokens, leading to incomplete representations. On the other hand, a large \\(\\alpha\\) keeps too many irrelevant tokens, weakening the focus and limiting the network's ability to reduce noise." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.606, + 0.48, + 0.655 + ], + "angle": 0, + "content": "
Focus ratio0.10.30.50.70.9
PSNR26.4826.5826.6226.6126.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.662, + 0.483, + 0.69 + ], + "angle": 0, + "content": "Table 4. Ablation study on focus ratio for \\( \\times 4 \\) SR,evaluated on Urban100." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Effects of different window sizes. The window size determines the model's scope of correlation extraction and significant impact on reconstruction performance. Previous studies have shown that larger windows yield better reconstruction results for image super-resolution tasks. However, due to the quadratic complexity of self-attention, previous methods find it challenging to use large windows effectively. Our PFA dynamically filters out patches irrelevant to the current query patch. This allows us to select the interaction scope before computing similarity. As a result, the overall computational load is greatly reduced. This enables us to use large windows while maintaining a low computational cost. As shown in Tab. 5, reconstruction performance" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.384, + 0.907, + 0.43 + ], + "angle": 0, + "content": "improves as the window size increases. We ultimately select a window size of \\(32 \\times 32\\) to balance performance, model parameters, and computational cost." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.436, + 0.907, + 0.514 + ], + "angle": 0, + "content": "
Window sizeSet5Urban100Manga109
8 × 832.3326.4030.71
16 × 1632.4126.6230.85
32 × 3232.4926.8130.93
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.518, + 0.907, + 0.547 + ], + "angle": 0, + "content": "Table 5. Ablation study on window sizes for \\( \\times 4 \\) SR,evaluated on the Urban100 dataset, with PSNR as the evaluation metric." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.555, + 0.634, + 0.57 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.58, + 0.907, + 0.807 + ], + "angle": 0, + "content": "We propose the PFT, which introduces a novel approach to linking attention maps across layers through the key innovation of the PFA mechanism, progressively refining the focus on relevant features. By inheriting and modifying attention maps from previous layers, the PFA mechanism reduces unnecessary similarity calculations, improving attention efficiency. This enables the model to prioritize the most relevant tokens while effectively suppressing the influence of irrelevant ones. Experiments show that PFT and PFT-light achieves leading performance in single-image super-resolution with lower computation. As a key component of the Progressive Focused Transformer, PFA has proven to be both effective and efficient for super-resolution tasks. We look forward to exploring its potential in other high-level vision tasks, as well as in natural language processing." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.821, + 0.673, + 0.838 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.845, + 0.907, + 0.888 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (No. 62476051) and the Sichuan Natural Science Foundation (No. 2024NSFTD0041)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2286" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. Fast, accurate, and lightweight super-resolution with cascading residual network. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12780–12791, 2023. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.907, + 0.741 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2288" + } + ] +] \ No newline at end of file diff --git a/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_origin.pdf b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4d9cb0060c020521047402ea10f5f831a5395247 --- /dev/null +++ b/2025/Progressive Focused Transformer for Single Image Super-Resolution/a3bd7da0-3f79-431d-b8a1-9a72e56058b5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9614a73882f9e0c293488940c4e1eb49059a708a4592062b74307340541446aa +size 7134790 diff --git a/2025/Progressive Focused Transformer for Single Image Super-Resolution/full.md b/2025/Progressive Focused Transformer for Single Image Super-Resolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4fe050f2e60fb0a3734f404084bacef9986bd41d --- /dev/null +++ b/2025/Progressive Focused Transformer for Single Image Super-Resolution/full.md @@ -0,0 +1,258 @@ +# Progressive Focused Transformer for Single Image Super-Resolution + +Wei Long $^{1}$ , Xingyu Zhou $^{1}$ , Leheng Zhang $^{1}$ , Shuhang Gu $^{1*}$ $^{1}$ University of Electronic Science and Technology of China + +weilong@std.uestc.edu.cn, shuhanggu@gmail.com + +https://github.com/LabShuHangGU/PFT-SR + +# Abstract + +Transformer-based methods have achieved remarkable results in image super-resolution tasks because they can capture non-local dependencies in low-quality input images. However, this feature-intensive modeling approach is computationally expensive because it calculates the similarities between numerous features that are irrelevant to the query features when obtaining attention weights. These unnecessary similarity calculations not only degrade the reconstruction performance but also introduce significant computational overhead. How to accurately identify the features that are important to the current query features and avoid similarity calculations between irrelevant features remains an urgent problem. To address this issue, we propose a novel and effective Progressive Focused Transformer (PFT) that links all isolated attention maps in the network through Progressive Focused Attention (PFA) to focus attention on the most important tokens. PFA not only enables the network to capture more critical similar features, but also significantly reduces the computational cost of the overall network by filtering out irrelevant features before calculating similarities. Extensive experiments demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance on various single image superresolution benchmarks. + +# 1. Introduction + +Image Super-Resolution (SR) aims to reconstruct high-resolution details and textures from Low-Resolution (LR) images. Effective SR techniques not only enhance visual quality but also enable more meaningful information extraction from high-resolution outputs. It has critical applications in fields such as medical imaging, satellite remote sensing, and video surveillance. + +Several classical Convolutional Neural Networks (CNNs) [10, 11, 15, 23] designed for SR have achieved + +![](images/36bb171c828feb9e4a8afd5a8e36ded71d1a3dad601c8af9ec6fb1a55be78341.jpg) +(a) Self-Attention + +![](images/1be1190e67514fdd1c155d4d4e4ba527619724909decb741136239f3fe66762b.jpg) +(b) Sparse Attention + +(c) Progressive Focused Attention (ours) +Figure 1. Comparison of different attention mechanisms. (a) Vanilla self-attention calculates attention weights in the whole window and generates non-zero weights for both highly relevant and less relevant tokens. (b) Sparse Attention is able to filter out the impact of less relevant tokens with small weights, but still requires the calculation of attention weights for all tokens. (c) Progressive Focused Attention connects isolated attention maps, leveraging attention weights to skip unnecessary computations and better aggregate relevant tokens. +![](images/be95d238a86e6dc13ee1fd1cab6d4ca0d5beee74c0cb09377569463cf2170fe4.jpg) +★Query patch Attention calculation region Attention weight + +promising reconstruction results. Due to the limitations of convolution operations, these methods can capture only local feature information. Many studies have focused on enabling networks to achieve broader feature interaction to improve image restoration. Recently, Transformer-based methods [6, 22, 42, 46] have been increasingly applied to image reconstruction, owing to their ability to effectively leverage long-range dependencies, thereby enhancing the recovery of detailed information in images. + +Transformer-based super-resolution methods utilize cascaded self-attention blocks to recover the missing High-Resolution (HR) details. At the core of the self-attention + +block is the attention map, which determines how the input features are aggregated to generate output features. Due to the quadratic computational complexity of the self-attention mechanism, most of the existing methods confine attention computation within local windows and only aggregate a limited number of tokens to update image features. Therefore, how to exploit information of relevant tokens while alleviating the disruption from irrelevant tokens is critical in Transformer-based SR models. For the pursuit of high-quality SR results, one category of research tries to enrich the information source by enlarging the window size [6, 46], leveraging cross-window information [7], and introducing an external token dictionary [41]. Since more information can be incorporated into the weighted feature updating process, these methods have shown promising capability in delivering superior SR results. However, calculating similarities between more tokens inevitably leads to extra computational footprint. These methods still need to compromise on model overhead and introduce limited extra information. Another category of studies investigates sophisticated weighting strategies to make better use of input information [5, 28]. Instead of combining all the tokens according to the normalized productive similarities, as in a vanilla self-attention block, various elaborately designed weighting mechanisms have been exploited to make better use of highly relevant tokens while at the same time filtering out less relevant tokens. While the overall concept of seeking more rational weights is highly appealing, the challenge of obtaining enhanced attention weights remains an open problem in the literature. + +In this paper, we link the attention maps between adjacent layers and propose a Progressive Focused Attention (PFA) block to better leverage input tokens across a wider range. Instead of combining input features merely according to the calculated attention map $\mathbf{A}_{cal}^{l}$ , we inherit attention information from the previous block in a productive manner $\mathbf{A}^{l} = \text{Norm}(\mathbf{A}^{l-1} \odot \mathbf{A}_{cal}^{l})$ , where $\text{Norm}(\cdot)$ is the row-wise normalization operation. Such an attention inheritance mechanism enables our method to make a comprehensive measurement of token similarity: tokens that are consistently similar to each other are empowered with larger weights to help each other while the weights of irrelevant tokens are suppressed during the cascaded multiplications. Furthermore, in addition to boosting weights for important tokens and suppressing weights for less relevant tokens, another advantage of our PFA lies in its calculation pre-filtering capability. Specifically, since the final attention map $\mathbf{A}^{l}$ will be multiplied by the previous attention map $\mathbf{A}^{l-1}$ , small weights in $\mathbf{A}^{l-1}$ are a sign of unimportant tokens, for which the weight calculation process can be skipped. As shown in Fig.1, the previous attention map not only helps our PFA block to generate better weights which emphasize highly relevant tokens, but also enables + +it to skip unnecessary similarity calculations so that we are able to afford the computational overhead of large window. Therefore, with comparable computational resources, our SR model could employ a larger window size to leverage input tokens from a broader range. + +The main contributions of this paper are as follows: + +- We propose the idea of Progressive Focused Attention (PFA) which inherits attention weights from previous layers in a productive manner. PFA not only avoids unnecessary similarity computation with less relevant tokens but also endows highly relevant tokens with larger weights to better enhance the input feature. +- We instantiate a Progressive Focused Transformer (PFT) for image super-resolution, which takes the progressive focusing benefits of PFA and systematically arranges computational resources for different layers. This property enables the PFT to leverage the merit of large window while maintaining model efficiency. +- We conduct extensive experiments on super-resolution benchmarks. Our superior experimental results over recent state-of-the-art methods as well as our detailed ablation studies demonstrate the effectiveness of our method. + +# 2. Related Work + +Transformer-based SR. Transformer models were initially used for natural language processing [9, 33]. Subsequently, they have attracted extensive research interest in the field of computer vision [3, 13, 14, 24, 36]. Due to its excellent feature extraction capabilities, Transformers have also been introduced to low-level visual tasks, including single image super-resolution [21, 37, 43]. Classical SR models [18, 19, 30, 40] based on CNN architectures were limited by narrow receptive fields and limited feature interaction capabilities, and their effectiveness was gradually surpassed by Transformer-based approaches. For example, IPT [4] implements a pre-trained Transformer-based model for better super-resolution. SwinIR [22] improves image quality by using shifted window attention and residual blocks, effectively capturing a broad range of features for restoration. Subsequently, CAT [7] improves image restoration by using rectangle-window self-attention and axial shifting to enhance cross-window interaction. To address the perceptual limitations of window-based methods, several approaches have been proposed. HAT [6] combines channel and window-based attention to overcome these limitations and enhance cross-window interactions for superior image reconstruction. Another approach is ATD [41], which addresses the limitations of local windows by using an Adaptive-Token Dictionary and category-based self-attention to incorporate global information and enhance features. In addition, IPG [31] improves SR by prioritizing detail-rich pixels and using flexible local and global graphs to enhance reconstruction. Unlike existing methods, we + +propose a PFT method that can better focus on key tokens and filter out irrelevant features through PFA, thereby reducing the impact of irrelevant features on SR results and the computational effort. + +Transformer with Sparse Attention. The dense attention maps in Transformers may introduce features from irrelevant locations, which interferes with the effectiveness of feature extraction. To address this, many approaches explore how to leverage sparse attention calculations to better utilize relevant information. For example, NLSA [28] combines non-local operations with sparse representations, using dynamic sparse attention to focus on pertinent features, thereby improving efficiency and robustness while reducing computational costs. ART [39] enhances image restoration by combining both dense and sparse attention mechanisms, expanding the receptive field to enable more effective interactions and better feature representation. Additionally, a class of methods [35, 45] explicitly selects the most relevant positions in the attention map for retention, filtering out irrelevant information that might interfere with feature aggregation. Building on this, DRSformer [5] further develops the idea of sparse selection by introducing a learnable top- $k$ -selection operator, that adaptively retains the most relevant self-attention values, thus improving image restoration. We propose the PFT method, which connects isolated attention maps across the entire network to efficiently identify the positions each attention map collectively focuses on. PFA performs a Hadamard product on adjacent attention maps to pinpoint the most relevant attention locations, thereby enhancing the filtering of irrelevant information. + +# 3. Progressive Focused Transformer + +# 3.1. Preliminaries + +Self-Attention. The self-attention mechanism [33] is a fundamental part of Transformer, which computes the similarity between tokens and aggregates features based on the corresponding attention weights. + +Given the query matrix $\mathbf{Q} \in \mathbb{R}^{N \times d}$ , key matrix $\mathbf{K} \in \mathbb{R}^{N \times d}$ , the attention weights are calculated as follows: + +$$ +\mathbf {A} _ {s a} = \operatorname {S o f t m a x} \left(\mathbf {Q K} ^ {\top} / \sqrt {d}\right), \tag {1} +$$ + +where the $i$ -th row in $\mathbf{A}_{sa}$ represents normalized weights to aggregate value tokens $\mathbf{V} \in \mathbb{R}^{N \times d}$ and the output of self-attention module is obtained by $\mathbf{O}_{SA} = \mathbf{A}_{sa}\mathbf{K}$ . Although the exponential function in Softmax could suppress irrelevant tokens to some extent, the above vanilla self-attention still apply dense weights which utilize all the input tokens in the window to generate the final output. Moreover, another feature of the above self-attention lies in its computational overhead. The complexity of Eq. (1) grows quadratically with the number of tokens $N$ . Therefore, most existing + +methods need to perform self-attention calculations in small windows to manage this computational burden. + +Sparse Attention. To mitigate the negative impact of irrelevant features in the dense attention map, numerous sparse attention methods have been proposed. Generally speaking, the overall idea of sparse attention is to introduce a selection operation to sparsify the attention weights: + +$$ +\mathbf {A} _ {s s a} = \operatorname {S o f t m a x} \left(\mathcal {S} \left(\mathbf {Q K} ^ {\top} / \sqrt {d}\right)\right), \tag {2} +$$ + +where $S(\cdot)$ is a sparsification operation which removes the weights for less relevant tokens. The most commonly adopted sparsify operation is the top- $k$ selection, which only allows $K$ non-zero values in each row. Despite its strong capability of irrelevant token suppression, top- $k$ selection only adjusts aggregation weights according to a single step of similarity calculation and has limited ability to make effective use of highly relevant tokens. + +# 3.2. Progressive Focused Attention + +As reviewed in the previous section, although sparse attention methods are able to improve the vanilla self-attention by alleviating the negative impact of irrelevant tokens, they still have limited capability in further distinguishing highly relevant tokens from mildly relevant tokens. Moreover, both the vanilla and sparse attention methods fail to identify the relevant feature regions prior to similarity calculation, resulting in a significant amount of unnecessary calculations, which impedes the incorporation of additional input tokens. + +In this paper, we propose Progressive Focused Attention, which links the attention maps between adjacent layers to better aggregate relevant features. Generally, the proposed PFA advances the existing methods in two aspects. Firstly, PFA makes use of attention maps from previous layers to better weight input features. The weights of highly relevant tokens that are consistently similar to each other across layers will be enhanced during the cascade multiplication process. Secondly, PFA leverages the attention map of previous layers to identify irrelevant features for saving computational overhead. This selective calculation mechanism enables us to conduct self-attention within a larger window. In the remaining part of this section, we first introduce the basic idea of our PFA, which inherits the attention map from the previous layers through a Hadamard product. Then, we introduce how we could further leverage previous attention maps to reduce computational overhead. + +Progressive Attention Across Layers. As introduced in Eq. (1) and (2), the previous methods obtain attention weights merely according to the calculated similarities between tokens from the current layer. The standard similarity calculation has limited discriminative capability in boosting highly relevant tokens while suppressing less relevant tokens. To address this issue, we propose to inherit attention + +![](images/89f3984760226f1a873b496ba83a32f8c367515bebc76c2e808fb4747ee198da.jpg) +Figure 2. The overall architecture of PFT. PFA Block consists of $M$ Progressive Focused Attention Layers (PFAL). Each PFA takes both image features and aggregated PFA maps from previous layers as input. Sparse Matrix Multiplication (SMM) ensures each row of $Q$ interacts only with sparse columns of $K^T$ , producing calculated attention maps. After applying the Hadamard product and sparse focusing, PFA maps of the current layer are obtained and used with the $V$ matrix in an SMM operation to generate attention-aggregated features. + +weights from previous layers in a productive manner: + +$$ +\mathbf {A} ^ {l} = \operatorname {N o r m} \left(\mathbf {A} ^ {l - 1} \odot \mathbf {A} _ {\text {c a l}} ^ {l}\right), \tag {3} +$$ + +where $\mathbf{A}_{cal}^{l}$ is the calculated attention map for the $l$ -th layer according to the vanilla self-attention mechanism as in Eq. (1); $\mathbf{A}^{l - 1}$ is the attention map of the previous layer; Norm(\cdot) represents the row-wise normalization operation, which ensures the summation of each row to be 1. As indicated in Eq. (3), the final attention map in the $l$ -th layer is obtained by multiplying the calculated similarities with the attention map from the previous layer. Such a mechanism enables us to make a comprehensive assessment of token similarity: the weights for less relevant tokens will be wiped out during the successive multiplication process, while important tokens with high similarity values across layers will be assigned with larger weights after normalization. As will be validated in our ablation studies, with improved feature aggregation weights, such a Progressive Attention mechanism could deliver better SR results over the top- $k$ sparse attention as well as the standard self-attention block. + +Progressive Focused Attention. Since all the normalized similarities are less than 1, the above strategy of multiplicative attention inheritance could gradually filter out the impact of irrelevant tokens and obtain sparse weights as the network depth increases. Actually, based on the previous attention map $\mathbf{A}^{l - 1}$ , we are able to identify unimportant positions before calculation. Therefore, we can avoid unnecessary computations with a Sparse Matrix Multiplica + +tion (SMM) operation: + +$$ +\mathbf {A} _ {s c} ^ {l} = \operatorname {S o f t m a x} \left(\boldsymbol {\Psi} \left(\mathbf {Q} ^ {l}, \left(\mathbf {K} ^ {l}\right) ^ {\top}, \mathbf {I} ^ {l - 1}\right)\right), \tag {4} +$$ + +where $\Psi$ denotes the SMM operation; $\mathbf{I}^{l - 1}\in \mathbb{R}^{N\times N}$ is a sparse index matrix; we calculate $\mathbf{A}_{sc}^l (i,j)$ with $\mathbf{Q}^l (i,:)$ and $\mathbf{K}^l (j,:)^T$ only if $\mathbf{I}^{l - 1}(i,j) = 1$ , otherwise we set $\mathbf{A}_{sc}^l (i,j) = 0$ . Note that after the SMM operation we still need to normalize each row of the calculation results using the Softmax function. For an all-ones indexing matrix, the SMM operation in Eq. (4) is equivalent to the standard attention calculation process as in Eq. (1); However, if we are able to obtain a sparse $\mathbf{I}^{l - 1}$ prior to the calculation process, a significant portion of computations can be skipped. Due to our progressive attention mechanism, we utilize $\mathbf{A}^{l - 1}$ to indicate skippable positions. Specifically, inspired by the success of top- $k$ sparse attention, we only keep $K^l$ non-zero attention weights for each layer and generate the indexing matrix $\mathbf{I}^l$ according to the non-zero positions in $\mathbf{A}^l$ . To sum up, the attention map of our progressive focused attention is achieved through the following formula: + +$$ +\left\{ \begin{array}{l l} \mathbf {A} _ {s c} ^ {l} = S o f t m a x (\boldsymbol {\Psi} (\mathbf {Q} ^ {l}, (\mathbf {K} ^ {l}) ^ {\top}, \mathbf {I} ^ {l - 1})), \\ \mathbf {A} ^ {l} = \mathcal {S} _ {K ^ {l}} (N o r m (\mathbf {A} _ {s c} ^ {l} \odot \mathbf {A} ^ {l - 1})), \\ \mathbf {I} ^ {l} = \operatorname {S i g n} (\mathbf {A} ^ {l}), \end{array} \right. \tag {5} +$$ + +Where $S_{K^l}(\cdot)$ is the sparsification operation that selects the top $K^l$ values in each row and $\mathrm{Sign}(\cdot)$ generates a binary index matrix according to the sign of input matrix. Then, + +we can also use the SMM operation to calculate the output matrix of the $l$ -th layer: + +$$ +\mathbf {O} ^ {l} = \Psi (\mathbf {A} ^ {l}, \mathbf {V} ^ {l}, \mathbf {I} ^ {l}). \tag {6} +$$ + +For the first attention block, in which we do not have previous attention map, we simply set $\mathbf{A}^0$ and $\mathbf{I}^0$ as allones matrix and calculate $\mathbf{A}^1$ as standard self-attention in Eq. (1) to aggregate input features. For subsequent layers, we exploit the attention map from previous layer to generate better weights and filter out unnecessary computations as in Eq. (5). Since tokens which have been determined as irrelevant tokens to a specific query token in previous layers will not be considered in the following layers at all, to avoid filtering-out important tokens at early stages, we set $K^1 = N$ and gradually reduce the nonzero values with a focus ratio: $K^l = \alpha K^{l - 1}$ , where $K$ represents the number of retained attention values within the window. With $0 < \alpha < 1$ , our cascade PFA layers gradually focus on important candidates and reduce the number of key-tokens to be considered for each input query-token, resulting in significant reduction in computational burden for each window. Notably, using standard matrix multiplication to implement the SMM operation is highly inefficient. Therefore, we developed efficient CUDA kernels for SMM. This implementation significantly enhances the efficiency of our model, enabling PFT to achieve inference speeds comparable to those of existing methods. + +# 3.3. The Overall Network Architecture + +As illustrated in Fig. 2, the overall architecture of PFT follows the structure adopted in recent state-of-the-art Transformer-based SR models [6, 22, 41]. While, we replace the standard self-attention blocks with our proposed PFA block for the pursuit of better SR results. Notably, we also incorporate the shifted window approach from the Swin Transformer, though it is omitted in the illustration for simplicity. Thus, the attention map in PFA is passed from the first layer to the last through two pathways, divided by the shift operation into even and odd layers for focused processing. Additionally, we incorporate LePE positional encoding [12] during attention computation. For classical SR, the PFT network consists of 6 blocks, with the number of attention layers in each block being [4, 4, 4, 6, 6, 6]. The model utilizes multi-head attention with 6 attention heads, and the total number of channels is 240. The window size is $32 \times 32$ , and the number of retained attention values in each block is [1024, 256, 128, 64, 32, 16], respectively. For lightweight SR, the PFT-light network is composed of five blocks, with the number of attention layers in each block being [2, 4, 6, 6, 6]. It employs 4 attention heads, with a total of 52 channels. The window size is $32 \times 32$ , and the number of retained attention values in each block follows the pattern [1024, 256, 128, 64, 32]. + +Analysis of Computational Complexity. Self-Attention and sparse attention have the same computational cost, as both measure similarity with neighboring positions by interacting with tokens within non-overlapping windows. When the input feature map size is $h \times w \times C$ and the window size is $W \times W$ , the feature map is divided into $\frac{h}{W} \times \frac{w}{W}$ windows, each with $W \times W$ tokens. Assuming that the network has a total of $L$ attention layers, the computational complexity of the attention component for the entire network is: + +$$ +\Omega (S A) = 4 h w L C ^ {2} + 2 W ^ {2} h w L C. \tag {7} +$$ + +PFA can control the proportion of key tokens that are most relevant to the query features by adjusting the retention ratio $\alpha$ . The index matrix $\mathbf{I}$ allows shallow attention aggregation information to be carried into deeper layers for further focusing, resulting in a gradually decreasing $K$ . For a network with $L$ attention layers, we assume that the number of retained attention values within the window decreases, as expressed by the following formula: $K^{l} = \alpha K^{l - 1}$ , where $0 < \alpha < 1$ and $K^{-1}$ is generally set to $W^2$ . It can be represented as $K^{l} = W^{2}\alpha^{l - 1}$ . The overall computational complexity of the model is: + +$$ +\Omega (P F A) = \sum_ {l = 1} ^ {L} \left(4 h w C ^ {2} + 2 \alpha^ {(l - 1)} W ^ {2} h w C\right), \tag {8} +$$ + +where $\alpha^{(l-1)}$ controls the decay of the focus ratio across layers, with $0 < \alpha < 1$ . As $l$ increases, the focus ratio progressively decreases. The first term, $4hwC^2$ , represents the computational complexity of the projection layers. The second term, $2\alpha^{(l-1)}W^2hwC$ , accounts for the complexity of computing the similarity between the query and the selected key tokens, as well as redistributing the corresponding value information at the focused positions. Obviously, since $\alpha$ is less than 1, the complexity of this term decreases exponentially with depth. For example, with $\alpha = 0.5$ , the computational complexity is reduced to just $6.25\%$ of the original after four decay steps. + +# 4. Experiments + +# 4.1. Experiment Setting + +We use the DF2K dataset, which combines DIV2K [32] and Flickr2K [23], as our training set. To ensure fair comparisons, we adopt the same training configuration as utilized in recent SR studies [6, 31, 41]. Our model is trained for 500K iterations using the AdamW optimizer and an initial learning rate of $2 \times 10^{-4}$ . The input patch size for training is fixed at $64 \times 64$ , and we employ a MultistepLR scheduler, which reduces the learning rate by half at specified iterations [250000, 400000, 450000, 475000]. The batch size is set to 32. We evaluate our method on five standard benchmark datasets: Set5 [2], Set14 [38], BSD100 [26], + +
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
EDSR [23]×242.6M22.14T38.110.960233.920.919532.320.901332.930.935139.100.9773
RCAN [44]×215.4M7.02T38.270.961434.120.921632.410.902733.340.938439.440.9786
HAN [29]×263.6M7.24T38.270.961434.160.921732.410.902733.350.938539.460.9785
IPT [4]×2115M7.38T38.37-34.43-32.48-33.76---
SwinIR [22]×211.8M3.04T38.420.962334.460.925032.530.904133.810.943339.920.9797
CAT-A [7]×216.5M5.08T38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [39]×216.4M7.04T38.560.962934.590.926732.580.904834.300.945240.240.9808
HAT [6]×220.6M5.81T38.630.963034.860.927432.620.905334.450.946640.260.9809
IPG [31]×218.1M5.35T38.610.963234.730.927032.600.905234.480.946440.240.9810
ATD [41]×220.1M6.07T38.610.962934.950.927632.650.905634.700.947640.370.9810
PFT (Ours)×219.6M5.03T38.680.963535.000.928032.670.905834.900.949040.490.9815
EDSR [23]×343.0M9.82T34.650.928030.520.846229.250.809328.800.865334.170.9476
RCAN [44]×315.6M3.12T34.740.929930.650.848229.320.811129.090.870234.440.9499
HAN [29]×364.2M3.21T34.750.929930.670.848329.320.811029.100.870534.480.9500
IPT [4]×3116M3.28T34.81-30.85-29.38-29.49---
SwinIR [22]×311.9M1.35T34.970.931830.930.853429.460.814529.750.882635.120.9537
CAT-A [7]×316.6M2.26T35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [39]×316.6M3.12T35.070.932531.020.854129.510.815930.100.887135.390.9548
HAT [6]×320.8M2.58T35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG [31]×318.3M2.39T35.100.933231.100.855429.530.816830.360.890135.530.9554
ATD [41]×320.3M2.69T35.110.933031.130.855629.570.817630.460.891735.630.9558
PFT (Ours)×319.8M2.23T35.150.933331.160.856129.580.817830.560.893135.670.9560
EDSR [23]×443.0M5.54T32.460.896828.800.787627.710.742026.640.803331.020.9148
RCAN [44]×415.6M1.76T32.630.900228.870.788927.770.743626.820.808731.220.9173
HAN [29]×464.2M1.81T32.640.900228.900.789027.800.744226.850.809431.420.9177
IPT [4]×4116M1.85T32.64-29.01-27.82-27.26---
SwinIR [22]×411.9M0.76T32.920.904429.090.795027.920.748927.450.825432.030.9260
CAT-A [7]×416.6M1.27T33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [39]×416.6M1.76T33.040.905129.160.795827.970.751027.770.832132.310.9283
HAT [6]×420.8M1.45T33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG [31]×417.0M1.30T33.150.906229.240.797327.990.751928.130.839232.530.9300
ATD [41]×420.3M1.52T33.100.905829.240.797428.010.752628.170.840432.620.9306
PFT (Ours)×419.8M1.26T33.150.906529.290.797828.020.752728.200.841232.630.9306
+ +Table 1. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on classical SR task. The best and second best results are colored with red and blue. + +Urban100 [16], and Manga109 [27]. In addition, the computational costs of all models in this paper are measured at an output resolution of $1280 \times 640$ . + +# 4.2. Comparison with State-of-the-Art Methods + +We compare the performance of our model with various SR baselines on widely used benchmark datasets, including Set5 [2], Set14 [38], BSD100 [26], Urban100 [16], and Manga109 [27]. These SR methods include both classical and state-of-the-art approaches, such as EDSR [23], RCAN [44], HAN [29], IPT [4], SwinIR [8], CAT [7], ART [39], HAT [6], IPG [31], and ATD [41]. We use PSNR and SSIM metrics to assess the performance of SR models at $\times 2$ , $\times 3$ , and $\times 4$ upscaling factors. All computational costs are calculated at the output resolution of $1280\times 640$ , and PFT uses a window size of $32\times 32$ . + +The results, shown in Tab. 1, indicate that the proposed PFT model achieves superior performance over ATD, with significantly reduced computational costs. Notably, PFT reduces computational load by $17.1\%$ compared to ATD, while attaining the highest PSNR in most datasets. For lightweight SR tasks, we further compare our model with other efficient SR methods, including CARN [1], IMDN [17], LAPAR [20], LatticeNet [25], SwinIR [8], SwinIR-NG [8], ELAN [42], and OmniSR [34]. As shown in Tab. 2, the proposed PFT-light outperforms the + +recently introduced ATD-light [41] on nearly all benchmark datasets, while reducing computational complexity by $20.1\%$ . On the $\times 2$ Urban100 benchmark, PFT-light outperforms ATD-light by 0.40dB and IPG-Tiny by 0.63dB. For the $\times 4$ SR experiments, PFT-light also outperforms IPG Tiny by 0.42dB and ATD-light by 0.23dB on the Urban100 test set. The superior performance of PFT can be attributed to its use of Progressive Focused Attention, which connects otherwise isolated attention maps across the network. This enables the model to focus on essential features, filter out irrelevant patches, substantially reduce computational costs, and support the use of larger window sizes. + +![](images/0ad7c72860c53ecd930625860b0371c1de4310305ccbb9a39d26f2d098faa37c.jpg) +Figure 3. Visual comparison of attention distributions in the 18th layer. SA and top- $k$ Attention distribute attention broadly, failing to focus on the most relevant areas. In contrast, PFA filters out irrelevant tokens and concentrates attention on key regions. By reducing computational costs, it enables the use of a larger $32 \times 32$ window for more extensive feature interactions. + +
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
CARN [1]×21,592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [17]×2694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [20]×2548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [25]×2756K169.5G38.150.961033.780.919332.250.900532.430.9302--
SwinIR-light [22]×2910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [42]×2582K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [8]×21181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
OmniSR [34]×2772K194.5G38.220.961333.980.921032.360.902033.050.936339.280.9784
IPG-Tiny [31]×2872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
ATD-light [41]×2753K348.6G38.280.961634.110.921732.390.902333.270.937639.510.9789
PFT-light (Ours)×2776K278.3G38.360.962034.190.923232.430.903033.670.941139.550.9792
CARN [1]×31,592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [17]×3703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [20]×3544K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [25]×3765K76.3G34.530.928130.390.842429.150.805928.330.8538--
SwinIR-light [22]×3918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [42]×3590K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [8]×31190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
OmniSR [34]×3780K88.4G34.700.929430.570.846929.280.809428.840.865634.220.9487
IPG-Tiny [31]×2878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
ATD-light [41]×3760K154.7G34.700.930030.680.848529.320.810929.160.871034.600.9505
PFT-light (ours)×3783K123.5G34.810.930530.750.849329.330.811629.430.875934.600.9510
CARN [1]×41,592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [17]×4715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [20]×4659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [25]×4777K43.6G32.300.896228.680.783027.620.736726.250.7873--
SwinIR-light [22]×4930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [42]×4582K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [8]×41201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
OmniSR [34]×4792K50.9G32.490.898828.780.785927.710.741526.650.801831.020.9151
IPG-Tiny [31]×4887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
ATD-light [41]×4769K87.1G32.620.899728.870.788427.770.743926.970.810731.470.9198
PFT-light (Ours)×4792K69.6G32.630.900528.920.789127.790.744527.200.817131.510.9204
+ +Visual comparison of attention distribution. The attention distribution visualizations are shown in Fig. 3. The attention distributions of the Vanilla Self-Attention and top-k Attention methods are relatively scattered, failing to allocate attention to the regions most relevant to the current query. In contrast, our PFA method filters out irrelevant tokens and focuses on most important positions. It also lowers computation costs, enabling larger $32 \times 32$ windows for broader feature interactions. + +Visual comparison of SR reconstruction results. To evaluate the quality of different super-resolution methods, we show visual examples in Fig. 4. These comparisons demonstrate the strength of our PFT approach in restoring sharp edges and fine textures from low-resolution images. For example, in img_001 and img_095, most methods struggle to reconstruct textures accurately, leading to noticeable distortions. Similarly, in the zebra and barbara images, many methods fail to recover details, resulting in blurry or incorrect textures. In contrast, our PFT effectively captures fine textures by focusing on the most relevant features. This ability to selectively attend helps restore clean edges and reduce artifacts, producing more accurate reconstructions. + +# 4.3. Ablation Study + +We conduct ablation studies on the proposed PFT-light model, with all models trained for 250k iterations on the DIV2K dataset at $\times 4$ scale. Except for the experiments on + +window size, all other experiments use a window size of $16 \times 16$ . In top- $k$ Attention, the value of $k$ is set to half the number of window elements, which is 128. + +Effectiveness of Progressive Focused Attention. We conducted experiments to demonstrate the effectiveness of the proposed Progressive Attention and Progressive Focused Attention, with results presented in Tab. 3. These experiments compare the quantitative performance of $\times 4$ super-resolution on the Set5, Urban100, and Manga109 datasets. Progressive Attention applies a straightforward Hadamard product connection of the attention maps. As shown, even the Progressive Attention provides notable performance improvements over Self-Attention and top- $k$ Attention. Progressive Focused Attention achieved the best results with a $27.69\%$ reduction in computation, and notably increasing PSNR by 0.36dB on the Urban100 dataset. The effectiveness of PFA lies in its ability to link adjacent attention maps across the network via the Hadamard product, allowing the model to reduce redundant computations and focus on the most relevant tokens. + +Table 2. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on lightweight SR task. The best and second best results are colored with red and blue. + +
MethodFLOPsSet5Urban100Manga109
Vanilla Self-Attention70.4G32.2826.2630.62
Top-k Attention70.4G32.3026.2930.67
Progressive Attention70.4G32.3526.4130.78
Progressive Focused Attention50.9G32.4126.6230.85
+ +Table 3. Ablation study on the proposed focused attention. + +![](images/dfd4ad0d0122ada1d7b87ecbcee880e5c6bfc2312408fad0c788fd0b09653ce7.jpg) +Figure 4. Visual comparison of SR reconstruction results. + +Effects of focus ratio. As discussed in Sec. 3.2, the parameter $\alpha$ controls the focus degree of Progressive Focused Attention as network depth increases. A smaller $\alpha$ retains fewer attention positions, accelerating the focusing process. However, $\alpha$ is generally kept above 0.1, as a rapid reduction in attention retention may cause the network to make premature choices. As shown in Tab. 4, model performance is optimal when $\alpha$ is around 0.5. Experimental results indicate that both excessively large and small values of $\alpha$ can hinder effective attention focusing. A very small $\alpha$ may cause the network to overlook important tokens, leading to incomplete representations. On the other hand, a large $\alpha$ keeps too many irrelevant tokens, weakening the focus and limiting the network's ability to reduce noise. + +
Focus ratio0.10.30.50.70.9
PSNR26.4826.5826.6226.6126.56
+ +Effects of different window sizes. The window size determines the model's scope of correlation extraction and significant impact on reconstruction performance. Previous studies have shown that larger windows yield better reconstruction results for image super-resolution tasks. However, due to the quadratic complexity of self-attention, previous methods find it challenging to use large windows effectively. Our PFA dynamically filters out patches irrelevant to the current query patch. This allows us to select the interaction scope before computing similarity. As a result, the overall computational load is greatly reduced. This enables us to use large windows while maintaining a low computational cost. As shown in Tab. 5, reconstruction performance + +improves as the window size increases. We ultimately select a window size of $32 \times 32$ to balance performance, model parameters, and computational cost. + +Table 4. Ablation study on focus ratio for $\times 4$ SR,evaluated on Urban100. + +
Window sizeSet5Urban100Manga109
8 × 832.3326.4030.71
16 × 1632.4126.6230.85
32 × 3232.4926.8130.93
+ +Table 5. Ablation study on window sizes for $\times 4$ SR,evaluated on the Urban100 dataset, with PSNR as the evaluation metric. + +# 5. Conclusion + +We propose the PFT, which introduces a novel approach to linking attention maps across layers through the key innovation of the PFA mechanism, progressively refining the focus on relevant features. By inheriting and modifying attention maps from previous layers, the PFA mechanism reduces unnecessary similarity calculations, improving attention efficiency. This enables the model to prioritize the most relevant tokens while effectively suppressing the influence of irrelevant ones. Experiments show that PFT and PFT-light achieves leading performance in single-image super-resolution with lower computation. As a key component of the Progressive Focused Transformer, PFA has proven to be both effective and efficient for super-resolution tasks. We look forward to exploring its potential in other high-level vision tasks, as well as in natural language processing. + +# Acknowledgement + +This work was supported by the National Natural Science Foundation of China (No. 62476051) and the Sichuan Natural Science Foundation (No. 2024NSFTD0041). + +# References + +[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. Fast, accurate, and lightweight super-resolution with cascading residual network. In Proceedings of the European conference on computer vision, pages 252-268, 2018. 6, 7 +[2] Marco Bevilacqua, Aline Roumy, Christine Guillemot, and Marie Line Alberi-Morel. Low-complexity single-image super-resolution based on nonnegative neighbor embedding. 2012. 5, 6 +[3] Jiezhang Cao, Yawei Li, Kai Zhang, and Luc Van Gool. Video super-resolution transformer. arXiv preprint arXiv:2106.06847, 2021. 2 +[4] Hanting Chen, Yunhe Wang, Tianyu Guo, Chang Xu, Yiping Deng, Zhenhua Liu, Siwei Ma, Chunjing Xu, Chao Xu, and Wen Gao. 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Comparison of different attention mechanisms. (a) Vanilla self-attention calculates attention weights in the whole window and generates non-zero weights for both highly relevant and less relevant tokens. (b) Sparse Attention is able to filter out the impact of less relevant tokens with small weights, but still requires the calculation of attention weights for all tokens. (c) Progressive Focused Attention connects isolated attention maps, leveraging attention weights to skip unnecessary computations and better aggregate relevant tokens." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 566, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 555, + 674 + ], + "type": "text", + "content": "promising reconstruction results. Due to the limitations of convolution operations, these methods can capture only local feature information. Many studies have focused on enabling networks to achieve broader feature interaction to improve image restoration. Recently, Transformer-based methods [6, 22, 42, 46] have been increasingly applied to image reconstruction, owing to their ability to effectively leverage long-range dependencies, thereby enhancing the recovery of detailed information in images." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Transformer-based super-resolution methods utilize cascaded self-attention blocks to recover the missing High-Resolution (HR) details. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 143, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 143, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 143, + 712 + ], + "type": "text", + "content": "* Corresponding author" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2279" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "content": "block is the attention map, which determines how the input features are aggregated to generate output features. Due to the quadratic computational complexity of the self-attention mechanism, most of the existing methods confine attention computation within local windows and only aggregate a limited number of tokens to update image features. Therefore, how to exploit information of relevant tokens while alleviating the disruption from irrelevant tokens is critical in Transformer-based SR models. For the pursuit of high-quality SR results, one category of research tries to enrich the information source by enlarging the window size [6, 46], leveraging cross-window information [7], and introducing an external token dictionary [41]. Since more information can be incorporated into the weighted feature updating process, these methods have shown promising capability in delivering superior SR results. However, calculating similarities between more tokens inevitably leads to extra computational footprint. These methods still need to compromise on model overhead and introduce limited extra information. Another category of studies investigates sophisticated weighting strategies to make better use of input information [5, 28]. Instead of combining all the tokens according to the normalized productive similarities, as in a vanilla self-attention block, various elaborately designed weighting mechanisms have been exploited to make better use of highly relevant tokens while at the same time filtering out less relevant tokens. While the overall concept of seeking more rational weights is highly appealing, the challenge of obtaining enhanced attention weights remains an open problem in the literature." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": "In this paper, we link the attention maps between adjacent layers and propose a Progressive Focused Attention (PFA) block to better leverage input tokens across a wider range. Instead of combining input features merely according to the calculated attention map " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{cal}^{l}" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": ", we inherit attention information from the previous block in a productive manner " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l} = \\text{Norm}(\\mathbf{A}^{l-1} \\odot \\mathbf{A}_{cal}^{l})" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\text{Norm}(\\cdot)" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": " is the row-wise normalization operation. Such an attention inheritance mechanism enables our method to make a comprehensive measurement of token similarity: tokens that are consistently similar to each other are empowered with larger weights to help each other while the weights of irrelevant tokens are suppressed during the cascaded multiplications. Furthermore, in addition to boosting weights for important tokens and suppressing weights for less relevant tokens, another advantage of our PFA lies in its calculation pre-filtering capability. Specifically, since the final attention map " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l}" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": " will be multiplied by the previous attention map " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l-1}" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": ", small weights in " + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l-1}" + }, + { + "bbox": [ + 57, + 439, + 294, + 712 + ], + "type": "text", + "content": " are a sign of unimportant tokens, for which the weight calculation process can be skipped. As shown in Fig.1, the previous attention map not only helps our PFA block to generate better weights which emphasize highly relevant tokens, but also enables" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 317, + 73, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 73, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 553, + 132 + ], + "type": "text", + "content": "it to skip unnecessary similarity calculations so that we are able to afford the computational overhead of large window. Therefore, with comparable computational resources, our SR model could employ a larger window size to leverage input tokens from a broader range." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 328, + 133, + 534, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 133, + 534, + 144 + ], + "spans": [ + { + "bbox": [ + 328, + 133, + 534, + 144 + ], + "type": "text", + "content": "The main contributions of this paper are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 316, + 146, + 553, + 335 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 317, + 146, + 553, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 146, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 317, + 146, + 553, + 217 + ], + "type": "text", + "content": "- We propose the idea of Progressive Focused Attention (PFA) which inherits attention weights from previous layers in a productive manner. PFA not only avoids unnecessary similarity computation with less relevant tokens but also endows highly relevant tokens with larger weights to better enhance the input feature." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 316, + 217, + 553, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 217, + 553, + 288 + ], + "spans": [ + { + "bbox": [ + 316, + 217, + 553, + 288 + ], + "type": "text", + "content": "- We instantiate a Progressive Focused Transformer (PFT) for image super-resolution, which takes the progressive focusing benefits of PFA and systematically arranges computational resources for different layers. This property enables the PFT to leverage the merit of large window while maintaining model efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 289, + 553, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 289, + 553, + 335 + ], + "spans": [ + { + "bbox": [ + 316, + 289, + 553, + 335 + ], + "type": "text", + "content": "- We conduct extensive experiments on super-resolution benchmarks. Our superior experimental results over recent state-of-the-art methods as well as our detailed ablation studies demonstrate the effectiveness of our method." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 347, + 400, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 347, + 400, + 358 + ], + "spans": [ + { + "bbox": [ + 317, + 347, + 400, + 358 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 367, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 367, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 315, + 367, + 553, + 712 + ], + "type": "text", + "content": "Transformer-based SR. Transformer models were initially used for natural language processing [9, 33]. Subsequently, they have attracted extensive research interest in the field of computer vision [3, 13, 14, 24, 36]. Due to its excellent feature extraction capabilities, Transformers have also been introduced to low-level visual tasks, including single image super-resolution [21, 37, 43]. Classical SR models [18, 19, 30, 40] based on CNN architectures were limited by narrow receptive fields and limited feature interaction capabilities, and their effectiveness was gradually surpassed by Transformer-based approaches. For example, IPT [4] implements a pre-trained Transformer-based model for better super-resolution. SwinIR [22] improves image quality by using shifted window attention and residual blocks, effectively capturing a broad range of features for restoration. Subsequently, CAT [7] improves image restoration by using rectangle-window self-attention and axial shifting to enhance cross-window interaction. To address the perceptual limitations of window-based methods, several approaches have been proposed. HAT [6] combines channel and window-based attention to overcome these limitations and enhance cross-window interactions for superior image reconstruction. Another approach is ATD [41], which addresses the limitations of local windows by using an Adaptive-Token Dictionary and category-based self-attention to incorporate global information and enhance features. In addition, IPG [31] improves SR by prioritizing detail-rich pixels and using flexible local and global graphs to enhance reconstruction. Unlike existing methods, we" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "2280" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "propose a PFT method that can better focus on key tokens and filter out irrelevant features through PFA, thereby reducing the impact of irrelevant features on SR results and the computational effort." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 122, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 122, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 56, + 122, + 296, + 434 + ], + "type": "text", + "content": "Transformer with Sparse Attention. The dense attention maps in Transformers may introduce features from irrelevant locations, which interferes with the effectiveness of feature extraction. To address this, many approaches explore how to leverage sparse attention calculations to better utilize relevant information. For example, NLSA [28] combines non-local operations with sparse representations, using dynamic sparse attention to focus on pertinent features, thereby improving efficiency and robustness while reducing computational costs. ART [39] enhances image restoration by combining both dense and sparse attention mechanisms, expanding the receptive field to enable more effective interactions and better feature representation. Additionally, a class of methods [35, 45] explicitly selects the most relevant positions in the attention map for retention, filtering out irrelevant information that might interfere with feature aggregation. Building on this, DRSformer [5] further develops the idea of sparse selection by introducing a learnable top-" + }, + { + "bbox": [ + 56, + 122, + 296, + 434 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 56, + 122, + 296, + 434 + ], + "type": "text", + "content": "-selection operator, that adaptively retains the most relevant self-attention values, thus improving image restoration. We propose the PFT method, which connects isolated attention maps across the entire network to efficiently identify the positions each attention map collectively focuses on. PFA performs a Hadamard product on adjacent attention maps to pinpoint the most relevant attention locations, thereby enhancing the filtering of irrelevant information." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 445, + 242, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 242, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 242, + 458 + ], + "type": "text", + "content": "3. Progressive Focused Transformer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 465, + 141, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 141, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 141, + 477 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 483, + 295, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 530 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 530 + ], + "type": "text", + "content": "Self-Attention. The self-attention mechanism [33] is a fundamental part of Transformer, which computes the similarity between tokens and aggregates features based on the corresponding attention weights." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "text", + "content": "Given the query matrix " + }, + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "text", + "content": ", key matrix " + }, + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{K} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 55, + 530, + 295, + 555 + ], + "type": "text", + "content": ", the attention weights are calculated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 564, + 295, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 564, + 295, + 586 + ], + "spans": [ + { + "bbox": [ + 111, + 564, + 295, + 586 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {s a} = \\operatorname {S o f t m a x} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right), \\tag {1}", + "image_path": "b11620d447e1aa4aec0149e0ea4d1c9d3a7a12bb64ec0bcdd9840d5b81dfc9e8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "-th row in " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{sa}" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " represents normalized weights to aggregate value tokens " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " and the output of self-attention module is obtained by " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_{SA} = \\mathbf{A}_{sa}\\mathbf{K}" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": ". Although the exponential function in Softmax could suppress irrelevant tokens to some extent, the above vanilla self-attention still apply dense weights which utilize all the input tokens in the window to generate the final output. Moreover, another feature of the above self-attention lies in its computational overhead. The complexity of Eq. (1) grows quadratically with the number of tokens " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": ". Therefore, most existing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "content": "methods need to perform self-attention calculations in small windows to manage this computational burden." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 102, + 555, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 102, + 555, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 555, + 162 + ], + "type": "text", + "content": "Sparse Attention. To mitigate the negative impact of irrelevant features in the dense attention map, numerous sparse attention methods have been proposed. Generally speaking, the overall idea of sparse attention is to introduce a selection operation to sparsify the attention weights:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 358, + 166, + 555, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 166, + 555, + 186 + ], + "spans": [ + { + "bbox": [ + 358, + 166, + 555, + 186 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {s s a} = \\operatorname {S o f t m a x} \\left(\\mathcal {S} \\left(\\mathbf {Q K} ^ {\\top} / \\sqrt {d}\\right)\\right), \\tag {2}", + "image_path": "0983c9870fa7691ab6b356cdc5693721ccf4367c1b3076ccb54f892b66192a6d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "content": " is a sparsification operation which removes the weights for less relevant tokens. The most commonly adopted sparsify operation is the top-" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "content": " selection, which only allows " + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "content": " non-zero values in each row. Despite its strong capability of irrelevant token suppression, top-" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 191, + 555, + 287 + ], + "type": "text", + "content": " selection only adjusts aggregation weights according to a single step of similarity calculation and has limited ability to make effective use of highly relevant tokens." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 298, + 479, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 298, + 479, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 479, + 311 + ], + "type": "text", + "content": "3.2. Progressive Focused Attention" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 316, + 554, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 554, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 554, + 422 + ], + "type": "text", + "content": "As reviewed in the previous section, although sparse attention methods are able to improve the vanilla self-attention by alleviating the negative impact of irrelevant tokens, they still have limited capability in further distinguishing highly relevant tokens from mildly relevant tokens. Moreover, both the vanilla and sparse attention methods fail to identify the relevant feature regions prior to similarity calculation, resulting in a significant amount of unnecessary calculations, which impedes the incorporation of additional input tokens." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 424, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 424, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 424, + 555, + 628 + ], + "type": "text", + "content": "In this paper, we propose Progressive Focused Attention, which links the attention maps between adjacent layers to better aggregate relevant features. Generally, the proposed PFA advances the existing methods in two aspects. Firstly, PFA makes use of attention maps from previous layers to better weight input features. The weights of highly relevant tokens that are consistently similar to each other across layers will be enhanced during the cascade multiplication process. Secondly, PFA leverages the attention map of previous layers to identify irrelevant features for saving computational overhead. This selective calculation mechanism enables us to conduct self-attention within a larger window. In the remaining part of this section, we first introduce the basic idea of our PFA, which inherits the attention map from the previous layers through a Hadamard product. Then, we introduce how we could further leverage previous attention maps to reduce computational overhead." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 555, + 713 + ], + "type": "text", + "content": "Progressive Attention Across Layers. As introduced in Eq. (1) and (2), the previous methods obtain attention weights merely according to the calculated similarities between tokens from the current layer. The standard similarity calculation has limited discriminative capability in boosting highly relevant tokens while suppressing less relevant tokens. To address this issue, we propose to inherit attention" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "2281" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 78, + 531, + 293 + ], + "blocks": [ + { + "bbox": [ + 72, + 78, + 531, + 293 + ], + "lines": [ + { + "bbox": [ + 72, + 78, + 531, + 293 + ], + "spans": [ + { + "bbox": [ + 72, + 78, + 531, + 293 + ], + "type": "image", + "image_path": "89f3984760226f1a873b496ba83a32f8c367515bebc76c2e808fb4747ee198da.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "lines": [ + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "text", + "content": "Figure 2. The overall architecture of PFT. PFA Block consists of " + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "text", + "content": " Progressive Focused Attention Layers (PFAL). Each PFA takes both image features and aggregated PFA maps from previous layers as input. Sparse Matrix Multiplication (SMM) ensures each row of " + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "text", + "content": " interacts only with sparse columns of " + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "inline_equation", + "content": "K^T" + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "text", + "content": ", producing calculated attention maps. After applying the Hadamard product and sparse focusing, PFA maps of the current layer are obtained and used with the " + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 54, + 308, + 555, + 353 + ], + "type": "text", + "content": " matrix in an SMM operation to generate attention-aggregated features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 365, + 272, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 272, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 272, + 376 + ], + "type": "text", + "content": "weights from previous layers in a productive manner:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 386, + 295, + 402 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 386, + 295, + 402 + ], + "spans": [ + { + "bbox": [ + 115, + 386, + 295, + 402 + ], + "type": "interline_equation", + "content": "\\mathbf {A} ^ {l} = \\operatorname {N o r m} \\left(\\mathbf {A} ^ {l - 1} \\odot \\mathbf {A} _ {\\text {c a l}} ^ {l}\\right), \\tag {3}", + "image_path": "df02710b238e63ea9bcd5df5834fd4090555340f2bba31dd80444eeb147f87b2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{cal}^{l}" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": " is the calculated attention map for the " + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": "-th layer according to the vanilla self-attention mechanism as in Eq. (1); " + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l - 1}" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": " is the attention map of the previous layer; Norm(\\cdot) represents the row-wise normalization operation, which ensures the summation of each row to be 1. As indicated in Eq. (3), the final attention map in the " + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": "-th layer is obtained by multiplying the calculated similarities with the attention map from the previous layer. Such a mechanism enables us to make a comprehensive assessment of token similarity: the weights for less relevant tokens will be wiped out during the successive multiplication process, while important tokens with high similarity values across layers will be assigned with larger weights after normalization. As will be validated in our ablation studies, with improved feature aggregation weights, such a Progressive Attention mechanism could deliver better SR results over the top-" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 54, + 413, + 295, + 616 + ], + "type": "text", + "content": " sparse attention as well as the standard self-attention block." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "content": "Progressive Focused Attention. Since all the normalized similarities are less than 1, the above strategy of multiplicative attention inheritance could gradually filter out the impact of irrelevant tokens and obtain sparse weights as the network depth increases. Actually, based on the previous attention map " + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l - 1}" + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "content": ", we are able to identify unimportant positions before calculation. Therefore, we can avoid unnecessary computations with a Sparse Matrix Multiplica" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 365, + 408, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 408, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 408, + 376 + ], + "type": "text", + "content": "tion (SMM) operation:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 351, + 384, + 555, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 384, + 555, + 399 + ], + "spans": [ + { + "bbox": [ + 351, + 384, + 555, + 399 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {s c} ^ {l} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {\\Psi} \\left(\\mathbf {Q} ^ {l}, \\left(\\mathbf {K} ^ {l}\\right) ^ {\\top}, \\mathbf {I} ^ {l - 1}\\right)\\right), \\tag {4}", + "image_path": "dfe649daa2d2dd6ed02a6846fd850554c6ca7620d5711609dda9815bd0941285.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " denotes the SMM operation; " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{l - 1}\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " is a sparse index matrix; we calculate " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{sc}^l (i,j)" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^l (i,:)" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^l (j,:)^T" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " only if " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{l - 1}(i,j) = 1" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": ", otherwise we set " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{sc}^l (i,j) = 0" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": ". Note that after the SMM operation we still need to normalize each row of the calculation results using the Softmax function. For an all-ones indexing matrix, the SMM operation in Eq. (4) is equivalent to the standard attention calculation process as in Eq. (1); However, if we are able to obtain a sparse " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{l - 1}" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " prior to the calculation process, a significant portion of computations can be skipped. Due to our progressive attention mechanism, we utilize " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{l - 1}" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " to indicate skippable positions. Specifically, inspired by the success of top-" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " sparse attention, we only keep " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "K^l" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " non-zero attention weights for each layer and generate the indexing matrix " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^l" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": " according to the non-zero positions in " + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^l" + }, + { + "bbox": [ + 313, + 408, + 555, + 615 + ], + "type": "text", + "content": ". To sum up, the attention map of our progressive focused attention is achieved through the following formula:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 344, + 624, + 555, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 624, + 555, + 669 + ], + "spans": [ + { + "bbox": [ + 344, + 624, + 555, + 669 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l l} \\mathbf {A} _ {s c} ^ {l} = S o f t m a x (\\boldsymbol {\\Psi} (\\mathbf {Q} ^ {l}, (\\mathbf {K} ^ {l}) ^ {\\top}, \\mathbf {I} ^ {l - 1})), \\\\ \\mathbf {A} ^ {l} = \\mathcal {S} _ {K ^ {l}} (N o r m (\\mathbf {A} _ {s c} ^ {l} \\odot \\mathbf {A} ^ {l - 1})), \\\\ \\mathbf {I} ^ {l} = \\operatorname {S i g n} (\\mathbf {A} ^ {l}), \\end{array} \\right. \\tag {5}", + "image_path": "980e66667e0c3919712cbfe07de51e349028eb9113d02eeca86e72ba7d253443.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "S_{K^l}(\\cdot)" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " is the sparsification operation that selects the top " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "K^l" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " values in each row and " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Sign}(\\cdot)" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " generates a binary index matrix according to the sign of input matrix. Then," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2282" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": "we can also use the SMM operation to calculate the output matrix of the " + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": "-th layer:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 103, + 295, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 103, + 295, + 119 + ], + "spans": [ + { + "bbox": [ + 132, + 103, + 295, + 119 + ], + "type": "interline_equation", + "content": "\\mathbf {O} ^ {l} = \\Psi (\\mathbf {A} ^ {l}, \\mathbf {V} ^ {l}, \\mathbf {I} ^ {l}). \\tag {6}", + "image_path": "cb0a025190b77f752aff5f10694c51178207e8f808e7e7d4aade956368537820.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": "For the first attention block, in which we do not have previous attention map, we simply set " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^0" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^0" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": " as allones matrix and calculate " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^1" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": " as standard self-attention in Eq. (1) to aggregate input features. For subsequent layers, we exploit the attention map from previous layer to generate better weights and filter out unnecessary computations as in Eq. (5). Since tokens which have been determined as irrelevant tokens to a specific query token in previous layers will not be considered in the following layers at all, to avoid filtering-out important tokens at early stages, we set " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "K^1 = N" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": " and gradually reduce the nonzero values with a focus ratio: " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "K^l = \\alpha K^{l - 1}" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": " represents the number of retained attention values within the window. With " + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "inline_equation", + "content": "0 < \\alpha < 1" + }, + { + "bbox": [ + 55, + 126, + 296, + 403 + ], + "type": "text", + "content": ", our cascade PFA layers gradually focus on important candidates and reduce the number of key-tokens to be considered for each input query-token, resulting in significant reduction in computational burden for each window. Notably, using standard matrix multiplication to implement the SMM operation is highly inefficient. Therefore, we developed efficient CUDA kernels for SMM. This implementation significantly enhances the efficiency of our model, enabling PFT to achieve inference speeds comparable to those of existing methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 409, + 241, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 409, + 241, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 241, + 421 + ], + "type": "text", + "content": "3.3. The Overall Network Architecture" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "text", + "content": "As illustrated in Fig. 2, the overall architecture of PFT follows the structure adopted in recent state-of-the-art Transformer-based SR models [6, 22, 41]. While, we replace the standard self-attention blocks with our proposed PFA block for the pursuit of better SR results. Notably, we also incorporate the shifted window approach from the Swin Transformer, though it is omitted in the illustration for simplicity. Thus, the attention map in PFA is passed from the first layer to the last through two pathways, divided by the shift operation into even and odd layers for focused processing. Additionally, we incorporate LePE positional encoding [12] during attention computation. For classical SR, the PFT network consists of 6 blocks, with the number of attention layers in each block being [4, 4, 4, 6, 6, 6]. The model utilizes multi-head attention with 6 attention heads, and the total number of channels is 240. The window size is " + }, + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "text", + "content": ", and the number of retained attention values in each block is [1024, 256, 128, 64, 32, 16], respectively. For lightweight SR, the PFT-light network is composed of five blocks, with the number of attention layers in each block being [2, 4, 6, 6, 6]. It employs 4 attention heads, with a total of 52 channels. The window size is " + }, + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 55, + 426, + 296, + 714 + ], + "type": "text", + "content": ", and the number of retained attention values in each block follows the pattern [1024, 256, 128, 64, 32]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": "Analysis of Computational Complexity. Self-Attention and sparse attention have the same computational cost, as both measure similarity with neighboring positions by interacting with tokens within non-overlapping windows. When the input feature map size is " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "h \\times w \\times C" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " and the window size is " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "W \\times W" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": ", the feature map is divided into " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "\\frac{h}{W} \\times \\frac{w}{W}" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " windows, each with " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "W \\times W" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " tokens. Assuming that the network has a total of " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " attention layers, the computational complexity of the attention component for the entire network is:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 361, + 185, + 555, + 200 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 185, + 555, + 200 + ], + "spans": [ + { + "bbox": [ + 361, + 185, + 555, + 200 + ], + "type": "interline_equation", + "content": "\\Omega (S A) = 4 h w L C ^ {2} + 2 W ^ {2} h w L C. \\tag {7}", + "image_path": "26e7fe6417c90e75145fb657f6c288e3d6c9ec354aa9314e108c7dd04bd63a6d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": "PFA can control the proportion of key tokens that are most relevant to the query features by adjusting the retention ratio " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": ". The index matrix " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": " allows shallow attention aggregation information to be carried into deeper layers for further focusing, resulting in a gradually decreasing " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": ". For a network with " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": " attention layers, we assume that the number of retained attention values within the window decreases, as expressed by the following formula: " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "K^{l} = \\alpha K^{l - 1}" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "0 < \\alpha < 1" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "K^{-1}" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": " is generally set to " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "W^2" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": ". It can be represented as " + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "inline_equation", + "content": "K^{l} = W^{2}\\alpha^{l - 1}" + }, + { + "bbox": [ + 313, + 205, + 556, + 338 + ], + "type": "text", + "content": ". The overall computational complexity of the model is:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 329, + 350, + 555, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 350, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 329, + 350, + 555, + 384 + ], + "type": "interline_equation", + "content": "\\Omega (P F A) = \\sum_ {l = 1} ^ {L} \\left(4 h w C ^ {2} + 2 \\alpha^ {(l - 1)} W ^ {2} h w C\\right), \\tag {8}", + "image_path": "656acc267eb3b0a597e62e7509814995851ff39d9fc8655ebb6002204f0258d6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "\\alpha^{(l-1)}" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": " controls the decay of the focus ratio across layers, with " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "0 < \\alpha < 1" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": " increases, the focus ratio progressively decreases. The first term, " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "4hwC^2" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": ", represents the computational complexity of the projection layers. The second term, " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "2\\alpha^{(l-1)}W^2hwC" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": ", accounts for the complexity of computing the similarity between the query and the selected key tokens, as well as redistributing the corresponding value information at the focused positions. Obviously, since " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": " is less than 1, the complexity of this term decreases exponentially with depth. For example, with " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": ", the computational complexity is reduced to just " + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 313, + 389, + 556, + 535 + ], + "type": "text", + "content": " of the original after four decay steps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 544, + 397, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 397, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 397, + 558 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 564, + 429, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 429, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 429, + 578 + ], + "type": "text", + "content": "4.1. Experiment Setting" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "We use the DF2K dataset, which combines DIV2K [32] and Flickr2K [23], as our training set. To ensure fair comparisons, we adopt the same training configuration as utilized in recent SR studies [6, 31, 41]. Our model is trained for 500K iterations using the AdamW optimizer and an initial learning rate of " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": ". The input patch size for training is fixed at " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": ", and we employ a MultistepLR scheduler, which reduces the learning rate by half at specified iterations [250000, 400000, 450000, 475000]. The batch size is set to 32. We evaluate our method on five standard benchmark datasets: Set5 [2], Set14 [38], BSD100 [26]," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2283" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 64, + 541, + 353 + ], + "blocks": [ + { + "bbox": [ + 70, + 64, + 541, + 353 + ], + "lines": [ + { + "bbox": [ + 70, + 64, + 541, + 353 + ], + "spans": [ + { + "bbox": [ + 70, + 64, + 541, + 353 + ], + "type": "table", + "html": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
EDSR [23]×242.6M22.14T38.110.960233.920.919532.320.901332.930.935139.100.9773
RCAN [44]×215.4M7.02T38.270.961434.120.921632.410.902733.340.938439.440.9786
HAN [29]×263.6M7.24T38.270.961434.160.921732.410.902733.350.938539.460.9785
IPT [4]×2115M7.38T38.37-34.43-32.48-33.76---
SwinIR [22]×211.8M3.04T38.420.962334.460.925032.530.904133.810.943339.920.9797
CAT-A [7]×216.5M5.08T38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [39]×216.4M7.04T38.560.962934.590.926732.580.904834.300.945240.240.9808
HAT [6]×220.6M5.81T38.630.963034.860.927432.620.905334.450.946640.260.9809
IPG [31]×218.1M5.35T38.610.963234.730.927032.600.905234.480.946440.240.9810
ATD [41]×220.1M6.07T38.610.962934.950.927632.650.905634.700.947640.370.9810
PFT (Ours)×219.6M5.03T38.680.963535.000.928032.670.905834.900.949040.490.9815
EDSR [23]×343.0M9.82T34.650.928030.520.846229.250.809328.800.865334.170.9476
RCAN [44]×315.6M3.12T34.740.929930.650.848229.320.811129.090.870234.440.9499
HAN [29]×364.2M3.21T34.750.929930.670.848329.320.811029.100.870534.480.9500
IPT [4]×3116M3.28T34.81-30.85-29.38-29.49---
SwinIR [22]×311.9M1.35T34.970.931830.930.853429.460.814529.750.882635.120.9537
CAT-A [7]×316.6M2.26T35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [39]×316.6M3.12T35.070.932531.020.854129.510.815930.100.887135.390.9548
HAT [6]×320.8M2.58T35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG [31]×318.3M2.39T35.100.933231.100.855429.530.816830.360.890135.530.9554
ATD [41]×320.3M2.69T35.110.933031.130.855629.570.817630.460.891735.630.9558
PFT (Ours)×319.8M2.23T35.150.933331.160.856129.580.817830.560.893135.670.9560
EDSR [23]×443.0M5.54T32.460.896828.800.787627.710.742026.640.803331.020.9148
RCAN [44]×415.6M1.76T32.630.900228.870.788927.770.743626.820.808731.220.9173
HAN [29]×464.2M1.81T32.640.900228.900.789027.800.744226.850.809431.420.9177
IPT [4]×4116M1.85T32.64-29.01-27.82-27.26---
SwinIR [22]×411.9M0.76T32.920.904429.090.795027.920.748927.450.825432.030.9260
CAT-A [7]×416.6M1.27T33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [39]×416.6M1.76T33.040.905129.160.795827.970.751027.770.832132.310.9283
HAT [6]×420.8M1.45T33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG [31]×417.0M1.30T33.150.906229.240.797327.990.751928.130.839232.530.9300
ATD [41]×420.3M1.52T33.100.905829.240.797428.010.752628.170.840432.620.9306
PFT (Ours)×419.8M1.26T33.150.906529.290.797828.020.752728.200.841232.630.9306
", + "image_path": "a004fc6841d016abb23d427db65ad3bba33de8256dac09259f9695001aca7805.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 361, + 555, + 384 + ], + "lines": [ + { + "bbox": [ + 55, + 361, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 555, + 384 + ], + "type": "text", + "content": "Table 1. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on classical SR task. The best and second best results are colored with red and blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 394, + 296, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 394, + 296, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 394, + 296, + 430 + ], + "type": "text", + "content": "Urban100 [16], and Manga109 [27]. In addition, the computational costs of all models in this paper are measured at an output resolution of " + }, + { + "bbox": [ + 55, + 394, + 296, + 430 + ], + "type": "inline_equation", + "content": "1280 \\times 640" + }, + { + "bbox": [ + 55, + 394, + 296, + 430 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 442, + 281, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 442, + 281, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 442, + 281, + 455 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "spans": [ + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": "We compare the performance of our model with various SR baselines on widely used benchmark datasets, including Set5 [2], Set14 [38], BSD100 [26], Urban100 [16], and Manga109 [27]. These SR methods include both classical and state-of-the-art approaches, such as EDSR [23], RCAN [44], HAN [29], IPT [4], SwinIR [8], CAT [7], ART [39], HAT [6], IPG [31], and ATD [41]. We use PSNR and SSIM metrics to assess the performance of SR models at " + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\times 3" + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": " upscaling factors. All computational costs are calculated at the output resolution of " + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "inline_equation", + "content": "1280\\times 640" + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": ", and PFT uses a window size of " + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "inline_equation", + "content": "32\\times 32" + }, + { + "bbox": [ + 54, + 460, + 295, + 592 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": "The results, shown in Tab. 1, indicate that the proposed PFT model achieves superior performance over ATD, with significantly reduced computational costs. Notably, PFT reduces computational load by " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "17.1\\%" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " compared to ATD, while attaining the highest PSNR in most datasets. For lightweight SR tasks, we further compare our model with other efficient SR methods, including CARN [1], IMDN [17], LAPAR [20], LatticeNet [25], SwinIR [8], SwinIR-NG [8], ELAN [42], and OmniSR [34]. As shown in Tab. 2, the proposed PFT-light outperforms the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "text", + "content": "recently introduced ATD-light [41] on nearly all benchmark datasets, while reducing computational complexity by " + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "inline_equation", + "content": "20.1\\%" + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "text", + "content": ". On the " + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "text", + "content": " Urban100 benchmark, PFT-light outperforms ATD-light by 0.40dB and IPG-Tiny by 0.63dB. For the " + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 313, + 394, + 555, + 538 + ], + "type": "text", + "content": " SR experiments, PFT-light also outperforms IPG Tiny by 0.42dB and ATD-light by 0.23dB on the Urban100 test set. The superior performance of PFT can be attributed to its use of Progressive Focused Attention, which connects otherwise isolated attention maps across the network. This enables the model to focus on essential features, filter out irrelevant patches, substantially reduce computational costs, and support the use of larger window sizes." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 541, + 552, + 647 + ], + "blocks": [ + { + "bbox": [ + 317, + 541, + 552, + 647 + ], + "lines": [ + { + "bbox": [ + 317, + 541, + 552, + 647 + ], + "spans": [ + { + "bbox": [ + 317, + 541, + 552, + 647 + ], + "type": "image", + "image_path": "0ad7c72860c53ecd930625860b0371c1de4310305ccbb9a39d26f2d098faa37c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "lines": [ + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "type": "text", + "content": "Figure 3. Visual comparison of attention distributions in the 18th layer. SA and top-" + }, + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "type": "text", + "content": " Attention distribute attention broadly, failing to focus on the most relevant areas. In contrast, PFA filters out irrelevant tokens and concentrates attention on key regions. By reducing computational costs, it enables the use of a larger " + }, + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 313, + 647, + 555, + 712 + ], + "type": "text", + "content": " window for more extensive feature interactions." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2284" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 64, + 547, + 355 + ], + "blocks": [ + { + "bbox": [ + 65, + 64, + 547, + 355 + ], + "lines": [ + { + "bbox": [ + 65, + 64, + 547, + 355 + ], + "spans": [ + { + "bbox": [ + 65, + 64, + 547, + 355 + ], + "type": "table", + "html": "
MethodScaleParamsFLOPsSet5Set14BSD100Urban100Manga109
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
CARN [1]×21,592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [17]×2694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [20]×2548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [25]×2756K169.5G38.150.961033.780.919332.250.900532.430.9302--
SwinIR-light [22]×2910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [42]×2582K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [8]×21181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
OmniSR [34]×2772K194.5G38.220.961333.980.921032.360.902033.050.936339.280.9784
IPG-Tiny [31]×2872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
ATD-light [41]×2753K348.6G38.280.961634.110.921732.390.902333.270.937639.510.9789
PFT-light (Ours)×2776K278.3G38.360.962034.190.923232.430.903033.670.941139.550.9792
CARN [1]×31,592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [17]×3703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [20]×3544K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [25]×3765K76.3G34.530.928130.390.842429.150.805928.330.8538--
SwinIR-light [22]×3918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [42]×3590K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [8]×31190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
OmniSR [34]×3780K88.4G34.700.929430.570.846929.280.809428.840.865634.220.9487
IPG-Tiny [31]×2878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
ATD-light [41]×3760K154.7G34.700.930030.680.848529.320.810929.160.871034.600.9505
PFT-light (ours)×3783K123.5G34.810.930530.750.849329.330.811629.430.875934.600.9510
CARN [1]×41,592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [17]×4715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [20]×4659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [25]×4777K43.6G32.300.896228.680.783027.620.736726.250.7873--
SwinIR-light [22]×4930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [42]×4582K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [8]×41201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
OmniSR [34]×4792K50.9G32.490.898828.780.785927.710.741526.650.801831.020.9151
IPG-Tiny [31]×4887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
ATD-light [41]×4769K87.1G32.620.899728.870.788427.770.743926.970.810731.470.9198
PFT-light (Ours)×4792K69.6G32.630.900528.920.789127.790.744527.200.817131.510.9204
", + "image_path": "08111f7aa3313af65db2476a14a511a0997f90daf9ca3f5bf17977768ea36e5c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 391, + 294, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 391, + 294, + 498 + ], + "spans": [ + { + "bbox": [ + 54, + 391, + 294, + 498 + ], + "type": "text", + "content": "Visual comparison of attention distribution. The attention distribution visualizations are shown in Fig. 3. The attention distributions of the Vanilla Self-Attention and top-k Attention methods are relatively scattered, failing to allocate attention to the regions most relevant to the current query. In contrast, our PFA method filters out irrelevant tokens and focuses on most important positions. It also lowers computation costs, enabling larger " + }, + { + "bbox": [ + 54, + 391, + 294, + 498 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 54, + 391, + 294, + 498 + ], + "type": "text", + "content": " windows for broader feature interactions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 498, + 295, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 498, + 295, + 654 + ], + "spans": [ + { + "bbox": [ + 54, + 498, + 295, + 654 + ], + "type": "text", + "content": "Visual comparison of SR reconstruction results. To evaluate the quality of different super-resolution methods, we show visual examples in Fig. 4. These comparisons demonstrate the strength of our PFT approach in restoring sharp edges and fine textures from low-resolution images. For example, in img_001 and img_095, most methods struggle to reconstruct textures accurately, leading to noticeable distortions. Similarly, in the zebra and barbara images, many methods fail to recover details, resulting in blurry or incorrect textures. In contrast, our PFT effectively captures fine textures by focusing on the most relevant features. This ability to selectively attend helps restore clean edges and reduce artifacts, producing more accurate reconstructions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 660, + 149, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 660, + 149, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 660, + 149, + 673 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "We conduct ablation studies on the proposed PFT-light model, with all models trained for 250k iterations on the DIV2K dataset at " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": " scale. Except for the experiments on" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "text", + "content": "window size, all other experiments use a window size of " + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "text", + "content": ". In top-" + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "text", + "content": " Attention, the value of " + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 391, + 555, + 426 + ], + "type": "text", + "content": " is set to half the number of window elements, which is 128." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "text", + "content": "Effectiveness of Progressive Focused Attention. We conducted experiments to demonstrate the effectiveness of the proposed Progressive Attention and Progressive Focused Attention, with results presented in Tab. 3. These experiments compare the quantitative performance of " + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "text", + "content": " super-resolution on the Set5, Urban100, and Manga109 datasets. Progressive Attention applies a straightforward Hadamard product connection of the attention maps. As shown, even the Progressive Attention provides notable performance improvements over Self-Attention and top-" + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "text", + "content": " Attention. Progressive Focused Attention achieved the best results with a " + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "inline_equation", + "content": "27.69\\%" + }, + { + "bbox": [ + 313, + 430, + 556, + 634 + ], + "type": "text", + "content": " reduction in computation, and notably increasing PSNR by 0.36dB on the Urban100 dataset. The effectiveness of PFA lies in its ability to link adjacent attention maps across the network via the Hadamard product, allowing the model to reduce redundant computations and focus on the most relevant tokens." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 644, + 555, + 701 + ], + "blocks": [ + { + "bbox": [ + 55, + 358, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 55, + 358, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 555, + 381 + ], + "type": "text", + "content": "Table 2. Quantitative comparison (PSNR/SSIM) with state-of-the-art methods on lightweight SR task. The best and second best results are colored with red and blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 644, + 555, + 701 + ], + "lines": [ + { + "bbox": [ + 317, + 644, + 555, + 701 + ], + "spans": [ + { + "bbox": [ + 317, + 644, + 555, + 701 + ], + "type": "table", + "html": "
MethodFLOPsSet5Urban100Manga109
Vanilla Self-Attention70.4G32.2826.2630.62
Top-k Attention70.4G32.3026.2930.67
Progressive Attention70.4G32.3526.4130.78
Progressive Focused Attention50.9G32.4126.6230.85
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Focus ratio0.10.30.50.70.9
PSNR26.4826.5826.6226.6126.56
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Window sizeSet5Urban100Manga109
8 × 832.3326.4030.71
16 × 1632.4126.6230.85
32 × 3232.4926.8130.93
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Ablation study on window sizes for " + }, + { + "bbox": [ + 313, + 410, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 313, + 410, + 555, + 433 + ], + "type": "text", + "content": " SR,evaluated on the Urban100 dataset, with PSNR as the evaluation metric." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 439, + 388, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 439, + 388, + 451 + ], + "spans": [ + { + "bbox": [ + 313, + 439, + 388, + 451 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 459, + 555, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 459, + 555, + 639 + ], + "spans": [ + { + "bbox": [ + 312, + 459, + 555, + 639 + ], + "type": "text", + "content": "We propose the PFT, which introduces a novel approach to linking attention maps across layers through the key innovation of the PFA mechanism, progressively refining the focus on relevant features. By inheriting and modifying attention maps from previous layers, the PFA mechanism reduces unnecessary similarity calculations, improving attention efficiency. This enables the model to prioritize the most relevant tokens while effectively suppressing the influence of irrelevant ones. Experiments show that PFT and PFT-light achieves leading performance in single-image super-resolution with lower computation. As a key component of the Progressive Focused Transformer, PFA has proven to be both effective and efficient for super-resolution tasks. We look forward to exploring its potential in other high-level vision tasks, as well as in natural language processing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 650, + 411, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 650, + 411, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 650, + 411, + 663 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 669, + 555, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 555, + 703 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 555, + 703 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (No. 62476051) and the Sichuan Natural Science Foundation (No. 2024NSFTD0041)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2286" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12780–12791, 2023. 1, 2" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2288" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_content_list.json b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..07fe0a11898cd2f4ddcd5b4f44244a834488c583 --- /dev/null +++ b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_content_list.json @@ -0,0 +1,1381 @@ +[ + { + "type": "text", + "text": "Progressive Rendering Distillation: Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data", + "text_level": 1, + "bbox": [ + 169, + 130, + 828, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhiyuan Ma $^{1,2}$ Xinyue Liang $^{1,2}$ Rongyuan Wu $^{1}$ Xiangyu Zhu $^{3,4}$ Zhen Lei $^{1,2,3,4*}$ Lei Zhang $^{1*}$ $^{1}$ The Hong Kong Polytechnic University \n $^{2}$ Center for Artificial Intelligence and Robotics, HKISI CAS \n $^{3}$ State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA \n $^{4}$ School of Artificial Intelligence, University of Chinese Academy of Sciences, UCAS", + "bbox": [ + 116, + 200, + 885, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d18896515f3c1ce807f510adcf655d5349f24f8555be93062ae17f641a6dabc9.jpg", + "image_caption": [ + "Figure 1. Our method adapts Stable Diffusion [87] to generate high-fidelity textured meshes in 1.2 seconds." + ], + "image_footnote": [], + "bbox": [ + 116, + 329, + 885, + 558 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 597, + 326, + 613 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is highly desirable to obtain a model that can generate high-quality 3D meshes from text prompts in just seconds. While recent attempts have adapted pre-trained text-to-image diffusion models, such as Stable Diffusion (SD), into generators of 3D representations (e.g., Triplane), they often suffer from poor quality due to the lack of sufficient high-quality 3D training data. Aiming at overcoming the data shortage, we propose a novel training scheme, termed as Progressive Rendering Distillation (PRD), eliminating the need for 3D ground-truths by distilling multi-view diffusion models and adapting SD into a native 3D generator. In each iteration of training, PRD uses the U-Net to progressively denoise the latent from random noise for a few steps, and in each step it decodes the denoised latent into 3D output. Multi-view diffusion models, including MVDream and RichDreamer, are used in joint with SD", + "bbox": [ + 88, + 631, + 485, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to distill text-consistent textures and geometries into the 3D outputs through score distillation. Since PRD supports training without 3D ground-truths, we can easily scale up the training data and improve generation quality for challenging text prompts with creative concepts. Meanwhile, PRD can accelerate the inference speed of the generation model in just a few steps. With PRD, we train a Triplane generator, namely TriplaneTurbo, which adds only $2.5\\%$ trainable parameters to adapt SD for Triplane generation. TriplaneTurbo outperforms previous text-to-3D generators in both efficiency and quality. Specifically, it can produce high-quality 3D meshes in 1.2 seconds and generalize well for challenging text input. The code is available at github.com/theEricMa/TriplaneTurbo.", + "bbox": [ + 511, + 599, + 908, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 843, + 645, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-3D aims to create 3D contents faithful to the given textual descriptions. The optimization-based text-to-3D", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 109, + 887, + 241, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11036", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "methods can achieve high generation fidelity by using image diffusion priors [52, 62, 66, 68, 71, 84, 94, 110] and score distillation techniques [42, 56, 73, 82, 111, 115, 143, 153] to optimize 3D representations [10, 29, 59, 60, 105]. However, these approaches encounter bottlenecks in computational efficiency since they take hours to generate 3D textured meshes. Recent researches have shifted towards learning-based methods [7, 25, 37, 49, 80], which generate 3D contents through feed-forward networks, reducing the latency to a few seconds per output. Unfortunately, existing 3D datasets [16-18, 81, 123] are much smaller compared to those used in training text-to-image generation models, while the 3D data therein suffer from texture quality and inconsistent object poses [61]. Consequently, these approaches struggle to produce high-quality 3D outputs. As a promising alternative to the above mentioned methods, one can adapt pretrained text-to-image models, such as Stable Diffusion (SD) [87], into generators of 3D representations [54, 65, 76]. Recent studies have enabled the use of SD to generate 2D planes for 3D representations such as Triplane [8]. PI3D [65] adapts SD to generate six 2D planes pre-optimized for 3D object reconstruction. HexaGen [76] first trains a VAE to compress 3D objects into latent space, then adapts SD to generate the desired latents from text prompts. These methods leverage SD's prior knowledge for diverse text prompts while reducing training costs. However, their reliance on data-driven training limits the generalization performance.", + "bbox": [ + 89, + 90, + 485, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose to address the data shortage problem by using high-quality multi-view diffusion models [66, 84, 94] as teachers and performing multi-view distillation to adapt SD into an instant text-to-mesh generator without using 3D ground-truth data. Data-free distillation techniques [69, 154] have been applied in previous methods [51, 70, 73, 130] to train native 3D generators from scratch, whereas they struggle to produce high-quality 3D outputs. We argue that if we can adapt SD for native 3D generation, instead of training from scratch, not only the training efficiency can be improved but also the generation quality can be enhanced. To our best knowledge, however, no such attempt has been made before. The primary obstacle lies in the training scheme of SD, which requires 3D ground-truth data to supervise the denoising process. This requirement, unfortunately, conflicts with our goal to eliminate the dependency on 3D training data.", + "bbox": [ + 89, + 518, + 483, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above challenges, we propose Progressive Rendering Distillation (PRD), which enables 3D data-free distillation. PRD achieves this goal by denoising the latent from random noise rather than 3D groundtruths. In each training iteration, PRD uses a few steps to progressively reverse noise to latent space using the adapted U-Net of SD. Then the denoised latent of each step is decoded to 3D contents via the adapted VAE decoder. Multi-", + "bbox": [ + 89, + 780, + 483, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "view teacher models are used to distill high-quality renderings through efficient score distillation techniques such as ASD [73]. An additional benefit of PRD is that by adapting the SD to generate 3D contents in just four steps, the overall generation process can be much accelerated.", + "bbox": [ + 511, + 90, + 906, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "PRD is flexible in the choices of multi-view teacher models and the types of 3D representations. Unlike existing approaches using SD alone as the teacher [59, 104, 115, 140, 153], which risk the multi-view inconsistency and the Janus problem [4], we employ multiple teachers in training. Specifically, we employ MVDream [94] and SD to suppress the Janus problem and ensure text consistency in 3D content supervision. Additionally, we use RichDreamer [84] for geometry supervision through normal and depth. With PRD, we adapt SD into a native 3D generator to produce geometry and texture Triplanes in 4 steps, which is named as TriplaneTurbo in the following context. To enhance TriplaneTurbo's textured mesh quality, we employ SDF-based volumetric rendering [138] and mesh rasterization [118] for multi-view teacher supervision.", + "bbox": [ + 511, + 167, + 908, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, to address the high GPU memory usage caused by multiple teachers and multi-view renderings in the training process, we introduce the Parameter-Efficient Triplane Adapter (PETA), which adds only $2.5\\%$ trainable parameters to the frozen SD and effectively adapts it for 3D generation. Some results are shown in Fig. 1. To our knowledge, this is the first parameter-efficient training method for direct 3D content generation from 2D diffusion models, departing from full-parameter adaptation approaches. Our key contributions are summarized as follows:", + "bbox": [ + 511, + 393, + 908, + 542 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We make the first attempt to adapt the pretrained 2D SD model into a native 3D generator without 3D data. With the proposed PRD scheme, we use multi-view diffusion models as teachers and distill SD into a four-step native 3D generator, namely TriplaneTurbo.", + "- TriplaneTurbo adds only $2.5\\%$ additional trainable parameters to the frozen SD for Triplane adaptation. It marks the first use of parameter-efficient training to adapt 2D diffusion models for native 3D generation.", + "- TriplaneTurbo surpasses existing text-to-3D models not only in quality but also in speed, reducing text-to-mesh generation time to just 1.2 seconds. In addition, by scaling up the text training data, the model can generalize much better to complex text input." + ], + "bbox": [ + 511, + 545, + 906, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 768, + 656, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data-Driven Models for 3D Generation. Employing 3D data to train generators has shown its effectiveness for single-category 3D generation such as human faces [2, 8, 31, 72, 98, 125, 128], body shapes [34, 57, 89, 134], everyday objects [3, 39, 64, 78], and structured room layouts [5, 21, 75, 86, 107, 126]. This is mainly because for these specific categories, the training data are relatively", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11037", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "easy to collect. However, text-to-3D generation requires open-category generation, bringing a rather different challenge. The difficulties in obtaining sufficient 3D training data largely limit the model generalizability across diverse text prompts [73], regardless of the type of used generation models (e.g., GAN [24, 79, 91] or diffusion models [28, 40, 96]) or 3D representations (e.g., NeRF [6, 77] or Gaussian Splatting [44, 144]). The publicly available 3D datasets [16–18, 81, 123] mostly contain only hundreds or thousands of samples, which are very hard, if not impossible, to train a generalized text-to-3D generation model.", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2D Diffusion Models for 3D Generation. The difficulty of text-to-3D generation can be alleviated by leveraging 2D diffusion models as priors, thanks to their training on vast text-image pairs. Early approaches like SDS [104] and VSD [13] pioneered zero-shot text-to-3D generation by optimizing 3D representations (NeRF [59, 62, 82, 111], mesh [11, 59, 115, 136], 3DGS [56, 105, 140, 141]) through score distillation [1, 36, 41, 55, 56, 73, 82, 103, 113, 115, 117, 127, 142, 150, 152, 155], which serves as a bridge to transfer the generative capability of 2D diffusion models to 3D representations through rendered views. However, pre-trained text-to-image models like SD lack multiview consistency, leading to the Janus problem [4]. MVDream [94] and subsequent works [35, 67] address this issue by camera-aware adaptations and synchronized multiview generation, and they incorporate additional modalities such as normal [84], depth [22, 43], and CCM [63, 131] to enhance geometric quality. While achieving improved 3D generation results, these methods require computationally intensive score distillation [12, 84, 90, 94] or 3D reconstruction [32, 53, 68, 93, 106, 116, 135, 146]. Native 3D generators [17, 26, 34, 49, 50, 58, 74, 108, 122, 129, 145, 148, 148, 151, 151] can reduce the generation time to seconds by directly producing 3D content without view rendering as proxies. For example, LN3Diff [49] and GVGEN [26] compress NeRF [77] and 3DGS [44] into latent spaces using VAEs [47], then train text-conditioned latent diffusion models [28]. However, these methods show limited generalizability across text prompts, as their performance is constrained by the insufficient text-3D training pairs.", + "bbox": [ + 91, + 261, + 483, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some methods [65, 76, 84, 94] leverage SD as their backbone to transfer text-to-image knowledge into text-to-3D generation. SD provides strong generative prior and improves the model generalizability [9, 19, 58, 99–102, 120, 121, 137, 147]. Approaches like PI3D [65] adapt SD to generate multiple planes for constructing 3D space, yet their performance remains limited due to the insufficient 3D training data. Instead of adapting SD for multiview generation, native 3D generation requires substantially more 3D data for effective adaptation. We propose to address the data insufficiency challenge by distilling knowledge from multi-view diffusion models into an SD-adapted", + "bbox": [ + 89, + 719, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "native 3D generator, eliminating the need for 3D training data. While previous works like ATT3D [70] and ScaleDreamer [73] have investigated such a data-free training strategy, they employ multi-view distillation to train generators from scratch, and show limited performance due to the insufficient training scale. To overcome the huge training cost, we propose a cost-effective solution that combines multi-view distillation with SD-based native 3D generation. A fundamental challenge to achieve this goal is how to adapt SD for 3D generation without ground-truth data. We address this by proposing a novel Progressive Rendering Distillation scheme, which not only eliminates the need of 3d ground-truths but also enables few-step generation.", + "bbox": [ + 511, + 90, + 903, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 303, + 604, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 328, + 643, + 344 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stable Diffusion (SD) performs diffusion in latent space for efficient text-to-image generation. Its VAE encoder $E_{\\phi^{\\mathrm{SD}}}$ compresses an image $x$ into a latent code $z$ , while its decoder $D_{\\phi^{\\mathrm{SD}}}$ reconstructs the image. Given text prompt $y$ , a U-net $\\epsilon_{\\phi^{\\mathrm{SD}}}$ predicts noise $\\epsilon$ , which is added to $z_t = \\alpha_t z + \\sigma_t \\epsilon$ , where timestep $t \\in 1, \\ldots, T$ controls noise level via scalars $\\alpha_t$ and $\\sigma_t$ . Generation proceeds by iteratively denoising from $z_T$ to prompt-aligned $z_0$ . At each step, the U-net estimates noise $\\hat{\\epsilon} = \\epsilon_{\\phi^{\\mathrm{SD}}}(z_t; t, y)$ to compute $\\hat{z}_0 = \\frac{\\hat{z}_t - \\sigma_t \\hat{\\epsilon}}{\\alpha_t}$ , denoted as $\\hat{z}_0 = z_{\\phi^{\\mathrm{SD}}}(z_t; t, y)$ . Results can be refined through additional diffusion steps $t' < t$ . The final latent is decoded to an image via $\\hat{x} = D_{\\phi^{\\mathrm{SD}}}(\\hat{z}_0)$ .", + "bbox": [ + 511, + 349, + 906, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score Distillation. 2D diffusion models can optimize 3D representations $\\theta$ through differentiable rendering $x_{\\pi} = g(\\theta, \\pi)$ [45, 92, 95], which produces images $x_{\\pi}$ from camera view $\\pi$ . Here 2D diffusion models serve as a metric $\\mathcal{L}(x_{\\pi}; \\pi, y)$ that measures the consistency between $x_{\\pi}$ and the text conditions $y$ . The 3D representation is optimized using gradient $\\nabla_{\\theta} \\mathcal{L}(x_{\\pi}; \\pi, y) = \\nabla x_{\\pi} \\mathcal{L}(x_{\\pi}; \\pi, y) \\frac{\\partial x_{\\pi}}{\\partial \\theta}$ , which also trains the native 3D generator. The computation of $\\nabla x_{\\pi} \\mathcal{L}$ depends on the chosen score distillation method.", + "bbox": [ + 511, + 534, + 908, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Progressive Rendering Distillation", + "text_level": 1, + "bbox": [ + 511, + 681, + 812, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now detail our proposed training scheme for adapting SD as a native 3D generator. Traditional adaptation approaches require preparing ground-truth 3D representations $\\theta$ and their corresponding latents $z$ for each 3D sample in the dataset. The U-net is adapted to denoise diffused latents $z_{t}$ by minimizing the noise prediction mean squared error (MSE). Fig. 2(a) illustrates this paradigm, which has been used by several native 3D generators [65, 114, 122, 148]. However, this paradigm faces limitations in both the quantity and quality of available 3D representations $\\theta$ , as existing 3D datasets lack sufficient high-quality data for training text-to-3D generators. Actually, the pretrained SD models already possess denoising capabilities for image generation.", + "bbox": [ + 511, + 704, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11038", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c1ac498931652cc33bbbb3cc7826ce8d1a9646fe1500089a8d291fe068630e80.jpg", + "image_caption": [ + "(a) Vanilla SD Adaptation / Diffusion Model Training" + ], + "image_footnote": [], + "bbox": [ + 114, + 109, + 442, + 276 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/563b13dc3fbcad2cb77db81a628fc18dccb08d12a58a25dda7ef0a5c82170b32.jpg", + "image_caption": [ + "(b) Progressive Rendering Distillation (Ours)", + "Figure 2. Comparison between (a) traditional SD adaptation and (b) our proposed progressive rendering distillation (PRD) for native 3D generation. Traditional approach requires ground-truth 3D representations $\\theta$ and their latents $z_0$ for each 3D sample to generate $z_0$ . Our proposed PRD scheme progressively denoises latents $z_t$ initialized from random noise into $z_0$ , which are decoded to $\\theta$ , using multi-view diffusion models as teachers for distillation, eliminating the need for 3D data during adaptation and overcoming data scarcity." + ], + "image_footnote": [], + "bbox": [ + 464, + 104, + 903, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In other words, pretrained SD is well-trained for a Markov Chain to reverse $\\boldsymbol{z}_T = \\epsilon \\sim \\mathcal{N}(0, I)$ to $\\boldsymbol{z}_0$ with its U-net $\\boldsymbol{z}_{\\phi^{\\mathrm{SD}}}$ , and decode $\\boldsymbol{z}_0$ to image with its decoder $D_{\\phi^{\\mathrm{SD}}}$ . Our goal is to modify the Markov chain by transforming $\\boldsymbol{z}_{\\phi^{\\mathrm{SD}}}$ and $D_{\\phi^{\\mathrm{SD}}}$ into 3D generators $\\boldsymbol{z}_{\\phi^{3\\mathrm{D}}}$ and $D_{\\phi^{3\\mathrm{D}}}$ , from which the 3D representations $\\theta$ can be decoded. Note that our modification of the Markov chain differs from the traditional diffusion model adaptation objectives, as it requires neither ground-truth latents $\\boldsymbol{z}_0$ nor their noise-diffused variants $\\boldsymbol{z}_t$ in the training process.", + "bbox": [ + 88, + 371, + 483, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, at the beginning of the Markov chain, the network takes random noise $\\epsilon$ as input to represent $\\mathbf{z}_T$ . At each step, current state $\\mathbf{z}_t$ is used to estimate $\\hat{\\mathbf{z}}_0$ through $\\mathbf{z}_{\\phi^{\\mathrm{SD}}}$ , which is then decoded to 3D output $\\hat{\\theta}$ with $D_{\\phi^{\\mathrm{SD}}}$ . The 3D output $\\hat{\\theta}$ is used to render images $\\mathbf{x}_{\\pi_1}, \\mathbf{x}_{\\pi_2}, \\ldots$ at camera views $\\pi_1, \\pi_2, \\ldots$ and receive supervision from multiview teachers via score distillation, while the estimated $\\hat{\\mathbf{z}}_0$ is diffused to the next timestep $t'$ as $\\mathbf{z}_{t'} = \\alpha_{t'} \\hat{\\mathbf{z}}_0 + \\sigma_{t'} \\epsilon$ for subsequent operations. We name this training scheme as Progressive Rendering Distillation (PRD), as illustrated in Fig. 2(b). From the total $T$ timesteps, we select a decreasing sequence of $K$ timesteps $T = t_1 > t_2 > \\dots > t_K = T / K$ with uniform spacing to perform score distillation from multi-view teachers. The gradient at each step is not backpropagated to previous steps; therefore, we can largely reduce the GPU memory usage and prevent gradient explosion [15, 83, 124, 133]. Since $\\phi^{\\mathrm{3D}}$ is initialized from $\\phi^{\\mathrm{SD}}$ , this specialized gradient detachment strategy still maintains good convergence. The pseudo code of our algorithm is provided in the supplementary material. While the time cost of our training strategy increases with the increase of $K$ , we can ensure the model to generate high quality results in just a few steps, thereby accelerating inference. We set $K = 4$ to balance quality and speed.", + "bbox": [ + 91, + 536, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Parameter-Efficient Triplane Adaptation", + "text_level": 1, + "bbox": [ + 511, + 371, + 862, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While various 3D representations could be employed by our PRD scheme, in this paper we demonstrate an exemplar solution using Triplanes as the representation. We denote our adapted model as TriplaneTurbo with parameters $\\phi^{3\\mathrm{D}}$ . Specifically, TriplaneTurbo adapts SD to generate a 3D representation consisting of two Triplanes [8] $\\theta = (\\theta_{\\mathrm{geo}},\\theta_{\\mathrm{tex}})$ : a geometry Triplane $\\theta_{\\mathrm{geo}}$ storing Signed Distance Function (SDF) and deformation values for mesh extraction, and a texture Triplane $\\theta_{\\mathrm{tex}}$ containing RGB attributes for painting texture on the mesh. For each point in 3D space, we use a two-layer MLP to decode its SDF value. The same process applies to texture and mesh deformation [92, 118]. This separation of geometry and texture planes follows the work in [23, 97, 119]. We set the Triplane resolution as $256\\times 256$ , and replace the last convolution in SD's decoder to output 32 channels. The Triplanes' output has a dimension of $6\\times 256\\times 256\\times 32$ in feature space. Due to the $8\\times$ compression of the VAE, this corresponds to $6\\times 32\\times 32\\times 4$ in latent space, distinct from the $1\\times 64\\times 64\\times 4$ latent generated by pretrained SD. To enable interaction between the six feature planes, we follow existing approaches [68, 93, 94, 112] to adapt the U-nets' self-attention [87, 109] to allow cross-plane attention. Unlike existing works that fully retrain SD [12, 54, 65, 76, 94], which can lead to catastrophic forgetting [65, 94], we propose a parameter-efficient adaptation approach. The core of our design lies in the fact that each of the six feature planes maintains its own unique feature distribution. Therefore, plane-specific characteristics must be incorporated into the adaptation process. As illustrated in Fig. 3, our adaptation modifies the convolution, self-attention, and cross-attention layers. We name our approach Parameter-Efficient Triplane Adaptation (PETA).", + "bbox": [ + 511, + 401, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11039", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/746feac01c63a3330237dbd27e8b8ca4a77e15c35731a90b900354ad64b049d2.jpg", + "image_caption": [ + "Figure 3. Illustration of TriplaneTurbo: an SD-adapted native 3D generator using our PRD scheme. Our model generates six feature planes comprising geometry Triplane $\\theta_{\\mathrm{geo}}$ and texture Triplane $\\theta_{\\mathrm{tex}}$ in 4 steps. We introduce Parameter Efficient Triplane Adaptation (PETA), which requires only $2.5\\%$ additional parameters for adaptation. The parameter arrangement is illustrated in the figure." + ], + "image_footnote": [], + "bbox": [ + 91, + 92, + 867, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 3, for the convolution blocks (Res-Blocks) and cross-attention layers, we implement LoRA [33, 139] for parameter-efficient adaptation, and process the six planes uniformly. The plane-specific adaptations are then applied to the self-attention. For the self-attention blocks, we apply distinct LoRA layers [33] to the to_Q, to_K, to_V, and to_Out linear layers when processing each of the six feature planes. In each linear transformation within a self-attention block, the linear projection with multiple LoRAs is implemented in two steps. First, the frozen linear layer batch processes the features extracted from all the six planes together. Then, separate LoRA transformations are applied independently to the features of each plane. This adaptation maintains low computational overhead while effectively introducing plane-specific processing during attention calculations across the six feature planes. It can be applied with other techniques like AdaLoRa [149] and Vera [48]. We leave this for further exploration. We set the LoRA rank to 16 by default. While this adaptation adds only $2.5\\%$ of the parameters to the SD model, it effectively enables native 3D generation.", + "bbox": [ + 91, + 412, + 483, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Distillation Details", + "text_level": 1, + "bbox": [ + 89, + 741, + 269, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since PRD eliminates the need for 3D data by referring to multi-view teachers for distillation, using multiple teachers allows us to combine their strengths while mitigating individual biases. Most previous works [14, 59, 70, 82, 105] use SD model (parametrized by $\\phi^{\\mathrm{SD}}$ ) as the teacher for its ability to generate high-fidelity, text-consistent images. However, SD lacks camera-awareness, which can lead to the Janus problem [4]. MVDream [94] (MV, parametrized by $\\phi^{\\mathrm{MV}}$ ) addresses this by generating four", + "bbox": [ + 89, + 763, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "camera-conditioned views simultaneously, but at the cost of reduced prompt consistency [112]. While SD and MV complement each other, both of them focus on RGB rendering and provide no direct supervision on geometry. We further incorporate RichDreamer [84] (RD, parameterized by $\\phi^{\\mathrm{RD}}$ ), a model that generates four-view normal and depth maps based on text prompts. The score distillation guidance $\\mathcal{L}(\\pmb{x}_{\\pi};\\pi ,y)$ in our implementation thus integrates SD, MV, and RD. At each PRD step (see Sec. 3.2 and Fig. 2), given a text prompt $y$ and generated 3D representation $\\hat{\\theta}$ from $z_{\\phi^{3\\mathrm{D}}}$ and $D_{\\phi^{3\\mathrm{D}}}$ , we sample four views $\\pi_1,\\dots ,\\pi_4$ at uniform azimuth intervals. We sample one view $\\pi$ from $\\pi_1,\\ldots ,\\pi_4$ to compute $\\mathcal{L}_{\\mathrm{SD}} = \\mathcal{L}_{\\phi^{\\mathrm{SD}}}(x_{\\pi};\\pi ,y)$ . For MV, all the four views are used to compute $\\mathcal{L}_{\\mathrm{MV}} = \\mathcal{L}_{\\phi^{\\mathrm{MV}}}(x_{\\pi_1},\\dots,x_{\\pi_4};\\pi_1,\\dots,\\pi_4,y)$ . RD operates on concatenated normal and depth renderings $x_{\\pi_1}'$ $\\dots ,x_{\\pi_4}'$ and its objective is $\\mathcal{L}_{\\mathrm{RD}} = \\mathcal{L}_{\\phi^{RD}}(x_{\\pi_1}'$ $\\dots ,x_{\\pi_4}'$ $\\pi_1,\\dots,\\pi_4,y)$ . Among existing score distillation methods [36, 41, 55, 56, 73, 82, 115, 117, 127, 142], we adopt Asynchronous Score Distillation (ASD) [73] for its pioneered efficiency in training deep text-to-3D generators. For 3D rendering, as illustrated in Fig. 3, we combine volumetric rendering [138] at $64\\times 64$ resolution with mesh rasterization [46] at $512\\times 512$ to overcome the instability of pure mesh supervision [132].", + "bbox": [ + 511, + 412, + 906, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 792, + 645, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 511, + 818, + 720, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. For a fair comparison with existing methods, we use captions of the 3D objects [17] provided by [30] to train our model, which comprises a total of 360K text prompts. We employ SD v2.1-base [88] as the", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11040", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b7550ed971a14bbc9043de9ee481e939d5c04a13b9a0990454404120aac2e697.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of text-to-mesh generation results by competing methods. Please refer to Sec. 4.2 for details." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 901, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "base model. Our model is trained for 15K iterations with a learning rate of 2e-4, costing 40 hours on 8 NVIDIA H20 GPUs. We further collect 1.6 million text prompts to evaluate the benefit of data scaling supported by our method. Additional training details and loss weights are provided in the supplementary material.", + "bbox": [ + 89, + 619, + 483, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared Methods. Our proposed PRD aims for fast text-to-mesh generation. Therefore, we compare it against state-of-the-art approaches that can generate textured meshes within one minute, including Shape-E [38], Direct3D [61], 3DTopia [30], GVGEN [26], LN3Diff [49], LGM [106] and PI3D [65]. Note that we do not compare with some relevant works [76, 130] since their codes/models are not publicly available and they employ different evaluation protocols. In our experiments, the results of Shape-E, Direct3D, 3DTopia, GVGEN, LN3Diff and LGM are obtained by running their publicly available models. For PI3D, we can only perform quantitative com", + "bbox": [ + 89, + 719, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "parisons with it by copying its results from the original paper, but we cannot perform visual comparisons with it since its code/model is not yet publicly available.", + "bbox": [ + 511, + 619, + 906, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Protocol. We employ the protocol used in our competing methods [26, 30, 38, 49, 65, 106] to evaluate our PRD model. Specifically, we use the ViT-B/34 CLIP model [85] to evaluate the test prompts from the DreamFusion gallery [82]. As in [65], we render the generated 3D results at 512 resolution from four viewpoints at $15^{\\circ}$ elevation across four azimuth angles: $0^{\\circ}$ , $90^{\\circ}$ , $180^{\\circ}$ and $270^{\\circ}$ . Under these views, we evaluate the performance of competing methods using CLIP Score [27] (C.S.) and CLIP R-precision $(\\mathbb{R}@\\mathbb{1})$ . To ensure a fair comparison for instant text-to-mesh generation, we exclude the post-processing steps such as SDS refinement [82], as they will prolong the generation time by several minutes. For models [26, 106] using Gaussian Splatting representations, we use the conversion script from [106] to generate textured meshes.", + "bbox": [ + 511, + 672, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11041", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 90, + 294, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We showcase qualitative comparisons of the competing methods in Fig. 4 using challenging test prompts. One can see that most of the existing methods struggle to generate satisfactory outputs. Our method, in comparison, produces better quality results with complete and vivid meshes. The quantitative results are reported in Tab. 1. Again, our method demonstrates superior performance to its competitors in all the metrics. Existing methods fall short in the consistency of object poses and in the capability of handling complex prompts. Our PRD method addresses these challenges, enabling faster inference speed and improving the model performance by data scaling.", + "bbox": [ + 88, + 113, + 480, + 294 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Handling Inconsistent Generation Poses. As shown in Fig. 4, existing models often generate objects with incorrect poses. For prompts like 'A teal moped', the competing methods like Direct3D [122], Shape-E [38] and GVGEN [26] generate objects with misaligned orientations, such as facing sideways or backwards. This issue stems from the inconsistent object orientations in 3D training datasets, which are difficult to detect and correct automatically. Current methods struggle with noisy training data, leading to pose ambiguity and geometric defects. Our approach addresses this challenge by learning from multiview teachers. Though our teachers are trained on noisy 3D datasets and may occasionally provide incorrect directional guidance, our PRD scheme exposes the 3D outputs to multi-view teachers $K$ times per iteration (see Sec. 3.2). Through the iterative distillation process, we substantially decrease the impact of incorrect directional guidance, ensuring consistent pose alignment in the 3D outputs.", + "bbox": [ + 91, + 296, + 483, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Handling Complex Text Prompts. The failure of our competing methods mainly stems from their reliance on the existing text-3D paired datasets, which are not comprehensive enough compared to the diverse user inputs. Therefore, trained on these data, existing methods fail to produce good results when the input is complex. For example, existing methods might perform well when the input prompt is 'A robot' but fail when the prompt becomes 'A robot tiger'. The quality of existing 3D datasets is also compromised by the absence of creative concepts. Creating 3D models for imaginative concepts like 'A robot tiger' demands significant time and expertise from 3D artists. As a result, existing 3D datasets are largely limited to common everyday objects. Models trained on these limited datasets fail to generalize effectively to imaginative or complex prompts. We solve this problem by adapting SD as a 3D generator and inheriting its generative power, and more crucially, by introducing a training scheme that completely eliminates the need of 3D data. Our training scheme not only improves the quality of results on the existing training corpus, as shown by the qualitative and quantitative results in Fig. 4 and Tab. 1, but also enhances the capability to handle complex prompts by", + "bbox": [ + 91, + 569, + 486, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/61f7ee0e7d24a11e8df8c101385dd8b4cabcf60769aaf4e3d868a0c7b7815d2f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
C.S. ↑R@1↑Latency (/sec)
Shape-E [38]55.127.113.0
Direct3D60.84.3316.0
3DTopia [30]59.711.223.7
PI3D* [65]65.925.23.00
GVGEN [26]51.12.4449.2
LN3Diff [49]55.95.098.16
LGM [106]67.428.356.1
Ours68.232.31.23
+More Text Data75.146.01.23
", + "bbox": [ + 532, + 88, + 887, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quality and speed comparison for text-to-mesh generation. *indicates that the values are quoted from the original papers.", + "bbox": [ + 511, + 265, + 906, + 295 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "expanding the available training data, as detailed below.", + "bbox": [ + 511, + 306, + 882, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fast Inference Speed. Our PRD method also demonstrates superior computational efficiency. As shown in Tab. 1, we evaluate the average inference latency from text input to textured mesh output across all test prompts on the H20 GPU device. While some methods [26, 106] require dozens of steps, our PRD approach enables the native 3D generator to produce quality results in just $K$ steps. With the suggested setting of $K = 4$ , as shown in Tab. 1, our model achieves sub-second latency for text-to-mesh generation, significantly outperforming previous methods.", + "bbox": [ + 511, + 323, + 906, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Scaling Up Training Corpus. Since our method is free from the constraints of 3D training data, it can be easily scaled to accommodate more complex and creative text prompts during training. It preserves the SD model's ability to handle creative concepts throughout the 3D adaptation process, generating 3D outputs that faithfully represent the input prompts. As can be seen in the +More Text Data column, when we scale up the training text data from 360K to 1.6M, the CLIP similarity improves by as much as $7\\%$ , leading to more consistent generation for challenging text prompts such as A lion reading the newspaper and A tray of Sushi containing pugs. This is because our collected text data covers a wider range of creative concepts than the existing 3D datasets [17, 123], thus providing more sufficient training and improving the generalizability of the model. More visual examples are partially presented in Fig. 1 and detailed in the supplementary materials.", + "bbox": [ + 511, + 474, + 908, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 742, + 668, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Effectiveness of PRD. We validate our PRD algorithm by testing a simplified configuration with $\\mathbf{K} = \\mathbf{1}$ , which reduces our method to a single-step generation process that is equivalent to a vanilla native 3D generator trained by score distillation [73]. As shown in Fig. 5 and quantified in Tab. 2, this configuration fails to generate proper 3D structures because it needs to simultaneously handle two complex challenges: adapting SD for 3D generation and performing single-step generation. In contrast, our PRD scheme can", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11042", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c9574b850015534b8784ae70a56b6fcc3f5da82b22672050fbc14021579f8dec.jpg", + "image_caption": [ + "Figure 5. Visualizations on the ablation studies of PRD algorithm." + ], + "image_footnote": [], + "bbox": [ + 96, + 85, + 486, + 270 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/aeedd00ade5f6985cba285532b18e0bd99df09dd2074e9abf0865e8f04e1b466.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
C.S. ↑R@1 ↑
K=150.914.4
K=262.622.4
K=4 (Proposed)68.232.3
", + "bbox": [ + 168, + 310, + 406, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "use alternative step configurations such as $\\mathbf{K} = 2$ , which produces suboptimal yet acceptable results. We found that the configuration of $\\mathbf{K} = 4$ provides the best trade-off between output quality and computational efficiency, which is used as the default setting of PRD.", + "bbox": [ + 89, + 443, + 482, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Effectiveness of PETA. We first compare our proposed PETA method with conventional full parameter fine-tuning (shown as Full Param Tuning in Fig. 6 and Tab. 3). We see that full parameter fine-tuning exhibits training instability and catastrophic forgetting, resulting in text-inconsistent outputs. We then conduct additional ablation studies using vanilla LoRA tuning, maintaining an equivalent parameter size (22.6M), shown as the configuration of w/ Basic LoRA. We see that this vanilla adaptation produces degraded geometric structures and textures, and lacks the capability to handle the unique characteristics of each plane. Since different geometry and texture planes (see Fig. 3) exhibit distinct feature distributions, they require specialized consideration. Our solution (denoted as w/ PETA) considers plane dependency using multiple LoRAs in self-attention blocks, enabling each plane to maintain its unique representation while allowing cross-plane interactions during self-attention computation. As shown in Fig. 5 and Tab. 2, PETA achieves enhanced 3D generation quality with good text consistency.", + "bbox": [ + 89, + 521, + 482, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also perform ablation studies to investigate the impact of multiple multi-view teachers in training, the choice of LoRA rank, our hybrid rendering approach that combines volumetric rendering and rasterization for multi-view distillation in PRD training scheme. The details can be found in", + "bbox": [ + 89, + 824, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe3bb0ff1296f13213667bda6dc75ce3cdd106658ab0656927c0ea72fac9f0be.jpg", + "image_caption": [ + "Figure 6. Visualizations on the ablation study of PETA." + ], + "image_footnote": [], + "bbox": [ + 519, + 90, + 903, + 270 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9bf2c876db40115ba95d1d51a9e763b9034d5d92933720b547e5052247c9d9a6.jpg", + "table_caption": [ + "Table 2. Ablation study on the hyper-parameters of PRD." + ], + "table_footnote": [], + "table_body": "
C.S. ↑R@1 ↑
Full Param Tuning35.80.35
w/ Basic LoRA54.211.1
w/ PETA (Proposed)68.232.3
", + "bbox": [ + 576, + 306, + 844, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study on the effectiveness of PETA.", + "bbox": [ + 547, + 395, + 870, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the supplementary materials.", + "text_level": 1, + "bbox": [ + 511, + 438, + 712, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Limitation", + "text_level": 1, + "bbox": [ + 511, + 469, + 764, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented Progressive Rendering Distillation (PRD), a novel training scheme that adapts Stable Diffusion (SD) for instant text-to-mesh generation without relying on 3D data. We also introduced PETA (Parameter-Efficient Triplane Adaptation), a parameter-efficient method that introduces only $2.5\\%$ additional parameters to effectively enable SD for instant text-to-mesh generation. Our model, namely TriplaneTurbo, can produce text-consistent textured meshes in only 1.2 second. Through comprehensive experiments, we validated the effectiveness of our approach. Our methodology has the potential to be extended to 3D scene generation and image-to-3D tasks. While currently implemented with SD, the PRD approach can also be applied to other pre-trained models like DiT [20]. We hope our work can inspire new directions in 3D generation to overcome the dependency on 3D data.", + "bbox": [ + 511, + 494, + 906, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. One limitation of our method lies in the generation of precise numbers of multiple 3D objects, which may require more sophisticated multi-view teachers, potentially enhanced with layout guidance. Besides, our results for full-body humans might exhibit limited facial and hand details, which can be improved by extending SD adaptation to more advanced 3D structures than Triplane.", + "bbox": [ + 511, + 737, + 908, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 513, + 859, + 666, + 876 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the InnoHK program.", + "bbox": [ + 511, + 885, + 834, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11043", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Thiemo Alldieck, Nikos Kolotouros, and Cristian Sminchisescu. 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Springer, 2024. 3" + ], + "bbox": [ + 89, + 90, + 486, + 204 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "11050", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 14 + } +] \ No newline at end of file diff --git a/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_model.json b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e1127baba683d1574186b907b4ed4ae143b12864 --- /dev/null +++ b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_model.json @@ -0,0 +1,3035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.17, + 0.131, + 0.83, + 0.175 + ], + "angle": 0, + "content": "Progressive Rendering Distillation: Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.202, + 0.886, + 0.294 + ], + "angle": 0, + "content": "Zhiyuan Ma\\(^{1,2}\\) Xinyue Liang\\(^{1,2}\\) Rongyuan Wu\\(^{1}\\) Xiangyu Zhu\\(^{3,4}\\) Zhen Lei\\(^{1,2,3,4*}\\) Lei Zhang\\(^{1*}\\) \n\\(^{1}\\)The Hong Kong Polytechnic University \n\\(^{2}\\)Center for Artificial Intelligence and Robotics, HKISI CAS \n\\(^{3}\\)State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA \n\\(^{4}\\)School of Artificial Intelligence, University of Chinese Academy of Sciences, UCAS" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.33, + 0.886, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.571, + 0.816, + 0.586 + ], + "angle": 0, + "content": "Figure 1. Our method adapts Stable Diffusion [87] to generate high-fidelity textured meshes in 1.2 seconds." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.598, + 0.327, + 0.614 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.632, + 0.486, + 0.875 + ], + "angle": 0, + "content": "It is highly desirable to obtain a model that can generate high-quality 3D meshes from text prompts in just seconds. While recent attempts have adapted pre-trained text-to-image diffusion models, such as Stable Diffusion (SD), into generators of 3D representations (e.g., Triplane), they often suffer from poor quality due to the lack of sufficient high-quality 3D training data. Aiming at overcoming the data shortage, we propose a novel training scheme, termed as Progressive Rendering Distillation (PRD), eliminating the need for 3D ground-truths by distilling multi-view diffusion models and adapting SD into a native 3D generator. In each iteration of training, PRD uses the U-Net to progressively denoise the latent from random noise for a few steps, and in each step it decodes the denoised latent into 3D output. Multi-view diffusion models, including MVDream and RichDreamer, are used in joint with SD" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.6, + 0.909, + 0.812 + ], + "angle": 0, + "content": "to distill text-consistent textures and geometries into the 3D outputs through score distillation. Since PRD supports training without 3D ground-truths, we can easily scale up the training data and improve generation quality for challenging text prompts with creative concepts. Meanwhile, PRD can accelerate the inference speed of the generation model in just a few steps. With PRD, we train a Triplane generator, namely TriplaneTurbo, which adds only \\(2.5\\%\\) trainable parameters to adapt SD for Triplane generation. TriplaneTurbo outperforms previous text-to-3D generators in both efficiency and quality. Specifically, it can produce high-quality 3D meshes in 1.2 seconds and generalize well for challenging text input. The code is available at github.com/theEricMa/TriplaneTurbo." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.844, + 0.646, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Text-to-3D aims to create 3D contents faithful to the given textual descriptions. The optimization-based text-to-3D" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.242, + 0.901 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11036" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.514 + ], + "angle": 0, + "content": "methods can achieve high generation fidelity by using image diffusion priors [52, 62, 66, 68, 71, 84, 94, 110] and score distillation techniques [42, 56, 73, 82, 111, 115, 143, 153] to optimize 3D representations [10, 29, 59, 60, 105]. However, these approaches encounter bottlenecks in computational efficiency since they take hours to generate 3D textured meshes. Recent researches have shifted towards learning-based methods [7, 25, 37, 49, 80], which generate 3D contents through feed-forward networks, reducing the latency to a few seconds per output. Unfortunately, existing 3D datasets [16-18, 81, 123] are much smaller compared to those used in training text-to-image generation models, while the 3D data therein suffer from texture quality and inconsistent object poses [61]. Consequently, these approaches struggle to produce high-quality 3D outputs. As a promising alternative to the above mentioned methods, one can adapt pretrained text-to-image models, such as Stable Diffusion (SD) [87], into generators of 3D representations [54, 65, 76]. Recent studies have enabled the use of SD to generate 2D planes for 3D representations such as Triplane [8]. PI3D [65] adapts SD to generate six 2D planes pre-optimized for 3D object reconstruction. HexaGen [76] first trains a VAE to compress 3D objects into latent space, then adapts SD to generate the desired latents from text prompts. These methods leverage SD's prior knowledge for diverse text prompts while reducing training costs. However, their reliance on data-driven training limits the generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.519, + 0.485, + 0.777 + ], + "angle": 0, + "content": "In this paper, we propose to address the data shortage problem by using high-quality multi-view diffusion models [66, 84, 94] as teachers and performing multi-view distillation to adapt SD into an instant text-to-mesh generator without using 3D ground-truth data. Data-free distillation techniques [69, 154] have been applied in previous methods [51, 70, 73, 130] to train native 3D generators from scratch, whereas they struggle to produce high-quality 3D outputs. We argue that if we can adapt SD for native 3D generation, instead of training from scratch, not only the training efficiency can be improved but also the generation quality can be enhanced. To our best knowledge, however, no such attempt has been made before. The primary obstacle lies in the training scheme of SD, which requires 3D ground-truth data to supervise the denoising process. This requirement, unfortunately, conflicts with our goal to eliminate the dependency on 3D training data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.485, + 0.903 + ], + "angle": 0, + "content": "To address the above challenges, we propose Progressive Rendering Distillation (PRD), which enables 3D data-free distillation. PRD achieves this goal by denoising the latent from random noise rather than 3D groundtruths. In each training iteration, PRD uses a few steps to progressively reverse noise to latent space using the adapted U-Net of SD. Then the denoised latent of each step is decoded to 3D contents via the adapted VAE decoder. Multi-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.168 + ], + "angle": 0, + "content": "view teacher models are used to distill high-quality renderings through efficient score distillation techniques such as ASD [73]. An additional benefit of PRD is that by adapting the SD to generate 3D contents in just four steps, the overall generation process can be much accelerated." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.909, + 0.394 + ], + "angle": 0, + "content": "PRD is flexible in the choices of multi-view teacher models and the types of 3D representations. Unlike existing approaches using SD alone as the teacher [59, 104, 115, 140, 153], which risk the multi-view inconsistency and the Janus problem [4], we employ multiple teachers in training. Specifically, we employ MVDream [94] and SD to suppress the Janus problem and ensure text consistency in 3D content supervision. Additionally, we use RichDreamer [84] for geometry supervision through normal and depth. With PRD, we adapt SD into a native 3D generator to produce geometry and texture Triplanes in 4 steps, which is named as TriplaneTurbo in the following context. To enhance TriplaneTurbo's textured mesh quality, we employ SDF-based volumetric rendering [138] and mesh rasterization [118] for multi-view teacher supervision." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.394, + 0.909, + 0.544 + ], + "angle": 0, + "content": "In addition, to address the high GPU memory usage caused by multiple teachers and multi-view renderings in the training process, we introduce the Parameter-Efficient Triplane Adapter (PETA), which adds only \\(2.5\\%\\) trainable parameters to the frozen SD and effectively adapts it for 3D generation. Some results are shown in Fig. 1. To our knowledge, this is the first parameter-efficient training method for direct 3D content generation from 2D diffusion models, departing from full-parameter adaptation approaches. Our key contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.546, + 0.907, + 0.621 + ], + "angle": 0, + "content": "- We make the first attempt to adapt the pretrained 2D SD model into a native 3D generator without 3D data. With the proposed PRD scheme, we use multi-view diffusion models as teachers and distill SD into a four-step native 3D generator, namely TriplaneTurbo." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.622, + 0.906, + 0.681 + ], + "angle": 0, + "content": "- TriplaneTurbo adds only \\(2.5\\%\\) additional trainable parameters to the frozen SD for Triplane adaptation. It marks the first use of parameter-efficient training to adapt 2D diffusion models for native 3D generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.682, + 0.906, + 0.758 + ], + "angle": 0, + "content": "- TriplaneTurbo surpasses existing text-to-3D models not only in quality but also in speed, reducing text-to-mesh generation time to just 1.2 seconds. In addition, by scaling up the text training data, the model can generalize much better to complex text input." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.546, + 0.907, + 0.758 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.77, + 0.658, + 0.785 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Data-Driven Models for 3D Generation. Employing 3D data to train generators has shown its effectiveness for single-category 3D generation such as human faces [2, 8, 31, 72, 98, 125, 128], body shapes [34, 57, 89, 134], everyday objects [3, 39, 64, 78], and structured room layouts [5, 21, 75, 86, 107, 126]. This is mainly because for these specific categories, the training data are relatively" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11037" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "easy to collect. However, text-to-3D generation requires open-category generation, bringing a rather different challenge. The difficulties in obtaining sufficient 3D training data largely limit the model generalizability across diverse text prompts [73], regardless of the type of used generation models (e.g., GAN [24, 79, 91] or diffusion models [28, 40, 96]) or 3D representations (e.g., NeRF [6, 77] or Gaussian Splatting [44, 144]). The publicly available 3D datasets [16–18, 81, 123] mostly contain only hundreds or thousands of samples, which are very hard, if not impossible, to train a generalized text-to-3D generation model." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.262, + 0.485, + 0.716 + ], + "angle": 0, + "content": "2D Diffusion Models for 3D Generation. The difficulty of text-to-3D generation can be alleviated by leveraging 2D diffusion models as priors, thanks to their training on vast text-image pairs. Early approaches like SDS [104] and VSD [13] pioneered zero-shot text-to-3D generation by optimizing 3D representations (NeRF [59, 62, 82, 111], mesh [11, 59, 115, 136], 3DGS [56, 105, 140, 141]) through score distillation [1, 36, 41, 55, 56, 73, 82, 103, 113, 115, 117, 127, 142, 150, 152, 155], which serves as a bridge to transfer the generative capability of 2D diffusion models to 3D representations through rendered views. However, pre-trained text-to-image models like SD lack multiview consistency, leading to the Janus problem [4]. MVDream [94] and subsequent works [35, 67] address this issue by camera-aware adaptations and synchronized multiview generation, and they incorporate additional modalities such as normal [84], depth [22, 43], and CCM [63, 131] to enhance geometric quality. While achieving improved 3D generation results, these methods require computationally intensive score distillation [12, 84, 90, 94] or 3D reconstruction [32, 53, 68, 93, 106, 116, 135, 146]. Native 3D generators [17, 26, 34, 49, 50, 58, 74, 108, 122, 129, 145, 148, 148, 151, 151] can reduce the generation time to seconds by directly producing 3D content without view rendering as proxies. For example, LN3Diff [49] and GVGEN [26] compress NeRF [77] and 3DGS [44] into latent spaces using VAEs [47], then train text-conditioned latent diffusion models [28]. However, these methods show limited generalizability across text prompts, as their performance is constrained by the insufficient text-3D training pairs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Some methods [65, 76, 84, 94] leverage SD as their backbone to transfer text-to-image knowledge into text-to-3D generation. SD provides strong generative prior and improves the model generalizability [9, 19, 58, 99–102, 120, 121, 137, 147]. Approaches like PI3D [65] adapt SD to generate multiple planes for constructing 3D space, yet their performance remains limited due to the insufficient 3D training data. Instead of adapting SD for multiview generation, native 3D generation requires substantially more 3D data for effective adaptation. We propose to address the data insufficiency challenge by distilling knowledge from multi-view diffusion models into an SD-adapted" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.289 + ], + "angle": 0, + "content": "native 3D generator, eliminating the need for 3D training data. While previous works like ATT3D [70] and ScaleDreamer [73] have investigated such a data-free training strategy, they employ multi-view distillation to train generators from scratch, and show limited performance due to the insufficient training scale. To overcome the huge training cost, we propose a cost-effective solution that combines multi-view distillation with SD-based native 3D generation. A fundamental challenge to achieve this goal is how to adapt SD for 3D generation without ground-truth data. We address this by proposing a novel Progressive Rendering Distillation scheme, which not only eliminates the need of 3d ground-truths but also enables few-step generation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.304, + 0.605, + 0.318 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.329, + 0.644, + 0.345 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.907, + 0.534 + ], + "angle": 0, + "content": "Stable Diffusion (SD) performs diffusion in latent space for efficient text-to-image generation. Its VAE encoder \\( E_{\\phi^{\\mathrm{SD}}} \\) compresses an image \\( x \\) into a latent code \\( z \\), while its decoder \\( D_{\\phi^{\\mathrm{SD}}} \\) reconstructs the image. Given text prompt \\( y \\), a U-net \\( \\epsilon_{\\phi^{\\mathrm{SD}}} \\) predicts noise \\( \\epsilon \\), which is added to \\( z_t = \\alpha_t z + \\sigma_t \\epsilon \\), where timestep \\( t \\in 1, \\ldots, T \\) controls noise level via scalars \\( \\alpha_t \\) and \\( \\sigma_t \\). Generation proceeds by iteratively denoising from \\( z_T \\) to prompt-aligned \\( z_0 \\). At each step, the U-net estimates noise \\( \\hat{\\epsilon} = \\epsilon_{\\phi^{\\mathrm{SD}}}(z_t; t, y) \\) to compute \\( \\hat{z}_0 = \\frac{\\hat{z}_t - \\sigma_t \\hat{\\epsilon}}{\\alpha_t} \\), denoted as \\( \\hat{z}_0 = z_{\\phi^{\\mathrm{SD}}}(z_t; t, y) \\). Results can be refined through additional diffusion steps \\( t' < t \\). The final latent is decoded to an image via \\( \\hat{x} = D_{\\phi^{\\mathrm{SD}}}(\\hat{z}_0) \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.535, + 0.909, + 0.673 + ], + "angle": 0, + "content": "Score Distillation. 2D diffusion models can optimize 3D representations \\(\\theta\\) through differentiable rendering \\(x_{\\pi} = g(\\theta, \\pi)\\) [45, 92, 95], which produces images \\(x_{\\pi}\\) from camera view \\(\\pi\\). Here 2D diffusion models serve as a metric \\(\\mathcal{L}(x_{\\pi}; \\pi, y)\\) that measures the consistency between \\(x_{\\pi}\\) and the text conditions \\(y\\). The 3D representation is optimized using gradient \\(\\nabla_{\\theta} \\mathcal{L}(x_{\\pi}; \\pi, y) = \\nabla x_{\\pi} \\mathcal{L}(x_{\\pi}; \\pi, y) \\frac{\\partial x_{\\pi}}{\\partial \\theta}\\), which also trains the native 3D generator. The computation of \\(\\nabla x_{\\pi} \\mathcal{L}\\) depends on the chosen score distillation method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.682, + 0.813, + 0.699 + ], + "angle": 0, + "content": "3.2. Progressive Rendering Distillation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We now detail our proposed training scheme for adapting SD as a native 3D generator. Traditional adaptation approaches require preparing ground-truth 3D representations \\(\\theta\\) and their corresponding latents \\(z\\) for each 3D sample in the dataset. The U-net is adapted to denoise diffused latents \\(z_{t}\\) by minimizing the noise prediction mean squared error (MSE). Fig. 2(a) illustrates this paradigm, which has been used by several native 3D generators [65, 114, 122, 148]. However, this paradigm faces limitations in both the quantity and quality of available 3D representations \\(\\theta\\), as existing 3D datasets lack sufficient high-quality data for training text-to-3D generators. Actually, the pretrained SD models already possess denoising capabilities for image generation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11038" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.093, + 0.408, + 0.105 + ], + "angle": 0, + "content": "(a) Vanilla SD Adaptation / Diffusion Model Training" + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.111, + 0.443, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.093, + 0.75, + 0.105 + ], + "angle": 0, + "content": "(b) Progressive Rendering Distillation (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.106, + 0.904, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.289, + 0.908, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Comparison between (a) traditional SD adaptation and (b) our proposed progressive rendering distillation (PRD) for native 3D generation. Traditional approach requires ground-truth 3D representations \\(\\theta\\) and their latents \\(z_0\\) for each 3D sample to generate \\(z_0\\). Our proposed PRD scheme progressively denoises latents \\(z_t\\) initialized from random noise into \\(z_0\\), which are decoded to \\(\\theta\\), using multi-view diffusion models as teachers for distillation, eliminating the need for 3D data during adaptation and overcoming data scarcity." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.372, + 0.484, + 0.525 + ], + "angle": 0, + "content": "In other words, pretrained SD is well-trained for a Markov Chain to reverse \\( \\boldsymbol{z}_T = \\epsilon \\sim \\mathcal{N}(0, I) \\) to \\( \\boldsymbol{z}_0 \\) with its U-net \\( \\boldsymbol{z}_{\\phi^{\\mathrm{SD}}} \\), and decode \\( \\boldsymbol{z}_0 \\) to image with its decoder \\( D_{\\phi^{\\mathrm{SD}}} \\). Our goal is to modify the Markov chain by transforming \\( \\boldsymbol{z}_{\\phi^{\\mathrm{SD}}} \\) and \\( D_{\\phi^{\\mathrm{SD}}} \\) into 3D generators \\( \\boldsymbol{z}_{\\phi^{3\\mathrm{D}}} \\) and \\( D_{\\phi^{3\\mathrm{D}}} \\), from which the 3D representations \\( \\theta \\) can be decoded. Note that our modification of the Markov chain differs from the traditional diffusion model adaptation objectives, as it requires neither ground-truth latents \\( \\boldsymbol{z}_0 \\) nor their noise-diffused variants \\( \\boldsymbol{z}_t \\) in the training process." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.537, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Specifically, at the beginning of the Markov chain, the network takes random noise \\(\\epsilon\\) as input to represent \\(\\mathbf{z}_T\\). At each step, current state \\(\\mathbf{z}_t\\) is used to estimate \\(\\hat{\\mathbf{z}}_0\\) through \\(\\mathbf{z}_{\\phi^{\\mathrm{SD}}}\\), which is then decoded to 3D output \\(\\hat{\\theta}\\) with \\(D_{\\phi^{\\mathrm{SD}}}\\). The 3D output \\(\\hat{\\theta}\\) is used to render images \\(\\mathbf{x}_{\\pi_1}, \\mathbf{x}_{\\pi_2}, \\ldots\\) at camera views \\(\\pi_1, \\pi_2, \\ldots\\) and receive supervision from multiview teachers via score distillation, while the estimated \\(\\hat{\\mathbf{z}}_0\\) is diffused to the next timestep \\(t'\\) as \\(\\mathbf{z}_{t'} = \\alpha_{t'} \\hat{\\mathbf{z}}_0 + \\sigma_{t'} \\epsilon\\) for subsequent operations. We name this training scheme as Progressive Rendering Distillation (PRD), as illustrated in Fig. 2(b). From the total \\(T\\) timesteps, we select a decreasing sequence of \\(K\\) timesteps \\(T = t_1 > t_2 > \\dots > t_K = T / K\\) with uniform spacing to perform score distillation from multi-view teachers. The gradient at each step is not backpropagated to previous steps; therefore, we can largely reduce the GPU memory usage and prevent gradient explosion [15, 83, 124, 133]. Since \\(\\phi^{\\mathrm{3D}}\\) is initialized from \\(\\phi^{\\mathrm{SD}}\\), this specialized gradient detachment strategy still maintains good convergence. The pseudo code of our algorithm is provided in the supplementary material. While the time cost of our training strategy increases with the increase of \\(K\\), we can ensure the model to generate high quality results in just a few steps, thereby accelerating inference. We set \\(K = 4\\) to balance quality and speed." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.372, + 0.863, + 0.389 + ], + "angle": 0, + "content": "3.3. Parameter-Efficient Triplane Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.402, + 0.908, + 0.902 + ], + "angle": 0, + "content": "While various 3D representations could be employed by our PRD scheme, in this paper we demonstrate an exemplar solution using Triplanes as the representation. We denote our adapted model as TriplaneTurbo with parameters \\(\\phi^{3\\mathrm{D}}\\). Specifically, TriplaneTurbo adapts SD to generate a 3D representation consisting of two Triplanes [8] \\(\\theta = (\\theta_{\\mathrm{geo}},\\theta_{\\mathrm{tex}})\\): a geometry Triplane \\(\\theta_{\\mathrm{geo}}\\) storing Signed Distance Function (SDF) and deformation values for mesh extraction, and a texture Triplane \\(\\theta_{\\mathrm{tex}}\\) containing RGB attributes for painting texture on the mesh. For each point in 3D space, we use a two-layer MLP to decode its SDF value. The same process applies to texture and mesh deformation [92, 118]. This separation of geometry and texture planes follows the work in [23, 97, 119]. We set the Triplane resolution as \\(256\\times 256\\), and replace the last convolution in SD's decoder to output 32 channels. The Triplanes' output has a dimension of \\(6\\times 256\\times 256\\times 32\\) in feature space. Due to the \\(8\\times\\) compression of the VAE, this corresponds to \\(6\\times 32\\times 32\\times 4\\) in latent space, distinct from the \\(1\\times 64\\times 64\\times 4\\) latent generated by pretrained SD. To enable interaction between the six feature planes, we follow existing approaches [68, 93, 94, 112] to adapt the U-nets' self-attention [87, 109] to allow cross-plane attention. Unlike existing works that fully retrain SD [12, 54, 65, 76, 94], which can lead to catastrophic forgetting [65, 94], we propose a parameter-efficient adaptation approach. The core of our design lies in the fact that each of the six feature planes maintains its own unique feature distribution. Therefore, plane-specific characteristics must be incorporated into the adaptation process. As illustrated in Fig. 3, our adaptation modifies the convolution, self-attention, and cross-attention layers. We name our approach Parameter-Efficient Triplane Adaptation (PETA)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11039" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.093, + 0.868, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.344, + 0.908, + 0.388 + ], + "angle": 0, + "content": "Figure 3. Illustration of TriplaneTurbo: an SD-adapted native 3D generator using our PRD scheme. Our model generates six feature planes comprising geometry Triplane \\(\\theta_{\\mathrm{geo}}\\) and texture Triplane \\(\\theta_{\\mathrm{tex}}\\) in 4 steps. We introduce Parameter Efficient Triplane Adaptation (PETA), which requires only \\(2.5\\%\\) additional parameters for adaptation. The parameter arrangement is illustrated in the figure." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.413, + 0.485, + 0.732 + ], + "angle": 0, + "content": "As shown in Fig. 3, for the convolution blocks (Res-Blocks) and cross-attention layers, we implement LoRA [33, 139] for parameter-efficient adaptation, and process the six planes uniformly. The plane-specific adaptations are then applied to the self-attention. For the self-attention blocks, we apply distinct LoRA layers [33] to the to_Q, to_K, to_V, and to_Out linear layers when processing each of the six feature planes. In each linear transformation within a self-attention block, the linear projection with multiple LoRAs is implemented in two steps. First, the frozen linear layer batch processes the features extracted from all the six planes together. Then, separate LoRA transformations are applied independently to the features of each plane. This adaptation maintains low computational overhead while effectively introducing plane-specific processing during attention calculations across the six feature planes. It can be applied with other techniques like AdaLoRa [149] and Vera [48]. We leave this for further exploration. We set the LoRA rank to 16 by default. While this adaptation adds only \\(2.5\\%\\) of the parameters to the SD model, it effectively enables native 3D generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.271, + 0.757 + ], + "angle": 0, + "content": "3.4. Distillation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Since PRD eliminates the need for 3D data by referring to multi-view teachers for distillation, using multiple teachers allows us to combine their strengths while mitigating individual biases. Most previous works [14, 59, 70, 82, 105] use SD model (parametrized by \\(\\phi^{\\mathrm{SD}}\\)) as the teacher for its ability to generate high-fidelity, text-consistent images. However, SD lacks camera-awareness, which can lead to the Janus problem [4]. MVDream [94] (MV, parametrized by \\(\\phi^{\\mathrm{MV}}\\)) addresses this by generating four" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.908, + 0.782 + ], + "angle": 0, + "content": "camera-conditioned views simultaneously, but at the cost of reduced prompt consistency [112]. While SD and MV complement each other, both of them focus on RGB rendering and provide no direct supervision on geometry. We further incorporate RichDreamer [84] (RD, parameterized by \\(\\phi^{\\mathrm{RD}}\\)), a model that generates four-view normal and depth maps based on text prompts. The score distillation guidance \\(\\mathcal{L}(\\pmb{x}_{\\pi};\\pi ,y)\\) in our implementation thus integrates SD, MV, and RD. At each PRD step (see Sec. 3.2 and Fig. 2), given a text prompt \\(y\\) and generated 3D representation \\(\\hat{\\theta}\\) from \\(z_{\\phi^{3\\mathrm{D}}}\\) and \\(D_{\\phi^{3\\mathrm{D}}}\\), we sample four views \\(\\pi_1,\\dots ,\\pi_4\\) at uniform azimuth intervals. We sample one view \\(\\pi\\) from \\(\\pi_1,\\ldots ,\\pi_4\\) to compute \\(\\mathcal{L}_{\\mathrm{SD}} = \\mathcal{L}_{\\phi^{\\mathrm{SD}}}(x_{\\pi};\\pi ,y)\\). For MV, all the four views are used to compute \\(\\mathcal{L}_{\\mathrm{MV}} = \\mathcal{L}_{\\phi^{\\mathrm{MV}}}(x_{\\pi_1},\\dots,x_{\\pi_4};\\pi_1,\\dots,\\pi_4,y)\\). RD operates on concatenated normal and depth renderings \\(x_{\\pi_1}'\\) \\(\\dots ,x_{\\pi_4}'\\) and its objective is \\(\\mathcal{L}_{\\mathrm{RD}} = \\mathcal{L}_{\\phi^{RD}}(x_{\\pi_1}'\\) \\(\\dots ,x_{\\pi_4}'\\) \\(\\pi_1,\\dots,\\pi_4,y)\\). Among existing score distillation methods [36, 41, 55, 56, 73, 82, 115, 117, 127, 142], we adopt Asynchronous Score Distillation (ASD) [73] for its pioneered efficiency in training deep text-to-3D generators. For 3D rendering, as illustrated in Fig. 3, we combine volumetric rendering [138] at \\(64\\times 64\\) resolution with mesh rasterization [46] at \\(512\\times 512\\) to overcome the instability of pure mesh supervision [132]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.794, + 0.646, + 0.811 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.722, + 0.835 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. For a fair comparison with existing methods, we use captions of the 3D objects [17] provided by [30] to train our model, which comprises a total of 360K text prompts. We employ SD v2.1-base [88] as the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11040" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.903, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.58, + 0.871, + 0.596 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of text-to-mesh generation results by competing methods. Please refer to Sec. 4.2 for details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.484, + 0.713 + ], + "angle": 0, + "content": "base model. Our model is trained for 15K iterations with a learning rate of 2e-4, costing 40 hours on 8 NVIDIA H20 GPUs. We further collect 1.6 million text prompts to evaluate the benefit of data scaling supported by our method. Additional training details and loss weights are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Compared Methods. Our proposed PRD aims for fast text-to-mesh generation. Therefore, we compare it against state-of-the-art approaches that can generate textured meshes within one minute, including Shape-E [38], Direct3D [61], 3DTopia [30], GVGEN [26], LN3Diff [49], LGM [106] and PI3D [65]. Note that we do not compare with some relevant works [76, 130] since their codes/models are not publicly available and they employ different evaluation protocols. In our experiments, the results of Shape-E, Direct3D, 3DTopia, GVGEN, LN3Diff and LGM are obtained by running their publicly available models. For PI3D, we can only perform quantitative com" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.907, + 0.667 + ], + "angle": 0, + "content": "parisons with it by copying its results from the original paper, but we cannot perform visual comparisons with it since its code/model is not yet publicly available." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Evaluation Protocol. We employ the protocol used in our competing methods [26, 30, 38, 49, 65, 106] to evaluate our PRD model. Specifically, we use the ViT-B/34 CLIP model [85] to evaluate the test prompts from the DreamFusion gallery [82]. As in [65], we render the generated 3D results at 512 resolution from four viewpoints at \\(15^{\\circ}\\) elevation across four azimuth angles: \\(0^{\\circ}\\), \\(90^{\\circ}\\), \\(180^{\\circ}\\) and \\(270^{\\circ}\\). Under these views, we evaluate the performance of competing methods using CLIP Score [27] (C.S.) and CLIP R-precision \\((\\mathbb{R}@\\mathbb{1})\\). To ensure a fair comparison for instant text-to-mesh generation, we exclude the post-processing steps such as SDS refinement [82], as they will prolong the generation time by several minutes. For models [26, 106] using Gaussian Splatting representations, we use the conversion script from [106] to generate textured meshes." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11041" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.295, + 0.108 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.114, + 0.482, + 0.295 + ], + "angle": 0, + "content": "We showcase qualitative comparisons of the competing methods in Fig. 4 using challenging test prompts. One can see that most of the existing methods struggle to generate satisfactory outputs. Our method, in comparison, produces better quality results with complete and vivid meshes. The quantitative results are reported in Tab. 1. Again, our method demonstrates superior performance to its competitors in all the metrics. Existing methods fall short in the consistency of object poses and in the capability of handling complex prompts. Our PRD method addresses these challenges, enabling faster inference speed and improving the model performance by data scaling." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.297, + 0.485, + 0.568 + ], + "angle": 0, + "content": "Handling Inconsistent Generation Poses. As shown in Fig. 4, existing models often generate objects with incorrect poses. For prompts like 'A teal moped', the competing methods like Direct3D [122], Shape-E [38] and GVGEN [26] generate objects with misaligned orientations, such as facing sideways or backwards. This issue stems from the inconsistent object orientations in 3D training datasets, which are difficult to detect and correct automatically. Current methods struggle with noisy training data, leading to pose ambiguity and geometric defects. Our approach addresses this challenge by learning from multiview teachers. Though our teachers are trained on noisy 3D datasets and may occasionally provide incorrect directional guidance, our PRD scheme exposes the 3D outputs to multi-view teachers \\( K \\) times per iteration (see Sec. 3.2). Through the iterative distillation process, we substantially decrease the impact of incorrect directional guidance, ensuring consistent pose alignment in the 3D outputs." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.57, + 0.487, + 0.904 + ], + "angle": 0, + "content": "Handling Complex Text Prompts. The failure of our competing methods mainly stems from their reliance on the existing text-3D paired datasets, which are not comprehensive enough compared to the diverse user inputs. Therefore, trained on these data, existing methods fail to produce good results when the input is complex. For example, existing methods might perform well when the input prompt is 'A robot' but fail when the prompt becomes 'A robot tiger'. The quality of existing 3D datasets is also compromised by the absence of creative concepts. Creating 3D models for imaginative concepts like 'A robot tiger' demands significant time and expertise from 3D artists. As a result, existing 3D datasets are largely limited to common everyday objects. Models trained on these limited datasets fail to generalize effectively to imaginative or complex prompts. We solve this problem by adapting SD as a 3D generator and inheriting its generative power, and more crucially, by introducing a training scheme that completely eliminates the need of 3D data. Our training scheme not only improves the quality of results on the existing training corpus, as shown by the qualitative and quantitative results in Fig. 4 and Tab. 1, but also enhances the capability to handle complex prompts by" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.089, + 0.888, + 0.264 + ], + "angle": 0, + "content": "
C.S. ↑R@1↑Latency (/sec)
Shape-E [38]55.127.113.0
Direct3D60.84.3316.0
3DTopia [30]59.711.223.7
PI3D* [65]65.925.23.00
GVGEN [26]51.12.4449.2
LN3Diff [49]55.95.098.16
LGM [106]67.428.356.1
Ours68.232.31.23
+More Text Data75.146.01.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.266, + 0.907, + 0.296 + ], + "angle": 0, + "content": "Table 1. Quality and speed comparison for text-to-mesh generation. *indicates that the values are quoted from the original papers." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.308, + 0.883, + 0.323 + ], + "angle": 0, + "content": "expanding the available training data, as detailed below." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.907, + 0.475 + ], + "angle": 0, + "content": "Fast Inference Speed. Our PRD method also demonstrates superior computational efficiency. As shown in Tab. 1, we evaluate the average inference latency from text input to textured mesh output across all test prompts on the H20 GPU device. While some methods [26, 106] require dozens of steps, our PRD approach enables the native 3D generator to produce quality results in just \\( K \\) steps. With the suggested setting of \\( K = 4 \\), as shown in Tab. 1, our model achieves sub-second latency for text-to-mesh generation, significantly outperforming previous methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.476, + 0.909, + 0.732 + ], + "angle": 0, + "content": "Scaling Up Training Corpus. Since our method is free from the constraints of 3D training data, it can be easily scaled to accommodate more complex and creative text prompts during training. It preserves the SD model's ability to handle creative concepts throughout the 3D adaptation process, generating 3D outputs that faithfully represent the input prompts. As can be seen in the +More Text Data column, when we scale up the training text data from 360K to 1.6M, the CLIP similarity improves by as much as \\(7\\%\\), leading to more consistent generation for challenging text prompts such as A lion reading the newspaper and A tray of Sushi containing pugs. This is because our collected text data covers a wider range of creative concepts than the existing 3D datasets [17, 123], thus providing more sufficient training and improving the generalizability of the model. More visual examples are partially presented in Fig. 1 and detailed in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.743, + 0.669, + 0.759 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The Effectiveness of PRD. We validate our PRD algorithm by testing a simplified configuration with \\(\\mathbf{K} = \\mathbf{1}\\), which reduces our method to a single-step generation process that is equivalent to a vanilla native 3D generator trained by score distillation [73]. As shown in Fig. 5 and quantified in Tab. 2, this configuration fails to generate proper 3D structures because it needs to simultaneously handle two complex challenges: adapting SD for 3D generation and performing single-step generation. In contrast, our PRD scheme can" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11042" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.087, + 0.488, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.279, + 0.483, + 0.296 + ], + "angle": 0, + "content": "Figure 5. Visualizations on the ablation studies of PRD algorithm." + }, + { + "type": "table", + "bbox": [ + 0.169, + 0.311, + 0.408, + 0.391 + ], + "angle": 0, + "content": "
C.S. ↑R@1 ↑
K=150.914.4
K=262.622.4
K=4 (Proposed)68.232.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.399, + 0.458, + 0.415 + ], + "angle": 0, + "content": "Table 2. Ablation study on the hyper-parameters of PRD." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.483, + 0.52 + ], + "angle": 0, + "content": "use alternative step configurations such as \\(\\mathbf{K} = 2\\), which produces suboptimal yet acceptable results. We found that the configuration of \\(\\mathbf{K} = 4\\) provides the best trade-off between output quality and computational efficiency, which is used as the default setting of PRD." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.522, + 0.483, + 0.824 + ], + "angle": 0, + "content": "The Effectiveness of PETA. We first compare our proposed PETA method with conventional full parameter fine-tuning (shown as Full Param Tuning in Fig. 6 and Tab. 3). We see that full parameter fine-tuning exhibits training instability and catastrophic forgetting, resulting in text-inconsistent outputs. We then conduct additional ablation studies using vanilla LoRA tuning, maintaining an equivalent parameter size (22.6M), shown as the configuration of w/ Basic LoRA. We see that this vanilla adaptation produces degraded geometric structures and textures, and lacks the capability to handle the unique characteristics of each plane. Since different geometry and texture planes (see Fig. 3) exhibit distinct feature distributions, they require specialized consideration. Our solution (denoted as w/ PETA) considers plane dependency using multiple LoRAs in self-attention blocks, enabling each plane to maintain its unique representation while allowing cross-plane interactions during self-attention computation. As shown in Fig. 5 and Tab. 2, PETA achieves enhanced 3D generation quality with good text consistency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.903 + ], + "angle": 0, + "content": "We also perform ablation studies to investigate the impact of multiple multi-view teachers in training, the choice of LoRA rank, our hybrid rendering approach that combines volumetric rendering and rasterization for multi-view distillation in PRD training scheme. The details can be found in" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.091, + 0.905, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.279, + 0.875, + 0.295 + ], + "angle": 0, + "content": "Figure 6. Visualizations on the ablation study of PETA." + }, + { + "type": "table", + "bbox": [ + 0.577, + 0.308, + 0.846, + 0.386 + ], + "angle": 0, + "content": "
C.S. ↑R@1 ↑
Full Param Tuning35.80.35
w/ Basic LoRA54.211.1
w/ PETA (Proposed)68.232.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.549, + 0.396, + 0.871, + 0.411 + ], + "angle": 0, + "content": "Table 3. Ablation study on the effectiveness of PETA." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.439, + 0.714, + 0.455 + ], + "angle": 0, + "content": "the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.47, + 0.766, + 0.485 + ], + "angle": 0, + "content": "5. Conclusion and Limitation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.496, + 0.907, + 0.737 + ], + "angle": 0, + "content": "In this paper, we presented Progressive Rendering Distillation (PRD), a novel training scheme that adapts Stable Diffusion (SD) for instant text-to-mesh generation without relying on 3D data. We also introduced PETA (Parameter-Efficient Triplane Adaptation), a parameter-efficient method that introduces only \\(2.5\\%\\) additional parameters to effectively enable SD for instant text-to-mesh generation. Our model, namely TriplaneTurbo, can produce text-consistent textured meshes in only 1.2 second. Through comprehensive experiments, we validated the effectiveness of our approach. Our methodology has the potential to be extended to 3D scene generation and image-to-3D tasks. While currently implemented with SD, the PRD approach can also be applied to other pre-trained models like DiT [20]. We hope our work can inspire new directions in 3D generation to overcome the dependency on 3D data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.738, + 0.909, + 0.845 + ], + "angle": 0, + "content": "Limitations. One limitation of our method lies in the generation of precise numbers of multiple 3D objects, which may require more sophisticated multi-view teachers, potentially enhanced with layout guidance. Besides, our results for full-body humans might exhibit limited facial and hand details, which can be improved by extending SD adaptation to more advanced 3D structures than Triplane." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.86, + 0.667, + 0.877 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.835, + 0.902 + ], + "angle": 0, + "content": "This work is supported by the InnoHK program." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11043" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.115, + 0.483, + 0.156 + ], + "angle": 0, + "content": "[1] Thiemo Alldieck, Nikos Kolotouros, and Cristian Sminchisescu. 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Springer, 2024. 3" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.092, + 0.487, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11050" + } + ] +] \ No newline at end of file diff --git a/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_origin.pdf b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6eac79b4ad0198d354f2525740c34c1551bd1b8b --- /dev/null +++ b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/64be8fea-91f9-4a05-a3e4-a20e757ee9ee_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:657dffccdaad91f13433317f2c88e06cb08831faec6a829ff1182b3fa32dcbf2 +size 8900983 diff --git a/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/full.md b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e1ee121e39bcef7a32b555e19ec03a5378ac40e7 --- /dev/null +++ b/2025/Progressive Rendering Distillation_ Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data/full.md @@ -0,0 +1,329 @@ +# Progressive Rendering Distillation: Adapting Stable Diffusion for Instant Text-to-Mesh Generation without 3D Data + +Zhiyuan Ma $^{1,2}$ Xinyue Liang $^{1,2}$ Rongyuan Wu $^{1}$ Xiangyu Zhu $^{3,4}$ Zhen Lei $^{1,2,3,4*}$ Lei Zhang $^{1*}$ $^{1}$ The Hong Kong Polytechnic University + $^{2}$ Center for Artificial Intelligence and Robotics, HKISI CAS + $^{3}$ State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA + $^{4}$ School of Artificial Intelligence, University of Chinese Academy of Sciences, UCAS + +![](images/d18896515f3c1ce807f510adcf655d5349f24f8555be93062ae17f641a6dabc9.jpg) +Figure 1. Our method adapts Stable Diffusion [87] to generate high-fidelity textured meshes in 1.2 seconds. + +# Abstract + +It is highly desirable to obtain a model that can generate high-quality 3D meshes from text prompts in just seconds. While recent attempts have adapted pre-trained text-to-image diffusion models, such as Stable Diffusion (SD), into generators of 3D representations (e.g., Triplane), they often suffer from poor quality due to the lack of sufficient high-quality 3D training data. Aiming at overcoming the data shortage, we propose a novel training scheme, termed as Progressive Rendering Distillation (PRD), eliminating the need for 3D ground-truths by distilling multi-view diffusion models and adapting SD into a native 3D generator. In each iteration of training, PRD uses the U-Net to progressively denoise the latent from random noise for a few steps, and in each step it decodes the denoised latent into 3D output. Multi-view diffusion models, including MVDream and RichDreamer, are used in joint with SD + +to distill text-consistent textures and geometries into the 3D outputs through score distillation. Since PRD supports training without 3D ground-truths, we can easily scale up the training data and improve generation quality for challenging text prompts with creative concepts. Meanwhile, PRD can accelerate the inference speed of the generation model in just a few steps. With PRD, we train a Triplane generator, namely TriplaneTurbo, which adds only $2.5\%$ trainable parameters to adapt SD for Triplane generation. TriplaneTurbo outperforms previous text-to-3D generators in both efficiency and quality. Specifically, it can produce high-quality 3D meshes in 1.2 seconds and generalize well for challenging text input. The code is available at github.com/theEricMa/TriplaneTurbo. + +# 1. Introduction + +Text-to-3D aims to create 3D contents faithful to the given textual descriptions. The optimization-based text-to-3D + +methods can achieve high generation fidelity by using image diffusion priors [52, 62, 66, 68, 71, 84, 94, 110] and score distillation techniques [42, 56, 73, 82, 111, 115, 143, 153] to optimize 3D representations [10, 29, 59, 60, 105]. However, these approaches encounter bottlenecks in computational efficiency since they take hours to generate 3D textured meshes. Recent researches have shifted towards learning-based methods [7, 25, 37, 49, 80], which generate 3D contents through feed-forward networks, reducing the latency to a few seconds per output. Unfortunately, existing 3D datasets [16-18, 81, 123] are much smaller compared to those used in training text-to-image generation models, while the 3D data therein suffer from texture quality and inconsistent object poses [61]. Consequently, these approaches struggle to produce high-quality 3D outputs. As a promising alternative to the above mentioned methods, one can adapt pretrained text-to-image models, such as Stable Diffusion (SD) [87], into generators of 3D representations [54, 65, 76]. Recent studies have enabled the use of SD to generate 2D planes for 3D representations such as Triplane [8]. PI3D [65] adapts SD to generate six 2D planes pre-optimized for 3D object reconstruction. HexaGen [76] first trains a VAE to compress 3D objects into latent space, then adapts SD to generate the desired latents from text prompts. These methods leverage SD's prior knowledge for diverse text prompts while reducing training costs. However, their reliance on data-driven training limits the generalization performance. + +In this paper, we propose to address the data shortage problem by using high-quality multi-view diffusion models [66, 84, 94] as teachers and performing multi-view distillation to adapt SD into an instant text-to-mesh generator without using 3D ground-truth data. Data-free distillation techniques [69, 154] have been applied in previous methods [51, 70, 73, 130] to train native 3D generators from scratch, whereas they struggle to produce high-quality 3D outputs. We argue that if we can adapt SD for native 3D generation, instead of training from scratch, not only the training efficiency can be improved but also the generation quality can be enhanced. To our best knowledge, however, no such attempt has been made before. The primary obstacle lies in the training scheme of SD, which requires 3D ground-truth data to supervise the denoising process. This requirement, unfortunately, conflicts with our goal to eliminate the dependency on 3D training data. + +To address the above challenges, we propose Progressive Rendering Distillation (PRD), which enables 3D data-free distillation. PRD achieves this goal by denoising the latent from random noise rather than 3D groundtruths. In each training iteration, PRD uses a few steps to progressively reverse noise to latent space using the adapted U-Net of SD. Then the denoised latent of each step is decoded to 3D contents via the adapted VAE decoder. Multi- + +view teacher models are used to distill high-quality renderings through efficient score distillation techniques such as ASD [73]. An additional benefit of PRD is that by adapting the SD to generate 3D contents in just four steps, the overall generation process can be much accelerated. + +PRD is flexible in the choices of multi-view teacher models and the types of 3D representations. Unlike existing approaches using SD alone as the teacher [59, 104, 115, 140, 153], which risk the multi-view inconsistency and the Janus problem [4], we employ multiple teachers in training. Specifically, we employ MVDream [94] and SD to suppress the Janus problem and ensure text consistency in 3D content supervision. Additionally, we use RichDreamer [84] for geometry supervision through normal and depth. With PRD, we adapt SD into a native 3D generator to produce geometry and texture Triplanes in 4 steps, which is named as TriplaneTurbo in the following context. To enhance TriplaneTurbo's textured mesh quality, we employ SDF-based volumetric rendering [138] and mesh rasterization [118] for multi-view teacher supervision. + +In addition, to address the high GPU memory usage caused by multiple teachers and multi-view renderings in the training process, we introduce the Parameter-Efficient Triplane Adapter (PETA), which adds only $2.5\%$ trainable parameters to the frozen SD and effectively adapts it for 3D generation. Some results are shown in Fig. 1. To our knowledge, this is the first parameter-efficient training method for direct 3D content generation from 2D diffusion models, departing from full-parameter adaptation approaches. Our key contributions are summarized as follows: + +- We make the first attempt to adapt the pretrained 2D SD model into a native 3D generator without 3D data. With the proposed PRD scheme, we use multi-view diffusion models as teachers and distill SD into a four-step native 3D generator, namely TriplaneTurbo. +- TriplaneTurbo adds only $2.5\%$ additional trainable parameters to the frozen SD for Triplane adaptation. It marks the first use of parameter-efficient training to adapt 2D diffusion models for native 3D generation. +- TriplaneTurbo surpasses existing text-to-3D models not only in quality but also in speed, reducing text-to-mesh generation time to just 1.2 seconds. In addition, by scaling up the text training data, the model can generalize much better to complex text input. + +# 2. Related Work + +Data-Driven Models for 3D Generation. Employing 3D data to train generators has shown its effectiveness for single-category 3D generation such as human faces [2, 8, 31, 72, 98, 125, 128], body shapes [34, 57, 89, 134], everyday objects [3, 39, 64, 78], and structured room layouts [5, 21, 75, 86, 107, 126]. This is mainly because for these specific categories, the training data are relatively + +easy to collect. However, text-to-3D generation requires open-category generation, bringing a rather different challenge. The difficulties in obtaining sufficient 3D training data largely limit the model generalizability across diverse text prompts [73], regardless of the type of used generation models (e.g., GAN [24, 79, 91] or diffusion models [28, 40, 96]) or 3D representations (e.g., NeRF [6, 77] or Gaussian Splatting [44, 144]). The publicly available 3D datasets [16–18, 81, 123] mostly contain only hundreds or thousands of samples, which are very hard, if not impossible, to train a generalized text-to-3D generation model. + +2D Diffusion Models for 3D Generation. The difficulty of text-to-3D generation can be alleviated by leveraging 2D diffusion models as priors, thanks to their training on vast text-image pairs. Early approaches like SDS [104] and VSD [13] pioneered zero-shot text-to-3D generation by optimizing 3D representations (NeRF [59, 62, 82, 111], mesh [11, 59, 115, 136], 3DGS [56, 105, 140, 141]) through score distillation [1, 36, 41, 55, 56, 73, 82, 103, 113, 115, 117, 127, 142, 150, 152, 155], which serves as a bridge to transfer the generative capability of 2D diffusion models to 3D representations through rendered views. However, pre-trained text-to-image models like SD lack multiview consistency, leading to the Janus problem [4]. MVDream [94] and subsequent works [35, 67] address this issue by camera-aware adaptations and synchronized multiview generation, and they incorporate additional modalities such as normal [84], depth [22, 43], and CCM [63, 131] to enhance geometric quality. While achieving improved 3D generation results, these methods require computationally intensive score distillation [12, 84, 90, 94] or 3D reconstruction [32, 53, 68, 93, 106, 116, 135, 146]. Native 3D generators [17, 26, 34, 49, 50, 58, 74, 108, 122, 129, 145, 148, 148, 151, 151] can reduce the generation time to seconds by directly producing 3D content without view rendering as proxies. For example, LN3Diff [49] and GVGEN [26] compress NeRF [77] and 3DGS [44] into latent spaces using VAEs [47], then train text-conditioned latent diffusion models [28]. However, these methods show limited generalizability across text prompts, as their performance is constrained by the insufficient text-3D training pairs. + +Some methods [65, 76, 84, 94] leverage SD as their backbone to transfer text-to-image knowledge into text-to-3D generation. SD provides strong generative prior and improves the model generalizability [9, 19, 58, 99–102, 120, 121, 137, 147]. Approaches like PI3D [65] adapt SD to generate multiple planes for constructing 3D space, yet their performance remains limited due to the insufficient 3D training data. Instead of adapting SD for multiview generation, native 3D generation requires substantially more 3D data for effective adaptation. We propose to address the data insufficiency challenge by distilling knowledge from multi-view diffusion models into an SD-adapted + +native 3D generator, eliminating the need for 3D training data. While previous works like ATT3D [70] and ScaleDreamer [73] have investigated such a data-free training strategy, they employ multi-view distillation to train generators from scratch, and show limited performance due to the insufficient training scale. To overcome the huge training cost, we propose a cost-effective solution that combines multi-view distillation with SD-based native 3D generation. A fundamental challenge to achieve this goal is how to adapt SD for 3D generation without ground-truth data. We address this by proposing a novel Progressive Rendering Distillation scheme, which not only eliminates the need of 3d ground-truths but also enables few-step generation. + +# 3. Method + +# 3.1. Preliminary + +Stable Diffusion (SD) performs diffusion in latent space for efficient text-to-image generation. Its VAE encoder $E_{\phi^{\mathrm{SD}}}$ compresses an image $x$ into a latent code $z$ , while its decoder $D_{\phi^{\mathrm{SD}}}$ reconstructs the image. Given text prompt $y$ , a U-net $\epsilon_{\phi^{\mathrm{SD}}}$ predicts noise $\epsilon$ , which is added to $z_t = \alpha_t z + \sigma_t \epsilon$ , where timestep $t \in 1, \ldots, T$ controls noise level via scalars $\alpha_t$ and $\sigma_t$ . Generation proceeds by iteratively denoising from $z_T$ to prompt-aligned $z_0$ . At each step, the U-net estimates noise $\hat{\epsilon} = \epsilon_{\phi^{\mathrm{SD}}}(z_t; t, y)$ to compute $\hat{z}_0 = \frac{\hat{z}_t - \sigma_t \hat{\epsilon}}{\alpha_t}$ , denoted as $\hat{z}_0 = z_{\phi^{\mathrm{SD}}}(z_t; t, y)$ . Results can be refined through additional diffusion steps $t' < t$ . The final latent is decoded to an image via $\hat{x} = D_{\phi^{\mathrm{SD}}}(\hat{z}_0)$ . + +Score Distillation. 2D diffusion models can optimize 3D representations $\theta$ through differentiable rendering $x_{\pi} = g(\theta, \pi)$ [45, 92, 95], which produces images $x_{\pi}$ from camera view $\pi$ . Here 2D diffusion models serve as a metric $\mathcal{L}(x_{\pi}; \pi, y)$ that measures the consistency between $x_{\pi}$ and the text conditions $y$ . The 3D representation is optimized using gradient $\nabla_{\theta} \mathcal{L}(x_{\pi}; \pi, y) = \nabla x_{\pi} \mathcal{L}(x_{\pi}; \pi, y) \frac{\partial x_{\pi}}{\partial \theta}$ , which also trains the native 3D generator. The computation of $\nabla x_{\pi} \mathcal{L}$ depends on the chosen score distillation method. + +# 3.2. Progressive Rendering Distillation + +We now detail our proposed training scheme for adapting SD as a native 3D generator. Traditional adaptation approaches require preparing ground-truth 3D representations $\theta$ and their corresponding latents $z$ for each 3D sample in the dataset. The U-net is adapted to denoise diffused latents $z_{t}$ by minimizing the noise prediction mean squared error (MSE). Fig. 2(a) illustrates this paradigm, which has been used by several native 3D generators [65, 114, 122, 148]. However, this paradigm faces limitations in both the quantity and quality of available 3D representations $\theta$ , as existing 3D datasets lack sufficient high-quality data for training text-to-3D generators. Actually, the pretrained SD models already possess denoising capabilities for image generation. + +![](images/c1ac498931652cc33bbbb3cc7826ce8d1a9646fe1500089a8d291fe068630e80.jpg) +(a) Vanilla SD Adaptation / Diffusion Model Training + +![](images/563b13dc3fbcad2cb77db81a628fc18dccb08d12a58a25dda7ef0a5c82170b32.jpg) +(b) Progressive Rendering Distillation (Ours) +Figure 2. Comparison between (a) traditional SD adaptation and (b) our proposed progressive rendering distillation (PRD) for native 3D generation. Traditional approach requires ground-truth 3D representations $\theta$ and their latents $z_0$ for each 3D sample to generate $z_0$ . Our proposed PRD scheme progressively denoises latents $z_t$ initialized from random noise into $z_0$ , which are decoded to $\theta$ , using multi-view diffusion models as teachers for distillation, eliminating the need for 3D data during adaptation and overcoming data scarcity. + +In other words, pretrained SD is well-trained for a Markov Chain to reverse $\boldsymbol{z}_T = \epsilon \sim \mathcal{N}(0, I)$ to $\boldsymbol{z}_0$ with its U-net $\boldsymbol{z}_{\phi^{\mathrm{SD}}}$ , and decode $\boldsymbol{z}_0$ to image with its decoder $D_{\phi^{\mathrm{SD}}}$ . Our goal is to modify the Markov chain by transforming $\boldsymbol{z}_{\phi^{\mathrm{SD}}}$ and $D_{\phi^{\mathrm{SD}}}$ into 3D generators $\boldsymbol{z}_{\phi^{3\mathrm{D}}}$ and $D_{\phi^{3\mathrm{D}}}$ , from which the 3D representations $\theta$ can be decoded. Note that our modification of the Markov chain differs from the traditional diffusion model adaptation objectives, as it requires neither ground-truth latents $\boldsymbol{z}_0$ nor their noise-diffused variants $\boldsymbol{z}_t$ in the training process. + +Specifically, at the beginning of the Markov chain, the network takes random noise $\epsilon$ as input to represent $\mathbf{z}_T$ . At each step, current state $\mathbf{z}_t$ is used to estimate $\hat{\mathbf{z}}_0$ through $\mathbf{z}_{\phi^{\mathrm{SD}}}$ , which is then decoded to 3D output $\hat{\theta}$ with $D_{\phi^{\mathrm{SD}}}$ . The 3D output $\hat{\theta}$ is used to render images $\mathbf{x}_{\pi_1}, \mathbf{x}_{\pi_2}, \ldots$ at camera views $\pi_1, \pi_2, \ldots$ and receive supervision from multiview teachers via score distillation, while the estimated $\hat{\mathbf{z}}_0$ is diffused to the next timestep $t'$ as $\mathbf{z}_{t'} = \alpha_{t'} \hat{\mathbf{z}}_0 + \sigma_{t'} \epsilon$ for subsequent operations. We name this training scheme as Progressive Rendering Distillation (PRD), as illustrated in Fig. 2(b). From the total $T$ timesteps, we select a decreasing sequence of $K$ timesteps $T = t_1 > t_2 > \dots > t_K = T / K$ with uniform spacing to perform score distillation from multi-view teachers. The gradient at each step is not backpropagated to previous steps; therefore, we can largely reduce the GPU memory usage and prevent gradient explosion [15, 83, 124, 133]. Since $\phi^{\mathrm{3D}}$ is initialized from $\phi^{\mathrm{SD}}$ , this specialized gradient detachment strategy still maintains good convergence. The pseudo code of our algorithm is provided in the supplementary material. While the time cost of our training strategy increases with the increase of $K$ , we can ensure the model to generate high quality results in just a few steps, thereby accelerating inference. We set $K = 4$ to balance quality and speed. + +# 3.3. Parameter-Efficient Triplane Adaptation + +While various 3D representations could be employed by our PRD scheme, in this paper we demonstrate an exemplar solution using Triplanes as the representation. We denote our adapted model as TriplaneTurbo with parameters $\phi^{3\mathrm{D}}$ . Specifically, TriplaneTurbo adapts SD to generate a 3D representation consisting of two Triplanes [8] $\theta = (\theta_{\mathrm{geo}},\theta_{\mathrm{tex}})$ : a geometry Triplane $\theta_{\mathrm{geo}}$ storing Signed Distance Function (SDF) and deformation values for mesh extraction, and a texture Triplane $\theta_{\mathrm{tex}}$ containing RGB attributes for painting texture on the mesh. For each point in 3D space, we use a two-layer MLP to decode its SDF value. The same process applies to texture and mesh deformation [92, 118]. This separation of geometry and texture planes follows the work in [23, 97, 119]. We set the Triplane resolution as $256\times 256$ , and replace the last convolution in SD's decoder to output 32 channels. The Triplanes' output has a dimension of $6\times 256\times 256\times 32$ in feature space. Due to the $8\times$ compression of the VAE, this corresponds to $6\times 32\times 32\times 4$ in latent space, distinct from the $1\times 64\times 64\times 4$ latent generated by pretrained SD. To enable interaction between the six feature planes, we follow existing approaches [68, 93, 94, 112] to adapt the U-nets' self-attention [87, 109] to allow cross-plane attention. Unlike existing works that fully retrain SD [12, 54, 65, 76, 94], which can lead to catastrophic forgetting [65, 94], we propose a parameter-efficient adaptation approach. The core of our design lies in the fact that each of the six feature planes maintains its own unique feature distribution. Therefore, plane-specific characteristics must be incorporated into the adaptation process. As illustrated in Fig. 3, our adaptation modifies the convolution, self-attention, and cross-attention layers. We name our approach Parameter-Efficient Triplane Adaptation (PETA). + +![](images/746feac01c63a3330237dbd27e8b8ca4a77e15c35731a90b900354ad64b049d2.jpg) +Figure 3. Illustration of TriplaneTurbo: an SD-adapted native 3D generator using our PRD scheme. Our model generates six feature planes comprising geometry Triplane $\theta_{\mathrm{geo}}$ and texture Triplane $\theta_{\mathrm{tex}}$ in 4 steps. We introduce Parameter Efficient Triplane Adaptation (PETA), which requires only $2.5\%$ additional parameters for adaptation. The parameter arrangement is illustrated in the figure. + +As shown in Fig. 3, for the convolution blocks (Res-Blocks) and cross-attention layers, we implement LoRA [33, 139] for parameter-efficient adaptation, and process the six planes uniformly. The plane-specific adaptations are then applied to the self-attention. For the self-attention blocks, we apply distinct LoRA layers [33] to the to_Q, to_K, to_V, and to_Out linear layers when processing each of the six feature planes. In each linear transformation within a self-attention block, the linear projection with multiple LoRAs is implemented in two steps. First, the frozen linear layer batch processes the features extracted from all the six planes together. Then, separate LoRA transformations are applied independently to the features of each plane. This adaptation maintains low computational overhead while effectively introducing plane-specific processing during attention calculations across the six feature planes. It can be applied with other techniques like AdaLoRa [149] and Vera [48]. We leave this for further exploration. We set the LoRA rank to 16 by default. While this adaptation adds only $2.5\%$ of the parameters to the SD model, it effectively enables native 3D generation. + +# 3.4. Distillation Details + +Since PRD eliminates the need for 3D data by referring to multi-view teachers for distillation, using multiple teachers allows us to combine their strengths while mitigating individual biases. Most previous works [14, 59, 70, 82, 105] use SD model (parametrized by $\phi^{\mathrm{SD}}$ ) as the teacher for its ability to generate high-fidelity, text-consistent images. However, SD lacks camera-awareness, which can lead to the Janus problem [4]. MVDream [94] (MV, parametrized by $\phi^{\mathrm{MV}}$ ) addresses this by generating four + +camera-conditioned views simultaneously, but at the cost of reduced prompt consistency [112]. While SD and MV complement each other, both of them focus on RGB rendering and provide no direct supervision on geometry. We further incorporate RichDreamer [84] (RD, parameterized by $\phi^{\mathrm{RD}}$ ), a model that generates four-view normal and depth maps based on text prompts. The score distillation guidance $\mathcal{L}(\pmb{x}_{\pi};\pi ,y)$ in our implementation thus integrates SD, MV, and RD. At each PRD step (see Sec. 3.2 and Fig. 2), given a text prompt $y$ and generated 3D representation $\hat{\theta}$ from $z_{\phi^{3\mathrm{D}}}$ and $D_{\phi^{3\mathrm{D}}}$ , we sample four views $\pi_1,\dots ,\pi_4$ at uniform azimuth intervals. We sample one view $\pi$ from $\pi_1,\ldots ,\pi_4$ to compute $\mathcal{L}_{\mathrm{SD}} = \mathcal{L}_{\phi^{\mathrm{SD}}}(x_{\pi};\pi ,y)$ . For MV, all the four views are used to compute $\mathcal{L}_{\mathrm{MV}} = \mathcal{L}_{\phi^{\mathrm{MV}}}(x_{\pi_1},\dots,x_{\pi_4};\pi_1,\dots,\pi_4,y)$ . RD operates on concatenated normal and depth renderings $x_{\pi_1}'$ $\dots ,x_{\pi_4}'$ and its objective is $\mathcal{L}_{\mathrm{RD}} = \mathcal{L}_{\phi^{RD}}(x_{\pi_1}'$ $\dots ,x_{\pi_4}'$ $\pi_1,\dots,\pi_4,y)$ . Among existing score distillation methods [36, 41, 55, 56, 73, 82, 115, 117, 127, 142], we adopt Asynchronous Score Distillation (ASD) [73] for its pioneered efficiency in training deep text-to-3D generators. For 3D rendering, as illustrated in Fig. 3, we combine volumetric rendering [138] at $64\times 64$ resolution with mesh rasterization [46] at $512\times 512$ to overcome the instability of pure mesh supervision [132]. + +# 4. Experiments + +# 4.1. Experimental Settings + +Implementation Details. For a fair comparison with existing methods, we use captions of the 3D objects [17] provided by [30] to train our model, which comprises a total of 360K text prompts. We employ SD v2.1-base [88] as the + +![](images/b7550ed971a14bbc9043de9ee481e939d5c04a13b9a0990454404120aac2e697.jpg) +Figure 4. Qualitative comparison of text-to-mesh generation results by competing methods. Please refer to Sec. 4.2 for details. + +base model. Our model is trained for 15K iterations with a learning rate of 2e-4, costing 40 hours on 8 NVIDIA H20 GPUs. We further collect 1.6 million text prompts to evaluate the benefit of data scaling supported by our method. Additional training details and loss weights are provided in the supplementary material. + +Compared Methods. Our proposed PRD aims for fast text-to-mesh generation. Therefore, we compare it against state-of-the-art approaches that can generate textured meshes within one minute, including Shape-E [38], Direct3D [61], 3DTopia [30], GVGEN [26], LN3Diff [49], LGM [106] and PI3D [65]. Note that we do not compare with some relevant works [76, 130] since their codes/models are not publicly available and they employ different evaluation protocols. In our experiments, the results of Shape-E, Direct3D, 3DTopia, GVGEN, LN3Diff and LGM are obtained by running their publicly available models. For PI3D, we can only perform quantitative com + +parisons with it by copying its results from the original paper, but we cannot perform visual comparisons with it since its code/model is not yet publicly available. + +Evaluation Protocol. We employ the protocol used in our competing methods [26, 30, 38, 49, 65, 106] to evaluate our PRD model. Specifically, we use the ViT-B/34 CLIP model [85] to evaluate the test prompts from the DreamFusion gallery [82]. As in [65], we render the generated 3D results at 512 resolution from four viewpoints at $15^{\circ}$ elevation across four azimuth angles: $0^{\circ}$ , $90^{\circ}$ , $180^{\circ}$ and $270^{\circ}$ . Under these views, we evaluate the performance of competing methods using CLIP Score [27] (C.S.) and CLIP R-precision $(\mathbb{R}@\mathbb{1})$ . To ensure a fair comparison for instant text-to-mesh generation, we exclude the post-processing steps such as SDS refinement [82], as they will prolong the generation time by several minutes. For models [26, 106] using Gaussian Splatting representations, we use the conversion script from [106] to generate textured meshes. + +# 4.2. Experimental Results + +We showcase qualitative comparisons of the competing methods in Fig. 4 using challenging test prompts. One can see that most of the existing methods struggle to generate satisfactory outputs. Our method, in comparison, produces better quality results with complete and vivid meshes. The quantitative results are reported in Tab. 1. Again, our method demonstrates superior performance to its competitors in all the metrics. Existing methods fall short in the consistency of object poses and in the capability of handling complex prompts. Our PRD method addresses these challenges, enabling faster inference speed and improving the model performance by data scaling. + +Handling Inconsistent Generation Poses. As shown in Fig. 4, existing models often generate objects with incorrect poses. For prompts like 'A teal moped', the competing methods like Direct3D [122], Shape-E [38] and GVGEN [26] generate objects with misaligned orientations, such as facing sideways or backwards. This issue stems from the inconsistent object orientations in 3D training datasets, which are difficult to detect and correct automatically. Current methods struggle with noisy training data, leading to pose ambiguity and geometric defects. Our approach addresses this challenge by learning from multiview teachers. Though our teachers are trained on noisy 3D datasets and may occasionally provide incorrect directional guidance, our PRD scheme exposes the 3D outputs to multi-view teachers $K$ times per iteration (see Sec. 3.2). Through the iterative distillation process, we substantially decrease the impact of incorrect directional guidance, ensuring consistent pose alignment in the 3D outputs. + +Handling Complex Text Prompts. The failure of our competing methods mainly stems from their reliance on the existing text-3D paired datasets, which are not comprehensive enough compared to the diverse user inputs. Therefore, trained on these data, existing methods fail to produce good results when the input is complex. For example, existing methods might perform well when the input prompt is 'A robot' but fail when the prompt becomes 'A robot tiger'. The quality of existing 3D datasets is also compromised by the absence of creative concepts. Creating 3D models for imaginative concepts like 'A robot tiger' demands significant time and expertise from 3D artists. As a result, existing 3D datasets are largely limited to common everyday objects. Models trained on these limited datasets fail to generalize effectively to imaginative or complex prompts. We solve this problem by adapting SD as a 3D generator and inheriting its generative power, and more crucially, by introducing a training scheme that completely eliminates the need of 3D data. Our training scheme not only improves the quality of results on the existing training corpus, as shown by the qualitative and quantitative results in Fig. 4 and Tab. 1, but also enhances the capability to handle complex prompts by + +
C.S. ↑R@1↑Latency (/sec)
Shape-E [38]55.127.113.0
Direct3D60.84.3316.0
3DTopia [30]59.711.223.7
PI3D* [65]65.925.23.00
GVGEN [26]51.12.4449.2
LN3Diff [49]55.95.098.16
LGM [106]67.428.356.1
Ours68.232.31.23
+More Text Data75.146.01.23
+ +Table 1. Quality and speed comparison for text-to-mesh generation. *indicates that the values are quoted from the original papers. + +expanding the available training data, as detailed below. + +Fast Inference Speed. Our PRD method also demonstrates superior computational efficiency. As shown in Tab. 1, we evaluate the average inference latency from text input to textured mesh output across all test prompts on the H20 GPU device. While some methods [26, 106] require dozens of steps, our PRD approach enables the native 3D generator to produce quality results in just $K$ steps. With the suggested setting of $K = 4$ , as shown in Tab. 1, our model achieves sub-second latency for text-to-mesh generation, significantly outperforming previous methods. + +Scaling Up Training Corpus. Since our method is free from the constraints of 3D training data, it can be easily scaled to accommodate more complex and creative text prompts during training. It preserves the SD model's ability to handle creative concepts throughout the 3D adaptation process, generating 3D outputs that faithfully represent the input prompts. As can be seen in the +More Text Data column, when we scale up the training text data from 360K to 1.6M, the CLIP similarity improves by as much as $7\%$ , leading to more consistent generation for challenging text prompts such as A lion reading the newspaper and A tray of Sushi containing pugs. This is because our collected text data covers a wider range of creative concepts than the existing 3D datasets [17, 123], thus providing more sufficient training and improving the generalizability of the model. More visual examples are partially presented in Fig. 1 and detailed in the supplementary materials. + +# 4.3. Ablation Study + +The Effectiveness of PRD. We validate our PRD algorithm by testing a simplified configuration with $\mathbf{K} = \mathbf{1}$ , which reduces our method to a single-step generation process that is equivalent to a vanilla native 3D generator trained by score distillation [73]. As shown in Fig. 5 and quantified in Tab. 2, this configuration fails to generate proper 3D structures because it needs to simultaneously handle two complex challenges: adapting SD for 3D generation and performing single-step generation. In contrast, our PRD scheme can + +![](images/c9574b850015534b8784ae70a56b6fcc3f5da82b22672050fbc14021579f8dec.jpg) +Figure 5. Visualizations on the ablation studies of PRD algorithm. + +
C.S. ↑R@1 ↑
K=150.914.4
K=262.622.4
K=4 (Proposed)68.232.3
+ +use alternative step configurations such as $\mathbf{K} = 2$ , which produces suboptimal yet acceptable results. We found that the configuration of $\mathbf{K} = 4$ provides the best trade-off between output quality and computational efficiency, which is used as the default setting of PRD. + +The Effectiveness of PETA. We first compare our proposed PETA method with conventional full parameter fine-tuning (shown as Full Param Tuning in Fig. 6 and Tab. 3). We see that full parameter fine-tuning exhibits training instability and catastrophic forgetting, resulting in text-inconsistent outputs. We then conduct additional ablation studies using vanilla LoRA tuning, maintaining an equivalent parameter size (22.6M), shown as the configuration of w/ Basic LoRA. We see that this vanilla adaptation produces degraded geometric structures and textures, and lacks the capability to handle the unique characteristics of each plane. Since different geometry and texture planes (see Fig. 3) exhibit distinct feature distributions, they require specialized consideration. Our solution (denoted as w/ PETA) considers plane dependency using multiple LoRAs in self-attention blocks, enabling each plane to maintain its unique representation while allowing cross-plane interactions during self-attention computation. As shown in Fig. 5 and Tab. 2, PETA achieves enhanced 3D generation quality with good text consistency. + +We also perform ablation studies to investigate the impact of multiple multi-view teachers in training, the choice of LoRA rank, our hybrid rendering approach that combines volumetric rendering and rasterization for multi-view distillation in PRD training scheme. The details can be found in + +![](images/fe3bb0ff1296f13213667bda6dc75ce3cdd106658ab0656927c0ea72fac9f0be.jpg) +Figure 6. Visualizations on the ablation study of PETA. + +Table 2. Ablation study on the hyper-parameters of PRD. + +
C.S. ↑R@1 ↑
Full Param Tuning35.80.35
w/ Basic LoRA54.211.1
w/ PETA (Proposed)68.232.3
+ +Table 3. Ablation study on the effectiveness of PETA. + +# the supplementary materials. + +# 5. Conclusion and Limitation + +In this paper, we presented Progressive Rendering Distillation (PRD), a novel training scheme that adapts Stable Diffusion (SD) for instant text-to-mesh generation without relying on 3D data. We also introduced PETA (Parameter-Efficient Triplane Adaptation), a parameter-efficient method that introduces only $2.5\%$ additional parameters to effectively enable SD for instant text-to-mesh generation. Our model, namely TriplaneTurbo, can produce text-consistent textured meshes in only 1.2 second. Through comprehensive experiments, we validated the effectiveness of our approach. Our methodology has the potential to be extended to 3D scene generation and image-to-3D tasks. While currently implemented with SD, the PRD approach can also be applied to other pre-trained models like DiT [20]. We hope our work can inspire new directions in 3D generation to overcome the dependency on 3D data. + +Limitations. One limitation of our method lies in the generation of precise numbers of multiple 3D objects, which may require more sophisticated multi-view teachers, potentially enhanced with layout guidance. Besides, our results for full-body humans might exhibit limited facial and hand details, which can be improved by extending SD adaptation to more advanced 3D structures than Triplane. + +# Acknowledgment + +This work is supported by the InnoHK program. + +# References + +[1] Thiemo Alldieck, Nikos Kolotouros, and Cristian Sminchisescu. Score distillation sampling with learned manifold corrective, 2024. 3 +[2] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y Ogras, and Linjie Luo. Panohead: Geometry-aware 3d fullhead synthesis in 360deg. 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Our method adapts Stable Diffusion [87] to generate high-fidelity textured meshes in 1.2 seconds." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 473, + 200, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 473, + 200, + 486 + ], + "spans": [ + { + "bbox": [ + 151, + 473, + 200, + 486 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 500, + 297, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 500, + 297, + 693 + ], + "spans": [ + { + "bbox": [ + 54, + 500, + 297, + 693 + ], + "type": "text", + "content": "It is highly desirable to obtain a model that can generate high-quality 3D meshes from text prompts in just seconds. While recent attempts have adapted pre-trained text-to-image diffusion models, such as Stable Diffusion (SD), into generators of 3D representations (e.g., Triplane), they often suffer from poor quality due to the lack of sufficient high-quality 3D training data. Aiming at overcoming the data shortage, we propose a novel training scheme, termed as Progressive Rendering Distillation (PRD), eliminating the need for 3D ground-truths by distilling multi-view diffusion models and adapting SD into a native 3D generator. In each iteration of training, PRD uses the U-Net to progressively denoise the latent from random noise for a few steps, and in each step it decodes the denoised latent into 3D output. Multi-view diffusion models, including MVDream and RichDreamer, are used in joint with SD" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 475, + 556, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 556, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 556, + 643 + ], + "type": "text", + "content": "to distill text-consistent textures and geometries into the 3D outputs through score distillation. Since PRD supports training without 3D ground-truths, we can easily scale up the training data and improve generation quality for challenging text prompts with creative concepts. Meanwhile, PRD can accelerate the inference speed of the generation model in just a few steps. With PRD, we train a Triplane generator, namely TriplaneTurbo, which adds only " + }, + { + "bbox": [ + 313, + 475, + 556, + 643 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 313, + 475, + 556, + 643 + ], + "type": "text", + "content": " trainable parameters to adapt SD for Triplane generation. TriplaneTurbo outperforms previous text-to-3D generators in both efficiency and quality. Specifically, it can produce high-quality 3D meshes in 1.2 seconds and generalize well for challenging text input. The code is available at github.com/theEricMa/TriplaneTurbo." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "spans": [ + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Text-to-3D aims to create 3D contents faithful to the given textual descriptions. The optimization-based text-to-3D" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 148, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 148, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 148, + 713 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11036" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 407 + ], + "type": "text", + "content": "methods can achieve high generation fidelity by using image diffusion priors [52, 62, 66, 68, 71, 84, 94, 110] and score distillation techniques [42, 56, 73, 82, 111, 115, 143, 153] to optimize 3D representations [10, 29, 59, 60, 105]. However, these approaches encounter bottlenecks in computational efficiency since they take hours to generate 3D textured meshes. Recent researches have shifted towards learning-based methods [7, 25, 37, 49, 80], which generate 3D contents through feed-forward networks, reducing the latency to a few seconds per output. Unfortunately, existing 3D datasets [16-18, 81, 123] are much smaller compared to those used in training text-to-image generation models, while the 3D data therein suffer from texture quality and inconsistent object poses [61]. Consequently, these approaches struggle to produce high-quality 3D outputs. As a promising alternative to the above mentioned methods, one can adapt pretrained text-to-image models, such as Stable Diffusion (SD) [87], into generators of 3D representations [54, 65, 76]. Recent studies have enabled the use of SD to generate 2D planes for 3D representations such as Triplane [8]. PI3D [65] adapts SD to generate six 2D planes pre-optimized for 3D object reconstruction. HexaGen [76] first trains a VAE to compress 3D objects into latent space, then adapts SD to generate the desired latents from text prompts. These methods leverage SD's prior knowledge for diverse text prompts while reducing training costs. However, their reliance on data-driven training limits the generalization performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 411, + 296, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 615 + ], + "type": "text", + "content": "In this paper, we propose to address the data shortage problem by using high-quality multi-view diffusion models [66, 84, 94] as teachers and performing multi-view distillation to adapt SD into an instant text-to-mesh generator without using 3D ground-truth data. Data-free distillation techniques [69, 154] have been applied in previous methods [51, 70, 73, 130] to train native 3D generators from scratch, whereas they struggle to produce high-quality 3D outputs. We argue that if we can adapt SD for native 3D generation, instead of training from scratch, not only the training efficiency can be improved but also the generation quality can be enhanced. To our best knowledge, however, no such attempt has been made before. The primary obstacle lies in the training scheme of SD, which requires 3D ground-truth data to supervise the denoising process. This requirement, unfortunately, conflicts with our goal to eliminate the dependency on 3D training data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 618, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 715 + ], + "type": "text", + "content": "To address the above challenges, we propose Progressive Rendering Distillation (PRD), which enables 3D data-free distillation. PRD achieves this goal by denoising the latent from random noise rather than 3D groundtruths. In each training iteration, PRD uses a few steps to progressively reverse noise to latent space using the adapted U-Net of SD. Then the denoised latent of each step is decoded to 3D contents via the adapted VAE decoder. Multi-" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 133 + ], + "type": "text", + "content": "view teacher models are used to distill high-quality renderings through efficient score distillation techniques such as ASD [73]. An additional benefit of PRD is that by adapting the SD to generate 3D contents in just four steps, the overall generation process can be much accelerated." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 133, + 556, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 556, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 556, + 312 + ], + "type": "text", + "content": "PRD is flexible in the choices of multi-view teacher models and the types of 3D representations. Unlike existing approaches using SD alone as the teacher [59, 104, 115, 140, 153], which risk the multi-view inconsistency and the Janus problem [4], we employ multiple teachers in training. Specifically, we employ MVDream [94] and SD to suppress the Janus problem and ensure text consistency in 3D content supervision. Additionally, we use RichDreamer [84] for geometry supervision through normal and depth. With PRD, we adapt SD into a native 3D generator to produce geometry and texture Triplanes in 4 steps, which is named as TriplaneTurbo in the following context. To enhance TriplaneTurbo's textured mesh quality, we employ SDF-based volumetric rendering [138] and mesh rasterization [118] for multi-view teacher supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 312, + 556, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 556, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 556, + 430 + ], + "type": "text", + "content": "In addition, to address the high GPU memory usage caused by multiple teachers and multi-view renderings in the training process, we introduce the Parameter-Efficient Triplane Adapter (PETA), which adds only " + }, + { + "bbox": [ + 313, + 312, + 556, + 430 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 313, + 312, + 556, + 430 + ], + "type": "text", + "content": " trainable parameters to the frozen SD and effectively adapts it for 3D generation. Some results are shown in Fig. 1. To our knowledge, this is the first parameter-efficient training method for direct 3D content generation from 2D diffusion models, departing from full-parameter adaptation approaches. Our key contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 432, + 555, + 600 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 432, + 555, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 432, + 555, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 432, + 555, + 491 + ], + "type": "text", + "content": "- We make the first attempt to adapt the pretrained 2D SD model into a native 3D generator without 3D data. With the proposed PRD scheme, we use multi-view diffusion models as teachers and distill SD into a four-step native 3D generator, namely TriplaneTurbo." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 492, + 554, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 554, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 554, + 539 + ], + "type": "text", + "content": "- TriplaneTurbo adds only " + }, + { + "bbox": [ + 313, + 492, + 554, + 539 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 313, + 492, + 554, + 539 + ], + "type": "text", + "content": " additional trainable parameters to the frozen SD for Triplane adaptation. It marks the first use of parameter-efficient training to adapt 2D diffusion models for native 3D generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 540, + 554, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 554, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 554, + 600 + ], + "type": "text", + "content": "- TriplaneTurbo surpasses existing text-to-3D models not only in quality but also in speed, reducing text-to-mesh generation time to just 1.2 seconds. In addition, by scaling up the text training data, the model can generalize much better to complex text input." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 609, + 402, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 609, + 402, + 621 + ], + "spans": [ + { + "bbox": [ + 314, + 609, + 402, + 621 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": "Data-Driven Models for 3D Generation. Employing 3D data to train generators has shown its effectiveness for single-category 3D generation such as human faces [2, 8, 31, 72, 98, 125, 128], body shapes [34, 57, 89, 134], everyday objects [3, 39, 64, 78], and structured room layouts [5, 21, 75, 86, 107, 126]. This is mainly because for these specific categories, the training data are relatively" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11037" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "easy to collect. However, text-to-3D generation requires open-category generation, bringing a rather different challenge. The difficulties in obtaining sufficient 3D training data largely limit the model generalizability across diverse text prompts [73], regardless of the type of used generation models (e.g., GAN [24, 79, 91] or diffusion models [28, 40, 96]) or 3D representations (e.g., NeRF [6, 77] or Gaussian Splatting [44, 144]). The publicly available 3D datasets [16–18, 81, 123] mostly contain only hundreds or thousands of samples, which are very hard, if not impossible, to train a generalized text-to-3D generation model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 207, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 207, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 56, + 207, + 296, + 567 + ], + "type": "text", + "content": "2D Diffusion Models for 3D Generation. The difficulty of text-to-3D generation can be alleviated by leveraging 2D diffusion models as priors, thanks to their training on vast text-image pairs. Early approaches like SDS [104] and VSD [13] pioneered zero-shot text-to-3D generation by optimizing 3D representations (NeRF [59, 62, 82, 111], mesh [11, 59, 115, 136], 3DGS [56, 105, 140, 141]) through score distillation [1, 36, 41, 55, 56, 73, 82, 103, 113, 115, 117, 127, 142, 150, 152, 155], which serves as a bridge to transfer the generative capability of 2D diffusion models to 3D representations through rendered views. However, pre-trained text-to-image models like SD lack multiview consistency, leading to the Janus problem [4]. MVDream [94] and subsequent works [35, 67] address this issue by camera-aware adaptations and synchronized multiview generation, and they incorporate additional modalities such as normal [84], depth [22, 43], and CCM [63, 131] to enhance geometric quality. While achieving improved 3D generation results, these methods require computationally intensive score distillation [12, 84, 90, 94] or 3D reconstruction [32, 53, 68, 93, 106, 116, 135, 146]. Native 3D generators [17, 26, 34, 49, 50, 58, 74, 108, 122, 129, 145, 148, 148, 151, 151] can reduce the generation time to seconds by directly producing 3D content without view rendering as proxies. For example, LN3Diff [49] and GVGEN [26] compress NeRF [77] and 3DGS [44] into latent spaces using VAEs [47], then train text-conditioned latent diffusion models [28]. However, these methods show limited generalizability across text prompts, as their performance is constrained by the insufficient text-3D training pairs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": "Some methods [65, 76, 84, 94] leverage SD as their backbone to transfer text-to-image knowledge into text-to-3D generation. SD provides strong generative prior and improves the model generalizability [9, 19, 58, 99–102, 120, 121, 137, 147]. Approaches like PI3D [65] adapt SD to generate multiple planes for constructing 3D space, yet their performance remains limited due to the insufficient 3D training data. Instead of adapting SD for multiview generation, native 3D generation requires substantially more 3D data for effective adaptation. We propose to address the data insufficiency challenge by distilling knowledge from multi-view diffusion models into an SD-adapted" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "content": "native 3D generator, eliminating the need for 3D training data. While previous works like ATT3D [70] and ScaleDreamer [73] have investigated such a data-free training strategy, they employ multi-view distillation to train generators from scratch, and show limited performance due to the insufficient training scale. To overcome the huge training cost, we propose a cost-effective solution that combines multi-view distillation with SD-based native 3D generation. A fundamental challenge to achieve this goal is how to adapt SD for 3D generation without ground-truth data. We address this by proposing a novel Progressive Rendering Distillation scheme, which not only eliminates the need of 3d ground-truths but also enables few-step generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 240, + 370, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 240, + 370, + 251 + ], + "spans": [ + { + "bbox": [ + 314, + 240, + 370, + 251 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 260, + 394, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 260, + 394, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 260, + 394, + 273 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": "Stable Diffusion (SD) performs diffusion in latent space for efficient text-to-image generation. Its VAE encoder " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "E_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " compresses an image " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " into a latent code " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ", while its decoder " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "D_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " reconstructs the image. Given text prompt " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ", a U-net " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " predicts noise " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ", which is added to " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "z_t = \\alpha_t z + \\sigma_t \\epsilon" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ", where timestep " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "t \\in 1, \\ldots, T" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " controls noise level via scalars " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\alpha_t" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ". Generation proceeds by iteratively denoising from " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "z_T" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " to prompt-aligned " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ". At each step, the U-net estimates noise " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon} = \\epsilon_{\\phi^{\\mathrm{SD}}}(z_t; t, y)" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": " to compute " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\hat{z}_0 = \\frac{\\hat{z}_t - \\sigma_t \\hat{\\epsilon}}{\\alpha_t}" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\hat{z}_0 = z_{\\phi^{\\mathrm{SD}}}(z_t; t, y)" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ". Results can be refined through additional diffusion steps " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "t' < t" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": ". The final latent is decoded to an image via " + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\hat{x} = D_{\\phi^{\\mathrm{SD}}}(\\hat{z}_0)" + }, + { + "bbox": [ + 313, + 277, + 555, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": "Score Distillation. 2D diffusion models can optimize 3D representations " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " through differentiable rendering " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "x_{\\pi} = g(\\theta, \\pi)" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " [45, 92, 95], which produces images " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "x_{\\pi}" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " from camera view " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": ". Here 2D diffusion models serve as a metric " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(x_{\\pi}; \\pi, y)" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " that measures the consistency between " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "x_{\\pi}" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " and the text conditions " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": ". The 3D representation is optimized using gradient " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta} \\mathcal{L}(x_{\\pi}; \\pi, y) = \\nabla x_{\\pi} \\mathcal{L}(x_{\\pi}; \\pi, y) \\frac{\\partial x_{\\pi}}{\\partial \\theta}" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": ", which also trains the native 3D generator. The computation of " + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "inline_equation", + "content": "\\nabla x_{\\pi} \\mathcal{L}" + }, + { + "bbox": [ + 313, + 423, + 556, + 533 + ], + "type": "text", + "content": " depends on the chosen score distillation method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 540, + 497, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 497, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 497, + 553 + ], + "type": "text", + "content": "3.2. Progressive Rendering Distillation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": "We now detail our proposed training scheme for adapting SD as a native 3D generator. Traditional adaptation approaches require preparing ground-truth 3D representations " + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": " and their corresponding latents " + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": " for each 3D sample in the dataset. The U-net is adapted to denoise diffused latents " + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": " by minimizing the noise prediction mean squared error (MSE). Fig. 2(a) illustrates this paradigm, which has been used by several native 3D generators [65, 114, 122, 148]. However, this paradigm faces limitations in both the quantity and quality of available 3D representations " + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 558, + 555, + 715 + ], + "type": "text", + "content": ", as existing 3D datasets lack sufficient high-quality data for training text-to-3D generators. Actually, the pretrained SD models already possess denoising capabilities for image generation." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11038" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 87, + 271, + 219 + ], + "blocks": [ + { + "bbox": [ + 91, + 73, + 249, + 83 + ], + "lines": [ + { + "bbox": [ + 91, + 73, + 249, + 83 + ], + "spans": [ + { + "bbox": [ + 91, + 73, + 249, + 83 + ], + "type": "text", + "content": "(a) Vanilla SD Adaptation / Diffusion Model Training" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 70, + 87, + 271, + 219 + ], + "lines": [ + { + "bbox": [ + 70, + 87, + 271, + 219 + ], + "spans": [ + { + "bbox": [ + 70, + 87, + 271, + 219 + ], + "type": "image", + "image_path": "c1ac498931652cc33bbbb3cc7826ce8d1a9646fe1500089a8d291fe068630e80.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 284, + 83, + 553, + 217 + ], + "blocks": [ + { + "bbox": [ + 325, + 73, + 459, + 83 + ], + "lines": [ + { + "bbox": [ + 325, + 73, + 459, + 83 + ], + "spans": [ + { + "bbox": [ + 325, + 73, + 459, + 83 + ], + "type": "text", + "content": "(b) Progressive Rendering Distillation (Ours)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 284, + 83, + 553, + 217 + ], + "lines": [ + { + "bbox": [ + 284, + 83, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 284, + 83, + 553, + 217 + ], + "type": "image", + "image_path": "563b13dc3fbcad2cb77db81a628fc18dccb08d12a58a25dda7ef0a5c82170b32.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "lines": [ + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": "Figure 2. Comparison between (a) traditional SD adaptation and (b) our proposed progressive rendering distillation (PRD) for native 3D generation. Traditional approach requires ground-truth 3D representations " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": " and their latents " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": " for each 3D sample to generate " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": ". Our proposed PRD scheme progressively denoises latents " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": " initialized from random noise into " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": ", which are decoded to " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": ", using multi-view diffusion models as teachers for distillation, eliminating the need for 3D data during adaptation and overcoming data scarcity." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "spans": [ + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": "In other words, pretrained SD is well-trained for a Markov Chain to reverse " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_T = \\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_0" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " with its U-net " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": ", and decode " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_0" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " to image with its decoder " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "D_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": ". Our goal is to modify the Markov chain by transforming " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "D_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " into 3D generators " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_{\\phi^{3\\mathrm{D}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "D_{\\phi^{3\\mathrm{D}}}" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": ", from which the 3D representations " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " can be decoded. Note that our modification of the Markov chain differs from the traditional diffusion model adaptation objectives, as it requires neither ground-truth latents " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_0" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " nor their noise-diffused variants " + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_t" + }, + { + "bbox": [ + 54, + 294, + 296, + 415 + ], + "type": "text", + "content": " in the training process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": "Specifically, at the beginning of the Markov chain, the network takes random noise " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " as input to represent " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": ". At each step, current state " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " is used to estimate " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_0" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " through " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": ", which is then decoded to 3D output " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "D_{\\phi^{\\mathrm{SD}}}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": ". The 3D output " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " is used to render images " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\pi_1}, \\mathbf{x}_{\\pi_2}, \\ldots" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " at camera views " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pi_1, \\pi_2, \\ldots" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " and receive supervision from multiview teachers via score distillation, while the estimated " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_0" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " is diffused to the next timestep " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t'} = \\alpha_{t'} \\hat{\\mathbf{z}}_0 + \\sigma_{t'} \\epsilon" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " for subsequent operations. We name this training scheme as Progressive Rendering Distillation (PRD), as illustrated in Fig. 2(b). From the total " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " timesteps, we select a decreasing sequence of " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " timesteps " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "T = t_1 > t_2 > \\dots > t_K = T / K" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " with uniform spacing to perform score distillation from multi-view teachers. The gradient at each step is not backpropagated to previous steps; therefore, we can largely reduce the GPU memory usage and prevent gradient explosion [15, 83, 124, 133]. Since " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\phi^{\\mathrm{3D}}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " is initialized from " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\phi^{\\mathrm{SD}}" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": ", this specialized gradient detachment strategy still maintains good convergence. The pseudo code of our algorithm is provided in the supplementary material. While the time cost of our training strategy increases with the increase of " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": ", we can ensure the model to generate high quality results in just a few steps, thereby accelerating inference. We set " + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 56, + 425, + 296, + 714 + ], + "type": "text", + "content": " to balance quality and speed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 294, + 528, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 294, + 528, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 528, + 308 + ], + "type": "text", + "content": "3.3. Parameter-Efficient Triplane Adaptation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": "While various 3D representations could be employed by our PRD scheme, in this paper we demonstrate an exemplar solution using Triplanes as the representation. We denote our adapted model as TriplaneTurbo with parameters " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\phi^{3\\mathrm{D}}" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": ". Specifically, TriplaneTurbo adapts SD to generate a 3D representation consisting of two Triplanes [8] " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\theta = (\\theta_{\\mathrm{geo}},\\theta_{\\mathrm{tex}})" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": ": a geometry Triplane " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{geo}}" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " storing Signed Distance Function (SDF) and deformation values for mesh extraction, and a texture Triplane " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{tex}}" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " containing RGB attributes for painting texture on the mesh. For each point in 3D space, we use a two-layer MLP to decode its SDF value. The same process applies to texture and mesh deformation [92, 118]. This separation of geometry and texture planes follows the work in [23, 97, 119]. We set the Triplane resolution as " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": ", and replace the last convolution in SD's decoder to output 32 channels. The Triplanes' output has a dimension of " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "6\\times 256\\times 256\\times 32" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " in feature space. Due to the " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " compression of the VAE, this corresponds to " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "6\\times 32\\times 32\\times 4" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " in latent space, distinct from the " + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "inline_equation", + "content": "1\\times 64\\times 64\\times 4" + }, + { + "bbox": [ + 313, + 318, + 555, + 714 + ], + "type": "text", + "content": " latent generated by pretrained SD. To enable interaction between the six feature planes, we follow existing approaches [68, 93, 94, 112] to adapt the U-nets' self-attention [87, 109] to allow cross-plane attention. Unlike existing works that fully retrain SD [12, 54, 65, 76, 94], which can lead to catastrophic forgetting [65, 94], we propose a parameter-efficient adaptation approach. The core of our design lies in the fact that each of the six feature planes maintains its own unique feature distribution. Therefore, plane-specific characteristics must be incorporated into the adaptation process. As illustrated in Fig. 3, our adaptation modifies the convolution, self-attention, and cross-attention layers. We name our approach Parameter-Efficient Triplane Adaptation (PETA)." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11039" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 73, + 531, + 262 + ], + "blocks": [ + { + "bbox": [ + 56, + 73, + 531, + 262 + ], + "lines": [ + { + "bbox": [ + 56, + 73, + 531, + 262 + ], + "spans": [ + { + "bbox": [ + 56, + 73, + 531, + 262 + ], + "type": "image", + "image_path": "746feac01c63a3330237dbd27e8b8ca4a77e15c35731a90b900354ad64b049d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "lines": [ + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "spans": [ + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "text", + "content": "Figure 3. Illustration of TriplaneTurbo: an SD-adapted native 3D generator using our PRD scheme. Our model generates six feature planes comprising geometry Triplane " + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{geo}}" + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "text", + "content": " and texture Triplane " + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{tex}}" + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "text", + "content": " in 4 steps. We introduce Parameter Efficient Triplane Adaptation (PETA), which requires only " + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 54, + 272, + 555, + 307 + ], + "type": "text", + "content": " additional parameters for adaptation. The parameter arrangement is illustrated in the figure." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 327, + 296, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 327, + 296, + 579 + ], + "spans": [ + { + "bbox": [ + 56, + 327, + 296, + 579 + ], + "type": "text", + "content": "As shown in Fig. 3, for the convolution blocks (Res-Blocks) and cross-attention layers, we implement LoRA [33, 139] for parameter-efficient adaptation, and process the six planes uniformly. The plane-specific adaptations are then applied to the self-attention. For the self-attention blocks, we apply distinct LoRA layers [33] to the to_Q, to_K, to_V, and to_Out linear layers when processing each of the six feature planes. In each linear transformation within a self-attention block, the linear projection with multiple LoRAs is implemented in two steps. First, the frozen linear layer batch processes the features extracted from all the six planes together. Then, separate LoRA transformations are applied independently to the features of each plane. This adaptation maintains low computational overhead while effectively introducing plane-specific processing during attention calculations across the six feature planes. It can be applied with other techniques like AdaLoRa [149] and Vera [48]. We leave this for further exploration. We set the LoRA rank to 16 by default. While this adaptation adds only " + }, + { + "bbox": [ + 56, + 327, + 296, + 579 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 56, + 327, + 296, + 579 + ], + "type": "text", + "content": " of the parameters to the SD model, it effectively enables native 3D generation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 587, + 165, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 165, + 599 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 165, + 599 + ], + "type": "text", + "content": "3.4. Distillation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": "Since PRD eliminates the need for 3D data by referring to multi-view teachers for distillation, using multiple teachers allows us to combine their strengths while mitigating individual biases. Most previous works [14, 59, 70, 82, 105] use SD model (parametrized by " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\phi^{\\mathrm{SD}}" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": ") as the teacher for its ability to generate high-fidelity, text-consistent images. However, SD lacks camera-awareness, which can lead to the Janus problem [4]. MVDream [94] (MV, parametrized by " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\phi^{\\mathrm{MV}}" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": ") addresses this by generating four" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": "camera-conditioned views simultaneously, but at the cost of reduced prompt consistency [112]. While SD and MV complement each other, both of them focus on RGB rendering and provide no direct supervision on geometry. We further incorporate RichDreamer [84] (RD, parameterized by " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\phi^{\\mathrm{RD}}" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": "), a model that generates four-view normal and depth maps based on text prompts. The score distillation guidance " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\pmb{x}_{\\pi};\\pi ,y)" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " in our implementation thus integrates SD, MV, and RD. At each PRD step (see Sec. 3.2 and Fig. 2), given a text prompt " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " and generated 3D representation " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "z_{\\phi^{3\\mathrm{D}}}" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "D_{\\phi^{3\\mathrm{D}}}" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": ", we sample four views " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\pi_1,\\dots ,\\pi_4" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " at uniform azimuth intervals. We sample one view " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\pi_1,\\ldots ,\\pi_4" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " to compute " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SD}} = \\mathcal{L}_{\\phi^{\\mathrm{SD}}}(x_{\\pi};\\pi ,y)" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": ". For MV, all the four views are used to compute " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MV}} = \\mathcal{L}_{\\phi^{\\mathrm{MV}}}(x_{\\pi_1},\\dots,x_{\\pi_4};\\pi_1,\\dots,\\pi_4,y)" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": ". RD operates on concatenated normal and depth renderings " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "x_{\\pi_1}'" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\dots ,x_{\\pi_4}'" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " and its objective is " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RD}} = \\mathcal{L}_{\\phi^{RD}}(x_{\\pi_1}'" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\dots ,x_{\\pi_4}'" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\pi_1,\\dots,\\pi_4,y)" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": ". Among existing score distillation methods [36, 41, 55, 56, 73, 82, 115, 117, 127, 142], we adopt Asynchronous Score Distillation (ASD) [73] for its pioneered efficiency in training deep text-to-3D generators. For 3D rendering, as illustrated in Fig. 3, we combine volumetric rendering [138] at " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " resolution with mesh rasterization [46] at " + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 313, + 327, + 555, + 619 + ], + "type": "text", + "content": " to overcome the instability of pure mesh supervision [132]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 628, + 395, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 628, + 395, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 628, + 395, + 642 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 648, + 441, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 441, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 441, + 661 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "Implementation Details. For a fair comparison with existing methods, we use captions of the 3D objects [17] provided by [30] to train our model, which comprises a total of 360K text prompts. We employ SD v2.1-base [88] as the" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11040" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 552, + 449 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 552, + 449 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 552, + 449 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 552, + 449 + ], + "type": "image", + "image_path": "b7550ed971a14bbc9043de9ee481e939d5c04a13b9a0990454404120aac2e697.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 459, + 533, + 472 + ], + "lines": [ + { + "bbox": [ + 76, + 459, + 533, + 472 + ], + "spans": [ + { + "bbox": [ + 76, + 459, + 533, + 472 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of text-to-mesh generation results by competing methods. Please refer to Sec. 4.2 for details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 491, + 296, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 296, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 296, + 564 + ], + "type": "text", + "content": "base model. Our model is trained for 15K iterations with a learning rate of 2e-4, costing 40 hours on 8 NVIDIA H20 GPUs. We further collect 1.6 million text prompts to evaluate the benefit of data scaling supported by our method. Additional training details and loss weights are provided in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "type": "text", + "content": "Compared Methods. Our proposed PRD aims for fast text-to-mesh generation. Therefore, we compare it against state-of-the-art approaches that can generate textured meshes within one minute, including Shape-E [38], Direct3D [61], 3DTopia [30], GVGEN [26], LN3Diff [49], LGM [106] and PI3D [65]. Note that we do not compare with some relevant works [76, 130] since their codes/models are not publicly available and they employ different evaluation protocols. In our experiments, the results of Shape-E, Direct3D, 3DTopia, GVGEN, LN3Diff and LGM are obtained by running their publicly available models. For PI3D, we can only perform quantitative com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 555, + 528 + ], + "type": "text", + "content": "parisons with it by copying its results from the original paper, but we cannot perform visual comparisons with it since its code/model is not yet publicly available." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": "Evaluation Protocol. We employ the protocol used in our competing methods [26, 30, 38, 49, 65, 106] to evaluate our PRD model. Specifically, we use the ViT-B/34 CLIP model [85] to evaluate the test prompts from the DreamFusion gallery [82]. As in [65], we render the generated 3D results at 512 resolution from four viewpoints at " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "15^{\\circ}" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": " elevation across four azimuth angles: " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "270^{\\circ}" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": ". Under these views, we evaluate the performance of competing methods using CLIP Score [27] (C.S.) and CLIP R-precision " + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbb{R}@\\mathbb{1})" + }, + { + "bbox": [ + 313, + 533, + 556, + 715 + ], + "type": "text", + "content": ". To ensure a fair comparison for instant text-to-mesh generation, we exclude the post-processing steps such as SDS refinement [82], as they will prolong the generation time by several minutes. For models [26, 106] using Gaussian Splatting representations, we use the conversion script from [106] to generate textured meshes." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11041" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 180, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 180, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 180, + 85 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 90, + 294, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 90, + 294, + 233 + ], + "spans": [ + { + "bbox": [ + 54, + 90, + 294, + 233 + ], + "type": "text", + "content": "We showcase qualitative comparisons of the competing methods in Fig. 4 using challenging test prompts. One can see that most of the existing methods struggle to generate satisfactory outputs. Our method, in comparison, produces better quality results with complete and vivid meshes. The quantitative results are reported in Tab. 1. Again, our method demonstrates superior performance to its competitors in all the metrics. Existing methods fall short in the consistency of object poses and in the capability of handling complex prompts. Our PRD method addresses these challenges, enabling faster inference speed and improving the model performance by data scaling." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 235, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 235, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 56, + 235, + 296, + 449 + ], + "type": "text", + "content": "Handling Inconsistent Generation Poses. As shown in Fig. 4, existing models often generate objects with incorrect poses. For prompts like 'A teal moped', the competing methods like Direct3D [122], Shape-E [38] and GVGEN [26] generate objects with misaligned orientations, such as facing sideways or backwards. This issue stems from the inconsistent object orientations in 3D training datasets, which are difficult to detect and correct automatically. Current methods struggle with noisy training data, leading to pose ambiguity and geometric defects. Our approach addresses this challenge by learning from multiview teachers. Though our teachers are trained on noisy 3D datasets and may occasionally provide incorrect directional guidance, our PRD scheme exposes the 3D outputs to multi-view teachers " + }, + { + "bbox": [ + 56, + 235, + 296, + 449 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 56, + 235, + 296, + 449 + ], + "type": "text", + "content": " times per iteration (see Sec. 3.2). Through the iterative distillation process, we substantially decrease the impact of incorrect directional guidance, ensuring consistent pose alignment in the 3D outputs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 451, + 298, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 451, + 298, + 715 + ], + "spans": [ + { + "bbox": [ + 56, + 451, + 298, + 715 + ], + "type": "text", + "content": "Handling Complex Text Prompts. The failure of our competing methods mainly stems from their reliance on the existing text-3D paired datasets, which are not comprehensive enough compared to the diverse user inputs. Therefore, trained on these data, existing methods fail to produce good results when the input is complex. For example, existing methods might perform well when the input prompt is 'A robot' but fail when the prompt becomes 'A robot tiger'. The quality of existing 3D datasets is also compromised by the absence of creative concepts. Creating 3D models for imaginative concepts like 'A robot tiger' demands significant time and expertise from 3D artists. As a result, existing 3D datasets are largely limited to common everyday objects. Models trained on these limited datasets fail to generalize effectively to imaginative or complex prompts. We solve this problem by adapting SD as a 3D generator and inheriting its generative power, and more crucially, by introducing a training scheme that completely eliminates the need of 3D data. Our training scheme not only improves the quality of results on the existing training corpus, as shown by the qualitative and quantitative results in Fig. 4 and Tab. 1, but also enhances the capability to handle complex prompts by" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 326, + 70, + 543, + 209 + ], + "blocks": [ + { + "bbox": [ + 326, + 70, + 543, + 209 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 543, + 209 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 543, + 209 + ], + "type": "table", + "html": "
C.S. ↑R@1↑Latency (/sec)
Shape-E [38]55.127.113.0
Direct3D60.84.3316.0
3DTopia [30]59.711.223.7
PI3D* [65]65.925.23.00
GVGEN [26]51.12.4449.2
LN3Diff [49]55.95.098.16
LGM [106]67.428.356.1
Ours68.232.31.23
+More Text Data75.146.01.23
", + "image_path": "61f7ee0e7d24a11e8df8c101385dd8b4cabcf60769aaf4e3d868a0c7b7815d2f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 210, + 555, + 234 + ], + "lines": [ + { + "bbox": [ + 313, + 210, + 555, + 234 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 555, + 234 + ], + "type": "text", + "content": "Table 1. Quality and speed comparison for text-to-mesh generation. *indicates that the values are quoted from the original papers." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 243, + 540, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 540, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 540, + 255 + ], + "type": "text", + "content": "expanding the available training data, as detailed below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": "Fast Inference Speed. Our PRD method also demonstrates superior computational efficiency. As shown in Tab. 1, we evaluate the average inference latency from text input to textured mesh output across all test prompts on the H20 GPU device. While some methods [26, 106] require dozens of steps, our PRD approach enables the native 3D generator to produce quality results in just " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": " steps. With the suggested setting of " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": ", as shown in Tab. 1, our model achieves sub-second latency for text-to-mesh generation, significantly outperforming previous methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 376, + 556, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 556, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 556, + 579 + ], + "type": "text", + "content": "Scaling Up Training Corpus. Since our method is free from the constraints of 3D training data, it can be easily scaled to accommodate more complex and creative text prompts during training. It preserves the SD model's ability to handle creative concepts throughout the 3D adaptation process, generating 3D outputs that faithfully represent the input prompts. As can be seen in the +More Text Data column, when we scale up the training text data from 360K to 1.6M, the CLIP similarity improves by as much as " + }, + { + "bbox": [ + 313, + 376, + 556, + 579 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 313, + 376, + 556, + 579 + ], + "type": "text", + "content": ", leading to more consistent generation for challenging text prompts such as A lion reading the newspaper and A tray of Sushi containing pugs. This is because our collected text data covers a wider range of creative concepts than the existing 3D datasets [17, 123], thus providing more sufficient training and improving the generalizability of the model. More visual examples are partially presented in Fig. 1 and detailed in the supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 588, + 409, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 409, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 409, + 601 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "The Effectiveness of PRD. We validate our PRD algorithm by testing a simplified configuration with " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{K} = \\mathbf{1}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": ", which reduces our method to a single-step generation process that is equivalent to a vanilla native 3D generator trained by score distillation [73]. As shown in Fig. 5 and quantified in Tab. 2, this configuration fails to generate proper 3D structures because it needs to simultaneously handle two complex challenges: adapting SD for 3D generation and performing single-step generation. In contrast, our PRD scheme can" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11042" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 68, + 298, + 214 + ], + "blocks": [ + { + "bbox": [ + 59, + 68, + 298, + 214 + ], + "lines": [ + { + "bbox": [ + 59, + 68, + 298, + 214 + ], + "spans": [ + { + "bbox": [ + 59, + 68, + 298, + 214 + ], + "type": "image", + "image_path": "c9574b850015534b8784ae70a56b6fcc3f5da82b22672050fbc14021579f8dec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 220, + 295, + 234 + ], + "lines": [ + { + "bbox": [ + 55, + 220, + 295, + 234 + ], + "spans": [ + { + "bbox": [ + 55, + 220, + 295, + 234 + ], + "type": "text", + "content": "Figure 5. Visualizations on the ablation studies of PRD algorithm." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 103, + 246, + 249, + 309 + ], + "blocks": [ + { + "bbox": [ + 103, + 246, + 249, + 309 + ], + "lines": [ + { + "bbox": [ + 103, + 246, + 249, + 309 + ], + "spans": [ + { + "bbox": [ + 103, + 246, + 249, + 309 + ], + "type": "table", + "html": "
C.S. ↑R@1 ↑
K=150.914.4
K=262.622.4
K=4 (Proposed)68.232.3
", + "image_path": "aeedd00ade5f6985cba285532b18e0bd99df09dd2074e9abf0865e8f04e1b466.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "text", + "content": "use alternative step configurations such as " + }, + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{K} = 2" + }, + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "text", + "content": ", which produces suboptimal yet acceptable results. We found that the configuration of " + }, + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{K} = 4" + }, + { + "bbox": [ + 55, + 351, + 295, + 411 + ], + "type": "text", + "content": " provides the best trade-off between output quality and computational efficiency, which is used as the default setting of PRD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "text", + "content": "The Effectiveness of PETA. We first compare our proposed PETA method with conventional full parameter fine-tuning (shown as Full Param Tuning in Fig. 6 and Tab. 3). We see that full parameter fine-tuning exhibits training instability and catastrophic forgetting, resulting in text-inconsistent outputs. We then conduct additional ablation studies using vanilla LoRA tuning, maintaining an equivalent parameter size (22.6M), shown as the configuration of w/ Basic LoRA. We see that this vanilla adaptation produces degraded geometric structures and textures, and lacks the capability to handle the unique characteristics of each plane. Since different geometry and texture planes (see Fig. 3) exhibit distinct feature distributions, they require specialized consideration. Our solution (denoted as w/ PETA) considers plane dependency using multiple LoRAs in self-attention blocks, enabling each plane to maintain its unique representation while allowing cross-plane interactions during self-attention computation. As shown in Fig. 5 and Tab. 2, PETA achieves enhanced 3D generation quality with good text consistency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "text", + "content": "We also perform ablation studies to investigate the impact of multiple multi-view teachers in training, the choice of LoRA rank, our hybrid rendering approach that combines volumetric rendering and rasterization for multi-view distillation in PRD training scheme. The details can be found in" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 318, + 72, + 553, + 214 + ], + "blocks": [ + { + "bbox": [ + 318, + 72, + 553, + 214 + ], + "lines": [ + { + "bbox": [ + 318, + 72, + 553, + 214 + ], + "spans": [ + { + "bbox": [ + 318, + 72, + 553, + 214 + ], + "type": "image", + "image_path": "fe3bb0ff1296f13213667bda6dc75ce3cdd106658ab0656927c0ea72fac9f0be.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 220, + 535, + 233 + ], + "lines": [ + { + "bbox": [ + 332, + 220, + 535, + 233 + ], + "spans": [ + { + "bbox": [ + 332, + 220, + 535, + 233 + ], + "type": "text", + "content": "Figure 6. Visualizations on the ablation study of PETA." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 353, + 243, + 517, + 305 + ], + "blocks": [ + { + "bbox": [ + 71, + 316, + 280, + 328 + ], + "lines": [ + { + "bbox": [ + 71, + 316, + 280, + 328 + ], + "spans": [ + { + "bbox": [ + 71, + 316, + 280, + 328 + ], + "type": "text", + "content": "Table 2. Ablation study on the hyper-parameters of PRD." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 353, + 243, + 517, + 305 + ], + "lines": [ + { + "bbox": [ + 353, + 243, + 517, + 305 + ], + "spans": [ + { + "bbox": [ + 353, + 243, + 517, + 305 + ], + "type": "table", + "html": "
C.S. ↑R@1 ↑
Full Param Tuning35.80.35
w/ Basic LoRA54.211.1
w/ PETA (Proposed)68.232.3
", + "image_path": "9bf2c876db40115ba95d1d51a9e763b9034d5d92933720b547e5052247c9d9a6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 335, + 313, + 533, + 325 + ], + "lines": [ + { + "bbox": [ + 335, + 313, + 533, + 325 + ], + "spans": [ + { + "bbox": [ + 335, + 313, + 533, + 325 + ], + "type": "text", + "content": "Table 3. Ablation study on the effectiveness of PETA." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 347, + 436, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 436, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 436, + 360 + ], + "type": "text", + "content": "the supplementary materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 372, + 468, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 468, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 468, + 384 + ], + "type": "text", + "content": "5. Conclusion and Limitation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 392, + 555, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 583 + ], + "type": "text", + "content": "In this paper, we presented Progressive Rendering Distillation (PRD), a novel training scheme that adapts Stable Diffusion (SD) for instant text-to-mesh generation without relying on 3D data. We also introduced PETA (Parameter-Efficient Triplane Adaptation), a parameter-efficient method that introduces only " + }, + { + "bbox": [ + 313, + 392, + 555, + 583 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 313, + 392, + 555, + 583 + ], + "type": "text", + "content": " additional parameters to effectively enable SD for instant text-to-mesh generation. Our model, namely TriplaneTurbo, can produce text-consistent textured meshes in only 1.2 second. Through comprehensive experiments, we validated the effectiveness of our approach. Our methodology has the potential to be extended to 3D scene generation and image-to-3D tasks. While currently implemented with SD, the PRD approach can also be applied to other pre-trained models like DiT [20]. We hope our work can inspire new directions in 3D generation to overcome the dependency on 3D data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 584, + 556, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 584, + 556, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 584, + 556, + 669 + ], + "type": "text", + "content": "Limitations. One limitation of our method lies in the generation of precise numbers of multiple 3D objects, which may require more sophisticated multi-view teachers, potentially enhanced with layout guidance. Besides, our results for full-body humans might exhibit limited facial and hand details, which can be improved by extending SD adaptation to more advanced 3D structures than Triplane." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 681, + 408, + 694 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 681, + 408, + 694 + ], + "spans": [ + { + "bbox": [ + 314, + 681, + 408, + 694 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 701, + 511, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 511, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 511, + 714 + ], + "type": "text", + "content": "This work is supported by the InnoHK program." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11043" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 91, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 66, + 91, + 295, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 91, + 295, + 123 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 295, + 123 + ], + "type": "text", + "content": "[1] Thiemo Alldieck, Nikos Kolotouros, and Cristian Sminchisescu. 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However, these attacks often struggle to impersonate multiple targets and frequently fail to bypass liveness detection. For example, attacks using human-skin masks [28] are challenging to fabricate, inconvenient to swap between users, and often fail liveness detection due to facial occlusions. A projector, however, can generate content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Thus, we propose a novel physical adversarial attack using a projector and explore the superposition of projected and natural light to create adversarial facial images. This approach eliminates the need for physical artifacts on the face, effectively overcoming these limitations. Specifically, our proposed ProjAttacker generates adversarial 3D textures that are projected onto human faces. To ensure physical realizability, we introduce a light reflection function that models complex optical interactions between projected light and human skin, accounting for reflection and diffraction effects. Furthermore, we incorporate camera Image Signal Processing (ISP) simulation to maintain the robustness of adversarial perturbations across real-world diverse imaging conditions. Comprehensive evaluations conducted in both digital and physical scenarios validate the effectiveness of our method.", + "bbox": [ + 88, + 395, + 485, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 818, + 220, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Face recognition has become a widely adopted technology for authentication and access control [2, 13]. De", + "bbox": [ + 89, + 844, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0d93a70c5c0150b7583935591cbb284f88fc483f2969b97f62d659129b007569.jpg", + "image_caption": [ + "(a) Existing Attack Methods" + ], + "image_footnote": [], + "bbox": [ + 519, + 361, + 901, + 428 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/aec9f27e02e800285acb22e138763c00b4736c1460f370e78d1ecd8b7165aff5.jpg", + "image_caption": [ + "(b) Our Attack Method", + "Figure 1. Comparison of our ProjAttacker with existing attack methods. While existing methods [10, 18, 28] can successfully attack face recognition, they are difficult to fabricate, inconvenient to swap between targets, and unable to bypass liveness detection due to facial occlusions. In contrast, our ProjAttacker projects light-based adversarial textures onto the face, enabling a non-intrusive attack via projector that overcomes these limitations, allowing real-time, configurable face swaps that simultaneously deceive both liveness detection and recognition models." + ], + "image_footnote": [], + "bbox": [ + 519, + 443, + 901, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "spite its prevalence, significant security vulnerabilities remain. Recent studies have shown that imperceptible, carefully crafted perturbations can deceive deep neural network based face recognition models, leading to incorrect predictions [5, 20, 25, 30]. These attacks remain effective in the physical world [24], exposing substantial security risks. Developing physical adversarial attack methods to identify weaknesses and assess the robustness of these systems is essential for secure real-world deployment.", + "bbox": [ + 509, + 729, + 906, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing physical adversarial attacks on face recognition systems largely rely on physical artifacts like textured", + "bbox": [ + 511, + 869, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution † Corresponding author", + "bbox": [ + 114, + 886, + 362, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21248", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0fe86138bcd980b73eb144213639643192649123b5a68bdaa36b674d176932dc.jpg", + "image_caption": [ + "Figure 2. Workflow of our ProjAttacker. ProjAttacker works in four steps: (1) generating a light-based adversarial 3D mask; (2) deploying the attack in the real world using projection devices; (3) capturing the attacker's image with a camera; and (4) executing the attack during model inference. This workflow mirrors our attack pipeline in the digital domain." + ], + "image_footnote": [], + "bbox": [ + 94, + 87, + 297, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f92a9c19fe6ef15fb6fd241099f63b6fd1bb2bef986cbd56fac3fd1a7df1654c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 87, + 478, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/407506bbfededf98af80ff0161bdf545de772ffca56d82f249c2fe0188118941.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 478, + 88, + 658, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/45b09106044e3a81523ddc7a8e0fb1126e7a71174f93d46f163536b3feba57a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 88, + 903, + 215 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eyeglasses [18, 19], human-skin masks [28], stickers [25], forehead-covering hats [10], and makeup [29]. While these approaches can successfully fool recognition models, they face notable limitations: 1) they are user-specific, difficult to adapt for multiple individuals, and often require complex fabrication processes (e.g., 2D or 3D printing) and high-quality materials to accurately replicate designed adversarial textures, making them impractical for multi-user scenarios; and 2) their occlusive nature makes it difficult to bypass liveness detection, reducing their attack effectiveness in real-world settings.", + "bbox": [ + 88, + 277, + 480, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A projector can produce content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Leveraging this advantage, we introduce ProjAttacker, a novel and configurable physical adversarial attack for face recognition. ProjAttacker explores the superposition of projected and natural light to create adversarial facial images. This approach effectively addresses both aforementioned limitations, simultaneously enabling multi-target impersonation and circumvention of liveness detection. Fig. 1 presents a comparison between our method and existing state-of-the-art (SOTA) approaches.", + "bbox": [ + 88, + 446, + 482, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To ensure real-world attack effectiveness, we analyze the workflow of ProjAttacker, which comprises four steps (see Fig. 2). For the adversarial 3D mask generated in step (1) to remain effective through step (4), it must successfully traverse two critical domain transitions: the projector-mediated transition from digital domain to physical space, and the camera-mediated transition from physical space back to digital images. Maintaining resilience across these domain transitions is crucial for attack success. Therefore, we first incorporate a light reflection function into the adversarial 3D mask generation pipeline, ensuring robustness against projection inconsistencies. To mitigate camera-induced color shifts in real-world scenarios, we develop a differentiable proxy network that simulates camera Image Signal Processing (ISP) modules. Specifically, this proxy network transforms the camera's internal denoising and color correction units into differentiable modules, and through stochastic sampling of conditional input parameters during optimization, generates adversarial patterns", + "bbox": [ + 89, + 613, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that remain effective under various camera capture conditions. Extensive experiments in both digital and physical scenarios demonstrate that our proposed method effectively compromises mainstream models and APIs. The main contributions are summarized as follows:", + "bbox": [ + 511, + 279, + 903, + 353 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Real-world configurable face swap. We present ProjAttacker, the first light-based attack that leverages projected 3D masks with adversarial patterns to simultaneously deceive face recognition models and liveness detection systems, enabling efficient and cost-effective face-swapping attacks.", + "- Physically realizable attack pipeline. We bridge the digital-physical gap through: (i) a light reflection simulation function that ensures robustness against projection inconsistencies, and (ii) a differentiable camera ISP proxy network that accurately models the image capture process, guaranteeing the real-world effectiveness of the adversarial 3D mask.", + "- Exceptional attack effectiveness. Our ProjAttacker achieves superior performance in both digital and physical domains. Comprehensive experimental results validate our approach and reveal significant security vulnerabilities in contemporary face recognition systems." + ], + "bbox": [ + 511, + 358, + 906, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 647, + 661, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Physical Adversarial Attack for Face Recognition. Face recognition systems have been extensively deployed in safety-critical applications, making the study of physical-world adversarial attacks against such systems increasingly crucial. Prior works have predominantly explored the integration of adversarial perturbations with physical accessories, including hats [10], glasses [18, 19, 27], and stickers [25, 26]. Additionally, alternative approaches such as Adv-Makeup [29] demonstrate successful attacks through subtle eye-area cosmetic modifications, while AT3D [28] employs 3D-printed masks with adversarial textures. However, these methodologies either suffer from diminished effectiveness when transitioning from digital to physical domains or require complex, time-intensive preparation processes. Furthermore, their reliance on material-based facial", + "bbox": [ + 511, + 672, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21249", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a064d28d17cc98cd79087b2bc212e418bd8acd9fbc0d65e02ab6bd8650e87831.jpg", + "image_caption": [ + "Figure 3. Overview of ProjAttacker. (a) Initially, we employ CNN to extract features and perform parameter fitting on the image, precisely regressing the 3D Morphable Model (3DMM) coefficients. These coefficients are then rendered and cropped to produce the initial 3D adversarial pattern. (b) Subsequently, we simulate the realistic projection of the pattern in the physical space using the Light Reflection Function (LRF), and employ an camera ISP proxy model to emulate adversarial face images under various camera imaging systems. The adversarial pattern is dynamically updated through multiple iterations of optimization using an ensemble learning model. (c) Finally, we utilize the optimized adversarial face image for black-box attacks. If the attack fails, we dynamically adjust the weight distribution of the ensemble model through a reinforcement learning-based reward function and repeat step (b) to continually refine the attack strategy and enhance the success rate." + ], + "image_footnote": [], + "bbox": [ + 130, + 89, + 852, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "artifacts often fails to circumvent liveness detection mechanisms. In this work, we propose a light-based attack that addresses these limitations by simultaneously compromising both face recognition and liveness detection systems.", + "bbox": [ + 88, + 457, + 482, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Light-Based Attack. Light has emerged as a promising adversarial medium for projecting attack patterns onto human faces [24]. Current light-based attacks against face recognition systems are limited to two primary approaches: Zhou et al. [31]'s infrared light projection method and Nguyen et al. [14]'s 2D RGB adversarial pattern projection. While these approaches represent significant advances, they fail to adequately account for light distortion and reflection on facial surfaces, resulting in suboptimal attack success rates and performance. We systematically re-examine the light-based attack pipeline, as illustrated in Fig. 2, and introduce novel light reflection and camera capture simulation modules. These innovations enable the generation of robust light-based adversarial patterns that maintain effectiveness throughout both projection and capture processes, ensuring high attack success rates in real-world scenarios.", + "bbox": [ + 88, + 520, + 482, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Domain Transition. Since Sharif et al. [18] first demonstrated adversarial attacks in the physical world, the research community has increasingly focused on exploring the effectiveness of adversarial examples under real-world conditions [7, 21, 23]. This process involves two domain transformations. As shown in Fig. 2, the first domain transformation occurs during the attack deployment stage, where the adversarial pattern transitions from the digital space to the physical world. The second domain transfor", + "bbox": [ + 88, + 763, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mation takes place during the camera capture stage, where the adversarial pattern transitions back from the physical world to the digital space. Existing methods have primarily addressed the former, such as non-printability score (NPS) [18] and D2P [8], which aim to mitigate the impact of the digital-to-physical transformation on attacks. To the best of our knowledge, no method has yet addressed the latter transformation, i.e., from physical to digital. We have designed a comprehensive attack pipeline that incorporates a light reflection function and a camera ISP proxy network to accurately simulate the real-world workflow, thereby enhancing the attack effectiveness in the physical world.", + "bbox": [ + 511, + 457, + 906, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 511, + 651, + 650, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 511, + 675, + 718, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Threat Model. Let $\\mathcal{X}$ denote the space of all possible facial images. Given a black-box facial recognition system $f:\\mathcal{X}\\to \\mathbb{R}^d$ that maps an input image to a $d$ -dimensional embedding space, our goal is to generate physical adversarial patterns that can be projected onto an attacker's face to impersonate a target victim. Formally, for an attacker's face image $x^{a}\\in \\mathcal{X}$ and a victim's face image $x^{v}\\in \\mathcal{X}$ , we aim to find an adversarial perturbation function $F(\\cdot)$ that generates a physically realizable adversarial example $x^{adv}$ such that:", + "bbox": [ + 511, + 696, + 906, + 834 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {a d v} = F \\left(x ^ {a}, x ^ {v}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 842, + 906, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $F(\\cdot)$ consists of a 3D mask $M$ and a light-based perturbation pattern $\\tilde{x}$ .", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21250", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Attack Objective. The attack is considered successful if the following conditions are satisfied: (1) Impersonation Success: The adversarial example should be verified as the victim: $\\text{Ver}(x^{adv}, x^v) = 1$ where $\\text{Ver}(x^1, x^2) = \\mathbb{I}\\left(\\frac{\\langle f(x^1), f(x^2)\\rangle}{|f(x^1)| \\cdot |f(x^2)|} > \\tau\\right)$ . (2) Physical Realizability: The adversarial perturbation must be physically realizable through light projection:", + "bbox": [ + 89, + 90, + 483, + 204 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 210, + 482, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T_{l}(\\cdot)$ represents the Light Reflection Function that models real-world lighting effects. The complete optimization can be formulated as:", + "bbox": [ + 89, + 234, + 483, + 279 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {M, \\tilde {x}} L _ {F} \\left[ T _ {c} \\left(x ^ {a d v}\\right), x ^ {v} \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 282, + 357, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {s . t .} x ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M \\quad M \\in \\mathcal {M}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 311, + 480, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{F}[\\cdot ,\\cdot ]$ is the objective function measuring the dissimilarity between the adversarial example and victim, $T_{c}(\\cdot)$ represents the camera capture simulation, $\\mathcal{M}$ is the space of valid 3D masks obtained through 3D face reconstruction, $\\odot$ denotes element-wise multiplication.", + "bbox": [ + 89, + 342, + 483, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This optimization problem is solved through a reinforcement learning framework [11], where the agent learns an optimal perturbation policy through interactions with an environment constructed from white-box face recognition model ensembles, ultimately generalizing to attack the black-box target model.", + "bbox": [ + 89, + 417, + 483, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overall Framework", + "text_level": 1, + "bbox": [ + 89, + 516, + 279, + 530 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a victim's facial image $x^{v}$ , we first construct a 3D face model using a pre-trained 3D face reconstruction network. This network decomposes the facial attributes into multiple components, and then used them to reconstruct a complete 3D face model of the victim. To obtain the projection area for the adversarial pattern, we perform 3D cropping on the reconstructed face model to generate the initial 3D mask $M \\in \\mathcal{M}$ . This mask defines the spatial region where the light-based perturbation will be applied.", + "bbox": [ + 89, + 537, + 483, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core of our framework lies in the optimization stage, where we iteratively refine the adversarial pattern through a reinforcement learning approach. This stage involves several key components: Light Reflection Function $T_{l}(\\cdot)$ : We design a differentiable light reflection function that simulates how projected patterns interact with the attacker's face under various physical conditions. This function models the transformation of the initial perturbation $\\tilde{x}$ when projected onto the 3D mask $M$ and combines it with the attacker's face image $x^{a}$ according to Eq. 2. Camera ISP Proxy Network $T_{c}(\\cdot)$ : To bridge the gap between digital and physical domains, we incorporate a Camera ISP (Image Signal Processing) proxy network that simulates real-world image capture effects. This network ensures that the generated patterns remain effective under real camera conditions. Agent", + "bbox": [ + 89, + 674, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Models: We construct an environment using an ensemble of white-box face recognition models. The agent interacts with these models to learn an optimal perturbation strategy that can generalize to black-box scenarios. The learning process is guided by a reward signal derived from the cosine similarity scores between the adversarial example and the victim's embedding.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the final stage, we evaluate the effectiveness of our attack against the target black-box face recognition model. The attacker's face, augmented with the optimized adversarial pattern projected through the 3D mask, is presented to the target system. The success of the attack is measured by the verification result $\\text{Ver}(x^{adv}, x^v)$ . This stage validates whether our generated adversarial pattern can successfully fool the target system while maintaining physical realizability. The entire framework operates in an end-to-end manner, with loss gradients propagating backward through the optimization stage to continuously refine the adversarial pattern.", + "bbox": [ + 511, + 198, + 905, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. 3D Mask Initialization", + "text_level": 1, + "bbox": [ + 511, + 390, + 723, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Face recognition systems capture the 3D structure of facial features, such as surface protrusions and recesses. However, most existing attack methods [10, 18, 19, 25] rely on 2D perturbation simulations, which struggle to effectively map onto 3D facial features in real-world applications. This dimensional mismatch reduces the effectiveness of physical-space attacks. To address this limitation, we introduce a high-dimensional, geometric parameter-driven 3D facial projection construction. Starting from facial images, we employ a convolutional neural network (CNN) regression model to extract 3D Morphable Model (3DMM) coefficients that encode individual-specific facial geometry. These coefficients then guide a facial mesh reconstruction module, applying 3D deformation and topological mapping to accurately generate a 3D mesh model aligned with the individual's facial structure. Spatial coordinate transformations are then applied to map the mesh vertices from object coordinates to camera coordinates, and an intrinsic camera matrix enables perspective projection, which normalizes depth information into 2D pixel coordinates for precise 3D-to-2D mapping on the image plane.", + "bbox": [ + 511, + 412, + 906, + 731 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx = \\mathcal {T} \\left(K \\cdot \\mathcal {R} \\left(B \\cdot [ \\Theta_ {i d}, \\Theta_ {e x p}, \\Theta_ {t e x}, \\dots ] ^ {T} + \\overline {{S}}\\right)\\right). (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 741, + 906, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this formulation, $\\Theta$ represents various 3DMM coefficients. $B$ is the matrix containing the basis shape vectors, which is used to map the coefficients to the corresponding shape space, while $\\overline{S}$ serves as the mean facial shape. $\\mathcal{R}$ is the spatial transformation function mapping 3D mesh vertices from object to camera coordinates, while the intrinsic camera matrix $K$ enables perspective projection, and $\\mathcal{T}$ normalizes depth information to 2D pixel coordinates.", + "bbox": [ + 511, + 779, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21251", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through this process, we effectively simulate digital-space attack patterns in the physical domain by projecting refined 2D adversarial patterns onto 3D faces, substantially enhancing attack success rates.", + "bbox": [ + 89, + 90, + 482, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Light Reflection Function", + "text_level": 1, + "bbox": [ + 89, + 159, + 323, + 175 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The efficacy of light-based adversarial attacks hinges on the faithful conversion of digital adversarial patterns into physical light projections. Two primary factors influence this process: (1) the alteration of received light wavelengths due to specular reflection, diffuse reflection, and absorption of adversarial light on facial surfaces, and (2) the interaction between projected light and ambient illumination, resulting in the reception of reflected ambient light. These phenomena modulate the pixel values of the digital pattern. Consequently, formulating these transformations is crucial for mitigating their impacts and preserving attack effectiveness.", + "bbox": [ + 89, + 180, + 483, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a Light Reflection Function (LRF) that models the process of pattern projection, reflection on skin, and camera capture, formulated as the transformation $T_{l}(\\cdot)$ :", + "bbox": [ + 89, + 347, + 482, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {\\text {m a s k}} = T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 401, + 480, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This process primarily involves modeling the following physical phenomena: the projector emits light patterns corresponding to the RGB values of each pixel in the image. Both projected and ambient light strike the human face and, after absorption and reflection, produce new light patterns. The camera then captures these patterns and converts them into RGB format. This process is principally determined by three factors ( $\\lambda$ denotes the wavelength of light):", + "bbox": [ + 89, + 426, + 483, + 547 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $S(\\lambda)$ : the spectral power distribution of the projector.", + "- $\\rho (\\lambda)$ : the spectral reflectance of the skin.", + "- $\\sigma(\\lambda)$ : the sensitivity of the camera's photodetectors, with $\\sigma_x(\\lambda)$ , $\\sigma_y(\\lambda)$ , and $\\sigma_z(\\lambda)$ representing the impact on red, green, and blue components respectively." + ], + "bbox": [ + 89, + 547, + 480, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To simulate and quantify human visual response to colors, we utilize the CIE XYZ color space model, integrating the color matching functions to calculate an image's coordinates within this space: $X = \\int S(\\lambda) \\rho(\\lambda) \\sigma_x(\\lambda) d\\lambda, Y = \\int S(\\lambda) \\rho(\\lambda) \\sigma_y(\\lambda) d\\lambda, Z = \\int S(\\lambda) \\rho(\\lambda) \\sigma_z(\\lambda) d\\lambda$ . The interaction between ambient and projected light is considered through linear superposition of their spectral intensities:", + "bbox": [ + 89, + 625, + 483, + 729 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS (\\lambda) = S _ {\\text {n a t u r a l}} (\\lambda) + S _ {\\text {p r o j e c t o r}} (\\lambda). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 738, + 482, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, XYZ coordinates are converted to RGB coordinates. Using the PAL standard RGB system as an example, the transformation is:", + "bbox": [ + 89, + 763, + 482, + 808 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{l} R \\\\ G \\\\ B \\end{array} \\right] = \\left[ \\begin{array}{c c c} X _ {r} & Y _ {r} & Z _ {r} \\\\ X _ {g} & Y _ {g} & Z _ {g} \\\\ X _ {b} & Y _ {b} & Z _ {b} \\end{array} \\right] \\left[ \\begin{array}{l} X \\\\ Y \\\\ Z \\end{array} \\right]. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 813, + 482, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$S(\\lambda)$ , $\\rho (\\lambda)$ , $\\sigma (\\lambda)$ , and PAL color conversion matrix $(X_{r}$ etc.) can all be obtained from technical documentation and", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4ec31b0b06a26443f0f649e7ae6eb558b00e5cb25a03d27e5ec18a3323204719.jpg", + "image_caption": [ + "Figure 4. Light Reflection Function. (c) is obtained by applying our light reflection function to (b), while (d), obtained by projecting (a) in the real world, demonstrates consistency with (c)." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 890, + 171 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "official standards. As shown in Fig. 4, our LRF enables the transformed adversarial 3D mask to closely align with its real-world counterpart. Integrating the LRF within our optimization pipeline ensures that the adversarial 3D mask, when projected into the physical world, maintains its attack effectiveness.", + "bbox": [ + 511, + 229, + 903, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Camera Capture Simulation", + "text_level": 1, + "bbox": [ + 511, + 332, + 767, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The camera's internal Image Signal Processing (ISP) pipeline plays a crucial role in transforming physical scenes into digital RGB images. Variations in ISP configurations can lead to divergent visual characteristics of the same adversarial texture across devices, potentially affecting attack performance. Therefore, we introduce ISP simulation $T_{c}(\\cdot)$ to model the camera capturing process. To address the non-differentiable nature of traditional ISP processes, we build a differentiable camera ISP proxy network that enables gradient propagation during optimization. The camera ISP proxy network simulates various ISP processes through conditional inputs, focusing on representative parameters from color and tone correction modules, as well as the denoising module, which significantly impact image quality.", + "bbox": [ + 511, + 354, + 906, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our camera ISP proxy network is based on the U-Net architecture [16], comprising $3 \\times 3$ convolutions and $2 \\times 2$ max pooling operations in its encoder and decoder. The feature channels expand progressively through \\{32, 64, 128, 256, 512\\}. This structure enables the ISP proxy network to maintain differentiability while simulating diverse camera ISP parameter configurations, thus adapting to various hardware environments.", + "bbox": [ + 511, + 566, + 905, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We normalize ISP parameters (e.g., brightness, contrast, gamma correction) to [0,1] and concatenate them with feature maps, enabling the ISP proxy network to dynamically adjust image tone, contrast, color balance, and denoising characteristics to flexibly simulate diverse device imaging profiles. To train our camera ISP proxy network, we utilize an undifferentiable camera ISP simulator [15] along with the COCO dataset [12], generating a total of 2,270 data pairs. During training, we employ a composite loss function—including pixel-level MSE loss, perceptual loss, and regularization loss—to ensure high image fidelity and sensitivity to conditional ISP parameters, while maintaining full differentiability for gradient optimization. Our framework leverages the ISP network simulating various lighting ef", + "bbox": [ + 511, + 689, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21252", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ac58b178d8b453613e2c8c86a05c44ceacab59038bafe5b95d04169fae84419d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SourceLFW datasetCelebA-HQ dataset
ArcFaceMoblieNetResNetIRAPIArcFaceMoblieNetResNetIRAPI
ArcFace [1]-40.40%25.37%39.22%12.37%-60.80%64.32%62.12%16.49%
MobileNet [4]13.28%-46.98%24.71%12.05%49.50%-66.33%40.80%12.86%
ResNet [3]25.37%54.31%-33.14%18.33%63.49%75.50%-56.35%12.35%
IR [3]22.32%41.44%42.37%-17.86%78.79%78.39%58.79%-14.29%
Ensemble59.09%72.91%75.28%53.52%38.78%90.50%88.29%88.37%88.50%32.84%
", + "bbox": [ + 106, + 88, + 885, + 202 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/949f29de3c1c60d5e55bf2c4e6a7d0cccdc4e700ad8ad33839e0b125c03611e1.jpg", + "table_caption": [ + "Table 1. Evaluation of black-box impersonation attack. We report the attack success rates (ASR) on ArcFace, MobileNet, ResNet, IR, and a commercial API. Each row represents results using a different source model for the attack. In the ensemble setting, the target model corresponding to each column is excluded from the ensemble used to generate the attack." + ], + "table_footnote": [], + "table_body": "
DatasetTypeMethodArcFaceFaceNetMobileNetResNetCosFaceAPIAverage
LFWTransfer-basedTAP [27] \\( _{CVPR'21} \\)53.50%46.00%--50.00%10.00%39.89%
AT3D [28] \\( _{CVPR'23} \\)86.25%-91.50%86.50%63.00%45.25%74.50%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-51.11%--48.06%-49.59%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours78.07%52.17%79.49%82.98%78.17%41.43%68.72%
CelebA-HQTransfer-basedTAP [27] \\( _{CVPR'21} \\)65.75%52.50%--58.25%20.00%49.13%
AT3D [28] \\( _{CVPR'23} \\)92.50%-96.25%93.75%87.50%50.25%84.05%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-48.96%--47.73%-48.35%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours95.15%84.47%98.13%97.20%93.20%44.03%85.36%
", + "bbox": [ + 106, + 261, + 885, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison with existing methods. All methods are evaluated under a black-box setting, where TAP [27] and AT3D [28] are transfer-based attacks, while AdvSticker [25], SOPP [26], and ProjAttacker are query-based attacks. The highest and second-highest Attack Success Rates (ASRs) across both datasets are highlighted in red and blue, respectively.", + "bbox": [ + 89, + 433, + 903, + 476 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "fects in the physical world to enhance the robustness of adversarial patterns and improve attack efficacy.", + "bbox": [ + 89, + 502, + 482, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 547, + 223, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 89, + 571, + 282, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Targeted Models. We selected seven face recognition models as our target models, including six representative open-source models (ArcFace [1], MobileNet [4], ResNet [3], FaceNet [17], CosFace [22], IR [3]) and a commercial face recognition API*. For attacking the API, we employed other open-source models as an ensemble of surrogate models. When performing an ensemble attack on one of the models, the remaining models served as surrogate models. In our experiments, we evaluate the attack effectiveness by calculating the cosine similarity of the vectors obtained from the input image pairs. Each model adheres to its respective threshold: if the similarity between two images exceeds the threshold, they are considered the same identity; otherwise, they are considered different identities. Notably, each model is well-trained, achieving an accuracy exceeding $99\\%$ on the LFW dataset.", + "bbox": [ + 89, + 593, + 482, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conducted experiments in the digital domain on two extensively employed benchmark datasets: the La-", + "bbox": [ + 89, + 835, + 482, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "beled Faces in the Wild (LFW) [6] and the CelebFaces Attributes High Quality (CelebA-HQ) [9]. For evasion attacks, we randomly selected several pairs of images with the same identity from the dataset, aiming to push the attacker's features away from their true identity. For impersonation attacks, we randomly chose an attacker from the dataset and paired them with several randomly selected victims, creating multiple pairs of images with different identities.", + "bbox": [ + 511, + 502, + 903, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison methods. We compare our proposed ProjAttacker with the following four methods: TAP [27], AdvSticker [25], SOPP [26], and AT3D [28]. All methods are physically realizable.", + "bbox": [ + 511, + 623, + 903, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. All experiments were conducted on a Linux server equipped with two NVIDIA GeForce RTX 3090 GPUs, with all code and algorithms implemented in PyTorch. We set the number of iterations per round to 300 and the learning rate to 0.45. Within the overall framework, the reward step size is set to 0.1. The total number of queries is 25, and if no result is obtained within 25 queries, the attempt is deemed unsuccessful.", + "bbox": [ + 511, + 685, + 903, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Attacks in the Digital World", + "text_level": 1, + "bbox": [ + 511, + 816, + 764, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Black-box Attack. To assess the effectiveness of the attacks, we employ the Attack Success Rate (ASR), a metric that measures the efficacy of attack methodologies by indicating the proportion of successful attacks relative to the", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "\\*https://intl.cloud.tencent.com/product/ facerecognition", + "bbox": [ + 89, + 875, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21253", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe71e0915d9a6343c6d6264bd8b0d5aadbdd8ca8575703150445b58d893f6053.jpg", + "image_caption": [ + "Figure 5. Attack results of our ProjAttacker in both digital and physical domains. By projecting diverse adversarial patterns onto facial regions, an attacker can induce the face recognition model (CosFace [22]) to misidentify the subject as various victims. Our method exhibits superior flexibility and cost-effectiveness compared to approaches based on wearable material artifacts. Green indicates successful attacks, while red denotes unsuccessful attacks." + ], + "image_footnote": [], + "bbox": [ + 133, + 89, + 864, + 419 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "total samples. Tab. 1 displays the quantitative results of impersonation attacks under black-box conditions against five different target models.", + "bbox": [ + 88, + 491, + 482, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 1, we can observe: (1) The proposed model ensemble method demonstrates significant efficacy against impersonation attacks on both the LFW and CelebA-HQ datasets. Notably, the highest attack success rate achieved on the LFW dataset is $75.28\\%$ , while on the CelebA-HQ dataset, it reaches $90.50\\%$ . (2) The attack success rates on the CelebA-HQ dataset are generally higher than those on the LFW dataset. This can be attributed to the higher quality and resolution of facial images in the CelebA-HQ dataset, which facilitates more effective feature extraction by the models. (3) The ensemble method consistently outperforms models trained individually, indicating that our approach can adaptively adjust model weights to achieve optimal performance.", + "bbox": [ + 88, + 537, + 482, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons with SOTA Methods. We compare ProjAttacker attack with five existing physically realizable black-box attack methods, as shown in Tab. 2. We conducted experiments on a set of images from the CelebA-HQ dataset. Each target model in the columns is excluded from our ensemble model, strictly adhering to the principles of black-box attacks. Our method outperforms the two baseline query-based approaches, AdvSticker and SOPP, across both datasets. Regarding transfer-based methods, our approach surpasses TAP on the LFW dataset but falls short of", + "bbox": [ + 88, + 750, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/18c7c79c287e8d3a5a4e800c92cf0f31f362c32ef449d246c2f0041fd897db0e.jpg", + "table_caption": [], + "table_footnote": [ + "- \"3D\" represents the 3D mask form, as opposed to the 2D mask.", + "- \"LRF\" means the light reflection function in our pipeline.", + "- \"ISP\" means the camera ISP proxy network in our pipeline." + ], + "table_body": "
3DLRFISPArcFaceMobileNetResNetAPI
✓✓56%54%52%34%
✓✓38%32%32%12%
✓✓44%42%48%22%
✓✓✓68%60%62%38%
", + "bbox": [ + 517, + 488, + 901, + 573 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study in the physical world. We report the ASR of our ProjAttacker attack.", + "bbox": [ + 513, + 609, + 905, + 637 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AT3D. However, on the CelebA-HQ dataset, our method outperforms both TAP and AT3D. These results demonstrate the excellent attack performance of our approach in black-box settings.", + "bbox": [ + 511, + 667, + 906, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Attacks in the Physical World", + "text_level": 1, + "bbox": [ + 511, + 739, + 777, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Analysis. As shown in Fig. 5, we present an attacker, six victims, and their corresponding digital and physical space attacks. Without the light reflection function, the optimized adversarial patterns exhibit diverse colors with high saturation, impeding physical space reproduction. Incorporating the light reflection function facilitates the transfer of digital space adversarial patterns to the physical domain. Physical space attacks demonstrate our method's efficacy in misleading CosFace to misiden", + "bbox": [ + 509, + 763, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21254", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/84a652497147d894a18e0f18e989c759ae24c830eb7df60aec48534b4c76529b.jpg", + "image_caption": [ + "Figure 6. Comparison with existing methods. We compare the hiPAA [24] of three physical adversarial attack methods." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 478, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tify the attacker as different victims with high confidence. Notably, transitioning between victims merely requires altering the projected pattern, offering significant operational convenience. These results highlight our method's flexibility in executing effective attacks in real-world scenarios.", + "bbox": [ + 88, + 234, + 482, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Study. To quantify the contribution of each module within our proposed framework to the success rate of physical space attacks, we conducted ablation experiments. We systematically removed the 3D, RLF, and ISP modules from a set of attacker-victim image pairs, generating four distinct adversarial patterns for physical testing, including those from the complete framework. The experiments encompassed 50 attacker-victim pairs, with statistical results presented in Tab. 3. We observe that the removal of any single module results in a decrease in Attack Success Rate (ASR). These findings validate the rationale and necessity of each module within our method.", + "bbox": [ + 89, + 310, + 483, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation using hiPAA Metrics. To comprehensively evaluate the performance of physical adversarial attacks, Wei et al. [24] proposed the hiPAA metric, which includes six dimensions: Effectiveness, Stealthiness, Robustness, Practicability, Aesthetics, and Economics. We assess and compare the hiPAA scores of various methods, as illustrated in Fig. 6. Note that Stealthiness, Practicability, and Aesthetics are evaluated through a user study; refer to the supplementary material for more details of our evaluation. We observe that our ProjAttacker attack outperforms TAP in robustness and surpasses AT3D in effectiveness. Additionally, our method significantly outperforms in the Practicability dimension, as it does not require manually crafted 3D-printed masks or patches. For an attacker to mislead the facial recognition system into identifying them as different victims, only the adversarial pattern needs to be switched. This not only reduces costs but also eliminates the need for complex manufacturing processes, enhancing the practicality of real-world applications.", + "bbox": [ + 89, + 491, + 483, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Liveness Detection", + "text_level": 1, + "bbox": [ + 89, + 787, + 269, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Liveness detection technology primarily encompasses four methods: (1) Transform: Analysis of image Fourier transforms or Local Binary Patterns to discern whether a presented face is genuine or merely a static image. (2) Depth: Utilization of depth sensors or stereo cameras to assess the three-dimensional structure of a face, thereby verifying its", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0c4448ffdb2021fdcd76eb96537058bc3b4bd1b2aaec76d4afe97d1feaf14597.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTransformDepthMotionMultiBio
TAP [27] CVPR'21✓XXX
AdvSticker [25] TPAMI'22✓✓✓X
SOPP [26] TPAMI'22✓✓✓X
AT3D [28] CVPR'23✓✓XX
ProjAttacker Ours✓✓✓✓
", + "bbox": [ + 517, + 88, + 903, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c4abdce232fbcb4e0934292f0ade24a5cec65abd66301dc5631f1337d05c4781.jpg", + "table_caption": [ + "Table 4. Liveness detection analysis. Our light-based attack outperforms existing methods by successfully deceiving all liveness detection strategies." + ], + "table_footnote": [], + "table_body": "
CTyunBaiduTencentAliyun
Physical Evaluation55/5555/5548/5152/55
", + "bbox": [ + 517, + 244, + 903, + 289 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Bypass rate. The number of successful bypasses achieved by our method across four commercial liveness detection APIs.", + "bbox": [ + 511, + 292, + 903, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "authenticity. (3) Motion: Examination and tracking of eye movements, lip motions, and blink frequency to validate the presence of a live subject. (4) MultiBio: Integration of facial vascular flow detection with other biometric identification technologies, such as iris scanning, to provide a multi-tiered security validation approach.", + "bbox": [ + 511, + 348, + 903, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 4 shows that existing physical attack modalities typically require a tangible medium and often rely on partially obstructing the facial features to create adversarial perturbations. In contrast, our method utilizes light as the medium and adopts a non-intrusive attack. This approach avoids obscuring facial biometric features, thus demonstrating higher effectiveness against various liveness detection technologies. Tab. 5 shows that our method achieved successful bypasses across all four commercial liveness detection APIs, with a $100\\%$ success rate on CTyun and Baidu in particular.", + "bbox": [ + 511, + 439, + 905, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 603, + 633, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced ProjAttacker, a novel adversarial light attack that effectively compromises both face recognition systems and liveness detection models. Extensive experiments in both digital and physical space demonstrate that ProjAttacker outperforms existing methods, highlighting the vulnerability of current face recognition systems to sophisticated physical attacks. Our findings underscore the pressing need for more robust defense mechanisms to secure biometric systems against potential threats.", + "bbox": [ + 511, + 628, + 905, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethics Statement. Our research investigates the vulnerabilities of face recognition systems through physical adversarial attacks. Aware of the dual-use potential, we conducted all experiments under strict ethical guidelines, ensuring no compromise of personal data or real-world systems. Our goal is to contribute to the development of more secure face recognition systems. We urge the community to consider both defensive and offensive aspects, promoting responsible application.", + "bbox": [ + 511, + 763, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21255", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by Hubei Key R&D Project (2022BAA033) and National Natural Science Foundation of China (62171325, 62402365). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.", + "bbox": [ + 89, + 90, + 485, + 183 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 193, + 187, + 209 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jiankang Deng, Jia Guo, Jing Yang, Niannan Xue, Irene Kotsia, and Stefanos Zafeiriou. 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Invisible mask: Practical attacks on face recognition with infrared. arXiv preprint arXiv:1803.04683, 2018. 3" + ], + "bbox": [ + 91, + 90, + 483, + 598 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21257", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/ProjAttacker_ A Configurable Physical Adversarial Attack for Face Recognition via Projector/4340b920-658a-4e45-bed9-f9bb84d4699c_model.json b/2025/ProjAttacker_ A Configurable Physical Adversarial Attack for Face Recognition via Projector/4340b920-658a-4e45-bed9-f9bb84d4699c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..803435b364d5a26b6712b615fa7fafaf9aee3649 --- /dev/null +++ b/2025/ProjAttacker_ A Configurable Physical Adversarial Attack for Face Recognition via Projector/4340b920-658a-4e45-bed9-f9bb84d4699c_model.json @@ -0,0 +1,1936 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.817, + 0.177 + ], + "angle": 0, + "content": "ProjAttacker: A Configurable Physical Adversarial Attack for Face Recognition via Projector" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.203, + 0.786, + 0.24 + ], + "angle": 0, + "content": "Yuanwei Liu\\(^{1,2*}\\) Hui Wei\\(^{1,2*}\\) Chengyu Jia\\(^{1,2}\\) Ruqi Xiao\\(^{1,2}\\) Weijian Ruan\\(^{3,4}\\) Xingxing Wei\\(^{5}\\) Joey Tianyi Zhou\\(^{6}\\) Zheng Wang\\(^{1,2\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.242, + 0.894, + 0.329 + ], + "angle": 0, + "content": "\\(^{1}\\)National Engineering Research Center for Multimedia Software, Institute of Artificial Intelligence, School of Computer Science, Wuhan University, Wuhan, China \\(^{2}\\)Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan, China \\(^{3}\\)Hangzhou Research Institute of Xidian University, Hangzhou, China \\(^{4}\\)Smart City Research Institute of China Electronics Technology Group Corporation, Shenzhen, China \\(^{5}\\)Institute of Artificial Intelligence, Beihang University, Beijing, China \\(^{6}\\)Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR), Singapore" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.362, + 0.327, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.396, + 0.486, + 0.789 + ], + "angle": 0, + "content": "Previous physical adversarial attacks have shown that carefully crafted perturbations can deceive face recognition systems, revealing critical security vulnerabilities. However, these attacks often struggle to impersonate multiple targets and frequently fail to bypass liveness detection. For example, attacks using human-skin masks [28] are challenging to fabricate, inconvenient to swap between users, and often fail liveness detection due to facial occlusions. A projector, however, can generate content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Thus, we propose a novel physical adversarial attack using a projector and explore the superposition of projected and natural light to create adversarial facial images. This approach eliminates the need for physical artifacts on the face, effectively overcoming these limitations. Specifically, our proposed ProjAttacker generates adversarial 3D textures that are projected onto human faces. To ensure physical realizability, we introduce a light reflection function that models complex optical interactions between projected light and human skin, accounting for reflection and diffraction effects. Furthermore, we incorporate camera Image Signal Processing (ISP) simulation to maintain the robustness of adversarial perturbations across real-world diverse imaging conditions. Comprehensive evaluations conducted in both digital and physical scenarios validate the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.819, + 0.222, + 0.835 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.845, + 0.485, + 0.876 + ], + "angle": 0, + "content": "Face recognition has become a widely adopted technology for authentication and access control [2, 13]. De" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.362, + 0.903, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.43, + 0.785, + 0.442 + ], + "angle": 0, + "content": "(a) Existing Attack Methods" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.444, + 0.902, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.654, + 0.571, + 0.771, + 0.582 + ], + "angle": 0, + "content": "(b) Our Attack Method" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.587, + 0.907, + 0.713 + ], + "angle": 0, + "content": "Figure 1. Comparison of our ProjAttacker with existing attack methods. While existing methods [10, 18, 28] can successfully attack face recognition, they are difficult to fabricate, inconvenient to swap between targets, and unable to bypass liveness detection due to facial occlusions. In contrast, our ProjAttacker projects light-based adversarial textures onto the face, enabling a non-intrusive attack via projector that overcomes these limitations, allowing real-time, configurable face swaps that simultaneously deceive both liveness detection and recognition models." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.731, + 0.907, + 0.868 + ], + "angle": 0, + "content": "spite its prevalence, significant security vulnerabilities remain. Recent studies have shown that imperceptible, carefully crafted perturbations can deceive deep neural network based face recognition models, leading to incorrect predictions [5, 20, 25, 30]. These attacks remain effective in the physical world [24], exposing substantial security risks. Developing physical adversarial attack methods to identify weaknesses and assess the robustness of these systems is essential for secure real-world deployment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Existing physical adversarial attacks on face recognition systems largely rely on physical artifacts like textured" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.887, + 0.364, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution † Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21248" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.088, + 0.299, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.299, + 0.088, + 0.48, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.48, + 0.089, + 0.66, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.089, + 0.904, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.225, + 0.908, + 0.268 + ], + "angle": 0, + "content": "Figure 2. Workflow of our ProjAttacker. ProjAttacker works in four steps: (1) generating a light-based adversarial 3D mask; (2) deploying the attack in the real world using projection devices; (3) capturing the attacker's image with a camera; and (4) executing the attack during model inference. This workflow mirrors our attack pipeline in the digital domain." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.279, + 0.482, + 0.446 + ], + "angle": 0, + "content": "eyeglasses [18, 19], human-skin masks [28], stickers [25], forehead-covering hats [10], and makeup [29]. While these approaches can successfully fool recognition models, they face notable limitations: 1) they are user-specific, difficult to adapt for multiple individuals, and often require complex fabrication processes (e.g., 2D or 3D printing) and high-quality materials to accurately replicate designed adversarial textures, making them impractical for multi-user scenarios; and 2) their occlusive nature makes it difficult to bypass liveness detection, reducing their attack effectiveness in real-world settings." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.447, + 0.483, + 0.612 + ], + "angle": 0, + "content": "A projector can produce content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Leveraging this advantage, we introduce ProjAttacker, a novel and configurable physical adversarial attack for face recognition. ProjAttacker explores the superposition of projected and natural light to create adversarial facial images. This approach effectively addresses both aforementioned limitations, simultaneously enabling multi-target impersonation and circumvention of liveness detection. Fig. 1 presents a comparison between our method and existing state-of-the-art (SOTA) approaches." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To ensure real-world attack effectiveness, we analyze the workflow of ProjAttacker, which comprises four steps (see Fig. 2). For the adversarial 3D mask generated in step (1) to remain effective through step (4), it must successfully traverse two critical domain transitions: the projector-mediated transition from digital domain to physical space, and the camera-mediated transition from physical space back to digital images. Maintaining resilience across these domain transitions is crucial for attack success. Therefore, we first incorporate a light reflection function into the adversarial 3D mask generation pipeline, ensuring robustness against projection inconsistencies. To mitigate camera-induced color shifts in real-world scenarios, we develop a differentiable proxy network that simulates camera Image Signal Processing (ISP) modules. Specifically, this proxy network transforms the camera's internal denoising and color correction units into differentiable modules, and through stochastic sampling of conditional input parameters during optimization, generates adversarial patterns" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.28, + 0.905, + 0.354 + ], + "angle": 0, + "content": "that remain effective under various camera capture conditions. Extensive experiments in both digital and physical scenarios demonstrate that our proposed method effectively compromises mainstream models and APIs. The main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.359, + 0.907, + 0.449 + ], + "angle": 0, + "content": "- Real-world configurable face swap. We present ProjAttacker, the first light-based attack that leverages projected 3D masks with adversarial patterns to simultaneously deceive face recognition models and liveness detection systems, enabling efficient and cost-effective face-swapping attacks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.449, + 0.906, + 0.553 + ], + "angle": 0, + "content": "- Physically realizable attack pipeline. We bridge the digital-physical gap through: (i) a light reflection simulation function that ensures robustness against projection inconsistencies, and (ii) a differentiable camera ISP proxy network that accurately models the image capture process, guaranteeing the real-world effectiveness of the adversarial 3D mask." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.555, + 0.905, + 0.631 + ], + "angle": 0, + "content": "- Exceptional attack effectiveness. Our ProjAttacker achieves superior performance in both digital and physical domains. Comprehensive experimental results validate our approach and reveal significant security vulnerabilities in contemporary face recognition systems." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.359, + 0.907, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.648, + 0.663, + 0.664 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Physical Adversarial Attack for Face Recognition. Face recognition systems have been extensively deployed in safety-critical applications, making the study of physical-world adversarial attacks against such systems increasingly crucial. Prior works have predominantly explored the integration of adversarial perturbations with physical accessories, including hats [10], glasses [18, 19, 27], and stickers [25, 26]. Additionally, alternative approaches such as Adv-Makeup [29] demonstrate successful attacks through subtle eye-area cosmetic modifications, while AT3D [28] employs 3D-printed masks with adversarial textures. However, these methodologies either suffer from diminished effectiveness when transitioning from digital to physical domains or require complex, time-intensive preparation processes. Furthermore, their reliance on material-based facial" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21249" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.131, + 0.09, + 0.854, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.334, + 0.907, + 0.446 + ], + "angle": 0, + "content": "Figure 3. Overview of ProjAttacker. (a) Initially, we employ CNN to extract features and perform parameter fitting on the image, precisely regressing the 3D Morphable Model (3DMM) coefficients. These coefficients are then rendered and cropped to produce the initial 3D adversarial pattern. (b) Subsequently, we simulate the realistic projection of the pattern in the physical space using the Light Reflection Function (LRF), and employ an camera ISP proxy model to emulate adversarial face images under various camera imaging systems. The adversarial pattern is dynamically updated through multiple iterations of optimization using an ensemble learning model. (c) Finally, we utilize the optimized adversarial face image for black-box attacks. If the attack fails, we dynamically adjust the weight distribution of the ensemble model through a reinforcement learning-based reward function and repeat step (b) to continually refine the attack strategy and enhance the success rate." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.458, + 0.483, + 0.518 + ], + "angle": 0, + "content": "artifacts often fails to circumvent liveness detection mechanisms. In this work, we propose a light-based attack that addresses these limitations by simultaneously compromising both face recognition and liveness detection systems." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.521, + 0.483, + 0.763 + ], + "angle": 0, + "content": "Light-Based Attack. Light has emerged as a promising adversarial medium for projecting attack patterns onto human faces [24]. Current light-based attacks against face recognition systems are limited to two primary approaches: Zhou et al. [31]'s infrared light projection method and Nguyen et al. [14]'s 2D RGB adversarial pattern projection. While these approaches represent significant advances, they fail to adequately account for light distortion and reflection on facial surfaces, resulting in suboptimal attack success rates and performance. We systematically re-examine the light-based attack pipeline, as illustrated in Fig. 2, and introduce novel light reflection and camera capture simulation modules. These innovations enable the generation of robust light-based adversarial patterns that maintain effectiveness throughout both projection and capture processes, ensuring high attack success rates in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Domain Transition. Since Sharif et al. [18] first demonstrated adversarial attacks in the physical world, the research community has increasingly focused on exploring the effectiveness of adversarial examples under real-world conditions [7, 21, 23]. This process involves two domain transformations. As shown in Fig. 2, the first domain transformation occurs during the attack deployment stage, where the adversarial pattern transitions from the digital space to the physical world. The second domain transfor" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.907, + 0.64 + ], + "angle": 0, + "content": "mation takes place during the camera capture stage, where the adversarial pattern transitions back from the physical world to the digital space. Existing methods have primarily addressed the former, such as non-printability score (NPS) [18] and D2P [8], which aim to mitigate the impact of the digital-to-physical transformation on attacks. To the best of our knowledge, no method has yet addressed the latter transformation, i.e., from physical to digital. We have designed a comprehensive attack pipeline that incorporates a light reflection function and a camera ISP proxy network to accurately simulate the real-world workflow, thereby enhancing the attack effectiveness in the physical world." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.652, + 0.651, + 0.67 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.676, + 0.719, + 0.691 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.698, + 0.907, + 0.835 + ], + "angle": 0, + "content": "Threat Model. Let \\(\\mathcal{X}\\) denote the space of all possible facial images. Given a black-box facial recognition system \\(f:\\mathcal{X}\\to \\mathbb{R}^d\\) that maps an input image to a \\(d\\)-dimensional embedding space, our goal is to generate physical adversarial patterns that can be projected onto an attacker's face to impersonate a target victim. Formally, for an attacker's face image \\(x^{a}\\in \\mathcal{X}\\) and a victim's face image \\(x^{v}\\in \\mathcal{X}\\), we aim to find an adversarial perturbation function \\(F(\\cdot)\\) that generates a physically realizable adversarial example \\(x^{adv}\\) such that:" + }, + { + "type": "equation", + "bbox": [ + 0.644, + 0.843, + 0.907, + 0.862 + ], + "angle": 0, + "content": "\\[\nx ^ {a d v} = F \\left(x ^ {a}, x ^ {v}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(F(\\cdot)\\) consists of a 3D mask \\(M\\) and a light-based perturbation pattern \\(\\tilde{x}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21250" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.205 + ], + "angle": 0, + "content": "Attack Objective. The attack is considered successful if the following conditions are satisfied: (1) Impersonation Success: The adversarial example should be verified as the victim: \\( \\text{Ver}(x^{adv}, x^v) = 1 \\) where \\( \\text{Ver}(x^1, x^2) = \\mathbb{I}\\left(\\frac{\\langle f(x^1), f(x^2)\\rangle}{|f(x^1)| \\cdot |f(x^2)|} > \\tau\\right) \\). (2) Physical Realizability: The adversarial perturbation must be physically realizable through light projection:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.211, + 0.483, + 0.23 + ], + "angle": 0, + "content": "\\[\nx ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.235, + 0.484, + 0.28 + ], + "angle": 0, + "content": "where \\( T_{l}(\\cdot) \\) represents the Light Reflection Function that models real-world lighting effects. The complete optimization can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.284, + 0.359, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\min _ {M, \\tilde {x}} L _ {F} \\left[ T _ {c} \\left(x ^ {a d v}\\right), x ^ {v} \\right]\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.312, + 0.482, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\text {s . t .} x ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M \\quad M \\in \\mathcal {M}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.343, + 0.484, + 0.418 + ], + "angle": 0, + "content": "where \\(L_{F}[\\cdot ,\\cdot ]\\) is the objective function measuring the dissimilarity between the adversarial example and victim, \\(T_{c}(\\cdot)\\) represents the camera capture simulation, \\(\\mathcal{M}\\) is the space of valid 3D masks obtained through 3D face reconstruction, \\(\\odot\\) denotes element-wise multiplication." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.419, + 0.484, + 0.509 + ], + "angle": 0, + "content": "This optimization problem is solved through a reinforcement learning framework [11], where the agent learns an optimal perturbation policy through interactions with an environment constructed from white-box face recognition model ensembles, ultimately generalizing to attack the black-box target model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.517, + 0.281, + 0.531 + ], + "angle": 0, + "content": "3.2. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.484, + 0.675 + ], + "angle": 0, + "content": "Given a victim's facial image \\( x^{v} \\), we first construct a 3D face model using a pre-trained 3D face reconstruction network. This network decomposes the facial attributes into multiple components, and then used them to reconstruct a complete 3D face model of the victim. To obtain the projection area for the adversarial pattern, we perform 3D cropping on the reconstructed face model to generate the initial 3D mask \\( M \\in \\mathcal{M} \\). This mask defines the spatial region where the light-based perturbation will be applied." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The core of our framework lies in the optimization stage, where we iteratively refine the adversarial pattern through a reinforcement learning approach. This stage involves several key components: Light Reflection Function \\( T_{l}(\\cdot) \\): We design a differentiable light reflection function that simulates how projected patterns interact with the attacker's face under various physical conditions. This function models the transformation of the initial perturbation \\( \\tilde{x} \\) when projected onto the 3D mask \\( M \\) and combines it with the attacker's face image \\( x^{a} \\) according to Eq. 2. Camera ISP Proxy Network \\( T_{c}(\\cdot) \\): To bridge the gap between digital and physical domains, we incorporate a Camera ISP (Image Signal Processing) proxy network that simulates real-world image capture effects. This network ensures that the generated patterns remain effective under real camera conditions. Agent" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "Models: We construct an environment using an ensemble of white-box face recognition models. The agent interacts with these models to learn an optimal perturbation strategy that can generalize to black-box scenarios. The learning process is guided by a reward signal derived from the cosine similarity scores between the adversarial example and the victim's embedding." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.906, + 0.38 + ], + "angle": 0, + "content": "In the final stage, we evaluate the effectiveness of our attack against the target black-box face recognition model. The attacker's face, augmented with the optimized adversarial pattern projected through the 3D mask, is presented to the target system. The success of the attack is measured by the verification result \\( \\text{Ver}(x^{adv}, x^v) \\). This stage validates whether our generated adversarial pattern can successfully fool the target system while maintaining physical realizability. The entire framework operates in an end-to-end manner, with loss gradients propagating backward through the optimization stage to continuously refine the adversarial pattern." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.391, + 0.724, + 0.405 + ], + "angle": 0, + "content": "3.3. 3D Mask Initialization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.907, + 0.732 + ], + "angle": 0, + "content": "Face recognition systems capture the 3D structure of facial features, such as surface protrusions and recesses. However, most existing attack methods [10, 18, 19, 25] rely on 2D perturbation simulations, which struggle to effectively map onto 3D facial features in real-world applications. This dimensional mismatch reduces the effectiveness of physical-space attacks. To address this limitation, we introduce a high-dimensional, geometric parameter-driven 3D facial projection construction. Starting from facial images, we employ a convolutional neural network (CNN) regression model to extract 3D Morphable Model (3DMM) coefficients that encode individual-specific facial geometry. These coefficients then guide a facial mesh reconstruction module, applying 3D deformation and topological mapping to accurately generate a 3D mesh model aligned with the individual's facial structure. Spatial coordinate transformations are then applied to map the mesh vertices from object coordinates to camera coordinates, and an intrinsic camera matrix enables perspective projection, which normalizes depth information into 2D pixel coordinates for precise 3D-to-2D mapping on the image plane." + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.742, + 0.907, + 0.77 + ], + "angle": 0, + "content": "\\[\nx = \\mathcal {T} \\left(K \\cdot \\mathcal {R} \\left(B \\cdot [ \\Theta_ {i d}, \\Theta_ {e x p}, \\Theta_ {t e x}, \\dots ] ^ {T} + \\overline {{S}}\\right)\\right). (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In this formulation, \\(\\Theta\\) represents various 3DMM coefficients. \\(B\\) is the matrix containing the basis shape vectors, which is used to map the coefficients to the corresponding shape space, while \\(\\overline{S}\\) serves as the mean facial shape. \\(\\mathcal{R}\\) is the spatial transformation function mapping 3D mesh vertices from object to camera coordinates, while the intrinsic camera matrix \\(K\\) enables perspective projection, and \\(\\mathcal{T}\\) normalizes depth information to 2D pixel coordinates." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21251" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.152 + ], + "angle": 0, + "content": "Through this process, we effectively simulate digital-space attack patterns in the physical domain by projecting refined 2D adversarial patterns onto 3D faces, substantially enhancing attack success rates." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.16, + 0.325, + 0.176 + ], + "angle": 0, + "content": "3.4. Light Reflection Function" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.181, + 0.484, + 0.348 + ], + "angle": 0, + "content": "The efficacy of light-based adversarial attacks hinges on the faithful conversion of digital adversarial patterns into physical light projections. Two primary factors influence this process: (1) the alteration of received light wavelengths due to specular reflection, diffuse reflection, and absorption of adversarial light on facial surfaces, and (2) the interaction between projected light and ambient illumination, resulting in the reception of reflected ambient light. These phenomena modulate the pixel values of the digital pattern. Consequently, formulating these transformations is crucial for mitigating their impacts and preserving attack effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.348, + 0.483, + 0.395 + ], + "angle": 0, + "content": "We propose a Light Reflection Function (LRF) that models the process of pattern projection, reflection on skin, and camera capture, formulated as the transformation \\( T_{l}(\\cdot) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.402, + 0.482, + 0.42 + ], + "angle": 0, + "content": "\\[\nx ^ {\\text {m a s k}} = T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.428, + 0.484, + 0.548 + ], + "angle": 0, + "content": "This process primarily involves modeling the following physical phenomena: the projector emits light patterns corresponding to the RGB values of each pixel in the image. Both projected and ambient light strike the human face and, after absorption and reflection, produce new light patterns. The camera then captures these patterns and converts them into RGB format. This process is principally determined by three factors (\\(\\lambda\\) denotes the wavelength of light):" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.549, + 0.458, + 0.564 + ], + "angle": 0, + "content": "- \\( S(\\lambda) \\): the spectral power distribution of the projector." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.564, + 0.376, + 0.578 + ], + "angle": 0, + "content": "- \\(\\rho (\\lambda)\\): the spectral reflectance of the skin." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.579, + 0.481, + 0.623 + ], + "angle": 0, + "content": "- \\(\\sigma(\\lambda)\\): the sensitivity of the camera's photodetectors, with \\(\\sigma_x(\\lambda)\\), \\(\\sigma_y(\\lambda)\\), and \\(\\sigma_z(\\lambda)\\) representing the impact on red, green, and blue components respectively." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.549, + 0.481, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.625, + 0.484, + 0.73 + ], + "angle": 0, + "content": "To simulate and quantify human visual response to colors, we utilize the CIE XYZ color space model, integrating the color matching functions to calculate an image's coordinates within this space: \\( X = \\int S(\\lambda) \\rho(\\lambda) \\sigma_x(\\lambda) d\\lambda, Y = \\int S(\\lambda) \\rho(\\lambda) \\sigma_y(\\lambda) d\\lambda, Z = \\int S(\\lambda) \\rho(\\lambda) \\sigma_z(\\lambda) d\\lambda \\). The interaction between ambient and projected light is considered through linear superposition of their spectral intensities:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.739, + 0.483, + 0.757 + ], + "angle": 0, + "content": "\\[\nS (\\lambda) = S _ {\\text {n a t u r a l}} (\\lambda) + S _ {\\text {p r o j e c t o r}} (\\lambda). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Finally, XYZ coordinates are converted to RGB coordinates. Using the PAL standard RGB system as an example, the transformation is:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.814, + 0.483, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{l} R \\\\ G \\\\ B \\end{array} \\right] = \\left[ \\begin{array}{c c c} X _ {r} & Y _ {r} & Z _ {r} \\\\ X _ {g} & Y _ {g} & Z _ {g} \\\\ X _ {b} & Y _ {b} & Z _ {b} \\end{array} \\right] \\left[ \\begin{array}{l} X \\\\ Y \\\\ Z \\end{array} \\right]. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "\\(S(\\lambda)\\), \\(\\rho (\\lambda)\\), \\(\\sigma (\\lambda)\\), and PAL color conversion matrix \\((X_{r}\\) etc.) can all be obtained from technical documentation and" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.891, + 0.172 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.178, + 0.905, + 0.218 + ], + "angle": 0, + "content": "Figure 4. Light Reflection Function. (c) is obtained by applying our light reflection function to (b), while (d), obtained by projecting (a) in the real world, demonstrates consistency with (c)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.231, + 0.905, + 0.32 + ], + "angle": 0, + "content": "official standards. As shown in Fig. 4, our LRF enables the transformed adversarial 3D mask to closely align with its real-world counterpart. Integrating the LRF within our optimization pipeline ensures that the adversarial 3D mask, when projected into the physical world, maintains its attack effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.333, + 0.769, + 0.349 + ], + "angle": 0, + "content": "3.5. Camera Capture Simulation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.356, + 0.907, + 0.568 + ], + "angle": 0, + "content": "The camera's internal Image Signal Processing (ISP) pipeline plays a crucial role in transforming physical scenes into digital RGB images. Variations in ISP configurations can lead to divergent visual characteristics of the same adversarial texture across devices, potentially affecting attack performance. Therefore, we introduce ISP simulation \\( T_{c}(\\cdot) \\) to model the camera capturing process. To address the non-differentiable nature of traditional ISP processes, we build a differentiable camera ISP proxy network that enables gradient propagation during optimization. The camera ISP proxy network simulates various ISP processes through conditional inputs, focusing on representative parameters from color and tone correction modules, as well as the denoising module, which significantly impact image quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.906, + 0.688 + ], + "angle": 0, + "content": "Our camera ISP proxy network is based on the U-Net architecture [16], comprising \\(3 \\times 3\\) convolutions and \\(2 \\times 2\\) max pooling operations in its encoder and decoder. The feature channels expand progressively through \\{32, 64, 128, 256, 512\\}. This structure enables the ISP proxy network to maintain differentiability while simulating diverse camera ISP parameter configurations, thus adapting to various hardware environments." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We normalize ISP parameters (e.g., brightness, contrast, gamma correction) to [0,1] and concatenate them with feature maps, enabling the ISP proxy network to dynamically adjust image tone, contrast, color balance, and denoising characteristics to flexibly simulate diverse device imaging profiles. To train our camera ISP proxy network, we utilize an undifferentiable camera ISP simulator [15] along with the COCO dataset [12], generating a total of 2,270 data pairs. During training, we employ a composite loss function—including pixel-level MSE loss, perceptual loss, and regularization loss—to ensure high image fidelity and sensitivity to conditional ISP parameters, while maintaining full differentiability for gradient optimization. Our framework leverages the ISP network simulating various lighting ef" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21252" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.887, + 0.203 + ], + "angle": 0, + "content": "
SourceLFW datasetCelebA-HQ dataset
ArcFaceMoblieNetResNetIRAPIArcFaceMoblieNetResNetIRAPI
ArcFace [1]-40.40%25.37%39.22%12.37%-60.80%64.32%62.12%16.49%
MobileNet [4]13.28%-46.98%24.71%12.05%49.50%-66.33%40.80%12.86%
ResNet [3]25.37%54.31%-33.14%18.33%63.49%75.50%-56.35%12.35%
IR [3]22.32%41.44%42.37%-17.86%78.79%78.39%58.79%-14.29%
Ensemble59.09%72.91%75.28%53.52%38.78%90.50%88.29%88.37%88.50%32.84%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.207, + 0.905, + 0.248 + ], + "angle": 0, + "content": "Table 1. Evaluation of black-box impersonation attack. We report the attack success rates (ASR) on ArcFace, MobileNet, ResNet, IR, and a commercial API. Each row represents results using a different source model for the attack. In the ensemble setting, the target model corresponding to each column is excluded from the ensemble used to generate the attack." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.262, + 0.887, + 0.43 + ], + "angle": 0, + "content": "
DatasetTypeMethodArcFaceFaceNetMobileNetResNetCosFaceAPIAverage
LFWTransfer-basedTAP [27] \\( _{CVPR'21} \\)53.50%46.00%--50.00%10.00%39.89%
AT3D [28] \\( _{CVPR'23} \\)86.25%-91.50%86.50%63.00%45.25%74.50%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-51.11%--48.06%-49.59%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours78.07%52.17%79.49%82.98%78.17%41.43%68.72%
CelebA-HQTransfer-basedTAP [27] \\( _{CVPR'21} \\)65.75%52.50%--58.25%20.00%49.13%
AT3D [28] \\( _{CVPR'23} \\)92.50%-96.25%93.75%87.50%50.25%84.05%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-48.96%--47.73%-48.35%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours95.15%84.47%98.13%97.20%93.20%44.03%85.36%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.434, + 0.905, + 0.477 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with existing methods. All methods are evaluated under a black-box setting, where TAP [27] and AT3D [28] are transfer-based attacks, while AdvSticker [25], SOPP [26], and ProjAttacker are query-based attacks. The highest and second-highest Attack Success Rates (ASRs) across both datasets are highlighted in red and blue, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.503, + 0.483, + 0.534 + ], + "angle": 0, + "content": "fects in the physical world to enhance the robustness of adversarial patterns and improve attack efficacy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.548, + 0.224, + 0.563 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.572, + 0.284, + 0.589 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.594, + 0.483, + 0.835 + ], + "angle": 0, + "content": "Targeted Models. We selected seven face recognition models as our target models, including six representative open-source models (ArcFace [1], MobileNet [4], ResNet [3], FaceNet [17], CosFace [22], IR [3]) and a commercial face recognition API*. For attacking the API, we employed other open-source models as an ensemble of surrogate models. When performing an ensemble attack on one of the models, the remaining models served as surrogate models. In our experiments, we evaluate the attack effectiveness by calculating the cosine similarity of the vectors obtained from the input image pairs. Each model adheres to its respective threshold: if the similarity between two images exceeds the threshold, they are considered the same identity; otherwise, they are considered different identities. Notably, each model is well-trained, achieving an accuracy exceeding \\(99\\%\\) on the LFW dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.836, + 0.483, + 0.866 + ], + "angle": 0, + "content": "Datasets. We conducted experiments in the digital domain on two extensively employed benchmark datasets: the La-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.905, + 0.623 + ], + "angle": 0, + "content": "beled Faces in the Wild (LFW) [6] and the CelebFaces Attributes High Quality (CelebA-HQ) [9]. For evasion attacks, we randomly selected several pairs of images with the same identity from the dataset, aiming to push the attacker's features away from their true identity. For impersonation attacks, we randomly chose an attacker from the dataset and paired them with several randomly selected victims, creating multiple pairs of images with different identities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.624, + 0.905, + 0.685 + ], + "angle": 0, + "content": "Comparison methods. We compare our proposed ProjAttacker with the following four methods: TAP [27], AdvSticker [25], SOPP [26], and AT3D [28]. All methods are physically realizable." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.686, + 0.905, + 0.806 + ], + "angle": 0, + "content": "Implementation details. All experiments were conducted on a Linux server equipped with two NVIDIA GeForce RTX 3090 GPUs, with all code and algorithms implemented in PyTorch. We set the number of iterations per round to 300 and the learning rate to 0.45. Within the overall framework, the reward step size is set to 0.1. The total number of queries is 25, and if no result is obtained within 25 queries, the attempt is deemed unsuccessful." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.818, + 0.766, + 0.833 + ], + "angle": 0, + "content": "4.2. Attacks in the Digital World" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Black-box Attack. To assess the effectiveness of the attacks, we employ the Attack Success Rate (ASR), a metric that measures the efficacy of attack methodologies by indicating the proportion of successful attacks relative to the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.875, + 0.483, + 0.901 + ], + "angle": 0, + "content": "\\*https://intl.cloud.tencent.com/product/ facerecognition" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21253" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.09, + 0.865, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.422, + 0.908, + 0.477 + ], + "angle": 0, + "content": "Figure 5. Attack results of our ProjAttacker in both digital and physical domains. By projecting diverse adversarial patterns onto facial regions, an attacker can induce the face recognition model (CosFace [22]) to misidentify the subject as various victims. Our method exhibits superior flexibility and cost-effectiveness compared to approaches based on wearable material artifacts. Green indicates successful attacks, while red denotes unsuccessful attacks." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.492, + 0.483, + 0.537 + ], + "angle": 0, + "content": "total samples. Tab. 1 displays the quantitative results of impersonation attacks under black-box conditions against five different target models." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.539, + 0.483, + 0.749 + ], + "angle": 0, + "content": "As shown in Tab. 1, we can observe: (1) The proposed model ensemble method demonstrates significant efficacy against impersonation attacks on both the LFW and CelebA-HQ datasets. Notably, the highest attack success rate achieved on the LFW dataset is \\(75.28\\%\\), while on the CelebA-HQ dataset, it reaches \\(90.50\\%\\). (2) The attack success rates on the CelebA-HQ dataset are generally higher than those on the LFW dataset. This can be attributed to the higher quality and resolution of facial images in the CelebA-HQ dataset, which facilitates more effective feature extraction by the models. (3) The ensemble method consistently outperforms models trained individually, indicating that our approach can adaptively adjust model weights to achieve optimal performance." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Comparisons with SOTA Methods. We compare ProjAttacker attack with five existing physically realizable black-box attack methods, as shown in Tab. 2. We conducted experiments on a set of images from the CelebA-HQ dataset. Each target model in the columns is excluded from our ensemble model, strictly adhering to the principles of black-box attacks. Our method outperforms the two baseline query-based approaches, AdvSticker and SOPP, across both datasets. Regarding transfer-based methods, our approach surpasses TAP on the LFW dataset but falls short of" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.489, + 0.903, + 0.574 + ], + "angle": 0, + "content": "
3DLRFISPArcFaceMobileNetResNetAPI
✓✓56%54%52%34%
✓✓38%32%32%12%
✓✓44%42%48%22%
✓✓✓68%60%62%38%
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.516, + 0.575, + 0.833, + 0.587 + ], + "angle": 0, + "content": "- \"3D\" represents the 3D mask form, as opposed to the 2D mask." + }, + { + "type": "table_footnote", + "bbox": [ + 0.521, + 0.587, + 0.807, + 0.597 + ], + "angle": 0, + "content": "- \"LRF\" means the light reflection function in our pipeline." + }, + { + "type": "table_footnote", + "bbox": [ + 0.52, + 0.597, + 0.816, + 0.609 + ], + "angle": 0, + "content": "- \"ISP\" means the camera ISP proxy network in our pipeline." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.575, + 0.833, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.61, + 0.906, + 0.638 + ], + "angle": 0, + "content": "Table 3. Ablation study in the physical world. We report the ASR of our ProjAttacker attack." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.668, + 0.907, + 0.729 + ], + "angle": 0, + "content": "AT3D. However, on the CelebA-HQ dataset, our method outperforms both TAP and AT3D. These results demonstrate the excellent attack performance of our approach in black-box settings." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.741, + 0.779, + 0.758 + ], + "angle": 0, + "content": "4.3. Attacks in the Physical World" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.765, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Qualitative Analysis. As shown in Fig. 5, we present an attacker, six victims, and their corresponding digital and physical space attacks. Without the light reflection function, the optimized adversarial patterns exhibit diverse colors with high saturation, impeding physical space reproduction. Incorporating the light reflection function facilitates the transfer of digital space adversarial patterns to the physical domain. Physical space attacks demonstrate our method's efficacy in misleading CosFace to misiden" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21254" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.48, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.191, + 0.483, + 0.22 + ], + "angle": 0, + "content": "Figure 6. Comparison with existing methods. We compare the hiPAA [24] of three physical adversarial attack methods." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.235, + 0.483, + 0.31 + ], + "angle": 0, + "content": "tify the attacker as different victims with high confidence. Notably, transitioning between victims merely requires altering the projected pattern, offering significant operational convenience. These results highlight our method's flexibility in executing effective attacks in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.311, + 0.484, + 0.491 + ], + "angle": 0, + "content": "Ablation Study. To quantify the contribution of each module within our proposed framework to the success rate of physical space attacks, we conducted ablation experiments. We systematically removed the 3D, RLF, and ISP modules from a set of attacker-victim image pairs, generating four distinct adversarial patterns for physical testing, including those from the complete framework. The experiments encompassed 50 attacker-victim pairs, with statistical results presented in Tab. 3. We observe that the removal of any single module results in a decrease in Attack Success Rate (ASR). These findings validate the rationale and necessity of each module within our method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.484, + 0.78 + ], + "angle": 0, + "content": "Evaluation using hiPAA Metrics. To comprehensively evaluate the performance of physical adversarial attacks, Wei et al. [24] proposed the hiPAA metric, which includes six dimensions: Effectiveness, Stealthiness, Robustness, Practicability, Aesthetics, and Economics. We assess and compare the hiPAA scores of various methods, as illustrated in Fig. 6. Note that Stealthiness, Practicability, and Aesthetics are evaluated through a user study; refer to the supplementary material for more details of our evaluation. We observe that our ProjAttacker attack outperforms TAP in robustness and surpasses AT3D in effectiveness. Additionally, our method significantly outperforms in the Practicability dimension, as it does not require manually crafted 3D-printed masks or patches. For an attacker to mislead the facial recognition system into identifying them as different victims, only the adversarial pattern needs to be switched. This not only reduces costs but also eliminates the need for complex manufacturing processes, enhancing the practicality of real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.271, + 0.803 + ], + "angle": 0, + "content": "4.4. Liveness Detection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Liveness detection technology primarily encompasses four methods: (1) Transform: Analysis of image Fourier transforms or Local Binary Patterns to discern whether a presented face is genuine or merely a static image. (2) Depth: Utilization of depth sensors or stereo cameras to assess the three-dimensional structure of a face, thereby verifying its" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.905, + 0.187 + ], + "angle": 0, + "content": "
MethodTransformDepthMotionMultiBio
TAP [27] CVPR'21✓XXX
AdvSticker [25] TPAMI'22✓✓✓X
SOPP [26] TPAMI'22✓✓✓X
AT3D [28] CVPR'23✓✓XX
ProjAttacker Ours✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.191, + 0.905, + 0.233 + ], + "angle": 0, + "content": "Table 4. Liveness detection analysis. Our light-based attack outperforms existing methods by successfully deceiving all liveness detection strategies." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.246, + 0.905, + 0.29 + ], + "angle": 0, + "content": "
CTyunBaiduTencentAliyun
Physical Evaluation55/5555/5548/5152/55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.294, + 0.905, + 0.322 + ], + "angle": 0, + "content": "Table 5. Bypass rate. The number of successful bypasses achieved by our method across four commercial liveness detection APIs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.905, + 0.44 + ], + "angle": 0, + "content": "authenticity. (3) Motion: Examination and tracking of eye movements, lip motions, and blink frequency to validate the presence of a live subject. (4) MultiBio: Integration of facial vascular flow detection with other biometric identification technologies, such as iris scanning, to provide a multi-tiered security validation approach." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.44, + 0.906, + 0.591 + ], + "angle": 0, + "content": "Tab. 4 shows that existing physical attack modalities typically require a tangible medium and often rely on partially obstructing the facial features to create adversarial perturbations. In contrast, our method utilizes light as the medium and adopts a non-intrusive attack. This approach avoids obscuring facial biometric features, thus demonstrating higher effectiveness against various liveness detection technologies. Tab. 5 shows that our method achieved successful bypasses across all four commercial liveness detection APIs, with a \\(100\\%\\) success rate on CTyun and Baidu in particular." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.634, + 0.62 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.906, + 0.765 + ], + "angle": 0, + "content": "We introduced ProjAttacker, a novel adversarial light attack that effectively compromises both face recognition systems and liveness detection models. Extensive experiments in both digital and physical space demonstrate that ProjAttacker outperforms existing methods, highlighting the vulnerability of current face recognition systems to sophisticated physical attacks. Our findings underscore the pressing need for more robust defense mechanisms to secure biometric systems against potential threats." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Ethics Statement. Our research investigates the vulnerabilities of face recognition systems through physical adversarial attacks. Aware of the dual-use potential, we conducted all experiments under strict ethical guidelines, ensuring no compromise of personal data or real-world systems. Our goal is to contribute to the development of more secure face recognition systems. We urge the community to consider both defensive and offensive aspects, promoting responsible application." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21255" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.184 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by Hubei Key R&D Project (2022BAA033) and National Natural Science Foundation of China (62171325, 62402365). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.194, + 0.188, + 0.21 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.219, + 0.482, + 0.288 + ], + "angle": 0, + "content": "[1] Jiankang Deng, Jia Guo, Jing Yang, Niannan Xue, Irene Kotsia, and Stefanos Zafeiriou. 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However, these attacks often struggle to impersonate multiple targets and frequently fail to bypass liveness detection. For example, attacks using human-skin masks [28] are challenging to fabricate, inconvenient to swap between users, and often fail liveness detection due to facial occlusions. A projector, however, can generate content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Thus, we propose a novel physical adversarial attack using a projector and explore the superposition of projected and natural light to create adversarial facial images. This approach eliminates the need for physical artifacts on the face, effectively overcoming these limitations. Specifically, our proposed ProjAttacker generates adversarial 3D textures that are projected onto human faces. To ensure physical realizability, we introduce a light reflection function that models complex optical interactions between projected light and human skin, accounting for reflection and diffraction effects. Furthermore, we incorporate camera Image Signal Processing (ISP) simulation to maintain the robustness of adversarial perturbations across real-world diverse imaging conditions. Comprehensive evaluations conducted in both digital and physical scenarios validate the effectiveness of our method. + +# 1. Introduction + +Face recognition has become a widely adopted technology for authentication and access control [2, 13]. De + +![](images/0d93a70c5c0150b7583935591cbb284f88fc483f2969b97f62d659129b007569.jpg) +(a) Existing Attack Methods + +![](images/aec9f27e02e800285acb22e138763c00b4736c1460f370e78d1ecd8b7165aff5.jpg) +(b) Our Attack Method +Figure 1. Comparison of our ProjAttacker with existing attack methods. While existing methods [10, 18, 28] can successfully attack face recognition, they are difficult to fabricate, inconvenient to swap between targets, and unable to bypass liveness detection due to facial occlusions. In contrast, our ProjAttacker projects light-based adversarial textures onto the face, enabling a non-intrusive attack via projector that overcomes these limitations, allowing real-time, configurable face swaps that simultaneously deceive both liveness detection and recognition models. + +spite its prevalence, significant security vulnerabilities remain. Recent studies have shown that imperceptible, carefully crafted perturbations can deceive deep neural network based face recognition models, leading to incorrect predictions [5, 20, 25, 30]. These attacks remain effective in the physical world [24], exposing substantial security risks. Developing physical adversarial attack methods to identify weaknesses and assess the robustness of these systems is essential for secure real-world deployment. + +Existing physical adversarial attacks on face recognition systems largely rely on physical artifacts like textured + +![](images/0fe86138bcd980b73eb144213639643192649123b5a68bdaa36b674d176932dc.jpg) +Figure 2. Workflow of our ProjAttacker. ProjAttacker works in four steps: (1) generating a light-based adversarial 3D mask; (2) deploying the attack in the real world using projection devices; (3) capturing the attacker's image with a camera; and (4) executing the attack during model inference. This workflow mirrors our attack pipeline in the digital domain. + +![](images/f92a9c19fe6ef15fb6fd241099f63b6fd1bb2bef986cbd56fac3fd1a7df1654c.jpg) + +![](images/407506bbfededf98af80ff0161bdf545de772ffca56d82f249c2fe0188118941.jpg) + +![](images/45b09106044e3a81523ddc7a8e0fb1126e7a71174f93d46f163536b3feba57a2.jpg) + +eyeglasses [18, 19], human-skin masks [28], stickers [25], forehead-covering hats [10], and makeup [29]. While these approaches can successfully fool recognition models, they face notable limitations: 1) they are user-specific, difficult to adapt for multiple individuals, and often require complex fabrication processes (e.g., 2D or 3D printing) and high-quality materials to accurately replicate designed adversarial textures, making them impractical for multi-user scenarios; and 2) their occlusive nature makes it difficult to bypass liveness detection, reducing their attack effectiveness in real-world settings. + +A projector can produce content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Leveraging this advantage, we introduce ProjAttacker, a novel and configurable physical adversarial attack for face recognition. ProjAttacker explores the superposition of projected and natural light to create adversarial facial images. This approach effectively addresses both aforementioned limitations, simultaneously enabling multi-target impersonation and circumvention of liveness detection. Fig. 1 presents a comparison between our method and existing state-of-the-art (SOTA) approaches. + +To ensure real-world attack effectiveness, we analyze the workflow of ProjAttacker, which comprises four steps (see Fig. 2). For the adversarial 3D mask generated in step (1) to remain effective through step (4), it must successfully traverse two critical domain transitions: the projector-mediated transition from digital domain to physical space, and the camera-mediated transition from physical space back to digital images. Maintaining resilience across these domain transitions is crucial for attack success. Therefore, we first incorporate a light reflection function into the adversarial 3D mask generation pipeline, ensuring robustness against projection inconsistencies. To mitigate camera-induced color shifts in real-world scenarios, we develop a differentiable proxy network that simulates camera Image Signal Processing (ISP) modules. Specifically, this proxy network transforms the camera's internal denoising and color correction units into differentiable modules, and through stochastic sampling of conditional input parameters during optimization, generates adversarial patterns + +that remain effective under various camera capture conditions. Extensive experiments in both digital and physical scenarios demonstrate that our proposed method effectively compromises mainstream models and APIs. The main contributions are summarized as follows: + +- Real-world configurable face swap. We present ProjAttacker, the first light-based attack that leverages projected 3D masks with adversarial patterns to simultaneously deceive face recognition models and liveness detection systems, enabling efficient and cost-effective face-swapping attacks. +- Physically realizable attack pipeline. We bridge the digital-physical gap through: (i) a light reflection simulation function that ensures robustness against projection inconsistencies, and (ii) a differentiable camera ISP proxy network that accurately models the image capture process, guaranteeing the real-world effectiveness of the adversarial 3D mask. +- Exceptional attack effectiveness. Our ProjAttacker achieves superior performance in both digital and physical domains. Comprehensive experimental results validate our approach and reveal significant security vulnerabilities in contemporary face recognition systems. + +# 2. Related Works + +Physical Adversarial Attack for Face Recognition. Face recognition systems have been extensively deployed in safety-critical applications, making the study of physical-world adversarial attacks against such systems increasingly crucial. Prior works have predominantly explored the integration of adversarial perturbations with physical accessories, including hats [10], glasses [18, 19, 27], and stickers [25, 26]. Additionally, alternative approaches such as Adv-Makeup [29] demonstrate successful attacks through subtle eye-area cosmetic modifications, while AT3D [28] employs 3D-printed masks with adversarial textures. However, these methodologies either suffer from diminished effectiveness when transitioning from digital to physical domains or require complex, time-intensive preparation processes. Furthermore, their reliance on material-based facial + +![](images/a064d28d17cc98cd79087b2bc212e418bd8acd9fbc0d65e02ab6bd8650e87831.jpg) +Figure 3. Overview of ProjAttacker. (a) Initially, we employ CNN to extract features and perform parameter fitting on the image, precisely regressing the 3D Morphable Model (3DMM) coefficients. These coefficients are then rendered and cropped to produce the initial 3D adversarial pattern. (b) Subsequently, we simulate the realistic projection of the pattern in the physical space using the Light Reflection Function (LRF), and employ an camera ISP proxy model to emulate adversarial face images under various camera imaging systems. The adversarial pattern is dynamically updated through multiple iterations of optimization using an ensemble learning model. (c) Finally, we utilize the optimized adversarial face image for black-box attacks. If the attack fails, we dynamically adjust the weight distribution of the ensemble model through a reinforcement learning-based reward function and repeat step (b) to continually refine the attack strategy and enhance the success rate. + +artifacts often fails to circumvent liveness detection mechanisms. In this work, we propose a light-based attack that addresses these limitations by simultaneously compromising both face recognition and liveness detection systems. + +Light-Based Attack. Light has emerged as a promising adversarial medium for projecting attack patterns onto human faces [24]. Current light-based attacks against face recognition systems are limited to two primary approaches: Zhou et al. [31]'s infrared light projection method and Nguyen et al. [14]'s 2D RGB adversarial pattern projection. While these approaches represent significant advances, they fail to adequately account for light distortion and reflection on facial surfaces, resulting in suboptimal attack success rates and performance. We systematically re-examine the light-based attack pipeline, as illustrated in Fig. 2, and introduce novel light reflection and camera capture simulation modules. These innovations enable the generation of robust light-based adversarial patterns that maintain effectiveness throughout both projection and capture processes, ensuring high attack success rates in real-world scenarios. + +Domain Transition. Since Sharif et al. [18] first demonstrated adversarial attacks in the physical world, the research community has increasingly focused on exploring the effectiveness of adversarial examples under real-world conditions [7, 21, 23]. This process involves two domain transformations. As shown in Fig. 2, the first domain transformation occurs during the attack deployment stage, where the adversarial pattern transitions from the digital space to the physical world. The second domain transfor + +mation takes place during the camera capture stage, where the adversarial pattern transitions back from the physical world to the digital space. Existing methods have primarily addressed the former, such as non-printability score (NPS) [18] and D2P [8], which aim to mitigate the impact of the digital-to-physical transformation on attacks. To the best of our knowledge, no method has yet addressed the latter transformation, i.e., from physical to digital. We have designed a comprehensive attack pipeline that incorporates a light reflection function and a camera ISP proxy network to accurately simulate the real-world workflow, thereby enhancing the attack effectiveness in the physical world. + +# 3. Methodology + +# 3.1. Problem Formulation + +Threat Model. Let $\mathcal{X}$ denote the space of all possible facial images. Given a black-box facial recognition system $f:\mathcal{X}\to \mathbb{R}^d$ that maps an input image to a $d$ -dimensional embedding space, our goal is to generate physical adversarial patterns that can be projected onto an attacker's face to impersonate a target victim. Formally, for an attacker's face image $x^{a}\in \mathcal{X}$ and a victim's face image $x^{v}\in \mathcal{X}$ , we aim to find an adversarial perturbation function $F(\cdot)$ that generates a physically realizable adversarial example $x^{adv}$ such that: + +$$ +x ^ {a d v} = F \left(x ^ {a}, x ^ {v}\right), \tag {1} +$$ + +where $F(\cdot)$ consists of a 3D mask $M$ and a light-based perturbation pattern $\tilde{x}$ . + +Attack Objective. The attack is considered successful if the following conditions are satisfied: (1) Impersonation Success: The adversarial example should be verified as the victim: $\text{Ver}(x^{adv}, x^v) = 1$ where $\text{Ver}(x^1, x^2) = \mathbb{I}\left(\frac{\langle f(x^1), f(x^2)\rangle}{|f(x^1)| \cdot |f(x^2)|} > \tau\right)$ . (2) Physical Realizability: The adversarial perturbation must be physically realizable through light projection: + +$$ +x ^ {a d v} = x ^ {a} \odot (1 - M) + T _ {l} \left(x ^ {a} + \tilde {x}\right) \odot M, \tag {2} +$$ + +where $T_{l}(\cdot)$ represents the Light Reflection Function that models real-world lighting effects. The complete optimization can be formulated as: + +$$ +\min _ {M, \tilde {x}} L _ {F} \left[ T _ {c} \left(x ^ {a d v}\right), x ^ {v} \right] +$$ + +$$ +\text {s . t .} x ^ {a d v} = x ^ {a} \odot (1 - M) + T _ {l} \left(x ^ {a} + \tilde {x}\right) \odot M \quad M \in \mathcal {M}, \tag {3} +$$ + +where $L_{F}[\cdot ,\cdot ]$ is the objective function measuring the dissimilarity between the adversarial example and victim, $T_{c}(\cdot)$ represents the camera capture simulation, $\mathcal{M}$ is the space of valid 3D masks obtained through 3D face reconstruction, $\odot$ denotes element-wise multiplication. + +This optimization problem is solved through a reinforcement learning framework [11], where the agent learns an optimal perturbation policy through interactions with an environment constructed from white-box face recognition model ensembles, ultimately generalizing to attack the black-box target model. + +# 3.2. Overall Framework + +Given a victim's facial image $x^{v}$ , we first construct a 3D face model using a pre-trained 3D face reconstruction network. This network decomposes the facial attributes into multiple components, and then used them to reconstruct a complete 3D face model of the victim. To obtain the projection area for the adversarial pattern, we perform 3D cropping on the reconstructed face model to generate the initial 3D mask $M \in \mathcal{M}$ . This mask defines the spatial region where the light-based perturbation will be applied. + +The core of our framework lies in the optimization stage, where we iteratively refine the adversarial pattern through a reinforcement learning approach. This stage involves several key components: Light Reflection Function $T_{l}(\cdot)$ : We design a differentiable light reflection function that simulates how projected patterns interact with the attacker's face under various physical conditions. This function models the transformation of the initial perturbation $\tilde{x}$ when projected onto the 3D mask $M$ and combines it with the attacker's face image $x^{a}$ according to Eq. 2. Camera ISP Proxy Network $T_{c}(\cdot)$ : To bridge the gap between digital and physical domains, we incorporate a Camera ISP (Image Signal Processing) proxy network that simulates real-world image capture effects. This network ensures that the generated patterns remain effective under real camera conditions. Agent + +Models: We construct an environment using an ensemble of white-box face recognition models. The agent interacts with these models to learn an optimal perturbation strategy that can generalize to black-box scenarios. The learning process is guided by a reward signal derived from the cosine similarity scores between the adversarial example and the victim's embedding. + +In the final stage, we evaluate the effectiveness of our attack against the target black-box face recognition model. The attacker's face, augmented with the optimized adversarial pattern projected through the 3D mask, is presented to the target system. The success of the attack is measured by the verification result $\text{Ver}(x^{adv}, x^v)$ . This stage validates whether our generated adversarial pattern can successfully fool the target system while maintaining physical realizability. The entire framework operates in an end-to-end manner, with loss gradients propagating backward through the optimization stage to continuously refine the adversarial pattern. + +# 3.3. 3D Mask Initialization + +Face recognition systems capture the 3D structure of facial features, such as surface protrusions and recesses. However, most existing attack methods [10, 18, 19, 25] rely on 2D perturbation simulations, which struggle to effectively map onto 3D facial features in real-world applications. This dimensional mismatch reduces the effectiveness of physical-space attacks. To address this limitation, we introduce a high-dimensional, geometric parameter-driven 3D facial projection construction. Starting from facial images, we employ a convolutional neural network (CNN) regression model to extract 3D Morphable Model (3DMM) coefficients that encode individual-specific facial geometry. These coefficients then guide a facial mesh reconstruction module, applying 3D deformation and topological mapping to accurately generate a 3D mesh model aligned with the individual's facial structure. Spatial coordinate transformations are then applied to map the mesh vertices from object coordinates to camera coordinates, and an intrinsic camera matrix enables perspective projection, which normalizes depth information into 2D pixel coordinates for precise 3D-to-2D mapping on the image plane. + +$$ +x = \mathcal {T} \left(K \cdot \mathcal {R} \left(B \cdot [ \Theta_ {i d}, \Theta_ {e x p}, \Theta_ {t e x}, \dots ] ^ {T} + \overline {{S}}\right)\right). (4) +$$ + +In this formulation, $\Theta$ represents various 3DMM coefficients. $B$ is the matrix containing the basis shape vectors, which is used to map the coefficients to the corresponding shape space, while $\overline{S}$ serves as the mean facial shape. $\mathcal{R}$ is the spatial transformation function mapping 3D mesh vertices from object to camera coordinates, while the intrinsic camera matrix $K$ enables perspective projection, and $\mathcal{T}$ normalizes depth information to 2D pixel coordinates. + +Through this process, we effectively simulate digital-space attack patterns in the physical domain by projecting refined 2D adversarial patterns onto 3D faces, substantially enhancing attack success rates. + +# 3.4. Light Reflection Function + +The efficacy of light-based adversarial attacks hinges on the faithful conversion of digital adversarial patterns into physical light projections. Two primary factors influence this process: (1) the alteration of received light wavelengths due to specular reflection, diffuse reflection, and absorption of adversarial light on facial surfaces, and (2) the interaction between projected light and ambient illumination, resulting in the reception of reflected ambient light. These phenomena modulate the pixel values of the digital pattern. Consequently, formulating these transformations is crucial for mitigating their impacts and preserving attack effectiveness. + +We propose a Light Reflection Function (LRF) that models the process of pattern projection, reflection on skin, and camera capture, formulated as the transformation $T_{l}(\cdot)$ : + +$$ +x ^ {\text {m a s k}} = T _ {l} \left(x ^ {a} + \tilde {x}\right) \odot M. \tag {5} +$$ + +This process primarily involves modeling the following physical phenomena: the projector emits light patterns corresponding to the RGB values of each pixel in the image. Both projected and ambient light strike the human face and, after absorption and reflection, produce new light patterns. The camera then captures these patterns and converts them into RGB format. This process is principally determined by three factors ( $\lambda$ denotes the wavelength of light): + +- $S(\lambda)$ : the spectral power distribution of the projector. +- $\rho (\lambda)$ : the spectral reflectance of the skin. +- $\sigma(\lambda)$ : the sensitivity of the camera's photodetectors, with $\sigma_x(\lambda)$ , $\sigma_y(\lambda)$ , and $\sigma_z(\lambda)$ representing the impact on red, green, and blue components respectively. + +To simulate and quantify human visual response to colors, we utilize the CIE XYZ color space model, integrating the color matching functions to calculate an image's coordinates within this space: $X = \int S(\lambda) \rho(\lambda) \sigma_x(\lambda) d\lambda, Y = \int S(\lambda) \rho(\lambda) \sigma_y(\lambda) d\lambda, Z = \int S(\lambda) \rho(\lambda) \sigma_z(\lambda) d\lambda$ . The interaction between ambient and projected light is considered through linear superposition of their spectral intensities: + +$$ +S (\lambda) = S _ {\text {n a t u r a l}} (\lambda) + S _ {\text {p r o j e c t o r}} (\lambda). \tag {6} +$$ + +Finally, XYZ coordinates are converted to RGB coordinates. Using the PAL standard RGB system as an example, the transformation is: + +$$ +\left[ \begin{array}{l} R \\ G \\ B \end{array} \right] = \left[ \begin{array}{c c c} X _ {r} & Y _ {r} & Z _ {r} \\ X _ {g} & Y _ {g} & Z _ {g} \\ X _ {b} & Y _ {b} & Z _ {b} \end{array} \right] \left[ \begin{array}{l} X \\ Y \\ Z \end{array} \right]. \tag {7} +$$ + +$S(\lambda)$ , $\rho (\lambda)$ , $\sigma (\lambda)$ , and PAL color conversion matrix $(X_{r}$ etc.) can all be obtained from technical documentation and + +![](images/4ec31b0b06a26443f0f649e7ae6eb558b00e5cb25a03d27e5ec18a3323204719.jpg) +Figure 4. Light Reflection Function. (c) is obtained by applying our light reflection function to (b), while (d), obtained by projecting (a) in the real world, demonstrates consistency with (c). + +official standards. As shown in Fig. 4, our LRF enables the transformed adversarial 3D mask to closely align with its real-world counterpart. Integrating the LRF within our optimization pipeline ensures that the adversarial 3D mask, when projected into the physical world, maintains its attack effectiveness. + +# 3.5. Camera Capture Simulation + +The camera's internal Image Signal Processing (ISP) pipeline plays a crucial role in transforming physical scenes into digital RGB images. Variations in ISP configurations can lead to divergent visual characteristics of the same adversarial texture across devices, potentially affecting attack performance. Therefore, we introduce ISP simulation $T_{c}(\cdot)$ to model the camera capturing process. To address the non-differentiable nature of traditional ISP processes, we build a differentiable camera ISP proxy network that enables gradient propagation during optimization. The camera ISP proxy network simulates various ISP processes through conditional inputs, focusing on representative parameters from color and tone correction modules, as well as the denoising module, which significantly impact image quality. + +Our camera ISP proxy network is based on the U-Net architecture [16], comprising $3 \times 3$ convolutions and $2 \times 2$ max pooling operations in its encoder and decoder. The feature channels expand progressively through \{32, 64, 128, 256, 512\}. This structure enables the ISP proxy network to maintain differentiability while simulating diverse camera ISP parameter configurations, thus adapting to various hardware environments. + +We normalize ISP parameters (e.g., brightness, contrast, gamma correction) to [0,1] and concatenate them with feature maps, enabling the ISP proxy network to dynamically adjust image tone, contrast, color balance, and denoising characteristics to flexibly simulate diverse device imaging profiles. To train our camera ISP proxy network, we utilize an undifferentiable camera ISP simulator [15] along with the COCO dataset [12], generating a total of 2,270 data pairs. During training, we employ a composite loss function—including pixel-level MSE loss, perceptual loss, and regularization loss—to ensure high image fidelity and sensitivity to conditional ISP parameters, while maintaining full differentiability for gradient optimization. Our framework leverages the ISP network simulating various lighting ef + +
SourceLFW datasetCelebA-HQ dataset
ArcFaceMoblieNetResNetIRAPIArcFaceMoblieNetResNetIRAPI
ArcFace [1]-40.40%25.37%39.22%12.37%-60.80%64.32%62.12%16.49%
MobileNet [4]13.28%-46.98%24.71%12.05%49.50%-66.33%40.80%12.86%
ResNet [3]25.37%54.31%-33.14%18.33%63.49%75.50%-56.35%12.35%
IR [3]22.32%41.44%42.37%-17.86%78.79%78.39%58.79%-14.29%
Ensemble59.09%72.91%75.28%53.52%38.78%90.50%88.29%88.37%88.50%32.84%
+ +Table 1. Evaluation of black-box impersonation attack. We report the attack success rates (ASR) on ArcFace, MobileNet, ResNet, IR, and a commercial API. Each row represents results using a different source model for the attack. In the ensemble setting, the target model corresponding to each column is excluded from the ensemble used to generate the attack. + +
DatasetTypeMethodArcFaceFaceNetMobileNetResNetCosFaceAPIAverage
LFWTransfer-basedTAP [27] \( _{CVPR'21} \)53.50%46.00%--50.00%10.00%39.89%
AT3D [28] \( _{CVPR'23} \)86.25%-91.50%86.50%63.00%45.25%74.50%
Query-basedAdvSticker [25] \( _{TPAMI'22} \)-51.11%--48.06%-49.59%
SOPP [26] \( _{TPAMI'22} \)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours78.07%52.17%79.49%82.98%78.17%41.43%68.72%
CelebA-HQTransfer-basedTAP [27] \( _{CVPR'21} \)65.75%52.50%--58.25%20.00%49.13%
AT3D [28] \( _{CVPR'23} \)92.50%-96.25%93.75%87.50%50.25%84.05%
Query-basedAdvSticker [25] \( _{TPAMI'22} \)-48.96%--47.73%-48.35%
SOPP [26] \( _{TPAMI'22} \)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours95.15%84.47%98.13%97.20%93.20%44.03%85.36%
+ +Table 2. Quantitative comparison with existing methods. All methods are evaluated under a black-box setting, where TAP [27] and AT3D [28] are transfer-based attacks, while AdvSticker [25], SOPP [26], and ProjAttacker are query-based attacks. The highest and second-highest Attack Success Rates (ASRs) across both datasets are highlighted in red and blue, respectively. + +fects in the physical world to enhance the robustness of adversarial patterns and improve attack efficacy. + +# 4. Experiments + +# 4.1. Experiment Settings + +Targeted Models. We selected seven face recognition models as our target models, including six representative open-source models (ArcFace [1], MobileNet [4], ResNet [3], FaceNet [17], CosFace [22], IR [3]) and a commercial face recognition API*. For attacking the API, we employed other open-source models as an ensemble of surrogate models. When performing an ensemble attack on one of the models, the remaining models served as surrogate models. In our experiments, we evaluate the attack effectiveness by calculating the cosine similarity of the vectors obtained from the input image pairs. Each model adheres to its respective threshold: if the similarity between two images exceeds the threshold, they are considered the same identity; otherwise, they are considered different identities. Notably, each model is well-trained, achieving an accuracy exceeding $99\%$ on the LFW dataset. + +Datasets. We conducted experiments in the digital domain on two extensively employed benchmark datasets: the La- + +beled Faces in the Wild (LFW) [6] and the CelebFaces Attributes High Quality (CelebA-HQ) [9]. For evasion attacks, we randomly selected several pairs of images with the same identity from the dataset, aiming to push the attacker's features away from their true identity. For impersonation attacks, we randomly chose an attacker from the dataset and paired them with several randomly selected victims, creating multiple pairs of images with different identities. + +Comparison methods. We compare our proposed ProjAttacker with the following four methods: TAP [27], AdvSticker [25], SOPP [26], and AT3D [28]. All methods are physically realizable. + +Implementation details. All experiments were conducted on a Linux server equipped with two NVIDIA GeForce RTX 3090 GPUs, with all code and algorithms implemented in PyTorch. We set the number of iterations per round to 300 and the learning rate to 0.45. Within the overall framework, the reward step size is set to 0.1. The total number of queries is 25, and if no result is obtained within 25 queries, the attempt is deemed unsuccessful. + +# 4.2. Attacks in the Digital World + +Black-box Attack. To assess the effectiveness of the attacks, we employ the Attack Success Rate (ASR), a metric that measures the efficacy of attack methodologies by indicating the proportion of successful attacks relative to the + +![](images/fe71e0915d9a6343c6d6264bd8b0d5aadbdd8ca8575703150445b58d893f6053.jpg) +Figure 5. Attack results of our ProjAttacker in both digital and physical domains. By projecting diverse adversarial patterns onto facial regions, an attacker can induce the face recognition model (CosFace [22]) to misidentify the subject as various victims. Our method exhibits superior flexibility and cost-effectiveness compared to approaches based on wearable material artifacts. Green indicates successful attacks, while red denotes unsuccessful attacks. + +total samples. Tab. 1 displays the quantitative results of impersonation attacks under black-box conditions against five different target models. + +As shown in Tab. 1, we can observe: (1) The proposed model ensemble method demonstrates significant efficacy against impersonation attacks on both the LFW and CelebA-HQ datasets. Notably, the highest attack success rate achieved on the LFW dataset is $75.28\%$ , while on the CelebA-HQ dataset, it reaches $90.50\%$ . (2) The attack success rates on the CelebA-HQ dataset are generally higher than those on the LFW dataset. This can be attributed to the higher quality and resolution of facial images in the CelebA-HQ dataset, which facilitates more effective feature extraction by the models. (3) The ensemble method consistently outperforms models trained individually, indicating that our approach can adaptively adjust model weights to achieve optimal performance. + +Comparisons with SOTA Methods. We compare ProjAttacker attack with five existing physically realizable black-box attack methods, as shown in Tab. 2. We conducted experiments on a set of images from the CelebA-HQ dataset. Each target model in the columns is excluded from our ensemble model, strictly adhering to the principles of black-box attacks. Our method outperforms the two baseline query-based approaches, AdvSticker and SOPP, across both datasets. Regarding transfer-based methods, our approach surpasses TAP on the LFW dataset but falls short of + +
3DLRFISPArcFaceMobileNetResNetAPI
✓✓56%54%52%34%
✓✓38%32%32%12%
✓✓44%42%48%22%
✓✓✓68%60%62%38%
+ +- "3D" represents the 3D mask form, as opposed to the 2D mask. +- "LRF" means the light reflection function in our pipeline. +- "ISP" means the camera ISP proxy network in our pipeline. + +Table 3. Ablation study in the physical world. We report the ASR of our ProjAttacker attack. + +AT3D. However, on the CelebA-HQ dataset, our method outperforms both TAP and AT3D. These results demonstrate the excellent attack performance of our approach in black-box settings. + +# 4.3. Attacks in the Physical World + +Qualitative Analysis. As shown in Fig. 5, we present an attacker, six victims, and their corresponding digital and physical space attacks. Without the light reflection function, the optimized adversarial patterns exhibit diverse colors with high saturation, impeding physical space reproduction. Incorporating the light reflection function facilitates the transfer of digital space adversarial patterns to the physical domain. Physical space attacks demonstrate our method's efficacy in misleading CosFace to misiden + +![](images/84a652497147d894a18e0f18e989c759ae24c830eb7df60aec48534b4c76529b.jpg) +Figure 6. Comparison with existing methods. We compare the hiPAA [24] of three physical adversarial attack methods. + +tify the attacker as different victims with high confidence. Notably, transitioning between victims merely requires altering the projected pattern, offering significant operational convenience. These results highlight our method's flexibility in executing effective attacks in real-world scenarios. + +Ablation Study. To quantify the contribution of each module within our proposed framework to the success rate of physical space attacks, we conducted ablation experiments. We systematically removed the 3D, RLF, and ISP modules from a set of attacker-victim image pairs, generating four distinct adversarial patterns for physical testing, including those from the complete framework. The experiments encompassed 50 attacker-victim pairs, with statistical results presented in Tab. 3. We observe that the removal of any single module results in a decrease in Attack Success Rate (ASR). These findings validate the rationale and necessity of each module within our method. + +Evaluation using hiPAA Metrics. To comprehensively evaluate the performance of physical adversarial attacks, Wei et al. [24] proposed the hiPAA metric, which includes six dimensions: Effectiveness, Stealthiness, Robustness, Practicability, Aesthetics, and Economics. We assess and compare the hiPAA scores of various methods, as illustrated in Fig. 6. Note that Stealthiness, Practicability, and Aesthetics are evaluated through a user study; refer to the supplementary material for more details of our evaluation. We observe that our ProjAttacker attack outperforms TAP in robustness and surpasses AT3D in effectiveness. Additionally, our method significantly outperforms in the Practicability dimension, as it does not require manually crafted 3D-printed masks or patches. For an attacker to mislead the facial recognition system into identifying them as different victims, only the adversarial pattern needs to be switched. This not only reduces costs but also eliminates the need for complex manufacturing processes, enhancing the practicality of real-world applications. + +# 4.4. Liveness Detection + +Liveness detection technology primarily encompasses four methods: (1) Transform: Analysis of image Fourier transforms or Local Binary Patterns to discern whether a presented face is genuine or merely a static image. (2) Depth: Utilization of depth sensors or stereo cameras to assess the three-dimensional structure of a face, thereby verifying its + +
MethodTransformDepthMotionMultiBio
TAP [27] CVPR'21✓XXX
AdvSticker [25] TPAMI'22✓✓✓X
SOPP [26] TPAMI'22✓✓✓X
AT3D [28] CVPR'23✓✓XX
ProjAttacker Ours✓✓✓✓
+ +Table 4. Liveness detection analysis. Our light-based attack outperforms existing methods by successfully deceiving all liveness detection strategies. + +
CTyunBaiduTencentAliyun
Physical Evaluation55/5555/5548/5152/55
+ +Table 5. Bypass rate. The number of successful bypasses achieved by our method across four commercial liveness detection APIs. + +authenticity. (3) Motion: Examination and tracking of eye movements, lip motions, and blink frequency to validate the presence of a live subject. (4) MultiBio: Integration of facial vascular flow detection with other biometric identification technologies, such as iris scanning, to provide a multi-tiered security validation approach. + +Tab. 4 shows that existing physical attack modalities typically require a tangible medium and often rely on partially obstructing the facial features to create adversarial perturbations. In contrast, our method utilizes light as the medium and adopts a non-intrusive attack. This approach avoids obscuring facial biometric features, thus demonstrating higher effectiveness against various liveness detection technologies. Tab. 5 shows that our method achieved successful bypasses across all four commercial liveness detection APIs, with a $100\%$ success rate on CTyun and Baidu in particular. + +# 5. Conclusion + +We introduced ProjAttacker, a novel adversarial light attack that effectively compromises both face recognition systems and liveness detection models. Extensive experiments in both digital and physical space demonstrate that ProjAttacker outperforms existing methods, highlighting the vulnerability of current face recognition systems to sophisticated physical attacks. Our findings underscore the pressing need for more robust defense mechanisms to secure biometric systems against potential threats. + +Ethics Statement. Our research investigates the vulnerabilities of face recognition systems through physical adversarial attacks. Aware of the dual-use potential, we conducted all experiments under strict ethical guidelines, ensuring no compromise of personal data or real-world systems. Our goal is to contribute to the development of more secure face recognition systems. We urge the community to consider both defensive and offensive aspects, promoting responsible application. + +Acknowledgements. This work was supported by Hubei Key R&D Project (2022BAA033) and National Natural Science Foundation of China (62171325, 62402365). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University. + +# References + +[1] Jiankang Deng, Jia Guo, Jing Yang, Niannan Xue, Irene Kotsia, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(10):5962-5979, 2022. 6 +[2] Hang Du, Hailin Shi, Dan Zeng, Xiao-Ping Zhang, and Tao Mei. The elements of end-to-end deep face recognition: A survey of recent advances. 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However, these attacks often struggle to impersonate multiple targets and frequently fail to bypass liveness detection. For example, attacks using human-skin masks [28] are challenging to fabricate, inconvenient to swap between users, and often fail liveness detection due to facial occlusions. A projector, however, can generate content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Thus, we propose a novel physical adversarial attack using a projector and explore the superposition of projected and natural light to create adversarial facial images. This approach eliminates the need for physical artifacts on the face, effectively overcoming these limitations. Specifically, our proposed ProjAttacker generates adversarial 3D textures that are projected onto human faces. To ensure physical realizability, we introduce a light reflection function that models complex optical interactions between projected light and human skin, accounting for reflection and diffraction effects. Furthermore, we incorporate camera Image Signal Processing (ISP) simulation to maintain the robustness of adversarial perturbations across real-world diverse imaging conditions. Comprehensive evaluations conducted in both digital and physical scenarios validate the effectiveness of our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 648, + 135, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 648, + 135, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 648, + 135, + 661 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "type": "text", + "content": "Face recognition has become a widely adopted technology for authentication and access control [2, 13]. De" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 318, + 286, + 552, + 339 + ], + "blocks": [ + { + "bbox": [ + 318, + 286, + 552, + 339 + ], + "lines": [ + { + "bbox": [ + 318, + 286, + 552, + 339 + ], + "spans": [ + { + "bbox": [ + 318, + 286, + 552, + 339 + ], + "type": "image", + "image_path": "0d93a70c5c0150b7583935591cbb284f88fc483f2969b97f62d659129b007569.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 340, + 480, + 350 + ], + "lines": [ + { + "bbox": [ + 392, + 340, + 480, + 350 + ], + "spans": [ + { + "bbox": [ + 392, + 340, + 480, + 350 + ], + "type": "text", + "content": "(a) Existing Attack Methods" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 351, + 552, + 450 + ], + "blocks": [ + { + "bbox": [ + 318, + 351, + 552, + 450 + ], + "lines": [ + { + "bbox": [ + 318, + 351, + 552, + 450 + ], + "spans": [ + { + "bbox": [ + 318, + 351, + 552, + 450 + ], + "type": "image", + "image_path": "aec9f27e02e800285acb22e138763c00b4736c1460f370e78d1ecd8b7165aff5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 452, + 471, + 460 + ], + "lines": [ + { + "bbox": [ + 400, + 452, + 471, + 460 + ], + "spans": [ + { + "bbox": [ + 400, + 452, + 471, + 460 + ], + "type": "text", + "content": "(b) Our Attack Method" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "type": "text", + "content": "Figure 1. Comparison of our ProjAttacker with existing attack methods. While existing methods [10, 18, 28] can successfully attack face recognition, they are difficult to fabricate, inconvenient to swap between targets, and unable to bypass liveness detection due to facial occlusions. In contrast, our ProjAttacker projects light-based adversarial textures onto the face, enabling a non-intrusive attack via projector that overcomes these limitations, allowing real-time, configurable face swaps that simultaneously deceive both liveness detection and recognition models." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 578, + 555, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 578, + 555, + 687 + ], + "spans": [ + { + "bbox": [ + 312, + 578, + 555, + 687 + ], + "type": "text", + "content": "spite its prevalence, significant security vulnerabilities remain. Recent studies have shown that imperceptible, carefully crafted perturbations can deceive deep neural network based face recognition models, leading to incorrect predictions [5, 20, 25, 30]. These attacks remain effective in the physical world [24], exposing substantial security risks. Developing physical adversarial attack methods to identify weaknesses and assess the robustness of these systems is essential for secure real-world deployment." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "type": "text", + "content": "Existing physical adversarial attacks on face recognition systems largely rely on physical artifacts like textured" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 222, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 222, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 222, + 713 + ], + "type": "text", + "content": "*Equal contribution † Corresponding author" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21248" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 69, + 182, + 171 + ], + "blocks": [ + { + "bbox": [ + 58, + 69, + 182, + 171 + ], + "lines": [ + { + "bbox": [ + 58, + 69, + 182, + 171 + ], + "spans": [ + { + "bbox": [ + 58, + 69, + 182, + 171 + ], + "type": "image", + "image_path": "0fe86138bcd980b73eb144213639643192649123b5a68bdaa36b674d176932dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 178, + 555, + 212 + ], + "lines": [ + { + "bbox": [ + 55, + 178, + 555, + 212 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 555, + 212 + ], + "type": "text", + "content": "Figure 2. Workflow of our ProjAttacker. ProjAttacker works in four steps: (1) generating a light-based adversarial 3D mask; (2) deploying the attack in the real world using projection devices; (3) capturing the attacker's image with a camera; and (4) executing the attack during model inference. This workflow mirrors our attack pipeline in the digital domain." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 182, + 69, + 293, + 171 + ], + "blocks": [ + { + "bbox": [ + 182, + 69, + 293, + 171 + ], + "lines": [ + { + "bbox": [ + 182, + 69, + 293, + 171 + ], + "spans": [ + { + "bbox": [ + 182, + 69, + 293, + 171 + ], + "type": "image", + "image_path": "f92a9c19fe6ef15fb6fd241099f63b6fd1bb2bef986cbd56fac3fd1a7df1654c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 293, + 70, + 403, + 171 + ], + "blocks": [ + { + "bbox": [ + 293, + 70, + 403, + 171 + ], + "lines": [ + { + "bbox": [ + 293, + 70, + 403, + 171 + ], + "spans": [ + { + "bbox": [ + 293, + 70, + 403, + 171 + ], + "type": "image", + "image_path": "407506bbfededf98af80ff0161bdf545de772ffca56d82f249c2fe0188118941.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 403, + 70, + 553, + 171 + ], + "blocks": [ + { + "bbox": [ + 403, + 70, + 553, + 171 + ], + "lines": [ + { + "bbox": [ + 403, + 70, + 553, + 171 + ], + "spans": [ + { + "bbox": [ + 403, + 70, + 553, + 171 + ], + "type": "image", + "image_path": "45b09106044e3a81523ddc7a8e0fb1126e7a71174f93d46f163536b3feba57a2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 220, + 294, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 220, + 294, + 353 + ], + "spans": [ + { + "bbox": [ + 54, + 220, + 294, + 353 + ], + "type": "text", + "content": "eyeglasses [18, 19], human-skin masks [28], stickers [25], forehead-covering hats [10], and makeup [29]. While these approaches can successfully fool recognition models, they face notable limitations: 1) they are user-specific, difficult to adapt for multiple individuals, and often require complex fabrication processes (e.g., 2D or 3D printing) and high-quality materials to accurately replicate designed adversarial textures, making them impractical for multi-user scenarios; and 2) their occlusive nature makes it difficult to bypass liveness detection, reducing their attack effectiveness in real-world settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 354, + 295, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 354, + 295, + 484 + ], + "spans": [ + { + "bbox": [ + 54, + 354, + 295, + 484 + ], + "type": "text", + "content": "A projector can produce content-rich light without obstructing the face, making it ideal for non-intrusive attacks. Leveraging this advantage, we introduce ProjAttacker, a novel and configurable physical adversarial attack for face recognition. ProjAttacker explores the superposition of projected and natural light to create adversarial facial images. This approach effectively addresses both aforementioned limitations, simultaneously enabling multi-target impersonation and circumvention of liveness detection. Fig. 1 presents a comparison between our method and existing state-of-the-art (SOTA) approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "text", + "content": "To ensure real-world attack effectiveness, we analyze the workflow of ProjAttacker, which comprises four steps (see Fig. 2). For the adversarial 3D mask generated in step (1) to remain effective through step (4), it must successfully traverse two critical domain transitions: the projector-mediated transition from digital domain to physical space, and the camera-mediated transition from physical space back to digital images. Maintaining resilience across these domain transitions is crucial for attack success. Therefore, we first incorporate a light reflection function into the adversarial 3D mask generation pipeline, ensuring robustness against projection inconsistencies. To mitigate camera-induced color shifts in real-world scenarios, we develop a differentiable proxy network that simulates camera Image Signal Processing (ISP) modules. Specifically, this proxy network transforms the camera's internal denoising and color correction units into differentiable modules, and through stochastic sampling of conditional input parameters during optimization, generates adversarial patterns" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 221, + 553, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 221, + 553, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 553, + 280 + ], + "type": "text", + "content": "that remain effective under various camera capture conditions. Extensive experiments in both digital and physical scenarios demonstrate that our proposed method effectively compromises mainstream models and APIs. The main contributions are summarized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 284, + 555, + 499 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 313, + 284, + 555, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 284, + 555, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 555, + 355 + ], + "type": "text", + "content": "- Real-world configurable face swap. We present ProjAttacker, the first light-based attack that leverages projected 3D masks with adversarial patterns to simultaneously deceive face recognition models and liveness detection systems, enabling efficient and cost-effective face-swapping attacks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 355, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 355, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 355, + 554, + 437 + ], + "type": "text", + "content": "- Physically realizable attack pipeline. We bridge the digital-physical gap through: (i) a light reflection simulation function that ensures robustness against projection inconsistencies, and (ii) a differentiable camera ISP proxy network that accurately models the image capture process, guaranteeing the real-world effectiveness of the adversarial 3D mask." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 439, + 553, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 439, + 553, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 439, + 553, + 499 + ], + "type": "text", + "content": "- Exceptional attack effectiveness. Our ProjAttacker achieves superior performance in both digital and physical domains. Comprehensive experimental results validate our approach and reveal significant security vulnerabilities in contemporary face recognition systems." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 513, + 405, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 513, + 405, + 525 + ], + "spans": [ + { + "bbox": [ + 314, + 513, + 405, + 525 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "text", + "content": "Physical Adversarial Attack for Face Recognition. Face recognition systems have been extensively deployed in safety-critical applications, making the study of physical-world adversarial attacks against such systems increasingly crucial. Prior works have predominantly explored the integration of adversarial perturbations with physical accessories, including hats [10], glasses [18, 19, 27], and stickers [25, 26]. Additionally, alternative approaches such as Adv-Makeup [29] demonstrate successful attacks through subtle eye-area cosmetic modifications, while AT3D [28] employs 3D-printed masks with adversarial textures. However, these methodologies either suffer from diminished effectiveness when transitioning from digital to physical domains or require complex, time-intensive preparation processes. Furthermore, their reliance on material-based facial" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21249" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 71, + 522, + 261 + ], + "blocks": [ + { + "bbox": [ + 80, + 71, + 522, + 261 + ], + "lines": [ + { + "bbox": [ + 80, + 71, + 522, + 261 + ], + "spans": [ + { + "bbox": [ + 80, + 71, + 522, + 261 + ], + "type": "image", + "image_path": "a064d28d17cc98cd79087b2bc212e418bd8acd9fbc0d65e02ab6bd8650e87831.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 264, + 555, + 353 + ], + "lines": [ + { + "bbox": [ + 54, + 264, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 54, + 264, + 555, + 353 + ], + "type": "text", + "content": "Figure 3. Overview of ProjAttacker. (a) Initially, we employ CNN to extract features and perform parameter fitting on the image, precisely regressing the 3D Morphable Model (3DMM) coefficients. These coefficients are then rendered and cropped to produce the initial 3D adversarial pattern. (b) Subsequently, we simulate the realistic projection of the pattern in the physical space using the Light Reflection Function (LRF), and employ an camera ISP proxy model to emulate adversarial face images under various camera imaging systems. The adversarial pattern is dynamically updated through multiple iterations of optimization using an ensemble learning model. (c) Finally, we utilize the optimized adversarial face image for black-box attacks. If the attack fails, we dynamically adjust the weight distribution of the ensemble model through a reinforcement learning-based reward function and repeat step (b) to continually refine the attack strategy and enhance the success rate." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 362, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 362, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 54, + 362, + 295, + 410 + ], + "type": "text", + "content": "artifacts often fails to circumvent liveness detection mechanisms. In this work, we propose a light-based attack that addresses these limitations by simultaneously compromising both face recognition and liveness detection systems." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 412, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 412, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 54, + 412, + 295, + 604 + ], + "type": "text", + "content": "Light-Based Attack. Light has emerged as a promising adversarial medium for projecting attack patterns onto human faces [24]. Current light-based attacks against face recognition systems are limited to two primary approaches: Zhou et al. [31]'s infrared light projection method and Nguyen et al. [14]'s 2D RGB adversarial pattern projection. While these approaches represent significant advances, they fail to adequately account for light distortion and reflection on facial surfaces, resulting in suboptimal attack success rates and performance. We systematically re-examine the light-based attack pipeline, as illustrated in Fig. 2, and introduce novel light reflection and camera capture simulation modules. These innovations enable the generation of robust light-based adversarial patterns that maintain effectiveness throughout both projection and capture processes, ensuring high attack success rates in real-world scenarios." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": "Domain Transition. Since Sharif et al. [18] first demonstrated adversarial attacks in the physical world, the research community has increasingly focused on exploring the effectiveness of adversarial examples under real-world conditions [7, 21, 23]. This process involves two domain transformations. As shown in Fig. 2, the first domain transformation occurs during the attack deployment stage, where the adversarial pattern transitions from the digital space to the physical world. The second domain transfor" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 362, + 555, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 555, + 506 + ], + "type": "text", + "content": "mation takes place during the camera capture stage, where the adversarial pattern transitions back from the physical world to the digital space. Existing methods have primarily addressed the former, such as non-printability score (NPS) [18] and D2P [8], which aim to mitigate the impact of the digital-to-physical transformation on attacks. To the best of our knowledge, no method has yet addressed the latter transformation, i.e., from physical to digital. We have designed a comprehensive attack pipeline that incorporates a light reflection function and a camera ISP proxy network to accurately simulate the real-world workflow, thereby enhancing the attack effectiveness in the physical world." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 516, + 398, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 398, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 398, + 530 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 535, + 440, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 535, + 440, + 547 + ], + "spans": [ + { + "bbox": [ + 313, + 535, + 440, + 547 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": "Threat Model. Let " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " denote the space of all possible facial images. Given a black-box facial recognition system " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "f:\\mathcal{X}\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " that maps an input image to a " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": "-dimensional embedding space, our goal is to generate physical adversarial patterns that can be projected onto an attacker's face to impersonate a target victim. Formally, for an attacker's face image " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "x^{a}\\in \\mathcal{X}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " and a victim's face image " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "x^{v}\\in \\mathcal{X}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": ", we aim to find an adversarial perturbation function " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " that generates a physically realizable adversarial example " + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "inline_equation", + "content": "x^{adv}" + }, + { + "bbox": [ + 313, + 552, + 555, + 661 + ], + "type": "text", + "content": " such that:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 394, + 667, + 555, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 667, + 555, + 682 + ], + "spans": [ + { + "bbox": [ + 394, + 667, + 555, + 682 + ], + "type": "interline_equation", + "content": "x ^ {a d v} = F \\left(x ^ {a}, x ^ {v}\\right), \\tag {1}", + "image_path": "5b1d9104276bf8d64db32ea7706406a2e670fe8f2ce2f0f5663403ab48fa2c9d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " consists of a 3D mask " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " and a light-based perturbation pattern " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21250" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "text", + "content": "Attack Objective. The attack is considered successful if the following conditions are satisfied: (1) Impersonation Success: The adversarial example should be verified as the victim: " + }, + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "inline_equation", + "content": "\\text{Ver}(x^{adv}, x^v) = 1" + }, + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "inline_equation", + "content": "\\text{Ver}(x^1, x^2) = \\mathbb{I}\\left(\\frac{\\langle f(x^1), f(x^2)\\rangle}{|f(x^1)| \\cdot |f(x^2)|} > \\tau\\right)" + }, + { + "bbox": [ + 55, + 72, + 296, + 162 + ], + "type": "text", + "content": ". (2) Physical Realizability: The adversarial perturbation must be physically realizable through light projection:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 87, + 167, + 295, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 167, + 295, + 182 + ], + "spans": [ + { + "bbox": [ + 87, + 167, + 295, + 182 + ], + "type": "interline_equation", + "content": "x ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M, \\tag {2}", + "image_path": "819839fa91b41ae0960948da09d79183f7625f521e591c2ca60dd342dc4436ac.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 186, + 296, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 296, + 221 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 296, + 221 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 186, + 296, + 221 + ], + "type": "inline_equation", + "content": "T_{l}(\\cdot)" + }, + { + "bbox": [ + 55, + 186, + 296, + 221 + ], + "type": "text", + "content": " represents the Light Reflection Function that models real-world lighting effects. The complete optimization can be formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 126, + 224, + 219, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 224, + 219, + 243 + ], + "spans": [ + { + "bbox": [ + 126, + 224, + 219, + 243 + ], + "type": "interline_equation", + "content": "\\min _ {M, \\tilde {x}} L _ {F} \\left[ T _ {c} \\left(x ^ {a d v}\\right), x ^ {v} \\right]", + "image_path": "2338de0a3f1675b45a5b49b5b25009fd5ffe30284bd379f8203b08aba1f2c3e8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 247, + 294, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 247, + 294, + 270 + ], + "spans": [ + { + "bbox": [ + 59, + 247, + 294, + 270 + ], + "type": "interline_equation", + "content": "\\text {s . t .} x ^ {a d v} = x ^ {a} \\odot (1 - M) + T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M \\quad M \\in \\mathcal {M}, \\tag {3}", + "image_path": "ea0d82c616d43648ce9bb936a10b9a2186d8871c9fd17260c2b2afe57d03bcc8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "inline_equation", + "content": "L_{F}[\\cdot ,\\cdot ]" + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "content": " is the objective function measuring the dissimilarity between the adversarial example and victim, " + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "inline_equation", + "content": "T_{c}(\\cdot)" + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "content": " represents the camera capture simulation, " + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "content": " is the space of valid 3D masks obtained through 3D face reconstruction, " + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 271, + 296, + 331 + ], + "type": "text", + "content": " denotes element-wise multiplication." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 331, + 296, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 403 + ], + "type": "text", + "content": "This optimization problem is solved through a reinforcement learning framework [11], where the agent learns an optimal perturbation policy through interactions with an environment constructed from white-box face recognition model ensembles, ultimately generalizing to attack the black-box target model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 409, + 171, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 409, + 171, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 171, + 420 + ], + "type": "text", + "content": "3.2. Overall Framework" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "text", + "content": "Given a victim's facial image " + }, + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "inline_equation", + "content": "x^{v}" + }, + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "text", + "content": ", we first construct a 3D face model using a pre-trained 3D face reconstruction network. This network decomposes the facial attributes into multiple components, and then used them to reconstruct a complete 3D face model of the victim. To obtain the projection area for the adversarial pattern, we perform 3D cropping on the reconstructed face model to generate the initial 3D mask " + }, + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "inline_equation", + "content": "M \\in \\mathcal{M}" + }, + { + "bbox": [ + 55, + 426, + 296, + 534 + ], + "type": "text", + "content": ". This mask defines the spatial region where the light-based perturbation will be applied." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": "The core of our framework lies in the optimization stage, where we iteratively refine the adversarial pattern through a reinforcement learning approach. This stage involves several key components: Light Reflection Function " + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "inline_equation", + "content": "T_{l}(\\cdot)" + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": ": We design a differentiable light reflection function that simulates how projected patterns interact with the attacker's face under various physical conditions. This function models the transformation of the initial perturbation " + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": " when projected onto the 3D mask " + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": " and combines it with the attacker's face image " + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "inline_equation", + "content": "x^{a}" + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": " according to Eq. 2. Camera ISP Proxy Network " + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "inline_equation", + "content": "T_{c}(\\cdot)" + }, + { + "bbox": [ + 55, + 534, + 296, + 713 + ], + "type": "text", + "content": ": To bridge the gap between digital and physical domains, we incorporate a Camera ISP (Image Signal Processing) proxy network that simulates real-world image capture effects. This network ensures that the generated patterns remain effective under real camera conditions. Agent" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "Models: We construct an environment using an ensemble of white-box face recognition models. The agent interacts with these models to learn an optimal perturbation strategy that can generalize to black-box scenarios. The learning process is guided by a reward signal derived from the cosine similarity scores between the adversarial example and the victim's embedding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 157, + 554, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 554, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 554, + 300 + ], + "type": "text", + "content": "In the final stage, we evaluate the effectiveness of our attack against the target black-box face recognition model. The attacker's face, augmented with the optimized adversarial pattern projected through the 3D mask, is presented to the target system. The success of the attack is measured by the verification result " + }, + { + "bbox": [ + 313, + 157, + 554, + 300 + ], + "type": "inline_equation", + "content": "\\text{Ver}(x^{adv}, x^v)" + }, + { + "bbox": [ + 313, + 157, + 554, + 300 + ], + "type": "text", + "content": ". This stage validates whether our generated adversarial pattern can successfully fool the target system while maintaining physical realizability. The entire framework operates in an end-to-end manner, with loss gradients propagating backward through the optimization stage to continuously refine the adversarial pattern." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 309, + 443, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 309, + 443, + 320 + ], + "spans": [ + { + "bbox": [ + 313, + 309, + 443, + 320 + ], + "type": "text", + "content": "3.3. 3D Mask Initialization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 327, + 555, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 555, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 555, + 579 + ], + "type": "text", + "content": "Face recognition systems capture the 3D structure of facial features, such as surface protrusions and recesses. However, most existing attack methods [10, 18, 19, 25] rely on 2D perturbation simulations, which struggle to effectively map onto 3D facial features in real-world applications. This dimensional mismatch reduces the effectiveness of physical-space attacks. To address this limitation, we introduce a high-dimensional, geometric parameter-driven 3D facial projection construction. Starting from facial images, we employ a convolutional neural network (CNN) regression model to extract 3D Morphable Model (3DMM) coefficients that encode individual-specific facial geometry. These coefficients then guide a facial mesh reconstruction module, applying 3D deformation and topological mapping to accurately generate a 3D mesh model aligned with the individual's facial structure. Spatial coordinate transformations are then applied to map the mesh vertices from object coordinates to camera coordinates, and an intrinsic camera matrix enables perspective projection, which normalizes depth information into 2D pixel coordinates for precise 3D-to-2D mapping on the image plane." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 323, + 587, + 555, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 587, + 555, + 609 + ], + "spans": [ + { + "bbox": [ + 323, + 587, + 555, + 609 + ], + "type": "interline_equation", + "content": "x = \\mathcal {T} \\left(K \\cdot \\mathcal {R} \\left(B \\cdot [ \\Theta_ {i d}, \\Theta_ {e x p}, \\Theta_ {t e x}, \\dots ] ^ {T} + \\overline {{S}}\\right)\\right). (4)", + "image_path": "b3884d2533fc530c183f69e7fa6b96a160be4132a76d30dc33f9c14980256fed.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": "In this formulation, " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " represents various 3DMM coefficients. " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " is the matrix containing the basis shape vectors, which is used to map the coefficients to the corresponding shape space, while " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\overline{S}" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " serves as the mean facial shape. " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " is the spatial transformation function mapping 3D mesh vertices from object to camera coordinates, while the intrinsic camera matrix " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " enables perspective projection, and " + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": " normalizes depth information to 2D pixel coordinates." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21251" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": "Through this process, we effectively simulate digital-space attack patterns in the physical domain by projecting refined 2D adversarial patterns onto 3D faces, substantially enhancing attack success rates." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 126, + 198, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 126, + 198, + 139 + ], + "spans": [ + { + "bbox": [ + 55, + 126, + 198, + 139 + ], + "type": "text", + "content": "3.4. Light Reflection Function" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 143, + 296, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 143, + 296, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 143, + 296, + 275 + ], + "type": "text", + "content": "The efficacy of light-based adversarial attacks hinges on the faithful conversion of digital adversarial patterns into physical light projections. Two primary factors influence this process: (1) the alteration of received light wavelengths due to specular reflection, diffuse reflection, and absorption of adversarial light on facial surfaces, and (2) the interaction between projected light and ambient illumination, resulting in the reception of reflected ambient light. These phenomena modulate the pixel values of the digital pattern. Consequently, formulating these transformations is crucial for mitigating their impacts and preserving attack effectiveness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "text", + "content": "We propose a Light Reflection Function (LRF) that models the process of pattern projection, reflection on skin, and camera capture, formulated as the transformation " + }, + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "inline_equation", + "content": "T_{l}(\\cdot)" + }, + { + "bbox": [ + 55, + 275, + 295, + 312 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 119, + 318, + 294, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 318, + 294, + 332 + ], + "spans": [ + { + "bbox": [ + 119, + 318, + 294, + 332 + ], + "type": "interline_equation", + "content": "x ^ {\\text {m a s k}} = T _ {l} \\left(x ^ {a} + \\tilde {x}\\right) \\odot M. \\tag {5}", + "image_path": "abd7e8d36029d6aaea3c14ef0b2ac3b1c3b6660d60784016b2b6fd6490b81184.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 338, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 434 + ], + "type": "text", + "content": "This process primarily involves modeling the following physical phenomena: the projector emits light patterns corresponding to the RGB values of each pixel in the image. Both projected and ambient light strike the human face and, after absorption and reflection, produce new light patterns. The camera then captures these patterns and converts them into RGB format. This process is principally determined by three factors (" + }, + { + "bbox": [ + 55, + 338, + 296, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 338, + 296, + 434 + ], + "type": "text", + "content": " denotes the wavelength of light):" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 434, + 294, + 493 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 55, + 434, + 280, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 280, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 280, + 446 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 434, + 280, + 446 + ], + "type": "inline_equation", + "content": "S(\\lambda)" + }, + { + "bbox": [ + 55, + 434, + 280, + 446 + ], + "type": "text", + "content": ": the spectral power distribution of the projector." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 446, + 230, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 230, + 457 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 230, + 457 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 446, + 230, + 457 + ], + "type": "inline_equation", + "content": "\\rho (\\lambda)" + }, + { + "bbox": [ + 55, + 446, + 230, + 457 + ], + "type": "text", + "content": ": the spectral reflectance of the skin." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "inline_equation", + "content": "\\sigma(\\lambda)" + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "content": ": the sensitivity of the camera's photodetectors, with " + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "inline_equation", + "content": "\\sigma_x(\\lambda)" + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "inline_equation", + "content": "\\sigma_y(\\lambda)" + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "inline_equation", + "content": "\\sigma_z(\\lambda)" + }, + { + "bbox": [ + 55, + 458, + 294, + 493 + ], + "type": "text", + "content": " representing the impact on red, green, and blue components respectively." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 495, + 296, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 578 + ], + "type": "text", + "content": "To simulate and quantify human visual response to colors, we utilize the CIE XYZ color space model, integrating the color matching functions to calculate an image's coordinates within this space: " + }, + { + "bbox": [ + 55, + 495, + 296, + 578 + ], + "type": "inline_equation", + "content": "X = \\int S(\\lambda) \\rho(\\lambda) \\sigma_x(\\lambda) d\\lambda, Y = \\int S(\\lambda) \\rho(\\lambda) \\sigma_y(\\lambda) d\\lambda, Z = \\int S(\\lambda) \\rho(\\lambda) \\sigma_z(\\lambda) d\\lambda" + }, + { + "bbox": [ + 55, + 495, + 296, + 578 + ], + "type": "text", + "content": ". The interaction between ambient and projected light is considered through linear superposition of their spectral intensities:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 98, + 585, + 295, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 585, + 295, + 599 + ], + "spans": [ + { + "bbox": [ + 98, + 585, + 295, + 599 + ], + "type": "interline_equation", + "content": "S (\\lambda) = S _ {\\text {n a t u r a l}} (\\lambda) + S _ {\\text {p r o j e c t o r}} (\\lambda). \\tag {6}", + "image_path": "65a90c34549b1911147a682e757d609f92f8fc89cb75a350c3c07f7258380f12.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": "Finally, XYZ coordinates are converted to RGB coordinates. Using the PAL standard RGB system as an example, the transformation is:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 110, + 644, + 295, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 644, + 295, + 684 + ], + "spans": [ + { + "bbox": [ + 110, + 644, + 295, + 684 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{l} R \\\\ G \\\\ B \\end{array} \\right] = \\left[ \\begin{array}{c c c} X _ {r} & Y _ {r} & Z _ {r} \\\\ X _ {g} & Y _ {g} & Z _ {g} \\\\ X _ {b} & Y _ {b} & Z _ {b} \\end{array} \\right] \\left[ \\begin{array}{l} X \\\\ Y \\\\ Z \\end{array} \\right]. \\tag {7}", + "image_path": "a2ec6fdb98097c984010ceed6897a7e5cc52eb8f775ef8f1a19f428239c46355.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "S(\\lambda)" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\rho (\\lambda)" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\sigma (\\lambda)" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": ", and PAL color conversion matrix " + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "(X_{r}" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": " etc.) can all be obtained from technical documentation and" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 545, + 136 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 545, + 136 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 545, + 136 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 545, + 136 + ], + "type": "image", + "image_path": "4ec31b0b06a26443f0f649e7ae6eb558b00e5cb25a03d27e5ec18a3323204719.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 140, + 553, + 172 + ], + "lines": [ + { + "bbox": [ + 313, + 140, + 553, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 553, + 172 + ], + "type": "text", + "content": "Figure 4. Light Reflection Function. (c) is obtained by applying our light reflection function to (b), while (d), obtained by projecting (a) in the real world, demonstrates consistency with (c)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 182, + 553, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 553, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 553, + 253 + ], + "type": "text", + "content": "official standards. As shown in Fig. 4, our LRF enables the transformed adversarial 3D mask to closely align with its real-world counterpart. Integrating the LRF within our optimization pipeline ensures that the adversarial 3D mask, when projected into the physical world, maintains its attack effectiveness." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 263, + 470, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 470, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 470, + 276 + ], + "type": "text", + "content": "3.5. Camera Capture Simulation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "content": "The camera's internal Image Signal Processing (ISP) pipeline plays a crucial role in transforming physical scenes into digital RGB images. Variations in ISP configurations can lead to divergent visual characteristics of the same adversarial texture across devices, potentially affecting attack performance. Therefore, we introduce ISP simulation " + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "inline_equation", + "content": "T_{c}(\\cdot)" + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "content": " to model the camera capturing process. To address the non-differentiable nature of traditional ISP processes, we build a differentiable camera ISP proxy network that enables gradient propagation during optimization. The camera ISP proxy network simulates various ISP processes through conditional inputs, focusing on representative parameters from color and tone correction modules, as well as the denoising module, which significantly impact image quality." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "content": "Our camera ISP proxy network is based on the U-Net architecture [16], comprising " + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "content": " convolutions and " + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "content": " max pooling operations in its encoder and decoder. The feature channels expand progressively through \\{32, 64, 128, 256, 512\\}. This structure enables the ISP proxy network to maintain differentiability while simulating diverse camera ISP parameter configurations, thus adapting to various hardware environments." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "content": "We normalize ISP parameters (e.g., brightness, contrast, gamma correction) to [0,1] and concatenate them with feature maps, enabling the ISP proxy network to dynamically adjust image tone, contrast, color balance, and denoising characteristics to flexibly simulate diverse device imaging profiles. To train our camera ISP proxy network, we utilize an undifferentiable camera ISP simulator [15] along with the COCO dataset [12], generating a total of 2,270 data pairs. During training, we employ a composite loss function—including pixel-level MSE loss, perceptual loss, and regularization loss—to ensure high image fidelity and sensitivity to conditional ISP parameters, while maintaining full differentiability for gradient optimization. Our framework leverages the ISP network simulating various lighting ef" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21252" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 542, + 160 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 542, + 160 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 542, + 160 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 542, + 160 + ], + "type": "table", + "html": "
SourceLFW datasetCelebA-HQ dataset
ArcFaceMoblieNetResNetIRAPIArcFaceMoblieNetResNetIRAPI
ArcFace [1]-40.40%25.37%39.22%12.37%-60.80%64.32%62.12%16.49%
MobileNet [4]13.28%-46.98%24.71%12.05%49.50%-66.33%40.80%12.86%
ResNet [3]25.37%54.31%-33.14%18.33%63.49%75.50%-56.35%12.35%
IR [3]22.32%41.44%42.37%-17.86%78.79%78.39%58.79%-14.29%
Ensemble59.09%72.91%75.28%53.52%38.78%90.50%88.29%88.37%88.50%32.84%
", + "image_path": "ac58b178d8b453613e2c8c86a05c44ceacab59038bafe5b95d04169fae84419d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 207, + 542, + 340 + ], + "blocks": [ + { + "bbox": [ + 55, + 163, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 553, + 196 + ], + "type": "text", + "content": "Table 1. Evaluation of black-box impersonation attack. We report the attack success rates (ASR) on ArcFace, MobileNet, ResNet, IR, and a commercial API. Each row represents results using a different source model for the attack. In the ensemble setting, the target model corresponding to each column is excluded from the ensemble used to generate the attack." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 207, + 542, + 340 + ], + "lines": [ + { + "bbox": [ + 65, + 207, + 542, + 340 + ], + "spans": [ + { + "bbox": [ + 65, + 207, + 542, + 340 + ], + "type": "table", + "html": "
DatasetTypeMethodArcFaceFaceNetMobileNetResNetCosFaceAPIAverage
LFWTransfer-basedTAP [27] \\( _{CVPR'21} \\)53.50%46.00%--50.00%10.00%39.89%
AT3D [28] \\( _{CVPR'23} \\)86.25%-91.50%86.50%63.00%45.25%74.50%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-51.11%--48.06%-49.59%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours78.07%52.17%79.49%82.98%78.17%41.43%68.72%
CelebA-HQTransfer-basedTAP [27] \\( _{CVPR'21} \\)65.75%52.50%--58.25%20.00%49.13%
AT3D [28] \\( _{CVPR'23} \\)92.50%-96.25%93.75%87.50%50.25%84.05%
Query-basedAdvSticker [25] \\( _{TPAMI'22} \\)-48.96%--47.73%-48.35%
SOPP [26] \\( _{TPAMI'22} \\)50.28%72.83%--40.08%37.56%50.19%
ProjAttacker Ours95.15%84.47%98.13%97.20%93.20%44.03%85.36%
", + "image_path": "949f29de3c1c60d5e55bf2c4e6a7d0cccdc4e700ad8ad33839e0b125c03611e1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 343, + 553, + 377 + ], + "lines": [ + { + "bbox": [ + 55, + 343, + 553, + 377 + ], + "spans": [ + { + "bbox": [ + 55, + 343, + 553, + 377 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with existing methods. All methods are evaluated under a black-box setting, where TAP [27] and AT3D [28] are transfer-based attacks, while AdvSticker [25], SOPP [26], and ProjAttacker are query-based attacks. The highest and second-highest Attack Success Rates (ASRs) across both datasets are highlighted in red and blue, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 398, + 295, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 398, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 398, + 295, + 422 + ], + "type": "text", + "content": "fects in the physical world to enhance the robustness of adversarial patterns and improve attack efficacy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 434, + 137, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 137, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 137, + 445 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 453, + 173, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 173, + 466 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 173, + 466 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 470, + 295, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 470, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 470, + 295, + 661 + ], + "type": "text", + "content": "Targeted Models. We selected seven face recognition models as our target models, including six representative open-source models (ArcFace [1], MobileNet [4], ResNet [3], FaceNet [17], CosFace [22], IR [3]) and a commercial face recognition API*. For attacking the API, we employed other open-source models as an ensemble of surrogate models. When performing an ensemble attack on one of the models, the remaining models served as surrogate models. In our experiments, we evaluate the attack effectiveness by calculating the cosine similarity of the vectors obtained from the input image pairs. Each model adheres to its respective threshold: if the similarity between two images exceeds the threshold, they are considered the same identity; otherwise, they are considered different identities. Notably, each model is well-trained, achieving an accuracy exceeding " + }, + { + "bbox": [ + 55, + 470, + 295, + 661 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 55, + 470, + 295, + 661 + ], + "type": "text", + "content": " on the LFW dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 662, + 295, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 662, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 662, + 295, + 685 + ], + "type": "text", + "content": "Datasets. We conducted experiments in the digital domain on two extensively employed benchmark datasets: the La-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 398, + 553, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 553, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 553, + 493 + ], + "type": "text", + "content": "beled Faces in the Wild (LFW) [6] and the CelebFaces Attributes High Quality (CelebA-HQ) [9]. For evasion attacks, we randomly selected several pairs of images with the same identity from the dataset, aiming to push the attacker's features away from their true identity. For impersonation attacks, we randomly chose an attacker from the dataset and paired them with several randomly selected victims, creating multiple pairs of images with different identities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 494, + 553, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 553, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 553, + 542 + ], + "type": "text", + "content": "Comparison methods. We compare our proposed ProjAttacker with the following four methods: TAP [27], AdvSticker [25], SOPP [26], and AT3D [28]. All methods are physically realizable." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 543, + 553, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 553, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 553, + 638 + ], + "type": "text", + "content": "Implementation details. All experiments were conducted on a Linux server equipped with two NVIDIA GeForce RTX 3090 GPUs, with all code and algorithms implemented in PyTorch. We set the number of iterations per round to 300 and the learning rate to 0.45. Within the overall framework, the reward step size is set to 0.1. The total number of queries is 25, and if no result is obtained within 25 queries, the attempt is deemed unsuccessful." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 647, + 468, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 468, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 468, + 659 + ], + "type": "text", + "content": "4.2. Attacks in the Digital World" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Black-box Attack. To assess the effectiveness of the attacks, we employ the Attack Success Rate (ASR), a metric that measures the efficacy of attack methodologies by indicating the proportion of successful attacks relative to the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "text", + "content": "\\*https://intl.cloud.tencent.com/product/ facerecognition" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21253" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 71, + 529, + 332 + ], + "blocks": [ + { + "bbox": [ + 82, + 71, + 529, + 332 + ], + "lines": [ + { + "bbox": [ + 82, + 71, + 529, + 332 + ], + "spans": [ + { + "bbox": [ + 82, + 71, + 529, + 332 + ], + "type": "image", + "image_path": "fe71e0915d9a6343c6d6264bd8b0d5aadbdd8ca8575703150445b58d893f6053.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 334, + 555, + 377 + ], + "lines": [ + { + "bbox": [ + 55, + 334, + 555, + 377 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 555, + 377 + ], + "type": "text", + "content": "Figure 5. Attack results of our ProjAttacker in both digital and physical domains. By projecting diverse adversarial patterns onto facial regions, an attacker can induce the face recognition model (CosFace [22]) to misidentify the subject as various victims. Our method exhibits superior flexibility and cost-effectiveness compared to approaches based on wearable material artifacts. Green indicates successful attacks, while red denotes unsuccessful attacks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 389, + 295, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 389, + 295, + 425 + ], + "spans": [ + { + "bbox": [ + 54, + 389, + 295, + 425 + ], + "type": "text", + "content": "total samples. Tab. 1 displays the quantitative results of impersonation attacks under black-box conditions against five different target models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "text", + "content": "As shown in Tab. 1, we can observe: (1) The proposed model ensemble method demonstrates significant efficacy against impersonation attacks on both the LFW and CelebA-HQ datasets. Notably, the highest attack success rate achieved on the LFW dataset is " + }, + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "inline_equation", + "content": "75.28\\%" + }, + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "text", + "content": ", while on the CelebA-HQ dataset, it reaches " + }, + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "inline_equation", + "content": "90.50\\%" + }, + { + "bbox": [ + 54, + 426, + 295, + 593 + ], + "type": "text", + "content": ". (2) The attack success rates on the CelebA-HQ dataset are generally higher than those on the LFW dataset. This can be attributed to the higher quality and resolution of facial images in the CelebA-HQ dataset, which facilitates more effective feature extraction by the models. (3) The ensemble method consistently outperforms models trained individually, indicating that our approach can adaptively adjust model weights to achieve optimal performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 594, + 295, + 713 + ], + "type": "text", + "content": "Comparisons with SOTA Methods. We compare ProjAttacker attack with five existing physically realizable black-box attack methods, as shown in Tab. 2. We conducted experiments on a set of images from the CelebA-HQ dataset. Each target model in the columns is excluded from our ensemble model, strictly adhering to the principles of black-box attacks. Our method outperforms the two baseline query-based approaches, AdvSticker and SOPP, across both datasets. Regarding transfer-based methods, our approach surpasses TAP on the LFW dataset but falls short of" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 317, + 387, + 552, + 454 + ], + "blocks": [ + { + "bbox": [ + 317, + 387, + 552, + 454 + ], + "lines": [ + { + "bbox": [ + 317, + 387, + 552, + 454 + ], + "spans": [ + { + "bbox": [ + 317, + 387, + 552, + 454 + ], + "type": "table", + "html": "
3DLRFISPArcFaceMobileNetResNetAPI
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", + "image_path": "18c7c79c287e8d3a5a4e800c92cf0f31f362c32ef449d246c2f0041fd897db0e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 315, + 455, + 509, + 464 + ], + "lines": [ + { + "bbox": [ + 315, + 455, + 509, + 464 + ], + "spans": [ + { + "bbox": [ + 315, + 455, + 509, + 464 + ], + "type": "text", + "content": "- \"3D\" represents the 3D mask form, as opposed to the 2D mask." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 318, + 464, + 493, + 472 + ], + "lines": [ + { + "bbox": [ + 318, + 464, + 493, + 472 + ], + "spans": [ + { + "bbox": [ + 318, + 464, + 493, + 472 + ], + "type": "text", + "content": "- \"LRF\" means the light reflection function in our pipeline." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 318, + 472, + 499, + 482 + ], + "lines": [ + { + "bbox": [ + 318, + 472, + 499, + 482 + ], + "spans": [ + { + "bbox": [ + 318, + 472, + 499, + 482 + ], + "type": "text", + "content": "- \"ISP\" means the camera ISP proxy network in our pipeline." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 483, + 554, + 505 + ], + "lines": [ + { + "bbox": [ + 314, + 483, + 554, + 505 + ], + "spans": [ + { + "bbox": [ + 314, + 483, + 554, + 505 + ], + "type": "text", + "content": "Table 3. Ablation study in the physical world. We report the ASR of our ProjAttacker attack." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 529, + 555, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 555, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 555, + 577 + ], + "type": "text", + "content": "AT3D. However, on the CelebA-HQ dataset, our method outperforms both TAP and AT3D. These results demonstrate the excellent attack performance of our approach in black-box settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 586, + 476, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 586, + 476, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 586, + 476, + 600 + ], + "type": "text", + "content": "4.3. Attacks in the Physical World" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 605, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 605, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 605, + 555, + 713 + ], + "type": "text", + "content": "Qualitative Analysis. As shown in Fig. 5, we present an attacker, six victims, and their corresponding digital and physical space attacks. Without the light reflection function, the optimized adversarial patterns exhibit diverse colors with high saturation, impeding physical space reproduction. Incorporating the light reflection function facilitates the transfer of digital space adversarial patterns to the physical domain. Physical space attacks demonstrate our method's efficacy in misleading CosFace to misiden" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21254" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 293, + 148 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 293, + 148 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 293, + 148 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 293, + 148 + ], + "type": "image", + "image_path": "84a652497147d894a18e0f18e989c759ae24c830eb7df60aec48534b4c76529b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 151, + 295, + 174 + ], + "lines": [ + { + "bbox": [ + 55, + 151, + 295, + 174 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 295, + 174 + ], + "type": "text", + "content": "Figure 6. Comparison with existing methods. We compare the hiPAA [24] of three physical adversarial attack methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 186, + 295, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 186, + 295, + 245 + ], + "spans": [ + { + "bbox": [ + 54, + 186, + 295, + 245 + ], + "type": "text", + "content": "tify the attacker as different victims with high confidence. Notably, transitioning between victims merely requires altering the projected pattern, offering significant operational convenience. These results highlight our method's flexibility in executing effective attacks in real-world scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 246, + 296, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 246, + 296, + 388 + ], + "spans": [ + { + "bbox": [ + 55, + 246, + 296, + 388 + ], + "type": "text", + "content": "Ablation Study. To quantify the contribution of each module within our proposed framework to the success rate of physical space attacks, we conducted ablation experiments. We systematically removed the 3D, RLF, and ISP modules from a set of attacker-victim image pairs, generating four distinct adversarial patterns for physical testing, including those from the complete framework. The experiments encompassed 50 attacker-victim pairs, with statistical results presented in Tab. 3. We observe that the removal of any single module results in a decrease in Attack Success Rate (ASR). These findings validate the rationale and necessity of each module within our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 389, + 296, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 296, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 296, + 617 + ], + "type": "text", + "content": "Evaluation using hiPAA Metrics. To comprehensively evaluate the performance of physical adversarial attacks, Wei et al. [24] proposed the hiPAA metric, which includes six dimensions: Effectiveness, Stealthiness, Robustness, Practicability, Aesthetics, and Economics. We assess and compare the hiPAA scores of various methods, as illustrated in Fig. 6. Note that Stealthiness, Practicability, and Aesthetics are evaluated through a user study; refer to the supplementary material for more details of our evaluation. We observe that our ProjAttacker attack outperforms TAP in robustness and surpasses AT3D in effectiveness. Additionally, our method significantly outperforms in the Practicability dimension, as it does not require manually crafted 3D-printed masks or patches. For an attacker to mislead the facial recognition system into identifying them as different victims, only the adversarial pattern needs to be switched. This not only reduces costs but also eliminates the need for complex manufacturing processes, enhancing the practicality of real-world applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 624, + 165, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 165, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 165, + 635 + ], + "type": "text", + "content": "4.4. Liveness Detection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "Liveness detection technology primarily encompasses four methods: (1) Transform: Analysis of image Fourier transforms or Local Binary Patterns to discern whether a presented face is genuine or merely a static image. (2) Depth: Utilization of depth sensors or stereo cameras to assess the three-dimensional structure of a face, thereby verifying its" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 553, + 148 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 553, + 148 + ], + "type": "table", + "html": "
MethodTransformDepthMotionMultiBio
TAP [27] CVPR'21✓XXX
AdvSticker [25] TPAMI'22✓✓✓X
SOPP [26] TPAMI'22✓✓✓X
AT3D [28] CVPR'23✓✓XX
ProjAttacker Ours✓✓✓✓
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CTyunBaiduTencentAliyun
Physical Evaluation55/5555/5548/5152/55
", + "image_path": "c4abdce232fbcb4e0934292f0ade24a5cec65abd66301dc5631f1337d05c4781.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 232, + 553, + 255 + ], + "lines": [ + { + "bbox": [ + 313, + 232, + 553, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 553, + 255 + ], + "type": "text", + "content": "Table 5. Bypass rate. The number of successful bypasses achieved by our method across four commercial liveness detection APIs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 276, + 553, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 553, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 553, + 348 + ], + "type": "text", + "content": "authenticity. (3) Motion: Examination and tracking of eye movements, lip motions, and blink frequency to validate the presence of a live subject. (4) MultiBio: Integration of facial vascular flow detection with other biometric identification technologies, such as iris scanning, to provide a multi-tiered security validation approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 348, + 554, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 554, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 554, + 468 + ], + "type": "text", + "content": "Tab. 4 shows that existing physical attack modalities typically require a tangible medium and often rely on partially obstructing the facial features to create adversarial perturbations. In contrast, our method utilizes light as the medium and adopts a non-intrusive attack. This approach avoids obscuring facial biometric features, thus demonstrating higher effectiveness against various liveness detection technologies. Tab. 5 shows that our method achieved successful bypasses across all four commercial liveness detection APIs, with a " + }, + { + "bbox": [ + 313, + 348, + 554, + 468 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 348, + 554, + 468 + ], + "type": "text", + "content": " success rate on CTyun and Baidu in particular." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": "We introduced ProjAttacker, a novel adversarial light attack that effectively compromises both face recognition systems and liveness detection models. Extensive experiments in both digital and physical space demonstrate that ProjAttacker outperforms existing methods, highlighting the vulnerability of current face recognition systems to sophisticated physical attacks. Our findings underscore the pressing need for more robust defense mechanisms to secure biometric systems against potential threats." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": "Ethics Statement. Our research investigates the vulnerabilities of face recognition systems through physical adversarial attacks. Aware of the dual-use potential, we conducted all experiments under strict ethical guidelines, ensuring no compromise of personal data or real-world systems. Our goal is to contribute to the development of more secure face recognition systems. We urge the community to consider both defensive and offensive aspects, promoting responsible application." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21255" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by Hubei Key R&D Project (2022BAA033) and National Natural Science Foundation of China (62171325, 62402365). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 153, + 115, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 153, + 115, + 166 + ], + "spans": [ + { + "bbox": [ + 56, + 153, + 115, + 166 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 173, + 294, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 173, + 294, + 228 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 173, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 173, + 294, + 228 + ], + "type": "text", + "content": "[1] Jiankang Deng, Jia Guo, Jing Yang, Niannan Xue, Irene Kotsia, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. 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To address this issue, we propose a simple three-step approach-Project-Probe-Aggregate (PPA)-that enables parameter-efficient fine-tuning for foundation models without relying on group annotations. Building upon the failure-based debiasing scheme, our method, PPA, improves its two key components: minority samples identification and the robust training algorithm. Specifically, we first train biased classifiers by projecting image features onto the nullspace of class proxies from text encoders. Next, we infer group labels using the biased classifier and probe group targets with prior correction. Finally, we aggregate group weights of each class to produce the debiased classifier. Our theoretical analysis shows that our PPA enhances minority group identification and is Bayes optimal for minimizing the balanced group error, mitigating spurious correlations. Extensive experimental results confirm the effectiveness of our PPA: it outperforms the state-of-the-art by an average worst-group accuracy while requiring less than $0.01\\%$ tunable parameters without training group labels.", + "bbox": [ + 88, + 300, + 485, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 660, + 220, + 676 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-text foundation models [12, 31, 40]—large models pre-trained on web-scale data—are becoming increasingly prevalent in real-world deployments. However, adapting these models to downstream tasks, whether through zero-shot transfer or fine-tuning, remains challenging due to fundamental issues of group robustness: they achieve low average test error but incur high risk on certain groups of examples [3, 44, 47, 48]. This issue becomes particularly pronounced in the presence of spurious correlations [8], where a classifier relies on non-causal relationships that happen to align with class labels in training but break down during deployment. For example, consider the case where \"water", + "bbox": [ + 89, + 685, + 482, + 867 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/98ddfd37b139ea8a93d91224ae93bdb90acf617c3af6cf8027449d6f0894ea84.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodWorst-group Recall (%)Worst-group Precision (%)
CA [48]46.415.6
JTT [21]78.624.1
PPA (ours)80.444.3
", + "bbox": [ + 571, + 266, + 849, + 353 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Table 1. The precision and recall of the worst-group examples (i.e., the group with lowest validation accuracy) identified by biased models on the Waterbird training set [32] using CLIP ResNet-50. Our PPA is more susceptible to supurious features, achieving higher worst-group recall and precision compared to previous methods.", + "bbox": [ + 511, + 363, + 906, + 434 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "birds” predominantly appear in images with a “water” background. When trained on such a dataset, neural networks often rely on the background to recognize the objects.", + "bbox": [ + 511, + 460, + 906, + 507 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a result, several fine-tuning methods have emerged to improve group robustness in foundation models [3, 29, 44, 47, 48]. Unlike conventional robust training frameworks, which typically re-train the entire model [21, 22, 26, 27] (which is computationally expensive) and/or require group labels [1, 32] (which demands additional annotation costs), these fine-tuning methods prioritize parameter and annotation efficiency. They address spurious correlations by optimizing only a small subset of parameters without relying on training group labels. For instance, Zhang and Ré [48] fine-tune a lightweight adapter and You et al. [47] propose to optimize projection layers to improve distributional robustness. In this paper, we build on these ideas by focusing on efficient fine-tuning to enhance group robustness, i.e., training linear probes.", + "bbox": [ + 509, + 507, + 908, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "At a high level, in the absence of group annotations, a common strategy [5, 19, 21, 22, 26, 48, 49] involves first identifying minority groups by training a biased model that easily overfits to spurious features. Subsequently, a debiased model is trained using the inferred group labels. To improve the identification of minority groups, prior work proposes various strategies: [22, 26] employ generalized cross-entropy loss to amplify the model bias, JTT [21] simply trains a model with empirical risk minimization (ERM) and tunes hyperparameters to exacerbate bias, CA [48] leverages the correctness of zero-shot pre", + "bbox": [ + 509, + 734, + 910, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work was done during Beier Zhu's visit at AGI Lab, Westlake University. $\\dagger$ denotes corresponding author.", + "bbox": [ + 89, + 875, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25487", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dictions and [5] uses low-capacity networks to capture spurious features. In this paper, we leverage the pre-trained knowledge from the image-text foundation models to effectively induce bias, further enhancing the identification of minority groups. Specifically, we project out class proxies, provided by the text encoders, from the input image features and use only the remaining information to train the biased classifiers. Intuitively, removing class information forces the model to rely more heavily on spurious features for predictions. We provide theoretical analysis to support this intuition in Proposition 1. Empirically, in Tab. 1, we evaluate the quality of the inferred groups in the training datasets obtained by our method, and compare it to prior approaches [21, 48]. Specifically, we measure precision—the fraction of examples within the identified minor groups that belong to the worst-performing group, and recall—the fraction of examples from the worst-performing group that are captured by the identified minor groups. As expected, our method achieves higher precision and recall, demonstrating superior group identification.", + "bbox": [ + 89, + 90, + 480, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given the inferred groups, typical debiased learning algorithms up-weight/up-sample minority group samples to enhance performance on these challenging instances [5, 10, 17, 21, 26]. However, determining the optimal weights requires careful hyper-parameter tuning and lacks theoretical guidance. Since the goal of debiased training is to minimize the Balanced Group Error (BGE) [22, 36], we propose a methodology designed to achieve this objective directly. Rather than predicting class labels, our method is trained to probe for group targets by compensating group priors into the softmax cross-entropy during training. Afterward, we aggregate group weights of each class to produce the final debiased classifier. We dub our overall debiasing framework Project-Probe-Aggregate (PPA), and demonstrate that it is Bayes optimal for minimizing BGE in Proposition 2.", + "bbox": [ + 89, + 396, + 482, + 623 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 109, + 626, + 341, + 641 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We project out the class proxies offered by the text encoder and train the biased model on the residual image features, with theoretical analysis showing this approach increases reliance on spurious features, improving minority group identification.", + "- We propose a novel debiasing method that is consistent for minimizing the balanced group error. The debiased classifier predicts group labels compensated by group priors and uses weight-space aggregation after fine-tuning to avoid group inference overhead.", + "- We confirm the effectiveness of our proposal across five benchmarks with spurious correlations. With less than $0.01\\%$ of the foundation model parameters, our approach PPA improves the worst group accuracy over the state-of-the-art without training group annotations. Beyond linear probes, we also adapt other parameter-efficient finetuning paradigms (e.g., prompt tuning and adapters) to" + ], + "bbox": [ + 89, + 643, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "show the versatility of the proposed method.", + "bbox": [ + 527, + 90, + 821, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 119, + 653, + 133 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Improving group robustness. There have been numerous works aimed at improving group robustness, which broadly fall into two categories based on whether group labels are available during training. (i) Group supervised methods focus on balancing the contribution of each group during the training phase, such as through re-sampling/reweighting [10, 11, 13, 17, 24, 39], or robust optimization [1, 32, 34]. However, this approach requires additional annotation costs for group labels. In this paper, we focus on (ii) group unsupervised methods, which do not assume the availability of group labels during training [2, 14, 15, 18, 35, 42, 43, 46]. Without group labels, a common strategy is to first train an easily biased model, and then infer groups based on its biased predictions. A robust model is subsequently trained using the inferred group labels through techniques such as importance weighting [21, 26, 30], robust optimization [4, 27], or by learning similar representations for groups within the same class [49]. In this paper, we leverage the general knowledge from image-text foundation models to train a biased classifier by excluding the class proxy information generated by the CLIP text encoder. Note that classifier in [39] also predicts group labels, our approach differs in two key aspects: 1) We further incorporate logit offsets during training, which compensates for group imbalances and leads to lower balanced error. 2) Unlike [39], our method does not require access to ground-truth group labels.", + "bbox": [ + 511, + 143, + 906, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efficient robust fine-tuning for foundation models. The advent of image-text foundation models has led to several efforts to develop efficient group-robust fine-tuning methods [3, 6, 16, 17, 28, 44, 47, 48, 50, 55]. Kirichenko et al. [17] demonstrate that last-layer retraining significantly improves group robustness in pretrained models. Zhang and Ré [48] use contrastive objectives to train adapters, bringing same-class embeddings closer together. Chuang et al. [3] reduce bias in image-text models by removing biased directions in text embeddings. Other works [44, 47] focus on lightweight fine-tuning by optimizing only the projection layers of the vision branch for distributional robustness. Our approach builds on efficient fine-tuning by training only a linear classification head for group targets and further introduces weight-space ensembling after fine-tuning to eliminate the overhead of group inference.", + "bbox": [ + 511, + 551, + 908, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 513, + 806, + 651, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Setup", + "text_level": 1, + "bbox": [ + 513, + 832, + 594, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Considering a classification problem with instances $\\mathbf{x} \\in \\mathcal{X} \\subseteq \\mathbb{R}^d$ and labels $y \\in \\mathcal{Y} = [K]$ . Each data point $(\\mathbf{x}, y)$ has an input attribute $a(\\mathbf{x}) \\in \\mathcal{A}$ that is spuriously correlated", + "bbox": [ + 511, + 854, + 906, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25488", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with the target $y$ . We form $|\\mathcal{G}| = |\\mathcal{A}|\\times |\\mathcal{Y}|$ groups, where each group label $g\\in \\mathcal{G}$ is the combination of the attribute $a$ and the class label $y$ , i.e., $g\\coloneqq (a,y)$ . Given a training dataset $\\mathcal{D} = \\{\\mathbf{x}_i,y_i\\}_{i = 1}^N$ drawn from some unknown distribution $\\mathbb{P}$ , and let $\\mathbb{P}_g$ be the distribution conditioned on $g$ for any $g\\in \\mathcal{G}$ . We assume that spurious attribute annotations are not available for the samples in the training set. Our goal is to train a model $f_{\\theta}:\\mathcal{X}\\to \\mathbb{R}^{K}$ that outputs prediction score, such that it achieves low expected error:", + "bbox": [ + 89, + 90, + 483, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} = \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 237, + 483, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and, more importantly, exhibits group robust, i.e., achieving low worst-group error:", + "bbox": [ + 89, + 273, + 483, + 303 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {\\mathrm {w g}} = \\max _ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P} _ {g}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 313, + 482, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For example, in the Waterbirds [32] dataset, the task is to classify birds $y \\in \\{\\text{waterbird}, \\text{landbird}\\}$ , with the background serving as a spurious attribute ( $a \\in \\{\\text{water}, \\text{land}\\}$ ). A notable pattern is that about $95\\%$ of waterbird images have a water background, causing models to rely on the \"water\" background to predict \"waterbird\". This reliance leads to poor performance on minority groups, such as landbirds with water backgrounds $g =$ (water, landbird). Unlike domain generalization or out-of-distribution evaluation, all groups are present in the training, validation, and test splits. However, the training groups are imbalanced, which can result in poor group robustness on the test set.", + "bbox": [ + 89, + 348, + 483, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Common Strategy for Improving Unsupervised Group Robustness", + "text_level": 1, + "bbox": [ + 89, + 539, + 483, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At a high level, typical methods without access to group labels first train a biased model and then use its biased predictions to infer the groups. Subsequently, a robust model is trained using the inferred group labels. $^{1}$", + "bbox": [ + 89, + 578, + 483, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Taking JTT [21] as an example, it identifies the misclassified samples from ERM model $f_{\\mathrm{erm}}$ as the error set $\\mathcal{E}$ :", + "bbox": [ + 89, + 638, + 483, + 669 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\text {s . t .} f _ {\\operatorname {e r m}} \\left(\\mathbf {x} _ {i}\\right) \\neq y _ {i} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 679, + 482, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "then trains a robust model by weighting the samples in $\\mathcal{E}$ :", + "bbox": [ + 89, + 705, + 483, + 722 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {J T T}} (\\theta , \\mathcal {E}) = \\lambda \\sum_ {(\\mathbf {x}, y) \\in \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta) + \\sum_ {(\\mathbf {x}, y) \\notin \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 743, + 482, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda \\in \\mathbb{R}_+$ is a hyperparameter. The core idea behind JTT is that ERM models tend to fit groups with easily learnable spurious correlations. The samples in $\\mathcal{E}$ are primarily from minority groups where these correlations fail. Upweighting such challenging samples improves the model's performance on the worst-performing groups.", + "bbox": [ + 89, + 787, + 483, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Remark. Improving group robustness without access to group labels hinges on identifying minority groups by training a biased model that overfits on spurious features. Prior work amplifies this bias through various strategies: LfF [26] employs generalized cross-entropy (GCE) loss to bias the first-stage model, JTT [21] tunes hyperparameters to induce bias, and [5] uses low-capacity networks to capture spurious features. In this paper, we enhance bias by projecting out the class proxies from the input features, using only the remaining information for classification. In Sec. 5.1, we prove that this operation increases susceptibility to spurious features, aiding the identification of minority groups.", + "bbox": [ + 511, + 90, + 903, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another key factor is the robust learning algorithm given the pseudo groups. Prior methods address this through importance weighting [21, 26], robust optimization [4, 27], or aligning representations within the same class [49]. Our approach, PPA, predicts pseudo group labels and applies a group prior offset to correct for imbalance. In Sec. 5.2, we prove that our training algorithm effectively mitigates spurious correlations.", + "bbox": [ + 511, + 273, + 905, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methods", + "text_level": 1, + "bbox": [ + 513, + 407, + 612, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Tuning entire pre-trained models is both time-consuming and computationally costly. Recent work [17] shows that simple last-layer retraining performs well on spurious correlation benchmarks. In our approach, the input $\\mathbf{x}$ represents image features encoded by CLIP. We freeze the backbone and learn linear classifiers for efficient fine-tuning.", + "bbox": [ + 511, + 431, + 905, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now present PPA, a simple three-step approach following the common strategy in Sec. 3.2. First, we train a biased classifier by removing the class proxies generated by the CLIP text encoder. Next, we group samples by classification correctness and train a robust model to predict group labels using our proposed group logit adjustment. Finally, we aggregate group weights to produce the final classifier.", + "bbox": [ + 511, + 523, + 905, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Step 1: Project out class proxies. We compute the matrix $Z = [\\mathbf{z}_1, \\ldots, \\mathbf{z}_K]^\\top \\in \\mathbb{R}^{K \\times d}$ whose rows are the text embeddings of the $K$ class names. Specifically, each $\\mathbf{z}_j$ is derived from a prompt like \"a photo of a [CLASS].\" with the class token [CLASS] replaced by the $j$ -th class name. Let $\\Pi \\in \\mathbb{R}^{d \\times d}$ be the projection operator onto the null space of $Z$ , given by:", + "bbox": [ + 511, + 628, + 905, + 736 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Pi = I - Z ^ {\\top} \\left(Z Z ^ {\\top}\\right) ^ {- 1} Z \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 744, + 903, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With $\\Pi$ , the biased model $f_{\\mathsf{b}}: \\mathcal{X} \\to \\mathbb{R}^{K}$ is formulated as a linear classifier parameterized by a matrix $W_{\\mathsf{b}} \\in \\mathbb{R}^{K \\times d}$ :", + "bbox": [ + 511, + 773, + 905, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\mathrm {b}} (\\mathbf {x}) = W _ {\\mathrm {b}} \\Pi \\mathbf {x} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 653, + 818, + 903, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To account for potential class imbalance $^2$ , we apply the logit-adjustment loss [25, 54] to ensure $f_{\\mathrm{b}}$ focuses on spu", + "bbox": [ + 511, + 845, + 905, + 878 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "It is also known as the failure-based debiasing scheme. [26]", + "bbox": [ + 107, + 886, + 431, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "Datasets like Waterbirds [32] and CelebA [23] are class imbalanced.", + "bbox": [ + 529, + 886, + 898, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25489", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "rious features rather than class priors:", + "bbox": [ + 89, + 90, + 341, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathrm {l a}} (y, f _ {\\mathrm {b}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y}}{\\sum_ {y ^ {\\prime} \\in \\mathcal {Y}} \\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y ^ {\\prime}}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 114, + 482, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pi_y$ is the prior of class $y$ . In Proposition 1, we show that our biased model is more easily influenced by spurious correlation.", + "bbox": [ + 89, + 160, + 482, + 203 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 2: Probe with group target. We follow the heuristic of JTT [21] to identify minority groups that $f_{\\mathrm{b}}$ misclassifies:", + "bbox": [ + 89, + 205, + 482, + 236 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {a} (\\mathbf {x}) = \\mathbb {1} [ y \\neq \\operatorname {a r g m a x} _ {y ^ {\\prime} \\in \\mathcal {Y}} f _ {\\mathrm {b}} (\\mathbf {x}) _ {y ^ {\\prime}} ], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 250, + 482, + 275 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}[\\cdot ]$ is the indicator function. Then, each training sample is augmented as $(\\mathbf{x},y,\\hat{a})$ , with the pseudo group defined as the combination of $y$ and $\\hat{a}$ : $\\hat{g} \\coloneqq (y,\\hat{a}) \\in \\hat{\\mathcal{G}}$ .", + "bbox": [ + 89, + 281, + 482, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our approach PPA uses a group scorer, implemented via linear probing, to predict pseudo group labels. Specifically, the group score $h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x}:\\mathcal{X}\\to \\mathbb{R}^{|\\hat{\\mathcal{G}}|}$ is parameterized by $W_{\\mathrm{d}}\\in \\mathbb{R}^{|\\hat{\\mathcal{G}}|\\times d}$ . Let $\\hat{\\beta}$ denote the group priors, we propose the group logit adjustment loss to achieve balanced group performance.:", + "bbox": [ + 89, + 327, + 483, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathbf {g l a}} (\\hat {g}, h _ {\\mathbf {d}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {\\hat {g}}}{\\sum_ {g ^ {\\prime} \\in \\hat {\\mathcal {G}}} \\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {g ^ {\\prime}}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 431, + 482, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau \\in \\mathbb{R}_+$ is a hyper-parameter.", + "bbox": [ + 89, + 484, + 331, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 3: Aggregate weights. The final debiased classifier $f_{\\mathrm{d}}(\\mathbf{x}) : \\mathcal{X} \\to \\mathbb{R}^{K}$ is constructed by aggregating the weights corresponding to each class:", + "bbox": [ + 89, + 500, + 483, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\mathbf {w} _ {y} ^ {\\top} \\mathbf {x}, \\text {w h e r e} \\mathbf {w} _ {y} ^ {\\top} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 566, + 482, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $W_{\\mathrm{d},g}$ represents the weight vector in $W_{\\mathrm{d}}$ associated with group $g$ . This weight-space aggregation transforms group classification into class prediction, eliminating the need for group inference overhead.", + "bbox": [ + 89, + 612, + 482, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Proposition 2, we prove that the debiased model $f_{\\mathrm{d}}(\\mathbf{x})$ is the Bayes optimal classifier for minimizing the balanced group error. Beyond linear classifiers, we also employ other parameter-efficient fine-tuning paradigms (e.g., prompt tuning and adapters) to implement our debiased classifier $f_{\\mathrm{d}}(\\mathbf{x})$ , as detailed in Sec. 6.5. The full pipeline is outlined in Algorithm 1.", + "bbox": [ + 89, + 672, + 483, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Theoretical Analysis", + "text_level": 1, + "bbox": [ + 89, + 791, + 285, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Removal of Class Proxies Amplifies Model Bias", + "text_level": 1, + "bbox": [ + 89, + 816, + 482, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, removing class information forces the model $f_{\\mathrm{b}}$ to rely more on spurious features for predicting class labels. To support this intuition, we provide theoretical evidence in a linear regression setup. Let $\\mathbf{c}$ denote the core features", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Pipeline of PPA", + "text_level": 1, + "bbox": [ + 514, + 90, + 710, + 104 + ], + "page_idx": 3 + }, + { + "type": "ref_text", + "text": "1: Given: Training dataset $\\mathcal{D} = \\{\\mathbf{x}_i, y_i\\}_{i=1}^N$ , class proxies $\\{\\mathbf{z}_j\\}_{j=1}^K$ .", + "bbox": [ + 521, + 111, + 905, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 1: Project", + "bbox": [ + 542, + 143, + 651, + 157 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2: Compute the projection matrix $\\Pi$ using Eq. (5).", + "3: Build $f_{\\mathrm{b}}(\\mathbf{x}) = W_{\\mathrm{b}} \\Pi \\mathbf{x}$ and optimize $W_{\\mathrm{b}}$ using Eq. (7)." + ], + "bbox": [ + 522, + 157, + 897, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 2: Probe", + "bbox": [ + 542, + 188, + 640, + 202 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "4: Identify pseudo groups $\\{\\hat{g}\\}$ via Eq. (8).", + "5: Build $h_{\\mathsf{d}}(\\mathbf{x}) = W_{\\mathsf{d}}\\mathbf{x}$ and optimize $W_{\\mathsf{d}}$ using Eq. (9)." + ], + "bbox": [ + 522, + 203, + 887, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 3: Aggregate", + "bbox": [ + 542, + 234, + 671, + 247 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "6: Construct $f_{\\mathbf{d}}(\\mathbf{x})$ by aggregating weights of $W_{\\mathrm{d}}$ , as in Eq. (10).", + "7: Return $f_{\\mathrm{d}}(\\mathbf{x})$ ." + ], + "bbox": [ + 522, + 247, + 903, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which are stable for predicting the target $y$ and $s$ be a spurious feature. The spurious feature is correlated with the target in the training set, but this correlation may not hold during testing. Suppose we observe $n$ features, stacked as $C = [\\mathbf{c}_1,\\dots ,\\mathbf{c}_n]^\\top \\in \\mathbb{R}^{N\\times d}$ and $\\mathbf{s} = [s_1,\\ldots ,s_n]^\\top \\in \\mathbb{R}^N$ . We are interested in the contribution of the spurious feature $s$ across the following two models:", + "bbox": [ + 511, + 323, + 905, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Full model: Linear regression on the core features $\\mathbf{c}$ and the spurious feature $s$ :", + "bbox": [ + 513, + 428, + 905, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = C \\boldsymbol {\\beta} + \\gamma \\mathbf {s} + \\varepsilon , \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 468, + 903, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ and $\\gamma$ are the weights associated with the core features and the spurious feature, respectively. $\\varepsilon$ is a noise term with an expected value of 0.", + "bbox": [ + 524, + 494, + 905, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Projected model: Applying the projection matrix $\\Pi$ to $C$ to obtain $\\tilde{C} = C\\Pi$ , followed by linear regression on $\\tilde{\\mathbf{c}}$ and $s$ :", + "bbox": [ + 513, + 539, + 905, + 582 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = \\tilde {C} \\tilde {\\boldsymbol {\\beta}} + \\gamma^ {\\prime} \\mathbf {s} + \\varepsilon^ {\\prime}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 583, + 903, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{\\beta}$ and $\\gamma^\\prime$ are the weights for the projected core features and the spurious feature, respectively.", + "bbox": [ + 524, + 604, + 903, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (11), the core features $C$ can be decomposed into the remaining part $\\tilde{C}$ and the projected-out part $C_{\\mathrm{o}}$ .", + "bbox": [ + 511, + 636, + 903, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC = C \\Pi + C (I - \\Pi) = \\tilde {C} + C _ {\\circ}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 674, + 903, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{y}_{\\circ} = C_{\\circ}\\beta$ denote the contribution of the projected-out core features in the full model. Define $M = I - \\tilde{C} (\\tilde{C}^{\\top}\\tilde{C})^{-1}\\tilde{C}^{\\top}$ , $\\mathbf{r_{y_o}} = M\\mathbf{y_o}$ and $\\mathbf{r_s} = M\\mathbf{s}$ . The following proposition states that projecting out core features can make the model more susceptible to spurious feature (proof in Appendix A.1).", + "bbox": [ + 511, + 702, + 905, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1. The weight of the spurious feature after projection is", + "bbox": [ + 511, + 800, + 903, + 828 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma^ {\\prime} = \\gamma + \\frac {\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {y _ {o}}}}{\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {s}}}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 829, + 903, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. Since the denominator $\\mathbf{r_s}^\\top \\mathbf{r_s}$ is non-negative, the model relies more on spurious feature, i.e., $\\gamma^{\\prime} > \\gamma$ , if", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25490", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{r_s}^\\top \\mathbf{r_y_o} > 0$ . In other words, if the spurious feature $s$ is positively correlated with the contribution of projected-out core features $\\mathbf{c}_o$ in the space of $M$ , the weight of the spurious feature will increase. For instance, consider the Waterbirds dataset [32], the spurious feature water background is positively correlated with the core feature waterbird (about $95\\%$ of waterbird images have a water background). If we remove the contribution of waterbird by projection, the weight of the spurious feature water will increase.", + "bbox": [ + 89, + 90, + 483, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Group Classification and Aggregation Mitigate Spurious Correlation", + "text_level": 1, + "bbox": [ + 89, + 234, + 483, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The goal of training a debiased model to avoid spurious correlation is to minimize the Balanced Group Error (BGE) rates [22]:", + "bbox": [ + 89, + 272, + 483, + 316 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {B G E} (f) = \\frac {1}{| \\mathcal {G} |} \\sum_ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x} \\mid g} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 321, + 483, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A natural question is: what is the Bayes optimal classifier for this problem, i.e., $f^{*} \\in \\arg \\min_{f} \\mathsf{BGE}(f)$ . Suppose the underlying group-probabilities $\\mathbb{P}(g|\\mathbf{x}) \\propto \\exp (h^{*}(\\mathbf{x})_{g})$ for unknown scorer: $h^{*}: \\mathcal{X} \\to \\mathbb{R}^{|G|}$ . The Bayes optimal classifier $f^{*}$ is derived from the following Proposition (proof in Appendix A.2):", + "bbox": [ + 89, + 364, + 483, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 2. Let $\\mathcal{G}(y)$ denote the set of groups with class label $y$ , i.e., $\\mathcal{G}(y) := \\{g = (y', a) \\in \\mathcal{G} | y' = y\\}$ . Let $\\beta$ denote the group priors, i.e., $\\beta_g = \\mathbb{P}(g)$ . The prediction:", + "bbox": [ + 89, + 460, + 483, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\ln \\beta\\right) _ {g} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 513, + 480, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is Bayes optimal for the problem in Eq. (15).", + "bbox": [ + 89, + 553, + 385, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark. We translate the unknown distributional class scores based on group logits $h(\\mathbf{x})$ and group priors $\\beta$ . To obtain $f^{*}$ , we can learn the ERM solution for group logits $h(\\mathbf{x})$ . Then, we can minus the logarithm of the group prior $\\ln \\beta$ and aggregate the logits that belongs to $\\mathcal{G}(y)$ to yield the prediction for each class $y$ . In practice, instead predict Eq. (47), we introduce a hyper-parameter $\\tau \\in \\mathbb{R}_{+}$ :", + "bbox": [ + 89, + 574, + 483, + 680 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\tau \\cdot \\ln \\beta\\right) _ {g} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 686, + 483, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by Menon et al. [25], we incorporate logit adjustment into the softmax cross-entropy $\\ell_{\\mathrm{ce}}$ . To do so, we directly enforce group priors offset while learning the group classifier $h_{\\mathrm{d}}(\\mathbf{x})$ . We refer to this as the group logit adjustment loss:", + "bbox": [ + 89, + 726, + 483, + 800 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathrm {g l a}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x})) = \\ell_ {\\mathrm {c e}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 806, + 480, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which is equivalent to Eq. (9). Now, the estimated debiased classifier $f_{\\mathrm{d}}(\\mathbf{x})$ becomes:", + "bbox": [ + 89, + 830, + 483, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} h _ {\\mathrm {d}} (\\mathbf {x}) _ {g} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g} \\mathbf {x} \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 867, + 483, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since $h_{\\mathrm{d}}$ is linear, summing over the output-space is equivalent to aggregating in weight-space, eliminating the overhead of group inference.", + "bbox": [ + 511, + 90, + 905, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 513, + 152, + 645, + 169 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate the effectiveness of our method across five benchmarks: Waterbirds [32], CelebA [23], MetaShift [20], BAR [26], and Living-17 [33]. For brevity, we provide an overview of our experimental setup here; further details can be found in Appendix B.", + "bbox": [ + 511, + 178, + 905, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1. Datasets", + "text_level": 1, + "bbox": [ + 513, + 265, + 614, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Waterbirds [32] was created by overlaying bird images from the Caltech-UCSD Birds [38] dataset onto background scenes from the Places [51] dataset. The target classes are bird types $(\\mathcal{Y} = \\{\\text{waterbird, landbird}\\})$ , while the spurious attribute is the scene type $(A = \\{\\text{water, land}\\})$ . Approximately $95\\%$ of the waterbird training samples are associated with a water background.", + "bbox": [ + 511, + 287, + 905, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CelebA [23] is a real-world dataset comprising 200K celebrity portrait images. The objective is to classify hair color ( $\\mathcal{Y} = \\{\\text{not blond, blond}\\}$ ), with gender ( $\\mathcal{A} = \\{\\text{male, female}\\}$ ) as a spurious attribute. Notably, over $94\\%$ of the blond-haired training images feature women.", + "bbox": [ + 511, + 395, + 905, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MetaShift [20]: The classification objective of MetaShift is to distinguish between cats and dogs, with background type $(\\mathcal{A} = \\{\\mathrm{indoor}, \\mathrm{outdoor}\\})$ as a spurious attribute. Following [45], we use a pre-processed version of MetaShift. In the training set, an inherent bias emerges: cats predominantly appear in indoor scenes, while dogs are more frequently seen in outdoor settings.", + "bbox": [ + 511, + 470, + 905, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BAR [26] is a real-world dataset designed to classify six actions that are each biased toward specific locations. In the original training set, the six action-location pairs are {climbing, rock wall}, {diving, underwater}, {fishing, water surface}, {racing, paved track}, {throwing, playing Field}, and {vaulting, sky}. However, the test set features different locations than the training set. We adapted the dataset for a group robustness setting by incorporating $5\\%$ of the test set images into the training set.", + "bbox": [ + 511, + 577, + 905, + 713 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Living-17 [33]: Each class in the Living-17 represents a broad animal category that encompasses several fine-grained groups. The groups in the training and testing sets can exhibit noticeable visual differences, e.g., the bear class includes images of sloth bear and ice bear. Following [48], $5\\%$ of the images in each testing group are added to the training groups.", + "bbox": [ + 511, + 713, + 905, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.2. Baselines", + "text_level": 1, + "bbox": [ + 513, + 830, + 620, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our PPA against 14 baselines: (1) Zero-shot prompting [31], which matches image features with classification weights by extending class names into pre", + "bbox": [ + 511, + 854, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25491", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/56ad3b33050fe9e116b17808f27f347655b5c1bba8f10348c72708856ef8c956.jpg", + "table_caption": [ + "Table 2. Evaluation of methods for improving group robustness of CLIP models across the Waterbirds, CelebA, and MetaShift benchmarks. Best worst-group accuracy (WGA) of the methods without group labels are in bold." + ], + "table_footnote": [], + "table_body": "
Group labels in train sets?MethodCLIP ResNet-50CLIP ViT-L/14
WaterbirdsCelebAMetaShiftWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvgWGAAvgWGAAvgWGAAvg
✓GroupDRO [32]75.183.884.189.583.287.390.896.488.391.293.997.4
S-CS [44]77.583.275.280.481.289.889.195.786.189.392.397.1
S-CL [44]75.286.075.680.481.588.889.996.087.890.593.196.9
DFR [17]73.283.880.092.883.188.389.797.885.690.892.397.0
XZero-Shot (ZS) [31]54.292.455.088.086.295.426.588.227.085.993.296.2
Group Prompt ZS [31]46.491.753.473.584.695.225.485.866.983.193.996.7
ERM [37]7.993.511.994.775.494.465.997.628.394.784.696.7
WiSE-FT [41]49.891.085.688.686.295.465.997.680.087.493.997.2
Orth-Cali [3]74.078.782.284.486.294.868.884.576.186.292.796.2
AFR [30]48.489.353.494.376.986.873.488.270.085.290.397.1
JTT [21]61.790.660.279.978.589.483.697.375.693.391.294.2
CnC [49]61.287.163.990.378.387.184.597.579.289.392.294.7
CA [48]83.789.490.090.777.985.586.996.284.690.491.393.4
CFR [47]76.977.673.781.181.589.588.296.884.887.893.795.5
PPA (ours)84.388.391.192.190.894.787.294.690.491.094.896.8
", + "bbox": [ + 112, + 128, + 885, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "defined prompts, e.g., \"a photo of a waterbird\". (2) Group-informed prompting [31], which incorporates group descriptions into the prompts, e.g., \"a photo of a waterbird on land\". (3) ERM [37], a linear classifier trained using cross-entropy loss, (4) WiSE-FT [41], which interpolates zero-shot and ERM models in weight-space, (5) Orth-Cali [3], a debiased zero-shot model that removes biased direction in the text embedding. (6) AFR [30], retrans the last layer of an ERM model with a weighted loss that emphasizes examples where the ERM model performs poorly, (7) JTT [21], (see details in Sec. 3.2), (8) CnC [49], which builds upon JTT [21], but it uses a contrastive loss to train the debiased model, (9) CA [48], trains contrastive adapters by learning similar representations across different groups, (10) CFR [47], refines the representation by aligning them with the class centroids via contrastive loss. We also compare with three group-supervised methods - (11) Group-DRO [32], (12) DFR [17], (13) S-CS [44] and (14) S-SL [44].", + "bbox": [ + 91, + 426, + 483, + 713 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.3. Training and Evaluation Details", + "text_level": 1, + "bbox": [ + 89, + 724, + 372, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each method, we evaluate both its worst-group accuracy and average (in-distribution) accuracy on the test sets. We use CLIP ResNet-50 and CLIP ViT-L/14 as primary models, while also reporting results for CLIP ResNet-101, ViT-B/32, and ViT-B/16. Following prior work [44, 47, 48], we freeze the model backbones and train all models using the SGD optimizer for 100 epochs. The hyperparameter $\\tau$ is set to $\\{1.2, 1.0, 0.9, 1.0, 1.0\\}$ for Waterbirds, CelebA, MetaShift, Living-17, and BAR, respectively. Model selection is based on the highest worst-group validation ac", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0a69ffca772b8f70d325d6a67be2ca56f3bef756429522d0e56fc85cea830256.jpg", + "table_caption": [ + "Table 3. Experimental results on Living-17 and BAR benchmarks." + ], + "table_footnote": [], + "table_body": "
MethodCLIP ResNet-50CLIP ViT-L/14
Living-17BARLiving-17BAR
WGAAvgWGAWGAAvgWGA
ZS [31]38.083.274.448.092.381.7
ERM [37]53.390.854.984.098.689.0
JTT [21]44.086.458.578.797.390.2
CA [48]62.090.9-80.097.5-
PPA (ours)65.092.576.885.098.191.5
", + "bbox": [ + 524, + 449, + 895, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "curacy, except for BAR, which lacks a validation set; for BAR, we evaluate the checkpoint from the last epoch. Additionally, since the majority groups in training set do not appear in testing, we measure only the worst-group accuracy for BAR. Further implementation details are provided in Appendix B.", + "bbox": [ + 511, + 621, + 906, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.4. Main Results", + "text_level": 1, + "bbox": [ + 511, + 724, + 651, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 2 presents the worst-group accuracy (WGA) and average (in-distribution) accuracy for all methods on Waterbirds [32], CelebA [23] and MetaShift [20] datasets. Compared to other group-unsupervised debiasing approaches, our PPA achieves superior performance with less than $0.1\\%$ trainable parameters (CLIP ResNet-50 has 25,557,032 parameters, while our model $f_{\\mathrm{d}}(\\cdot)$ has only 4,096 trainable parameters). Specifically, PPA based on CLIP ResNet-50 outperforms the previous state-of-the-art, CFR [47], with improvements of $\\{7.4\\%, 17.4\\%, 9.3\\%$ on Water", + "bbox": [ + 511, + 750, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25492", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ed38fc158e415d5b0585fee8e90f8d82a7fc9ebf3ffd1507c65b146a97549fff.jpg", + "table_caption": [ + "Table 4. PPA consistently improves group robustness for across different efficient fine-tuning paradigms using CLIP ResNet-50. The results using CLIP ViT-L/14 are reported in Appendix B.3." + ], + "table_footnote": [], + "table_body": "
MethodWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvg
Linear Probe + ERM7.993.511.994.775.494.4
Linear Probe + PPA84.388.391.192.190.894.7
CoOp + ERM61.796.235.094.875.492.8
CoOp + PPA83.087.690.092.289.093.3
Adapter + ERM61.496.760.694.484.693.9
Adapter + PPA78.291.891.592.587.793.4
", + "bbox": [ + 91, + 142, + 480, + 271 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8968710afca1d231e08b4fc7e2edb8ce9e694799fc29f531dd3c7bf619f1129e.jpg", + "table_caption": [ + "Table 5. PPA consistently improves group robustness on Waterbirds across different architectures." + ], + "table_footnote": [], + "table_body": "
MethodCLIP RN-101CLIP ViT-B/32CLIP ViT-B/16
WGAAvgWGAAvgWGAAvg
Zero-shot33.690.047.088.834.088.1
ERM LP62.996.556.895.666.596.4
PPA83.689.783.589.184.489.9
", + "bbox": [ + 91, + 321, + 483, + 410 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "birds, CelebA, and MetaShift, respectively. Moreover, PPA is competitive with group-supervised methods that rely on group annotations. Notably, our improvements in worst-group accuracy come at the cost of a modest reduction in in-distribution accuracy, with an average drop of 1.8 points compared to ERM models using CLIP ViT-L/14. In Tab. 3, we report results for the Living-17 [33] and BAR [26] datasets. We again observe that PPA achieves the highest worst-group performance. Notably, for the BAR dataset, where model selection is not performed and only the last checkpoint is used (due to the absence of a validation set), PPA still attains the highest worst-group accuracy.", + "bbox": [ + 88, + 433, + 482, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.5. Further Analysis and Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 625, + 421, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct comprehensive studies to (1) confirm the versatility of our proposed method—specifically, its compatibility with other efficient fine-tuning paradigms and model architectures—and (2) to understand the contribution of each component to the overall improvement.", + "bbox": [ + 89, + 647, + 482, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Extending PPA to other parameter-efficient fine-tuning paradigms. In this paper, we adopt linear probes for efficient fine-tuning of foundation models. We also explore the applicability of PPA to other efficient fine-tuning methods, such as prompt tuning [52, 53] (CoOp) and adapter-based tuning [7, 9, 48] (small bottleneck MLPs). Specifically, we replace the linear probe $h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x}$ in Step 2 of Algorithm 1 with the following models:", + "bbox": [ + 89, + 723, + 482, + 843 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Prompt tuning (CoOp). The prompt for group $i$ is designed as:", + "bbox": [ + 89, + 844, + 482, + 873 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {t} _ {i} = \\left[ V _ {1} ^ {i} \\right] \\left[ V _ {2} ^ {i} \\right] \\dots \\left[ V _ {M} ^ {i} \\right] [ \\mathrm {C L A S S} ], \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 883, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Main component analysis. We present the worst group accuracies using CLIP ResNet-50. \"Proj.\" and \"GLA\" stands for the projection operation in Eq. (6) and group logit adjustment loss in Eq. (9), respectively. \"GT\" means we use the ground-truth group labels for training debiased models.", + "bbox": [ + 511, + 89, + 905, + 159 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6e1688be0758e1acdf7388d0161b314da47d4345ea0c0e25df756dff8474dc1c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Proj.GLAGTWaterbirdsCelebAMetaShift
(a)7.911.975.4
(b)✓54.429.486.2
(c)✓81.670.089.2
(d)✓✓84.391.190.8
(e)✓✓86.891.591.3
", + "bbox": [ + 514, + 169, + 903, + 271 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/968d3613caf16a9b380d8310061728d61acd41c75e257ba572392ddd7eb610ab.jpg", + "image_caption": [ + "(a) Worst Group Recall" + ], + "image_footnote": [], + "bbox": [ + 517, + 286, + 710, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c11a75be58e87d5a88f315b76747205af2449ab235ce7bd0e237e67b8d7e7d4.jpg", + "image_caption": [ + "(b) Worst Group Precision", + "Figure 1. The precision and recall of the worst-group examples on Waterbirds and CelebA using CLIP ResNet-50." + ], + "image_footnote": [], + "bbox": [ + 712, + 286, + 900, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $[V_m^i]$ is a vector with the same dimensionality as the word embedding and serves as a parameter to be optimized. We follow CoOp to set $M = 16$ . [CLASS] represents the word embedding of the class name. Let $\\Phi(\\cdot)$ denote the CLIP text encoder. The group scorer for group $i$ is then defined as:", + "bbox": [ + 524, + 483, + 906, + 573 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nh _ {\\mathrm {d}} ^ {\\mathrm {p t}} (\\mathbf {x}; \\mathbf {t}) _ {i} = \\Phi \\left(\\mathbf {t} _ {i}\\right) ^ {\\top} \\mathbf {x} / \\tau_ {\\text {c l i p}}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 583, + 903, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\tau_{\\mathrm{clip}}$ is the temperature.", + "bbox": [ + 526, + 613, + 725, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Adapter-based tuning. We adopt [7] to transform the visual embeddings $\\mathbf{x} \\in \\mathbb{R}^D$ and the text embedding $Z \\in \\mathbb{R}^{K \\times D}$ using simple 2-layer bottleneck MLPs. Let $H$ denote the feature the hidden-layer dimension. We follow [48] to set $H = 128$ . With ReLU function $\\sigma(\\cdot)$ , visual adapter weights $W_{\\mathrm{v}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{v}}^{2} \\in \\mathbb{R}^{D \\times H}$ and textual adapter weights $W_{\\mathrm{t}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{t}}^{2} \\in \\mathbb{R}^{D \\times H}$ , the input $\\mathbf{x}$ and text embeddings $Z$ are adapted as:", + "bbox": [ + 513, + 628, + 905, + 750 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {x}} = W _ {\\mathrm {v}} ^ {2} \\sigma \\left(W _ {\\mathrm {v}} ^ {1} \\mathbf {x}\\right), \\quad \\tilde {Z} ^ {\\top} = W _ {\\mathrm {t}} ^ {2} \\sigma \\left(W _ {\\mathrm {t}} ^ {1} Z ^ {\\top}\\right). \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 757, + 903, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We then use the normalized adapted embeddings and the temperature $\\tau_{\\mathrm{clip}}$ to output the final scorer:", + "bbox": [ + 526, + 786, + 906, + 816 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nh _ {\\mathrm {d}} ^ {\\mathrm {a t}} (\\mathbf {x}) _ {i} = \\tilde {\\mathbf {z}} ^ {\\top} \\tilde {\\mathbf {x}} / \\tau_ {\\mathrm {c l i p}} \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 825, + 903, + 844 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 4 demonstrates consistent improvements in worstgroup accuracy over the ERM-trained CLIP ResNet-50 model across three benchmarks, highlighting the versatility", + "bbox": [ + 511, + 854, + 905, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25493", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/871b5df7dc7a49b25578953ea1c10f4472d1e9a729297b9c4da76f85e036cd07.jpg", + "image_caption": [ + "Figure 2. Study on the effect of $\\tau$ using CLIP ResNet-50. The optimal worst group accuracy is typically observed around $\\tau = 1.0$ ." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 370, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe5498182cc46adb6652dbb3307426c729a5b6cdf775fd0d330d8db5ab6250f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 88, + 630, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3c4fdc8f48cde3c20fc5f0dd64a7f0d18b289a24cb3fe8ab008e323068914598.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 88, + 883, + 220 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of our PPA across various efficient fine-tuning paradigms. For instance, on the CelebA dataset, our PPA achieves worst-group accuracy improvements of $55.0\\%$ with CoOp and $30.9\\%$ with Adapter. Additionally, integrating PPA with these three fine-tuning methods yields comparable performance. However, linear probing is more computationally efficient than prompt tuning, as the latter requires both forward and backward passes through the large text encoder to update the prompts. It is also more storage-efficient than Adapter-based methods, which introduce additional training parameters, i.e., $\\theta$ and $\\phi$ .", + "bbox": [ + 88, + 272, + 482, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study on model versatility. In Tab. 5, we implement our PPA to various backbone architectures, including CLIP ResNet-101, CLIP ViT-B/32 and CLIP ViT-B/16. We observe consistent performance gains on the worst group accuracy, indicating the model versatility of our PPA.", + "bbox": [ + 88, + 441, + 483, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Main component analysis. In Tab. 6, we provide an ablation study to assess the impact of the projection operation (Proj.) and group logit adjustment (GLA) loss on worst-group accuracy using CLIP ResNet-50. Row (a) represents the ERM-trained linear probing model; Row (b) probes group targets without prior correction; and Row (c) omits the projection operation during training. Row (d) shows results from our proposed method (PPA), while Row (e) replaces estimated group labels with ground-truth labels. Comparing Rows (b) and (d), we observe that adjusting the margin significantly improves worst-group accuracy. In the comparison of Rows (c) and (d), projecting out class proxies enhances group identification, resulting in better worst-group performance. Finally, Row (e) demonstrates the oracle performance using ground-truth labels, revealing that PPA approximates the maximum achievable accuracy, underscoring the importance of accurate pseudo-group labels.", + "bbox": [ + 91, + 518, + 482, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study on the quality of estimated group labels. In the absence of training group labels, we rely on the quality of pseudo group labels inferred from the biased model $f_{\\mathrm{b}}(\\mathbf{x})$ . To evaluate the quality of identified minority groups within the training set, we measure two metrics: precision, defined as the fraction of examples within the identified minority groups that belong to the worst-performing group, and recall, the fraction of examples from the worst-performing", + "bbox": [ + 88, + 780, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "group captured by the identified minority groups. Here, the worst-performing group is defined as the group on which the ERM model achieves the lowest validation accuracy. In Fig. 1, we compare our method with two baselines: (1) ERM, which uses standard empirical risk minimization to train biased models, and (2) CA [48], which leverages zero-shot models to identify minority groups. Our method, PPA, achieves significantly higher recall and precision than both ERM and CA. This improvement is attributed to our biased model $f_{\\mathrm{b}}$ , which relies more heavily on spurious features to make predictions.", + "bbox": [ + 511, + 272, + 903, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study on the hyper-parameter $\\tau$ . We examine the effect of $\\tau \\in \\mathbb{R}_+$ in Eq. (9), as illustrated in Fig. 2 (more details are in Appendix B.6). Specifically, we vary $\\tau$ from 0.0 to 2.0 and report both the worst-group accuracy and average accuracy on the Waterbirds, CelebA, and MetaShift datasets using CLIP ResNet-50. A larger $\\tau$ promotes a greater margin for the minority groups, while $\\tau = 0$ reduces to the standard cross-entropy loss. Our findings reveal that (1) average accuracy decreases monotonically as $\\tau$ increases, and (2) the optimal worst-group accuracy is generally achieved around $\\tau = 1.0$ . For example, the optimal values of $\\tau$ are 1.2, 1.0 and 0.9 for Waterbirds, CelebA and MetaShift, respectively. This aligns with our theoretical analysis, which suggests that the Bayes optimal classifier for minimizing the balanced group error is attained when $\\tau = 1$ .", + "bbox": [ + 511, + 438, + 906, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 679, + 633, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce Project-Probe-Aggregate (PPA), a novel, parameter-efficient fine-tuning framework for enhancing the group robustness of image-text foundation models without relying on training group labels. Our approach improves the identification of minority groups by projecting image features onto the null space of class proxies. Additionally, we design a group logit adjustment loss to minimize balanced group error and mitigate spurious correlations. Through theoretical analysis and empirical evaluations across diverse benchmarks, fine-tuning paradigms and model architectures, we demonstrate that the proposed method effectively enhances robust group performance of foundation models.", + "bbox": [ + 511, + 703, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25494", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 91, + 90, + 240, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore.", + "bbox": [ + 89, + 114, + 483, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 190, + 187, + 205 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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In NeurIPS, 2024. 2" + ], + "bbox": [ + 514, + 90, + 905, + 488 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "25496", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_model.json b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..29f00f1ad7e8356822c1fe84b1641dc027c375e4 --- /dev/null +++ b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_model.json @@ -0,0 +1,2662 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.144, + 0.131, + 0.856, + 0.154 + ], + "angle": 0, + "content": "Project-Probe-Aggregate: Efficient Fine-Tuning for Group Robustness" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.18, + 0.754, + 0.22 + ], + "angle": 0, + "content": "Beier Zhu\\(^{1,2}\\) Jiequan Cui\\(^{1}\\) Hanwang Zhang\\(^{1}\\) Chi Zhang\\(^{2\\dagger}\\) \n\\(^{1}\\)Nanyang Technological University, \\(^{2}\\)Westlake University" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.22, + 0.83, + 0.235 + ], + "angle": 0, + "content": "{beier.zhu, jiequan.cui, hanwangzhang}@ntu.edu.sg, chizhang@westlake.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.301, + 0.486, + 0.633 + ], + "angle": 0, + "content": "While image-text foundation models have succeeded across diverse downstream tasks, they still face challenges in the presence of spurious correlations between the input and label. To address this issue, we propose a simple three-step approach-Project-Probe-Aggregate (PPA)-that enables parameter-efficient fine-tuning for foundation models without relying on group annotations. Building upon the failure-based debiasing scheme, our method, PPA, improves its two key components: minority samples identification and the robust training algorithm. Specifically, we first train biased classifiers by projecting image features onto the nullspace of class proxies from text encoders. Next, we infer group labels using the biased classifier and probe group targets with prior correction. Finally, we aggregate group weights of each class to produce the debiased classifier. Our theoretical analysis shows that our PPA enhances minority group identification and is Bayes optimal for minimizing the balanced group error, mitigating spurious correlations. Extensive experimental results confirm the effectiveness of our PPA: it outperforms the state-of-the-art by an average worst-group accuracy while requiring less than \\(0.01\\%\\) tunable parameters without training group labels." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.661, + 0.222, + 0.677 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.686, + 0.483, + 0.868 + ], + "angle": 0, + "content": "Image-text foundation models [12, 31, 40]—large models pre-trained on web-scale data—are becoming increasingly prevalent in real-world deployments. However, adapting these models to downstream tasks, whether through zero-shot transfer or fine-tuning, remains challenging due to fundamental issues of group robustness: they achieve low average test error but incur high risk on certain groups of examples [3, 44, 47, 48]. This issue becomes particularly pronounced in the presence of spurious correlations [8], where a classifier relies on non-causal relationships that happen to align with class labels in training but break down during deployment. For example, consider the case where \"water" + }, + { + "type": "table", + "bbox": [ + 0.572, + 0.267, + 0.851, + 0.354 + ], + "angle": 0, + "content": "
MethodWorst-group Recall (%)Worst-group Precision (%)
CA [48]46.415.6
JTT [21]78.624.1
PPA (ours)80.444.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.364, + 0.907, + 0.435 + ], + "angle": 0, + "content": "Table 1. The precision and recall of the worst-group examples (i.e., the group with lowest validation accuracy) identified by biased models on the Waterbird training set [32] using CLIP ResNet-50. Our PPA is more susceptible to supurious features, achieving higher worst-group recall and precision compared to previous methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.462, + 0.907, + 0.508 + ], + "angle": 0, + "content": "birds” predominantly appear in images with a “water” background. When trained on such a dataset, neural networks often rely on the background to recognize the objects." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.508, + 0.909, + 0.735 + ], + "angle": 0, + "content": "As a result, several fine-tuning methods have emerged to improve group robustness in foundation models [3, 29, 44, 47, 48]. Unlike conventional robust training frameworks, which typically re-train the entire model [21, 22, 26, 27] (which is computationally expensive) and/or require group labels [1, 32] (which demands additional annotation costs), these fine-tuning methods prioritize parameter and annotation efficiency. They address spurious correlations by optimizing only a small subset of parameters without relying on training group labels. For instance, Zhang and Ré [48] fine-tune a lightweight adapter and You et al. [47] propose to optimize projection layers to improve distributional robustness. In this paper, we build on these ideas by focusing on efficient fine-tuning to enhance group robustness, i.e., training linear probes." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.735, + 0.911, + 0.903 + ], + "angle": 0, + "content": "At a high level, in the absence of group annotations, a common strategy [5, 19, 21, 22, 26, 48, 49] involves first identifying minority groups by training a biased model that easily overfits to spurious features. Subsequently, a debiased model is trained using the inferred group labels. To improve the identification of minority groups, prior work proposes various strategies: [22, 26] employ generalized cross-entropy loss to amplify the model bias, JTT [21] simply trains a model with empirical risk minimization (ERM) and tunes hyperparameters to exacerbate bias, CA [48] leverages the correctness of zero-shot pre" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.875, + 0.483, + 0.901 + ], + "angle": 0, + "content": "This work was done during Beier Zhu's visit at AGI Lab, Westlake University. \\(\\dagger\\) denotes corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25487" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.394 + ], + "angle": 0, + "content": "dictions and [5] uses low-capacity networks to capture spurious features. In this paper, we leverage the pre-trained knowledge from the image-text foundation models to effectively induce bias, further enhancing the identification of minority groups. Specifically, we project out class proxies, provided by the text encoders, from the input image features and use only the remaining information to train the biased classifiers. Intuitively, removing class information forces the model to rely more heavily on spurious features for predictions. We provide theoretical analysis to support this intuition in Proposition 1. Empirically, in Tab. 1, we evaluate the quality of the inferred groups in the training datasets obtained by our method, and compare it to prior approaches [21, 48]. Specifically, we measure precision—the fraction of examples within the identified minor groups that belong to the worst-performing group, and recall—the fraction of examples from the worst-performing group that are captured by the identified minor groups. As expected, our method achieves higher precision and recall, demonstrating superior group identification." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.483, + 0.624 + ], + "angle": 0, + "content": "Given the inferred groups, typical debiased learning algorithms up-weight/up-sample minority group samples to enhance performance on these challenging instances [5, 10, 17, 21, 26]. However, determining the optimal weights requires careful hyper-parameter tuning and lacks theoretical guidance. Since the goal of debiased training is to minimize the Balanced Group Error (BGE) [22, 36], we propose a methodology designed to achieve this objective directly. Rather than predicting class labels, our method is trained to probe for group targets by compensating group priors into the softmax cross-entropy during training. Afterward, we aggregate group weights of each class to produce the final debiased classifier. We dub our overall debiasing framework Project-Probe-Aggregate (PPA), and demonstrate that it is Bayes optimal for minimizing BGE in Proposition 2." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.627, + 0.342, + 0.642 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.645, + 0.483, + 0.719 + ], + "angle": 0, + "content": "- We project out the class proxies offered by the text encoder and train the biased model on the residual image features, with theoretical analysis showing this approach increases reliance on spurious features, improving minority group identification." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.72, + 0.483, + 0.795 + ], + "angle": 0, + "content": "- We propose a novel debiasing method that is consistent for minimizing the balanced group error. The debiased classifier predicts group labels compensated by group priors and uses weight-space aggregation after fine-tuning to avoid group inference overhead." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.796, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- We confirm the effectiveness of our proposal across five benchmarks with spurious correlations. With less than \\(0.01\\%\\) of the foundation model parameters, our approach PPA improves the worst group accuracy over the state-of-the-art without training group annotations. Beyond linear probes, we also adapt other parameter-efficient finetuning paradigms (e.g., prompt tuning and adapters) to" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.645, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.092, + 0.822, + 0.107 + ], + "angle": 0, + "content": "show the versatility of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.12, + 0.655, + 0.135 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.145, + 0.907, + 0.553 + ], + "angle": 0, + "content": "Improving group robustness. There have been numerous works aimed at improving group robustness, which broadly fall into two categories based on whether group labels are available during training. (i) Group supervised methods focus on balancing the contribution of each group during the training phase, such as through re-sampling/reweighting [10, 11, 13, 17, 24, 39], or robust optimization [1, 32, 34]. However, this approach requires additional annotation costs for group labels. In this paper, we focus on (ii) group unsupervised methods, which do not assume the availability of group labels during training [2, 14, 15, 18, 35, 42, 43, 46]. Without group labels, a common strategy is to first train an easily biased model, and then infer groups based on its biased predictions. A robust model is subsequently trained using the inferred group labels through techniques such as importance weighting [21, 26, 30], robust optimization [4, 27], or by learning similar representations for groups within the same class [49]. In this paper, we leverage the general knowledge from image-text foundation models to train a biased classifier by excluding the class proxy information generated by the CLIP text encoder. Note that classifier in [39] also predicts group labels, our approach differs in two key aspects: 1) We further incorporate logit offsets during training, which compensates for group imbalances and leads to lower balanced error. 2) Unlike [39], our method does not require access to ground-truth group labels." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.553, + 0.909, + 0.795 + ], + "angle": 0, + "content": "Efficient robust fine-tuning for foundation models. The advent of image-text foundation models has led to several efforts to develop efficient group-robust fine-tuning methods [3, 6, 16, 17, 28, 44, 47, 48, 50, 55]. Kirichenko et al. [17] demonstrate that last-layer retraining significantly improves group robustness in pretrained models. Zhang and Ré [48] use contrastive objectives to train adapters, bringing same-class embeddings closer together. Chuang et al. [3] reduce bias in image-text models by removing biased directions in text embeddings. Other works [44, 47] focus on lightweight fine-tuning by optimizing only the projection layers of the vision branch for distributional robustness. Our approach builds on efficient fine-tuning by training only a linear classification head for group targets and further introduces weight-space ensembling after fine-tuning to eliminate the overhead of group inference." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.808, + 0.652, + 0.823 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.833, + 0.596, + 0.849 + ], + "angle": 0, + "content": "3.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Considering a classification problem with instances \\(\\mathbf{x} \\in \\mathcal{X} \\subseteq \\mathbb{R}^d\\) and labels \\(y \\in \\mathcal{Y} = [K]\\). Each data point \\((\\mathbf{x}, y)\\) has an input attribute \\(a(\\mathbf{x}) \\in \\mathcal{A}\\) that is spuriously correlated" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25488" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.228 + ], + "angle": 0, + "content": "with the target \\(y\\). We form \\(|\\mathcal{G}| = |\\mathcal{A}|\\times |\\mathcal{Y}|\\) groups, where each group label \\(g\\in \\mathcal{G}\\) is the combination of the attribute \\(a\\) and the class label \\(y\\), i.e., \\(g\\coloneqq (a,y)\\). Given a training dataset \\(\\mathcal{D} = \\{\\mathbf{x}_i,y_i\\}_{i = 1}^N\\) drawn from some unknown distribution \\(\\mathbb{P}\\), and let \\(\\mathbb{P}_g\\) be the distribution conditioned on \\(g\\) for any \\(g\\in \\mathcal{G}\\). We assume that spurious attribute annotations are not available for the samples in the training set. Our goal is to train a model \\(f_{\\theta}:\\mathcal{X}\\to \\mathbb{R}^{K}\\) that outputs prediction score, such that it achieves low expected error:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.238, + 0.484, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} = \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.274, + 0.484, + 0.304 + ], + "angle": 0, + "content": "and, more importantly, exhibits group robust, i.e., achieving low worst-group error:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.314, + 0.483, + 0.34 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {\\mathrm {w g}} = \\max _ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P} _ {g}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.349, + 0.484, + 0.532 + ], + "angle": 0, + "content": "For example, in the Waterbirds [32] dataset, the task is to classify birds \\( y \\in \\{\\text{waterbird}, \\text{landbird}\\} \\), with the background serving as a spurious attribute (\\( a \\in \\{\\text{water}, \\text{land}\\} \\)). A notable pattern is that about \\( 95\\% \\) of waterbird images have a water background, causing models to rely on the \"water\" background to predict \"waterbird\". This reliance leads to poor performance on minority groups, such as landbirds with water backgrounds \\( g = \\) (water, landbird). Unlike domain generalization or out-of-distribution evaluation, all groups are present in the training, validation, and test splits. However, the training groups are imbalanced, which can result in poor group robustness on the test set." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.54, + 0.484, + 0.571 + ], + "angle": 0, + "content": "3.2. Common Strategy for Improving Unsupervised Group Robustness" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.579, + 0.484, + 0.638 + ], + "angle": 0, + "content": "At a high level, typical methods without access to group labels first train a biased model and then use its biased predictions to infer the groups. Subsequently, a robust model is trained using the inferred group labels.\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.639, + 0.484, + 0.67 + ], + "angle": 0, + "content": "Taking JTT [21] as an example, it identifies the misclassified samples from ERM model \\( f_{\\mathrm{erm}} \\) as the error set \\( \\mathcal{E} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.68, + 0.483, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\text {s . t .} f _ {\\operatorname {e r m}} \\left(\\mathbf {x} _ {i}\\right) \\neq y _ {i} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.706, + 0.484, + 0.723 + ], + "angle": 0, + "content": "then trains a robust model by weighting the samples in \\(\\mathcal{E}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.744, + 0.483, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {J T T}} (\\theta , \\mathcal {E}) = \\lambda \\sum_ {(\\mathbf {x}, y) \\in \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta) + \\sum_ {(\\mathbf {x}, y) \\notin \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.788, + 0.484, + 0.88 + ], + "angle": 0, + "content": "where \\(\\lambda \\in \\mathbb{R}_+\\) is a hyperparameter. The core idea behind JTT is that ERM models tend to fit groups with easily learnable spurious correlations. The samples in \\(\\mathcal{E}\\) are primarily from minority groups where these correlations fail. Upweighting such challenging samples improves the model's performance on the worst-performing groups." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.273 + ], + "angle": 0, + "content": "Remark. Improving group robustness without access to group labels hinges on identifying minority groups by training a biased model that overfits on spurious features. Prior work amplifies this bias through various strategies: LfF [26] employs generalized cross-entropy (GCE) loss to bias the first-stage model, JTT [21] tunes hyperparameters to induce bias, and [5] uses low-capacity networks to capture spurious features. In this paper, we enhance bias by projecting out the class proxies from the input features, using only the remaining information for classification. In Sec. 5.1, we prove that this operation increases susceptibility to spurious features, aiding the identification of minority groups." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.274, + 0.906, + 0.393 + ], + "angle": 0, + "content": "Another key factor is the robust learning algorithm given the pseudo groups. Prior methods address this through importance weighting [21, 26], robust optimization [4, 27], or aligning representations within the same class [49]. Our approach, PPA, predicts pseudo group labels and applies a group prior offset to correct for imbalance. In Sec. 5.2, we prove that our training algorithm effectively mitigates spurious correlations." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.408, + 0.613, + 0.423 + ], + "angle": 0, + "content": "4. Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.906, + 0.524 + ], + "angle": 0, + "content": "Tuning entire pre-trained models is both time-consuming and computationally costly. Recent work [17] shows that simple last-layer retraining performs well on spurious correlation benchmarks. In our approach, the input \\(\\mathbf{x}\\) represents image features encoded by CLIP. We freeze the backbone and learn linear classifiers for efficient fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.524, + 0.906, + 0.63 + ], + "angle": 0, + "content": "We now present PPA, a simple three-step approach following the common strategy in Sec. 3.2. First, we train a biased classifier by removing the class proxies generated by the CLIP text encoder. Next, we group samples by classification correctness and train a robust model to predict group labels using our proposed group logit adjustment. Finally, we aggregate group weights to produce the final classifier." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.906, + 0.737 + ], + "angle": 0, + "content": "Step 1: Project out class proxies. We compute the matrix \\( Z = [\\mathbf{z}_1, \\ldots, \\mathbf{z}_K]^\\top \\in \\mathbb{R}^{K \\times d} \\) whose rows are the text embeddings of the \\( K \\) class names. Specifically, each \\( \\mathbf{z}_j \\) is derived from a prompt like \"a photo of a [CLASS].\" with the class token [CLASS] replaced by the \\( j \\)-th class name. Let \\( \\Pi \\in \\mathbb{R}^{d \\times d} \\) be the projection operator onto the null space of \\( Z \\), given by:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.746, + 0.905, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\Pi = I - Z ^ {\\top} \\left(Z Z ^ {\\top}\\right) ^ {- 1} Z \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.775, + 0.906, + 0.807 + ], + "angle": 0, + "content": "With \\(\\Pi\\), the biased model \\(f_{\\mathsf{b}}: \\mathcal{X} \\to \\mathbb{R}^{K}\\) is formulated as a linear classifier parameterized by a matrix \\(W_{\\mathsf{b}} \\in \\mathbb{R}^{K \\times d}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.655, + 0.819, + 0.905, + 0.836 + ], + "angle": 0, + "content": "\\[\nf _ {\\mathrm {b}} (\\mathbf {x}) = W _ {\\mathrm {b}} \\Pi \\mathbf {x} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.847, + 0.906, + 0.879 + ], + "angle": 0, + "content": "To account for potential class imbalance\\(^2\\), we apply the logit-adjustment loss [25, 54] to ensure \\( f_{\\mathrm{b}} \\) focuses on spu" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.432, + 0.901 + ], + "angle": 0, + "content": "It is also known as the failure-based debiasing scheme. [26]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.531, + 0.887, + 0.9, + 0.901 + ], + "angle": 0, + "content": "Datasets like Waterbirds [32] and CelebA [23] are class imbalanced." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25489" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.342, + 0.106 + ], + "angle": 0, + "content": "rious features rather than class priors:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.116, + 0.483, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathrm {l a}} (y, f _ {\\mathrm {b}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y}}{\\sum_ {y ^ {\\prime} \\in \\mathcal {Y}} \\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y ^ {\\prime}}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.161, + 0.483, + 0.204 + ], + "angle": 0, + "content": "where \\(\\pi_y\\) is the prior of class \\(y\\). In Proposition 1, we show that our biased model is more easily influenced by spurious correlation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.206, + 0.483, + 0.237 + ], + "angle": 0, + "content": "Step 2: Probe with group target. We follow the heuristic of JTT [21] to identify minority groups that \\( f_{\\mathrm{b}} \\) misclassifies:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.25, + 0.483, + 0.276 + ], + "angle": 0, + "content": "\\[\n\\hat {a} (\\mathbf {x}) = \\mathbb {1} [ y \\neq \\operatorname {a r g m a x} _ {y ^ {\\prime} \\in \\mathcal {Y}} f _ {\\mathrm {b}} (\\mathbf {x}) _ {y ^ {\\prime}} ], \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.282, + 0.483, + 0.328 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}[\\cdot ]\\) is the indicator function. Then, each training sample is augmented as \\((\\mathbf{x},y,\\hat{a})\\), with the pseudo group defined as the combination of \\(y\\) and \\(\\hat{a}\\): \\(\\hat{g} \\coloneqq (y,\\hat{a}) \\in \\hat{\\mathcal{G}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.328, + 0.484, + 0.422 + ], + "angle": 0, + "content": "Our approach PPA uses a group scorer, implemented via linear probing, to predict pseudo group labels. Specifically, the group score \\( h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x}:\\mathcal{X}\\to \\mathbb{R}^{|\\hat{\\mathcal{G}}|} \\) is parameterized by \\( W_{\\mathrm{d}}\\in \\mathbb{R}^{|\\hat{\\mathcal{G}}|\\times d} \\). Let \\( \\hat{\\beta} \\) denote the group priors, we propose the group logit adjustment loss to achieve balanced group performance.:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.433, + 0.483, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathbf {g l a}} (\\hat {g}, h _ {\\mathbf {d}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {\\hat {g}}}{\\sum_ {g ^ {\\prime} \\in \\hat {\\mathcal {G}}} \\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {g ^ {\\prime}}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.485, + 0.333, + 0.499 + ], + "angle": 0, + "content": "where \\(\\tau \\in \\mathbb{R}_+\\) is a hyper-parameter." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.484, + 0.545 + ], + "angle": 0, + "content": "Step 3: Aggregate weights. The final debiased classifier \\( f_{\\mathrm{d}}(\\mathbf{x}) : \\mathcal{X} \\to \\mathbb{R}^{K} \\) is constructed by aggregating the weights corresponding to each class:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.568, + 0.483, + 0.605 + ], + "angle": 0, + "content": "\\[\nf _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\mathbf {w} _ {y} ^ {\\top} \\mathbf {x}, \\text {w h e r e} \\mathbf {w} _ {y} ^ {\\top} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.483, + 0.673 + ], + "angle": 0, + "content": "Here, \\( W_{\\mathrm{d},g} \\) represents the weight vector in \\( W_{\\mathrm{d}} \\) associated with group \\( g \\). This weight-space aggregation transforms group classification into class prediction, eliminating the need for group inference overhead." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.484, + 0.78 + ], + "angle": 0, + "content": "In Proposition 2, we prove that the debiased model \\( f_{\\mathrm{d}}(\\mathbf{x}) \\) is the Bayes optimal classifier for minimizing the balanced group error. Beyond linear classifiers, we also employ other parameter-efficient fine-tuning paradigms (e.g., prompt tuning and adapters) to implement our debiased classifier \\( f_{\\mathrm{d}}(\\mathbf{x}) \\), as detailed in Sec. 6.5. The full pipeline is outlined in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.792, + 0.287, + 0.809 + ], + "angle": 0, + "content": "5. Theoretical Analysis" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.817, + 0.483, + 0.833 + ], + "angle": 0, + "content": "5.1. Removal of Class Proxies Amplifies Model Bias" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Intuitively, removing class information forces the model \\( f_{\\mathrm{b}} \\) to rely more on spurious features for predicting class labels. To support this intuition, we provide theoretical evidence in a linear regression setup. Let \\( \\mathbf{c} \\) denote the core features" + }, + { + "type": "title", + "bbox": [ + 0.516, + 0.092, + 0.712, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Pipeline of PPA" + }, + { + "type": "ref_text", + "bbox": [ + 0.522, + 0.112, + 0.906, + 0.145 + ], + "angle": 0, + "content": "1: Given: Training dataset \\(\\mathcal{D} = \\{\\mathbf{x}_i, y_i\\}_{i=1}^N\\), class proxies \\(\\{\\mathbf{z}_j\\}_{j=1}^K\\)." + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.145, + 0.652, + 0.158 + ], + "angle": 0, + "content": "Step 1: Project" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.158, + 0.856, + 0.173 + ], + "angle": 0, + "content": "2: Compute the projection matrix \\(\\Pi\\) using Eq. (5)." + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.173, + 0.898, + 0.188 + ], + "angle": 0, + "content": "3: Build \\( f_{\\mathrm{b}}(\\mathbf{x}) = W_{\\mathrm{b}} \\Pi \\mathbf{x} \\) and optimize \\( W_{\\mathrm{b}} \\) using Eq. (7)." + }, + { + "type": "list", + "bbox": [ + 0.524, + 0.158, + 0.898, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.189, + 0.642, + 0.203 + ], + "angle": 0, + "content": "Step 2: Probe" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.204, + 0.803, + 0.219 + ], + "angle": 0, + "content": "4: Identify pseudo groups \\(\\{\\hat{g}\\}\\) via Eq. (8)." + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.219, + 0.888, + 0.234 + ], + "angle": 0, + "content": "5: Build \\( h_{\\mathsf{d}}(\\mathbf{x}) = W_{\\mathsf{d}}\\mathbf{x} \\) and optimize \\( W_{\\mathsf{d}} \\) using Eq. (9)." + }, + { + "type": "list", + "bbox": [ + 0.524, + 0.204, + 0.888, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.235, + 0.672, + 0.248 + ], + "angle": 0, + "content": "Step 3: Aggregate" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.248, + 0.905, + 0.279 + ], + "angle": 0, + "content": "6: Construct \\( f_{\\mathbf{d}}(\\mathbf{x}) \\) by aggregating weights of \\( W_{\\mathrm{d}} \\), as in Eq. (10)." + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.28, + 0.641, + 0.294 + ], + "angle": 0, + "content": "7: Return \\( f_{\\mathrm{d}}(\\mathbf{x}) \\)." + }, + { + "type": "list", + "bbox": [ + 0.524, + 0.248, + 0.905, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.906, + 0.428 + ], + "angle": 0, + "content": "which are stable for predicting the target \\(y\\) and \\(s\\) be a spurious feature. The spurious feature is correlated with the target in the training set, but this correlation may not hold during testing. Suppose we observe \\(n\\) features, stacked as \\(C = [\\mathbf{c}_1,\\dots ,\\mathbf{c}_n]^\\top \\in \\mathbb{R}^{N\\times d}\\) and \\(\\mathbf{s} = [s_1,\\ldots ,s_n]^\\top \\in \\mathbb{R}^N\\). We are interested in the contribution of the spurious feature \\(s\\) across the following two models:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.429, + 0.906, + 0.459 + ], + "angle": 0, + "content": "- Full model: Linear regression on the core features \\(\\mathbf{c}\\) and the spurious feature \\(s\\):" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.469, + 0.905, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = C \\boldsymbol {\\beta} + \\gamma \\mathbf {s} + \\varepsilon , \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.495, + 0.906, + 0.539 + ], + "angle": 0, + "content": "where \\(\\beta\\) and \\(\\gamma\\) are the weights associated with the core features and the spurious feature, respectively. \\(\\varepsilon\\) is a noise term with an expected value of 0." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.54, + 0.906, + 0.583 + ], + "angle": 0, + "content": "- Projected model: Applying the projection matrix \\(\\Pi\\) to \\(C\\) to obtain \\(\\tilde{C} = C\\Pi\\), followed by linear regression on \\(\\tilde{\\mathbf{c}}\\) and \\(s\\):" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.584, + 0.905, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = \\tilde {C} \\tilde {\\boldsymbol {\\beta}} + \\gamma^ {\\prime} \\mathbf {s} + \\varepsilon^ {\\prime}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.605, + 0.905, + 0.636 + ], + "angle": 0, + "content": "where \\(\\tilde{\\beta}\\) and \\(\\gamma^\\prime\\) are the weights for the projected core features and the spurious feature, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.637, + 0.905, + 0.667 + ], + "angle": 0, + "content": "In Eq. (11), the core features \\(C\\) can be decomposed into the remaining part \\(\\tilde{C}\\) and the projected-out part \\(C_{\\mathrm{o}}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.675, + 0.905, + 0.693 + ], + "angle": 0, + "content": "\\[\nC = C \\Pi + C (I - \\Pi) = \\tilde {C} + C _ {\\circ}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.906, + 0.793 + ], + "angle": 0, + "content": "Let \\(\\mathbf{y}_{\\circ} = C_{\\circ}\\beta\\) denote the contribution of the projected-out core features in the full model. Define \\(M = I - \\tilde{C} (\\tilde{C}^{\\top}\\tilde{C})^{-1}\\tilde{C}^{\\top}\\), \\(\\mathbf{r_{y_o}} = M\\mathbf{y_o}\\) and \\(\\mathbf{r_s} = M\\mathbf{s}\\). The following proposition states that projecting out core features can make the model more susceptible to spurious feature (proof in Appendix A.1)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.801, + 0.905, + 0.829 + ], + "angle": 0, + "content": "Proposition 1. The weight of the spurious feature after projection is" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.83, + 0.905, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\gamma^ {\\prime} = \\gamma + \\frac {\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {y _ {o}}}}{\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {s}}}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Remark. Since the denominator \\(\\mathbf{r_s}^\\top \\mathbf{r_s}\\) is non-negative, the model relies more on spurious feature, i.e., \\(\\gamma^{\\prime} > \\gamma\\), if" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25490" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.228 + ], + "angle": 0, + "content": "\\(\\mathbf{r_s}^\\top \\mathbf{r_y_o} > 0\\). In other words, if the spurious feature \\(s\\) is positively correlated with the contribution of projected-out core features \\(\\mathbf{c}_o\\) in the space of \\(M\\), the weight of the spurious feature will increase. For instance, consider the Waterbirds dataset [32], the spurious feature water background is positively correlated with the core feature waterbird (about \\(95\\%\\) of waterbird images have a water background). If we remove the contribution of waterbird by projection, the weight of the spurious feature water will increase." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.235, + 0.484, + 0.266 + ], + "angle": 0, + "content": "5.2. Group Classification and Aggregation Mitigate Spurious Correlation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.273, + 0.484, + 0.318 + ], + "angle": 0, + "content": "The goal of training a debiased model to avoid spurious correlation is to minimize the Balanced Group Error (BGE) rates [22]:" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.323, + 0.484, + 0.36 + ], + "angle": 0, + "content": "\\[\n\\operatorname {B G E} (f) = \\frac {1}{| \\mathcal {G} |} \\sum_ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x} \\mid g} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.365, + 0.484, + 0.456 + ], + "angle": 0, + "content": "A natural question is: what is the Bayes optimal classifier for this problem, i.e., \\( f^{*} \\in \\arg \\min_{f} \\mathsf{BGE}(f) \\). Suppose the underlying group-probabilities \\( \\mathbb{P}(g|\\mathbf{x}) \\propto \\exp (h^{*}(\\mathbf{x})_{g}) \\) for unknown scorer: \\( h^{*}: \\mathcal{X} \\to \\mathbb{R}^{|G|} \\). The Bayes optimal classifier \\( f^{*} \\) is derived from the following Proposition (proof in Appendix A.2):" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.484, + 0.509 + ], + "angle": 0, + "content": "Proposition 2. Let \\(\\mathcal{G}(y)\\) denote the set of groups with class label \\(y\\), i.e., \\(\\mathcal{G}(y) := \\{g = (y', a) \\in \\mathcal{G} | y' = y\\}\\). Let \\(\\beta\\) denote the group priors, i.e., \\(\\beta_g = \\mathbb{P}(g)\\). The prediction:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.514, + 0.482, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\ln \\beta\\right) _ {g} \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.554, + 0.387, + 0.57 + ], + "angle": 0, + "content": "is Bayes optimal for the problem in Eq. (15)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.484, + 0.681 + ], + "angle": 0, + "content": "Remark. We translate the unknown distributional class scores based on group logits \\( h(\\mathbf{x}) \\) and group priors \\( \\beta \\). To obtain \\( f^{*} \\), we can learn the ERM solution for group logits \\( h(\\mathbf{x}) \\). Then, we can minus the logarithm of the group prior \\( \\ln \\beta \\) and aggregate the logits that belongs to \\( \\mathcal{G}(y) \\) to yield the prediction for each class \\( y \\). In practice, instead predict Eq. (47), we introduce a hyper-parameter \\( \\tau \\in \\mathbb{R}_{+} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.688, + 0.484, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\tau \\cdot \\ln \\beta\\right) _ {g} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.484, + 0.801 + ], + "angle": 0, + "content": "Inspired by Menon et al. [25], we incorporate logit adjustment into the softmax cross-entropy \\(\\ell_{\\mathrm{ce}}\\). To do so, we directly enforce group priors offset while learning the group classifier \\(h_{\\mathrm{d}}(\\mathbf{x})\\). We refer to this as the group logit adjustment loss:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.807, + 0.482, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathrm {g l a}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x})) = \\ell_ {\\mathrm {c e}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.832, + 0.484, + 0.862 + ], + "angle": 0, + "content": "which is equivalent to Eq. (9). Now, the estimated debiased classifier \\( f_{\\mathrm{d}}(\\mathbf{x}) \\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.868, + 0.484, + 0.905 + ], + "angle": 0, + "content": "\\[\nf _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} h _ {\\mathrm {d}} (\\mathbf {x}) _ {g} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g} \\mathbf {x} \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.138 + ], + "angle": 0, + "content": "Since \\( h_{\\mathrm{d}} \\) is linear, summing over the output-space is equivalent to aggregating in weight-space, eliminating the overhead of group inference." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.153, + 0.646, + 0.17 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.179, + 0.906, + 0.255 + ], + "angle": 0, + "content": "In this section, we evaluate the effectiveness of our method across five benchmarks: Waterbirds [32], CelebA [23], MetaShift [20], BAR [26], and Living-17 [33]. For brevity, we provide an overview of our experimental setup here; further details can be found in Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.266, + 0.616, + 0.28 + ], + "angle": 0, + "content": "6.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.289, + 0.906, + 0.395 + ], + "angle": 0, + "content": "Waterbirds [32] was created by overlaying bird images from the Caltech-UCSD Birds [38] dataset onto background scenes from the Places [51] dataset. The target classes are bird types \\((\\mathcal{Y} = \\{\\text{waterbird, landbird}\\})\\), while the spurious attribute is the scene type \\((A = \\{\\text{water, land}\\})\\). Approximately \\(95\\%\\) of the waterbird training samples are associated with a water background." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.396, + 0.906, + 0.47 + ], + "angle": 0, + "content": "CelebA [23] is a real-world dataset comprising 200K celebrity portrait images. The objective is to classify hair color (\\(\\mathcal{Y} = \\{\\text{not blond, blond}\\}\\)), with gender (\\(\\mathcal{A} = \\{\\text{male, female}\\}\\)) as a spurious attribute. Notably, over \\(94\\%\\) of the blond-haired training images feature women." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.471, + 0.906, + 0.577 + ], + "angle": 0, + "content": "MetaShift [20]: The classification objective of MetaShift is to distinguish between cats and dogs, with background type \\((\\mathcal{A} = \\{\\mathrm{indoor}, \\mathrm{outdoor}\\})\\) as a spurious attribute. Following [45], we use a pre-processed version of MetaShift. In the training set, an inherent bias emerges: cats predominantly appear in indoor scenes, while dogs are more frequently seen in outdoor settings." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.578, + 0.906, + 0.714 + ], + "angle": 0, + "content": "BAR [26] is a real-world dataset designed to classify six actions that are each biased toward specific locations. In the original training set, the six action-location pairs are {climbing, rock wall}, {diving, underwater}, {fishing, water surface}, {racing, paved track}, {throwing, playing Field}, and {vaulting, sky}. However, the test set features different locations than the training set. We adapted the dataset for a group robustness setting by incorporating \\(5\\%\\) of the test set images into the training set." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.714, + 0.906, + 0.821 + ], + "angle": 0, + "content": "Living-17 [33]: Each class in the Living-17 represents a broad animal category that encompasses several fine-grained groups. The groups in the training and testing sets can exhibit noticeable visual differences, e.g., the bear class includes images of sloth bear and ice bear. Following [48], \\(5\\%\\) of the images in each testing group are added to the training groups." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.832, + 0.622, + 0.846 + ], + "angle": 0, + "content": "6.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.902 + ], + "angle": 0, + "content": "We compare our PPA against 14 baselines: (1) Zero-shot prompting [31], which matches image features with classification weights by extending class names into pre" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25491" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.119 + ], + "angle": 0, + "content": "Table 2. Evaluation of methods for improving group robustness of CLIP models across the Waterbirds, CelebA, and MetaShift benchmarks. Best worst-group accuracy (WGA) of the methods without group labels are in bold." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.129, + 0.887, + 0.389 + ], + "angle": 0, + "content": "
Group labels in train sets?MethodCLIP ResNet-50CLIP ViT-L/14
WaterbirdsCelebAMetaShiftWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvgWGAAvgWGAAvgWGAAvg
✓GroupDRO [32]75.183.884.189.583.287.390.896.488.391.293.997.4
S-CS [44]77.583.275.280.481.289.889.195.786.189.392.397.1
S-CL [44]75.286.075.680.481.588.889.996.087.890.593.196.9
DFR [17]73.283.880.092.883.188.389.797.885.690.892.397.0
XZero-Shot (ZS) [31]54.292.455.088.086.295.426.588.227.085.993.296.2
Group Prompt ZS [31]46.491.753.473.584.695.225.485.866.983.193.996.7
ERM [37]7.993.511.994.775.494.465.997.628.394.784.696.7
WiSE-FT [41]49.891.085.688.686.295.465.997.680.087.493.997.2
Orth-Cali [3]74.078.782.284.486.294.868.884.576.186.292.796.2
AFR [30]48.489.353.494.376.986.873.488.270.085.290.397.1
JTT [21]61.790.660.279.978.589.483.697.375.693.391.294.2
CnC [49]61.287.163.990.378.387.184.597.579.289.392.294.7
CA [48]83.789.490.090.777.985.586.996.284.690.491.393.4
CFR [47]76.977.673.781.181.589.588.296.884.887.893.795.5
PPA (ours)84.388.391.192.190.894.787.294.690.491.094.896.8
" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.427, + 0.485, + 0.714 + ], + "angle": 0, + "content": "defined prompts, e.g., \"a photo of a waterbird\". (2) Group-informed prompting [31], which incorporates group descriptions into the prompts, e.g., \"a photo of a waterbird on land\". (3) ERM [37], a linear classifier trained using cross-entropy loss, (4) WiSE-FT [41], which interpolates zero-shot and ERM models in weight-space, (5) Orth-Cali [3], a debiased zero-shot model that removes biased direction in the text embedding. (6) AFR [30], retrans the last layer of an ERM model with a weighted loss that emphasizes examples where the ERM model performs poorly, (7) JTT [21], (see details in Sec. 3.2), (8) CnC [49], which builds upon JTT [21], but it uses a contrastive loss to train the debiased model, (9) CA [48], trains contrastive adapters by learning similar representations across different groups, (10) CFR [47], refines the representation by aligning them with the class centroids via contrastive loss. We also compare with three group-supervised methods - (11) Group-DRO [32], (12) DFR [17], (13) S-CS [44] and (14) S-SL [44]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.726, + 0.373, + 0.741 + ], + "angle": 0, + "content": "6.3. Training and Evaluation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "For each method, we evaluate both its worst-group accuracy and average (in-distribution) accuracy on the test sets. We use CLIP ResNet-50 and CLIP ViT-L/14 as primary models, while also reporting results for CLIP ResNet-101, ViT-B/32, and ViT-B/16. Following prior work [44, 47, 48], we freeze the model backbones and train all models using the SGD optimizer for 100 epochs. The hyperparameter \\(\\tau\\) is set to \\(\\{1.2, 1.0, 0.9, 1.0, 1.0\\}\\) for Waterbirds, CelebA, MetaShift, Living-17, and BAR, respectively. Model selection is based on the highest worst-group validation ac" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.425, + 0.904, + 0.439 + ], + "angle": 0, + "content": "Table 3. Experimental results on Living-17 and BAR benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.45, + 0.897, + 0.581 + ], + "angle": 0, + "content": "
MethodCLIP ResNet-50CLIP ViT-L/14
Living-17BARLiving-17BAR
WGAAvgWGAWGAAvgWGA
ZS [31]38.083.274.448.092.381.7
ERM [37]53.390.854.984.098.689.0
JTT [21]44.086.458.578.797.390.2
CA [48]62.090.9-80.097.5-
PPA (ours)65.092.576.885.098.191.5
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.907, + 0.713 + ], + "angle": 0, + "content": "curacy, except for BAR, which lacks a validation set; for BAR, we evaluate the checkpoint from the last epoch. Additionally, since the majority groups in training set do not appear in testing, we measure only the worst-group accuracy for BAR. Further implementation details are provided in Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.652, + 0.74 + ], + "angle": 0, + "content": "6.4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Tab. 2 presents the worst-group accuracy (WGA) and average (in-distribution) accuracy for all methods on Waterbirds [32], CelebA [23] and MetaShift [20] datasets. Compared to other group-unsupervised debiasing approaches, our PPA achieves superior performance with less than \\(0.1\\%\\) trainable parameters (CLIP ResNet-50 has 25,557,032 parameters, while our model \\(f_{\\mathrm{d}}(\\cdot)\\) has only 4,096 trainable parameters). Specifically, PPA based on CLIP ResNet-50 outperforms the previous state-of-the-art, CFR [47], with improvements of \\(\\{7.4\\%, 17.4\\%, 9.3\\%\\) on Water" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25492" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.132 + ], + "angle": 0, + "content": "Table 4. PPA consistently improves group robustness for across different efficient fine-tuning paradigms using CLIP ResNet-50. The results using CLIP ViT-L/14 are reported in Appendix B.3." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.143, + 0.482, + 0.272 + ], + "angle": 0, + "content": "
MethodWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvg
Linear Probe + ERM7.993.511.994.775.494.4
Linear Probe + PPA84.388.391.192.190.894.7
CoOp + ERM61.796.235.094.875.492.8
CoOp + PPA83.087.690.092.289.093.3
Adapter + ERM61.496.760.694.484.693.9
Adapter + PPA78.291.891.592.587.793.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.283, + 0.483, + 0.311 + ], + "angle": 0, + "content": "Table 5. PPA consistently improves group robustness on Waterbirds across different architectures." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.322, + 0.485, + 0.411 + ], + "angle": 0, + "content": "
MethodCLIP RN-101CLIP ViT-B/32CLIP ViT-B/16
WGAAvgWGAAvgWGAAvg
Zero-shot33.690.047.088.834.088.1
ERM LP62.996.556.895.666.596.4
PPA83.689.783.589.184.489.9
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.434, + 0.483, + 0.618 + ], + "angle": 0, + "content": "birds, CelebA, and MetaShift, respectively. Moreover, PPA is competitive with group-supervised methods that rely on group annotations. Notably, our improvements in worst-group accuracy come at the cost of a modest reduction in in-distribution accuracy, with an average drop of 1.8 points compared to ERM models using CLIP ViT-L/14. In Tab. 3, we report results for the Living-17 [33] and BAR [26] datasets. We again observe that PPA achieves the highest worst-group performance. Notably, for the BAR dataset, where model selection is not performed and only the last checkpoint is used (due to the absence of a validation set), PPA still attains the highest worst-group accuracy." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.625, + 0.423, + 0.642 + ], + "angle": 0, + "content": "6.5. Further Analysis and Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.648, + 0.483, + 0.723 + ], + "angle": 0, + "content": "We conduct comprehensive studies to (1) confirm the versatility of our proposed method—specifically, its compatibility with other efficient fine-tuning paradigms and model architectures—and (2) to understand the contribution of each component to the overall improvement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.724, + 0.483, + 0.844 + ], + "angle": 0, + "content": "Extending PPA to other parameter-efficient fine-tuning paradigms. In this paper, we adopt linear probes for efficient fine-tuning of foundation models. We also explore the applicability of PPA to other efficient fine-tuning methods, such as prompt tuning [52, 53] (CoOp) and adapter-based tuning [7, 9, 48] (small bottleneck MLPs). Specifically, we replace the linear probe \\( h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x} \\) in Step 2 of Algorithm 1 with the following models:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.845, + 0.483, + 0.874 + ], + "angle": 0, + "content": "- Prompt tuning (CoOp). The prompt for group \\( i \\) is designed as:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.884, + 0.483, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {t} _ {i} = \\left[ V _ {1} ^ {i} \\right] \\left[ V _ {2} ^ {i} \\right] \\dots \\left[ V _ {M} ^ {i} \\right] [ \\mathrm {C L A S S} ], \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.09, + 0.906, + 0.16 + ], + "angle": 0, + "content": "Table 6. Main component analysis. We present the worst group accuracies using CLIP ResNet-50. \"Proj.\" and \"GLA\" stands for the projection operation in Eq. (6) and group logit adjustment loss in Eq. (9), respectively. \"GT\" means we use the ground-truth group labels for training debiased models." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.17, + 0.905, + 0.272 + ], + "angle": 0, + "content": "
Proj.GLAGTWaterbirdsCelebAMetaShift
(a)7.911.975.4
(b)✓54.429.486.2
(c)✓81.670.089.2
(d)✓✓84.391.190.8
(e)✓✓86.891.591.3
" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.287, + 0.712, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.408, + 0.674, + 0.419 + ], + "angle": 0, + "content": "(a) Worst Group Recall" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.287, + 0.901, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.408, + 0.874, + 0.419 + ], + "angle": 0, + "content": "(b) Worst Group Precision" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.43, + 0.906, + 0.459 + ], + "angle": 0, + "content": "Figure 1. The precision and recall of the worst-group examples on Waterbirds and CelebA using CLIP ResNet-50." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.484, + 0.907, + 0.574 + ], + "angle": 0, + "content": "where \\([V_m^i]\\) is a vector with the same dimensionality as the word embedding and serves as a parameter to be optimized. We follow CoOp to set \\(M = 16\\). [CLASS] represents the word embedding of the class name. Let \\(\\Phi(\\cdot)\\) denote the CLIP text encoder. The group scorer for group \\(i\\) is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.584, + 0.905, + 0.603 + ], + "angle": 0, + "content": "\\[\nh _ {\\mathrm {d}} ^ {\\mathrm {p t}} (\\mathbf {x}; \\mathbf {t}) _ {i} = \\Phi \\left(\\mathbf {t} _ {i}\\right) ^ {\\top} \\mathbf {x} / \\tau_ {\\text {c l i p}}, \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.614, + 0.726, + 0.628 + ], + "angle": 0, + "content": "where \\(\\tau_{\\mathrm{clip}}\\) is the temperature." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.629, + 0.906, + 0.75 + ], + "angle": 0, + "content": "- Adapter-based tuning. We adopt [7] to transform the visual embeddings \\(\\mathbf{x} \\in \\mathbb{R}^D\\) and the text embedding \\(Z \\in \\mathbb{R}^{K \\times D}\\) using simple 2-layer bottleneck MLPs. Let \\(H\\) denote the feature the hidden-layer dimension. We follow [48] to set \\(H = 128\\). With ReLU function \\(\\sigma(\\cdot)\\), visual adapter weights \\(W_{\\mathrm{v}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{v}}^{2} \\in \\mathbb{R}^{D \\times H}\\) and textual adapter weights \\(W_{\\mathrm{t}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{t}}^{2} \\in \\mathbb{R}^{D \\times H}\\), the input \\(\\mathbf{x}\\) and text embeddings \\(Z\\) are adapted as:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.758, + 0.905, + 0.777 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {x}} = W _ {\\mathrm {v}} ^ {2} \\sigma \\left(W _ {\\mathrm {v}} ^ {1} \\mathbf {x}\\right), \\quad \\tilde {Z} ^ {\\top} = W _ {\\mathrm {t}} ^ {2} \\sigma \\left(W _ {\\mathrm {t}} ^ {1} Z ^ {\\top}\\right). \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.787, + 0.907, + 0.818 + ], + "angle": 0, + "content": "We then use the normalized adapted embeddings and the temperature \\(\\tau_{\\mathrm{clip}}\\) to output the final scorer:" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.827, + 0.905, + 0.845 + ], + "angle": 0, + "content": "\\[\nh _ {\\mathrm {d}} ^ {\\mathrm {a t}} (\\mathbf {x}) _ {i} = \\tilde {\\mathbf {z}} ^ {\\top} \\tilde {\\mathbf {x}} / \\tau_ {\\mathrm {c l i p}} \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Tab. 4 demonstrates consistent improvements in worstgroup accuracy over the ERM-trained CLIP ResNet-50 model across three benchmarks, highlighting the versatility" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25493" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.372, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.631, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.089, + 0.885, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.231, + 0.89, + 0.246 + ], + "angle": 0, + "content": "Figure 2. Study on the effect of \\(\\tau\\) using CLIP ResNet-50. The optimal worst group accuracy is typically observed around \\(\\tau = 1.0\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.273, + 0.483, + 0.439 + ], + "angle": 0, + "content": "of our PPA across various efficient fine-tuning paradigms. For instance, on the CelebA dataset, our PPA achieves worst-group accuracy improvements of \\(55.0\\%\\) with CoOp and \\(30.9\\%\\) with Adapter. Additionally, integrating PPA with these three fine-tuning methods yields comparable performance. However, linear probing is more computationally efficient than prompt tuning, as the latter requires both forward and backward passes through the large text encoder to update the prompts. It is also more storage-efficient than Adapter-based methods, which introduce additional training parameters, i.e., \\(\\theta\\) and \\(\\phi\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.442, + 0.484, + 0.517 + ], + "angle": 0, + "content": "Study on model versatility. In Tab. 5, we implement our PPA to various backbone architectures, including CLIP ResNet-101, CLIP ViT-B/32 and CLIP ViT-B/16. We observe consistent performance gains on the worst group accuracy, indicating the model versatility of our PPA." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.52, + 0.483, + 0.777 + ], + "angle": 0, + "content": "Main component analysis. In Tab. 6, we provide an ablation study to assess the impact of the projection operation (Proj.) and group logit adjustment (GLA) loss on worst-group accuracy using CLIP ResNet-50. Row (a) represents the ERM-trained linear probing model; Row (b) probes group targets without prior correction; and Row (c) omits the projection operation during training. Row (d) shows results from our proposed method (PPA), while Row (e) replaces estimated group labels with ground-truth labels. Comparing Rows (b) and (d), we observe that adjusting the margin significantly improves worst-group accuracy. In the comparison of Rows (c) and (d), projecting out class proxies enhances group identification, resulting in better worst-group performance. Finally, Row (e) demonstrates the oracle performance using ground-truth labels, revealing that PPA approximates the maximum achievable accuracy, underscoring the importance of accurate pseudo-group labels." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.781, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Study on the quality of estimated group labels. In the absence of training group labels, we rely on the quality of pseudo group labels inferred from the biased model \\( f_{\\mathrm{b}}(\\mathbf{x}) \\). To evaluate the quality of identified minority groups within the training set, we measure two metrics: precision, defined as the fraction of examples within the identified minority groups that belong to the worst-performing group, and recall, the fraction of examples from the worst-performing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.273, + 0.905, + 0.438 + ], + "angle": 0, + "content": "group captured by the identified minority groups. Here, the worst-performing group is defined as the group on which the ERM model achieves the lowest validation accuracy. In Fig. 1, we compare our method with two baselines: (1) ERM, which uses standard empirical risk minimization to train biased models, and (2) CA [48], which leverages zero-shot models to identify minority groups. Our method, PPA, achieves significantly higher recall and precision than both ERM and CA. This improvement is attributed to our biased model \\( f_{\\mathrm{b}} \\), which relies more heavily on spurious features to make predictions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.439, + 0.907, + 0.665 + ], + "angle": 0, + "content": "Study on the hyper-parameter \\(\\tau\\). We examine the effect of \\(\\tau \\in \\mathbb{R}_+\\) in Eq. (9), as illustrated in Fig. 2 (more details are in Appendix B.6). Specifically, we vary \\(\\tau\\) from 0.0 to 2.0 and report both the worst-group accuracy and average accuracy on the Waterbirds, CelebA, and MetaShift datasets using CLIP ResNet-50. A larger \\(\\tau\\) promotes a greater margin for the minority groups, while \\(\\tau = 0\\) reduces to the standard cross-entropy loss. Our findings reveal that (1) average accuracy decreases monotonically as \\(\\tau\\) increases, and (2) the optimal worst-group accuracy is generally achieved around \\(\\tau = 1.0\\). For example, the optimal values of \\(\\tau\\) are 1.2, 1.0 and 0.9 for Waterbirds, CelebA and MetaShift, respectively. This aligns with our theoretical analysis, which suggests that the Bayes optimal classifier for minimizing the balanced group error is attained when \\(\\tau = 1\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.68, + 0.634, + 0.695 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.9 + ], + "angle": 0, + "content": "In this paper, we introduce Project-Probe-Aggregate (PPA), a novel, parameter-efficient fine-tuning framework for enhancing the group robustness of image-text foundation models without relying on training group labels. Our approach improves the identification of minority groups by projecting image features onto the null space of class proxies. Additionally, we design a group logit adjustment loss to minimize balanced group error and mitigate spurious correlations. Through theoretical analysis and empirical evaluations across diverse benchmarks, fine-tuning paradigms and model architectures, we demonstrate that the proposed method effectively enhances robust group performance of foundation models." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25494" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.241, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.178 + ], + "angle": 0, + "content": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.191, + 0.188, + 0.207 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.216, + 0.484, + 0.258 + ], + "angle": 0, + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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In NeurIPS, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.092, + 0.906, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "25496" + } + ] +] \ No newline at end of file diff --git a/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_origin.pdf b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bf281c78aba9ff0f6d75c7ca96503514024b539e --- /dev/null +++ b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/5e368750-4958-49b1-b258-1956bba6e2a9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f6c9a8f28dba46ea460d8e478278fc271423c5f27546606db4f254bcfa9938c2 +size 515510 diff --git a/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/full.md b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a2bd975eed748a1b857e004c61cec75f711a03b7 --- /dev/null +++ b/2025/Project-Probe-Aggregate_ Efficient Fine-Tuning for Group Robustness/full.md @@ -0,0 +1,419 @@ +# Project-Probe-Aggregate: Efficient Fine-Tuning for Group Robustness + +Beier Zhu $^{1,2}$ Jiequan Cui $^{1}$ Hanwang Zhang $^{1}$ Chi Zhang $^{2\dagger}$ $^{1}$ Nanyang Technological University, $^{2}$ Westlake University + +{beier.zhu, jiequan.cui, hanwangzhang}@ntu.edu.sg, chizhang@westlake.edu.cn + +# Abstract + +While image-text foundation models have succeeded across diverse downstream tasks, they still face challenges in the presence of spurious correlations between the input and label. To address this issue, we propose a simple three-step approach-Project-Probe-Aggregate (PPA)-that enables parameter-efficient fine-tuning for foundation models without relying on group annotations. Building upon the failure-based debiasing scheme, our method, PPA, improves its two key components: minority samples identification and the robust training algorithm. Specifically, we first train biased classifiers by projecting image features onto the nullspace of class proxies from text encoders. Next, we infer group labels using the biased classifier and probe group targets with prior correction. Finally, we aggregate group weights of each class to produce the debiased classifier. Our theoretical analysis shows that our PPA enhances minority group identification and is Bayes optimal for minimizing the balanced group error, mitigating spurious correlations. Extensive experimental results confirm the effectiveness of our PPA: it outperforms the state-of-the-art by an average worst-group accuracy while requiring less than $0.01\%$ tunable parameters without training group labels. + +# 1. Introduction + +Image-text foundation models [12, 31, 40]—large models pre-trained on web-scale data—are becoming increasingly prevalent in real-world deployments. However, adapting these models to downstream tasks, whether through zero-shot transfer or fine-tuning, remains challenging due to fundamental issues of group robustness: they achieve low average test error but incur high risk on certain groups of examples [3, 44, 47, 48]. This issue becomes particularly pronounced in the presence of spurious correlations [8], where a classifier relies on non-causal relationships that happen to align with class labels in training but break down during deployment. For example, consider the case where "water + +
MethodWorst-group Recall (%)Worst-group Precision (%)
CA [48]46.415.6
JTT [21]78.624.1
PPA (ours)80.444.3
+ +Table 1. The precision and recall of the worst-group examples (i.e., the group with lowest validation accuracy) identified by biased models on the Waterbird training set [32] using CLIP ResNet-50. Our PPA is more susceptible to supurious features, achieving higher worst-group recall and precision compared to previous methods. + +birds” predominantly appear in images with a “water” background. When trained on such a dataset, neural networks often rely on the background to recognize the objects. + +As a result, several fine-tuning methods have emerged to improve group robustness in foundation models [3, 29, 44, 47, 48]. Unlike conventional robust training frameworks, which typically re-train the entire model [21, 22, 26, 27] (which is computationally expensive) and/or require group labels [1, 32] (which demands additional annotation costs), these fine-tuning methods prioritize parameter and annotation efficiency. They address spurious correlations by optimizing only a small subset of parameters without relying on training group labels. For instance, Zhang and Ré [48] fine-tune a lightweight adapter and You et al. [47] propose to optimize projection layers to improve distributional robustness. In this paper, we build on these ideas by focusing on efficient fine-tuning to enhance group robustness, i.e., training linear probes. + +At a high level, in the absence of group annotations, a common strategy [5, 19, 21, 22, 26, 48, 49] involves first identifying minority groups by training a biased model that easily overfits to spurious features. Subsequently, a debiased model is trained using the inferred group labels. To improve the identification of minority groups, prior work proposes various strategies: [22, 26] employ generalized cross-entropy loss to amplify the model bias, JTT [21] simply trains a model with empirical risk minimization (ERM) and tunes hyperparameters to exacerbate bias, CA [48] leverages the correctness of zero-shot pre + +dictions and [5] uses low-capacity networks to capture spurious features. In this paper, we leverage the pre-trained knowledge from the image-text foundation models to effectively induce bias, further enhancing the identification of minority groups. Specifically, we project out class proxies, provided by the text encoders, from the input image features and use only the remaining information to train the biased classifiers. Intuitively, removing class information forces the model to rely more heavily on spurious features for predictions. We provide theoretical analysis to support this intuition in Proposition 1. Empirically, in Tab. 1, we evaluate the quality of the inferred groups in the training datasets obtained by our method, and compare it to prior approaches [21, 48]. Specifically, we measure precision—the fraction of examples within the identified minor groups that belong to the worst-performing group, and recall—the fraction of examples from the worst-performing group that are captured by the identified minor groups. As expected, our method achieves higher precision and recall, demonstrating superior group identification. + +Given the inferred groups, typical debiased learning algorithms up-weight/up-sample minority group samples to enhance performance on these challenging instances [5, 10, 17, 21, 26]. However, determining the optimal weights requires careful hyper-parameter tuning and lacks theoretical guidance. Since the goal of debiased training is to minimize the Balanced Group Error (BGE) [22, 36], we propose a methodology designed to achieve this objective directly. Rather than predicting class labels, our method is trained to probe for group targets by compensating group priors into the softmax cross-entropy during training. Afterward, we aggregate group weights of each class to produce the final debiased classifier. We dub our overall debiasing framework Project-Probe-Aggregate (PPA), and demonstrate that it is Bayes optimal for minimizing BGE in Proposition 2. + +In summary, our contributions are: + +- We project out the class proxies offered by the text encoder and train the biased model on the residual image features, with theoretical analysis showing this approach increases reliance on spurious features, improving minority group identification. +- We propose a novel debiasing method that is consistent for minimizing the balanced group error. The debiased classifier predicts group labels compensated by group priors and uses weight-space aggregation after fine-tuning to avoid group inference overhead. +- We confirm the effectiveness of our proposal across five benchmarks with spurious correlations. With less than $0.01\%$ of the foundation model parameters, our approach PPA improves the worst group accuracy over the state-of-the-art without training group annotations. Beyond linear probes, we also adapt other parameter-efficient finetuning paradigms (e.g., prompt tuning and adapters) to + +show the versatility of the proposed method. + +# 2. Related Work + +Improving group robustness. There have been numerous works aimed at improving group robustness, which broadly fall into two categories based on whether group labels are available during training. (i) Group supervised methods focus on balancing the contribution of each group during the training phase, such as through re-sampling/reweighting [10, 11, 13, 17, 24, 39], or robust optimization [1, 32, 34]. However, this approach requires additional annotation costs for group labels. In this paper, we focus on (ii) group unsupervised methods, which do not assume the availability of group labels during training [2, 14, 15, 18, 35, 42, 43, 46]. Without group labels, a common strategy is to first train an easily biased model, and then infer groups based on its biased predictions. A robust model is subsequently trained using the inferred group labels through techniques such as importance weighting [21, 26, 30], robust optimization [4, 27], or by learning similar representations for groups within the same class [49]. In this paper, we leverage the general knowledge from image-text foundation models to train a biased classifier by excluding the class proxy information generated by the CLIP text encoder. Note that classifier in [39] also predicts group labels, our approach differs in two key aspects: 1) We further incorporate logit offsets during training, which compensates for group imbalances and leads to lower balanced error. 2) Unlike [39], our method does not require access to ground-truth group labels. + +Efficient robust fine-tuning for foundation models. The advent of image-text foundation models has led to several efforts to develop efficient group-robust fine-tuning methods [3, 6, 16, 17, 28, 44, 47, 48, 50, 55]. Kirichenko et al. [17] demonstrate that last-layer retraining significantly improves group robustness in pretrained models. Zhang and Ré [48] use contrastive objectives to train adapters, bringing same-class embeddings closer together. Chuang et al. [3] reduce bias in image-text models by removing biased directions in text embeddings. Other works [44, 47] focus on lightweight fine-tuning by optimizing only the projection layers of the vision branch for distributional robustness. Our approach builds on efficient fine-tuning by training only a linear classification head for group targets and further introduces weight-space ensembling after fine-tuning to eliminate the overhead of group inference. + +# 3. Preliminaries + +# 3.1. Setup + +Considering a classification problem with instances $\mathbf{x} \in \mathcal{X} \subseteq \mathbb{R}^d$ and labels $y \in \mathcal{Y} = [K]$ . Each data point $(\mathbf{x}, y)$ has an input attribute $a(\mathbf{x}) \in \mathcal{A}$ that is spuriously correlated + +with the target $y$ . We form $|\mathcal{G}| = |\mathcal{A}|\times |\mathcal{Y}|$ groups, where each group label $g\in \mathcal{G}$ is the combination of the attribute $a$ and the class label $y$ , i.e., $g\coloneqq (a,y)$ . Given a training dataset $\mathcal{D} = \{\mathbf{x}_i,y_i\}_{i = 1}^N$ drawn from some unknown distribution $\mathbb{P}$ , and let $\mathbb{P}_g$ be the distribution conditioned on $g$ for any $g\in \mathcal{G}$ . We assume that spurious attribute annotations are not available for the samples in the training set. Our goal is to train a model $f_{\theta}:\mathcal{X}\to \mathbb{R}^{K}$ that outputs prediction score, such that it achieves low expected error: + +$$ +\mathcal {R} = \mathbb {E} _ {\mathbf {x}, y \sim \mathbb {P}} [ y \neq \underset {y ^ {\prime} \in \mathcal {Y}} {\operatorname {a r g m a x}} f _ {\theta} (\mathbf {x}) _ {y ^ {\prime}} ] \tag {1} +$$ + +and, more importantly, exhibits group robust, i.e., achieving low worst-group error: + +$$ +\mathcal {R} _ {\mathrm {w g}} = \max _ {g \in \mathcal {G}} \mathbb {E} _ {\mathbf {x}, y \sim \mathbb {P} _ {g}} [ y \neq \underset {y ^ {\prime} \in \mathcal {Y}} {\operatorname {a r g m a x}} f _ {\theta} (\mathbf {x}) _ {y ^ {\prime}} ] \tag {2} +$$ + +For example, in the Waterbirds [32] dataset, the task is to classify birds $y \in \{\text{waterbird}, \text{landbird}\}$ , with the background serving as a spurious attribute ( $a \in \{\text{water}, \text{land}\}$ ). A notable pattern is that about $95\%$ of waterbird images have a water background, causing models to rely on the "water" background to predict "waterbird". This reliance leads to poor performance on minority groups, such as landbirds with water backgrounds $g =$ (water, landbird). Unlike domain generalization or out-of-distribution evaluation, all groups are present in the training, validation, and test splits. However, the training groups are imbalanced, which can result in poor group robustness on the test set. + +# 3.2. Common Strategy for Improving Unsupervised Group Robustness + +At a high level, typical methods without access to group labels first train a biased model and then use its biased predictions to infer the groups. Subsequently, a robust model is trained using the inferred group labels. $^{1}$ + +Taking JTT [21] as an example, it identifies the misclassified samples from ERM model $f_{\mathrm{erm}}$ as the error set $\mathcal{E}$ : + +$$ +\mathcal {E} = \left\{\left(\mathbf {x} _ {i}, y _ {i}\right) \text {s . t .} f _ {\operatorname {e r m}} \left(\mathbf {x} _ {i}\right) \neq y _ {i} \right\}, \tag {3} +$$ + +then trains a robust model by weighting the samples in $\mathcal{E}$ : + +$$ +\mathcal {L} _ {\mathrm {J T T}} (\theta , \mathcal {E}) = \lambda \sum_ {(\mathbf {x}, y) \in \mathcal {E}} \ell (\mathbf {x}, y; \theta) + \sum_ {(\mathbf {x}, y) \notin \mathcal {E}} \ell (\mathbf {x}, y; \theta), \tag {4} +$$ + +where $\lambda \in \mathbb{R}_+$ is a hyperparameter. The core idea behind JTT is that ERM models tend to fit groups with easily learnable spurious correlations. The samples in $\mathcal{E}$ are primarily from minority groups where these correlations fail. Upweighting such challenging samples improves the model's performance on the worst-performing groups. + +Remark. Improving group robustness without access to group labels hinges on identifying minority groups by training a biased model that overfits on spurious features. Prior work amplifies this bias through various strategies: LfF [26] employs generalized cross-entropy (GCE) loss to bias the first-stage model, JTT [21] tunes hyperparameters to induce bias, and [5] uses low-capacity networks to capture spurious features. In this paper, we enhance bias by projecting out the class proxies from the input features, using only the remaining information for classification. In Sec. 5.1, we prove that this operation increases susceptibility to spurious features, aiding the identification of minority groups. + +Another key factor is the robust learning algorithm given the pseudo groups. Prior methods address this through importance weighting [21, 26], robust optimization [4, 27], or aligning representations within the same class [49]. Our approach, PPA, predicts pseudo group labels and applies a group prior offset to correct for imbalance. In Sec. 5.2, we prove that our training algorithm effectively mitigates spurious correlations. + +# 4. Methods + +Tuning entire pre-trained models is both time-consuming and computationally costly. Recent work [17] shows that simple last-layer retraining performs well on spurious correlation benchmarks. In our approach, the input $\mathbf{x}$ represents image features encoded by CLIP. We freeze the backbone and learn linear classifiers for efficient fine-tuning. + +We now present PPA, a simple three-step approach following the common strategy in Sec. 3.2. First, we train a biased classifier by removing the class proxies generated by the CLIP text encoder. Next, we group samples by classification correctness and train a robust model to predict group labels using our proposed group logit adjustment. Finally, we aggregate group weights to produce the final classifier. + +Step 1: Project out class proxies. We compute the matrix $Z = [\mathbf{z}_1, \ldots, \mathbf{z}_K]^\top \in \mathbb{R}^{K \times d}$ whose rows are the text embeddings of the $K$ class names. Specifically, each $\mathbf{z}_j$ is derived from a prompt like "a photo of a [CLASS]." with the class token [CLASS] replaced by the $j$ -th class name. Let $\Pi \in \mathbb{R}^{d \times d}$ be the projection operator onto the null space of $Z$ , given by: + +$$ +\Pi = I - Z ^ {\top} \left(Z Z ^ {\top}\right) ^ {- 1} Z \tag {5} +$$ + +With $\Pi$ , the biased model $f_{\mathsf{b}}: \mathcal{X} \to \mathbb{R}^{K}$ is formulated as a linear classifier parameterized by a matrix $W_{\mathsf{b}} \in \mathbb{R}^{K \times d}$ : + +$$ +f _ {\mathrm {b}} (\mathbf {x}) = W _ {\mathrm {b}} \Pi \mathbf {x} \tag {6} +$$ + +To account for potential class imbalance $^2$ , we apply the logit-adjustment loss [25, 54] to ensure $f_{\mathrm{b}}$ focuses on spu + +rious features rather than class priors: + +$$ +\ell_ {\mathrm {l a}} (y, f _ {\mathrm {b}} (\mathbf {x})) = - \ln \frac {\exp \left(f _ {\mathrm {b}} (\mathbf {x}) + \ln \pi\right) _ {y}}{\sum_ {y ^ {\prime} \in \mathcal {Y}} \exp \left(f _ {\mathrm {b}} (\mathbf {x}) + \ln \pi\right) _ {y ^ {\prime}}}, \tag {7} +$$ + +where $\pi_y$ is the prior of class $y$ . In Proposition 1, we show that our biased model is more easily influenced by spurious correlation. + +Step 2: Probe with group target. We follow the heuristic of JTT [21] to identify minority groups that $f_{\mathrm{b}}$ misclassifies: + +$$ +\hat {a} (\mathbf {x}) = \mathbb {1} [ y \neq \operatorname {a r g m a x} _ {y ^ {\prime} \in \mathcal {Y}} f _ {\mathrm {b}} (\mathbf {x}) _ {y ^ {\prime}} ], \tag {8} +$$ + +where $\mathbb{1}[\cdot ]$ is the indicator function. Then, each training sample is augmented as $(\mathbf{x},y,\hat{a})$ , with the pseudo group defined as the combination of $y$ and $\hat{a}$ : $\hat{g} \coloneqq (y,\hat{a}) \in \hat{\mathcal{G}}$ . + +Our approach PPA uses a group scorer, implemented via linear probing, to predict pseudo group labels. Specifically, the group score $h_{\mathrm{d}}(\mathbf{x}) = W_{\mathrm{d}}\mathbf{x}:\mathcal{X}\to \mathbb{R}^{|\hat{\mathcal{G}}|}$ is parameterized by $W_{\mathrm{d}}\in \mathbb{R}^{|\hat{\mathcal{G}}|\times d}$ . Let $\hat{\beta}$ denote the group priors, we propose the group logit adjustment loss to achieve balanced group performance.: + +$$ +\ell_ {\mathbf {g l a}} (\hat {g}, h _ {\mathbf {d}} (\mathbf {x})) = - \ln \frac {\exp \left(h _ {\mathbf {d}} (\mathbf {x}) + \tau \cdot \ln \hat {\boldsymbol {\beta}}\right) _ {\hat {g}}}{\sum_ {g ^ {\prime} \in \hat {\mathcal {G}}} \exp \left(h _ {\mathbf {d}} (\mathbf {x}) + \tau \cdot \ln \hat {\boldsymbol {\beta}}\right) _ {g ^ {\prime}}}, \tag {9} +$$ + +where $\tau \in \mathbb{R}_+$ is a hyper-parameter. + +Step 3: Aggregate weights. The final debiased classifier $f_{\mathrm{d}}(\mathbf{x}) : \mathcal{X} \to \mathbb{R}^{K}$ is constructed by aggregating the weights corresponding to each class: + +$$ +f _ {\mathrm {d}} (\mathbf {x}) _ {y} = \mathbf {w} _ {y} ^ {\top} \mathbf {x}, \text {w h e r e} \mathbf {w} _ {y} ^ {\top} = \sum_ {g \in \hat {\mathcal {G}} (y)} W _ {\mathrm {d}, g}. \tag {10} +$$ + +Here, $W_{\mathrm{d},g}$ represents the weight vector in $W_{\mathrm{d}}$ associated with group $g$ . This weight-space aggregation transforms group classification into class prediction, eliminating the need for group inference overhead. + +In Proposition 2, we prove that the debiased model $f_{\mathrm{d}}(\mathbf{x})$ is the Bayes optimal classifier for minimizing the balanced group error. Beyond linear classifiers, we also employ other parameter-efficient fine-tuning paradigms (e.g., prompt tuning and adapters) to implement our debiased classifier $f_{\mathrm{d}}(\mathbf{x})$ , as detailed in Sec. 6.5. The full pipeline is outlined in Algorithm 1. + +# 5. Theoretical Analysis + +# 5.1. Removal of Class Proxies Amplifies Model Bias + +Intuitively, removing class information forces the model $f_{\mathrm{b}}$ to rely more on spurious features for predicting class labels. To support this intuition, we provide theoretical evidence in a linear regression setup. Let $\mathbf{c}$ denote the core features + +# Algorithm 1 Pipeline of PPA + +1: Given: Training dataset $\mathcal{D} = \{\mathbf{x}_i, y_i\}_{i=1}^N$ , class proxies $\{\mathbf{z}_j\}_{j=1}^K$ . + +Step 1: Project + +2: Compute the projection matrix $\Pi$ using Eq. (5). +3: Build $f_{\mathrm{b}}(\mathbf{x}) = W_{\mathrm{b}} \Pi \mathbf{x}$ and optimize $W_{\mathrm{b}}$ using Eq. (7). + +Step 2: Probe + +4: Identify pseudo groups $\{\hat{g}\}$ via Eq. (8). +5: Build $h_{\mathsf{d}}(\mathbf{x}) = W_{\mathsf{d}}\mathbf{x}$ and optimize $W_{\mathsf{d}}$ using Eq. (9). + +Step 3: Aggregate + +6: Construct $f_{\mathbf{d}}(\mathbf{x})$ by aggregating weights of $W_{\mathrm{d}}$ , as in Eq. (10). +7: Return $f_{\mathrm{d}}(\mathbf{x})$ . + +which are stable for predicting the target $y$ and $s$ be a spurious feature. The spurious feature is correlated with the target in the training set, but this correlation may not hold during testing. Suppose we observe $n$ features, stacked as $C = [\mathbf{c}_1,\dots ,\mathbf{c}_n]^\top \in \mathbb{R}^{N\times d}$ and $\mathbf{s} = [s_1,\ldots ,s_n]^\top \in \mathbb{R}^N$ . We are interested in the contribution of the spurious feature $s$ across the following two models: + +- Full model: Linear regression on the core features $\mathbf{c}$ and the spurious feature $s$ : + +$$ +\mathbf {y} = C \boldsymbol {\beta} + \gamma \mathbf {s} + \varepsilon , \tag {11} +$$ + +where $\beta$ and $\gamma$ are the weights associated with the core features and the spurious feature, respectively. $\varepsilon$ is a noise term with an expected value of 0. + +- Projected model: Applying the projection matrix $\Pi$ to $C$ to obtain $\tilde{C} = C\Pi$ , followed by linear regression on $\tilde{\mathbf{c}}$ and $s$ : + +$$ +\mathbf {y} = \tilde {C} \tilde {\boldsymbol {\beta}} + \gamma^ {\prime} \mathbf {s} + \varepsilon^ {\prime}, \tag {12} +$$ + +where $\tilde{\beta}$ and $\gamma^\prime$ are the weights for the projected core features and the spurious feature, respectively. + +In Eq. (11), the core features $C$ can be decomposed into the remaining part $\tilde{C}$ and the projected-out part $C_{\mathrm{o}}$ . + +$$ +C = C \Pi + C (I - \Pi) = \tilde {C} + C _ {\circ}. \tag {13} +$$ + +Let $\mathbf{y}_{\circ} = C_{\circ}\beta$ denote the contribution of the projected-out core features in the full model. Define $M = I - \tilde{C} (\tilde{C}^{\top}\tilde{C})^{-1}\tilde{C}^{\top}$ , $\mathbf{r_{y_o}} = M\mathbf{y_o}$ and $\mathbf{r_s} = M\mathbf{s}$ . The following proposition states that projecting out core features can make the model more susceptible to spurious feature (proof in Appendix A.1). + +Proposition 1. The weight of the spurious feature after projection is + +$$ +\gamma^ {\prime} = \gamma + \frac {\mathbf {r _ {s}} ^ {\top} \mathbf {r _ {y _ {o}}}}{\mathbf {r _ {s}} ^ {\top} \mathbf {r _ {s}}}. \tag {14} +$$ + +Remark. Since the denominator $\mathbf{r_s}^\top \mathbf{r_s}$ is non-negative, the model relies more on spurious feature, i.e., $\gamma^{\prime} > \gamma$ , if + +$\mathbf{r_s}^\top \mathbf{r_y_o} > 0$ . In other words, if the spurious feature $s$ is positively correlated with the contribution of projected-out core features $\mathbf{c}_o$ in the space of $M$ , the weight of the spurious feature will increase. For instance, consider the Waterbirds dataset [32], the spurious feature water background is positively correlated with the core feature waterbird (about $95\%$ of waterbird images have a water background). If we remove the contribution of waterbird by projection, the weight of the spurious feature water will increase. + +# 5.2. Group Classification and Aggregation Mitigate Spurious Correlation + +The goal of training a debiased model to avoid spurious correlation is to minimize the Balanced Group Error (BGE) rates [22]: + +$$ +\operatorname {B G E} (f) = \frac {1}{| \mathcal {G} |} \sum_ {g \in \mathcal {G}} \mathbb {E} _ {\mathbf {x} \mid g} [ y \neq \underset {y ^ {\prime} \in \mathcal {Y}} {\operatorname {a r g m a x}} f (\mathbf {x}) _ {y ^ {\prime}} ] \tag {15} +$$ + +A natural question is: what is the Bayes optimal classifier for this problem, i.e., $f^{*} \in \arg \min_{f} \mathsf{BGE}(f)$ . Suppose the underlying group-probabilities $\mathbb{P}(g|\mathbf{x}) \propto \exp (h^{*}(\mathbf{x})_{g})$ for unknown scorer: $h^{*}: \mathcal{X} \to \mathbb{R}^{|G|}$ . The Bayes optimal classifier $f^{*}$ is derived from the following Proposition (proof in Appendix A.2): + +Proposition 2. Let $\mathcal{G}(y)$ denote the set of groups with class label $y$ , i.e., $\mathcal{G}(y) := \{g = (y', a) \in \mathcal{G} | y' = y\}$ . Let $\beta$ denote the group priors, i.e., $\beta_g = \mathbb{P}(g)$ . The prediction: + +$$ +\arg \max _ {y \in \mathcal {Y}} f ^ {*} (\mathbf {x}) _ {y} = \arg \max _ {y \in \mathcal {Y}} \sum_ {g \in \mathcal {G} (y)} \left(h (\mathbf {x}) - \ln \beta\right) _ {g} \tag {16} +$$ + +is Bayes optimal for the problem in Eq. (15). + +Remark. We translate the unknown distributional class scores based on group logits $h(\mathbf{x})$ and group priors $\beta$ . To obtain $f^{*}$ , we can learn the ERM solution for group logits $h(\mathbf{x})$ . Then, we can minus the logarithm of the group prior $\ln \beta$ and aggregate the logits that belongs to $\mathcal{G}(y)$ to yield the prediction for each class $y$ . In practice, instead predict Eq. (47), we introduce a hyper-parameter $\tau \in \mathbb{R}_{+}$ : + +$$ +\arg \max _ {y \in \mathcal {Y}} f ^ {*} (\mathbf {x}) _ {y} = \arg \max _ {y \in \mathcal {Y}} \sum_ {g \in \mathcal {G} (y)} \left(h (\mathbf {x}) - \tau \cdot \ln \beta\right) _ {g} \tag {17} +$$ + +Inspired by Menon et al. [25], we incorporate logit adjustment into the softmax cross-entropy $\ell_{\mathrm{ce}}$ . To do so, we directly enforce group priors offset while learning the group classifier $h_{\mathrm{d}}(\mathbf{x})$ . We refer to this as the group logit adjustment loss: + +$$ +\ell_ {\mathrm {g l a}} (\hat {g}, h _ {\mathrm {d}} (\mathbf {x})) = \ell_ {\mathrm {c e}} (\hat {g}, h _ {\mathrm {d}} (\mathbf {x}) + \tau \cdot \ln \hat {\boldsymbol {\beta}}), \tag {18} +$$ + +which is equivalent to Eq. (9). Now, the estimated debiased classifier $f_{\mathrm{d}}(\mathbf{x})$ becomes: + +$$ +f _ {\mathrm {d}} (\mathbf {x}) _ {y} = \sum_ {g \in \hat {\mathcal {G}} (y)} h _ {\mathrm {d}} (\mathbf {x}) _ {g} = \sum_ {g \in \hat {\mathcal {G}} (y)} W _ {\mathrm {d}, g} \mathbf {x} \tag {19} +$$ + +Since $h_{\mathrm{d}}$ is linear, summing over the output-space is equivalent to aggregating in weight-space, eliminating the overhead of group inference. + +# 6. Experiments + +In this section, we evaluate the effectiveness of our method across five benchmarks: Waterbirds [32], CelebA [23], MetaShift [20], BAR [26], and Living-17 [33]. For brevity, we provide an overview of our experimental setup here; further details can be found in Appendix B. + +# 6.1. Datasets + +Waterbirds [32] was created by overlaying bird images from the Caltech-UCSD Birds [38] dataset onto background scenes from the Places [51] dataset. The target classes are bird types $(\mathcal{Y} = \{\text{waterbird, landbird}\})$ , while the spurious attribute is the scene type $(A = \{\text{water, land}\})$ . Approximately $95\%$ of the waterbird training samples are associated with a water background. + +CelebA [23] is a real-world dataset comprising 200K celebrity portrait images. The objective is to classify hair color ( $\mathcal{Y} = \{\text{not blond, blond}\}$ ), with gender ( $\mathcal{A} = \{\text{male, female}\}$ ) as a spurious attribute. Notably, over $94\%$ of the blond-haired training images feature women. + +MetaShift [20]: The classification objective of MetaShift is to distinguish between cats and dogs, with background type $(\mathcal{A} = \{\mathrm{indoor}, \mathrm{outdoor}\})$ as a spurious attribute. Following [45], we use a pre-processed version of MetaShift. In the training set, an inherent bias emerges: cats predominantly appear in indoor scenes, while dogs are more frequently seen in outdoor settings. + +BAR [26] is a real-world dataset designed to classify six actions that are each biased toward specific locations. In the original training set, the six action-location pairs are {climbing, rock wall}, {diving, underwater}, {fishing, water surface}, {racing, paved track}, {throwing, playing Field}, and {vaulting, sky}. However, the test set features different locations than the training set. We adapted the dataset for a group robustness setting by incorporating $5\%$ of the test set images into the training set. + +Living-17 [33]: Each class in the Living-17 represents a broad animal category that encompasses several fine-grained groups. The groups in the training and testing sets can exhibit noticeable visual differences, e.g., the bear class includes images of sloth bear and ice bear. Following [48], $5\%$ of the images in each testing group are added to the training groups. + +# 6.2. Baselines + +We compare our PPA against 14 baselines: (1) Zero-shot prompting [31], which matches image features with classification weights by extending class names into pre + +Table 2. Evaluation of methods for improving group robustness of CLIP models across the Waterbirds, CelebA, and MetaShift benchmarks. Best worst-group accuracy (WGA) of the methods without group labels are in bold. + +
Group labels in train sets?MethodCLIP ResNet-50CLIP ViT-L/14
WaterbirdsCelebAMetaShiftWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvgWGAAvgWGAAvgWGAAvg
✓GroupDRO [32]75.183.884.189.583.287.390.896.488.391.293.997.4
S-CS [44]77.583.275.280.481.289.889.195.786.189.392.397.1
S-CL [44]75.286.075.680.481.588.889.996.087.890.593.196.9
DFR [17]73.283.880.092.883.188.389.797.885.690.892.397.0
XZero-Shot (ZS) [31]54.292.455.088.086.295.426.588.227.085.993.296.2
Group Prompt ZS [31]46.491.753.473.584.695.225.485.866.983.193.996.7
ERM [37]7.993.511.994.775.494.465.997.628.394.784.696.7
WiSE-FT [41]49.891.085.688.686.295.465.997.680.087.493.997.2
Orth-Cali [3]74.078.782.284.486.294.868.884.576.186.292.796.2
AFR [30]48.489.353.494.376.986.873.488.270.085.290.397.1
JTT [21]61.790.660.279.978.589.483.697.375.693.391.294.2
CnC [49]61.287.163.990.378.387.184.597.579.289.392.294.7
CA [48]83.789.490.090.777.985.586.996.284.690.491.393.4
CFR [47]76.977.673.781.181.589.588.296.884.887.893.795.5
PPA (ours)84.388.391.192.190.894.787.294.690.491.094.896.8
+ +defined prompts, e.g., "a photo of a waterbird". (2) Group-informed prompting [31], which incorporates group descriptions into the prompts, e.g., "a photo of a waterbird on land". (3) ERM [37], a linear classifier trained using cross-entropy loss, (4) WiSE-FT [41], which interpolates zero-shot and ERM models in weight-space, (5) Orth-Cali [3], a debiased zero-shot model that removes biased direction in the text embedding. (6) AFR [30], retrans the last layer of an ERM model with a weighted loss that emphasizes examples where the ERM model performs poorly, (7) JTT [21], (see details in Sec. 3.2), (8) CnC [49], which builds upon JTT [21], but it uses a contrastive loss to train the debiased model, (9) CA [48], trains contrastive adapters by learning similar representations across different groups, (10) CFR [47], refines the representation by aligning them with the class centroids via contrastive loss. We also compare with three group-supervised methods - (11) Group-DRO [32], (12) DFR [17], (13) S-CS [44] and (14) S-SL [44]. + +# 6.3. Training and Evaluation Details + +For each method, we evaluate both its worst-group accuracy and average (in-distribution) accuracy on the test sets. We use CLIP ResNet-50 and CLIP ViT-L/14 as primary models, while also reporting results for CLIP ResNet-101, ViT-B/32, and ViT-B/16. Following prior work [44, 47, 48], we freeze the model backbones and train all models using the SGD optimizer for 100 epochs. The hyperparameter $\tau$ is set to $\{1.2, 1.0, 0.9, 1.0, 1.0\}$ for Waterbirds, CelebA, MetaShift, Living-17, and BAR, respectively. Model selection is based on the highest worst-group validation ac + +Table 3. Experimental results on Living-17 and BAR benchmarks. + +
MethodCLIP ResNet-50CLIP ViT-L/14
Living-17BARLiving-17BAR
WGAAvgWGAWGAAvgWGA
ZS [31]38.083.274.448.092.381.7
ERM [37]53.390.854.984.098.689.0
JTT [21]44.086.458.578.797.390.2
CA [48]62.090.9-80.097.5-
PPA (ours)65.092.576.885.098.191.5
+ +curacy, except for BAR, which lacks a validation set; for BAR, we evaluate the checkpoint from the last epoch. Additionally, since the majority groups in training set do not appear in testing, we measure only the worst-group accuracy for BAR. Further implementation details are provided in Appendix B. + +# 6.4. Main Results + +Tab. 2 presents the worst-group accuracy (WGA) and average (in-distribution) accuracy for all methods on Waterbirds [32], CelebA [23] and MetaShift [20] datasets. Compared to other group-unsupervised debiasing approaches, our PPA achieves superior performance with less than $0.1\%$ trainable parameters (CLIP ResNet-50 has 25,557,032 parameters, while our model $f_{\mathrm{d}}(\cdot)$ has only 4,096 trainable parameters). Specifically, PPA based on CLIP ResNet-50 outperforms the previous state-of-the-art, CFR [47], with improvements of $\{7.4\%, 17.4\%, 9.3\%$ on Water + +Table 4. PPA consistently improves group robustness for across different efficient fine-tuning paradigms using CLIP ResNet-50. The results using CLIP ViT-L/14 are reported in Appendix B.3. + +
MethodWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvg
Linear Probe + ERM7.993.511.994.775.494.4
Linear Probe + PPA84.388.391.192.190.894.7
CoOp + ERM61.796.235.094.875.492.8
CoOp + PPA83.087.690.092.289.093.3
Adapter + ERM61.496.760.694.484.693.9
Adapter + PPA78.291.891.592.587.793.4
+ +Table 5. PPA consistently improves group robustness on Waterbirds across different architectures. + +
MethodCLIP RN-101CLIP ViT-B/32CLIP ViT-B/16
WGAAvgWGAAvgWGAAvg
Zero-shot33.690.047.088.834.088.1
ERM LP62.996.556.895.666.596.4
PPA83.689.783.589.184.489.9
+ +birds, CelebA, and MetaShift, respectively. Moreover, PPA is competitive with group-supervised methods that rely on group annotations. Notably, our improvements in worst-group accuracy come at the cost of a modest reduction in in-distribution accuracy, with an average drop of 1.8 points compared to ERM models using CLIP ViT-L/14. In Tab. 3, we report results for the Living-17 [33] and BAR [26] datasets. We again observe that PPA achieves the highest worst-group performance. Notably, for the BAR dataset, where model selection is not performed and only the last checkpoint is used (due to the absence of a validation set), PPA still attains the highest worst-group accuracy. + +# 6.5. Further Analysis and Ablation Studies + +We conduct comprehensive studies to (1) confirm the versatility of our proposed method—specifically, its compatibility with other efficient fine-tuning paradigms and model architectures—and (2) to understand the contribution of each component to the overall improvement. + +Extending PPA to other parameter-efficient fine-tuning paradigms. In this paper, we adopt linear probes for efficient fine-tuning of foundation models. We also explore the applicability of PPA to other efficient fine-tuning methods, such as prompt tuning [52, 53] (CoOp) and adapter-based tuning [7, 9, 48] (small bottleneck MLPs). Specifically, we replace the linear probe $h_{\mathrm{d}}(\mathbf{x}) = W_{\mathrm{d}}\mathbf{x}$ in Step 2 of Algorithm 1 with the following models: + +- Prompt tuning (CoOp). The prompt for group $i$ is designed as: + +$$ +\mathbf {t} _ {i} = \left[ V _ {1} ^ {i} \right] \left[ V _ {2} ^ {i} \right] \dots \left[ V _ {M} ^ {i} \right] [ \mathrm {C L A S S} ], \tag {20} +$$ + +Table 6. Main component analysis. We present the worst group accuracies using CLIP ResNet-50. "Proj." and "GLA" stands for the projection operation in Eq. (6) and group logit adjustment loss in Eq. (9), respectively. "GT" means we use the ground-truth group labels for training debiased models. + +
Proj.GLAGTWaterbirdsCelebAMetaShift
(a)7.911.975.4
(b)✓54.429.486.2
(c)✓81.670.089.2
(d)✓✓84.391.190.8
(e)✓✓86.891.591.3
+ +![](images/968d3613caf16a9b380d8310061728d61acd41c75e257ba572392ddd7eb610ab.jpg) +(a) Worst Group Recall + +![](images/8c11a75be58e87d5a88f315b76747205af2449ab235ce7bd0e237e67b8d7e7d4.jpg) +(b) Worst Group Precision +Figure 1. The precision and recall of the worst-group examples on Waterbirds and CelebA using CLIP ResNet-50. + +where $[V_m^i]$ is a vector with the same dimensionality as the word embedding and serves as a parameter to be optimized. We follow CoOp to set $M = 16$ . [CLASS] represents the word embedding of the class name. Let $\Phi(\cdot)$ denote the CLIP text encoder. The group scorer for group $i$ is then defined as: + +$$ +h _ {\mathrm {d}} ^ {\mathrm {p t}} (\mathbf {x}; \mathbf {t}) _ {i} = \Phi \left(\mathbf {t} _ {i}\right) ^ {\top} \mathbf {x} / \tau_ {\text {c l i p}}, \tag {21} +$$ + +where $\tau_{\mathrm{clip}}$ is the temperature. + +- Adapter-based tuning. We adopt [7] to transform the visual embeddings $\mathbf{x} \in \mathbb{R}^D$ and the text embedding $Z \in \mathbb{R}^{K \times D}$ using simple 2-layer bottleneck MLPs. Let $H$ denote the feature the hidden-layer dimension. We follow [48] to set $H = 128$ . With ReLU function $\sigma(\cdot)$ , visual adapter weights $W_{\mathrm{v}}^{1} \in \mathbb{R}^{H \times D}, W_{\mathrm{v}}^{2} \in \mathbb{R}^{D \times H}$ and textual adapter weights $W_{\mathrm{t}}^{1} \in \mathbb{R}^{H \times D}, W_{\mathrm{t}}^{2} \in \mathbb{R}^{D \times H}$ , the input $\mathbf{x}$ and text embeddings $Z$ are adapted as: + +$$ +\tilde {\mathbf {x}} = W _ {\mathrm {v}} ^ {2} \sigma \left(W _ {\mathrm {v}} ^ {1} \mathbf {x}\right), \quad \tilde {Z} ^ {\top} = W _ {\mathrm {t}} ^ {2} \sigma \left(W _ {\mathrm {t}} ^ {1} Z ^ {\top}\right). \tag {22} +$$ + +We then use the normalized adapted embeddings and the temperature $\tau_{\mathrm{clip}}$ to output the final scorer: + +$$ +h _ {\mathrm {d}} ^ {\mathrm {a t}} (\mathbf {x}) _ {i} = \tilde {\mathbf {z}} ^ {\top} \tilde {\mathbf {x}} / \tau_ {\mathrm {c l i p}} \tag {23} +$$ + +Tab. 4 demonstrates consistent improvements in worstgroup accuracy over the ERM-trained CLIP ResNet-50 model across three benchmarks, highlighting the versatility + +![](images/871b5df7dc7a49b25578953ea1c10f4472d1e9a729297b9c4da76f85e036cd07.jpg) +Figure 2. Study on the effect of $\tau$ using CLIP ResNet-50. The optimal worst group accuracy is typically observed around $\tau = 1.0$ . + +![](images/fe5498182cc46adb6652dbb3307426c729a5b6cdf775fd0d330d8db5ab6250f1.jpg) + +![](images/3c4fdc8f48cde3c20fc5f0dd64a7f0d18b289a24cb3fe8ab008e323068914598.jpg) + +of our PPA across various efficient fine-tuning paradigms. For instance, on the CelebA dataset, our PPA achieves worst-group accuracy improvements of $55.0\%$ with CoOp and $30.9\%$ with Adapter. Additionally, integrating PPA with these three fine-tuning methods yields comparable performance. However, linear probing is more computationally efficient than prompt tuning, as the latter requires both forward and backward passes through the large text encoder to update the prompts. It is also more storage-efficient than Adapter-based methods, which introduce additional training parameters, i.e., $\theta$ and $\phi$ . + +Study on model versatility. In Tab. 5, we implement our PPA to various backbone architectures, including CLIP ResNet-101, CLIP ViT-B/32 and CLIP ViT-B/16. We observe consistent performance gains on the worst group accuracy, indicating the model versatility of our PPA. + +Main component analysis. In Tab. 6, we provide an ablation study to assess the impact of the projection operation (Proj.) and group logit adjustment (GLA) loss on worst-group accuracy using CLIP ResNet-50. Row (a) represents the ERM-trained linear probing model; Row (b) probes group targets without prior correction; and Row (c) omits the projection operation during training. Row (d) shows results from our proposed method (PPA), while Row (e) replaces estimated group labels with ground-truth labels. Comparing Rows (b) and (d), we observe that adjusting the margin significantly improves worst-group accuracy. In the comparison of Rows (c) and (d), projecting out class proxies enhances group identification, resulting in better worst-group performance. Finally, Row (e) demonstrates the oracle performance using ground-truth labels, revealing that PPA approximates the maximum achievable accuracy, underscoring the importance of accurate pseudo-group labels. + +Study on the quality of estimated group labels. In the absence of training group labels, we rely on the quality of pseudo group labels inferred from the biased model $f_{\mathrm{b}}(\mathbf{x})$ . To evaluate the quality of identified minority groups within the training set, we measure two metrics: precision, defined as the fraction of examples within the identified minority groups that belong to the worst-performing group, and recall, the fraction of examples from the worst-performing + +group captured by the identified minority groups. Here, the worst-performing group is defined as the group on which the ERM model achieves the lowest validation accuracy. In Fig. 1, we compare our method with two baselines: (1) ERM, which uses standard empirical risk minimization to train biased models, and (2) CA [48], which leverages zero-shot models to identify minority groups. Our method, PPA, achieves significantly higher recall and precision than both ERM and CA. This improvement is attributed to our biased model $f_{\mathrm{b}}$ , which relies more heavily on spurious features to make predictions. + +Study on the hyper-parameter $\tau$ . We examine the effect of $\tau \in \mathbb{R}_+$ in Eq. (9), as illustrated in Fig. 2 (more details are in Appendix B.6). Specifically, we vary $\tau$ from 0.0 to 2.0 and report both the worst-group accuracy and average accuracy on the Waterbirds, CelebA, and MetaShift datasets using CLIP ResNet-50. A larger $\tau$ promotes a greater margin for the minority groups, while $\tau = 0$ reduces to the standard cross-entropy loss. Our findings reveal that (1) average accuracy decreases monotonically as $\tau$ increases, and (2) the optimal worst-group accuracy is generally achieved around $\tau = 1.0$ . For example, the optimal values of $\tau$ are 1.2, 1.0 and 0.9 for Waterbirds, CelebA and MetaShift, respectively. This aligns with our theoretical analysis, which suggests that the Bayes optimal classifier for minimizing the balanced group error is attained when $\tau = 1$ . + +# 7. Conclusion + +In this paper, we introduce Project-Probe-Aggregate (PPA), a novel, parameter-efficient fine-tuning framework for enhancing the group robustness of image-text foundation models without relying on training group labels. Our approach improves the identification of minority groups by projecting image features onto the null space of class proxies. Additionally, we design a group logit adjustment loss to minimize balanced group error and mitigate spurious correlations. Through theoretical analysis and empirical evaluations across diverse benchmarks, fine-tuning paradigms and model architectures, we demonstrate that the proposed method effectively enhances robust group performance of foundation models. + +# Acknowledgment + +This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore. + +# References + +[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. 1, 2 +[2] Saeid Asgari, Aliasghar Khani, Fereshte Khani, Ali Gholami, Linh Tran, Ali Mahdavi Amiri, and Ghassan Hamarneh. Masktune: Mitigating spurious correlations by forcing to explore. 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To address this issue, we propose a simple three-step approach-Project-Probe-Aggregate (PPA)-that enables parameter-efficient fine-tuning for foundation models without relying on group annotations. Building upon the failure-based debiasing scheme, our method, PPA, improves its two key components: minority samples identification and the robust training algorithm. Specifically, we first train biased classifiers by projecting image features onto the nullspace of class proxies from text encoders. Next, we infer group labels using the biased classifier and probe group targets with prior correction. Finally, we aggregate group weights of each class to produce the debiased classifier. Our theoretical analysis shows that our PPA enhances minority group identification and is Bayes optimal for minimizing the balanced group error, mitigating spurious correlations. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 543, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 543, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 543, + 295, + 687 + ], + "type": "text", + "content": "Image-text foundation models [12, 31, 40]—large models pre-trained on web-scale data—are becoming increasingly prevalent in real-world deployments. However, adapting these models to downstream tasks, whether through zero-shot transfer or fine-tuning, remains challenging due to fundamental issues of group robustness: they achieve low average test error but incur high risk on certain groups of examples [3, 44, 47, 48]. This issue becomes particularly pronounced in the presence of spurious correlations [8], where a classifier relies on non-causal relationships that happen to align with class labels in training but break down during deployment. 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MethodWorst-group Recall (%)Worst-group Precision (%)
CA [48]46.415.6
JTT [21]78.624.1
PPA (ours)80.444.3
", + "image_path": "98ddfd37b139ea8a93d91224ae93bdb90acf617c3af6cf8027449d6f0894ea84.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 288, + 555, + 344 + ], + "lines": [ + { + "bbox": [ + 313, + 288, + 555, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 555, + 344 + ], + "type": "text", + "content": "Table 1. The precision and recall of the worst-group examples (i.e., the group with lowest validation accuracy) identified by biased models on the Waterbird training set [32] using CLIP ResNet-50. Our PPA is more susceptible to supurious features, achieving higher worst-group recall and precision compared to previous methods." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 365, + 555, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 402 + ], + "type": "text", + "content": "birds” predominantly appear in images with a “water” background. When trained on such a dataset, neural networks often rely on the background to recognize the objects." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 402, + 556, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 402, + 556, + 582 + ], + "spans": [ + { + "bbox": [ + 312, + 402, + 556, + 582 + ], + "type": "text", + "content": "As a result, several fine-tuning methods have emerged to improve group robustness in foundation models [3, 29, 44, 47, 48]. Unlike conventional robust training frameworks, which typically re-train the entire model [21, 22, 26, 27] (which is computationally expensive) and/or require group labels [1, 32] (which demands additional annotation costs), these fine-tuning methods prioritize parameter and annotation efficiency. They address spurious correlations by optimizing only a small subset of parameters without relying on training group labels. For instance, Zhang and Ré [48] fine-tune a lightweight adapter and You et al. [47] propose to optimize projection layers to improve distributional robustness. In this paper, we build on these ideas by focusing on efficient fine-tuning to enhance group robustness, i.e., training linear probes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "type": "text", + "content": "At a high level, in the absence of group annotations, a common strategy [5, 19, 21, 22, 26, 48, 49] involves first identifying minority groups by training a biased model that easily overfits to spurious features. Subsequently, a debiased model is trained using the inferred group labels. To improve the identification of minority groups, prior work proposes various strategies: [22, 26] employ generalized cross-entropy loss to amplify the model bias, JTT [21] simply trains a model with empirical risk minimization (ERM) and tunes hyperparameters to exacerbate bias, CA [48] leverages the correctness of zero-shot pre" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "text", + "content": "This work was done during Beier Zhu's visit at AGI Lab, Westlake University. " + }, + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "text", + "content": " denotes corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25487" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 312 + ], + "type": "text", + "content": "dictions and [5] uses low-capacity networks to capture spurious features. In this paper, we leverage the pre-trained knowledge from the image-text foundation models to effectively induce bias, further enhancing the identification of minority groups. Specifically, we project out class proxies, provided by the text encoders, from the input image features and use only the remaining information to train the biased classifiers. Intuitively, removing class information forces the model to rely more heavily on spurious features for predictions. We provide theoretical analysis to support this intuition in Proposition 1. Empirically, in Tab. 1, we evaluate the quality of the inferred groups in the training datasets obtained by our method, and compare it to prior approaches [21, 48]. Specifically, we measure precision—the fraction of examples within the identified minor groups that belong to the worst-performing group, and recall—the fraction of examples from the worst-performing group that are captured by the identified minor groups. As expected, our method achieves higher precision and recall, demonstrating superior group identification." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 314, + 295, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 295, + 494 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 295, + 494 + ], + "type": "text", + "content": "Given the inferred groups, typical debiased learning algorithms up-weight/up-sample minority group samples to enhance performance on these challenging instances [5, 10, 17, 21, 26]. However, determining the optimal weights requires careful hyper-parameter tuning and lacks theoretical guidance. Since the goal of debiased training is to minimize the Balanced Group Error (BGE) [22, 36], we propose a methodology designed to achieve this objective directly. Rather than predicting class labels, our method is trained to probe for group targets by compensating group priors into the softmax cross-entropy during training. Afterward, we aggregate group weights of each class to produce the final debiased classifier. We dub our overall debiasing framework Project-Probe-Aggregate (PPA), and demonstrate that it is Bayes optimal for minimizing BGE in Proposition 2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 496, + 209, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 496, + 209, + 508 + ], + "spans": [ + { + "bbox": [ + 67, + 496, + 209, + 508 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 510, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 510, + 295, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 569 + ], + "type": "text", + "content": "- We project out the class proxies offered by the text encoder and train the biased model on the residual image features, with theoretical analysis showing this approach increases reliance on spurious features, improving minority group identification." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 570, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 629 + ], + "type": "text", + "content": "- We propose a novel debiasing method that is consistent for minimizing the balanced group error. The debiased classifier predicts group labels compensated by group priors and uses weight-space aggregation after fine-tuning to avoid group inference overhead." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "content": "- We confirm the effectiveness of our proposal across five benchmarks with spurious correlations. With less than " + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "content": " of the foundation model parameters, our approach PPA improves the worst group accuracy over the state-of-the-art without training group annotations. Beyond linear probes, we also adapt other parameter-efficient finetuning paradigms (e.g., prompt tuning and adapters) to" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 72, + 503, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 72, + 503, + 84 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 503, + 84 + ], + "type": "text", + "content": "show the versatility of the proposed method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 95, + 400, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 95, + 400, + 106 + ], + "spans": [ + { + "bbox": [ + 314, + 95, + 400, + 106 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 114, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 114, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 114, + 555, + 437 + ], + "type": "text", + "content": "Improving group robustness. There have been numerous works aimed at improving group robustness, which broadly fall into two categories based on whether group labels are available during training. (i) Group supervised methods focus on balancing the contribution of each group during the training phase, such as through re-sampling/reweighting [10, 11, 13, 17, 24, 39], or robust optimization [1, 32, 34]. However, this approach requires additional annotation costs for group labels. In this paper, we focus on (ii) group unsupervised methods, which do not assume the availability of group labels during training [2, 14, 15, 18, 35, 42, 43, 46]. Without group labels, a common strategy is to first train an easily biased model, and then infer groups based on its biased predictions. A robust model is subsequently trained using the inferred group labels through techniques such as importance weighting [21, 26, 30], robust optimization [4, 27], or by learning similar representations for groups within the same class [49]. In this paper, we leverage the general knowledge from image-text foundation models to train a biased classifier by excluding the class proxy information generated by the CLIP text encoder. Note that classifier in [39] also predicts group labels, our approach differs in two key aspects: 1) We further incorporate logit offsets during training, which compensates for group imbalances and leads to lower balanced error. 2) Unlike [39], our method does not require access to ground-truth group labels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "type": "text", + "content": "Efficient robust fine-tuning for foundation models. The advent of image-text foundation models has led to several efforts to develop efficient group-robust fine-tuning methods [3, 6, 16, 17, 28, 44, 47, 48, 50, 55]. Kirichenko et al. [17] demonstrate that last-layer retraining significantly improves group robustness in pretrained models. Zhang and Ré [48] use contrastive objectives to train adapters, bringing same-class embeddings closer together. Chuang et al. [3] reduce bias in image-text models by removing biased directions in text embeddings. Other works [44, 47] focus on lightweight fine-tuning by optimizing only the projection layers of the vision branch for distributional robustness. Our approach builds on efficient fine-tuning by training only a linear classification head for group targets and further introduces weight-space ensembling after fine-tuning to eliminate the overhead of group inference." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 639, + 399, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 639, + 399, + 651 + ], + "spans": [ + { + "bbox": [ + 314, + 639, + 399, + 651 + ], + "type": "text", + "content": "3. 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Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": "Considering a classification problem with instances " + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathcal{X} \\subseteq \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": " and labels " + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{Y} = [K]" + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": ". Each data point " + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}, y)" + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": " has an input attribute " + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "inline_equation", + "content": "a(\\mathbf{x}) \\in \\mathcal{A}" + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": " that is spuriously correlated" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25488" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": "with the target " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ". We form " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "|\\mathcal{G}| = |\\mathcal{A}|\\times |\\mathcal{Y}|" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " groups, where each group label " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "g\\in \\mathcal{G}" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " is the combination of the attribute " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " and the class label " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "g\\coloneqq (a,y)" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ". Given a training dataset " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathbf{x}_i,y_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " drawn from some unknown distribution " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "\\mathbb{P}" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ", and let " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_g" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " be the distribution conditioned on " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "g\\in \\mathcal{G}" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ". We assume that spurious attribute annotations are not available for the samples in the training set. Our goal is to train a model " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "f_{\\theta}:\\mathcal{X}\\to \\mathbb{R}^{K}" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " that outputs prediction score, such that it achieves low expected error:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 188, + 296, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 188, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 104, + 188, + 296, + 209 + ], + "type": "interline_equation", + "content": "\\mathcal {R} = \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {1}", + "image_path": "407817dc37d194b221b204ee033d03b4fe4cf7845fca4ec8a6105126449f813c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 217, + 296, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 240 + ], + "type": "text", + "content": "and, more importantly, exhibits group robust, i.e., achieving low worst-group error:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 248, + 295, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 248, + 295, + 269 + ], + "spans": [ + { + "bbox": [ + 86, + 248, + 295, + 269 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {\\mathrm {w g}} = \\max _ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\mathbb {P} _ {g}} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f _ {\\theta} (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {2}", + "image_path": "e87445ee896b4a6ecabe32cc0ac6592ababb852fedafe744f245d1fe0729d09e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "content": "For example, in the Waterbirds [32] dataset, the task is to classify birds " + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "inline_equation", + "content": "y \\in \\{\\text{waterbird}, \\text{landbird}\\}" + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "content": ", with the background serving as a spurious attribute (" + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "inline_equation", + "content": "a \\in \\{\\text{water}, \\text{land}\\}" + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "content": "). A notable pattern is that about " + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "content": " of waterbird images have a water background, causing models to rely on the \"water\" background to predict \"waterbird\". This reliance leads to poor performance on minority groups, such as landbirds with water backgrounds " + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "inline_equation", + "content": "g =" + }, + { + "bbox": [ + 55, + 276, + 296, + 421 + ], + "type": "text", + "content": " (water, landbird). Unlike domain generalization or out-of-distribution evaluation, all groups are present in the training, validation, and test splits. However, the training groups are imbalanced, which can result in poor group robustness on the test set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 427, + 296, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 452 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 452 + ], + "type": "text", + "content": "3.2. Common Strategy for Improving Unsupervised Group Robustness" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 458, + 296, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 296, + 505 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 296, + 505 + ], + "type": "text", + "content": "At a high level, typical methods without access to group labels first train a biased model and then use its biased predictions to infer the groups. Subsequently, a robust model is trained using the inferred group labels." + }, + { + "bbox": [ + 55, + 458, + 296, + 505 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "text", + "content": "Taking JTT [21] as an example, it identifies the misclassified samples from ERM model " + }, + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{erm}}" + }, + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "text", + "content": " as the error set " + }, + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 506, + 296, + 530 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 538, + 295, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 538, + 295, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 295, + 552 + ], + "type": "interline_equation", + "content": "\\mathcal {E} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\text {s . t .} f _ {\\operatorname {e r m}} \\left(\\mathbf {x} _ {i}\\right) \\neq y _ {i} \\right\\}, \\tag {3}", + "image_path": "777b6a915acc82b9a0cad759acd0a881a12e57cfe71bd96b6c6dcf0ef23a2e9d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 559, + 296, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 559, + 296, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 296, + 572 + ], + "type": "text", + "content": "then trains a robust model by weighting the samples in " + }, + { + "bbox": [ + 55, + 559, + 296, + 572 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 559, + 296, + 572 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 589, + 295, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 589, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 61, + 589, + 295, + 617 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {J T T}} (\\theta , \\mathcal {E}) = \\lambda \\sum_ {(\\mathbf {x}, y) \\in \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta) + \\sum_ {(\\mathbf {x}, y) \\notin \\mathcal {E}} \\ell (\\mathbf {x}, y; \\theta), \\tag {4}", + "image_path": "54b35ee107b4f20035fc9c9fc012d094c0a71fee036bfb5deef728b1a187ca46.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "inline_equation", + "content": "\\lambda \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "text", + "content": " is a hyperparameter. The core idea behind JTT is that ERM models tend to fit groups with easily learnable spurious correlations. The samples in " + }, + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 624, + 296, + 696 + ], + "type": "text", + "content": " are primarily from minority groups where these correlations fail. Upweighting such challenging samples improves the model's performance on the worst-performing groups." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "type": "text", + "content": "Remark. Improving group robustness without access to group labels hinges on identifying minority groups by training a biased model that overfits on spurious features. Prior work amplifies this bias through various strategies: LfF [26] employs generalized cross-entropy (GCE) loss to bias the first-stage model, JTT [21] tunes hyperparameters to induce bias, and [5] uses low-capacity networks to capture spurious features. In this paper, we enhance bias by projecting out the class proxies from the input features, using only the remaining information for classification. In Sec. 5.1, we prove that this operation increases susceptibility to spurious features, aiding the identification of minority groups." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 217, + 554, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 554, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 554, + 311 + ], + "type": "text", + "content": "Another key factor is the robust learning algorithm given the pseudo groups. Prior methods address this through importance weighting [21, 26], robust optimization [4, 27], or aligning representations within the same class [49]. Our approach, PPA, predicts pseudo group labels and applies a group prior offset to correct for imbalance. In Sec. 5.2, we prove that our training algorithm effectively mitigates spurious correlations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 323, + 375, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 323, + 375, + 335 + ], + "spans": [ + { + "bbox": [ + 314, + 323, + 375, + 335 + ], + "type": "text", + "content": "4. Methods" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 342, + 554, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 554, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 554, + 415 + ], + "type": "text", + "content": "Tuning entire pre-trained models is both time-consuming and computationally costly. Recent work [17] shows that simple last-layer retraining performs well on spurious correlation benchmarks. In our approach, the input " + }, + { + "bbox": [ + 313, + 342, + 554, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 342, + 554, + 415 + ], + "type": "text", + "content": " represents image features encoded by CLIP. We freeze the backbone and learn linear classifiers for efficient fine-tuning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 415, + 554, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 554, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 554, + 498 + ], + "type": "text", + "content": "We now present PPA, a simple three-step approach following the common strategy in Sec. 3.2. First, we train a biased classifier by removing the class proxies generated by the CLIP text encoder. Next, we group samples by classification correctness and train a robust model to predict group labels using our proposed group logit adjustment. Finally, we aggregate group weights to produce the final classifier." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": "Step 1: Project out class proxies. We compute the matrix " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "Z = [\\mathbf{z}_1, \\ldots, \\mathbf{z}_K]^\\top \\in \\mathbb{R}^{K \\times d}" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": " whose rows are the text embeddings of the " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": " class names. Specifically, each " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_j" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": " is derived from a prompt like \"a photo of a [CLASS].\" with the class token [CLASS] replaced by the " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": "-th class name. Let " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "\\Pi \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": " be the projection operator onto the null space of " + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 313, + 498, + 554, + 583 + ], + "type": "text", + "content": ", given by:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 382, + 590, + 553, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 590, + 553, + 605 + ], + "spans": [ + { + "bbox": [ + 382, + 590, + 553, + 605 + ], + "type": "interline_equation", + "content": "\\Pi = I - Z ^ {\\top} \\left(Z Z ^ {\\top}\\right) ^ {- 1} Z \\tag {5}", + "image_path": "ced77d4acc771297500fb51d9ff4cb5fa22a85ea46cf75b44f49511187644238.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "text", + "content": ", the biased model " + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "inline_equation", + "content": "f_{\\mathsf{b}}: \\mathcal{X} \\to \\mathbb{R}^{K}" + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "text", + "content": " is formulated as a linear classifier parameterized by a matrix " + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "inline_equation", + "content": "W_{\\mathsf{b}} \\in \\mathbb{R}^{K \\times d}" + }, + { + "bbox": [ + 313, + 613, + 554, + 639 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 400, + 648, + 553, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 648, + 553, + 662 + ], + "spans": [ + { + "bbox": [ + 400, + 648, + 553, + 662 + ], + "type": "interline_equation", + "content": "f _ {\\mathrm {b}} (\\mathbf {x}) = W _ {\\mathrm {b}} \\Pi \\mathbf {x} \\tag {6}", + "image_path": "3fd9253cd652b78c5d11de26c654438de306280e93862c883b7655ff949d08ea.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "text", + "content": "To account for potential class imbalance" + }, + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "text", + "content": ", we apply the logit-adjustment loss [25, 54] to ensure " + }, + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}" + }, + { + "bbox": [ + 313, + 670, + 554, + 696 + ], + "type": "text", + "content": " focuses on spu" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 702, + 264, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 264, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 264, + 713 + ], + "type": "text", + "content": "It is also known as the failure-based debiasing scheme. [26]" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 324, + 702, + 550, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 702, + 550, + 713 + ], + "spans": [ + { + "bbox": [ + 324, + 702, + 550, + 713 + ], + "type": "text", + "content": "Datasets like Waterbirds [32] and CelebA [23] are class imbalanced." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25489" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 209, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 209, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 209, + 83 + ], + "type": "text", + "content": "rious features rather than class priors:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 91, + 295, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 91, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 67, + 91, + 295, + 120 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathrm {l a}} (y, f _ {\\mathrm {b}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y}}{\\sum_ {y ^ {\\prime} \\in \\mathcal {Y}} \\exp \\left(f _ {\\mathrm {b}} (\\mathbf {x}) + \\ln \\pi\\right) _ {y ^ {\\prime}}}, \\tag {7}", + "image_path": "6d8fd22cbc79c0009cc4906ada052976ed61f9559e971727102b0971627b54b6.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "spans": [ + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "inline_equation", + "content": "\\pi_y" + }, + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "text", + "content": " is the prior of class " + }, + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 127, + 295, + 161 + ], + "type": "text", + "content": ". In Proposition 1, we show that our biased model is more easily influenced by spurious correlation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "text", + "content": "Step 2: Probe with group target. We follow the heuristic of JTT [21] to identify minority groups that " + }, + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}" + }, + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "text", + "content": " misclassifies:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 198, + 295, + 218 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 198, + 295, + 218 + ], + "spans": [ + { + "bbox": [ + 108, + 198, + 295, + 218 + ], + "type": "interline_equation", + "content": "\\hat {a} (\\mathbf {x}) = \\mathbb {1} [ y \\neq \\operatorname {a r g m a x} _ {y ^ {\\prime} \\in \\mathcal {Y}} f _ {\\mathrm {b}} (\\mathbf {x}) _ {y ^ {\\prime}} ], \\tag {8}", + "image_path": "955aefd94667a9a5b8a7a803bb93ace34338882b99d23d1bb67378504203611e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "inline_equation", + "content": "\\mathbb{1}[\\cdot ]" + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": " is the indicator function. Then, each training sample is augmented as " + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},y,\\hat{a})" + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": ", with the pseudo group defined as the combination of " + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "inline_equation", + "content": "\\hat{a}" + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "inline_equation", + "content": "\\hat{g} \\coloneqq (y,\\hat{a}) \\in \\hat{\\mathcal{G}}" + }, + { + "bbox": [ + 55, + 223, + 295, + 259 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "spans": [ + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "text", + "content": "Our approach PPA uses a group scorer, implemented via linear probing, to predict pseudo group labels. Specifically, the group score " + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "inline_equation", + "content": "h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x}:\\mathcal{X}\\to \\mathbb{R}^{|\\hat{\\mathcal{G}}|}" + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "text", + "content": " is parameterized by " + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{d}}\\in \\mathbb{R}^{|\\hat{\\mathcal{G}}|\\times d}" + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "inline_equation", + "content": "\\hat{\\beta}" + }, + { + "bbox": [ + 55, + 259, + 296, + 334 + ], + "type": "text", + "content": " denote the group priors, we propose the group logit adjustment loss to achieve balanced group performance.:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 64, + 342, + 295, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 342, + 295, + 383 + ], + "spans": [ + { + "bbox": [ + 64, + 342, + 295, + 383 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathbf {g l a}} (\\hat {g}, h _ {\\mathbf {d}} (\\mathbf {x})) = - \\ln \\frac {\\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {\\hat {g}}}{\\sum_ {g ^ {\\prime} \\in \\hat {\\mathcal {G}}} \\exp \\left(h _ {\\mathbf {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}\\right) _ {g ^ {\\prime}}}, \\tag {9}", + "image_path": "df4305a32f66044f9e750b4d86f83c21b9a3563011f83a4a5993ac844e59aed4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 384, + 203, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 203, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 203, + 395 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 384, + 203, + 395 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 384, + 203, + 395 + ], + "type": "text", + "content": " is a hyper-parameter." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 396, + 296, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 431 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 431 + ], + "type": "text", + "content": "Step 3: Aggregate weights. The final debiased classifier " + }, + { + "bbox": [ + 55, + 396, + 296, + 431 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\mathbf{x}) : \\mathcal{X} \\to \\mathbb{R}^{K}" + }, + { + "bbox": [ + 55, + 396, + 296, + 431 + ], + "type": "text", + "content": " is constructed by aggregating the weights corresponding to each class:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 78, + 449, + 295, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 449, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 78, + 449, + 295, + 479 + ], + "type": "interline_equation", + "content": "f _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\mathbf {w} _ {y} ^ {\\top} \\mathbf {x}, \\text {w h e r e} \\mathbf {w} _ {y} ^ {\\top} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g}. \\tag {10}", + "image_path": "d8289384b7e456fe8bb609d8f25973582b4c6a5c27ce912d56c0769eb4c37fd0.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{d},g}" + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "text", + "content": " represents the weight vector in " + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{d}}" + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "text", + "content": " associated with group " + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 485, + 295, + 533 + ], + "type": "text", + "content": ". This weight-space aggregation transforms group classification into class prediction, eliminating the need for group inference overhead." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "text", + "content": "In Proposition 2, we prove that the debiased model " + }, + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "text", + "content": " is the Bayes optimal classifier for minimizing the balanced group error. Beyond linear classifiers, we also employ other parameter-efficient fine-tuning paradigms (e.g., prompt tuning and adapters) to implement our debiased classifier " + }, + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 533, + 296, + 617 + ], + "type": "text", + "content": ", as detailed in Sec. 6.5. The full pipeline is outlined in Algorithm 1." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 627, + 175, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 627, + 175, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 627, + 175, + 640 + ], + "type": "text", + "content": "5. Theoretical Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 647, + 295, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 295, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 295, + 659 + ], + "type": "text", + "content": "5.1. Removal of Class Proxies Amplifies Model Bias" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "Intuitively, removing class information forces the model " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " to rely more on spurious features for predicting class labels. To support this intuition, we provide theoretical evidence in a linear regression setup. Let " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " denote the core features" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 72, + 435, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 72, + 435, + 83 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 435, + 83 + ], + "type": "text", + "content": "Algorithm 1 Pipeline of PPA" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "spans": [ + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "text", + "content": "1: Given: Training dataset " + }, + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathbf{x}_i, y_i\\}_{i=1}^N" + }, + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "text", + "content": ", class proxies " + }, + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_j\\}_{j=1}^K" + }, + { + "bbox": [ + 319, + 88, + 554, + 114 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 332, + 114, + 399, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 114, + 399, + 125 + ], + "spans": [ + { + "bbox": [ + 332, + 114, + 399, + 125 + ], + "type": "text", + "content": "Step 1: Project" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 320, + 125, + 549, + 148 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 320, + 125, + 523, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 125, + 523, + 137 + ], + "spans": [ + { + "bbox": [ + 320, + 125, + 523, + 137 + ], + "type": "text", + "content": "2: Compute the projection matrix " + }, + { + "bbox": [ + 320, + 125, + 523, + 137 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 320, + 125, + 523, + 137 + ], + "type": "text", + "content": " using Eq. (5)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "spans": [ + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "text", + "content": "3: Build " + }, + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}(\\mathbf{x}) = W_{\\mathrm{b}} \\Pi \\mathbf{x}" + }, + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "text", + "content": " and optimize " + }, + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{b}}" + }, + { + "bbox": [ + 320, + 137, + 549, + 148 + ], + "type": "text", + "content": " using Eq. (7)." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 332, + 149, + 392, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 149, + 392, + 160 + ], + "spans": [ + { + "bbox": [ + 332, + 149, + 392, + 160 + ], + "type": "text", + "content": "Step 2: Probe" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 320, + 161, + 543, + 185 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 320, + 161, + 491, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 161, + 491, + 173 + ], + "spans": [ + { + "bbox": [ + 320, + 161, + 491, + 173 + ], + "type": "text", + "content": "4: Identify pseudo groups " + }, + { + "bbox": [ + 320, + 161, + 491, + 173 + ], + "type": "inline_equation", + "content": "\\{\\hat{g}\\}" + }, + { + "bbox": [ + 320, + 161, + 491, + 173 + ], + "type": "text", + "content": " via Eq. (8)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "spans": [ + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "text", + "content": "5: Build " + }, + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "inline_equation", + "content": "h_{\\mathsf{d}}(\\mathbf{x}) = W_{\\mathsf{d}}\\mathbf{x}" + }, + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "text", + "content": " and optimize " + }, + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "inline_equation", + "content": "W_{\\mathsf{d}}" + }, + { + "bbox": [ + 320, + 173, + 543, + 185 + ], + "type": "text", + "content": " using Eq. (9)." + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 332, + 186, + 411, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 186, + 411, + 196 + ], + "spans": [ + { + "bbox": [ + 332, + 186, + 411, + 196 + ], + "type": "text", + "content": "Step 3: Aggregate" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 320, + 196, + 553, + 232 + ], + "type": "list", + "angle": 0, + "index": 29, + "blocks": [ + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "spans": [ + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "text", + "content": "6: Construct " + }, + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "text", + "content": " by aggregating weights of " + }, + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{d}}" + }, + { + "bbox": [ + 320, + 196, + 553, + 220 + ], + "type": "text", + "content": ", as in Eq. (10)." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 320, + 221, + 392, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 221, + 392, + 232 + ], + "spans": [ + { + "bbox": [ + 320, + 221, + 392, + 232 + ], + "type": "text", + "content": "7: Return " + }, + { + "bbox": [ + 320, + 221, + 392, + 232 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 320, + 221, + 392, + 232 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": "which are stable for predicting the target " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": " be a spurious feature. The spurious feature is correlated with the target in the training set, but this correlation may not hold during testing. Suppose we observe " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": " features, stacked as " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "C = [\\mathbf{c}_1,\\dots ,\\mathbf{c}_n]^\\top \\in \\mathbb{R}^{N\\times d}" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = [s_1,\\ldots ,s_n]^\\top \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": ". We are interested in the contribution of the spurious feature " + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 256, + 554, + 338 + ], + "type": "text", + "content": " across the following two models:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "spans": [ + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "text", + "content": "- Full model: Linear regression on the core features " + }, + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "text", + "content": " and the spurious feature " + }, + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 314, + 339, + 554, + 363 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 398, + 371, + 553, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 371, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 398, + 371, + 553, + 384 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = C \\boldsymbol {\\beta} + \\gamma \\mathbf {s} + \\varepsilon , \\tag {11}", + "image_path": "fa332bff6cc559a248fc988584724f33b809e8574db82032c0d61505561cc113.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "text", + "content": " are the weights associated with the core features and the spurious feature, respectively. " + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 321, + 392, + 554, + 426 + ], + "type": "text", + "content": " is a noise term with an expected value of 0." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "spans": [ + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": "- Projected model: Applying the projection matrix " + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "inline_equation", + "content": "\\tilde{C} = C\\Pi" + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": ", followed by linear regression on " + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{c}}" + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 314, + 427, + 554, + 461 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 394, + 462, + 553, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 462, + 553, + 475 + ], + "spans": [ + { + "bbox": [ + 394, + 462, + 553, + 475 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = \\tilde {C} \\tilde {\\boldsymbol {\\beta}} + \\gamma^ {\\prime} \\mathbf {s} + \\varepsilon^ {\\prime}, \\tag {12}", + "image_path": "c5eddde67e28428c8c8691c39e573ef3ddaf4e99bcf23a937aef4dadf0cbf03a.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "spans": [ + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "inline_equation", + "content": "\\tilde{\\beta}" + }, + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "inline_equation", + "content": "\\gamma^\\prime" + }, + { + "bbox": [ + 321, + 479, + 553, + 503 + ], + "type": "text", + "content": " are the weights for the projected core features and the spurious feature, respectively." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "text", + "content": "In Eq. (11), the core features " + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "text", + "content": " can be decomposed into the remaining part " + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "inline_equation", + "content": "\\tilde{C}" + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "text", + "content": " and the projected-out part " + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{o}}" + }, + { + "bbox": [ + 313, + 504, + 553, + 528 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 364, + 534, + 553, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 534, + 553, + 548 + ], + "spans": [ + { + "bbox": [ + 364, + 534, + 553, + 548 + ], + "type": "interline_equation", + "content": "C = C \\Pi + C (I - \\Pi) = \\tilde {C} + C _ {\\circ}. \\tag {13}", + "image_path": "a25e70b9f6f808f31b6859511ad32068105fa213261ea7a5a1f647cc6ad8ca94.jpg" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\circ} = C_{\\circ}\\beta" + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "content": " denote the contribution of the projected-out core features in the full model. Define " + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "inline_equation", + "content": "M = I - \\tilde{C} (\\tilde{C}^{\\top}\\tilde{C})^{-1}\\tilde{C}^{\\top}" + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{r_{y_o}} = M\\mathbf{y_o}" + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{r_s} = M\\mathbf{s}" + }, + { + "bbox": [ + 313, + 556, + 554, + 628 + ], + "type": "text", + "content": ". The following proposition states that projecting out core features can make the model more susceptible to spurious feature (proof in Appendix A.1)." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 313, + 634, + 553, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 553, + 656 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 553, + 656 + ], + "type": "text", + "content": "Proposition 1. The weight of the spurious feature after projection is" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 397, + 657, + 553, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 657, + 553, + 684 + ], + "spans": [ + { + "bbox": [ + 397, + 657, + 553, + 684 + ], + "type": "interline_equation", + "content": "\\gamma^ {\\prime} = \\gamma + \\frac {\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {y _ {o}}}}{\\mathbf {r _ {s}} ^ {\\top} \\mathbf {r _ {s}}}. \\tag {14}", + "image_path": "00ffaa1dd7832e9522fe5185f9401bc100fb88123b67c62e0eaf5218ce34f361.jpg" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "Remark. Since the denominator " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{r_s}^\\top \\mathbf{r_s}" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " is non-negative, the model relies more on spurious feature, i.e., " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\gamma^{\\prime} > \\gamma" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": ", if" + } + ] + } + ], + "index": 42 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25490" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{r_s}^\\top \\mathbf{r_y_o} > 0" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ". In other words, if the spurious feature " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " is positively correlated with the contribution of projected-out core features " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_o" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " in the space of " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": ", the weight of the spurious feature will increase. For instance, consider the Waterbirds dataset [32], the spurious feature water background is positively correlated with the core feature waterbird (about " + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": " of waterbird images have a water background). If we remove the contribution of waterbird by projection, the weight of the spurious feature water will increase." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 186, + 296, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 296, + 210 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 296, + 210 + ], + "type": "text", + "content": "5.2. Group Classification and Aggregation Mitigate Spurious Correlation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 216, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 216, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 296, + 251 + ], + "type": "text", + "content": "The goal of training a debiased model to avoid spurious correlation is to minimize the Balanced Group Error (BGE) rates [22]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 74, + 255, + 296, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 255, + 296, + 285 + ], + "spans": [ + { + "bbox": [ + 74, + 255, + 296, + 285 + ], + "type": "interline_equation", + "content": "\\operatorname {B G E} (f) = \\frac {1}{| \\mathcal {G} |} \\sum_ {g \\in \\mathcal {G}} \\mathbb {E} _ {\\mathbf {x} \\mid g} [ y \\neq \\underset {y ^ {\\prime} \\in \\mathcal {Y}} {\\operatorname {a r g m a x}} f (\\mathbf {x}) _ {y ^ {\\prime}} ] \\tag {15}", + "image_path": "c8e53716b1e25b6a623dbb32b5deff8987276ef00932fa78d527bf8020627126.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": "A natural question is: what is the Bayes optimal classifier for this problem, i.e., " + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "inline_equation", + "content": "f^{*} \\in \\arg \\min_{f} \\mathsf{BGE}(f)" + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": ". Suppose the underlying group-probabilities " + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(g|\\mathbf{x}) \\propto \\exp (h^{*}(\\mathbf{x})_{g})" + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": " for unknown scorer: " + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "inline_equation", + "content": "h^{*}: \\mathcal{X} \\to \\mathbb{R}^{|G|}" + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": ". The Bayes optimal classifier " + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "inline_equation", + "content": "f^{*}" + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": " is derived from the following Proposition (proof in Appendix A.2):" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": "Proposition 2. Let " + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(y)" + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": " denote the set of groups with class label " + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(y) := \\{g = (y', a) \\in \\mathcal{G} | y' = y\\}" + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": " denote the group priors, i.e., " + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "inline_equation", + "content": "\\beta_g = \\mathbb{P}(g)" + }, + { + "bbox": [ + 55, + 365, + 296, + 403 + ], + "type": "text", + "content": ". The prediction:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 407, + 294, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 407, + 294, + 434 + ], + "spans": [ + { + "bbox": [ + 64, + 407, + 294, + 434 + ], + "type": "interline_equation", + "content": "\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\ln \\beta\\right) _ {g} \\tag {16}", + "image_path": "049d996c0f2fd1a920147fe29d903421d2c0f2d14f4a2b3893cd135372c4746e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 438, + 236, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 438, + 236, + 451 + ], + "spans": [ + { + "bbox": [ + 55, + 438, + 236, + 451 + ], + "type": "text", + "content": "is Bayes optimal for the problem in Eq. (15)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": "Remark. We translate the unknown distributional class scores based on group logits " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": " and group priors " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": ". To obtain " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "f^{*}" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": ", we can learn the ERM solution for group logits " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": ". Then, we can minus the logarithm of the group prior " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "\\ln \\beta" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": " and aggregate the logits that belongs to " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(y)" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": " to yield the prediction for each class " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": ". In practice, instead predict Eq. (47), we introduce a hyper-parameter " + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_{+}" + }, + { + "bbox": [ + 55, + 455, + 296, + 539 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 60, + 544, + 296, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 544, + 296, + 571 + ], + "spans": [ + { + "bbox": [ + 60, + 544, + 296, + 571 + ], + "type": "interline_equation", + "content": "\\arg \\max _ {y \\in \\mathcal {Y}} f ^ {*} (\\mathbf {x}) _ {y} = \\arg \\max _ {y \\in \\mathcal {Y}} \\sum_ {g \\in \\mathcal {G} (y)} \\left(h (\\mathbf {x}) - \\tau \\cdot \\ln \\beta\\right) _ {g} \\tag {17}", + "image_path": "22f13bd2cd663ec215a818f7adffb7101f355880b28cb2a4f1792d46eded7ca1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "text", + "content": "Inspired by Menon et al. [25], we incorporate logit adjustment into the softmax cross-entropy " + }, + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "inline_equation", + "content": "\\ell_{\\mathrm{ce}}" + }, + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "text", + "content": ". To do so, we directly enforce group priors offset while learning the group classifier " + }, + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "inline_equation", + "content": "h_{\\mathrm{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 575, + 296, + 634 + ], + "type": "text", + "content": ". We refer to this as the group logit adjustment loss:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 91, + 639, + 294, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 639, + 294, + 654 + ], + "spans": [ + { + "bbox": [ + 91, + 639, + 294, + 654 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathrm {g l a}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x})) = \\ell_ {\\mathrm {c e}} (\\hat {g}, h _ {\\mathrm {d}} (\\mathbf {x}) + \\tau \\cdot \\ln \\hat {\\boldsymbol {\\beta}}), \\tag {18}", + "image_path": "15c463f95372a5ee290cb2fc80b4a9791f9d25956d3dfcb868ca60a96e92134a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 658, + 296, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 296, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 296, + 682 + ], + "type": "text", + "content": "which is equivalent to Eq. (9). Now, the estimated debiased classifier " + }, + { + "bbox": [ + 55, + 658, + 296, + 682 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 658, + 296, + 682 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 687, + 296, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 687, + 296, + 716 + ], + "spans": [ + { + "bbox": [ + 91, + 687, + 296, + 716 + ], + "type": "interline_equation", + "content": "f _ {\\mathrm {d}} (\\mathbf {x}) _ {y} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} h _ {\\mathrm {d}} (\\mathbf {x}) _ {g} = \\sum_ {g \\in \\hat {\\mathcal {G}} (y)} W _ {\\mathrm {d}, g} \\mathbf {x} \\tag {19}", + "image_path": "8d9ad388a9e6ae2a1b9945026cf29fc705b95f2e15343468014dc91dc47a028f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "h_{\\mathrm{d}}" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " is linear, summing over the output-space is equivalent to aggregating in weight-space, eliminating the overhead of group inference." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 121, + 395, + 134 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 395, + 134 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 395, + 134 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 141, + 554, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 141, + 554, + 201 + ], + "spans": [ + { + "bbox": [ + 313, + 141, + 554, + 201 + ], + "type": "text", + "content": "In this section, we evaluate the effectiveness of our method across five benchmarks: Waterbirds [32], CelebA [23], MetaShift [20], BAR [26], and Living-17 [33]. For brevity, we provide an overview of our experimental setup here; further details can be found in Appendix B." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 210, + 376, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 210, + 376, + 221 + ], + "spans": [ + { + "bbox": [ + 314, + 210, + 376, + 221 + ], + "type": "text", + "content": "6.1. Datasets" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "text", + "content": "Waterbirds [32] was created by overlaying bird images from the Caltech-UCSD Birds [38] dataset onto background scenes from the Places [51] dataset. The target classes are bird types " + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "inline_equation", + "content": "(\\mathcal{Y} = \\{\\text{waterbird, landbird}\\})" + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "text", + "content": ", while the spurious attribute is the scene type " + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "inline_equation", + "content": "(A = \\{\\text{water, land}\\})" + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "text", + "content": ". Approximately " + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 313, + 228, + 554, + 312 + ], + "type": "text", + "content": " of the waterbird training samples are associated with a water background." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "text", + "content": "CelebA [23] is a real-world dataset comprising 200K celebrity portrait images. The objective is to classify hair color (" + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = \\{\\text{not blond, blond}\\}" + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "text", + "content": "), with gender (" + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{\\text{male, female}\\}" + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "text", + "content": ") as a spurious attribute. Notably, over " + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 313, + 313, + 554, + 372 + ], + "type": "text", + "content": " of the blond-haired training images feature women." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 373, + 554, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 554, + 456 + ], + "type": "text", + "content": "MetaShift [20]: The classification objective of MetaShift is to distinguish between cats and dogs, with background type " + }, + { + "bbox": [ + 313, + 373, + 554, + 456 + ], + "type": "inline_equation", + "content": "(\\mathcal{A} = \\{\\mathrm{indoor}, \\mathrm{outdoor}\\})" + }, + { + "bbox": [ + 313, + 373, + 554, + 456 + ], + "type": "text", + "content": " as a spurious attribute. Following [45], we use a pre-processed version of MetaShift. In the training set, an inherent bias emerges: cats predominantly appear in indoor scenes, while dogs are more frequently seen in outdoor settings." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 457, + 554, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 554, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 554, + 565 + ], + "type": "text", + "content": "BAR [26] is a real-world dataset designed to classify six actions that are each biased toward specific locations. In the original training set, the six action-location pairs are {climbing, rock wall}, {diving, underwater}, {fishing, water surface}, {racing, paved track}, {throwing, playing Field}, and {vaulting, sky}. However, the test set features different locations than the training set. We adapted the dataset for a group robustness setting by incorporating " + }, + { + "bbox": [ + 313, + 457, + 554, + 565 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 457, + 554, + 565 + ], + "type": "text", + "content": " of the test set images into the training set." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 565, + 554, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 565, + 554, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 565, + 554, + 650 + ], + "type": "text", + "content": "Living-17 [33]: Each class in the Living-17 represents a broad animal category that encompasses several fine-grained groups. The groups in the training and testing sets can exhibit noticeable visual differences, e.g., the bear class includes images of sloth bear and ice bear. Following [48], " + }, + { + "bbox": [ + 313, + 565, + 554, + 650 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 565, + 554, + 650 + ], + "type": "text", + "content": " of the images in each testing group are added to the training groups." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 658, + 380, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 658, + 380, + 670 + ], + "spans": [ + { + "bbox": [ + 314, + 658, + 380, + 670 + ], + "type": "text", + "content": "6.2. Baselines" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": "We compare our PPA against 14 baselines: (1) Zero-shot prompting [31], which matches image features with classification weights by extending class names into pre" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25491" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 102, + 542, + 308 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 2. Evaluation of methods for improving group robustness of CLIP models across the Waterbirds, CelebA, and MetaShift benchmarks. Best worst-group accuracy (WGA) of the methods without group labels are in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 102, + 542, + 308 + ], + "lines": [ + { + "bbox": [ + 69, + 102, + 542, + 308 + ], + "spans": [ + { + "bbox": [ + 69, + 102, + 542, + 308 + ], + "type": "table", + "html": "
Group labels in train sets?MethodCLIP ResNet-50CLIP ViT-L/14
WaterbirdsCelebAMetaShiftWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvgWGAAvgWGAAvgWGAAvg
✓GroupDRO [32]75.183.884.189.583.287.390.896.488.391.293.997.4
S-CS [44]77.583.275.280.481.289.889.195.786.189.392.397.1
S-CL [44]75.286.075.680.481.588.889.996.087.890.593.196.9
DFR [17]73.283.880.092.883.188.389.797.885.690.892.397.0
XZero-Shot (ZS) [31]54.292.455.088.086.295.426.588.227.085.993.296.2
Group Prompt ZS [31]46.491.753.473.584.695.225.485.866.983.193.996.7
ERM [37]7.993.511.994.775.494.465.997.628.394.784.696.7
WiSE-FT [41]49.891.085.688.686.295.465.997.680.087.493.997.2
Orth-Cali [3]74.078.782.284.486.294.868.884.576.186.292.796.2
AFR [30]48.489.353.494.376.986.873.488.270.085.290.397.1
JTT [21]61.790.660.279.978.589.483.697.375.693.391.294.2
CnC [49]61.287.163.990.378.387.184.597.579.289.392.294.7
CA [48]83.789.490.090.777.985.586.996.284.690.491.393.4
CFR [47]76.977.673.781.181.589.588.296.884.887.893.795.5
PPA (ours)84.388.391.192.190.894.787.294.690.491.094.896.8
", + "image_path": "56ad3b33050fe9e116b17808f27f347655b5c1bba8f10348c72708856ef8c956.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 338, + 296, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 338, + 296, + 565 + ], + "spans": [ + { + "bbox": [ + 56, + 338, + 296, + 565 + ], + "type": "text", + "content": "defined prompts, e.g., \"a photo of a waterbird\". (2) Group-informed prompting [31], which incorporates group descriptions into the prompts, e.g., \"a photo of a waterbird on land\". (3) ERM [37], a linear classifier trained using cross-entropy loss, (4) WiSE-FT [41], which interpolates zero-shot and ERM models in weight-space, (5) Orth-Cali [3], a debiased zero-shot model that removes biased direction in the text embedding. (6) AFR [30], retrans the last layer of an ERM model with a weighted loss that emphasizes examples where the ERM model performs poorly, (7) JTT [21], (see details in Sec. 3.2), (8) CnC [49], which builds upon JTT [21], but it uses a contrastive loss to train the debiased model, (9) CA [48], trains contrastive adapters by learning similar representations across different groups, (10) CFR [47], refines the representation by aligning them with the class centroids via contrastive loss. We also compare with three group-supervised methods - (11) Group-DRO [32], (12) DFR [17], (13) S-CS [44] and (14) S-SL [44]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 574, + 228, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 228, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 228, + 586 + ], + "type": "text", + "content": "6.3. Training and Evaluation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "For each method, we evaluate both its worst-group accuracy and average (in-distribution) accuracy on the test sets. We use CLIP ResNet-50 and CLIP ViT-L/14 as primary models, while also reporting results for CLIP ResNet-101, ViT-B/32, and ViT-B/16. Following prior work [44, 47, 48], we freeze the model backbones and train all models using the SGD optimizer for 100 epochs. The hyperparameter " + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\{1.2, 1.0, 0.9, 1.0, 1.0\\}" + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": " for Waterbirds, CelebA, MetaShift, Living-17, and BAR, respectively. Model selection is based on the highest worst-group validation ac" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 321, + 356, + 548, + 460 + ], + "blocks": [ + { + "bbox": [ + 314, + 336, + 553, + 347 + ], + "lines": [ + { + "bbox": [ + 314, + 336, + 553, + 347 + ], + "spans": [ + { + "bbox": [ + 314, + 336, + 553, + 347 + ], + "type": "text", + "content": "Table 3. Experimental results on Living-17 and BAR benchmarks." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 356, + 548, + 460 + ], + "lines": [ + { + "bbox": [ + 321, + 356, + 548, + 460 + ], + "spans": [ + { + "bbox": [ + 321, + 356, + 548, + 460 + ], + "type": "table", + "html": "
MethodCLIP ResNet-50CLIP ViT-L/14
Living-17BARLiving-17BAR
WGAAvgWGAWGAAvgWGA
ZS [31]38.083.274.448.092.381.7
ERM [37]53.390.854.984.098.689.0
JTT [21]44.086.458.578.797.390.2
CA [48]62.090.9-80.097.5-
PPA (ours)65.092.576.885.098.191.5
", + "image_path": "0a69ffca772b8f70d325d6a67be2ca56f3bef756429522d0e56fc85cea830256.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 492, + 555, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 555, + 564 + ], + "type": "text", + "content": "curacy, except for BAR, which lacks a validation set; for BAR, we evaluate the checkpoint from the last epoch. Additionally, since the majority groups in training set do not appear in testing, we measure only the worst-group accuracy for BAR. Further implementation details are provided in Appendix B." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 574, + 399, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 399, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 399, + 586 + ], + "type": "text", + "content": "6.4. Main Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": "Tab. 2 presents the worst-group accuracy (WGA) and average (in-distribution) accuracy for all methods on Waterbirds [32], CelebA [23] and MetaShift [20] datasets. Compared to other group-unsupervised debiasing approaches, our PPA achieves superior performance with less than " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " trainable parameters (CLIP ResNet-50 has 25,557,032 parameters, while our model " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{d}}(\\cdot)" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " has only 4,096 trainable parameters). Specifically, PPA based on CLIP ResNet-50 outperforms the previous state-of-the-art, CFR [47], with improvements of " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\{7.4\\%, 17.4\\%, 9.3\\%" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " on Water" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "25492" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 113, + 294, + 215 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 104 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 104 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 104 + ], + "type": "text", + "content": "Table 4. PPA consistently improves group robustness for across different efficient fine-tuning paradigms using CLIP ResNet-50. The results using CLIP ViT-L/14 are reported in Appendix B.3." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 113, + 294, + 215 + ], + "lines": [ + { + "bbox": [ + 56, + 113, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 56, + 113, + 294, + 215 + ], + "type": "table", + "html": "
MethodWaterbirdsCelebAMetaShift
WGAAvgWGAAvgWGAAvg
Linear Probe + ERM7.993.511.994.775.494.4
Linear Probe + PPA84.388.391.192.190.894.7
CoOp + ERM61.796.235.094.875.492.8
CoOp + PPA83.087.690.092.289.093.3
Adapter + ERM61.496.760.694.484.693.9
Adapter + PPA78.291.891.592.587.793.4
", + "image_path": "ed38fc158e415d5b0585fee8e90f8d82a7fc9ebf3ffd1507c65b146a97549fff.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 255, + 296, + 325 + ], + "blocks": [ + { + "bbox": [ + 55, + 224, + 295, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 224, + 295, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 224, + 295, + 246 + ], + "type": "text", + "content": "Table 5. PPA consistently improves group robustness on Waterbirds across different architectures." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 255, + 296, + 325 + ], + "lines": [ + { + "bbox": [ + 56, + 255, + 296, + 325 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 296, + 325 + ], + "type": "table", + "html": "
MethodCLIP RN-101CLIP ViT-B/32CLIP ViT-B/16
WGAAvgWGAAvgWGAAvg
Zero-shot33.690.047.088.834.088.1
ERM LP62.996.556.895.666.596.4
PPA83.689.783.589.184.489.9
", + "image_path": "8968710afca1d231e08b4fc7e2edb8ce9e694799fc29f531dd3c7bf619f1129e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 343, + 295, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 343, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 54, + 343, + 295, + 489 + ], + "type": "text", + "content": "birds, CelebA, and MetaShift, respectively. Moreover, PPA is competitive with group-supervised methods that rely on group annotations. Notably, our improvements in worst-group accuracy come at the cost of a modest reduction in in-distribution accuracy, with an average drop of 1.8 points compared to ERM models using CLIP ViT-L/14. In Tab. 3, we report results for the Living-17 [33] and BAR [26] datasets. We again observe that PPA achieves the highest worst-group performance. Notably, for the BAR dataset, where model selection is not performed and only the last checkpoint is used (due to the absence of a validation set), PPA still attains the highest worst-group accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 495, + 258, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 258, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 258, + 508 + ], + "type": "text", + "content": "6.5. Further Analysis and Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 513, + 295, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 513, + 295, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 513, + 295, + 572 + ], + "type": "text", + "content": "We conduct comprehensive studies to (1) confirm the versatility of our proposed method—specifically, its compatibility with other efficient fine-tuning paradigms and model architectures—and (2) to understand the contribution of each component to the overall improvement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 573, + 295, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 573, + 295, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 573, + 295, + 668 + ], + "type": "text", + "content": "Extending PPA to other parameter-efficient fine-tuning paradigms. In this paper, we adopt linear probes for efficient fine-tuning of foundation models. We also explore the applicability of PPA to other efficient fine-tuning methods, such as prompt tuning [52, 53] (CoOp) and adapter-based tuning [7, 9, 48] (small bottleneck MLPs). Specifically, we replace the linear probe " + }, + { + "bbox": [ + 55, + 573, + 295, + 668 + ], + "type": "inline_equation", + "content": "h_{\\mathrm{d}}(\\mathbf{x}) = W_{\\mathrm{d}}\\mathbf{x}" + }, + { + "bbox": [ + 55, + 573, + 295, + 668 + ], + "type": "text", + "content": " in Step 2 of Algorithm 1 with the following models:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 669, + 295, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 295, + 692 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 295, + 692 + ], + "type": "text", + "content": "- Prompt tuning (CoOp). The prompt for group " + }, + { + "bbox": [ + 55, + 669, + 295, + 692 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 669, + 295, + 692 + ], + "type": "text", + "content": " is designed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 116, + 700, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 700, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 116, + 700, + 295, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {t} _ {i} = \\left[ V _ {1} ^ {i} \\right] \\left[ V _ {2} ^ {i} \\right] \\dots \\left[ V _ {M} ^ {i} \\right] [ \\mathrm {C L A S S} ], \\tag {20}", + "image_path": "65660d96a4984d025db2331ce09e00e9f59734acfd49b1a146dec42170dca908.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 71, + 554, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 71, + 554, + 126 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 554, + 126 + ], + "type": "text", + "content": "Table 6. Main component analysis. We present the worst group accuracies using CLIP ResNet-50. \"Proj.\" and \"GLA\" stands for the projection operation in Eq. (6) and group logit adjustment loss in Eq. (9), respectively. \"GT\" means we use the ground-truth group labels for training debiased models." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 134, + 553, + 215 + ], + "blocks": [ + { + "bbox": [ + 315, + 134, + 553, + 215 + ], + "lines": [ + { + "bbox": [ + 315, + 134, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 315, + 134, + 553, + 215 + ], + "type": "table", + "html": "
Proj.GLAGTWaterbirdsCelebAMetaShift
(a)7.911.975.4
(b)✓54.429.486.2
(c)✓81.670.089.2
(d)✓✓84.391.190.8
(e)✓✓86.891.591.3
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The precision and recall of the worst-group examples on Waterbirds and CelebA using CLIP ResNet-50." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "spans": [ + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "inline_equation", + "content": "[V_m^i]" + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "content": " is a vector with the same dimensionality as the word embedding and serves as a parameter to be optimized. We follow CoOp to set " + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "inline_equation", + "content": "M = 16" + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "content": ". [CLASS] represents the word embedding of the class name. Let " + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot)" + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "content": " denote the CLIP text encoder. The group scorer for group " + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 321, + 383, + 555, + 454 + ], + "type": "text", + "content": " is then defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 381, + 462, + 553, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 462, + 553, + 477 + ], + "spans": [ + { + "bbox": [ + 381, + 462, + 553, + 477 + ], + "type": "interline_equation", + "content": "h _ {\\mathrm {d}} ^ {\\mathrm {p t}} (\\mathbf {x}; \\mathbf {t}) _ {i} = \\Phi \\left(\\mathbf {t} _ {i}\\right) ^ {\\top} \\mathbf {x} / \\tau_ {\\text {c l i p}}, \\tag {21}", + "image_path": "6cb6bc63494ded9e7a5946ff7b46d9b52d1a33682443ee7e3e9cc19d29fc0aca.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 322, + 486, + 444, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 486, + 444, + 497 + ], + "spans": [ + { + "bbox": [ + 322, + 486, + 444, + 497 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 322, + 486, + 444, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{clip}}" + }, + { + "bbox": [ + 322, + 486, + 444, + 497 + ], + "type": "text", + "content": " is the temperature." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": "- Adapter-based tuning. We adopt [7] to transform the visual embeddings " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " and the text embedding " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " using simple 2-layer bottleneck MLPs. Let " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " denote the feature the hidden-layer dimension. We follow [48] to set " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "H = 128" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": ". With ReLU function " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": ", visual adapter weights " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{v}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{v}}^{2} \\in \\mathbb{R}^{D \\times H}" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " and textual adapter weights " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "W_{\\mathrm{t}}^{1} \\in \\mathbb{R}^{H \\times D}, W_{\\mathrm{t}}^{2} \\in \\mathbb{R}^{D \\times H}" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": ", the input " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " and text embeddings " + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 314, + 498, + 554, + 594 + ], + "type": "text", + "content": " are adapted as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 341, + 600, + 553, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 600, + 553, + 615 + ], + "spans": [ + { + "bbox": [ + 341, + 600, + 553, + 615 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {x}} = W _ {\\mathrm {v}} ^ {2} \\sigma \\left(W _ {\\mathrm {v}} ^ {1} \\mathbf {x}\\right), \\quad \\tilde {Z} ^ {\\top} = W _ {\\mathrm {t}} ^ {2} \\sigma \\left(W _ {\\mathrm {t}} ^ {1} Z ^ {\\top}\\right). \\tag {22}", + "image_path": "ed06adefba4ed761f3906bed6499ff96c162e6963c800d4b7beec97e870b9344.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 322, + 623, + 555, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 623, + 555, + 647 + ], + "spans": [ + { + "bbox": [ + 322, + 623, + 555, + 647 + ], + "type": "text", + "content": "We then use the normalized adapted embeddings and the temperature " + }, + { + "bbox": [ + 322, + 623, + 555, + 647 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{clip}}" + }, + { + "bbox": [ + 322, + 623, + 555, + 647 + ], + "type": "text", + "content": " to output the final scorer:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 395, + 654, + 553, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 654, + 553, + 669 + ], + "spans": [ + { + "bbox": [ + 395, + 654, + 553, + 669 + ], + "type": "interline_equation", + "content": "h _ {\\mathrm {d}} ^ {\\mathrm {a t}} (\\mathbf {x}) _ {i} = \\tilde {\\mathbf {z}} ^ {\\top} \\tilde {\\mathbf {x}} / \\tau_ {\\mathrm {c l i p}} \\tag {23}", + "image_path": "bb8da59e3be15295e256c77a61bdaa6ea99fe9e72d999a6cc1e27baef9b6927a.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": "Tab. 4 demonstrates consistent improvements in worstgroup accuracy over the ERM-trained CLIP ResNet-50 model across three benchmarks, highlighting the versatility" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25493" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 227, + 175 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 227, + 175 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 227, + 175 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 227, + 175 + ], + "type": "image", + "image_path": "871b5df7dc7a49b25578953ea1c10f4472d1e9a729297b9c4da76f85e036cd07.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 182, + 544, + 194 + ], + "lines": [ + { + "bbox": [ + 64, + 182, + 544, + 194 + ], + "spans": [ + { + "bbox": [ + 64, + 182, + 544, + 194 + ], + "type": "text", + "content": "Figure 2. Study on the effect of " + }, + { + "bbox": [ + 64, + 182, + 544, + 194 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 64, + 182, + 544, + 194 + ], + "type": "text", + "content": " using CLIP ResNet-50. 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For instance, on the CelebA dataset, our PPA achieves worst-group accuracy improvements of " + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "inline_equation", + "content": "55.0\\%" + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "text", + "content": " with CoOp and " + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "inline_equation", + "content": "30.9\\%" + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "text", + "content": " with Adapter. Additionally, integrating PPA with these three fine-tuning methods yields comparable performance. However, linear probing is more computationally efficient than prompt tuning, as the latter requires both forward and backward passes through the large text encoder to update the prompts. It is also more storage-efficient than Adapter-based methods, which introduce additional training parameters, i.e., " + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 54, + 216, + 295, + 347 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 350, + 296, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 350, + 296, + 409 + ], + "spans": [ + { + "bbox": [ + 54, + 350, + 296, + 409 + ], + "type": "text", + "content": "Study on model versatility. In Tab. 5, we implement our PPA to various backbone architectures, including CLIP ResNet-101, CLIP ViT-B/32 and CLIP ViT-B/16. We observe consistent performance gains on the worst group accuracy, indicating the model versatility of our PPA." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 411, + 295, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 411, + 295, + 615 + ], + "spans": [ + { + "bbox": [ + 56, + 411, + 295, + 615 + ], + "type": "text", + "content": "Main component analysis. In Tab. 6, we provide an ablation study to assess the impact of the projection operation (Proj.) and group logit adjustment (GLA) loss on worst-group accuracy using CLIP ResNet-50. Row (a) represents the ERM-trained linear probing model; Row (b) probes group targets without prior correction; and Row (c) omits the projection operation during training. Row (d) shows results from our proposed method (PPA), while Row (e) replaces estimated group labels with ground-truth labels. Comparing Rows (b) and (d), we observe that adjusting the margin significantly improves worst-group accuracy. In the comparison of Rows (c) and (d), projecting out class proxies enhances group identification, resulting in better worst-group performance. Finally, Row (e) demonstrates the oracle performance using ground-truth labels, revealing that PPA approximates the maximum achievable accuracy, underscoring the importance of accurate pseudo-group labels." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 618, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 618, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 618, + 295, + 714 + ], + "type": "text", + "content": "Study on the quality of estimated group labels. In the absence of training group labels, we rely on the quality of pseudo group labels inferred from the biased model " + }, + { + "bbox": [ + 54, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}(\\mathbf{x})" + }, + { + "bbox": [ + 54, + 618, + 295, + 714 + ], + "type": "text", + "content": ". To evaluate the quality of identified minority groups within the training set, we measure two metrics: precision, defined as the fraction of examples within the identified minority groups that belong to the worst-performing group, and recall, the fraction of examples from the worst-performing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 216, + 553, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 216, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 216, + 553, + 346 + ], + "type": "text", + "content": "group captured by the identified minority groups. Here, the worst-performing group is defined as the group on which the ERM model achieves the lowest validation accuracy. In Fig. 1, we compare our method with two baselines: (1) ERM, which uses standard empirical risk minimization to train biased models, and (2) CA [48], which leverages zero-shot models to identify minority groups. Our method, PPA, achieves significantly higher recall and precision than both ERM and CA. This improvement is attributed to our biased model " + }, + { + "bbox": [ + 313, + 216, + 553, + 346 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{b}}" + }, + { + "bbox": [ + 313, + 216, + 553, + 346 + ], + "type": "text", + "content": ", which relies more heavily on spurious features to make predictions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": "Study on the hyper-parameter " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": ". We examine the effect of " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " in Eq. (9), as illustrated in Fig. 2 (more details are in Appendix B.6). Specifically, we vary " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " from 0.0 to 2.0 and report both the worst-group accuracy and average accuracy on the Waterbirds, CelebA, and MetaShift datasets using CLIP ResNet-50. A larger " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " promotes a greater margin for the minority groups, while " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau = 0" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " reduces to the standard cross-entropy loss. Our findings reveal that (1) average accuracy decreases monotonically as " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " increases, and (2) the optimal worst-group accuracy is generally achieved around " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau = 1.0" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": ". For example, the optimal values of " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": " are 1.2, 1.0 and 0.9 for Waterbirds, CelebA and MetaShift, respectively. This aligns with our theoretical analysis, which suggests that the Bayes optimal classifier for minimizing the balanced group error is attained when " + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 313, + 347, + 555, + 526 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 538, + 388, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 388, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 388, + 550 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 557, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 712 + ], + "type": "text", + "content": "In this paper, we introduce Project-Probe-Aggregate (PPA), a novel, parameter-efficient fine-tuning framework for enhancing the group robustness of image-text foundation models without relying on training group labels. Our approach improves the identification of minority groups by projecting image features onto the null space of class proxies. Additionally, we design a group logit adjustment loss to minimize balanced group error and mitigate spurious correlations. Through theoretical analysis and empirical evaluations across diverse benchmarks, fine-tuning paradigms and model architectures, we demonstrate that the proposed method effectively enhances robust group performance of foundation models." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25494" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "content": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 151, + 115, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 151, + 115, + 163 + ], + "spans": [ + { + "bbox": [ + 56, + 151, + 115, + 163 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 171, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 171, + 296, + 204 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 171, + 296, + 204 + ], + "spans": [ + { + "bbox": [ + 61, + 171, + 296, + 204 + ], + "type": "text", + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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We present Prometheus, a novel method for feed-forward scene-level 3D generation. At its core, our approach harnesses the power of 2D priors to fuel generalizable and efficient 3D synthesis - hence our name, Prometheus." + ], + "image_footnote": [], + "bbox": [ + 138, + 273, + 815, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 789, + 326, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we introduce Prometheus, a 3D-aware latent diffusion model for text-to-3D generation at both ob", + "bbox": [ + 89, + 835, + 485, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ject and scene levels in seconds. We formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within the latent diffusion paradigm. To ensure generalizability, we build our model upon pretrained text-to-image generation model with only minimal adjustments, and further train it using a large number of images from both single-view and multi-view datasets. Fur", + "bbox": [ + 511, + 791, + 910, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* denotes equal contribution.", + "bbox": [ + 107, + 875, + 264, + 888 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† corresponding author.", + "bbox": [ + 109, + 888, + 236, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2857", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thermore, we introduce an RGB-D latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feed-forward generation of 3D Gaussians with better fidelity and geometry. Extensive experimental results demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation. Project page: Prometheus.", + "bbox": [ + 89, + 90, + 485, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 224, + 222, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D assets play a crucial role in a wide range of applications, including AR/VR, gaming, and simulation. Developing 3D generative models capable of efficiently producing versatile 3D content has become a key objective, drawing substantial interest in the field. Despite rapid progress in 2D image and video generation, 3D generative models continue to fall short of the progress seen in 2D generation.", + "bbox": [ + 89, + 251, + 482, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One line of existing 3D generative models learn from 3D/multi-view data [8, 89], or single-view images of a single category [5, 59]. This allows them for directly learning 3D representations in a feed-forward manner. Despite achieving excellent multi-view consistency with good geometry, their generalizability is limited due to the scarcity of the training data. Another line of approaches seeks to use models trained on large amounts of 2D data for 3D generation — while the largest multi-view datasets contain around 100K samples, single-view datasets and pretrained models based on them can reach scales of 100M to 2B samples. Most methods in this area obtain 3D representations through optimization. Some approaches use score distillation [40, 54, 70, 80, 93] or incremental inpainting [14, 64, 75, 97]. However, since 2D models lack a complete understanding of 3D, their outputs sometimes face the Janus problem and tend to produce results with low fidelity. Another set of methods fine-tunes 2D models to generate multi-view images, requiring multi-view reconstruction to form the 3D representation [18, 47, 58, 63, 84]. In both cases, the optimization process can be time-consuming, thereby lacking efficiency.", + "bbox": [ + 89, + 357, + 482, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the aforementioned issues, we introduce Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels. Our key idea is to exploiting vast amount of 2D data as well as 2D generative models to facilitate feed-forward 3D generation while maintaining generalization ability - taming the fire of 2D priors to streamline 3D generation. Specifically, we formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within latent diffusion paradigm. To ensure generalizability, we not only build our model upon pre-trained text-to-image generation model (Stable Diffusion) with only minimal adjustments but also train it using both single-view images and multi-view images. Furthermore, we introduce an RGB-D", + "bbox": [ + 89, + 688, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feedforward generation of 3D Gaussians with better fidelity and geometry.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following the standard latent diffusion paradigm [57], we separate training into two distinct stages. In the first stage, we train a 3D Gaussian Variational Autoencoder (GS-VAE) that takes multi-view or single-view RGB-D images as input and predicts per-pixel aligned 3D Gaussians. Here, the input depth map during training is estimated using an off-the-shelf monocular depth estimator. Additionally, the encoder of our GS-VAE directly re-uses the Stable Diffusion encoder, predicting latent codes for both RGB images and depth maps. We subsequently train a multi-view GS decoder to generate multi-view 3D Gaussians from the RGB-D latent codes conditioned on camera poses. In the second stage, we train a multi-view LDM that jointly predicts multi-view RGB-D latent codes, conditioned on both camera pose and text prompt. Furthermore, our full model is trained on a combination of 9 multi-view and single-view datasets, aiming for generalizability comparable to Stable Diffusion. We demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation, showcasing that our model can generate 3D scenes in seconds while generalizing well to a variety of 3D objects and scenes.", + "bbox": [ + 511, + 152, + 906, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 513, + 498, + 651, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Generative Models: 3D generative models have attracted great attention in recent years. Many approaches learn from single-category images or 3D supervisions [5, 10, 51, 59, 73, 100], utilizing either GANs or diffusion models. However, these studies primarily concentrate on domain-specific, object-centric scenes, such as those involving Carla Cars [16] and human faces [29]. Despite recent progress that has further extended these methods to model scene-level generation [1, 53, 88, 91], these methods are yet confined to a specific domain with limited generalization capability. This is mainly due to the scarcity of 3D supervision. We aim to tackle this problem by combining multi-view supervision with a vast amount of 2D images.", + "bbox": [ + 511, + 530, + 906, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Generation with 2D priors: Thanks to the rapid progress in 2D generation models like Stable Diffusion [57] and SoRA [3], there is a large many works have explored the potential of large 2D diffusion models for 3D-aware generation. One line of works fine-tune 2D diffusion models to enable pose controllability for objects [46, 47] or scenes [18, 20, 58, 81], where the output still lies in the 2D image space. Additionally, some works [13, 34, 34, 44, 52, 68, 95, 98, 105] aim to incorporate underlying 3D prior knowledge to assist in synthesis. Since the aforementioned methods generate only 2D images, a separate 3D re", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2858", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "construction step is still needed, which can add time and introduce errors. In contrast, we explore directly generating 3D representations in a feed-forward manner.", + "bbox": [ + 89, + 90, + 482, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another line of methods utilize the 2D priors for 3D generation through optimization, e.g., using Score Distillation Sampling (SDS) [54, 54, 70, 74, 80, 93]. In parallel, several works [14, 17, 36, 64, 75, 96, 103] formulate scene synthesis as \"perpetual view generation\" [43], synthesizing the effects of navigating a 3D world by stitching and rendering images based on camera motions. These methods do not require retraining 2D generative models, but they are inefficient due to per-scene optimization. The generated content's quality is limited by the 2D backbone, causing issues like multi-view inconsistency and artifacts in geometry and texture during image inpainting and score distillation.", + "bbox": [ + 89, + 137, + 483, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feed-Forward 3D Gaussian Generation: Unlike view synthesis-based methods that focus on synthesizing multiview images followed by 3D reconstruction, a more intuitive approach is to directly generate 3D representations. Following this idea, many works [6, 26, 76, 89] concentrate on the direct synthesis of 3D representations, such as NeRF [48], which generates meshes from single or few-view image inputs. Recently, numerous works [7, 8, 11, 12, 69, 71, 82, 86, 87, 87, 94, 102] have adopted 3D Gaussian Splatting [32] as the underlying representation. Pixel-Splat [7] is the first feed-forward model that learns to reconstruct 3D Gaussian splats from pairs of images. GS-LRM [102] builds on this idea and utilizing a larger reconstruction model (LRM [26]), achieving improved results.", + "bbox": [ + 89, + 327, + 483, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this challenge, several works [21, 23, 35, 37, 38, 56, 60, 106] propose Large Diffusion Models as powerful generators for 3D representations. WildFusion [60] introduces a novel approach for achieving 3D-aware image synthesis from in-the-wild datasets using latent diffusion models. Director3D [38], which is closely related to our work, presents a robust open-world text-to-3D generation framework designed to create both real-world 3D scenes and adaptive camera trajectories. Unlike Director3D, which requires supervision in the image space, we follow common practices in 2D image generation and adopt a latent diffusion framework. This approach significantly reduces computational overhead, making larger-scale training feasible, and better leverages the 2D latent space, enhancing the generalizability of our method.", + "bbox": [ + 89, + 539, + 483, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 782, + 181, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we provide the technical details of our method. As illustrated in Fig. 2, Prometheus follows the common latent diffusion framework [57], which involves two training stages. In the first stage (Sec. 3.1), our 3D autoencoder, GS-VAE, learns a compressed and abstracted latent space from multi-view images. Subsequently, it de", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "codes this latent space into pixel-aligned 3DGS representations, serving as scene-level representations. In the second stage (Sec. 3.2), a latent multi-view diffusion model (MV-LDM) is trained on the latent representations derived from the first stage's autoencoder. This process results in a fully generative model. Finally, we elaborate on our sampling strategy (Sec. 3.3) for sampling 3D scenes in seconds while maintaining consistency and visual fidelity.", + "bbox": [ + 511, + 90, + 905, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Stage 1: GS-VAE", + "text_level": 1, + "bbox": [ + 511, + 224, + 684, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Stage 1, our objective is to train a 3D autoencoder capable of compressing data into a latent space and subsequently reconstructing it into a 3D representation. Given multi-view input images with camera poses, our GS-VAE outputs multi-view pixel-aligned 3DGS. These outputs are then merged into a scene-level 3D representation.", + "bbox": [ + 511, + 248, + 905, + 338 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Encoding Multi-View RGB-D Images. We propose to encode both, RGB images and their predicted monocular depth maps, into the latent space, considering that monocular depth maps provide clues for the later 3D Gaussian decoding process and can be easily obtained. Given a set of multi-view images $\\mathcal{I} = \\{I_i\\in \\mathbb{R}^{H\\times W\\times 3}|i = 1,2,\\dots ,N\\}$ with each image $I_{i}$ being an observation of an underlying 3D scene, we first employ an off-the-shelf depth estimator [90] to obtain their corresponding monocular depth maps $\\mathcal{D} = \\{D_i\\in \\mathbb{R}^{H\\times W\\times 1}|i = 1,2,\\dots ,N\\}$ . Next, we utilize a pre-trained image encoder $\\mathcal{E}_{\\phi}$ to encode both the multi-view images $\\mathcal{I}$ and their depth maps $\\mathcal{D}$ into a latent representation:", + "bbox": [ + 511, + 339, + 906, + 536 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} _ {\\phi}: (\\mathcal {I}, \\mathcal {D}) \\mapsto \\mathcal {Z} \\in \\mathbb {R} ^ {N \\times h \\times w \\times c}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 549, + 903, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h \\times w$ is the downsampled resolution. In practice, we use a pre-trained Stable Diffusion (SD) image encoder and freeze it during training. Recent methods, such as Marigold [31], indicate that the SD encoder exhibits robust generalization capabilities with depth maps. Consequently, we opt to employ the same SD encoder to independently encode both images and depths without the need for fine-tuning. Subsequently, we concatenate these encoded representations to obtain the full multi-view latent $\\mathcal{Z}$ which can be used for 3D reconstruction. Our diffusion model is additionally trained within this joint RGB-D latent space.", + "bbox": [ + 511, + 580, + 905, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fusing Multi-View Latent Images. Recent advancements [26, 35, 77, 101, 102] underscore the significant potential of transformer-based models in integrating multiview information. Since our latent codes for each view in $\\mathcal{Z}$ are derived individually, we employ a multi-view transformer to facilitate cross-view information exchange.", + "bbox": [ + 511, + 750, + 905, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We further inject $N$ camera poses into our multiview transformer. Inspired by recent works [18, 35, 38, 89], we choose Plücker coordinates as camera representation [65], specifically $\\mathbf{r} = (\\mathbf{d},\\mathbf{p}\\times \\mathbf{d})\\in \\mathbb{R}^6$", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2859", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3bf7985b354b7a3ce0070def4f49b1279c986fac85404c17dc30f13ee5ad03fb.jpg", + "image_caption": [ + "Figure 2. Method Overview. Our training process is divided into two stages. In stage 1, our objective is to train a GS-VAE. Utilizing multi-view images along with their corresponding pseudo depth maps and camera poses, our GS-VAE is designed to encode these multi-view RGB-D images, integrate cross-view information, and ultimately decode them into pixel-aligned 3DGS. In stage 2, we focus on training a MV-LDM. We can generate multi-view RGB-D latents by sampling from randomly-sampled noise with trained MV-LDM." + ], + "image_footnote": [], + "bbox": [ + 93, + 85, + 630, + 290 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/39a6c12b98a75e2fc297c663a32124cef8d7f45ff27a8f2127705fab14ba0b30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 85, + 903, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{d}$ denotes the normalized ray direction and $\\mathbf{p}$ denotes the camera origin. Thus, initial $N$ camera poses can be re-parameterized as multi-view ray maps $\\mathcal{R} = \\{R_i\\in \\mathbb{R}^{H\\times W\\times 6}|i = 1,2,\\ldots ,N\\}$ . We combine the multiview latent codes $\\mathcal{Z}$ and the camera ray maps $\\mathcal{R}$ via concatenation along the feature channel and feed them into the cross-view transformer to obtain the fused latent codes $\\tilde{\\mathcal{Z}}\\in \\mathbb{R}^{h\\times w\\times c}$ that merges multi-view context:", + "bbox": [ + 89, + 385, + 483, + 506 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) \\mapsto \\tilde {\\mathcal {Z}} \\in \\mathbb {R} ^ {h \\times w \\times c}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 516, + 482, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoding into Gaussian Scenes. Finally, we concatenate the raw image latent codes $\\mathcal{Z}$ , ray maps $\\mathcal{R}$ , and the fused latent codes $\\tilde{\\mathcal{Z}}$ , and feed them into the decoder, thereby obtaining the pixel-aligned multi-view 3D Gaussians $\\mathcal{F} = \\{F_i \\in \\mathbb{R}^{H \\times W \\times C_G} | i = 1, 2, \\ldots, N\\}$", + "bbox": [ + 89, + 546, + 483, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) \\mapsto \\mathcal {F} \\in \\mathbb {R} ^ {N \\times H \\times W \\times C _ {G}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 633, + 482, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $F_{i}$ is the pixel-aligned 3D Gaussians corresponding to each image. A 3D Gaussian is parameterized by 1-channel depth, 4-channel rotation quaternion, 3-channel scale, 1-channel opacity, and 3-channel spherical harmonics coefficients respectively. Thus $C_G = 12$ in our formulation. After aggregating multi-view 3D Gaussians, we can get the final scene-level 3D Gaussians $G$ as in Eq. (4)", + "bbox": [ + 89, + 662, + 483, + 770 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {M} (\\mathcal {F}) \\mapsto G \\in \\mathbb {R} ^ {N _ {G} \\times C _ {G}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 780, + 482, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\mathbb{M}(\\cdot)$ denotes the aggregation operation, which is achieved by transforming all 3D Gaussians into a global coordinate system. $N_{G}$ represents the number of full Gaussian primitives, which is equivalent to $N\\times H\\times W$ .", + "bbox": [ + 89, + 810, + 482, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, this architecture is also applicable to single-view images, where $N$ equals to 1. During training, we", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sample from both single-view and multi-view images. Besides, to maximize the usage of 2D generative priors, we follow Director3D [38] and repurpose a pre-trained Stable Diffusion image decoder with minor modifications as our Gaussian decoder $\\mathcal{D}_{\\phi}$ . Specifically, we only adjust the number of channels in the first and last convolutional layers.", + "bbox": [ + 511, + 385, + 906, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss Function. Given the reconstructed scene-level 3D Gaussians $\\hat{G}$ , we can render them from arbitrary viewpoints. Let $\\mathbf{c}$ denote a given viewpoint, we can render the corresponding RGB image and depth map from $\\hat{G}$ :", + "bbox": [ + 511, + 476, + 906, + 537 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {R} (\\hat {G}, \\mathbf {c}) \\mapsto \\{\\hat {I}, \\hat {D} \\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 642, + 541, + 903, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{R}(\\cdot)$ denotes the differentiable rendering of 3D Gaussian Splatting. We can subsequently apply render loss, which integrates MSE (Mean Squared Error) loss and perceptual [28] loss:", + "bbox": [ + 511, + 566, + 906, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e n d e r}} = \\mathcal {L} _ {\\text {m s e}} (\\hat {I}, I) + \\mathcal {L} _ {\\text {v g g}} (\\hat {I}, I). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 633, + 903, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to the rendering loss on the RGB domain, we also impose a loss between our rendered expected depth $\\hat{D}$ and the monocular depth $\\bar{D}$ which serve as pseudo geometry ground truth as below:", + "bbox": [ + 511, + 657, + 905, + 718 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} = \\| (w \\hat {D} + q) - \\bar {D} \\| _ {2}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 724, + 903, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{depth}$ is the scale invariant depth loss following [55]. Here, $w$ and $q$ are the scale and shift used to align $\\hat{D}$ with $\\bar{D}$ since $\\bar{D}$ is defined only up to a scale and a shift. We determine $w$ and $q$ using a least-squares criterion [55].", + "bbox": [ + 511, + 750, + 905, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our full loss function of the GS-VAE is as follows:", + "bbox": [ + 532, + 810, + 870, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\phi) = \\lambda_ {1} \\mathcal {L} _ {m s e} + \\lambda_ {2} \\mathcal {L} _ {v g g} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 832, + 903, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\phi$ denotes the estimizable parameters in GS-VAE, and $\\lambda_1, \\lambda_2, \\lambda_3$ are employed to balance the weight of each loss term.", + "bbox": [ + 511, + 854, + 905, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2860", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Stage 2: Geometry-Aware Multi-View Denoiser", + "text_level": 1, + "bbox": [ + 89, + 90, + 480, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the training of stage 1, we obtain a GS-VAE capable of i) efficiently compressing images into a compact latent space and ii) bridging the gap between 2D and 3D via a 3D Gaussian decoder. This capability enables us to train the multi-view diffusion model (MV-LDM) in the latent space.", + "bbox": [ + 89, + 112, + 482, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We aim to jointly generate multix-view RGB-D latent codes $\\mathcal{Z} \\in \\mathbb{R}^{N \\times h \\times w \\times c}$ to provide richer geometric cues for decoding 3DGS. Therefore, we formulate a continuous-time denoising diffusion [30, 66] conditioned on the text prompt $\\mathbf{y}$ and camera poses $\\mathcal{R}$ . The diffusion model consists of a stochastic forward pass to inject one noise level noise Gaussian noise into input latent codes and a reverse process to remove noise with a learnable denoiser $\\mathcal{G}_{\\theta}$ .", + "bbox": [ + 89, + 188, + 483, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. For each training step, we sample one noise level $\\sigma_{t}$ , where $\\log \\sigma_{t} \\sim \\mathcal{N}(P_{mean}, P_{std}^{2})$ [30]. Next, we add noise of this level to the clean multi-view latents $\\mathcal{Z}_{0}$ to obtain the noisy latents $\\mathcal{Z}_{t}$ as", + "bbox": [ + 89, + 309, + 483, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Z} _ {t} = \\mathcal {Z} _ {0} + \\sigma_ {t} ^ {2} \\boldsymbol {\\epsilon}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 378, + 480, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the reverse process, diffusion model denoises $\\mathcal{Z}_t$ towards predicted clean $\\hat{\\mathcal{Z}}_0$ with a learnable multi-view denoiser $\\mathcal{G}_{\\theta}$ as", + "bbox": [ + 89, + 404, + 482, + 446 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {Z}} _ {0} = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 448, + 480, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{y}$ and $\\mathcal{R}$ are the text and camera poses condition respectively. Our MV-LDM is trained in latent space via denoising score matching (DSM) [72]", + "bbox": [ + 89, + 470, + 483, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\theta) = \\mathbb {E} _ {\\mathcal {Z}, \\mathcal {R}, \\mathbf {y}, \\sigma_ {t}} \\left[ \\lambda (\\sigma_ {t}) \\| \\hat {\\mathcal {Z}} _ {0} - \\mathcal {Z} _ {0} \\| _ {2} ^ {2} \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 523, + 482, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with weighting function $\\lambda (\\sigma) = (1 + \\sigma^2)\\sigma^{-2}$ . In this work, we follow EDM [30] and parameterize the denoiser $\\mathcal{G}_{\\theta}$ as", + "bbox": [ + 89, + 559, + 482, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right) = c _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathcal {Z} _ {t} + \\tag {12} \\\\ c _ {\\text {o u t}} (\\sigma_ {t}) F _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma_ {t}) \\mathcal {Z} _ {t}; c _ {\\text {n o i s e}} (\\sigma_ {t}), \\mathbf {y}, \\mathcal {R}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 599, + 480, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{\\theta}$ is a UNet to be trained in our case, and $c_{\\mathrm{skip}}$ , $c_{\\mathrm{out}}$ , $c_{\\mathrm{in}}$ , and $c_{\\mathrm{noise}}$ are preconditioning functions. Furthermore, consistent with Stage 1 Eq. (3), we employ ray maps as the pose representation and incorporate them into the network by concatenating them with the noisy latents $\\mathcal{Z}_t$ along feature channel. Additionally, the text prompt conditioning is introduced via cross-attention mechanisms.", + "bbox": [ + 89, + 643, + 482, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by recent multi-view diffusions [18, 38, 63], we replace the self-attention blocks in the original UNet with 3D cross-view self-attention blocks to capture multi-view correlations. In practice, to leverage the pre-trained text-to-image prior, we initialize the model $\\mathcal{G}_{\\theta}$ from a pre-trained text-to-image diffusion model's, specifically the UNet from Stable Diffusion [57].", + "bbox": [ + 89, + 750, + 482, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sampling. At sampling time, multi-view latents $\\mathcal{Z}_0$ is restored from a randomly-sampled Gaussian noise $\\mathcal{Z}_T$ conditioning on text prompt and camera poses by iteratively", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ea2d942b8e29d341876d93f0f5b27249796004d32eca937d7ef0afef3d627cca.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetScene type# of frames# of Scenes
SAM-1B [33]Single view11M-
MVImgNet [99]Object6.8M230K
DL3DV-10K [42]Indoor / Outdoor2.2M6K
Objaverse [15]Object11.5M784K
ACID [43]Indoor510K11K
RealEstate10K [107]Indoor2.8M57K
KITTI [19]Driving42K0.8K
KITTI-360 [39]Driving69K1.2K
nuScenes [4]Driving340K0.85K
Waymo [67]Driving200K1K
", + "bbox": [ + 524, + 89, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Training datasets We collect a large, multi-domain dataset for training, including single-view and multi-view data, all paired with detailed captions.", + "bbox": [ + 511, + 228, + 903, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "applying the denoising process with trained MV-LDM $\\mathcal{G}_{\\theta}$", + "bbox": [ + 511, + 276, + 893, + 291 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Z} _ {T} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma_ {T} ^ {2} \\mathbf {I}) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 297, + 903, + 316 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {Z} _ {t - 1} = \\frac {\\mathcal {Z} _ {t} - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {T} ; \\sigma_ {t} , \\mathbf {y} , \\mathcal {R}\\right)}{\\sigma_ {t}} \\left(\\sigma_ {t - 1} - \\sigma_ {t}\\right) \\tag {14} \\\\ + \\mathcal {Z} _ {t}, \\quad 0 < t \\leq T \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 343, + 903, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma_0,\\dots,\\sigma_T$ are sampled from a fixed variance schedule of a denoising process with $T$ steps.", + "bbox": [ + 511, + 402, + 903, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Importance of Noise Level. Inspired by insights from recent works [2, 13, 62], we recognize that a lower Signal-to-Noise Ratio (SNR) during the denoising step is crucial for determining the global low-frequency structure of the content. Furthermore, this lower SNR during sampling is essential for achieving multi-view consistency in the multiview diffusion model $\\mathcal{G}_{\\theta}$ . Therefore, we adopt a relatively large noise distribution with $P_{mean} = 1.5$ and $P_{std} = 2.0$ during multi-view training of MV-LDM $\\mathcal{G}_{\\theta}$ and $P_{mean} = -0.5$ and $P_{std} = 1.2$ during single-view training.", + "bbox": [ + 511, + 431, + 906, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Text to 3D Scene Generation in Sceonds", + "text_level": 1, + "bbox": [ + 511, + 590, + 854, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the model above, we can achieve feed-forward text to 3D scene generation by sampling multi-view RGB-D latents $\\mathcal{Z}$ from randomly-sampled Gaussian noise $\\mathcal{Z}_T$ in latent space using MV-LDM $\\mathcal{G}_{\\theta}$ , and subsequently decode into a 3D Gaussian Scene $G$ using GS-VAE decoder:", + "bbox": [ + 511, + 613, + 905, + 688 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\mathcal {G} _ {\\theta}: (\\mathcal {Z} _ {T}; \\mathbf {y}, \\mathcal {R}) & \\mapsto \\mathcal {Z}, \\\\ \\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) & \\mapsto \\tilde {\\mathcal {Z}}, \\\\ \\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) & \\mapsto G. \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 696, + 903, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To sample that with high quality and align with the condition, we use classifier-free-guidance (CFG) [25] to guide multi-view generation toward condition signal $\\mathbf{y}$ .", + "bbox": [ + 511, + 758, + 905, + 805 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = w \\cdot \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\tag {16} \\\\ + (w - 1) \\cdot \\mathcal {G} _ {\\theta} (\\mathcal {Z} _ {t}; \\mathcal {R}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 811, + 903, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w \\geq 0$ represents the guidance strength. However, if we simply apply the naive CFG Eq. (16), as commonly practiced in most text-to-image methods, increasing", + "bbox": [ + 511, + 854, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2861", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4c0f2239c83bf1ff8a393ef1e4d1d3f744c3f9d0e29fa584619c1754c981bdfb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTartanair (Easy)Tartanair (Medium)Tartanair (Hard)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
pixelSplat[7]21.650.6810.2930.6500.37320.300.6280.3370.8060.32319.350.5890.3710.8710.307
MVSplat [11]19.380.5690.3700.8090.28318.500.5310.4090.8720.26517.870.5000.4450.9070.272
Ours20.950.5890.2890.4350.53620.150.5600.3140.4930.51419.490.5320.3410.5260.505
", + "bbox": [ + 109, + 88, + 885, + 152 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison for Stage 1. We compare our GS-VAE with baselines for generalizable reconstruction on Tartanair.", + "bbox": [ + 96, + 152, + 898, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0cb67c6b9f20d0d01452e683003e7eaae8b05e9cc591dc1a62d80e36591bd5b8.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison for Stage 1. We compare Prometheus against baselines under varying difficulty settings. As overlap gradually decreases, the advantages of our method continue to grow. Moreover, as shown in the depth map, our method exhibits superior geometry quality across all settings." + ], + "image_footnote": [], + "bbox": [ + 109, + 169, + 887, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$w$ would lead to multi-view inconsistency in the generated results. This naive design described above causes the model to overfit to the text condition while compromising multi-view consistency, in line with the findings in [83, 85]. To balance multi-view consistency and fidelity during sampling, we follow HarmonyView [83] and adapt hybrid sampling guidance, which rewrites Eq. (16) as below:", + "bbox": [ + 88, + 443, + 483, + 549 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\\\ + w _ {1} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathcal {R}\\right)\\right) \\\\ + w _ {2} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}\\right)\\right), \\tag {17} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 564, + 480, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $w_{1}$ and $w_{2}$ denote the weight of text and pose guidance respectively with $w = w_{1} + w_{2}$ , thereby better maintaining fidelity and consistency across generated views. In addition, we also use CFG-rescale as proposed in [41] to avoid over-saturation issues during conditional sampling.", + "bbox": [ + 89, + 633, + 483, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 89, + 729, + 215, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Training Datasets", + "text_level": 1, + "bbox": [ + 89, + 755, + 263, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train our method on large-scale single-view and multiview datasets, see Tab. 1. Regarding the single view dataset, we use a high-quality SAM-1B [33] dataset with detailed captions [45] which was present in PixArt- $\\alpha$ [9]. Our model is trained on a combination of 9 multi-view datasets, including object-centric, indoor, outdoor, and driving scenarios, text prompts for each scene are generated using the multimodal large language model [45].", + "bbox": [ + 89, + 779, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implement Details", + "text_level": 1, + "bbox": [ + 511, + 441, + 691, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During GS-VAE training (Stage 1), we set both the number of input and novel views to $N = 4$ for each multi-view scene. To improve model generalizability, we also sample 2 single-view images alongside the multi-view ones, applying the loss to the input views only for single-view images. The GS-VAE was trained on 8 A800 GPUs with a batch size of 32. The final model is trained for 200,000 iterations with approximately 4 days. We use gsplat [92] as our 3D Gaussian renderer. We initialize the weights of our cross-view transformer from a pretrained RayDiff [101].", + "bbox": [ + 511, + 465, + 906, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the MV-LDM (Stage 2), we employ Stable Diffusion 2.1 [57] as our base model. During training, we set $N = 8$ for each multi-view scene. Similarly to Stage 1, we sample $M = 4$ single-view images alongside multi-view ones. For each iteration, we sample a batch size of 8 on each GPU. The final MV-LDM model was trained on 32 A800 GPUs, resulting in a total batch size of 3072 images. The model underwent 350,000 iterations, which took about 7 days. We utilize a DepthAnything-V2-S [90] model to estimate depth map on the fly. To achieve classifier-free guidance during sampling, we randomly drop text condition $y$ and pose condition $\\mathcal{R}$ with the probability $10\\%$ during training.", + "bbox": [ + 511, + 619, + 908, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation Protocols", + "text_level": 1, + "bbox": [ + 511, + 816, + 709, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3D Reconstruction (Stage-1). To demonstrate the 3D reconstruction generalization of our GS-VAE, we employed Tartanair [78] for our evaluation, which is a diverse synthetic dataset with 18 scenes not included in our training set,", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2862", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c21cbdb7e5efcd896fa33b108b5dd8e5da975f99288906730bc3d1f3cfb0725f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSingle-ObjectSingle-Object-with-SurroundingsScene-LevelTime
BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑
GaussianDreamer [93]107.818.790.386110.818.160.389-≈ 15min
MVDream [63]+LGM [71]74.6414.960.37977.5014.030.343-≈ 10s
Director3D [38]49.9113.560.39749.7713.640.40550.8814.970.357≈ 22s
Ours59.4314.230.32958.8814.000.36949.6314.010.370≈ 8s
", + "bbox": [ + 111, + 88, + 893, + 165 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative comparison for 3D generation. We compare Prometheus with baselines for text-to-3D generation utilizing text prompts from T3Bench.", + "bbox": [ + 89, + 167, + 906, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0980da7f515248b6d68d77d8189f106ace893a19b7b4ee1984db2c28de19ae7e.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison for Stage2: Object-level 3D generation. Prometheus generates objects that align with the given description, incorporating rich background information and intricate details." + ], + "image_footnote": [], + "bbox": [ + 109, + 196, + 890, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "covering both indoor and outdoor scenarios. Based on the degree of overlap and distance among input views, we categorize them into three distinct modes: Easy, Medium, and Hard, each comprising 4 context views and 3 target views.", + "bbox": [ + 88, + 434, + 482, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use the metrics PSNR, SSIM [79] and LPIPS [104] for evaluating the reconstructed images. To better compare the reconstructed geometry, we evaluate the rendered depth maps. Follow [27, 61], we align rendered depth maps with the ground truth with per-scene scale and shift and calculate two widely recognized metrics [55] for evaluation, Absolute Mean Relative Error (AbsRel) and $\\delta 1$ accuracy with a specified threshold value of 1.25.", + "bbox": [ + 88, + 496, + 482, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3D Generation (Stage-2). To assess the text-to-3D generation capabilities of our model, we employ two text prompt sets from T3Bench [22] — Single-Object and Single-Object-with-Surroundings. These sets collectively evaluate the model's proficiency in object-level, and scene-level generation tasks. Additionally, we collected 80 diverse scene-level text prompts covering indoor and outdoor scenarios.", + "bbox": [ + 88, + 619, + 482, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The quantitative results are evaluated using the CLIP-Score [24], NIQE [50], and BRISQUE [49] metrics. CLIP-Score assesses the alignment between the generated images and the textual prompts, whereas NIQE and BRISQUE indicate the image quality.", + "bbox": [ + 88, + 726, + 482, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison with Baselines", + "text_level": 1, + "bbox": [ + 89, + 816, + 336, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3D Reconstruction. We compare the GS-VAE of Prometheus against two sparse-view reconstruction models — namely, pixelSplat [7] and MVSplat [11]. Our quantitative findings are shown in Tab. 2, where we accen", + "bbox": [ + 88, + 839, + 485, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tuate the best, second-best, and third-best scores across all metrics. Beginning with geometry, Prometheus surpasses the other two baselines, and this advantage becomes more pronounced as the degree of overlap among input views diminishes — see the $\\delta 1$ , which exhibits a relative enhancement of $44\\%$ on Easy mode and a substantial $64\\%$ on Hard mode against pixelSplat. Regarding the reconstructed images, Prometheus delivers comparable outcomes on Easy mode and notably outperforms its counterparts as the mode intensifies, particularly in Hard mode. We also provide qualitative results in Fig. 3. These findings on geometry and image reconstruction suggest that Prometheus is more robust to variations in input view overlap than its baselines, a key factor for the success of our downstream 3D generation task.", + "bbox": [ + 511, + 434, + 906, + 661 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3D Generation. We compare Prometheus with three text-to-3D baseline methods, covering both optimization-based method and feed-forward method. Gaussian-Dreamer [93] is a state-of-the-art SDS-based method for 3DGS. We additionally implement a baseline that applies a multi-view to 3D method, LGM [71] to images generated by MVDream [63]. We also compare to a feed-forward method, Director3D [38] (without refiner). Fig. 4 and Fig. 5 show that our method is capable of generating both, object and scene-level contents, containing background and rich details, outperforms both optimization-based and feedforward baselines. Tab. 3 shows our overall metrics are suboptimal compared with Director3D for object level while leading in other cases. This is attributed to failure cases in the object-centric setting, see supplementary material for", + "bbox": [ + 511, + 674, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2863", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A bedroom scene displays a bed covered by a quilt and a window located near the end of the bed", + "bbox": [ + 112, + 101, + 282, + 133 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A coastal town with white buildings and green vegetation is seen in the image", + "bbox": [ + 116, + 160, + 277, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebb8d392e38e2369b58b5cd1728d46091d1ff3d909938a3e70f127e28b31361c.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison for Stage 2: Scene-level 3D generation with diverse scene-level prompt. Our result better aligns with the text prompt and captures more details." + ], + "image_footnote": [], + "bbox": [ + 295, + 88, + 883, + 218 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8f59bd1557a0befab9c82f4e3cb82ab989b894c32c2670210fa22cfddeaf8196.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VariantsTartanair (4 views)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
Ours(w/o RGB-D)18.380.4750.3830.7610.324
Ours(w/o single-view)18.630.4800.4240.5420.475
Ours19.490.5320.3410.5260.505
", + "bbox": [ + 94, + 252, + 478, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c32a293d994f2724222e8984add9394434cf3e97fbc0474ec4f9a98587e4811e.jpg", + "image_caption": [ + "Figure 6. Qualitative ablation results of GS-VAE for generalizable reconstruction." + ], + "image_footnote": [], + "bbox": [ + 101, + 359, + 473, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "more details. Note that our method takes only 8 seconds for generation, outperforming all baselines.", + "bbox": [ + 89, + 556, + 482, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablations of GS-VAE (Stage 1)", + "text_level": 1, + "bbox": [ + 89, + 609, + 362, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 4, we run ablation studies on the Hard mode of Tartanair, analyzing the following factors of GS-VAE.", + "bbox": [ + 89, + 635, + 482, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effectiveness of Depth Prior for GS-VAE. We investigate the impact of RGB-D latent space during our stage 1 training. Our result in Tab. 4 highlights that training without RGB-D latent space — only RGB latent space — yields worse results over our full model on geometry. Additionally, this bad geometry will lead to sub-optimal quality on reconstructed images, see qualitative results in Fig. 6.", + "bbox": [ + 89, + 669, + 482, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "If large scale matters in Generalizable Reconstruction. Next, we ablate the effectiveness of large-scale dataset, denoted as w/o single-view in Tab. 4. The exclusion of the single-view dataset results in diminished performance across both reconstructed images and geometry. This underscores the significant role of large-scale datasets in achieving robust Generalizable Reconstruction. We also visualize the qualitative results in Fig. 6.", + "bbox": [ + 89, + 780, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a0489913ba0769e209af1dbb6a2a786a873835c684b1c0fd2f5f9308b9c1d23f.jpg", + "table_caption": [ + "Table 4. Quantitative ablation results of GS-VAE for generalizable reconstruction." + ], + "table_footnote": [], + "table_body": "
VariantsBRISQUE↓NIQE↓CLIP-Score↑
Training strategyw/o single-view data59.4514.570.342
w/o high noise level63.0613.880.343
Inference strategyw/o hybrid sampling66.1913.920.329
w/o CFG-rescale89.7015.150.303
Ours (full)58.8814.000.369
", + "bbox": [ + 526, + 252, + 901, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Quantitative ablation results of MV-LDM on text-to-3D generation.", + "bbox": [ + 513, + 342, + 903, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablations of MV-LDM (Stage 2)", + "text_level": 1, + "bbox": [ + 511, + 377, + 795, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 5, we conduct ablation studies on the Single-Object-with-Surroundings subset of T3Bench, examining both training and inference strategies of MV-LDM.", + "bbox": [ + 511, + 401, + 905, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Single-View Dataset. We assess the impact of single-view data. Excluding this training strategy by solely training with multi-view data (w/o single-view data) results in performance degradation. We attribute this to the lack of single-view data, which reduces the model's generalizability, aligning with the observations in MVDream [63].", + "bbox": [ + 511, + 446, + 905, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "High Noise Level. As mentioned in Zero123++ [46] and Sec. 3.2, it is crucial for the model to learn high-level structures in the low-frequency space. Therefore, we also evaluate the effectiveness of a high noise level by setting $P_{mean} = -0.5$ and $P_{std} = 1.2$ during multi-view training (w/o high-noise level). The results in Tab. 3 show that both visual quality and CLIP score decline in this setting.", + "bbox": [ + 511, + 539, + 906, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hybrid Sampling and CFG-Rescale. Finally, we evaluate the design of our inference strategy Sec. 3.2 on hybrid CFG sampling and CFG-rescale by applying CFG solely on the text prompt(w/o hybrid sampling) and set the CFG-rescale factor to 0 (w/o CFG-rescale). Tab. 5 shows that the absence of hybrid sampling and CFG-rescale results in varying degrees of metric decline.", + "bbox": [ + 511, + 645, + 905, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 768, + 633, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels in seconds. We demonstrate the effectiveness of our method in feed-forward reconstruction and 3D generation with extensive experiments. We believe our work offers valuable contributions to text-to-3D scene generation, improving generalizability, fidelity, and efficiency.", + "bbox": [ + 511, + 794, + 905, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2864", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work is supported by NSFC under grant 62441223 and 62202418. This work was supported by Ant Group Research Fund.", + "bbox": [ + 89, + 90, + 485, + 137 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 152, + 187, + 167 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sherwin Bahmani, Jeong Joon Park, Despoina Paschalidou, Xingguang Yan, Gordon Wetzstein, Leonidas J. Guibas, and Andrea Tagliasacchi. 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ACM Trans. on Graphics, 37, 2018. 5" + ], + "bbox": [ + 91, + 90, + 482, + 472 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "2869", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_model.json b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_model.json new file mode 100644 index 0000000000000000000000000000000000000000..525797cf1eaa947b2a6b99003b67eb1b89a4eeeb --- /dev/null +++ b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_model.json @@ -0,0 +1,2987 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.163, + 0.131, + 0.838, + 0.175 + ], + "angle": 0, + "content": "Prometheus: 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.202, + 0.88, + 0.224 + ], + "angle": 0, + "content": "Yuanbo Yang\\(^{1*}\\) Jiahao Shao\\(^{1*}\\) Xinyang Li\\(^{2}\\) Yujun Shen\\(^{3}\\) Andreas Geiger\\(^{4}\\) Yiyi Liao\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.228, + 0.837, + 0.249 + ], + "angle": 0, + "content": "\\(^{1}\\)Zhejiang University \\(^{2}\\)Xiamen University \\(^{3}\\)Ant Group \\(^{4}\\)University of Tübingen" + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.275, + 0.816, + 0.735 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.739, + 0.908, + 0.768 + ], + "angle": 0, + "content": "Figure 1. We present Prometheus, a novel method for feed-forward scene-level 3D generation. At its core, our approach harnesses the power of 2D priors to fuel generalizable and efficient 3D synthesis - hence our name, Prometheus." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.79, + 0.327, + 0.807 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.837, + 0.486, + 0.868 + ], + "angle": 0, + "content": "In this work, we introduce Prometheus, a 3D-aware latent diffusion model for text-to-3D generation at both ob" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.792, + 0.911, + 0.899 + ], + "angle": 0, + "content": "ject and scene levels in seconds. We formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within the latent diffusion paradigm. To ensure generalizability, we build our model upon pretrained text-to-image generation model with only minimal adjustments, and further train it using a large number of images from both single-view and multi-view datasets. Fur" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.876, + 0.265, + 0.889 + ], + "angle": 0, + "content": "* denotes equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.89, + 0.237, + 0.901 + ], + "angle": 0, + "content": "† corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.876, + 0.265, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2857" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.198 + ], + "angle": 0, + "content": "thermore, we introduce an RGB-D latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feed-forward generation of 3D Gaussians with better fidelity and geometry. Extensive experimental results demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation. Project page: Prometheus." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.226, + 0.223, + 0.243 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.252, + 0.483, + 0.357 + ], + "angle": 0, + "content": "3D assets play a crucial role in a wide range of applications, including AR/VR, gaming, and simulation. Developing 3D generative models capable of efficiently producing versatile 3D content has become a key objective, drawing substantial interest in the field. Despite rapid progress in 2D image and video generation, 3D generative models continue to fall short of the progress seen in 2D generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.689 + ], + "angle": 0, + "content": "One line of existing 3D generative models learn from 3D/multi-view data [8, 89], or single-view images of a single category [5, 59]. This allows them for directly learning 3D representations in a feed-forward manner. Despite achieving excellent multi-view consistency with good geometry, their generalizability is limited due to the scarcity of the training data. Another line of approaches seeks to use models trained on large amounts of 2D data for 3D generation — while the largest multi-view datasets contain around 100K samples, single-view datasets and pretrained models based on them can reach scales of 100M to 2B samples. Most methods in this area obtain 3D representations through optimization. Some approaches use score distillation [40, 54, 70, 80, 93] or incremental inpainting [14, 64, 75, 97]. However, since 2D models lack a complete understanding of 3D, their outputs sometimes face the Janus problem and tend to produce results with low fidelity. Another set of methods fine-tunes 2D models to generate multi-view images, requiring multi-view reconstruction to form the 3D representation [18, 47, 58, 63, 84]. In both cases, the optimization process can be time-consuming, thereby lacking efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To address the aforementioned issues, we introduce Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels. Our key idea is to exploiting vast amount of 2D data as well as 2D generative models to facilitate feed-forward 3D generation while maintaining generalization ability - taming the fire of 2D priors to streamline 3D generation. Specifically, we formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within latent diffusion paradigm. To ensure generalizability, we not only build our model upon pre-trained text-to-image generation model (Stable Diffusion) with only minimal adjustments but also train it using both single-view images and multi-view images. Furthermore, we introduce an RGB-D" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feedforward generation of 3D Gaussians with better fidelity and geometry." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.153, + 0.907, + 0.485 + ], + "angle": 0, + "content": "Following the standard latent diffusion paradigm [57], we separate training into two distinct stages. In the first stage, we train a 3D Gaussian Variational Autoencoder (GS-VAE) that takes multi-view or single-view RGB-D images as input and predicts per-pixel aligned 3D Gaussians. Here, the input depth map during training is estimated using an off-the-shelf monocular depth estimator. Additionally, the encoder of our GS-VAE directly re-uses the Stable Diffusion encoder, predicting latent codes for both RGB images and depth maps. We subsequently train a multi-view GS decoder to generate multi-view 3D Gaussians from the RGB-D latent codes conditioned on camera poses. In the second stage, we train a multi-view LDM that jointly predicts multi-view RGB-D latent codes, conditioned on both camera pose and text prompt. Furthermore, our full model is trained on a combination of 9 multi-view and single-view datasets, aiming for generalizability comparable to Stable Diffusion. We demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation, showcasing that our model can generate 3D scenes in seconds while generalizing well to a variety of 3D objects and scenes." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.499, + 0.652, + 0.515 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.531, + 0.907, + 0.728 + ], + "angle": 0, + "content": "3D Generative Models: 3D generative models have attracted great attention in recent years. Many approaches learn from single-category images or 3D supervisions [5, 10, 51, 59, 73, 100], utilizing either GANs or diffusion models. However, these studies primarily concentrate on domain-specific, object-centric scenes, such as those involving Carla Cars [16] and human faces [29]. Despite recent progress that has further extended these methods to model scene-level generation [1, 53, 88, 91], these methods are yet confined to a specific domain with limited generalization capability. This is mainly due to the scarcity of 3D supervision. We aim to tackle this problem by combining multi-view supervision with a vast amount of 2D images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "3D Generation with 2D priors: Thanks to the rapid progress in 2D generation models like Stable Diffusion [57] and SoRA [3], there is a large many works have explored the potential of large 2D diffusion models for 3D-aware generation. One line of works fine-tune 2D diffusion models to enable pose controllability for objects [46, 47] or scenes [18, 20, 58, 81], where the output still lies in the 2D image space. Additionally, some works [13, 34, 34, 44, 52, 68, 95, 98, 105] aim to incorporate underlying 3D prior knowledge to assist in synthesis. Since the aforementioned methods generate only 2D images, a separate 3D re" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2858" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.137 + ], + "angle": 0, + "content": "construction step is still needed, which can add time and introduce errors. In contrast, we explore directly generating 3D representations in a feed-forward manner." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.484, + 0.32 + ], + "angle": 0, + "content": "Another line of methods utilize the 2D priors for 3D generation through optimization, e.g., using Score Distillation Sampling (SDS) [54, 54, 70, 74, 80, 93]. In parallel, several works [14, 17, 36, 64, 75, 96, 103] formulate scene synthesis as \"perpetual view generation\" [43], synthesizing the effects of navigating a 3D world by stitching and rendering images based on camera motions. These methods do not require retraining 2D generative models, but they are inefficient due to per-scene optimization. The generated content's quality is limited by the 2D backbone, causing issues like multi-view inconsistency and artifacts in geometry and texture during image inpainting and score distillation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.328, + 0.484, + 0.539 + ], + "angle": 0, + "content": "Feed-Forward 3D Gaussian Generation: Unlike view synthesis-based methods that focus on synthesizing multiview images followed by 3D reconstruction, a more intuitive approach is to directly generate 3D representations. Following this idea, many works [6, 26, 76, 89] concentrate on the direct synthesis of 3D representations, such as NeRF [48], which generates meshes from single or few-view image inputs. Recently, numerous works [7, 8, 11, 12, 69, 71, 82, 86, 87, 87, 94, 102] have adopted 3D Gaussian Splatting [32] as the underlying representation. Pixel-Splat [7] is the first feed-forward model that learns to reconstruct 3D Gaussian splats from pairs of images. GS-LRM [102] builds on this idea and utilizing a larger reconstruction model (LRM [26]), achieving improved results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.484, + 0.768 + ], + "angle": 0, + "content": "To address this challenge, several works [21, 23, 35, 37, 38, 56, 60, 106] propose Large Diffusion Models as powerful generators for 3D representations. WildFusion [60] introduces a novel approach for achieving 3D-aware image synthesis from in-the-wild datasets using latent diffusion models. Director3D [38], which is closely related to our work, presents a robust open-world text-to-3D generation framework designed to create both real-world 3D scenes and adaptive camera trajectories. Unlike Director3D, which requires supervision in the image space, we follow common practices in 2D image generation and adopt a latent diffusion framework. This approach significantly reduces computational overhead, making larger-scale training feasible, and better leverages the 2D latent space, enhancing the generalizability of our method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.784, + 0.182, + 0.8 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In this section, we provide the technical details of our method. As illustrated in Fig. 2, Prometheus follows the common latent diffusion framework [57], which involves two training stages. In the first stage (Sec. 3.1), our 3D autoencoder, GS-VAE, learns a compressed and abstracted latent space from multi-view images. Subsequently, it de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.213 + ], + "angle": 0, + "content": "codes this latent space into pixel-aligned 3DGS representations, serving as scene-level representations. In the second stage (Sec. 3.2), a latent multi-view diffusion model (MV-LDM) is trained on the latent representations derived from the first stage's autoencoder. This process results in a fully generative model. Finally, we elaborate on our sampling strategy (Sec. 3.3) for sampling 3D scenes in seconds while maintaining consistency and visual fidelity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.225, + 0.685, + 0.241 + ], + "angle": 0, + "content": "3.1. Stage 1: GS-VAE" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.906, + 0.339 + ], + "angle": 0, + "content": "In Stage 1, our objective is to train a 3D autoencoder capable of compressing data into a latent space and subsequently reconstructing it into a 3D representation. Given multi-view input images with camera poses, our GS-VAE outputs multi-view pixel-aligned 3DGS. These outputs are then merged into a scene-level 3D representation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.907, + 0.537 + ], + "angle": 0, + "content": "Encoding Multi-View RGB-D Images. We propose to encode both, RGB images and their predicted monocular depth maps, into the latent space, considering that monocular depth maps provide clues for the later 3D Gaussian decoding process and can be easily obtained. Given a set of multi-view images \\(\\mathcal{I} = \\{I_i\\in \\mathbb{R}^{H\\times W\\times 3}|i = 1,2,\\dots ,N\\}\\) with each image \\(I_{i}\\) being an observation of an underlying 3D scene, we first employ an off-the-shelf depth estimator [90] to obtain their corresponding monocular depth maps \\(\\mathcal{D} = \\{D_i\\in \\mathbb{R}^{H\\times W\\times 1}|i = 1,2,\\dots ,N\\}\\). Next, we utilize a pre-trained image encoder \\(\\mathcal{E}_{\\phi}\\) to encode both the multi-view images \\(\\mathcal{I}\\) and their depth maps \\(\\mathcal{D}\\) into a latent representation:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.55, + 0.905, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} _ {\\phi}: (\\mathcal {I}, \\mathcal {D}) \\mapsto \\mathcal {Z} \\in \\mathbb {R} ^ {N \\times h \\times w \\times c}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.906, + 0.748 + ], + "angle": 0, + "content": "where \\( h \\times w \\) is the downsampled resolution. In practice, we use a pre-trained Stable Diffusion (SD) image encoder and freeze it during training. Recent methods, such as Marigold [31], indicate that the SD encoder exhibits robust generalization capabilities with depth maps. Consequently, we opt to employ the same SD encoder to independently encode both images and depths without the need for fine-tuning. Subsequently, we concatenate these encoded representations to obtain the full multi-view latent \\( \\mathcal{Z} \\) which can be used for 3D reconstruction. Our diffusion model is additionally trained within this joint RGB-D latent space." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.75, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Fusing Multi-View Latent Images. Recent advancements [26, 35, 77, 101, 102] underscore the significant potential of transformer-based models in integrating multiview information. Since our latent codes for each view in \\(\\mathcal{Z}\\) are derived individually, we employ a multi-view transformer to facilitate cross-view information exchange." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "We further inject \\(N\\) camera poses into our multiview transformer. Inspired by recent works [18, 35, 38, 89], we choose Plücker coordinates as camera representation [65], specifically \\(\\mathbf{r} = (\\mathbf{d},\\mathbf{p}\\times \\mathbf{d})\\in \\mathbb{R}^6\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2859" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.087, + 0.631, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.087, + 0.905, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.303, + 0.908, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Method Overview. Our training process is divided into two stages. In stage 1, our objective is to train a GS-VAE. Utilizing multi-view images along with their corresponding pseudo depth maps and camera poses, our GS-VAE is designed to encode these multi-view RGB-D images, integrate cross-view information, and ultimately decode them into pixel-aligned 3DGS. In stage 2, we focus on training a MV-LDM. We can generate multi-view RGB-D latents by sampling from randomly-sampled noise with trained MV-LDM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.386, + 0.484, + 0.507 + ], + "angle": 0, + "content": "where \\(\\mathbf{d}\\) denotes the normalized ray direction and \\(\\mathbf{p}\\) denotes the camera origin. Thus, initial \\(N\\) camera poses can be re-parameterized as multi-view ray maps \\(\\mathcal{R} = \\{R_i\\in \\mathbb{R}^{H\\times W\\times 6}|i = 1,2,\\ldots ,N\\}\\). We combine the multiview latent codes \\(\\mathcal{Z}\\) and the camera ray maps \\(\\mathcal{R}\\) via concatenation along the feature channel and feed them into the cross-view transformer to obtain the fused latent codes \\(\\tilde{\\mathcal{Z}}\\in \\mathbb{R}^{h\\times w\\times c}\\) that merges multi-view context:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.517, + 0.483, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) \\mapsto \\tilde {\\mathcal {Z}} \\in \\mathbb {R} ^ {h \\times w \\times c}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.547, + 0.484, + 0.625 + ], + "angle": 0, + "content": "Decoding into Gaussian Scenes. Finally, we concatenate the raw image latent codes \\(\\mathcal{Z}\\), ray maps \\(\\mathcal{R}\\), and the fused latent codes \\(\\tilde{\\mathcal{Z}}\\), and feed them into the decoder, thereby obtaining the pixel-aligned multi-view 3D Gaussians \\(\\mathcal{F} = \\{F_i \\in \\mathbb{R}^{H \\times W \\times C_G} | i = 1, 2, \\ldots, N\\}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.634, + 0.483, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) \\mapsto \\mathcal {F} \\in \\mathbb {R} ^ {N \\times H \\times W \\times C _ {G}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.664, + 0.484, + 0.771 + ], + "angle": 0, + "content": "where \\(F_{i}\\) is the pixel-aligned 3D Gaussians corresponding to each image. A 3D Gaussian is parameterized by 1-channel depth, 4-channel rotation quaternion, 3-channel scale, 1-channel opacity, and 3-channel spherical harmonics coefficients respectively. Thus \\(C_G = 12\\) in our formulation. After aggregating multi-view 3D Gaussians, we can get the final scene-level 3D Gaussians \\(G\\) as in Eq. (4)" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.781, + 0.483, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\mathbb {M} (\\mathcal {F}) \\mapsto G \\in \\mathbb {R} ^ {N _ {G} \\times C _ {G}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Here, \\(\\mathbb{M}(\\cdot)\\) denotes the aggregation operation, which is achieved by transforming all 3D Gaussians into a global coordinate system. \\(N_{G}\\) represents the number of full Gaussian primitives, which is equivalent to \\(N\\times H\\times W\\)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In practice, this architecture is also applicable to single-view images, where \\( N \\) equals to 1. During training, we" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.386, + 0.907, + 0.476 + ], + "angle": 0, + "content": "sample from both single-view and multi-view images. Besides, to maximize the usage of 2D generative priors, we follow Director3D [38] and repurpose a pre-trained Stable Diffusion image decoder with minor modifications as our Gaussian decoder \\(\\mathcal{D}_{\\phi}\\). Specifically, we only adjust the number of channels in the first and last convolutional layers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.907, + 0.538 + ], + "angle": 0, + "content": "Loss Function. Given the reconstructed scene-level 3D Gaussians \\(\\hat{G}\\), we can render them from arbitrary viewpoints. Let \\(\\mathbf{c}\\) denote a given viewpoint, we can render the corresponding RGB image and depth map from \\(\\hat{G}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.643, + 0.542, + 0.905, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\mathbb {R} (\\hat {G}, \\mathbf {c}) \\mapsto \\{\\hat {I}, \\hat {D} \\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.907, + 0.629 + ], + "angle": 0, + "content": "where \\( \\mathbb{R}(\\cdot) \\) denotes the differentiable rendering of 3D Gaussian Splatting. We can subsequently apply render loss, which integrates MSE (Mean Squared Error) loss and perceptual [28] loss:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.634, + 0.905, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e n d e r}} = \\mathcal {L} _ {\\text {m s e}} (\\hat {I}, I) + \\mathcal {L} _ {\\text {v g g}} (\\hat {I}, I). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.906, + 0.719 + ], + "angle": 0, + "content": "In addition to the rendering loss on the RGB domain, we also impose a loss between our rendered expected depth \\(\\hat{D}\\) and the monocular depth \\(\\bar{D}\\) which serve as pseudo geometry ground truth as below:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.726, + 0.905, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} = \\| (w \\hat {D} + q) - \\bar {D} \\| _ {2}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.75, + 0.906, + 0.811 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{depth}\\) is the scale invariant depth loss following [55]. Here, \\(w\\) and \\(q\\) are the scale and shift used to align \\(\\hat{D}\\) with \\(\\bar{D}\\) since \\(\\bar{D}\\) is defined only up to a scale and a shift. We determine \\(w\\) and \\(q\\) using a least-squares criterion [55]." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.811, + 0.871, + 0.824 + ], + "angle": 0, + "content": "Our full loss function of the GS-VAE is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.833, + 0.905, + 0.85 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\phi) = \\lambda_ {1} \\mathcal {L} _ {m s e} + \\lambda_ {2} \\mathcal {L} _ {v g g} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.9 + ], + "angle": 0, + "content": "where \\(\\phi\\) denotes the estimizable parameters in GS-VAE, and \\(\\lambda_1, \\lambda_2, \\lambda_3\\) are employed to balance the weight of each loss term." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2860" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.482, + 0.107 + ], + "angle": 0, + "content": "3.2. Stage 2: Geometry-Aware Multi-View Denoiser" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.483, + 0.188 + ], + "angle": 0, + "content": "After the training of stage 1, we obtain a GS-VAE capable of i) efficiently compressing images into a compact latent space and ii) bridging the gap between 2D and 3D via a 3D Gaussian decoder. This capability enables us to train the multi-view diffusion model (MV-LDM) in the latent space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.189, + 0.484, + 0.308 + ], + "angle": 0, + "content": "We aim to jointly generate multix-view RGB-D latent codes \\(\\mathcal{Z} \\in \\mathbb{R}^{N \\times h \\times w \\times c}\\) to provide richer geometric cues for decoding 3DGS. Therefore, we formulate a continuous-time denoising diffusion [30, 66] conditioned on the text prompt \\(\\mathbf{y}\\) and camera poses \\(\\mathcal{R}\\). The diffusion model consists of a stochastic forward pass to inject one noise level noise Gaussian noise into input latent codes and a reverse process to remove noise with a learnable denoiser \\(\\mathcal{G}_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.31, + 0.484, + 0.369 + ], + "angle": 0, + "content": "Training. For each training step, we sample one noise level \\(\\sigma_{t}\\), where \\(\\log \\sigma_{t} \\sim \\mathcal{N}(P_{mean}, P_{std}^{2})\\) [30]. Next, we add noise of this level to the clean multi-view latents \\(\\mathcal{Z}_{0}\\) to obtain the noisy latents \\(\\mathcal{Z}_{t}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.379, + 0.482, + 0.396 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Z} _ {t} = \\mathcal {Z} _ {0} + \\sigma_ {t} ^ {2} \\boldsymbol {\\epsilon}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.405, + 0.483, + 0.448 + ], + "angle": 0, + "content": "In the reverse process, diffusion model denoises \\(\\mathcal{Z}_t\\) towards predicted clean \\(\\hat{\\mathcal{Z}}_0\\) with a learnable multi-view denoiser \\(\\mathcal{G}_{\\theta}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.449, + 0.482, + 0.467 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {Z}} _ {0} = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.472, + 0.484, + 0.518 + ], + "angle": 0, + "content": "where \\(\\mathbf{y}\\) and \\(\\mathcal{R}\\) are the text and camera poses condition respectively. Our MV-LDM is trained in latent space via denoising score matching (DSM) [72]" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.525, + 0.483, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\theta) = \\mathbb {E} _ {\\mathcal {Z}, \\mathcal {R}, \\mathbf {y}, \\sigma_ {t}} \\left[ \\lambda (\\sigma_ {t}) \\| \\hat {\\mathcal {Z}} _ {0} - \\mathcal {Z} _ {0} \\| _ {2} ^ {2} \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.56, + 0.483, + 0.592 + ], + "angle": 0, + "content": "with weighting function \\(\\lambda (\\sigma) = (1 + \\sigma^2)\\sigma^{-2}\\). In this work, we follow EDM [30] and parameterize the denoiser \\(\\mathcal{G}_{\\theta}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.6, + 0.482, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right) = c _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathcal {Z} _ {t} + \\tag {12} \\\\ c _ {\\text {o u t}} (\\sigma_ {t}) F _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma_ {t}) \\mathcal {Z} _ {t}; c _ {\\text {n o i s e}} (\\sigma_ {t}), \\mathbf {y}, \\mathcal {R}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.483, + 0.748 + ], + "angle": 0, + "content": "where \\(F_{\\theta}\\) is a UNet to be trained in our case, and \\(c_{\\mathrm{skip}}\\), \\(c_{\\mathrm{out}}\\), \\(c_{\\mathrm{in}}\\), and \\(c_{\\mathrm{noise}}\\) are preconditioning functions. Furthermore, consistent with Stage 1 Eq. (3), we employ ray maps as the pose representation and incorporate them into the network by concatenating them with the noisy latents \\(\\mathcal{Z}_t\\) along feature channel. Additionally, the text prompt conditioning is introduced via cross-attention mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.855 + ], + "angle": 0, + "content": "Inspired by recent multi-view diffusions [18, 38, 63], we replace the self-attention blocks in the original UNet with 3D cross-view self-attention blocks to capture multi-view correlations. In practice, to leverage the pre-trained text-to-image prior, we initialize the model \\(\\mathcal{G}_{\\theta}\\) from a pre-trained text-to-image diffusion model's, specifically the UNet from Stable Diffusion [57]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Sampling. At sampling time, multi-view latents \\(\\mathcal{Z}_0\\) is restored from a randomly-sampled Gaussian noise \\(\\mathcal{Z}_T\\) conditioning on text prompt and camera poses by iteratively" + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.09, + 0.895, + 0.228 + ], + "angle": 0, + "content": "
DatasetScene type# of frames# of Scenes
SAM-1B [33]Single view11M-
MVImgNet [99]Object6.8M230K
DL3DV-10K [42]Indoor / Outdoor2.2M6K
Objaverse [15]Object11.5M784K
ACID [43]Indoor510K11K
RealEstate10K [107]Indoor2.8M57K
KITTI [19]Driving42K0.8K
KITTI-360 [39]Driving69K1.2K
nuScenes [4]Driving340K0.85K
Waymo [67]Driving200K1K
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.229, + 0.905, + 0.271 + ], + "angle": 0, + "content": "Table 1. Training datasets We collect a large, multi-domain dataset for training, including single-view and multi-view data, all paired with detailed captions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.277, + 0.894, + 0.292 + ], + "angle": 0, + "content": "applying the denoising process with trained MV-LDM \\(\\mathcal{G}_{\\theta}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.299, + 0.905, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Z} _ {T} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma_ {T} ^ {2} \\mathbf {I}) \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.344, + 0.905, + 0.394 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {Z} _ {t - 1} = \\frac {\\mathcal {Z} _ {t} - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {T} ; \\sigma_ {t} , \\mathbf {y} , \\mathcal {R}\\right)}{\\sigma_ {t}} \\left(\\sigma_ {t - 1} - \\sigma_ {t}\\right) \\tag {14} \\\\ + \\mathcal {Z} _ {t}, \\quad 0 < t \\leq T \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.403, + 0.905, + 0.432 + ], + "angle": 0, + "content": "where \\(\\sigma_0,\\dots,\\sigma_T\\) are sampled from a fixed variance schedule of a denoising process with \\(T\\) steps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.907, + 0.584 + ], + "angle": 0, + "content": "The Importance of Noise Level. Inspired by insights from recent works [2, 13, 62], we recognize that a lower Signal-to-Noise Ratio (SNR) during the denoising step is crucial for determining the global low-frequency structure of the content. Furthermore, this lower SNR during sampling is essential for achieving multi-view consistency in the multiview diffusion model \\(\\mathcal{G}_{\\theta}\\). Therefore, we adopt a relatively large noise distribution with \\(P_{mean} = 1.5\\) and \\(P_{std} = 2.0\\) during multi-view training of MV-LDM \\(\\mathcal{G}_{\\theta}\\) and \\(P_{mean} = -0.5\\) and \\(P_{std} = 1.2\\) during single-view training." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.592, + 0.855, + 0.607 + ], + "angle": 0, + "content": "3.3. Text to 3D Scene Generation in Sceonds" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.689 + ], + "angle": 0, + "content": "Based on the model above, we can achieve feed-forward text to 3D scene generation by sampling multi-view RGB-D latents \\(\\mathcal{Z}\\) from randomly-sampled Gaussian noise \\(\\mathcal{Z}_T\\) in latent space using MV-LDM \\(\\mathcal{G}_{\\theta}\\), and subsequently decode into a 3D Gaussian Scene \\(G\\) using GS-VAE decoder:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.697, + 0.905, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l l} \\mathcal {G} _ {\\theta}: (\\mathcal {Z} _ {T}; \\mathbf {y}, \\mathcal {R}) & \\mapsto \\mathcal {Z}, \\\\ \\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) & \\mapsto \\tilde {\\mathcal {Z}}, \\\\ \\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) & \\mapsto G. \\end{array} \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.76, + 0.906, + 0.806 + ], + "angle": 0, + "content": "To sample that with high quality and align with the condition, we use classifier-free-guidance (CFG) [25] to guide multi-view generation toward condition signal \\(\\mathbf{y}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.813, + 0.905, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = w \\cdot \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\tag {16} \\\\ + (w - 1) \\cdot \\mathcal {G} _ {\\theta} (\\mathcal {Z} _ {t}; \\mathcal {R}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(w \\geq 0\\) represents the guidance strength. However, if we simply apply the naive CFG Eq. (16), as commonly practiced in most text-to-image methods, increasing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2861" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.111, + 0.089, + 0.887, + 0.153 + ], + "angle": 0, + "content": "
MethodTartanair (Easy)Tartanair (Medium)Tartanair (Hard)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
pixelSplat[7]21.650.6810.2930.6500.37320.300.6280.3370.8060.32319.350.5890.3710.8710.307
MVSplat [11]19.380.5690.3700.8090.28318.500.5310.4090.8720.26517.870.5000.4450.9070.272
Ours20.950.5890.2890.4350.53620.150.5600.3140.4930.51419.490.5320.3410.5260.505
" + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.154, + 0.899, + 0.168 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison for Stage 1. We compare our GS-VAE with baselines for generalizable reconstruction on Tartanair." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.17, + 0.888, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.386, + 0.908, + 0.43 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison for Stage 1. We compare Prometheus against baselines under varying difficulty settings. As overlap gradually decreases, the advantages of our method continue to grow. Moreover, as shown in the depth map, our method exhibits superior geometry quality across all settings." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.444, + 0.484, + 0.55 + ], + "angle": 0, + "content": "\\(w\\) would lead to multi-view inconsistency in the generated results. This naive design described above causes the model to overfit to the text condition while compromising multi-view consistency, in line with the findings in [83, 85]. To balance multi-view consistency and fidelity during sampling, we follow HarmonyView [83] and adapt hybrid sampling guidance, which rewrites Eq. (16) as below:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.565, + 0.482, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\\\ + w _ {1} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathcal {R}\\right)\\right) \\\\ + w _ {2} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}\\right)\\right), \\tag {17} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.635, + 0.484, + 0.711 + ], + "angle": 0, + "content": "where \\( w_{1} \\) and \\( w_{2} \\) denote the weight of text and pose guidance respectively with \\( w = w_{1} + w_{2} \\), thereby better maintaining fidelity and consistency across generated views. In addition, we also use CFG-rescale as proposed in [41] to avoid over-saturation issues during conditional sampling." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.73, + 0.216, + 0.747 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.756, + 0.264, + 0.772 + ], + "angle": 0, + "content": "4.1. Training Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We train our method on large-scale single-view and multiview datasets, see Tab. 1. Regarding the single view dataset, we use a high-quality SAM-1B [33] dataset with detailed captions [45] which was present in PixArt-\\(\\alpha\\) [9]. Our model is trained on a combination of 9 multi-view datasets, including object-centric, indoor, outdoor, and driving scenarios, text prompts for each scene are generated using the multimodal large language model [45]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.443, + 0.692, + 0.459 + ], + "angle": 0, + "content": "4.2. Implement Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.467, + 0.907, + 0.619 + ], + "angle": 0, + "content": "During GS-VAE training (Stage 1), we set both the number of input and novel views to \\( N = 4 \\) for each multi-view scene. To improve model generalizability, we also sample 2 single-view images alongside the multi-view ones, applying the loss to the input views only for single-view images. The GS-VAE was trained on 8 A800 GPUs with a batch size of 32. The final model is trained for 200,000 iterations with approximately 4 days. We use gsplat [92] as our 3D Gaussian renderer. We initialize the weights of our cross-view transformer from a pretrained RayDiff [101]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.62, + 0.909, + 0.801 + ], + "angle": 0, + "content": "For the MV-LDM (Stage 2), we employ Stable Diffusion 2.1 [57] as our base model. During training, we set \\( N = 8 \\) for each multi-view scene. Similarly to Stage 1, we sample \\( M = 4 \\) single-view images alongside multi-view ones. For each iteration, we sample a batch size of 8 on each GPU. The final MV-LDM model was trained on 32 A800 GPUs, resulting in a total batch size of 3072 images. The model underwent 350,000 iterations, which took about 7 days. We utilize a DepthAnything-V2-S [90] model to estimate depth map on the fly. To achieve classifier-free guidance during sampling, we randomly drop text condition \\( y \\) and pose condition \\( \\mathcal{R} \\) with the probability \\( 10\\% \\) during training." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.71, + 0.831 + ], + "angle": 0, + "content": "4.3. Evaluation Protocols" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.908, + 0.903 + ], + "angle": 0, + "content": "3D Reconstruction (Stage-1). To demonstrate the 3D reconstruction generalization of our GS-VAE, we employed Tartanair [78] for our evaluation, which is a diverse synthetic dataset with 18 scenes not included in our training set," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2862" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.112, + 0.089, + 0.895, + 0.166 + ], + "angle": 0, + "content": "
MethodSingle-ObjectSingle-Object-with-SurroundingsScene-LevelTime
BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑
GaussianDreamer [93]107.818.790.386110.818.160.389-≈ 15min
MVDream [63]+LGM [71]74.6414.960.37977.5014.030.343-≈ 10s
Director3D [38]49.9113.560.39749.7713.640.40550.8814.970.357≈ 22s
Ours59.4314.230.32958.8814.000.36949.6314.010.370≈ 8s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.168, + 0.907, + 0.194 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison for 3D generation. We compare Prometheus with baselines for text-to-3D generation utilizing text prompts from T3Bench." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.197, + 0.891, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.391, + 0.908, + 0.421 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison for Stage2: Object-level 3D generation. Prometheus generates objects that align with the given description, incorporating rich background information and intricate details." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.435, + 0.483, + 0.496 + ], + "angle": 0, + "content": "covering both indoor and outdoor scenarios. Based on the degree of overlap and distance among input views, we categorize them into three distinct modes: Easy, Medium, and Hard, each comprising 4 context views and 3 target views." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.497, + 0.483, + 0.618 + ], + "angle": 0, + "content": "We use the metrics PSNR, SSIM [79] and LPIPS [104] for evaluating the reconstructed images. To better compare the reconstructed geometry, we evaluate the rendered depth maps. Follow [27, 61], we align rendered depth maps with the ground truth with per-scene scale and shift and calculate two widely recognized metrics [55] for evaluation, Absolute Mean Relative Error (AbsRel) and \\(\\delta 1\\) accuracy with a specified threshold value of 1.25." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.62, + 0.483, + 0.725 + ], + "angle": 0, + "content": "3D Generation (Stage-2). To assess the text-to-3D generation capabilities of our model, we employ two text prompt sets from T3Bench [22] — Single-Object and Single-Object-with-Surroundings. These sets collectively evaluate the model's proficiency in object-level, and scene-level generation tasks. Additionally, we collected 80 diverse scene-level text prompts covering indoor and outdoor scenarios." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.727, + 0.483, + 0.803 + ], + "angle": 0, + "content": "The quantitative results are evaluated using the CLIP-Score [24], NIQE [50], and BRISQUE [49] metrics. CLIP-Score assesses the alignment between the generated images and the textual prompts, whereas NIQE and BRISQUE indicate the image quality." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.817, + 0.338, + 0.833 + ], + "angle": 0, + "content": "4.4. Comparison with Baselines" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.84, + 0.486, + 0.903 + ], + "angle": 0, + "content": "3D Reconstruction. We compare the GS-VAE of Prometheus against two sparse-view reconstruction models — namely, pixelSplat [7] and MVSplat [11]. Our quantitative findings are shown in Tab. 2, where we accen" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.907, + 0.662 + ], + "angle": 0, + "content": "tuate the best, second-best, and third-best scores across all metrics. Beginning with geometry, Prometheus surpasses the other two baselines, and this advantage becomes more pronounced as the degree of overlap among input views diminishes — see the \\(\\delta 1\\), which exhibits a relative enhancement of \\(44\\%\\) on Easy mode and a substantial \\(64\\%\\) on Hard mode against pixelSplat. Regarding the reconstructed images, Prometheus delivers comparable outcomes on Easy mode and notably outperforms its counterparts as the mode intensifies, particularly in Hard mode. We also provide qualitative results in Fig. 3. These findings on geometry and image reconstruction suggest that Prometheus is more robust to variations in input view overlap than its baselines, a key factor for the success of our downstream 3D generation task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.902 + ], + "angle": 0, + "content": "3D Generation. We compare Prometheus with three text-to-3D baseline methods, covering both optimization-based method and feed-forward method. Gaussian-Dreamer [93] is a state-of-the-art SDS-based method for 3DGS. We additionally implement a baseline that applies a multi-view to 3D method, LGM [71] to images generated by MVDream [63]. We also compare to a feed-forward method, Director3D [38] (without refiner). Fig. 4 and Fig. 5 show that our method is capable of generating both, object and scene-level contents, containing background and rich details, outperforms both optimization-based and feedforward baselines. Tab. 3 shows our overall metrics are suboptimal compared with Director3D for object level while leading in other cases. This is attributed to failure cases in the object-centric setting, see supplementary material for" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2863" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.102, + 0.284, + 0.134 + ], + "angle": 0, + "content": "A bedroom scene displays a bed covered by a quilt and a window located near the end of the bed" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.161, + 0.279, + 0.193 + ], + "angle": 0, + "content": "A coastal town with white buildings and green vegetation is seen in the image" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.089, + 0.885, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.22, + 0.905, + 0.248 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison for Stage 2: Scene-level 3D generation with diverse scene-level prompt. Our result better aligns with the text prompt and captures more details." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.253, + 0.479, + 0.324 + ], + "angle": 0, + "content": "
VariantsTartanair (4 views)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
Ours(w/o RGB-D)18.380.4750.3830.7610.324
Ours(w/o single-view)18.630.4800.4240.5420.475
Ours19.490.5320.3410.5260.505
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.325, + 0.482, + 0.352 + ], + "angle": 0, + "content": "Table 4. Quantitative ablation results of GS-VAE for generalizable reconstruction." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.36, + 0.475, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.514, + 0.483, + 0.54 + ], + "angle": 0, + "content": "Figure 6. Qualitative ablation results of GS-VAE for generalizable reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.558, + 0.483, + 0.589 + ], + "angle": 0, + "content": "more details. Note that our method takes only 8 seconds for generation, outperforming all baselines." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.61, + 0.363, + 0.627 + ], + "angle": 0, + "content": "4.5. Ablations of GS-VAE (Stage 1)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.636, + 0.483, + 0.667 + ], + "angle": 0, + "content": "In Tab. 4, we run ablation studies on the Hard mode of Tartanair, analyzing the following factors of GS-VAE." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.777 + ], + "angle": 0, + "content": "The effectiveness of Depth Prior for GS-VAE. We investigate the impact of RGB-D latent space during our stage 1 training. Our result in Tab. 4 highlights that training without RGB-D latent space — only RGB latent space — yields worse results over our full model on geometry. Additionally, this bad geometry will lead to sub-optimal quality on reconstructed images, see qualitative results in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.483, + 0.901 + ], + "angle": 0, + "content": "If large scale matters in Generalizable Reconstruction. Next, we ablate the effectiveness of large-scale dataset, denoted as w/o single-view in Tab. 4. The exclusion of the single-view dataset results in diminished performance across both reconstructed images and geometry. This underscores the significant role of large-scale datasets in achieving robust Generalizable Reconstruction. We also visualize the qualitative results in Fig. 6." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.253, + 0.903, + 0.342 + ], + "angle": 0, + "content": "
VariantsBRISQUE↓NIQE↓CLIP-Score↑
Training strategyw/o single-view data59.4514.570.342
w/o high noise level63.0613.880.343
Inference strategyw/o hybrid sampling66.1913.920.329
w/o CFG-rescale89.7015.150.303
Ours (full)58.8814.000.369
" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.343, + 0.905, + 0.371 + ], + "angle": 0, + "content": "Table 5. Quantitative ablation results of MV-LDM on text-to-3D generation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.378, + 0.797, + 0.394 + ], + "angle": 0, + "content": "4.6. Ablations of MV-LDM (Stage 2)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.402, + 0.906, + 0.446 + ], + "angle": 0, + "content": "In Tab. 5, we conduct ablation studies on the Single-Object-with-Surroundings subset of T3Bench, examining both training and inference strategies of MV-LDM." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.906, + 0.538 + ], + "angle": 0, + "content": "Single-View Dataset. We assess the impact of single-view data. Excluding this training strategy by solely training with multi-view data (w/o single-view data) results in performance degradation. We attribute this to the lack of single-view data, which reduces the model's generalizability, aligning with the observations in MVDream [63]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.54, + 0.907, + 0.646 + ], + "angle": 0, + "content": "High Noise Level. As mentioned in Zero123++ [46] and Sec. 3.2, it is crucial for the model to learn high-level structures in the low-frequency space. Therefore, we also evaluate the effectiveness of a high noise level by setting \\( P_{mean} = -0.5 \\) and \\( P_{std} = 1.2 \\) during multi-view training (w/o high-noise level). The results in Tab. 3 show that both visual quality and CLIP score decline in this setting." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.906, + 0.752 + ], + "angle": 0, + "content": "Hybrid Sampling and CFG-Rescale. Finally, we evaluate the design of our inference strategy Sec. 3.2 on hybrid CFG sampling and CFG-rescale by applying CFG solely on the text prompt(w/o hybrid sampling) and set the CFG-rescale factor to 0 (w/o CFG-rescale). Tab. 5 shows that the absence of hybrid sampling and CFG-rescale results in varying degrees of metric decline." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.769, + 0.634, + 0.785 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.903 + ], + "angle": 0, + "content": "We present Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels in seconds. We demonstrate the effectiveness of our method in feed-forward reconstruction and 3D generation with extensive experiments. We believe our work offers valuable contributions to text-to-3D scene generation, improving generalizability, fidelity, and efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2864" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.486, + 0.138 + ], + "angle": 0, + "content": "Acknowledgements: This work is supported by NSFC under grant 62441223 and 62202418. This work was supported by Ant Group Research Fund." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.153, + 0.188, + 0.168 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.178, + 0.484, + 0.234 + ], + "angle": 0, + "content": "[1] Sherwin Bahmani, Jeong Joon Park, Despoina Paschalidou, Xingguang Yan, Gordon Wetzstein, Leonidas J. Guibas, and Andrea Tagliasacchi. 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ACM Trans. on Graphics, 37, 2018. 5" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.483, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2869" + } + ] +] \ No newline at end of file diff --git a/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_origin.pdf b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..99fcb7cf57c1be04ab771ebee45194df609a14e1 --- /dev/null +++ b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/f7239594-bff6-466c-a34f-3ffb021b8e29_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bf0e77842217bdc7c32cfb30856f667ed46e6582484de73417bf2052082a052d +size 7098190 diff --git a/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/full.md b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..58d2f3a5f08a7c2931751f1bcf80b05cb249ffc4 --- /dev/null +++ b/2025/Prometheus_ 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation/full.md @@ -0,0 +1,411 @@ +# Prometheus: 3D-Aware Latent Diffusion Models for Feed-Forward Text-to-3D Scene Generation + +Yuanbo Yang $^{1*}$ Jiahao Shao $^{1*}$ Xinyang Li $^{2}$ Yujun Shen $^{3}$ Andreas Geiger $^{4}$ Yiyi Liao $^{1\dagger}$ + +$^{1}$ Zhejiang University $^{2}$ Xiamen University $^{3}$ Ant Group $^{4}$ University of Tübingen + +![](images/15dee114f762fcb11d8ea429669df3655af25b88171c254cd9ff91f5e63d40e7.jpg) +Figure 1. We present Prometheus, a novel method for feed-forward scene-level 3D generation. At its core, our approach harnesses the power of 2D priors to fuel generalizable and efficient 3D synthesis - hence our name, Prometheus. + +# Abstract + +In this work, we introduce Prometheus, a 3D-aware latent diffusion model for text-to-3D generation at both ob + +ject and scene levels in seconds. We formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within the latent diffusion paradigm. To ensure generalizability, we build our model upon pretrained text-to-image generation model with only minimal adjustments, and further train it using a large number of images from both single-view and multi-view datasets. Fur + +thermore, we introduce an RGB-D latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feed-forward generation of 3D Gaussians with better fidelity and geometry. Extensive experimental results demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation. Project page: Prometheus. + +# 1. Introduction + +3D assets play a crucial role in a wide range of applications, including AR/VR, gaming, and simulation. Developing 3D generative models capable of efficiently producing versatile 3D content has become a key objective, drawing substantial interest in the field. Despite rapid progress in 2D image and video generation, 3D generative models continue to fall short of the progress seen in 2D generation. + +One line of existing 3D generative models learn from 3D/multi-view data [8, 89], or single-view images of a single category [5, 59]. This allows them for directly learning 3D representations in a feed-forward manner. Despite achieving excellent multi-view consistency with good geometry, their generalizability is limited due to the scarcity of the training data. Another line of approaches seeks to use models trained on large amounts of 2D data for 3D generation — while the largest multi-view datasets contain around 100K samples, single-view datasets and pretrained models based on them can reach scales of 100M to 2B samples. Most methods in this area obtain 3D representations through optimization. Some approaches use score distillation [40, 54, 70, 80, 93] or incremental inpainting [14, 64, 75, 97]. However, since 2D models lack a complete understanding of 3D, their outputs sometimes face the Janus problem and tend to produce results with low fidelity. Another set of methods fine-tunes 2D models to generate multi-view images, requiring multi-view reconstruction to form the 3D representation [18, 47, 58, 63, 84]. In both cases, the optimization process can be time-consuming, thereby lacking efficiency. + +To address the aforementioned issues, we introduce Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels. Our key idea is to exploiting vast amount of 2D data as well as 2D generative models to facilitate feed-forward 3D generation while maintaining generalization ability - taming the fire of 2D priors to streamline 3D generation. Specifically, we formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within latent diffusion paradigm. To ensure generalizability, we not only build our model upon pre-trained text-to-image generation model (Stable Diffusion) with only minimal adjustments but also train it using both single-view images and multi-view images. Furthermore, we introduce an RGB-D + +latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feedforward generation of 3D Gaussians with better fidelity and geometry. + +Following the standard latent diffusion paradigm [57], we separate training into two distinct stages. In the first stage, we train a 3D Gaussian Variational Autoencoder (GS-VAE) that takes multi-view or single-view RGB-D images as input and predicts per-pixel aligned 3D Gaussians. Here, the input depth map during training is estimated using an off-the-shelf monocular depth estimator. Additionally, the encoder of our GS-VAE directly re-uses the Stable Diffusion encoder, predicting latent codes for both RGB images and depth maps. We subsequently train a multi-view GS decoder to generate multi-view 3D Gaussians from the RGB-D latent codes conditioned on camera poses. In the second stage, we train a multi-view LDM that jointly predicts multi-view RGB-D latent codes, conditioned on both camera pose and text prompt. Furthermore, our full model is trained on a combination of 9 multi-view and single-view datasets, aiming for generalizability comparable to Stable Diffusion. We demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation, showcasing that our model can generate 3D scenes in seconds while generalizing well to a variety of 3D objects and scenes. + +# 2. Related work + +3D Generative Models: 3D generative models have attracted great attention in recent years. Many approaches learn from single-category images or 3D supervisions [5, 10, 51, 59, 73, 100], utilizing either GANs or diffusion models. However, these studies primarily concentrate on domain-specific, object-centric scenes, such as those involving Carla Cars [16] and human faces [29]. Despite recent progress that has further extended these methods to model scene-level generation [1, 53, 88, 91], these methods are yet confined to a specific domain with limited generalization capability. This is mainly due to the scarcity of 3D supervision. We aim to tackle this problem by combining multi-view supervision with a vast amount of 2D images. + +3D Generation with 2D priors: Thanks to the rapid progress in 2D generation models like Stable Diffusion [57] and SoRA [3], there is a large many works have explored the potential of large 2D diffusion models for 3D-aware generation. One line of works fine-tune 2D diffusion models to enable pose controllability for objects [46, 47] or scenes [18, 20, 58, 81], where the output still lies in the 2D image space. Additionally, some works [13, 34, 34, 44, 52, 68, 95, 98, 105] aim to incorporate underlying 3D prior knowledge to assist in synthesis. Since the aforementioned methods generate only 2D images, a separate 3D re + +construction step is still needed, which can add time and introduce errors. In contrast, we explore directly generating 3D representations in a feed-forward manner. + +Another line of methods utilize the 2D priors for 3D generation through optimization, e.g., using Score Distillation Sampling (SDS) [54, 54, 70, 74, 80, 93]. In parallel, several works [14, 17, 36, 64, 75, 96, 103] formulate scene synthesis as "perpetual view generation" [43], synthesizing the effects of navigating a 3D world by stitching and rendering images based on camera motions. These methods do not require retraining 2D generative models, but they are inefficient due to per-scene optimization. The generated content's quality is limited by the 2D backbone, causing issues like multi-view inconsistency and artifacts in geometry and texture during image inpainting and score distillation. + +Feed-Forward 3D Gaussian Generation: Unlike view synthesis-based methods that focus on synthesizing multiview images followed by 3D reconstruction, a more intuitive approach is to directly generate 3D representations. Following this idea, many works [6, 26, 76, 89] concentrate on the direct synthesis of 3D representations, such as NeRF [48], which generates meshes from single or few-view image inputs. Recently, numerous works [7, 8, 11, 12, 69, 71, 82, 86, 87, 87, 94, 102] have adopted 3D Gaussian Splatting [32] as the underlying representation. Pixel-Splat [7] is the first feed-forward model that learns to reconstruct 3D Gaussian splats from pairs of images. GS-LRM [102] builds on this idea and utilizing a larger reconstruction model (LRM [26]), achieving improved results. + +To address this challenge, several works [21, 23, 35, 37, 38, 56, 60, 106] propose Large Diffusion Models as powerful generators for 3D representations. WildFusion [60] introduces a novel approach for achieving 3D-aware image synthesis from in-the-wild datasets using latent diffusion models. Director3D [38], which is closely related to our work, presents a robust open-world text-to-3D generation framework designed to create both real-world 3D scenes and adaptive camera trajectories. Unlike Director3D, which requires supervision in the image space, we follow common practices in 2D image generation and adopt a latent diffusion framework. This approach significantly reduces computational overhead, making larger-scale training feasible, and better leverages the 2D latent space, enhancing the generalizability of our method. + +# 3. Method + +In this section, we provide the technical details of our method. As illustrated in Fig. 2, Prometheus follows the common latent diffusion framework [57], which involves two training stages. In the first stage (Sec. 3.1), our 3D autoencoder, GS-VAE, learns a compressed and abstracted latent space from multi-view images. Subsequently, it de + +codes this latent space into pixel-aligned 3DGS representations, serving as scene-level representations. In the second stage (Sec. 3.2), a latent multi-view diffusion model (MV-LDM) is trained on the latent representations derived from the first stage's autoencoder. This process results in a fully generative model. Finally, we elaborate on our sampling strategy (Sec. 3.3) for sampling 3D scenes in seconds while maintaining consistency and visual fidelity. + +# 3.1. Stage 1: GS-VAE + +In Stage 1, our objective is to train a 3D autoencoder capable of compressing data into a latent space and subsequently reconstructing it into a 3D representation. Given multi-view input images with camera poses, our GS-VAE outputs multi-view pixel-aligned 3DGS. These outputs are then merged into a scene-level 3D representation. + +Encoding Multi-View RGB-D Images. We propose to encode both, RGB images and their predicted monocular depth maps, into the latent space, considering that monocular depth maps provide clues for the later 3D Gaussian decoding process and can be easily obtained. Given a set of multi-view images $\mathcal{I} = \{I_i\in \mathbb{R}^{H\times W\times 3}|i = 1,2,\dots ,N\}$ with each image $I_{i}$ being an observation of an underlying 3D scene, we first employ an off-the-shelf depth estimator [90] to obtain their corresponding monocular depth maps $\mathcal{D} = \{D_i\in \mathbb{R}^{H\times W\times 1}|i = 1,2,\dots ,N\}$ . Next, we utilize a pre-trained image encoder $\mathcal{E}_{\phi}$ to encode both the multi-view images $\mathcal{I}$ and their depth maps $\mathcal{D}$ into a latent representation: + +$$ +\mathcal {E} _ {\phi}: (\mathcal {I}, \mathcal {D}) \mapsto \mathcal {Z} \in \mathbb {R} ^ {N \times h \times w \times c}, \tag {1} +$$ + +where $h \times w$ is the downsampled resolution. In practice, we use a pre-trained Stable Diffusion (SD) image encoder and freeze it during training. Recent methods, such as Marigold [31], indicate that the SD encoder exhibits robust generalization capabilities with depth maps. Consequently, we opt to employ the same SD encoder to independently encode both images and depths without the need for fine-tuning. Subsequently, we concatenate these encoded representations to obtain the full multi-view latent $\mathcal{Z}$ which can be used for 3D reconstruction. Our diffusion model is additionally trained within this joint RGB-D latent space. + +Fusing Multi-View Latent Images. Recent advancements [26, 35, 77, 101, 102] underscore the significant potential of transformer-based models in integrating multiview information. Since our latent codes for each view in $\mathcal{Z}$ are derived individually, we employ a multi-view transformer to facilitate cross-view information exchange. + +We further inject $N$ camera poses into our multiview transformer. Inspired by recent works [18, 35, 38, 89], we choose Plücker coordinates as camera representation [65], specifically $\mathbf{r} = (\mathbf{d},\mathbf{p}\times \mathbf{d})\in \mathbb{R}^6$ + +![](images/3bf7985b354b7a3ce0070def4f49b1279c986fac85404c17dc30f13ee5ad03fb.jpg) +Figure 2. Method Overview. Our training process is divided into two stages. In stage 1, our objective is to train a GS-VAE. Utilizing multi-view images along with their corresponding pseudo depth maps and camera poses, our GS-VAE is designed to encode these multi-view RGB-D images, integrate cross-view information, and ultimately decode them into pixel-aligned 3DGS. In stage 2, we focus on training a MV-LDM. We can generate multi-view RGB-D latents by sampling from randomly-sampled noise with trained MV-LDM. + +![](images/39a6c12b98a75e2fc297c663a32124cef8d7f45ff27a8f2127705fab14ba0b30.jpg) + +where $\mathbf{d}$ denotes the normalized ray direction and $\mathbf{p}$ denotes the camera origin. Thus, initial $N$ camera poses can be re-parameterized as multi-view ray maps $\mathcal{R} = \{R_i\in \mathbb{R}^{H\times W\times 6}|i = 1,2,\ldots ,N\}$ . We combine the multiview latent codes $\mathcal{Z}$ and the camera ray maps $\mathcal{R}$ via concatenation along the feature channel and feed them into the cross-view transformer to obtain the fused latent codes $\tilde{\mathcal{Z}}\in \mathbb{R}^{h\times w\times c}$ that merges multi-view context: + +$$ +\mathcal {C} _ {\phi}: (\mathcal {Z}, \mathcal {R}) \mapsto \tilde {\mathcal {Z}} \in \mathbb {R} ^ {h \times w \times c}. \tag {2} +$$ + +Decoding into Gaussian Scenes. Finally, we concatenate the raw image latent codes $\mathcal{Z}$ , ray maps $\mathcal{R}$ , and the fused latent codes $\tilde{\mathcal{Z}}$ , and feed them into the decoder, thereby obtaining the pixel-aligned multi-view 3D Gaussians $\mathcal{F} = \{F_i \in \mathbb{R}^{H \times W \times C_G} | i = 1, 2, \ldots, N\}$ + +$$ +\mathcal {D} _ {\phi}: (\mathcal {Z}, \tilde {\mathcal {Z}}, \mathcal {R}) \mapsto \mathcal {F} \in \mathbb {R} ^ {N \times H \times W \times C _ {G}}, \tag {3} +$$ + +where $F_{i}$ is the pixel-aligned 3D Gaussians corresponding to each image. A 3D Gaussian is parameterized by 1-channel depth, 4-channel rotation quaternion, 3-channel scale, 1-channel opacity, and 3-channel spherical harmonics coefficients respectively. Thus $C_G = 12$ in our formulation. After aggregating multi-view 3D Gaussians, we can get the final scene-level 3D Gaussians $G$ as in Eq. (4) + +$$ +\mathbb {M} (\mathcal {F}) \mapsto G \in \mathbb {R} ^ {N _ {G} \times C _ {G}}. \tag {4} +$$ + +Here, $\mathbb{M}(\cdot)$ denotes the aggregation operation, which is achieved by transforming all 3D Gaussians into a global coordinate system. $N_{G}$ represents the number of full Gaussian primitives, which is equivalent to $N\times H\times W$ . + +In practice, this architecture is also applicable to single-view images, where $N$ equals to 1. During training, we + +sample from both single-view and multi-view images. Besides, to maximize the usage of 2D generative priors, we follow Director3D [38] and repurpose a pre-trained Stable Diffusion image decoder with minor modifications as our Gaussian decoder $\mathcal{D}_{\phi}$ . Specifically, we only adjust the number of channels in the first and last convolutional layers. + +Loss Function. Given the reconstructed scene-level 3D Gaussians $\hat{G}$ , we can render them from arbitrary viewpoints. Let $\mathbf{c}$ denote a given viewpoint, we can render the corresponding RGB image and depth map from $\hat{G}$ : + +$$ +\mathbb {R} (\hat {G}, \mathbf {c}) \mapsto \{\hat {I}, \hat {D} \}, \tag {5} +$$ + +where $\mathbb{R}(\cdot)$ denotes the differentiable rendering of 3D Gaussian Splatting. We can subsequently apply render loss, which integrates MSE (Mean Squared Error) loss and perceptual [28] loss: + +$$ +\mathcal {L} _ {\text {r e n d e r}} = \mathcal {L} _ {\text {m s e}} (\hat {I}, I) + \mathcal {L} _ {\text {v g g}} (\hat {I}, I). \tag {6} +$$ + +In addition to the rendering loss on the RGB domain, we also impose a loss between our rendered expected depth $\hat{D}$ and the monocular depth $\bar{D}$ which serve as pseudo geometry ground truth as below: + +$$ +\mathcal {L} _ {\text {d e p t h}} = \| (w \hat {D} + q) - \bar {D} \| _ {2}, \tag {7} +$$ + +where $\mathcal{L}_{depth}$ is the scale invariant depth loss following [55]. Here, $w$ and $q$ are the scale and shift used to align $\hat{D}$ with $\bar{D}$ since $\bar{D}$ is defined only up to a scale and a shift. We determine $w$ and $q$ using a least-squares criterion [55]. + +Our full loss function of the GS-VAE is as follows: + +$$ +\mathcal {L} (\phi) = \lambda_ {1} \mathcal {L} _ {m s e} + \lambda_ {2} \mathcal {L} _ {v g g} + \lambda_ {3} \mathcal {L} _ {\text {d e p t h}}, \tag {8} +$$ + +where $\phi$ denotes the estimizable parameters in GS-VAE, and $\lambda_1, \lambda_2, \lambda_3$ are employed to balance the weight of each loss term. + +# 3.2. Stage 2: Geometry-Aware Multi-View Denoiser + +After the training of stage 1, we obtain a GS-VAE capable of i) efficiently compressing images into a compact latent space and ii) bridging the gap between 2D and 3D via a 3D Gaussian decoder. This capability enables us to train the multi-view diffusion model (MV-LDM) in the latent space. + +We aim to jointly generate multix-view RGB-D latent codes $\mathcal{Z} \in \mathbb{R}^{N \times h \times w \times c}$ to provide richer geometric cues for decoding 3DGS. Therefore, we formulate a continuous-time denoising diffusion [30, 66] conditioned on the text prompt $\mathbf{y}$ and camera poses $\mathcal{R}$ . The diffusion model consists of a stochastic forward pass to inject one noise level noise Gaussian noise into input latent codes and a reverse process to remove noise with a learnable denoiser $\mathcal{G}_{\theta}$ . + +Training. For each training step, we sample one noise level $\sigma_{t}$ , where $\log \sigma_{t} \sim \mathcal{N}(P_{mean}, P_{std}^{2})$ [30]. Next, we add noise of this level to the clean multi-view latents $\mathcal{Z}_{0}$ to obtain the noisy latents $\mathcal{Z}_{t}$ as + +$$ +\mathcal {Z} _ {t} = \mathcal {Z} _ {0} + \sigma_ {t} ^ {2} \boldsymbol {\epsilon}, \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {9} +$$ + +In the reverse process, diffusion model denoises $\mathcal{Z}_t$ towards predicted clean $\hat{\mathcal{Z}}_0$ with a learnable multi-view denoiser $\mathcal{G}_{\theta}$ as + +$$ +\hat {\mathcal {Z}} _ {0} = \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \sigma_ {t}, \mathbf {y}, \mathcal {R}\right), \tag {10} +$$ + +where $\mathbf{y}$ and $\mathcal{R}$ are the text and camera poses condition respectively. Our MV-LDM is trained in latent space via denoising score matching (DSM) [72] + +$$ +\mathcal {L} (\theta) = \mathbb {E} _ {\mathcal {Z}, \mathcal {R}, \mathbf {y}, \sigma_ {t}} \left[ \lambda (\sigma_ {t}) \| \hat {\mathcal {Z}} _ {0} - \mathcal {Z} _ {0} \| _ {2} ^ {2} \right], \tag {11} +$$ + +with weighting function $\lambda (\sigma) = (1 + \sigma^2)\sigma^{-2}$ . In this work, we follow EDM [30] and parameterize the denoiser $\mathcal{G}_{\theta}$ as + +$$ +\begin{array}{l} \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \sigma_ {t}, \mathbf {y}, \mathcal {R}\right) = c _ {\text {s k i p}} \left(\sigma_ {t}\right) \mathcal {Z} _ {t} + \tag {12} \\ c _ {\text {o u t}} (\sigma_ {t}) F _ {\theta} \left(c _ {\text {i n}} (\sigma_ {t}) \mathcal {Z} _ {t}; c _ {\text {n o i s e}} (\sigma_ {t}), \mathbf {y}, \mathcal {R}\right), \\ \end{array} +$$ + +where $F_{\theta}$ is a UNet to be trained in our case, and $c_{\mathrm{skip}}$ , $c_{\mathrm{out}}$ , $c_{\mathrm{in}}$ , and $c_{\mathrm{noise}}$ are preconditioning functions. Furthermore, consistent with Stage 1 Eq. (3), we employ ray maps as the pose representation and incorporate them into the network by concatenating them with the noisy latents $\mathcal{Z}_t$ along feature channel. Additionally, the text prompt conditioning is introduced via cross-attention mechanisms. + +Inspired by recent multi-view diffusions [18, 38, 63], we replace the self-attention blocks in the original UNet with 3D cross-view self-attention blocks to capture multi-view correlations. In practice, to leverage the pre-trained text-to-image prior, we initialize the model $\mathcal{G}_{\theta}$ from a pre-trained text-to-image diffusion model's, specifically the UNet from Stable Diffusion [57]. + +Sampling. At sampling time, multi-view latents $\mathcal{Z}_0$ is restored from a randomly-sampled Gaussian noise $\mathcal{Z}_T$ conditioning on text prompt and camera poses by iteratively + +
DatasetScene type# of frames# of Scenes
SAM-1B [33]Single view11M-
MVImgNet [99]Object6.8M230K
DL3DV-10K [42]Indoor / Outdoor2.2M6K
Objaverse [15]Object11.5M784K
ACID [43]Indoor510K11K
RealEstate10K [107]Indoor2.8M57K
KITTI [19]Driving42K0.8K
KITTI-360 [39]Driving69K1.2K
nuScenes [4]Driving340K0.85K
Waymo [67]Driving200K1K
+ +Table 1. Training datasets We collect a large, multi-domain dataset for training, including single-view and multi-view data, all paired with detailed captions. + +applying the denoising process with trained MV-LDM $\mathcal{G}_{\theta}$ + +$$ +\mathcal {Z} _ {T} \sim \mathcal {N} (\mathbf {0}, \sigma_ {T} ^ {2} \mathbf {I}) \tag {13} +$$ + +$$ +\begin{array}{l} \mathcal {Z} _ {t - 1} = \frac {\mathcal {Z} _ {t} - \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {T} ; \sigma_ {t} , \mathbf {y} , \mathcal {R}\right)}{\sigma_ {t}} \left(\sigma_ {t - 1} - \sigma_ {t}\right) \tag {14} \\ + \mathcal {Z} _ {t}, \quad 0 < t \leq T \\ \end{array} +$$ + +where $\sigma_0,\dots,\sigma_T$ are sampled from a fixed variance schedule of a denoising process with $T$ steps. + +The Importance of Noise Level. Inspired by insights from recent works [2, 13, 62], we recognize that a lower Signal-to-Noise Ratio (SNR) during the denoising step is crucial for determining the global low-frequency structure of the content. Furthermore, this lower SNR during sampling is essential for achieving multi-view consistency in the multiview diffusion model $\mathcal{G}_{\theta}$ . Therefore, we adopt a relatively large noise distribution with $P_{mean} = 1.5$ and $P_{std} = 2.0$ during multi-view training of MV-LDM $\mathcal{G}_{\theta}$ and $P_{mean} = -0.5$ and $P_{std} = 1.2$ during single-view training. + +# 3.3. Text to 3D Scene Generation in Sceonds + +Based on the model above, we can achieve feed-forward text to 3D scene generation by sampling multi-view RGB-D latents $\mathcal{Z}$ from randomly-sampled Gaussian noise $\mathcal{Z}_T$ in latent space using MV-LDM $\mathcal{G}_{\theta}$ , and subsequently decode into a 3D Gaussian Scene $G$ using GS-VAE decoder: + +$$ +\left\{ \begin{array}{l l} \mathcal {G} _ {\theta}: (\mathcal {Z} _ {T}; \mathbf {y}, \mathcal {R}) & \mapsto \mathcal {Z}, \\ \mathcal {C} _ {\phi}: (\mathcal {Z}, \mathcal {R}) & \mapsto \tilde {\mathcal {Z}}, \\ \mathcal {D} _ {\phi}: (\mathcal {Z}, \tilde {\mathcal {Z}}, \mathcal {R}) & \mapsto G. \end{array} \right. \tag {15} +$$ + +To sample that with high quality and align with the condition, we use classifier-free-guidance (CFG) [25] to guide multi-view generation toward condition signal $\mathbf{y}$ . + +$$ +\begin{array}{l} \mathcal {G} _ {\theta} ^ {w} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) = w \cdot \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) \tag {16} \\ + (w - 1) \cdot \mathcal {G} _ {\theta} (\mathcal {Z} _ {t}; \mathcal {R}), \\ \end{array} +$$ + +where $w \geq 0$ represents the guidance strength. However, if we simply apply the naive CFG Eq. (16), as commonly practiced in most text-to-image methods, increasing + +
MethodTartanair (Easy)Tartanair (Medium)Tartanair (Hard)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
pixelSplat[7]21.650.6810.2930.6500.37320.300.6280.3370.8060.32319.350.5890.3710.8710.307
MVSplat [11]19.380.5690.3700.8090.28318.500.5310.4090.8720.26517.870.5000.4450.9070.272
Ours20.950.5890.2890.4350.53620.150.5600.3140.4930.51419.490.5320.3410.5260.505
+ +Table 2. Quantitative comparison for Stage 1. We compare our GS-VAE with baselines for generalizable reconstruction on Tartanair. + +![](images/0cb67c6b9f20d0d01452e683003e7eaae8b05e9cc591dc1a62d80e36591bd5b8.jpg) +Figure 3. Qualitative comparison for Stage 1. We compare Prometheus against baselines under varying difficulty settings. As overlap gradually decreases, the advantages of our method continue to grow. Moreover, as shown in the depth map, our method exhibits superior geometry quality across all settings. + +$w$ would lead to multi-view inconsistency in the generated results. This naive design described above causes the model to overfit to the text condition while compromising multi-view consistency, in line with the findings in [83, 85]. To balance multi-view consistency and fidelity during sampling, we follow HarmonyView [83] and adapt hybrid sampling guidance, which rewrites Eq. (16) as below: + +$$ +\begin{array}{l} \mathcal {G} _ {\theta} ^ {w} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) = \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) \\ + w _ {1} \cdot \left(\mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) - \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathcal {R}\right)\right) \\ + w _ {2} \cdot \left(\mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathbf {y}, \mathcal {R}\right) - \mathcal {G} _ {\theta} \left(\mathcal {Z} _ {t}; \mathbf {y}\right)\right), \tag {17} \\ \end{array} +$$ + +where $w_{1}$ and $w_{2}$ denote the weight of text and pose guidance respectively with $w = w_{1} + w_{2}$ , thereby better maintaining fidelity and consistency across generated views. In addition, we also use CFG-rescale as proposed in [41] to avoid over-saturation issues during conditional sampling. + +# 4. Experiment + +# 4.1. Training Datasets + +We train our method on large-scale single-view and multiview datasets, see Tab. 1. Regarding the single view dataset, we use a high-quality SAM-1B [33] dataset with detailed captions [45] which was present in PixArt- $\alpha$ [9]. Our model is trained on a combination of 9 multi-view datasets, including object-centric, indoor, outdoor, and driving scenarios, text prompts for each scene are generated using the multimodal large language model [45]. + +# 4.2. Implement Details + +During GS-VAE training (Stage 1), we set both the number of input and novel views to $N = 4$ for each multi-view scene. To improve model generalizability, we also sample 2 single-view images alongside the multi-view ones, applying the loss to the input views only for single-view images. The GS-VAE was trained on 8 A800 GPUs with a batch size of 32. The final model is trained for 200,000 iterations with approximately 4 days. We use gsplat [92] as our 3D Gaussian renderer. We initialize the weights of our cross-view transformer from a pretrained RayDiff [101]. + +For the MV-LDM (Stage 2), we employ Stable Diffusion 2.1 [57] as our base model. During training, we set $N = 8$ for each multi-view scene. Similarly to Stage 1, we sample $M = 4$ single-view images alongside multi-view ones. For each iteration, we sample a batch size of 8 on each GPU. The final MV-LDM model was trained on 32 A800 GPUs, resulting in a total batch size of 3072 images. The model underwent 350,000 iterations, which took about 7 days. We utilize a DepthAnything-V2-S [90] model to estimate depth map on the fly. To achieve classifier-free guidance during sampling, we randomly drop text condition $y$ and pose condition $\mathcal{R}$ with the probability $10\%$ during training. + +# 4.3. Evaluation Protocols + +3D Reconstruction (Stage-1). To demonstrate the 3D reconstruction generalization of our GS-VAE, we employed Tartanair [78] for our evaluation, which is a diverse synthetic dataset with 18 scenes not included in our training set, + +
MethodSingle-ObjectSingle-Object-with-SurroundingsScene-LevelTime
BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑
GaussianDreamer [93]107.818.790.386110.818.160.389-≈ 15min
MVDream [63]+LGM [71]74.6414.960.37977.5014.030.343-≈ 10s
Director3D [38]49.9113.560.39749.7713.640.40550.8814.970.357≈ 22s
Ours59.4314.230.32958.8814.000.36949.6314.010.370≈ 8s
+ +Table 3. Quantitative comparison for 3D generation. We compare Prometheus with baselines for text-to-3D generation utilizing text prompts from T3Bench. + +![](images/0980da7f515248b6d68d77d8189f106ace893a19b7b4ee1984db2c28de19ae7e.jpg) +Figure 4. Qualitative comparison for Stage2: Object-level 3D generation. Prometheus generates objects that align with the given description, incorporating rich background information and intricate details. + +covering both indoor and outdoor scenarios. Based on the degree of overlap and distance among input views, we categorize them into three distinct modes: Easy, Medium, and Hard, each comprising 4 context views and 3 target views. + +We use the metrics PSNR, SSIM [79] and LPIPS [104] for evaluating the reconstructed images. To better compare the reconstructed geometry, we evaluate the rendered depth maps. Follow [27, 61], we align rendered depth maps with the ground truth with per-scene scale and shift and calculate two widely recognized metrics [55] for evaluation, Absolute Mean Relative Error (AbsRel) and $\delta 1$ accuracy with a specified threshold value of 1.25. + +3D Generation (Stage-2). To assess the text-to-3D generation capabilities of our model, we employ two text prompt sets from T3Bench [22] — Single-Object and Single-Object-with-Surroundings. These sets collectively evaluate the model's proficiency in object-level, and scene-level generation tasks. Additionally, we collected 80 diverse scene-level text prompts covering indoor and outdoor scenarios. + +The quantitative results are evaluated using the CLIP-Score [24], NIQE [50], and BRISQUE [49] metrics. CLIP-Score assesses the alignment between the generated images and the textual prompts, whereas NIQE and BRISQUE indicate the image quality. + +# 4.4. Comparison with Baselines + +3D Reconstruction. We compare the GS-VAE of Prometheus against two sparse-view reconstruction models — namely, pixelSplat [7] and MVSplat [11]. Our quantitative findings are shown in Tab. 2, where we accen + +tuate the best, second-best, and third-best scores across all metrics. Beginning with geometry, Prometheus surpasses the other two baselines, and this advantage becomes more pronounced as the degree of overlap among input views diminishes — see the $\delta 1$ , which exhibits a relative enhancement of $44\%$ on Easy mode and a substantial $64\%$ on Hard mode against pixelSplat. Regarding the reconstructed images, Prometheus delivers comparable outcomes on Easy mode and notably outperforms its counterparts as the mode intensifies, particularly in Hard mode. We also provide qualitative results in Fig. 3. These findings on geometry and image reconstruction suggest that Prometheus is more robust to variations in input view overlap than its baselines, a key factor for the success of our downstream 3D generation task. + +3D Generation. We compare Prometheus with three text-to-3D baseline methods, covering both optimization-based method and feed-forward method. Gaussian-Dreamer [93] is a state-of-the-art SDS-based method for 3DGS. We additionally implement a baseline that applies a multi-view to 3D method, LGM [71] to images generated by MVDream [63]. We also compare to a feed-forward method, Director3D [38] (without refiner). Fig. 4 and Fig. 5 show that our method is capable of generating both, object and scene-level contents, containing background and rich details, outperforms both optimization-based and feedforward baselines. Tab. 3 shows our overall metrics are suboptimal compared with Director3D for object level while leading in other cases. This is attributed to failure cases in the object-centric setting, see supplementary material for + +A bedroom scene displays a bed covered by a quilt and a window located near the end of the bed + +A coastal town with white buildings and green vegetation is seen in the image + +![](images/ebb8d392e38e2369b58b5cd1728d46091d1ff3d909938a3e70f127e28b31361c.jpg) +Figure 5. Qualitative comparison for Stage 2: Scene-level 3D generation with diverse scene-level prompt. Our result better aligns with the text prompt and captures more details. + +
VariantsTartanair (4 views)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
Ours(w/o RGB-D)18.380.4750.3830.7610.324
Ours(w/o single-view)18.630.4800.4240.5420.475
Ours19.490.5320.3410.5260.505
+ +![](images/c32a293d994f2724222e8984add9394434cf3e97fbc0474ec4f9a98587e4811e.jpg) +Figure 6. Qualitative ablation results of GS-VAE for generalizable reconstruction. + +more details. Note that our method takes only 8 seconds for generation, outperforming all baselines. + +# 4.5. Ablations of GS-VAE (Stage 1) + +In Tab. 4, we run ablation studies on the Hard mode of Tartanair, analyzing the following factors of GS-VAE. + +The effectiveness of Depth Prior for GS-VAE. We investigate the impact of RGB-D latent space during our stage 1 training. Our result in Tab. 4 highlights that training without RGB-D latent space — only RGB latent space — yields worse results over our full model on geometry. Additionally, this bad geometry will lead to sub-optimal quality on reconstructed images, see qualitative results in Fig. 6. + +If large scale matters in Generalizable Reconstruction. Next, we ablate the effectiveness of large-scale dataset, denoted as w/o single-view in Tab. 4. The exclusion of the single-view dataset results in diminished performance across both reconstructed images and geometry. This underscores the significant role of large-scale datasets in achieving robust Generalizable Reconstruction. We also visualize the qualitative results in Fig. 6. + +Table 4. Quantitative ablation results of GS-VAE for generalizable reconstruction. + +
VariantsBRISQUE↓NIQE↓CLIP-Score↑
Training strategyw/o single-view data59.4514.570.342
w/o high noise level63.0613.880.343
Inference strategyw/o hybrid sampling66.1913.920.329
w/o CFG-rescale89.7015.150.303
Ours (full)58.8814.000.369
+ +Table 5. Quantitative ablation results of MV-LDM on text-to-3D generation. + +# 4.6. Ablations of MV-LDM (Stage 2) + +In Tab. 5, we conduct ablation studies on the Single-Object-with-Surroundings subset of T3Bench, examining both training and inference strategies of MV-LDM. + +Single-View Dataset. We assess the impact of single-view data. Excluding this training strategy by solely training with multi-view data (w/o single-view data) results in performance degradation. We attribute this to the lack of single-view data, which reduces the model's generalizability, aligning with the observations in MVDream [63]. + +High Noise Level. As mentioned in Zero123++ [46] and Sec. 3.2, it is crucial for the model to learn high-level structures in the low-frequency space. Therefore, we also evaluate the effectiveness of a high noise level by setting $P_{mean} = -0.5$ and $P_{std} = 1.2$ during multi-view training (w/o high-noise level). The results in Tab. 3 show that both visual quality and CLIP score decline in this setting. + +Hybrid Sampling and CFG-Rescale. Finally, we evaluate the design of our inference strategy Sec. 3.2 on hybrid CFG sampling and CFG-rescale by applying CFG solely on the text prompt(w/o hybrid sampling) and set the CFG-rescale factor to 0 (w/o CFG-rescale). Tab. 5 shows that the absence of hybrid sampling and CFG-rescale results in varying degrees of metric decline. + +# 5. Conclusion + +We present Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels in seconds. We demonstrate the effectiveness of our method in feed-forward reconstruction and 3D generation with extensive experiments. We believe our work offers valuable contributions to text-to-3D scene generation, improving generalizability, fidelity, and efficiency. + +Acknowledgements: This work is supported by NSFC under grant 62441223 and 62202418. 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We present Prometheus, a novel method for feed-forward scene-level 3D generation. At its core, our approach harnesses the power of 2D priors to fuel generalizable and efficient 3D synthesis - hence our name, Prometheus." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 152, + 625, + 200, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 625, + 200, + 639 + ], + "spans": [ + { + "bbox": [ + 152, + 625, + 200, + 639 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 662, + 297, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 662, + 297, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 662, + 297, + 687 + ], + "type": "text", + "content": "In this work, we introduce Prometheus, a 3D-aware latent diffusion model for text-to-3D generation at both ob" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 627, + 557, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 627, + 557, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 627, + 557, + 712 + ], + "type": "text", + "content": "ject and scene levels in seconds. We formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within the latent diffusion paradigm. To ensure generalizability, we build our model upon pretrained text-to-image generation model with only minimal adjustments, and further train it using a large number of images from both single-view and multi-view datasets. Fur" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 162, + 704 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 162, + 704 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 162, + 704 + ], + "type": "text", + "content": "* denotes equal contribution." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 704, + 145, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 704, + 145, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 704, + 145, + 713 + ], + "type": "text", + "content": "† corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2857" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "type": "text", + "content": "thermore, we introduce an RGB-D latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feed-forward generation of 3D Gaussians with better fidelity and geometry. Extensive experimental results demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation. Project page: Prometheus." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 178, + 136, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 178, + 136, + 192 + ], + "spans": [ + { + "bbox": [ + 56, + 178, + 136, + 192 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 199, + 295, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 199, + 295, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 199, + 295, + 282 + ], + "type": "text", + "content": "3D assets play a crucial role in a wide range of applications, including AR/VR, gaming, and simulation. Developing 3D generative models capable of efficiently producing versatile 3D content has become a key objective, drawing substantial interest in the field. Despite rapid progress in 2D image and video generation, 3D generative models continue to fall short of the progress seen in 2D generation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 283, + 295, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 545 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 545 + ], + "type": "text", + "content": "One line of existing 3D generative models learn from 3D/multi-view data [8, 89], or single-view images of a single category [5, 59]. This allows them for directly learning 3D representations in a feed-forward manner. Despite achieving excellent multi-view consistency with good geometry, their generalizability is limited due to the scarcity of the training data. Another line of approaches seeks to use models trained on large amounts of 2D data for 3D generation — while the largest multi-view datasets contain around 100K samples, single-view datasets and pretrained models based on them can reach scales of 100M to 2B samples. Most methods in this area obtain 3D representations through optimization. Some approaches use score distillation [40, 54, 70, 80, 93] or incremental inpainting [14, 64, 75, 97]. However, since 2D models lack a complete understanding of 3D, their outputs sometimes face the Janus problem and tend to produce results with low fidelity. Another set of methods fine-tunes 2D models to generate multi-view images, requiring multi-view reconstruction to form the 3D representation [18, 47, 58, 63, 84]. In both cases, the optimization process can be time-consuming, thereby lacking efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "content": "To address the aforementioned issues, we introduce Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels. Our key idea is to exploiting vast amount of 2D data as well as 2D generative models to facilitate feed-forward 3D generation while maintaining generalization ability - taming the fire of 2D priors to streamline 3D generation. Specifically, we formulate 3D scene generation as multi-view, feed-forward, pixel-aligned 3D Gaussian generation within latent diffusion paradigm. To ensure generalizability, we not only build our model upon pre-trained text-to-image generation model (Stable Diffusion) with only minimal adjustments but also train it using both single-view images and multi-view images. Furthermore, we introduce an RGB-D" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "latent space into 3D Gaussian generation to disentangle appearance and geometry information, enabling efficient feedforward generation of 3D Gaussians with better fidelity and geometry." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 121, + 555, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 555, + 384 + ], + "type": "text", + "content": "Following the standard latent diffusion paradigm [57], we separate training into two distinct stages. In the first stage, we train a 3D Gaussian Variational Autoencoder (GS-VAE) that takes multi-view or single-view RGB-D images as input and predicts per-pixel aligned 3D Gaussians. Here, the input depth map during training is estimated using an off-the-shelf monocular depth estimator. Additionally, the encoder of our GS-VAE directly re-uses the Stable Diffusion encoder, predicting latent codes for both RGB images and depth maps. We subsequently train a multi-view GS decoder to generate multi-view 3D Gaussians from the RGB-D latent codes conditioned on camera poses. In the second stage, we train a multi-view LDM that jointly predicts multi-view RGB-D latent codes, conditioned on both camera pose and text prompt. Furthermore, our full model is trained on a combination of 9 multi-view and single-view datasets, aiming for generalizability comparable to Stable Diffusion. We demonstrate the effectiveness of our method in both feed-forward 3D Gaussian reconstruction and text-to-3D generation, showcasing that our model can generate 3D scenes in seconds while generalizing well to a variety of 3D objects and scenes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 395, + 399, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 395, + 399, + 407 + ], + "spans": [ + { + "bbox": [ + 314, + 395, + 399, + 407 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 420, + 555, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 555, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 555, + 576 + ], + "type": "text", + "content": "3D Generative Models: 3D generative models have attracted great attention in recent years. Many approaches learn from single-category images or 3D supervisions [5, 10, 51, 59, 73, 100], utilizing either GANs or diffusion models. However, these studies primarily concentrate on domain-specific, object-centric scenes, such as those involving Carla Cars [16] and human faces [29]. Despite recent progress that has further extended these methods to model scene-level generation [1, 53, 88, 91], these methods are yet confined to a specific domain with limited generalization capability. This is mainly due to the scarcity of 3D supervision. We aim to tackle this problem by combining multi-view supervision with a vast amount of 2D images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "3D Generation with 2D priors: Thanks to the rapid progress in 2D generation models like Stable Diffusion [57] and SoRA [3], there is a large many works have explored the potential of large 2D diffusion models for 3D-aware generation. One line of works fine-tune 2D diffusion models to enable pose controllability for objects [46, 47] or scenes [18, 20, 58, 81], where the output still lies in the 2D image space. Additionally, some works [13, 34, 34, 44, 52, 68, 95, 98, 105] aim to incorporate underlying 3D prior knowledge to assist in synthesis. Since the aforementioned methods generate only 2D images, a separate 3D re" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2858" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": "construction step is still needed, which can add time and introduce errors. In contrast, we explore directly generating 3D representations in a feed-forward manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 109, + 296, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 296, + 253 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 296, + 253 + ], + "type": "text", + "content": "Another line of methods utilize the 2D priors for 3D generation through optimization, e.g., using Score Distillation Sampling (SDS) [54, 54, 70, 74, 80, 93]. In parallel, several works [14, 17, 36, 64, 75, 96, 103] formulate scene synthesis as \"perpetual view generation\" [43], synthesizing the effects of navigating a 3D world by stitching and rendering images based on camera motions. These methods do not require retraining 2D generative models, but they are inefficient due to per-scene optimization. The generated content's quality is limited by the 2D backbone, causing issues like multi-view inconsistency and artifacts in geometry and texture during image inpainting and score distillation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 259, + 296, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 259, + 296, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 259, + 296, + 426 + ], + "type": "text", + "content": "Feed-Forward 3D Gaussian Generation: Unlike view synthesis-based methods that focus on synthesizing multiview images followed by 3D reconstruction, a more intuitive approach is to directly generate 3D representations. Following this idea, many works [6, 26, 76, 89] concentrate on the direct synthesis of 3D representations, such as NeRF [48], which generates meshes from single or few-view image inputs. Recently, numerous works [7, 8, 11, 12, 69, 71, 82, 86, 87, 87, 94, 102] have adopted 3D Gaussian Splatting [32] as the underlying representation. Pixel-Splat [7] is the first feed-forward model that learns to reconstruct 3D Gaussian splats from pairs of images. GS-LRM [102] builds on this idea and utilizing a larger reconstruction model (LRM [26]), achieving improved results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 427, + 296, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 608 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 608 + ], + "type": "text", + "content": "To address this challenge, several works [21, 23, 35, 37, 38, 56, 60, 106] propose Large Diffusion Models as powerful generators for 3D representations. WildFusion [60] introduces a novel approach for achieving 3D-aware image synthesis from in-the-wild datasets using latent diffusion models. Director3D [38], which is closely related to our work, presents a robust open-world text-to-3D generation framework designed to create both real-world 3D scenes and adaptive camera trajectories. Unlike Director3D, which requires supervision in the image space, we follow common practices in 2D image generation and adopt a latent diffusion framework. This approach significantly reduces computational overhead, making larger-scale training feasible, and better leverages the 2D latent space, enhancing the generalizability of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 620, + 111, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 620, + 111, + 633 + ], + "spans": [ + { + "bbox": [ + 55, + 620, + 111, + 633 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "In this section, we provide the technical details of our method. As illustrated in Fig. 2, Prometheus follows the common latent diffusion framework [57], which involves two training stages. In the first stage (Sec. 3.1), our 3D autoencoder, GS-VAE, learns a compressed and abstracted latent space from multi-view images. Subsequently, it de" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "type": "text", + "content": "codes this latent space into pixel-aligned 3DGS representations, serving as scene-level representations. In the second stage (Sec. 3.2), a latent multi-view diffusion model (MV-LDM) is trained on the latent representations derived from the first stage's autoencoder. This process results in a fully generative model. Finally, we elaborate on our sampling strategy (Sec. 3.3) for sampling 3D scenes in seconds while maintaining consistency and visual fidelity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 178, + 419, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 178, + 419, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 419, + 190 + ], + "type": "text", + "content": "3.1. Stage 1: GS-VAE" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 197, + 554, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 554, + 268 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 554, + 268 + ], + "type": "text", + "content": "In Stage 1, our objective is to train a 3D autoencoder capable of compressing data into a latent space and subsequently reconstructing it into a 3D representation. Given multi-view input images with camera poses, our GS-VAE outputs multi-view pixel-aligned 3DGS. These outputs are then merged into a scene-level 3D representation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": "Encoding Multi-View RGB-D Images. We propose to encode both, RGB images and their predicted monocular depth maps, into the latent space, considering that monocular depth maps provide clues for the later 3D Gaussian decoding process and can be easily obtained. Given a set of multi-view images " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I_i\\in \\mathbb{R}^{H\\times W\\times 3}|i = 1,2,\\dots ,N\\}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": " with each image " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": " being an observation of an underlying 3D scene, we first employ an off-the-shelf depth estimator [90] to obtain their corresponding monocular depth maps " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{D_i\\in \\mathbb{R}^{H\\times W\\times 1}|i = 1,2,\\dots ,N\\}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": ". Next, we utilize a pre-trained image encoder " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\phi}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": " to encode both the multi-view images " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": " and their depth maps " + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 269, + 555, + 425 + ], + "type": "text", + "content": " into a latent representation:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 366, + 435, + 553, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 435, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 366, + 435, + 553, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {E} _ {\\phi}: (\\mathcal {I}, \\mathcal {D}) \\mapsto \\mathcal {Z} \\in \\mathbb {R} ^ {N \\times h \\times w \\times c}, \\tag {1}", + "image_path": "cac8565cb1c479928491ceb69f92764a2f92585b6fa98369f6eda2eff5c82e08.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "text", + "content": " is the downsampled resolution. In practice, we use a pre-trained Stable Diffusion (SD) image encoder and freeze it during training. Recent methods, such as Marigold [31], indicate that the SD encoder exhibits robust generalization capabilities with depth maps. Consequently, we opt to employ the same SD encoder to independently encode both images and depths without the need for fine-tuning. Subsequently, we concatenate these encoded representations to obtain the full multi-view latent " + }, + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 313, + 460, + 554, + 592 + ], + "type": "text", + "content": " which can be used for 3D reconstruction. Our diffusion model is additionally trained within this joint RGB-D latent space." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "text", + "content": "Fusing Multi-View Latent Images. Recent advancements [26, 35, 77, 101, 102] underscore the significant potential of transformer-based models in integrating multiview information. Since our latent codes for each view in " + }, + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "text", + "content": " are derived individually, we employ a multi-view transformer to facilitate cross-view information exchange." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "We further inject " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": " camera poses into our multiview transformer. Inspired by recent works [18, 35, 38, 89], we choose Plücker coordinates as camera representation [65], specifically " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = (\\mathbf{d},\\mathbf{p}\\times \\mathbf{d})\\in \\mathbb{R}^6" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2859" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 68, + 386, + 230 + ], + "blocks": [ + { + "bbox": [ + 57, + 68, + 386, + 230 + ], + "lines": [ + { + "bbox": [ + 57, + 68, + 386, + 230 + ], + "spans": [ + { + "bbox": [ + 57, + 68, + 386, + 230 + ], + "type": "image", + "image_path": "3bf7985b354b7a3ce0070def4f49b1279c986fac85404c17dc30f13ee5ad03fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 239, + 555, + 285 + ], + "lines": [ + { + "bbox": [ + 55, + 239, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 555, + 285 + ], + "type": "text", + "content": "Figure 2. Method Overview. Our training process is divided into two stages. In stage 1, our objective is to train a GS-VAE. Utilizing multi-view images along with their corresponding pseudo depth maps and camera poses, our GS-VAE is designed to encode these multi-view RGB-D images, integrate cross-view information, and ultimately decode them into pixel-aligned 3DGS. In stage 2, we focus on training a MV-LDM. We can generate multi-view RGB-D latents by sampling from randomly-sampled noise with trained MV-LDM." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 389, + 68, + 553, + 230 + ], + "blocks": [ + { + "bbox": [ + 389, + 68, + 553, + 230 + ], + "lines": [ + { + "bbox": [ + 389, + 68, + 553, + 230 + ], + "spans": [ + { + "bbox": [ + 389, + 68, + 553, + 230 + ], + "type": "image", + "image_path": "39a6c12b98a75e2fc297c663a32124cef8d7f45ff27a8f2127705fab14ba0b30.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " denotes the normalized ray direction and " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " denotes the camera origin. Thus, initial " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " camera poses can be re-parameterized as multi-view ray maps " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{R_i\\in \\mathbb{R}^{H\\times W\\times 6}|i = 1,2,\\ldots ,N\\}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": ". We combine the multiview latent codes " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " and the camera ray maps " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " via concatenation along the feature channel and feed them into the cross-view transformer to obtain the fused latent codes " + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{Z}}\\in \\mathbb{R}^{h\\times w\\times c}" + }, + { + "bbox": [ + 55, + 305, + 296, + 401 + ], + "type": "text", + "content": " that merges multi-view context:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 409, + 295, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 409, + 295, + 423 + ], + "spans": [ + { + "bbox": [ + 113, + 409, + 295, + 423 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) \\mapsto \\tilde {\\mathcal {Z}} \\in \\mathbb {R} ^ {h \\times w \\times c}. \\tag {2}", + "image_path": "e1901b09c9a7aade169776a9718dc266aa3688d42fce04adcd8c508146bf3c0c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "text", + "content": "Decoding into Gaussian Scenes. Finally, we concatenate the raw image latent codes " + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "text", + "content": ", ray maps " + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "text", + "content": ", and the fused latent codes " + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{Z}}" + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "text", + "content": ", and feed them into the decoder, thereby obtaining the pixel-aligned multi-view 3D Gaussians " + }, + { + "bbox": [ + 55, + 433, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{F} = \\{F_i \\in \\mathbb{R}^{H \\times W \\times C_G} | i = 1, 2, \\ldots, N\\}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 93, + 502, + 295, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 502, + 295, + 517 + ], + "spans": [ + { + "bbox": [ + 93, + 502, + 295, + 517 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) \\mapsto \\mathcal {F} \\in \\mathbb {R} ^ {N \\times H \\times W \\times C _ {G}}, \\tag {3}", + "image_path": "1c1018db93a753f7c9aeb0c92f6b26b2d180894da35173388e94b6de2d031631.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "text", + "content": " is the pixel-aligned 3D Gaussians corresponding to each image. A 3D Gaussian is parameterized by 1-channel depth, 4-channel rotation quaternion, 3-channel scale, 1-channel opacity, and 3-channel spherical harmonics coefficients respectively. Thus " + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "inline_equation", + "content": "C_G = 12" + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "text", + "content": " in our formulation. After aggregating multi-view 3D Gaussians, we can get the final scene-level 3D Gaussians " + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 525, + 296, + 610 + ], + "type": "text", + "content": " as in Eq. (4)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 618, + 295, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 618, + 295, + 632 + ], + "spans": [ + { + "bbox": [ + 124, + 618, + 295, + 632 + ], + "type": "interline_equation", + "content": "\\mathbb {M} (\\mathcal {F}) \\mapsto G \\in \\mathbb {R} ^ {N _ {G} \\times C _ {G}}. \\tag {4}", + "image_path": "7ed98da3da0cfb4cb49cbf98f32026fb6d2434c9b815797b46f40c306dd165bd.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbb{M}(\\cdot)" + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": " denotes the aggregation operation, which is achieved by transforming all 3D Gaussians into a global coordinate system. " + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "inline_equation", + "content": "N_{G}" + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": " represents the number of full Gaussian primitives, which is equivalent to " + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "inline_equation", + "content": "N\\times H\\times W" + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "In practice, this architecture is also applicable to single-view images, where " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " equals to 1. During training, we" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 305, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 305, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 305, + 555, + 376 + ], + "type": "text", + "content": "sample from both single-view and multi-view images. Besides, to maximize the usage of 2D generative priors, we follow Director3D [38] and repurpose a pre-trained Stable Diffusion image decoder with minor modifications as our Gaussian decoder " + }, + { + "bbox": [ + 313, + 305, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\phi}" + }, + { + "bbox": [ + 313, + 305, + 555, + 376 + ], + "type": "text", + "content": ". Specifically, we only adjust the number of channels in the first and last convolutional layers." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "text", + "content": "Loss Function. Given the reconstructed scene-level 3D Gaussians " + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\hat{G}" + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "text", + "content": ", we can render them from arbitrary viewpoints. Let " + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "text", + "content": " denote a given viewpoint, we can render the corresponding RGB image and depth map from " + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\hat{G}" + }, + { + "bbox": [ + 313, + 377, + 555, + 426 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 393, + 429, + 553, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 429, + 553, + 444 + ], + "spans": [ + { + "bbox": [ + 393, + 429, + 553, + 444 + ], + "type": "interline_equation", + "content": "\\mathbb {R} (\\hat {G}, \\mathbf {c}) \\mapsto \\{\\hat {I}, \\hat {D} \\}, \\tag {5}", + "image_path": "899dec3f79bd0ddfc69239383c94f29def7a70e43d71d7515e7674b6f061806a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 449, + 555, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 449, + 555, + 498 + ], + "type": "inline_equation", + "content": "\\mathbb{R}(\\cdot)" + }, + { + "bbox": [ + 313, + 449, + 555, + 498 + ], + "type": "text", + "content": " denotes the differentiable rendering of 3D Gaussian Splatting. We can subsequently apply render loss, which integrates MSE (Mean Squared Error) loss and perceptual [28] loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 359, + 502, + 553, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 502, + 553, + 517 + ], + "spans": [ + { + "bbox": [ + 359, + 502, + 553, + 517 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e n d e r}} = \\mathcal {L} _ {\\text {m s e}} (\\hat {I}, I) + \\mathcal {L} _ {\\text {v g g}} (\\hat {I}, I). \\tag {6}", + "image_path": "9ac2cd028d70beb9bde08d34fb04485aeae4eaeef68233099f1ed21e212762f4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "text", + "content": "In addition to the rendering loss on the RGB domain, we also impose a loss between our rendered expected depth " + }, + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "inline_equation", + "content": "\\hat{D}" + }, + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "text", + "content": " and the monocular depth " + }, + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "inline_equation", + "content": "\\bar{D}" + }, + { + "bbox": [ + 313, + 521, + 554, + 569 + ], + "type": "text", + "content": " which serve as pseudo geometry ground truth as below:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 373, + 574, + 553, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 574, + 553, + 588 + ], + "spans": [ + { + "bbox": [ + 373, + 574, + 553, + 588 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e p t h}} = \\| (w \\hat {D} + q) - \\bar {D} \\| _ {2}, \\tag {7}", + "image_path": "9a4bb1daa798e6cff89fc102484872c56f57a8dcbfe7b394bb468900f5b93432.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{depth}" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " is the scale invariant depth loss following [55]. Here, " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " are the scale and shift used to align " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "\\hat{D}" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "\\bar{D}" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " since " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "\\bar{D}" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " is defined only up to a scale and a shift. We determine " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " using a least-squares criterion [55]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 326, + 642, + 533, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 642, + 533, + 652 + ], + "spans": [ + { + "bbox": [ + 326, + 642, + 533, + 652 + ], + "type": "text", + "content": "Our full loss function of the GS-VAE is as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 659, + 553, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 659, + 553, + 673 + ], + "spans": [ + { + "bbox": [ + 351, + 659, + 553, + 673 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\phi) = \\lambda_ {1} \\mathcal {L} _ {m s e} + \\lambda_ {2} \\mathcal {L} _ {v g g} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {8}", + "image_path": "f4aaf69261c8e7d6ab816ef8c9bc14c42b1e1dffe7a08cf96820bf38989e5eaf.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "text", + "content": " denotes the estimizable parameters in GS-VAE, and " + }, + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3" + }, + { + "bbox": [ + 313, + 677, + 554, + 712 + ], + "type": "text", + "content": " are employed to balance the weight of each loss term." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2860" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 84 + ], + "type": "text", + "content": "3.2. Stage 2: Geometry-Aware Multi-View Denoiser" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 295, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 295, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 295, + 148 + ], + "type": "text", + "content": "After the training of stage 1, we obtain a GS-VAE capable of i) efficiently compressing images into a compact latent space and ii) bridging the gap between 2D and 3D via a 3D Gaussian decoder. This capability enables us to train the multi-view diffusion model (MV-LDM) in the latent space." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "content": "We aim to jointly generate multix-view RGB-D latent codes " + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{Z} \\in \\mathbb{R}^{N \\times h \\times w \\times c}" + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "content": " to provide richer geometric cues for decoding 3DGS. Therefore, we formulate a continuous-time denoising diffusion [30, 66] conditioned on the text prompt " + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "content": " and camera poses " + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "content": ". The diffusion model consists of a stochastic forward pass to inject one noise level noise Gaussian noise into input latent codes and a reverse process to remove noise with a learnable denoiser " + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 55, + 149, + 296, + 243 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "content": "Training. For each training step, we sample one noise level " + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "inline_equation", + "content": "\\log \\sigma_{t} \\sim \\mathcal{N}(P_{mean}, P_{std}^{2})" + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "content": " [30]. Next, we add noise of this level to the clean multi-view latents " + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{0}" + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "content": " to obtain the noisy latents " + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{t}" + }, + { + "bbox": [ + 55, + 245, + 296, + 292 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 112, + 300, + 294, + 313 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 300, + 294, + 313 + ], + "spans": [ + { + "bbox": [ + 112, + 300, + 294, + 313 + ], + "type": "interline_equation", + "content": "\\mathcal {Z} _ {t} = \\mathcal {Z} _ {0} + \\sigma_ {t} ^ {2} \\boldsymbol {\\epsilon}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {9}", + "image_path": "867ec4209db39479d803d070801ce2bb87f51b881efb9fb1ed0554e703960902.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "text", + "content": "In the reverse process, diffusion model denoises " + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_t" + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "text", + "content": " towards predicted clean " + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Z}}_0" + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "text", + "content": " with a learnable multi-view denoiser " + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 55, + 320, + 295, + 354 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 127, + 355, + 294, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 355, + 294, + 369 + ], + "spans": [ + { + "bbox": [ + 127, + 355, + 294, + 369 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {Z}} _ {0} = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right), \\tag {10}", + "image_path": "0e6020cb9c7ae3c876a45171706c722551032442e5307da60d33502cef5dff3d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 55, + 373, + 296, + 410 + ], + "type": "text", + "content": " are the text and camera poses condition respectively. Our MV-LDM is trained in latent space via denoising score matching (DSM) [72]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 415, + 295, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 415, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 93, + 415, + 295, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\theta) = \\mathbb {E} _ {\\mathcal {Z}, \\mathcal {R}, \\mathbf {y}, \\sigma_ {t}} \\left[ \\lambda (\\sigma_ {t}) \\| \\hat {\\mathcal {Z}} _ {0} - \\mathcal {Z} _ {0} \\| _ {2} ^ {2} \\right], \\tag {11}", + "image_path": "31252f18407b5da5f707eb73d6da7a62bb62aa031034fecd950b36e9a615949d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "text", + "content": "with weighting function " + }, + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "inline_equation", + "content": "\\lambda (\\sigma) = (1 + \\sigma^2)\\sigma^{-2}" + }, + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "text", + "content": ". In this work, we follow EDM [30] and parameterize the denoiser " + }, + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 55, + 443, + 295, + 468 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 475, + 294, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 475, + 294, + 502 + ], + "spans": [ + { + "bbox": [ + 61, + 475, + 294, + 502 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\sigma_ {t}, \\mathbf {y}, \\mathcal {R}\\right) = c _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathcal {Z} _ {t} + \\tag {12} \\\\ c _ {\\text {o u t}} (\\sigma_ {t}) F _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma_ {t}) \\mathcal {Z} _ {t}; c _ {\\text {n o i s e}} (\\sigma_ {t}), \\mathbf {y}, \\mathcal {R}\\right), \\\\ \\end{array}", + "image_path": "05c44addd7b677bb036abb67efa419d4fec5841c87d7e54164a71b9525c60263.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": " is a UNet to be trained in our case, and " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{skip}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{out}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{noise}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": " are preconditioning functions. Furthermore, consistent with Stage 1 Eq. (3), we employ ray maps as the pose representation and incorporate them into the network by concatenating them with the noisy latents " + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_t" + }, + { + "bbox": [ + 55, + 510, + 295, + 592 + ], + "type": "text", + "content": " along feature channel. Additionally, the text prompt conditioning is introduced via cross-attention mechanisms." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 594, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 677 + ], + "type": "text", + "content": "Inspired by recent multi-view diffusions [18, 38, 63], we replace the self-attention blocks in the original UNet with 3D cross-view self-attention blocks to capture multi-view correlations. In practice, to leverage the pre-trained text-to-image prior, we initialize the model " + }, + { + "bbox": [ + 55, + 594, + 295, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 55, + 594, + 295, + 677 + ], + "type": "text", + "content": " from a pre-trained text-to-image diffusion model's, specifically the UNet from Stable Diffusion [57]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Sampling. At sampling time, multi-view latents " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_0" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " is restored from a randomly-sampled Gaussian noise " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_T" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " conditioning on text prompt and camera poses by iteratively" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 321, + 71, + 547, + 180 + ], + "blocks": [ + { + "bbox": [ + 321, + 71, + 547, + 180 + ], + "lines": [ + { + "bbox": [ + 321, + 71, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 321, + 71, + 547, + 180 + ], + "type": "table", + "html": "
DatasetScene type# of frames# of Scenes
SAM-1B [33]Single view11M-
MVImgNet [99]Object6.8M230K
DL3DV-10K [42]Indoor / Outdoor2.2M6K
Objaverse [15]Object11.5M784K
ACID [43]Indoor510K11K
RealEstate10K [107]Indoor2.8M57K
KITTI [19]Driving42K0.8K
KITTI-360 [39]Driving69K1.2K
nuScenes [4]Driving340K0.85K
Waymo [67]Driving200K1K
", + "image_path": "ea2d942b8e29d341876d93f0f5b27249796004d32eca937d7ef0afef3d627cca.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 181, + 553, + 214 + ], + "lines": [ + { + "bbox": [ + 313, + 181, + 553, + 214 + ], + "spans": [ + { + "bbox": [ + 313, + 181, + 553, + 214 + ], + "type": "text", + "content": "Table 1. Training datasets We collect a large, multi-domain dataset for training, including single-view and multi-view data, all paired with detailed captions." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 219, + 547, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 547, + 231 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 547, + 231 + ], + "type": "text", + "content": "applying the denoising process with trained MV-LDM " + }, + { + "bbox": [ + 313, + 219, + 547, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 397, + 236, + 553, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 236, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 397, + 236, + 553, + 251 + ], + "type": "interline_equation", + "content": "\\mathcal {Z} _ {T} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma_ {T} ^ {2} \\mathbf {I}) \\tag {13}", + "image_path": "74b0f4b6fa8f6ae8795627288414d1e6f1dba029b3958cf422fbd486d857fbe2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 336, + 272, + 553, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 272, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 336, + 272, + 553, + 312 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {Z} _ {t - 1} = \\frac {\\mathcal {Z} _ {t} - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {T} ; \\sigma_ {t} , \\mathbf {y} , \\mathcal {R}\\right)}{\\sigma_ {t}} \\left(\\sigma_ {t - 1} - \\sigma_ {t}\\right) \\tag {14} \\\\ + \\mathcal {Z} _ {t}, \\quad 0 < t \\leq T \\\\ \\end{array}", + "image_path": "a3dfe9011a64327b049874132267e4d44eb5f6c89b60c57b37fc7a1da8156e52.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\sigma_0,\\dots,\\sigma_T" + }, + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "text", + "content": " are sampled from a fixed variance schedule of a denoising process with " + }, + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 319, + 553, + 342 + ], + "type": "text", + "content": " steps." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": "The Importance of Noise Level. Inspired by insights from recent works [2, 13, 62], we recognize that a lower Signal-to-Noise Ratio (SNR) during the denoising step is crucial for determining the global low-frequency structure of the content. Furthermore, this lower SNR during sampling is essential for achieving multi-view consistency in the multiview diffusion model " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": ". Therefore, we adopt a relatively large noise distribution with " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "P_{mean} = 1.5" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "P_{std} = 2.0" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": " during multi-view training of MV-LDM " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "P_{mean} = -0.5" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "inline_equation", + "content": "P_{std} = 1.2" + }, + { + "bbox": [ + 313, + 342, + 555, + 462 + ], + "type": "text", + "content": " during single-view training." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 468, + 523, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 523, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 523, + 480 + ], + "type": "text", + "content": "3.3. Text to 3D Scene Generation in Sceonds" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "content": "Based on the model above, we can achieve feed-forward text to 3D scene generation by sampling multi-view RGB-D latents " + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "content": " from randomly-sampled Gaussian noise " + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_T" + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "content": " in latent space using MV-LDM " + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "content": ", and subsequently decode into a 3D Gaussian Scene " + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 486, + 554, + 545 + ], + "type": "text", + "content": " using GS-VAE decoder:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 380, + 552, + 553, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 552, + 553, + 596 + ], + "spans": [ + { + "bbox": [ + 380, + 552, + 553, + 596 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l l} \\mathcal {G} _ {\\theta}: (\\mathcal {Z} _ {T}; \\mathbf {y}, \\mathcal {R}) & \\mapsto \\mathcal {Z}, \\\\ \\mathcal {C} _ {\\phi}: (\\mathcal {Z}, \\mathcal {R}) & \\mapsto \\tilde {\\mathcal {Z}}, \\\\ \\mathcal {D} _ {\\phi}: (\\mathcal {Z}, \\tilde {\\mathcal {Z}}, \\mathcal {R}) & \\mapsto G. \\end{array} \\right. \\tag {15}", + "image_path": "536497bdef3261aaaf1185b62f6fbf94416969d4284e7b97902ed0b83bfe662f.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 601, + 554, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 601, + 554, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 601, + 554, + 638 + ], + "type": "text", + "content": "To sample that with high quality and align with the condition, we use classifier-free-guidance (CFG) [25] to guide multi-view generation toward condition signal " + }, + { + "bbox": [ + 313, + 601, + 554, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 601, + 554, + 638 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 329, + 643, + 553, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 643, + 553, + 671 + ], + "spans": [ + { + "bbox": [ + 329, + 643, + 553, + 671 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = w \\cdot \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\tag {16} \\\\ + (w - 1) \\cdot \\mathcal {G} _ {\\theta} (\\mathcal {Z} _ {t}; \\mathcal {R}), \\\\ \\end{array}", + "image_path": "42930b01cafdf91be6a5f84c75c0396791a3cb40c6b8d1fc063415132a9ef904.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "inline_equation", + "content": "w \\geq 0" + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": " represents the guidance strength. However, if we simply apply the naive CFG Eq. (16), as commonly practiced in most text-to-image methods, increasing" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2861" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 542, + 121 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 542, + 121 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 542, + 121 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 542, + 121 + ], + "type": "table", + "html": "
MethodTartanair (Easy)Tartanair (Medium)Tartanair (Hard)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
pixelSplat[7]21.650.6810.2930.6500.37320.300.6280.3370.8060.32319.350.5890.3710.8710.307
MVSplat [11]19.380.5690.3700.8090.28318.500.5310.4090.8720.26517.870.5000.4450.9070.272
Ours20.950.5890.2890.4350.53620.150.5600.3140.4930.51419.490.5320.3410.5260.505
", + "image_path": "4c0f2239c83bf1ff8a393ef1e4d1d3f744c3f9d0e29fa584619c1754c981bdfb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 121, + 550, + 133 + ], + "lines": [ + { + "bbox": [ + 59, + 121, + 550, + 133 + ], + "spans": [ + { + "bbox": [ + 59, + 121, + 550, + 133 + ], + "type": "text", + "content": "Table 2. Quantitative comparison for Stage 1. We compare our GS-VAE with baselines for generalizable reconstruction on Tartanair." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 67, + 134, + 543, + 300 + ], + "blocks": [ + { + "bbox": [ + 67, + 134, + 543, + 300 + ], + "lines": [ + { + "bbox": [ + 67, + 134, + 543, + 300 + ], + "spans": [ + { + "bbox": [ + 67, + 134, + 543, + 300 + ], + "type": "image", + "image_path": "0cb67c6b9f20d0d01452e683003e7eaae8b05e9cc591dc1a62d80e36591bd5b8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 305, + 555, + 340 + ], + "lines": [ + { + "bbox": [ + 54, + 305, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 54, + 305, + 555, + 340 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison for Stage 1. We compare Prometheus against baselines under varying difficulty settings. As overlap gradually decreases, the advantages of our method continue to grow. Moreover, as shown in the depth map, our method exhibits superior geometry quality across all settings." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 351, + 296, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 351, + 296, + 435 + ], + "spans": [ + { + "bbox": [ + 54, + 351, + 296, + 435 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 54, + 351, + 296, + 435 + ], + "type": "text", + "content": " would lead to multi-view inconsistency in the generated results. This naive design described above causes the model to overfit to the text condition while compromising multi-view consistency, in line with the findings in [83, 85]. To balance multi-view consistency and fidelity during sampling, we follow HarmonyView [83] and adapt hybrid sampling guidance, which rewrites Eq. (16) as below:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 70, + 447, + 294, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 447, + 294, + 491 + ], + "spans": [ + { + "bbox": [ + 70, + 447, + 294, + 491 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {G} _ {\\theta} ^ {w} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) = \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) \\\\ + w _ {1} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathcal {R}\\right)\\right) \\\\ + w _ {2} \\cdot \\left(\\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}, \\mathcal {R}\\right) - \\mathcal {G} _ {\\theta} \\left(\\mathcal {Z} _ {t}; \\mathbf {y}\\right)\\right), \\tag {17} \\\\ \\end{array}", + "image_path": "d8d518cf19fd2a3e8b5dfc012297355877919f2123770412ffdfed2be74c8808.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "text", + "content": " denote the weight of text and pose guidance respectively with " + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "inline_equation", + "content": "w = w_{1} + w_{2}" + }, + { + "bbox": [ + 55, + 502, + 296, + 563 + ], + "type": "text", + "content": ", thereby better maintaining fidelity and consistency across generated views. In addition, we also use CFG-rescale as proposed in [41] to avoid over-saturation issues during conditional sampling." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 578, + 132, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 132, + 591 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 132, + 591 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 598, + 161, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 161, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 161, + 611 + ], + "type": "text", + "content": "4.1. Training Datasets" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "text", + "content": "We train our method on large-scale single-view and multiview datasets, see Tab. 1. Regarding the single view dataset, we use a high-quality SAM-1B [33] dataset with detailed captions [45] which was present in PixArt-" + }, + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "text", + "content": " [9]. Our model is trained on a combination of 9 multi-view datasets, including object-centric, indoor, outdoor, and driving scenarios, text prompts for each scene are generated using the multimodal large language model [45]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 350, + 423, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 423, + 363 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 423, + 363 + ], + "type": "text", + "content": "4.2. Implement Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 369, + 555, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 490 + ], + "type": "text", + "content": "During GS-VAE training (Stage 1), we set both the number of input and novel views to " + }, + { + "bbox": [ + 313, + 369, + 555, + 490 + ], + "type": "inline_equation", + "content": "N = 4" + }, + { + "bbox": [ + 313, + 369, + 555, + 490 + ], + "type": "text", + "content": " for each multi-view scene. To improve model generalizability, we also sample 2 single-view images alongside the multi-view ones, applying the loss to the input views only for single-view images. The GS-VAE was trained on 8 A800 GPUs with a batch size of 32. The final model is trained for 200,000 iterations with approximately 4 days. We use gsplat [92] as our 3D Gaussian renderer. We initialize the weights of our cross-view transformer from a pretrained RayDiff [101]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": "For the MV-LDM (Stage 2), we employ Stable Diffusion 2.1 [57] as our base model. During training, we set " + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "inline_equation", + "content": "N = 8" + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": " for each multi-view scene. Similarly to Stage 1, we sample " + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "inline_equation", + "content": "M = 4" + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": " single-view images alongside multi-view ones. For each iteration, we sample a batch size of 8 on each GPU. The final MV-LDM model was trained on 32 A800 GPUs, resulting in a total batch size of 3072 images. The model underwent 350,000 iterations, which took about 7 days. We utilize a DepthAnything-V2-S [90] model to estimate depth map on the fly. To achieve classifier-free guidance during sampling, we randomly drop text condition " + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": " and pose condition " + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": " with the probability " + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 491, + 556, + 634 + ], + "type": "text", + "content": " during training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 647, + 434, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 434, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 434, + 658 + ], + "type": "text", + "content": "4.3. Evaluation Protocols" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "3D Reconstruction (Stage-1). To demonstrate the 3D reconstruction generalization of our GS-VAE, we employed Tartanair [78] for our evaluation, which is a diverse synthetic dataset with 18 scenes not included in our training set," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2862" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 68, + 70, + 547, + 131 + ], + "blocks": [ + { + "bbox": [ + 68, + 70, + 547, + 131 + ], + "lines": [ + { + "bbox": [ + 68, + 70, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 68, + 70, + 547, + 131 + ], + "type": "table", + "html": "
MethodSingle-ObjectSingle-Object-with-SurroundingsScene-LevelTime
BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑BRISQUE↓NIQE↓CLIP-Score↑
GaussianDreamer [93]107.818.790.386110.818.160.389-≈ 15min
MVDream [63]+LGM [71]74.6414.960.37977.5014.030.343-≈ 10s
Director3D [38]49.9113.560.39749.7713.640.40550.8814.970.357≈ 22s
Ours59.4314.230.32958.8814.000.36949.6314.010.370≈ 8s
", + "image_path": "c21cbdb7e5efcd896fa33b108b5dd8e5da975f99288906730bc3d1f3cfb0725f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 133, + 555, + 153 + ], + "lines": [ + { + "bbox": [ + 55, + 133, + 555, + 153 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 555, + 153 + ], + "type": "text", + "content": "Table 3. Quantitative comparison for 3D generation. We compare Prometheus with baselines for text-to-3D generation utilizing text prompts from T3Bench." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 67, + 156, + 545, + 305 + ], + "blocks": [ + { + "bbox": [ + 67, + 156, + 545, + 305 + ], + "lines": [ + { + "bbox": [ + 67, + 156, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 67, + 156, + 545, + 305 + ], + "type": "image", + "image_path": "0980da7f515248b6d68d77d8189f106ace893a19b7b4ee1984db2c28de19ae7e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 309, + 555, + 333 + ], + "lines": [ + { + "bbox": [ + 54, + 309, + 555, + 333 + ], + "spans": [ + { + "bbox": [ + 54, + 309, + 555, + 333 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison for Stage2: Object-level 3D generation. Prometheus generates objects that align with the given description, incorporating rich background information and intricate details." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 344, + 295, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 344, + 295, + 392 + ], + "spans": [ + { + "bbox": [ + 54, + 344, + 295, + 392 + ], + "type": "text", + "content": "covering both indoor and outdoor scenarios. Based on the degree of overlap and distance among input views, we categorize them into three distinct modes: Easy, Medium, and Hard, each comprising 4 context views and 3 target views." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 393, + 295, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 393, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 54, + 393, + 295, + 489 + ], + "type": "text", + "content": "We use the metrics PSNR, SSIM [79] and LPIPS [104] for evaluating the reconstructed images. To better compare the reconstructed geometry, we evaluate the rendered depth maps. Follow [27, 61], we align rendered depth maps with the ground truth with per-scene scale and shift and calculate two widely recognized metrics [55] for evaluation, Absolute Mean Relative Error (AbsRel) and " + }, + { + "bbox": [ + 54, + 393, + 295, + 489 + ], + "type": "inline_equation", + "content": "\\delta 1" + }, + { + "bbox": [ + 54, + 393, + 295, + 489 + ], + "type": "text", + "content": " accuracy with a specified threshold value of 1.25." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 491, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 491, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 54, + 491, + 295, + 574 + ], + "type": "text", + "content": "3D Generation (Stage-2). To assess the text-to-3D generation capabilities of our model, we employ two text prompt sets from T3Bench [22] — Single-Object and Single-Object-with-Surroundings. These sets collectively evaluate the model's proficiency in object-level, and scene-level generation tasks. Additionally, we collected 80 diverse scene-level text prompts covering indoor and outdoor scenarios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 575, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 575, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 54, + 575, + 295, + 635 + ], + "type": "text", + "content": "The quantitative results are evaluated using the CLIP-Score [24], NIQE [50], and BRISQUE [49] metrics. CLIP-Score assesses the alignment between the generated images and the textual prompts, whereas NIQE and BRISQUE indicate the image quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 647, + 206, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 206, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 206, + 659 + ], + "type": "text", + "content": "4.4. Comparison with Baselines" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 665, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 665, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 665, + 297, + 715 + ], + "type": "text", + "content": "3D Reconstruction. We compare the GS-VAE of Prometheus against two sparse-view reconstruction models — namely, pixelSplat [7] and MVSplat [11]. Our quantitative findings are shown in Tab. 2, where we accen" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "text", + "content": "tuate the best, second-best, and third-best scores across all metrics. Beginning with geometry, Prometheus surpasses the other two baselines, and this advantage becomes more pronounced as the degree of overlap among input views diminishes — see the " + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "inline_equation", + "content": "\\delta 1" + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "text", + "content": ", which exhibits a relative enhancement of " + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "inline_equation", + "content": "44\\%" + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "text", + "content": " on Easy mode and a substantial " + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "inline_equation", + "content": "64\\%" + }, + { + "bbox": [ + 313, + 344, + 555, + 524 + ], + "type": "text", + "content": " on Hard mode against pixelSplat. Regarding the reconstructed images, Prometheus delivers comparable outcomes on Easy mode and notably outperforms its counterparts as the mode intensifies, particularly in Hard mode. We also provide qualitative results in Fig. 3. These findings on geometry and image reconstruction suggest that Prometheus is more robust to variations in input view overlap than its baselines, a key factor for the success of our downstream 3D generation task." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "content": "3D Generation. We compare Prometheus with three text-to-3D baseline methods, covering both optimization-based method and feed-forward method. Gaussian-Dreamer [93] is a state-of-the-art SDS-based method for 3DGS. We additionally implement a baseline that applies a multi-view to 3D method, LGM [71] to images generated by MVDream [63]. We also compare to a feed-forward method, Director3D [38] (without refiner). Fig. 4 and Fig. 5 show that our method is capable of generating both, object and scene-level contents, containing background and rich details, outperforms both optimization-based and feedforward baselines. Tab. 3 shows our overall metrics are suboptimal compared with Director3D for object level while leading in other cases. This is attributed to failure cases in the object-centric setting, see supplementary material for" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2863" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 80, + 173, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 80, + 173, + 106 + ], + "spans": [ + { + "bbox": [ + 69, + 80, + 173, + 106 + ], + "type": "text", + "content": "A bedroom scene displays a bed covered by a quilt and a window located near the end of the bed" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 127, + 170, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 127, + 170, + 152 + ], + "spans": [ + { + "bbox": [ + 71, + 127, + 170, + 152 + ], + "type": "text", + "content": "A coastal town with white buildings and green vegetation is seen in the image" + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 181, + 70, + 541, + 173 + ], + "blocks": [ + { + "bbox": [ + 181, + 70, + 541, + 173 + ], + "lines": [ + { + "bbox": [ + 181, + 70, + 541, + 173 + ], + "spans": [ + { + "bbox": [ + 181, + 70, + 541, + 173 + ], + "type": "image", + "image_path": "ebb8d392e38e2369b58b5cd1728d46091d1ff3d909938a3e70f127e28b31361c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 174, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 174, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 553, + 196 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison for Stage 2: Scene-level 3D generation with diverse scene-level prompt. Our result better aligns with the text prompt and captures more details." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 58, + 200, + 293, + 256 + ], + "blocks": [ + { + "bbox": [ + 58, + 200, + 293, + 256 + ], + "lines": [ + { + "bbox": [ + 58, + 200, + 293, + 256 + ], + "spans": [ + { + "bbox": [ + 58, + 200, + 293, + 256 + ], + "type": "table", + "html": "
VariantsTartanair (4 views)
PSNR↑SSIM↑LPIPS↓AbsRel↓δ1↑
Ours(w/o RGB-D)18.380.4750.3830.7610.324
Ours(w/o single-view)18.630.4800.4240.5420.475
Ours19.490.5320.3410.5260.505
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VariantsBRISQUE↓NIQE↓CLIP-Score↑
Training strategyw/o single-view data59.4514.570.342
w/o high noise level63.0613.880.343
Inference strategyw/o hybrid sampling66.1913.920.329
w/o CFG-rescale89.7015.150.303
Ours (full)58.8814.000.369
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Ablations of MV-LDM (Stage 2)" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 318, + 554, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 318, + 554, + 353 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 554, + 353 + ], + "type": "text", + "content": "In Tab. 5, we conduct ablation studies on the Single-Object-with-Surroundings subset of T3Bench, examining both training and inference strategies of MV-LDM." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 354, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 426 + ], + "type": "text", + "content": "Single-View Dataset. We assess the impact of single-view data. Excluding this training strategy by solely training with multi-view data (w/o single-view data) results in performance degradation. We attribute this to the lack of single-view data, which reduces the model's generalizability, aligning with the observations in MVDream [63]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "text", + "content": "High Noise Level. As mentioned in Zero123++ [46] and Sec. 3.2, it is crucial for the model to learn high-level structures in the low-frequency space. Therefore, we also evaluate the effectiveness of a high noise level by setting " + }, + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "inline_equation", + "content": "P_{mean} = -0.5" + }, + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "inline_equation", + "content": "P_{std} = 1.2" + }, + { + "bbox": [ + 313, + 427, + 555, + 511 + ], + "type": "text", + "content": " during multi-view training (w/o high-noise level). The results in Tab. 3 show that both visual quality and CLIP score decline in this setting." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 511, + 554, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 554, + 595 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 554, + 595 + ], + "type": "text", + "content": "Hybrid Sampling and CFG-Rescale. Finally, we evaluate the design of our inference strategy Sec. 3.2 on hybrid CFG sampling and CFG-rescale by applying CFG solely on the text prompt(w/o hybrid sampling) and set the CFG-rescale factor to 0 (w/o CFG-rescale). Tab. 5 shows that the absence of hybrid sampling and CFG-rescale results in varying degrees of metric decline." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 609, + 388, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 609, + 388, + 621 + ], + "spans": [ + { + "bbox": [ + 313, + 609, + 388, + 621 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": "We present Prometheus, a 3D-aware latent diffusion model tailored for text-to-3D generation at both object and scene levels in seconds. We demonstrate the effectiveness of our method in feed-forward reconstruction and 3D generation with extensive experiments. We believe our work offers valuable contributions to text-to-3D scene generation, improving generalizability, fidelity, and efficiency." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2864" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "content": "Acknowledgements: This work is supported by NSFC under grant 62441223 and 62202418. This work was supported by Ant Group Research Fund." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 121, + 115, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 121, + 115, + 133 + ], + "spans": [ + { + "bbox": [ + 56, + 121, + 115, + 133 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 140, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 66, + 140, + 296, + 185 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 140, + 296, + 185 + ], + "spans": [ + { + "bbox": [ + 66, + 140, + 296, + 185 + ], + "type": "text", + "content": "[1] Sherwin Bahmani, Jeong Joon Park, Despoina Paschalidou, Xingguang Yan, Gordon Wetzstein, Leonidas J. Guibas, and Andrea Tagliasacchi. 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Campolongo1, Daniel Rubenstein4, Charles V. Stewart5, Anuj Karpatne3, Tanya Berger-Wolf1, Yu Su1, Wei-Lun Chao1", + "bbox": [ + 135, + 202, + 859, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1The Ohio State University, 2University of Tsukuba, 3Virginia Tech, 4Princeton University, 5Rensselaer Polytechnic Institute", + "bbox": [ + 140, + 266, + 857, + 303 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c68c428d5d8d835e28d968e957616918fb9933eaf4492010577e7bfdbe52e8a1.jpg", + "image_caption": [ + "Figure 1. Illustration of PROMPT-CAM. By learning class-specific prompts for a pre-trained Vision Transformer (ViT), PROMPT-CAM enables multiple functionalities. (a) PROMPT-CAM achieves fine-grained image classification using the output logits from the class-specific prompts. (b) PROMPT-CAM enables trait localization by visualizing the multi-head attention maps queried by the true-class prompt. (c) PROMPT-CAM identifies common traits shared between species by visualizing the attention maps queried by another-class prompt. (d) PROMPT-CAM can identify the most discriminative traits per species (e.g., distinctive yellow chest and black neck for \"Scott Oriole\") by systematically masking out the least important attention heads. See subsection 2.3 for details." + ], + "image_footnote": [], + "bbox": [ + 91, + 338, + 903, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 628, + 326, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a simple approach to make pre-trained Vision Transformers (ViTs) interpretable for fine-grained analysis, aiming to identify and localize the traits that distinguish visually similar categories, such as bird species. Pre-trained ViTs, such as DINO, have demonstrated remarkable capabilities in extracting localized, discriminative features. However, saliency maps like Grad-CAM often fail to identify these traits, producing blurred, coarse heatmaps that highlight entire objects instead. We propose a novel approach, Prompt Class Attention Map (PROMPT-CAM), to address this limitation. PROMPT-CAM learns class-specific prompts for a pre-trained ViT and uses the corresponding outputs for classification. To correctly classify an image, the true-class prompt must attend to unique image patches not present in other classes' images (i.e., traits). As", + "bbox": [ + 88, + 674, + 486, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a result, the true class's multi-head attention maps reveal traits and their locations. Implementation-wise, PROMPT-CAM is almost a \"free lunch,\" requiring only a modification to the prediction head of Visual Prompt Tuning (VPT). This makes PROMPT-CAM easy to train and apply, in stark contrast to other interpretable methods that require designing specific models and training processes. Extensive empirical studies on a dozen datasets from various domains (e.g., birds, fishes, insects, fungi, flowers, food, and cars) validate the superior interpretation capability of PROMPT-CAM. The source code and demo are available at https://github.com/Imageomics/Prompt_CAM.", + "bbox": [ + 511, + 630, + 908, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 843, + 645, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision Transformers (ViT) [9] pre-trained on huge datasets have greatly improved vision recognition, even for fine", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4375", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "grained objects [10, 40, 48, 54]. DINO [4] and DINOv2 [29] further showed remarkable abilities to extract features that are localized and informative, precisely representing the corresponding coordinates in the input image. These advancements open up the possibility of using pre-trained ViTs to discover \"traits\" that highlight each category's identity and distinguish it from other visually close ones.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One popular approach to this is saliency maps, for example, Class Activation Map (CAM) [13, 25, 37, 52]. After extracting the feature maps from an image, CAM highlights the spatial grids whose feature vectors align with the target class's fully connected weight. While easy to implement and efficient, the reported CAM saliency on ViTs is often far from expectation. It frequently locates the whole object with a blurred, coarse heatmap, instead of focusing on subtle traits that tell visually similar objects (e.g., birds) apart. One may argue that CAM was not originally developed for ViTs, but even with dedicated variants like attention rollout [1, 5, 14], the issue is only mildly attenuated.", + "bbox": [ + 89, + 198, + 480, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "What if we look at the attention maps? ViTs rely on self-attention to relate image patches; the [CLS] token aggregates image features by attending to informative patches. As shown in [7, 27, 39], the attention maps of the [CLS] token do highlight local regions inside the object. However, these regions are not \"class-specific.\" Instead, they often focus on the same object regions across different categories, such as body parts like heads, wings, and tails of bird species. While these are where traits usually reside, they are not traits. For example, the distinction between \"Red-winged Blackbird\" and other bird species is the red spot on the wing, having little to do with other body parts.", + "bbox": [ + 89, + 378, + 480, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "How can we leverage pre-trained ViTs, particularly their localized and informative patch features, to identify traits that are so special for each category?", + "text_level": 1, + "bbox": [ + 96, + 571, + 478, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our proposal is to prompt ViTs with learnable \"class-specific\" tokens, one for each class, inspired by [17, 20, 31, 50]. These \"class-specific\" tokens, once inputted into ViTs, attend to image patches via self-attention, similar to the [CLS] token. However, unlike the [CLS] token, which is \"class-agnostic,\" these \"class-specific\" tokens can attend to the same image differently, with the potential to highlight regions specific to the corresponding classes, i.e., traits.", + "bbox": [ + 89, + 628, + 480, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We implement our approach, named Prompt Class Attention Map (PROMPT-CAM), as follows. Given a pretrained ViT and a fine-grained classification dataset with $C$ classes, we add $C$ learnable tokens as additional inputs alongside the input image. To make these tokens \"class-specific,\" we collect their corresponding output vectors after the final Transformer layer and perform inner products with a shared vector (also learnable) to obtain $C$ \"class-specific\" scores, following [31]. One may interpret each class-specific score as how clearly the corresponding class's", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "traits are visible in the input image. Intuitively, the input image's ground-truth class should possess the highest score, and we encourage this by minimizing a cross-entropy loss, treating the scores as logits. We keep the whole pre-trained ViT frozen and only optimize the $C$ tokens and the shared scoring vector. See section 2 for details and variants.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For interpretation during inference, we input the image and the $C$ tokens simultaneously to the ViT to obtain the $C$ scores. One can then select a specific class (e.g., the highest-score class) and visualize its multi-head attention maps over the image patches. See Figure 1 for an illustration and section 2 for how to rank these maps to highlight the most discriminative traits. When the highest-score class is the ground-truth class, the attention maps reveal its traits. Otherwise, comparing the attention maps of the highest-score class with those of the ground-truth class helps explain why the image is misclassified. Possible reasons include the object being partially occluded or in an unusual pose, making its traits invisible, or the appearance being too similar to a wrong class, possibly due to lighting conditions (Figure 5).", + "bbox": [ + 511, + 185, + 903, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "PROMPT-CAM is fairly easy to implement and train. It requires no change to pre-trained ViTs and no specially designed loss function or training strategy—just the standard cross-entropy loss and SGD. Indeed, building upon Visual Prompt Tuning (VPT) [12], one merely needs to adjust a few lines of code and can enjoy fine-grained interpretation. This simplicity sharply contrasts other interpretable methods like ProtoPNet [6] and ProtoTree [26]. Compared to INterpretable TRansformer (INTR) [31], which also featured simplicity, PROMPT-CAM has three notable advantages. First, PROMPT-CAM is encoder-only and can potentially utilize any ViT encoder. In contrast, INTR is built upon an encoder-decoder model pre-trained on object detection datasets. As a result, PROMPT-CAM can more easily leverage up-to-date pre-trained models. Second, PROMPT-CAM can be trained much faster—only the prompts and the shared vector need to be learned. In contrast, INTR typically requires full fine-tuning. Third, PROMPT-CAM produces cleaner and sharper attention maps than INTR, which we attribute to the use of state-of-the-art ViTs like DINO [4] or DINOv2 [29]. Taken together, we view PROMPT-CAM as a simpler yet more powerful interpretable Transformer.", + "bbox": [ + 511, + 398, + 903, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We validate PROMPT-CAM on over a dozen datasets: CUB-200-2011 [45], Birds-525 [33], Oxford Pet [30], Stanford Dogs [15], Stanford Cars [16], iNaturalist-2021-Moths [43], Fish Vista [24], Rare Species [41], Insects-2 [49], iNaturalist-2021-Fungi [43], Oxford Flowers [28], Medicinal Leaf [36], Stanford Cars [16], and Food 101 [2]. PROMPT-CAM can identify different traits of a category through multi-head attention and consistently localize them in images. To our knowledge, PROMPT-CAM is the only explainable or interpretable method for vision that has been evaluated on such a broad range of domains. We further", + "bbox": [ + 511, + 734, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4376", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/87245fe056e18b62979132a84efea39d703a805f89ff5a55722d3889d0798548.jpg", + "image_caption": [ + "(a) VPT" + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 282, + 195 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b50a3236717178e5f04ec850e74aa8bc1508831d6303129af91b6c6c2b621d6f.jpg", + "image_caption": [ + "(b) PROMPT-CAM", + "Figure 2. PROMPT-CAM vs. Visual Prompt Tuning (VPT). (a) VPT [12] adds the prediction head on top of the [CLS] token's output, a default design to use ViTs for classification. (b) PROMPT-CAM adds the prediction head on top of the injected prompts' outputs, making them class-specific to identify and localize traits." + ], + "image_footnote": [], + "bbox": [ + 297, + 88, + 473, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "show PROMPT-CAM's extendability by applying it to discovering taxonomy keys. Our contributions are two-fold.", + "bbox": [ + 89, + 311, + 482, + 340 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present PROMPT-CAM, an easily implementable, trainable, and reproducible interpretable method that leverages the representations of pre-trained ViTs to identify and localize traits for fine-grained analysis.", + "- We conduct extensive experiments on more than a dozen datasets to validate PROMPT-CAM's interpretation quality, wide applicability, and extendability." + ], + "bbox": [ + 89, + 347, + 482, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Comparison to closely related work. Besides INTR [31], our class-specific attentions are inspired by two other works in different contexts, MCTformer for weakly supervised semantic segmentation [50] and Query2Label for multi-label classification [20]. Both of them learned class-specific tokens but aimed to localize visually distinct common objects (e.g., people, horses, and flights). In contrast, we focus on fine-grained analysis: supervised by class labels of visually similar objects (e.g., bird species), we aim to localize their traits (e.g., red spots on wings). One particular feature of PROMPT-CAM is its simplicity, in both implementation and compatibility with pre-trained backbones, without extra modules, loss terms, and changes to the backbones, making it an almost plug-and-pay approach to interpretation.", + "bbox": [ + 89, + 462, + 482, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to space constraints, we provide a detailed related work section in the Supplementary Material (Suppl.).", + "bbox": [ + 89, + 676, + 482, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Approach", + "text_level": 1, + "bbox": [ + 89, + 734, + 199, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose Prompt Class Attention Map (PROMPT-CAM) to leverage pre-trained Vision Transformers (ViTs) [9] for fine-grained analysis. The goal is to identify and localize traits that highlight an object category's identity. PROMPT-CAM adds learnable class-specific tokens to prompt ViTs, producing class-specific attention maps that reveal traits. The overall framework is presented in Figure 3. We deliberately follow the notation and naming of Visual Prompt Tuning (VPT) [12] for ease of reference.", + "bbox": [ + 89, + 763, + 485, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Preliminaries", + "text_level": 1, + "bbox": [ + 513, + 90, + 653, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A ViT typically contains $N$ Transformer layers [44]. Each consists of a Multi-head Self-Attention (MSA) block, a Multi-Layer Perceptron (MLP) block, and several other operations like layer normalization and residual connections.", + "bbox": [ + 511, + 112, + 905, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The input image $\\pmb{I}$ to ViTs is first divided into $M$ fixed-sized patches. Each is then projected into a $D$ -dimensional feature space with positional encoding, denoted by $e_0^j$ , with $1 \\leq j \\leq M$ . We use $E_0 = [e_0^1, \\dots, e_0^M] \\in \\mathbb{R}^{D \\times M}$ to denote their column-wise concatenation.", + "bbox": [ + 511, + 172, + 905, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Together with a learnable [CLS] token $\\pmb{x}_0 \\in \\mathbb{R}^D$ , the whole ViT is formulated as:", + "bbox": [ + 511, + 247, + 905, + 277 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ \\pmb {E} _ {i}, \\pmb {x} _ {i} ] = L _ {i} ([ \\pmb {E} _ {i - 1}, \\pmb {x} _ {i - 1} ]), \\quad i = 1, \\dots , N,\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 289, + 864, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L_{i}$ denotes the $i$ -th Transformer layer. The final $\\mathbf{x}_N$ is typically used to represent the whole image and fed into a prediction head for classification.", + "bbox": [ + 511, + 316, + 905, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Prompt Class Attention Map (PROMPT-CAM)", + "text_level": 1, + "bbox": [ + 511, + 371, + 890, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a pre-trained ViT and a downstream classification dataset with $C$ classes, we introduce a set of $C$ learnable $D$ -dimensional vectors to prompt the ViT. These vectors are learned to be \"class-specific\" by minimizing the cross-entropy loss, during which the ViT backbone is frozen. In the following, we first introduce the baseline version.", + "bbox": [ + 511, + 393, + 905, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PROMPT-CAM-SHALLOW. The $C$ class-specific prompts are injected into the first Transformer layer $L_{1}$ . We denote each prompt by $\\pmb{p}^{c} \\in \\mathbb{R}^{D}$ , where $1 \\leq c \\leq C$ , and use $\\pmb{P} = [\\pmb{p}^{1}, \\dots, \\pmb{p}^{C}] \\in \\mathbb{R}^{D \\times C}$ to indicate their column-wise concatenation. The prompted ViT is:", + "bbox": [ + 511, + 487, + 905, + 564 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} [ \\boldsymbol {Z} _ {1}, \\boldsymbol {E} _ {1}, \\boldsymbol {x} _ {1} ] = L _ {1} ([ \\boldsymbol {P}, \\boldsymbol {E} _ {0}, \\boldsymbol {x} _ {0} ]) \\\\ [ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {Z} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 2, \\dots , N, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 573, + 898, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $Z_{i}$ represents the features corresponding to $P$ , computed by the $i$ -th Transformer layer $L_{i}$ . The order among $x_{0}, E_{0}$ , and $P$ does not matter since the positional encoding of patch locations has already been inserted into $E_{0}$ .", + "bbox": [ + 511, + 619, + 905, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make $\\pmb{P} = [\\pmb{p}^{1},\\dots ,\\pmb{p}^{C}]$ class-specific, we employ a cross-entropy loss on top of the corresponding ViT's output, i.e., $Z_{N} = [z_{N}^{1},\\dots ,z_{N}^{C}]$ . Given a labeled training example $(\\pmb {I},y\\in \\{1,\\dots ,C\\})$ , we calculate the logit of each class by:", + "bbox": [ + 511, + 680, + 905, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns [ c ] = \\boldsymbol {w} ^ {\\top} \\boldsymbol {z} _ {N} ^ {c}, \\quad 1 \\leq c \\leq C, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 765, + 903, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\boldsymbol{w} \\in \\mathbb{R}^{D}$ is a learnable vector. $\\pmb{P}$ can then be updated by minimizing the loss:", + "bbox": [ + 511, + 794, + 905, + 825 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n- \\log \\left(\\frac {\\exp (s [ y ])}{\\sum_ {c} \\exp (s [ c ])}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 835, + 903, + 876 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PROMPT-CAM-DEEP. While straightforward, PROMPT", + "bbox": [ + 511, + 885, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4377", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/541dd0ed751b12e4958f3bfd538e0a0903b6d619209337852b520b5ad329d72a.jpg", + "image_caption": [ + "Figure 3. Overview of Prompt Class Attention Map (PROMPT-CAM). We explore two variants, given a pre-trained ViT with $N$ layers and a downstream task with $C$ classes: (a) PROMPT-CAM-DEEP: insert $C$ learnable \"class-specific\" tokens to the last layer's input and $C$ learnable \"class-agnostic\" tokens to each of the other $N - 1$ layers' input; (b) PROMPT-CAM-SHALLOW: insert $C$ learnable \"class-specific\" tokens to the first layer's input. During training, only the prompts and the prediction head are updated; the whole ViT is frozen." + ], + "image_footnote": [], + "bbox": [ + 125, + 104, + 867, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CAM-SHALLOW has two potential drawbacks. First, the class-specific prompts attend to every layer's patch features, i.e., $E_{i}$ , $i = 0, \\dots, N - 1$ . However, features of the early layers are often not informative enough but noisy for differentiating classes. Second, the prompts $p^{1}, \\dots, p^{C}$ have a \"double duty.\" Individually, each needs to highlight class-specific traits. Collectively, they need to adapt pre-trained ViTs to downstream tasks, which is the original purpose of VPT [12]. In our case, the downstream task is a new usage of ViTs on a specific fine-grained dataset.", + "bbox": [ + 88, + 397, + 483, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these issues, we resort to the VPT-Deep's design while deliberately decoupling injected prompts' roles. VPT-Deep adds learnable prompts to every layer's input. Denote by $\\pmb{P}_{i - 1} = [\\pmb{p}_{i - 1}^{1},\\dots ,\\pmb{p}_{i - 1}^{C}]$ the prompts to the $i$ -th Transformer layer, the deep-prompted ViT is formulated as:", + "bbox": [ + 89, + 549, + 483, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n[ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {P} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 1, \\dots , N, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 648, + 482, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is worth noting that the features $Z_{i}$ after the $i$ -th layer are not inputted to the next layer, and are typically disregarded.", + "bbox": [ + 89, + 688, + 482, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In PROMPT-CAM-DEEP, we repurpose $Z_{N}$ for classification, following Equation 1. As such, after minimizing the cross entropy loss in Equation 2, the corresponding prompts $P_{N - 1} = [\\pmb{p}_{N - 1}^{1},\\dots ,\\pmb{p}_{N - 1}^{C}]$ will be class-specific. Prompts to the other layers' inputs, i.e., $P_{i} = [p_{i}^{1},\\dots ,p_{i}^{C}]$ for $i = 0,\\dots ,N - 2$ , remain class-agnostic, because $p_i^c$ does not particularly serve for the $c$ -th class, unlike $p_{N - 1}^{c}$ . In other words, PROMPT-CAM-DEEP learns both class-specific prompts for trait localization and class-agnostic prompts for adaptation. The class-specific prompts $P_{N - 1}$ only attend to the patch features $E_{N - 1}$ inputted to the last Transformer layer $L_{N}$ , further addressing the other issue in", + "bbox": [ + 89, + 719, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "PROMPT-CAM-SHALLOW.", + "bbox": [ + 513, + 398, + 702, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the following, we focus on PROMPT-CAM-DEEP.", + "bbox": [ + 531, + 412, + 880, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.3. Trait Identification and Localization", + "text_level": 1, + "bbox": [ + 511, + 440, + 828, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During inference, given an image $\\pmb{I}$ , PROMPT-CAM-DEEP extracts patch embeddings $\\pmb{E}_0 = [e_0^1,\\dots ,e_0^M ]$ and follows Equation 3 to obtain $Z_{N}$ and Equation 1 to obtain $s[c]$ for $c\\in \\{1,\\dots ,C\\}$ . The predicted label $\\hat{y}$ is:", + "bbox": [ + 511, + 463, + 906, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\arg \\max _ {c \\in \\{1, \\dots , C \\}} s [ c ]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 537, + 906, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "What are the traits of class $c$ ? To answer this question, one could collect images whose true and predicted classes are both class $c$ (i.e., correctly classified) and visualize the multi-head attention maps queried by $\\pmb{p}_{N-1}^c$ in layer $L_N$ .", + "bbox": [ + 511, + 571, + 905, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, in layer $L_{N}$ with $R$ attention heads, the patch features $\\pmb{E}_{N - 1} \\in \\mathbb{R}^{D \\times M}$ are projected into $R$ key matrices, denoted by $\\pmb{K}_{N - 1}^{r} \\in \\mathbb{R}^{D' \\times M}$ , $r = 1, \\dots, R$ . The $j$ -th column corresponds to the $j$ -th patch in $\\pmb{I}$ . Meanwhile, the prompt $\\pmb{p}_{N - 1}^{c}$ is projected into $R$ query vectors $\\pmb{q}_{N - 1}^{c,r} \\in \\mathbb{R}^{D'}$ , $r = 1, \\dots, R$ . Queried by $\\pmb{p}_{N - 1}^{c}$ , the $r$ -th head's attention map $\\alpha_{N - 1}^{c,r} \\in \\mathbb{R}^{M}$ is computed by:", + "bbox": [ + 511, + 633, + 905, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\alpha} _ {N - 1} ^ {c, r} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {K} _ {N - 1} ^ {r} \\mathbin {\\text {T}} \\boldsymbol {q} _ {N - 1} ^ {c , r}}{D ^ {\\prime}}\\right) \\in \\mathbb {R} ^ {M}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 757, + 906, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conceptually, from the $r$ -th head's perspective, the weight $\\alpha_{N - 1}^{c,r}[j]$ indicates how important the $j$ -th patch is for classifying class $c$ , hence localizing traits in the image. Ideally, each head should attend to different (sets of) patches to look for multiple traits that together highlight class $c$ 's identity. By visualizing each attention map $\\alpha_{N - 1}^{c,r}$ , $r = 1,\\dots ,R$", + "bbox": [ + 511, + 810, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4378", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "instead of pooling them averagely, PROMPT-CAM can potentially identify up to $R$ different traits for class $c$ .", + "bbox": [ + 89, + 90, + 482, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Which traits are more discriminative? For categories that are so distinctive, like \"Red-winged Blackbird,\" a few traits are sufficient to distinguish them from others. To automatically identify these most discriminative traits, we take a greedy approach, progressively blurring the least important attention maps until the image is misclassified. The remaining ones highlight traits that are sufficient for classification.", + "bbox": [ + 89, + 125, + 483, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Suppose class $c$ is the true class and the image is correctly classified. In each greedy step, for each of the unblurred heads indexed by $r'$ , we iteratively replace $\\alpha_{N-1}^{c,r'}$ with $\\frac{1}{M}\\mathbf{1}$ and recalculate $s[c]$ in Equation 1, where $\\mathbf{1} \\in \\mathbb{R}^M$ is an all-one vector. Doing so essentially blurs the $r'$ -th head for class $c$ , preventing it from focusing. The head with the highest blurred $s[c]$ is thus the least important, as blurring it degrades classification the least. See Suppl. for details.", + "bbox": [ + 89, + 231, + 483, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Why is an image wrongly classified? When $\\hat{y} \\neq y$ for a labeled image $(I, y)$ , one could visualize both $\\{\\alpha_{N-1}^{y,r}\\}_{r=1}^{R}$ and $\\{\\alpha_{N-1}^{\\hat{y},r}\\}_{r=1}^{R}$ to understand why the classifier made such a prediction. For example, some traits of class $y$ may be invisible or unclear in $I$ ; the object in $I$ may possess class $\\hat{y}$ 's visual traits, for example, due to light conditions.", + "bbox": [ + 89, + 359, + 483, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.4. Variants and Extensions", + "text_level": 1, + "bbox": [ + 89, + 462, + 313, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Other PROMPT-CAM designs. Besides injecting class-specific prompts to the first layer (i.e., PROMPT-CAM-SHALLOW) or the last (i.e., PROMPT-CAM-DEEP), we also explore their interpolation. We introduce class-specific prompts like PROMPT-CAM-SHALLOW to the $i$ -th layer and class-agnostic prompts like PROMPT-CAM-DEEP to the first $i - 1$ layers. See the Suppl. for a comparison.", + "bbox": [ + 89, + 488, + 483, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PROMPT-CAM for discovering taxonomy keys. So far, we have focused on a \"flat\" comparison over all the categories. In domains like biology that are full of fine-grained categories, researchers often have built hierarchical decision trees to ease manual categorization, such as taxonomy. The role of each intermediate \"tree node\" is to dichotomize a subset of categories into multiple groups, each possessing certain group-level characteristics (i.e., taxonomy keys).", + "bbox": [ + 89, + 598, + 483, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The simplicity of PROMPT-CAM allows us to efficiently train multiple sets of prompts, one for each intermediate tree node, potentially (re-)discovering the taxonomy keys. One just needs to relabel categories of the same group by a single label, before training. In expectation, along the path from the root to a leaf node, each of the intermediate tree nodes should look at different group-level traits on the same image of that leaf node. See Figure 9 for a preliminary result.", + "bbox": [ + 89, + 719, + 483, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.5. What is PROMPT-CAM suited for?", + "text_level": 1, + "bbox": [ + 89, + 848, + 380, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As our paper is titled, PROMPT-CAM is dedicated to fine-grained analysis, aiming to identify and, more importantly,", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "localize traits useful for differentiating categories. This, however, does not mean that PROMPT-CAM would excel in fine-grained classification accuracy. Modern neural networks easily have millions if not billions of parameters. How a model predicts is thus still an unanswered question, at least, not fully. It is known if a model is trained mainly to chase accuracies with no constraints, it will inevitably discover \"shortcuts\" in the collected data that are useful for classification but not analysis [8, 11]. We thus argue:", + "bbox": [ + 511, + 90, + 905, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To make a model suitable for fine-grained analysis, one must constrain its capacity, while knowing that doing so would unavoidably hurt its classification accuracy.", + "text_level": 1, + "bbox": [ + 522, + 236, + 895, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PROMPT-CAM is designed with this mindset. Unlike conventional classifiers that employ a fully connected layer on top, PROMPT-CAM follows [31] and learns a shared vector $\\boldsymbol{w}$ in Equation 1. The goal of $\\boldsymbol{w}$ is NOT to capture class-specific information BUT to answer a \"binary\" question: Based on where a class-specific prompt attends, does the class recognize itself in the input image?", + "bbox": [ + 511, + 289, + 905, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To elucidate the difference, let us consider a simplified single-head-attention Transformer layer with no layer normalization, residual connection, MLP block, and other nonlinear operations. Let $V = \\{\\pmb{v}^1,\\dots ,\\pmb{v}^M\\} \\in \\mathbb{R}^{D\\times M}$ be the $M$ input patches' value features, $\\alpha^c\\in \\mathbb{R}^M$ be the attention weights of class $c$ , and $\\alpha^{\\star}\\in \\mathbb{R}^{M}$ be the attention weights of the [CLS] token. Conventional models predict classes by:", + "bbox": [ + 511, + 396, + 906, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} _ {c} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\left(\\boldsymbol {w} _ {c} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 523, + 905, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\boldsymbol{w}_c$ stores the fully connected weights for class $c$ . We argue that this formulation allows for a potential \"detour,\" enabling the model to correctly classify an image $I$ of class $y$ even without meaningful attention weights. In essence, the model can choose to produce holistically discriminative value features from $I$ without preserving spatial resolution, such that $v^j$ aligns with $\\boldsymbol{w}_y$ but $v^j = v^{j'}$ , $\\forall j \\neq j'$ . In this case, regardless of the specific values of $\\alpha^\\star$ , as long as they sum to one—as is default in the softmax formulation—the prediction remains unaffected.", + "bbox": [ + 511, + 601, + 905, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In contrast, PROMPT-CAM predicts classes by:", + "bbox": [ + 532, + 753, + 846, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {c} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {c} [ j ] \\times \\left(\\boldsymbol {w} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 776, + 905, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{w}$ is the shared binary classifier. (For brevity, we assume no self-attention among the prompts.) While the difference between Equation 7 and Equation 6 is subtle at", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4379", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "first glance, it fundamentally changes the model's behavior. In essence, it becomes less effective to store class discriminative information in the channels of $\\pmb{v}^j$ , because there is no $\\pmb{w}_c$ to align with. Moreover, the model can no longer produce holistic features with no spatial resolution; otherwise, it cannot distinguish among classes since all of their scores $s[c]$ will be exactly the same, no matter what $\\alpha^c$ is.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In response, the model must be equipped with two capabilities to minimize the cross-entropy error:", + "bbox": [ + 89, + 200, + 482, + 233 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Generate localized features $\\mathbf{v}^j$ that highlight discriminative patches (e.g., the red spot on the wing) of an image.", + "- Generate distinctive attention weights $\\alpha^c$ across classes, each focusing on traits frequently seen in class $c$ ." + ], + "bbox": [ + 89, + 239, + 482, + 299 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These properties are what fine-grained analysis needs.", + "bbox": [ + 89, + 306, + 447, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In sum, PROMPT-CAM discourages patch features from encoding class-discriminative holistic information (e.g., the whole object shapes or mysterious long-distance pixel correlations), even if such information can be \"beneficial\" to a conventional classifier. To this end, PROMPT-CAM needs to distill localized, trait-specific information from the pretrained ViT's patch features, which is achieved through the injected class-agnostic prompts in PROMPT-CAM-DEEP.", + "bbox": [ + 89, + 328, + 483, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3. Experiments", + "text_level": 1, + "bbox": [ + 89, + 477, + 223, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 507, + 281, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We comprehensively evaluate the performance of PROMPT-CAM on 13 diverse fine-grained image classification datasets across three domains: (1) animal-based: CUB-200-2011 (CUB) [45], Birds-525 (Bird) [33], Stanford Dogs (Dog) [15], Oxford Pet (Pet) [30], iNaturalist-2021-Moths (Moth) [43], Fish Vista (Fish) [24], Rare Species (RareS.) [41] and Insects-2 (Insects) [49]; (2) plant and fungi-based: iNaturalist-2021-Fungi (Fungi) [43], Oxford Flowers (Flower) [28] and Medicinal Leaf (MedLeaf) [36]; (3) object-based: Stanford Cars (Car) [16] and Food 101 (Food) [2]. We provide details about data processing and statistics in Suppl.", + "bbox": [ + 89, + 534, + 483, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model. We consider three pre-trained ViT backbones, DINO [4], DINOv2 [29], and BioCLIP [38] across different scales including ViT-B (the main one we use) and ViTS. The backbones are kept completely frozen when applying PROMPT-CAM. We mainly used DINO, unless stated otherwise. More details can be found in Suppl.", + "bbox": [ + 89, + 724, + 482, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline Methods. We compared PROMPT-CAM with explainable methods like Grad-CAM [37], Layer-CAM [13] and Eigen-CAM [25] as well as with interpretable methods like ProtoPFormer [51], TesNet [47], ProtoConcepts [21] and INTR [31]. More details are in Suppl.", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/41dcffcc56468aaa61d2007340f8b80a6c31229c057f8122139583eafb243a20.jpg", + "table_caption": [ + "Table 1. Faithfulness evaluation based on insertion and deletion scores. A higher insertion score and a lower deletion score indicate better results. The results are obtained from the validation images of CUB using the DINO backbone." + ], + "table_footnote": [], + "table_body": "
MethodInsertion↑Deletion↓
Grad-CAM [37]0.520.17
Layer-CAM[13]0.540.13
Eigen-CAM [25]0.560.22
Attention roll-out [14]0.550.27
PROMPT-CAM0.610.09
", + "bbox": [ + 566, + 148, + 854, + 238 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5101e4ff432ab8a389284c47c23f840b2ee30cd0ce0992aedbd794a7f88f7dfc.jpg", + "table_caption": [ + "Table 2. Accuracy (%) comparison using the DINO backbone." + ], + "table_footnote": [], + "table_body": "
BirdCUBDogPet
Linear Probing99.278.682.492.4
PROMPT-CAM98.873.281.191.3
", + "bbox": [ + 570, + 263, + 849, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.2. Experiment Results", + "text_level": 1, + "bbox": [ + 513, + 330, + 700, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Is PROMPT-CAM faithful? We first investigate whether PROMPT-CAM highlights the image regions that the corresponding classifier focuses on when making predictions. We use PROMPT-CAM to rank pixels based on the aggregated attention maps over the top heads. We then employ the insertion and deletion metrics [32], manipulating highly ranked pixels to measure confidence increase and drop.", + "bbox": [ + 511, + 358, + 903, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For comparison, we consider post-hoc explainable methods like Grad-CAM [37], Eigen-CAM [25], Layer-CAM [13], and attention roll-out [14], based on the same ViT backbone with Linear Probing. As summarized in Table 1, PROMPT-CAM yields higher insertion scores and lower deletion scores, indicating a stronger focus on discriminative image traits and highlighting PROMPT-CAM's enhanced interpretability over standard post-hoc algorithms.", + "bbox": [ + 511, + 465, + 905, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PROMPT-CAM excels in trait identification (human assessment). We then conduct a quantitative human study to evaluate trait identification quality for PROMPT-CAM, TesNet [47], and ProtoConcepts [21]. Participants with no prior knowledge about the algorithms were instructed to compare the expert-identified traits (in text, such as orange belly) and the top heatmaps generated by each method. If an expert-identified trait is seen in the heatmaps, it is considered identified by the algorithm. On average, participants recognized $60.49\\%$ of traits for PROMPT-CAM, significantly outperforming TesNet and ProtoConcepts whose recognition rates are $39.14\\%$ and $30.39\\%$ , respectively. The results highlight PROMPT-CAM's superiority in emphasizing and conveying relevant traits effectively. More details are in Suppl.", + "bbox": [ + 511, + 592, + 905, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classification accuracy comparison. We observe that PROMPT-CAM shows a slight accuracy drop compared to Linear Probing (see Table 2). However, the images misclassified by PROMPT-CAM but correctly classified by Linear Probing align with our design philosophy: PROMPT-CAM classifies images based on the presence of class-specific, lo", + "bbox": [ + 511, + 809, + 905, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4380", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b164b82b6fff0e27a3bed5ae19facd5ce1f47cfed2a62059d3232c4dd26e890f.jpg", + "image_caption": [ + "Figure 4. Visualization of PROMPT-CAM on different datasets. We show the top four attention maps (from left to right) per correctly classified test example triggered by the ground-truth classes." + ], + "image_footnote": [], + "bbox": [ + 133, + 90, + 869, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e40450824f803a72e1bba42c8365db1b958698d2e4aaada45c4b6aeedfae0897.jpg", + "image_caption": [ + "Figure 5. Images misclassified by PROMPT-CAM but correctly classified by Linear Probing. Species-specific traits—such as the red breast of \"Red-breasted Grosbeak\"—are barely visible in misclassified images while Linear Probing uses global features such as body shapes, poses, and backgrounds for correct predictions." + ], + "image_footnote": [], + "bbox": [ + 112, + 428, + 460, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "calized traits and would fail if they are invisible. As shown in Figure 5, discriminative traits—such as the red breast of the Red-breasted Grosbeak—are barely visible in images misclassified by PROMPT-CAM due to occlusion, unusual poses, or lighting conditions. Linear Probing correctly classifies them by leveraging global information such as body shapes and backgrounds. Please see more analysis in Suppl.", + "bbox": [ + 89, + 618, + 483, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to interpretable models. We conduct a qualitative analysis to compare PROMPT-CAM with other interpretable methods—ProtoPFormer, INTR, TesNet, and ProtoConcepts. Figure 6 shows the top-ranked attention maps or prototypes generated by each method. PROMPT-CAM can capture a more extensive range of distinct, fine-grained traits, in contrast to other methods that often focus on a narrower or repetitive set of attributes (for example, ProtoConcepts in the first three ranks of the fifth row). This highlights PROMPT-CAM's ability to identify and localize different traits that collectively define a category's identity.", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dd20db4fc1d4f17480a0371b5ac88d4b7a8ba71d5399d63d16042496a82c652e.jpg", + "image_caption": [ + "Figure 6. Comparison of interpretable models. Visual demonstration (heatmaps and bounding boxes) of the four most activated responses of attention heads (PROMPT-CAM and INTR) or prototypes of each method on a \"Lazuli Bunting\" example image." + ], + "image_footnote": [], + "bbox": [ + 517, + 428, + 906, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.3. Further Analysis and Discussion", + "text_level": 1, + "bbox": [ + 511, + 717, + 799, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PROMPT-CAM on different backbones. Figure 7 illustrates that PROMPT-CAM is compatible with different ViT backbones. We show the top three attention maps generated by PROMPT-CAM using different ViT backbones on an image of Scott Oriole, highlighting consistent identification of traits for species recognition, irrespective of the backbones. Please see the caption and Suppl. for details.", + "bbox": [ + 511, + 744, + 906, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PROMPT-CAM on different datasets. Figure 4 presents the top four attention maps generated by PROMPT-CAM across various datasets spanning diverse domains, includ", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4381", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0906c7178dba438a5dc859c08fcb5a90a122cfa9fdfcd4282bd4f95f5b708ae5.jpg", + "image_caption": [ + "Figure 7. PROMPT-CAM on different backbones. Here we show the top attention maps for PROMPT-CAM on (a) DINO, (b) DINOv2, and (c) BioCLIP backbone. All three sets of attention heads point to consistent key traits of the species \"Scott Oriole\"—yellow belly, black head, and black chest." + ], + "image_footnote": [], + "bbox": [ + 169, + 87, + 406, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a29c3242880362df17324e7e575acc58a6b0a3063d5dc5e62d7bad9e0f60d532.jpg", + "image_caption": [ + "Figure 8. Trait manipulation. The top row shows attention maps for a correctly classified \"Red-winged Blackbird\" image. In the second row, the red spot on the bird's wings was removed, and PROMPT-CAM subsequently classified it as a \"Boat-tailed Grackle,\" as depicted in the reference column." + ], + "image_footnote": [], + "bbox": [ + 94, + 287, + 480, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing animals, plants, and objects. PROMPT-CAM effectively captures the most important traits in each case to accurately identify species, demonstrating its remarkable generalizability and wide applicability.", + "bbox": [ + 89, + 500, + 483, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PROMPT-CAM can detect biologically meaningful traits. As shown in Figure 4, PROMPT-CAM consistently identifies traits from images of the same species (e.g., the red breast and white belly for Rose-breasted Grosbeak). This is further demonstrated in Figure 1 (d), where we progressively mask attention heads (detailed in subsection 2.3) until the model can no longer generate high-confidence predictions for correctly classifying images of Scott Oriole. The remaining heads 1 and 11 highlight the essential traits, i.e., the black head and yellow belly. PROMPT-CAM also enables identifying common traits between species. This is achieved by visualizing the image of one class (e.g., Scott Oriole) using other classes' prompts (e.g., Brewer Blackbird or Baltimore Oriole). As shown in Figure 1 (c), Brewer Blackbird shares the head and neck color with Scott Oriole. These results demonstrate PROMPT-CAM ability to recognize species in a biologically meaningful way.", + "bbox": [ + 89, + 564, + 483, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PROMPT-CAM can identify and interpret trait manipulation. We conduct a counterfactual-style analysis to investigate whether PROMPT-CAM truly relies on the identified traits for making predictions. For instance, to correctly classify the Red-winged Blackbird, it highlights the red-wing", + "bbox": [ + 89, + 825, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/09e3cb314af842ade141bb347fe8f0a42ef6581a27f8f67c84335d70c80930e1.jpg", + "image_caption": [ + "Figure 9. PROMPT-CAM can detect taxonomically meaningful traits. Give an image of the species \"Amophiprion Clarkii,\" PROMPT-CAM highlights the pelvic fin and double stripe to distinguish it from \"Amophiprion Melanopus\" at the species level. When it goes to the genus level, PROMPT-CAM looks at the pattern in the body and tail to classify the image as the \"Amophiprion\" genus. As we go up, fishes at the family level become visually dissimilar. PROMPT-CAM only needs to look at the tail and pelvic fin to classify the image as the \"Pomacentridae\" family." + ], + "image_footnote": [], + "bbox": [ + 521, + 93, + 874, + 296 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "patch (the first row of Figure 8), consistent with the field guide provided by the Cornell Lab of Ornithology. When we remove this red spot from the image to resemble a Boat-tailed Grackle, the model no longer highlights the original position of the red patch. As such, it does not predict the image as a Red-winged Blackbird but a Boat-tailed Grackle (the second row of Figure 8). This shows PROMPT-CAM's sensitivity to trait differences, showcasing its interpretability in fine-grained recognition.", + "bbox": [ + 511, + 443, + 906, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PROMPT-CAM can detect taxonomically meaningful traits. We train PROMPT-CAM based on a hierarchical framework, considering four levels of taxonomic hierarchy: Order $\\rightarrow$ Family $\\rightarrow$ Genus $\\rightarrow$ Species of Fish Dataset. In this setup, PROMPT-CAM progressively shifts its focus from coarse-grained traits at the Family level to fine-grained traits at the Species level to distinguish categories (shown in Figure 9). This progression suggests PROMPT-CAM's potential to automatically identify and localize taxonomy keys to aid in biological and ecological research domains. We provide more details in Suppl.", + "bbox": [ + 511, + 584, + 908, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 763, + 633, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present Prompt Class Attention Map (PROMPT-CAM), a simple yet effective interpretable approach that leverages pre-trained ViTs to identify and localize discriminative traits for fine-grained classification. PROMPT-CAM is easy to implement and train. Extensive empirical studies highlight both the strong performance of PROMPT-CAM and the promise of repurposing standard models for interpretability.", + "bbox": [ + 511, + 787, + 906, + 893 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4382", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 91, + 90, + 240, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research is supported in part by grants from the National Science Foundation (OAC-2118240, HDR Institute:Imageomics). The authors are grateful for the generous support of the computational resources from the Ohio Supercomputer Center.", + "bbox": [ + 89, + 114, + 483, + 191 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 207, + 187, + 223 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samira Abnar and Willem Zuidema. Quantifying attention flow in transformers. arXiv preprint arXiv:2005.00928, 2020. 2", + "[2] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer vision-ECCV 2014: 13th European conference, zurich, Switzerland, September 6-12, 2014, proceedings, part VI 13, pages 446-461. Springer, 2014. 2, 6", + "[3] Tom B. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4692–4702, 2022. 2" + ], + "bbox": [ + 91, + 92, + 485, + 570 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4385", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Prompt-CAM_ Making Vision Transformers Interpretable for Fine-Grained Analysis/88b2374b-97f1-4093-aedd-5058cdff0e06_model.json b/2025/Prompt-CAM_ Making Vision Transformers Interpretable for Fine-Grained Analysis/88b2374b-97f1-4093-aedd-5058cdff0e06_model.json new file mode 100644 index 0000000000000000000000000000000000000000..513db5984e54b4df1a2b2a3ba12e5809c9248d6a --- /dev/null +++ b/2025/Prompt-CAM_ Making Vision Transformers Interpretable for Fine-Grained Analysis/88b2374b-97f1-4093-aedd-5058cdff0e06_model.json @@ -0,0 +1,2268 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.197, + 0.131, + 0.803, + 0.176 + ], + "angle": 0, + "content": "PROMPT-CAM: Making Vision Transformers Interpretable for Fine-Grained Analysis" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.203, + 0.861, + 0.258 + ], + "angle": 0, + "content": "Arpita Chowdhury1, Dipanjyoti Paul2, Zheda Mai1, Jianyang Gu1, Ziheng Zhang1, Kazi Sajeed Mehrab3, Elizabeth G. Campolongo1, Daniel Rubenstein4, Charles V. Stewart5, Anuj Karpatne3, Tanya Berger-Wolf1, Yu Su1, Wei-Lun Chao1" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.267, + 0.858, + 0.304 + ], + "angle": 0, + "content": "1The Ohio State University, 2University of Tsukuba, 3Virginia Tech, 4Princeton University, 5Rensselaer Polytechnic Institute" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.339, + 0.905, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.533, + 0.908, + 0.618 + ], + "angle": 0, + "content": "Figure 1. Illustration of PROMPT-CAM. By learning class-specific prompts for a pre-trained Vision Transformer (ViT), PROMPT-CAM enables multiple functionalities. (a) PROMPT-CAM achieves fine-grained image classification using the output logits from the class-specific prompts. (b) PROMPT-CAM enables trait localization by visualizing the multi-head attention maps queried by the true-class prompt. (c) PROMPT-CAM identifies common traits shared between species by visualizing the attention maps queried by another-class prompt. (d) PROMPT-CAM can identify the most discriminative traits per species (e.g., distinctive yellow chest and black neck for \"Scott Oriole\") by systematically masking out the least important attention heads. See subsection 2.3 for details." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.629, + 0.328, + 0.645 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.675, + 0.487, + 0.902 + ], + "angle": 0, + "content": "We present a simple approach to make pre-trained Vision Transformers (ViTs) interpretable for fine-grained analysis, aiming to identify and localize the traits that distinguish visually similar categories, such as bird species. Pre-trained ViTs, such as DINO, have demonstrated remarkable capabilities in extracting localized, discriminative features. However, saliency maps like Grad-CAM often fail to identify these traits, producing blurred, coarse heatmaps that highlight entire objects instead. We propose a novel approach, Prompt Class Attention Map (PROMPT-CAM), to address this limitation. PROMPT-CAM learns class-specific prompts for a pre-trained ViT and uses the corresponding outputs for classification. To correctly classify an image, the true-class prompt must attend to unique image patches not present in other classes' images (i.e., traits). As" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.631, + 0.909, + 0.813 + ], + "angle": 0, + "content": "a result, the true class's multi-head attention maps reveal traits and their locations. Implementation-wise, PROMPT-CAM is almost a \"free lunch,\" requiring only a modification to the prediction head of Visual Prompt Tuning (VPT). This makes PROMPT-CAM easy to train and apply, in stark contrast to other interpretable methods that require designing specific models and training processes. Extensive empirical studies on a dozen datasets from various domains (e.g., birds, fishes, insects, fungi, flowers, food, and cars) validate the superior interpretation capability of PROMPT-CAM. The source code and demo are available at https://github.com/Imageomics/Prompt_CAM." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.844, + 0.646, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Vision Transformers (ViT) [9] pre-trained on huge datasets have greatly improved vision recognition, even for fine" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4375" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "grained objects [10, 40, 48, 54]. DINO [4] and DINOv2 [29] further showed remarkable abilities to extract features that are localized and informative, precisely representing the corresponding coordinates in the input image. These advancements open up the possibility of using pre-trained ViTs to discover \"traits\" that highlight each category's identity and distinguish it from other visually close ones." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.199, + 0.482, + 0.379 + ], + "angle": 0, + "content": "One popular approach to this is saliency maps, for example, Class Activation Map (CAM) [13, 25, 37, 52]. After extracting the feature maps from an image, CAM highlights the spatial grids whose feature vectors align with the target class's fully connected weight. While easy to implement and efficient, the reported CAM saliency on ViTs is often far from expectation. It frequently locates the whole object with a blurred, coarse heatmap, instead of focusing on subtle traits that tell visually similar objects (e.g., birds) apart. One may argue that CAM was not originally developed for ViTs, but even with dedicated variants like attention rollout [1, 5, 14], the issue is only mildly attenuated." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.38, + 0.482, + 0.561 + ], + "angle": 0, + "content": "What if we look at the attention maps? ViTs rely on self-attention to relate image patches; the [CLS] token aggregates image features by attending to informative patches. As shown in [7, 27, 39], the attention maps of the [CLS] token do highlight local regions inside the object. However, these regions are not \"class-specific.\" Instead, they often focus on the same object regions across different categories, such as body parts like heads, wings, and tails of bird species. While these are where traits usually reside, they are not traits. For example, the distinction between \"Red-winged Blackbird\" and other bird species is the red spot on the wing, having little to do with other body parts." + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.573, + 0.48, + 0.618 + ], + "angle": 0, + "content": "How can we leverage pre-trained ViTs, particularly their localized and informative patch features, to identify traits that are so special for each category?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.482, + 0.75 + ], + "angle": 0, + "content": "Our proposal is to prompt ViTs with learnable \"class-specific\" tokens, one for each class, inspired by [17, 20, 31, 50]. These \"class-specific\" tokens, once inputted into ViTs, attend to image patches via self-attention, similar to the [CLS] token. However, unlike the [CLS] token, which is \"class-agnostic,\" these \"class-specific\" tokens can attend to the same image differently, with the potential to highlight regions specific to the corresponding classes, i.e., traits." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.751, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We implement our approach, named Prompt Class Attention Map (PROMPT-CAM), as follows. Given a pretrained ViT and a fine-grained classification dataset with \\( C \\) classes, we add \\( C \\) learnable tokens as additional inputs alongside the input image. To make these tokens \"class-specific,\" we collect their corresponding output vectors after the final Transformer layer and perform inner products with a shared vector (also learnable) to obtain \\( C \\) \"class-specific\" scores, following [31]. One may interpret each class-specific score as how clearly the corresponding class's" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "traits are visible in the input image. Intuitively, the input image's ground-truth class should possess the highest score, and we encourage this by minimizing a cross-entropy loss, treating the scores as logits. We keep the whole pre-trained ViT frozen and only optimize the \\(C\\) tokens and the shared scoring vector. See section 2 for details and variants." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.186, + 0.905, + 0.397 + ], + "angle": 0, + "content": "For interpretation during inference, we input the image and the \\(C\\) tokens simultaneously to the ViT to obtain the \\(C\\) scores. One can then select a specific class (e.g., the highest-score class) and visualize its multi-head attention maps over the image patches. See Figure 1 for an illustration and section 2 for how to rank these maps to highlight the most discriminative traits. When the highest-score class is the ground-truth class, the attention maps reveal its traits. Otherwise, comparing the attention maps of the highest-score class with those of the ground-truth class helps explain why the image is misclassified. Possible reasons include the object being partially occluded or in an unusual pose, making its traits invisible, or the appearance being too similar to a wrong class, possibly due to lighting conditions (Figure 5)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.4, + 0.905, + 0.732 + ], + "angle": 0, + "content": "PROMPT-CAM is fairly easy to implement and train. It requires no change to pre-trained ViTs and no specially designed loss function or training strategy—just the standard cross-entropy loss and SGD. Indeed, building upon Visual Prompt Tuning (VPT) [12], one merely needs to adjust a few lines of code and can enjoy fine-grained interpretation. This simplicity sharply contrasts other interpretable methods like ProtoPNet [6] and ProtoTree [26]. Compared to INterpretable TRansformer (INTR) [31], which also featured simplicity, PROMPT-CAM has three notable advantages. First, PROMPT-CAM is encoder-only and can potentially utilize any ViT encoder. In contrast, INTR is built upon an encoder-decoder model pre-trained on object detection datasets. As a result, PROMPT-CAM can more easily leverage up-to-date pre-trained models. Second, PROMPT-CAM can be trained much faster—only the prompts and the shared vector need to be learned. In contrast, INTR typically requires full fine-tuning. Third, PROMPT-CAM produces cleaner and sharper attention maps than INTR, which we attribute to the use of state-of-the-art ViTs like DINO [4] or DINOv2 [29]. Taken together, we view PROMPT-CAM as a simpler yet more powerful interpretable Transformer." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.905, + 0.901 + ], + "angle": 0, + "content": "We validate PROMPT-CAM on over a dozen datasets: CUB-200-2011 [45], Birds-525 [33], Oxford Pet [30], Stanford Dogs [15], Stanford Cars [16], iNaturalist-2021-Moths [43], Fish Vista [24], Rare Species [41], Insects-2 [49], iNaturalist-2021-Fungi [43], Oxford Flowers [28], Medicinal Leaf [36], Stanford Cars [16], and Food 101 [2]. PROMPT-CAM can identify different traits of a category through multi-head attention and consistently localize them in images. To our knowledge, PROMPT-CAM is the only explainable or interpretable method for vision that has been evaluated on such a broad range of domains. We further" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4376" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.283, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.202, + 0.214, + 0.214 + ], + "angle": 0, + "content": "(a) VPT" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.089, + 0.475, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.343, + 0.201, + 0.43, + 0.213 + ], + "angle": 0, + "content": "(b) PROMPT-CAM" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.219, + 0.483, + 0.29 + ], + "angle": 0, + "content": "Figure 2. PROMPT-CAM vs. Visual Prompt Tuning (VPT). (a) VPT [12] adds the prediction head on top of the [CLS] token's output, a default design to use ViTs for classification. (b) PROMPT-CAM adds the prediction head on top of the injected prompts' outputs, making them class-specific to identify and localize traits." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.312, + 0.483, + 0.342 + ], + "angle": 0, + "content": "show PROMPT-CAM's extendability by applying it to discovering taxonomy keys. Our contributions are two-fold." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.348, + 0.483, + 0.408 + ], + "angle": 0, + "content": "- We present PROMPT-CAM, an easily implementable, trainable, and reproducible interpretable method that leverages the representations of pre-trained ViTs to identify and localize traits for fine-grained analysis." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.408, + 0.483, + 0.455 + ], + "angle": 0, + "content": "- We conduct extensive experiments on more than a dozen datasets to validate PROMPT-CAM's interpretation quality, wide applicability, and extendability." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.348, + 0.483, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.675 + ], + "angle": 0, + "content": "Comparison to closely related work. Besides INTR [31], our class-specific attentions are inspired by two other works in different contexts, MCTformer for weakly supervised semantic segmentation [50] and Query2Label for multi-label classification [20]. Both of them learned class-specific tokens but aimed to localize visually distinct common objects (e.g., people, horses, and flights). In contrast, we focus on fine-grained analysis: supervised by class labels of visually similar objects (e.g., bird species), we aim to localize their traits (e.g., red spots on wings). One particular feature of PROMPT-CAM is its simplicity, in both implementation and compatibility with pre-trained backbones, without extra modules, loss terms, and changes to the backbones, making it an almost plug-and-pay approach to interpretation." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.678, + 0.483, + 0.71 + ], + "angle": 0, + "content": "Due to space constraints, we provide a detailed related work section in the Supplementary Material (Suppl.)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.735, + 0.2, + 0.753 + ], + "angle": 0, + "content": "2. Approach" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.486, + 0.902 + ], + "angle": 0, + "content": "We propose Prompt Class Attention Map (PROMPT-CAM) to leverage pre-trained Vision Transformers (ViTs) [9] for fine-grained analysis. The goal is to identify and localize traits that highlight an object category's identity. PROMPT-CAM adds learnable class-specific tokens to prompt ViTs, producing class-specific attention maps that reveal traits. The overall framework is presented in Figure 3. We deliberately follow the notation and naming of Visual Prompt Tuning (VPT) [12] for ease of reference." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.655, + 0.105 + ], + "angle": 0, + "content": "2.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.113, + 0.906, + 0.173 + ], + "angle": 0, + "content": "A ViT typically contains \\(N\\) Transformer layers [44]. Each consists of a Multi-head Self-Attention (MSA) block, a Multi-Layer Perceptron (MLP) block, and several other operations like layer normalization and residual connections." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.174, + 0.906, + 0.248 + ], + "angle": 0, + "content": "The input image \\( \\pmb{I} \\) to ViTs is first divided into \\( M \\) fixed-sized patches. Each is then projected into a \\( D \\)-dimensional feature space with positional encoding, denoted by \\( e_0^j \\), with \\( 1 \\leq j \\leq M \\). We use \\( E_0 = [e_0^1, \\dots, e_0^M] \\in \\mathbb{R}^{D \\times M} \\) to denote their column-wise concatenation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.248, + 0.906, + 0.278 + ], + "angle": 0, + "content": "Together with a learnable [CLS] token \\( \\pmb{x}_0 \\in \\mathbb{R}^D \\), the whole ViT is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.29, + 0.866, + 0.308 + ], + "angle": 0, + "content": "\\[\n[ \\pmb {E} _ {i}, \\pmb {x} _ {i} ] = L _ {i} ([ \\pmb {E} _ {i - 1}, \\pmb {x} _ {i - 1} ]), \\quad i = 1, \\dots , N,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.317, + 0.906, + 0.363 + ], + "angle": 0, + "content": "where \\(L_{i}\\) denotes the \\(i\\)-th Transformer layer. The final \\(\\mathbf{x}_N\\) is typically used to represent the whole image and fed into a prediction head for classification." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.372, + 0.892, + 0.387 + ], + "angle": 0, + "content": "2.2. Prompt Class Attention Map (PROMPT-CAM)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.394, + 0.906, + 0.485 + ], + "angle": 0, + "content": "Given a pre-trained ViT and a downstream classification dataset with \\( C \\) classes, we introduce a set of \\( C \\) learnable \\( D \\)-dimensional vectors to prompt the ViT. These vectors are learned to be \"class-specific\" by minimizing the cross-entropy loss, during which the ViT backbone is frozen. In the following, we first introduce the baseline version." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.488, + 0.906, + 0.565 + ], + "angle": 0, + "content": "PROMPT-CAM-SHALLOW. The \\(C\\) class-specific prompts are injected into the first Transformer layer \\(L_{1}\\). We denote each prompt by \\(\\pmb{p}^{c} \\in \\mathbb{R}^{D}\\), where \\(1 \\leq c \\leq C\\), and use \\(\\pmb{P} = [\\pmb{p}^{1}, \\dots, \\pmb{p}^{C}] \\in \\mathbb{R}^{D \\times C}\\) to indicate their column-wise concatenation. The prompted ViT is:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.574, + 0.9, + 0.611 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} [ \\boldsymbol {Z} _ {1}, \\boldsymbol {E} _ {1}, \\boldsymbol {x} _ {1} ] = L _ {1} ([ \\boldsymbol {P}, \\boldsymbol {E} _ {0}, \\boldsymbol {x} _ {0} ]) \\\\ [ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {Z} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 2, \\dots , N, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.906, + 0.681 + ], + "angle": 0, + "content": "where \\( Z_{i} \\) represents the features corresponding to \\( P \\), computed by the \\( i \\)-th Transformer layer \\( L_{i} \\). The order among \\( x_{0}, E_{0} \\), and \\( P \\) does not matter since the positional encoding of patch locations has already been inserted into \\( E_{0} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.681, + 0.906, + 0.743 + ], + "angle": 0, + "content": "To make \\( \\pmb{P} = [\\pmb{p}^{1},\\dots ,\\pmb{p}^{C}] \\) class-specific, we employ a cross-entropy loss on top of the corresponding ViT's output, i.e., \\( Z_{N} = [z_{N}^{1},\\dots ,z_{N}^{C}] \\). Given a labeled training example \\( (\\pmb {I},y\\in \\{1,\\dots ,C\\}) \\), we calculate the logit of each class by:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.766, + 0.905, + 0.786 + ], + "angle": 0, + "content": "\\[\ns [ c ] = \\boldsymbol {w} ^ {\\top} \\boldsymbol {z} _ {N} ^ {c}, \\quad 1 \\leq c \\leq C, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.827 + ], + "angle": 0, + "content": "where \\(\\boldsymbol{w} \\in \\mathbb{R}^{D}\\) is a learnable vector. \\(\\pmb{P}\\) can then be updated by minimizing the loss:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.836, + 0.905, + 0.877 + ], + "angle": 0, + "content": "\\[\n- \\log \\left(\\frac {\\exp (s [ y ])}{\\sum_ {c} \\exp (s [ c ])}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "PROMPT-CAM-DEEP. While straightforward, PROMPT" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4377" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.105, + 0.868, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.322, + 0.907, + 0.381 + ], + "angle": 0, + "content": "Figure 3. Overview of Prompt Class Attention Map (PROMPT-CAM). We explore two variants, given a pre-trained ViT with \\(N\\) layers and a downstream task with \\(C\\) classes: (a) PROMPT-CAM-DEEP: insert \\(C\\) learnable \"class-specific\" tokens to the last layer's input and \\(C\\) learnable \"class-agnostic\" tokens to each of the other \\(N - 1\\) layers' input; (b) PROMPT-CAM-SHALLOW: insert \\(C\\) learnable \"class-specific\" tokens to the first layer's input. During training, only the prompts and the prediction head are updated; the whole ViT is frozen." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.398, + 0.484, + 0.549 + ], + "angle": 0, + "content": "CAM-SHALLOW has two potential drawbacks. First, the class-specific prompts attend to every layer's patch features, i.e., \\( E_{i} \\), \\( i = 0, \\dots, N - 1 \\). However, features of the early layers are often not informative enough but noisy for differentiating classes. Second, the prompts \\( p^{1}, \\dots, p^{C} \\) have a \"double duty.\" Individually, each needs to highlight class-specific traits. Collectively, they need to adapt pre-trained ViTs to downstream tasks, which is the original purpose of VPT [12]. In our case, the downstream task is a new usage of ViTs on a specific fine-grained dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.484, + 0.626 + ], + "angle": 0, + "content": "To address these issues, we resort to the VPT-Deep's design while deliberately decoupling injected prompts' roles. VPT-Deep adds learnable prompts to every layer's input. Denote by \\( \\pmb{P}_{i - 1} = [\\pmb{p}_{i - 1}^{1},\\dots ,\\pmb{p}_{i - 1}^{C}] \\) the prompts to the \\( i \\)-th Transformer layer, the deep-prompted ViT is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.649, + 0.483, + 0.68 + ], + "angle": 0, + "content": "\\[\n[ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {P} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 1, \\dots , N, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.72 + ], + "angle": 0, + "content": "It is worth noting that the features \\( Z_{i} \\) after the \\( i \\)-th layer are not inputted to the next layer, and are typically disregarded." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In PROMPT-CAM-DEEP, we repurpose \\( Z_{N} \\) for classification, following Equation 1. As such, after minimizing the cross entropy loss in Equation 2, the corresponding prompts \\( P_{N - 1} = [\\pmb{p}_{N - 1}^{1},\\dots ,\\pmb{p}_{N - 1}^{C}] \\) will be class-specific. Prompts to the other layers' inputs, i.e., \\( P_{i} = [p_{i}^{1},\\dots ,p_{i}^{C}] \\) for \\( i = 0,\\dots ,N - 2 \\), remain class-agnostic, because \\( p_i^c \\) does not particularly serve for the \\( c \\)-th class, unlike \\( p_{N - 1}^{c} \\). In other words, PROMPT-CAM-DEEP learns both class-specific prompts for trait localization and class-agnostic prompts for adaptation. The class-specific prompts \\( P_{N - 1} \\) only attend to the patch features \\( E_{N - 1} \\) inputted to the last Transformer layer \\( L_{N} \\), further addressing the other issue in" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.399, + 0.704, + 0.412 + ], + "angle": 0, + "content": "PROMPT-CAM-SHALLOW." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.414, + 0.881, + 0.43 + ], + "angle": 0, + "content": "In the following, we focus on PROMPT-CAM-DEEP." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.441, + 0.83, + 0.456 + ], + "angle": 0, + "content": "2.3. Trait Identification and Localization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.464, + 0.907, + 0.525 + ], + "angle": 0, + "content": "During inference, given an image \\(\\pmb{I}\\), PROMPT-CAM-DEEP extracts patch embeddings \\(\\pmb{E}_0 = [e_0^1,\\dots ,e_0^M ]\\) and follows Equation 3 to obtain \\(Z_{N}\\) and Equation 1 to obtain \\(s[c]\\) for \\(c\\in \\{1,\\dots ,C\\}\\). The predicted label \\(\\hat{y}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.538, + 0.907, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\arg \\max _ {c \\in \\{1, \\dots , C \\}} s [ c ]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.573, + 0.906, + 0.634 + ], + "angle": 0, + "content": "What are the traits of class \\( c \\)? To answer this question, one could collect images whose true and predicted classes are both class \\( c \\) (i.e., correctly classified) and visualize the multi-head attention maps queried by \\( \\pmb{p}_{N-1}^c \\) in layer \\( L_N \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.635, + 0.906, + 0.746 + ], + "angle": 0, + "content": "Specifically, in layer \\(L_{N}\\) with \\(R\\) attention heads, the patch features \\(\\pmb{E}_{N - 1} \\in \\mathbb{R}^{D \\times M}\\) are projected into \\(R\\) key matrices, denoted by \\(\\pmb{K}_{N - 1}^{r} \\in \\mathbb{R}^{D' \\times M}\\), \\(r = 1, \\dots, R\\). The \\(j\\)-th column corresponds to the \\(j\\)-th patch in \\(\\pmb{I}\\). Meanwhile, the prompt \\(\\pmb{p}_{N - 1}^{c}\\) is projected into \\(R\\) query vectors \\(\\pmb{q}_{N - 1}^{c,r} \\in \\mathbb{R}^{D'}\\), \\(r = 1, \\dots, R\\). Queried by \\(\\pmb{p}_{N - 1}^{c}\\), the \\(r\\)-th head's attention map \\(\\alpha_{N - 1}^{c,r} \\in \\mathbb{R}^{M}\\) is computed by:" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.758, + 0.907, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\alpha} _ {N - 1} ^ {c, r} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {K} _ {N - 1} ^ {r} \\mathbin {\\text {T}} \\boldsymbol {q} _ {N - 1} ^ {c , r}}{D ^ {\\prime}}\\right) \\in \\mathbb {R} ^ {M}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Conceptually, from the \\(r\\)-th head's perspective, the weight \\(\\alpha_{N - 1}^{c,r}[j]\\) indicates how important the \\(j\\)-th patch is for classifying class \\(c\\), hence localizing traits in the image. Ideally, each head should attend to different (sets of) patches to look for multiple traits that together highlight class \\(c\\)'s identity. By visualizing each attention map \\(\\alpha_{N - 1}^{c,r}\\), \\(r = 1,\\dots ,R\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4378" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.122 + ], + "angle": 0, + "content": "instead of pooling them averagely, PROMPT-CAM can potentially identify up to \\( R \\) different traits for class \\( c \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.126, + 0.484, + 0.232 + ], + "angle": 0, + "content": "Which traits are more discriminative? For categories that are so distinctive, like \"Red-winged Blackbird,\" a few traits are sufficient to distinguish them from others. To automatically identify these most discriminative traits, we take a greedy approach, progressively blurring the least important attention maps until the image is misclassified. The remaining ones highlight traits that are sufficient for classification." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.232, + 0.484, + 0.357 + ], + "angle": 0, + "content": "Suppose class \\( c \\) is the true class and the image is correctly classified. In each greedy step, for each of the unblurred heads indexed by \\( r' \\), we iteratively replace \\( \\alpha_{N-1}^{c,r'} \\) with \\( \\frac{1}{M}\\mathbf{1} \\) and recalculate \\( s[c] \\) in Equation 1, where \\( \\mathbf{1} \\in \\mathbb{R}^M \\) is an all-one vector. Doing so essentially blurs the \\( r' \\)-th head for class \\( c \\), preventing it from focusing. The head with the highest blurred \\( s[c] \\) is thus the least important, as blurring it degrades classification the least. See Suppl. for details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.36, + 0.484, + 0.455 + ], + "angle": 0, + "content": "Why is an image wrongly classified? When \\(\\hat{y} \\neq y\\) for a labeled image \\((I, y)\\), one could visualize both \\(\\{\\alpha_{N-1}^{y,r}\\}_{r=1}^{R}\\) and \\(\\{\\alpha_{N-1}^{\\hat{y},r}\\}_{r=1}^{R}\\) to understand why the classifier made such a prediction. For example, some traits of class \\(y\\) may be invisible or unclear in \\(I\\); the object in \\(I\\) may possess class \\(\\hat{y}\\)'s visual traits, for example, due to light conditions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.463, + 0.315, + 0.478 + ], + "angle": 0, + "content": "2.4. Variants and Extensions" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.595 + ], + "angle": 0, + "content": "Other PROMPT-CAM designs. Besides injecting class-specific prompts to the first layer (i.e., PROMPT-CAM-SHALLOW) or the last (i.e., PROMPT-CAM-DEEP), we also explore their interpolation. We introduce class-specific prompts like PROMPT-CAM-SHALLOW to the \\( i \\)-th layer and class-agnostic prompts like PROMPT-CAM-DEEP to the first \\( i - 1 \\) layers. See the Suppl. for a comparison." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.484, + 0.719 + ], + "angle": 0, + "content": "PROMPT-CAM for discovering taxonomy keys. So far, we have focused on a \"flat\" comparison over all the categories. In domains like biology that are full of fine-grained categories, researchers often have built hierarchical decision trees to ease manual categorization, such as taxonomy. The role of each intermediate \"tree node\" is to dichotomize a subset of categories into multiple groups, each possessing certain group-level characteristics (i.e., taxonomy keys)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.841 + ], + "angle": 0, + "content": "The simplicity of PROMPT-CAM allows us to efficiently train multiple sets of prompts, one for each intermediate tree node, potentially (re-)discovering the taxonomy keys. One just needs to relabel categories of the same group by a single label, before training. In expectation, along the path from the root to a leaf node, each of the intermediate tree nodes should look at different group-level traits on the same image of that leaf node. See Figure 9 for a preliminary result." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.382, + 0.864 + ], + "angle": 0, + "content": "2.5. What is PROMPT-CAM suited for?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "As our paper is titled, PROMPT-CAM is dedicated to fine-grained analysis, aiming to identify and, more importantly," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.228 + ], + "angle": 0, + "content": "localize traits useful for differentiating categories. This, however, does not mean that PROMPT-CAM would excel in fine-grained classification accuracy. Modern neural networks easily have millions if not billions of parameters. How a model predicts is thus still an unanswered question, at least, not fully. It is known if a model is trained mainly to chase accuracies with no constraints, it will inevitably discover \"shortcuts\" in the collected data that are useful for classification but not analysis [8, 11]. We thus argue:" + }, + { + "type": "title", + "bbox": [ + 0.523, + 0.237, + 0.896, + 0.282 + ], + "angle": 0, + "content": "To make a model suitable for fine-grained analysis, one must constrain its capacity, while knowing that doing so would unavoidably hurt its classification accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.906, + 0.396 + ], + "angle": 0, + "content": "PROMPT-CAM is designed with this mindset. Unlike conventional classifiers that employ a fully connected layer on top, PROMPT-CAM follows [31] and learns a shared vector \\(\\boldsymbol{w}\\) in Equation 1. The goal of \\(\\boldsymbol{w}\\) is NOT to capture class-specific information BUT to answer a \"binary\" question: Based on where a class-specific prompt attends, does the class recognize itself in the input image?" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.397, + 0.907, + 0.502 + ], + "angle": 0, + "content": "To elucidate the difference, let us consider a simplified single-head-attention Transformer layer with no layer normalization, residual connection, MLP block, and other nonlinear operations. Let \\(V = \\{\\pmb{v}^1,\\dots ,\\pmb{v}^M\\} \\in \\mathbb{R}^{D\\times M}\\) be the \\(M\\) input patches' value features, \\(\\alpha^c\\in \\mathbb{R}^M\\) be the attention weights of class \\(c\\), and \\(\\alpha^{\\star}\\in \\mathbb{R}^{M}\\) be the attention weights of the [CLS] token. Conventional models predict classes by:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.524, + 0.906, + 0.594 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} _ {c} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\left(\\boldsymbol {w} _ {c} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.602, + 0.906, + 0.753 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{w}_c \\) stores the fully connected weights for class \\( c \\). We argue that this formulation allows for a potential \"detour,\" enabling the model to correctly classify an image \\( I \\) of class \\( y \\) even without meaningful attention weights. In essence, the model can choose to produce holistically discriminative value features from \\( I \\) without preserving spatial resolution, such that \\( v^j \\) aligns with \\( \\boldsymbol{w}_y \\) but \\( v^j = v^{j'} \\), \\( \\forall j \\neq j' \\). In this case, regardless of the specific values of \\( \\alpha^\\star \\), as long as they sum to one—as is default in the softmax formulation—the prediction remains unaffected." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.754, + 0.848, + 0.769 + ], + "angle": 0, + "content": "In contrast, PROMPT-CAM predicts classes by:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.777, + 0.906, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {c} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {c} [ j ] \\times \\left(\\boldsymbol {w} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "where \\( \\mathbf{w} \\) is the shared binary classifier. (For brevity, we assume no self-attention among the prompts.) While the difference between Equation 7 and Equation 6 is subtle at" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4379" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "first glance, it fundamentally changes the model's behavior. In essence, it becomes less effective to store class discriminative information in the channels of \\(\\pmb{v}^j\\), because there is no \\(\\pmb{w}_c\\) to align with. Moreover, the model can no longer produce holistic features with no spatial resolution; otherwise, it cannot distinguish among classes since all of their scores \\(s[c]\\) will be exactly the same, no matter what \\(\\alpha^c\\) is." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.202, + 0.483, + 0.234 + ], + "angle": 0, + "content": "In response, the model must be equipped with two capabilities to minimize the cross-entropy error:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.24, + 0.483, + 0.27 + ], + "angle": 0, + "content": "- Generate localized features \\( \\mathbf{v}^j \\) that highlight discriminative patches (e.g., the red spot on the wing) of an image." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.271, + 0.482, + 0.3 + ], + "angle": 0, + "content": "- Generate distinctive attention weights \\(\\alpha^c\\) across classes, each focusing on traits frequently seen in class \\(c\\)." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.24, + 0.483, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.308, + 0.449, + 0.324 + ], + "angle": 0, + "content": "These properties are what fine-grained analysis needs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.329, + 0.484, + 0.451 + ], + "angle": 0, + "content": "In sum, PROMPT-CAM discourages patch features from encoding class-discriminative holistic information (e.g., the whole object shapes or mysterious long-distance pixel correlations), even if such information can be \"beneficial\" to a conventional classifier. To this end, PROMPT-CAM needs to distill localized, trait-specific information from the pretrained ViT's patch features, which is achieved through the injected class-agnostic prompts in PROMPT-CAM-DEEP." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.478, + 0.224, + 0.495 + ], + "angle": 0, + "content": "3. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.508, + 0.282, + 0.525 + ], + "angle": 0, + "content": "3.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.535, + 0.484, + 0.716 + ], + "angle": 0, + "content": "Dataset. We comprehensively evaluate the performance of PROMPT-CAM on 13 diverse fine-grained image classification datasets across three domains: (1) animal-based: CUB-200-2011 (CUB) [45], Birds-525 (Bird) [33], Stanford Dogs (Dog) [15], Oxford Pet (Pet) [30], iNaturalist-2021-Moths (Moth) [43], Fish Vista (Fish) [24], Rare Species (RareS.) [41] and Insects-2 (Insects) [49]; (2) plant and fungi-based: iNaturalist-2021-Fungi (Fungi) [43], Oxford Flowers (Flower) [28] and Medicinal Leaf (MedLeaf) [36]; (3) object-based: Stanford Cars (Car) [16] and Food 101 (Food) [2]. We provide details about data processing and statistics in Suppl." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.725, + 0.483, + 0.817 + ], + "angle": 0, + "content": "Model. We consider three pre-trained ViT backbones, DINO [4], DINOv2 [29], and BioCLIP [38] across different scales including ViT-B (the main one we use) and ViTS. The backbones are kept completely frozen when applying PROMPT-CAM. We mainly used DINO, unless stated otherwise. More details can be found in Suppl." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Baseline Methods. We compared PROMPT-CAM with explainable methods like Grad-CAM [37], Layer-CAM [13] and Eigen-CAM [25] as well as with interpretable methods like ProtoPFormer [51], TesNet [47], ProtoConcepts [21] and INTR [31]. More details are in Suppl." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.905, + 0.146 + ], + "angle": 0, + "content": "Table 1. Faithfulness evaluation based on insertion and deletion scores. A higher insertion score and a lower deletion score indicate better results. The results are obtained from the validation images of CUB using the DINO backbone." + }, + { + "type": "table", + "bbox": [ + 0.568, + 0.15, + 0.855, + 0.239 + ], + "angle": 0, + "content": "
MethodInsertion↑Deletion↓
Grad-CAM [37]0.520.17
Layer-CAM[13]0.540.13
Eigen-CAM [25]0.560.22
Attention roll-out [14]0.550.27
PROMPT-CAM0.610.09
" + }, + { + "type": "table_caption", + "bbox": [ + 0.525, + 0.249, + 0.894, + 0.262 + ], + "angle": 0, + "content": "Table 2. Accuracy (%) comparison using the DINO backbone." + }, + { + "type": "table", + "bbox": [ + 0.571, + 0.264, + 0.851, + 0.317 + ], + "angle": 0, + "content": "
BirdCUBDogPet
Linear Probing99.278.682.492.4
PROMPT-CAM98.873.281.191.3
" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.332, + 0.702, + 0.348 + ], + "angle": 0, + "content": "3.2. Experiment Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.359, + 0.905, + 0.465 + ], + "angle": 0, + "content": "Is PROMPT-CAM faithful? We first investigate whether PROMPT-CAM highlights the image regions that the corresponding classifier focuses on when making predictions. We use PROMPT-CAM to rank pixels based on the aggregated attention maps over the top heads. We then employ the insertion and deletion metrics [32], manipulating highly ranked pixels to measure confidence increase and drop." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.467, + 0.906, + 0.588 + ], + "angle": 0, + "content": "For comparison, we consider post-hoc explainable methods like Grad-CAM [37], Eigen-CAM [25], Layer-CAM [13], and attention roll-out [14], based on the same ViT backbone with Linear Probing. As summarized in Table 1, PROMPT-CAM yields higher insertion scores and lower deletion scores, indicating a stronger focus on discriminative image traits and highlighting PROMPT-CAM's enhanced interpretability over standard post-hoc algorithms." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.906, + 0.805 + ], + "angle": 0, + "content": "PROMPT-CAM excels in trait identification (human assessment). We then conduct a quantitative human study to evaluate trait identification quality for PROMPT-CAM, TesNet [47], and ProtoConcepts [21]. Participants with no prior knowledge about the algorithms were instructed to compare the expert-identified traits (in text, such as orange belly) and the top heatmaps generated by each method. If an expert-identified trait is seen in the heatmaps, it is considered identified by the algorithm. On average, participants recognized \\(60.49\\%\\) of traits for PROMPT-CAM, significantly outperforming TesNet and ProtoConcepts whose recognition rates are \\(39.14\\%\\) and \\(30.39\\%\\), respectively. The results highlight PROMPT-CAM's superiority in emphasizing and conveying relevant traits effectively. More details are in Suppl." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Classification accuracy comparison. We observe that PROMPT-CAM shows a slight accuracy drop compared to Linear Probing (see Table 2). However, the images misclassified by PROMPT-CAM but correctly classified by Linear Probing align with our design philosophy: PROMPT-CAM classifies images based on the presence of class-specific, lo" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4380" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.092, + 0.87, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.387, + 0.908, + 0.416 + ], + "angle": 0, + "content": "Figure 4. Visualization of PROMPT-CAM on different datasets. We show the top four attention maps (from left to right) per correctly classified test example triggered by the ground-truth classes." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.429, + 0.462, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.523, + 0.484, + 0.592 + ], + "angle": 0, + "content": "Figure 5. Images misclassified by PROMPT-CAM but correctly classified by Linear Probing. Species-specific traits—such as the red breast of \"Red-breasted Grosbeak\"—are barely visible in misclassified images while Linear Probing uses global features such as body shapes, poses, and backgrounds for correct predictions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.619, + 0.484, + 0.726 + ], + "angle": 0, + "content": "calized traits and would fail if they are invisible. As shown in Figure 5, discriminative traits—such as the red breast of the Red-breasted Grosbeak—are barely visible in images misclassified by PROMPT-CAM due to occlusion, unusual poses, or lighting conditions. Linear Probing correctly classifies them by leveraging global information such as body shapes and backgrounds. Please see more analysis in Suppl." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Comparison to interpretable models. We conduct a qualitative analysis to compare PROMPT-CAM with other interpretable methods—ProtoPFormer, INTR, TesNet, and ProtoConcepts. Figure 6 shows the top-ranked attention maps or prototypes generated by each method. PROMPT-CAM can capture a more extensive range of distinct, fine-grained traits, in contrast to other methods that often focus on a narrower or repetitive set of attributes (for example, ProtoConcepts in the first three ranks of the fifth row). This highlights PROMPT-CAM's ability to identify and localize different traits that collectively define a category's identity." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.429, + 0.907, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.647, + 0.908, + 0.704 + ], + "angle": 0, + "content": "Figure 6. Comparison of interpretable models. Visual demonstration (heatmaps and bounding boxes) of the four most activated responses of attention heads (PROMPT-CAM and INTR) or prototypes of each method on a \"Lazuli Bunting\" example image." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.718, + 0.8, + 0.734 + ], + "angle": 0, + "content": "3.3. Further Analysis and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.745, + 0.907, + 0.852 + ], + "angle": 0, + "content": "PROMPT-CAM on different backbones. Figure 7 illustrates that PROMPT-CAM is compatible with different ViT backbones. We show the top three attention maps generated by PROMPT-CAM using different ViT backbones on an image of Scott Oriole, highlighting consistent identification of traits for species recognition, irrespective of the backbones. Please see the caption and Suppl. for details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "PROMPT-CAM on different datasets. Figure 4 presents the top four attention maps generated by PROMPT-CAM across various datasets spanning diverse domains, includ" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4381" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.17, + 0.088, + 0.408, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.216, + 0.484, + 0.284 + ], + "angle": 0, + "content": "Figure 7. PROMPT-CAM on different backbones. Here we show the top attention maps for PROMPT-CAM on (a) DINO, (b) DINOv2, and (c) BioCLIP backbone. All three sets of attention heads point to consistent key traits of the species \"Scott Oriole\"—yellow belly, black head, and black chest." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.289, + 0.482, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.416, + 0.484, + 0.485 + ], + "angle": 0, + "content": "Figure 8. Trait manipulation. The top row shows attention maps for a correctly classified \"Red-winged Blackbird\" image. In the second row, the red spot on the bird's wings was removed, and PROMPT-CAM subsequently classified it as a \"Boat-tailed Grackle,\" as depicted in the reference column." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.484, + 0.56 + ], + "angle": 0, + "content": "ing animals, plants, and objects. PROMPT-CAM effectively captures the most important traits in each case to accurately identify species, demonstrating its remarkable generalizability and wide applicability." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.484, + 0.821 + ], + "angle": 0, + "content": "PROMPT-CAM can detect biologically meaningful traits. As shown in Figure 4, PROMPT-CAM consistently identifies traits from images of the same species (e.g., the red breast and white belly for Rose-breasted Grosbeak). This is further demonstrated in Figure 1 (d), where we progressively mask attention heads (detailed in subsection 2.3) until the model can no longer generate high-confidence predictions for correctly classifying images of Scott Oriole. The remaining heads 1 and 11 highlight the essential traits, i.e., the black head and yellow belly. PROMPT-CAM also enables identifying common traits between species. This is achieved by visualizing the image of one class (e.g., Scott Oriole) using other classes' prompts (e.g., Brewer Blackbird or Baltimore Oriole). As shown in Figure 1 (c), Brewer Blackbird shares the head and neck color with Scott Oriole. These results demonstrate PROMPT-CAM ability to recognize species in a biologically meaningful way." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.903 + ], + "angle": 0, + "content": "PROMPT-CAM can identify and interpret trait manipulation. We conduct a counterfactual-style analysis to investigate whether PROMPT-CAM truly relies on the identified traits for making predictions. For instance, to correctly classify the Red-winged Blackbird, it highlights the red-wing" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.094, + 0.875, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.305, + 0.907, + 0.43 + ], + "angle": 0, + "content": "Figure 9. PROMPT-CAM can detect taxonomically meaningful traits. Give an image of the species \"Amophiprion Clarkii,\" PROMPT-CAM highlights the pelvic fin and double stripe to distinguish it from \"Amophiprion Melanopus\" at the species level. When it goes to the genus level, PROMPT-CAM looks at the pattern in the body and tail to classify the image as the \"Amophiprion\" genus. As we go up, fishes at the family level become visually dissimilar. PROMPT-CAM only needs to look at the tail and pelvic fin to classify the image as the \"Pomacentridae\" family." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.444, + 0.907, + 0.581 + ], + "angle": 0, + "content": "patch (the first row of Figure 8), consistent with the field guide provided by the Cornell Lab of Ornithology. When we remove this red spot from the image to resemble a Boat-tailed Grackle, the model no longer highlights the original position of the red patch. As such, it does not predict the image as a Red-winged Blackbird but a Boat-tailed Grackle (the second row of Figure 8). This shows PROMPT-CAM's sensitivity to trait differences, showcasing its interpretability in fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.909, + 0.751 + ], + "angle": 0, + "content": "PROMPT-CAM can detect taxonomically meaningful traits. We train PROMPT-CAM based on a hierarchical framework, considering four levels of taxonomic hierarchy: Order \\(\\rightarrow\\) Family \\(\\rightarrow\\) Genus \\(\\rightarrow\\) Species of Fish Dataset. In this setup, PROMPT-CAM progressively shifts its focus from coarse-grained traits at the Family level to fine-grained traits at the Species level to distinguish categories (shown in Figure 9). This progression suggests PROMPT-CAM's potential to automatically identify and localize taxonomy keys to aid in biological and ecological research domains. We provide more details in Suppl." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.764, + 0.634, + 0.779 + ], + "angle": 0, + "content": "4. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.789, + 0.907, + 0.895 + ], + "angle": 0, + "content": "We present Prompt Class Attention Map (PROMPT-CAM), a simple yet effective interpretable approach that leverages pre-trained ViTs to identify and localize discriminative traits for fine-grained classification. PROMPT-CAM is easy to implement and train. Extensive empirical studies highlight both the strong performance of PROMPT-CAM and the promise of repurposing standard models for interpretability." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4382" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.241, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.484, + 0.193 + ], + "angle": 0, + "content": "This research is supported in part by grants from the National Science Foundation (OAC-2118240, HDR Institute:Imageomics). The authors are grateful for the generous support of the computational resources from the Ohio Supercomputer Center." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.208, + 0.188, + 0.224 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.233, + 0.484, + 0.274 + ], + "angle": 0, + "content": "[1] Samira Abnar and Willem Zuidema. Quantifying attention flow in transformers. arXiv preprint arXiv:2005.00928, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.277, + 0.484, + 0.348 + ], + "angle": 0, + "content": "[2] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer vision-ECCV 2014: 13th European conference, zurich, Switzerland, September 6-12, 2014, proceedings, part VI 13, pages 446-461. Springer, 2014. 2, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.349, + 0.485, + 0.514 + ], + "angle": 0, + "content": "[3] Tom B. 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Campolongo1, Daniel Rubenstein4, Charles V. Stewart5, Anuj Karpatne3, Tanya Berger-Wolf1, Yu Su1, Wei-Lun Chao1 + +1The Ohio State University, 2University of Tsukuba, 3Virginia Tech, 4Princeton University, 5Rensselaer Polytechnic Institute + +![](images/c68c428d5d8d835e28d968e957616918fb9933eaf4492010577e7bfdbe52e8a1.jpg) +Figure 1. Illustration of PROMPT-CAM. By learning class-specific prompts for a pre-trained Vision Transformer (ViT), PROMPT-CAM enables multiple functionalities. (a) PROMPT-CAM achieves fine-grained image classification using the output logits from the class-specific prompts. (b) PROMPT-CAM enables trait localization by visualizing the multi-head attention maps queried by the true-class prompt. (c) PROMPT-CAM identifies common traits shared between species by visualizing the attention maps queried by another-class prompt. (d) PROMPT-CAM can identify the most discriminative traits per species (e.g., distinctive yellow chest and black neck for "Scott Oriole") by systematically masking out the least important attention heads. See subsection 2.3 for details. + +# Abstract + +We present a simple approach to make pre-trained Vision Transformers (ViTs) interpretable for fine-grained analysis, aiming to identify and localize the traits that distinguish visually similar categories, such as bird species. Pre-trained ViTs, such as DINO, have demonstrated remarkable capabilities in extracting localized, discriminative features. However, saliency maps like Grad-CAM often fail to identify these traits, producing blurred, coarse heatmaps that highlight entire objects instead. We propose a novel approach, Prompt Class Attention Map (PROMPT-CAM), to address this limitation. PROMPT-CAM learns class-specific prompts for a pre-trained ViT and uses the corresponding outputs for classification. To correctly classify an image, the true-class prompt must attend to unique image patches not present in other classes' images (i.e., traits). As + +a result, the true class's multi-head attention maps reveal traits and their locations. Implementation-wise, PROMPT-CAM is almost a "free lunch," requiring only a modification to the prediction head of Visual Prompt Tuning (VPT). This makes PROMPT-CAM easy to train and apply, in stark contrast to other interpretable methods that require designing specific models and training processes. Extensive empirical studies on a dozen datasets from various domains (e.g., birds, fishes, insects, fungi, flowers, food, and cars) validate the superior interpretation capability of PROMPT-CAM. The source code and demo are available at https://github.com/Imageomics/Prompt_CAM. + +# 1. Introduction + +Vision Transformers (ViT) [9] pre-trained on huge datasets have greatly improved vision recognition, even for fine + +grained objects [10, 40, 48, 54]. DINO [4] and DINOv2 [29] further showed remarkable abilities to extract features that are localized and informative, precisely representing the corresponding coordinates in the input image. These advancements open up the possibility of using pre-trained ViTs to discover "traits" that highlight each category's identity and distinguish it from other visually close ones. + +One popular approach to this is saliency maps, for example, Class Activation Map (CAM) [13, 25, 37, 52]. After extracting the feature maps from an image, CAM highlights the spatial grids whose feature vectors align with the target class's fully connected weight. While easy to implement and efficient, the reported CAM saliency on ViTs is often far from expectation. It frequently locates the whole object with a blurred, coarse heatmap, instead of focusing on subtle traits that tell visually similar objects (e.g., birds) apart. One may argue that CAM was not originally developed for ViTs, but even with dedicated variants like attention rollout [1, 5, 14], the issue is only mildly attenuated. + +What if we look at the attention maps? ViTs rely on self-attention to relate image patches; the [CLS] token aggregates image features by attending to informative patches. As shown in [7, 27, 39], the attention maps of the [CLS] token do highlight local regions inside the object. However, these regions are not "class-specific." Instead, they often focus on the same object regions across different categories, such as body parts like heads, wings, and tails of bird species. While these are where traits usually reside, they are not traits. For example, the distinction between "Red-winged Blackbird" and other bird species is the red spot on the wing, having little to do with other body parts. + +# How can we leverage pre-trained ViTs, particularly their localized and informative patch features, to identify traits that are so special for each category? + +Our proposal is to prompt ViTs with learnable "class-specific" tokens, one for each class, inspired by [17, 20, 31, 50]. These "class-specific" tokens, once inputted into ViTs, attend to image patches via self-attention, similar to the [CLS] token. However, unlike the [CLS] token, which is "class-agnostic," these "class-specific" tokens can attend to the same image differently, with the potential to highlight regions specific to the corresponding classes, i.e., traits. + +We implement our approach, named Prompt Class Attention Map (PROMPT-CAM), as follows. Given a pretrained ViT and a fine-grained classification dataset with $C$ classes, we add $C$ learnable tokens as additional inputs alongside the input image. To make these tokens "class-specific," we collect their corresponding output vectors after the final Transformer layer and perform inner products with a shared vector (also learnable) to obtain $C$ "class-specific" scores, following [31]. One may interpret each class-specific score as how clearly the corresponding class's + +traits are visible in the input image. Intuitively, the input image's ground-truth class should possess the highest score, and we encourage this by minimizing a cross-entropy loss, treating the scores as logits. We keep the whole pre-trained ViT frozen and only optimize the $C$ tokens and the shared scoring vector. See section 2 for details and variants. + +For interpretation during inference, we input the image and the $C$ tokens simultaneously to the ViT to obtain the $C$ scores. One can then select a specific class (e.g., the highest-score class) and visualize its multi-head attention maps over the image patches. See Figure 1 for an illustration and section 2 for how to rank these maps to highlight the most discriminative traits. When the highest-score class is the ground-truth class, the attention maps reveal its traits. Otherwise, comparing the attention maps of the highest-score class with those of the ground-truth class helps explain why the image is misclassified. Possible reasons include the object being partially occluded or in an unusual pose, making its traits invisible, or the appearance being too similar to a wrong class, possibly due to lighting conditions (Figure 5). + +PROMPT-CAM is fairly easy to implement and train. It requires no change to pre-trained ViTs and no specially designed loss function or training strategy—just the standard cross-entropy loss and SGD. Indeed, building upon Visual Prompt Tuning (VPT) [12], one merely needs to adjust a few lines of code and can enjoy fine-grained interpretation. This simplicity sharply contrasts other interpretable methods like ProtoPNet [6] and ProtoTree [26]. Compared to INterpretable TRansformer (INTR) [31], which also featured simplicity, PROMPT-CAM has three notable advantages. First, PROMPT-CAM is encoder-only and can potentially utilize any ViT encoder. In contrast, INTR is built upon an encoder-decoder model pre-trained on object detection datasets. As a result, PROMPT-CAM can more easily leverage up-to-date pre-trained models. Second, PROMPT-CAM can be trained much faster—only the prompts and the shared vector need to be learned. In contrast, INTR typically requires full fine-tuning. Third, PROMPT-CAM produces cleaner and sharper attention maps than INTR, which we attribute to the use of state-of-the-art ViTs like DINO [4] or DINOv2 [29]. Taken together, we view PROMPT-CAM as a simpler yet more powerful interpretable Transformer. + +We validate PROMPT-CAM on over a dozen datasets: CUB-200-2011 [45], Birds-525 [33], Oxford Pet [30], Stanford Dogs [15], Stanford Cars [16], iNaturalist-2021-Moths [43], Fish Vista [24], Rare Species [41], Insects-2 [49], iNaturalist-2021-Fungi [43], Oxford Flowers [28], Medicinal Leaf [36], Stanford Cars [16], and Food 101 [2]. PROMPT-CAM can identify different traits of a category through multi-head attention and consistently localize them in images. To our knowledge, PROMPT-CAM is the only explainable or interpretable method for vision that has been evaluated on such a broad range of domains. We further + +![](images/87245fe056e18b62979132a84efea39d703a805f89ff5a55722d3889d0798548.jpg) +(a) VPT + +![](images/b50a3236717178e5f04ec850e74aa8bc1508831d6303129af91b6c6c2b621d6f.jpg) +(b) PROMPT-CAM +Figure 2. PROMPT-CAM vs. Visual Prompt Tuning (VPT). (a) VPT [12] adds the prediction head on top of the [CLS] token's output, a default design to use ViTs for classification. (b) PROMPT-CAM adds the prediction head on top of the injected prompts' outputs, making them class-specific to identify and localize traits. + +show PROMPT-CAM's extendability by applying it to discovering taxonomy keys. Our contributions are two-fold. + +- We present PROMPT-CAM, an easily implementable, trainable, and reproducible interpretable method that leverages the representations of pre-trained ViTs to identify and localize traits for fine-grained analysis. +- We conduct extensive experiments on more than a dozen datasets to validate PROMPT-CAM's interpretation quality, wide applicability, and extendability. + +Comparison to closely related work. Besides INTR [31], our class-specific attentions are inspired by two other works in different contexts, MCTformer for weakly supervised semantic segmentation [50] and Query2Label for multi-label classification [20]. Both of them learned class-specific tokens but aimed to localize visually distinct common objects (e.g., people, horses, and flights). In contrast, we focus on fine-grained analysis: supervised by class labels of visually similar objects (e.g., bird species), we aim to localize their traits (e.g., red spots on wings). One particular feature of PROMPT-CAM is its simplicity, in both implementation and compatibility with pre-trained backbones, without extra modules, loss terms, and changes to the backbones, making it an almost plug-and-pay approach to interpretation. + +Due to space constraints, we provide a detailed related work section in the Supplementary Material (Suppl.). + +# 2. Approach + +We propose Prompt Class Attention Map (PROMPT-CAM) to leverage pre-trained Vision Transformers (ViTs) [9] for fine-grained analysis. The goal is to identify and localize traits that highlight an object category's identity. PROMPT-CAM adds learnable class-specific tokens to prompt ViTs, producing class-specific attention maps that reveal traits. The overall framework is presented in Figure 3. We deliberately follow the notation and naming of Visual Prompt Tuning (VPT) [12] for ease of reference. + +# 2.1. Preliminaries + +A ViT typically contains $N$ Transformer layers [44]. Each consists of a Multi-head Self-Attention (MSA) block, a Multi-Layer Perceptron (MLP) block, and several other operations like layer normalization and residual connections. + +The input image $\pmb{I}$ to ViTs is first divided into $M$ fixed-sized patches. Each is then projected into a $D$ -dimensional feature space with positional encoding, denoted by $e_0^j$ , with $1 \leq j \leq M$ . We use $E_0 = [e_0^1, \dots, e_0^M] \in \mathbb{R}^{D \times M}$ to denote their column-wise concatenation. + +Together with a learnable [CLS] token $\pmb{x}_0 \in \mathbb{R}^D$ , the whole ViT is formulated as: + +$$ +[ \pmb {E} _ {i}, \pmb {x} _ {i} ] = L _ {i} ([ \pmb {E} _ {i - 1}, \pmb {x} _ {i - 1} ]), \quad i = 1, \dots , N, +$$ + +where $L_{i}$ denotes the $i$ -th Transformer layer. The final $\mathbf{x}_N$ is typically used to represent the whole image and fed into a prediction head for classification. + +# 2.2. Prompt Class Attention Map (PROMPT-CAM) + +Given a pre-trained ViT and a downstream classification dataset with $C$ classes, we introduce a set of $C$ learnable $D$ -dimensional vectors to prompt the ViT. These vectors are learned to be "class-specific" by minimizing the cross-entropy loss, during which the ViT backbone is frozen. In the following, we first introduce the baseline version. + +PROMPT-CAM-SHALLOW. The $C$ class-specific prompts are injected into the first Transformer layer $L_{1}$ . We denote each prompt by $\pmb{p}^{c} \in \mathbb{R}^{D}$ , where $1 \leq c \leq C$ , and use $\pmb{P} = [\pmb{p}^{1}, \dots, \pmb{p}^{C}] \in \mathbb{R}^{D \times C}$ to indicate their column-wise concatenation. The prompted ViT is: + +$$ +\begin{array}{l} [ \boldsymbol {Z} _ {1}, \boldsymbol {E} _ {1}, \boldsymbol {x} _ {1} ] = L _ {1} ([ \boldsymbol {P}, \boldsymbol {E} _ {0}, \boldsymbol {x} _ {0} ]) \\ [ \boldsymbol {Z} _ {i}, \boldsymbol {E} _ {i}, \boldsymbol {x} _ {i} ] = L _ {i} ([ \boldsymbol {Z} _ {i - 1}, \boldsymbol {E} _ {i - 1}, \boldsymbol {x} _ {i - 1} ]), \quad i = 2, \dots , N, \\ \end{array} +$$ + +where $Z_{i}$ represents the features corresponding to $P$ , computed by the $i$ -th Transformer layer $L_{i}$ . The order among $x_{0}, E_{0}$ , and $P$ does not matter since the positional encoding of patch locations has already been inserted into $E_{0}$ . + +To make $\pmb{P} = [\pmb{p}^{1},\dots ,\pmb{p}^{C}]$ class-specific, we employ a cross-entropy loss on top of the corresponding ViT's output, i.e., $Z_{N} = [z_{N}^{1},\dots ,z_{N}^{C}]$ . Given a labeled training example $(\pmb {I},y\in \{1,\dots ,C\})$ , we calculate the logit of each class by: + +$$ +s [ c ] = \boldsymbol {w} ^ {\top} \boldsymbol {z} _ {N} ^ {c}, \quad 1 \leq c \leq C, \tag {1} +$$ + +where $\boldsymbol{w} \in \mathbb{R}^{D}$ is a learnable vector. $\pmb{P}$ can then be updated by minimizing the loss: + +$$ +- \log \left(\frac {\exp (s [ y ])}{\sum_ {c} \exp (s [ c ])}\right). \tag {2} +$$ + +PROMPT-CAM-DEEP. While straightforward, PROMPT + +![](images/541dd0ed751b12e4958f3bfd538e0a0903b6d619209337852b520b5ad329d72a.jpg) +Figure 3. Overview of Prompt Class Attention Map (PROMPT-CAM). We explore two variants, given a pre-trained ViT with $N$ layers and a downstream task with $C$ classes: (a) PROMPT-CAM-DEEP: insert $C$ learnable "class-specific" tokens to the last layer's input and $C$ learnable "class-agnostic" tokens to each of the other $N - 1$ layers' input; (b) PROMPT-CAM-SHALLOW: insert $C$ learnable "class-specific" tokens to the first layer's input. During training, only the prompts and the prediction head are updated; the whole ViT is frozen. + +CAM-SHALLOW has two potential drawbacks. First, the class-specific prompts attend to every layer's patch features, i.e., $E_{i}$ , $i = 0, \dots, N - 1$ . However, features of the early layers are often not informative enough but noisy for differentiating classes. Second, the prompts $p^{1}, \dots, p^{C}$ have a "double duty." Individually, each needs to highlight class-specific traits. Collectively, they need to adapt pre-trained ViTs to downstream tasks, which is the original purpose of VPT [12]. In our case, the downstream task is a new usage of ViTs on a specific fine-grained dataset. + +To address these issues, we resort to the VPT-Deep's design while deliberately decoupling injected prompts' roles. VPT-Deep adds learnable prompts to every layer's input. Denote by $\pmb{P}_{i - 1} = [\pmb{p}_{i - 1}^{1},\dots ,\pmb{p}_{i - 1}^{C}]$ the prompts to the $i$ -th Transformer layer, the deep-prompted ViT is formulated as: + +$$ +[ \boldsymbol {Z} _ {i}, \boldsymbol {E} _ {i}, \boldsymbol {x} _ {i} ] = L _ {i} ([ \boldsymbol {P} _ {i - 1}, \boldsymbol {E} _ {i - 1}, \boldsymbol {x} _ {i - 1} ]), \quad i = 1, \dots , N, \tag {3} +$$ + +It is worth noting that the features $Z_{i}$ after the $i$ -th layer are not inputted to the next layer, and are typically disregarded. + +In PROMPT-CAM-DEEP, we repurpose $Z_{N}$ for classification, following Equation 1. As such, after minimizing the cross entropy loss in Equation 2, the corresponding prompts $P_{N - 1} = [\pmb{p}_{N - 1}^{1},\dots ,\pmb{p}_{N - 1}^{C}]$ will be class-specific. Prompts to the other layers' inputs, i.e., $P_{i} = [p_{i}^{1},\dots ,p_{i}^{C}]$ for $i = 0,\dots ,N - 2$ , remain class-agnostic, because $p_i^c$ does not particularly serve for the $c$ -th class, unlike $p_{N - 1}^{c}$ . In other words, PROMPT-CAM-DEEP learns both class-specific prompts for trait localization and class-agnostic prompts for adaptation. The class-specific prompts $P_{N - 1}$ only attend to the patch features $E_{N - 1}$ inputted to the last Transformer layer $L_{N}$ , further addressing the other issue in + +PROMPT-CAM-SHALLOW. + +In the following, we focus on PROMPT-CAM-DEEP. + +# 2.3. Trait Identification and Localization + +During inference, given an image $\pmb{I}$ , PROMPT-CAM-DEEP extracts patch embeddings $\pmb{E}_0 = [e_0^1,\dots ,e_0^M ]$ and follows Equation 3 to obtain $Z_{N}$ and Equation 1 to obtain $s[c]$ for $c\in \{1,\dots ,C\}$ . The predicted label $\hat{y}$ is: + +$$ +\hat {y} = \arg \max _ {c \in \{1, \dots , C \}} s [ c ]. \tag {4} +$$ + +What are the traits of class $c$ ? To answer this question, one could collect images whose true and predicted classes are both class $c$ (i.e., correctly classified) and visualize the multi-head attention maps queried by $\pmb{p}_{N-1}^c$ in layer $L_N$ . + +Specifically, in layer $L_{N}$ with $R$ attention heads, the patch features $\pmb{E}_{N - 1} \in \mathbb{R}^{D \times M}$ are projected into $R$ key matrices, denoted by $\pmb{K}_{N - 1}^{r} \in \mathbb{R}^{D' \times M}$ , $r = 1, \dots, R$ . The $j$ -th column corresponds to the $j$ -th patch in $\pmb{I}$ . Meanwhile, the prompt $\pmb{p}_{N - 1}^{c}$ is projected into $R$ query vectors $\pmb{q}_{N - 1}^{c,r} \in \mathbb{R}^{D'}$ , $r = 1, \dots, R$ . Queried by $\pmb{p}_{N - 1}^{c}$ , the $r$ -th head's attention map $\alpha_{N - 1}^{c,r} \in \mathbb{R}^{M}$ is computed by: + +$$ +\boldsymbol {\alpha} _ {N - 1} ^ {c, r} = \operatorname {s o f t m a x} \left(\frac {\boldsymbol {K} _ {N - 1} ^ {r} \mathbin {\text {T}} \boldsymbol {q} _ {N - 1} ^ {c , r}}{D ^ {\prime}}\right) \in \mathbb {R} ^ {M}. \tag {5} +$$ + +Conceptually, from the $r$ -th head's perspective, the weight $\alpha_{N - 1}^{c,r}[j]$ indicates how important the $j$ -th patch is for classifying class $c$ , hence localizing traits in the image. Ideally, each head should attend to different (sets of) patches to look for multiple traits that together highlight class $c$ 's identity. By visualizing each attention map $\alpha_{N - 1}^{c,r}$ , $r = 1,\dots ,R$ + +instead of pooling them averagely, PROMPT-CAM can potentially identify up to $R$ different traits for class $c$ . + +Which traits are more discriminative? For categories that are so distinctive, like "Red-winged Blackbird," a few traits are sufficient to distinguish them from others. To automatically identify these most discriminative traits, we take a greedy approach, progressively blurring the least important attention maps until the image is misclassified. The remaining ones highlight traits that are sufficient for classification. + +Suppose class $c$ is the true class and the image is correctly classified. In each greedy step, for each of the unblurred heads indexed by $r'$ , we iteratively replace $\alpha_{N-1}^{c,r'}$ with $\frac{1}{M}\mathbf{1}$ and recalculate $s[c]$ in Equation 1, where $\mathbf{1} \in \mathbb{R}^M$ is an all-one vector. Doing so essentially blurs the $r'$ -th head for class $c$ , preventing it from focusing. The head with the highest blurred $s[c]$ is thus the least important, as blurring it degrades classification the least. See Suppl. for details. + +Why is an image wrongly classified? When $\hat{y} \neq y$ for a labeled image $(I, y)$ , one could visualize both $\{\alpha_{N-1}^{y,r}\}_{r=1}^{R}$ and $\{\alpha_{N-1}^{\hat{y},r}\}_{r=1}^{R}$ to understand why the classifier made such a prediction. For example, some traits of class $y$ may be invisible or unclear in $I$ ; the object in $I$ may possess class $\hat{y}$ 's visual traits, for example, due to light conditions. + +# 2.4. Variants and Extensions + +Other PROMPT-CAM designs. Besides injecting class-specific prompts to the first layer (i.e., PROMPT-CAM-SHALLOW) or the last (i.e., PROMPT-CAM-DEEP), we also explore their interpolation. We introduce class-specific prompts like PROMPT-CAM-SHALLOW to the $i$ -th layer and class-agnostic prompts like PROMPT-CAM-DEEP to the first $i - 1$ layers. See the Suppl. for a comparison. + +PROMPT-CAM for discovering taxonomy keys. So far, we have focused on a "flat" comparison over all the categories. In domains like biology that are full of fine-grained categories, researchers often have built hierarchical decision trees to ease manual categorization, such as taxonomy. The role of each intermediate "tree node" is to dichotomize a subset of categories into multiple groups, each possessing certain group-level characteristics (i.e., taxonomy keys). + +The simplicity of PROMPT-CAM allows us to efficiently train multiple sets of prompts, one for each intermediate tree node, potentially (re-)discovering the taxonomy keys. One just needs to relabel categories of the same group by a single label, before training. In expectation, along the path from the root to a leaf node, each of the intermediate tree nodes should look at different group-level traits on the same image of that leaf node. See Figure 9 for a preliminary result. + +# 2.5. What is PROMPT-CAM suited for? + +As our paper is titled, PROMPT-CAM is dedicated to fine-grained analysis, aiming to identify and, more importantly, + +localize traits useful for differentiating categories. This, however, does not mean that PROMPT-CAM would excel in fine-grained classification accuracy. Modern neural networks easily have millions if not billions of parameters. How a model predicts is thus still an unanswered question, at least, not fully. It is known if a model is trained mainly to chase accuracies with no constraints, it will inevitably discover "shortcuts" in the collected data that are useful for classification but not analysis [8, 11]. We thus argue: + +# To make a model suitable for fine-grained analysis, one must constrain its capacity, while knowing that doing so would unavoidably hurt its classification accuracy. + +PROMPT-CAM is designed with this mindset. Unlike conventional classifiers that employ a fully connected layer on top, PROMPT-CAM follows [31] and learns a shared vector $\boldsymbol{w}$ in Equation 1. The goal of $\boldsymbol{w}$ is NOT to capture class-specific information BUT to answer a "binary" question: Based on where a class-specific prompt attends, does the class recognize itself in the input image? + +To elucidate the difference, let us consider a simplified single-head-attention Transformer layer with no layer normalization, residual connection, MLP block, and other nonlinear operations. Let $V = \{\pmb{v}^1,\dots ,\pmb{v}^M\} \in \mathbb{R}^{D\times M}$ be the $M$ input patches' value features, $\alpha^c\in \mathbb{R}^M$ be the attention weights of class $c$ , and $\alpha^{\star}\in \mathbb{R}^{M}$ be the attention weights of the [CLS] token. Conventional models predict classes by: + +$$ +\begin{array}{l} \hat {y} = \arg \max _ {c} \boldsymbol {w} _ {c} ^ {\top} \left(\sum_ {j} \alpha^ {\star} [ j ] \times \boldsymbol {v} ^ {j}\right) \\ = \arg \max _ {c} \sum_ {j} \alpha^ {\star} [ j ] \times \left(\boldsymbol {w} _ {c} ^ {\top} \boldsymbol {v} ^ {j}\right), \tag {6} \\ \end{array} +$$ + +where $\boldsymbol{w}_c$ stores the fully connected weights for class $c$ . We argue that this formulation allows for a potential "detour," enabling the model to correctly classify an image $I$ of class $y$ even without meaningful attention weights. In essence, the model can choose to produce holistically discriminative value features from $I$ without preserving spatial resolution, such that $v^j$ aligns with $\boldsymbol{w}_y$ but $v^j = v^{j'}$ , $\forall j \neq j'$ . In this case, regardless of the specific values of $\alpha^\star$ , as long as they sum to one—as is default in the softmax formulation—the prediction remains unaffected. + +In contrast, PROMPT-CAM predicts classes by: + +$$ +\begin{array}{l} \hat {y} = \arg \max _ {c} \boldsymbol {w} ^ {\top} \left(\sum_ {j} \alpha^ {c} [ j ] \times \boldsymbol {v} ^ {j}\right) \\ = \arg \max _ {c} \sum_ {j} \alpha^ {c} [ j ] \times \left(\boldsymbol {w} ^ {\top} \boldsymbol {v} ^ {j}\right), \tag {7} \\ \end{array} +$$ + +where $\mathbf{w}$ is the shared binary classifier. (For brevity, we assume no self-attention among the prompts.) While the difference between Equation 7 and Equation 6 is subtle at + +first glance, it fundamentally changes the model's behavior. In essence, it becomes less effective to store class discriminative information in the channels of $\pmb{v}^j$ , because there is no $\pmb{w}_c$ to align with. Moreover, the model can no longer produce holistic features with no spatial resolution; otherwise, it cannot distinguish among classes since all of their scores $s[c]$ will be exactly the same, no matter what $\alpha^c$ is. + +In response, the model must be equipped with two capabilities to minimize the cross-entropy error: + +- Generate localized features $\mathbf{v}^j$ that highlight discriminative patches (e.g., the red spot on the wing) of an image. +- Generate distinctive attention weights $\alpha^c$ across classes, each focusing on traits frequently seen in class $c$ . + +These properties are what fine-grained analysis needs. + +In sum, PROMPT-CAM discourages patch features from encoding class-discriminative holistic information (e.g., the whole object shapes or mysterious long-distance pixel correlations), even if such information can be "beneficial" to a conventional classifier. To this end, PROMPT-CAM needs to distill localized, trait-specific information from the pretrained ViT's patch features, which is achieved through the injected class-agnostic prompts in PROMPT-CAM-DEEP. + +# 3. Experiments + +# 3.1. Experimental Setup + +Dataset. We comprehensively evaluate the performance of PROMPT-CAM on 13 diverse fine-grained image classification datasets across three domains: (1) animal-based: CUB-200-2011 (CUB) [45], Birds-525 (Bird) [33], Stanford Dogs (Dog) [15], Oxford Pet (Pet) [30], iNaturalist-2021-Moths (Moth) [43], Fish Vista (Fish) [24], Rare Species (RareS.) [41] and Insects-2 (Insects) [49]; (2) plant and fungi-based: iNaturalist-2021-Fungi (Fungi) [43], Oxford Flowers (Flower) [28] and Medicinal Leaf (MedLeaf) [36]; (3) object-based: Stanford Cars (Car) [16] and Food 101 (Food) [2]. We provide details about data processing and statistics in Suppl. + +Model. We consider three pre-trained ViT backbones, DINO [4], DINOv2 [29], and BioCLIP [38] across different scales including ViT-B (the main one we use) and ViTS. The backbones are kept completely frozen when applying PROMPT-CAM. We mainly used DINO, unless stated otherwise. More details can be found in Suppl. + +Baseline Methods. We compared PROMPT-CAM with explainable methods like Grad-CAM [37], Layer-CAM [13] and Eigen-CAM [25] as well as with interpretable methods like ProtoPFormer [51], TesNet [47], ProtoConcepts [21] and INTR [31]. More details are in Suppl. + +Table 1. Faithfulness evaluation based on insertion and deletion scores. A higher insertion score and a lower deletion score indicate better results. The results are obtained from the validation images of CUB using the DINO backbone. + +
MethodInsertion↑Deletion↓
Grad-CAM [37]0.520.17
Layer-CAM[13]0.540.13
Eigen-CAM [25]0.560.22
Attention roll-out [14]0.550.27
PROMPT-CAM0.610.09
+ +Table 2. Accuracy (%) comparison using the DINO backbone. + +
BirdCUBDogPet
Linear Probing99.278.682.492.4
PROMPT-CAM98.873.281.191.3
+ +# 3.2. Experiment Results + +Is PROMPT-CAM faithful? We first investigate whether PROMPT-CAM highlights the image regions that the corresponding classifier focuses on when making predictions. We use PROMPT-CAM to rank pixels based on the aggregated attention maps over the top heads. We then employ the insertion and deletion metrics [32], manipulating highly ranked pixels to measure confidence increase and drop. + +For comparison, we consider post-hoc explainable methods like Grad-CAM [37], Eigen-CAM [25], Layer-CAM [13], and attention roll-out [14], based on the same ViT backbone with Linear Probing. As summarized in Table 1, PROMPT-CAM yields higher insertion scores and lower deletion scores, indicating a stronger focus on discriminative image traits and highlighting PROMPT-CAM's enhanced interpretability over standard post-hoc algorithms. + +PROMPT-CAM excels in trait identification (human assessment). We then conduct a quantitative human study to evaluate trait identification quality for PROMPT-CAM, TesNet [47], and ProtoConcepts [21]. Participants with no prior knowledge about the algorithms were instructed to compare the expert-identified traits (in text, such as orange belly) and the top heatmaps generated by each method. If an expert-identified trait is seen in the heatmaps, it is considered identified by the algorithm. On average, participants recognized $60.49\%$ of traits for PROMPT-CAM, significantly outperforming TesNet and ProtoConcepts whose recognition rates are $39.14\%$ and $30.39\%$ , respectively. The results highlight PROMPT-CAM's superiority in emphasizing and conveying relevant traits effectively. More details are in Suppl. + +Classification accuracy comparison. We observe that PROMPT-CAM shows a slight accuracy drop compared to Linear Probing (see Table 2). However, the images misclassified by PROMPT-CAM but correctly classified by Linear Probing align with our design philosophy: PROMPT-CAM classifies images based on the presence of class-specific, lo + +![](images/b164b82b6fff0e27a3bed5ae19facd5ce1f47cfed2a62059d3232c4dd26e890f.jpg) +Figure 4. Visualization of PROMPT-CAM on different datasets. We show the top four attention maps (from left to right) per correctly classified test example triggered by the ground-truth classes. + +![](images/e40450824f803a72e1bba42c8365db1b958698d2e4aaada45c4b6aeedfae0897.jpg) +Figure 5. Images misclassified by PROMPT-CAM but correctly classified by Linear Probing. Species-specific traits—such as the red breast of "Red-breasted Grosbeak"—are barely visible in misclassified images while Linear Probing uses global features such as body shapes, poses, and backgrounds for correct predictions. + +calized traits and would fail if they are invisible. As shown in Figure 5, discriminative traits—such as the red breast of the Red-breasted Grosbeak—are barely visible in images misclassified by PROMPT-CAM due to occlusion, unusual poses, or lighting conditions. Linear Probing correctly classifies them by leveraging global information such as body shapes and backgrounds. Please see more analysis in Suppl. + +Comparison to interpretable models. We conduct a qualitative analysis to compare PROMPT-CAM with other interpretable methods—ProtoPFormer, INTR, TesNet, and ProtoConcepts. Figure 6 shows the top-ranked attention maps or prototypes generated by each method. PROMPT-CAM can capture a more extensive range of distinct, fine-grained traits, in contrast to other methods that often focus on a narrower or repetitive set of attributes (for example, ProtoConcepts in the first three ranks of the fifth row). This highlights PROMPT-CAM's ability to identify and localize different traits that collectively define a category's identity. + +![](images/dd20db4fc1d4f17480a0371b5ac88d4b7a8ba71d5399d63d16042496a82c652e.jpg) +Figure 6. Comparison of interpretable models. Visual demonstration (heatmaps and bounding boxes) of the four most activated responses of attention heads (PROMPT-CAM and INTR) or prototypes of each method on a "Lazuli Bunting" example image. + +# 3.3. Further Analysis and Discussion + +PROMPT-CAM on different backbones. Figure 7 illustrates that PROMPT-CAM is compatible with different ViT backbones. We show the top three attention maps generated by PROMPT-CAM using different ViT backbones on an image of Scott Oriole, highlighting consistent identification of traits for species recognition, irrespective of the backbones. Please see the caption and Suppl. for details. + +PROMPT-CAM on different datasets. Figure 4 presents the top four attention maps generated by PROMPT-CAM across various datasets spanning diverse domains, includ + +![](images/0906c7178dba438a5dc859c08fcb5a90a122cfa9fdfcd4282bd4f95f5b708ae5.jpg) +Figure 7. PROMPT-CAM on different backbones. Here we show the top attention maps for PROMPT-CAM on (a) DINO, (b) DINOv2, and (c) BioCLIP backbone. All three sets of attention heads point to consistent key traits of the species "Scott Oriole"—yellow belly, black head, and black chest. + +![](images/a29c3242880362df17324e7e575acc58a6b0a3063d5dc5e62d7bad9e0f60d532.jpg) +Figure 8. Trait manipulation. The top row shows attention maps for a correctly classified "Red-winged Blackbird" image. In the second row, the red spot on the bird's wings was removed, and PROMPT-CAM subsequently classified it as a "Boat-tailed Grackle," as depicted in the reference column. + +ing animals, plants, and objects. PROMPT-CAM effectively captures the most important traits in each case to accurately identify species, demonstrating its remarkable generalizability and wide applicability. + +PROMPT-CAM can detect biologically meaningful traits. As shown in Figure 4, PROMPT-CAM consistently identifies traits from images of the same species (e.g., the red breast and white belly for Rose-breasted Grosbeak). This is further demonstrated in Figure 1 (d), where we progressively mask attention heads (detailed in subsection 2.3) until the model can no longer generate high-confidence predictions for correctly classifying images of Scott Oriole. The remaining heads 1 and 11 highlight the essential traits, i.e., the black head and yellow belly. PROMPT-CAM also enables identifying common traits between species. This is achieved by visualizing the image of one class (e.g., Scott Oriole) using other classes' prompts (e.g., Brewer Blackbird or Baltimore Oriole). As shown in Figure 1 (c), Brewer Blackbird shares the head and neck color with Scott Oriole. These results demonstrate PROMPT-CAM ability to recognize species in a biologically meaningful way. + +PROMPT-CAM can identify and interpret trait manipulation. We conduct a counterfactual-style analysis to investigate whether PROMPT-CAM truly relies on the identified traits for making predictions. For instance, to correctly classify the Red-winged Blackbird, it highlights the red-wing + +![](images/09e3cb314af842ade141bb347fe8f0a42ef6581a27f8f67c84335d70c80930e1.jpg) +Figure 9. PROMPT-CAM can detect taxonomically meaningful traits. Give an image of the species "Amophiprion Clarkii," PROMPT-CAM highlights the pelvic fin and double stripe to distinguish it from "Amophiprion Melanopus" at the species level. When it goes to the genus level, PROMPT-CAM looks at the pattern in the body and tail to classify the image as the "Amophiprion" genus. As we go up, fishes at the family level become visually dissimilar. PROMPT-CAM only needs to look at the tail and pelvic fin to classify the image as the "Pomacentridae" family. + +patch (the first row of Figure 8), consistent with the field guide provided by the Cornell Lab of Ornithology. When we remove this red spot from the image to resemble a Boat-tailed Grackle, the model no longer highlights the original position of the red patch. As such, it does not predict the image as a Red-winged Blackbird but a Boat-tailed Grackle (the second row of Figure 8). This shows PROMPT-CAM's sensitivity to trait differences, showcasing its interpretability in fine-grained recognition. + +PROMPT-CAM can detect taxonomically meaningful traits. We train PROMPT-CAM based on a hierarchical framework, considering four levels of taxonomic hierarchy: Order $\rightarrow$ Family $\rightarrow$ Genus $\rightarrow$ Species of Fish Dataset. In this setup, PROMPT-CAM progressively shifts its focus from coarse-grained traits at the Family level to fine-grained traits at the Species level to distinguish categories (shown in Figure 9). This progression suggests PROMPT-CAM's potential to automatically identify and localize taxonomy keys to aid in biological and ecological research domains. We provide more details in Suppl. + +# 4. Conclusion + +We present Prompt Class Attention Map (PROMPT-CAM), a simple yet effective interpretable approach that leverages pre-trained ViTs to identify and localize discriminative traits for fine-grained classification. PROMPT-CAM is easy to implement and train. Extensive empirical studies highlight both the strong performance of PROMPT-CAM and the promise of repurposing standard models for interpretability. + +# Acknowledgment + +This research is supported in part by grants from the National Science Foundation (OAC-2118240, HDR Institute:Imageomics). 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Illustration of PROMPT-CAM. By learning class-specific prompts for a pre-trained Vision Transformer (ViT), PROMPT-CAM enables multiple functionalities. (a) PROMPT-CAM achieves fine-grained image classification using the output logits from the class-specific prompts. (b) PROMPT-CAM enables trait localization by visualizing the multi-head attention maps queried by the true-class prompt. (c) PROMPT-CAM identifies common traits shared between species by visualizing the attention maps queried by another-class prompt. (d) PROMPT-CAM can identify the most discriminative traits per species (e.g., distinctive yellow chest and black neck for \"Scott Oriole\") by systematically masking out the least important attention heads. See subsection 2.3 for details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 498, + 200, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 498, + 200, + 510 + ], + "spans": [ + { + "bbox": [ + 151, + 498, + 200, + 510 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 534, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 534, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 534, + 298, + 714 + ], + "type": "text", + "content": "We present a simple approach to make pre-trained Vision Transformers (ViTs) interpretable for fine-grained analysis, aiming to identify and localize the traits that distinguish visually similar categories, such as bird species. Pre-trained ViTs, such as DINO, have demonstrated remarkable capabilities in extracting localized, discriminative features. However, saliency maps like Grad-CAM often fail to identify these traits, producing blurred, coarse heatmaps that highlight entire objects instead. We propose a novel approach, Prompt Class Attention Map (PROMPT-CAM), to address this limitation. PROMPT-CAM learns class-specific prompts for a pre-trained ViT and uses the corresponding outputs for classification. To correctly classify an image, the true-class prompt must attend to unique image patches not present in other classes' images (i.e., traits). As" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 499, + 556, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 499, + 556, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 499, + 556, + 643 + ], + "type": "text", + "content": "a result, the true class's multi-head attention maps reveal traits and their locations. Implementation-wise, PROMPT-CAM is almost a \"free lunch,\" requiring only a modification to the prediction head of Visual Prompt Tuning (VPT). This makes PROMPT-CAM easy to train and apply, in stark contrast to other interpretable methods that require designing specific models and training processes. Extensive empirical studies on a dozen datasets from various domains (e.g., birds, fishes, insects, fungi, flowers, food, and cars) validate the superior interpretation capability of PROMPT-CAM. The source code and demo are available at https://github.com/Imageomics/Prompt_CAM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "spans": [ + { + "bbox": [ + 314, + 668, + 395, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Vision Transformers (ViT) [9] pre-trained on huge datasets have greatly improved vision recognition, even for fine" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4375" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "grained objects [10, 40, 48, 54]. DINO [4] and DINOv2 [29] further showed remarkable abilities to extract features that are localized and informative, precisely representing the corresponding coordinates in the input image. These advancements open up the possibility of using pre-trained ViTs to discover \"traits\" that highlight each category's identity and distinguish it from other visually close ones." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 157, + 294, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 157, + 294, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 157, + 294, + 300 + ], + "type": "text", + "content": "One popular approach to this is saliency maps, for example, Class Activation Map (CAM) [13, 25, 37, 52]. After extracting the feature maps from an image, CAM highlights the spatial grids whose feature vectors align with the target class's fully connected weight. While easy to implement and efficient, the reported CAM saliency on ViTs is often far from expectation. It frequently locates the whole object with a blurred, coarse heatmap, instead of focusing on subtle traits that tell visually similar objects (e.g., birds) apart. One may argue that CAM was not originally developed for ViTs, but even with dedicated variants like attention rollout [1, 5, 14], the issue is only mildly attenuated." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 300, + 294, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 294, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 294, + 444 + ], + "type": "text", + "content": "What if we look at the attention maps? ViTs rely on self-attention to relate image patches; the [CLS] token aggregates image features by attending to informative patches. As shown in [7, 27, 39], the attention maps of the [CLS] token do highlight local regions inside the object. However, these regions are not \"class-specific.\" Instead, they often focus on the same object regions across different categories, such as body parts like heads, wings, and tails of bird species. While these are where traits usually reside, they are not traits. For example, the distinction between \"Red-winged Blackbird\" and other bird species is the red spot on the wing, having little to do with other body parts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 453, + 293, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 453, + 293, + 489 + ], + "spans": [ + { + "bbox": [ + 59, + 453, + 293, + 489 + ], + "type": "text", + "content": "How can we leverage pre-trained ViTs, particularly their localized and informative patch features, to identify traits that are so special for each category?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 498, + 294, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 294, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 294, + 594 + ], + "type": "text", + "content": "Our proposal is to prompt ViTs with learnable \"class-specific\" tokens, one for each class, inspired by [17, 20, 31, 50]. These \"class-specific\" tokens, once inputted into ViTs, attend to image patches via self-attention, similar to the [CLS] token. However, unlike the [CLS] token, which is \"class-agnostic,\" these \"class-specific\" tokens can attend to the same image differently, with the potential to highlight regions specific to the corresponding classes, i.e., traits." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "We implement our approach, named Prompt Class Attention Map (PROMPT-CAM), as follows. Given a pretrained ViT and a fine-grained classification dataset with " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " classes, we add " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " learnable tokens as additional inputs alongside the input image. To make these tokens \"class-specific,\" we collect their corresponding output vectors after the final Transformer layer and perform inner products with a shared vector (also learnable) to obtain " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " \"class-specific\" scores, following [31]. One may interpret each class-specific score as how clearly the corresponding class's" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "traits are visible in the input image. Intuitively, the input image's ground-truth class should possess the highest score, and we encourage this by minimizing a cross-entropy loss, treating the scores as logits. We keep the whole pre-trained ViT frozen and only optimize the " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " tokens and the shared scoring vector. See section 2 for details and variants." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "text", + "content": "For interpretation during inference, we input the image and the " + }, + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "text", + "content": " tokens simultaneously to the ViT to obtain the " + }, + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 147, + 553, + 314 + ], + "type": "text", + "content": " scores. One can then select a specific class (e.g., the highest-score class) and visualize its multi-head attention maps over the image patches. See Figure 1 for an illustration and section 2 for how to rank these maps to highlight the most discriminative traits. When the highest-score class is the ground-truth class, the attention maps reveal its traits. Otherwise, comparing the attention maps of the highest-score class with those of the ground-truth class helps explain why the image is misclassified. Possible reasons include the object being partially occluded or in an unusual pose, making its traits invisible, or the appearance being too similar to a wrong class, possibly due to lighting conditions (Figure 5)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 316, + 553, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 553, + 579 + ], + "type": "text", + "content": "PROMPT-CAM is fairly easy to implement and train. It requires no change to pre-trained ViTs and no specially designed loss function or training strategy—just the standard cross-entropy loss and SGD. Indeed, building upon Visual Prompt Tuning (VPT) [12], one merely needs to adjust a few lines of code and can enjoy fine-grained interpretation. This simplicity sharply contrasts other interpretable methods like ProtoPNet [6] and ProtoTree [26]. Compared to INterpretable TRansformer (INTR) [31], which also featured simplicity, PROMPT-CAM has three notable advantages. First, PROMPT-CAM is encoder-only and can potentially utilize any ViT encoder. In contrast, INTR is built upon an encoder-decoder model pre-trained on object detection datasets. As a result, PROMPT-CAM can more easily leverage up-to-date pre-trained models. Second, PROMPT-CAM can be trained much faster—only the prompts and the shared vector need to be learned. In contrast, INTR typically requires full fine-tuning. Third, PROMPT-CAM produces cleaner and sharper attention maps than INTR, which we attribute to the use of state-of-the-art ViTs like DINO [4] or DINOv2 [29]. Taken together, we view PROMPT-CAM as a simpler yet more powerful interpretable Transformer." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "type": "text", + "content": "We validate PROMPT-CAM on over a dozen datasets: CUB-200-2011 [45], Birds-525 [33], Oxford Pet [30], Stanford Dogs [15], Stanford Cars [16], iNaturalist-2021-Moths [43], Fish Vista [24], Rare Species [41], Insects-2 [49], iNaturalist-2021-Fungi [43], Oxford Flowers [28], Medicinal Leaf [36], Stanford Cars [16], and Food 101 [2]. PROMPT-CAM can identify different traits of a category through multi-head attention and consistently localize them in images. To our knowledge, PROMPT-CAM is the only explainable or interpretable method for vision that has been evaluated on such a broad range of domains. We further" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4376" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 173, + 155 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 173, + 155 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 173, + 155 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 173, + 155 + ], + "type": "image", + "image_path": "87245fe056e18b62979132a84efea39d703a805f89ff5a55722d3889d0798548.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 105, + 159, + 130, + 169 + ], + "lines": [ + { + "bbox": [ + 105, + 159, + 130, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 130, + 169 + ], + "type": "text", + "content": "(a) VPT" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 182, + 70, + 290, + 156 + ], + "blocks": [ + { + "bbox": [ + 182, + 70, + 290, + 156 + ], + "lines": [ + { + "bbox": [ + 182, + 70, + 290, + 156 + ], + "spans": [ + { + "bbox": [ + 182, + 70, + 290, + 156 + ], + "type": "image", + "image_path": "b50a3236717178e5f04ec850e74aa8bc1508831d6303129af91b6c6c2b621d6f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 209, + 159, + 263, + 168 + ], + "lines": [ + { + "bbox": [ + 209, + 159, + 263, + 168 + ], + "spans": [ + { + "bbox": [ + 209, + 159, + 263, + 168 + ], + "type": "text", + "content": "(b) PROMPT-CAM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 173, + 295, + 229 + ], + "lines": [ + { + "bbox": [ + 55, + 173, + 295, + 229 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 295, + 229 + ], + "type": "text", + "content": "Figure 2. PROMPT-CAM vs. Visual Prompt Tuning (VPT). (a) VPT [12] adds the prediction head on top of the [CLS] token's output, a default design to use ViTs for classification. (b) PROMPT-CAM adds the prediction head on top of the injected prompts' outputs, making them class-specific to identify and localize traits." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 247, + 295, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 295, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 295, + 270 + ], + "type": "text", + "content": "show PROMPT-CAM's extendability by applying it to discovering taxonomy keys. Our contributions are two-fold." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 275, + 295, + 360 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 55, + 275, + 295, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 275, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 295, + 323 + ], + "type": "text", + "content": "- We present PROMPT-CAM, an easily implementable, trainable, and reproducible interpretable method that leverages the representations of pre-trained ViTs to identify and localize traits for fine-grained analysis." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 323, + 295, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 323, + 295, + 360 + ], + "spans": [ + { + "bbox": [ + 56, + 323, + 295, + 360 + ], + "type": "text", + "content": "- We conduct extensive experiments on more than a dozen datasets to validate PROMPT-CAM's interpretation quality, wide applicability, and extendability." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 366, + 295, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 534 + ], + "type": "text", + "content": "Comparison to closely related work. Besides INTR [31], our class-specific attentions are inspired by two other works in different contexts, MCTformer for weakly supervised semantic segmentation [50] and Query2Label for multi-label classification [20]. Both of them learned class-specific tokens but aimed to localize visually distinct common objects (e.g., people, horses, and flights). In contrast, we focus on fine-grained analysis: supervised by class labels of visually similar objects (e.g., bird species), we aim to localize their traits (e.g., red spots on wings). One particular feature of PROMPT-CAM is its simplicity, in both implementation and compatibility with pre-trained backbones, without extra modules, loss terms, and changes to the backbones, making it an almost plug-and-pay approach to interpretation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 536, + 295, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 295, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 295, + 562 + ], + "type": "text", + "content": "Due to space constraints, we provide a detailed related work section in the Supplementary Material (Suppl.)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 582, + 122, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 122, + 596 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 122, + 596 + ], + "type": "text", + "content": "2. Approach" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 605, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 297, + 714 + ], + "type": "text", + "content": "We propose Prompt Class Attention Map (PROMPT-CAM) to leverage pre-trained Vision Transformers (ViTs) [9] for fine-grained analysis. The goal is to identify and localize traits that highlight an object category's identity. PROMPT-CAM adds learnable class-specific tokens to prompt ViTs, producing class-specific attention maps that reveal traits. The overall framework is presented in Figure 3. We deliberately follow the notation and naming of Visual Prompt Tuning (VPT) [12] for ease of reference." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "type": "text", + "content": "2.1. Preliminaries" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 89, + 554, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 554, + 137 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 554, + 137 + ], + "type": "text", + "content": "A ViT typically contains " + }, + { + "bbox": [ + 313, + 89, + 554, + 137 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 89, + 554, + 137 + ], + "type": "text", + "content": " Transformer layers [44]. Each consists of a Multi-head Self-Attention (MSA) block, a Multi-Layer Perceptron (MLP) block, and several other operations like layer normalization and residual connections." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": "The input image " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": " to ViTs is first divided into " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": " fixed-sized patches. Each is then projected into a " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": "-dimensional feature space with positional encoding, denoted by " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "e_0^j" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "1 \\leq j \\leq M" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "inline_equation", + "content": "E_0 = [e_0^1, \\dots, e_0^M] \\in \\mathbb{R}^{D \\times M}" + }, + { + "bbox": [ + 313, + 137, + 554, + 196 + ], + "type": "text", + "content": " to denote their column-wise concatenation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 196, + 554, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 196, + 554, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 196, + 554, + 220 + ], + "type": "text", + "content": "Together with a learnable [CLS] token " + }, + { + "bbox": [ + 313, + 196, + 554, + 220 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0 \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 313, + 196, + 554, + 220 + ], + "type": "text", + "content": ", the whole ViT is formulated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 339, + 229, + 529, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 229, + 529, + 243 + ], + "spans": [ + { + "bbox": [ + 339, + 229, + 529, + 243 + ], + "type": "interline_equation", + "content": "[ \\pmb {E} _ {i}, \\pmb {x} _ {i} ] = L _ {i} ([ \\pmb {E} _ {i - 1}, \\pmb {x} _ {i - 1} ]), \\quad i = 1, \\dots , N,", + "image_path": "0d8a903821e8a88b748f46a7d7fe0319413d429dd6e2a4c03aa4bcffa85fbcc9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "text", + "content": "-th Transformer layer. The final " + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_N" + }, + { + "bbox": [ + 313, + 251, + 554, + 287 + ], + "type": "text", + "content": " is typically used to represent the whole image and fed into a prediction head for classification." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 294, + 545, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 294, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 545, + 306 + ], + "type": "text", + "content": "2.2. Prompt Class Attention Map (PROMPT-CAM)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "text", + "content": "Given a pre-trained ViT and a downstream classification dataset with " + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "text", + "content": " classes, we introduce a set of " + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "text", + "content": " learnable " + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 312, + 554, + 384 + ], + "type": "text", + "content": "-dimensional vectors to prompt the ViT. These vectors are learned to be \"class-specific\" by minimizing the cross-entropy loss, during which the ViT backbone is frozen. In the following, we first introduce the baseline version." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": "PROMPT-CAM-SHALLOW. The " + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": " class-specific prompts are injected into the first Transformer layer " + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": ". We denote each prompt by " + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "inline_equation", + "content": "\\pmb{p}^{c} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "inline_equation", + "content": "1 \\leq c \\leq C" + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": ", and use " + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "inline_equation", + "content": "\\pmb{P} = [\\pmb{p}^{1}, \\dots, \\pmb{p}^{C}] \\in \\mathbb{R}^{D \\times C}" + }, + { + "bbox": [ + 313, + 386, + 554, + 447 + ], + "type": "text", + "content": " to indicate their column-wise concatenation. The prompted ViT is:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 454, + 550, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 454, + 550, + 483 + ], + "spans": [ + { + "bbox": [ + 318, + 454, + 550, + 483 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} [ \\boldsymbol {Z} _ {1}, \\boldsymbol {E} _ {1}, \\boldsymbol {x} _ {1} ] = L _ {1} ([ \\boldsymbol {P}, \\boldsymbol {E} _ {0}, \\boldsymbol {x} _ {0} ]) \\\\ [ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {Z} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 2, \\dots , N, \\\\ \\end{array}", + "image_path": "741fe1c4ba6968985cd73c4d53e99c87b87470b4469e7ee578360cc020f133b4.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "Z_{i}" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": " represents the features corresponding to " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": ", computed by the " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": "-th Transformer layer " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": ". The order among " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "x_{0}, E_{0}" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": " does not matter since the positional encoding of patch locations has already been inserted into " + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "inline_equation", + "content": "E_{0}" + }, + { + "bbox": [ + 313, + 491, + 554, + 539 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "text", + "content": "To make " + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "inline_equation", + "content": "\\pmb{P} = [\\pmb{p}^{1},\\dots ,\\pmb{p}^{C}]" + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "text", + "content": " class-specific, we employ a cross-entropy loss on top of the corresponding ViT's output, i.e., " + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "inline_equation", + "content": "Z_{N} = [z_{N}^{1},\\dots ,z_{N}^{C}]" + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "text", + "content": ". Given a labeled training example " + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "inline_equation", + "content": "(\\pmb {I},y\\in \\{1,\\dots ,C\\})" + }, + { + "bbox": [ + 313, + 539, + 554, + 588 + ], + "type": "text", + "content": ", we calculate the logit of each class by:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 374, + 606, + 553, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 606, + 553, + 622 + ], + "spans": [ + { + "bbox": [ + 374, + 606, + 553, + 622 + ], + "type": "interline_equation", + "content": "s [ c ] = \\boldsymbol {w} ^ {\\top} \\boldsymbol {z} _ {N} ^ {c}, \\quad 1 \\leq c \\leq C, \\tag {1}", + "image_path": "4a0142add0c5be7a8d0e4f320d2bdf207cfcdcb8984007575ee5fe0bbb8952f6.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "text", + "content": " is a learnable vector. " + }, + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "inline_equation", + "content": "\\pmb{P}" + }, + { + "bbox": [ + 313, + 629, + 554, + 654 + ], + "type": "text", + "content": " can then be updated by minimizing the loss:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 382, + 662, + 553, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 662, + 553, + 694 + ], + "spans": [ + { + "bbox": [ + 382, + 662, + 553, + 694 + ], + "type": "interline_equation", + "content": "- \\log \\left(\\frac {\\exp (s [ y ])}{\\sum_ {c} \\exp (s [ c ])}\\right). \\tag {2}", + "image_path": "2dd99a1512dbbde0a1a27679842a18dc5a5928d6a97ab279337706eebb51832a.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "content": "PROMPT-CAM-DEEP. While straightforward, PROMPT" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4377" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 83, + 531, + 252 + ], + "blocks": [ + { + "bbox": [ + 77, + 83, + 531, + 252 + ], + "lines": [ + { + "bbox": [ + 77, + 83, + 531, + 252 + ], + "spans": [ + { + "bbox": [ + 77, + 83, + 531, + 252 + ], + "type": "image", + "image_path": "541dd0ed751b12e4958f3bfd538e0a0903b6d619209337852b520b5ad329d72a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "lines": [ + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": "Figure 3. Overview of Prompt Class Attention Map (PROMPT-CAM). We explore two variants, given a pre-trained ViT with " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " layers and a downstream task with " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " classes: (a) PROMPT-CAM-DEEP: insert " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " learnable \"class-specific\" tokens to the last layer's input and " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " learnable \"class-agnostic\" tokens to each of the other " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "N - 1" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " layers' input; (b) PROMPT-CAM-SHALLOW: insert " + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 255, + 555, + 301 + ], + "type": "text", + "content": " learnable \"class-specific\" tokens to the first layer's input. During training, only the prompts and the prediction head are updated; the whole ViT is frozen." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "text", + "content": "CAM-SHALLOW has two potential drawbacks. First, the class-specific prompts attend to every layer's patch features, i.e., " + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "inline_equation", + "content": "E_{i}" + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "inline_equation", + "content": "i = 0, \\dots, N - 1" + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "text", + "content": ". However, features of the early layers are often not informative enough but noisy for differentiating classes. Second, the prompts " + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "inline_equation", + "content": "p^{1}, \\dots, p^{C}" + }, + { + "bbox": [ + 54, + 315, + 296, + 434 + ], + "type": "text", + "content": " have a \"double duty.\" Individually, each needs to highlight class-specific traits. Collectively, they need to adapt pre-trained ViTs to downstream tasks, which is the original purpose of VPT [12]. In our case, the downstream task is a new usage of ViTs on a specific fine-grained dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "text", + "content": "To address these issues, we resort to the VPT-Deep's design while deliberately decoupling injected prompts' roles. VPT-Deep adds learnable prompts to every layer's input. Denote by " + }, + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{i - 1} = [\\pmb{p}_{i - 1}^{1},\\dots ,\\pmb{p}_{i - 1}^{C}]" + }, + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "text", + "content": " the prompts to the " + }, + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 435, + 296, + 495 + ], + "type": "text", + "content": "-th Transformer layer, the deep-prompted ViT is formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 514, + 295, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 514, + 295, + 538 + ], + "spans": [ + { + "bbox": [ + 61, + 514, + 295, + 538 + ], + "type": "interline_equation", + "content": "[ \\boldsymbol {Z} _ {i}, \\boldsymbol {E} _ {i}, \\boldsymbol {x} _ {i} ] = L _ {i} ([ \\boldsymbol {P} _ {i - 1}, \\boldsymbol {E} _ {i - 1}, \\boldsymbol {x} _ {i - 1} ]), \\quad i = 1, \\dots , N, \\tag {3}", + "image_path": "e698f8de7f9bbd64f5167585b10f3a2d6e05e79959794599e5fed3d2d67d0911.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "text", + "content": "It is worth noting that the features " + }, + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "inline_equation", + "content": "Z_{i}" + }, + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "text", + "content": " after the " + }, + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 545, + 295, + 570 + ], + "type": "text", + "content": "-th layer are not inputted to the next layer, and are typically disregarded." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": "In PROMPT-CAM-DEEP, we repurpose " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "Z_{N}" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " for classification, following Equation 1. As such, after minimizing the cross entropy loss in Equation 2, the corresponding prompts " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "P_{N - 1} = [\\pmb{p}_{N - 1}^{1},\\dots ,\\pmb{p}_{N - 1}^{C}]" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " will be class-specific. Prompts to the other layers' inputs, i.e., " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "P_{i} = [p_{i}^{1},\\dots ,p_{i}^{C}]" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "i = 0,\\dots ,N - 2" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": ", remain class-agnostic, because " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " does not particularly serve for the " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": "-th class, unlike " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "p_{N - 1}^{c}" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": ". In other words, PROMPT-CAM-DEEP learns both class-specific prompts for trait localization and class-agnostic prompts for adaptation. The class-specific prompts " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "P_{N - 1}" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " only attend to the patch features " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "E_{N - 1}" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": " inputted to the last Transformer layer " + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "inline_equation", + "content": "L_{N}" + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": ", further addressing the other issue in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 316, + 430, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 316, + 430, + 326 + ], + "spans": [ + { + "bbox": [ + 314, + 316, + 430, + 326 + ], + "type": "text", + "content": "PROMPT-CAM-SHALLOW." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 325, + 327, + 539, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 327, + 539, + 340 + ], + "spans": [ + { + "bbox": [ + 325, + 327, + 539, + 340 + ], + "type": "text", + "content": "In the following, we focus on PROMPT-CAM-DEEP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 349, + 507, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 349, + 507, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 349, + 507, + 361 + ], + "type": "text", + "content": "2.3. Trait Identification and Localization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": "During inference, given an image " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": ", PROMPT-CAM-DEEP extracts patch embeddings " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\pmb{E}_0 = [e_0^1,\\dots ,e_0^M ]" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": " and follows Equation 3 to obtain " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "Z_{N}" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": " and Equation 1 to obtain " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "s[c]" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "c\\in \\{1,\\dots ,C\\}" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": ". The predicted label " + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 313, + 367, + 555, + 415 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 426, + 555, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 426, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 375, + 426, + 555, + 441 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\arg \\max _ {c \\in \\{1, \\dots , C \\}} s [ c ]. \\tag {4}", + "image_path": "6bc9be81d0c0092c2af94872c07a420d4ef46330633ae0087cc5bbd31affdb20.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "content": "What are the traits of class " + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "content": "? To answer this question, one could collect images whose true and predicted classes are both class " + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "content": " (i.e., correctly classified) and visualize the multi-head attention maps queried by " + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{N-1}^c" + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "content": " in layer " + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "inline_equation", + "content": "L_N" + }, + { + "bbox": [ + 313, + 453, + 554, + 502 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": "Specifically, in layer " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "L_{N}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " attention heads, the patch features " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{E}_{N - 1} \\in \\mathbb{R}^{D \\times M}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " are projected into " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " key matrices, denoted by " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{K}_{N - 1}^{r} \\in \\mathbb{R}^{D' \\times M}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "r = 1, \\dots, R" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": "-th column corresponds to the " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": "-th patch in " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ". Meanwhile, the prompt " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{N - 1}^{c}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " is projected into " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " query vectors " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{q}_{N - 1}^{c,r} \\in \\mathbb{R}^{D'}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "r = 1, \\dots, R" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ". Queried by " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{N - 1}^{c}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": "-th head's attention map " + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\alpha_{N - 1}^{c,r} \\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 313, + 502, + 554, + 590 + ], + "type": "text", + "content": " is computed by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 600, + 555, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 600, + 555, + 633 + ], + "spans": [ + { + "bbox": [ + 342, + 600, + 555, + 633 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\alpha} _ {N - 1} ^ {c, r} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {K} _ {N - 1} ^ {r} \\mathbin {\\text {T}} \\boldsymbol {q} _ {N - 1} ^ {c , r}}{D ^ {\\prime}}\\right) \\in \\mathbb {R} ^ {M}. \\tag {5}", + "image_path": "72fe9196f206a7b2d13bf8beada34a4d12f1fbdcb9f6b851de9447fc2ffaaef1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "Conceptually, from the " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "-th head's perspective, the weight " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{N - 1}^{c,r}[j]" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": " indicates how important the " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "-th patch is for classifying class " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": ", hence localizing traits in the image. Ideally, each head should attend to different (sets of) patches to look for multiple traits that together highlight class " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "'s identity. By visualizing each attention map " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{N - 1}^{c,r}" + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "inline_equation", + "content": "r = 1,\\dots ,R" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4378" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": "instead of pooling them averagely, PROMPT-CAM can potentially identify up to " + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": " different traits for class " + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 99, + 296, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 99, + 296, + 183 + ], + "spans": [ + { + "bbox": [ + 55, + 99, + 296, + 183 + ], + "type": "text", + "content": "Which traits are more discriminative? For categories that are so distinctive, like \"Red-winged Blackbird,\" a few traits are sufficient to distinguish them from others. To automatically identify these most discriminative traits, we take a greedy approach, progressively blurring the least important attention maps until the image is misclassified. The remaining ones highlight traits that are sufficient for classification." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": "Suppose class " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " is the true class and the image is correctly classified. In each greedy step, for each of the unblurred heads indexed by " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "r'" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": ", we iteratively replace " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "\\alpha_{N-1}^{c,r'}" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "\\frac{1}{M}\\mathbf{1}" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " and recalculate " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "s[c]" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " in Equation 1, where " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{1} \\in \\mathbb{R}^M" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " is an all-one vector. Doing so essentially blurs the " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "r'" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": "-th head for class " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": ", preventing it from focusing. The head with the highest blurred " + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "inline_equation", + "content": "s[c]" + }, + { + "bbox": [ + 55, + 183, + 296, + 282 + ], + "type": "text", + "content": " is thus the least important, as blurring it degrades classification the least. See Suppl. for details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": "Why is an image wrongly classified? When " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\hat{y} \\neq y" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": " for a labeled image " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "(I, y)" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": ", one could visualize both " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\{\\alpha_{N-1}^{y,r}\\}_{r=1}^{R}" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\{\\alpha_{N-1}^{\\hat{y},r}\\}_{r=1}^{R}" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": " to understand why the classifier made such a prediction. For example, some traits of class " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": " may be invisible or unclear in " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": "; the object in " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": " may possess class " + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 55, + 285, + 296, + 360 + ], + "type": "text", + "content": "'s visual traits, for example, due to light conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 366, + 192, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 192, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 192, + 378 + ], + "type": "text", + "content": "2.4. Variants and Extensions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "content": "Other PROMPT-CAM designs. Besides injecting class-specific prompts to the first layer (i.e., PROMPT-CAM-SHALLOW) or the last (i.e., PROMPT-CAM-DEEP), we also explore their interpolation. We introduce class-specific prompts like PROMPT-CAM-SHALLOW to the " + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "content": "-th layer and class-agnostic prompts like PROMPT-CAM-DEEP to the first " + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "inline_equation", + "content": "i - 1" + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "content": " layers. See the Suppl. for a comparison." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 474, + 296, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 296, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 296, + 569 + ], + "type": "text", + "content": "PROMPT-CAM for discovering taxonomy keys. So far, we have focused on a \"flat\" comparison over all the categories. In domains like biology that are full of fine-grained categories, researchers often have built hierarchical decision trees to ease manual categorization, such as taxonomy. The role of each intermediate \"tree node\" is to dichotomize a subset of categories into multiple groups, each possessing certain group-level characteristics (i.e., taxonomy keys)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 570, + 296, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 666 + ], + "type": "text", + "content": "The simplicity of PROMPT-CAM allows us to efficiently train multiple sets of prompts, one for each intermediate tree node, potentially (re-)discovering the taxonomy keys. One just needs to relabel categories of the same group by a single label, before training. In expectation, along the path from the root to a leaf node, each of the intermediate tree nodes should look at different group-level traits on the same image of that leaf node. See Figure 9 for a preliminary result." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 672, + 233, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 233, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 233, + 684 + ], + "type": "text", + "content": "2.5. What is PROMPT-CAM suited for?" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "As our paper is titled, PROMPT-CAM is dedicated to fine-grained analysis, aiming to identify and, more importantly," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": "localize traits useful for differentiating categories. This, however, does not mean that PROMPT-CAM would excel in fine-grained classification accuracy. Modern neural networks easily have millions if not billions of parameters. How a model predicts is thus still an unanswered question, at least, not fully. It is known if a model is trained mainly to chase accuracies with no constraints, it will inevitably discover \"shortcuts\" in the collected data that are useful for classification but not analysis [8, 11]. We thus argue:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 187, + 548, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 187, + 548, + 223 + ], + "spans": [ + { + "bbox": [ + 320, + 187, + 548, + 223 + ], + "type": "text", + "content": "To make a model suitable for fine-grained analysis, one must constrain its capacity, while knowing that doing so would unavoidably hurt its classification accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "text", + "content": "PROMPT-CAM is designed with this mindset. Unlike conventional classifiers that employ a fully connected layer on top, PROMPT-CAM follows [31] and learns a shared vector " + }, + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "text", + "content": " in Equation 1. The goal of " + }, + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 313, + 229, + 554, + 313 + ], + "type": "text", + "content": " is NOT to capture class-specific information BUT to answer a \"binary\" question: Based on where a class-specific prompt attends, does the class recognize itself in the input image?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": "To elucidate the difference, let us consider a simplified single-head-attention Transformer layer with no layer normalization, residual connection, MLP block, and other nonlinear operations. Let " + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "inline_equation", + "content": "V = \\{\\pmb{v}^1,\\dots ,\\pmb{v}^M\\} \\in \\mathbb{R}^{D\\times M}" + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": " be the " + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": " input patches' value features, " + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "inline_equation", + "content": "\\alpha^c\\in \\mathbb{R}^M" + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": " be the attention weights of class " + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "inline_equation", + "content": "\\alpha^{\\star}\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 313, + 314, + 555, + 397 + ], + "type": "text", + "content": " be the attention weights of the [CLS] token. Conventional models predict classes by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 361, + 415, + 554, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 415, + 554, + 470 + ], + "spans": [ + { + "bbox": [ + 361, + 415, + 554, + 470 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} _ {c} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {\\star} [ j ] \\times \\left(\\boldsymbol {w} _ {c} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {6} \\\\ \\end{array}", + "image_path": "989b38a77e0f0517ae8b009a7c1eba458ceec9611ad3ef0b04792150d141a784.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_c" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " stores the fully connected weights for class " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": ". We argue that this formulation allows for a potential \"detour,\" enabling the model to correctly classify an image " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " even without meaningful attention weights. In essence, the model can choose to produce holistically discriminative value features from " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " without preserving spatial resolution, such that " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "v^j" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " aligns with " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_y" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": " but " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "v^j = v^{j'}" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "\\forall j \\neq j'" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": ". In this case, regardless of the specific values of " + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "inline_equation", + "content": "\\alpha^\\star" + }, + { + "bbox": [ + 313, + 476, + 554, + 596 + ], + "type": "text", + "content": ", as long as they sum to one—as is default in the softmax formulation—the prediction remains unaffected." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 597, + 518, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 597, + 518, + 609 + ], + "spans": [ + { + "bbox": [ + 326, + 597, + 518, + 609 + ], + "type": "text", + "content": "In contrast, PROMPT-CAM predicts classes by:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 361, + 615, + 554, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 615, + 554, + 670 + ], + "spans": [ + { + "bbox": [ + 361, + 615, + 554, + 670 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {y} = \\arg \\max _ {c} \\boldsymbol {w} ^ {\\top} \\left(\\sum_ {j} \\alpha^ {c} [ j ] \\times \\boldsymbol {v} ^ {j}\\right) \\\\ = \\arg \\max _ {c} \\sum_ {j} \\alpha^ {c} [ j ] \\times \\left(\\boldsymbol {w} ^ {\\top} \\boldsymbol {v} ^ {j}\\right), \\tag {7} \\\\ \\end{array}", + "image_path": "b797ab734d0345ce9d6bcf9076b94771484ec0d7c2370b9333902d126784ce77.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": " is the shared binary classifier. (For brevity, we assume no self-attention among the prompts.) While the difference between Equation 7 and Equation 6 is subtle at" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4379" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "first glance, it fundamentally changes the model's behavior. In essence, it becomes less effective to store class discriminative information in the channels of " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\pmb{v}^j" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": ", because there is no " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\pmb{w}_c" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " to align with. Moreover, the model can no longer produce holistic features with no spatial resolution; otherwise, it cannot distinguish among classes since all of their scores " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "s[c]" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " will be exactly the same, no matter what " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\alpha^c" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " is." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 159, + 295, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 159, + 295, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 295, + 185 + ], + "type": "text", + "content": "In response, the model must be equipped with two capabilities to minimize the cross-entropy error:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 55, + 190, + 295, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 295, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 295, + 213 + ], + "type": "text", + "content": "- Generate localized features " + }, + { + "bbox": [ + 55, + 190, + 295, + 213 + ], + "type": "inline_equation", + "content": "\\mathbf{v}^j" + }, + { + "bbox": [ + 55, + 190, + 295, + 213 + ], + "type": "text", + "content": " that highlight discriminative patches (e.g., the red spot on the wing) of an image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "spans": [ + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "text", + "content": "- Generate distinctive attention weights " + }, + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "inline_equation", + "content": "\\alpha^c" + }, + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "text", + "content": " across classes, each focusing on traits frequently seen in class " + }, + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 214, + 294, + 237 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 243, + 274, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 243, + 274, + 256 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 274, + 256 + ], + "type": "text", + "content": "These properties are what fine-grained analysis needs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 260, + 296, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 260, + 296, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 296, + 357 + ], + "type": "text", + "content": "In sum, PROMPT-CAM discourages patch features from encoding class-discriminative holistic information (e.g., the whole object shapes or mysterious long-distance pixel correlations), even if such information can be \"beneficial\" to a conventional classifier. To this end, PROMPT-CAM needs to distill localized, trait-specific information from the pretrained ViT's patch features, which is achieved through the injected class-agnostic prompts in PROMPT-CAM-DEEP." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "type": "text", + "content": "3. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 402, + 172, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 172, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 172, + 415 + ], + "type": "text", + "content": "3.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 423, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 296, + 567 + ], + "type": "text", + "content": "Dataset. We comprehensively evaluate the performance of PROMPT-CAM on 13 diverse fine-grained image classification datasets across three domains: (1) animal-based: CUB-200-2011 (CUB) [45], Birds-525 (Bird) [33], Stanford Dogs (Dog) [15], Oxford Pet (Pet) [30], iNaturalist-2021-Moths (Moth) [43], Fish Vista (Fish) [24], Rare Species (RareS.) [41] and Insects-2 (Insects) [49]; (2) plant and fungi-based: iNaturalist-2021-Fungi (Fungi) [43], Oxford Flowers (Flower) [28] and Medicinal Leaf (MedLeaf) [36]; (3) object-based: Stanford Cars (Car) [16] and Food 101 (Food) [2]. We provide details about data processing and statistics in Suppl." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 574, + 295, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 295, + 647 + ], + "type": "text", + "content": "Model. We consider three pre-trained ViT backbones, DINO [4], DINOv2 [29], and BioCLIP [38] across different scales including ViT-B (the main one we use) and ViTS. The backbones are kept completely frozen when applying PROMPT-CAM. We mainly used DINO, unless stated otherwise. More details can be found in Suppl." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "Baseline Methods. We compared PROMPT-CAM with explainable methods like Grad-CAM [37], Layer-CAM [13] and Eigen-CAM [25] as well as with interpretable methods like ProtoPFormer [51], TesNet [47], ProtoConcepts [21] and INTR [31]. More details are in Suppl." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 347, + 118, + 523, + 189 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 553, + 115 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 553, + 115 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 553, + 115 + ], + "type": "text", + "content": "Table 1. Faithfulness evaluation based on insertion and deletion scores. A higher insertion score and a lower deletion score indicate better results. The results are obtained from the validation images of CUB using the DINO backbone." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 347, + 118, + 523, + 189 + ], + "lines": [ + { + "bbox": [ + 347, + 118, + 523, + 189 + ], + "spans": [ + { + "bbox": [ + 347, + 118, + 523, + 189 + ], + "type": "table", + "html": "
MethodInsertion↑Deletion↓
Grad-CAM [37]0.520.17
Layer-CAM[13]0.540.13
Eigen-CAM [25]0.560.22
Attention roll-out [14]0.550.27
PROMPT-CAM0.610.09
", + "image_path": "41dcffcc56468aaa61d2007340f8b80a6c31229c057f8122139583eafb243a20.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 349, + 209, + 520, + 251 + ], + "blocks": [ + { + "bbox": [ + 321, + 197, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 321, + 197, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 321, + 197, + 547, + 207 + ], + "type": "text", + "content": "Table 2. Accuracy (%) comparison using the DINO backbone." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 349, + 209, + 520, + 251 + ], + "lines": [ + { + "bbox": [ + 349, + 209, + 520, + 251 + ], + "spans": [ + { + "bbox": [ + 349, + 209, + 520, + 251 + ], + "type": "table", + "html": "
BirdCUBDogPet
Linear Probing99.278.682.492.4
PROMPT-CAM98.873.281.191.3
", + "image_path": "5101e4ff432ab8a389284c47c23f840b2ee30cd0ce0992aedbd794a7f88f7dfc.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 262, + 429, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 262, + 429, + 275 + ], + "spans": [ + { + "bbox": [ + 314, + 262, + 429, + 275 + ], + "type": "text", + "content": "3.2. Experiment Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 284, + 553, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 284, + 553, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 553, + 368 + ], + "type": "text", + "content": "Is PROMPT-CAM faithful? We first investigate whether PROMPT-CAM highlights the image regions that the corresponding classifier focuses on when making predictions. We use PROMPT-CAM to rank pixels based on the aggregated attention maps over the top heads. We then employ the insertion and deletion metrics [32], manipulating highly ranked pixels to measure confidence increase and drop." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 369, + 554, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 554, + 465 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 554, + 465 + ], + "type": "text", + "content": "For comparison, we consider post-hoc explainable methods like Grad-CAM [37], Eigen-CAM [25], Layer-CAM [13], and attention roll-out [14], based on the same ViT backbone with Linear Probing. As summarized in Table 1, PROMPT-CAM yields higher insertion scores and lower deletion scores, indicating a stronger focus on discriminative image traits and highlighting PROMPT-CAM's enhanced interpretability over standard post-hoc algorithms." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "text", + "content": "PROMPT-CAM excels in trait identification (human assessment). We then conduct a quantitative human study to evaluate trait identification quality for PROMPT-CAM, TesNet [47], and ProtoConcepts [21]. Participants with no prior knowledge about the algorithms were instructed to compare the expert-identified traits (in text, such as orange belly) and the top heatmaps generated by each method. If an expert-identified trait is seen in the heatmaps, it is considered identified by the algorithm. On average, participants recognized " + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "inline_equation", + "content": "60.49\\%" + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "text", + "content": " of traits for PROMPT-CAM, significantly outperforming TesNet and ProtoConcepts whose recognition rates are " + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "inline_equation", + "content": "39.14\\%" + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "inline_equation", + "content": "30.39\\%" + }, + { + "bbox": [ + 313, + 469, + 554, + 637 + ], + "type": "text", + "content": ", respectively. The results highlight PROMPT-CAM's superiority in emphasizing and conveying relevant traits effectively. More details are in Suppl." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "content": "Classification accuracy comparison. We observe that PROMPT-CAM shows a slight accuracy drop compared to Linear Probing (see Table 2). However, the images misclassified by PROMPT-CAM but correctly classified by Linear Probing align with our design philosophy: PROMPT-CAM classifies images based on the presence of class-specific, lo" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4380" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 72, + 532, + 300 + ], + "blocks": [ + { + "bbox": [ + 82, + 72, + 532, + 300 + ], + "lines": [ + { + "bbox": [ + 82, + 72, + 532, + 300 + ], + "spans": [ + { + "bbox": [ + 82, + 72, + 532, + 300 + ], + "type": "image", + "image_path": "b164b82b6fff0e27a3bed5ae19facd5ce1f47cfed2a62059d3232c4dd26e890f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "lines": [ + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "type": "text", + "content": "Figure 4. Visualization of PROMPT-CAM on different datasets. We show the top four attention maps (from left to right) per correctly classified test example triggered by the ground-truth classes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 339, + 282, + 408 + ], + "blocks": [ + { + "bbox": [ + 69, + 339, + 282, + 408 + ], + "lines": [ + { + "bbox": [ + 69, + 339, + 282, + 408 + ], + "spans": [ + { + "bbox": [ + 69, + 339, + 282, + 408 + ], + "type": "image", + "image_path": "e40450824f803a72e1bba42c8365db1b958698d2e4aaada45c4b6aeedfae0897.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 414, + 296, + 468 + ], + "lines": [ + { + "bbox": [ + 55, + 414, + 296, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 414, + 296, + 468 + ], + "type": "text", + "content": "Figure 5. Images misclassified by PROMPT-CAM but correctly classified by Linear Probing. Species-specific traits—such as the red breast of \"Red-breasted Grosbeak\"—are barely visible in misclassified images while Linear Probing uses global features such as body shapes, poses, and backgrounds for correct predictions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 490, + 296, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 296, + 574 + ], + "type": "text", + "content": "calized traits and would fail if they are invisible. As shown in Figure 5, discriminative traits—such as the red breast of the Red-breasted Grosbeak—are barely visible in images misclassified by PROMPT-CAM due to occlusion, unusual poses, or lighting conditions. Linear Probing correctly classifies them by leveraging global information such as body shapes and backgrounds. Please see more analysis in Suppl." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "Comparison to interpretable models. We conduct a qualitative analysis to compare PROMPT-CAM with other interpretable methods—ProtoPFormer, INTR, TesNet, and ProtoConcepts. Figure 6 shows the top-ranked attention maps or prototypes generated by each method. PROMPT-CAM can capture a more extensive range of distinct, fine-grained traits, in contrast to other methods that often focus on a narrower or repetitive set of attributes (for example, ProtoConcepts in the first three ranks of the fifth row). This highlights PROMPT-CAM's ability to identify and localize different traits that collectively define a category's identity." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 339, + 555, + 509 + ], + "blocks": [ + { + "bbox": [ + 317, + 339, + 555, + 509 + ], + "lines": [ + { + "bbox": [ + 317, + 339, + 555, + 509 + ], + "spans": [ + { + "bbox": [ + 317, + 339, + 555, + 509 + ], + "type": "image", + "image_path": "dd20db4fc1d4f17480a0371b5ac88d4b7a8ba71d5399d63d16042496a82c652e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 512, + 555, + 557 + ], + "lines": [ + { + "bbox": [ + 313, + 512, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 555, + 557 + ], + "type": "text", + "content": "Figure 6. Comparison of interpretable models. Visual demonstration (heatmaps and bounding boxes) of the four most activated responses of attention heads (PROMPT-CAM and INTR) or prototypes of each method on a \"Lazuli Bunting\" example image." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 568, + 489, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 489, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 489, + 581 + ], + "type": "text", + "content": "3.3. Further Analysis and Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": "PROMPT-CAM on different backbones. Figure 7 illustrates that PROMPT-CAM is compatible with different ViT backbones. We show the top three attention maps generated by PROMPT-CAM using different ViT backbones on an image of Scott Oriole, highlighting consistent identification of traits for species recognition, irrespective of the backbones. Please see the caption and Suppl. for details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "PROMPT-CAM on different datasets. Figure 4 presents the top four attention maps generated by PROMPT-CAM across various datasets spanning diverse domains, includ" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4381" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 69, + 249, + 166 + ], + "blocks": [ + { + "bbox": [ + 104, + 69, + 249, + 166 + ], + "lines": [ + { + "bbox": [ + 104, + 69, + 249, + 166 + ], + "spans": [ + { + "bbox": [ + 104, + 69, + 249, + 166 + ], + "type": "image", + "image_path": "0906c7178dba438a5dc859c08fcb5a90a122cfa9fdfcd4282bd4f95f5b708ae5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 171, + 296, + 224 + ], + "lines": [ + { + "bbox": [ + 55, + 171, + 296, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 296, + 224 + ], + "type": "text", + "content": "Figure 7. PROMPT-CAM on different backbones. Here we show the top attention maps for PROMPT-CAM on (a) DINO, (b) DINOv2, and (c) BioCLIP backbone. All three sets of attention heads point to consistent key traits of the species \"Scott Oriole\"—yellow belly, black head, and black chest." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 228, + 294, + 326 + ], + "blocks": [ + { + "bbox": [ + 58, + 228, + 294, + 326 + ], + "lines": [ + { + "bbox": [ + 58, + 228, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 58, + 228, + 294, + 326 + ], + "type": "image", + "image_path": "a29c3242880362df17324e7e575acc58a6b0a3063d5dc5e62d7bad9e0f60d532.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 329, + 296, + 384 + ], + "lines": [ + { + "bbox": [ + 55, + 329, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 296, + 384 + ], + "type": "text", + "content": "Figure 8. Trait manipulation. The top row shows attention maps for a correctly classified \"Red-winged Blackbird\" image. In the second row, the red spot on the bird's wings was removed, and PROMPT-CAM subsequently classified it as a \"Boat-tailed Grackle,\" as depicted in the reference column." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 296, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 443 + ], + "type": "text", + "content": "ing animals, plants, and objects. PROMPT-CAM effectively captures the most important traits in each case to accurately identify species, demonstrating its remarkable generalizability and wide applicability." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 447, + 296, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 650 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 650 + ], + "type": "text", + "content": "PROMPT-CAM can detect biologically meaningful traits. As shown in Figure 4, PROMPT-CAM consistently identifies traits from images of the same species (e.g., the red breast and white belly for Rose-breasted Grosbeak). This is further demonstrated in Figure 1 (d), where we progressively mask attention heads (detailed in subsection 2.3) until the model can no longer generate high-confidence predictions for correctly classifying images of Scott Oriole. The remaining heads 1 and 11 highlight the essential traits, i.e., the black head and yellow belly. PROMPT-CAM also enables identifying common traits between species. This is achieved by visualizing the image of one class (e.g., Scott Oriole) using other classes' prompts (e.g., Brewer Blackbird or Baltimore Oriole). As shown in Figure 1 (c), Brewer Blackbird shares the head and neck color with Scott Oriole. These results demonstrate PROMPT-CAM ability to recognize species in a biologically meaningful way." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": "PROMPT-CAM can identify and interpret trait manipulation. We conduct a counterfactual-style analysis to investigate whether PROMPT-CAM truly relies on the identified traits for making predictions. For instance, to correctly classify the Red-winged Blackbird, it highlights the red-wing" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 74, + 535, + 235 + ], + "blocks": [ + { + "bbox": [ + 319, + 74, + 535, + 235 + ], + "lines": [ + { + "bbox": [ + 319, + 74, + 535, + 235 + ], + "spans": [ + { + "bbox": [ + 319, + 74, + 535, + 235 + ], + "type": "image", + "image_path": "09e3cb314af842ade141bb347fe8f0a42ef6581a27f8f67c84335d70c80930e1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 241, + 555, + 340 + ], + "lines": [ + { + "bbox": [ + 313, + 241, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 555, + 340 + ], + "type": "text", + "content": "Figure 9. PROMPT-CAM can detect taxonomically meaningful traits. Give an image of the species \"Amophiprion Clarkii,\" PROMPT-CAM highlights the pelvic fin and double stripe to distinguish it from \"Amophiprion Melanopus\" at the species level. When it goes to the genus level, PROMPT-CAM looks at the pattern in the body and tail to classify the image as the \"Amophiprion\" genus. As we go up, fishes at the family level become visually dissimilar. PROMPT-CAM only needs to look at the tail and pelvic fin to classify the image as the \"Pomacentridae\" family." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 351, + 555, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 351, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 351, + 555, + 460 + ], + "type": "text", + "content": "patch (the first row of Figure 8), consistent with the field guide provided by the Cornell Lab of Ornithology. When we remove this red spot from the image to resemble a Boat-tailed Grackle, the model no longer highlights the original position of the red patch. As such, it does not predict the image as a Red-winged Blackbird but a Boat-tailed Grackle (the second row of Figure 8). This shows PROMPT-CAM's sensitivity to trait differences, showcasing its interpretability in fine-grained recognition." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "text", + "content": "PROMPT-CAM can detect taxonomically meaningful traits. We train PROMPT-CAM based on a hierarchical framework, considering four levels of taxonomic hierarchy: Order " + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "text", + "content": " Family " + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "text", + "content": " Genus " + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 463, + 556, + 594 + ], + "type": "text", + "content": " Species of Fish Dataset. In this setup, PROMPT-CAM progressively shifts its focus from coarse-grained traits at the Family level to fine-grained traits at the Species level to distinguish categories (shown in Figure 9). This progression suggests PROMPT-CAM's potential to automatically identify and localize taxonomy keys to aid in biological and ecological research domains. We provide more details in Suppl." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 388, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 388, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 388, + 616 + ], + "type": "text", + "content": "4. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 624, + 555, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 555, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 555, + 708 + ], + "type": "text", + "content": "We present Prompt Class Attention Map (PROMPT-CAM), a simple yet effective interpretable approach that leverages pre-trained ViTs to identify and localize discriminative traits for fine-grained classification. PROMPT-CAM is easy to implement and train. Extensive empirical studies highlight both the strong performance of PROMPT-CAM and the promise of repurposing standard models for interpretability." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4382" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "type": "text", + "content": "This research is supported in part by grants from the National Science Foundation (OAC-2118240, HDR Institute:Imageomics). The authors are grateful for the generous support of the computational resources from the Ohio Supercomputer Center." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 164, + 115, + 177 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 164, + 115, + 177 + ], + "spans": [ + { + "bbox": [ + 56, + 164, + 115, + 177 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 184, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 184, + 296, + 217 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 184, + 296, + 217 + ], + "spans": [ + { + "bbox": [ + 61, + 184, + 296, + 217 + ], + "type": "text", + "content": "[1] Samira Abnar and Willem Zuidema. 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However, these models are highly susceptible to adversarial attacks—small, imperceptible changes that can mislead classifiers—raising critical concerns about their reliability and security. Traditional attacks rely on fixed-norm perturbations, misaligning with human perception. In contrast, diffusion-based attacks require pre-trained models, demanding substantial data when these models are unavailable, limiting practical use in data-scarce scenarios. In medical imaging, however, this is often unfeasible due to the limited availability of datasets. Building on recent advancements in learnable prompts, we propose Prompt2Perturb $(P2P)$ , a novel language-guided attack method capable of generating meaningful attack examples driven by text instructions. During the prompt learning phase, our approach leverages learnable prompts within the text encoder to create subtle, yet impactful, perturbations that remain imperceptible while guiding the model towards targeted outcomes. In contrast to current prompt learning-based approaches, our $P2P$ stands out by directly updating text embeddings, avoiding the need for retraining diffusion models. Further, we leverage the finding that optimizing only the early diffusion steps boosts efficiency while ensuring that the generated adversarial examples incorporate subtle noise, thus preserving ultrasound image quality without introducing noticeable artifacts. We show that our method outperforms state-of-the-art attack techniques across three breast ultrasound datasets in FID and LPIPS. Moreover, the generated images are both more natural in appearance and more effective compared to existing adversarial attacks. Our Code is publicly available on GitHub.", + "bbox": [ + 88, + 398, + 485, + 883 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d323c553b7d7cb4ca5a950325c613ebb35b589f3b1098c79a88f236e3c675353.jpg", + "image_caption": [ + "Figure 1. Illustration of P2P in an adversarial attack against Diff-PGD; note there is no exhibited change of image semantics in our method." + ], + "image_footnote": [], + "bbox": [ + 521, + 349, + 901, + 439 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 527, + 643, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mammography remains the primary tool for breast cancer screening, offering widespread accessibility and proven effectiveness in detecting early-stage tumors [16]. However, it has some limitations, including patient discomfort and reduced diagnostic accuracy in individuals with dense breast tissue [33]. Ultrasound has become a useful supplementary technique, as it provides better patient comfort and avoids the risks associated with radiation exposure. Its ability to capture real-time images makes it beneficial for further investigating abnormalities observed on mammograms [16]. Nonetheless, the performance of ultrasound can be inconsistent, with sensitivity and specificity affected by the operator's expertise, device configuration, and changes in tissue characteristics due to breast density. Furthermore, variability in interpretation among different radiologists poses additional challenges [51]. In response to these issues, computational approaches, especially deep learning models, are gaining traction as promising tools to improve diagnostic outcomes and address these existing gaps [12, 31, 51].", + "bbox": [ + 511, + 551, + 906, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ensuring the security and robustness of medical deep neural networks (DNNs) is a key concern in healthcare. Recent research in medical imaging tasks has revealed that even state-of-the-art DNNs are highly susceptible to adversar", + "bbox": [ + 511, + 840, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28564", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ial attacks [39]. Specifically, medical imaging DNNs are more susceptible to adversarial threats than those designed for natural images [39]. In addition, the limited availability of publicly accessible medical images, which poses a challenge for effective training, has pushed modern algorithms to rely on pre-trained models based on large datasets of natural images—a technique known as transfer learning. However, due to the substantial difference between natural and medical images, deep learning models developed through transfer learning tend to be more vulnerable to adversarial attacks [10].", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this vulnerability, various adversarial attack methods have been developed. Traditional gradient-based methods such as fast gradient sign method (FGSM) [20], Carlini-wagner [8], and projected gradient descent (PGD) [40] perturb original images within predefined perturbation bounds. Although they can be easily generated using gradient-based techniques, these attacks often deviate significantly from the true data distribution of natural images, leading to a compromise between their effectiveness and subtlety [61]. Generative models such as generative adversarial networks (GANs) [19] have been used to generate adversarial examples, based on their ability to produce high-quality images, by perturbing latent space [3, 49, 64]. However, modifying latent codes changes the high-level semantics of generated images in a way that is easily noticeable to human observers [30]. Recently, diffusion-based models have been employed in the literature to generate realistic adversarial images [11, 36, 61]. In models like AdvDiffuser [11] and Diff-PGD [61], the PGD method is incorporated into the diffusion process to enhance the realism of the generated images. Furthermore, approaches such as Instruct2Attack [37] leverage latent diffusion models [46] to deceive the target model by optimizing over input prompts. These text-guided attacks aim to produce adversarial semantic image edits, such as altering the color of a truck in an image. While image editing holds significant value in natural image domains, it is less applicable in the medical field, as altering the semantics of medical images can result in unrealistic representations. Additionally, these models are often not well-adapted to clinical terminology, making such modifications less meaningful in medical contexts [57].", + "bbox": [ + 91, + 256, + 483, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These limitations can be addressed by reversing the diffusion model to obtain context-relevant text tokens, or prompts, specifically designed for the medical domain to generate adversarial images. Optimizing these prompts presents a challenge due to the intricate structure of the generative model, which includes a two-part pipeline: a conditioning network (the CLIP text encoder [44]) and a generative unit (U-Net [47]), both of which complicate gradient flow to the input layer. To tackle these obstacles, we freeze the generative model and make the following contributions:", + "bbox": [ + 89, + 739, + 482, + 891 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our method requires no fine-tuning and efficiently generates attack images by directly updating text embeddings, unlike previous diffusion-based approaches reliant on large pre-trained models on the same domain. Additionally, we find that optimizing only the initial forward diffusion steps is sufficient, improving efficiency and maintaining image quality without the need for all reverse diffusion phases.", + "- Based on our findings, we proposed Prompt2Perturb (P2P) to create challenging adversarial examples optimized for clinical terminology that are particularly challenging to distinguish as attacked, thus highlighting limitations in current adversarial attack mechanisms.", + "- We demonstrate empirically that our method produces semantically significant attack images that are perceptually similar but varied versions of a target image (see Fig. 1). By incorporating relevant clinical terminology into the text embedding of Stable Diffusion, we ensure that the generated images retain clinical accuracy and realism, thereby enhancing the effectiveness of the attack in a medical context." + ], + "bbox": [ + 511, + 90, + 906, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 421, + 653, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial attack. DNN models are widely recognized as being susceptible to adversarial attacks [45]. These attacks can manipulate the model's predictions by introducing subtle modifications that are imperceptible to human observers. Adversarial attacks pose a major barrier to the widespread adoption of deep learning models in real-world applications, and considerable research has been dedicated to addressing this ongoing challenge. Adversarial attacks can be broadly classified into black-box and white-box types. White-box attacks, such as limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) [52], FGSM [20], PGD [40], C-W [8], and DeepFool [42], rely on full access to the target model's architecture and parameters, making them gradient-based. In contrast, black-box attacks do not require this level of access and generate adversarial samples through query-based methods. Despite these differences, many white-box attacks are still effective in black-box settings due to the transferability of adversarial examples across models. Adversarial training, which involves training a model using adversariably generated examples, is one of the limited methods available to defend against adversarial attacks [5]. In medical domain, several approaches have been developed to generate adversarial examples targeting computer-aided diagnosis models which can be consistently taxonomized with that of adversarial attacks [15]. Specifically, Zhou et al. [65] introduced two GAN-based models operating at different resolutions, capable of generating highly realistic adversarial images that can mislead breast cancer diagnosis. MIRST [50] was proposed to defend untargeted adversarial attacks", + "bbox": [ + 511, + 446, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28565", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/68f6b89a0fba1940bc379c80ee12300eca6779e33f79b04c9d797a90eabbd1ff.jpg", + "image_caption": [ + "Figure 2. Overall framework of the proposed method. Image adapted from [36]" + ], + "image_footnote": [], + "bbox": [ + 147, + 95, + 848, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "on breast ultrasound images. Lastly, Hao et al. [22] introduce an adversarially robust feature learning method where a feature correlation metric is included as an objective function to promote the learning of robust features while minimizing the influence of spurious ones for the application of breast cancer diagnosis.", + "bbox": [ + 88, + 290, + 482, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial attack with diffusion models. The success of diffusion models has motivated their exploration in adversarial deep learning, demonstrating potential for both attacking [60, 66] and defending [58, 59] against adversarial examples. These methods are broadly used to enhance the imperceptibility of unconstrained adversarial perturbations [9], transfer the style from the reference image into the original image to create natural-looking adversarial images [56], or attack the diffusion-based purification method [29].", + "bbox": [ + 89, + 381, + 482, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt learning. Recent progress in controllable image generation and editing using diffusion models [25, 48] has created new possibilities for developing semantic adversarial attacks. Prompt learning was initially introduced as an alternative to full fine-tuning and linear probing, aiming to leverage pre-trained language models in natural language processing (NLP) [34]. Recently, prompt learning techniques have been adapted for adversarial purposes. For instance, BadCLIP [4] targets the CLIP [44] model by injecting a backdoor during the prompt learning phase. In the medical field, BAPLe [21] utilizes learnable prompts within the text encoder and introduces imperceptible learnable noise triggers into input images, effectively leveraging the full capabilities of medical foundation models. Additionally, PromptSmooth [27] uses prompt learning to efficiently achieve certified robustness in medical vision-language models by leveraging semantic concepts.", + "bbox": [ + 89, + 517, + 482, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 89, + 789, + 225, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 89, + 815, + 220, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We explore the challenge of image classification. Consider an image sample $\\pmb{x} \\in \\mathcal{X} \\coloneqq \\mathbb{R}^{H \\times W \\times C}$ , paired with its label $y \\in \\mathcal{Y} \\coloneqq \\{1, \\dots, |\\mathcal{Y}|\\}$ , where $H, W,$ and $C$ represent the image's height, width, and number of channels, respec", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tively. Let $f: \\mathcal{X} \\to \\mathcal{Y}$ denote the image classifier. Given a clean input image $\\pmb{x}$ and its true label $y$ , the attacker's objective is to generate an adversarial version $\\pmb{x}_{\\mathrm{adv}}$ of $\\pmb{x}$ that misleads $f$ , so that $f(\\pmb{x}_{\\mathrm{adv}}) \\neq y$ . Traditional approaches either necessitate adding pixel-level adversarial noise $\\delta$ [8, 20] to the input image $\\pmb{x}$ , resulting in $\\pmb{x}_{\\mathrm{adv}} = \\pmb{x} + \\delta$ , or manipulating data to embed subtle biases or vulnerabilities. In this work, we instead focus on prompt-guided semantic attacks, aiming to create meaningful, interpretable perturbed images guided by language descriptions.", + "bbox": [ + 511, + 290, + 906, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Prompt2Perturb (P2P)", + "text_level": 1, + "bbox": [ + 511, + 452, + 725, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 provides a high-level overview of the proposed approach. Our approach seeks to generate an adversarial image, $\\pmb{x}_{\\mathrm{adv}}$ , such that the modification from the original image $\\pmb{x}$ is guided by a text-based embedding instruction $C$ . The core idea of Prompt2Perturb (P2P) is to update these text embeddings specifically for the modified input to steer the classifier toward an incorrect prediction. In the subsequent sections, we will provide a detailed breakdown of each component of our proposed method.", + "bbox": [ + 511, + 477, + 906, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent Diffusion Models. We utilize the learned latent space of a generative model, defined as $\\mathcal{Z} = z\\mid z = \\mathcal{E}(\\boldsymbol {x}),\\boldsymbol {x}\\in \\mathcal{X}\\subseteq \\mathbb{R}^{h\\times w\\times c}$ , where $\\mathcal{E}$ represents the image encoder and $h\\times w\\times c$ denotes the dimensions of the latent space. Unlike the image space, this latent space offers a compact, lower-dimensional representation that emphasizes the critical semantic details, making it ideal for controlled semantic alterations. These modifications are enabled through a pretrained conditional latent diffusion model (LDM) [6, 46], which facilitates meaningful and guided editing in the latent domain.", + "bbox": [ + 511, + 613, + 905, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The encoder is regularized via either a KL-divergence penalty or vector quantization, as suggested by prior works [53]. The corresponding decoder, denoted as $\\mathcal{D}$ , learns to reconstruct input images from the latent representations, ensuring $\\mathcal{D}(\\mathcal{E}(x)) \\approx x$ , for high fidelity reconstruction. Subsequently, a diffusion model is trained to generate latent codes that reside within the learned latent space. This diffusion model is flexible and can be conditioned using", + "bbox": [ + 511, + 779, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28566", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "auxiliary information, such as class labels, segmentation masks, or features from a co-trained text-embedding model. Specifically, let $c_{\\theta}(p)$ represent a network mapping conditioning input $p$ to its respective conditioning vector. The objective function for the Latent Diffusion Model (LDM) can thus be formulated as:", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {z \\sim \\mathcal {E} (x), p, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, c _ {\\theta} (p)) \\| _ {2} ^ {2} \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 186, + 473, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ is the time step, $z_{t}$ is the noisy latent at $t$ , $\\epsilon$ is the unscaled noise sample, and $\\epsilon_{\\theta}$ is the denoising network. Intuitively, the objective here is to correctly remove the noise added to a latent representation of an image. While training, $c_{\\theta}$ and $\\epsilon_{\\theta}$ are jointly optimized to minimize the LDM loss. At inference time, a random noise tensor is sampled and iteratively denoised to produce a new image latent, $z_{0}$ . Finally, this latent code is transformed into an image through the pre-trained decoder $x' = \\mathcal{D}(z_0)$ . Previous diffusion-based attack methods leverage extensively pretrained models on natural images, incorporating specialized attack strategies and employing a reverse diffusion process to generate adversarial examples that resemble the underlying data distribution. However, this approach is impractical in the medical domain due to the lack of extensively trained models caused by inherent data scarcity and the presence of diverse imaging modalities. Unlike these previous approaches, our method is well-suited to handle this diversity without requiring retraining of a diffusion model or relying on large-scale pre-trained models. This robustness stems from our approach, which involves updating the text embeddings directly, rather than merely adding noise to the latent space. We next review the early stages of such a text encoder, and our choice of attack space.", + "bbox": [ + 89, + 220, + 483, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text optimization. The text encoder processes the input prompt $\\mathbf{P}$ , which is fed into the latent diffusion model. A text tokenizer transforms the prompt strings into tokens, representing indices in a predefined vocabulary of size $|V|$ . Each token is then mapped to its corresponding embedding vector $\\mathbf{c}_i \\in \\mathbf{C}$ , where $i \\in 1, \\dots, |V|$ within the embedding space $\\mathcal{C}$ . Previous work on textual inversion in the embedding space $\\mathcal{C}$ [17, 55] attempts to learn new concepts for a set of images by associating placeholder strings with newly learned embedding vectors. This effectively expands the existing vocabulary with additional concepts. However, these newly learned concepts have been found to be uninformative in the medical domain, as the learned embeddings are often distant from the embeddings corresponding to the original vocabulary. In contrast, our approach aims to optimize the embedding vectors $\\mathbf{c}_i$ , $i \\in 1, \\dots, L$ , from the existing vocabulary for a prompt of maximum length $L$ specific to the medical domain. This adaptation addresses the limitations of existing diffusion model vocabularies that lack specific medical terms (e.g., the word \"benign\" is not present in the vocabulary of the Stable Diffusion text encoder, despite", + "bbox": [ + 89, + 584, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "its frequent use in medical contexts). Therefore, our method ensures applicability across diverse imaging modalities and scenarios within the medical domain, as it remains independent of the specific encoder choice and is instead reliant on the latent diffusion backbone used for prompt optimization. Minimal reversal steps. Previous studies [41] have demonstrated that the diffusion model's sensitivity to conditioning intensifies significantly during the later stages of the diffusion process, particularly when noise levels are higher. Conversely, in the initial timesteps, the diffusion loss remains relatively stable across various prompts applied to the same image. Inspired by this observation, we hypothesize that not all reverse diffusion steps are necessary for generating an adversarial image. Optimizing only for the early timesteps of diffusion process (akin to later timesteps of denoising process) has two-fold advantage. First, given that we are optimizing the early layers of a very deep neural network, the resulting gradients tend to be quite small which contributes to our method's efficiency compared to others that require training the entire diffusion model. Additionally, early timesteps (the start of the diffusion process) are associated with high-frequency components, focusing on reconstructing edges, textures, and fine-grained structures [43]. By introducing adversarial perturbations during this stage, our strategy generates examples that effectively mimic common scenarios in ultrasound imaging, where acquisition settings—such as the transducer's operating frequency and its orientation relative to the anatomy—significantly influence the high-frequency content captured in the images [35]. We provide more details in the next sections.", + "bbox": [ + 511, + 90, + 906, + 544 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Text-Guided Diffusion-Based Attack Pipeline for Single Image" + ], + "code_body": "Input: Attacked classifier $f$ , Image $x$ , Prompt $p$ Label $y$ \nOutput: Adversarily perturbed image $x_{\\mathrm{adv\\_best}}$ $d_{\\mathrm{best}}\\gets \\infty$ . \nfor $i\\in$ range(num_iterations) do \n $t\\gets$ randint(0,50); \n $z\\gets$ vae.encode(x), $C\\gets$ textencoder(p); \n $\\epsilon \\gets$ randn_like(z), $z_{t}\\gets$ add_noise(z, $\\epsilon ,t)$ $\\tilde{z}\\gets \\sqrt{\\frac{1}{\\bar{\\alpha}_t}} (z_t - \\sqrt{1 - \\bar{\\alpha}_t}\\cdot \\epsilon_\\theta (z_t,t,C));$ $x_{\\mathrm{adv}}\\gets$ vaedecode( $\\tilde{z}$ ), $x_{\\mathrm{adv}}\\gets (x_{\\mathrm{adv}} + 1) / 2;$ $x_{\\mathrm{adv}}$ .Normalize(mean, std), $\\tilde{y}\\gets f(x_{\\mathrm{adv}})$ \nLoss $\\leftarrow -10^{10}\\times$ CrossEntropyLoss(y,y)+ mse(ε,εθzt,C)); \nLoss-backward(), textencoder_optimizer.step(); \n $d\\gets$ mse(x,xadv); \nif $d < d_{best}$ then \n $\\begin{array}{r}\\lfloor d_{\\mathrm{best}}\\leftarrow d,x_{\\mathrm{adv\\_best}}\\leftarrow x_{\\mathrm{adv}}; \\end{array}$ \nreturn $x_{\\mathrm{adv\\_best}}$", + "bbox": [ + 519, + 595, + 875, + 890 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28567", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attacking policy setup. Given a target image $\\pmb{x}$ and a latent diffusion model parameterized by $\\epsilon_{\\theta}$ , our goal is to optimize the text encoder to best represent the visual content of the image while simultaneously crafting an adversarial attack on the classifier. To determine the optimal text encoder for generating an adversarial image, we formulate the problem with two components. First, we employ a cross-entropy loss to measure the difference between the classifier's predicted output and the actual image class. Second, we include a loss that captures the discrepancy between the predicted noise from the network and the noise originally added to the image under a specific prompt condition, thereby ensuring semantic similarity between the adversarial image and the original image. Our objective is to recover the set of embeddings that align our objective of generating an adversarial image. Note that we freeze the diffusion model parameters throughout this optimization except the text encoder part. As discussed previously, instead of optimizing over all diffusion time steps, we restrict the range of $t$ to early diffusion timesteps $(t \\leq 50)$ . Subsequently, the image that shows the highest similarity to the original input is selected as the adversarial output. The complete approach of our method is illustrated in Algorithm 1.", + "bbox": [ + 89, + 90, + 485, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 450, + 225, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section starts by outlining the experimental setup, the comparison framework, and the evaluation metrics used. We then present both quantitative and qualitative comparisons against the current state-of-the-art methods, focusing on the stealthiness of the perturbations introduced and the realism of the generated examples. Finally, we conduct ablation and sensitivity analyses to evaluate the influence of key components and hyperparameters.", + "bbox": [ + 89, + 476, + 483, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental settings", + "text_level": 1, + "bbox": [ + 89, + 606, + 294, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and Models. We leverage three publicly available breast ultrasound datasets and experiment with three widely recognized classifier architectures—ResNet34 [23], SqueezeNet1.1 [28], and DenseNet121 [26]—which are commonly used as baselines in medical imaging research [1, 32]. Given the relatively small dataset sizes, we apply five-fold cross-validation across all classes to ensure robust evaluation. For consistency with the classifier architectures, all images are resized to $224 \\times 224$ pixels. Additionally, we incorporate a pre-trained LDM from Hugging Face, specifically utilizing the Stable-Diffusion-v-1-4 variant [13].", + "bbox": [ + 89, + 628, + 485, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BUSI (Breast Ultrasound Images). Collected in 2018, this dataset comprises ultrasound scans from 600 female patients between the ages of 25 and 75, gathered for breast cancer detection. The dataset includes a total of 780 images, each with an average resolution of $500 \\times 500$ pixels, categorized into three classes: normal (133 images), benign", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(437 images), and malignant (210 images) [2].", + "bbox": [ + 511, + 90, + 821, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BUS-BRA. BUS-BRA [18] dataset includes 1875 anonymized images from 1,064 female patients, acquired with four different ultrasound scanners as part of systematic studies conducted at the National Institute of Cancer in Rio de Janeiro, Brazil. This dataset includes biopsy-confirmed tumor cases, with 1268 benign and 607 malignant cases.", + "bbox": [ + 511, + 106, + 903, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "UDIAT. Collected in 2012 at the UDIAT Diagnostic Centre of the Parc Taulí Corporation in Sabadell, Spain, this dataset [62] was gathered using a Siemens ACUSON Sequoia C512 system with a 17L5 HD linear array transducer operating at $8.5\\mathrm{MHz}$ . It comprises 163 images from 163 female patients, with an average resolution of $760\\times 570$ pixels, categorized into 53 malignant and 110 benign lesions.", + "bbox": [ + 511, + 196, + 903, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hyperparameters. In our experiments, we train the model for 500 iterations with a learning rate of $5 \\times 10^{-4}$ using the AdamW optimizer [38]. For adversarial methods, we set the FGSM attack parameter to $\\epsilon = 0.05$ . For the PGD attack, we configure $\\epsilon = 0.03$ with a step size of $\\alpha = 0.007$ over 200 iterations. We utilize Diff-PGD with the same setting as it used for ImageNet [14]. We run our experiments on a single NVIDIA RTX V100 GPU with 32GB memory.", + "bbox": [ + 511, + 316, + 906, + 454 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/246dd51a187acb5cad1758fb9d248be4318ca8c075424aa12388e9ae3d1b5276.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.880.400.81123.51
PGD0.570.290.45378.62
Diff-PGD1.00.300.87111.03
P2P (Ours)0.980.130.8545.84
ResNet34
FGSM0.960.410.81131.62
PGD0.550.250.37332.01
Diff-PGD1.00.310.84117.49
P2P (Ours)0.970.120.8143.03
SqueezeNet1.1
FGSM0.490.160.40118.03
PGD0.330.200.30250.38
Diff-PGD0.740.140.5679.51
P2P (Ours)0.960.090.6347.64
", + "bbox": [ + 514, + 465, + 911, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Evaluation of adversarial attacks on different attack models for BUSI dataset [2] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples.", + "bbox": [ + 511, + 747, + 906, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation of Adversarial Examples", + "text_level": 1, + "bbox": [ + 511, + 816, + 828, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the quality of adversarial examples generated by our proposed P2P method, we benchmark it against the leading Diffusion-Based Projected Gradient Descent (Diff-PGD) attack and conventional techniques like FGSM and", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28568", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d702d8fb76952d7638ba5683dfbe92f63c6878c0b16323734cea5beb43f0c936.jpg", + "image_caption": [ + "Figure 3. Visual comparison of different attack methods on a benign image from the BUSI dataset, using DenseNet121 as the classifier. The second row displays the perturbations, calculated as the difference between the original image and the attacked example." + ], + "image_footnote": [], + "bbox": [ + 127, + 97, + 867, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d17d6949b37dcde8e1df7a1ebc65faa2d157eaa5134cf12c5233625a3ffc0119.jpg", + "image_caption": [ + "Figure 4. Comparison of original and P2P-attacked ultrasound images from BUS-BRA Dataset, using DenseNet121 as the classifier. The top row shows the original images with their diagnostic labels, while the bottom row displays the same images after applying the P2P attack. Green boxes indicate the true labels, while red boxes show the labels predicted by the classifier after the attack." + ], + "image_footnote": [], + "bbox": [ + 151, + 309, + 864, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PGD. We assess each attack's performance across metrics including Success Rate, LPIPS, SSIM, and FID, enabling a comprehensive analysis of both adversarial efficacy and the perceptual integrity of the generated adversarial samples.", + "bbox": [ + 89, + 584, + 482, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our setting, each attack baseline is applied to validation set images that were initially classified correctly, with adversarial examples retained only when successful in misleading the classifiers. Accordingly, all metrics presented in Tabs. 1 to 3 reflect measurements derived exclusively from these modified images.", + "bbox": [ + 89, + 645, + 482, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Across all datasets and classifier architectures, our P2P approach consistently attains high Success Rates [7] comparable to those achieved by Diff-PGD, while surpassing baseline methods in Fréchet Inception Distance (FID) [24], reflecting the imperceptibility of the crafted adversarial examples, and in Learned Perceptual Image Patch Similarity (LPIPS) [63], indicating reduced distortion in our attacks. These results highlight the superior perceptual quality of adversarial examples generated by our method.", + "bbox": [ + 89, + 734, + 482, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In terms of Structural Similarity Index Measure (SSIM),", + "bbox": [ + 99, + 871, + 482, + 886 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which evaluates the structural alignment between adversarial and original images, our method achieves competitive performance. Although Diff-PGD occasionally marginally outperforms P2P in SSIM for specific models, P2P consistently maintains strong SSIM values across all datasets, as shown in Tabs. 1 to 3. This reflects high visual similarity between the generated adversarial examples $x_{\\mathrm{adv}}$ and the original clean images $x$ , capturing low perceived visual distortion by preserving luminance, contrast, and structural details. The combination of high SSIM with low LPIPS and FID scores underscores P2P's ability to preserve structural consistency while producing perceptually aligned adversarial examples.", + "bbox": [ + 511, + 584, + 906, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the DenseNet121 and ResNet34 classifiers, P2P achieves a strong balance of high Success Rate, low LPIPS, and favorable SSIM and FID scores, surpassing traditional methods. With SqueezeNet1.1, P2P exhibits particularly robust performance on perceptual metrics, reaching the lowest LPIPS and FID values across all datasets, as shown in Tabs. 1 to 3, highlighting its ability to generate realistic and", + "bbox": [ + 511, + 780, + 908, + 886 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28569", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e96dc4e6379cbf602026c178e84d0539cc351ea22fe32bfad9b4cf93c9eaa570.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Evaluation of adversarial attacks on different attack models for BUS-BRA dataset [18] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + ], + "table_body": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.930.400.77112.11
PGD0.430.190.56213.65
Diff-PGD1.00.290.8290.5
P2P (Ours)0.940.120.7838.00
ResNet34
FGSM0.810.350.66133.17
PGD0.310.120.24158.24
Diff-PGD1.00.290.78100.2
P2P (Ours)0.930.110.7244.09
SqueezeNet1.1
FGSM0.690.160.77120.14
PGD0.430.260.40292.99
Diff-PGD0.750.120.4789.47
P2P (Ours)0.740.080.4958.60
", + "bbox": [ + 91, + 88, + 486, + 358 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "structurally consistent adversarial images.", + "bbox": [ + 89, + 440, + 370, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Overall, P2P demonstrates competitive Success Rates while consistently producing high-quality adversarial examples with enhanced visual fidelity and structural similarity. The results underscore P2P's effectiveness as a balanced approach for crafting effective and perceptually similar adversarial images across various datasets and classifiers. We will further elaborate on these results qualitatively in the subsequent section.", + "bbox": [ + 88, + 455, + 482, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Results of Adversarial Examples", + "text_level": 1, + "bbox": [ + 89, + 589, + 467, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 3 presents visual comparisons of images and adversarial perturbations generated by different attack methods. Notably, our method (P2P) produces attack examples that more closely follow the distribution of the original medical images, resulting in a more natural and less detectable alteration. In contrast, other attack methods, such as FGSM, PGD, and Diff-PGD, introduce high-frequency noise with a distinct \"textured\" appearance. This textured noise can make these adversarial examples appear less natural, potentially revealing them as manipulated images, exhibit noisy artifacts. Besides, Fig. 4 shows that the P2P attack successfully changes the diagnostic labels of ultrasound images with minimal alteration to the images' semantic appearance, demonstrating label vulnerability despite preserved image semantics. Moreover, the t-SNE [54] visualization of clean and attacked image features further confirms the effect of our prompt learning method. Figure 5 compares four attack methods—FGSM, PGD, Diff-PGD, and P2P (Ours)—in terms of how well they blend attack samples", + "bbox": [ + 91, + 613, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6a2484c6d80d5dc4b4967eb7aefdf6b7543e8f51d765c8d5edb89ce3f26d2dce.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Evaluation of adversarial attacks on different attack models for UDIAT dataset [62] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + ], + "table_body": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.970.370.77103.07
PGD0.170.070.11147.84
Diff-PGD1.00.270.8081.31
P2P (Ours)0.860.120.6227.18
ResNet34
FGSM0.980.410.75103.68
PGD0.230.100.19135.95
Diff-PGD1.00.310.7780.89
P2P (Ours)0.970.150.7420.3
SqueezeNet1.1
FGSM0.590.200.4272.51
PGD0.160.140.19292.21
Diff-PGD0.770.160.5432.47
P2P (Ours)0.760.100.5223.50
", + "bbox": [ + 514, + 88, + 910, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with clean data clusters. Diff-PGD shows limited effectiveness, with noticeable separations between attack and clean samples. FGSM and PGD improve blending but still leaves isolated clusters of attack points. P2P achieves the best integration, with attack samples closely interwoven with clean data, indicating superior performance in making adversarial examples indistinguishable from clean data.", + "bbox": [ + 511, + 440, + 906, + 545 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To gain further insights, we examined attacked examples from the training set, focusing on images that the classifier identifies with high confidence. Figure 6 presents malignant cases from the BUSI training set alongside their attacked versions generated by Diff-PGD and our method, P2P. As illustrated, the Diff-PGD attack introduces a noticeable noise pattern, while our method produces images that closely resemble the originals. Interestingly, additional examples reveal that Diff-PGD's image quality deteriorates as the classifier's confidence increases. While attack experiments are generally performed on validation sets, we analyzed training set images here to understand the performance of different attack models in varied scenarios.", + "bbox": [ + 511, + 546, + 908, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 755, + 668, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This section disentangles the effects of design choices to assess their individual contributions to our approach's effectiveness. All ablation experiments are conducted on the BUSI dataset, using ResNet34 as the classifier, with results averaged over 5-fold cross-validation.", + "bbox": [ + 511, + 779, + 906, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Loss Function. Ablation study results on the effect of MSE loss function are reported in Tab. 4 (second row) and Fig. 7. Although using an MSE loss does not necessarily lead to", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28570", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b9e04771152a544718fdac5a49a53352d553652871567ad76580ba12ef282405.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ComponentLoss FunctionTime StepSuccess RateLPIPSSSIMFIDTime (second)
Baseline0.970.120.8143.03178
W/O MSE✓0.960.120.8043.58178
T=20✓0.830.100.7149.9798
T=100✓0.970.120.8138.06280
", + "bbox": [ + 122, + 88, + 874, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of the ablation study on different components of the P2P pipeline. The baseline configuration uses T=50 with MSE in the loss function. In each row, only one component is modified from the baseline. 'Time' indicates the duration of the generation process for the attack per image.", + "bbox": [ + 89, + 196, + 906, + 241 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f63cccf1255402eae4d5589ea5d20d368f97f292f90b56d241d5642fd9fb693.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 262, + 284, + 368 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e3b35e1289e69bfab5b8003c6eb459cf21366e64ed43e35b1bfd11b091a3ca0.jpg", + "image_caption": [ + "b) PGD" + ], + "image_footnote": [], + "bbox": [ + 290, + 263, + 475, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/033234e36d8a24664daf7b200425eef120552e9d692ade817c0718254c5f9fbc.jpg", + "image_caption": [ + "a) FGSM", + "c) Diff-PGD" + ], + "image_footnote": [], + "bbox": [ + 99, + 378, + 284, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2c069aaeb41fbd4121ebce889d05b4845545b693694f15d0e56652540856a74.jpg", + "image_caption": [ + "d) P2P (Ours)" + ], + "image_footnote": [], + "bbox": [ + 290, + 378, + 475, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e004de72efc40b46bb54cf1f54a859f597d9b8a1159f7848aabbde15eb4166d.jpg", + "image_caption": [ + "Figure 5. t-SNE visualization of last-layer ResNet34 features on the BUSI dataset for FGSM, PGD, Diff-PGD, and our P2P. Clean examples are shown in blue, and adversarial examples in orange.", + "a) Original", + "Figure 6. Attack examples of a malignant image of Dataset BUSI from Diff-PGD and P2P with ResNet34 as a classifier." + ], + "image_footnote": [], + "bbox": [ + 102, + 561, + 222, + 684 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d35b9d7f6b11addbcb870b46a082c0e94970d3f467a068a2004eab75d7033e1a.jpg", + "image_caption": [ + "b) Diff-PGD" + ], + "image_footnote": [], + "bbox": [ + 227, + 561, + 346, + 684 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6633feb668a9b5f7b4148bf6d511b179f75b4d494786140a4d1be6fc48dde402.jpg", + "image_caption": [ + "c) P2P" + ], + "image_footnote": [], + "bbox": [ + 351, + 561, + 470, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "better quantitative metrics, Fig. 7 shows that it attempts to mitigate artifacts and retain the semantic integrity of the ultrasound image. Specifically, the middle image (without MSE) exhibits enhanced linear or streak-like artifacts, which may disrupt the homogeneity of tissue appearance (highlighted in the red rectangular region) and obscure finer structural details in the ultrasound image. Incorporating the MSE loss helps to reduce intensity fluctuations, creating a smoother and more consistent appearance, particularly", + "bbox": [ + 89, + 763, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f962d471b65ff11e9af8c98564aa13307303fa6d12ebc6bea0c7d7b0e213080.jpg", + "image_caption": [ + "a) Original", + "Figure 7. Impact of MSE loss in the P2P framework. Image (a) shows the clean reference image, image (b) shows the P2P result without MSE loss, and image (c) includes the MSE loss function." + ], + "image_footnote": [], + "bbox": [ + 526, + 262, + 645, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/786f0c3772e3d62738244519aecfcb82402f5b334e9a628c47a8eda9dcf70d9b.jpg", + "image_caption": [ + "b) W/O MSE" + ], + "image_footnote": [], + "bbox": [ + 651, + 262, + 769, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/185fd600c6119b5769f11348799fb2ade3f2a0e5dc4dca01470c70dc5b0317e6.jpg", + "image_caption": [ + "c) MSE" + ], + "image_footnote": [], + "bbox": [ + 774, + 262, + 893, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "beneficial in areas with subtle tissue boundaries.", + "bbox": [ + 511, + 464, + 831, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Step Selection To justify the choices for P2P with optimization for different timesteps, we show in Tab. 4 the performance of our method with different settings. Using 20 steps, the approach yields prompts that generate attack images with relatively low success, SSIM and LPIPS. However, when optimizing with more timesteps ( $T = 100$ ) even though, the FID of the generated attack images is better, other metrics are comparable to that of ( $T = 50$ ), but with longer time to generate attack images. Therefore, given the efficiency dilemma and the results presented, selecting 50 steps appears to be a reasonable choice.", + "bbox": [ + 511, + 479, + 906, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 676, + 633, + 693 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We designed P2P, an effective adversarial attack method for synthesizing adversarial breast ultrasound images using prompt learning in text-to-image diffusion models. We showcase the effectiveness of our approach across various attack scenarios, especially valuable in data-limited medical applications. Our adversarial images surpass previous methods, appearing more clinically natural and harder to detect. They also maintain lower perceptual differences and achieve greater structural similarity. P2P enables significantly easier attacks on classifiers in the medical domain, eliminating the need for pre-trained models in a specific domain by facilitating the construction of effective textual examples.", + "bbox": [ + 511, + 703, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28571", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgment", + "text_level": 1, + "bbox": [ + 89, + 90, + 263, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 265, + 187, + 280 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Barsha Abhisheka, Saroj Kumar Biswas, and Biswajit Purkayastha. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2385-2392, 2023. 3", + "bbox": [ + 516, + 90, + 903, + 148 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "28574", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/98c943d3-1292-44ba-a2e7-68b21f76d5b2_model.json b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/98c943d3-1292-44ba-a2e7-68b21f76d5b2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5f144f28959072849a9a64259873eb8bf45d1389 --- /dev/null +++ b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/98c943d3-1292-44ba-a2e7-68b21f76d5b2_model.json @@ -0,0 +1,2158 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.13, + 0.888, + 0.177 + ], + "angle": 0, + "content": "Prompt2Perturb (P2P): Text-Guided Diffusion-Based Adversarial Attacks on Breast Ultrasound Images" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.203, + 0.899, + 0.257 + ], + "angle": 0, + "content": "Yasamin Medghalchi1 Moein Heidari1 Clayton Allard1 Leonid Sigal1,2 Ilker Hacihaliloglu1 \n1University of British Columbia, Vancouver, BC, Canada \n2Vector Institute for AI, Toronto, ON, Canada" + }, + { + "type": "text", + "bbox": [ + 0.303, + 0.261, + 0.694, + 0.31 + ], + "angle": 0, + "content": "yasimed@student.ubc.ca{moein.heidari, ilker.hacihaliloglu}@ubc.ca clayton.allard@stat.ubc.ca, lsignal@cs.ubc.ca" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.345, + 0.327, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.4, + 0.486, + 0.884 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) offer significant promise for improving breast cancer diagnosis in medical imaging. However, these models are highly susceptible to adversarial attacks—small, imperceptible changes that can mislead classifiers—raising critical concerns about their reliability and security. Traditional attacks rely on fixed-norm perturbations, misaligning with human perception. In contrast, diffusion-based attacks require pre-trained models, demanding substantial data when these models are unavailable, limiting practical use in data-scarce scenarios. In medical imaging, however, this is often unfeasible due to the limited availability of datasets. Building on recent advancements in learnable prompts, we propose Prompt2Perturb \\((P2P)\\), a novel language-guided attack method capable of generating meaningful attack examples driven by text instructions. During the prompt learning phase, our approach leverages learnable prompts within the text encoder to create subtle, yet impactful, perturbations that remain imperceptible while guiding the model towards targeted outcomes. In contrast to current prompt learning-based approaches, our \\(P2P\\) stands out by directly updating text embeddings, avoiding the need for retraining diffusion models. Further, we leverage the finding that optimizing only the early diffusion steps boosts efficiency while ensuring that the generated adversarial examples incorporate subtle noise, thus preserving ultrasound image quality without introducing noticeable artifacts. We show that our method outperforms state-of-the-art attack techniques across three breast ultrasound datasets in FID and LPIPS. Moreover, the generated images are both more natural in appearance and more effective compared to existing adversarial attacks. Our Code is publicly available on GitHub." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.351, + 0.902, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.46, + 0.908, + 0.501 + ], + "angle": 0, + "content": "Figure 1. Illustration of P2P in an adversarial attack against Diff-PGD; note there is no exhibited change of image semantics in our method." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.528, + 0.645, + 0.543 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.907, + 0.841 + ], + "angle": 0, + "content": "Mammography remains the primary tool for breast cancer screening, offering widespread accessibility and proven effectiveness in detecting early-stage tumors [16]. However, it has some limitations, including patient discomfort and reduced diagnostic accuracy in individuals with dense breast tissue [33]. Ultrasound has become a useful supplementary technique, as it provides better patient comfort and avoids the risks associated with radiation exposure. Its ability to capture real-time images makes it beneficial for further investigating abnormalities observed on mammograms [16]. Nonetheless, the performance of ultrasound can be inconsistent, with sensitivity and specificity affected by the operator's expertise, device configuration, and changes in tissue characteristics due to breast density. Furthermore, variability in interpretation among different radiologists poses additional challenges [51]. In response to these issues, computational approaches, especially deep learning models, are gaining traction as promising tools to improve diagnostic outcomes and address these existing gaps [12, 31, 51]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Ensuring the security and robustness of medical deep neural networks (DNNs) is a key concern in healthcare. Recent research in medical imaging tasks has revealed that even state-of-the-art DNNs are highly susceptible to adversar" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "28564" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "ial attacks [39]. Specifically, medical imaging DNNs are more susceptible to adversarial threats than those designed for natural images [39]. In addition, the limited availability of publicly accessible medical images, which poses a challenge for effective training, has pushed modern algorithms to rely on pre-trained models based on large datasets of natural images—a technique known as transfer learning. However, due to the substantial difference between natural and medical images, deep learning models developed through transfer learning tend to be more vulnerable to adversarial attacks [10]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.257, + 0.485, + 0.74 + ], + "angle": 0, + "content": "To address this vulnerability, various adversarial attack methods have been developed. Traditional gradient-based methods such as fast gradient sign method (FGSM) [20], Carlini-wagner [8], and projected gradient descent (PGD) [40] perturb original images within predefined perturbation bounds. Although they can be easily generated using gradient-based techniques, these attacks often deviate significantly from the true data distribution of natural images, leading to a compromise between their effectiveness and subtlety [61]. Generative models such as generative adversarial networks (GANs) [19] have been used to generate adversarial examples, based on their ability to produce high-quality images, by perturbing latent space [3, 49, 64]. However, modifying latent codes changes the high-level semantics of generated images in a way that is easily noticeable to human observers [30]. Recently, diffusion-based models have been employed in the literature to generate realistic adversarial images [11, 36, 61]. In models like AdvDiffuser [11] and Diff-PGD [61], the PGD method is incorporated into the diffusion process to enhance the realism of the generated images. Furthermore, approaches such as Instruct2Attack [37] leverage latent diffusion models [46] to deceive the target model by optimizing over input prompts. These text-guided attacks aim to produce adversarial semantic image edits, such as altering the color of a truck in an image. While image editing holds significant value in natural image domains, it is less applicable in the medical field, as altering the semantics of medical images can result in unrealistic representations. Additionally, these models are often not well-adapted to clinical terminology, making such modifications less meaningful in medical contexts [57]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.741, + 0.483, + 0.892 + ], + "angle": 0, + "content": "These limitations can be addressed by reversing the diffusion model to obtain context-relevant text tokens, or prompts, specifically designed for the medical domain to generate adversarial images. Optimizing these prompts presents a challenge due to the intricate structure of the generative model, which includes a two-part pipeline: a conditioning network (the CLIP text encoder [44]) and a generative unit (U-Net [47]), both of which complicate gradient flow to the input layer. To tackle these obstacles, we freeze the generative model and make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "- Our method requires no fine-tuning and efficiently generates attack images by directly updating text embeddings, unlike previous diffusion-based approaches reliant on large pre-trained models on the same domain. Additionally, we find that optimizing only the initial forward diffusion steps is sufficient, improving efficiency and maintaining image quality without the need for all reverse diffusion phases." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.213, + 0.905, + 0.287 + ], + "angle": 0, + "content": "- Based on our findings, we proposed Prompt2Perturb (P2P) to create challenging adversarial examples optimized for clinical terminology that are particularly challenging to distinguish as attacked, thus highlighting limitations in current adversarial attack mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.288, + 0.907, + 0.408 + ], + "angle": 0, + "content": "- We demonstrate empirically that our method produces semantically significant attack images that are perceptually similar but varied versions of a target image (see Fig. 1). By incorporating relevant clinical terminology into the text embedding of Stable Diffusion, we ensure that the generated images retain clinical accuracy and realism, thereby enhancing the effectiveness of the attack in a medical context." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.422, + 0.655, + 0.438 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Adversarial attack. DNN models are widely recognized as being susceptible to adversarial attacks [45]. These attacks can manipulate the model's predictions by introducing subtle modifications that are imperceptible to human observers. Adversarial attacks pose a major barrier to the widespread adoption of deep learning models in real-world applications, and considerable research has been dedicated to addressing this ongoing challenge. Adversarial attacks can be broadly classified into black-box and white-box types. White-box attacks, such as limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) [52], FGSM [20], PGD [40], C-W [8], and DeepFool [42], rely on full access to the target model's architecture and parameters, making them gradient-based. In contrast, black-box attacks do not require this level of access and generate adversarial samples through query-based methods. Despite these differences, many white-box attacks are still effective in black-box settings due to the transferability of adversarial examples across models. Adversarial training, which involves training a model using adversariably generated examples, is one of the limited methods available to defend against adversarial attacks [5]. In medical domain, several approaches have been developed to generate adversarial examples targeting computer-aided diagnosis models which can be consistently taxonomized with that of adversarial attacks [15]. Specifically, Zhou et al. [65] introduced two GAN-based models operating at different resolutions, capable of generating highly realistic adversarial images that can mislead breast cancer diagnosis. MIRST [50] was proposed to defend untargeted adversarial attacks" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28565" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.148, + 0.096, + 0.849, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.268, + 0.735, + 0.284 + ], + "angle": 0, + "content": "Figure 2. Overall framework of the proposed method. Image adapted from [36]" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.291, + 0.483, + 0.382 + ], + "angle": 0, + "content": "on breast ultrasound images. Lastly, Hao et al. [22] introduce an adversarially robust feature learning method where a feature correlation metric is included as an objective function to promote the learning of robust features while minimizing the influence of spurious ones for the application of breast cancer diagnosis." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.382, + 0.483, + 0.517 + ], + "angle": 0, + "content": "Adversarial attack with diffusion models. The success of diffusion models has motivated their exploration in adversarial deep learning, demonstrating potential for both attacking [60, 66] and defending [58, 59] against adversarial examples. These methods are broadly used to enhance the imperceptibility of unconstrained adversarial perturbations [9], transfer the style from the reference image into the original image to create natural-looking adversarial images [56], or attack the diffusion-based purification method [29]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.518, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Prompt learning. Recent progress in controllable image generation and editing using diffusion models [25, 48] has created new possibilities for developing semantic adversarial attacks. Prompt learning was initially introduced as an alternative to full fine-tuning and linear probing, aiming to leverage pre-trained language models in natural language processing (NLP) [34]. Recently, prompt learning techniques have been adapted for adversarial purposes. For instance, BadCLIP [4] targets the CLIP [44] model by injecting a backdoor during the prompt learning phase. In the medical field, BAPLe [21] utilizes learnable prompts within the text encoder and introduces imperceptible learnable noise triggers into input images, effectively leveraging the full capabilities of medical foundation models. Additionally, PromptSmooth [27] uses prompt learning to efficiently achieve certified robustness in medical vision-language models by leveraging semantic concepts." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.79, + 0.226, + 0.808 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.816, + 0.221, + 0.833 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We explore the challenge of image classification. Consider an image sample \\( \\pmb{x} \\in \\mathcal{X} \\coloneqq \\mathbb{R}^{H \\times W \\times C} \\), paired with its label \\( y \\in \\mathcal{Y} \\coloneqq \\{1, \\dots, |\\mathcal{Y}|\\} \\), where \\( H, W, \\) and \\( C \\) represent the image's height, width, and number of channels, respec" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.291, + 0.907, + 0.444 + ], + "angle": 0, + "content": "tively. Let \\( f: \\mathcal{X} \\to \\mathcal{Y} \\) denote the image classifier. Given a clean input image \\( \\pmb{x} \\) and its true label \\( y \\), the attacker's objective is to generate an adversarial version \\( \\pmb{x}_{\\mathrm{adv}} \\) of \\( \\pmb{x} \\) that misleads \\( f \\), so that \\( f(\\pmb{x}_{\\mathrm{adv}}) \\neq y \\). Traditional approaches either necessitate adding pixel-level adversarial noise \\( \\delta \\) [8, 20] to the input image \\( \\pmb{x} \\), resulting in \\( \\pmb{x}_{\\mathrm{adv}} = \\pmb{x} + \\delta \\), or manipulating data to embed subtle biases or vulnerabilities. In this work, we instead focus on prompt-guided semantic attacks, aiming to create meaningful, interpretable perturbed images guided by language descriptions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.453, + 0.727, + 0.47 + ], + "angle": 0, + "content": "3.2. Prompt2Perturb (P2P)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.907, + 0.613 + ], + "angle": 0, + "content": "Figure 2 provides a high-level overview of the proposed approach. Our approach seeks to generate an adversarial image, \\( \\pmb{x}_{\\mathrm{adv}} \\), such that the modification from the original image \\( \\pmb{x} \\) is guided by a text-based embedding instruction \\( C \\). The core idea of Prompt2Perturb (P2P) is to update these text embeddings specifically for the modified input to steer the classifier toward an incorrect prediction. In the subsequent sections, we will provide a detailed breakdown of each component of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.779 + ], + "angle": 0, + "content": "Latent Diffusion Models. We utilize the learned latent space of a generative model, defined as \\(\\mathcal{Z} = z\\mid z = \\mathcal{E}(\\boldsymbol {x}),\\boldsymbol {x}\\in \\mathcal{X}\\subseteq \\mathbb{R}^{h\\times w\\times c}\\), where \\(\\mathcal{E}\\) represents the image encoder and \\(h\\times w\\times c\\) denotes the dimensions of the latent space. Unlike the image space, this latent space offers a compact, lower-dimensional representation that emphasizes the critical semantic details, making it ideal for controlled semantic alterations. These modifications are enabled through a pretrained conditional latent diffusion model (LDM) [6, 46], which facilitates meaningful and guided editing in the latent domain." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.902 + ], + "angle": 0, + "content": "The encoder is regularized via either a KL-divergence penalty or vector quantization, as suggested by prior works [53]. The corresponding decoder, denoted as \\(\\mathcal{D}\\), learns to reconstruct input images from the latent representations, ensuring \\(\\mathcal{D}(\\mathcal{E}(x)) \\approx x\\), for high fidelity reconstruction. Subsequently, a diffusion model is trained to generate latent codes that reside within the learned latent space. This diffusion model is flexible and can be conditioned using" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28566" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "auxiliary information, such as class labels, segmentation masks, or features from a co-trained text-embedding model. Specifically, let \\( c_{\\theta}(p) \\) represent a network mapping conditioning input \\( p \\) to its respective conditioning vector. The objective function for the Latent Diffusion Model (LDM) can thus be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.188, + 0.474, + 0.215 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {z \\sim \\mathcal {E} (x), p, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, c _ {\\theta} (p)) \\| _ {2} ^ {2} \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.222, + 0.485, + 0.584 + ], + "angle": 0, + "content": "where \\( t \\) is the time step, \\( z_{t} \\) is the noisy latent at \\( t \\), \\( \\epsilon \\) is the unscaled noise sample, and \\( \\epsilon_{\\theta} \\) is the denoising network. Intuitively, the objective here is to correctly remove the noise added to a latent representation of an image. While training, \\( c_{\\theta} \\) and \\( \\epsilon_{\\theta} \\) are jointly optimized to minimize the LDM loss. At inference time, a random noise tensor is sampled and iteratively denoised to produce a new image latent, \\( z_{0} \\). Finally, this latent code is transformed into an image through the pre-trained decoder \\( x' = \\mathcal{D}(z_0) \\). Previous diffusion-based attack methods leverage extensively pretrained models on natural images, incorporating specialized attack strategies and employing a reverse diffusion process to generate adversarial examples that resemble the underlying data distribution. However, this approach is impractical in the medical domain due to the lack of extensively trained models caused by inherent data scarcity and the presence of diverse imaging modalities. Unlike these previous approaches, our method is well-suited to handle this diversity without requiring retraining of a diffusion model or relying on large-scale pre-trained models. This robustness stems from our approach, which involves updating the text embeddings directly, rather than merely adding noise to the latent space. We next review the early stages of such a text encoder, and our choice of attack space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Text optimization. The text encoder processes the input prompt \\(\\mathbf{P}\\), which is fed into the latent diffusion model. A text tokenizer transforms the prompt strings into tokens, representing indices in a predefined vocabulary of size \\(|V|\\). Each token is then mapped to its corresponding embedding vector \\(\\mathbf{c}_i \\in \\mathbf{C}\\), where \\(i \\in 1, \\dots, |V|\\) within the embedding space \\(\\mathcal{C}\\). Previous work on textual inversion in the embedding space \\(\\mathcal{C}\\) [17, 55] attempts to learn new concepts for a set of images by associating placeholder strings with newly learned embedding vectors. This effectively expands the existing vocabulary with additional concepts. However, these newly learned concepts have been found to be uninformative in the medical domain, as the learned embeddings are often distant from the embeddings corresponding to the original vocabulary. In contrast, our approach aims to optimize the embedding vectors \\(\\mathbf{c}_i\\), \\(i \\in 1, \\dots, L\\), from the existing vocabulary for a prompt of maximum length \\(L\\) specific to the medical domain. This adaptation addresses the limitations of existing diffusion model vocabularies that lack specific medical terms (e.g., the word \"benign\" is not present in the vocabulary of the Stable Diffusion text encoder, despite" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.545 + ], + "angle": 0, + "content": "its frequent use in medical contexts). Therefore, our method ensures applicability across diverse imaging modalities and scenarios within the medical domain, as it remains independent of the specific encoder choice and is instead reliant on the latent diffusion backbone used for prompt optimization. Minimal reversal steps. Previous studies [41] have demonstrated that the diffusion model's sensitivity to conditioning intensifies significantly during the later stages of the diffusion process, particularly when noise levels are higher. Conversely, in the initial timesteps, the diffusion loss remains relatively stable across various prompts applied to the same image. Inspired by this observation, we hypothesize that not all reverse diffusion steps are necessary for generating an adversarial image. Optimizing only for the early timesteps of diffusion process (akin to later timesteps of denoising process) has two-fold advantage. First, given that we are optimizing the early layers of a very deep neural network, the resulting gradients tend to be quite small which contributes to our method's efficiency compared to others that require training the entire diffusion model. Additionally, early timesteps (the start of the diffusion process) are associated with high-frequency components, focusing on reconstructing edges, textures, and fine-grained structures [43]. By introducing adversarial perturbations during this stage, our strategy generates examples that effectively mimic common scenarios in ultrasound imaging, where acquisition settings—such as the transducer's operating frequency and its orientation relative to the anatomy—significantly influence the high-frequency content captured in the images [35]. We provide more details in the next sections." + }, + { + "type": "code_caption", + "bbox": [ + 0.523, + 0.565, + 0.862, + 0.595 + ], + "angle": 0, + "content": "Algorithm 1: Text-Guided Diffusion-Based Attack Pipeline for Single Image" + }, + { + "type": "algorithm", + "bbox": [ + 0.52, + 0.597, + 0.877, + 0.891 + ], + "angle": 0, + "content": "Input: Attacked classifier \\(f\\) , Image \\(x\\) , Prompt \\(p\\) Label \\(y\\) \nOutput: Adversarily perturbed image \\(x_{\\mathrm{adv\\_best}}\\) \n\\(d_{\\mathrm{best}}\\gets \\infty\\) . \nfor \\(i\\in\\) range(num_iterations) do \n\\(t\\gets\\) randint(0,50); \n\\(z\\gets\\) vae.encode(x), \\(C\\gets\\) textencoder(p); \n\\(\\epsilon \\gets\\) randn_like(z), \\(z_{t}\\gets\\) add_noise(z, \\(\\epsilon ,t)\\) \n\\(\\tilde{z}\\gets \\sqrt{\\frac{1}{\\bar{\\alpha}_t}} (z_t - \\sqrt{1 - \\bar{\\alpha}_t}\\cdot \\epsilon_\\theta (z_t,t,C));\\) \n\\(x_{\\mathrm{adv}}\\gets\\) vaedecode(\\(\\tilde{z}\\) ), \\(x_{\\mathrm{adv}}\\gets (x_{\\mathrm{adv}} + 1) / 2;\\) \n\\(x_{\\mathrm{adv}}\\) .Normalize(mean, std), \\(\\tilde{y}\\gets f(x_{\\mathrm{adv}})\\) \nLoss \\(\\leftarrow -10^{10}\\times\\) CrossEntropyLoss(y,y)+ mse(ε,εθzt,C)); \nLoss-backward(), textencoder_optimizer.step(); \n\\(d\\gets\\) mse(x,xadv); \nif \\(d < d_{best}\\) then \n\\(\\begin{array}{r}\\lfloor d_{\\mathrm{best}}\\leftarrow d,x_{\\mathrm{adv\\_best}}\\leftarrow x_{\\mathrm{adv}}; \\end{array}\\) \nreturn \\(x_{\\mathrm{adv\\_best}}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28567" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.44 + ], + "angle": 0, + "content": "Attacking policy setup. Given a target image \\( \\pmb{x} \\) and a latent diffusion model parameterized by \\( \\epsilon_{\\theta} \\), our goal is to optimize the text encoder to best represent the visual content of the image while simultaneously crafting an adversarial attack on the classifier. To determine the optimal text encoder for generating an adversarial image, we formulate the problem with two components. First, we employ a cross-entropy loss to measure the difference between the classifier's predicted output and the actual image class. Second, we include a loss that captures the discrepancy between the predicted noise from the network and the noise originally added to the image under a specific prompt condition, thereby ensuring semantic similarity between the adversarial image and the original image. Our objective is to recover the set of embeddings that align our objective of generating an adversarial image. Note that we freeze the diffusion model parameters throughout this optimization except the text encoder part. As discussed previously, instead of optimizing over all diffusion time steps, we restrict the range of \\( t \\) to early diffusion timesteps \\( (t \\leq 50) \\). Subsequently, the image that shows the highest similarity to the original input is selected as the adversarial output. The complete approach of our method is illustrated in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.452, + 0.226, + 0.469 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.477, + 0.485, + 0.599 + ], + "angle": 0, + "content": "This section starts by outlining the experimental setup, the comparison framework, and the evaluation metrics used. We then present both quantitative and qualitative comparisons against the current state-of-the-art methods, focusing on the stealthiness of the perturbations introduced and the realism of the generated examples. Finally, we conduct ablation and sensitivity analyses to evaluate the influence of key components and hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.607, + 0.295, + 0.623 + ], + "angle": 0, + "content": "4.1. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.486, + 0.81 + ], + "angle": 0, + "content": "Dataset and Models. We leverage three publicly available breast ultrasound datasets and experiment with three widely recognized classifier architectures—ResNet34 [23], SqueezeNet1.1 [28], and DenseNet121 [26]—which are commonly used as baselines in medical imaging research [1, 32]. Given the relatively small dataset sizes, we apply five-fold cross-validation across all classes to ensure robust evaluation. For consistency with the classifier architectures, all images are resized to \\(224 \\times 224\\) pixels. Additionally, we incorporate a pre-trained LDM from Hugging Face, specifically utilizing the Stable-Diffusion-v-1-4 variant [13]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.485, + 0.902 + ], + "angle": 0, + "content": "BUSI (Breast Ultrasound Images). Collected in 2018, this dataset comprises ultrasound scans from 600 female patients between the ages of 25 and 75, gathered for breast cancer detection. The dataset includes a total of 780 images, each with an average resolution of \\(500 \\times 500\\) pixels, categorized into three classes: normal (133 images), benign" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.823, + 0.107 + ], + "angle": 0, + "content": "(437 images), and malignant (210 images) [2]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.107, + 0.905, + 0.197 + ], + "angle": 0, + "content": "BUS-BRA. BUS-BRA [18] dataset includes 1875 anonymized images from 1,064 female patients, acquired with four different ultrasound scanners as part of systematic studies conducted at the National Institute of Cancer in Rio de Janeiro, Brazil. This dataset includes biopsy-confirmed tumor cases, with 1268 benign and 607 malignant cases." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.198, + 0.905, + 0.317 + ], + "angle": 0, + "content": "UDIAT. Collected in 2012 at the UDIAT Diagnostic Centre of the Parc Taulí Corporation in Sabadell, Spain, this dataset [62] was gathered using a Siemens ACUSON Sequoia C512 system with a 17L5 HD linear array transducer operating at \\(8.5\\mathrm{MHz}\\). It comprises 163 images from 163 female patients, with an average resolution of \\(760\\times 570\\) pixels, categorized into 53 malignant and 110 benign lesions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.908, + 0.455 + ], + "angle": 0, + "content": "Hyperparameters. In our experiments, we train the model for 500 iterations with a learning rate of \\(5 \\times 10^{-4}\\) using the AdamW optimizer [38]. For adversarial methods, we set the FGSM attack parameter to \\(\\epsilon = 0.05\\). For the PGD attack, we configure \\(\\epsilon = 0.03\\) with a step size of \\(\\alpha = 0.007\\) over 200 iterations. We utilize Diff-PGD with the same setting as it used for ImageNet [14]. We run our experiments on a single NVIDIA RTX V100 GPU with 32GB memory." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.467, + 0.912, + 0.737 + ], + "angle": 0, + "content": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.880.400.81123.51
PGD0.570.290.45378.62
Diff-PGD1.00.300.87111.03
P2P (Ours)0.980.130.8545.84
ResNet34
FGSM0.960.410.81131.62
PGD0.550.250.37332.01
Diff-PGD1.00.310.84117.49
P2P (Ours)0.970.120.8143.03
SqueezeNet1.1
FGSM0.490.160.40118.03
PGD0.330.200.30250.38
Diff-PGD0.740.140.5679.51
P2P (Ours)0.960.090.6347.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.748, + 0.908, + 0.791 + ], + "angle": 0, + "content": "Table 1. Evaluation of adversarial attacks on different attack models for BUSI dataset [2] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.829, + 0.833 + ], + "angle": 0, + "content": "4.2. Evaluation of Adversarial Examples" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.908, + 0.903 + ], + "angle": 0, + "content": "To evaluate the quality of adversarial examples generated by our proposed P2P method, we benchmark it against the leading Diffusion-Based Projected Gradient Descent (Diff-PGD) attack and conventional techniques like FGSM and" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "28568" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.098, + 0.868, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.268, + 0.908, + 0.298 + ], + "angle": 0, + "content": "Figure 3. Visual comparison of different attack methods on a benign image from the BUSI dataset, using DenseNet121 as the classifier. The second row displays the perturbations, calculated as the difference between the original image and the attacked example." + }, + { + "type": "image", + "bbox": [ + 0.153, + 0.31, + 0.866, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.529, + 0.908, + 0.571 + ], + "angle": 0, + "content": "Figure 4. Comparison of original and P2P-attacked ultrasound images from BUS-BRA Dataset, using DenseNet121 as the classifier. The top row shows the original images with their diagnostic labels, while the bottom row displays the same images after applying the P2P attack. Green boxes indicate the true labels, while red boxes show the labels predicted by the classifier after the attack." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.483, + 0.645 + ], + "angle": 0, + "content": "PGD. We assess each attack's performance across metrics including Success Rate, LPIPS, SSIM, and FID, enabling a comprehensive analysis of both adversarial efficacy and the perceptual integrity of the generated adversarial samples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.646, + 0.483, + 0.735 + ], + "angle": 0, + "content": "In our setting, each attack baseline is applied to validation set images that were initially classified correctly, with adversarial examples retained only when successful in misleading the classifiers. Accordingly, all metrics presented in Tabs. 1 to 3 reflect measurements derived exclusively from these modified images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.736, + 0.483, + 0.871 + ], + "angle": 0, + "content": "Across all datasets and classifier architectures, our P2P approach consistently attains high Success Rates [7] comparable to those achieved by Diff-PGD, while surpassing baseline methods in Fréchet Inception Distance (FID) [24], reflecting the imperceptibility of the crafted adversarial examples, and in Learned Perceptual Image Patch Similarity (LPIPS) [63], indicating reduced distortion in our attacks. These results highlight the superior perceptual quality of adversarial examples generated by our method." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.872, + 0.483, + 0.887 + ], + "angle": 0, + "content": "In terms of Structural Similarity Index Measure (SSIM)," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.907, + 0.78 + ], + "angle": 0, + "content": "which evaluates the structural alignment between adversarial and original images, our method achieves competitive performance. Although Diff-PGD occasionally marginally outperforms P2P in SSIM for specific models, P2P consistently maintains strong SSIM values across all datasets, as shown in Tabs. 1 to 3. This reflects high visual similarity between the generated adversarial examples \\( x_{\\mathrm{adv}} \\) and the original clean images \\( x \\), capturing low perceived visual distortion by preserving luminance, contrast, and structural details. The combination of high SSIM with low LPIPS and FID scores underscores P2P's ability to preserve structural consistency while producing perceptually aligned adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.887 + ], + "angle": 0, + "content": "For the DenseNet121 and ResNet34 classifiers, P2P achieves a strong balance of high Success Rate, low LPIPS, and favorable SSIM and FID scores, surpassing traditional methods. With SqueezeNet1.1, P2P exhibits particularly robust performance on perceptual metrics, reaching the lowest LPIPS and FID values across all datasets, as shown in Tabs. 1 to 3, highlighting its ability to generate realistic and" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28569" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.487, + 0.359 + ], + "angle": 0, + "content": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.930.400.77112.11
PGD0.430.190.56213.65
Diff-PGD1.00.290.8290.5
P2P (Ours)0.940.120.7838.00
ResNet34
FGSM0.810.350.66133.17
PGD0.310.120.24158.24
Diff-PGD1.00.290.78100.2
P2P (Ours)0.930.110.7244.09
SqueezeNet1.1
FGSM0.690.160.77120.14
PGD0.430.260.40292.99
Diff-PGD0.750.120.4789.47
P2P (Ours)0.740.080.4958.60
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.37, + 0.483, + 0.414 + ], + "angle": 0, + "content": "Table 2. Evaluation of adversarial attacks on different attack models for BUS-BRA dataset [18] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.441, + 0.371, + 0.457 + ], + "angle": 0, + "content": "structurally consistent adversarial images." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.457, + 0.483, + 0.577 + ], + "angle": 0, + "content": "Overall, P2P demonstrates competitive Success Rates while consistently producing high-quality adversarial examples with enhanced visual fidelity and structural similarity. The results underscore P2P's effectiveness as a balanced approach for crafting effective and perceptually similar adversarial images across various datasets and classifiers. We will further elaborate on these results qualitatively in the subsequent section." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.59, + 0.468, + 0.607 + ], + "angle": 0, + "content": "4.3. Qualitative Results of Adversarial Examples" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.614, + 0.485, + 0.901 + ], + "angle": 0, + "content": "Figure 3 presents visual comparisons of images and adversarial perturbations generated by different attack methods. Notably, our method (P2P) produces attack examples that more closely follow the distribution of the original medical images, resulting in a more natural and less detectable alteration. In contrast, other attack methods, such as FGSM, PGD, and Diff-PGD, introduce high-frequency noise with a distinct \"textured\" appearance. This textured noise can make these adversarial examples appear less natural, potentially revealing them as manipulated images, exhibit noisy artifacts. Besides, Fig. 4 shows that the P2P attack successfully changes the diagnostic labels of ultrasound images with minimal alteration to the images' semantic appearance, demonstrating label vulnerability despite preserved image semantics. Moreover, the t-SNE [54] visualization of clean and attacked image features further confirms the effect of our prompt learning method. Figure 5 compares four attack methods—FGSM, PGD, Diff-PGD, and P2P (Ours)—in terms of how well they blend attack samples" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.089, + 0.911, + 0.36 + ], + "angle": 0, + "content": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.970.370.77103.07
PGD0.170.070.11147.84
Diff-PGD1.00.270.8081.31
P2P (Ours)0.860.120.6227.18
ResNet34
FGSM0.980.410.75103.68
PGD0.230.100.19135.95
Diff-PGD1.00.310.7780.89
P2P (Ours)0.970.150.7420.3
SqueezeNet1.1
FGSM0.590.200.4272.51
PGD0.160.140.19292.21
Diff-PGD0.770.160.5432.47
P2P (Ours)0.760.100.5223.50
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.513, + 0.37, + 0.908, + 0.413 + ], + "angle": 0, + "content": "Table 3. Evaluation of adversarial attacks on different attack models for UDIAT dataset [62] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.441, + 0.907, + 0.546 + ], + "angle": 0, + "content": "with clean data clusters. Diff-PGD shows limited effectiveness, with noticeable separations between attack and clean samples. FGSM and PGD improve blending but still leaves isolated clusters of attack points. P2P achieves the best integration, with attack samples closely interwoven with clean data, indicating superior performance in making adversarial examples indistinguishable from clean data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.547, + 0.909, + 0.743 + ], + "angle": 0, + "content": "To gain further insights, we examined attacked examples from the training set, focusing on images that the classifier identifies with high confidence. Figure 6 presents malignant cases from the BUSI training set alongside their attacked versions generated by Diff-PGD and our method, P2P. As illustrated, the Diff-PGD attack introduces a noticeable noise pattern, while our method produces images that closely resemble the originals. Interestingly, additional examples reveal that Diff-PGD's image quality deteriorates as the classifier's confidence increases. While attack experiments are generally performed on validation sets, we analyzed training set images here to understand the performance of different attack models in varied scenarios." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.756, + 0.669, + 0.772 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.855 + ], + "angle": 0, + "content": "This section disentangles the effects of design choices to assess their individual contributions to our approach's effectiveness. All ablation experiments are conducted on the BUSI dataset, using ResNet34 as the classifier, with results averaged over 5-fold cross-validation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Loss Function. Ablation study results on the effect of MSE loss function are reported in Tab. 4 (second row) and Fig. 7. Although using an MSE loss does not necessarily lead to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28570" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.875, + 0.187 + ], + "angle": 0, + "content": "
ComponentLoss FunctionTime StepSuccess RateLPIPSSSIMFIDTime (second)
Baseline0.970.120.8143.03178
W/O MSE✓0.960.120.8043.58178
T=20✓0.830.100.7149.9798
T=100✓0.970.120.8138.06280
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.197, + 0.908, + 0.242 + ], + "angle": 0, + "content": "Table 4. Comparison of the ablation study on different components of the P2P pipeline. The baseline configuration uses T=50 with MSE in the loss function. In each row, only one component is modified from the baseline. 'Time' indicates the duration of the generation process for the attack per image." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.263, + 0.285, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.371, + 0.218, + 0.38 + ], + "angle": 0, + "content": "a) FGSM" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.264, + 0.476, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.37, + 0.404, + 0.38 + ], + "angle": 0, + "content": "b) PGD" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.38, + 0.285, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.484, + 0.226, + 0.494 + ], + "angle": 0, + "content": "c) Diff-PGD" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.38, + 0.476, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.484, + 0.42, + 0.495 + ], + "angle": 0, + "content": "d) P2P (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.505, + 0.483, + 0.548 + ], + "angle": 0, + "content": "Figure 5. t-SNE visualization of last-layer ResNet34 features on the BUSI dataset for FGSM, PGD, Diff-PGD, and our P2P. Clean examples are shown in blue, and adversarial examples in orange." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.562, + 0.223, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.686, + 0.194, + 0.697 + ], + "angle": 0, + "content": "a) Original" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.562, + 0.347, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.686, + 0.323, + 0.697 + ], + "angle": 0, + "content": "b) Diff-PGD" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.562, + 0.472, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.686, + 0.431, + 0.697 + ], + "angle": 0, + "content": "c) P2P" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.709, + 0.483, + 0.736 + ], + "angle": 0, + "content": "Figure 6. Attack examples of a malignant image of Dataset BUSI from Diff-PGD and P2P with ResNet34 as a classifier." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "better quantitative metrics, Fig. 7 shows that it attempts to mitigate artifacts and retain the semantic integrity of the ultrasound image. Specifically, the middle image (without MSE) exhibits enhanced linear or streak-like artifacts, which may disrupt the homogeneity of tissue appearance (highlighted in the red rectangular region) and obscure finer structural details in the ultrasound image. Incorporating the MSE loss helps to reduce intensity fluctuations, creating a smoother and more consistent appearance, particularly" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.263, + 0.646, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.557, + 0.371, + 0.616, + 0.383 + ], + "angle": 0, + "content": "a) Original" + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.263, + 0.77, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.371, + 0.747, + 0.382 + ], + "angle": 0, + "content": "b) W/O MSE" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.263, + 0.895, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.371, + 0.856, + 0.382 + ], + "angle": 0, + "content": "c) MSE" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.394, + 0.907, + 0.436 + ], + "angle": 0, + "content": "Figure 7. Impact of MSE loss in the P2P framework. Image (a) shows the clean reference image, image (b) shows the P2P result without MSE loss, and image (c) includes the MSE loss function." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.465, + 0.833, + 0.479 + ], + "angle": 0, + "content": "beneficial in areas with subtle tissue boundaries." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.907, + 0.646 + ], + "angle": 0, + "content": "Step Selection To justify the choices for P2P with optimization for different timesteps, we show in Tab. 4 the performance of our method with different settings. Using 20 steps, the approach yields prompts that generate attack images with relatively low success, SSIM and LPIPS. However, when optimizing with more timesteps (\\(T = 100\\)) even though, the FID of the generated attack images is better, other metrics are comparable to that of (\\(T = 50\\)), but with longer time to generate attack images. Therefore, given the efficiency dilemma and the results presented, selecting 50 steps appears to be a reasonable choice." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.678, + 0.634, + 0.694 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We designed P2P, an effective adversarial attack method for synthesizing adversarial breast ultrasound images using prompt learning in text-to-image diffusion models. We showcase the effectiveness of our approach across various attack scenarios, especially valuable in data-limited medical applications. Our adversarial images surpass previous methods, appearing more clinically natural and harder to detect. They also maintain lower perceptual differences and achieve greater structural similarity. P2P enables significantly easier attacks on classifiers in the medical domain, eliminating the need for pre-trained models in a specific domain by facilitating the construction of effective textual examples." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28571" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.264, + 0.108 + ], + "angle": 0, + "content": "6. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.114, + 0.486, + 0.241 + ], + "angle": 0, + "content": "This work was supported by the Canadian Foundation for Innovation-John R. Evans Leaders Fund (CFI-JELF) program grant number 42816. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [RGPIN-2023-03575]. Cette recherche a eté financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG), [RGPIN-2023-03575]. 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However, these models are highly susceptible to adversarial attacks—small, imperceptible changes that can mislead classifiers—raising critical concerns about their reliability and security. Traditional attacks rely on fixed-norm perturbations, misaligning with human perception. In contrast, diffusion-based attacks require pre-trained models, demanding substantial data when these models are unavailable, limiting practical use in data-scarce scenarios. In medical imaging, however, this is often unfeasible due to the limited availability of datasets. Building on recent advancements in learnable prompts, we propose Prompt2Perturb $(P2P)$ , a novel language-guided attack method capable of generating meaningful attack examples driven by text instructions. During the prompt learning phase, our approach leverages learnable prompts within the text encoder to create subtle, yet impactful, perturbations that remain imperceptible while guiding the model towards targeted outcomes. In contrast to current prompt learning-based approaches, our $P2P$ stands out by directly updating text embeddings, avoiding the need for retraining diffusion models. Further, we leverage the finding that optimizing only the early diffusion steps boosts efficiency while ensuring that the generated adversarial examples incorporate subtle noise, thus preserving ultrasound image quality without introducing noticeable artifacts. We show that our method outperforms state-of-the-art attack techniques across three breast ultrasound datasets in FID and LPIPS. Moreover, the generated images are both more natural in appearance and more effective compared to existing adversarial attacks. Our Code is publicly available on GitHub. + +![](images/d323c553b7d7cb4ca5a950325c613ebb35b589f3b1098c79a88f236e3c675353.jpg) +Figure 1. Illustration of P2P in an adversarial attack against Diff-PGD; note there is no exhibited change of image semantics in our method. + +# 1. Introduction + +Mammography remains the primary tool for breast cancer screening, offering widespread accessibility and proven effectiveness in detecting early-stage tumors [16]. However, it has some limitations, including patient discomfort and reduced diagnostic accuracy in individuals with dense breast tissue [33]. Ultrasound has become a useful supplementary technique, as it provides better patient comfort and avoids the risks associated with radiation exposure. Its ability to capture real-time images makes it beneficial for further investigating abnormalities observed on mammograms [16]. Nonetheless, the performance of ultrasound can be inconsistent, with sensitivity and specificity affected by the operator's expertise, device configuration, and changes in tissue characteristics due to breast density. Furthermore, variability in interpretation among different radiologists poses additional challenges [51]. In response to these issues, computational approaches, especially deep learning models, are gaining traction as promising tools to improve diagnostic outcomes and address these existing gaps [12, 31, 51]. + +Ensuring the security and robustness of medical deep neural networks (DNNs) is a key concern in healthcare. Recent research in medical imaging tasks has revealed that even state-of-the-art DNNs are highly susceptible to adversar + +ial attacks [39]. Specifically, medical imaging DNNs are more susceptible to adversarial threats than those designed for natural images [39]. In addition, the limited availability of publicly accessible medical images, which poses a challenge for effective training, has pushed modern algorithms to rely on pre-trained models based on large datasets of natural images—a technique known as transfer learning. However, due to the substantial difference between natural and medical images, deep learning models developed through transfer learning tend to be more vulnerable to adversarial attacks [10]. + +To address this vulnerability, various adversarial attack methods have been developed. Traditional gradient-based methods such as fast gradient sign method (FGSM) [20], Carlini-wagner [8], and projected gradient descent (PGD) [40] perturb original images within predefined perturbation bounds. Although they can be easily generated using gradient-based techniques, these attacks often deviate significantly from the true data distribution of natural images, leading to a compromise between their effectiveness and subtlety [61]. Generative models such as generative adversarial networks (GANs) [19] have been used to generate adversarial examples, based on their ability to produce high-quality images, by perturbing latent space [3, 49, 64]. However, modifying latent codes changes the high-level semantics of generated images in a way that is easily noticeable to human observers [30]. Recently, diffusion-based models have been employed in the literature to generate realistic adversarial images [11, 36, 61]. In models like AdvDiffuser [11] and Diff-PGD [61], the PGD method is incorporated into the diffusion process to enhance the realism of the generated images. Furthermore, approaches such as Instruct2Attack [37] leverage latent diffusion models [46] to deceive the target model by optimizing over input prompts. These text-guided attacks aim to produce adversarial semantic image edits, such as altering the color of a truck in an image. While image editing holds significant value in natural image domains, it is less applicable in the medical field, as altering the semantics of medical images can result in unrealistic representations. Additionally, these models are often not well-adapted to clinical terminology, making such modifications less meaningful in medical contexts [57]. + +These limitations can be addressed by reversing the diffusion model to obtain context-relevant text tokens, or prompts, specifically designed for the medical domain to generate adversarial images. Optimizing these prompts presents a challenge due to the intricate structure of the generative model, which includes a two-part pipeline: a conditioning network (the CLIP text encoder [44]) and a generative unit (U-Net [47]), both of which complicate gradient flow to the input layer. To tackle these obstacles, we freeze the generative model and make the following contributions: + +- Our method requires no fine-tuning and efficiently generates attack images by directly updating text embeddings, unlike previous diffusion-based approaches reliant on large pre-trained models on the same domain. Additionally, we find that optimizing only the initial forward diffusion steps is sufficient, improving efficiency and maintaining image quality without the need for all reverse diffusion phases. +- Based on our findings, we proposed Prompt2Perturb (P2P) to create challenging adversarial examples optimized for clinical terminology that are particularly challenging to distinguish as attacked, thus highlighting limitations in current adversarial attack mechanisms. +- We demonstrate empirically that our method produces semantically significant attack images that are perceptually similar but varied versions of a target image (see Fig. 1). By incorporating relevant clinical terminology into the text embedding of Stable Diffusion, we ensure that the generated images retain clinical accuracy and realism, thereby enhancing the effectiveness of the attack in a medical context. + +# 2. Related Work + +Adversarial attack. DNN models are widely recognized as being susceptible to adversarial attacks [45]. These attacks can manipulate the model's predictions by introducing subtle modifications that are imperceptible to human observers. Adversarial attacks pose a major barrier to the widespread adoption of deep learning models in real-world applications, and considerable research has been dedicated to addressing this ongoing challenge. Adversarial attacks can be broadly classified into black-box and white-box types. White-box attacks, such as limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) [52], FGSM [20], PGD [40], C-W [8], and DeepFool [42], rely on full access to the target model's architecture and parameters, making them gradient-based. In contrast, black-box attacks do not require this level of access and generate adversarial samples through query-based methods. Despite these differences, many white-box attacks are still effective in black-box settings due to the transferability of adversarial examples across models. Adversarial training, which involves training a model using adversariably generated examples, is one of the limited methods available to defend against adversarial attacks [5]. In medical domain, several approaches have been developed to generate adversarial examples targeting computer-aided diagnosis models which can be consistently taxonomized with that of adversarial attacks [15]. Specifically, Zhou et al. [65] introduced two GAN-based models operating at different resolutions, capable of generating highly realistic adversarial images that can mislead breast cancer diagnosis. MIRST [50] was proposed to defend untargeted adversarial attacks + +![](images/68f6b89a0fba1940bc379c80ee12300eca6779e33f79b04c9d797a90eabbd1ff.jpg) +Figure 2. Overall framework of the proposed method. Image adapted from [36] + +on breast ultrasound images. Lastly, Hao et al. [22] introduce an adversarially robust feature learning method where a feature correlation metric is included as an objective function to promote the learning of robust features while minimizing the influence of spurious ones for the application of breast cancer diagnosis. + +Adversarial attack with diffusion models. The success of diffusion models has motivated their exploration in adversarial deep learning, demonstrating potential for both attacking [60, 66] and defending [58, 59] against adversarial examples. These methods are broadly used to enhance the imperceptibility of unconstrained adversarial perturbations [9], transfer the style from the reference image into the original image to create natural-looking adversarial images [56], or attack the diffusion-based purification method [29]. + +Prompt learning. Recent progress in controllable image generation and editing using diffusion models [25, 48] has created new possibilities for developing semantic adversarial attacks. Prompt learning was initially introduced as an alternative to full fine-tuning and linear probing, aiming to leverage pre-trained language models in natural language processing (NLP) [34]. Recently, prompt learning techniques have been adapted for adversarial purposes. For instance, BadCLIP [4] targets the CLIP [44] model by injecting a backdoor during the prompt learning phase. In the medical field, BAPLe [21] utilizes learnable prompts within the text encoder and introduces imperceptible learnable noise triggers into input images, effectively leveraging the full capabilities of medical foundation models. Additionally, PromptSmooth [27] uses prompt learning to efficiently achieve certified robustness in medical vision-language models by leveraging semantic concepts. + +# 3. Methodology + +# 3.1. Preliminary + +We explore the challenge of image classification. Consider an image sample $\pmb{x} \in \mathcal{X} \coloneqq \mathbb{R}^{H \times W \times C}$ , paired with its label $y \in \mathcal{Y} \coloneqq \{1, \dots, |\mathcal{Y}|\}$ , where $H, W,$ and $C$ represent the image's height, width, and number of channels, respec + +tively. Let $f: \mathcal{X} \to \mathcal{Y}$ denote the image classifier. Given a clean input image $\pmb{x}$ and its true label $y$ , the attacker's objective is to generate an adversarial version $\pmb{x}_{\mathrm{adv}}$ of $\pmb{x}$ that misleads $f$ , so that $f(\pmb{x}_{\mathrm{adv}}) \neq y$ . Traditional approaches either necessitate adding pixel-level adversarial noise $\delta$ [8, 20] to the input image $\pmb{x}$ , resulting in $\pmb{x}_{\mathrm{adv}} = \pmb{x} + \delta$ , or manipulating data to embed subtle biases or vulnerabilities. In this work, we instead focus on prompt-guided semantic attacks, aiming to create meaningful, interpretable perturbed images guided by language descriptions. + +# 3.2. Prompt2Perturb (P2P) + +Figure 2 provides a high-level overview of the proposed approach. Our approach seeks to generate an adversarial image, $\pmb{x}_{\mathrm{adv}}$ , such that the modification from the original image $\pmb{x}$ is guided by a text-based embedding instruction $C$ . The core idea of Prompt2Perturb (P2P) is to update these text embeddings specifically for the modified input to steer the classifier toward an incorrect prediction. In the subsequent sections, we will provide a detailed breakdown of each component of our proposed method. + +Latent Diffusion Models. We utilize the learned latent space of a generative model, defined as $\mathcal{Z} = z\mid z = \mathcal{E}(\boldsymbol {x}),\boldsymbol {x}\in \mathcal{X}\subseteq \mathbb{R}^{h\times w\times c}$ , where $\mathcal{E}$ represents the image encoder and $h\times w\times c$ denotes the dimensions of the latent space. Unlike the image space, this latent space offers a compact, lower-dimensional representation that emphasizes the critical semantic details, making it ideal for controlled semantic alterations. These modifications are enabled through a pretrained conditional latent diffusion model (LDM) [6, 46], which facilitates meaningful and guided editing in the latent domain. + +The encoder is regularized via either a KL-divergence penalty or vector quantization, as suggested by prior works [53]. The corresponding decoder, denoted as $\mathcal{D}$ , learns to reconstruct input images from the latent representations, ensuring $\mathcal{D}(\mathcal{E}(x)) \approx x$ , for high fidelity reconstruction. Subsequently, a diffusion model is trained to generate latent codes that reside within the learned latent space. This diffusion model is flexible and can be conditioned using + +auxiliary information, such as class labels, segmentation masks, or features from a co-trained text-embedding model. Specifically, let $c_{\theta}(p)$ represent a network mapping conditioning input $p$ to its respective conditioning vector. The objective function for the Latent Diffusion Model (LDM) can thus be formulated as: + +$$ +\mathcal {L} _ {\mathrm {L D M}} := \mathbb {E} _ {z \sim \mathcal {E} (x), p, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (z _ {t}, t, c _ {\theta} (p)) \| _ {2} ^ {2} \right], +$$ + +where $t$ is the time step, $z_{t}$ is the noisy latent at $t$ , $\epsilon$ is the unscaled noise sample, and $\epsilon_{\theta}$ is the denoising network. Intuitively, the objective here is to correctly remove the noise added to a latent representation of an image. While training, $c_{\theta}$ and $\epsilon_{\theta}$ are jointly optimized to minimize the LDM loss. At inference time, a random noise tensor is sampled and iteratively denoised to produce a new image latent, $z_{0}$ . Finally, this latent code is transformed into an image through the pre-trained decoder $x' = \mathcal{D}(z_0)$ . Previous diffusion-based attack methods leverage extensively pretrained models on natural images, incorporating specialized attack strategies and employing a reverse diffusion process to generate adversarial examples that resemble the underlying data distribution. However, this approach is impractical in the medical domain due to the lack of extensively trained models caused by inherent data scarcity and the presence of diverse imaging modalities. Unlike these previous approaches, our method is well-suited to handle this diversity without requiring retraining of a diffusion model or relying on large-scale pre-trained models. This robustness stems from our approach, which involves updating the text embeddings directly, rather than merely adding noise to the latent space. We next review the early stages of such a text encoder, and our choice of attack space. + +Text optimization. The text encoder processes the input prompt $\mathbf{P}$ , which is fed into the latent diffusion model. A text tokenizer transforms the prompt strings into tokens, representing indices in a predefined vocabulary of size $|V|$ . Each token is then mapped to its corresponding embedding vector $\mathbf{c}_i \in \mathbf{C}$ , where $i \in 1, \dots, |V|$ within the embedding space $\mathcal{C}$ . Previous work on textual inversion in the embedding space $\mathcal{C}$ [17, 55] attempts to learn new concepts for a set of images by associating placeholder strings with newly learned embedding vectors. This effectively expands the existing vocabulary with additional concepts. However, these newly learned concepts have been found to be uninformative in the medical domain, as the learned embeddings are often distant from the embeddings corresponding to the original vocabulary. In contrast, our approach aims to optimize the embedding vectors $\mathbf{c}_i$ , $i \in 1, \dots, L$ , from the existing vocabulary for a prompt of maximum length $L$ specific to the medical domain. This adaptation addresses the limitations of existing diffusion model vocabularies that lack specific medical terms (e.g., the word "benign" is not present in the vocabulary of the Stable Diffusion text encoder, despite + +its frequent use in medical contexts). Therefore, our method ensures applicability across diverse imaging modalities and scenarios within the medical domain, as it remains independent of the specific encoder choice and is instead reliant on the latent diffusion backbone used for prompt optimization. Minimal reversal steps. Previous studies [41] have demonstrated that the diffusion model's sensitivity to conditioning intensifies significantly during the later stages of the diffusion process, particularly when noise levels are higher. Conversely, in the initial timesteps, the diffusion loss remains relatively stable across various prompts applied to the same image. Inspired by this observation, we hypothesize that not all reverse diffusion steps are necessary for generating an adversarial image. Optimizing only for the early timesteps of diffusion process (akin to later timesteps of denoising process) has two-fold advantage. First, given that we are optimizing the early layers of a very deep neural network, the resulting gradients tend to be quite small which contributes to our method's efficiency compared to others that require training the entire diffusion model. Additionally, early timesteps (the start of the diffusion process) are associated with high-frequency components, focusing on reconstructing edges, textures, and fine-grained structures [43]. By introducing adversarial perturbations during this stage, our strategy generates examples that effectively mimic common scenarios in ultrasound imaging, where acquisition settings—such as the transducer's operating frequency and its orientation relative to the anatomy—significantly influence the high-frequency content captured in the images [35]. We provide more details in the next sections. + +Algorithm 1: Text-Guided Diffusion-Based Attack Pipeline for Single Image +Input: Attacked classifier $f$ , Image $x$ , Prompt $p$ Label $y$ +Output: Adversarily perturbed image $x_{\mathrm{adv\_best}}$ $d_{\mathrm{best}}\gets \infty$ . +for $i\in$ range(num_iterations) do + $t\gets$ randint(0,50); + $z\gets$ vae.encode(x), $C\gets$ textencoder(p); + $\epsilon \gets$ randn_like(z), $z_{t}\gets$ add_noise(z, $\epsilon ,t)$ $\tilde{z}\gets \sqrt{\frac{1}{\bar{\alpha}_t}} (z_t - \sqrt{1 - \bar{\alpha}_t}\cdot \epsilon_\theta (z_t,t,C));$ $x_{\mathrm{adv}}\gets$ vaedecode( $\tilde{z}$ ), $x_{\mathrm{adv}}\gets (x_{\mathrm{adv}} + 1) / 2;$ $x_{\mathrm{adv}}$ .Normalize(mean, std), $\tilde{y}\gets f(x_{\mathrm{adv}})$ +Loss $\leftarrow -10^{10}\times$ CrossEntropyLoss(y,y)+ mse(ε,εθzt,C)); +Loss-backward(), textencoder_optimizer.step(); + $d\gets$ mse(x,xadv); +if $d < d_{best}$ then + $\begin{array}{r}\lfloor d_{\mathrm{best}}\leftarrow d,x_{\mathrm{adv\_best}}\leftarrow x_{\mathrm{adv}}; \end{array}$ +return $x_{\mathrm{adv\_best}}$ + +Attacking policy setup. Given a target image $\pmb{x}$ and a latent diffusion model parameterized by $\epsilon_{\theta}$ , our goal is to optimize the text encoder to best represent the visual content of the image while simultaneously crafting an adversarial attack on the classifier. To determine the optimal text encoder for generating an adversarial image, we formulate the problem with two components. First, we employ a cross-entropy loss to measure the difference between the classifier's predicted output and the actual image class. Second, we include a loss that captures the discrepancy between the predicted noise from the network and the noise originally added to the image under a specific prompt condition, thereby ensuring semantic similarity between the adversarial image and the original image. Our objective is to recover the set of embeddings that align our objective of generating an adversarial image. Note that we freeze the diffusion model parameters throughout this optimization except the text encoder part. As discussed previously, instead of optimizing over all diffusion time steps, we restrict the range of $t$ to early diffusion timesteps $(t \leq 50)$ . Subsequently, the image that shows the highest similarity to the original input is selected as the adversarial output. The complete approach of our method is illustrated in Algorithm 1. + +# 4. Experiments + +This section starts by outlining the experimental setup, the comparison framework, and the evaluation metrics used. We then present both quantitative and qualitative comparisons against the current state-of-the-art methods, focusing on the stealthiness of the perturbations introduced and the realism of the generated examples. Finally, we conduct ablation and sensitivity analyses to evaluate the influence of key components and hyperparameters. + +# 4.1. Experimental settings + +Dataset and Models. We leverage three publicly available breast ultrasound datasets and experiment with three widely recognized classifier architectures—ResNet34 [23], SqueezeNet1.1 [28], and DenseNet121 [26]—which are commonly used as baselines in medical imaging research [1, 32]. Given the relatively small dataset sizes, we apply five-fold cross-validation across all classes to ensure robust evaluation. For consistency with the classifier architectures, all images are resized to $224 \times 224$ pixels. Additionally, we incorporate a pre-trained LDM from Hugging Face, specifically utilizing the Stable-Diffusion-v-1-4 variant [13]. + +BUSI (Breast Ultrasound Images). Collected in 2018, this dataset comprises ultrasound scans from 600 female patients between the ages of 25 and 75, gathered for breast cancer detection. The dataset includes a total of 780 images, each with an average resolution of $500 \times 500$ pixels, categorized into three classes: normal (133 images), benign + +(437 images), and malignant (210 images) [2]. + +BUS-BRA. BUS-BRA [18] dataset includes 1875 anonymized images from 1,064 female patients, acquired with four different ultrasound scanners as part of systematic studies conducted at the National Institute of Cancer in Rio de Janeiro, Brazil. This dataset includes biopsy-confirmed tumor cases, with 1268 benign and 607 malignant cases. + +UDIAT. Collected in 2012 at the UDIAT Diagnostic Centre of the Parc Taulí Corporation in Sabadell, Spain, this dataset [62] was gathered using a Siemens ACUSON Sequoia C512 system with a 17L5 HD linear array transducer operating at $8.5\mathrm{MHz}$ . It comprises 163 images from 163 female patients, with an average resolution of $760\times 570$ pixels, categorized into 53 malignant and 110 benign lesions. + +Hyperparameters. In our experiments, we train the model for 500 iterations with a learning rate of $5 \times 10^{-4}$ using the AdamW optimizer [38]. For adversarial methods, we set the FGSM attack parameter to $\epsilon = 0.05$ . For the PGD attack, we configure $\epsilon = 0.03$ with a step size of $\alpha = 0.007$ over 200 iterations. We utilize Diff-PGD with the same setting as it used for ImageNet [14]. We run our experiments on a single NVIDIA RTX V100 GPU with 32GB memory. + +
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.880.400.81123.51
PGD0.570.290.45378.62
Diff-PGD1.00.300.87111.03
P2P (Ours)0.980.130.8545.84
ResNet34
FGSM0.960.410.81131.62
PGD0.550.250.37332.01
Diff-PGD1.00.310.84117.49
P2P (Ours)0.970.120.8143.03
SqueezeNet1.1
FGSM0.490.160.40118.03
PGD0.330.200.30250.38
Diff-PGD0.740.140.5679.51
P2P (Ours)0.960.090.6347.64
+ +Table 1. Evaluation of adversarial attacks on different attack models for BUSI dataset [2] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples. + +# 4.2. Evaluation of Adversarial Examples + +To evaluate the quality of adversarial examples generated by our proposed P2P method, we benchmark it against the leading Diffusion-Based Projected Gradient Descent (Diff-PGD) attack and conventional techniques like FGSM and + +![](images/d702d8fb76952d7638ba5683dfbe92f63c6878c0b16323734cea5beb43f0c936.jpg) +Figure 3. Visual comparison of different attack methods on a benign image from the BUSI dataset, using DenseNet121 as the classifier. The second row displays the perturbations, calculated as the difference between the original image and the attacked example. + +![](images/d17d6949b37dcde8e1df7a1ebc65faa2d157eaa5134cf12c5233625a3ffc0119.jpg) +Figure 4. Comparison of original and P2P-attacked ultrasound images from BUS-BRA Dataset, using DenseNet121 as the classifier. The top row shows the original images with their diagnostic labels, while the bottom row displays the same images after applying the P2P attack. Green boxes indicate the true labels, while red boxes show the labels predicted by the classifier after the attack. + +PGD. We assess each attack's performance across metrics including Success Rate, LPIPS, SSIM, and FID, enabling a comprehensive analysis of both adversarial efficacy and the perceptual integrity of the generated adversarial samples. + +In our setting, each attack baseline is applied to validation set images that were initially classified correctly, with adversarial examples retained only when successful in misleading the classifiers. Accordingly, all metrics presented in Tabs. 1 to 3 reflect measurements derived exclusively from these modified images. + +Across all datasets and classifier architectures, our P2P approach consistently attains high Success Rates [7] comparable to those achieved by Diff-PGD, while surpassing baseline methods in Fréchet Inception Distance (FID) [24], reflecting the imperceptibility of the crafted adversarial examples, and in Learned Perceptual Image Patch Similarity (LPIPS) [63], indicating reduced distortion in our attacks. These results highlight the superior perceptual quality of adversarial examples generated by our method. + +In terms of Structural Similarity Index Measure (SSIM), + +which evaluates the structural alignment between adversarial and original images, our method achieves competitive performance. Although Diff-PGD occasionally marginally outperforms P2P in SSIM for specific models, P2P consistently maintains strong SSIM values across all datasets, as shown in Tabs. 1 to 3. This reflects high visual similarity between the generated adversarial examples $x_{\mathrm{adv}}$ and the original clean images $x$ , capturing low perceived visual distortion by preserving luminance, contrast, and structural details. The combination of high SSIM with low LPIPS and FID scores underscores P2P's ability to preserve structural consistency while producing perceptually aligned adversarial examples. + +For the DenseNet121 and ResNet34 classifiers, P2P achieves a strong balance of high Success Rate, low LPIPS, and favorable SSIM and FID scores, surpassing traditional methods. With SqueezeNet1.1, P2P exhibits particularly robust performance on perceptual metrics, reaching the lowest LPIPS and FID values across all datasets, as shown in Tabs. 1 to 3, highlighting its ability to generate realistic and + +
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.930.400.77112.11
PGD0.430.190.56213.65
Diff-PGD1.00.290.8290.5
P2P (Ours)0.940.120.7838.00
ResNet34
FGSM0.810.350.66133.17
PGD0.310.120.24158.24
Diff-PGD1.00.290.78100.2
P2P (Ours)0.930.110.7244.09
SqueezeNet1.1
FGSM0.690.160.77120.14
PGD0.430.260.40292.99
Diff-PGD0.750.120.4789.47
P2P (Ours)0.740.080.4958.60
+ +Table 2. Evaluation of adversarial attacks on different attack models for BUS-BRA dataset [18] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples. + +structurally consistent adversarial images. + +Overall, P2P demonstrates competitive Success Rates while consistently producing high-quality adversarial examples with enhanced visual fidelity and structural similarity. The results underscore P2P's effectiveness as a balanced approach for crafting effective and perceptually similar adversarial images across various datasets and classifiers. We will further elaborate on these results qualitatively in the subsequent section. + +# 4.3. Qualitative Results of Adversarial Examples + +Figure 3 presents visual comparisons of images and adversarial perturbations generated by different attack methods. Notably, our method (P2P) produces attack examples that more closely follow the distribution of the original medical images, resulting in a more natural and less detectable alteration. In contrast, other attack methods, such as FGSM, PGD, and Diff-PGD, introduce high-frequency noise with a distinct "textured" appearance. This textured noise can make these adversarial examples appear less natural, potentially revealing them as manipulated images, exhibit noisy artifacts. Besides, Fig. 4 shows that the P2P attack successfully changes the diagnostic labels of ultrasound images with minimal alteration to the images' semantic appearance, demonstrating label vulnerability despite preserved image semantics. Moreover, the t-SNE [54] visualization of clean and attacked image features further confirms the effect of our prompt learning method. Figure 5 compares four attack methods—FGSM, PGD, Diff-PGD, and P2P (Ours)—in terms of how well they blend attack samples + +
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.970.370.77103.07
PGD0.170.070.11147.84
Diff-PGD1.00.270.8081.31
P2P (Ours)0.860.120.6227.18
ResNet34
FGSM0.980.410.75103.68
PGD0.230.100.19135.95
Diff-PGD1.00.310.7780.89
P2P (Ours)0.970.150.7420.3
SqueezeNet1.1
FGSM0.590.200.4272.51
PGD0.160.140.19292.21
Diff-PGD0.770.160.5432.47
P2P (Ours)0.760.100.5223.50
+ +Table 3. Evaluation of adversarial attacks on different attack models for UDIAT dataset [62] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples. + +with clean data clusters. Diff-PGD shows limited effectiveness, with noticeable separations between attack and clean samples. FGSM and PGD improve blending but still leaves isolated clusters of attack points. P2P achieves the best integration, with attack samples closely interwoven with clean data, indicating superior performance in making adversarial examples indistinguishable from clean data. + +To gain further insights, we examined attacked examples from the training set, focusing on images that the classifier identifies with high confidence. Figure 6 presents malignant cases from the BUSI training set alongside their attacked versions generated by Diff-PGD and our method, P2P. As illustrated, the Diff-PGD attack introduces a noticeable noise pattern, while our method produces images that closely resemble the originals. Interestingly, additional examples reveal that Diff-PGD's image quality deteriorates as the classifier's confidence increases. While attack experiments are generally performed on validation sets, we analyzed training set images here to understand the performance of different attack models in varied scenarios. + +# 4.4. Ablation Study + +This section disentangles the effects of design choices to assess their individual contributions to our approach's effectiveness. All ablation experiments are conducted on the BUSI dataset, using ResNet34 as the classifier, with results averaged over 5-fold cross-validation. + +Loss Function. Ablation study results on the effect of MSE loss function are reported in Tab. 4 (second row) and Fig. 7. Although using an MSE loss does not necessarily lead to + +
ComponentLoss FunctionTime StepSuccess RateLPIPSSSIMFIDTime (second)
Baseline0.970.120.8143.03178
W/O MSE✓0.960.120.8043.58178
T=20✓0.830.100.7149.9798
T=100✓0.970.120.8138.06280
+ +Table 4. Comparison of the ablation study on different components of the P2P pipeline. The baseline configuration uses T=50 with MSE in the loss function. In each row, only one component is modified from the baseline. 'Time' indicates the duration of the generation process for the attack per image. + +![](images/3f63cccf1255402eae4d5589ea5d20d368f97f292f90b56d241d5642fd9fb693.jpg) + +![](images/4e3b35e1289e69bfab5b8003c6eb459cf21366e64ed43e35b1bfd11b091a3ca0.jpg) +b) PGD + +![](images/033234e36d8a24664daf7b200425eef120552e9d692ade817c0718254c5f9fbc.jpg) +a) FGSM +c) Diff-PGD + +![](images/a2c069aaeb41fbd4121ebce889d05b4845545b693694f15d0e56652540856a74.jpg) +d) P2P (Ours) + +![](images/2e004de72efc40b46bb54cf1f54a859f597d9b8a1159f7848aabbde15eb4166d.jpg) +Figure 5. t-SNE visualization of last-layer ResNet34 features on the BUSI dataset for FGSM, PGD, Diff-PGD, and our P2P. Clean examples are shown in blue, and adversarial examples in orange. +a) Original +Figure 6. Attack examples of a malignant image of Dataset BUSI from Diff-PGD and P2P with ResNet34 as a classifier. + +![](images/d35b9d7f6b11addbcb870b46a082c0e94970d3f467a068a2004eab75d7033e1a.jpg) +b) Diff-PGD + +![](images/6633feb668a9b5f7b4148bf6d511b179f75b4d494786140a4d1be6fc48dde402.jpg) +c) P2P + +better quantitative metrics, Fig. 7 shows that it attempts to mitigate artifacts and retain the semantic integrity of the ultrasound image. Specifically, the middle image (without MSE) exhibits enhanced linear or streak-like artifacts, which may disrupt the homogeneity of tissue appearance (highlighted in the red rectangular region) and obscure finer structural details in the ultrasound image. Incorporating the MSE loss helps to reduce intensity fluctuations, creating a smoother and more consistent appearance, particularly + +![](images/2f962d471b65ff11e9af8c98564aa13307303fa6d12ebc6bea0c7d7b0e213080.jpg) +a) Original +Figure 7. Impact of MSE loss in the P2P framework. Image (a) shows the clean reference image, image (b) shows the P2P result without MSE loss, and image (c) includes the MSE loss function. + +![](images/786f0c3772e3d62738244519aecfcb82402f5b334e9a628c47a8eda9dcf70d9b.jpg) +b) W/O MSE + +![](images/185fd600c6119b5769f11348799fb2ade3f2a0e5dc4dca01470c70dc5b0317e6.jpg) +c) MSE + +beneficial in areas with subtle tissue boundaries. + +Step Selection To justify the choices for P2P with optimization for different timesteps, we show in Tab. 4 the performance of our method with different settings. Using 20 steps, the approach yields prompts that generate attack images with relatively low success, SSIM and LPIPS. However, when optimizing with more timesteps ( $T = 100$ ) even though, the FID of the generated attack images is better, other metrics are comparable to that of ( $T = 50$ ), but with longer time to generate attack images. Therefore, given the efficiency dilemma and the results presented, selecting 50 steps appears to be a reasonable choice. + +# 5. Conclusion + +We designed P2P, an effective adversarial attack method for synthesizing adversarial breast ultrasound images using prompt learning in text-to-image diffusion models. We showcase the effectiveness of our approach across various attack scenarios, especially valuable in data-limited medical applications. Our adversarial images surpass previous methods, appearing more clinically natural and harder to detect. They also maintain lower perceptual differences and achieve greater structural similarity. P2P enables significantly easier attacks on classifiers in the medical domain, eliminating the need for pre-trained models in a specific domain by facilitating the construction of effective textual examples. + +# 6. Acknowledgment + +# References + +[1] Barsha Abhisheka, Saroj Kumar Biswas, and Biswajit Purkayastha. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2385-2392, 2023. 3 \ No newline at end of file diff --git a/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/images.zip b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..503319a1b9d1a986136f5f30e4ecb3c1027dc10e --- /dev/null +++ b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b277475d180b4c5cd132324f30dae41994c242df6508cc22f22ca1799c1fd72c +size 492523 diff --git a/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/layout.json b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c2ee004f70ef844989ddaca89e76489b0da6671a --- /dev/null +++ b/2025/Prompt2Perturb (P2P)_ Text-Guided Diffusion-Based Adversarial Attack on Breast Ultrasound Images/layout.json @@ -0,0 +1,8299 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 67, + 102, + 543, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 102, + 543, + 140 + ], + "spans": [ + { + "bbox": [ + 67, + 102, + 543, + 140 + ], + "type": "text", + "content": "Prompt2Perturb (P2P): Text-Guided Diffusion-Based Adversarial Attacks on Breast Ultrasound Images" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 160, + 550, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 160, + 550, + 203 + ], + "spans": [ + { + "bbox": [ + 62, + 160, + 550, + 203 + ], + "type": "text", + "content": "Yasamin Medghalchi1 Moein Heidari1 Clayton Allard1 Leonid Sigal1,2 Ilker Hacihaliloglu1 \n1University of British Columbia, Vancouver, BC, Canada \n2Vector Institute for AI, Toronto, ON, Canada" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 185, + 206, + 424, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 185, + 206, + 424, + 245 + ], + "spans": [ + { + "bbox": [ + 185, + 206, + 424, + 245 + ], + "type": "text", + "content": "yasimed@student.ubc.ca{moein.heidari, ilker.hacihaliloglu}@ubc.ca clayton.allard@stat.ubc.ca, lsignal@cs.ubc.ca" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 152, + 273, + 200, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 273, + 200, + 285 + ], + "spans": [ + { + "bbox": [ + 152, + 273, + 200, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "spans": [ + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "text", + "content": "Deep neural networks (DNNs) offer significant promise for improving breast cancer diagnosis in medical imaging. However, these models are highly susceptible to adversarial attacks—small, imperceptible changes that can mislead classifiers—raising critical concerns about their reliability and security. Traditional attacks rely on fixed-norm perturbations, misaligning with human perception. In contrast, diffusion-based attacks require pre-trained models, demanding substantial data when these models are unavailable, limiting practical use in data-scarce scenarios. In medical imaging, however, this is often unfeasible due to the limited availability of datasets. Building on recent advancements in learnable prompts, we propose Prompt2Perturb " + }, + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "inline_equation", + "content": "(P2P)" + }, + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "text", + "content": ", a novel language-guided attack method capable of generating meaningful attack examples driven by text instructions. During the prompt learning phase, our approach leverages learnable prompts within the text encoder to create subtle, yet impactful, perturbations that remain imperceptible while guiding the model towards targeted outcomes. In contrast to current prompt learning-based approaches, our " + }, + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "inline_equation", + "content": "P2P" + }, + { + "bbox": [ + 54, + 316, + 297, + 700 + ], + "type": "text", + "content": " stands out by directly updating text embeddings, avoiding the need for retraining diffusion models. Further, we leverage the finding that optimizing only the early diffusion steps boosts efficiency while ensuring that the generated adversarial examples incorporate subtle noise, thus preserving ultrasound image quality without introducing noticeable artifacts. We show that our method outperforms state-of-the-art attack techniques across three breast ultrasound datasets in FID and LPIPS. Moreover, the generated images are both more natural in appearance and more effective compared to existing adversarial attacks. Our Code is publicly available on GitHub." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 277, + 552, + 348 + ], + "blocks": [ + { + "bbox": [ + 319, + 277, + 552, + 348 + ], + "lines": [ + { + "bbox": [ + 319, + 277, + 552, + 348 + ], + "spans": [ + { + "bbox": [ + 319, + 277, + 552, + 348 + ], + "type": "image", + "image_path": "d323c553b7d7cb4ca5a950325c613ebb35b589f3b1098c79a88f236e3c675353.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 364, + 555, + 396 + ], + "lines": [ + { + "bbox": [ + 313, + 364, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 555, + 396 + ], + "type": "text", + "content": "Figure 1. Illustration of P2P in an adversarial attack against Diff-PGD; note there is no exhibited change of image semantics in our method." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 418, + 394, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 418, + 394, + 430 + ], + "spans": [ + { + "bbox": [ + 314, + 418, + 394, + 430 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 437, + 555, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 666 + ], + "type": "text", + "content": "Mammography remains the primary tool for breast cancer screening, offering widespread accessibility and proven effectiveness in detecting early-stage tumors [16]. However, it has some limitations, including patient discomfort and reduced diagnostic accuracy in individuals with dense breast tissue [33]. Ultrasound has become a useful supplementary technique, as it provides better patient comfort and avoids the risks associated with radiation exposure. Its ability to capture real-time images makes it beneficial for further investigating abnormalities observed on mammograms [16]. Nonetheless, the performance of ultrasound can be inconsistent, with sensitivity and specificity affected by the operator's expertise, device configuration, and changes in tissue characteristics due to breast density. Furthermore, variability in interpretation among different radiologists poses additional challenges [51]. 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Recent research in medical imaging tasks has revealed that even state-of-the-art DNNs are highly susceptible to adversar" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28564" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "ial attacks [39]. Specifically, medical imaging DNNs are more susceptible to adversarial threats than those designed for natural images [39]. In addition, the limited availability of publicly accessible medical images, which poses a challenge for effective training, has pushed modern algorithms to rely on pre-trained models based on large datasets of natural images—a technique known as transfer learning. However, due to the substantial difference between natural and medical images, deep learning models developed through transfer learning tend to be more vulnerable to adversarial attacks [10]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 203, + 296, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 203, + 296, + 586 + ], + "spans": [ + { + "bbox": [ + 56, + 203, + 296, + 586 + ], + "type": "text", + "content": "To address this vulnerability, various adversarial attack methods have been developed. Traditional gradient-based methods such as fast gradient sign method (FGSM) [20], Carlini-wagner [8], and projected gradient descent (PGD) [40] perturb original images within predefined perturbation bounds. Although they can be easily generated using gradient-based techniques, these attacks often deviate significantly from the true data distribution of natural images, leading to a compromise between their effectiveness and subtlety [61]. Generative models such as generative adversarial networks (GANs) [19] have been used to generate adversarial examples, based on their ability to produce high-quality images, by perturbing latent space [3, 49, 64]. However, modifying latent codes changes the high-level semantics of generated images in a way that is easily noticeable to human observers [30]. Recently, diffusion-based models have been employed in the literature to generate realistic adversarial images [11, 36, 61]. In models like AdvDiffuser [11] and Diff-PGD [61], the PGD method is incorporated into the diffusion process to enhance the realism of the generated images. Furthermore, approaches such as Instruct2Attack [37] leverage latent diffusion models [46] to deceive the target model by optimizing over input prompts. These text-guided attacks aim to produce adversarial semantic image edits, such as altering the color of a truck in an image. While image editing holds significant value in natural image domains, it is less applicable in the medical field, as altering the semantics of medical images can result in unrealistic representations. Additionally, these models are often not well-adapted to clinical terminology, making such modifications less meaningful in medical contexts [57]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 586, + 295, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 295, + 706 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 295, + 706 + ], + "type": "text", + "content": "These limitations can be addressed by reversing the diffusion model to obtain context-relevant text tokens, or prompts, specifically designed for the medical domain to generate adversarial images. Optimizing these prompts presents a challenge due to the intricate structure of the generative model, which includes a two-part pipeline: a conditioning network (the CLIP text encoder [44]) and a generative unit (U-Net [47]), both of which complicate gradient flow to the input layer. To tackle these obstacles, we freeze the generative model and make the following contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 555, + 323 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 314, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 167 + ], + "type": "text", + "content": "- Our method requires no fine-tuning and efficiently generates attack images by directly updating text embeddings, unlike previous diffusion-based approaches reliant on large pre-trained models on the same domain. Additionally, we find that optimizing only the initial forward diffusion steps is sufficient, improving efficiency and maintaining image quality without the need for all reverse diffusion phases." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 168, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 227 + ], + "type": "text", + "content": "- Based on our findings, we proposed Prompt2Perturb (P2P) to create challenging adversarial examples optimized for clinical terminology that are particularly challenging to distinguish as attacked, thus highlighting limitations in current adversarial attack mechanisms." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 228, + 555, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 555, + 323 + ], + "type": "text", + "content": "- We demonstrate empirically that our method produces semantically significant attack images that are perceptually similar but varied versions of a target image (see Fig. 1). By incorporating relevant clinical terminology into the text embedding of Stable Diffusion, we ensure that the generated images retain clinical accuracy and realism, thereby enhancing the effectiveness of the attack in a medical context." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 334, + 400, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 334, + 400, + 346 + ], + "spans": [ + { + "bbox": [ + 314, + 334, + 400, + 346 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "type": "text", + "content": "Adversarial attack. DNN models are widely recognized as being susceptible to adversarial attacks [45]. These attacks can manipulate the model's predictions by introducing subtle modifications that are imperceptible to human observers. Adversarial attacks pose a major barrier to the widespread adoption of deep learning models in real-world applications, and considerable research has been dedicated to addressing this ongoing challenge. Adversarial attacks can be broadly classified into black-box and white-box types. White-box attacks, such as limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) [52], FGSM [20], PGD [40], C-W [8], and DeepFool [42], rely on full access to the target model's architecture and parameters, making them gradient-based. In contrast, black-box attacks do not require this level of access and generate adversarial samples through query-based methods. Despite these differences, many white-box attacks are still effective in black-box settings due to the transferability of adversarial examples across models. Adversarial training, which involves training a model using adversariably generated examples, is one of the limited methods available to defend against adversarial attacks [5]. In medical domain, several approaches have been developed to generate adversarial examples targeting computer-aided diagnosis models which can be consistently taxonomized with that of adversarial attacks [15]. Specifically, Zhou et al. [65] introduced two GAN-based models operating at different resolutions, capable of generating highly realistic adversarial images that can mislead breast cancer diagnosis. MIRST [50] was proposed to defend untargeted adversarial attacks" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28565" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 90, + 76, + 519, + 208 + ], + "blocks": [ + { + "bbox": [ + 90, + 76, + 519, + 208 + ], + "lines": [ + { + "bbox": [ + 90, + 76, + 519, + 208 + ], + "spans": [ + { + "bbox": [ + 90, + 76, + 519, + 208 + ], + "type": "image", + "image_path": "68f6b89a0fba1940bc379c80ee12300eca6779e33f79b04c9d797a90eabbd1ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 212, + 449, + 224 + ], + "lines": [ + { + "bbox": [ + 160, + 212, + 449, + 224 + ], + "spans": [ + { + "bbox": [ + 160, + 212, + 449, + 224 + ], + "type": "text", + "content": "Figure 2. Overall framework of the proposed method. Image adapted from [36]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 230, + 295, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 230, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 54, + 230, + 295, + 302 + ], + "type": "text", + "content": "on breast ultrasound images. Lastly, Hao et al. [22] introduce an adversarially robust feature learning method where a feature correlation metric is included as an objective function to promote the learning of robust features while minimizing the influence of spurious ones for the application of breast cancer diagnosis." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 302, + 295, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 302, + 295, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 302, + 295, + 409 + ], + "type": "text", + "content": "Adversarial attack with diffusion models. The success of diffusion models has motivated their exploration in adversarial deep learning, demonstrating potential for both attacking [60, 66] and defending [58, 59] against adversarial examples. These methods are broadly used to enhance the imperceptibility of unconstrained adversarial perturbations [9], transfer the style from the reference image into the original image to create natural-looking adversarial images [56], or attack the diffusion-based purification method [29]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 410, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 410, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 410, + 295, + 613 + ], + "type": "text", + "content": "Prompt learning. Recent progress in controllable image generation and editing using diffusion models [25, 48] has created new possibilities for developing semantic adversarial attacks. Prompt learning was initially introduced as an alternative to full fine-tuning and linear probing, aiming to leverage pre-trained language models in natural language processing (NLP) [34]. Recently, prompt learning techniques have been adapted for adversarial purposes. For instance, BadCLIP [4] targets the CLIP [44] model by injecting a backdoor during the prompt learning phase. In the medical field, BAPLe [21] utilizes learnable prompts within the text encoder and introduces imperceptible learnable noise triggers into input images, effectively leveraging the full capabilities of medical foundation models. Additionally, PromptSmooth [27] uses prompt learning to efficiently achieve certified robustness in medical vision-language models by leveraging semantic concepts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 625, + 138, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 625, + 138, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 625, + 138, + 639 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "We explore the challenge of image classification. Consider an image sample " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathcal{X} \\coloneqq \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ", paired with its label " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{Y} \\coloneqq \\{1, \\dots, |\\mathcal{Y}|\\}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "H, W," + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " represent the image's height, width, and number of channels, respec" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": "tively. Let " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathcal{Y}" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": " denote the image classifier. Given a clean input image " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": " and its true label " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": ", the attacker's objective is to generate an adversarial version " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": " that misleads " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": ", so that " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "f(\\pmb{x}_{\\mathrm{adv}}) \\neq y" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": ". Traditional approaches either necessitate adding pixel-level adversarial noise " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": " [8, 20] to the input image " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": ", resulting in " + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{adv}} = \\pmb{x} + \\delta" + }, + { + "bbox": [ + 313, + 230, + 555, + 351 + ], + "type": "text", + "content": ", or manipulating data to embed subtle biases or vulnerabilities. In this work, we instead focus on prompt-guided semantic attacks, aiming to create meaningful, interpretable perturbed images guided by language descriptions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 358, + 444, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 444, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 444, + 372 + ], + "type": "text", + "content": "3.2. Prompt2Perturb (P2P)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "text", + "content": "Figure 2 provides a high-level overview of the proposed approach. Our approach seeks to generate an adversarial image, " + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "text", + "content": ", such that the modification from the original image " + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "text", + "content": " is guided by a text-based embedding instruction " + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 378, + 555, + 485 + ], + "type": "text", + "content": ". The core idea of Prompt2Perturb (P2P) is to update these text embeddings specifically for the modified input to steer the classifier toward an incorrect prediction. In the subsequent sections, we will provide a detailed breakdown of each component of our proposed method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "text", + "content": "Latent Diffusion Models. We utilize the learned latent space of a generative model, defined as " + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{Z} = z\\mid z = \\mathcal{E}(\\boldsymbol {x}),\\boldsymbol {x}\\in \\mathcal{X}\\subseteq \\mathbb{R}^{h\\times w\\times c}" + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "text", + "content": " represents the image encoder and " + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "inline_equation", + "content": "h\\times w\\times c" + }, + { + "bbox": [ + 313, + 486, + 554, + 616 + ], + "type": "text", + "content": " denotes the dimensions of the latent space. Unlike the image space, this latent space offers a compact, lower-dimensional representation that emphasizes the critical semantic details, making it ideal for controlled semantic alterations. These modifications are enabled through a pretrained conditional latent diffusion model (LDM) [6, 46], which facilitates meaningful and guided editing in the latent domain." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "content": "The encoder is regularized via either a KL-divergence penalty or vector quantization, as suggested by prior works [53]. The corresponding decoder, denoted as " + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "content": ", learns to reconstruct input images from the latent representations, ensuring " + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(x)) \\approx x" + }, + { + "bbox": [ + 313, + 617, + 556, + 714 + ], + "type": "text", + "content": ", for high fidelity reconstruction. Subsequently, a diffusion model is trained to generate latent codes that reside within the learned latent space. This diffusion model is flexible and can be conditioned using" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28566" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "auxiliary information, such as class labels, segmentation masks, or features from a co-trained text-embedding model. Specifically, let " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "c_{\\theta}(p)" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " represent a network mapping conditioning input " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " to its respective conditioning vector. The objective function for the Latent Diffusion Model (LDM) can thus be formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 148, + 290, + 170 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 148, + 290, + 170 + ], + "spans": [ + { + "bbox": [ + 61, + 148, + 290, + 170 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {z \\sim \\mathcal {E} (x), p, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, c _ {\\theta} (p)) \\| _ {2} ^ {2} \\right],", + "image_path": "613ded02123f539251c1cf7b843b2368da5521d099436a4662b5bb3c2c419c50.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " is the time step, " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " is the noisy latent at " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " is the unscaled noise sample, and " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " is the denoising network. Intuitively, the objective here is to correctly remove the noise added to a latent representation of an image. While training, " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "c_{\\theta}" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": " are jointly optimized to minimize the LDM loss. At inference time, a random noise tensor is sampled and iteratively denoised to produce a new image latent, " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "z_{0}" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": ". Finally, this latent code is transformed into an image through the pre-trained decoder " + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "inline_equation", + "content": "x' = \\mathcal{D}(z_0)" + }, + { + "bbox": [ + 55, + 175, + 296, + 462 + ], + "type": "text", + "content": ". Previous diffusion-based attack methods leverage extensively pretrained models on natural images, incorporating specialized attack strategies and employing a reverse diffusion process to generate adversarial examples that resemble the underlying data distribution. However, this approach is impractical in the medical domain due to the lack of extensively trained models caused by inherent data scarcity and the presence of diverse imaging modalities. Unlike these previous approaches, our method is well-suited to handle this diversity without requiring retraining of a diffusion model or relying on large-scale pre-trained models. This robustness stems from our approach, which involves updating the text embeddings directly, rather than merely adding noise to the latent space. We next review the early stages of such a text encoder, and our choice of attack space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": "Text optimization. The text encoder processes the input prompt " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ", which is fed into the latent diffusion model. A text tokenizer transforms the prompt strings into tokens, representing indices in a predefined vocabulary of size " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "|V|" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ". Each token is then mapped to its corresponding embedding vector " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i \\in \\mathbf{C}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "i \\in 1, \\dots, |V|" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": " within the embedding space " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ". Previous work on textual inversion in the embedding space " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": " [17, 55] attempts to learn new concepts for a set of images by associating placeholder strings with newly learned embedding vectors. This effectively expands the existing vocabulary with additional concepts. However, these newly learned concepts have been found to be uninformative in the medical domain, as the learned embeddings are often distant from the embeddings corresponding to the original vocabulary. In contrast, our approach aims to optimize the embedding vectors " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "i \\in 1, \\dots, L" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ", from the existing vocabulary for a prompt of maximum length " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": " specific to the medical domain. This adaptation addresses the limitations of existing diffusion model vocabularies that lack specific medical terms (e.g., the word \"benign\" is not present in the vocabulary of the Stable Diffusion text encoder, despite" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 431 + ], + "type": "text", + "content": "its frequent use in medical contexts). Therefore, our method ensures applicability across diverse imaging modalities and scenarios within the medical domain, as it remains independent of the specific encoder choice and is instead reliant on the latent diffusion backbone used for prompt optimization. Minimal reversal steps. Previous studies [41] have demonstrated that the diffusion model's sensitivity to conditioning intensifies significantly during the later stages of the diffusion process, particularly when noise levels are higher. Conversely, in the initial timesteps, the diffusion loss remains relatively stable across various prompts applied to the same image. Inspired by this observation, we hypothesize that not all reverse diffusion steps are necessary for generating an adversarial image. Optimizing only for the early timesteps of diffusion process (akin to later timesteps of denoising process) has two-fold advantage. First, given that we are optimizing the early layers of a very deep neural network, the resulting gradients tend to be quite small which contributes to our method's efficiency compared to others that require training the entire diffusion model. Additionally, early timesteps (the start of the diffusion process) are associated with high-frequency components, focusing on reconstructing edges, textures, and fine-grained structures [43]. By introducing adversarial perturbations during this stage, our strategy generates examples that effectively mimic common scenarios in ultrasound imaging, where acquisition settings—such as the transducer's operating frequency and its orientation relative to the anatomy—significantly influence the high-frequency content captured in the images [35]. We provide more details in the next sections." + } + ] + } + ], + "index": 4 + }, + { + "type": "code", + "bbox": [ + 318, + 472, + 536, + 705 + ], + "blocks": [ + { + "bbox": [ + 320, + 447, + 527, + 471 + ], + "lines": [ + { + "bbox": [ + 320, + 447, + 527, + 471 + ], + "spans": [ + { + "bbox": [ + 320, + 447, + 527, + 471 + ], + "type": "text", + "content": "Algorithm 1: Text-Guided Diffusion-Based Attack Pipeline for Single Image" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "lines": [ + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "spans": [ + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": "Input: Attacked classifier " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " , Image " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " , Prompt " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " Label " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " \nOutput: Adversarily perturbed image " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv\\_best}}" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{best}}\\gets \\infty" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " . \nfor " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "i\\in" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " range(num_iterations) do \n" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "t\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " randint(0,50); \n" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "z\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " vae.encode(x), " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "C\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " textencoder(p); \n" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\epsilon \\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " randn_like(z), " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "z_{t}\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " add_noise(z, " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\epsilon ,t)" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\tilde{z}\\gets \\sqrt{\\frac{1}{\\bar{\\alpha}_t}} (z_t - \\sqrt{1 - \\bar{\\alpha}_t}\\cdot \\epsilon_\\theta (z_t,t,C));" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " vaedecode(" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\tilde{z}" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " ), " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}\\gets (x_{\\mathrm{adv}} + 1) / 2;" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " .Normalize(mean, std), " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\tilde{y}\\gets f(x_{\\mathrm{adv}})" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " \nLoss " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\leftarrow -10^{10}\\times" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " CrossEntropyLoss(y,y)+ mse(ε,εθzt,C)); \nLoss-backward(), textencoder_optimizer.step(); \n" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "d\\gets" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " mse(x,xadv); \nif " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "d < d_{best}" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " then \n" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\lfloor d_{\\mathrm{best}}\\leftarrow d,x_{\\mathrm{adv\\_best}}\\leftarrow x_{\\mathrm{adv}}; \\end{array}" + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "text", + "content": " \nreturn " + }, + { + "bbox": [ + 318, + 472, + 536, + 705 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv\\_best}}" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_body" + } + ], + "index": 6, + "sub_type": "algorithm" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28567" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "content": "Attacking policy setup. Given a target image " + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "content": " and a latent diffusion model parameterized by " + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "content": ", our goal is to optimize the text encoder to best represent the visual content of the image while simultaneously crafting an adversarial attack on the classifier. To determine the optimal text encoder for generating an adversarial image, we formulate the problem with two components. First, we employ a cross-entropy loss to measure the difference between the classifier's predicted output and the actual image class. Second, we include a loss that captures the discrepancy between the predicted noise from the network and the noise originally added to the image under a specific prompt condition, thereby ensuring semantic similarity between the adversarial image and the original image. Our objective is to recover the set of embeddings that align our objective of generating an adversarial image. Note that we freeze the diffusion model parameters throughout this optimization except the text encoder part. As discussed previously, instead of optimizing over all diffusion time steps, we restrict the range of " + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "content": " to early diffusion timesteps " + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "inline_equation", + "content": "(t \\leq 50)" + }, + { + "bbox": [ + 55, + 72, + 297, + 348 + ], + "type": "text", + "content": ". Subsequently, the image that shows the highest similarity to the original input is selected as the adversarial output. The complete approach of our method is illustrated in Algorithm 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 357, + 138, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 138, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 138, + 371 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 377, + 296, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 296, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 296, + 474 + ], + "type": "text", + "content": "This section starts by outlining the experimental setup, the comparison framework, and the evaluation metrics used. We then present both quantitative and qualitative comparisons against the current state-of-the-art methods, focusing on the stealthiness of the perturbations introduced and the realism of the generated examples. Finally, we conduct ablation and sensitivity analyses to evaluate the influence of key components and hyperparameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 480, + 180, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 180, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 180, + 493 + ], + "type": "text", + "content": "4.1. Experimental settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 498, + 297, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 297, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 297, + 641 + ], + "type": "text", + "content": "Dataset and Models. We leverage three publicly available breast ultrasound datasets and experiment with three widely recognized classifier architectures—ResNet34 [23], SqueezeNet1.1 [28], and DenseNet121 [26]—which are commonly used as baselines in medical imaging research [1, 32]. Given the relatively small dataset sizes, we apply five-fold cross-validation across all classes to ensure robust evaluation. For consistency with the classifier architectures, all images are resized to " + }, + { + "bbox": [ + 55, + 498, + 297, + 641 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 55, + 498, + 297, + 641 + ], + "type": "text", + "content": " pixels. Additionally, we incorporate a pre-trained LDM from Hugging Face, specifically utilizing the Stable-Diffusion-v-1-4 variant [13]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "BUSI (Breast Ultrasound Images). Collected in 2018, this dataset comprises ultrasound scans from 600 female patients between the ages of 25 and 75, gathered for breast cancer detection. The dataset includes a total of 780 images, each with an average resolution of " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "500 \\times 500" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " pixels, categorized into three classes: normal (133 images), benign" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 503, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 503, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 503, + 84 + ], + "type": "text", + "content": "(437 images), and malignant (210 images) [2]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 553, + 156 + ], + "type": "text", + "content": "BUS-BRA. BUS-BRA [18] dataset includes 1875 anonymized images from 1,064 female patients, acquired with four different ultrasound scanners as part of systematic studies conducted at the National Institute of Cancer in Rio de Janeiro, Brazil. This dataset includes biopsy-confirmed tumor cases, with 1268 benign and 607 malignant cases." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "text", + "content": "UDIAT. Collected in 2012 at the UDIAT Diagnostic Centre of the Parc Taulí Corporation in Sabadell, Spain, this dataset [62] was gathered using a Siemens ACUSON Sequoia C512 system with a 17L5 HD linear array transducer operating at " + }, + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "inline_equation", + "content": "8.5\\mathrm{MHz}" + }, + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "text", + "content": ". It comprises 163 images from 163 female patients, with an average resolution of " + }, + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "inline_equation", + "content": "760\\times 570" + }, + { + "bbox": [ + 313, + 156, + 553, + 251 + ], + "type": "text", + "content": " pixels, categorized into 53 malignant and 110 benign lesions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "content": "Hyperparameters. In our experiments, we train the model for 500 iterations with a learning rate of " + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "content": " using the AdamW optimizer [38]. For adversarial methods, we set the FGSM attack parameter to " + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.05" + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "content": ". For the PGD attack, we configure " + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.03" + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "content": " with a step size of " + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\alpha = 0.007" + }, + { + "bbox": [ + 313, + 251, + 555, + 360 + ], + "type": "text", + "content": " over 200 iterations. We utilize Diff-PGD with the same setting as it used for ImageNet [14]. We run our experiments on a single NVIDIA RTX V100 GPU with 32GB memory." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 315, + 369, + 558, + 583 + ], + "blocks": [ + { + "bbox": [ + 315, + 369, + 558, + 583 + ], + "lines": [ + { + "bbox": [ + 315, + 369, + 558, + 583 + ], + "spans": [ + { + "bbox": [ + 315, + 369, + 558, + 583 + ], + "type": "table", + "html": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.880.400.81123.51
PGD0.570.290.45378.62
Diff-PGD1.00.300.87111.03
P2P (Ours)0.980.130.8545.84
ResNet34
FGSM0.960.410.81131.62
PGD0.550.250.37332.01
Diff-PGD1.00.310.84117.49
P2P (Ours)0.970.120.8143.03
SqueezeNet1.1
FGSM0.490.160.40118.03
PGD0.330.200.30250.38
Diff-PGD0.740.140.5679.51
P2P (Ours)0.960.090.6347.64
", + "image_path": "246dd51a187acb5cad1758fb9d248be4318ca8c075424aa12388e9ae3d1b5276.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 592, + 555, + 626 + ], + "lines": [ + { + "bbox": [ + 313, + 592, + 555, + 626 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 555, + 626 + ], + "type": "text", + "content": "Table 1. Evaluation of adversarial attacks on different attack models for BUSI dataset [2] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 647, + 507, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 507, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 507, + 659 + ], + "type": "text", + "content": "4.2. Evaluation of Adversarial Examples" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "To evaluate the quality of adversarial examples generated by our proposed P2P method, we benchmark it against the leading Diffusion-Based Projected Gradient Descent (Diff-PGD) attack and conventional techniques like FGSM and" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28568" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 77, + 531, + 205 + ], + "blocks": [ + { + "bbox": [ + 78, + 77, + 531, + 205 + ], + "lines": [ + { + "bbox": [ + 78, + 77, + 531, + 205 + ], + "spans": [ + { + "bbox": [ + 78, + 77, + 531, + 205 + ], + "type": "image", + "image_path": "d702d8fb76952d7638ba5683dfbe92f63c6878c0b16323734cea5beb43f0c936.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 212, + 555, + 236 + ], + "lines": [ + { + "bbox": [ + 55, + 212, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 555, + 236 + ], + "type": "text", + "content": "Figure 3. Visual comparison of different attack methods on a benign image from the BUSI dataset, using DenseNet121 as the classifier. The second row displays the perturbations, calculated as the difference between the original image and the attacked example." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 93, + 245, + 529, + 415 + ], + "blocks": [ + { + "bbox": [ + 93, + 245, + 529, + 415 + ], + "lines": [ + { + "bbox": [ + 93, + 245, + 529, + 415 + ], + "spans": [ + { + "bbox": [ + 93, + 245, + 529, + 415 + ], + "type": "image", + "image_path": "d17d6949b37dcde8e1df7a1ebc65faa2d157eaa5134cf12c5233625a3ffc0119.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 418, + 555, + 452 + ], + "lines": [ + { + "bbox": [ + 55, + 418, + 555, + 452 + ], + "spans": [ + { + "bbox": [ + 55, + 418, + 555, + 452 + ], + "type": "text", + "content": "Figure 4. Comparison of original and P2P-attacked ultrasound images from BUS-BRA Dataset, using DenseNet121 as the classifier. The top row shows the original images with their diagnostic labels, while the bottom row displays the same images after applying the P2P attack. Green boxes indicate the true labels, while red boxes show the labels predicted by the classifier after the attack." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 463, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 295, + 510 + ], + "type": "text", + "content": "PGD. We assess each attack's performance across metrics including Success Rate, LPIPS, SSIM, and FID, enabling a comprehensive analysis of both adversarial efficacy and the perceptual integrity of the generated adversarial samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 511, + 295, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 511, + 295, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 511, + 295, + 582 + ], + "type": "text", + "content": "In our setting, each attack baseline is applied to validation set images that were initially classified correctly, with adversarial examples retained only when successful in misleading the classifiers. Accordingly, all metrics presented in Tabs. 1 to 3 reflect measurements derived exclusively from these modified images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 689 + ], + "type": "text", + "content": "Across all datasets and classifier architectures, our P2P approach consistently attains high Success Rates [7] comparable to those achieved by Diff-PGD, while surpassing baseline methods in Fréchet Inception Distance (FID) [24], reflecting the imperceptibility of the crafted adversarial examples, and in Learned Perceptual Image Patch Similarity (LPIPS) [63], indicating reduced distortion in our attacks. These results highlight the superior perceptual quality of adversarial examples generated by our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 690, + 295, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 690, + 295, + 702 + ], + "spans": [ + { + "bbox": [ + 61, + 690, + 295, + 702 + ], + "type": "text", + "content": "In terms of Structural Similarity Index Measure (SSIM)," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "text", + "content": "which evaluates the structural alignment between adversarial and original images, our method achieves competitive performance. Although Diff-PGD occasionally marginally outperforms P2P in SSIM for specific models, P2P consistently maintains strong SSIM values across all datasets, as shown in Tabs. 1 to 3. This reflects high visual similarity between the generated adversarial examples " + }, + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "text", + "content": " and the original clean images " + }, + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 463, + 555, + 617 + ], + "type": "text", + "content": ", capturing low perceived visual distortion by preserving luminance, contrast, and structural details. The combination of high SSIM with low LPIPS and FID scores underscores P2P's ability to preserve structural consistency while producing perceptually aligned adversarial examples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 618, + 556, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 702 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 702 + ], + "type": "text", + "content": "For the DenseNet121 and ResNet34 classifiers, P2P achieves a strong balance of high Success Rate, low LPIPS, and favorable SSIM and FID scores, surpassing traditional methods. With SqueezeNet1.1, P2P exhibits particularly robust performance on perceptual metrics, reaching the lowest LPIPS and FID values across all datasets, as shown in Tabs. 1 to 3, highlighting its ability to generate realistic and" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28569" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 298, + 284 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 298, + 284 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 298, + 284 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 298, + 284 + ], + "type": "table", + "html": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.930.400.77112.11
PGD0.430.190.56213.65
Diff-PGD1.00.290.8290.5
P2P (Ours)0.940.120.7838.00
ResNet34
FGSM0.810.350.66133.17
PGD0.310.120.24158.24
Diff-PGD1.00.290.78100.2
P2P (Ours)0.930.110.7244.09
SqueezeNet1.1
FGSM0.690.160.77120.14
PGD0.430.260.40292.99
Diff-PGD0.750.120.4789.47
P2P (Ours)0.740.080.4958.60
", + "image_path": "e96dc4e6379cbf602026c178e84d0539cc351ea22fe32bfad9b4cf93c9eaa570.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 293, + 295, + 327 + ], + "lines": [ + { + "bbox": [ + 55, + 293, + 295, + 327 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 295, + 327 + ], + "type": "text", + "content": "Table 2. Evaluation of adversarial attacks on different attack models for BUS-BRA dataset [18] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 349, + 227, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 227, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 227, + 361 + ], + "type": "text", + "content": "structurally consistent adversarial images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 361, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 361, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 54, + 361, + 295, + 456 + ], + "type": "text", + "content": "Overall, P2P demonstrates competitive Success Rates while consistently producing high-quality adversarial examples with enhanced visual fidelity and structural similarity. The results underscore P2P's effectiveness as a balanced approach for crafting effective and perceptually similar adversarial images across various datasets and classifiers. We will further elaborate on these results qualitatively in the subsequent section." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 467, + 286, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 467, + 286, + 480 + ], + "spans": [ + { + "bbox": [ + 55, + 467, + 286, + 480 + ], + "type": "text", + "content": "4.3. Qualitative Results of Adversarial Examples" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 486, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 486, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 486, + 296, + 713 + ], + "type": "text", + "content": "Figure 3 presents visual comparisons of images and adversarial perturbations generated by different attack methods. Notably, our method (P2P) produces attack examples that more closely follow the distribution of the original medical images, resulting in a more natural and less detectable alteration. In contrast, other attack methods, such as FGSM, PGD, and Diff-PGD, introduce high-frequency noise with a distinct \"textured\" appearance. This textured noise can make these adversarial examples appear less natural, potentially revealing them as manipulated images, exhibit noisy artifacts. Besides, Fig. 4 shows that the P2P attack successfully changes the diagnostic labels of ultrasound images with minimal alteration to the images' semantic appearance, demonstrating label vulnerability despite preserved image semantics. Moreover, the t-SNE [54] visualization of clean and attacked image features further confirms the effect of our prompt learning method. Figure 5 compares four attack methods—FGSM, PGD, Diff-PGD, and P2P (Ours)—in terms of how well they blend attack samples" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 557, + 285 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 557, + 285 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 557, + 285 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 557, + 285 + ], + "type": "table", + "html": "
AttackerSuccess RateLPIPSSSIMFID
DenseNet121
FGSM0.970.370.77103.07
PGD0.170.070.11147.84
Diff-PGD1.00.270.8081.31
P2P (Ours)0.860.120.6227.18
ResNet34
FGSM0.980.410.75103.68
PGD0.230.100.19135.95
Diff-PGD1.00.310.7780.89
P2P (Ours)0.970.150.7420.3
SqueezeNet1.1
FGSM0.590.200.4272.51
PGD0.160.140.19292.21
Diff-PGD0.770.160.5432.47
P2P (Ours)0.760.100.5223.50
", + "image_path": "6a2484c6d80d5dc4b4967eb7aefdf6b7543e8f51d765c8d5edb89ce3f26d2dce.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 293, + 555, + 327 + ], + "lines": [ + { + "bbox": [ + 313, + 293, + 555, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 555, + 327 + ], + "type": "text", + "content": "Table 3. Evaluation of adversarial attacks on different attack models for UDIAT dataset [62] with 3 classifiers. LPIPS, SSIM, and FID are reported on successful attack examples." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 349, + 555, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 349, + 555, + 432 + ], + "spans": [ + { + "bbox": [ + 313, + 349, + 555, + 432 + ], + "type": "text", + "content": "with clean data clusters. Diff-PGD shows limited effectiveness, with noticeable separations between attack and clean samples. FGSM and PGD improve blending but still leaves isolated clusters of attack points. P2P achieves the best integration, with attack samples closely interwoven with clean data, indicating superior performance in making adversarial examples indistinguishable from clean data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 433, + 556, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 556, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 556, + 588 + ], + "type": "text", + "content": "To gain further insights, we examined attacked examples from the training set, focusing on images that the classifier identifies with high confidence. Figure 6 presents malignant cases from the BUSI training set alongside their attacked versions generated by Diff-PGD and our method, P2P. As illustrated, the Diff-PGD attack introduces a noticeable noise pattern, while our method produces images that closely resemble the originals. Interestingly, additional examples reveal that Diff-PGD's image quality deteriorates as the classifier's confidence increases. While attack experiments are generally performed on validation sets, we analyzed training set images here to understand the performance of different attack models in varied scenarios." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 598, + 409, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 598, + 409, + 611 + ], + "spans": [ + { + "bbox": [ + 313, + 598, + 409, + 611 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 617, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 677 + ], + "type": "text", + "content": "This section disentangles the effects of design choices to assess their individual contributions to our approach's effectiveness. All ablation experiments are conducted on the BUSI dataset, using ResNet34 as the classifier, with results averaged over 5-fold cross-validation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Loss Function. Ablation study results on the effect of MSE loss function are reported in Tab. 4 (second row) and Fig. 7. Although using an MSE loss does not necessarily lead to" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28570" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 535, + 148 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 535, + 148 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 535, + 148 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 535, + 148 + ], + "type": "table", + "html": "
ComponentLoss FunctionTime StepSuccess RateLPIPSSSIMFIDTime (second)
Baseline0.970.120.8143.03178
W/O MSE✓0.960.120.8043.58178
T=20✓0.830.100.7149.9798
T=100✓0.970.120.8138.06280
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'Time' indicates the duration of the generation process for the attack per image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 61, + 208, + 174, + 292 + ], + "blocks": [ + { + "bbox": [ + 61, + 208, + 174, + 292 + ], + "lines": [ + { + "bbox": [ + 61, + 208, + 174, + 292 + ], + "spans": [ + { + "bbox": [ + 61, + 208, + 174, + 292 + ], + "type": "image", + "image_path": "3f63cccf1255402eae4d5589ea5d20d368f97f292f90b56d241d5642fd9fb693.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 178, + 209, + 291, + 293 + ], + "blocks": [ + { + "bbox": [ + 178, + 209, + 291, + 293 + ], + "lines": [ + { + "bbox": [ + 178, + 209, + 291, + 293 + ], + "spans": [ + { + "bbox": [ + 178, + 209, + 291, + 293 + ], + "type": "image", + "image_path": "4e3b35e1289e69bfab5b8003c6eb459cf21366e64ed43e35b1bfd11b091a3ca0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 221, + 293, + 247, + 300 + ], + "lines": [ + { + "bbox": [ + 221, + 293, + 247, + 300 + ], + "spans": [ + { + "bbox": [ + 221, + 293, + 247, + 300 + ], + "type": "text", + "content": "b) PGD" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 61, + 300, + 174, + 383 + ], + "blocks": [ + { + "bbox": [ + 102, + 293, + 133, + 300 + ], + "lines": [ + { + "bbox": [ + 102, + 293, + 133, + 300 + ], + "spans": [ + { + "bbox": [ + 102, + 293, + 133, + 300 + ], + "type": "text", + "content": "a) FGSM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 300, + 174, + 383 + ], + "lines": [ + { + "bbox": [ + 61, + 300, + 174, + 383 + ], + "spans": [ + { + "bbox": [ + 61, + 300, + 174, + 383 + ], + "type": "image", + "image_path": "033234e36d8a24664daf7b200425eef120552e9d692ade817c0718254c5f9fbc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 383, + 138, + 391 + ], + "lines": [ + { + "bbox": [ + 97, + 383, + 138, + 391 + ], + "spans": [ + { + "bbox": [ + 97, + 383, + 138, + 391 + ], + "type": "text", + "content": "c) Diff-PGD" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 178, + 300, + 291, + 383 + ], + "blocks": [ + { + "bbox": [ + 178, + 300, + 291, + 383 + ], + "lines": [ + { + "bbox": [ + 178, + 300, + 291, + 383 + ], + "spans": [ + { + "bbox": [ + 178, + 300, + 291, + 383 + ], + "type": "image", + "image_path": "a2c069aaeb41fbd4121ebce889d05b4845545b693694f15d0e56652540856a74.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 383, + 257, + 392 + ], + "lines": [ + { + "bbox": [ + 211, + 383, + 257, + 392 + ], + "spans": [ + { + "bbox": [ + 211, + 383, + 257, + 392 + ], + "type": "text", + "content": "d) P2P (Ours)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 63, + 445, + 136, + 542 + ], + "blocks": [ + { + "bbox": [ + 55, + 399, + 295, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 399, + 295, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 295, + 434 + ], + "type": "text", + "content": "Figure 5. t-SNE visualization of last-layer ResNet34 features on the BUSI dataset for FGSM, PGD, Diff-PGD, and our P2P. Clean examples are shown in blue, and adversarial examples in orange." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 63, + 445, + 136, + 542 + ], + "lines": [ + { + "bbox": [ + 63, + 445, + 136, + 542 + ], + "spans": [ + { + "bbox": [ + 63, + 445, + 136, + 542 + ], + "type": "image", + "image_path": "2e004de72efc40b46bb54cf1f54a859f597d9b8a1159f7848aabbde15eb4166d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 543, + 118, + 552 + ], + "lines": [ + { + "bbox": [ + 81, + 543, + 118, + 552 + ], + "spans": [ + { + "bbox": [ + 81, + 543, + 118, + 552 + ], + "type": "text", + "content": "a) Original" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 561, + 295, + 582 + ], + "lines": [ + { + "bbox": [ + 55, + 561, + 295, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 295, + 582 + ], + "type": "text", + "content": "Figure 6. Attack examples of a malignant image of Dataset BUSI from Diff-PGD and P2P with ResNet34 as a classifier." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 139, + 445, + 212, + 542 + ], + "blocks": [ + { + "bbox": [ + 139, + 445, + 212, + 542 + ], + "lines": [ + { + "bbox": [ + 139, + 445, + 212, + 542 + ], + "spans": [ + { + "bbox": [ + 139, + 445, + 212, + 542 + ], + "type": "image", + "image_path": "d35b9d7f6b11addbcb870b46a082c0e94970d3f467a068a2004eab75d7033e1a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 543, + 197, + 552 + ], + "lines": [ + { + "bbox": [ + 154, + 543, + 197, + 552 + ], + "spans": [ + { + "bbox": [ + 154, + 543, + 197, + 552 + ], + "type": "text", + "content": "b) Diff-PGD" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 215, + 445, + 288, + 542 + ], + "blocks": [ + { + "bbox": [ + 215, + 445, + 288, + 542 + ], + "lines": [ + { + "bbox": [ + 215, + 445, + 288, + 542 + ], + "spans": [ + { + "bbox": [ + 215, + 445, + 288, + 542 + ], + "type": "image", + "image_path": "6633feb668a9b5f7b4148bf6d511b179f75b4d494786140a4d1be6fc48dde402.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 240, + 543, + 263, + 552 + ], + "lines": [ + { + "bbox": [ + 240, + 543, + 263, + 552 + ], + "spans": [ + { + "bbox": [ + 240, + 543, + 263, + 552 + ], + "type": "text", + "content": "c) P2P" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": "better quantitative metrics, Fig. 7 shows that it attempts to mitigate artifacts and retain the semantic integrity of the ultrasound image. Specifically, the middle image (without MSE) exhibits enhanced linear or streak-like artifacts, which may disrupt the homogeneity of tissue appearance (highlighted in the red rectangular region) and obscure finer structural details in the ultrasound image. Incorporating the MSE loss helps to reduce intensity fluctuations, creating a smoother and more consistent appearance, particularly" + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 322, + 208, + 395, + 293 + ], + "blocks": [ + { + "bbox": [ + 322, + 208, + 395, + 293 + ], + "lines": [ + { + "bbox": [ + 322, + 208, + 395, + 293 + ], + "spans": [ + { + "bbox": [ + 322, + 208, + 395, + 293 + ], + "type": "image", + "image_path": "2f962d471b65ff11e9af8c98564aa13307303fa6d12ebc6bea0c7d7b0e213080.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 293, + 376, + 303 + ], + "lines": [ + { + "bbox": [ + 340, + 293, + 376, + 303 + ], + "spans": [ + { + "bbox": [ + 340, + 293, + 376, + 303 + ], + "type": "text", + "content": "a) Original" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 312, + 555, + 345 + ], + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 345 + ], + "type": "text", + "content": "Figure 7. Impact of MSE loss in the P2P framework. Image (a) shows the clean reference image, image (b) shows the P2P result without MSE loss, and image (c) includes the MSE loss function." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 399, + 208, + 471, + 293 + ], + "blocks": [ + { + "bbox": [ + 399, + 208, + 471, + 293 + ], + "lines": [ + { + "bbox": [ + 399, + 208, + 471, + 293 + ], + "spans": [ + { + "bbox": [ + 399, + 208, + 471, + 293 + ], + "type": "image", + "image_path": "786f0c3772e3d62738244519aecfcb82402f5b334e9a628c47a8eda9dcf70d9b.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 412, + 293, + 457, + 302 + ], + "lines": [ + { + "bbox": [ + 412, + 293, + 457, + 302 + ], + "spans": [ + { + "bbox": [ + 412, + 293, + 457, + 302 + ], + "type": "text", + "content": "b) W/O MSE" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 474, + 208, + 547, + 293 + ], + "blocks": [ + { + "bbox": [ + 474, + 208, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 474, + 208, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 474, + 208, + 547, + 293 + ], + "type": "image", + "image_path": "185fd600c6119b5769f11348799fb2ade3f2a0e5dc4dca01470c70dc5b0317e6.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 497, + 293, + 523, + 302 + ], + "lines": [ + { + "bbox": [ + 497, + 293, + 523, + 302 + ], + "spans": [ + { + "bbox": [ + 497, + 293, + 523, + 302 + ], + "type": "text", + "content": "c) MSE" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 368, + 509, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 368, + 509, + 379 + ], + "spans": [ + { + "bbox": [ + 313, + 368, + 509, + 379 + ], + "type": "text", + "content": "beneficial in areas with subtle tissue boundaries." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "content": "Step Selection To justify the choices for P2P with optimization for different timesteps, we show in Tab. 4 the performance of our method with different settings. Using 20 steps, the approach yields prompts that generate attack images with relatively low success, SSIM and LPIPS. However, when optimizing with more timesteps (" + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "content": ") even though, the FID of the generated attack images is better, other metrics are comparable to that of (" + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "inline_equation", + "content": "T = 50" + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "content": "), but with longer time to generate attack images. Therefore, given the efficiency dilemma and the results presented, selecting 50 steps appears to be a reasonable choice." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "spans": [ + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "content": "We designed P2P, an effective adversarial attack method for synthesizing adversarial breast ultrasound images using prompt learning in text-to-image diffusion models. We showcase the effectiveness of our approach across various attack scenarios, especially valuable in data-limited medical applications. Our adversarial images surpass previous methods, appearing more clinically natural and harder to detect. They also maintain lower perceptual differences and achieve greater structural similarity. P2P enables significantly easier attacks on classifiers in the medical domain, eliminating the need for pre-trained models in a specific domain by facilitating the construction of effective textual examples." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28571" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "type": "text", + "content": "6. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2385-2392, 2023. 3" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28574" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_content_list.json b/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..db5e3387c70975e991f880f6641f06ebe7b76dd9 --- /dev/null +++ b/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_content_list.json @@ -0,0 +1,1809 @@ +[ + { + "type": "text", + "text": "PromptHMR: Promptable Human Mesh Recovery", + "text_level": 1, + "bbox": [ + 241, + 130, + 756, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yufu Wang $^{1,4}$ Yu Sun $^{1}$ Priyanka Patel $^{1}$ Kostas Daniilidis $^{4,5}$", + "bbox": [ + 238, + 179, + 756, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Michael J. Black1,2 Muhammed Kocabas1,2,3", + "bbox": [ + 313, + 198, + 681, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Meshcapade $^{2}$ MPI for Intelligent Systems $^{3}$ ETH Zürich $^{4}$ University of Pennsylvania $^{5}$ Archimedes", + "bbox": [ + 102, + 215, + 880, + 234 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ea57a6b5418d647e90d39ee8171a09d7e2c754f331b237f857309d2d07146c1.jpg", + "image_caption": [ + "image $\\downarrow$ box prompts" + ], + "image_footnote": [], + "bbox": [ + 127, + 250, + 339, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be9343463bf96acd4f8244d7f857449379a2aa84da0e1a9881ba4601702fc205.jpg", + "image_caption": [ + "PromptHMR" + ], + "image_footnote": [], + "bbox": [ + 127, + 426, + 338, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/558ab4fd1be2e1d09c658b84738575efafe760a9ebfbcae282bc07e18e4f7f76.jpg", + "image_caption": [ + "image $\\downarrow$ box prompts" + ], + "image_footnote": [], + "bbox": [ + 349, + 250, + 575, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c688a0cd5f13e1806152dc103c989787d868b8228a8b74a9dcfcde525815441.jpg", + "image_caption": [ + "PromptHMR", + "Figure 1. PromptHMR is a promptable human pose and shape (HPS) estimation method that processes images with spatial or semantic prompts. It takes \"side information\" readily available from vision-language models or user input to improve the accuracy and robustness of 3D HPS. PromptHMR recovers human pose and shape from spatial prompts such as (a) face bounding boxes, (b) partial or complete person detection boxes, or (c) segmentation masks. It refines its predictions using semantic prompts such as (c) person-person interaction labels for close contact scenarios, or (d) natural language descriptions of body shape to improve body shape predictions. Both image and video versions of PromptHMR achieve state-of-the-art accuracy. https://yufu-wang.github.io/phmr-page" + ], + "image_footnote": [], + "bbox": [ + 349, + 426, + 575, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5e1de9b86be207d1dc0218a369085eda5b7e9baecbf158546e647520b9ca2018.jpg", + "image_caption": [ + "image ↓ masks" + ], + "image_footnote": [], + "bbox": [ + 588, + 250, + 700, + 359 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/145e269221490644537bd771e62275f0879e53b37a177d56d0a31cf8b876fc58.jpg", + "image_caption": [ + "image $\\downarrow$ box $^+$ text" + ], + "image_footnote": [], + "bbox": [ + 725, + 250, + 861, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/edc9a72aed113623aedcf57605e936369a6b8762655ef8aea36ee2463dcb008d.jpg", + "image_caption": [ + "PromptHMR", + "PromptHMR" + ], + "image_footnote": [], + "bbox": [ + 725, + 417, + 797, + 430 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d2bf6200a1aaa296d11e489d8590bea6eda69f48551b2aef83e23e9bcc957bda.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 444, + 861, + 544 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 670, + 326, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human pose and shape (HPS) estimation presents challenges in diverse scenarios such as crowded scenes, person-person interactions, and single-view reconstruction. Existing approaches lack mechanisms to incorporate auxiliary \"side information\" that could enhance reconstruction accuracy in such challenging scenarios. Furthermore, the most accurate methods rely on cropped person detections and cannot exploit scene context while methods that process the whole image often fail to detect people and are less accurate than methods that use crops. While recent language-based methods explore HPS reasoning through large language or vision-language models, their metric accuracy is well below the state of the art. In contrast, we present PromptHMR,", + "bbox": [ + 89, + 704, + 485, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a transformer-based promptable method that reformulates HPS estimation through spatial and semantic prompts. Our method processes full images to maintain scene context and accepts multiple input modalities: spatial prompts like bounding boxes and masks, and semantic prompts like language descriptions or interaction labels. PromptHMR demonstrates robust performance across challenging scenarios: estimating people from bounding boxes as small as faces in crowded scenes, improving body shape estimation through language descriptions, modeling person-person interactions, and producing temporally coherent motions in videos. Experiments on benchmarks show that PromptHMR achieves state-of-the-art performance while offering flexible prompt-based control over the HPS estimation process.", + "bbox": [ + 511, + 672, + 908, + 885 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1148", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 89, + 222, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The estimation of 3D human pose and shape (HPS) is classically viewed as regressing the parameters of shape and pose from pixels. In particular, most methods take a tightly cropped image of a person and output the pose and shape in camera coordinates. While the accuracy of such methods has increased rapidly, they do not address the whole problem. In particular, an HPS method should be able to take an image or video containing complex human-human and human-scene interactions, return the parameters of every person in the scene, and place these people in a consistent global coordinate frame.", + "bbox": [ + 89, + 114, + 480, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key observation is that the classical \"pixels to parameters\" formulation of the problem is too narrow. Today, we have large vision-language foundation models (VLMs) that understand a great deal about images and what people are doing in them. What these models lack, however, is an understanding of 3D human pose and shape. Recent work [10, 15] has tried to bring together VLMs and 3D HPS but with 3D accuracy well below the best classical methods.", + "bbox": [ + 89, + 281, + 480, + 401 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consequently, we need to think about the problem in a different way and ask whether we can exploit readily available side information (e.g. provided by a VLM) to improve 3D HPS regression robustness, usefulness, and accuracy. To that end, we develop a novel \"promptable\" HPS architecture called PromptHMR. Consider the sample images shown in Fig. 1. In crowded scenes, existing person detection methods struggle, while face detection methods remain reliable. When people closely interact, their body parts overlap and occlude each other, introducing ambiguity in pose estimation. Moreover, 3D body shape estimation from monocular views is challenging due to perspective ambiguity. In all these cases, we can extract cues, or prompts, that provide \"side information\" that can help an HPS method better analyze the scene. PromptHMR formalizes this intuition by combining image evidence with different types of spatial and semantic information that can come from either humans or AI systems such as VLMs.", + "bbox": [ + 89, + 402, + 482, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, our approach combines three key components: (1) a vision transformer that extracts features from high-resolution full images to preserve scene context, (2) a multi-modal prompt encoder that processes spatial and semantic inputs, and (3) a transformer decoder that attends to both prompt and image tokens to generate SMPL-X [45] body parameters. This design addresses the limitations of cropped-image HPS methods by processing full images using side information in the form of prompts. It addresses the challenges that full-image HPS methods have in detecting all people in a scene by accepting readily available bounding boxes. Last, our method incorporates auxiliary semantic information through text descriptions or interaction labels.", + "bbox": [ + 89, + 674, + 482, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By combining spatial and semantic prompting, our method offers a powerful and versatile approach to 3D HPS", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "estimation from the whole image. At test time, we show that this promptable structure (1) can take various bounding boxes or segmentation masks to recover full body HPS in a robust way, (2) improve its body shape predictions by using textual descriptions as input, (3) is capable of modeling person-person close interaction directly in the regression process, and (4) uses full image context to reconstruct people coherently in the camera space and the world space. Our model can handle video by incorporating temporal transformer layers at the SMPL-X decoding phase, yielding temporally stable and smooth motions. Last, following TRAM [65], we combine the temporal version of our model with metric SLAM to estimate human motion in world coordinates.", + "bbox": [ + 511, + 90, + 903, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We make several key design choices that make PromptHMR successful. To achieve robustness to different spatial inputs, we train our model by simulating noisy full-body and face-region bounding boxes. For improved body shape estimation, we leverage SHAPY [8] to generate automatic body shape descriptions for training samples and process them with a pretrained text encoder [48]. To enhance person-person interaction reconstruction, we use segmentation masks as more precise spatial prompts and develop person-person attention layers that operate between prompted people, producing coherent reconstructions of close interactions. Through random masking of different input types during training, our model learns to work with any combination of prompts at test time.", + "bbox": [ + 511, + 301, + 903, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quantitative experiments on the EMDB [24], 3DPW [63], RICH [20], Hi4D [68], CHI3D [16] and HBW [8] benchmark datasets demonstrate that our method outperforms state-of-the-art (SOTA) approaches and strong baselines. We also provide many qualitative examples of in-the-wild images and videos that illustrate the robustness and generalization of PromptHMR.", + "bbox": [ + 511, + 513, + 903, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By moving away from the pure pixels-to-parameters approach, PromptHMR not only achieves a new SOTA, it shows a new way of improving both accuracy and robustness by leveraging side information that is easily available. One can think of this as a collaboration between VLMs, which know a lot about people in images but not in 3D, and a metric regressor that knows a lot about 3D humans but not about the semantics of what they do. We show that this combination has significant upside potential to increase both generality and accuracy. Our code and model are available for research purposes.", + "bbox": [ + 511, + 619, + 903, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 799, + 653, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human pose and shape estimation from images. Existing methods for human pose and shape (HPS) estimation can be broadly categorized into two main approaches. The first [6, 17, 22, 27, 28, 30-32, 39, 64, 70] uses a tightly cropped image of an individual as input, and estimates", + "bbox": [ + 511, + 825, + 903, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1149", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pose and shape in camera coordinates. While effective for isolated individuals, this approach discards scene context that is essential to resolve human pose in cases of occlusion, severe overlap and close interaction in multi-person scenes [16, 68].", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The second category [2, 21, 55, 57-59] build upon object detection frameworks [5, 12] to jointly detect humans and estimate their pose and shape parameters. Having access to the entire image, they can better perceive occluded individuals and infer depth relationships, but they often suffer from detection failures due to the difficulty in simultaneously performing detection and reconstruction. Our \"promptable\" architecture leverages detection box prompts to resolve such conflicts while having access to the entire scene context.", + "bbox": [ + 89, + 169, + 480, + 304 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human pose and shape estimation from video. Methods for human motion estimation from video can also be divided into two main categories. The first [7, 23, 26, 36, 56] focuses on estimating smooth human motion in camera space. These methods build upon single-person HPS estimation approaches [22, 30] by adding temporal layers during the SMPL decoding phase to introduce temporal coherence.", + "bbox": [ + 89, + 306, + 480, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More recent methods estimate human motion in world coordinates from videos captured with dynamic cameras. These methods follow a two-stage approach, first estimating camera motion using SLAM techniques [18, 19, 40, 41, 60, 61], and then leveraging human motion priors to optimize the human world motion [29, 67, 69]. Others [51, 52] learn temporal models to directly regress human world motion from image and camera features. Still others [65, 71] use monocular metric depth estimation to solve for the scale of camera motion and transform human motion from camera space to world coordinates.", + "bbox": [ + 89, + 412, + 480, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our approach, we extend PromptHMR to video by taking the SMPL-X output tokens and utilizing a temporal transformer module to estimate temporally stable and smooth human motion and translation in camera space. We follow TRAM [65] to transform human motion to world coordinates due to its simplicity and effectiveness.", + "bbox": [ + 89, + 582, + 480, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic reasoning about 3D humans in images. Recent methods explore combining different types of semantic information, such as language descriptions and knowledge of person-person interactions, to improve reasoning about 3D humans from images and videos. For example, ChatPose [15] follows the common approach of visual language models (VLMs) [34] by fine-tuning a large language model (LLM) with a combination of images and tokens to estimate SMPL parameters. In a similar direction, PoseEmbroider [10] is a multi-modal framework that aligns image, 3D pose, and text representations in a shared latent space. While ChatPose focuses on combining high-level scene reasoning with 3D HPS, PoseEmbroider exploits detailed language descriptions of human pose. While promising, neither method achieves SOTA accuracy on the HPS task. Note", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that many other methods relate language to human pose or motion, without considering images [1, 9, 35, 46, 62], but these are outside our scope.", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Additionally, several methods [8, 47, 53] focus on modeling the relationship between SMPL body shape and natural language descriptions. These methods show that language descriptions and images can provide complementary information to solve this task. Other approaches, such as BUDDI [38] and ProsePose [54], address the challenge of estimating person-person interactions. BUDDI is an optimization-based approach that leverages diffusion model as a prior over interacting people, while ProsePose queries a VLM to estimate contact points on the human body surface and uses these contact points to guide an optimization process for improving human interaction.", + "bbox": [ + 511, + 136, + 903, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overall, methods like ChatPose [15] and PoseEmbroider [10] are promising steps toward jointly learning the relationship between vision, language, and 3D humans, but their understanding of 3D humans remains limited, as indicated by their relatively low 3D pose accuracy. Meanwhile, SHAPY [8], BodyShapeGPT [47], and BodyTalk [53] focus solely on exploring the relationship between SMPL body shape and natural language. BUDDI and ProsePose are post-processing approaches for interaction that do not directly reason using image information.", + "bbox": [ + 511, + 316, + 903, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach addresses the limitations of these methods by training a single model capable of flexible prompting that achieves state-of-the-art (SOTA) performance, not only on standard HPS benchmarks but also on benchmarks tailored to body shape and person-person interaction.", + "bbox": [ + 511, + 469, + 903, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 556, + 604, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an image $I$ containing $N$ people and a set of prompts, our main goal is to recover the pose, shape, and locations of the people in the camera space to form a coherent human-centric 3D scene. Figure 2 shows an overview.", + "bbox": [ + 511, + 580, + 903, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Promptable mesh regression", + "text_level": 1, + "bbox": [ + 511, + 648, + 767, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We adopt SMPL-X [45] to represent each person $i$ in the 3D space, including the orientation $\\phi_i \\in \\mathbb{R}^3$ , local body pose $\\theta_i \\in \\mathbb{R}^{22 \\times 3}$ , shape $\\beta_i \\in \\mathbb{R}^{10}$ , and translation $\\tau_i \\in \\mathbb{R}^3$ in the camera space. We do not include face and hand parameters in this work. Each human $H_i$ is mapped to a 3D mesh with the differentiable SMPL-X layer.", + "bbox": [ + 511, + 672, + 903, + 763 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH _ {i} = \\left\\{\\phi_ {i}, \\theta_ {i}, \\beta_ {i}, \\tau_ {i} \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 770, + 903, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Each person can be prompted with spatial and semantic prompts. Spatial prompts include a bounding box $b_{i} \\in \\mathbb{R}^{2 \\times 2}$ (the two corners) and a segmentation mask $m_{i} \\in \\mathbb{R}^{h \\times w}$ . Semantic prompts consist of text and two-person interaction labels. The text prompt is the CLIP embedding $t_{i}$ of a sentence describing the body shape. The interaction prompt is a binary variable $k_{i}$ indicating whether two", + "bbox": [ + 511, + 795, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1150", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d599869071b1bf25b431691619e1796dbe8c792619a59e6e36f426fa5ae4f60d.jpg", + "image_caption": [ + "Figure 2. Method overview. PromptHMR estimates SMPL-X parameters for each person in an image based on various types of prompts, such as boxes, language descriptions, and person-person interaction cues. Given an image and prompts, we utilize a vision transformer to generate image embeddings and mask and prompt encoders to map different types of prompts to tokens. Optionally, camera intrinsics can be embedded along with the image embeddings. The image embeddings and prompt tokens are then fed to the SMPL-X decoder. The SMPL-X decoder is a transformer-based module that attends to both the image and prompt tokens to estimate SMPL-X parameters. Note that the language and interaction prompts are optional, but providing them enhances the accuracy of the estimated SMPL-X parameters." + ], + "image_footnote": [], + "bbox": [ + 94, + 90, + 898, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "people are in close contact. While semantic prompts are optional, each human needs at least one spatial prompt to be reconstructed. Overall, the input prompts are represented as $P_{i}$ :", + "bbox": [ + 89, + 345, + 483, + 405 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i} \\subseteq \\left\\{b _ {i}, m _ {i}, t _ {i}, k _ {i} \\right\\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 411, + 480, + 434 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nb _ {i} \\in P _ {i} \\text {o r} m _ {i} \\in P _ {i}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 431, + 354, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Promptable human mesh recovery (PromptHMR) is defined as a learnable function that maps an image and a set of prompts to a set of 3D humans", + "bbox": [ + 89, + 450, + 483, + 496 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf: \\left(I, \\left\\{P _ {i} \\right\\} _ {i = 1} ^ {N}\\right)\\rightarrow \\left\\{H _ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 501, + 480, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This task definition integrates all available contexts to locate and reconstruct prompted humans in the image.", + "bbox": [ + 89, + 525, + 483, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Model", + "text_level": 1, + "bbox": [ + 89, + 561, + 176, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image encoder. The image is first encoded as tokens by a vision transformer (ViT) encoder from DINOv2 [11, 42]:", + "bbox": [ + 89, + 585, + 483, + 616 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF = \\operatorname {E n c o d e r} (I), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 622, + 480, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure sufficient resolution for modeling humans at both near and far distances, we use $896 \\times 896$ images. The encoder is run once per frame regardless of the number of people prompted. When camera intrinsics are provided, we add positional encoding of the camera rays to the image tokens to make them camera-aware [2, 14].", + "bbox": [ + 89, + 645, + 483, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mask encoder. When available, masks are first processed by an encoder consisting of stripped convolutional layers that downsample the masks. The output mask features are added to the image tokens. If no mask is provided, a learned \"no mask\" token is added instead.", + "bbox": [ + 89, + 736, + 483, + 810 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {i} = \\operatorname {E n c o d e r} _ {\\mathrm {m}} \\left(m _ {i}\\right) + F. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 818, + 480, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt encoder. The prompt encoder consists of a set of transformations that map different types of prompts to token vectors of the same dimension. When a prompt is not available, it is replaced with a learned null token.", + "bbox": [ + 89, + 840, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For bounding boxes, we encode $b_{i}$ using positional encoding summed with learned embeddings to form the box prompt tokens $T_{bi} = \\mathrm{PE}(b_{i})$ , with $T_{bi} \\in \\mathbb{R}^{2 \\times d}$ . We design different box transformations during training to allow the model to use different boxes as a human identifier. In the training phase, each instance is prompted with either a whole-body bounding box, a face bounding box, or a truncated box covering part of the body. Gaussian noise is added to both corners. At inference time, the model accepts boxes without needing to know the box types.", + "bbox": [ + 511, + 345, + 906, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Language is a natural way to supply semantic information, and in this paper, we use language to supplement spatial prompts with information on body shape. A sentence such as \"a muscular and tall male\" is encoded with the CLIP text encoder $T_{ti} = \\mathrm{CLIP}(t_i)$ , with $T_{ti} \\in \\mathbb{R}^{d}$ . To generate paired (image, text) data, we run SHAPY's [8] shape-to-attribute method on the ground truth shape parameters to obtain shape attribute scores and randomly pick a subset of top attributes to form a sentence.", + "bbox": [ + 511, + 496, + 905, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The interaction prompt $k_{i}$ passes through the prompt encoder without modification and directly switches on-off the cross-person attention that is described in Sec. 3.3.", + "bbox": [ + 511, + 632, + 905, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SMPL-X decoder. The SMPL-X decoder appends two query tokens $T_{\\mathrm{spl}}, T_{\\mathrm{depth}}$ with the prompt tokens $T_{bi}, T_{ti}$ to form the person-specific prompt $T_i \\in \\mathbb{R}^{5 \\times d}$ .", + "bbox": [ + 511, + 676, + 905, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we use a standard transformer decoder and two MLP heads to produce the final output", + "bbox": [ + 511, + 723, + 905, + 753 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {s m p l} ^ {\\prime}, T _ {d e p t h} ^ {\\prime} = \\mathrm {D e c o d e r} (F _ {i}, T _ {i})\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 758, + 812, + 779 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {i}, \\theta_ {i}, \\beta_ {i} = \\operatorname {H e a d} _ {s m p l} \\left(T _ {s m p l} ^ {\\prime}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 781, + 903, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tau_ {i} = \\operatorname {H e a d} _ {d e p t h} (T _ {d e p t h} ^ {\\prime}).\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 801, + 830, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The transformer consists of three attention blocks. Each block applies self-attention on the tokens, cross-person attention (described in Sec. 3.3), and then two-way cross-attention between the tokens and the image embeddings [25]. The self-attention and cross-attention with the", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1151", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "image are applied to each prompted person independently. We use separate tokens $T_{\\mathrm{spl}}$ and $T_{\\mathrm{depth}}$ to make the location representation invariant to the 3D human pose and shape representation.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regressing the location of the human in the camera space is much more challenging than most prior work that models humans in a cropped image space. Therefore, we do not regress $\\tau$ directly. We regress focal length normalized 2D translation $p_{xy} \\in \\mathbb{R}^2$ and inverse depth $p_z \\in \\mathbb{R}$ , and then transform them to $\\tau$ as follows", + "bbox": [ + 89, + 152, + 482, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt _ {x y} = \\frac {p _ {x y}}{p _ {z}} \\quad t _ {z} = \\frac {1}{p _ {z}} \\times \\frac {f}{f _ {c}} \\quad \\tau = [ t _ {x y}, t z ], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 250, + 482, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f$ is the ground truth or estimated focal length of the image, and $f_{c}$ is the canonical focal length. Predicting the normalized inverse depth follows the recent monocular depth literature [49] and is also intuitive since the inverse depth is linearly related to the size of the human in the image. Predicting $p_{xy}$ is equivalent to predicting the 2D location of the human in a normalized image plane.", + "bbox": [ + 89, + 291, + 483, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Two-person interaction", + "text_level": 1, + "bbox": [ + 89, + 406, + 305, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We introduce promptable layers in the decoder to model two-person interaction. We describe the case where there are two people in the image, but the implementation can extend to model an interacting pair in a larger group.", + "bbox": [ + 89, + 429, + 482, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The promptability is modeled as a flow control with a residual connection (Fig. 3). Specifically, if two humans are interacting (as indicated by $k_{i}$ ), their query tokens pass through an additional self-attention layer; otherwise, non-interacting humans skip this.", + "bbox": [ + 89, + 489, + 482, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Applying attention to every person often creates unnecessary dependency in crowded scenes, and there is limited training data for large-group scenarios. However, there is high-quality data featuring two-person social interactions. By making the interaction layers promptable, we mitigate data diversity issues and increase flexibility, regardless of the number of people in the scene.", + "bbox": [ + 89, + 566, + 482, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed interaction layer uses a standard self-attention mechanism. First, we add positional encodings to the query tokens to distinguish the two individuals. The encoded tokens then go through a self-attention layer, whose output is combined with the original tokens via a residual connection. Our experiments demonstrate that including these interaction layers significantly improves inter-person pose accuracy in two-person interaction benchmarks.", + "bbox": [ + 89, + 671, + 482, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. PromptHMR video version", + "text_level": 1, + "bbox": [ + 89, + 801, + 334, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the single-image variant of PromptHMR, we train an extended version that processes videos to estimate human motion in world coordinates. To achieve this, we introduce a simple and efficient temporal transformer module. Given a monocular video sequence $\\{I^t\\}_{t=0}^T$ , we first run", + "bbox": [ + 89, + 824, + 482, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/40583d3d4a212eca68f9d26bdff69156d79a47247c0ae986bf506b27ded37f66.jpg", + "image_caption": [ + "Figure 3. SMPL-X decoder. The top row shows one attention block in the decoder. The cross-person interaction module can be turned on/off. The bottom row shows the cross-person attention." + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 898, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PromptHMR to obtain per-subject SMPL-X decoder output tokens $T_{\\mathrm{spl}}^{\\prime}$ and $T_{\\mathrm{depth}}^{\\prime}$ , assuming that the subject identities are provided with the prompts. These tokens, along with the positional encoding of time $t$ , are fed to a decoder-only temporal transformer module with twelve attention blocks. The output tokens are converted to SMPL-X parameters $\\phi_t, \\theta_t, \\beta_t$ , translation $\\tau_t$ , and joint contact probabilities $c_t$ . The contact probabilities indicate whether a given joint is in contact with the ground plane similar to [50-52].", + "bbox": [ + 511, + 268, + 905, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain results in world coordinates, we adopt the approach from TRAM [65]. Specifically, we use DROID-SLAM [60] and a monocular metric depth estimation model, ZoeDepth [3], to estimate camera motion in metric world coordinates. The translation parameters $\\tau_{t}$ are then transformed to world coordinates using the estimated camera motion. To refine the human trajectory and mitigate foot-skating artifacts, we leverage the estimated contact probabilities and run a fast postprocessing that optimizes the contact joints to have zero velocity.", + "bbox": [ + 511, + 407, + 905, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Losses", + "text_level": 1, + "bbox": [ + 513, + 574, + 601, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PromptHMR is trained with a combination of 2D and 3D losses, following traditional HMR methods [22, 30]:", + "bbox": [ + 511, + 599, + 905, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {2 D} + \\lambda_ {2} \\mathcal {L} _ {3 D} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {4} \\mathcal {L} _ {V} + \\lambda_ {5} \\mathcal {L} _ {t}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 645, + 883, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with each term calculated as", + "bbox": [ + 511, + 676, + 702, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {2 D} = \\left\\| \\hat {\\mathcal {J}} _ {2 D} - \\Pi \\left(\\mathcal {J} _ {3 D}\\right) \\right\\| _ {F} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 707, + 779, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {3 D} = \\left\\| \\hat {\\mathcal {J}} _ {3 D} - \\mathcal {J} _ {3 D} \\right\\| _ {F} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 728, + 754, + 746 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S M P L}} = | | \\hat {\\Theta} - \\Theta | | _ {2} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 750, + 718, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {V} = \\left\\| \\hat {V} - V \\right\\| _ {F} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 772, + 720, + 789 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\left| \\left| \\hat {p} _ {x y} - p _ {x y} \\right| \\right| _ {F} ^ {2} + \\left| \\left| \\hat {p} _ {z} - p _ {z} \\right| \\right| _ {F} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 792, + 843, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{J}_{3D}$ and $V$ are the 3D joints and vertices of the SMPL-X model, with the hat operator denoting the ground truth. $\\Pi$ is the camera reprojection operator. Additionally, on datasets with ground truth translation labels, we supervise the normalized translation $p_{xy}$ and inverse depth $p_z$ .", + "bbox": [ + 511, + 824, + 905, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1152", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 89, + 223, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We train PromptHMR with standard datasets: BEDLAM [4], AGORA [44], 3DPW [63], COCO [33], and MPII [37]. Following 4DHumans, we add AIC [66] and InstaVariety [23] as in-the-wild data, with pseudoground truth from CamSMPLify [43]. Additionally, we add CHI3D [16] and HI4D [68] to enable learning two-person interaction following the train-test splits from BUDDI [38]. Including CHI3D and HI4D does not improve performance on other benchmarks.", + "bbox": [ + 89, + 114, + 483, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We train PromptHMR with AdamW with a batch size of 96 images of resolution $896 \\times 896$ . We use a learning rate of $1e^{-5}$ for the image encoder and $3e^{-5}$ for the prompt encoder and the SMPL-X decoder, with a weight decay of $5e^{-5}$ . The training converges within 350K steps.", + "bbox": [ + 89, + 253, + 483, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. We evaluate camera space reconstruction accuracy on 3DPW [63], EMDB [24] and RICH [20], using MPJPE, Procrustes-aligned MPJPE (PA-MPJPE) and Per Vertex Error (PVE) [22]. We evaluate inter-person accuracy on HI4D and CHI3D by Pair-PA-MPJPE, which aligns the two people as a whole with the ground truth [38].", + "bbox": [ + 89, + 330, + 483, + 420 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate world-grounded motion on EMDB with PromptHMR video (PromptHMR-vid), we compute World-aligned MPJPE $(\\mathrm{WA - MPJPE}_{100})$ , World MPJPE $(\\mathrm{W - MPJPE}_{100})$ and Root Translation Error (RTE in %) [52, 67].", + "bbox": [ + 89, + 422, + 483, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Reconstruction accuracy", + "text_level": 1, + "bbox": [ + 89, + 496, + 316, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For camera space reconstruction, as shown in Table 1, PromptHMR and PromptHMR-Vid demonstrate state-of-the-art performance, matching crop-based methods while achieving better results than other full-image methods. PromptHMR and CameraHMR use the same training data and have similar performance, which validates that this prompt-based approach can achieve metrically accurate results. For representative results, see Fig. 7, where PromptHMR recovers coherent 3D scenes of people.", + "bbox": [ + 89, + 520, + 483, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For interaction reconstruction, PromptHMR achieves good accuracy as indicated in Table 2. Compared to BUDDI which is also trained on CHI3D and HI4D, our method achieves better overall accuracy on per-person and interperson metrics. We show qualitative results in Fig. 8. As a monocular regression method, PromptHMR still cannot avoid interpenetration between closely interacting people.", + "bbox": [ + 89, + 657, + 483, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PromptHMR-Vid achieves SOTA performance among methods that estimate human motion in world coordinates, as shown in Table 4. Unlike TRAM, we estimate the joint contact probabilities similar to [51, 52]. Therefore, we achieve lower foot skating than TRAM, even though we use the same metric SLAM method to transform motion in camera space to world coordinates. Please refer to our supplementary material (SupMat) for qualitative results of PromptHMR-Vid.", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/76765d0a6a3a88ed783d150a61768340fbb14079662abbd07fae52512a29a113.jpg", + "image_caption": [ + "Figure 4. Effect of box prompts. Our method remains stable with different boxes, including noisy truncated boxes." + ], + "image_footnote": [], + "bbox": [ + 517, + 88, + 900, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45cd98a2e74dde29e3e811469d3fa51fbc4a9d8865b796168422773625ece09d.jpg", + "image_caption": [ + "Figure 5. Effect of mask prompts. Results are from the same model with different prompt inputs. Masks are better for close interaction scenarios where boxes are ambiguous." + ], + "image_footnote": [], + "bbox": [ + 516, + 204, + 900, + 287 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0455387cbb7dea4c820714e8a040a3978a2731be3dbf1bed6d7449c3af85372a.jpg", + "image_caption": [ + "Figure 6. Effect of shape prompts. Compared to the baseline that does not incorporate shape description during training and testing, the model with shape prompts has better accuracy on HBW, especially in ambiguous images." + ], + "image_footnote": [], + "bbox": [ + 519, + 335, + 898, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Effect of multimodal prompts", + "text_level": 1, + "bbox": [ + 511, + 678, + 777, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct qualitative and quantitative evaluations of the multimodal prompts. For efficient ablation, we train models with $448 \\times 448$ input resolution and select the best model within 150K steps of training.", + "bbox": [ + 511, + 702, + 905, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For box prompts, as shown in rows 3-4 of Fig. 7, our method is able to take a combination of different boxes from in-the-wild images to reconstruct crowded scenes. Figure 4 also shows an example with varying box inputs. PromptHMR remains stable when the boxes change and uses full image context to reconstruct the human even when the boxes are truncated.", + "bbox": [ + 511, + 763, + 905, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The mask prompt is more effective than boxes when people closely overlap (Fig. 5), as boxes are ambiguous in such", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1153", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ba87ce3ed2ade4199326cf7ec0cb4f2ab1d3f690b7e1c877373c8eaac657afe0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Models3DPW (14)EMDB (24)RICH (24)
PA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVE
cropped imageCLIFF* [31]43.069.081.268.3103.3123.768.1103.3128.0
HMR2.0a [17]44.469.882.261.597.8120.060.798.3120.8
TokenHMR [13]44.371.084.655.691.7109.4---
CameraHMR [43]35.156.065.943.370.281.734.055.764.4
full imageBEV [58]46.978.592.370.9112.2133.4---
Multi-HMR* [2]45.973.187.150.181.695.746.373.883.0
PromptHMR*36.658.769.441.071.784.537.356.665.5
videoWHAM [52]37.559.871.552.081.696.944.380.091.2
TRAM [65]35.659.369.645.774.486.6---
GVHMR [51]37.056.668.744.574.285.939.566.074.4
PromptHMR-Vid35.556.967.340.168.179.237.057.465.8
", + "bbox": [ + 153, + 90, + 841, + 316 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aa23c2cdd57b42e2175fd626a2e69dfc4179502569d5b8e94893682946233122.jpg", + "table_caption": [ + "Table 1. Comparison of mesh reconstruction on the 3DPW, EMDB and RICH datasets, with the number of joints in parenthesis. $\\star$ denotes methods that use ground truth focal length during inference. Note that we remove the test-time flip augmentation from all of the video methods to ensure a fair comparison. All metrics are in mm." + ], + "table_footnote": [], + "table_body": "
ModelsHI4D (14)CHI3D (14)
PA-MPJPEMPJPEPair-PA-MPJPEPA-MPJPEMPJPEPair-PA-MPJPE
BEV* [58]81-13651-96
BUDDI [38]73-9847-68
Multi-HMR* [2]49.867.880.631.754.0100.0
PromptHMR*39.263.978.127.248.058.5
PromptHMR30.139.639.524.746.545.3
", + "bbox": [ + 94, + 380, + 477, + 481 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9a93e84104db7099870847c217097b9fbece44908e0b217074b1c174b4bf512a.jpg", + "table_caption": [ + "Table 2. Comparison on interaction reconstruction. PromptHMR is more accurate in per-person and inter-person accuracy. * denote a method or baseline is not trained on HI4D or CHI3D. All metrics are in mm. The impact of HI4D and the interaction prompt are evaluated in Table 5." + ], + "table_footnote": [], + "table_body": "
Train w/ textTest w/ textHBW
HeightChestWaistHipP2P-20k
××6951886326
✓×6948866026
✓✓6243765824
", + "bbox": [ + 94, + 566, + 475, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cases. Ablation of HI4D (rows 1-2 in Tab. 5) shows that using masks as the spatial prompt improves accuracy.", + "bbox": [ + 89, + 763, + 482, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiments on the HBW validation set (Tab. 3) show that text prompts effectively improve shape accuracy when used during both training and testing. Moreover, training with shape descriptions alone provides an accuracy boost even if prompts are not given at test time. As illustrated in Fig. 6, text prompts provide notable improvements, especially when large perspective effects create ambiguity.", + "bbox": [ + 89, + 795, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/90ae2f57c0fdc058081ff3ab4b3377b36e4a7ccbf224d6e0b98c3fbd4cee6db3.jpg", + "table_caption": [ + "Table 3. Ablation of shape prompts using text. Training with shape prompts improves shape accuracy. Using shape prompts during inference further improves shape accuracy. The ablation study is conducted with a $448 \\times 448$ model. Errors are in mm." + ], + "table_footnote": [], + "table_body": "
ModelsEMDB-2 (24)
WA-MPJPE100W-MPJPE100RTEJitterFoot Skating
WHAM [52]135.6354.86.022.54.4
TRAM [65]76.4222.41.418.523.4
GVHMR [51]111.0276.52.016.73.5
PromptHMR-Vid71.0216.51.316.33.5
", + "bbox": [ + 519, + 380, + 898, + 467 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9d490488d1aa1ed7a16399089be73109b9b2939a55fef2a092f6ad4fe9d97aa1.jpg", + "table_caption": [ + "Table 4. Evaluation of motion in world coordinates. PromptHMR-Vid combined with metric SLAM from TRAM [65] surpasses SOTA methods at predicting human motion in world coordinates." + ], + "table_footnote": [], + "table_body": "
Trained withHI4D (14)
MaskInteractionHI4DPA-MPJPEMPJPEPair-PA-MPJPE
×××47.071.487.2
✓××43.460.583.0
×✓×43.761.373.0
××✓36.349.452.6
✓✓✓36.547.147.9
", + "bbox": [ + 517, + 549, + 903, + 675 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation on interaction prompt. The interaction module improves inter-person reconstruction metrics Pair-PA-MPJPE on HI4D, especially when the method does not include HI4D in training. Ablation is conducted with a $448 \\times 448$ model. All metrics are in mm.", + "bbox": [ + 511, + 683, + 906, + 752 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For interaction prompts, we show an ablation in Table 5. The proposed interaction module is beneficial and largely improves inter-person accuracy on HI4D even without HI4D training, indicating out-off-domain generalization. When trained on HI4D, the interaction module does not improve per-person PA-MPJPE but still improves interperson Pair-PA-MPJPE. Please refer to our SupMat for more qualitative results on interaction prompts.", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1154", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a845a1ad594881ec9d8ab80a5d9c550aa3b3adb337a13fb5501266f7a87634b9.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison: Multi-HMR vs PromptHMR. Our model can recover coherent 3D scenes of people. In crowded scenes, face detection provides reliable box prompts for our model. Please zoom in to see the details." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 897, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7db2160aff5f5160604adec48ce4f0c51cfe225426774259d35b6ba76b1d46e6.jpg", + "image_caption": [ + "Figure 8. Qualitative results. PromptHMR recovers coherent two-person close interaction. Despite suffering from some interpenetration, the relative positions of the interacting people are accurately recovered. More examples are provided in the Supplementary." + ], + "image_footnote": [], + "bbox": [ + 96, + 484, + 880, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 89, + 726, + 212, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We see PromptHMR as a step towards a holistic perception model for 3D humans, but several limitations need to be addressed in future work. Currently, the shape description and interaction prompts are not automatically generated and need to be supplied by the user. Future work should explore how to effectively integrate our promptable model with VLMs to automate prompting. We show how semantic prompts can improve reconstruction accuracy, but many other potential types of side information such as action descriptions, 3D scene context, or body measurements may", + "bbox": [ + 89, + 750, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "provide additional benefits in different scenarios.", + "bbox": [ + 513, + 727, + 836, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 753, + 633, + 770 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented PromptHMR, a promptable HPS estimation approach that leverages full image context with spatial and semantic prompts to infer 3D humans in the scene. Our method demonstrates state-of-the-art accuracy across diverse benchmarks and generalizes well in the wild. Our experiments show that incorporating diverse input information through flexible prompting enables robustness and adaptability in challenging scenarios.", + "bbox": [ + 511, + 779, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1155", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. The authors would like to thank Yan Zhang, Yao Feng, and Nitin Saini for their suggestions. The majority of the work was done when Yufu was an intern at Meshcapade. Yufu and Kostas thank the support of NSF NCS-FO 2124355, NSF FRR 2220868, and NSF IISRI 2212433.", + "bbox": [ + 89, + 90, + 480, + 180 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Disclosure. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society.", + "bbox": [ + 89, + 181, + 480, + 242 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 255, + 187, + 271 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nikos Athanasiou, Alpár Ceske, Markos Diomataris, Michael J. Black, and Gül Varol. MotionFix: Text-driven 3D human motion editing. In SIGGRAPH Asia, 2024. 3", + "[2] Fabien Baradel, Matthieu Armando, Salma Galaoui, Romain Brégier, Philippe Weinzaepfel, Grégory Rogez, and Thomas Lucas. Multi-HMR: Multi-person whole-body human mesh recovery in a single shot. European Conference on Computer Vision, 2024. 3, 4, 7", + "[3] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1216-1226, 2024. 3", + "bbox": [ + 91, + 90, + 482, + 161 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "1159", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_model.json b/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..939286b748d95d4c08285a21812b587f81442d8a --- /dev/null +++ b/2025/PromptHMR_ Promptable Human Mesh Recovery/5b944c82-9867-4899-8aca-e1b6957dfaa1_model.json @@ -0,0 +1,2666 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.243, + 0.131, + 0.757, + 0.155 + ], + "angle": 0, + "content": "PromptHMR: Promptable Human Mesh Recovery" + }, + { + "type": "text", + "bbox": [ + 0.239, + 0.18, + 0.758, + 0.199 + ], + "angle": 0, + "content": "Yufu Wang\\(^{1,4}\\) Yu Sun\\(^{1}\\) Priyanka Patel\\(^{1}\\) Kostas Daniilidis\\(^{4,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.315, + 0.199, + 0.683, + 0.216 + ], + "angle": 0, + "content": "Michael J. 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PromptHMR is a promptable human pose and shape (HPS) estimation method that processes images with spatial or semantic prompts. It takes \"side information\" readily available from vision-language models or user input to improve the accuracy and robustness of 3D HPS. PromptHMR recovers human pose and shape from spatial prompts such as (a) face bounding boxes, (b) partial or complete person detection boxes, or (c) segmentation masks. It refines its predictions using semantic prompts such as (c) person-person interaction labels for close contact scenarios, or (d) natural language descriptions of body shape to improve body shape predictions. Both image and video versions of PromptHMR achieve state-of-the-art accuracy. https://yufu-wang.github.io/phmr-page" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.671, + 0.327, + 0.687 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Human pose and shape (HPS) estimation presents challenges in diverse scenarios such as crowded scenes, person-person interactions, and single-view reconstruction. Existing approaches lack mechanisms to incorporate auxiliary \"side information\" that could enhance reconstruction accuracy in such challenging scenarios. Furthermore, the most accurate methods rely on cropped person detections and cannot exploit scene context while methods that process the whole image often fail to detect people and are less accurate than methods that use crops. While recent language-based methods explore HPS reasoning through large language or vision-language models, their metric accuracy is well below the state of the art. In contrast, we present PromptHMR," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.909, + 0.886 + ], + "angle": 0, + "content": "a transformer-based promptable method that reformulates HPS estimation through spatial and semantic prompts. Our method processes full images to maintain scene context and accepts multiple input modalities: spatial prompts like bounding boxes and masks, and semantic prompts like language descriptions or interaction labels. PromptHMR demonstrates robust performance across challenging scenarios: estimating people from bounding boxes as small as faces in crowded scenes, improving body shape estimation through language descriptions, modeling person-person interactions, and producing temporally coherent motions in videos. Experiments on benchmarks show that PromptHMR achieves state-of-the-art performance while offering flexible prompt-based control over the HPS estimation process." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1148" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.223, + 0.107 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.482, + 0.281 + ], + "angle": 0, + "content": "The estimation of 3D human pose and shape (HPS) is classically viewed as regressing the parameters of shape and pose from pixels. In particular, most methods take a tightly cropped image of a person and output the pose and shape in camera coordinates. While the accuracy of such methods has increased rapidly, they do not address the whole problem. In particular, an HPS method should be able to take an image or video containing complex human-human and human-scene interactions, return the parameters of every person in the scene, and place these people in a consistent global coordinate frame." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.282, + 0.482, + 0.402 + ], + "angle": 0, + "content": "Our key observation is that the classical \"pixels to parameters\" formulation of the problem is too narrow. Today, we have large vision-language foundation models (VLMs) that understand a great deal about images and what people are doing in them. What these models lack, however, is an understanding of 3D human pose and shape. Recent work [10, 15] has tried to bring together VLMs and 3D HPS but with 3D accuracy well below the best classical methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.403, + 0.483, + 0.674 + ], + "angle": 0, + "content": "Consequently, we need to think about the problem in a different way and ask whether we can exploit readily available side information (e.g. provided by a VLM) to improve 3D HPS regression robustness, usefulness, and accuracy. To that end, we develop a novel \"promptable\" HPS architecture called PromptHMR. Consider the sample images shown in Fig. 1. In crowded scenes, existing person detection methods struggle, while face detection methods remain reliable. When people closely interact, their body parts overlap and occlude each other, introducing ambiguity in pose estimation. Moreover, 3D body shape estimation from monocular views is challenging due to perspective ambiguity. In all these cases, we can extract cues, or prompts, that provide \"side information\" that can help an HPS method better analyze the scene. PromptHMR formalizes this intuition by combining image evidence with different types of spatial and semantic information that can come from either humans or AI systems such as VLMs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Specifically, our approach combines three key components: (1) a vision transformer that extracts features from high-resolution full images to preserve scene context, (2) a multi-modal prompt encoder that processes spatial and semantic inputs, and (3) a transformer decoder that attends to both prompt and image tokens to generate SMPL-X [45] body parameters. This design addresses the limitations of cropped-image HPS methods by processing full images using side information in the form of prompts. It addresses the challenges that full-image HPS methods have in detecting all people in a scene by accepting readily available bounding boxes. Last, our method incorporates auxiliary semantic information through text descriptions or interaction labels." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "By combining spatial and semantic prompting, our method offers a powerful and versatile approach to 3D HPS" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.302 + ], + "angle": 0, + "content": "estimation from the whole image. At test time, we show that this promptable structure (1) can take various bounding boxes or segmentation masks to recover full body HPS in a robust way, (2) improve its body shape predictions by using textual descriptions as input, (3) is capable of modeling person-person close interaction directly in the regression process, and (4) uses full image context to reconstruct people coherently in the camera space and the world space. Our model can handle video by incorporating temporal transformer layers at the SMPL-X decoding phase, yielding temporally stable and smooth motions. Last, following TRAM [65], we combine the temporal version of our model with metric SLAM to estimate human motion in world coordinates." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.303, + 0.905, + 0.514 + ], + "angle": 0, + "content": "We make several key design choices that make PromptHMR successful. To achieve robustness to different spatial inputs, we train our model by simulating noisy full-body and face-region bounding boxes. For improved body shape estimation, we leverage SHAPY [8] to generate automatic body shape descriptions for training samples and process them with a pretrained text encoder [48]. To enhance person-person interaction reconstruction, we use segmentation masks as more precise spatial prompts and develop person-person attention layers that operate between prompted people, producing coherent reconstructions of close interactions. Through random masking of different input types during training, our model learns to work with any combination of prompts at test time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.905, + 0.62 + ], + "angle": 0, + "content": "Quantitative experiments on the EMDB [24], 3DPW [63], RICH [20], Hi4D [68], CHI3D [16] and HBW [8] benchmark datasets demonstrate that our method outperforms state-of-the-art (SOTA) approaches and strong baselines. We also provide many qualitative examples of in-the-wild images and videos that illustrate the robustness and generalization of PromptHMR." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.905, + 0.786 + ], + "angle": 0, + "content": "By moving away from the pure pixels-to-parameters approach, PromptHMR not only achieves a new SOTA, it shows a new way of improving both accuracy and robustness by leveraging side information that is easily available. One can think of this as a collaboration between VLMs, which know a lot about people in images but not in 3D, and a metric regressor that knows a lot about 3D humans but not about the semantics of what they do. We show that this combination has significant upside potential to increase both generality and accuracy. Our code and model are available for research purposes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.8, + 0.655, + 0.815 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.903 + ], + "angle": 0, + "content": "Human pose and shape estimation from images. Existing methods for human pose and shape (HPS) estimation can be broadly categorized into two main approaches. The first [6, 17, 22, 27, 28, 30-32, 39, 64, 70] uses a tightly cropped image of an individual as input, and estimates" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1149" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "pose and shape in camera coordinates. While effective for isolated individuals, this approach discards scene context that is essential to resolve human pose in cases of occlusion, severe overlap and close interaction in multi-person scenes [16, 68]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.17, + 0.482, + 0.305 + ], + "angle": 0, + "content": "The second category [2, 21, 55, 57-59] build upon object detection frameworks [5, 12] to jointly detect humans and estimate their pose and shape parameters. Having access to the entire image, they can better perceive occluded individuals and infer depth relationships, but they often suffer from detection failures due to the difficulty in simultaneously performing detection and reconstruction. Our \"promptable\" architecture leverages detection box prompts to resolve such conflicts while having access to the entire scene context." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.307, + 0.482, + 0.412 + ], + "angle": 0, + "content": "Human pose and shape estimation from video. Methods for human motion estimation from video can also be divided into two main categories. The first [7, 23, 26, 36, 56] focuses on estimating smooth human motion in camera space. These methods build upon single-person HPS estimation approaches [22, 30] by adding temporal layers during the SMPL decoding phase to introduce temporal coherence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.414, + 0.482, + 0.581 + ], + "angle": 0, + "content": "More recent methods estimate human motion in world coordinates from videos captured with dynamic cameras. These methods follow a two-stage approach, first estimating camera motion using SLAM techniques [18, 19, 40, 41, 60, 61], and then leveraging human motion priors to optimize the human world motion [29, 67, 69]. Others [51, 52] learn temporal models to directly regress human world motion from image and camera features. Still others [65, 71] use monocular metric depth estimation to solve for the scale of camera motion and transform human motion from camera space to world coordinates." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.482, + 0.673 + ], + "angle": 0, + "content": "In our approach, we extend PromptHMR to video by taking the SMPL-X output tokens and utilizing a temporal transformer module to estimate temporally stable and smooth human motion and translation in camera space. We follow TRAM [65] to transform human motion to world coordinates due to its simplicity and effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Semantic reasoning about 3D humans in images. Recent methods explore combining different types of semantic information, such as language descriptions and knowledge of person-person interactions, to improve reasoning about 3D humans from images and videos. For example, ChatPose [15] follows the common approach of visual language models (VLMs) [34] by fine-tuning a large language model (LLM) with a combination of images and tokens to estimate SMPL parameters. In a similar direction, PoseEmbroider [10] is a multi-modal framework that aligns image, 3D pose, and text representations in a shared latent space. While ChatPose focuses on combining high-level scene reasoning with 3D HPS, PoseEmbroider exploits detailed language descriptions of human pose. While promising, neither method achieves SOTA accuracy on the HPS task. Note" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "that many other methods relate language to human pose or motion, without considering images [1, 9, 35, 46, 62], but these are outside our scope." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.137, + 0.905, + 0.318 + ], + "angle": 0, + "content": "Additionally, several methods [8, 47, 53] focus on modeling the relationship between SMPL body shape and natural language descriptions. These methods show that language descriptions and images can provide complementary information to solve this task. Other approaches, such as BUDDI [38] and ProsePose [54], address the challenge of estimating person-person interactions. BUDDI is an optimization-based approach that leverages diffusion model as a prior over interacting people, while ProsePose queries a VLM to estimate contact points on the human body surface and uses these contact points to guide an optimization process for improving human interaction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.905, + 0.469 + ], + "angle": 0, + "content": "Overall, methods like ChatPose [15] and PoseEmbroider [10] are promising steps toward jointly learning the relationship between vision, language, and 3D humans, but their understanding of 3D humans remains limited, as indicated by their relatively low 3D pose accuracy. Meanwhile, SHAPY [8], BodyShapeGPT [47], and BodyTalk [53] focus solely on exploring the relationship between SMPL body shape and natural language. BUDDI and ProsePose are post-processing approaches for interaction that do not directly reason using image information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.905, + 0.545 + ], + "angle": 0, + "content": "Our approach addresses the limitations of these methods by training a single model capable of flexible prompting that achieves state-of-the-art (SOTA) performance, not only on standard HPS benchmarks but also on benchmarks tailored to body shape and person-person interaction." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.557, + 0.605, + 0.571 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.905, + 0.643 + ], + "angle": 0, + "content": "Given an image \\(I\\) containing \\(N\\) people and a set of prompts, our main goal is to recover the pose, shape, and locations of the people in the camera space to form a coherent human-centric 3D scene. Figure 2 shows an overview." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.65, + 0.768, + 0.667 + ], + "angle": 0, + "content": "3.1. Promptable mesh regression" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.905, + 0.764 + ], + "angle": 0, + "content": "We adopt SMPL-X [45] to represent each person \\(i\\) in the 3D space, including the orientation \\(\\phi_i \\in \\mathbb{R}^3\\), local body pose \\(\\theta_i \\in \\mathbb{R}^{22 \\times 3}\\), shape \\(\\beta_i \\in \\mathbb{R}^{10}\\), and translation \\(\\tau_i \\in \\mathbb{R}^3\\) in the camera space. We do not include face and hand parameters in this work. Each human \\(H_i\\) is mapped to a 3D mesh with the differentiable SMPL-X layer." + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.771, + 0.905, + 0.789 + ], + "angle": 0, + "content": "\\[\nH _ {i} = \\left\\{\\phi_ {i}, \\theta_ {i}, \\beta_ {i}, \\tau_ {i} \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.796, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Each person can be prompted with spatial and semantic prompts. Spatial prompts include a bounding box \\( b_{i} \\in \\mathbb{R}^{2 \\times 2} \\) (the two corners) and a segmentation mask \\( m_{i} \\in \\mathbb{R}^{h \\times w} \\). Semantic prompts consist of text and two-person interaction labels. The text prompt is the CLIP embedding \\( t_{i} \\) of a sentence describing the body shape. The interaction prompt is a binary variable \\( k_{i} \\) indicating whether two" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1150" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.092, + 0.9, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.243, + 0.907, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Method overview. PromptHMR estimates SMPL-X parameters for each person in an image based on various types of prompts, such as boxes, language descriptions, and person-person interaction cues. Given an image and prompts, we utilize a vision transformer to generate image embeddings and mask and prompt encoders to map different types of prompts to tokens. Optionally, camera intrinsics can be embedded along with the image embeddings. The image embeddings and prompt tokens are then fed to the SMPL-X decoder. The SMPL-X decoder is a transformer-based module that attends to both the image and prompt tokens to estimate SMPL-X parameters. Note that the language and interaction prompts are optional, but providing them enhances the accuracy of the estimated SMPL-X parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.346, + 0.484, + 0.406 + ], + "angle": 0, + "content": "people are in close contact. While semantic prompts are optional, each human needs at least one spatial prompt to be reconstructed. Overall, the input prompts are represented as \\( P_{i} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.412, + 0.482, + 0.435 + ], + "angle": 0, + "content": "\\[\nP _ {i} \\subseteq \\left\\{b _ {i}, m _ {i}, t _ {i}, k _ {i} \\right\\} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.433, + 0.356, + 0.446 + ], + "angle": 0, + "content": "\\[\nb _ {i} \\in P _ {i} \\text {o r} m _ {i} \\in P _ {i}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.497 + ], + "angle": 0, + "content": "Promptable human mesh recovery (PromptHMR) is defined as a learnable function that maps an image and a set of prompts to a set of 3D humans" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.502, + 0.482, + 0.521 + ], + "angle": 0, + "content": "\\[\nf: \\left(I, \\left\\{P _ {i} \\right\\} _ {i = 1} ^ {N}\\right)\\rightarrow \\left\\{H _ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.526, + 0.484, + 0.557 + ], + "angle": 0, + "content": "This task definition integrates all available contexts to locate and reconstruct prompted humans in the image." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.563, + 0.178, + 0.578 + ], + "angle": 0, + "content": "3.2. Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.587, + 0.484, + 0.617 + ], + "angle": 0, + "content": "Image encoder. The image is first encoded as tokens by a vision transformer (ViT) encoder from DINOv2 [11, 42]:" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.623, + 0.482, + 0.64 + ], + "angle": 0, + "content": "\\[\nF = \\operatorname {E n c o d e r} (I), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.646, + 0.484, + 0.736 + ], + "angle": 0, + "content": "To ensure sufficient resolution for modeling humans at both near and far distances, we use \\(896 \\times 896\\) images. The encoder is run once per frame regardless of the number of people prompted. When camera intrinsics are provided, we add positional encoding of the camera rays to the image tokens to make them camera-aware [2, 14]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.737, + 0.484, + 0.811 + ], + "angle": 0, + "content": "Mask encoder. When available, masks are first processed by an encoder consisting of stripped convolutional layers that downsample the masks. The output mask features are added to the image tokens. If no mask is provided, a learned \"no mask\" token is added instead." + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.819, + 0.482, + 0.835 + ], + "angle": 0, + "content": "\\[\nF _ {i} = \\operatorname {E n c o d e r} _ {\\mathrm {m}} \\left(m _ {i}\\right) + F. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Prompt encoder. The prompt encoder consists of a set of transformations that map different types of prompts to token vectors of the same dimension. When a prompt is not available, it is replaced with a learned null token." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.346, + 0.907, + 0.497 + ], + "angle": 0, + "content": "For bounding boxes, we encode \\( b_{i} \\) using positional encoding summed with learned embeddings to form the box prompt tokens \\( T_{bi} = \\mathrm{PE}(b_{i}) \\), with \\( T_{bi} \\in \\mathbb{R}^{2 \\times d} \\). We design different box transformations during training to allow the model to use different boxes as a human identifier. In the training phase, each instance is prompted with either a whole-body bounding box, a face bounding box, or a truncated box covering part of the body. Gaussian noise is added to both corners. At inference time, the model accepts boxes without needing to know the box types." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.497, + 0.906, + 0.633 + ], + "angle": 0, + "content": "Language is a natural way to supply semantic information, and in this paper, we use language to supplement spatial prompts with information on body shape. A sentence such as \"a muscular and tall male\" is encoded with the CLIP text encoder \\( T_{ti} = \\mathrm{CLIP}(t_i) \\), with \\( T_{ti} \\in \\mathbb{R}^{d} \\). To generate paired (image, text) data, we run SHAPY's [8] shape-to-attribute method on the ground truth shape parameters to obtain shape attribute scores and randomly pick a subset of top attributes to form a sentence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.633, + 0.906, + 0.678 + ], + "angle": 0, + "content": "The interaction prompt \\( k_{i} \\) passes through the prompt encoder without modification and directly switches on-off the cross-person attention that is described in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.678, + 0.906, + 0.723 + ], + "angle": 0, + "content": "SMPL-X decoder. The SMPL-X decoder appends two query tokens \\( T_{\\mathrm{spl}}, T_{\\mathrm{depth}} \\) with the prompt tokens \\( T_{bi}, T_{ti} \\) to form the person-specific prompt \\( T_i \\in \\mathbb{R}^{5 \\times d} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.724, + 0.906, + 0.754 + ], + "angle": 0, + "content": "Finally, we use a standard transformer decoder and two MLP heads to produce the final output" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.76, + 0.813, + 0.78 + ], + "angle": 0, + "content": "\\[\nT _ {s m p l} ^ {\\prime}, T _ {d e p t h} ^ {\\prime} = \\mathrm {D e c o d e r} (F _ {i}, T _ {i})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.782, + 0.905, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\phi_ {i}, \\theta_ {i}, \\beta_ {i} = \\operatorname {H e a d} _ {s m p l} \\left(T _ {s m p l} ^ {\\prime}\\right) \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.664, + 0.802, + 0.831, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\tau_ {i} = \\operatorname {H e a d} _ {d e p t h} (T _ {d e p t h} ^ {\\prime}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "The transformer consists of three attention blocks. Each block applies self-attention on the tokens, cross-person attention (described in Sec. 3.3), and then two-way cross-attention between the tokens and the image embeddings [25]. The self-attention and cross-attention with the" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1151" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "image are applied to each prompted person independently. We use separate tokens \\( T_{\\mathrm{spl}} \\) and \\( T_{\\mathrm{depth}} \\) to make the location representation invariant to the 3D human pose and shape representation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.243 + ], + "angle": 0, + "content": "Regressing the location of the human in the camera space is much more challenging than most prior work that models humans in a cropped image space. Therefore, we do not regress \\(\\tau\\) directly. We regress focal length normalized 2D translation \\(p_{xy} \\in \\mathbb{R}^2\\) and inverse depth \\(p_z \\in \\mathbb{R}\\), and then transform them to \\(\\tau\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.25, + 0.483, + 0.283 + ], + "angle": 0, + "content": "\\[\nt _ {x y} = \\frac {p _ {x y}}{p _ {z}} \\quad t _ {z} = \\frac {1}{p _ {z}} \\times \\frac {f}{f _ {c}} \\quad \\tau = [ t _ {x y}, t z ], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.292, + 0.484, + 0.399 + ], + "angle": 0, + "content": "where \\( f \\) is the ground truth or estimated focal length of the image, and \\( f_{c} \\) is the canonical focal length. Predicting the normalized inverse depth follows the recent monocular depth literature [49] and is also intuitive since the inverse depth is linearly related to the size of the human in the image. Predicting \\( p_{xy} \\) is equivalent to predicting the 2D location of the human in a normalized image plane." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.407, + 0.307, + 0.423 + ], + "angle": 0, + "content": "3.3. Two-person interaction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.43, + 0.483, + 0.492 + ], + "angle": 0, + "content": "We introduce promptable layers in the decoder to model two-person interaction. We describe the case where there are two people in the image, but the implementation can extend to model an interacting pair in a larger group." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.491, + 0.483, + 0.567 + ], + "angle": 0, + "content": "The promptability is modeled as a flow control with a residual connection (Fig. 3). Specifically, if two humans are interacting (as indicated by \\( k_{i} \\)), their query tokens pass through an additional self-attention layer; otherwise, non-interacting humans skip this." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.567, + 0.483, + 0.672 + ], + "angle": 0, + "content": "Applying attention to every person often creates unnecessary dependency in crowded scenes, and there is limited training data for large-group scenarios. However, there is high-quality data featuring two-person social interactions. By making the interaction layers promptable, we mitigate data diversity issues and increase flexibility, regardless of the number of people in the scene." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Our proposed interaction layer uses a standard self-attention mechanism. First, we add positional encodings to the query tokens to distinguish the two individuals. The encoded tokens then go through a self-attention layer, whose output is combined with the original tokens via a residual connection. Our experiments demonstrate that including these interaction layers significantly improves inter-person pose accuracy in two-person interaction benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.802, + 0.336, + 0.818 + ], + "angle": 0, + "content": "3.4. PromptHMR video version" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.903 + ], + "angle": 0, + "content": "In addition to the single-image variant of PromptHMR, we train an extended version that processes videos to estimate human motion in world coordinates. To achieve this, we introduce a simple and efficient temporal transformer module. Given a monocular video sequence \\(\\{I^t\\}_{t=0}^T\\), we first run" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.091, + 0.9, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.208, + 0.906, + 0.251 + ], + "angle": 0, + "content": "Figure 3. SMPL-X decoder. The top row shows one attention block in the decoder. The cross-person interaction module can be turned on/off. The bottom row shows the cross-person attention." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.27, + 0.906, + 0.407 + ], + "angle": 0, + "content": "PromptHMR to obtain per-subject SMPL-X decoder output tokens \\( T_{\\mathrm{spl}}^{\\prime} \\) and \\( T_{\\mathrm{depth}}^{\\prime} \\), assuming that the subject identities are provided with the prompts. These tokens, along with the positional encoding of time \\( t \\), are fed to a decoder-only temporal transformer module with twelve attention blocks. The output tokens are converted to SMPL-X parameters \\( \\phi_t, \\theta_t, \\beta_t \\), translation \\( \\tau_t \\), and joint contact probabilities \\( c_t \\). The contact probabilities indicate whether a given joint is in contact with the ground plane similar to [50-52]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.408, + 0.906, + 0.56 + ], + "angle": 0, + "content": "To obtain results in world coordinates, we adopt the approach from TRAM [65]. Specifically, we use DROID-SLAM [60] and a monocular metric depth estimation model, ZoeDepth [3], to estimate camera motion in metric world coordinates. The translation parameters \\(\\tau_{t}\\) are then transformed to world coordinates using the estimated camera motion. To refine the human trajectory and mitigate foot-skating artifacts, we leverage the estimated contact probabilities and run a fast postprocessing that optimizes the contact joints to have zero velocity." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.575, + 0.602, + 0.589 + ], + "angle": 0, + "content": "3.5. Losses" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.6, + 0.906, + 0.631 + ], + "angle": 0, + "content": "PromptHMR is trained with a combination of 2D and 3D losses, following traditional HMR methods [22, 30]:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.646, + 0.884, + 0.663 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {2 D} + \\lambda_ {2} \\mathcal {L} _ {3 D} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {4} \\mathcal {L} _ {V} + \\lambda_ {5} \\mathcal {L} _ {t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.678, + 0.704, + 0.692 + ], + "angle": 0, + "content": "with each term calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.708, + 0.78, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {2 D} = \\left\\| \\hat {\\mathcal {J}} _ {2 D} - \\Pi \\left(\\mathcal {J} _ {3 D}\\right) \\right\\| _ {F} ^ {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.729, + 0.755, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {3 D} = \\left\\| \\hat {\\mathcal {J}} _ {3 D} - \\mathcal {J} _ {3 D} \\right\\| _ {F} ^ {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.751, + 0.72, + 0.769 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {S M P L}} = | | \\hat {\\Theta} - \\Theta | | _ {2} ^ {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.773, + 0.722, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {V} = \\left\\| \\hat {V} - V \\right\\| _ {F} ^ {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.793, + 0.844, + 0.811 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\left| \\left| \\hat {p} _ {x y} - p _ {x y} \\right| \\right| _ {F} ^ {2} + \\left| \\left| \\hat {p} _ {z} - p _ {z} \\right| \\right| _ {F} ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathcal{J}_{3D}\\) and \\(V\\) are the 3D joints and vertices of the SMPL-X model, with the hat operator denoting the ground truth. \\(\\Pi\\) is the camera reprojection operator. Additionally, on datasets with ground truth translation labels, we supervise the normalized translation \\(p_{xy}\\) and inverse depth \\(p_z\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1152" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.224, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.484, + 0.252 + ], + "angle": 0, + "content": "Datasets. We train PromptHMR with standard datasets: BEDLAM [4], AGORA [44], 3DPW [63], COCO [33], and MPII [37]. Following 4DHumans, we add AIC [66] and InstaVariety [23] as in-the-wild data, with pseudoground truth from CamSMPLify [43]. Additionally, we add CHI3D [16] and HI4D [68] to enable learning two-person interaction following the train-test splits from BUDDI [38]. Including CHI3D and HI4D does not improve performance on other benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.254, + 0.484, + 0.33 + ], + "angle": 0, + "content": "Implementation. We train PromptHMR with AdamW with a batch size of 96 images of resolution \\(896 \\times 896\\). We use a learning rate of \\(1e^{-5}\\) for the image encoder and \\(3e^{-5}\\) for the prompt encoder and the SMPL-X decoder, with a weight decay of \\(5e^{-5}\\). The training converges within 350K steps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.331, + 0.484, + 0.421 + ], + "angle": 0, + "content": "Evaluation. We evaluate camera space reconstruction accuracy on 3DPW [63], EMDB [24] and RICH [20], using MPJPE, Procrustes-aligned MPJPE (PA-MPJPE) and Per Vertex Error (PVE) [22]. We evaluate inter-person accuracy on HI4D and CHI3D by Pair-PA-MPJPE, which aligns the two people as a whole with the ground truth [38]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.423, + 0.484, + 0.484 + ], + "angle": 0, + "content": "To evaluate world-grounded motion on EMDB with PromptHMR video (PromptHMR-vid), we compute World-aligned MPJPE \\((\\mathrm{WA - MPJPE}_{100})\\), World MPJPE \\((\\mathrm{W - MPJPE}_{100})\\) and Root Translation Error (RTE in %) [52, 67]." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.497, + 0.318, + 0.513 + ], + "angle": 0, + "content": "4.1. Reconstruction accuracy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.521, + 0.484, + 0.657 + ], + "angle": 0, + "content": "For camera space reconstruction, as shown in Table 1, PromptHMR and PromptHMR-Vid demonstrate state-of-the-art performance, matching crop-based methods while achieving better results than other full-image methods. PromptHMR and CameraHMR use the same training data and have similar performance, which validates that this prompt-based approach can achieve metrically accurate results. For representative results, see Fig. 7, where PromptHMR recovers coherent 3D scenes of people." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.484, + 0.764 + ], + "angle": 0, + "content": "For interaction reconstruction, PromptHMR achieves good accuracy as indicated in Table 2. Compared to BUDDI which is also trained on CHI3D and HI4D, our method achieves better overall accuracy on per-person and interperson metrics. We show qualitative results in Fig. 8. As a monocular regression method, PromptHMR still cannot avoid interpenetration between closely interacting people." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "PromptHMR-Vid achieves SOTA performance among methods that estimate human motion in world coordinates, as shown in Table 4. Unlike TRAM, we estimate the joint contact probabilities similar to [51, 52]. Therefore, we achieve lower foot skating than TRAM, even though we use the same metric SLAM method to transform motion in camera space to world coordinates. Please refer to our supplementary material (SupMat) for qualitative results of PromptHMR-Vid." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.089, + 0.901, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.168, + 0.906, + 0.196 + ], + "angle": 0, + "content": "Figure 4. Effect of box prompts. Our method remains stable with different boxes, including noisy truncated boxes." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.205, + 0.901, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.291, + 0.906, + 0.334 + ], + "angle": 0, + "content": "Figure 5. Effect of mask prompts. Results are from the same model with different prompt inputs. Masks are better for close interaction scenarios where boxes are ambiguous." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.337, + 0.9, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.603, + 0.906, + 0.659 + ], + "angle": 0, + "content": "Figure 6. Effect of shape prompts. Compared to the baseline that does not incorporate shape description during training and testing, the model with shape prompts has better accuracy on HBW, especially in ambiguous images." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.679, + 0.779, + 0.696 + ], + "angle": 0, + "content": "4.2. Effect of multimodal prompts" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.906, + 0.764 + ], + "angle": 0, + "content": "We conduct qualitative and quantitative evaluations of the multimodal prompts. For efficient ablation, we train models with \\(448 \\times 448\\) input resolution and select the best model within 150K steps of training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.869 + ], + "angle": 0, + "content": "For box prompts, as shown in rows 3-4 of Fig. 7, our method is able to take a combination of different boxes from in-the-wild images to reconstruct crowded scenes. Figure 4 also shows an example with varying box inputs. PromptHMR remains stable when the boxes change and uses full image context to reconstruct the human even when the boxes are truncated." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "The mask prompt is more effective than boxes when people closely overlap (Fig. 5), as boxes are ambiguous in such" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1153" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.155, + 0.091, + 0.842, + 0.317 + ], + "angle": 0, + "content": "
Models3DPW (14)EMDB (24)RICH (24)
PA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVE
cropped imageCLIFF* [31]43.069.081.268.3103.3123.768.1103.3128.0
HMR2.0a [17]44.469.882.261.597.8120.060.798.3120.8
TokenHMR [13]44.371.084.655.691.7109.4---
CameraHMR [43]35.156.065.943.370.281.734.055.764.4
full imageBEV [58]46.978.592.370.9112.2133.4---
Multi-HMR* [2]45.973.187.150.181.695.746.373.883.0
PromptHMR*36.658.769.441.071.784.537.356.665.5
videoWHAM [52]37.559.871.552.081.696.944.380.091.2
TRAM [65]35.659.369.645.774.486.6---
GVHMR [51]37.056.668.744.574.285.939.566.074.4
PromptHMR-Vid35.556.967.340.168.179.237.057.465.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.324, + 0.907, + 0.368 + ], + "angle": 0, + "content": "Table 1. Comparison of mesh reconstruction on the 3DPW, EMDB and RICH datasets, with the number of joints in parenthesis. \\(\\star\\) denotes methods that use ground truth focal length during inference. Note that we remove the test-time flip augmentation from all of the video methods to ensure a fair comparison. All metrics are in mm." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.381, + 0.478, + 0.482 + ], + "angle": 0, + "content": "
ModelsHI4D (14)CHI3D (14)
PA-MPJPEMPJPEPair-PA-MPJPEPA-MPJPEMPJPEPair-PA-MPJPE
BEV* [58]81-13651-96
BUDDI [38]73-9847-68
Multi-HMR* [2]49.867.880.631.754.0100.0
PromptHMR*39.263.978.127.248.058.5
PromptHMR30.139.639.524.746.545.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.557 + ], + "angle": 0, + "content": "Table 2. Comparison on interaction reconstruction. PromptHMR is more accurate in per-person and inter-person accuracy. * denote a method or baseline is not trained on HI4D or CHI3D. All metrics are in mm. The impact of HI4D and the interaction prompt are evaluated in Table 5." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.568, + 0.476, + 0.674 + ], + "angle": 0, + "content": "
Train w/ textTest w/ textHBW
HeightChestWaistHipP2P-20k
××6951886326
✓×6948866026
✓✓6243765824
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.683, + 0.483, + 0.741 + ], + "angle": 0, + "content": "Table 3. Ablation of shape prompts using text. Training with shape prompts improves shape accuracy. Using shape prompts during inference further improves shape accuracy. The ablation study is conducted with a \\(448 \\times 448\\) model. Errors are in mm." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.794 + ], + "angle": 0, + "content": "cases. Ablation of HI4D (rows 1-2 in Tab. 5) shows that using masks as the spatial prompt improves accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Experiments on the HBW validation set (Tab. 3) show that text prompts effectively improve shape accuracy when used during both training and testing. Moreover, training with shape descriptions alone provides an accuracy boost even if prompts are not given at test time. As illustrated in Fig. 6, text prompts provide notable improvements, especially when large perspective effects create ambiguity." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.381, + 0.899, + 0.468 + ], + "angle": 0, + "content": "
ModelsEMDB-2 (24)
WA-MPJPE100W-MPJPE100RTEJitterFoot Skating
WHAM [52]135.6354.86.022.54.4
TRAM [65]76.4222.41.418.523.4
GVHMR [51]111.0276.52.016.73.5
PromptHMR-Vid71.0216.51.316.33.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.475, + 0.907, + 0.53 + ], + "angle": 0, + "content": "Table 4. Evaluation of motion in world coordinates. PromptHMR-Vid combined with metric SLAM from TRAM [65] surpasses SOTA methods at predicting human motion in world coordinates." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.55, + 0.905, + 0.676 + ], + "angle": 0, + "content": "
Trained withHI4D (14)
MaskInteractionHI4DPA-MPJPEMPJPEPair-PA-MPJPE
×××47.071.487.2
✓××43.460.583.0
×✓×43.761.373.0
××✓36.349.452.6
✓✓✓36.547.147.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.684, + 0.907, + 0.753 + ], + "angle": 0, + "content": "Table 5. Ablation on interaction prompt. The interaction module improves inter-person reconstruction metrics Pair-PA-MPJPE on HI4D, especially when the method does not include HI4D in training. Ablation is conducted with a \\(448 \\times 448\\) model. All metrics are in mm." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "For interaction prompts, we show an ablation in Table 5. The proposed interaction module is beneficial and largely improves inter-person accuracy on HI4D even without HI4D training, indicating out-off-domain generalization. When trained on HI4D, the interaction module does not improve per-person PA-MPJPE but still improves interperson Pair-PA-MPJPE. Please refer to our SupMat for more qualitative results on interaction prompts." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1154" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.898, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.443, + 0.908, + 0.473 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison: Multi-HMR vs PromptHMR. Our model can recover coherent 3D scenes of people. In crowded scenes, face detection provides reliable box prompts for our model. Please zoom in to see the details." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.486, + 0.881, + 0.677 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.681, + 0.908, + 0.71 + ], + "angle": 0, + "content": "Figure 8. Qualitative results. PromptHMR recovers coherent two-person close interaction. Despite suffering from some interpenetration, the relative positions of the interacting people are accurately recovered. More examples are provided in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.727, + 0.214, + 0.743 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We see PromptHMR as a step towards a holistic perception model for 3D humans, but several limitations need to be addressed in future work. Currently, the shape description and interaction prompts are not automatically generated and need to be supplied by the user. Future work should explore how to effectively integrate our promptable model with VLMs to automate prompting. We show how semantic prompts can improve reconstruction accuracy, but many other potential types of side information such as action descriptions, 3D scene context, or body measurements may" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.728, + 0.838, + 0.743 + ], + "angle": 0, + "content": "provide additional benefits in different scenarios." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.755, + 0.634, + 0.771 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We have presented PromptHMR, a promptable HPS estimation approach that leverages full image context with spatial and semantic prompts to infer 3D humans in the scene. Our method demonstrates state-of-the-art accuracy across diverse benchmarks and generalizes well in the wild. Our experiments show that incorporating diverse input information through flexible prompting enables robustness and adaptability in challenging scenarios." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1155" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.181 + ], + "angle": 0, + "content": "Acknowledgement. The authors would like to thank Yan Zhang, Yao Feng, and Nitin Saini for their suggestions. The majority of the work was done when Yufu was an intern at Meshcapade. Yufu and Kostas thank the support of NSF NCS-FO 2124355, NSF FRR 2220868, and NSF IISRI 2212433." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.182, + 0.482, + 0.243 + ], + "angle": 0, + "content": "Disclosure. 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Black1,2 Muhammed Kocabas1,2,3 + +$^{1}$ Meshcapade $^{2}$ MPI for Intelligent Systems $^{3}$ ETH Zürich $^{4}$ University of Pennsylvania $^{5}$ Archimedes + +![](images/1ea57a6b5418d647e90d39ee8171a09d7e2c754f331b237f857309d2d07146c1.jpg) +image $\downarrow$ box prompts + +![](images/be9343463bf96acd4f8244d7f857449379a2aa84da0e1a9881ba4601702fc205.jpg) +PromptHMR + +![](images/558ab4fd1be2e1d09c658b84738575efafe760a9ebfbcae282bc07e18e4f7f76.jpg) +image $\downarrow$ box prompts + +![](images/3c688a0cd5f13e1806152dc103c989787d868b8228a8b74a9dcfcde525815441.jpg) +PromptHMR +Figure 1. PromptHMR is a promptable human pose and shape (HPS) estimation method that processes images with spatial or semantic prompts. It takes "side information" readily available from vision-language models or user input to improve the accuracy and robustness of 3D HPS. PromptHMR recovers human pose and shape from spatial prompts such as (a) face bounding boxes, (b) partial or complete person detection boxes, or (c) segmentation masks. It refines its predictions using semantic prompts such as (c) person-person interaction labels for close contact scenarios, or (d) natural language descriptions of body shape to improve body shape predictions. Both image and video versions of PromptHMR achieve state-of-the-art accuracy. https://yufu-wang.github.io/phmr-page + +![](images/5e1de9b86be207d1dc0218a369085eda5b7e9baecbf158546e647520b9ca2018.jpg) +image ↓ masks + +![](images/145e269221490644537bd771e62275f0879e53b37a177d56d0a31cf8b876fc58.jpg) +image $\downarrow$ box $^+$ text + +![](images/edc9a72aed113623aedcf57605e936369a6b8762655ef8aea36ee2463dcb008d.jpg) +PromptHMR +PromptHMR + +![](images/d2bf6200a1aaa296d11e489d8590bea6eda69f48551b2aef83e23e9bcc957bda.jpg) + +# Abstract + +Human pose and shape (HPS) estimation presents challenges in diverse scenarios such as crowded scenes, person-person interactions, and single-view reconstruction. Existing approaches lack mechanisms to incorporate auxiliary "side information" that could enhance reconstruction accuracy in such challenging scenarios. Furthermore, the most accurate methods rely on cropped person detections and cannot exploit scene context while methods that process the whole image often fail to detect people and are less accurate than methods that use crops. While recent language-based methods explore HPS reasoning through large language or vision-language models, their metric accuracy is well below the state of the art. In contrast, we present PromptHMR, + +a transformer-based promptable method that reformulates HPS estimation through spatial and semantic prompts. Our method processes full images to maintain scene context and accepts multiple input modalities: spatial prompts like bounding boxes and masks, and semantic prompts like language descriptions or interaction labels. PromptHMR demonstrates robust performance across challenging scenarios: estimating people from bounding boxes as small as faces in crowded scenes, improving body shape estimation through language descriptions, modeling person-person interactions, and producing temporally coherent motions in videos. Experiments on benchmarks show that PromptHMR achieves state-of-the-art performance while offering flexible prompt-based control over the HPS estimation process. + +# 1. Introduction + +The estimation of 3D human pose and shape (HPS) is classically viewed as regressing the parameters of shape and pose from pixels. In particular, most methods take a tightly cropped image of a person and output the pose and shape in camera coordinates. While the accuracy of such methods has increased rapidly, they do not address the whole problem. In particular, an HPS method should be able to take an image or video containing complex human-human and human-scene interactions, return the parameters of every person in the scene, and place these people in a consistent global coordinate frame. + +Our key observation is that the classical "pixels to parameters" formulation of the problem is too narrow. Today, we have large vision-language foundation models (VLMs) that understand a great deal about images and what people are doing in them. What these models lack, however, is an understanding of 3D human pose and shape. Recent work [10, 15] has tried to bring together VLMs and 3D HPS but with 3D accuracy well below the best classical methods. + +Consequently, we need to think about the problem in a different way and ask whether we can exploit readily available side information (e.g. provided by a VLM) to improve 3D HPS regression robustness, usefulness, and accuracy. To that end, we develop a novel "promptable" HPS architecture called PromptHMR. Consider the sample images shown in Fig. 1. In crowded scenes, existing person detection methods struggle, while face detection methods remain reliable. When people closely interact, their body parts overlap and occlude each other, introducing ambiguity in pose estimation. Moreover, 3D body shape estimation from monocular views is challenging due to perspective ambiguity. In all these cases, we can extract cues, or prompts, that provide "side information" that can help an HPS method better analyze the scene. PromptHMR formalizes this intuition by combining image evidence with different types of spatial and semantic information that can come from either humans or AI systems such as VLMs. + +Specifically, our approach combines three key components: (1) a vision transformer that extracts features from high-resolution full images to preserve scene context, (2) a multi-modal prompt encoder that processes spatial and semantic inputs, and (3) a transformer decoder that attends to both prompt and image tokens to generate SMPL-X [45] body parameters. This design addresses the limitations of cropped-image HPS methods by processing full images using side information in the form of prompts. It addresses the challenges that full-image HPS methods have in detecting all people in a scene by accepting readily available bounding boxes. Last, our method incorporates auxiliary semantic information through text descriptions or interaction labels. + +By combining spatial and semantic prompting, our method offers a powerful and versatile approach to 3D HPS + +estimation from the whole image. At test time, we show that this promptable structure (1) can take various bounding boxes or segmentation masks to recover full body HPS in a robust way, (2) improve its body shape predictions by using textual descriptions as input, (3) is capable of modeling person-person close interaction directly in the regression process, and (4) uses full image context to reconstruct people coherently in the camera space and the world space. Our model can handle video by incorporating temporal transformer layers at the SMPL-X decoding phase, yielding temporally stable and smooth motions. Last, following TRAM [65], we combine the temporal version of our model with metric SLAM to estimate human motion in world coordinates. + +We make several key design choices that make PromptHMR successful. To achieve robustness to different spatial inputs, we train our model by simulating noisy full-body and face-region bounding boxes. For improved body shape estimation, we leverage SHAPY [8] to generate automatic body shape descriptions for training samples and process them with a pretrained text encoder [48]. To enhance person-person interaction reconstruction, we use segmentation masks as more precise spatial prompts and develop person-person attention layers that operate between prompted people, producing coherent reconstructions of close interactions. Through random masking of different input types during training, our model learns to work with any combination of prompts at test time. + +Quantitative experiments on the EMDB [24], 3DPW [63], RICH [20], Hi4D [68], CHI3D [16] and HBW [8] benchmark datasets demonstrate that our method outperforms state-of-the-art (SOTA) approaches and strong baselines. We also provide many qualitative examples of in-the-wild images and videos that illustrate the robustness and generalization of PromptHMR. + +By moving away from the pure pixels-to-parameters approach, PromptHMR not only achieves a new SOTA, it shows a new way of improving both accuracy and robustness by leveraging side information that is easily available. One can think of this as a collaboration between VLMs, which know a lot about people in images but not in 3D, and a metric regressor that knows a lot about 3D humans but not about the semantics of what they do. We show that this combination has significant upside potential to increase both generality and accuracy. Our code and model are available for research purposes. + +# 2. Related Work + +Human pose and shape estimation from images. Existing methods for human pose and shape (HPS) estimation can be broadly categorized into two main approaches. The first [6, 17, 22, 27, 28, 30-32, 39, 64, 70] uses a tightly cropped image of an individual as input, and estimates + +pose and shape in camera coordinates. While effective for isolated individuals, this approach discards scene context that is essential to resolve human pose in cases of occlusion, severe overlap and close interaction in multi-person scenes [16, 68]. + +The second category [2, 21, 55, 57-59] build upon object detection frameworks [5, 12] to jointly detect humans and estimate their pose and shape parameters. Having access to the entire image, they can better perceive occluded individuals and infer depth relationships, but they often suffer from detection failures due to the difficulty in simultaneously performing detection and reconstruction. Our "promptable" architecture leverages detection box prompts to resolve such conflicts while having access to the entire scene context. + +Human pose and shape estimation from video. Methods for human motion estimation from video can also be divided into two main categories. The first [7, 23, 26, 36, 56] focuses on estimating smooth human motion in camera space. These methods build upon single-person HPS estimation approaches [22, 30] by adding temporal layers during the SMPL decoding phase to introduce temporal coherence. + +More recent methods estimate human motion in world coordinates from videos captured with dynamic cameras. These methods follow a two-stage approach, first estimating camera motion using SLAM techniques [18, 19, 40, 41, 60, 61], and then leveraging human motion priors to optimize the human world motion [29, 67, 69]. Others [51, 52] learn temporal models to directly regress human world motion from image and camera features. Still others [65, 71] use monocular metric depth estimation to solve for the scale of camera motion and transform human motion from camera space to world coordinates. + +In our approach, we extend PromptHMR to video by taking the SMPL-X output tokens and utilizing a temporal transformer module to estimate temporally stable and smooth human motion and translation in camera space. We follow TRAM [65] to transform human motion to world coordinates due to its simplicity and effectiveness. + +Semantic reasoning about 3D humans in images. Recent methods explore combining different types of semantic information, such as language descriptions and knowledge of person-person interactions, to improve reasoning about 3D humans from images and videos. For example, ChatPose [15] follows the common approach of visual language models (VLMs) [34] by fine-tuning a large language model (LLM) with a combination of images and tokens to estimate SMPL parameters. In a similar direction, PoseEmbroider [10] is a multi-modal framework that aligns image, 3D pose, and text representations in a shared latent space. While ChatPose focuses on combining high-level scene reasoning with 3D HPS, PoseEmbroider exploits detailed language descriptions of human pose. While promising, neither method achieves SOTA accuracy on the HPS task. Note + +that many other methods relate language to human pose or motion, without considering images [1, 9, 35, 46, 62], but these are outside our scope. + +Additionally, several methods [8, 47, 53] focus on modeling the relationship between SMPL body shape and natural language descriptions. These methods show that language descriptions and images can provide complementary information to solve this task. Other approaches, such as BUDDI [38] and ProsePose [54], address the challenge of estimating person-person interactions. BUDDI is an optimization-based approach that leverages diffusion model as a prior over interacting people, while ProsePose queries a VLM to estimate contact points on the human body surface and uses these contact points to guide an optimization process for improving human interaction. + +Overall, methods like ChatPose [15] and PoseEmbroider [10] are promising steps toward jointly learning the relationship between vision, language, and 3D humans, but their understanding of 3D humans remains limited, as indicated by their relatively low 3D pose accuracy. Meanwhile, SHAPY [8], BodyShapeGPT [47], and BodyTalk [53] focus solely on exploring the relationship between SMPL body shape and natural language. BUDDI and ProsePose are post-processing approaches for interaction that do not directly reason using image information. + +Our approach addresses the limitations of these methods by training a single model capable of flexible prompting that achieves state-of-the-art (SOTA) performance, not only on standard HPS benchmarks but also on benchmarks tailored to body shape and person-person interaction. + +# 3. Method + +Given an image $I$ containing $N$ people and a set of prompts, our main goal is to recover the pose, shape, and locations of the people in the camera space to form a coherent human-centric 3D scene. Figure 2 shows an overview. + +# 3.1. Promptable mesh regression + +We adopt SMPL-X [45] to represent each person $i$ in the 3D space, including the orientation $\phi_i \in \mathbb{R}^3$ , local body pose $\theta_i \in \mathbb{R}^{22 \times 3}$ , shape $\beta_i \in \mathbb{R}^{10}$ , and translation $\tau_i \in \mathbb{R}^3$ in the camera space. We do not include face and hand parameters in this work. Each human $H_i$ is mapped to a 3D mesh with the differentiable SMPL-X layer. + +$$ +H _ {i} = \left\{\phi_ {i}, \theta_ {i}, \beta_ {i}, \tau_ {i} \right\}. \tag {1} +$$ + +Each person can be prompted with spatial and semantic prompts. Spatial prompts include a bounding box $b_{i} \in \mathbb{R}^{2 \times 2}$ (the two corners) and a segmentation mask $m_{i} \in \mathbb{R}^{h \times w}$ . Semantic prompts consist of text and two-person interaction labels. The text prompt is the CLIP embedding $t_{i}$ of a sentence describing the body shape. The interaction prompt is a binary variable $k_{i}$ indicating whether two + +![](images/d599869071b1bf25b431691619e1796dbe8c792619a59e6e36f426fa5ae4f60d.jpg) +Figure 2. Method overview. PromptHMR estimates SMPL-X parameters for each person in an image based on various types of prompts, such as boxes, language descriptions, and person-person interaction cues. Given an image and prompts, we utilize a vision transformer to generate image embeddings and mask and prompt encoders to map different types of prompts to tokens. Optionally, camera intrinsics can be embedded along with the image embeddings. The image embeddings and prompt tokens are then fed to the SMPL-X decoder. The SMPL-X decoder is a transformer-based module that attends to both the image and prompt tokens to estimate SMPL-X parameters. Note that the language and interaction prompts are optional, but providing them enhances the accuracy of the estimated SMPL-X parameters. + +people are in close contact. While semantic prompts are optional, each human needs at least one spatial prompt to be reconstructed. Overall, the input prompts are represented as $P_{i}$ : + +$$ +P _ {i} \subseteq \left\{b _ {i}, m _ {i}, t _ {i}, k _ {i} \right\} \tag {2} +$$ + +$$ +b _ {i} \in P _ {i} \text {o r} m _ {i} \in P _ {i} +$$ + +Promptable human mesh recovery (PromptHMR) is defined as a learnable function that maps an image and a set of prompts to a set of 3D humans + +$$ +f: \left(I, \left\{P _ {i} \right\} _ {i = 1} ^ {N}\right)\rightarrow \left\{H _ {i} \right\} _ {i = 1} ^ {N}. \tag {3} +$$ + +This task definition integrates all available contexts to locate and reconstruct prompted humans in the image. + +# 3.2. Model + +Image encoder. The image is first encoded as tokens by a vision transformer (ViT) encoder from DINOv2 [11, 42]: + +$$ +F = \operatorname {E n c o d e r} (I), \tag {4} +$$ + +To ensure sufficient resolution for modeling humans at both near and far distances, we use $896 \times 896$ images. The encoder is run once per frame regardless of the number of people prompted. When camera intrinsics are provided, we add positional encoding of the camera rays to the image tokens to make them camera-aware [2, 14]. + +Mask encoder. When available, masks are first processed by an encoder consisting of stripped convolutional layers that downsample the masks. The output mask features are added to the image tokens. If no mask is provided, a learned "no mask" token is added instead. + +$$ +F _ {i} = \operatorname {E n c o d e r} _ {\mathrm {m}} \left(m _ {i}\right) + F. \tag {5} +$$ + +Prompt encoder. The prompt encoder consists of a set of transformations that map different types of prompts to token vectors of the same dimension. When a prompt is not available, it is replaced with a learned null token. + +For bounding boxes, we encode $b_{i}$ using positional encoding summed with learned embeddings to form the box prompt tokens $T_{bi} = \mathrm{PE}(b_{i})$ , with $T_{bi} \in \mathbb{R}^{2 \times d}$ . We design different box transformations during training to allow the model to use different boxes as a human identifier. In the training phase, each instance is prompted with either a whole-body bounding box, a face bounding box, or a truncated box covering part of the body. Gaussian noise is added to both corners. At inference time, the model accepts boxes without needing to know the box types. + +Language is a natural way to supply semantic information, and in this paper, we use language to supplement spatial prompts with information on body shape. A sentence such as "a muscular and tall male" is encoded with the CLIP text encoder $T_{ti} = \mathrm{CLIP}(t_i)$ , with $T_{ti} \in \mathbb{R}^{d}$ . To generate paired (image, text) data, we run SHAPY's [8] shape-to-attribute method on the ground truth shape parameters to obtain shape attribute scores and randomly pick a subset of top attributes to form a sentence. + +The interaction prompt $k_{i}$ passes through the prompt encoder without modification and directly switches on-off the cross-person attention that is described in Sec. 3.3. + +SMPL-X decoder. The SMPL-X decoder appends two query tokens $T_{\mathrm{spl}}, T_{\mathrm{depth}}$ with the prompt tokens $T_{bi}, T_{ti}$ to form the person-specific prompt $T_i \in \mathbb{R}^{5 \times d}$ . + +Finally, we use a standard transformer decoder and two MLP heads to produce the final output + +$$ +T _ {s m p l} ^ {\prime}, T _ {d e p t h} ^ {\prime} = \mathrm {D e c o d e r} (F _ {i}, T _ {i}) +$$ + +$$ +\phi_ {i}, \theta_ {i}, \beta_ {i} = \operatorname {H e a d} _ {s m p l} \left(T _ {s m p l} ^ {\prime}\right) \tag {6} +$$ + +$$ +\tau_ {i} = \operatorname {H e a d} _ {d e p t h} (T _ {d e p t h} ^ {\prime}). +$$ + +The transformer consists of three attention blocks. Each block applies self-attention on the tokens, cross-person attention (described in Sec. 3.3), and then two-way cross-attention between the tokens and the image embeddings [25]. The self-attention and cross-attention with the + +image are applied to each prompted person independently. We use separate tokens $T_{\mathrm{spl}}$ and $T_{\mathrm{depth}}$ to make the location representation invariant to the 3D human pose and shape representation. + +Regressing the location of the human in the camera space is much more challenging than most prior work that models humans in a cropped image space. Therefore, we do not regress $\tau$ directly. We regress focal length normalized 2D translation $p_{xy} \in \mathbb{R}^2$ and inverse depth $p_z \in \mathbb{R}$ , and then transform them to $\tau$ as follows + +$$ +t _ {x y} = \frac {p _ {x y}}{p _ {z}} \quad t _ {z} = \frac {1}{p _ {z}} \times \frac {f}{f _ {c}} \quad \tau = [ t _ {x y}, t z ], \tag {7} +$$ + +where $f$ is the ground truth or estimated focal length of the image, and $f_{c}$ is the canonical focal length. Predicting the normalized inverse depth follows the recent monocular depth literature [49] and is also intuitive since the inverse depth is linearly related to the size of the human in the image. Predicting $p_{xy}$ is equivalent to predicting the 2D location of the human in a normalized image plane. + +# 3.3. Two-person interaction + +We introduce promptable layers in the decoder to model two-person interaction. We describe the case where there are two people in the image, but the implementation can extend to model an interacting pair in a larger group. + +The promptability is modeled as a flow control with a residual connection (Fig. 3). Specifically, if two humans are interacting (as indicated by $k_{i}$ ), their query tokens pass through an additional self-attention layer; otherwise, non-interacting humans skip this. + +Applying attention to every person often creates unnecessary dependency in crowded scenes, and there is limited training data for large-group scenarios. However, there is high-quality data featuring two-person social interactions. By making the interaction layers promptable, we mitigate data diversity issues and increase flexibility, regardless of the number of people in the scene. + +Our proposed interaction layer uses a standard self-attention mechanism. First, we add positional encodings to the query tokens to distinguish the two individuals. The encoded tokens then go through a self-attention layer, whose output is combined with the original tokens via a residual connection. Our experiments demonstrate that including these interaction layers significantly improves inter-person pose accuracy in two-person interaction benchmarks. + +# 3.4. PromptHMR video version + +In addition to the single-image variant of PromptHMR, we train an extended version that processes videos to estimate human motion in world coordinates. To achieve this, we introduce a simple and efficient temporal transformer module. Given a monocular video sequence $\{I^t\}_{t=0}^T$ , we first run + +![](images/40583d3d4a212eca68f9d26bdff69156d79a47247c0ae986bf506b27ded37f66.jpg) +Figure 3. SMPL-X decoder. The top row shows one attention block in the decoder. The cross-person interaction module can be turned on/off. The bottom row shows the cross-person attention. + +PromptHMR to obtain per-subject SMPL-X decoder output tokens $T_{\mathrm{spl}}^{\prime}$ and $T_{\mathrm{depth}}^{\prime}$ , assuming that the subject identities are provided with the prompts. These tokens, along with the positional encoding of time $t$ , are fed to a decoder-only temporal transformer module with twelve attention blocks. The output tokens are converted to SMPL-X parameters $\phi_t, \theta_t, \beta_t$ , translation $\tau_t$ , and joint contact probabilities $c_t$ . The contact probabilities indicate whether a given joint is in contact with the ground plane similar to [50-52]. + +To obtain results in world coordinates, we adopt the approach from TRAM [65]. Specifically, we use DROID-SLAM [60] and a monocular metric depth estimation model, ZoeDepth [3], to estimate camera motion in metric world coordinates. The translation parameters $\tau_{t}$ are then transformed to world coordinates using the estimated camera motion. To refine the human trajectory and mitigate foot-skating artifacts, we leverage the estimated contact probabilities and run a fast postprocessing that optimizes the contact joints to have zero velocity. + +# 3.5. Losses + +PromptHMR is trained with a combination of 2D and 3D losses, following traditional HMR methods [22, 30]: + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {2 D} + \lambda_ {2} \mathcal {L} _ {3 D} + \lambda_ {3} \mathcal {L} _ {\mathrm {S M P L}} + \lambda_ {4} \mathcal {L} _ {V} + \lambda_ {5} \mathcal {L} _ {t} +$$ + +with each term calculated as + +$$ +\mathcal {L} _ {2 D} = \left\| \hat {\mathcal {J}} _ {2 D} - \Pi \left(\mathcal {J} _ {3 D}\right) \right\| _ {F} ^ {2} +$$ + +$$ +\mathcal {L} _ {3 D} = \left\| \hat {\mathcal {J}} _ {3 D} - \mathcal {J} _ {3 D} \right\| _ {F} ^ {2} +$$ + +$$ +\mathcal {L} _ {\mathrm {S M P L}} = | | \hat {\Theta} - \Theta | | _ {2} ^ {2} +$$ + +$$ +\mathcal {L} _ {V} = \left\| \hat {V} - V \right\| _ {F} ^ {2} +$$ + +$$ +\mathcal {L} _ {t} = \left| \left| \hat {p} _ {x y} - p _ {x y} \right| \right| _ {F} ^ {2} + \left| \left| \hat {p} _ {z} - p _ {z} \right| \right| _ {F} ^ {2} +$$ + +where $\mathcal{J}_{3D}$ and $V$ are the 3D joints and vertices of the SMPL-X model, with the hat operator denoting the ground truth. $\Pi$ is the camera reprojection operator. Additionally, on datasets with ground truth translation labels, we supervise the normalized translation $p_{xy}$ and inverse depth $p_z$ . + +# 4. Experiments + +Datasets. We train PromptHMR with standard datasets: BEDLAM [4], AGORA [44], 3DPW [63], COCO [33], and MPII [37]. Following 4DHumans, we add AIC [66] and InstaVariety [23] as in-the-wild data, with pseudoground truth from CamSMPLify [43]. Additionally, we add CHI3D [16] and HI4D [68] to enable learning two-person interaction following the train-test splits from BUDDI [38]. Including CHI3D and HI4D does not improve performance on other benchmarks. + +Implementation. We train PromptHMR with AdamW with a batch size of 96 images of resolution $896 \times 896$ . We use a learning rate of $1e^{-5}$ for the image encoder and $3e^{-5}$ for the prompt encoder and the SMPL-X decoder, with a weight decay of $5e^{-5}$ . The training converges within 350K steps. + +Evaluation. We evaluate camera space reconstruction accuracy on 3DPW [63], EMDB [24] and RICH [20], using MPJPE, Procrustes-aligned MPJPE (PA-MPJPE) and Per Vertex Error (PVE) [22]. We evaluate inter-person accuracy on HI4D and CHI3D by Pair-PA-MPJPE, which aligns the two people as a whole with the ground truth [38]. + +To evaluate world-grounded motion on EMDB with PromptHMR video (PromptHMR-vid), we compute World-aligned MPJPE $(\mathrm{WA - MPJPE}_{100})$ , World MPJPE $(\mathrm{W - MPJPE}_{100})$ and Root Translation Error (RTE in %) [52, 67]. + +# 4.1. Reconstruction accuracy + +For camera space reconstruction, as shown in Table 1, PromptHMR and PromptHMR-Vid demonstrate state-of-the-art performance, matching crop-based methods while achieving better results than other full-image methods. PromptHMR and CameraHMR use the same training data and have similar performance, which validates that this prompt-based approach can achieve metrically accurate results. For representative results, see Fig. 7, where PromptHMR recovers coherent 3D scenes of people. + +For interaction reconstruction, PromptHMR achieves good accuracy as indicated in Table 2. Compared to BUDDI which is also trained on CHI3D and HI4D, our method achieves better overall accuracy on per-person and interperson metrics. We show qualitative results in Fig. 8. As a monocular regression method, PromptHMR still cannot avoid interpenetration between closely interacting people. + +PromptHMR-Vid achieves SOTA performance among methods that estimate human motion in world coordinates, as shown in Table 4. Unlike TRAM, we estimate the joint contact probabilities similar to [51, 52]. Therefore, we achieve lower foot skating than TRAM, even though we use the same metric SLAM method to transform motion in camera space to world coordinates. Please refer to our supplementary material (SupMat) for qualitative results of PromptHMR-Vid. + +![](images/76765d0a6a3a88ed783d150a61768340fbb14079662abbd07fae52512a29a113.jpg) +Figure 4. Effect of box prompts. Our method remains stable with different boxes, including noisy truncated boxes. + +![](images/45cd98a2e74dde29e3e811469d3fa51fbc4a9d8865b796168422773625ece09d.jpg) +Figure 5. Effect of mask prompts. Results are from the same model with different prompt inputs. Masks are better for close interaction scenarios where boxes are ambiguous. + +![](images/0455387cbb7dea4c820714e8a040a3978a2731be3dbf1bed6d7449c3af85372a.jpg) +Figure 6. Effect of shape prompts. Compared to the baseline that does not incorporate shape description during training and testing, the model with shape prompts has better accuracy on HBW, especially in ambiguous images. + +# 4.2. Effect of multimodal prompts + +We conduct qualitative and quantitative evaluations of the multimodal prompts. For efficient ablation, we train models with $448 \times 448$ input resolution and select the best model within 150K steps of training. + +For box prompts, as shown in rows 3-4 of Fig. 7, our method is able to take a combination of different boxes from in-the-wild images to reconstruct crowded scenes. Figure 4 also shows an example with varying box inputs. PromptHMR remains stable when the boxes change and uses full image context to reconstruct the human even when the boxes are truncated. + +The mask prompt is more effective than boxes when people closely overlap (Fig. 5), as boxes are ambiguous in such + +
Models3DPW (14)EMDB (24)RICH (24)
PA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVE
cropped imageCLIFF* [31]43.069.081.268.3103.3123.768.1103.3128.0
HMR2.0a [17]44.469.882.261.597.8120.060.798.3120.8
TokenHMR [13]44.371.084.655.691.7109.4---
CameraHMR [43]35.156.065.943.370.281.734.055.764.4
full imageBEV [58]46.978.592.370.9112.2133.4---
Multi-HMR* [2]45.973.187.150.181.695.746.373.883.0
PromptHMR*36.658.769.441.071.784.537.356.665.5
videoWHAM [52]37.559.871.552.081.696.944.380.091.2
TRAM [65]35.659.369.645.774.486.6---
GVHMR [51]37.056.668.744.574.285.939.566.074.4
PromptHMR-Vid35.556.967.340.168.179.237.057.465.8
+ +Table 1. Comparison of mesh reconstruction on the 3DPW, EMDB and RICH datasets, with the number of joints in parenthesis. $\star$ denotes methods that use ground truth focal length during inference. Note that we remove the test-time flip augmentation from all of the video methods to ensure a fair comparison. All metrics are in mm. + +
ModelsHI4D (14)CHI3D (14)
PA-MPJPEMPJPEPair-PA-MPJPEPA-MPJPEMPJPEPair-PA-MPJPE
BEV* [58]81-13651-96
BUDDI [38]73-9847-68
Multi-HMR* [2]49.867.880.631.754.0100.0
PromptHMR*39.263.978.127.248.058.5
PromptHMR30.139.639.524.746.545.3
+ +Table 2. Comparison on interaction reconstruction. PromptHMR is more accurate in per-person and inter-person accuracy. * denote a method or baseline is not trained on HI4D or CHI3D. All metrics are in mm. The impact of HI4D and the interaction prompt are evaluated in Table 5. + +
Train w/ textTest w/ textHBW
HeightChestWaistHipP2P-20k
××6951886326
✓×6948866026
✓✓6243765824
+ +cases. Ablation of HI4D (rows 1-2 in Tab. 5) shows that using masks as the spatial prompt improves accuracy. + +Experiments on the HBW validation set (Tab. 3) show that text prompts effectively improve shape accuracy when used during both training and testing. Moreover, training with shape descriptions alone provides an accuracy boost even if prompts are not given at test time. As illustrated in Fig. 6, text prompts provide notable improvements, especially when large perspective effects create ambiguity. + +Table 3. Ablation of shape prompts using text. Training with shape prompts improves shape accuracy. Using shape prompts during inference further improves shape accuracy. The ablation study is conducted with a $448 \times 448$ model. Errors are in mm. + +
ModelsEMDB-2 (24)
WA-MPJPE100W-MPJPE100RTEJitterFoot Skating
WHAM [52]135.6354.86.022.54.4
TRAM [65]76.4222.41.418.523.4
GVHMR [51]111.0276.52.016.73.5
PromptHMR-Vid71.0216.51.316.33.5
+ +Table 4. Evaluation of motion in world coordinates. PromptHMR-Vid combined with metric SLAM from TRAM [65] surpasses SOTA methods at predicting human motion in world coordinates. + +
Trained withHI4D (14)
MaskInteractionHI4DPA-MPJPEMPJPEPair-PA-MPJPE
×××47.071.487.2
✓××43.460.583.0
×✓×43.761.373.0
××✓36.349.452.6
✓✓✓36.547.147.9
+ +Table 5. Ablation on interaction prompt. The interaction module improves inter-person reconstruction metrics Pair-PA-MPJPE on HI4D, especially when the method does not include HI4D in training. Ablation is conducted with a $448 \times 448$ model. All metrics are in mm. + +For interaction prompts, we show an ablation in Table 5. The proposed interaction module is beneficial and largely improves inter-person accuracy on HI4D even without HI4D training, indicating out-off-domain generalization. When trained on HI4D, the interaction module does not improve per-person PA-MPJPE but still improves interperson Pair-PA-MPJPE. Please refer to our SupMat for more qualitative results on interaction prompts. + +![](images/a845a1ad594881ec9d8ab80a5d9c550aa3b3adb337a13fb5501266f7a87634b9.jpg) +Figure 7. Qualitative comparison: Multi-HMR vs PromptHMR. Our model can recover coherent 3D scenes of people. In crowded scenes, face detection provides reliable box prompts for our model. Please zoom in to see the details. + +![](images/7db2160aff5f5160604adec48ce4f0c51cfe225426774259d35b6ba76b1d46e6.jpg) +Figure 8. Qualitative results. PromptHMR recovers coherent two-person close interaction. Despite suffering from some interpenetration, the relative positions of the interacting people are accurately recovered. More examples are provided in the Supplementary. + +# 5. Limitations + +We see PromptHMR as a step towards a holistic perception model for 3D humans, but several limitations need to be addressed in future work. Currently, the shape description and interaction prompts are not automatically generated and need to be supplied by the user. Future work should explore how to effectively integrate our promptable model with VLMs to automate prompting. We show how semantic prompts can improve reconstruction accuracy, but many other potential types of side information such as action descriptions, 3D scene context, or body measurements may + +provide additional benefits in different scenarios. + +# 6. Conclusion + +We have presented PromptHMR, a promptable HPS estimation approach that leverages full image context with spatial and semantic prompts to infer 3D humans in the scene. Our method demonstrates state-of-the-art accuracy across diverse benchmarks and generalizes well in the wild. Our experiments show that incorporating diverse input information through flexible prompting enables robustness and adaptability in challenging scenarios. + +Acknowledgement. The authors would like to thank Yan Zhang, Yao Feng, and Nitin Saini for their suggestions. The majority of the work was done when Yufu was an intern at Meshcapade. Yufu and Kostas thank the support of NSF NCS-FO 2124355, NSF FRR 2220868, and NSF IISRI 2212433. + +Disclosure. 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PromptHMR is a promptable human pose and shape (HPS) estimation method that processes images with spatial or semantic prompts. It takes \"side information\" readily available from vision-language models or user input to improve the accuracy and robustness of 3D HPS. PromptHMR recovers human pose and shape from spatial prompts such as (a) face bounding boxes, (b) partial or complete person detection boxes, or (c) segmentation masks. It refines its predictions using semantic prompts such as (c) person-person interaction labels for close contact scenarios, or (d) natural language descriptions of body shape to improve body shape predictions. 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Existing approaches lack mechanisms to incorporate auxiliary \"side information\" that could enhance reconstruction accuracy in such challenging scenarios. Furthermore, the most accurate methods rely on cropped person detections and cannot exploit scene context while methods that process the whole image often fail to detect people and are less accurate than methods that use crops. While recent language-based methods explore HPS reasoning through large language or vision-language models, their metric accuracy is well below the state of the art. In contrast, we present PromptHMR," + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 533, + 556, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 556, + 701 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 556, + 701 + ], + "type": "text", + "content": "a transformer-based promptable method that reformulates HPS estimation through spatial and semantic prompts. Our method processes full images to maintain scene context and accepts multiple input modalities: spatial prompts like bounding boxes and masks, and semantic prompts like language descriptions or interaction labels. PromptHMR demonstrates robust performance across challenging scenarios: estimating people from bounding boxes as small as faces in crowded scenes, improving body shape estimation through language descriptions, modeling person-person interactions, and producing temporally coherent motions in videos. Experiments on benchmarks show that PromptHMR achieves state-of-the-art performance while offering flexible prompt-based control over the HPS estimation process." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1148" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 136, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 136, + 84 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 136, + 84 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 294, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 294, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 294, + 222 + ], + "type": "text", + "content": "The estimation of 3D human pose and shape (HPS) is classically viewed as regressing the parameters of shape and pose from pixels. In particular, most methods take a tightly cropped image of a person and output the pose and shape in camera coordinates. While the accuracy of such methods has increased rapidly, they do not address the whole problem. In particular, an HPS method should be able to take an image or video containing complex human-human and human-scene interactions, return the parameters of every person in the scene, and place these people in a consistent global coordinate frame." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 223, + 294, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 294, + 318 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 294, + 318 + ], + "type": "text", + "content": "Our key observation is that the classical \"pixels to parameters\" formulation of the problem is too narrow. Today, we have large vision-language foundation models (VLMs) that understand a great deal about images and what people are doing in them. What these models lack, however, is an understanding of 3D human pose and shape. Recent work [10, 15] has tried to bring together VLMs and 3D HPS but with 3D accuracy well below the best classical methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 319, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 295, + 533 + ], + "type": "text", + "content": "Consequently, we need to think about the problem in a different way and ask whether we can exploit readily available side information (e.g. provided by a VLM) to improve 3D HPS regression robustness, usefulness, and accuracy. To that end, we develop a novel \"promptable\" HPS architecture called PromptHMR. Consider the sample images shown in Fig. 1. In crowded scenes, existing person detection methods struggle, while face detection methods remain reliable. When people closely interact, their body parts overlap and occlude each other, introducing ambiguity in pose estimation. Moreover, 3D body shape estimation from monocular views is challenging due to perspective ambiguity. In all these cases, we can extract cues, or prompts, that provide \"side information\" that can help an HPS method better analyze the scene. PromptHMR formalizes this intuition by combining image evidence with different types of spatial and semantic information that can come from either humans or AI systems such as VLMs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 534, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 689 + ], + "type": "text", + "content": "Specifically, our approach combines three key components: (1) a vision transformer that extracts features from high-resolution full images to preserve scene context, (2) a multi-modal prompt encoder that processes spatial and semantic inputs, and (3) a transformer decoder that attends to both prompt and image tokens to generate SMPL-X [45] body parameters. This design addresses the limitations of cropped-image HPS methods by processing full images using side information in the form of prompts. It addresses the challenges that full-image HPS methods have in detecting all people in a scene by accepting readily available bounding boxes. Last, our method incorporates auxiliary semantic information through text descriptions or interaction labels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "By combining spatial and semantic prompting, our method offers a powerful and versatile approach to 3D HPS" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "content": "estimation from the whole image. At test time, we show that this promptable structure (1) can take various bounding boxes or segmentation masks to recover full body HPS in a robust way, (2) improve its body shape predictions by using textual descriptions as input, (3) is capable of modeling person-person close interaction directly in the regression process, and (4) uses full image context to reconstruct people coherently in the camera space and the world space. Our model can handle video by incorporating temporal transformer layers at the SMPL-X decoding phase, yielding temporally stable and smooth motions. Last, following TRAM [65], we combine the temporal version of our model with metric SLAM to estimate human motion in world coordinates." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 239, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 553, + 407 + ], + "type": "text", + "content": "We make several key design choices that make PromptHMR successful. To achieve robustness to different spatial inputs, we train our model by simulating noisy full-body and face-region bounding boxes. For improved body shape estimation, we leverage SHAPY [8] to generate automatic body shape descriptions for training samples and process them with a pretrained text encoder [48]. To enhance person-person interaction reconstruction, we use segmentation masks as more precise spatial prompts and develop person-person attention layers that operate between prompted people, producing coherent reconstructions of close interactions. Through random masking of different input types during training, our model learns to work with any combination of prompts at test time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 407, + 553, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 553, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 553, + 491 + ], + "type": "text", + "content": "Quantitative experiments on the EMDB [24], 3DPW [63], RICH [20], Hi4D [68], CHI3D [16] and HBW [8] benchmark datasets demonstrate that our method outperforms state-of-the-art (SOTA) approaches and strong baselines. We also provide many qualitative examples of in-the-wild images and videos that illustrate the robustness and generalization of PromptHMR." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 491, + 553, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 553, + 622 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 553, + 622 + ], + "type": "text", + "content": "By moving away from the pure pixels-to-parameters approach, PromptHMR not only achieves a new SOTA, it shows a new way of improving both accuracy and robustness by leveraging side information that is easily available. One can think of this as a collaboration between VLMs, which know a lot about people in images but not in 3D, and a metric regressor that knows a lot about 3D humans but not about the semantics of what they do. We show that this combination has significant upside potential to increase both generality and accuracy. Our code and model are available for research purposes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 633, + 400, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 400, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 400, + 645 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 654, + 553, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 715 + ], + "type": "text", + "content": "Human pose and shape estimation from images. Existing methods for human pose and shape (HPS) estimation can be broadly categorized into two main approaches. The first [6, 17, 22, 27, 28, 30-32, 39, 64, 70] uses a tightly cropped image of an individual as input, and estimates" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1149" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "pose and shape in camera coordinates. While effective for isolated individuals, this approach discards scene context that is essential to resolve human pose in cases of occlusion, severe overlap and close interaction in multi-person scenes [16, 68]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 134, + 294, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 134, + 294, + 241 + ], + "spans": [ + { + "bbox": [ + 55, + 134, + 294, + 241 + ], + "type": "text", + "content": "The second category [2, 21, 55, 57-59] build upon object detection frameworks [5, 12] to jointly detect humans and estimate their pose and shape parameters. Having access to the entire image, they can better perceive occluded individuals and infer depth relationships, but they often suffer from detection failures due to the difficulty in simultaneously performing detection and reconstruction. Our \"promptable\" architecture leverages detection box prompts to resolve such conflicts while having access to the entire scene context." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 243, + 294, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 243, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 294, + 326 + ], + "type": "text", + "content": "Human pose and shape estimation from video. Methods for human motion estimation from video can also be divided into two main categories. The first [7, 23, 26, 36, 56] focuses on estimating smooth human motion in camera space. These methods build upon single-person HPS estimation approaches [22, 30] by adding temporal layers during the SMPL decoding phase to introduce temporal coherence." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 327, + 294, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 294, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 294, + 460 + ], + "type": "text", + "content": "More recent methods estimate human motion in world coordinates from videos captured with dynamic cameras. These methods follow a two-stage approach, first estimating camera motion using SLAM techniques [18, 19, 40, 41, 60, 61], and then leveraging human motion priors to optimize the human world motion [29, 67, 69]. Others [51, 52] learn temporal models to directly regress human world motion from image and camera features. Still others [65, 71] use monocular metric depth estimation to solve for the scale of camera motion and transform human motion from camera space to world coordinates." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 461, + 294, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 294, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 294, + 533 + ], + "type": "text", + "content": "In our approach, we extend PromptHMR to video by taking the SMPL-X output tokens and utilizing a temporal transformer module to estimate temporally stable and smooth human motion and translation in camera space. We follow TRAM [65] to transform human motion to world coordinates due to its simplicity and effectiveness." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "Semantic reasoning about 3D humans in images. Recent methods explore combining different types of semantic information, such as language descriptions and knowledge of person-person interactions, to improve reasoning about 3D humans from images and videos. For example, ChatPose [15] follows the common approach of visual language models (VLMs) [34] by fine-tuning a large language model (LLM) with a combination of images and tokens to estimate SMPL parameters. In a similar direction, PoseEmbroider [10] is a multi-modal framework that aligns image, 3D pose, and text representations in a shared latent space. While ChatPose focuses on combining high-level scene reasoning with 3D HPS, PoseEmbroider exploits detailed language descriptions of human pose. While promising, neither method achieves SOTA accuracy on the HPS task. Note" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "that many other methods relate language to human pose or motion, without considering images [1, 9, 35, 46, 62], but these are outside our scope." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 108, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 108, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 108, + 553, + 251 + ], + "type": "text", + "content": "Additionally, several methods [8, 47, 53] focus on modeling the relationship between SMPL body shape and natural language descriptions. These methods show that language descriptions and images can provide complementary information to solve this task. Other approaches, such as BUDDI [38] and ProsePose [54], address the challenge of estimating person-person interactions. BUDDI is an optimization-based approach that leverages diffusion model as a prior over interacting people, while ProsePose queries a VLM to estimate contact points on the human body surface and uses these contact points to guide an optimization process for improving human interaction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 251, + 553, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 553, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 553, + 371 + ], + "type": "text", + "content": "Overall, methods like ChatPose [15] and PoseEmbroider [10] are promising steps toward jointly learning the relationship between vision, language, and 3D humans, but their understanding of 3D humans remains limited, as indicated by their relatively low 3D pose accuracy. Meanwhile, SHAPY [8], BodyShapeGPT [47], and BodyTalk [53] focus solely on exploring the relationship between SMPL body shape and natural language. BUDDI and ProsePose are post-processing approaches for interaction that do not directly reason using image information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 372, + 553, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 553, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 553, + 431 + ], + "type": "text", + "content": "Our approach addresses the limitations of these methods by training a single model capable of flexible prompting that achieves state-of-the-art (SOTA) performance, not only on standard HPS benchmarks but also on benchmarks tailored to body shape and person-person interaction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 441, + 370, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 441, + 370, + 452 + ], + "spans": [ + { + "bbox": [ + 314, + 441, + 370, + 452 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "text", + "content": " containing " + }, + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 460, + 553, + 509 + ], + "type": "text", + "content": " people and a set of prompts, our main goal is to recover the pose, shape, and locations of the people in the camera space to form a coherent human-centric 3D scene. Figure 2 shows an overview." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 514, + 470, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 470, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 470, + 528 + ], + "type": "text", + "content": "3.1. Promptable mesh regression" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": "We adopt SMPL-X [45] to represent each person " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": " in the 3D space, including the orientation " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "\\phi_i \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": ", local body pose " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "\\theta_i \\in \\mathbb{R}^{22 \\times 3}" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": ", shape " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "\\beta_i \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": ", and translation " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "\\tau_i \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": " in the camera space. We do not include face and hand parameters in this work. Each human " + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "inline_equation", + "content": "H_i" + }, + { + "bbox": [ + 313, + 533, + 553, + 605 + ], + "type": "text", + "content": " is mapped to a 3D mesh with the differentiable SMPL-X layer." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 390, + 610, + 553, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 610, + 553, + 624 + ], + "spans": [ + { + "bbox": [ + 390, + 610, + 553, + 624 + ], + "type": "interline_equation", + "content": "H _ {i} = \\left\\{\\phi_ {i}, \\theta_ {i}, \\beta_ {i}, \\tau_ {i} \\right\\}. \\tag {1}", + "image_path": "b2b4331cc2661ddf1b4a21e32d8040ddc9252ba045c193fe48e2c76bfb56907d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "content": "Each person can be prompted with spatial and semantic prompts. Spatial prompts include a bounding box " + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "inline_equation", + "content": "b_{i} \\in \\mathbb{R}^{2 \\times 2}" + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "content": " (the two corners) and a segmentation mask " + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "inline_equation", + "content": "m_{i} \\in \\mathbb{R}^{h \\times w}" + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "content": ". Semantic prompts consist of text and two-person interaction labels. The text prompt is the CLIP embedding " + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "content": " of a sentence describing the body shape. The interaction prompt is a binary variable " + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 313, + 630, + 555, + 714 + ], + "type": "text", + "content": " indicating whether two" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1150" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 72, + 550, + 188 + ], + "blocks": [ + { + "bbox": [ + 58, + 72, + 550, + 188 + ], + "lines": [ + { + "bbox": [ + 58, + 72, + 550, + 188 + ], + "spans": [ + { + "bbox": [ + 58, + 72, + 550, + 188 + ], + "type": "image", + "image_path": "d599869071b1bf25b431691619e1796dbe8c792619a59e6e36f426fa5ae4f60d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 192, + 555, + 258 + ], + "lines": [ + { + "bbox": [ + 55, + 192, + 555, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 192, + 555, + 258 + ], + "type": "text", + "content": "Figure 2. Method overview. PromptHMR estimates SMPL-X parameters for each person in an image based on various types of prompts, such as boxes, language descriptions, and person-person interaction cues. Given an image and prompts, we utilize a vision transformer to generate image embeddings and mask and prompt encoders to map different types of prompts to tokens. Optionally, camera intrinsics can be embedded along with the image embeddings. The image embeddings and prompt tokens are then fed to the SMPL-X decoder. The SMPL-X decoder is a transformer-based module that attends to both the image and prompt tokens to estimate SMPL-X parameters. Note that the language and interaction prompts are optional, but providing them enhances the accuracy of the estimated SMPL-X parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 274, + 296, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 274, + 296, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 296, + 321 + ], + "type": "text", + "content": "people are in close contact. While semantic prompts are optional, each human needs at least one spatial prompt to be reconstructed. Overall, the input prompts are represented as " + }, + { + "bbox": [ + 55, + 274, + 296, + 321 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 55, + 274, + 296, + 321 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 133, + 326, + 294, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 326, + 294, + 344 + ], + "spans": [ + { + "bbox": [ + 133, + 326, + 294, + 344 + ], + "type": "interline_equation", + "content": "P _ {i} \\subseteq \\left\\{b _ {i}, m _ {i}, t _ {i}, k _ {i} \\right\\} \\tag {2}", + "image_path": "3eceb3923ef687102e0d2da6fcda7fdb44e53653c4498c2f51f7fb08912f949f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 138, + 342, + 217, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 342, + 217, + 353 + ], + "spans": [ + { + "bbox": [ + 138, + 342, + 217, + 353 + ], + "type": "interline_equation", + "content": "b _ {i} \\in P _ {i} \\text {o r} m _ {i} \\in P _ {i}", + "image_path": "9ec7ae0c4e4f0a2c92643d95d6ea43b911e66bea1e3f0cd07a628423baf029b7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 357, + 296, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 393 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 393 + ], + "type": "text", + "content": "Promptable human mesh recovery (PromptHMR) is defined as a learnable function that maps an image and a set of prompts to a set of 3D humans" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 397, + 294, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 397, + 294, + 412 + ], + "spans": [ + { + "bbox": [ + 115, + 397, + 294, + 412 + ], + "type": "interline_equation", + "content": "f: \\left(I, \\left\\{P _ {i} \\right\\} _ {i = 1} ^ {N}\\right)\\rightarrow \\left\\{H _ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}", + "image_path": "36f1ad60a6140e08e98b5d8723c25e496c67b3cc579710cf8c253b68e59b645a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 416, + 296, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 416, + 296, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 416, + 296, + 441 + ], + "type": "text", + "content": "This task definition integrates all available contexts to locate and reconstruct prompted humans in the image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 445, + 108, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 108, + 457 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 108, + 457 + ], + "type": "text", + "content": "3.2. Model" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 464, + 296, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 296, + 488 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 296, + 488 + ], + "type": "text", + "content": "Image encoder. The image is first encoded as tokens by a vision transformer (ViT) encoder from DINOv2 [11, 42]:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 137, + 493, + 294, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 493, + 294, + 506 + ], + "spans": [ + { + "bbox": [ + 137, + 493, + 294, + 506 + ], + "type": "interline_equation", + "content": "F = \\operatorname {E n c o d e r} (I), \\tag {4}", + "image_path": "5e87df8a0ae3ad8ac2269db61b437b088ae35985bc421964db8bb74260d437e9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 511, + 296, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 511, + 296, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 511, + 296, + 582 + ], + "type": "text", + "content": "To ensure sufficient resolution for modeling humans at both near and far distances, we use " + }, + { + "bbox": [ + 55, + 511, + 296, + 582 + ], + "type": "inline_equation", + "content": "896 \\times 896" + }, + { + "bbox": [ + 55, + 511, + 296, + 582 + ], + "type": "text", + "content": " images. The encoder is run once per frame regardless of the number of people prompted. When camera intrinsics are provided, we add positional encoding of the camera rays to the image tokens to make them camera-aware [2, 14]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 583, + 296, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 583, + 296, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 583, + 296, + 642 + ], + "type": "text", + "content": "Mask encoder. When available, masks are first processed by an encoder consisting of stripped convolutional layers that downsample the masks. The output mask features are added to the image tokens. If no mask is provided, a learned \"no mask\" token is added instead." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 121, + 648, + 294, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 648, + 294, + 661 + ], + "spans": [ + { + "bbox": [ + 121, + 648, + 294, + 661 + ], + "type": "interline_equation", + "content": "F _ {i} = \\operatorname {E n c o d e r} _ {\\mathrm {m}} \\left(m _ {i}\\right) + F. \\tag {5}", + "image_path": "5c4b0ee16f17fe31dccaed185a8c2c9c56da537d294718c89f94db299b35745c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 713 + ], + "type": "text", + "content": "Prompt encoder. The prompt encoder consists of a set of transformations that map different types of prompts to token vectors of the same dimension. When a prompt is not available, it is replaced with a learned null token." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "text", + "content": "For bounding boxes, we encode " + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "text", + "content": " using positional encoding summed with learned embeddings to form the box prompt tokens " + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "inline_equation", + "content": "T_{bi} = \\mathrm{PE}(b_{i})" + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "inline_equation", + "content": "T_{bi} \\in \\mathbb{R}^{2 \\times d}" + }, + { + "bbox": [ + 313, + 274, + 555, + 393 + ], + "type": "text", + "content": ". We design different box transformations during training to allow the model to use different boxes as a human identifier. In the training phase, each instance is prompted with either a whole-body bounding box, a face bounding box, or a truncated box covering part of the body. Gaussian noise is added to both corners. At inference time, the model accepts boxes without needing to know the box types." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "text", + "content": "Language is a natural way to supply semantic information, and in this paper, we use language to supplement spatial prompts with information on body shape. A sentence such as \"a muscular and tall male\" is encoded with the CLIP text encoder " + }, + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "inline_equation", + "content": "T_{ti} = \\mathrm{CLIP}(t_i)" + }, + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "inline_equation", + "content": "T_{ti} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 313, + 393, + 554, + 501 + ], + "type": "text", + "content": ". To generate paired (image, text) data, we run SHAPY's [8] shape-to-attribute method on the ground truth shape parameters to obtain shape attribute scores and randomly pick a subset of top attributes to form a sentence." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 501, + 554, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 554, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 554, + 536 + ], + "type": "text", + "content": "The interaction prompt " + }, + { + "bbox": [ + 313, + 501, + 554, + 536 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 313, + 501, + 554, + 536 + ], + "type": "text", + "content": " passes through the prompt encoder without modification and directly switches on-off the cross-person attention that is described in Sec. 3.3." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": "SMPL-X decoder. The SMPL-X decoder appends two query tokens " + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{spl}}, T_{\\mathrm{depth}}" + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": " with the prompt tokens " + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "inline_equation", + "content": "T_{bi}, T_{ti}" + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": " to form the person-specific prompt " + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "inline_equation", + "content": "T_i \\in \\mathbb{R}^{5 \\times d}" + }, + { + "bbox": [ + 313, + 536, + 554, + 572 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 573, + 554, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 573, + 554, + 597 + ], + "spans": [ + { + "bbox": [ + 313, + 573, + 554, + 597 + ], + "type": "text", + "content": "Finally, we use a standard transformer decoder and two MLP heads to produce the final output" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 358, + 601, + 497, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 601, + 497, + 617 + ], + "spans": [ + { + "bbox": [ + 358, + 601, + 497, + 617 + ], + "type": "interline_equation", + "content": "T _ {s m p l} ^ {\\prime}, T _ {d e p t h} ^ {\\prime} = \\mathrm {D e c o d e r} (F _ {i}, T _ {i})", + "image_path": "359f3be5460a0a6486e8ee209c4278c96503f5c2f7b251968c910ade55f822e5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 378, + 619, + 553, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 619, + 553, + 632 + ], + "spans": [ + { + "bbox": [ + 378, + 619, + 553, + 632 + ], + "type": "interline_equation", + "content": "\\phi_ {i}, \\theta_ {i}, \\beta_ {i} = \\operatorname {H e a d} _ {s m p l} \\left(T _ {s m p l} ^ {\\prime}\\right) \\tag {6}", + "image_path": "d5667d299ffd6eb1354fb5a8462383f63581ab41961cb56cb9b66fe14d1e2b7c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 406, + 635, + 508, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 635, + 508, + 649 + ], + "spans": [ + { + "bbox": [ + 406, + 635, + 508, + 649 + ], + "type": "interline_equation", + "content": "\\tau_ {i} = \\operatorname {H e a d} _ {d e p t h} (T _ {d e p t h} ^ {\\prime}).", + "image_path": "21dbc6ec15b4d0a5a3da069b4e0985a41175ef22c66d28c4ad37571113f83b6d.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "The transformer consists of three attention blocks. Each block applies self-attention on the tokens, cross-person attention (described in Sec. 3.3), and then two-way cross-attention between the tokens and the image embeddings [25]. The self-attention and cross-attention with the" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1151" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "image are applied to each prompted person independently. We use separate tokens " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{spl}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{depth}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " to make the location representation invariant to the 3D human pose and shape representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "content": "Regressing the location of the human in the camera space is much more challenging than most prior work that models humans in a cropped image space. Therefore, we do not regress " + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "content": " directly. We regress focal length normalized 2D translation " + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "inline_equation", + "content": "p_{xy} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "content": " and inverse depth " + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "inline_equation", + "content": "p_z \\in \\mathbb{R}" + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "content": ", and then transform them to " + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 121, + 295, + 192 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 198, + 295, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 198, + 295, + 224 + ], + "spans": [ + { + "bbox": [ + 86, + 198, + 295, + 224 + ], + "type": "interline_equation", + "content": "t _ {x y} = \\frac {p _ {x y}}{p _ {z}} \\quad t _ {z} = \\frac {1}{p _ {z}} \\times \\frac {f}{f _ {c}} \\quad \\tau = [ t _ {x y}, t z ], \\tag {7}", + "image_path": "abffc3fe223dad6e9b6ded536cfcdc6e74f000e67ca938de976b5ba1f079029a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "text", + "content": " is the ground truth or estimated focal length of the image, and " + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "text", + "content": " is the canonical focal length. Predicting the normalized inverse depth follows the recent monocular depth literature [49] and is also intuitive since the inverse depth is linearly related to the size of the human in the image. Predicting " + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "inline_equation", + "content": "p_{xy}" + }, + { + "bbox": [ + 55, + 231, + 296, + 316 + ], + "type": "text", + "content": " is equivalent to predicting the 2D location of the human in a normalized image plane." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 322, + 187, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 322, + 187, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 187, + 335 + ], + "type": "text", + "content": "3.3. Two-person interaction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 340, + 295, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 340, + 295, + 389 + ], + "spans": [ + { + "bbox": [ + 55, + 340, + 295, + 389 + ], + "type": "text", + "content": "We introduce promptable layers in the decoder to model two-person interaction. We describe the case where there are two people in the image, but the implementation can extend to model an interacting pair in a larger group." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 388, + 295, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 449 + ], + "type": "text", + "content": "The promptability is modeled as a flow control with a residual connection (Fig. 3). Specifically, if two humans are interacting (as indicated by " + }, + { + "bbox": [ + 55, + 388, + 295, + 449 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 55, + 388, + 295, + 449 + ], + "type": "text", + "content": "), their query tokens pass through an additional self-attention layer; otherwise, non-interacting humans skip this." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 449, + 295, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 295, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 295, + 532 + ], + "type": "text", + "content": "Applying attention to every person often creates unnecessary dependency in crowded scenes, and there is limited training data for large-group scenarios. However, there is high-quality data featuring two-person social interactions. By making the interaction layers promptable, we mitigate data diversity issues and increase flexibility, regardless of the number of people in the scene." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 532, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 628 + ], + "type": "text", + "content": "Our proposed interaction layer uses a standard self-attention mechanism. First, we add positional encodings to the query tokens to distinguish the two individuals. The encoded tokens then go through a self-attention layer, whose output is combined with the original tokens via a residual connection. Our experiments demonstrate that including these interaction layers significantly improves inter-person pose accuracy in two-person interaction benchmarks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 635, + 205, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 205, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 205, + 647 + ], + "type": "text", + "content": "3.4. PromptHMR video version" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "text", + "content": "In addition to the single-image variant of PromptHMR, we train an extended version that processes videos to estimate human motion in world coordinates. To achieve this, we introduce a simple and efficient temporal transformer module. Given a monocular video sequence " + }, + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\{I^t\\}_{t=0}^T" + }, + { + "bbox": [ + 55, + 653, + 295, + 715 + ], + "type": "text", + "content": ", we first run" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 550, + 159 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 550, + 159 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 550, + 159 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 550, + 159 + ], + "type": "image", + "image_path": "40583d3d4a212eca68f9d26bdff69156d79a47247c0ae986bf506b27ded37f66.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 164, + 554, + 198 + ], + "lines": [ + { + "bbox": [ + 313, + 164, + 554, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 554, + 198 + ], + "type": "text", + "content": "Figure 3. SMPL-X decoder. The top row shows one attention block in the decoder. The cross-person interaction module can be turned on/off. The bottom row shows the cross-person attention." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": "PromptHMR to obtain per-subject SMPL-X decoder output tokens " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{spl}}^{\\prime}" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{depth}}^{\\prime}" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": ", assuming that the subject identities are provided with the prompts. These tokens, along with the positional encoding of time " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": ", are fed to a decoder-only temporal transformer module with twelve attention blocks. The output tokens are converted to SMPL-X parameters " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "\\phi_t, \\theta_t, \\beta_t" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": ", translation " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "\\tau_t" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": ", and joint contact probabilities " + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 313, + 213, + 554, + 322 + ], + "type": "text", + "content": ". The contact probabilities indicate whether a given joint is in contact with the ground plane similar to [50-52]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 323, + 554, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 554, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 554, + 443 + ], + "type": "text", + "content": "To obtain results in world coordinates, we adopt the approach from TRAM [65]. Specifically, we use DROID-SLAM [60] and a monocular metric depth estimation model, ZoeDepth [3], to estimate camera motion in metric world coordinates. The translation parameters " + }, + { + "bbox": [ + 313, + 323, + 554, + 443 + ], + "type": "inline_equation", + "content": "\\tau_{t}" + }, + { + "bbox": [ + 313, + 323, + 554, + 443 + ], + "type": "text", + "content": " are then transformed to world coordinates using the estimated camera motion. To refine the human trajectory and mitigate foot-skating artifacts, we leverage the estimated contact probabilities and run a fast postprocessing that optimizes the contact joints to have zero velocity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 455, + 368, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 455, + 368, + 466 + ], + "spans": [ + { + "bbox": [ + 314, + 455, + 368, + 466 + ], + "type": "text", + "content": "3.5. Losses" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "content": "PromptHMR is trained with a combination of 2D and 3D losses, following traditional HMR methods [22, 30]:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 327, + 511, + 541, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 511, + 541, + 525 + ], + "spans": [ + { + "bbox": [ + 327, + 511, + 541, + 525 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {2 D} + \\lambda_ {2} \\mathcal {L} _ {3 D} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {4} \\mathcal {L} _ {V} + \\lambda_ {5} \\mathcal {L} _ {t}", + "image_path": "ee39c48fdaabab8f561caa515b44e69a35ca9e79c5a53194c35cf0c769113144.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 536, + 430, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 430, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 430, + 548 + ], + "type": "text", + "content": "with each term calculated as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 365, + 560, + 477, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 560, + 477, + 574 + ], + "spans": [ + { + "bbox": [ + 365, + 560, + 477, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {2 D} = \\left\\| \\hat {\\mathcal {J}} _ {2 D} - \\Pi \\left(\\mathcal {J} _ {3 D}\\right) \\right\\| _ {F} ^ {2}", + "image_path": "9bae6bf90d566b985679303b44bb9e02a744f1611e0db6d7eee9f9be837c5f00.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 365, + 577, + 462, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 577, + 462, + 591 + ], + "spans": [ + { + "bbox": [ + 365, + 577, + 462, + 591 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {3 D} = \\left\\| \\hat {\\mathcal {J}} _ {3 D} - \\mathcal {J} _ {3 D} \\right\\| _ {F} ^ {2}", + "image_path": "025da68599d4e3aac4c07846fb641285d1916d1a79c6d6a2254b03c55dec1fc7.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 353, + 594, + 440, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 594, + 440, + 609 + ], + "spans": [ + { + "bbox": [ + 353, + 594, + 440, + 609 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {S M P L}} = | | \\hat {\\Theta} - \\Theta | | _ {2} ^ {2}", + "image_path": "30cf1435a76e5a4f05fa4220aeed87f197c65a1b4bea20bb3ede05a3011e1831.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 369, + 612, + 441, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 612, + 441, + 625 + ], + "spans": [ + { + "bbox": [ + 369, + 612, + 441, + 625 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {V} = \\left\\| \\hat {V} - V \\right\\| _ {F} ^ {2}", + "image_path": "1e91ca1bc7407844c44d683a3e0284293d93017ed571d52c397edf570dd30f0f.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 371, + 628, + 516, + 642 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 628, + 516, + 642 + ], + "spans": [ + { + "bbox": [ + 371, + 628, + 516, + 642 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = \\left| \\left| \\hat {p} _ {x y} - p _ {x y} \\right| \\right| _ {F} ^ {2} + \\left| \\left| \\hat {p} _ {z} - p _ {z} \\right| \\right| _ {F} ^ {2}", + "image_path": "ddda5a5f167b4535283b055c023aa78de7cafc7c30d8d526043b7c85c58574bf.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{J}_{3D}" + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": " are the 3D joints and vertices of the SMPL-X model, with the hat operator denoting the ground truth. " + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": " is the camera reprojection operator. Additionally, on datasets with ground truth translation labels, we supervise the normalized translation " + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "inline_equation", + "content": "p_{xy}" + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": " and inverse depth " + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "inline_equation", + "content": "p_z" + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1152" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 137, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 137, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 137, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "content": "Datasets. We train PromptHMR with standard datasets: BEDLAM [4], AGORA [44], 3DPW [63], COCO [33], and MPII [37]. Following 4DHumans, we add AIC [66] and InstaVariety [23] as in-the-wild data, with pseudoground truth from CamSMPLify [43]. Additionally, we add CHI3D [16] and HI4D [68] to enable learning two-person interaction following the train-test splits from BUDDI [38]. Including CHI3D and HI4D does not improve performance on other benchmarks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "content": "Implementation. We train PromptHMR with AdamW with a batch size of 96 images of resolution " + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "inline_equation", + "content": "896 \\times 896" + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "content": ". We use a learning rate of " + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "inline_equation", + "content": "1e^{-5}" + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "content": " for the image encoder and " + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "inline_equation", + "content": "3e^{-5}" + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "content": " for the prompt encoder and the SMPL-X decoder, with a weight decay of " + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "inline_equation", + "content": "5e^{-5}" + }, + { + "bbox": [ + 55, + 201, + 296, + 261 + ], + "type": "text", + "content": ". The training converges within 350K steps." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 262, + 296, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 296, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 296, + 333 + ], + "type": "text", + "content": "Evaluation. We evaluate camera space reconstruction accuracy on 3DPW [63], EMDB [24] and RICH [20], using MPJPE, Procrustes-aligned MPJPE (PA-MPJPE) and Per Vertex Error (PVE) [22]. We evaluate inter-person accuracy on HI4D and CHI3D by Pair-PA-MPJPE, which aligns the two people as a whole with the ground truth [38]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "text", + "content": "To evaluate world-grounded motion on EMDB with PromptHMR video (PromptHMR-vid), we compute World-aligned MPJPE " + }, + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "inline_equation", + "content": "(\\mathrm{WA - MPJPE}_{100})" + }, + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "text", + "content": ", World MPJPE " + }, + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "inline_equation", + "content": "(\\mathrm{W - MPJPE}_{100})" + }, + { + "bbox": [ + 55, + 335, + 296, + 383 + ], + "type": "text", + "content": " and Root Translation Error (RTE in %) [52, 67]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 393, + 194, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 194, + 406 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 194, + 406 + ], + "type": "text", + "content": "4.1. Reconstruction accuracy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 412, + 296, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 296, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 296, + 520 + ], + "type": "text", + "content": "For camera space reconstruction, as shown in Table 1, PromptHMR and PromptHMR-Vid demonstrate state-of-the-art performance, matching crop-based methods while achieving better results than other full-image methods. PromptHMR and CameraHMR use the same training data and have similar performance, which validates that this prompt-based approach can achieve metrically accurate results. For representative results, see Fig. 7, where PromptHMR recovers coherent 3D scenes of people." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 521, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 296, + 605 + ], + "type": "text", + "content": "For interaction reconstruction, PromptHMR achieves good accuracy as indicated in Table 2. Compared to BUDDI which is also trained on CHI3D and HI4D, our method achieves better overall accuracy on per-person and interperson metrics. We show qualitative results in Fig. 8. As a monocular regression method, PromptHMR still cannot avoid interpenetration between closely interacting people." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "PromptHMR-Vid achieves SOTA performance among methods that estimate human motion in world coordinates, as shown in Table 4. Unlike TRAM, we estimate the joint contact probabilities similar to [51, 52]. Therefore, we achieve lower foot skating than TRAM, even though we use the same metric SLAM method to transform motion in camera space to world coordinates. Please refer to our supplementary material (SupMat) for qualitative results of PromptHMR-Vid." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 70, + 551, + 129 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 551, + 129 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 551, + 129 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 551, + 129 + ], + "type": "image", + "image_path": "76765d0a6a3a88ed783d150a61768340fbb14079662abbd07fae52512a29a113.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 133, + 554, + 155 + ], + "lines": [ + { + "bbox": [ + 313, + 133, + 554, + 155 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 554, + 155 + ], + "type": "text", + "content": "Figure 4. Effect of box prompts. Our method remains stable with different boxes, including noisy truncated boxes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 162, + 551, + 228 + ], + "blocks": [ + { + "bbox": [ + 316, + 162, + 551, + 228 + ], + "lines": [ + { + "bbox": [ + 316, + 162, + 551, + 228 + ], + "spans": [ + { + "bbox": [ + 316, + 162, + 551, + 228 + ], + "type": "image", + "image_path": "45cd98a2e74dde29e3e811469d3fa51fbc4a9d8865b796168422773625ece09d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 230, + 554, + 264 + ], + "lines": [ + { + "bbox": [ + 313, + 230, + 554, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 554, + 264 + ], + "type": "text", + "content": "Figure 5. Effect of mask prompts. Results are from the same model with different prompt inputs. Masks are better for close interaction scenarios where boxes are ambiguous." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 318, + 266, + 550, + 472 + ], + "blocks": [ + { + "bbox": [ + 318, + 266, + 550, + 472 + ], + "lines": [ + { + "bbox": [ + 318, + 266, + 550, + 472 + ], + "spans": [ + { + "bbox": [ + 318, + 266, + 550, + 472 + ], + "type": "image", + "image_path": "0455387cbb7dea4c820714e8a040a3978a2731be3dbf1bed6d7449c3af85372a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 477, + 554, + 521 + ], + "lines": [ + { + "bbox": [ + 313, + 477, + 554, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 554, + 521 + ], + "type": "text", + "content": "Figure 6. Effect of shape prompts. Compared to the baseline that does not incorporate shape description during training and testing, the model with shape prompts has better accuracy on HBW, especially in ambiguous images." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 537, + 476, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 537, + 476, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 537, + 476, + 551 + ], + "type": "text", + "content": "4.2. Effect of multimodal prompts" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 556, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 554, + 605 + ], + "type": "text", + "content": "We conduct qualitative and quantitative evaluations of the multimodal prompts. For efficient ablation, we train models with " + }, + { + "bbox": [ + 313, + 556, + 554, + 605 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 313, + 556, + 554, + 605 + ], + "type": "text", + "content": " input resolution and select the best model within 150K steps of training." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 605, + 554, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 688 + ], + "type": "text", + "content": "For box prompts, as shown in rows 3-4 of Fig. 7, our method is able to take a combination of different boxes from in-the-wild images to reconstruct crowded scenes. Figure 4 also shows an example with varying box inputs. PromptHMR remains stable when the boxes change and uses full image context to reconstruct the human even when the boxes are truncated." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "The mask prompt is more effective than boxes when people closely overlap (Fig. 5), as boxes are ambiguous in such" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1153" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 72, + 515, + 251 + ], + "blocks": [ + { + "bbox": [ + 94, + 72, + 515, + 251 + ], + "lines": [ + { + "bbox": [ + 94, + 72, + 515, + 251 + ], + "spans": [ + { + "bbox": [ + 94, + 72, + 515, + 251 + ], + "type": "table", + "html": "
Models3DPW (14)EMDB (24)RICH (24)
PA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVEPA-MPJPEMPJPEPVE
cropped imageCLIFF* [31]43.069.081.268.3103.3123.768.1103.3128.0
HMR2.0a [17]44.469.882.261.597.8120.060.798.3120.8
TokenHMR [13]44.371.084.655.691.7109.4---
CameraHMR [43]35.156.065.943.370.281.734.055.764.4
full imageBEV [58]46.978.592.370.9112.2133.4---
Multi-HMR* [2]45.973.187.150.181.695.746.373.883.0
PromptHMR*36.658.769.441.071.784.537.356.665.5
videoWHAM [52]37.559.871.552.081.696.944.380.091.2
TRAM [65]35.659.369.645.774.486.6---
GVHMR [51]37.056.668.744.574.285.939.566.074.4
PromptHMR-Vid35.556.967.340.168.179.237.057.465.8
", + "image_path": "ba87ce3ed2ade4199326cf7ec0cb4f2ab1d3f690b7e1c877373c8eaac657afe0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 301, + 292, + 381 + ], + "blocks": [ + { + "bbox": [ + 55, + 256, + 555, + 291 + ], + "lines": [ + { + "bbox": [ + 55, + 256, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 256, + 555, + 291 + ], + "type": "text", + "content": "Table 1. Comparison of mesh reconstruction on the 3DPW, EMDB and RICH datasets, with the number of joints in parenthesis. " + }, + { + "bbox": [ + 55, + 256, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 55, + 256, + 555, + 291 + ], + "type": "text", + "content": " denotes methods that use ground truth focal length during inference. Note that we remove the test-time flip augmentation from all of the video methods to ensure a fair comparison. All metrics are in mm." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 301, + 292, + 381 + ], + "lines": [ + { + "bbox": [ + 58, + 301, + 292, + 381 + ], + "spans": [ + { + "bbox": [ + 58, + 301, + 292, + 381 + ], + "type": "table", + "html": "
ModelsHI4D (14)CHI3D (14)
PA-MPJPEMPJPEPair-PA-MPJPEPA-MPJPEMPJPEPair-PA-MPJPE
BEV* [58]81-13651-96
BUDDI [38]73-9847-68
Multi-HMR* [2]49.867.880.631.754.0100.0
PromptHMR*39.263.978.127.248.058.5
PromptHMR30.139.639.524.746.545.3
", + "image_path": "aa23c2cdd57b42e2175fd626a2e69dfc4179502569d5b8e94893682946233122.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 58, + 449, + 291, + 533 + ], + "blocks": [ + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "type": "text", + "content": "Table 2. Comparison on interaction reconstruction. PromptHMR is more accurate in per-person and inter-person accuracy. * denote a method or baseline is not trained on HI4D or CHI3D. All metrics are in mm. The impact of HI4D and the interaction prompt are evaluated in Table 5." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 449, + 291, + 533 + ], + "lines": [ + { + "bbox": [ + 58, + 449, + 291, + 533 + ], + "spans": [ + { + "bbox": [ + 58, + 449, + 291, + 533 + ], + "type": "table", + "html": "
Train w/ textTest w/ textHBW
HeightChestWaistHipP2P-20k
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", + "image_path": "9a93e84104db7099870847c217097b9fbece44908e0b217074b1c174b4bf512a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "content": "cases. Ablation of HI4D (rows 1-2 in Tab. 5) shows that using masks as the spatial prompt improves accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "content": "Experiments on the HBW validation set (Tab. 3) show that text prompts effectively improve shape accuracy when used during both training and testing. Moreover, training with shape descriptions alone provides an accuracy boost even if prompts are not given at test time. As illustrated in Fig. 6, text prompts provide notable improvements, especially when large perspective effects create ambiguity." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 318, + 301, + 550, + 370 + ], + "blocks": [ + { + "bbox": [ + 55, + 540, + 295, + 586 + ], + "lines": [ + { + "bbox": [ + 55, + 540, + 295, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 295, + 586 + ], + "type": "text", + "content": "Table 3. Ablation of shape prompts using text. Training with shape prompts improves shape accuracy. Using shape prompts during inference further improves shape accuracy. The ablation study is conducted with a " + }, + { + "bbox": [ + 55, + 540, + 295, + 586 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 55, + 540, + 295, + 586 + ], + "type": "text", + "content": " model. Errors are in mm." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 301, + 550, + 370 + ], + "lines": [ + { + "bbox": [ + 318, + 301, + 550, + 370 + ], + "spans": [ + { + "bbox": [ + 318, + 301, + 550, + 370 + ], + "type": "table", + "html": "
ModelsEMDB-2 (24)
WA-MPJPE100W-MPJPE100RTEJitterFoot Skating
WHAM [52]135.6354.86.022.54.4
TRAM [65]76.4222.41.418.523.4
GVHMR [51]111.0276.52.016.73.5
PromptHMR-Vid71.0216.51.316.33.5
", + "image_path": "90ae2f57c0fdc058081ff3ab4b3377b36e4a7ccbf224d6e0b98c3fbd4cee6db3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 435, + 553, + 535 + ], + "blocks": [ + { + "bbox": [ + 313, + 376, + 555, + 419 + ], + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 419 + ], + "type": "text", + "content": "Table 4. Evaluation of motion in world coordinates. PromptHMR-Vid combined with metric SLAM from TRAM [65] surpasses SOTA methods at predicting human motion in world coordinates." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 435, + 553, + 535 + ], + "lines": [ + { + "bbox": [ + 317, + 435, + 553, + 535 + ], + "spans": [ + { + "bbox": [ + 317, + 435, + 553, + 535 + ], + "type": "table", + "html": "
Trained withHI4D (14)
MaskInteractionHI4DPA-MPJPEMPJPEPair-PA-MPJPE
×××47.071.487.2
✓××43.460.583.0
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", + "image_path": "9d490488d1aa1ed7a16399089be73109b9b2939a55fef2a092f6ad4fe9d97aa1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 541, + 555, + 596 + ], + "lines": [ + { + "bbox": [ + 313, + 541, + 555, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 541, + 555, + 596 + ], + "type": "text", + "content": "Table 5. Ablation on interaction prompt. The interaction module improves inter-person reconstruction metrics Pair-PA-MPJPE on HI4D, especially when the method does not include HI4D in training. Ablation is conducted with a " + }, + { + "bbox": [ + 313, + 541, + 555, + 596 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 313, + 541, + 555, + 596 + ], + "type": "text", + "content": " model. All metrics are in mm." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "For interaction prompts, we show an ablation in Table 5. The proposed interaction module is beneficial and largely improves inter-person accuracy on HI4D even without HI4D training, indicating out-off-domain generalization. When trained on HI4D, the interaction module does not improve per-person PA-MPJPE but still improves interperson Pair-PA-MPJPE. Please refer to our SupMat for more qualitative results on interaction prompts." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1154" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 549, + 350 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 549, + 350 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 549, + 350 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 549, + 350 + ], + "type": "image", + "image_path": "a845a1ad594881ec9d8ab80a5d9c550aa3b3adb337a13fb5501266f7a87634b9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 350, + 555, + 374 + ], + "lines": [ + { + "bbox": [ + 55, + 350, + 555, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 555, + 374 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison: Multi-HMR vs PromptHMR. Our model can recover coherent 3D scenes of people. In crowded scenes, face detection provides reliable box prompts for our model. Please zoom in to see the details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 384, + 539, + 536 + ], + "blocks": [ + { + "bbox": [ + 59, + 384, + 539, + 536 + ], + "lines": [ + { + "bbox": [ + 59, + 384, + 539, + 536 + ], + "spans": [ + { + "bbox": [ + 59, + 384, + 539, + 536 + ], + "type": "image", + "image_path": "7db2160aff5f5160604adec48ce4f0c51cfe225426774259d35b6ba76b1d46e6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 539, + 555, + 562 + ], + "lines": [ + { + "bbox": [ + 55, + 539, + 555, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 555, + 562 + ], + "type": "text", + "content": "Figure 8. Qualitative results. PromptHMR recovers coherent two-person close interaction. Despite suffering from some interpenetration, the relative positions of the interacting people are accurately recovered. More examples are provided in the Supplementary." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 575, + 130, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 130, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 130, + 588 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "text", + "content": "We see PromptHMR as a step towards a holistic perception model for 3D humans, but several limitations need to be addressed in future work. Currently, the shape description and interaction prompts are not automatically generated and need to be supplied by the user. Future work should explore how to effectively integrate our promptable model with VLMs to automate prompting. We show how semantic prompts can improve reconstruction accuracy, but many other potential types of side information such as action descriptions, 3D scene context, or body measurements may" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 576, + 512, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 576, + 512, + 588 + ], + "spans": [ + { + "bbox": [ + 314, + 576, + 512, + 588 + ], + "type": "text", + "content": "provide additional benefits in different scenarios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 597, + 388, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 597, + 388, + 610 + ], + "spans": [ + { + "bbox": [ + 314, + 597, + 388, + 610 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "content": "We have presented PromptHMR, a promptable HPS estimation approach that leverages full image context with spatial and semantic prompts to infer 3D humans in the scene. Our method demonstrates state-of-the-art accuracy across diverse benchmarks and generalizes well in the wild. Our experiments show that incorporating diverse input information through flexible prompting enables robustness and adaptability in challenging scenarios." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1155" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "content": "Acknowledgement. The authors would like to thank Yan Zhang, Yao Feng, and Nitin Saini for their suggestions. The majority of the work was done when Yufu was an intern at Meshcapade. Yufu and Kostas thank the support of NSF NCS-FO 2124355, NSF FRR 2220868, and NSF IISRI 2212433." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 294, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 294, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 294, + 192 + ], + "type": "text", + "content": "Disclosure. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 202, + 115, + 215 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 202, + 115, + 215 + ], + "spans": [ + { + "bbox": [ + 56, + 202, + 115, + 215 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 222, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 222, + 295, + 255 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 222, + 295, + 255 + ], + "spans": [ + { + "bbox": [ + 61, + 222, + 295, + 255 + ], + "type": "text", + "content": "[1] Nikos Athanasiou, Alpár Ceske, Markos Diomataris, Michael J. Black, and Gül Varol. MotionFix: Text-driven 3D human motion editing. 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However, contemporary methods exhibit significant limitations in semantic preservation, contextual integrity, and information redundancy, which constrains retrieval efficacy. We present PromptHash, an innovative framework leveraging affinity prompt-aware collaborative learning for adaptive cross-modal hashing. We propose an end-to-end framework for affinity-prompted collaborative hashing, with the following fundamental technical contributions: (i) a text affinity prompt learning mechanism that preserves contextual information while maintaining parameter efficiency, (ii) an adaptive gated selection fusion architecture that synthesizes State Space Model with Transformer network for precise cross-modal feature integration, and (iii) a prompt affinity alignment strategy that bridges modal heterogeneity through hierarchical contrastive learning. To the best of our knowledge, this study presents the first investigation into affinity prompt awareness within collaborative cross-modal adaptive hash learning, establishing a paradigm for enhanced semantic consistency across modalities. Through comprehensive evaluation on three benchmark multi-label datasets, PromptHash demonstrates substantial performance improvements over existing approaches. Notably, on the NUS-WIDE dataset, our method achieves significant gains of $18.22\\%$ and $18.65\\%$ in image-to-text and text-to-image retrieval tasks, respectively. The code is publicly available at https://github.com/ShiShuMo/PromptHash.", + "bbox": [ + 86, + 323, + 485, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 790, + 220, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid proliferation of social media platforms, multimodal data has grown exponentially, making cross-modal retrieval an increasingly promising field with broad application prospects [29].", + "bbox": [ + 89, + 816, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7d191359806e6d9d2478b06266e79bbf034a8b9c62e05d99d16d7f311248c62b.jpg", + "image_caption": [ + "Figure 1. Compare with existing frameworks. (a) Previous methods used dual Transformers for cross modal hashing contrastive learning. (b) We compare and learn images and texts separately by setting learnable affinity prompts." + ], + "image_footnote": [], + "bbox": [ + 516, + 290, + 924, + 491 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the inherent modal heterogeneity of multimodal data presents significant challenges, indicating substantial room for improvement in both academic research and industrial applications of cross-modal retrieval [45]. Cross-modal hashing employs shared hash functions with strong representational capacities, mapping data from different modalities into a common hash space. As a result, data with similar semantic content across modalities can be mapped to proximate binary hash codes, effectively bridging the semantic gap between modalities and enabling rapid and accurate cross-modal data retrieval [1, 9, 12, 16, 17, 26, 31, 33, 41]. Existing cross-modal hashing methods are generally divided into unsupervised and supervised approaches, with supervised methods typically outperforming unsupervised ones by leveraging supervisory information, such as pairwise similarity matrices or semantic labels. Despite the considerable progress made in deep supervised cross-modal hashing, there are still fundamental challenges to address.", + "bbox": [ + 511, + 582, + 906, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, CLIP (Contrastive Language-Image Pretraining) [27] has emerged as a powerful backbone for cross-modal feature extraction in many hashing methods due to", + "bbox": [ + 511, + 854, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 109, + 887, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19649", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "its strong zero-shot capabilities and alignment between visual and textual representations. However, adopting CLIP introduces several critical challenges that limit performance in real-world applications.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A notable challenge is the context-length limitation in CLIP pre-trained models, where the current maximum context length is limited to 77 characters, whereas real-world text data often far exceeds this limit. This discrepancy leads to context loss and semantic truncation, especially when retrieving textual information. Furthermore, effectively fusing cross-modal features remains an open challenge, particularly in enhancing semantic feature weights relevant to retrieval while suppressing irrelevant information. For instance, the widely used MS COCO dataset [22] exemplifies this challenge, as its text lengths range from 169 to 625 characters, significantly exceeding CLIP's 77-character capacity for text encoding. To address the CLIP context-length limitation, our approach incorporates foreground target text into adaptive affinity prompts and implements a dynamic weighting mechanism between these prompts and the original text. This strategy effectively preserves critical semantic information while circumventing CLIP's 77-character constraint, enabling comprehensive processing of lengthy real-world texts without semantic truncation. Previous approaches have employed various methods to address this: the Bag-of-Words (BoW) model, which disregards contextual word relationships; pre-trained Transformer [36] models such as Vision Transformer(ViT) [7] and BERT [6], which still face truncation; and VTPH's [4] use of large language models [19, 25] to reconstruct text as prompts, although this method introduces significant computational overhead without fully resolving the semantic truncation issue.", + "bbox": [ + 91, + 152, + 483, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another challenge lies in the feature fusion of different modalities, where existing cross-modal hashing methods often incorporate contrastive learning to capture intermodal consistency. However, benchmark datasets commonly used in cross-modal retrieval suffer from context loss and semantic redundancy, especially in textual representation. For example, the textual content in MIRFLICKR-25K [13] and NUS-WIDE [5] is generated through direct label concatenation, resulting in limited contextual depth. Additionally, MS COCO's text data, derived from merged manual descriptions, can introduce semantic redundancy.", + "bbox": [ + 89, + 592, + 482, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose a Adaptive Affinity-Prompted Collaborative Cross-Modal Learning (PromptHash) for Hashing Retrieval in Fig. 1. Ours framework that integrates text affinity prompts with State Space Model(SSM) and Transformer-based adaptive gated selection fusion, supported by a novel Prompt Affinity Contrastive Loss (PACL) to better align cross-modal semantics. Our contributions can be summarized as follows:", + "bbox": [ + 89, + 758, + 482, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- To mitigate semantic truncation caused by CLIP's", + "bbox": [ + 89, + 885, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "context-length limitation, adaptive text prompts are introduced that incorporate foreground target text essential for retrieval. This approach implements a dynamic weighting mechanism between prompts and original text, effectively preserving critical semantic information while circumventing length constraints for improved retrieval performance.", + "bbox": [ + 524, + 90, + 903, + 195 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The framework also incorporates an SSM-Transformer adaptive gated selection fusion module to refine cross-modal feature integration, preserving relevant semantic information while filtering out redundant content.", + "- To balance prompt semantics with the original image-text semantics, a novel Prompt Affinity Contrastive Loss (PACL) is introduced, bridging modality heterogeneity and semantic gaps through global and local prompt contrast.", + "- Extensive experiments on three benchmark datasets demonstrate that the proposed PromptHash framework significantly outperforms state-of-the-art methods, underscoring its effectiveness in cross-modal retrieval." + ], + "bbox": [ + 511, + 196, + 903, + 392 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 410, + 653, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep Cross-Modal Hashing", + "text_level": 1, + "bbox": [ + 511, + 436, + 761, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cross-modal hashing has made significant strides in information retrieval by mapping heterogeneous data into a unified Hamming space via hash functions. The literature typically categorizes approaches into unsupervised and supervised methods.", + "bbox": [ + 511, + 459, + 903, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised methods maintain semantic similarity without explicit supervision by leveraging cross-modal correlations. Notable works include DAEH [30] with deep adaptive enhancement, UKD's [10] teacher-student framework, and UCMFH's [40] CLIP-based feature extraction. Additionally, UCCH [11] addresses binary-continuous relaxation constraints, while NRCH [37] advances through robust contrastive loss and dynamic noise separation.", + "bbox": [ + 511, + 536, + 905, + 656 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Supervised methods utilize label information to establish semantic consistency within a shared hash space. DCMH [16] pioneered end-to-end deep cross-modal hashing, followed by CMHH's [3] focal loss approach and AGAH's [9] adversarial learning with attention mechanisms. Recent innovations include DCHUC's [34] joint optimization, MIAN's [42] modality-invariant networks, and GCDH's [2] graph convolutional networks. DCHMT [32] and MITH [23] leverage CLIP for fine-grained feature extraction.", + "bbox": [ + 511, + 657, + 905, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Proxy learning has emerged as another significant direction, with DAPH's [35] data-aware networks, DSPH's [14] fine-grained semantic relations, and DHaPH's [15] hierarchical learning. Notable approaches also include CMCL's [39] multi-bit collaboration and VTPH's [4] large model optimization. Distinct from existing methods, we in", + "bbox": [ + 511, + 810, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19650", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tegrate both global and local prompt alignments while minimizing feature divergence to alleviate modality heterogeneity and semantic gaps.", + "bbox": [ + 89, + 90, + 480, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Prompt Learning", + "text_level": 1, + "bbox": [ + 89, + 147, + 261, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt learning originated in NLP, integrating handcrafted templates into input data for downstream tasks. Recent studies have extended this concept to vision-language models, with CoCoOp [43] introducing Conditional Context Optimization, MaPLe [18] implementing Multi-modal Prompt Learning, and CoPrompt [28] enhancing performance through consistency constraints. While PromptKD [20] explores Unsupervised Prompt Distillation, prompt learning's effectiveness in cross-modal hashing remains underexplored.", + "bbox": [ + 89, + 169, + 482, + 320 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Contrastive Learning", + "text_level": 1, + "bbox": [ + 89, + 330, + 292, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive learning has demonstrated substantial efficacy in feature representation by maximizing similarity between positive pairs while minimizing negative pair similarity. Several cross-modal hashing methods have adopted this paradigm: UCCH [11] pioneered unsupervised contrastive learning, UniHash [38] facilitates instance-level learning, and CMCL [39] optimizes through token alignment. However, existing methods often overlook explicit fine-grained token-level semantic alignment. Our work addresses this through prompt-based contrastive learning for both instance and token-level representations.", + "bbox": [ + 89, + 353, + 482, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. State Space Models", + "text_level": 1, + "bbox": [ + 89, + 530, + 276, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While contrastive learning effectively aligns semantic representations across modalities, distinguishing between foreground (relevant) and background (irrelevant) information in multimodal contexts remains challenging. State Space Models (SSM) [8] offer a promising solution through their selective sequence modeling capabilities with linear computational complexity. Unlike Transformers that attend to all tokens equally, SSM's selective scan mechanism can dynamically focus on informative elements while filtering out noise. Vim [44] pioneered SSM in visual domains, demonstrating their ability to selectively process visual information. VMamba [24] extended this capability with 2D Selective Scanning that effectively separates foreground objects from background elements. Jamba [21] further showed how SSM's selective attention, when integrated with Transformer layers, enables more efficient sequence feature processing.", + "bbox": [ + 89, + 551, + 482, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite these advances, the potential of SSM, when combined with contrastive learning, to effectively address the foreground-background confusion problem in cross-modal hashing retrieval remains unexplored. Our work integrates these two paradigms, utilizing SSM for precise separation of foreground and background information and con", + "bbox": [ + 89, + 810, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "trastive mechanisms for accurate cross-modal alignment.", + "bbox": [ + 511, + 90, + 887, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 513, + 119, + 648, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Notations and Problem Definition", + "text_level": 1, + "bbox": [ + 513, + 145, + 805, + 160 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This paper adopts a framework analogous to conventional cross-modal hashing methodologies, utilizing image-text pairs as input modalities. Let $\\mathcal{O} = \\{o_i\\}_{i=1}^N$ denote a collection of $N$ training sample pairs, where each sample $o_i = (x_i^v, x_i^t, l_i, p_i)$ comprises a visual feature vector $x_i^v \\in \\mathbb{R}^{d^v}$ , a textual feature vector $x_i^t \\in \\mathbb{R}^{d^t}$ , a multi-label annotation $l_i \\in \\{0, 1\\}^{1 \\times C}$ (where $l_{i,c} = 1$ if sample $o_i$ belongs to category $c$ ; otherwise, $l_{i,c} = 0$ ), and a prompt word $p_i$ . We construct a similarity matrix $S$ where $S_{ij} = 1$ if samples share at least one category, indicating semantic affinity; otherwise, $S_{ij} = 0$ . The primary objective is to project heterogeneous features into a unified $K$ -bit Hamming space through two hashing functions: $b_i^v = H^v(f_i^v; \\theta^v) \\in \\{-1, +1\\}^K$ and $b_i^{pt} = H^t(f_i^{pt}; \\theta^t) \\in \\{-1, +1\\}^K$ , where $b_i^v$ and $b_i^{pt}$ denote the hash codes for visual and textual modalities, while $\\theta^v$ and $\\theta^t$ represent the learnable parameters of the corresponding functions. Throughout this paper, $M$ denotes the mini-batch size, and $D$ represents the feature embedding dimension. We use $f$ for initial feature representations (e.g., $f_i^v, f_i^t, f_i^p, f_i^{pt}$ ), $h$ for continuous hash representations prior to quantization (e.g., $h_i^v, h_i^{pt}, h_i^p$ ), and $b$ for binary hash codes (e.g., $b_i^v, b_i^{pt}$ ). For similarity metrics, $\\Theta_{ij}$ represents prompt-visual similarity, $\\Phi_{ij}$ denotes visual-prompt similarity, and $\\Omega_{ij}$ indicates intra-modal prompt similarity.", + "bbox": [ + 511, + 167, + 906, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Feature Extraction", + "text_level": 1, + "bbox": [ + 513, + 542, + 694, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 illustrates the detailed workflow of our proposed PromptHash framework. To leverage the latest advances in deep neural networks and Transformer-based models, we employ a two-branch Transformer architecture for the extraction of image and text features. Additionally, we introduce a dedicated Transformer network designed to extract prompt features, which are then used to compute prompt-weighted similarities. To further enhance the quality of the image and text representations, we utilize pretrained ViT and BERT as the visual encoder and text encoder, respectively. These models extract the image and text embeddings, denoted as $f_{i}^{v} = \\{G_{i}^{v}\\} \\in \\mathbb{R}^{L^{\\nu} \\times D}$ and $f_{i}^{t} = \\{G_{i}^{t}\\} \\in \\mathbb{R}^{L^{t} \\times D}$ . Similarly, the constructed masked fused prompt embeddings, denoted as $f_{i}^{pt} = \\{G_{i}^{p}\\} \\in \\mathbb{R}^{L^{p} \\times D}$ , are used to represent the fused prompt.", + "bbox": [ + 511, + 564, + 906, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Text Affinity-Aware Prompt Learning", + "text_level": 1, + "bbox": [ + 511, + 803, + 839, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In cross-modal hashing tasks, negative textual features can significantly degrade retrieval performance by hindering the effective distinction between foreground and background information. To address this issue, we propose a Text Affinity-Aware Prompt (TAAP) module, which dynami-", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19651", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/66af3efc14c7d701d2ea5d9a0588863154e48277e9363921a82c808afcca603b.jpg", + "image_caption": [ + "Figure 2. Overall Framework of PromptHash. Our framework consists of five key components: 1) Image and Text Encoders for modality-specific feature extraction; 2) Adaptive Gated State Selection and Fusion Module for feature filtering and cross-modal fusion between image features and hybrid prompt-enhanced textual features; 3) Text Affinity-Aware Prompting that dynamically learns and distinguishes retrieval-beneficial foreground information while optimizing textual feature representations through dynamic prompting mechanisms; 4) Cross-Modal Prompt Alignment Mechanism incorporating both global and local alignments, where global alignment facilitates image-to-text and image-to-prompt representation alignments with intra-class and inter-class affinity losses; 5) Hash Learning with quantization and reconstruction losses." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 903, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cally learns and differentiates foreground information that aids retrieval, and optimizes textual feature representations through a dynamic prompt mechanism.", + "bbox": [ + 88, + 530, + 482, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $l_{i}$ represent the category label set corresponding to image-text pairs $o_{i}$ and $o_{t}$ . We generate prompt text using a template: \"This is an image containing {class_name_i}\", where {class_name_i} corresponds to label $l_{i}$ . The complete prompt text is formulated as $\\text{prompt}_i =$ \"This is an image containing {class_name_i}\" which is then tokenized using Byte Pair Encoding (BPE): token_prompt_i = Tokenizer(prompt_i).", + "bbox": [ + 89, + 575, + 482, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The token sequence is encoded into an embedding vector $p_i$ : $p_i = \\text{embed}(\\text{token\\_prompt}_i)$ , $p_i \\in \\mathbb{R}^D$ (1)", + "bbox": [ + 89, + 696, + 482, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D$ denotes CLIP's embedding dimension. Then $f_{i}^{p}$ combines this with a learnable context vector $C_{\\mathrm{ctx}}$ :", + "bbox": [ + 89, + 739, + 482, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {p} = p _ {i} + C _ {\\mathrm {c t x}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 243, + 773, + 482, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This dynamic prompt mechanism enables effective distinction between foreground and background features through a learnable mask, optimizing the feature representation for retrieval tasks. The generated prompt features $f_{i}^{p}$ are then processed by the TAAP module's Transformer encoder layers, fusing them with the original text features $f_{i}^{t}$ :", + "bbox": [ + 89, + 796, + 482, + 878 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {f} _ {i} ^ {p} = \\text {T r a n s f o r m e r L a y e r} \\left(f _ {i} ^ {p}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 878, + 482, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we obtain the weighted feature representation through element-wise multiplication and global average pooling:", + "bbox": [ + 511, + 531, + 903, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {p t} = \\left(\\widehat {f} _ {i} ^ {p} \\times f _ {i} ^ {t}\\right) \\otimes \\eta , \\quad f _ {i} ^ {p t} \\in \\mathbb {R} ^ {D} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 561, + 903, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\eta$ represent learnable weight, respectively, with $\\otimes$ denoting matrix multiplication. This integration process effectively preserves foreground information while suppressing background noise, significantly improving cross-modal hashing retrieval performance.", + "bbox": [ + 511, + 585, + 905, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Adaptive Gated State Space Fusion Module", + "text_level": 1, + "bbox": [ + 511, + 664, + 883, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we integrate the State Space Model (SSM) with adaptive gating mechanisms to design an adaptive filtering feature fusion module, which we refer to as the Adaptive Gated State Space Fusion Module(AGSF). The textual features are weighted through the aforementioned prompt learning module, yielding a refined textual feature representation. However, image features must also undergo filtering and fusion with the resulting mixed prompt-text features. This process is formalized as follows:", + "bbox": [ + 511, + 685, + 905, + 796 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {\\mathrm {c l s} _ {m}} = \\operatorname {S i L U} \\left(\\operatorname {M L P} \\left(\\operatorname {G R N} \\left(f _ {i} ^ {m}\\right)\\right)\\right) \\mid m \\in \\{v, p t \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 800, + 903, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {\\text {f u s i o n}} = \\operatorname {C o n c a t} \\left(f _ {i} ^ {\\mathrm {c l s} _ {v}}, f _ {i} ^ {\\mathrm {c l s} _ {p t}}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 820, + 740, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Concat represents the concatenation operation, GRN denotes Global Response Normalization, MLP refers to a multi-layer perceptron, and SiLU is the activation function. In the Global Response Normalization (GRN) layer, for input $x \\in \\mathbb{R}^{B \\times N \\times D}$ , the", + "bbox": [ + 511, + 844, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19652", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "L2 norm $G_{x}$ and normalization factor $N_{x}$ are computed sequentially:", + "bbox": [ + 89, + 92, + 482, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {x} = \\| x \\| _ {2} = \\sqrt {\\sum_ {d = 1} ^ {D} x _ {d} ^ {2}}, \\quad N _ {x} = \\frac {G _ {x}}{\\frac {1}{N} \\sum_ {i = 1} ^ {N} G _ {x i}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 127, + 482, + 171 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final output with learnable parameters $\\lambda$ and $\\kappa$ is:", + "bbox": [ + 89, + 181, + 413, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G R N} (x) = \\lambda \\cdot \\left(x \\cdot N _ {x}\\right) + \\kappa + x \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 205, + 482, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the fused features, they are fed into the SSM adaptive selection module, expressed as:", + "bbox": [ + 89, + 232, + 482, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {\\text {f l i p} _ {\\text {a x i s}} = \\psi} = \\operatorname {F l i p} _ {\\text {a x i s}} ^ {T} (\\operatorname {S S M} (\\operatorname {F l i p} _ {\\text {a x i s}} = \\psi (f _ {i} ^ {\\text {f u s i o n}}))) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 267, + 482, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\psi \\in \\{1,2,(1,2)\\}$ . Here, $\\mathrm{Flip}_{\\mathrm{axis} = \\psi}$ denotes a flipping operation along different axes, and $\\mathrm{Flip}^T$ represents its inverse. The term SSM refers to the State Space Model. After obtaining the final three features, we apply an adaptive weighted filtering process. The parameter $\\tau$ serves as a learnable temperature coefficient, which balances the relative importance of the four features derived from flipped and unflipped orientations:", + "bbox": [ + 89, + 297, + 483, + 398 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {\\mathrm {f i t}} = \\theta \\tau \\sum_ {j \\in \\omega} f _ {i} ^ {\\mathrm {f l i p} _ {\\mathrm {a x i s} = j}} + (1 - \\theta) f _ {i} ^ {\\text {f u s i o n}}, \\omega = \\{1, 2, (1, 2) \\} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 405, + 482, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where, $\\theta$ denotes a set of learnable parameters. The filtered features are subsequently passed through a Transformer encoder layer, yielding:", + "bbox": [ + 89, + 446, + 483, + 488 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {f _ {i} ^ {v}}, \\widetilde {f _ {i} ^ {\\mathrm {p t}}} = \\operatorname {S p l i t} \\left(\\operatorname {T r a n s f o r m e r L a y e r} \\left(\\operatorname {M L P} \\left(f _ {i} ^ {\\mathrm {f i t}}\\right)\\right)\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 496, + 482, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The resulting features $\\widetilde{f_i^v}$ and $\\widetilde{f_i^{\\mathrm{pt}}}$ represent the outputs obtained through the adaptive SSM gating and selection fusion module. Here, Split denotes an operation that separates the individual visual and textual features from the fused representation. Through the aforementioned operations, we simultaneously adaptively filter and dynamically weight redundant information in both images and text, significantly enhancing the quality and effectiveness of retrieval.", + "bbox": [ + 89, + 529, + 483, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Prompt Alignment Contrastive Learning", + "text_level": 1, + "bbox": [ + 89, + 654, + 441, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To effectively bridge the semantic gaps between different modalities, we propose prompt alignment contrastive learning (PACL), a learning mechanism that enables fine-grained alignment between modalities. This mechanism operates through two key components: cross-modal prompt alignment and affinity-aware loss function.", + "bbox": [ + 89, + 676, + 483, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.1. Cross-Modal Prompt Alignment", + "text_level": 1, + "bbox": [ + 89, + 768, + 362, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further mitigate heterogeneity and semantic gaps, we leverage contrastive learning to explicitly align the fine-grained semantic concept representations. Our alignment strategy comprises two key components: global-local prompt alignment and affinity-aware loss functions.", + "bbox": [ + 89, + 787, + 482, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For global prompt alignment, we adopt symmetric InfoNCE losses to align image representations with textual and prompt representations:", + "bbox": [ + 89, + 858, + 483, + 898 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i} ^ {a \\rightarrow b} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {i} ^ {b}} / \\tau_ {1}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {c} ^ {b}} / \\tau_ {1}\\right)} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 88, + 905, + 150 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal{L}_{\\mathrm{gpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{a,b\\in \\{v,pt\\} \\\\ a\\neq b}}\\mathcal{L}_{i}^{a\\to b}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 151, + 777, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau_{1}$ is a temperature hyperparameter, and the subscript $c$ indexes over all samples in the batch. Here, $a, b \\in \\{v, pt\\}, a \\neq b$ , corresponding to visual and textual features.", + "bbox": [ + 511, + 213, + 906, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For local prompt alignment, we employ a dynamic temperature mechanism adjusted by modality distributions:", + "bbox": [ + 511, + 256, + 905, + 284 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tau_ {2} = \\tau \\times \\frac {1}{1 + \\mathrm {J S - d i v} \\left(f _ {i} ^ {v} , f _ {i} ^ {p}\\right)} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 292, + 905, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is the base temperature and JS-div measures the Jensen-Shannon divergence between modality distributions. Here, $\\tau$ and $\\tau_{1}$ denote the temperature hyperparameters with a default value of 0.07.", + "bbox": [ + 511, + 335, + 906, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The local alignment losses are then formulated as:", + "bbox": [ + 532, + 392, + 834, + 406 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i} ^ {e \\rightarrow f} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {i} ^ {f}} / \\tau_ {2}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {c} ^ {f}} / \\tau_ {2}\\right)} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 415, + 903, + 478 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal{L}_{\\mathrm{lpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{e,f\\in \\{v,p\\} \\\\ e\\neq f}}\\mathcal{L}_{i}^{e\\to f}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 479, + 772, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $e, f \\in \\{v, p\\}$ , $e \\neq f$ , corresponding to visual and prompt features. $\\tau$ and $\\tau_1$ denote the temperature hyperparameters with a default value of 0.07.", + "bbox": [ + 511, + 540, + 906, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.2. Affinity-Aware Loss Function", + "text_level": 1, + "bbox": [ + 511, + 593, + 766, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To preserve semantic consistency, we design inter-class and intra-class affinity losses:", + "bbox": [ + 511, + 613, + 905, + 641 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n t e r}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\sum_ {k = 1} ^ {Q} \\left(S _ {i j} k - \\log \\left(1 + e ^ {\\Theta_ {i j}}\\right)\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 652, + 905, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q \\in \\{\\Theta_{ij}, \\Phi_{ij}\\}$ , $\\Theta_{ij} \\neq \\Phi_{ij}$ , $\\Theta_{ij} = \\frac{1}{2} (h_i^p)^T h_j^v$ and $\\Phi_{ij} = \\frac{1}{2} (h_i^v)^T h_j^p$ denote cross-modal similarities, where $h_i^p$ and $h_j^v$ represent the real-valued hash codes of prompt and visual features respectively, before passing through the sign function, $N$ is the number of samples, and $S_{ij} \\in \\{0, 1\\}$ is the ground truth similarity matrix.", + "bbox": [ + 511, + 704, + 905, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The intra-class affinity loss is defined as:", + "bbox": [ + 532, + 794, + 777, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n t r a}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\left(\\mathcal {S} _ {i j} \\Omega_ {i j} - \\log \\left(1 + e ^ {\\Omega_ {i j}}\\right)\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 818, + 903, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Omega_{ij} = \\frac{1}{2}\\left(h_i^p\\right)^T h_j^p$ represents intra-modal similarity between prompt features.", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19653", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Hashing Learning", + "text_level": 1, + "bbox": [ + 91, + 90, + 267, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1) Quantization Loss: The quantization loss aims to learn a unified semantic representation and generate high-quality, distinguishable hash codes. It is mathematically formulated as follows:", + "bbox": [ + 89, + 112, + 482, + 154 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {q u a n}} = \\frac {1}{N M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| b _ {i} ^ {v} - \\frac {1}{2} \\left(h _ {i} ^ {v} + f _ {i} ^ {v}\\right) \\right\\| _ {2} ^ {2} + \\left\\| b _ {i} ^ {p t} - \\frac {1}{2} \\left(h _ {i} ^ {p t} + f _ {i} ^ {p t}\\right) \\right\\| _ {2} ^ {2}\\right) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 171, + 482, + 203 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This loss function encourages the hash codes $b_{i}^{v}$ and $b_{i}^{pt}$ to closely approximate the average of the visual and textual feature representations, facilitating a unified and discriminative semantic embedding.", + "bbox": [ + 89, + 214, + 482, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2) Reconstruction Loss: The reconstruction loss seeks to enhance the representational capacity and retrieval performance of the hash codes by ensuring that the generated hash codes are more distinguishable and closely approximate the original semantic features. The loss is expressed as:", + "bbox": [ + 89, + 271, + 483, + 340 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| h _ {i} ^ {v} - b _ {i} ^ {v} \\right\\| _ {2} ^ {2} + \\left\\| h _ {i} ^ {p t} - b _ {i} ^ {p t} \\right\\| _ {2} ^ {2}\\right) \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 345, + 482, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The reconstruction loss minimizes the difference between the hash codes and their corresponding feature representations, promoting the generation of hash codes that effectively retain semantic information for accurate retrieval.", + "bbox": [ + 89, + 392, + 482, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, the total loss function for the proposed PromptHash method is computed as the weighted sum of the individual loss components, $\\alpha, \\beta, \\gamma, \\mu, \\sigma, \\zeta$ represent hyperparameters:", + "bbox": [ + 89, + 448, + 483, + 491 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\alpha \\mathcal {L} _ {\\mathrm {g p a}} + \\beta \\mathcal {L} _ {\\mathrm {l p a}} + \\gamma \\mathcal {L} _ {\\text {i n t e r}} \\tag {18} \\\\ + \\mu \\mathcal {L} _ {\\text {i n t r a}} + \\sigma \\mathcal {L} _ {\\text {q u a n}} + \\zeta \\mathcal {L} _ {\\text {r e c o n}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 494, + 482, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 540, + 223, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To rigorously evaluate the effectiveness of the proposed PromptHash method, we conducted extensive experiments on three widely used cross-modal multi-label retrieval datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. We compared PromptHash against twelve state-of-the-art cross-modal hashing retrieval methods, including DCMH [16], CMHH [3], GCDH [2], DCHMT [32], MITH [23], DSPH [14], TwDH [33], DNpH [26], DHaPH [15], CMCL [39], and VTPH [4]. All methods were tested under identical experimental conditions, with consistent dataset splits, retrieval, and query sets aligned with our experimental setup.", + "bbox": [ + 89, + 565, + 482, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The following sections provide a comprehensive analysis of the experimental results obtained from each of the eleven competing algorithms. Additionally, we offer detailed descriptions of the three datasets used for training and testing, outline the experimental procedures specific to PromptHash, and discuss the metrics used to assess its performance. The experimental environment specifications are also documented to ensure reproducibility and transparency.", + "bbox": [ + 89, + 717, + 483, + 829 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 837, + 192, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 presents an overview of the datasets used in our experiments and details their respective partitioning strategies. For our evaluations, we applied a consistent sampling strategy across the three", + "bbox": [ + 89, + 858, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "large-scale, multi-label datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. Each dataset was partitioned into training, testing, and retrieval sets. Image and text data were processed uniformly across all datasets: images were resized to an input resolution of $224 \\times 224$ pixels, while text data were encoded using byte pair encoding (BPE) before being input into the network.", + "bbox": [ + 511, + 90, + 905, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Details", + "text_level": 1, + "bbox": [ + 511, + 184, + 712, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this study, we employ CLIP-B16 as the backbone network, with experiments conducted on a single NVIDIA RTX 4090 GPU (24GB) using PyTorch V2.3.1. Input images across all datasets are resized to $224 \\times 224$ pixels. The learning rate is set to $1\\mathrm{e} - 6$ for the backbone network and $1\\mathrm{e} - 5$ for both the prompt model and fusion module, with a batch size of 128. The loss terms are defined as follows: $\\alpha$ represents the global prompt alignment loss, $\\beta$ denotes the local prompt alignment loss, $\\gamma$ indicates the inter-class affinity loss, $\\mu$ represents the intra-class affinity loss, $\\sigma$ denotes the quantization loss, and $\\zeta$ represents the reconstruction loss. For the MIRFLICKR-25K and NUS-WIDE datasets, these hyperparameters are set to 5.0, 5.0, 0.005, 5.0, 0.1, and 0.001, respectively. For the MS COCO dataset, the corresponding values are 5.0, 5.0, 0.005, 20.0, 1.0, and 0.001. Throughout all tables, bold typeface indicates the best performance, while underlined values represent the second-best results.", + "bbox": [ + 511, + 205, + 906, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct comprehensive ablation studies to systematically evaluate the effectiveness of each component in our proposed PromptHash framework, with results presented in Tab. 2. The experiments examine five distinct variants: (a) a baseline implementation utilizing only the CLIP feature extraction network and hash function, excluding TAAP, AGSF, and PACL modules; (b) PromptHash w/o (PACL + AGSF), which retains only the TAAP module; (c) PromptHash w/o (TAAP + PACL), maintaining only the AGSF module; (d) PromptHash w/o AGSF, preserving TAAP and PACL modules; and (e) PromptHash w/o PACL, retaining TAAP and AGSF modules.", + "bbox": [ + 511, + 429, + 908, + 580 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a8e90691e2ea46bb95a3177b344863927e00c215492b1d189dcb079a7f763d23.jpg", + "table_caption": [ + "Table 1. Summary of Feature Statistics for the Three Benchmark Datasets" + ], + "table_footnote": [], + "table_body": "
Dataset detailsMIRFLICKR-25KNUS-WIDEMS COCO
Dataset Size24581192779122218
Training Size100001050010000
Retrieval Size22581190679117218
Query Size200021005000
Number of Categories242180
", + "bbox": [ + 527, + 631, + 893, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Analysis of Experimental Results", + "text_level": 1, + "bbox": [ + 511, + 720, + 803, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 742, + 676, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The experimental results demonstrate that incorporating the TAAP module significantly enhances retrieval performance by effectively addressing text semantic truncation through adaptive weighting of original text semantic features, thereby preserving retrieval-relevant semantic information while minimizing the impact of irrelevant features. Implementation of the AGSF module reveals the effectiveness of cross-modal semantic fusion in selectively retaining beneficial semantic information while filtering out redundant contextual information. The combination of TAAP and PACL modules demonstrates that PACL's alignment of global and local", + "bbox": [ + 511, + 761, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19654", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0b39a16c866c6df38dc444318d9613b9497d0dc0ef09f093db2c604f00660098.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 88, + 227, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/82c8941a456cba94fd2ac77cf0b27440b3172f6c7e8f1ae829ee864a4e144953.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 89, + 362, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d72e4a605c28ff6aa707d7de3dc24ffd2e48b23da25493cce4dee557a24b831.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 90, + 496, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e46822a69577689c33a6fb24228dc22e3a933680e8c4962bd79f772f95f60ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 90, + 632, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2907f008048b09b16550860185315f80def21995c5b012e190c66a284108f852.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 90, + 766, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e12d4aaa8062cb14d8a3062ac97c50a1bf19380f82ba706183399e3021bbb20d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 90, + 900, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4915d63ba173e5f1c0068d1d28d89bc723e2e8279f5aa6766c125f46a949a0aa.jpg", + "image_caption": [ + "Figure 3. Ablation study results of six key hyperparameters $(\\alpha, \\beta, \\gamma, \\lambda, \\mu, \\nu)$ evaluated on three benchmark datasets (MIRFLICKR-25K, NUS-WIDE, and MS COCO)." + ], + "image_footnote": [], + "bbox": [ + 93, + 207, + 228, + 296 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/368f54402dc1948855372a739ce69275fe11c4f526a2328abe39af829dd4aa41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 209, + 362, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9a13e340cba41a5244c132505182f4b6e904c301c26fb01be2536f91cc46e33c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 209, + 496, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7cd186766ab8280499aef0cbe24f9c5633d592dfde5a2236f82df4141f8c9829.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 209, + 632, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cc401a172c2d53c39c386eb6a6dc1a8eebb8d6f981d5e6d23abade9bf12f34c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 209, + 767, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ae4c47773b5ea6a954c59a23d7eec664fe639ddae3d1d0c9ff0e97d39c521c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 209, + 903, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2011a8639e1dd5113515a9dc9c052a4c5e353ae2c307dbde6b415eb515211815.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 299, + 227, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/882a0250fdab842dd816e4697be81830e0d0d2fd0c6f94b78ca2d6e269d7258d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 299, + 362, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ea91ed8af515f068b0f7b1494c0fb269cb8d2dd30c536c8e637c5759b526aeaa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 299, + 496, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f8d3c42c05cb624e4203f84e7df59f1847f939b78ed97eb0cc4c7ddb1cfa787.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 299, + 632, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/15c02fb8261893d3688a22fbe5520a779817a85280e15bf536afcb958c8fc678.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 299, + 767, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ce7b2fb6e16ff8423ab3f91cd79fa0db12a8ecc77e5080deccbd781360e50eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 299, + 903, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17b38d7002fe7a92a7bbe21587b723839be77d001347182cbc6b16a8bf7d787d.jpg", + "image_caption": [ + "Figure 4. Precision-Recall curves of different hash code lengths (16, 32, and 64 bits) on three benchmark datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO." + ], + "image_footnote": [], + "bbox": [ + 93, + 391, + 227, + 478 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8451a076d48848ecab2cf979c944e7f35a9cbbce326399e47491a2e60964108b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 391, + 362, + 478 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0dd442dd161f7b7af985b428d79c4048eab9969a089f71b95138937fe6a09ee0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 391, + 496, + 478 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8af4f8a5bb0d92e10ca288fc985f9a4f8a9447b843aa8130e1934d95c2138859.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 391, + 632, + 478 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e136d5daba7d388a1c35da02a249839275cf2b5e817c0472ff98c92255aee0e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 391, + 767, + 478 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3d4e6b7e3ea66095b6b2c6a8cd61ba862cb10f13de65e4d0bd61017cc942eab0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 391, + 903, + 478 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/205cc49acdf2d16cc5bd5bc1b3ffb0c844053a8f1f3e12bff97df6481d54e6ce.jpg", + "table_caption": [ + "Table 2. Ablation study results of different components in the proposed method." + ], + "table_footnote": [], + "table_body": "
MethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bit16bit32bit64bit16bit32bit64bit
I2Tbaseline0.84440.85900.86660.72280.73770.74880.70990.75940.7793
w/o (PACL+AGSF)0.87670.88550.89080.82780.85550.86560.72220.79100.8207
w/o (TAAP+PACL)0.91390.92690.93290.76680.78380.78930.71170.76870.7933
w/o AGSF0.93460.95120.95930.83770.85840.87090.74240.81110.8444
w/o PACL0.97200.98590.99240.90130.94500.96390.72460.82280.8725
PromptHash(Ours)0.98180.99600.99950.93130.97590.99310.76730.87820.9263
T2Ibaseline0.83830.84880.85240.73030.74770.75880.72010.75950.7885
w/o (PACL+AGSF)0.85580.86410.87040.79960.82720.83380.72050.78040.8103
w/o (TAAP+PACL)0.91400.92760.93310.76960.78410.79020.71410.77550.7973
w/o AGSF0.94200.95910.96700.81570.83130.84600.75090.80920.8414
w/o PACL0.97200.98590.99250.90600.95170.96760.72270.82720.8731
PromptHash(Ours)0.98160.99550.99950.93810.97610.99340.76670.87900.9283
", + "bbox": [ + 138, + 547, + 859, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "prompt tokens optimizes prompt text semantics and original text semantics with image semantics as the center, resulting in high-quality hash codes. While results from PACL indicate that TAAP and AGSF modules substantially improve retrieval performance for high-bit hash codes, they are less effective for low-bit scenarios. Notably, the complete PromptHash framework, incorporating all three modules, successfully leverages their complementary strengths to enhance retrieval performance across all hash code lengths, validating the superiority of our designed modules.", + "bbox": [ + 89, + 766, + 482, + 891 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.2. Hyperparameter Analysis", + "text_level": 1, + "bbox": [ + 513, + 765, + 740, + 780 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct a comprehensive analysis of hyperparameters in our proposed PromptHash method, with results illustrated in Fig. 3 for the six hyperparameters in our overall objective function. The experimental results demonstrate optimal performance across all datasets when setting $\\{\\alpha = 5.0, \\beta = 5.0, \\gamma = 0.005, \\mu = 5.0, \\sigma = 0.1, \\zeta = 0.001\\}$ . Our analysis reveals that gradually increasing parameters while maintaining default values for others yields optimal mean Average Precision (mAP) across the three", + "bbox": [ + 511, + 789, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19655", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c4ebeee554201452bf9ccf207dca6914b50404751dae094ca509440c5afaa5e8.jpg", + "table_caption": [ + "Table 3. For the Mean Average Precision (MAP) evaluation on the MIRFLICKR25K, NUS-WIDE, and MS COCO datasets (MAP@ALL), the best performance is in bold, the second-best is underlined, and results from original papers are marked with an asterisk (*)." + ], + "table_footnote": [], + "table_body": "
NetworkMethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bitAvg16bit32bit64bitAvg16bit32bit64bitAvg
I2TCNNDCMH [16]0.72880.74110.74900.73960.52380.59950.61950.58090.51770.53110.54710.5320
CMHH [3]0.66490.66770.67310.66860.53120.54760.52990.53620.56570.55820.55400.5593
GCDH [2]0.79910.81230.82040.81060.71420.73670.74980.73360.72970.76510.79050.7618
CLIPDCHMT [32]0.82540.82840.82570.82650.68320.68920.70250.69160.64400.64650.65520.6486
MITH [23]0.83770.84910.85760.84810.70620.71800.71860.71430.71490.73730.75800.7367
DSPH [14]0.80810.83870.85050.83240.69530.70310.71610.70480.70490.75830.77280.7453
TwDH [33]0.77660.79150.80160.78990.66490.68550.69330.68120.65640.72070.74720.7081
DNpH [26]0.83990.84860.85000.84620.71350.71690.72470.71840.67540.68970.68620.6838
DHaPH [15]0.82710.83510.83240.83150.72150.73330.74100.73190.73100.74020.74960.7403
CMCL [39]0.84870.86110.86920.85970.71540.73140.74400.73030.74200.77010.79360.7686
VTPH* [4]0.90560.92490.93280.92110.77330.78700.79360.78460.72020.74770.77860.7488
PromptHash(Ours)0.98180.99600.99950.99240.93130.97590.99310.96680.76730.87820.92630.8573
T2ICNNDCMH [16]0.75200.76960.77760.76640.54400.59010.59560.57660.55100.58830.60500.5814
CMHH [3]0.66150.68510.69430.68030.48260.48680.47110.48020.50980.50710.50970.5089
GCDH [2]0.78490.80220.80670.79790.72150.74230.75340.73910.72610.76500.78850.7599
CLIPDCHMT [32]0.81150.81790.82000.81650.69200.70810.72080.70700.62820.63610.76740.6772
MITH [23]0.82880.84080.84830.83930.71220.72810.73350.72460.70450.73190.71680.7177
DSPH [14]0.79090.82150.83340.81530.70280.71650.73290.71740.70470.75520.75250.7375
TwDH [33]0.77580.78950.80300.78940.67190.71260.71530.69990.66030.72050.69900.6933
DNpH [26]0.81510.82490.83290.82430.72220.72650.73130.72670.65950.68010.69900.6795
DHaPH [15]0.80890.81700.81940.81510.72030.72840.73880.72920.69990.70370.79190.7318
CMCL [39]0.82900.83620.84020.83510.72900.74380.75110.74130.73960.76890.79620.7682
VTPH* [4]0.90200.92260.92780.91750.77080.78400.79330.78270.71850.75150.77430.7481
PromptHash(Ours)0.98160.99550.99950.99220.93810.97610.99340.96920.76670.87900.92830.8580
", + "bbox": [ + 94, + 127, + 906, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "datasets. However, reducing $\\sigma$ to 0.1 while simultaneously increasing $\\gamma$ results in decreased mAP performance. Furthermore, when attempting to optimize all hyperparameters independently for each dataset, the resulting average mAP values prove inferior to those achieved by solely reducing $\\sigma$ to 0.1. Additional experiments show that further reducing $\\sigma$ to 0.05 also leads to degraded average mAP performance. These findings suggest that maintaining default values for all hyperparameters except the quantization loss weight $\\sigma$ (set to 0.1) yields optimal average mAP across all three datasets. We hypothesize that this phenomenon occurs because PromptHash effectively aligns image-text features extracted by CLIP, resulting in high similarity between related image-text pairs and natural dissimilarity between unrelated pairs in the common Hamming space, thus requiring lower emphasis on quantization loss.", + "bbox": [ + 89, + 455, + 480, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.3. Comparison with State-of-the-Art", + "text_level": 1, + "bbox": [ + 89, + 672, + 372, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As demonstrated in Tab. 3, our proposed PromptHash method achieves superior performance across all metrics on three public datasets. Using the mAP@all metric as a primary indicator, we observe significant improvements over the previous state-of-the-art methods. On the MIRFLICKR-25K dataset, PromptHash outperforms the second-best method (VTPH) by margins of $7.13\\%$ and $7.47\\%$ for I2T and T2I tasks, respectively. For the NUS-WIDE dataset, we achieve even more substantial improvements over VTPH, with gains of $18.22\\%$ for I2T and $18.65\\%$ for T2I tasks. On the MS COCO dataset, our method surpasses the previous best performer (CMCL) by $8.87\\%$ and $8.98\\%$ for I2T and T2I tasks, respectively.", + "bbox": [ + 89, + 691, + 482, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Precision-Recall curves in Fig. 4 demonstrate particularly notable improvements on MIRFLICKR-25K and NUS-WIDE datasets, where PromptHash significantly outperforms ex", + "bbox": [ + 89, + 858, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "isting methods. This superior performance can be attributed to our method's effective handling of discrete word-based texts through affinity prompt learning and adaptive weighting modules, coupled with image-centric feature discrimination between foreground retrieval targets and background information. However, we observe relatively modest improvements on the MS COCO dataset, which we attribute to its unique characteristics: text annotations comprise complete sentences rather than discrete words, with annotations extending up to 625 words, of which only 3-5 words typically represent retrieval targets. This high noise data presents a particular challenge that could potentially be addressed in future work through text reconstruction.", + "bbox": [ + 511, + 455, + 906, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 638, + 633, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Most existing cross-modal hashing methods primarily focus on hashing function design and optimizing distances between different samples, while overlooking inherent issues within the sample sets themselves. Specifically, problems such as text semantic truncation and negative semantic information within the sample set can significantly limit retrieval performance.", + "bbox": [ + 511, + 664, + 903, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our proposed PromptHash framework addresses these limitations through two key innovations. First, it introduces prompt learning for adaptively weighted learning of truncated text semantics, effectively improving retrieval performance under limited character encoding constraints. Second, it combines SSM and Transformer architectures with adaptive gated selection fusion, enabling efficient filtering and weighting of fused features. Furthermore, our novel Prompt Affinity Contrastive Learning module (PACL) balances prompt, textual, and visual features while bridging modality heterogeneity through feature alignment, significantly enhancing retrieval accuracy.", + "bbox": [ + 511, + 748, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19656", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the Scientific and Technological Innovation 2030 Major Project under Grant 2022ZD0115800, the National Natural Science Foundation of China under Grant 62441213, and the Key Laboratory Open Projects in Xinjiang Uygur Autonomous Region under Grant 2023D04028.", + "bbox": [ + 89, + 114, + 483, + 184 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 196, + 187, + 213 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Cong Bai, Chao Zeng, Qing Ma, Jinglin Zhang, and Shengyong Chen. 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IEEE TKDE, 36(1): 239-260, 2024. 1" + ], + "bbox": [ + 514, + 92, + 903, + 244 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19658", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_model.json b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5624c1a839dd6bc8b8faca0f814751e0ebccf2c5 --- /dev/null +++ b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_model.json @@ -0,0 +1,2486 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.13, + 0.872, + 0.177 + ], + "angle": 0, + "content": "PromptHash: Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.321, + 0.204, + 0.676, + 0.222 + ], + "angle": 0, + "content": "Qiang Zou Shuli Cheng* Jiayi Chen" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.223, + 0.788, + 0.24 + ], + "angle": 0, + "content": "School of Computer Science and Technology, Xinjiang University, China" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.24, + 0.823, + 0.257 + ], + "angle": 0, + "content": "zouq@stu.xju.edu.cn cslxju@xju.edu.cn 107552203982@stu.xju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.324, + 0.486, + 0.764 + ], + "angle": 0, + "content": "Cross-modal hashing is a promising approach for efficient data retrieval and storage optimization. However, contemporary methods exhibit significant limitations in semantic preservation, contextual integrity, and information redundancy, which constrains retrieval efficacy. We present PromptHash, an innovative framework leveraging affinity prompt-aware collaborative learning for adaptive cross-modal hashing. We propose an end-to-end framework for affinity-prompted collaborative hashing, with the following fundamental technical contributions: (i) a text affinity prompt learning mechanism that preserves contextual information while maintaining parameter efficiency, (ii) an adaptive gated selection fusion architecture that synthesizes State Space Model with Transformer network for precise cross-modal feature integration, and (iii) a prompt affinity alignment strategy that bridges modal heterogeneity through hierarchical contrastive learning. To the best of our knowledge, this study presents the first investigation into affinity prompt awareness within collaborative cross-modal adaptive hash learning, establishing a paradigm for enhanced semantic consistency across modalities. Through comprehensive evaluation on three benchmark multi-label datasets, PromptHash demonstrates substantial performance improvements over existing approaches. Notably, on the NUS-WIDE dataset, our method achieves significant gains of \\(18.22\\%\\) and \\(18.65\\%\\) in image-to-text and text-to-image retrieval tasks, respectively. The code is publicly available at https://github.com/ShiShuMo/PromptHash." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.791, + 0.222, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.817, + 0.484, + 0.879 + ], + "angle": 0, + "content": "With the rapid proliferation of social media platforms, multimodal data has grown exponentially, making cross-modal retrieval an increasingly promising field with broad application prospects [29]." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.291, + 0.925, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.501, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Figure 1. Compare with existing frameworks. (a) Previous methods used dual Transformers for cross modal hashing contrastive learning. (b) We compare and learn images and texts separately by setting learnable affinity prompts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.856 + ], + "angle": 0, + "content": "However, the inherent modal heterogeneity of multimodal data presents significant challenges, indicating substantial room for improvement in both academic research and industrial applications of cross-modal retrieval [45]. Cross-modal hashing employs shared hash functions with strong representational capacities, mapping data from different modalities into a common hash space. As a result, data with similar semantic content across modalities can be mapped to proximate binary hash codes, effectively bridging the semantic gap between modalities and enabling rapid and accurate cross-modal data retrieval [1, 9, 12, 16, 17, 26, 31, 33, 41]. Existing cross-modal hashing methods are generally divided into unsupervised and supervised approaches, with supervised methods typically outperforming unsupervised ones by leveraging supervisory information, such as pairwise similarity matrices or semantic labels. Despite the considerable progress made in deep supervised cross-modal hashing, there are still fundamental challenges to address." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Recently, CLIP (Contrastive Language-Image Pretraining) [27] has emerged as a powerful backbone for cross-modal feature extraction in many hashing methods due to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.239, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19649" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "its strong zero-shot capabilities and alignment between visual and textual representations. However, adopting CLIP introduces several critical challenges that limit performance in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.153, + 0.485, + 0.59 + ], + "angle": 0, + "content": "A notable challenge is the context-length limitation in CLIP pre-trained models, where the current maximum context length is limited to 77 characters, whereas real-world text data often far exceeds this limit. This discrepancy leads to context loss and semantic truncation, especially when retrieving textual information. Furthermore, effectively fusing cross-modal features remains an open challenge, particularly in enhancing semantic feature weights relevant to retrieval while suppressing irrelevant information. For instance, the widely used MS COCO dataset [22] exemplifies this challenge, as its text lengths range from 169 to 625 characters, significantly exceeding CLIP's 77-character capacity for text encoding. To address the CLIP context-length limitation, our approach incorporates foreground target text into adaptive affinity prompts and implements a dynamic weighting mechanism between these prompts and the original text. This strategy effectively preserves critical semantic information while circumventing CLIP's 77-character constraint, enabling comprehensive processing of lengthy real-world texts without semantic truncation. Previous approaches have employed various methods to address this: the Bag-of-Words (BoW) model, which disregards contextual word relationships; pre-trained Transformer [36] models such as Vision Transformer(ViT) [7] and BERT [6], which still face truncation; and VTPH's [4] use of large language models [19, 25] to reconstruct text as prompts, although this method introduces significant computational overhead without fully resolving the semantic truncation issue." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.593, + 0.483, + 0.759 + ], + "angle": 0, + "content": "Another challenge lies in the feature fusion of different modalities, where existing cross-modal hashing methods often incorporate contrastive learning to capture intermodal consistency. However, benchmark datasets commonly used in cross-modal retrieval suffer from context loss and semantic redundancy, especially in textual representation. For example, the textual content in MIRFLICKR-25K [13] and NUS-WIDE [5] is generated through direct label concatenation, resulting in limited contextual depth. Additionally, MS COCO's text data, derived from merged manual descriptions, can introduce semantic redundancy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.76, + 0.483, + 0.88 + ], + "angle": 0, + "content": "To address these challenges, we propose a Adaptive Affinity-Prompted Collaborative Cross-Modal Learning (PromptHash) for Hashing Retrieval in Fig. 1. Ours framework that integrates text affinity prompts with State Space Model(SSM) and Transformer-based adaptive gated selection fusion, supported by a novel Prompt Affinity Contrastive Loss (PACL) to better align cross-modal semantics. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- To mitigate semantic truncation caused by CLIP's" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.092, + 0.905, + 0.196 + ], + "angle": 0, + "content": "context-length limitation, adaptive text prompts are introduced that incorporate foreground target text essential for retrieval. This approach implements a dynamic weighting mechanism between prompts and original text, effectively preserving critical semantic information while circumventing length constraints for improved retrieval performance." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.198, + 0.905, + 0.258 + ], + "angle": 0, + "content": "- The framework also incorporates an SSM-Transformer adaptive gated selection fusion module to refine cross-modal feature integration, preserving relevant semantic information while filtering out redundant content." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.258, + 0.905, + 0.331 + ], + "angle": 0, + "content": "- To balance prompt semantics with the original image-text semantics, a novel Prompt Affinity Contrastive Loss (PACL) is introduced, bridging modality heterogeneity and semantic gaps through global and local prompt contrast." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.333, + 0.905, + 0.393 + ], + "angle": 0, + "content": "- Extensive experiments on three benchmark datasets demonstrate that the proposed PromptHash framework significantly outperforms state-of-the-art methods, underscoring its effectiveness in cross-modal retrieval." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.198, + 0.905, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.411, + 0.655, + 0.426 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.437, + 0.762, + 0.453 + ], + "angle": 0, + "content": "2.1. Deep Cross-Modal Hashing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.905, + 0.534 + ], + "angle": 0, + "content": "Cross-modal hashing has made significant strides in information retrieval by mapping heterogeneous data into a unified Hamming space via hash functions. The literature typically categorizes approaches into unsupervised and supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.906, + 0.657 + ], + "angle": 0, + "content": "Unsupervised methods maintain semantic similarity without explicit supervision by leveraging cross-modal correlations. Notable works include DAEH [30] with deep adaptive enhancement, UKD's [10] teacher-student framework, and UCMFH's [40] CLIP-based feature extraction. Additionally, UCCH [11] addresses binary-continuous relaxation constraints, while NRCH [37] advances through robust contrastive loss and dynamic noise separation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.906, + 0.809 + ], + "angle": 0, + "content": "Supervised methods utilize label information to establish semantic consistency within a shared hash space. DCMH [16] pioneered end-to-end deep cross-modal hashing, followed by CMHH's [3] focal loss approach and AGAH's [9] adversarial learning with attention mechanisms. Recent innovations include DCHUC's [34] joint optimization, MIAN's [42] modality-invariant networks, and GCDH's [2] graph convolutional networks. DCHMT [32] and MITH [23] leverage CLIP for fine-grained feature extraction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Proxy learning has emerged as another significant direction, with DAPH's [35] data-aware networks, DSPH's [14] fine-grained semantic relations, and DHaPH's [15] hierarchical learning. Notable approaches also include CMCL's [39] multi-bit collaboration and VTPH's [4] large model optimization. Distinct from existing methods, we in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19650" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.138 + ], + "angle": 0, + "content": "tegrate both global and local prompt alignments while minimizing feature divergence to alleviate modality heterogeneity and semantic gaps." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.148, + 0.263, + 0.164 + ], + "angle": 0, + "content": "2.2. Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.17, + 0.483, + 0.321 + ], + "angle": 0, + "content": "Prompt learning originated in NLP, integrating handcrafted templates into input data for downstream tasks. Recent studies have extended this concept to vision-language models, with CoCoOp [43] introducing Conditional Context Optimization, MaPLe [18] implementing Multi-modal Prompt Learning, and CoPrompt [28] enhancing performance through consistency constraints. While PromptKD [20] explores Unsupervised Prompt Distillation, prompt learning's effectiveness in cross-modal hashing remains underexplored." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.332, + 0.293, + 0.348 + ], + "angle": 0, + "content": "2.3. Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.354, + 0.483, + 0.52 + ], + "angle": 0, + "content": "Contrastive learning has demonstrated substantial efficacy in feature representation by maximizing similarity between positive pairs while minimizing negative pair similarity. Several cross-modal hashing methods have adopted this paradigm: UCCH [11] pioneered unsupervised contrastive learning, UniHash [38] facilitates instance-level learning, and CMCL [39] optimizes through token alignment. However, existing methods often overlook explicit fine-grained token-level semantic alignment. Our work addresses this through prompt-based contrastive learning for both instance and token-level representations." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.531, + 0.277, + 0.547 + ], + "angle": 0, + "content": "2.4. State Space Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.483, + 0.81 + ], + "angle": 0, + "content": "While contrastive learning effectively aligns semantic representations across modalities, distinguishing between foreground (relevant) and background (irrelevant) information in multimodal contexts remains challenging. State Space Models (SSM) [8] offer a promising solution through their selective sequence modeling capabilities with linear computational complexity. Unlike Transformers that attend to all tokens equally, SSM's selective scan mechanism can dynamically focus on informative elements while filtering out noise. Vim [44] pioneered SSM in visual domains, demonstrating their ability to selectively process visual information. VMamba [24] extended this capability with 2D Selective Scanning that effectively separates foreground objects from background elements. Jamba [21] further showed how SSM's selective attention, when integrated with Transformer layers, enables more efficient sequence feature processing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Despite these advances, the potential of SSM, when combined with contrastive learning, to effectively address the foreground-background confusion problem in cross-modal hashing retrieval remains unexplored. Our work integrates these two paradigms, utilizing SSM for precise separation of foreground and background information and con" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.888, + 0.107 + ], + "angle": 0, + "content": "trastive mechanisms for accurate cross-modal alignment." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.121, + 0.649, + 0.138 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.146, + 0.807, + 0.161 + ], + "angle": 0, + "content": "3.1. Notations and Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.169, + 0.907, + 0.533 + ], + "angle": 0, + "content": "This paper adopts a framework analogous to conventional cross-modal hashing methodologies, utilizing image-text pairs as input modalities. Let \\(\\mathcal{O} = \\{o_i\\}_{i=1}^N\\) denote a collection of \\(N\\) training sample pairs, where each sample \\(o_i = (x_i^v, x_i^t, l_i, p_i)\\) comprises a visual feature vector \\(x_i^v \\in \\mathbb{R}^{d^v}\\), a textual feature vector \\(x_i^t \\in \\mathbb{R}^{d^t}\\), a multi-label annotation \\(l_i \\in \\{0, 1\\}^{1 \\times C}\\) (where \\(l_{i,c} = 1\\) if sample \\(o_i\\) belongs to category \\(c\\); otherwise, \\(l_{i,c} = 0\\)), and a prompt word \\(p_i\\). We construct a similarity matrix \\(S\\) where \\(S_{ij} = 1\\) if samples share at least one category, indicating semantic affinity; otherwise, \\(S_{ij} = 0\\). The primary objective is to project heterogeneous features into a unified \\(K\\)-bit Hamming space through two hashing functions: \\(b_i^v = H^v(f_i^v; \\theta^v) \\in \\{-1, +1\\}^K\\) and \\(b_i^{pt} = H^t(f_i^{pt}; \\theta^t) \\in \\{-1, +1\\}^K\\), where \\(b_i^v\\) and \\(b_i^{pt}\\) denote the hash codes for visual and textual modalities, while \\(\\theta^v\\) and \\(\\theta^t\\) represent the learnable parameters of the corresponding functions. Throughout this paper, \\(M\\) denotes the mini-batch size, and \\(D\\) represents the feature embedding dimension. We use \\(f\\) for initial feature representations (e.g., \\(f_i^v, f_i^t, f_i^p, f_i^{pt}\\)), \\(h\\) for continuous hash representations prior to quantization (e.g., \\(h_i^v, h_i^{pt}, h_i^p\\)), and \\(b\\) for binary hash codes (e.g., \\(b_i^v, b_i^{pt}\\)). For similarity metrics, \\(\\Theta_{ij}\\) represents prompt-visual similarity, \\(\\Phi_{ij}\\) denotes visual-prompt similarity, and \\(\\Omega_{ij}\\) indicates intra-modal prompt similarity." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.543, + 0.695, + 0.557 + ], + "angle": 0, + "content": "3.2. Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.565, + 0.907, + 0.793 + ], + "angle": 0, + "content": "Fig. 2 illustrates the detailed workflow of our proposed PromptHash framework. To leverage the latest advances in deep neural networks and Transformer-based models, we employ a two-branch Transformer architecture for the extraction of image and text features. Additionally, we introduce a dedicated Transformer network designed to extract prompt features, which are then used to compute prompt-weighted similarities. To further enhance the quality of the image and text representations, we utilize pretrained ViT and BERT as the visual encoder and text encoder, respectively. These models extract the image and text embeddings, denoted as \\( f_{i}^{v} = \\{G_{i}^{v}\\} \\in \\mathbb{R}^{L^{\\nu} \\times D} \\) and \\( f_{i}^{t} = \\{G_{i}^{t}\\} \\in \\mathbb{R}^{L^{t} \\times D} \\). Similarly, the constructed masked fused prompt embeddings, denoted as \\( f_{i}^{pt} = \\{G_{i}^{p}\\} \\in \\mathbb{R}^{L^{p} \\times D} \\), are used to represent the fused prompt." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.804, + 0.84, + 0.82 + ], + "angle": 0, + "content": "3.3. Text Affinity-Aware Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In cross-modal hashing tasks, negative textual features can significantly degrade retrieval performance by hindering the effective distinction between foreground and background information. To address this issue, we propose a Text Affinity-Aware Prompt (TAAP) module, which dynami-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19651" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.905, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.414, + 0.907, + 0.511 + ], + "angle": 0, + "content": "Figure 2. Overall Framework of PromptHash. Our framework consists of five key components: 1) Image and Text Encoders for modality-specific feature extraction; 2) Adaptive Gated State Selection and Fusion Module for feature filtering and cross-modal fusion between image features and hybrid prompt-enhanced textual features; 3) Text Affinity-Aware Prompting that dynamically learns and distinguishes retrieval-beneficial foreground information while optimizing textual feature representations through dynamic prompting mechanisms; 4) Cross-Modal Prompt Alignment Mechanism incorporating both global and local alignments, where global alignment facilitates image-to-text and image-to-prompt representation alignments with intra-class and inter-class affinity losses; 5) Hash Learning with quantization and reconstruction losses." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.531, + 0.483, + 0.576 + ], + "angle": 0, + "content": "cally learns and differentiates foreground information that aids retrieval, and optimizes textual feature representations through a dynamic prompt mechanism." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.577, + 0.483, + 0.697 + ], + "angle": 0, + "content": "Let \\( l_{i} \\) represent the category label set corresponding to image-text pairs \\( o_{i} \\) and \\( o_{t} \\). We generate prompt text using a template: \"This is an image containing {class_name_i}\", where {class_name_i} corresponds to label \\( l_{i} \\). The complete prompt text is formulated as \\( \\text{prompt}_i = \\) \"This is an image containing {class_name_i}\" which is then tokenized using Byte Pair Encoding (BPE): token_prompt_i = Tokenizer(prompt_i)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.483, + 0.734 + ], + "angle": 0, + "content": "The token sequence is encoded into an embedding vector \\(p_i\\): \\(p_i = \\text{embed}(\\text{token\\_prompt}_i)\\), \\(p_i \\in \\mathbb{R}^D\\) (1)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.741, + 0.483, + 0.769 + ], + "angle": 0, + "content": "where \\(D\\) denotes CLIP's embedding dimension. Then \\(f_{i}^{p}\\) combines this with a learnable context vector \\(C_{\\mathrm{ctx}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.244, + 0.775, + 0.483, + 0.79 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {p} = p _ {i} + C _ {\\mathrm {c t x}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.797, + 0.483, + 0.879 + ], + "angle": 0, + "content": "This dynamic prompt mechanism enables effective distinction between foreground and background features through a learnable mask, optimizing the feature representation for retrieval tasks. The generated prompt features \\( f_{i}^{p} \\) are then processed by the TAAP module's Transformer encoder layers, fusing them with the original text features \\( f_{i}^{t} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.88, + 0.483, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\widetilde {f} _ {i} ^ {p} = \\text {T r a n s f o r m e r L a y e r} \\left(f _ {i} ^ {p}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.532, + 0.905, + 0.56 + ], + "angle": 0, + "content": "Finally, we obtain the weighted feature representation through element-wise multiplication and global average pooling:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.563, + 0.905, + 0.582 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {p t} = \\left(\\widehat {f} _ {i} ^ {p} \\times f _ {i} ^ {t}\\right) \\otimes \\eta , \\quad f _ {i} ^ {p t} \\in \\mathbb {R} ^ {D} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.906, + 0.656 + ], + "angle": 0, + "content": "where \\(\\eta\\) represent learnable weight, respectively, with \\(\\otimes\\) denoting matrix multiplication. This integration process effectively preserves foreground information while suppressing background noise, significantly improving cross-modal hashing retrieval performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.665, + 0.884, + 0.681 + ], + "angle": 0, + "content": "3.4. Adaptive Gated State Space Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.686, + 0.906, + 0.797 + ], + "angle": 0, + "content": "In this work, we integrate the State Space Model (SSM) with adaptive gating mechanisms to design an adaptive filtering feature fusion module, which we refer to as the Adaptive Gated State Space Fusion Module(AGSF). The textual features are weighted through the aforementioned prompt learning module, yielding a refined textual feature representation. However, image features must also undergo filtering and fusion with the resulting mixed prompt-text features. This process is formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.801, + 0.905, + 0.826 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {\\mathrm {c l s} _ {m}} = \\operatorname {S i L U} \\left(\\operatorname {M L P} \\left(\\operatorname {G R N} \\left(f _ {i} ^ {m}\\right)\\right)\\right) \\mid m \\in \\{v, p t \\}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.821, + 0.741, + 0.839 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {\\text {f u s i o n}} = \\operatorname {C o n c a t} \\left(f _ {i} ^ {\\mathrm {c l s} _ {v}}, f _ {i} ^ {\\mathrm {c l s} _ {p t}}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.845, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where Concat represents the concatenation operation, GRN denotes Global Response Normalization, MLP refers to a multi-layer perceptron, and SiLU is the activation function. In the Global Response Normalization (GRN) layer, for input \\( x \\in \\mathbb{R}^{B \\times N \\times D} \\), the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19652" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.093, + 0.483, + 0.121 + ], + "angle": 0, + "content": "L2 norm \\( G_{x} \\) and normalization factor \\( N_{x} \\) are computed sequentially:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.128, + 0.483, + 0.172 + ], + "angle": 0, + "content": "\\[\nG _ {x} = \\| x \\| _ {2} = \\sqrt {\\sum_ {d = 1} ^ {D} x _ {d} ^ {2}}, \\quad N _ {x} = \\frac {G _ {x}}{\\frac {1}{N} \\sum_ {i = 1} ^ {N} G _ {x i}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.183, + 0.414, + 0.197 + ], + "angle": 0, + "content": "The final output with learnable parameters \\(\\lambda\\) and \\(\\kappa\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.207, + 0.483, + 0.221 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G R N} (x) = \\lambda \\cdot \\left(x \\cdot N _ {x}\\right) + \\kappa + x \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.233, + 0.483, + 0.26 + ], + "angle": 0, + "content": "After obtaining the fused features, they are fed into the SSM adaptive selection module, expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.268, + 0.483, + 0.288 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {\\text {f l i p} _ {\\text {a x i s}} = \\psi} = \\operatorname {F l i p} _ {\\text {a x i s}} ^ {T} (\\operatorname {S S M} (\\operatorname {F l i p} _ {\\text {a x i s}} = \\psi (f _ {i} ^ {\\text {f u s i o n}}))) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.298, + 0.484, + 0.399 + ], + "angle": 0, + "content": "where \\(\\psi \\in \\{1,2,(1,2)\\}\\). Here, \\(\\mathrm{Flip}_{\\mathrm{axis} = \\psi}\\) denotes a flipping operation along different axes, and \\(\\mathrm{Flip}^T\\) represents its inverse. The term SSM refers to the State Space Model. After obtaining the final three features, we apply an adaptive weighted filtering process. The parameter \\(\\tau\\) serves as a learnable temperature coefficient, which balances the relative importance of the four features derived from flipped and unflipped orientations:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.406, + 0.483, + 0.437 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {\\mathrm {f i t}} = \\theta \\tau \\sum_ {j \\in \\omega} f _ {i} ^ {\\mathrm {f l i p} _ {\\mathrm {a x i s} = j}} + (1 - \\theta) f _ {i} ^ {\\text {f u s i o n}}, \\omega = \\{1, 2, (1, 2) \\} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.447, + 0.484, + 0.489 + ], + "angle": 0, + "content": "Where, \\(\\theta\\) denotes a set of learnable parameters. The filtered features are subsequently passed through a Transformer encoder layer, yielding:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.497, + 0.483, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\widetilde {f _ {i} ^ {v}}, \\widetilde {f _ {i} ^ {\\mathrm {p t}}} = \\operatorname {S p l i t} \\left(\\operatorname {T r a n s f o r m e r L a y e r} \\left(\\operatorname {M L P} \\left(f _ {i} ^ {\\mathrm {f i t}}\\right)\\right)\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.53, + 0.484, + 0.645 + ], + "angle": 0, + "content": "The resulting features \\(\\widetilde{f_i^v}\\) and \\(\\widetilde{f_i^{\\mathrm{pt}}}\\) represent the outputs obtained through the adaptive SSM gating and selection fusion module. Here, Split denotes an operation that separates the individual visual and textual features from the fused representation. Through the aforementioned operations, we simultaneously adaptively filter and dynamically weight redundant information in both images and text, significantly enhancing the quality and effectiveness of retrieval." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.655, + 0.442, + 0.672 + ], + "angle": 0, + "content": "3.5. Prompt Alignment Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.678, + 0.484, + 0.76 + ], + "angle": 0, + "content": "To effectively bridge the semantic gaps between different modalities, we propose prompt alignment contrastive learning (PACL), a learning mechanism that enables fine-grained alignment between modalities. This mechanism operates through two key components: cross-modal prompt alignment and affinity-aware loss function." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.77, + 0.364, + 0.786 + ], + "angle": 0, + "content": "3.5.1. Cross-Modal Prompt Alignment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.789, + 0.483, + 0.857 + ], + "angle": 0, + "content": "To further mitigate heterogeneity and semantic gaps, we leverage contrastive learning to explicitly align the fine-grained semantic concept representations. Our alignment strategy comprises two key components: global-local prompt alignment and affinity-aware loss functions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.859, + 0.484, + 0.9 + ], + "angle": 0, + "content": "For global prompt alignment, we adopt symmetric InfoNCE losses to align image representations with textual and prompt representations:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.089, + 0.906, + 0.151 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i} ^ {a \\rightarrow b} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {i} ^ {b}} / \\tau_ {1}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {c} ^ {b}} / \\tau_ {1}\\right)} \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.152, + 0.778, + 0.199 + ], + "angle": 0, + "content": "\\[\n\\mathcal{L}_{\\mathrm{gpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{a,b\\in \\{v,pt\\} \\\\ a\\neq b}}\\mathcal{L}_{i}^{a\\to b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.214, + 0.907, + 0.256 + ], + "angle": 0, + "content": "where \\(\\tau_{1}\\) is a temperature hyperparameter, and the subscript \\(c\\) indexes over all samples in the batch. Here, \\(a, b \\in \\{v, pt\\}, a \\neq b\\), corresponding to visual and textual features." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.257, + 0.906, + 0.285 + ], + "angle": 0, + "content": "For local prompt alignment, we employ a dynamic temperature mechanism adjusted by modality distributions:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.294, + 0.906, + 0.325 + ], + "angle": 0, + "content": "\\[\n\\tau_ {2} = \\tau \\times \\frac {1}{1 + \\mathrm {J S - d i v} \\left(f _ {i} ^ {v} , f _ {i} ^ {p}\\right)} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.336, + 0.907, + 0.39 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the base temperature and JS-div measures the Jensen-Shannon divergence between modality distributions. Here, \\(\\tau\\) and \\(\\tau_{1}\\) denote the temperature hyperparameters with a default value of 0.07." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.393, + 0.835, + 0.407 + ], + "angle": 0, + "content": "The local alignment losses are then formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.416, + 0.905, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i} ^ {e \\rightarrow f} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {i} ^ {f}} / \\tau_ {2}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {c} ^ {f}} / \\tau_ {2}\\right)} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.481, + 0.774, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\mathcal{L}_{\\mathrm{lpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{e,f\\in \\{v,p\\} \\\\ e\\neq f}}\\mathcal{L}_{i}^{e\\to f}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.541, + 0.907, + 0.583 + ], + "angle": 0, + "content": "where \\( e, f \\in \\{v, p\\} \\), \\( e \\neq f \\), corresponding to visual and prompt features. \\( \\tau \\) and \\( \\tau_1 \\) denote the temperature hyperparameters with a default value of 0.07." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.594, + 0.767, + 0.609 + ], + "angle": 0, + "content": "3.5.2. Affinity-Aware Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.642 + ], + "angle": 0, + "content": "To preserve semantic consistency, we design inter-class and intra-class affinity losses:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.653, + 0.906, + 0.692 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n t e r}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\sum_ {k = 1} ^ {Q} \\left(S _ {i j} k - \\log \\left(1 + e ^ {\\Theta_ {i j}}\\right)\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.705, + 0.906, + 0.793 + ], + "angle": 0, + "content": "where \\(Q \\in \\{\\Theta_{ij}, \\Phi_{ij}\\}\\), \\(\\Theta_{ij} \\neq \\Phi_{ij}\\), \\(\\Theta_{ij} = \\frac{1}{2} (h_i^p)^T h_j^v\\) and \\(\\Phi_{ij} = \\frac{1}{2} (h_i^v)^T h_j^p\\) denote cross-modal similarities, where \\(h_i^p\\) and \\(h_j^v\\) represent the real-valued hash codes of prompt and visual features respectively, before passing through the sign function, \\(N\\) is the number of samples, and \\(S_{ij} \\in \\{0, 1\\}\\) is the ground truth similarity matrix." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.795, + 0.778, + 0.808 + ], + "angle": 0, + "content": "The intra-class affinity loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.819, + 0.905, + 0.857 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n t r a}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\left(\\mathcal {S} _ {i j} \\Omega_ {i j} - \\log \\left(1 + e ^ {\\Omega_ {i j}}\\right)\\right) \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(\\Omega_{ij} = \\frac{1}{2}\\left(h_i^p\\right)^T h_j^p\\) represents intra-modal similarity between prompt features." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19653" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.268, + 0.108 + ], + "angle": 0, + "content": "3.6. Hashing Learning" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.113, + 0.483, + 0.155 + ], + "angle": 0, + "content": "1) Quantization Loss: The quantization loss aims to learn a unified semantic representation and generate high-quality, distinguishable hash codes. It is mathematically formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.172, + 0.483, + 0.204 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {q u a n}} = \\frac {1}{N M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| b _ {i} ^ {v} - \\frac {1}{2} \\left(h _ {i} ^ {v} + f _ {i} ^ {v}\\right) \\right\\| _ {2} ^ {2} + \\left\\| b _ {i} ^ {p t} - \\frac {1}{2} \\left(h _ {i} ^ {p t} + f _ {i} ^ {p t}\\right) \\right\\| _ {2} ^ {2}\\right) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.215, + 0.483, + 0.271 + ], + "angle": 0, + "content": "This loss function encourages the hash codes \\( b_{i}^{v} \\) and \\( b_{i}^{pt} \\) to closely approximate the average of the visual and textual feature representations, facilitating a unified and discriminative semantic embedding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.272, + 0.484, + 0.342 + ], + "angle": 0, + "content": "2) Reconstruction Loss: The reconstruction loss seeks to enhance the representational capacity and retrieval performance of the hash codes by ensuring that the generated hash codes are more distinguishable and closely approximate the original semantic features. The loss is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.346, + 0.483, + 0.383 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c o n}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| h _ {i} ^ {v} - b _ {i} ^ {v} \\right\\| _ {2} ^ {2} + \\left\\| h _ {i} ^ {p t} - b _ {i} ^ {p t} \\right\\| _ {2} ^ {2}\\right) \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.393, + 0.483, + 0.447 + ], + "angle": 0, + "content": "The reconstruction loss minimizes the difference between the hash codes and their corresponding feature representations, promoting the generation of hash codes that effectively retain semantic information for accurate retrieval." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.449, + 0.484, + 0.492 + ], + "angle": 0, + "content": "Finally, the total loss function for the proposed PromptHash method is computed as the weighted sum of the individual loss components, \\(\\alpha, \\beta, \\gamma, \\mu, \\sigma, \\zeta\\) represent hyperparameters:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.496, + 0.483, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\alpha \\mathcal {L} _ {\\mathrm {g p a}} + \\beta \\mathcal {L} _ {\\mathrm {l p a}} + \\gamma \\mathcal {L} _ {\\text {i n t e r}} \\tag {18} \\\\ + \\mu \\mathcal {L} _ {\\text {i n t r a}} + \\sigma \\mathcal {L} _ {\\text {q u a n}} + \\zeta \\mathcal {L} _ {\\text {r e c o n}} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.541, + 0.224, + 0.558 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.566, + 0.483, + 0.717 + ], + "angle": 0, + "content": "To rigorously evaluate the effectiveness of the proposed PromptHash method, we conducted extensive experiments on three widely used cross-modal multi-label retrieval datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. We compared PromptHash against twelve state-of-the-art cross-modal hashing retrieval methods, including DCMH [16], CMHH [3], GCDH [2], DCHMT [32], MITH [23], DSPH [14], TwDH [33], DNpH [26], DHaPH [15], CMCL [39], and VTPH [4]. All methods were tested under identical experimental conditions, with consistent dataset splits, retrieval, and query sets aligned with our experimental setup." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.484, + 0.83 + ], + "angle": 0, + "content": "The following sections provide a comprehensive analysis of the experimental results obtained from each of the eleven competing algorithms. Additionally, we offer detailed descriptions of the three datasets used for training and testing, outline the experimental procedures specific to PromptHash, and discuss the metrics used to assess its performance. The experimental environment specifications are also documented to ensure reproducibility and transparency." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.838, + 0.193, + 0.853 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.859, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Tab. 1 presents an overview of the datasets used in our experiments and details their respective partitioning strategies. For our evaluations, we applied a consistent sampling strategy across the three" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.177 + ], + "angle": 0, + "content": "large-scale, multi-label datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. Each dataset was partitioned into training, testing, and retrieval sets. Image and text data were processed uniformly across all datasets: images were resized to an input resolution of \\(224 \\times 224\\) pixels, while text data were encoded using byte pair encoding (BPE) before being input into the network." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.185, + 0.714, + 0.201 + ], + "angle": 0, + "content": "4.2. Experimental Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.207, + 0.907, + 0.428 + ], + "angle": 0, + "content": "In this study, we employ CLIP-B16 as the backbone network, with experiments conducted on a single NVIDIA RTX 4090 GPU (24GB) using PyTorch V2.3.1. Input images across all datasets are resized to \\(224 \\times 224\\) pixels. The learning rate is set to \\(1\\mathrm{e} - 6\\) for the backbone network and \\(1\\mathrm{e} - 5\\) for both the prompt model and fusion module, with a batch size of 128. The loss terms are defined as follows: \\(\\alpha\\) represents the global prompt alignment loss, \\(\\beta\\) denotes the local prompt alignment loss, \\(\\gamma\\) indicates the inter-class affinity loss, \\(\\mu\\) represents the intra-class affinity loss, \\(\\sigma\\) denotes the quantization loss, and \\(\\zeta\\) represents the reconstruction loss. For the MIRFLICKR-25K and NUS-WIDE datasets, these hyperparameters are set to 5.0, 5.0, 0.005, 5.0, 0.1, and 0.001, respectively. For the MS COCO dataset, the corresponding values are 5.0, 5.0, 0.005, 20.0, 1.0, and 0.001. Throughout all tables, bold typeface indicates the best performance, while underlined values represent the second-best results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.43, + 0.909, + 0.581 + ], + "angle": 0, + "content": "We conduct comprehensive ablation studies to systematically evaluate the effectiveness of each component in our proposed PromptHash framework, with results presented in Tab. 2. The experiments examine five distinct variants: (a) a baseline implementation utilizing only the CLIP feature extraction network and hash function, excluding TAAP, AGSF, and PACL modules; (b) PromptHash w/o (PACL + AGSF), which retains only the TAAP module; (c) PromptHash w/o (TAAP + PACL), maintaining only the AGSF module; (d) PromptHash w/o AGSF, preserving TAAP and PACL modules; and (e) PromptHash w/o PACL, retaining TAAP and AGSF modules." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.593, + 0.907, + 0.62 + ], + "angle": 0, + "content": "Table 1. Summary of Feature Statistics for the Three Benchmark Datasets" + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.632, + 0.895, + 0.703 + ], + "angle": 0, + "content": "
Dataset detailsMIRFLICKR-25KNUS-WIDEMS COCO
Dataset Size24581192779122218
Training Size100001050010000
Retrieval Size22581190679117218
Query Size200021005000
Number of Categories242180
" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.722, + 0.805, + 0.739 + ], + "angle": 0, + "content": "4.3. Analysis of Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.743, + 0.677, + 0.758 + ], + "angle": 0, + "content": "4.3.1. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The experimental results demonstrate that incorporating the TAAP module significantly enhances retrieval performance by effectively addressing text semantic truncation through adaptive weighting of original text semantic features, thereby preserving retrieval-relevant semantic information while minimizing the impact of irrelevant features. Implementation of the AGSF module reveals the effectiveness of cross-modal semantic fusion in selectively retaining beneficial semantic information while filtering out redundant contextual information. The combination of TAAP and PACL modules demonstrates that PACL's alignment of global and local" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19654" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.089, + 0.228, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.232, + 0.09, + 0.363, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.091, + 0.498, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.091, + 0.633, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.091, + 0.767, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.091, + 0.901, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.178, + 0.907, + 0.204 + ], + "angle": 0, + "content": "Figure 3. Ablation study results of six key hyperparameters \\((\\alpha, \\beta, \\gamma, \\lambda, \\mu, \\nu)\\) evaluated on three benchmark datasets (MIRFLICKR-25K, NUS-WIDE, and MS COCO)." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.208, + 0.229, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.21, + 0.364, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.21, + 0.498, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.21, + 0.633, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.21, + 0.768, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.21, + 0.904, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.3, + 0.228, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.3, + 0.364, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.3, + 0.498, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.3, + 0.633, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.3, + 0.768, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.3, + 0.904, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.392, + 0.228, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.392, + 0.364, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.392, + 0.498, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.392, + 0.633, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.392, + 0.768, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.392, + 0.904, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.491, + 0.907, + 0.518 + ], + "angle": 0, + "content": "Figure 4. Precision-Recall curves of different hash code lengths (16, 32, and 64 bits) on three benchmark datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO." + }, + { + "type": "table_caption", + "bbox": [ + 0.26, + 0.523, + 0.735, + 0.538 + ], + "angle": 0, + "content": "Table 2. Ablation study results of different components in the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.139, + 0.548, + 0.86, + 0.748 + ], + "angle": 0, + "content": "
MethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bit16bit32bit64bit16bit32bit64bit
I2Tbaseline0.84440.85900.86660.72280.73770.74880.70990.75940.7793
w/o (PACL+AGSF)0.87670.88550.89080.82780.85550.86560.72220.79100.8207
w/o (TAAP+PACL)0.91390.92690.93290.76680.78380.78930.71170.76870.7933
w/o AGSF0.93460.95120.95930.83770.85840.87090.74240.81110.8444
w/o PACL0.97200.98590.99240.90130.94500.96390.72460.82280.8725
PromptHash(Ours)0.98180.99600.99950.93130.97590.99310.76730.87820.9263
T2Ibaseline0.83830.84880.85240.73030.74770.75880.72010.75950.7885
w/o (PACL+AGSF)0.85580.86410.87040.79960.82720.83380.72050.78040.8103
w/o (TAAP+PACL)0.91400.92760.93310.76960.78410.79020.71410.77550.7973
w/o AGSF0.94200.95910.96700.81570.83130.84600.75090.80920.8414
w/o PACL0.97200.98590.99250.90600.95170.96760.72270.82720.8731
PromptHash(Ours)0.98160.99550.99950.93810.97610.99340.76670.87900.9283
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.483, + 0.892 + ], + "angle": 0, + "content": "prompt tokens optimizes prompt text semantics and original text semantics with image semantics as the center, resulting in high-quality hash codes. While results from PACL indicate that TAAP and AGSF modules substantially improve retrieval performance for high-bit hash codes, they are less effective for low-bit scenarios. Notably, the complete PromptHash framework, incorporating all three modules, successfully leverages their complementary strengths to enhance retrieval performance across all hash code lengths, validating the superiority of our designed modules." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.766, + 0.741, + 0.781 + ], + "angle": 0, + "content": "4.3.2. Hyperparameter Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.79, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We conduct a comprehensive analysis of hyperparameters in our proposed PromptHash method, with results illustrated in Fig. 3 for the six hyperparameters in our overall objective function. The experimental results demonstrate optimal performance across all datasets when setting \\(\\{\\alpha = 5.0, \\beta = 5.0, \\gamma = 0.005, \\mu = 5.0, \\sigma = 0.1, \\zeta = 0.001\\}\\). Our analysis reveals that gradually increasing parameters while maintaining default values for others yields optimal mean Average Precision (mAP) across the three" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19655" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.09, + 0.905, + 0.118 + ], + "angle": 0, + "content": "Table 3. For the Mean Average Precision (MAP) evaluation on the MIRFLICKR25K, NUS-WIDE, and MS COCO datasets (MAP@ALL), the best performance is in bold, the second-best is underlined, and results from original papers are marked with an asterisk (*)." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.128, + 0.907, + 0.439 + ], + "angle": 0, + "content": "
NetworkMethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bitAvg16bit32bit64bitAvg16bit32bit64bitAvg
I2TCNNDCMH [16]0.72880.74110.74900.73960.52380.59950.61950.58090.51770.53110.54710.5320
CMHH [3]0.66490.66770.67310.66860.53120.54760.52990.53620.56570.55820.55400.5593
GCDH [2]0.79910.81230.82040.81060.71420.73670.74980.73360.72970.76510.79050.7618
CLIPDCHMT [32]0.82540.82840.82570.82650.68320.68920.70250.69160.64400.64650.65520.6486
MITH [23]0.83770.84910.85760.84810.70620.71800.71860.71430.71490.73730.75800.7367
DSPH [14]0.80810.83870.85050.83240.69530.70310.71610.70480.70490.75830.77280.7453
TwDH [33]0.77660.79150.80160.78990.66490.68550.69330.68120.65640.72070.74720.7081
DNpH [26]0.83990.84860.85000.84620.71350.71690.72470.71840.67540.68970.68620.6838
DHaPH [15]0.82710.83510.83240.83150.72150.73330.74100.73190.73100.74020.74960.7403
CMCL [39]0.84870.86110.86920.85970.71540.73140.74400.73030.74200.77010.79360.7686
VTPH* [4]0.90560.92490.93280.92110.77330.78700.79360.78460.72020.74770.77860.7488
PromptHash(Ours)0.98180.99600.99950.99240.93130.97590.99310.96680.76730.87820.92630.8573
T2ICNNDCMH [16]0.75200.76960.77760.76640.54400.59010.59560.57660.55100.58830.60500.5814
CMHH [3]0.66150.68510.69430.68030.48260.48680.47110.48020.50980.50710.50970.5089
GCDH [2]0.78490.80220.80670.79790.72150.74230.75340.73910.72610.76500.78850.7599
CLIPDCHMT [32]0.81150.81790.82000.81650.69200.70810.72080.70700.62820.63610.76740.6772
MITH [23]0.82880.84080.84830.83930.71220.72810.73350.72460.70450.73190.71680.7177
DSPH [14]0.79090.82150.83340.81530.70280.71650.73290.71740.70470.75520.75250.7375
TwDH [33]0.77580.78950.80300.78940.67190.71260.71530.69990.66030.72050.69900.6933
DNpH [26]0.81510.82490.83290.82430.72220.72650.73130.72670.65950.68010.69900.6795
DHaPH [15]0.80890.81700.81940.81510.72030.72840.73880.72920.69990.70370.79190.7318
CMCL [39]0.82900.83620.84020.83510.72900.74380.75110.74130.73960.76890.79620.7682
VTPH* [4]0.90200.92260.92780.91750.77080.78400.79330.78270.71850.75150.77430.7481
PromptHash(Ours)0.98160.99550.99950.99220.93810.97610.99340.96920.76670.87900.92830.8580
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.482, + 0.664 + ], + "angle": 0, + "content": "datasets. However, reducing \\(\\sigma\\) to 0.1 while simultaneously increasing \\(\\gamma\\) results in decreased mAP performance. Furthermore, when attempting to optimize all hyperparameters independently for each dataset, the resulting average mAP values prove inferior to those achieved by solely reducing \\(\\sigma\\) to 0.1. Additional experiments show that further reducing \\(\\sigma\\) to 0.05 also leads to degraded average mAP performance. These findings suggest that maintaining default values for all hyperparameters except the quantization loss weight \\(\\sigma\\) (set to 0.1) yields optimal average mAP across all three datasets. We hypothesize that this phenomenon occurs because PromptHash effectively aligns image-text features extracted by CLIP, resulting in high similarity between related image-text pairs and natural dissimilarity between unrelated pairs in the common Hamming space, thus requiring lower emphasis on quantization loss." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.673, + 0.373, + 0.688 + ], + "angle": 0, + "content": "4.3.3. Comparison with State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.692, + 0.483, + 0.858 + ], + "angle": 0, + "content": "As demonstrated in Tab. 3, our proposed PromptHash method achieves superior performance across all metrics on three public datasets. Using the mAP@all metric as a primary indicator, we observe significant improvements over the previous state-of-the-art methods. On the MIRFLICKR-25K dataset, PromptHash outperforms the second-best method (VTPH) by margins of \\(7.13\\%\\) and \\(7.47\\%\\) for I2T and T2I tasks, respectively. For the NUS-WIDE dataset, we achieve even more substantial improvements over VTPH, with gains of \\(18.22\\%\\) for I2T and \\(18.65\\%\\) for T2I tasks. On the MS COCO dataset, our method surpasses the previous best performer (CMCL) by \\(8.87\\%\\) and \\(8.98\\%\\) for I2T and T2I tasks, respectively." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.859, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The Precision-Recall curves in Fig. 4 demonstrate particularly notable improvements on MIRFLICKR-25K and NUS-WIDE datasets, where PromptHash significantly outperforms ex" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.907, + 0.624 + ], + "angle": 0, + "content": "isting methods. This superior performance can be attributed to our method's effective handling of discrete word-based texts through affinity prompt learning and adaptive weighting modules, coupled with image-centric feature discrimination between foreground retrieval targets and background information. However, we observe relatively modest improvements on the MS COCO dataset, which we attribute to its unique characteristics: text annotations comprise complete sentences rather than discrete words, with annotations extending up to 625 words, of which only 3-5 words typically represent retrieval targets. This high noise data presents a particular challenge that could potentially be addressed in future work through text reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.639, + 0.634, + 0.655 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.665, + 0.905, + 0.748 + ], + "angle": 0, + "content": "Most existing cross-modal hashing methods primarily focus on hashing function design and optimizing distances between different samples, while overlooking inherent issues within the sample sets themselves. Specifically, problems such as text semantic truncation and negative semantic information within the sample set can significantly limit retrieval performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Our proposed PromptHash framework addresses these limitations through two key innovations. First, it introduces prompt learning for adaptively weighted learning of truncated text semantics, effectively improving retrieval performance under limited character encoding constraints. Second, it combines SSM and Transformer architectures with adaptive gated selection fusion, enabling efficient filtering and weighting of fused features. Furthermore, our novel Prompt Affinity Contrastive Learning module (PACL) balances prompt, textual, and visual features while bridging modality heterogeneity through feature alignment, significantly enhancing retrieval accuracy." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19656" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.185 + ], + "angle": 0, + "content": "This work was supported by the Scientific and Technological Innovation 2030 Major Project under Grant 2022ZD0115800, the National Natural Science Foundation of China under Grant 62441213, and the Key Laboratory Open Projects in Xinjiang Uygur Autonomous Region under Grant 2023D04028." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.198, + 0.188, + 0.214 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.223, + 0.484, + 0.265 + ], + "angle": 0, + "content": "[1] Cong Bai, Chao Zeng, Qing Ma, Jinglin Zhang, and Shengyong Chen. 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IEEE TKDE, 36(1): 239-260, 2024. 1" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.093, + 0.905, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19658" + } + ] +] \ No newline at end of file diff --git a/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_origin.pdf b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7cc3f2e1b71a073cfde80bd1d2e832d2fe30db12 --- /dev/null +++ b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/64d85235-28eb-4b3d-9010-9b6834181937_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f3e30281710b8ffd76f84050648c811d3912bcc6017e37f09048a47a07d4d9cc +size 7327744 diff --git a/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/full.md b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e3a6bbc6850e0e9936383452a2aff355f3a0b272 --- /dev/null +++ b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/full.md @@ -0,0 +1,403 @@ +# PromptHash: Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval + +Qiang Zou Shuli Cheng* Jiayi Chen + +School of Computer Science and Technology, Xinjiang University, China + +zouq@stu.xju.edu.cn cslxju@xju.edu.cn 107552203982@stu.xju.edu.cn + +# Abstract + +Cross-modal hashing is a promising approach for efficient data retrieval and storage optimization. However, contemporary methods exhibit significant limitations in semantic preservation, contextual integrity, and information redundancy, which constrains retrieval efficacy. We present PromptHash, an innovative framework leveraging affinity prompt-aware collaborative learning for adaptive cross-modal hashing. We propose an end-to-end framework for affinity-prompted collaborative hashing, with the following fundamental technical contributions: (i) a text affinity prompt learning mechanism that preserves contextual information while maintaining parameter efficiency, (ii) an adaptive gated selection fusion architecture that synthesizes State Space Model with Transformer network for precise cross-modal feature integration, and (iii) a prompt affinity alignment strategy that bridges modal heterogeneity through hierarchical contrastive learning. To the best of our knowledge, this study presents the first investigation into affinity prompt awareness within collaborative cross-modal adaptive hash learning, establishing a paradigm for enhanced semantic consistency across modalities. Through comprehensive evaluation on three benchmark multi-label datasets, PromptHash demonstrates substantial performance improvements over existing approaches. Notably, on the NUS-WIDE dataset, our method achieves significant gains of $18.22\%$ and $18.65\%$ in image-to-text and text-to-image retrieval tasks, respectively. The code is publicly available at https://github.com/ShiShuMo/PromptHash. + +# 1. Introduction + +With the rapid proliferation of social media platforms, multimodal data has grown exponentially, making cross-modal retrieval an increasingly promising field with broad application prospects [29]. + +![](images/7d191359806e6d9d2478b06266e79bbf034a8b9c62e05d99d16d7f311248c62b.jpg) +Figure 1. Compare with existing frameworks. (a) Previous methods used dual Transformers for cross modal hashing contrastive learning. (b) We compare and learn images and texts separately by setting learnable affinity prompts. + +However, the inherent modal heterogeneity of multimodal data presents significant challenges, indicating substantial room for improvement in both academic research and industrial applications of cross-modal retrieval [45]. Cross-modal hashing employs shared hash functions with strong representational capacities, mapping data from different modalities into a common hash space. As a result, data with similar semantic content across modalities can be mapped to proximate binary hash codes, effectively bridging the semantic gap between modalities and enabling rapid and accurate cross-modal data retrieval [1, 9, 12, 16, 17, 26, 31, 33, 41]. Existing cross-modal hashing methods are generally divided into unsupervised and supervised approaches, with supervised methods typically outperforming unsupervised ones by leveraging supervisory information, such as pairwise similarity matrices or semantic labels. Despite the considerable progress made in deep supervised cross-modal hashing, there are still fundamental challenges to address. + +Recently, CLIP (Contrastive Language-Image Pretraining) [27] has emerged as a powerful backbone for cross-modal feature extraction in many hashing methods due to + +its strong zero-shot capabilities and alignment between visual and textual representations. However, adopting CLIP introduces several critical challenges that limit performance in real-world applications. + +A notable challenge is the context-length limitation in CLIP pre-trained models, where the current maximum context length is limited to 77 characters, whereas real-world text data often far exceeds this limit. This discrepancy leads to context loss and semantic truncation, especially when retrieving textual information. Furthermore, effectively fusing cross-modal features remains an open challenge, particularly in enhancing semantic feature weights relevant to retrieval while suppressing irrelevant information. For instance, the widely used MS COCO dataset [22] exemplifies this challenge, as its text lengths range from 169 to 625 characters, significantly exceeding CLIP's 77-character capacity for text encoding. To address the CLIP context-length limitation, our approach incorporates foreground target text into adaptive affinity prompts and implements a dynamic weighting mechanism between these prompts and the original text. This strategy effectively preserves critical semantic information while circumventing CLIP's 77-character constraint, enabling comprehensive processing of lengthy real-world texts without semantic truncation. Previous approaches have employed various methods to address this: the Bag-of-Words (BoW) model, which disregards contextual word relationships; pre-trained Transformer [36] models such as Vision Transformer(ViT) [7] and BERT [6], which still face truncation; and VTPH's [4] use of large language models [19, 25] to reconstruct text as prompts, although this method introduces significant computational overhead without fully resolving the semantic truncation issue. + +Another challenge lies in the feature fusion of different modalities, where existing cross-modal hashing methods often incorporate contrastive learning to capture intermodal consistency. However, benchmark datasets commonly used in cross-modal retrieval suffer from context loss and semantic redundancy, especially in textual representation. For example, the textual content in MIRFLICKR-25K [13] and NUS-WIDE [5] is generated through direct label concatenation, resulting in limited contextual depth. Additionally, MS COCO's text data, derived from merged manual descriptions, can introduce semantic redundancy. + +To address these challenges, we propose a Adaptive Affinity-Prompted Collaborative Cross-Modal Learning (PromptHash) for Hashing Retrieval in Fig. 1. Ours framework that integrates text affinity prompts with State Space Model(SSM) and Transformer-based adaptive gated selection fusion, supported by a novel Prompt Affinity Contrastive Loss (PACL) to better align cross-modal semantics. Our contributions can be summarized as follows: + +- To mitigate semantic truncation caused by CLIP's + +context-length limitation, adaptive text prompts are introduced that incorporate foreground target text essential for retrieval. This approach implements a dynamic weighting mechanism between prompts and original text, effectively preserving critical semantic information while circumventing length constraints for improved retrieval performance. + +- The framework also incorporates an SSM-Transformer adaptive gated selection fusion module to refine cross-modal feature integration, preserving relevant semantic information while filtering out redundant content. +- To balance prompt semantics with the original image-text semantics, a novel Prompt Affinity Contrastive Loss (PACL) is introduced, bridging modality heterogeneity and semantic gaps through global and local prompt contrast. +- Extensive experiments on three benchmark datasets demonstrate that the proposed PromptHash framework significantly outperforms state-of-the-art methods, underscoring its effectiveness in cross-modal retrieval. + +# 2. Related Work + +# 2.1. Deep Cross-Modal Hashing + +Cross-modal hashing has made significant strides in information retrieval by mapping heterogeneous data into a unified Hamming space via hash functions. The literature typically categorizes approaches into unsupervised and supervised methods. + +Unsupervised methods maintain semantic similarity without explicit supervision by leveraging cross-modal correlations. Notable works include DAEH [30] with deep adaptive enhancement, UKD's [10] teacher-student framework, and UCMFH's [40] CLIP-based feature extraction. Additionally, UCCH [11] addresses binary-continuous relaxation constraints, while NRCH [37] advances through robust contrastive loss and dynamic noise separation. + +Supervised methods utilize label information to establish semantic consistency within a shared hash space. DCMH [16] pioneered end-to-end deep cross-modal hashing, followed by CMHH's [3] focal loss approach and AGAH's [9] adversarial learning with attention mechanisms. Recent innovations include DCHUC's [34] joint optimization, MIAN's [42] modality-invariant networks, and GCDH's [2] graph convolutional networks. DCHMT [32] and MITH [23] leverage CLIP for fine-grained feature extraction. + +Proxy learning has emerged as another significant direction, with DAPH's [35] data-aware networks, DSPH's [14] fine-grained semantic relations, and DHaPH's [15] hierarchical learning. Notable approaches also include CMCL's [39] multi-bit collaboration and VTPH's [4] large model optimization. Distinct from existing methods, we in + +tegrate both global and local prompt alignments while minimizing feature divergence to alleviate modality heterogeneity and semantic gaps. + +# 2.2. Prompt Learning + +Prompt learning originated in NLP, integrating handcrafted templates into input data for downstream tasks. Recent studies have extended this concept to vision-language models, with CoCoOp [43] introducing Conditional Context Optimization, MaPLe [18] implementing Multi-modal Prompt Learning, and CoPrompt [28] enhancing performance through consistency constraints. While PromptKD [20] explores Unsupervised Prompt Distillation, prompt learning's effectiveness in cross-modal hashing remains underexplored. + +# 2.3. Contrastive Learning + +Contrastive learning has demonstrated substantial efficacy in feature representation by maximizing similarity between positive pairs while minimizing negative pair similarity. Several cross-modal hashing methods have adopted this paradigm: UCCH [11] pioneered unsupervised contrastive learning, UniHash [38] facilitates instance-level learning, and CMCL [39] optimizes through token alignment. However, existing methods often overlook explicit fine-grained token-level semantic alignment. Our work addresses this through prompt-based contrastive learning for both instance and token-level representations. + +# 2.4. State Space Models + +While contrastive learning effectively aligns semantic representations across modalities, distinguishing between foreground (relevant) and background (irrelevant) information in multimodal contexts remains challenging. State Space Models (SSM) [8] offer a promising solution through their selective sequence modeling capabilities with linear computational complexity. Unlike Transformers that attend to all tokens equally, SSM's selective scan mechanism can dynamically focus on informative elements while filtering out noise. Vim [44] pioneered SSM in visual domains, demonstrating their ability to selectively process visual information. VMamba [24] extended this capability with 2D Selective Scanning that effectively separates foreground objects from background elements. Jamba [21] further showed how SSM's selective attention, when integrated with Transformer layers, enables more efficient sequence feature processing. + +Despite these advances, the potential of SSM, when combined with contrastive learning, to effectively address the foreground-background confusion problem in cross-modal hashing retrieval remains unexplored. Our work integrates these two paradigms, utilizing SSM for precise separation of foreground and background information and con + +trastive mechanisms for accurate cross-modal alignment. + +# 3. Methodology + +# 3.1. Notations and Problem Definition + +This paper adopts a framework analogous to conventional cross-modal hashing methodologies, utilizing image-text pairs as input modalities. Let $\mathcal{O} = \{o_i\}_{i=1}^N$ denote a collection of $N$ training sample pairs, where each sample $o_i = (x_i^v, x_i^t, l_i, p_i)$ comprises a visual feature vector $x_i^v \in \mathbb{R}^{d^v}$ , a textual feature vector $x_i^t \in \mathbb{R}^{d^t}$ , a multi-label annotation $l_i \in \{0, 1\}^{1 \times C}$ (where $l_{i,c} = 1$ if sample $o_i$ belongs to category $c$ ; otherwise, $l_{i,c} = 0$ ), and a prompt word $p_i$ . We construct a similarity matrix $S$ where $S_{ij} = 1$ if samples share at least one category, indicating semantic affinity; otherwise, $S_{ij} = 0$ . The primary objective is to project heterogeneous features into a unified $K$ -bit Hamming space through two hashing functions: $b_i^v = H^v(f_i^v; \theta^v) \in \{-1, +1\}^K$ and $b_i^{pt} = H^t(f_i^{pt}; \theta^t) \in \{-1, +1\}^K$ , where $b_i^v$ and $b_i^{pt}$ denote the hash codes for visual and textual modalities, while $\theta^v$ and $\theta^t$ represent the learnable parameters of the corresponding functions. Throughout this paper, $M$ denotes the mini-batch size, and $D$ represents the feature embedding dimension. We use $f$ for initial feature representations (e.g., $f_i^v, f_i^t, f_i^p, f_i^{pt}$ ), $h$ for continuous hash representations prior to quantization (e.g., $h_i^v, h_i^{pt}, h_i^p$ ), and $b$ for binary hash codes (e.g., $b_i^v, b_i^{pt}$ ). For similarity metrics, $\Theta_{ij}$ represents prompt-visual similarity, $\Phi_{ij}$ denotes visual-prompt similarity, and $\Omega_{ij}$ indicates intra-modal prompt similarity. + +# 3.2. Feature Extraction + +Fig. 2 illustrates the detailed workflow of our proposed PromptHash framework. To leverage the latest advances in deep neural networks and Transformer-based models, we employ a two-branch Transformer architecture for the extraction of image and text features. Additionally, we introduce a dedicated Transformer network designed to extract prompt features, which are then used to compute prompt-weighted similarities. To further enhance the quality of the image and text representations, we utilize pretrained ViT and BERT as the visual encoder and text encoder, respectively. These models extract the image and text embeddings, denoted as $f_{i}^{v} = \{G_{i}^{v}\} \in \mathbb{R}^{L^{\nu} \times D}$ and $f_{i}^{t} = \{G_{i}^{t}\} \in \mathbb{R}^{L^{t} \times D}$ . Similarly, the constructed masked fused prompt embeddings, denoted as $f_{i}^{pt} = \{G_{i}^{p}\} \in \mathbb{R}^{L^{p} \times D}$ , are used to represent the fused prompt. + +# 3.3. Text Affinity-Aware Prompt Learning + +In cross-modal hashing tasks, negative textual features can significantly degrade retrieval performance by hindering the effective distinction between foreground and background information. To address this issue, we propose a Text Affinity-Aware Prompt (TAAP) module, which dynami- + +![](images/66af3efc14c7d701d2ea5d9a0588863154e48277e9363921a82c808afcca603b.jpg) +Figure 2. Overall Framework of PromptHash. Our framework consists of five key components: 1) Image and Text Encoders for modality-specific feature extraction; 2) Adaptive Gated State Selection and Fusion Module for feature filtering and cross-modal fusion between image features and hybrid prompt-enhanced textual features; 3) Text Affinity-Aware Prompting that dynamically learns and distinguishes retrieval-beneficial foreground information while optimizing textual feature representations through dynamic prompting mechanisms; 4) Cross-Modal Prompt Alignment Mechanism incorporating both global and local alignments, where global alignment facilitates image-to-text and image-to-prompt representation alignments with intra-class and inter-class affinity losses; 5) Hash Learning with quantization and reconstruction losses. + +cally learns and differentiates foreground information that aids retrieval, and optimizes textual feature representations through a dynamic prompt mechanism. + +Let $l_{i}$ represent the category label set corresponding to image-text pairs $o_{i}$ and $o_{t}$ . We generate prompt text using a template: "This is an image containing {class_name_i}", where {class_name_i} corresponds to label $l_{i}$ . The complete prompt text is formulated as $\text{prompt}_i =$ "This is an image containing {class_name_i}" which is then tokenized using Byte Pair Encoding (BPE): token_prompt_i = Tokenizer(prompt_i). + +The token sequence is encoded into an embedding vector $p_i$ : $p_i = \text{embed}(\text{token\_prompt}_i)$ , $p_i \in \mathbb{R}^D$ (1) + +where $D$ denotes CLIP's embedding dimension. Then $f_{i}^{p}$ combines this with a learnable context vector $C_{\mathrm{ctx}}$ : + +$$ +f _ {i} ^ {p} = p _ {i} + C _ {\mathrm {c t x}} \tag {2} +$$ + +This dynamic prompt mechanism enables effective distinction between foreground and background features through a learnable mask, optimizing the feature representation for retrieval tasks. The generated prompt features $f_{i}^{p}$ are then processed by the TAAP module's Transformer encoder layers, fusing them with the original text features $f_{i}^{t}$ : + +$$ +\widetilde {f} _ {i} ^ {p} = \text {T r a n s f o r m e r L a y e r} \left(f _ {i} ^ {p}\right) \tag {3} +$$ + +Finally, we obtain the weighted feature representation through element-wise multiplication and global average pooling: + +$$ +f _ {i} ^ {p t} = \left(\widehat {f} _ {i} ^ {p} \times f _ {i} ^ {t}\right) \otimes \eta , \quad f _ {i} ^ {p t} \in \mathbb {R} ^ {D} \tag {4} +$$ + +where $\eta$ represent learnable weight, respectively, with $\otimes$ denoting matrix multiplication. This integration process effectively preserves foreground information while suppressing background noise, significantly improving cross-modal hashing retrieval performance. + +# 3.4. Adaptive Gated State Space Fusion Module + +In this work, we integrate the State Space Model (SSM) with adaptive gating mechanisms to design an adaptive filtering feature fusion module, which we refer to as the Adaptive Gated State Space Fusion Module(AGSF). The textual features are weighted through the aforementioned prompt learning module, yielding a refined textual feature representation. However, image features must also undergo filtering and fusion with the resulting mixed prompt-text features. This process is formalized as follows: + +$$ +f _ {i} ^ {\mathrm {c l s} _ {m}} = \operatorname {S i L U} \left(\operatorname {M L P} \left(\operatorname {G R N} \left(f _ {i} ^ {m}\right)\right)\right) \mid m \in \{v, p t \} +$$ + +$$ +f _ {i} ^ {\text {f u s i o n}} = \operatorname {C o n c a t} \left(f _ {i} ^ {\mathrm {c l s} _ {v}}, f _ {i} ^ {\mathrm {c l s} _ {p t}}\right) +$$ + +where Concat represents the concatenation operation, GRN denotes Global Response Normalization, MLP refers to a multi-layer perceptron, and SiLU is the activation function. In the Global Response Normalization (GRN) layer, for input $x \in \mathbb{R}^{B \times N \times D}$ , the + +L2 norm $G_{x}$ and normalization factor $N_{x}$ are computed sequentially: + +$$ +G _ {x} = \| x \| _ {2} = \sqrt {\sum_ {d = 1} ^ {D} x _ {d} ^ {2}}, \quad N _ {x} = \frac {G _ {x}}{\frac {1}{N} \sum_ {i = 1} ^ {N} G _ {x i}} \tag {6} +$$ + +The final output with learnable parameters $\lambda$ and $\kappa$ is: + +$$ +\operatorname {G R N} (x) = \lambda \cdot \left(x \cdot N _ {x}\right) + \kappa + x \tag {7} +$$ + +After obtaining the fused features, they are fed into the SSM adaptive selection module, expressed as: + +$$ +f _ {i} ^ {\text {f l i p} _ {\text {a x i s}} = \psi} = \operatorname {F l i p} _ {\text {a x i s}} ^ {T} (\operatorname {S S M} (\operatorname {F l i p} _ {\text {a x i s}} = \psi (f _ {i} ^ {\text {f u s i o n}}))) \tag {8} +$$ + +where $\psi \in \{1,2,(1,2)\}$ . Here, $\mathrm{Flip}_{\mathrm{axis} = \psi}$ denotes a flipping operation along different axes, and $\mathrm{Flip}^T$ represents its inverse. The term SSM refers to the State Space Model. After obtaining the final three features, we apply an adaptive weighted filtering process. The parameter $\tau$ serves as a learnable temperature coefficient, which balances the relative importance of the four features derived from flipped and unflipped orientations: + +$$ +f _ {i} ^ {\mathrm {f i t}} = \theta \tau \sum_ {j \in \omega} f _ {i} ^ {\mathrm {f l i p} _ {\mathrm {a x i s} = j}} + (1 - \theta) f _ {i} ^ {\text {f u s i o n}}, \omega = \{1, 2, (1, 2) \} \tag {9} +$$ + +Where, $\theta$ denotes a set of learnable parameters. The filtered features are subsequently passed through a Transformer encoder layer, yielding: + +$$ +\widetilde {f _ {i} ^ {v}}, \widetilde {f _ {i} ^ {\mathrm {p t}}} = \operatorname {S p l i t} \left(\operatorname {T r a n s f o r m e r L a y e r} \left(\operatorname {M L P} \left(f _ {i} ^ {\mathrm {f i t}}\right)\right)\right) \tag {10} +$$ + +The resulting features $\widetilde{f_i^v}$ and $\widetilde{f_i^{\mathrm{pt}}}$ represent the outputs obtained through the adaptive SSM gating and selection fusion module. Here, Split denotes an operation that separates the individual visual and textual features from the fused representation. Through the aforementioned operations, we simultaneously adaptively filter and dynamically weight redundant information in both images and text, significantly enhancing the quality and effectiveness of retrieval. + +# 3.5. Prompt Alignment Contrastive Learning + +To effectively bridge the semantic gaps between different modalities, we propose prompt alignment contrastive learning (PACL), a learning mechanism that enables fine-grained alignment between modalities. This mechanism operates through two key components: cross-modal prompt alignment and affinity-aware loss function. + +# 3.5.1. Cross-Modal Prompt Alignment + +To further mitigate heterogeneity and semantic gaps, we leverage contrastive learning to explicitly align the fine-grained semantic concept representations. Our alignment strategy comprises two key components: global-local prompt alignment and affinity-aware loss functions. + +For global prompt alignment, we adopt symmetric InfoNCE losses to align image representations with textual and prompt representations: + +$$ +\mathcal {L} _ {i} ^ {a \rightarrow b} = - \log \frac {\exp \left(\left(\widetilde {f _ {i} ^ {a}}\right) ^ {T} \widetilde {f _ {i} ^ {b}} / \tau_ {1}\right)}{\sum_ {c = 1} ^ {M} \exp \left(\left(\widetilde {f _ {i} ^ {a}}\right) ^ {T} \widetilde {f _ {c} ^ {b}} / \tau_ {1}\right)} \tag {11} +$$ + +$$ +\mathcal{L}_{\mathrm{gpa}} = \frac{1}{M}\sum_{i = 1}^{M}\sum_{\substack{a,b\in \{v,pt\} \\ a\neq b}}\mathcal{L}_{i}^{a\to b} +$$ + +where $\tau_{1}$ is a temperature hyperparameter, and the subscript $c$ indexes over all samples in the batch. Here, $a, b \in \{v, pt\}, a \neq b$ , corresponding to visual and textual features. + +For local prompt alignment, we employ a dynamic temperature mechanism adjusted by modality distributions: + +$$ +\tau_ {2} = \tau \times \frac {1}{1 + \mathrm {J S - d i v} \left(f _ {i} ^ {v} , f _ {i} ^ {p}\right)} \tag {12} +$$ + +where $\tau$ is the base temperature and JS-div measures the Jensen-Shannon divergence between modality distributions. Here, $\tau$ and $\tau_{1}$ denote the temperature hyperparameters with a default value of 0.07. + +The local alignment losses are then formulated as: + +$$ +\mathcal {L} _ {i} ^ {e \rightarrow f} = - \log \frac {\exp \left(\left(\widetilde {f _ {i} ^ {e}}\right) ^ {T} \widetilde {f _ {i} ^ {f}} / \tau_ {2}\right)}{\sum_ {c = 1} ^ {M} \exp \left(\left(\widetilde {f _ {i} ^ {e}}\right) ^ {T} \widetilde {f _ {c} ^ {f}} / \tau_ {2}\right)} \tag {13} +$$ + +$$ +\mathcal{L}_{\mathrm{lpa}} = \frac{1}{M}\sum_{i = 1}^{M}\sum_{\substack{e,f\in \{v,p\} \\ e\neq f}}\mathcal{L}_{i}^{e\to f} +$$ + +where $e, f \in \{v, p\}$ , $e \neq f$ , corresponding to visual and prompt features. $\tau$ and $\tau_1$ denote the temperature hyperparameters with a default value of 0.07. + +# 3.5.2. Affinity-Aware Loss Function + +To preserve semantic consistency, we design inter-class and intra-class affinity losses: + +$$ +\mathcal {L} _ {\text {i n t e r}} = - \frac {1}{M N} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {M} \sum_ {k = 1} ^ {Q} \left(S _ {i j} k - \log \left(1 + e ^ {\Theta_ {i j}}\right)\right) \tag {14} +$$ + +where $Q \in \{\Theta_{ij}, \Phi_{ij}\}$ , $\Theta_{ij} \neq \Phi_{ij}$ , $\Theta_{ij} = \frac{1}{2} (h_i^p)^T h_j^v$ and $\Phi_{ij} = \frac{1}{2} (h_i^v)^T h_j^p$ denote cross-modal similarities, where $h_i^p$ and $h_j^v$ represent the real-valued hash codes of prompt and visual features respectively, before passing through the sign function, $N$ is the number of samples, and $S_{ij} \in \{0, 1\}$ is the ground truth similarity matrix. + +The intra-class affinity loss is defined as: + +$$ +\mathcal {L} _ {\text {i n t r a}} = - \frac {1}{M N} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {M} \left(\mathcal {S} _ {i j} \Omega_ {i j} - \log \left(1 + e ^ {\Omega_ {i j}}\right)\right) \tag {15} +$$ + +where $\Omega_{ij} = \frac{1}{2}\left(h_i^p\right)^T h_j^p$ represents intra-modal similarity between prompt features. + +# 3.6. Hashing Learning + +1) Quantization Loss: The quantization loss aims to learn a unified semantic representation and generate high-quality, distinguishable hash codes. It is mathematically formulated as follows: + +$$ +\mathcal {L} _ {\text {q u a n}} = \frac {1}{N M} \sum_ {i = 1} ^ {M} \left(\left\| b _ {i} ^ {v} - \frac {1}{2} \left(h _ {i} ^ {v} + f _ {i} ^ {v}\right) \right\| _ {2} ^ {2} + \left\| b _ {i} ^ {p t} - \frac {1}{2} \left(h _ {i} ^ {p t} + f _ {i} ^ {p t}\right) \right\| _ {2} ^ {2}\right) \tag {16} +$$ + +This loss function encourages the hash codes $b_{i}^{v}$ and $b_{i}^{pt}$ to closely approximate the average of the visual and textual feature representations, facilitating a unified and discriminative semantic embedding. + +2) Reconstruction Loss: The reconstruction loss seeks to enhance the representational capacity and retrieval performance of the hash codes by ensuring that the generated hash codes are more distinguishable and closely approximate the original semantic features. The loss is expressed as: + +$$ +\mathcal {L} _ {\text {r e c o n}} = \frac {1}{M} \sum_ {i = 1} ^ {M} \left(\left\| h _ {i} ^ {v} - b _ {i} ^ {v} \right\| _ {2} ^ {2} + \left\| h _ {i} ^ {p t} - b _ {i} ^ {p t} \right\| _ {2} ^ {2}\right) \tag {17} +$$ + +The reconstruction loss minimizes the difference between the hash codes and their corresponding feature representations, promoting the generation of hash codes that effectively retain semantic information for accurate retrieval. + +Finally, the total loss function for the proposed PromptHash method is computed as the weighted sum of the individual loss components, $\alpha, \beta, \gamma, \mu, \sigma, \zeta$ represent hyperparameters: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {T o t a l}} = \alpha \mathcal {L} _ {\mathrm {g p a}} + \beta \mathcal {L} _ {\mathrm {l p a}} + \gamma \mathcal {L} _ {\text {i n t e r}} \tag {18} \\ + \mu \mathcal {L} _ {\text {i n t r a}} + \sigma \mathcal {L} _ {\text {q u a n}} + \zeta \mathcal {L} _ {\text {r e c o n}} \\ \end{array} +$$ + +# 4. Experiments + +To rigorously evaluate the effectiveness of the proposed PromptHash method, we conducted extensive experiments on three widely used cross-modal multi-label retrieval datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. We compared PromptHash against twelve state-of-the-art cross-modal hashing retrieval methods, including DCMH [16], CMHH [3], GCDH [2], DCHMT [32], MITH [23], DSPH [14], TwDH [33], DNpH [26], DHaPH [15], CMCL [39], and VTPH [4]. All methods were tested under identical experimental conditions, with consistent dataset splits, retrieval, and query sets aligned with our experimental setup. + +The following sections provide a comprehensive analysis of the experimental results obtained from each of the eleven competing algorithms. Additionally, we offer detailed descriptions of the three datasets used for training and testing, outline the experimental procedures specific to PromptHash, and discuss the metrics used to assess its performance. The experimental environment specifications are also documented to ensure reproducibility and transparency. + +# 4.1. Datasets + +Tab. 1 presents an overview of the datasets used in our experiments and details their respective partitioning strategies. For our evaluations, we applied a consistent sampling strategy across the three + +large-scale, multi-label datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. Each dataset was partitioned into training, testing, and retrieval sets. Image and text data were processed uniformly across all datasets: images were resized to an input resolution of $224 \times 224$ pixels, while text data were encoded using byte pair encoding (BPE) before being input into the network. + +# 4.2. Experimental Details + +In this study, we employ CLIP-B16 as the backbone network, with experiments conducted on a single NVIDIA RTX 4090 GPU (24GB) using PyTorch V2.3.1. Input images across all datasets are resized to $224 \times 224$ pixels. The learning rate is set to $1\mathrm{e} - 6$ for the backbone network and $1\mathrm{e} - 5$ for both the prompt model and fusion module, with a batch size of 128. The loss terms are defined as follows: $\alpha$ represents the global prompt alignment loss, $\beta$ denotes the local prompt alignment loss, $\gamma$ indicates the inter-class affinity loss, $\mu$ represents the intra-class affinity loss, $\sigma$ denotes the quantization loss, and $\zeta$ represents the reconstruction loss. For the MIRFLICKR-25K and NUS-WIDE datasets, these hyperparameters are set to 5.0, 5.0, 0.005, 5.0, 0.1, and 0.001, respectively. For the MS COCO dataset, the corresponding values are 5.0, 5.0, 0.005, 20.0, 1.0, and 0.001. Throughout all tables, bold typeface indicates the best performance, while underlined values represent the second-best results. + +We conduct comprehensive ablation studies to systematically evaluate the effectiveness of each component in our proposed PromptHash framework, with results presented in Tab. 2. The experiments examine five distinct variants: (a) a baseline implementation utilizing only the CLIP feature extraction network and hash function, excluding TAAP, AGSF, and PACL modules; (b) PromptHash w/o (PACL + AGSF), which retains only the TAAP module; (c) PromptHash w/o (TAAP + PACL), maintaining only the AGSF module; (d) PromptHash w/o AGSF, preserving TAAP and PACL modules; and (e) PromptHash w/o PACL, retaining TAAP and AGSF modules. + +Table 1. Summary of Feature Statistics for the Three Benchmark Datasets + +
Dataset detailsMIRFLICKR-25KNUS-WIDEMS COCO
Dataset Size24581192779122218
Training Size100001050010000
Retrieval Size22581190679117218
Query Size200021005000
Number of Categories242180
+ +# 4.3. Analysis of Experimental Results + +# 4.3.1. Ablation Studies + +The experimental results demonstrate that incorporating the TAAP module significantly enhances retrieval performance by effectively addressing text semantic truncation through adaptive weighting of original text semantic features, thereby preserving retrieval-relevant semantic information while minimizing the impact of irrelevant features. Implementation of the AGSF module reveals the effectiveness of cross-modal semantic fusion in selectively retaining beneficial semantic information while filtering out redundant contextual information. The combination of TAAP and PACL modules demonstrates that PACL's alignment of global and local + +![](images/0b39a16c866c6df38dc444318d9613b9497d0dc0ef09f093db2c604f00660098.jpg) + +![](images/82c8941a456cba94fd2ac77cf0b27440b3172f6c7e8f1ae829ee864a4e144953.jpg) + +![](images/4d72e4a605c28ff6aa707d7de3dc24ffd2e48b23da25493cce4dee557a24b831.jpg) + +![](images/0e46822a69577689c33a6fb24228dc22e3a933680e8c4962bd79f772f95f60ac.jpg) + +![](images/2907f008048b09b16550860185315f80def21995c5b012e190c66a284108f852.jpg) + +![](images/e12d4aaa8062cb14d8a3062ac97c50a1bf19380f82ba706183399e3021bbb20d.jpg) + +![](images/4915d63ba173e5f1c0068d1d28d89bc723e2e8279f5aa6766c125f46a949a0aa.jpg) +Figure 3. Ablation study results of six key hyperparameters $(\alpha, \beta, \gamma, \lambda, \mu, \nu)$ evaluated on three benchmark datasets (MIRFLICKR-25K, NUS-WIDE, and MS COCO). + +![](images/368f54402dc1948855372a739ce69275fe11c4f526a2328abe39af829dd4aa41.jpg) + +![](images/9a13e340cba41a5244c132505182f4b6e904c301c26fb01be2536f91cc46e33c.jpg) + +![](images/7cd186766ab8280499aef0cbe24f9c5633d592dfde5a2236f82df4141f8c9829.jpg) + +![](images/cc401a172c2d53c39c386eb6a6dc1a8eebb8d6f981d5e6d23abade9bf12f34c2.jpg) + +![](images/7ae4c47773b5ea6a954c59a23d7eec664fe639ddae3d1d0c9ff0e97d39c521c0.jpg) + +![](images/2011a8639e1dd5113515a9dc9c052a4c5e353ae2c307dbde6b415eb515211815.jpg) + +![](images/882a0250fdab842dd816e4697be81830e0d0d2fd0c6f94b78ca2d6e269d7258d.jpg) + +![](images/ea91ed8af515f068b0f7b1494c0fb269cb8d2dd30c536c8e637c5759b526aeaa.jpg) + +![](images/0f8d3c42c05cb624e4203f84e7df59f1847f939b78ed97eb0cc4c7ddb1cfa787.jpg) + +![](images/15c02fb8261893d3688a22fbe5520a779817a85280e15bf536afcb958c8fc678.jpg) + +![](images/7ce7b2fb6e16ff8423ab3f91cd79fa0db12a8ecc77e5080deccbd781360e50eb.jpg) + +![](images/17b38d7002fe7a92a7bbe21587b723839be77d001347182cbc6b16a8bf7d787d.jpg) +Figure 4. Precision-Recall curves of different hash code lengths (16, 32, and 64 bits) on three benchmark datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. + +![](images/8451a076d48848ecab2cf979c944e7f35a9cbbce326399e47491a2e60964108b.jpg) + +![](images/0dd442dd161f7b7af985b428d79c4048eab9969a089f71b95138937fe6a09ee0.jpg) + +![](images/8af4f8a5bb0d92e10ca288fc985f9a4f8a9447b843aa8130e1934d95c2138859.jpg) + +![](images/e136d5daba7d388a1c35da02a249839275cf2b5e817c0472ff98c92255aee0e4.jpg) + +![](images/3d4e6b7e3ea66095b6b2c6a8cd61ba862cb10f13de65e4d0bd61017cc942eab0.jpg) + +Table 2. Ablation study results of different components in the proposed method. + +
MethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bit16bit32bit64bit16bit32bit64bit
I2Tbaseline0.84440.85900.86660.72280.73770.74880.70990.75940.7793
w/o (PACL+AGSF)0.87670.88550.89080.82780.85550.86560.72220.79100.8207
w/o (TAAP+PACL)0.91390.92690.93290.76680.78380.78930.71170.76870.7933
w/o AGSF0.93460.95120.95930.83770.85840.87090.74240.81110.8444
w/o PACL0.97200.98590.99240.90130.94500.96390.72460.82280.8725
PromptHash(Ours)0.98180.99600.99950.93130.97590.99310.76730.87820.9263
T2Ibaseline0.83830.84880.85240.73030.74770.75880.72010.75950.7885
w/o (PACL+AGSF)0.85580.86410.87040.79960.82720.83380.72050.78040.8103
w/o (TAAP+PACL)0.91400.92760.93310.76960.78410.79020.71410.77550.7973
w/o AGSF0.94200.95910.96700.81570.83130.84600.75090.80920.8414
w/o PACL0.97200.98590.99250.90600.95170.96760.72270.82720.8731
PromptHash(Ours)0.98160.99550.99950.93810.97610.99340.76670.87900.9283
+ +prompt tokens optimizes prompt text semantics and original text semantics with image semantics as the center, resulting in high-quality hash codes. While results from PACL indicate that TAAP and AGSF modules substantially improve retrieval performance for high-bit hash codes, they are less effective for low-bit scenarios. Notably, the complete PromptHash framework, incorporating all three modules, successfully leverages their complementary strengths to enhance retrieval performance across all hash code lengths, validating the superiority of our designed modules. + +# 4.3.2. Hyperparameter Analysis + +We conduct a comprehensive analysis of hyperparameters in our proposed PromptHash method, with results illustrated in Fig. 3 for the six hyperparameters in our overall objective function. The experimental results demonstrate optimal performance across all datasets when setting $\{\alpha = 5.0, \beta = 5.0, \gamma = 0.005, \mu = 5.0, \sigma = 0.1, \zeta = 0.001\}$ . Our analysis reveals that gradually increasing parameters while maintaining default values for others yields optimal mean Average Precision (mAP) across the three + +Table 3. For the Mean Average Precision (MAP) evaluation on the MIRFLICKR25K, NUS-WIDE, and MS COCO datasets (MAP@ALL), the best performance is in bold, the second-best is underlined, and results from original papers are marked with an asterisk (*). + +
NetworkMethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bitAvg16bit32bit64bitAvg16bit32bit64bitAvg
I2TCNNDCMH [16]0.72880.74110.74900.73960.52380.59950.61950.58090.51770.53110.54710.5320
CMHH [3]0.66490.66770.67310.66860.53120.54760.52990.53620.56570.55820.55400.5593
GCDH [2]0.79910.81230.82040.81060.71420.73670.74980.73360.72970.76510.79050.7618
CLIPDCHMT [32]0.82540.82840.82570.82650.68320.68920.70250.69160.64400.64650.65520.6486
MITH [23]0.83770.84910.85760.84810.70620.71800.71860.71430.71490.73730.75800.7367
DSPH [14]0.80810.83870.85050.83240.69530.70310.71610.70480.70490.75830.77280.7453
TwDH [33]0.77660.79150.80160.78990.66490.68550.69330.68120.65640.72070.74720.7081
DNpH [26]0.83990.84860.85000.84620.71350.71690.72470.71840.67540.68970.68620.6838
DHaPH [15]0.82710.83510.83240.83150.72150.73330.74100.73190.73100.74020.74960.7403
CMCL [39]0.84870.86110.86920.85970.71540.73140.74400.73030.74200.77010.79360.7686
VTPH* [4]0.90560.92490.93280.92110.77330.78700.79360.78460.72020.74770.77860.7488
PromptHash(Ours)0.98180.99600.99950.99240.93130.97590.99310.96680.76730.87820.92630.8573
T2ICNNDCMH [16]0.75200.76960.77760.76640.54400.59010.59560.57660.55100.58830.60500.5814
CMHH [3]0.66150.68510.69430.68030.48260.48680.47110.48020.50980.50710.50970.5089
GCDH [2]0.78490.80220.80670.79790.72150.74230.75340.73910.72610.76500.78850.7599
CLIPDCHMT [32]0.81150.81790.82000.81650.69200.70810.72080.70700.62820.63610.76740.6772
MITH [23]0.82880.84080.84830.83930.71220.72810.73350.72460.70450.73190.71680.7177
DSPH [14]0.79090.82150.83340.81530.70280.71650.73290.71740.70470.75520.75250.7375
TwDH [33]0.77580.78950.80300.78940.67190.71260.71530.69990.66030.72050.69900.6933
DNpH [26]0.81510.82490.83290.82430.72220.72650.73130.72670.65950.68010.69900.6795
DHaPH [15]0.80890.81700.81940.81510.72030.72840.73880.72920.69990.70370.79190.7318
CMCL [39]0.82900.83620.84020.83510.72900.74380.75110.74130.73960.76890.79620.7682
VTPH* [4]0.90200.92260.92780.91750.77080.78400.79330.78270.71850.75150.77430.7481
PromptHash(Ours)0.98160.99550.99950.99220.93810.97610.99340.96920.76670.87900.92830.8580
+ +datasets. However, reducing $\sigma$ to 0.1 while simultaneously increasing $\gamma$ results in decreased mAP performance. Furthermore, when attempting to optimize all hyperparameters independently for each dataset, the resulting average mAP values prove inferior to those achieved by solely reducing $\sigma$ to 0.1. Additional experiments show that further reducing $\sigma$ to 0.05 also leads to degraded average mAP performance. These findings suggest that maintaining default values for all hyperparameters except the quantization loss weight $\sigma$ (set to 0.1) yields optimal average mAP across all three datasets. We hypothesize that this phenomenon occurs because PromptHash effectively aligns image-text features extracted by CLIP, resulting in high similarity between related image-text pairs and natural dissimilarity between unrelated pairs in the common Hamming space, thus requiring lower emphasis on quantization loss. + +# 4.3.3. Comparison with State-of-the-Art + +As demonstrated in Tab. 3, our proposed PromptHash method achieves superior performance across all metrics on three public datasets. Using the mAP@all metric as a primary indicator, we observe significant improvements over the previous state-of-the-art methods. On the MIRFLICKR-25K dataset, PromptHash outperforms the second-best method (VTPH) by margins of $7.13\%$ and $7.47\%$ for I2T and T2I tasks, respectively. For the NUS-WIDE dataset, we achieve even more substantial improvements over VTPH, with gains of $18.22\%$ for I2T and $18.65\%$ for T2I tasks. On the MS COCO dataset, our method surpasses the previous best performer (CMCL) by $8.87\%$ and $8.98\%$ for I2T and T2I tasks, respectively. + +The Precision-Recall curves in Fig. 4 demonstrate particularly notable improvements on MIRFLICKR-25K and NUS-WIDE datasets, where PromptHash significantly outperforms ex + +isting methods. This superior performance can be attributed to our method's effective handling of discrete word-based texts through affinity prompt learning and adaptive weighting modules, coupled with image-centric feature discrimination between foreground retrieval targets and background information. However, we observe relatively modest improvements on the MS COCO dataset, which we attribute to its unique characteristics: text annotations comprise complete sentences rather than discrete words, with annotations extending up to 625 words, of which only 3-5 words typically represent retrieval targets. This high noise data presents a particular challenge that could potentially be addressed in future work through text reconstruction. + +# 5. Conclusion + +Most existing cross-modal hashing methods primarily focus on hashing function design and optimizing distances between different samples, while overlooking inherent issues within the sample sets themselves. Specifically, problems such as text semantic truncation and negative semantic information within the sample set can significantly limit retrieval performance. + +Our proposed PromptHash framework addresses these limitations through two key innovations. First, it introduces prompt learning for adaptively weighted learning of truncated text semantics, effectively improving retrieval performance under limited character encoding constraints. Second, it combines SSM and Transformer architectures with adaptive gated selection fusion, enabling efficient filtering and weighting of fused features. Furthermore, our novel Prompt Affinity Contrastive Learning module (PACL) balances prompt, textual, and visual features while bridging modality heterogeneity through feature alignment, significantly enhancing retrieval accuracy. + +# Acknowledgments + +This work was supported by the Scientific and Technological Innovation 2030 Major Project under Grant 2022ZD0115800, the National Natural Science Foundation of China under Grant 62441213, and the Key Laboratory Open Projects in Xinjiang Uygur Autonomous Region under Grant 2023D04028. + +# References + +[1] Cong Bai, Chao Zeng, Qing Ma, Jinglin Zhang, and Shengyong Chen. Deep adversarial discrete hashing for cross-modal retrieval. In ICMR, pages 525-531, 2020. 1 +[2] Cong Bai, Chao Zeng, Qing Ma, and Jinglin Zhang. Graph convolutional network discrete hashing for cross-modal retrieval. IEEE TNNLS, 35(4):4756-4767, 2024. 2, 6, 8 +[3] Yue Cao, Bin Liu, Mingsheng Long, and Jianmin Wang. Cross-modal hamming hashing. 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IEEE TKDE, 36(1): 239-260, 2024. 1 \ No newline at end of file diff --git a/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/images.zip b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..391450ef23ba1b5937de44dd37793d984e18ab92 --- /dev/null +++ b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:49f6c629328cd51cf97c10828d105123c38ad8ef809e2fbebc3a41c04da2dd61 +size 900211 diff --git a/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/layout.json b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4c52689555b9def9c582cb525dfb13e62ea814b8 --- /dev/null +++ b/2025/PromptHash_Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval/layout.json @@ -0,0 +1,9964 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 102, + 533, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 102, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 78, + 102, + 533, + 140 + ], + "type": "text", + "content": "PromptHash: Affinity-Prompted Collaborative Cross-Modal Learning for Adaptive Hashing Retrieval" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 196, + 161, + 413, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 196, + 161, + 413, + 175 + ], + "spans": [ + { + "bbox": [ + 196, + 161, + 413, + 175 + ], + "type": "text", + "content": "Qiang Zou Shuli Cheng* Jiayi Chen" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 128, + 176, + 482, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 176, + 482, + 190 + ], + "spans": [ + { + "bbox": [ + 128, + 176, + 482, + 190 + ], + "type": "text", + "content": "School of Computer Science and Technology, Xinjiang University, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 190, + 503, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 190, + 503, + 203 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 503, + 203 + ], + "type": "text", + "content": "zouq@stu.xju.edu.cn cslxju@xju.edu.cn 107552203982@stu.xju.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "spans": [ + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "text", + "content": "Cross-modal hashing is a promising approach for efficient data retrieval and storage optimization. However, contemporary methods exhibit significant limitations in semantic preservation, contextual integrity, and information redundancy, which constrains retrieval efficacy. We present PromptHash, an innovative framework leveraging affinity prompt-aware collaborative learning for adaptive cross-modal hashing. We propose an end-to-end framework for affinity-prompted collaborative hashing, with the following fundamental technical contributions: (i) a text affinity prompt learning mechanism that preserves contextual information while maintaining parameter efficiency, (ii) an adaptive gated selection fusion architecture that synthesizes State Space Model with Transformer network for precise cross-modal feature integration, and (iii) a prompt affinity alignment strategy that bridges modal heterogeneity through hierarchical contrastive learning. To the best of our knowledge, this study presents the first investigation into affinity prompt awareness within collaborative cross-modal adaptive hash learning, establishing a paradigm for enhanced semantic consistency across modalities. Through comprehensive evaluation on three benchmark multi-label datasets, PromptHash demonstrates substantial performance improvements over existing approaches. Notably, on the NUS-WIDE dataset, our method achieves significant gains of " + }, + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "inline_equation", + "content": "18.22\\%" + }, + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "inline_equation", + "content": "18.65\\%" + }, + { + "bbox": [ + 53, + 256, + 297, + 605 + ], + "type": "text", + "content": " in image-to-text and text-to-image retrieval tasks, respectively. The code is publicly available at https://github.com/ShiShuMo/PromptHash." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 626, + 135, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 626, + 135, + 639 + ], + "spans": [ + { + "bbox": [ + 56, + 626, + 135, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 647, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 296, + 696 + ], + "type": "text", + "content": "With the rapid proliferation of social media platforms, multimodal data has grown exponentially, making cross-modal retrieval an increasingly promising field with broad application prospects [29]." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 230, + 566, + 389 + ], + "blocks": [ + { + "bbox": [ + 316, + 230, + 566, + 389 + ], + "lines": [ + { + "bbox": [ + 316, + 230, + 566, + 389 + ], + "spans": [ + { + "bbox": [ + 316, + 230, + 566, + 389 + ], + "type": "image", + "image_path": "7d191359806e6d9d2478b06266e79bbf034a8b9c62e05d99d16d7f311248c62b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "type": "text", + "content": "Figure 1. Compare with existing frameworks. (a) Previous methods used dual Transformers for cross modal hashing contrastive learning. (b) We compare and learn images and texts separately by setting learnable affinity prompts." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 461, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 677 + ], + "type": "text", + "content": "However, the inherent modal heterogeneity of multimodal data presents significant challenges, indicating substantial room for improvement in both academic research and industrial applications of cross-modal retrieval [45]. Cross-modal hashing employs shared hash functions with strong representational capacities, mapping data from different modalities into a common hash space. As a result, data with similar semantic content across modalities can be mapped to proximate binary hash codes, effectively bridging the semantic gap between modalities and enabling rapid and accurate cross-modal data retrieval [1, 9, 12, 16, 17, 26, 31, 33, 41]. Existing cross-modal hashing methods are generally divided into unsupervised and supervised approaches, with supervised methods typically outperforming unsupervised ones by leveraging supervisory information, such as pairwise similarity matrices or semantic labels. Despite the considerable progress made in deep supervised cross-modal hashing, there are still fundamental challenges to address." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "content": "Recently, CLIP (Contrastive Language-Image Pretraining) [27] has emerged as a powerful backbone for cross-modal feature extraction in many hashing methods due to" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19649" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "its strong zero-shot capabilities and alignment between visual and textual representations. However, adopting CLIP introduces several critical challenges that limit performance in real-world applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 121, + 296, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 121, + 296, + 467 + ], + "spans": [ + { + "bbox": [ + 56, + 121, + 296, + 467 + ], + "type": "text", + "content": "A notable challenge is the context-length limitation in CLIP pre-trained models, where the current maximum context length is limited to 77 characters, whereas real-world text data often far exceeds this limit. This discrepancy leads to context loss and semantic truncation, especially when retrieving textual information. Furthermore, effectively fusing cross-modal features remains an open challenge, particularly in enhancing semantic feature weights relevant to retrieval while suppressing irrelevant information. For instance, the widely used MS COCO dataset [22] exemplifies this challenge, as its text lengths range from 169 to 625 characters, significantly exceeding CLIP's 77-character capacity for text encoding. To address the CLIP context-length limitation, our approach incorporates foreground target text into adaptive affinity prompts and implements a dynamic weighting mechanism between these prompts and the original text. This strategy effectively preserves critical semantic information while circumventing CLIP's 77-character constraint, enabling comprehensive processing of lengthy real-world texts without semantic truncation. Previous approaches have employed various methods to address this: the Bag-of-Words (BoW) model, which disregards contextual word relationships; pre-trained Transformer [36] models such as Vision Transformer(ViT) [7] and BERT [6], which still face truncation; and VTPH's [4] use of large language models [19, 25] to reconstruct text as prompts, although this method introduces significant computational overhead without fully resolving the semantic truncation issue." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 469, + 295, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 295, + 601 + ], + "type": "text", + "content": "Another challenge lies in the feature fusion of different modalities, where existing cross-modal hashing methods often incorporate contrastive learning to capture intermodal consistency. However, benchmark datasets commonly used in cross-modal retrieval suffer from context loss and semantic redundancy, especially in textual representation. For example, the textual content in MIRFLICKR-25K [13] and NUS-WIDE [5] is generated through direct label concatenation, resulting in limited contextual depth. Additionally, MS COCO's text data, derived from merged manual descriptions, can introduce semantic redundancy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 601, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 601, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 601, + 295, + 696 + ], + "type": "text", + "content": "To address these challenges, we propose a Adaptive Affinity-Prompted Collaborative Cross-Modal Learning (PromptHash) for Hashing Retrieval in Fig. 1. Ours framework that integrates text affinity prompts with State Space Model(SSM) and Transformer-based adaptive gated selection fusion, supported by a novel Prompt Affinity Contrastive Loss (PACL) to better align cross-modal semantics. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "- To mitigate semantic truncation caused by CLIP's" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 321, + 72, + 553, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 553, + 155 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 553, + 155 + ], + "type": "text", + "content": "context-length limitation, adaptive text prompts are introduced that incorporate foreground target text essential for retrieval. This approach implements a dynamic weighting mechanism between prompts and original text, effectively preserving critical semantic information while circumventing length constraints for improved retrieval performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 156, + 553, + 311 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 156, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 156, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 314, + 156, + 553, + 204 + ], + "type": "text", + "content": "- The framework also incorporates an SSM-Transformer adaptive gated selection fusion module to refine cross-modal feature integration, preserving relevant semantic information while filtering out redundant content." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 204, + 553, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 204, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 204, + 553, + 262 + ], + "type": "text", + "content": "- To balance prompt semantics with the original image-text semantics, a novel Prompt Affinity Contrastive Loss (PACL) is introduced, bridging modality heterogeneity and semantic gaps through global and local prompt contrast." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 263, + 553, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 553, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 553, + 311 + ], + "type": "text", + "content": "- Extensive experiments on three benchmark datasets demonstrate that the proposed PromptHash framework significantly outperforms state-of-the-art methods, underscoring its effectiveness in cross-modal retrieval." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "spans": [ + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 346, + 466, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 466, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 466, + 358 + ], + "type": "text", + "content": "2.1. Deep Cross-Modal Hashing" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 364, + 553, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 553, + 422 + ], + "type": "text", + "content": "Cross-modal hashing has made significant strides in information retrieval by mapping heterogeneous data into a unified Hamming space via hash functions. The literature typically categorizes approaches into unsupervised and supervised methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 425, + 554, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 554, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 554, + 520 + ], + "type": "text", + "content": "Unsupervised methods maintain semantic similarity without explicit supervision by leveraging cross-modal correlations. Notable works include DAEH [30] with deep adaptive enhancement, UKD's [10] teacher-student framework, and UCMFH's [40] CLIP-based feature extraction. Additionally, UCCH [11] addresses binary-continuous relaxation constraints, while NRCH [37] advances through robust contrastive loss and dynamic noise separation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 554, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 554, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 554, + 640 + ], + "type": "text", + "content": "Supervised methods utilize label information to establish semantic consistency within a shared hash space. DCMH [16] pioneered end-to-end deep cross-modal hashing, followed by CMHH's [3] focal loss approach and AGAH's [9] adversarial learning with attention mechanisms. Recent innovations include DCHUC's [34] joint optimization, MIAN's [42] modality-invariant networks, and GCDH's [2] graph convolutional networks. DCHMT [32] and MITH [23] leverage CLIP for fine-grained feature extraction." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": "Proxy learning has emerged as another significant direction, with DAPH's [35] data-aware networks, DSPH's [14] fine-grained semantic relations, and DHaPH's [15] hierarchical learning. Notable approaches also include CMCL's [39] multi-bit collaboration and VTPH's [4] large model optimization. Distinct from existing methods, we in" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19650" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "type": "text", + "content": "tegrate both global and local prompt alignments while minimizing feature divergence to alleviate modality heterogeneity and semantic gaps." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 117, + 160, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 117, + 160, + 129 + ], + "spans": [ + { + "bbox": [ + 55, + 117, + 160, + 129 + ], + "type": "text", + "content": "2.2. Prompt Learning" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 134, + 295, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 134, + 295, + 254 + ], + "spans": [ + { + "bbox": [ + 55, + 134, + 295, + 254 + ], + "type": "text", + "content": "Prompt learning originated in NLP, integrating handcrafted templates into input data for downstream tasks. Recent studies have extended this concept to vision-language models, with CoCoOp [43] introducing Conditional Context Optimization, MaPLe [18] implementing Multi-modal Prompt Learning, and CoPrompt [28] enhancing performance through consistency constraints. While PromptKD [20] explores Unsupervised Prompt Distillation, prompt learning's effectiveness in cross-modal hashing remains underexplored." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 262, + 179, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 179, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 179, + 275 + ], + "type": "text", + "content": "2.3. Contrastive Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 280, + 295, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 280, + 295, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 280, + 295, + 411 + ], + "type": "text", + "content": "Contrastive learning has demonstrated substantial efficacy in feature representation by maximizing similarity between positive pairs while minimizing negative pair similarity. Several cross-modal hashing methods have adopted this paradigm: UCCH [11] pioneered unsupervised contrastive learning, UniHash [38] facilitates instance-level learning, and CMCL [39] optimizes through token alignment. However, existing methods often overlook explicit fine-grained token-level semantic alignment. Our work addresses this through prompt-based contrastive learning for both instance and token-level representations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 420, + 169, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 169, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 169, + 433 + ], + "type": "text", + "content": "2.4. State Space Models" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 437, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 641 + ], + "type": "text", + "content": "While contrastive learning effectively aligns semantic representations across modalities, distinguishing between foreground (relevant) and background (irrelevant) information in multimodal contexts remains challenging. State Space Models (SSM) [8] offer a promising solution through their selective sequence modeling capabilities with linear computational complexity. Unlike Transformers that attend to all tokens equally, SSM's selective scan mechanism can dynamically focus on informative elements while filtering out noise. Vim [44] pioneered SSM in visual domains, demonstrating their ability to selectively process visual information. VMamba [24] extended this capability with 2D Selective Scanning that effectively separates foreground objects from background elements. Jamba [21] further showed how SSM's selective attention, when integrated with Transformer layers, enables more efficient sequence feature processing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "content": "Despite these advances, the potential of SSM, when combined with contrastive learning, to effectively address the foreground-background confusion problem in cross-modal hashing retrieval remains unexplored. Our work integrates these two paradigms, utilizing SSM for precise separation of foreground and background information and con" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 543, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 543, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 543, + 84 + ], + "type": "text", + "content": "trastive mechanisms for accurate cross-modal alignment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "spans": [ + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 115, + 493, + 127 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 115, + 493, + 127 + ], + "spans": [ + { + "bbox": [ + 314, + 115, + 493, + 127 + ], + "type": "text", + "content": "3.1. Notations and Problem Definition" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "This paper adopts a framework analogous to conventional cross-modal hashing methodologies, utilizing image-text pairs as input modalities. Let " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = \\{o_i\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " denote a collection of " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " training sample pairs, where each sample " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "o_i = (x_i^v, x_i^t, l_i, p_i)" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " comprises a visual feature vector " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "x_i^v \\in \\mathbb{R}^{d^v}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": ", a textual feature vector " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "x_i^t \\in \\mathbb{R}^{d^t}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": ", a multi-label annotation " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "l_i \\in \\{0, 1\\}^{1 \\times C}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " (where " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "l_{i,c} = 1" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " if sample " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " belongs to category " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "; otherwise, " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "l_{i,c} = 0" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "), and a prompt word " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": ". We construct a similarity matrix " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "S_{ij} = 1" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " if samples share at least one category, indicating semantic affinity; otherwise, " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "S_{ij} = 0" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": ". The primary objective is to project heterogeneous features into a unified " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "-bit Hamming space through two hashing functions: " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b_i^v = H^v(f_i^v; \\theta^v) \\in \\{-1, +1\\}^K" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b_i^{pt} = H^t(f_i^{pt}; \\theta^t) \\in \\{-1, +1\\}^K" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b_i^v" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b_i^{pt}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " denote the hash codes for visual and textual modalities, while " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\theta^v" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " represent the learnable parameters of the corresponding functions. Throughout this paper, " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " denotes the mini-batch size, and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " represents the feature embedding dimension. We use " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " for initial feature representations (e.g., " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "f_i^v, f_i^t, f_i^p, f_i^{pt}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " for continuous hash representations prior to quantization (e.g., " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "h_i^v, h_i^{pt}, h_i^p" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " for binary hash codes (e.g., " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "b_i^v, b_i^{pt}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": "). For similarity metrics, " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\Theta_{ij}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " represents prompt-visual similarity, " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\Phi_{ij}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " denotes visual-prompt similarity, and " + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\Omega_{ij}" + }, + { + "bbox": [ + 313, + 133, + 555, + 422 + ], + "type": "text", + "content": " indicates intra-modal prompt similarity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 430, + 425, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 430, + 425, + 441 + ], + "spans": [ + { + "bbox": [ + 314, + 430, + 425, + 441 + ], + "type": "text", + "content": "3.2. Feature Extraction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "text", + "content": "Fig. 2 illustrates the detailed workflow of our proposed PromptHash framework. To leverage the latest advances in deep neural networks and Transformer-based models, we employ a two-branch Transformer architecture for the extraction of image and text features. Additionally, we introduce a dedicated Transformer network designed to extract prompt features, which are then used to compute prompt-weighted similarities. To further enhance the quality of the image and text representations, we utilize pretrained ViT and BERT as the visual encoder and text encoder, respectively. These models extract the image and text embeddings, denoted as " + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "inline_equation", + "content": "f_{i}^{v} = \\{G_{i}^{v}\\} \\in \\mathbb{R}^{L^{\\nu} \\times D}" + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "inline_equation", + "content": "f_{i}^{t} = \\{G_{i}^{t}\\} \\in \\mathbb{R}^{L^{t} \\times D}" + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "text", + "content": ". Similarly, the constructed masked fused prompt embeddings, denoted as " + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "inline_equation", + "content": "f_{i}^{pt} = \\{G_{i}^{p}\\} \\in \\mathbb{R}^{L^{p} \\times D}" + }, + { + "bbox": [ + 313, + 447, + 555, + 628 + ], + "type": "text", + "content": ", are used to represent the fused prompt." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 636, + 514, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 514, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 514, + 649 + ], + "type": "text", + "content": "3.3. Text Affinity-Aware Prompt Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "In cross-modal hashing tasks, negative textual features can significantly degrade retrieval performance by hindering the effective distinction between foreground and background information. To address this issue, we propose a Text Affinity-Aware Prompt (TAAP) module, which dynami-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19651" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 553, + 322 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 322 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 322 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 322 + ], + "type": "image", + "image_path": "66af3efc14c7d701d2ea5d9a0588863154e48277e9363921a82c808afcca603b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 327, + 555, + 404 + ], + "lines": [ + { + "bbox": [ + 54, + 327, + 555, + 404 + ], + "spans": [ + { + "bbox": [ + 54, + 327, + 555, + 404 + ], + "type": "text", + "content": "Figure 2. Overall Framework of PromptHash. Our framework consists of five key components: 1) Image and Text Encoders for modality-specific feature extraction; 2) Adaptive Gated State Selection and Fusion Module for feature filtering and cross-modal fusion between image features and hybrid prompt-enhanced textual features; 3) Text Affinity-Aware Prompting that dynamically learns and distinguishes retrieval-beneficial foreground information while optimizing textual feature representations through dynamic prompting mechanisms; 4) Cross-Modal Prompt Alignment Mechanism incorporating both global and local alignments, where global alignment facilitates image-to-text and image-to-prompt representation alignments with intra-class and inter-class affinity losses; 5) Hash Learning with quantization and reconstruction losses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 420, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 420, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 54, + 420, + 295, + 456 + ], + "type": "text", + "content": "cally learns and differentiates foreground information that aids retrieval, and optimizes textual feature representations through a dynamic prompt mechanism." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": " represent the category label set corresponding to image-text pairs " + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "inline_equation", + "content": "o_{t}" + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": ". We generate prompt text using a template: \"This is an image containing {class_name_i}\", where {class_name_i} corresponds to label " + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": ". The complete prompt text is formulated as " + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "inline_equation", + "content": "\\text{prompt}_i =" + }, + { + "bbox": [ + 55, + 456, + 295, + 552 + ], + "type": "text", + "content": " \"This is an image containing {class_name_i}\" which is then tokenized using Byte Pair Encoding (BPE): token_prompt_i = Tokenizer(prompt_i)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "text", + "content": "The token sequence is encoded into an embedding vector " + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "inline_equation", + "content": "p_i = \\text{embed}(\\text{token\\_prompt}_i)" + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "inline_equation", + "content": "p_i \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 55, + 552, + 295, + 581 + ], + "type": "text", + "content": " (1)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "text", + "content": " denotes CLIP's embedding dimension. Then " + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "inline_equation", + "content": "f_{i}^{p}" + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "text", + "content": " combines this with a learnable context vector " + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{ctx}}" + }, + { + "bbox": [ + 55, + 586, + 295, + 609 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 149, + 613, + 295, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 613, + 295, + 625 + ], + "spans": [ + { + "bbox": [ + 149, + 613, + 295, + 625 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {p} = p _ {i} + C _ {\\mathrm {c t x}} \\tag {2}", + "image_path": "54c9e30360ade10d51a95e2a79d58a1bcc8db86d8cadabd336ceaa8559f815c2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "text", + "content": "This dynamic prompt mechanism enables effective distinction between foreground and background features through a learnable mask, optimizing the feature representation for retrieval tasks. The generated prompt features " + }, + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "inline_equation", + "content": "f_{i}^{p}" + }, + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "text", + "content": " are then processed by the TAAP module's Transformer encoder layers, fusing them with the original text features " + }, + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "inline_equation", + "content": "f_{i}^{t}" + }, + { + "bbox": [ + 55, + 631, + 295, + 696 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 123, + 696, + 295, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 696, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 123, + 696, + 295, + 711 + ], + "type": "interline_equation", + "content": "\\widetilde {f} _ {i} ^ {p} = \\text {T r a n s f o r m e r L a y e r} \\left(f _ {i} ^ {p}\\right) \\tag {3}", + "image_path": "fee7a59715fc8a79805fab9122dd1a67e875054f0fb8e7f9d9456a865b9c9fc0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 421, + 553, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 421, + 553, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 421, + 553, + 443 + ], + "type": "text", + "content": "Finally, we obtain the weighted feature representation through element-wise multiplication and global average pooling:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 368, + 445, + 553, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 445, + 553, + 460 + ], + "spans": [ + { + "bbox": [ + 368, + 445, + 553, + 460 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {p t} = \\left(\\widehat {f} _ {i} ^ {p} \\times f _ {i} ^ {t}\\right) \\otimes \\eta , \\quad f _ {i} ^ {p t} \\in \\mathbb {R} ^ {D} \\tag {4}", + "image_path": "0821382f3301113fc1f7a776af5f7f4216fe1956a5b90c555e40f85884c1c709.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "text", + "content": " represent learnable weight, respectively, with " + }, + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 313, + 464, + 554, + 519 + ], + "type": "text", + "content": " denoting matrix multiplication. This integration process effectively preserves foreground information while suppressing background noise, significantly improving cross-modal hashing retrieval performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 526, + 541, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 541, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 541, + 539 + ], + "type": "text", + "content": "3.4. Adaptive Gated State Space Fusion Module" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 543, + 554, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 554, + 631 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 554, + 631 + ], + "type": "text", + "content": "In this work, we integrate the State Space Model (SSM) with adaptive gating mechanisms to design an adaptive filtering feature fusion module, which we refer to as the Adaptive Gated State Space Fusion Module(AGSF). The textual features are weighted through the aforementioned prompt learning module, yielding a refined textual feature representation. However, image features must also undergo filtering and fusion with the resulting mixed prompt-text features. This process is formalized as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 344, + 634, + 553, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 634, + 553, + 654 + ], + "spans": [ + { + "bbox": [ + 344, + 634, + 553, + 654 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {\\mathrm {c l s} _ {m}} = \\operatorname {S i L U} \\left(\\operatorname {M L P} \\left(\\operatorname {G R N} \\left(f _ {i} ^ {m}\\right)\\right)\\right) \\mid m \\in \\{v, p t \\}", + "image_path": "9077c0c40fca24c3fe51b8703b5761a0338fd17551eb852afe51a637469756d1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 344, + 650, + 453, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 650, + 453, + 664 + ], + "spans": [ + { + "bbox": [ + 344, + 650, + 453, + 664 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {\\text {f u s i o n}} = \\operatorname {C o n c a t} \\left(f _ {i} ^ {\\mathrm {c l s} _ {v}}, f _ {i} ^ {\\mathrm {c l s} _ {p t}}\\right)", + "image_path": "0954e10cded0a82c013c849d279c9ecc6d3ed0307d48b2958cea51ff4daee7b9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 669, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 555, + 714 + ], + "type": "text", + "content": "where Concat represents the concatenation operation, GRN denotes Global Response Normalization, MLP refers to a multi-layer perceptron, and SiLU is the activation function. In the Global Response Normalization (GRN) layer, for input " + }, + { + "bbox": [ + 313, + 669, + 555, + 714 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{B \\times N \\times D}" + }, + { + "bbox": [ + 313, + 669, + 555, + 714 + ], + "type": "text", + "content": ", the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19652" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "text", + "content": "L2 norm " + }, + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "inline_equation", + "content": "G_{x}" + }, + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "text", + "content": " and normalization factor " + }, + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "inline_equation", + "content": "N_{x}" + }, + { + "bbox": [ + 55, + 73, + 295, + 95 + ], + "type": "text", + "content": " are computed sequentially:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 101, + 295, + 136 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 101, + 295, + 136 + ], + "spans": [ + { + "bbox": [ + 80, + 101, + 295, + 136 + ], + "type": "interline_equation", + "content": "G _ {x} = \\| x \\| _ {2} = \\sqrt {\\sum_ {d = 1} ^ {D} x _ {d} ^ {2}}, \\quad N _ {x} = \\frac {G _ {x}}{\\frac {1}{N} \\sum_ {i = 1} ^ {N} G _ {x i}} \\tag {6}", + "image_path": "9af9ede78a91cceab7808fb0fa46b751082a6db158d255fec67ca5a7f8333b46.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "text", + "content": "The final output with learnable parameters " + }, + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 144, + 253, + 156 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 119, + 163, + 295, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 163, + 295, + 175 + ], + "spans": [ + { + "bbox": [ + 119, + 163, + 295, + 175 + ], + "type": "interline_equation", + "content": "\\operatorname {G R N} (x) = \\lambda \\cdot \\left(x \\cdot N _ {x}\\right) + \\kappa + x \\tag {7}", + "image_path": "1dcd7937429e44fbad1dbff5f899a5a036a21f3100c54c195b5fa0bf70c2dce6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 184, + 295, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 184, + 295, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 184, + 295, + 205 + ], + "type": "text", + "content": "After obtaining the fused features, they are fed into the SSM adaptive selection module, expressed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 81, + 212, + 295, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 212, + 295, + 228 + ], + "spans": [ + { + "bbox": [ + 81, + 212, + 295, + 228 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {\\text {f l i p} _ {\\text {a x i s}} = \\psi} = \\operatorname {F l i p} _ {\\text {a x i s}} ^ {T} (\\operatorname {S S M} (\\operatorname {F l i p} _ {\\text {a x i s}} = \\psi (f _ {i} ^ {\\text {f u s i o n}}))) \\tag {8}", + "image_path": "fd5d5e9eedbdced42b48424fa6539838b34470d156d178319d6e83105be2a005.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\psi \\in \\{1,2,(1,2)\\}" + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\mathrm{Flip}_{\\mathrm{axis} = \\psi}" + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "content": " denotes a flipping operation along different axes, and " + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\mathrm{Flip}^T" + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "content": " represents its inverse. The term SSM refers to the State Space Model. After obtaining the final three features, we apply an adaptive weighted filtering process. The parameter " + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 236, + 296, + 316 + ], + "type": "text", + "content": " serves as a learnable temperature coefficient, which balances the relative importance of the four features derived from flipped and unflipped orientations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 321, + 295, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 321, + 295, + 346 + ], + "spans": [ + { + "bbox": [ + 63, + 321, + 295, + 346 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {\\mathrm {f i t}} = \\theta \\tau \\sum_ {j \\in \\omega} f _ {i} ^ {\\mathrm {f l i p} _ {\\mathrm {a x i s} = j}} + (1 - \\theta) f _ {i} ^ {\\text {f u s i o n}}, \\omega = \\{1, 2, (1, 2) \\} \\tag {9}", + "image_path": "43798a16966f503e95ae04320262647f9e80707a58ffec9dd6b20c555e3e9f48.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 354, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 387 + ], + "type": "text", + "content": "Where, " + }, + { + "bbox": [ + 55, + 354, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 354, + 296, + 387 + ], + "type": "text", + "content": " denotes a set of learnable parameters. The filtered features are subsequently passed through a Transformer encoder layer, yielding:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 393, + 295, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 393, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 88, + 393, + 295, + 410 + ], + "type": "interline_equation", + "content": "\\widetilde {f _ {i} ^ {v}}, \\widetilde {f _ {i} ^ {\\mathrm {p t}}} = \\operatorname {S p l i t} \\left(\\operatorname {T r a n s f o r m e r L a y e r} \\left(\\operatorname {M L P} \\left(f _ {i} ^ {\\mathrm {f i t}}\\right)\\right)\\right) \\tag {10}", + "image_path": "c87774beb0bcfa085d338c88897c374eeeb98abb6b9c7b0fb807c9065f7020f6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "text", + "content": "The resulting features " + }, + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "inline_equation", + "content": "\\widetilde{f_i^v}" + }, + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "inline_equation", + "content": "\\widetilde{f_i^{\\mathrm{pt}}}" + }, + { + "bbox": [ + 55, + 419, + 296, + 510 + ], + "type": "text", + "content": " represent the outputs obtained through the adaptive SSM gating and selection fusion module. Here, Split denotes an operation that separates the individual visual and textual features from the fused representation. Through the aforementioned operations, we simultaneously adaptively filter and dynamically weight redundant information in both images and text, significantly enhancing the quality and effectiveness of retrieval." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 518, + 270, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 270, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 270, + 532 + ], + "type": "text", + "content": "3.5. Prompt Alignment Contrastive Learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 536, + 296, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 296, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 296, + 601 + ], + "type": "text", + "content": "To effectively bridge the semantic gaps between different modalities, we propose prompt alignment contrastive learning (PACL), a learning mechanism that enables fine-grained alignment between modalities. This mechanism operates through two key components: cross-modal prompt alignment and affinity-aware loss function." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 609, + 222, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 222, + 622 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 222, + 622 + ], + "type": "text", + "content": "3.5.1. Cross-Modal Prompt Alignment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 624, + 295, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 295, + 678 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 295, + 678 + ], + "type": "text", + "content": "To further mitigate heterogeneity and semantic gaps, we leverage contrastive learning to explicitly align the fine-grained semantic concept representations. Our alignment strategy comprises two key components: global-local prompt alignment and affinity-aware loss functions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 680, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 680, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 680, + 296, + 712 + ], + "type": "text", + "content": "For global prompt alignment, we adopt symmetric InfoNCE losses to align image representations with textual and prompt representations:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 351, + 70, + 554, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 70, + 554, + 119 + ], + "spans": [ + { + "bbox": [ + 351, + 70, + 554, + 119 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i} ^ {a \\rightarrow b} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {i} ^ {b}} / \\tau_ {1}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {a}}\\right) ^ {T} \\widetilde {f _ {c} ^ {b}} / \\tau_ {1}\\right)} \\tag {11}", + "image_path": "6e747811c3d1513fae4a65927ffe7421c5f5437fe69374052fae2b010e5a67a8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 358, + 120, + 476, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 120, + 476, + 157 + ], + "spans": [ + { + "bbox": [ + 358, + 120, + 476, + 157 + ], + "type": "interline_equation", + "content": "\\mathcal{L}_{\\mathrm{gpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{a,b\\in \\{v,pt\\} \\\\ a\\neq b}}\\mathcal{L}_{i}^{a\\to b}", + "image_path": "216911b86cb87ce02b12917c09d978ea394e67b05e94b88efa344c51d01cde43.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "inline_equation", + "content": "\\tau_{1}" + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "text", + "content": " is a temperature hyperparameter, and the subscript " + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "text", + "content": " indexes over all samples in the batch. Here, " + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "inline_equation", + "content": "a, b \\in \\{v, pt\\}, a \\neq b" + }, + { + "bbox": [ + 313, + 169, + 555, + 202 + ], + "type": "text", + "content": ", corresponding to visual and textual features." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 203, + 554, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 203, + 554, + 225 + ], + "spans": [ + { + "bbox": [ + 313, + 203, + 554, + 225 + ], + "type": "text", + "content": "For local prompt alignment, we employ a dynamic temperature mechanism adjusted by modality distributions:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 378, + 232, + 554, + 257 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 232, + 554, + 257 + ], + "spans": [ + { + "bbox": [ + 378, + 232, + 554, + 257 + ], + "type": "interline_equation", + "content": "\\tau_ {2} = \\tau \\times \\frac {1}{1 + \\mathrm {J S - d i v} \\left(f _ {i} ^ {v} , f _ {i} ^ {p}\\right)} \\tag {12}", + "image_path": "5530a7138f39addd0a80e77dc42eada2826945d1368b7713ace5aa7bef515805.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "text", + "content": " is the base temperature and JS-div measures the Jensen-Shannon divergence between modality distributions. Here, " + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\tau_{1}" + }, + { + "bbox": [ + 313, + 266, + 555, + 308 + ], + "type": "text", + "content": " denote the temperature hyperparameters with a default value of 0.07." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 326, + 311, + 511, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 311, + 511, + 322 + ], + "spans": [ + { + "bbox": [ + 326, + 311, + 511, + 322 + ], + "type": "text", + "content": "The local alignment losses are then formulated as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 350, + 329, + 553, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 329, + 553, + 379 + ], + "spans": [ + { + "bbox": [ + 350, + 329, + 553, + 379 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i} ^ {e \\rightarrow f} = - \\log \\frac {\\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {i} ^ {f}} / \\tau_ {2}\\right)}{\\sum_ {c = 1} ^ {M} \\exp \\left(\\left(\\widetilde {f _ {i} ^ {e}}\\right) ^ {T} \\widetilde {f _ {c} ^ {f}} / \\tau_ {2}\\right)} \\tag {13}", + "image_path": "9710942bac7b324bc09adad2de3e44eb14ff3c04d6dd77c5c3eab5fddd3b1367.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 359, + 380, + 473, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 380, + 473, + 418 + ], + "spans": [ + { + "bbox": [ + 359, + 380, + 473, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal{L}_{\\mathrm{lpa}} = \\frac{1}{M}\\sum_{i = 1}^{M}\\sum_{\\substack{e,f\\in \\{v,p\\} \\\\ e\\neq f}}\\mathcal{L}_{i}^{e\\to f}", + "image_path": "ea387435081300772d198a49cc5406c592cc243dcc8119ad0652f218be022df4.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "inline_equation", + "content": "e, f \\in \\{v, p\\}" + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "inline_equation", + "content": "e \\neq f" + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "content": ", corresponding to visual and prompt features. " + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "inline_equation", + "content": "\\tau_1" + }, + { + "bbox": [ + 313, + 428, + 555, + 461 + ], + "type": "text", + "content": " denote the temperature hyperparameters with a default value of 0.07." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 470, + 469, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 469, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 469, + 482 + ], + "type": "text", + "content": "3.5.2. Affinity-Aware Loss Function" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 486, + 554, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 508 + ], + "type": "text", + "content": "To preserve semantic consistency, we design inter-class and intra-class affinity losses:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 318, + 517, + 554, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 517, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 318, + 517, + 554, + 548 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n t e r}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\sum_ {k = 1} ^ {Q} \\left(S _ {i j} k - \\log \\left(1 + e ^ {\\Theta_ {i j}}\\right)\\right) \\tag {14}", + "image_path": "b569ff21c86c6559f222fec95cc24a2e3823d9210b6bf6c1058dc852ad3409c5.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "Q \\in \\{\\Theta_{ij}, \\Phi_{ij}\\}" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\Theta_{ij} \\neq \\Phi_{ij}" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\Theta_{ij} = \\frac{1}{2} (h_i^p)^T h_j^v" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\Phi_{ij} = \\frac{1}{2} (h_i^v)^T h_j^p" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " denote cross-modal similarities, where " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "h_i^p" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "h_j^v" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " represent the real-valued hash codes of prompt and visual features respectively, before passing through the sign function, " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " is the number of samples, and " + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "inline_equation", + "content": "S_{ij} \\in \\{0, 1\\}" + }, + { + "bbox": [ + 313, + 558, + 554, + 628 + ], + "type": "text", + "content": " is the ground truth similarity matrix." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 326, + 629, + 476, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 629, + 476, + 639 + ], + "spans": [ + { + "bbox": [ + 326, + 629, + 476, + 639 + ], + "type": "text", + "content": "The intra-class affinity loss is defined as:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 328, + 648, + 553, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 648, + 553, + 678 + ], + "spans": [ + { + "bbox": [ + 328, + 648, + 553, + 678 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n t r a}} = - \\frac {1}{M N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {M} \\left(\\mathcal {S} _ {i j} \\Omega_ {i j} - \\log \\left(1 + e ^ {\\Omega_ {i j}}\\right)\\right) \\tag {15}", + "image_path": "5b817c8488e175530ddb50327d7db9f679ec821750c2aee963b5b89300a95e29.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\Omega_{ij} = \\frac{1}{2}\\left(h_i^p\\right)^T h_j^p" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " represents intra-modal similarity between prompt features." + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19653" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 164, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 164, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 164, + 85 + ], + "type": "text", + "content": "3.6. Hashing Learning" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 295, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 295, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 295, + 122 + ], + "type": "text", + "content": "1) Quantization Loss: The quantization loss aims to learn a unified semantic representation and generate high-quality, distinguishable hash codes. It is mathematically formulated as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 136, + 295, + 161 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 136, + 295, + 161 + ], + "spans": [ + { + "bbox": [ + 55, + 136, + 295, + 161 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {q u a n}} = \\frac {1}{N M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| b _ {i} ^ {v} - \\frac {1}{2} \\left(h _ {i} ^ {v} + f _ {i} ^ {v}\\right) \\right\\| _ {2} ^ {2} + \\left\\| b _ {i} ^ {p t} - \\frac {1}{2} \\left(h _ {i} ^ {p t} + f _ {i} ^ {p t}\\right) \\right\\| _ {2} ^ {2}\\right) \\tag {16}", + "image_path": "4a3c2b102964173ba633eade005d1cd63cc432201c65a56eaea299c84b1d35df.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "text", + "content": "This loss function encourages the hash codes " + }, + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "inline_equation", + "content": "b_{i}^{v}" + }, + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "inline_equation", + "content": "b_{i}^{pt}" + }, + { + "bbox": [ + 55, + 170, + 295, + 214 + ], + "type": "text", + "content": " to closely approximate the average of the visual and textual feature representations, facilitating a unified and discriminative semantic embedding." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 215, + 296, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 215, + 296, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 215, + 296, + 270 + ], + "type": "text", + "content": "2) Reconstruction Loss: The reconstruction loss seeks to enhance the representational capacity and retrieval performance of the hash codes by ensuring that the generated hash codes are more distinguishable and closely approximate the original semantic features. The loss is expressed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 274, + 295, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 274, + 295, + 303 + ], + "spans": [ + { + "bbox": [ + 85, + 274, + 295, + 303 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c o n}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\left(\\left\\| h _ {i} ^ {v} - b _ {i} ^ {v} \\right\\| _ {2} ^ {2} + \\left\\| h _ {i} ^ {p t} - b _ {i} ^ {p t} \\right\\| _ {2} ^ {2}\\right) \\tag {17}", + "image_path": "656b943eabc76790f46cf373bc9dcbee8a2d91038709377edff9636290e24cf6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 311, + 295, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 311, + 295, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 311, + 295, + 354 + ], + "type": "text", + "content": "The reconstruction loss minimizes the difference between the hash codes and their corresponding feature representations, promoting the generation of hash codes that effectively retain semantic information for accurate retrieval." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 355, + 296, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 355, + 296, + 389 + ], + "spans": [ + { + "bbox": [ + 55, + 355, + 296, + 389 + ], + "type": "text", + "content": "Finally, the total loss function for the proposed PromptHash method is computed as the weighted sum of the individual loss components, " + }, + { + "bbox": [ + 55, + 355, + 296, + 389 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma, \\mu, \\sigma, \\zeta" + }, + { + "bbox": [ + 55, + 355, + 296, + 389 + ], + "type": "text", + "content": " represent hyperparameters:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 392, + 295, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 392, + 295, + 418 + ], + "spans": [ + { + "bbox": [ + 111, + 392, + 295, + 418 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\alpha \\mathcal {L} _ {\\mathrm {g p a}} + \\beta \\mathcal {L} _ {\\mathrm {l p a}} + \\gamma \\mathcal {L} _ {\\text {i n t e r}} \\tag {18} \\\\ + \\mu \\mathcal {L} _ {\\text {i n t r a}} + \\sigma \\mathcal {L} _ {\\text {q u a n}} + \\zeta \\mathcal {L} _ {\\text {r e c o n}} \\\\ \\end{array}", + "image_path": "fdcbfa5e1cf7e46ff92f99a39fd0207a367970c9fe10f85b8be818c35a22788e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 428, + 137, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 428, + 137, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 428, + 137, + 441 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 448, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 295, + 567 + ], + "type": "text", + "content": "To rigorously evaluate the effectiveness of the proposed PromptHash method, we conducted extensive experiments on three widely used cross-modal multi-label retrieval datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. We compared PromptHash against twelve state-of-the-art cross-modal hashing retrieval methods, including DCMH [16], CMHH [3], GCDH [2], DCHMT [32], MITH [23], DSPH [14], TwDH [33], DNpH [26], DHaPH [15], CMCL [39], and VTPH [4]. All methods were tested under identical experimental conditions, with consistent dataset splits, retrieval, and query sets aligned with our experimental setup." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 568, + 296, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 296, + 657 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 296, + 657 + ], + "type": "text", + "content": "The following sections provide a comprehensive analysis of the experimental results obtained from each of the eleven competing algorithms. Additionally, we offer detailed descriptions of the three datasets used for training and testing, outline the experimental procedures specific to PromptHash, and discuss the metrics used to assess its performance. The experimental environment specifications are also documented to ensure reproducibility and transparency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 663, + 118, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 663, + 118, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 663, + 118, + 675 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 680, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 680, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 680, + 296, + 714 + ], + "type": "text", + "content": "Tab. 1 presents an overview of the datasets used in our experiments and details their respective partitioning strategies. For our evaluations, we applied a consistent sampling strategy across the three" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 554, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 140 + ], + "type": "text", + "content": "large-scale, multi-label datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO. Each dataset was partitioned into training, testing, and retrieval sets. Image and text data were processed uniformly across all datasets: images were resized to an input resolution of " + }, + { + "bbox": [ + 313, + 72, + 554, + 140 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 313, + 72, + 554, + 140 + ], + "type": "text", + "content": " pixels, while text data were encoded using byte pair encoding (BPE) before being input into the network." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 146, + 436, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 146, + 436, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 146, + 436, + 159 + ], + "type": "text", + "content": "4.2. Experimental Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": "In this study, we employ CLIP-B16 as the backbone network, with experiments conducted on a single NVIDIA RTX 4090 GPU (24GB) using PyTorch V2.3.1. Input images across all datasets are resized to " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " pixels. The learning rate is set to " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "1\\mathrm{e} - 6" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " for the backbone network and " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "1\\mathrm{e} - 5" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " for both the prompt model and fusion module, with a batch size of 128. The loss terms are defined as follows: " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " represents the global prompt alignment loss, " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " denotes the local prompt alignment loss, " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " indicates the inter-class affinity loss, " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " represents the intra-class affinity loss, " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " denotes the quantization loss, and " + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 313, + 163, + 555, + 338 + ], + "type": "text", + "content": " represents the reconstruction loss. For the MIRFLICKR-25K and NUS-WIDE datasets, these hyperparameters are set to 5.0, 5.0, 0.005, 5.0, 0.1, and 0.001, respectively. For the MS COCO dataset, the corresponding values are 5.0, 5.0, 0.005, 20.0, 1.0, and 0.001. Throughout all tables, bold typeface indicates the best performance, while underlined values represent the second-best results." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 340, + 556, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 340, + 556, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 340, + 556, + 460 + ], + "type": "text", + "content": "We conduct comprehensive ablation studies to systematically evaluate the effectiveness of each component in our proposed PromptHash framework, with results presented in Tab. 2. The experiments examine five distinct variants: (a) a baseline implementation utilizing only the CLIP feature extraction network and hash function, excluding TAAP, AGSF, and PACL modules; (b) PromptHash w/o (PACL + AGSF), which retains only the TAAP module; (c) PromptHash w/o (TAAP + PACL), maintaining only the AGSF module; (d) PromptHash w/o AGSF, preserving TAAP and PACL modules; and (e) PromptHash w/o PACL, retaining TAAP and AGSF modules." + } + ] + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 323, + 500, + 547, + 556 + ], + "blocks": [ + { + "bbox": [ + 313, + 469, + 555, + 491 + ], + "lines": [ + { + "bbox": [ + 313, + 469, + 555, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 555, + 491 + ], + "type": "text", + "content": "Table 1. Summary of Feature Statistics for the Three Benchmark Datasets" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 500, + 547, + 556 + ], + "lines": [ + { + "bbox": [ + 323, + 500, + 547, + 556 + ], + "spans": [ + { + "bbox": [ + 323, + 500, + 547, + 556 + ], + "type": "table", + "html": "
Dataset detailsMIRFLICKR-25KNUS-WIDEMS COCO
Dataset Size24581192779122218
Training Size100001050010000
Retrieval Size22581190679117218
Query Size200021005000
Number of Categories242180
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Precision-Recall curves of different hash code lengths (16, 32, and 64 bits) on three benchmark datasets: MIRFLICKR-25K, NUS-WIDE, and MS COCO." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 141, + 310, + 222, + 379 + ], + "blocks": [ + { + "bbox": [ + 141, + 310, + 222, + 379 + ], + "lines": [ + { + "bbox": [ + 141, + 310, + 222, + 379 + ], + "spans": [ + { + "bbox": [ + 141, + 310, + 222, + 379 + ], + "type": "image", + "image_path": "8451a076d48848ecab2cf979c944e7f35a9cbbce326399e47491a2e60964108b.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 223, + 310, + 304, + 379 + ], + "blocks": [ + { + "bbox": [ + 223, + 310, + 304, + 379 + ], + "lines": [ + { + "bbox": [ + 223, + 310, + 304, + 379 + ], + "spans": [ + { + "bbox": [ + 223, + 310, + 304, + 379 + ], + "type": "image", + "image_path": "0dd442dd161f7b7af985b428d79c4048eab9969a089f71b95138937fe6a09ee0.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 306, + 310, + 387, + 379 + ], + "blocks": [ + { + "bbox": [ + 306, + 310, + 387, + 379 + ], + "lines": [ + { + "bbox": [ + 306, + 310, + 387, + 379 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 387, + 379 + ], + "type": "image", + "image_path": "8af4f8a5bb0d92e10ca288fc985f9a4f8a9447b843aa8130e1934d95c2138859.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 389, + 310, + 470, + 379 + ], + "blocks": [ + { + "bbox": [ + 389, + 310, + 470, + 379 + ], + "lines": [ + { + "bbox": [ + 389, + 310, + 470, + 379 + ], + "spans": [ + { + "bbox": [ + 389, + 310, + 470, + 379 + ], + "type": "image", + "image_path": "e136d5daba7d388a1c35da02a249839275cf2b5e817c0472ff98c92255aee0e4.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 471, + 310, + 553, + 379 + ], + "blocks": [ + { + "bbox": [ + 471, + 310, + 553, + 379 + ], + "lines": [ + { + "bbox": [ + 471, + 310, + 553, + 379 + ], + "spans": [ + { + "bbox": [ + 471, + 310, + 553, + 379 + ], + "type": "image", + "image_path": "3d4e6b7e3ea66095b6b2c6a8cd61ba862cb10f13de65e4d0bd61017cc942eab0.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 85, + 434, + 526, + 592 + ], + "blocks": [ + { + "bbox": [ + 159, + 414, + 449, + 426 + ], + "lines": [ + { + "bbox": [ + 159, + 414, + 449, + 426 + ], + "spans": [ + { + "bbox": [ + 159, + 414, + 449, + 426 + ], + "type": "text", + "content": "Table 2. Ablation study results of different components in the proposed method." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 434, + 526, + 592 + ], + "lines": [ + { + "bbox": [ + 85, + 434, + 526, + 592 + ], + "spans": [ + { + "bbox": [ + 85, + 434, + 526, + 592 + ], + "type": "table", + "html": "
MethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bit16bit32bit64bit16bit32bit64bit
I2Tbaseline0.84440.85900.86660.72280.73770.74880.70990.75940.7793
w/o (PACL+AGSF)0.87670.88550.89080.82780.85550.86560.72220.79100.8207
w/o (TAAP+PACL)0.91390.92690.93290.76680.78380.78930.71170.76870.7933
w/o AGSF0.93460.95120.95930.83770.85840.87090.74240.81110.8444
w/o PACL0.97200.98590.99240.90130.94500.96390.72460.82280.8725
PromptHash(Ours)0.98180.99600.99950.93130.97590.99310.76730.87820.9263
T2Ibaseline0.83830.84880.85240.73030.74770.75880.72010.75950.7885
w/o (PACL+AGSF)0.85580.86410.87040.79960.82720.83380.72050.78040.8103
w/o (TAAP+PACL)0.91400.92760.93310.76960.78410.79020.71410.77550.7973
w/o AGSF0.94200.95910.96700.81570.83130.84600.75090.80920.8414
w/o PACL0.97200.98590.99250.90600.95170.96760.72270.82720.8731
PromptHash(Ours)0.98160.99550.99950.93810.97610.99340.76670.87900.9283
", + "image_path": "205cc49acdf2d16cc5bd5bc1b3ffb0c844053a8f1f3e12bff97df6481d54e6ce.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 55, + 607, + 295, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 295, + 706 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 295, + 706 + ], + "type": "text", + "content": "prompt tokens optimizes prompt text semantics and original text semantics with image semantics as the center, resulting in high-quality hash codes. While results from PACL indicate that TAAP and AGSF modules substantially improve retrieval performance for high-bit hash codes, they are less effective for low-bit scenarios. Notably, the complete PromptHash framework, incorporating all three modules, successfully leverages their complementary strengths to enhance retrieval performance across all hash code lengths, validating the superiority of our designed modules." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 314, + 606, + 453, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 606, + 453, + 618 + ], + "spans": [ + { + "bbox": [ + 314, + 606, + 453, + 618 + ], + "type": "text", + "content": "4.3.2. Hyperparameter Analysis" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 625, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 625, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 625, + 555, + 713 + ], + "type": "text", + "content": "We conduct a comprehensive analysis of hyperparameters in our proposed PromptHash method, with results illustrated in Fig. 3 for the six hyperparameters in our overall objective function. The experimental results demonstrate optimal performance across all datasets when setting " + }, + { + "bbox": [ + 313, + 625, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\{\\alpha = 5.0, \\beta = 5.0, \\gamma = 0.005, \\mu = 5.0, \\sigma = 0.1, \\zeta = 0.001\\}" + }, + { + "bbox": [ + 313, + 625, + 555, + 713 + ], + "type": "text", + "content": ". Our analysis reveals that gradually increasing parameters while maintaining default values for others yields optimal mean Average Precision (mAP) across the three" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19655" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 101, + 555, + 347 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 553, + 93 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 553, + 93 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 553, + 93 + ], + "type": "text", + "content": "Table 3. For the Mean Average Precision (MAP) evaluation on the MIRFLICKR25K, NUS-WIDE, and MS COCO datasets (MAP@ALL), the best performance is in bold, the second-best is underlined, and results from original papers are marked with an asterisk (*)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 101, + 555, + 347 + ], + "lines": [ + { + "bbox": [ + 58, + 101, + 555, + 347 + ], + "spans": [ + { + "bbox": [ + 58, + 101, + 555, + 347 + ], + "type": "table", + "html": "
NetworkMethodsMIRFLICKR-25KNUS-WIDEMS COCO
16bit32bit64bitAvg16bit32bit64bitAvg16bit32bit64bitAvg
I2TCNNDCMH [16]0.72880.74110.74900.73960.52380.59950.61950.58090.51770.53110.54710.5320
CMHH [3]0.66490.66770.67310.66860.53120.54760.52990.53620.56570.55820.55400.5593
GCDH [2]0.79910.81230.82040.81060.71420.73670.74980.73360.72970.76510.79050.7618
CLIPDCHMT [32]0.82540.82840.82570.82650.68320.68920.70250.69160.64400.64650.65520.6486
MITH [23]0.83770.84910.85760.84810.70620.71800.71860.71430.71490.73730.75800.7367
DSPH [14]0.80810.83870.85050.83240.69530.70310.71610.70480.70490.75830.77280.7453
TwDH [33]0.77660.79150.80160.78990.66490.68550.69330.68120.65640.72070.74720.7081
DNpH [26]0.83990.84860.85000.84620.71350.71690.72470.71840.67540.68970.68620.6838
DHaPH [15]0.82710.83510.83240.83150.72150.73330.74100.73190.73100.74020.74960.7403
CMCL [39]0.84870.86110.86920.85970.71540.73140.74400.73030.74200.77010.79360.7686
VTPH* [4]0.90560.92490.93280.92110.77330.78700.79360.78460.72020.74770.77860.7488
PromptHash(Ours)0.98180.99600.99950.99240.93130.97590.99310.96680.76730.87820.92630.8573
T2ICNNDCMH [16]0.75200.76960.77760.76640.54400.59010.59560.57660.55100.58830.60500.5814
CMHH [3]0.66150.68510.69430.68030.48260.48680.47110.48020.50980.50710.50970.5089
GCDH [2]0.78490.80220.80670.79790.72150.74230.75340.73910.72610.76500.78850.7599
CLIPDCHMT [32]0.81150.81790.82000.81650.69200.70810.72080.70700.62820.63610.76740.6772
MITH [23]0.82880.84080.84830.83930.71220.72810.73350.72460.70450.73190.71680.7177
DSPH [14]0.79090.82150.83340.81530.70280.71650.73290.71740.70470.75520.75250.7375
TwDH [33]0.77580.78950.80300.78940.67190.71260.71530.69990.66030.72050.69900.6933
DNpH [26]0.81510.82490.83290.82430.72220.72650.73130.72670.65950.68010.69900.6795
DHaPH [15]0.80890.81700.81940.81510.72030.72840.73880.72920.69990.70370.79190.7318
CMCL [39]0.82900.83620.84020.83510.72900.74380.75110.74130.73960.76890.79620.7682
VTPH* [4]0.90200.92260.92780.91750.77080.78400.79330.78270.71850.75150.77430.7481
PromptHash(Ours)0.98160.99550.99950.99220.93810.97610.99340.96920.76670.87900.92830.8580
", + "image_path": "c4ebeee554201452bf9ccf207dca6914b50404751dae094ca509440c5afaa5e8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": "datasets. However, reducing " + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": " to 0.1 while simultaneously increasing " + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": " results in decreased mAP performance. Furthermore, when attempting to optimize all hyperparameters independently for each dataset, the resulting average mAP values prove inferior to those achieved by solely reducing " + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": " to 0.1. Additional experiments show that further reducing " + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": " to 0.05 also leads to degraded average mAP performance. These findings suggest that maintaining default values for all hyperparameters except the quantization loss weight " + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 361, + 294, + 525 + ], + "type": "text", + "content": " (set to 0.1) yields optimal average mAP across all three datasets. We hypothesize that this phenomenon occurs because PromptHash effectively aligns image-text features extracted by CLIP, resulting in high similarity between related image-text pairs and natural dissimilarity between unrelated pairs in the common Hamming space, thus requiring lower emphasis on quantization loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 533, + 228, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 228, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 228, + 544 + ], + "type": "text", + "content": "4.3.3. Comparison with State-of-the-Art" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": "As demonstrated in Tab. 3, our proposed PromptHash method achieves superior performance across all metrics on three public datasets. Using the mAP@all metric as a primary indicator, we observe significant improvements over the previous state-of-the-art methods. On the MIRFLICKR-25K dataset, PromptHash outperforms the second-best method (VTPH) by margins of " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "7.13\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "7.47\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " for I2T and T2I tasks, respectively. For the NUS-WIDE dataset, we achieve even more substantial improvements over VTPH, with gains of " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "18.22\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " for I2T and " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "18.65\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " for T2I tasks. On the MS COCO dataset, our method surpasses the previous best performer (CMCL) by " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "8.87\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "inline_equation", + "content": "8.98\\%" + }, + { + "bbox": [ + 55, + 548, + 295, + 679 + ], + "type": "text", + "content": " for I2T and T2I tasks, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 680, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 680, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 680, + 295, + 713 + ], + "type": "text", + "content": "The Precision-Recall curves in Fig. 4 demonstrate particularly notable improvements on MIRFLICKR-25K and NUS-WIDE datasets, where PromptHash significantly outperforms ex" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 361, + 555, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 555, + 494 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 555, + 494 + ], + "type": "text", + "content": "isting methods. This superior performance can be attributed to our method's effective handling of discrete word-based texts through affinity prompt learning and adaptive weighting modules, coupled with image-centric feature discrimination between foreground retrieval targets and background information. However, we observe relatively modest improvements on the MS COCO dataset, which we attribute to its unique characteristics: text annotations comprise complete sentences rather than discrete words, with annotations extending up to 625 words, of which only 3-5 words typically represent retrieval targets. This high noise data presents a particular challenge that could potentially be addressed in future work through text reconstruction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 506, + 388, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 506, + 388, + 518 + ], + "spans": [ + { + "bbox": [ + 314, + 506, + 388, + 518 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 526, + 553, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 553, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 553, + 592 + ], + "type": "text", + "content": "Most existing cross-modal hashing methods primarily focus on hashing function design and optimizing distances between different samples, while overlooking inherent issues within the sample sets themselves. Specifically, problems such as text semantic truncation and negative semantic information within the sample set can significantly limit retrieval performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "type": "text", + "content": "Our proposed PromptHash framework addresses these limitations through two key innovations. First, it introduces prompt learning for adaptively weighted learning of truncated text semantics, effectively improving retrieval performance under limited character encoding constraints. Second, it combines SSM and Transformer architectures with adaptive gated selection fusion, enabling efficient filtering and weighting of fused features. Furthermore, our novel Prompt Affinity Contrastive Learning module (PACL) balances prompt, textual, and visual features while bridging modality heterogeneity through feature alignment, significantly enhancing retrieval accuracy." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19656" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 146 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 146 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 146 + ], + "type": "text", + "content": "This work was supported by the Scientific and Technological Innovation 2030 Major Project under Grant 2022ZD0115800, the National Natural Science Foundation of China under Grant 62441213, and the Key Laboratory Open Projects in Xinjiang Uygur Autonomous Region under Grant 2023D04028." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 156, + 115, + 169 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 156, + 115, + 169 + ], + "spans": [ + { + "bbox": [ + 56, + 156, + 115, + 169 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 176, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 176, + 296, + 209 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 176, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 61, + 176, + 296, + 209 + ], + "type": "text", + "content": "[1] Cong Bai, Chao Zeng, Qing Ma, Jinglin Zhang, and Shengyong Chen. 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IEEE TKDE, 36(1): 239-260, 2024. 1" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19658" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_content_list.json b/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6f4db41c5c8363df96e1649335e533f5bd7068f1 --- /dev/null +++ b/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_content_list.json @@ -0,0 +1,1741 @@ +[ + { + "type": "text", + "text": "Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation", + "text_level": 1, + "bbox": [ + 91, + 130, + 906, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haotong Lin $^{1,2}$ Sida Peng $^{1\\dagger}$ Jingxiao Chen $^{3}$ Songyou Peng $^{4}$ Jiaming Sun $^{1}$ Minghuan Liu $^{3}$ Hujun Bao $^{1}$ Jiashi Feng $^{2}$ Xiaowei Zhou $^{1}$ Bingyi Kang $^{2}$", + "bbox": [ + 168, + 172, + 825, + 210 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Zhejiang University 2ByteDance Seed 3Shanghai Jiao Tong University 4ETH Zurich", + "bbox": [ + 133, + 215, + 864, + 236 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://PromptDA.github.io/", + "bbox": [ + 361, + 241, + 629, + 257 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2d5ca732a96357d869d3b8185285e1c75e3971622776938bd937167972981cc7.jpg", + "image_caption": [ + "(a) Prompt Depth Anything", + "Image & Low-cost LiDAR" + ], + "image_footnote": [], + "bbox": [ + 101, + 296, + 225, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8165f281835905ac8744dcade00ed0c4df41bf33ea10f2a7c7032ce12f4683e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 296, + 364, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a2b65c1fe65876089efb2fc4d28b6fe461af215c3b92b0f956b41f7f63599760.jpg", + "image_caption": [ + "Accurate metric depth" + ], + "image_footnote": [], + "bbox": [ + 364, + 296, + 486, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8593b736b08299cfa83b1c874aa79f0e02cf5fcaaf609a684bba1bd96ef702b6.jpg", + "image_caption": [ + "(c) High-res Accurate Depth Estimation for Dynamic Scenes", + "ARKit Depth: low-res & noisy", + "Figure 1. Illustration and capabilities of Prompt Depth Anything. (a) Prompt Depth Anything is a new paradigm for metric depth estimation, which is formulated as prompting a depth foundation model with a metric prompt, specifically utilizing a low-cost LiDAR as the prompt. (b) Our method enables consistent depth estimation, addressing the limitations of Metric3D v2 [25] that suffer from inaccurate scale and inconsistency. (c) It achieves accurate 4K accurate depth estimation, significantly surpassing ARKit LiDAR Depth $(240 \\times 320)$ ." + ], + "image_footnote": [], + "bbox": [ + 114, + 402, + 279, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8120958f7b4753aa472641b46be5b9c0ce951aa9ff65f22420a7a3674e223cce.jpg", + "image_caption": [ + "Ours: high-res & accurate" + ], + "image_footnote": [], + "bbox": [ + 308, + 402, + 475, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0d7683f264672980ee8a01fac9e093e94c909b28bc467da72e3750935261cd4c.jpg", + "image_caption": [ + "(b) Consistent Multi-view Depth Estimation for Static Scenes" + ], + "image_footnote": [], + "bbox": [ + 511, + 297, + 637, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2df15b1045dc2a795dcd79346fbe2f5b3a933d5b3d819f67a61c057590f8c3ed.jpg", + "image_caption": [ + "Groundtruth distance", + "Input viewpoints" + ], + "image_footnote": [], + "bbox": [ + 511, + 382, + 637, + 464 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a8ccb18b7b882c80235e3fc33a6d02a81ff6b980b29c814c357624f1a46b7140.jpg", + "image_caption": [ + "Err rate: $0.8\\% - 1.3\\%$", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 643, + 297, + 764, + 464 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/93f65daa27c7895954180e909383f1a61b71828b501347e7fd44154490c134f1.jpg", + "image_caption": [ + "Err rate: $14\\% -34\\%$", + "Metric3D v2" + ], + "image_footnote": [], + "bbox": [ + 774, + 299, + 895, + 464 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 585, + 326, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prompts play a critical role in unleashing the power of language and vision foundation models for specific tasks. For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation termed Prompt Depth Anything. Specifically, we use a low-cost LiDAR as the prompt to guide the Depth Anything model for accurate metric depth output, achieving up to 4K resolution. Our approach centers on a concise prompt fusion design that integrates the LiDAR at multiple scales within the depth decoder. To address training challenges posed by limited datasets containing both LiDAR depth and precise GT depth, we propose a scalable data pipeline that includes synthetic data LiDAR simulation and real data pseudo GT depth generation. Our approach sets new state-of-the-arts on the ARKitScenes and ScanNet++ datasets and benefits downstream applications, including", + "bbox": [ + 88, + 621, + 485, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D reconstruction and generalized robotic grasping.", + "bbox": [ + 513, + 573, + 859, + 588 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 617, + 643, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "High-quality depth perception is a fundamental challenge in computer vision and robotics. Recent monocular depth estimation has experienced a significant leap by scaling the model or data, leading to the flourishing of depth foundation models [19, 29, 72, 73]. These models demonstrate strong abilities in producing high-quality relative depth, but suffer from scale ambiguity, hindering their practical applications in autonomous driving and robotic manipulation, etc. Therefore, significant efforts have been made to achieve metric depth estimation, by either finetuning depth foundation models [6, 20] on metric datasets or training metric depth models with image intrinsics as additional inputs [8, 25, 45, 77]. However, neither of them can address the problem properly, as illustrated in Fig. 1(b).", + "bbox": [ + 509, + 643, + 906, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A natural question thus arises: Do these foundation models truly lack utility in accurate metric depth estimation? This reminds us to closely examine the foundation models", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author: Sida Peng.", + "bbox": [ + 114, + 886, + 303, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17070", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in natural language [1, 9] and vision [38, 39, 50], which often involve pre-training and instruction tuning stages. A properly designed prompt and a instruction dataset can unlock the power of foundation models on downstream tasks. Inspired by these successes, we propose a new paradigm for metric depth estimation by treating it as a downstream task, i.e., prompting a depth foundation model with metric information. We believe this prompt can take any form as long as the scale information is provided, e.g., camera intrinsics. In this paper, we validate the feasibility of the paradigm by choosing low-cost LiDAR as the prompt for two reasons. First, it provides precise metric scale information. Second, it is widely available, even in common mobile devices (e.g., Apple iPhone has a LiDAR).", + "bbox": [ + 89, + 90, + 480, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, based on Depth Anything [73], we propose Prompt Depth Anything, which achieves 4K resolution accurate metric depth estimation. At the core of our method is a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models [8, 73]. The prompt fusion architecture integrates the LiDAR depth at multiple scales within the DPT decoder, fusing the LiDAR features for depth decoding. The metric prompt provides precise spatial distance information, making the depth foundation model particularly serve as a local shape learner, resulting in accurate and high-resolution metric depth estimation.", + "bbox": [ + 89, + 304, + 480, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training Prompt Depth Anything requires both LiDAR depth and precise GT depth. However, existing synthetic data [49] lacks LiDAR depth, and real-world data [75] with LiDAR only has an imprecise GT depth of bad edges. To solve this challenge, we propose a scalable data pipeline that simulates low-resolution, noisy LiDAR for synthetic data and generates pseudo GT depth with high-quality edges for real data using a reconstruction method [2]. To mitigate errors in the pseudo GT depth from the 3D reconstruction, we introduce an edge-aware depth loss that leverages only the gradient of pseudo GT depth, which is prominent at edges. We experimentally demonstrate that these efforts result in highly accurate depth estimation.", + "bbox": [ + 89, + 472, + 480, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate the proposed method on ARKitScenes [3] and ScanNet++ [75] datasets containing iPhone ARKit depth. It consistently exhibits state-of-the-art performance across datasets and metrics. Even our zero-shot model achieves better performance compared to other methods [6, 73] in non-zero-shot testing, highlighting the generalization ability of prompting a foundation model. We also show that the foundation model and prompt of Prompt Depth Anything can be replaced with DepthPro [8] and vehicle LiDAR [53], respectively. Furthermore, we demonstrate that it benefits several downstream applications, including 3D reconstruction and generalized robotic object grasping.", + "bbox": [ + 89, + 670, + 480, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, this work has the following contributions:", + "bbox": [ + 109, + 853, + 472, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Prompt Depth Anything, a new paradigm for metric depth estimation by prompting a depth foundation model with a", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "low-cost LiDAR as the metric prompt.", + "bbox": [ + 526, + 90, + 782, + 106 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A concise prompt fusion architecture for depth foundation models, a scalable data pipeline, and an edge-aware depth loss to train Prompt Depth Anything.", + "- State-of-the-art performance on depth estimation benchmarks [3, 75], showing the extensibility of replacing depth foundation models and LiDAR sensors, and highlighting benefits for several downstream applications including 3D reconstruction and robotic object grasping." + ], + "bbox": [ + 513, + 107, + 903, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 244, + 653, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular depth estimation. Traditional methods [24, 52] rely on hand-crafted features for depth estimation. With the advent of deep learning, this field has seen significant advancements. Early learning-based approaches [15, 16] are often limited to a single dataset, lacking generalization capabilities. To enhance generalization, diverse datasets [13, 33, 58-60, 62, 63, 74], affine-invariant loss [46], and more powerful network architectures [47] have been introduced. More recently, latent diffusion models [50], pre-trained on extensive image generation tasks, have been applied to depth estimation [22, 29]. These models exhibit good generalization, estimating relative depth effectively, though they remain scale-agnostic. To achieve metric depth estimation, early methods either model the problem as global distribution classification [4, 5, 18, 36] or fine-tune a depth model on metric depth datasets [6, 34, 35]. Recent methods [20, 25, 45, 76, 77] discuss the ambiguity in monocular metric depth estimation and address it by incorporating camera intrinsic parameters. Although recent methods [8, 22, 25, 29, 45, 73, 77] exhibit strong generalization ability and claim to be depth foundation models [8, 19, 25, 73], metric depth estimation remains a challenge as shown in Fig. 1(b). We seek to address this challenge by prompting the depth foundation models with a metric prompt, inspired by the success of prompting in vision and vision-language models [38, 39, 79].", + "bbox": [ + 511, + 276, + 903, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth estimation with auxiliary sensors. Obtaining dense depth information through active sensors typically demands high power consumption [10, 65-69]. A more practical approach involves utilizing a low-power active sensor to capture sparse depth, which can then be completed into dense maps. Many studies investigate methods to fill in sparse depth data. Early works rely on filter-based [23, 27, 31] and optimization-based [17, 71] techniques for depth completion. More recent studies [11, 12, 14, 21, 37, 40, 54-56, 69, 80] adopt learning-based approaches for depth completion. Typically, these methods are not tested on real indoor LiDAR data but rather on simulated sparse lidar for depth datasets such as NYUv2 [16] to reconstruct complete depth. This is because real testing setups require both low-power and high-power LiDAR sensors. More recent", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17071", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6739d4056a8898d8508a7a040fc8ea193beeaf68dbed40a6730cb09da17a3ae0.jpg", + "image_caption": [ + "Figure 2. Overview of Prompt Depth Anything. (a) Prompt Depth Anything builds on a depth foundation model [73] with a ViT encoder and a DPT decoder, and adds a multi-scale prompt fusion design, using a prompt fusion block to fuse the metric information at each scale. (b) Since training requires both low-cost LiDAR and precise GT depth, we propose a scalable data pipeline that simulates LiDAR depth for synthetic data with precise GT depth, and generates pseudo GT depth for real data with LiDAR. An edge-aware depth loss is proposed to merge accurate edges from pseudo GT depth with accurate depth in textureless areas from FARO annotated GT depth on real data." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 493, + 276 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c94af6fcc796006d6bdd40b18cf94d91826c67fc6940c5c069e3f48603262813.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 898, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "works have collected both low-power and high-power Li-DAR data. To collect such data, DELTA [32] builds a suite to collect data using L5 and Intel RealSense 435i, while three other datasets [3, 48, 75] are collected using iPhone LiDAR and FARO LiDAR. We focus on the latter, as iPhone is widely available. A recent work similar to ours is Depth Prompting [42]. Our approach differs in that we use a network to take sparse depth as a prompt for the depth foundation model, achieving specific output. In contrast, they fuse sparse depth with features from the depth foundation model to post-process the foundation model output, which does not constitute prompting a foundation model.", + "bbox": [ + 88, + 369, + 483, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 566, + 181, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Monocular depth estimation models [8, 72, 73] are becoming depth foundation models for their generalization ability obtained from large-scale data. However, due to the inherent ambiguities, they cannot achieve high accuracy on metric depth estimation as shown in Fig. 1(b). Inspired by the success of prompting for vision [30, 39, 50] and language [1] foundation models, we propose Prompt Depth Anything prompting the depth foundation model with a metric prompt to achieve metric depth estimation. We take the low-cost LiDAR as the metric prompt in this work, as it has recently been integrated into lots of smartphones, making this setup highly practical. To be specific, we aim to prompt the depth foundation model to unleash its power for accurate metric depth estimation.", + "bbox": [ + 88, + 593, + 482, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary: Depth Foundation Model", + "text_level": 1, + "bbox": [ + 89, + 816, + 424, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current depth foundation models [7, 72, 73, 77] generally share similar network structures of DPT [47] networks. Specifically, given an image $\\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W}$ , they take a vision transformer (ViT) with multiple stages to extract to", + "bbox": [ + 88, + 839, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "kenized image features $\\{\\mathbf{T}_i\\}$ , where $\\mathbf{T}_i \\in \\mathbb{R}^{C_i \\times (\\frac{H}{p} \\times \\frac{W}{p} + 1)}$ represents the feature map at stage $S_i$ , $D_i$ is the feature dimension at stage $S_i$ , and $p$ is the patch size. The DPT decoder reassembles features from different stages into image-like representations $\\mathbf{F}_i \\in \\mathbb{R}^{D_i \\times \\frac{H}{p} \\times \\frac{W}{p}}$ with the reassemble operation [47]. Finally, a sequence of convolutional blending steps are applied to merge features $\\mathbf{F}_i$ across different stages, predicting a dense depth map $\\mathbf{D} \\in \\mathbb{R}^{H \\times W}$ .", + "bbox": [ + 511, + 367, + 906, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We note that there exists another line of depth foundation models [19, 22, 29] that use the image diffusion model [51] to estimate depth maps. Due to the high computational cost of diffusion models, we only consider DPT-based depth foundation models [8, 73] as our base model for real-time performance in this work.", + "bbox": [ + 511, + 496, + 906, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Prompt Depth Anything", + "text_level": 1, + "bbox": [ + 511, + 603, + 736, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we seek to find a concise way to incorporate a low-cost LiDAR (i.e., a low-resolution and noisy depth map) as a prompt into the depth foundation model. To this end, we propose a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models to integrate low-resolution depth information. As shown in Fig. 2(a), the prompt fusion architecture integrates low-resolution depth information at multiple scales within the DPT Decoder. Specifically, for each scale $S_{i}$ in the DPT Decoder, a low-resolution depth map $\\mathbf{L} \\in \\mathbb{R}^{1 \\times H_{\\mathrm{L}} \\times W_{\\mathrm{L}}}$ is firstly bilinearly resized to match the spatial dimensions of the current scale $\\mathbb{R}^{1 \\times H_{i} \\times W_{i}}$ . Then, the resized depth map is passed through a shallow convolutional network to extract depth features. After that, the extracted features are projected to the same dimension as the image features $\\mathbf{F}_{i} \\in \\mathbb{R}^{C_{i} \\times H_{i} \\times W_{i}}$ using a zero-initialized convolutional layer. Finally, the depth features are added to the DPT intermediate features for depth decoding. The illustration of", + "bbox": [ + 511, + 628, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17072", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f4be7cedfa4089ef4c1f076f7eda05818a28f35bd96a27749f4e254b96e1fa5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 88, + 480, + 164 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/493326964741bce62ecdb3c2cb091df7cbfe91a58575104c6cd165e606b9f845.jpg", + "image_caption": [ + "Reference Image & LiDAR w/ Sparse anchor Interp. w/ Linear Down. Interp.", + "Reference Image & LiDAR w/ Pseudo GT & Edge Loss w/ Anno. GT", + "Figure 3. Effects on the synthetic data lidar simulation and real data pseudo GT generation with the edge-aware depth loss. The middle and right columns are the depth prediction results of our different models. The two rows highlight the significance of sparse anchor interpolation for lidar simulation and pseudo GT generation with edge-aware depth loss, respectively." + ], + "image_footnote": [], + "bbox": [ + 93, + 175, + 480, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "this block design is shown in Fig. 2.", + "bbox": [ + 89, + 383, + 328, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed design has the following advantages. Firstly, it introduces only $5.7\\%$ additional computational overhead (1.789 TFLOPs v.s. 1.691 TFLOPs for a $756 \\times 1008$ image) to the original depth foundation model, and effectively addresses the ambiguity issue inherent in the depth foundation model as demonstrated in Tab. 3(b). Secondly, it fully inherits the capabilities of the depth foundation model because its encoder and decoder are initialized from the foundation model [73], and the proposed fusion architecture is zero-initialized, ensuring that the initial output is identical to that of the foundation model. We experimentally verify the importance of inheriting from a pretrained depth foundation model as shown in Tab. 3(c).", + "bbox": [ + 88, + 398, + 482, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "**Optional designs.** Inspired by conditional image generation methods [28, 43, 79], we also explore various potential prompt conditioning designs into the depth foundation model. Specifically, we experimented with the following designs: a) Adaptive LayerNorm [28, 44] which adapts the layer normalization parameters of the encoder blocks based on the conditioning input, b) CrossAttention [57] which injects a cross attention block after each self-attention block and integrates the conditioning input through cross-attention mechanisms, and c) ControlNet [79] which copies the encoder blocks and inputs control signals to the copied blocks to control the output depth. As shown in Tab. 3(d,e,f), our experiments reveal that these designs do not perform as well as the proposed fusion block. A plausible reason is that they are designed to integrate cross-modal information (e.g., text prompts), which does not effectively utilize the pixel alignment characteristics between the input low-res LiDAR and the output depth. We detail these optional designs in the supp.", + "bbox": [ + 89, + 598, + 482, + 885 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training Prompt Depth Anything", + "text_level": 1, + "bbox": [ + 513, + 90, + 807, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Prompt Depth Anything simultaneously requires a low-cost LiDAR and precise GT depth. However, synthetic data [49] do not contain LiDAR depth, real-world data with noisy LiDAR depth [75] only have imprecise depth annotations. Therefore, we propose a LiDAR simulation method for synthetic data and generate pseudo GT depth from Zip-NeRF [2] with an edge-aware depth loss for real data. Note that more effective approaches [64, 70] can be applied.", + "bbox": [ + 511, + 118, + 903, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Synthetic data: LiDAR simulation. A LiDAR depth map is low-resolution and noisy. The naive approach for simulating it is to directly downsample the synthetic data depth map. However, this method leads to the model learning depth super-resolution, as shown in Fig. 3, meaning that the model does not correct the LiDAR noise. To simulate the noise, we introduce a sparse anchor interpolation method. Specifically, we first downsample the GT depth map to low-resolution (192 × 256, exactly the depth resolution of iPhone ARKit Depth). Then we sample points on this depth map using a distorted grid with a stride (7 in practice). The remaining depth values are interpolated from these points using RGB similarity with KNN. As shown in Fig. 3, it effectively simulates LiDAR noise and results in better depth prediction. We provide visualization results of the simulated LiDAR in the supp.", + "bbox": [ + 511, + 248, + 906, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Real Data: Pseudo GT depth generation. We also add real data [75] to our training data. The annotated depth in ScanNet++ [75] is re-rendered from a mesh scanned by a high-power LiDAR sensor (FARO Focus Premium laser scanner). Due to the presence of many occlusions in the scene, several scan positions (typically 4 in a medium-sized scene in ScanNet++) result in an incomplete scanned mesh, leading to depth maps with numerous holes and poor edge quality, as illustrated in Fig. 2(b). Motivated by the success of reconstruction methods [2, 41], we propose using Zip-NeRF [2] to recover high-quality depth maps. Specifically, we train Zip-NeRF for each scene in ScanNet++ and re-rendered pseudo GT depth. To provide Zip-NeRF with high-quality and dense observations, we detect unblurred frames in Scannet++iPhone videos, and additionally utilize DSLR videos to provide high-quality dense-view images.", + "bbox": [ + 511, + 500, + 905, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Real Data: Edge-aware depth loss. Although Zip-NeRF can generate high-quality edge depth, reconstructing textureless and reflective regions remains challenging as shown in Fig. 2(b). In contrast, these areas (e.g., walls, floors, and ceilings etc.) are usually planar with few occlusions, and the annotations depth in FARO rendered depth is good in these regions. This motivates us to leverage the strengths of both. We propose an edge-aware depth loss to meet these requirements. Specifically, we use the FARO scanned mesh depth and the gradient of the pseudo GT depth to supervise output", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17073", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "depth and the gradient of the output depth, respectively:", + "bbox": [ + 89, + 90, + 460, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e d g e}} = L _ {1} \\left(\\mathbf {D} _ {\\mathrm {g t}}, \\hat {\\mathbf {D}}\\right) + \\lambda \\cdot \\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 118, + 480, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right) = \\left(| \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial x} | + | \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial y} |\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 148, + 480, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we set $\\lambda = 0.5$ . The depth gradient is mainly prominent at the edges, which is exactly where the pseudo GT depth excels. The gradient loss encourages the model to learn the accurate edges from the pseudo GT depth, while the L1 loss encourages the model to learn the overall depth, ultimately leading to excellent depth prediction. We experimentally verify the effectiveness of the edge-aware depth loss in Tab. 3(j) and Fig. 3.", + "bbox": [ + 89, + 175, + 482, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 305, + 307, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we provide essential information about the network design, depth normalization, and training details. Please refer to the supp. for more details.", + "bbox": [ + 89, + 328, + 482, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network details. We utilize the ViT-large model as our backbone model. The shallow convolutional network comprises two convolutional layers with a kernel size of 3 and a stride of 1. More details can be found in the supp. Detailed running time analysis can be found in Sec. 4.3.", + "bbox": [ + 89, + 377, + 483, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth normalization. The irregular range of input depth data can hinder network convergence. To address this, we normalize the LiDAR data using linear scaling to the range [0, 1], based on its minimum and maximum values. The network output is also normalized with the same scaling factor from LiDAR data, ensuring consistent scales and facilitating easier convergence during training.", + "bbox": [ + 89, + 457, + 483, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. We initiate training from the metric model released by Depth Anything v2 [73], incorporating a 10K step warm-up phase. During this warm-up phase, we fine-tune this metric model to output a normalized depth derived from the linear scaling of LiDAR data. Subsequently, we train our model for 200K steps. During the training process, the batch size is set to 2, utilizing 8 GPUs. We employ the AdamW optimizer, with a learning rate of 5e-6 for the ViT backbone and 5e-5 for the other parameters.", + "bbox": [ + 89, + 566, + 483, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 715, + 220, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 741, + 279, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We mainly conduct experiments on the HyperSim synthetic dataset [49] and two real-world datasets: ScanNet++ [75] and ARKitScenes [3], which provide iPhone RGB-LiDAR data $(192 \\times 256$ resolution) and annotated depth from a high-power LiDAR $(1440 \\times 1920$ resolution). We follow the suggested training and evaluation protocol in [3] for ARKitScenes, where $40\\mathrm{K}$ images are used for training and $5\\mathrm{K}$ images for evaluation. For the ScanNet++ dataset, we randomly select 20 scenes from its 50 validation scenes,", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/caa309fcc853b4327d24e693a78b620391fc57494380a4639ef2c00764687c72.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Zero ShotNet. / Post. / w/o LiDAR384 × 512768x10241440x1920
L1 ↓RMSE ↓L1 ↓RMSE ↓L1 ↓RMSE ↓
NoOurs0.01350.03260.01320.03150.01380.0316
MSPF0.01530.03690.01490.03620.01520.0363
Depth Pro*0.04370.06720.04350.06650.04250.0654
DepthAny. v2*0.04640.07150.04230.06600.04970.0764
ZoeDepth*0.08310.28730.06790.14210.05290.0793
Depth Pro*0.12220.14240.12250.14270.12440.1444
DepthAny. v2*0.09780.11800.07710.06470.09060.1125
ZoeDepth*0.21010.27840.17800.23190.15660.1788
YesOurssyn0.01610.03760.01630.03710.01700.0376
D.P.0.02510.04220.02530.04220.02490.0422
BPNet0.14940.21060.14930.21070.14910.2100
ARKit Depth0.02510.04240.02500.04230.02540.0426
DepthAny. v20.07160.16860.06160.13680.04940.0764
DepthAny. v10.07330.17570.06530.15300.05270.0859
Metric3D v20.06260.21040.05240.17210.04020.1045
ZoeDepth0.10070.19170.08900.16270.07620.1135
Lotus0.08530.17930.10380.17820.19410.2741
Marigold0.09080.18490.08070.15650.06920.1065
Metric3D v20.17770.27660.16630.24910.16150.2131
ZoeDepth0.61580.95770.56880.61290.53160.5605
", + "bbox": [ + 517, + 89, + 903, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons on ARKitScenes dataset. The terms Net., Post. and w/o LiDAR refer to the LiDAR depth usage of models, where \"Net.\" denotes network fusion, \"Post.\" indicates post-alignment using RANSAC, and \"w/o LiDAR\" means the output is metric depth. Methods marked with * are finetuned with their released models and code on ARKitScenes [3] and ScanNet++ [75] datasets.", + "bbox": [ + 511, + 349, + 906, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "amounting to approximately 5K images for our validation and the training set are from its 230 training scenes, containing about 60K images. To ensure a fair comparison, we additionally train a model with HyperSim training set to achieve zero-shot testing on ScanNet++ and ARKitScenes datasets. Besides depth accuracy metrics, we also report the TSDF reconstruction results of our method on ScanNet++, which reflects the depth consistency. We describe the details of the evaluation metrics in the supp.", + "bbox": [ + 511, + 458, + 906, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparisons with the State of the Art", + "text_level": 1, + "bbox": [ + 511, + 604, + 841, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our method against the current SOTA depth estimation methods from two classes: Monocular depth estimation (MDE) and depth completion/upsampling. For MDE methods, we compare our method with Metric3D v2 [25], ZoeDepth [6], DepthPro [8], Depth Anything v1 and v2 [72, 73] (short for DepthAny. v1 and v2), Marigold [29] and Lotus [22]. For depth completion/upsampling methods, we compare our method with BPNet [56], Depth Prompting [42] (short for D.P.), MSPF [61]. To make a fair comparison with MDE methods, we align their predictions with ARKit LiDAR depth using the RANSAC align method. According to whether they have seen the testing data types during training, we divide methods into two categories: zero-shot and non zero-shot. We train a model $\\mathrm{Ours}_{\\mathrm{syn}}$ only with HyperSim training set to make comparisons with the zero-shot methods. As shown in Tabs. 1 and 2 and Figs. 4 and 5, our method consistently outperforms the existing methods. Note that", + "bbox": [ + 511, + 628, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17074", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1894ea3f4088d3d69218ba928cc70b2bd94fa8bb06b2cc05a637935dd16065f1.jpg", + "image_caption": [ + "Figure 4. Qualitative comparisons with the state-of-the-art. \"Metric3D v2\" and \"Depth Any. v2\" are scale-shift corrected with ARKit depth. The pink boxes denote the GT depth and depth percentage error map, where red represents high error, and blue indicates low error." + ], + "image_footnote": [], + "bbox": [ + 124, + 88, + 870, + 559 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c72c263ab080252f495209221f6bfcf351d0d5f1234674177db8ebf36c542085.jpg", + "image_caption": [ + "Figure 5. Qualitative comparisons of TSDF reconstruction. * align denotes the scale-shift corrected depth with ARKit depth." + ], + "image_footnote": [], + "bbox": [ + 122, + 604, + 874, + 852 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17075", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/97a58a5b3f3c6480ff4bc562004ca2b2275aa337b6968b71399b3194b2237128.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Zero ShotNet. / Post. / w/o LiDARDepth EstimationTSDF Reconstruction
L1 ↓RMSE ↓AbsRel ↓δ0.5 ↑Acc ↓Comp ↓Prec ↑Recall ↑F-score ↑
NoOurs0.02500.08290.01750.97810.06990.06160.72550.81870.7619
MSPF*0.03260.09750.02260.96740.07720.06950.67380.77610.7133
DepthAny. v2*0.05100.10100.03710.94370.08080.07350.62750.71070.6595
ZoeDepth*0.05820.10690.04160.93250.08810.08010.57210.66400.6083
DepthAny. v2*0.09030.13470.06240.86570.12640.09170.42560.59540.4882
ZoeDepth*0.16750.19840.12780.58070.15670.15530.21640.25530.2323
YesOurssyn0.03270.09660.02240.97000.07460.06660.69030.79310.7307
D.P.0.03530.09830.02420.96570.08200.07470.64310.72340.6734
ARKit Depth0.03510.09870.02410.96590.08110.07430.64840.72800.6785
DepthAny. v20.05920.11450.04020.94040.08810.07470.55620.69460.6127
Depth Pro0.06380.12120.05100.92120.09040.07600.56950.69160.6187
Metric3D v20.05850.30870.04190.95290.07850.07520.62160.69940.6515
Marigold0.08280.14120.06030.87180.09990.07810.51280.66940.5740
DepthPro0.24060.28360.20150.52160.15370.14670.26840.37520.3086
Metric3D v20.12260.34030.08410.80090.08810.08010.57210.66400.6083
", + "bbox": [ + 153, + 88, + 841, + 313 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7c73292a30d95f7683466a45d441ba4db2a7eecef3248810f7d8122b30e017d2.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on ScanNet++ dataset. The terms Net, Post and w/o LiDAR refer to the LiDAR depth usage of models as the last table. Methods marked with * are finetuned with their released code on ARKitScenes [3] and ScanNet++ [75] datasets." + ], + "table_footnote": [], + "table_body": "
ARKitScenesScanNet++
L1 ↓AbsRel ↓Acc ↓Comp ↓F-Score ↑
(a) Oursyn (synthetic data)0.01630.01420.07460.06660.7307
(b) w/o prompting0.06050.05050.09230.08010.5696
(c) w/o foundation model0.01940.01690.07740.07130.7077
(d) AdaLN prompting0.01970.01650.07950.07250.6943
(e) Cross-atten. prompting0.05230.04430.09320.08190.5595
(f) Controlnet prompting0.02390.02060.07850.07260.6899
(g) a + ARKitScenes data0.01340.01150.07440.06620.7341
(h) g + ScanNet++ anno. GT0.01320.01140.06700.06140.7647
(i) g + ScanNet++ pseudo GT0.01390.01210.08350.07660.6505
(j) Ours (h,i+edge loss)0.01320.01150.06990.06160.7619
", + "bbox": [ + 94, + 362, + 480, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative ablations on ARKitScenes and ScanNet++ datasets. Please refer to Sec. 4.3 for detailed descriptions.", + "bbox": [ + 89, + 511, + 482, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Oursyn achieves better performance than all non-zero-shot models [61, 73] on ScanNet++, highlighting the generalization ability of prompting a depth foundation model.", + "bbox": [ + 89, + 554, + 482, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablations and Analysis", + "text_level": 1, + "bbox": [ + 89, + 608, + 305, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Prompting a depth foundation model. We assess its importance with two experiments: 1) Removing the prompting. Tab. 3(b) shows a significant performance drop. 2) Removing the foundation model initialization [73]. Tab. 3(c) shows a noticeable performance decline.", + "bbox": [ + 89, + 636, + 482, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Prompting architecture design. We study different designs: AdaLN, Cross-attention, and ControlNet as discussed in Sec. 3.2. Tab. 3(d,e,f) reveals that ControlNet performs best but still falls short of our method.", + "bbox": [ + 89, + 715, + 482, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training data and edge-aware depth loss. We initially incorporate ARKitScenes data, which only enhances performance on ARKitScenes (Tab. 3(g)). Then we add ScanNet++, which improves results on both ARKitScenes and ScanNet++ (Tab. 3(h)). However, the depth visualization remains less than ideal (Fig. 3). Tab. 3(i) show that direct supervision with pseudo GT depth from reconstruction methods decreases performance. Ultimately, employ", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f0cbae75084fc5da7f533290ca2bc1139cff113390458f0d1d8a805073d394d5.jpg", + "image_caption": [ + "Figure 6. Outdoor reconstruction by taking the vehicle LiDAR as metric prompt. Please refer to the supp. for more video results." + ], + "image_footnote": [], + "bbox": [ + 516, + 361, + 903, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing the edge-aware depth loss that utilizes pseudo GT depth and FARO annotated GT achieves comparable performance with Tab. 3(h) but with superior thin structure depth performance as shown in Fig. 3. We provide more qualitative ablation results in the supp.", + "bbox": [ + 511, + 513, + 906, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Running time analysis. Our model with ViT-L runs at 20.4 FPS for an image resolution of $768 \\times 1024$ on a A100 GPU. As ARKit6 supports 4K image recording, we test our model at a resolution of $2160 \\times 3840$ and achieve 2.0 FPS. Note that our model can also be implemented with ViT-S, where the corresponding speeds are 80.0 and 10.3 FPS. More testing results can be found in the supp.", + "bbox": [ + 511, + 592, + 908, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Zero-shot Testing on Diverse Scenes", + "text_level": 1, + "bbox": [ + 511, + 708, + 823, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Although our model is trained on indoor scenes, it generalizes well to various scenarios, including new rooms, gyms with thin structures, poorly lit museums, human and outdoor environments, as shown in Fig. 7, highlighting the effectiveness of prompting a depth foundation model. Please refer to the supp. for video results.", + "bbox": [ + 511, + 731, + 906, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Application: 3D Reconstruction", + "text_level": 1, + "bbox": [ + 511, + 830, + 795, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our consistent and scale-accurate depth estimation benefits the indoor 3D reconstruction as shown in Tab. 2 and Fig. 5. Besides, the prompt of our model can be easily replaced", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17076", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce3b85d05a2632a2ad85eeff1a0e5b04a8946a86d67c9a487385af10f5a0ec06.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 238, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32221f05ba826aa51bbfa024ecb1602a3048b6fb0bef12a2154cd89e261357c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 238, + 88, + 370, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0ff369aa5b5366acfec20eb6ee81429851da9e0f29c4b5946a603d4e0f40e9b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 88, + 460, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48a7c8bcef15e64eb5ba3c3da6b2fa391193b000829b4e1e01a681c0da356b82.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 88, + 607, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b5a052c384357a135c06142a4a986539bf4d968a1f21f720adf702f7f574c338.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 88, + 751, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2ae9ee77f2aad1943ae0521c775e95c7e0baeeb56e8345fd15c5daea04573f0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 88, + 898, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/29b80770a23124d022e867231f50039e3543a9a56e20de7de60e215a7abc8e26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 172, + 236, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0227ff15eb9ee56f77eb23669df4187eb4aa781f19b19a569cb7f85230e4528c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 238, + 172, + 370, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d0a43e9a3f9610daaccf8360397538c40acec53dd67686688acb579936a16e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 172, + 462, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3cdeb52ebdcb3de327185696e86100b24fa9bdfd6b910fe6334784f7cb6c3425.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 172, + 607, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/768a43cb292b9cac0df752d82c1e67755adbce3df2d4e67317c98284a4ca5786.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 172, + 751, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed488c368182431f1d775fcc463dadcb52a53a5eadd38a7b5171b9d2af3edafb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 172, + 898, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/389da1a51a4a9cfe1b35a328d38729c92fbeb3a30b39516d9e6d20485e27915a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 258, + 233, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b5a8d182b51269f993ddc013b456e7da4ecfa607513fd6c0cf8a9a77d9c6d209.jpg", + "image_caption": [ + "Figure 7. Zero-shot testing on diverse scenes." + ], + "image_footnote": [], + "bbox": [ + 238, + 258, + 370, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f8e2171c80abd63e170c94834cc3e30f6f61ec2fde114baac1bda14c0a2d8396.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 258, + 460, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/baddb5471700ba2394250fe119f9f33d60d82003e5105dcc49a816870f20a477.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 258, + 607, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7007a975fadc75766524929b2b52370881dad2d942022ef99f61bbd8b2f0638f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 258, + 751, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79fdeebbfea7b29e33826b182a604eaa7fbc472f023fea8d3c78c1113de25224.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 258, + 898, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f245ca7811fc55a5028d28ae613881c1a3b3bd1e906de4c3803710e7a954497d.jpg", + "image_caption": [ + "Figure 8. Robotic grasping setup and input signal types. Our goal is to grasp objects of various types using image/LiDAR/depth inputs. Red rectangles indicate potential object positions." + ], + "image_footnote": [], + "bbox": [ + 93, + 376, + 336, + 542 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79ddd2f611b37f79a0b90654981df45b5aac5b13e4e9e2b457d63841f5181668.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 336, + 377, + 480, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with vehicle LiDAR, which enables our model to achieve large-scale outdoor scene reconstruction as shown in Fig. 6. We detail the setup and include more video results for dynamic streets in the supp.", + "bbox": [ + 89, + 611, + 482, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Application: Generalized Robotic Grasping", + "text_level": 1, + "bbox": [ + 89, + 680, + 464, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We set up a robotic platform to test our model in generalized robotic manipulation (Fig. 8), which typically requires depth or RGB as observations. Good depth estimation enhances the generalization ability because it accurately describes the 3D information of surroundings [26, 78]. Specifically, we train an ACT policy [81] to grasp various objects into the box, using different types of input signals such as RGB, LiDAR, and depth data from our model. We empirically find that our model generalizes well to unseen objects like transparent and specular objects when trained on diffusive objects, outperforming RGB and LiDAR inputs as shown in Tab. 4. This is because RGB is dominated by color, which leads to poor generalization across objects, and", + "bbox": [ + 89, + 704, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5364eda7a4092a88f25ad337c181eee37d4f2eb217a858f132f6b71ff066ab06.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Input SignalDiffusiveTransparentSpecular
Red CanGreen Can
Ours1.0/1.0/1.01.0/1.0/1.00.3/1.0/1.00.8/1.0/0.9
LiDAR1.0/1.0/1.01.0/1.0/0.20.5/0.4/0.00.7/1.0/0.0
RGB1.0/1.0/0.01.0/1.0/0.00.2/1.0/0.00.0/0.9/0.9
", + "bbox": [ + 517, + 376, + 905, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Grasping success rate on various objects. Three numbers indicate objects placed at near, middle, and far positions. The grasping policy is trained on diffusive and tested on all objects.", + "bbox": [ + 511, + 452, + 906, + 496 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the iPhone LiDAR depth is noisy and lacks the capability to perceive transparent objects. Please refer to the supp. for detailed setup descriptions and videos.", + "bbox": [ + 511, + 502, + 906, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Discussions", + "text_level": 1, + "bbox": [ + 511, + 566, + 769, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduced a new paradigm for metric depth estimation, formulated as prompting a depth foundation model with metric information. We validated the feasibility of the paradigm by choosing the low-cost LiDAR depth as the prompt. A scalable data pipeline was proposed to generate synthetic LiDAR depth and pseudo GT depth for training. Extensive experiments demonstrate the superiority of our method against existing monocular depth estimation and depth completion/upsampling methods. Furthermore, we showed that it benefits for downstream tasks including 3D reconstruction and generalized robotic grasping.", + "bbox": [ + 511, + 593, + 906, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. This work has some known limitations. For instance, when using the iPhone LiDAR as the prompt, it cannot handle long-range depth, as the iPhone LiDAR detects very noisy depth for far objects. Additionally, we observed some temporal flickering of LiDAR depth, leading to a flickering depth prediction. These issues can be addressed in future works by considering more advanced prompt learning techniques that can extend the effective range and temporal prompt tuning.", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17077", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was partially supported by NSFC (No. 62402427, U24B20154, 623B2091), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), Information Technology Center and State Key Lab of CAD&CG, and Zhejiang University Education Foundation Qizhen Scholar Foundation.", + "bbox": [ + 89, + 90, + 485, + 183 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 195, + 187, + 210 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv, 2023. 2, 3", + "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Zip-nerf: Anti-aliased grid-based neural radiance fields. 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Robotics: Science and Systems, 2023. 8" + ], + "bbox": [ + 516, + 90, + 903, + 202 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17080", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_model.json b/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3f20901ca4244636403ce5c0d6d79a25ec698e78 --- /dev/null +++ b/2025/Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation/5ba6a389-8293-4209-b8d7-39d2a373b186_model.json @@ -0,0 +1,2719 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.131, + 0.908, + 0.153 + ], + "angle": 0, + "content": "Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation" + }, + { + "type": "text", + "bbox": [ + 0.169, + 0.173, + 0.826, + 0.212 + ], + "angle": 0, + "content": "Haotong Lin\\(^{1,2}\\) Sida Peng\\(^{1\\dagger}\\) Jingxiao Chen\\(^{3}\\) Songyou Peng\\(^{4}\\) Jiaming Sun\\(^{1}\\) Minghuan Liu\\(^{3}\\) Hujun Bao\\(^{1}\\) Jiashi Feng\\(^{2}\\) Xiaowei Zhou\\(^{1}\\) Bingyi Kang\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.217, + 0.865, + 0.237 + ], + "angle": 0, + "content": "1Zhejiang University 2ByteDance Seed 3Shanghai Jiao Tong University 4ETH Zurich" + }, + { + "type": "text", + "bbox": [ + 0.362, + 0.242, + 0.63, + 0.258 + ], + "angle": 0, + "content": "https://PromptDA.github.io/" + }, + { + "type": "image_caption", + "bbox": [ + 0.208, + 0.281, + 0.381, + 0.295 + ], + "angle": 0, + "content": "(a) Prompt Depth Anything" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.297, + 0.226, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.366, + 0.226, + 0.375 + ], + "angle": 0, + "content": "Image & Low-cost LiDAR" + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.297, + 0.365, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.297, + 0.487, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.366, + 0.482, + 0.375 + ], + "angle": 0, + "content": "Accurate metric depth" + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.389, + 0.482, + 0.403 + ], + "angle": 0, + "content": "(c) High-res Accurate Depth Estimation for Dynamic Scenes" + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.404, + 0.28, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.477, + 0.266, + 0.488 + ], + "angle": 0, + "content": "ARKit Depth: low-res & noisy" + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.404, + 0.477, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.477, + 0.457, + 0.488 + ], + "angle": 0, + "content": "Ours: high-res & accurate" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.281, + 0.895, + 0.295 + ], + "angle": 0, + "content": "(b) Consistent Multi-view Depth Estimation for Static Scenes" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.299, + 0.638, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.383, + 0.638, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.466, + 0.621, + 0.474 + ], + "angle": 0, + "content": "Groundtruth distance" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.477, + 0.619, + 0.488 + ], + "angle": 0, + "content": "Input viewpoints" + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.299, + 0.765, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.661, + 0.466, + 0.749, + 0.474 + ], + "angle": 0, + "content": "Err rate: \\(0.8\\% - 1.3\\%\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.477, + 0.718, + 0.486 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.3, + 0.897, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.466, + 0.877, + 0.474 + ], + "angle": 0, + "content": "Err rate: \\(14\\% -34\\%\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.803, + 0.477, + 0.866, + 0.486 + ], + "angle": 0, + "content": "Metric3D v2" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.5, + 0.907, + 0.557 + ], + "angle": 0, + "content": "Figure 1. Illustration and capabilities of Prompt Depth Anything. (a) Prompt Depth Anything is a new paradigm for metric depth estimation, which is formulated as prompting a depth foundation model with a metric prompt, specifically utilizing a low-cost LiDAR as the prompt. (b) Our method enables consistent depth estimation, addressing the limitations of Metric3D v2 [25] that suffer from inaccurate scale and inconsistency. (c) It achieves accurate 4K accurate depth estimation, significantly surpassing ARKit LiDAR Depth \\((240 \\times 320)\\)." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.587, + 0.327, + 0.603 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.622, + 0.486, + 0.864 + ], + "angle": 0, + "content": "Prompts play a critical role in unleashing the power of language and vision foundation models for specific tasks. For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation termed Prompt Depth Anything. Specifically, we use a low-cost LiDAR as the prompt to guide the Depth Anything model for accurate metric depth output, achieving up to 4K resolution. Our approach centers on a concise prompt fusion design that integrates the LiDAR at multiple scales within the depth decoder. To address training challenges posed by limited datasets containing both LiDAR depth and precise GT depth, we propose a scalable data pipeline that includes synthetic data LiDAR simulation and real data pseudo GT depth generation. Our approach sets new state-of-the-arts on the ARKitScenes and ScanNet++ datasets and benefits downstream applications, including" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.574, + 0.86, + 0.589 + ], + "angle": 0, + "content": "3D reconstruction and generalized robotic grasping." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.618, + 0.644, + 0.633 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.644, + 0.907, + 0.854 + ], + "angle": 0, + "content": "High-quality depth perception is a fundamental challenge in computer vision and robotics. Recent monocular depth estimation has experienced a significant leap by scaling the model or data, leading to the flourishing of depth foundation models [19, 29, 72, 73]. These models demonstrate strong abilities in producing high-quality relative depth, but suffer from scale ambiguity, hindering their practical applications in autonomous driving and robotic manipulation, etc. Therefore, significant efforts have been made to achieve metric depth estimation, by either finetuning depth foundation models [6, 20] on metric datasets or training metric depth models with image intrinsics as additional inputs [8, 25, 45, 77]. However, neither of them can address the problem properly, as illustrated in Fig. 1(b)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "A natural question thus arises: Do these foundation models truly lack utility in accurate metric depth estimation? This reminds us to closely examine the foundation models" + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.887, + 0.304, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author: Sida Peng." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17070" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.302 + ], + "angle": 0, + "content": "in natural language [1, 9] and vision [38, 39, 50], which often involve pre-training and instruction tuning stages. A properly designed prompt and a instruction dataset can unlock the power of foundation models on downstream tasks. Inspired by these successes, we propose a new paradigm for metric depth estimation by treating it as a downstream task, i.e., prompting a depth foundation model with metric information. We believe this prompt can take any form as long as the scale information is provided, e.g., camera intrinsics. In this paper, we validate the feasibility of the paradigm by choosing low-cost LiDAR as the prompt for two reasons. First, it provides precise metric scale information. Second, it is widely available, even in common mobile devices (e.g., Apple iPhone has a LiDAR)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.305, + 0.482, + 0.472 + ], + "angle": 0, + "content": "Specifically, based on Depth Anything [73], we propose Prompt Depth Anything, which achieves 4K resolution accurate metric depth estimation. At the core of our method is a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models [8, 73]. The prompt fusion architecture integrates the LiDAR depth at multiple scales within the DPT decoder, fusing the LiDAR features for depth decoding. The metric prompt provides precise spatial distance information, making the depth foundation model particularly serve as a local shape learner, resulting in accurate and high-resolution metric depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.473, + 0.482, + 0.669 + ], + "angle": 0, + "content": "Training Prompt Depth Anything requires both LiDAR depth and precise GT depth. However, existing synthetic data [49] lacks LiDAR depth, and real-world data [75] with LiDAR only has an imprecise GT depth of bad edges. To solve this challenge, we propose a scalable data pipeline that simulates low-resolution, noisy LiDAR for synthetic data and generates pseudo GT depth with high-quality edges for real data using a reconstruction method [2]. To mitigate errors in the pseudo GT depth from the 3D reconstruction, we introduce an edge-aware depth loss that leverages only the gradient of pseudo GT depth, which is prominent at edges. We experimentally demonstrate that these efforts result in highly accurate depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.671, + 0.482, + 0.852 + ], + "angle": 0, + "content": "We evaluate the proposed method on ARKitScenes [3] and ScanNet++ [75] datasets containing iPhone ARKit depth. It consistently exhibits state-of-the-art performance across datasets and metrics. Even our zero-shot model achieves better performance compared to other methods [6, 73] in non-zero-shot testing, highlighting the generalization ability of prompting a foundation model. We also show that the foundation model and prompt of Prompt Depth Anything can be replaced with DepthPro [8] and vehicle LiDAR [53], respectively. Furthermore, we demonstrate that it benefits several downstream applications, including 3D reconstruction and generalized robotic object grasping." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.854, + 0.473, + 0.869 + ], + "angle": 0, + "content": "In summary, this work has the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- Prompt Depth Anything, a new paradigm for metric depth estimation by prompting a depth foundation model with a" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.092, + 0.783, + 0.107 + ], + "angle": 0, + "content": "low-cost LiDAR as the metric prompt." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.108, + 0.905, + 0.151 + ], + "angle": 0, + "content": "- A concise prompt fusion architecture for depth foundation models, a scalable data pipeline, and an edge-aware depth loss to train Prompt Depth Anything." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.153, + 0.905, + 0.228 + ], + "angle": 0, + "content": "- State-of-the-art performance on depth estimation benchmarks [3, 75], showing the extensibility of replacing depth foundation models and LiDAR sensors, and highlighting benefits for several downstream applications including 3D reconstruction and robotic object grasping." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.108, + 0.905, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.246, + 0.655, + 0.261 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.277, + 0.905, + 0.669 + ], + "angle": 0, + "content": "Monocular depth estimation. Traditional methods [24, 52] rely on hand-crafted features for depth estimation. With the advent of deep learning, this field has seen significant advancements. Early learning-based approaches [15, 16] are often limited to a single dataset, lacking generalization capabilities. To enhance generalization, diverse datasets [13, 33, 58-60, 62, 63, 74], affine-invariant loss [46], and more powerful network architectures [47] have been introduced. More recently, latent diffusion models [50], pre-trained on extensive image generation tasks, have been applied to depth estimation [22, 29]. These models exhibit good generalization, estimating relative depth effectively, though they remain scale-agnostic. To achieve metric depth estimation, early methods either model the problem as global distribution classification [4, 5, 18, 36] or fine-tune a depth model on metric depth datasets [6, 34, 35]. Recent methods [20, 25, 45, 76, 77] discuss the ambiguity in monocular metric depth estimation and address it by incorporating camera intrinsic parameters. Although recent methods [8, 22, 25, 29, 45, 73, 77] exhibit strong generalization ability and claim to be depth foundation models [8, 19, 25, 73], metric depth estimation remains a challenge as shown in Fig. 1(b). We seek to address this challenge by prompting the depth foundation models with a metric prompt, inspired by the success of prompting in vision and vision-language models [38, 39, 79]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Depth estimation with auxiliary sensors. Obtaining dense depth information through active sensors typically demands high power consumption [10, 65-69]. A more practical approach involves utilizing a low-power active sensor to capture sparse depth, which can then be completed into dense maps. Many studies investigate methods to fill in sparse depth data. Early works rely on filter-based [23, 27, 31] and optimization-based [17, 71] techniques for depth completion. More recent studies [11, 12, 14, 21, 37, 40, 54-56, 69, 80] adopt learning-based approaches for depth completion. Typically, these methods are not tested on real indoor LiDAR data but rather on simulated sparse lidar for depth datasets such as NYUv2 [16] to reconstruct complete depth. This is because real testing setups require both low-power and high-power LiDAR sensors. More recent" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17071" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.495, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.9, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.285, + 0.907, + 0.356 + ], + "angle": 0, + "content": "Figure 2. Overview of Prompt Depth Anything. (a) Prompt Depth Anything builds on a depth foundation model [73] with a ViT encoder and a DPT decoder, and adds a multi-scale prompt fusion design, using a prompt fusion block to fuse the metric information at each scale. (b) Since training requires both low-cost LiDAR and precise GT depth, we propose a scalable data pipeline that simulates LiDAR depth for synthetic data with precise GT depth, and generates pseudo GT depth for real data with LiDAR. An edge-aware depth loss is proposed to merge accurate edges from pseudo GT depth with accurate depth in textureless areas from FARO annotated GT depth on real data." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.371, + 0.485, + 0.552 + ], + "angle": 0, + "content": "works have collected both low-power and high-power Li-DAR data. To collect such data, DELTA [32] builds a suite to collect data using L5 and Intel RealSense 435i, while three other datasets [3, 48, 75] are collected using iPhone LiDAR and FARO LiDAR. We focus on the latter, as iPhone is widely available. A recent work similar to ours is Depth Prompting [42]. Our approach differs in that we use a network to take sparse depth as a prompt for the depth foundation model, achieving specific output. In contrast, they fuse sparse depth with features from the depth foundation model to post-process the foundation model output, which does not constitute prompting a foundation model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.567, + 0.182, + 0.584 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.594, + 0.483, + 0.806 + ], + "angle": 0, + "content": "Monocular depth estimation models [8, 72, 73] are becoming depth foundation models for their generalization ability obtained from large-scale data. However, due to the inherent ambiguities, they cannot achieve high accuracy on metric depth estimation as shown in Fig. 1(b). Inspired by the success of prompting for vision [30, 39, 50] and language [1] foundation models, we propose Prompt Depth Anything prompting the depth foundation model with a metric prompt to achieve metric depth estimation. We take the low-cost LiDAR as the metric prompt in this work, as it has recently been integrated into lots of smartphones, making this setup highly practical. To be specific, we aim to prompt the depth foundation model to unleash its power for accurate metric depth estimation." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.817, + 0.426, + 0.833 + ], + "angle": 0, + "content": "3.1. Preliminary: Depth Foundation Model" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.84, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Current depth foundation models [7, 72, 73, 77] generally share similar network structures of DPT [47] networks. Specifically, given an image \\(\\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W}\\), they take a vision transformer (ViT) with multiple stages to extract to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.368, + 0.907, + 0.496 + ], + "angle": 0, + "content": "kenized image features \\(\\{\\mathbf{T}_i\\}\\), where \\(\\mathbf{T}_i \\in \\mathbb{R}^{C_i \\times (\\frac{H}{p} \\times \\frac{W}{p} + 1)}\\) represents the feature map at stage \\(S_i\\), \\(D_i\\) is the feature dimension at stage \\(S_i\\), and \\(p\\) is the patch size. The DPT decoder reassembles features from different stages into image-like representations \\(\\mathbf{F}_i \\in \\mathbb{R}^{D_i \\times \\frac{H}{p} \\times \\frac{W}{p}}\\) with the reassemble operation [47]. Finally, a sequence of convolutional blending steps are applied to merge features \\(\\mathbf{F}_i\\) across different stages, predicting a dense depth map \\(\\mathbf{D} \\in \\mathbb{R}^{H \\times W}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.497, + 0.907, + 0.587 + ], + "angle": 0, + "content": "We note that there exists another line of depth foundation models [19, 22, 29] that use the image diffusion model [51] to estimate depth maps. Due to the high computational cost of diffusion models, we only consider DPT-based depth foundation models [8, 73] as our base model for real-time performance in this work." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.738, + 0.621 + ], + "angle": 0, + "content": "3.2. Prompt Depth Anything" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.902 + ], + "angle": 0, + "content": "In this section, we seek to find a concise way to incorporate a low-cost LiDAR (i.e., a low-resolution and noisy depth map) as a prompt into the depth foundation model. To this end, we propose a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models to integrate low-resolution depth information. As shown in Fig. 2(a), the prompt fusion architecture integrates low-resolution depth information at multiple scales within the DPT Decoder. Specifically, for each scale \\( S_{i} \\) in the DPT Decoder, a low-resolution depth map \\( \\mathbf{L} \\in \\mathbb{R}^{1 \\times H_{\\mathrm{L}} \\times W_{\\mathrm{L}}} \\) is firstly bilinearly resized to match the spatial dimensions of the current scale \\( \\mathbb{R}^{1 \\times H_{i} \\times W_{i}} \\). Then, the resized depth map is passed through a shallow convolutional network to extract depth features. After that, the extracted features are projected to the same dimension as the image features \\( \\mathbf{F}_{i} \\in \\mathbb{R}^{C_{i} \\times H_{i} \\times W_{i}} \\) using a zero-initialized convolutional layer. Finally, the depth features are added to the DPT intermediate features for depth decoding. The illustration of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17072" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.166, + 0.475, + 0.176 + ], + "angle": 0, + "content": "Reference Image & LiDAR w/ Sparse anchor Interp. w/ Linear Down. Interp." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.176, + 0.482, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.253, + 0.448, + 0.263 + ], + "angle": 0, + "content": "Reference Image & LiDAR w/ Pseudo GT & Edge Loss w/ Anno. GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.275, + 0.483, + 0.358 + ], + "angle": 0, + "content": "Figure 3. Effects on the synthetic data lidar simulation and real data pseudo GT generation with the edge-aware depth loss. The middle and right columns are the depth prediction results of our different models. The two rows highlight the significance of sparse anchor interpolation for lidar simulation and pseudo GT generation with edge-aware depth loss, respectively." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.384, + 0.33, + 0.399 + ], + "angle": 0, + "content": "this block design is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.4, + 0.483, + 0.595 + ], + "angle": 0, + "content": "The proposed design has the following advantages. Firstly, it introduces only \\(5.7\\%\\) additional computational overhead (1.789 TFLOPs v.s. 1.691 TFLOPs for a \\(756 \\times 1008\\) image) to the original depth foundation model, and effectively addresses the ambiguity issue inherent in the depth foundation model as demonstrated in Tab. 3(b). Secondly, it fully inherits the capabilities of the depth foundation model because its encoder and decoder are initialized from the foundation model [73], and the proposed fusion architecture is zero-initialized, ensuring that the initial output is identical to that of the foundation model. We experimentally verify the importance of inheriting from a pretrained depth foundation model as shown in Tab. 3(c)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.886 + ], + "angle": 0, + "content": "**Optional designs.** Inspired by conditional image generation methods [28, 43, 79], we also explore various potential prompt conditioning designs into the depth foundation model. Specifically, we experimented with the following designs: a) Adaptive LayerNorm [28, 44] which adapts the layer normalization parameters of the encoder blocks based on the conditioning input, b) CrossAttention [57] which injects a cross attention block after each self-attention block and integrates the conditioning input through cross-attention mechanisms, and c) ControlNet [79] which copies the encoder blocks and inputs control signals to the copied blocks to control the output depth. As shown in Tab. 3(d,e,f), our experiments reveal that these designs do not perform as well as the proposed fusion block. A plausible reason is that they are designed to integrate cross-modal information (e.g., text prompts), which does not effectively utilize the pixel alignment characteristics between the input low-res LiDAR and the output depth. We detail these optional designs in the supp." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.808, + 0.108 + ], + "angle": 0, + "content": "3.3. Training Prompt Depth Anything" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.119, + 0.905, + 0.241 + ], + "angle": 0, + "content": "Training Prompt Depth Anything simultaneously requires a low-cost LiDAR and precise GT depth. However, synthetic data [49] do not contain LiDAR depth, real-world data with noisy LiDAR depth [75] only have imprecise depth annotations. Therefore, we propose a LiDAR simulation method for synthetic data and generate pseudo GT depth from Zip-NeRF [2] with an edge-aware depth loss for real data. Note that more effective approaches [64, 70] can be applied." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.907, + 0.492 + ], + "angle": 0, + "content": "Synthetic data: LiDAR simulation. A LiDAR depth map is low-resolution and noisy. The naive approach for simulating it is to directly downsample the synthetic data depth map. However, this method leads to the model learning depth super-resolution, as shown in Fig. 3, meaning that the model does not correct the LiDAR noise. To simulate the noise, we introduce a sparse anchor interpolation method. Specifically, we first downsample the GT depth map to low-resolution (192 × 256, exactly the depth resolution of iPhone ARKit Depth). Then we sample points on this depth map using a distorted grid with a stride (7 in practice). The remaining depth values are interpolated from these points using RGB similarity with KNN. As shown in Fig. 3, it effectively simulates LiDAR noise and results in better depth prediction. We provide visualization results of the simulated LiDAR in the supp." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.5, + 0.906, + 0.742 + ], + "angle": 0, + "content": "Real Data: Pseudo GT depth generation. We also add real data [75] to our training data. The annotated depth in ScanNet++ [75] is re-rendered from a mesh scanned by a high-power LiDAR sensor (FARO Focus Premium laser scanner). Due to the presence of many occlusions in the scene, several scan positions (typically 4 in a medium-sized scene in ScanNet++) result in an incomplete scanned mesh, leading to depth maps with numerous holes and poor edge quality, as illustrated in Fig. 2(b). Motivated by the success of reconstruction methods [2, 41], we propose using Zip-NeRF [2] to recover high-quality depth maps. Specifically, we train Zip-NeRF for each scene in ScanNet++ and re-rendered pseudo GT depth. To provide Zip-NeRF with high-quality and dense observations, we detect unblurred frames in Scannet++iPhone videos, and additionally utilize DSLR videos to provide high-quality dense-view images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Real Data: Edge-aware depth loss. Although Zip-NeRF can generate high-quality edge depth, reconstructing textureless and reflective regions remains challenging as shown in Fig. 2(b). In contrast, these areas (e.g., walls, floors, and ceilings etc.) are usually planar with few occlusions, and the annotations depth in FARO rendered depth is good in these regions. This motivates us to leverage the strengths of both. We propose an edge-aware depth loss to meet these requirements. Specifically, we use the FARO scanned mesh depth and the gradient of the pseudo GT depth to supervise output" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17073" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.461, + 0.108 + ], + "angle": 0, + "content": "depth and the gradient of the output depth, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.119, + 0.482, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e d g e}} = L _ {1} \\left(\\mathbf {D} _ {\\mathrm {g t}}, \\hat {\\mathbf {D}}\\right) + \\lambda \\cdot \\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.149, + 0.482, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right) = \\left(| \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial x} | + | \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial y} |\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.176, + 0.483, + 0.297 + ], + "angle": 0, + "content": "In practice, we set \\(\\lambda = 0.5\\). The depth gradient is mainly prominent at the edges, which is exactly where the pseudo GT depth excels. The gradient loss encourages the model to learn the accurate edges from the pseudo GT depth, while the L1 loss encourages the model to learn the overall depth, ultimately leading to excellent depth prediction. We experimentally verify the effectiveness of the edge-aware depth loss in Tab. 3(j) and Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.306, + 0.308, + 0.322 + ], + "angle": 0, + "content": "3.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.329, + 0.483, + 0.375 + ], + "angle": 0, + "content": "In this section, we provide essential information about the network design, depth normalization, and training details. Please refer to the supp. for more details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.378, + 0.484, + 0.455 + ], + "angle": 0, + "content": "Network details. We utilize the ViT-large model as our backbone model. The shallow convolutional network comprises two convolutional layers with a kernel size of 3 and a stride of 1. More details can be found in the supp. Detailed running time analysis can be found in Sec. 4.3." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.484, + 0.564 + ], + "angle": 0, + "content": "Depth normalization. The irregular range of input depth data can hinder network convergence. To address this, we normalize the LiDAR data using linear scaling to the range [0, 1], based on its minimum and maximum values. The network output is also normalized with the same scaling factor from LiDAR data, ensuring consistent scales and facilitating easier convergence during training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.567, + 0.484, + 0.704 + ], + "angle": 0, + "content": "Training details. We initiate training from the metric model released by Depth Anything v2 [73], incorporating a 10K step warm-up phase. During this warm-up phase, we fine-tune this metric model to output a normalized depth derived from the linear scaling of LiDAR data. Subsequently, we train our model for 200K steps. During the training process, the batch size is set to 2, utilizing 8 GPUs. We employ the AdamW optimizer, with a learning rate of 5e-6 for the ViT backbone and 5e-5 for the other parameters." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.717, + 0.222, + 0.734 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.281, + 0.759 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We mainly conduct experiments on the HyperSim synthetic dataset [49] and two real-world datasets: ScanNet++ [75] and ARKitScenes [3], which provide iPhone RGB-LiDAR data \\((192 \\times 256\\) resolution) and annotated depth from a high-power LiDAR \\((1440 \\times 1920\\) resolution). We follow the suggested training and evaluation protocol in [3] for ARKitScenes, where \\(40\\mathrm{K}\\) images are used for training and \\(5\\mathrm{K}\\) images for evaluation. For the ScanNet++ dataset, we randomly select 20 scenes from its 50 validation scenes," + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.09, + 0.905, + 0.34 + ], + "angle": 0, + "content": "
Zero ShotNet. / Post. / w/o LiDAR384 × 512768x10241440x1920
L1 ↓RMSE ↓L1 ↓RMSE ↓L1 ↓RMSE ↓
NoOurs0.01350.03260.01320.03150.01380.0316
MSPF0.01530.03690.01490.03620.01520.0363
Depth Pro*0.04370.06720.04350.06650.04250.0654
DepthAny. v2*0.04640.07150.04230.06600.04970.0764
ZoeDepth*0.08310.28730.06790.14210.05290.0793
Depth Pro*0.12220.14240.12250.14270.12440.1444
DepthAny. v2*0.09780.11800.07710.06470.09060.1125
ZoeDepth*0.21010.27840.17800.23190.15660.1788
YesOurssyn0.01610.03760.01630.03710.01700.0376
D.P.0.02510.04220.02530.04220.02490.0422
BPNet0.14940.21060.14930.21070.14910.2100
ARKit Depth0.02510.04240.02500.04230.02540.0426
DepthAny. v20.07160.16860.06160.13680.04940.0764
DepthAny. v10.07330.17570.06530.15300.05270.0859
Metric3D v20.06260.21040.05240.17210.04020.1045
ZoeDepth0.10070.19170.08900.16270.07620.1135
Lotus0.08530.17930.10380.17820.19410.2741
Marigold0.09080.18490.08070.15650.06920.1065
Metric3D v20.17770.27660.16630.24910.16150.2131
ZoeDepth0.61580.95770.56880.61290.53160.5605
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.351, + 0.907, + 0.448 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on ARKitScenes dataset. The terms Net., Post. and w/o LiDAR refer to the LiDAR depth usage of models, where \"Net.\" denotes network fusion, \"Post.\" indicates post-alignment using RANSAC, and \"w/o LiDAR\" means the output is metric depth. Methods marked with * are finetuned with their released models and code on ARKitScenes [3] and ScanNet++ [75] datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.907, + 0.596 + ], + "angle": 0, + "content": "amounting to approximately 5K images for our validation and the training set are from its 230 training scenes, containing about 60K images. To ensure a fair comparison, we additionally train a model with HyperSim training set to achieve zero-shot testing on ScanNet++ and ARKitScenes datasets. Besides depth accuracy metrics, we also report the TSDF reconstruction results of our method on ScanNet++, which reflects the depth consistency. We describe the details of the evaluation metrics in the supp." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.606, + 0.842, + 0.621 + ], + "angle": 0, + "content": "4.2. Comparisons with the State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.901 + ], + "angle": 0, + "content": "We compare our method against the current SOTA depth estimation methods from two classes: Monocular depth estimation (MDE) and depth completion/upsampling. For MDE methods, we compare our method with Metric3D v2 [25], ZoeDepth [6], DepthPro [8], Depth Anything v1 and v2 [72, 73] (short for DepthAny. v1 and v2), Marigold [29] and Lotus [22]. For depth completion/upsampling methods, we compare our method with BPNet [56], Depth Prompting [42] (short for D.P.), MSPF [61]. To make a fair comparison with MDE methods, we align their predictions with ARKit LiDAR depth using the RANSAC align method. According to whether they have seen the testing data types during training, we divide methods into two categories: zero-shot and non zero-shot. We train a model \\(\\mathrm{Ours}_{\\mathrm{syn}}\\) only with HyperSim training set to make comparisons with the zero-shot methods. As shown in Tabs. 1 and 2 and Figs. 4 and 5, our method consistently outperforms the existing methods. Note that" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17074" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.089, + 0.871, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.564, + 0.908, + 0.594 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparisons with the state-of-the-art. \"Metric3D v2\" and \"Depth Any. v2\" are scale-shift corrected with ARKit depth. The pink boxes denote the GT depth and depth percentage error map, where red represents high error, and blue indicates low error." + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.606, + 0.875, + 0.853 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.857, + 0.877, + 0.873 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons of TSDF reconstruction. * align denotes the scale-shift corrected depth with ARKit depth." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17075" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.155, + 0.089, + 0.842, + 0.314 + ], + "angle": 0, + "content": "
Zero ShotNet. / Post. / w/o LiDARDepth EstimationTSDF Reconstruction
L1 ↓RMSE ↓AbsRel ↓δ0.5 ↑Acc ↓Comp ↓Prec ↑Recall ↑F-score ↑
NoOurs0.02500.08290.01750.97810.06990.06160.72550.81870.7619
MSPF*0.03260.09750.02260.96740.07720.06950.67380.77610.7133
DepthAny. v2*0.05100.10100.03710.94370.08080.07350.62750.71070.6595
ZoeDepth*0.05820.10690.04160.93250.08810.08010.57210.66400.6083
DepthAny. v2*0.09030.13470.06240.86570.12640.09170.42560.59540.4882
ZoeDepth*0.16750.19840.12780.58070.15670.15530.21640.25530.2323
YesOurssyn0.03270.09660.02240.97000.07460.06660.69030.79310.7307
D.P.0.03530.09830.02420.96570.08200.07470.64310.72340.6734
ARKit Depth0.03510.09870.02410.96590.08110.07430.64840.72800.6785
DepthAny. v20.05920.11450.04020.94040.08810.07470.55620.69460.6127
Depth Pro0.06380.12120.05100.92120.09040.07600.56950.69160.6187
Metric3D v20.05850.30870.04190.95290.07850.07520.62160.69940.6515
Marigold0.08280.14120.06030.87180.09990.07810.51280.66940.5740
DepthPro0.24060.28360.20150.52160.15370.14670.26840.37520.3086
Metric3D v20.12260.34030.08410.80090.08810.08010.57210.66400.6083
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.318, + 0.907, + 0.348 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on ScanNet++ dataset. The terms Net, Post and w/o LiDAR refer to the LiDAR depth usage of models as the last table. Methods marked with * are finetuned with their released code on ARKitScenes [3] and ScanNet++ [75] datasets." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.363, + 0.481, + 0.508 + ], + "angle": 0, + "content": "
ARKitScenesScanNet++
L1 ↓AbsRel ↓Acc ↓Comp ↓F-Score ↑
(a) Oursyn (synthetic data)0.01630.01420.07460.06660.7307
(b) w/o prompting0.06050.05050.09230.08010.5696
(c) w/o foundation model0.01940.01690.07740.07130.7077
(d) AdaLN prompting0.01970.01650.07950.07250.6943
(e) Cross-atten. prompting0.05230.04430.09320.08190.5595
(f) Controlnet prompting0.02390.02060.07850.07260.6899
(g) a + ARKitScenes data0.01340.01150.07440.06620.7341
(h) g + ScanNet++ anno. GT0.01320.01140.06700.06140.7647
(i) g + ScanNet++ pseudo GT0.01390.01210.08350.07660.6505
(j) Ours (h,i+edge loss)0.01320.01150.06990.06160.7619
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.512, + 0.483, + 0.542 + ], + "angle": 0, + "content": "Table 3. Quantitative ablations on ARKitScenes and ScanNet++ datasets. Please refer to Sec. 4.3 for detailed descriptions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.555, + 0.483, + 0.603 + ], + "angle": 0, + "content": "Oursyn achieves better performance than all non-zero-shot models [61, 73] on ScanNet++, highlighting the generalization ability of prompting a depth foundation model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.609, + 0.306, + 0.627 + ], + "angle": 0, + "content": "4.3. Ablations and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.637, + 0.483, + 0.713 + ], + "angle": 0, + "content": "Prompting a depth foundation model. We assess its importance with two experiments: 1) Removing the prompting. Tab. 3(b) shows a significant performance drop. 2) Removing the foundation model initialization [73]. Tab. 3(c) shows a noticeable performance decline." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.716, + 0.483, + 0.776 + ], + "angle": 0, + "content": "Prompting architecture design. We study different designs: AdaLN, Cross-attention, and ControlNet as discussed in Sec. 3.2. Tab. 3(d,e,f) reveals that ControlNet performs best but still falls short of our method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Training data and edge-aware depth loss. We initially incorporate ARKitScenes data, which only enhances performance on ARKitScenes (Tab. 3(g)). Then we add ScanNet++, which improves results on both ARKitScenes and ScanNet++ (Tab. 3(h)). However, the depth visualization remains less than ideal (Fig. 3). Tab. 3(i) show that direct supervision with pseudo GT depth from reconstruction methods decreases performance. Ultimately, employ" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.362, + 0.905, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.469, + 0.907, + 0.498 + ], + "angle": 0, + "content": "Figure 6. Outdoor reconstruction by taking the vehicle LiDAR as metric prompt. Please refer to the supp. for more video results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.514, + 0.907, + 0.59 + ], + "angle": 0, + "content": "ing the edge-aware depth loss that utilizes pseudo GT depth and FARO annotated GT achieves comparable performance with Tab. 3(h) but with superior thin structure depth performance as shown in Fig. 3. We provide more qualitative ablation results in the supp." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.909, + 0.701 + ], + "angle": 0, + "content": "Running time analysis. Our model with ViT-L runs at 20.4 FPS for an image resolution of \\(768 \\times 1024\\) on a A100 GPU. As ARKit6 supports 4K image recording, we test our model at a resolution of \\(2160 \\times 3840\\) and achieve 2.0 FPS. Note that our model can also be implemented with ViT-S, where the corresponding speeds are 80.0 and 10.3 FPS. More testing results can be found in the supp." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.709, + 0.825, + 0.725 + ], + "angle": 0, + "content": "4.4. Zero-shot Testing on Diverse Scenes" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.732, + 0.907, + 0.824 + ], + "angle": 0, + "content": "Although our model is trained on indoor scenes, it generalizes well to various scenarios, including new rooms, gyms with thin structures, poorly lit museums, human and outdoor environments, as shown in Fig. 7, highlighting the effectiveness of prompting a depth foundation model. Please refer to the supp. for video results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.832, + 0.796, + 0.849 + ], + "angle": 0, + "content": "4.5. Application: 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Our consistent and scale-accurate depth estimation benefits the indoor 3D reconstruction as shown in Tab. 2 and Fig. 5. Besides, the prompt of our model can be easily replaced" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17076" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.239, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.089, + 0.371, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.462, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.463, + 0.089, + 0.608, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.089, + 0.753, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.089, + 0.899, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.174, + 0.238, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.174, + 0.372, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.174, + 0.463, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.174, + 0.608, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.174, + 0.753, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.174, + 0.899, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.26, + 0.234, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.26, + 0.372, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.26, + 0.462, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.463, + 0.26, + 0.608, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.26, + 0.753, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.26, + 0.899, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.357, + 0.353, + 0.64, + 0.368 + ], + "angle": 0, + "content": "Figure 7. Zero-shot testing on diverse scenes." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.377, + 0.338, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.378, + 0.482, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.554, + 0.483, + 0.598 + ], + "angle": 0, + "content": "Figure 8. Robotic grasping setup and input signal types. Our goal is to grasp objects of various types using image/LiDAR/depth inputs. Red rectangles indicate potential object positions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.675 + ], + "angle": 0, + "content": "with vehicle LiDAR, which enables our model to achieve large-scale outdoor scene reconstruction as shown in Fig. 6. We detail the setup and include more video results for dynamic streets in the supp." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.681, + 0.465, + 0.699 + ], + "angle": 0, + "content": "4.6. Application: Generalized Robotic Grasping" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We set up a robotic platform to test our model in generalized robotic manipulation (Fig. 8), which typically requires depth or RGB as observations. Good depth estimation enhances the generalization ability because it accurately describes the 3D information of surroundings [26, 78]. Specifically, we train an ACT policy [81] to grasp various objects into the box, using different types of input signals such as RGB, LiDAR, and depth data from our model. We empirically find that our model generalizes well to unseen objects like transparent and specular objects when trained on diffusive objects, outperforming RGB and LiDAR inputs as shown in Tab. 4. This is because RGB is dominated by color, which leads to poor generalization across objects, and" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.377, + 0.906, + 0.449 + ], + "angle": 0, + "content": "
Input SignalDiffusiveTransparentSpecular
Red CanGreen Can
Ours1.0/1.0/1.01.0/1.0/1.00.3/1.0/1.00.8/1.0/0.9
LiDAR1.0/1.0/1.01.0/1.0/0.20.5/0.4/0.00.7/1.0/0.0
RGB1.0/1.0/0.01.0/1.0/0.00.2/1.0/0.00.0/0.9/0.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.453, + 0.907, + 0.497 + ], + "angle": 0, + "content": "Table 4. Grasping success rate on various objects. Three numbers indicate objects placed at near, middle, and far positions. The grasping policy is trained on diffusive and tested on all objects." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.907, + 0.549 + ], + "angle": 0, + "content": "the iPhone LiDAR depth is noisy and lacks the capability to perceive transparent objects. Please refer to the supp. for detailed setup descriptions and videos." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.567, + 0.771, + 0.584 + ], + "angle": 0, + "content": "5. Conclusion and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.594, + 0.907, + 0.761 + ], + "angle": 0, + "content": "This paper introduced a new paradigm for metric depth estimation, formulated as prompting a depth foundation model with metric information. We validated the feasibility of the paradigm by choosing the low-cost LiDAR depth as the prompt. A scalable data pipeline was proposed to generate synthetic LiDAR depth and pseudo GT depth for training. Extensive experiments demonstrate the superiority of our method against existing monocular depth estimation and depth completion/upsampling methods. Furthermore, we showed that it benefits for downstream tasks including 3D reconstruction and generalized robotic grasping." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Limitations and future work. This work has some known limitations. For instance, when using the iPhone LiDAR as the prompt, it cannot handle long-range depth, as the iPhone LiDAR detects very noisy depth for far objects. Additionally, we observed some temporal flickering of LiDAR depth, leading to a flickering depth prediction. These issues can be addressed in future works by considering more advanced prompt learning techniques that can extend the effective range and temporal prompt tuning." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17077" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.184 + ], + "angle": 0, + "content": "Acknowledgements. This work was partially supported by NSFC (No. 62402427, U24B20154, 623B2091), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), Information Technology Center and State Key Lab of CAD&CG, and Zhejiang University Education Foundation Qizhen Scholar Foundation." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.196, + 0.188, + 0.212 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.221, + 0.482, + 0.276 + ], + "angle": 0, + "content": "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv, 2023. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.278, + 0.482, + 0.332 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Zip-nerf: Anti-aliased grid-based neural radiance fields. 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Illustration and capabilities of Prompt Depth Anything. (a) Prompt Depth Anything is a new paradigm for metric depth estimation, which is formulated as prompting a depth foundation model with a metric prompt, specifically utilizing a low-cost LiDAR as the prompt. (b) Our method enables consistent depth estimation, addressing the limitations of Metric3D v2 [25] that suffer from inaccurate scale and inconsistency. (c) It achieves accurate 4K accurate depth estimation, significantly surpassing ARKit LiDAR Depth $(240 \times 320)$ . + +![](images/8120958f7b4753aa472641b46be5b9c0ce951aa9ff65f22420a7a3674e223cce.jpg) +Ours: high-res & accurate + +![](images/0d7683f264672980ee8a01fac9e093e94c909b28bc467da72e3750935261cd4c.jpg) +(b) Consistent Multi-view Depth Estimation for Static Scenes + +![](images/2df15b1045dc2a795dcd79346fbe2f5b3a933d5b3d819f67a61c057590f8c3ed.jpg) +Groundtruth distance +Input viewpoints + +![](images/a8ccb18b7b882c80235e3fc33a6d02a81ff6b980b29c814c357624f1a46b7140.jpg) +Err rate: $0.8\% - 1.3\%$ +Ours + +![](images/93f65daa27c7895954180e909383f1a61b71828b501347e7fd44154490c134f1.jpg) +Err rate: $14\% -34\%$ +Metric3D v2 + +# Abstract + +Prompts play a critical role in unleashing the power of language and vision foundation models for specific tasks. For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation termed Prompt Depth Anything. Specifically, we use a low-cost LiDAR as the prompt to guide the Depth Anything model for accurate metric depth output, achieving up to 4K resolution. Our approach centers on a concise prompt fusion design that integrates the LiDAR at multiple scales within the depth decoder. To address training challenges posed by limited datasets containing both LiDAR depth and precise GT depth, we propose a scalable data pipeline that includes synthetic data LiDAR simulation and real data pseudo GT depth generation. Our approach sets new state-of-the-arts on the ARKitScenes and ScanNet++ datasets and benefits downstream applications, including + +3D reconstruction and generalized robotic grasping. + +# 1. Introduction + +High-quality depth perception is a fundamental challenge in computer vision and robotics. Recent monocular depth estimation has experienced a significant leap by scaling the model or data, leading to the flourishing of depth foundation models [19, 29, 72, 73]. These models demonstrate strong abilities in producing high-quality relative depth, but suffer from scale ambiguity, hindering their practical applications in autonomous driving and robotic manipulation, etc. Therefore, significant efforts have been made to achieve metric depth estimation, by either finetuning depth foundation models [6, 20] on metric datasets or training metric depth models with image intrinsics as additional inputs [8, 25, 45, 77]. However, neither of them can address the problem properly, as illustrated in Fig. 1(b). + +A natural question thus arises: Do these foundation models truly lack utility in accurate metric depth estimation? This reminds us to closely examine the foundation models + +in natural language [1, 9] and vision [38, 39, 50], which often involve pre-training and instruction tuning stages. A properly designed prompt and a instruction dataset can unlock the power of foundation models on downstream tasks. Inspired by these successes, we propose a new paradigm for metric depth estimation by treating it as a downstream task, i.e., prompting a depth foundation model with metric information. We believe this prompt can take any form as long as the scale information is provided, e.g., camera intrinsics. In this paper, we validate the feasibility of the paradigm by choosing low-cost LiDAR as the prompt for two reasons. First, it provides precise metric scale information. Second, it is widely available, even in common mobile devices (e.g., Apple iPhone has a LiDAR). + +Specifically, based on Depth Anything [73], we propose Prompt Depth Anything, which achieves 4K resolution accurate metric depth estimation. At the core of our method is a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models [8, 73]. The prompt fusion architecture integrates the LiDAR depth at multiple scales within the DPT decoder, fusing the LiDAR features for depth decoding. The metric prompt provides precise spatial distance information, making the depth foundation model particularly serve as a local shape learner, resulting in accurate and high-resolution metric depth estimation. + +Training Prompt Depth Anything requires both LiDAR depth and precise GT depth. However, existing synthetic data [49] lacks LiDAR depth, and real-world data [75] with LiDAR only has an imprecise GT depth of bad edges. To solve this challenge, we propose a scalable data pipeline that simulates low-resolution, noisy LiDAR for synthetic data and generates pseudo GT depth with high-quality edges for real data using a reconstruction method [2]. To mitigate errors in the pseudo GT depth from the 3D reconstruction, we introduce an edge-aware depth loss that leverages only the gradient of pseudo GT depth, which is prominent at edges. We experimentally demonstrate that these efforts result in highly accurate depth estimation. + +We evaluate the proposed method on ARKitScenes [3] and ScanNet++ [75] datasets containing iPhone ARKit depth. It consistently exhibits state-of-the-art performance across datasets and metrics. Even our zero-shot model achieves better performance compared to other methods [6, 73] in non-zero-shot testing, highlighting the generalization ability of prompting a foundation model. We also show that the foundation model and prompt of Prompt Depth Anything can be replaced with DepthPro [8] and vehicle LiDAR [53], respectively. Furthermore, we demonstrate that it benefits several downstream applications, including 3D reconstruction and generalized robotic object grasping. + +In summary, this work has the following contributions: + +- Prompt Depth Anything, a new paradigm for metric depth estimation by prompting a depth foundation model with a + +low-cost LiDAR as the metric prompt. + +- A concise prompt fusion architecture for depth foundation models, a scalable data pipeline, and an edge-aware depth loss to train Prompt Depth Anything. +- State-of-the-art performance on depth estimation benchmarks [3, 75], showing the extensibility of replacing depth foundation models and LiDAR sensors, and highlighting benefits for several downstream applications including 3D reconstruction and robotic object grasping. + +# 2. Related Work + +Monocular depth estimation. Traditional methods [24, 52] rely on hand-crafted features for depth estimation. With the advent of deep learning, this field has seen significant advancements. Early learning-based approaches [15, 16] are often limited to a single dataset, lacking generalization capabilities. To enhance generalization, diverse datasets [13, 33, 58-60, 62, 63, 74], affine-invariant loss [46], and more powerful network architectures [47] have been introduced. More recently, latent diffusion models [50], pre-trained on extensive image generation tasks, have been applied to depth estimation [22, 29]. These models exhibit good generalization, estimating relative depth effectively, though they remain scale-agnostic. To achieve metric depth estimation, early methods either model the problem as global distribution classification [4, 5, 18, 36] or fine-tune a depth model on metric depth datasets [6, 34, 35]. Recent methods [20, 25, 45, 76, 77] discuss the ambiguity in monocular metric depth estimation and address it by incorporating camera intrinsic parameters. Although recent methods [8, 22, 25, 29, 45, 73, 77] exhibit strong generalization ability and claim to be depth foundation models [8, 19, 25, 73], metric depth estimation remains a challenge as shown in Fig. 1(b). We seek to address this challenge by prompting the depth foundation models with a metric prompt, inspired by the success of prompting in vision and vision-language models [38, 39, 79]. + +Depth estimation with auxiliary sensors. Obtaining dense depth information through active sensors typically demands high power consumption [10, 65-69]. A more practical approach involves utilizing a low-power active sensor to capture sparse depth, which can then be completed into dense maps. Many studies investigate methods to fill in sparse depth data. Early works rely on filter-based [23, 27, 31] and optimization-based [17, 71] techniques for depth completion. More recent studies [11, 12, 14, 21, 37, 40, 54-56, 69, 80] adopt learning-based approaches for depth completion. Typically, these methods are not tested on real indoor LiDAR data but rather on simulated sparse lidar for depth datasets such as NYUv2 [16] to reconstruct complete depth. This is because real testing setups require both low-power and high-power LiDAR sensors. More recent + +![](images/6739d4056a8898d8508a7a040fc8ea193beeaf68dbed40a6730cb09da17a3ae0.jpg) +Figure 2. Overview of Prompt Depth Anything. (a) Prompt Depth Anything builds on a depth foundation model [73] with a ViT encoder and a DPT decoder, and adds a multi-scale prompt fusion design, using a prompt fusion block to fuse the metric information at each scale. (b) Since training requires both low-cost LiDAR and precise GT depth, we propose a scalable data pipeline that simulates LiDAR depth for synthetic data with precise GT depth, and generates pseudo GT depth for real data with LiDAR. An edge-aware depth loss is proposed to merge accurate edges from pseudo GT depth with accurate depth in textureless areas from FARO annotated GT depth on real data. + +![](images/c94af6fcc796006d6bdd40b18cf94d91826c67fc6940c5c069e3f48603262813.jpg) + +works have collected both low-power and high-power Li-DAR data. To collect such data, DELTA [32] builds a suite to collect data using L5 and Intel RealSense 435i, while three other datasets [3, 48, 75] are collected using iPhone LiDAR and FARO LiDAR. We focus on the latter, as iPhone is widely available. A recent work similar to ours is Depth Prompting [42]. Our approach differs in that we use a network to take sparse depth as a prompt for the depth foundation model, achieving specific output. In contrast, they fuse sparse depth with features from the depth foundation model to post-process the foundation model output, which does not constitute prompting a foundation model. + +# 3. Method + +Monocular depth estimation models [8, 72, 73] are becoming depth foundation models for their generalization ability obtained from large-scale data. However, due to the inherent ambiguities, they cannot achieve high accuracy on metric depth estimation as shown in Fig. 1(b). Inspired by the success of prompting for vision [30, 39, 50] and language [1] foundation models, we propose Prompt Depth Anything prompting the depth foundation model with a metric prompt to achieve metric depth estimation. We take the low-cost LiDAR as the metric prompt in this work, as it has recently been integrated into lots of smartphones, making this setup highly practical. To be specific, we aim to prompt the depth foundation model to unleash its power for accurate metric depth estimation. + +# 3.1. Preliminary: Depth Foundation Model + +Current depth foundation models [7, 72, 73, 77] generally share similar network structures of DPT [47] networks. Specifically, given an image $\mathbf{I} \in \mathbb{R}^{C \times H \times W}$ , they take a vision transformer (ViT) with multiple stages to extract to + +kenized image features $\{\mathbf{T}_i\}$ , where $\mathbf{T}_i \in \mathbb{R}^{C_i \times (\frac{H}{p} \times \frac{W}{p} + 1)}$ represents the feature map at stage $S_i$ , $D_i$ is the feature dimension at stage $S_i$ , and $p$ is the patch size. The DPT decoder reassembles features from different stages into image-like representations $\mathbf{F}_i \in \mathbb{R}^{D_i \times \frac{H}{p} \times \frac{W}{p}}$ with the reassemble operation [47]. Finally, a sequence of convolutional blending steps are applied to merge features $\mathbf{F}_i$ across different stages, predicting a dense depth map $\mathbf{D} \in \mathbb{R}^{H \times W}$ . + +We note that there exists another line of depth foundation models [19, 22, 29] that use the image diffusion model [51] to estimate depth maps. Due to the high computational cost of diffusion models, we only consider DPT-based depth foundation models [8, 73] as our base model for real-time performance in this work. + +# 3.2. Prompt Depth Anything + +In this section, we seek to find a concise way to incorporate a low-cost LiDAR (i.e., a low-resolution and noisy depth map) as a prompt into the depth foundation model. To this end, we propose a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models to integrate low-resolution depth information. As shown in Fig. 2(a), the prompt fusion architecture integrates low-resolution depth information at multiple scales within the DPT Decoder. Specifically, for each scale $S_{i}$ in the DPT Decoder, a low-resolution depth map $\mathbf{L} \in \mathbb{R}^{1 \times H_{\mathrm{L}} \times W_{\mathrm{L}}}$ is firstly bilinearly resized to match the spatial dimensions of the current scale $\mathbb{R}^{1 \times H_{i} \times W_{i}}$ . Then, the resized depth map is passed through a shallow convolutional network to extract depth features. After that, the extracted features are projected to the same dimension as the image features $\mathbf{F}_{i} \in \mathbb{R}^{C_{i} \times H_{i} \times W_{i}}$ using a zero-initialized convolutional layer. Finally, the depth features are added to the DPT intermediate features for depth decoding. The illustration of + +![](images/8f4be7cedfa4089ef4c1f076f7eda05818a28f35bd96a27749f4e254b96e1fa5.jpg) + +![](images/493326964741bce62ecdb3c2cb091df7cbfe91a58575104c6cd165e606b9f845.jpg) +Reference Image & LiDAR w/ Sparse anchor Interp. w/ Linear Down. Interp. +Reference Image & LiDAR w/ Pseudo GT & Edge Loss w/ Anno. GT +Figure 3. Effects on the synthetic data lidar simulation and real data pseudo GT generation with the edge-aware depth loss. The middle and right columns are the depth prediction results of our different models. The two rows highlight the significance of sparse anchor interpolation for lidar simulation and pseudo GT generation with edge-aware depth loss, respectively. + +this block design is shown in Fig. 2. + +The proposed design has the following advantages. Firstly, it introduces only $5.7\%$ additional computational overhead (1.789 TFLOPs v.s. 1.691 TFLOPs for a $756 \times 1008$ image) to the original depth foundation model, and effectively addresses the ambiguity issue inherent in the depth foundation model as demonstrated in Tab. 3(b). Secondly, it fully inherits the capabilities of the depth foundation model because its encoder and decoder are initialized from the foundation model [73], and the proposed fusion architecture is zero-initialized, ensuring that the initial output is identical to that of the foundation model. We experimentally verify the importance of inheriting from a pretrained depth foundation model as shown in Tab. 3(c). + +**Optional designs.** Inspired by conditional image generation methods [28, 43, 79], we also explore various potential prompt conditioning designs into the depth foundation model. Specifically, we experimented with the following designs: a) Adaptive LayerNorm [28, 44] which adapts the layer normalization parameters of the encoder blocks based on the conditioning input, b) CrossAttention [57] which injects a cross attention block after each self-attention block and integrates the conditioning input through cross-attention mechanisms, and c) ControlNet [79] which copies the encoder blocks and inputs control signals to the copied blocks to control the output depth. As shown in Tab. 3(d,e,f), our experiments reveal that these designs do not perform as well as the proposed fusion block. A plausible reason is that they are designed to integrate cross-modal information (e.g., text prompts), which does not effectively utilize the pixel alignment characteristics between the input low-res LiDAR and the output depth. We detail these optional designs in the supp. + +# 3.3. Training Prompt Depth Anything + +Training Prompt Depth Anything simultaneously requires a low-cost LiDAR and precise GT depth. However, synthetic data [49] do not contain LiDAR depth, real-world data with noisy LiDAR depth [75] only have imprecise depth annotations. Therefore, we propose a LiDAR simulation method for synthetic data and generate pseudo GT depth from Zip-NeRF [2] with an edge-aware depth loss for real data. Note that more effective approaches [64, 70] can be applied. + +Synthetic data: LiDAR simulation. A LiDAR depth map is low-resolution and noisy. The naive approach for simulating it is to directly downsample the synthetic data depth map. However, this method leads to the model learning depth super-resolution, as shown in Fig. 3, meaning that the model does not correct the LiDAR noise. To simulate the noise, we introduce a sparse anchor interpolation method. Specifically, we first downsample the GT depth map to low-resolution (192 × 256, exactly the depth resolution of iPhone ARKit Depth). Then we sample points on this depth map using a distorted grid with a stride (7 in practice). The remaining depth values are interpolated from these points using RGB similarity with KNN. As shown in Fig. 3, it effectively simulates LiDAR noise and results in better depth prediction. We provide visualization results of the simulated LiDAR in the supp. + +Real Data: Pseudo GT depth generation. We also add real data [75] to our training data. The annotated depth in ScanNet++ [75] is re-rendered from a mesh scanned by a high-power LiDAR sensor (FARO Focus Premium laser scanner). Due to the presence of many occlusions in the scene, several scan positions (typically 4 in a medium-sized scene in ScanNet++) result in an incomplete scanned mesh, leading to depth maps with numerous holes and poor edge quality, as illustrated in Fig. 2(b). Motivated by the success of reconstruction methods [2, 41], we propose using Zip-NeRF [2] to recover high-quality depth maps. Specifically, we train Zip-NeRF for each scene in ScanNet++ and re-rendered pseudo GT depth. To provide Zip-NeRF with high-quality and dense observations, we detect unblurred frames in Scannet++iPhone videos, and additionally utilize DSLR videos to provide high-quality dense-view images. + +Real Data: Edge-aware depth loss. Although Zip-NeRF can generate high-quality edge depth, reconstructing textureless and reflective regions remains challenging as shown in Fig. 2(b). In contrast, these areas (e.g., walls, floors, and ceilings etc.) are usually planar with few occlusions, and the annotations depth in FARO rendered depth is good in these regions. This motivates us to leverage the strengths of both. We propose an edge-aware depth loss to meet these requirements. Specifically, we use the FARO scanned mesh depth and the gradient of the pseudo GT depth to supervise output + +depth and the gradient of the output depth, respectively: + +$$ +\mathcal {L} _ {\text {e d g e}} = L _ {1} \left(\mathbf {D} _ {\mathrm {g t}}, \hat {\mathbf {D}}\right) + \lambda \cdot \mathcal {L} _ {\text {g r a d}} \left(\mathbf {D} _ {\text {p s e u d o}}, \hat {\mathbf {D}}\right), \tag {1} +$$ + +$$ +\mathcal {L} _ {\text {g r a d}} \left(\mathbf {D} _ {\text {p s e u d o}}, \hat {\mathbf {D}}\right) = \left(| \frac {\partial (\hat {\mathbf {D}} - \mathbf {D} _ {\text {p s e u d o}})}{\partial x} | + | \frac {\partial (\hat {\mathbf {D}} - \mathbf {D} _ {\text {p s e u d o}})}{\partial y} |\right). \tag {2} +$$ + +In practice, we set $\lambda = 0.5$ . The depth gradient is mainly prominent at the edges, which is exactly where the pseudo GT depth excels. The gradient loss encourages the model to learn the accurate edges from the pseudo GT depth, while the L1 loss encourages the model to learn the overall depth, ultimately leading to excellent depth prediction. We experimentally verify the effectiveness of the edge-aware depth loss in Tab. 3(j) and Fig. 3. + +# 3.4. Implementation Details + +In this section, we provide essential information about the network design, depth normalization, and training details. Please refer to the supp. for more details. + +Network details. We utilize the ViT-large model as our backbone model. The shallow convolutional network comprises two convolutional layers with a kernel size of 3 and a stride of 1. More details can be found in the supp. Detailed running time analysis can be found in Sec. 4.3. + +Depth normalization. The irregular range of input depth data can hinder network convergence. To address this, we normalize the LiDAR data using linear scaling to the range [0, 1], based on its minimum and maximum values. The network output is also normalized with the same scaling factor from LiDAR data, ensuring consistent scales and facilitating easier convergence during training. + +Training details. We initiate training from the metric model released by Depth Anything v2 [73], incorporating a 10K step warm-up phase. During this warm-up phase, we fine-tune this metric model to output a normalized depth derived from the linear scaling of LiDAR data. Subsequently, we train our model for 200K steps. During the training process, the batch size is set to 2, utilizing 8 GPUs. We employ the AdamW optimizer, with a learning rate of 5e-6 for the ViT backbone and 5e-5 for the other parameters. + +# 4. Experiments + +# 4.1. Experimental Setup + +We mainly conduct experiments on the HyperSim synthetic dataset [49] and two real-world datasets: ScanNet++ [75] and ARKitScenes [3], which provide iPhone RGB-LiDAR data $(192 \times 256$ resolution) and annotated depth from a high-power LiDAR $(1440 \times 1920$ resolution). We follow the suggested training and evaluation protocol in [3] for ARKitScenes, where $40\mathrm{K}$ images are used for training and $5\mathrm{K}$ images for evaluation. For the ScanNet++ dataset, we randomly select 20 scenes from its 50 validation scenes, + +
Zero ShotNet. / Post. / w/o LiDAR384 × 512768x10241440x1920
L1 ↓RMSE ↓L1 ↓RMSE ↓L1 ↓RMSE ↓
NoOurs0.01350.03260.01320.03150.01380.0316
MSPF0.01530.03690.01490.03620.01520.0363
Depth Pro*0.04370.06720.04350.06650.04250.0654
DepthAny. v2*0.04640.07150.04230.06600.04970.0764
ZoeDepth*0.08310.28730.06790.14210.05290.0793
Depth Pro*0.12220.14240.12250.14270.12440.1444
DepthAny. v2*0.09780.11800.07710.06470.09060.1125
ZoeDepth*0.21010.27840.17800.23190.15660.1788
YesOurssyn0.01610.03760.01630.03710.01700.0376
D.P.0.02510.04220.02530.04220.02490.0422
BPNet0.14940.21060.14930.21070.14910.2100
ARKit Depth0.02510.04240.02500.04230.02540.0426
DepthAny. v20.07160.16860.06160.13680.04940.0764
DepthAny. v10.07330.17570.06530.15300.05270.0859
Metric3D v20.06260.21040.05240.17210.04020.1045
ZoeDepth0.10070.19170.08900.16270.07620.1135
Lotus0.08530.17930.10380.17820.19410.2741
Marigold0.09080.18490.08070.15650.06920.1065
Metric3D v20.17770.27660.16630.24910.16150.2131
ZoeDepth0.61580.95770.56880.61290.53160.5605
+ +Table 1. Quantitative comparisons on ARKitScenes dataset. The terms Net., Post. and w/o LiDAR refer to the LiDAR depth usage of models, where "Net." denotes network fusion, "Post." indicates post-alignment using RANSAC, and "w/o LiDAR" means the output is metric depth. Methods marked with * are finetuned with their released models and code on ARKitScenes [3] and ScanNet++ [75] datasets. + +amounting to approximately 5K images for our validation and the training set are from its 230 training scenes, containing about 60K images. To ensure a fair comparison, we additionally train a model with HyperSim training set to achieve zero-shot testing on ScanNet++ and ARKitScenes datasets. Besides depth accuracy metrics, we also report the TSDF reconstruction results of our method on ScanNet++, which reflects the depth consistency. We describe the details of the evaluation metrics in the supp. + +# 4.2. Comparisons with the State of the Art + +We compare our method against the current SOTA depth estimation methods from two classes: Monocular depth estimation (MDE) and depth completion/upsampling. For MDE methods, we compare our method with Metric3D v2 [25], ZoeDepth [6], DepthPro [8], Depth Anything v1 and v2 [72, 73] (short for DepthAny. v1 and v2), Marigold [29] and Lotus [22]. For depth completion/upsampling methods, we compare our method with BPNet [56], Depth Prompting [42] (short for D.P.), MSPF [61]. To make a fair comparison with MDE methods, we align their predictions with ARKit LiDAR depth using the RANSAC align method. According to whether they have seen the testing data types during training, we divide methods into two categories: zero-shot and non zero-shot. We train a model $\mathrm{Ours}_{\mathrm{syn}}$ only with HyperSim training set to make comparisons with the zero-shot methods. As shown in Tabs. 1 and 2 and Figs. 4 and 5, our method consistently outperforms the existing methods. Note that + +![](images/1894ea3f4088d3d69218ba928cc70b2bd94fa8bb06b2cc05a637935dd16065f1.jpg) +Figure 4. Qualitative comparisons with the state-of-the-art. "Metric3D v2" and "Depth Any. v2" are scale-shift corrected with ARKit depth. The pink boxes denote the GT depth and depth percentage error map, where red represents high error, and blue indicates low error. + +![](images/c72c263ab080252f495209221f6bfcf351d0d5f1234674177db8ebf36c542085.jpg) +Figure 5. Qualitative comparisons of TSDF reconstruction. * align denotes the scale-shift corrected depth with ARKit depth. + +
Zero ShotNet. / Post. / w/o LiDARDepth EstimationTSDF Reconstruction
L1 ↓RMSE ↓AbsRel ↓δ0.5 ↑Acc ↓Comp ↓Prec ↑Recall ↑F-score ↑
NoOurs0.02500.08290.01750.97810.06990.06160.72550.81870.7619
MSPF*0.03260.09750.02260.96740.07720.06950.67380.77610.7133
DepthAny. v2*0.05100.10100.03710.94370.08080.07350.62750.71070.6595
ZoeDepth*0.05820.10690.04160.93250.08810.08010.57210.66400.6083
DepthAny. v2*0.09030.13470.06240.86570.12640.09170.42560.59540.4882
ZoeDepth*0.16750.19840.12780.58070.15670.15530.21640.25530.2323
YesOurssyn0.03270.09660.02240.97000.07460.06660.69030.79310.7307
D.P.0.03530.09830.02420.96570.08200.07470.64310.72340.6734
ARKit Depth0.03510.09870.02410.96590.08110.07430.64840.72800.6785
DepthAny. v20.05920.11450.04020.94040.08810.07470.55620.69460.6127
Depth Pro0.06380.12120.05100.92120.09040.07600.56950.69160.6187
Metric3D v20.05850.30870.04190.95290.07850.07520.62160.69940.6515
Marigold0.08280.14120.06030.87180.09990.07810.51280.66940.5740
DepthPro0.24060.28360.20150.52160.15370.14670.26840.37520.3086
Metric3D v20.12260.34030.08410.80090.08810.08010.57210.66400.6083
+ +Table 2. Quantitative comparisons on ScanNet++ dataset. The terms Net, Post and w/o LiDAR refer to the LiDAR depth usage of models as the last table. Methods marked with * are finetuned with their released code on ARKitScenes [3] and ScanNet++ [75] datasets. + +
ARKitScenesScanNet++
L1 ↓AbsRel ↓Acc ↓Comp ↓F-Score ↑
(a) Oursyn (synthetic data)0.01630.01420.07460.06660.7307
(b) w/o prompting0.06050.05050.09230.08010.5696
(c) w/o foundation model0.01940.01690.07740.07130.7077
(d) AdaLN prompting0.01970.01650.07950.07250.6943
(e) Cross-atten. prompting0.05230.04430.09320.08190.5595
(f) Controlnet prompting0.02390.02060.07850.07260.6899
(g) a + ARKitScenes data0.01340.01150.07440.06620.7341
(h) g + ScanNet++ anno. GT0.01320.01140.06700.06140.7647
(i) g + ScanNet++ pseudo GT0.01390.01210.08350.07660.6505
(j) Ours (h,i+edge loss)0.01320.01150.06990.06160.7619
+ +Table 3. Quantitative ablations on ARKitScenes and ScanNet++ datasets. Please refer to Sec. 4.3 for detailed descriptions. + +Oursyn achieves better performance than all non-zero-shot models [61, 73] on ScanNet++, highlighting the generalization ability of prompting a depth foundation model. + +# 4.3. Ablations and Analysis + +Prompting a depth foundation model. We assess its importance with two experiments: 1) Removing the prompting. Tab. 3(b) shows a significant performance drop. 2) Removing the foundation model initialization [73]. Tab. 3(c) shows a noticeable performance decline. + +Prompting architecture design. We study different designs: AdaLN, Cross-attention, and ControlNet as discussed in Sec. 3.2. Tab. 3(d,e,f) reveals that ControlNet performs best but still falls short of our method. + +Training data and edge-aware depth loss. We initially incorporate ARKitScenes data, which only enhances performance on ARKitScenes (Tab. 3(g)). Then we add ScanNet++, which improves results on both ARKitScenes and ScanNet++ (Tab. 3(h)). However, the depth visualization remains less than ideal (Fig. 3). Tab. 3(i) show that direct supervision with pseudo GT depth from reconstruction methods decreases performance. Ultimately, employ + +![](images/f0cbae75084fc5da7f533290ca2bc1139cff113390458f0d1d8a805073d394d5.jpg) +Figure 6. Outdoor reconstruction by taking the vehicle LiDAR as metric prompt. Please refer to the supp. for more video results. + +ing the edge-aware depth loss that utilizes pseudo GT depth and FARO annotated GT achieves comparable performance with Tab. 3(h) but with superior thin structure depth performance as shown in Fig. 3. We provide more qualitative ablation results in the supp. + +Running time analysis. Our model with ViT-L runs at 20.4 FPS for an image resolution of $768 \times 1024$ on a A100 GPU. As ARKit6 supports 4K image recording, we test our model at a resolution of $2160 \times 3840$ and achieve 2.0 FPS. Note that our model can also be implemented with ViT-S, where the corresponding speeds are 80.0 and 10.3 FPS. More testing results can be found in the supp. + +# 4.4. Zero-shot Testing on Diverse Scenes + +Although our model is trained on indoor scenes, it generalizes well to various scenarios, including new rooms, gyms with thin structures, poorly lit museums, human and outdoor environments, as shown in Fig. 7, highlighting the effectiveness of prompting a depth foundation model. Please refer to the supp. for video results. + +# 4.5. Application: 3D Reconstruction + +Our consistent and scale-accurate depth estimation benefits the indoor 3D reconstruction as shown in Tab. 2 and Fig. 5. Besides, the prompt of our model can be easily replaced + +![](images/ce3b85d05a2632a2ad85eeff1a0e5b04a8946a86d67c9a487385af10f5a0ec06.jpg) + +![](images/32221f05ba826aa51bbfa024ecb1602a3048b6fb0bef12a2154cd89e261357c8.jpg) + +![](images/a0ff369aa5b5366acfec20eb6ee81429851da9e0f29c4b5946a603d4e0f40e9b.jpg) + +![](images/48a7c8bcef15e64eb5ba3c3da6b2fa391193b000829b4e1e01a681c0da356b82.jpg) + +![](images/b5a052c384357a135c06142a4a986539bf4d968a1f21f720adf702f7f574c338.jpg) + +![](images/2ae9ee77f2aad1943ae0521c775e95c7e0baeeb56e8345fd15c5daea04573f0d.jpg) + +![](images/29b80770a23124d022e867231f50039e3543a9a56e20de7de60e215a7abc8e26.jpg) + +![](images/0227ff15eb9ee56f77eb23669df4187eb4aa781f19b19a569cb7f85230e4528c.jpg) + +![](images/8d0a43e9a3f9610daaccf8360397538c40acec53dd67686688acb579936a16e8.jpg) + +![](images/3cdeb52ebdcb3de327185696e86100b24fa9bdfd6b910fe6334784f7cb6c3425.jpg) + +![](images/768a43cb292b9cac0df752d82c1e67755adbce3df2d4e67317c98284a4ca5786.jpg) + +![](images/ed488c368182431f1d775fcc463dadcb52a53a5eadd38a7b5171b9d2af3edafb.jpg) + +![](images/389da1a51a4a9cfe1b35a328d38729c92fbeb3a30b39516d9e6d20485e27915a.jpg) + +![](images/b5a8d182b51269f993ddc013b456e7da4ecfa607513fd6c0cf8a9a77d9c6d209.jpg) +Figure 7. Zero-shot testing on diverse scenes. + +![](images/f8e2171c80abd63e170c94834cc3e30f6f61ec2fde114baac1bda14c0a2d8396.jpg) + +![](images/baddb5471700ba2394250fe119f9f33d60d82003e5105dcc49a816870f20a477.jpg) + +![](images/7007a975fadc75766524929b2b52370881dad2d942022ef99f61bbd8b2f0638f.jpg) + +![](images/79fdeebbfea7b29e33826b182a604eaa7fbc472f023fea8d3c78c1113de25224.jpg) + +![](images/f245ca7811fc55a5028d28ae613881c1a3b3bd1e906de4c3803710e7a954497d.jpg) +Figure 8. Robotic grasping setup and input signal types. Our goal is to grasp objects of various types using image/LiDAR/depth inputs. Red rectangles indicate potential object positions. + +![](images/79ddd2f611b37f79a0b90654981df45b5aac5b13e4e9e2b457d63841f5181668.jpg) + +with vehicle LiDAR, which enables our model to achieve large-scale outdoor scene reconstruction as shown in Fig. 6. We detail the setup and include more video results for dynamic streets in the supp. + +# 4.6. Application: Generalized Robotic Grasping + +We set up a robotic platform to test our model in generalized robotic manipulation (Fig. 8), which typically requires depth or RGB as observations. Good depth estimation enhances the generalization ability because it accurately describes the 3D information of surroundings [26, 78]. Specifically, we train an ACT policy [81] to grasp various objects into the box, using different types of input signals such as RGB, LiDAR, and depth data from our model. We empirically find that our model generalizes well to unseen objects like transparent and specular objects when trained on diffusive objects, outperforming RGB and LiDAR inputs as shown in Tab. 4. This is because RGB is dominated by color, which leads to poor generalization across objects, and + +
Input SignalDiffusiveTransparentSpecular
Red CanGreen Can
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RGB1.0/1.0/0.01.0/1.0/0.00.2/1.0/0.00.0/0.9/0.9
+ +Table 4. Grasping success rate on various objects. Three numbers indicate objects placed at near, middle, and far positions. The grasping policy is trained on diffusive and tested on all objects. + +the iPhone LiDAR depth is noisy and lacks the capability to perceive transparent objects. Please refer to the supp. for detailed setup descriptions and videos. + +# 5. Conclusion and Discussions + +This paper introduced a new paradigm for metric depth estimation, formulated as prompting a depth foundation model with metric information. We validated the feasibility of the paradigm by choosing the low-cost LiDAR depth as the prompt. A scalable data pipeline was proposed to generate synthetic LiDAR depth and pseudo GT depth for training. Extensive experiments demonstrate the superiority of our method against existing monocular depth estimation and depth completion/upsampling methods. Furthermore, we showed that it benefits for downstream tasks including 3D reconstruction and generalized robotic grasping. + +Limitations and future work. This work has some known limitations. For instance, when using the iPhone LiDAR as the prompt, it cannot handle long-range depth, as the iPhone LiDAR detects very noisy depth for far objects. Additionally, we observed some temporal flickering of LiDAR depth, leading to a flickering depth prediction. These issues can be addressed in future works by considering more advanced prompt learning techniques that can extend the effective range and temporal prompt tuning. + +Acknowledgements. This work was partially supported by NSFC (No. 62402427, U24B20154, 623B2091), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), Information Technology Center and State Key Lab of CAD&CG, and Zhejiang University Education Foundation Qizhen Scholar Foundation. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv, 2023. 2, 3 +[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Zip-nerf: Anti-aliased grid-based neural radiance fields. In ICCV, pages 19697-19705, 2023. 2, 4 +[3] Gilad Baruch, Zhuoyuan Chen, Afshin Dehghan, Tal Dimry, Yuri Feigin, Peter Fu, Thomas Gebauer, Brandon Joffe, Daniel Kurz, Arik Schwartz, et al. Arkitsscenes: A diverse real-world dataset for 3d indoor scene understanding using mobile rgb-d data. 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Illustration and capabilities of Prompt Depth Anything. (a) Prompt Depth Anything is a new paradigm for metric depth estimation, which is formulated as prompting a depth foundation model with a metric prompt, specifically utilizing a low-cost LiDAR as the prompt. (b) Our method enables consistent depth estimation, addressing the limitations of Metric3D v2 [25] that suffer from inaccurate scale and inconsistency. 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For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation termed Prompt Depth Anything. Specifically, we use a low-cost LiDAR as the prompt to guide the Depth Anything model for accurate metric depth output, achieving up to 4K resolution. Our approach centers on a concise prompt fusion design that integrates the LiDAR at multiple scales within the depth decoder. To address training challenges posed by limited datasets containing both LiDAR depth and precise GT depth, we propose a scalable data pipeline that includes synthetic data LiDAR simulation and real data pseudo GT depth generation. Our approach sets new state-of-the-arts on the ARKitScenes and ScanNet++ datasets and benefits downstream applications, including" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 314, + 454, + 526, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 454, + 526, + 466 + ], + "spans": [ + { + "bbox": [ + 314, + 454, + 526, + 466 + ], + "type": "text", + "content": "3D reconstruction and generalized robotic grasping." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 314, + 489, + 394, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 489, + 394, + 501 + ], + "spans": [ + { + "bbox": [ + 314, + 489, + 394, + 501 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 312, + 510, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 510, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 312, + 510, + 555, + 676 + ], + "type": "text", + "content": "High-quality depth perception is a fundamental challenge in computer vision and robotics. Recent monocular depth estimation has experienced a significant leap by scaling the model or data, leading to the flourishing of depth foundation models [19, 29, 72, 73]. These models demonstrate strong abilities in producing high-quality relative depth, but suffer from scale ambiguity, hindering their practical applications in autonomous driving and robotic manipulation, etc. Therefore, significant efforts have been made to achieve metric depth estimation, by either finetuning depth foundation models [6, 20] on metric datasets or training metric depth models with image intrinsics as additional inputs [8, 25, 45, 77]. However, neither of them can address the problem properly, as illustrated in Fig. 1(b)." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "A natural question thus arises: Do these foundation models truly lack utility in accurate metric depth estimation? This reminds us to closely examine the foundation models" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 186, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 186, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 186, + 713 + ], + "type": "text", + "content": "†Corresponding author: Sida Peng." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17070" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 239 + ], + "type": "text", + "content": "in natural language [1, 9] and vision [38, 39, 50], which often involve pre-training and instruction tuning stages. A properly designed prompt and a instruction dataset can unlock the power of foundation models on downstream tasks. Inspired by these successes, we propose a new paradigm for metric depth estimation by treating it as a downstream task, i.e., prompting a depth foundation model with metric information. We believe this prompt can take any form as long as the scale information is provided, e.g., camera intrinsics. In this paper, we validate the feasibility of the paradigm by choosing low-cost LiDAR as the prompt for two reasons. First, it provides precise metric scale information. Second, it is widely available, even in common mobile devices (e.g., Apple iPhone has a LiDAR)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 241, + 294, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 241, + 294, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 241, + 294, + 373 + ], + "type": "text", + "content": "Specifically, based on Depth Anything [73], we propose Prompt Depth Anything, which achieves 4K resolution accurate metric depth estimation. At the core of our method is a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models [8, 73]. The prompt fusion architecture integrates the LiDAR depth at multiple scales within the DPT decoder, fusing the LiDAR features for depth decoding. The metric prompt provides precise spatial distance information, making the depth foundation model particularly serve as a local shape learner, resulting in accurate and high-resolution metric depth estimation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 374, + 294, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 374, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 294, + 529 + ], + "type": "text", + "content": "Training Prompt Depth Anything requires both LiDAR depth and precise GT depth. However, existing synthetic data [49] lacks LiDAR depth, and real-world data [75] with LiDAR only has an imprecise GT depth of bad edges. To solve this challenge, we propose a scalable data pipeline that simulates low-resolution, noisy LiDAR for synthetic data and generates pseudo GT depth with high-quality edges for real data using a reconstruction method [2]. To mitigate errors in the pseudo GT depth from the 3D reconstruction, we introduce an edge-aware depth loss that leverages only the gradient of pseudo GT depth, which is prominent at edges. We experimentally demonstrate that these efforts result in highly accurate depth estimation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 531, + 294, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 531, + 294, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 531, + 294, + 674 + ], + "type": "text", + "content": "We evaluate the proposed method on ARKitScenes [3] and ScanNet++ [75] datasets containing iPhone ARKit depth. It consistently exhibits state-of-the-art performance across datasets and metrics. Even our zero-shot model achieves better performance compared to other methods [6, 73] in non-zero-shot testing, highlighting the generalization ability of prompting a foundation model. We also show that the foundation model and prompt of Prompt Depth Anything can be replaced with DepthPro [8] and vehicle LiDAR [53], respectively. Furthermore, we demonstrate that it benefits several downstream applications, including 3D reconstruction and generalized robotic object grasping." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 676, + 289, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 676, + 289, + 688 + ], + "spans": [ + { + "bbox": [ + 67, + 676, + 289, + 688 + ], + "type": "text", + "content": "In summary, this work has the following contributions:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "- Prompt Depth Anything, a new paradigm for metric depth estimation by prompting a depth foundation model with a" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 322, + 72, + 479, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 72, + 479, + 84 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 479, + 84 + ], + "type": "text", + "content": "low-cost LiDAR as the metric prompt." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 85, + 553, + 180 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 85, + 553, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 85, + 553, + 119 + ], + "spans": [ + { + "bbox": [ + 314, + 85, + 553, + 119 + ], + "type": "text", + "content": "- A concise prompt fusion architecture for depth foundation models, a scalable data pipeline, and an edge-aware depth loss to train Prompt Depth Anything." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "content": "- State-of-the-art performance on depth estimation benchmarks [3, 75], showing the extensibility of replacing depth foundation models and LiDAR sensors, and highlighting benefits for several downstream applications including 3D reconstruction and robotic object grasping." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 194, + 400, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 194, + 400, + 206 + ], + "spans": [ + { + "bbox": [ + 314, + 194, + 400, + 206 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 219, + 553, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 553, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 553, + 529 + ], + "type": "text", + "content": "Monocular depth estimation. Traditional methods [24, 52] rely on hand-crafted features for depth estimation. With the advent of deep learning, this field has seen significant advancements. Early learning-based approaches [15, 16] are often limited to a single dataset, lacking generalization capabilities. To enhance generalization, diverse datasets [13, 33, 58-60, 62, 63, 74], affine-invariant loss [46], and more powerful network architectures [47] have been introduced. More recently, latent diffusion models [50], pre-trained on extensive image generation tasks, have been applied to depth estimation [22, 29]. These models exhibit good generalization, estimating relative depth effectively, though they remain scale-agnostic. To achieve metric depth estimation, early methods either model the problem as global distribution classification [4, 5, 18, 36] or fine-tune a depth model on metric depth datasets [6, 34, 35]. Recent methods [20, 25, 45, 76, 77] discuss the ambiguity in monocular metric depth estimation and address it by incorporating camera intrinsic parameters. Although recent methods [8, 22, 25, 29, 45, 73, 77] exhibit strong generalization ability and claim to be depth foundation models [8, 19, 25, 73], metric depth estimation remains a challenge as shown in Fig. 1(b). We seek to address this challenge by prompting the depth foundation models with a metric prompt, inspired by the success of prompting in vision and vision-language models [38, 39, 79]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "Depth estimation with auxiliary sensors. Obtaining dense depth information through active sensors typically demands high power consumption [10, 65-69]. A more practical approach involves utilizing a low-power active sensor to capture sparse depth, which can then be completed into dense maps. Many studies investigate methods to fill in sparse depth data. Early works rely on filter-based [23, 27, 31] and optimization-based [17, 71] techniques for depth completion. More recent studies [11, 12, 14, 21, 37, 40, 54-56, 69, 80] adopt learning-based approaches for depth completion. Typically, these methods are not tested on real indoor LiDAR data but rather on simulated sparse lidar for depth datasets such as NYUv2 [16] to reconstruct complete depth. This is because real testing setups require both low-power and high-power LiDAR sensors. More recent" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17071" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 302, + 219 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 302, + 219 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 302, + 219 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 302, + 219 + ], + "type": "image", + "image_path": "6739d4056a8898d8508a7a040fc8ea193beeaf68dbed40a6730cb09da17a3ae0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 225, + 555, + 281 + ], + "lines": [ + { + "bbox": [ + 54, + 225, + 555, + 281 + ], + "spans": [ + { + "bbox": [ + 54, + 225, + 555, + 281 + ], + "type": "text", + "content": "Figure 2. Overview of Prompt Depth Anything. (a) Prompt Depth Anything builds on a depth foundation model [73] with a ViT encoder and a DPT decoder, and adds a multi-scale prompt fusion design, using a prompt fusion block to fuse the metric information at each scale. (b) Since training requires both low-cost LiDAR and precise GT depth, we propose a scalable data pipeline that simulates LiDAR depth for synthetic data with precise GT depth, and generates pseudo GT depth for real data with LiDAR. An edge-aware depth loss is proposed to merge accurate edges from pseudo GT depth with accurate depth in textureless areas from FARO annotated GT depth on real data." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 550, + 220 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 550, + 220 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 550, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 550, + 220 + ], + "type": "image", + "image_path": "c94af6fcc796006d6bdd40b18cf94d91826c67fc6940c5c069e3f48603262813.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 293, + 296, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 293, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 54, + 293, + 296, + 437 + ], + "type": "text", + "content": "works have collected both low-power and high-power Li-DAR data. To collect such data, DELTA [32] builds a suite to collect data using L5 and Intel RealSense 435i, while three other datasets [3, 48, 75] are collected using iPhone LiDAR and FARO LiDAR. We focus on the latter, as iPhone is widely available. A recent work similar to ours is Depth Prompting [42]. Our approach differs in that we use a network to take sparse depth as a prompt for the depth foundation model, achieving specific output. In contrast, they fuse sparse depth with features from the depth foundation model to post-process the foundation model output, which does not constitute prompting a foundation model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 449, + 111, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 111, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 111, + 462 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 470, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 470, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 54, + 470, + 295, + 638 + ], + "type": "text", + "content": "Monocular depth estimation models [8, 72, 73] are becoming depth foundation models for their generalization ability obtained from large-scale data. However, due to the inherent ambiguities, they cannot achieve high accuracy on metric depth estimation as shown in Fig. 1(b). Inspired by the success of prompting for vision [30, 39, 50] and language [1] foundation models, we propose Prompt Depth Anything prompting the depth foundation model with a metric prompt to achieve metric depth estimation. We take the low-cost LiDAR as the metric prompt in this work, as it has recently been integrated into lots of smartphones, making this setup highly practical. To be specific, we aim to prompt the depth foundation model to unleash its power for accurate metric depth estimation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 647, + 260, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 260, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 260, + 659 + ], + "type": "text", + "content": "3.1. Preliminary: Depth Foundation Model" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 665, + 296, + 715 + ], + "type": "text", + "content": "Current depth foundation models [7, 72, 73, 77] generally share similar network structures of DPT [47] networks. Specifically, given an image " + }, + { + "bbox": [ + 54, + 665, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W}" + }, + { + "bbox": [ + 54, + 665, + 296, + 715 + ], + "type": "text", + "content": ", they take a vision transformer (ViT) with multiple stages to extract to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": "kenized image features " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{T}_i\\}" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i \\in \\mathbb{R}^{C_i \\times (\\frac{H}{p} \\times \\frac{W}{p} + 1)}" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": " represents the feature map at stage " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "D_i" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": " is the feature dimension at stage " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": " is the patch size. The DPT decoder reassembles features from different stages into image-like representations " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i \\in \\mathbb{R}^{D_i \\times \\frac{H}{p} \\times \\frac{W}{p}}" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": " with the reassemble operation [47]. Finally, a sequence of convolutional blending steps are applied to merge features " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": " across different stages, predicting a dense depth map " + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 313, + 291, + 555, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 393, + 555, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 555, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 555, + 464 + ], + "type": "text", + "content": "We note that there exists another line of depth foundation models [19, 22, 29] that use the image diffusion model [51] to estimate depth maps. Due to the high computational cost of diffusion models, we only consider DPT-based depth foundation models [8, 73] as our base model for real-time performance in this work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 478, + 451, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 451, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 451, + 491 + ], + "type": "text", + "content": "3.2. Prompt Depth Anything" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": "In this section, we seek to find a concise way to incorporate a low-cost LiDAR (i.e., a low-resolution and noisy depth map) as a prompt into the depth foundation model. To this end, we propose a concise prompt fusion architecture tailored for the DPT-based [47] depth foundation models to integrate low-resolution depth information. As shown in Fig. 2(a), the prompt fusion architecture integrates low-resolution depth information at multiple scales within the DPT Decoder. Specifically, for each scale " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " in the DPT Decoder, a low-resolution depth map " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{L} \\in \\mathbb{R}^{1 \\times H_{\\mathrm{L}} \\times W_{\\mathrm{L}}}" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " is firstly bilinearly resized to match the spatial dimensions of the current scale " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{1 \\times H_{i} \\times W_{i}}" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": ". Then, the resized depth map is passed through a shallow convolutional network to extract depth features. After that, the extracted features are projected to the same dimension as the image features " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{i} \\in \\mathbb{R}^{C_{i} \\times H_{i} \\times W_{i}}" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " using a zero-initialized convolutional layer. Finally, the depth features are added to the DPT intermediate features for depth decoding. The illustration of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17072" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 294, + 130 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 130 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 130 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 130 + ], + "type": "image", + "image_path": "8f4be7cedfa4089ef4c1f076f7eda05818a28f35bd96a27749f4e254b96e1fa5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 57, + 139, + 294, + 199 + ], + "blocks": [ + { + "bbox": [ + 58, + 131, + 290, + 139 + ], + "lines": [ + { + "bbox": [ + 58, + 131, + 290, + 139 + ], + "spans": [ + { + "bbox": [ + 58, + 131, + 290, + 139 + ], + "type": "text", + "content": "Reference Image & LiDAR w/ Sparse anchor Interp. w/ Linear Down. Interp." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 57, + 139, + 294, + 199 + ], + "lines": [ + { + "bbox": [ + 57, + 139, + 294, + 199 + ], + "spans": [ + { + "bbox": [ + 57, + 139, + 294, + 199 + ], + "type": "image", + "image_path": "493326964741bce62ecdb3c2cb091df7cbfe91a58575104c6cd165e606b9f845.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 200, + 274, + 208 + ], + "lines": [ + { + "bbox": [ + 59, + 200, + 274, + 208 + ], + "spans": [ + { + "bbox": [ + 59, + 200, + 274, + 208 + ], + "type": "text", + "content": "Reference Image & LiDAR w/ Pseudo GT & Edge Loss w/ Anno. GT" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 217, + 295, + 283 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 295, + 283 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 295, + 283 + ], + "type": "text", + "content": "Figure 3. Effects on the synthetic data lidar simulation and real data pseudo GT generation with the edge-aware depth loss. The middle and right columns are the depth prediction results of our different models. The two rows highlight the significance of sparse anchor interpolation for lidar simulation and pseudo GT generation with edge-aware depth loss, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 304, + 201, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 201, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 201, + 316 + ], + "type": "text", + "content": "this block design is shown in Fig. 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "spans": [ + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "text", + "content": "The proposed design has the following advantages. Firstly, it introduces only " + }, + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "text", + "content": " additional computational overhead (1.789 TFLOPs v.s. 1.691 TFLOPs for a " + }, + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "inline_equation", + "content": "756 \\times 1008" + }, + { + "bbox": [ + 54, + 316, + 295, + 471 + ], + "type": "text", + "content": " image) to the original depth foundation model, and effectively addresses the ambiguity issue inherent in the depth foundation model as demonstrated in Tab. 3(b). Secondly, it fully inherits the capabilities of the depth foundation model because its encoder and decoder are initialized from the foundation model [73], and the proposed fusion architecture is zero-initialized, ensuring that the initial output is identical to that of the foundation model. We experimentally verify the importance of inheriting from a pretrained depth foundation model as shown in Tab. 3(c)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 474, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 701 + ], + "type": "text", + "content": "**Optional designs.** Inspired by conditional image generation methods [28, 43, 79], we also explore various potential prompt conditioning designs into the depth foundation model. Specifically, we experimented with the following designs: a) Adaptive LayerNorm [28, 44] which adapts the layer normalization parameters of the encoder blocks based on the conditioning input, b) CrossAttention [57] which injects a cross attention block after each self-attention block and integrates the conditioning input through cross-attention mechanisms, and c) ControlNet [79] which copies the encoder blocks and inputs control signals to the copied blocks to control the output depth. As shown in Tab. 3(d,e,f), our experiments reveal that these designs do not perform as well as the proposed fusion block. A plausible reason is that they are designed to integrate cross-modal information (e.g., text prompts), which does not effectively utilize the pixel alignment characteristics between the input low-res LiDAR and the output depth. We detail these optional designs in the supp." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 72, + 494, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 494, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 494, + 85 + ], + "type": "text", + "content": "3.3. Training Prompt Depth Anything" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 94, + 553, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 94, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 94, + 553, + 190 + ], + "type": "text", + "content": "Training Prompt Depth Anything simultaneously requires a low-cost LiDAR and precise GT depth. However, synthetic data [49] do not contain LiDAR depth, real-world data with noisy LiDAR depth [75] only have imprecise depth annotations. Therefore, we propose a LiDAR simulation method for synthetic data and generate pseudo GT depth from Zip-NeRF [2] with an edge-aware depth loss for real data. Note that more effective approaches [64, 70] can be applied." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 197, + 555, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 555, + 389 + ], + "type": "text", + "content": "Synthetic data: LiDAR simulation. A LiDAR depth map is low-resolution and noisy. The naive approach for simulating it is to directly downsample the synthetic data depth map. However, this method leads to the model learning depth super-resolution, as shown in Fig. 3, meaning that the model does not correct the LiDAR noise. To simulate the noise, we introduce a sparse anchor interpolation method. Specifically, we first downsample the GT depth map to low-resolution (192 × 256, exactly the depth resolution of iPhone ARKit Depth). Then we sample points on this depth map using a distorted grid with a stride (7 in practice). The remaining depth values are interpolated from these points using RGB similarity with KNN. As shown in Fig. 3, it effectively simulates LiDAR noise and results in better depth prediction. We provide visualization results of the simulated LiDAR in the supp." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 396, + 554, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 554, + 587 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 554, + 587 + ], + "type": "text", + "content": "Real Data: Pseudo GT depth generation. We also add real data [75] to our training data. The annotated depth in ScanNet++ [75] is re-rendered from a mesh scanned by a high-power LiDAR sensor (FARO Focus Premium laser scanner). Due to the presence of many occlusions in the scene, several scan positions (typically 4 in a medium-sized scene in ScanNet++) result in an incomplete scanned mesh, leading to depth maps with numerous holes and poor edge quality, as illustrated in Fig. 2(b). Motivated by the success of reconstruction methods [2, 41], we propose using Zip-NeRF [2] to recover high-quality depth maps. Specifically, we train Zip-NeRF for each scene in ScanNet++ and re-rendered pseudo GT depth. To provide Zip-NeRF with high-quality and dense observations, we detect unblurred frames in Scannet++iPhone videos, and additionally utilize DSLR videos to provide high-quality dense-view images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "Real Data: Edge-aware depth loss. Although Zip-NeRF can generate high-quality edge depth, reconstructing textureless and reflective regions remains challenging as shown in Fig. 2(b). In contrast, these areas (e.g., walls, floors, and ceilings etc.) are usually planar with few occlusions, and the annotations depth in FARO rendered depth is good in these regions. This motivates us to leverage the strengths of both. We propose an edge-aware depth loss to meet these requirements. Specifically, we use the FARO scanned mesh depth and the gradient of the pseudo GT depth to supervise output" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17073" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "type": "text", + "content": "depth and the gradient of the output depth, respectively:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 94, + 294, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 94, + 294, + 107 + ], + "spans": [ + { + "bbox": [ + 86, + 94, + 294, + 107 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e d g e}} = L _ {1} \\left(\\mathbf {D} _ {\\mathrm {g t}}, \\hat {\\mathbf {D}}\\right) + \\lambda \\cdot \\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right), \\tag {1}", + "image_path": "9bc126b0dd20caed842ab4bc2c6281e305e31b2afa8cf59a6d5118f4d1ece1e1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 118, + 294, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 118, + 294, + 135 + ], + "spans": [ + { + "bbox": [ + 63, + 118, + 294, + 135 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g r a d}} \\left(\\mathbf {D} _ {\\text {p s e u d o}}, \\hat {\\mathbf {D}}\\right) = \\left(| \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial x} | + | \\frac {\\partial (\\hat {\\mathbf {D}} - \\mathbf {D} _ {\\text {p s e u d o}})}{\\partial y} |\\right). \\tag {2}", + "image_path": "37ac37dde22ae37b191128c24407463d05fa2f93dd1df552472a59dfd31782f6.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 139, + 295, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 139, + 295, + 235 + ], + "spans": [ + { + "bbox": [ + 55, + 139, + 295, + 235 + ], + "type": "text", + "content": "In practice, we set " + }, + { + "bbox": [ + 55, + 139, + 295, + 235 + ], + "type": "inline_equation", + "content": "\\lambda = 0.5" + }, + { + "bbox": [ + 55, + 139, + 295, + 235 + ], + "type": "text", + "content": ". The depth gradient is mainly prominent at the edges, which is exactly where the pseudo GT depth excels. The gradient loss encourages the model to learn the accurate edges from the pseudo GT depth, while the L1 loss encourages the model to learn the overall depth, ultimately leading to excellent depth prediction. We experimentally verify the effectiveness of the edge-aware depth loss in Tab. 3(j) and Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 242, + 188, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 242, + 188, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 242, + 188, + 255 + ], + "type": "text", + "content": "3.4. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 260, + 295, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 260, + 295, + 297 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 295, + 297 + ], + "type": "text", + "content": "In this section, we provide essential information about the network design, depth normalization, and training details. Please refer to the supp. for more details." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 299, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 299, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 299, + 296, + 360 + ], + "type": "text", + "content": "Network details. We utilize the ViT-large model as our backbone model. The shallow convolutional network comprises two convolutional layers with a kernel size of 3 and a stride of 1. More details can be found in the supp. Detailed running time analysis can be found in Sec. 4.3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 362, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 296, + 446 + ], + "type": "text", + "content": "Depth normalization. The irregular range of input depth data can hinder network convergence. To address this, we normalize the LiDAR data using linear scaling to the range [0, 1], based on its minimum and maximum values. The network output is also normalized with the same scaling factor from LiDAR data, ensuring consistent scales and facilitating easier convergence during training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 449, + 296, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 296, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 296, + 557 + ], + "type": "text", + "content": "Training details. We initiate training from the metric model released by Depth Anything v2 [73], incorporating a 10K step warm-up phase. During this warm-up phase, we fine-tune this metric model to output a normalized depth derived from the linear scaling of LiDAR data. Subsequently, we train our model for 200K steps. During the training process, the batch size is set to 2, utilizing 8 GPUs. We employ the AdamW optimizer, with a learning rate of 5e-6 for the ViT backbone and 5e-5 for the other parameters." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 567, + 135, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 135, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 135, + 581 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 587, + 171, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 171, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 171, + 601 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "We mainly conduct experiments on the HyperSim synthetic dataset [49] and two real-world datasets: ScanNet++ [75] and ARKitScenes [3], which provide iPhone RGB-LiDAR data " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "(192 \\times 256" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " resolution) and annotated depth from a high-power LiDAR " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "(1440 \\times 1920" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " resolution). We follow the suggested training and evaluation protocol in [3] for ARKitScenes, where " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "40\\mathrm{K}" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " images are used for training and " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "5\\mathrm{K}" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " images for evaluation. For the ScanNet++ dataset, we randomly select 20 scenes from its 50 validation scenes," + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 317, + 71, + 553, + 269 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 553, + 269 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 553, + 269 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 553, + 269 + ], + "type": "table", + "html": "
Zero ShotNet. / Post. / w/o LiDAR384 × 512768x10241440x1920
L1 ↓RMSE ↓L1 ↓RMSE ↓L1 ↓RMSE ↓
NoOurs0.01350.03260.01320.03150.01380.0316
MSPF0.01530.03690.01490.03620.01520.0363
Depth Pro*0.04370.06720.04350.06650.04250.0654
DepthAny. v2*0.04640.07150.04230.06600.04970.0764
ZoeDepth*0.08310.28730.06790.14210.05290.0793
Depth Pro*0.12220.14240.12250.14270.12440.1444
DepthAny. v2*0.09780.11800.07710.06470.09060.1125
ZoeDepth*0.21010.27840.17800.23190.15660.1788
YesOurssyn0.01610.03760.01630.03710.01700.0376
D.P.0.02510.04220.02530.04220.02490.0422
BPNet0.14940.21060.14930.21070.14910.2100
ARKit Depth0.02510.04240.02500.04230.02540.0426
DepthAny. v20.07160.16860.06160.13680.04940.0764
DepthAny. v10.07330.17570.06530.15300.05270.0859
Metric3D v20.06260.21040.05240.17210.04020.1045
ZoeDepth0.10070.19170.08900.16270.07620.1135
Lotus0.08530.17930.10380.17820.19410.2741
Marigold0.09080.18490.08070.15650.06920.1065
Metric3D v20.17770.27660.16630.24910.16150.2131
ZoeDepth0.61580.95770.56880.61290.53160.5605
", + "image_path": "caa309fcc853b4327d24e693a78b620391fc57494380a4639ef2c00764687c72.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 277, + 555, + 354 + ], + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 354 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on ARKitScenes dataset. The terms Net., Post. and w/o LiDAR refer to the LiDAR depth usage of models, where \"Net.\" denotes network fusion, \"Post.\" indicates post-alignment using RANSAC, and \"w/o LiDAR\" means the output is metric depth. Methods marked with * are finetuned with their released models and code on ARKitScenes [3] and ScanNet++ [75] datasets." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 363, + 555, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 472 + ], + "type": "text", + "content": "amounting to approximately 5K images for our validation and the training set are from its 230 training scenes, containing about 60K images. To ensure a fair comparison, we additionally train a model with HyperSim training set to achieve zero-shot testing on ScanNet++ and ARKitScenes datasets. Besides depth accuracy metrics, we also report the TSDF reconstruction results of our method on ScanNet++, which reflects the depth consistency. We describe the details of the evaluation metrics in the supp." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 479, + 515, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 515, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 515, + 491 + ], + "type": "text", + "content": "4.2. Comparisons with the State of the Art" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 498, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 713 + ], + "type": "text", + "content": "We compare our method against the current SOTA depth estimation methods from two classes: Monocular depth estimation (MDE) and depth completion/upsampling. For MDE methods, we compare our method with Metric3D v2 [25], ZoeDepth [6], DepthPro [8], Depth Anything v1 and v2 [72, 73] (short for DepthAny. v1 and v2), Marigold [29] and Lotus [22]. For depth completion/upsampling methods, we compare our method with BPNet [56], Depth Prompting [42] (short for D.P.), MSPF [61]. To make a fair comparison with MDE methods, we align their predictions with ARKit LiDAR depth using the RANSAC align method. According to whether they have seen the testing data types during training, we divide methods into two categories: zero-shot and non zero-shot. We train a model " + }, + { + "bbox": [ + 313, + 498, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Ours}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 313, + 498, + 556, + 713 + ], + "type": "text", + "content": " only with HyperSim training set to make comparisons with the zero-shot methods. As shown in Tabs. 1 and 2 and Figs. 4 and 5, our method consistently outperforms the existing methods. Note that" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17074" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 70, + 533, + 443 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 533, + 443 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 533, + 443 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 533, + 443 + ], + "type": "image", + "image_path": "1894ea3f4088d3d69218ba928cc70b2bd94fa8bb06b2cc05a637935dd16065f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 446, + 555, + 470 + ], + "lines": [ + { + "bbox": [ + 55, + 446, + 555, + 470 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 555, + 470 + ], + "type": "text", + "content": "Figure 4. Qualitative comparisons with the state-of-the-art. \"Metric3D v2\" and \"Depth Any. v2\" are scale-shift corrected with ARKit depth. The pink boxes denote the GT depth and depth percentage error map, where red represents high error, and blue indicates low error." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 75, + 479, + 535, + 675 + ], + "blocks": [ + { + "bbox": [ + 75, + 479, + 535, + 675 + ], + "lines": [ + { + "bbox": [ + 75, + 479, + 535, + 675 + ], + "spans": [ + { + "bbox": [ + 75, + 479, + 535, + 675 + ], + "type": "image", + "image_path": "c72c263ab080252f495209221f6bfcf351d0d5f1234674177db8ebf36c542085.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 678, + 536, + 691 + ], + "lines": [ + { + "bbox": [ + 72, + 678, + 536, + 691 + ], + "spans": [ + { + "bbox": [ + 72, + 678, + 536, + 691 + ], + "type": "text", + "content": "Figure 5. Qualitative comparisons of TSDF reconstruction. * align denotes the scale-shift corrected depth with ARKit depth." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17075" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 70, + 515, + 248 + ], + "blocks": [ + { + "bbox": [ + 94, + 70, + 515, + 248 + ], + "lines": [ + { + "bbox": [ + 94, + 70, + 515, + 248 + ], + "spans": [ + { + "bbox": [ + 94, + 70, + 515, + 248 + ], + "type": "table", + "html": "
Zero ShotNet. / Post. / w/o LiDARDepth EstimationTSDF Reconstruction
L1 ↓RMSE ↓AbsRel ↓δ0.5 ↑Acc ↓Comp ↓Prec ↑Recall ↑F-score ↑
NoOurs0.02500.08290.01750.97810.06990.06160.72550.81870.7619
MSPF*0.03260.09750.02260.96740.07720.06950.67380.77610.7133
DepthAny. v2*0.05100.10100.03710.94370.08080.07350.62750.71070.6595
ZoeDepth*0.05820.10690.04160.93250.08810.08010.57210.66400.6083
DepthAny. v2*0.09030.13470.06240.86570.12640.09170.42560.59540.4882
ZoeDepth*0.16750.19840.12780.58070.15670.15530.21640.25530.2323
YesOurssyn0.03270.09660.02240.97000.07460.06660.69030.79310.7307
D.P.0.03530.09830.02420.96570.08200.07470.64310.72340.6734
ARKit Depth0.03510.09870.02410.96590.08110.07430.64840.72800.6785
DepthAny. v20.05920.11450.04020.94040.08810.07470.55620.69460.6127
Depth Pro0.06380.12120.05100.92120.09040.07600.56950.69160.6187
Metric3D v20.05850.30870.04190.95290.07850.07520.62160.69940.6515
Marigold0.08280.14120.06030.87180.09990.07810.51280.66940.5740
DepthPro0.24060.28360.20150.52160.15370.14670.26840.37520.3086
Metric3D v20.12260.34030.08410.80090.08810.08010.57210.66400.6083
", + "image_path": "97a58a5b3f3c6480ff4bc562004ca2b2275aa337b6968b71399b3194b2237128.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 287, + 294, + 402 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 555, + 275 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 555, + 275 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on ScanNet++ dataset. The terms Net, Post and w/o LiDAR refer to the LiDAR depth usage of models as the last table. Methods marked with * are finetuned with their released code on ARKitScenes [3] and ScanNet++ [75] datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 287, + 294, + 402 + ], + "lines": [ + { + "bbox": [ + 58, + 287, + 294, + 402 + ], + "spans": [ + { + "bbox": [ + 58, + 287, + 294, + 402 + ], + "type": "table", + "html": "
ARKitScenesScanNet++
L1 ↓AbsRel ↓Acc ↓Comp ↓F-Score ↑
(a) Oursyn (synthetic data)0.01630.01420.07460.06660.7307
(b) w/o prompting0.06050.05050.09230.08010.5696
(c) w/o foundation model0.01940.01690.07740.07130.7077
(d) AdaLN prompting0.01970.01650.07950.07250.6943
(e) Cross-atten. prompting0.05230.04430.09320.08190.5595
(f) Controlnet prompting0.02390.02060.07850.07260.6899
(g) a + ARKitScenes data0.01340.01150.07440.06620.7341
(h) g + ScanNet++ anno. GT0.01320.01140.06700.06140.7647
(i) g + ScanNet++ pseudo GT0.01390.01210.08350.07660.6505
(j) Ours (h,i+edge loss)0.01320.01150.06990.06160.7619
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Please refer to Sec. 4.3 for detailed descriptions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 439, + 295, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 439, + 295, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 439, + 295, + 477 + ], + "type": "text", + "content": "Oursyn achieves better performance than all non-zero-shot models [61, 73] on ScanNet++, highlighting the generalization ability of prompting a depth foundation model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 482, + 187, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 482, + 187, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 482, + 187, + 496 + ], + "type": "text", + "content": "4.3. Ablations and Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 504, + 295, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 504, + 295, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 504, + 295, + 564 + ], + "type": "text", + "content": "Prompting a depth foundation model. We assess its importance with two experiments: 1) Removing the prompting. Tab. 3(b) shows a significant performance drop. 2) Removing the foundation model initialization [73]. Tab. 3(c) shows a noticeable performance decline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 567, + 295, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 614 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 614 + ], + "type": "text", + "content": "Prompting architecture design. We study different designs: AdaLN, Cross-attention, and ControlNet as discussed in Sec. 3.2. Tab. 3(d,e,f) reveals that ControlNet performs best but still falls short of our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": "Training data and edge-aware depth loss. We initially incorporate ARKitScenes data, which only enhances performance on ARKitScenes (Tab. 3(g)). Then we add ScanNet++, which improves results on both ARKitScenes and ScanNet++ (Tab. 3(h)). However, the depth visualization remains less than ideal (Fig. 3). Tab. 3(i) show that direct supervision with pseudo GT depth from reconstruction methods decreases performance. Ultimately, employ" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 286, + 553, + 363 + ], + "blocks": [ + { + "bbox": [ + 316, + 286, + 553, + 363 + ], + "lines": [ + { + "bbox": [ + 316, + 286, + 553, + 363 + ], + "spans": [ + { + "bbox": [ + 316, + 286, + 553, + 363 + ], + "type": "image", + "image_path": "f0cbae75084fc5da7f533290ca2bc1139cff113390458f0d1d8a805073d394d5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 371, + 555, + 394 + ], + "lines": [ + { + "bbox": [ + 313, + 371, + 555, + 394 + ], + "spans": [ + { + "bbox": [ + 313, + 371, + 555, + 394 + ], + "type": "text", + "content": "Figure 6. Outdoor reconstruction by taking the vehicle LiDAR as metric prompt. Please refer to the supp. for more video results." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "content": "ing the edge-aware depth loss that utilizes pseudo GT depth and FARO annotated GT achieves comparable performance with Tab. 3(h) but with superior thin structure depth performance as shown in Fig. 3. We provide more qualitative ablation results in the supp." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "text", + "content": "Running time analysis. Our model with ViT-L runs at 20.4 FPS for an image resolution of " + }, + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "inline_equation", + "content": "768 \\times 1024" + }, + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "text", + "content": " on a A100 GPU. As ARKit6 supports 4K image recording, we test our model at a resolution of " + }, + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "inline_equation", + "content": "2160 \\times 3840" + }, + { + "bbox": [ + 313, + 469, + 556, + 555 + ], + "type": "text", + "content": " and achieve 2.0 FPS. Note that our model can also be implemented with ViT-S, where the corresponding speeds are 80.0 and 10.3 FPS. More testing results can be found in the supp." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 561, + 504, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 504, + 574 + ], + "type": "text", + "content": "4.4. Zero-shot Testing on Diverse Scenes" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 579, + 555, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 579, + 555, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 579, + 555, + 652 + ], + "type": "text", + "content": "Although our model is trained on indoor scenes, it generalizes well to various scenarios, including new rooms, gyms with thin structures, poorly lit museums, human and outdoor environments, as shown in Fig. 7, highlighting the effectiveness of prompting a depth foundation model. Please refer to the supp. for video results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 658, + 487, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 487, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 487, + 672 + ], + "type": "text", + "content": "4.5. Application: 3D Reconstruction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "Our consistent and scale-accurate depth estimation benefits the indoor 3D reconstruction as shown in Tab. 2 and Fig. 5. 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Robotic grasping setup and input signal types. Our goal is to grasp objects of various types using image/LiDAR/depth inputs. Red rectangles indicate potential object positions." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 206, + 299, + 294, + 430 + ], + "blocks": [ + { + "bbox": [ + 206, + 299, + 294, + 430 + ], + "lines": [ + { + "bbox": [ + 206, + 299, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 206, + 299, + 294, + 430 + ], + "type": "image", + "image_path": "79ddd2f611b37f79a0b90654981df45b5aac5b13e4e9e2b457d63841f5181668.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 55, + 484, + 295, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 534 + ], + "type": "text", + "content": "with vehicle LiDAR, which enables our model to achieve large-scale outdoor scene reconstruction as shown in Fig. 6. We detail the setup and include more video results for dynamic streets in the supp." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 55, + 539, + 284, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 539, + 284, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 284, + 553 + ], + "type": "text", + "content": "4.6. Application: Generalized Robotic Grasping" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "content": "We set up a robotic platform to test our model in generalized robotic manipulation (Fig. 8), which typically requires depth or RGB as observations. Good depth estimation enhances the generalization ability because it accurately describes the 3D information of surroundings [26, 78]. Specifically, we train an ACT policy [81] to grasp various objects into the box, using different types of input signals such as RGB, LiDAR, and depth data from our model. We empirically find that our model generalizes well to unseen objects like transparent and specular objects when trained on diffusive objects, outperforming RGB and LiDAR inputs as shown in Tab. 4. This is because RGB is dominated by color, which leads to poor generalization across objects, and" + } + ] + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 317, + 298, + 554, + 355 + ], + "blocks": [ + { + "bbox": [ + 317, + 298, + 554, + 355 + ], + "lines": [ + { + "bbox": [ + 317, + 298, + 554, + 355 + ], + "spans": [ + { + "bbox": [ + 317, + 298, + 554, + 355 + ], + "type": "table", + "html": "
Input SignalDiffusiveTransparentSpecular
Red CanGreen Can
Ours1.0/1.0/1.01.0/1.0/1.00.3/1.0/1.00.8/1.0/0.9
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", + "image_path": "5364eda7a4092a88f25ad337c181eee37d4f2eb217a858f132f6b71ff066ab06.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 358, + 555, + 393 + ], + "lines": [ + { + "bbox": [ + 313, + 358, + 555, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 555, + 393 + ], + "type": "text", + "content": "Table 4. Grasping success rate on various objects. Three numbers indicate objects placed at near, middle, and far positions. The grasping policy is trained on diffusive and tested on all objects." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 398, + 555, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 555, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 555, + 434 + ], + "type": "text", + "content": "the iPhone LiDAR depth is noisy and lacks the capability to perceive transparent objects. Please refer to the supp. for detailed setup descriptions and videos." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 449, + 471, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 471, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 471, + 462 + ], + "type": "text", + "content": "5. Conclusion and Discussions" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 470, + 555, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 555, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 555, + 602 + ], + "type": "text", + "content": "This paper introduced a new paradigm for metric depth estimation, formulated as prompting a depth foundation model with metric information. We validated the feasibility of the paradigm by choosing the low-cost LiDAR depth as the prompt. A scalable data pipeline was proposed to generate synthetic LiDAR depth and pseudo GT depth for training. Extensive experiments demonstrate the superiority of our method against existing monocular depth estimation and depth completion/upsampling methods. Furthermore, we showed that it benefits for downstream tasks including 3D reconstruction and generalized robotic grasping." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Limitations and future work. This work has some known limitations. For instance, when using the iPhone LiDAR as the prompt, it cannot handle long-range depth, as the iPhone LiDAR detects very noisy depth for far objects. Additionally, we observed some temporal flickering of LiDAR depth, leading to a flickering depth prediction. These issues can be addressed in future works by considering more advanced prompt learning techniques that can extend the effective range and temporal prompt tuning." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17077" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "content": "Acknowledgements. This work was partially supported by NSFC (No. 62402427, U24B20154, 623B2091), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), Information Technology Center and State Key Lab of CAD&CG, and Zhejiang University Education Foundation Qizhen Scholar Foundation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "spans": [ + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 175, + 294, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 175, + 294, + 218 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 175, + 294, + 218 + ], + "spans": [ + { + "bbox": [ + 61, + 175, + 294, + 218 + ], + "type": "text", + "content": "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Learning fine-grained bimanual manipulation with low-cost hardware. 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This task demands the model bridge character performances and complicated prosody structures to build a high-quality video-synchronized dubbing track. The limited scale of movie dubbing datasets, along with the background noise inherent in audio data, hinder the acoustic modeling performance of trained models. To address these issues, we propose an acoustic-prosody disentangled two-stage method to achieve high-quality dubbing generation with precise prosody alignment. First, we propose a prosody-enhanced acoustic pre-training to develop robust acoustic modeling capabilities. Then, we freeze the pre-trained acoustic system and design an acoustic-disentangled framework to model prosodic text features and dubbing style while maintaining acoustic quality. Additionally, we incorporate an in-domain emotion analysis module to reduce the impact of visual domain shifts across different movies, thereby enhancing emotion-prosody alignment. Extensive experiments show that our method performs favorably against the state-of-the-art models on two primary benchmarks. The project is available at https://zzdoog.github.io/ProDubber/.", + "bbox": [ + 89, + 340, + 483, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 732, + 220, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Movie Dubbing, also known as Visual Voice Cloning (V2C) [5], aims to generate speech from scripts using a specified voice conditioned by a single short reference audio while ensuring prosody alignment with the character's performance in terms of both pronunciation duration and intonation (as shown in Figure 1 (a)). It promises significant potential in real-world applications such as film post-", + "bbox": [ + 89, + 758, + 482, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77134cc1fa0f21cd3932d79018a9194c0cd0a14bda7767f80d151ed9e60937a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 313, + 890, + 400 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5b5d420c4f529c118468a19fdb5d877278ccbf37f97e9798c1e0fb9ae9e145d3.jpg", + "image_caption": [ + "(a) Visual Voice Cloning (V2C) task", + "(b) Illustration of our proposed method", + "Figure 1. (a) Illustration of the V2C task. (b) Illustration of the proposed acoustic pre-training stage (Stage I) and prosody adapting stage (Stage II), which aim to generate dubbing with high acoustic quality and aligned prosody." + ], + "image_footnote": [], + "bbox": [ + 532, + 419, + 895, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "production, media production, and personal speech AIGC.", + "bbox": [ + 511, + 597, + 898, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared to traditional speech synthesis [4, 27, 30, 35, 36] or Voice Cloning [1] tasks, movie dubbing presents greater challenges. It demands the ability not only to align the prosody with complex character performances but also to maintain high acoustic quality even when managing diverse and exaggerated prosody inherent in dubbing.", + "bbox": [ + 511, + 613, + 905, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous works achieve significant progress in aligning prosody with the performances of movie characters. V2C-Net [5] incorporates visual features from each frame of the movie clip into the mel-spectrogram frame-level prosody modeling. HPMDubbing [6] employs a hierarchical design, where lip, face, and video-level features correspond to pronunciation duration, prosody, and the overall video atmosphere, respectively. StyleDubber [8] uses a fine-grained adaptor to bridge the speaker's style and character's emotion states at the phoneme level, facilitating joint modeling of prosody. However, existing methods overlook the visual domain discrepancies arising from variations in movie styles and other visual elements, such as color grading,", + "bbox": [ + 511, + 704, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work is done during the intern in VIPL group, ICT, CAS.", + "bbox": [ + 107, + 875, + 442, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "172", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "which impact the stability of prosody alignment.", + "bbox": [ + 89, + 90, + 413, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The nature of film acting means movie dubbing inherently involves more exaggerated and diverse prosody variations compared to traditional speech, yet the difficulty of its acoustic modeling is often underestimated. In addition, certain characteristics of movie dubbing datasets, such as their limited scale (primarily due to copyright restrictions) and the suboptimal audio quality caused by unavoidable movie background noise [54], further hinder methods that solely rely on dubbing datasets for training to achieve satisfied acoustic quality [5, 6, 8, 24]. Speaker2Dubber [54] attempts to enhance the model's acoustic modeling capability by pre-training the phoneme encoder on a large-scale text-to-speech corpus. This two-stage training strategy improves the model's pronunciation accuracy, however, the pre-trained phoneme encoder alone cannot eliminate the impact of low audio quality in dubbing datasets, or modeling complex prosody variation, leading to a significant degradation in final acoustic quality.", + "bbox": [ + 89, + 108, + 483, + 380 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we propose a dubbing method that incorporates a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to achieve high-quality dubbing with well-aligned prosody (as shown in Figure 1 (b)). Specifically, in the prosody-enhanced acoustic pre-training stage, we pre-train the entire acoustic system of the model using a text-speech corpus with enhanced prosody. This ensures the acoustic modeling capability in audio quality and managing the complex dubbing prosody variations. We thus freeze the acoustic system in the second stage and design a disentangled framework to model prosodic features from the dubbing script and audio by introducing a prosodic text BERT encoder and a prosodic style diffusion module. These disentangled prosodic features are further bridged with the in-domain emotion analysis output feature, aligning the prosody with the character's emotion. Lip motion features are then utilized to predict pronunciation duration and upsample the text content to match the mel-spectrogram length. Finally, the pre-trained audio decoder takes the upsampled text content and predicted prosody as input, integrating the speaker voice via AdaIN layer [15], and generates dubbing with high acoustic quality and aligned prosody.", + "bbox": [ + 89, + 383, + 483, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of the paper are as follows:", + "bbox": [ + 109, + 732, + 447, + 747 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a two-stage dubbing method with a prosody-enhanced acoustic pre-training to enhance the model's ability in high-quality acoustic modeling and handling complex prosodic variations.", + "- To maintain the acoustic quality in the prosody adapting stage, we freeze the pre-trained acoustic system and devise an acoustic-disentangled prosody adapting framework by introducing prosodic modeling modules corresponding to both the script and the required dubbing style.", + "- We design an in-domain emotion analysis module in the" + ], + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prosody adapting stage to reduce the instability caused by visual domain discrepancies across different movies.", + "bbox": [ + 526, + 90, + 903, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments demonstrate the proposed method achieves favorable performance compared to several state-of-the-art approaches on two major benchmarks, validating the effectiveness of our approach.", + "bbox": [ + 513, + 121, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 194, + 655, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Speech Synthesis", + "text_level": 1, + "bbox": [ + 511, + 219, + 679, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the rapid development of deep learning [7, 10, 11, 16, 29, 32, 40, 42-45, 48, 50, 53, 56], the speech synthesis task has advanced significantly in recent years. From the autoregressive generation architecture of models like WaveNet [46] to the non-autoregressive parallel architecture of the FastSpeech series [35, 36], both the quality and speed of speech generation have improved substantially. Recently, the NaturalSpeech [18, 38, 39] and StyleTTS [25, 27] series have utilized factorized codec and diffusion models, as well as adversarial training with large speech language models, respectively, to achieve high-quality speech synthesis that more closely approaches human-level performance. Additionally, many other works based on other generative models [13, 14, 17, 19, 33, 47] such as flow matching [12, 20, 28] are also advancing the progress in speech synthesis. Despite the progress has been made, they cannot be directly applied to movie dubbing tasks because they lack the design of modeling prosody from input movie clips.", + "bbox": [ + 511, + 239, + 906, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Visual Voice Cloning", + "text_level": 1, + "bbox": [ + 511, + 521, + 710, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The V2C task [5] requires the model to align the prosody of the generated speech with the input video to achieve automatic movie dubbing. To this end, HPMDubbing [6] proposes a hierarchical prosody learning structure, aligning the dubbing duration, prosody, and overall tone with the lip movements, facial expressions, and overall context of the video. Some works [8, 55], on the other hand, design a fine-grained prosody matching module for character voice, incorporating phoneme-level features and emotional variations to model the dubbing style of the characters. Subsequently, Speaker2Dubber [54] addresses the difficulty of learning accurate pronunciation through training solely on dubbing datasets by pre-training its phoneme encoder on text-speech corpus. Despite these advancements, current dubbing models are still significantly influenced by the quality of the dubbing dataset and struggle to achieve high acoustic quality.", + "bbox": [ + 511, + 542, + 908, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 511, + 813, + 604, + 828 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 511, + 837, + 624, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The target of the overall movie dubbing task is:", + "bbox": [ + 511, + 859, + 826, + 875 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {A} _ {D u b} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {d}, V _ {m}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 883, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "173", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d87b9aa0b59d04745cc6c83851f3f02076b4b2ffc7fef72982399e3f2d11cfbc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 89, + 903, + 251 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/07ff39d8d8cc4a9c98ac2f2780943f978d5fc508084a6c9762e602c0811d605e.jpg", + "image_caption": [ + "Figure 2. The main architecture of the proposed method. In the Prosody-Enhanced Acoustic Pre-training stage (Section 3.2), we pre-train the acoustic system using a prosody-enhanced text-speech corpus. In the Acoustic-Disentangled Prosody Adapting stage (Section 3.4), we freeze the acoustic system and employ a disentangled framework to bridge the prosody of dubbing with the character's performance using In-Domain Emotion Analysis (Section 3.3), thus generating dubbing with aligned prosody and maintain high acoustic quality." + ], + "image_footnote": [], + "bbox": [ + 94, + 252, + 903, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the $\\tilde{A}_{Dub}$ is the generated dubbing and $A_{Ref}, T_d, V_m$ are the reference audio, dubbing scripts, and the input silent movie clip respectively.", + "bbox": [ + 89, + 486, + 482, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main architecture of the proposed two-stage method is shown in Figure 2. In the prosody-enhanced acoustic pre-training stage, we first design a prosody enhancement strategy to address the prosody domain differences between movie dubbing and traditional speech and apply it to a large-scale, high-quality text-speech corpus. Then, we use the enhanced corpus to pre-train the acoustic style encoder (ASE), acoustic text encoder, and end-to-end audio decoder of the dubbing model, enabling the acoustic system to accurately generate high-quality speech with corresponding content and speaker voice. Next, in the acoustic-disentangled prosody adapting stage, we utilize an acoustic-prosodic disentangled framework by introducing the prosodic style diffusion and prosodic text BERT encoder. This framework adapts the prosody while keeping the acoustic system frozen, thus maintaining the acoustic quality of generated dubbing. We also propose In-Domain Emotion Analysis to better bridge the dubbing prosody with the character's emotion, which improves the audiovisual consistency. We detail each module below.", + "bbox": [ + 89, + 532, + 483, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Prosody-Enhanced Acoustic Pre-training", + "text_level": 1, + "bbox": [ + 89, + 847, + 442, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Acoustic quality forms the foundation of movie dubbing. The goal of prosody-enhanced acoustic pre-training is to", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "provide a solid basis for high-quality acoustic modeling for movie dubbing through the pre-training of the acoustic system in the dubbing model. Below, we detail this pre-training approach in two aspects: the pre-training objectives and the prosody enhancement strategy.", + "bbox": [ + 511, + 487, + 906, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1. Pre-training Objectives", + "text_level": 1, + "bbox": [ + 511, + 570, + 723, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike the target of the movie dubbing task, the input of this stage does not contain the movie clip:", + "bbox": [ + 511, + 588, + 905, + 619 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {A} _ {s p e e c h} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {s}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 628, + 906, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the $T_{s}$ is the script from the text-speech corpus. Nevertheless, the acoustic information ultimately used to generate speech audio comprises three components which are the same as the movie dubbing: content information derived from the text, speaker voice obtained from reference audio, and the prosody of the speech. The only difference lies in whether the prosody and duration of each phoneme need to align with the given video. Since the text-speech corpus used in this stage does not include the corresponding video clip, we directly utilize the ground truth duration and prosody during this stage.", + "bbox": [ + 511, + 657, + 906, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We adopt an architecture similar to StyleTTS [25] for acoustic pre-training. First, the text in the corpus is converted from a grapheme sequence to a phoneme sequence using a G2P module. We then use a bidirectional LSTM network to extract acoustic text features from the phoneme", + "bbox": [ + 511, + 825, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "174", + "bbox": [ + 486, + 944, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sequence. Next, an acoustic style encoder extracts timbre features from either the ground truth or other speech samples from the same speaker. A prosody extractor is employed to extract mel-spectrogram frame-level prosody (pitch and energy curve) from the mel-spectrogram of the ground truth speech. To upsample the acoustic text sequence to match the length of the mel-spectrogram, we use a monotonic aligner pre-trained on the LibriSpeech dataset for the automatic speech recognition (ASR) task to obtain the ground truth duration of each phoneme:", + "bbox": [ + 89, + 90, + 483, + 243 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {p h o} = \\mathrm {G 2 P} (T _ {s}) \\in \\mathbb {R} ^ {L _ {p h o}},\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 251, + 287, + 268 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {a} = \\operatorname {A c o u s t i c T e x t E n c o d e r} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}},\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 271, + 436, + 289 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {a} = \\text {A c o u s t i c S t y l e E n c o d e r} \\left(A _ {R e f}\\right) \\in \\mathbb {R} ^ {d _ {m}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 292, + 480, + 310 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A l i g n} = \\operatorname {T e x t A l i g n e r} (M e l _ {s}, T _ {P h o}) \\in \\mathbb {R} ^ {L _ {p h o} \\times L _ {m e l}},\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 313, + 449, + 330 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np, n = \\operatorname {P r o s o d y E x t r a c t o r} (M e l _ {s}) \\in \\mathbb {R} ^ {L _ {m e l}},\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 334, + 395, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T_{a}$ and $S_{a}$ are the acoustic text feature and acoustic style feature, respectively. $L_{pho}$ and $L_{mel}$ denote the length of the phoneme sequence and desired mel-spectrogram, respectively. $d_{m}$ denotes the hidden size of the model. Align is the monotonic attention map between the phoneme sequence and the mel-spectrogram of ground truth speech $Mel_{s}$ . $p, n$ is the ground truth pitch and energy curve.", + "bbox": [ + 89, + 359, + 483, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, a HiFi-GAN [22] based end-to-end audio decoder takes the extracted prosody and the upsampled acoustic text features as inputs, while using Adaptive Instance Normalization (AdaIN) [15] to integrate the acoustic style information and reconstruct the original ground truth waveform:", + "bbox": [ + 89, + 465, + 483, + 542 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A d a I N} \\left(c, S _ {a}\\right) = P _ {\\sigma} \\left(S _ {a}\\right) \\frac {c - \\mu (c)}{\\sigma (c)} + P _ {\\mu} \\left(S _ {a}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 550, + 480, + 584 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {A} _ {\\text {s p e e c h}} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot \\operatorname {A l i n g}, p, n, S _ {a}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 585, + 439, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c$ is the single channel of the feature maps, $\\mu (\\cdot)$ and $\\sigma (\\cdot)$ denote the channel mean and standard deviation. $P_{\\mu}$ and $P_{\\sigma}$ are the linear projections for predicting the adaptive gain and bias using the acoustic style feature $S_{a}$ .", + "bbox": [ + 89, + 612, + 483, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training objective at this stage is a reconstruction loss for speech:", + "bbox": [ + 89, + 672, + 483, + 702 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R e c} = \\left\\| A _ {s p e e c h} - \\tilde {A} _ {s p e e c h} \\right\\| _ {1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 710, + 482, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2. Prosody Enhancement Strategy", + "text_level": 1, + "bbox": [ + 89, + 746, + 356, + 761 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By pre-training the acoustic system using a text-speech corpus as mentioned above, the dubbing model gains the ability to convert text into high-quality speech. However, the speech in traditional text-to-speech corpora typically comes from recordings of audiobooks or blogs, which often exhibit flat and monotonous prosody. In contrast, the prosody of movie dubbing tends to vary significantly depending on the plot or performance, particularly in terms of pitch variation and the duration of certain lines.", + "bbox": [ + 89, + 763, + 483, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We design two prosody enhancement strategies to address the prosodic domain discrepancy between movie dubbing and traditional speech: pitch shifting and duration stretching. Pitch shifting alters the overall pitch of the speech by shifting it to higher or lower frequency bands, simulating the pitch variations found in dubbing. Duration stretching scales the length of the speech to simulate the varied speech pace observed in movie dubbing.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the implementation, we find that directly manipulating pitch or duration in the time domain significantly degrades speech quality and reduces its naturalness. Therefore, we choose to convert the speech into mel-spectrograms and apply the enhancements in the frequency domain. We then use a vocoder [22] to convert the modified speech back to the time domain for end-to-end pre-training. Specifically, for the pitch shifting operation, we shift the entire spectrogram up or down by a specified number of frequency bands and fill the excess frequency bands with -80db to maintain the shape of spectrogram. For duration stretching, we use linear interpolation and downsampling operations to expand or shorten the length of spectrograms.", + "bbox": [ + 511, + 213, + 906, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. In-Domain Emotion Analysis", + "text_level": 1, + "bbox": [ + 511, + 422, + 774, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To obtain fine-grained character emotion features at the video frame level, we first extract the face region of each frame of movie clip $V_{face}$ via S $^3$ FD face detection [52], then utilize an emotion face-alignment network (EmoFAN [41]) to encode the face region to emotion features $V_{emo}$ following [6]:", + "bbox": [ + 511, + 445, + 905, + 536 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {e m o} = \\operatorname {E m o F A N} \\left(\\mathrm {S} ^ {3} \\mathrm {F D} \\left(V _ {m}\\right)\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 547, + 903, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $L_{v}$ denotes the frame number of the video.", + "bbox": [ + 511, + 580, + 864, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure that the fine-grained video frame-level emotion features more accurately reflect emotional changes rather than visual characteristics of the movie, we first normalize them:", + "bbox": [ + 511, + 595, + 905, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {e m o} ^ {\\prime} = \\Sigma^ {- \\frac {1}{2}} \\left(V _ {e m o} - \\mu\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 669, + 903, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{emo}'$ denotes the normalized feature, $\\mu$ is the mean of the feature sequence, and $\\Sigma$ is the covariance matrix of sequence. The term $\\Sigma^{-\\frac{1}{2}}$ represents the inverse square root of the covariance matrix, which ensures that the normalized features have zero mean and unit covariance.", + "bbox": [ + 511, + 700, + 905, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Simultaneously, to reflect the absolute emotional state of characters in the video, we use a video-level atmosphere feature [6] to adjust the normalized emotion features, thereby capturing the character's emotional state and changes:", + "bbox": [ + 511, + 777, + 905, + 853 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {p} = \\alpha \\cdot V _ {e m o} ^ {\\prime} + \\beta \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 866, + 903, + 891 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha = f _ {\\alpha} (V _ {a t o}), \\quad \\beta = f _ {\\beta} (V _ {a t o}),\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 888, + 815, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "175", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{ato} \\in \\mathbb{R}^{d_m}$ is the video-level atmosphere feature, $f_{\\alpha}$ and $f_{\\beta}$ are learnable linear projections. $V_{p}$ denotes the video-frame level emotion prosodic features.", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Acoustic-Disentangled Prosody Adapting", + "text_level": 1, + "bbox": [ + 89, + 146, + 442, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ensure that the model does not compromise acoustic quality during training on the dubbing dataset, we freeze the entire pre-trained acoustic system at this stage. Unlike traditional TTS tasks that only require modeling prosody from the input text and the voice of reference audio, movie dubbing demands a more complex prosody modeling that bridges the character's facial expressions from visual modality. Relying solely on the frozen acoustic text encoder and acoustic style encoder is insufficient to handle the complex prosody alignment.", + "bbox": [ + 88, + 167, + 482, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To this end, we propose an acoustic-disentangled framework by introducing a prosodic text BERT encoder (PTBE) [26] and a prosodic style encoder (PSE) to extract prosodic features from the script text and non-timbre prosodic features from ground truth dubbing, respectively:", + "bbox": [ + 89, + 319, + 483, + 396 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {p} = \\operatorname {P T B E} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 402, + 480, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {p} = \\mathrm {P r o s o d i c S t y l e E n c o d e r} (A _ {D u b}) \\in \\mathbb {R} ^ {d _ {m}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 425, + 437, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After extracting prosodic features from both the text and the dubbing audio, we employ a multi-head cross-attention module to connect phoneme-level text prosodic features with emotion features, enabling the modeling of prosody at the phoneme level based on character emotion variations:", + "bbox": [ + 89, + 454, + 483, + 529 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} T _ {F u s i o n} ^ {k} = s o f t m a x (\\frac {Q _ {p h o} ^ {\\top} K _ {e m o}}{\\sqrt {d _ {m}}}) V _ {e m o} \\in \\mathbb {R} ^ {L _ {p h o} \\times \\frac {d _ {m}}{n _ {h e a d}}}, \\\\ Q _ {p h o} = W _ {j} ^ {Q} T _ {p} ^ {\\top}, K _ {e m o} = W _ {j} ^ {K _ {p}} V _ {p} ^ {\\top}, V _ {p} = W _ {j} ^ {V _ {p}} V _ {p} ^ {\\top}, \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 532, + 480, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $k$ denotes $k$ -th head's output, $W_{j}^{*}$ are learnable parameter matrix, and $T_{Fusion}$ is phoneme-level prosodic feature with emotion variation information.", + "bbox": [ + 89, + 613, + 482, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To model the prosodic style feature of dubbing, we design a prosodic dstyle diffusion module that takes $T_{Fusion}$ as input and samples the prosodic style feature from noise:", + "bbox": [ + 89, + 659, + 483, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p _ {\\theta} \\left(S _ {t - 1} \\mid S _ {t}\\right) = \\mathcal {N} \\left(S _ {t - 1}; \\mu_ {\\theta} \\left(S _ {t}, t\\right), \\Sigma_ {\\theta} \\left(S _ {t}, t\\right)\\right), \\tag {11} \\\\ \\tilde {S} _ {p} = p _ {\\theta} \\left(S _ {0} \\mid T _ {F u s i o n}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 715, + 480, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $p_{\\theta}$ is the learnable denoise distribution and the $S_{t-1}$ is the feature of previous time step. Specifically, in the first half of the training process, we train the prosodic style encoder to better assist the prosody predictor in prosody prediction. In the second half of the training, we introduce the prosodic style diffusion module. This approach ensures more stable convergence during training.", + "bbox": [ + 89, + 763, + 482, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, we employ the AdaIN module to integrate the predicted prosodic style feature into the $T_{Fusion}$ , which", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is then input into the prosody predictor for specific prosody prediction:", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {p}, \\tilde {n} = \\text {P r o s o d y P r e d i c t o r} (\\text {A d a I N} (T _ {\\text {F u s i o n}}, \\tilde {S} _ {p})), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 132, + 903, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\tilde{p},\\tilde{n}\\in \\mathbb{R}^{L_{pho}}$ are the prediction of prosody attributes (pitch and energy) based on the prosodic features and the visual emotion feature.", + "bbox": [ + 511, + 159, + 903, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In terms of aligning the duration of pronunciation with lip movements, since this alignment is solely related to the prosody of pronunciation and lip movements, which is independent of character emotions and both kinds of style, the input to the duration predictor is the cross-attention fusion of the prosodic text feature and the lip motion feature. Then, we upsample the acoustic text features to the spectrogram length based on the alignment built from the duration prediction, and the audio decoder takes the upsampled acoustic text feature, the acoustic style feature, and the prosody prediction as input, generating the dubbing audio:", + "bbox": [ + 511, + 205, + 906, + 372 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {d} = \\text {D u r a t i o n P r e d i c t o r} (\\underset {\\sim} {\\mathrm {C A}} (T _ {p}, V _ {d}, V _ {d})) \\in \\mathbb {R} ^ {L _ {p h o}}, \\tag {13} \\\\ \\tilde {A} _ {D u b} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot A l i g n, \\tilde {p}, \\tilde {n}, S _ {a}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 381, + 903, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $V_{d} \\in \\mathbb{R}^{L_{v} \\times d_{m}}$ is the lip motion feature extracted from the lip region of movie clips following [6]. $\\mathrm{CA}(\\cdot)$ denotes the cross-attention, we use $T_{p}$ as query and $V_{d}$ as key and value here to get the phoneme-level duration features. The duration prediction is scaled according to the length of the movie clip to ensure the alignment between total video duration and total dubbing duration. It is noteworthy that $\\tilde{p}$ and $\\tilde{n}$ are also upsampled before being input into the decoder to match the spectrogram length.", + "bbox": [ + 511, + 431, + 906, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training", + "text_level": 1, + "bbox": [ + 513, + 579, + 617, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the acoustic-disentangled prosody adapting stage, since we freeze all acoustic modules, the training objective for this stage is the sum of the losses for different prosody attributes:", + "bbox": [ + 511, + 601, + 905, + 659 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D u b} = \\lambda_ {1} \\mathcal {L} _ {p} + \\lambda_ {2} \\mathcal {L} _ {n} + \\lambda_ {3} \\mathcal {L} _ {d} + \\lambda_ {4} \\mathcal {L} _ {S _ {p}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 675, + 903, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\mathcal{L}_p, \\mathcal{L}_n,$ and $\\mathcal{L}_d$ are the L1-Loss for pitch, energy and duration respectively. The $\\mathcal{L}_{S_p}$ is the diffusion loss for prosodic style feature modeling.", + "bbox": [ + 511, + 704, + 905, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 762, + 637, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 511, + 787, + 614, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "V2C-Animation dataset [5] is a collection of 10,217 video clips from 26 animated movies, featuring aligned text, audio, and video clips from real movies along with speaker emotion annotations. Our main experimental results are validated on this dataset due to its authenticity and more detailed annotations.", + "bbox": [ + 511, + 809, + 905, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "176", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c38aa8a49f596aa294da652832d3dc9dc9744b838a4b02df55acb998a21e2e19.jpg", + "table_caption": [ + "Table 1. Results on V2C-Animation benchmark. For the Dub 1.0 setting, we use the ground truth audio as reference audio, for the Dub 2.0 setting, we use the non-ground truth audio from the same speaker within the dataset as the reference audio which is more aligned with practical usage in dubbing. The method with “*” refers to a variant taking video embedding as an additional input following [5]. “T-S” indicates whether this method employs a two-stage training approach same as [54]. The same setup is applied to the GRID benchmark." + ], + "table_footnote": [], + "table_body": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%)↑WER (%)↓UT-MOS ↑EMO-ACC (%)↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%)↑WER (%)↓UT-MOS ↑
GT-100.0025.552.2699.960.000.00100.0022.552.26
GT Mel + Vocoder-96.9624.402.1897.093.773.8096.9624.402.18
StyleSpeech* [30]X42.53108.001.4142.5311.6214.2375.6782.481.81
Zero-shot TTS* [57]X48.9368.051.7243.9710.0312.0147.5558.811.63
V2C-Net [5]X40.6173.081.3243.0814.1218.4934.0761.611.30
HPMDubbing [6]X53.76164.161.3146.6111.1211.2231.42171.031.30
Face-TTS [24]X52.81201.131.3144.0413.4426.9451.98200.181.31
StyleDubber [8]X82.2631.491.8945.629.379.4681.2731.701.95
StyleSpeech* [30]✓58.9438.352.4446.2710.1013.1255.9063.971.89
V2C-Net [5]✓69.0023.022.3546.159.9710.9769.3023.152.32
Speaker2Dubber [54]✓81.5017.512.4146.809.469.6579.8617.332.42
Ours✓75.468.043.1048.939.299.3275.3911.503.09
", + "bbox": [ + 93, + 148, + 903, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GRID dataset [9] is a basic benchmark for multi-speaker dubbing. It comprises high-quality video recordings of 33 speakers performing 1,000 scripted sentences each, resulting in a total of 33,000 utterances. All participants are recorded in a noise-free studio with a unified screen background. V2C-Animation and GRID benchmarks respectively correspond to animated films and basic real-person dubbing, covering a wide range of application scenarios.", + "bbox": [ + 88, + 339, + 480, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LibriTTS dataset [51] is a substantial collection of speech data designed for training and evaluating multi-speaker text-to-speech (TTS) systems derived from the LibriSpeech [31]. It includes multi-speaker recordings, offering a diverse range of voices and speaking styles and meticulously segmented and annotated with text transcripts. We employ LibriTTS as the text-speech corpus used in the prosody-enhance acoustic pre-training stage.", + "bbox": [ + 88, + 460, + 482, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 590, + 308, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following [5, 6, 8, 54], all the video frames are sampled at 25 FPS. During training, we resample all audio file in $24\\mathrm{kHz}$ and convert them into mel-spectrograms using FFT size of 2048, hop size of 300, window size of 1200, and frequency bins of 80. We employ a pre-trained JDC network [23] as the pitch extractor and use the log norm to calculate the energy following [25, 27]. For the text aligner, we adopt the ASR model fine-tuned for the TTS task by [25] to get the ground truth alignment between phoneme and mel-spectrogram.", + "bbox": [ + 88, + 613, + 482, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use Libri-TTS-460 following [27] for the acoustic pre-training and apply a $3\\%$ prosody enhancement ratio to trade off the audio quality and prosody variations. We use the official pre-trained HiFi-GAN [22] as the vocoder for the prosody enhancement. We train the acoustic system with 20 epochs in the pre-training stage. For the prosody adapting stage, we train the model with 30 epochs on the V2C-Animation dataset and 20 epochs for GRID dataset. An Adam [21] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.98$ , $\\epsilon = 10^{-9}$ is used", + "bbox": [ + 88, + 763, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as the optimizer in both the training stages. The learning rate is set to 0.00625. The weight in Equation 14 are set to $\\lambda_1 = 1$ , $\\lambda_2 = 1$ , $\\lambda_3 = 1$ , $\\lambda_4 = 1$ . For a fair comparison, all comparison models are re-trained on the same dataset.", + "bbox": [ + 511, + 339, + 906, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 511, + 407, + 697, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ diverse metrics to comprehensively evaluate the model's performance in the movie dubbing task:", + "bbox": [ + 511, + 429, + 905, + 459 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MCD-DTW & MCD-DTW-SL. The Mel Cepstral Distortion Dynamic Time Warping (MCD-DTW) metric and its variant MCD-DTW-SL which adjusts the weights based on duration measure the distance between the generated dubbing and the ground truth following [5].", + "bbox": [ + 511, + 459, + 905, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SECS. The speaker encoder cosine similarity (SECS) evaluates the similarity of speaker voice between the generated dubbing and the reference audio following [2, 3].", + "bbox": [ + 511, + 535, + 905, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "WER. The Word Error Rate (WER) ${}^{1}$ assesses the model's pronunciation accuracy by using an advanced ASR model ${\\text{Whisper}}^{2}\\left\\lbrack {34}\\right\\rbrack$ to transcribe the generated dubbing into text and compare it with the original dubbing script.", + "bbox": [ + 511, + 580, + 905, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "UT-MOS. UT-MOS [37] is a speech mean opinion score (MOS) predictor to measure the acoustic quality and naturalness of the generated dubbing following [18, 49].", + "bbox": [ + 511, + 641, + 905, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "EMO-ACC. Emotion accuracy uses an emotion classifier to determine whether the emotion of the generated dubbing aligns with the ground truth labels following [8]. Note that this metric is only applicable to the V2C-Animation dataset, as the GRID dataset does not include emotion labels.", + "bbox": [ + 511, + 686, + 905, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MOS-N & MOS-S. MOS-Naturalness (MOS-N) and MOS-Similarity (MOS-S) are mean option scores reported with a $95\\%$ confidence interval based on ratings from 20 native English speakers using a scale from 1 to 5. Each participant is required to listen to 30 randomly selected generated dubbing and rate the dubbing according to the speech naturalness and voice similarity following [49].", + "bbox": [ + 511, + 761, + 905, + 868 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1 https://github.com/jitsi/jiwer", + "bbox": [ + 529, + 875, + 692, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2https://huggingface.co/openai/whisper-large", + "bbox": [ + 529, + 887, + 769, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "177", + "bbox": [ + 486, + 944, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3ba77f4848d022bfcc163f9a1a45648b3fceebbcfeb508ecba56c82a832fccf7.jpg", + "table_caption": [ + "Table 2. Results on GRID benchmark." + ], + "table_footnote": [], + "table_body": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%) ↑WER (%) ↓UT-MOS ↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%) ↑WER (%) ↓UT-MOS ↑
GT-100.0022.413.940.000.00100.0022.553.94
GT Mel + Vocoder-97.5721.413.574.104.1597.5721.413.57
StyleSpeech* [30]X91.0624.833.715.875.9882.5721.423.57
Zero-shot TTS* [57]X86.5419.133.605.715.9972.9119.353.62
V2C-Net [5]X80.9847.822.416.797.2375.9249.092.40
HPMDubbing [6]X85.1145.512.146.496.7861.3244.152.11
Face-TTS [24]X82.9744.372.537.448.1678.2439.152.48
StyleDubber [8]X93.7918.883.735.615.6986.6719.583.71
StyleSpeech* [30]✓91.4219.633.735.775.8983.7322.383.66
V2C-Net [5]✓89.7519.043.705.796.0680.1119.923.64
Ours✓89.0318.603.875.605.6381.7219.173.86
", + "bbox": [ + 94, + 107, + 903, + 292 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1314eeec4f8971ec509c45d80cdc71c16d83fb23379abe6eda62e133c09a001b.jpg", + "table_caption": [ + "Table 3. Subjective evaluation on V2C-Animation and GRID benchmarks." + ], + "table_footnote": [], + "table_body": "
DatasetV2C-AnimationGRID
MethodsMOS-N ↑MOS-S ↑CMOS ↑MOS-N ↑MOS-S ↑CMOS ↑
GT4.52±0.13-+0.194.69±0.07-+0.10
GT Mel + Vocoder4.39±0.164.41±0.18+0.174.66±0.084.53±0.10+0.11
StyleSpeech* [30]3.31±0.213.35±0.12-0.253.50±0.103.58±0.11-0.29
Zero-shot TTS* [57]3.40±0.123.47±0.18-0.293.58±0.213.52±0.15-0.26
V2C-Net [5]3.54±0.163.51±0.18-0.243.62±0.063.67±0.11-0.22
HPMDubbing [6]3.57±0.173.54±0.12-0.243.77±0.203.74±0.13-0.19
Face-TTS [24]3.18±0.133.24±0.16-0.373.39±0.213.32±0.17-0.32
StyleDubber [8]3.88±0.143.90±0.14-0.154.02±0.114.06±0.05-0.09
StyleSpeech* [30]3.31±0.213.35±0.12-0.203.50±0.103.58±0.11-0.23
V2C-Net [5]3.54±0.163.51±0.18-0.213.62±0.063.67±0.11-0.17
Speaker2Dubber [54]3.92±0.193.87±0.14-0.104.10±0.094.05±0.11-0.16
Ours4.03±0.123.99±0.080.004.12±0.074.07±0.100.00
", + "bbox": [ + 94, + 332, + 480, + 474 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/325886ca62e12eeded3be870d2c691d64d17e0b9d39b5fb55dccb98dc59e3b03.jpg", + "table_caption": [ + "Table 4. Results on zero-shot test." + ], + "table_footnote": [], + "table_body": "
MethodT-SSECS(%) ↑WER(%) ↓UT-MOS ↑CMOS ↑
StyleSpeech* [30]X58.71105.641.91-0.21
Zero-shot TTS* [57]X61.1235.102.13-0.23
V2C-Net [5]X41.8638.721.99-0.19
HPMDubbing [6]X49.31106.451.35-0.21
FaceTTS [24]X33.80231.631.31-0.35
StyleDubber [8]X71.5213.452.51-0.09
StyleSpeech* [30]✓61.0121.512.72-0.18
V2C-Net [5]✓52.5320.842.96-0.17
Speaker2Dubber [54]✓73.4416.053.08-0.12
Ours✓75.959.853.630.0
", + "bbox": [ + 94, + 494, + 480, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CMOS. Comparative mean option score (CMOS) asks the participants to compare the dubbing generated by two models using the same input and rate them on a scale from -5 to 5 based on the criterion of matched degree between the generated dubbing with the video clip.", + "bbox": [ + 89, + 632, + 482, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison with SOTA", + "text_level": 1, + "bbox": [ + 89, + 720, + 310, + 736 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.1. Results on V2C-Animation Benchmark", + "text_level": 1, + "bbox": [ + 89, + 744, + 410, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 1, our proposed method outperforms the current state-of-the-art models and achieves the best performance across the majority of metrics. Our method achieves the best pronunciation accuracy in both dubbing settings, surpasses all others including two-stage methods using the same pre-training strategy following [54]. In terms of acoustic quality, due to the impact of inherent background noise in the movie dubbing dataset, other methods do not perform well in this aspect even with the pre-trained", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "phoneme encoder. However, our proposed method achieves a score improvement of 0.73-1.86 on the UT-MOS metric, bringing a significant improvement in the acoustic quality of generated dubbing. Concurrently, our model achieves the lowest MCD-DTW and MCD-DTW-SL, indicating that the generated dubbing exhibits the smallest discrepancy and the best duration alignment with the real dubbing. The best dubbing emotion accuracy rate which outperforms the current state-of-the-art models with a $+2.58\\%$ margin indicating the best prosody alignment performance of our method.", + "bbox": [ + 511, + 301, + 903, + 453 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Although we fall short in voice similarity compared to StyleDubber [8], which learns fine-grained speaker styles, our method attains the highest score in MOS-S in subjective evaluation. Additionally, our proposed method also achieves the highest scores in MOS-N and CMOS, indicating the best overall dubbing quality and alignment.", + "bbox": [ + 511, + 454, + 906, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.2. Results on GRID Benchmark", + "text_level": 1, + "bbox": [ + 511, + 551, + 764, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since the dubbing in the GRID benchmark is closer to traditional speech, the gap between different models is not as significant as in the V2C-Animation benchmark. Nevertheless, as shown in Table 2, we still achieve state-of-the-art performance in pronunciation clarity, speech quality, and discrepancy from ground truth in both dubbing settings while maintaining advanced voice similarity. Moreover, our model also outperforms other state-of-the-art models in subjective evaluation scores on the GRID benchmark, demonstrating the effectiveness of our method across diverse dubbing benchmarks and scenarios.", + "bbox": [ + 511, + 571, + 905, + 737 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.3. Results on Zero-shot Test", + "text_level": 1, + "bbox": [ + 511, + 744, + 736, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to dubbing benchmarks, we also conduct the zero-shot test to evaluate the generalization performance of models. We use audio from the GRID dataset (which is out of domain) as reference audio to dub movie clips from the V2C-Animation dataset. Due to the absence of corresponding ground truth, we only calculate WER, UT-MOS, and SECS for objective evaluation.", + "bbox": [ + 511, + 763, + 905, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 4, our proposed method surpasses the current state-of-the-art models and achieves the best per", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "178", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7250ee8cd64b9c88be82fdd28bee298ec0007d02f4ebabef7e38cd7fcc19468e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 88, + 145, + 132 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/df95ebe57a08cb2efa9afbdb4ffc801626bc161391531c46aa4e2cbd3857ea2a.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 151, + 88, + 326, + 138 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/69e55d4c4c93c60fdea5cc4daf65b18e959862abd3e79c14d292f3315c126ca5.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 330, + 88, + 509, + 138 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/919a2c0e6cc88f842bda9229095318bf5559ac50f4de54d18b412c98b213f514.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 88, + 560, + 132 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd0f0e8e16f0407d0b3b9547d4d333f8d2600bba44ff30e12fdde96095115f4d.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 563, + 88, + 732, + 138 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/05ffb72c342c1200c03f5d6be96366cbea52a44905ae269b4bf297a4e33a9ecd.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 733, + 88, + 901, + 138 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/103aedbb26a79faee7e9d3e9cbdc7862532c581e1ee85e5de2115b8f14719a48.jpg", + "image_caption": [ + "Figure 3. The visualization of the mel-spectrograms of ground truth and synthesized dubbing by different models. The red and white bounding boxes highlight regions where different models exhibit significant differences in audio quality and pronunciation details." + ], + "image_footnote": [], + "bbox": [ + 96, + 148, + 148, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb3e72b22cce34c961463ce09db2f7caf1c0aa4fe7b7a37b9ae417ac34c15f1d.jpg", + "image_caption": [ + "Speaker2Dubber" + ], + "image_footnote": [], + "bbox": [ + 151, + 148, + 326, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f50f382c54f57cfe56ed547a83b4160478b404f17505469bd13a25ad46b7f72.jpg", + "image_caption": [ + "StyleDubber" + ], + "image_footnote": [], + "bbox": [ + 330, + 148, + 508, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/742caadba741477b9765b51601d206bb868b00f93174290e4663cd32b2ff9f58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 148, + 563, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4afe7905f3fd1edc6956ac40586aa4824d903beb7b393344525c5efab6794c0.jpg", + "image_caption": [ + "Speaker2Dubber" + ], + "image_footnote": [], + "bbox": [ + 563, + 147, + 730, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8f65cca7cc2565836c39419a02e28361f9f2ce0a7db0b56d2c8b3362f29a8c1c.jpg", + "image_caption": [ + "StyleDubber" + ], + "image_footnote": [], + "bbox": [ + 733, + 148, + 901, + 196 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a09ef4cdb419618b97984f1010ca4a95cba2c4fdc988351834d1dc821a3c327a.jpg", + "table_caption": [ + "Table 5. Results of ablation study" + ], + "table_footnote": [], + "table_body": "
#MethodWER ↓UT-MOS ↑EMO-ACC ↑MCD-DTW ↓MCD-DTW-SL ↓
-GT22.552.2699.960.000.00
-GT Mel+ Vocoder24.402.1897.093.773.80
1w/o AP21.452.3845.209.789.83
2w/o PE9.843.0946.129.359.38
3w/o IDEA8.383.0747.639.499.52
4w/o PSD10.633.0547.069.619.64
5w/o PTBE8.632.6046.089.849.87
6Full Model8.043.1048.939.299.32
", + "bbox": [ + 93, + 256, + 483, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance across all metrics. Specifically, our proposed method still ensures accurate pronunciation and the best acoustic quality of the generated dubbing when facing out-of-domain reference audio. In terms of voice similarity, our model achieves the best cloning effect in both objective and subjective evaluations. The zero-shot experimental results substantiate the superiority of the generalization performance of our proposed method.", + "bbox": [ + 89, + 354, + 483, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 89, + 484, + 282, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the mel-spectrograms of ground truth and dubbing generated by different models for comparison in Figure 3. (More visualization results are presented in the Appendix.) The red bounding boxes represent regions where different models exhibit significant differences in audio quality and the white regions present the difference in pronunciation details. Through the observation of the red bounding box, it is evident that our method exhibits less noise in the non-pronunciation intervals of dubbing compared to other models, indicating better acoustic quality. Additionally, the clearer spectrum lines in the white bounding box and the closer resemblance to the ground truth in terms of prosody (the shape of spectrum lines) show that our method also achieves better pronunciation quality and prosody alignment performance.", + "bbox": [ + 88, + 506, + 483, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 742, + 254, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further investigate the specific effects of each module in our proposed method, we conduct ablation studies on the Dub 1.0 setting of the V2C-Animation benchmark.", + "bbox": [ + 89, + 763, + 482, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Acoustic Pre-training (AP). As shown in Row 1 of Table 5, acoustic pre-training significantly improves the acoustic quality and pronunciation accuracy. It noticeably enhances the model's performance on the UTMOS and WER. The clearer pronunciation and speech quality are also reflected in the improvement of dubbing accu", + "bbox": [ + 89, + 810, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "racy indicated by MCD-DTW and MCD-DTW-SL.", + "bbox": [ + 511, + 244, + 851, + 260 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Prosody Enhancement (PE). Row 2 of Table 5 shows that the prosody enhancement strategy can reduce the difference between the generated dubbing and the ground truth, enhancing the model's performance on the MCD-DTW and MCD-DTW-SL metrics. The results demonstrate it improves the model's acoustic modeling capability in handling complex prosody variations.", + "bbox": [ + 511, + 261, + 905, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of In-Domain Emotion Analysis (IDEA). As shown in Row 3 of Table 5, the IDEA module provides a more stable and accurate alignment between the emotion of characters and the dubbing prosody, enhancing performance on emotion accuracy. The better prosody alignment brought by IDEA also reduces the discrepancy between the generated dubbing with ground truth.", + "bbox": [ + 511, + 367, + 905, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Prosodic Style Diffusion (PSD). The modeling of prosodic style features allows the model to focus on non-timbre prosodic characteristics during the prosody adapting stage, improving the overall dubbing accuracy as shown in Row 4 of Table 5. Additionally, the disentangled design on prosodic style also enhances the model's performance in acoustic and pronunciation quality. Effectiveness of Prosodic Text BERT Encoder (PTBE). Compared to previous works that use a single text encoder output feature for both acoustic and prosodic modeling, the introduction of the Prosodic Text BERT Encoder brings disentangled text prosodic features. This approach not only enhances the quality of text prosodic modeling but also ensures the acoustic quality of the generated dubbing. As shown in Row 5 of Table 5, the PTBE module significantly improves the dubbing accuracy and the acoustic quality.", + "bbox": [ + 511, + 473, + 905, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 723, + 633, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a method with a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to generate high-quality movie dubbing with aligned prosody. The first stage equips the model with the acoustic modeling capability to handle complex dubbing prosody. The second stage employs a disentangled prosody adapting framework to bridge character performances with dubbing prosody while maintaining the acoustic quality. Extensive experimental results demonstrate the effectiveness of our proposed method.", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "179", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China: 62322211, 62336008, U21B2024, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (2024C01023, 2023C01046, 2023C01038), Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of Music), Ministry of Culture and Tourism (2023DMKLB004). Yuankai Qi and Anton van den Hengel are not supported by the aforementioned fundings.", + "bbox": [ + 89, + 114, + 483, + 251 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 263, + 187, + 277 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sercan Ömer Arik, Jitong Chen, Kainan Peng, Wei Ping, and Yanqi Zhou. Neural voice cloning with a few samples. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, pages 10040-10050, 2018. 1", + "[2] Edresson Casanova, Christopher Shulby, Eren Gölge, Nicolas Michael Müller, Frederico Santos de Oliveira, Arnaldo Candido Jr., Anderson da Silva Soares, Sandra Maria Aluísio, and Moacir Antonelli Ponti. Sc-glowts: An efficient zero-shot multi-speaker text-to-speech model. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.844, + 0.177 + ], + "angle": 0, + "content": "Prosody-Enhanced Acoustic Pre-training and Acoustic-Disentangled Prosody Adapting for Movie Dubbing" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.203, + 0.764, + 0.221 + ], + "angle": 0, + "content": "Zhedong Zhang\\(^{1,2*}\\) Liang Li\\(^{2\\dagger}\\) Chenggang Yan\\(^{1}\\) Chunshan Liu\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.356, + 0.222, + 0.663, + 0.239 + ], + "angle": 0, + "content": "Anton van den Hengel3 Yuankai Qi4" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.24, + 0.89, + 0.258 + ], + "angle": 0, + "content": "\\(^{1}\\)Hangzhou Dianzi University \\(^{2}\\)Institute of Computing Technology, Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.258, + 0.697, + 0.275 + ], + "angle": 0, + "content": "3 University of Adelaide 4 Macquarie University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.309, + 0.327, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.342, + 0.485, + 0.705 + ], + "angle": 0, + "content": "Movie dubbing describes the process of transforming a script into speech that aligns temporally and emotionally with a given movie clip while exemplifying the speaker's voice demonstrated in a short reference audio clip. This task demands the model bridge character performances and complicated prosody structures to build a high-quality video-synchronized dubbing track. The limited scale of movie dubbing datasets, along with the background noise inherent in audio data, hinder the acoustic modeling performance of trained models. To address these issues, we propose an acoustic-prosody disentangled two-stage method to achieve high-quality dubbing generation with precise prosody alignment. First, we propose a prosody-enhanced acoustic pre-training to develop robust acoustic modeling capabilities. Then, we freeze the pre-trained acoustic system and design an acoustic-disentangled framework to model prosodic text features and dubbing style while maintaining acoustic quality. Additionally, we incorporate an in-domain emotion analysis module to reduce the impact of visual domain shifts across different movies, thereby enhancing emotion-prosody alignment. Extensive experiments show that our method performs favorably against the state-of-the-art models on two primary benchmarks. The project is available at https://zzdoog.github.io/ProDubber/." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.733, + 0.222, + 0.75 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.759, + 0.483, + 0.866 + ], + "angle": 0, + "content": "Movie Dubbing, also known as Visual Voice Cloning (V2C) [5], aims to generate speech from scripts using a specified voice conditioned by a single short reference audio while ensuring prosody alignment with the character's performance in terms of both pronunciation duration and intonation (as shown in Figure 1 (a)). It promises significant potential in real-world applications such as film post-" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.314, + 0.891, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.407, + 0.799, + 0.419 + ], + "angle": 0, + "content": "(a) Visual Voice Cloning (V2C) task" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.42, + 0.896, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.506, + 0.813, + 0.517 + ], + "angle": 0, + "content": "(b) Illustration of our proposed method" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.529, + 0.906, + 0.586 + ], + "angle": 0, + "content": "Figure 1. (a) Illustration of the V2C task. (b) Illustration of the proposed acoustic pre-training stage (Stage I) and prosody adapting stage (Stage II), which aim to generate dubbing with high acoustic quality and aligned prosody." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.598, + 0.899, + 0.613 + ], + "angle": 0, + "content": "production, media production, and personal speech AIGC." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.704 + ], + "angle": 0, + "content": "Compared to traditional speech synthesis [4, 27, 30, 35, 36] or Voice Cloning [1] tasks, movie dubbing presents greater challenges. It demands the ability not only to align the prosody with complex character performances but also to maintain high acoustic quality even when managing diverse and exaggerated prosody inherent in dubbing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Previous works achieve significant progress in aligning prosody with the performances of movie characters. V2C-Net [5] incorporates visual features from each frame of the movie clip into the mel-spectrogram frame-level prosody modeling. HPMDubbing [6] employs a hierarchical design, where lip, face, and video-level features correspond to pronunciation duration, prosody, and the overall video atmosphere, respectively. StyleDubber [8] uses a fine-grained adaptor to bridge the speaker's style and character's emotion states at the phoneme level, facilitating joint modeling of prosody. However, existing methods overlook the visual domain discrepancies arising from variations in movie styles and other visual elements, such as color grading," + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.444, + 0.888 + ], + "angle": 0, + "content": "*This work is done during the intern in VIPL group, ICT, CAS." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.444, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "172" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.414, + 0.107 + ], + "angle": 0, + "content": "which impact the stability of prosody alignment." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.109, + 0.484, + 0.381 + ], + "angle": 0, + "content": "The nature of film acting means movie dubbing inherently involves more exaggerated and diverse prosody variations compared to traditional speech, yet the difficulty of its acoustic modeling is often underestimated. In addition, certain characteristics of movie dubbing datasets, such as their limited scale (primarily due to copyright restrictions) and the suboptimal audio quality caused by unavoidable movie background noise [54], further hinder methods that solely rely on dubbing datasets for training to achieve satisfied acoustic quality [5, 6, 8, 24]. Speaker2Dubber [54] attempts to enhance the model's acoustic modeling capability by pre-training the phoneme encoder on a large-scale text-to-speech corpus. This two-stage training strategy improves the model's pronunciation accuracy, however, the pre-trained phoneme encoder alone cannot eliminate the impact of low audio quality in dubbing datasets, or modeling complex prosody variation, leading to a significant degradation in final acoustic quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.384, + 0.484, + 0.732 + ], + "angle": 0, + "content": "To address these issues, we propose a dubbing method that incorporates a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to achieve high-quality dubbing with well-aligned prosody (as shown in Figure 1 (b)). Specifically, in the prosody-enhanced acoustic pre-training stage, we pre-train the entire acoustic system of the model using a text-speech corpus with enhanced prosody. This ensures the acoustic modeling capability in audio quality and managing the complex dubbing prosody variations. We thus freeze the acoustic system in the second stage and design a disentangled framework to model prosodic features from the dubbing script and audio by introducing a prosodic text BERT encoder and a prosodic style diffusion module. These disentangled prosodic features are further bridged with the in-domain emotion analysis output feature, aligning the prosody with the character's emotion. Lip motion features are then utilized to predict pronunciation duration and upsample the text content to match the mel-spectrogram length. Finally, the pre-trained audio decoder takes the upsampled text content and predicted prosody as input, integrating the speaker voice via AdaIN layer [15], and generates dubbing with high acoustic quality and aligned prosody." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.733, + 0.449, + 0.748 + ], + "angle": 0, + "content": "The main contributions of the paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.75, + 0.483, + 0.81 + ], + "angle": 0, + "content": "- We propose a two-stage dubbing method with a prosody-enhanced acoustic pre-training to enhance the model's ability in high-quality acoustic modeling and handling complex prosodic variations." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.483, + 0.886 + ], + "angle": 0, + "content": "- To maintain the acoustic quality in the prosody adapting stage, we freeze the pre-trained acoustic system and devise an acoustic-disentangled prosody adapting framework by introducing prosodic modeling modules corresponding to both the script and the required dubbing style." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.887, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- We design an in-domain emotion analysis module in the" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "prosody adapting stage to reduce the instability caused by visual domain discrepancies across different movies." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.122, + 0.905, + 0.183 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the proposed method achieves favorable performance compared to several state-of-the-art approaches on two major benchmarks, validating the effectiveness of our approach." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.195, + 0.656, + 0.21 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.22, + 0.681, + 0.236 + ], + "angle": 0, + "content": "2.1. Speech Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.241, + 0.907, + 0.514 + ], + "angle": 0, + "content": "With the rapid development of deep learning [7, 10, 11, 16, 29, 32, 40, 42-45, 48, 50, 53, 56], the speech synthesis task has advanced significantly in recent years. From the autoregressive generation architecture of models like WaveNet [46] to the non-autoregressive parallel architecture of the FastSpeech series [35, 36], both the quality and speed of speech generation have improved substantially. Recently, the NaturalSpeech [18, 38, 39] and StyleTTS [25, 27] series have utilized factorized codec and diffusion models, as well as adversarial training with large speech language models, respectively, to achieve high-quality speech synthesis that more closely approaches human-level performance. Additionally, many other works based on other generative models [13, 14, 17, 19, 33, 47] such as flow matching [12, 20, 28] are also advancing the progress in speech synthesis. Despite the progress has been made, they cannot be directly applied to movie dubbing tasks because they lack the design of modeling prosody from input movie clips." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.522, + 0.712, + 0.538 + ], + "angle": 0, + "content": "2.2. Visual Voice Cloning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.544, + 0.909, + 0.802 + ], + "angle": 0, + "content": "The V2C task [5] requires the model to align the prosody of the generated speech with the input video to achieve automatic movie dubbing. To this end, HPMDubbing [6] proposes a hierarchical prosody learning structure, aligning the dubbing duration, prosody, and overall tone with the lip movements, facial expressions, and overall context of the video. Some works [8, 55], on the other hand, design a fine-grained prosody matching module for character voice, incorporating phoneme-level features and emotional variations to model the dubbing style of the characters. Subsequently, Speaker2Dubber [54] addresses the difficulty of learning accurate pronunciation through training solely on dubbing datasets by pre-training its phoneme encoder on text-speech corpus. Despite these advancements, current dubbing models are still significantly influenced by the quality of the dubbing dataset and struggle to achieve high acoustic quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.814, + 0.606, + 0.829 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.838, + 0.625, + 0.853 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.861, + 0.828, + 0.876 + ], + "angle": 0, + "content": "The target of the overall movie dubbing task is:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.884, + 0.907, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\tilde {A} _ {D u b} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {d}, V _ {m}\\right), \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "173" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.904, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.253, + 0.904, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.419, + 0.908, + 0.477 + ], + "angle": 0, + "content": "Figure 2. The main architecture of the proposed method. In the Prosody-Enhanced Acoustic Pre-training stage (Section 3.2), we pre-train the acoustic system using a prosody-enhanced text-speech corpus. In the Acoustic-Disentangled Prosody Adapting stage (Section 3.4), we freeze the acoustic system and employ a disentangled framework to bridge the prosody of dubbing with the character's performance using In-Domain Emotion Analysis (Section 3.3), thus generating dubbing with aligned prosody and maintain high acoustic quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.534 + ], + "angle": 0, + "content": "where the \\(\\tilde{A}_{Dub}\\) is the generated dubbing and \\(A_{Ref}, T_d, V_m\\) are the reference audio, dubbing scripts, and the input silent movie clip respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.484, + 0.835 + ], + "angle": 0, + "content": "The main architecture of the proposed two-stage method is shown in Figure 2. In the prosody-enhanced acoustic pre-training stage, we first design a prosody enhancement strategy to address the prosody domain differences between movie dubbing and traditional speech and apply it to a large-scale, high-quality text-speech corpus. Then, we use the enhanced corpus to pre-train the acoustic style encoder (ASE), acoustic text encoder, and end-to-end audio decoder of the dubbing model, enabling the acoustic system to accurately generate high-quality speech with corresponding content and speaker voice. Next, in the acoustic-disentangled prosody adapting stage, we utilize an acoustic-prosodic disentangled framework by introducing the prosodic style diffusion and prosodic text BERT encoder. This framework adapts the prosody while keeping the acoustic system frozen, thus maintaining the acoustic quality of generated dubbing. We also propose In-Domain Emotion Analysis to better bridge the dubbing prosody with the character's emotion, which improves the audiovisual consistency. We detail each module below." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.443, + 0.865 + ], + "angle": 0, + "content": "3.2. Prosody-Enhanced Acoustic Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Acoustic quality forms the foundation of movie dubbing. The goal of prosody-enhanced acoustic pre-training is to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.907, + 0.565 + ], + "angle": 0, + "content": "provide a solid basis for high-quality acoustic modeling for movie dubbing through the pre-training of the acoustic system in the dubbing model. Below, we detail this pre-training approach in two aspects: the pre-training objectives and the prosody enhancement strategy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.571, + 0.724, + 0.587 + ], + "angle": 0, + "content": "3.2.1. Pre-training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.589, + 0.906, + 0.621 + ], + "angle": 0, + "content": "Unlike the target of the movie dubbing task, the input of this stage does not contain the movie clip:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.63, + 0.907, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\tilde {A} _ {s p e e c h} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {s}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.825 + ], + "angle": 0, + "content": "where the \\( T_{s} \\) is the script from the text-speech corpus. Nevertheless, the acoustic information ultimately used to generate speech audio comprises three components which are the same as the movie dubbing: content information derived from the text, speaker voice obtained from reference audio, and the prosody of the speech. The only difference lies in whether the prosody and duration of each phoneme need to align with the given video. Since the text-speech corpus used in this stage does not include the corresponding video clip, we directly utilize the ground truth duration and prosody during this stage." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We adopt an architecture similar to StyleTTS [25] for acoustic pre-training. First, the text in the corpus is converted from a grapheme sequence to a phoneme sequence using a G2P module. We then use a bidirectional LSTM network to extract acoustic text features from the phoneme" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.945, + 0.511, + 0.956 + ], + "angle": 0, + "content": "174" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.244 + ], + "angle": 0, + "content": "sequence. Next, an acoustic style encoder extracts timbre features from either the ground truth or other speech samples from the same speaker. A prosody extractor is employed to extract mel-spectrogram frame-level prosody (pitch and energy curve) from the mel-spectrogram of the ground truth speech. To upsample the acoustic text sequence to match the length of the mel-spectrogram, we use a monotonic aligner pre-trained on the LibriSpeech dataset for the automatic speech recognition (ASR) task to obtain the ground truth duration of each phoneme:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.252, + 0.289, + 0.269 + ], + "angle": 0, + "content": "\\[\nT _ {p h o} = \\mathrm {G 2 P} (T _ {s}) \\in \\mathbb {R} ^ {L _ {p h o}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.272, + 0.437, + 0.29 + ], + "angle": 0, + "content": "\\[\nT _ {a} = \\operatorname {A c o u s t i c T e x t E n c o d e r} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.293, + 0.482, + 0.311 + ], + "angle": 0, + "content": "\\[\nS _ {a} = \\text {A c o u s t i c S t y l e E n c o d e r} \\left(A _ {R e f}\\right) \\in \\mathbb {R} ^ {d _ {m}}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.314, + 0.45, + 0.331 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A l i g n} = \\operatorname {T e x t A l i g n e r} (M e l _ {s}, T _ {P h o}) \\in \\mathbb {R} ^ {L _ {p h o} \\times L _ {m e l}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.335, + 0.397, + 0.352 + ], + "angle": 0, + "content": "\\[\np, n = \\operatorname {P r o s o d y E x t r a c t o r} (M e l _ {s}) \\in \\mathbb {R} ^ {L _ {m e l}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.361, + 0.484, + 0.466 + ], + "angle": 0, + "content": "where \\( T_{a} \\) and \\( S_{a} \\) are the acoustic text feature and acoustic style feature, respectively. \\( L_{pho} \\) and \\( L_{mel} \\) denote the length of the phoneme sequence and desired mel-spectrogram, respectively. \\( d_{m} \\) denotes the hidden size of the model. Align is the monotonic attention map between the phoneme sequence and the mel-spectrogram of ground truth speech \\( Mel_{s} \\). \\( p, n \\) is the ground truth pitch and energy curve." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.467, + 0.484, + 0.543 + ], + "angle": 0, + "content": "Then, a HiFi-GAN [22] based end-to-end audio decoder takes the extracted prosody and the upsampled acoustic text features as inputs, while using Adaptive Instance Normalization (AdaIN) [15] to integrate the acoustic style information and reconstruct the original ground truth waveform:" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.551, + 0.482, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A d a I N} \\left(c, S _ {a}\\right) = P _ {\\sigma} \\left(S _ {a}\\right) \\frac {c - \\mu (c)}{\\sigma (c)} + P _ {\\mu} \\left(S _ {a}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.586, + 0.44, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\tilde {A} _ {\\text {s p e e c h}} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot \\operatorname {A l i n g}, p, n, S _ {a}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.674 + ], + "angle": 0, + "content": "where \\(c\\) is the single channel of the feature maps, \\(\\mu (\\cdot)\\) and \\(\\sigma (\\cdot)\\) denote the channel mean and standard deviation. \\(P_{\\mu}\\) and \\(P_{\\sigma}\\) are the linear projections for predicting the adaptive gain and bias using the acoustic style feature \\(S_{a}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.484, + 0.703 + ], + "angle": 0, + "content": "The training objective at this stage is a reconstruction loss for speech:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.712, + 0.483, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R e c} = \\left\\| A _ {s p e e c h} - \\tilde {A} _ {s p e e c h} \\right\\| _ {1}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.747, + 0.357, + 0.762 + ], + "angle": 0, + "content": "3.2.2. Prosody Enhancement Strategy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.9 + ], + "angle": 0, + "content": "By pre-training the acoustic system using a text-speech corpus as mentioned above, the dubbing model gains the ability to convert text into high-quality speech. However, the speech in traditional text-to-speech corpora typically comes from recordings of audiobooks or blogs, which often exhibit flat and monotonous prosody. In contrast, the prosody of movie dubbing tends to vary significantly depending on the plot or performance, particularly in terms of pitch variation and the duration of certain lines." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "We design two prosody enhancement strategies to address the prosodic domain discrepancy between movie dubbing and traditional speech: pitch shifting and duration stretching. Pitch shifting alters the overall pitch of the speech by shifting it to higher or lower frequency bands, simulating the pitch variations found in dubbing. Duration stretching scales the length of the speech to simulate the varied speech pace observed in movie dubbing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.214, + 0.907, + 0.41 + ], + "angle": 0, + "content": "During the implementation, we find that directly manipulating pitch or duration in the time domain significantly degrades speech quality and reduces its naturalness. Therefore, we choose to convert the speech into mel-spectrograms and apply the enhancements in the frequency domain. We then use a vocoder [22] to convert the modified speech back to the time domain for end-to-end pre-training. Specifically, for the pitch shifting operation, we shift the entire spectrogram up or down by a specified number of frequency bands and fill the excess frequency bands with -80db to maintain the shape of spectrogram. For duration stretching, we use linear interpolation and downsampling operations to expand or shorten the length of spectrograms." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.423, + 0.776, + 0.438 + ], + "angle": 0, + "content": "3.3. In-Domain Emotion Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.446, + 0.906, + 0.537 + ], + "angle": 0, + "content": "To obtain fine-grained character emotion features at the video frame level, we first extract the face region of each frame of movie clip \\( V_{face} \\) via S\\(^3\\)FD face detection [52], then utilize an emotion face-alignment network (EmoFAN [41]) to encode the face region to emotion features \\( V_{emo} \\) following [6]:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.549, + 0.905, + 0.567 + ], + "angle": 0, + "content": "\\[\nV _ {e m o} = \\operatorname {E m o F A N} \\left(\\mathrm {S} ^ {3} \\mathrm {F D} \\left(V _ {m}\\right)\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.581, + 0.865, + 0.596 + ], + "angle": 0, + "content": "where the \\(L_{v}\\) denotes the frame number of the video." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.597, + 0.906, + 0.656 + ], + "angle": 0, + "content": "To ensure that the fine-grained video frame-level emotion features more accurately reflect emotional changes rather than visual characteristics of the movie, we first normalize them:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.67, + 0.905, + 0.689 + ], + "angle": 0, + "content": "\\[\nV _ {e m o} ^ {\\prime} = \\Sigma^ {- \\frac {1}{2}} \\left(V _ {e m o} - \\mu\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.702, + 0.906, + 0.776 + ], + "angle": 0, + "content": "where \\( V_{emo}' \\) denotes the normalized feature, \\( \\mu \\) is the mean of the feature sequence, and \\( \\Sigma \\) is the covariance matrix of sequence. The term \\( \\Sigma^{-\\frac{1}{2}} \\) represents the inverse square root of the covariance matrix, which ensures that the normalized features have zero mean and unit covariance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.778, + 0.906, + 0.854 + ], + "angle": 0, + "content": "Simultaneously, to reflect the absolute emotional state of characters in the video, we use a video-level atmosphere feature [6] to adjust the normalized emotion features, thereby capturing the character's emotional state and changes:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.867, + 0.905, + 0.892 + ], + "angle": 0, + "content": "\\[\nV _ {p} = \\alpha \\cdot V _ {e m o} ^ {\\prime} + \\beta \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.889, + 0.816, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\alpha = f _ {\\alpha} (V _ {a t o}), \\quad \\beta = f _ {\\beta} (V _ {a t o}),\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "175" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.483, + 0.138 + ], + "angle": 0, + "content": "where \\(V_{ato} \\in \\mathbb{R}^{d_m}\\) is the video-level atmosphere feature, \\(f_{\\alpha}\\) and \\(f_{\\beta}\\) are learnable linear projections. \\(V_{p}\\) denotes the video-frame level emotion prosodic features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.147, + 0.443, + 0.164 + ], + "angle": 0, + "content": "3.4. Acoustic-Disentangled Prosody Adapting" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.169, + 0.483, + 0.319 + ], + "angle": 0, + "content": "To ensure that the model does not compromise acoustic quality during training on the dubbing dataset, we freeze the entire pre-trained acoustic system at this stage. Unlike traditional TTS tasks that only require modeling prosody from the input text and the voice of reference audio, movie dubbing demands a more complex prosody modeling that bridges the character's facial expressions from visual modality. Relying solely on the frozen acoustic text encoder and acoustic style encoder is insufficient to handle the complex prosody alignment." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.32, + 0.484, + 0.397 + ], + "angle": 0, + "content": "To this end, we propose an acoustic-disentangled framework by introducing a prosodic text BERT encoder (PTBE) [26] and a prosodic style encoder (PSE) to extract prosodic features from the script text and non-timbre prosodic features from ground truth dubbing, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.404, + 0.482, + 0.424 + ], + "angle": 0, + "content": "\\[\nT _ {p} = \\operatorname {P T B E} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.426, + 0.438, + 0.445 + ], + "angle": 0, + "content": "\\[\nS _ {p} = \\mathrm {P r o s o d i c S t y l e E n c o d e r} (A _ {D u b}) \\in \\mathbb {R} ^ {d _ {m}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.455, + 0.484, + 0.53 + ], + "angle": 0, + "content": "After extracting prosodic features from both the text and the dubbing audio, we employ a multi-head cross-attention module to connect phoneme-level text prosodic features with emotion features, enabling the modeling of prosody at the phoneme level based on character emotion variations:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.534, + 0.482, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} T _ {F u s i o n} ^ {k} = s o f t m a x (\\frac {Q _ {p h o} ^ {\\top} K _ {e m o}}{\\sqrt {d _ {m}}}) V _ {e m o} \\in \\mathbb {R} ^ {L _ {p h o} \\times \\frac {d _ {m}}{n _ {h e a d}}}, \\\\ Q _ {p h o} = W _ {j} ^ {Q} T _ {p} ^ {\\top}, K _ {e m o} = W _ {j} ^ {K _ {p}} V _ {p} ^ {\\top}, V _ {p} = W _ {j} ^ {V _ {p}} V _ {p} ^ {\\top}, \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.658 + ], + "angle": 0, + "content": "where \\(k\\) denotes \\(k\\)-th head's output, \\(W_{j}^{*}\\) are learnable parameter matrix, and \\(T_{Fusion}\\) is phoneme-level prosodic feature with emotion variation information." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.706 + ], + "angle": 0, + "content": "To model the prosodic style feature of dubbing, we design a prosodic dstyle diffusion module that takes \\( T_{Fusion} \\) as input and samples the prosodic style feature from noise:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.716, + 0.482, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p _ {\\theta} \\left(S _ {t - 1} \\mid S _ {t}\\right) = \\mathcal {N} \\left(S _ {t - 1}; \\mu_ {\\theta} \\left(S _ {t}, t\\right), \\Sigma_ {\\theta} \\left(S _ {t}, t\\right)\\right), \\tag {11} \\\\ \\tilde {S} _ {p} = p _ {\\theta} \\left(S _ {0} \\mid T _ {F u s i o n}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.87 + ], + "angle": 0, + "content": "where the \\( p_{\\theta} \\) is the learnable denoise distribution and the \\( S_{t-1} \\) is the feature of previous time step. Specifically, in the first half of the training process, we train the prosodic style encoder to better assist the prosody predictor in prosody prediction. In the second half of the training, we introduce the prosodic style diffusion module. This approach ensures more stable convergence during training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Subsequently, we employ the AdaIN module to integrate the predicted prosodic style feature into the \\(T_{Fusion}\\), which" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "is then input into the prosody predictor for specific prosody prediction:" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.133, + 0.905, + 0.151 + ], + "angle": 0, + "content": "\\[\n\\tilde {p}, \\tilde {n} = \\text {P r o s o d y P r e d i c t o r} (\\text {A d a I N} (T _ {\\text {F u s i o n}}, \\tilde {S} _ {p})), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.16, + 0.905, + 0.205 + ], + "angle": 0, + "content": "where the \\(\\tilde{p},\\tilde{n}\\in \\mathbb{R}^{L_{pho}}\\) are the prediction of prosody attributes (pitch and energy) based on the prosodic features and the visual emotion feature." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.207, + 0.907, + 0.373 + ], + "angle": 0, + "content": "In terms of aligning the duration of pronunciation with lip movements, since this alignment is solely related to the prosody of pronunciation and lip movements, which is independent of character emotions and both kinds of style, the input to the duration predictor is the cross-attention fusion of the prosodic text feature and the lip motion feature. Then, we upsample the acoustic text features to the spectrogram length based on the alignment built from the duration prediction, and the audio decoder takes the upsampled acoustic text feature, the acoustic style feature, and the prosody prediction as input, generating the dubbing audio:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.382, + 0.905, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {d} = \\text {D u r a t i o n P r e d i c t o r} (\\underset {\\sim} {\\mathrm {C A}} (T _ {p}, V _ {d}, V _ {d})) \\in \\mathbb {R} ^ {L _ {p h o}}, \\tag {13} \\\\ \\tilde {A} _ {D u b} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot A l i g n, \\tilde {p}, \\tilde {n}, S _ {a}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.907, + 0.571 + ], + "angle": 0, + "content": "where the \\( V_{d} \\in \\mathbb{R}^{L_{v} \\times d_{m}} \\) is the lip motion feature extracted from the lip region of movie clips following [6]. \\( \\mathrm{CA}(\\cdot) \\) denotes the cross-attention, we use \\( T_{p} \\) as query and \\( V_{d} \\) as key and value here to get the phoneme-level duration features. The duration prediction is scaled according to the length of the movie clip to ensure the alignment between total video duration and total dubbing duration. It is noteworthy that \\( \\tilde{p} \\) and \\( \\tilde{n} \\) are also upsampled before being input into the decoder to match the spectrogram length." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.58, + 0.619, + 0.596 + ], + "angle": 0, + "content": "3.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.602, + 0.906, + 0.66 + ], + "angle": 0, + "content": "In the acoustic-disentangled prosody adapting stage, since we freeze all acoustic modules, the training objective for this stage is the sum of the losses for different prosody attributes:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.676, + 0.905, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D u b} = \\lambda_ {1} \\mathcal {L} _ {p} + \\lambda_ {2} \\mathcal {L} _ {n} + \\lambda_ {3} \\mathcal {L} _ {d} + \\lambda_ {4} \\mathcal {L} _ {S _ {p}}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.906, + 0.751 + ], + "angle": 0, + "content": "where the \\(\\mathcal{L}_p, \\mathcal{L}_n,\\) and \\(\\mathcal{L}_d\\) are the L1-Loss for pitch, energy and duration respectively. The \\(\\mathcal{L}_{S_p}\\) is the diffusion loss for prosodic style feature modeling." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.763, + 0.638, + 0.78 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.789, + 0.616, + 0.803 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.9 + ], + "angle": 0, + "content": "V2C-Animation dataset [5] is a collection of 10,217 video clips from 26 animated movies, featuring aligned text, audio, and video clips from real movies along with speaker emotion annotations. Our main experimental results are validated on this dataset due to its authenticity and more detailed annotations." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.513, + 0.957 + ], + "angle": 0, + "content": "176" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.146 + ], + "angle": 0, + "content": "Table 1. Results on V2C-Animation benchmark. For the Dub 1.0 setting, we use the ground truth audio as reference audio, for the Dub 2.0 setting, we use the non-ground truth audio from the same speaker within the dataset as the reference audio which is more aligned with practical usage in dubbing. The method with “*” refers to a variant taking video embedding as an additional input following [5]. “T-S” indicates whether this method employs a two-stage training approach same as [54]. The same setup is applied to the GRID benchmark." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.15, + 0.905, + 0.324 + ], + "angle": 0, + "content": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%)↑WER (%)↓UT-MOS ↑EMO-ACC (%)↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%)↑WER (%)↓UT-MOS ↑
GT-100.0025.552.2699.960.000.00100.0022.552.26
GT Mel + Vocoder-96.9624.402.1897.093.773.8096.9624.402.18
StyleSpeech* [30]X42.53108.001.4142.5311.6214.2375.6782.481.81
Zero-shot TTS* [57]X48.9368.051.7243.9710.0312.0147.5558.811.63
V2C-Net [5]X40.6173.081.3243.0814.1218.4934.0761.611.30
HPMDubbing [6]X53.76164.161.3146.6111.1211.2231.42171.031.30
Face-TTS [24]X52.81201.131.3144.0413.4426.9451.98200.181.31
StyleDubber [8]X82.2631.491.8945.629.379.4681.2731.701.95
StyleSpeech* [30]✓58.9438.352.4446.2710.1013.1255.9063.971.89
V2C-Net [5]✓69.0023.022.3546.159.9710.9769.3023.152.32
Speaker2Dubber [54]✓81.5017.512.4146.809.469.6579.8617.332.42
Ours✓75.468.043.1048.939.299.3275.3911.503.09
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.34, + 0.482, + 0.461 + ], + "angle": 0, + "content": "GRID dataset [9] is a basic benchmark for multi-speaker dubbing. It comprises high-quality video recordings of 33 speakers performing 1,000 scripted sentences each, resulting in a total of 33,000 utterances. All participants are recorded in a noise-free studio with a unified screen background. V2C-Animation and GRID benchmarks respectively correspond to animated films and basic real-person dubbing, covering a wide range of application scenarios." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.461, + 0.483, + 0.584 + ], + "angle": 0, + "content": "LibriTTS dataset [51] is a substantial collection of speech data designed for training and evaluating multi-speaker text-to-speech (TTS) systems derived from the LibriSpeech [31]. It includes multi-speaker recordings, offering a diverse range of voices and speaking styles and meticulously segmented and annotated with text transcripts. We employ LibriTTS as the text-speech corpus used in the prosody-enhance acoustic pre-training stage." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.592, + 0.31, + 0.608 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.614, + 0.483, + 0.765 + ], + "angle": 0, + "content": "Following [5, 6, 8, 54], all the video frames are sampled at 25 FPS. During training, we resample all audio file in \\(24\\mathrm{kHz}\\) and convert them into mel-spectrograms using FFT size of 2048, hop size of 300, window size of 1200, and frequency bins of 80. We employ a pre-trained JDC network [23] as the pitch extractor and use the log norm to calculate the energy following [25, 27]. For the text aligner, we adopt the ASR model fine-tuned for the TTS task by [25] to get the ground truth alignment between phoneme and mel-spectrogram." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We use Libri-TTS-460 following [27] for the acoustic pre-training and apply a \\(3\\%\\) prosody enhancement ratio to trade off the audio quality and prosody variations. We use the official pre-trained HiFi-GAN [22] as the vocoder for the prosody enhancement. We train the acoustic system with 20 epochs in the pre-training stage. For the prosody adapting stage, we train the model with 30 epochs on the V2C-Animation dataset and 20 epochs for GRID dataset. An Adam [21] with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.98\\), \\(\\epsilon = 10^{-9}\\) is used" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.907, + 0.402 + ], + "angle": 0, + "content": "as the optimizer in both the training stages. The learning rate is set to 0.00625. The weight in Equation 14 are set to \\(\\lambda_1 = 1\\), \\(\\lambda_2 = 1\\), \\(\\lambda_3 = 1\\), \\(\\lambda_4 = 1\\). For a fair comparison, all comparison models are re-trained on the same dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.408, + 0.698, + 0.423 + ], + "angle": 0, + "content": "4.3. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.43, + 0.906, + 0.46 + ], + "angle": 0, + "content": "We employ diverse metrics to comprehensively evaluate the model's performance in the movie dubbing task:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.906, + 0.536 + ], + "angle": 0, + "content": "MCD-DTW & MCD-DTW-SL. The Mel Cepstral Distortion Dynamic Time Warping (MCD-DTW) metric and its variant MCD-DTW-SL which adjusts the weights based on duration measure the distance between the generated dubbing and the ground truth following [5]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.536, + 0.906, + 0.581 + ], + "angle": 0, + "content": "SECS. The speaker encoder cosine similarity (SECS) evaluates the similarity of speaker voice between the generated dubbing and the reference audio following [2, 3]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.906, + 0.642 + ], + "angle": 0, + "content": "WER. The Word Error Rate (WER) \\( {}^{1} \\) assesses the model's pronunciation accuracy by using an advanced ASR model \\( {\\text{Whisper}}^{2}\\left\\lbrack {34}\\right\\rbrack \\) to transcribe the generated dubbing into text and compare it with the original dubbing script." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.642, + 0.906, + 0.687 + ], + "angle": 0, + "content": "UT-MOS. UT-MOS [37] is a speech mean opinion score (MOS) predictor to measure the acoustic quality and naturalness of the generated dubbing following [18, 49]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.906, + 0.762 + ], + "angle": 0, + "content": "EMO-ACC. Emotion accuracy uses an emotion classifier to determine whether the emotion of the generated dubbing aligns with the ground truth labels following [8]. Note that this metric is only applicable to the V2C-Animation dataset, as the GRID dataset does not include emotion labels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.906, + 0.869 + ], + "angle": 0, + "content": "MOS-N & MOS-S. MOS-Naturalness (MOS-N) and MOS-Similarity (MOS-S) are mean option scores reported with a \\(95\\%\\) confidence interval based on ratings from 20 native English speakers using a scale from 1 to 5. Each participant is required to listen to 30 randomly selected generated dubbing and rate the dubbing according to the speech naturalness and voice similarity following [49]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.531, + 0.875, + 0.693, + 0.888 + ], + "angle": 0, + "content": "1 https://github.com/jitsi/jiwer" + }, + { + "type": "page_footnote", + "bbox": [ + 0.531, + 0.888, + 0.771, + 0.901 + ], + "angle": 0, + "content": "2https://huggingface.co/openai/whisper-large" + }, + { + "type": "list", + "bbox": [ + 0.531, + 0.875, + 0.771, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.945, + 0.511, + 0.956 + ], + "angle": 0, + "content": "177" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.384, + 0.09, + 0.612, + 0.103 + ], + "angle": 0, + "content": "Table 2. Results on GRID benchmark." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.108, + 0.904, + 0.293 + ], + "angle": 0, + "content": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%) ↑WER (%) ↓UT-MOS ↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%) ↑WER (%) ↓UT-MOS ↑
GT-100.0022.413.940.000.00100.0022.553.94
GT Mel + Vocoder-97.5721.413.574.104.1597.5721.413.57
StyleSpeech* [30]X91.0624.833.715.875.9882.5721.423.57
Zero-shot TTS* [57]X86.5419.133.605.715.9972.9119.353.62
V2C-Net [5]X80.9847.822.416.797.2375.9249.092.40
HPMDubbing [6]X85.1145.512.146.496.7861.3244.152.11
Face-TTS [24]X82.9744.372.537.448.1678.2439.152.48
StyleDubber [8]X93.7918.883.735.615.6986.6719.583.71
StyleSpeech* [30]✓91.4219.633.735.775.8983.7322.383.66
V2C-Net [5]✓89.7519.043.705.796.0680.1119.923.64
Ours✓89.0318.603.875.605.6381.7219.173.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.301, + 0.482, + 0.328 + ], + "angle": 0, + "content": "Table 3. Subjective evaluation on V2C-Animation and GRID benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.333, + 0.481, + 0.475 + ], + "angle": 0, + "content": "
DatasetV2C-AnimationGRID
MethodsMOS-N ↑MOS-S ↑CMOS ↑MOS-N ↑MOS-S ↑CMOS ↑
GT4.52±0.13-+0.194.69±0.07-+0.10
GT Mel + Vocoder4.39±0.164.41±0.18+0.174.66±0.084.53±0.10+0.11
StyleSpeech* [30]3.31±0.213.35±0.12-0.253.50±0.103.58±0.11-0.29
Zero-shot TTS* [57]3.40±0.123.47±0.18-0.293.58±0.213.52±0.15-0.26
V2C-Net [5]3.54±0.163.51±0.18-0.243.62±0.063.67±0.11-0.22
HPMDubbing [6]3.57±0.173.54±0.12-0.243.77±0.203.74±0.13-0.19
Face-TTS [24]3.18±0.133.24±0.16-0.373.39±0.213.32±0.17-0.32
StyleDubber [8]3.88±0.143.90±0.14-0.154.02±0.114.06±0.05-0.09
StyleSpeech* [30]3.31±0.213.35±0.12-0.203.50±0.103.58±0.11-0.23
V2C-Net [5]3.54±0.163.51±0.18-0.213.62±0.063.67±0.11-0.17
Speaker2Dubber [54]3.92±0.193.87±0.14-0.104.10±0.094.05±0.11-0.16
Ours4.03±0.123.99±0.080.004.12±0.074.07±0.100.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.186, + 0.478, + 0.388, + 0.49 + ], + "angle": 0, + "content": "Table 4. Results on zero-shot test." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.495, + 0.482, + 0.627 + ], + "angle": 0, + "content": "
MethodT-SSECS(%) ↑WER(%) ↓UT-MOS ↑CMOS ↑
StyleSpeech* [30]X58.71105.641.91-0.21
Zero-shot TTS* [57]X61.1235.102.13-0.23
V2C-Net [5]X41.8638.721.99-0.19
HPMDubbing [6]X49.31106.451.35-0.21
FaceTTS [24]X33.80231.631.31-0.35
StyleDubber [8]X71.5213.452.51-0.09
StyleSpeech* [30]✓61.0121.512.72-0.18
V2C-Net [5]✓52.5320.842.96-0.17
Speaker2Dubber [54]✓73.4416.053.08-0.12
Ours✓75.959.853.630.0
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.633, + 0.483, + 0.71 + ], + "angle": 0, + "content": "CMOS. Comparative mean option score (CMOS) asks the participants to compare the dubbing generated by two models using the same input and rate them on a scale from -5 to 5 based on the criterion of matched degree between the generated dubbing with the video clip." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.722, + 0.312, + 0.737 + ], + "angle": 0, + "content": "4.4. Comparison with SOTA" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.745, + 0.411, + 0.759 + ], + "angle": 0, + "content": "4.4.1. Results on V2C-Animation Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 1, our proposed method outperforms the current state-of-the-art models and achieves the best performance across the majority of metrics. Our method achieves the best pronunciation accuracy in both dubbing settings, surpasses all others including two-stage methods using the same pre-training strategy following [54]. In terms of acoustic quality, due to the impact of inherent background noise in the movie dubbing dataset, other methods do not perform well in this aspect even with the pre-trained" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.303, + 0.905, + 0.454 + ], + "angle": 0, + "content": "phoneme encoder. However, our proposed method achieves a score improvement of 0.73-1.86 on the UT-MOS metric, bringing a significant improvement in the acoustic quality of generated dubbing. Concurrently, our model achieves the lowest MCD-DTW and MCD-DTW-SL, indicating that the generated dubbing exhibits the smallest discrepancy and the best duration alignment with the real dubbing. The best dubbing emotion accuracy rate which outperforms the current state-of-the-art models with a \\(+2.58\\%\\) margin indicating the best prosody alignment performance of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.455, + 0.907, + 0.545 + ], + "angle": 0, + "content": "Although we fall short in voice similarity compared to StyleDubber [8], which learns fine-grained speaker styles, our method attains the highest score in MOS-S in subjective evaluation. Additionally, our proposed method also achieves the highest scores in MOS-N and CMOS, indicating the best overall dubbing quality and alignment." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.553, + 0.765, + 0.566 + ], + "angle": 0, + "content": "4.4.2. Results on GRID Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.572, + 0.906, + 0.738 + ], + "angle": 0, + "content": "Since the dubbing in the GRID benchmark is closer to traditional speech, the gap between different models is not as significant as in the V2C-Animation benchmark. Nevertheless, as shown in Table 2, we still achieve state-of-the-art performance in pronunciation clarity, speech quality, and discrepancy from ground truth in both dubbing settings while maintaining advanced voice similarity. Moreover, our model also outperforms other state-of-the-art models in subjective evaluation scores on the GRID benchmark, demonstrating the effectiveness of our method across diverse dubbing benchmarks and scenarios." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.746, + 0.738, + 0.76 + ], + "angle": 0, + "content": "4.4.3. Results on Zero-shot Test" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.87 + ], + "angle": 0, + "content": "In addition to dubbing benchmarks, we also conduct the zero-shot test to evaluate the generalization performance of models. We use audio from the GRID dataset (which is out of domain) as reference audio to dub movie clips from the V2C-Animation dataset. Due to the absence of corresponding ground truth, we only calculate WER, UT-MOS, and SECS for objective evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 4, our proposed method surpasses the current state-of-the-art models and achieves the best per" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "178" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.147, + 0.133 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.089, + 0.328, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.229, + 0.14, + 0.246, + 0.147 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.089, + 0.51, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.14, + 0.43, + 0.147 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.089, + 0.561, + 0.133 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.089, + 0.733, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.14, + 0.657, + 0.147 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.089, + 0.903, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.807, + 0.14, + 0.83, + 0.147 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.15, + 0.15, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.149, + 0.328, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.198, + 0.274, + 0.208 + ], + "angle": 0, + "content": "Speaker2Dubber" + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.149, + 0.509, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.198, + 0.448, + 0.207 + ], + "angle": 0, + "content": "StyleDubber" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.15, + 0.565, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.148, + 0.732, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.616, + 0.198, + 0.694, + 0.207 + ], + "angle": 0, + "content": "Speaker2Dubber" + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.149, + 0.902, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.198, + 0.851, + 0.207 + ], + "angle": 0, + "content": "StyleDubber" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.213, + 0.907, + 0.241 + ], + "angle": 0, + "content": "Figure 3. The visualization of the mel-spectrograms of ground truth and synthesized dubbing by different models. The red and white bounding boxes highlight regions where different models exhibit significant differences in audio quality and pronunciation details." + }, + { + "type": "table_caption", + "bbox": [ + 0.186, + 0.245, + 0.388, + 0.257 + ], + "angle": 0, + "content": "Table 5. Results of ablation study" + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.257, + 0.484, + 0.35 + ], + "angle": 0, + "content": "
#MethodWER ↓UT-MOS ↑EMO-ACC ↑MCD-DTW ↓MCD-DTW-SL ↓
-GT22.552.2699.960.000.00
-GT Mel+ Vocoder24.402.1897.093.773.80
1w/o AP21.452.3845.209.789.83
2w/o PE9.843.0946.129.359.38
3w/o IDEA8.383.0747.639.499.52
4w/o PSD10.633.0547.069.619.64
5w/o PTBE8.632.6046.089.849.87
6Full Model8.043.1048.939.299.32
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.484, + 0.476 + ], + "angle": 0, + "content": "formance across all metrics. Specifically, our proposed method still ensures accurate pronunciation and the best acoustic quality of the generated dubbing when facing out-of-domain reference audio. In terms of voice similarity, our model achieves the best cloning effect in both objective and subjective evaluations. The zero-shot experimental results substantiate the superiority of the generalization performance of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.485, + 0.283, + 0.501 + ], + "angle": 0, + "content": "4.5. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.507, + 0.484, + 0.735 + ], + "angle": 0, + "content": "We visualize the mel-spectrograms of ground truth and dubbing generated by different models for comparison in Figure 3. (More visualization results are presented in the Appendix.) The red bounding boxes represent regions where different models exhibit significant differences in audio quality and the white regions present the difference in pronunciation details. Through the observation of the red bounding box, it is evident that our method exhibits less noise in the non-pronunciation intervals of dubbing compared to other models, indicating better acoustic quality. Additionally, the clearer spectrum lines in the white bounding box and the closer resemblance to the ground truth in terms of prosody (the shape of spectrum lines) show that our method also achieves better pronunciation quality and prosody alignment performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.743, + 0.255, + 0.758 + ], + "angle": 0, + "content": "4.6. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.81 + ], + "angle": 0, + "content": "To further investigate the specific effects of each module in our proposed method, we conduct ablation studies on the Dub 1.0 setting of the V2C-Animation benchmark." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of Acoustic Pre-training (AP). As shown in Row 1 of Table 5, acoustic pre-training significantly improves the acoustic quality and pronunciation accuracy. It noticeably enhances the model's performance on the UTMOS and WER. The clearer pronunciation and speech quality are also reflected in the improvement of dubbing accu" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.246, + 0.852, + 0.261 + ], + "angle": 0, + "content": "racy indicated by MCD-DTW and MCD-DTW-SL." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.262, + 0.906, + 0.368 + ], + "angle": 0, + "content": "Effectiveness of Prosody Enhancement (PE). Row 2 of Table 5 shows that the prosody enhancement strategy can reduce the difference between the generated dubbing and the ground truth, enhancing the model's performance on the MCD-DTW and MCD-DTW-SL metrics. The results demonstrate it improves the model's acoustic modeling capability in handling complex prosody variations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.368, + 0.906, + 0.473 + ], + "angle": 0, + "content": "Effectiveness of In-Domain Emotion Analysis (IDEA). As shown in Row 3 of Table 5, the IDEA module provides a more stable and accurate alignment between the emotion of characters and the dubbing prosody, enhancing performance on emotion accuracy. The better prosody alignment brought by IDEA also reduces the discrepancy between the generated dubbing with ground truth." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.474, + 0.906, + 0.717 + ], + "angle": 0, + "content": "Effectiveness of Prosodic Style Diffusion (PSD). The modeling of prosodic style features allows the model to focus on non-timbre prosodic characteristics during the prosody adapting stage, improving the overall dubbing accuracy as shown in Row 4 of Table 5. Additionally, the disentangled design on prosodic style also enhances the model's performance in acoustic and pronunciation quality. Effectiveness of Prosodic Text BERT Encoder (PTBE). Compared to previous works that use a single text encoder output feature for both acoustic and prosodic modeling, the introduction of the Prosodic Text BERT Encoder brings disentangled text prosodic features. This approach not only enhances the quality of text prosodic modeling but also ensures the acoustic quality of the generated dubbing. As shown in Row 5 of Table 5, the PTBE module significantly improves the dubbing accuracy and the acoustic quality." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.724, + 0.634, + 0.74 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this work, we propose a method with a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to generate high-quality movie dubbing with aligned prosody. The first stage equips the model with the acoustic modeling capability to handle complex dubbing prosody. The second stage employs a disentangled prosody adapting framework to bridge character performances with dubbing prosody while maintaining the acoustic quality. Extensive experimental results demonstrate the effectiveness of our proposed method." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "179" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.252 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China: 62322211, 62336008, U21B2024, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (2024C01023, 2023C01046, 2023C01038), Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of Music), Ministry of Culture and Tourism (2023DMKLB004). Yuankai Qi and Anton van den Hengel are not supported by the aforementioned fundings." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.264, + 0.188, + 0.279 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.288, + 0.484, + 0.371 + ], + "angle": 0, + "content": "[1] Sercan Ömer Arik, Jitong Chen, Kainan Peng, Wei Ping, and Yanqi Zhou. Neural voice cloning with a few samples. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, pages 10040-10050, 2018. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.372, + 0.484, + 0.483 + ], + "angle": 0, + "content": "[2] Edresson Casanova, Christopher Shulby, Eren Gölge, Nicolas Michael Müller, Frederico Santos de Oliveira, Arnaldo Candido Jr., Anderson da Silva Soares, Sandra Maria Aluísio, and Moacir Antonelli Ponti. 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This task demands the model bridge character performances and complicated prosody structures to build a high-quality video-synchronized dubbing track. The limited scale of movie dubbing datasets, along with the background noise inherent in audio data, hinder the acoustic modeling performance of trained models. To address these issues, we propose an acoustic-prosody disentangled two-stage method to achieve high-quality dubbing generation with precise prosody alignment. First, we propose a prosody-enhanced acoustic pre-training to develop robust acoustic modeling capabilities. Then, we freeze the pre-trained acoustic system and design an acoustic-disentangled framework to model prosodic text features and dubbing style while maintaining acoustic quality. Additionally, we incorporate an in-domain emotion analysis module to reduce the impact of visual domain shifts across different movies, thereby enhancing emotion-prosody alignment. Extensive experiments show that our method performs favorably against the state-of-the-art models on two primary benchmarks. The project is available at https://zzdoog.github.io/ProDubber/. + +# 1. Introduction + +Movie Dubbing, also known as Visual Voice Cloning (V2C) [5], aims to generate speech from scripts using a specified voice conditioned by a single short reference audio while ensuring prosody alignment with the character's performance in terms of both pronunciation duration and intonation (as shown in Figure 1 (a)). It promises significant potential in real-world applications such as film post- + +![](images/77134cc1fa0f21cd3932d79018a9194c0cd0a14bda7767f80d151ed9e60937a4.jpg) + +![](images/5b5d420c4f529c118468a19fdb5d877278ccbf37f97e9798c1e0fb9ae9e145d3.jpg) +(a) Visual Voice Cloning (V2C) task +(b) Illustration of our proposed method +Figure 1. (a) Illustration of the V2C task. (b) Illustration of the proposed acoustic pre-training stage (Stage I) and prosody adapting stage (Stage II), which aim to generate dubbing with high acoustic quality and aligned prosody. + +production, media production, and personal speech AIGC. + +Compared to traditional speech synthesis [4, 27, 30, 35, 36] or Voice Cloning [1] tasks, movie dubbing presents greater challenges. It demands the ability not only to align the prosody with complex character performances but also to maintain high acoustic quality even when managing diverse and exaggerated prosody inherent in dubbing. + +Previous works achieve significant progress in aligning prosody with the performances of movie characters. V2C-Net [5] incorporates visual features from each frame of the movie clip into the mel-spectrogram frame-level prosody modeling. HPMDubbing [6] employs a hierarchical design, where lip, face, and video-level features correspond to pronunciation duration, prosody, and the overall video atmosphere, respectively. StyleDubber [8] uses a fine-grained adaptor to bridge the speaker's style and character's emotion states at the phoneme level, facilitating joint modeling of prosody. However, existing methods overlook the visual domain discrepancies arising from variations in movie styles and other visual elements, such as color grading, + +which impact the stability of prosody alignment. + +The nature of film acting means movie dubbing inherently involves more exaggerated and diverse prosody variations compared to traditional speech, yet the difficulty of its acoustic modeling is often underestimated. In addition, certain characteristics of movie dubbing datasets, such as their limited scale (primarily due to copyright restrictions) and the suboptimal audio quality caused by unavoidable movie background noise [54], further hinder methods that solely rely on dubbing datasets for training to achieve satisfied acoustic quality [5, 6, 8, 24]. Speaker2Dubber [54] attempts to enhance the model's acoustic modeling capability by pre-training the phoneme encoder on a large-scale text-to-speech corpus. This two-stage training strategy improves the model's pronunciation accuracy, however, the pre-trained phoneme encoder alone cannot eliminate the impact of low audio quality in dubbing datasets, or modeling complex prosody variation, leading to a significant degradation in final acoustic quality. + +To address these issues, we propose a dubbing method that incorporates a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to achieve high-quality dubbing with well-aligned prosody (as shown in Figure 1 (b)). Specifically, in the prosody-enhanced acoustic pre-training stage, we pre-train the entire acoustic system of the model using a text-speech corpus with enhanced prosody. This ensures the acoustic modeling capability in audio quality and managing the complex dubbing prosody variations. We thus freeze the acoustic system in the second stage and design a disentangled framework to model prosodic features from the dubbing script and audio by introducing a prosodic text BERT encoder and a prosodic style diffusion module. These disentangled prosodic features are further bridged with the in-domain emotion analysis output feature, aligning the prosody with the character's emotion. Lip motion features are then utilized to predict pronunciation duration and upsample the text content to match the mel-spectrogram length. Finally, the pre-trained audio decoder takes the upsampled text content and predicted prosody as input, integrating the speaker voice via AdaIN layer [15], and generates dubbing with high acoustic quality and aligned prosody. + +The main contributions of the paper are as follows: + +- We propose a two-stage dubbing method with a prosody-enhanced acoustic pre-training to enhance the model's ability in high-quality acoustic modeling and handling complex prosodic variations. +- To maintain the acoustic quality in the prosody adapting stage, we freeze the pre-trained acoustic system and devise an acoustic-disentangled prosody adapting framework by introducing prosodic modeling modules corresponding to both the script and the required dubbing style. +- We design an in-domain emotion analysis module in the + +prosody adapting stage to reduce the instability caused by visual domain discrepancies across different movies. + +- Extensive experiments demonstrate the proposed method achieves favorable performance compared to several state-of-the-art approaches on two major benchmarks, validating the effectiveness of our approach. + +# 2. Related Work + +# 2.1. Speech Synthesis + +With the rapid development of deep learning [7, 10, 11, 16, 29, 32, 40, 42-45, 48, 50, 53, 56], the speech synthesis task has advanced significantly in recent years. From the autoregressive generation architecture of models like WaveNet [46] to the non-autoregressive parallel architecture of the FastSpeech series [35, 36], both the quality and speed of speech generation have improved substantially. Recently, the NaturalSpeech [18, 38, 39] and StyleTTS [25, 27] series have utilized factorized codec and diffusion models, as well as adversarial training with large speech language models, respectively, to achieve high-quality speech synthesis that more closely approaches human-level performance. Additionally, many other works based on other generative models [13, 14, 17, 19, 33, 47] such as flow matching [12, 20, 28] are also advancing the progress in speech synthesis. Despite the progress has been made, they cannot be directly applied to movie dubbing tasks because they lack the design of modeling prosody from input movie clips. + +# 2.2. Visual Voice Cloning + +The V2C task [5] requires the model to align the prosody of the generated speech with the input video to achieve automatic movie dubbing. To this end, HPMDubbing [6] proposes a hierarchical prosody learning structure, aligning the dubbing duration, prosody, and overall tone with the lip movements, facial expressions, and overall context of the video. Some works [8, 55], on the other hand, design a fine-grained prosody matching module for character voice, incorporating phoneme-level features and emotional variations to model the dubbing style of the characters. Subsequently, Speaker2Dubber [54] addresses the difficulty of learning accurate pronunciation through training solely on dubbing datasets by pre-training its phoneme encoder on text-speech corpus. Despite these advancements, current dubbing models are still significantly influenced by the quality of the dubbing dataset and struggle to achieve high acoustic quality. + +# 3. Method + +# 3.1. Overview + +The target of the overall movie dubbing task is: + +$$ +\tilde {A} _ {D u b} = \operatorname {M o d e l} \left(A _ {R e f}, T _ {d}, V _ {m}\right), \tag {1} +$$ + +![](images/d87b9aa0b59d04745cc6c83851f3f02076b4b2ffc7fef72982399e3f2d11cfbc.jpg) + +![](images/07ff39d8d8cc4a9c98ac2f2780943f978d5fc508084a6c9762e602c0811d605e.jpg) +Figure 2. The main architecture of the proposed method. In the Prosody-Enhanced Acoustic Pre-training stage (Section 3.2), we pre-train the acoustic system using a prosody-enhanced text-speech corpus. In the Acoustic-Disentangled Prosody Adapting stage (Section 3.4), we freeze the acoustic system and employ a disentangled framework to bridge the prosody of dubbing with the character's performance using In-Domain Emotion Analysis (Section 3.3), thus generating dubbing with aligned prosody and maintain high acoustic quality. + +where the $\tilde{A}_{Dub}$ is the generated dubbing and $A_{Ref}, T_d, V_m$ are the reference audio, dubbing scripts, and the input silent movie clip respectively. + +The main architecture of the proposed two-stage method is shown in Figure 2. In the prosody-enhanced acoustic pre-training stage, we first design a prosody enhancement strategy to address the prosody domain differences between movie dubbing and traditional speech and apply it to a large-scale, high-quality text-speech corpus. Then, we use the enhanced corpus to pre-train the acoustic style encoder (ASE), acoustic text encoder, and end-to-end audio decoder of the dubbing model, enabling the acoustic system to accurately generate high-quality speech with corresponding content and speaker voice. Next, in the acoustic-disentangled prosody adapting stage, we utilize an acoustic-prosodic disentangled framework by introducing the prosodic style diffusion and prosodic text BERT encoder. This framework adapts the prosody while keeping the acoustic system frozen, thus maintaining the acoustic quality of generated dubbing. We also propose In-Domain Emotion Analysis to better bridge the dubbing prosody with the character's emotion, which improves the audiovisual consistency. We detail each module below. + +# 3.2. Prosody-Enhanced Acoustic Pre-training + +Acoustic quality forms the foundation of movie dubbing. The goal of prosody-enhanced acoustic pre-training is to + +provide a solid basis for high-quality acoustic modeling for movie dubbing through the pre-training of the acoustic system in the dubbing model. Below, we detail this pre-training approach in two aspects: the pre-training objectives and the prosody enhancement strategy. + +# 3.2.1. Pre-training Objectives + +Unlike the target of the movie dubbing task, the input of this stage does not contain the movie clip: + +$$ +\tilde {A} _ {s p e e c h} = \operatorname {M o d e l} \left(A _ {R e f}, T _ {s}\right), \tag {2} +$$ + +where the $T_{s}$ is the script from the text-speech corpus. Nevertheless, the acoustic information ultimately used to generate speech audio comprises three components which are the same as the movie dubbing: content information derived from the text, speaker voice obtained from reference audio, and the prosody of the speech. The only difference lies in whether the prosody and duration of each phoneme need to align with the given video. Since the text-speech corpus used in this stage does not include the corresponding video clip, we directly utilize the ground truth duration and prosody during this stage. + +We adopt an architecture similar to StyleTTS [25] for acoustic pre-training. First, the text in the corpus is converted from a grapheme sequence to a phoneme sequence using a G2P module. We then use a bidirectional LSTM network to extract acoustic text features from the phoneme + +sequence. Next, an acoustic style encoder extracts timbre features from either the ground truth or other speech samples from the same speaker. A prosody extractor is employed to extract mel-spectrogram frame-level prosody (pitch and energy curve) from the mel-spectrogram of the ground truth speech. To upsample the acoustic text sequence to match the length of the mel-spectrogram, we use a monotonic aligner pre-trained on the LibriSpeech dataset for the automatic speech recognition (ASR) task to obtain the ground truth duration of each phoneme: + +$$ +T _ {p h o} = \mathrm {G 2 P} (T _ {s}) \in \mathbb {R} ^ {L _ {p h o}}, +$$ + +$$ +T _ {a} = \operatorname {A c o u s t i c T e x t E n c o d e r} \left(T _ {p h o}\right) \in \mathbb {R} ^ {L _ {p h o} \times d _ {m}}, +$$ + +$$ +S _ {a} = \text {A c o u s t i c S t y l e E n c o d e r} \left(A _ {R e f}\right) \in \mathbb {R} ^ {d _ {m}}, \tag {3} +$$ + +$$ +\operatorname {A l i g n} = \operatorname {T e x t A l i g n e r} (M e l _ {s}, T _ {P h o}) \in \mathbb {R} ^ {L _ {p h o} \times L _ {m e l}}, +$$ + +$$ +p, n = \operatorname {P r o s o d y E x t r a c t o r} (M e l _ {s}) \in \mathbb {R} ^ {L _ {m e l}}, +$$ + +where $T_{a}$ and $S_{a}$ are the acoustic text feature and acoustic style feature, respectively. $L_{pho}$ and $L_{mel}$ denote the length of the phoneme sequence and desired mel-spectrogram, respectively. $d_{m}$ denotes the hidden size of the model. Align is the monotonic attention map between the phoneme sequence and the mel-spectrogram of ground truth speech $Mel_{s}$ . $p, n$ is the ground truth pitch and energy curve. + +Then, a HiFi-GAN [22] based end-to-end audio decoder takes the extracted prosody and the upsampled acoustic text features as inputs, while using Adaptive Instance Normalization (AdaIN) [15] to integrate the acoustic style information and reconstruct the original ground truth waveform: + +$$ +\operatorname {A d a I N} \left(c, S _ {a}\right) = P _ {\sigma} \left(S _ {a}\right) \frac {c - \mu (c)}{\sigma (c)} + P _ {\mu} \left(S _ {a}\right), \tag {4} +$$ + +$$ +\tilde {A} _ {\text {s p e e c h}} = \operatorname {A u i d o D e c o d e r} \left(T _ {a} \cdot \operatorname {A l i n g}, p, n, S _ {a}\right), +$$ + +where $c$ is the single channel of the feature maps, $\mu (\cdot)$ and $\sigma (\cdot)$ denote the channel mean and standard deviation. $P_{\mu}$ and $P_{\sigma}$ are the linear projections for predicting the adaptive gain and bias using the acoustic style feature $S_{a}$ . + +The training objective at this stage is a reconstruction loss for speech: + +$$ +\mathcal {L} _ {R e c} = \left\| A _ {s p e e c h} - \tilde {A} _ {s p e e c h} \right\| _ {1}. \tag {5} +$$ + +# 3.2.2. Prosody Enhancement Strategy + +By pre-training the acoustic system using a text-speech corpus as mentioned above, the dubbing model gains the ability to convert text into high-quality speech. However, the speech in traditional text-to-speech corpora typically comes from recordings of audiobooks or blogs, which often exhibit flat and monotonous prosody. In contrast, the prosody of movie dubbing tends to vary significantly depending on the plot or performance, particularly in terms of pitch variation and the duration of certain lines. + +We design two prosody enhancement strategies to address the prosodic domain discrepancy between movie dubbing and traditional speech: pitch shifting and duration stretching. Pitch shifting alters the overall pitch of the speech by shifting it to higher or lower frequency bands, simulating the pitch variations found in dubbing. Duration stretching scales the length of the speech to simulate the varied speech pace observed in movie dubbing. + +During the implementation, we find that directly manipulating pitch or duration in the time domain significantly degrades speech quality and reduces its naturalness. Therefore, we choose to convert the speech into mel-spectrograms and apply the enhancements in the frequency domain. We then use a vocoder [22] to convert the modified speech back to the time domain for end-to-end pre-training. Specifically, for the pitch shifting operation, we shift the entire spectrogram up or down by a specified number of frequency bands and fill the excess frequency bands with -80db to maintain the shape of spectrogram. For duration stretching, we use linear interpolation and downsampling operations to expand or shorten the length of spectrograms. + +# 3.3. In-Domain Emotion Analysis + +To obtain fine-grained character emotion features at the video frame level, we first extract the face region of each frame of movie clip $V_{face}$ via S $^3$ FD face detection [52], then utilize an emotion face-alignment network (EmoFAN [41]) to encode the face region to emotion features $V_{emo}$ following [6]: + +$$ +V _ {e m o} = \operatorname {E m o F A N} \left(\mathrm {S} ^ {3} \mathrm {F D} \left(V _ {m}\right)\right) \in \mathbb {R} ^ {L _ {v} \times d _ {m}}, \tag {6} +$$ + +where the $L_{v}$ denotes the frame number of the video. + +To ensure that the fine-grained video frame-level emotion features more accurately reflect emotional changes rather than visual characteristics of the movie, we first normalize them: + +$$ +V _ {e m o} ^ {\prime} = \Sigma^ {- \frac {1}{2}} \left(V _ {e m o} - \mu\right) \in \mathbb {R} ^ {L _ {v} \times d _ {m}}, \tag {7} +$$ + +where $V_{emo}'$ denotes the normalized feature, $\mu$ is the mean of the feature sequence, and $\Sigma$ is the covariance matrix of sequence. The term $\Sigma^{-\frac{1}{2}}$ represents the inverse square root of the covariance matrix, which ensures that the normalized features have zero mean and unit covariance. + +Simultaneously, to reflect the absolute emotional state of characters in the video, we use a video-level atmosphere feature [6] to adjust the normalized emotion features, thereby capturing the character's emotional state and changes: + +$$ +V _ {p} = \alpha \cdot V _ {e m o} ^ {\prime} + \beta \in \mathbb {R} ^ {L _ {v} \times d _ {m}}, \tag {8} +$$ + +$$ +\alpha = f _ {\alpha} (V _ {a t o}), \quad \beta = f _ {\beta} (V _ {a t o}), +$$ + +where $V_{ato} \in \mathbb{R}^{d_m}$ is the video-level atmosphere feature, $f_{\alpha}$ and $f_{\beta}$ are learnable linear projections. $V_{p}$ denotes the video-frame level emotion prosodic features. + +# 3.4. Acoustic-Disentangled Prosody Adapting + +To ensure that the model does not compromise acoustic quality during training on the dubbing dataset, we freeze the entire pre-trained acoustic system at this stage. Unlike traditional TTS tasks that only require modeling prosody from the input text and the voice of reference audio, movie dubbing demands a more complex prosody modeling that bridges the character's facial expressions from visual modality. Relying solely on the frozen acoustic text encoder and acoustic style encoder is insufficient to handle the complex prosody alignment. + +To this end, we propose an acoustic-disentangled framework by introducing a prosodic text BERT encoder (PTBE) [26] and a prosodic style encoder (PSE) to extract prosodic features from the script text and non-timbre prosodic features from ground truth dubbing, respectively: + +$$ +T _ {p} = \operatorname {P T B E} \left(T _ {p h o}\right) \in \mathbb {R} ^ {L _ {p h o} \times d _ {m}}, \tag {9} +$$ + +$$ +S _ {p} = \mathrm {P r o s o d i c S t y l e E n c o d e r} (A _ {D u b}) \in \mathbb {R} ^ {d _ {m}}. +$$ + +After extracting prosodic features from both the text and the dubbing audio, we employ a multi-head cross-attention module to connect phoneme-level text prosodic features with emotion features, enabling the modeling of prosody at the phoneme level based on character emotion variations: + +$$ +\begin{array}{l} T _ {F u s i o n} ^ {k} = s o f t m a x (\frac {Q _ {p h o} ^ {\top} K _ {e m o}}{\sqrt {d _ {m}}}) V _ {e m o} \in \mathbb {R} ^ {L _ {p h o} \times \frac {d _ {m}}{n _ {h e a d}}}, \\ Q _ {p h o} = W _ {j} ^ {Q} T _ {p} ^ {\top}, K _ {e m o} = W _ {j} ^ {K _ {p}} V _ {p} ^ {\top}, V _ {p} = W _ {j} ^ {V _ {p}} V _ {p} ^ {\top}, \tag {10} \\ \end{array} +$$ + +where $k$ denotes $k$ -th head's output, $W_{j}^{*}$ are learnable parameter matrix, and $T_{Fusion}$ is phoneme-level prosodic feature with emotion variation information. + +To model the prosodic style feature of dubbing, we design a prosodic dstyle diffusion module that takes $T_{Fusion}$ as input and samples the prosodic style feature from noise: + +$$ +\begin{array}{l} p _ {\theta} \left(S _ {t - 1} \mid S _ {t}\right) = \mathcal {N} \left(S _ {t - 1}; \mu_ {\theta} \left(S _ {t}, t\right), \Sigma_ {\theta} \left(S _ {t}, t\right)\right), \tag {11} \\ \tilde {S} _ {p} = p _ {\theta} \left(S _ {0} \mid T _ {F u s i o n}\right), \\ \end{array} +$$ + +where the $p_{\theta}$ is the learnable denoise distribution and the $S_{t-1}$ is the feature of previous time step. Specifically, in the first half of the training process, we train the prosodic style encoder to better assist the prosody predictor in prosody prediction. In the second half of the training, we introduce the prosodic style diffusion module. This approach ensures more stable convergence during training. + +Subsequently, we employ the AdaIN module to integrate the predicted prosodic style feature into the $T_{Fusion}$ , which + +is then input into the prosody predictor for specific prosody prediction: + +$$ +\tilde {p}, \tilde {n} = \text {P r o s o d y P r e d i c t o r} (\text {A d a I N} (T _ {\text {F u s i o n}}, \tilde {S} _ {p})), \tag {12} +$$ + +where the $\tilde{p},\tilde{n}\in \mathbb{R}^{L_{pho}}$ are the prediction of prosody attributes (pitch and energy) based on the prosodic features and the visual emotion feature. + +In terms of aligning the duration of pronunciation with lip movements, since this alignment is solely related to the prosody of pronunciation and lip movements, which is independent of character emotions and both kinds of style, the input to the duration predictor is the cross-attention fusion of the prosodic text feature and the lip motion feature. Then, we upsample the acoustic text features to the spectrogram length based on the alignment built from the duration prediction, and the audio decoder takes the upsampled acoustic text feature, the acoustic style feature, and the prosody prediction as input, generating the dubbing audio: + +$$ +\begin{array}{l} \tilde {d} = \text {D u r a t i o n P r e d i c t o r} (\underset {\sim} {\mathrm {C A}} (T _ {p}, V _ {d}, V _ {d})) \in \mathbb {R} ^ {L _ {p h o}}, \tag {13} \\ \tilde {A} _ {D u b} = \operatorname {A u i d o D e c o d e r} \left(T _ {a} \cdot A l i g n, \tilde {p}, \tilde {n}, S _ {a}\right), \\ \end{array} +$$ + +where the $V_{d} \in \mathbb{R}^{L_{v} \times d_{m}}$ is the lip motion feature extracted from the lip region of movie clips following [6]. $\mathrm{CA}(\cdot)$ denotes the cross-attention, we use $T_{p}$ as query and $V_{d}$ as key and value here to get the phoneme-level duration features. The duration prediction is scaled according to the length of the movie clip to ensure the alignment between total video duration and total dubbing duration. It is noteworthy that $\tilde{p}$ and $\tilde{n}$ are also upsampled before being input into the decoder to match the spectrogram length. + +# 3.5. Training + +In the acoustic-disentangled prosody adapting stage, since we freeze all acoustic modules, the training objective for this stage is the sum of the losses for different prosody attributes: + +$$ +\mathcal {L} _ {D u b} = \lambda_ {1} \mathcal {L} _ {p} + \lambda_ {2} \mathcal {L} _ {n} + \lambda_ {3} \mathcal {L} _ {d} + \lambda_ {4} \mathcal {L} _ {S _ {p}}, \tag {14} +$$ + +where the $\mathcal{L}_p, \mathcal{L}_n,$ and $\mathcal{L}_d$ are the L1-Loss for pitch, energy and duration respectively. The $\mathcal{L}_{S_p}$ is the diffusion loss for prosodic style feature modeling. + +# 4. Experiment + +# 4.1. Datasets + +V2C-Animation dataset [5] is a collection of 10,217 video clips from 26 animated movies, featuring aligned text, audio, and video clips from real movies along with speaker emotion annotations. Our main experimental results are validated on this dataset due to its authenticity and more detailed annotations. + +Table 1. Results on V2C-Animation benchmark. For the Dub 1.0 setting, we use the ground truth audio as reference audio, for the Dub 2.0 setting, we use the non-ground truth audio from the same speaker within the dataset as the reference audio which is more aligned with practical usage in dubbing. The method with “*” refers to a variant taking video embedding as an additional input following [5]. “T-S” indicates whether this method employs a two-stage training approach same as [54]. The same setup is applied to the GRID benchmark. + +
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%)↑WER (%)↓UT-MOS ↑EMO-ACC (%)↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%)↑WER (%)↓UT-MOS ↑
GT-100.0025.552.2699.960.000.00100.0022.552.26
GT Mel + Vocoder-96.9624.402.1897.093.773.8096.9624.402.18
StyleSpeech* [30]X42.53108.001.4142.5311.6214.2375.6782.481.81
Zero-shot TTS* [57]X48.9368.051.7243.9710.0312.0147.5558.811.63
V2C-Net [5]X40.6173.081.3243.0814.1218.4934.0761.611.30
HPMDubbing [6]X53.76164.161.3146.6111.1211.2231.42171.031.30
Face-TTS [24]X52.81201.131.3144.0413.4426.9451.98200.181.31
StyleDubber [8]X82.2631.491.8945.629.379.4681.2731.701.95
StyleSpeech* [30]✓58.9438.352.4446.2710.1013.1255.9063.971.89
V2C-Net [5]✓69.0023.022.3546.159.9710.9769.3023.152.32
Speaker2Dubber [54]✓81.5017.512.4146.809.469.6579.8617.332.42
Ours✓75.468.043.1048.939.299.3275.3911.503.09
+ +GRID dataset [9] is a basic benchmark for multi-speaker dubbing. It comprises high-quality video recordings of 33 speakers performing 1,000 scripted sentences each, resulting in a total of 33,000 utterances. All participants are recorded in a noise-free studio with a unified screen background. V2C-Animation and GRID benchmarks respectively correspond to animated films and basic real-person dubbing, covering a wide range of application scenarios. + +LibriTTS dataset [51] is a substantial collection of speech data designed for training and evaluating multi-speaker text-to-speech (TTS) systems derived from the LibriSpeech [31]. It includes multi-speaker recordings, offering a diverse range of voices and speaking styles and meticulously segmented and annotated with text transcripts. We employ LibriTTS as the text-speech corpus used in the prosody-enhance acoustic pre-training stage. + +# 4.2. Implementation Details + +Following [5, 6, 8, 54], all the video frames are sampled at 25 FPS. During training, we resample all audio file in $24\mathrm{kHz}$ and convert them into mel-spectrograms using FFT size of 2048, hop size of 300, window size of 1200, and frequency bins of 80. We employ a pre-trained JDC network [23] as the pitch extractor and use the log norm to calculate the energy following [25, 27]. For the text aligner, we adopt the ASR model fine-tuned for the TTS task by [25] to get the ground truth alignment between phoneme and mel-spectrogram. + +We use Libri-TTS-460 following [27] for the acoustic pre-training and apply a $3\%$ prosody enhancement ratio to trade off the audio quality and prosody variations. We use the official pre-trained HiFi-GAN [22] as the vocoder for the prosody enhancement. We train the acoustic system with 20 epochs in the pre-training stage. For the prosody adapting stage, we train the model with 30 epochs on the V2C-Animation dataset and 20 epochs for GRID dataset. An Adam [21] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.98$ , $\epsilon = 10^{-9}$ is used + +as the optimizer in both the training stages. The learning rate is set to 0.00625. The weight in Equation 14 are set to $\lambda_1 = 1$ , $\lambda_2 = 1$ , $\lambda_3 = 1$ , $\lambda_4 = 1$ . For a fair comparison, all comparison models are re-trained on the same dataset. + +# 4.3. Evaluation Metrics + +We employ diverse metrics to comprehensively evaluate the model's performance in the movie dubbing task: + +MCD-DTW & MCD-DTW-SL. The Mel Cepstral Distortion Dynamic Time Warping (MCD-DTW) metric and its variant MCD-DTW-SL which adjusts the weights based on duration measure the distance between the generated dubbing and the ground truth following [5]. + +SECS. The speaker encoder cosine similarity (SECS) evaluates the similarity of speaker voice between the generated dubbing and the reference audio following [2, 3]. + +WER. The Word Error Rate (WER) ${}^{1}$ assesses the model's pronunciation accuracy by using an advanced ASR model ${\text{Whisper}}^{2}\left\lbrack {34}\right\rbrack$ to transcribe the generated dubbing into text and compare it with the original dubbing script. + +UT-MOS. UT-MOS [37] is a speech mean opinion score (MOS) predictor to measure the acoustic quality and naturalness of the generated dubbing following [18, 49]. + +EMO-ACC. Emotion accuracy uses an emotion classifier to determine whether the emotion of the generated dubbing aligns with the ground truth labels following [8]. Note that this metric is only applicable to the V2C-Animation dataset, as the GRID dataset does not include emotion labels. + +MOS-N & MOS-S. MOS-Naturalness (MOS-N) and MOS-Similarity (MOS-S) are mean option scores reported with a $95\%$ confidence interval based on ratings from 20 native English speakers using a scale from 1 to 5. Each participant is required to listen to 30 randomly selected generated dubbing and rate the dubbing according to the speech naturalness and voice similarity following [49]. + +Table 2. Results on GRID benchmark. + +
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%) ↑WER (%) ↓UT-MOS ↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%) ↑WER (%) ↓UT-MOS ↑
GT-100.0022.413.940.000.00100.0022.553.94
GT Mel + Vocoder-97.5721.413.574.104.1597.5721.413.57
StyleSpeech* [30]X91.0624.833.715.875.9882.5721.423.57
Zero-shot TTS* [57]X86.5419.133.605.715.9972.9119.353.62
V2C-Net [5]X80.9847.822.416.797.2375.9249.092.40
HPMDubbing [6]X85.1145.512.146.496.7861.3244.152.11
Face-TTS [24]X82.9744.372.537.448.1678.2439.152.48
StyleDubber [8]X93.7918.883.735.615.6986.6719.583.71
StyleSpeech* [30]✓91.4219.633.735.775.8983.7322.383.66
V2C-Net [5]✓89.7519.043.705.796.0680.1119.923.64
Ours✓89.0318.603.875.605.6381.7219.173.86
+ +Table 3. Subjective evaluation on V2C-Animation and GRID benchmarks. + +
DatasetV2C-AnimationGRID
MethodsMOS-N ↑MOS-S ↑CMOS ↑MOS-N ↑MOS-S ↑CMOS ↑
GT4.52±0.13-+0.194.69±0.07-+0.10
GT Mel + Vocoder4.39±0.164.41±0.18+0.174.66±0.084.53±0.10+0.11
StyleSpeech* [30]3.31±0.213.35±0.12-0.253.50±0.103.58±0.11-0.29
Zero-shot TTS* [57]3.40±0.123.47±0.18-0.293.58±0.213.52±0.15-0.26
V2C-Net [5]3.54±0.163.51±0.18-0.243.62±0.063.67±0.11-0.22
HPMDubbing [6]3.57±0.173.54±0.12-0.243.77±0.203.74±0.13-0.19
Face-TTS [24]3.18±0.133.24±0.16-0.373.39±0.213.32±0.17-0.32
StyleDubber [8]3.88±0.143.90±0.14-0.154.02±0.114.06±0.05-0.09
StyleSpeech* [30]3.31±0.213.35±0.12-0.203.50±0.103.58±0.11-0.23
V2C-Net [5]3.54±0.163.51±0.18-0.213.62±0.063.67±0.11-0.17
Speaker2Dubber [54]3.92±0.193.87±0.14-0.104.10±0.094.05±0.11-0.16
Ours4.03±0.123.99±0.080.004.12±0.074.07±0.100.00
+ +Table 4. Results on zero-shot test. + +
MethodT-SSECS(%) ↑WER(%) ↓UT-MOS ↑CMOS ↑
StyleSpeech* [30]X58.71105.641.91-0.21
Zero-shot TTS* [57]X61.1235.102.13-0.23
V2C-Net [5]X41.8638.721.99-0.19
HPMDubbing [6]X49.31106.451.35-0.21
FaceTTS [24]X33.80231.631.31-0.35
StyleDubber [8]X71.5213.452.51-0.09
StyleSpeech* [30]✓61.0121.512.72-0.18
V2C-Net [5]✓52.5320.842.96-0.17
Speaker2Dubber [54]✓73.4416.053.08-0.12
Ours✓75.959.853.630.0
+ +CMOS. Comparative mean option score (CMOS) asks the participants to compare the dubbing generated by two models using the same input and rate them on a scale from -5 to 5 based on the criterion of matched degree between the generated dubbing with the video clip. + +# 4.4. Comparison with SOTA + +# 4.4.1. Results on V2C-Animation Benchmark + +As shown in Table 1, our proposed method outperforms the current state-of-the-art models and achieves the best performance across the majority of metrics. Our method achieves the best pronunciation accuracy in both dubbing settings, surpasses all others including two-stage methods using the same pre-training strategy following [54]. In terms of acoustic quality, due to the impact of inherent background noise in the movie dubbing dataset, other methods do not perform well in this aspect even with the pre-trained + +phoneme encoder. However, our proposed method achieves a score improvement of 0.73-1.86 on the UT-MOS metric, bringing a significant improvement in the acoustic quality of generated dubbing. Concurrently, our model achieves the lowest MCD-DTW and MCD-DTW-SL, indicating that the generated dubbing exhibits the smallest discrepancy and the best duration alignment with the real dubbing. The best dubbing emotion accuracy rate which outperforms the current state-of-the-art models with a $+2.58\%$ margin indicating the best prosody alignment performance of our method. + +Although we fall short in voice similarity compared to StyleDubber [8], which learns fine-grained speaker styles, our method attains the highest score in MOS-S in subjective evaluation. Additionally, our proposed method also achieves the highest scores in MOS-N and CMOS, indicating the best overall dubbing quality and alignment. + +# 4.4.2. Results on GRID Benchmark + +Since the dubbing in the GRID benchmark is closer to traditional speech, the gap between different models is not as significant as in the V2C-Animation benchmark. Nevertheless, as shown in Table 2, we still achieve state-of-the-art performance in pronunciation clarity, speech quality, and discrepancy from ground truth in both dubbing settings while maintaining advanced voice similarity. Moreover, our model also outperforms other state-of-the-art models in subjective evaluation scores on the GRID benchmark, demonstrating the effectiveness of our method across diverse dubbing benchmarks and scenarios. + +# 4.4.3. Results on Zero-shot Test + +In addition to dubbing benchmarks, we also conduct the zero-shot test to evaluate the generalization performance of models. We use audio from the GRID dataset (which is out of domain) as reference audio to dub movie clips from the V2C-Animation dataset. Due to the absence of corresponding ground truth, we only calculate WER, UT-MOS, and SECS for objective evaluation. + +As shown in Table 4, our proposed method surpasses the current state-of-the-art models and achieves the best per + +![](images/7250ee8cd64b9c88be82fdd28bee298ec0007d02f4ebabef7e38cd7fcc19468e.jpg) + +![](images/df95ebe57a08cb2efa9afbdb4ffc801626bc161391531c46aa4e2cbd3857ea2a.jpg) +GT + +![](images/69e55d4c4c93c60fdea5cc4daf65b18e959862abd3e79c14d292f3315c126ca5.jpg) +Ours + +![](images/919a2c0e6cc88f842bda9229095318bf5559ac50f4de54d18b412c98b213f514.jpg) + +![](images/cd0f0e8e16f0407d0b3b9547d4d333f8d2600bba44ff30e12fdde96095115f4d.jpg) +GT + +![](images/05ffb72c342c1200c03f5d6be96366cbea52a44905ae269b4bf297a4e33a9ecd.jpg) +Ours + +![](images/103aedbb26a79faee7e9d3e9cbdc7862532c581e1ee85e5de2115b8f14719a48.jpg) +Figure 3. The visualization of the mel-spectrograms of ground truth and synthesized dubbing by different models. The red and white bounding boxes highlight regions where different models exhibit significant differences in audio quality and pronunciation details. + +![](images/bb3e72b22cce34c961463ce09db2f7caf1c0aa4fe7b7a37b9ae417ac34c15f1d.jpg) +Speaker2Dubber + +![](images/5f50f382c54f57cfe56ed547a83b4160478b404f17505469bd13a25ad46b7f72.jpg) +StyleDubber + +![](images/742caadba741477b9765b51601d206bb868b00f93174290e4663cd32b2ff9f58.jpg) + +![](images/b4afe7905f3fd1edc6956ac40586aa4824d903beb7b393344525c5efab6794c0.jpg) +Speaker2Dubber + +![](images/8f65cca7cc2565836c39419a02e28361f9f2ce0a7db0b56d2c8b3362f29a8c1c.jpg) +StyleDubber + +Table 5. Results of ablation study + +
#MethodWER ↓UT-MOS ↑EMO-ACC ↑MCD-DTW ↓MCD-DTW-SL ↓
-GT22.552.2699.960.000.00
-GT Mel+ Vocoder24.402.1897.093.773.80
1w/o AP21.452.3845.209.789.83
2w/o PE9.843.0946.129.359.38
3w/o IDEA8.383.0747.639.499.52
4w/o PSD10.633.0547.069.619.64
5w/o PTBE8.632.6046.089.849.87
6Full Model8.043.1048.939.299.32
+ +formance across all metrics. Specifically, our proposed method still ensures accurate pronunciation and the best acoustic quality of the generated dubbing when facing out-of-domain reference audio. In terms of voice similarity, our model achieves the best cloning effect in both objective and subjective evaluations. The zero-shot experimental results substantiate the superiority of the generalization performance of our proposed method. + +# 4.5. Qualitative Analysis + +We visualize the mel-spectrograms of ground truth and dubbing generated by different models for comparison in Figure 3. (More visualization results are presented in the Appendix.) The red bounding boxes represent regions where different models exhibit significant differences in audio quality and the white regions present the difference in pronunciation details. Through the observation of the red bounding box, it is evident that our method exhibits less noise in the non-pronunciation intervals of dubbing compared to other models, indicating better acoustic quality. Additionally, the clearer spectrum lines in the white bounding box and the closer resemblance to the ground truth in terms of prosody (the shape of spectrum lines) show that our method also achieves better pronunciation quality and prosody alignment performance. + +# 4.6. Ablation Studies + +To further investigate the specific effects of each module in our proposed method, we conduct ablation studies on the Dub 1.0 setting of the V2C-Animation benchmark. + +Effectiveness of Acoustic Pre-training (AP). As shown in Row 1 of Table 5, acoustic pre-training significantly improves the acoustic quality and pronunciation accuracy. It noticeably enhances the model's performance on the UTMOS and WER. The clearer pronunciation and speech quality are also reflected in the improvement of dubbing accu + +racy indicated by MCD-DTW and MCD-DTW-SL. + +Effectiveness of Prosody Enhancement (PE). Row 2 of Table 5 shows that the prosody enhancement strategy can reduce the difference between the generated dubbing and the ground truth, enhancing the model's performance on the MCD-DTW and MCD-DTW-SL metrics. The results demonstrate it improves the model's acoustic modeling capability in handling complex prosody variations. + +Effectiveness of In-Domain Emotion Analysis (IDEA). As shown in Row 3 of Table 5, the IDEA module provides a more stable and accurate alignment between the emotion of characters and the dubbing prosody, enhancing performance on emotion accuracy. The better prosody alignment brought by IDEA also reduces the discrepancy between the generated dubbing with ground truth. + +Effectiveness of Prosodic Style Diffusion (PSD). The modeling of prosodic style features allows the model to focus on non-timbre prosodic characteristics during the prosody adapting stage, improving the overall dubbing accuracy as shown in Row 4 of Table 5. Additionally, the disentangled design on prosodic style also enhances the model's performance in acoustic and pronunciation quality. Effectiveness of Prosodic Text BERT Encoder (PTBE). Compared to previous works that use a single text encoder output feature for both acoustic and prosodic modeling, the introduction of the Prosodic Text BERT Encoder brings disentangled text prosodic features. This approach not only enhances the quality of text prosodic modeling but also ensures the acoustic quality of the generated dubbing. As shown in Row 5 of Table 5, the PTBE module significantly improves the dubbing accuracy and the acoustic quality. + +# 5. Conclusion + +In this work, we propose a method with a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to generate high-quality movie dubbing with aligned prosody. The first stage equips the model with the acoustic modeling capability to handle complex dubbing prosody. The second stage employs a disentangled prosody adapting framework to bridge character performances with dubbing prosody while maintaining the acoustic quality. Extensive experimental results demonstrate the effectiveness of our proposed method. + +# Acknowledgement + +This work was supported by National Natural Science Foundation of China: 62322211, 62336008, U21B2024, "Pioneer" and "Leading Goose" R&D Program of Zhejiang Province (2024C01023, 2023C01046, 2023C01038), Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of Music), Ministry of Culture and Tourism (2023DMKLB004). 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This task demands the model bridge character performances and complicated prosody structures to build a high-quality video-synchronized dubbing track. The limited scale of movie dubbing datasets, along with the background noise inherent in audio data, hinder the acoustic modeling performance of trained models. To address these issues, we propose an acoustic-prosody disentangled two-stage method to achieve high-quality dubbing generation with precise prosody alignment. First, we propose a prosody-enhanced acoustic pre-training to develop robust acoustic modeling capabilities. Then, we freeze the pre-trained acoustic system and design an acoustic-disentangled framework to model prosodic text features and dubbing style while maintaining acoustic quality. Additionally, we incorporate an in-domain emotion analysis module to reduce the impact of visual domain shifts across different movies, thereby enhancing emotion-prosody alignment. Extensive experiments show that our method performs favorably against the state-of-the-art models on two primary benchmarks. The project is available at https://zzdoog.github.io/ProDubber/." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 580, + 135, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 135, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 135, + 594 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 601, + 295, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 601, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 601, + 295, + 685 + ], + "type": "text", + "content": "Movie Dubbing, also known as Visual Voice Cloning (V2C) [5], aims to generate speech from scripts using a specified voice conditioned by a single short reference audio while ensuring prosody alignment with the character's performance in terms of both pronunciation duration and intonation (as shown in Figure 1 (a)). It promises significant potential in real-world applications such as film post-" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 326, + 248, + 545, + 317 + ], + "blocks": [ + { + "bbox": [ + 326, + 248, + 545, + 317 + ], + "lines": [ + { + "bbox": [ + 326, + 248, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 326, + 248, + 545, + 317 + ], + "type": "image", + "image_path": "77134cc1fa0f21cd3932d79018a9194c0cd0a14bda7767f80d151ed9e60937a4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 326, + 332, + 548, + 399 + ], + "blocks": [ + { + "bbox": [ + 374, + 322, + 488, + 331 + ], + "lines": [ + { + "bbox": [ + 374, + 322, + 488, + 331 + ], + "spans": [ + { + "bbox": [ + 374, + 322, + 488, + 331 + ], + "type": "text", + "content": "(a) Visual Voice Cloning (V2C) task" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 326, + 332, + 548, + 399 + ], + "lines": [ + { + "bbox": [ + 326, + 332, + 548, + 399 + ], + "spans": [ + { + "bbox": [ + 326, + 332, + 548, + 399 + ], + "type": "image", + "image_path": "5b5d420c4f529c118468a19fdb5d877278ccbf37f97e9798c1e0fb9ae9e145d3.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 400, + 497, + 409 + ], + "lines": [ + { + "bbox": [ + 371, + 400, + 497, + 409 + ], + "spans": [ + { + "bbox": [ + 371, + 400, + 497, + 409 + ], + "type": "text", + "content": "(b) Illustration of our proposed method" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 418, + 554, + 464 + ], + "lines": [ + { + "bbox": [ + 313, + 418, + 554, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 554, + 464 + ], + "type": "text", + "content": "Figure 1. (a) Illustration of the V2C task. (b) Illustration of the proposed acoustic pre-training stage (Stage I) and prosody adapting stage (Stage II), which aim to generate dubbing with high acoustic quality and aligned prosody." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 473, + 550, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 550, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 550, + 485 + ], + "type": "text", + "content": "production, media production, and personal speech AIGC." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 486, + 554, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 557 + ], + "type": "text", + "content": "Compared to traditional speech synthesis [4, 27, 30, 35, 36] or Voice Cloning [1] tasks, movie dubbing presents greater challenges. It demands the ability not only to align the prosody with complex character performances but also to maintain high acoustic quality even when managing diverse and exaggerated prosody inherent in dubbing." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 558, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 714 + ], + "type": "text", + "content": "Previous works achieve significant progress in aligning prosody with the performances of movie characters. V2C-Net [5] incorporates visual features from each frame of the movie clip into the mel-spectrogram frame-level prosody modeling. HPMDubbing [6] employs a hierarchical design, where lip, face, and video-level features correspond to pronunciation duration, prosody, and the overall video atmosphere, respectively. StyleDubber [8] uses a fine-grained adaptor to bridge the speaker's style and character's emotion states at the phoneme level, facilitating joint modeling of prosody. However, existing methods overlook the visual domain discrepancies arising from variations in movie styles and other visual elements, such as color grading," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 271, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 271, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 271, + 703 + ], + "type": "text", + "content": "*This work is done during the intern in VIPL group, ICT, CAS." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "172" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 253, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 253, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 253, + 84 + ], + "type": "text", + "content": "which impact the stability of prosody alignment." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 86, + 296, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 86, + 296, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 86, + 296, + 301 + ], + "type": "text", + "content": "The nature of film acting means movie dubbing inherently involves more exaggerated and diverse prosody variations compared to traditional speech, yet the difficulty of its acoustic modeling is often underestimated. In addition, certain characteristics of movie dubbing datasets, such as their limited scale (primarily due to copyright restrictions) and the suboptimal audio quality caused by unavoidable movie background noise [54], further hinder methods that solely rely on dubbing datasets for training to achieve satisfied acoustic quality [5, 6, 8, 24]. Speaker2Dubber [54] attempts to enhance the model's acoustic modeling capability by pre-training the phoneme encoder on a large-scale text-to-speech corpus. This two-stage training strategy improves the model's pronunciation accuracy, however, the pre-trained phoneme encoder alone cannot eliminate the impact of low audio quality in dubbing datasets, or modeling complex prosody variation, leading to a significant degradation in final acoustic quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 304, + 296, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 296, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 296, + 579 + ], + "type": "text", + "content": "To address these issues, we propose a dubbing method that incorporates a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to achieve high-quality dubbing with well-aligned prosody (as shown in Figure 1 (b)). Specifically, in the prosody-enhanced acoustic pre-training stage, we pre-train the entire acoustic system of the model using a text-speech corpus with enhanced prosody. This ensures the acoustic modeling capability in audio quality and managing the complex dubbing prosody variations. We thus freeze the acoustic system in the second stage and design a disentangled framework to model prosodic features from the dubbing script and audio by introducing a prosodic text BERT encoder and a prosodic style diffusion module. These disentangled prosodic features are further bridged with the in-domain emotion analysis output feature, aligning the prosody with the character's emotion. Lip motion features are then utilized to predict pronunciation duration and upsample the text content to match the mel-spectrogram length. Finally, the pre-trained audio decoder takes the upsampled text content and predicted prosody as input, integrating the speaker voice via AdaIN layer [15], and generates dubbing with high acoustic quality and aligned prosody." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 580, + 274, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 580, + 274, + 592 + ], + "spans": [ + { + "bbox": [ + 67, + 580, + 274, + 592 + ], + "type": "text", + "content": "The main contributions of the paper are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 594, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 641 + ], + "type": "text", + "content": "- We propose a two-stage dubbing method with a prosody-enhanced acoustic pre-training to enhance the model's ability in high-quality acoustic modeling and handling complex prosodic variations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "content": "- To maintain the acoustic quality in the prosody adapting stage, we freeze the pre-trained acoustic system and devise an acoustic-disentangled prosody adapting framework by introducing prosodic modeling modules corresponding to both the script and the required dubbing style." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 702, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 702, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 702, + 295, + 714 + ], + "type": "text", + "content": "- We design an in-domain emotion analysis module in the" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "type": "text", + "content": "prosody adapting stage to reduce the instability caused by visual domain discrepancies across different movies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 96, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 96, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 314, + 96, + 553, + 144 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the proposed method achieves favorable performance compared to several state-of-the-art approaches on two major benchmarks, validating the effectiveness of our approach." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 154, + 401, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 154, + 401, + 166 + ], + "spans": [ + { + "bbox": [ + 313, + 154, + 401, + 166 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 174, + 416, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 174, + 416, + 186 + ], + "spans": [ + { + "bbox": [ + 313, + 174, + 416, + 186 + ], + "type": "text", + "content": "2.1. Speech Synthesis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 190, + 555, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 555, + 407 + ], + "type": "text", + "content": "With the rapid development of deep learning [7, 10, 11, 16, 29, 32, 40, 42-45, 48, 50, 53, 56], the speech synthesis task has advanced significantly in recent years. From the autoregressive generation architecture of models like WaveNet [46] to the non-autoregressive parallel architecture of the FastSpeech series [35, 36], both the quality and speed of speech generation have improved substantially. Recently, the NaturalSpeech [18, 38, 39] and StyleTTS [25, 27] series have utilized factorized codec and diffusion models, as well as adversarial training with large speech language models, respectively, to achieve high-quality speech synthesis that more closely approaches human-level performance. Additionally, many other works based on other generative models [13, 14, 17, 19, 33, 47] such as flow matching [12, 20, 28] are also advancing the progress in speech synthesis. Despite the progress has been made, they cannot be directly applied to movie dubbing tasks because they lack the design of modeling prosody from input movie clips." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 413, + 435, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 435, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 435, + 426 + ], + "type": "text", + "content": "2.2. Visual Voice Cloning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 430, + 556, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 556, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 556, + 635 + ], + "type": "text", + "content": "The V2C task [5] requires the model to align the prosody of the generated speech with the input video to achieve automatic movie dubbing. To this end, HPMDubbing [6] proposes a hierarchical prosody learning structure, aligning the dubbing duration, prosody, and overall tone with the lip movements, facial expressions, and overall context of the video. Some works [8, 55], on the other hand, design a fine-grained prosody matching module for character voice, incorporating phoneme-level features and emotional variations to model the dubbing style of the characters. Subsequently, Speaker2Dubber [54] addresses the difficulty of learning accurate pronunciation through training solely on dubbing datasets by pre-training its phoneme encoder on text-speech corpus. Despite these advancements, current dubbing models are still significantly influenced by the quality of the dubbing dataset and struggle to achieve high acoustic quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 644, + 370, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 644, + 370, + 656 + ], + "spans": [ + { + "bbox": [ + 313, + 644, + 370, + 656 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 663, + 382, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 663, + 382, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 663, + 382, + 675 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 681, + 506, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 681, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 681, + 506, + 693 + ], + "type": "text", + "content": "The target of the overall movie dubbing task is:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 368, + 700, + 555, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 700, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 368, + 700, + 555, + 715 + ], + "type": "interline_equation", + "content": "\\tilde {A} _ {D u b} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {d}, V _ {m}\\right), \\tag {1}", + "image_path": "b86145af05b5dee6e4f83124ca04ef204ecb1a33f4980956ee88a5b7cc9d2445.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "173" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 553, + 199 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 553, + 199 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 553, + 199 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 553, + 199 + ], + "type": "image", + "image_path": "d87b9aa0b59d04745cc6c83851f3f02076b4b2ffc7fef72982399e3f2d11cfbc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 200, + 553, + 322 + ], + "blocks": [ + { + "bbox": [ + 58, + 200, + 553, + 322 + ], + "lines": [ + { + "bbox": [ + 58, + 200, + 553, + 322 + ], + "spans": [ + { + "bbox": [ + 58, + 200, + 553, + 322 + ], + "type": "image", + "image_path": "07ff39d8d8cc4a9c98ac2f2780943f978d5fc508084a6c9762e602c0811d605e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 331, + 555, + 377 + ], + "lines": [ + { + "bbox": [ + 55, + 331, + 555, + 377 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 555, + 377 + ], + "type": "text", + "content": "Figure 2. The main architecture of the proposed method. In the Prosody-Enhanced Acoustic Pre-training stage (Section 3.2), we pre-train the acoustic system using a prosody-enhanced text-speech corpus. In the Acoustic-Disentangled Prosody Adapting stage (Section 3.4), we freeze the acoustic system and employ a disentangled framework to bridge the prosody of dubbing with the character's performance using In-Domain Emotion Analysis (Section 3.3), thus generating dubbing with aligned prosody and maintain high acoustic quality." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "inline_equation", + "content": "\\tilde{A}_{Dub}" + }, + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "text", + "content": " is the generated dubbing and " + }, + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "inline_equation", + "content": "A_{Ref}, T_d, V_m" + }, + { + "bbox": [ + 55, + 385, + 295, + 422 + ], + "type": "text", + "content": " are the reference audio, dubbing scripts, and the input silent movie clip respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 422, + 296, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 661 + ], + "type": "text", + "content": "The main architecture of the proposed two-stage method is shown in Figure 2. In the prosody-enhanced acoustic pre-training stage, we first design a prosody enhancement strategy to address the prosody domain differences between movie dubbing and traditional speech and apply it to a large-scale, high-quality text-speech corpus. Then, we use the enhanced corpus to pre-train the acoustic style encoder (ASE), acoustic text encoder, and end-to-end audio decoder of the dubbing model, enabling the acoustic system to accurately generate high-quality speech with corresponding content and speaker voice. Next, in the acoustic-disentangled prosody adapting stage, we utilize an acoustic-prosodic disentangled framework by introducing the prosodic style diffusion and prosodic text BERT encoder. This framework adapts the prosody while keeping the acoustic system frozen, thus maintaining the acoustic quality of generated dubbing. We also propose In-Domain Emotion Analysis to better bridge the dubbing prosody with the character's emotion, which improves the audiovisual consistency. We detail each module below." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 671, + 271, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 271, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 271, + 685 + ], + "type": "text", + "content": "3.2. Prosody-Enhanced Acoustic Pre-training" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "Acoustic quality forms the foundation of movie dubbing. The goal of prosody-enhanced acoustic pre-training is to" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 386, + 555, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 555, + 447 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 555, + 447 + ], + "type": "text", + "content": "provide a solid basis for high-quality acoustic modeling for movie dubbing through the pre-training of the acoustic system in the dubbing model. Below, we detail this pre-training approach in two aspects: the pre-training objectives and the prosody enhancement strategy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 452, + 443, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 452, + 443, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 452, + 443, + 464 + ], + "type": "text", + "content": "3.2.1. Pre-training Objectives" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 466, + 554, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 466, + 554, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 466, + 554, + 491 + ], + "type": "text", + "content": "Unlike the target of the movie dubbing task, the input of this stage does not contain the movie clip:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 372, + 498, + 555, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 498, + 555, + 514 + ], + "spans": [ + { + "bbox": [ + 372, + 498, + 555, + 514 + ], + "type": "interline_equation", + "content": "\\tilde {A} _ {s p e e c h} = \\operatorname {M o d e l} \\left(A _ {R e f}, T _ {s}\\right), \\tag {2}", + "image_path": "7715e9b05ea342f42af118983042bff6cc989138f0bc0160226893b7bbb1adb3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 521, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 653 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 521, + 555, + 653 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 313, + 521, + 555, + 653 + ], + "type": "text", + "content": " is the script from the text-speech corpus. Nevertheless, the acoustic information ultimately used to generate speech audio comprises three components which are the same as the movie dubbing: content information derived from the text, speaker voice obtained from reference audio, and the prosody of the speech. The only difference lies in whether the prosody and duration of each phoneme need to align with the given video. Since the text-speech corpus used in this stage does not include the corresponding video clip, we directly utilize the ground truth duration and prosody during this stage." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "content": "We adopt an architecture similar to StyleTTS [25] for acoustic pre-training. First, the text in the corpus is converted from a grapheme sequence to a phoneme sequence using a G2P module. We then use a bidirectional LSTM network to extract acoustic text features from the phoneme" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "text", + "content": "174" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": "sequence. Next, an acoustic style encoder extracts timbre features from either the ground truth or other speech samples from the same speaker. A prosody extractor is employed to extract mel-spectrogram frame-level prosody (pitch and energy curve) from the mel-spectrogram of the ground truth speech. To upsample the acoustic text sequence to match the length of the mel-spectrogram, we use a monotonic aligner pre-trained on the LibriSpeech dataset for the automatic speech recognition (ASR) task to obtain the ground truth duration of each phoneme:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 199, + 176, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 199, + 176, + 213 + ], + "spans": [ + { + "bbox": [ + 62, + 199, + 176, + 213 + ], + "type": "interline_equation", + "content": "T _ {p h o} = \\mathrm {G 2 P} (T _ {s}) \\in \\mathbb {R} ^ {L _ {p h o}},", + "image_path": "e483345bda34cc8d759aacb4084d6c206d7b5f3f36d9ea118c422be292450b61.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 215, + 267, + 229 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 215, + 267, + 229 + ], + "spans": [ + { + "bbox": [ + 62, + 215, + 267, + 229 + ], + "type": "interline_equation", + "content": "T _ {a} = \\operatorname {A c o u s t i c T e x t E n c o d e r} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}},", + "image_path": "7dce7580ccad54776eee2132c5e42b518cd6904e5e75a0c6dacc840fa90291fa.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 232, + 294, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 232, + 294, + 246 + ], + "spans": [ + { + "bbox": [ + 63, + 232, + 294, + 246 + ], + "type": "interline_equation", + "content": "S _ {a} = \\text {A c o u s t i c S t y l e E n c o d e r} \\left(A _ {R e f}\\right) \\in \\mathbb {R} ^ {d _ {m}}, \\tag {3}", + "image_path": "344c6b44316205a1611ee0695ce5391d13bf6b4f38774e364b2e0cb7112e9fd7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 248, + 275, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 248, + 275, + 262 + ], + "spans": [ + { + "bbox": [ + 63, + 248, + 275, + 262 + ], + "type": "interline_equation", + "content": "\\operatorname {A l i g n} = \\operatorname {T e x t A l i g n e r} (M e l _ {s}, T _ {P h o}) \\in \\mathbb {R} ^ {L _ {p h o} \\times L _ {m e l}},", + "image_path": "26b585c2fa0866ac26c63e33a8738681eba4c5f385f3a0f97e9b0dd427b61191.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 63, + 265, + 242, + 278 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 265, + 242, + 278 + ], + "spans": [ + { + "bbox": [ + 63, + 265, + 242, + 278 + ], + "type": "interline_equation", + "content": "p, n = \\operatorname {P r o s o d y E x t r a c t o r} (M e l _ {s}) \\in \\mathbb {R} ^ {L _ {m e l}},", + "image_path": "aab837e15068d34f4d509d2a30a2aa426756f276930bfb00df6ccfe81152b575.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "T_{a}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "S_{a}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " are the acoustic text feature and acoustic style feature, respectively. " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "L_{pho}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "L_{mel}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " denote the length of the phoneme sequence and desired mel-spectrogram, respectively. " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "d_{m}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " denotes the hidden size of the model. Align is the monotonic attention map between the phoneme sequence and the mel-spectrogram of ground truth speech " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "Mel_{s}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "p, n" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " is the ground truth pitch and energy curve." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 369, + 296, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 296, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 296, + 430 + ], + "type": "text", + "content": "Then, a HiFi-GAN [22] based end-to-end audio decoder takes the extracted prosody and the upsampled acoustic text features as inputs, while using Adaptive Instance Normalization (AdaIN) [15] to integrate the acoustic style information and reconstruct the original ground truth waveform:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 436, + 294, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 436, + 294, + 463 + ], + "spans": [ + { + "bbox": [ + 69, + 436, + 294, + 463 + ], + "type": "interline_equation", + "content": "\\operatorname {A d a I N} \\left(c, S _ {a}\\right) = P _ {\\sigma} \\left(S _ {a}\\right) \\frac {c - \\mu (c)}{\\sigma (c)} + P _ {\\mu} \\left(S _ {a}\\right), \\tag {4}", + "image_path": "ae5dfbbe119b043ae7e1fa9b98f20f32f72e671b80f5f633d066444743ad1942.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 70, + 464, + 269, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 464, + 269, + 478 + ], + "spans": [ + { + "bbox": [ + 70, + 464, + 269, + 478 + ], + "type": "interline_equation", + "content": "\\tilde {A} _ {\\text {s p e e c h}} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot \\operatorname {A l i n g}, p, n, S _ {a}\\right),", + "image_path": "628dcd1c09c4c7cd85ea93bd0a6fda0c54f67e742078b87d4425e340b13b4823.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": " is the single channel of the feature maps, " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\mu (\\cdot)" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": " denote the channel mean and standard deviation. " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "P_{\\mu}" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "P_{\\sigma}" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": " are the linear projections for predicting the adaptive gain and bias using the acoustic style feature " + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "inline_equation", + "content": "S_{a}" + }, + { + "bbox": [ + 55, + 485, + 296, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 533, + 296, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 296, + 556 + ], + "type": "text", + "content": "The training objective at this stage is a reconstruction loss for speech:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 108, + 563, + 295, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 563, + 295, + 585 + ], + "spans": [ + { + "bbox": [ + 108, + 563, + 295, + 585 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R e c} = \\left\\| A _ {s p e e c h} - \\tilde {A} _ {s p e e c h} \\right\\| _ {1}. \\tag {5}", + "image_path": "bdcc965cffd03e4d11d90a786ceff3c5900e8cfa0f2d193e6964965f9b956c2b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 591, + 218, + 603 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 591, + 218, + 603 + ], + "spans": [ + { + "bbox": [ + 55, + 591, + 218, + 603 + ], + "type": "text", + "content": "3.2.2. Prosody Enhancement Strategy" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 605, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 712 + ], + "type": "text", + "content": "By pre-training the acoustic system using a text-speech corpus as mentioned above, the dubbing model gains the ability to convert text into high-quality speech. However, the speech in traditional text-to-speech corpora typically comes from recordings of audiobooks or blogs, which often exhibit flat and monotonous prosody. In contrast, the prosody of movie dubbing tends to vary significantly depending on the plot or performance, particularly in terms of pitch variation and the duration of certain lines." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "We design two prosody enhancement strategies to address the prosodic domain discrepancy between movie dubbing and traditional speech: pitch shifting and duration stretching. Pitch shifting alters the overall pitch of the speech by shifting it to higher or lower frequency bands, simulating the pitch variations found in dubbing. Duration stretching scales the length of the speech to simulate the varied speech pace observed in movie dubbing." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 169, + 555, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 169, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 169, + 555, + 324 + ], + "type": "text", + "content": "During the implementation, we find that directly manipulating pitch or duration in the time domain significantly degrades speech quality and reduces its naturalness. Therefore, we choose to convert the speech into mel-spectrograms and apply the enhancements in the frequency domain. We then use a vocoder [22] to convert the modified speech back to the time domain for end-to-end pre-training. Specifically, for the pitch shifting operation, we shift the entire spectrogram up or down by a specified number of frequency bands and fill the excess frequency bands with -80db to maintain the shape of spectrogram. For duration stretching, we use linear interpolation and downsampling operations to expand or shorten the length of spectrograms." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 335, + 474, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 474, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 474, + 346 + ], + "type": "text", + "content": "3.3. In-Domain Emotion Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": "To obtain fine-grained character emotion features at the video frame level, we first extract the face region of each frame of movie clip " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "V_{face}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " via S" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": "FD face detection [52], then utilize an emotion face-alignment network (EmoFAN [41]) to encode the face region to emotion features " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "V_{emo}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " following [6]:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 343, + 434, + 553, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 434, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 343, + 434, + 553, + 449 + ], + "type": "interline_equation", + "content": "V _ {e m o} = \\operatorname {E m o F A N} \\left(\\mathrm {S} ^ {3} \\mathrm {F D} \\left(V _ {m}\\right)\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {6}", + "image_path": "022370d864302a99ca9dcd8c92c9b0317109a5c13e15f8311e2de76134d4f846.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 460, + 529, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 529, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 529, + 472 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 460, + 529, + 472 + ], + "type": "inline_equation", + "content": "L_{v}" + }, + { + "bbox": [ + 313, + 460, + 529, + 472 + ], + "type": "text", + "content": " denotes the frame number of the video." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 472, + 554, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 554, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 554, + 519 + ], + "type": "text", + "content": "To ensure that the fine-grained video frame-level emotion features more accurately reflect emotional changes rather than visual characteristics of the movie, we first normalize them:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 357, + 530, + 553, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 530, + 553, + 545 + ], + "spans": [ + { + "bbox": [ + 357, + 530, + 553, + 545 + ], + "type": "interline_equation", + "content": "V _ {e m o} ^ {\\prime} = \\Sigma^ {- \\frac {1}{2}} \\left(V _ {e m o} - \\mu\\right) \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {7}", + "image_path": "164096206f74af21849c9b8fd767c3a142adb5d808bb6a85b1f2848859ad64b8.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "inline_equation", + "content": "V_{emo}'" + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "content": " denotes the normalized feature, " + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "content": " is the mean of the feature sequence, and " + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "content": " is the covariance matrix of sequence. The term " + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 313, + 555, + 554, + 614 + ], + "type": "text", + "content": " represents the inverse square root of the covariance matrix, which ensures that the normalized features have zero mean and unit covariance." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 616, + 554, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 554, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 554, + 676 + ], + "type": "text", + "content": "Simultaneously, to reflect the absolute emotional state of characters in the video, we use a video-level atmosphere feature [6] to adjust the normalized emotion features, thereby capturing the character's emotional state and changes:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 368, + 686, + 553, + 706 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 686, + 553, + 706 + ], + "spans": [ + { + "bbox": [ + 368, + 686, + 553, + 706 + ], + "type": "interline_equation", + "content": "V _ {p} = \\alpha \\cdot V _ {e m o} ^ {\\prime} + \\beta \\in \\mathbb {R} ^ {L _ {v} \\times d _ {m}}, \\tag {8}", + "image_path": "39658d81805b889a70fe3404f9eb1095dce674e87c959b7565df4d819505017c.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 370, + 704, + 499, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 704, + 499, + 715 + ], + "spans": [ + { + "bbox": [ + 370, + 704, + 499, + 715 + ], + "type": "interline_equation", + "content": "\\alpha = f _ {\\alpha} (V _ {a t o}), \\quad \\beta = f _ {\\beta} (V _ {a t o}),", + "image_path": "a434672789e4dfcf667db77bf3ed2831b0a25323b94ef7d4bc34aa75ea3351a4.jpg" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "175" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "V_{ato} \\in \\mathbb{R}^{d_m}" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " is the video-level atmosphere feature, " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "f_{\\alpha}" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "f_{\\beta}" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " are learnable linear projections. " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "V_{p}" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " denotes the video-frame level emotion prosodic features." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 116, + 271, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 116, + 271, + 129 + ], + "spans": [ + { + "bbox": [ + 55, + 116, + 271, + 129 + ], + "type": "text", + "content": "3.4. Acoustic-Disentangled Prosody Adapting" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 133, + 295, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 133, + 295, + 252 + ], + "spans": [ + { + "bbox": [ + 54, + 133, + 295, + 252 + ], + "type": "text", + "content": "To ensure that the model does not compromise acoustic quality during training on the dubbing dataset, we freeze the entire pre-trained acoustic system at this stage. Unlike traditional TTS tasks that only require modeling prosody from the input text and the voice of reference audio, movie dubbing demands a more complex prosody modeling that bridges the character's facial expressions from visual modality. Relying solely on the frozen acoustic text encoder and acoustic style encoder is insufficient to handle the complex prosody alignment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 253, + 296, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 296, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 296, + 314 + ], + "type": "text", + "content": "To this end, we propose an acoustic-disentangled framework by introducing a prosodic text BERT encoder (PTBE) [26] and a prosodic style encoder (PSE) to extract prosodic features from the script text and non-timbre prosodic features from ground truth dubbing, respectively:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 82, + 319, + 294, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 319, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 82, + 319, + 294, + 335 + ], + "type": "interline_equation", + "content": "T _ {p} = \\operatorname {P T B E} \\left(T _ {p h o}\\right) \\in \\mathbb {R} ^ {L _ {p h o} \\times d _ {m}}, \\tag {9}", + "image_path": "1e90f063ff9d423d48f1f8ea773d140cc0f7fcf556e370bbc0ff65cdc8bc5666.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 337, + 268, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 337, + 268, + 352 + ], + "spans": [ + { + "bbox": [ + 83, + 337, + 268, + 352 + ], + "type": "interline_equation", + "content": "S _ {p} = \\mathrm {P r o s o d i c S t y l e E n c o d e r} (A _ {D u b}) \\in \\mathbb {R} ^ {d _ {m}}.", + "image_path": "71df7cb7780e920004a63368c5dca478678bc85d83880e63c5c85ac19a72f486.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 360, + 296, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 296, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 296, + 419 + ], + "type": "text", + "content": "After extracting prosodic features from both the text and the dubbing audio, we employ a multi-head cross-attention module to connect phoneme-level text prosodic features with emotion features, enabling the modeling of prosody at the phoneme level based on character emotion variations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 422, + 294, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 422, + 294, + 480 + ], + "spans": [ + { + "bbox": [ + 58, + 422, + 294, + 480 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} T _ {F u s i o n} ^ {k} = s o f t m a x (\\frac {Q _ {p h o} ^ {\\top} K _ {e m o}}{\\sqrt {d _ {m}}}) V _ {e m o} \\in \\mathbb {R} ^ {L _ {p h o} \\times \\frac {d _ {m}}{n _ {h e a d}}}, \\\\ Q _ {p h o} = W _ {j} ^ {Q} T _ {p} ^ {\\top}, K _ {e m o} = W _ {j} ^ {K _ {p}} V _ {p} ^ {\\top}, V _ {p} = W _ {j} ^ {V _ {p}} V _ {p} ^ {\\top}, \\tag {10} \\\\ \\end{array}", + "image_path": "660a2405101431fae62fc1627d6bcf4bfc8459d46ee7a1660684221daa29f17e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "content": "-th head's output, " + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "inline_equation", + "content": "W_{j}^{*}" + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "content": " are learnable parameter matrix, and " + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "inline_equation", + "content": "T_{Fusion}" + }, + { + "bbox": [ + 55, + 486, + 295, + 521 + ], + "type": "text", + "content": " is phoneme-level prosodic feature with emotion variation information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 522, + 296, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 559 + ], + "type": "text", + "content": "To model the prosodic style feature of dubbing, we design a prosodic dstyle diffusion module that takes " + }, + { + "bbox": [ + 55, + 522, + 296, + 559 + ], + "type": "inline_equation", + "content": "T_{Fusion}" + }, + { + "bbox": [ + 55, + 522, + 296, + 559 + ], + "type": "text", + "content": " as input and samples the prosodic style feature from noise:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 72, + 567, + 294, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 567, + 294, + 597 + ], + "spans": [ + { + "bbox": [ + 72, + 567, + 294, + 597 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p _ {\\theta} \\left(S _ {t - 1} \\mid S _ {t}\\right) = \\mathcal {N} \\left(S _ {t - 1}; \\mu_ {\\theta} \\left(S _ {t}, t\\right), \\Sigma_ {\\theta} \\left(S _ {t}, t\\right)\\right), \\tag {11} \\\\ \\tilde {S} _ {p} = p _ {\\theta} \\left(S _ {0} \\mid T _ {F u s i o n}\\right), \\\\ \\end{array}", + "image_path": "c264594b19927767ac88abf45e2814819836f1bd080ab7beeb3f887e1c59c4dd.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "content": " is the learnable denoise distribution and the " + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "inline_equation", + "content": "S_{t-1}" + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "content": " is the feature of previous time step. Specifically, in the first half of the training process, we train the prosodic style encoder to better assist the prosody predictor in prosody prediction. In the second half of the training, we introduce the prosodic style diffusion module. This approach ensures more stable convergence during training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Subsequently, we employ the AdaIN module to integrate the predicted prosodic style feature into the " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "T_{Fusion}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ", which" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "is then input into the prosody predictor for specific prosody prediction:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 323, + 105, + 553, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 105, + 553, + 119 + ], + "spans": [ + { + "bbox": [ + 323, + 105, + 553, + 119 + ], + "type": "interline_equation", + "content": "\\tilde {p}, \\tilde {n} = \\text {P r o s o d y P r e d i c t o r} (\\text {A d a I N} (T _ {\\text {F u s i o n}}, \\tilde {S} _ {p})), \\tag {12}", + "image_path": "4462f72fa062fe596288c8109f7473e3f0e43d6f95afa8974a6aaef406423f0a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 126, + 553, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 126, + 553, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 126, + 553, + 162 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 126, + 553, + 162 + ], + "type": "inline_equation", + "content": "\\tilde{p},\\tilde{n}\\in \\mathbb{R}^{L_{pho}}" + }, + { + "bbox": [ + 313, + 126, + 553, + 162 + ], + "type": "text", + "content": " are the prediction of prosody attributes (pitch and energy) based on the prosodic features and the visual emotion feature." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 163, + 555, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 555, + 295 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 555, + 295 + ], + "type": "text", + "content": "In terms of aligning the duration of pronunciation with lip movements, since this alignment is solely related to the prosody of pronunciation and lip movements, which is independent of character emotions and both kinds of style, the input to the duration predictor is the cross-attention fusion of the prosodic text feature and the lip motion feature. Then, we upsample the acoustic text features to the spectrogram length based on the alignment built from the duration prediction, and the audio decoder takes the upsampled acoustic text feature, the acoustic style feature, and the prosody prediction as input, generating the dubbing audio:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 319, + 302, + 553, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 302, + 553, + 334 + ], + "spans": [ + { + "bbox": [ + 319, + 302, + 553, + 334 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {d} = \\text {D u r a t i o n P r e d i c t o r} (\\underset {\\sim} {\\mathrm {C A}} (T _ {p}, V _ {d}, V _ {d})) \\in \\mathbb {R} ^ {L _ {p h o}}, \\tag {13} \\\\ \\tilde {A} _ {D u b} = \\operatorname {A u i d o D e c o d e r} \\left(T _ {a} \\cdot A l i g n, \\tilde {p}, \\tilde {n}, S _ {a}\\right), \\\\ \\end{array}", + "image_path": "b2a8f67ec4c4390ebb05621ec3b6ec1a58c56ec2dca3d8c5668cece7834f5164.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "V_{d} \\in \\mathbb{R}^{L_{v} \\times d_{m}}" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " is the lip motion feature extracted from the lip region of movie clips following [6]. " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\mathrm{CA}(\\cdot)" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " denotes the cross-attention, we use " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "T_{p}" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " as query and " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "V_{d}" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " as key and value here to get the phoneme-level duration features. The duration prediction is scaled according to the length of the movie clip to ensure the alignment between total video duration and total dubbing duration. It is noteworthy that " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\tilde{n}" + }, + { + "bbox": [ + 313, + 342, + 555, + 452 + ], + "type": "text", + "content": " are also upsampled before being input into the decoder to match the spectrogram length." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 459, + 378, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 459, + 378, + 472 + ], + "spans": [ + { + "bbox": [ + 314, + 459, + 378, + 472 + ], + "type": "text", + "content": "3.5. Training" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 476, + 554, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 476, + 554, + 522 + ], + "spans": [ + { + "bbox": [ + 313, + 476, + 554, + 522 + ], + "type": "text", + "content": "In the acoustic-disentangled prosody adapting stage, since we freeze all acoustic modules, the training objective for this stage is the sum of the losses for different prosody attributes:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 348, + 535, + 553, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 535, + 553, + 548 + ], + "spans": [ + { + "bbox": [ + 348, + 535, + 553, + 548 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D u b} = \\lambda_ {1} \\mathcal {L} _ {p} + \\lambda_ {2} \\mathcal {L} _ {n} + \\lambda_ {3} \\mathcal {L} _ {d} + \\lambda_ {4} \\mathcal {L} _ {S _ {p}}, \\tag {14}", + "image_path": "3559db1488d97a4f39179f60cde7e87c76d02c944d87936cdf601f8f0b507754.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p, \\mathcal{L}_n," + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "text", + "content": " are the L1-Loss for pitch, energy and duration respectively. The " + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{S_p}" + }, + { + "bbox": [ + 313, + 558, + 554, + 594 + ], + "type": "text", + "content": " is the diffusion loss for prosodic style feature modeling." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 604, + 390, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 390, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 390, + 617 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 624, + 376, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 376, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 376, + 635 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "type": "text", + "content": "V2C-Animation dataset [5] is a collection of 10,217 video clips from 26 animated movies, featuring aligned text, audio, and video clips from real movies along with speaker emotion annotations. Our main experimental results are validated on this dataset due to its authenticity and more detailed annotations." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "176" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 118, + 553, + 256 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "type": "text", + "content": "Table 1. Results on V2C-Animation benchmark. For the Dub 1.0 setting, we use the ground truth audio as reference audio, for the Dub 2.0 setting, we use the non-ground truth audio from the same speaker within the dataset as the reference audio which is more aligned with practical usage in dubbing. The method with “*” refers to a variant taking video embedding as an additional input following [5]. “T-S” indicates whether this method employs a two-stage training approach same as [54]. The same setup is applied to the GRID benchmark." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 118, + 553, + 256 + ], + "lines": [ + { + "bbox": [ + 57, + 118, + 553, + 256 + ], + "spans": [ + { + "bbox": [ + 57, + 118, + 553, + 256 + ], + "type": "table", + "html": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%)↑WER (%)↓UT-MOS ↑EMO-ACC (%)↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%)↑WER (%)↓UT-MOS ↑
GT-100.0025.552.2699.960.000.00100.0022.552.26
GT Mel + Vocoder-96.9624.402.1897.093.773.8096.9624.402.18
StyleSpeech* [30]X42.53108.001.4142.5311.6214.2375.6782.481.81
Zero-shot TTS* [57]X48.9368.051.7243.9710.0312.0147.5558.811.63
V2C-Net [5]X40.6173.081.3243.0814.1218.4934.0761.611.30
HPMDubbing [6]X53.76164.161.3146.6111.1211.2231.42171.031.30
Face-TTS [24]X52.81201.131.3144.0413.4426.9451.98200.181.31
StyleDubber [8]X82.2631.491.8945.629.379.4681.2731.701.95
StyleSpeech* [30]✓58.9438.352.4446.2710.1013.1255.9063.971.89
V2C-Net [5]✓69.0023.022.3546.159.9710.9769.3023.152.32
Speaker2Dubber [54]✓81.5017.512.4146.809.469.6579.8617.332.42
Ours✓75.468.043.1048.939.299.3275.3911.503.09
", + "image_path": "c38aa8a49f596aa294da652832d3dc9dc9744b838a4b02df55acb998a21e2e19.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 269, + 294, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 269, + 294, + 365 + ], + "spans": [ + { + "bbox": [ + 54, + 269, + 294, + 365 + ], + "type": "text", + "content": "GRID dataset [9] is a basic benchmark for multi-speaker dubbing. It comprises high-quality video recordings of 33 speakers performing 1,000 scripted sentences each, resulting in a total of 33,000 utterances. All participants are recorded in a noise-free studio with a unified screen background. V2C-Animation and GRID benchmarks respectively correspond to animated films and basic real-person dubbing, covering a wide range of application scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 365, + 295, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 365, + 295, + 462 + ], + "spans": [ + { + "bbox": [ + 54, + 365, + 295, + 462 + ], + "type": "text", + "content": "LibriTTS dataset [51] is a substantial collection of speech data designed for training and evaluating multi-speaker text-to-speech (TTS) systems derived from the LibriSpeech [31]. It includes multi-speaker recordings, offering a diverse range of voices and speaking styles and meticulously segmented and annotated with text transcripts. We employ LibriTTS as the text-speech corpus used in the prosody-enhance acoustic pre-training stage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 468, + 189, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 189, + 481 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 189, + 481 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 486, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 486, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 54, + 486, + 295, + 605 + ], + "type": "text", + "content": "Following [5, 6, 8, 54], all the video frames are sampled at 25 FPS. During training, we resample all audio file in " + }, + { + "bbox": [ + 54, + 486, + 295, + 605 + ], + "type": "inline_equation", + "content": "24\\mathrm{kHz}" + }, + { + "bbox": [ + 54, + 486, + 295, + 605 + ], + "type": "text", + "content": " and convert them into mel-spectrograms using FFT size of 2048, hop size of 300, window size of 1200, and frequency bins of 80. We employ a pre-trained JDC network [23] as the pitch extractor and use the log norm to calculate the energy following [25, 27]. For the text aligner, we adopt the ASR model fine-tuned for the TTS task by [25] to get the ground truth alignment between phoneme and mel-spectrogram." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": "We use Libri-TTS-460 following [27] for the acoustic pre-training and apply a " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " prosody enhancement ratio to trade off the audio quality and prosody variations. We use the official pre-trained HiFi-GAN [22] as the vocoder for the prosody enhancement. We train the acoustic system with 20 epochs in the pre-training stage. For the prosody adapting stage, we train the model with 30 epochs on the V2C-Animation dataset and 20 epochs for GRID dataset. An Adam [21] with " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.98" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-9}" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " is used" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "content": "as the optimizer in both the training stages. The learning rate is set to 0.00625. The weight in Equation 14 are set to " + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 1" + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\lambda_2 = 1" + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\lambda_3 = 1" + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\lambda_4 = 1" + }, + { + "bbox": [ + 313, + 269, + 555, + 318 + ], + "type": "text", + "content": ". For a fair comparison, all comparison models are re-trained on the same dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 323, + 427, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 427, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 427, + 335 + ], + "type": "text", + "content": "4.3. Evaluation Metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 340, + 554, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 340, + 554, + 364 + ], + "spans": [ + { + "bbox": [ + 313, + 340, + 554, + 364 + ], + "type": "text", + "content": "We employ diverse metrics to comprehensively evaluate the model's performance in the movie dubbing task:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 364, + 554, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 554, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 554, + 424 + ], + "type": "text", + "content": "MCD-DTW & MCD-DTW-SL. The Mel Cepstral Distortion Dynamic Time Warping (MCD-DTW) metric and its variant MCD-DTW-SL which adjusts the weights based on duration measure the distance between the generated dubbing and the ground truth following [5]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 424, + 554, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 424, + 554, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 424, + 554, + 460 + ], + "type": "text", + "content": "SECS. The speaker encoder cosine similarity (SECS) evaluates the similarity of speaker voice between the generated dubbing and the reference audio following [2, 3]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "text", + "content": "WER. The Word Error Rate (WER) " + }, + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "inline_equation", + "content": "{}^{1}" + }, + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "text", + "content": " assesses the model's pronunciation accuracy by using an advanced ASR model " + }, + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "inline_equation", + "content": "{\\text{Whisper}}^{2}\\left\\lbrack {34}\\right\\rbrack" + }, + { + "bbox": [ + 313, + 460, + 554, + 508 + ], + "type": "text", + "content": " to transcribe the generated dubbing into text and compare it with the original dubbing script." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 508, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 508, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 508, + 554, + 544 + ], + "type": "text", + "content": "UT-MOS. UT-MOS [37] is a speech mean opinion score (MOS) predictor to measure the acoustic quality and naturalness of the generated dubbing following [18, 49]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 544, + 554, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 554, + 603 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 554, + 603 + ], + "type": "text", + "content": "EMO-ACC. Emotion accuracy uses an emotion classifier to determine whether the emotion of the generated dubbing aligns with the ground truth labels following [8]. Note that this metric is only applicable to the V2C-Animation dataset, as the GRID dataset does not include emotion labels." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 603, + 554, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 554, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 554, + 688 + ], + "type": "text", + "content": "MOS-N & MOS-S. MOS-Naturalness (MOS-N) and MOS-Similarity (MOS-S) are mean option scores reported with a " + }, + { + "bbox": [ + 313, + 603, + 554, + 688 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 313, + 603, + 554, + 688 + ], + "type": "text", + "content": " confidence interval based on ratings from 20 native English speakers using a scale from 1 to 5. Each participant is required to listen to 30 randomly selected generated dubbing and rate the dubbing according to the speech naturalness and voice similarity following [49]." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 324, + 693, + 424, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 693, + 424, + 703 + ], + "spans": [ + { + "bbox": [ + 324, + 693, + 424, + 703 + ], + "type": "text", + "content": "1 https://github.com/jitsi/jiwer" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 324, + 703, + 471, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 703, + 471, + 713 + ], + "spans": [ + { + "bbox": [ + 324, + 703, + 471, + 713 + ], + "type": "text", + "content": "2https://huggingface.co/openai/whisper-large" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "text", + "content": "177" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 85, + 553, + 232 + ], + "blocks": [ + { + "bbox": [ + 235, + 71, + 374, + 81 + ], + "lines": [ + { + "bbox": [ + 235, + 71, + 374, + 81 + ], + "spans": [ + { + "bbox": [ + 235, + 71, + 374, + 81 + ], + "type": "text", + "content": "Table 2. Results on GRID benchmark." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 85, + 553, + 232 + ], + "lines": [ + { + "bbox": [ + 58, + 85, + 553, + 232 + ], + "spans": [ + { + "bbox": [ + 58, + 85, + 553, + 232 + ], + "type": "table", + "html": "
SettingDub 1.0Dub 2.0
MethodsT-SSECS (%) ↑WER (%) ↓UT-MOS ↑MCD-DTW ↓MCD-DTW-SL ↓SECS (%) ↑WER (%) ↓UT-MOS ↑
GT-100.0022.413.940.000.00100.0022.553.94
GT Mel + Vocoder-97.5721.413.574.104.1597.5721.413.57
StyleSpeech* [30]X91.0624.833.715.875.9882.5721.423.57
Zero-shot TTS* [57]X86.5419.133.605.715.9972.9119.353.62
V2C-Net [5]X80.9847.822.416.797.2375.9249.092.40
HPMDubbing [6]X85.1145.512.146.496.7861.3244.152.11
Face-TTS [24]X82.9744.372.537.448.1678.2439.152.48
StyleDubber [8]X93.7918.883.735.615.6986.6719.583.71
StyleSpeech* [30]✓91.4219.633.735.775.8983.7322.383.66
V2C-Net [5]✓89.7519.043.705.796.0680.1119.923.64
Ours✓89.0318.603.875.605.6381.7219.173.86
", + "image_path": "3ba77f4848d022bfcc163f9a1a45648b3fceebbcfeb508ecba56c82a832fccf7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 58, + 263, + 294, + 376 + ], + "blocks": [ + { + "bbox": [ + 56, + 238, + 294, + 259 + ], + "lines": [ + { + "bbox": [ + 56, + 238, + 294, + 259 + ], + "spans": [ + { + "bbox": [ + 56, + 238, + 294, + 259 + ], + "type": "text", + "content": "Table 3. Subjective evaluation on V2C-Animation and GRID benchmarks." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 263, + 294, + 376 + ], + "lines": [ + { + "bbox": [ + 58, + 263, + 294, + 376 + ], + "spans": [ + { + "bbox": [ + 58, + 263, + 294, + 376 + ], + "type": "table", + "html": "
DatasetV2C-AnimationGRID
MethodsMOS-N ↑MOS-S ↑CMOS ↑MOS-N ↑MOS-S ↑CMOS ↑
GT4.52±0.13-+0.194.69±0.07-+0.10
GT Mel + Vocoder4.39±0.164.41±0.18+0.174.66±0.084.53±0.10+0.11
StyleSpeech* [30]3.31±0.213.35±0.12-0.253.50±0.103.58±0.11-0.29
Zero-shot TTS* [57]3.40±0.123.47±0.18-0.293.58±0.213.52±0.15-0.26
V2C-Net [5]3.54±0.163.51±0.18-0.243.62±0.063.67±0.11-0.22
HPMDubbing [6]3.57±0.173.54±0.12-0.243.77±0.203.74±0.13-0.19
Face-TTS [24]3.18±0.133.24±0.16-0.373.39±0.213.32±0.17-0.32
StyleDubber [8]3.88±0.143.90±0.14-0.154.02±0.114.06±0.05-0.09
StyleSpeech* [30]3.31±0.213.35±0.12-0.203.50±0.103.58±0.11-0.23
V2C-Net [5]3.54±0.163.51±0.18-0.213.62±0.063.67±0.11-0.17
Speaker2Dubber [54]3.92±0.193.87±0.14-0.104.10±0.094.05±0.11-0.16
Ours4.03±0.123.99±0.080.004.12±0.074.07±0.100.00
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MethodT-SSECS(%) ↑WER(%) ↓UT-MOS ↑CMOS ↑
StyleSpeech* [30]X58.71105.641.91-0.21
Zero-shot TTS* [57]X61.1235.102.13-0.23
V2C-Net [5]X41.8638.721.99-0.19
HPMDubbing [6]X49.31106.451.35-0.21
FaceTTS [24]X33.80231.631.31-0.35
StyleDubber [8]X71.5213.452.51-0.09
StyleSpeech* [30]✓61.0121.512.72-0.18
V2C-Net [5]✓52.5320.842.96-0.17
Speaker2Dubber [54]✓73.4416.053.08-0.12
Ours✓75.959.853.630.0
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Comparison with SOTA" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 590, + 251, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 590, + 251, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 590, + 251, + 601 + ], + "type": "text", + "content": "4.4.1. Results on V2C-Animation Benchmark" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "As shown in Table 1, our proposed method outperforms the current state-of-the-art models and achieves the best performance across the majority of metrics. Our method achieves the best pronunciation accuracy in both dubbing settings, surpasses all others including two-stage methods using the same pre-training strategy following [54]. In terms of acoustic quality, due to the impact of inherent background noise in the movie dubbing dataset, other methods do not perform well in this aspect even with the pre-trained" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 239, + 553, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 553, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 553, + 359 + ], + "type": "text", + "content": "phoneme encoder. However, our proposed method achieves a score improvement of 0.73-1.86 on the UT-MOS metric, bringing a significant improvement in the acoustic quality of generated dubbing. Concurrently, our model achieves the lowest MCD-DTW and MCD-DTW-SL, indicating that the generated dubbing exhibits the smallest discrepancy and the best duration alignment with the real dubbing. The best dubbing emotion accuracy rate which outperforms the current state-of-the-art models with a " + }, + { + "bbox": [ + 313, + 239, + 553, + 359 + ], + "type": "inline_equation", + "content": "+2.58\\%" + }, + { + "bbox": [ + 313, + 239, + 553, + 359 + ], + "type": "text", + "content": " margin indicating the best prosody alignment performance of our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 360, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 555, + 431 + ], + "type": "text", + "content": "Although we fall short in voice similarity compared to StyleDubber [8], which learns fine-grained speaker styles, our method attains the highest score in MOS-S in subjective evaluation. Additionally, our proposed method also achieves the highest scores in MOS-N and CMOS, indicating the best overall dubbing quality and alignment." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 437, + 468, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 468, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 468, + 448 + ], + "type": "text", + "content": "4.4.2. Results on GRID Benchmark" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 453, + 554, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 554, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 554, + 584 + ], + "type": "text", + "content": "Since the dubbing in the GRID benchmark is closer to traditional speech, the gap between different models is not as significant as in the V2C-Animation benchmark. Nevertheless, as shown in Table 2, we still achieve state-of-the-art performance in pronunciation clarity, speech quality, and discrepancy from ground truth in both dubbing settings while maintaining advanced voice similarity. Moreover, our model also outperforms other state-of-the-art models in subjective evaluation scores on the GRID benchmark, demonstrating the effectiveness of our method across diverse dubbing benchmarks and scenarios." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 590, + 451, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 451, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 451, + 601 + ], + "type": "text", + "content": "4.4.3. Results on Zero-shot Test" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 605, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 689 + ], + "type": "text", + "content": "In addition to dubbing benchmarks, we also conduct the zero-shot test to evaluate the generalization performance of models. We use audio from the GRID dataset (which is out of domain) as reference audio to dub movie clips from the V2C-Animation dataset. Due to the absence of corresponding ground truth, we only calculate WER, UT-MOS, and SECS for objective evaluation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "As shown in Table 4, our proposed method surpasses the current state-of-the-art models and achieves the best per" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "178" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 89, + 105 + ], + 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The visualization of the mel-spectrograms of ground truth and synthesized dubbing by different models. The red and white bounding boxes highlight regions where different models exhibit significant differences in audio quality and pronunciation details." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 93, + 118, + 200, + 156 + ], + "blocks": [ + { + "bbox": [ + 93, + 118, + 200, + 156 + ], + "lines": [ + { + "bbox": [ + 93, + 118, + 200, + 156 + ], + "spans": [ + { + "bbox": [ + 93, + 118, + 200, + 156 + ], + "type": "image", + "image_path": "bb3e72b22cce34c961463ce09db2f7caf1c0aa4fe7b7a37b9ae417ac34c15f1d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 120, + 156, + 167, + 164 + ], + "lines": [ + { + "bbox": [ + 120, + 156, + 167, + 164 + ], + "spans": [ + { + "bbox": [ + 120, + 156, + 167, + 164 + ], + "type": "text", + "content": "Speaker2Dubber" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 202, + 118, + 311, + 156 + ], + "blocks": [ + { + "bbox": [ + 202, + 118, + 311, + 156 + ], + "lines": [ + { + "bbox": [ + 202, + 118, + 311, + 156 + ], + "spans": [ + { + "bbox": [ + 202, + 118, + 311, + 156 + ], + "type": "image", + "image_path": "5f50f382c54f57cfe56ed547a83b4160478b404f17505469bd13a25ad46b7f72.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 156, + 274, + 163 + ], + "lines": [ + { + "bbox": [ + 238, + 156, + 274, + 163 + ], + "spans": [ + { + "bbox": [ + 238, + 156, + 274, + 163 + ], + "type": "text", + "content": "StyleDubber" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 313, + 118, + 345, + 152 + ], + "blocks": [ + { + "bbox": [ + 313, + 118, + 345, + 152 + ], + "lines": [ + { + "bbox": [ + 313, + 118, + 345, + 152 + ], + "spans": [ + { + "bbox": [ + 313, + 118, + 345, + 152 + ], + "type": "image", + "image_path": "742caadba741477b9765b51601d206bb868b00f93174290e4663cd32b2ff9f58.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 345, + 117, + 447, + 156 + ], + "blocks": [ + { + "bbox": [ + 345, + 117, + 447, + 156 + ], + "lines": [ + { + "bbox": [ + 345, + 117, + 447, + 156 + ], + "spans": [ + { + "bbox": [ + 345, + 117, + 447, + 156 + ], + "type": "image", + "image_path": "b4afe7905f3fd1edc6956ac40586aa4824d903beb7b393344525c5efab6794c0.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 376, + 156, + 424, + 163 + ], + "lines": [ + { + "bbox": [ + 376, + 156, + 424, + 163 + ], + "spans": [ + { + "bbox": [ + 376, + 156, + 424, + 163 + ], + "type": "text", + "content": "Speaker2Dubber" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 449, + 118, + 552, + 156 + ], + "blocks": [ + { + "bbox": [ + 449, + 118, + 552, + 156 + ], + "lines": [ + { + "bbox": [ + 449, + 118, + 552, + 156 + ], + "spans": [ + { + "bbox": [ + 449, + 118, + 552, + 156 + ], + "type": "image", + "image_path": "8f65cca7cc2565836c39419a02e28361f9f2ce0a7db0b56d2c8b3362f29a8c1c.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 156, + 520, + 163 + ], + "lines": [ + { + "bbox": [ + 484, + 156, + 520, + 163 + ], + "spans": [ + { + "bbox": [ + 484, + 156, + 520, + 163 + ], + "type": "text", + "content": "StyleDubber" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 57, + 203, + 296, + 277 + ], + "blocks": [ + { + "bbox": [ + 113, + 194, + 237, + 203 + ], + "lines": [ + { + "bbox": [ + 113, + 194, + 237, + 203 + ], + "spans": [ + { + "bbox": [ + 113, + 194, + 237, + 203 + ], + "type": "text", + "content": "Table 5. Results of ablation study" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 203, + 296, + 277 + ], + "lines": [ + { + "bbox": [ + 57, + 203, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 57, + 203, + 296, + 277 + ], + "type": "table", + "html": "
#MethodWER ↓UT-MOS ↑EMO-ACC ↑MCD-DTW ↓MCD-DTW-SL ↓
-GT22.552.2699.960.000.00
-GT Mel+ Vocoder24.402.1897.093.773.80
1w/o AP21.452.3845.209.789.83
2w/o PE9.843.0946.129.359.38
3w/o IDEA8.383.0747.639.499.52
4w/o PSD10.633.0547.069.619.64
5w/o PTBE8.632.6046.089.849.87
6Full Model8.043.1048.939.299.32
", + "image_path": "a09ef4cdb419618b97984f1010ca4a95cba2c4fdc988351834d1dc821a3c327a.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 55, + 281, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 376 + ], + "type": "text", + "content": "formance across all metrics. Specifically, our proposed method still ensures accurate pronunciation and the best acoustic quality of the generated dubbing when facing out-of-domain reference audio. In terms of voice similarity, our model achieves the best cloning effect in both objective and subjective evaluations. The zero-shot experimental results substantiate the superiority of the generalization performance of our proposed method." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 55, + 384, + 173, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 173, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 173, + 396 + ], + "type": "text", + "content": "4.5. Qualitative Analysis" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 54, + 401, + 296, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 401, + 296, + 582 + ], + "spans": [ + { + "bbox": [ + 54, + 401, + 296, + 582 + ], + "type": "text", + "content": "We visualize the mel-spectrograms of ground truth and dubbing generated by different models for comparison in Figure 3. (More visualization results are presented in the Appendix.) The red bounding boxes represent regions where different models exhibit significant differences in audio quality and the white regions present the difference in pronunciation details. Through the observation of the red bounding box, it is evident that our method exhibits less noise in the non-pronunciation intervals of dubbing compared to other models, indicating better acoustic quality. Additionally, the clearer spectrum lines in the white bounding box and the closer resemblance to the ground truth in terms of prosody (the shape of spectrum lines) show that our method also achieves better pronunciation quality and prosody alignment performance." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 55, + 588, + 156, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 588, + 156, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 588, + 156, + 600 + ], + "type": "text", + "content": "4.6. Ablation Studies" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 55, + 605, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 641 + ], + "type": "text", + "content": "To further investigate the specific effects of each module in our proposed method, we conduct ablation studies on the Dub 1.0 setting of the V2C-Animation benchmark." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": "Effectiveness of Acoustic Pre-training (AP). As shown in Row 1 of Table 5, acoustic pre-training significantly improves the acoustic quality and pronunciation accuracy. It noticeably enhances the model's performance on the UTMOS and WER. The clearer pronunciation and speech quality are also reflected in the improvement of dubbing accu" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 194, + 521, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 521, + 206 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 521, + 206 + ], + "type": "text", + "content": "racy indicated by MCD-DTW and MCD-DTW-SL." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 207, + 554, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 207, + 554, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 554, + 291 + ], + "type": "text", + "content": "Effectiveness of Prosody Enhancement (PE). Row 2 of Table 5 shows that the prosody enhancement strategy can reduce the difference between the generated dubbing and the ground truth, enhancing the model's performance on the MCD-DTW and MCD-DTW-SL metrics. The results demonstrate it improves the model's acoustic modeling capability in handling complex prosody variations." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 291, + 554, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 291, + 554, + 374 + ], + "spans": [ + { + "bbox": [ + 313, + 291, + 554, + 374 + ], + "type": "text", + "content": "Effectiveness of In-Domain Emotion Analysis (IDEA). As shown in Row 3 of Table 5, the IDEA module provides a more stable and accurate alignment between the emotion of characters and the dubbing prosody, enhancing performance on emotion accuracy. The better prosody alignment brought by IDEA also reduces the discrepancy between the generated dubbing with ground truth." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 375, + 554, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 375, + 554, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 375, + 554, + 567 + ], + "type": "text", + "content": "Effectiveness of Prosodic Style Diffusion (PSD). The modeling of prosodic style features allows the model to focus on non-timbre prosodic characteristics during the prosody adapting stage, improving the overall dubbing accuracy as shown in Row 4 of Table 5. Additionally, the disentangled design on prosodic style also enhances the model's performance in acoustic and pronunciation quality. Effectiveness of Prosodic Text BERT Encoder (PTBE). Compared to previous works that use a single text encoder output feature for both acoustic and prosodic modeling, the introduction of the Prosodic Text BERT Encoder brings disentangled text prosodic features. This approach not only enhances the quality of text prosodic modeling but also ensures the acoustic quality of the generated dubbing. As shown in Row 5 of Table 5, the PTBE module significantly improves the dubbing accuracy and the acoustic quality." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "spans": [ + { + "bbox": [ + 314, + 573, + 388, + 586 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "In this work, we propose a method with a prosody-enhanced acoustic pre-training stage and an acoustic-disentangled prosody adapting stage to generate high-quality movie dubbing with aligned prosody. The first stage equips the model with the acoustic modeling capability to handle complex dubbing prosody. The second stage employs a disentangled prosody adapting framework to bridge character performances with dubbing prosody while maintaining the acoustic quality. Extensive experimental results demonstrate the effectiveness of our proposed method." + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "179" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China: 62322211, 62336008, U21B2024, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (2024C01023, 2023C01046, 2023C01038), Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of Music), Ministry of Culture and Tourism (2023DMKLB004). 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In *Interspeech* 2022, 23rd Annual Conference of the International Speech Communication Association, Incheon, Korea, 18-22 September 2022, pages 2573-2577, 2022. 6, 7" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "182" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_content_list.json b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..50d38904aaed502f7745f530a16a7319c8248dac --- /dev/null +++ b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_content_list.json @@ -0,0 +1,1418 @@ +[ + { + "type": "text", + "text": "Protecting Your Video Content: Disrupting Automated Video-based LLM Annotations", + "text_level": 1, + "bbox": [ + 127, + 128, + 870, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haitong Liu $^{1*}$ , Kuofeng Gao $^{1*}$ , Yang Bai $^{2\\dagger}$ , Jinmin Li $^{1}$ , Jinxiao Shan $^{3}$ , Tao Dai $^{4\\dagger}$ , Shu-Tao Xia $^{1,5}$ $^{1}$ Tsinghua University $^{2}$ ByteDance $^{3}$ Digital Center, China Merchants Group Limited \n $^{4}$ Shenzhen University $^{5}$ Peng Cheng Laboratory", + "bbox": [ + 106, + 202, + 888, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{liuhaito24,gkf21,ljm22}@mails.tsinghua.edu.cn，baiyang0522@gmail.com", + "bbox": [ + 191, + 258, + 803, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shanjinxiao@cmhk.com, daitao.edu@gmail.com, xiast@sz.tsinghua.edu.cn", + "bbox": [ + 191, + 277, + 795, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 325, + 326, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, video-based large language models (video-based LLMs) have achieved impressive performance across various video comprehension tasks. However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content. Our code is available at https://github.com/ttthhl/Protecting_Your_Video_Content.", + "bbox": [ + 88, + 357, + 483, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 763, + 220, + 780 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed significant advancements in both video-based large language models (video-based LLMs) [18, 27, 35, 44-46] and text-to-video generation models [6, 16, 23, 26, 37]. These two types of models demonstrate a close relationship: text-to-video models", + "bbox": [ + 89, + 789, + 483, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c1d8f54acf8dac49e30dd18d5bdf7dc7efb7d061902fdb39f8d13a0537158b07.jpg", + "image_caption": [ + "Figure 1. We propose two strategies to protect the video content: Ramblings and Mutes. The Ramblings approach misleads videobased large language models into generating inaccurate captions. Besides, Mutes prompt these models to produce shorter and even NULL captions, lacking descriptive detail. The answers in the figure are excerpts." + ], + "image_footnote": [], + "bbox": [ + 524, + 325, + 895, + 501 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rely heavily on high-quality video-text pairs for fine-tuning, while video-based LLMs can enhance video-text pairs quality through advanced annotation capabilities. By leveraging the power of large language models [4, 14, 15, 36, 41], video-based LLMs have revolutionized video content interpretation and annotation. This advancement directly contributes to the improvement of video data annotation quality. However, alongside these technological advances, concerns about data safety and privacy [2, 8, 19-22, 40] have emerged. Given the vast amount of personal video content available on multimedia platforms, protecting this data from unauthorized annotation has become an urgent challenge that requires immediate attention. In this paper, we aim to protect personal videos from being unauthorizedly and automatically annotated by video-based LLMs. To tackle this significant and challenging issue, we propose two series of protective and imperceptible watermarks added to videos. In each scenario, we propose two methods in order to add", + "bbox": [ + 511, + 628, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 107, + 875, + 220, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 109, + 887, + 240, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24056", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "diversity and adaptability for widespread applications.", + "bbox": [ + 89, + 90, + 447, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we aim to mislead video-based LLMs into generating entirely incorrect annotations in the first scenario. To achieve this, we propose two methods, Rambling-F and Rambling-L, from different perspectives. Rambling-F operates at the feature level, increasing the discrepancy of video and LLM features. Rambling-L manipulates the logit-level by increasing the auto-regressive loss. These adversarial strategies serve to protect personal video content from unauthorized exploitation. Furthermore, fine-tuning text-to-video models on these adversarial video-text pairs will degrade the quality of generated videos.", + "bbox": [ + 88, + 108, + 480, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second scenario is designed to make the video-based LLMs effectively \"mute\", which means they are induced to generate shorter output on the given video. We also propose two methods, called Mute-S and Mute-N, relying on the probability of the End-of-Sequence (EOS) token, which, when generated, halts the LLM's inference process. Mute-S aims to cause the video-based LLMs to generate short and incomplete text sequences. For example, the generated text is \"The video is a\". Mute-N aims to return a NULL response by increasing the EOS probability of the first generated token. Overall, these methods can either fragment the sentences or result in a null output, preventing meaningful information from being leveraged by the video-based LLMs. These disruptions in the video-text pairs can then influence the text-to-video model's training and reduce your information leakage.", + "bbox": [ + 91, + 276, + 483, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our two scenarios are evaluated across three datasets and three different video-based LLMs, providing comprehensive validation of our methods' effectiveness and adaptability. The text output demonstrates that our Ramblings method can effectively induce the video-based LLMs to generate completely incorrect annotations for the videos, while our Mutes method successfully limits the model's output, reducing the amount of useful information generated. Additionally, we use the annotated video-text pairs to fine-tune a text-to-video model, and the results clearly show that the model's performance degrades by our watermarking methods. Finally, a series of ablation studies, including prompt transferability, further validate the effectiveness and robustness of our proposed methods.", + "bbox": [ + 91, + 520, + 483, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contribution can be outlined as follows:", + "bbox": [ + 107, + 732, + 480, + 747 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We investigate the security and privacy risks faced by video annotation with video-based LLMs. To address these risks, we introduce two series of novel video watermarks that prevent unauthorized automated annotation. And we emphasize that the video-text pairs' quality influenced by our watermarks is important for downstream tasks such as text-to-video models.", + "- Our two series of watermarking methodologies demonstrate distinct strategies for disrupting video-based LLMs: inducing either inaccurate or short captions. These" + ], + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "methodologies expand the scope of video privacy protection techniques and establish a foundation for developing robust defenses against unauthorized content analysis.", + "bbox": [ + 524, + 90, + 903, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Through extensive experiments, our methods have been proven to perform effectively across three state-of-the-art video-based LLMs, namely Video-ChatGPT [27], Video-LLaMA [46], and Video-Vicuna (change the backbone of Video-LLaMA), as well as three diverse datasets: OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. These demonstrate the robustness and generalization capability of our approach, showing its ability to adapt to various models and datasets while consistently preventing unauthorized video annotation.", + "bbox": [ + 511, + 136, + 906, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 301, + 653, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Video-based Large Language Models", + "text_level": 1, + "bbox": [ + 511, + 328, + 834, + 344 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recent advancements in video-based LLMs [18, 27, 35, 44-46] have significantly enhanced their capabilities in various video-related tasks [38, 47, 48]. These models, such as Video-ChatGPT [27] and Video-LLaMA [46], effectively leverage both spatial and temporal features from video data and the generation ability of LLMs, enabling them to achieve impressive zero-shot performance. The integration of the video modality into LLMs allows for visual context-aware interaction, surpassing the capabilities of existing LLMs. The impressive performance of these models has led to their widespread use in generating dense captions [44] for unannotated videos, which can be used subsequently in downstream tasks, such as text-to-video generation models [6, 16, 23, 26, 37]. However, the widespread use of video-based LLMs raises privacy concerns regarding the potential for the unauthorized annotation of personal videos. As these models become more prevalent, it is crucial to address the ethical implications involving sensitive or private video content. To address these issues, we propose protective video watermarking methods that can prevent personal video from unauthorized and automated annotation by video-based LLMs.", + "bbox": [ + 511, + 352, + 906, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Adversarial Attack", + "text_level": 1, + "bbox": [ + 511, + 695, + 696, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial attacks [1, 7, 9-13, 17, 19, 25, 39, 42, 50] typically craft imperceptible adversarial perturbations that can mislead the models into making incorrect predictions. With the development of multi-modal LLMs, researchers have begun exploring how these attacks can be applied in more complex generation settings. Concretely, recent studies show that adversarial attacks can be used to jailbreak multi-modal LLMs, causing them to generate harmful content [32] or induce targeted captions [49]. In contrast to these adversarial attacks, which aim to manipulate the model to an attacking goal, we adopt them as a pioneering watermarking strategy. It is designed to protect the privacy", + "bbox": [ + 511, + 719, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24057", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and security of video content within these models. Specifically, our watermarking approach is crafted to safeguard the video data against unauthorized annotation.", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 89, + 148, + 225, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 89, + 172, + 200, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To prevent unauthorized annotation by video-based LLMs, we propose two protective scenarios. First, video-based LLMs can be misled to generate inaccurate captions that significantly diverge the video content when provided with protected video input. Second, video-based LLMs are induced to generate shorter, less detailed captions compared to those generated from clean videos which means less information leakage. Fine-tuning text-to-video models on such video-text pairs can degrade the quality of generated videos, due to the low quality of video-text pairs. For each scenario, we propose to adopt imperceptible adversarial perturbations as watermarks to protect videos from unauthorized annotation.", + "bbox": [ + 89, + 196, + 483, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Threat Model", + "text_level": 1, + "bbox": [ + 89, + 400, + 233, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Goals and Capabilities. The goal is to craft an imperceptible adversarial perturbation as a protective watermark for the video, which can induce video-based LLMs to generate totally incorrect or shorter sequences during the victim model's deployment. Following the most commonly used constraint for the involved perturbation [5], it is restricted within a predefined magnitude in the $l_{p}$ norm, ensuring perturbation is difficult to detect.", + "bbox": [ + 89, + 422, + 483, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge and Background. Following previous works [13, 31], we assume that the victim video-based LLMs can be accessed in full knowledge, including architectures and parameters. Additionally, we consider a more challenging scenario where the victim video-based LLMs are inaccessible, as detailed in the Appendix.", + "bbox": [ + 89, + 544, + 483, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Problem Formulation", + "text_level": 1, + "bbox": [ + 89, + 642, + 294, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To safeguard the video from unauthorized annotation by video-based LLMs, we propose to craft adversarial perturbations that can be added to a sequence of frames from the original videos. Given an original video $\\pmb{x}$ and an adversarial video $\\pmb{x}'$ with a watermark, the optimization problem can be formulated as follows:", + "bbox": [ + 89, + 666, + 482, + 755 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\underset {\\boldsymbol {x} ^ {\\prime}} {\\arg \\max } \\mathcal {L} \\left(\\boldsymbol {x} ^ {\\prime}\\right), \\tag {1} \\\\ s. t. \\left| \\left| \\boldsymbol {x} ^ {\\prime} - \\boldsymbol {x} \\right| \\right| _ {\\infty} < \\epsilon , \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 760, + 482, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}(\\cdot)$ denotes the loss objective function to achieve different protective scenarios. To ensure the stealthiness of the adversarial perturbations, we introduce the $l_{\\infty}$ restriction within a value of $\\epsilon$ . For optimization, the projected gradient descent (PGD) algorithm [28] is adopted to update the adversarial perturbations at each iteration.", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Typically, when a video $\\mathbf{x}$ and an input prompt $c_{\\mathrm{in}}$ are provided as inputs to the video-based LLMs $\\mathcal{F}(\\cdot)$ , the video-based LLMs first utilize vision encoders $g(\\cdot)$ to extract visual features from the video. These extracted video features are then fed into the base LLMs $h(\\cdot)$ with $c_{\\mathrm{in}}$ as inputs, which generate the hidden states from its final layer. Finally, the hidden states are projected into the probability distribution of all generated tokens, which can obtain a sequence of generated output tokens. We denote $f_{i}(\\cdot)$ as the probability distribution after the Softmax $(\\cdot)$ layer over the $i$ -th generated token.", + "bbox": [ + 511, + 90, + 903, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.4. Ramblings for Incorrect Generation of Video-based LLMs", + "text_level": 1, + "bbox": [ + 511, + 265, + 903, + 295 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we optimize adversarial videos that can mislead video-based LLMs to generate incorrect captions. To achieve this goal, we develop two different methods for video watermarks from the feature level and the logit level of the video-based LLMs, dubbed Rambling-F and Rambling-L.", + "bbox": [ + 511, + 303, + 903, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rambling-F (Feature). To induce the video-based LLMs to generate incorrect captions, we propose a feature-level adversarial strategy called Rambling-F. The core idea behind this approach is to deviate the features of adversarial videos from the original ones in the latent representation space. During the inference stage, the video-based LLMs extract visual features from the input video and also generate LLM features from the combination of the input video and text queries. Hence, in the Rambling-F, we propose to increase the $l_{2}$ distance for both the video features and the LLM features between the original and adversarial videos. As a result, the disrupted features will result in the model's inability to accurately generate the captions correlated with the videos. The loss objective function for the Rambling-F can be formulated as follows:", + "bbox": [ + 511, + 393, + 905, + 619 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {v i d e o}} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left(g \\left(\\boldsymbol {x} ^ {\\prime}\\right) _ {i} - g (\\boldsymbol {x}) _ {i}\\right) ^ {2}, \\\\ \\mathcal {L} _ {L L M} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\left(h \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right) _ {j} - h \\left(\\boldsymbol {x}, c _ {\\text {i n}}\\right) _ {j}\\right) ^ {2}, \\tag {2} \\\\ \\mathcal {L} _ {R F} (\\pmb {x} ^ {\\prime}) = \\alpha * \\mathcal {L} _ {v i d e o} (\\pmb {x} ^ {\\prime}) + \\beta * \\mathcal {L} _ {L L M} (\\pmb {x} ^ {\\prime}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 625, + 903, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $n$ and $m$ are the total number of elements in the video and LLM features, respectively. In addition, $g(\\cdot)_i$ represents the $i$ -th dimension of video features and $h(\\cdot)_j$ represents the $j$ -th dimension of LLM features.", + "bbox": [ + 511, + 734, + 903, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rambling-L (Logit). In addition to the feature-level Rambling-F attack, we propose another adversarial strategy called Rambling-L, which manipulates the logit-level outputs, i.e., probability distributions over the generated tokens. Typically, based on the probability distribution over generated tokens, video-based LLMs can generate one token at one time in an auto-regressive manner to obtain the", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24058", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/78f8b76a772ce97e785971601170cf62712ad39cd6e21a83dbcf08aee8023590.jpg", + "image_caption": [ + "Text-to-video model" + ], + "image_footnote": [], + "bbox": [ + 99, + 108, + 488, + 378 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9c5258d5edd36eed731d4af266321e3c8b36083d323093da4bb724f829acde7f.jpg", + "image_caption": [ + "Figure 2. The pipeline of Ramblings and Mutes. While Rambling-F focuses on feature-level perturbations of the original content, Rambling-L increases auto-regressive loss to manipulate video-based LLMs into generating incorrect descriptions. Mutes, on the other hand, tend to increase the probability of the EOS token. Finally, these video-text pairs can influence downstream tasks, such as the capacity of text-to-video models fine-tuned on these data." + ], + "image_footnote": [], + "bbox": [ + 493, + 107, + 897, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "caption. Therefore, for the generation of incorrect captions, we can increase the distance between the adversarial video $\\pmb{x}^{\\prime}$ and the original ground-truth caption $y$ generated from the original video $\\pmb{x}$ by the auto-regressive loss $\\mathcal{L}_{ar}(\\cdot)$ . The loss objective function for the Rambling-L attack can be expressed as follows:", + "bbox": [ + 88, + 517, + 482, + 607 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R L} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), y\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 616, + 482, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By increasing Eq. (3), we can shift the model's token probability distribution away from the correct captions, causing the video-based LLMs to generate incorrect textual outputs.", + "bbox": [ + 89, + 642, + 483, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Mutes for Shorter even NULL Generation of Video-based LLMs", + "text_level": 1, + "bbox": [ + 89, + 696, + 483, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we craft adversarial videos that can induce video-based LLMs to generate shorter captions or even no captions at all, including Mute-S and Mute-N. To this end, we propose manipulating the probability of the End-of-Sequence (EOS) token of video-based LLMs for two protective goals.", + "bbox": [ + 89, + 734, + 482, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mute-S (Short Caption). During the auto-regressive generation process of video-based LLMs, the occurrence of an End-of-Sequence (EOS) token serves as a signal to stop generating further tokens. To decrease the length of generated sequences, one straightforward approach is to in", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "duce the occurrence of the EOS token during the prediction process. However, the auto-regressive prediction is a non-deterministic random process [13], making it challenging to directly determine the exact position where the EOS token is generated. To address this challenge, we propose Mute-S, which aims to increase the probability of the EOS token at all positions of generated sequences $y_{\\mathrm{out}}$ . The loss function can be formulated as follows:", + "bbox": [ + 511, + 517, + 906, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M S} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} f _ {i} ^ {\\mathrm {E O S}} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}} \\oplus y _ {\\text {o u t}}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 648, + 906, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{i}^{\\mathrm{EOS}}(\\cdot)$ is EOS token probability of the probability distribution after the Softmax(\\cdot) layer over the $i$ -th generated token and $N$ is the length of generated sequences $y_{\\mathrm{out}}$ . Note that $y_{\\mathrm{out}}$ is updated at each iteration during the optimization. By increasing Eq. (4), Mute-S can effectively manipulate video-based LLMs to terminate the caption generation process in advance, resulting in shorter and potentially less informative captions.", + "bbox": [ + 511, + 702, + 906, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mute-N (NULL Caption). Considering a more extreme case, we can directly induce video-based LLMs to become highly confident in predicting the EOS token as the very first token during generation, resulting in generating NULL or empty captions. To this end, we propose Mute-N, which", + "bbox": [ + 511, + 825, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24059", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "increases the probability of the EOS token at the first predicted token position, rather than optimizing the mean probability of the EOS token across generated sequences as Mute-S. Given the auto-regressive generation process of video-based LLMs, we can force video-based LLMs to approach the EOS token in an auto-regressive manner. The loss function for Mute-N can be formulated as follows:", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M N} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = - \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), [ \\mathrm {E O S} ]\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 208, + 482, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{ar}(\\cdot)$ denotes the auto-regressive loss function and [EOS] is the EOS token. By optimizing Eq. (5), we can fool the video-based LLMs into generating the EOS token at the beginning, causing the generation process of video-based LLMs to halt immediately.", + "bbox": [ + 89, + 234, + 483, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 89, + 324, + 215, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 348, + 307, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Models and Datasets. We elaborately select three state-of-the-art video-based LLMs as annotation models: VideoChatGPT [27], Video-LLaMA [46], and Video-Vicuna (a variant of Video-LLaMA with a modified backbone). The default inference prompt template is used to obtain video annotations, with the user input prompt set to \"What is this video about?\" Detailed settings for these models are available in the Appendix. For datasets, we use data from OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. They are all high-quality collections of videos paired with corresponding captions. By calculating similarity with the dataset captions, we can evaluate the performance of the annotations. To accommodate the limited memory of GPUs, each video is preprocessed to consist of 8 frames.", + "bbox": [ + 89, + 372, + 482, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines and Setups. We use original videos and videos added with random perturbations as baselines. For the setup, the perturbation magnitude is set to 16/255 using the $l_{\\infty}$ norm to make the perturbation imperceptible, and the optimization step size is set to 1/255, using the projected gradient descent (PGD) algorithm [28]. The optimization iteration is set to 200 for Ramblings and 500 for Mutes, respectively. For video-based LLM configurations, we set a sampling temperature of 0.2 and limit the output to a maximum of 512 tokens for three models and the others are default. Additional setup details are provided in the Appendix.", + "bbox": [ + 89, + 584, + 482, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. For the evaluation of Ramblings, we employ two metrics: CLIP score (RN101) and BLEU. CLIP score [33] measures the similarity between the model's post-attack inferences and the original dataset captions, with a higher score indicating greater similarity and better annotation performance. BLEU [30] assesses the alignment between the model's outputs and reference texts, where a higher BLEU indicates a closer match and improved annotation performance. Our adversarial objective is to reduce these scores.", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the evaluation of Mutes, we use two metrics: length and EOS rate (NULL caption rate). We compare the lengths of outputs generated from clean and adversarial videos to assess the effectiveness of the Mutes approach. A shorter length indicates less information leakage from the videos. The EOS rate measures how often video-based LLMs output the EOS token early, signifying that no information is leaked from the videos. A higher EOS rate means video-based LLMs output NULL captions more frequently.", + "bbox": [ + 511, + 90, + 903, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 511, + 237, + 651, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Tab. 1, the CLIP score and BLEU are similar between original videos and those with random noise across three models, indicating that random noise does not reduce annotation performance and is therefore ineffective at protecting videos from unauthorized annotation. In contrast, the evaluation scores for Ramblings in Tab. 1 show a substantial decrease compared to the baselines, indicating significant alterations in the semantic information generated by the video-based LLMs. These results demonstrate that adversarial attack on the feature level or logit level effectively misleads the models into generating incorrect annotations for the videos. And our two methods offer great adaptability and flexibility to accommodate various circumstances.", + "bbox": [ + 511, + 261, + 903, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Tab. 2, the videos with random noise are ineffective in protecting video content compared to the original videos, as the output length is high and the EOS rate is zero, indicating that a gradient optimization algorithm is necessary to achieve meaningful perturbation. In contrast, our Mute-S effectively disrupts sentence integrity, for example, video-based LLMs may output fragmented text such as \"The video is a\" without forming a coherent description. Further examples are provided in the Appendix. Specifically, for Video-LLaMA, Mute-S reduces text length nearly tenfold, with the EOS rate around $10\\%$ . Additionally, our Mute-S significantly reduces the length of generated texts while maintaining a relatively low EOS rate, representing an untargeted attack strategy. Meanwhile, our Mute-N successfully prompts the model to output NULL captions, meaning that video-based LLMs extract no information from the videos, achieving a targeted attack. This analysis underscores the exceptional effectiveness of both Mute-S and Mute-N, resulting in minimal information being extracted by video-based LLMs and ultimately protecting videos from unauthorized and automated annotation.", + "bbox": [ + 511, + 458, + 903, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Influence on Downstream Work: Text-to-video Models", + "text_level": 1, + "bbox": [ + 511, + 786, + 903, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further demonstrate the impact of our watermarking methods on downstream tasks, we fine-tune text-to-video models using our annotated video-text pairs. After finetuning, we evaluate the model's performance on established benchmarks to demonstrate that our protective watermark", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24060", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/86f970d2f3cf05d588c627afada8e9aeb7caef8551d131513976f912d52dbe2f.jpg", + "table_caption": [ + "Table 1. The CLIP score and BLEU between texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna, and clean captions in datasets are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Video-ChatGPTOriginal0.762210.017030.673830.024050.609380.01040
Noise0.757810.013980.675290.026710.613770.01123
Rambling-F0.667970.011970.603520.015610.495610.00514
Rambling-L0.627440.002710.603030.003500.483150.00169
Video-LLaMAOriginal0.787600.051210.623540.004820.608890.00316
Noise0.799800.047610.622560.004720.601560.00292
Rambling-F0.583010.016000.492920.003500.428960.00205
Rambling-L0.609380.020680.492190.003130.433840.00189
Video-VicunaOriginal0.757320.019690.621580.026040.601070.01332
Noise0.763670.022750.617680.022110.601070.01435
Rambling-F0.625000.023170.507320.007840.423100.00363
Rambling-L0.635250.016440.501950.009080.441890.00449
", + "bbox": [ + 91, + 131, + 906, + 371 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f6bff26203268d2b76106900f5851359d588289d46bc6ab0900975220696bb4c.jpg", + "table_caption": [ + "Table 2. The length and EOS rate of texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Video-ChatGPTOriginal30.470.030.290.031.210.0
Noise30.200.031.240.024.280.0
Mute-S13.6011.012.2813.011.3921.0
Mute-N0.00100.00.00100.00.00100.0
Video-LLaMAOriginal203.540.0208.620.0214.490.0
Noise224.230.0213.470.0209.300.0
Mute-S11.587.017.2813.037.749.0
Mute-N0.00100.00.00100.00.00100.0
Video-VicunaOriginal32.900.046.540.028.640.0
Noise38.270.040.080.034.370.0
Mute-S7.381.06.450.05.560.0
Mute-N0.00100.00.00100.00.00100.0
", + "bbox": [ + 91, + 412, + 906, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing methods can significantly degrade the model's ability to generate high-quality videos.", + "bbox": [ + 89, + 676, + 482, + 707 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiment Setups. The text-to-video framework we used isAnimateDiff [16], which is based on diffusion model [34]. The dataset we used to fine-tune the text-to-video model consists of video-text pairs annotated by Video-LLaMA based on OpenVid-1M. We follow theAnimateDiff training script. The pre-trained model used is stable-diffusion-v1-51. For image fine-tuning in theAnimateDiff pipeline, the learning rate and training steps are set to $2 \\times 10^{-6}$ and 500, respectively. During the training process of the motion module in theAnimateDiff pipeline, we set the learning rate to $5 \\times 10^{-5}$ and the training steps", + "bbox": [ + 89, + 707, + 482, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to 10,000. For text-to-video generation, we set the guidance scale as 8 and the steps as 25. To evaluate conveniently, we still use stable-diffusion-v1-5 as the base model.", + "bbox": [ + 511, + 676, + 906, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. For the evaluation of the text-to-video models, we use two metrics: $\\mathrm{VQA}_{\\mathrm{A}}$ and $\\mathrm{VQAT}_{\\mathrm{T}}$ . We adopt these metrics from EvalCrafter [24] as benchmarks to evaluate the performance of text-to-video models fine-tuned on videos with annotations generated by video-based LLMs. Specifically, $\\mathrm{VQA}_{\\mathrm{A}}$ measures the aesthetic quality of generated videos, while $\\mathrm{VQAT}_{\\mathrm{T}}$ assesses technical quality. Higher $\\mathrm{VQA}_{\\mathrm{A}}$ and $\\mathrm{VQAT}_{\\mathrm{T}}$ indicate better quality of the generated videos by text-to-video models.", + "bbox": [ + 511, + 727, + 908, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. As illustrated in Tab. 5, the $\\mathrm{VQA_A}$ and $\\mathrm{VQAT}_{\\mathrm{T}}$ [24] decrease whenAnimateDiff is fine-tuned using adversar", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1 https://huggingface.co/stable-diffusion-v1-5/stable-diffusion-v1-5", + "bbox": [ + 107, + 886, + 462, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24061", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/32941edf2c34643115e750b805e09a358672108edfe033acceae939389712ae9.jpg", + "table_caption": [ + "Table 3. Prompt transferability: The CLIP score and BLEU between texts annotated by Video-LLaMA and clean captions are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts:\"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Original0.787600.051210.793460.044110.767580.03146
Noise0.799800.047610.796880.040810.771970.03459
Rambling-F0.583010.016000.600100.015850.606450.01514
Rambling-L0.609380.020680.612790.019420.625000.01828
", + "bbox": [ + 91, + 146, + 911, + 266 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bc31f32a54d7d2a869d414b58b1c245bdea5a1c2e53e2839f400c290f7111d63.jpg", + "table_caption": [ + "Table 4. Prompt transferability: The length and EOS rate of texts annotated by Video-LLaMA are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts: \"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Original203.540.0221.310.0299.120.0
Noise224.230.0236.850.0300.920.0
Mute-S11.587.024.165.036.4410.0
Mute-N0.00100.064.0473.0230.7419.0
", + "bbox": [ + 91, + 335, + 911, + 455 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53d1ef5b94e1f692697fc81e4d14b91df3199827d89c05d2fbc21e186322ff5a.jpg", + "table_caption": [ + "Table 5. The VQA and VQAT are evaluated forAnimateDiff fine-tuned on different adversarial video-text pairs. All the video-text pairs are annotated by Video-LLaMA on the OpenVid-1M dataset. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodVQAAVQAT
Original60.43051.302
Noise46.71835.392
Rambling-F39.38328.231
Rambling-L38.04227.394
Mute-S43.61024.487
Mute-N43.46831.009
", + "bbox": [ + 148, + 546, + 423, + 669 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ial video-text pairs compared to those with original or randomly perturbed video-text pairs. This notable reduction demonstrates that the quality of text-to-video models degrades significantly by our watermarking methods.", + "bbox": [ + 89, + 696, + 483, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 768, + 254, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transferability. Video-based LLMs generate corresponding responses according to different user prompts. In this section, we conduct the transferability experiments [25] to assess whether adversarial watermarks can protect videos from unauthorized annotation under varying user inference prompts. In this experiment, we adopt the inference prompts: \"What is this video about?\", \"What happens in", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the video?”, and “Can you describe the video in detail?”", + "bbox": [ + 511, + 479, + 883, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 3, changing the inference prompt still results in a significant reduction in both CLIP score and BLEU when using our Ramblings method, indicating that Rambling-F and Rambling-L effectively protect videos from unauthorized annotation across varied prompts. Similarly, as shown in Tab. 4, even with differing inference prompts, Mute-S and Mute-N significantly reduce the length of generated texts, preventing information leakage from the videos. Additionally, the EOS rate remains high, suggesting that Mute-N leads video-based LLMs to produce null captions. Notably, when the inference prompt differs from the prompt used during the attack phase, Mute-N shows a certain degree of performance reduction against Video-LLaMA. We speculate this may be due to Mute-N's focus on the EOS probability of a single token, potentially reducing its stability across different inference prompts. So, we introduce Mute-N2 in the Appendix to enhance its performance. These findings further emphasize the necessity of using both Mute-S and Mute-N, as Mute-S remains stable under different circumstances, while Mute-N performs optimally when the inference prompt matches the one used during the attack phase. Overall, the experiments above demonstrate that our methods have a certain degree of prompt transferability.", + "bbox": [ + 511, + 502, + 906, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on Rambling-F. Our Rambling-F integrates both $\\mathcal{L}_{video}$ and $\\mathcal{L}_{LLM}$ . To thoroughly evaluate the", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24062", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e48b43bb5f65a06ff8569742c9aa34e1ed7a70ce924409c7af81424bf93833bc.jpg", + "image_caption": [ + "Figure 3. Comparison of CLIP score (left) and BLEU (right) on Rambling-F to evaluate different parameters' influence. When the parameter is too small, the CLIP score and BLEU are high, indicating poor protective performance. Meanwhile, the evaluation scores decrease under $\\alpha = 1$ , $\\beta = 1$ compared to $\\alpha = 1$ , $\\beta = 0$ or $\\alpha = 0$ , $\\beta = 1$ , suggesting that the combination of feature losses is effective and necessary. All the videos are annotated by VideoLLaMA on the OpenVid-1M dataset. $\\alpha = 0$ , $\\beta = 0$ represents original video." + ], + "image_footnote": [], + "bbox": [ + 109, + 93, + 287, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd0a667231aa79bdddaaa88ee04a66b6a9d4219066716424630050b66b8d68e0.jpg", + "image_caption": [ + "Figure 4. CLIP score about Ramblings on different perturbation magnitudes. When the perturbation magnitude is small, the CLIP score is higher, indicating poor protective performance for the videos. With the increase of perturbation magnitude, the protective performance of Ramblings is better." + ], + "image_footnote": [], + "bbox": [ + 300, + 93, + 478, + 218 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "individual and combined impact of each feature loss, we conduct a parameter experiment to explore the influence of $\\alpha$ and $\\beta$ in Eq. (2). As outlined in Fig. 3, the combination of $\\alpha = 1, \\beta = 1$ outperforms the combination of $\\alpha = 1, \\beta = 0$ or $\\alpha = 0, \\beta = 1$ which means that it is effective to add these features together to get better protective performance. Additionally, larger values for these parameters generally lead to better performance in reducing annotation quality. However, when increased to a certain extent, the performance does not show improvement even reduction. These findings highlight the synergy between the two feature losses, suggesting that their integration enhances the method's ability to strengthen adversarial attacks and more effectively protect video content. And to get better performance, the proper parameters are needed. Actually, $\\alpha = 1, \\beta = 1$ is a suitable parameter combination.", + "bbox": [ + 88, + 383, + 482, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Study on Perturbation Magnitude. We conduct additional experiments with varying perturbation magnitudes to investigate their influence on adversarial performance. We select perturbation magnitudes of 2/255, 4/255, 8/255, and 16/255 for evaluation. As illustrated in Fig. 4, a perturbation magnitude of 2/255 yields the worst performance and a perturbation magnitude of 16/255 yields the best performance to protect the videos. Overall, an increase in the perturbation magnitude correlates with an enhancement in the Ramblings performance. Meanwhile, as illustrated in Fig. 5, lower perturbation magnitude tends to result in increased output length. Overall, reduced perturbation magnitudes may compromise the performance of Ramblings and Mutes, yet they have the benefit of minimizing deviations from the original videos. Consequently, finding an optimal balance in perturbation magnitude is essential to achieve both effective performance in adversarial attacks and imperceptible deviations from original videos. More", + "bbox": [ + 89, + 628, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d48dd283e46b60b5509b9703659d54114414484c28076ee4d176b55e4ffa239.jpg", + "image_caption": [ + "Figure 5. The length of the textual output for Mutes varies across different perturbation magnitudes. When the perturbation magnitude is small, the text length is longer, indicating more information leakage from the videos. With the increase of perturbation magnitude, the information leakage of Mutes is less." + ], + "image_footnote": [], + "bbox": [ + 514, + 87, + 694, + 224 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/27c25ebf86dd0182f95bda8113d27834247a63091290f4c699c7ea28ad160a28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 89, + 895, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "experiment results can be found in the Appendix. And all the videos used in experiments are annotated by VideoLLaMA on the OpenVid-1M dataset.", + "bbox": [ + 511, + 422, + 903, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 484, + 632, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we have successfully developed two series of novel watermarking methods aimed at safeguarding video content from unauthorized and automated annotation by video-based large language models. Through our exploration of adversarial attacks, we propose two series of video watermarks named Ramblings and Mutes, respectively. On the one hand, Ramblings are designed to fool video-based LLMs into generating completely incorrect annotations. On the other hand, Mutes, which focus on the EOS token, can shorten annotations by video-based LLMs. Extensive experiments demonstrate the effectiveness of our watermarking methods in misleading or silencing video-based LLMs. Furthermore, evaluations of text-to-video models using different protective approaches show that our methods can impact downstream tasks. Finally, we hope that our Ramblings and Mutes can serve as a protective paradigm to help safeguard videos from unauthorized annotation.", + "bbox": [ + 511, + 510, + 906, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethics Statement", + "text_level": 1, + "bbox": [ + 511, + 782, + 660, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our proposed Ramblings and Mutes are designed solely for protective purposes not to be applied maliciously, and their application in this context is intended to benefit video data privacy. We hope that our work can inform both academic researchers and industry professionals on safeguarding personal video content from misuse.", + "bbox": [ + 511, + 809, + 905, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24063", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported in part by the National Natural Science Foundation of China, under Grant (62302309, 62171248), Shenzhen Science and Technology Program (JCYJ20220818101014030, JCYJ20220818101012025), and the PCNL KEY project (PCL2023AS6-1).", + "bbox": [ + 89, + 114, + 483, + 191 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 205, + 187, + 222 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jiawang Bai, Bin Chen, Yiming Li, Dongxian Wu, Weiwei Guo, Shu-tao Xia, and En-hui Yang. 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In ICML, pages 62892-62913, 2024. 2" + ], + "bbox": [ + 516, + 90, + 903, + 728 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24065", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_model.json b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..32485d2ee21be14ce240e20610583072deaba850 --- /dev/null +++ b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_model.json @@ -0,0 +1,2013 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.13, + 0.872, + 0.175 + ], + "angle": 0, + "content": "Protecting Your Video Content: Disrupting Automated Video-based LLM Annotations" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.203, + 0.89, + 0.258 + ], + "angle": 0, + "content": "Haitong Liu\\(^{1*}\\), Kuofeng Gao\\(^{1*}\\), Yang Bai\\(^{2\\dagger}\\), Jinmin Li\\(^{1}\\), Jinxiao Shan\\(^{3}\\), Tao Dai\\(^{4\\dagger}\\), Shu-Tao Xia\\(^{1,5}\\) \n\\(^{1}\\) Tsinghua University \\(^{2}\\) ByteDance \\(^{3}\\) Digital Center, China Merchants Group Limited \n\\(^{4}\\) Shenzhen University \\(^{5}\\) Peng Cheng Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.26, + 0.804, + 0.275 + ], + "angle": 0, + "content": "{liuhaito24,gkf21,ljm22}@mails.tsinghua.edu.cn，baiyang0522@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.278, + 0.796, + 0.292 + ], + "angle": 0, + "content": "shanjinxiao@cmhk.com, daitao.edu@gmail.com, xiast@sz.tsinghua.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.327, + 0.327, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.358, + 0.485, + 0.737 + ], + "angle": 0, + "content": "Recently, video-based large language models (video-based LLMs) have achieved impressive performance across various video comprehension tasks. However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content. Our code is available at https://github.com/ttthhl/Protecting_Your_Video_Content." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.765, + 0.222, + 0.781 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.79, + 0.484, + 0.866 + ], + "angle": 0, + "content": "Recent years have witnessed significant advancements in both video-based large language models (video-based LLMs) [18, 27, 35, 44-46] and text-to-video generation models [6, 16, 23, 26, 37]. These two types of models demonstrate a close relationship: text-to-video models" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.327, + 0.897, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.511, + 0.908, + 0.596 + ], + "angle": 0, + "content": "Figure 1. We propose two strategies to protect the video content: Ramblings and Mutes. The Ramblings approach misleads videobased large language models into generating inaccurate captions. Besides, Mutes prompt these models to produce shorter and even NULL captions, lacking descriptive detail. The answers in the figure are excerpts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.903 + ], + "angle": 0, + "content": "rely heavily on high-quality video-text pairs for fine-tuning, while video-based LLMs can enhance video-text pairs quality through advanced annotation capabilities. By leveraging the power of large language models [4, 14, 15, 36, 41], video-based LLMs have revolutionized video content interpretation and annotation. This advancement directly contributes to the improvement of video data annotation quality. However, alongside these technological advances, concerns about data safety and privacy [2, 8, 19-22, 40] have emerged. Given the vast amount of personal video content available on multimedia platforms, protecting this data from unauthorized annotation has become an urgent challenge that requires immediate attention. In this paper, we aim to protect personal videos from being unauthorizedly and automatically annotated by video-based LLMs. To tackle this significant and challenging issue, we propose two series of protective and imperceptible watermarks added to videos. In each scenario, we propose two methods in order to add" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.221, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.241, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.241, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24056" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.449, + 0.107 + ], + "angle": 0, + "content": "diversity and adaptability for widespread applications." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.109, + 0.482, + 0.275 + ], + "angle": 0, + "content": "Specifically, we aim to mislead video-based LLMs into generating entirely incorrect annotations in the first scenario. To achieve this, we propose two methods, Rambling-F and Rambling-L, from different perspectives. Rambling-F operates at the feature level, increasing the discrepancy of video and LLM features. Rambling-L manipulates the logit-level by increasing the auto-regressive loss. These adversarial strategies serve to protect personal video content from unauthorized exploitation. Furthermore, fine-tuning text-to-video models on these adversarial video-text pairs will degrade the quality of generated videos." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.277, + 0.485, + 0.518 + ], + "angle": 0, + "content": "The second scenario is designed to make the video-based LLMs effectively \"mute\", which means they are induced to generate shorter output on the given video. We also propose two methods, called Mute-S and Mute-N, relying on the probability of the End-of-Sequence (EOS) token, which, when generated, halts the LLM's inference process. Mute-S aims to cause the video-based LLMs to generate short and incomplete text sequences. For example, the generated text is \"The video is a\". Mute-N aims to return a NULL response by increasing the EOS probability of the first generated token. Overall, these methods can either fragment the sentences or result in a null output, preventing meaningful information from being leveraged by the video-based LLMs. These disruptions in the video-text pairs can then influence the text-to-video model's training and reduce your information leakage." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.521, + 0.485, + 0.732 + ], + "angle": 0, + "content": "Our two scenarios are evaluated across three datasets and three different video-based LLMs, providing comprehensive validation of our methods' effectiveness and adaptability. The text output demonstrates that our Ramblings method can effectively induce the video-based LLMs to generate completely incorrect annotations for the videos, while our Mutes method successfully limits the model's output, reducing the amount of useful information generated. Additionally, we use the annotated video-text pairs to fine-tune a text-to-video model, and the results clearly show that the model's performance degrades by our watermarking methods. Finally, a series of ablation studies, including prompt transferability, further validate the effectiveness and robustness of our proposed methods." + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.733, + 0.482, + 0.748 + ], + "angle": 0, + "content": "In summary, our contribution can be outlined as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.75, + 0.483, + 0.854 + ], + "angle": 0, + "content": "- We investigate the security and privacy risks faced by video annotation with video-based LLMs. To address these risks, we introduce two series of novel video watermarks that prevent unauthorized automated annotation. And we emphasize that the video-text pairs' quality influenced by our watermarks is important for downstream tasks such as text-to-video models." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- Our two series of watermarking methodologies demonstrate distinct strategies for disrupting video-based LLMs: inducing either inaccurate or short captions. These" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "methodologies expand the scope of video privacy protection techniques and establish a foundation for developing robust defenses against unauthorized content analysis." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.137, + 0.907, + 0.289 + ], + "angle": 0, + "content": "- Through extensive experiments, our methods have been proven to perform effectively across three state-of-the-art video-based LLMs, namely Video-ChatGPT [27], Video-LLaMA [46], and Video-Vicuna (change the backbone of Video-LLaMA), as well as three diverse datasets: OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. These demonstrate the robustness and generalization capability of our approach, showing its ability to adapt to various models and datasets while consistently preventing unauthorized video annotation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.303, + 0.655, + 0.319 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.329, + 0.836, + 0.345 + ], + "angle": 0, + "content": "2.1. Video-based Large Language Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.908, + 0.685 + ], + "angle": 0, + "content": "The recent advancements in video-based LLMs [18, 27, 35, 44-46] have significantly enhanced their capabilities in various video-related tasks [38, 47, 48]. These models, such as Video-ChatGPT [27] and Video-LLaMA [46], effectively leverage both spatial and temporal features from video data and the generation ability of LLMs, enabling them to achieve impressive zero-shot performance. The integration of the video modality into LLMs allows for visual context-aware interaction, surpassing the capabilities of existing LLMs. The impressive performance of these models has led to their widespread use in generating dense captions [44] for unannotated videos, which can be used subsequently in downstream tasks, such as text-to-video generation models [6, 16, 23, 26, 37]. However, the widespread use of video-based LLMs raises privacy concerns regarding the potential for the unauthorized annotation of personal videos. As these models become more prevalent, it is crucial to address the ethical implications involving sensitive or private video content. To address these issues, we propose protective video watermarking methods that can prevent personal video from unauthorized and automated annotation by video-based LLMs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.696, + 0.697, + 0.712 + ], + "angle": 0, + "content": "2.2. Adversarial Attack" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Adversarial attacks [1, 7, 9-13, 17, 19, 25, 39, 42, 50] typically craft imperceptible adversarial perturbations that can mislead the models into making incorrect predictions. With the development of multi-modal LLMs, researchers have begun exploring how these attacks can be applied in more complex generation settings. Concretely, recent studies show that adversarial attacks can be used to jailbreak multi-modal LLMs, causing them to generate harmful content [32] or induce targeted captions [49]. In contrast to these adversarial attacks, which aim to manipulate the model to an attacking goal, we adopt them as a pioneering watermarking strategy. It is designed to protect the privacy" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24057" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "and security of video content within these models. Specifically, our watermarking approach is crafted to safeguard the video data against unauthorized annotation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.149, + 0.226, + 0.166 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.173, + 0.201, + 0.188 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.197, + 0.484, + 0.392 + ], + "angle": 0, + "content": "To prevent unauthorized annotation by video-based LLMs, we propose two protective scenarios. First, video-based LLMs can be misled to generate inaccurate captions that significantly diverge the video content when provided with protected video input. Second, video-based LLMs are induced to generate shorter, less detailed captions compared to those generated from clean videos which means less information leakage. Fine-tuning text-to-video models on such video-text pairs can degrade the quality of generated videos, due to the low quality of video-text pairs. For each scenario, we propose to adopt imperceptible adversarial perturbations as watermarks to protect videos from unauthorized annotation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.401, + 0.235, + 0.415 + ], + "angle": 0, + "content": "3.2. Threat Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.484, + 0.544 + ], + "angle": 0, + "content": "Goals and Capabilities. The goal is to craft an imperceptible adversarial perturbation as a protective watermark for the video, which can induce video-based LLMs to generate totally incorrect or shorter sequences during the victim model's deployment. Following the most commonly used constraint for the involved perturbation [5], it is restricted within a predefined magnitude in the \\( l_{p} \\) norm, ensuring perturbation is difficult to detect." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.545, + 0.484, + 0.636 + ], + "angle": 0, + "content": "Knowledge and Background. Following previous works [13, 31], we assume that the victim video-based LLMs can be accessed in full knowledge, including architectures and parameters. Additionally, we consider a more challenging scenario where the victim video-based LLMs are inaccessible, as detailed in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.643, + 0.295, + 0.658 + ], + "angle": 0, + "content": "3.3. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.483, + 0.756 + ], + "angle": 0, + "content": "To safeguard the video from unauthorized annotation by video-based LLMs, we propose to craft adversarial perturbations that can be added to a sequence of frames from the original videos. Given an original video \\( \\pmb{x} \\) and an adversarial video \\( \\pmb{x}' \\) with a watermark, the optimization problem can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.761, + 0.483, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\underset {\\boldsymbol {x} ^ {\\prime}} {\\arg \\max } \\mathcal {L} \\left(\\boldsymbol {x} ^ {\\prime}\\right), \\tag {1} \\\\ s. t. \\left| \\left| \\boldsymbol {x} ^ {\\prime} - \\boldsymbol {x} \\right| \\right| _ {\\infty} < \\epsilon , \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}(\\cdot)\\) denotes the loss objective function to achieve different protective scenarios. To ensure the stealthiness of the adversarial perturbations, we introduce the \\(l_{\\infty}\\) restriction within a value of \\(\\epsilon\\). For optimization, the projected gradient descent (PGD) algorithm [28] is adopted to update the adversarial perturbations at each iteration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.258 + ], + "angle": 0, + "content": "Typically, when a video \\( \\mathbf{x} \\) and an input prompt \\( c_{\\mathrm{in}} \\) are provided as inputs to the video-based LLMs \\( \\mathcal{F}(\\cdot) \\), the video-based LLMs first utilize vision encoders \\( g(\\cdot) \\) to extract visual features from the video. These extracted video features are then fed into the base LLMs \\( h(\\cdot) \\) with \\( c_{\\mathrm{in}} \\) as inputs, which generate the hidden states from its final layer. Finally, the hidden states are projected into the probability distribution of all generated tokens, which can obtain a sequence of generated output tokens. We denote \\( f_{i}(\\cdot) \\) as the probability distribution after the Softmax \\( (\\cdot) \\) layer over the \\( i \\)-th generated token." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.266, + 0.905, + 0.296 + ], + "angle": 0, + "content": "3.4. Ramblings for Incorrect Generation of Video-based LLMs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.304, + 0.905, + 0.394 + ], + "angle": 0, + "content": "In this section, we optimize adversarial videos that can mislead video-based LLMs to generate incorrect captions. To achieve this goal, we develop two different methods for video watermarks from the feature level and the logit level of the video-based LLMs, dubbed Rambling-F and Rambling-L." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.395, + 0.906, + 0.621 + ], + "angle": 0, + "content": "Rambling-F (Feature). To induce the video-based LLMs to generate incorrect captions, we propose a feature-level adversarial strategy called Rambling-F. The core idea behind this approach is to deviate the features of adversarial videos from the original ones in the latent representation space. During the inference stage, the video-based LLMs extract visual features from the input video and also generate LLM features from the combination of the input video and text queries. Hence, in the Rambling-F, we propose to increase the \\( l_{2} \\) distance for both the video features and the LLM features between the original and adversarial videos. As a result, the disrupted features will result in the model's inability to accurately generate the captions correlated with the videos. The loss objective function for the Rambling-F can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.626, + 0.905, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {v i d e o}} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left(g \\left(\\boldsymbol {x} ^ {\\prime}\\right) _ {i} - g (\\boldsymbol {x}) _ {i}\\right) ^ {2}, \\\\ \\mathcal {L} _ {L L M} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\left(h \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right) _ {j} - h \\left(\\boldsymbol {x}, c _ {\\text {i n}}\\right) _ {j}\\right) ^ {2}, \\tag {2} \\\\ \\mathcal {L} _ {R F} (\\pmb {x} ^ {\\prime}) = \\alpha * \\mathcal {L} _ {v i d e o} (\\pmb {x} ^ {\\prime}) + \\beta * \\mathcal {L} _ {L L M} (\\pmb {x} ^ {\\prime}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.905, + 0.795 + ], + "angle": 0, + "content": "where \\( n \\) and \\( m \\) are the total number of elements in the video and LLM features, respectively. In addition, \\( g(\\cdot)_i \\) represents the \\( i \\)-th dimension of video features and \\( h(\\cdot)_j \\) represents the \\( j \\)-th dimension of LLM features." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Rambling-L (Logit). In addition to the feature-level Rambling-F attack, we propose another adversarial strategy called Rambling-L, which manipulates the logit-level outputs, i.e., probability distributions over the generated tokens. Typically, based on the probability distribution over generated tokens, video-based LLMs can generate one token at one time in an auto-regressive manner to obtain the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24058" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.109, + 0.49, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.108, + 0.898, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.416, + 0.391, + 0.593, + 0.409 + ], + "angle": 0, + "content": "Text-to-video model" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.435, + 0.908, + 0.492 + ], + "angle": 0, + "content": "Figure 2. The pipeline of Ramblings and Mutes. While Rambling-F focuses on feature-level perturbations of the original content, Rambling-L increases auto-regressive loss to manipulate video-based LLMs into generating incorrect descriptions. Mutes, on the other hand, tend to increase the probability of the EOS token. Finally, these video-text pairs can influence downstream tasks, such as the capacity of text-to-video models fine-tuned on these data." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.518, + 0.483, + 0.608 + ], + "angle": 0, + "content": "caption. Therefore, for the generation of incorrect captions, we can increase the distance between the adversarial video \\( \\pmb{x}^{\\prime} \\) and the original ground-truth caption \\( y \\) generated from the original video \\( \\pmb{x} \\) by the auto-regressive loss \\( \\mathcal{L}_{ar}(\\cdot) \\). The loss objective function for the Rambling-L attack can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.617, + 0.483, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R L} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), y\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.484, + 0.69 + ], + "angle": 0, + "content": "By increasing Eq. (3), we can shift the model's token probability distribution away from the correct captions, causing the video-based LLMs to generate incorrect textual outputs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.697, + 0.485, + 0.726 + ], + "angle": 0, + "content": "3.5. Mutes for Shorter even NULL Generation of Video-based LLMs" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.825 + ], + "angle": 0, + "content": "In this section, we craft adversarial videos that can induce video-based LLMs to generate shorter captions or even no captions at all, including Mute-S and Mute-N. To this end, we propose manipulating the probability of the End-of-Sequence (EOS) token of video-based LLMs for two protective goals." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Mute-S (Short Caption). During the auto-regressive generation process of video-based LLMs, the occurrence of an End-of-Sequence (EOS) token serves as a signal to stop generating further tokens. To decrease the length of generated sequences, one straightforward approach is to in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.907, + 0.639 + ], + "angle": 0, + "content": "duce the occurrence of the EOS token during the prediction process. However, the auto-regressive prediction is a non-deterministic random process [13], making it challenging to directly determine the exact position where the EOS token is generated. To address this challenge, we propose Mute-S, which aims to increase the probability of the EOS token at all positions of generated sequences \\( y_{\\mathrm{out}} \\). The loss function can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.649, + 0.907, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M S} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} f _ {i} ^ {\\mathrm {E O S}} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}} \\oplus y _ {\\text {o u t}}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.907, + 0.825 + ], + "angle": 0, + "content": "where \\( f_{i}^{\\mathrm{EOS}}(\\cdot) \\) is EOS token probability of the probability distribution after the Softmax(\\cdot) layer over the \\( i \\)-th generated token and \\( N \\) is the length of generated sequences \\( y_{\\mathrm{out}} \\). Note that \\( y_{\\mathrm{out}} \\) is updated at each iteration during the optimization. By increasing Eq. (4), Mute-S can effectively manipulate video-based LLMs to terminate the caption generation process in advance, resulting in shorter and potentially less informative captions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Mute-N (NULL Caption). Considering a more extreme case, we can directly induce video-based LLMs to become highly confident in predicting the EOS token as the very first token during generation, resulting in generating NULL or empty captions. To this end, we propose Mute-N, which" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24059" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "increases the probability of the EOS token at the first predicted token position, rather than optimizing the mean probability of the EOS token across generated sequences as Mute-S. Given the auto-regressive generation process of video-based LLMs, we can force video-based LLMs to approach the EOS token in an auto-regressive manner. The loss function for Mute-N can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.209, + 0.483, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M N} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = - \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), [ \\mathrm {E O S} ]\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.235, + 0.484, + 0.312 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{ar}(\\cdot)\\) denotes the auto-regressive loss function and [EOS] is the EOS token. By optimizing Eq. (5), we can fool the video-based LLMs into generating the EOS token at the beginning, causing the generation process of video-based LLMs to halt immediately." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.325, + 0.216, + 0.342 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.349, + 0.308, + 0.366 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.373, + 0.483, + 0.584 + ], + "angle": 0, + "content": "Models and Datasets. We elaborately select three state-of-the-art video-based LLMs as annotation models: VideoChatGPT [27], Video-LLaMA [46], and Video-Vicuna (a variant of Video-LLaMA with a modified backbone). The default inference prompt template is used to obtain video annotations, with the user input prompt set to \"What is this video about?\" Detailed settings for these models are available in the Appendix. For datasets, we use data from OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. They are all high-quality collections of videos paired with corresponding captions. By calculating similarity with the dataset captions, we can evaluate the performance of the annotations. To accommodate the limited memory of GPUs, each video is preprocessed to consist of 8 frames." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.483, + 0.75 + ], + "angle": 0, + "content": "Baselines and Setups. We use original videos and videos added with random perturbations as baselines. For the setup, the perturbation magnitude is set to 16/255 using the \\( l_{\\infty} \\) norm to make the perturbation imperceptible, and the optimization step size is set to 1/255, using the projected gradient descent (PGD) algorithm [28]. The optimization iteration is set to 200 for Ramblings and 500 for Mutes, respectively. For video-based LLM configurations, we set a sampling temperature of 0.2 and limit the output to a maximum of 512 tokens for three models and the others are default. Additional setup details are provided in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.751, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. For the evaluation of Ramblings, we employ two metrics: CLIP score (RN101) and BLEU. CLIP score [33] measures the similarity between the model's post-attack inferences and the original dataset captions, with a higher score indicating greater similarity and better annotation performance. BLEU [30] assesses the alignment between the model's outputs and reference texts, where a higher BLEU indicates a closer match and improved annotation performance. Our adversarial objective is to reduce these scores." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.228 + ], + "angle": 0, + "content": "For the evaluation of Mutes, we use two metrics: length and EOS rate (NULL caption rate). We compare the lengths of outputs generated from clean and adversarial videos to assess the effectiveness of the Mutes approach. A shorter length indicates less information leakage from the videos. The EOS rate measures how often video-based LLMs output the EOS token early, signifying that no information is leaked from the videos. A higher EOS rate means video-based LLMs output NULL captions more frequently." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.238, + 0.652, + 0.253 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.262, + 0.905, + 0.457 + ], + "angle": 0, + "content": "As shown in Tab. 1, the CLIP score and BLEU are similar between original videos and those with random noise across three models, indicating that random noise does not reduce annotation performance and is therefore ineffective at protecting videos from unauthorized annotation. In contrast, the evaluation scores for Ramblings in Tab. 1 show a substantial decrease compared to the baselines, indicating significant alterations in the semantic information generated by the video-based LLMs. These results demonstrate that adversarial attack on the feature level or logit level effectively misleads the models into generating incorrect annotations for the videos. And our two methods offer great adaptability and flexibility to accommodate various circumstances." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.905, + 0.777 + ], + "angle": 0, + "content": "As shown in Tab. 2, the videos with random noise are ineffective in protecting video content compared to the original videos, as the output length is high and the EOS rate is zero, indicating that a gradient optimization algorithm is necessary to achieve meaningful perturbation. In contrast, our Mute-S effectively disrupts sentence integrity, for example, video-based LLMs may output fragmented text such as \"The video is a\" without forming a coherent description. Further examples are provided in the Appendix. Specifically, for Video-LLaMA, Mute-S reduces text length nearly tenfold, with the EOS rate around \\(10\\%\\). Additionally, our Mute-S significantly reduces the length of generated texts while maintaining a relatively low EOS rate, representing an untargeted attack strategy. Meanwhile, our Mute-N successfully prompts the model to output NULL captions, meaning that video-based LLMs extract no information from the videos, achieving a targeted attack. This analysis underscores the exceptional effectiveness of both Mute-S and Mute-N, resulting in minimal information being extracted by video-based LLMs and ultimately protecting videos from unauthorized and automated annotation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.787, + 0.905, + 0.816 + ], + "angle": 0, + "content": "4.3. Influence on Downstream Work: Text-to-video Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "To further demonstrate the impact of our watermarking methods on downstream tasks, we fine-tune text-to-video models using our annotated video-text pairs. After finetuning, we evaluate the model's performance on established benchmarks to demonstrate that our protective watermark" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24060" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.131 + ], + "angle": 0, + "content": "Table 1. The CLIP score and BLEU between texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna, and clean captions in datasets are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.132, + 0.907, + 0.372 + ], + "angle": 0, + "content": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Video-ChatGPTOriginal0.762210.017030.673830.024050.609380.01040
Noise0.757810.013980.675290.026710.613770.01123
Rambling-F0.667970.011970.603520.015610.495610.00514
Rambling-L0.627440.002710.603030.003500.483150.00169
Video-LLaMAOriginal0.787600.051210.623540.004820.608890.00316
Noise0.799800.047610.622560.004720.601560.00292
Rambling-F0.583010.016000.492920.003500.428960.00205
Rambling-L0.609380.020680.492190.003130.433840.00189
Video-VicunaOriginal0.757320.019690.621580.026040.601070.01332
Noise0.763670.022750.617680.022110.601070.01435
Rambling-F0.625000.023170.507320.007840.423100.00363
Rambling-L0.635250.016440.501950.009080.441890.00449
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.384, + 0.907, + 0.412 + ], + "angle": 0, + "content": "Table 2. The length and EOS rate of texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.413, + 0.907, + 0.653 + ], + "angle": 0, + "content": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Video-ChatGPTOriginal30.470.030.290.031.210.0
Noise30.200.031.240.024.280.0
Mute-S13.6011.012.2813.011.3921.0
Mute-N0.00100.00.00100.00.00100.0
Video-LLaMAOriginal203.540.0208.620.0214.490.0
Noise224.230.0213.470.0209.300.0
Mute-S11.587.017.2813.037.749.0
Mute-N0.00100.00.00100.00.00100.0
Video-VicunaOriginal32.900.046.540.028.640.0
Noise38.270.040.080.034.370.0
Mute-S7.381.06.450.05.560.0
Mute-N0.00100.00.00100.00.00100.0
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.677, + 0.483, + 0.708 + ], + "angle": 0, + "content": "ing methods can significantly degrade the model's ability to generate high-quality videos." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.708, + 0.483, + 0.875 + ], + "angle": 0, + "content": "Experiment Setups. The text-to-video framework we used isAnimateDiff [16], which is based on diffusion model [34]. The dataset we used to fine-tune the text-to-video model consists of video-text pairs annotated by Video-LLaMA based on OpenVid-1M. We follow theAnimateDiff training script. The pre-trained model used is stable-diffusion-v1-51. For image fine-tuning in theAnimateDiff pipeline, the learning rate and training steps are set to \\(2 \\times 10^{-6}\\) and 500, respectively. During the training process of the motion module in theAnimateDiff pipeline, we set the learning rate to \\(5 \\times 10^{-5}\\) and the training steps" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.677, + 0.907, + 0.722 + ], + "angle": 0, + "content": "to 10,000. For text-to-video generation, we set the guidance scale as 8 and the steps as 25. To evaluate conveniently, we still use stable-diffusion-v1-5 as the base model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.728, + 0.909, + 0.865 + ], + "angle": 0, + "content": "Evaluation Metrics. For the evaluation of the text-to-video models, we use two metrics: \\(\\mathrm{VQA}_{\\mathrm{A}}\\) and \\(\\mathrm{VQAT}_{\\mathrm{T}}\\). We adopt these metrics from EvalCrafter [24] as benchmarks to evaluate the performance of text-to-video models fine-tuned on videos with annotations generated by video-based LLMs. Specifically, \\(\\mathrm{VQA}_{\\mathrm{A}}\\) measures the aesthetic quality of generated videos, while \\(\\mathrm{VQAT}_{\\mathrm{T}}\\) assesses technical quality. Higher \\(\\mathrm{VQA}_{\\mathrm{A}}\\) and \\(\\mathrm{VQAT}_{\\mathrm{T}}\\) indicate better quality of the generated videos by text-to-video models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Results. As illustrated in Tab. 5, the \\(\\mathrm{VQA_A}\\) and \\(\\mathrm{VQAT}_{\\mathrm{T}}\\) [24] decrease whenAnimateDiff is fine-tuned using adversar" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.463, + 0.902 + ], + "angle": 0, + "content": "1 https://huggingface.co/stable-diffusion-v1-5/stable-diffusion-v1-5" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24061" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.146 + ], + "angle": 0, + "content": "Table 3. Prompt transferability: The CLIP score and BLEU between texts annotated by Video-LLaMA and clean captions are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts:\"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.147, + 0.912, + 0.267 + ], + "angle": 0, + "content": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Original0.787600.051210.793460.044110.767580.03146
Noise0.799800.047610.796880.040810.771970.03459
Rambling-F0.583010.016000.600100.015850.606450.01514
Rambling-L0.609380.020680.612790.019420.625000.01828
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.279, + 0.907, + 0.336 + ], + "angle": 0, + "content": "Table 4. Prompt transferability: The length and EOS rate of texts annotated by Video-LLaMA are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts: \"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.336, + 0.912, + 0.457 + ], + "angle": 0, + "content": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Original203.540.0221.310.0299.120.0
Noise224.230.0236.850.0300.920.0
Mute-S11.587.024.165.036.4410.0
Mute-N0.00100.064.0473.0230.7419.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.48, + 0.486, + 0.537 + ], + "angle": 0, + "content": "Table 5. The VQA and VQAT are evaluated forAnimateDiff fine-tuned on different adversarial video-text pairs. All the video-text pairs are annotated by Video-LLaMA on the OpenVid-1M dataset. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.149, + 0.547, + 0.424, + 0.67 + ], + "angle": 0, + "content": "
MethodVQAAVQAT
Original60.43051.302
Noise46.71835.392
Rambling-F39.38328.231
Rambling-L38.04227.394
Mute-S43.61024.487
Mute-N43.46831.009
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.485, + 0.759 + ], + "angle": 0, + "content": "ial video-text pairs compared to those with original or randomly perturbed video-text pairs. This notable reduction demonstrates that the quality of text-to-video models degrades significantly by our watermarking methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.77, + 0.255, + 0.787 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Transferability. Video-based LLMs generate corresponding responses according to different user prompts. In this section, we conduct the transferability experiments [25] to assess whether adversarial watermarks can protect videos from unauthorized annotation under varying user inference prompts. In this experiment, we adopt the inference prompts: \"What is this video about?\", \"What happens in" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.481, + 0.885, + 0.497 + ], + "angle": 0, + "content": "the video?”, and “Can you describe the video in detail?”" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.907, + 0.867 + ], + "angle": 0, + "content": "As shown in Tab. 3, changing the inference prompt still results in a significant reduction in both CLIP score and BLEU when using our Ramblings method, indicating that Rambling-F and Rambling-L effectively protect videos from unauthorized annotation across varied prompts. Similarly, as shown in Tab. 4, even with differing inference prompts, Mute-S and Mute-N significantly reduce the length of generated texts, preventing information leakage from the videos. Additionally, the EOS rate remains high, suggesting that Mute-N leads video-based LLMs to produce null captions. Notably, when the inference prompt differs from the prompt used during the attack phase, Mute-N shows a certain degree of performance reduction against Video-LLaMA. We speculate this may be due to Mute-N's focus on the EOS probability of a single token, potentially reducing its stability across different inference prompts. So, we introduce Mute-N2 in the Appendix to enhance its performance. These findings further emphasize the necessity of using both Mute-S and Mute-N, as Mute-S remains stable under different circumstances, while Mute-N performs optimally when the inference prompt matches the one used during the attack phase. Overall, the experiments above demonstrate that our methods have a certain degree of prompt transferability." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Ablation Study on Rambling-F. Our Rambling-F integrates both \\(\\mathcal{L}_{video}\\) and \\(\\mathcal{L}_{LLM}\\). To thoroughly evaluate the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24062" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.094, + 0.289, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.094, + 0.48, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.227, + 0.483, + 0.352 + ], + "angle": 0, + "content": "Figure 3. Comparison of CLIP score (left) and BLEU (right) on Rambling-F to evaluate different parameters' influence. When the parameter is too small, the CLIP score and BLEU are high, indicating poor protective performance. Meanwhile, the evaluation scores decrease under \\(\\alpha = 1\\), \\(\\beta = 1\\) compared to \\(\\alpha = 1\\), \\(\\beta = 0\\) or \\(\\alpha = 0\\), \\(\\beta = 1\\), suggesting that the combination of feature losses is effective and necessary. All the videos are annotated by VideoLLaMA on the OpenVid-1M dataset. \\(\\alpha = 0\\), \\(\\beta = 0\\) represents original video." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.385, + 0.483, + 0.626 + ], + "angle": 0, + "content": "individual and combined impact of each feature loss, we conduct a parameter experiment to explore the influence of \\(\\alpha\\) and \\(\\beta\\) in Eq. (2). As outlined in Fig. 3, the combination of \\(\\alpha = 1, \\beta = 1\\) outperforms the combination of \\(\\alpha = 1, \\beta = 0\\) or \\(\\alpha = 0, \\beta = 1\\) which means that it is effective to add these features together to get better protective performance. Additionally, larger values for these parameters generally lead to better performance in reducing annotation quality. However, when increased to a certain extent, the performance does not show improvement even reduction. These findings highlight the synergy between the two feature losses, suggesting that their integration enhances the method's ability to strengthen adversarial attacks and more effectively protect video content. And to get better performance, the proper parameters are needed. Actually, \\(\\alpha = 1, \\beta = 1\\) is a suitable parameter combination." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Ablation Study on Perturbation Magnitude. We conduct additional experiments with varying perturbation magnitudes to investigate their influence on adversarial performance. We select perturbation magnitudes of 2/255, 4/255, 8/255, and 16/255 for evaluation. As illustrated in Fig. 4, a perturbation magnitude of 2/255 yields the worst performance and a perturbation magnitude of 16/255 yields the best performance to protect the videos. Overall, an increase in the perturbation magnitude correlates with an enhancement in the Ramblings performance. Meanwhile, as illustrated in Fig. 5, lower perturbation magnitude tends to result in increased output length. Overall, reduced perturbation magnitudes may compromise the performance of Ramblings and Mutes, yet they have the benefit of minimizing deviations from the original videos. Consequently, finding an optimal balance in perturbation magnitude is essential to achieve both effective performance in adversarial attacks and imperceptible deviations from original videos. More" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.088, + 0.695, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.09, + 0.897, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.242, + 0.695, + 0.394 + ], + "angle": 0, + "content": "Figure 4. CLIP score about Ramblings on different perturbation magnitudes. When the perturbation magnitude is small, the CLIP score is higher, indicating poor protective performance for the videos. With the increase of perturbation magnitude, the protective performance of Ramblings is better." + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.242, + 0.903, + 0.394 + ], + "angle": 0, + "content": "Figure 5. The length of the textual output for Mutes varies across different perturbation magnitudes. When the perturbation magnitude is small, the text length is longer, indicating more information leakage from the videos. With the increase of perturbation magnitude, the information leakage of Mutes is less." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.424, + 0.905, + 0.468 + ], + "angle": 0, + "content": "experiment results can be found in the Appendix. And all the videos used in experiments are annotated by VideoLLaMA on the OpenVid-1M dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.485, + 0.633, + 0.5 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.511, + 0.907, + 0.768 + ], + "angle": 0, + "content": "In this study, we have successfully developed two series of novel watermarking methods aimed at safeguarding video content from unauthorized and automated annotation by video-based large language models. Through our exploration of adversarial attacks, we propose two series of video watermarks named Ramblings and Mutes, respectively. On the one hand, Ramblings are designed to fool video-based LLMs into generating completely incorrect annotations. On the other hand, Mutes, which focus on the EOS token, can shorten annotations by video-based LLMs. Extensive experiments demonstrate the effectiveness of our watermarking methods in misleading or silencing video-based LLMs. Furthermore, evaluations of text-to-video models using different protective approaches show that our methods can impact downstream tasks. Finally, we hope that our Ramblings and Mutes can serve as a protective paradigm to help safeguard videos from unauthorized annotation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.784, + 0.661, + 0.8 + ], + "angle": 0, + "content": "Ethics Statement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.9 + ], + "angle": 0, + "content": "Our proposed Ramblings and Mutes are designed solely for protective purposes not to be applied maliciously, and their application in this context is intended to benefit video data privacy. We hope that our work can inform both academic researchers and industry professionals on safeguarding personal video content from misuse." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24063" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.484, + 0.192 + ], + "angle": 0, + "content": "This work is supported in part by the National Natural Science Foundation of China, under Grant (62302309, 62171248), Shenzhen Science and Technology Program (JCYJ20220818101014030, JCYJ20220818101012025), and the PCNL KEY project (PCL2023AS6-1)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.207, + 0.188, + 0.223 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.232, + 0.484, + 0.274 + ], + "angle": 0, + "content": "[1] Jiawang Bai, Bin Chen, Yiming Li, Dongxian Wu, Weiwei Guo, Shu-tao Xia, and En-hui Yang. 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In ICML, pages 62892-62913, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.905, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24065" + } + ] +] \ No newline at end of file diff --git a/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_origin.pdf b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..94f75d23b9637136a63a41c22edb2997a8bbbe39 --- /dev/null +++ b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/3e55fb27-6e40-4d5b-80e6-37b2f1422af5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c729185d3b10a48e5abc134e1cdd950be99fd5f29f213d54ff6edb4f49bbcbb7 +size 1421968 diff --git a/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/full.md b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..beb71a11ed41f76d0c5c9d5089005fb4cf9c316a --- /dev/null +++ b/2025/Protecting Your Video Content_ Disrupting Automated Video-based LLM Annotations/full.md @@ -0,0 +1,276 @@ +# Protecting Your Video Content: Disrupting Automated Video-based LLM Annotations + +Haitong Liu $^{1*}$ , Kuofeng Gao $^{1*}$ , Yang Bai $^{2\dagger}$ , Jinmin Li $^{1}$ , Jinxiao Shan $^{3}$ , Tao Dai $^{4\dagger}$ , Shu-Tao Xia $^{1,5}$ $^{1}$ Tsinghua University $^{2}$ ByteDance $^{3}$ Digital Center, China Merchants Group Limited + $^{4}$ Shenzhen University $^{5}$ Peng Cheng Laboratory + +{liuhaito24,gkf21,ljm22}@mails.tsinghua.edu.cn，baiyang0522@gmail.com + +shanjinxiao@cmhk.com, daitao.edu@gmail.com, xiast@sz.tsinghua.edu.cn + +# Abstract + +Recently, video-based large language models (video-based LLMs) have achieved impressive performance across various video comprehension tasks. However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content. Our code is available at https://github.com/ttthhl/Protecting_Your_Video_Content. + +# 1. Introduction + +Recent years have witnessed significant advancements in both video-based large language models (video-based LLMs) [18, 27, 35, 44-46] and text-to-video generation models [6, 16, 23, 26, 37]. These two types of models demonstrate a close relationship: text-to-video models + +![](images/c1d8f54acf8dac49e30dd18d5bdf7dc7efb7d061902fdb39f8d13a0537158b07.jpg) +Figure 1. We propose two strategies to protect the video content: Ramblings and Mutes. The Ramblings approach misleads videobased large language models into generating inaccurate captions. Besides, Mutes prompt these models to produce shorter and even NULL captions, lacking descriptive detail. The answers in the figure are excerpts. + +rely heavily on high-quality video-text pairs for fine-tuning, while video-based LLMs can enhance video-text pairs quality through advanced annotation capabilities. By leveraging the power of large language models [4, 14, 15, 36, 41], video-based LLMs have revolutionized video content interpretation and annotation. This advancement directly contributes to the improvement of video data annotation quality. However, alongside these technological advances, concerns about data safety and privacy [2, 8, 19-22, 40] have emerged. Given the vast amount of personal video content available on multimedia platforms, protecting this data from unauthorized annotation has become an urgent challenge that requires immediate attention. In this paper, we aim to protect personal videos from being unauthorizedly and automatically annotated by video-based LLMs. To tackle this significant and challenging issue, we propose two series of protective and imperceptible watermarks added to videos. In each scenario, we propose two methods in order to add + +diversity and adaptability for widespread applications. + +Specifically, we aim to mislead video-based LLMs into generating entirely incorrect annotations in the first scenario. To achieve this, we propose two methods, Rambling-F and Rambling-L, from different perspectives. Rambling-F operates at the feature level, increasing the discrepancy of video and LLM features. Rambling-L manipulates the logit-level by increasing the auto-regressive loss. These adversarial strategies serve to protect personal video content from unauthorized exploitation. Furthermore, fine-tuning text-to-video models on these adversarial video-text pairs will degrade the quality of generated videos. + +The second scenario is designed to make the video-based LLMs effectively "mute", which means they are induced to generate shorter output on the given video. We also propose two methods, called Mute-S and Mute-N, relying on the probability of the End-of-Sequence (EOS) token, which, when generated, halts the LLM's inference process. Mute-S aims to cause the video-based LLMs to generate short and incomplete text sequences. For example, the generated text is "The video is a". Mute-N aims to return a NULL response by increasing the EOS probability of the first generated token. Overall, these methods can either fragment the sentences or result in a null output, preventing meaningful information from being leveraged by the video-based LLMs. These disruptions in the video-text pairs can then influence the text-to-video model's training and reduce your information leakage. + +Our two scenarios are evaluated across three datasets and three different video-based LLMs, providing comprehensive validation of our methods' effectiveness and adaptability. The text output demonstrates that our Ramblings method can effectively induce the video-based LLMs to generate completely incorrect annotations for the videos, while our Mutes method successfully limits the model's output, reducing the amount of useful information generated. Additionally, we use the annotated video-text pairs to fine-tune a text-to-video model, and the results clearly show that the model's performance degrades by our watermarking methods. Finally, a series of ablation studies, including prompt transferability, further validate the effectiveness and robustness of our proposed methods. + +In summary, our contribution can be outlined as follows: + +- We investigate the security and privacy risks faced by video annotation with video-based LLMs. To address these risks, we introduce two series of novel video watermarks that prevent unauthorized automated annotation. And we emphasize that the video-text pairs' quality influenced by our watermarks is important for downstream tasks such as text-to-video models. +- Our two series of watermarking methodologies demonstrate distinct strategies for disrupting video-based LLMs: inducing either inaccurate or short captions. These + +methodologies expand the scope of video privacy protection techniques and establish a foundation for developing robust defenses against unauthorized content analysis. + +- Through extensive experiments, our methods have been proven to perform effectively across three state-of-the-art video-based LLMs, namely Video-ChatGPT [27], Video-LLaMA [46], and Video-Vicuna (change the backbone of Video-LLaMA), as well as three diverse datasets: OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. These demonstrate the robustness and generalization capability of our approach, showing its ability to adapt to various models and datasets while consistently preventing unauthorized video annotation. + +# 2. Related Work + +# 2.1. Video-based Large Language Models + +The recent advancements in video-based LLMs [18, 27, 35, 44-46] have significantly enhanced their capabilities in various video-related tasks [38, 47, 48]. These models, such as Video-ChatGPT [27] and Video-LLaMA [46], effectively leverage both spatial and temporal features from video data and the generation ability of LLMs, enabling them to achieve impressive zero-shot performance. The integration of the video modality into LLMs allows for visual context-aware interaction, surpassing the capabilities of existing LLMs. The impressive performance of these models has led to their widespread use in generating dense captions [44] for unannotated videos, which can be used subsequently in downstream tasks, such as text-to-video generation models [6, 16, 23, 26, 37]. However, the widespread use of video-based LLMs raises privacy concerns regarding the potential for the unauthorized annotation of personal videos. As these models become more prevalent, it is crucial to address the ethical implications involving sensitive or private video content. To address these issues, we propose protective video watermarking methods that can prevent personal video from unauthorized and automated annotation by video-based LLMs. + +# 2.2. Adversarial Attack + +Adversarial attacks [1, 7, 9-13, 17, 19, 25, 39, 42, 50] typically craft imperceptible adversarial perturbations that can mislead the models into making incorrect predictions. With the development of multi-modal LLMs, researchers have begun exploring how these attacks can be applied in more complex generation settings. Concretely, recent studies show that adversarial attacks can be used to jailbreak multi-modal LLMs, causing them to generate harmful content [32] or induce targeted captions [49]. In contrast to these adversarial attacks, which aim to manipulate the model to an attacking goal, we adopt them as a pioneering watermarking strategy. It is designed to protect the privacy + +and security of video content within these models. Specifically, our watermarking approach is crafted to safeguard the video data against unauthorized annotation. + +# 3. Methodology + +# 3.1. Overview + +To prevent unauthorized annotation by video-based LLMs, we propose two protective scenarios. First, video-based LLMs can be misled to generate inaccurate captions that significantly diverge the video content when provided with protected video input. Second, video-based LLMs are induced to generate shorter, less detailed captions compared to those generated from clean videos which means less information leakage. Fine-tuning text-to-video models on such video-text pairs can degrade the quality of generated videos, due to the low quality of video-text pairs. For each scenario, we propose to adopt imperceptible adversarial perturbations as watermarks to protect videos from unauthorized annotation. + +# 3.2. Threat Model + +Goals and Capabilities. The goal is to craft an imperceptible adversarial perturbation as a protective watermark for the video, which can induce video-based LLMs to generate totally incorrect or shorter sequences during the victim model's deployment. Following the most commonly used constraint for the involved perturbation [5], it is restricted within a predefined magnitude in the $l_{p}$ norm, ensuring perturbation is difficult to detect. + +Knowledge and Background. Following previous works [13, 31], we assume that the victim video-based LLMs can be accessed in full knowledge, including architectures and parameters. Additionally, we consider a more challenging scenario where the victim video-based LLMs are inaccessible, as detailed in the Appendix. + +# 3.3. Problem Formulation + +To safeguard the video from unauthorized annotation by video-based LLMs, we propose to craft adversarial perturbations that can be added to a sequence of frames from the original videos. Given an original video $\pmb{x}$ and an adversarial video $\pmb{x}'$ with a watermark, the optimization problem can be formulated as follows: + +$$ +\begin{array}{l} \underset {\boldsymbol {x} ^ {\prime}} {\arg \max } \mathcal {L} \left(\boldsymbol {x} ^ {\prime}\right), \tag {1} \\ s. t. \left| \left| \boldsymbol {x} ^ {\prime} - \boldsymbol {x} \right| \right| _ {\infty} < \epsilon , \\ \end{array} +$$ + +where $\mathcal{L}(\cdot)$ denotes the loss objective function to achieve different protective scenarios. To ensure the stealthiness of the adversarial perturbations, we introduce the $l_{\infty}$ restriction within a value of $\epsilon$ . For optimization, the projected gradient descent (PGD) algorithm [28] is adopted to update the adversarial perturbations at each iteration. + +Typically, when a video $\mathbf{x}$ and an input prompt $c_{\mathrm{in}}$ are provided as inputs to the video-based LLMs $\mathcal{F}(\cdot)$ , the video-based LLMs first utilize vision encoders $g(\cdot)$ to extract visual features from the video. These extracted video features are then fed into the base LLMs $h(\cdot)$ with $c_{\mathrm{in}}$ as inputs, which generate the hidden states from its final layer. Finally, the hidden states are projected into the probability distribution of all generated tokens, which can obtain a sequence of generated output tokens. We denote $f_{i}(\cdot)$ as the probability distribution after the Softmax $(\cdot)$ layer over the $i$ -th generated token. + +# 3.4. Ramblings for Incorrect Generation of Video-based LLMs + +In this section, we optimize adversarial videos that can mislead video-based LLMs to generate incorrect captions. To achieve this goal, we develop two different methods for video watermarks from the feature level and the logit level of the video-based LLMs, dubbed Rambling-F and Rambling-L. + +Rambling-F (Feature). To induce the video-based LLMs to generate incorrect captions, we propose a feature-level adversarial strategy called Rambling-F. The core idea behind this approach is to deviate the features of adversarial videos from the original ones in the latent representation space. During the inference stage, the video-based LLMs extract visual features from the input video and also generate LLM features from the combination of the input video and text queries. Hence, in the Rambling-F, we propose to increase the $l_{2}$ distance for both the video features and the LLM features between the original and adversarial videos. As a result, the disrupted features will result in the model's inability to accurately generate the captions correlated with the videos. The loss objective function for the Rambling-F can be formulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {v i d e o}} \left(\boldsymbol {x} ^ {\prime}\right) = \frac {1}{n} \sum_ {i = 1} ^ {n} \left(g \left(\boldsymbol {x} ^ {\prime}\right) _ {i} - g (\boldsymbol {x}) _ {i}\right) ^ {2}, \\ \mathcal {L} _ {L L M} \left(\boldsymbol {x} ^ {\prime}\right) = \frac {1}{m} \sum_ {j = 1} ^ {m} \left(h \left(\boldsymbol {x} ^ {\prime}, c _ {\text {i n}}\right) _ {j} - h \left(\boldsymbol {x}, c _ {\text {i n}}\right) _ {j}\right) ^ {2}, \tag {2} \\ \mathcal {L} _ {R F} (\pmb {x} ^ {\prime}) = \alpha * \mathcal {L} _ {v i d e o} (\pmb {x} ^ {\prime}) + \beta * \mathcal {L} _ {L L M} (\pmb {x} ^ {\prime}), \\ \end{array} +$$ + +where $n$ and $m$ are the total number of elements in the video and LLM features, respectively. In addition, $g(\cdot)_i$ represents the $i$ -th dimension of video features and $h(\cdot)_j$ represents the $j$ -th dimension of LLM features. + +Rambling-L (Logit). In addition to the feature-level Rambling-F attack, we propose another adversarial strategy called Rambling-L, which manipulates the logit-level outputs, i.e., probability distributions over the generated tokens. Typically, based on the probability distribution over generated tokens, video-based LLMs can generate one token at one time in an auto-regressive manner to obtain the + +![](images/78f8b76a772ce97e785971601170cf62712ad39cd6e21a83dbcf08aee8023590.jpg) +Text-to-video model + +![](images/9c5258d5edd36eed731d4af266321e3c8b36083d323093da4bb724f829acde7f.jpg) +Figure 2. The pipeline of Ramblings and Mutes. While Rambling-F focuses on feature-level perturbations of the original content, Rambling-L increases auto-regressive loss to manipulate video-based LLMs into generating incorrect descriptions. Mutes, on the other hand, tend to increase the probability of the EOS token. Finally, these video-text pairs can influence downstream tasks, such as the capacity of text-to-video models fine-tuned on these data. + +caption. Therefore, for the generation of incorrect captions, we can increase the distance between the adversarial video $\pmb{x}^{\prime}$ and the original ground-truth caption $y$ generated from the original video $\pmb{x}$ by the auto-regressive loss $\mathcal{L}_{ar}(\cdot)$ . The loss objective function for the Rambling-L attack can be expressed as follows: + +$$ +\mathcal {L} _ {R L} \left(\boldsymbol {x} ^ {\prime}\right) = \mathcal {L} _ {a r} \left(\mathcal {F} \left(\boldsymbol {x} ^ {\prime}, c _ {\text {i n}}\right), y\right). \tag {3} +$$ + +By increasing Eq. (3), we can shift the model's token probability distribution away from the correct captions, causing the video-based LLMs to generate incorrect textual outputs. + +# 3.5. Mutes for Shorter even NULL Generation of Video-based LLMs + +In this section, we craft adversarial videos that can induce video-based LLMs to generate shorter captions or even no captions at all, including Mute-S and Mute-N. To this end, we propose manipulating the probability of the End-of-Sequence (EOS) token of video-based LLMs for two protective goals. + +Mute-S (Short Caption). During the auto-regressive generation process of video-based LLMs, the occurrence of an End-of-Sequence (EOS) token serves as a signal to stop generating further tokens. To decrease the length of generated sequences, one straightforward approach is to in + +duce the occurrence of the EOS token during the prediction process. However, the auto-regressive prediction is a non-deterministic random process [13], making it challenging to directly determine the exact position where the EOS token is generated. To address this challenge, we propose Mute-S, which aims to increase the probability of the EOS token at all positions of generated sequences $y_{\mathrm{out}}$ . The loss function can be formulated as follows: + +$$ +\mathcal {L} _ {M S} \left(\boldsymbol {x} ^ {\prime}\right) = \frac {1}{N} \sum_ {i = 1} ^ {N} f _ {i} ^ {\mathrm {E O S}} \left(\boldsymbol {x} ^ {\prime}, c _ {\text {i n}} \oplus y _ {\text {o u t}}\right), \tag {4} +$$ + +where $f_{i}^{\mathrm{EOS}}(\cdot)$ is EOS token probability of the probability distribution after the Softmax(\cdot) layer over the $i$ -th generated token and $N$ is the length of generated sequences $y_{\mathrm{out}}$ . Note that $y_{\mathrm{out}}$ is updated at each iteration during the optimization. By increasing Eq. (4), Mute-S can effectively manipulate video-based LLMs to terminate the caption generation process in advance, resulting in shorter and potentially less informative captions. + +Mute-N (NULL Caption). Considering a more extreme case, we can directly induce video-based LLMs to become highly confident in predicting the EOS token as the very first token during generation, resulting in generating NULL or empty captions. To this end, we propose Mute-N, which + +increases the probability of the EOS token at the first predicted token position, rather than optimizing the mean probability of the EOS token across generated sequences as Mute-S. Given the auto-regressive generation process of video-based LLMs, we can force video-based LLMs to approach the EOS token in an auto-regressive manner. The loss function for Mute-N can be formulated as follows: + +$$ +\mathcal {L} _ {M N} \left(\boldsymbol {x} ^ {\prime}\right) = - \mathcal {L} _ {a r} \left(\mathcal {F} \left(\boldsymbol {x} ^ {\prime}, c _ {\text {i n}}\right), [ \mathrm {E O S} ]\right), \tag {5} +$$ + +where $\mathcal{L}_{ar}(\cdot)$ denotes the auto-regressive loss function and [EOS] is the EOS token. By optimizing Eq. (5), we can fool the video-based LLMs into generating the EOS token at the beginning, causing the generation process of video-based LLMs to halt immediately. + +# 4. Experiment + +# 4.1. Implementation Details + +Models and Datasets. We elaborately select three state-of-the-art video-based LLMs as annotation models: VideoChatGPT [27], Video-LLaMA [46], and Video-Vicuna (a variant of Video-LLaMA with a modified backbone). The default inference prompt template is used to obtain video annotations, with the user input prompt set to "What is this video about?" Detailed settings for these models are available in the Appendix. For datasets, we use data from OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. They are all high-quality collections of videos paired with corresponding captions. By calculating similarity with the dataset captions, we can evaluate the performance of the annotations. To accommodate the limited memory of GPUs, each video is preprocessed to consist of 8 frames. + +Baselines and Setups. We use original videos and videos added with random perturbations as baselines. For the setup, the perturbation magnitude is set to 16/255 using the $l_{\infty}$ norm to make the perturbation imperceptible, and the optimization step size is set to 1/255, using the projected gradient descent (PGD) algorithm [28]. The optimization iteration is set to 200 for Ramblings and 500 for Mutes, respectively. For video-based LLM configurations, we set a sampling temperature of 0.2 and limit the output to a maximum of 512 tokens for three models and the others are default. Additional setup details are provided in the Appendix. + +Evaluation Metrics. For the evaluation of Ramblings, we employ two metrics: CLIP score (RN101) and BLEU. CLIP score [33] measures the similarity between the model's post-attack inferences and the original dataset captions, with a higher score indicating greater similarity and better annotation performance. BLEU [30] assesses the alignment between the model's outputs and reference texts, where a higher BLEU indicates a closer match and improved annotation performance. Our adversarial objective is to reduce these scores. + +For the evaluation of Mutes, we use two metrics: length and EOS rate (NULL caption rate). We compare the lengths of outputs generated from clean and adversarial videos to assess the effectiveness of the Mutes approach. A shorter length indicates less information leakage from the videos. The EOS rate measures how often video-based LLMs output the EOS token early, signifying that no information is leaked from the videos. A higher EOS rate means video-based LLMs output NULL captions more frequently. + +# 4.2. Main Results + +As shown in Tab. 1, the CLIP score and BLEU are similar between original videos and those with random noise across three models, indicating that random noise does not reduce annotation performance and is therefore ineffective at protecting videos from unauthorized annotation. In contrast, the evaluation scores for Ramblings in Tab. 1 show a substantial decrease compared to the baselines, indicating significant alterations in the semantic information generated by the video-based LLMs. These results demonstrate that adversarial attack on the feature level or logit level effectively misleads the models into generating incorrect annotations for the videos. And our two methods offer great adaptability and flexibility to accommodate various circumstances. + +As shown in Tab. 2, the videos with random noise are ineffective in protecting video content compared to the original videos, as the output length is high and the EOS rate is zero, indicating that a gradient optimization algorithm is necessary to achieve meaningful perturbation. In contrast, our Mute-S effectively disrupts sentence integrity, for example, video-based LLMs may output fragmented text such as "The video is a" without forming a coherent description. Further examples are provided in the Appendix. Specifically, for Video-LLaMA, Mute-S reduces text length nearly tenfold, with the EOS rate around $10\%$ . Additionally, our Mute-S significantly reduces the length of generated texts while maintaining a relatively low EOS rate, representing an untargeted attack strategy. Meanwhile, our Mute-N successfully prompts the model to output NULL captions, meaning that video-based LLMs extract no information from the videos, achieving a targeted attack. This analysis underscores the exceptional effectiveness of both Mute-S and Mute-N, resulting in minimal information being extracted by video-based LLMs and ultimately protecting videos from unauthorized and automated annotation. + +# 4.3. Influence on Downstream Work: Text-to-video Models + +To further demonstrate the impact of our watermarking methods on downstream tasks, we fine-tune text-to-video models using our annotated video-text pairs. After finetuning, we evaluate the model's performance on established benchmarks to demonstrate that our protective watermark + +Table 1. The CLIP score and BLEU between texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna, and clean captions in datasets are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold. + +
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Video-ChatGPTOriginal0.762210.017030.673830.024050.609380.01040
Noise0.757810.013980.675290.026710.613770.01123
Rambling-F0.667970.011970.603520.015610.495610.00514
Rambling-L0.627440.002710.603030.003500.483150.00169
Video-LLaMAOriginal0.787600.051210.623540.004820.608890.00316
Noise0.799800.047610.622560.004720.601560.00292
Rambling-F0.583010.016000.492920.003500.428960.00205
Rambling-L0.609380.020680.492190.003130.433840.00189
Video-VicunaOriginal0.757320.019690.621580.026040.601070.01332
Noise0.763670.022750.617680.022110.601070.01435
Rambling-F0.625000.023170.507320.007840.423100.00363
Rambling-L0.635250.016440.501950.009080.441890.00449
+ +Table 2. The length and EOS rate of texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold. + +
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Video-ChatGPTOriginal30.470.030.290.031.210.0
Noise30.200.031.240.024.280.0
Mute-S13.6011.012.2813.011.3921.0
Mute-N0.00100.00.00100.00.00100.0
Video-LLaMAOriginal203.540.0208.620.0214.490.0
Noise224.230.0213.470.0209.300.0
Mute-S11.587.017.2813.037.749.0
Mute-N0.00100.00.00100.00.00100.0
Video-VicunaOriginal32.900.046.540.028.640.0
Noise38.270.040.080.034.370.0
Mute-S7.381.06.450.05.560.0
Mute-N0.00100.00.00100.00.00100.0
+ +ing methods can significantly degrade the model's ability to generate high-quality videos. + +Experiment Setups. The text-to-video framework we used isAnimateDiff [16], which is based on diffusion model [34]. The dataset we used to fine-tune the text-to-video model consists of video-text pairs annotated by Video-LLaMA based on OpenVid-1M. We follow theAnimateDiff training script. The pre-trained model used is stable-diffusion-v1-51. For image fine-tuning in theAnimateDiff pipeline, the learning rate and training steps are set to $2 \times 10^{-6}$ and 500, respectively. During the training process of the motion module in theAnimateDiff pipeline, we set the learning rate to $5 \times 10^{-5}$ and the training steps + +to 10,000. For text-to-video generation, we set the guidance scale as 8 and the steps as 25. To evaluate conveniently, we still use stable-diffusion-v1-5 as the base model. + +Evaluation Metrics. For the evaluation of the text-to-video models, we use two metrics: $\mathrm{VQA}_{\mathrm{A}}$ and $\mathrm{VQAT}_{\mathrm{T}}$ . We adopt these metrics from EvalCrafter [24] as benchmarks to evaluate the performance of text-to-video models fine-tuned on videos with annotations generated by video-based LLMs. Specifically, $\mathrm{VQA}_{\mathrm{A}}$ measures the aesthetic quality of generated videos, while $\mathrm{VQAT}_{\mathrm{T}}$ assesses technical quality. Higher $\mathrm{VQA}_{\mathrm{A}}$ and $\mathrm{VQAT}_{\mathrm{T}}$ indicate better quality of the generated videos by text-to-video models. + +Results. As illustrated in Tab. 5, the $\mathrm{VQA_A}$ and $\mathrm{VQAT}_{\mathrm{T}}$ [24] decrease whenAnimateDiff is fine-tuned using adversar + +Table 3. Prompt transferability: The CLIP score and BLEU between texts annotated by Video-LLaMA and clean captions are measured on OpenVid-1M dataset. The prompt used during the attack phase is "What is this video about?". After the attack, we apply three different prompts:"What is this video about?", "What happens in the video?", and "Can you describe the video in detail?" to generate annotations for videos. The best results are highlighted in bold. + +
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Original0.787600.051210.793460.044110.767580.03146
Noise0.799800.047610.796880.040810.771970.03459
Rambling-F0.583010.016000.600100.015850.606450.01514
Rambling-L0.609380.020680.612790.019420.625000.01828
+ +Table 4. Prompt transferability: The length and EOS rate of texts annotated by Video-LLaMA are measured on OpenVid-1M dataset. The prompt used during the attack phase is "What is this video about?". After the attack, we apply three different prompts: "What is this video about?", "What happens in the video?", and "Can you describe the video in detail?" to generate annotations for videos. The best results are highlighted in bold. + +
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Original203.540.0221.310.0299.120.0
Noise224.230.0236.850.0300.920.0
Mute-S11.587.024.165.036.4410.0
Mute-N0.00100.064.0473.0230.7419.0
+ +Table 5. The VQA and VQAT are evaluated forAnimateDiff fine-tuned on different adversarial video-text pairs. All the video-text pairs are annotated by Video-LLaMA on the OpenVid-1M dataset. The best results are highlighted in bold. + +
MethodVQAAVQAT
Original60.43051.302
Noise46.71835.392
Rambling-F39.38328.231
Rambling-L38.04227.394
Mute-S43.61024.487
Mute-N43.46831.009
+ +ial video-text pairs compared to those with original or randomly perturbed video-text pairs. This notable reduction demonstrates that the quality of text-to-video models degrades significantly by our watermarking methods. + +# 4.4. Ablation Studies + +Transferability. Video-based LLMs generate corresponding responses according to different user prompts. In this section, we conduct the transferability experiments [25] to assess whether adversarial watermarks can protect videos from unauthorized annotation under varying user inference prompts. In this experiment, we adopt the inference prompts: "What is this video about?", "What happens in + +the video?”, and “Can you describe the video in detail?” + +As shown in Tab. 3, changing the inference prompt still results in a significant reduction in both CLIP score and BLEU when using our Ramblings method, indicating that Rambling-F and Rambling-L effectively protect videos from unauthorized annotation across varied prompts. Similarly, as shown in Tab. 4, even with differing inference prompts, Mute-S and Mute-N significantly reduce the length of generated texts, preventing information leakage from the videos. Additionally, the EOS rate remains high, suggesting that Mute-N leads video-based LLMs to produce null captions. Notably, when the inference prompt differs from the prompt used during the attack phase, Mute-N shows a certain degree of performance reduction against Video-LLaMA. We speculate this may be due to Mute-N's focus on the EOS probability of a single token, potentially reducing its stability across different inference prompts. So, we introduce Mute-N2 in the Appendix to enhance its performance. These findings further emphasize the necessity of using both Mute-S and Mute-N, as Mute-S remains stable under different circumstances, while Mute-N performs optimally when the inference prompt matches the one used during the attack phase. Overall, the experiments above demonstrate that our methods have a certain degree of prompt transferability. + +Ablation Study on Rambling-F. Our Rambling-F integrates both $\mathcal{L}_{video}$ and $\mathcal{L}_{LLM}$ . To thoroughly evaluate the + +![](images/e48b43bb5f65a06ff8569742c9aa34e1ed7a70ce924409c7af81424bf93833bc.jpg) +Figure 3. Comparison of CLIP score (left) and BLEU (right) on Rambling-F to evaluate different parameters' influence. When the parameter is too small, the CLIP score and BLEU are high, indicating poor protective performance. Meanwhile, the evaluation scores decrease under $\alpha = 1$ , $\beta = 1$ compared to $\alpha = 1$ , $\beta = 0$ or $\alpha = 0$ , $\beta = 1$ , suggesting that the combination of feature losses is effective and necessary. All the videos are annotated by VideoLLaMA on the OpenVid-1M dataset. $\alpha = 0$ , $\beta = 0$ represents original video. + +![](images/fd0a667231aa79bdddaaa88ee04a66b6a9d4219066716424630050b66b8d68e0.jpg) +Figure 4. CLIP score about Ramblings on different perturbation magnitudes. When the perturbation magnitude is small, the CLIP score is higher, indicating poor protective performance for the videos. With the increase of perturbation magnitude, the protective performance of Ramblings is better. + +individual and combined impact of each feature loss, we conduct a parameter experiment to explore the influence of $\alpha$ and $\beta$ in Eq. (2). As outlined in Fig. 3, the combination of $\alpha = 1, \beta = 1$ outperforms the combination of $\alpha = 1, \beta = 0$ or $\alpha = 0, \beta = 1$ which means that it is effective to add these features together to get better protective performance. Additionally, larger values for these parameters generally lead to better performance in reducing annotation quality. However, when increased to a certain extent, the performance does not show improvement even reduction. These findings highlight the synergy between the two feature losses, suggesting that their integration enhances the method's ability to strengthen adversarial attacks and more effectively protect video content. And to get better performance, the proper parameters are needed. Actually, $\alpha = 1, \beta = 1$ is a suitable parameter combination. + +Ablation Study on Perturbation Magnitude. We conduct additional experiments with varying perturbation magnitudes to investigate their influence on adversarial performance. We select perturbation magnitudes of 2/255, 4/255, 8/255, and 16/255 for evaluation. As illustrated in Fig. 4, a perturbation magnitude of 2/255 yields the worst performance and a perturbation magnitude of 16/255 yields the best performance to protect the videos. Overall, an increase in the perturbation magnitude correlates with an enhancement in the Ramblings performance. Meanwhile, as illustrated in Fig. 5, lower perturbation magnitude tends to result in increased output length. Overall, reduced perturbation magnitudes may compromise the performance of Ramblings and Mutes, yet they have the benefit of minimizing deviations from the original videos. Consequently, finding an optimal balance in perturbation magnitude is essential to achieve both effective performance in adversarial attacks and imperceptible deviations from original videos. More + +![](images/3d48dd283e46b60b5509b9703659d54114414484c28076ee4d176b55e4ffa239.jpg) +Figure 5. The length of the textual output for Mutes varies across different perturbation magnitudes. When the perturbation magnitude is small, the text length is longer, indicating more information leakage from the videos. With the increase of perturbation magnitude, the information leakage of Mutes is less. + +![](images/27c25ebf86dd0182f95bda8113d27834247a63091290f4c699c7ea28ad160a28.jpg) + +experiment results can be found in the Appendix. And all the videos used in experiments are annotated by VideoLLaMA on the OpenVid-1M dataset. + +# 5. Conclusion + +In this study, we have successfully developed two series of novel watermarking methods aimed at safeguarding video content from unauthorized and automated annotation by video-based large language models. Through our exploration of adversarial attacks, we propose two series of video watermarks named Ramblings and Mutes, respectively. On the one hand, Ramblings are designed to fool video-based LLMs into generating completely incorrect annotations. On the other hand, Mutes, which focus on the EOS token, can shorten annotations by video-based LLMs. Extensive experiments demonstrate the effectiveness of our watermarking methods in misleading or silencing video-based LLMs. Furthermore, evaluations of text-to-video models using different protective approaches show that our methods can impact downstream tasks. Finally, we hope that our Ramblings and Mutes can serve as a protective paradigm to help safeguard videos from unauthorized annotation. + +# Ethics Statement + +Our proposed Ramblings and Mutes are designed solely for protective purposes not to be applied maliciously, and their application in this context is intended to benefit video data privacy. 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Efficient self-supervised video hashing with selective state spaces. In AAAI, 2025. 2 +[39] Zefeng Wang, Zhen Han, Shuo Chen, Fan Xue, Zifeng Ding, Xun Xiao, Volker Tresp, Philip Torr, and Jindong Gu. Stop reasoning! when multimodal llms with chain-of-thought reasoning meets adversarial images. arXiv preprint arXiv:2402.14899, 2024. 2 + +[40] Cheng Wei, Yang Wang, Kuofeng Gao, Shuo Shao, Yiming Li, Zhibo Wang, and Zhan Qin. Pointncbw: Towards dataset ownership verification for point clouds via negative clean-label backdoor watermark. IEEE Transactions on Information Forensics and Security, 2024. 1 +[41] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. In NeurIPS, pages 24824-24837, 2022. 1 +[42] Baoyuan Wu, Shaokui Wei, Mingli Zhu, Meixi Zheng, Zihao Zhu, Mingda Zhang, Hongrui Chen, Danni Yuan, Li Liu, and Qingshan Liu. Defenses in adversarial machine learning: A survey. arXiv preprint arXiv:2312.08890, 2023. 2 +[43] Jun Xu, Tao Mei, Ting Yao, and Yong Rui. Msr-vtt: A large video description dataset for bridging video and language. In CVPR, 2016. 2, 5 +[44] Lin Xu, Yilin Zhao, Daquan Zhou, Zhijie Lin, See Kiong Ng, and Jiashi Feng. Pllava: Parameter-free llava extension from images to videos for video dense captioning. arXiv preprint arXiv:2404.16994, 2024. 1, 2 +[45] Antoine Yang, Arsha Nagrani, Paul Hongsuck Seo, Antoine Miech, Jordi Pont-Tuset, Ivan Laptev, Josef Sivic, and Cordelia Schmid. Vid2seq: Large-scale pretraining of a visual language model for dense video captioning. In CVPR, pages 10714-10726, 2023. +[46] Hang Zhang, Xin Li, and Lidong Bing. Video-llama: An instruction-tuned audio-visual language model for video understanding. arXiv preprint arXiv:2306.02858, 2023. 1, 2, 5 +[47] Tong Zhang, Xiankai Lu, Hao Zhang, Xiushan Nie, Yilong Yin, and Jianbing Shen. Relational network via cascade crf for video language grounding. IEEE Transactions on Multimedia, 26:8297-8311, 2023. 2 +[48] Tong Zhang, Hao Fang, Hao Zhang, Jialin Gao, Xiankai Lu, Xiushan Nie, and Yilong Yin. Learning feature semantic matching for spatio-temporal video grounding. IEEE Transactions on Multimedia, 2024. 2 +[49] Yunqing Zhao, Tianyu Pang, Chao Du, Xiao Yang, Chongxuan Li, Ngai-Man Man Cheung, and Min Lin. On evaluating adversarial robustness of large vision-language models. In NeurIPS, 2023. 2 +[50] Yongshuo Zong, Tingyang Yu, Ruchika Chavhan, Bingchen Zhao, and Timothy Hospedales. Fool your (vision and) language model with embarrassingly simple permutations. 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However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content. Our code is available at https://github.com/ttthhl/Protecting_Your_Video_Content." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 135, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 135, + 618 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 135, + 618 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 625, + 296, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 625, + 296, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 625, + 296, + 685 + ], + "type": "text", + "content": "Recent years have witnessed significant advancements in both video-based large language models (video-based LLMs) [18, 27, 35, 44-46] and text-to-video generation models [6, 16, 23, 26, 37]. These two types of models demonstrate a close relationship: text-to-video models" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 321, + 258, + 548, + 397 + ], + "blocks": [ + { + "bbox": [ + 321, + 258, + 548, + 397 + ], + "lines": [ + { + "bbox": [ + 321, + 258, + 548, + 397 + ], + "spans": [ + { + "bbox": [ + 321, + 258, + 548, + 397 + ], + "type": "image", + "image_path": "c1d8f54acf8dac49e30dd18d5bdf7dc7efb7d061902fdb39f8d13a0537158b07.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 404, + 555, + 472 + ], + "lines": [ + { + "bbox": [ + 313, + 404, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 404, + 555, + 472 + ], + "type": "text", + "content": "Figure 1. We propose two strategies to protect the video content: Ramblings and Mutes. The Ramblings approach misleads videobased large language models into generating inaccurate captions. Besides, Mutes prompt these models to produce shorter and even NULL captions, lacking descriptive detail. The answers in the figure are excerpts." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "content": "rely heavily on high-quality video-text pairs for fine-tuning, while video-based LLMs can enhance video-text pairs quality through advanced annotation capabilities. By leveraging the power of large language models [4, 14, 15, 36, 41], video-based LLMs have revolutionized video content interpretation and annotation. This advancement directly contributes to the improvement of video data annotation quality. However, alongside these technological advances, concerns about data safety and privacy [2, 8, 19-22, 40] have emerged. Given the vast amount of personal video content available on multimedia platforms, protecting this data from unauthorized annotation has become an urgent challenge that requires immediate attention. In this paper, we aim to protect personal videos from being unauthorizedly and automatically annotated by video-based LLMs. To tackle this significant and challenging issue, we propose two series of protective and imperceptible watermarks added to videos. In each scenario, we propose two methods in order to add" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 135, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 135, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 135, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24056" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 274, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 274, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 274, + 84 + ], + "type": "text", + "content": "diversity and adaptability for widespread applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 86, + 294, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 86, + 294, + 217 + ], + "spans": [ + { + "bbox": [ + 54, + 86, + 294, + 217 + ], + "type": "text", + "content": "Specifically, we aim to mislead video-based LLMs into generating entirely incorrect annotations in the first scenario. To achieve this, we propose two methods, Rambling-F and Rambling-L, from different perspectives. Rambling-F operates at the feature level, increasing the discrepancy of video and LLM features. Rambling-L manipulates the logit-level by increasing the auto-regressive loss. These adversarial strategies serve to protect personal video content from unauthorized exploitation. Furthermore, fine-tuning text-to-video models on these adversarial video-text pairs will degrade the quality of generated videos." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 219, + 296, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 219, + 296, + 410 + ], + "spans": [ + { + "bbox": [ + 56, + 219, + 296, + 410 + ], + "type": "text", + "content": "The second scenario is designed to make the video-based LLMs effectively \"mute\", which means they are induced to generate shorter output on the given video. We also propose two methods, called Mute-S and Mute-N, relying on the probability of the End-of-Sequence (EOS) token, which, when generated, halts the LLM's inference process. Mute-S aims to cause the video-based LLMs to generate short and incomplete text sequences. For example, the generated text is \"The video is a\". Mute-N aims to return a NULL response by increasing the EOS probability of the first generated token. Overall, these methods can either fragment the sentences or result in a null output, preventing meaningful information from being leveraged by the video-based LLMs. These disruptions in the video-text pairs can then influence the text-to-video model's training and reduce your information leakage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 412, + 296, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 412, + 296, + 579 + ], + "spans": [ + { + "bbox": [ + 56, + 412, + 296, + 579 + ], + "type": "text", + "content": "Our two scenarios are evaluated across three datasets and three different video-based LLMs, providing comprehensive validation of our methods' effectiveness and adaptability. The text output demonstrates that our Ramblings method can effectively induce the video-based LLMs to generate completely incorrect annotations for the videos, while our Mutes method successfully limits the model's output, reducing the amount of useful information generated. Additionally, we use the annotated video-text pairs to fine-tune a text-to-video model, and the results clearly show that the model's performance degrades by our watermarking methods. Finally, a series of ablation studies, including prompt transferability, further validate the effectiveness and robustness of our proposed methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 580, + 294, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 580, + 294, + 592 + ], + "spans": [ + { + "bbox": [ + 66, + 580, + 294, + 592 + ], + "type": "text", + "content": "In summary, our contribution can be outlined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "type": "text", + "content": "- We investigate the security and privacy risks faced by video annotation with video-based LLMs. To address these risks, we introduce two series of novel video watermarks that prevent unauthorized automated annotation. And we emphasize that the video-text pairs' quality influenced by our watermarks is important for downstream tasks such as text-to-video models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "- Our two series of watermarking methodologies demonstrate distinct strategies for disrupting video-based LLMs: inducing either inaccurate or short captions. These" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 553, + 108 + ], + "type": "text", + "content": "methodologies expand the scope of video privacy protection techniques and establish a foundation for developing robust defenses against unauthorized content analysis." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 108, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 108, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 108, + 555, + 228 + ], + "type": "text", + "content": "- Through extensive experiments, our methods have been proven to perform effectively across three state-of-the-art video-based LLMs, namely Video-ChatGPT [27], Video-LLaMA [46], and Video-Vicuna (change the backbone of Video-LLaMA), as well as three diverse datasets: OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. These demonstrate the robustness and generalization capability of our approach, showing its ability to adapt to various models and datasets while consistently preventing unauthorized video annotation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 239, + 400, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 400, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 400, + 252 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 260, + 511, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 260, + 511, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 260, + 511, + 273 + ], + "type": "text", + "content": "2.1. Video-based Large Language Models" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 279, + 555, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 555, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 555, + 542 + ], + "type": "text", + "content": "The recent advancements in video-based LLMs [18, 27, 35, 44-46] have significantly enhanced their capabilities in various video-related tasks [38, 47, 48]. These models, such as Video-ChatGPT [27] and Video-LLaMA [46], effectively leverage both spatial and temporal features from video data and the generation ability of LLMs, enabling them to achieve impressive zero-shot performance. The integration of the video modality into LLMs allows for visual context-aware interaction, surpassing the capabilities of existing LLMs. The impressive performance of these models has led to their widespread use in generating dense captions [44] for unannotated videos, which can be used subsequently in downstream tasks, such as text-to-video generation models [6, 16, 23, 26, 37]. However, the widespread use of video-based LLMs raises privacy concerns regarding the potential for the unauthorized annotation of personal videos. As these models become more prevalent, it is crucial to address the ethical implications involving sensitive or private video content. To address these issues, we propose protective video watermarking methods that can prevent personal video from unauthorized and automated annotation by video-based LLMs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 551, + 426, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 551, + 426, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 551, + 426, + 563 + ], + "type": "text", + "content": "2.2. Adversarial Attack" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "content": "Adversarial attacks [1, 7, 9-13, 17, 19, 25, 39, 42, 50] typically craft imperceptible adversarial perturbations that can mislead the models into making incorrect predictions. With the development of multi-modal LLMs, researchers have begun exploring how these attacks can be applied in more complex generation settings. Concretely, recent studies show that adversarial attacks can be used to jailbreak multi-modal LLMs, causing them to generate harmful content [32] or induce targeted captions [49]. In contrast to these adversarial attacks, which aim to manipulate the model to an attacking goal, we adopt them as a pioneering watermarking strategy. It is designed to protect the privacy" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24057" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "and security of video content within these models. Specifically, our watermarking approach is crafted to safeguard the video data against unauthorized annotation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 118, + 138, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 118, + 138, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 118, + 138, + 131 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 137, + 123, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 137, + 123, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 137, + 123, + 148 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 156, + 296, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 156, + 296, + 310 + ], + "spans": [ + { + "bbox": [ + 55, + 156, + 296, + 310 + ], + "type": "text", + "content": "To prevent unauthorized annotation by video-based LLMs, we propose two protective scenarios. First, video-based LLMs can be misled to generate inaccurate captions that significantly diverge the video content when provided with protected video input. Second, video-based LLMs are induced to generate shorter, less detailed captions compared to those generated from clean videos which means less information leakage. Fine-tuning text-to-video models on such video-text pairs can degrade the quality of generated videos, due to the low quality of video-text pairs. For each scenario, we propose to adopt imperceptible adversarial perturbations as watermarks to protect videos from unauthorized annotation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 317, + 143, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 317, + 143, + 328 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 143, + 328 + ], + "type": "text", + "content": "3.2. Threat Model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "content": "Goals and Capabilities. The goal is to craft an imperceptible adversarial perturbation as a protective watermark for the video, which can induce video-based LLMs to generate totally incorrect or shorter sequences during the victim model's deployment. Following the most commonly used constraint for the involved perturbation [5], it is restricted within a predefined magnitude in the " + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "inline_equation", + "content": "l_{p}" + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "content": " norm, ensuring perturbation is difficult to detect." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 431, + 296, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 296, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 296, + 503 + ], + "type": "text", + "content": "Knowledge and Background. Following previous works [13, 31], we assume that the victim video-based LLMs can be accessed in full knowledge, including architectures and parameters. Additionally, we consider a more challenging scenario where the victim video-based LLMs are inaccessible, as detailed in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 509, + 180, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 180, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 180, + 521 + ], + "type": "text", + "content": "3.3. Problem Formulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "text", + "content": "To safeguard the video from unauthorized annotation by video-based LLMs, we propose to craft adversarial perturbations that can be added to a sequence of frames from the original videos. Given an original video " + }, + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "text", + "content": " and an adversarial video " + }, + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "inline_equation", + "content": "\\pmb{x}'" + }, + { + "bbox": [ + 55, + 528, + 295, + 598 + ], + "type": "text", + "content": " with a watermark, the optimization problem can be formulated as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 133, + 602, + 295, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 602, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 133, + 602, + 295, + 635 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\underset {\\boldsymbol {x} ^ {\\prime}} {\\arg \\max } \\mathcal {L} \\left(\\boldsymbol {x} ^ {\\prime}\\right), \\tag {1} \\\\ s. t. \\left| \\left| \\boldsymbol {x} ^ {\\prime} - \\boldsymbol {x} \\right| \\right| _ {\\infty} < \\epsilon , \\\\ \\end{array}", + "image_path": "99eb27ce4fb493c1231fe3332ed6873190b8719546c8bae8f358c86f5c9d0a6b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\cdot)" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " denotes the loss objective function to achieve different protective scenarios. To ensure the stealthiness of the adversarial perturbations, we introduce the " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "l_{\\infty}" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " restriction within a value of " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": ". For optimization, the projected gradient descent (PGD) algorithm [28] is adopted to update the adversarial perturbations at each iteration." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": "Typically, when a video " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " and an input prompt " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " are provided as inputs to the video-based LLMs " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": ", the video-based LLMs first utilize vision encoders " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " to extract visual features from the video. These extracted video features are then fed into the base LLMs " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " as inputs, which generate the hidden states from its final layer. Finally, the hidden states are projected into the probability distribution of all generated tokens, which can obtain a sequence of generated output tokens. We denote " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "f_{i}(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " as the probability distribution after the Softmax " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": " layer over the " + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 553, + 204 + ], + "type": "text", + "content": "-th generated token." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 210, + 553, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 553, + 234 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 553, + 234 + ], + "type": "text", + "content": "3.4. Ramblings for Incorrect Generation of Video-based LLMs" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 240, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 553, + 312 + ], + "type": "text", + "content": "In this section, we optimize adversarial videos that can mislead video-based LLMs to generate incorrect captions. To achieve this goal, we develop two different methods for video watermarks from the feature level and the logit level of the video-based LLMs, dubbed Rambling-F and Rambling-L." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 312, + 554, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 554, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 554, + 491 + ], + "type": "text", + "content": "Rambling-F (Feature). To induce the video-based LLMs to generate incorrect captions, we propose a feature-level adversarial strategy called Rambling-F. The core idea behind this approach is to deviate the features of adversarial videos from the original ones in the latent representation space. During the inference stage, the video-based LLMs extract visual features from the input video and also generate LLM features from the combination of the input video and text queries. Hence, in the Rambling-F, we propose to increase the " + }, + { + "bbox": [ + 313, + 312, + 554, + 491 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 313, + 312, + 554, + 491 + ], + "type": "text", + "content": " distance for both the video features and the LLM features between the original and adversarial videos. As a result, the disrupted features will result in the model's inability to accurately generate the captions correlated with the videos. The loss objective function for the Rambling-F can be formulated as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 338, + 495, + 553, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 495, + 553, + 578 + ], + "spans": [ + { + "bbox": [ + 338, + 495, + 553, + 578 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {v i d e o}} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left(g \\left(\\boldsymbol {x} ^ {\\prime}\\right) _ {i} - g (\\boldsymbol {x}) _ {i}\\right) ^ {2}, \\\\ \\mathcal {L} _ {L L M} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\left(h \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right) _ {j} - h \\left(\\boldsymbol {x}, c _ {\\text {i n}}\\right) _ {j}\\right) ^ {2}, \\tag {2} \\\\ \\mathcal {L} _ {R F} (\\pmb {x} ^ {\\prime}) = \\alpha * \\mathcal {L} _ {v i d e o} (\\pmb {x} ^ {\\prime}) + \\beta * \\mathcal {L} _ {L L M} (\\pmb {x} ^ {\\prime}), \\\\ \\end{array}", + "image_path": "97ce60e2ada54411455c789980e82f7d35b66d1e6ef660647f3890ccd866dee2.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": " are the total number of elements in the video and LLM features, respectively. In addition, " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "g(\\cdot)_i" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": "-th dimension of video features and " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "h(\\cdot)_j" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 582, + 553, + 629 + ], + "type": "text", + "content": "-th dimension of LLM features." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Rambling-L (Logit). In addition to the feature-level Rambling-F attack, we propose another adversarial strategy called Rambling-L, which manipulates the logit-level outputs, i.e., probability distributions over the generated tokens. Typically, based on the probability distribution over generated tokens, video-based LLMs can generate one token at one time in an auto-regressive manner to obtain the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24058" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 86, + 299, + 300 + ], + "blocks": [ + { + "bbox": [ + 61, + 86, + 299, + 300 + ], + "lines": [ + { + "bbox": [ + 61, + 86, + 299, + 300 + ], + "spans": [ + { + "bbox": [ + 61, + 86, + 299, + 300 + ], + "type": "image", + "image_path": "78f8b76a772ce97e785971601170cf62712ad39cd6e21a83dbcf08aee8023590.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 254, + 309, + 362, + 323 + ], + "lines": [ + { + "bbox": [ + 254, + 309, + 362, + 323 + ], + "spans": [ + { + "bbox": [ + 254, + 309, + 362, + 323 + ], + "type": "text", + "content": "Text-to-video model" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 302, + 85, + 549, + 300 + ], + "blocks": [ + { + "bbox": [ + 302, + 85, + 549, + 300 + ], + "lines": [ + { + "bbox": [ + 302, + 85, + 549, + 300 + ], + "spans": [ + { + "bbox": [ + 302, + 85, + 549, + 300 + ], + "type": "image", + "image_path": "9c5258d5edd36eed731d4af266321e3c8b36083d323093da4bb724f829acde7f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 344, + 555, + 389 + ], + "lines": [ + { + "bbox": [ + 54, + 344, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 54, + 344, + 555, + 389 + ], + "type": "text", + "content": "Figure 2. The pipeline of Ramblings and Mutes. While Rambling-F focuses on feature-level perturbations of the original content, Rambling-L increases auto-regressive loss to manipulate video-based LLMs into generating incorrect descriptions. Mutes, on the other hand, tend to increase the probability of the EOS token. Finally, these video-text pairs can influence downstream tasks, such as the capacity of text-to-video models fine-tuned on these data." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "spans": [ + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "content": "caption. Therefore, for the generation of incorrect captions, we can increase the distance between the adversarial video " + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{\\prime}" + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "content": " and the original ground-truth caption " + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "content": " generated from the original video " + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "content": " by the auto-regressive loss " + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ar}(\\cdot)" + }, + { + "bbox": [ + 54, + 410, + 295, + 481 + ], + "type": "text", + "content": ". The loss objective function for the Rambling-L attack can be expressed as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 488, + 295, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 488, + 295, + 504 + ], + "spans": [ + { + "bbox": [ + 111, + 488, + 295, + 504 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R L} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), y\\right). \\tag {3}", + "image_path": "5a12e5d93e5b682bb6765fb05160a40e981fd39b5b49d37cbd24a6aea4c0c536.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 509, + 296, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 296, + 546 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 296, + 546 + ], + "type": "text", + "content": "By increasing Eq. (3), we can shift the model's token probability distribution away from the correct captions, causing the video-based LLMs to generate incorrect textual outputs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 552, + 296, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 574 + ], + "type": "text", + "content": "3.5. Mutes for Shorter even NULL Generation of Video-based LLMs" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 653 + ], + "type": "text", + "content": "In this section, we craft adversarial videos that can induce video-based LLMs to generate shorter captions or even no captions at all, including Mute-S and Mute-N. To this end, we propose manipulating the probability of the End-of-Sequence (EOS) token of video-based LLMs for two protective goals." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "Mute-S (Short Caption). During the auto-regressive generation process of video-based LLMs, the occurrence of an End-of-Sequence (EOS) token serves as a signal to stop generating further tokens. To decrease the length of generated sequences, one straightforward approach is to in" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 410, + 555, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 555, + 506 + ], + "type": "text", + "content": "duce the occurrence of the EOS token during the prediction process. However, the auto-regressive prediction is a non-deterministic random process [13], making it challenging to directly determine the exact position where the EOS token is generated. To address this challenge, we propose Mute-S, which aims to increase the probability of the EOS token at all positions of generated sequences " + }, + { + "bbox": [ + 313, + 410, + 555, + 506 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{out}}" + }, + { + "bbox": [ + 313, + 410, + 555, + 506 + ], + "type": "text", + "content": ". The loss function can be formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 348, + 514, + 555, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 514, + 555, + 546 + ], + "spans": [ + { + "bbox": [ + 348, + 514, + 555, + 546 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M S} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} f _ {i} ^ {\\mathrm {E O S}} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}} \\oplus y _ {\\text {o u t}}\\right), \\tag {4}", + "image_path": "26796e522ec69a39504ce55d172ab7fc6929b28efaab7a70fabf26ff0279c85a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "inline_equation", + "content": "f_{i}^{\\mathrm{EOS}}(\\cdot)" + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": " is EOS token probability of the probability distribution after the Softmax(\\cdot) layer over the " + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": "-th generated token and " + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": " is the length of generated sequences " + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{out}}" + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{out}}" + }, + { + "bbox": [ + 313, + 556, + 555, + 653 + ], + "type": "text", + "content": " is updated at each iteration during the optimization. By increasing Eq. (4), Mute-S can effectively manipulate video-based LLMs to terminate the caption generation process in advance, resulting in shorter and potentially less informative captions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 714 + ], + "type": "text", + "content": "Mute-N (NULL Caption). Considering a more extreme case, we can directly induce video-based LLMs to become highly confident in predicting the EOS token as the very first token during generation, resulting in generating NULL or empty captions. To this end, we propose Mute-N, which" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24059" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "increases the probability of the EOS token at the first predicted token position, rather than optimizing the mean probability of the EOS token across generated sequences as Mute-S. Given the auto-regressive generation process of video-based LLMs, we can force video-based LLMs to approach the EOS token in an auto-regressive manner. The loss function for Mute-N can be formulated as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 93, + 165, + 295, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 165, + 295, + 178 + ], + "spans": [ + { + "bbox": [ + 93, + 165, + 295, + 178 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M N} \\left(\\boldsymbol {x} ^ {\\prime}\\right) = - \\mathcal {L} _ {a r} \\left(\\mathcal {F} \\left(\\boldsymbol {x} ^ {\\prime}, c _ {\\text {i n}}\\right), [ \\mathrm {E O S} ]\\right), \\tag {5}", + "image_path": "63814a2fe71a3892351e95ff5a3a1663eeccd7ca20796c9b0db3f287fe799da1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 186, + 296, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 296, + 247 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 296, + 247 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 186, + 296, + 247 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ar}(\\cdot)" + }, + { + "bbox": [ + 55, + 186, + 296, + 247 + ], + "type": "text", + "content": " denotes the auto-regressive loss function and [EOS] is the EOS token. By optimizing Eq. (5), we can fool the video-based LLMs into generating the EOS token at the beginning, causing the generation process of video-based LLMs to halt immediately." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 257, + 132, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 132, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 132, + 270 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 276, + 188, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 276, + 188, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 276, + 188, + 289 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 295, + 295, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 295, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 295, + 462 + ], + "type": "text", + "content": "Models and Datasets. We elaborately select three state-of-the-art video-based LLMs as annotation models: VideoChatGPT [27], Video-LLaMA [46], and Video-Vicuna (a variant of Video-LLaMA with a modified backbone). The default inference prompt template is used to obtain video annotations, with the user input prompt set to \"What is this video about?\" Detailed settings for these models are available in the Appendix. For datasets, we use data from OpenVid-1M [29], MSR-VTT [43], and WebVid-10M [3]. They are all high-quality collections of videos paired with corresponding captions. By calculating similarity with the dataset captions, we can evaluate the performance of the annotations. To accommodate the limited memory of GPUs, each video is preprocessed to consist of 8 frames." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 463, + 295, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 295, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 295, + 594 + ], + "type": "text", + "content": "Baselines and Setups. We use original videos and videos added with random perturbations as baselines. For the setup, the perturbation magnitude is set to 16/255 using the " + }, + { + "bbox": [ + 55, + 463, + 295, + 594 + ], + "type": "inline_equation", + "content": "l_{\\infty}" + }, + { + "bbox": [ + 55, + 463, + 295, + 594 + ], + "type": "text", + "content": " norm to make the perturbation imperceptible, and the optimization step size is set to 1/255, using the projected gradient descent (PGD) algorithm [28]. The optimization iteration is set to 200 for Ramblings and 500 for Mutes, respectively. For video-based LLM configurations, we set a sampling temperature of 0.2 and limit the output to a maximum of 512 tokens for three models and the others are default. Additional setup details are provided in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. For the evaluation of Ramblings, we employ two metrics: CLIP score (RN101) and BLEU. CLIP score [33] measures the similarity between the model's post-attack inferences and the original dataset captions, with a higher score indicating greater similarity and better annotation performance. BLEU [30] assesses the alignment between the model's outputs and reference texts, where a higher BLEU indicates a closer match and improved annotation performance. Our adversarial objective is to reduce these scores." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "content": "For the evaluation of Mutes, we use two metrics: length and EOS rate (NULL caption rate). We compare the lengths of outputs generated from clean and adversarial videos to assess the effectiveness of the Mutes approach. A shorter length indicates less information leakage from the videos. The EOS rate measures how often video-based LLMs output the EOS token early, signifying that no information is leaked from the videos. A higher EOS rate means video-based LLMs output NULL captions more frequently." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 188, + 399, + 200 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 188, + 399, + 200 + ], + "spans": [ + { + "bbox": [ + 313, + 188, + 399, + 200 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 207, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 207, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 553, + 361 + ], + "type": "text", + "content": "As shown in Tab. 1, the CLIP score and BLEU are similar between original videos and those with random noise across three models, indicating that random noise does not reduce annotation performance and is therefore ineffective at protecting videos from unauthorized annotation. In contrast, the evaluation scores for Ramblings in Tab. 1 show a substantial decrease compared to the baselines, indicating significant alterations in the semantic information generated by the video-based LLMs. These results demonstrate that adversarial attack on the feature level or logit level effectively misleads the models into generating incorrect annotations for the videos. And our two methods offer great adaptability and flexibility to accommodate various circumstances." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 363, + 553, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 553, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 553, + 615 + ], + "type": "text", + "content": "As shown in Tab. 2, the videos with random noise are ineffective in protecting video content compared to the original videos, as the output length is high and the EOS rate is zero, indicating that a gradient optimization algorithm is necessary to achieve meaningful perturbation. In contrast, our Mute-S effectively disrupts sentence integrity, for example, video-based LLMs may output fragmented text such as \"The video is a\" without forming a coherent description. Further examples are provided in the Appendix. Specifically, for Video-LLaMA, Mute-S reduces text length nearly tenfold, with the EOS rate around " + }, + { + "bbox": [ + 313, + 363, + 553, + 615 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 363, + 553, + 615 + ], + "type": "text", + "content": ". Additionally, our Mute-S significantly reduces the length of generated texts while maintaining a relatively low EOS rate, representing an untargeted attack strategy. Meanwhile, our Mute-N successfully prompts the model to output NULL captions, meaning that video-based LLMs extract no information from the videos, achieving a targeted attack. This analysis underscores the exceptional effectiveness of both Mute-S and Mute-N, resulting in minimal information being extracted by video-based LLMs and ultimately protecting videos from unauthorized and automated annotation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 623, + 553, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 623, + 553, + 646 + ], + "spans": [ + { + "bbox": [ + 313, + 623, + 553, + 646 + ], + "type": "text", + "content": "4.3. Influence on Downstream Work: Text-to-video Models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "To further demonstrate the impact of our watermarking methods on downstream tasks, we fine-tune text-to-video models using our annotated video-text pairs. After finetuning, we evaluate the model's performance on established benchmarks to demonstrate that our protective watermark" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24060" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 104, + 555, + 294 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "type": "text", + "content": "Table 1. The CLIP score and BLEU between texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna, and clean captions in datasets are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 104, + 555, + 294 + ], + "lines": [ + { + "bbox": [ + 56, + 104, + 555, + 294 + ], + "spans": [ + { + "bbox": [ + 56, + 104, + 555, + 294 + ], + "type": "table", + "html": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Video-ChatGPTOriginal0.762210.017030.673830.024050.609380.01040
Noise0.757810.013980.675290.026710.613770.01123
Rambling-F0.667970.011970.603520.015610.495610.00514
Rambling-L0.627440.002710.603030.003500.483150.00169
Video-LLaMAOriginal0.787600.051210.623540.004820.608890.00316
Noise0.799800.047610.622560.004720.601560.00292
Rambling-F0.583010.016000.492920.003500.428960.00205
Rambling-L0.609380.020680.492190.003130.433840.00189
Video-VicunaOriginal0.757320.019690.621580.026040.601070.01332
Noise0.763670.022750.617680.022110.601070.01435
Rambling-F0.625000.023170.507320.007840.423100.00363
Rambling-L0.635250.016440.501950.009080.441890.00449
", + "image_path": "86f970d2f3cf05d588c627afada8e9aeb7caef8551d131513976f912d52dbe2f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 327, + 555, + 517 + ], + "blocks": [ + { + "bbox": [ + 55, + 304, + 555, + 326 + ], + "lines": [ + { + "bbox": [ + 55, + 304, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 555, + 326 + ], + "type": "text", + "content": "Table 2. The length and EOS rate of texts annotated by three video-based LLMs: Video-ChatGPT, Video-LLaMA, and Video-Vicuna are measured on three datasets: OpenVid-1M, MSR-VTT, and WebVid-10M. The best results are highlighted in bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 327, + 555, + 517 + ], + "lines": [ + { + "bbox": [ + 56, + 327, + 555, + 517 + ], + "spans": [ + { + "bbox": [ + 56, + 327, + 555, + 517 + ], + "type": "table", + "html": "
Base modelMethodOpenVid-1MMSR-VTTWebVid-10M
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Video-ChatGPTOriginal30.470.030.290.031.210.0
Noise30.200.031.240.024.280.0
Mute-S13.6011.012.2813.011.3921.0
Mute-N0.00100.00.00100.00.00100.0
Video-LLaMAOriginal203.540.0208.620.0214.490.0
Noise224.230.0213.470.0209.300.0
Mute-S11.587.017.2813.037.749.0
Mute-N0.00100.00.00100.00.00100.0
Video-VicunaOriginal32.900.046.540.028.640.0
Noise38.270.040.080.034.370.0
Mute-S7.381.06.450.05.560.0
Mute-N0.00100.00.00100.00.00100.0
", + "image_path": "f6bff26203268d2b76106900f5851359d588289d46bc6ab0900975220696bb4c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 536, + 295, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 295, + 560 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 295, + 560 + ], + "type": "text", + "content": "ing methods can significantly degrade the model's ability to generate high-quality videos." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "text", + "content": "Experiment Setups. The text-to-video framework we used isAnimateDiff [16], which is based on diffusion model [34]. The dataset we used to fine-tune the text-to-video model consists of video-text pairs annotated by Video-LLaMA based on OpenVid-1M. We follow theAnimateDiff training script. The pre-trained model used is stable-diffusion-v1-51. For image fine-tuning in theAnimateDiff pipeline, the learning rate and training steps are set to " + }, + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-6}" + }, + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "text", + "content": " and 500, respectively. During the training process of the motion module in theAnimateDiff pipeline, we set the learning rate to " + }, + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 55, + 560, + 295, + 693 + ], + "type": "text", + "content": " and the training steps" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 536, + 555, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 555, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 555, + 571 + ], + "type": "text", + "content": "to 10,000. For text-to-video generation, we set the guidance scale as 8 and the steps as 25. To evaluate conveniently, we still use stable-diffusion-v1-5 as the base model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": "Evaluation Metrics. For the evaluation of the text-to-video models, we use two metrics: " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQA}_{\\mathrm{A}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQAT}_{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": ". We adopt these metrics from EvalCrafter [24] as benchmarks to evaluate the performance of text-to-video models fine-tuned on videos with annotations generated by video-based LLMs. Specifically, " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQA}_{\\mathrm{A}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": " measures the aesthetic quality of generated videos, while " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQAT}_{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": " assesses technical quality. Higher " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQA}_{\\mathrm{A}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{VQAT}_{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 576, + 556, + 685 + ], + "type": "text", + "content": " indicate better quality of the generated videos by text-to-video models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Results. As illustrated in Tab. 5, the " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{VQA_A}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{VQAT}_{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " [24] decrease whenAnimateDiff is fine-tuned using adversar" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 702, + 283, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 283, + 714 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 283, + 714 + ], + "type": "text", + "content": "1 https://huggingface.co/stable-diffusion-v1-5/stable-diffusion-v1-5" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24061" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 116, + 558, + 211 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 115 + ], + "type": "text", + "content": "Table 3. Prompt transferability: The CLIP score and BLEU between texts annotated by Video-LLaMA and clean captions are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts:\"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 116, + 558, + 211 + ], + "lines": [ + { + "bbox": [ + 56, + 116, + 558, + 211 + ], + "spans": [ + { + "bbox": [ + 56, + 116, + 558, + 211 + ], + "type": "table", + "html": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
CLIP ScoreBLEUCLIP ScoreBLEUCLIP ScoreBLEU
Original0.787600.051210.793460.044110.767580.03146
Noise0.799800.047610.796880.040810.771970.03459
Rambling-F0.583010.016000.600100.015850.606450.01514
Rambling-L0.609380.020680.612790.019420.625000.01828
", + "image_path": "32941edf2c34643115e750b805e09a358672108edfe033acceae939389712ae9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 266, + 558, + 361 + ], + "blocks": [ + { + "bbox": [ + 55, + 220, + 555, + 266 + ], + "lines": [ + { + "bbox": [ + 55, + 220, + 555, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 220, + 555, + 266 + ], + "type": "text", + "content": "Table 4. Prompt transferability: The length and EOS rate of texts annotated by Video-LLaMA are measured on OpenVid-1M dataset. The prompt used during the attack phase is \"What is this video about?\". After the attack, we apply three different prompts: \"What is this video about?\", \"What happens in the video?\", and \"Can you describe the video in detail?\" to generate annotations for videos. The best results are highlighted in bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 266, + 558, + 361 + ], + "lines": [ + { + "bbox": [ + 56, + 266, + 558, + 361 + ], + "spans": [ + { + "bbox": [ + 56, + 266, + 558, + 361 + ], + "type": "table", + "html": "
MethodWhat is this video about?What happens in the video?Can you describe the video in detail?
LengthEOS Rate(%)LengthEOS Rate(%)LengthEOS Rate(%)
Original203.540.0221.310.0299.120.0
Noise224.230.0236.850.0300.920.0
Mute-S11.587.024.165.036.4410.0
Mute-N0.00100.064.0473.0230.7419.0
", + "image_path": "bc31f32a54d7d2a869d414b58b1c245bdea5a1c2e53e2839f400c290f7111d63.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 91, + 433, + 259, + 530 + ], + "blocks": [ + { + "bbox": [ + 55, + 380, + 297, + 425 + ], + "lines": [ + { + "bbox": [ + 55, + 380, + 297, + 425 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 297, + 425 + ], + "type": "text", + "content": "Table 5. The VQA and VQAT are evaluated forAnimateDiff fine-tuned on different adversarial video-text pairs. All the video-text pairs are annotated by Video-LLaMA on the OpenVid-1M dataset. The best results are highlighted in bold." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 91, + 433, + 259, + 530 + ], + "lines": [ + { + "bbox": [ + 91, + 433, + 259, + 530 + ], + "spans": [ + { + "bbox": [ + 91, + 433, + 259, + 530 + ], + "type": "table", + "html": "
MethodVQAAVQAT
Original60.43051.302
Noise46.71835.392
Rambling-F39.38328.231
Rambling-L38.04227.394
Mute-S43.61024.487
Mute-N43.46831.009
", + "image_path": "53d1ef5b94e1f692697fc81e4d14b91df3199827d89c05d2fbc21e186322ff5a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 552, + 296, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 601 + ], + "type": "text", + "content": "ial video-text pairs compared to those with original or randomly perturbed video-text pairs. This notable reduction demonstrates that the quality of text-to-video models degrades significantly by our watermarking methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 609, + 156, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 156, + 623 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 156, + 623 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "Transferability. Video-based LLMs generate corresponding responses according to different user prompts. In this section, we conduct the transferability experiments [25] to assess whether adversarial watermarks can protect videos from unauthorized annotation under varying user inference prompts. In this experiment, we adopt the inference prompts: \"What is this video about?\", \"What happens in" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 380, + 541, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 541, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 541, + 393 + ], + "type": "text", + "content": "the video?”, and “Can you describe the video in detail?”" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 398, + 555, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 555, + 686 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 555, + 686 + ], + "type": "text", + "content": "As shown in Tab. 3, changing the inference prompt still results in a significant reduction in both CLIP score and BLEU when using our Ramblings method, indicating that Rambling-F and Rambling-L effectively protect videos from unauthorized annotation across varied prompts. Similarly, as shown in Tab. 4, even with differing inference prompts, Mute-S and Mute-N significantly reduce the length of generated texts, preventing information leakage from the videos. Additionally, the EOS rate remains high, suggesting that Mute-N leads video-based LLMs to produce null captions. Notably, when the inference prompt differs from the prompt used during the attack phase, Mute-N shows a certain degree of performance reduction against Video-LLaMA. We speculate this may be due to Mute-N's focus on the EOS probability of a single token, potentially reducing its stability across different inference prompts. So, we introduce Mute-N2 in the Appendix to enhance its performance. These findings further emphasize the necessity of using both Mute-S and Mute-N, as Mute-S remains stable under different circumstances, while Mute-N performs optimally when the inference prompt matches the one used during the attack phase. Overall, the experiments above demonstrate that our methods have a certain degree of prompt transferability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Ablation Study on Rambling-F. Our Rambling-F integrates both " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{video}" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LLM}" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": ". To thoroughly evaluate the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24062" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 74, + 176, + 172 + ], + "blocks": [ + { + "bbox": [ + 67, + 74, + 176, + 172 + ], + "lines": [ + { + "bbox": [ + 67, + 74, + 176, + 172 + ], + "spans": [ + { + "bbox": [ + 67, + 74, + 176, + 172 + ], + "type": "image", + "image_path": "e48b43bb5f65a06ff8569742c9aa34e1ed7a70ce924409c7af81424bf93833bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "lines": [ + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "spans": [ + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": "Figure 3. Comparison of CLIP score (left) and BLEU (right) on Rambling-F to evaluate different parameters' influence. When the parameter is too small, the CLIP score and BLEU are high, indicating poor protective performance. Meanwhile, the evaluation scores decrease under " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": " compared to " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": ", suggesting that the combination of feature losses is effective and necessary. All the videos are annotated by VideoLLaMA on the OpenVid-1M dataset. " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 55, + 179, + 295, + 278 + ], + "type": "text", + "content": " represents original video." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 184, + 74, + 293, + 173 + ], + "blocks": [ + { + "bbox": [ + 184, + 74, + 293, + 173 + ], + "lines": [ + { + "bbox": [ + 184, + 74, + 293, + 173 + ], + "spans": [ + { + "bbox": [ + 184, + 74, + 293, + 173 + ], + "type": "image", + "image_path": "fd0a667231aa79bdddaaa88ee04a66b6a9d4219066716424630050b66b8d68e0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 191, + 425, + 312 + ], + "lines": [ + { + "bbox": [ + 313, + 191, + 425, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 191, + 425, + 312 + ], + "type": "text", + "content": "Figure 4. CLIP score about Ramblings on different perturbation magnitudes. When the perturbation magnitude is small, the CLIP score is higher, indicating poor protective performance for the videos. With the increase of perturbation magnitude, the protective performance of Ramblings is better." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "spans": [ + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": "individual and combined impact of each feature loss, we conduct a parameter experiment to explore the influence of " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " in Eq. (2). As outlined in Fig. 3, the combination of " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\alpha = 1, \\beta = 1" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " outperforms the combination of " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\alpha = 1, \\beta = 0" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\alpha = 0, \\beta = 1" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " which means that it is effective to add these features together to get better protective performance. Additionally, larger values for these parameters generally lead to better performance in reducing annotation quality. However, when increased to a certain extent, the performance does not show improvement even reduction. These findings highlight the synergy between the two feature losses, suggesting that their integration enhances the method's ability to strengthen adversarial attacks and more effectively protect video content. And to get better performance, the proper parameters are needed. Actually, " + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "inline_equation", + "content": "\\alpha = 1, \\beta = 1" + }, + { + "bbox": [ + 54, + 304, + 295, + 495 + ], + "type": "text", + "content": " is a suitable parameter combination." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": "Ablation Study on Perturbation Magnitude. We conduct additional experiments with varying perturbation magnitudes to investigate their influence on adversarial performance. We select perturbation magnitudes of 2/255, 4/255, 8/255, and 16/255 for evaluation. As illustrated in Fig. 4, a perturbation magnitude of 2/255 yields the worst performance and a perturbation magnitude of 16/255 yields the best performance to protect the videos. Overall, an increase in the perturbation magnitude correlates with an enhancement in the Ramblings performance. Meanwhile, as illustrated in Fig. 5, lower perturbation magnitude tends to result in increased output length. Overall, reduced perturbation magnitudes may compromise the performance of Ramblings and Mutes, yet they have the benefit of minimizing deviations from the original videos. Consequently, finding an optimal balance in perturbation magnitude is essential to achieve both effective performance in adversarial attacks and imperceptible deviations from original videos. More" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 315, + 69, + 425, + 178 + ], + "blocks": [ + { + "bbox": [ + 315, + 69, + 425, + 178 + ], + "lines": [ + { + "bbox": [ + 315, + 69, + 425, + 178 + ], + "spans": [ + { + "bbox": [ + 315, + 69, + 425, + 178 + ], + "type": "image", + "image_path": "3d48dd283e46b60b5509b9703659d54114414484c28076ee4d176b55e4ffa239.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 434, + 191, + 552, + 312 + ], + "lines": [ + { + "bbox": [ + 434, + 191, + 552, + 312 + ], + "spans": [ + { + "bbox": [ + 434, + 191, + 552, + 312 + ], + "type": "text", + "content": "Figure 5. The length of the textual output for Mutes varies across different perturbation magnitudes. When the perturbation magnitude is small, the text length is longer, indicating more information leakage from the videos. With the increase of perturbation magnitude, the information leakage of Mutes is less." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 439, + 71, + 548, + 178 + ], + "blocks": [ + { + "bbox": [ + 439, + 71, + 548, + 178 + ], + "lines": [ + { + "bbox": [ + 439, + 71, + 548, + 178 + ], + "spans": [ + { + "bbox": [ + 439, + 71, + 548, + 178 + ], + "type": "image", + "image_path": "27c25ebf86dd0182f95bda8113d27834247a63091290f4c699c7ea28ad160a28.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 335, + 553, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 553, + 370 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 553, + 370 + ], + "type": "text", + "content": "experiment results can be found in the Appendix. And all the videos used in experiments are annotated by VideoLLaMA on the OpenVid-1M dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 384, + 387, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 387, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 387, + 396 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 404, + 555, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 404, + 555, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 404, + 555, + 608 + ], + "type": "text", + "content": "In this study, we have successfully developed two series of novel watermarking methods aimed at safeguarding video content from unauthorized and automated annotation by video-based large language models. Through our exploration of adversarial attacks, we propose two series of video watermarks named Ramblings and Mutes, respectively. On the one hand, Ramblings are designed to fool video-based LLMs into generating completely incorrect annotations. On the other hand, Mutes, which focus on the EOS token, can shorten annotations by video-based LLMs. Extensive experiments demonstrate the effectiveness of our watermarking methods in misleading or silencing video-based LLMs. Furthermore, evaluations of text-to-video models using different protective approaches show that our methods can impact downstream tasks. Finally, we hope that our Ramblings and Mutes can serve as a protective paradigm to help safeguard videos from unauthorized annotation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 620, + 404, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 620, + 404, + 633 + ], + "spans": [ + { + "bbox": [ + 313, + 620, + 404, + 633 + ], + "type": "text", + "content": "Ethics Statement" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 712 + ], + "type": "text", + "content": "Our proposed Ramblings and Mutes are designed solely for protective purposes not to be applied maliciously, and their application in this context is intended to benefit video data privacy. We hope that our work can inform both academic researchers and industry professionals on safeguarding personal video content from misuse." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24063" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 152 + ], + "type": "text", + "content": "This work is supported in part by the National Natural Science Foundation of China, under Grant (62302309, 62171248), Shenzhen Science and Technology Program (JCYJ20220818101014030, JCYJ20220818101012025), and the PCNL KEY project (PCL2023AS6-1)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 163, + 115, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 163, + 115, + 176 + ], + "spans": [ + { + "bbox": [ + 56, + 163, + 115, + 176 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 183, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 183, + 296, + 217 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 183, + 296, + 217 + ], + "spans": [ + { + "bbox": [ + 61, + 183, + 296, + 217 + ], + "type": "text", + "content": "[1] Jiawang Bai, Bin Chen, Yiming Li, Dongxian Wu, Weiwei Guo, Shu-tao Xia, and En-hui Yang. 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Gangopadhyay Ziyao Zeng Younjoon Chung Alex Wong Yale Vision Lab", + "bbox": [ + 109, + 180, + 880, + 226 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 261, + 328, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present ProtoDepth, a novel prototype-based approach for continual learning of unsupervised depth completion, the multimodal 3D reconstruction task of predicting dense depth maps from RGB images and sparse point clouds. The unsupervised learning paradigm is well-suited for continual learning, as ground truth is not needed. However, when training on new non-stationary distributions, depth completion models will catastrophically forget previously learned information. We address forgetting by learning prototype sets that adapt the latent features of a frozen pretrained model to new domains. Since the original weights are not modified, ProtoDepth does not forget when test-time domain identity is known. To extend ProtoDepth to the challenging setting where the test-time domain identity is withheld, we propose to learn domain descriptors that enable the model to select the appropriate prototype set for inference. We evaluate ProtoDepth on benchmark dataset sequences, where we reduce forgetting compared to baselines by $52.2\\%$ for indoor and $53.2\\%$ for outdoor to achieve the state of the art. Project Page: https://protodepth.github.io/.", + "bbox": [ + 88, + 292, + 485, + 597 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 618, + 220, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstructing three-dimensional (3D) environments facilitates spatial applications such as autonomous navigation, robotic manipulation, and AR/VR. These applications typically utilize platforms equipped with heterogeneous sensors, such as cameras and sparse range sensors (e.g., LiDAR, ToF) which yield RGB images and point clouds. To reconstruct 3D scenes from an ego-centric point of view in the form of depth maps, the point clouds are typically projected onto the image plane. However, their projections tend to be sparse, which is unlike RGB images that comprise irradiance measured at each pixel. These complementary modalities can be used to predict dense depth maps; this multimodal 3D reconstruction task is called depth completion.", + "bbox": [ + 89, + 643, + 485, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Depth completion models can be trained in a supervised (using ground truth) or unsupervised (using Structure-from-Motion) manner. As ground truth is prohibitively expensive to acquire, we subscribe to the unsupervised learning", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d3992e7a6e62904b1febe2810704257ea19d212ab7fe07854755378b2c6432e.jpg", + "image_caption": [ + "Figure 1. Results on KITTI validation set during continual training on outdoor dataset sequence (KITTI $\\rightarrow$ Waymo $\\rightarrow$ VKITTI)." + ], + "image_footnote": [], + "bbox": [ + 524, + 263, + 897, + 405 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "paradigm, which enables one to learn without human intervention. While this suggests the potential to continuously learn, existing models are trained and evaluated on single datasets under the assumption of a stationary data distribution. However, sequences of multiple datasets exhibit non-stationary distributions and are captured by sensors with varying calibrations. Hence, fitting to new data samples inevitably causes the model to \"catastrophically forget\" [19, 54, 63, 82] previously learned information, where the model performance degrades significantly on data from distributions that it had already observed.", + "bbox": [ + 511, + 462, + 908, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enable pretrained models to adapt to new environments or domains in an unsupervised manner, we consider continual learning, where training strategies aim to mitigate catastrophic forgetting of previously observed training distributions when learning from a continuous stream of non-stationary data. One school of thought is to constrain updates to parameters deemed \"important\" for previous domains based on a regularization term controlled by a weight chosen as a hyperparameter. Another is to incur memory costs by storing previously observed training data and incorporating them during learning of new domains, akin to rehearsals. The trade-off is in the sensitivity of optimization (and forgetting) to the choice of hyperparameter and in the size of storage and data privacy. Both schools perform updates to the full set of model parameters, which is computationally expensive. Unlike them, we opt to freeze the pretrained model to ensure zero forgetting and learn a small set of parameters, which we term \"prototypes,\" that modulate", + "bbox": [ + 511, + 628, + 910, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6304", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the latent features for each new domain encountered.", + "bbox": [ + 89, + 90, + 439, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We model the change in distribution as a domain-specific bias to be learned by global multiplicative and local additive prototypes that transform the latent features to fit the new distribution. In the same vein are learnable prompts or tokens [92] used in continual learning for vision transformers, where the model itself is similarly frozen. Yet, there is no natural scale at which to discretize images, unlike discrete text tokens. In contrast, our proposed prototypes lift the requirements of tokenized inputs and can thus be applied to convolutional neural networks, which are prevalently used in unsupervised depth completion, as well as transformers.", + "bbox": [ + 88, + 106, + 480, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose ProtoDepth, a novel prototype-based method for unsupervised continual depth completion. Instead of prompts in input space, we deploy lightweight prototypes to a frozen pretrained model to encode prototypical information of each domain. These prototypes model global and local biases, where global prototypes learn a transformation from the latent pretrained data distribution to that of the new domain, and local prototypes capture fine-grained features that can be selectively queried depending on the input. Naturally, when the test-time domain identity is known, i.e., domain-incremental, ProtoDepth exhibits no forgetting and learns the new data distribution with high fidelity. We further encode each domain as a descriptor to enable inference when test-time domain identity is withheld, i.e., domain-agnostic, where the prototype set corresponding to the highest affinity domain descriptor for a given sample is chosen.", + "bbox": [ + 91, + 273, + 485, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions: We propose (1) a novel prototype-based paradigm for unsupervised continual depth completion that incurs no forgetting in the domain-incremental setting, and (2) a prototype set selection mechanism that extends the prototype paradigm to domain-agnostic settings with minimal forgetting. This is facilitated by (3) a novel training objective that learns descriptors for each domain, which can be used to determine the prototype set suitable for inference without knowledge of domain identity. (4) Our method, ProtoDepth, reduces forgetting over baselines by over $50\\%$ across six datasets; to the best of our knowledge, this is the first unsupervised continual depth completion method.", + "bbox": [ + 89, + 513, + 483, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 709, + 232, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continual learning is the process of incrementally adapting the weights of a parameterized model to perform new tasks involving non-stationary distributions, while preserving information learned from previous tasks.", + "bbox": [ + 89, + 734, + 482, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Regularization-based methods aim to mitigate forgetting by restricting the plasticity of model parameters that are important for previously learned tasks. [1, 7, 36, 113] introduce regularization terms to the loss function to identify and penalize changes to important weights while new tasks are learned. [14, 15, 28, 39, 42, 68, 114] attempt to preserve output behavior on previous tasks using knowledge", + "bbox": [ + 89, + 795, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "distillation [26, 70]. [55, 57, 61, 83] regularize the space of learned functions to encourage similarity between outputs of task-specific heads. However, while they perform well in simpler continual learning settings, regularization-based methods can struggle with more challenging tasks [52] and larger domain shifts between datasets [64, 101].", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rehearsal-based methods use a memory buffer to store a limited amount of data from previous tasks, allowing the model to periodically re-train on this data during continual learning. [7, 25, 69] introduce the strategy of retaining a subset of previous \"experiences\" (i.e., data) to \"replay\" (i.e., re-train on) while learning new tasks. [8, 31, 49, 64, 65, 87] employ various sampling strategies, [29, 47, 117] reduce memory by storing latent features rather than inputs, and generative replay methods [3, 24, 33, 56, 59, 66, 71, 74, 102] create synthetic rehearsal data from previous task domains. Some recent works utilize techniques such as self-supervision [6, 60] and knowledge distillation [4, 9, 64, 101]. [10] introduces a rehearsal-based continual single image-based depth estimation method, the first such work for a 3D vision task. Rehearsal-based methods can reduce forgetting but are unsuitable when data storage is limited by memory or privacy constraints [76]. Additionally, their performance degrades significantly as memory buffer size shrinks [6].", + "bbox": [ + 511, + 184, + 906, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Architecture-based methods [32, 34, 41, 48, 53, 62, 72, 73, 89, 110, 116] allocate task-specific parameters or subnetworks, aiming to enable learning of new tasks while minimizing changes to parameters assigned to previous tasks. Most of these methods require task identity to be known at test-time, which prevents their use in the more realistic domain-agnostic setting where new data is not restricted to a certain domain. Other methods [16, 90] rely on a rehearsal buffer in addition to task-specific parameters. Furthermore, architecture-based methods often introduce a significant number of additional parameters for each task [60, 100, 105], which can even exceed the parameter count of the original model [32, 89]. In contrast, our method can be used for inference without task identity, does not require a rehearsal buffer, and only introduces a very small number of additional parameters (<5% of original model) per task.", + "bbox": [ + 511, + 459, + 908, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt-based methods introduce learnable prompts that encode task-specific information. [92] learns a pool of tokens, from which a set is selected using a query mechanism and prepended to the input. [91] refines this by using both task-specific and shared prompts. Subsequent approaches replace prompt selection with an attention mechanism [79] or with intermediate embeddings [35]. However, these prompt-based methods are designed for 2D classification tasks that use vision transformers (ViTs), borrowing the concept of prompting from the field of natural language processing (NLP). The idea of prepending prompts to tokenized inputs does not naturally extend to convolutional neural networks (CNNs), limiting their applicability to 3D vision tasks where", + "bbox": [ + 511, + 704, + 908, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6305", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CNNs are primarily used. In contrast, our method learns prototypes, which serve as representative features, offering a more intuitive mechanism for adding a lightweight selective bias than prepending abstract prompts in image space. Unlike prompt-based methods, our method is fully architecture-agnostic and can be applied to any model that has a latent space without modifying the underlying architecture.", + "bbox": [ + 89, + 90, + 483, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prototypes have predominantly been explored in the context of few-shot learning of 2D tasks [22, 23, 44, 45, 80, 107] and representation learning [5, 11, 40]. For continual learning, prototypes have been deployed for supervised classification tasks as discriminative class representations [2, 13, 27, 43, 93, 115]. In contrast, we leverage prototypes as a mechanism for encoding domain-specific information to facilitate continual learning for unsupervised reconstruction.", + "bbox": [ + 89, + 198, + 483, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised depth completion is a multimodal, 3D reconstruction problem of predicting a depth map from an image and its associated sparse point cloud. In lieu of training signals from ground-truth depth annotations, unsupervised depth completion methods [17, 18, 30, 38, 46, 51, 75, 78, 94, 96-99, 106, 109] minimize the reconstruction error of the sparse depth, the reprojection error of the image from temporally adjacent views, and a local smoothness regularizer. Some works [50, 85, 109] utilize synthetic data to learn priors, while other works [97, 98] densify then refine the sparse point cloud by constructing a coarse piecewise scaffolding. [95] uses backprojection layers to map image features to the 3D scene using camera calibration. These methods are prone to catastrophic forgetting in continual learning settings since they must update their learned model weights to fit to new data, causing performance degradation on previously seen data domains. In contrast, our method freezes the entire model and learns a lightweight selective bias for each dataset, allowing it to adapt effectively to new data domains while mitigating forgetting.", + "bbox": [ + 91, + 318, + 483, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "UnCLe [21] proposes a benchmark and adapts existing methods [36, 42, 69] for unsupervised continual depth completion. To the best of our knowledge, we propose the first continual learning method for unsupervised depth completion and are the first to explore prototypes in this context.", + "bbox": [ + 89, + 619, + 483, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 710, + 228, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised Depth Completion. Assuming we are given an RGB image $I:\\Omega \\subset \\mathbb{R}^2\\to \\mathbb{R}^3$ and its associated sparse depth map $z:\\Omega \\rightarrow \\mathbb{R}_+$ obtained by projecting the sparse point cloud onto the image plane, we wish to train a depth completion model $f_{\\theta}$ to predict the dense depth map $\\hat{d}$ in an unsupervised manner (i.e., without access to ground-truth depth). Unsupervised depth completion models [51, 95, 97, 98] typically minimize a loss function in the form of Eq. (1), which comprises a linear combination of three terms:", + "bbox": [ + 89, + 736, + 483, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 885, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\ell_{ph}$ denotes photometric consistency, $\\ell_{sz}$ sparse depth consistency, and $\\ell_{sm}$ a local smoothness regularizer.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Photometric Consistency term leverages image reconstruction as the training signal. Specifically, given an image $I_{t}$ at time $t$ , its reconstruction $\\hat{I}_{t\\tau}$ from a temporally adjacent image $I_{\\tau}$ at time $\\tau$ for $\\tau \\in \\{t - 1, t + 1\\}$ is given by", + "bbox": [ + 511, + 122, + 906, + 181 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {I} _ {t \\tau} (x, \\hat {d}, g _ {\\tau t}) = I _ {\\tau} \\left(\\pi g _ {\\tau t} K ^ {- 1} \\bar {x} \\hat {d} (x)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 191, + 906, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\bar{x} = [x^{\\top},1]^{\\top}$ is the homogeneous coordinates of $x\\in \\Omega$ $K$ is the camera intrinsic calibration matrix, $g_{\\tau t}\\in$ $SE(3)$ is the estimated relative camera pose matrix from time $t$ to $\\tau$ , and $\\pi$ is the canonical perspective projection matrix. Given $I_{t}$ and its reconstruction $\\hat{I}_{t\\tau}$ , the photometric consistency loss measures the $L1$ difference and structural similarity (SSIM [88]) between $I_{t}$ and $\\hat{I}_{t\\tau}$ ..", + "bbox": [ + 511, + 220, + 906, + 329 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {p h} = \\frac {1}{| \\Omega |} \\sum_ {\\tau \\in T} \\sum_ {x \\in \\Omega} w _ {c o} \\left| \\hat {I} _ {t \\tau} (x) - I (x) \\right| + \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 338, + 906, + 376 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw _ {s t} \\big (1 - \\operatorname {S S I M} (\\hat {I} _ {t \\tau} (x), I (x)) \\big).\n$$\n", + "text_format": "latex", + "bbox": [ + 658, + 378, + 864, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sparse Depth Consistency. However, photometric reconstruction recovers depth only up to an unknown scale. To ground predictions to a metric scale, we minimize an $L1$ loss between the predicted depth $\\hat{d}$ and sparse depth $z$ for $x\\in \\Omega$ where points exist as denoted by $M:\\Omega \\mapsto \\{0,1\\}$ :", + "bbox": [ + 511, + 406, + 906, + 482 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {s z} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} | M (x) \\cdot (\\hat {d} (x) - z (x)) |. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 492, + 906, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Smoothness. To address ambiguities in regions where the predicted depth is not constrained by photometric or sparse depth reconstruction terms, we rely on a regularizer that enforces local smoothness in predictions by applying an $L1$ penalty on the depth gradients in both the $x$ -direction $(\\partial_{X})$ and $y$ -direction $(\\partial_{Y})$ . To allow for depth discontinuities along object boundaries, these penalties are weighted by their corresponding image gradients, $\\lambda_{X} = e^{-|\\partial_{X}I_{t}(x)|}$ and $\\lambda_{Y} = e^{-|\\partial_{Y}I_{t}(x)|}$ . Larger image gradients result in smaller weights, allowing for sharp transitions in depth along edges:", + "bbox": [ + 511, + 539, + 906, + 691 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {s m} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} \\lambda_ {X} (x) \\left| \\partial_ {X} \\hat {d} (x) \\right| + \\lambda_ {Y} (x) \\left| \\partial_ {Y} \\hat {d} (x) \\right|. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 700, + 906, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised Continual Depth Completion. For continual learning, we consider a task sequence of domains $\\mathcal{D}_1,\\mathcal{D}_2,\\dots ,\\mathcal{D}_T$ . Starting with a depth completion model $f_{\\theta}$ pretrained on the initial dataset $\\mathcal{D}_1$ , we aim to incrementally adapt $f_{\\theta}$ to each subsequent dataset $\\mathcal{D}_2,\\dots ,\\mathcal{D}_k,\\dots ,\\mathcal{D}_T$ . The key challenge is to learn the data distribution of each new dataset $\\mathcal{D}_k$ without \"forgetting,\" as measured by performance degradation on previously learned datasets $\\mathcal{D}_{j < k}$ . We denote each dataset as $\\mathcal{D}_k = \\{(I_k^{(i)},z_k^{(i)},K_k^{(i)})\\}_{i = 1}^{n_k}$ , which comprises $n_k$ training samples of image, sparse depth, and", + "bbox": [ + 511, + 746, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6306", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f7bda9c664577cb155d046f3118a9e9542f026dd5864cddb754ed73b6c0e2f15.jpg", + "image_caption": [ + "Figure 2. Overview of ProtoDepth. (a) In the agnostic setting, a prototype set is selected by maximizing the cosine similarity between an input sample descriptor and the learned domain descriptors. In the incremental setting, the domain identity is known. (b) At inference, the similarity between the frozen queries and the keys of the selected prototype set determines how the learned prototypes contribute as local (additive) biases to the latent features. Additionally, a global (multiplicative) bias is applied using a $1 \\times 1$ depthwise convolution." + ], + "image_footnote": [], + "bbox": [ + 117, + 93, + 424, + 281 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/aa81f6dc0df6fad71f74b3474a61e8929fe516e7dbb3f7f1d25d08d0f8292470.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 437, + 93, + 880, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "calibration, with no ground-truth depth. We assume that the relative camera pose $g_{t\\tau}$ is given, or is estimated; if estimated by a pose network, we allow it to forget as we focus on continual learning for depth completion, and not pose estimation, which is outside the focus of this work.", + "bbox": [ + 88, + 359, + 486, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 89, + 446, + 183, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present ProtoDepth, a novel approach for unsupervised continual depth completion that mitigates catastrophic forgetting by leveraging prototype sets as selective biases. Given a pretrained depth completion model $f_{\\theta}$ , which we freeze to prevent any forgetting, we adapt it to new datasets by deploying lightweight, domain-specific prototype sets that learn to selectively bias the latent features; note that this only adds minimal additional parameters per dataset or domain. Our method is applicable to the domain-incremental (\"incremental\") setting, where dataset identity is known at test-time, and the more challenging domain-agnostic (\"agnostic\") setting, where the test-time domain identity is unknown, through a proposed prototype set selection mechanism (see Sec. 4.3).", + "bbox": [ + 88, + 472, + 483, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Prototype Learning", + "text_level": 1, + "bbox": [ + 89, + 676, + 277, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enable the model to adapt to new datasets without forgetting, we learn layer-specific prototype sets for each dataset that serve as multiplicative (global) and additive (local) biases in the latent feature space. For simplicity, we consider an input sample from a single dataset $\\mathcal{D}_k$ at a single layer $l$ , which is encoded into the latent features $X \\in \\mathbb{R}^{h \\times w \\times c}$ . We assume a linear transformation from the learned latent space of $\\mathcal{D}_1$ to that of $\\mathcal{D}_k$ ; hence, we formulate the adaptation as", + "bbox": [ + 88, + 699, + 485, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} = A \\odot X + B, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 828, + 483, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ denotes a (broadcasted) Hadamard product between the global prototype $A\\in \\mathbb{R}^c$ and the features $X$ ; $B$ is an additive bias constructed from a set of local prototypes $P$ .", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we flatten the latent features $X$ to get $Q \\in \\mathbb{R}^{(h \\times w) \\times c}$ . Since the model $f_{\\theta}$ is frozen, $Q$ serves as a set of $h \\times w$ deterministic queries, where each query is a $c$ -dimensional vector. We introduce $N$ learnable additive prototypes $P = [p_1, p_2, \\dots, p_N]^\\top \\in \\mathbb{R}^{N \\times c}$ , where each $p_i$ is a $c$ -dimensional vector representing a \"prototypical\" local feature of the dataset. To learn the keys associated with each prototype, we define a projection matrix $W$ that learns to map the prototypes $P$ back into the query space, i.e., the latent feature space. This yields $K \\in \\mathbb{R}^{N \\times c}$ , where", + "bbox": [ + 511, + 359, + 906, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nK = \\operatorname {S t o p G r a d} (P) \\times W. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 517, + 906, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "StopGrad (stop gradient) facilitates decoupled optimization, enabling prototypes to learn appropriate additive biases while keys learn to assign relevant prototypes to queries. We compute the similarity scores between the queries $Q$ and the keys $K$ using scaled dot-product attention [86]. To obtain the additive bias $b \\in \\mathbb{R}^{(h \\times w) \\times c}$ , the scores are used to compute a convex combination of prototypes $P$ :", + "bbox": [ + 511, + 539, + 908, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nb = \\operatorname {s o f t m a x} \\left(Q \\times K ^ {\\top} / \\sqrt {c}\\right) \\times P. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 650, + 906, + 669 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We reshape $b$ back to the spatial dimensions of $X$ to obtain the local additive bias $B \\in \\mathbb{R}^{h \\times w \\times c}$ . To model the global transformation, we learn a $c$ -dimensional multiplicative prototype $A$ , applied element-wise as $A \\odot X$ , which can be efficiently implemented as a $1 \\times 1$ depthwise convolution. The result is further adapted to the new dataset distribution, still without altering the original model parameters, by incorporating the local domain-specific transformation $B$ as an additive bias, i.e., $\\hat{X} = A \\odot X + B$ . As $f_{\\theta}$ is frozen and a new prototype set (local and global prototypes $P_{k}$ and $A_{k}$ , and projection matrix $W_{k}$ ) is learned for each dataset $\\mathcal{D}_k$ , this naturally facilitates continual learning and ensures no forgetting in the incremental setting, where the prototype set corresponding to the domain identity is selected. We further extend this to the agnostic setting in Sec. 4.3.", + "bbox": [ + 511, + 674, + 910, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6307", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/9e85daff7bdafc62f2218a49e2828bd905357b0899d8b1cae4d765cfa628a2cf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned8.8286.1316.9517.04263.352125.2815.46135.05352.453108.43415.36035.357
EWC [36]9.4398.0145.1836.17463.787126.70615.22934.36753.614110.95615.09134.039
LwF [42]8.5918.4569.61321.77465.135126.96816.22138.00253.517108.84515.40234.729
Replay [69]6.1544.6889.47111.71364.305126.71416.37336.72954.326112.21816.64037.671
ProtoDepth-A2.4393.5984.6304.51956.971118.13213.55430.55447.367103.01513.51731.623
ProtoDepth0.0000.0000.0000.00056.359115.15313.58930.33246.934101.32613.68431.925
FusionNetFinetuned24.9289.77532.33316.79966.523130.14215.82933.88154.252110.66615.31733.726
EWC [36]11.2568.78217.94417.84764.487130.89015.26434.20351.345109.22314.27632.781
LwF [42]6.8632.8657.3361.93961.204123.57314.07530.87950.159106.38613.87931.608
Replay [69]5.7022.86212.19611.18661.467125.58714.75033.27950.273108.60814.35133.658
ProtoDepth-A1.2820.6861.3040.44657.742119.98813.27430.13947.674104.34913.12831.058
ProtoDepth0.0000.0000.0000.00057.486119.16813.32329.93647.335102.84513.09130.474
KBNetFinetuned16.08015.4638.1889.17058.577124.60613.47431.40947.890105.80713.26631.742
EWC [36]14.91511.87810.3985.64057.414122.07513.74131.55248.031106.66114.12933.096
LwF [42]9.7176.3246.1685.25457.511119.09314.11932.16547.154103.16414.30433.838
Replay [69]7.2004.8199.2029.53956.208117.84813.98332.34146.700103.63113.84433.326
ProtoDepth-A3.2041.3044.9112.94354.254115.54813.20130.49945.264101.09713.28131.718
ProtoDepth0.0000.0000.0000.00052.497113.54812.84529.99044.09299.78813.08131.503
", + "bbox": [ + 91, + 88, + 903, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative results on indoor datasets. Models are initially trained on NYUv2 and continually trained on ScanNet, then VOID. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21].", + "bbox": [ + 89, + 409, + 906, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. ProtoDepth Architecture", + "text_level": 1, + "bbox": [ + 89, + 455, + 318, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Current unsupervised depth completion models [95, 97, 98] adopt an encoder-decoder CNN architecture, which consists of separate image and sparse depth encoders with skip connections to the decoder. We refer to the bottleneck and the skip connections as the latent space layers (see Fig. 2).", + "bbox": [ + 89, + 482, + 482, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To extend the prototype mechanism (Sec. 4.1) across multiple layers, for each new dataset $D_{k}$ , we introduce a prototype set of local and global prototypes $P^{(l)}$ and $A^{(l)}$ , and projection matrix $W^{(l)}$ for each layer $l$ in the latent space. For each new dataset, the latent feature adaptation (Eqs. (6) and (8)) is applied independently to each layer $l$ .", + "bbox": [ + 89, + 561, + 482, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As different modalities in multimodal tasks (e.g., RGB image and sparse depth map in depth completion) may experience varying degrees of covariate shift across domains, we propose to deploy a different number of prototypes $N^{(I)}$ and $N^{(z)}$ for the RGB image and sparse depth modalities, respectively. Based on the observation that RGB images undergo a larger covariate shift than sparse depth [58], we choose $N^{(I)} > N^{(z)}$ to capture their prototypical features; this choice reduces the parameter overhead.", + "bbox": [ + 89, + 655, + 482, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed prototype-based continual learning mechanism operates on the latent feature space and does not depend on the specific architecture of the model. This architecture-agnostic flexibility stems from the fact that our queries $Q \\in \\mathbb{R}^{(h \\times w) \\times c}$ mirror the general structure of latent features across commonly used model architectures, where $h \\times w$ can be replaced by the number of tokens $n$ in the", + "bbox": [ + 89, + 795, + 482, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "case of transformers [86]. Thus, it can be applied generically to models with latent feature representations [37, 103], providing a general framework for mitigating catastrophic forgetting across various tasks and modalities.", + "bbox": [ + 511, + 457, + 906, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Prototype Set Selection", + "text_level": 1, + "bbox": [ + 511, + 529, + 725, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As the prototypes are learned for a specific domain, we cannot easily select the appropriate prototype set for inference if the test-time domain identity is withheld, i.e., in the domain-agnostic setting. To address this challenging scenario, we introduce a prototype set selection mechanism that chooses the most relevant prototype set for a given input.", + "bbox": [ + 511, + 551, + 906, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, we introduce a domain descriptor $r_k \\in \\mathbb{R}^c$ for each dataset $\\mathcal{D}_k$ , which adds negligible overhead in terms of number of parameters. For an input from $\\mathcal{D}_k$ , we obtain a sample descriptor $s_k \\in \\mathbb{R}^c$ by applying global average pooling (GAP) to the bottleneck latent features (with channel dimension $c$ ) before applying the prototype set. Importantly, since both encoders are always frozen during continual training, $s_k$ is a deterministic mapping of the input.", + "bbox": [ + 511, + 643, + 908, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each new dataset $\\mathcal{D}_k$ , we deploy a new domain descriptor $r_k$ and freeze all existing learned domain descriptors. The deployed domain descriptor $r_k$ is trained by minimizing cosine distance between itself and sample descriptors $s_k$ for $\\mathcal{D}_k$ , while maximizing the cosine distance to all other learned domain descriptors $\\{r_{j \\neq k}\\}$ . This naturally yields domain descriptors that are discriminative across datasets, allowing us to use the projection of sample descriptors onto domain descriptors as a prototype set selection mechanism.", + "bbox": [ + 511, + 765, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6308", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7bfcb49e9758bbe9267c0a43288ded58a6d5402dce60a7ec383bbf843a391cb6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned499.598162.188467.472208.6931620.4293072.1294.0406.144914.2232993.2281.9554.503
EWC [36]555.925190.152540.109247.9431796.3003346.0574.4906.685962.9373209.7591.9624.739
LwF [42]631.119221.535524.976233.7581973.9723612.7004.5336.648985.9953236.2442.0624.722
Replay [69]17.2414.05016.6625.478524.1141875.8971.3333.359618.6682366.5771.2923.348
ProtoDepth-A2.4272.8632.0792.153458.5201832.6901.1333.213548.2402294.3991.0803.159
ProtoDepth0.0000.0000.0000.000445.4191804.1581.1063.169531.6892262.9431.0433.110
FusionNetFinetuned11.3368.43517.44717.991437.7301785.2121.1933.724501.3622138.4221.1113.978
EWC [36]21.00610.49420.43116.535431.4401760.4601.1443.181486.1702117.0301.0292.986
LwF [42]12.3685.20213.59313.117442.8781759.2021.1783.352526.5282168.9611.1563.451
Replay [69]8.29011.1342.7697.975419.0441774.3611.0443.032479.1682122.9970.9662.906
ProtoDepth-A2.2002.2822.6027.203404.9561702.9451.0413.028464.9762052.4130.9522.864
ProtoDepth0.0000.0000.0000.000400.8881683.2021.0222.899461.0432048.9420.9322.792
KBNetFinetuned27.15318.20852.96933.370469.6581943.2591.3383.683541.3832411.1691.1443.505
EWC [36]23.5178.58330.07718.991456.8281806.7611.2213.321526.3662210.4241.1333.158
LwF [42]21.1844.04943.50019.951460.0971749.7341.3623.555541.9322142.9991.3593.731
Replay [69]25.42329.3036.3627.274454.8961935.6671.1023.203525.6962318.3631.0943.246
ProtoDepth-A4.5133.1002.9601.878409.9031730.7201.0453.044478.7902138.3471.0083.066
ProtoDepth0.0000.0000.0000.000401.0751710.0741.0292.993471.4372125.9570.9963.015
", + "bbox": [ + 91, + 88, + 903, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative results on outdoor datasets. Models are initially trained on KITTI and continually trained on Waymo, then VKITTI. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21].", + "bbox": [ + 89, + 388, + 906, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To this end, we propose to minimize an additional objective:", + "bbox": [ + 89, + 436, + 483, + 452 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {d r} = 1 - \\left(\\frac {s _ {k}}{\\| s _ {k} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right) + \\frac {1}{w _ {j k}} \\sum_ {j \\neq k} \\left(\\frac {r _ {j}}{\\| r _ {j} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 457, + 483, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $||\\cdot||$ denotes the $L2$ -norm and $w_{jk} \\propto |j \\neq k|$ is a tunable normalization constant. As the previously learned domain descriptors are frozen, their alignment to their respective datasets or domains is preserved, allowing us to continually learn new domain descriptors that can distinguish new datasets. Eq. (9) is incorporated into Eq. (1) as an additional term weighted by $w_{dr}$ to yield a novel loss function for training of unsupervised continual depth completion models in the agnostic setting:", + "bbox": [ + 89, + 500, + 483, + 636 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m} + w _ {d r} \\ell_ {d r}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 643, + 483, + 660 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "At test-time, we compute the sample descriptor $s$ for an input without dataset identity and select the domain descriptor $r_{k^*}$ that maximizes cosine similarity with $s$ :", + "bbox": [ + 89, + 666, + 483, + 710 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nk ^ {*} = \\arg \\max _ {k} \\left(\\frac {s}{\\| s \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 715, + 483, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each latent space layer, we use the prototype set corresponding to the selected domain descriptor. While this does not eliminate forgetting due to the evolving set of domain descriptors and possible overlap between domains, it does minimize forgetting as each prototype set is learned independently for each dataset, but can still be selectively used for inference without knowing the test-time dataset identity. The trade-off is shown in Tabs. 1 and 2 (ProtoDepth-A) where we incur forgetting in exchange for the flexibility to support both the incremental and agnostic settings.", + "bbox": [ + 89, + 750, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 435, + 643, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Indoor dataset sequence: NYUv2 [77] contains household, office, and commercial scenes captured with a Microsoft Kinect; ScanNet [12] is a diverse, large-scale dataset captured using a Structure Sensor; Void [97] contains laboratory, classroom, and garden scenes captured using XIVO. Outdoor dataset sequence: KITTI [84] is a daytime autonomous driving benchmark captured using a Velodyne LiDAR sensor; Waymo [81] contains road scenes with a wide variety of driving conditions; VKITTI [20] is a synthetic dataset that replicates and augments KITTI scenes.", + "bbox": [ + 509, + 464, + 906, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Models. We evaluate using three recent unsupervised depth completion models in the continual learning setting: VOICES [97], FusionNet [98], and KBNet [95].", + "bbox": [ + 511, + 618, + 906, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline Methods. We compare ProtoDepth against EWC [36], LwF [42], and Experience Replay (\"Re-play\") [69] as milestone works of their respective class of continual learning approaches. We include full finetuning (\"Finetuned\") as a baseline of performance with no continual learning strategy. All baseline methods achieve identical performance in the incremental and agnostic settings.", + "bbox": [ + 511, + 667, + 908, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics are computed across four standard depth completion metrics (MAE, RMSE, iMAE, iRMSE). We define the following evaluation metrics in terms of $a_{j}^{k}$ , denoting any one of the four depth completion metrics on dataset $\\mathcal{D}_j$ after training on $\\mathcal{D}_k$ . Given $T$ total datasets:", + "bbox": [ + 511, + 776, + 908, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Average Forgetting $(\\bar{F})$ is the scale-invariant mean of how much performance on previous datasets $\\mathcal{D}_{j < k}$ deteriorates (i.e., increases in $\\%$ ) after training on each new $\\mathcal{D}_k$ :", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6309", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9acda1ef2bb737c62ecc7bdaad76910468cc71920fa5f4f0f962bf45ac5e085a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 179, + 90, + 397, + 138 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8ff5728ed6306d29ae74641b42862c137625b3049fb30d92190f4b85a24b4c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 400, + 90, + 601, + 138 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6c67b92dc2e21fc0977676d72adaae3b5a6310dac2076d9da40db1ff016d2556.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 90, + 805, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb033faad52b899f869f917bbf1e2f601d33f3c6df2ef8b2d515ead3a3ab9123.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 96, + 142, + 496, + 281 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/60fff9d3172d60991c1654339b5a831cabd007fd2b7443b4028567a962b3697b.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison of ProtoDepth and baseline methods using VOICESED on KITTI after continual training on Waymo. (a) Input sample from KITTI, (b) Baseline methods exhibit significant forgetting, particularly for small-surface-area objects (e.g., street signs and lamp posts) where sparse depth is limited, and photometric priors from KITTI are critical. In contrast, ProtoDepth produces high-fidelity depth predictions, effectively mitigating forgetting despite the large domain gap between KITTI and Waymo." + ], + "image_footnote": [], + "bbox": [ + 501, + 141, + 903, + 281 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {F} = \\frac {2}{T (T - 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j < k} \\frac {a _ {j} ^ {k} - a _ {j} ^ {j}}{a _ {j} ^ {j}}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 375, + 483, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Average Performance $(\\bar{\\mu})$ is the mean of performance on all seen datasets $\\mathcal{D}_{j\\leq k}$ after training on each new $\\mathcal{D}_k$ :", + "bbox": [ + 89, + 425, + 483, + 455 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mu} = \\frac {2}{T (T + 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j \\leq k} a _ {j} ^ {k}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 468, + 483, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Stability-Plasticity Trade-off (SPTO) captures the balance between retaining learned knowledge (stability) and adapting to new domains (plasticity) as a harmonic mean:", + "bbox": [ + 89, + 518, + 483, + 565 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {S P T O} = \\frac {2 \\times S \\times P}{S + P}, \\left\\{ \\begin{array}{l} S = \\sum_ {k = 1} ^ {T} a _ {k} ^ {T} \\\\ P = \\sum_ {k = 1} ^ {T} a _ {k} ^ {k}, \\end{array} \\right. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 575, + 483, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $S$ is performance across all datasets after completing training on the dataset sequence, and $P$ is performance on each new dataset after training on it for the first time.", + "bbox": [ + 89, + 625, + 483, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Main Results", + "text_level": 1, + "bbox": [ + 89, + 681, + 228, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method, evaluated in both the incremental (ProtoDepth) and agnostic (ProtoDepth-A) settings, against baseline methods for the indoor dataset sequence in Tab. 1 and for the outdoor dataset sequence in Tab. 2.", + "bbox": [ + 89, + 704, + 483, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results in Incremental Setting. In both indoor and outdoor settings, ProtoDepth achieves a $100\\%$ improvement in Average Forgetting compared to all baseline methods across all models and metrics. This is, of course, because ProtoDepth exhibits zero forgetting as it freezes all model parameters and learns dataset-specific prototypes. For the indoor sequence, compared to the best baseline method, ProtoDepth improves Average Performance by $5.15\\%$ and SPTO by $6.59\\%$ , averaged across all models and metrics.", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Similarly, for the outdoor sequence, we improve Average Performance by $6.88\\%$ and SPTO by $6.94\\%$ .", + "bbox": [ + 511, + 362, + 906, + 392 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the reduced forgetting achieved by ProtoDepth, we qualitatively compare against all baseline methods using VOICESED on KITTI after continual training on Waymo (see Fig. 3). ProtoDepth yields better depth predictions for small-surface-area objects with limited sparse depth measurements for which the model must rely on photometric priors learned from images. Unlike KITTI, which consists exclusively of daytime scenes, Waymo includes many evening and overcast scenes, introducing variations in lighting and pixel intensities. Additionally, Waymo was captured using a higher-resolution camera which causes objects to appear bigger in terms of number of pixels occupied. Due to this large distributional shift, the model forgets the projected shapes of objects in KITTI after training on Waymo, even if the objects exist in both datasets. This forgetting is apparent in the highlighted street sign and lamp posts, where baseline methods struggle to accurately predict depth.", + "bbox": [ + 509, + 395, + 908, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results in Agnostic Setting. For the indoor sequence, compared to the best baseline method, ProtoDepth-A improves Average Forgetting by $52.22\\%$ , Average Performance by $4.26\\%$ , and SPTO by $5.40\\%$ , averaged across all models and metrics. Notably, ProtoDepth-A outperforms ProtoDepth in some metrics, meaning the model appropriately selects prototypes of different domains when there is domain overlap, thereby enhancing its generalization capabilities.", + "bbox": [ + 511, + 655, + 908, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the outdoor sequence, ProtoDepth-A shows an average improvement of $53.21\\%$ in Average Forgetting across all models and metrics. In contrast to the indoor sequence, ProtoDepth-A does not outperform ProtoDepth in any metric, likely due to the larger domain gaps between the outdoor datasets. Selecting prototypes from a different outdoor dataset is more likely to be erroneous, leading to performance degradation rather than generalization.", + "bbox": [ + 511, + 779, + 910, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6310", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/35f38a1648c5b230257134c09aefb60bd904cc7f9d31cde759709f06ffb982d9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodN(I)N(z)# ParamsScanNetVOID
MAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
Pretrained--0M (0%)4114.044626.00390.78447.3142.94106.3929.2664.04
ProtoDepth110.24M (3.5%)19.68±0.6860.10±0.7110.44±0.4827.86±0.7437.81±0.5293.72±0.9022.82±0.2752.58±0.32
550.25M (3.6%)16.49±0.1557.51±0.196.84±0.0322.07±0.0334.02±0.2587.72±0.4317.92±0.1443.95±0.28
1050.25M (3.6%)14.59±0.1742.20±0.095.57±0.1417.10±0.1533.63±0.2387.30±0.5717.55±0.3243.24±0.63
10100.25M (3.7%)15.25±0.3943.31±0.725.85±0.2217.57±0.3834.39±0.8288.73±1.8318.49±0.8545.23±1.60
1001000.38M (5.5%)16.35±0.3747.61±0.165.90±0.1720.11±0.1934.29±0.5888.22±0.8618.16±0.6244.51±1.07
", + "bbox": [ + 91, + 88, + 903, + 231 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c7cc58c7e45eb7cf00a418c6916605b1338acef721e6a91e8e1a3bd6e6758904.jpg", + "table_caption": [ + "Table 3. Sensitivity study of prototype set sizes $(N^{(I)}$ and $N^{(z)}$ ) on ProtoDepth using KBNet for indoor datasets (ScanNet and VOID). KBNet is pretrained on the initial dataset (NYUv2). Parameter overhead is reported as a percentage of the full KBNet model's parameters." + ], + "table_footnote": [], + "table_body": "
ScanNetWaymo
Ablated ComponentMAERMSEMAERMSE
global prototypes18.1258.91505.011715.21
projection matrix W17.5957.61495.051690.51
decoupled K and P16.3645.10491.591675.57
no ablations14.5942.20486.951664.18
", + "bbox": [ + 91, + 277, + 480, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation studies using KBNet for indoor and outdoor.", + "bbox": [ + 96, + 411, + 475, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Furthermore, we refer back to Fig. 3 (ProtoDepth-A) for head-to-head comparison of our method against other baselines in the agnostic setting. The error maps for Finetuned, EWC, and LwF display significant errors, indicating substantial forgetting of previously learned information. While Replay yields an improved error map, it still experiences forgetting in small-surface-area objects. For example, Replay fails to reconstruct the upper portions of the highlighted street sign and lamp posts due to forgetting of learned photometric priors from KITTI, whereas ProtoDepth-A recalls them from KITTI prototypes. Additionally, ProtoDepth-A predicts the depth of the highlighted small fence poles with higher fidelity than the incoherent prediction of Replay.", + "bbox": [ + 88, + 443, + 485, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Design Choice Studies", + "text_level": 1, + "bbox": [ + 89, + 650, + 297, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Prototype Set Sizes. We investigate the impact of varying the prototype set sizes (i.e., number of prototypes) for the image and sparse depth layers (denoted as $N^{(I)}$ and $N^{(z)}$ , respectively) on the performance of our method. The set size experiments for the indoor sequence are shown in Tab. 3, based on which we selected $N^{(I)} = 10$ , $N^{(z)} = 5$ for the main experiments. Smaller set sizes perform worse as there is insufficient capacity to capture the diversity of features in each dataset. There is also performance degradation with larger set sizes; intuitively, unnecessary additional parameters may learn noise and cause overfitting. Notably, best performance is achieved when $N^{(I)} > N^{(z)}$ , which can be attributed to the larger distributional shift between scenes in the image modality compared to the sparse depth modality [58]. Since the bottleneck layer fuses both modalities,", + "bbox": [ + 91, + 674, + 485, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we use $N^{(I)}$ for the bottleneck layer prototypes. As a lower bound, we show that the frozen base model pretrained on NYUv2 (\"Pretrained\") performs poorly, motivating the need for continual learning. We perform similar set size experiments for the outdoor dataset sequence (see Supp. Mat.), based on which we choose $N^{(I)} = 25$ , $N^{(z)} = 10$ .", + "bbox": [ + 511, + 280, + 906, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablations. We assess the impact of the components of ProtoDepth on both indoor (ScanNet) and outdoor (Waymo) in Tab. 4. Removing the $1 \\times 1$ depthwise convolutions results in performance degradation, demonstrating their effectiveness as lightweight global prototypes. Learning the keys $K$ independently from the prototypes $P$ without the projection matrix $W$ hurts performance, suggesting that the projection matrix effectively learns to map the prototypes into latent feature space, fulfilling the intended role of keys. Furthermore, performance decreases without the stop gradient operation on $P$ when computing $K$ , indicating the importance of decoupled optimization of keys and prototypes.", + "bbox": [ + 511, + 372, + 908, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 511, + 571, + 627, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ProtoDepth leverages prototypes as a mechanism for mitigating catastrophic forgetting. While we demonstrate it on unsupervised depth completion, ProtoDepth does not assume specific modalities and thus can be relevant to other multimodal problems [67, 104, 108, 111]. Our promising results on both indoor and outdoor domains illustrate the potential for ProtoDepth to enable unsupervised continual learning for multimodal 3D reconstruction. Our architecture-agnostic approach can also be extended to other tasks involving models that produce latent feature representations [37, 112], offering a general framework for continual learning.", + "bbox": [ + 511, + 597, + 908, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. ProtoDepth relies on knowledge of dataset boundaries to instantiate new prototype sets, which may not be feasible in online training settings where there are no defined boundaries between domains. In the same vein, we do not consider scenarios where domain gaps between datasets are small or where there are significant distributional shifts within a dataset. Addressing these limitations would require mechanisms to dynamically detect domain shifts and instantiate new prototypes when appropriate.", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6311", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by NSF-2112562 Athena AI Institute.", + "bbox": [ + 89, + 114, + 485, + 130 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 143, + 187, + 157 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9296-9305, 2022. 2" + ], + "bbox": [ + 516, + 92, + 906, + 247 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "6316", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_model.json b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_model.json new file mode 100644 index 0000000000000000000000000000000000000000..37fb0a7bbaeb003ff09c84ba166f433d92e1b67f --- /dev/null +++ b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_model.json @@ -0,0 +1,2932 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.131, + 0.868, + 0.154 + ], + "angle": 0, + "content": "ProtoDepth: Unsupervised Continual Depth Completion with Prototypes" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.181, + 0.882, + 0.227 + ], + "angle": 0, + "content": "Patrick Rim Hyoungseob Park S. Gangopadhyay Ziyao Zeng Younjoon Chung Alex Wong Yale Vision Lab" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.262, + 0.329, + 0.279 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.294, + 0.486, + 0.598 + ], + "angle": 0, + "content": "We present ProtoDepth, a novel prototype-based approach for continual learning of unsupervised depth completion, the multimodal 3D reconstruction task of predicting dense depth maps from RGB images and sparse point clouds. The unsupervised learning paradigm is well-suited for continual learning, as ground truth is not needed. However, when training on new non-stationary distributions, depth completion models will catastrophically forget previously learned information. We address forgetting by learning prototype sets that adapt the latent features of a frozen pretrained model to new domains. Since the original weights are not modified, ProtoDepth does not forget when test-time domain identity is known. To extend ProtoDepth to the challenging setting where the test-time domain identity is withheld, we propose to learn domain descriptors that enable the model to select the appropriate prototype set for inference. We evaluate ProtoDepth on benchmark dataset sequences, where we reduce forgetting compared to baselines by \\(52.2\\%\\) for indoor and \\(53.2\\%\\) for outdoor to achieve the state of the art. Project Page: https://protodepth.github.io/." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.619, + 0.222, + 0.635 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.486, + 0.84 + ], + "angle": 0, + "content": "Reconstructing three-dimensional (3D) environments facilitates spatial applications such as autonomous navigation, robotic manipulation, and AR/VR. These applications typically utilize platforms equipped with heterogeneous sensors, such as cameras and sparse range sensors (e.g., LiDAR, ToF) which yield RGB images and point clouds. To reconstruct 3D scenes from an ego-centric point of view in the form of depth maps, the point clouds are typically projected onto the image plane. However, their projections tend to be sparse, which is unlike RGB images that comprise irradiance measured at each pixel. These complementary modalities can be used to predict dense depth maps; this multimodal 3D reconstruction task is called depth completion." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Depth completion models can be trained in a supervised (using ground truth) or unsupervised (using Structure-from-Motion) manner. As ground truth is prohibitively expensive to acquire, we subscribe to the unsupervised learning" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.264, + 0.898, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.413, + 0.907, + 0.443 + ], + "angle": 0, + "content": "Figure 1. Results on KITTI validation set during continual training on outdoor dataset sequence (KITTI \\(\\rightarrow\\) Waymo \\(\\rightarrow\\) VKITTI)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.909, + 0.629 + ], + "angle": 0, + "content": "paradigm, which enables one to learn without human intervention. While this suggests the potential to continuously learn, existing models are trained and evaluated on single datasets under the assumption of a stationary data distribution. However, sequences of multiple datasets exhibit non-stationary distributions and are captured by sensors with varying calibrations. Hence, fitting to new data samples inevitably causes the model to \"catastrophically forget\" [19, 54, 63, 82] previously learned information, where the model performance degrades significantly on data from distributions that it had already observed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.911, + 0.902 + ], + "angle": 0, + "content": "To enable pretrained models to adapt to new environments or domains in an unsupervised manner, we consider continual learning, where training strategies aim to mitigate catastrophic forgetting of previously observed training distributions when learning from a continuous stream of non-stationary data. One school of thought is to constrain updates to parameters deemed \"important\" for previous domains based on a regularization term controlled by a weight chosen as a hyperparameter. Another is to incur memory costs by storing previously observed training data and incorporating them during learning of new domains, akin to rehearsals. The trade-off is in the sensitivity of optimization (and forgetting) to the choice of hyperparameter and in the size of storage and data privacy. Both schools perform updates to the full set of model parameters, which is computationally expensive. Unlike them, we opt to freeze the pretrained model to ensure zero forgetting and learn a small set of parameters, which we term \"prototypes,\" that modulate" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6304" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.441, + 0.106 + ], + "angle": 0, + "content": "the latent features for each new domain encountered." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.107, + 0.482, + 0.272 + ], + "angle": 0, + "content": "We model the change in distribution as a domain-specific bias to be learned by global multiplicative and local additive prototypes that transform the latent features to fit the new distribution. In the same vein are learnable prompts or tokens [92] used in continual learning for vision transformers, where the model itself is similarly frozen. Yet, there is no natural scale at which to discretize images, unlike discrete text tokens. In contrast, our proposed prototypes lift the requirements of tokenized inputs and can thus be applied to convolutional neural networks, which are prevalently used in unsupervised depth completion, as well as transformers." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.274, + 0.486, + 0.514 + ], + "angle": 0, + "content": "To this end, we propose ProtoDepth, a novel prototype-based method for unsupervised continual depth completion. Instead of prompts in input space, we deploy lightweight prototypes to a frozen pretrained model to encode prototypical information of each domain. These prototypes model global and local biases, where global prototypes learn a transformation from the latent pretrained data distribution to that of the new domain, and local prototypes capture fine-grained features that can be selectively queried depending on the input. Naturally, when the test-time domain identity is known, i.e., domain-incremental, ProtoDepth exhibits no forgetting and learns the new data distribution with high fidelity. We further encode each domain as a descriptor to enable inference when test-time domain identity is withheld, i.e., domain-agnostic, where the prototype set corresponding to the highest affinity domain descriptor for a given sample is chosen." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.515, + 0.485, + 0.696 + ], + "angle": 0, + "content": "Our contributions: We propose (1) a novel prototype-based paradigm for unsupervised continual depth completion that incurs no forgetting in the domain-incremental setting, and (2) a prototype set selection mechanism that extends the prototype paradigm to domain-agnostic settings with minimal forgetting. This is facilitated by (3) a novel training objective that learns descriptors for each domain, which can be used to determine the prototype set suitable for inference without knowledge of domain identity. (4) Our method, ProtoDepth, reduces forgetting over baselines by over \\(50\\%\\) across six datasets; to the best of our knowledge, this is the first unsupervised continual depth completion method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.233, + 0.725 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.795 + ], + "angle": 0, + "content": "Continual learning is the process of incrementally adapting the weights of a parameterized model to perform new tasks involving non-stationary distributions, while preserving information learned from previous tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Regularization-based methods aim to mitigate forgetting by restricting the plasticity of model parameters that are important for previously learned tasks. [1, 7, 36, 113] introduce regularization terms to the loss function to identify and penalize changes to important weights while new tasks are learned. [14, 15, 28, 39, 42, 68, 114] attempt to preserve output behavior on previous tasks using knowledge" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "distillation [26, 70]. [55, 57, 61, 83] regularize the space of learned functions to encourage similarity between outputs of task-specific heads. However, while they perform well in simpler continual learning settings, regularization-based methods can struggle with more challenging tasks [52] and larger domain shifts between datasets [64, 101]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.185, + 0.908, + 0.457 + ], + "angle": 0, + "content": "Rehearsal-based methods use a memory buffer to store a limited amount of data from previous tasks, allowing the model to periodically re-train on this data during continual learning. [7, 25, 69] introduce the strategy of retaining a subset of previous \"experiences\" (i.e., data) to \"replay\" (i.e., re-train on) while learning new tasks. [8, 31, 49, 64, 65, 87] employ various sampling strategies, [29, 47, 117] reduce memory by storing latent features rather than inputs, and generative replay methods [3, 24, 33, 56, 59, 66, 71, 74, 102] create synthetic rehearsal data from previous task domains. Some recent works utilize techniques such as self-supervision [6, 60] and knowledge distillation [4, 9, 64, 101]. [10] introduces a rehearsal-based continual single image-based depth estimation method, the first such work for a 3D vision task. Rehearsal-based methods can reduce forgetting but are unsuitable when data storage is limited by memory or privacy constraints [76]. Additionally, their performance degrades significantly as memory buffer size shrinks [6]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.909, + 0.702 + ], + "angle": 0, + "content": "Architecture-based methods [32, 34, 41, 48, 53, 62, 72, 73, 89, 110, 116] allocate task-specific parameters or subnetworks, aiming to enable learning of new tasks while minimizing changes to parameters assigned to previous tasks. Most of these methods require task identity to be known at test-time, which prevents their use in the more realistic domain-agnostic setting where new data is not restricted to a certain domain. Other methods [16, 90] rely on a rehearsal buffer in addition to task-specific parameters. Furthermore, architecture-based methods often introduce a significant number of additional parameters for each task [60, 100, 105], which can even exceed the parameter count of the original model [32, 89]. In contrast, our method can be used for inference without task identity, does not require a rehearsal buffer, and only introduces a very small number of additional parameters (<5% of original model) per task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Prompt-based methods introduce learnable prompts that encode task-specific information. [92] learns a pool of tokens, from which a set is selected using a query mechanism and prepended to the input. [91] refines this by using both task-specific and shared prompts. Subsequent approaches replace prompt selection with an attention mechanism [79] or with intermediate embeddings [35]. However, these prompt-based methods are designed for 2D classification tasks that use vision transformers (ViTs), borrowing the concept of prompting from the field of natural language processing (NLP). The idea of prepending prompts to tokenized inputs does not naturally extend to convolutional neural networks (CNNs), limiting their applicability to 3D vision tasks where" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6305" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.198 + ], + "angle": 0, + "content": "CNNs are primarily used. In contrast, our method learns prototypes, which serve as representative features, offering a more intuitive mechanism for adding a lightweight selective bias than prepending abstract prompts in image space. Unlike prompt-based methods, our method is fully architecture-agnostic and can be applied to any model that has a latent space without modifying the underlying architecture." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.199, + 0.484, + 0.318 + ], + "angle": 0, + "content": "Prototypes have predominantly been explored in the context of few-shot learning of 2D tasks [22, 23, 44, 45, 80, 107] and representation learning [5, 11, 40]. For continual learning, prototypes have been deployed for supervised classification tasks as discriminative class representations [2, 13, 27, 43, 93, 115]. In contrast, we leverage prototypes as a mechanism for encoding domain-specific information to facilitate continual learning for unsupervised reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.319, + 0.485, + 0.621 + ], + "angle": 0, + "content": "Unsupervised depth completion is a multimodal, 3D reconstruction problem of predicting a depth map from an image and its associated sparse point cloud. In lieu of training signals from ground-truth depth annotations, unsupervised depth completion methods [17, 18, 30, 38, 46, 51, 75, 78, 94, 96-99, 106, 109] minimize the reconstruction error of the sparse depth, the reprojection error of the image from temporally adjacent views, and a local smoothness regularizer. Some works [50, 85, 109] utilize synthetic data to learn priors, while other works [97, 98] densify then refine the sparse point cloud by constructing a coarse piecewise scaffolding. [95] uses backprojection layers to map image features to the 3D scene using camera calibration. These methods are prone to catastrophic forgetting in continual learning settings since they must update their learned model weights to fit to new data, causing performance degradation on previously seen data domains. In contrast, our method freezes the entire model and learns a lightweight selective bias for each dataset, allowing it to adapt effectively to new data domains while mitigating forgetting." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.484, + 0.697 + ], + "angle": 0, + "content": "UnCLe [21] proposes a benchmark and adapts existing methods [36, 42, 69] for unsupervised continual depth completion. To the best of our knowledge, we propose the first continual learning method for unsupervised depth completion and are the first to explore prototypes in this context." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.711, + 0.229, + 0.727 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.737, + 0.484, + 0.873 + ], + "angle": 0, + "content": "Unsupervised Depth Completion. Assuming we are given an RGB image \\(I:\\Omega \\subset \\mathbb{R}^2\\to \\mathbb{R}^3\\) and its associated sparse depth map \\(z:\\Omega \\rightarrow \\mathbb{R}_+\\) obtained by projecting the sparse point cloud onto the image plane, we wish to train a depth completion model \\(f_{\\theta}\\) to predict the dense depth map \\(\\hat{d}\\) in an unsupervised manner (i.e., without access to ground-truth depth). Unsupervised depth completion models [51, 95, 97, 98] typically minimize a loss function in the form of Eq. (1), which comprises a linear combination of three terms:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.886, + 0.484, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "where \\(\\ell_{ph}\\) denotes photometric consistency, \\(\\ell_{sz}\\) sparse depth consistency, and \\(\\ell_{sm}\\) a local smoothness regularizer." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.123, + 0.907, + 0.183 + ], + "angle": 0, + "content": "Photometric Consistency term leverages image reconstruction as the training signal. Specifically, given an image \\(I_{t}\\) at time \\(t\\), its reconstruction \\(\\hat{I}_{t\\tau}\\) from a temporally adjacent image \\(I_{\\tau}\\) at time \\(\\tau\\) for \\(\\tau \\in \\{t - 1, t + 1\\}\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.193, + 0.907, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\hat {I} _ {t \\tau} (x, \\hat {d}, g _ {\\tau t}) = I _ {\\tau} \\left(\\pi g _ {\\tau t} K ^ {- 1} \\bar {x} \\hat {d} (x)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.222, + 0.907, + 0.33 + ], + "angle": 0, + "content": "where \\(\\bar{x} = [x^{\\top},1]^{\\top}\\) is the homogeneous coordinates of \\(x\\in \\Omega\\) \\(K\\) is the camera intrinsic calibration matrix, \\(g_{\\tau t}\\in\\) \\(SE(3)\\) is the estimated relative camera pose matrix from time \\(t\\) to \\(\\tau\\) , and \\(\\pi\\) is the canonical perspective projection matrix. Given \\(I_{t}\\) and its reconstruction \\(\\hat{I}_{t\\tau}\\) , the photometric consistency loss measures the \\(L1\\) difference and structural similarity (SSIM [88]) between \\(I_{t}\\) and \\(\\hat{I}_{t\\tau}\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.339, + 0.907, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\ell_ {p h} = \\frac {1}{| \\Omega |} \\sum_ {\\tau \\in T} \\sum_ {x \\in \\Omega} w _ {c o} \\left| \\hat {I} _ {t \\tau} (x) - I (x) \\right| + \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.66, + 0.379, + 0.866, + 0.397 + ], + "angle": 0, + "content": "\\[\nw _ {s t} \\big (1 - \\operatorname {S S I M} (\\hat {I} _ {t \\tau} (x), I (x)) \\big).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.407, + 0.907, + 0.483 + ], + "angle": 0, + "content": "Sparse Depth Consistency. However, photometric reconstruction recovers depth only up to an unknown scale. To ground predictions to a metric scale, we minimize an \\(L1\\) loss between the predicted depth \\(\\hat{d}\\) and sparse depth \\(z\\) for \\(x\\in \\Omega\\) where points exist as denoted by \\(M:\\Omega \\mapsto \\{0,1\\}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.493, + 0.907, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\ell_ {s z} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} | M (x) \\cdot (\\hat {d} (x) - z (x)) |. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.54, + 0.907, + 0.692 + ], + "angle": 0, + "content": "Local Smoothness. To address ambiguities in regions where the predicted depth is not constrained by photometric or sparse depth reconstruction terms, we rely on a regularizer that enforces local smoothness in predictions by applying an \\(L1\\) penalty on the depth gradients in both the \\(x\\)-direction \\((\\partial_{X})\\) and \\(y\\)-direction \\((\\partial_{Y})\\). To allow for depth discontinuities along object boundaries, these penalties are weighted by their corresponding image gradients, \\(\\lambda_{X} = e^{-|\\partial_{X}I_{t}(x)|}\\) and \\(\\lambda_{Y} = e^{-|\\partial_{Y}I_{t}(x)|}\\). Larger image gradients result in smaller weights, allowing for sharp transitions in depth along edges:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.701, + 0.907, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\ell_ {s m} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} \\lambda_ {X} (x) \\left| \\partial_ {X} \\hat {d} (x) \\right| + \\lambda_ {Y} (x) \\left| \\partial_ {Y} \\hat {d} (x) \\right|. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Unsupervised Continual Depth Completion. For continual learning, we consider a task sequence of domains \\(\\mathcal{D}_1,\\mathcal{D}_2,\\dots ,\\mathcal{D}_T\\). Starting with a depth completion model \\(f_{\\theta}\\) pretrained on the initial dataset \\(\\mathcal{D}_1\\), we aim to incrementally adapt \\(f_{\\theta}\\) to each subsequent dataset \\(\\mathcal{D}_2,\\dots ,\\mathcal{D}_k,\\dots ,\\mathcal{D}_T\\). The key challenge is to learn the data distribution of each new dataset \\(\\mathcal{D}_k\\) without \"forgetting,\" as measured by performance degradation on previously learned datasets \\(\\mathcal{D}_{j < k}\\). We denote each dataset as \\(\\mathcal{D}_k = \\{(I_k^{(i)},z_k^{(i)},K_k^{(i)})\\}_{i = 1}^{n_k}\\), which comprises \\(n_k\\) training samples of image, sparse depth, and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.094, + 0.425, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.439, + 0.094, + 0.882, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.289, + 0.908, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Overview of ProtoDepth. (a) In the agnostic setting, a prototype set is selected by maximizing the cosine similarity between an input sample descriptor and the learned domain descriptors. In the incremental setting, the domain identity is known. (b) At inference, the similarity between the frozen queries and the keys of the selected prototype set determines how the learned prototypes contribute as local (additive) biases to the latent features. Additionally, a global (multiplicative) bias is applied using a \\(1 \\times 1\\) depthwise convolution." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.36, + 0.487, + 0.437 + ], + "angle": 0, + "content": "calibration, with no ground-truth depth. We assume that the relative camera pose \\( g_{t\\tau} \\) is given, or is estimated; if estimated by a pose network, we allow it to forget as we focus on continual learning for depth completion, and not pose estimation, which is outside the focus of this work." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.448, + 0.184, + 0.464 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.473, + 0.485, + 0.671 + ], + "angle": 0, + "content": "We present ProtoDepth, a novel approach for unsupervised continual depth completion that mitigates catastrophic forgetting by leveraging prototype sets as selective biases. Given a pretrained depth completion model \\( f_{\\theta} \\), which we freeze to prevent any forgetting, we adapt it to new datasets by deploying lightweight, domain-specific prototype sets that learn to selectively bias the latent features; note that this only adds minimal additional parameters per dataset or domain. Our method is applicable to the domain-incremental (\"incremental\") setting, where dataset identity is known at test-time, and the more challenging domain-agnostic (\"agnostic\") setting, where the test-time domain identity is unknown, through a proposed prototype set selection mechanism (see Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.678, + 0.279, + 0.695 + ], + "angle": 0, + "content": "4.1. Prototype Learning" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.7, + 0.486, + 0.822 + ], + "angle": 0, + "content": "To enable the model to adapt to new datasets without forgetting, we learn layer-specific prototype sets for each dataset that serve as multiplicative (global) and additive (local) biases in the latent feature space. For simplicity, we consider an input sample from a single dataset \\(\\mathcal{D}_k\\) at a single layer \\(l\\), which is encoded into the latent features \\(X \\in \\mathbb{R}^{h \\times w \\times c}\\). We assume a linear transformation from the learned latent space of \\(\\mathcal{D}_1\\) to that of \\(\\mathcal{D}_k\\); hence, we formulate the adaptation as" + }, + { + "type": "equation", + "bbox": [ + 0.224, + 0.829, + 0.484, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\hat {X} = A \\odot X + B, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.903 + ], + "angle": 0, + "content": "where \\(\\odot\\) denotes a (broadcasted) Hadamard product between the global prototype \\(A\\in \\mathbb{R}^c\\) and the features \\(X\\); \\(B\\) is an additive bias constructed from a set of local prototypes \\(P\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.36, + 0.907, + 0.512 + ], + "angle": 0, + "content": "To this end, we flatten the latent features \\(X\\) to get \\(Q \\in \\mathbb{R}^{(h \\times w) \\times c}\\). Since the model \\(f_{\\theta}\\) is frozen, \\(Q\\) serves as a set of \\(h \\times w\\) deterministic queries, where each query is a \\(c\\)-dimensional vector. We introduce \\(N\\) learnable additive prototypes \\(P = [p_1, p_2, \\dots, p_N]^\\top \\in \\mathbb{R}^{N \\times c}\\), where each \\(p_i\\) is a \\(c\\)-dimensional vector representing a \"prototypical\" local feature of the dataset. To learn the keys associated with each prototype, we define a projection matrix \\(W\\) that learns to map the prototypes \\(P\\) back into the query space, i.e., the latent feature space. This yields \\(K \\in \\mathbb{R}^{N \\times c}\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.518, + 0.907, + 0.535 + ], + "angle": 0, + "content": "\\[\nK = \\operatorname {S t o p G r a d} (P) \\times W. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.54, + 0.909, + 0.648 + ], + "angle": 0, + "content": "StopGrad (stop gradient) facilitates decoupled optimization, enabling prototypes to learn appropriate additive biases while keys learn to assign relevant prototypes to queries. We compute the similarity scores between the queries \\( Q \\) and the keys \\( K \\) using scaled dot-product attention [86]. To obtain the additive bias \\( b \\in \\mathbb{R}^{(h \\times w) \\times c} \\), the scores are used to compute a convex combination of prototypes \\( P \\):" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.651, + 0.907, + 0.67 + ], + "angle": 0, + "content": "\\[\nb = \\operatorname {s o f t m a x} \\left(Q \\times K ^ {\\top} / \\sqrt {c}\\right) \\times P. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.911, + 0.902 + ], + "angle": 0, + "content": "We reshape \\( b \\) back to the spatial dimensions of \\( X \\) to obtain the local additive bias \\( B \\in \\mathbb{R}^{h \\times w \\times c} \\). To model the global transformation, we learn a \\( c \\)-dimensional multiplicative prototype \\( A \\), applied element-wise as \\( A \\odot X \\), which can be efficiently implemented as a \\( 1 \\times 1 \\) depthwise convolution. The result is further adapted to the new dataset distribution, still without altering the original model parameters, by incorporating the local domain-specific transformation \\( B \\) as an additive bias, i.e., \\( \\hat{X} = A \\odot X + B \\). As \\( f_{\\theta} \\) is frozen and a new prototype set (local and global prototypes \\( P_{k} \\) and \\( A_{k} \\), and projection matrix \\( W_{k} \\)) is learned for each dataset \\( \\mathcal{D}_k \\), this naturally facilitates continual learning and ensures no forgetting in the incremental setting, where the prototype set corresponding to the domain identity is selected. We further extend this to the agnostic setting in Sec. 4.3." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6307" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.905, + 0.403 + ], + "angle": 0, + "content": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned8.8286.1316.9517.04263.352125.2815.46135.05352.453108.43415.36035.357
EWC [36]9.4398.0145.1836.17463.787126.70615.22934.36753.614110.95615.09134.039
LwF [42]8.5918.4569.61321.77465.135126.96816.22138.00253.517108.84515.40234.729
Replay [69]6.1544.6889.47111.71364.305126.71416.37336.72954.326112.21816.64037.671
ProtoDepth-A2.4393.5984.6304.51956.971118.13213.55430.55447.367103.01513.51731.623
ProtoDepth0.0000.0000.0000.00056.359115.15313.58930.33246.934101.32613.68431.925
FusionNetFinetuned24.9289.77532.33316.79966.523130.14215.82933.88154.252110.66615.31733.726
EWC [36]11.2568.78217.94417.84764.487130.89015.26434.20351.345109.22314.27632.781
LwF [42]6.8632.8657.3361.93961.204123.57314.07530.87950.159106.38613.87931.608
Replay [69]5.7022.86212.19611.18661.467125.58714.75033.27950.273108.60814.35133.658
ProtoDepth-A1.2820.6861.3040.44657.742119.98813.27430.13947.674104.34913.12831.058
ProtoDepth0.0000.0000.0000.00057.486119.16813.32329.93647.335102.84513.09130.474
KBNetFinetuned16.08015.4638.1889.17058.577124.60613.47431.40947.890105.80713.26631.742
EWC [36]14.91511.87810.3985.64057.414122.07513.74131.55248.031106.66114.12933.096
LwF [42]9.7176.3246.1685.25457.511119.09314.11932.16547.154103.16414.30433.838
Replay [69]7.2004.8199.2029.53956.208117.84813.98332.34146.700103.63113.84433.326
ProtoDepth-A3.2041.3044.9112.94354.254115.54813.20130.49945.264101.09713.28131.718
ProtoDepth0.0000.0000.0000.00052.497113.54812.84529.99044.09299.78813.08131.503
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.41, + 0.908, + 0.44 + ], + "angle": 0, + "content": "Table 1. Quantitative results on indoor datasets. Models are initially trained on NYUv2 and continually trained on ScanNet, then VOID. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.457, + 0.32, + 0.473 + ], + "angle": 0, + "content": "4.2. ProtoDepth Architecture" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.483, + 0.483, + 0.559 + ], + "angle": 0, + "content": "Current unsupervised depth completion models [95, 97, 98] adopt an encoder-decoder CNN architecture, which consists of separate image and sparse depth encoders with skip connections to the decoder. We refer to the bottleneck and the skip connections as the latent space layers (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.562, + 0.483, + 0.653 + ], + "angle": 0, + "content": "To extend the prototype mechanism (Sec. 4.1) across multiple layers, for each new dataset \\(D_{k}\\), we introduce a prototype set of local and global prototypes \\(P^{(l)}\\) and \\(A^{(l)}\\), and projection matrix \\(W^{(l)}\\) for each layer \\(l\\) in the latent space. For each new dataset, the latent feature adaptation (Eqs. (6) and (8)) is applied independently to each layer \\(l\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.656, + 0.483, + 0.793 + ], + "angle": 0, + "content": "As different modalities in multimodal tasks (e.g., RGB image and sparse depth map in depth completion) may experience varying degrees of covariate shift across domains, we propose to deploy a different number of prototypes \\( N^{(I)} \\) and \\( N^{(z)} \\) for the RGB image and sparse depth modalities, respectively. Based on the observation that RGB images undergo a larger covariate shift than sparse depth [58], we choose \\( N^{(I)} > N^{(z)} \\) to capture their prototypical features; this choice reduces the parameter overhead." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.903 + ], + "angle": 0, + "content": "The proposed prototype-based continual learning mechanism operates on the latent feature space and does not depend on the specific architecture of the model. This architecture-agnostic flexibility stems from the fact that our queries \\( Q \\in \\mathbb{R}^{(h \\times w) \\times c} \\) mirror the general structure of latent features across commonly used model architectures, where \\( h \\times w \\) can be replaced by the number of tokens \\( n \\) in the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.908, + 0.52 + ], + "angle": 0, + "content": "case of transformers [86]. Thus, it can be applied generically to models with latent feature representations [37, 103], providing a general framework for mitigating catastrophic forgetting across various tasks and modalities." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.53, + 0.727, + 0.546 + ], + "angle": 0, + "content": "4.3. Prototype Set Selection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.908, + 0.644 + ], + "angle": 0, + "content": "As the prototypes are learned for a specific domain, we cannot easily select the appropriate prototype set for inference if the test-time domain identity is withheld, i.e., in the domain-agnostic setting. To address this challenging scenario, we introduce a prototype set selection mechanism that chooses the most relevant prototype set for a given input." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.909, + 0.765 + ], + "angle": 0, + "content": "During training, we introduce a domain descriptor \\(r_k \\in \\mathbb{R}^c\\) for each dataset \\(\\mathcal{D}_k\\), which adds negligible overhead in terms of number of parameters. For an input from \\(\\mathcal{D}_k\\), we obtain a sample descriptor \\(s_k \\in \\mathbb{R}^c\\) by applying global average pooling (GAP) to the bottleneck latent features (with channel dimension \\(c\\)) before applying the prototype set. Importantly, since both encoders are always frozen during continual training, \\(s_k\\) is a deterministic mapping of the input." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.909, + 0.903 + ], + "angle": 0, + "content": "For each new dataset \\(\\mathcal{D}_k\\), we deploy a new domain descriptor \\(r_k\\) and freeze all existing learned domain descriptors. The deployed domain descriptor \\(r_k\\) is trained by minimizing cosine distance between itself and sample descriptors \\(s_k\\) for \\(\\mathcal{D}_k\\), while maximizing the cosine distance to all other learned domain descriptors \\(\\{r_{j \\neq k}\\}\\). This naturally yields domain descriptors that are discriminative across datasets, allowing us to use the projection of sample descriptors onto domain descriptors as a prototype set selection mechanism." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6308" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.905, + 0.381 + ], + "angle": 0, + "content": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned499.598162.188467.472208.6931620.4293072.1294.0406.144914.2232993.2281.9554.503
EWC [36]555.925190.152540.109247.9431796.3003346.0574.4906.685962.9373209.7591.9624.739
LwF [42]631.119221.535524.976233.7581973.9723612.7004.5336.648985.9953236.2442.0624.722
Replay [69]17.2414.05016.6625.478524.1141875.8971.3333.359618.6682366.5771.2923.348
ProtoDepth-A2.4272.8632.0792.153458.5201832.6901.1333.213548.2402294.3991.0803.159
ProtoDepth0.0000.0000.0000.000445.4191804.1581.1063.169531.6892262.9431.0433.110
FusionNetFinetuned11.3368.43517.44717.991437.7301785.2121.1933.724501.3622138.4221.1113.978
EWC [36]21.00610.49420.43116.535431.4401760.4601.1443.181486.1702117.0301.0292.986
LwF [42]12.3685.20213.59313.117442.8781759.2021.1783.352526.5282168.9611.1563.451
Replay [69]8.29011.1342.7697.975419.0441774.3611.0443.032479.1682122.9970.9662.906
ProtoDepth-A2.2002.2822.6027.203404.9561702.9451.0413.028464.9762052.4130.9522.864
ProtoDepth0.0000.0000.0000.000400.8881683.2021.0222.899461.0432048.9420.9322.792
KBNetFinetuned27.15318.20852.96933.370469.6581943.2591.3383.683541.3832411.1691.1443.505
EWC [36]23.5178.58330.07718.991456.8281806.7611.2213.321526.3662210.4241.1333.158
LwF [42]21.1844.04943.50019.951460.0971749.7341.3623.555541.9322142.9991.3593.731
Replay [69]25.42329.3036.3627.274454.8961935.6671.1023.203525.6962318.3631.0943.246
ProtoDepth-A4.5133.1002.9601.878409.9031730.7201.0453.044478.7902138.3471.0083.066
ProtoDepth0.0000.0000.0000.000401.0751710.0741.0292.993471.4372125.9570.9963.015
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.39, + 0.908, + 0.418 + ], + "angle": 0, + "content": "Table 2. Quantitative results on outdoor datasets. Models are initially trained on KITTI and continually trained on Waymo, then VKITTI. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.438, + 0.484, + 0.453 + ], + "angle": 0, + "content": "To this end, we propose to minimize an additional objective:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.458, + 0.484, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\ell_ {d r} = 1 - \\left(\\frac {s _ {k}}{\\| s _ {k} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right) + \\frac {1}{w _ {j k}} \\sum_ {j \\neq k} \\left(\\frac {r _ {j}}{\\| r _ {j} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.484, + 0.637 + ], + "angle": 0, + "content": "where \\( ||\\cdot|| \\) denotes the \\( L2 \\)-norm and \\( w_{jk} \\propto |j \\neq k| \\) is a tunable normalization constant. As the previously learned domain descriptors are frozen, their alignment to their respective datasets or domains is preserved, allowing us to continually learn new domain descriptors that can distinguish new datasets. Eq. (9) is incorporated into Eq. (1) as an additional term weighted by \\( w_{dr} \\) to yield a novel loss function for training of unsupervised continual depth completion models in the agnostic setting:" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.644, + 0.484, + 0.661 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m} + w _ {d r} \\ell_ {d r}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.484, + 0.711 + ], + "angle": 0, + "content": "At test-time, we compute the sample descriptor \\( s \\) for an input without dataset identity and select the domain descriptor \\( r_{k^*} \\) that maximizes cosine similarity with \\( s \\):" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.716, + 0.484, + 0.746 + ], + "angle": 0, + "content": "\\[\nk ^ {*} = \\arg \\max _ {k} \\left(\\frac {s}{\\| s \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.751, + 0.484, + 0.901 + ], + "angle": 0, + "content": "For each latent space layer, we use the prototype set corresponding to the selected domain descriptor. While this does not eliminate forgetting due to the evolving set of domain descriptors and possible overlap between domains, it does minimize forgetting as each prototype set is learned independently for each dataset, but can still be selectively used for inference without knowing the test-time dataset identity. The trade-off is shown in Tabs. 1 and 2 (ProtoDepth-A) where we incur forgetting in exchange for the flexibility to support both the incremental and agnostic settings." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.436, + 0.645, + 0.453 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.465, + 0.907, + 0.617 + ], + "angle": 0, + "content": "Datasets. Indoor dataset sequence: NYUv2 [77] contains household, office, and commercial scenes captured with a Microsoft Kinect; ScanNet [12] is a diverse, large-scale dataset captured using a Structure Sensor; Void [97] contains laboratory, classroom, and garden scenes captured using XIVO. Outdoor dataset sequence: KITTI [84] is a daytime autonomous driving benchmark captured using a Velodyne LiDAR sensor; Waymo [81] contains road scenes with a wide variety of driving conditions; VKITTI [20] is a synthetic dataset that replicates and augments KITTI scenes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.619, + 0.907, + 0.665 + ], + "angle": 0, + "content": "Models. We evaluate using three recent unsupervised depth completion models in the continual learning setting: VOICES [97], FusionNet [98], and KBNet [95]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.668, + 0.909, + 0.774 + ], + "angle": 0, + "content": "Baseline Methods. We compare ProtoDepth against EWC [36], LwF [42], and Experience Replay (\"Re-play\") [69] as milestone works of their respective class of continual learning approaches. We include full finetuning (\"Finetuned\") as a baseline of performance with no continual learning strategy. All baseline methods achieve identical performance in the incremental and agnostic settings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.777, + 0.909, + 0.853 + ], + "angle": 0, + "content": "Evaluation Metrics are computed across four standard depth completion metrics (MAE, RMSE, iMAE, iRMSE). We define the following evaluation metrics in terms of \\( a_{j}^{k} \\), denoting any one of the four depth completion metrics on dataset \\( \\mathcal{D}_j \\) after training on \\( \\mathcal{D}_k \\). Given \\( T \\) total datasets:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "Average Forgetting \\((\\bar{F})\\) is the scale-invariant mean of how much performance on previous datasets \\(\\mathcal{D}_{j < k}\\) deteriorates (i.e., increases in \\(\\%\\) ) after training on each new \\(\\mathcal{D}_k\\):" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6309" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.18, + 0.091, + 0.398, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.091, + 0.602, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.092, + 0.806, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.133, + 0.115, + 0.142 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.143, + 0.498, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.142, + 0.905, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.291, + 0.908, + 0.348 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison of ProtoDepth and baseline methods using VOICESED on KITTI after continual training on Waymo. (a) Input sample from KITTI, (b) Baseline methods exhibit significant forgetting, particularly for small-surface-area objects (e.g., street signs and lamp posts) where sparse depth is limited, and photometric priors from KITTI are critical. In contrast, ProtoDepth produces high-fidelity depth predictions, effectively mitigating forgetting despite the large domain gap between KITTI and Waymo." + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.375, + 0.484, + 0.418 + ], + "angle": 0, + "content": "\\[\n\\bar {F} = \\frac {2}{T (T - 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j < k} \\frac {a _ {j} ^ {k} - a _ {j} ^ {j}}{a _ {j} ^ {j}}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.426, + 0.484, + 0.457 + ], + "angle": 0, + "content": "Average Performance \\((\\bar{\\mu})\\) is the mean of performance on all seen datasets \\(\\mathcal{D}_{j\\leq k}\\) after training on each new \\(\\mathcal{D}_k\\):" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.469, + 0.484, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mu} = \\frac {2}{T (T + 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j \\leq k} a _ {j} ^ {k}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.519, + 0.484, + 0.566 + ], + "angle": 0, + "content": "Stability-Plasticity Trade-off (SPTO) captures the balance between retaining learned knowledge (stability) and adapting to new domains (plasticity) as a harmonic mean:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.577, + 0.484, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\mathrm {S P T O} = \\frac {2 \\times S \\times P}{S + P}, \\left\\{ \\begin{array}{l} S = \\sum_ {k = 1} ^ {T} a _ {k} ^ {T} \\\\ P = \\sum_ {k = 1} ^ {T} a _ {k} ^ {k}, \\end{array} \\right. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.626, + 0.485, + 0.672 + ], + "angle": 0, + "content": "where \\( S \\) is performance across all datasets after completing training on the dataset sequence, and \\( P \\) is performance on each new dataset after training on it for the first time." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.229, + 0.696 + ], + "angle": 0, + "content": "5.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.764 + ], + "angle": 0, + "content": "We compare our method, evaluated in both the incremental (ProtoDepth) and agnostic (ProtoDepth-A) settings, against baseline methods for the indoor dataset sequence in Tab. 1 and for the outdoor dataset sequence in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Results in Incremental Setting. In both indoor and outdoor settings, ProtoDepth achieves a \\(100\\%\\) improvement in Average Forgetting compared to all baseline methods across all models and metrics. This is, of course, because ProtoDepth exhibits zero forgetting as it freezes all model parameters and learns dataset-specific prototypes. For the indoor sequence, compared to the best baseline method, ProtoDepth improves Average Performance by \\(5.15\\%\\) and SPTO by \\(6.59\\%\\), averaged across all models and metrics." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.363, + 0.907, + 0.393 + ], + "angle": 0, + "content": "Similarly, for the outdoor sequence, we improve Average Performance by \\(6.88\\%\\) and SPTO by \\(6.94\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.396, + 0.909, + 0.654 + ], + "angle": 0, + "content": "To demonstrate the reduced forgetting achieved by ProtoDepth, we qualitatively compare against all baseline methods using VOICESED on KITTI after continual training on Waymo (see Fig. 3). ProtoDepth yields better depth predictions for small-surface-area objects with limited sparse depth measurements for which the model must rely on photometric priors learned from images. Unlike KITTI, which consists exclusively of daytime scenes, Waymo includes many evening and overcast scenes, introducing variations in lighting and pixel intensities. Additionally, Waymo was captured using a higher-resolution camera which causes objects to appear bigger in terms of number of pixels occupied. Due to this large distributional shift, the model forgets the projected shapes of objects in KITTI after training on Waymo, even if the objects exist in both datasets. This forgetting is apparent in the highlighted street sign and lamp posts, where baseline methods struggle to accurately predict depth." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.656, + 0.909, + 0.779 + ], + "angle": 0, + "content": "Results in Agnostic Setting. For the indoor sequence, compared to the best baseline method, ProtoDepth-A improves Average Forgetting by \\(52.22\\%\\), Average Performance by \\(4.26\\%\\), and SPTO by \\(5.40\\%\\), averaged across all models and metrics. Notably, ProtoDepth-A outperforms ProtoDepth in some metrics, meaning the model appropriately selects prototypes of different domains when there is domain overlap, thereby enhancing its generalization capabilities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.911, + 0.902 + ], + "angle": 0, + "content": "For the outdoor sequence, ProtoDepth-A shows an average improvement of \\(53.21\\%\\) in Average Forgetting across all models and metrics. In contrast to the indoor sequence, ProtoDepth-A does not outperform ProtoDepth in any metric, likely due to the larger domain gaps between the outdoor datasets. Selecting prototypes from a different outdoor dataset is more likely to be erroneous, leading to performance degradation rather than generalization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6310" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.905, + 0.232 + ], + "angle": 0, + "content": "
MethodN(I)N(z)# ParamsScanNetVOID
MAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
Pretrained--0M (0%)4114.044626.00390.78447.3142.94106.3929.2664.04
ProtoDepth110.24M (3.5%)19.68±0.6860.10±0.7110.44±0.4827.86±0.7437.81±0.5293.72±0.9022.82±0.2752.58±0.32
550.25M (3.6%)16.49±0.1557.51±0.196.84±0.0322.07±0.0334.02±0.2587.72±0.4317.92±0.1443.95±0.28
1050.25M (3.6%)14.59±0.1742.20±0.095.57±0.1417.10±0.1533.63±0.2387.30±0.5717.55±0.3243.24±0.63
10100.25M (3.7%)15.25±0.3943.31±0.725.85±0.2217.57±0.3834.39±0.8288.73±1.8318.49±0.8545.23±1.60
1001000.38M (5.5%)16.35±0.3747.61±0.165.90±0.1720.11±0.1934.29±0.5888.22±0.8618.16±0.6244.51±1.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.237, + 0.908, + 0.267 + ], + "angle": 0, + "content": "Table 3. Sensitivity study of prototype set sizes \\((N^{(I)}\\) and \\(N^{(z)}\\) ) on ProtoDepth using KBNet for indoor datasets (ScanNet and VOID). KBNet is pretrained on the initial dataset (NYUv2). Parameter overhead is reported as a percentage of the full KBNet model's parameters." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.279, + 0.481, + 0.407 + ], + "angle": 0, + "content": "
ScanNetWaymo
Ablated ComponentMAERMSEMAERMSE
global prototypes18.1258.91505.011715.21
projection matrix W17.5957.61495.051690.51
decoupled K and P16.3645.10491.591675.57
no ablations14.5942.20486.951664.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.097, + 0.412, + 0.476, + 0.426 + ], + "angle": 0, + "content": "Table 4. Ablation studies using KBNet for indoor and outdoor." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.444, + 0.486, + 0.641 + ], + "angle": 0, + "content": "Furthermore, we refer back to Fig. 3 (ProtoDepth-A) for head-to-head comparison of our method against other baselines in the agnostic setting. The error maps for Finetuned, EWC, and LwF display significant errors, indicating substantial forgetting of previously learned information. While Replay yields an improved error map, it still experiences forgetting in small-surface-area objects. For example, Replay fails to reconstruct the upper portions of the highlighted street sign and lamp posts due to forgetting of learned photometric priors from KITTI, whereas ProtoDepth-A recalls them from KITTI prototypes. Additionally, ProtoDepth-A predicts the depth of the highlighted small fence poles with higher fidelity than the incoherent prediction of Replay." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.651, + 0.299, + 0.668 + ], + "angle": 0, + "content": "5.2. Design Choice Studies" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.675, + 0.486, + 0.901 + ], + "angle": 0, + "content": "Prototype Set Sizes. We investigate the impact of varying the prototype set sizes (i.e., number of prototypes) for the image and sparse depth layers (denoted as \\( N^{(I)} \\) and \\( N^{(z)} \\), respectively) on the performance of our method. The set size experiments for the indoor sequence are shown in Tab. 3, based on which we selected \\( N^{(I)} = 10 \\), \\( N^{(z)} = 5 \\) for the main experiments. Smaller set sizes perform worse as there is insufficient capacity to capture the diversity of features in each dataset. There is also performance degradation with larger set sizes; intuitively, unnecessary additional parameters may learn noise and cause overfitting. Notably, best performance is achieved when \\( N^{(I)} > N^{(z)} \\), which can be attributed to the larger distributional shift between scenes in the image modality compared to the sparse depth modality [58]. Since the bottleneck layer fuses both modalities," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.281, + 0.908, + 0.371 + ], + "angle": 0, + "content": "we use \\( N^{(I)} \\) for the bottleneck layer prototypes. As a lower bound, we show that the frozen base model pretrained on NYUv2 (\"Pretrained\") performs poorly, motivating the need for continual learning. We perform similar set size experiments for the outdoor dataset sequence (see Supp. Mat.), based on which we choose \\( N^{(I)} = 25 \\), \\( N^{(z)} = 10 \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.373, + 0.909, + 0.555 + ], + "angle": 0, + "content": "Ablations. We assess the impact of the components of ProtoDepth on both indoor (ScanNet) and outdoor (Waymo) in Tab. 4. Removing the \\(1 \\times 1\\) depthwise convolutions results in performance degradation, demonstrating their effectiveness as lightweight global prototypes. Learning the keys \\(K\\) independently from the prototypes \\(P\\) without the projection matrix \\(W\\) hurts performance, suggesting that the projection matrix effectively learns to map the prototypes into latent feature space, fulfilling the intended role of keys. Furthermore, performance decreases without the stop gradient operation on \\(P\\) when computing \\(K\\), indicating the importance of decoupled optimization of keys and prototypes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.572, + 0.628, + 0.587 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.598, + 0.909, + 0.764 + ], + "angle": 0, + "content": "ProtoDepth leverages prototypes as a mechanism for mitigating catastrophic forgetting. While we demonstrate it on unsupervised depth completion, ProtoDepth does not assume specific modalities and thus can be relevant to other multimodal problems [67, 104, 108, 111]. Our promising results on both indoor and outdoor domains illustrate the potential for ProtoDepth to enable unsupervised continual learning for multimodal 3D reconstruction. Our architecture-agnostic approach can also be extended to other tasks involving models that produce latent feature representations [37, 112], offering a general framework for continual learning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Limitations. ProtoDepth relies on knowledge of dataset boundaries to instantiate new prototype sets, which may not be feasible in online training settings where there are no defined boundaries between domains. In the same vein, we do not consider scenarios where domain gaps between datasets are small or where there are significant distributional shifts within a dataset. Addressing these limitations would require mechanisms to dynamically detect domain shifts and instantiate new prototypes when appropriate." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "6311" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.486, + 0.131 + ], + "angle": 0, + "content": "This work is supported by NSF-2112562 Athena AI Institute." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.144, + 0.188, + 0.159 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.169, + 0.486, + 0.238 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9296-9305, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.908, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6316" + } + ] +] \ No newline at end of file diff --git a/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_origin.pdf b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8c47745f998ebd397b1764138fbc17095cf9911d --- /dev/null +++ b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/739ff3ca-b993-42db-9cbe-a91a1fb89d52_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1da99289fcf2817ba2bd5f572887c02023444af495714145124790a391d9f30f +size 2101487 diff --git a/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/full.md b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a9bf47950067e6939b633d2d62c6a7c85330690e --- /dev/null +++ b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/full.md @@ -0,0 +1,391 @@ +# ProtoDepth: Unsupervised Continual Depth Completion with Prototypes + +Patrick Rim Hyoungseob Park S. Gangopadhyay Ziyao Zeng Younjoon Chung Alex Wong Yale Vision Lab + +# Abstract + +We present ProtoDepth, a novel prototype-based approach for continual learning of unsupervised depth completion, the multimodal 3D reconstruction task of predicting dense depth maps from RGB images and sparse point clouds. The unsupervised learning paradigm is well-suited for continual learning, as ground truth is not needed. However, when training on new non-stationary distributions, depth completion models will catastrophically forget previously learned information. We address forgetting by learning prototype sets that adapt the latent features of a frozen pretrained model to new domains. Since the original weights are not modified, ProtoDepth does not forget when test-time domain identity is known. To extend ProtoDepth to the challenging setting where the test-time domain identity is withheld, we propose to learn domain descriptors that enable the model to select the appropriate prototype set for inference. We evaluate ProtoDepth on benchmark dataset sequences, where we reduce forgetting compared to baselines by $52.2\%$ for indoor and $53.2\%$ for outdoor to achieve the state of the art. Project Page: https://protodepth.github.io/. + +# 1. Introduction + +Reconstructing three-dimensional (3D) environments facilitates spatial applications such as autonomous navigation, robotic manipulation, and AR/VR. These applications typically utilize platforms equipped with heterogeneous sensors, such as cameras and sparse range sensors (e.g., LiDAR, ToF) which yield RGB images and point clouds. To reconstruct 3D scenes from an ego-centric point of view in the form of depth maps, the point clouds are typically projected onto the image plane. However, their projections tend to be sparse, which is unlike RGB images that comprise irradiance measured at each pixel. These complementary modalities can be used to predict dense depth maps; this multimodal 3D reconstruction task is called depth completion. + +Depth completion models can be trained in a supervised (using ground truth) or unsupervised (using Structure-from-Motion) manner. As ground truth is prohibitively expensive to acquire, we subscribe to the unsupervised learning + +![](images/8d3992e7a6e62904b1febe2810704257ea19d212ab7fe07854755378b2c6432e.jpg) +Figure 1. Results on KITTI validation set during continual training on outdoor dataset sequence (KITTI $\rightarrow$ Waymo $\rightarrow$ VKITTI). + +paradigm, which enables one to learn without human intervention. While this suggests the potential to continuously learn, existing models are trained and evaluated on single datasets under the assumption of a stationary data distribution. However, sequences of multiple datasets exhibit non-stationary distributions and are captured by sensors with varying calibrations. Hence, fitting to new data samples inevitably causes the model to "catastrophically forget" [19, 54, 63, 82] previously learned information, where the model performance degrades significantly on data from distributions that it had already observed. + +To enable pretrained models to adapt to new environments or domains in an unsupervised manner, we consider continual learning, where training strategies aim to mitigate catastrophic forgetting of previously observed training distributions when learning from a continuous stream of non-stationary data. One school of thought is to constrain updates to parameters deemed "important" for previous domains based on a regularization term controlled by a weight chosen as a hyperparameter. Another is to incur memory costs by storing previously observed training data and incorporating them during learning of new domains, akin to rehearsals. The trade-off is in the sensitivity of optimization (and forgetting) to the choice of hyperparameter and in the size of storage and data privacy. Both schools perform updates to the full set of model parameters, which is computationally expensive. Unlike them, we opt to freeze the pretrained model to ensure zero forgetting and learn a small set of parameters, which we term "prototypes," that modulate + +the latent features for each new domain encountered. + +We model the change in distribution as a domain-specific bias to be learned by global multiplicative and local additive prototypes that transform the latent features to fit the new distribution. In the same vein are learnable prompts or tokens [92] used in continual learning for vision transformers, where the model itself is similarly frozen. Yet, there is no natural scale at which to discretize images, unlike discrete text tokens. In contrast, our proposed prototypes lift the requirements of tokenized inputs and can thus be applied to convolutional neural networks, which are prevalently used in unsupervised depth completion, as well as transformers. + +To this end, we propose ProtoDepth, a novel prototype-based method for unsupervised continual depth completion. Instead of prompts in input space, we deploy lightweight prototypes to a frozen pretrained model to encode prototypical information of each domain. These prototypes model global and local biases, where global prototypes learn a transformation from the latent pretrained data distribution to that of the new domain, and local prototypes capture fine-grained features that can be selectively queried depending on the input. Naturally, when the test-time domain identity is known, i.e., domain-incremental, ProtoDepth exhibits no forgetting and learns the new data distribution with high fidelity. We further encode each domain as a descriptor to enable inference when test-time domain identity is withheld, i.e., domain-agnostic, where the prototype set corresponding to the highest affinity domain descriptor for a given sample is chosen. + +Our contributions: We propose (1) a novel prototype-based paradigm for unsupervised continual depth completion that incurs no forgetting in the domain-incremental setting, and (2) a prototype set selection mechanism that extends the prototype paradigm to domain-agnostic settings with minimal forgetting. This is facilitated by (3) a novel training objective that learns descriptors for each domain, which can be used to determine the prototype set suitable for inference without knowledge of domain identity. (4) Our method, ProtoDepth, reduces forgetting over baselines by over $50\%$ across six datasets; to the best of our knowledge, this is the first unsupervised continual depth completion method. + +# 2. Related Work + +Continual learning is the process of incrementally adapting the weights of a parameterized model to perform new tasks involving non-stationary distributions, while preserving information learned from previous tasks. + +Regularization-based methods aim to mitigate forgetting by restricting the plasticity of model parameters that are important for previously learned tasks. [1, 7, 36, 113] introduce regularization terms to the loss function to identify and penalize changes to important weights while new tasks are learned. [14, 15, 28, 39, 42, 68, 114] attempt to preserve output behavior on previous tasks using knowledge + +distillation [26, 70]. [55, 57, 61, 83] regularize the space of learned functions to encourage similarity between outputs of task-specific heads. However, while they perform well in simpler continual learning settings, regularization-based methods can struggle with more challenging tasks [52] and larger domain shifts between datasets [64, 101]. + +Rehearsal-based methods use a memory buffer to store a limited amount of data from previous tasks, allowing the model to periodically re-train on this data during continual learning. [7, 25, 69] introduce the strategy of retaining a subset of previous "experiences" (i.e., data) to "replay" (i.e., re-train on) while learning new tasks. [8, 31, 49, 64, 65, 87] employ various sampling strategies, [29, 47, 117] reduce memory by storing latent features rather than inputs, and generative replay methods [3, 24, 33, 56, 59, 66, 71, 74, 102] create synthetic rehearsal data from previous task domains. Some recent works utilize techniques such as self-supervision [6, 60] and knowledge distillation [4, 9, 64, 101]. [10] introduces a rehearsal-based continual single image-based depth estimation method, the first such work for a 3D vision task. Rehearsal-based methods can reduce forgetting but are unsuitable when data storage is limited by memory or privacy constraints [76]. Additionally, their performance degrades significantly as memory buffer size shrinks [6]. + +Architecture-based methods [32, 34, 41, 48, 53, 62, 72, 73, 89, 110, 116] allocate task-specific parameters or subnetworks, aiming to enable learning of new tasks while minimizing changes to parameters assigned to previous tasks. Most of these methods require task identity to be known at test-time, which prevents their use in the more realistic domain-agnostic setting where new data is not restricted to a certain domain. Other methods [16, 90] rely on a rehearsal buffer in addition to task-specific parameters. Furthermore, architecture-based methods often introduce a significant number of additional parameters for each task [60, 100, 105], which can even exceed the parameter count of the original model [32, 89]. In contrast, our method can be used for inference without task identity, does not require a rehearsal buffer, and only introduces a very small number of additional parameters (<5% of original model) per task. + +Prompt-based methods introduce learnable prompts that encode task-specific information. [92] learns a pool of tokens, from which a set is selected using a query mechanism and prepended to the input. [91] refines this by using both task-specific and shared prompts. Subsequent approaches replace prompt selection with an attention mechanism [79] or with intermediate embeddings [35]. However, these prompt-based methods are designed for 2D classification tasks that use vision transformers (ViTs), borrowing the concept of prompting from the field of natural language processing (NLP). The idea of prepending prompts to tokenized inputs does not naturally extend to convolutional neural networks (CNNs), limiting their applicability to 3D vision tasks where + +CNNs are primarily used. In contrast, our method learns prototypes, which serve as representative features, offering a more intuitive mechanism for adding a lightweight selective bias than prepending abstract prompts in image space. Unlike prompt-based methods, our method is fully architecture-agnostic and can be applied to any model that has a latent space without modifying the underlying architecture. + +Prototypes have predominantly been explored in the context of few-shot learning of 2D tasks [22, 23, 44, 45, 80, 107] and representation learning [5, 11, 40]. For continual learning, prototypes have been deployed for supervised classification tasks as discriminative class representations [2, 13, 27, 43, 93, 115]. In contrast, we leverage prototypes as a mechanism for encoding domain-specific information to facilitate continual learning for unsupervised reconstruction. + +Unsupervised depth completion is a multimodal, 3D reconstruction problem of predicting a depth map from an image and its associated sparse point cloud. In lieu of training signals from ground-truth depth annotations, unsupervised depth completion methods [17, 18, 30, 38, 46, 51, 75, 78, 94, 96-99, 106, 109] minimize the reconstruction error of the sparse depth, the reprojection error of the image from temporally adjacent views, and a local smoothness regularizer. Some works [50, 85, 109] utilize synthetic data to learn priors, while other works [97, 98] densify then refine the sparse point cloud by constructing a coarse piecewise scaffolding. [95] uses backprojection layers to map image features to the 3D scene using camera calibration. These methods are prone to catastrophic forgetting in continual learning settings since they must update their learned model weights to fit to new data, causing performance degradation on previously seen data domains. In contrast, our method freezes the entire model and learns a lightweight selective bias for each dataset, allowing it to adapt effectively to new data domains while mitigating forgetting. + +UnCLe [21] proposes a benchmark and adapts existing methods [36, 42, 69] for unsupervised continual depth completion. To the best of our knowledge, we propose the first continual learning method for unsupervised depth completion and are the first to explore prototypes in this context. + +# 3. Preliminaries + +Unsupervised Depth Completion. Assuming we are given an RGB image $I:\Omega \subset \mathbb{R}^2\to \mathbb{R}^3$ and its associated sparse depth map $z:\Omega \rightarrow \mathbb{R}_+$ obtained by projecting the sparse point cloud onto the image plane, we wish to train a depth completion model $f_{\theta}$ to predict the dense depth map $\hat{d}$ in an unsupervised manner (i.e., without access to ground-truth depth). Unsupervised depth completion models [51, 95, 97, 98] typically minimize a loss function in the form of Eq. (1), which comprises a linear combination of three terms: + +$$ +\mathcal {L} = w _ {p h} \ell_ {p h} + w _ {s z} \ell_ {s z} + w _ {s m} \ell_ {s m}, \tag {1} +$$ + +where $\ell_{ph}$ denotes photometric consistency, $\ell_{sz}$ sparse depth consistency, and $\ell_{sm}$ a local smoothness regularizer. + +Photometric Consistency term leverages image reconstruction as the training signal. Specifically, given an image $I_{t}$ at time $t$ , its reconstruction $\hat{I}_{t\tau}$ from a temporally adjacent image $I_{\tau}$ at time $\tau$ for $\tau \in \{t - 1, t + 1\}$ is given by + +$$ +\hat {I} _ {t \tau} (x, \hat {d}, g _ {\tau t}) = I _ {\tau} \left(\pi g _ {\tau t} K ^ {- 1} \bar {x} \hat {d} (x)\right), \tag {2} +$$ + +where $\bar{x} = [x^{\top},1]^{\top}$ is the homogeneous coordinates of $x\in \Omega$ $K$ is the camera intrinsic calibration matrix, $g_{\tau t}\in$ $SE(3)$ is the estimated relative camera pose matrix from time $t$ to $\tau$ , and $\pi$ is the canonical perspective projection matrix. Given $I_{t}$ and its reconstruction $\hat{I}_{t\tau}$ , the photometric consistency loss measures the $L1$ difference and structural similarity (SSIM [88]) between $I_{t}$ and $\hat{I}_{t\tau}$ .. + +$$ +\ell_ {p h} = \frac {1}{| \Omega |} \sum_ {\tau \in T} \sum_ {x \in \Omega} w _ {c o} \left| \hat {I} _ {t \tau} (x) - I (x) \right| + \tag {3} +$$ + +$$ +w _ {s t} \big (1 - \operatorname {S S I M} (\hat {I} _ {t \tau} (x), I (x)) \big). +$$ + +Sparse Depth Consistency. However, photometric reconstruction recovers depth only up to an unknown scale. To ground predictions to a metric scale, we minimize an $L1$ loss between the predicted depth $\hat{d}$ and sparse depth $z$ for $x\in \Omega$ where points exist as denoted by $M:\Omega \mapsto \{0,1\}$ : + +$$ +\ell_ {s z} = \frac {1}{| \Omega |} \sum_ {x \in \Omega} | M (x) \cdot (\hat {d} (x) - z (x)) |. \tag {4} +$$ + +Local Smoothness. To address ambiguities in regions where the predicted depth is not constrained by photometric or sparse depth reconstruction terms, we rely on a regularizer that enforces local smoothness in predictions by applying an $L1$ penalty on the depth gradients in both the $x$ -direction $(\partial_{X})$ and $y$ -direction $(\partial_{Y})$ . To allow for depth discontinuities along object boundaries, these penalties are weighted by their corresponding image gradients, $\lambda_{X} = e^{-|\partial_{X}I_{t}(x)|}$ and $\lambda_{Y} = e^{-|\partial_{Y}I_{t}(x)|}$ . Larger image gradients result in smaller weights, allowing for sharp transitions in depth along edges: + +$$ +\ell_ {s m} = \frac {1}{| \Omega |} \sum_ {x \in \Omega} \lambda_ {X} (x) \left| \partial_ {X} \hat {d} (x) \right| + \lambda_ {Y} (x) \left| \partial_ {Y} \hat {d} (x) \right|. \tag {5} +$$ + +Unsupervised Continual Depth Completion. For continual learning, we consider a task sequence of domains $\mathcal{D}_1,\mathcal{D}_2,\dots ,\mathcal{D}_T$ . Starting with a depth completion model $f_{\theta}$ pretrained on the initial dataset $\mathcal{D}_1$ , we aim to incrementally adapt $f_{\theta}$ to each subsequent dataset $\mathcal{D}_2,\dots ,\mathcal{D}_k,\dots ,\mathcal{D}_T$ . The key challenge is to learn the data distribution of each new dataset $\mathcal{D}_k$ without "forgetting," as measured by performance degradation on previously learned datasets $\mathcal{D}_{j < k}$ . We denote each dataset as $\mathcal{D}_k = \{(I_k^{(i)},z_k^{(i)},K_k^{(i)})\}_{i = 1}^{n_k}$ , which comprises $n_k$ training samples of image, sparse depth, and + +![](images/f7bda9c664577cb155d046f3118a9e9542f026dd5864cddb754ed73b6c0e2f15.jpg) +Figure 2. Overview of ProtoDepth. (a) In the agnostic setting, a prototype set is selected by maximizing the cosine similarity between an input sample descriptor and the learned domain descriptors. In the incremental setting, the domain identity is known. (b) At inference, the similarity between the frozen queries and the keys of the selected prototype set determines how the learned prototypes contribute as local (additive) biases to the latent features. Additionally, a global (multiplicative) bias is applied using a $1 \times 1$ depthwise convolution. + +![](images/aa81f6dc0df6fad71f74b3474a61e8929fe516e7dbb3f7f1d25d08d0f8292470.jpg) + +calibration, with no ground-truth depth. We assume that the relative camera pose $g_{t\tau}$ is given, or is estimated; if estimated by a pose network, we allow it to forget as we focus on continual learning for depth completion, and not pose estimation, which is outside the focus of this work. + +# 4. Method + +We present ProtoDepth, a novel approach for unsupervised continual depth completion that mitigates catastrophic forgetting by leveraging prototype sets as selective biases. Given a pretrained depth completion model $f_{\theta}$ , which we freeze to prevent any forgetting, we adapt it to new datasets by deploying lightweight, domain-specific prototype sets that learn to selectively bias the latent features; note that this only adds minimal additional parameters per dataset or domain. Our method is applicable to the domain-incremental ("incremental") setting, where dataset identity is known at test-time, and the more challenging domain-agnostic ("agnostic") setting, where the test-time domain identity is unknown, through a proposed prototype set selection mechanism (see Sec. 4.3). + +# 4.1. Prototype Learning + +To enable the model to adapt to new datasets without forgetting, we learn layer-specific prototype sets for each dataset that serve as multiplicative (global) and additive (local) biases in the latent feature space. For simplicity, we consider an input sample from a single dataset $\mathcal{D}_k$ at a single layer $l$ , which is encoded into the latent features $X \in \mathbb{R}^{h \times w \times c}$ . We assume a linear transformation from the learned latent space of $\mathcal{D}_1$ to that of $\mathcal{D}_k$ ; hence, we formulate the adaptation as + +$$ +\hat {X} = A \odot X + B, \tag {6} +$$ + +where $\odot$ denotes a (broadcasted) Hadamard product between the global prototype $A\in \mathbb{R}^c$ and the features $X$ ; $B$ is an additive bias constructed from a set of local prototypes $P$ . + +To this end, we flatten the latent features $X$ to get $Q \in \mathbb{R}^{(h \times w) \times c}$ . Since the model $f_{\theta}$ is frozen, $Q$ serves as a set of $h \times w$ deterministic queries, where each query is a $c$ -dimensional vector. We introduce $N$ learnable additive prototypes $P = [p_1, p_2, \dots, p_N]^\top \in \mathbb{R}^{N \times c}$ , where each $p_i$ is a $c$ -dimensional vector representing a "prototypical" local feature of the dataset. To learn the keys associated with each prototype, we define a projection matrix $W$ that learns to map the prototypes $P$ back into the query space, i.e., the latent feature space. This yields $K \in \mathbb{R}^{N \times c}$ , where + +$$ +K = \operatorname {S t o p G r a d} (P) \times W. \tag {7} +$$ + +StopGrad (stop gradient) facilitates decoupled optimization, enabling prototypes to learn appropriate additive biases while keys learn to assign relevant prototypes to queries. We compute the similarity scores between the queries $Q$ and the keys $K$ using scaled dot-product attention [86]. To obtain the additive bias $b \in \mathbb{R}^{(h \times w) \times c}$ , the scores are used to compute a convex combination of prototypes $P$ : + +$$ +b = \operatorname {s o f t m a x} \left(Q \times K ^ {\top} / \sqrt {c}\right) \times P. \tag {8} +$$ + +We reshape $b$ back to the spatial dimensions of $X$ to obtain the local additive bias $B \in \mathbb{R}^{h \times w \times c}$ . To model the global transformation, we learn a $c$ -dimensional multiplicative prototype $A$ , applied element-wise as $A \odot X$ , which can be efficiently implemented as a $1 \times 1$ depthwise convolution. The result is further adapted to the new dataset distribution, still without altering the original model parameters, by incorporating the local domain-specific transformation $B$ as an additive bias, i.e., $\hat{X} = A \odot X + B$ . As $f_{\theta}$ is frozen and a new prototype set (local and global prototypes $P_{k}$ and $A_{k}$ , and projection matrix $W_{k}$ ) is learned for each dataset $\mathcal{D}_k$ , this naturally facilitates continual learning and ensures no forgetting in the incremental setting, where the prototype set corresponding to the domain identity is selected. We further extend this to the agnostic setting in Sec. 4.3. + +
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned8.8286.1316.9517.04263.352125.2815.46135.05352.453108.43415.36035.357
EWC [36]9.4398.0145.1836.17463.787126.70615.22934.36753.614110.95615.09134.039
LwF [42]8.5918.4569.61321.77465.135126.96816.22138.00253.517108.84515.40234.729
Replay [69]6.1544.6889.47111.71364.305126.71416.37336.72954.326112.21816.64037.671
ProtoDepth-A2.4393.5984.6304.51956.971118.13213.55430.55447.367103.01513.51731.623
ProtoDepth0.0000.0000.0000.00056.359115.15313.58930.33246.934101.32613.68431.925
FusionNetFinetuned24.9289.77532.33316.79966.523130.14215.82933.88154.252110.66615.31733.726
EWC [36]11.2568.78217.94417.84764.487130.89015.26434.20351.345109.22314.27632.781
LwF [42]6.8632.8657.3361.93961.204123.57314.07530.87950.159106.38613.87931.608
Replay [69]5.7022.86212.19611.18661.467125.58714.75033.27950.273108.60814.35133.658
ProtoDepth-A1.2820.6861.3040.44657.742119.98813.27430.13947.674104.34913.12831.058
ProtoDepth0.0000.0000.0000.00057.486119.16813.32329.93647.335102.84513.09130.474
KBNetFinetuned16.08015.4638.1889.17058.577124.60613.47431.40947.890105.80713.26631.742
EWC [36]14.91511.87810.3985.64057.414122.07513.74131.55248.031106.66114.12933.096
LwF [42]9.7176.3246.1685.25457.511119.09314.11932.16547.154103.16414.30433.838
Replay [69]7.2004.8199.2029.53956.208117.84813.98332.34146.700103.63113.84433.326
ProtoDepth-A3.2041.3044.9112.94354.254115.54813.20130.49945.264101.09713.28131.718
ProtoDepth0.0000.0000.0000.00052.497113.54812.84529.99044.09299.78813.08131.503
+ +Table 1. Quantitative results on indoor datasets. Models are initially trained on NYUv2 and continually trained on ScanNet, then VOID. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]. + +# 4.2. ProtoDepth Architecture + +Current unsupervised depth completion models [95, 97, 98] adopt an encoder-decoder CNN architecture, which consists of separate image and sparse depth encoders with skip connections to the decoder. We refer to the bottleneck and the skip connections as the latent space layers (see Fig. 2). + +To extend the prototype mechanism (Sec. 4.1) across multiple layers, for each new dataset $D_{k}$ , we introduce a prototype set of local and global prototypes $P^{(l)}$ and $A^{(l)}$ , and projection matrix $W^{(l)}$ for each layer $l$ in the latent space. For each new dataset, the latent feature adaptation (Eqs. (6) and (8)) is applied independently to each layer $l$ . + +As different modalities in multimodal tasks (e.g., RGB image and sparse depth map in depth completion) may experience varying degrees of covariate shift across domains, we propose to deploy a different number of prototypes $N^{(I)}$ and $N^{(z)}$ for the RGB image and sparse depth modalities, respectively. Based on the observation that RGB images undergo a larger covariate shift than sparse depth [58], we choose $N^{(I)} > N^{(z)}$ to capture their prototypical features; this choice reduces the parameter overhead. + +The proposed prototype-based continual learning mechanism operates on the latent feature space and does not depend on the specific architecture of the model. This architecture-agnostic flexibility stems from the fact that our queries $Q \in \mathbb{R}^{(h \times w) \times c}$ mirror the general structure of latent features across commonly used model architectures, where $h \times w$ can be replaced by the number of tokens $n$ in the + +case of transformers [86]. Thus, it can be applied generically to models with latent feature representations [37, 103], providing a general framework for mitigating catastrophic forgetting across various tasks and modalities. + +# 4.3. Prototype Set Selection + +As the prototypes are learned for a specific domain, we cannot easily select the appropriate prototype set for inference if the test-time domain identity is withheld, i.e., in the domain-agnostic setting. To address this challenging scenario, we introduce a prototype set selection mechanism that chooses the most relevant prototype set for a given input. + +During training, we introduce a domain descriptor $r_k \in \mathbb{R}^c$ for each dataset $\mathcal{D}_k$ , which adds negligible overhead in terms of number of parameters. For an input from $\mathcal{D}_k$ , we obtain a sample descriptor $s_k \in \mathbb{R}^c$ by applying global average pooling (GAP) to the bottleneck latent features (with channel dimension $c$ ) before applying the prototype set. Importantly, since both encoders are always frozen during continual training, $s_k$ is a deterministic mapping of the input. + +For each new dataset $\mathcal{D}_k$ , we deploy a new domain descriptor $r_k$ and freeze all existing learned domain descriptors. The deployed domain descriptor $r_k$ is trained by minimizing cosine distance between itself and sample descriptors $s_k$ for $\mathcal{D}_k$ , while maximizing the cosine distance to all other learned domain descriptors $\{r_{j \neq k}\}$ . This naturally yields domain descriptors that are discriminative across datasets, allowing us to use the projection of sample descriptors onto domain descriptors as a prototype set selection mechanism. + +
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned499.598162.188467.472208.6931620.4293072.1294.0406.144914.2232993.2281.9554.503
EWC [36]555.925190.152540.109247.9431796.3003346.0574.4906.685962.9373209.7591.9624.739
LwF [42]631.119221.535524.976233.7581973.9723612.7004.5336.648985.9953236.2442.0624.722
Replay [69]17.2414.05016.6625.478524.1141875.8971.3333.359618.6682366.5771.2923.348
ProtoDepth-A2.4272.8632.0792.153458.5201832.6901.1333.213548.2402294.3991.0803.159
ProtoDepth0.0000.0000.0000.000445.4191804.1581.1063.169531.6892262.9431.0433.110
FusionNetFinetuned11.3368.43517.44717.991437.7301785.2121.1933.724501.3622138.4221.1113.978
EWC [36]21.00610.49420.43116.535431.4401760.4601.1443.181486.1702117.0301.0292.986
LwF [42]12.3685.20213.59313.117442.8781759.2021.1783.352526.5282168.9611.1563.451
Replay [69]8.29011.1342.7697.975419.0441774.3611.0443.032479.1682122.9970.9662.906
ProtoDepth-A2.2002.2822.6027.203404.9561702.9451.0413.028464.9762052.4130.9522.864
ProtoDepth0.0000.0000.0000.000400.8881683.2021.0222.899461.0432048.9420.9322.792
KBNetFinetuned27.15318.20852.96933.370469.6581943.2591.3383.683541.3832411.1691.1443.505
EWC [36]23.5178.58330.07718.991456.8281806.7611.2213.321526.3662210.4241.1333.158
LwF [42]21.1844.04943.50019.951460.0971749.7341.3623.555541.9322142.9991.3593.731
Replay [69]25.42329.3036.3627.274454.8961935.6671.1023.203525.6962318.3631.0943.246
ProtoDepth-A4.5133.1002.9601.878409.9031730.7201.0453.044478.7902138.3471.0083.066
ProtoDepth0.0000.0000.0000.000401.0751710.0741.0292.993471.4372125.9570.9963.015
+ +Table 2. Quantitative results on outdoor datasets. Models are initially trained on KITTI and continually trained on Waymo, then VKITTI. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]. + +To this end, we propose to minimize an additional objective: + +$$ +\ell_ {d r} = 1 - \left(\frac {s _ {k}}{\| s _ {k} \|} \cdot \frac {r _ {k}}{\| r _ {k} \|}\right) + \frac {1}{w _ {j k}} \sum_ {j \neq k} \left(\frac {r _ {j}}{\| r _ {j} \|} \cdot \frac {r _ {k}}{\| r _ {k} \|}\right), \tag {9} +$$ + +where $||\cdot||$ denotes the $L2$ -norm and $w_{jk} \propto |j \neq k|$ is a tunable normalization constant. As the previously learned domain descriptors are frozen, their alignment to their respective datasets or domains is preserved, allowing us to continually learn new domain descriptors that can distinguish new datasets. Eq. (9) is incorporated into Eq. (1) as an additional term weighted by $w_{dr}$ to yield a novel loss function for training of unsupervised continual depth completion models in the agnostic setting: + +$$ +\mathcal {L} = w _ {p h} \ell_ {p h} + w _ {s z} \ell_ {s z} + w _ {s m} \ell_ {s m} + w _ {d r} \ell_ {d r}. \tag {10} +$$ + +At test-time, we compute the sample descriptor $s$ for an input without dataset identity and select the domain descriptor $r_{k^*}$ that maximizes cosine similarity with $s$ : + +$$ +k ^ {*} = \arg \max _ {k} \left(\frac {s}{\| s \|} \cdot \frac {r _ {k}}{\| r _ {k} \|}\right). \tag {11} +$$ + +For each latent space layer, we use the prototype set corresponding to the selected domain descriptor. While this does not eliminate forgetting due to the evolving set of domain descriptors and possible overlap between domains, it does minimize forgetting as each prototype set is learned independently for each dataset, but can still be selectively used for inference without knowing the test-time dataset identity. The trade-off is shown in Tabs. 1 and 2 (ProtoDepth-A) where we incur forgetting in exchange for the flexibility to support both the incremental and agnostic settings. + +# 5. Experiments + +Datasets. Indoor dataset sequence: NYUv2 [77] contains household, office, and commercial scenes captured with a Microsoft Kinect; ScanNet [12] is a diverse, large-scale dataset captured using a Structure Sensor; Void [97] contains laboratory, classroom, and garden scenes captured using XIVO. Outdoor dataset sequence: KITTI [84] is a daytime autonomous driving benchmark captured using a Velodyne LiDAR sensor; Waymo [81] contains road scenes with a wide variety of driving conditions; VKITTI [20] is a synthetic dataset that replicates and augments KITTI scenes. + +Models. We evaluate using three recent unsupervised depth completion models in the continual learning setting: VOICES [97], FusionNet [98], and KBNet [95]. + +Baseline Methods. We compare ProtoDepth against EWC [36], LwF [42], and Experience Replay ("Re-play") [69] as milestone works of their respective class of continual learning approaches. We include full finetuning ("Finetuned") as a baseline of performance with no continual learning strategy. All baseline methods achieve identical performance in the incremental and agnostic settings. + +Evaluation Metrics are computed across four standard depth completion metrics (MAE, RMSE, iMAE, iRMSE). We define the following evaluation metrics in terms of $a_{j}^{k}$ , denoting any one of the four depth completion metrics on dataset $\mathcal{D}_j$ after training on $\mathcal{D}_k$ . Given $T$ total datasets: + +Average Forgetting $(\bar{F})$ is the scale-invariant mean of how much performance on previous datasets $\mathcal{D}_{j < k}$ deteriorates (i.e., increases in $\%$ ) after training on each new $\mathcal{D}_k$ : + +![](images/9acda1ef2bb737c62ecc7bdaad76910468cc71920fa5f4f0f962bf45ac5e085a.jpg) + +![](images/f8ff5728ed6306d29ae74641b42862c137625b3049fb30d92190f4b85a24b4c1.jpg) + +![](images/6c67b92dc2e21fc0977676d72adaae3b5a6310dac2076d9da40db1ff016d2556.jpg) + +![](images/cb033faad52b899f869f917bbf1e2f601d33f3c6df2ef8b2d515ead3a3ab9123.jpg) +(b) + +![](images/60fff9d3172d60991c1654339b5a831cabd007fd2b7443b4028567a962b3697b.jpg) +Figure 3. Qualitative comparison of ProtoDepth and baseline methods using VOICESED on KITTI after continual training on Waymo. (a) Input sample from KITTI, (b) Baseline methods exhibit significant forgetting, particularly for small-surface-area objects (e.g., street signs and lamp posts) where sparse depth is limited, and photometric priors from KITTI are critical. In contrast, ProtoDepth produces high-fidelity depth predictions, effectively mitigating forgetting despite the large domain gap between KITTI and Waymo. + +$$ +\bar {F} = \frac {2}{T (T - 1)} \sum_ {k = 1} ^ {T} \sum_ {j < k} \frac {a _ {j} ^ {k} - a _ {j} ^ {j}}{a _ {j} ^ {j}}. \tag {12} +$$ + +Average Performance $(\bar{\mu})$ is the mean of performance on all seen datasets $\mathcal{D}_{j\leq k}$ after training on each new $\mathcal{D}_k$ : + +$$ +\bar {\mu} = \frac {2}{T (T + 1)} \sum_ {k = 1} ^ {T} \sum_ {j \leq k} a _ {j} ^ {k}. \tag {13} +$$ + +Stability-Plasticity Trade-off (SPTO) captures the balance between retaining learned knowledge (stability) and adapting to new domains (plasticity) as a harmonic mean: + +$$ +\mathrm {S P T O} = \frac {2 \times S \times P}{S + P}, \left\{ \begin{array}{l} S = \sum_ {k = 1} ^ {T} a _ {k} ^ {T} \\ P = \sum_ {k = 1} ^ {T} a _ {k} ^ {k}, \end{array} \right. \tag {14} +$$ + +where $S$ is performance across all datasets after completing training on the dataset sequence, and $P$ is performance on each new dataset after training on it for the first time. + +# 5.1. Main Results + +We compare our method, evaluated in both the incremental (ProtoDepth) and agnostic (ProtoDepth-A) settings, against baseline methods for the indoor dataset sequence in Tab. 1 and for the outdoor dataset sequence in Tab. 2. + +Results in Incremental Setting. In both indoor and outdoor settings, ProtoDepth achieves a $100\%$ improvement in Average Forgetting compared to all baseline methods across all models and metrics. This is, of course, because ProtoDepth exhibits zero forgetting as it freezes all model parameters and learns dataset-specific prototypes. For the indoor sequence, compared to the best baseline method, ProtoDepth improves Average Performance by $5.15\%$ and SPTO by $6.59\%$ , averaged across all models and metrics. + +Similarly, for the outdoor sequence, we improve Average Performance by $6.88\%$ and SPTO by $6.94\%$ . + +To demonstrate the reduced forgetting achieved by ProtoDepth, we qualitatively compare against all baseline methods using VOICESED on KITTI after continual training on Waymo (see Fig. 3). ProtoDepth yields better depth predictions for small-surface-area objects with limited sparse depth measurements for which the model must rely on photometric priors learned from images. Unlike KITTI, which consists exclusively of daytime scenes, Waymo includes many evening and overcast scenes, introducing variations in lighting and pixel intensities. Additionally, Waymo was captured using a higher-resolution camera which causes objects to appear bigger in terms of number of pixels occupied. Due to this large distributional shift, the model forgets the projected shapes of objects in KITTI after training on Waymo, even if the objects exist in both datasets. This forgetting is apparent in the highlighted street sign and lamp posts, where baseline methods struggle to accurately predict depth. + +Results in Agnostic Setting. For the indoor sequence, compared to the best baseline method, ProtoDepth-A improves Average Forgetting by $52.22\%$ , Average Performance by $4.26\%$ , and SPTO by $5.40\%$ , averaged across all models and metrics. Notably, ProtoDepth-A outperforms ProtoDepth in some metrics, meaning the model appropriately selects prototypes of different domains when there is domain overlap, thereby enhancing its generalization capabilities. + +For the outdoor sequence, ProtoDepth-A shows an average improvement of $53.21\%$ in Average Forgetting across all models and metrics. In contrast to the indoor sequence, ProtoDepth-A does not outperform ProtoDepth in any metric, likely due to the larger domain gaps between the outdoor datasets. Selecting prototypes from a different outdoor dataset is more likely to be erroneous, leading to performance degradation rather than generalization. + +
MethodN(I)N(z)# ParamsScanNetVOID
MAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
Pretrained--0M (0%)4114.044626.00390.78447.3142.94106.3929.2664.04
ProtoDepth110.24M (3.5%)19.68±0.6860.10±0.7110.44±0.4827.86±0.7437.81±0.5293.72±0.9022.82±0.2752.58±0.32
550.25M (3.6%)16.49±0.1557.51±0.196.84±0.0322.07±0.0334.02±0.2587.72±0.4317.92±0.1443.95±0.28
1050.25M (3.6%)14.59±0.1742.20±0.095.57±0.1417.10±0.1533.63±0.2387.30±0.5717.55±0.3243.24±0.63
10100.25M (3.7%)15.25±0.3943.31±0.725.85±0.2217.57±0.3834.39±0.8288.73±1.8318.49±0.8545.23±1.60
1001000.38M (5.5%)16.35±0.3747.61±0.165.90±0.1720.11±0.1934.29±0.5888.22±0.8618.16±0.6244.51±1.07
+ +Table 3. Sensitivity study of prototype set sizes $(N^{(I)}$ and $N^{(z)}$ ) on ProtoDepth using KBNet for indoor datasets (ScanNet and VOID). KBNet is pretrained on the initial dataset (NYUv2). Parameter overhead is reported as a percentage of the full KBNet model's parameters. + +
ScanNetWaymo
Ablated ComponentMAERMSEMAERMSE
global prototypes18.1258.91505.011715.21
projection matrix W17.5957.61495.051690.51
decoupled K and P16.3645.10491.591675.57
no ablations14.5942.20486.951664.18
+ +Table 4. Ablation studies using KBNet for indoor and outdoor. + +Furthermore, we refer back to Fig. 3 (ProtoDepth-A) for head-to-head comparison of our method against other baselines in the agnostic setting. The error maps for Finetuned, EWC, and LwF display significant errors, indicating substantial forgetting of previously learned information. While Replay yields an improved error map, it still experiences forgetting in small-surface-area objects. For example, Replay fails to reconstruct the upper portions of the highlighted street sign and lamp posts due to forgetting of learned photometric priors from KITTI, whereas ProtoDepth-A recalls them from KITTI prototypes. Additionally, ProtoDepth-A predicts the depth of the highlighted small fence poles with higher fidelity than the incoherent prediction of Replay. + +# 5.2. Design Choice Studies + +Prototype Set Sizes. We investigate the impact of varying the prototype set sizes (i.e., number of prototypes) for the image and sparse depth layers (denoted as $N^{(I)}$ and $N^{(z)}$ , respectively) on the performance of our method. The set size experiments for the indoor sequence are shown in Tab. 3, based on which we selected $N^{(I)} = 10$ , $N^{(z)} = 5$ for the main experiments. Smaller set sizes perform worse as there is insufficient capacity to capture the diversity of features in each dataset. There is also performance degradation with larger set sizes; intuitively, unnecessary additional parameters may learn noise and cause overfitting. Notably, best performance is achieved when $N^{(I)} > N^{(z)}$ , which can be attributed to the larger distributional shift between scenes in the image modality compared to the sparse depth modality [58]. Since the bottleneck layer fuses both modalities, + +we use $N^{(I)}$ for the bottleneck layer prototypes. As a lower bound, we show that the frozen base model pretrained on NYUv2 ("Pretrained") performs poorly, motivating the need for continual learning. We perform similar set size experiments for the outdoor dataset sequence (see Supp. Mat.), based on which we choose $N^{(I)} = 25$ , $N^{(z)} = 10$ . + +Ablations. We assess the impact of the components of ProtoDepth on both indoor (ScanNet) and outdoor (Waymo) in Tab. 4. Removing the $1 \times 1$ depthwise convolutions results in performance degradation, demonstrating their effectiveness as lightweight global prototypes. Learning the keys $K$ independently from the prototypes $P$ without the projection matrix $W$ hurts performance, suggesting that the projection matrix effectively learns to map the prototypes into latent feature space, fulfilling the intended role of keys. Furthermore, performance decreases without the stop gradient operation on $P$ when computing $K$ , indicating the importance of decoupled optimization of keys and prototypes. + +# 6. Discussion + +ProtoDepth leverages prototypes as a mechanism for mitigating catastrophic forgetting. While we demonstrate it on unsupervised depth completion, ProtoDepth does not assume specific modalities and thus can be relevant to other multimodal problems [67, 104, 108, 111]. Our promising results on both indoor and outdoor domains illustrate the potential for ProtoDepth to enable unsupervised continual learning for multimodal 3D reconstruction. Our architecture-agnostic approach can also be extended to other tasks involving models that produce latent feature representations [37, 112], offering a general framework for continual learning. + +Limitations. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9296-9305, 2022. 2 \ No newline at end of file diff --git a/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/images.zip b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2325aa6d09728fad1e12e4223837324008269b8a --- /dev/null +++ b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2ad23901cbdf02369e4b814470053651a8b6dda8bd98c7c0ea1c2734691447ab +size 791401 diff --git a/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/layout.json b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..522c535c7a0bd77bda6f629d4e6f6c7ebf887868 --- /dev/null +++ b/2025/ProtoDepth_ Unsupervised Continual Depth Completion with Prototypes/layout.json @@ -0,0 +1,12114 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 80, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 80, + 103, + 531, + 121 + ], + "type": "text", + "content": "ProtoDepth: Unsupervised Continual Depth Completion with Prototypes" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 143, + 539, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 143, + 539, + 179 + ], + "spans": [ + { + "bbox": [ + 67, + 143, + 539, + 179 + ], + "type": "text", + "content": "Patrick Rim Hyoungseob Park S. Gangopadhyay Ziyao Zeng Younjoon Chung Alex Wong Yale Vision Lab" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 207, + 201, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 207, + 201, + 220 + ], + "spans": [ + { + "bbox": [ + 151, + 207, + 201, + 220 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "spans": [ + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "text", + "content": "We present ProtoDepth, a novel prototype-based approach for continual learning of unsupervised depth completion, the multimodal 3D reconstruction task of predicting dense depth maps from RGB images and sparse point clouds. The unsupervised learning paradigm is well-suited for continual learning, as ground truth is not needed. However, when training on new non-stationary distributions, depth completion models will catastrophically forget previously learned information. We address forgetting by learning prototype sets that adapt the latent features of a frozen pretrained model to new domains. Since the original weights are not modified, ProtoDepth does not forget when test-time domain identity is known. To extend ProtoDepth to the challenging setting where the test-time domain identity is withheld, we propose to learn domain descriptors that enable the model to select the appropriate prototype set for inference. We evaluate ProtoDepth on benchmark dataset sequences, where we reduce forgetting compared to baselines by " + }, + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "inline_equation", + "content": "52.2\\%" + }, + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "text", + "content": " for indoor and " + }, + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "inline_equation", + "content": "53.2\\%" + }, + { + "bbox": [ + 54, + 232, + 297, + 473 + ], + "type": "text", + "content": " for outdoor to achieve the state of the art. Project Page: https://protodepth.github.io/." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 135, + 502 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 510, + 297, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 297, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 297, + 665 + ], + "type": "text", + "content": "Reconstructing three-dimensional (3D) environments facilitates spatial applications such as autonomous navigation, robotic manipulation, and AR/VR. These applications typically utilize platforms equipped with heterogeneous sensors, such as cameras and sparse range sensors (e.g., LiDAR, ToF) which yield RGB images and point clouds. To reconstruct 3D scenes from an ego-centric point of view in the form of depth maps, the point clouds are typically projected onto the image plane. However, their projections tend to be sparse, which is unlike RGB images that comprise irradiance measured at each pixel. These complementary modalities can be used to predict dense depth maps; this multimodal 3D reconstruction task is called depth completion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Depth completion models can be trained in a supervised (using ground truth) or unsupervised (using Structure-from-Motion) manner. As ground truth is prohibitively expensive to acquire, we subscribe to the unsupervised learning" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 209, + 549, + 321 + ], + "blocks": [ + { + "bbox": [ + 321, + 209, + 549, + 321 + ], + "lines": [ + { + "bbox": [ + 321, + 209, + 549, + 321 + ], + "spans": [ + { + "bbox": [ + 321, + 209, + 549, + 321 + ], + "type": "image", + "image_path": "8d3992e7a6e62904b1febe2810704257ea19d212ab7fe07854755378b2c6432e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "lines": [ + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "type": "text", + "content": "Figure 1. Results on KITTI validation set during continual training on outdoor dataset sequence (KITTI " + }, + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "type": "text", + "content": " Waymo " + }, + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 327, + 555, + 350 + ], + "type": "text", + "content": " VKITTI)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 366, + 556, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 556, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 556, + 498 + ], + "type": "text", + "content": "paradigm, which enables one to learn without human intervention. While this suggests the potential to continuously learn, existing models are trained and evaluated on single datasets under the assumption of a stationary data distribution. However, sequences of multiple datasets exhibit non-stationary distributions and are captured by sensors with varying calibrations. Hence, fitting to new data samples inevitably causes the model to \"catastrophically forget\" [19, 54, 63, 82] previously learned information, where the model performance degrades significantly on data from distributions that it had already observed." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 498, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 557, + 714 + ], + "type": "text", + "content": "To enable pretrained models to adapt to new environments or domains in an unsupervised manner, we consider continual learning, where training strategies aim to mitigate catastrophic forgetting of previously observed training distributions when learning from a continuous stream of non-stationary data. One school of thought is to constrain updates to parameters deemed \"important\" for previous domains based on a regularization term controlled by a weight chosen as a hyperparameter. Another is to incur memory costs by storing previously observed training data and incorporating them during learning of new domains, akin to rehearsals. The trade-off is in the sensitivity of optimization (and forgetting) to the choice of hyperparameter and in the size of storage and data privacy. Both schools perform updates to the full set of model parameters, which is computationally expensive. Unlike them, we opt to freeze the pretrained model to ensure zero forgetting and learn a small set of parameters, which we term \"prototypes,\" that modulate" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6304" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 269, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 269, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 269, + 83 + ], + "type": "text", + "content": "the latent features for each new domain encountered." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 84, + 294, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 84, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 54, + 84, + 294, + 215 + ], + "type": "text", + "content": "We model the change in distribution as a domain-specific bias to be learned by global multiplicative and local additive prototypes that transform the latent features to fit the new distribution. In the same vein are learnable prompts or tokens [92] used in continual learning for vision transformers, where the model itself is similarly frozen. Yet, there is no natural scale at which to discretize images, unlike discrete text tokens. In contrast, our proposed prototypes lift the requirements of tokenized inputs and can thus be applied to convolutional neural networks, which are prevalently used in unsupervised depth completion, as well as transformers." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 217, + 297, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 217, + 297, + 407 + ], + "spans": [ + { + "bbox": [ + 56, + 217, + 297, + 407 + ], + "type": "text", + "content": "To this end, we propose ProtoDepth, a novel prototype-based method for unsupervised continual depth completion. Instead of prompts in input space, we deploy lightweight prototypes to a frozen pretrained model to encode prototypical information of each domain. These prototypes model global and local biases, where global prototypes learn a transformation from the latent pretrained data distribution to that of the new domain, and local prototypes capture fine-grained features that can be selectively queried depending on the input. Naturally, when the test-time domain identity is known, i.e., domain-incremental, ProtoDepth exhibits no forgetting and learns the new data distribution with high fidelity. We further encode each domain as a descriptor to enable inference when test-time domain identity is withheld, i.e., domain-agnostic, where the prototype set corresponding to the highest affinity domain descriptor for a given sample is chosen." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 407, + 296, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 296, + 551 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 296, + 551 + ], + "type": "text", + "content": "Our contributions: We propose (1) a novel prototype-based paradigm for unsupervised continual depth completion that incurs no forgetting in the domain-incremental setting, and (2) a prototype set selection mechanism that extends the prototype paradigm to domain-agnostic settings with minimal forgetting. This is facilitated by (3) a novel training objective that learns descriptors for each domain, which can be used to determine the prototype set suitable for inference without knowledge of domain identity. (4) Our method, ProtoDepth, reduces forgetting over baselines by over " + }, + { + "bbox": [ + 55, + 407, + 296, + 551 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 407, + 296, + 551 + ], + "type": "text", + "content": " across six datasets; to the best of our knowledge, this is the first unsupervised continual depth completion method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 562, + 142, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 142, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 142, + 574 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 582, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 629 + ], + "type": "text", + "content": "Continual learning is the process of incrementally adapting the weights of a parameterized model to perform new tasks involving non-stationary distributions, while preserving information learned from previous tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "content": "Regularization-based methods aim to mitigate forgetting by restricting the plasticity of model parameters that are important for previously learned tasks. [1, 7, 36, 113] introduce regularization terms to the loss function to identify and penalize changes to important weights while new tasks are learned. [14, 15, 28, 39, 42, 68, 114] attempt to preserve output behavior on previous tasks using knowledge" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "distillation [26, 70]. [55, 57, 61, 83] regularize the space of learned functions to encourage similarity between outputs of task-specific heads. However, while they perform well in simpler continual learning settings, regularization-based methods can struggle with more challenging tasks [52] and larger domain shifts between datasets [64, 101]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 146, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 146, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 146, + 555, + 361 + ], + "type": "text", + "content": "Rehearsal-based methods use a memory buffer to store a limited amount of data from previous tasks, allowing the model to periodically re-train on this data during continual learning. [7, 25, 69] introduce the strategy of retaining a subset of previous \"experiences\" (i.e., data) to \"replay\" (i.e., re-train on) while learning new tasks. [8, 31, 49, 64, 65, 87] employ various sampling strategies, [29, 47, 117] reduce memory by storing latent features rather than inputs, and generative replay methods [3, 24, 33, 56, 59, 66, 71, 74, 102] create synthetic rehearsal data from previous task domains. Some recent works utilize techniques such as self-supervision [6, 60] and knowledge distillation [4, 9, 64, 101]. [10] introduces a rehearsal-based continual single image-based depth estimation method, the first such work for a 3D vision task. Rehearsal-based methods can reduce forgetting but are unsuitable when data storage is limited by memory or privacy constraints [76]. Additionally, their performance degrades significantly as memory buffer size shrinks [6]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 364, + 556, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 556, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 556, + 555 + ], + "type": "text", + "content": "Architecture-based methods [32, 34, 41, 48, 53, 62, 72, 73, 89, 110, 116] allocate task-specific parameters or subnetworks, aiming to enable learning of new tasks while minimizing changes to parameters assigned to previous tasks. Most of these methods require task identity to be known at test-time, which prevents their use in the more realistic domain-agnostic setting where new data is not restricted to a certain domain. Other methods [16, 90] rely on a rehearsal buffer in addition to task-specific parameters. Furthermore, architecture-based methods often introduce a significant number of additional parameters for each task [60, 100, 105], which can even exceed the parameter count of the original model [32, 89]. In contrast, our method can be used for inference without task identity, does not require a rehearsal buffer, and only introduces a very small number of additional parameters (<5% of original model) per task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "type": "text", + "content": "Prompt-based methods introduce learnable prompts that encode task-specific information. [92] learns a pool of tokens, from which a set is selected using a query mechanism and prepended to the input. [91] refines this by using both task-specific and shared prompts. Subsequent approaches replace prompt selection with an attention mechanism [79] or with intermediate embeddings [35]. However, these prompt-based methods are designed for 2D classification tasks that use vision transformers (ViTs), borrowing the concept of prompting from the field of natural language processing (NLP). The idea of prepending prompts to tokenized inputs does not naturally extend to convolutional neural networks (CNNs), limiting their applicability to 3D vision tasks where" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6305" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": "CNNs are primarily used. In contrast, our method learns prototypes, which serve as representative features, offering a more intuitive mechanism for adding a lightweight selective bias than prepending abstract prompts in image space. Unlike prompt-based methods, our method is fully architecture-agnostic and can be applied to any model that has a latent space without modifying the underlying architecture." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 157, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 157, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 157, + 296, + 251 + ], + "type": "text", + "content": "Prototypes have predominantly been explored in the context of few-shot learning of 2D tasks [22, 23, 44, 45, 80, 107] and representation learning [5, 11, 40]. For continual learning, prototypes have been deployed for supervised classification tasks as discriminative class representations [2, 13, 27, 43, 93, 115]. In contrast, we leverage prototypes as a mechanism for encoding domain-specific information to facilitate continual learning for unsupervised reconstruction." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 252, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 252, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 56, + 252, + 296, + 491 + ], + "type": "text", + "content": "Unsupervised depth completion is a multimodal, 3D reconstruction problem of predicting a depth map from an image and its associated sparse point cloud. In lieu of training signals from ground-truth depth annotations, unsupervised depth completion methods [17, 18, 30, 38, 46, 51, 75, 78, 94, 96-99, 106, 109] minimize the reconstruction error of the sparse depth, the reprojection error of the image from temporally adjacent views, and a local smoothness regularizer. Some works [50, 85, 109] utilize synthetic data to learn priors, while other works [97, 98] densify then refine the sparse point cloud by constructing a coarse piecewise scaffolding. [95] uses backprojection layers to map image features to the 3D scene using camera calibration. These methods are prone to catastrophic forgetting in continual learning settings since they must update their learned model weights to fit to new data, causing performance degradation on previously seen data domains. In contrast, our method freezes the entire model and learns a lightweight selective bias for each dataset, allowing it to adapt effectively to new data domains while mitigating forgetting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "content": "UnCLe [21] proposes a benchmark and adapts existing methods [36, 42, 69] for unsupervised continual depth completion. To the best of our knowledge, we propose the first continual learning method for unsupervised depth completion and are the first to explore prototypes in this context." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 563, + 140, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 140, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 140, + 575 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "spans": [ + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "content": "Unsupervised Depth Completion. Assuming we are given an RGB image " + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "inline_equation", + "content": "I:\\Omega \\subset \\mathbb{R}^2\\to \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "content": " and its associated sparse depth map " + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "inline_equation", + "content": "z:\\Omega \\rightarrow \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "content": " obtained by projecting the sparse point cloud onto the image plane, we wish to train a depth completion model " + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "content": " to predict the dense depth map " + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\hat{d}" + }, + { + "bbox": [ + 55, + 583, + 296, + 691 + ], + "type": "text", + "content": " in an unsupervised manner (i.e., without access to ground-truth depth). Unsupervised depth completion models [51, 95, 97, 98] typically minimize a loss function in the form of Eq. (1), which comprises a linear combination of three terms:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 701, + 296, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 701, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 104, + 701, + 296, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m}, \\tag {1}", + "image_path": "e6525eb4cb2bab51a97374fc80069e33c4c214f1e943bbbb90a3d4853c45f332.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\ell_{ph}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " denotes photometric consistency, " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\ell_{sz}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " sparse depth consistency, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\ell_{sm}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " a local smoothness regularizer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": "Photometric Consistency term leverages image reconstruction as the training signal. Specifically, given an image " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": ", its reconstruction " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "\\hat{I}_{t\\tau}" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": " from a temporally adjacent image " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "I_{\\tau}" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "inline_equation", + "content": "\\tau \\in \\{t - 1, t + 1\\}" + }, + { + "bbox": [ + 313, + 97, + 555, + 144 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 358, + 152, + 555, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 152, + 555, + 168 + ], + "spans": [ + { + "bbox": [ + 358, + 152, + 555, + 168 + ], + "type": "interline_equation", + "content": "\\hat {I} _ {t \\tau} (x, \\hat {d}, g _ {\\tau t}) = I _ {\\tau} \\left(\\pi g _ {\\tau t} K ^ {- 1} \\bar {x} \\hat {d} (x)\\right), \\tag {2}", + "image_path": "9a17ef4bfe77a7baf1fe2163a8119bd0fe001debbdb19dac91a99d979644d5bb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\bar{x} = [x^{\\top},1]^{\\top}" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " is the homogeneous coordinates of " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "x\\in \\Omega" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " is the camera intrinsic calibration matrix, " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "g_{\\tau t}\\in" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "SE(3)" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " is the estimated relative camera pose matrix from time " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " is the canonical perspective projection matrix. Given " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " and its reconstruction " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\hat{I}_{t\\tau}" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " , the photometric consistency loss measures the " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " difference and structural similarity (SSIM [88]) between " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\hat{I}_{t\\tau}" + }, + { + "bbox": [ + 313, + 175, + 555, + 261 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 326, + 268, + 555, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 268, + 555, + 298 + ], + "spans": [ + { + "bbox": [ + 326, + 268, + 555, + 298 + ], + "type": "interline_equation", + "content": "\\ell_ {p h} = \\frac {1}{| \\Omega |} \\sum_ {\\tau \\in T} \\sum_ {x \\in \\Omega} w _ {c o} \\left| \\hat {I} _ {t \\tau} (x) - I (x) \\right| + \\tag {3}", + "image_path": "b2cbb3af9545df8e7bd2a36102058e592690e316119037acfe7daf4e234c9fc5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 403, + 300, + 529, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 403, + 300, + 529, + 314 + ], + "spans": [ + { + "bbox": [ + 403, + 300, + 529, + 314 + ], + "type": "interline_equation", + "content": "w _ {s t} \\big (1 - \\operatorname {S S I M} (\\hat {I} _ {t \\tau} (x), I (x)) \\big).", + "image_path": "7f8a1798fe73c863704b585f0a23f28f4f6ddaa1c8f1700723e56ebd74418eef.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": "Sparse Depth Consistency. However, photometric reconstruction recovers depth only up to an unknown scale. To ground predictions to a metric scale, we minimize an " + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": " loss between the predicted depth " + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "inline_equation", + "content": "\\hat{d}" + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": " and sparse depth " + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "inline_equation", + "content": "x\\in \\Omega" + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": " where points exist as denoted by " + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "inline_equation", + "content": "M:\\Omega \\mapsto \\{0,1\\}" + }, + { + "bbox": [ + 313, + 322, + 555, + 382 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 353, + 390, + 555, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 390, + 555, + 418 + ], + "spans": [ + { + "bbox": [ + 353, + 390, + 555, + 418 + ], + "type": "interline_equation", + "content": "\\ell_ {s z} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} | M (x) \\cdot (\\hat {d} (x) - z (x)) |. \\tag {4}", + "image_path": "60f2f17402a215adc8d906bc5d1ec30cadc732ce2c2aa2fe1f6a9e1012750d69.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": "Local Smoothness. To address ambiguities in regions where the predicted depth is not constrained by photometric or sparse depth reconstruction terms, we rely on a regularizer that enforces local smoothness in predictions by applying an " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": " penalty on the depth gradients in both the " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": "-direction " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "(\\partial_{X})" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": "-direction " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "(\\partial_{Y})" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": ". To allow for depth discontinuities along object boundaries, these penalties are weighted by their corresponding image gradients, " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "\\lambda_{X} = e^{-|\\partial_{X}I_{t}(x)|}" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "inline_equation", + "content": "\\lambda_{Y} = e^{-|\\partial_{Y}I_{t}(x)|}" + }, + { + "bbox": [ + 313, + 427, + 555, + 548 + ], + "type": "text", + "content": ". Larger image gradients result in smaller weights, allowing for sharp transitions in depth along edges:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 324, + 555, + 555, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 555, + 555, + 583 + ], + "spans": [ + { + "bbox": [ + 324, + 555, + 555, + 583 + ], + "type": "interline_equation", + "content": "\\ell_ {s m} = \\frac {1}{| \\Omega |} \\sum_ {x \\in \\Omega} \\lambda_ {X} (x) \\left| \\partial_ {X} \\hat {d} (x) \\right| + \\lambda_ {Y} (x) \\left| \\partial_ {Y} \\hat {d} (x) \\right|. \\tag {5}", + "image_path": "5219601ed9064fc6947420cf4ddec042d9bae980350afbdea5038f456c55245e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": "Unsupervised Continual Depth Completion. For continual learning, we consider a task sequence of domains " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1,\\mathcal{D}_2,\\dots ,\\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": ". Starting with a depth completion model " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": " pretrained on the initial dataset " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": ", we aim to incrementally adapt " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": " to each subsequent dataset " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_2,\\dots ,\\mathcal{D}_k,\\dots ,\\mathcal{D}_T" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": ". The key challenge is to learn the data distribution of each new dataset " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": " without \"forgetting,\" as measured by performance degradation on previously learned datasets " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{j < k}" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": ". We denote each dataset as " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k = \\{(I_k^{(i)},z_k^{(i)},K_k^{(i)})\\}_{i = 1}^{n_k}" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": ", which comprises " + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "inline_equation", + "content": "n_k" + }, + { + "bbox": [ + 313, + 591, + 556, + 715 + ], + "type": "text", + "content": " training samples of image, sparse depth, and" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6306" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 74, + 260, + 223 + ], + "blocks": [ + { + "bbox": [ + 72, + 74, + 260, + 223 + ], + "lines": [ + { + "bbox": [ + 72, + 74, + 260, + 223 + ], + "spans": [ + { + "bbox": [ + 72, + 74, + 260, + 223 + ], + "type": "image", + "image_path": "f7bda9c664577cb155d046f3118a9e9542f026dd5864cddb754ed73b6c0e2f15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "lines": [ + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": "Figure 2. Overview of ProtoDepth. (a) In the agnostic setting, a prototype set is selected by maximizing the cosine similarity between an input sample descriptor and the learned domain descriptors. In the incremental setting, the domain identity is known. (b) At inference, the similarity between the frozen queries and the keys of the selected prototype set determines how the learned prototypes contribute as local (additive) biases to the latent features. Additionally, a global (multiplicative) bias is applied using a " + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 54, + 228, + 555, + 275 + ], + "type": "text", + "content": " depthwise convolution." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 268, + 74, + 539, + 222 + ], + "blocks": [ + { + "bbox": [ + 268, + 74, + 539, + 222 + ], + "lines": [ + { + "bbox": [ + 268, + 74, + 539, + 222 + ], + "spans": [ + { + "bbox": [ + 268, + 74, + 539, + 222 + ], + "type": "image", + "image_path": "aa81f6dc0df6fad71f74b3474a61e8929fe516e7dbb3f7f1d25d08d0f8292470.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 285, + 298, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 285, + 298, + 346 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 298, + 346 + ], + "type": "text", + "content": "calibration, with no ground-truth depth. We assume that the relative camera pose " + }, + { + "bbox": [ + 54, + 285, + 298, + 346 + ], + "type": "inline_equation", + "content": "g_{t\\tau}" + }, + { + "bbox": [ + 54, + 285, + 298, + 346 + ], + "type": "text", + "content": " is given, or is estimated; if estimated by a pose network, we allow it to forget as we focus on continual learning for depth completion, and not pose estimation, which is outside the focus of this work." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 354, + 112, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 112, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 112, + 367 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 374, + 296, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 374, + 296, + 531 + ], + "spans": [ + { + "bbox": [ + 54, + 374, + 296, + 531 + ], + "type": "text", + "content": "We present ProtoDepth, a novel approach for unsupervised continual depth completion that mitigates catastrophic forgetting by leveraging prototype sets as selective biases. Given a pretrained depth completion model " + }, + { + "bbox": [ + 54, + 374, + 296, + 531 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 54, + 374, + 296, + 531 + ], + "type": "text", + "content": ", which we freeze to prevent any forgetting, we adapt it to new datasets by deploying lightweight, domain-specific prototype sets that learn to selectively bias the latent features; note that this only adds minimal additional parameters per dataset or domain. Our method is applicable to the domain-incremental (\"incremental\") setting, where dataset identity is known at test-time, and the more challenging domain-agnostic (\"agnostic\") setting, where the test-time domain identity is unknown, through a proposed prototype set selection mechanism (see Sec. 4.3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 536, + 170, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 170, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 170, + 550 + ], + "type": "text", + "content": "4.1. Prototype Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "spans": [ + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": "To enable the model to adapt to new datasets without forgetting, we learn layer-specific prototype sets for each dataset that serve as multiplicative (global) and additive (local) biases in the latent feature space. For simplicity, we consider an input sample from a single dataset " + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": " at a single layer " + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": ", which is encoded into the latent features " + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": ". We assume a linear transformation from the learned latent space of " + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": " to that of " + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 54, + 554, + 297, + 651 + ], + "type": "text", + "content": "; hence, we formulate the adaptation as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 137, + 656, + 296, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 656, + 296, + 670 + ], + "spans": [ + { + "bbox": [ + 137, + 656, + 296, + 670 + ], + "type": "interline_equation", + "content": "\\hat {X} = A \\odot X + B, \\tag {6}", + "image_path": "2352c67b3aaa6a7c028fe69763254108a230336ef6ef14613a61c9d67b220e71.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": " denotes a (broadcasted) Hadamard product between the global prototype " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "A\\in \\mathbb{R}^c" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": " and the features " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": " is an additive bias constructed from a set of local prototypes " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": "To this end, we flatten the latent features " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{(h \\times w) \\times c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": ". Since the model " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " is frozen, " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " serves as a set of " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " deterministic queries, where each query is a " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": "-dimensional vector. We introduce " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " learnable additive prototypes " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "P = [p_1, p_2, \\dots, p_N]^\\top \\in \\mathbb{R}^{N \\times c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": "-dimensional vector representing a \"prototypical\" local feature of the dataset. To learn the keys associated with each prototype, we define a projection matrix " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " that learns to map the prototypes " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": " back into the query space, i.e., the latent feature space. This yields " + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{R}^{N \\times c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 405 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 382, + 410, + 555, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 410, + 555, + 423 + ], + "spans": [ + { + "bbox": [ + 382, + 410, + 555, + 423 + ], + "type": "interline_equation", + "content": "K = \\operatorname {S t o p G r a d} (P) \\times W. \\tag {7}", + "image_path": "74f991fe074b54021f684b4c8d3142311bb749a02685f9b2cd02cc6414d843b3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "content": "StopGrad (stop gradient) facilitates decoupled optimization, enabling prototypes to learn appropriate additive biases while keys learn to assign relevant prototypes to queries. We compute the similarity scores between the queries " + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "content": " and the keys " + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "content": " using scaled dot-product attention [86]. To obtain the additive bias " + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "inline_equation", + "content": "b \\in \\mathbb{R}^{(h \\times w) \\times c}" + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "content": ", the scores are used to compute a convex combination of prototypes " + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 427, + 556, + 513 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 362, + 515, + 555, + 530 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 515, + 555, + 530 + ], + "spans": [ + { + "bbox": [ + 362, + 515, + 555, + 530 + ], + "type": "interline_equation", + "content": "b = \\operatorname {s o f t m a x} \\left(Q \\times K ^ {\\top} / \\sqrt {c}\\right) \\times P. \\tag {8}", + "image_path": "9b76b1f36ee9f488149bdebe290232afc5311fb60657a5bfe09e78b0d616ef4a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": "We reshape " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " back to the spatial dimensions of " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " to obtain the local additive bias " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ". To model the global transformation, we learn a " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": "-dimensional multiplicative prototype " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ", applied element-wise as " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "A \\odot X" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ", which can be efficiently implemented as a " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " depthwise convolution. The result is further adapted to the new dataset distribution, still without altering the original model parameters, by incorporating the local domain-specific transformation " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " as an additive bias, i.e., " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "\\hat{X} = A \\odot X + B" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " is frozen and a new prototype set (local and global prototypes " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "P_{k}" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "A_{k}" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ", and projection matrix " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "W_{k}" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ") is learned for each dataset " + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 534, + 557, + 714 + ], + "type": "text", + "content": ", this naturally facilitates continual learning and ensures no forgetting in the incremental setting, where the prototype set corresponding to the domain identity is selected. We further extend this to the agnostic setting in Sec. 4.3." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6307" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 553, + 319 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 319 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 319 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 319 + ], + "type": "table", + "html": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned8.8286.1316.9517.04263.352125.2815.46135.05352.453108.43415.36035.357
EWC [36]9.4398.0145.1836.17463.787126.70615.22934.36753.614110.95615.09134.039
LwF [42]8.5918.4569.61321.77465.135126.96816.22138.00253.517108.84515.40234.729
Replay [69]6.1544.6889.47111.71364.305126.71416.37336.72954.326112.21816.64037.671
ProtoDepth-A2.4393.5984.6304.51956.971118.13213.55430.55447.367103.01513.51731.623
ProtoDepth0.0000.0000.0000.00056.359115.15313.58930.33246.934101.32613.68431.925
FusionNetFinetuned24.9289.77532.33316.79966.523130.14215.82933.88154.252110.66615.31733.726
EWC [36]11.2568.78217.94417.84764.487130.89015.26434.20351.345109.22314.27632.781
LwF [42]6.8632.8657.3361.93961.204123.57314.07530.87950.159106.38613.87931.608
Replay [69]5.7022.86212.19611.18661.467125.58714.75033.27950.273108.60814.35133.658
ProtoDepth-A1.2820.6861.3040.44657.742119.98813.27430.13947.674104.34913.12831.058
ProtoDepth0.0000.0000.0000.00057.486119.16813.32329.93647.335102.84513.09130.474
KBNetFinetuned16.08015.4638.1889.17058.577124.60613.47431.40947.890105.80713.26631.742
EWC [36]14.91511.87810.3985.64057.414122.07513.74131.55248.031106.66114.12933.096
LwF [42]9.7176.3246.1685.25457.511119.09314.11932.16547.154103.16414.30433.838
Replay [69]7.2004.8199.2029.53956.208117.84813.98332.34146.700103.63113.84433.326
ProtoDepth-A3.2041.3044.9112.94354.254115.54813.20130.49945.264101.09713.28131.718
ProtoDepth0.0000.0000.0000.00052.497113.54812.84529.99044.09299.78813.08131.503
", + "image_path": "9e85daff7bdafc62f2218a49e2828bd905357b0899d8b1cae4d765cfa628a2cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 324, + 555, + 348 + ], + "lines": [ + { + "bbox": [ + 55, + 324, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 555, + 348 + ], + "type": "text", + "content": "Table 1. Quantitative results on indoor datasets. Models are initially trained on NYUv2 and continually trained on ScanNet, then VOID. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 361, + 195, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 195, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 195, + 374 + ], + "type": "text", + "content": "4.2. ProtoDepth Architecture" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 382, + 295, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 382, + 295, + 442 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 295, + 442 + ], + "type": "text", + "content": "Current unsupervised depth completion models [95, 97, 98] adopt an encoder-decoder CNN architecture, which consists of separate image and sparse depth encoders with skip connections to the decoder. We refer to the bottleneck and the skip connections as the latent space layers (see Fig. 2)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": "To extend the prototype mechanism (Sec. 4.1) across multiple layers, for each new dataset " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "D_{k}" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": ", we introduce a prototype set of local and global prototypes " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "P^{(l)}" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "A^{(l)}" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": ", and projection matrix " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "W^{(l)}" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": " for each layer " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": " in the latent space. For each new dataset, the latent feature adaptation (Eqs. (6) and (8)) is applied independently to each layer " + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 445, + 295, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "text", + "content": "As different modalities in multimodal tasks (e.g., RGB image and sparse depth map in depth completion) may experience varying degrees of covariate shift across domains, we propose to deploy a different number of prototypes " + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "inline_equation", + "content": "N^{(I)}" + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "inline_equation", + "content": "N^{(z)}" + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "text", + "content": " for the RGB image and sparse depth modalities, respectively. Based on the observation that RGB images undergo a larger covariate shift than sparse depth [58], we choose " + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "inline_equation", + "content": "N^{(I)} > N^{(z)}" + }, + { + "bbox": [ + 55, + 519, + 295, + 628 + ], + "type": "text", + "content": " to capture their prototypical features; this choice reduces the parameter overhead." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "content": "The proposed prototype-based continual learning mechanism operates on the latent feature space and does not depend on the specific architecture of the model. This architecture-agnostic flexibility stems from the fact that our queries " + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{(h \\times w) \\times c}" + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "content": " mirror the general structure of latent features across commonly used model architectures, where " + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "content": " can be replaced by the number of tokens " + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 630, + 295, + 715 + ], + "type": "text", + "content": " in the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 362, + 555, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 555, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 555, + 411 + ], + "type": "text", + "content": "case of transformers [86]. Thus, it can be applied generically to models with latent feature representations [37, 103], providing a general framework for mitigating catastrophic forgetting across various tasks and modalities." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 419, + 444, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 444, + 432 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 444, + 432 + ], + "type": "text", + "content": "4.3. Prototype Set Selection" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 437, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 510 + ], + "type": "text", + "content": "As the prototypes are learned for a specific domain, we cannot easily select the appropriate prototype set for inference if the test-time domain identity is withheld, i.e., in the domain-agnostic setting. To address this challenging scenario, we introduce a prototype set selection mechanism that chooses the most relevant prototype set for a given input." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": "During training, we introduce a domain descriptor " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "r_k \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": " for each dataset " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": ", which adds negligible overhead in terms of number of parameters. For an input from " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": ", we obtain a sample descriptor " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "s_k \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": " by applying global average pooling (GAP) to the bottleneck latent features (with channel dimension " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": ") before applying the prototype set. Importantly, since both encoders are always frozen during continual training, " + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 313, + 510, + 556, + 605 + ], + "type": "text", + "content": " is a deterministic mapping of the input." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": "For each new dataset " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": ", we deploy a new domain descriptor " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": " and freeze all existing learned domain descriptors. The deployed domain descriptor " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": " is trained by minimizing cosine distance between itself and sample descriptors " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": ", while maximizing the cosine distance to all other learned domain descriptors " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{r_{j \\neq k}\\}" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": ". This naturally yields domain descriptors that are discriminative across datasets, allowing us to use the projection of sample descriptors onto domain descriptors as a prototype set selection mechanism." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6308" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 553, + 301 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 301 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 301 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 301 + ], + "type": "table", + "html": "
Average Forgetting (%)Average Performance (mm)SPTO (mm)
ModelMethodMAERMSEiMAEiRMSEMAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
VOICEDFinetuned499.598162.188467.472208.6931620.4293072.1294.0406.144914.2232993.2281.9554.503
EWC [36]555.925190.152540.109247.9431796.3003346.0574.4906.685962.9373209.7591.9624.739
LwF [42]631.119221.535524.976233.7581973.9723612.7004.5336.648985.9953236.2442.0624.722
Replay [69]17.2414.05016.6625.478524.1141875.8971.3333.359618.6682366.5771.2923.348
ProtoDepth-A2.4272.8632.0792.153458.5201832.6901.1333.213548.2402294.3991.0803.159
ProtoDepth0.0000.0000.0000.000445.4191804.1581.1063.169531.6892262.9431.0433.110
FusionNetFinetuned11.3368.43517.44717.991437.7301785.2121.1933.724501.3622138.4221.1113.978
EWC [36]21.00610.49420.43116.535431.4401760.4601.1443.181486.1702117.0301.0292.986
LwF [42]12.3685.20213.59313.117442.8781759.2021.1783.352526.5282168.9611.1563.451
Replay [69]8.29011.1342.7697.975419.0441774.3611.0443.032479.1682122.9970.9662.906
ProtoDepth-A2.2002.2822.6027.203404.9561702.9451.0413.028464.9762052.4130.9522.864
ProtoDepth0.0000.0000.0000.000400.8881683.2021.0222.899461.0432048.9420.9322.792
KBNetFinetuned27.15318.20852.96933.370469.6581943.2591.3383.683541.3832411.1691.1443.505
EWC [36]23.5178.58330.07718.991456.8281806.7611.2213.321526.3662210.4241.1333.158
LwF [42]21.1844.04943.50019.951460.0971749.7341.3623.555541.9322142.9991.3593.731
Replay [69]25.42329.3036.3627.274454.8961935.6671.1023.203525.6962318.3631.0943.246
ProtoDepth-A4.5133.1002.9601.878409.9031730.7201.0453.044478.7902138.3471.0083.066
ProtoDepth0.0000.0000.0000.000401.0751710.0741.0292.993471.4372125.9570.9963.015
", + "image_path": "7bfcb49e9758bbe9267c0a43288ded58a6d5402dce60a7ec383bbf843a391cb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "lines": [ + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "type": "text", + "content": "Table 2. Quantitative results on outdoor datasets. Models are initially trained on KITTI and continually trained on Waymo, then VKITTI. Bold indicates the best performance, while underline indicates the second-best performance. Baseline results are obtained from UnCLe [21]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 346, + 296, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 346, + 296, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 296, + 358 + ], + "type": "text", + "content": "To this end, we propose to minimize an additional objective:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 362, + 296, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 362, + 296, + 392 + ], + "spans": [ + { + "bbox": [ + 61, + 362, + 296, + 392 + ], + "type": "interline_equation", + "content": "\\ell_ {d r} = 1 - \\left(\\frac {s _ {k}}{\\| s _ {k} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right) + \\frac {1}{w _ {j k}} \\sum_ {j \\neq k} \\left(\\frac {r _ {j}}{\\| r _ {j} \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right), \\tag {9}", + "image_path": "589870604ebbe7353964368429e99826cda629693c0811b81eee10a031847fc6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "inline_equation", + "content": "||\\cdot||" + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "content": "-norm and " + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "inline_equation", + "content": "w_{jk} \\propto |j \\neq k|" + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "content": " is a tunable normalization constant. As the previously learned domain descriptors are frozen, their alignment to their respective datasets or domains is preserved, allowing us to continually learn new domain descriptors that can distinguish new datasets. Eq. (9) is incorporated into Eq. (1) as an additional term weighted by " + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "inline_equation", + "content": "w_{dr}" + }, + { + "bbox": [ + 55, + 396, + 296, + 504 + ], + "type": "text", + "content": " to yield a novel loss function for training of unsupervised continual depth completion models in the agnostic setting:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 510, + 296, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 510, + 296, + 523 + ], + "spans": [ + { + "bbox": [ + 76, + 510, + 296, + 523 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = w _ {p h} \\ell_ {p h} + w _ {s z} \\ell_ {s z} + w _ {s m} \\ell_ {s m} + w _ {d r} \\ell_ {d r}. \\tag {10}", + "image_path": "4bd685a66626266fe5b22b2f28fe752d95c46bf2bc013936e04887cb40766cf7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "text", + "content": "At test-time, we compute the sample descriptor " + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "text", + "content": " for an input without dataset identity and select the domain descriptor " + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "inline_equation", + "content": "r_{k^*}" + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "text", + "content": " that maximizes cosine similarity with " + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 528, + 296, + 563 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 114, + 567, + 296, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 567, + 296, + 590 + ], + "spans": [ + { + "bbox": [ + 114, + 567, + 296, + 590 + ], + "type": "interline_equation", + "content": "k ^ {*} = \\arg \\max _ {k} \\left(\\frac {s}{\\| s \\|} \\cdot \\frac {r _ {k}}{\\| r _ {k} \\|}\\right). \\tag {11}", + "image_path": "f2992662f153951e4455dfef96a1ac2d2a5b71112703951f16246a38f4cab360.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": "For each latent space layer, we use the prototype set corresponding to the selected domain descriptor. While this does not eliminate forgetting due to the evolving set of domain descriptors and possible overlap between domains, it does minimize forgetting as each prototype set is learned independently for each dataset, but can still be selectively used for inference without knowing the test-time dataset identity. The trade-off is shown in Tabs. 1 and 2 (ProtoDepth-A) where we incur forgetting in exchange for the flexibility to support both the incremental and agnostic settings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 345, + 394, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 345, + 394, + 358 + ], + "spans": [ + { + "bbox": [ + 314, + 345, + 394, + 358 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 368, + 555, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 368, + 555, + 488 + ], + "spans": [ + { + "bbox": [ + 312, + 368, + 555, + 488 + ], + "type": "text", + "content": "Datasets. Indoor dataset sequence: NYUv2 [77] contains household, office, and commercial scenes captured with a Microsoft Kinect; ScanNet [12] is a diverse, large-scale dataset captured using a Structure Sensor; Void [97] contains laboratory, classroom, and garden scenes captured using XIVO. Outdoor dataset sequence: KITTI [84] is a daytime autonomous driving benchmark captured using a Velodyne LiDAR sensor; Waymo [81] contains road scenes with a wide variety of driving conditions; VKITTI [20] is a synthetic dataset that replicates and augments KITTI scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "content": "Models. We evaluate using three recent unsupervised depth completion models in the continual learning setting: VOICES [97], FusionNet [98], and KBNet [95]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 529, + 556, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 556, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 556, + 613 + ], + "type": "text", + "content": "Baseline Methods. We compare ProtoDepth against EWC [36], LwF [42], and Experience Replay (\"Re-play\") [69] as milestone works of their respective class of continual learning approaches. We include full finetuning (\"Finetuned\") as a baseline of performance with no continual learning strategy. All baseline methods achieve identical performance in the incremental and agnostic settings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "content": "Evaluation Metrics are computed across four standard depth completion metrics (MAE, RMSE, iMAE, iRMSE). We define the following evaluation metrics in terms of " + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "inline_equation", + "content": "a_{j}^{k}" + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "content": ", denoting any one of the four depth completion metrics on dataset " + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_j" + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "content": " after training on " + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 615, + 556, + 675 + ], + "type": "text", + "content": " total datasets:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Average Forgetting " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "(\\bar{F})" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": " is the scale-invariant mean of how much performance on previous datasets " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{j < k}" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": " deteriorates (i.e., increases in " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": " ) after training on each new " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6309" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 72, + 243, + 110 + ], + "blocks": [ + { + "bbox": [ + 110, + 72, + 243, + 110 + ], + "lines": [ + { + "bbox": [ + 110, + 72, + 243, + 110 + ], + "spans": [ + { + "bbox": [ + 110, + 72, + 243, + 110 + ], + "type": "image", + "image_path": "9acda1ef2bb737c62ecc7bdaad76910468cc71920fa5f4f0f962bf45ac5e085a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 245, + 72, + 368, + 110 + ], + "blocks": [ + { + "bbox": [ + 245, + 72, + 368, + 110 + ], + "lines": [ + { + "bbox": [ + 245, + 72, + 368, + 110 + ], + "spans": [ + { + "bbox": [ + 245, + 72, + 368, + 110 + ], + "type": "image", + "image_path": "f8ff5728ed6306d29ae74641b42862c137625b3049fb30d92190f4b85a24b4c1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 370, + 72, + 493, + 109 + ], + "blocks": [ + { + "bbox": [ + 370, + 72, + 493, + 109 + ], + "lines": [ + { + "bbox": [ + 370, + 72, + 493, + 109 + ], + "spans": [ + { + "bbox": [ + 370, + 72, + 493, + 109 + ], + "type": "image", + "image_path": "6c67b92dc2e21fc0977676d72adaae3b5a6310dac2076d9da40db1ff016d2556.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 59, + 113, + 304, + 223 + ], + "blocks": [ + { + "bbox": [ + 59, + 105, + 70, + 112 + ], + "lines": [ + { + "bbox": [ + 59, + 105, + 70, + 112 + ], + "spans": [ + { + "bbox": [ + 59, + 105, + 70, + 112 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 113, + 304, + 223 + ], + "lines": [ + { + "bbox": [ + 59, + 113, + 304, + 223 + ], + "spans": [ + { + "bbox": [ + 59, + 113, + 304, + 223 + ], + "type": "image", + "image_path": "cb033faad52b899f869f917bbf1e2f601d33f3c6df2ef8b2d515ead3a3ab9123.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 112, + 553, + 223 + ], + "blocks": [ + { + "bbox": [ + 307, + 112, + 553, + 223 + ], + "lines": [ + { + "bbox": [ + 307, + 112, + 553, + 223 + ], + "spans": [ + { + "bbox": [ + 307, + 112, + 553, + 223 + ], + "type": "image", + "image_path": "60fff9d3172d60991c1654339b5a831cabd007fd2b7443b4028567a962b3697b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 230, + 555, + 275 + ], + "lines": [ + { + "bbox": [ + 55, + 230, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 555, + 275 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison of ProtoDepth and baseline methods using VOICESED on KITTI after continual training on Waymo. (a) Input sample from KITTI, (b) Baseline methods exhibit significant forgetting, particularly for small-surface-area objects (e.g., street signs and lamp posts) where sparse depth is limited, and photometric priors from KITTI are critical. In contrast, ProtoDepth produces high-fidelity depth predictions, effectively mitigating forgetting despite the large domain gap between KITTI and Waymo." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 297, + 296, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 297, + 296, + 331 + ], + "spans": [ + { + "bbox": [ + 104, + 297, + 296, + 331 + ], + "type": "interline_equation", + "content": "\\bar {F} = \\frac {2}{T (T - 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j < k} \\frac {a _ {j} ^ {k} - a _ {j} ^ {j}}{a _ {j} ^ {j}}. \\tag {12}", + "image_path": "4f52278c4ea6cd0694f9cbe7e9bf5bd66ec29dad893881058f48eb6d98f53f00.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "text", + "content": "Average Performance " + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "inline_equation", + "content": "(\\bar{\\mu})" + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "text", + "content": " is the mean of performance on all seen datasets " + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{j\\leq k}" + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "text", + "content": " after training on each new " + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 55, + 337, + 296, + 361 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 116, + 371, + 296, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 371, + 296, + 404 + ], + "spans": [ + { + "bbox": [ + 116, + 371, + 296, + 404 + ], + "type": "interline_equation", + "content": "\\bar {\\mu} = \\frac {2}{T (T + 1)} \\sum_ {k = 1} ^ {T} \\sum_ {j \\leq k} a _ {j} ^ {k}. \\tag {13}", + "image_path": "8bea28ce31a1a28e03f85f671eea94ddbdd79b26def54b21d49f00e9d0b1b450.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 411, + 296, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 448 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 448 + ], + "type": "text", + "content": "Stability-Plasticity Trade-off (SPTO) captures the balance between retaining learned knowledge (stability) and adapting to new domains (plasticity) as a harmonic mean:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 88, + 456, + 296, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 456, + 296, + 489 + ], + "spans": [ + { + "bbox": [ + 88, + 456, + 296, + 489 + ], + "type": "interline_equation", + "content": "\\mathrm {S P T O} = \\frac {2 \\times S \\times P}{S + P}, \\left\\{ \\begin{array}{l} S = \\sum_ {k = 1} ^ {T} a _ {k} ^ {T} \\\\ P = \\sum_ {k = 1} ^ {T} a _ {k} ^ {k}, \\end{array} \\right. \\tag {14}", + "image_path": "952fe432ce3ff483cb4e7ef351c30ddf73eaf65d73613c15aeaa67d8a88a2dfb.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "text", + "content": " is performance across all datasets after completing training on the dataset sequence, and " + }, + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 495, + 296, + 532 + ], + "type": "text", + "content": " is performance on each new dataset after training on it for the first time." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 540, + 140, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 140, + 551 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 140, + 551 + ], + "type": "text", + "content": "5.1. Main Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 558, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 605 + ], + "type": "text", + "content": "We compare our method, evaluated in both the incremental (ProtoDepth) and agnostic (ProtoDepth-A) settings, against baseline methods for the indoor dataset sequence in Tab. 1 and for the outdoor dataset sequence in Tab. 2." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "Results in Incremental Setting. In both indoor and outdoor settings, ProtoDepth achieves a " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " improvement in Average Forgetting compared to all baseline methods across all models and metrics. This is, of course, because ProtoDepth exhibits zero forgetting as it freezes all model parameters and learns dataset-specific prototypes. For the indoor sequence, compared to the best baseline method, ProtoDepth improves Average Performance by " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "5.15\\%" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " and SPTO by " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "6.59\\%" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": ", averaged across all models and metrics." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "text", + "content": "Similarly, for the outdoor sequence, we improve Average Performance by " + }, + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "inline_equation", + "content": "6.88\\%" + }, + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "text", + "content": " and SPTO by " + }, + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "inline_equation", + "content": "6.94\\%" + }, + { + "bbox": [ + 313, + 287, + 555, + 311 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 313, + 556, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 313, + 556, + 517 + ], + "spans": [ + { + "bbox": [ + 312, + 313, + 556, + 517 + ], + "type": "text", + "content": "To demonstrate the reduced forgetting achieved by ProtoDepth, we qualitatively compare against all baseline methods using VOICESED on KITTI after continual training on Waymo (see Fig. 3). ProtoDepth yields better depth predictions for small-surface-area objects with limited sparse depth measurements for which the model must rely on photometric priors learned from images. Unlike KITTI, which consists exclusively of daytime scenes, Waymo includes many evening and overcast scenes, introducing variations in lighting and pixel intensities. Additionally, Waymo was captured using a higher-resolution camera which causes objects to appear bigger in terms of number of pixels occupied. Due to this large distributional shift, the model forgets the projected shapes of objects in KITTI after training on Waymo, even if the objects exist in both datasets. This forgetting is apparent in the highlighted street sign and lamp posts, where baseline methods struggle to accurately predict depth." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "text", + "content": "Results in Agnostic Setting. For the indoor sequence, compared to the best baseline method, ProtoDepth-A improves Average Forgetting by " + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "inline_equation", + "content": "52.22\\%" + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "text", + "content": ", Average Performance by " + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "inline_equation", + "content": "4.26\\%" + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "text", + "content": ", and SPTO by " + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "inline_equation", + "content": "5.40\\%" + }, + { + "bbox": [ + 313, + 519, + 556, + 616 + ], + "type": "text", + "content": ", averaged across all models and metrics. Notably, ProtoDepth-A outperforms ProtoDepth in some metrics, meaning the model appropriately selects prototypes of different domains when there is domain overlap, thereby enhancing its generalization capabilities." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": "For the outdoor sequence, ProtoDepth-A shows an average improvement of " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "53.21\\%" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " in Average Forgetting across all models and metrics. In contrast to the indoor sequence, ProtoDepth-A does not outperform ProtoDepth in any metric, likely due to the larger domain gaps between the outdoor datasets. Selecting prototypes from a different outdoor dataset is more likely to be erroneous, leading to performance degradation rather than generalization." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6310" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 553, + 183 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 183 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 183 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 183 + ], + "type": "table", + "html": "
MethodN(I)N(z)# ParamsScanNetVOID
MAERMSEiMAEiRMSEMAERMSEiMAEiRMSE
Pretrained--0M (0%)4114.044626.00390.78447.3142.94106.3929.2664.04
ProtoDepth110.24M (3.5%)19.68±0.6860.10±0.7110.44±0.4827.86±0.7437.81±0.5293.72±0.9022.82±0.2752.58±0.32
550.25M (3.6%)16.49±0.1557.51±0.196.84±0.0322.07±0.0334.02±0.2587.72±0.4317.92±0.1443.95±0.28
1050.25M (3.6%)14.59±0.1742.20±0.095.57±0.1417.10±0.1533.63±0.2387.30±0.5717.55±0.3243.24±0.63
10100.25M (3.7%)15.25±0.3943.31±0.725.85±0.2217.57±0.3834.39±0.8288.73±1.8318.49±0.8545.23±1.60
1001000.38M (5.5%)16.35±0.3747.61±0.165.90±0.1720.11±0.1934.29±0.5888.22±0.8618.16±0.6244.51±1.07
", + "image_path": "35f38a1648c5b230257134c09aefb60bd904cc7f9d31cde759709f06ffb982d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 220, + 294, + 322 + ], + "blocks": [ + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "lines": [ + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "type": "text", + "content": "Table 3. Sensitivity study of prototype set sizes " + }, + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "type": "inline_equation", + "content": "(N^{(I)}" + }, + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "type": "inline_equation", + "content": "N^{(z)}" + }, + { + "bbox": [ + 55, + 187, + 555, + 211 + ], + "type": "text", + "content": " ) on ProtoDepth using KBNet for indoor datasets (ScanNet and VOID). KBNet is pretrained on the initial dataset (NYUv2). Parameter overhead is reported as a percentage of the full KBNet model's parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 220, + 294, + 322 + ], + "lines": [ + { + "bbox": [ + 56, + 220, + 294, + 322 + ], + "spans": [ + { + "bbox": [ + 56, + 220, + 294, + 322 + ], + "type": "table", + "html": "
ScanNetWaymo
Ablated ComponentMAERMSEMAERMSE
global prototypes18.1258.91505.011715.21
projection matrix W17.5957.61495.051690.51
decoupled K and P16.3645.10491.591675.57
no ablations14.5942.20486.951664.18
", + "image_path": "c7cc58c7e45eb7cf00a418c6916605b1338acef721e6a91e8e1a3bd6e6758904.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 326, + 291, + 337 + ], + "lines": [ + { + "bbox": [ + 59, + 326, + 291, + 337 + ], + "spans": [ + { + "bbox": [ + 59, + 326, + 291, + 337 + ], + "type": "text", + "content": "Table 4. Ablation studies using KBNet for indoor and outdoor." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 351, + 297, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 351, + 297, + 507 + ], + "spans": [ + { + "bbox": [ + 54, + 351, + 297, + 507 + ], + "type": "text", + "content": "Furthermore, we refer back to Fig. 3 (ProtoDepth-A) for head-to-head comparison of our method against other baselines in the agnostic setting. The error maps for Finetuned, EWC, and LwF display significant errors, indicating substantial forgetting of previously learned information. While Replay yields an improved error map, it still experiences forgetting in small-surface-area objects. For example, Replay fails to reconstruct the upper portions of the highlighted street sign and lamp posts due to forgetting of learned photometric priors from KITTI, whereas ProtoDepth-A recalls them from KITTI prototypes. Additionally, ProtoDepth-A predicts the depth of the highlighted small fence poles with higher fidelity than the incoherent prediction of Replay." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 515, + 182, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 182, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 182, + 529 + ], + "type": "text", + "content": "5.2. Design Choice Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": "Prototype Set Sizes. We investigate the impact of varying the prototype set sizes (i.e., number of prototypes) for the image and sparse depth layers (denoted as " + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "inline_equation", + "content": "N^{(I)}" + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "inline_equation", + "content": "N^{(z)}" + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": ", respectively) on the performance of our method. The set size experiments for the indoor sequence are shown in Tab. 3, based on which we selected " + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "inline_equation", + "content": "N^{(I)} = 10" + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "inline_equation", + "content": "N^{(z)} = 5" + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": " for the main experiments. Smaller set sizes perform worse as there is insufficient capacity to capture the diversity of features in each dataset. There is also performance degradation with larger set sizes; intuitively, unnecessary additional parameters may learn noise and cause overfitting. Notably, best performance is achieved when " + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "inline_equation", + "content": "N^{(I)} > N^{(z)}" + }, + { + "bbox": [ + 56, + 534, + 297, + 713 + ], + "type": "text", + "content": ", which can be attributed to the larger distributional shift between scenes in the image modality compared to the sparse depth modality [58]. Since the bottleneck layer fuses both modalities," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "text", + "content": "we use " + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "inline_equation", + "content": "N^{(I)}" + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "text", + "content": " for the bottleneck layer prototypes. As a lower bound, we show that the frozen base model pretrained on NYUv2 (\"Pretrained\") performs poorly, motivating the need for continual learning. We perform similar set size experiments for the outdoor dataset sequence (see Supp. Mat.), based on which we choose " + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "inline_equation", + "content": "N^{(I)} = 25" + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "inline_equation", + "content": "N^{(z)} = 10" + }, + { + "bbox": [ + 313, + 222, + 555, + 293 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": "Ablations. We assess the impact of the components of ProtoDepth on both indoor (ScanNet) and outdoor (Waymo) in Tab. 4. Removing the " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": " depthwise convolutions results in performance degradation, demonstrating their effectiveness as lightweight global prototypes. Learning the keys " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": " independently from the prototypes " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": " without the projection matrix " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": " hurts performance, suggesting that the projection matrix effectively learns to map the prototypes into latent feature space, fulfilling the intended role of keys. Furthermore, performance decreases without the stop gradient operation on " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": " when computing " + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 295, + 556, + 439 + ], + "type": "text", + "content": ", indicating the importance of decoupled optimization of keys and prototypes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 453, + 384, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 384, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 384, + 464 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 473, + 556, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 556, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 556, + 605 + ], + "type": "text", + "content": "ProtoDepth leverages prototypes as a mechanism for mitigating catastrophic forgetting. While we demonstrate it on unsupervised depth completion, ProtoDepth does not assume specific modalities and thus can be relevant to other multimodal problems [67, 104, 108, 111]. Our promising results on both indoor and outdoor domains illustrate the potential for ProtoDepth to enable unsupervised continual learning for multimodal 3D reconstruction. Our architecture-agnostic approach can also be extended to other tasks involving models that produce latent feature representations [37, 112], offering a general framework for continual learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Limitations. ProtoDepth relies on knowledge of dataset boundaries to instantiate new prototype sets, which may not be feasible in online training settings where there are no defined boundaries between domains. In the same vein, we do not consider scenarios where domain gaps between datasets are small or where there are significant distributional shifts within a dataset. Addressing these limitations would require mechanisms to dynamically detect domain shifts and instantiate new prototypes when appropriate." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6311" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 103 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 103 + ], + "type": "text", + "content": "This work is supported by NSF-2112562 Athena AI Institute." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "spans": [ + { + "bbox": [ + 56, + 114, + 115, + 125 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 133, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 66, + 133, + 297, + 188 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 133, + 297, + 188 + ], + "spans": [ + { + "bbox": [ + 66, + 133, + 297, + 188 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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Traditional methods using Class Activation Maps (CAMs) often highlight only the most discriminative regions, leading to incomplete masks. Recent approaches that introduce textual information struggle with histopathological images due to inter-class homogeneity and intraclass heterogeneity. In this paper, we propose a prototype-based image prompting framework for histopathological image segmentation. It constructs an image bank from the training set using clustering, extracting multiple prototype features per class to capture intra-class heterogeneity. By designing a matching loss between input features and class-specific prototypes using contrastive learning, our method addresses inter-class homogeneity and guides the model to generate more accurate CAMs. Experiments on four datasets (LUAD-HistoSeg, BCSS-WSSS, GCSS, and BCSS) show that our method outperforms existing weakly supervised segmentation approaches, setting new benchmarks in histopathological image segmentation. $^{1}$", + "bbox": [ + 88, + 323, + 485, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 656, + 220, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automated segmentation of histopathology images plays a crucial role in computer-aided diagnosis, assisting in the identification of abnormal tissue regions, quantification of tumor microenvironments [58], and the support of tumor grading and prognosis [11-14, 51]. Existing methods largely depend on extensive high-quality annotated data [28, 30, 41], while pixel-level annotations present particular challenges due to the significant domain expertise and time required for their creation [15, 33, 62]. To reduce this requirement, weakly supervised segmentation (WSS) frameworks [20, 56, 57] have been proposed as a more label-efficient alternative, utilizing weak but easily acces", + "bbox": [ + 89, + 681, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69a37f233894a9c8ea5832a71a64c0a20910480d8fd395095b549a668f5939fa.jpg", + "image_caption": [ + "a" + ], + "image_footnote": [], + "bbox": [ + 522, + 309, + 645, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77e5ead71ad4844a7b639ca85f0992cd0e6c82b3397c896e88b8f99a39ca76f2.jpg", + "image_caption": [ + "b" + ], + "image_footnote": [], + "bbox": [ + 647, + 308, + 769, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bd457940bea09c32f336d78a7a4e2d081cb50bbc6d71222adf315ab829301851.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 306, + 895, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bd3a02ed4ccef791acb8bc1d93dd2efd18539991b41663813afb94da1bbee66d.jpg", + "image_caption": [ + "Figure 1. a. Four supervision frameworks for histopathological image segmentation: fully supervised with pixel-level masks, CAM-based WSS using image labels, textural-based WSS, and our image prompt-based framework. b. The challenges of inter-class homogeneity (variable texture and staining within classes) and intra-class heterogeneity (similar appearances across classes). Cosine similarities are computed using features extracted by the MedCLIP model [47]." + ], + "image_footnote": [], + "bbox": [ + 524, + 373, + 645, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0d4e34ae5667d945ed7d677c88dd60d3bfbca0564c4da91a4d6ea0a58df323bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 371, + 767, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/10dc851bf0a42bcf02599499ed88142267797b96e1c6a565a4de62b08587e926.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 776, + 369, + 895, + 430 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sible labels such as bounding boxes [21, 35], scribbles [29], point annotations [34], and image-level labels [56, 57]. Typically, WSS methods employ a two-stage process: a classification network is first trained using weak labels to generate pseudo-labels, such as class activation maps (CAMs) [59]. These pseudo-labels are then utilized as refined supervision signals to train a fully supervised network [17, 57, 59].", + "bbox": [ + 511, + 566, + 906, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, CAMs generated from image-level labels often focus on the most discriminative regions, leading to incomplete localization of target objects and confusion between target and non-target areas [23, 50]. This limitation arises from a domain gap in pre-trained models, which are often trained on source domains (e.g., ImageNet [8]) that differ from the target domain (e.g., histopathology), causing CAMs to focus on features misaligned with those of the target domain. Early studies have explored various strategies to improve CAM quality, such as pixel affinity models [1] and saliency map integration [24]. Recent studies have utilized textual information to bridge the gap between image-level labels and pixel-level segmentation [9, 50, 57]. As illustrated in Figure 1, these approaches incorporate textual descriptions (e.g., object type, colour, structure) into", + "bbox": [ + 511, + 674, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 107, + 875, + 218, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/QingchenTang/PBIP", + "bbox": [ + 109, + 887, + 400, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "30271", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the model via pre-trained vision-language models, such as CLIP model [36].", + "bbox": [ + 89, + 90, + 480, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While these methods have shown strong performance on popular segmentation benchmarks [9, 50], they face challenges in histopathological image segmentation. Tissue segmentation involves larger anatomical structures compared to general images or cell nucleus segmentation, with complex spatial arrangements, significant inter-class homogeneity, and intra-class heterogeneity [6, 25]. As illustrated in Figure 1.b, inter-class homogeneity refers to the visual similarity between different tissue types, making it difficult to differentiate target regions from surrounding tissues. For instance, non-tumor tissues may closely resemble tumor tissues, causing CAM-based methods [3, 17] to activate on irrelevant areas erroneously. Intra-class heterogeneity involves significant variability within the same tissue type, such as differences in staining, shape, and texture, which hampers text-based methods [9, 50, 57] from capturing fine-grained details, leading to misalignment between textual descriptions and pixel-level features.", + "bbox": [ + 89, + 123, + 482, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose a Prototype-Based Image Prompting (PBIP) framework for WSS in histopathological segmentation. Unlike methods that rely on text prompts, we utilize image-level labels and their corresponding images to construct visual prototypes. This approach enables the model to discern nuanced visual variations that are challenging for text-based methods. The visual prototypes are achieved through a feature bank that serves as an additional supervisory signal to guide CAM refinement. More specifically, the PBIP framework consists of two main components: a classification network and a prototype-guided feature matching network. The classification network, based on a pre-trained model, extracts multiscale feature representations from the query image to produce pseudo-segmentation masks that indicate class-specific pixel regions. The prototype-guided network constructs a feature bank containing multiple prototypes for each tissue class to capture intra-class heterogeneity. The feature bank is constructed from the training set by organizing images into distinct prototypes based on their labels and employing a CLIP-based image encoder to extract semantically rich, pixel-level features. In addition, a contrastive learning-based similarity loss is computed between the prototypes and class-specific pixel regions, mitigating inter-class homogeneity and yielding high-precision CAMs in the first stage of WSS, which then serve as pseudo-labels for subsequent supervised training.", + "bbox": [ + 89, + 397, + 482, + 805 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper are as follows:", + "bbox": [ + 109, + 806, + 450, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- To the best of our knowledge, the proposed PBIP framework is the first WSS model in the histopathology domain that utilizes image prompts. By integrating a prototype-guided feature prompting mechanism through an image library, it addresses intra-class heterogeneity", + "bbox": [ + 93, + 824, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and inter-class homogeneity.", + "bbox": [ + 529, + 92, + 720, + 106 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a CLIP-based image matching method that uses a contrastive learning approach to encourage the alignment of foreground features with their respective prototypes while maintaining distance from non-target prototypes, enhancing pixel-level segmentation in weakly supervised tasks.", + "- Extensive experiments on the LUAD-HistoSeg [17], BCSS-wsss [17], GCSS [39], and BCSS [2] demonstrate that our method outperforms the current state-of-the-art methods in weakly supervised tissue segmentation." + ], + "bbox": [ + 516, + 106, + 903, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 272, + 653, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Weakly Supervised Segmentation", + "text_level": 1, + "bbox": [ + 511, + 297, + 805, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "WSS methods aim to infer pixel-level segmentation from simpler labels such as image-level classification tags [7, 33], bounding boxes [22], or point annotations [16, 53]. Subsequent research has focused on generating higher-quality pseudo labels from these weak annotations, leading to the development of numerous CAM-based approaches [43, 46], such as the Grad-CAM model [37], pixel affinity models [1], and saliency maps [24]. These CAM-based models have been used in early histopathological image segmentation studies, including HistoSegNet [3], OEEN [26], and the MLPS model [17].", + "bbox": [ + 511, + 321, + 903, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With advances in multimodal learning [40, 44], particularly the development of CLIP [36], which effectively aligns image and text embeddings, recent studies have incorporated textual information as additional supervision to reduce the discrepancy between image-level labels and pixel-level predictions in WSS. For instance, Xie et al. proposed CLIMS [50] and Deng et al. introduced QA-CLIMS [9], integrating textual information into WSS models using the pre-trained CLIP model [36]. In histopathological image segmentation, Zhang et al. proposed TPRO [57], which incorporates general descriptions of tissue characteristics into image features via an attention mechanism [42] to produce more accurate CAMs by aligning image features with textual descriptions. In contrast, our method utilizes image-level labels and the corresponding images to provide finer-grained guidance compared to text-based approaches, addressing the challenges of homogeneity and heterogeneity in histopathological images.", + "bbox": [ + 511, + 488, + 903, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Prompt Learning", + "text_level": 1, + "bbox": [ + 511, + 771, + 684, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt learning initially gained traction in Natural Language Processing (NLP) [10, 27], where models were guided in specific tasks through designed or learned prompts. With the rise of large-scale pre-trained multimodal models like CLIP [36], prompt engineering has extended to vision tasks [60, 61]. Early approaches relied on manually defined text templates (e.g., \"a photo of {class", + "bbox": [ + 511, + 794, + 903, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "30272", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "name}\") to describe classes of interest and extract relevant knowledge [9, 50]. However, this trial-and-error process is time-consuming and requires specific expertise.", + "bbox": [ + 89, + 90, + 482, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address these limitations, learnable prompt-based methods were introduced for vision tasks [52, 60], replacing manual templates with a set of learnable text vectors preceding class names, thus automating the prompt generation process [60]. Additionally, some methods attempted to introduce image prompts through prototypes for few-shot image tasks [18, 48]. For example, Wang et al. [45] and Shen et al. [38] effectively utilized image prototypes for few-shot image segmentation.", + "bbox": [ + 89, + 137, + 483, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our method, we leverage prototype-based image prompts instead of text-based prompts. These image prompts offer finer-grained and more direct guidance, allowing the model to capture subtle visual differences that are challenging to describe using text alone.", + "bbox": [ + 89, + 273, + 483, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 363, + 181, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 89, + 388, + 200, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key idea of our proposed PBIP framework is to leverage image-level labels and corresponding images to create a high-quality visual prototype feature bank, guiding the generation of more accurate CAMs as pseudo masks for WSS. As illustrated in Figure 2, the PBIP framework consists of two main components: a Classification Network (ClassNet) and an Image Feature Matching Network (ImgMatchNet).", + "bbox": [ + 89, + 412, + 483, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ClassNet takes a histopathology image $\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times C}$ from the dataset and the prototype feature vectors $\\mathbf{P}_i$ from ImgMatchNet (as detailed in Section 3.4), where $H$ , $W$ , and $C$ denote the height, width, and number of channels, respectively. ClassNet performs a classification task to generate initial pseudo-segmentation masks $\\mathbf{M} \\in \\mathbb{R}^{H \\times W \\times N}$ and is optimized by a classification loss $\\mathcal{L}_{\\mathrm{CLS}}$ , where $N$ denotes the number of classes in the dataset.", + "bbox": [ + 89, + 518, + 483, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ImgMatchNet receives the input histopathology image $\\mathbf{X}$ , an image bank constructed from the training set through clustering, and the pseudo-segmentation masks $\\mathbf{M}$ generated by the ClassNet. ImgMatchNet extracts prototype features $\\mathbf{P}$ using a CLIP image encoder from the image bank and refines the pseudo-segmentation masks $\\mathbf{M}$ through a similarity matching loss $\\mathcal{L}_{\\mathrm{SIM}}$ . The refined masks $\\mathbf{M}$ are merged via an argmax operation over the channel dimension to produce the final activation map for the first stage of WSS. These masks are subsequently used to train a fully supervised segmentation model in the second stage, generating the final segmentation masks.", + "bbox": [ + 89, + 640, + 483, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Construction of Image Bank", + "text_level": 1, + "bbox": [ + 89, + 830, + 344, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We construct an image bank that captures diverse visual prototypes for each class, which is automatically assembled from the training set. Specifically, we select tissue images", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "based on image-level labels that indicate the patch contains only one class (e.g., only tumor) and exclude images with excessive white regions automatically. These patches are grouped into $N$ categories corresponding to the $N$ classes in the dataset. To capture intra-class heterogeneity, $K$ -Means clustering is applied within each category to partition the patches into $K$ subcategories. For each subcategory, the top $N_K$ images closest to the cluster center are selected as prototypes for the image bank. The distance metric used for clustering is defined as:", + "bbox": [ + 511, + 90, + 906, + 242 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD _ {t} (x _ {1}, x _ {2}) = 1 - \\frac {\\phi_ {e} (x _ {1}) \\cdot \\phi_ {e} (x _ {2})}{\\| \\phi_ {e} (x _ {1}) \\| \\| \\phi_ {e} (x _ {2}) \\|}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 251, + 906, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x_{1}$ and $x_{2}$ are two image patches, $\\phi_{e}$ denotes the feature extraction function of the CLIP image encoder, and the symbol $\\cdot$ denotes the dot product operation between vectors. This process results in an image bank comprising $N$ classes, each containing $K$ subcategories, with each subcategory holding $N_{K}$ representative images.", + "bbox": [ + 511, + 292, + 905, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Classification Network", + "text_level": 1, + "bbox": [ + 511, + 391, + 723, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ClassNet generates the initial pseudo-segmentation masks $\\mathbf{M}$ by leveraging both the input image $\\mathbf{X}$ and the prototype features $\\mathbf{P}$ . We adopt SegFormer [49] as the backbone due to its efficacy in capturing multi-scale contextual information through its hierarchical transformer encoder.", + "bbox": [ + 511, + 414, + 905, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an input histopathology image $\\mathbf{X}$ , hierarchical feature maps $\\mathbf{F}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times C_i}$ are extracted across different stages $i = 1,2,3$ with $C_{i + 1} > C_i$ , where $C_i$ corresponds to the number of channels at each hierarchical level $i$ of the feature maps. To generate the initial pseudo masks, the cosine similarity is computed (SIM) between each pixel feature vector in $\\mathbf{F}_i$ and the prototype feature vectors in $\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}$ . This computation produces confidence scores for each pixel across all classes, forming the pseudo-segmentation masks $\\mathbf{M}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times N}$ . The confidence score for pixel $p$ and class $n$ at level $i$ is calculated as:", + "bbox": [ + 511, + 489, + 906, + 674 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {i} (p, n) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {\\mathbf {F} _ {i} (p) \\cdot \\mathbf {P} _ {i} (n , k)}{\\| \\mathbf {F} _ {i} (p) \\| \\left. \\mathbf {P} _ {i} (n , k) \\right\\|}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 681, + 906, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{F}_i(p)$ is the feature vector of pixel $p$ in $\\mathbf{F}_i$ , and $\\mathbf{P}_i(n, k)$ is the $k$ -th prototype feature vector for class $n$ . By averaging the cosine similarities over all prototypes $K$ for each class, it effectively captures intra-class variations and obtains a robust confidence score that reflects the likelihood of the pixel $p$ belonging to the class $n$ .", + "bbox": [ + 511, + 732, + 905, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.4. Image Feature Matching Network", + "text_level": 1, + "bbox": [ + 511, + 832, + 810, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ImgMatchNet introduces image prompts through a prototype-based approach. It generates prototype features $\\mathbf{P}$ from the image bank, and then ClassNet is used to", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "30273", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4900ad11ed4e68559000ec2eaa861d112b0f6a6f15e0e82c8fd2b57ee06c5932.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 90, + 470, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f60bb0cd826f84ce2e8413e2f0481d328f55205c31425171aae6bb4a6d3f7bb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 478, + 90, + 898, + 227 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ec8d5f4ebbba4c48168186720114465f2a70bff887552893306b18545238655a.jpg", + "image_caption": [ + "Figure 2. Structure of the proposed PBIP framework. Overview. PBIP consists of two main components: a Classification Network(ClassNet) and an Image Feature Matching Network(ImgMatchNet), which leverage an external image bank to provide image prompts in the form of prototypes. Image Bank. Training images are grouped by their labels and clustered into $K$ subclasses per class. For each subclass, $N_K$ representative images are selected to build the image bank. ClassNet. It receives an input image $\\mathbf{X}$ and prototype features $\\mathbf{P}$ , performing a classification task to generate the pseudo-segmentation mask $\\mathbf{M}$ . ImgMatchNet. It processes the input image $\\mathbf{X}$ and the initial pseudo-segmentation mask $\\mathbf{M}$ , extracting foreground and background regions. These regions are then matched with $\\mathbf{P}$ from the image bank to refine the pseudo mask generation." + ], + "image_footnote": [], + "bbox": [ + 94, + 229, + 475, + 345 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3d4da5fafc154f904e853f7a6d3713933ec48e40f8e6ae74863ad29b3216ea7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 231, + 898, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "compute pixel-level class confidences in the feature maps. To extract these prototype features, we employ the image encoder from the pre-trained MedCLIP model [47], a variant of the CLIP architecture tailored for medical images and trained on large-scale medical image-text pairs.", + "bbox": [ + 88, + 470, + 482, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "All images in the image bank are encoded using the MedCLIP image encoder, producing feature representations denoted as $\\mathbf{F}_p\\in \\mathbb{R}^{N\\times K\\times N_K\\times d}$ , where $N$ is the number of classes in the dataset, $K$ is the number of subclasses per class determined by the clustering, $N_{K}$ is the number of images per subclass, and $d$ is the dimension of the feature space. The mean feature vector is computed for each subclass across its images to obtain the prototype features, yielding $\\mathbf{P}\\in \\mathbb{R}^{N\\times K\\times d}$ . To align these prototype features with the hierarchical feature maps generated by the ClassNet, we employ a Multi-Layer Perceptron (MLP) composed of fully connected layers and ReLU activations. The MLP projects the prototype features to match the dimensionality of each feature level, producing $\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}$ .", + "bbox": [ + 88, + 550, + 482, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ImgMatchNet includes a foreground-background separation module to further refine the pseudo-masks obtained from the ClassNet. Specifically, this module upsamples and aggregates the hierarchical pseudo-masks from different feature levels to obtain a comprehensive pseudo-mask:", + "bbox": [ + 88, + 765, + 482, + 842 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {\\prime} = \\sum_ {i = 1} ^ {3} \\operatorname {U p} \\left(\\mathbf {M} _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 862, + 482, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{M}' \\in \\mathbb{R}^{H \\times W \\times N}$ , and $\\mathrm{Up}(\\cdot)$ denotes the upsampling operation to match the original image resolution.", + "bbox": [ + 511, + 469, + 903, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ an adaptive thresholding module to separate foreground and background regions. This module computes an adaptive threshold $\\tau$ based on the intensity distribution of the pseudo-mask, dynamically distinguishing between foreground and background to reduce noise. The adaptive threshold is computed as:", + "bbox": [ + 511, + 501, + 905, + 592 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tau = \\delta \\cdot \\max (\\mathbf {M}), \\quad \\delta \\in [ 0, 1 ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 599, + 903, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta$ is a scaling parameter that controls the threshold level. Applying this threshold to the activation map yields a binary mask $b\\in \\mathbb{R}^{H\\times W\\times N}$ , where pixel values greater than or equal to $\\tau$ are set to 1 (foreground), and values below $\\tau$ are set to 0 (background). We then separate foreground and background images through element-wise multiplication:", + "bbox": [ + 511, + 625, + 905, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {\\mathrm {F G}} = b \\cdot \\mathbf {M} \\cdot \\mathbf {X}, \\quad \\mathbf {X} _ {\\mathrm {B G}} = (1 - b) \\cdot (1 - \\mathbf {M}) \\cdot \\mathbf {X}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 723, + 903, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}_{\\mathrm{FG}},\\mathbf{X}_{\\mathrm{BG}}\\in \\mathbb{R}^{H\\times W\\times N}$ represent the separated foreground and background regions. By using the same MedCLIP image encoder and MLP, we extract hierarchical foreground and background features $\\mathbf{F}_{\\mathrm{FG}_i},\\mathbf{F}_{\\mathrm{BG}_i}\\in \\mathbb{R}^{N\\times C_i}$ . These features are then utilized in a similarity matching loss to optimize the generation of the pseudo-masks further.", + "bbox": [ + 511, + 747, + 905, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Optimization Objectives", + "text_level": 1, + "bbox": [ + 511, + 847, + 736, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our model is jointly optimized by two objectives: the classification loss $\\mathcal{L}_{\\mathrm{CLS}}$ , which ensures consistency between pre", + "bbox": [ + 511, + 869, + 905, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "30274", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dicted labels and image-level annotations, and the similarity loss $\\mathcal{L}_{\\mathrm{SIM}}$ , which promotes alignment between the encoded features of the foreground and background regions with their respective prototype features $\\mathbf{P}$ . The total loss function is defined as:", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C L S}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S I M}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 178, + 482, + 194 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are weighting coefficients that balance the contribution of each loss term.", + "bbox": [ + 89, + 205, + 482, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Classification Loss. Image-level class predictions $\\hat{y} \\in \\mathbb{R}^{3 \\times N}$ are obtained by applying global average pooling to the pseudo-segmentation masks $\\mathbf{M}$ from each hierarchical level in the ClassNet, where 3 corresponds to the levels and $N$ is the number of classes. The predictions are compared with the ground-truth labels $y \\in \\mathbb{R}^{1 \\times N}$ , and the classification loss for each level $i$ is:", + "bbox": [ + 89, + 236, + 483, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L S}} [ i ] = \\operatorname {C o s s E n t r o p y} (y, \\hat {y} [ i ]) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 353, + 482, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma$ is the sigmoid function. The total classification loss is a weighted sum:", + "bbox": [ + 89, + 381, + 483, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L S}} = \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {\\mathrm {C L S}} [ i ]. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 422, + 482, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarity Loss. The similarity loss $\\mathcal{L}_{\\mathrm{SIM}}$ is divided into two components: the foreground similarity loss $\\mathcal{L}_{\\mathrm{FGS}}$ and the background similarity loss $\\mathcal{L}_{\\mathrm{BGS}}$ .", + "bbox": [ + 89, + 473, + 483, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The foreground similarity loss $\\mathcal{L}_{\\mathrm{FGS}}$ aligns the foreground image features with the corresponding foreground prototype features, while distinguishing them from the background prototype features. Formally, given the foreground image feature $F_{\\mathrm{FG}}[j]$ for the $j$ -th class, foreground prototype feature $P_{\\mathrm{FG}} = P[j]$ , and the background prototype features $P_{\\mathrm{BG}} = P[m]$ where $1 \\leq m \\leq N$ and $m \\neq j$ , the loss is defined as:", + "bbox": [ + 89, + 518, + 483, + 638 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {F G S}} = - \\log \\left(\\frac {\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right)}{\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right) + \\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} / \\tau\\right)}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 111, + 661, + 482, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 89, + 724, + 137, + 736 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {F G}}\\right), \\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 748, + 482, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FF}}$ is the sum of similarity scores between the foreground feature and the foreground prototype of the $j$ -th class, while $\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FB}}$ is the sum of similarity scores between the foreground feature of the $j$ -th class and the background prototype. The temperature parameter $\\tau$ controls the concentration level of the distribution.", + "bbox": [ + 89, + 779, + 482, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, $\\mathcal{L}_{\\mathrm{BGS}}$ aligns background image features with background prototype features while distinguishing them", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "from foreground prototype features. Given the background image feature $F_{\\mathrm{BG}}[j]$ , the background prototype feature $P_{\\mathrm{BG}} = P[j]$ for the $j$ -th region, and the foreground prototype features $P_{\\mathrm{FG}} = P[m]$ , the loss is defined as:", + "bbox": [ + 511, + 90, + 906, + 152 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {B G S}} = - \\log \\left(\\frac {\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}{\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j} , \\mathrm {j}} ^ {\\mathrm {B F}} / \\tau\\right) + \\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 175, + 906, + 228 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} = \\operatorname {m e a n} \\left(F _ {\\mathrm {B G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 241, + 906, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{s}}_j^{\\mathrm{BB}}$ is the mean of similarity scores between the background feature of the $j$ -th class and the background prototype. The total similarity loss is the combination of the two components:", + "bbox": [ + 511, + 268, + 906, + 329 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S I M}} = \\theta_ {1} \\cdot \\mathcal {L} _ {\\mathrm {F G S}} + \\theta_ {2} \\cdot \\mathcal {L} _ {\\mathrm {B G S}}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 340, + 905, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\theta_{1}$ and $\\theta_{2}$ are weights that balance the importance of the foreground and background similarity terms.", + "bbox": [ + 511, + 369, + 906, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 513, + 414, + 648, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 513, + 438, + 702, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluated our method on four histopathological datasets. BCSS [2] consists of 151 H&E-stained breast cancer images from TCGA-BRCA, annotated with four classes (Tumor, Stroma, Lymphocytic infiltrate, Necrosis), and includes 30,000 training patches, 2,500 validation patches and 2,500 testing patches.", + "bbox": [ + 511, + 462, + 905, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BCSS-WSSS [17] is derived from BCSS for WSS with 23,422 training patches, 3,418 validation patches and 4,986 testing patches.", + "bbox": [ + 511, + 551, + 905, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LUAD-HistoSeg [17] contains 17,291 H&E-stained lung adenocarcinoma patches, annotated with four classes (Tumor Epithelium, Stroma, Necrosis, and Lymphocytes), with 16,678 training patches, 306 validation patches and 307 testing patches.", + "bbox": [ + 511, + 598, + 905, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GCSS [39] comprises 100 H&E-stained Gastric cancer images from TCGA-STAD gastric cancer images, annotated with four classes (Tumor, Lymphoid Stroma, Desmoplastic Stroma, Smooth Muscle Necrosis) providing 20,000 training, 2,500 validation patches and 2,500 testing patches.", + "bbox": [ + 511, + 672, + 905, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BCSS-WSSS and LUAD-HistoSeg are used exclusively for weakly supervised segmentation tasks, as the training images are labelled only at the image level, with the validation and test sets still including ground truth masks for evaluation purposes. More details about datasets are in the Supplementary Material.", + "bbox": [ + 511, + 750, + 905, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. The ClassNet utilizes the Mix Transformer from SegFormer [49] as its backbone, which is pretrained on ImageNet-1K. The ImgMatchNet is built upon an image bank assembled from the training set, where", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "30275", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2ed76f2ea1705f2592b794c68e81d9a8f8bf8abd8bf85385759fbe65ed1a24c9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetBCSS-WSSS [17]LUAD-HistoSeg [17]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
WHistoSegNet [3]32.19±5.835.69±5.919.24±1.748.70±6.845.32±4.345.08±3.918.36±1.162.37±4.3
TransWS [56]40.25±0.0--57.39±0.056.27±0.0--72.02±0.0
OEEN [26]59.93±0.561.11±0.825.09±1.274.95±0.472.54±0.271.65±0.226.15±1.484.08±0.2
MLPS [17]65.17±1.769.65±1.935.19±0.578.91±1.173.54±2.173.15±1.127.77±0.984.75±1.4
TPRO [57]63.92±0.464.45±0.225.79±0.577.99±0.374.14±0.874.01±0.227.46±0.385.14±0.5
CLIMS [50]38.98±2.437.58±2.113.52±0.956.09±2.639.45±3.138.92±2.717.55±1.656.58±3.0
QA-CLIMS [9]22.45±9.724.87±8.211.15±2.436.67±11.221.97±8.620.63±8.910.67±2.136.03±10.0
Proto2Seg [32]67.86±0.9*72.48±1.1*35.54±0.4*81.00±0.9*74.91±1.2*74.52±1.0*30.71±0.5*85.97±1.2*
PBLP (Ours)69.54±0.674.52±0.537.17±0.482.03±0.576.44±0.575.19±0.530.64±0.386.64±0.3
DatasetGCSS [39]BCSS [2]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
F&SSSPCL [39]51.63±0.0--68.10±0.062.47±0.0--76.90±0.0
SAM-Path [54]58.78±0.959.01±0.758.78±0.973.11±0.363.27±0.863.35±0.725.10±0.777.50±0.6
SAM2-Path [55]57.06±0.656.50±0.622.32±0.472.66±0.761.57±0.662.01±0.623.77±0.476.21±0.5
WHistoSegNet [3]30.02±6.231.25±5.410.10±3.646.15±7.022.15±7.822.80±8.012.11±4.136.27±8.9
OEEN [26]45.89±2.847.14±2.515.33±1.862.91±3.147.50±0.448.21±0.314.00±0.264.41±0.4
MLPS [17]51.20±1.752.85±1.519.10±1.367.72±2.449.32±1.151.31±1.321.08±0.766.06±0.9
TPRO [57]50.12±1.951.73±1.718.50±1.169.84±1.850.97±0.351.01±0.317.88±0.467.52±0.2
CLIMS [50]32.03±3.031.89±2.715.22±1.848.52±3.336.12±4.636.77±3.012.16±1.153.07±4.2
QA-CLIMS [9]25.01±8.326.54±7.612.34±4.240.02±9.023.00±9.924.07±9.110.27±3.637.39±12.2
Proto2Seg [32]53.23±2.853.97±2.922.34±1.770.84±2.055.34±2.056.72±2.022.40±1.570.78±2.1
PBLP (Ours)55.10±1.357.05±1.221.40±0.971.05±1.455.28±0.856.30±0.823.65±0.371.20±0.7
", + "bbox": [ + 96, + 88, + 903, + 425 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b076516922a010a9c966b96a08cea004cee356796b4ec524c7d4a0081462f5c8.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of various methods on four histopathological datasets. The best results are highlighted in bold. \"Sup.\" denotes the type of supervision used: $\\mathcal{F} \\& \\mathcal{S}$ represents fully and semi-supervised methods, while $\\mathcal{W}$ indicates weakly supervised methods. Except for CLIMS and QA-CLIMS (designed for natural image segmentation), all methods are specifically tailored for histopathological image segmentation. For the BCSS-WSSS and LUAD-HistoSeg, the $p$ -values from t-tests comparing our model with the second-best results* were calculated, and all $p$ -values were less than 0.05." + ], + "table_footnote": [], + "table_body": "
CLCSFGMBGMmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓62.08±0.363.00±0.425.73±0.276.60±0.3
✓✓55.01±2.859.47±2.520.44±1.070.98±3.0
✓✓50.23±2.452.11±1.719.20±0.766.87±2.7
✓✓62.34±1.664.08±1.925.68±0.776.80±1.5
✓✓✓67.54±0.669.42±0.733.00±0.480.63±0.4
", + "bbox": [ + 94, + 517, + 480, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Ablation study of different loss function combinations on the initial pseudo masks quality (mIoU%) for the BCSS-WSSS dataset.", + "bbox": [ + 89, + 595, + 482, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the number of clusters $K$ in $K$ -Means was set to 3, and each subclass contains $N_K = 100$ . The scaling parameter $\\delta$ in the adaptive thresholding module was 0.15.", + "bbox": [ + 89, + 652, + 482, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During training, we utilized the AdamW optimizer with an initial learning rate of $1 \\times 10^{-5}$ and a weight decay of 0.003. The total loss function combines the classification loss and similarity loss with weighting factors $\\alpha = 1$ and $\\beta = 0.5$ , respectively. The temperature parameter in both $\\mathcal{L}_{\\mathrm{FGS}}$ and $\\mathcal{L}_{\\mathrm{BGS}}$ was set to 1, while $\\theta_{1}$ and $\\theta_{2}$ were set to 1 and 0.5, respectively. The model was trained for 10 epochs, with a batch size of 10 during the first stage. In the second stage in WSS, an unmodified Deeplab-v2 model [5] was trained as a fully supervised segmentation model. All models were trained on a single 4090 GPU.", + "bbox": [ + 89, + 700, + 482, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To quantitatively evaluate our method, we employed four standard metrics: Mean Intersection over Union (mIoU),", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Frequency Weighted IoU (FWIoU), Boundary IoU (bIoU), and Dice Coefficient. We also calculated p-values from t-tests to indicate the statistical significance of our results, measuring the probability that the observed differences occurred by chance.", + "bbox": [ + 511, + 520, + 906, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 513, + 608, + 607, + 625 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ca609d1a25878ea3d1857ef9c4cc1ddc156d9ef813e7030535731a92d157819e.jpg", + "image_caption": [ + "(a) Analysis of $\\beta /\\alpha$" + ], + "image_footnote": [], + "bbox": [ + 514, + 643, + 705, + 747 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9e4ad25ac8b61f3914274545a617c8c3c18599310fd2c2ef3b9f70e700d02c34.jpg", + "image_caption": [ + "(b) Analysis of $\\theta_{2} / \\theta_{1}$", + "Figure 3. Ablation study on hyperparameter ratios. The mIoU values are reported on initial pseudo masks for BCSS-WSSS." + ], + "image_footnote": [], + "bbox": [ + 712, + 643, + 903, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared our model with ten advanced methods, including three supervised models and five weakly supervised models, two state-of-the-art text-prompted weakly supervised models. We used the reported results for SSPCL and TransWS due to the unavailability of publicly available", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "30276", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/33a45ef645fe089db1cf6f6fce77e23cba359cb42621dccb6045e0707ed9382d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetBCSS
EncoderBackbonemIoU(%)FwIoU(%)bIoU(%)dice(%)
CLIP [36]SegFormer66.45±0.372.42±0.327.05±0.280.56±0.2
ResNet1865.87±0.270.40±0.323.23±0.378.95±0.2
ResNet3866.10±0.471.22±0.426.56±0.279.86±0.3
ResNet5065.30±0.470.21±0.423.31±0.378.27±0.3
TransUNet60.17±0.463.52±0.517.81±0.275.12±0.5
MedCLIP [47]SegFormer68.01±0.673.20±0.536.88±0.481.62±0.5
ResNet1867.17±0.472.60±0.333.99±0.380.64±0.4
ResNet3867.18±0.572.57±0.535.18±0.380.93±0.4
ResNet5067.03±0.372.11±0.233.98±0.480.26±0.2
TransUNet62.09±0.566.89±0.520.15±0.376.61±0.5
PLIP [19]SegFormer67.16±0.773.53±0.537.21±0.481.77±0.5
ResNet1866.89±0.673.00±0.433.01±0.480.16±0.5
ResNet3867.02±0.573.24±0.535.85±0.480.25±0.4
ResNet5066.75±0.472.48±0.332.17±0.280.05±0.4
TransUNet61.98±0.666.01±0.521.54±0.376.53±0.6
DINOv2 [31]SegFormer66.37±0.872.38±0.932.01±0.380.24±0.8
ResNet3865.01±0.670.47±0.631.90±0.479.23±0.6
TransUNet61.00±0.462.71±0.520.22±0.276.64±0.4
", + "bbox": [ + 94, + 88, + 480, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "code. All other models were retrained and tested with five random seeds for robustness. Proto2Seg is a model based on human feedback; in our comparison with Proto2Seg, we carefully selected patches that met the required criteria using existing patch-level and image-level annotations instead of performing manual cutting and human feedback labelling. This might lead to a performance improvement for the Proto2Seg model.", + "bbox": [ + 88, + 378, + 482, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 1, our PBIP framework generally outperforms state-of-the-art weakly supervised methods across the four datasets. Specifically, on BCSS-WSSS, LUAD-HistoSeg and GCSS, our method outperforms Proto2Seg by $1.68\\%$ , $1.53\\%$ and $1.87\\%$ in mIoU, achieving the best weakly supervised performance. All $p$ -values between our model and the second best on BCSS-WSSS and LUAD-HistoSeg are below 0.05, confirming the statistical significance of our improvements.", + "bbox": [ + 88, + 500, + 482, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 shows the pseudo masks generated during the first stage of WSS models. We compared PBIP with MLPS, TPRO, and CLIMS. MLPS ranks third on BCSS-WSSS, while TPRO achieves the third-best on LUAD based. CLIMS is a text-supervised segmentation model for natural images. The results indicate that PBIP activates more complete object content and fewer background regions, while TPRO offers slight improvement over MLPS and CLIMS shows many errors. Text features do not enhance histopathological segmentation, and text supervision can mislead the model due to inter-class homogeneity and intra-class heterogeneity in histopathological images.", + "bbox": [ + 89, + 637, + 482, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 830, + 254, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study of Image Bank. We investigated the impact of the number of prototype images by randomly selecting images without clustering, using 10 different random", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8f962fd1783e4654fa8a9b2b42e06d2f707ab44c3c8667ef1c6e1e1c40d503b1.jpg", + "table_caption": [ + "Table 3. Performance comparison of different combinations of image encoders (CLIP, MedCLIP, PLIP, DINOv2) and backbones (SegFormer, ResNet variants, TransUNet) on initial pseudo masks for BCSS-WSSS." + ], + "table_footnote": [], + "table_body": "
K12345
DatasetmIoU(%)mIoU(%)mIoU(%)mIoU(%)mIoU(%)
BCSS-WSSS67.03±0.467.15±0.468.01±0.667.81±0.767.53±0.7
LUAD-HistoSeg74.91±0.575.12±0.574.87±0.673.72±1.274.07±0.8
GCSS51.26±0.852.07±0.853.21±1.253.91±1.053.54±0.9
BCSS54.01±0.653.97±0.854.05±0.853.87±1.053.50±0.9
", + "bbox": [ + 517, + 88, + 903, + 154 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "seeds for robustness. In Figure 4, \"Proto Num\" represents the number of images per sub-bank per category. The results show that the average mIoU improves as the number of prototype images increases. Using all eligible training images yielded a mIoU of $69.15\\%$ , suggesting that more images help reduce noise in prototype computation. However, due to inter-class homogeneity, simply increasing the number is not the most effective approach. The highest mIoU of $69.52\\%$ was achieved with 100 images per sub-bank. When clustering was applied to select 100 images, the mIoU further increased to $69.60\\%$ . This demonstrates that selecting representative images through clustering is more effective than merely increasing quantity, as clustering captures the most discriminative features and mitigates challenges posed by inter-class homogeneity.", + "bbox": [ + 511, + 251, + 906, + 478 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additionally, we analyzed the impact of the number of clusters $K$ in $K$ -Means. As shown in Table 4, the best results across all datasets were obtained when $K$ was set between 2 and 4, indicating that the optimal choice of $K$ may depend on the level of inter-class homogeneity and intra-class heterogeneity within the dataset. Specifically, a small $K$ prevents the model from adequately capturing intra-class heterogeneity, and an excessively high $K$ amplifies the influence of inter-class homogeneity.", + "bbox": [ + 511, + 479, + 905, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study of the Loss Function. We analyzed the impact of different loss function configurations. Specifically, we varied the weighting ratios $\\beta/\\alpha$ (for $\\mathcal{L}_{\\mathrm{SIM}}$ and $\\mathcal{L}_{\\mathrm{CLS}}$ ) and $\\theta_{2}/\\theta_{1}$ (for $\\mathcal{L}_{\\mathrm{BGS}}$ and $\\mathcal{L}_{\\mathrm{FGS}}$ ), as illustrated in Figure 3. The results indicate that extreme values of these ratios lead to a decline in performance. Furthermore, excluding either $\\mathcal{L}_{\\mathrm{FGS}}$ or $\\mathcal{L}_{\\mathrm{BGS}}$ causes the mIoU to drop significantly from $67.54\\%$ to $50.23\\%$ and $55.01\\%$ , respectively. This substantial decrease suggests that both components are essential; relying solely on one causes the model to focus excessively on either the foreground or background, lead", + "bbox": [ + 511, + 618, + 905, + 785 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/78d256ea707e3431e2361fc211adc0a37ca616844d0ad39a33845cd35e738d29.jpg", + "table_caption": [ + "Table 4. Ablation study on the number of clusters $K$ in $\\mathrm{k}$ -means across different datasets. The mIoU values on initial pseudo masks for BCSS-WSSS are reported with standard deviation. The optimal $K$ value varies per dataset,with $K = 2$ to $K = 4$ generally achieving the highest performance." + ], + "table_footnote": [], + "table_body": "
SIMATmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓63.25±0.566.80±0.425.89±0.377.98±0.4
✓67.09±0.673.01±0.627.48±0.579.92±0.6
✓✓68.01±0.673.20±0.536.88±0.481.62±0.5
", + "bbox": [ + 517, + 800, + 903, + 858 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation study on the impact of SIM and Adaptive Thresholding (AT) on initial pseudo masks for BCSS-WSSS.", + "bbox": [ + 511, + 867, + 903, + 896 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "30277", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9d1a4eb718b8a8fa2c9ab6503d2fa79259adb0f53abb213f78e471b1e902c943.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PromptModelTUMSTRLYMNECMean
TextCLIP [36]0.0050.0010.1350.0020.035
PLIP [19]0.7780.0080.3190.1360.310
MedCLIP [47]0.4230.0200.1650.2050.203
ImageCLIP [36]0.7160.2140.5290.0190.370
PLIP [19]0.9240.9200.8160.8350.874
MedCLIP [47]0.8810.8950.7900.6710.809
", + "bbox": [ + 94, + 87, + 480, + 179 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Zero-shot classification F1 scores $(\\%)$ on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with text and image prompts.", + "bbox": [ + 89, + 189, + 482, + 233 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbc81cecd43f5609ff21276b10bbef31dc8c19f5560daf797d936385c242c70e.jpg", + "image_caption": [ + "Figure 4. Ablation study of the number of prototype images. Proto Num represents the number of prototype images per sub-bank for each category. We report the mIoU values with Standard Deviation obtained over 10 runs with different random seeds." + ], + "image_footnote": [], + "bbox": [ + 99, + 247, + 478, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing to incomplete or erroneous activations.", + "bbox": [ + 89, + 478, + 372, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study of the Modules. We analyzed the effectiveness of different modules within PBLP. As shown in Table 5, both the SIM and the Adaptive Thresholding Module significantly enhance model performance. Specifically, when the SIM module is removed, we substitute it with a simple $1 \\times 1$ convolutional layer to generate the pseudo-segmentation masks. The results demonstrate a noticeable decline in performance without the SIM and AT module. The SIM module captures intra-class heterogeneity and inter-class homogeneity better than the $1 \\times 1$ convolutional layer. Furthermore, Figure 1 illustrates the foreground images generated by the model with and without the AT module. The results demonstrate that AT effectively reduces noise in background regions.", + "bbox": [ + 88, + 492, + 482, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additionally, we evaluated the performance of our model using different image encoders and backbones, as summarized in Table 3. The combination of MedCLIP [47] and SegFormer achieved the best results in terms of mIoU metric. We observed that the PLIP [19] and SegFormer pairing performed best on the bIoU, FWIoU, and Dice coefficient. The TransUNet model [4], with its end-to-end architecture that does not utilize the SIM module for pseudo-mask computation, exhibited inferior performance. These results suggest that the absence of the SIM module may contribute to the lower effectiveness. Moreover, the relatively poor performance of CLIP [36] and DINOv2 [31] further highlights the importance of external knowledge from pretraining in", + "bbox": [ + 89, + 704, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ada068df4a82c0fe6d0f3b43424424ba5eea4ab816908c1944780ebe37eeff31.jpg", + "image_caption": [ + "Figure 5. a. Visualization of the pseudo-segmentation masks generated by models in the first stage on BCSS-WSSS. The masks are overlaid on the input images, with the raw pseudo-segmentation mask shown in the top-left corner. b. The foreground images generated by PBIP for the four segmentation targets. More visualizations are in Supplementary Material." + ], + "image_footnote": [], + "bbox": [ + 517, + 89, + 906, + 276 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "histopathology, as these more generic encoders appear less effective for the specialized task of tissue segmentation.", + "bbox": [ + 511, + 388, + 903, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Text prompt and Image prompt. To explore the challenges of image-text matching in histopathology, we conducted zero-shot classification experiments on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with both text and image prompts (see Table 6). For text prompts, we used the common format: \"a photo of {class name} \", while for image prompts, we utilized our prototype image features. The results show that PLIP and MedCLIP significantly outperform CLIP when using image prompts, but all models perform poorly with text prompts. This highlights the substantial challenges of text prompting in histopathology, where textual descriptions struggle to capture complex visual patterns and inter-class homogeneity. In contrast, image prompts effectively guide the models by aligning with the intricate characteristics of histopathological images through prototype features.", + "bbox": [ + 511, + 420, + 906, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 679, + 633, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a novel Prototype-Based Image Prompting (PBIP) framework to address the challenges of inter-class homogeneity and intra-class heterogeneity in weakly supervised histopathological image segmentation. PBIP leverages image-based labels and corresponding images in histopathology datasets by extracting class prototype features through clustering methods. By incorporating class prototypes, our approach effectively mitigates inter-class homogeneity, while multiple sub-prototypes for each class address intra-class heterogeneity. Validation on four datasets demonstrated that PBIP achieves state-of-the-art performance and robustness in weakly supervised histopathological segmentation.", + "bbox": [ + 511, + 705, + 906, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "30278", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. 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National science review, 5(1):44-53, 2018. 1" + ], + "bbox": [ + 516, + 92, + 903, + 830 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "30280", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_model.json b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f5a6b9b22f3ab5f722588f41987f6fcb5d286d9f --- /dev/null +++ b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_model.json @@ -0,0 +1,2475 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.13, + 0.885, + 0.177 + ], + "angle": 0, + "content": "Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.26, + 0.204, + 0.738, + 0.24 + ], + "angle": 0, + "content": "Qingchen Tang* Lei Fan* Maurice Pagnucco Yang Song University of New South Wales" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.242, + 0.807, + 0.258 + ], + "angle": 0, + "content": "{qingchen.tang@student, lei.fanl@, morri@cse, yang.song1@}.unsw.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.324, + 0.486, + 0.627 + ], + "angle": 0, + "content": "Weakly supervised image segmentation with image-level labels has drawn attention due to the high cost of pixel-level annotations. Traditional methods using Class Activation Maps (CAMs) often highlight only the most discriminative regions, leading to incomplete masks. Recent approaches that introduce textual information struggle with histopathological images due to inter-class homogeneity and intraclass heterogeneity. In this paper, we propose a prototype-based image prompting framework for histopathological image segmentation. It constructs an image bank from the training set using clustering, extracting multiple prototype features per class to capture intra-class heterogeneity. By designing a matching loss between input features and class-specific prototypes using contrastive learning, our method addresses inter-class homogeneity and guides the model to generate more accurate CAMs. Experiments on four datasets (LUAD-HistoSeg, BCSS-WSSS, GCSS, and BCSS) show that our method outperforms existing weakly supervised segmentation approaches, setting new benchmarks in histopathological image segmentation.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.657, + 0.222, + 0.673 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.682, + 0.485, + 0.864 + ], + "angle": 0, + "content": "Automated segmentation of histopathology images plays a crucial role in computer-aided diagnosis, assisting in the identification of abnormal tissue regions, quantification of tumor microenvironments [58], and the support of tumor grading and prognosis [11-14, 51]. Existing methods largely depend on extensive high-quality annotated data [28, 30, 41], while pixel-level annotations present particular challenges due to the significant domain expertise and time required for their creation [15, 33, 62]. To reduce this requirement, weakly supervised segmentation (WSS) frameworks [20, 56, 57] have been proposed as a more label-efficient alternative, utilizing weak but easily acces" + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.296, + 0.537, + 0.306 + ], + "angle": 0, + "content": "a" + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.31, + 0.646, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.309, + 0.77, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.293, + 0.787, + 0.305 + ], + "angle": 0, + "content": "b" + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.308, + 0.896, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.374, + 0.646, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.372, + 0.769, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.37, + 0.896, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.56 + ], + "angle": 0, + "content": "Figure 1. a. Four supervision frameworks for histopathological image segmentation: fully supervised with pixel-level masks, CAM-based WSS using image labels, textural-based WSS, and our image prompt-based framework. b. The challenges of inter-class homogeneity (variable texture and staining within classes) and intra-class heterogeneity (similar appearances across classes). Cosine similarities are computed using features extracted by the MedCLIP model [47]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.674 + ], + "angle": 0, + "content": "sible labels such as bounding boxes [21, 35], scribbles [29], point annotations [34], and image-level labels [56, 57]. Typically, WSS methods employ a two-stage process: a classification network is first trained using weak labels to generate pseudo-labels, such as class activation maps (CAMs) [59]. These pseudo-labels are then utilized as refined supervision signals to train a fully supervised network [17, 57, 59]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.902 + ], + "angle": 0, + "content": "However, CAMs generated from image-level labels often focus on the most discriminative regions, leading to incomplete localization of target objects and confusion between target and non-target areas [23, 50]. This limitation arises from a domain gap in pre-trained models, which are often trained on source domains (e.g., ImageNet [8]) that differ from the target domain (e.g., histopathology), causing CAMs to focus on features misaligned with those of the target domain. Early studies have explored various strategies to improve CAM quality, such as pixel affinity models [1] and saliency map integration [24]. Recent studies have utilized textual information to bridge the gap between image-level labels and pixel-level segmentation [9, 50, 57]. As illustrated in Figure 1, these approaches incorporate textual descriptions (e.g., object type, colour, structure) into" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.22, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.401, + 0.901 + ], + "angle": 0, + "content": "1https://github.com/QingchenTang/PBIP" + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.401, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30271" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.122 + ], + "angle": 0, + "content": "the model via pre-trained vision-language models, such as CLIP model [36]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.124, + 0.483, + 0.395 + ], + "angle": 0, + "content": "While these methods have shown strong performance on popular segmentation benchmarks [9, 50], they face challenges in histopathological image segmentation. Tissue segmentation involves larger anatomical structures compared to general images or cell nucleus segmentation, with complex spatial arrangements, significant inter-class homogeneity, and intra-class heterogeneity [6, 25]. As illustrated in Figure 1.b, inter-class homogeneity refers to the visual similarity between different tissue types, making it difficult to differentiate target regions from surrounding tissues. For instance, non-tumor tissues may closely resemble tumor tissues, causing CAM-based methods [3, 17] to activate on irrelevant areas erroneously. Intra-class heterogeneity involves significant variability within the same tissue type, such as differences in staining, shape, and texture, which hampers text-based methods [9, 50, 57] from capturing fine-grained details, leading to misalignment between textual descriptions and pixel-level features." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.398, + 0.483, + 0.806 + ], + "angle": 0, + "content": "To address these challenges, we propose a Prototype-Based Image Prompting (PBIP) framework for WSS in histopathological segmentation. Unlike methods that rely on text prompts, we utilize image-level labels and their corresponding images to construct visual prototypes. This approach enables the model to discern nuanced visual variations that are challenging for text-based methods. The visual prototypes are achieved through a feature bank that serves as an additional supervisory signal to guide CAM refinement. More specifically, the PBIP framework consists of two main components: a classification network and a prototype-guided feature matching network. The classification network, based on a pre-trained model, extracts multiscale feature representations from the query image to produce pseudo-segmentation masks that indicate class-specific pixel regions. The prototype-guided network constructs a feature bank containing multiple prototypes for each tissue class to capture intra-class heterogeneity. The feature bank is constructed from the training set by organizing images into distinct prototypes based on their labels and employing a CLIP-based image encoder to extract semantically rich, pixel-level features. In addition, a contrastive learning-based similarity loss is computed between the prototypes and class-specific pixel regions, mitigating inter-class homogeneity and yielding high-precision CAMs in the first stage of WSS, which then serve as pseudo-labels for subsequent supervised training." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.808, + 0.451, + 0.823 + ], + "angle": 0, + "content": "The main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.825, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- To the best of our knowledge, the proposed PBIP framework is the first WSS model in the histopathology domain that utilizes image prompts. By integrating a prototype-guided feature prompting mechanism through an image library, it addresses intra-class heterogeneity" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.093, + 0.722, + 0.107 + ], + "angle": 0, + "content": "and inter-class homogeneity." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.107, + 0.905, + 0.197 + ], + "angle": 0, + "content": "- We design a CLIP-based image matching method that uses a contrastive learning approach to encourage the alignment of foreground features with their respective prototypes while maintaining distance from non-target prototypes, enhancing pixel-level segmentation in weakly supervised tasks." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.198, + 0.905, + 0.258 + ], + "angle": 0, + "content": "- Extensive experiments on the LUAD-HistoSeg [17], BCSS-wsss [17], GCSS [39], and BCSS [2] demonstrate that our method outperforms the current state-of-the-art methods in weakly supervised tissue segmentation." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.107, + 0.905, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.273, + 0.655, + 0.289 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.298, + 0.806, + 0.315 + ], + "angle": 0, + "content": "2.1. Weakly Supervised Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.322, + 0.905, + 0.488 + ], + "angle": 0, + "content": "WSS methods aim to infer pixel-level segmentation from simpler labels such as image-level classification tags [7, 33], bounding boxes [22], or point annotations [16, 53]. Subsequent research has focused on generating higher-quality pseudo labels from these weak annotations, leading to the development of numerous CAM-based approaches [43, 46], such as the Grad-CAM model [37], pixel affinity models [1], and saliency maps [24]. These CAM-based models have been used in early histopathological image segmentation studies, including HistoSegNet [3], OEEN [26], and the MLPS model [17]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.489, + 0.905, + 0.761 + ], + "angle": 0, + "content": "With advances in multimodal learning [40, 44], particularly the development of CLIP [36], which effectively aligns image and text embeddings, recent studies have incorporated textual information as additional supervision to reduce the discrepancy between image-level labels and pixel-level predictions in WSS. For instance, Xie et al. proposed CLIMS [50] and Deng et al. introduced QA-CLIMS [9], integrating textual information into WSS models using the pre-trained CLIP model [36]. In histopathological image segmentation, Zhang et al. proposed TPRO [57], which incorporates general descriptions of tissue characteristics into image features via an attention mechanism [42] to produce more accurate CAMs by aligning image features with textual descriptions. In contrast, our method utilizes image-level labels and the corresponding images to provide finer-grained guidance compared to text-based approaches, addressing the challenges of homogeneity and heterogeneity in histopathological images." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.772, + 0.685, + 0.788 + ], + "angle": 0, + "content": "2.2. Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.905, + 0.903 + ], + "angle": 0, + "content": "Prompt learning initially gained traction in Natural Language Processing (NLP) [10, 27], where models were guided in specific tasks through designed or learned prompts. With the rise of large-scale pre-trained multimodal models like CLIP [36], prompt engineering has extended to vision tasks [60, 61]. Early approaches relied on manually defined text templates (e.g., \"a photo of {class" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30272" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.137 + ], + "angle": 0, + "content": "name}\") to describe classes of interest and extract relevant knowledge [9, 50]. However, this trial-and-error process is time-consuming and requires specific expertise." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.484, + 0.273 + ], + "angle": 0, + "content": "To address these limitations, learnable prompt-based methods were introduced for vision tasks [52, 60], replacing manual templates with a set of learnable text vectors preceding class names, thus automating the prompt generation process [60]. Additionally, some methods attempted to introduce image prompts through prototypes for few-shot image tasks [18, 48]. For example, Wang et al. [45] and Shen et al. [38] effectively utilized image prototypes for few-shot image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.274, + 0.484, + 0.35 + ], + "angle": 0, + "content": "In our method, we leverage prototype-based image prompts instead of text-based prompts. These image prompts offer finer-grained and more direct guidance, allowing the model to capture subtle visual differences that are challenging to describe using text alone." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.364, + 0.182, + 0.379 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.389, + 0.201, + 0.403 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.413, + 0.484, + 0.518 + ], + "angle": 0, + "content": "The key idea of our proposed PBIP framework is to leverage image-level labels and corresponding images to create a high-quality visual prototype feature bank, guiding the generation of more accurate CAMs as pseudo masks for WSS. As illustrated in Figure 2, the PBIP framework consists of two main components: a Classification Network (ClassNet) and an Image Feature Matching Network (ImgMatchNet)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.519, + 0.484, + 0.64 + ], + "angle": 0, + "content": "The ClassNet takes a histopathology image \\(\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times C}\\) from the dataset and the prototype feature vectors \\(\\mathbf{P}_i\\) from ImgMatchNet (as detailed in Section 3.4), where \\(H\\), \\(W\\), and \\(C\\) denote the height, width, and number of channels, respectively. ClassNet performs a classification task to generate initial pseudo-segmentation masks \\(\\mathbf{M} \\in \\mathbb{R}^{H \\times W \\times N}\\) and is optimized by a classification loss \\(\\mathcal{L}_{\\mathrm{CLS}}\\), where \\(N\\) denotes the number of classes in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.641, + 0.484, + 0.822 + ], + "angle": 0, + "content": "The ImgMatchNet receives the input histopathology image \\(\\mathbf{X}\\), an image bank constructed from the training set through clustering, and the pseudo-segmentation masks \\(\\mathbf{M}\\) generated by the ClassNet. ImgMatchNet extracts prototype features \\(\\mathbf{P}\\) using a CLIP image encoder from the image bank and refines the pseudo-segmentation masks \\(\\mathbf{M}\\) through a similarity matching loss \\(\\mathcal{L}_{\\mathrm{SIM}}\\). The refined masks \\(\\mathbf{M}\\) are merged via an argmax operation over the channel dimension to produce the final activation map for the first stage of WSS. These masks are subsequently used to train a fully supervised segmentation model in the second stage, generating the final segmentation masks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.832, + 0.345, + 0.848 + ], + "angle": 0, + "content": "3.2. Construction of Image Bank" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We construct an image bank that captures diverse visual prototypes for each class, which is automatically assembled from the training set. Specifically, we select tissue images" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.243 + ], + "angle": 0, + "content": "based on image-level labels that indicate the patch contains only one class (e.g., only tumor) and exclude images with excessive white regions automatically. These patches are grouped into \\( N \\) categories corresponding to the \\( N \\) classes in the dataset. To capture intra-class heterogeneity, \\( K \\)-Means clustering is applied within each category to partition the patches into \\( K \\) subcategories. For each subcategory, the top \\( N_K \\) images closest to the cluster center are selected as prototypes for the image bank. The distance metric used for clustering is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.252, + 0.907, + 0.287 + ], + "angle": 0, + "content": "\\[\nD _ {t} (x _ {1}, x _ {2}) = 1 - \\frac {\\phi_ {e} (x _ {1}) \\cdot \\phi_ {e} (x _ {2})}{\\| \\phi_ {e} (x _ {1}) \\| \\| \\phi_ {e} (x _ {2}) \\|}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.293, + 0.906, + 0.385 + ], + "angle": 0, + "content": "where \\( x_{1} \\) and \\( x_{2} \\) are two image patches, \\( \\phi_{e} \\) denotes the feature extraction function of the CLIP image encoder, and the symbol \\( \\cdot \\) denotes the dot product operation between vectors. This process results in an image bank comprising \\( N \\) classes, each containing \\( K \\) subcategories, with each subcategory holding \\( N_{K} \\) representative images." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.392, + 0.724, + 0.407 + ], + "angle": 0, + "content": "3.3. Classification Network" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.415, + 0.906, + 0.491 + ], + "angle": 0, + "content": "The ClassNet generates the initial pseudo-segmentation masks \\(\\mathbf{M}\\) by leveraging both the input image \\(\\mathbf{X}\\) and the prototype features \\(\\mathbf{P}\\). We adopt SegFormer [49] as the backbone due to its efficacy in capturing multi-scale contextual information through its hierarchical transformer encoder." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.491, + 0.907, + 0.675 + ], + "angle": 0, + "content": "Given an input histopathology image \\(\\mathbf{X}\\), hierarchical feature maps \\(\\mathbf{F}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times C_i}\\) are extracted across different stages \\(i = 1,2,3\\) with \\(C_{i + 1} > C_i\\), where \\(C_i\\) corresponds to the number of channels at each hierarchical level \\(i\\) of the feature maps. To generate the initial pseudo masks, the cosine similarity is computed (SIM) between each pixel feature vector in \\(\\mathbf{F}_i\\) and the prototype feature vectors in \\(\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}\\). This computation produces confidence scores for each pixel across all classes, forming the pseudo-segmentation masks \\(\\mathbf{M}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times N}\\). The confidence score for pixel \\(p\\) and class \\(n\\) at level \\(i\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.683, + 0.907, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {i} (p, n) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {\\mathbf {F} _ {i} (p) \\cdot \\mathbf {P} _ {i} (n , k)}{\\| \\mathbf {F} _ {i} (p) \\| \\left. \\mathbf {P} _ {i} (n , k) \\right\\|}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.906, + 0.825 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}_i(p)\\) is the feature vector of pixel \\(p\\) in \\(\\mathbf{F}_i\\), and \\(\\mathbf{P}_i(n, k)\\) is the \\(k\\)-th prototype feature vector for class \\(n\\). By averaging the cosine similarities over all prototypes \\(K\\) for each class, it effectively captures intra-class variations and obtains a robust confidence score that reflects the likelihood of the pixel \\(p\\) belonging to the class \\(n\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.812, + 0.849 + ], + "angle": 0, + "content": "3.4. Image Feature Matching Network" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "ImgMatchNet introduces image prompts through a prototype-based approach. It generates prototype features \\(\\mathbf{P}\\) from the image bank, and then ClassNet is used to" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30273" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.092, + 0.472, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.48, + 0.092, + 0.899, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.231, + 0.476, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.232, + 0.899, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.361, + 0.907, + 0.462 + ], + "angle": 0, + "content": "Figure 2. Structure of the proposed PBIP framework. Overview. PBIP consists of two main components: a Classification Network(ClassNet) and an Image Feature Matching Network(ImgMatchNet), which leverage an external image bank to provide image prompts in the form of prototypes. Image Bank. Training images are grouped by their labels and clustered into \\( K \\) subclasses per class. For each subclass, \\( N_K \\) representative images are selected to build the image bank. ClassNet. It receives an input image \\( \\mathbf{X} \\) and prototype features \\( \\mathbf{P} \\), performing a classification task to generate the pseudo-segmentation mask \\( \\mathbf{M} \\). ImgMatchNet. It processes the input image \\( \\mathbf{X} \\) and the initial pseudo-segmentation mask \\( \\mathbf{M} \\), extracting foreground and background regions. These regions are then matched with \\( \\mathbf{P} \\) from the image bank to refine the pseudo mask generation." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.472, + 0.483, + 0.547 + ], + "angle": 0, + "content": "compute pixel-level class confidences in the feature maps. To extract these prototype features, we employ the image encoder from the pre-trained MedCLIP model [47], a variant of the CLIP architecture tailored for medical images and trained on large-scale medical image-text pairs." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.551, + 0.483, + 0.763 + ], + "angle": 0, + "content": "All images in the image bank are encoded using the MedCLIP image encoder, producing feature representations denoted as \\(\\mathbf{F}_p\\in \\mathbb{R}^{N\\times K\\times N_K\\times d}\\), where \\(N\\) is the number of classes in the dataset, \\(K\\) is the number of subclasses per class determined by the clustering, \\(N_{K}\\) is the number of images per subclass, and \\(d\\) is the dimension of the feature space. The mean feature vector is computed for each subclass across its images to obtain the prototype features, yielding \\(\\mathbf{P}\\in \\mathbb{R}^{N\\times K\\times d}\\). To align these prototype features with the hierarchical feature maps generated by the ClassNet, we employ a Multi-Layer Perceptron (MLP) composed of fully connected layers and ReLU activations. The MLP projects the prototype features to match the dimensionality of each feature level, producing \\(\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.766, + 0.483, + 0.843 + ], + "angle": 0, + "content": "ImgMatchNet includes a foreground-background separation module to further refine the pseudo-masks obtained from the ClassNet. Specifically, this module upsamples and aggregates the hierarchical pseudo-masks from different feature levels to obtain a comprehensive pseudo-mask:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.863, + 0.483, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {\\prime} = \\sum_ {i = 1} ^ {3} \\operatorname {U p} \\left(\\mathbf {M} _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.905, + 0.502 + ], + "angle": 0, + "content": "where \\(\\mathbf{M}' \\in \\mathbb{R}^{H \\times W \\times N}\\), and \\(\\mathrm{Up}(\\cdot)\\) denotes the upsampling operation to match the original image resolution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.502, + 0.906, + 0.593 + ], + "angle": 0, + "content": "We employ an adaptive thresholding module to separate foreground and background regions. This module computes an adaptive threshold \\(\\tau\\) based on the intensity distribution of the pseudo-mask, dynamically distinguishing between foreground and background to reduce noise. The adaptive threshold is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.601, + 0.905, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\tau = \\delta \\cdot \\max (\\mathbf {M}), \\quad \\delta \\in [ 0, 1 ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.906, + 0.718 + ], + "angle": 0, + "content": "where \\(\\delta\\) is a scaling parameter that controls the threshold level. Applying this threshold to the activation map yields a binary mask \\(b\\in \\mathbb{R}^{H\\times W\\times N}\\), where pixel values greater than or equal to \\(\\tau\\) are set to 1 (foreground), and values below \\(\\tau\\) are set to 0 (background). We then separate foreground and background images through element-wise multiplication:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.724, + 0.905, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {\\mathrm {F G}} = b \\cdot \\mathbf {M} \\cdot \\mathbf {X}, \\quad \\mathbf {X} _ {\\mathrm {B G}} = (1 - b) \\cdot (1 - \\mathbf {M}) \\cdot \\mathbf {X}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.748, + 0.906, + 0.84 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}_{\\mathrm{FG}},\\mathbf{X}_{\\mathrm{BG}}\\in \\mathbb{R}^{H\\times W\\times N}\\) represent the separated foreground and background regions. By using the same MedCLIP image encoder and MLP, we extract hierarchical foreground and background features \\(\\mathbf{F}_{\\mathrm{FG}_i},\\mathbf{F}_{\\mathrm{BG}_i}\\in \\mathbb{R}^{N\\times C_i}\\). These features are then utilized in a similarity matching loss to optimize the generation of the pseudo-masks further." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.848, + 0.738, + 0.865 + ], + "angle": 0, + "content": "3.5. Optimization Objectives" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Our model is jointly optimized by two objectives: the classification loss \\(\\mathcal{L}_{\\mathrm{CLS}}\\), which ensures consistency between pre" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30274" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "dicted labels and image-level annotations, and the similarity loss \\(\\mathcal{L}_{\\mathrm{SIM}}\\), which promotes alignment between the encoded features of the foreground and background regions with their respective prototype features \\(\\mathbf{P}\\). The total loss function is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.179, + 0.483, + 0.195 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C L S}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S I M}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.206, + 0.483, + 0.236 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are weighting coefficients that balance the contribution of each loss term." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.237, + 0.484, + 0.342 + ], + "angle": 0, + "content": "Classification Loss. Image-level class predictions \\(\\hat{y} \\in \\mathbb{R}^{3 \\times N}\\) are obtained by applying global average pooling to the pseudo-segmentation masks \\(\\mathbf{M}\\) from each hierarchical level in the ClassNet, where 3 corresponds to the levels and \\(N\\) is the number of classes. The predictions are compared with the ground-truth labels \\(y \\in \\mathbb{R}^{1 \\times N}\\), and the classification loss for each level \\(i\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.354, + 0.483, + 0.371 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L S}} [ i ] = \\operatorname {C o s s E n t r o p y} (y, \\hat {y} [ i ]) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.382, + 0.484, + 0.412 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the sigmoid function. The total classification loss is a weighted sum:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.423, + 0.483, + 0.464 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L S}} = \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {\\mathrm {C L S}} [ i ]. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.474, + 0.484, + 0.519 + ], + "angle": 0, + "content": "Similarity Loss. The similarity loss \\(\\mathcal{L}_{\\mathrm{SIM}}\\) is divided into two components: the foreground similarity loss \\(\\mathcal{L}_{\\mathrm{FGS}}\\) and the background similarity loss \\(\\mathcal{L}_{\\mathrm{BGS}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.484, + 0.64 + ], + "angle": 0, + "content": "The foreground similarity loss \\(\\mathcal{L}_{\\mathrm{FGS}}\\) aligns the foreground image features with the corresponding foreground prototype features, while distinguishing them from the background prototype features. Formally, given the foreground image feature \\(F_{\\mathrm{FG}}[j]\\) for the \\(j\\)-th class, foreground prototype feature \\(P_{\\mathrm{FG}} = P[j]\\), and the background prototype features \\(P_{\\mathrm{BG}} = P[m]\\) where \\(1 \\leq m \\leq N\\) and \\(m \\neq j\\), the loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.112, + 0.662, + 0.483, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {F G S}} = - \\log \\left(\\frac {\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right)}{\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right) + \\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} / \\tau\\right)}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.725, + 0.138, + 0.737 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.749, + 0.483, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {F G}}\\right), \\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.87 + ], + "angle": 0, + "content": "where \\(\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FF}}\\) is the sum of similarity scores between the foreground feature and the foreground prototype of the \\(j\\)-th class, while \\(\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FB}}\\) is the sum of similarity scores between the foreground feature of the \\(j\\)-th class and the background prototype. The temperature parameter \\(\\tau\\) controls the concentration level of the distribution." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Similarly, \\(\\mathcal{L}_{\\mathrm{BGS}}\\) aligns background image features with background prototype features while distinguishing them" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.153 + ], + "angle": 0, + "content": "from foreground prototype features. Given the background image feature \\( F_{\\mathrm{BG}}[j] \\), the background prototype feature \\( P_{\\mathrm{BG}} = P[j] \\) for the \\( j \\)-th region, and the foreground prototype features \\( P_{\\mathrm{FG}} = P[m] \\), the loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.176, + 0.907, + 0.229 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {B G S}} = - \\log \\left(\\frac {\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}{\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j} , \\mathrm {j}} ^ {\\mathrm {B F}} / \\tau\\right) + \\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}\\right), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.242, + 0.907, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} = \\operatorname {m e a n} \\left(F _ {\\mathrm {B G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.269, + 0.907, + 0.33 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{s}}_j^{\\mathrm{BB}}\\) is the mean of similarity scores between the background feature of the \\(j\\)-th class and the background prototype. The total similarity loss is the combination of the two components:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.342, + 0.906, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {S I M}} = \\theta_ {1} \\cdot \\mathcal {L} _ {\\mathrm {F G S}} + \\theta_ {2} \\cdot \\mathcal {L} _ {\\mathrm {B G S}}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.371, + 0.907, + 0.402 + ], + "angle": 0, + "content": "where \\(\\theta_{1}\\) and \\(\\theta_{2}\\) are weights that balance the importance of the foreground and background similarity terms." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.415, + 0.649, + 0.431 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.439, + 0.704, + 0.456 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.906, + 0.553 + ], + "angle": 0, + "content": "Datasets. We evaluated our method on four histopathological datasets. BCSS [2] consists of 151 H&E-stained breast cancer images from TCGA-BRCA, annotated with four classes (Tumor, Stroma, Lymphocytic infiltrate, Necrosis), and includes 30,000 training patches, 2,500 validation patches and 2,500 testing patches." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.553, + 0.906, + 0.599 + ], + "angle": 0, + "content": "BCSS-WSSS [17] is derived from BCSS for WSS with 23,422 training patches, 3,418 validation patches and 4,986 testing patches." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.599, + 0.906, + 0.674 + ], + "angle": 0, + "content": "LUAD-HistoSeg [17] contains 17,291 H&E-stained lung adenocarcinoma patches, annotated with four classes (Tumor Epithelium, Stroma, Necrosis, and Lymphocytes), with 16,678 training patches, 306 validation patches and 307 testing patches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.906, + 0.75 + ], + "angle": 0, + "content": "GCSS [39] comprises 100 H&E-stained Gastric cancer images from TCGA-STAD gastric cancer images, annotated with four classes (Tumor, Lymphoid Stroma, Desmoplastic Stroma, Smooth Muscle Necrosis) providing 20,000 training, 2,500 validation patches and 2,500 testing patches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.84 + ], + "angle": 0, + "content": "BCSS-WSSS and LUAD-HistoSeg are used exclusively for weakly supervised segmentation tasks, as the training images are labelled only at the image level, with the validation and test sets still including ground truth masks for evaluation purposes. More details about datasets are in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Implementation Details. The ClassNet utilizes the Mix Transformer from SegFormer [49] as its backbone, which is pretrained on ImageNet-1K. The ImgMatchNet is built upon an image bank assembled from the training set, where" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30275" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.904, + 0.426 + ], + "angle": 0, + "content": "
DatasetBCSS-WSSS [17]LUAD-HistoSeg [17]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
WHistoSegNet [3]32.19±5.835.69±5.919.24±1.748.70±6.845.32±4.345.08±3.918.36±1.162.37±4.3
TransWS [56]40.25±0.0--57.39±0.056.27±0.0--72.02±0.0
OEEN [26]59.93±0.561.11±0.825.09±1.274.95±0.472.54±0.271.65±0.226.15±1.484.08±0.2
MLPS [17]65.17±1.769.65±1.935.19±0.578.91±1.173.54±2.173.15±1.127.77±0.984.75±1.4
TPRO [57]63.92±0.464.45±0.225.79±0.577.99±0.374.14±0.874.01±0.227.46±0.385.14±0.5
CLIMS [50]38.98±2.437.58±2.113.52±0.956.09±2.639.45±3.138.92±2.717.55±1.656.58±3.0
QA-CLIMS [9]22.45±9.724.87±8.211.15±2.436.67±11.221.97±8.620.63±8.910.67±2.136.03±10.0
Proto2Seg [32]67.86±0.9*72.48±1.1*35.54±0.4*81.00±0.9*74.91±1.2*74.52±1.0*30.71±0.5*85.97±1.2*
PBLP (Ours)69.54±0.674.52±0.537.17±0.482.03±0.576.44±0.575.19±0.530.64±0.386.64±0.3
DatasetGCSS [39]BCSS [2]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
F&SSSPCL [39]51.63±0.0--68.10±0.062.47±0.0--76.90±0.0
SAM-Path [54]58.78±0.959.01±0.758.78±0.973.11±0.363.27±0.863.35±0.725.10±0.777.50±0.6
SAM2-Path [55]57.06±0.656.50±0.622.32±0.472.66±0.761.57±0.662.01±0.623.77±0.476.21±0.5
WHistoSegNet [3]30.02±6.231.25±5.410.10±3.646.15±7.022.15±7.822.80±8.012.11±4.136.27±8.9
OEEN [26]45.89±2.847.14±2.515.33±1.862.91±3.147.50±0.448.21±0.314.00±0.264.41±0.4
MLPS [17]51.20±1.752.85±1.519.10±1.367.72±2.449.32±1.151.31±1.321.08±0.766.06±0.9
TPRO [57]50.12±1.951.73±1.718.50±1.169.84±1.850.97±0.351.01±0.317.88±0.467.52±0.2
CLIMS [50]32.03±3.031.89±2.715.22±1.848.52±3.336.12±4.636.77±3.012.16±1.153.07±4.2
QA-CLIMS [9]25.01±8.326.54±7.612.34±4.240.02±9.023.00±9.924.07±9.110.27±3.637.39±12.2
Proto2Seg [32]53.23±2.853.97±2.922.34±1.770.84±2.055.34±2.056.72±2.022.40±1.570.78±2.1
PBLP (Ours)55.10±1.357.05±1.221.40±0.971.05±1.455.28±0.856.30±0.823.65±0.371.20±0.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.436, + 0.907, + 0.507 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of various methods on four histopathological datasets. The best results are highlighted in bold. \"Sup.\" denotes the type of supervision used: \\( \\mathcal{F} \\& \\mathcal{S} \\) represents fully and semi-supervised methods, while \\( \\mathcal{W} \\) indicates weakly supervised methods. Except for CLIMS and QA-CLIMS (designed for natural image segmentation), all methods are specifically tailored for histopathological image segmentation. For the BCSS-WSSS and LUAD-HistoSeg, the \\( p \\)-values from t-tests comparing our model with the second-best results* were calculated, and all \\( p \\)-values were less than 0.05." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.518, + 0.482, + 0.588 + ], + "angle": 0, + "content": "
CLCSFGMBGMmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓62.08±0.363.00±0.425.73±0.276.60±0.3
✓✓55.01±2.859.47±2.520.44±1.070.98±3.0
✓✓50.23±2.452.11±1.719.20±0.766.87±2.7
✓✓62.34±1.664.08±1.925.68±0.776.80±1.5
✓✓✓67.54±0.669.42±0.733.00±0.480.63±0.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.597, + 0.483, + 0.639 + ], + "angle": 0, + "content": "Table 2. Ablation study of different loss function combinations on the initial pseudo masks quality (mIoU%) for the BCSS-WSSS dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.654, + 0.483, + 0.699 + ], + "angle": 0, + "content": "the number of clusters \\( K \\) in \\( K \\)-Means was set to 3, and each subclass contains \\( N_K = 100 \\). The scaling parameter \\( \\delta \\) in the adaptive thresholding module was 0.15." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.483, + 0.868 + ], + "angle": 0, + "content": "During training, we utilized the AdamW optimizer with an initial learning rate of \\(1 \\times 10^{-5}\\) and a weight decay of 0.003. The total loss function combines the classification loss and similarity loss with weighting factors \\(\\alpha = 1\\) and \\(\\beta = 0.5\\), respectively. The temperature parameter in both \\(\\mathcal{L}_{\\mathrm{FGS}}\\) and \\(\\mathcal{L}_{\\mathrm{BGS}}\\) was set to 1, while \\(\\theta_{1}\\) and \\(\\theta_{2}\\) were set to 1 and 0.5, respectively. The model was trained for 10 epochs, with a batch size of 10 during the first stage. In the second stage in WSS, an unmodified Deeplab-v2 model [5] was trained as a fully supervised segmentation model. All models were trained on a single 4090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To quantitatively evaluate our method, we employed four standard metrics: Mean Intersection over Union (mIoU)," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.521, + 0.907, + 0.598 + ], + "angle": 0, + "content": "Frequency Weighted IoU (FWIoU), Boundary IoU (bIoU), and Dice Coefficient. We also calculated p-values from t-tests to indicate the statistical significance of our results, measuring the probability that the observed differences occurred by chance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.609, + 0.608, + 0.625 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.645, + 0.707, + 0.748 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.752, + 0.666, + 0.765 + ], + "angle": 0, + "content": "(a) Analysis of \\(\\beta /\\alpha\\)" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.645, + 0.905, + 0.75 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.749, + 0.752, + 0.869, + 0.765 + ], + "angle": 0, + "content": "(b) Analysis of \\(\\theta_{2} / \\theta_{1}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.776, + 0.907, + 0.806 + ], + "angle": 0, + "content": "Figure 3. Ablation study on hyperparameter ratios. The mIoU values are reported on initial pseudo masks for BCSS-WSSS." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We compared our model with ten advanced methods, including three supervised models and five weakly supervised models, two state-of-the-art text-prompted weakly supervised models. We used the reported results for SSPCL and TransWS due to the unavailability of publicly available" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30276" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.482, + 0.302 + ], + "angle": 0, + "content": "
DatasetBCSS
EncoderBackbonemIoU(%)FwIoU(%)bIoU(%)dice(%)
CLIP [36]SegFormer66.45±0.372.42±0.327.05±0.280.56±0.2
ResNet1865.87±0.270.40±0.323.23±0.378.95±0.2
ResNet3866.10±0.471.22±0.426.56±0.279.86±0.3
ResNet5065.30±0.470.21±0.423.31±0.378.27±0.3
TransUNet60.17±0.463.52±0.517.81±0.275.12±0.5
MedCLIP [47]SegFormer68.01±0.673.20±0.536.88±0.481.62±0.5
ResNet1867.17±0.472.60±0.333.99±0.380.64±0.4
ResNet3867.18±0.572.57±0.535.18±0.380.93±0.4
ResNet5067.03±0.372.11±0.233.98±0.480.26±0.2
TransUNet62.09±0.566.89±0.520.15±0.376.61±0.5
PLIP [19]SegFormer67.16±0.773.53±0.537.21±0.481.77±0.5
ResNet1866.89±0.673.00±0.433.01±0.480.16±0.5
ResNet3867.02±0.573.24±0.535.85±0.480.25±0.4
ResNet5066.75±0.472.48±0.332.17±0.280.05±0.4
TransUNet61.98±0.666.01±0.521.54±0.376.53±0.6
DINOv2 [31]SegFormer66.37±0.872.38±0.932.01±0.380.24±0.8
ResNet3865.01±0.670.47±0.631.90±0.479.23±0.6
TransUNet61.00±0.462.71±0.520.22±0.276.64±0.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.312, + 0.483, + 0.368 + ], + "angle": 0, + "content": "Table 3. Performance comparison of different combinations of image encoders (CLIP, MedCLIP, PLIP, DINOv2) and backbones (SegFormer, ResNet variants, TransUNet) on initial pseudo masks for BCSS-WSSS." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.379, + 0.483, + 0.501 + ], + "angle": 0, + "content": "code. All other models were retrained and tested with five random seeds for robustness. Proto2Seg is a model based on human feedback; in our comparison with Proto2Seg, we carefully selected patches that met the required criteria using existing patch-level and image-level annotations instead of performing manual cutting and human feedback labelling. This might lead to a performance improvement for the Proto2Seg model." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.501, + 0.483, + 0.637 + ], + "angle": 0, + "content": "As shown in Table 1, our PBIP framework generally outperforms state-of-the-art weakly supervised methods across the four datasets. Specifically, on BCSS-WSSS, LUAD-HistoSeg and GCSS, our method outperforms Proto2Seg by \\(1.68\\%\\), \\(1.53\\%\\) and \\(1.87\\%\\) in mIoU, achieving the best weakly supervised performance. All \\(p\\)-values between our model and the second best on BCSS-WSSS and LUAD-HistoSeg are below 0.05, confirming the statistical significance of our improvements." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.483, + 0.82 + ], + "angle": 0, + "content": "Figure 5 shows the pseudo masks generated during the first stage of WSS models. We compared PBIP with MLPS, TPRO, and CLIMS. MLPS ranks third on BCSS-WSSS, while TPRO achieves the third-best on LUAD based. CLIMS is a text-supervised segmentation model for natural images. The results indicate that PBIP activates more complete object content and fewer background regions, while TPRO offers slight improvement over MLPS and CLIMS shows many errors. Text features do not enhance histopathological segmentation, and text supervision can mislead the model due to inter-class homogeneity and intra-class heterogeneity in histopathological images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.832, + 0.255, + 0.846 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Ablation study of Image Bank. We investigated the impact of the number of prototype images by randomly selecting images without clustering, using 10 different random" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.905, + 0.155 + ], + "angle": 0, + "content": "
K12345
DatasetmIoU(%)mIoU(%)mIoU(%)mIoU(%)mIoU(%)
BCSS-WSSS67.03±0.467.15±0.468.01±0.667.81±0.767.53±0.7
LUAD-HistoSeg74.91±0.575.12±0.574.87±0.673.72±1.274.07±0.8
GCSS51.26±0.852.07±0.853.21±1.253.91±1.053.54±0.9
BCSS54.01±0.653.97±0.854.05±0.853.87±1.053.50±0.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.166, + 0.905, + 0.235 + ], + "angle": 0, + "content": "Table 4. Ablation study on the number of clusters \\( K \\) in \\( \\mathrm{k} \\) -means across different datasets. The mIoU values on initial pseudo masks for BCSS-WSSS are reported with standard deviation. The optimal \\( K \\) value varies per dataset,with \\( K = 2 \\) to \\( K = 4 \\) generally achieving the highest performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.252, + 0.907, + 0.479 + ], + "angle": 0, + "content": "seeds for robustness. In Figure 4, \"Proto Num\" represents the number of images per sub-bank per category. The results show that the average mIoU improves as the number of prototype images increases. Using all eligible training images yielded a mIoU of \\(69.15\\%\\), suggesting that more images help reduce noise in prototype computation. However, due to inter-class homogeneity, simply increasing the number is not the most effective approach. The highest mIoU of \\(69.52\\%\\) was achieved with 100 images per sub-bank. When clustering was applied to select 100 images, the mIoU further increased to \\(69.60\\%\\). This demonstrates that selecting representative images through clustering is more effective than merely increasing quantity, as clustering captures the most discriminative features and mitigates challenges posed by inter-class homogeneity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.481, + 0.906, + 0.618 + ], + "angle": 0, + "content": "Additionally, we analyzed the impact of the number of clusters \\( K \\) in \\( K \\)-Means. As shown in Table 4, the best results across all datasets were obtained when \\( K \\) was set between 2 and 4, indicating that the optimal choice of \\( K \\) may depend on the level of inter-class homogeneity and intra-class heterogeneity within the dataset. Specifically, a small \\( K \\) prevents the model from adequately capturing intra-class heterogeneity, and an excessively high \\( K \\) amplifies the influence of inter-class homogeneity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.619, + 0.906, + 0.786 + ], + "angle": 0, + "content": "Ablation study of the Loss Function. We analyzed the impact of different loss function configurations. Specifically, we varied the weighting ratios \\(\\beta/\\alpha\\) (for \\(\\mathcal{L}_{\\mathrm{SIM}}\\) and \\(\\mathcal{L}_{\\mathrm{CLS}}\\)) and \\(\\theta_{2}/\\theta_{1}\\) (for \\(\\mathcal{L}_{\\mathrm{BGS}}\\) and \\(\\mathcal{L}_{\\mathrm{FGS}}\\)), as illustrated in Figure 3. The results indicate that extreme values of these ratios lead to a decline in performance. Furthermore, excluding either \\(\\mathcal{L}_{\\mathrm{FGS}}\\) or \\(\\mathcal{L}_{\\mathrm{BGS}}\\) causes the mIoU to drop significantly from \\(67.54\\%\\) to \\(50.23\\%\\) and \\(55.01\\%\\), respectively. This substantial decrease suggests that both components are essential; relying solely on one causes the model to focus excessively on either the foreground or background, lead" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.801, + 0.905, + 0.859 + ], + "angle": 0, + "content": "
SIMATmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓63.25±0.566.80±0.425.89±0.377.98±0.4
✓67.09±0.673.01±0.627.48±0.579.92±0.6
✓✓68.01±0.673.20±0.536.88±0.481.62±0.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.868, + 0.905, + 0.897 + ], + "angle": 0, + "content": "Table 5. Ablation study on the impact of SIM and Adaptive Thresholding (AT) on initial pseudo masks for BCSS-WSSS." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30277" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.088, + 0.482, + 0.18 + ], + "angle": 0, + "content": "
PromptModelTUMSTRLYMNECMean
TextCLIP [36]0.0050.0010.1350.0020.035
PLIP [19]0.7780.0080.3190.1360.310
MedCLIP [47]0.4230.0200.1650.2050.203
ImageCLIP [36]0.7160.2140.5290.0190.370
PLIP [19]0.9240.9200.8160.8350.874
MedCLIP [47]0.8810.8950.7900.6710.809
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.19, + 0.483, + 0.234 + ], + "angle": 0, + "content": "Table 6. Zero-shot classification F1 scores \\((\\%)\\) on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with text and image prompts." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.248, + 0.48, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.466 + ], + "angle": 0, + "content": "Figure 4. Ablation study of the number of prototype images. Proto Num represents the number of prototype images per sub-bank for each category. We report the mIoU values with Standard Deviation obtained over 10 runs with different random seeds." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.479, + 0.373, + 0.493 + ], + "angle": 0, + "content": "ing to incomplete or erroneous activations." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.493, + 0.483, + 0.705 + ], + "angle": 0, + "content": "Ablation study of the Modules. We analyzed the effectiveness of different modules within PBLP. As shown in Table 5, both the SIM and the Adaptive Thresholding Module significantly enhance model performance. Specifically, when the SIM module is removed, we substitute it with a simple \\(1 \\times 1\\) convolutional layer to generate the pseudo-segmentation masks. The results demonstrate a noticeable decline in performance without the SIM and AT module. The SIM module captures intra-class heterogeneity and inter-class homogeneity better than the \\(1 \\times 1\\) convolutional layer. Furthermore, Figure 1 illustrates the foreground images generated by the model with and without the AT module. The results demonstrate that AT effectively reduces noise in background regions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Additionally, we evaluated the performance of our model using different image encoders and backbones, as summarized in Table 3. The combination of MedCLIP [47] and SegFormer achieved the best results in terms of mIoU metric. We observed that the PLIP [19] and SegFormer pairing performed best on the bIoU, FWIoU, and Dice coefficient. The TransUNet model [4], with its end-to-end architecture that does not utilize the SIM module for pseudo-mask computation, exhibited inferior performance. These results suggest that the absence of the SIM module may contribute to the lower effectiveness. Moreover, the relatively poor performance of CLIP [36] and DINOv2 [31] further highlights the importance of external knowledge from pretraining in" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.09, + 0.907, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.287, + 0.907, + 0.371 + ], + "angle": 0, + "content": "Figure 5. a. Visualization of the pseudo-segmentation masks generated by models in the first stage on BCSS-WSSS. The masks are overlaid on the input images, with the raw pseudo-segmentation mask shown in the top-left corner. b. The foreground images generated by PBIP for the four segmentation targets. More visualizations are in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.905, + 0.42 + ], + "angle": 0, + "content": "histopathology, as these more generic encoders appear less effective for the specialized task of tissue segmentation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.421, + 0.907, + 0.663 + ], + "angle": 0, + "content": "Text prompt and Image prompt. To explore the challenges of image-text matching in histopathology, we conducted zero-shot classification experiments on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with both text and image prompts (see Table 6). For text prompts, we used the common format: \"a photo of {class name} \", while for image prompts, we utilized our prototype image features. The results show that PLIP and MedCLIP significantly outperform CLIP when using image prompts, but all models perform poorly with text prompts. This highlights the substantial challenges of text prompting in histopathology, where textual descriptions struggle to capture complex visual patterns and inter-class homogeneity. In contrast, image prompts effectively guide the models by aligning with the intricate characteristics of histopathological images through prototype features." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.68, + 0.634, + 0.696 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.706, + 0.907, + 0.889 + ], + "angle": 0, + "content": "We proposed a novel Prototype-Based Image Prompting (PBIP) framework to address the challenges of inter-class homogeneity and intra-class heterogeneity in weakly supervised histopathological image segmentation. PBIP leverages image-based labels and corresponding images in histopathology datasets by extracting class prototype features through clustering methods. By incorporating class prototypes, our approach effectively mitigates inter-class homogeneity, while multiple sub-prototypes for each class address intra-class heterogeneity. Validation on four datasets demonstrated that PBIP achieves state-of-the-art performance and robustness in weakly supervised histopathological segmentation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30278" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.483, + 0.156 + ], + "angle": 0, + "content": "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. 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National science review, 5(1):44-53, 2018. 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30280" + } + ] +] \ No newline at end of file diff --git a/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_origin.pdf b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9e5b519bf28a4c1559d7c14ecacd5f86808d896d --- /dev/null +++ b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/3d418639-aae6-43b4-aad7-bbaf79e8d3c9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:373a8e8b8c5342432bedde8be793e333fe64378419d9ae9a04954901677b4f3a +size 5801371 diff --git a/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/full.md b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..53c33409ea4cf79ee5da8bae3c692d6246a28ea2 --- /dev/null +++ b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/full.md @@ -0,0 +1,362 @@ +# Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation + +Qingchen Tang* Lei Fan* Maurice Pagnucco Yang Song University of New South Wales + +{qingchen.tang@student, lei.fanl@, morri@cse, yang.song1@}.unsw.edu.au + +# Abstract + +Weakly supervised image segmentation with image-level labels has drawn attention due to the high cost of pixel-level annotations. Traditional methods using Class Activation Maps (CAMs) often highlight only the most discriminative regions, leading to incomplete masks. Recent approaches that introduce textual information struggle with histopathological images due to inter-class homogeneity and intraclass heterogeneity. In this paper, we propose a prototype-based image prompting framework for histopathological image segmentation. It constructs an image bank from the training set using clustering, extracting multiple prototype features per class to capture intra-class heterogeneity. By designing a matching loss between input features and class-specific prototypes using contrastive learning, our method addresses inter-class homogeneity and guides the model to generate more accurate CAMs. Experiments on four datasets (LUAD-HistoSeg, BCSS-WSSS, GCSS, and BCSS) show that our method outperforms existing weakly supervised segmentation approaches, setting new benchmarks in histopathological image segmentation. $^{1}$ + +# 1. Introduction + +Automated segmentation of histopathology images plays a crucial role in computer-aided diagnosis, assisting in the identification of abnormal tissue regions, quantification of tumor microenvironments [58], and the support of tumor grading and prognosis [11-14, 51]. Existing methods largely depend on extensive high-quality annotated data [28, 30, 41], while pixel-level annotations present particular challenges due to the significant domain expertise and time required for their creation [15, 33, 62]. To reduce this requirement, weakly supervised segmentation (WSS) frameworks [20, 56, 57] have been proposed as a more label-efficient alternative, utilizing weak but easily acces + +![](images/69a37f233894a9c8ea5832a71a64c0a20910480d8fd395095b549a668f5939fa.jpg) +a + +![](images/77e5ead71ad4844a7b639ca85f0992cd0e6c82b3397c896e88b8f99a39ca76f2.jpg) +b + +![](images/bd457940bea09c32f336d78a7a4e2d081cb50bbc6d71222adf315ab829301851.jpg) + +![](images/bd3a02ed4ccef791acb8bc1d93dd2efd18539991b41663813afb94da1bbee66d.jpg) +Figure 1. a. Four supervision frameworks for histopathological image segmentation: fully supervised with pixel-level masks, CAM-based WSS using image labels, textural-based WSS, and our image prompt-based framework. b. The challenges of inter-class homogeneity (variable texture and staining within classes) and intra-class heterogeneity (similar appearances across classes). Cosine similarities are computed using features extracted by the MedCLIP model [47]. + +![](images/0d4e34ae5667d945ed7d677c88dd60d3bfbca0564c4da91a4d6ea0a58df323bf.jpg) + +![](images/10dc851bf0a42bcf02599499ed88142267797b96e1c6a565a4de62b08587e926.jpg) + +sible labels such as bounding boxes [21, 35], scribbles [29], point annotations [34], and image-level labels [56, 57]. Typically, WSS methods employ a two-stage process: a classification network is first trained using weak labels to generate pseudo-labels, such as class activation maps (CAMs) [59]. These pseudo-labels are then utilized as refined supervision signals to train a fully supervised network [17, 57, 59]. + +However, CAMs generated from image-level labels often focus on the most discriminative regions, leading to incomplete localization of target objects and confusion between target and non-target areas [23, 50]. This limitation arises from a domain gap in pre-trained models, which are often trained on source domains (e.g., ImageNet [8]) that differ from the target domain (e.g., histopathology), causing CAMs to focus on features misaligned with those of the target domain. Early studies have explored various strategies to improve CAM quality, such as pixel affinity models [1] and saliency map integration [24]. Recent studies have utilized textual information to bridge the gap between image-level labels and pixel-level segmentation [9, 50, 57]. As illustrated in Figure 1, these approaches incorporate textual descriptions (e.g., object type, colour, structure) into + +the model via pre-trained vision-language models, such as CLIP model [36]. + +While these methods have shown strong performance on popular segmentation benchmarks [9, 50], they face challenges in histopathological image segmentation. Tissue segmentation involves larger anatomical structures compared to general images or cell nucleus segmentation, with complex spatial arrangements, significant inter-class homogeneity, and intra-class heterogeneity [6, 25]. As illustrated in Figure 1.b, inter-class homogeneity refers to the visual similarity between different tissue types, making it difficult to differentiate target regions from surrounding tissues. For instance, non-tumor tissues may closely resemble tumor tissues, causing CAM-based methods [3, 17] to activate on irrelevant areas erroneously. Intra-class heterogeneity involves significant variability within the same tissue type, such as differences in staining, shape, and texture, which hampers text-based methods [9, 50, 57] from capturing fine-grained details, leading to misalignment between textual descriptions and pixel-level features. + +To address these challenges, we propose a Prototype-Based Image Prompting (PBIP) framework for WSS in histopathological segmentation. Unlike methods that rely on text prompts, we utilize image-level labels and their corresponding images to construct visual prototypes. This approach enables the model to discern nuanced visual variations that are challenging for text-based methods. The visual prototypes are achieved through a feature bank that serves as an additional supervisory signal to guide CAM refinement. More specifically, the PBIP framework consists of two main components: a classification network and a prototype-guided feature matching network. The classification network, based on a pre-trained model, extracts multiscale feature representations from the query image to produce pseudo-segmentation masks that indicate class-specific pixel regions. The prototype-guided network constructs a feature bank containing multiple prototypes for each tissue class to capture intra-class heterogeneity. The feature bank is constructed from the training set by organizing images into distinct prototypes based on their labels and employing a CLIP-based image encoder to extract semantically rich, pixel-level features. In addition, a contrastive learning-based similarity loss is computed between the prototypes and class-specific pixel regions, mitigating inter-class homogeneity and yielding high-precision CAMs in the first stage of WSS, which then serve as pseudo-labels for subsequent supervised training. + +The main contributions of this paper are as follows: + +- To the best of our knowledge, the proposed PBIP framework is the first WSS model in the histopathology domain that utilizes image prompts. By integrating a prototype-guided feature prompting mechanism through an image library, it addresses intra-class heterogeneity + +and inter-class homogeneity. + +- We design a CLIP-based image matching method that uses a contrastive learning approach to encourage the alignment of foreground features with their respective prototypes while maintaining distance from non-target prototypes, enhancing pixel-level segmentation in weakly supervised tasks. +- Extensive experiments on the LUAD-HistoSeg [17], BCSS-wsss [17], GCSS [39], and BCSS [2] demonstrate that our method outperforms the current state-of-the-art methods in weakly supervised tissue segmentation. + +# 2. Related Work + +# 2.1. Weakly Supervised Segmentation + +WSS methods aim to infer pixel-level segmentation from simpler labels such as image-level classification tags [7, 33], bounding boxes [22], or point annotations [16, 53]. Subsequent research has focused on generating higher-quality pseudo labels from these weak annotations, leading to the development of numerous CAM-based approaches [43, 46], such as the Grad-CAM model [37], pixel affinity models [1], and saliency maps [24]. These CAM-based models have been used in early histopathological image segmentation studies, including HistoSegNet [3], OEEN [26], and the MLPS model [17]. + +With advances in multimodal learning [40, 44], particularly the development of CLIP [36], which effectively aligns image and text embeddings, recent studies have incorporated textual information as additional supervision to reduce the discrepancy between image-level labels and pixel-level predictions in WSS. For instance, Xie et al. proposed CLIMS [50] and Deng et al. introduced QA-CLIMS [9], integrating textual information into WSS models using the pre-trained CLIP model [36]. In histopathological image segmentation, Zhang et al. proposed TPRO [57], which incorporates general descriptions of tissue characteristics into image features via an attention mechanism [42] to produce more accurate CAMs by aligning image features with textual descriptions. In contrast, our method utilizes image-level labels and the corresponding images to provide finer-grained guidance compared to text-based approaches, addressing the challenges of homogeneity and heterogeneity in histopathological images. + +# 2.2. Prompt Learning + +Prompt learning initially gained traction in Natural Language Processing (NLP) [10, 27], where models were guided in specific tasks through designed or learned prompts. With the rise of large-scale pre-trained multimodal models like CLIP [36], prompt engineering has extended to vision tasks [60, 61]. Early approaches relied on manually defined text templates (e.g., "a photo of {class + +name}") to describe classes of interest and extract relevant knowledge [9, 50]. However, this trial-and-error process is time-consuming and requires specific expertise. + +To address these limitations, learnable prompt-based methods were introduced for vision tasks [52, 60], replacing manual templates with a set of learnable text vectors preceding class names, thus automating the prompt generation process [60]. Additionally, some methods attempted to introduce image prompts through prototypes for few-shot image tasks [18, 48]. For example, Wang et al. [45] and Shen et al. [38] effectively utilized image prototypes for few-shot image segmentation. + +In our method, we leverage prototype-based image prompts instead of text-based prompts. These image prompts offer finer-grained and more direct guidance, allowing the model to capture subtle visual differences that are challenging to describe using text alone. + +# 3. Method + +# 3.1. Overview + +The key idea of our proposed PBIP framework is to leverage image-level labels and corresponding images to create a high-quality visual prototype feature bank, guiding the generation of more accurate CAMs as pseudo masks for WSS. As illustrated in Figure 2, the PBIP framework consists of two main components: a Classification Network (ClassNet) and an Image Feature Matching Network (ImgMatchNet). + +The ClassNet takes a histopathology image $\mathbf{X} \in \mathbb{R}^{H \times W \times C}$ from the dataset and the prototype feature vectors $\mathbf{P}_i$ from ImgMatchNet (as detailed in Section 3.4), where $H$ , $W$ , and $C$ denote the height, width, and number of channels, respectively. ClassNet performs a classification task to generate initial pseudo-segmentation masks $\mathbf{M} \in \mathbb{R}^{H \times W \times N}$ and is optimized by a classification loss $\mathcal{L}_{\mathrm{CLS}}$ , where $N$ denotes the number of classes in the dataset. + +The ImgMatchNet receives the input histopathology image $\mathbf{X}$ , an image bank constructed from the training set through clustering, and the pseudo-segmentation masks $\mathbf{M}$ generated by the ClassNet. ImgMatchNet extracts prototype features $\mathbf{P}$ using a CLIP image encoder from the image bank and refines the pseudo-segmentation masks $\mathbf{M}$ through a similarity matching loss $\mathcal{L}_{\mathrm{SIM}}$ . The refined masks $\mathbf{M}$ are merged via an argmax operation over the channel dimension to produce the final activation map for the first stage of WSS. These masks are subsequently used to train a fully supervised segmentation model in the second stage, generating the final segmentation masks. + +# 3.2. Construction of Image Bank + +We construct an image bank that captures diverse visual prototypes for each class, which is automatically assembled from the training set. Specifically, we select tissue images + +based on image-level labels that indicate the patch contains only one class (e.g., only tumor) and exclude images with excessive white regions automatically. These patches are grouped into $N$ categories corresponding to the $N$ classes in the dataset. To capture intra-class heterogeneity, $K$ -Means clustering is applied within each category to partition the patches into $K$ subcategories. For each subcategory, the top $N_K$ images closest to the cluster center are selected as prototypes for the image bank. The distance metric used for clustering is defined as: + +$$ +D _ {t} (x _ {1}, x _ {2}) = 1 - \frac {\phi_ {e} (x _ {1}) \cdot \phi_ {e} (x _ {2})}{\| \phi_ {e} (x _ {1}) \| \| \phi_ {e} (x _ {2}) \|}, \tag {1} +$$ + +where $x_{1}$ and $x_{2}$ are two image patches, $\phi_{e}$ denotes the feature extraction function of the CLIP image encoder, and the symbol $\cdot$ denotes the dot product operation between vectors. This process results in an image bank comprising $N$ classes, each containing $K$ subcategories, with each subcategory holding $N_{K}$ representative images. + +# 3.3. Classification Network + +The ClassNet generates the initial pseudo-segmentation masks $\mathbf{M}$ by leveraging both the input image $\mathbf{X}$ and the prototype features $\mathbf{P}$ . We adopt SegFormer [49] as the backbone due to its efficacy in capturing multi-scale contextual information through its hierarchical transformer encoder. + +Given an input histopathology image $\mathbf{X}$ , hierarchical feature maps $\mathbf{F}_i\in \mathbb{R}^{(H / 2^{i + 1})\times (W / 2^{i + 1})\times C_i}$ are extracted across different stages $i = 1,2,3$ with $C_{i + 1} > C_i$ , where $C_i$ corresponds to the number of channels at each hierarchical level $i$ of the feature maps. To generate the initial pseudo masks, the cosine similarity is computed (SIM) between each pixel feature vector in $\mathbf{F}_i$ and the prototype feature vectors in $\mathbf{P}_i\in \mathbb{R}^{N\times K\times C_i}$ . This computation produces confidence scores for each pixel across all classes, forming the pseudo-segmentation masks $\mathbf{M}_i\in \mathbb{R}^{(H / 2^{i + 1})\times (W / 2^{i + 1})\times N}$ . The confidence score for pixel $p$ and class $n$ at level $i$ is calculated as: + +$$ +\mathbf {M} _ {i} (p, n) = \frac {1}{K} \sum_ {k = 1} ^ {K} \frac {\mathbf {F} _ {i} (p) \cdot \mathbf {P} _ {i} (n , k)}{\| \mathbf {F} _ {i} (p) \| \left. \mathbf {P} _ {i} (n , k) \right\|}, \tag {2} +$$ + +where $\mathbf{F}_i(p)$ is the feature vector of pixel $p$ in $\mathbf{F}_i$ , and $\mathbf{P}_i(n, k)$ is the $k$ -th prototype feature vector for class $n$ . By averaging the cosine similarities over all prototypes $K$ for each class, it effectively captures intra-class variations and obtains a robust confidence score that reflects the likelihood of the pixel $p$ belonging to the class $n$ . + +# 3.4. Image Feature Matching Network + +ImgMatchNet introduces image prompts through a prototype-based approach. It generates prototype features $\mathbf{P}$ from the image bank, and then ClassNet is used to + +![](images/4900ad11ed4e68559000ec2eaa861d112b0f6a6f15e0e82c8fd2b57ee06c5932.jpg) + +![](images/f60bb0cd826f84ce2e8413e2f0481d328f55205c31425171aae6bb4a6d3f7bb3.jpg) + +![](images/ec8d5f4ebbba4c48168186720114465f2a70bff887552893306b18545238655a.jpg) +Figure 2. Structure of the proposed PBIP framework. Overview. PBIP consists of two main components: a Classification Network(ClassNet) and an Image Feature Matching Network(ImgMatchNet), which leverage an external image bank to provide image prompts in the form of prototypes. Image Bank. Training images are grouped by their labels and clustered into $K$ subclasses per class. For each subclass, $N_K$ representative images are selected to build the image bank. ClassNet. It receives an input image $\mathbf{X}$ and prototype features $\mathbf{P}$ , performing a classification task to generate the pseudo-segmentation mask $\mathbf{M}$ . ImgMatchNet. It processes the input image $\mathbf{X}$ and the initial pseudo-segmentation mask $\mathbf{M}$ , extracting foreground and background regions. These regions are then matched with $\mathbf{P}$ from the image bank to refine the pseudo mask generation. + +![](images/3d4da5fafc154f904e853f7a6d3713933ec48e40f8e6ae74863ad29b3216ea7c.jpg) + +compute pixel-level class confidences in the feature maps. To extract these prototype features, we employ the image encoder from the pre-trained MedCLIP model [47], a variant of the CLIP architecture tailored for medical images and trained on large-scale medical image-text pairs. + +All images in the image bank are encoded using the MedCLIP image encoder, producing feature representations denoted as $\mathbf{F}_p\in \mathbb{R}^{N\times K\times N_K\times d}$ , where $N$ is the number of classes in the dataset, $K$ is the number of subclasses per class determined by the clustering, $N_{K}$ is the number of images per subclass, and $d$ is the dimension of the feature space. The mean feature vector is computed for each subclass across its images to obtain the prototype features, yielding $\mathbf{P}\in \mathbb{R}^{N\times K\times d}$ . To align these prototype features with the hierarchical feature maps generated by the ClassNet, we employ a Multi-Layer Perceptron (MLP) composed of fully connected layers and ReLU activations. The MLP projects the prototype features to match the dimensionality of each feature level, producing $\mathbf{P}_i\in \mathbb{R}^{N\times K\times C_i}$ . + +ImgMatchNet includes a foreground-background separation module to further refine the pseudo-masks obtained from the ClassNet. Specifically, this module upsamples and aggregates the hierarchical pseudo-masks from different feature levels to obtain a comprehensive pseudo-mask: + +$$ +\mathbf {M} ^ {\prime} = \sum_ {i = 1} ^ {3} \operatorname {U p} \left(\mathbf {M} _ {i}\right), \tag {3} +$$ + +where $\mathbf{M}' \in \mathbb{R}^{H \times W \times N}$ , and $\mathrm{Up}(\cdot)$ denotes the upsampling operation to match the original image resolution. + +We employ an adaptive thresholding module to separate foreground and background regions. This module computes an adaptive threshold $\tau$ based on the intensity distribution of the pseudo-mask, dynamically distinguishing between foreground and background to reduce noise. The adaptive threshold is computed as: + +$$ +\tau = \delta \cdot \max (\mathbf {M}), \quad \delta \in [ 0, 1 ], \tag {4} +$$ + +where $\delta$ is a scaling parameter that controls the threshold level. Applying this threshold to the activation map yields a binary mask $b\in \mathbb{R}^{H\times W\times N}$ , where pixel values greater than or equal to $\tau$ are set to 1 (foreground), and values below $\tau$ are set to 0 (background). We then separate foreground and background images through element-wise multiplication: + +$$ +\mathbf {X} _ {\mathrm {F G}} = b \cdot \mathbf {M} \cdot \mathbf {X}, \quad \mathbf {X} _ {\mathrm {B G}} = (1 - b) \cdot (1 - \mathbf {M}) \cdot \mathbf {X}, \tag {5} +$$ + +where $\mathbf{X}_{\mathrm{FG}},\mathbf{X}_{\mathrm{BG}}\in \mathbb{R}^{H\times W\times N}$ represent the separated foreground and background regions. By using the same MedCLIP image encoder and MLP, we extract hierarchical foreground and background features $\mathbf{F}_{\mathrm{FG}_i},\mathbf{F}_{\mathrm{BG}_i}\in \mathbb{R}^{N\times C_i}$ . These features are then utilized in a similarity matching loss to optimize the generation of the pseudo-masks further. + +# 3.5. Optimization Objectives + +Our model is jointly optimized by two objectives: the classification loss $\mathcal{L}_{\mathrm{CLS}}$ , which ensures consistency between pre + +dicted labels and image-level annotations, and the similarity loss $\mathcal{L}_{\mathrm{SIM}}$ , which promotes alignment between the encoded features of the foreground and background regions with their respective prototype features $\mathbf{P}$ . The total loss function is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \cdot \mathcal {L} _ {\mathrm {C L S}} + \beta \cdot \mathcal {L} _ {\mathrm {S I M}}, \tag {6} +$$ + +where $\alpha$ and $\beta$ are weighting coefficients that balance the contribution of each loss term. + +Classification Loss. Image-level class predictions $\hat{y} \in \mathbb{R}^{3 \times N}$ are obtained by applying global average pooling to the pseudo-segmentation masks $\mathbf{M}$ from each hierarchical level in the ClassNet, where 3 corresponds to the levels and $N$ is the number of classes. The predictions are compared with the ground-truth labels $y \in \mathbb{R}^{1 \times N}$ , and the classification loss for each level $i$ is: + +$$ +\mathcal {L} _ {\mathrm {C L S}} [ i ] = \operatorname {C o s s E n t r o p y} (y, \hat {y} [ i ]) \tag {7} +$$ + +where $\sigma$ is the sigmoid function. The total classification loss is a weighted sum: + +$$ +\mathcal {L} _ {\mathrm {C L S}} = \sum_ {i = 1} ^ {3} \mathcal {L} _ {\mathrm {C L S}} [ i ]. \tag {8} +$$ + +Similarity Loss. The similarity loss $\mathcal{L}_{\mathrm{SIM}}$ is divided into two components: the foreground similarity loss $\mathcal{L}_{\mathrm{FGS}}$ and the background similarity loss $\mathcal{L}_{\mathrm{BGS}}$ . + +The foreground similarity loss $\mathcal{L}_{\mathrm{FGS}}$ aligns the foreground image features with the corresponding foreground prototype features, while distinguishing them from the background prototype features. Formally, given the foreground image feature $F_{\mathrm{FG}}[j]$ for the $j$ -th class, foreground prototype feature $P_{\mathrm{FG}} = P[j]$ , and the background prototype features $P_{\mathrm{BG}} = P[m]$ where $1 \leq m \leq N$ and $m \neq j$ , the loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {F G S}} = - \log \left(\frac {\exp \left(\mathbf {s} _ {\mathrm {j}} ^ {\mathrm {F F}} / \tau\right)}{\exp \left(\mathbf {s} _ {\mathrm {j}} ^ {\mathrm {F F}} / \tau\right) + \exp \left(\mathbf {s} _ {\mathrm {j}} ^ {\mathrm {F B}} / \tau\right)}\right), \tag {9} +$$ + +where + +$$ +\mathbf {s} _ {\mathrm {j}} ^ {\mathrm {F F}} = \operatorname {s u m} \left(F _ {\mathrm {F G}} [ j ] \cdot P _ {\mathrm {F G}}\right), \mathbf {s} _ {\mathrm {j}} ^ {\mathrm {F B}} = \operatorname {s u m} \left(F _ {\mathrm {F G}} [ j ] \cdot P _ {\mathrm {B G}}\right), \tag {10} +$$ + +where $\mathbf{s}_{\mathrm{j}}^{\mathrm{FF}}$ is the sum of similarity scores between the foreground feature and the foreground prototype of the $j$ -th class, while $\mathbf{s}_{\mathrm{j}}^{\mathrm{FB}}$ is the sum of similarity scores between the foreground feature of the $j$ -th class and the background prototype. The temperature parameter $\tau$ controls the concentration level of the distribution. + +Similarly, $\mathcal{L}_{\mathrm{BGS}}$ aligns background image features with background prototype features while distinguishing them + +from foreground prototype features. Given the background image feature $F_{\mathrm{BG}}[j]$ , the background prototype feature $P_{\mathrm{BG}} = P[j]$ for the $j$ -th region, and the foreground prototype features $P_{\mathrm{FG}} = P[m]$ , the loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {B G S}} = - \log \left(\frac {\exp \left(\bar {\mathbf {s}} _ {\mathrm {j}} ^ {\mathrm {B B}} / \tau\right)}{\exp \left(\bar {\mathbf {s}} _ {\mathrm {j} , \mathrm {j}} ^ {\mathrm {B F}} / \tau\right) + \exp \left(\bar {\mathbf {s}} _ {\mathrm {j}} ^ {\mathrm {B B}} / \tau\right)}\right), \tag {11} +$$ + +$$ +\bar {\mathbf {s}} _ {\mathrm {j}} ^ {\mathrm {B B}} = \operatorname {m e a n} \left(F _ {\mathrm {B G}} [ j ] \cdot P _ {\mathrm {B G}}\right), \tag {12} +$$ + +where $\bar{\mathbf{s}}_j^{\mathrm{BB}}$ is the mean of similarity scores between the background feature of the $j$ -th class and the background prototype. The total similarity loss is the combination of the two components: + +$$ +\mathcal {L} _ {\mathrm {S I M}} = \theta_ {1} \cdot \mathcal {L} _ {\mathrm {F G S}} + \theta_ {2} \cdot \mathcal {L} _ {\mathrm {B G S}}. \tag {13} +$$ + +where $\theta_{1}$ and $\theta_{2}$ are weights that balance the importance of the foreground and background similarity terms. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. We evaluated our method on four histopathological datasets. BCSS [2] consists of 151 H&E-stained breast cancer images from TCGA-BRCA, annotated with four classes (Tumor, Stroma, Lymphocytic infiltrate, Necrosis), and includes 30,000 training patches, 2,500 validation patches and 2,500 testing patches. + +BCSS-WSSS [17] is derived from BCSS for WSS with 23,422 training patches, 3,418 validation patches and 4,986 testing patches. + +LUAD-HistoSeg [17] contains 17,291 H&E-stained lung adenocarcinoma patches, annotated with four classes (Tumor Epithelium, Stroma, Necrosis, and Lymphocytes), with 16,678 training patches, 306 validation patches and 307 testing patches. + +GCSS [39] comprises 100 H&E-stained Gastric cancer images from TCGA-STAD gastric cancer images, annotated with four classes (Tumor, Lymphoid Stroma, Desmoplastic Stroma, Smooth Muscle Necrosis) providing 20,000 training, 2,500 validation patches and 2,500 testing patches. + +BCSS-WSSS and LUAD-HistoSeg are used exclusively for weakly supervised segmentation tasks, as the training images are labelled only at the image level, with the validation and test sets still including ground truth masks for evaluation purposes. More details about datasets are in the Supplementary Material. + +Implementation Details. The ClassNet utilizes the Mix Transformer from SegFormer [49] as its backbone, which is pretrained on ImageNet-1K. The ImgMatchNet is built upon an image bank assembled from the training set, where + +
DatasetBCSS-WSSS [17]LUAD-HistoSeg [17]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
WHistoSegNet [3]32.19±5.835.69±5.919.24±1.748.70±6.845.32±4.345.08±3.918.36±1.162.37±4.3
TransWS [56]40.25±0.0--57.39±0.056.27±0.0--72.02±0.0
OEEN [26]59.93±0.561.11±0.825.09±1.274.95±0.472.54±0.271.65±0.226.15±1.484.08±0.2
MLPS [17]65.17±1.769.65±1.935.19±0.578.91±1.173.54±2.173.15±1.127.77±0.984.75±1.4
TPRO [57]63.92±0.464.45±0.225.79±0.577.99±0.374.14±0.874.01±0.227.46±0.385.14±0.5
CLIMS [50]38.98±2.437.58±2.113.52±0.956.09±2.639.45±3.138.92±2.717.55±1.656.58±3.0
QA-CLIMS [9]22.45±9.724.87±8.211.15±2.436.67±11.221.97±8.620.63±8.910.67±2.136.03±10.0
Proto2Seg [32]67.86±0.9*72.48±1.1*35.54±0.4*81.00±0.9*74.91±1.2*74.52±1.0*30.71±0.5*85.97±1.2*
PBLP (Ours)69.54±0.674.52±0.537.17±0.482.03±0.576.44±0.575.19±0.530.64±0.386.64±0.3
DatasetGCSS [39]BCSS [2]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
F&SSSPCL [39]51.63±0.0--68.10±0.062.47±0.0--76.90±0.0
SAM-Path [54]58.78±0.959.01±0.758.78±0.973.11±0.363.27±0.863.35±0.725.10±0.777.50±0.6
SAM2-Path [55]57.06±0.656.50±0.622.32±0.472.66±0.761.57±0.662.01±0.623.77±0.476.21±0.5
WHistoSegNet [3]30.02±6.231.25±5.410.10±3.646.15±7.022.15±7.822.80±8.012.11±4.136.27±8.9
OEEN [26]45.89±2.847.14±2.515.33±1.862.91±3.147.50±0.448.21±0.314.00±0.264.41±0.4
MLPS [17]51.20±1.752.85±1.519.10±1.367.72±2.449.32±1.151.31±1.321.08±0.766.06±0.9
TPRO [57]50.12±1.951.73±1.718.50±1.169.84±1.850.97±0.351.01±0.317.88±0.467.52±0.2
CLIMS [50]32.03±3.031.89±2.715.22±1.848.52±3.336.12±4.636.77±3.012.16±1.153.07±4.2
QA-CLIMS [9]25.01±8.326.54±7.612.34±4.240.02±9.023.00±9.924.07±9.110.27±3.637.39±12.2
Proto2Seg [32]53.23±2.853.97±2.922.34±1.770.84±2.055.34±2.056.72±2.022.40±1.570.78±2.1
PBLP (Ours)55.10±1.357.05±1.221.40±0.971.05±1.455.28±0.856.30±0.823.65±0.371.20±0.7
+ +Table 1. Quantitative comparison of various methods on four histopathological datasets. The best results are highlighted in bold. "Sup." denotes the type of supervision used: $\mathcal{F} \& \mathcal{S}$ represents fully and semi-supervised methods, while $\mathcal{W}$ indicates weakly supervised methods. Except for CLIMS and QA-CLIMS (designed for natural image segmentation), all methods are specifically tailored for histopathological image segmentation. For the BCSS-WSSS and LUAD-HistoSeg, the $p$ -values from t-tests comparing our model with the second-best results* were calculated, and all $p$ -values were less than 0.05. + +
CLCSFGMBGMmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓62.08±0.363.00±0.425.73±0.276.60±0.3
✓✓55.01±2.859.47±2.520.44±1.070.98±3.0
✓✓50.23±2.452.11±1.719.20±0.766.87±2.7
✓✓62.34±1.664.08±1.925.68±0.776.80±1.5
✓✓✓67.54±0.669.42±0.733.00±0.480.63±0.4
+ +Table 2. Ablation study of different loss function combinations on the initial pseudo masks quality (mIoU%) for the BCSS-WSSS dataset. + +the number of clusters $K$ in $K$ -Means was set to 3, and each subclass contains $N_K = 100$ . The scaling parameter $\delta$ in the adaptive thresholding module was 0.15. + +During training, we utilized the AdamW optimizer with an initial learning rate of $1 \times 10^{-5}$ and a weight decay of 0.003. The total loss function combines the classification loss and similarity loss with weighting factors $\alpha = 1$ and $\beta = 0.5$ , respectively. The temperature parameter in both $\mathcal{L}_{\mathrm{FGS}}$ and $\mathcal{L}_{\mathrm{BGS}}$ was set to 1, while $\theta_{1}$ and $\theta_{2}$ were set to 1 and 0.5, respectively. The model was trained for 10 epochs, with a batch size of 10 during the first stage. In the second stage in WSS, an unmodified Deeplab-v2 model [5] was trained as a fully supervised segmentation model. All models were trained on a single 4090 GPU. + +To quantitatively evaluate our method, we employed four standard metrics: Mean Intersection over Union (mIoU), + +Frequency Weighted IoU (FWIoU), Boundary IoU (bIoU), and Dice Coefficient. We also calculated p-values from t-tests to indicate the statistical significance of our results, measuring the probability that the observed differences occurred by chance. + +# 4.2. Results + +![](images/ca609d1a25878ea3d1857ef9c4cc1ddc156d9ef813e7030535731a92d157819e.jpg) +(a) Analysis of $\beta /\alpha$ + +![](images/9e4ad25ac8b61f3914274545a617c8c3c18599310fd2c2ef3b9f70e700d02c34.jpg) +(b) Analysis of $\theta_{2} / \theta_{1}$ +Figure 3. Ablation study on hyperparameter ratios. The mIoU values are reported on initial pseudo masks for BCSS-WSSS. + +We compared our model with ten advanced methods, including three supervised models and five weakly supervised models, two state-of-the-art text-prompted weakly supervised models. We used the reported results for SSPCL and TransWS due to the unavailability of publicly available + +
DatasetBCSS
EncoderBackbonemIoU(%)FwIoU(%)bIoU(%)dice(%)
CLIP [36]SegFormer66.45±0.372.42±0.327.05±0.280.56±0.2
ResNet1865.87±0.270.40±0.323.23±0.378.95±0.2
ResNet3866.10±0.471.22±0.426.56±0.279.86±0.3
ResNet5065.30±0.470.21±0.423.31±0.378.27±0.3
TransUNet60.17±0.463.52±0.517.81±0.275.12±0.5
MedCLIP [47]SegFormer68.01±0.673.20±0.536.88±0.481.62±0.5
ResNet1867.17±0.472.60±0.333.99±0.380.64±0.4
ResNet3867.18±0.572.57±0.535.18±0.380.93±0.4
ResNet5067.03±0.372.11±0.233.98±0.480.26±0.2
TransUNet62.09±0.566.89±0.520.15±0.376.61±0.5
PLIP [19]SegFormer67.16±0.773.53±0.537.21±0.481.77±0.5
ResNet1866.89±0.673.00±0.433.01±0.480.16±0.5
ResNet3867.02±0.573.24±0.535.85±0.480.25±0.4
ResNet5066.75±0.472.48±0.332.17±0.280.05±0.4
TransUNet61.98±0.666.01±0.521.54±0.376.53±0.6
DINOv2 [31]SegFormer66.37±0.872.38±0.932.01±0.380.24±0.8
ResNet3865.01±0.670.47±0.631.90±0.479.23±0.6
TransUNet61.00±0.462.71±0.520.22±0.276.64±0.4
+ +code. All other models were retrained and tested with five random seeds for robustness. Proto2Seg is a model based on human feedback; in our comparison with Proto2Seg, we carefully selected patches that met the required criteria using existing patch-level and image-level annotations instead of performing manual cutting and human feedback labelling. This might lead to a performance improvement for the Proto2Seg model. + +As shown in Table 1, our PBIP framework generally outperforms state-of-the-art weakly supervised methods across the four datasets. Specifically, on BCSS-WSSS, LUAD-HistoSeg and GCSS, our method outperforms Proto2Seg by $1.68\%$ , $1.53\%$ and $1.87\%$ in mIoU, achieving the best weakly supervised performance. All $p$ -values between our model and the second best on BCSS-WSSS and LUAD-HistoSeg are below 0.05, confirming the statistical significance of our improvements. + +Figure 5 shows the pseudo masks generated during the first stage of WSS models. We compared PBIP with MLPS, TPRO, and CLIMS. MLPS ranks third on BCSS-WSSS, while TPRO achieves the third-best on LUAD based. CLIMS is a text-supervised segmentation model for natural images. The results indicate that PBIP activates more complete object content and fewer background regions, while TPRO offers slight improvement over MLPS and CLIMS shows many errors. Text features do not enhance histopathological segmentation, and text supervision can mislead the model due to inter-class homogeneity and intra-class heterogeneity in histopathological images. + +# 4.3. Ablation Studies + +Ablation study of Image Bank. We investigated the impact of the number of prototype images by randomly selecting images without clustering, using 10 different random + +Table 3. Performance comparison of different combinations of image encoders (CLIP, MedCLIP, PLIP, DINOv2) and backbones (SegFormer, ResNet variants, TransUNet) on initial pseudo masks for BCSS-WSSS. + +
K12345
DatasetmIoU(%)mIoU(%)mIoU(%)mIoU(%)mIoU(%)
BCSS-WSSS67.03±0.467.15±0.468.01±0.667.81±0.767.53±0.7
LUAD-HistoSeg74.91±0.575.12±0.574.87±0.673.72±1.274.07±0.8
GCSS51.26±0.852.07±0.853.21±1.253.91±1.053.54±0.9
BCSS54.01±0.653.97±0.854.05±0.853.87±1.053.50±0.9
+ +seeds for robustness. In Figure 4, "Proto Num" represents the number of images per sub-bank per category. The results show that the average mIoU improves as the number of prototype images increases. Using all eligible training images yielded a mIoU of $69.15\%$ , suggesting that more images help reduce noise in prototype computation. However, due to inter-class homogeneity, simply increasing the number is not the most effective approach. The highest mIoU of $69.52\%$ was achieved with 100 images per sub-bank. When clustering was applied to select 100 images, the mIoU further increased to $69.60\%$ . This demonstrates that selecting representative images through clustering is more effective than merely increasing quantity, as clustering captures the most discriminative features and mitigates challenges posed by inter-class homogeneity. + +Additionally, we analyzed the impact of the number of clusters $K$ in $K$ -Means. As shown in Table 4, the best results across all datasets were obtained when $K$ was set between 2 and 4, indicating that the optimal choice of $K$ may depend on the level of inter-class homogeneity and intra-class heterogeneity within the dataset. Specifically, a small $K$ prevents the model from adequately capturing intra-class heterogeneity, and an excessively high $K$ amplifies the influence of inter-class homogeneity. + +Ablation study of the Loss Function. We analyzed the impact of different loss function configurations. Specifically, we varied the weighting ratios $\beta/\alpha$ (for $\mathcal{L}_{\mathrm{SIM}}$ and $\mathcal{L}_{\mathrm{CLS}}$ ) and $\theta_{2}/\theta_{1}$ (for $\mathcal{L}_{\mathrm{BGS}}$ and $\mathcal{L}_{\mathrm{FGS}}$ ), as illustrated in Figure 3. The results indicate that extreme values of these ratios lead to a decline in performance. Furthermore, excluding either $\mathcal{L}_{\mathrm{FGS}}$ or $\mathcal{L}_{\mathrm{BGS}}$ causes the mIoU to drop significantly from $67.54\%$ to $50.23\%$ and $55.01\%$ , respectively. This substantial decrease suggests that both components are essential; relying solely on one causes the model to focus excessively on either the foreground or background, lead + +Table 4. Ablation study on the number of clusters $K$ in $\mathrm{k}$ -means across different datasets. The mIoU values on initial pseudo masks for BCSS-WSSS are reported with standard deviation. The optimal $K$ value varies per dataset,with $K = 2$ to $K = 4$ generally achieving the highest performance. + +
SIMATmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓63.25±0.566.80±0.425.89±0.377.98±0.4
✓67.09±0.673.01±0.627.48±0.579.92±0.6
✓✓68.01±0.673.20±0.536.88±0.481.62±0.5
+ +Table 5. Ablation study on the impact of SIM and Adaptive Thresholding (AT) on initial pseudo masks for BCSS-WSSS. + +
PromptModelTUMSTRLYMNECMean
TextCLIP [36]0.0050.0010.1350.0020.035
PLIP [19]0.7780.0080.3190.1360.310
MedCLIP [47]0.4230.0200.1650.2050.203
ImageCLIP [36]0.7160.2140.5290.0190.370
PLIP [19]0.9240.9200.8160.8350.874
MedCLIP [47]0.8810.8950.7900.6710.809
+ +Table 6. Zero-shot classification F1 scores $(\%)$ on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with text and image prompts. + +![](images/bbc81cecd43f5609ff21276b10bbef31dc8c19f5560daf797d936385c242c70e.jpg) +Figure 4. Ablation study of the number of prototype images. Proto Num represents the number of prototype images per sub-bank for each category. We report the mIoU values with Standard Deviation obtained over 10 runs with different random seeds. + +ing to incomplete or erroneous activations. + +Ablation study of the Modules. We analyzed the effectiveness of different modules within PBLP. As shown in Table 5, both the SIM and the Adaptive Thresholding Module significantly enhance model performance. Specifically, when the SIM module is removed, we substitute it with a simple $1 \times 1$ convolutional layer to generate the pseudo-segmentation masks. The results demonstrate a noticeable decline in performance without the SIM and AT module. The SIM module captures intra-class heterogeneity and inter-class homogeneity better than the $1 \times 1$ convolutional layer. Furthermore, Figure 1 illustrates the foreground images generated by the model with and without the AT module. The results demonstrate that AT effectively reduces noise in background regions. + +Additionally, we evaluated the performance of our model using different image encoders and backbones, as summarized in Table 3. The combination of MedCLIP [47] and SegFormer achieved the best results in terms of mIoU metric. We observed that the PLIP [19] and SegFormer pairing performed best on the bIoU, FWIoU, and Dice coefficient. The TransUNet model [4], with its end-to-end architecture that does not utilize the SIM module for pseudo-mask computation, exhibited inferior performance. These results suggest that the absence of the SIM module may contribute to the lower effectiveness. Moreover, the relatively poor performance of CLIP [36] and DINOv2 [31] further highlights the importance of external knowledge from pretraining in + +![](images/ada068df4a82c0fe6d0f3b43424424ba5eea4ab816908c1944780ebe37eeff31.jpg) +Figure 5. a. Visualization of the pseudo-segmentation masks generated by models in the first stage on BCSS-WSSS. The masks are overlaid on the input images, with the raw pseudo-segmentation mask shown in the top-left corner. b. The foreground images generated by PBIP for the four segmentation targets. More visualizations are in Supplementary Material. + +histopathology, as these more generic encoders appear less effective for the specialized task of tissue segmentation. + +Text prompt and Image prompt. To explore the challenges of image-text matching in histopathology, we conducted zero-shot classification experiments on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with both text and image prompts (see Table 6). For text prompts, we used the common format: "a photo of {class name} ", while for image prompts, we utilized our prototype image features. The results show that PLIP and MedCLIP significantly outperform CLIP when using image prompts, but all models perform poorly with text prompts. This highlights the substantial challenges of text prompting in histopathology, where textual descriptions struggle to capture complex visual patterns and inter-class homogeneity. In contrast, image prompts effectively guide the models by aligning with the intricate characteristics of histopathological images through prototype features. + +# 5. Conclusion + +We proposed a novel Prototype-Based Image Prompting (PBIP) framework to address the challenges of inter-class homogeneity and intra-class heterogeneity in weakly supervised histopathological image segmentation. 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National science review, 5(1):44-53, 2018. 1 \ No newline at end of file diff --git a/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/images.zip b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a55157567f3a48200880590c623e6a2efe290a36 --- /dev/null +++ b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed463a351056f1810c8c962daaa29731bb8704245d244aefa9369708c9606af3 +size 705325 diff --git a/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/layout.json b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..81919a145d3ad206949cf99c23874914e6fa08d2 --- /dev/null +++ b/2025/Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation/layout.json @@ -0,0 +1,10776 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "spans": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "type": "text", + "content": "Prototype-Based Image Prompting for Weakly Supervised Histopathological Image Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 159, + 161, + 451, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 161, + 451, + 190 + ], + "spans": [ + { + "bbox": [ + 159, + 161, + 451, + 190 + ], + "type": "text", + "content": "Qingchen Tang* Lei Fan* Maurice Pagnucco Yang Song University of New South Wales" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 114, + 191, + 493, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 191, + 493, + 204 + ], + "spans": [ + { + "bbox": [ + 114, + 191, + 493, + 204 + ], + "type": "text", + "content": "{qingchen.tang@student, lei.fanl@, morri@cse, yang.song1@}.unsw.edu.au" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 256, + 297, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 256, + 297, + 496 + ], + "spans": [ + { + "bbox": [ + 54, + 256, + 297, + 496 + ], + "type": "text", + "content": "Weakly supervised image segmentation with image-level labels has drawn attention due to the high cost of pixel-level annotations. Traditional methods using Class Activation Maps (CAMs) often highlight only the most discriminative regions, leading to incomplete masks. Recent approaches that introduce textual information struggle with histopathological images due to inter-class homogeneity and intraclass heterogeneity. In this paper, we propose a prototype-based image prompting framework for histopathological image segmentation. It constructs an image bank from the training set using clustering, extracting multiple prototype features per class to capture intra-class heterogeneity. By designing a matching loss between input features and class-specific prototypes using contrastive learning, our method addresses inter-class homogeneity and guides the model to generate more accurate CAMs. Experiments on four datasets (LUAD-HistoSeg, BCSS-WSSS, GCSS, and BCSS) show that our method outperforms existing weakly supervised segmentation approaches, setting new benchmarks in histopathological image segmentation." + }, + { + "bbox": [ + 54, + 256, + 297, + 496 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 520, + 135, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 520, + 135, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 520, + 135, + 533 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 540, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 296, + 684 + ], + "type": "text", + "content": "Automated segmentation of histopathology images plays a crucial role in computer-aided diagnosis, assisting in the identification of abnormal tissue regions, quantification of tumor microenvironments [58], and the support of tumor grading and prognosis [11-14, 51]. Existing methods largely depend on extensive high-quality annotated data [28, 30, 41], while pixel-level annotations present particular challenges due to the significant domain expertise and time required for their creation [15, 33, 62]. 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Four supervision frameworks for histopathological image segmentation: fully supervised with pixel-level masks, CAM-based WSS using image labels, textural-based WSS, and our image prompt-based framework. b. The challenges of inter-class homogeneity (variable texture and staining within classes) and intra-class heterogeneity (similar appearances across classes). Cosine similarities are computed using features extracted by the MedCLIP model [47]." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 396, + 294, + 470, + 342 + ], + "blocks": [ + { + "bbox": [ + 396, + 294, + 470, + 342 + ], + "lines": [ + { + "bbox": [ + 396, + 294, + 470, + 342 + ], + "spans": [ + { + "bbox": [ + 396, + 294, + 470, + 342 + ], + "type": "image", + "image_path": "0d4e34ae5667d945ed7d677c88dd60d3bfbca0564c4da91a4d6ea0a58df323bf.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 475, + 293, + 548, + 341 + ], + "blocks": [ + { + "bbox": [ + 475, + 293, + 548, + 341 + ], + "lines": [ + { + "bbox": [ + 475, + 293, + 548, + 341 + ], + "spans": [ + { + "bbox": [ + 475, + 293, + 548, + 341 + ], + "type": "image", + "image_path": "10dc851bf0a42bcf02599499ed88142267797b96e1c6a565a4de62b08587e926.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": "sible labels such as bounding boxes [21, 35], scribbles [29], point annotations [34], and image-level labels [56, 57]. Typically, WSS methods employ a two-stage process: a classification network is first trained using weak labels to generate pseudo-labels, such as class activation maps (CAMs) [59]. These pseudo-labels are then utilized as refined supervision signals to train a fully supervised network [17, 57, 59]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "content": "However, CAMs generated from image-level labels often focus on the most discriminative regions, leading to incomplete localization of target objects and confusion between target and non-target areas [23, 50]. This limitation arises from a domain gap in pre-trained models, which are often trained on source domains (e.g., ImageNet [8]) that differ from the target domain (e.g., histopathology), causing CAMs to focus on features misaligned with those of the target domain. Early studies have explored various strategies to improve CAM quality, such as pixel affinity models [1] and saliency map integration [24]. Recent studies have utilized textual information to bridge the gap between image-level labels and pixel-level segmentation [9, 50, 57]. As illustrated in Figure 1, these approaches incorporate textual descriptions (e.g., object type, colour, structure) into" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 67, + 703, + 245, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 245, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 245, + 713 + ], + "type": "text", + "content": "1https://github.com/QingchenTang/PBIP" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30271" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 96 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 96 + ], + "type": "text", + "content": "the model via pre-trained vision-language models, such as CLIP model [36]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 98, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 98, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 98, + 295, + 312 + ], + "type": "text", + "content": "While these methods have shown strong performance on popular segmentation benchmarks [9, 50], they face challenges in histopathological image segmentation. Tissue segmentation involves larger anatomical structures compared to general images or cell nucleus segmentation, with complex spatial arrangements, significant inter-class homogeneity, and intra-class heterogeneity [6, 25]. As illustrated in Figure 1.b, inter-class homogeneity refers to the visual similarity between different tissue types, making it difficult to differentiate target regions from surrounding tissues. For instance, non-tumor tissues may closely resemble tumor tissues, causing CAM-based methods [3, 17] to activate on irrelevant areas erroneously. Intra-class heterogeneity involves significant variability within the same tissue type, such as differences in staining, shape, and texture, which hampers text-based methods [9, 50, 57] from capturing fine-grained details, leading to misalignment between textual descriptions and pixel-level features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 315, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 315, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 295, + 638 + ], + "type": "text", + "content": "To address these challenges, we propose a Prototype-Based Image Prompting (PBIP) framework for WSS in histopathological segmentation. Unlike methods that rely on text prompts, we utilize image-level labels and their corresponding images to construct visual prototypes. This approach enables the model to discern nuanced visual variations that are challenging for text-based methods. The visual prototypes are achieved through a feature bank that serves as an additional supervisory signal to guide CAM refinement. More specifically, the PBIP framework consists of two main components: a classification network and a prototype-guided feature matching network. The classification network, based on a pre-trained model, extracts multiscale feature representations from the query image to produce pseudo-segmentation masks that indicate class-specific pixel regions. The prototype-guided network constructs a feature bank containing multiple prototypes for each tissue class to capture intra-class heterogeneity. The feature bank is constructed from the training set by organizing images into distinct prototypes based on their labels and employing a CLIP-based image encoder to extract semantically rich, pixel-level features. In addition, a contrastive learning-based similarity loss is computed between the prototypes and class-specific pixel regions, mitigating inter-class homogeneity and yielding high-precision CAMs in the first stage of WSS, which then serve as pseudo-labels for subsequent supervised training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 639, + 276, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 639, + 276, + 651 + ], + "spans": [ + { + "bbox": [ + 67, + 639, + 276, + 651 + ], + "type": "text", + "content": "The main contributions of this paper are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 653, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 653, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 57, + 653, + 295, + 714 + ], + "type": "text", + "content": "- To the best of our knowledge, the proposed PBIP framework is the first WSS model in the histopathology domain that utilizes image prompts. By integrating a prototype-guided feature prompting mechanism through an image library, it addresses intra-class heterogeneity" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 324, + 73, + 441, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 73, + 441, + 84 + ], + "spans": [ + { + "bbox": [ + 324, + 73, + 441, + 84 + ], + "type": "text", + "content": "and inter-class homogeneity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 84, + 553, + 204 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 316, + 84, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 84, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 316, + 84, + 553, + 156 + ], + "type": "text", + "content": "- We design a CLIP-based image matching method that uses a contrastive learning approach to encourage the alignment of foreground features with their respective prototypes while maintaining distance from non-target prototypes, enhancing pixel-level segmentation in weakly supervised tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 156, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 156, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 316, + 156, + 553, + 204 + ], + "type": "text", + "content": "- Extensive experiments on the LUAD-HistoSeg [17], BCSS-wsss [17], GCSS [39], and BCSS [2] demonstrate that our method outperforms the current state-of-the-art methods in weakly supervised tissue segmentation." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 216, + 400, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 216, + 400, + 228 + ], + "spans": [ + { + "bbox": [ + 314, + 216, + 400, + 228 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 236, + 493, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 493, + 249 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 493, + 249 + ], + "type": "text", + "content": "2.1. Weakly Supervised Segmentation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 255, + 553, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 255, + 553, + 386 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 553, + 386 + ], + "type": "text", + "content": "WSS methods aim to infer pixel-level segmentation from simpler labels such as image-level classification tags [7, 33], bounding boxes [22], or point annotations [16, 53]. Subsequent research has focused on generating higher-quality pseudo labels from these weak annotations, leading to the development of numerous CAM-based approaches [43, 46], such as the Grad-CAM model [37], pixel affinity models [1], and saliency maps [24]. These CAM-based models have been used in early histopathological image segmentation studies, including HistoSegNet [3], OEEN [26], and the MLPS model [17]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 387, + 553, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 553, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 553, + 602 + ], + "type": "text", + "content": "With advances in multimodal learning [40, 44], particularly the development of CLIP [36], which effectively aligns image and text embeddings, recent studies have incorporated textual information as additional supervision to reduce the discrepancy between image-level labels and pixel-level predictions in WSS. For instance, Xie et al. proposed CLIMS [50] and Deng et al. introduced QA-CLIMS [9], integrating textual information into WSS models using the pre-trained CLIP model [36]. In histopathological image segmentation, Zhang et al. proposed TPRO [57], which incorporates general descriptions of tissue characteristics into image features via an attention mechanism [42] to produce more accurate CAMs by aligning image features with textual descriptions. In contrast, our method utilizes image-level labels and the corresponding images to provide finer-grained guidance compared to text-based approaches, addressing the challenges of homogeneity and heterogeneity in histopathological images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 611, + 419, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 419, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 419, + 624 + ], + "type": "text", + "content": "2.2. Prompt Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 629, + 553, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 553, + 715 + ], + "type": "text", + "content": "Prompt learning initially gained traction in Natural Language Processing (NLP) [10, 27], where models were guided in specific tasks through designed or learned prompts. With the rise of large-scale pre-trained multimodal models like CLIP [36], prompt engineering has extended to vision tasks [60, 61]. Early approaches relied on manually defined text templates (e.g., \"a photo of {class" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30272" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": "name}\") to describe classes of interest and extract relevant knowledge [9, 50]. However, this trial-and-error process is time-consuming and requires specific expertise." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 109, + 296, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 296, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 296, + 216 + ], + "type": "text", + "content": "To address these limitations, learnable prompt-based methods were introduced for vision tasks [52, 60], replacing manual templates with a set of learnable text vectors preceding class names, thus automating the prompt generation process [60]. Additionally, some methods attempted to introduce image prompts through prototypes for few-shot image tasks [18, 48]. For example, Wang et al. [45] and Shen et al. [38] effectively utilized image prototypes for few-shot image segmentation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 217, + 296, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 277 + ], + "type": "text", + "content": "In our method, we leverage prototype-based image prompts instead of text-based prompts. These image prompts offer finer-grained and more direct guidance, allowing the model to capture subtle visual differences that are challenging to describe using text alone." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 288, + 111, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 288, + 111, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 288, + 111, + 300 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 308, + 123, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 308, + 123, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 123, + 319 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 327, + 296, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 296, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 296, + 410 + ], + "type": "text", + "content": "The key idea of our proposed PBIP framework is to leverage image-level labels and corresponding images to create a high-quality visual prototype feature bank, guiding the generation of more accurate CAMs as pseudo masks for WSS. As illustrated in Figure 2, the PBIP framework consists of two main components: a Classification Network (ClassNet) and an Image Feature Matching Network (ImgMatchNet)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": "The ClassNet takes a histopathology image " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " from the dataset and the prototype feature vectors " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " from ImgMatchNet (as detailed in Section 3.4), where " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " denote the height, width, and number of channels, respectively. ClassNet performs a classification task to generate initial pseudo-segmentation masks " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{H \\times W \\times N}" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " and is optimized by a classification loss " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CLS}}" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " denotes the number of classes in the dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": "The ImgMatchNet receives the input histopathology image " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": ", an image bank constructed from the training set through clustering, and the pseudo-segmentation masks " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": " generated by the ClassNet. ImgMatchNet extracts prototype features " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": " using a CLIP image encoder from the image bank and refines the pseudo-segmentation masks " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": " through a similarity matching loss " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SIM}}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": ". The refined masks " + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 507, + 296, + 651 + ], + "type": "text", + "content": " are merged via an argmax operation over the channel dimension to produce the final activation map for the first stage of WSS. These masks are subsequently used to train a fully supervised segmentation model in the second stage, generating the final segmentation masks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 658, + 211, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 211, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 211, + 671 + ], + "type": "text", + "content": "3.2. Construction of Image Bank" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "We construct an image bank that captures diverse visual prototypes for each class, which is automatically assembled from the training set. Specifically, we select tissue images" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": "based on image-level labels that indicate the patch contains only one class (e.g., only tumor) and exclude images with excessive white regions automatically. These patches are grouped into " + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": " categories corresponding to the " + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": " classes in the dataset. To capture intra-class heterogeneity, " + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": "-Means clustering is applied within each category to partition the patches into " + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": " subcategories. For each subcategory, the top " + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "inline_equation", + "content": "N_K" + }, + { + "bbox": [ + 313, + 72, + 555, + 192 + ], + "type": "text", + "content": " images closest to the cluster center are selected as prototypes for the image bank. The distance metric used for clustering is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 354, + 199, + 555, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 199, + 555, + 227 + ], + "spans": [ + { + "bbox": [ + 354, + 199, + 555, + 227 + ], + "type": "interline_equation", + "content": "D _ {t} (x _ {1}, x _ {2}) = 1 - \\frac {\\phi_ {e} (x _ {1}) \\cdot \\phi_ {e} (x _ {2})}{\\| \\phi_ {e} (x _ {1}) \\| \\| \\phi_ {e} (x _ {2}) \\|}, \\tag {1}", + "image_path": "2ff0e298e1934a396a257b96faa9e213fc7df774c6c020d61da893b95e9240dc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "x_{2}" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " are two image patches, " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "\\phi_{e}" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " denotes the feature extraction function of the CLIP image encoder, and the symbol " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " denotes the dot product operation between vectors. This process results in an image bank comprising " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " classes, each containing " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " subcategories, with each subcategory holding " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "N_{K}" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " representative images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 310, + 443, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 443, + 322 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 443, + 322 + ], + "type": "text", + "content": "3.3. Classification Network" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "text", + "content": "The ClassNet generates the initial pseudo-segmentation masks " + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "text", + "content": " by leveraging both the input image " + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "text", + "content": " and the prototype features " + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 328, + 554, + 388 + ], + "type": "text", + "content": ". We adopt SegFormer [49] as the backbone due to its efficacy in capturing multi-scale contextual information through its hierarchical transformer encoder." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": "Given an input histopathology image " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": ", hierarchical feature maps " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times C_i}" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " are extracted across different stages " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "i = 1,2,3" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "C_{i + 1} > C_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " corresponds to the number of channels at each hierarchical level " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " of the feature maps. To generate the initial pseudo masks, the cosine similarity is computed (SIM) between each pixel feature vector in " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " and the prototype feature vectors in " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": ". This computation produces confidence scores for each pixel across all classes, forming the pseudo-segmentation masks " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_i\\in \\mathbb{R}^{(H / 2^{i + 1})\\times (W / 2^{i + 1})\\times N}" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": ". The confidence score for pixel " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " and class " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " at level " + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 388, + 555, + 534 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 351, + 540, + 555, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 540, + 555, + 572 + ], + "spans": [ + { + "bbox": [ + 351, + 540, + 555, + 572 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {i} (p, n) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {\\mathbf {F} _ {i} (p) \\cdot \\mathbf {P} _ {i} (n , k)}{\\| \\mathbf {F} _ {i} (p) \\| \\left. \\mathbf {P} _ {i} (n , k) \\right\\|}, \\tag {2}", + "image_path": "a4427108cbe44128f90ce38230373b0c06d7c8e08042c36165d31f2398c38f81.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i(p)" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": " is the feature vector of pixel " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i(n, k)" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": "-th prototype feature vector for class " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": ". By averaging the cosine similarities over all prototypes " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": " for each class, it effectively captures intra-class variations and obtains a robust confidence score that reflects the likelihood of the pixel " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": " belonging to the class " + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 580, + 554, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 659, + 496, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 496, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 496, + 672 + ], + "type": "text", + "content": "3.4. Image Feature Matching Network" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "ImgMatchNet introduces image prompts through a prototype-based approach. It generates prototype features " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": " from the image bank, and then ClassNet is used to" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30273" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 288, + 178 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 288, + 178 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 288, + 178 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 288, + 178 + ], + "type": "image", + "image_path": "4900ad11ed4e68559000ec2eaa861d112b0f6a6f15e0e82c8fd2b57ee06c5932.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 293, + 72, + 550, + 180 + ], + "blocks": [ + { + "bbox": [ + 293, + 72, + 550, + 180 + ], + "lines": [ + { + "bbox": [ + 293, + 72, + 550, + 180 + ], + "spans": [ + { + "bbox": [ + 293, + 72, + 550, + 180 + ], + "type": "image", + "image_path": "f60bb0cd826f84ce2e8413e2f0481d328f55205c31425171aae6bb4a6d3f7bb3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 182, + 291, + 274 + ], + "blocks": [ + { + "bbox": [ + 58, + 182, + 291, + 274 + ], + "lines": [ + { + "bbox": [ + 58, + 182, + 291, + 274 + ], + "spans": [ + { + "bbox": [ + 58, + 182, + 291, + 274 + ], + "type": "image", + "image_path": "ec8d5f4ebbba4c48168186720114465f2a70bff887552893306b18545238655a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "lines": [ + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": "Figure 2. Structure of the proposed PBIP framework. Overview. PBIP consists of two main components: a Classification Network(ClassNet) and an Image Feature Matching Network(ImgMatchNet), which leverage an external image bank to provide image prompts in the form of prototypes. Image Bank. Training images are grouped by their labels and clustered into " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": " subclasses per class. For each subclass, " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "N_K" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": " representative images are selected to build the image bank. ClassNet. It receives an input image " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": " and prototype features " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": ", performing a classification task to generate the pseudo-segmentation mask " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": ". ImgMatchNet. It processes the input image " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": " and the initial pseudo-segmentation mask " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": ", extracting foreground and background regions. These regions are then matched with " + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 54, + 285, + 555, + 365 + ], + "type": "text", + "content": " from the image bank to refine the pseudo mask generation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 294, + 183, + 550, + 274 + ], + "blocks": [ + { + "bbox": [ + 294, + 183, + 550, + 274 + ], + "lines": [ + { + "bbox": [ + 294, + 183, + 550, + 274 + ], + "spans": [ + { + "bbox": [ + 294, + 183, + 550, + 274 + ], + "type": "image", + "image_path": "3d4da5fafc154f904e853f7a6d3713933ec48e40f8e6ae74863ad29b3216ea7c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 373, + 295, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 373, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 54, + 373, + 295, + 433 + ], + "type": "text", + "content": "compute pixel-level class confidences in the feature maps. To extract these prototype features, we employ the image encoder from the pre-trained MedCLIP model [47], a variant of the CLIP architecture tailored for medical images and trained on large-scale medical image-text pairs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": "All images in the image bank are encoded using the MedCLIP image encoder, producing feature representations denoted as " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_p\\in \\mathbb{R}^{N\\times K\\times N_K\\times d}" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": " is the number of classes in the dataset, " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": " is the number of subclasses per class determined by the clustering, " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "N_{K}" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": " is the number of images per subclass, and " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": " is the dimension of the feature space. The mean feature vector is computed for each subclass across its images to obtain the prototype features, yielding " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{P}\\in \\mathbb{R}^{N\\times K\\times d}" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": ". To align these prototype features with the hierarchical feature maps generated by the ClassNet, we employ a Multi-Layer Perceptron (MLP) composed of fully connected layers and ReLU activations. The MLP projects the prototype features to match the dimensionality of each feature level, producing " + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i\\in \\mathbb{R}^{N\\times K\\times C_i}" + }, + { + "bbox": [ + 54, + 436, + 295, + 604 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 606, + 295, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 606, + 295, + 667 + ], + "spans": [ + { + "bbox": [ + 54, + 606, + 295, + 667 + ], + "type": "text", + "content": "ImgMatchNet includes a foreground-background separation module to further refine the pseudo-masks obtained from the ClassNet. Specifically, this module upsamples and aggregates the hierarchical pseudo-masks from different feature levels to obtain a comprehensive pseudo-mask:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 133, + 683, + 295, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 683, + 295, + 716 + ], + "spans": [ + { + "bbox": [ + 133, + 683, + 295, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {\\prime} = \\sum_ {i = 1} ^ {3} \\operatorname {U p} \\left(\\mathbf {M} _ {i}\\right), \\tag {3}", + "image_path": "cf70bc8b773905ace2048dea3993b257d9a09031e5281e58d91bf23a47c68b7f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "inline_equation", + "content": "\\mathbf{M}' \\in \\mathbb{R}^{H \\times W \\times N}" + }, + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "inline_equation", + "content": "\\mathrm{Up}(\\cdot)" + }, + { + "bbox": [ + 313, + 372, + 553, + 397 + ], + "type": "text", + "content": " denotes the upsampling operation to match the original image resolution." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 397, + 554, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 397, + 554, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 397, + 554, + 469 + ], + "type": "text", + "content": "We employ an adaptive thresholding module to separate foreground and background regions. This module computes an adaptive threshold " + }, + { + "bbox": [ + 313, + 397, + 554, + 469 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 397, + 554, + 469 + ], + "type": "text", + "content": " based on the intensity distribution of the pseudo-mask, dynamically distinguishing between foreground and background to reduce noise. The adaptive threshold is computed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 371, + 475, + 553, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 475, + 553, + 489 + ], + "spans": [ + { + "bbox": [ + 371, + 475, + 553, + 489 + ], + "type": "interline_equation", + "content": "\\tau = \\delta \\cdot \\max (\\mathbf {M}), \\quad \\delta \\in [ 0, 1 ], \\tag {4}", + "image_path": "982ce384d48896a8cfe24514384af357ee794354adefdcffb027bc4bfcce6eb9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "content": " is a scaling parameter that controls the threshold level. Applying this threshold to the activation map yields a binary mask " + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "inline_equation", + "content": "b\\in \\mathbb{R}^{H\\times W\\times N}" + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "content": ", where pixel values greater than or equal to " + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "content": " are set to 1 (foreground), and values below " + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 495, + 554, + 568 + ], + "type": "text", + "content": " are set to 0 (background). We then separate foreground and background images through element-wise multiplication:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 323, + 573, + 553, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 573, + 553, + 587 + ], + "spans": [ + { + "bbox": [ + 323, + 573, + 553, + 587 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {\\mathrm {F G}} = b \\cdot \\mathbf {M} \\cdot \\mathbf {X}, \\quad \\mathbf {X} _ {\\mathrm {B G}} = (1 - b) \\cdot (1 - \\mathbf {M}) \\cdot \\mathbf {X}, \\tag {5}", + "image_path": "2f4801c395bf069653cde041e6ff0bb23fc4bcb3df816ab98dbd843f8f51bce1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{FG}},\\mathbf{X}_{\\mathrm{BG}}\\in \\mathbb{R}^{H\\times W\\times N}" + }, + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "text", + "content": " represent the separated foreground and background regions. By using the same MedCLIP image encoder and MLP, we extract hierarchical foreground and background features " + }, + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{FG}_i},\\mathbf{F}_{\\mathrm{BG}_i}\\in \\mathbb{R}^{N\\times C_i}" + }, + { + "bbox": [ + 313, + 592, + 554, + 665 + ], + "type": "text", + "content": ". These features are then utilized in a similarity matching loss to optimize the generation of the pseudo-masks further." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 671, + 451, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 671, + 451, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 671, + 451, + 685 + ], + "type": "text", + "content": "3.5. Optimization Objectives" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": "Our model is jointly optimized by two objectives: the classification loss " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CLS}}" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": ", which ensures consistency between pre" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30274" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "dicted labels and image-level annotations, and the similarity loss " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SIM}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": ", which promotes alignment between the encoded features of the foreground and background regions with their respective prototype features " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": ". The total loss function is defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 141, + 295, + 154 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 141, + 295, + 154 + ], + "spans": [ + { + "bbox": [ + 116, + 141, + 295, + 154 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C L S}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {S I M}}, \\tag {6}", + "image_path": "fca4c1803d8efd218c44d30f72fee0f4c671384ad2ee2c1b7020e426cd45f6d4.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 163, + 295, + 186 + ], + "type": "text", + "content": " are weighting coefficients that balance the contribution of each loss term." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": "Classification Loss. Image-level class predictions " + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "inline_equation", + "content": "\\hat{y} \\in \\mathbb{R}^{3 \\times N}" + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": " are obtained by applying global average pooling to the pseudo-segmentation masks " + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": " from each hierarchical level in the ClassNet, where 3 corresponds to the levels and " + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": " is the number of classes. The predictions are compared with the ground-truth labels " + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{1 \\times N}" + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": ", and the classification loss for each level " + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 187, + 296, + 270 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 280, + 295, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 280, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 111, + 280, + 295, + 293 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C L S}} [ i ] = \\operatorname {C o s s E n t r o p y} (y, \\hat {y} [ i ]) \\tag {7}", + "image_path": "2d5fcf395b801ca48d4d3bbcbe1f616ce4f526df1904e894d152f234ad007db8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 302, + 296, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 302, + 296, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 302, + 296, + 326 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 302, + 296, + 326 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 302, + 296, + 326 + ], + "type": "text", + "content": " is the sigmoid function. The total classification loss is a weighted sum:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 133, + 335, + 295, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 335, + 295, + 367 + ], + "spans": [ + { + "bbox": [ + 133, + 335, + 295, + 367 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C L S}} = \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {\\mathrm {C L S}} [ i ]. \\tag {8}", + "image_path": "91a45c4a532fd87cf227746bc440a390f6528177a05e6c9a868af51acc494dae.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "text", + "content": "Similarity Loss. The similarity loss " + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SIM}}" + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "text", + "content": " is divided into two components: the foreground similarity loss " + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{FGS}}" + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "text", + "content": " and the background similarity loss " + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BGS}}" + }, + { + "bbox": [ + 55, + 375, + 296, + 411 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": "The foreground similarity loss " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{FGS}}" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " aligns the foreground image features with the corresponding foreground prototype features, while distinguishing them from the background prototype features. Formally, given the foreground image feature " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{FG}}[j]" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": "-th class, foreground prototype feature " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{FG}} = P[j]" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": ", and the background prototype features " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{BG}} = P[m]" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "1 \\leq m \\leq N" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "inline_equation", + "content": "m \\neq j" + }, + { + "bbox": [ + 55, + 411, + 296, + 506 + ], + "type": "text", + "content": ", the loss is defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 524, + 295, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 524, + 295, + 566 + ], + "spans": [ + { + "bbox": [ + 68, + 524, + 295, + 566 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {F G S}} = - \\log \\left(\\frac {\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right)}{\\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} / \\tau\\right) + \\exp \\left(\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} / \\tau\\right)}\\right), \\tag {9}", + "image_path": "204c501fd178434794e28a73fe0e8575aa5766515d802f35171b8a736d3e798f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 574, + 84, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 84, + 583 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 84, + 583 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 593, + 295, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 593, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 59, + 593, + 295, + 609 + ], + "type": "interline_equation", + "content": "\\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F F}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {F G}}\\right), \\mathbf {s} _ {\\mathrm {j}} ^ {\\mathrm {F B}} = \\operatorname {s u m} \\left(F _ {\\mathrm {F G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {10}", + "image_path": "8c211fd487d136e989fbcb60b280fa7cb3976dbb1b9e20176270834d6c4da3e9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FF}}" + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": " is the sum of similarity scores between the foreground feature and the foreground prototype of the " + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": "-th class, while " + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\mathrm{j}}^{\\mathrm{FB}}" + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": " is the sum of similarity scores between the foreground feature of the " + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": "-th class and the background prototype. The temperature parameter " + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 617, + 295, + 689 + ], + "type": "text", + "content": " controls the concentration level of the distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Similarly, " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BGS}}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " aligns background image features with background prototype features while distinguishing them" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "content": "from foreground prototype features. Given the background image feature " + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{BG}}[j]" + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "content": ", the background prototype feature " + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{BG}} = P[j]" + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "content": "-th region, and the foreground prototype features " + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{FG}} = P[m]" + }, + { + "bbox": [ + 313, + 72, + 555, + 121 + ], + "type": "text", + "content": ", the loss is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 323, + 139, + 555, + 181 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 139, + 555, + 181 + ], + "spans": [ + { + "bbox": [ + 323, + 139, + 555, + 181 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {B G S}} = - \\log \\left(\\frac {\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}{\\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j} , \\mathrm {j}} ^ {\\mathrm {B F}} / \\tau\\right) + \\exp \\left(\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} / \\tau\\right)}\\right), \\tag {11}", + "image_path": "5ee696aa59c94c3b82d97e59113dac192e4510b920bc5b714f89d3e358b73902.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 375, + 191, + 555, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 191, + 555, + 208 + ], + "spans": [ + { + "bbox": [ + 375, + 191, + 555, + 208 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {s}} _ {\\mathrm {j}} ^ {\\mathrm {B B}} = \\operatorname {m e a n} \\left(F _ {\\mathrm {B G}} [ j ] \\cdot P _ {\\mathrm {B G}}\\right), \\tag {12}", + "image_path": "8bec3fe72d5b1ce56e662e84200fc500e5d0991d2de0fe90ddf710495df0ef13.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{s}}_j^{\\mathrm{BB}}" + }, + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "text", + "content": " is the mean of similarity scores between the background feature of the " + }, + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 213, + 555, + 261 + ], + "type": "text", + "content": "-th class and the background prototype. The total similarity loss is the combination of the two components:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 372, + 270, + 554, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 270, + 554, + 283 + ], + "spans": [ + { + "bbox": [ + 372, + 270, + 554, + 283 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {S I M}} = \\theta_ {1} \\cdot \\mathcal {L} _ {\\mathrm {F G S}} + \\theta_ {2} \\cdot \\mathcal {L} _ {\\mathrm {B G S}}. \\tag {13}", + "image_path": "d3800cb19966c31bc463e55c2de50fb567989361799bacac36ac6b1bb6f14f68.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\theta_{1}" + }, + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "inline_equation", + "content": "\\theta_{2}" + }, + { + "bbox": [ + 313, + 293, + 555, + 318 + ], + "type": "text", + "content": " are weights that balance the importance of the foreground and background similarity terms." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 328, + 397, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 328, + 397, + 341 + ], + "spans": [ + { + "bbox": [ + 314, + 328, + 397, + 341 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 347, + 430, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 347, + 430, + 361 + ], + "spans": [ + { + "bbox": [ + 314, + 347, + 430, + 361 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 366, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 554, + 437 + ], + "type": "text", + "content": "Datasets. We evaluated our method on four histopathological datasets. BCSS [2] consists of 151 H&E-stained breast cancer images from TCGA-BRCA, annotated with four classes (Tumor, Stroma, Lymphocytic infiltrate, Necrosis), and includes 30,000 training patches, 2,500 validation patches and 2,500 testing patches." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 437, + 554, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 474 + ], + "type": "text", + "content": "BCSS-WSSS [17] is derived from BCSS for WSS with 23,422 training patches, 3,418 validation patches and 4,986 testing patches." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 474, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 554, + 533 + ], + "type": "text", + "content": "LUAD-HistoSeg [17] contains 17,291 H&E-stained lung adenocarcinoma patches, annotated with four classes (Tumor Epithelium, Stroma, Necrosis, and Lymphocytes), with 16,678 training patches, 306 validation patches and 307 testing patches." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 533, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 554, + 594 + ], + "type": "text", + "content": "GCSS [39] comprises 100 H&E-stained Gastric cancer images from TCGA-STAD gastric cancer images, annotated with four classes (Tumor, Lymphoid Stroma, Desmoplastic Stroma, Smooth Muscle Necrosis) providing 20,000 training, 2,500 validation patches and 2,500 testing patches." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 665 + ], + "type": "text", + "content": "BCSS-WSSS and LUAD-HistoSeg are used exclusively for weakly supervised segmentation tasks, as the training images are labelled only at the image level, with the validation and test sets still including ground truth masks for evaluation purposes. More details about datasets are in the Supplementary Material." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "Implementation Details. The ClassNet utilizes the Mix Transformer from SegFormer [49] as its backbone, which is pretrained on ImageNet-1K. The ImgMatchNet is built upon an image bank assembled from the training set, where" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30275" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 553, + 337 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 553, + 337 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 553, + 337 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 553, + 337 + ], + "type": "table", + "html": "
DatasetBCSS-WSSS [17]LUAD-HistoSeg [17]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
WHistoSegNet [3]32.19±5.835.69±5.919.24±1.748.70±6.845.32±4.345.08±3.918.36±1.162.37±4.3
TransWS [56]40.25±0.0--57.39±0.056.27±0.0--72.02±0.0
OEEN [26]59.93±0.561.11±0.825.09±1.274.95±0.472.54±0.271.65±0.226.15±1.484.08±0.2
MLPS [17]65.17±1.769.65±1.935.19±0.578.91±1.173.54±2.173.15±1.127.77±0.984.75±1.4
TPRO [57]63.92±0.464.45±0.225.79±0.577.99±0.374.14±0.874.01±0.227.46±0.385.14±0.5
CLIMS [50]38.98±2.437.58±2.113.52±0.956.09±2.639.45±3.138.92±2.717.55±1.656.58±3.0
QA-CLIMS [9]22.45±9.724.87±8.211.15±2.436.67±11.221.97±8.620.63±8.910.67±2.136.03±10.0
Proto2Seg [32]67.86±0.9*72.48±1.1*35.54±0.4*81.00±0.9*74.91±1.2*74.52±1.0*30.71±0.5*85.97±1.2*
PBLP (Ours)69.54±0.674.52±0.537.17±0.482.03±0.576.44±0.575.19±0.530.64±0.386.64±0.3
DatasetGCSS [39]BCSS [2]
Sup.MethodmIoU(%)FwIoU(%)bIoU(%)dice(%)mIoU(%)FwIoU(%)bIoU(%)dice(%)
F&SSSPCL [39]51.63±0.0--68.10±0.062.47±0.0--76.90±0.0
SAM-Path [54]58.78±0.959.01±0.758.78±0.973.11±0.363.27±0.863.35±0.725.10±0.777.50±0.6
SAM2-Path [55]57.06±0.656.50±0.622.32±0.472.66±0.761.57±0.662.01±0.623.77±0.476.21±0.5
WHistoSegNet [3]30.02±6.231.25±5.410.10±3.646.15±7.022.15±7.822.80±8.012.11±4.136.27±8.9
OEEN [26]45.89±2.847.14±2.515.33±1.862.91±3.147.50±0.448.21±0.314.00±0.264.41±0.4
MLPS [17]51.20±1.752.85±1.519.10±1.367.72±2.449.32±1.151.31±1.321.08±0.766.06±0.9
TPRO [57]50.12±1.951.73±1.718.50±1.169.84±1.850.97±0.351.01±0.317.88±0.467.52±0.2
CLIMS [50]32.03±3.031.89±2.715.22±1.848.52±3.336.12±4.636.77±3.012.16±1.153.07±4.2
QA-CLIMS [9]25.01±8.326.54±7.612.34±4.240.02±9.023.00±9.924.07±9.110.27±3.637.39±12.2
Proto2Seg [32]53.23±2.853.97±2.922.34±1.770.84±2.055.34±2.056.72±2.022.40±1.570.78±2.1
PBLP (Ours)55.10±1.357.05±1.221.40±0.971.05±1.455.28±0.856.30±0.823.65±0.371.20±0.7
", + "image_path": "2ed76f2ea1705f2592b794c68e81d9a8f8bf8abd8bf85385759fbe65ed1a24c9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 410, + 294, + 465 + ], + "blocks": [ + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "lines": [ + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of various methods on four histopathological datasets. The best results are highlighted in bold. \"Sup.\" denotes the type of supervision used: " + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{F} \\& \\mathcal{S}" + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "text", + "content": " represents fully and semi-supervised methods, while " + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "text", + "content": " indicates weakly supervised methods. Except for CLIMS and QA-CLIMS (designed for natural image segmentation), all methods are specifically tailored for histopathological image segmentation. For the BCSS-WSSS and LUAD-HistoSeg, the " + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "text", + "content": "-values from t-tests comparing our model with the second-best results* were calculated, and all " + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 345, + 555, + 401 + ], + "type": "text", + "content": "-values were less than 0.05." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 410, + 294, + 465 + ], + "lines": [ + { + "bbox": [ + 58, + 410, + 294, + 465 + ], + "spans": [ + { + "bbox": [ + 58, + 410, + 294, + 465 + ], + "type": "table", + "html": "
CLCSFGMBGMmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓62.08±0.363.00±0.425.73±0.276.60±0.3
✓✓55.01±2.859.47±2.520.44±1.070.98±3.0
✓✓50.23±2.452.11±1.719.20±0.766.87±2.7
✓✓62.34±1.664.08±1.925.68±0.776.80±1.5
✓✓✓67.54±0.669.42±0.733.00±0.480.63±0.4
", + "image_path": "b076516922a010a9c966b96a08cea004cee356796b4ec524c7d4a0081462f5c8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 472, + 295, + 506 + ], + "lines": [ + { + "bbox": [ + 55, + 472, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 295, + 506 + ], + "type": "text", + "content": "Table 2. Ablation study of different loss function combinations on the initial pseudo masks quality (mIoU%) for the BCSS-WSSS dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": "the number of clusters " + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": "-Means was set to 3, and each subclass contains " + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "inline_equation", + "content": "N_K = 100" + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": ". The scaling parameter " + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 517, + 295, + 553 + ], + "type": "text", + "content": " in the adaptive thresholding module was 0.15." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": "During training, we utilized the AdamW optimizer with an initial learning rate of " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " and a weight decay of 0.003. The total loss function combines the classification loss and similarity loss with weighting factors " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": ", respectively. The temperature parameter in both " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{FGS}}" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BGS}}" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " was set to 1, while " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\theta_{1}" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\theta_{2}" + }, + { + "bbox": [ + 55, + 555, + 295, + 687 + ], + "type": "text", + "content": " were set to 1 and 0.5, respectively. The model was trained for 10 epochs, with a batch size of 10 during the first stage. In the second stage in WSS, an unmodified Deeplab-v2 model [5] was trained as a fully supervised segmentation model. All models were trained on a single 4090 GPU." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "To quantitatively evaluate our method, we employed four standard metrics: Mean Intersection over Union (mIoU)," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 412, + 555, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 412, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 412, + 555, + 473 + ], + "type": "text", + "content": "Frequency Weighted IoU (FWIoU), Boundary IoU (bIoU), and Dice Coefficient. We also calculated p-values from t-tests to indicate the statistical significance of our results, measuring the probability that the observed differences occurred by chance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 482, + 372, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 482, + 372, + 495 + ], + "spans": [ + { + "bbox": [ + 314, + 482, + 372, + 495 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 510, + 432, + 592 + ], + "blocks": [ + { + "bbox": [ + 315, + 510, + 432, + 592 + ], + "lines": [ + { + "bbox": [ + 315, + 510, + 432, + 592 + ], + "spans": [ + { + "bbox": [ + 315, + 510, + 432, + 592 + ], + "type": "image", + "image_path": "ca609d1a25878ea3d1857ef9c4cc1ddc156d9ef813e7030535731a92d157819e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 595, + 407, + 605 + ], + "lines": [ + { + "bbox": [ + 339, + 595, + 407, + 605 + ], + "spans": [ + { + "bbox": [ + 339, + 595, + 407, + 605 + ], + "type": "text", + "content": "(a) Analysis of " + }, + { + "bbox": [ + 339, + 595, + 407, + 605 + ], + "type": "inline_equation", + "content": "\\beta /\\alpha" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 436, + 510, + 553, + 594 + ], + "blocks": [ + { + "bbox": [ + 436, + 510, + 553, + 594 + ], + "lines": [ + { + "bbox": [ + 436, + 510, + 553, + 594 + ], + "spans": [ + { + "bbox": [ + 436, + 510, + 553, + 594 + ], + "type": "image", + "image_path": "9e4ad25ac8b61f3914274545a617c8c3c18599310fd2c2ef3b9f70e700d02c34.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 458, + 595, + 531, + 605 + ], + "lines": [ + { + "bbox": [ + 458, + 595, + 531, + 605 + ], + "spans": [ + { + "bbox": [ + 458, + 595, + 531, + 605 + ], + "type": "text", + "content": "(b) Analysis of " + }, + { + "bbox": [ + 458, + 595, + 531, + 605 + ], + "type": "inline_equation", + "content": "\\theta_{2} / \\theta_{1}" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 614, + 555, + 638 + ], + "lines": [ + { + "bbox": [ + 313, + 614, + 555, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 614, + 555, + 638 + ], + "type": "text", + "content": "Figure 3. Ablation study on hyperparameter ratios. The mIoU values are reported on initial pseudo masks for BCSS-WSSS." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "We compared our model with ten advanced methods, including three supervised models and five weakly supervised models, two state-of-the-art text-prompted weakly supervised models. We used the reported results for SSPCL and TransWS due to the unavailability of publicly available" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30276" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 294, + 239 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 294, + 239 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 294, + 239 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 294, + 239 + ], + "type": "table", + "html": "
DatasetBCSS
EncoderBackbonemIoU(%)FwIoU(%)bIoU(%)dice(%)
CLIP [36]SegFormer66.45±0.372.42±0.327.05±0.280.56±0.2
ResNet1865.87±0.270.40±0.323.23±0.378.95±0.2
ResNet3866.10±0.471.22±0.426.56±0.279.86±0.3
ResNet5065.30±0.470.21±0.423.31±0.378.27±0.3
TransUNet60.17±0.463.52±0.517.81±0.275.12±0.5
MedCLIP [47]SegFormer68.01±0.673.20±0.536.88±0.481.62±0.5
ResNet1867.17±0.472.60±0.333.99±0.380.64±0.4
ResNet3867.18±0.572.57±0.535.18±0.380.93±0.4
ResNet5067.03±0.372.11±0.233.98±0.480.26±0.2
TransUNet62.09±0.566.89±0.520.15±0.376.61±0.5
PLIP [19]SegFormer67.16±0.773.53±0.537.21±0.481.77±0.5
ResNet1866.89±0.673.00±0.433.01±0.480.16±0.5
ResNet3867.02±0.573.24±0.535.85±0.480.25±0.4
ResNet5066.75±0.472.48±0.332.17±0.280.05±0.4
TransUNet61.98±0.666.01±0.521.54±0.376.53±0.6
DINOv2 [31]SegFormer66.37±0.872.38±0.932.01±0.380.24±0.8
ResNet3865.01±0.670.47±0.631.90±0.479.23±0.6
TransUNet61.00±0.462.71±0.520.22±0.276.64±0.4
", + "image_path": "33a45ef645fe089db1cf6f6fce77e23cba359cb42621dccb6045e0707ed9382d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 300, + 295, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 300, + 295, + 396 + ], + "spans": [ + { + "bbox": [ + 54, + 300, + 295, + 396 + ], + "type": "text", + "content": "code. All other models were retrained and tested with five random seeds for robustness. Proto2Seg is a model based on human feedback; in our comparison with Proto2Seg, we carefully selected patches that met the required criteria using existing patch-level and image-level annotations instead of performing manual cutting and human feedback labelling. This might lead to a performance improvement for the Proto2Seg model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "spans": [ + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "content": "As shown in Table 1, our PBIP framework generally outperforms state-of-the-art weakly supervised methods across the four datasets. Specifically, on BCSS-WSSS, LUAD-HistoSeg and GCSS, our method outperforms Proto2Seg by " + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "inline_equation", + "content": "1.68\\%" + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "inline_equation", + "content": "1.53\\%" + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "inline_equation", + "content": "1.87\\%" + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "content": " in mIoU, achieving the best weakly supervised performance. All " + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 54, + 396, + 295, + 504 + ], + "type": "text", + "content": "-values between our model and the second best on BCSS-WSSS and LUAD-HistoSeg are below 0.05, confirming the statistical significance of our improvements." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 505, + 295, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 295, + 649 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 295, + 649 + ], + "type": "text", + "content": "Figure 5 shows the pseudo masks generated during the first stage of WSS models. We compared PBIP with MLPS, TPRO, and CLIMS. MLPS ranks third on BCSS-WSSS, while TPRO achieves the third-best on LUAD based. CLIMS is a text-supervised segmentation model for natural images. The results indicate that PBIP activates more complete object content and fewer background regions, while TPRO offers slight improvement over MLPS and CLIMS shows many errors. Text features do not enhance histopathological segmentation, and text supervision can mislead the model due to inter-class homogeneity and intra-class heterogeneity in histopathological images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 658, + 156, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 156, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 156, + 670 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Ablation study of Image Bank. We investigated the impact of the number of prototype images by randomly selecting images without clustering, using 10 different random" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 553, + 122 + ], + "blocks": [ + { + "bbox": [ + 55, + 247, + 295, + 291 + ], + "lines": [ + { + "bbox": [ + 55, + 247, + 295, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 295, + 291 + ], + "type": "text", + "content": "Table 3. Performance comparison of different combinations of image encoders (CLIP, MedCLIP, PLIP, DINOv2) and backbones (SegFormer, ResNet variants, TransUNet) on initial pseudo masks for BCSS-WSSS." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 70, + 553, + 122 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 553, + 122 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 553, + 122 + ], + "type": "table", + "html": "
K12345
DatasetmIoU(%)mIoU(%)mIoU(%)mIoU(%)mIoU(%)
BCSS-WSSS67.03±0.467.15±0.468.01±0.667.81±0.767.53±0.7
LUAD-HistoSeg74.91±0.575.12±0.574.87±0.673.72±1.274.07±0.8
GCSS51.26±0.852.07±0.853.21±1.253.91±1.053.54±0.9
BCSS54.01±0.653.97±0.854.05±0.853.87±1.053.50±0.9
", + "image_path": "8f962fd1783e4654fa8a9b2b42e06d2f707ab44c3c8667ef1c6e1e1c40d503b1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "spans": [ + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "text", + "content": "seeds for robustness. In Figure 4, \"Proto Num\" represents the number of images per sub-bank per category. The results show that the average mIoU improves as the number of prototype images increases. Using all eligible training images yielded a mIoU of " + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "inline_equation", + "content": "69.15\\%" + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "text", + "content": ", suggesting that more images help reduce noise in prototype computation. However, due to inter-class homogeneity, simply increasing the number is not the most effective approach. The highest mIoU of " + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "inline_equation", + "content": "69.52\\%" + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "text", + "content": " was achieved with 100 images per sub-bank. When clustering was applied to select 100 images, the mIoU further increased to " + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "inline_equation", + "content": "69.60\\%" + }, + { + "bbox": [ + 313, + 199, + 555, + 379 + ], + "type": "text", + "content": ". This demonstrates that selecting representative images through clustering is more effective than merely increasing quantity, as clustering captures the most discriminative features and mitigates challenges posed by inter-class homogeneity." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": "Additionally, we analyzed the impact of the number of clusters " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": "-Means. As shown in Table 4, the best results across all datasets were obtained when " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": " was set between 2 and 4, indicating that the optimal choice of " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": " may depend on the level of inter-class homogeneity and intra-class heterogeneity within the dataset. Specifically, a small " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": " prevents the model from adequately capturing intra-class heterogeneity, and an excessively high " + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 380, + 554, + 489 + ], + "type": "text", + "content": " amplifies the influence of inter-class homogeneity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": "Ablation study of the Loss Function. We analyzed the impact of different loss function configurations. Specifically, we varied the weighting ratios " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\beta/\\alpha" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " (for " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SIM}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CLS}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\theta_{2}/\\theta_{1}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " (for " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BGS}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{FGS}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": "), as illustrated in Figure 3. The results indicate that extreme values of these ratios lead to a decline in performance. Furthermore, excluding either " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{FGS}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{BGS}}" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " causes the mIoU to drop significantly from " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "67.54\\%" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "50.23\\%" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "inline_equation", + "content": "55.01\\%" + }, + { + "bbox": [ + 313, + 490, + 554, + 622 + ], + "type": "text", + "content": ", respectively. This substantial decrease suggests that both components are essential; relying solely on one causes the model to focus excessively on either the foreground or background, lead" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 317, + 634, + 553, + 680 + ], + "blocks": [ + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "lines": [ + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "spans": [ + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": "Table 4. Ablation study on the number of clusters " + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "inline_equation", + "content": "\\mathrm{k}" + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": " -means across different datasets. The mIoU values on initial pseudo masks for BCSS-WSSS are reported with standard deviation. The optimal " + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": " value varies per dataset,with " + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 313, + 131, + 553, + 186 + ], + "type": "text", + "content": " generally achieving the highest performance." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 634, + 553, + 680 + ], + "lines": [ + { + "bbox": [ + 317, + 634, + 553, + 680 + ], + "spans": [ + { + "bbox": [ + 317, + 634, + 553, + 680 + ], + "type": "table", + "html": "
SIMATmIoU(%)FwIoU(%)bIoU(%)dice(%)
✓63.25±0.566.80±0.425.89±0.377.98±0.4
✓67.09±0.673.01±0.627.48±0.579.92±0.6
✓✓68.01±0.673.20±0.536.88±0.481.62±0.5
", + "image_path": "78d256ea707e3431e2361fc211adc0a37ca616844d0ad39a33845cd35e738d29.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 687, + 553, + 710 + ], + "lines": [ + { + "bbox": [ + 313, + 687, + 553, + 710 + ], + "spans": [ + { + "bbox": [ + 313, + 687, + 553, + 710 + ], + "type": "text", + "content": "Table 5. Ablation study on the impact of SIM and Adaptive Thresholding (AT) on initial pseudo masks for BCSS-WSSS." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30277" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 69, + 294, + 142 + ], + "blocks": [ + { + "bbox": [ + 58, + 69, + 294, + 142 + ], + "lines": [ + { + "bbox": [ + 58, + 69, + 294, + 142 + ], + "spans": [ + { + "bbox": [ + 58, + 69, + 294, + 142 + ], + "type": "table", + "html": "
PromptModelTUMSTRLYMNECMean
TextCLIP [36]0.0050.0010.1350.0020.035
PLIP [19]0.7780.0080.3190.1360.310
MedCLIP [47]0.4230.0200.1650.2050.203
ImageCLIP [36]0.7160.2140.5290.0190.370
PLIP [19]0.9240.9200.8160.8350.874
MedCLIP [47]0.8810.8950.7900.6710.809
", + "image_path": "9d1a4eb718b8a8fa2c9ab6503d2fa79259adb0f53abb213f78e471b1e902c943.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 150, + 295, + 185 + ], + "lines": [ + { + "bbox": [ + 55, + 150, + 295, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 150, + 295, + 185 + ], + "type": "text", + "content": "Table 6. Zero-shot classification F1 scores " + }, + { + "bbox": [ + 55, + 150, + 295, + 185 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 55, + 150, + 295, + 185 + ], + "type": "text", + "content": " on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with text and image prompts." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 61, + 196, + 293, + 316 + ], + "blocks": [ + { + "bbox": [ + 61, + 196, + 293, + 316 + ], + "lines": [ + { + "bbox": [ + 61, + 196, + 293, + 316 + ], + "spans": [ + { + "bbox": [ + 61, + 196, + 293, + 316 + ], + "type": "image", + "image_path": "bbc81cecd43f5609ff21276b10bbef31dc8c19f5560daf797d936385c242c70e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 324, + 296, + 369 + ], + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 369 + ], + "type": "text", + "content": "Figure 4. Ablation study of the number of prototype images. Proto Num represents the number of prototype images per sub-bank for each category. We report the mIoU values with Standard Deviation obtained over 10 runs with different random seeds." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 379, + 228, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 379, + 228, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 379, + 228, + 390 + ], + "type": "text", + "content": "ing to incomplete or erroneous activations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "spans": [ + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "text", + "content": "Ablation study of the Modules. We analyzed the effectiveness of different modules within PBLP. As shown in Table 5, both the SIM and the Adaptive Thresholding Module significantly enhance model performance. Specifically, when the SIM module is removed, we substitute it with a simple " + }, + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "text", + "content": " convolutional layer to generate the pseudo-segmentation masks. The results demonstrate a noticeable decline in performance without the SIM and AT module. The SIM module captures intra-class heterogeneity and inter-class homogeneity better than the " + }, + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 54, + 390, + 295, + 558 + ], + "type": "text", + "content": " convolutional layer. Furthermore, Figure 1 illustrates the foreground images generated by the model with and without the AT module. The results demonstrate that AT effectively reduces noise in background regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 558, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 714 + ], + "type": "text", + "content": "Additionally, we evaluated the performance of our model using different image encoders and backbones, as summarized in Table 3. The combination of MedCLIP [47] and SegFormer achieved the best results in terms of mIoU metric. We observed that the PLIP [19] and SegFormer pairing performed best on the bIoU, FWIoU, and Dice coefficient. The TransUNet model [4], with its end-to-end architecture that does not utilize the SIM module for pseudo-mask computation, exhibited inferior performance. These results suggest that the absence of the SIM module may contribute to the lower effectiveness. Moreover, the relatively poor performance of CLIP [36] and DINOv2 [31] further highlights the importance of external knowledge from pretraining in" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 71, + 555, + 219 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 555, + 219 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 555, + 219 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 555, + 219 + ], + "type": "image", + "image_path": "ada068df4a82c0fe6d0f3b43424424ba5eea4ab816908c1944780ebe37eeff31.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 227, + 555, + 293 + ], + "lines": [ + { + "bbox": [ + 313, + 227, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 555, + 293 + ], + "type": "text", + "content": "Figure 5. a. Visualization of the pseudo-segmentation masks generated by models in the first stage on BCSS-WSSS. The masks are overlaid on the input images, with the raw pseudo-segmentation mask shown in the top-left corner. b. The foreground images generated by PBIP for the four segmentation targets. More visualizations are in Supplementary Material." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 308, + 553, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 553, + 332 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 553, + 332 + ], + "type": "text", + "content": "histopathology, as these more generic encoders appear less effective for the specialized task of tissue segmentation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 333, + 555, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 333, + 555, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 333, + 555, + 525 + ], + "type": "text", + "content": "Text prompt and Image prompt. To explore the challenges of image-text matching in histopathology, we conducted zero-shot classification experiments on the BCSS-WSSS dataset using CLIP, PLIP, and MedCLIP with both text and image prompts (see Table 6). For text prompts, we used the common format: \"a photo of {class name} \", while for image prompts, we utilized our prototype image features. The results show that PLIP and MedCLIP significantly outperform CLIP when using image prompts, but all models perform poorly with text prompts. This highlights the substantial challenges of text prompting in histopathology, where textual descriptions struggle to capture complex visual patterns and inter-class homogeneity. In contrast, image prompts effectively guide the models by aligning with the intricate characteristics of histopathological images through prototype features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 538, + 388, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 388, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 388, + 551 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 559, + 555, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 555, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 555, + 704 + ], + "type": "text", + "content": "We proposed a novel Prototype-Based Image Prompting (PBIP) framework to address the challenges of inter-class homogeneity and intra-class heterogeneity in weakly supervised histopathological image segmentation. PBIP leverages image-based labels and corresponding images in histopathology datasets by extracting class prototype features through clustering methods. By incorporating class prototypes, our approach effectively mitigates inter-class homogeneity, while multiple sub-prototypes for each class address intra-class heterogeneity. Validation on four datasets demonstrated that PBIP achieves state-of-the-art performance and robustness in weakly supervised histopathological segmentation." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30278" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "type": "text", + "content": "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. 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This paper investigates ICL on Large Vision-Language Models (LVLMs) and explores the policies of multi-modal demonstration selection. Existing research efforts in ICL face significant challenges: First, they rely on pre-defined demonstrations or heuristic selecting strategies based on human intuition, which are usually inadequate for covering diverse task requirements, leading to sub-optimal solutions; Second, individually selecting each demonstration fails in modeling the interactions between them, resulting in information redundancy. Unlike these prevailing efforts, we propose a new exploration-exploitation reinforcement learning framework, which explores policies to fuse multi-modal information and adaptively select adequate demonstrations as an integrated whole. The framework allows LVLMs to optimize themselves by continually refining their demonstrations through self-exploration, enabling the ability to autonomously identify and generate the most effective selection policies for in-context learning. Experimental results verify the superior performance of our approach on four Visual Question-Answering (VQA) datasets, demonstrating its effectiveness in enhancing the generalization capability of few-shot LVLMs.", + "bbox": [ + 88, + 358, + 483, + 751 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 779, + 220, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed remarkable advancements in Large Vision-Language Models (LVLMs) [43]. Powered by the rapid development of Language Models (LMs) and extensive pretraining on large-scale vision-language datasets,", + "bbox": [ + 89, + 804, + 483, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7b895d1976718ff9720a14842ce1b18d2d41c9ea6072c87ff5c5eedb0b3e8e72.jpg", + "image_caption": [ + "Figure 1. The motivation of the proposed method. The method consists of two stages: exploration and exploitation. In the exploration stage, a stochastic beam search is conducted to generate multiple selection strategies for the query. We reason the output with a large language model and comprehensively evaluate these multiple demonstration sets. In the exploitation stage, the policy is optimized based on evaluation, making it more likely to select the optimal combination. These two stages iterate continuously, resulting in seeking the optimal strategy." + ], + "image_footnote": [], + "bbox": [ + 517, + 325, + 906, + 577 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LVLMs have demonstrated exceptional capabilities on various tasks, including generation [1, 3, 9, 29, 36], translation [15, 16, 21, 23, 40], and beyond [12, 14, 24, 38]. Despite their impressive performance, LVLMs still encounter substantial challenges in adapting to novel scenarios, primarily due to the resource-intensive nature of fine-tuning procedures.", + "bbox": [ + 511, + 744, + 906, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle this problem, In-Context Learning (ICL) offers a training-free alternative to conventional fine-tuning approaches. Specifically, ICL augments the prompt with", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work.", + "bbox": [ + 107, + 875, + 364, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 109, + 887, + 241, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3826", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a few high-quality examples, i.e., demonstrations, allowing models to learn from them efficiently during inference. This enables LVLMs to leverage analogical reasoning and effectively generalize to novel tasks. Consequently, ICL is becoming a widely-used technique for easily improving the performance of both LLMs and VLMs [10, 19, 28, 37, 41].", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The selection of demonstrations plays a crucial role in ICL for LVLMs. Current approaches predominantly rely on heuristic selection strategies, which can be categorized into two main lines. The first line adopts query-independent selection, utilizing predefined demonstrations for simplicity and stability. However, this static approach fails to cover the diverse range of task requirements, leading to suboptimal performance when handling novel vision-language tasks [5, 37, 41]. The second line employs dynamic selection strategies, typically retrieving demonstrations with higher embedding similarity to the query. While similarity-based methods have shown promise in language-only domains, they face significant limitations in multi-modal scenarios. First, high similarity scores do not guarantee high demonstration utility, potentially overlooking valuable demonstrations while retrieving samples with limited reference value. Second, the individual selection of demonstrations results in substantial information redundancy among retrieved top-similar samples, since it doesn't consider the inter-sample relationships. This severely hampers the model's generation capability. These heuristic approaches, whether through manual curation or fixed strategies, suffer from a lack of learning capability, failing to fully exploit appropriate demonstrations and thus severely limiting the potential of ICL. Moreover, the inherent difficulty of vision-language alignment poses additional challenges for demonstration selection, as it requires effectively capturing both visual and textual semantic relationships.", + "bbox": [ + 91, + 186, + 486, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper investigates the multi-modal demonstration selection for in-context learning of LVLMs. Departing from heuristic selection approaches, we introduce an end-to-end learnable framework that automatically optimizes the demonstration combinations. To address the redundancy issues, we reformulate demonstration selection as a combinatorial optimization problem rather than independent sample selection. However, unlike conventional supervised learning tasks, this combinatorial optimization problem is particularly challenging as the optimal demonstration combinations cannot be manually annotated, resulting in the absence of direct supervision signals. To address the challenge, we propose a novel exploration-exploitation framework that adaptively learns to choose demonstrations in a reinforcement-like manner. As illustrated in Figure 1, our framework iteratively conducts an exploration phase to efficiently explore good demonstration combinations and an exploitation phase to reinforce the sampling-policy network. Given a query (image-question pair) and a candi", + "bbox": [ + 89, + 613, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "date demonstration set, the sampling-policy network first leverages interaction encoding to establish cross-modal relationships, then performs auto-regressive demonstration selection, where each selection decision is informed by the ensemble of previously selected samples. In the exploration phase, the framework applies stochastic beam search to the sampling-policy network, generating multiple possible demonstration combinations. These combinations are then evaluated by feeding them along with the query into the LVLM to obtain effective rewards. In the exploitation phase, the sampling policy is optimized using policy gradient reinforcement learning based on the rewards of different combinations. This process strengthens the joint probability of high-performing combinations while suppressing that of less effective ones. Through alternating between exploration and exploitation phases, the framework enables models to autonomously identify and generate the most effective demonstration sets for input queries. This approach reduces the dependence on manual intervention and significantly improves generalization and adaptability.", + "bbox": [ + 511, + 90, + 903, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are summarized below:", + "bbox": [ + 532, + 393, + 893, + 409 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We view ICL demonstration selection from a new perspective of combinatorial optimization. It mitigates the drawbacks of individual selection by interaction among samples, thereby reducing information redundancy and enhancing demo utility.", + "- We introduce a multi-modal exploration-exploitation framework. It iteratively conducts an exploration phase to explore better demonstration combinations by stochastic tree search, and an exploitation phase to adaptively optimize the sampling-policy network in a reinforcement manner.", + "- Extensive experiments on four representative VQA datasets across multiple LVLMs demonstrate the effectiveness of our methods." + ], + "bbox": [ + 511, + 410, + 903, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 638, + 663, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. In-context Learning", + "text_level": 1, + "bbox": [ + 513, + 664, + 705, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pre-trained VLMs show the ability to understand and reason. Consequently, in-context learning (ICL) uses examples related to the input query to activate the few-shot ability of models and predict the answers through analogy. Many methods have been explored. Brown et al. [5] first explore the few-shot ability of the language models and propose in-context learning with fixed demonstrations. Recent works have shown that dynamical retrieval leads to better improvement compared with the fixed. The dynamical retrieval shares similar ideas with retrieval-augmented generation (RAG), for example, MuRAG [8] selects multi-modal references related to questions, while the different motivations lead to different optimization goals and evaluations. Wang et al. [37] propose a method that retrieves instances", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3827", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/937cce982f2b544e1f55ef59329b91dbd7508943539516124b371e7dc1387c49.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed framework. It comprises three parts: multi-modal interactive encoding, self-exploration, and self-exploitation. First, the questions and images of queries and candidate demonstrations are encoded to generate multi-modal features, which are subsequently processed through a fusion encoder to output the interactive features. Following this, we employ auto-regressive decoder to generate multiple demonstration combinations that are suitable for the query. These combinations are used in few-shot inference. Finally, the predicted outputs are compared against the ground-truth to get responsive rewards, leveraged to optimize the selection policy." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 903, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "similar to the query. Zemlyanskiy et al. [41] also propose retrieval methods based on similarity but it considers both input and output. Besides similarity, diversity has been proven effective [10, 19, 28]. For example, Itay et al. [19] find that various structures encourage the model to generalize and propose methods to select diverse demonstrations. Gao et al. [10] find that ambiguous examples can better improve ICL performance compared to selecting semantically similar ones only. Li et al. [22] propose a unified retriever by training a model on multiple tasks with ranking loss. While most works focus on LLMs, we extend the research to the LVLMs and further investigate efficient information utilization for better demonstration combination strategies.", + "bbox": [ + 88, + 469, + 483, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Large Vision-Language Model", + "text_level": 1, + "bbox": [ + 89, + 679, + 362, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Building upon the success of LLMs, researchers are focusing on large vision-language models (LVLMs) and have achieved substantial advancements, which enable the understanding of complex interactions between images and text [42]. GPT-4 (Vision) [29] and Gemini [35] first explore the region, showing impressive multi-modal understanding and generation capabilities. Liu et al. [25] train a large multimodal model LLaVA that connects vision and language for general understanding. Similar work includes Minigpt-4 [45], BLIP-2 [20] and others. Later, new work explores how to enable LVLMs to predict multimodal outputs, such as Koh et al. [18] and Zheng et al. [44], they enable the LLMs to predict visual outputs with the text representations.", + "bbox": [ + 89, + 703, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Early ICL work primarily focuses on LLMs. With the development of LVLMs, there has been growing attention on how to utilize multimodal information and propose more effective ICL strategies on LVLMs.", + "bbox": [ + 511, + 469, + 906, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. LLM with Reinforcement Learning", + "text_level": 1, + "bbox": [ + 511, + 541, + 821, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the realm of reinforcement learning, the concepts of exploration and exploitation are the foundation to make decisions. Recent advancements in exploration and exploitation strategies have led to several notable algorithms. Schulman et al. [32] propose an effective PPO algorithm, which allows for effective exploration while ensuring that the agent does not deviate far from a learned policy. Rafailov et al. [30] simplify the complex RL algorithm and propose DPO to solve the standard RLHF problem by using a simple classification loss. Later, Shao et al. [33] introduce a variant of PPO, i.e., GRPO, replacing value function approximation with the average reward of multiple samples. These methods exemplify the significant progress in balancing exploration and exploitation, substantially advancing the efficiency of reinforcement learning.", + "bbox": [ + 511, + 565, + 906, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 511, + 806, + 612, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation and Overview", + "text_level": 1, + "bbox": [ + 511, + 830, + 764, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denote the tasks $\\mathcal{T}$ , $(\\mathbf{t},\\mathcal{I},\\mathbf{y})\\sim \\mathcal{T}$ a query with answer, and the large vision-language model as $\\mathcal{F}:\\mathbf{x},\\mathcal{I}\\mapsto \\mathbf{y}$ that receives a prompt $\\mathbf{t}$ and its associated RGB images sequence", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3828", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathcal{I} = \\{\\mathbf{I}_1,\\mathbf{I}_2,\\ldots \\}$ , where $\\mathbf{I}_{(\\cdot)}\\in \\mathbb{R}^{CHW}$ , to predict the textual output $\\mathbf{y}$ .", + "bbox": [ + 89, + 89, + 482, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denote $\\mathcal{D}$ as the candidate demonstrations, our few-shot in-context learning tries to find an adaptive policy", + "bbox": [ + 89, + 121, + 482, + 152 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P}: \\mathbf {t} _ {q}, \\mathcal {I} _ {q} \\mapsto \\mathcal {E} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 162, + 482, + 180 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to select optimal demonstration combination", + "bbox": [ + 89, + 191, + 392, + 205 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} = \\left\\{\\mathbf {d} _ {1}, \\mathbf {d} _ {2}, \\dots , \\mathbf {d} _ {m} \\right\\} \\subset \\mathcal {D} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 217, + 482, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for a query $(\\mathbf{t}_q,\\mathcal{I}_q)$ , where $\\mathbf{d}_i = (\\mathbf{t}_i,\\mathcal{I}_i,\\mathbf{y}_i)$ is a demonstration and $\\mathbf{y}$ is the associated answer to its query $\\mathbf{t}$ . With $\\mathcal{E}$ , VLM $\\mathcal{F}$ predicts the improved output by feeding an input $P(\\mathbf{t}_q,\\mathcal{E})$ of the form", + "bbox": [ + 89, + 244, + 483, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(\\mathbf {t} _ {q}, \\mathcal {E}\\right) = \\mathbf {t} _ {1} \\quad \\mathbf {y} _ {1} \\quad \\mathbf {t} _ {2} \\quad \\mathbf {y} _ {2} \\quad \\dots \\quad \\mathbf {t} _ {m} \\quad \\mathbf {y} _ {m} \\quad \\mathbf {t} _ {q}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 316, + 482, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To sum up, our objective is to find a policy for demonstration selection:", + "bbox": [ + 89, + 345, + 482, + 375 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {*} = \\arg \\max _ {\\mathcal {P}} \\mathbb {E} _ {(\\mathbf {t}, \\mathcal {I}, \\mathbf {y}) \\sim \\mathcal {T}} \\xi (\\mathcal {F} (P (\\mathbf {t} _ {q}, \\mathcal {E}), \\cup \\mathcal {I}), \\mathbf {y}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 387, + 482, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\cup \\mathcal{I}$ contain all images from demonstrations and the query, and $\\xi$ is the evaluation criterion, e.g., VQAScore.", + "bbox": [ + 89, + 415, + 482, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivation and Framework As aforementioned, the interactions between demonstrations matter in ICL, and multiple factors affect the behaviors of demonstrations on the few-shot inference. Intuitively, we propose to view demonstration selection as a combinatorial optimization problem, and introduce exploration-exploitation to iteratively find the optimal policies, which relies on the three-fold framework: 1) Multi-modal Fusion Encoder to catch the rich features interactively; 2) Stochastic Beam Search with auto-regressive decoder to find possible strategies for demonstration combination selection; 3) Responsive Reinforcement to exploit those strategies for finding the optimal policy.", + "bbox": [ + 89, + 446, + 483, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Multi-modal Interactive Encoding", + "text_level": 1, + "bbox": [ + 89, + 635, + 390, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While in vanilla ICL fixed demonstrations can be embedded into prompts for VLMs inference [5], several works have explored heuristic methods as better strategies, such as selecting according to similarity [37, 41] or diversity [10, 19]. Although these methods have achieved improvements, they do not cover two major problems that theoretically limit the potential of VLMs: a) These methods do not explore dynamic multimodal relationships, which mainly focus on hand-crafted heuristic strategies. b) Selection of demonstrations is independent, failing to consider the interaction between demonstrations. This is also prone to issues such as information redundancy.", + "bbox": [ + 89, + 657, + 482, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To tackle the problems, we therefore propose our Multimodal Interactive Encoding, which includes two parts, multi-modal encoder $f_{e}$ and fusion encoder $f_{f}$ . Given query $(\\mathbf{t},\\mathcal{I})$ and candidate demonstrations $\\mathcal{D}$ , different", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "modalities are first fed into multi-modal encoder $f_{e}$ to get the textual feature $\\{\\mathbf{f}_{\\mathbf{t}_q},\\mathbf{f}_{\\mathbf{t}_1},\\mathbf{f}_{\\mathbf{t}_2},\\ldots \\}$ and image features $\\{\\mathbf{f}_{\\mathbf{I}_q},\\mathbf{f}_{\\mathbf{I}_1},\\mathbf{f}_{\\mathbf{I}_2},\\ldots \\}$ , it has the following form:", + "bbox": [ + 511, + 90, + 905, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\mathbf {f} _ {\\mathbf {t} _ {q}}, \\mathbf {f} _ {\\mathbf {t} _ {1}}, \\mathbf {f} _ {\\mathbf {t} _ {2}}, \\dots \\right\\} = \\left\\{f _ {e} \\left(\\mathbf {t} _ {q}\\right), f _ {e} \\left(\\mathbf {t} _ {1}\\right), f _ {e} \\left(\\mathbf {t} _ {2}\\right), \\dots \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 148, + 903, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\mathbf {f} _ {\\mathbf {I} _ {q}}, \\mathbf {f} _ {\\mathbf {I} _ {1}}, \\mathbf {f} _ {\\mathbf {I} _ {2}}, \\ldots \\} = \\{f _ {e} (\\mathbf {I} _ {q}), f _ {e} (\\mathbf {I} _ {1}), f _ {e} (\\mathbf {I} _ {2}), \\ldots \\}. \\quad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 167, + 903, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To account for the interaction between multi-modal features, as well as the interaction between candidate demonstrations and queries, we implement $f_{f}$ as a transformer encoder, thereby ensuring global interactions among tokens. Features of different modalities are first embedded with separate functional embedding $\\Delta_{\\{t,i\\}}^{f}$ to distinguish them. Subsequently, positional encodings $\\Delta_{i}^{p}$ are respectively added to features of different modalities, thereby establishing correlations among corresponding features", + "bbox": [ + 511, + 199, + 906, + 338 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} + \\Delta_ {\\{t, i \\}} ^ {f}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 349, + 903, + 371 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} + \\Delta_ {\\{t, i \\}} ^ {f} + \\Delta_ {k} ^ {p}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 375, + 903, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, the queries and examples are fed into the fusion encoder $f_{f}$ to obtain interactive feature $\\mathbf{M}$ .", + "bbox": [ + 511, + 405, + 905, + 435 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} = f _ {f} \\left(\\left[ \\begin{array}{l l l l l l l} \\mathbf {f} _ {\\mathbf {t} _ {q}} & \\mathbf {f} _ {\\mathbf {I} _ {q}} & \\mathbf {f} _ {\\mathbf {t} _ {1}} & \\mathbf {f} _ {\\mathbf {I} _ {1}} & \\mathbf {f} _ {\\mathbf {t} _ {2}} & \\mathbf {f} _ {\\mathbf {I} _ {2}} & \\dots \\end{array} \\right]\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 446, + 903, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During this process, features of different modalities of queries and candidate demonstrations are fused to learn the characteristics of multi-modal tasks.", + "bbox": [ + 511, + 478, + 906, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Stochastic Beam Search Exploration", + "text_level": 1, + "bbox": [ + 511, + 535, + 828, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Auto-regressive Decoding Given the black-box nature of both the problem characteristics and VLMs, it is challenging for humans to manually design appropriate demonstration sets and selection strategies. To frame demonstration selection as a combinatorial optimization problem, we introduce an auto-regressive transformer decoder $f_{d}$ .", + "bbox": [ + 511, + 560, + 905, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $\\mathbf{M}$ by interactive encoder, decoder $f_{d}$ then predicts the $i$ -th demonstration $\\mathbf{d}_i$ based on the queries, candidates and other $i - 1$ demonstrations $\\mathcal{E}$ by", + "bbox": [ + 511, + 651, + 905, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} = \\alpha_ {t} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {t} _ {i}}\\right) + \\alpha_ {i} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {I} _ {i}}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 710, + 903, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni = \\arg \\max _ {i} [ p _ {i} \\leq \\min \\{p _ {j} \\} ], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 744, + 903, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{dist}()$ is the cosine similarity in our implementation, $\\alpha_{\\{t,i\\}}$ are weight coefficients. This process is autoregressive to achieve the policy $\\pi_{\\theta}$", + "bbox": [ + 511, + 775, + 905, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {\\theta} (\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {d} _ {i} \\mid \\mathbf {d} _ {1}, \\mathbf {d} _ {2}, \\dots , \\mathbf {d} _ {i - 1}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 833, + 903, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus the selection is modeled as a combinatorial problem.", + "bbox": [ + 511, + 885, + 897, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3829", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Stochastic beam search" + ], + "code_body": "Data: policy $\\pi_{\\theta}$ , candidate demonstration $\\mathcal{D}$ size of demonstration combination $m$ \nResult: $B_{m}$ , set of candidate demonstration sets. \n $B_0\\gets \\{(1,\\emptyset)\\}$ . \nfor $i\\gets 1$ to m do \n $B\\gets \\varnothing$ \nfor $(s,\\mathcal{E})\\in B_{t - 1}$ do /\\* Enumerate and concatenate every demonstration \\*/ for $\\mathbf{d}\\in \\mathcal{D}$ do $s\\gets s\\cdot \\pi_{\\theta}(\\mathbf{d}\\mid \\mathcal{E},\\mathbf{t}_q,\\mathcal{I}_q);$ $B\\gets B\\cup \\{(s,\\mathcal{E}\\cup \\mathbf{d})\\}$ end \nend \n/\\*Normalize the possibility \\*/ $S\\gets 0$ \nfor $(s,\\mathcal{E})\\in B$ do $S\\gets S + |s|$ \nend \n $s\\gets \\frac{s}{|S|}$ for each item in $B$ sample from $B$ with possibility $s$ to get $B_{i}$", + "bbox": [ + 109, + 112, + 459, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stochastic Beam Search To facilitate exploration, we incorporate beam search into our algorithm as a method for exploring various policies. Beam Search is a heuristic search algorithm widely adopted in NLP tasks such as sequence generation. However, due to beam search always expanding the highest probability option at each step, it is not suitable for policy exploration. We modify the traditional beam search to a stochastic sampling version, allowing for stochastic exploration. The algorithm is listed in Algorithm 1. Intuitively, it does not always accept the current \"optimal\" options, thereby introducing the exploration.", + "bbox": [ + 89, + 493, + 483, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through this algorithm, the model can start from a random policy, continuously explore various strategies, and provide potential optimization directions for the framework.", + "bbox": [ + 89, + 664, + 483, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Responsive Reinforcement Exploitation", + "text_level": 1, + "bbox": [ + 89, + 732, + 429, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After establishing a sufficiently flexible model and exploration algorithm, we introduce our Responsive Reinforcement Exploitation to continuously optimize the superior policies.", + "bbox": [ + 89, + 758, + 483, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a query $(\\mathbf{t}_q,\\mathcal{I}_q)$ , the exploration phase first explores and sample multiple candidate demonstration combinations $\\mathcal{E}_1,\\mathcal{E}_2,\\ldots ,\\mathcal{E}_c$ by the stochastic beam search with policy $\\pi_{\\theta}$ . Based on the combinations, the framework optimizes the policy model $\\pi_{\\theta}$ by maximizing the following", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2: Training Algorithm" + ], + "code_body": "Data: task $\\mathcal{T}$ , candidate demonstrations $\\mathcal{D}$ size of demonstration sets $m$ \nResult: policy $\\pi_{\\theta}$ \ninit $\\pi_{\\theta}$ randomly; \nfor $(\\mathbf{t}_q,\\mathcal{I}_q,\\mathbf{y})\\sim \\mathcal{T}$ do $\\{(s_i,\\mathcal{E}_i)\\}_{i = 1}^c\\gets$ beam-search $(\\pi_{\\theta},\\mathcal{D},m,c)$ . $\\mathbf{o}_i\\gets \\mathcal{F}(P(\\mathbf{t}_q,\\mathcal{E}_i),\\bigcup_{\\mathcal{I}_j\\in \\mathcal{E}_i}\\mathcal{I}_j);$ $A_{i}\\gets r(\\mathbf{o}_{i},\\mathbf{y})$ . $\\hat{A}_i\\gets \\frac{A_i - \\mathrm{mean}(\\mathbf{A})}{\\mathrm{var}(\\mathbf{A})};$ Optimize $\\pi_{\\theta}$ to maximize $\\mathcal{L}$ \nend", + "bbox": [ + 526, + 111, + 874, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "objective:", + "bbox": [ + 513, + 325, + 581, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\left(\\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right) \\sim \\mathcal {T}, \\left\\{\\mathcal {E} _ {i} \\right\\} _ {i = 1} ^ {c} \\sim \\pi_ {\\theta} \\left(\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right)} \\\\ = \\frac {1}{c} \\sum_ {i = 1} ^ {c} \\hat {A} _ {i} \\cdot \\sum_ {k = 1} ^ {m} \\log \\pi_ {\\theta} \\left(\\mathbf {d} _ {i, k} \\mid \\mathbf {d} _ {i, < k}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 354, + 903, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by policy gradient methods [17, 33], this optimization objective aims to adaptively optimize the joint probability of various demonstration combinations under the policy model. The advantage term $\\hat{A}_i$ represents the relative benefit of each combination, where a larger advantage value indicates a more beneficial combination, thus warranting an increase in its corresponding joint probability. Specifically, the advantage $\\hat{A}_i$ is responsively calculated as", + "bbox": [ + 511, + 428, + 906, + 549 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {i} = r \\left(\\mathcal {F} \\left(P \\left(\\mathbf {t} _ {q}, \\mathcal {E} _ {i}\\right), \\mathcal {I} _ {q} \\cup \\bigcup_ {\\mathcal {I} _ {j} \\in \\mathcal {E} _ {i}} \\mathcal {I} _ {j}\\right), \\mathbf {y}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 561, + 906, + 611 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {A} _ {i} = \\frac {A _ {i} - \\operatorname {m e a n} (\\mathbf {A})}{\\operatorname {v a r} (\\mathbf {A})}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 612, + 905, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $r(\\cdot)$ is reward function and $A_{i}$ is the original advantages for each combination. $\\mathbf{A} = [A_1, \\dots, A_c]$ denotes the original advantages of all explored combinations for one query. Based on $\\mathbf{A}$ , the final advantage $\\hat{A}_i$ is obtained through query-wise standard normalization. It mitigates the distributional discrepancies across queries while ensuring a balanced distribution of positive and negative advantage values. For our experiments, we simply implement $r(\\cdot)$ as", + "bbox": [ + 511, + 657, + 906, + 780 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr (\\mathbf {o}, \\mathbf {y}) = \\mathbb {1} _ {[ \\mathbf {o} \\text {i s e q u i v a l e n t t o} \\mathbf {y} ]}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 794, + 903, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}_{[condition]}$ is the indicator function, equaling 1 if and only if the output o matches the ground-truth y; otherwise, 0. In this way, our approach is able to leverage the explored strategies to gradually uncover adaptive sampling policies that are suitable for various types of queries.", + "bbox": [ + 511, + 824, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3830", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/98f18e62c93ceed8c9d38bd9aacb104a074438931437f484b8d913e892ed40c5.jpg", + "table_caption": [ + "Table 1. Experimental comparison using VQAScore with the state-of-the-art methods on four VQA benchmarks." + ], + "table_footnote": [], + "table_body": "
MethodsOKVQATextVQAVizwizMMStarAvg.
CPFPIRLRSTMA
zero-shot57.565.232.852.037.647.625.317.933.241.0
random61.167.440.557.233.946.726.620.528.842.5
similarity (Qwen [2])60.667.248.757.231.447.232.826.227.144.3
BM25 [31]60.366.943.659.834.151.130.623.624.943.9
Ours (Qwen [2])64.767.453.656.836.246.634.124.929.345.9
similarity (LLaVA [25])22.733.619.848.528.443.733.623.627.531.3
Ours (LLaVA [25])44.350.145.654.638.049.836.720.128.440.8
", + "bbox": [ + 107, + 114, + 890, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 297, + 223, + 314 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Setups", + "text_level": 1, + "bbox": [ + 89, + 323, + 272, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. To demonstrate the generality of our method, following the previous studies [2], we conduct experiments on four representative VQA benchmarks, i.e., OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. OKVQA is a large-scale VQA benchmark constructed based on the MS-COCO dataset, which contains 14k question-answer pairs and 14k images. TextVQA dataset contains 28k images and associated questions with human-annotated answers. Vizwiz dataset contains 24k image/question pairs collected from the blind. MMStar is designed to evaluate the multi-modal capacities with carefully balanced challenge samples. These datasets include images and diverse text questions, reflecting ICL performance and showcasing the adaptability of methods to various tasks.", + "bbox": [ + 88, + 347, + 482, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline and Evaluation Metrics. We adopt a heuristic similarity policy as baseline, which selects demonstrations by cosine similarities of the embeddings. For fair comparisons, we follow previous studies [2] to use VQAScore as the main metric. The results are reported on validation sets.", + "bbox": [ + 89, + 560, + 482, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 648, + 307, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data Processing. Following previous studies [2], we adopt the official validation sets of OKVQA, TextVQA, and Vizwiz benchmarks to evaluate the performance. As no splits are provided for MMStar, following convention, we divide it into training and validation sets in a 7:3 ratio, treating the training sets as candidate demonstrations for both training and validation sets.", + "bbox": [ + 89, + 672, + 482, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Details. We adopt ImageBind [11] as $f_{e}$ in the interactive encoding. We use Qwen-VL [2] and LLaVA [25] as LVLMs. We implement $\\Delta$ as learnable functional and positional encoding following [6]. AdamW optimizer is adopted to train models for 10 epochs. The learning rate is $5 \\times 10^{-5}$ . The batch size is set as 8. The hyperparameter $c$ in responsive reinforcement is set as 4. The beam width and temperature are set as 9 and 1.0. The selection model", + "bbox": [ + 89, + 779, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9ed708a776e4843540af4b16ced078e4d74be7d19d88b26b92c5259f24278784.jpg", + "table_caption": [ + "Table 2. Ablation studies of different modules on the OKVQA benchmark. SBS: Stochastic beam search. AR: Auto-regressive. RR: Responsive Reinforcement." + ], + "table_footnote": [], + "table_body": "
Training Alg.SBSARVQAScoreΔ
RR✓63.31.4 ↓
RR✓63.31.4 ↓
Preference✓✓62.91.8 ↓
RR✓✓64.7-
", + "bbox": [ + 531, + 349, + 888, + 449 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "consists of 6-layer transformers with 8 attention heads and 2048 hidden dimensions. As we evaluate LVLMs locally, all experiments are conducted on 8 NVIDIA A800 GPUs.", + "bbox": [ + 511, + 474, + 903, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with Representative Methods", + "text_level": 1, + "bbox": [ + 511, + 530, + 872, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We respectively compare our methods with four methods, zero-shot, random, similarity, BM25, on four datasets including OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. Table 1 show the comparisons of VQAScore between ours and other methods. Our method surpasses other representative methods on four datasets. Especially on OKVQA and VizWiz, it improves significantly, increasing by 4.1 and 4.9 compared to similarity. The average performance is improved by 1.6. Additionally, it is noteworthy that our method achieves improvements in fine-grained perception compared to coarse perception, as well as in logical reasoning compared to instance reasoning. For coarse perception and instance reasoning tasks, directly selecting similar demonstrations yields better performance, whereas our proposed reinforcement method is unstable in fitting this fixed strategy. Furthermore, Table 1 shows our method's lower performance on math tasks. The math problems follow rigid rules where minor variations can lead to completely different solution paths. Related but non-isomorphic demonstrations interfere with LVLMs' understanding. In general, the experimental results show that our method is more effective than various heuristic approaches. It provides more significant improvement for weaker models [7],", + "bbox": [ + 511, + 553, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3831", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c9f91952e46dddd8f134fc14f87dfeddf35af92763138a96c49607a72071bb11.jpg", + "image_caption": [ + "Figure 3. Left: VQAScore on OKVQA benchmark of our method with different number of demonstrations. Right: VQAScore on OKVQA benchmark of our method with different temperature values in stochastic beam search." + ], + "image_footnote": [], + "bbox": [ + 98, + 93, + 473, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "e.g., LLaVA. By treating the selection as a combinatorial optimization problem, we achieve better results than the independent selection strategy.", + "bbox": [ + 89, + 332, + 482, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Performance Analysis", + "text_level": 1, + "bbox": [ + 89, + 390, + 294, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Studies of Components. To verify the effectiveness, we conduct extensive ablation experiments. The results are shown in Table 2. Without auto-regressive generation, the selection of each demonstration is independent, leading to a significant decrease in performance. This indicates that the interactions between demonstrations play a crucial role in analogical understanding. Stochastic beam search not employed, the limited self-exploration restricts the variety of strategies and declines the performance. When using preference loss, the optimization is not stable to converge to the better solutions found by responsive reinforcement. Our proposed framework shows strong performance in promoting in-context learning.", + "bbox": [ + 89, + 415, + 482, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of Numbers of Demonstrations. The number of demos impacts ICL. We conduct experiments to investigate the contribution of demo sizes to the performance. From Figure 3(left), it can be observed that as the number increases, the performance gradually improves. However, when the demonstration set becomes too large, performance shows a certain decline. We believe that while a larger number of demonstrations provides more information, it challenges the reinforcement learning process, thereby decreasing the performance. Additionally, too many demonstrations also add a number of tokens, raising inference costs. Therefore, in our method, we set the size to 2.", + "bbox": [ + 89, + 612, + 482, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In beam search, temperature controls the gap between high- and low-probability demonstrations during sampling, thus affecting policy exploration. We conduct experiments with several different temperatures. The performance in Figure 3(right) shows a general trend. It first rises then declines as temperature increases, thus we set temperature as 1. This hyper-parameter should be adjusted based on the", + "bbox": [ + 89, + 795, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/524eb066d0cd4caeb51155c69880a73683577fc183c118cbe18bffa7b9e92af4.jpg", + "image_caption": [ + "Figure 4. The similarity distribution of demonstrations that correct wrong predictions on the OKVQA benchmark. The demonstrations selected with ours are dissimilar to the queries but correct the predictions." + ], + "image_footnote": [], + "bbox": [ + 542, + 94, + 879, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45d43e9bcf6e51554eaa6fe4ccc221e4d32e0caaa5574354889ee7783c68bf41.jpg", + "image_caption": [ + "Figure 5. The relationships in cosine similarity of two demonstrations selected with ours on the OKVQA dataset. The yellow dot and white dot represent the centroid (0.5, 0.5) and the data centroid, respectively. The data exhibits an overall leftward shift." + ], + "image_footnote": [], + "bbox": [ + 562, + 335, + 857, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "characteristics of the downstream tasks.", + "bbox": [ + 511, + 657, + 776, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inefficient Similarity Strategy. For the similarity-based strategy, we conduct more detailed experiments to verify its effects. In Figure 4, we illustrate the queries corrected by our method on the OKVQA dataset. Our method selects demonstrations with lower similarity for these examples and predicts the correct answer; the similarity-based strategy, on the other hand, selects more similar demonstrations but misleads the predictions. In this manner, we verify that similar demonstrations are not necessarily the most effective. We observe the similarity relationships between two selected demonstrations. As shown in Figure 5, our method tends to select a dissimilar demonstration first, followed by a similar one. This suggests a complex selection strategy that maintains both similarity and diversity. Next, we observe the demonstration ordering as many re", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3832", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c6f07ce82cbbfa0f485ed9cee7cc547d8f76f8346e840f6dbd2984ef907978a7.jpg", + "image_caption": [ + "Figure 6. Demonstrations selected with our method, similarity, and random strategies on the OKVQA dataset. The demos selected based on criteria such as similarity are closer to queries, but differ in structure or in key objects, which are ineffective in analogical reasoning. Our approach adaptively learns to identify and utilize demonstration combinations that maximize both complementarity and utility." + ], + "image_footnote": [], + "bbox": [ + 133, + 85, + 867, + 369 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6f82f1cb0b8ea9adf7b3a723ec38ce18ad94e237cf64d15ae8313b06e6d7ead5.jpg", + "table_caption": [ + "Table 3. The effect of the orders of demonstrations on the OKVQA benchmark." + ], + "table_footnote": [], + "table_body": "
Methodsnormal perm.reversed perm.Δ
Similarity60.6360.92+0.29
Ours64.6664.69+0.03
", + "bbox": [ + 91, + 484, + 483, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cent works [13, 26, 39] treat it as one main factor affecting efficiency. The results in Table 3 suggest that ordering effects are specific to certain strategies. Only similarity-based strategy is affected and improved when the query is closer to a more similar demo. The results indicate that our method captures robust characteristics of similarity and diversity.", + "bbox": [ + 89, + 579, + 482, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "What Makes A Better Demonstrations? Table 1 indicates that policies based on human intuition, such as rank by similarity, are not optimal. Then what makes a better demonstration? To verify this issue, we conduct an in-depth examination of the policies learned by models. The results are shown in Figure 6. In the first set of images, the similarity strategy correctly selects indoor scenes and gameplay images. However, the query does not address the main object of the image. The similar demonstrations fail to provide relevant information but mislead LVLMs, causing them to focus on irrelevant salient objects. The random strategy further demonstrates that LVLMs are easily disturbed by salient objects. In contrast, the demonstrations selected by our method direct the attention to small background instruments. Similarly, in the second set of images,", + "bbox": [ + 89, + 674, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the similarity strategy selects two food images according to the query. However, it does not lead to effective inference for query questioning the types. Random strategy reveals that LVLMs tend to predict incorrect answers. The demonstrations selected by ours prompt LVLMs to focus on the type characteristics. The use of a single or heuristic strategy fails to account for the multiple factors, including queries, semantics, and image content. Our proposed reinforcement learning framework allows for a more comprehensive exploration of effective policies.", + "bbox": [ + 511, + 446, + 906, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions and Limitations", + "text_level": 1, + "bbox": [ + 511, + 614, + 779, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In this paper, we focus on the problem of demonstration selection in in-context learning. We view the selection from a new perspective considering it as a combinatorial optimization problem to model the interactions among the demonstrations. In our framework, we propose multi-modal interactive encoding to catch the relationships between different modalities of queries and candidate demonstrations. We propose auto-regressive decoder with stochastic beam search to enable exploring policies for selection, and responsive reinforcement to exploit them. Experimental results demonstrate our proposed framework achieves superior performance.", + "bbox": [ + 511, + 642, + 906, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our proposed method explores language-vision multimodal ICL only. As research progresses, LLMs are incorporating more modalities such as video and audio, and the exploration of ICL within them remains a pressing area for investigation, leaving for our future work.", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3833", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rohan Anil et al. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models, 2023. 3" + ], + "bbox": [ + 516, + 92, + 906, + 680 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3835", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_model.json b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ebd9dad5996b3d66fab71b9064abc1cd300049bf --- /dev/null +++ b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_model.json @@ -0,0 +1,2068 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.13, + 0.853, + 0.177 + ], + "angle": 0, + "content": "Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.203, + 0.842, + 0.258 + ], + "angle": 0, + "content": "Cheng Chen\\* 1,2, Yunpeng Zhai\\* 2, Yifan Zhao\\* 1, Jinyang Gao2, Bolin Ding2, Jia Li\\* 1 \n1State Key Laboratory of Virtual Reality Technology and Systems \n2Tongyi Lab, Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.26, + 0.662, + 0.275 + ], + "angle": 0, + "content": "{chengchen, zhaoyf, jiali}@cvteam.net" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.278, + 0.753, + 0.293 + ], + "angle": 0, + "content": "{zhaiyunpeng.zyp, jinyang.gjy, bolin.ding}@alibaba-inc.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.327, + 0.327, + 0.343 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.359, + 0.485, + 0.752 + ], + "angle": 0, + "content": "In-context learning (ICL), a predominant trend in instruction learning, aims at enhancing the performance of large language models by providing clear task guidance and examples, improving their capability in task understanding and execution. This paper investigates ICL on Large Vision-Language Models (LVLMs) and explores the policies of multi-modal demonstration selection. Existing research efforts in ICL face significant challenges: First, they rely on pre-defined demonstrations or heuristic selecting strategies based on human intuition, which are usually inadequate for covering diverse task requirements, leading to sub-optimal solutions; Second, individually selecting each demonstration fails in modeling the interactions between them, resulting in information redundancy. Unlike these prevailing efforts, we propose a new exploration-exploitation reinforcement learning framework, which explores policies to fuse multi-modal information and adaptively select adequate demonstrations as an integrated whole. The framework allows LVLMs to optimize themselves by continually refining their demonstrations through self-exploration, enabling the ability to autonomously identify and generate the most effective selection policies for in-context learning. Experimental results verify the superior performance of our approach on four Visual Question-Answering (VQA) datasets, demonstrating its effectiveness in enhancing the generalization capability of few-shot LVLMs." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.78, + 0.222, + 0.795 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.805, + 0.484, + 0.867 + ], + "angle": 0, + "content": "Recent years have witnessed remarkable advancements in Large Vision-Language Models (LVLMs) [43]. Powered by the rapid development of Language Models (LMs) and extensive pretraining on large-scale vision-language datasets," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.327, + 0.907, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.587, + 0.907, + 0.713 + ], + "angle": 0, + "content": "Figure 1. The motivation of the proposed method. The method consists of two stages: exploration and exploitation. In the exploration stage, a stochastic beam search is conducted to generate multiple selection strategies for the query. We reason the output with a large language model and comprehensively evaluate these multiple demonstration sets. In the exploitation stage, the policy is optimized based on evaluation, making it more likely to select the optimal combination. These two stages iterate continuously, resulting in seeking the optimal strategy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.746, + 0.907, + 0.852 + ], + "angle": 0, + "content": "LVLMs have demonstrated exceptional capabilities on various tasks, including generation [1, 3, 9, 29, 36], translation [15, 16, 21, 23, 40], and beyond [12, 14, 24, 38]. Despite their impressive performance, LVLMs still encounter substantial challenges in adapting to novel scenarios, primarily due to the resource-intensive nature of fine-tuning procedures." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "To tackle this problem, In-Context Learning (ICL) offers a training-free alternative to conventional fine-tuning approaches. Specifically, ICL augments the prompt with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.365, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.242, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.365, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3826" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.183 + ], + "angle": 0, + "content": "a few high-quality examples, i.e., demonstrations, allowing models to learn from them efficiently during inference. This enables LVLMs to leverage analogical reasoning and effectively generalize to novel tasks. Consequently, ICL is becoming a widely-used technique for easily improving the performance of both LLMs and VLMs [10, 19, 28, 37, 41]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.188, + 0.487, + 0.61 + ], + "angle": 0, + "content": "The selection of demonstrations plays a crucial role in ICL for LVLMs. Current approaches predominantly rely on heuristic selection strategies, which can be categorized into two main lines. The first line adopts query-independent selection, utilizing predefined demonstrations for simplicity and stability. However, this static approach fails to cover the diverse range of task requirements, leading to suboptimal performance when handling novel vision-language tasks [5, 37, 41]. The second line employs dynamic selection strategies, typically retrieving demonstrations with higher embedding similarity to the query. While similarity-based methods have shown promise in language-only domains, they face significant limitations in multi-modal scenarios. First, high similarity scores do not guarantee high demonstration utility, potentially overlooking valuable demonstrations while retrieving samples with limited reference value. Second, the individual selection of demonstrations results in substantial information redundancy among retrieved top-similar samples, since it doesn't consider the inter-sample relationships. This severely hampers the model's generation capability. These heuristic approaches, whether through manual curation or fixed strategies, suffer from a lack of learning capability, failing to fully exploit appropriate demonstrations and thus severely limiting the potential of ICL. Moreover, the inherent difficulty of vision-language alignment poses additional challenges for demonstration selection, as it requires effectively capturing both visual and textual semantic relationships." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.485, + 0.901 + ], + "angle": 0, + "content": "This paper investigates the multi-modal demonstration selection for in-context learning of LVLMs. Departing from heuristic selection approaches, we introduce an end-to-end learnable framework that automatically optimizes the demonstration combinations. To address the redundancy issues, we reformulate demonstration selection as a combinatorial optimization problem rather than independent sample selection. However, unlike conventional supervised learning tasks, this combinatorial optimization problem is particularly challenging as the optimal demonstration combinations cannot be manually annotated, resulting in the absence of direct supervision signals. To address the challenge, we propose a novel exploration-exploitation framework that adaptively learns to choose demonstrations in a reinforcement-like manner. As illustrated in Figure 1, our framework iteratively conducts an exploration phase to efficiently explore good demonstration combinations and an exploitation phase to reinforce the sampling-policy network. Given a query (image-question pair) and a candi" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.394 + ], + "angle": 0, + "content": "date demonstration set, the sampling-policy network first leverages interaction encoding to establish cross-modal relationships, then performs auto-regressive demonstration selection, where each selection decision is informed by the ensemble of previously selected samples. In the exploration phase, the framework applies stochastic beam search to the sampling-policy network, generating multiple possible demonstration combinations. These combinations are then evaluated by feeding them along with the query into the LVLM to obtain effective rewards. In the exploitation phase, the sampling policy is optimized using policy gradient reinforcement learning based on the rewards of different combinations. This process strengthens the joint probability of high-performing combinations while suppressing that of less effective ones. Through alternating between exploration and exploitation phases, the framework enables models to autonomously identify and generate the most effective demonstration sets for input queries. This approach reduces the dependence on manual intervention and significantly improves generalization and adaptability." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.395, + 0.895, + 0.41 + ], + "angle": 0, + "content": "The contributions of this paper are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.411, + 0.905, + 0.486 + ], + "angle": 0, + "content": "- We view ICL demonstration selection from a new perspective of combinatorial optimization. It mitigates the drawbacks of individual selection by interaction among samples, thereby reducing information redundancy and enhancing demo utility." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.486, + 0.905, + 0.576 + ], + "angle": 0, + "content": "- We introduce a multi-modal exploration-exploitation framework. It iteratively conducts an exploration phase to explore better demonstration combinations by stochastic tree search, and an exploitation phase to adaptively optimize the sampling-policy network in a reinforcement manner." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.577, + 0.905, + 0.622 + ], + "angle": 0, + "content": "- Extensive experiments on four representative VQA datasets across multiple LVLMs demonstrate the effectiveness of our methods." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.411, + 0.905, + 0.622 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.639, + 0.665, + 0.656 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.665, + 0.707, + 0.682 + ], + "angle": 0, + "content": "2.1. In-context Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Pre-trained VLMs show the ability to understand and reason. Consequently, in-context learning (ICL) uses examples related to the input query to activate the few-shot ability of models and predict the answers through analogy. Many methods have been explored. Brown et al. [5] first explore the few-shot ability of the language models and propose in-context learning with fixed demonstrations. Recent works have shown that dynamical retrieval leads to better improvement compared with the fixed. The dynamical retrieval shares similar ideas with retrieval-augmented generation (RAG), for example, MuRAG [8] selects multi-modal references related to questions, while the different motivations lead to different optimization goals and evaluations. Wang et al. [37] propose a method that retrieves instances" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3827" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.086, + 0.905, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.374, + 0.908, + 0.446 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed framework. It comprises three parts: multi-modal interactive encoding, self-exploration, and self-exploitation. First, the questions and images of queries and candidate demonstrations are encoded to generate multi-modal features, which are subsequently processed through a fusion encoder to output the interactive features. Following this, we employ auto-regressive decoder to generate multiple demonstration combinations that are suitable for the query. These combinations are used in few-shot inference. Finally, the predicted outputs are compared against the ground-truth to get responsive rewards, leveraged to optimize the selection policy." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.47, + 0.484, + 0.669 + ], + "angle": 0, + "content": "similar to the query. Zemlyanskiy et al. [41] also propose retrieval methods based on similarity but it considers both input and output. Besides similarity, diversity has been proven effective [10, 19, 28]. For example, Itay et al. [19] find that various structures encourage the model to generalize and propose methods to select diverse demonstrations. Gao et al. [10] find that ambiguous examples can better improve ICL performance compared to selecting semantically similar ones only. Li et al. [22] propose a unified retriever by training a model on multiple tasks with ranking loss. While most works focus on LLMs, we extend the research to the LVLMs and further investigate efficient information utilization for better demonstration combination strategies." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.68, + 0.363, + 0.697 + ], + "angle": 0, + "content": "2.2. Large Vision-Language Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Building upon the success of LLMs, researchers are focusing on large vision-language models (LVLMs) and have achieved substantial advancements, which enable the understanding of complex interactions between images and text [42]. GPT-4 (Vision) [29] and Gemini [35] first explore the region, showing impressive multi-modal understanding and generation capabilities. Liu et al. [25] train a large multimodal model LLaVA that connects vision and language for general understanding. Similar work includes Minigpt-4 [45], BLIP-2 [20] and others. Later, new work explores how to enable LVLMs to predict multimodal outputs, such as Koh et al. [18] and Zheng et al. [44], they enable the LLMs to predict visual outputs with the text representations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.907, + 0.532 + ], + "angle": 0, + "content": "Early ICL work primarily focuses on LLMs. With the development of LVLMs, there has been growing attention on how to utilize multimodal information and propose more effective ICL strategies on LVLMs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.542, + 0.822, + 0.559 + ], + "angle": 0, + "content": "2.3. LLM with Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.907, + 0.793 + ], + "angle": 0, + "content": "In the realm of reinforcement learning, the concepts of exploration and exploitation are the foundation to make decisions. Recent advancements in exploration and exploitation strategies have led to several notable algorithms. Schulman et al. [32] propose an effective PPO algorithm, which allows for effective exploration while ensuring that the agent does not deviate far from a learned policy. Rafailov et al. [30] simplify the complex RL algorithm and propose DPO to solve the standard RLHF problem by using a simple classification loss. Later, Shao et al. [33] introduce a variant of PPO, i.e., GRPO, replacing value function approximation with the average reward of multiple samples. These methods exemplify the significant progress in balancing exploration and exploitation, substantially advancing the efficiency of reinforcement learning." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.807, + 0.613, + 0.822 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.832, + 0.765, + 0.848 + ], + "angle": 0, + "content": "3.1. Formulation and Overview" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Denote the tasks \\(\\mathcal{T}\\), \\((\\mathbf{t},\\mathcal{I},\\mathbf{y})\\sim \\mathcal{T}\\) a query with answer, and the large vision-language model as \\(\\mathcal{F}:\\mathbf{x},\\mathcal{I}\\mapsto \\mathbf{y}\\) that receives a prompt \\(\\mathbf{t}\\) and its associated RGB images sequence" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3828" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.09, + 0.483, + 0.121 + ], + "angle": 0, + "content": "\\(\\mathcal{I} = \\{\\mathbf{I}_1,\\mathbf{I}_2,\\ldots \\}\\), where \\(\\mathbf{I}_{(\\cdot)}\\in \\mathbb{R}^{CHW}\\), to predict the textual output \\(\\mathbf{y}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.122, + 0.483, + 0.153 + ], + "angle": 0, + "content": "Denote \\(\\mathcal{D}\\) as the candidate demonstrations, our few-shot in-context learning tries to find an adaptive policy" + }, + { + "type": "equation", + "bbox": [ + 0.235, + 0.164, + 0.483, + 0.181 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P}: \\mathbf {t} _ {q}, \\mathcal {I} _ {q} \\mapsto \\mathcal {E} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.192, + 0.393, + 0.206 + ], + "angle": 0, + "content": "to select optimal demonstration combination" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.218, + 0.483, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} = \\left\\{\\mathbf {d} _ {1}, \\mathbf {d} _ {2}, \\dots , \\mathbf {d} _ {m} \\right\\} \\subset \\mathcal {D} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.245, + 0.484, + 0.307 + ], + "angle": 0, + "content": "for a query \\((\\mathbf{t}_q,\\mathcal{I}_q)\\), where \\(\\mathbf{d}_i = (\\mathbf{t}_i,\\mathcal{I}_i,\\mathbf{y}_i)\\) is a demonstration and \\(\\mathbf{y}\\) is the associated answer to its query \\(\\mathbf{t}\\). With \\(\\mathcal{E}\\), VLM \\(\\mathcal{F}\\) predicts the improved output by feeding an input \\(P(\\mathbf{t}_q,\\mathcal{E})\\) of the form" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.318, + 0.483, + 0.337 + ], + "angle": 0, + "content": "\\[\nP \\left(\\mathbf {t} _ {q}, \\mathcal {E}\\right) = \\mathbf {t} _ {1} \\quad \\mathbf {y} _ {1} \\quad \\mathbf {t} _ {2} \\quad \\mathbf {y} _ {2} \\quad \\dots \\quad \\mathbf {t} _ {m} \\quad \\mathbf {y} _ {m} \\quad \\mathbf {t} _ {q}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.346, + 0.483, + 0.375 + ], + "angle": 0, + "content": "To sum up, our objective is to find a policy for demonstration selection:" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.388, + 0.483, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {*} = \\arg \\max _ {\\mathcal {P}} \\mathbb {E} _ {(\\mathbf {t}, \\mathcal {I}, \\mathbf {y}) \\sim \\mathcal {T}} \\xi (\\mathcal {F} (P (\\mathbf {t} _ {q}, \\mathcal {E}), \\cup \\mathcal {I}), \\mathbf {y}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.416, + 0.483, + 0.446 + ], + "angle": 0, + "content": "where \\(\\cup \\mathcal{I}\\) contain all images from demonstrations and the query, and \\(\\xi\\) is the evaluation criterion, e.g., VQAScore." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.447, + 0.484, + 0.629 + ], + "angle": 0, + "content": "Motivation and Framework As aforementioned, the interactions between demonstrations matter in ICL, and multiple factors affect the behaviors of demonstrations on the few-shot inference. Intuitively, we propose to view demonstration selection as a combinatorial optimization problem, and introduce exploration-exploitation to iteratively find the optimal policies, which relies on the three-fold framework: 1) Multi-modal Fusion Encoder to catch the rich features interactively; 2) Stochastic Beam Search with auto-regressive decoder to find possible strategies for demonstration combination selection; 3) Responsive Reinforcement to exploit those strategies for finding the optimal policy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.636, + 0.391, + 0.653 + ], + "angle": 0, + "content": "3.2. Multi-modal Interactive Encoding" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.839 + ], + "angle": 0, + "content": "While in vanilla ICL fixed demonstrations can be embedded into prompts for VLMs inference [5], several works have explored heuristic methods as better strategies, such as selecting according to similarity [37, 41] or diversity [10, 19]. Although these methods have achieved improvements, they do not cover two major problems that theoretically limit the potential of VLMs: a) These methods do not explore dynamic multimodal relationships, which mainly focus on hand-crafted heuristic strategies. b) Selection of demonstrations is independent, failing to consider the interaction between demonstrations. This is also prone to issues such as information redundancy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To tackle the problems, we therefore propose our Multimodal Interactive Encoding, which includes two parts, multi-modal encoder \\( f_{e} \\) and fusion encoder \\( f_{f} \\). Given query \\( (\\mathbf{t},\\mathcal{I}) \\) and candidate demonstrations \\( \\mathcal{D} \\), different" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.138 + ], + "angle": 0, + "content": "modalities are first fed into multi-modal encoder \\(f_{e}\\) to get the textual feature \\(\\{\\mathbf{f}_{\\mathbf{t}_q},\\mathbf{f}_{\\mathbf{t}_1},\\mathbf{f}_{\\mathbf{t}_2},\\ldots \\}\\) and image features \\(\\{\\mathbf{f}_{\\mathbf{I}_q},\\mathbf{f}_{\\mathbf{I}_1},\\mathbf{f}_{\\mathbf{I}_2},\\ldots \\}\\), it has the following form:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.15, + 0.905, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\mathbf {f} _ {\\mathbf {t} _ {q}}, \\mathbf {f} _ {\\mathbf {t} _ {1}}, \\mathbf {f} _ {\\mathbf {t} _ {2}}, \\dots \\right\\} = \\left\\{f _ {e} \\left(\\mathbf {t} _ {q}\\right), f _ {e} \\left(\\mathbf {t} _ {1}\\right), f _ {e} \\left(\\mathbf {t} _ {2}\\right), \\dots \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.169, + 0.905, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\{\\mathbf {f} _ {\\mathbf {I} _ {q}}, \\mathbf {f} _ {\\mathbf {I} _ {1}}, \\mathbf {f} _ {\\mathbf {I} _ {2}}, \\ldots \\} = \\{f _ {e} (\\mathbf {I} _ {q}), f _ {e} (\\mathbf {I} _ {1}), f _ {e} (\\mathbf {I} _ {2}), \\ldots \\}. \\quad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.2, + 0.907, + 0.339 + ], + "angle": 0, + "content": "To account for the interaction between multi-modal features, as well as the interaction between candidate demonstrations and queries, we implement \\( f_{f} \\) as a transformer encoder, thereby ensuring global interactions among tokens. Features of different modalities are first embedded with separate functional embedding \\( \\Delta_{\\{t,i\\}}^{f} \\) to distinguish them. Subsequently, positional encodings \\( \\Delta_{i}^{p} \\) are respectively added to features of different modalities, thereby establishing correlations among corresponding features" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.35, + 0.905, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} + \\Delta_ {\\{t, i \\}} ^ {f}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.375, + 0.905, + 0.396 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} + \\Delta_ {\\{t, i \\}} ^ {f} + \\Delta_ {k} ^ {p}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.406, + 0.906, + 0.436 + ], + "angle": 0, + "content": "Next, the queries and examples are fed into the fusion encoder \\( f_{f} \\) to obtain interactive feature \\( \\mathbf{M} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.448, + 0.905, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} = f _ {f} \\left(\\left[ \\begin{array}{l l l l l l l} \\mathbf {f} _ {\\mathbf {t} _ {q}} & \\mathbf {f} _ {\\mathbf {I} _ {q}} & \\mathbf {f} _ {\\mathbf {t} _ {1}} & \\mathbf {f} _ {\\mathbf {I} _ {1}} & \\mathbf {f} _ {\\mathbf {t} _ {2}} & \\mathbf {f} _ {\\mathbf {I} _ {2}} & \\dots \\end{array} \\right]\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.479, + 0.907, + 0.524 + ], + "angle": 0, + "content": "During this process, features of different modalities of queries and candidate demonstrations are fused to learn the characteristics of multi-modal tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.536, + 0.83, + 0.552 + ], + "angle": 0, + "content": "3.3. Stochastic Beam Search Exploration" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.561, + 0.906, + 0.651 + ], + "angle": 0, + "content": "Auto-regressive Decoding Given the black-box nature of both the problem characteristics and VLMs, it is challenging for humans to manually design appropriate demonstration sets and selection strategies. To frame demonstration selection as a combinatorial optimization problem, we introduce an auto-regressive transformer decoder \\( f_{d} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.652, + 0.906, + 0.697 + ], + "angle": 0, + "content": "With \\(\\mathbf{M}\\) by interactive encoder, decoder \\(f_{d}\\) then predicts the \\(i\\)-th demonstration \\(\\mathbf{d}_i\\) based on the queries, candidates and other \\(i - 1\\) demonstrations \\(\\mathcal{E}\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.711, + 0.905, + 0.742 + ], + "angle": 0, + "content": "\\[\np _ {i} = \\alpha_ {t} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {t} _ {i}}\\right) + \\alpha_ {i} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {I} _ {i}}\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.746, + 0.905, + 0.763 + ], + "angle": 0, + "content": "\\[\ni = \\arg \\max _ {i} [ p _ {i} \\leq \\min \\{p _ {j} \\} ], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.776, + 0.906, + 0.822 + ], + "angle": 0, + "content": "where \\(\\mathrm{dist}()\\) is the cosine similarity in our implementation, \\(\\alpha_{\\{t,i\\}}\\) are weight coefficients. This process is autoregressive to achieve the policy \\(\\pi_{\\theta}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.834, + 0.905, + 0.885 + ], + "angle": 0, + "content": "\\[\n\\pi_ {\\theta} (\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {d} _ {i} \\mid \\mathbf {d} _ {1}, \\mathbf {d} _ {2}, \\dots , \\mathbf {d} _ {i - 1}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.898, + 0.901 + ], + "angle": 0, + "content": "Thus the selection is modeled as a combinatorial problem." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3829" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.103, + 0.096, + 0.353, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Stochastic beam search" + }, + { + "type": "algorithm", + "bbox": [ + 0.11, + 0.113, + 0.46, + 0.453 + ], + "angle": 0, + "content": "Data: policy \\(\\pi_{\\theta}\\) , candidate demonstration \\(\\mathcal{D}\\) size of demonstration combination \\(m\\) \nResult: \\(B_{m}\\) , set of candidate demonstration sets. \n\\(B_0\\gets \\{(1,\\emptyset)\\}\\) . \nfor \\(i\\gets 1\\) to m do \n\\(B\\gets \\varnothing\\) \nfor \\((s,\\mathcal{E})\\in B_{t - 1}\\) do /\\* Enumerate and concatenate every demonstration \\*/ for \\(\\mathbf{d}\\in \\mathcal{D}\\) do \\(s\\gets s\\cdot \\pi_{\\theta}(\\mathbf{d}\\mid \\mathcal{E},\\mathbf{t}_q,\\mathcal{I}_q);\\) \\(B\\gets B\\cup \\{(s,\\mathcal{E}\\cup \\mathbf{d})\\}\\) end \nend \n/\\*Normalize the possibility \\*/ \\(S\\gets 0\\) \nfor \\((s,\\mathcal{E})\\in B\\) do \\(S\\gets S + |s|\\) \nend \n\\(s\\gets \\frac{s}{|S|}\\) for each item in \\(B\\) sample from \\(B\\) with possibility \\(s\\) to get \\(B_{i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.494, + 0.484, + 0.661 + ], + "angle": 0, + "content": "Stochastic Beam Search To facilitate exploration, we incorporate beam search into our algorithm as a method for exploring various policies. Beam Search is a heuristic search algorithm widely adopted in NLP tasks such as sequence generation. However, due to beam search always expanding the highest probability option at each step, it is not suitable for policy exploration. We modify the traditional beam search to a stochastic sampling version, allowing for stochastic exploration. The algorithm is listed in Algorithm 1. Intuitively, it does not always accept the current \"optimal\" options, thereby introducing the exploration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.665, + 0.484, + 0.711 + ], + "angle": 0, + "content": "Through this algorithm, the model can start from a random policy, continuously explore various strategies, and provide potential optimization directions for the framework." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.733, + 0.43, + 0.75 + ], + "angle": 0, + "content": "3.4. Responsive Reinforcement Exploitation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.76, + 0.484, + 0.822 + ], + "angle": 0, + "content": "After establishing a sufficiently flexible model and exploration algorithm, we introduce our Responsive Reinforcement Exploitation to continuously optimize the superior policies." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Given a query \\((\\mathbf{t}_q,\\mathcal{I}_q)\\), the exploration phase first explores and sample multiple candidate demonstration combinations \\(\\mathcal{E}_1,\\mathcal{E}_2,\\ldots ,\\mathcal{E}_c\\) by the stochastic beam search with policy \\(\\pi_{\\theta}\\). Based on the combinations, the framework optimizes the policy model \\(\\pi_{\\theta}\\) by maximizing the following" + }, + { + "type": "code_caption", + "bbox": [ + 0.525, + 0.096, + 0.751, + 0.11 + ], + "angle": 0, + "content": "Algorithm 2: Training Algorithm" + }, + { + "type": "algorithm", + "bbox": [ + 0.527, + 0.112, + 0.875, + 0.291 + ], + "angle": 0, + "content": "Data: task \\(\\mathcal{T}\\) , candidate demonstrations \\(\\mathcal{D}\\) size of demonstration sets \\(m\\) \nResult: policy \\(\\pi_{\\theta}\\) \ninit \\(\\pi_{\\theta}\\) randomly; \nfor \\((\\mathbf{t}_q,\\mathcal{I}_q,\\mathbf{y})\\sim \\mathcal{T}\\) do \\(\\{(s_i,\\mathcal{E}_i)\\}_{i = 1}^c\\gets\\) beam-search \\((\\pi_{\\theta},\\mathcal{D},m,c)\\) . \\(\\mathbf{o}_i\\gets \\mathcal{F}(P(\\mathbf{t}_q,\\mathcal{E}_i),\\bigcup_{\\mathcal{I}_j\\in \\mathcal{E}_i}\\mathcal{I}_j);\\) \\(A_{i}\\gets r(\\mathbf{o}_{i},\\mathbf{y})\\) . \\(\\hat{A}_i\\gets \\frac{A_i - \\mathrm{mean}(\\mathbf{A})}{\\mathrm{var}(\\mathbf{A})};\\) Optimize \\(\\pi_{\\theta}\\) to maximize \\(\\mathcal{L}\\) \nend" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.327, + 0.583, + 0.341 + ], + "angle": 0, + "content": "objective:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.356, + 0.905, + 0.416 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\left(\\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right) \\sim \\mathcal {T}, \\left\\{\\mathcal {E} _ {i} \\right\\} _ {i = 1} ^ {c} \\sim \\pi_ {\\theta} \\left(\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right)} \\\\ = \\frac {1}{c} \\sum_ {i = 1} ^ {c} \\hat {A} _ {i} \\cdot \\sum_ {k = 1} ^ {m} \\log \\pi_ {\\theta} \\left(\\mathbf {d} _ {i, k} \\mid \\mathbf {d} _ {i, < k}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.907, + 0.55 + ], + "angle": 0, + "content": "Inspired by policy gradient methods [17, 33], this optimization objective aims to adaptively optimize the joint probability of various demonstration combinations under the policy model. The advantage term \\(\\hat{A}_i\\) represents the relative benefit of each combination, where a larger advantage value indicates a more beneficial combination, thus warranting an increase in its corresponding joint probability. Specifically, the advantage \\(\\hat{A}_i\\) is responsively calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.562, + 0.907, + 0.612 + ], + "angle": 0, + "content": "\\[\nA _ {i} = r \\left(\\mathcal {F} \\left(P \\left(\\mathbf {t} _ {q}, \\mathcal {E} _ {i}\\right), \\mathcal {I} _ {q} \\cup \\bigcup_ {\\mathcal {I} _ {j} \\in \\mathcal {E} _ {i}} \\mathcal {I} _ {j}\\right), \\mathbf {y}\\right), \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.613, + 0.906, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\hat {A} _ {i} = \\frac {A _ {i} - \\operatorname {m e a n} (\\mathbf {A})}{\\operatorname {v a r} (\\mathbf {A})}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.781 + ], + "angle": 0, + "content": "where \\( r(\\cdot) \\) is reward function and \\( A_{i} \\) is the original advantages for each combination. \\( \\mathbf{A} = [A_1, \\dots, A_c] \\) denotes the original advantages of all explored combinations for one query. Based on \\( \\mathbf{A} \\), the final advantage \\( \\hat{A}_i \\) is obtained through query-wise standard normalization. It mitigates the distributional discrepancies across queries while ensuring a balanced distribution of positive and negative advantage values. For our experiments, we simply implement \\( r(\\cdot) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.795, + 0.905, + 0.814 + ], + "angle": 0, + "content": "\\[\nr (\\mathbf {o}, \\mathbf {y}) = \\mathbb {1} _ {[ \\mathbf {o} \\text {i s e q u i v a l e n t t o} \\mathbf {y} ]}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}_{[condition]}\\) is the indicator function, equaling 1 if and only if the output o matches the ground-truth y; otherwise, 0. In this way, our approach is able to leverage the explored strategies to gradually uncover adaptive sampling policies that are suitable for various types of queries." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3830" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.165, + 0.089, + 0.832, + 0.104 + ], + "angle": 0, + "content": "Table 1. Experimental comparison using VQAScore with the state-of-the-art methods on four VQA benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.115, + 0.891, + 0.276 + ], + "angle": 0, + "content": "
MethodsOKVQATextVQAVizwizMMStarAvg.
CPFPIRLRSTMA
zero-shot57.565.232.852.037.647.625.317.933.241.0
random61.167.440.557.233.946.726.620.528.842.5
similarity (Qwen [2])60.667.248.757.231.447.232.826.227.144.3
BM25 [31]60.366.943.659.834.151.130.623.624.943.9
Ours (Qwen [2])64.767.453.656.836.246.634.124.929.345.9
similarity (LLaVA [25])22.733.619.848.528.443.733.623.627.531.3
Ours (LLaVA [25])44.350.145.654.638.049.836.720.128.440.8
" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.298, + 0.224, + 0.315 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.324, + 0.274, + 0.34 + ], + "angle": 0, + "content": "4.1. Experiment Setups" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.348, + 0.483, + 0.56 + ], + "angle": 0, + "content": "Datasets. To demonstrate the generality of our method, following the previous studies [2], we conduct experiments on four representative VQA benchmarks, i.e., OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. OKVQA is a large-scale VQA benchmark constructed based on the MS-COCO dataset, which contains 14k question-answer pairs and 14k images. TextVQA dataset contains 28k images and associated questions with human-annotated answers. Vizwiz dataset contains 24k image/question pairs collected from the blind. MMStar is designed to evaluate the multi-modal capacities with carefully balanced challenge samples. These datasets include images and diverse text questions, reflecting ICL performance and showcasing the adaptability of methods to various tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.561, + 0.483, + 0.637 + ], + "angle": 0, + "content": "Baseline and Evaluation Metrics. We adopt a heuristic similarity policy as baseline, which selects demonstrations by cosine similarities of the embeddings. For fair comparisons, we follow previous studies [2] to use VQAScore as the main metric. The results are reported on validation sets." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.649, + 0.308, + 0.665 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.673, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Data Processing. Following previous studies [2], we adopt the official validation sets of OKVQA, TextVQA, and Vizwiz benchmarks to evaluate the performance. As no splits are provided for MMStar, following convention, we divide it into training and validation sets in a 7:3 ratio, treating the training sets as candidate demonstrations for both training and validation sets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Training Details. We adopt ImageBind [11] as \\( f_{e} \\) in the interactive encoding. We use Qwen-VL [2] and LLaVA [25] as LVLMs. We implement \\( \\Delta \\) as learnable functional and positional encoding following [6]. AdamW optimizer is adopted to train models for 10 epochs. The learning rate is \\( 5 \\times 10^{-5} \\). The batch size is set as 8. The hyperparameter \\( c \\) in responsive reinforcement is set as 4. The beam width and temperature are set as 9 and 1.0. The selection model" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.297, + 0.905, + 0.339 + ], + "angle": 0, + "content": "Table 2. Ablation studies of different modules on the OKVQA benchmark. SBS: Stochastic beam search. AR: Auto-regressive. RR: Responsive Reinforcement." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.35, + 0.89, + 0.45 + ], + "angle": 0, + "content": "
Training Alg.SBSARVQAScoreΔ
RR✓63.31.4 ↓
RR✓63.31.4 ↓
Preference✓✓62.91.8 ↓
RR✓✓64.7-
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.905, + 0.52 + ], + "angle": 0, + "content": "consists of 6-layer transformers with 8 attention heads and 2048 hidden dimensions. As we evaluate LVLMs locally, all experiments are conducted on 8 NVIDIA A800 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.531, + 0.874, + 0.547 + ], + "angle": 0, + "content": "4.3. Comparison with Representative Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We respectively compare our methods with four methods, zero-shot, random, similarity, BM25, on four datasets including OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. Table 1 show the comparisons of VQAScore between ours and other methods. Our method surpasses other representative methods on four datasets. Especially on OKVQA and VizWiz, it improves significantly, increasing by 4.1 and 4.9 compared to similarity. The average performance is improved by 1.6. Additionally, it is noteworthy that our method achieves improvements in fine-grained perception compared to coarse perception, as well as in logical reasoning compared to instance reasoning. For coarse perception and instance reasoning tasks, directly selecting similar demonstrations yields better performance, whereas our proposed reinforcement method is unstable in fitting this fixed strategy. Furthermore, Table 1 shows our method's lower performance on math tasks. The math problems follow rigid rules where minor variations can lead to completely different solution paths. Related but non-isomorphic demonstrations interfere with LVLMs' understanding. In general, the experimental results show that our method is more effective than various heuristic approaches. It provides more significant improvement for weaker models [7]," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "3831" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.094, + 0.475, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.248, + 0.483, + 0.304 + ], + "angle": 0, + "content": "Figure 3. Left: VQAScore on OKVQA benchmark of our method with different number of demonstrations. Right: VQAScore on OKVQA benchmark of our method with different temperature values in stochastic beam search." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.333, + 0.483, + 0.38 + ], + "angle": 0, + "content": "e.g., LLaVA. By treating the selection as a combinatorial optimization problem, we achieve better results than the independent selection strategy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.391, + 0.295, + 0.407 + ], + "angle": 0, + "content": "4.4. Performance Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.416, + 0.483, + 0.612 + ], + "angle": 0, + "content": "Ablation Studies of Components. To verify the effectiveness, we conduct extensive ablation experiments. The results are shown in Table 2. Without auto-regressive generation, the selection of each demonstration is independent, leading to a significant decrease in performance. This indicates that the interactions between demonstrations play a crucial role in analogical understanding. Stochastic beam search not employed, the limited self-exploration restricts the variety of strategies and declines the performance. When using preference loss, the optimization is not stable to converge to the better solutions found by responsive reinforcement. Our proposed framework shows strong performance in promoting in-context learning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.483, + 0.794 + ], + "angle": 0, + "content": "Effects of Numbers of Demonstrations. The number of demos impacts ICL. We conduct experiments to investigate the contribution of demo sizes to the performance. From Figure 3(left), it can be observed that as the number increases, the performance gradually improves. However, when the demonstration set becomes too large, performance shows a certain decline. We believe that while a larger number of demonstrations provides more information, it challenges the reinforcement learning process, thereby decreasing the performance. Additionally, too many demonstrations also add a number of tokens, raising inference costs. Therefore, in our method, we set the size to 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.902 + ], + "angle": 0, + "content": "In beam search, temperature controls the gap between high- and low-probability demonstrations during sampling, thus affecting policy exploration. We conduct experiments with several different temperatures. The performance in Figure 3(right) shows a general trend. It first rises then declines as temperature increases, thus we set temperature as 1. This hyper-parameter should be adjusted based on the" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.095, + 0.88, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.257, + 0.907, + 0.313 + ], + "angle": 0, + "content": "Figure 4. The similarity distribution of demonstrations that correct wrong predictions on the OKVQA benchmark. The demonstrations selected with ours are dissimilar to the queries but correct the predictions." + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.337, + 0.858, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.573, + 0.907, + 0.629 + ], + "angle": 0, + "content": "Figure 5. The relationships in cosine similarity of two demonstrations selected with ours on the OKVQA dataset. The yellow dot and white dot represent the centroid (0.5, 0.5) and the data centroid, respectively. The data exhibits an overall leftward shift." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.658, + 0.777, + 0.672 + ], + "angle": 0, + "content": "characteristics of the downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Inefficient Similarity Strategy. For the similarity-based strategy, we conduct more detailed experiments to verify its effects. In Figure 4, we illustrate the queries corrected by our method on the OKVQA dataset. Our method selects demonstrations with lower similarity for these examples and predicts the correct answer; the similarity-based strategy, on the other hand, selects more similar demonstrations but misleads the predictions. In this manner, we verify that similar demonstrations are not necessarily the most effective. We observe the similarity relationships between two selected demonstrations. As shown in Figure 5, our method tends to select a dissimilar demonstration first, followed by a similar one. This suggests a complex selection strategy that maintains both similarity and diversity. Next, we observe the demonstration ordering as many re" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3832" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.086, + 0.868, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.379, + 0.907, + 0.423 + ], + "angle": 0, + "content": "Figure 6. Demonstrations selected with our method, similarity, and random strategies on the OKVQA dataset. The demos selected based on criteria such as similarity are closer to queries, but differ in structure or in key objects, which are ineffective in analogical reasoning. Our approach adaptively learns to identify and utilize demonstration combinations that maximize both complementarity and utility." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.446, + 0.483, + 0.473 + ], + "angle": 0, + "content": "Table 3. The effect of the orders of demonstrations on the OKVQA benchmark." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.485, + 0.485, + 0.548 + ], + "angle": 0, + "content": "
Methodsnormal perm.reversed perm.Δ
Similarity60.6360.92+0.29
Ours64.6664.69+0.03
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.483, + 0.673 + ], + "angle": 0, + "content": "cent works [13, 26, 39] treat it as one main factor affecting efficiency. The results in Table 3 suggest that ordering effects are specific to certain strategies. Only similarity-based strategy is affected and improved when the query is closer to a more similar demo. The results indicate that our method captures robust characteristics of similarity and diversity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.903 + ], + "angle": 0, + "content": "What Makes A Better Demonstrations? Table 1 indicates that policies based on human intuition, such as rank by similarity, are not optimal. Then what makes a better demonstration? To verify this issue, we conduct an in-depth examination of the policies learned by models. The results are shown in Figure 6. In the first set of images, the similarity strategy correctly selects indoor scenes and gameplay images. However, the query does not address the main object of the image. The similar demonstrations fail to provide relevant information but mislead LVLMs, causing them to focus on irrelevant salient objects. The random strategy further demonstrates that LVLMs are easily disturbed by salient objects. In contrast, the demonstrations selected by our method direct the attention to small background instruments. Similarly, in the second set of images," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.6 + ], + "angle": 0, + "content": "the similarity strategy selects two food images according to the query. However, it does not lead to effective inference for query questioning the types. Random strategy reveals that LVLMs tend to predict incorrect answers. The demonstrations selected by ours prompt LVLMs to focus on the type characteristics. The use of a single or heuristic strategy fails to account for the multiple factors, including queries, semantics, and image content. Our proposed reinforcement learning framework allows for a more comprehensive exploration of effective policies." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.616, + 0.78, + 0.633 + ], + "angle": 0, + "content": "5. Conclusions and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.825 + ], + "angle": 0, + "content": "Conclusion. In this paper, we focus on the problem of demonstration selection in in-context learning. We view the selection from a new perspective considering it as a combinatorial optimization problem to model the interactions among the demonstrations. In our framework, we propose multi-modal interactive encoding to catch the relationships between different modalities of queries and candidate demonstrations. We propose auto-regressive decoder with stochastic beam search to enable exploring policies for selection, and responsive reinforcement to exploit them. Experimental results demonstrate our proposed framework achieves superior performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Limitations. Our proposed method explores language-vision multimodal ICL only. As research progresses, LLMs are incorporating more modalities such as video and audio, and the exploration of ICL within them remains a pressing area for investigation, leaving for our future work." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3833" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.422, + 0.128 + ], + "angle": 0, + "content": "[1] Rohan Anil et al. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.907, + 0.681 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3835" + } + ] +] \ No newline at end of file diff --git a/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_origin.pdf b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..891302baf106c5e9318d379d440525b8f013a7e9 --- /dev/null +++ b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/b91a6ee3-ca22-45bc-888a-12a0ccc4e9d0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd459c2516dcf80808454155e1dedfdebef9ae1254d3d5cbca33e6644cd11788 +size 2109233 diff --git a/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/full.md b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..790efd8e0def9488b9af73d7ac3369aa01d5884f --- /dev/null +++ b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/full.md @@ -0,0 +1,327 @@ +# Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning + +Cheng Chen\* 1,2, Yunpeng Zhai\* 2, Yifan Zhao\* 1, Jinyang Gao2, Bolin Ding2, Jia Li\* 1 +1State Key Laboratory of Virtual Reality Technology and Systems +2Tongyi Lab, Alibaba Group + +{chengchen, zhaoyf, jiali}@cvteam.net + +{zhaiyunpeng.zyp, jinyang.gjy, bolin.ding}@alibaba-inc.com + +# Abstract + +In-context learning (ICL), a predominant trend in instruction learning, aims at enhancing the performance of large language models by providing clear task guidance and examples, improving their capability in task understanding and execution. This paper investigates ICL on Large Vision-Language Models (LVLMs) and explores the policies of multi-modal demonstration selection. Existing research efforts in ICL face significant challenges: First, they rely on pre-defined demonstrations or heuristic selecting strategies based on human intuition, which are usually inadequate for covering diverse task requirements, leading to sub-optimal solutions; Second, individually selecting each demonstration fails in modeling the interactions between them, resulting in information redundancy. Unlike these prevailing efforts, we propose a new exploration-exploitation reinforcement learning framework, which explores policies to fuse multi-modal information and adaptively select adequate demonstrations as an integrated whole. The framework allows LVLMs to optimize themselves by continually refining their demonstrations through self-exploration, enabling the ability to autonomously identify and generate the most effective selection policies for in-context learning. Experimental results verify the superior performance of our approach on four Visual Question-Answering (VQA) datasets, demonstrating its effectiveness in enhancing the generalization capability of few-shot LVLMs. + +# 1. Introduction + +Recent years have witnessed remarkable advancements in Large Vision-Language Models (LVLMs) [43]. Powered by the rapid development of Language Models (LMs) and extensive pretraining on large-scale vision-language datasets, + +![](images/7b895d1976718ff9720a14842ce1b18d2d41c9ea6072c87ff5c5eedb0b3e8e72.jpg) +Figure 1. The motivation of the proposed method. The method consists of two stages: exploration and exploitation. In the exploration stage, a stochastic beam search is conducted to generate multiple selection strategies for the query. We reason the output with a large language model and comprehensively evaluate these multiple demonstration sets. In the exploitation stage, the policy is optimized based on evaluation, making it more likely to select the optimal combination. These two stages iterate continuously, resulting in seeking the optimal strategy. + +LVLMs have demonstrated exceptional capabilities on various tasks, including generation [1, 3, 9, 29, 36], translation [15, 16, 21, 23, 40], and beyond [12, 14, 24, 38]. Despite their impressive performance, LVLMs still encounter substantial challenges in adapting to novel scenarios, primarily due to the resource-intensive nature of fine-tuning procedures. + +To tackle this problem, In-Context Learning (ICL) offers a training-free alternative to conventional fine-tuning approaches. Specifically, ICL augments the prompt with + +a few high-quality examples, i.e., demonstrations, allowing models to learn from them efficiently during inference. This enables LVLMs to leverage analogical reasoning and effectively generalize to novel tasks. Consequently, ICL is becoming a widely-used technique for easily improving the performance of both LLMs and VLMs [10, 19, 28, 37, 41]. + +The selection of demonstrations plays a crucial role in ICL for LVLMs. Current approaches predominantly rely on heuristic selection strategies, which can be categorized into two main lines. The first line adopts query-independent selection, utilizing predefined demonstrations for simplicity and stability. However, this static approach fails to cover the diverse range of task requirements, leading to suboptimal performance when handling novel vision-language tasks [5, 37, 41]. The second line employs dynamic selection strategies, typically retrieving demonstrations with higher embedding similarity to the query. While similarity-based methods have shown promise in language-only domains, they face significant limitations in multi-modal scenarios. First, high similarity scores do not guarantee high demonstration utility, potentially overlooking valuable demonstrations while retrieving samples with limited reference value. Second, the individual selection of demonstrations results in substantial information redundancy among retrieved top-similar samples, since it doesn't consider the inter-sample relationships. This severely hampers the model's generation capability. These heuristic approaches, whether through manual curation or fixed strategies, suffer from a lack of learning capability, failing to fully exploit appropriate demonstrations and thus severely limiting the potential of ICL. Moreover, the inherent difficulty of vision-language alignment poses additional challenges for demonstration selection, as it requires effectively capturing both visual and textual semantic relationships. + +This paper investigates the multi-modal demonstration selection for in-context learning of LVLMs. Departing from heuristic selection approaches, we introduce an end-to-end learnable framework that automatically optimizes the demonstration combinations. To address the redundancy issues, we reformulate demonstration selection as a combinatorial optimization problem rather than independent sample selection. However, unlike conventional supervised learning tasks, this combinatorial optimization problem is particularly challenging as the optimal demonstration combinations cannot be manually annotated, resulting in the absence of direct supervision signals. To address the challenge, we propose a novel exploration-exploitation framework that adaptively learns to choose demonstrations in a reinforcement-like manner. As illustrated in Figure 1, our framework iteratively conducts an exploration phase to efficiently explore good demonstration combinations and an exploitation phase to reinforce the sampling-policy network. Given a query (image-question pair) and a candi + +date demonstration set, the sampling-policy network first leverages interaction encoding to establish cross-modal relationships, then performs auto-regressive demonstration selection, where each selection decision is informed by the ensemble of previously selected samples. In the exploration phase, the framework applies stochastic beam search to the sampling-policy network, generating multiple possible demonstration combinations. These combinations are then evaluated by feeding them along with the query into the LVLM to obtain effective rewards. In the exploitation phase, the sampling policy is optimized using policy gradient reinforcement learning based on the rewards of different combinations. This process strengthens the joint probability of high-performing combinations while suppressing that of less effective ones. Through alternating between exploration and exploitation phases, the framework enables models to autonomously identify and generate the most effective demonstration sets for input queries. This approach reduces the dependence on manual intervention and significantly improves generalization and adaptability. + +The contributions of this paper are summarized below: + +- We view ICL demonstration selection from a new perspective of combinatorial optimization. It mitigates the drawbacks of individual selection by interaction among samples, thereby reducing information redundancy and enhancing demo utility. +- We introduce a multi-modal exploration-exploitation framework. It iteratively conducts an exploration phase to explore better demonstration combinations by stochastic tree search, and an exploitation phase to adaptively optimize the sampling-policy network in a reinforcement manner. +- Extensive experiments on four representative VQA datasets across multiple LVLMs demonstrate the effectiveness of our methods. + +# 2. Related Works + +# 2.1. In-context Learning + +Pre-trained VLMs show the ability to understand and reason. Consequently, in-context learning (ICL) uses examples related to the input query to activate the few-shot ability of models and predict the answers through analogy. Many methods have been explored. Brown et al. [5] first explore the few-shot ability of the language models and propose in-context learning with fixed demonstrations. Recent works have shown that dynamical retrieval leads to better improvement compared with the fixed. The dynamical retrieval shares similar ideas with retrieval-augmented generation (RAG), for example, MuRAG [8] selects multi-modal references related to questions, while the different motivations lead to different optimization goals and evaluations. Wang et al. [37] propose a method that retrieves instances + +![](images/937cce982f2b544e1f55ef59329b91dbd7508943539516124b371e7dc1387c49.jpg) +Figure 2. The pipeline of the proposed framework. It comprises three parts: multi-modal interactive encoding, self-exploration, and self-exploitation. First, the questions and images of queries and candidate demonstrations are encoded to generate multi-modal features, which are subsequently processed through a fusion encoder to output the interactive features. Following this, we employ auto-regressive decoder to generate multiple demonstration combinations that are suitable for the query. These combinations are used in few-shot inference. Finally, the predicted outputs are compared against the ground-truth to get responsive rewards, leveraged to optimize the selection policy. + +similar to the query. Zemlyanskiy et al. [41] also propose retrieval methods based on similarity but it considers both input and output. Besides similarity, diversity has been proven effective [10, 19, 28]. For example, Itay et al. [19] find that various structures encourage the model to generalize and propose methods to select diverse demonstrations. Gao et al. [10] find that ambiguous examples can better improve ICL performance compared to selecting semantically similar ones only. Li et al. [22] propose a unified retriever by training a model on multiple tasks with ranking loss. While most works focus on LLMs, we extend the research to the LVLMs and further investigate efficient information utilization for better demonstration combination strategies. + +# 2.2. Large Vision-Language Model + +Building upon the success of LLMs, researchers are focusing on large vision-language models (LVLMs) and have achieved substantial advancements, which enable the understanding of complex interactions between images and text [42]. GPT-4 (Vision) [29] and Gemini [35] first explore the region, showing impressive multi-modal understanding and generation capabilities. Liu et al. [25] train a large multimodal model LLaVA that connects vision and language for general understanding. Similar work includes Minigpt-4 [45], BLIP-2 [20] and others. Later, new work explores how to enable LVLMs to predict multimodal outputs, such as Koh et al. [18] and Zheng et al. [44], they enable the LLMs to predict visual outputs with the text representations. + +Early ICL work primarily focuses on LLMs. With the development of LVLMs, there has been growing attention on how to utilize multimodal information and propose more effective ICL strategies on LVLMs. + +# 2.3. LLM with Reinforcement Learning + +In the realm of reinforcement learning, the concepts of exploration and exploitation are the foundation to make decisions. Recent advancements in exploration and exploitation strategies have led to several notable algorithms. Schulman et al. [32] propose an effective PPO algorithm, which allows for effective exploration while ensuring that the agent does not deviate far from a learned policy. Rafailov et al. [30] simplify the complex RL algorithm and propose DPO to solve the standard RLHF problem by using a simple classification loss. Later, Shao et al. [33] introduce a variant of PPO, i.e., GRPO, replacing value function approximation with the average reward of multiple samples. These methods exemplify the significant progress in balancing exploration and exploitation, substantially advancing the efficiency of reinforcement learning. + +# 3. Methods + +# 3.1. Formulation and Overview + +Denote the tasks $\mathcal{T}$ , $(\mathbf{t},\mathcal{I},\mathbf{y})\sim \mathcal{T}$ a query with answer, and the large vision-language model as $\mathcal{F}:\mathbf{x},\mathcal{I}\mapsto \mathbf{y}$ that receives a prompt $\mathbf{t}$ and its associated RGB images sequence + +$\mathcal{I} = \{\mathbf{I}_1,\mathbf{I}_2,\ldots \}$ , where $\mathbf{I}_{(\cdot)}\in \mathbb{R}^{CHW}$ , to predict the textual output $\mathbf{y}$ . + +Denote $\mathcal{D}$ as the candidate demonstrations, our few-shot in-context learning tries to find an adaptive policy + +$$ +\mathcal {P}: \mathbf {t} _ {q}, \mathcal {I} _ {q} \mapsto \mathcal {E} \tag {1} +$$ + +to select optimal demonstration combination + +$$ +\mathcal {E} = \left\{\mathbf {d} _ {1}, \mathbf {d} _ {2}, \dots , \mathbf {d} _ {m} \right\} \subset \mathcal {D} \tag {2} +$$ + +for a query $(\mathbf{t}_q,\mathcal{I}_q)$ , where $\mathbf{d}_i = (\mathbf{t}_i,\mathcal{I}_i,\mathbf{y}_i)$ is a demonstration and $\mathbf{y}$ is the associated answer to its query $\mathbf{t}$ . With $\mathcal{E}$ , VLM $\mathcal{F}$ predicts the improved output by feeding an input $P(\mathbf{t}_q,\mathcal{E})$ of the form + +$$ +P \left(\mathbf {t} _ {q}, \mathcal {E}\right) = \mathbf {t} _ {1} \quad \mathbf {y} _ {1} \quad \mathbf {t} _ {2} \quad \mathbf {y} _ {2} \quad \dots \quad \mathbf {t} _ {m} \quad \mathbf {y} _ {m} \quad \mathbf {t} _ {q}. \tag {3} +$$ + +To sum up, our objective is to find a policy for demonstration selection: + +$$ +\mathcal {P} _ {*} = \arg \max _ {\mathcal {P}} \mathbb {E} _ {(\mathbf {t}, \mathcal {I}, \mathbf {y}) \sim \mathcal {T}} \xi (\mathcal {F} (P (\mathbf {t} _ {q}, \mathcal {E}), \cup \mathcal {I}), \mathbf {y}), \tag {4} +$$ + +where $\cup \mathcal{I}$ contain all images from demonstrations and the query, and $\xi$ is the evaluation criterion, e.g., VQAScore. + +Motivation and Framework As aforementioned, the interactions between demonstrations matter in ICL, and multiple factors affect the behaviors of demonstrations on the few-shot inference. Intuitively, we propose to view demonstration selection as a combinatorial optimization problem, and introduce exploration-exploitation to iteratively find the optimal policies, which relies on the three-fold framework: 1) Multi-modal Fusion Encoder to catch the rich features interactively; 2) Stochastic Beam Search with auto-regressive decoder to find possible strategies for demonstration combination selection; 3) Responsive Reinforcement to exploit those strategies for finding the optimal policy. + +# 3.2. Multi-modal Interactive Encoding + +While in vanilla ICL fixed demonstrations can be embedded into prompts for VLMs inference [5], several works have explored heuristic methods as better strategies, such as selecting according to similarity [37, 41] or diversity [10, 19]. Although these methods have achieved improvements, they do not cover two major problems that theoretically limit the potential of VLMs: a) These methods do not explore dynamic multimodal relationships, which mainly focus on hand-crafted heuristic strategies. b) Selection of demonstrations is independent, failing to consider the interaction between demonstrations. This is also prone to issues such as information redundancy. + +To tackle the problems, we therefore propose our Multimodal Interactive Encoding, which includes two parts, multi-modal encoder $f_{e}$ and fusion encoder $f_{f}$ . Given query $(\mathbf{t},\mathcal{I})$ and candidate demonstrations $\mathcal{D}$ , different + +modalities are first fed into multi-modal encoder $f_{e}$ to get the textual feature $\{\mathbf{f}_{\mathbf{t}_q},\mathbf{f}_{\mathbf{t}_1},\mathbf{f}_{\mathbf{t}_2},\ldots \}$ and image features $\{\mathbf{f}_{\mathbf{I}_q},\mathbf{f}_{\mathbf{I}_1},\mathbf{f}_{\mathbf{I}_2},\ldots \}$ , it has the following form: + +$$ +\left\{\mathbf {f} _ {\mathbf {t} _ {q}}, \mathbf {f} _ {\mathbf {t} _ {1}}, \mathbf {f} _ {\mathbf {t} _ {2}}, \dots \right\} = \left\{f _ {e} \left(\mathbf {t} _ {q}\right), f _ {e} \left(\mathbf {t} _ {1}\right), f _ {e} \left(\mathbf {t} _ {2}\right), \dots \right\}, \tag {5} +$$ + +$$ +\{\mathbf {f} _ {\mathbf {I} _ {q}}, \mathbf {f} _ {\mathbf {I} _ {1}}, \mathbf {f} _ {\mathbf {I} _ {2}}, \ldots \} = \{f _ {e} (\mathbf {I} _ {q}), f _ {e} (\mathbf {I} _ {1}), f _ {e} (\mathbf {I} _ {2}), \ldots \}. \quad (6) +$$ + +To account for the interaction between multi-modal features, as well as the interaction between candidate demonstrations and queries, we implement $f_{f}$ as a transformer encoder, thereby ensuring global interactions among tokens. Features of different modalities are first embedded with separate functional embedding $\Delta_{\{t,i\}}^{f}$ to distinguish them. Subsequently, positional encodings $\Delta_{i}^{p}$ are respectively added to features of different modalities, thereby establishing correlations among corresponding features + +$$ +\mathbf {f} _ {\{\mathbf {t}, \mathbf {I} \} _ {q}} \leftarrow \mathbf {f} _ {\{\mathbf {t}, \mathbf {I} \} _ {q}} + \Delta_ {\{t, i \}} ^ {f}, \tag {7} +$$ + +$$ +\mathbf {f} _ {\{\mathbf {t}, \mathbf {I} \} _ {k}} \leftarrow \mathbf {f} _ {\{\mathbf {t}, \mathbf {I} \} _ {k}} + \Delta_ {\{t, i \}} ^ {f} + \Delta_ {k} ^ {p}. \tag {8} +$$ + +Next, the queries and examples are fed into the fusion encoder $f_{f}$ to obtain interactive feature $\mathbf{M}$ . + +$$ +\mathbf {M} = f _ {f} \left(\left[ \begin{array}{l l l l l l l} \mathbf {f} _ {\mathbf {t} _ {q}} & \mathbf {f} _ {\mathbf {I} _ {q}} & \mathbf {f} _ {\mathbf {t} _ {1}} & \mathbf {f} _ {\mathbf {I} _ {1}} & \mathbf {f} _ {\mathbf {t} _ {2}} & \mathbf {f} _ {\mathbf {I} _ {2}} & \dots \end{array} \right]\right). \tag {9} +$$ + +During this process, features of different modalities of queries and candidate demonstrations are fused to learn the characteristics of multi-modal tasks. + +# 3.3. Stochastic Beam Search Exploration + +Auto-regressive Decoding Given the black-box nature of both the problem characteristics and VLMs, it is challenging for humans to manually design appropriate demonstration sets and selection strategies. To frame demonstration selection as a combinatorial optimization problem, we introduce an auto-regressive transformer decoder $f_{d}$ . + +With $\mathbf{M}$ by interactive encoder, decoder $f_{d}$ then predicts the $i$ -th demonstration $\mathbf{d}_i$ based on the queries, candidates and other $i - 1$ demonstrations $\mathcal{E}$ by + +$$ +p _ {i} = \alpha_ {t} \operatorname {d i s t} \left(f _ {d} (\mathbf {M}, \mathcal {E}), \mathbf {f} _ {\mathbf {t} _ {i}}\right) + \alpha_ {i} \operatorname {d i s t} \left(f _ {d} (\mathbf {M}, \mathcal {E}), \mathbf {f} _ {\mathbf {I} _ {i}}\right), \tag {10} +$$ + +$$ +i = \arg \max _ {i} [ p _ {i} \leq \min \{p _ {j} \} ], \tag {11} +$$ + +where $\mathrm{dist}()$ is the cosine similarity in our implementation, $\alpha_{\{t,i\}}$ are weight coefficients. This process is autoregressive to achieve the policy $\pi_{\theta}$ + +$$ +\pi_ {\theta} (\mathcal {E} \mid \mathbf {t} _ {q}, \mathcal {I} _ {q}) = \prod_ {i = 1} ^ {m} p \left(\mathbf {d} _ {i} \mid \mathbf {d} _ {1}, \mathbf {d} _ {2}, \dots , \mathbf {d} _ {i - 1}, \mathbf {t} _ {q}, \mathcal {I} _ {q}\right). \tag {12} +$$ + +Thus the selection is modeled as a combinatorial problem. + +Algorithm 1: Stochastic beam search +Data: policy $\pi_{\theta}$ , candidate demonstration $\mathcal{D}$ size of demonstration combination $m$ +Result: $B_{m}$ , set of candidate demonstration sets. + $B_0\gets \{(1,\emptyset)\}$ . +for $i\gets 1$ to m do + $B\gets \varnothing$ +for $(s,\mathcal{E})\in B_{t - 1}$ do /\* Enumerate and concatenate every demonstration \*/ for $\mathbf{d}\in \mathcal{D}$ do $s\gets s\cdot \pi_{\theta}(\mathbf{d}\mid \mathcal{E},\mathbf{t}_q,\mathcal{I}_q);$ $B\gets B\cup \{(s,\mathcal{E}\cup \mathbf{d})\}$ end +end +/\*Normalize the possibility \*/ $S\gets 0$ +for $(s,\mathcal{E})\in B$ do $S\gets S + |s|$ +end + $s\gets \frac{s}{|S|}$ for each item in $B$ sample from $B$ with possibility $s$ to get $B_{i}$ + +Stochastic Beam Search To facilitate exploration, we incorporate beam search into our algorithm as a method for exploring various policies. Beam Search is a heuristic search algorithm widely adopted in NLP tasks such as sequence generation. However, due to beam search always expanding the highest probability option at each step, it is not suitable for policy exploration. We modify the traditional beam search to a stochastic sampling version, allowing for stochastic exploration. The algorithm is listed in Algorithm 1. Intuitively, it does not always accept the current "optimal" options, thereby introducing the exploration. + +Through this algorithm, the model can start from a random policy, continuously explore various strategies, and provide potential optimization directions for the framework. + +# 3.4. Responsive Reinforcement Exploitation + +After establishing a sufficiently flexible model and exploration algorithm, we introduce our Responsive Reinforcement Exploitation to continuously optimize the superior policies. + +Given a query $(\mathbf{t}_q,\mathcal{I}_q)$ , the exploration phase first explores and sample multiple candidate demonstration combinations $\mathcal{E}_1,\mathcal{E}_2,\ldots ,\mathcal{E}_c$ by the stochastic beam search with policy $\pi_{\theta}$ . Based on the combinations, the framework optimizes the policy model $\pi_{\theta}$ by maximizing the following + +Algorithm 2: Training Algorithm +Data: task $\mathcal{T}$ , candidate demonstrations $\mathcal{D}$ size of demonstration sets $m$ +Result: policy $\pi_{\theta}$ +init $\pi_{\theta}$ randomly; +for $(\mathbf{t}_q,\mathcal{I}_q,\mathbf{y})\sim \mathcal{T}$ do $\{(s_i,\mathcal{E}_i)\}_{i = 1}^c\gets$ beam-search $(\pi_{\theta},\mathcal{D},m,c)$ . $\mathbf{o}_i\gets \mathcal{F}(P(\mathbf{t}_q,\mathcal{E}_i),\bigcup_{\mathcal{I}_j\in \mathcal{E}_i}\mathcal{I}_j);$ $A_{i}\gets r(\mathbf{o}_{i},\mathbf{y})$ . $\hat{A}_i\gets \frac{A_i - \mathrm{mean}(\mathbf{A})}{\mathrm{var}(\mathbf{A})};$ Optimize $\pi_{\theta}$ to maximize $\mathcal{L}$ +end + +objective: + +$$ +\begin{array}{l} \mathbb {E} _ {\left(\mathbf {t} _ {q}, \mathcal {I} _ {q}\right) \sim \mathcal {T}, \left\{\mathcal {E} _ {i} \right\} _ {i = 1} ^ {c} \sim \pi_ {\theta} \left(\mathcal {E} \mid \mathbf {t} _ {q}, \mathcal {I} _ {q}\right)} \\ = \frac {1}{c} \sum_ {i = 1} ^ {c} \hat {A} _ {i} \cdot \sum_ {k = 1} ^ {m} \log \pi_ {\theta} \left(\mathbf {d} _ {i, k} \mid \mathbf {d} _ {i, < k}, \mathbf {t} _ {q}, \mathcal {I} _ {q}\right). \tag {13} \\ \end{array} +$$ + +Inspired by policy gradient methods [17, 33], this optimization objective aims to adaptively optimize the joint probability of various demonstration combinations under the policy model. The advantage term $\hat{A}_i$ represents the relative benefit of each combination, where a larger advantage value indicates a more beneficial combination, thus warranting an increase in its corresponding joint probability. Specifically, the advantage $\hat{A}_i$ is responsively calculated as + +$$ +A _ {i} = r \left(\mathcal {F} \left(P \left(\mathbf {t} _ {q}, \mathcal {E} _ {i}\right), \mathcal {I} _ {q} \cup \bigcup_ {\mathcal {I} _ {j} \in \mathcal {E} _ {i}} \mathcal {I} _ {j}\right), \mathbf {y}\right), \tag {14} +$$ + +$$ +\hat {A} _ {i} = \frac {A _ {i} - \operatorname {m e a n} (\mathbf {A})}{\operatorname {v a r} (\mathbf {A})}, \tag {15} +$$ + +where $r(\cdot)$ is reward function and $A_{i}$ is the original advantages for each combination. $\mathbf{A} = [A_1, \dots, A_c]$ denotes the original advantages of all explored combinations for one query. Based on $\mathbf{A}$ , the final advantage $\hat{A}_i$ is obtained through query-wise standard normalization. It mitigates the distributional discrepancies across queries while ensuring a balanced distribution of positive and negative advantage values. For our experiments, we simply implement $r(\cdot)$ as + +$$ +r (\mathbf {o}, \mathbf {y}) = \mathbb {1} _ {[ \mathbf {o} \text {i s e q u i v a l e n t t o} \mathbf {y} ]}, \tag {16} +$$ + +where $\mathbb{1}_{[condition]}$ is the indicator function, equaling 1 if and only if the output o matches the ground-truth y; otherwise, 0. In this way, our approach is able to leverage the explored strategies to gradually uncover adaptive sampling policies that are suitable for various types of queries. + +Table 1. Experimental comparison using VQAScore with the state-of-the-art methods on four VQA benchmarks. + +
MethodsOKVQATextVQAVizwizMMStarAvg.
CPFPIRLRSTMA
zero-shot57.565.232.852.037.647.625.317.933.241.0
random61.167.440.557.233.946.726.620.528.842.5
similarity (Qwen [2])60.667.248.757.231.447.232.826.227.144.3
BM25 [31]60.366.943.659.834.151.130.623.624.943.9
Ours (Qwen [2])64.767.453.656.836.246.634.124.929.345.9
similarity (LLaVA [25])22.733.619.848.528.443.733.623.627.531.3
Ours (LLaVA [25])44.350.145.654.638.049.836.720.128.440.8
+ +# 4. Experiments + +# 4.1. Experiment Setups + +Datasets. To demonstrate the generality of our method, following the previous studies [2], we conduct experiments on four representative VQA benchmarks, i.e., OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. OKVQA is a large-scale VQA benchmark constructed based on the MS-COCO dataset, which contains 14k question-answer pairs and 14k images. TextVQA dataset contains 28k images and associated questions with human-annotated answers. Vizwiz dataset contains 24k image/question pairs collected from the blind. MMStar is designed to evaluate the multi-modal capacities with carefully balanced challenge samples. These datasets include images and diverse text questions, reflecting ICL performance and showcasing the adaptability of methods to various tasks. + +Baseline and Evaluation Metrics. We adopt a heuristic similarity policy as baseline, which selects demonstrations by cosine similarities of the embeddings. For fair comparisons, we follow previous studies [2] to use VQAScore as the main metric. The results are reported on validation sets. + +# 4.2. Implementation Details + +Data Processing. Following previous studies [2], we adopt the official validation sets of OKVQA, TextVQA, and Vizwiz benchmarks to evaluate the performance. As no splits are provided for MMStar, following convention, we divide it into training and validation sets in a 7:3 ratio, treating the training sets as candidate demonstrations for both training and validation sets. + +Training Details. We adopt ImageBind [11] as $f_{e}$ in the interactive encoding. We use Qwen-VL [2] and LLaVA [25] as LVLMs. We implement $\Delta$ as learnable functional and positional encoding following [6]. AdamW optimizer is adopted to train models for 10 epochs. The learning rate is $5 \times 10^{-5}$ . The batch size is set as 8. The hyperparameter $c$ in responsive reinforcement is set as 4. The beam width and temperature are set as 9 and 1.0. The selection model + +Table 2. Ablation studies of different modules on the OKVQA benchmark. SBS: Stochastic beam search. AR: Auto-regressive. RR: Responsive Reinforcement. + +
Training Alg.SBSARVQAScoreΔ
RR✓63.31.4 ↓
RR✓63.31.4 ↓
Preference✓✓62.91.8 ↓
RR✓✓64.7-
+ +consists of 6-layer transformers with 8 attention heads and 2048 hidden dimensions. As we evaluate LVLMs locally, all experiments are conducted on 8 NVIDIA A800 GPUs. + +# 4.3. Comparison with Representative Methods + +We respectively compare our methods with four methods, zero-shot, random, similarity, BM25, on four datasets including OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. Table 1 show the comparisons of VQAScore between ours and other methods. Our method surpasses other representative methods on four datasets. Especially on OKVQA and VizWiz, it improves significantly, increasing by 4.1 and 4.9 compared to similarity. The average performance is improved by 1.6. Additionally, it is noteworthy that our method achieves improvements in fine-grained perception compared to coarse perception, as well as in logical reasoning compared to instance reasoning. For coarse perception and instance reasoning tasks, directly selecting similar demonstrations yields better performance, whereas our proposed reinforcement method is unstable in fitting this fixed strategy. Furthermore, Table 1 shows our method's lower performance on math tasks. The math problems follow rigid rules where minor variations can lead to completely different solution paths. Related but non-isomorphic demonstrations interfere with LVLMs' understanding. In general, the experimental results show that our method is more effective than various heuristic approaches. It provides more significant improvement for weaker models [7], + +![](images/c9f91952e46dddd8f134fc14f87dfeddf35af92763138a96c49607a72071bb11.jpg) +Figure 3. Left: VQAScore on OKVQA benchmark of our method with different number of demonstrations. Right: VQAScore on OKVQA benchmark of our method with different temperature values in stochastic beam search. + +e.g., LLaVA. By treating the selection as a combinatorial optimization problem, we achieve better results than the independent selection strategy. + +# 4.4. Performance Analysis + +Ablation Studies of Components. To verify the effectiveness, we conduct extensive ablation experiments. The results are shown in Table 2. Without auto-regressive generation, the selection of each demonstration is independent, leading to a significant decrease in performance. This indicates that the interactions between demonstrations play a crucial role in analogical understanding. Stochastic beam search not employed, the limited self-exploration restricts the variety of strategies and declines the performance. When using preference loss, the optimization is not stable to converge to the better solutions found by responsive reinforcement. Our proposed framework shows strong performance in promoting in-context learning. + +Effects of Numbers of Demonstrations. The number of demos impacts ICL. We conduct experiments to investigate the contribution of demo sizes to the performance. From Figure 3(left), it can be observed that as the number increases, the performance gradually improves. However, when the demonstration set becomes too large, performance shows a certain decline. We believe that while a larger number of demonstrations provides more information, it challenges the reinforcement learning process, thereby decreasing the performance. Additionally, too many demonstrations also add a number of tokens, raising inference costs. Therefore, in our method, we set the size to 2. + +In beam search, temperature controls the gap between high- and low-probability demonstrations during sampling, thus affecting policy exploration. We conduct experiments with several different temperatures. The performance in Figure 3(right) shows a general trend. It first rises then declines as temperature increases, thus we set temperature as 1. This hyper-parameter should be adjusted based on the + +![](images/524eb066d0cd4caeb51155c69880a73683577fc183c118cbe18bffa7b9e92af4.jpg) +Figure 4. The similarity distribution of demonstrations that correct wrong predictions on the OKVQA benchmark. The demonstrations selected with ours are dissimilar to the queries but correct the predictions. + +![](images/45d43e9bcf6e51554eaa6fe4ccc221e4d32e0caaa5574354889ee7783c68bf41.jpg) +Figure 5. The relationships in cosine similarity of two demonstrations selected with ours on the OKVQA dataset. The yellow dot and white dot represent the centroid (0.5, 0.5) and the data centroid, respectively. The data exhibits an overall leftward shift. + +characteristics of the downstream tasks. + +Inefficient Similarity Strategy. For the similarity-based strategy, we conduct more detailed experiments to verify its effects. In Figure 4, we illustrate the queries corrected by our method on the OKVQA dataset. Our method selects demonstrations with lower similarity for these examples and predicts the correct answer; the similarity-based strategy, on the other hand, selects more similar demonstrations but misleads the predictions. In this manner, we verify that similar demonstrations are not necessarily the most effective. We observe the similarity relationships between two selected demonstrations. As shown in Figure 5, our method tends to select a dissimilar demonstration first, followed by a similar one. This suggests a complex selection strategy that maintains both similarity and diversity. Next, we observe the demonstration ordering as many re + +![](images/c6f07ce82cbbfa0f485ed9cee7cc547d8f76f8346e840f6dbd2984ef907978a7.jpg) +Figure 6. Demonstrations selected with our method, similarity, and random strategies on the OKVQA dataset. The demos selected based on criteria such as similarity are closer to queries, but differ in structure or in key objects, which are ineffective in analogical reasoning. Our approach adaptively learns to identify and utilize demonstration combinations that maximize both complementarity and utility. + +Table 3. The effect of the orders of demonstrations on the OKVQA benchmark. + +
Methodsnormal perm.reversed perm.Δ
Similarity60.6360.92+0.29
Ours64.6664.69+0.03
+ +cent works [13, 26, 39] treat it as one main factor affecting efficiency. The results in Table 3 suggest that ordering effects are specific to certain strategies. Only similarity-based strategy is affected and improved when the query is closer to a more similar demo. The results indicate that our method captures robust characteristics of similarity and diversity. + +What Makes A Better Demonstrations? Table 1 indicates that policies based on human intuition, such as rank by similarity, are not optimal. Then what makes a better demonstration? To verify this issue, we conduct an in-depth examination of the policies learned by models. The results are shown in Figure 6. In the first set of images, the similarity strategy correctly selects indoor scenes and gameplay images. However, the query does not address the main object of the image. The similar demonstrations fail to provide relevant information but mislead LVLMs, causing them to focus on irrelevant salient objects. The random strategy further demonstrates that LVLMs are easily disturbed by salient objects. In contrast, the demonstrations selected by our method direct the attention to small background instruments. Similarly, in the second set of images, + +the similarity strategy selects two food images according to the query. However, it does not lead to effective inference for query questioning the types. Random strategy reveals that LVLMs tend to predict incorrect answers. The demonstrations selected by ours prompt LVLMs to focus on the type characteristics. The use of a single or heuristic strategy fails to account for the multiple factors, including queries, semantics, and image content. Our proposed reinforcement learning framework allows for a more comprehensive exploration of effective policies. + +# 5. Conclusions and Limitations + +Conclusion. In this paper, we focus on the problem of demonstration selection in in-context learning. We view the selection from a new perspective considering it as a combinatorial optimization problem to model the interactions among the demonstrations. In our framework, we propose multi-modal interactive encoding to catch the relationships between different modalities of queries and candidate demonstrations. We propose auto-regressive decoder with stochastic beam search to enable exploring policies for selection, and responsive reinforcement to exploit them. Experimental results demonstrate our proposed framework achieves superior performance. + +Limitations. Our proposed method explores language-vision multimodal ICL only. As research progresses, LLMs are incorporating more modalities such as video and audio, and the exploration of ICL within them remains a pressing area for investigation, leaving for our future work. + +# References + +[1] Rohan Anil et al. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models, 2023. 3 \ No newline at end of file diff --git a/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/images.zip b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2d453de8067170f6f75c4c5483ad838d0a28f89d --- /dev/null +++ b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d8ee0990972fcfeda84f51fb0c0d67e9513849b695e3a9a2b1344f9167ac58dc +size 577559 diff --git a/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/layout.json b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bb9f8e41ae4781f76de496b2c3385f7ddf633c4a --- /dev/null +++ b/2025/Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning/layout.json @@ -0,0 +1,7989 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 102, + 522, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 102, + 522, + 140 + ], + "spans": [ + { + "bbox": [ + 88, + 102, + 522, + 140 + ], + "type": "text", + "content": "Provoking Multi-modal Few-Shot LVLM via Exploration-Exploitation In-Context Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 96, + 160, + 515, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 160, + 515, + 204 + ], + "spans": [ + { + "bbox": [ + 96, + 160, + 515, + 204 + ], + "type": "text", + "content": "Cheng Chen\\* 1,2, Yunpeng Zhai\\* 2, Yifan Zhao\\* 1, Jinyang Gao2, Bolin Ding2, Jia Li\\* 1 \n1State Key Laboratory of Virtual Reality Technology and Systems \n2Tongyi Lab, Alibaba Group" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 204, + 205, + 405, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 204, + 205, + 405, + 217 + ], + "spans": [ + { + "bbox": [ + 204, + 205, + 405, + 217 + ], + "type": "text", + "content": "{chengchen, zhaoyf, jiali}@cvteam.net" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 146, + 220, + 460, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 220, + 460, + 232 + ], + "spans": [ + { + "bbox": [ + 146, + 220, + 460, + 232 + ], + "type": "text", + "content": "{zhaiyunpeng.zyp, jinyang.gjy, bolin.ding}@alibaba-inc.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 258, + 200, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 258, + 200, + 271 + ], + "spans": [ + { + "bbox": [ + 151, + 258, + 200, + 271 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 284, + 296, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 284, + 296, + 595 + ], + "spans": [ + { + "bbox": [ + 54, + 284, + 296, + 595 + ], + "type": "text", + "content": "In-context learning (ICL), a predominant trend in instruction learning, aims at enhancing the performance of large language models by providing clear task guidance and examples, improving their capability in task understanding and execution. This paper investigates ICL on Large Vision-Language Models (LVLMs) and explores the policies of multi-modal demonstration selection. Existing research efforts in ICL face significant challenges: First, they rely on pre-defined demonstrations or heuristic selecting strategies based on human intuition, which are usually inadequate for covering diverse task requirements, leading to sub-optimal solutions; Second, individually selecting each demonstration fails in modeling the interactions between them, resulting in information redundancy. Unlike these prevailing efforts, we propose a new exploration-exploitation reinforcement learning framework, which explores policies to fuse multi-modal information and adaptively select adequate demonstrations as an integrated whole. 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Powered by the rapid development of Language Models (LMs) and extensive pretraining on large-scale vision-language datasets," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 258, + 555, + 457 + ], + "blocks": [ + { + "bbox": [ + 317, + 258, + 555, + 457 + ], + "lines": [ + { + "bbox": [ + 317, + 258, + 555, + 457 + ], + "spans": [ + { + "bbox": [ + 317, + 258, + 555, + 457 + ], + "type": "image", + "image_path": "7b895d1976718ff9720a14842ce1b18d2d41c9ea6072c87ff5c5eedb0b3e8e72.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 564 + ], + "type": "text", + "content": "Figure 1. The motivation of the proposed method. The method consists of two stages: exploration and exploitation. In the exploration stage, a stochastic beam search is conducted to generate multiple selection strategies for the query. We reason the output with a large language model and comprehensively evaluate these multiple demonstration sets. In the exploitation stage, the policy is optimized based on evaluation, making it more likely to select the optimal combination. These two stages iterate continuously, resulting in seeking the optimal strategy." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": "LVLMs have demonstrated exceptional capabilities on various tasks, including generation [1, 3, 9, 29, 36], translation [15, 16, 21, 23, 40], and beyond [12, 14, 24, 38]. Despite their impressive performance, LVLMs still encounter substantial challenges in adapting to novel scenarios, primarily due to the resource-intensive nature of fine-tuning procedures." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "To tackle this problem, In-Context Learning (ICL) offers a training-free alternative to conventional fine-tuning approaches. Specifically, ICL augments the prompt with" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 223, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 223, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 223, + 703 + ], + "type": "text", + "content": "*These authors contributed equally to this work." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3826" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "a few high-quality examples, i.e., demonstrations, allowing models to learn from them efficiently during inference. This enables LVLMs to leverage analogical reasoning and effectively generalize to novel tasks. Consequently, ICL is becoming a widely-used technique for easily improving the performance of both LLMs and VLMs [10, 19, 28, 37, 41]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 148, + 298, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 148, + 298, + 483 + ], + "spans": [ + { + "bbox": [ + 56, + 148, + 298, + 483 + ], + "type": "text", + "content": "The selection of demonstrations plays a crucial role in ICL for LVLMs. Current approaches predominantly rely on heuristic selection strategies, which can be categorized into two main lines. The first line adopts query-independent selection, utilizing predefined demonstrations for simplicity and stability. However, this static approach fails to cover the diverse range of task requirements, leading to suboptimal performance when handling novel vision-language tasks [5, 37, 41]. The second line employs dynamic selection strategies, typically retrieving demonstrations with higher embedding similarity to the query. While similarity-based methods have shown promise in language-only domains, they face significant limitations in multi-modal scenarios. First, high similarity scores do not guarantee high demonstration utility, potentially overlooking valuable demonstrations while retrieving samples with limited reference value. Second, the individual selection of demonstrations results in substantial information redundancy among retrieved top-similar samples, since it doesn't consider the inter-sample relationships. This severely hampers the model's generation capability. These heuristic approaches, whether through manual curation or fixed strategies, suffer from a lack of learning capability, failing to fully exploit appropriate demonstrations and thus severely limiting the potential of ICL. Moreover, the inherent difficulty of vision-language alignment poses additional challenges for demonstration selection, as it requires effectively capturing both visual and textual semantic relationships." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": "This paper investigates the multi-modal demonstration selection for in-context learning of LVLMs. Departing from heuristic selection approaches, we introduce an end-to-end learnable framework that automatically optimizes the demonstration combinations. To address the redundancy issues, we reformulate demonstration selection as a combinatorial optimization problem rather than independent sample selection. However, unlike conventional supervised learning tasks, this combinatorial optimization problem is particularly challenging as the optimal demonstration combinations cannot be manually annotated, resulting in the absence of direct supervision signals. To address the challenge, we propose a novel exploration-exploitation framework that adaptively learns to choose demonstrations in a reinforcement-like manner. As illustrated in Figure 1, our framework iteratively conducts an exploration phase to efficiently explore good demonstration combinations and an exploitation phase to reinforce the sampling-policy network. Given a query (image-question pair) and a candi" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 312 + ], + "type": "text", + "content": "date demonstration set, the sampling-policy network first leverages interaction encoding to establish cross-modal relationships, then performs auto-regressive demonstration selection, where each selection decision is informed by the ensemble of previously selected samples. In the exploration phase, the framework applies stochastic beam search to the sampling-policy network, generating multiple possible demonstration combinations. These combinations are then evaluated by feeding them along with the query into the LVLM to obtain effective rewards. In the exploitation phase, the sampling policy is optimized using policy gradient reinforcement learning based on the rewards of different combinations. This process strengthens the joint probability of high-performing combinations while suppressing that of less effective ones. Through alternating between exploration and exploitation phases, the framework enables models to autonomously identify and generate the most effective demonstration sets for input queries. This approach reduces the dependence on manual intervention and significantly improves generalization and adaptability." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 326, + 312, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 312, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 326, + 312, + 547, + 324 + ], + "type": "text", + "content": "The contributions of this paper are summarized below:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 325, + 553, + 492 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 325, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 325, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 314, + 325, + 553, + 384 + ], + "type": "text", + "content": "- We view ICL demonstration selection from a new perspective of combinatorial optimization. It mitigates the drawbacks of individual selection by interaction among samples, thereby reducing information redundancy and enhancing demo utility." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 384, + 553, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 553, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 553, + 456 + ], + "type": "text", + "content": "- We introduce a multi-modal exploration-exploitation framework. It iteratively conducts an exploration phase to explore better demonstration combinations by stochastic tree search, and an exploitation phase to adaptively optimize the sampling-policy network in a reinforcement manner." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 456, + 553, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 553, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 553, + 492 + ], + "type": "text", + "content": "- Extensive experiments on four representative VQA datasets across multiple LVLMs demonstrate the effectiveness of our methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 506, + 406, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 506, + 406, + 519 + ], + "spans": [ + { + "bbox": [ + 314, + 506, + 406, + 519 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 526, + 432, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 526, + 432, + 540 + ], + "spans": [ + { + "bbox": [ + 314, + 526, + 432, + 540 + ], + "type": "text", + "content": "2.1. In-context Learning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "Pre-trained VLMs show the ability to understand and reason. Consequently, in-context learning (ICL) uses examples related to the input query to activate the few-shot ability of models and predict the answers through analogy. Many methods have been explored. Brown et al. [5] first explore the few-shot ability of the language models and propose in-context learning with fixed demonstrations. Recent works have shown that dynamical retrieval leads to better improvement compared with the fixed. The dynamical retrieval shares similar ideas with retrieval-augmented generation (RAG), for example, MuRAG [8] selects multi-modal references related to questions, while the different motivations lead to different optimization goals and evaluations. Wang et al. [37] propose a method that retrieves instances" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3827" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 553, + 289 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 553, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 553, + 289 + ], + "type": "image", + "image_path": "937cce982f2b544e1f55ef59329b91dbd7508943539516124b371e7dc1387c49.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 296, + 555, + 353 + ], + "lines": [ + { + "bbox": [ + 54, + 296, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 54, + 296, + 555, + 353 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed framework. It comprises three parts: multi-modal interactive encoding, self-exploration, and self-exploitation. First, the questions and images of queries and candidate demonstrations are encoded to generate multi-modal features, which are subsequently processed through a fusion encoder to output the interactive features. Following this, we employ auto-regressive decoder to generate multiple demonstration combinations that are suitable for the query. These combinations are used in few-shot inference. Finally, the predicted outputs are compared against the ground-truth to get responsive rewards, leveraged to optimize the selection policy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 372, + 296, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 372, + 296, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 372, + 296, + 529 + ], + "type": "text", + "content": "similar to the query. Zemlyanskiy et al. [41] also propose retrieval methods based on similarity but it considers both input and output. Besides similarity, diversity has been proven effective [10, 19, 28]. For example, Itay et al. [19] find that various structures encourage the model to generalize and propose methods to select diverse demonstrations. Gao et al. [10] find that ambiguous examples can better improve ICL performance compared to selecting semantically similar ones only. Li et al. [22] propose a unified retriever by training a model on multiple tasks with ranking loss. While most works focus on LLMs, we extend the research to the LVLMs and further investigate efficient information utilization for better demonstration combination strategies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 538, + 222, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 538, + 222, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 538, + 222, + 552 + ], + "type": "text", + "content": "2.2. Large Vision-Language Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 557, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 296, + 714 + ], + "type": "text", + "content": "Building upon the success of LLMs, researchers are focusing on large vision-language models (LVLMs) and have achieved substantial advancements, which enable the understanding of complex interactions between images and text [42]. GPT-4 (Vision) [29] and Gemini [35] first explore the region, showing impressive multi-modal understanding and generation capabilities. Liu et al. [25] train a large multimodal model LLaVA that connects vision and language for general understanding. Similar work includes Minigpt-4 [45], BLIP-2 [20] and others. Later, new work explores how to enable LVLMs to predict multimodal outputs, such as Koh et al. [18] and Zheng et al. [44], they enable the LLMs to predict visual outputs with the text representations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 372, + 555, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 555, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 555, + 421 + ], + "type": "text", + "content": "Early ICL work primarily focuses on LLMs. With the development of LVLMs, there has been growing attention on how to utilize multimodal information and propose more effective ICL strategies on LVLMs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 429, + 503, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 429, + 503, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 503, + 442 + ], + "type": "text", + "content": "2.3. LLM with Reinforcement Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 448, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 555, + 628 + ], + "type": "text", + "content": "In the realm of reinforcement learning, the concepts of exploration and exploitation are the foundation to make decisions. Recent advancements in exploration and exploitation strategies have led to several notable algorithms. Schulman et al. [32] propose an effective PPO algorithm, which allows for effective exploration while ensuring that the agent does not deviate far from a learned policy. Rafailov et al. [30] simplify the complex RL algorithm and propose DPO to solve the standard RLHF problem by using a simple classification loss. Later, Shao et al. [33] introduce a variant of PPO, i.e., GRPO, replacing value function approximation with the average reward of multiple samples. These methods exemplify the significant progress in balancing exploration and exploitation, substantially advancing the efficiency of reinforcement learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 639, + 375, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 639, + 375, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 639, + 375, + 651 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 658, + 468, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 468, + 671 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 468, + 671 + ], + "type": "text", + "content": "3.1. 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243 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i = (\\mathbf{t}_i,\\mathcal{I}_i,\\mathbf{y}_i)" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": " is a demonstration and " + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": " is the associated answer to its query " + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": ". With " + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": ", VLM " + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": " predicts the improved output by feeding an input " + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "inline_equation", + "content": "P(\\mathbf{t}_q,\\mathcal{E})" + }, + { + "bbox": [ + 55, + 194, + 296, + 243 + ], + "type": "text", + "content": " of the form" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 251, + 295, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 251, + 295, + 266 + ], + "spans": [ + { + "bbox": [ + 63, + 251, + 295, + 266 + ], + "type": "interline_equation", + "content": "P \\left(\\mathbf {t} _ {q}, \\mathcal {E}\\right) = \\mathbf {t} _ {1} \\quad \\mathbf {y} _ {1} \\quad \\mathbf {t} _ {2} \\quad \\mathbf {y} _ {2} \\quad \\dots \\quad \\mathbf {t} _ {m} \\quad \\mathbf {y} _ {m} \\quad \\mathbf {t} _ {q}. \\tag {3}", + "image_path": "0c7461870fa709ba70c0a023c3bd78305025377b5a1f1e978601a91c0291cec2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 274, + 295, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 274, + 295, + 297 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 295, + 297 + ], + "type": "text", + "content": "To sum up, our objective is to find a policy for demonstration selection:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 307, + 295, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 307, + 295, + 321 + ], + "spans": [ + { + "bbox": [ + 66, + 307, + 295, + 321 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {*} = \\arg \\max _ {\\mathcal {P}} \\mathbb {E} _ {(\\mathbf {t}, \\mathcal {I}, \\mathbf {y}) \\sim \\mathcal {T}} \\xi (\\mathcal {F} (P (\\mathbf {t} _ {q}, \\mathcal {E}), \\cup \\mathcal {I}), \\mathbf {y}), \\tag {4}", + "image_path": "a81f6110e7fb203e6e25741def351166cf2f6e74e9c92bfe8a06b11a990898b0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "inline_equation", + "content": "\\cup \\mathcal{I}" + }, + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "text", + "content": " contain all images from demonstrations and the query, and " + }, + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 55, + 329, + 295, + 353 + ], + "type": "text", + "content": " is the evaluation criterion, e.g., VQAScore." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "type": "text", + "content": "Motivation and Framework As aforementioned, the interactions between demonstrations matter in ICL, and multiple factors affect the behaviors of demonstrations on the few-shot inference. Intuitively, we propose to view demonstration selection as a combinatorial optimization problem, and introduce exploration-exploitation to iteratively find the optimal policies, which relies on the three-fold framework: 1) Multi-modal Fusion Encoder to catch the rich features interactively; 2) Stochastic Beam Search with auto-regressive decoder to find possible strategies for demonstration combination selection; 3) Responsive Reinforcement to exploit those strategies for finding the optimal policy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 503, + 239, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 239, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 239, + 517 + ], + "type": "text", + "content": "3.2. Multi-modal Interactive Encoding" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": "While in vanilla ICL fixed demonstrations can be embedded into prompts for VLMs inference [5], several works have explored heuristic methods as better strategies, such as selecting according to similarity [37, 41] or diversity [10, 19]. Although these methods have achieved improvements, they do not cover two major problems that theoretically limit the potential of VLMs: a) These methods do not explore dynamic multimodal relationships, which mainly focus on hand-crafted heuristic strategies. b) Selection of demonstrations is independent, failing to consider the interaction between demonstrations. This is also prone to issues such as information redundancy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "To tackle the problems, we therefore propose our Multimodal Interactive Encoding, which includes two parts, multi-modal encoder " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_{e}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " and fusion encoder " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_{f}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ". Given query " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{t},\\mathcal{I})" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " and candidate demonstrations " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ", different" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": "modalities are first fed into multi-modal encoder " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "f_{e}" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " to get the textual feature " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{f}_{\\mathbf{t}_q},\\mathbf{f}_{\\mathbf{t}_1},\\mathbf{f}_{\\mathbf{t}_2},\\ldots \\}" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " and image features " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{f}_{\\mathbf{I}_q},\\mathbf{f}_{\\mathbf{I}_1},\\mathbf{f}_{\\mathbf{I}_2},\\ldots \\}" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": ", it has the following form:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 327, + 118, + 553, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 118, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 327, + 118, + 553, + 133 + ], + "type": "interline_equation", + "content": "\\left\\{\\mathbf {f} _ {\\mathbf {t} _ {q}}, \\mathbf {f} _ {\\mathbf {t} _ {1}}, \\mathbf {f} _ {\\mathbf {t} _ {2}}, \\dots \\right\\} = \\left\\{f _ {e} \\left(\\mathbf {t} _ {q}\\right), f _ {e} \\left(\\mathbf {t} _ {1}\\right), f _ {e} \\left(\\mathbf {t} _ {2}\\right), \\dots \\right\\}, \\tag {5}", + "image_path": "8829398a4a0af361ff15b02da9ab9f93ee2ba005dbf2b3b57d0f1e69d081de06.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 328, + 133, + 553, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 133, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 328, + 133, + 553, + 148 + ], + "type": "interline_equation", + "content": "\\{\\mathbf {f} _ {\\mathbf {I} _ {q}}, \\mathbf {f} _ {\\mathbf {I} _ {1}}, \\mathbf {f} _ {\\mathbf {I} _ {2}}, \\ldots \\} = \\{f _ {e} (\\mathbf {I} _ {q}), f _ {e} (\\mathbf {I} _ {1}), f _ {e} (\\mathbf {I} _ {2}), \\ldots \\}. \\quad (6)", + "image_path": "041e832d4a8a8d8eb58795a2daf95f27d2ea4181e7f93621ede5893822361b4d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "spans": [ + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "text", + "content": "To account for the interaction between multi-modal features, as well as the interaction between candidate demonstrations and queries, we implement " + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "inline_equation", + "content": "f_{f}" + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "text", + "content": " as a transformer encoder, thereby ensuring global interactions among tokens. Features of different modalities are first embedded with separate functional embedding " + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "inline_equation", + "content": "\\Delta_{\\{t,i\\}}^{f}" + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "text", + "content": " to distinguish them. Subsequently, positional encodings " + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "inline_equation", + "content": "\\Delta_{i}^{p}" + }, + { + "bbox": [ + 313, + 158, + 555, + 268 + ], + "type": "text", + "content": " are respectively added to features of different modalities, thereby establishing correlations among corresponding features" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 366, + 277, + 553, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 277, + 553, + 294 + ], + "spans": [ + { + "bbox": [ + 366, + 277, + 553, + 294 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {q}} + \\Delta_ {\\{t, i \\}} ^ {f}, \\tag {7}", + "image_path": "2b6c856106e67d7621efc4acd480a46707a28c13a2253981cb70b343a8286f1a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 366, + 297, + 553, + 313 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 297, + 553, + 313 + ], + "spans": [ + { + "bbox": [ + 366, + 297, + 553, + 313 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} \\leftarrow \\mathbf {f} _ {\\{\\mathbf {t}, \\mathbf {I} \\} _ {k}} + \\Delta_ {\\{t, i \\}} ^ {f} + \\Delta_ {k} ^ {p}. \\tag {8}", + "image_path": "af0c1afdfdff3f557804d0aa5f82ab9e6b1756381371f8a0686266c0194b02de.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "content": "Next, the queries and examples are fed into the fusion encoder " + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "inline_equation", + "content": "f_{f}" + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "content": " to obtain interactive feature " + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 330, + 354, + 553, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 354, + 553, + 370 + ], + "spans": [ + { + "bbox": [ + 330, + 354, + 553, + 370 + ], + "type": "interline_equation", + "content": "\\mathbf {M} = f _ {f} \\left(\\left[ \\begin{array}{l l l l l l l} \\mathbf {f} _ {\\mathbf {t} _ {q}} & \\mathbf {f} _ {\\mathbf {I} _ {q}} & \\mathbf {f} _ {\\mathbf {t} _ {1}} & \\mathbf {f} _ {\\mathbf {I} _ {1}} & \\mathbf {f} _ {\\mathbf {t} _ {2}} & \\mathbf {f} _ {\\mathbf {I} _ {2}} & \\dots \\end{array} \\right]\\right). \\tag {9}", + "image_path": "63ce23a431c33bf231ccde9ea1aff2794b4f29a9b6dcb37a4a013578751a91b3.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 379, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 379, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 379, + 555, + 415 + ], + "type": "text", + "content": "During this process, features of different modalities of queries and candidate demonstrations are fused to learn the characteristics of multi-modal tasks." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 424, + 507, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 424, + 507, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 424, + 507, + 437 + ], + "type": "text", + "content": "3.3. Stochastic Beam Search Exploration" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 444, + 554, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 554, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 554, + 515 + ], + "type": "text", + "content": "Auto-regressive Decoding Given the black-box nature of both the problem characteristics and VLMs, it is challenging for humans to manually design appropriate demonstration sets and selection strategies. To frame demonstration selection as a combinatorial optimization problem, we introduce an auto-regressive transformer decoder " + }, + { + "bbox": [ + 313, + 444, + 554, + 515 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 313, + 444, + 554, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": " by interactive encoder, decoder " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": " then predicts the " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": "-th demonstration " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": " based on the queries, candidates and other " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "i - 1" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": " demonstrations " + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 516, + 554, + 552 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 326, + 563, + 553, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 563, + 553, + 587 + ], + "spans": [ + { + "bbox": [ + 326, + 563, + 553, + 587 + ], + "type": "interline_equation", + "content": "p _ {i} = \\alpha_ {t} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {t} _ {i}}\\right) + \\alpha_ {i} \\operatorname {d i s t} \\left(f _ {d} (\\mathbf {M}, \\mathcal {E}), \\mathbf {f} _ {\\mathbf {I} _ {i}}\\right), \\tag {10}", + "image_path": "59bb287d306e2e67f42f8d06d58fb5014144891a5ef335e51d55e9317102295d.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 331, + 590, + 553, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 590, + 553, + 604 + ], + "spans": [ + { + "bbox": [ + 331, + 590, + 553, + 604 + ], + "type": "interline_equation", + "content": "i = \\arg \\max _ {i} [ p _ {i} \\leq \\min \\{p _ {j} \\} ], \\tag {11}", + "image_path": "fd0234e335191ebe98131155c8126ad34d6bdf424e4f72ea295ab8d220b68a66.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\mathrm{dist}()" + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "text", + "content": " is the cosine similarity in our implementation, " + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\alpha_{\\{t,i\\}}" + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "text", + "content": " are weight coefficients. This process is autoregressive to achieve the policy " + }, + { + "bbox": [ + 313, + 614, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 326, + 660, + 553, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 660, + 553, + 700 + ], + "spans": [ + { + "bbox": [ + 326, + 660, + 553, + 700 + ], + "type": "interline_equation", + "content": "\\pi_ {\\theta} (\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {d} _ {i} \\mid \\mathbf {d} _ {1}, \\mathbf {d} _ {2}, \\dots , \\mathbf {d} _ {i - 1}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {12}", + "image_path": "f6be0ffe3f5dd940d0a27b0e416e31e9bfc16fe3834a1bbc08f35f82db77116f.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 701, + 549, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 549, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 549, + 713 + ], + "type": "text", + "content": "Thus the selection is modeled as a combinatorial problem." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3829" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 67, + 89, + 281, + 358 + ], + "blocks": [ + { + "bbox": [ + 63, + 76, + 216, + 87 + ], + "lines": [ + { + "bbox": [ + 63, + 76, + 216, + 87 + ], + "spans": [ + { + "bbox": [ + 63, + 76, + 216, + 87 + ], + "type": "text", + "content": "Algorithm 1: Stochastic beam search" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "lines": [ + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "spans": [ + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": "Data: policy " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " , candidate demonstration " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " size of demonstration combination " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " \nResult: " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B_{m}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " , set of candidate demonstration sets. \n" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B_0\\gets \\{(1,\\emptyset)\\}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " . \nfor " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "i\\gets 1" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " to m do \n" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B\\gets \\varnothing" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " \nfor " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "(s,\\mathcal{E})\\in B_{t - 1}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " do /\\* Enumerate and concatenate every demonstration \\*/ for " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{d}\\in \\mathcal{D}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " do " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "s\\gets s\\cdot \\pi_{\\theta}(\\mathbf{d}\\mid \\mathcal{E},\\mathbf{t}_q,\\mathcal{I}_q);" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B\\gets B\\cup \\{(s,\\mathcal{E}\\cup \\mathbf{d})\\}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " end \nend \n/\\*Normalize the possibility \\*/ " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "S\\gets 0" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " \nfor " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "(s,\\mathcal{E})\\in B" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " do " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "S\\gets S + |s|" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " \nend \n" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "s\\gets \\frac{s}{|S|}" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " for each item in " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " sample from " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " with possibility " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 67, + 89, + 281, + 358 + ], + "type": "inline_equation", + "content": "B_{i}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 55, + 391, + 296, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 296, + 523 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 296, + 523 + ], + "type": "text", + "content": "Stochastic Beam Search To facilitate exploration, we incorporate beam search into our algorithm as a method for exploring various policies. Beam Search is a heuristic search algorithm widely adopted in NLP tasks such as sequence generation. However, due to beam search always expanding the highest probability option at each step, it is not suitable for policy exploration. We modify the traditional beam search to a stochastic sampling version, allowing for stochastic exploration. The algorithm is listed in Algorithm 1. Intuitively, it does not always accept the current \"optimal\" options, thereby introducing the exploration." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 526, + 296, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 526, + 296, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 526, + 296, + 563 + ], + "type": "text", + "content": "Through this algorithm, the model can start from a random policy, continuously explore various strategies, and provide potential optimization directions for the framework." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 580, + 263, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 263, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 263, + 594 + ], + "type": "text", + "content": "3.4. Responsive Reinforcement Exploitation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 601, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 601, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 601, + 296, + 651 + ], + "type": "text", + "content": "After establishing a sufficiently flexible model and exploration algorithm, we introduce our Responsive Reinforcement Exploitation to continuously optimize the superior policies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "Given a query " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{t}_q,\\mathcal{I}_q)" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": ", the exploration phase first explores and sample multiple candidate demonstration combinations " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_1,\\mathcal{E}_2,\\ldots ,\\mathcal{E}_c" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " by the stochastic beam search with policy " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": ". Based on the combinations, the framework optimizes the policy model " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " by maximizing the following" + } + ] + } + ], + "index": 6 + }, + { + "type": "code", + "bbox": [ + 322, + 88, + 535, + 230 + ], + "blocks": [ + { + "bbox": [ + 321, + 76, + 459, + 87 + ], + "lines": [ + { + "bbox": [ + 321, + 76, + 459, + 87 + ], + "spans": [ + { + "bbox": [ + 321, + 76, + 459, + 87 + ], + "type": "text", + "content": "Algorithm 2: Training Algorithm" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "lines": [ + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "spans": [ + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": "Data: task " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " , candidate demonstrations " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " size of demonstration sets " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " \nResult: policy " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " \ninit " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " randomly; \nfor " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "(\\mathbf{t}_q,\\mathcal{I}_q,\\mathbf{y})\\sim \\mathcal{T}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " do " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\{(s_i,\\mathcal{E}_i)\\}_{i = 1}^c\\gets" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " beam-search " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "(\\pi_{\\theta},\\mathcal{D},m,c)" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_i\\gets \\mathcal{F}(P(\\mathbf{t}_q,\\mathcal{E}_i),\\bigcup_{\\mathcal{I}_j\\in \\mathcal{E}_i}\\mathcal{I}_j);" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "A_{i}\\gets r(\\mathbf{o}_{i},\\mathbf{y})" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\hat{A}_i\\gets \\frac{A_i - \\mathrm{mean}(\\mathbf{A})}{\\mathrm{var}(\\mathbf{A})};" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " Optimize " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " to maximize " + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 322, + 88, + 535, + 230 + ], + "type": "text", + "content": " \nend" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_body" + } + ], + "index": 8, + "sub_type": "algorithm" + }, + { + "bbox": [ + 314, + 258, + 356, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 258, + 356, + 270 + ], + "spans": [ + { + "bbox": [ + 314, + 258, + 356, + 270 + ], + "type": "text", + "content": "objective:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 322, + 281, + 553, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 281, + 553, + 329 + ], + "spans": [ + { + "bbox": [ + 322, + 281, + 553, + 329 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\left(\\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right) \\sim \\mathcal {T}, \\left\\{\\mathcal {E} _ {i} \\right\\} _ {i = 1} ^ {c} \\sim \\pi_ {\\theta} \\left(\\mathcal {E} \\mid \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right)} \\\\ = \\frac {1}{c} \\sum_ {i = 1} ^ {c} \\hat {A} _ {i} \\cdot \\sum_ {k = 1} ^ {m} \\log \\pi_ {\\theta} \\left(\\mathbf {d} _ {i, k} \\mid \\mathbf {d} _ {i, < k}, \\mathbf {t} _ {q}, \\mathcal {I} _ {q}\\right). \\tag {13} \\\\ \\end{array}", + "image_path": "2fbf46dcdae4e97de46993ff20aee5a25f75c91d6d9f72c70491076a81d12801.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 339, + 555, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 555, + 435 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 555, + 435 + ], + "type": "text", + "content": "Inspired by policy gradient methods [17, 33], this optimization objective aims to adaptively optimize the joint probability of various demonstration combinations under the policy model. The advantage term " + }, + { + "bbox": [ + 313, + 339, + 555, + 435 + ], + "type": "inline_equation", + "content": "\\hat{A}_i" + }, + { + "bbox": [ + 313, + 339, + 555, + 435 + ], + "type": "text", + "content": " represents the relative benefit of each combination, where a larger advantage value indicates a more beneficial combination, thus warranting an increase in its corresponding joint probability. 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" + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "inline_equation", + "content": "\\mathbf{A} = [A_1, \\dots, A_c]" + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "text", + "content": " denotes the original advantages of all explored combinations for one query. Based on " + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "text", + "content": ", the final advantage " + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "inline_equation", + "content": "\\hat{A}_i" + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "text", + "content": " is obtained through query-wise standard normalization. It mitigates the distributional discrepancies across queries while ensuring a balanced distribution of positive and negative advantage values. For our experiments, we simply implement " + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 313, + 521, + 555, + 618 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 376, + 629, + 553, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 629, + 553, + 644 + ], + "spans": [ + { + "bbox": [ + 376, + 629, + 553, + 644 + ], + "type": "interline_equation", + "content": "r (\\mathbf {o}, \\mathbf {y}) = \\mathbb {1} _ {[ \\mathbf {o} \\text {i s e q u i v a l e n t t o} \\mathbf {y} ]}, \\tag {16}", + "image_path": "dabc04ff13fca24ecac65c4ad25f99d3431bdb2354bb20ff190ffd3ee5d83665.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 653, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 653, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{[condition]}" + }, + { + "bbox": [ + 313, + 653, + 555, + 714 + ], + "type": "text", + "content": " is the indicator function, equaling 1 if and only if the output o matches the ground-truth y; otherwise, 0. In this way, our approach is able to leverage the explored strategies to gradually uncover adaptive sampling policies that are suitable for various types of queries." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3830" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 91, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 100, + 70, + 509, + 82 + ], + "lines": [ + { + "bbox": [ + 100, + 70, + 509, + 82 + ], + "spans": [ + { + "bbox": [ + 100, + 70, + 509, + 82 + ], + "type": "text", + "content": "Table 1. Experimental comparison using VQAScore with the state-of-the-art methods on four VQA benchmarks." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 91, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 66, + 91, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 545, + 218 + ], + "type": "table", + "html": "
MethodsOKVQATextVQAVizwizMMStarAvg.
CPFPIRLRSTMA
zero-shot57.565.232.852.037.647.625.317.933.241.0
random61.167.440.557.233.946.726.620.528.842.5
similarity (Qwen [2])60.667.248.757.231.447.232.826.227.144.3
BM25 [31]60.366.943.659.834.151.130.623.624.943.9
Ours (Qwen [2])64.767.453.656.836.246.634.124.929.345.9
similarity (LLaVA [25])22.733.619.848.528.443.733.623.627.531.3
Ours (LLaVA [25])44.350.145.654.638.049.836.720.128.440.8
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To demonstrate the generality of our method, following the previous studies [2], we conduct experiments on four representative VQA benchmarks, i.e., OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. OKVQA is a large-scale VQA benchmark constructed based on the MS-COCO dataset, which contains 14k question-answer pairs and 14k images. TextVQA dataset contains 28k images and associated questions with human-annotated answers. Vizwiz dataset contains 24k image/question pairs collected from the blind. MMStar is designed to evaluate the multi-modal capacities with carefully balanced challenge samples. These datasets include images and diverse text questions, reflecting ICL performance and showcasing the adaptability of methods to various tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 444, + 295, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 444, + 295, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 295, + 504 + ], + "type": "text", + "content": "Baseline and Evaluation Metrics. We adopt a heuristic similarity policy as baseline, which selects demonstrations by cosine similarities of the embeddings. For fair comparisons, we follow previous studies [2] to use VQAScore as the main metric. The results are reported on validation sets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 514, + 188, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 188, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 188, + 526 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 533, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 616 + ], + "type": "text", + "content": "Data Processing. Following previous studies [2], we adopt the official validation sets of OKVQA, TextVQA, and Vizwiz benchmarks to evaluate the performance. As no splits are provided for MMStar, following convention, we divide it into training and validation sets in a 7:3 ratio, treating the training sets as candidate demonstrations for both training and validation sets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": "Training Details. We adopt ImageBind [11] as " + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "inline_equation", + "content": "f_{e}" + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": " in the interactive encoding. We use Qwen-VL [2] and LLaVA [25] as LVLMs. We implement " + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": " as learnable functional and positional encoding following [6]. AdamW optimizer is adopted to train models for 10 epochs. The learning rate is " + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": ". The batch size is set as 8. The hyperparameter " + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": " in responsive reinforcement is set as 4. The beam width and temperature are set as 9 and 1.0. The selection model" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 325, + 277, + 544, + 356 + ], + "blocks": [ + { + "bbox": [ + 313, + 235, + 553, + 268 + ], + "lines": [ + { + "bbox": [ + 313, + 235, + 553, + 268 + ], + "spans": [ + { + "bbox": [ + 313, + 235, + 553, + 268 + ], + "type": "text", + "content": "Table 2. Ablation studies of different modules on the OKVQA benchmark. SBS: Stochastic beam search. AR: Auto-regressive. RR: Responsive Reinforcement." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 277, + 544, + 356 + ], + "lines": [ + { + "bbox": [ + 325, + 277, + 544, + 356 + ], + "spans": [ + { + "bbox": [ + 325, + 277, + 544, + 356 + ], + "type": "table", + "html": "
Training Alg.SBSARVQAScoreΔ
RR✓63.31.4 ↓
RR✓63.31.4 ↓
Preference✓✓62.91.8 ↓
RR✓✓64.7-
", + "image_path": "9ed708a776e4843540af4b16ced078e4d74be7d19d88b26b92c5259f24278784.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 376, + 553, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 553, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 553, + 411 + ], + "type": "text", + "content": "consists of 6-layer transformers with 8 attention heads and 2048 hidden dimensions. As we evaluate LVLMs locally, all experiments are conducted on 8 NVIDIA A800 GPUs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 420, + 534, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 534, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 534, + 433 + ], + "type": "text", + "content": "4.3. Comparison with Representative Methods" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "content": "We respectively compare our methods with four methods, zero-shot, random, similarity, BM25, on four datasets including OKVQA [27], TextVQA [34], Vizwiz [4], and MMStar [7]. Table 1 show the comparisons of VQAScore between ours and other methods. Our method surpasses other representative methods on four datasets. Especially on OKVQA and VizWiz, it improves significantly, increasing by 4.1 and 4.9 compared to similarity. The average performance is improved by 1.6. Additionally, it is noteworthy that our method achieves improvements in fine-grained perception compared to coarse perception, as well as in logical reasoning compared to instance reasoning. For coarse perception and instance reasoning tasks, directly selecting similar demonstrations yields better performance, whereas our proposed reinforcement method is unstable in fitting this fixed strategy. Furthermore, Table 1 shows our method's lower performance on math tasks. The math problems follow rigid rules where minor variations can lead to completely different solution paths. Related but non-isomorphic demonstrations interfere with LVLMs' understanding. In general, the experimental results show that our method is more effective than various heuristic approaches. It provides more significant improvement for weaker models [7]," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3831" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 74, + 290, + 182 + ], + "blocks": [ + { + "bbox": [ + 60, + 74, + 290, + 182 + ], + "lines": [ + { + "bbox": [ + 60, + 74, + 290, + 182 + ], + "spans": [ + { + "bbox": [ + 60, + 74, + 290, + 182 + ], + "type": "image", + "image_path": "c9f91952e46dddd8f134fc14f87dfeddf35af92763138a96c49607a72071bb11.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 196, + 295, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 196, + 295, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 196, + 295, + 240 + ], + "type": "text", + "content": "Figure 3. Left: VQAScore on OKVQA benchmark of our method with different number of demonstrations. Right: VQAScore on OKVQA benchmark of our method with different temperature values in stochastic beam search." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 263, + 295, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 263, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 263, + 295, + 300 + ], + "type": "text", + "content": "e.g., LLaVA. By treating the selection as a combinatorial optimization problem, we achieve better results than the independent selection strategy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 309, + 180, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 309, + 180, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 180, + 322 + ], + "type": "text", + "content": "4.4. Performance Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 329, + 295, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 329, + 295, + 484 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 295, + 484 + ], + "type": "text", + "content": "Ablation Studies of Components. To verify the effectiveness, we conduct extensive ablation experiments. The results are shown in Table 2. Without auto-regressive generation, the selection of each demonstration is independent, leading to a significant decrease in performance. This indicates that the interactions between demonstrations play a crucial role in analogical understanding. Stochastic beam search not employed, the limited self-exploration restricts the variety of strategies and declines the performance. When using preference loss, the optimization is not stable to converge to the better solutions found by responsive reinforcement. Our proposed framework shows strong performance in promoting in-context learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 485, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 295, + 628 + ], + "type": "text", + "content": "Effects of Numbers of Demonstrations. The number of demos impacts ICL. We conduct experiments to investigate the contribution of demo sizes to the performance. From Figure 3(left), it can be observed that as the number increases, the performance gradually improves. However, when the demonstration set becomes too large, performance shows a certain decline. We believe that while a larger number of demonstrations provides more information, it challenges the reinforcement learning process, thereby decreasing the performance. Additionally, too many demonstrations also add a number of tokens, raising inference costs. Therefore, in our method, we set the size to 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "content": "In beam search, temperature controls the gap between high- and low-probability demonstrations during sampling, thus affecting policy exploration. We conduct experiments with several different temperatures. The performance in Figure 3(right) shows a general trend. It first rises then declines as temperature increases, thus we set temperature as 1. This hyper-parameter should be adjusted based on the" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 332, + 75, + 538, + 190 + ], + "blocks": [ + { + "bbox": [ + 332, + 75, + 538, + 190 + ], + "lines": [ + { + "bbox": [ + 332, + 75, + 538, + 190 + ], + "spans": [ + { + "bbox": [ + 332, + 75, + 538, + 190 + ], + "type": "image", + "image_path": "524eb066d0cd4caeb51155c69880a73683577fc183c118cbe18bffa7b9e92af4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 203, + 555, + 247 + ], + "lines": [ + { + "bbox": [ + 313, + 203, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 203, + 555, + 247 + ], + "type": "text", + "content": "Figure 4. The similarity distribution of demonstrations that correct wrong predictions on the OKVQA benchmark. The demonstrations selected with ours are dissimilar to the queries but correct the predictions." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 344, + 266, + 525, + 441 + ], + "blocks": [ + { + "bbox": [ + 344, + 266, + 525, + 441 + ], + "lines": [ + { + "bbox": [ + 344, + 266, + 525, + 441 + ], + "spans": [ + { + "bbox": [ + 344, + 266, + 525, + 441 + ], + "type": "image", + "image_path": "45d43e9bcf6e51554eaa6fe4ccc221e4d32e0caaa5574354889ee7783c68bf41.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 453, + 555, + 498 + ], + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 498 + ], + "type": "text", + "content": "Figure 5. The relationships in cosine similarity of two demonstrations selected with ours on the OKVQA dataset. The yellow dot and white dot represent the centroid (0.5, 0.5) and the data centroid, respectively. The data exhibits an overall leftward shift." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 521, + 475, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 475, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 475, + 532 + ], + "type": "text", + "content": "characteristics of the downstream tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "Inefficient Similarity Strategy. For the similarity-based strategy, we conduct more detailed experiments to verify its effects. In Figure 4, we illustrate the queries corrected by our method on the OKVQA dataset. Our method selects demonstrations with lower similarity for these examples and predicts the correct answer; the similarity-based strategy, on the other hand, selects more similar demonstrations but misleads the predictions. In this manner, we verify that similar demonstrations are not necessarily the most effective. We observe the similarity relationships between two selected demonstrations. As shown in Figure 5, our method tends to select a dissimilar demonstration first, followed by a similar one. This suggests a complex selection strategy that maintains both similarity and diversity. Next, we observe the demonstration ordering as many re" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3832" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 68, + 531, + 293 + ], + "blocks": [ + { + "bbox": [ + 82, + 68, + 531, + 293 + ], + "lines": [ + { + "bbox": [ + 82, + 68, + 531, + 293 + ], + "spans": [ + { + "bbox": [ + 82, + 68, + 531, + 293 + ], + "type": "image", + "image_path": "c6f07ce82cbbfa0f485ed9cee7cc547d8f76f8346e840f6dbd2984ef907978a7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 300, + 555, + 335 + ], + "lines": [ + { + "bbox": [ + 55, + 300, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 555, + 335 + ], + "type": "text", + "content": "Figure 6. Demonstrations selected with our method, similarity, and random strategies on the OKVQA dataset. The demos selected based on criteria such as similarity are closer to queries, but differ in structure or in key objects, which are ineffective in analogical reasoning. Our approach adaptively learns to identify and utilize demonstration combinations that maximize both complementarity and utility." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 384, + 296, + 434 + ], + "blocks": [ + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "lines": [ + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "type": "text", + "content": "Table 3. The effect of the orders of demonstrations on the OKVQA benchmark." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 384, + 296, + 434 + ], + "lines": [ + { + "bbox": [ + 56, + 384, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 56, + 384, + 296, + 434 + ], + "type": "table", + "html": "
Methodsnormal perm.reversed perm.Δ
Similarity60.6360.92+0.29
Ours64.6664.69+0.03
", + "image_path": "6f82f1cb0b8ea9adf7b3a723ec38ce18ad94e237cf64d15ae8313b06e6d7ead5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 459, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 533 + ], + "type": "text", + "content": "cent works [13, 26, 39] treat it as one main factor affecting efficiency. The results in Table 3 suggest that ordering effects are specific to certain strategies. Only similarity-based strategy is affected and improved when the query is closer to a more similar demo. The results indicate that our method captures robust characteristics of similarity and diversity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 534, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 715 + ], + "type": "text", + "content": "What Makes A Better Demonstrations? Table 1 indicates that policies based on human intuition, such as rank by similarity, are not optimal. Then what makes a better demonstration? To verify this issue, we conduct an in-depth examination of the policies learned by models. The results are shown in Figure 6. In the first set of images, the similarity strategy correctly selects indoor scenes and gameplay images. However, the query does not address the main object of the image. The similar demonstrations fail to provide relevant information but mislead LVLMs, causing them to focus on irrelevant salient objects. The random strategy further demonstrates that LVLMs are easily disturbed by salient objects. In contrast, the demonstrations selected by our method direct the attention to small background instruments. Similarly, in the second set of images," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 354, + 555, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 475 + ], + "type": "text", + "content": "the similarity strategy selects two food images according to the query. However, it does not lead to effective inference for query questioning the types. Random strategy reveals that LVLMs tend to predict incorrect answers. The demonstrations selected by ours prompt LVLMs to focus on the type characteristics. The use of a single or heuristic strategy fails to account for the multiple factors, including queries, semantics, and image content. Our proposed reinforcement learning framework allows for a more comprehensive exploration of effective policies." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 487, + 477, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 477, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 477, + 501 + ], + "type": "text", + "content": "5. Conclusions and Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "type": "text", + "content": "Conclusion. In this paper, we focus on the problem of demonstration selection in in-context learning. We view the selection from a new perspective considering it as a combinatorial optimization problem to model the interactions among the demonstrations. In our framework, we propose multi-modal interactive encoding to catch the relationships between different modalities of queries and candidate demonstrations. We propose auto-regressive decoder with stochastic beam search to enable exploring policies for selection, and responsive reinforcement to exploit them. Experimental results demonstrate our proposed framework achieves superior performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "Limitations. Our proposed method explores language-vision multimodal ICL only. As research progresses, LLMs are incorporating more modalities such as video and audio, and the exploration of ICL within them remains a pressing area for investigation, leaving for our future work." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3833" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 91, + 258, + 101 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 258, + 101 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 258, + 101 + ], + "type": "text", + "content": "[1] Rohan Anil et al. 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PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll.", + "bbox": [ + 89, + 306, + 485, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 729, + 220, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How many pixels does your camera actually need? Modern cameras typically require as many pixels as the image resolution demands. By contrast, single-pixel cameras need only one pixel, a light-sensitive detector, to capture images through multiple measurements. Single-pixel imaging (SPI) [13, 14, 20, 52, 67] technique measures the total light intensity of a scene coded by a series of spatially resolved", + "bbox": [ + 89, + 756, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/885ffbbe1646461c7c2c6e93214f5ca1f18fdbf19e69fae23a9951f8b4fda48f.jpg", + "image_caption": [ + "Figure 1. Average PSNR (left) of different methods at compressive ratios (CRs) $\\{0.01, 0.04, 0.10, 0.25\\}$ in which only methods in the yellow area can flexibly handle varying CRs with a single model. Optimization trajectories (right) of four classes of methods for solving inverse problems. Our ProxUnroll efficiently achieves SOTA performance with high flexibility and fast convergence." + ], + "image_footnote": [], + "bbox": [ + 514, + 273, + 905, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "masks on a single-pixel detector. Known masks and measurements, one can recover an image with the same resolution as the masks. SPI offers a competitive edge over mainstream CCD and CMOS cameras in certain scenarios, e.g., terahertz imaging [52] and non-visible 3D imaging [43].", + "bbox": [ + 511, + 536, + 906, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SPI cameras typical work under sub-Nyquist sampling rate to save acquisition time, leading to a compressed sensing problem [7, 8] of reconstructing a clean image $\\pmb{x} \\in \\mathbb{R}^n$ from its few measurements $\\pmb{y} \\in \\mathbb{R}^m$ obtained by the imaging model $\\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon}$ , where $\\Phi \\in \\mathbb{R}^{m\\times n}$ ( $m \\ll n$ ) is the measurement (i.e., degradation) matrix, $\\pmb{\\epsilon} \\in \\mathbb{R}^m$ the measurement noise. The inverse problem is formulated as", + "bbox": [ + 511, + 613, + 908, + 717 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {x}} = \\underset {\\boldsymbol {x}} {\\arg \\min } f (\\boldsymbol {x}) + \\lambda g (\\boldsymbol {x}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 720, + 903, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where $f(x) = \\frac{1}{2} \\| \\pmb{y} - \\pmb{\\Phi}\\pmb{x} \\|_2^2$ is a data fidelity term, $\\lambda g(x)$ a scaled regularization term that represents a prior knowledge on $x$ , e.g., sparsity [16]. In SPI cameras, $\\pmb{\\Phi}$ is usually set to be row-orthogonal and each row represents an optical mask. As a adjustable parameter, compressive ratio (CR) $\\eta = m/n$ affects the ill-posedness of Eq. (1), namely the degree to which images are degraded as illustrated in Fig. 2.", + "bbox": [ + 511, + 747, + 908, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A fruitful solution to Eq. (1) is first-order proximal algorithms [9], e.g., half quadratic splitting (HQS) [17] method and alternating direction method of multipliers", + "bbox": [ + 511, + 854, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 107, + 875, + 218, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author: Xin Yuan, xyuan@westlake.edu.cn", + "bbox": [ + 109, + 887, + 424, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "411", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/685e0d43c23e9f1a81eb27845eb1f7de2965798ffe63007450c1858088663d3d.jpg", + "image_caption": [ + "Figure 2. Degradations under different compressive ratios (CRs). (ADMM) [30], which individually perform the proximal operator $\\mathrm{Prox}$ on $f$ and $g$ . $\\mathrm{Prox}_h$ is defined as" + ], + "image_footnote": [], + "bbox": [ + 93, + 74, + 480, + 186 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {h} (z) = \\underset {\\boldsymbol {x}} {\\arg \\min } h (\\boldsymbol {x}) + \\frac {1}{2} \\| \\boldsymbol {x} - \\boldsymbol {z} \\| _ {2} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 250, + 482, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The properties of proximal operator guarantee the convergence of iterative algorithms [33]. $\\mathrm{Prox}_f$ has a closed form for a specific algorithm. $\\mathrm{Prox}_g$ can be loosely interpreted as a denoising step, which is explicitly implemented by the regularizer $g$ or implicitly by a deep neural network. By integrating proximal algorithms and deep neural networks, deep-unrolling (or unfolding) [1, 4, 11, 31, 61] and plug-and-play (PnP) [25, 44, 45, 64, 66] approaches have become the de-facto standard solvers for imaging inverse problems. PnP approaches constitute a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep Gaussian denoiser [63, 65, 66]. Unrolling approaches constitute a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network.", + "bbox": [ + 89, + 280, + 483, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In SPI cameras, degradations are signal-dependent and CR-dependent as illustrated in Fig. 2. PnP algorithms [46] have flexibility for varying CRs but typically achieve moderate accuracy with slow inference and cumbersome parameter adjustment. Latest works [15, 22-24, 37] reveal that, PnP deep denoiser or even deep restorer can approximate a proximal operator under certain assumptions or constraints to guarantee the convergence for various imaging tasks and varying degradations. Conversely, unrolling networks [35, 47] are typically trained end-to-end for a specific CR to achieve state-of-the-art (SOTA) accuracy with fast inference. However, when CR changes, they must be finetuned or even retrained due to the out-of-distribution (OOD) problem, thereby lacking flexibility. Besides, what has been learned from data is not interpretable for unrolling networks. As summarized in Tab. 1, PnP algorithms are highly flexible but are limited in accuracy and speed, whereas unrolling networks are too specialized to flexibly handle varying CRs. What hinders the flexibility and interpretability of unrolling networks is an open question.", + "bbox": [ + 89, + 507, + 483, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we address the challenge of integrating the strengths of PnP and unrolling approaches. The flexibility and interpretability are originated from proximal algorithms. The flexibility and interpretability of PnP and unrolling approaches depend on the extent to which the used neural networks approach proximal operators. To this end,", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/636472966db66020b9c7c558133d43e2d41111e300bbaf1cff9f5fc79fea460f.jpg", + "table_caption": [ + "Table 1. Comprehensive comparison among proximal algorithms, PnP algorithms, unrolling networks, and our ProxUnroll." + ], + "table_footnote": [], + "table_body": "
MethodAccuracySpeedFlexibilityInterpretability
ProximalLowLowHighHigh
PnPMiddleMiddleHighMiddle
UnrollingHighHighLowLow
ProxUnrollHighHighHighHigh
", + "bbox": [ + 537, + 107, + 879, + 186 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "we propose a proximal unrolling (ProxUnroll) approach to endow unrolling networks with flexibility and interpretability. Main contributions are summarized as follows:", + "bbox": [ + 511, + 196, + 903, + 239 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce HQS- and ADMM-unrolling networks for SPI, composed of a few iterations of an explicit proximal operator and an implicit deep image restorer (DIR).", + "- We design an efficient CNN-Transformer hybrid architecture as DIR, where the integration of window attention and dynamic CNN captures both low- and high-frequency information with high input dependency, and channel attention functions as a memory mechanism to propagate informative representations between adjacent iterations.", + "- More importantly, we propose a generic proximal trajectory (PT) loss function to train HQS/ADMM-unrolling networks into HQS/ADMM-ProxUnroll networks where learned DIRs approximate the proximal operator of an ideal explicit restoration regularizer.", + "- Extensive experiments demonstrate that the proposed HQS/ADMM-ProxUnroll efficiently achieves not only SOTA performance and fast convergence, but also the same flexibility as PnP algorithms (see Fig. 1)." + ], + "bbox": [ + 513, + 241, + 903, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 527, + 663, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SPI Reconstruction. SPI reconstruction is a classical inverse problem in the field of compressive imaging [48-50, 59]. Mainstream solvers involve iterative optimization algorithms [3, 5, 10, 16, 21, 26, 28, 30, 53], PnP algorithms [15, 22-24, 66], single-stage neural networks [27, 39, 40, 55], and unrolling (multi-stage) neural networks [18, 29, 32, 35, 38, 41, 42, 47, 51, 54, 56, 57, 61, 62, 68]. Iterative algorithms employ hand-crafted regularizers, e.g., sparsity [16], total variation [28], non-local low rank [10, 58], with a proximal algorithm, e.g., iterative shrinkage thresholding algorithm (ISTA) [3], approximate message passing (AMP) [30], HQS [17], and ADMM [53]. Single-stage networks generally achieve inferior performance due to the insufficient utilization of imaging model information. PnP algorithms are flexible for varying CRs and unrolling networks achieve superior performance, thus making both the de-facto standard tools for SPI reconstruction.", + "bbox": [ + 511, + 551, + 906, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Proximal learning. The objective of proximal learning is to train a neural network as the proximal operator of a explicit regularization function. Regularization by denoising [36] shows that under homogeneity, nonexpansiveness and Jacobian symmetry conditions, a denoiser can be written as a gradient descent step on a convex function. However, such", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "412", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "conditions are unrealistic for deep denoisers. Recently, a new type of gradient denoisers [15, 23, 24] has been proposed by training a denoiser as an explicit gradient step on a functional parameterized by a deep neural network. However, these denoisers must either be a contractive gradient [23, 24] or be constrained to input convex neural networks (ICNN) [15], inevitably sacrificing the expressivity. Proximal learning without assumptions and constraints remains an open challenge.", + "bbox": [ + 89, + 90, + 483, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 239, + 230, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce the inverse problem of SPI. Then, we extend two representative proximal algorithms (i.e., HQS and ADMM) to solve this problem. Finally, we compare PnP approaches with unrolling approaches.", + "bbox": [ + 89, + 263, + 483, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. SPI Inverse Problem", + "text_level": 1, + "bbox": [ + 89, + 333, + 285, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Typical SPI cameras capture 2D images. Following Eqs. (1) and (2), processing a 2D image in its vectorized form leads to large matrix calculation problems for all $\\Phi$ -related operations, particularly during model training. To this end, most previous works [18, 32, 41, 42, 51, 56, 57, 61, 62, 68] split a digital image into non-overlapping blocks to reduce the vectorized size, but block-wise sampling is impractical for real SPI cameras. A practical solution is Kronecker compressed sensing [6, 12], which processes 2D images in matrix form rather than vector form. Mathematically, $\\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon}$ is equivalent to $\\mathbf{Y} = \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top} + \\mathbf{E}$ with $\\pmb{y} = \\mathrm{vec}(\\mathbf{Y})$ , $\\pmb{x} = \\mathrm{vec}(\\mathbf{X})$ , $\\pmb{\\epsilon} = \\mathrm{vec}(\\mathbf{E})$ , $\\Phi = \\mathbf{W} \\otimes \\mathbf{H}$ , where $\\mathrm{vec}(\\cdot)$ denotes the vectorization operation, $\\otimes$ the Kronecker product. The large measurement matrix $\\Phi \\in \\mathbb{R}^{hw \\times HW}$ is replaced by two small matrices $\\mathbf{H} \\in \\mathbb{R}^{h \\times H}$ , $\\mathbf{W} \\in \\mathbb{R}^{w \\times W}$ to reconstruct an image $\\mathbf{X} \\in \\mathbb{R}^{H \\times W}$ from the measurements $\\mathbf{Y} \\in \\mathbb{R}^{hw}$ with a compressive ratio $\\eta = hw / HW$ . The inverse problem is therefore formulated as", + "bbox": [ + 89, + 356, + 483, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {X}} = \\underset {\\mathbf {X}} {\\arg \\min } f (\\mathbf {X}) + \\lambda g (\\mathbf {X}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 630, + 482, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f = \\frac{1}{2}\\| \\mathbf{Y} - \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top}\\|_{F}^{2},\\| \\cdot \\|_{F}$ denotes the Frobenius norm. As a result, large matrix calculations on $\\Phi$ are equivalent to efficient calculations on $\\mathbf{H}$ and $\\mathbf{W}$ , resulting in a significant decrease on space complexity from $\\mathcal{O}(\\eta H^2 W^2)$ to $\\mathcal{O}(\\sqrt{\\eta} H^2 +\\sqrt{\\eta} W^2)$ and time complexity from $\\mathcal{O}(\\eta H^2 W^2)$ to $\\mathcal{O}(\\eta H^2 W + \\sqrt{\\eta} HW^2)$ ( $H\\leq W$ ) [47]. Note that the physical masks in SPI cameras still correspond to the rows of $\\Phi = \\mathbf{W}\\otimes \\mathbf{H}$ .", + "bbox": [ + 89, + 659, + 483, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Proximal Algorithms: HQS and ADMM", + "text_level": 1, + "bbox": [ + 89, + 790, + 437, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "HQS and ADMM are generally developed to solve Eq. (1). Next, we exploit both towards Eq. (3). By introducing an auxiliary variable $\\mathbf{Z} \\in \\mathbb{R}^{H \\times W}$ , the unconstrained Eq. (3) can be rewritten as a constrained optimization problem:", + "bbox": [ + 89, + 813, + 483, + 875 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n(\\widehat {\\mathbf {X}}, \\widehat {\\mathbf {Z}}) = \\underset {\\mathbf {X}, \\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}), \\quad s. t. \\mathbf {Z} = \\mathbf {X}. \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 875, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "HQS handles the constraint of Eq. (4) as a penalty term by minimizing", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 123, + 903, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu > 0$ . The minimizer of Eq. (4) is the saddle point of $\\mathcal{L}$ , which can be found by alternative proximal operators as", + "bbox": [ + 511, + 150, + 903, + 180 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {f}: \\mathbf {Z} ^ {k + 1} = \\underset {\\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} ^ {k} \\| _ {F} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 181, + 903, + 210 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {g}: \\quad \\mathbf {X} ^ {k + 1} = \\underset {\\mathbf {X}} {\\arg \\min } \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {X} - \\mathbf {Z} ^ {k + 1} \\| _ {F} ^ {2}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 214, + 903, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{X}^0 = \\mathbf{H}^\\top \\mathbf{Y}\\mathbf{W}$ . Instead of adding a simple penalty term in HQS, ADMM re-formulates Eq. (4) using the augmented Lagrangian as", + "bbox": [ + 511, + 252, + 903, + 299 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}, \\mathbf {U}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\mathbf {U} ^ {\\top} (\\mathbf {Z} - \\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 300, + 903, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{U}$ is the Lagrange multiplier. Eq. (8) can also be solved by alternative proximal operators as", + "bbox": [ + 511, + 327, + 903, + 357 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {f}: \\mathbf {Z} ^ {k + 1} = \\underset {\\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\left(\\mathbf {X} ^ {k} - \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 358, + 903, + 390 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {g}: \\mathbf {X} ^ {k + 1} = \\underset {\\mathbf {X}} {\\arg \\min } \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {X} - \\left(\\mathbf {Z} ^ {k + 1} + \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 393, + 903, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $\\mathbf{U}^{k + 1} = \\mathbf{U}^k +\\mu (\\mathbf{Z}^{k + 1} - \\mathbf{X}^{k + 1})$", + "bbox": [ + 511, + 436, + 746, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In SPI paradigm, $f$ is a differentiable convex function and $\\Phi$ is generally set to be row-orthogonal, i.e., $\\mathbf{WW}^{\\top} \\otimes \\mathbf{HH}^{\\top} = \\mathbf{I}$ . In this case, $\\operatorname{Prox}_f$ has a closed form:", + "bbox": [ + 511, + 455, + 903, + 501 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {f} (\\mathbf {P}) = \\mathbf {V} + \\frac {1}{1 + \\mu} \\mathbf {H} ^ {\\top} (\\mathbf {Y} - \\mathbf {H P W} ^ {\\top}) \\mathbf {W}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 503, + 903, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{P} = \\mathbf{X}^k$ or $(\\mathbf{X}^k - \\frac{1}{\\mu}\\mathbf{U}^k)$ for HSQ or ADMM. Eq. (11) is also a gradient descent step. With a proper regularizer $g$ , HQS and ADMM could converge to stationary points of Eq. (3) by iterating", + "bbox": [ + 511, + 536, + 906, + 597 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {k + 1} = \\operatorname {P r o x} _ {g} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 598, + 903, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Plug-and-Play", + "text_level": 1, + "bbox": [ + 511, + 627, + 660, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PnP approaches typically replace $\\mathrm{Prox}_g$ in Eq. (12) with an off-the-shelf deep denoiser [63, 65, 66] $\\mathcal{D}_{\\theta}$ with learned weights $\\theta$ , namely iterating", + "bbox": [ + 511, + 651, + 906, + 696 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {k + 1} = \\mathcal {D} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 699, + 903, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the upside, $\\mathcal{D}_{\\theta}$ serves as a generic image prior to reduce unknown artifacts (including structural noises introduced by $\\mathrm{Prox}_f$ ) regardless of the imaging tasks and the degree of degradation, namely high generalization. For SPI cameras, the generalization makes PnP algorithms flexible for varying CRs. Besides, $\\mathcal{D}_{\\theta}$ can be interpreted as a proximal operator to guarantee the convergence under non-expansiveness assumptions or Lipschitz constraints [15, 22-24, 37]. On the downside, PnP approaches are typically limited in reconstruction accuracy and speed since pretrained $\\mathcal{D}_{\\theta}$ lacks task-specific knowledge and a large number of iterations and cumbersome parameter adjustment are necessary.", + "bbox": [ + 511, + 719, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "413", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/399ad9b3ffd8980e49cfbb0ae8d36facb481d9dca19ae1b8910ce74f6919c80b.jpg", + "image_caption": [ + "Figure 3. Proximal algorithm unrolling via trajectory loss." + ], + "image_footnote": [], + "bbox": [ + 132, + 74, + 767, + 234 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/91c3f000df1994a9964fabf2c86c2006a7e6cc72a017db585ab139e6cbeb96f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 87, + 861, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Unrolling", + "text_level": 1, + "bbox": [ + 89, + 268, + 200, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unrolling approaches first replace $\\mathbf{Prox}_g$ in Eq. (12) with a lightweight neural network $\\mathcal{N}$ , i.e., $\\mathbf{X}^{k + 1} = \\mathcal{N} \\circ \\mathbf{Prox}_f(\\mathbf{X}^k)$ , then unroll it with few iterations, finally train it end-to-end with degraded-clean image pairs produced by a specific degradation model $\\mathbf{Y} = \\mathbf{H}\\mathbf{X}\\mathbf{W}^\\top + \\mathbf{E}$ , therefore formulated as", + "bbox": [ + 89, + 292, + 483, + 367 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {K} = \\left[ \\begin{array}{l} K - 1 \\\\ \\bigcirc \\\\ k = 0 \\end{array} \\right. \\mathcal {N} _ {\\theta^ {k}} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {0}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 369, + 480, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}^0 = \\mathbf{H}^\\top \\mathbf{Y}\\mathbf{W}$ and $\\mathbf{X}^K$ denote the input and the output respectively, and $\\bigcirc$ is the compound composition operator. Instead of using a pretrained $\\mathcal{D}_{\\theta}$ in PnP algorithms, unrolling networks learn a small set of subnets $\\{\\mathcal{N}_{\\theta^k}\\}_{k=0}^{K-1}$ with a same structure but different weights, thereby belonging to multi-stage neural networks. Although unrolling networks resemble proximal algorithms that are widely known to be convergent, end-to-end training could only ensure that the final result $\\mathbf{X}^K$ is close to the ground truth $\\mathbf{X}$ but cannot guarantee that the intermediate results $\\{\\mathbf{X}^k\\}_{k=1}^{K-1}$ are improved step-by-step, thereby lacking the convergence guarantee [19] (see Fig. 7). After degradation-specific training, unrolling networks usually produce SOTA results with fast inference (due to very few iterations), but need be fine-tuned or even retrained when the degradation (e.g., CR in SPI) changes. Consequently, performance is achieved at the cost of generalization. How to make unrolling networks flexible for varying CRs is a key challenge in SPI.", + "bbox": [ + 89, + 405, + 483, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proximal Algorithm Unrolling", + "text_level": 1, + "bbox": [ + 89, + 691, + 370, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we first introduce a proximal algorithm unrolling approach with interpretability and convergence guarantees, named ProxUnroll, via a proximal trajectory (PT) loss function. Subsequently, we propose an efficient CNN-Transformer architecture to realize ProxUnroll.", + "bbox": [ + 89, + 717, + 483, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Proximal Unrolling via Trajectory Loss", + "text_level": 1, + "bbox": [ + 89, + 801, + 429, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The main differences between PnP in Eq. (13) and unrolling in Eq. (14) involve that, $(i)$ the iteration number is often large in PnP but small in unrolling; $(ii)$ one pretrained deep denoiser $\\mathcal{D}_{\\theta}$ is reused across iterations in PnP but $K$ subnets $\\{\\mathcal{N}_{\\theta^k}\\}_{k = 0}^{K - 1}$ are end-to-end optimized for $K$ iterations in un", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "rolling; (iii) $\\mathrm{PnP}\\mathcal{D}_{\\theta}$ could loosely correspond to $\\mathrm{Prox}_g$ but what unrolled $\\mathcal{N}_{\\theta^k}$ has learned is unclear. By integrating the characteristics of $\\mathrm{PnP}$ and unrolling, we define a proximal unrolling (ProxUnroll) framework as", + "bbox": [ + 511, + 270, + 905, + 330 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {K} = \\left[\\begin{array}{l}K - 1\\\\\\bigcirc\\\\k = 0\\end{array}\\right. \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {0}\\right), \\text {s . t .} \\mathcal {R} _ {\\theta} \\rightarrow \\operatorname {P r o x} _ {g}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 332, + 903, + 366 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{R}_{\\theta}$ is a neural network, which can be expressed as the proximal operator of a regularizer $g$ . In Eq. (15), the remaining challenge is to satisfy the condition $\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g$ .", + "bbox": [ + 511, + 367, + 905, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Essentially, $\\operatorname{Prox}_g$ is an input-to-output movement towards the minimum of a regularizer $g$ such that the output is between the input and the minimum. Given a degraded image as input, the output image is bound to be restored if the minimum is the corresponding clear image. In this case, $\\operatorname{Prox}_g$ is an image restoration operator. Motivated by this point, we define the squared Euclidean distance between a degraded image $\\mathbf{X}'$ and its clear image $\\mathbf{X}$ as an explicit regularization function:", + "bbox": [ + 511, + 417, + 905, + 550 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {g} \\left(\\mathbf {X} ^ {\\prime}\\right) = \\frac {1}{2} \\| \\mathbf {X} ^ {\\prime} - \\mathbf {X} \\| _ {F} ^ {2}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 551, + 903, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By inserting Eq. (16) into Eqs. (7) and (10), $\\mathrm{Prox}_{\\tilde{g}}$ has the following closed form:", + "bbox": [ + 511, + 580, + 903, + 611 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P r o x} _ {\\tilde {g}} (\\mathbf {Q}) = \\frac {\\mu \\mathbf {Q} + \\lambda \\mathbf {X}}{\\mu + \\lambda}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 612, + 903, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{Q} = \\mathbf{Z}^{k + 1}$ or $(\\mathbf{Z}^{k + 1} + \\frac{1}{\\mu}\\mathbf{U}^k)$ for HQS or ADMM, $\\mu$ and $\\lambda$ control the strength of being close to $\\mathbf{Q}$ and $\\mathbf{X}$ respectively. By combining Eqs. (11) and (17), an ideal explicit proximal algorithm is", + "bbox": [ + 511, + 646, + 905, + 707 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 709, + 903, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}^k\\rightarrow \\mathbf{X}$ if $k\\to \\infty$ . The convergence rate is closely related to $\\mu$ and $\\lambda$ . If $\\mu /\\lambda = 0$ , Proxg executes an one-step restoration from an arbitrarily degraded image to its clear image. Proxg is an explicit image restorer conditioned on the ground truth. During supervised training, we use Proxg to guide the optimization of $\\mathcal{R}_{\\theta}$ in Eq. (15) such that $\\mathcal{R}_{\\theta}$ serves as an implicit image restorer to approximate Proxg.", + "bbox": [ + 511, + 729, + 905, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3, a perfect proximal optimization trajectory $\\mathbf{X}^0\\rightarrow \\bar{\\mathbf{X}}^1\\rightarrow \\dots \\rightarrow \\bar{\\mathbf{X}}^{K - 1}\\rightarrow \\mathbf{X}$ can be produced from every $(\\mathbf{X}^0,\\mathbf{X})$ training pair via Eq. (18) to supervise the end-to-end training of algorithm unrolling in Eq. (15).", + "bbox": [ + 511, + 840, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "414", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/375973e91a60b3a88c8a66cdc5217a59c1fc33c8d70169553bf0511ea8a7d463.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 127, + 74, + 869, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b8bc180d36d817ef8b902c02f8bcd8250ee53be29f458cd1096a4a32c167af5.jpg", + "image_caption": [ + "Figure 4. Illustration of the proposed deep image restorer (DIR) $\\mathcal{R}_{\\theta}$ ." + ], + "image_footnote": [], + "bbox": [ + 156, + 223, + 450, + 416 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a1b994bb541f605f51bf223522bf8970c8431a94ea1e8e287c74b23fc056b4b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 470, + 223, + 849, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proximal iterations $\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_f$ are guaranteed with fast convergence towards the ground truth such that unrolled iterations $\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f$ are optimized to have the similar capability, namely $\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g$ . To this end, we propose a proximal trajectory (PT) loss function as", + "bbox": [ + 88, + 450, + 482, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {P L} = \\sum_ {k = 0} ^ {K - 1} \\alpha_ {k} \\| \\mathbf {X} ^ {k + 1} - \\bar {\\mathbf {X}} ^ {k + 1} \\| _ {F} ^ {2}, \\\\ s. t. \\left\\{ \\begin{array}{l} \\bar {\\mathbf {X}} ^ {k + 1} = \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right) \\\\ \\bar {\\mathbf {X}} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\bar {\\mathbf {X}} ^ {k}\\right) \\end{array} \\right. \\end{array} \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 529, + 480, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{X}}^0 = \\mathbf{X}^0$ , $\\bar{\\mathbf{X}}^K = \\mathbf{X}$ , $\\alpha_{k}$ controls the proximity strength of $k$ -th iteration. Trainable parameters involve $\\theta, \\{\\mu^{k}\\}_{k=0}^{K-1}$ in $\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_{f}$ and $\\{\\bar{\\mu}^{k}, \\bar{\\lambda}^{k}\\}_{k=0}^{K-2}$ in $\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_{f}$ . For $\\bar{\\mathbf{X}}^K = \\mathbf{X}$ , $(\\bar{\\mu}^{K-1}, \\bar{\\lambda}^{K-1})$ is set to be $(0,1)$ . PT loss function is designed to train any unrolled network $\\mathcal{R}_{\\theta}$ to approximate the proximal operator $\\mathrm{Prox}_{\\bar{g}}$ , thereby with interpretability. Since $\\mathrm{Prox}_{\\bar{g}}$ is an explicit image restorer, $\\mathcal{R}_{\\theta}$ functions as a deep image restorer (DIR).", + "bbox": [ + 89, + 595, + 483, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Deep Image Restorer", + "text_level": 1, + "bbox": [ + 89, + 726, + 290, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To unlock the potential of ProxUnroll, we propose an efficient CNN-Transformer architecture as DIR.", + "bbox": [ + 89, + 750, + 482, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall Pipeline. As shown in Fig. 4 (a), DIR is a 4-level asymmetric encoder-decoder architecture. Given a degraded image $\\mathbf{I}_{in} \\in \\mathbb{R}^{H \\times W \\times C_{in}}$ , one $3 \\times 3$ convolution layer is first applied to extract shallow features $\\mathbf{F}_0 \\in \\mathbb{R}^{H \\times W \\times C}$ . Next, $\\mathbf{F}_0$ are passed through 3 encoder stages, each of which contains one memory block, a stack of hybrid CNN-Transformer blocks, and one downsampling layer. From level-1 to level-3, the goal of the encoder is to progressively", + "bbox": [ + 89, + 779, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "reduce the spatial resolution by half while doubling channel capacity, thereby yielding multi-scale low-level features $\\{\\mathbf{F}_1,\\mathbf{F}_2,\\mathbf{F}_3\\}$ . For example, the encoder produces $\\mathbf{F}_3\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times 8C}$ at level-3. At level-4, a bottleneck stage is between the encoder and the decoder to produce $\\mathbf{F}_4$ . The decoder is similar to the encoder except for having no memory block and replacing the downsampling layer by one upsampling layer. Form level-3 to level-1, the decoder progressively produces high-level features $\\{\\mathbf{F}_5,\\mathbf{F}_6,\\mathbf{F}_7\\}$ while recovering the spatial resolution and channel capability. Finally, one $3\\times 3$ convolution layer transforms the features $\\mathbf{F}_7$ into the residual image $\\Delta \\mathbf{I}\\in \\mathbb{R}^{H\\times W\\times C_{in}}$ . The restored image is therefore obtained by $\\mathbf{I}_{out} = \\mathbf{I}_{in} + \\Delta \\mathbf{I}$ .", + "bbox": [ + 511, + 450, + 906, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In these downsampling and upsampling layers, one $2 \\times 2$ stripped convolution and one $2 \\times 2$ transposed convolution are employed respectively. Skip connections are built between the encoder and the decoder for efficient information propagation. Memory block and hybrid CNN-Transformer block are the core components. Next, we introduce them in detail.", + "bbox": [ + 511, + 654, + 908, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Memory Block. As mentioned previously, typical unrolling networks in Eq. (14) cannot guarantee the progressive refinement of intermediate results [19] (see Fig. 7) due to end-to-end training. That is also partially caused by that informative representations cannot be propagated across iterations. Hence, the artifacts in intermediate results may be the manifestations of informative representations in the image domain. As analyzed in the supplementary material, we attempt to reduce or remove the intermediate artifacts of SAUNet [47], and the resulting outputs become worse.", + "bbox": [ + 511, + 750, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "415", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this problem, we propose a memory block (MB) to propagate informative representations in a side path. MB is composed of one channel cross-attention (ChanCA), similar to existing multi-Dconv head transposed attention (MDTA) [60]. As shown in Fig. 4 (a), we directly consider the output features of the bottleneck and decoder at iteration $k$ as current memories $\\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\}$ . By producing queries from $\\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\}$ and keys/values from $\\{\\mathbf{F}_4^{k - 1},\\mathbf{F}_5^{k - 1},\\mathbf{F}_6^{k - 1},\\mathbf{F}_7^k\\}$ , MB adaptively aggregates previous useful representations into current iteration for efficient information propagation by ChanCA, formulated as", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {F} _ {\\text {o u t}} = \\operatorname {C h a n C A} \\left(\\mathbf {F} _ {q}, \\mathbf {F} _ {k v}\\right) = \\mathbf {W} _ {p} \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top}\\right) \\mathbf {V} \\right], \\\\ \\mathbf {Q} = \\mathbf {W} ^ {q} \\mathbf {E} \\mathbf {W} ^ {q} \\mathbf {K} = \\mathbf {W} ^ {k} \\mathbf {E} \\mathbf {W} ^ {k} \\mathbf {V} = \\mathbf {W} ^ {v} \\mathbf {E} \\mathbf {W} ^ {v} \\end{array} \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 258, + 480, + 287 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {W} _ {p} ^ {q} \\mathbf {F} _ {q} \\mathbf {W} _ {d} ^ {q}, \\mathbf {K} = \\mathbf {W} _ {p} ^ {k} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {k}, \\mathbf {V} = \\mathbf {W} _ {p} ^ {v} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {v}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 280, + 478, + 299 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{F}_q, \\mathbf{F}_{kv} \\in \\mathbb{R}^{d \\times HW}$ denote the heads of current and previous memory features respectively, $\\mathbf{Q}$ and $\\{\\mathbf{K}, \\mathbf{V}\\}$ are produced from $\\mathbf{F}_q$ and $\\mathbf{F}_{kv}$ by a point-wise convolution $\\mathbf{W}_p^{(\\cdot)}$ followed by a $3 \\times 3$ depth-wise convolution $\\mathbf{W}_d^{(\\cdot)}$ . At the first iteration, MB can automatically be invalid due to the lack of available memories, i.e. $\\mathbf{F}_{out} = 0$ if $\\mathbf{F}_{kv} = 0$ . Such design leads to two advantages: i) cross-iteration information propagation mechanism is built regardless iterations; ii) informative representations are adaptively activated.", + "bbox": [ + 89, + 301, + 480, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CNN-Transformer Block. We propose a hybrid CNN-Transformer block (CTB) as the basic processing unit. The core idea of CTB is to integrate high- and low-frequency modeling ability of CNN and Transformer [34] while keeping high dependency for input. As shown in Fig. 4 (a), an input feature is firstly split into two parts evenly, then Swin Transformer (SwinT) and gated dynamic CNN (GD-CNN) process them in parallel, finally two parts are fused by channel concatenation and a point-wise convolution.", + "bbox": [ + 89, + 444, + 480, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As depicted in Fig. 4 (b), SwinT is mainly powered by a shifted-window self-attention (SwinSA) and a feed-forward network (FFN) composed of a MLP with a $3 \\times 3$ depth-wise convolution inserted. SwinSA can be formulated as", + "bbox": [ + 89, + 584, + 480, + 643 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {\\text {o u t}} = \\operatorname {S w i n S A} \\left(\\mathbf {F} _ {\\text {i n}}\\right) = \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top} + \\mathbf {B}\\right) \\mathbf {V} \\right] \\mathbf {W}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 643, + 480, + 670 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {v},\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 666, + 421, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{F}_{in} \\in \\mathbb{R}^{p^2 \\times d}$ is the head at a $p \\times p$ window, $\\mathbf{W}^{(\\cdot)} \\in \\mathbb{R}^{d \\times d}$ denotes a learnable linear projection matrix, and $\\mathbf{B}$ denote a learnable relative position encoding (RPE). As opposed to ChanCA in Eq. (20), SwinSA performs self-attention mechanism on spatial dimensions.", + "bbox": [ + 89, + 686, + 480, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As depicted in Fig. 4 (c), GD-CNN is a gated structure of normal convolutions (Convs) and an adaptive convolution (AdaConv). AdaConv is a simple implementation of transforming a group of static (learned) convolution kernels into dynamic one varying with the input, formulated as", + "bbox": [ + 89, + 768, + 480, + 843 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} \\mathbf {F} & = \\text {R e s h a p e} (\\operatorname {C o n v} _ {3 \\times 3} (\\operatorname {R e L U} (\\operatorname {C o n v} _ {1 \\times 1} (\\mathbf {F} _ {i n})))) \\\\ \\mathbf {F} _ {\\text {o u t}} & = (\\mathbf {F W}) * \\mathbf {F} _ {\\text {i n}}, \\end{array} \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 845, + 480, + 877 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{F}_{in},\\mathbf{F}_{out}\\in \\mathbb{R}^{H\\times W\\times C}$ denote the input and the out", + "bbox": [ + 89, + 883, + 480, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "put, $\\mathbf{F} \\in \\mathbb{R}^{HW \\times n}$ the input-dependent kernel coefficients, $\\mathbf{W} \\in \\mathbb{R}^{n \\times C \\times 3^2}$ the kernel weights of $n \\times 3$ depth-wise convolutions, and $\\oplus$ performs the convolution operator. Similar to attention mechanism, AdaConv is also input-dependent. Differently, AdaConv updates convolution weights from a group of learned kernel weights while attention produces attention weights by the similarity between features.", + "bbox": [ + 511, + 90, + 903, + 198 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 212, + 643, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed DIR $\\mathcal{R}_{\\theta}$ in Sec. 4.2 is plugged in HQS- or ADMM-unrolling framework and then is end-to-end optimized using the proposed PL loss function in Sec. 4.1, leading to two proximal unrolling networks: HQS-ProxUnroll and ADMM-ProxUnroll. HQS/ADMM-ProxUnroll is composed of 6 iterations of $\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f$ . Next, we conduct experiments to estimate them. We adopt 400 images from BSD500 [2] to generate 20,000 training samples using data augmentation techniques following [32, 35, 38-42, 47, 68]. Similar to the training of PnP image denoisers [63, 65, 66], the compressive ratio varies within [0.01, 0.50] and the resolution varies from $256 \\times 256$ pixels to $512 \\times 512$ pixels to cover as wider degradations as possible. The initial learning rate is $1 \\times 10^{-3}$ and gradually reduced to $1 \\times 10^{-4}$ . We estimate HQS-ProxUnroll and ADMM-ProxUnroll on Set11 and BSD68 benchmark datasets and real captured SPI data. Regarding CBSD68, all experiments are performed on the luminance channel of YCbCr space, similar to [32, 39-42, 62, 68]. Following [35, 47], the measurement (i.e., degradation) matrices $(\\mathbf{H}, \\mathbf{W})$ are set to be floating-point and trainable for simulation experiments and are the reordered Hadamard matrices for real experiments. More experiment results are in the supplementary material.", + "bbox": [ + 511, + 238, + 906, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Results on Benchmark Datasets", + "text_level": 1, + "bbox": [ + 511, + 593, + 792, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SPI reconstruction approaches are closely related to a great number of image compressed sensing approaches. The proposed HQS-ProxUnroll and ADMM-ProxUnroll are compared with previous approaches on benchmark datasets at five widely-used CRs $\\{0.01, 0.04, 0.10, 0.25, 0.50\\}$ . Comparative approaches involve a single-stage network $(\\mathrm{CSNet}^{+}[39])$ , unrolling (multi-stage) networks (ISTA $\\mathrm{Net}^{+}[61]$ , OPINENet[62], AMP-Net [68], COAST [57], TransCS [38], MADUN [41], DGUNet[32], CSformer [56], OCTUF[42], SAUNet [47], CPP-Net [18], HATNet [35]), and PnP algorithms (PnP-DnCNN [37] and PnP-DRUNet [66]). Tab. 2 reports the reconstruction results of different approaches. Towards reconstruction accuracy, the proposed HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them outperform previous approaches on average. As visualized in Fig. 5, our HQS/ADMM-ProxUnroll can recover more image details. Towards the flexibility for CR, most previous approaches are separately trained for a specific CR and", + "bbox": [ + 511, + 613, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "416", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e3f02b984b6cb51036bbaeff554143eba504d9f0fe2f42b52d8d26fdf4b73a6.jpg", + "image_caption": [ + "Ground Truth PSNR/SSIM" + ], + "image_footnote": [], + "bbox": [ + 104, + 75, + 259, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0fa2fdacb8efd3b0ece62abf7b30e411cd543bd098f4fde2eefd2c198105e91a.jpg", + "image_caption": [ + "PnP-DRUNet 24.07/0.7243" + ], + "image_footnote": [], + "bbox": [ + 261, + 75, + 338, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5807ae6980418b931f98f964a95ecc7c31a8102c24bd359e010cf1e351c0c651.jpg", + "image_caption": [ + "OCTUF+ 25.13/0.7779" + ], + "image_footnote": [], + "bbox": [ + 339, + 75, + 416, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4ea8754e187b83f858298748fb4631e593ef81cd967af0978899c65d7d73d2e2.jpg", + "image_caption": [ + "DGUNet+ 26.13/0.8145" + ], + "image_footnote": [], + "bbox": [ + 418, + 75, + 496, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/683672773008efb2aeb2df935529b952fcc3926977497c998e1948d6e9df569e.jpg", + "image_caption": [ + "CPP-Net 27.35/0.8396" + ], + "image_footnote": [], + "bbox": [ + 496, + 75, + 573, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2dbd372ac923f908962c0278716495e7a5e0bf355ce8c84805a04afce48c7f4d.jpg", + "image_caption": [ + "SAUNet 27.65/0.8467", + "HATNet 28.17/0.867" + ], + "image_footnote": [], + "bbox": [ + 575, + 75, + 653, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0a657fdeff4e66677321884f868190ca6937939c73692b51992939f1ab259bb.jpg", + "image_caption": [ + "HQS-ProxUnroll Reference 29.54/0.8931" + ], + "image_footnote": [], + "bbox": [ + 653, + 75, + 732, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bd86abcbca9a0632638bbfa3e9322da0538241392170b661d6ada44e6aedc55d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 75, + 810, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/347f51b570bb294fbdbe2bcd9ab14162cf2defaeab7ea8e0b282099def23fa01.jpg", + "image_caption": [ + "Input", + "Figure 6. Visual comparisons on real SPI data \"resolution target\" reported in [35] at $\\mathrm{CR} = 0.15$" + ], + "image_footnote": [], + "bbox": [ + 104, + 243, + 217, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73220a75541267f55abf094ace383909a287bddf1a3212f208589de8b04a8454.jpg", + "image_caption": [ + "Figure 5. Visual comparisons on \"barbara\" from Set11 dataset at $\\mathrm{CR} = 0.04$", + "PnP-DRUNet" + ], + "image_footnote": [], + "bbox": [ + 218, + 243, + 330, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/68b44264dd70c511d01f924322bb194dddd58ef1bfacbcc8303b55c0cd0861dc.jpg", + "image_caption": [ + "SAUNet" + ], + "image_footnote": [], + "bbox": [ + 330, + 243, + 441, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/92d080dbca6bef121010e87382af4db7c9da6dd2319fe33a6baabdac536f2e30.jpg", + "image_caption": [ + "HATNet" + ], + "image_footnote": [], + "bbox": [ + 441, + 243, + 553, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/728ad005ae47793be90e0f0db0e24bb4a53f59fb72eb73bbda17ba7fa3e76614.jpg", + "image_caption": [ + "HQS-ProxUnroll" + ], + "image_footnote": [], + "bbox": [ + 553, + 243, + 663, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/68a6e873de7464b64c0e683428d93238d6afe6cd7161be818d064f372f62aed2.jpg", + "image_caption": [ + "ADMM-ProxUnroll" + ], + "image_footnote": [], + "bbox": [ + 665, + 243, + 777, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/192fabb064e01927e5e8d0f3a26b91bc09747a7df6629cafad8fc0ae02d8cd26.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 779, + 243, + 888, + 330 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/df314d47e86aef38205a9d11dddb439e682ae407e176b616bbb5151098ba1c17.jpg", + "table_caption": [ + "Table 2. Average PSNR/SSIM of different methods on Set11 and CBSD68 datasets with different compressive ratios. The best and second best results are highlighted and underlined. Blank cells (-) means that there is not an available model at the compressive ratio." + ], + "table_footnote": [], + "table_body": "
DatasetMethodFlexibilityCompressive Ratio (CR)Average
0.010.040.100.250.50
Set11ISTA-Net+ [61]Single17.42/0.402921.32/0.603726.64/0.808732.59/0.925438.11/0.970727.22/0.7423
CSNet+ [39]20.67/0.541124.83/0.748028.34/0.858033.34/0.938738.47/0.979629.13/0.8131
OPINE-Net+ [62]20.15/0.534025.69/0.792029.81/0.888434.86/0.950940.17/0.979732.63/0.9397
AMP-Net [68]20.21/0.542925.27/0.782129.43/0.888034.71/0.953240.66/0.982730.06/0.9679
TransCS [38]20.22/0.543125.41/0.788329.54/0.887735.06/0.954840.49/0.981529.42/0.8311
CSformer [56]21.58/0.607526.28/0.806229.79/0.888334.81/0.952740.73/0.982430.64/0.8474
MADUN [41]20.28/0.557225.71/0.804230.20/0.901635.76/0.960141.00/0.983730.59/0.8373
DGUNet+ [32]22.15/0.611326.82/0.823030.92/0.908836.18/0.961641.24/0.983731.46/0.8577
OCTUF+ [42]21.94/0.598926.54/0.815030.73/0.903636.10/0.960741.35/0.983831.33/0.8524
CPP-Net [18]22.19/0.613527.23/0.833731.27/0.913536.35/0.9631--
SAUNet [47]22.43/0.613427.80/0.835332.15/0.914737.11/0.962841.91/0.983832.28/0.8620
HATNet [35]22.54/0.616227.98/0.838232.26/0.918237.24/0.963442.05/0.983832.41/0.8640
COAST [57]Multiple10.45/0.2144*22.90/0.6971*28.69/0.861833.90/0.9399*38.94/0.974426.98/0.7375
PnP-DnCNN [37]Arbitrary21.68/0.568226.45/0.796929.57/0.871234.24/0.940239.78/0.973530.34/0.8300
PnP-DRUNet [66]21.75/0.573826.81/0.807430.16/0.886135.00/0.947640.54/0.976730.85/0.8383
HQS-ProxUnroll22.76/0.630028.23/0.845032.51/0.922537.33/0.963541.92/0.983732.55/0.8689
ADMM-ProxUnroll22.76/0.630728.30/0.845232.55/0.922637.35/0.963941.97/0.983832.59/0.8692
BSD68ISTA-Net+ [61]Single19.14/0.415822.17/0.548625.32/0.702229.36/0.852534.04/0.942426.01/0.6923
CSNet+ [39]22.21/0.510025.43/0.670627.91/0.793831.12/0.906036.76/0.963828.69/0.7688
OPINE-Net+ [62]22.11/0.514025.20/0.682527.82/0.804531.51/0.906136.35/0.966028.60/0.7746
AMP-Net [68]22.28/0.531925.27/0.693027.88/0.811831.80/0.915437.03/0.972228.85/0.7849
TransCS [38]22.28/0.531825.28/0.688127.86/0.808631.74/0.912136.81/0.969928.79/0.7821
CSformer [56]22.81/0.556625.73/0.695628.05/0.804531.82/0.910637.14/0.976629.11/0.7889
MADUN [41]22.08/0.524725.36/0.698528.18/0.821932.27/0.921937.23/0.973329.02/0.7880
DGUNet+ [32]22.13/0.521525.45/0.698628.13/0.816531.97/0.915837.04/0.971828.94/0.7848
OCTUF+ [42]22.78/0.541325.65/0.699928.28/0.817732.24/0.918537.41/0.972929.27/0.7900
CPP-Net [18]22.95/0.547525.81/0.706828.41/0.822732.25/0.9188--
SAUNet [47]23.11/0.546026.23/0.705029.25/0.825133.67/0.924339.28/0.975130.31/0.7951
COAST [57]Multiple12.08/0.2584*22.77/0.5953*26.28/0.742230.07/0.8703*34.74/0.949725.19/0.6832
PnP-DnCNN [37]Arbitrary22.27/0.522124.85/0.632727.22/0.765830.95/0.876236.47/0.960128.35/0.7514
PnP-DRUNet [66]22.81/0.530825.30/0.667027.79/0.785231.38/0.893136.86/0.962428.83/0.7677
HQS-ProxUnroll23.51/0.564526.52/0.719429.42/0.833233.76/0.928239.22/0.976030.49/0.8043
ADMM-ProxUnroll23.53/0.564926.54/0.720029.43/0.833433.77/0.928439.23/0.976130.50/0.8046
", + "bbox": [ + 96, + 401, + 897, + 893 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "417", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a4c2369ceb9cc1475bd195bcc3cb1c8203a05b1b6a04ae41b057c40f13f530c1.jpg", + "table_caption": [ + "Table 3. MACs (G), Params (M), and runtime (sec.) comparisons on $256 \\times 256$ images at CR = 0.25. PnP-DRUNet performs 50 iterations for best performance." + ], + "table_footnote": [], + "table_body": "
MetricCPP-Net [18]SAUNet [47]HATNet [35]PnP-DRUNet [66]HQS/ADMM-ProxUnroll
MACs153.47143.05494.427175.10 (143.5×50)107.73 (17.95×6)
Params12.3110.5331.2832.643.90
Runtime0.410.350.600.650.27
", + "bbox": [ + 94, + 118, + 480, + 198 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "thus cannot generalize to different CRs. COAST, trained on multiple CRs $\\{0.10, 0.20, 0.30, 0.40, 0.50\\}$ , is flexible only for seen CRs, not for unseen CRs (e.g. 0.01). Our HQS/ADMM-ProxUnroll and PnP algorithms (PnP-DnCNN, PnP-DRUNet) can flexibly handle arbitrary CRs with a single model. Moreover, we compare HQS/ADMM-ProxUnroll with several competitive approaches in terms of multiply-accumulate operations (MACs), model parameters (Params), and runtime. As reported in Tab. 3, our HQS/ADMM-ProxUnroll achieves an all-around superiority over these approaches. Overall, our HQS/ADMM-ProxUnroll achieve not only SOTA performance and efficiency but also the same flexibility as PnP algorithms.", + "bbox": [ + 88, + 207, + 482, + 404 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Results on Real Captured Data", + "text_level": 1, + "bbox": [ + 89, + 412, + 366, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We estimate the proposed HQS/ADMM-ProxUnroll on real captured SPI data. Among the networks mentioned previously, only SAUNet [47] and HATNet [35] are practical for real SPI cameras. The remaining networks are developed under the assumption that images can be compressively sampled block by block, which is out of line with real SPI cameras. Hence, we compare HQS/ADMM-ProxUnroll with SAUNet, HATNet, and PnP-DRUNet. As shown in Fig. 6, PnP-DRUNet can recovers well on low frequencies (e.g., shapes and edges) instead of high frequencies (e.g., textures and details), agreeing with that Gaussian denoisers could smooth out rather than remove unknown artifacts [66]. HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them have a better reconstruction ability than the competitors. In practice, SAUNet and HATNet need a separate model for a specific CR. A single model of HQS-ProxUnroll or ADMM-ProxUnroll is flexible enough for varying CRs, similar to PnP algorithms.", + "bbox": [ + 91, + 431, + 483, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 712, + 243, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To offer an insight into ProxUnroll, we conduct ablation experiments on PL loss function (Sec. 4.1) and DIR (Sec. 4.2). ProxUnroll uses PL loss function to train DIR as approximation of the proximal operator of an explicit restoration regularizer in Eq. (16) to guarantee the fast convergence.", + "bbox": [ + 89, + 733, + 482, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To demystify the influence of PL loss function, the convergence curves of different methods are depicted in Fig. 7. SAUNet and HATNet, both composed of 7 iterations, reconstruct images with twists and turns since their MSE loss function only ensure a satisfactory final result. This implies that their intermediate subnets cannot be interpreted", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/85a1d387c68057884f39d13d69a2b775be541f2c1c9874b976747da331d1b959.jpg", + "image_caption": [ + "Figure 7. Convergence curves of different unrolling methods." + ], + "image_footnote": [], + "bbox": [ + 560, + 74, + 854, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8addce41e725dc8f7b4fcac01958e77d28bb846831e00dea4bfa1a12bb9b0804.jpg", + "table_caption": [ + "Table 4. Ablation experiments for different components of our deep image restorer (DIR) on Set11 dataset at $\\mathrm{{CR}} = {0.10}$ ." + ], + "table_footnote": [], + "table_body": "
ChanCASwinTAdaConvPSNRMACsParamsRuntime
✓✓31.4294.853.100.22
✓✓32.25128.674.650.34
✓✓32.36101.993.850.21
✓✓✓32.51107.733.900.27
", + "bbox": [ + 517, + 271, + 893, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "as the proximal restoration operators and function more like black-box neural networks. Their lack of proximity also elucidates why prior unrolling networks require retraining when the degradation changes. With PL-based training, our HQS/ADMM-ProxUnroll achieves fast and stable convergence. By replacing PL loss with regular MSE loss during training, their convergence curves also become unstable.", + "bbox": [ + 511, + 352, + 905, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To demystify the influence of key designs in DIR, we conduct ablation experiments as shown in Tab. 4. The proposed DIR is mainly powered by three components: ChanCA in memory block, SwinT and GD-CNN in CNN-Transformer block. ChanCA is used to adaptively propagate informative representations between adjacent iterations. The combination of SwinT and GD-CNN is to integrate the high- and low-frequency modeling ability while keeping high dependency for input. GD-CNN is powered by the proposed AdaConv. Clearly, ChanCA results in a $1.09\\mathrm{dB}$ improvement in PSNR with a slight increase in MACs, parameters, and runtime. By discarding SwinT and doubling the channel capability of GD-CNN, the entire network becomes a CNN, leading to a $0.26\\mathrm{dB}$ decrease in PSNR and an all-round increase in other metrics. Replacing AdaConv with one depth-wise convolution causes a $0.15\\mathrm{dB}$ decrease in PSNR but has minimal impact on MACs, parameters, and runtime. These results validate the effectiveness and efficiency of ChanCA, SwinT, and AdaConv.", + "bbox": [ + 511, + 457, + 906, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 756, + 633, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose ProxUnroll to train any unrolled network to approximate the proximal operator of an explicit restoration regularizer using a proximal trajectory (PL) loss function. Besides, we propose an efficient CNN-Transformer architecture as deep image restorer (DIR) to arm ProxUnroll. Extensive experiments demonstrate that our ProxUnroll achieves not only SOTA performance and efficiency but also the same flexibility as PnP algorithms.", + "bbox": [ + 511, + 779, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "418", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 327, + 187, + 343 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hemant K Aggarwal, Merry P Mani, and Mathews Jacob. Modl: Model-based deep learning architecture for inverse problems. IEEE transactions on medical imaging, 38(2): 394-405, 2018. 2", + "[2] Pablo Arbeláez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. 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Amp-net: Denoising-based deep unfolding for compressive image sensing. IEEE Transactions on Image Processing, 30:1487-1500, 2020. 2, 3, 6, 7" + ], + "bbox": [ + 516, + 92, + 903, + 233 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "421", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Proximal Algorithm Unrolling_ Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging/b1aa96ba-e721-4e19-b13a-1d18da180bc8_model.json b/2025/Proximal Algorithm Unrolling_ Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging/b1aa96ba-e721-4e19-b13a-1d18da180bc8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2ca0e9018546c275cc8f7c341199d17a482a8d3e --- /dev/null +++ b/2025/Proximal Algorithm Unrolling_ Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging/b1aa96ba-e721-4e19-b13a-1d18da180bc8_model.json @@ -0,0 +1,2829 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.135, + 0.131, + 0.865, + 0.177 + ], + "angle": 0, + "content": "Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.203, + 0.866, + 0.242 + ], + "angle": 0, + "content": "Ping Wang\\(^{1,2*}\\) Lishun Wang\\(^{1*}\\) Gang Qu\\(^{1}\\) Xiaodong Wang\\(^{1,2}\\) Yulun Zhang\\(^{3}\\) Xin Yuan\\(^{1\\dagger}\\) \n\\(^{1}\\)Westlake University \\(^{2}\\)Zhejiang University \\(^{3}\\)Shanghai Jiao Tong University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.274, + 0.327, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.307, + 0.486, + 0.701 + ], + "angle": 0, + "content": "Deep-unrolling and plug-and-play (PnP) approaches have become the de-facto standard solvers for single-pixel imaging (SPI) inverse problem. PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.731, + 0.222, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.757, + 0.485, + 0.864 + ], + "angle": 0, + "content": "How many pixels does your camera actually need? Modern cameras typically require as many pixels as the image resolution demands. By contrast, single-pixel cameras need only one pixel, a light-sensitive detector, to capture images through multiple measurements. Single-pixel imaging (SPI) [13, 14, 20, 52, 67] technique measures the total light intensity of a scene coded by a series of spatially resolved" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.274, + 0.906, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.439, + 0.907, + 0.523 + ], + "angle": 0, + "content": "Figure 1. Average PSNR (left) of different methods at compressive ratios (CRs) \\(\\{0.01, 0.04, 0.10, 0.25\\}\\) in which only methods in the yellow area can flexibly handle varying CRs with a single model. Optimization trajectories (right) of four classes of methods for solving inverse problems. Our ProxUnroll efficiently achieves SOTA performance with high flexibility and fast convergence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.907, + 0.613 + ], + "angle": 0, + "content": "masks on a single-pixel detector. Known masks and measurements, one can recover an image with the same resolution as the masks. SPI offers a competitive edge over mainstream CCD and CMOS cameras in certain scenarios, e.g., terahertz imaging [52] and non-visible 3D imaging [43]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.718 + ], + "angle": 0, + "content": "SPI cameras typical work under sub-Nyquist sampling rate to save acquisition time, leading to a compressed sensing problem [7, 8] of reconstructing a clean image \\( \\pmb{x} \\in \\mathbb{R}^n \\) from its few measurements \\( \\pmb{y} \\in \\mathbb{R}^m \\) obtained by the imaging model \\( \\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon} \\), where \\( \\Phi \\in \\mathbb{R}^{m\\times n} \\) (\\( m \\ll n \\)) is the measurement (i.e., degradation) matrix, \\( \\pmb{\\epsilon} \\in \\mathbb{R}^m \\) the measurement noise. The inverse problem is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.722, + 0.905, + 0.746 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {x}} = \\underset {\\boldsymbol {x}} {\\arg \\min } f (\\boldsymbol {x}) + \\lambda g (\\boldsymbol {x}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.748, + 0.909, + 0.854 + ], + "angle": 0, + "content": "where \\( f(x) = \\frac{1}{2} \\| \\pmb{y} - \\pmb{\\Phi}\\pmb{x} \\|_2^2 \\) is a data fidelity term, \\( \\lambda g(x) \\) a scaled regularization term that represents a prior knowledge on \\( x \\), e.g., sparsity [16]. In SPI cameras, \\( \\pmb{\\Phi} \\) is usually set to be row-orthogonal and each row represents an optical mask. As a adjustable parameter, compressive ratio (CR) \\( \\eta = m/n \\) affects the ill-posedness of Eq. (1), namely the degree to which images are degraded as illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.901 + ], + "angle": 0, + "content": "A fruitful solution to Eq. (1) is first-order proximal algorithms [9], e.g., half quadratic splitting (HQS) [17] method and alternating direction method of multipliers" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.22, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.425, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author: Xin Yuan, xyuan@westlake.edu.cn" + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.425, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "411" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.075, + 0.482, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.196, + 0.482, + 0.248 + ], + "angle": 0, + "content": "Figure 2. Degradations under different compressive ratios (CRs). (ADMM) [30], which individually perform the proximal operator \\(\\mathrm{Prox}\\) on \\(f\\) and \\(g\\). \\(\\mathrm{Prox}_h\\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.25, + 0.483, + 0.279 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {h} (z) = \\underset {\\boldsymbol {x}} {\\arg \\min } h (\\boldsymbol {x}) + \\frac {1}{2} \\| \\boldsymbol {x} - \\boldsymbol {z} \\| _ {2} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.281, + 0.484, + 0.506 + ], + "angle": 0, + "content": "The properties of proximal operator guarantee the convergence of iterative algorithms [33]. \\(\\mathrm{Prox}_f\\) has a closed form for a specific algorithm. \\(\\mathrm{Prox}_g\\) can be loosely interpreted as a denoising step, which is explicitly implemented by the regularizer \\(g\\) or implicitly by a deep neural network. By integrating proximal algorithms and deep neural networks, deep-unrolling (or unfolding) [1, 4, 11, 31, 61] and plug-and-play (PnP) [25, 44, 45, 64, 66] approaches have become the de-facto standard solvers for imaging inverse problems. PnP approaches constitute a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep Gaussian denoiser [63, 65, 66]. Unrolling approaches constitute a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.484, + 0.81 + ], + "angle": 0, + "content": "In SPI cameras, degradations are signal-dependent and CR-dependent as illustrated in Fig. 2. PnP algorithms [46] have flexibility for varying CRs but typically achieve moderate accuracy with slow inference and cumbersome parameter adjustment. Latest works [15, 22-24, 37] reveal that, PnP deep denoiser or even deep restorer can approximate a proximal operator under certain assumptions or constraints to guarantee the convergence for various imaging tasks and varying degradations. Conversely, unrolling networks [35, 47] are typically trained end-to-end for a specific CR to achieve state-of-the-art (SOTA) accuracy with fast inference. However, when CR changes, they must be finetuned or even retrained due to the out-of-distribution (OOD) problem, thereby lacking flexibility. Besides, what has been learned from data is not interpretable for unrolling networks. As summarized in Tab. 1, PnP algorithms are highly flexible but are limited in accuracy and speed, whereas unrolling networks are too specialized to flexibly handle varying CRs. What hinders the flexibility and interpretability of unrolling networks is an open question." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In this paper, we address the challenge of integrating the strengths of PnP and unrolling approaches. The flexibility and interpretability are originated from proximal algorithms. The flexibility and interpretability of PnP and unrolling approaches depend on the extent to which the used neural networks approach proximal operators. To this end," + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.075, + 0.907, + 0.104 + ], + "angle": 0, + "content": "Table 1. Comprehensive comparison among proximal algorithms, PnP algorithms, unrolling networks, and our ProxUnroll." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.108, + 0.88, + 0.187 + ], + "angle": 0, + "content": "
MethodAccuracySpeedFlexibilityInterpretability
ProximalLowLowHighHigh
PnPMiddleMiddleHighMiddle
UnrollingHighHighLowLow
ProxUnrollHighHighHighHigh
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.197, + 0.905, + 0.241 + ], + "angle": 0, + "content": "we propose a proximal unrolling (ProxUnroll) approach to endow unrolling networks with flexibility and interpretability. Main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.242, + 0.905, + 0.287 + ], + "angle": 0, + "content": "- We introduce HQS- and ADMM-unrolling networks for SPI, composed of a few iterations of an explicit proximal operator and an implicit deep image restorer (DIR)." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.288, + 0.905, + 0.378 + ], + "angle": 0, + "content": "- We design an efficient CNN-Transformer hybrid architecture as DIR, where the integration of window attention and dynamic CNN captures both low- and high-frequency information with high input dependency, and channel attention functions as a memory mechanism to propagate informative representations between adjacent iterations." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.379, + 0.905, + 0.453 + ], + "angle": 0, + "content": "- More importantly, we propose a generic proximal trajectory (PT) loss function to train HQS/ADMM-unrolling networks into HQS/ADMM-ProxUnroll networks where learned DIRs approximate the proximal operator of an ideal explicit restoration regularizer." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.454, + 0.905, + 0.514 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that the proposed HQS/ADMM-ProxUnroll efficiently achieves not only SOTA performance and fast convergence, but also the same flexibility as PnP algorithms (see Fig. 1)." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.242, + 0.905, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.528, + 0.664, + 0.544 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.907, + 0.809 + ], + "angle": 0, + "content": "SPI Reconstruction. SPI reconstruction is a classical inverse problem in the field of compressive imaging [48-50, 59]. Mainstream solvers involve iterative optimization algorithms [3, 5, 10, 16, 21, 26, 28, 30, 53], PnP algorithms [15, 22-24, 66], single-stage neural networks [27, 39, 40, 55], and unrolling (multi-stage) neural networks [18, 29, 32, 35, 38, 41, 42, 47, 51, 54, 56, 57, 61, 62, 68]. Iterative algorithms employ hand-crafted regularizers, e.g., sparsity [16], total variation [28], non-local low rank [10, 58], with a proximal algorithm, e.g., iterative shrinkage thresholding algorithm (ISTA) [3], approximate message passing (AMP) [30], HQS [17], and ADMM [53]. Single-stage networks generally achieve inferior performance due to the insufficient utilization of imaging model information. PnP algorithms are flexible for varying CRs and unrolling networks achieve superior performance, thus making both the de-facto standard tools for SPI reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Proximal learning. The objective of proximal learning is to train a neural network as the proximal operator of a explicit regularization function. Regularization by denoising [36] shows that under homogeneity, nonexpansiveness and Jacobian symmetry conditions, a denoiser can be written as a gradient descent step on a convex function. However, such" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "412" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.228 + ], + "angle": 0, + "content": "conditions are unrealistic for deep denoisers. Recently, a new type of gradient denoisers [15, 23, 24] has been proposed by training a denoiser as an explicit gradient step on a functional parameterized by a deep neural network. However, these denoisers must either be a contractive gradient [23, 24] or be constrained to input convex neural networks (ICNN) [15], inevitably sacrificing the expressivity. Proximal learning without assumptions and constraints remains an open challenge." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.24, + 0.231, + 0.256 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.265, + 0.484, + 0.327 + ], + "angle": 0, + "content": "In this section, we first introduce the inverse problem of SPI. Then, we extend two representative proximal algorithms (i.e., HQS and ADMM) to solve this problem. Finally, we compare PnP approaches with unrolling approaches." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.334, + 0.287, + 0.348 + ], + "angle": 0, + "content": "3.1. SPI Inverse Problem" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.357, + 0.485, + 0.629 + ], + "angle": 0, + "content": "Typical SPI cameras capture 2D images. Following Eqs. (1) and (2), processing a 2D image in its vectorized form leads to large matrix calculation problems for all \\(\\Phi\\)-related operations, particularly during model training. To this end, most previous works [18, 32, 41, 42, 51, 56, 57, 61, 62, 68] split a digital image into non-overlapping blocks to reduce the vectorized size, but block-wise sampling is impractical for real SPI cameras. A practical solution is Kronecker compressed sensing [6, 12], which processes 2D images in matrix form rather than vector form. Mathematically, \\(\\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon}\\) is equivalent to \\(\\mathbf{Y} = \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top} + \\mathbf{E}\\) with \\(\\pmb{y} = \\mathrm{vec}(\\mathbf{Y})\\), \\(\\pmb{x} = \\mathrm{vec}(\\mathbf{X})\\), \\(\\pmb{\\epsilon} = \\mathrm{vec}(\\mathbf{E})\\), \\(\\Phi = \\mathbf{W} \\otimes \\mathbf{H}\\), where \\(\\mathrm{vec}(\\cdot)\\) denotes the vectorization operation, \\(\\otimes\\) the Kronecker product. The large measurement matrix \\(\\Phi \\in \\mathbb{R}^{hw \\times HW}\\) is replaced by two small matrices \\(\\mathbf{H} \\in \\mathbb{R}^{h \\times H}\\), \\(\\mathbf{W} \\in \\mathbb{R}^{w \\times W}\\) to reconstruct an image \\(\\mathbf{X} \\in \\mathbb{R}^{H \\times W}\\) from the measurements \\(\\mathbf{Y} \\in \\mathbb{R}^{hw}\\) with a compressive ratio \\(\\eta = hw / HW\\). The inverse problem is therefore formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.631, + 0.483, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {X}} = \\underset {\\mathbf {X}} {\\arg \\min } f (\\mathbf {X}) + \\lambda g (\\mathbf {X}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.783 + ], + "angle": 0, + "content": "where \\(f = \\frac{1}{2}\\| \\mathbf{Y} - \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top}\\|_{F}^{2},\\| \\cdot \\|_{F}\\) denotes the Frobenius norm. As a result, large matrix calculations on \\(\\Phi\\) are equivalent to efficient calculations on \\(\\mathbf{H}\\) and \\(\\mathbf{W}\\), resulting in a significant decrease on space complexity from \\(\\mathcal{O}(\\eta H^2 W^2)\\) to \\(\\mathcal{O}(\\sqrt{\\eta} H^2 +\\sqrt{\\eta} W^2)\\) and time complexity from \\(\\mathcal{O}(\\eta H^2 W^2)\\) to \\(\\mathcal{O}(\\eta H^2 W + \\sqrt{\\eta} HW^2)\\) (\\(H\\leq W\\)) [47]. Note that the physical masks in SPI cameras still correspond to the rows of \\(\\Phi = \\mathbf{W}\\otimes \\mathbf{H}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.791, + 0.439, + 0.807 + ], + "angle": 0, + "content": "3.2. Proximal Algorithms: HQS and ADMM" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.814, + 0.484, + 0.875 + ], + "angle": 0, + "content": "HQS and ADMM are generally developed to solve Eq. (1). Next, we exploit both towards Eq. (3). By introducing an auxiliary variable \\(\\mathbf{Z} \\in \\mathbb{R}^{H \\times W}\\), the unconstrained Eq. (3) can be rewritten as a constrained optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.876, + 0.483, + 0.903 + ], + "angle": 0, + "content": "\\[\n(\\widehat {\\mathbf {X}}, \\widehat {\\mathbf {Z}}) = \\underset {\\mathbf {X}, \\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}), \\quad s. t. \\mathbf {Z} = \\mathbf {X}. \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "HQS handles the constraint of Eq. (4) as a penalty term by minimizing" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.124, + 0.905, + 0.149 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.151, + 0.905, + 0.181 + ], + "angle": 0, + "content": "where \\(\\mu > 0\\). The minimizer of Eq. (4) is the saddle point of \\(\\mathcal{L}\\), which can be found by alternative proximal operators as" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.183, + 0.905, + 0.211 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {f}: \\mathbf {Z} ^ {k + 1} = \\underset {\\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} ^ {k} \\| _ {F} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.215, + 0.905, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {g}: \\quad \\mathbf {X} ^ {k + 1} = \\underset {\\mathbf {X}} {\\arg \\min } \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {X} - \\mathbf {Z} ^ {k + 1} \\| _ {F} ^ {2}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.253, + 0.905, + 0.3 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}^0 = \\mathbf{H}^\\top \\mathbf{Y}\\mathbf{W}\\). Instead of adding a simple penalty term in HQS, ADMM re-formulates Eq. (4) using the augmented Lagrangian as" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.301, + 0.905, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}, \\mathbf {U}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\mathbf {U} ^ {\\top} (\\mathbf {Z} - \\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.328, + 0.905, + 0.358 + ], + "angle": 0, + "content": "where \\(\\mathbf{U}\\) is the Lagrange multiplier. Eq. (8) can also be solved by alternative proximal operators as" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.359, + 0.905, + 0.391 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {f}: \\mathbf {Z} ^ {k + 1} = \\underset {\\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\left(\\mathbf {X} ^ {k} - \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.395, + 0.905, + 0.438 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {g}: \\mathbf {X} ^ {k + 1} = \\underset {\\mathbf {X}} {\\arg \\min } \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {X} - \\left(\\mathbf {Z} ^ {k + 1} + \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.438, + 0.747, + 0.455 + ], + "angle": 0, + "content": "with \\(\\mathbf{U}^{k + 1} = \\mathbf{U}^k +\\mu (\\mathbf{Z}^{k + 1} - \\mathbf{X}^{k + 1})\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.456, + 0.905, + 0.502 + ], + "angle": 0, + "content": "In SPI paradigm, \\(f\\) is a differentiable convex function and \\(\\Phi\\) is generally set to be row-orthogonal, i.e., \\(\\mathbf{WW}^{\\top} \\otimes \\mathbf{HH}^{\\top} = \\mathbf{I}\\). In this case, \\(\\operatorname{Prox}_f\\) has a closed form:" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.504, + 0.905, + 0.534 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {f} (\\mathbf {P}) = \\mathbf {V} + \\frac {1}{1 + \\mu} \\mathbf {H} ^ {\\top} (\\mathbf {Y} - \\mathbf {H P W} ^ {\\top}) \\mathbf {W}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.537, + 0.907, + 0.598 + ], + "angle": 0, + "content": "where \\(\\mathbf{P} = \\mathbf{X}^k\\) or \\((\\mathbf{X}^k - \\frac{1}{\\mu}\\mathbf{U}^k)\\) for HSQ or ADMM. Eq. (11) is also a gradient descent step. With a proper regularizer \\(g\\), HQS and ADMM could converge to stationary points of Eq. (3) by iterating" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.599, + 0.905, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {k + 1} = \\operatorname {P r o x} _ {g} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right). \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.628, + 0.661, + 0.644 + ], + "angle": 0, + "content": "3.3. Plug-and-Play" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.652, + 0.907, + 0.698 + ], + "angle": 0, + "content": "PnP approaches typically replace \\(\\mathrm{Prox}_g\\) in Eq. (12) with an off-the-shelf deep denoiser [63, 65, 66] \\(\\mathcal{D}_{\\theta}\\) with learned weights \\(\\theta\\), namely iterating" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.7, + 0.905, + 0.718 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {k + 1} = \\mathcal {D} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.902 + ], + "angle": 0, + "content": "On the upside, \\(\\mathcal{D}_{\\theta}\\) serves as a generic image prior to reduce unknown artifacts (including structural noises introduced by \\(\\mathrm{Prox}_f\\)) regardless of the imaging tasks and the degree of degradation, namely high generalization. For SPI cameras, the generalization makes PnP algorithms flexible for varying CRs. Besides, \\(\\mathcal{D}_{\\theta}\\) can be interpreted as a proximal operator to guarantee the convergence under non-expansiveness assumptions or Lipschitz constraints [15, 22-24, 37]. On the downside, PnP approaches are typically limited in reconstruction accuracy and speed since pretrained \\(\\mathcal{D}_{\\theta}\\) lacks task-specific knowledge and a large number of iterations and cumbersome parameter adjustment are necessary." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "413" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.133, + 0.075, + 0.768, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.088, + 0.862, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.24, + 0.673, + 0.255 + ], + "angle": 0, + "content": "Figure 3. Proximal algorithm unrolling via trajectory loss." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.27, + 0.202, + 0.287 + ], + "angle": 0, + "content": "3.4. Unrolling" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.293, + 0.484, + 0.368 + ], + "angle": 0, + "content": "Unrolling approaches first replace \\(\\mathbf{Prox}_g\\) in Eq. (12) with a lightweight neural network \\(\\mathcal{N}\\), i.e., \\(\\mathbf{X}^{k + 1} = \\mathcal{N} \\circ \\mathbf{Prox}_f(\\mathbf{X}^k)\\), then unroll it with few iterations, finally train it end-to-end with degraded-clean image pairs produced by a specific degradation model \\(\\mathbf{Y} = \\mathbf{H}\\mathbf{X}\\mathbf{W}^\\top + \\mathbf{E}\\), therefore formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.371, + 0.482, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {K} = \\left[ \\begin{array}{l} K - 1 \\\\ \\bigcirc \\\\ k = 0 \\end{array} \\right. \\mathcal {N} _ {\\theta^ {k}} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {0}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.406, + 0.484, + 0.68 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}^0 = \\mathbf{H}^\\top \\mathbf{Y}\\mathbf{W}\\) and \\(\\mathbf{X}^K\\) denote the input and the output respectively, and \\(\\bigcirc\\) is the compound composition operator. Instead of using a pretrained \\(\\mathcal{D}_{\\theta}\\) in PnP algorithms, unrolling networks learn a small set of subnets \\(\\{\\mathcal{N}_{\\theta^k}\\}_{k=0}^{K-1}\\) with a same structure but different weights, thereby belonging to multi-stage neural networks. Although unrolling networks resemble proximal algorithms that are widely known to be convergent, end-to-end training could only ensure that the final result \\(\\mathbf{X}^K\\) is close to the ground truth \\(\\mathbf{X}\\) but cannot guarantee that the intermediate results \\(\\{\\mathbf{X}^k\\}_{k=1}^{K-1}\\) are improved step-by-step, thereby lacking the convergence guarantee [19] (see Fig. 7). After degradation-specific training, unrolling networks usually produce SOTA results with fast inference (due to very few iterations), but need be fine-tuned or even retrained when the degradation (e.g., CR in SPI) changes. Consequently, performance is achieved at the cost of generalization. How to make unrolling networks flexible for varying CRs is a key challenge in SPI." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.692, + 0.371, + 0.71 + ], + "angle": 0, + "content": "4. Proximal Algorithm Unrolling" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.484, + 0.793 + ], + "angle": 0, + "content": "In this section, we first introduce a proximal algorithm unrolling approach with interpretability and convergence guarantees, named ProxUnroll, via a proximal trajectory (PT) loss function. Subsequently, we propose an efficient CNN-Transformer architecture to realize ProxUnroll." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.802, + 0.43, + 0.818 + ], + "angle": 0, + "content": "4.1. Proximal Unrolling via Trajectory Loss" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "The main differences between PnP in Eq. (13) and unrolling in Eq. (14) involve that, \\((i)\\) the iteration number is often large in PnP but small in unrolling; \\((ii)\\) one pretrained deep denoiser \\(\\mathcal{D}_{\\theta}\\) is reused across iterations in PnP but \\(K\\) subnets \\(\\{\\mathcal{N}_{\\theta^k}\\}_{k = 0}^{K - 1}\\) are end-to-end optimized for \\(K\\) iterations in un" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.271, + 0.906, + 0.331 + ], + "angle": 0, + "content": "rolling; (iii) \\(\\mathrm{PnP}\\mathcal{D}_{\\theta}\\) could loosely correspond to \\(\\mathrm{Prox}_g\\) but what unrolled \\(\\mathcal{N}_{\\theta^k}\\) has learned is unclear. By integrating the characteristics of \\(\\mathrm{PnP}\\) and unrolling, we define a proximal unrolling (ProxUnroll) framework as" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.333, + 0.905, + 0.367 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {K} = \\left[\\begin{array}{l}K - 1\\\\\\bigcirc\\\\k = 0\\end{array}\\right. \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {0}\\right), \\text {s . t .} \\mathcal {R} _ {\\theta} \\rightarrow \\operatorname {P r o x} _ {g}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.368, + 0.906, + 0.414 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}_{\\theta}\\) is a neural network, which can be expressed as the proximal operator of a regularizer \\(g\\). In Eq. (15), the remaining challenge is to satisfy the condition \\(\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.906, + 0.551 + ], + "angle": 0, + "content": "Essentially, \\(\\operatorname{Prox}_g\\) is an input-to-output movement towards the minimum of a regularizer \\(g\\) such that the output is between the input and the minimum. Given a degraded image as input, the output image is bound to be restored if the minimum is the corresponding clear image. In this case, \\(\\operatorname{Prox}_g\\) is an image restoration operator. Motivated by this point, we define the squared Euclidean distance between a degraded image \\(\\mathbf{X}'\\) and its clear image \\(\\mathbf{X}\\) as an explicit regularization function:" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.553, + 0.905, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\bar {g} \\left(\\mathbf {X} ^ {\\prime}\\right) = \\frac {1}{2} \\| \\mathbf {X} ^ {\\prime} - \\mathbf {X} \\| _ {F} ^ {2}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.582, + 0.905, + 0.612 + ], + "angle": 0, + "content": "By inserting Eq. (16) into Eqs. (7) and (10), \\(\\mathrm{Prox}_{\\tilde{g}}\\) has the following closed form:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.613, + 0.905, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P r o x} _ {\\tilde {g}} (\\mathbf {Q}) = \\frac {\\mu \\mathbf {Q} + \\lambda \\mathbf {X}}{\\mu + \\lambda}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.906, + 0.708 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q} = \\mathbf{Z}^{k + 1}\\) or \\((\\mathbf{Z}^{k + 1} + \\frac{1}{\\mu}\\mathbf{U}^k)\\) for HQS or ADMM, \\(\\mu\\) and \\(\\lambda\\) control the strength of being close to \\(\\mathbf{Q}\\) and \\(\\mathbf{X}\\) respectively. By combining Eqs. (11) and (17), an ideal explicit proximal algorithm is" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.71, + 0.905, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.73, + 0.906, + 0.837 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}^k\\rightarrow \\mathbf{X}\\) if \\(k\\to \\infty\\) . The convergence rate is closely related to \\(\\mu\\) and \\(\\lambda\\) . If \\(\\mu /\\lambda = 0\\) , Proxg executes an one-step restoration from an arbitrarily degraded image to its clear image. Proxg is an explicit image restorer conditioned on the ground truth. During supervised training, we use Proxg to guide the optimization of \\(\\mathcal{R}_{\\theta}\\) in Eq. (15) such that \\(\\mathcal{R}_{\\theta}\\) serves as an implicit image restorer to approximate Proxg." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 3, a perfect proximal optimization trajectory \\(\\mathbf{X}^0\\rightarrow \\bar{\\mathbf{X}}^1\\rightarrow \\dots \\rightarrow \\bar{\\mathbf{X}}^{K - 1}\\rightarrow \\mathbf{X}\\) can be produced from every \\((\\mathbf{X}^0,\\mathbf{X})\\) training pair via Eq. (18) to supervise the end-to-end training of algorithm unrolling in Eq. (15)." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "414" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.075, + 0.87, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.224, + 0.451, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.472, + 0.224, + 0.851, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.426, + 0.7, + 0.44 + ], + "angle": 0, + "content": "Figure 4. Illustration of the proposed deep image restorer (DIR) \\(\\mathcal{R}_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.452, + 0.483, + 0.528 + ], + "angle": 0, + "content": "The proximal iterations \\(\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_f\\) are guaranteed with fast convergence towards the ground truth such that unrolled iterations \\(\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f\\) are optimized to have the similar capability, namely \\(\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g\\). To this end, we propose a proximal trajectory (PT) loss function as" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.53, + 0.482, + 0.594 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {P L} = \\sum_ {k = 0} ^ {K - 1} \\alpha_ {k} \\| \\mathbf {X} ^ {k + 1} - \\bar {\\mathbf {X}} ^ {k + 1} \\| _ {F} ^ {2}, \\\\ s. t. \\left\\{ \\begin{array}{l} \\bar {\\mathbf {X}} ^ {k + 1} = \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right) \\\\ \\bar {\\mathbf {X}} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\bar {\\mathbf {X}} ^ {k}\\right) \\end{array} \\right. \\end{array} \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.484, + 0.718 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{X}}^0 = \\mathbf{X}^0\\), \\(\\bar{\\mathbf{X}}^K = \\mathbf{X}\\), \\(\\alpha_{k}\\) controls the proximity strength of \\(k\\)-th iteration. Trainable parameters involve \\(\\theta, \\{\\mu^{k}\\}_{k=0}^{K-1}\\) in \\(\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_{f}\\) and \\(\\{\\bar{\\mu}^{k}, \\bar{\\lambda}^{k}\\}_{k=0}^{K-2}\\) in \\(\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_{f}\\). For \\(\\bar{\\mathbf{X}}^K = \\mathbf{X}\\), \\((\\bar{\\mu}^{K-1}, \\bar{\\lambda}^{K-1})\\) is set to be \\((0,1)\\). PT loss function is designed to train any unrolled network \\(\\mathcal{R}_{\\theta}\\) to approximate the proximal operator \\(\\mathrm{Prox}_{\\bar{g}}\\), thereby with interpretability. Since \\(\\mathrm{Prox}_{\\bar{g}}\\) is an explicit image restorer, \\(\\mathcal{R}_{\\theta}\\) functions as a deep image restorer (DIR)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.727, + 0.291, + 0.743 + ], + "angle": 0, + "content": "4.2. Deep Image Restorer" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.779 + ], + "angle": 0, + "content": "To unlock the potential of ProxUnroll, we propose an efficient CNN-Transformer architecture as DIR." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Overall Pipeline. As shown in Fig. 4 (a), DIR is a 4-level asymmetric encoder-decoder architecture. Given a degraded image \\(\\mathbf{I}_{in} \\in \\mathbb{R}^{H \\times W \\times C_{in}}\\), one \\(3 \\times 3\\) convolution layer is first applied to extract shallow features \\(\\mathbf{F}_0 \\in \\mathbb{R}^{H \\times W \\times C}\\). Next, \\(\\mathbf{F}_0\\) are passed through 3 encoder stages, each of which contains one memory block, a stack of hybrid CNN-Transformer blocks, and one downsampling layer. From level-1 to level-3, the goal of the encoder is to progressively" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.452, + 0.907, + 0.651 + ], + "angle": 0, + "content": "reduce the spatial resolution by half while doubling channel capacity, thereby yielding multi-scale low-level features \\(\\{\\mathbf{F}_1,\\mathbf{F}_2,\\mathbf{F}_3\\}\\). For example, the encoder produces \\(\\mathbf{F}_3\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times 8C}\\) at level-3. At level-4, a bottleneck stage is between the encoder and the decoder to produce \\(\\mathbf{F}_4\\). The decoder is similar to the encoder except for having no memory block and replacing the downsampling layer by one upsampling layer. Form level-3 to level-1, the decoder progressively produces high-level features \\(\\{\\mathbf{F}_5,\\mathbf{F}_6,\\mathbf{F}_7\\}\\) while recovering the spatial resolution and channel capability. Finally, one \\(3\\times 3\\) convolution layer transforms the features \\(\\mathbf{F}_7\\) into the residual image \\(\\Delta \\mathbf{I}\\in \\mathbb{R}^{H\\times W\\times C_{in}}\\). The restored image is therefore obtained by \\(\\mathbf{I}_{out} = \\mathbf{I}_{in} + \\Delta \\mathbf{I}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.655, + 0.909, + 0.746 + ], + "angle": 0, + "content": "In these downsampling and upsampling layers, one \\(2 \\times 2\\) stripped convolution and one \\(2 \\times 2\\) transposed convolution are employed respectively. Skip connections are built between the encoder and the decoder for efficient information propagation. Memory block and hybrid CNN-Transformer block are the core components. Next, we introduce them in detail." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Memory Block. As mentioned previously, typical unrolling networks in Eq. (14) cannot guarantee the progressive refinement of intermediate results [19] (see Fig. 7) due to end-to-end training. That is also partially caused by that informative representations cannot be propagated across iterations. Hence, the artifacts in intermediate results may be the manifestations of informative representations in the image domain. As analyzed in the supplementary material, we attempt to reduce or remove the intermediate artifacts of SAUNet [47], and the resulting outputs become worse." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "415" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "To address this problem, we propose a memory block (MB) to propagate informative representations in a side path. MB is composed of one channel cross-attention (ChanCA), similar to existing multi-Dconv head transposed attention (MDTA) [60]. As shown in Fig. 4 (a), we directly consider the output features of the bottleneck and decoder at iteration \\( k \\) as current memories \\( \\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\} \\). By producing queries from \\( \\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\} \\) and keys/values from \\( \\{\\mathbf{F}_4^{k - 1},\\mathbf{F}_5^{k - 1},\\mathbf{F}_6^{k - 1},\\mathbf{F}_7^k\\} \\), MB adaptively aggregates previous useful representations into current iteration for efficient information propagation by ChanCA, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.26, + 0.482, + 0.288 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {F} _ {\\text {o u t}} = \\operatorname {C h a n C A} \\left(\\mathbf {F} _ {q}, \\mathbf {F} _ {k v}\\right) = \\mathbf {W} _ {p} \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top}\\right) \\mathbf {V} \\right], \\\\ \\mathbf {Q} = \\mathbf {W} ^ {q} \\mathbf {E} \\mathbf {W} ^ {q} \\mathbf {K} = \\mathbf {W} ^ {k} \\mathbf {E} \\mathbf {W} ^ {k} \\mathbf {V} = \\mathbf {W} ^ {v} \\mathbf {E} \\mathbf {W} ^ {v} \\end{array} \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.281, + 0.48, + 0.3 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {W} _ {p} ^ {q} \\mathbf {F} _ {q} \\mathbf {W} _ {d} ^ {q}, \\mathbf {K} = \\mathbf {W} _ {p} ^ {k} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {k}, \\mathbf {V} = \\mathbf {W} _ {p} ^ {v} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {v}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.302, + 0.482, + 0.442 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}_q, \\mathbf{F}_{kv} \\in \\mathbb{R}^{d \\times HW}\\) denote the heads of current and previous memory features respectively, \\(\\mathbf{Q}\\) and \\(\\{\\mathbf{K}, \\mathbf{V}\\}\\) are produced from \\(\\mathbf{F}_q\\) and \\(\\mathbf{F}_{kv}\\) by a point-wise convolution \\(\\mathbf{W}_p^{(\\cdot)}\\) followed by a \\(3 \\times 3\\) depth-wise convolution \\(\\mathbf{W}_d^{(\\cdot)}\\). At the first iteration, MB can automatically be invalid due to the lack of available memories, i.e. \\(\\mathbf{F}_{out} = 0\\) if \\(\\mathbf{F}_{kv} = 0\\). Such design leads to two advantages: i) cross-iteration information propagation mechanism is built regardless iterations; ii) informative representations are adaptively activated." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.445, + 0.482, + 0.581 + ], + "angle": 0, + "content": "CNN-Transformer Block. We propose a hybrid CNN-Transformer block (CTB) as the basic processing unit. The core idea of CTB is to integrate high- and low-frequency modeling ability of CNN and Transformer [34] while keeping high dependency for input. As shown in Fig. 4 (a), an input feature is firstly split into two parts evenly, then Swin Transformer (SwinT) and gated dynamic CNN (GD-CNN) process them in parallel, finally two parts are fused by channel concatenation and a point-wise convolution." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.482, + 0.645 + ], + "angle": 0, + "content": "As depicted in Fig. 4 (b), SwinT is mainly powered by a shifted-window self-attention (SwinSA) and a feed-forward network (FFN) composed of a MLP with a \\(3 \\times 3\\) depth-wise convolution inserted. SwinSA can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.645, + 0.482, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {\\text {o u t}} = \\operatorname {S w i n S A} \\left(\\mathbf {F} _ {\\text {i n}}\\right) = \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top} + \\mathbf {B}\\right) \\mathbf {V} \\right] \\mathbf {W}, \\tag {21}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.667, + 0.422, + 0.683 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {v},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.482, + 0.764 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}_{in} \\in \\mathbb{R}^{p^2 \\times d}\\) is the head at a \\(p \\times p\\) window, \\(\\mathbf{W}^{(\\cdot)} \\in \\mathbb{R}^{d \\times d}\\) denotes a learnable linear projection matrix, and \\(\\mathbf{B}\\) denote a learnable relative position encoding (RPE). As opposed to ChanCA in Eq. (20), SwinSA performs self-attention mechanism on spatial dimensions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.769, + 0.482, + 0.844 + ], + "angle": 0, + "content": "As depicted in Fig. 4 (c), GD-CNN is a gated structure of normal convolutions (Convs) and an adaptive convolution (AdaConv). AdaConv is a simple implementation of transforming a group of static (learned) convolution kernels into dynamic one varying with the input, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.847, + 0.482, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} \\mathbf {F} & = \\text {R e s h a p e} (\\operatorname {C o n v} _ {3 \\times 3} (\\operatorname {R e L U} (\\operatorname {C o n v} _ {1 \\times 1} (\\mathbf {F} _ {i n})))) \\\\ \\mathbf {F} _ {\\text {o u t}} & = (\\mathbf {F W}) * \\mathbf {F} _ {\\text {i n}}, \\end{array} \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.885, + 0.482, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}_{in},\\mathbf{F}_{out}\\in \\mathbb{R}^{H\\times W\\times C}\\) denote the input and the out" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.905, + 0.199 + ], + "angle": 0, + "content": "put, \\(\\mathbf{F} \\in \\mathbb{R}^{HW \\times n}\\) the input-dependent kernel coefficients, \\(\\mathbf{W} \\in \\mathbb{R}^{n \\times C \\times 3^2}\\) the kernel weights of \\(n \\times 3\\) depth-wise convolutions, and \\(\\oplus\\) performs the convolution operator. Similar to attention mechanism, AdaConv is also input-dependent. Differently, AdaConv updates convolution weights from a group of learned kernel weights while attention produces attention weights by the similarity between features." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.213, + 0.644, + 0.23 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.239, + 0.907, + 0.587 + ], + "angle": 0, + "content": "The proposed DIR \\(\\mathcal{R}_{\\theta}\\) in Sec. 4.2 is plugged in HQS- or ADMM-unrolling framework and then is end-to-end optimized using the proposed PL loss function in Sec. 4.1, leading to two proximal unrolling networks: HQS-ProxUnroll and ADMM-ProxUnroll. HQS/ADMM-ProxUnroll is composed of 6 iterations of \\(\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f\\). Next, we conduct experiments to estimate them. We adopt 400 images from BSD500 [2] to generate 20,000 training samples using data augmentation techniques following [32, 35, 38-42, 47, 68]. Similar to the training of PnP image denoisers [63, 65, 66], the compressive ratio varies within [0.01, 0.50] and the resolution varies from \\(256 \\times 256\\) pixels to \\(512 \\times 512\\) pixels to cover as wider degradations as possible. The initial learning rate is \\(1 \\times 10^{-3}\\) and gradually reduced to \\(1 \\times 10^{-4}\\). We estimate HQS-ProxUnroll and ADMM-ProxUnroll on Set11 and BSD68 benchmark datasets and real captured SPI data. Regarding CBSD68, all experiments are performed on the luminance channel of YCbCr space, similar to [32, 39-42, 62, 68]. Following [35, 47], the measurement (i.e., degradation) matrices \\((\\mathbf{H}, \\mathbf{W})\\) are set to be floating-point and trainable for simulation experiments and are the reordered Hadamard matrices for real experiments. More experiment results are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.594, + 0.794, + 0.608 + ], + "angle": 0, + "content": "5.1. Results on Benchmark Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.901 + ], + "angle": 0, + "content": "SPI reconstruction approaches are closely related to a great number of image compressed sensing approaches. The proposed HQS-ProxUnroll and ADMM-ProxUnroll are compared with previous approaches on benchmark datasets at five widely-used CRs \\(\\{0.01, 0.04, 0.10, 0.25, 0.50\\}\\). Comparative approaches involve a single-stage network \\((\\mathrm{CSNet}^{+}[39])\\), unrolling (multi-stage) networks (ISTA\\(\\mathrm{Net}^{+}[61]\\), OPINENet[62], AMP-Net [68], COAST [57], TransCS [38], MADUN [41], DGUNet[32], CSformer [56], OCTUF[42], SAUNet [47], CPP-Net [18], HATNet [35]), and PnP algorithms (PnP-DnCNN [37] and PnP-DRUNet [66]). Tab. 2 reports the reconstruction results of different approaches. Towards reconstruction accuracy, the proposed HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them outperform previous approaches on average. As visualized in Fig. 5, our HQS/ADMM-ProxUnroll can recover more image details. Towards the flexibility for CR, most previous approaches are separately trained for a specific CR and" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "416" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.105, + 0.076, + 0.261, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.197, + 0.221, + 0.22 + ], + "angle": 0, + "content": "Ground Truth PSNR/SSIM" + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.077, + 0.339, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.197, + 0.334, + 0.22 + ], + "angle": 0, + "content": "PnP-DRUNet 24.07/0.7243" + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.077, + 0.418, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.34, + 0.197, + 0.415, + 0.22 + ], + "angle": 0, + "content": "OCTUF+ 25.13/0.7779" + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.077, + 0.497, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.421, + 0.197, + 0.494, + 0.22 + ], + "angle": 0, + "content": "DGUNet+ 26.13/0.8145" + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.077, + 0.575, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.197, + 0.572, + 0.22 + ], + "angle": 0, + "content": "CPP-Net 27.35/0.8396" + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.077, + 0.654, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.197, + 0.649, + 0.22 + ], + "angle": 0, + "content": "SAUNet 27.65/0.8467" + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.077, + 0.733, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.197, + 0.72, + 0.22 + ], + "angle": 0, + "content": "HATNet 28.17/0.867" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.077, + 0.811, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.73, + 0.197, + 0.875, + 0.22 + ], + "angle": 0, + "content": "HQS-ProxUnroll Reference 29.54/0.8931" + }, + { + "type": "image_caption", + "bbox": [ + 0.269, + 0.224, + 0.726, + 0.238 + ], + "angle": 0, + "content": "Figure 5. Visual comparisons on \"barbara\" from Set11 dataset at \\(\\mathrm{CR} = 0.04\\)" + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.244, + 0.218, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.334, + 0.176, + 0.347 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.219, + 0.244, + 0.331, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.334, + 0.311, + 0.346 + ], + "angle": 0, + "content": "PnP-DRUNet" + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.244, + 0.442, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.334, + 0.412, + 0.345 + ], + "angle": 0, + "content": "SAUNet" + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.244, + 0.554, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.475, + 0.334, + 0.522, + 0.345 + ], + "angle": 0, + "content": "HATNet" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.244, + 0.665, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.334, + 0.655, + 0.345 + ], + "angle": 0, + "content": "HQS-ProxUnroll" + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.244, + 0.779, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.67, + 0.334, + 0.775, + 0.345 + ], + "angle": 0, + "content": "ADMM-ProxUnroll" + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.244, + 0.889, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.334, + 0.86, + 0.344 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.351, + 0.782, + 0.366 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons on real SPI data \"resolution target\" reported in [35] at \\(\\mathrm{CR} = 0.15\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.37, + 0.907, + 0.398 + ], + "angle": 0, + "content": "Table 2. Average PSNR/SSIM of different methods on Set11 and CBSD68 datasets with different compressive ratios. The best and second best results are highlighted and underlined. Blank cells (-) means that there is not an available model at the compressive ratio." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.402, + 0.898, + 0.895 + ], + "angle": 0, + "content": "
DatasetMethodFlexibilityCompressive Ratio (CR)Average
0.010.040.100.250.50
Set11ISTA-Net+ [61]Single17.42/0.402921.32/0.603726.64/0.808732.59/0.925438.11/0.970727.22/0.7423
CSNet+ [39]20.67/0.541124.83/0.748028.34/0.858033.34/0.938738.47/0.979629.13/0.8131
OPINE-Net+ [62]20.15/0.534025.69/0.792029.81/0.888434.86/0.950940.17/0.979732.63/0.9397
AMP-Net [68]20.21/0.542925.27/0.782129.43/0.888034.71/0.953240.66/0.982730.06/0.9679
TransCS [38]20.22/0.543125.41/0.788329.54/0.887735.06/0.954840.49/0.981529.42/0.8311
CSformer [56]21.58/0.607526.28/0.806229.79/0.888334.81/0.952740.73/0.982430.64/0.8474
MADUN [41]20.28/0.557225.71/0.804230.20/0.901635.76/0.960141.00/0.983730.59/0.8373
DGUNet+ [32]22.15/0.611326.82/0.823030.92/0.908836.18/0.961641.24/0.983731.46/0.8577
OCTUF+ [42]21.94/0.598926.54/0.815030.73/0.903636.10/0.960741.35/0.983831.33/0.8524
CPP-Net [18]22.19/0.613527.23/0.833731.27/0.913536.35/0.9631--
SAUNet [47]22.43/0.613427.80/0.835332.15/0.914737.11/0.962841.91/0.983832.28/0.8620
HATNet [35]22.54/0.616227.98/0.838232.26/0.918237.24/0.963442.05/0.983832.41/0.8640
COAST [57]Multiple10.45/0.2144*22.90/0.6971*28.69/0.861833.90/0.9399*38.94/0.974426.98/0.7375
PnP-DnCNN [37]Arbitrary21.68/0.568226.45/0.796929.57/0.871234.24/0.940239.78/0.973530.34/0.8300
PnP-DRUNet [66]21.75/0.573826.81/0.807430.16/0.886135.00/0.947640.54/0.976730.85/0.8383
HQS-ProxUnroll22.76/0.630028.23/0.845032.51/0.922537.33/0.963541.92/0.983732.55/0.8689
ADMM-ProxUnroll22.76/0.630728.30/0.845232.55/0.922637.35/0.963941.97/0.983832.59/0.8692
BSD68ISTA-Net+ [61]Single19.14/0.415822.17/0.548625.32/0.702229.36/0.852534.04/0.942426.01/0.6923
CSNet+ [39]22.21/0.510025.43/0.670627.91/0.793831.12/0.906036.76/0.963828.69/0.7688
OPINE-Net+ [62]22.11/0.514025.20/0.682527.82/0.804531.51/0.906136.35/0.966028.60/0.7746
AMP-Net [68]22.28/0.531925.27/0.693027.88/0.811831.80/0.915437.03/0.972228.85/0.7849
TransCS [38]22.28/0.531825.28/0.688127.86/0.808631.74/0.912136.81/0.969928.79/0.7821
CSformer [56]22.81/0.556625.73/0.695628.05/0.804531.82/0.910637.14/0.976629.11/0.7889
MADUN [41]22.08/0.524725.36/0.698528.18/0.821932.27/0.921937.23/0.973329.02/0.7880
DGUNet+ [32]22.13/0.521525.45/0.698628.13/0.816531.97/0.915837.04/0.971828.94/0.7848
OCTUF+ [42]22.78/0.541325.65/0.699928.28/0.817732.24/0.918537.41/0.972929.27/0.7900
CPP-Net [18]22.95/0.547525.81/0.706828.41/0.822732.25/0.9188--
SAUNet [47]23.11/0.546026.23/0.705029.25/0.825133.67/0.924339.28/0.975130.31/0.7951
COAST [57]Multiple12.08/0.2584*22.77/0.5953*26.28/0.742230.07/0.8703*34.74/0.949725.19/0.6832
PnP-DnCNN [37]Arbitrary22.27/0.522124.85/0.632727.22/0.765830.95/0.876236.47/0.960128.35/0.7514
PnP-DRUNet [66]22.81/0.530825.30/0.667027.79/0.785231.38/0.893136.86/0.962428.83/0.7677
HQS-ProxUnroll23.51/0.564526.52/0.719429.42/0.833233.76/0.928239.22/0.976030.49/0.8043
ADMM-ProxUnroll23.53/0.564926.54/0.720029.43/0.833433.77/0.928439.23/0.976130.50/0.8046
" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "417" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.075, + 0.483, + 0.117 + ], + "angle": 0, + "content": "Table 3. MACs (G), Params (M), and runtime (sec.) comparisons on \\(256 \\times 256\\) images at CR = 0.25. PnP-DRUNet performs 50 iterations for best performance." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.119, + 0.481, + 0.199 + ], + "angle": 0, + "content": "
MetricCPP-Net [18]SAUNet [47]HATNet [35]PnP-DRUNet [66]HQS/ADMM-ProxUnroll
MACs153.47143.05494.427175.10 (143.5×50)107.73 (17.95×6)
Params12.3110.5331.2832.643.90
Runtime0.410.350.600.650.27
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.208, + 0.483, + 0.405 + ], + "angle": 0, + "content": "thus cannot generalize to different CRs. COAST, trained on multiple CRs \\(\\{0.10, 0.20, 0.30, 0.40, 0.50\\}\\), is flexible only for seen CRs, not for unseen CRs (e.g. 0.01). Our HQS/ADMM-ProxUnroll and PnP algorithms (PnP-DnCNN, PnP-DRUNet) can flexibly handle arbitrary CRs with a single model. Moreover, we compare HQS/ADMM-ProxUnroll with several competitive approaches in terms of multiply-accumulate operations (MACs), model parameters (Params), and runtime. As reported in Tab. 3, our HQS/ADMM-ProxUnroll achieves an all-around superiority over these approaches. Overall, our HQS/ADMM-ProxUnroll achieve not only SOTA performance and efficiency but also the same flexibility as PnP algorithms." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.413, + 0.367, + 0.429 + ], + "angle": 0, + "content": "5.2. Results on Real Captured Data" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.433, + 0.485, + 0.706 + ], + "angle": 0, + "content": "We estimate the proposed HQS/ADMM-ProxUnroll on real captured SPI data. Among the networks mentioned previously, only SAUNet [47] and HATNet [35] are practical for real SPI cameras. The remaining networks are developed under the assumption that images can be compressively sampled block by block, which is out of line with real SPI cameras. Hence, we compare HQS/ADMM-ProxUnroll with SAUNet, HATNet, and PnP-DRUNet. As shown in Fig. 6, PnP-DRUNet can recovers well on low frequencies (e.g., shapes and edges) instead of high frequencies (e.g., textures and details), agreeing with that Gaussian denoisers could smooth out rather than remove unknown artifacts [66]. HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them have a better reconstruction ability than the competitors. In practice, SAUNet and HATNet need a separate model for a specific CR. A single model of HQS-ProxUnroll or ADMM-ProxUnroll is flexible enough for varying CRs, similar to PnP algorithms." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.713, + 0.245, + 0.729 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.81 + ], + "angle": 0, + "content": "To offer an insight into ProxUnroll, we conduct ablation experiments on PL loss function (Sec. 4.1) and DIR (Sec. 4.2). ProxUnroll uses PL loss function to train DIR as approximation of the proximal operator of an explicit restoration regularizer in Eq. (16) to guarantee the fast convergence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To demystify the influence of PL loss function, the convergence curves of different methods are depicted in Fig. 7. SAUNet and HATNet, both composed of 7 iterations, reconstruct images with twists and turns since their MSE loss function only ensure a satisfactory final result. This implies that their intermediate subnets cannot be interpreted" + }, + { + "type": "image", + "bbox": [ + 0.561, + 0.075, + 0.856, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.227, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Figure 7. Convergence curves of different unrolling methods." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.242, + 0.906, + 0.271 + ], + "angle": 0, + "content": "Table 4. Ablation experiments for different components of our deep image restorer (DIR) on Set11 dataset at \\( \\mathrm{{CR}} = {0.10} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.272, + 0.895, + 0.348 + ], + "angle": 0, + "content": "
ChanCASwinTAdaConvPSNRMACsParamsRuntime
✓✓31.4294.853.100.22
✓✓32.25128.674.650.34
✓✓32.36101.993.850.21
✓✓✓32.51107.733.900.27
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.906, + 0.457 + ], + "angle": 0, + "content": "as the proximal restoration operators and function more like black-box neural networks. Their lack of proximity also elucidates why prior unrolling networks require retraining when the degradation changes. With PL-based training, our HQS/ADMM-ProxUnroll achieves fast and stable convergence. By replacing PL loss with regular MSE loss during training, their convergence curves also become unstable." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.907, + 0.745 + ], + "angle": 0, + "content": "To demystify the influence of key designs in DIR, we conduct ablation experiments as shown in Tab. 4. The proposed DIR is mainly powered by three components: ChanCA in memory block, SwinT and GD-CNN in CNN-Transformer block. ChanCA is used to adaptively propagate informative representations between adjacent iterations. The combination of SwinT and GD-CNN is to integrate the high- and low-frequency modeling ability while keeping high dependency for input. GD-CNN is powered by the proposed AdaConv. Clearly, ChanCA results in a \\(1.09\\mathrm{dB}\\) improvement in PSNR with a slight increase in MACs, parameters, and runtime. By discarding SwinT and doubling the channel capability of GD-CNN, the entire network becomes a CNN, leading to a \\(0.26\\mathrm{dB}\\) decrease in PSNR and an all-round increase in other metrics. Replacing AdaConv with one depth-wise convolution causes a \\(0.15\\mathrm{dB}\\) decrease in PSNR but has minimal impact on MACs, parameters, and runtime. These results validate the effectiveness and efficiency of ChanCA, SwinT, and AdaConv." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.757, + 0.634, + 0.772 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We propose ProxUnroll to train any unrolled network to approximate the proximal operator of an explicit restoration regularizer using a proximal trajectory (PL) loss function. Besides, we propose an efficient CNN-Transformer architecture as deep image restorer (DIR) to arm ProxUnroll. Extensive experiments demonstrate that our ProxUnroll achieves not only SOTA performance and efficiency but also the same flexibility as PnP algorithms." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "418" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.486, + 0.298 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (2024YFF0505603), the National Natural Science Foundation of China (grant number 62271414), Zhejiang Provincial Distinguished Young Scientist Foundation (grant number LR23F010001), Zhejiang \"Pioneer\" and \"Leading Goose\" R&D Program (grant number 2024SDXHDX0006, 2024C03182), the Key Project of Westlake Institute for Optoelectronics (grant number 2023GD007), the 2023 International Sci-tech Cooperation Projects under the purview of the \"Innovation Yongjiang 2035\" Key R&D Program (grant number 2024Z126), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.328, + 0.188, + 0.344 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.1, + 0.353, + 0.482, + 0.408 + ], + "angle": 0, + "content": "[1] Hemant K Aggarwal, Merry P Mani, and Mathews Jacob. 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PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll. + +# 1. Introduction + +How many pixels does your camera actually need? Modern cameras typically require as many pixels as the image resolution demands. By contrast, single-pixel cameras need only one pixel, a light-sensitive detector, to capture images through multiple measurements. Single-pixel imaging (SPI) [13, 14, 20, 52, 67] technique measures the total light intensity of a scene coded by a series of spatially resolved + +![](images/885ffbbe1646461c7c2c6e93214f5ca1f18fdbf19e69fae23a9951f8b4fda48f.jpg) +Figure 1. Average PSNR (left) of different methods at compressive ratios (CRs) $\{0.01, 0.04, 0.10, 0.25\}$ in which only methods in the yellow area can flexibly handle varying CRs with a single model. Optimization trajectories (right) of four classes of methods for solving inverse problems. Our ProxUnroll efficiently achieves SOTA performance with high flexibility and fast convergence. + +masks on a single-pixel detector. Known masks and measurements, one can recover an image with the same resolution as the masks. SPI offers a competitive edge over mainstream CCD and CMOS cameras in certain scenarios, e.g., terahertz imaging [52] and non-visible 3D imaging [43]. + +SPI cameras typical work under sub-Nyquist sampling rate to save acquisition time, leading to a compressed sensing problem [7, 8] of reconstructing a clean image $\pmb{x} \in \mathbb{R}^n$ from its few measurements $\pmb{y} \in \mathbb{R}^m$ obtained by the imaging model $\pmb{y} = \pmb{\Phi}\pmb{x} + \pmb{\epsilon}$ , where $\Phi \in \mathbb{R}^{m\times n}$ ( $m \ll n$ ) is the measurement (i.e., degradation) matrix, $\pmb{\epsilon} \in \mathbb{R}^m$ the measurement noise. The inverse problem is formulated as + +$$ +\hat {\boldsymbol {x}} = \underset {\boldsymbol {x}} {\arg \min } f (\boldsymbol {x}) + \lambda g (\boldsymbol {x}), \tag {1} +$$ + +where $f(x) = \frac{1}{2} \| \pmb{y} - \pmb{\Phi}\pmb{x} \|_2^2$ is a data fidelity term, $\lambda g(x)$ a scaled regularization term that represents a prior knowledge on $x$ , e.g., sparsity [16]. In SPI cameras, $\pmb{\Phi}$ is usually set to be row-orthogonal and each row represents an optical mask. As a adjustable parameter, compressive ratio (CR) $\eta = m/n$ affects the ill-posedness of Eq. (1), namely the degree to which images are degraded as illustrated in Fig. 2. + +A fruitful solution to Eq. (1) is first-order proximal algorithms [9], e.g., half quadratic splitting (HQS) [17] method and alternating direction method of multipliers + +![](images/685e0d43c23e9f1a81eb27845eb1f7de2965798ffe63007450c1858088663d3d.jpg) +Figure 2. Degradations under different compressive ratios (CRs). (ADMM) [30], which individually perform the proximal operator $\mathrm{Prox}$ on $f$ and $g$ . $\mathrm{Prox}_h$ is defined as + +$$ +\operatorname {P r o x} _ {h} (z) = \underset {\boldsymbol {x}} {\arg \min } h (\boldsymbol {x}) + \frac {1}{2} \| \boldsymbol {x} - \boldsymbol {z} \| _ {2} ^ {2}. \tag {2} +$$ + +The properties of proximal operator guarantee the convergence of iterative algorithms [33]. $\mathrm{Prox}_f$ has a closed form for a specific algorithm. $\mathrm{Prox}_g$ can be loosely interpreted as a denoising step, which is explicitly implemented by the regularizer $g$ or implicitly by a deep neural network. By integrating proximal algorithms and deep neural networks, deep-unrolling (or unfolding) [1, 4, 11, 31, 61] and plug-and-play (PnP) [25, 44, 45, 64, 66] approaches have become the de-facto standard solvers for imaging inverse problems. PnP approaches constitute a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep Gaussian denoiser [63, 65, 66]. Unrolling approaches constitute a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network. + +In SPI cameras, degradations are signal-dependent and CR-dependent as illustrated in Fig. 2. PnP algorithms [46] have flexibility for varying CRs but typically achieve moderate accuracy with slow inference and cumbersome parameter adjustment. Latest works [15, 22-24, 37] reveal that, PnP deep denoiser or even deep restorer can approximate a proximal operator under certain assumptions or constraints to guarantee the convergence for various imaging tasks and varying degradations. Conversely, unrolling networks [35, 47] are typically trained end-to-end for a specific CR to achieve state-of-the-art (SOTA) accuracy with fast inference. However, when CR changes, they must be finetuned or even retrained due to the out-of-distribution (OOD) problem, thereby lacking flexibility. Besides, what has been learned from data is not interpretable for unrolling networks. As summarized in Tab. 1, PnP algorithms are highly flexible but are limited in accuracy and speed, whereas unrolling networks are too specialized to flexibly handle varying CRs. What hinders the flexibility and interpretability of unrolling networks is an open question. + +In this paper, we address the challenge of integrating the strengths of PnP and unrolling approaches. The flexibility and interpretability are originated from proximal algorithms. The flexibility and interpretability of PnP and unrolling approaches depend on the extent to which the used neural networks approach proximal operators. To this end, + +Table 1. Comprehensive comparison among proximal algorithms, PnP algorithms, unrolling networks, and our ProxUnroll. + +
MethodAccuracySpeedFlexibilityInterpretability
ProximalLowLowHighHigh
PnPMiddleMiddleHighMiddle
UnrollingHighHighLowLow
ProxUnrollHighHighHighHigh
+ +we propose a proximal unrolling (ProxUnroll) approach to endow unrolling networks with flexibility and interpretability. Main contributions are summarized as follows: + +- We introduce HQS- and ADMM-unrolling networks for SPI, composed of a few iterations of an explicit proximal operator and an implicit deep image restorer (DIR). +- We design an efficient CNN-Transformer hybrid architecture as DIR, where the integration of window attention and dynamic CNN captures both low- and high-frequency information with high input dependency, and channel attention functions as a memory mechanism to propagate informative representations between adjacent iterations. +- More importantly, we propose a generic proximal trajectory (PT) loss function to train HQS/ADMM-unrolling networks into HQS/ADMM-ProxUnroll networks where learned DIRs approximate the proximal operator of an ideal explicit restoration regularizer. +- Extensive experiments demonstrate that the proposed HQS/ADMM-ProxUnroll efficiently achieves not only SOTA performance and fast convergence, but also the same flexibility as PnP algorithms (see Fig. 1). + +# 2. Related Works + +SPI Reconstruction. SPI reconstruction is a classical inverse problem in the field of compressive imaging [48-50, 59]. Mainstream solvers involve iterative optimization algorithms [3, 5, 10, 16, 21, 26, 28, 30, 53], PnP algorithms [15, 22-24, 66], single-stage neural networks [27, 39, 40, 55], and unrolling (multi-stage) neural networks [18, 29, 32, 35, 38, 41, 42, 47, 51, 54, 56, 57, 61, 62, 68]. Iterative algorithms employ hand-crafted regularizers, e.g., sparsity [16], total variation [28], non-local low rank [10, 58], with a proximal algorithm, e.g., iterative shrinkage thresholding algorithm (ISTA) [3], approximate message passing (AMP) [30], HQS [17], and ADMM [53]. Single-stage networks generally achieve inferior performance due to the insufficient utilization of imaging model information. PnP algorithms are flexible for varying CRs and unrolling networks achieve superior performance, thus making both the de-facto standard tools for SPI reconstruction. + +Proximal learning. The objective of proximal learning is to train a neural network as the proximal operator of a explicit regularization function. Regularization by denoising [36] shows that under homogeneity, nonexpansiveness and Jacobian symmetry conditions, a denoiser can be written as a gradient descent step on a convex function. However, such + +conditions are unrealistic for deep denoisers. Recently, a new type of gradient denoisers [15, 23, 24] has been proposed by training a denoiser as an explicit gradient step on a functional parameterized by a deep neural network. However, these denoisers must either be a contractive gradient [23, 24] or be constrained to input convex neural networks (ICNN) [15], inevitably sacrificing the expressivity. Proximal learning without assumptions and constraints remains an open challenge. + +# 3. Preliminaries + +In this section, we first introduce the inverse problem of SPI. Then, we extend two representative proximal algorithms (i.e., HQS and ADMM) to solve this problem. Finally, we compare PnP approaches with unrolling approaches. + +# 3.1. SPI Inverse Problem + +Typical SPI cameras capture 2D images. Following Eqs. (1) and (2), processing a 2D image in its vectorized form leads to large matrix calculation problems for all $\Phi$ -related operations, particularly during model training. To this end, most previous works [18, 32, 41, 42, 51, 56, 57, 61, 62, 68] split a digital image into non-overlapping blocks to reduce the vectorized size, but block-wise sampling is impractical for real SPI cameras. A practical solution is Kronecker compressed sensing [6, 12], which processes 2D images in matrix form rather than vector form. Mathematically, $\pmb{y} = \pmb{\Phi}\pmb{x} + \pmb{\epsilon}$ is equivalent to $\mathbf{Y} = \mathbf{H}\mathbf{X}\mathbf{W}^{\top} + \mathbf{E}$ with $\pmb{y} = \mathrm{vec}(\mathbf{Y})$ , $\pmb{x} = \mathrm{vec}(\mathbf{X})$ , $\pmb{\epsilon} = \mathrm{vec}(\mathbf{E})$ , $\Phi = \mathbf{W} \otimes \mathbf{H}$ , where $\mathrm{vec}(\cdot)$ denotes the vectorization operation, $\otimes$ the Kronecker product. The large measurement matrix $\Phi \in \mathbb{R}^{hw \times HW}$ is replaced by two small matrices $\mathbf{H} \in \mathbb{R}^{h \times H}$ , $\mathbf{W} \in \mathbb{R}^{w \times W}$ to reconstruct an image $\mathbf{X} \in \mathbb{R}^{H \times W}$ from the measurements $\mathbf{Y} \in \mathbb{R}^{hw}$ with a compressive ratio $\eta = hw / HW$ . The inverse problem is therefore formulated as + +$$ +\widehat {\mathbf {X}} = \underset {\mathbf {X}} {\arg \min } f (\mathbf {X}) + \lambda g (\mathbf {X}), \tag {3} +$$ + +where $f = \frac{1}{2}\| \mathbf{Y} - \mathbf{H}\mathbf{X}\mathbf{W}^{\top}\|_{F}^{2},\| \cdot \|_{F}$ denotes the Frobenius norm. As a result, large matrix calculations on $\Phi$ are equivalent to efficient calculations on $\mathbf{H}$ and $\mathbf{W}$ , resulting in a significant decrease on space complexity from $\mathcal{O}(\eta H^2 W^2)$ to $\mathcal{O}(\sqrt{\eta} H^2 +\sqrt{\eta} W^2)$ and time complexity from $\mathcal{O}(\eta H^2 W^2)$ to $\mathcal{O}(\eta H^2 W + \sqrt{\eta} HW^2)$ ( $H\leq W$ ) [47]. Note that the physical masks in SPI cameras still correspond to the rows of $\Phi = \mathbf{W}\otimes \mathbf{H}$ . + +# 3.2. Proximal Algorithms: HQS and ADMM + +HQS and ADMM are generally developed to solve Eq. (1). Next, we exploit both towards Eq. (3). By introducing an auxiliary variable $\mathbf{Z} \in \mathbb{R}^{H \times W}$ , the unconstrained Eq. (3) can be rewritten as a constrained optimization problem: + +$$ +(\widehat {\mathbf {X}}, \widehat {\mathbf {Z}}) = \underset {\mathbf {X}, \mathbf {Z}} {\arg \min } f (\mathbf {Z}) + \lambda g (\mathbf {X}), \quad s. t. \mathbf {Z} = \mathbf {X}. \qquad (4) +$$ + +HQS handles the constraint of Eq. (4) as a penalty term by minimizing + +$$ +\mathcal {L} _ {\mu} (\mathbf {X}, \mathbf {Z}) = f (\mathbf {Z}) + \lambda g (\mathbf {X}) + \frac {\mu}{2} \| \mathbf {Z} - \mathbf {X} \| _ {F} ^ {2}, \tag {5} +$$ + +where $\mu > 0$ . The minimizer of Eq. (4) is the saddle point of $\mathcal{L}$ , which can be found by alternative proximal operators as + +$$ +\operatorname {P r o x} _ {f}: \mathbf {Z} ^ {k + 1} = \underset {\mathbf {Z}} {\arg \min } f (\mathbf {Z}) + \frac {\mu}{2} \| \mathbf {Z} - \mathbf {X} ^ {k} \| _ {F} ^ {2}, \tag {6} +$$ + +$$ +\operatorname {P r o x} _ {g}: \quad \mathbf {X} ^ {k + 1} = \underset {\mathbf {X}} {\arg \min } \lambda g (\mathbf {X}) + \frac {\mu}{2} \| \mathbf {X} - \mathbf {Z} ^ {k + 1} \| _ {F} ^ {2}, \tag {7} +$$ + +where $\mathbf{X}^0 = \mathbf{H}^\top \mathbf{Y}\mathbf{W}$ . Instead of adding a simple penalty term in HQS, ADMM re-formulates Eq. (4) using the augmented Lagrangian as + +$$ +\mathcal {L} _ {\mu} (\mathbf {X}, \mathbf {Z}, \mathbf {U}) = f (\mathbf {Z}) + \lambda g (\mathbf {X}) + \mathbf {U} ^ {\top} (\mathbf {Z} - \mathbf {X}) + \frac {\mu}{2} \| \mathbf {Z} - \mathbf {X} \| _ {F} ^ {2}, \tag {8} +$$ + +where $\mathbf{U}$ is the Lagrange multiplier. Eq. (8) can also be solved by alternative proximal operators as + +$$ +\operatorname {P r o x} _ {f}: \mathbf {Z} ^ {k + 1} = \underset {\mathbf {Z}} {\arg \min } f (\mathbf {Z}) + \frac {\mu}{2} \| \mathbf {Z} - \left(\mathbf {X} ^ {k} - \frac {1}{\mu} \mathbf {U} ^ {k}\right) \| _ {F} ^ {2}, \tag {9} +$$ + +$$ +\operatorname {P r o x} _ {g}: \mathbf {X} ^ {k + 1} = \underset {\mathbf {X}} {\arg \min } \lambda g (\mathbf {X}) + \frac {\mu}{2} \| \mathbf {X} - \left(\mathbf {Z} ^ {k + 1} + \frac {1}{\mu} \mathbf {U} ^ {k}\right) \| _ {F} ^ {2}, \tag {10} +$$ + +with $\mathbf{U}^{k + 1} = \mathbf{U}^k +\mu (\mathbf{Z}^{k + 1} - \mathbf{X}^{k + 1})$ + +In SPI paradigm, $f$ is a differentiable convex function and $\Phi$ is generally set to be row-orthogonal, i.e., $\mathbf{WW}^{\top} \otimes \mathbf{HH}^{\top} = \mathbf{I}$ . In this case, $\operatorname{Prox}_f$ has a closed form: + +$$ +\operatorname {P r o x} _ {f} (\mathbf {P}) = \mathbf {V} + \frac {1}{1 + \mu} \mathbf {H} ^ {\top} (\mathbf {Y} - \mathbf {H P W} ^ {\top}) \mathbf {W}, \tag {11} +$$ + +where $\mathbf{P} = \mathbf{X}^k$ or $(\mathbf{X}^k - \frac{1}{\mu}\mathbf{U}^k)$ for HSQ or ADMM. Eq. (11) is also a gradient descent step. With a proper regularizer $g$ , HQS and ADMM could converge to stationary points of Eq. (3) by iterating + +$$ +\mathbf {X} ^ {k + 1} = \operatorname {P r o x} _ {g} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {k}\right). \tag {12} +$$ + +# 3.3. Plug-and-Play + +PnP approaches typically replace $\mathrm{Prox}_g$ in Eq. (12) with an off-the-shelf deep denoiser [63, 65, 66] $\mathcal{D}_{\theta}$ with learned weights $\theta$ , namely iterating + +$$ +\mathbf {X} ^ {k + 1} = \mathcal {D} _ {\theta} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {k}\right). \tag {13} +$$ + +On the upside, $\mathcal{D}_{\theta}$ serves as a generic image prior to reduce unknown artifacts (including structural noises introduced by $\mathrm{Prox}_f$ ) regardless of the imaging tasks and the degree of degradation, namely high generalization. For SPI cameras, the generalization makes PnP algorithms flexible for varying CRs. Besides, $\mathcal{D}_{\theta}$ can be interpreted as a proximal operator to guarantee the convergence under non-expansiveness assumptions or Lipschitz constraints [15, 22-24, 37]. On the downside, PnP approaches are typically limited in reconstruction accuracy and speed since pretrained $\mathcal{D}_{\theta}$ lacks task-specific knowledge and a large number of iterations and cumbersome parameter adjustment are necessary. + +![](images/399ad9b3ffd8980e49cfbb0ae8d36facb481d9dca19ae1b8910ce74f6919c80b.jpg) +Figure 3. Proximal algorithm unrolling via trajectory loss. + +![](images/91c3f000df1994a9964fabf2c86c2006a7e6cc72a017db585ab139e6cbeb96f0.jpg) + +# 3.4. Unrolling + +Unrolling approaches first replace $\mathbf{Prox}_g$ in Eq. (12) with a lightweight neural network $\mathcal{N}$ , i.e., $\mathbf{X}^{k + 1} = \mathcal{N} \circ \mathbf{Prox}_f(\mathbf{X}^k)$ , then unroll it with few iterations, finally train it end-to-end with degraded-clean image pairs produced by a specific degradation model $\mathbf{Y} = \mathbf{H}\mathbf{X}\mathbf{W}^\top + \mathbf{E}$ , therefore formulated as + +$$ +\mathbf {X} ^ {K} = \left[ \begin{array}{l} K - 1 \\ \bigcirc \\ k = 0 \end{array} \right. \mathcal {N} _ {\theta^ {k}} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {0}\right), \tag {14} +$$ + +where $\mathbf{X}^0 = \mathbf{H}^\top \mathbf{Y}\mathbf{W}$ and $\mathbf{X}^K$ denote the input and the output respectively, and $\bigcirc$ is the compound composition operator. Instead of using a pretrained $\mathcal{D}_{\theta}$ in PnP algorithms, unrolling networks learn a small set of subnets $\{\mathcal{N}_{\theta^k}\}_{k=0}^{K-1}$ with a same structure but different weights, thereby belonging to multi-stage neural networks. Although unrolling networks resemble proximal algorithms that are widely known to be convergent, end-to-end training could only ensure that the final result $\mathbf{X}^K$ is close to the ground truth $\mathbf{X}$ but cannot guarantee that the intermediate results $\{\mathbf{X}^k\}_{k=1}^{K-1}$ are improved step-by-step, thereby lacking the convergence guarantee [19] (see Fig. 7). After degradation-specific training, unrolling networks usually produce SOTA results with fast inference (due to very few iterations), but need be fine-tuned or even retrained when the degradation (e.g., CR in SPI) changes. Consequently, performance is achieved at the cost of generalization. How to make unrolling networks flexible for varying CRs is a key challenge in SPI. + +# 4. Proximal Algorithm Unrolling + +In this section, we first introduce a proximal algorithm unrolling approach with interpretability and convergence guarantees, named ProxUnroll, via a proximal trajectory (PT) loss function. Subsequently, we propose an efficient CNN-Transformer architecture to realize ProxUnroll. + +# 4.1. Proximal Unrolling via Trajectory Loss + +The main differences between PnP in Eq. (13) and unrolling in Eq. (14) involve that, $(i)$ the iteration number is often large in PnP but small in unrolling; $(ii)$ one pretrained deep denoiser $\mathcal{D}_{\theta}$ is reused across iterations in PnP but $K$ subnets $\{\mathcal{N}_{\theta^k}\}_{k = 0}^{K - 1}$ are end-to-end optimized for $K$ iterations in un + +rolling; (iii) $\mathrm{PnP}\mathcal{D}_{\theta}$ could loosely correspond to $\mathrm{Prox}_g$ but what unrolled $\mathcal{N}_{\theta^k}$ has learned is unclear. By integrating the characteristics of $\mathrm{PnP}$ and unrolling, we define a proximal unrolling (ProxUnroll) framework as + +$$ +\mathbf {X} ^ {K} = \left[\begin{array}{l}K - 1\\\bigcirc\\k = 0\end{array}\right. \mathcal {R} _ {\theta} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {0}\right), \text {s . t .} \mathcal {R} _ {\theta} \rightarrow \operatorname {P r o x} _ {g}, \tag {15} +$$ + +where $\mathcal{R}_{\theta}$ is a neural network, which can be expressed as the proximal operator of a regularizer $g$ . In Eq. (15), the remaining challenge is to satisfy the condition $\mathcal{R}_{\theta} \to \mathrm{Prox}_g$ . + +Essentially, $\operatorname{Prox}_g$ is an input-to-output movement towards the minimum of a regularizer $g$ such that the output is between the input and the minimum. Given a degraded image as input, the output image is bound to be restored if the minimum is the corresponding clear image. In this case, $\operatorname{Prox}_g$ is an image restoration operator. Motivated by this point, we define the squared Euclidean distance between a degraded image $\mathbf{X}'$ and its clear image $\mathbf{X}$ as an explicit regularization function: + +$$ +\bar {g} \left(\mathbf {X} ^ {\prime}\right) = \frac {1}{2} \| \mathbf {X} ^ {\prime} - \mathbf {X} \| _ {F} ^ {2}. \tag {16} +$$ + +By inserting Eq. (16) into Eqs. (7) and (10), $\mathrm{Prox}_{\tilde{g}}$ has the following closed form: + +$$ +\operatorname {P r o x} _ {\tilde {g}} (\mathbf {Q}) = \frac {\mu \mathbf {Q} + \lambda \mathbf {X}}{\mu + \lambda}, \tag {17} +$$ + +where $\mathbf{Q} = \mathbf{Z}^{k + 1}$ or $(\mathbf{Z}^{k + 1} + \frac{1}{\mu}\mathbf{U}^k)$ for HQS or ADMM, $\mu$ and $\lambda$ control the strength of being close to $\mathbf{Q}$ and $\mathbf{X}$ respectively. By combining Eqs. (11) and (17), an ideal explicit proximal algorithm is + +$$ +\mathbf {X} ^ {k + 1} = \operatorname {P r o x} _ {\bar {g}} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {k}\right), \tag {18} +$$ + +where $\mathbf{X}^k\rightarrow \mathbf{X}$ if $k\to \infty$ . The convergence rate is closely related to $\mu$ and $\lambda$ . If $\mu /\lambda = 0$ , Proxg executes an one-step restoration from an arbitrarily degraded image to its clear image. Proxg is an explicit image restorer conditioned on the ground truth. During supervised training, we use Proxg to guide the optimization of $\mathcal{R}_{\theta}$ in Eq. (15) such that $\mathcal{R}_{\theta}$ serves as an implicit image restorer to approximate Proxg. + +As shown in Fig. 3, a perfect proximal optimization trajectory $\mathbf{X}^0\rightarrow \bar{\mathbf{X}}^1\rightarrow \dots \rightarrow \bar{\mathbf{X}}^{K - 1}\rightarrow \mathbf{X}$ can be produced from every $(\mathbf{X}^0,\mathbf{X})$ training pair via Eq. (18) to supervise the end-to-end training of algorithm unrolling in Eq. (15). + +![](images/375973e91a60b3a88c8a66cdc5217a59c1fc33c8d70169553bf0511ea8a7d463.jpg) + +![](images/0b8bc180d36d817ef8b902c02f8bcd8250ee53be29f458cd1096a4a32c167af5.jpg) +Figure 4. Illustration of the proposed deep image restorer (DIR) $\mathcal{R}_{\theta}$ . + +![](images/a1b994bb541f605f51bf223522bf8970c8431a94ea1e8e287c74b23fc056b4b6.jpg) + +The proximal iterations $\mathrm{Prox}_{\bar{g}} \circ \mathrm{Prox}_f$ are guaranteed with fast convergence towards the ground truth such that unrolled iterations $\mathcal{R}_{\theta} \circ \mathrm{Prox}_f$ are optimized to have the similar capability, namely $\mathcal{R}_{\theta} \to \mathrm{Prox}_g$ . To this end, we propose a proximal trajectory (PT) loss function as + +$$ +\begin{array}{l} \mathbf {P L} = \sum_ {k = 0} ^ {K - 1} \alpha_ {k} \| \mathbf {X} ^ {k + 1} - \bar {\mathbf {X}} ^ {k + 1} \| _ {F} ^ {2}, \\ s. t. \left\{ \begin{array}{l} \bar {\mathbf {X}} ^ {k + 1} = \mathcal {R} _ {\theta} \circ \operatorname {P r o x} _ {f} \left(\mathbf {X} ^ {k}\right) \\ \bar {\mathbf {X}} ^ {k + 1} = \operatorname {P r o x} _ {\bar {g}} \circ \operatorname {P r o x} _ {f} \left(\bar {\mathbf {X}} ^ {k}\right) \end{array} \right. \end{array} \tag {19} +$$ + +where $\bar{\mathbf{X}}^0 = \mathbf{X}^0$ , $\bar{\mathbf{X}}^K = \mathbf{X}$ , $\alpha_{k}$ controls the proximity strength of $k$ -th iteration. Trainable parameters involve $\theta, \{\mu^{k}\}_{k=0}^{K-1}$ in $\mathcal{R}_{\theta} \circ \mathrm{Prox}_{f}$ and $\{\bar{\mu}^{k}, \bar{\lambda}^{k}\}_{k=0}^{K-2}$ in $\mathrm{Prox}_{\bar{g}} \circ \mathrm{Prox}_{f}$ . For $\bar{\mathbf{X}}^K = \mathbf{X}$ , $(\bar{\mu}^{K-1}, \bar{\lambda}^{K-1})$ is set to be $(0,1)$ . PT loss function is designed to train any unrolled network $\mathcal{R}_{\theta}$ to approximate the proximal operator $\mathrm{Prox}_{\bar{g}}$ , thereby with interpretability. Since $\mathrm{Prox}_{\bar{g}}$ is an explicit image restorer, $\mathcal{R}_{\theta}$ functions as a deep image restorer (DIR). + +# 4.2. Deep Image Restorer + +To unlock the potential of ProxUnroll, we propose an efficient CNN-Transformer architecture as DIR. + +Overall Pipeline. As shown in Fig. 4 (a), DIR is a 4-level asymmetric encoder-decoder architecture. Given a degraded image $\mathbf{I}_{in} \in \mathbb{R}^{H \times W \times C_{in}}$ , one $3 \times 3$ convolution layer is first applied to extract shallow features $\mathbf{F}_0 \in \mathbb{R}^{H \times W \times C}$ . Next, $\mathbf{F}_0$ are passed through 3 encoder stages, each of which contains one memory block, a stack of hybrid CNN-Transformer blocks, and one downsampling layer. From level-1 to level-3, the goal of the encoder is to progressively + +reduce the spatial resolution by half while doubling channel capacity, thereby yielding multi-scale low-level features $\{\mathbf{F}_1,\mathbf{F}_2,\mathbf{F}_3\}$ . For example, the encoder produces $\mathbf{F}_3\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times 8C}$ at level-3. At level-4, a bottleneck stage is between the encoder and the decoder to produce $\mathbf{F}_4$ . The decoder is similar to the encoder except for having no memory block and replacing the downsampling layer by one upsampling layer. Form level-3 to level-1, the decoder progressively produces high-level features $\{\mathbf{F}_5,\mathbf{F}_6,\mathbf{F}_7\}$ while recovering the spatial resolution and channel capability. Finally, one $3\times 3$ convolution layer transforms the features $\mathbf{F}_7$ into the residual image $\Delta \mathbf{I}\in \mathbb{R}^{H\times W\times C_{in}}$ . The restored image is therefore obtained by $\mathbf{I}_{out} = \mathbf{I}_{in} + \Delta \mathbf{I}$ . + +In these downsampling and upsampling layers, one $2 \times 2$ stripped convolution and one $2 \times 2$ transposed convolution are employed respectively. Skip connections are built between the encoder and the decoder for efficient information propagation. Memory block and hybrid CNN-Transformer block are the core components. Next, we introduce them in detail. + +Memory Block. As mentioned previously, typical unrolling networks in Eq. (14) cannot guarantee the progressive refinement of intermediate results [19] (see Fig. 7) due to end-to-end training. That is also partially caused by that informative representations cannot be propagated across iterations. Hence, the artifacts in intermediate results may be the manifestations of informative representations in the image domain. As analyzed in the supplementary material, we attempt to reduce or remove the intermediate artifacts of SAUNet [47], and the resulting outputs become worse. + +To address this problem, we propose a memory block (MB) to propagate informative representations in a side path. MB is composed of one channel cross-attention (ChanCA), similar to existing multi-Dconv head transposed attention (MDTA) [60]. As shown in Fig. 4 (a), we directly consider the output features of the bottleneck and decoder at iteration $k$ as current memories $\{\mathbf{F}_4^k,\mathbf{F}_5^k,\mathbf{F}_6^k,\mathbf{F}_7^k\}$ . By producing queries from $\{\mathbf{F}_4^k,\mathbf{F}_5^k,\mathbf{F}_6^k,\mathbf{F}_7^k\}$ and keys/values from $\{\mathbf{F}_4^{k - 1},\mathbf{F}_5^{k - 1},\mathbf{F}_6^{k - 1},\mathbf{F}_7^k\}$ , MB adaptively aggregates previous useful representations into current iteration for efficient information propagation by ChanCA, formulated as + +$$ +\begin{array}{l} \mathbf {F} _ {\text {o u t}} = \operatorname {C h a n C A} \left(\mathbf {F} _ {q}, \mathbf {F} _ {k v}\right) = \mathbf {W} _ {p} \left[ \operatorname {s o f t m a t} \left(\mathbf {Q K} ^ {\top}\right) \mathbf {V} \right], \\ \mathbf {Q} = \mathbf {W} ^ {q} \mathbf {E} \mathbf {W} ^ {q} \mathbf {K} = \mathbf {W} ^ {k} \mathbf {E} \mathbf {W} ^ {k} \mathbf {V} = \mathbf {W} ^ {v} \mathbf {E} \mathbf {W} ^ {v} \end{array} \tag {20} +$$ + +$$ +\mathbf {Q} = \mathbf {W} _ {p} ^ {q} \mathbf {F} _ {q} \mathbf {W} _ {d} ^ {q}, \mathbf {K} = \mathbf {W} _ {p} ^ {k} \mathbf {F} _ {k v} \mathbf {W} _ {d} ^ {k}, \mathbf {V} = \mathbf {W} _ {p} ^ {v} \mathbf {F} _ {k v} \mathbf {W} _ {d} ^ {v}, \tag {20} +$$ + +where $\mathbf{F}_q, \mathbf{F}_{kv} \in \mathbb{R}^{d \times HW}$ denote the heads of current and previous memory features respectively, $\mathbf{Q}$ and $\{\mathbf{K}, \mathbf{V}\}$ are produced from $\mathbf{F}_q$ and $\mathbf{F}_{kv}$ by a point-wise convolution $\mathbf{W}_p^{(\cdot)}$ followed by a $3 \times 3$ depth-wise convolution $\mathbf{W}_d^{(\cdot)}$ . At the first iteration, MB can automatically be invalid due to the lack of available memories, i.e. $\mathbf{F}_{out} = 0$ if $\mathbf{F}_{kv} = 0$ . Such design leads to two advantages: i) cross-iteration information propagation mechanism is built regardless iterations; ii) informative representations are adaptively activated. + +CNN-Transformer Block. We propose a hybrid CNN-Transformer block (CTB) as the basic processing unit. The core idea of CTB is to integrate high- and low-frequency modeling ability of CNN and Transformer [34] while keeping high dependency for input. As shown in Fig. 4 (a), an input feature is firstly split into two parts evenly, then Swin Transformer (SwinT) and gated dynamic CNN (GD-CNN) process them in parallel, finally two parts are fused by channel concatenation and a point-wise convolution. + +As depicted in Fig. 4 (b), SwinT is mainly powered by a shifted-window self-attention (SwinSA) and a feed-forward network (FFN) composed of a MLP with a $3 \times 3$ depth-wise convolution inserted. SwinSA can be formulated as + +$$ +\mathbf {F} _ {\text {o u t}} = \operatorname {S w i n S A} \left(\mathbf {F} _ {\text {i n}}\right) = \left[ \operatorname {s o f t m a t} \left(\mathbf {Q K} ^ {\top} + \mathbf {B}\right) \mathbf {V} \right] \mathbf {W}, \tag {21} +$$ + +$$ +\mathbf {Q} = \mathbf {F} _ {i n} \mathbf {W} ^ {q}, \mathbf {K} = \mathbf {F} _ {i n} \mathbf {W} ^ {k}, \mathbf {V} = \mathbf {F} _ {i n} \mathbf {W} ^ {v}, +$$ + +where $\mathbf{F}_{in} \in \mathbb{R}^{p^2 \times d}$ is the head at a $p \times p$ window, $\mathbf{W}^{(\cdot)} \in \mathbb{R}^{d \times d}$ denotes a learnable linear projection matrix, and $\mathbf{B}$ denote a learnable relative position encoding (RPE). As opposed to ChanCA in Eq. (20), SwinSA performs self-attention mechanism on spatial dimensions. + +As depicted in Fig. 4 (c), GD-CNN is a gated structure of normal convolutions (Convs) and an adaptive convolution (AdaConv). AdaConv is a simple implementation of transforming a group of static (learned) convolution kernels into dynamic one varying with the input, formulated as + +$$ +\begin{array}{r l} \mathbf {F} & = \text {R e s h a p e} (\operatorname {C o n v} _ {3 \times 3} (\operatorname {R e L U} (\operatorname {C o n v} _ {1 \times 1} (\mathbf {F} _ {i n})))) \\ \mathbf {F} _ {\text {o u t}} & = (\mathbf {F W}) * \mathbf {F} _ {\text {i n}}, \end{array} \tag {22} +$$ + +where $\mathbf{F}_{in},\mathbf{F}_{out}\in \mathbb{R}^{H\times W\times C}$ denote the input and the out + +put, $\mathbf{F} \in \mathbb{R}^{HW \times n}$ the input-dependent kernel coefficients, $\mathbf{W} \in \mathbb{R}^{n \times C \times 3^2}$ the kernel weights of $n \times 3$ depth-wise convolutions, and $\oplus$ performs the convolution operator. Similar to attention mechanism, AdaConv is also input-dependent. Differently, AdaConv updates convolution weights from a group of learned kernel weights while attention produces attention weights by the similarity between features. + +# 5. Experiments + +The proposed DIR $\mathcal{R}_{\theta}$ in Sec. 4.2 is plugged in HQS- or ADMM-unrolling framework and then is end-to-end optimized using the proposed PL loss function in Sec. 4.1, leading to two proximal unrolling networks: HQS-ProxUnroll and ADMM-ProxUnroll. HQS/ADMM-ProxUnroll is composed of 6 iterations of $\mathcal{R}_{\theta} \circ \mathrm{Prox}_f$ . Next, we conduct experiments to estimate them. We adopt 400 images from BSD500 [2] to generate 20,000 training samples using data augmentation techniques following [32, 35, 38-42, 47, 68]. Similar to the training of PnP image denoisers [63, 65, 66], the compressive ratio varies within [0.01, 0.50] and the resolution varies from $256 \times 256$ pixels to $512 \times 512$ pixels to cover as wider degradations as possible. The initial learning rate is $1 \times 10^{-3}$ and gradually reduced to $1 \times 10^{-4}$ . We estimate HQS-ProxUnroll and ADMM-ProxUnroll on Set11 and BSD68 benchmark datasets and real captured SPI data. Regarding CBSD68, all experiments are performed on the luminance channel of YCbCr space, similar to [32, 39-42, 62, 68]. Following [35, 47], the measurement (i.e., degradation) matrices $(\mathbf{H}, \mathbf{W})$ are set to be floating-point and trainable for simulation experiments and are the reordered Hadamard matrices for real experiments. More experiment results are in the supplementary material. + +# 5.1. Results on Benchmark Datasets + +SPI reconstruction approaches are closely related to a great number of image compressed sensing approaches. The proposed HQS-ProxUnroll and ADMM-ProxUnroll are compared with previous approaches on benchmark datasets at five widely-used CRs $\{0.01, 0.04, 0.10, 0.25, 0.50\}$ . Comparative approaches involve a single-stage network $(\mathrm{CSNet}^{+}[39])$ , unrolling (multi-stage) networks (ISTA $\mathrm{Net}^{+}[61]$ , OPINENet[62], AMP-Net [68], COAST [57], TransCS [38], MADUN [41], DGUNet[32], CSformer [56], OCTUF[42], SAUNet [47], CPP-Net [18], HATNet [35]), and PnP algorithms (PnP-DnCNN [37] and PnP-DRUNet [66]). Tab. 2 reports the reconstruction results of different approaches. Towards reconstruction accuracy, the proposed HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them outperform previous approaches on average. As visualized in Fig. 5, our HQS/ADMM-ProxUnroll can recover more image details. Towards the flexibility for CR, most previous approaches are separately trained for a specific CR and + +![](images/2e3f02b984b6cb51036bbaeff554143eba504d9f0fe2f42b52d8d26fdf4b73a6.jpg) +Ground Truth PSNR/SSIM + +![](images/0fa2fdacb8efd3b0ece62abf7b30e411cd543bd098f4fde2eefd2c198105e91a.jpg) +PnP-DRUNet 24.07/0.7243 + +![](images/5807ae6980418b931f98f964a95ecc7c31a8102c24bd359e010cf1e351c0c651.jpg) +OCTUF+ 25.13/0.7779 + +![](images/4ea8754e187b83f858298748fb4631e593ef81cd967af0978899c65d7d73d2e2.jpg) +DGUNet+ 26.13/0.8145 + +![](images/683672773008efb2aeb2df935529b952fcc3926977497c998e1948d6e9df569e.jpg) +CPP-Net 27.35/0.8396 + +![](images/2dbd372ac923f908962c0278716495e7a5e0bf355ce8c84805a04afce48c7f4d.jpg) +SAUNet 27.65/0.8467 +HATNet 28.17/0.867 + +![](images/e0a657fdeff4e66677321884f868190ca6937939c73692b51992939f1ab259bb.jpg) +HQS-ProxUnroll Reference 29.54/0.8931 + +![](images/bd86abcbca9a0632638bbfa3e9322da0538241392170b661d6ada44e6aedc55d.jpg) + +![](images/347f51b570bb294fbdbe2bcd9ab14162cf2defaeab7ea8e0b282099def23fa01.jpg) +Input +Figure 6. Visual comparisons on real SPI data "resolution target" reported in [35] at $\mathrm{CR} = 0.15$ + +![](images/73220a75541267f55abf094ace383909a287bddf1a3212f208589de8b04a8454.jpg) +Figure 5. Visual comparisons on "barbara" from Set11 dataset at $\mathrm{CR} = 0.04$ +PnP-DRUNet + +![](images/68b44264dd70c511d01f924322bb194dddd58ef1bfacbcc8303b55c0cd0861dc.jpg) +SAUNet + +![](images/92d080dbca6bef121010e87382af4db7c9da6dd2319fe33a6baabdac536f2e30.jpg) +HATNet + +![](images/728ad005ae47793be90e0f0db0e24bb4a53f59fb72eb73bbda17ba7fa3e76614.jpg) +HQS-ProxUnroll + +![](images/68a6e873de7464b64c0e683428d93238d6afe6cd7161be818d064f372f62aed2.jpg) +ADMM-ProxUnroll + +![](images/192fabb064e01927e5e8d0f3a26b91bc09747a7df6629cafad8fc0ae02d8cd26.jpg) +Reference + +Table 2. Average PSNR/SSIM of different methods on Set11 and CBSD68 datasets with different compressive ratios. The best and second best results are highlighted and underlined. Blank cells (-) means that there is not an available model at the compressive ratio. + +
DatasetMethodFlexibilityCompressive Ratio (CR)Average
0.010.040.100.250.50
Set11ISTA-Net+ [61]Single17.42/0.402921.32/0.603726.64/0.808732.59/0.925438.11/0.970727.22/0.7423
CSNet+ [39]20.67/0.541124.83/0.748028.34/0.858033.34/0.938738.47/0.979629.13/0.8131
OPINE-Net+ [62]20.15/0.534025.69/0.792029.81/0.888434.86/0.950940.17/0.979732.63/0.9397
AMP-Net [68]20.21/0.542925.27/0.782129.43/0.888034.71/0.953240.66/0.982730.06/0.9679
TransCS [38]20.22/0.543125.41/0.788329.54/0.887735.06/0.954840.49/0.981529.42/0.8311
CSformer [56]21.58/0.607526.28/0.806229.79/0.888334.81/0.952740.73/0.982430.64/0.8474
MADUN [41]20.28/0.557225.71/0.804230.20/0.901635.76/0.960141.00/0.983730.59/0.8373
DGUNet+ [32]22.15/0.611326.82/0.823030.92/0.908836.18/0.961641.24/0.983731.46/0.8577
OCTUF+ [42]21.94/0.598926.54/0.815030.73/0.903636.10/0.960741.35/0.983831.33/0.8524
CPP-Net [18]22.19/0.613527.23/0.833731.27/0.913536.35/0.9631--
SAUNet [47]22.43/0.613427.80/0.835332.15/0.914737.11/0.962841.91/0.983832.28/0.8620
HATNet [35]22.54/0.616227.98/0.838232.26/0.918237.24/0.963442.05/0.983832.41/0.8640
COAST [57]Multiple10.45/0.2144*22.90/0.6971*28.69/0.861833.90/0.9399*38.94/0.974426.98/0.7375
PnP-DnCNN [37]Arbitrary21.68/0.568226.45/0.796929.57/0.871234.24/0.940239.78/0.973530.34/0.8300
PnP-DRUNet [66]21.75/0.573826.81/0.807430.16/0.886135.00/0.947640.54/0.976730.85/0.8383
HQS-ProxUnroll22.76/0.630028.23/0.845032.51/0.922537.33/0.963541.92/0.983732.55/0.8689
ADMM-ProxUnroll22.76/0.630728.30/0.845232.55/0.922637.35/0.963941.97/0.983832.59/0.8692
BSD68ISTA-Net+ [61]Single19.14/0.415822.17/0.548625.32/0.702229.36/0.852534.04/0.942426.01/0.6923
CSNet+ [39]22.21/0.510025.43/0.670627.91/0.793831.12/0.906036.76/0.963828.69/0.7688
OPINE-Net+ [62]22.11/0.514025.20/0.682527.82/0.804531.51/0.906136.35/0.966028.60/0.7746
AMP-Net [68]22.28/0.531925.27/0.693027.88/0.811831.80/0.915437.03/0.972228.85/0.7849
TransCS [38]22.28/0.531825.28/0.688127.86/0.808631.74/0.912136.81/0.969928.79/0.7821
CSformer [56]22.81/0.556625.73/0.695628.05/0.804531.82/0.910637.14/0.976629.11/0.7889
MADUN [41]22.08/0.524725.36/0.698528.18/0.821932.27/0.921937.23/0.973329.02/0.7880
DGUNet+ [32]22.13/0.521525.45/0.698628.13/0.816531.97/0.915837.04/0.971828.94/0.7848
OCTUF+ [42]22.78/0.541325.65/0.699928.28/0.817732.24/0.918537.41/0.972929.27/0.7900
CPP-Net [18]22.95/0.547525.81/0.706828.41/0.822732.25/0.9188--
SAUNet [47]23.11/0.546026.23/0.705029.25/0.825133.67/0.924339.28/0.975130.31/0.7951
COAST [57]Multiple12.08/0.2584*22.77/0.5953*26.28/0.742230.07/0.8703*34.74/0.949725.19/0.6832
PnP-DnCNN [37]Arbitrary22.27/0.522124.85/0.632727.22/0.765830.95/0.876236.47/0.960128.35/0.7514
PnP-DRUNet [66]22.81/0.530825.30/0.667027.79/0.785231.38/0.893136.86/0.962428.83/0.7677
HQS-ProxUnroll23.51/0.564526.52/0.719429.42/0.833233.76/0.928239.22/0.976030.49/0.8043
ADMM-ProxUnroll23.53/0.564926.54/0.720029.43/0.833433.77/0.928439.23/0.976130.50/0.8046
+ +Table 3. MACs (G), Params (M), and runtime (sec.) comparisons on $256 \times 256$ images at CR = 0.25. PnP-DRUNet performs 50 iterations for best performance. + +
MetricCPP-Net [18]SAUNet [47]HATNet [35]PnP-DRUNet [66]HQS/ADMM-ProxUnroll
MACs153.47143.05494.427175.10 (143.5×50)107.73 (17.95×6)
Params12.3110.5331.2832.643.90
Runtime0.410.350.600.650.27
+ +thus cannot generalize to different CRs. COAST, trained on multiple CRs $\{0.10, 0.20, 0.30, 0.40, 0.50\}$ , is flexible only for seen CRs, not for unseen CRs (e.g. 0.01). Our HQS/ADMM-ProxUnroll and PnP algorithms (PnP-DnCNN, PnP-DRUNet) can flexibly handle arbitrary CRs with a single model. Moreover, we compare HQS/ADMM-ProxUnroll with several competitive approaches in terms of multiply-accumulate operations (MACs), model parameters (Params), and runtime. As reported in Tab. 3, our HQS/ADMM-ProxUnroll achieves an all-around superiority over these approaches. Overall, our HQS/ADMM-ProxUnroll achieve not only SOTA performance and efficiency but also the same flexibility as PnP algorithms. + +# 5.2. Results on Real Captured Data + +We estimate the proposed HQS/ADMM-ProxUnroll on real captured SPI data. Among the networks mentioned previously, only SAUNet [47] and HATNet [35] are practical for real SPI cameras. The remaining networks are developed under the assumption that images can be compressively sampled block by block, which is out of line with real SPI cameras. Hence, we compare HQS/ADMM-ProxUnroll with SAUNet, HATNet, and PnP-DRUNet. As shown in Fig. 6, PnP-DRUNet can recovers well on low frequencies (e.g., shapes and edges) instead of high frequencies (e.g., textures and details), agreeing with that Gaussian denoisers could smooth out rather than remove unknown artifacts [66]. HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them have a better reconstruction ability than the competitors. In practice, SAUNet and HATNet need a separate model for a specific CR. A single model of HQS-ProxUnroll or ADMM-ProxUnroll is flexible enough for varying CRs, similar to PnP algorithms. + +# 5.3. Ablation Study + +To offer an insight into ProxUnroll, we conduct ablation experiments on PL loss function (Sec. 4.1) and DIR (Sec. 4.2). ProxUnroll uses PL loss function to train DIR as approximation of the proximal operator of an explicit restoration regularizer in Eq. (16) to guarantee the fast convergence. + +To demystify the influence of PL loss function, the convergence curves of different methods are depicted in Fig. 7. SAUNet and HATNet, both composed of 7 iterations, reconstruct images with twists and turns since their MSE loss function only ensure a satisfactory final result. This implies that their intermediate subnets cannot be interpreted + +![](images/85a1d387c68057884f39d13d69a2b775be541f2c1c9874b976747da331d1b959.jpg) +Figure 7. Convergence curves of different unrolling methods. + +Table 4. Ablation experiments for different components of our deep image restorer (DIR) on Set11 dataset at $\mathrm{{CR}} = {0.10}$ . + +
ChanCASwinTAdaConvPSNRMACsParamsRuntime
✓✓31.4294.853.100.22
✓✓32.25128.674.650.34
✓✓32.36101.993.850.21
✓✓✓32.51107.733.900.27
+ +as the proximal restoration operators and function more like black-box neural networks. Their lack of proximity also elucidates why prior unrolling networks require retraining when the degradation changes. With PL-based training, our HQS/ADMM-ProxUnroll achieves fast and stable convergence. By replacing PL loss with regular MSE loss during training, their convergence curves also become unstable. + +To demystify the influence of key designs in DIR, we conduct ablation experiments as shown in Tab. 4. The proposed DIR is mainly powered by three components: ChanCA in memory block, SwinT and GD-CNN in CNN-Transformer block. ChanCA is used to adaptively propagate informative representations between adjacent iterations. The combination of SwinT and GD-CNN is to integrate the high- and low-frequency modeling ability while keeping high dependency for input. GD-CNN is powered by the proposed AdaConv. Clearly, ChanCA results in a $1.09\mathrm{dB}$ improvement in PSNR with a slight increase in MACs, parameters, and runtime. By discarding SwinT and doubling the channel capability of GD-CNN, the entire network becomes a CNN, leading to a $0.26\mathrm{dB}$ decrease in PSNR and an all-round increase in other metrics. Replacing AdaConv with one depth-wise convolution causes a $0.15\mathrm{dB}$ decrease in PSNR but has minimal impact on MACs, parameters, and runtime. These results validate the effectiveness and efficiency of ChanCA, SwinT, and AdaConv. + +# 6. Conclusion + +We propose ProxUnroll to train any unrolled network to approximate the proximal operator of an explicit restoration regularizer using a proximal trajectory (PL) loss function. Besides, we propose an efficient CNN-Transformer architecture as deep image restorer (DIR) to arm ProxUnroll. 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Optimization-inspired compact deep compressive sensing. IEEE Journal of Selected Topics in Signal Processing, 14(4):765-774, 2020. 2, 3, 6, 7 +[63] Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang. Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE transactions on image processing, 26(7):3142-3155, 2017. 2, 3, 6 +[64] Kai Zhang, Wangmeng Zuo, Shuhang Gu, and Lei Zhang. Learning deep cnn denoiser prior for image restoration. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3929-3938, 2017. 2 +[65] Kai Zhang, Wangmeng Zuo, and Lei Zhang. Ffdnet: Toward a fast and flexible solution for cnn-based image denoising. IEEE Transactions on Image Processing, 27(9):4608-4622, 2018. 2, 3, 6 +[66] Kai Zhang, Yawei Li, Wangmeng Zuo, Lei Zhang, Luc Van Gool, and Radu Timofte. Plug-and-play image restoration with deep denoiser prior. IEEE Transactions on Pat- + +tern Analysis and Machine Intelligence, 44(10):6360-6376, 2021. 2, 3, 6, 7, 8 +[67] Zibang Zhang, Xueying Wang, Guoan Zheng, and Jinggang Zhong. Hadamard single-pixel imaging versus fourier single-pixel imaging. Optics Express, 25(16):19619-19639, 2017. 1 +[68] Zhonghao Zhang, Yipeng Liu, Jiani Liu, Fei Wen, and Ce Zhu. Amp-net: Denoising-based deep unfolding for compressive image sensing. 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PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "spans": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 599, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 599, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 599, + 296, + 684 + ], + "type": "text", + "content": "How many pixels does your camera actually need? Modern cameras typically require as many pixels as the image resolution demands. By contrast, single-pixel cameras need only one pixel, a light-sensitive detector, to capture images through multiple measurements. Single-pixel imaging (SPI) [13, 14, 20, 52, 67] technique measures the total light intensity of a scene coded by a series of spatially resolved" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 217, + 554, + 340 + ], + "blocks": [ + { + "bbox": [ + 315, + 217, + 554, + 340 + ], + "lines": [ + { + "bbox": [ + 315, + 217, + 554, + 340 + ], + "spans": [ + { + "bbox": [ + 315, + 217, + 554, + 340 + ], + "type": "image", + "image_path": "885ffbbe1646461c7c2c6e93214f5ca1f18fdbf19e69fae23a9951f8b4fda48f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 347, + 555, + 414 + ], + "lines": [ + { + "bbox": [ + 313, + 347, + 555, + 414 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 555, + 414 + ], + "type": "text", + "content": "Figure 1. Average PSNR (left) of different methods at compressive ratios (CRs) " + }, + { + "bbox": [ + 313, + 347, + 555, + 414 + ], + "type": "inline_equation", + "content": "\\{0.01, 0.04, 0.10, 0.25\\}" + }, + { + "bbox": [ + 313, + 347, + 555, + 414 + ], + "type": "text", + "content": " in which only methods in the yellow area can flexibly handle varying CRs with a single model. Optimization trajectories (right) of four classes of methods for solving inverse problems. Our ProxUnroll efficiently achieves SOTA performance with high flexibility and fast convergence." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 425, + 555, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 555, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 555, + 485 + ], + "type": "text", + "content": "masks on a single-pixel detector. Known masks and measurements, one can recover an image with the same resolution as the masks. SPI offers a competitive edge over mainstream CCD and CMOS cameras in certain scenarios, e.g., terahertz imaging [52] and non-visible 3D imaging [43]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": "SPI cameras typical work under sub-Nyquist sampling rate to save acquisition time, leading to a compressed sensing problem [7, 8] of reconstructing a clean image " + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": " from its few measurements " + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "\\pmb{y} \\in \\mathbb{R}^m" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": " obtained by the imaging model " + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "\\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon}" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "\\Phi \\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "m \\ll n" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": ") is the measurement (i.e., degradation) matrix, " + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon} \\in \\mathbb{R}^m" + }, + { + "bbox": [ + 313, + 486, + 556, + 568 + ], + "type": "text", + "content": " the measurement noise. The inverse problem is formulated as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 375, + 571, + 553, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 571, + 553, + 590 + ], + "spans": [ + { + "bbox": [ + 375, + 571, + 553, + 590 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {x}} = \\underset {\\boldsymbol {x}} {\\arg \\min } f (\\boldsymbol {x}) + \\lambda g (\\boldsymbol {x}), \\tag {1}", + "image_path": "c295430f491eee86de6fc1cabb451b9271f57b6e0e4aa277ed548a497de33240.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "inline_equation", + "content": "f(x) = \\frac{1}{2} \\| \\pmb{y} - \\pmb{\\Phi}\\pmb{x} \\|_2^2" + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": " is a data fidelity term, " + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "inline_equation", + "content": "\\lambda g(x)" + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": " a scaled regularization term that represents a prior knowledge on " + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": ", e.g., sparsity [16]. In SPI cameras, " + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "inline_equation", + "content": "\\pmb{\\Phi}" + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": " is usually set to be row-orthogonal and each row represents an optical mask. As a adjustable parameter, compressive ratio (CR) " + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "inline_equation", + "content": "\\eta = m/n" + }, + { + "bbox": [ + 313, + 592, + 556, + 676 + ], + "type": "text", + "content": " affects the ill-posedness of Eq. (1), namely the degree to which images are degraded as illustrated in Fig. 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "content": "A fruitful solution to Eq. (1) is first-order proximal algorithms [9], e.g., half quadratic splitting (HQS) [17] method and alternating direction method of multipliers" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 67, + 703, + 260, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 260, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 260, + 713 + ], + "type": "text", + "content": "† Corresponding author: Xin Yuan, xyuan@westlake.edu.cn" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "411" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 59, + 294, + 148 + ], + "blocks": [ + { + "bbox": [ + 57, + 59, + 294, + 148 + ], + "lines": [ + { + "bbox": [ + 57, + 59, + 294, + 148 + ], + "spans": [ + { + "bbox": [ + 57, + 59, + 294, + 148 + ], + "type": "image", + "image_path": "685e0d43c23e9f1a81eb27845eb1f7de2965798ffe63007450c1858088663d3d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "lines": [ + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "spans": [ + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "text", + "content": "Figure 2. Degradations under different compressive ratios (CRs). (ADMM) [30], which individually perform the proximal operator " + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}" + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_h" + }, + { + "bbox": [ + 56, + 155, + 294, + 196 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 91, + 198, + 295, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 198, + 295, + 220 + ], + "spans": [ + { + "bbox": [ + 91, + 198, + 295, + 220 + ], + "type": "interline_equation", + "content": "\\operatorname {P r o x} _ {h} (z) = \\underset {\\boldsymbol {x}} {\\arg \\min } h (\\boldsymbol {x}) + \\frac {1}{2} \\| \\boldsymbol {x} - \\boldsymbol {z} \\| _ {2} ^ {2}. \\tag {2}", + "image_path": "d88d470f437d31cf8f96caf1a0cfe58d842decf92f885392b85604f5908f1f49.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "spans": [ + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "text", + "content": "The properties of proximal operator guarantee the convergence of iterative algorithms [33]. " + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_f" + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "text", + "content": " has a closed form for a specific algorithm. " + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_g" + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "text", + "content": " can be loosely interpreted as a denoising step, which is explicitly implemented by the regularizer " + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 222, + 296, + 400 + ], + "type": "text", + "content": " or implicitly by a deep neural network. By integrating proximal algorithms and deep neural networks, deep-unrolling (or unfolding) [1, 4, 11, 31, 61] and plug-and-play (PnP) [25, 44, 45, 64, 66] approaches have become the de-facto standard solvers for imaging inverse problems. PnP approaches constitute a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep Gaussian denoiser [63, 65, 66]. Unrolling approaches constitute a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 402, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 296, + 641 + ], + "type": "text", + "content": "In SPI cameras, degradations are signal-dependent and CR-dependent as illustrated in Fig. 2. PnP algorithms [46] have flexibility for varying CRs but typically achieve moderate accuracy with slow inference and cumbersome parameter adjustment. Latest works [15, 22-24, 37] reveal that, PnP deep denoiser or even deep restorer can approximate a proximal operator under certain assumptions or constraints to guarantee the convergence for various imaging tasks and varying degradations. Conversely, unrolling networks [35, 47] are typically trained end-to-end for a specific CR to achieve state-of-the-art (SOTA) accuracy with fast inference. However, when CR changes, they must be finetuned or even retrained due to the out-of-distribution (OOD) problem, thereby lacking flexibility. Besides, what has been learned from data is not interpretable for unrolling networks. As summarized in Tab. 1, PnP algorithms are highly flexible but are limited in accuracy and speed, whereas unrolling networks are too specialized to flexibly handle varying CRs. What hinders the flexibility and interpretability of unrolling networks is an open question." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "In this paper, we address the challenge of integrating the strengths of PnP and unrolling approaches. The flexibility and interpretability are originated from proximal algorithms. The flexibility and interpretability of PnP and unrolling approaches depend on the extent to which the used neural networks approach proximal operators. To this end," + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 329, + 85, + 538, + 148 + ], + "blocks": [ + { + "bbox": [ + 313, + 59, + 555, + 82 + ], + "lines": [ + { + "bbox": [ + 313, + 59, + 555, + 82 + ], + "spans": [ + { + "bbox": [ + 313, + 59, + 555, + 82 + ], + "type": "text", + "content": "Table 1. Comprehensive comparison among proximal algorithms, PnP algorithms, unrolling networks, and our ProxUnroll." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 85, + 538, + 148 + ], + "lines": [ + { + "bbox": [ + 329, + 85, + 538, + 148 + ], + "spans": [ + { + "bbox": [ + 329, + 85, + 538, + 148 + ], + "type": "table", + "html": "
MethodAccuracySpeedFlexibilityInterpretability
ProximalLowLowHighHigh
PnPMiddleMiddleHighMiddle
UnrollingHighHighLowLow
ProxUnrollHighHighHighHigh
", + "image_path": "636472966db66020b9c7c558133d43e2d41111e300bbaf1cff9f5fc79fea460f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 156, + 553, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 156, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 553, + 190 + ], + "type": "text", + "content": "we propose a proximal unrolling (ProxUnroll) approach to endow unrolling networks with flexibility and interpretability. Main contributions are summarized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 191, + 553, + 407 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 314, + 191, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 191, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 314, + 191, + 553, + 227 + ], + "type": "text", + "content": "- We introduce HQS- and ADMM-unrolling networks for SPI, composed of a few iterations of an explicit proximal operator and an implicit deep image restorer (DIR)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 228, + 553, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 228, + 553, + 299 + ], + "spans": [ + { + "bbox": [ + 314, + 228, + 553, + 299 + ], + "type": "text", + "content": "- We design an efficient CNN-Transformer hybrid architecture as DIR, where the integration of window attention and dynamic CNN captures both low- and high-frequency information with high input dependency, and channel attention functions as a memory mechanism to propagate informative representations between adjacent iterations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 300, + 553, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 300, + 553, + 358 + ], + "spans": [ + { + "bbox": [ + 314, + 300, + 553, + 358 + ], + "type": "text", + "content": "- More importantly, we propose a generic proximal trajectory (PT) loss function to train HQS/ADMM-unrolling networks into HQS/ADMM-ProxUnroll networks where learned DIRs approximate the proximal operator of an ideal explicit restoration regularizer." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 359, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 359, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 314, + 359, + 553, + 407 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that the proposed HQS/ADMM-ProxUnroll efficiently achieves not only SOTA performance and fast convergence, but also the same flexibility as PnP algorithms (see Fig. 1)." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 418, + 406, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 418, + 406, + 430 + ], + "spans": [ + { + "bbox": [ + 314, + 418, + 406, + 430 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 437, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 640 + ], + "type": "text", + "content": "SPI Reconstruction. SPI reconstruction is a classical inverse problem in the field of compressive imaging [48-50, 59]. Mainstream solvers involve iterative optimization algorithms [3, 5, 10, 16, 21, 26, 28, 30, 53], PnP algorithms [15, 22-24, 66], single-stage neural networks [27, 39, 40, 55], and unrolling (multi-stage) neural networks [18, 29, 32, 35, 38, 41, 42, 47, 51, 54, 56, 57, 61, 62, 68]. Iterative algorithms employ hand-crafted regularizers, e.g., sparsity [16], total variation [28], non-local low rank [10, 58], with a proximal algorithm, e.g., iterative shrinkage thresholding algorithm (ISTA) [3], approximate message passing (AMP) [30], HQS [17], and ADMM [53]. Single-stage networks generally achieve inferior performance due to the insufficient utilization of imaging model information. PnP algorithms are flexible for varying CRs and unrolling networks achieve superior performance, thus making both the de-facto standard tools for SPI reconstruction." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "Proximal learning. The objective of proximal learning is to train a neural network as the proximal operator of a explicit regularization function. Regularization by denoising [36] shows that under homogeneity, nonexpansiveness and Jacobian symmetry conditions, a denoiser can be written as a gradient descent step on a convex function. However, such" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "412" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": "conditions are unrealistic for deep denoisers. Recently, a new type of gradient denoisers [15, 23, 24] has been proposed by training a denoiser as an explicit gradient step on a functional parameterized by a deep neural network. However, these denoisers must either be a contractive gradient [23, 24] or be constrained to input convex neural networks (ICNN) [15], inevitably sacrificing the expressivity. Proximal learning without assumptions and constraints remains an open challenge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 190, + 141, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 141, + 202 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 141, + 202 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 209, + 296, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 296, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 296, + 258 + ], + "type": "text", + "content": "In this section, we first introduce the inverse problem of SPI. Then, we extend two representative proximal algorithms (i.e., HQS and ADMM) to solve this problem. Finally, we compare PnP approaches with unrolling approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 264, + 175, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 175, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 175, + 275 + ], + "type": "text", + "content": "3.1. SPI Inverse Problem" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": "Typical SPI cameras capture 2D images. Following Eqs. (1) and (2), processing a 2D image in its vectorized form leads to large matrix calculation problems for all " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": "-related operations, particularly during model training. To this end, most previous works [18, 32, 41, 42, 51, 56, 57, 61, 62, 68] split a digital image into non-overlapping blocks to reduce the vectorized size, but block-wise sampling is impractical for real SPI cameras. A practical solution is Kronecker compressed sensing [6, 12], which processes 2D images in matrix form rather than vector form. Mathematically, " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{y} = \\pmb{\\Phi}\\pmb{x} + \\pmb{\\epsilon}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " is equivalent to " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top} + \\mathbf{E}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{y} = \\mathrm{vec}(\\mathbf{Y})" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{x} = \\mathrm{vec}(\\mathbf{X})" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon} = \\mathrm{vec}(\\mathbf{E})" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\Phi = \\mathbf{W} \\otimes \\mathbf{H}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathrm{vec}(\\cdot)" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " denotes the vectorization operation, " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " the Kronecker product. The large measurement matrix " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\Phi \\in \\mathbb{R}^{hw \\times HW}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " is replaced by two small matrices " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{H} \\in \\mathbb{R}^{h \\times H}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{w \\times W}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " to reconstruct an image " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " from the measurements " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\mathbb{R}^{hw}" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": " with a compressive ratio " + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "inline_equation", + "content": "\\eta = hw / HW" + }, + { + "bbox": [ + 55, + 282, + 296, + 498 + ], + "type": "text", + "content": ". The inverse problem is therefore formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 499, + 295, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 499, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 117, + 499, + 295, + 519 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {X}} = \\underset {\\mathbf {X}} {\\arg \\min } f (\\mathbf {X}) + \\lambda g (\\mathbf {X}), \\tag {3}", + "image_path": "b655438e09338f2165181e0bf4e507e3b3f58daf5a2d0796705510161e46349d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "f = \\frac{1}{2}\\| \\mathbf{Y} - \\mathbf{H}\\mathbf{X}\\mathbf{W}^{\\top}\\|_{F}^{2},\\| \\cdot \\|_{F}" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " denotes the Frobenius norm. As a result, large matrix calculations on " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " are equivalent to efficient calculations on " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": ", resulting in a significant decrease on space complexity from " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\eta H^2 W^2)" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\sqrt{\\eta} H^2 +\\sqrt{\\eta} W^2)" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " and time complexity from " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\eta H^2 W^2)" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\eta H^2 W + \\sqrt{\\eta} HW^2)" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "H\\leq W" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": ") [47]. Note that the physical masks in SPI cameras still correspond to the rows of " + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\Phi = \\mathbf{W}\\otimes \\mathbf{H}" + }, + { + "bbox": [ + 55, + 522, + 296, + 620 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 626, + 268, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 626, + 268, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 626, + 268, + 639 + ], + "type": "text", + "content": "3.2. Proximal Algorithms: HQS and ADMM" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 644, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 644, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 644, + 296, + 693 + ], + "type": "text", + "content": "HQS and ADMM are generally developed to solve Eq. (1). Next, we exploit both towards Eq. (3). By introducing an auxiliary variable " + }, + { + "bbox": [ + 55, + 644, + 296, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{Z} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 55, + 644, + 296, + 693 + ], + "type": "text", + "content": ", the unconstrained Eq. (3) can be rewritten as a constrained optimization problem:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 693, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 693, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 83, + 693, + 295, + 715 + ], + "type": "interline_equation", + "content": "(\\widehat {\\mathbf {X}}, \\widehat {\\mathbf {Z}}) = \\underset {\\mathbf {X}, \\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}), \\quad s. t. \\mathbf {Z} = \\mathbf {X}. \\qquad (4)", + "image_path": "a6813c892c20459a53258e9dfbfd006db085f152306f71376a4e6f70a1eb2a33.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "HQS handles the constraint of Eq. (4) as a penalty term by minimizing" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 348, + 98, + 553, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 98, + 553, + 118 + ], + "spans": [ + { + "bbox": [ + 348, + 98, + 553, + 118 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {5}", + "image_path": "0ffc32fa4711d088480895d64b0f46d8164d86e223df31bf0f3d15d757188fe9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 119, + 553, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 119, + 553, + 143 + ], + "spans": [ + { + "bbox": [ + 313, + 119, + 553, + 143 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 119, + 553, + 143 + ], + "type": "inline_equation", + "content": "\\mu > 0" + }, + { + "bbox": [ + 313, + 119, + 553, + 143 + ], + "type": "text", + "content": ". The minimizer of Eq. 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Instead of adding a simple penalty term in HQS, ADMM re-formulates Eq. (4) using the augmented Lagrangian as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 319, + 238, + 553, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 238, + 553, + 258 + ], + "spans": [ + { + "bbox": [ + 319, + 238, + 553, + 258 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mu} (\\mathbf {X}, \\mathbf {Z}, \\mathbf {U}) = f (\\mathbf {Z}) + \\lambda g (\\mathbf {X}) + \\mathbf {U} ^ {\\top} (\\mathbf {Z} - \\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\mathbf {X} \\| _ {F} ^ {2}, \\tag {8}", + "image_path": "7aa849478553010764039a3c6e0adb9cc30555aa715a98d4d74ddcff912e8d88.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 259, + 553, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 259, + 553, + 283 + ], + "spans": [ + { + "bbox": [ + 313, + 259, + 553, + 283 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 259, + 553, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 313, + 259, + 553, + 283 + ], + "type": "text", + "content": " is the Lagrange multiplier. Eq. (8) can also be solved by alternative proximal operators as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 284, + 553, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 284, + 553, + 309 + ], + "spans": [ + { + "bbox": [ + 318, + 284, + 553, + 309 + ], + "type": "interline_equation", + "content": "\\operatorname {P r o x} _ {f}: \\mathbf {Z} ^ {k + 1} = \\underset {\\mathbf {Z}} {\\arg \\min } f (\\mathbf {Z}) + \\frac {\\mu}{2} \\| \\mathbf {Z} - \\left(\\mathbf {X} ^ {k} - \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {9}", + "image_path": "cfa6d775e74552ca8f50c78b6a037edfa5192b5939c7a624048e9ebf5add2ba2.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 312, + 553, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 312, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 317, + 312, + 553, + 346 + ], + "type": "interline_equation", + "content": "\\operatorname {P r o x} _ {g}: \\mathbf {X} ^ {k + 1} = \\underset {\\mathbf {X}} {\\arg \\min } \\lambda g (\\mathbf {X}) + \\frac {\\mu}{2} \\| \\mathbf {X} - \\left(\\mathbf {Z} ^ {k + 1} + \\frac {1}{\\mu} \\mathbf {U} ^ {k}\\right) \\| _ {F} ^ {2}, \\tag {10}", + "image_path": "fb0d60684172330a259bd891e83e2f3eb028750131b8849331b4573113740900.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 346, + 457, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 457, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 457, + 360 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 313, + 346, + 457, + 360 + ], + "type": "inline_equation", + "content": "\\mathbf{U}^{k + 1} = \\mathbf{U}^k +\\mu (\\mathbf{Z}^{k + 1} - \\mathbf{X}^{k + 1})" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "content": "In SPI paradigm, " + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "content": " is a differentiable convex function and " + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "content": " is generally set to be row-orthogonal, i.e., " + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "inline_equation", + "content": "\\mathbf{WW}^{\\top} \\otimes \\mathbf{HH}^{\\top} = \\mathbf{I}" + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "content": ". In this case, " + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "inline_equation", + "content": "\\operatorname{Prox}_f" + }, + { + "bbox": [ + 313, + 361, + 553, + 397 + ], + "type": "text", + "content": " has a closed form:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 334, + 399, + 553, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 399, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 334, + 399, + 553, + 422 + ], + "type": "interline_equation", + "content": "\\operatorname {P r o x} _ {f} (\\mathbf {P}) = \\mathbf {V} + \\frac {1}{1 + \\mu} \\mathbf {H} ^ {\\top} (\\mathbf {Y} - \\mathbf {H P W} ^ {\\top}) \\mathbf {W}, \\tag {11}", + "image_path": "2f88606c962dc922205e3d6e44936b4fea2d1ebdb9617980737b3f669b9848df.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\mathbf{X}^k" + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}^k - \\frac{1}{\\mu}\\mathbf{U}^k)" + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "text", + "content": " for HSQ or ADMM. Eq. (11) is also a gradient descent step. With a proper regularizer " + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 425, + 555, + 473 + ], + "type": "text", + "content": ", HQS and ADMM could converge to stationary points of Eq. 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For SPI cameras, the generalization makes PnP algorithms flexible for varying CRs. Besides, " + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 313, + 570, + 555, + 714 + ], + "type": "text", + "content": " can be interpreted as a proximal operator to guarantee the convergence under non-expansiveness assumptions or Lipschitz constraints [15, 22-24, 37]. 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Proximal algorithm unrolling via trajectory loss." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 474, + 69, + 527, + 186 + ], + "blocks": [ + { + "bbox": [ + 474, + 69, + 527, + 186 + ], + "lines": [ + { + "bbox": [ + 474, + 69, + 527, + 186 + ], + "spans": [ + { + "bbox": [ + 474, + 69, + 527, + 186 + ], + "type": "image", + "image_path": "91c3f000df1994a9964fabf2c86c2006a7e6cc72a017db585ab139e6cbeb96f0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 213, + 123, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 123, + 227 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 123, + 227 + ], + "type": "text", + "content": "3.4. Unrolling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 232, + 296, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 232, + 296, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 296, + 291 + ], + "type": "text", + "content": "Unrolling approaches first replace " + }, + { + "bbox": [ + 55, + 232, + 296, + 291 + ], + "type": "inline_equation", + "content": "\\mathbf{Prox}_g" + }, + { + "bbox": [ + 55, + 232, + 296, + 291 + ], + "type": "text", + "content": " in Eq. 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Instead of using a pretrained " + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "text", + "content": " in PnP algorithms, unrolling networks learn a small set of subnets " + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}_{\\theta^k}\\}_{k=0}^{K-1}" + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "text", + "content": " with a same structure but different weights, thereby belonging to multi-stage neural networks. Although unrolling networks resemble proximal algorithms that are widely known to be convergent, end-to-end training could only ensure that the final result " + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^K" + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "text", + "content": " is close to the ground truth " + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "text", + "content": " but cannot guarantee that the intermediate results " + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}^k\\}_{k=1}^{K-1}" + }, + { + "bbox": [ + 55, + 321, + 296, + 538 + ], + "type": "text", + "content": " are improved step-by-step, thereby lacking the convergence guarantee [19] (see Fig. 7). After degradation-specific training, unrolling networks usually produce SOTA results with fast inference (due to very few iterations), but need be fine-tuned or even retrained when the degradation (e.g., CR in SPI) changes. Consequently, performance is achieved at the cost of generalization. How to make unrolling networks flexible for varying CRs is a key challenge in SPI." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 548, + 227, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 227, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 227, + 562 + ], + "type": "text", + "content": "4. Proximal Algorithm Unrolling" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 568, + 296, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 296, + 628 + ], + "type": "text", + "content": "In this section, we first introduce a proximal algorithm unrolling approach with interpretability and convergence guarantees, named ProxUnroll, via a proximal trajectory (PT) loss function. Subsequently, we propose an efficient CNN-Transformer architecture to realize ProxUnroll." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 635, + 263, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 263, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 263, + 647 + ], + "type": "text", + "content": "4.1. Proximal Unrolling via Trajectory Loss" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "The main differences between PnP in Eq. (13) and unrolling in Eq. (14) involve that, " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " the iteration number is often large in PnP but small in unrolling; " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "(ii)" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " one pretrained deep denoiser " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " is reused across iterations in PnP but " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " subnets " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}_{\\theta^k}\\}_{k = 0}^{K - 1}" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " are end-to-end optimized for " + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": " iterations in un" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "content": "rolling; (iii) " + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "inline_equation", + "content": "\\mathrm{PnP}\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "content": " could loosely correspond to " + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_g" + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "content": " but what unrolled " + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\theta^k}" + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "content": " has learned is unclear. By integrating the characteristics of " + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "inline_equation", + "content": "\\mathrm{PnP}" + }, + { + "bbox": [ + 313, + 214, + 554, + 262 + ], + "type": "text", + "content": " and unrolling, we define a proximal unrolling (ProxUnroll) framework as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 263, + 553, + 290 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 263, + 553, + 290 + ], + "spans": [ + { + "bbox": [ + 320, + 263, + 553, + 290 + ], + "type": "interline_equation", + "content": "\\mathbf {X} ^ {K} = \\left[\\begin{array}{l}K - 1\\\\\\bigcirc\\\\k = 0\\end{array}\\right. \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {0}\\right), \\text {s . t .} \\mathcal {R} _ {\\theta} \\rightarrow \\operatorname {P r o x} _ {g}, \\tag {15}", + "image_path": "42b83b7442bf0bbc386ffa964016a8cdfca63b7dc8457d12180090eef2a54e34.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "text", + "content": " is a neural network, which can be expressed as the proximal operator of a regularizer " + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "text", + "content": ". In Eq. (15), the remaining challenge is to satisfy the condition " + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g" + }, + { + "bbox": [ + 313, + 291, + 554, + 327 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": "Essentially, " + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\operatorname{Prox}_g" + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": " is an input-to-output movement towards the minimum of a regularizer " + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": " such that the output is between the input and the minimum. Given a degraded image as input, the output image is bound to be restored if the minimum is the corresponding clear image. In this case, " + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\operatorname{Prox}_g" + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": " is an image restoration operator. Motivated by this point, we define the squared Euclidean distance between a degraded image " + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{X}'" + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": " and its clear image " + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 331, + 554, + 436 + ], + "type": "text", + "content": " as an explicit regularization function:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 387, + 437, + 553, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 437, + 553, + 460 + ], + "spans": [ + { + "bbox": [ + 387, + 437, + 553, + 460 + ], + "type": "interline_equation", + "content": "\\bar {g} \\left(\\mathbf {X} ^ {\\prime}\\right) = \\frac {1}{2} \\| \\mathbf {X} ^ {\\prime} - \\mathbf {X} \\| _ {F} ^ {2}. \\tag {16}", + "image_path": "4290f31e30a5dfc38ba2b275ab00cd3542c2eade834e24d2d3b122e8c09b03e9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 460, + 553, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 553, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 553, + 484 + ], + "type": "text", + "content": "By inserting Eq. (16) into Eqs. (7) and (10), " + }, + { + "bbox": [ + 313, + 460, + 553, + 484 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_{\\tilde{g}}" + }, + { + "bbox": [ + 313, + 460, + 553, + 484 + ], + "type": "text", + "content": " has the following closed form:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 382, + 485, + 553, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 485, + 553, + 510 + ], + "spans": [ + { + "bbox": [ + 382, + 485, + 553, + 510 + ], + "type": "interline_equation", + "content": "\\operatorname {P r o x} _ {\\tilde {g}} (\\mathbf {Q}) = \\frac {\\mu \\mathbf {Q} + \\lambda \\mathbf {X}}{\\mu + \\lambda}, \\tag {17}", + "image_path": "30efc9e74da06ca583c5a6c30fa4bc01072bd57d22dfb68d7b34ee2d2846aa40.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} = \\mathbf{Z}^{k + 1}" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "(\\mathbf{Z}^{k + 1} + \\frac{1}{\\mu}\\mathbf{U}^k)" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " for HQS or ADMM, " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " control the strength of being close to " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 512, + 554, + 560 + ], + "type": "text", + "content": " respectively. By combining Eqs. (11) and (17), an ideal explicit proximal algorithm is" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 374, + 562, + 553, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 562, + 553, + 576 + ], + "spans": [ + { + "bbox": [ + 374, + 562, + 553, + 576 + ], + "type": "interline_equation", + "content": "\\mathbf {X} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right), \\tag {18}", + "image_path": "eefef6b97dc6b6a73e8c38485d3caa447859c4f9cb517aa5aa1ee7e7898d9348.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^k\\rightarrow \\mathbf{X}" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "k\\to \\infty" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " . The convergence rate is closely related to " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " . If " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\mu /\\lambda = 0" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " , Proxg executes an one-step restoration from an arbitrarily degraded image to its clear image. Proxg is an explicit image restorer conditioned on the ground truth. During supervised training, we use Proxg to guide the optimization of " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " in Eq. (15) such that " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " serves as an implicit image restorer to approximate Proxg." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": "As shown in Fig. 3, a perfect proximal optimization trajectory " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^0\\rightarrow \\bar{\\mathbf{X}}^1\\rightarrow \\dots \\rightarrow \\bar{\\mathbf{X}}^{K - 1}\\rightarrow \\mathbf{X}" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": " can be produced from every " + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}^0,\\mathbf{X})" + }, + { + "bbox": [ + 313, + 666, + 554, + 714 + ], + "type": "text", + "content": " training pair via Eq. (18) to supervise the end-to-end training of algorithm unrolling in Eq. (15)." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "414" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 59, + 532, + 175 + ], + "blocks": [ + { + "bbox": [ + 78, + 59, + 532, + 175 + ], + "lines": [ + { + "bbox": [ + 78, + 59, + 532, + 175 + ], + "spans": [ + { + "bbox": [ + 78, + 59, + 532, + 175 + ], + "type": "image", + "image_path": "375973e91a60b3a88c8a66cdc5217a59c1fc33c8d70169553bf0511ea8a7d463.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 96, + 177, + 276, + 330 + ], + "blocks": [ + { + "bbox": [ + 96, + 177, + 276, + 330 + ], + "lines": [ + { + "bbox": [ + 96, + 177, + 276, + 330 + ], + "spans": [ + { + "bbox": [ + 96, + 177, + 276, + 330 + ], + "type": "image", + "image_path": "0b8bc180d36d817ef8b902c02f8bcd8250ee53be29f458cd1096a4a32c167af5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 179, + 337, + 428, + 348 + ], + "lines": [ + { + "bbox": [ + 179, + 337, + 428, + 348 + ], + "spans": [ + { + "bbox": [ + 179, + 337, + 428, + 348 + ], + "type": "text", + "content": "Figure 4. Illustration of the proposed deep image restorer (DIR) " + }, + { + "bbox": [ + 179, + 337, + 428, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 179, + 337, + 428, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 288, + 177, + 520, + 330 + ], + "blocks": [ + { + "bbox": [ + 288, + 177, + 520, + 330 + ], + "lines": [ + { + "bbox": [ + 288, + 177, + 520, + 330 + ], + "spans": [ + { + "bbox": [ + 288, + 177, + 520, + 330 + ], + "type": "image", + "image_path": "a1b994bb541f605f51bf223522bf8970c8431a94ea1e8e287c74b23fc056b4b6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "spans": [ + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "text", + "content": "The proximal iterations " + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_f" + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "text", + "content": " are guaranteed with fast convergence towards the ground truth such that unrolled iterations " + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f" + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "text", + "content": " are optimized to have the similar capability, namely " + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta} \\to \\mathrm{Prox}_g" + }, + { + "bbox": [ + 54, + 357, + 295, + 418 + ], + "type": "text", + "content": ". To this end, we propose a proximal trajectory (PT) loss function as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 97, + 419, + 294, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 419, + 294, + 470 + ], + "spans": [ + { + "bbox": [ + 97, + 419, + 294, + 470 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {P L} = \\sum_ {k = 0} ^ {K - 1} \\alpha_ {k} \\| \\mathbf {X} ^ {k + 1} - \\bar {\\mathbf {X}} ^ {k + 1} \\| _ {F} ^ {2}, \\\\ s. t. \\left\\{ \\begin{array}{l} \\bar {\\mathbf {X}} ^ {k + 1} = \\mathcal {R} _ {\\theta} \\circ \\operatorname {P r o x} _ {f} \\left(\\mathbf {X} ^ {k}\\right) \\\\ \\bar {\\mathbf {X}} ^ {k + 1} = \\operatorname {P r o x} _ {\\bar {g}} \\circ \\operatorname {P r o x} _ {f} \\left(\\bar {\\mathbf {X}} ^ {k}\\right) \\end{array} \\right. \\end{array} \\tag {19}", + "image_path": "8ebb41360ed94ff2025aef5e7203d83044289a88400b9a730b695ea077150a04.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{X}}^0 = \\mathbf{X}^0" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{X}}^K = \\mathbf{X}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\alpha_{k}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " controls the proximity strength of " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": "-th iteration. Trainable parameters involve " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\theta, \\{\\mu^{k}\\}_{k=0}^{K-1}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_{f}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\mu}^{k}, \\bar{\\lambda}^{k}\\}_{k=0}^{K-2}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_{\\bar{g}} \\circ \\mathrm{Prox}_{f}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{X}}^K = \\mathbf{X}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "(\\bar{\\mu}^{K-1}, \\bar{\\lambda}^{K-1})" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " is set to be " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "(0,1)" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ". PT loss function is designed to train any unrolled network " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " to approximate the proximal operator " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_{\\bar{g}}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": ", thereby with interpretability. Since " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathrm{Prox}_{\\bar{g}}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " is an explicit image restorer, " + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 55, + 472, + 296, + 568 + ], + "type": "text", + "content": " functions as a deep image restorer (DIR)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 575, + 178, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 178, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 178, + 588 + ], + "type": "text", + "content": "4.2. Deep Image Restorer" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "content": "To unlock the potential of ProxUnroll, we propose an efficient CNN-Transformer architecture as DIR." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": "Overall Pipeline. As shown in Fig. 4 (a), DIR is a 4-level asymmetric encoder-decoder architecture. Given a degraded image " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{in} \\in \\mathbb{R}^{H \\times W \\times C_{in}}" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": ", one " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " convolution layer is first applied to extract shallow features " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_0 \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": ". Next, " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_0" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " are passed through 3 encoder stages, each of which contains one memory block, a stack of hybrid CNN-Transformer blocks, and one downsampling layer. From level-1 to level-3, the goal of the encoder is to progressively" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": "reduce the spatial resolution by half while doubling channel capacity, thereby yielding multi-scale low-level features " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_1,\\mathbf{F}_2,\\mathbf{F}_3\\}" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": ". For example, the encoder produces " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_3\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times 8C}" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": " at level-3. At level-4, a bottleneck stage is between the encoder and the decoder to produce " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_4" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": ". The decoder is similar to the encoder except for having no memory block and replacing the downsampling layer by one upsampling layer. Form level-3 to level-1, the decoder progressively produces high-level features " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_5,\\mathbf{F}_6,\\mathbf{F}_7\\}" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": " while recovering the spatial resolution and channel capability. Finally, one " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": " convolution layer transforms the features " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_7" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": " into the residual image " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{I}\\in \\mathbb{R}^{H\\times W\\times C_{in}}" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": ". The restored image is therefore obtained by " + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{out} = \\mathbf{I}_{in} + \\Delta \\mathbf{I}" + }, + { + "bbox": [ + 313, + 357, + 555, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "text", + "content": "In these downsampling and upsampling layers, one " + }, + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "text", + "content": " stripped convolution and one " + }, + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 518, + 556, + 590 + ], + "type": "text", + "content": " transposed convolution are employed respectively. Skip connections are built between the encoder and the decoder for efficient information propagation. Memory block and hybrid CNN-Transformer block are the core components. Next, we introduce them in detail." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": "Memory Block. As mentioned previously, typical unrolling networks in Eq. (14) cannot guarantee the progressive refinement of intermediate results [19] (see Fig. 7) due to end-to-end training. That is also partially caused by that informative representations cannot be propagated across iterations. Hence, the artifacts in intermediate results may be the manifestations of informative representations in the image domain. As analyzed in the supplementary material, we attempt to reduce or remove the intermediate artifacts of SAUNet [47], and the resulting outputs become worse." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "415" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "To address this problem, we propose a memory block (MB) to propagate informative representations in a side path. MB is composed of one channel cross-attention (ChanCA), similar to existing multi-Dconv head transposed attention (MDTA) [60]. As shown in Fig. 4 (a), we directly consider the output features of the bottleneck and decoder at iteration " + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": " as current memories " + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\}" + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": ". By producing queries from " + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_4^k,\\mathbf{F}_5^k,\\mathbf{F}_6^k,\\mathbf{F}_7^k\\}" + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": " and keys/values from " + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_4^{k - 1},\\mathbf{F}_5^{k - 1},\\mathbf{F}_6^{k - 1},\\mathbf{F}_7^k\\}" + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": ", MB adaptively aggregates previous useful representations into current iteration for efficient information propagation by ChanCA, formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 205, + 294, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 205, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 205, + 294, + 228 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {F} _ {\\text {o u t}} = \\operatorname {C h a n C A} \\left(\\mathbf {F} _ {q}, \\mathbf {F} _ {k v}\\right) = \\mathbf {W} _ {p} \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top}\\right) \\mathbf {V} \\right], \\\\ \\mathbf {Q} = \\mathbf {W} ^ {q} \\mathbf {E} \\mathbf {W} ^ {q} \\mathbf {K} = \\mathbf {W} ^ {k} \\mathbf {E} \\mathbf {W} ^ {k} \\mathbf {V} = \\mathbf {W} ^ {v} \\mathbf {E} \\mathbf {W} ^ {v} \\end{array} \\tag {20}", + "image_path": "205ffe8bfcd47a859bd24d8d9e132595e215a88b1c1c7497781641f64503c732.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 222, + 293, + 237 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 222, + 293, + 237 + ], + "spans": [ + { + "bbox": [ + 62, + 222, + 293, + 237 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {W} _ {p} ^ {q} \\mathbf {F} _ {q} \\mathbf {W} _ {d} ^ {q}, \\mathbf {K} = \\mathbf {W} _ {p} ^ {k} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {k}, \\mathbf {V} = \\mathbf {W} _ {p} ^ {v} \\mathbf {F} _ {k v} \\mathbf {W} _ {d} ^ {v}, \\tag {20}", + "image_path": "79e939a78fc88a081174ab6f3479be7b0255a64a72e93dcc1125b8ccb7e19336.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_q, \\mathbf{F}_{kv} \\in \\mathbb{R}^{d \\times HW}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " denote the heads of current and previous memory features respectively, " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{K}, \\mathbf{V}\\}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " are produced from " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_q" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{kv}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " by a point-wise convolution " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_p^{(\\cdot)}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " followed by a " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " depth-wise convolution " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_d^{(\\cdot)}" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": ". At the first iteration, MB can automatically be invalid due to the lack of available memories, i.e. " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{out} = 0" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{kv} = 0" + }, + { + "bbox": [ + 55, + 239, + 294, + 350 + ], + "type": "text", + "content": ". Such design leads to two advantages: i) cross-iteration information propagation mechanism is built regardless iterations; ii) informative representations are adaptively activated." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 352, + 294, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 294, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 294, + 460 + ], + "type": "text", + "content": "CNN-Transformer Block. We propose a hybrid CNN-Transformer block (CTB) as the basic processing unit. The core idea of CTB is to integrate high- and low-frequency modeling ability of CNN and Transformer [34] while keeping high dependency for input. As shown in Fig. 4 (a), an input feature is firstly split into two parts evenly, then Swin Transformer (SwinT) and gated dynamic CNN (GD-CNN) process them in parallel, finally two parts are fused by channel concatenation and a point-wise convolution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 463, + 294, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 294, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 294, + 510 + ], + "type": "text", + "content": "As depicted in Fig. 4 (b), SwinT is mainly powered by a shifted-window self-attention (SwinSA) and a feed-forward network (FFN) composed of a MLP with a " + }, + { + "bbox": [ + 55, + 463, + 294, + 510 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 463, + 294, + 510 + ], + "type": "text", + "content": " depth-wise convolution inserted. SwinSA can be formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 510, + 294, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 510, + 294, + 531 + ], + "spans": [ + { + "bbox": [ + 63, + 510, + 294, + 531 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {\\text {o u t}} = \\operatorname {S w i n S A} \\left(\\mathbf {F} _ {\\text {i n}}\\right) = \\left[ \\operatorname {s o f t m a t} \\left(\\mathbf {Q K} ^ {\\top} + \\mathbf {B}\\right) \\mathbf {V} \\right] \\mathbf {W}, \\tag {21}", + "image_path": "70fb029164a6e25018d21c4304f3a12b48df13531c5a2b825a41666a56082852.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 97, + 528, + 258, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 528, + 258, + 540 + ], + "spans": [ + { + "bbox": [ + 97, + 528, + 258, + 540 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {i n} \\mathbf {W} ^ {v},", + "image_path": "6d88497465d0e832c49d9a08ea2d48781595f1052eb8010aee000507425a1465.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{in} \\in \\mathbb{R}^{p^2 \\times d}" + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "content": " is the head at a " + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "inline_equation", + "content": "p \\times p" + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "content": " window, " + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\cdot)} \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "content": " denotes a learnable linear projection matrix, and " + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 55, + 544, + 294, + 605 + ], + "type": "text", + "content": " denote a learnable relative position encoding (RPE). As opposed to ChanCA in Eq. (20), SwinSA performs self-attention mechanism on spatial dimensions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 609, + 294, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 294, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 294, + 668 + ], + "type": "text", + "content": "As depicted in Fig. 4 (c), GD-CNN is a gated structure of normal convolutions (Convs) and an adaptive convolution (AdaConv). AdaConv is a simple implementation of transforming a group of static (learned) convolution kernels into dynamic one varying with the input, formulated as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 71, + 670, + 294, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 670, + 294, + 695 + ], + "spans": [ + { + "bbox": [ + 71, + 670, + 294, + 695 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} \\mathbf {F} & = \\text {R e s h a p e} (\\operatorname {C o n v} _ {3 \\times 3} (\\operatorname {R e L U} (\\operatorname {C o n v} _ {1 \\times 1} (\\mathbf {F} _ {i n})))) \\\\ \\mathbf {F} _ {\\text {o u t}} & = (\\mathbf {F W}) * \\mathbf {F} _ {\\text {i n}}, \\end{array} \\tag {22}", + "image_path": "a9b0bad5d533adacacd0dbda7e15df0351d61e82f12b945fa06f32c08ce0f7fe.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 700, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 700, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 700, + 294, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 700, + 294, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{in},\\mathbf{F}_{out}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 55, + 700, + 294, + 713 + ], + "type": "text", + "content": " denote the input and the out" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "content": "put, " + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{HW \\times n}" + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "content": " the input-dependent kernel coefficients, " + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{n \\times C \\times 3^2}" + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "content": " the kernel weights of " + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "inline_equation", + "content": "n \\times 3" + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "content": " depth-wise convolutions, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 313, + 72, + 553, + 157 + ], + "type": "text", + "content": " performs the convolution operator. Similar to attention mechanism, AdaConv is also input-dependent. Differently, AdaConv updates convolution weights from a group of learned kernel weights while attention produces attention weights by the similarity between features." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 168, + 394, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 168, + 394, + 182 + ], + "spans": [ + { + "bbox": [ + 314, + 168, + 394, + 182 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": "The proposed DIR " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": " in Sec. 4.2 is plugged in HQS- or ADMM-unrolling framework and then is end-to-end optimized using the proposed PL loss function in Sec. 4.1, leading to two proximal unrolling networks: HQS-ProxUnroll and ADMM-ProxUnroll. HQS/ADMM-ProxUnroll is composed of 6 iterations of " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta} \\circ \\mathrm{Prox}_f" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": ". Next, we conduct experiments to estimate them. We adopt 400 images from BSD500 [2] to generate 20,000 training samples using data augmentation techniques following [32, 35, 38-42, 47, 68]. Similar to the training of PnP image denoisers [63, 65, 66], the compressive ratio varies within [0.01, 0.50] and the resolution varies from " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": " pixels to " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": " pixels to cover as wider degradations as possible. The initial learning rate is " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": " and gradually reduced to " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": ". We estimate HQS-ProxUnroll and ADMM-ProxUnroll on Set11 and BSD68 benchmark datasets and real captured SPI data. Regarding CBSD68, all experiments are performed on the luminance channel of YCbCr space, similar to [32, 39-42, 62, 68]. Following [35, 47], the measurement (i.e., degradation) matrices " + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "inline_equation", + "content": "(\\mathbf{H}, \\mathbf{W})" + }, + { + "bbox": [ + 313, + 189, + 555, + 464 + ], + "type": "text", + "content": " are set to be floating-point and trainable for simulation experiments and are the reordered Hadamard matrices for real experiments. More experiment results are in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 470, + 485, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 485, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 485, + 481 + ], + "type": "text", + "content": "5.1. Results on Benchmark Datasets" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": "SPI reconstruction approaches are closely related to a great number of image compressed sensing approaches. The proposed HQS-ProxUnroll and ADMM-ProxUnroll are compared with previous approaches on benchmark datasets at five widely-used CRs " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\{0.01, 0.04, 0.10, 0.25, 0.50\\}" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ". Comparative approaches involve a single-stage network " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "(\\mathrm{CSNet}^{+}[39])" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ", unrolling (multi-stage) networks (ISTA" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Net}^{+}[61]" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ", OPINENet[62], AMP-Net [68], COAST [57], TransCS [38], MADUN [41], DGUNet[32], CSformer [56], OCTUF[42], SAUNet [47], CPP-Net [18], HATNet [35]), and PnP algorithms (PnP-DnCNN [37] and PnP-DRUNet [66]). Tab. 2 reports the reconstruction results of different approaches. Towards reconstruction accuracy, the proposed HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them outperform previous approaches on average. As visualized in Fig. 5, our HQS/ADMM-ProxUnroll can recover more image details. Towards the flexibility for CR, most previous approaches are separately trained for a specific CR and" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "416" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 64, + 60, + 159, + 155 + ], + "blocks": [ + { + "bbox": [ + 64, + 60, + 159, + 155 + ], + "lines": [ + { + "bbox": [ + 64, + 60, + 159, + 155 + ], + "spans": [ + { + "bbox": [ + 64, + 60, + 159, + 155 + ], + "type": "image", + "image_path": "2e3f02b984b6cb51036bbaeff554143eba504d9f0fe2f42b52d8d26fdf4b73a6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 90, + 156, + 135, + 174 + ], 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Average PSNR/SSIM of different methods on Set11 and CBSD68 datasets with different compressive ratios. The best and second best results are highlighted and underlined. Blank cells (-) means that there is not an available model at the compressive ratio." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 318, + 549, + 708 + ], + "lines": [ + { + "bbox": [ + 59, + 318, + 549, + 708 + ], + "spans": [ + { + "bbox": [ + 59, + 318, + 549, + 708 + ], + "type": "table", + "html": "
DatasetMethodFlexibilityCompressive Ratio (CR)Average
0.010.040.100.250.50
Set11ISTA-Net+ [61]Single17.42/0.402921.32/0.603726.64/0.808732.59/0.925438.11/0.970727.22/0.7423
CSNet+ [39]20.67/0.541124.83/0.748028.34/0.858033.34/0.938738.47/0.979629.13/0.8131
OPINE-Net+ [62]20.15/0.534025.69/0.792029.81/0.888434.86/0.950940.17/0.979732.63/0.9397
AMP-Net [68]20.21/0.542925.27/0.782129.43/0.888034.71/0.953240.66/0.982730.06/0.9679
TransCS [38]20.22/0.543125.41/0.788329.54/0.887735.06/0.954840.49/0.981529.42/0.8311
CSformer [56]21.58/0.607526.28/0.806229.79/0.888334.81/0.952740.73/0.982430.64/0.8474
MADUN [41]20.28/0.557225.71/0.804230.20/0.901635.76/0.960141.00/0.983730.59/0.8373
DGUNet+ [32]22.15/0.611326.82/0.823030.92/0.908836.18/0.961641.24/0.983731.46/0.8577
OCTUF+ [42]21.94/0.598926.54/0.815030.73/0.903636.10/0.960741.35/0.983831.33/0.8524
CPP-Net [18]22.19/0.613527.23/0.833731.27/0.913536.35/0.9631--
SAUNet [47]22.43/0.613427.80/0.835332.15/0.914737.11/0.962841.91/0.983832.28/0.8620
HATNet [35]22.54/0.616227.98/0.838232.26/0.918237.24/0.963442.05/0.983832.41/0.8640
COAST [57]Multiple10.45/0.2144*22.90/0.6971*28.69/0.861833.90/0.9399*38.94/0.974426.98/0.7375
PnP-DnCNN [37]Arbitrary21.68/0.568226.45/0.796929.57/0.871234.24/0.940239.78/0.973530.34/0.8300
PnP-DRUNet [66]21.75/0.573826.81/0.807430.16/0.886135.00/0.947640.54/0.976730.85/0.8383
HQS-ProxUnroll22.76/0.630028.23/0.845032.51/0.922537.33/0.963541.92/0.983732.55/0.8689
ADMM-ProxUnroll22.76/0.630728.30/0.845232.55/0.922637.35/0.963941.97/0.983832.59/0.8692
BSD68ISTA-Net+ [61]Single19.14/0.415822.17/0.548625.32/0.702229.36/0.852534.04/0.942426.01/0.6923
CSNet+ [39]22.21/0.510025.43/0.670627.91/0.793831.12/0.906036.76/0.963828.69/0.7688
OPINE-Net+ [62]22.11/0.514025.20/0.682527.82/0.804531.51/0.906136.35/0.966028.60/0.7746
AMP-Net [68]22.28/0.531925.27/0.693027.88/0.811831.80/0.915437.03/0.972228.85/0.7849
TransCS [38]22.28/0.531825.28/0.688127.86/0.808631.74/0.912136.81/0.969928.79/0.7821
CSformer [56]22.81/0.556625.73/0.695628.05/0.804531.82/0.910637.14/0.976629.11/0.7889
MADUN [41]22.08/0.524725.36/0.698528.18/0.821932.27/0.921937.23/0.973329.02/0.7880
DGUNet+ [32]22.13/0.521525.45/0.698628.13/0.816531.97/0.915837.04/0.971828.94/0.7848
OCTUF+ [42]22.78/0.541325.65/0.699928.28/0.817732.24/0.918537.41/0.972929.27/0.7900
CPP-Net [18]22.95/0.547525.81/0.706828.41/0.822732.25/0.9188--
SAUNet [47]23.11/0.546026.23/0.705029.25/0.825133.67/0.924339.28/0.975130.31/0.7951
COAST [57]Multiple12.08/0.2584*22.77/0.5953*26.28/0.742230.07/0.8703*34.74/0.949725.19/0.6832
PnP-DnCNN [37]Arbitrary22.27/0.522124.85/0.632727.22/0.765830.95/0.876236.47/0.960128.35/0.7514
PnP-DRUNet [66]22.81/0.530825.30/0.667027.79/0.785231.38/0.893136.86/0.962428.83/0.7677
HQS-ProxUnroll23.51/0.564526.52/0.719429.42/0.833233.76/0.928239.22/0.976030.49/0.8043
ADMM-ProxUnroll23.53/0.564926.54/0.720029.43/0.833433.77/0.928439.23/0.976130.50/0.8046
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MetricCPP-Net [18]SAUNet [47]HATNet [35]PnP-DRUNet [66]HQS/ADMM-ProxUnroll
MACs153.47143.05494.427175.10 (143.5×50)107.73 (17.95×6)
Params12.3110.5331.2832.643.90
Runtime0.410.350.600.650.27
", + "image_path": "a4c2369ceb9cc1475bd195bcc3cb1c8203a05b1b6a04ae41b057c40f13f530c1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 164, + 295, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 164, + 295, + 320 + ], + "spans": [ + { + "bbox": [ + 54, + 164, + 295, + 320 + ], + "type": "text", + "content": "thus cannot generalize to different CRs. COAST, trained on multiple CRs " + }, + { + "bbox": [ + 54, + 164, + 295, + 320 + ], + "type": "inline_equation", + "content": "\\{0.10, 0.20, 0.30, 0.40, 0.50\\}" + }, + { + "bbox": [ + 54, + 164, + 295, + 320 + ], + "type": "text", + "content": ", is flexible only for seen CRs, not for unseen CRs (e.g. 0.01). Our HQS/ADMM-ProxUnroll and PnP algorithms (PnP-DnCNN, PnP-DRUNet) can flexibly handle arbitrary CRs with a single model. Moreover, we compare HQS/ADMM-ProxUnroll with several competitive approaches in terms of multiply-accumulate operations (MACs), model parameters (Params), and runtime. As reported in Tab. 3, our HQS/ADMM-ProxUnroll achieves an all-around superiority over these approaches. Overall, our HQS/ADMM-ProxUnroll achieve not only SOTA performance and efficiency but also the same flexibility as PnP algorithms." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 327, + 224, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 224, + 339 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 224, + 339 + ], + "type": "text", + "content": "5.2. Results on Real Captured Data" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 342, + 296, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 342, + 296, + 559 + ], + "spans": [ + { + "bbox": [ + 56, + 342, + 296, + 559 + ], + "type": "text", + "content": "We estimate the proposed HQS/ADMM-ProxUnroll on real captured SPI data. Among the networks mentioned previously, only SAUNet [47] and HATNet [35] are practical for real SPI cameras. The remaining networks are developed under the assumption that images can be compressively sampled block by block, which is out of line with real SPI cameras. Hence, we compare HQS/ADMM-ProxUnroll with SAUNet, HATNet, and PnP-DRUNet. As shown in Fig. 6, PnP-DRUNet can recovers well on low frequencies (e.g., shapes and edges) instead of high frequencies (e.g., textures and details), agreeing with that Gaussian denoisers could smooth out rather than remove unknown artifacts [66]. HQS-ProxUnroll and ADMM-ProxUnroll are close and both of them have a better reconstruction ability than the competitors. In practice, SAUNet and HATNet need a separate model for a specific CR. A single model of HQS-ProxUnroll or ADMM-ProxUnroll is flexible enough for varying CRs, similar to PnP algorithms." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 564, + 149, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 564, + 149, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 564, + 149, + 577 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "content": "To offer an insight into ProxUnroll, we conduct ablation experiments on PL loss function (Sec. 4.1) and DIR (Sec. 4.2). ProxUnroll uses PL loss function to train DIR as approximation of the proximal operator of an explicit restoration regularizer in Eq. (16) to guarantee the fast convergence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "To demystify the influence of PL loss function, the convergence curves of different methods are depicted in Fig. 7. SAUNet and HATNet, both composed of 7 iterations, reconstruct images with twists and turns since their MSE loss function only ensure a satisfactory final result. This implies that their intermediate subnets cannot be interpreted" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 343, + 59, + 523, + 178 + ], + "blocks": [ + { + "bbox": [ + 343, + 59, + 523, + 178 + ], + "lines": [ + { + "bbox": [ + 343, + 59, + 523, + 178 + ], + "spans": [ + { + "bbox": [ + 343, + 59, + 523, + 178 + ], + "type": "image", + "image_path": "85a1d387c68057884f39d13d69a2b775be541f2c1c9874b976747da331d1b959.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 179, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 321, + 179, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 321, + 179, + 545, + 190 + ], + "type": "text", + "content": "Figure 7. Convergence curves of different unrolling methods." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 215, + 547, + 275 + ], + "blocks": [ + { + "bbox": [ + 313, + 191, + 554, + 214 + ], + "lines": [ + { + "bbox": [ + 313, + 191, + 554, + 214 + ], + "spans": [ + { + "bbox": [ + 313, + 191, + 554, + 214 + ], + "type": "text", + "content": "Table 4. Ablation experiments for different components of our deep image restorer (DIR) on Set11 dataset at " + }, + { + "bbox": [ + 313, + 191, + 554, + 214 + ], + "type": "inline_equation", + "content": "\\mathrm{{CR}} = {0.10}" + }, + { + "bbox": [ + 313, + 191, + 554, + 214 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 215, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 317, + 215, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 317, + 215, + 547, + 275 + ], + "type": "table", + "html": "
ChanCASwinTAdaConvPSNRMACsParamsRuntime
✓✓31.4294.853.100.22
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", + "image_path": "8addce41e725dc8f7b4fcac01958e77d28bb846831e00dea4bfa1a12bb9b0804.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 279, + 554, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 554, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 554, + 361 + ], + "type": "text", + "content": "as the proximal restoration operators and function more like black-box neural networks. Their lack of proximity also elucidates why prior unrolling networks require retraining when the degradation changes. With PL-based training, our HQS/ADMM-ProxUnroll achieves fast and stable convergence. By replacing PL loss with regular MSE loss during training, their convergence curves also become unstable." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "text", + "content": "To demystify the influence of key designs in DIR, we conduct ablation experiments as shown in Tab. 4. The proposed DIR is mainly powered by three components: ChanCA in memory block, SwinT and GD-CNN in CNN-Transformer block. ChanCA is used to adaptively propagate informative representations between adjacent iterations. The combination of SwinT and GD-CNN is to integrate the high- and low-frequency modeling ability while keeping high dependency for input. GD-CNN is powered by the proposed AdaConv. Clearly, ChanCA results in a " + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "inline_equation", + "content": "1.09\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "text", + "content": " improvement in PSNR with a slight increase in MACs, parameters, and runtime. By discarding SwinT and doubling the channel capability of GD-CNN, the entire network becomes a CNN, leading to a " + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "inline_equation", + "content": "0.26\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "text", + "content": " decrease in PSNR and an all-round increase in other metrics. Replacing AdaConv with one depth-wise convolution causes a " + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "inline_equation", + "content": "0.15\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 362, + 555, + 590 + ], + "type": "text", + "content": " decrease in PSNR but has minimal impact on MACs, parameters, and runtime. These results validate the effectiveness and efficiency of ChanCA, SwinT, and AdaConv." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 599, + 388, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 599, + 388, + 611 + ], + "spans": [ + { + "bbox": [ + 314, + 599, + 388, + 611 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 554, + 713 + ], + "type": "text", + "content": "We propose ProxUnroll to train any unrolled network to approximate the proximal operator of an explicit restoration regularizer using a proximal trajectory (PL) loss function. Besides, we propose an efficient CNN-Transformer architecture as deep image restorer (DIR) to arm ProxUnroll. Extensive experiments demonstrate that our ProxUnroll achieves not only SOTA performance and efficiency but also the same flexibility as PnP algorithms." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "418" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "spans": [ + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 279, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 279, + 294, + 323 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 279, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 61, + 279, + 294, + 323 + ], + "type": "text", + "content": "[1] Hemant K Aggarwal, Merry P Mani, and Mathews Jacob. 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IEEE Transactions on Image Processing, 30:1487-1500, 2020. 2, 3, 6, 7" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "421" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_content_list.json b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..024701873fc807e25ab3259222b2fa1160842a5f --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_content_list.json @@ -0,0 +1,1693 @@ +[ + { + "type": "text", + "text": "ProxyTransformation: Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding", + "text_level": 1, + "bbox": [ + 212, + 130, + 785, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qihang Peng", + "bbox": [ + 251, + 204, + 359, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Henry Zheng", + "bbox": [ + 447, + 204, + 555, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gao Huang*", + "bbox": [ + 643, + 204, + 745, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tsinghua University", + "bbox": [ + 419, + 238, + 584, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 309, + 326, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Embodied intelligence requires agents to interact with 3D environments in real time based on language instructions. A foundational task in this domain is ego-centric 3D visual grounding. However, the point clouds rendered from RGB-D images retain a large amount of redundant background data and inherent noise, both of which can interfere with the manifold structure of the target regions. Existing point cloud enhancement methods often require a tedious process to improve the manifold, which is not suitable for real-time tasks. We propose Proxy Transformation suitable for multimodal task to efficiently improve the point cloud manifold. Our method first leverages Deformable Point Clustering to identify the point cloud sub-manifolds in target regions. Then, we propose a Proxy Attention module that utilizes multimodal proxies to guide point cloud transformation. Built upon Proxy Attention, we design a submanifold transformation generation module where textual information globally guides translation vectors for different submanifolds, optimizing relative spatial relationships of target regions. Simultaneously, image information guides linear transformations within each submanifold, refining the local point cloud manifold of target regions. Extensive experiments demonstrate that Proxy Transformation significantly outperforms all existing methods, achieving an impressive improvement of $7.49\\%$ on easy targets and $4.60\\%$ on hard targets, while reducing the computational overhead of attention blocks by $40.6\\%$ . These results establish a new SOTA in ego-centric 3D visual grounding, showcasing the effectiveness and robustness of our approach.", + "bbox": [ + 88, + 340, + 485, + 781 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 806, + 220, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, the field of embodied AI has gained increasing attention, spurred by 3D visual grounding benchmarks [1, 5, 46] that have led to a surge of research [16, 20,", + "bbox": [ + 89, + 832, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "23, 46, 51, 57, 63]. The 3D visual grounding task, which involves locating target objects in real-world 3D environments based on natural language descriptions, is a core perception capability for embodied agents. This ability is crucial in enabling agents to interpret and interact with their surroundings via language, which supports applications in robotics and human-computer interaction.", + "bbox": [ + 511, + 310, + 906, + 415 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite these advancements, several significant challenges continue to hinder the performance of 3D visual grounding systems. One key challenge is the limited perception of embodied agents, who rely on ego-centric observations from multiple viewpoints, often lacking a holistic, scene-level understanding. While some methods attempt to improve scene-level perception using preconstructed 3D point clouds [16, 20, 23, 51, 57, 63], following previous 3D perception approaches [24, 50], they are impractical in real-world applications where comprehensive scene-level information is not readily available.", + "bbox": [ + 511, + 416, + 908, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In response, EmbodiedScan [46] was introduced, utilizing multi-view ego-centric RGB-D scans to enable models to process scenes directly from sparse, partial viewpoints. Previous methods[46, 65, 66, 70] decouple the encoding of RGB images and depth-reconstructed point clouds from ego-centric perspectives to extract both semantic and geometric information, which are then projected into 3D space using intrinsic and extrinsic matrices to form a semantically enriched point cloud for bounding box regression. While effective, these methods overlook the noise, such as errors in depth on non-lambertian surfaces, captured by the depth sensors [21, 22, 41] that causes suboptimal performance. Consequently, critical geometric details of corresponding target objects are lost, potentially distorting their original manifold and further compromising the model's grounding performance. Moreover, a substantial portion of the sampled points represents background regions, leading to a diminished density of foreground object points.", + "bbox": [ + 511, + 583, + 908, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In light of such critical challenges, previous works have focused on improving point cloud structure such as point cloud denoising [10, 11, 45] or completion methods [2, 26,", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 109, + 887, + 240, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24582", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b33eed93fe1c9240c69a03169c95d1f4471ed714f23876a99405a029b0bf579.jpg", + "image_caption": [ + "Figure 1. Illustration of our main idea and SOTA results. Ground truth and reference boxes are shown in green and purple respectively. Circular regions represent 3D areas where point cloud enhancement is applied. Black areas indicate regions that do not contribute to grounding performance and would increase unnecessary computation overhead. Traditional single-modality point cloud guidance would enhance these redundant areas. Red regions highlight areas where multimodal-guided point cloud enhancement is efficiently applied. Text modality, containing global relative position information among different critical objects, guides translation vectors for these region, while image modality, with local fine-grained semantic details, guides transformation matrices within each target regions. Our model achieves better results with reduced computation, about which details are in Tabs. 1 and 3." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 653, + 281 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d06c6cf044d438239d5d4c9b01dbbf95fc3e30d35cfbbf8a5a335eed5934cc2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 93, + 890, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "60, 61]. However, these methods often require extensive preprocessing the point cloud data, making them unsuitable for real-time ego-centric 3D visual grounding. Moreover, these methods rely on traditional statistical [43] methods or learning-based methods [31, 37] to enhance the point cloud structure in single modality, which cannot fully utilize the multimodal information available in our task.", + "bbox": [ + 88, + 416, + 480, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given the limitations of the above methods in ego-centric 3D visual grounding, we propose Proxy Transformation, which enhances point cloud manifolds before feature learning. This approach effectively reduces redundant computation in background point cloud regions and fully leverages the available multimodal information in current context to optimize the submanifolds of target regions. Notably, our method does not require pre-trained offline reconstruction of scene-level point clouds, making it better suited for real-time ego-centric 3D visual grounding task.", + "bbox": [ + 88, + 522, + 482, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, to generate transformations for point cloud submanifolds, reference points are first initialized as a uniform 3D grid for different scenes. Motivated by the success of deformable offsets in 2D domain [9, 52], a 3D offset network then takes the initial point cloud clusters centered on these reference points as input, producing offsets for each reference cluster center. In this way, these deformable cluster centers shift toward critical regions. Subsequently, they serve as cluster centers in a succeeding stage to select candidate submanifolds on the original point cloud for further transformations. For each submanifold, we employ a novel generalized attention mechanism, Proxy Attention, to learn the corresponding transformation matrixes and translation vectors. Specific proxy tokens can be selected based on task requirements (e.g. downsampling points after pooling,", + "bbox": [ + 89, + 674, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "multi-view image features or textual features).", + "bbox": [ + 511, + 416, + 818, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the context of online point cloud submanifold enhancement, we utilize text and image features as proxy tokens to guide submanifold transformations. In this approach, text information provides global positional relationships among different submanifolds, while image information offers local semantic details within each submanifold, as illustrated in Fig. 1. Leveraging these designs, our method supplies the subsequent 3D backbone with a higher-quality point cloud manifold, thereby enhancing the model's effectiveness and robustness.", + "bbox": [ + 511, + 431, + 906, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows. (1) We propose Proxy Transformation, enabling multimodal point cloud augmentation in the context of 3D visual grounding. (2) To obtain more desirable submanifolds for target regions, we design deformable point clustering, utilizing a 3D offset network to generate flexible and adaptive deformable clusters suited to diverse scenes. (3) We introduce a generalized proxy attention mechanism, allowing the selection of different proxy tokens based on task requirements, achieving linear computational complexity. (4) Our model significantly outperforms all existing methods, achieving an impressive improvement of $7.49\\%$ on easy targets and $4.60\\%$ on hard targets, while reducing the computational overhead of attention blocks by $40.6\\%$ , establishing a new SOTA in ego-centric 3D visual grounding.", + "bbox": [ + 511, + 585, + 908, + 811 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 511, + 828, + 663, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Visual Grounding. 3D visual grounding integrates multimodal data to localize target objects in 3D point clouds and it has gained significant attention in recent", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24583", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "years [12, 14, 47]. 3D visual grounding methods are divided into one-stage and two-stage architectures. One-stage approaches [15, 18, 27, 30] fuse textual and visual features to generate predictions in a single step, enabling end-to-end optimization and faster inference. However, they may struggle with complex scene layouts due to the absence of explicit object proposal refinement. In contrast, two-stage approaches [1, 4, 16, 20, 49, 58] follow a sequential process: they first utilize pre-trained object detectors [24, 49] to generate object proposals, which are subsequently matched with the linguistic input to identify the most likely target. This separation of detection and grounding allows for more precise alignment of visual and textual features, enhancing accuracy, particularly in complex scenes, but at the cost of increased computational overhead and inference time.", + "bbox": [ + 89, + 90, + 480, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent studies [4, 20, 23, 38, 40] have explored transformer-based structures for 3D visual grounding. BUTD-DETR [23] incorporates outputs from pre-trained detection networks, including predicted bounding boxes and their corresponding class labels, as additional inputs. Multi-View Transformer [20] projects the 3D scene into a multiview space to learn robust feature representations. MiKASA Transformer [4] integrates a scene-aware object encoder and an multi-key-anchor technique, enhancing object recognition accuracy and understanding of spatial relationships. In our paper, we focus on the more challenging one-stage methods with transformer modules.", + "bbox": [ + 89, + 319, + 480, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Point Cloud Enhancement. 3D point clouds provide rich geometric information and dense semantic details, playing a critical role in various domains [46, 54, 56, 60]. However, their inherent sparsity and irregularity limit model performance, and the deficiencies of existing sensors exacerbate issues such as high noise levels, sparsity, and incomplete structures in point clouds [32, 68]. These challenges make 3D point cloud augmentation a critical and challenging problem [35]. Traditional point cloud enhancement methods are often based on interpolation and optimization techniques [43], but their computational and memory overhead limits their applicability to large-scale datasets. Current deep learning-based point cloud augmentation methods can be broadly categorized into three main approaches: point cloud denoising, completion, and upsampling.", + "bbox": [ + 89, + 503, + 480, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Point cloud denoising [6, 10, 11, 45, 64] can eliminate noise in the point cloud while approximating and preserving the underlying surface geometry information and semantic details. Point cloud completion focuses mainly on completion for objects [7, 26, 60, 61] and scenes [48, 53, 55, 62]. And point cloud upsampling [13, 25, 28, 39, 59] aims to improve the resolution of point clouds while maintaining the integrity of the original geometric structure.", + "bbox": [ + 89, + 732, + 480, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, these methods are still confined to a single point cloud modality and are not well-suited for tasks with high real-time requirements. In the context of ego-centric", + "bbox": [ + 89, + 854, + 480, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D visual grounding, multimodal information is available. We leverage both textual and visual modalities as guidance to transform point cloud sub-manifolds. This approach enables simultaneous point cloud denoising and densification, providing higher-quality data for subsequent processing. Additionally, our method is designed with efficiency in mind, ensuring it meets the task's real-time requirements.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 511, + 212, + 648, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will introduce our network design. Firstly, we will give a brief introduction of the entire pipeline and what our module does in Sec. 3.1. Then, we introduce our effective yet efficient Proxy Attention in Sec. 3.2 and how deformable offsets are generated for reference points in Sec. 3.3. Finally, details of Proxy Transformation will be described in Sec. 3.4.", + "bbox": [ + 511, + 239, + 903, + 344 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Structure", + "text_level": 1, + "bbox": [ + 511, + 357, + 686, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We improve upon the previous SOTA in ego-centric 3D visual grounding [46]. Here we simply review the overall structure. First, the input RGB-D images from each view is transformed into a partial point cloud, which is then integrated into a holistic 3D point cloud $P \\in \\mathbb{R}^{N \\times 3}$ using global alignment matrices, thereby preserving geometric details. Next, multi-scale image and point features $\\{\\mathcal{F}_{\\mathrm{img}}^s\\}_{s=1}^S \\in \\mathbb{R}^{V \\times H_s \\times W_s \\times C_s}$ , $\\{\\mathcal{F}_{\\mathrm{point}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times C_s}$ , and text features $\\mathcal{T} \\in \\mathbb{R}^{L \\times C}$ are learned by respective backbone. Here, $N$ is the total number of points sampled from all perspective views $V$ , $S$ is the number of scale for the encoded feature maps and $L$ is the length of text sequence. The point features are then projected onto the 2D feature planes using intrinsic and extrinsic matrices to get semantic information. Further, they are concatenated to form sparse fusion features $\\{\\mathcal{F}_{\\mathrm{fusion}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times 2C_s}$ . Finally, they are fed into a DETR-like decoder and then finish 9-degree-of-freedom bounding box regression.", + "bbox": [ + 511, + 380, + 903, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, due to the large number of points in the depth-reconstructed point cloud and computational limitations, only a sparse subset (about $2\\%$ ) is sampled, resulting in a negative influence on the point cloud manifold. Due to the varying manifold structures in different local regions of scene-level point clouds, applying a global transformation to the entire point cloud is infeasible. To address this issue, we introduce Proxy Transformation to modify point cloud submanifolds with Proxy Attention, providing richer geometric information for subsequent feature learning.", + "bbox": [ + 511, + 655, + 905, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Proxy Attention", + "text_level": 1, + "bbox": [ + 511, + 818, + 671, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For simplicity, we use following formulation to represent Softmax attention:", + "bbox": [ + 511, + 840, + 903, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nO = \\sigma (Q K ^ {T}) V \\triangleq \\operatorname {A t t n} (Q, K, V) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 883, + 903, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24584", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f66e98551b6939bc3fe7c4ab248f9d50f6b5baef917da8560802ec209287109.jpg", + "image_caption": [ + "(a) Overall framework of Proxy Transformation" + ], + "image_footnote": [], + "bbox": [ + 117, + 85, + 880, + 313 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5d7d18f69d70dca8c2dbb9bac57eece4061aed3ebdf126cb272a3fa61cb095ef.jpg", + "image_caption": [ + "(b) Deformable Offset Network" + ], + "image_footnote": [], + "bbox": [ + 93, + 338, + 416, + 484 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7c3267cb4ec5f681e01698228b7659c04ba348839f9dcb7ae97356fd3593ef6a.jpg", + "image_caption": [ + "(c) Proxy Attention of Proxy Block", + "Figure 2. (a) shows the overall framework of Proxy Transformation. For simplicity, $\\dagger$ indicates that a 2D grid is used to represent the 3D spatial grid, with generated 3D offsets also expressed as 2D vectors for clarity. The Grid Prior spans the entire space, and we illustrate it with only four reference points for clearer visualization. In Proxy Transformation module, $\\mathcal{M}$ and $\\mathcal{T}$ are sets of transformation matrices and translation vectors for all clusters. (b) details the structure of our deformable offset network, and indicates the input and output shapes, where $M$ represents the number of clusters and $K$ represents the number of points per cluster. (c) illustrates the information flow in proxy attention. This module combines with FFN and skip connection in a standard Transformer architecture to form the Proxy Block." + ], + "image_footnote": [], + "bbox": [ + 437, + 338, + 874, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Q, K, V \\in \\mathbb{R}^{N \\times C}$ denote query, key and value matrices and $\\sigma(\\cdot)$ represents Softmax function. And our proxy attention consists of three components as follows.", + "bbox": [ + 89, + 619, + 482, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} O ^ {\\mathrm {P}} = \\operatorname {P r o x y A t t n} (Q, K, V, P) \\\\ = \\sigma (Q P ^ {T}) \\sigma (P K ^ {T}) V \\\\ = \\operatorname {A t t n} (Q, P, \\operatorname {A t t n} (P, K, V)). \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 672, + 482, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c} \\hline \\text {P r o x y C o m p r e s s i o n} \\\\ \\hline \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 259, + 732, + 408, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {P r o x y B r o a d c a s t}\n$$\n", + "text_format": "latex", + "bbox": [ + 258, + 758, + 356, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P\\in \\mathbb{R}^{n\\times C}$ is our proxy tokens.", + "bbox": [ + 89, + 777, + 346, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proxy Compression. Previous works [17, 33] have shown significant redundancy in query-key similarity computations within self-attention. To address this, we first compress the attention feature space using proxy tokens, whose number is substantially smaller than $N$ practically. This approach significantly alleviates computational overhead while preserving representational capacity, as shown", + "bbox": [ + 89, + 795, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Tab. 3. Specifically, we use proxy tokens as queries to compute similarity with initial keys, subsequently aggregating original values to obtain a compressed proxy value representation $V^{\\mathrm{P}}$ with reduced redundancy.", + "bbox": [ + 511, + 621, + 906, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proxy Broadcast. Subsequently, we treat proxy tokens $P$ and proxy values $V^{\\mathrm{P}}$ as keys and values for a second softmax operation with the original queries, allowing proxy features to be broadcast globally. This design preserves global contextual representation while reducing complexity to a linear scale. In practice, proxy tokens are selected based on the model's representational needs (e.g. downsampling points after pooting, multi-view image features or textual features). In these contexts, $n$ is much smaller than $N$ . Thus, this approach achieves generalized attention with a linear complexity of $\\mathcal{O}(Nnd)$ relative to the number of input features $N$ , balancing computational efficiency with high representational capacity as shown in Tab. 3.", + "bbox": [ + 511, + 684, + 906, + 881 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proxy Bias. Additionally, to compensate for the lack of po", + "bbox": [ + 511, + 885, + 903, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24585", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sitional information and the diversity of features, we introduce a novel proxy bias. To minimize parameter overhead, we merge two low-dimensional subspaces into a higher-dimensional space through a union operation of linear space. Specifically, we define two sets of low-dimensional learnable parameters, representing two subspaces $V_{c}$ and $V_{r}$ within feature space $V$ that satisfy $V = V_{c} \\cup V_{r}$ . After broadcasting these two parameter sets, they match the original feature dimensionality, enriching the feature space with positional information, and guiding Proxy Attention to focus on diverse regions.", + "bbox": [ + 89, + 90, + 483, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Deformable Point Clustering", + "text_level": 1, + "bbox": [ + 89, + 267, + 349, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To transform submanifolds, it is essential first to obtain suitable clusters. Motivated by [9, 19, 52, 71], we design a deformable clustering approach to identify optimal cluster center locations, capturing the desired target submanifolds.", + "bbox": [ + 89, + 287, + 483, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Grid Prior. As mentioned in Sec. 3.1, the randomly sampled sparse point cloud has already lost a significant amount of geometric information. To compensate for this loss, we first generate a 3D uniform grid and use its grid centers as reference points for the initial clustering:", + "bbox": [ + 89, + 349, + 483, + 425 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {Q} \\triangleq \\left\\{q _ {(i, j, k)} \\right\\} _ {i, j, k = 1} ^ {x _ {s}, y _ {s}, z _ {s}} \\sim U \\left[ \\mathcal {C} _ {\\min }, \\mathcal {C} _ {\\max } \\right], \\\\ \\mathcal {N} _ {(i, j, k)} \\triangleq \\{p _ {l} ^ {i, j, k} \\} _ {l = 1} ^ {m} = \\gamma (\\mathcal {Q} _ {(i, j, k)}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 436, + 480, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where reference points $\\mathcal{Q}$ are also the initial cluster centers. $U$ is a uniform distribution. $\\mathcal{C}$ is the 3D coordinate of points. $p_l^{i,j,k}$ is a specific point in corresponding cluster $\\mathcal{N}_{(i,j,k)}$ and $\\gamma$ is clustering function, e.g. ball query or kNN. $N$ and $m$ are respective numbers of point cloud and local cluster.", + "bbox": [ + 89, + 488, + 483, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To simplify, we regard $\\mathcal{N}_{(i,j,k)}$ as $\\mathcal{N}_t$ , where $t \\in [0, n-1]$ , where $n = x_s \\times y_s \\times z_s$ and $x_s, y_s, z_s$ are predefined as hyperparameter. Experimentally, we find that this approach does not affect performance, but provides greater stability in the training process compared to stochastic sampling.", + "bbox": [ + 89, + 564, + 483, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Deformable Offsets. To increase the diversity of submanifold selection, an offset network outputs the offset values for reference points respectively, allowing them to shift toward more relevant surrounding regions based on the current submanifold structure. Considering that each reference point covers a local $s$ ball region ( $s$ is the largest value for offset), the offset network is able to percept local features to learn reasonable offsets. In addition, we also provide global information to further enhance offset generation.", + "bbox": [ + 89, + 640, + 483, + 776 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {q} _ {t} = q _ {t} + \\Gamma_ {\\mathrm {o f f s e t}} (\\mathcal {N} _ {t}), \\\\ \\hat {\\mathcal {N}} _ {t} = \\gamma (\\hat {q} _ {t}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 787, + 480, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Gamma_{\\mathrm{offset}}(\\cdot)$ is our offset network. $\\hat{q}_t \\in \\hat{\\mathcal{Q}}$ is a new cluster center and $\\hat{\\mathcal{N}}_t$ is a new neighborhood.", + "bbox": [ + 89, + 839, + 482, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, for $\\mathcal{N}_t$ , we first concatenate the relative coordinates of sub-points with respect to the center and their", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "global coordinates. It's then passed through $1 \\times 1$ Conv2D and ReLU activation to extract point-wise features. We apply average pooling to obtain high-dimensional local-global features for each cluster, which are then fed into another $1 \\times 1$ convolution to generate the final offsets, as shown in Fig. 2. Notably, we set the bias of the $1 \\times 1$ convolution to zero to avoid introducing additional perturbations. Finally, we discard some clusters according to a predefined drop ratio $\\beta$ with a certain sampling method (e.g. random sampling or FPS), allowing us to obtain a more diverse neighborhood based on the new cluster centers.", + "bbox": [ + 511, + 90, + 906, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Proxy Transformation", + "text_level": 1, + "bbox": [ + 511, + 265, + 720, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each submanifold, we leverage the Proxy Block to learn a unique manifold transformation. Any arbitrary transformation in 3D space can be decomposed into a linear transformation and a translation. Then, these transformations are applied to each deformable cluster. Details about the transformation generation module are described below.", + "bbox": [ + 511, + 287, + 905, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proxy Block. Following the standard block design in Transformer architectures [42], we developed a Proxy Block based on proxy attention, aimed at cross-modal learning for subsequent manifold transformations. We denote $P_0$ and $F_0$ as a set of proxy tokens and cluster features. And $F_0$ is extracted by a simplified PointNet [34]. Then a transformer block comprises of proxy attention module and feedforward network:", + "bbox": [ + 511, + 378, + 906, + 497 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF = F _ {0} + B ^ {\\mathrm {P}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 506, + 903, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ = F W _ {Q}, K = F W _ {K}, V = F W _ {V}, P = P _ {0} W _ {P}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 532, + 903, + 547 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO ^ {\\mathrm {P}} = F + \\operatorname {P r o x y A t t n} (Q, K, V, P), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 551, + 903, + 569 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO = O ^ {\\mathrm {P}} + \\operatorname {F F N} \\left(O ^ {\\mathrm {P}}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 571, + 903, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $B^{\\mathrm{P}}$ is our proxy bias introduced in Sec. 3.2. $W_{Q}, W_{K}, W_{V}$ are projections for query, key and value. ProxyAttn(·) is a proxy attention module in Eq. (2). FFN(·) is a position-wise feedforward network.", + "bbox": [ + 511, + 594, + 905, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following sections, for simplicity, we use", + "bbox": [ + 532, + 655, + 846, + 670 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO = \\operatorname {P r o x y B l o c k} (F, P), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 680, + 903, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to represent the basic proxy block (Eqs. (5) to (8)).", + "bbox": [ + 511, + 704, + 849, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text Guided Translation. In ego-centric 3D visual grounding, the input text contains global relative positional information between the target object and other reference objects, while the remaining parts naturally correspond to background point clouds. Therefore, text features can effectively guide the model in learning translation vectors that establish spatial relationships between various submanifolds, thereby enhancing the global relational information embedded within the point cloud structure. Specifically, we leverage text features as proxies within the Proxy Block, allowing it to generate text-guided point cloud features that ultimately yield accurate and context-aware final translation", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24586", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "vectors for more precise grounding results.", + "bbox": [ + 89, + 90, + 375, + 106 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {T}\\right), l = 0,.., L - 1, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 116, + 480, + 133 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nT = F ^ {L} U _ {\\text {t e x t}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 235, + 143, + 480, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $P_{T}$ are text features $\\mathcal{F}_{\\mathrm{text}}\\in \\mathbb{R}^{S\\times C}$ . $L$ is number of layers and $U_{\\mathrm{text}}$ is a fully connected layer to generate final translation vectors $T\\in \\mathbb{R}^{n\\times 3}$ .", + "bbox": [ + 89, + 167, + 482, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image Guided Transformation. The input multi-view image contains rich fine-grained semantic information, compensating for the contextual loss caused by point cloud downsampling. Multi-view images provide pose information of the target object from various perspectives, guiding the model to learn internal transformations of each subpoints relative to the cluster center. Thus, we use pooled image features as proxies in the Proxy Block to generate reshaped image-guided point cloud features, which in turn yield the linear transformations for each submanifold:", + "bbox": [ + 89, + 214, + 483, + 364 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {I}\\right), l = 0,.., L - 1, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 376, + 482, + 393 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nM = F ^ {L} U _ {\\text {i m a g e}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 402, + 480, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $P_{I}\\in \\mathbb{R}^{V\\times C}$ are pooled image features from an additional attention pooling layer. And $L$ is the number of layers and $U_{\\mathrm{image}}$ is a fully connected layer to generate final transformation matrices $M\\in \\mathbb{R}^{n\\times 3\\times 3}$ .", + "bbox": [ + 89, + 426, + 482, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Submanifold Reshape. Once the transformation matrix, containing fine-grained semantic information from the image, and the translation vectors, encompassing precise global relative information from the text, are obtained, we can apply a Proxy Transformation to each submanifold and finally get a diverse enhanced point cloud manifold. To represent this process, we use concise set operations:", + "bbox": [ + 89, + 488, + 483, + 594 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {P}} = \\mathcal {M} \\odot \\mathcal {P} \\oplus \\mathcal {T}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 604, + 480, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{M}$ and $\\mathcal{T}$ are sets of transformation matrices and translation vectors for all clusters. $\\mathcal{P}$ is a union set of submanifolds of different neighborhoods $\\{\\mathcal{N}_i\\}_{i = 1}^n$ , namely a subset of original point cloud. $\\odot$ and $\\oplus$ represent elementwise multiplication and addition for sets.", + "bbox": [ + 89, + 633, + 482, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Equivalently, for a specific submanifold:", + "bbox": [ + 109, + 709, + 380, + 724 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {P} _ {i} = P _ {i} M _ {i} ^ {T} + T _ {i}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 734, + 480, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $P_{i}\\in \\mathcal{P}\\cap \\mathbb{R}^{m\\times 3}$ represent sub-points in $\\mathcal{N}_i$ . $M_{i}\\in$ $\\mathcal{M}\\cap \\mathbb{R}^{3\\times 3}$ and $T_{i}\\in \\mathcal{T}\\cap \\mathbb{R}^{3}$ are the specific transformation matrix and translation vector for this submanifold.", + "bbox": [ + 89, + 763, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, we replace the corresponding parts of the original point cloud with transformed submanifolds to obtain final enhanced point cloud, consisting of rich diversity in manifold structure, which is then fed into 3D backbone during training, enabling efficient multimodal-guided point cloud manifold enhancements.", + "bbox": [ + 89, + 810, + 483, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 513, + 90, + 645, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Benchmark. The EmbodiedScan dataset [46] used in our experiments is a large-scale, multi-modal, egocentric resource tailored for comprehensive 3D scene understanding. It comprises 5,185 scene scans from widely-used datasets like ScanNet [8], 3RScan [44], and Matterport3D [3]. This diverse dataset offers a rich foundation for 3D visual grounding, covering a broader range of scenes than previous datasets. The training set includes 801,711 language prompts, while the validation set contains 168,322 prompts, making EmbodiedScan notably larger and more challenging, thus providing a rigorous benchmark for egocentric 3D visual grounding tasks.", + "bbox": [ + 511, + 114, + 903, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Settings. Due to limited resources, we train on the official mini dataset. Despite this, our model outperforms the official baseline trained on the full training set, as shown in Tab. 1. For analysis experiments in Sec. 4.2, we also use the mini training and validation sets available through the official EmbodiedScan release [46].", + "bbox": [ + 511, + 296, + 903, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our reported accuracy uses the official IoU metric, focusing on cases where IoU exceeds $25\\%$ and $50\\%$ . We also assess model performance on both \"Easy\" and \"Hard\" scenes, where a \"Hard\" scene contains three or more target objects of the same category. The \"View-Dependent\" and \"View-Independent\" metrics further test the model's spatial reasoning by evaluating performance with and without perspective-specific descriptions.", + "bbox": [ + 511, + 387, + 905, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. This work builds upon the strong baseline from EmbodiedScan for ego-centric 3D visual grounding. We applied several techniques to enhance the original baseline. First, we replace the RoBERTa language encoder [29] with the CLIP encoder [36] to achieve superior alignment between language and vision. Additionally, we incorporate Class-Balanced Grouping and Sampling (CBGS) [67] during pretraining to address data imbalance and enhance detection accuracy across rare and common object categories. We follow EmbodiedScan's approach by using pretrained visual encoders. Finally, we also adopt text augmented by LLM to provide richer semantic context when training, proposed by [65]. Moreover, our Proxy Transformation is trained using the AdamW optimizer with a learning rate of 5e-4, weight decay of 5e-4, and a batch size of 48. Training spans 12 epochs, with the learning rate reduced by 0.1 at epochs 8 and 11.", + "bbox": [ + 511, + 507, + 905, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Main Results", + "text_level": 1, + "bbox": [ + 511, + 772, + 651, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the 3D visual grounding performance of our proposed method, Proxy Transformation, with results presented in Tab. 1, comparing it against established SOTA methods from the dataset benchmark. In addition, the upper methods with $\\dagger$ are trained on the full dataset, while the lower methods are trained on a mini dataset, approximately $20\\%$ of the full dataset.", + "bbox": [ + 511, + 794, + 903, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24587", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a266bfe2a283caea7627c001d9844239e7e3580c77387db31d735a487800e7be.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodEasy AP25Hard AP25Indep Dep AP25Overall AP25Easy AP50Hard AP50Indep Dep AP50Overall AP50
ScanRefer† [5]13.789.1213.4410.7712.85---
BUTD-DETR† [23]23.1218.2322.4720.9822.14---
L3Det† [69]24.0118.3423.5921.2223.07---
EmbodiedScan†39.8231.0240.3038.4839.1018.7914.9318.03
EmbodiedScan [46]33.8730.4933.5533.6133.5914.5812.4113.92
DenseG [65]40.1734.3838.7940.1839.7018.5215.8817.47
ProxyTransformation41.6634.3841.5740.8141.0819.4314.0918.65
", + "bbox": [ + 145, + 88, + 854, + 241 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 1, Proxy Transformation achieves a notable $7.49\\%$ and $4.60\\%$ improvement over the previous strongest baseline, EmbodiedScan, on the Overall@0.25 and Overall@0.50. Although only trained on the mini dataset, our method even surpasses the baseline trained on the full dataset. Through deformable point clustering, our model focuses on the most crucial target regions in the scene, reducing the extra computation overhead caused by redundant point clouds and improving efficiency. Additionally, a grid prior preserves essential original spatial information, mitigating early training instability. Recognizing that text information provides global positional relationships among different submanifolds and image information offers local semantic details within each submanifold, we designed generalized proxy attention to guide local transformations of the selected point cloud submanifolds. These transformations optimize local point cloud structures for each submanifold, ultimately providing higher-quality data for subsequent feature extraction and fusion.", + "bbox": [ + 88, + 333, + 480, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In summary, Proxy Transformation consistently outperforms the previous state-of-the-art across multiple evaluation metrics, including easy and hard samples as well as view-independent and view-dependent tasks. These consistent improvements across diverse metrics highlight not only the robustness and generalizability of our approach for 3D visual grounding tasks but also its adaptability to complex scenes and dynamic environments, making it an effective solution for advancing multimodal grounding capabilities in real-world embodied AI applications.", + "bbox": [ + 89, + 622, + 482, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Analysis Experiments", + "text_level": 1, + "bbox": [ + 89, + 786, + 294, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation on Proposed Modules. We conducted ablation studies on each module to verify their effectiveness as shown in Tab. 2. To ensure fair comparisons, the baseline is enhanced with several modules described in the implementation details. First, we introduce Proxy Transformation without deformable point clustering, resulting in a", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f3881558a7730385f3f9cc1068231a414cec31d31cec9550e91167845bbaef0f.jpg", + "table_caption": [ + "Table 1. Main Results on the official validation set. The table displays accuracy performance considering instances where IoU exceeds $25\\%$ and $50\\%$ under different circumstances as mentioned in Sec. 4. 'Indep' and 'Dep' mean the targets are view-independent and view-dependent. And $\\dagger$ denotes that models are trained on full train dataset. Although our model is trained on mini train dataset (approximately $20\\%$ of the full data), but it still surpasses previous methods trained on the full train dataset." + ], + "table_footnote": [], + "table_body": "
Grid PriorOffsetsPTEasyHardOverall
37.0530.6036.53
✓40.3932.6039.76
✓✓40.5932.1839.91
✓✓✓41.6634.3841.08
", + "bbox": [ + 521, + 330, + 898, + 422 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b53803725ee41e2906334e46ed83a84c17b85e4e821528b68a57d464ab11820a.jpg", + "table_caption": [ + "Table 2. Ablation of Proposed Modules. 'PT' represents 'Proxy Transformation'. The reported values are mAP for predictions greater than $25\\%$ IoU." + ], + "table_footnote": [], + "table_body": "
AttnFLOPs#ParamsEasyHardOverall
Vanilla8.36G2.52M40.7133.6540.14
Proxy4.97G2.71M41.6634.3841.08
", + "bbox": [ + 524, + 492, + 893, + 554 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/55ca8e69c429e181002f1ad5ce943278af20567722a552c4fafe487fe725fd6f.jpg", + "table_caption": [ + "Table 3. Ablation on Proxy Attention. Here, we compare the vanilla self-attention block with our Proxy Block. The FLOPs and parameters are computed over 3 transformer blocks with cluster features as input. We use a grid size of 12 and a drop radio of 0.6. The reported values are mAP for predictions greater than $25\\%$ IoU." + ], + "table_footnote": [], + "table_body": "
Grid SizeEasyHardOverall
w/o40.5932.1839.91
1040.9432.8140.29
1241.6634.3841.08
1441.1134.2840.56
", + "bbox": [ + 576, + 650, + 844, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation on the size of Grid Prior. The reported values are mAP for predictions greater than $25\\%$ IoU.", + "bbox": [ + 511, + 752, + 905, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "substantial improvement of $3.23\\%$ , which demonstrates the effectiveness and necessity of our multimodal point cloud enhancement. Then, we add deformable offsets, yielding an additional improvement on easy samples, indicating that offsets effectively guide cluster centers toward target regions. Finally, we incorporate grid prior, which improves", + "bbox": [ + 511, + 809, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24588", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8de7be3e9c60e296a5e84c3eb8ed8f3d25f5ca81b327d4cb11d2a974ceac7d37.jpg", + "image_caption": [ + "Figure 3. Visualization of ground truth and predictions. Ground truth boxes are shown in green, baseline in red, and ProxyTransformation's predictions in violet." + ], + "image_footnote": [], + "bbox": [ + 153, + 88, + 859, + 345 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/67f50c3b96060e4b47da9e54602eca39cee7a17b9b4fe1535d27a6e1074bddf1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LayersEasyHardOverall
141.6034.0740.99
241.5731.9740.79
341.6634.3841.08
441.7231.5540.90
", + "bbox": [ + 161, + 404, + 411, + 496 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation on the number of Proxy Layers. The reported values are mAP for predictions greater than $25\\%$ IoU.", + "bbox": [ + 89, + 507, + 482, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training stability and achieves an increase of $2.20\\%$ on hard samples. This result shows that the grid prior mitigates the randomness of offsets in the early stages of training, preserving essential scene information for the model.", + "bbox": [ + 89, + 561, + 482, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on Proxy Attention. We validate the effectiveness and efficiency of proxy attention by comparing the vanilla attention block with the proxy block. The input cluster features are aligned across both blocks. As discussed in Sec. 3.2, the number of proxy tokens is significantly smaller than the input sequence length. This reduction in proxy tokens compresses redundancy within the attention module, enhancing computational efficiency, which aligns with our experiment results. As shown in Tab. 3, our approach achieves higher performance than vanilla attention, while reducing the computation overhead by $40.6\\%$ .", + "bbox": [ + 89, + 625, + 482, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on Main Hyperparameters. Then, we ablate several hyperparameters in deformable point clustering and proxy transformation. As shown in Tab. 4, the size of the grid prior also influences performance by reducing instability during the early training stages, which can result from the randomness of the initial transformations. As shown in Tab. 5, we conduct several experiments to determine the", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "optimal layers of our proxy attention block for efficient learning. Based on these findings, we selected the optimal hyperparameters for our experiments. Moreover, further ablation studies are given in the supplementary material.", + "bbox": [ + 511, + 407, + 906, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative Results and Discussion", + "text_level": 1, + "bbox": [ + 511, + 488, + 815, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With our deformable point clustering and Proxy Transformation, the point cloud structure in target regions is optimized, providing higher-quality data for subsequent feature learning and fusion. As shown in Fig. 3, reference objects in these regions are small and difficult to distinguish, but with the enhanced manifold structure, our model effectively captures the relationships between target and reference objects, achieving improved grounding performance.", + "bbox": [ + 511, + 513, + 906, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 659, + 633, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose Proxy Transformation, a real-time multimodal point cloud enhancement model, to address issues of geometric loss and unexpected noise in 3D points within ego-centric 3D visual grounding. This approach yields a high-quality point cloud structure for feature learning. Extensive experiments show that our model not only outperforms all existing methods but also improves the computational efficiency of attention modules, setting a new SOTA on the EmbodiedScan benchmark. These results demonstrate the effectiveness and robustness of using multimodal information for real-time point cloud enhancement in ego-centric 3D visual grounding, offering fresh insights for advancing embodied AI and enabling human-computer interaction in real-world environments.", + "bbox": [ + 511, + 689, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24589", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The work is supported in part by the National Natural Science Foundation of China under Grant U24B2017, and Beijing Natural Science Foundation under Grant QY24257.", + "bbox": [ + 89, + 114, + 483, + 161 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 172, + 187, + 188 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. 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Densegrounding: Improving dense language-vision semantics for ego-centric 3d visual grounding. In The Thirteenth International Conference on Learning Representations, 2025. 1" + ], + "bbox": [ + 91, + 92, + 480, + 900 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[67] Benjin Zhu, Zhengkai Jiang, Xiangxin Zhou, Zeming Li, and Gang Yu. Class-balanced grouping and sampling for point cloud 3d object detection. arXiv preprint arXiv:1908.09492, 2019. 6", + "[68] Chen Zhu, Jianyu Yang, Zhanpeng Shao, and Chunping Liu. Vision based hand gesture recognition using 3d shape context. IEEE/CAA Journal of Automatica Sinica, 8(9):1600-1613, 2019. 3", + "[69] Chenming Zhu, Wenwei Zhang, Tai Wang, Xihui Liu, and Kai Chen. Object2scene: Putting objects in context for open-vocabulary 3d detection, 2023. 7", + "[70] Chenming Zhu, Tai Wang, Wenwei Zhang, Kai Chen, and Xihui Liu. Scanreason: Empowering 3d visual grounding with reasoning capabilities, 2024. 1", + "[71] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. In ICLR, 2021. 5" + ], + "bbox": [ + 516, + 92, + 903, + 332 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "24592", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_model.json b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4f52f72c2e5df650fc86b4e220b8d629dc65eec0 --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_model.json @@ -0,0 +1,2455 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.213, + 0.131, + 0.787, + 0.177 + ], + "angle": 0, + "content": "ProxyTransformation: Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.205, + 0.361, + 0.223 + ], + "angle": 0, + "content": "Qihang Peng" + }, + { + "type": "text", + "bbox": [ + 0.448, + 0.205, + 0.557, + 0.223 + ], + "angle": 0, + "content": "Henry Zheng" + }, + { + "type": "text", + "bbox": [ + 0.645, + 0.205, + 0.746, + 0.223 + ], + "angle": 0, + "content": "Gao Huang*" + }, + { + "type": "text", + "bbox": [ + 0.42, + 0.239, + 0.585, + 0.258 + ], + "angle": 0, + "content": "Tsinghua University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.31, + 0.327, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.342, + 0.486, + 0.782 + ], + "angle": 0, + "content": "Embodied intelligence requires agents to interact with 3D environments in real time based on language instructions. A foundational task in this domain is ego-centric 3D visual grounding. However, the point clouds rendered from RGB-D images retain a large amount of redundant background data and inherent noise, both of which can interfere with the manifold structure of the target regions. Existing point cloud enhancement methods often require a tedious process to improve the manifold, which is not suitable for real-time tasks. We propose Proxy Transformation suitable for multimodal task to efficiently improve the point cloud manifold. Our method first leverages Deformable Point Clustering to identify the point cloud sub-manifolds in target regions. Then, we propose a Proxy Attention module that utilizes multimodal proxies to guide point cloud transformation. Built upon Proxy Attention, we design a submanifold transformation generation module where textual information globally guides translation vectors for different submanifolds, optimizing relative spatial relationships of target regions. Simultaneously, image information guides linear transformations within each submanifold, refining the local point cloud manifold of target regions. Extensive experiments demonstrate that Proxy Transformation significantly outperforms all existing methods, achieving an impressive improvement of \\(7.49\\%\\) on easy targets and \\(4.60\\%\\) on hard targets, while reducing the computational overhead of attention blocks by \\(40.6\\%\\). These results establish a new SOTA in ego-centric 3D visual grounding, showcasing the effectiveness and robustness of our approach." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.808, + 0.222, + 0.823 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.833, + 0.484, + 0.88 + ], + "angle": 0, + "content": "In recent years, the field of embodied AI has gained increasing attention, spurred by 3D visual grounding benchmarks [1, 5, 46] that have led to a surge of research [16, 20," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.311, + 0.907, + 0.416 + ], + "angle": 0, + "content": "23, 46, 51, 57, 63]. The 3D visual grounding task, which involves locating target objects in real-world 3D environments based on natural language descriptions, is a core perception capability for embodied agents. This ability is crucial in enabling agents to interpret and interact with their surroundings via language, which supports applications in robotics and human-computer interaction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.417, + 0.909, + 0.583 + ], + "angle": 0, + "content": "Despite these advancements, several significant challenges continue to hinder the performance of 3D visual grounding systems. One key challenge is the limited perception of embodied agents, who rely on ego-centric observations from multiple viewpoints, often lacking a holistic, scene-level understanding. While some methods attempt to improve scene-level perception using preconstructed 3D point clouds [16, 20, 23, 51, 57, 63], following previous 3D perception approaches [24, 50], they are impractical in real-world applications where comprehensive scene-level information is not readily available." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.909, + 0.856 + ], + "angle": 0, + "content": "In response, EmbodiedScan [46] was introduced, utilizing multi-view ego-centric RGB-D scans to enable models to process scenes directly from sparse, partial viewpoints. Previous methods[46, 65, 66, 70] decouple the encoding of RGB images and depth-reconstructed point clouds from ego-centric perspectives to extract both semantic and geometric information, which are then projected into 3D space using intrinsic and extrinsic matrices to form a semantically enriched point cloud for bounding box regression. While effective, these methods overlook the noise, such as errors in depth on non-lambertian surfaces, captured by the depth sensors [21, 22, 41] that causes suboptimal performance. Consequently, critical geometric details of corresponding target objects are lost, potentially distorting their original manifold and further compromising the model's grounding performance. Moreover, a substantial portion of the sampled points represents background regions, leading to a diminished density of foreground object points." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In light of such critical challenges, previous works have focused on improving point cloud structure such as point cloud denoising [10, 11, 45] or completion methods [2, 26," + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.241, + 0.901 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24582" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.655, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.094, + 0.891, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.292, + 0.907, + 0.39 + ], + "angle": 0, + "content": "Figure 1. Illustration of our main idea and SOTA results. Ground truth and reference boxes are shown in green and purple respectively. Circular regions represent 3D areas where point cloud enhancement is applied. Black areas indicate regions that do not contribute to grounding performance and would increase unnecessary computation overhead. Traditional single-modality point cloud guidance would enhance these redundant areas. Red regions highlight areas where multimodal-guided point cloud enhancement is efficiently applied. Text modality, containing global relative position information among different critical objects, guides translation vectors for these region, while image modality, with local fine-grained semantic details, guides transformation matrices within each target regions. Our model achieves better results with reduced computation, about which details are in Tabs. 1 and 3." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.417, + 0.482, + 0.522 + ], + "angle": 0, + "content": "60, 61]. However, these methods often require extensive preprocessing the point cloud data, making them unsuitable for real-time ego-centric 3D visual grounding. Moreover, these methods rely on traditional statistical [43] methods or learning-based methods [31, 37] to enhance the point cloud structure in single modality, which cannot fully utilize the multimodal information available in our task." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.523, + 0.483, + 0.674 + ], + "angle": 0, + "content": "Given the limitations of the above methods in ego-centric 3D visual grounding, we propose Proxy Transformation, which enhances point cloud manifolds before feature learning. This approach effectively reduces redundant computation in background point cloud regions and fully leverages the available multimodal information in current context to optimize the submanifolds of target regions. Notably, our method does not require pre-trained offline reconstruction of scene-level point clouds, making it better suited for real-time ego-centric 3D visual grounding task." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Specifically, to generate transformations for point cloud submanifolds, reference points are first initialized as a uniform 3D grid for different scenes. Motivated by the success of deformable offsets in 2D domain [9, 52], a 3D offset network then takes the initial point cloud clusters centered on these reference points as input, producing offsets for each reference cluster center. In this way, these deformable cluster centers shift toward critical regions. Subsequently, they serve as cluster centers in a succeeding stage to select candidate submanifolds on the original point cloud for further transformations. For each submanifold, we employ a novel generalized attention mechanism, Proxy Attention, to learn the corresponding transformation matrixes and translation vectors. Specific proxy tokens can be selected based on task requirements (e.g. downsampling points after pooling," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.417, + 0.82, + 0.432 + ], + "angle": 0, + "content": "multi-view image features or textual features)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.907, + 0.583 + ], + "angle": 0, + "content": "In the context of online point cloud submanifold enhancement, we utilize text and image features as proxy tokens to guide submanifold transformations. In this approach, text information provides global positional relationships among different submanifolds, while image information offers local semantic details within each submanifold, as illustrated in Fig. 1. Leveraging these designs, our method supplies the subsequent 3D backbone with a higher-quality point cloud manifold, thereby enhancing the model's effectiveness and robustness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.586, + 0.909, + 0.813 + ], + "angle": 0, + "content": "In summary, our contributions are as follows. (1) We propose Proxy Transformation, enabling multimodal point cloud augmentation in the context of 3D visual grounding. (2) To obtain more desirable submanifolds for target regions, we design deformable point clustering, utilizing a 3D offset network to generate flexible and adaptive deformable clusters suited to diverse scenes. (3) We introduce a generalized proxy attention mechanism, allowing the selection of different proxy tokens based on task requirements, achieving linear computational complexity. (4) Our model significantly outperforms all existing methods, achieving an impressive improvement of \\(7.49\\%\\) on easy targets and \\(4.60\\%\\) on hard targets, while reducing the computational overhead of attention blocks by \\(40.6\\%\\), establishing a new SOTA in ego-centric 3D visual grounding." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.829, + 0.665, + 0.845 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "3D Visual Grounding. 3D visual grounding integrates multimodal data to localize target objects in 3D point clouds and it has gained significant attention in recent" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24583" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.318 + ], + "angle": 0, + "content": "years [12, 14, 47]. 3D visual grounding methods are divided into one-stage and two-stage architectures. One-stage approaches [15, 18, 27, 30] fuse textual and visual features to generate predictions in a single step, enabling end-to-end optimization and faster inference. However, they may struggle with complex scene layouts due to the absence of explicit object proposal refinement. In contrast, two-stage approaches [1, 4, 16, 20, 49, 58] follow a sequential process: they first utilize pre-trained object detectors [24, 49] to generate object proposals, which are subsequently matched with the linguistic input to identify the most likely target. This separation of detection and grounding allows for more precise alignment of visual and textual features, enhancing accuracy, particularly in complex scenes, but at the cost of increased computational overhead and inference time." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.32, + 0.482, + 0.501 + ], + "angle": 0, + "content": "Recent studies [4, 20, 23, 38, 40] have explored transformer-based structures for 3D visual grounding. BUTD-DETR [23] incorporates outputs from pre-trained detection networks, including predicted bounding boxes and their corresponding class labels, as additional inputs. Multi-View Transformer [20] projects the 3D scene into a multiview space to learn robust feature representations. MiKASA Transformer [4] integrates a scene-aware object encoder and an multi-key-anchor technique, enhancing object recognition accuracy and understanding of spatial relationships. In our paper, we focus on the more challenging one-stage methods with transformer modules." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.504, + 0.482, + 0.732 + ], + "angle": 0, + "content": "Point Cloud Enhancement. 3D point clouds provide rich geometric information and dense semantic details, playing a critical role in various domains [46, 54, 56, 60]. However, their inherent sparsity and irregularity limit model performance, and the deficiencies of existing sensors exacerbate issues such as high noise levels, sparsity, and incomplete structures in point clouds [32, 68]. These challenges make 3D point cloud augmentation a critical and challenging problem [35]. Traditional point cloud enhancement methods are often based on interpolation and optimization techniques [43], but their computational and memory overhead limits their applicability to large-scale datasets. Current deep learning-based point cloud augmentation methods can be broadly categorized into three main approaches: point cloud denoising, completion, and upsampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.733, + 0.482, + 0.853 + ], + "angle": 0, + "content": "Point cloud denoising [6, 10, 11, 45, 64] can eliminate noise in the point cloud while approximating and preserving the underlying surface geometry information and semantic details. Point cloud completion focuses mainly on completion for objects [7, 26, 60, 61] and scenes [48, 53, 55, 62]. And point cloud upsampling [13, 25, 28, 39, 59] aims to improve the resolution of point clouds while maintaining the integrity of the original geometric structure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.482, + 0.901 + ], + "angle": 0, + "content": "However, these methods are still confined to a single point cloud modality and are not well-suited for tasks with high real-time requirements. In the context of ego-centric" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "3D visual grounding, multimodal information is available. We leverage both textual and visual modalities as guidance to transform point cloud sub-manifolds. This approach enables simultaneous point cloud denoising and densification, providing higher-quality data for subsequent processing. Additionally, our method is designed with efficiency in mind, ensuring it meets the task's real-time requirements." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.213, + 0.649, + 0.231 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.24, + 0.905, + 0.345 + ], + "angle": 0, + "content": "In this section, we will introduce our network design. Firstly, we will give a brief introduction of the entire pipeline and what our module does in Sec. 3.1. Then, we introduce our effective yet efficient Proxy Attention in Sec. 3.2 and how deformable offsets are generated for reference points in Sec. 3.3. Finally, details of Proxy Transformation will be described in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.358, + 0.687, + 0.373 + ], + "angle": 0, + "content": "3.1. Overall Structure" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.905, + 0.655 + ], + "angle": 0, + "content": "We improve upon the previous SOTA in ego-centric 3D visual grounding [46]. Here we simply review the overall structure. First, the input RGB-D images from each view is transformed into a partial point cloud, which is then integrated into a holistic 3D point cloud \\( P \\in \\mathbb{R}^{N \\times 3} \\) using global alignment matrices, thereby preserving geometric details. Next, multi-scale image and point features \\( \\{\\mathcal{F}_{\\mathrm{img}}^s\\}_{s=1}^S \\in \\mathbb{R}^{V \\times H_s \\times W_s \\times C_s} \\), \\( \\{\\mathcal{F}_{\\mathrm{point}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times C_s} \\), and text features \\( \\mathcal{T} \\in \\mathbb{R}^{L \\times C} \\) are learned by respective backbone. Here, \\( N \\) is the total number of points sampled from all perspective views \\( V \\), \\( S \\) is the number of scale for the encoded feature maps and \\( L \\) is the length of text sequence. The point features are then projected onto the 2D feature planes using intrinsic and extrinsic matrices to get semantic information. Further, they are concatenated to form sparse fusion features \\( \\{\\mathcal{F}_{\\mathrm{fusion}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times 2C_s} \\). Finally, they are fed into a DETR-like decoder and then finish 9-degree-of-freedom bounding box regression." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.656, + 0.906, + 0.807 + ], + "angle": 0, + "content": "However, due to the large number of points in the depth-reconstructed point cloud and computational limitations, only a sparse subset (about \\(2\\%\\)) is sampled, resulting in a negative influence on the point cloud manifold. Due to the varying manifold structures in different local regions of scene-level point clouds, applying a global transformation to the entire point cloud is infeasible. To address this issue, we introduce Proxy Transformation to modify point cloud submanifolds with Proxy Attention, providing richer geometric information for subsequent feature learning." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.673, + 0.835 + ], + "angle": 0, + "content": "3.2. Proxy Attention" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.842, + 0.905, + 0.871 + ], + "angle": 0, + "content": "For simplicity, we use following formulation to represent Softmax attention:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.884, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\nO = \\sigma (Q K ^ {T}) V \\triangleq \\operatorname {A t t n} (Q, K, V) \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24584" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.087, + 0.881, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.319, + 0.568, + 0.33 + ], + "angle": 0, + "content": "(a) Overall framework of Proxy Transformation" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.339, + 0.418, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.488, + 0.293, + 0.498 + ], + "angle": 0, + "content": "(b) Deformable Offset Network" + }, + { + "type": "image", + "bbox": [ + 0.439, + 0.339, + 0.875, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.488, + 0.743, + 0.498 + ], + "angle": 0, + "content": "(c) Proxy Attention of Proxy Block" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.511, + 0.907, + 0.596 + ], + "angle": 0, + "content": "Figure 2. (a) shows the overall framework of Proxy Transformation. For simplicity, \\(\\dagger\\) indicates that a 2D grid is used to represent the 3D spatial grid, with generated 3D offsets also expressed as 2D vectors for clarity. The Grid Prior spans the entire space, and we illustrate it with only four reference points for clearer visualization. In Proxy Transformation module, \\(\\mathcal{M}\\) and \\(\\mathcal{T}\\) are sets of transformation matrices and translation vectors for all clusters. (b) details the structure of our deformable offset network, and indicates the input and output shapes, where \\(M\\) represents the number of clusters and \\(K\\) represents the number of points per cluster. (c) illustrates the information flow in proxy attention. This module combines with FFN and skip connection in a standard Transformer architecture to form the Proxy Block." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.483, + 0.667 + ], + "angle": 0, + "content": "where \\(Q, K, V \\in \\mathbb{R}^{N \\times C}\\) denote query, key and value matrices and \\(\\sigma(\\cdot)\\) represents Softmax function. And our proxy attention consists of three components as follows." + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.674, + 0.483, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} O ^ {\\mathrm {P}} = \\operatorname {P r o x y A t t n} (Q, K, V, P) \\\\ = \\sigma (Q P ^ {T}) \\sigma (P K ^ {T}) V \\\\ = \\operatorname {A t t n} (Q, P, \\operatorname {A t t n} (P, K, V)). \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.26, + 0.733, + 0.409, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c} \\hline \\text {P r o x y C o m p r e s s i o n} \\\\ \\hline \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.259, + 0.759, + 0.357, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\text {P r o x y B r o a d c a s t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.779, + 0.347, + 0.795 + ], + "angle": 0, + "content": "where \\(P\\in \\mathbb{R}^{n\\times C}\\) is our proxy tokens." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Proxy Compression. Previous works [17, 33] have shown significant redundancy in query-key similarity computations within self-attention. To address this, we first compress the attention feature space using proxy tokens, whose number is substantially smaller than \\(N\\) practically. This approach significantly alleviates computational overhead while preserving representational capacity, as shown" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.907, + 0.681 + ], + "angle": 0, + "content": "in Tab. 3. Specifically, we use proxy tokens as queries to compute similarity with initial keys, subsequently aggregating original values to obtain a compressed proxy value representation \\( V^{\\mathrm{P}} \\) with reduced redundancy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.685, + 0.907, + 0.882 + ], + "angle": 0, + "content": "Proxy Broadcast. Subsequently, we treat proxy tokens \\( P \\) and proxy values \\( V^{\\mathrm{P}} \\) as keys and values for a second softmax operation with the original queries, allowing proxy features to be broadcast globally. This design preserves global contextual representation while reducing complexity to a linear scale. In practice, proxy tokens are selected based on the model's representational needs (e.g. downsampling points after pooting, multi-view image features or textual features). In these contexts, \\( n \\) is much smaller than \\( N \\). Thus, this approach achieves generalized attention with a linear complexity of \\( \\mathcal{O}(Nnd) \\) relative to the number of input features \\( N \\), balancing computational efficiency with high representational capacity as shown in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Proxy Bias. Additionally, to compensate for the lack of po" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24585" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.258 + ], + "angle": 0, + "content": "sitional information and the diversity of features, we introduce a novel proxy bias. To minimize parameter overhead, we merge two low-dimensional subspaces into a higher-dimensional space through a union operation of linear space. Specifically, we define two sets of low-dimensional learnable parameters, representing two subspaces \\( V_{c} \\) and \\( V_{r} \\) within feature space \\( V \\) that satisfy \\( V = V_{c} \\cup V_{r} \\). After broadcasting these two parameter sets, they match the original feature dimensionality, enriching the feature space with positional information, and guiding Proxy Attention to focus on diverse regions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.268, + 0.35, + 0.284 + ], + "angle": 0, + "content": "3.3. Deformable Point Clustering" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.484, + 0.35 + ], + "angle": 0, + "content": "To transform submanifolds, it is essential first to obtain suitable clusters. Motivated by [9, 19, 52, 71], we design a deformable clustering approach to identify optimal cluster center locations, capturing the desired target submanifolds." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.351, + 0.484, + 0.426 + ], + "angle": 0, + "content": "Grid Prior. As mentioned in Sec. 3.1, the randomly sampled sparse point cloud has already lost a significant amount of geometric information. To compensate for this loss, we first generate a 3D uniform grid and use its grid centers as reference points for the initial clustering:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.438, + 0.482, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {Q} \\triangleq \\left\\{q _ {(i, j, k)} \\right\\} _ {i, j, k = 1} ^ {x _ {s}, y _ {s}, z _ {s}} \\sim U \\left[ \\mathcal {C} _ {\\min }, \\mathcal {C} _ {\\max } \\right], \\\\ \\mathcal {N} _ {(i, j, k)} \\triangleq \\{p _ {l} ^ {i, j, k} \\} _ {l = 1} ^ {m} = \\gamma (\\mathcal {Q} _ {(i, j, k)}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.564 + ], + "angle": 0, + "content": "where reference points \\(\\mathcal{Q}\\) are also the initial cluster centers. \\(U\\) is a uniform distribution. \\(\\mathcal{C}\\) is the 3D coordinate of points. \\(p_l^{i,j,k}\\) is a specific point in corresponding cluster \\(\\mathcal{N}_{(i,j,k)}\\) and \\(\\gamma\\) is clustering function, e.g. ball query or kNN. \\(N\\) and \\(m\\) are respective numbers of point cloud and local cluster." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.484, + 0.64 + ], + "angle": 0, + "content": "To simplify, we regard \\(\\mathcal{N}_{(i,j,k)}\\) as \\(\\mathcal{N}_t\\), where \\(t \\in [0, n-1]\\), where \\(n = x_s \\times y_s \\times z_s\\) and \\(x_s, y_s, z_s\\) are predefined as hyperparameter. Experimentally, we find that this approach does not affect performance, but provides greater stability in the training process compared to stochastic sampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.641, + 0.484, + 0.777 + ], + "angle": 0, + "content": "Deformable Offsets. To increase the diversity of submanifold selection, an offset network outputs the offset values for reference points respectively, allowing them to shift toward more relevant surrounding regions based on the current submanifold structure. Considering that each reference point covers a local \\(s\\) ball region (\\(s\\) is the largest value for offset), the offset network is able to percept local features to learn reasonable offsets. In addition, we also provide global information to further enhance offset generation." + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.789, + 0.482, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {q} _ {t} = q _ {t} + \\Gamma_ {\\mathrm {o f f s e t}} (\\mathcal {N} _ {t}), \\\\ \\hat {\\mathcal {N}} _ {t} = \\gamma (\\hat {q} _ {t}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.871 + ], + "angle": 0, + "content": "where \\(\\Gamma_{\\mathrm{offset}}(\\cdot)\\) is our offset network. \\(\\hat{q}_t \\in \\hat{\\mathcal{Q}}\\) is a new cluster center and \\(\\hat{\\mathcal{N}}_t\\) is a new neighborhood." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Specifically, for \\(\\mathcal{N}_t\\), we first concatenate the relative coordinates of sub-points with respect to the center and their" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.258 + ], + "angle": 0, + "content": "global coordinates. It's then passed through \\(1 \\times 1\\) Conv2D and ReLU activation to extract point-wise features. We apply average pooling to obtain high-dimensional local-global features for each cluster, which are then fed into another \\(1 \\times 1\\) convolution to generate the final offsets, as shown in Fig. 2. Notably, we set the bias of the \\(1 \\times 1\\) convolution to zero to avoid introducing additional perturbations. Finally, we discard some clusters according to a predefined drop ratio \\(\\beta\\) with a certain sampling method (e.g. random sampling or FPS), allowing us to obtain a more diverse neighborhood based on the new cluster centers." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.266, + 0.722, + 0.281 + ], + "angle": 0, + "content": "3.4. Proxy Transformation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.906, + 0.378 + ], + "angle": 0, + "content": "For each submanifold, we leverage the Proxy Block to learn a unique manifold transformation. Any arbitrary transformation in 3D space can be decomposed into a linear transformation and a translation. Then, these transformations are applied to each deformable cluster. Details about the transformation generation module are described below." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.379, + 0.907, + 0.498 + ], + "angle": 0, + "content": "Proxy Block. Following the standard block design in Transformer architectures [42], we developed a Proxy Block based on proxy attention, aimed at cross-modal learning for subsequent manifold transformations. We denote \\( P_0 \\) and \\( F_0 \\) as a set of proxy tokens and cluster features. And \\( F_0 \\) is extracted by a simplified PointNet [34]. Then a transformer block comprises of proxy attention module and feedforward network:" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.507, + 0.905, + 0.524 + ], + "angle": 0, + "content": "\\[\nF = F _ {0} + B ^ {\\mathrm {P}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.533, + 0.905, + 0.549 + ], + "angle": 0, + "content": "\\[\nQ = F W _ {Q}, K = F W _ {K}, V = F W _ {V}, P = P _ {0} W _ {P}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.552, + 0.905, + 0.57 + ], + "angle": 0, + "content": "\\[\nO ^ {\\mathrm {P}} = F + \\operatorname {P r o x y A t t n} (Q, K, V, P), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.573, + 0.905, + 0.59 + ], + "angle": 0, + "content": "\\[\nO = O ^ {\\mathrm {P}} + \\operatorname {F F N} \\left(O ^ {\\mathrm {P}}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.595, + 0.906, + 0.656 + ], + "angle": 0, + "content": "where \\( B^{\\mathrm{P}} \\) is our proxy bias introduced in Sec. 3.2. \\( W_{Q}, W_{K}, W_{V} \\) are projections for query, key and value. ProxyAttn(·) is a proxy attention module in Eq. (2). FFN(·) is a position-wise feedforward network." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.656, + 0.848, + 0.671 + ], + "angle": 0, + "content": "In the following sections, for simplicity, we use" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.681, + 0.905, + 0.696 + ], + "angle": 0, + "content": "\\[\nO = \\operatorname {P r o x y B l o c k} (F, P), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.705, + 0.85, + 0.719 + ], + "angle": 0, + "content": "to represent the basic proxy block (Eqs. (5) to (8))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Text Guided Translation. In ego-centric 3D visual grounding, the input text contains global relative positional information between the target object and other reference objects, while the remaining parts naturally correspond to background point clouds. Therefore, text features can effectively guide the model in learning translation vectors that establish spatial relationships between various submanifolds, thereby enhancing the global relational information embedded within the point cloud structure. Specifically, we leverage text features as proxies within the Proxy Block, allowing it to generate text-guided point cloud features that ultimately yield accurate and context-aware final translation" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24586" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.376, + 0.107 + ], + "angle": 0, + "content": "vectors for more precise grounding results." + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.117, + 0.482, + 0.135 + ], + "angle": 0, + "content": "\\[\nF ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {T}\\right), l = 0,.., L - 1, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.236, + 0.145, + 0.482, + 0.163 + ], + "angle": 0, + "content": "\\[\nT = F ^ {L} U _ {\\text {t e x t}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.169, + 0.483, + 0.214 + ], + "angle": 0, + "content": "where \\(P_{T}\\) are text features \\(\\mathcal{F}_{\\mathrm{text}}\\in \\mathbb{R}^{S\\times C}\\). \\(L\\) is number of layers and \\(U_{\\mathrm{text}}\\) is a fully connected layer to generate final translation vectors \\(T\\in \\mathbb{R}^{n\\times 3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.215, + 0.484, + 0.365 + ], + "angle": 0, + "content": "Image Guided Transformation. The input multi-view image contains rich fine-grained semantic information, compensating for the contextual loss caused by point cloud downsampling. Multi-view images provide pose information of the target object from various perspectives, guiding the model to learn internal transformations of each subpoints relative to the cluster center. Thus, we use pooled image features as proxies in the Proxy Block to generate reshaped image-guided point cloud features, which in turn yield the linear transformations for each submanifold:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.377, + 0.483, + 0.395 + ], + "angle": 0, + "content": "\\[\nF ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {I}\\right), l = 0,.., L - 1, \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.23, + 0.404, + 0.482, + 0.423 + ], + "angle": 0, + "content": "\\[\nM = F ^ {L} U _ {\\text {i m a g e}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.483, + 0.488 + ], + "angle": 0, + "content": "where \\(P_{I}\\in \\mathbb{R}^{V\\times C}\\) are pooled image features from an additional attention pooling layer. And \\(L\\) is the number of layers and \\(U_{\\mathrm{image}}\\) is a fully connected layer to generate final transformation matrices \\(M\\in \\mathbb{R}^{n\\times 3\\times 3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.595 + ], + "angle": 0, + "content": "Submanifold Reshape. Once the transformation matrix, containing fine-grained semantic information from the image, and the translation vectors, encompassing precise global relative information from the text, are obtained, we can apply a Proxy Transformation to each submanifold and finally get a diverse enhanced point cloud manifold. To represent this process, we use concise set operations:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.605, + 0.482, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {P}} = \\mathcal {M} \\odot \\mathcal {P} \\oplus \\mathcal {T}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.634, + 0.483, + 0.709 + ], + "angle": 0, + "content": "where \\(\\mathcal{M}\\) and \\(\\mathcal{T}\\) are sets of transformation matrices and translation vectors for all clusters. \\(\\mathcal{P}\\) is a union set of submanifolds of different neighborhoods \\(\\{\\mathcal{N}_i\\}_{i = 1}^n\\) , namely a subset of original point cloud. \\(\\odot\\) and \\(\\oplus\\) represent elementwise multiplication and addition for sets." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.71, + 0.381, + 0.725 + ], + "angle": 0, + "content": "Equivalently, for a specific submanifold:" + }, + { + "type": "equation", + "bbox": [ + 0.224, + 0.735, + 0.482, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\hat {P} _ {i} = P _ {i} M _ {i} ^ {T} + T _ {i}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.809 + ], + "angle": 0, + "content": "where \\(P_{i}\\in \\mathcal{P}\\cap \\mathbb{R}^{m\\times 3}\\) represent sub-points in \\(\\mathcal{N}_i\\). \\(M_{i}\\in\\) \\(\\mathcal{M}\\cap \\mathbb{R}^{3\\times 3}\\) and \\(T_{i}\\in \\mathcal{T}\\cap \\mathbb{R}^{3}\\) are the specific transformation matrix and translation vector for this submanifold." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.9 + ], + "angle": 0, + "content": "Finally, we replace the corresponding parts of the original point cloud with transformed submanifolds to obtain final enhanced point cloud, consisting of rich diversity in manifold structure, which is then fed into 3D backbone during training, enabling efficient multimodal-guided point cloud manifold enhancements." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.646, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.905, + 0.297 + ], + "angle": 0, + "content": "Dataset and Benchmark. The EmbodiedScan dataset [46] used in our experiments is a large-scale, multi-modal, egocentric resource tailored for comprehensive 3D scene understanding. It comprises 5,185 scene scans from widely-used datasets like ScanNet [8], 3RScan [44], and Matterport3D [3]. This diverse dataset offers a rich foundation for 3D visual grounding, covering a broader range of scenes than previous datasets. The training set includes 801,711 language prompts, while the validation set contains 168,322 prompts, making EmbodiedScan notably larger and more challenging, thus providing a rigorous benchmark for egocentric 3D visual grounding tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.297, + 0.905, + 0.387 + ], + "angle": 0, + "content": "Experimental Settings. Due to limited resources, we train on the official mini dataset. Despite this, our model outperforms the official baseline trained on the full training set, as shown in Tab. 1. For analysis experiments in Sec. 4.2, we also use the mini training and validation sets available through the official EmbodiedScan release [46]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.388, + 0.906, + 0.508 + ], + "angle": 0, + "content": "Our reported accuracy uses the official IoU metric, focusing on cases where IoU exceeds \\(25\\%\\) and \\(50\\%\\). We also assess model performance on both \"Easy\" and \"Hard\" scenes, where a \"Hard\" scene contains three or more target objects of the same category. The \"View-Dependent\" and \"View-Independent\" metrics further test the model's spatial reasoning by evaluating performance with and without perspective-specific descriptions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.906, + 0.765 + ], + "angle": 0, + "content": "Implementation Details. This work builds upon the strong baseline from EmbodiedScan for ego-centric 3D visual grounding. We applied several techniques to enhance the original baseline. First, we replace the RoBERTa language encoder [29] with the CLIP encoder [36] to achieve superior alignment between language and vision. Additionally, we incorporate Class-Balanced Grouping and Sampling (CBGS) [67] during pretraining to address data imbalance and enhance detection accuracy across rare and common object categories. We follow EmbodiedScan's approach by using pretrained visual encoders. Finally, we also adopt text augmented by LLM to provide richer semantic context when training, proposed by [65]. Moreover, our Proxy Transformation is trained using the AdamW optimizer with a learning rate of 5e-4, weight decay of 5e-4, and a batch size of 48. Training spans 12 epochs, with the learning rate reduced by 0.1 at epochs 8 and 11." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.773, + 0.653, + 0.789 + ], + "angle": 0, + "content": "4.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.905, + 0.9 + ], + "angle": 0, + "content": "We evaluate the 3D visual grounding performance of our proposed method, Proxy Transformation, with results presented in Tab. 1, comparing it against established SOTA methods from the dataset benchmark. In addition, the upper methods with \\(\\dagger\\) are trained on the full dataset, while the lower methods are trained on a mini dataset, approximately \\(20\\%\\) of the full dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24587" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.146, + 0.089, + 0.855, + 0.242 + ], + "angle": 0, + "content": "
MethodEasy AP25Hard AP25Indep Dep AP25Overall AP25Easy AP50Hard AP50Indep Dep AP50Overall AP50
ScanRefer† [5]13.789.1213.4410.7712.85---
BUTD-DETR† [23]23.1218.2322.4720.9822.14---
L3Det† [69]24.0118.3423.5921.2223.07---
EmbodiedScan†39.8231.0240.3038.4839.1018.7914.9318.03
EmbodiedScan [46]33.8730.4933.5533.6133.5914.5812.4113.92
DenseG [65]40.1734.3838.7940.1839.7018.5215.8817.47
ProxyTransformation41.6634.3841.5740.8141.0819.4314.0918.65
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.253, + 0.908, + 0.309 + ], + "angle": 0, + "content": "Table 1. Main Results on the official validation set. The table displays accuracy performance considering instances where IoU exceeds \\(25\\%\\) and \\(50\\%\\) under different circumstances as mentioned in Sec. 4. 'Indep' and 'Dep' mean the targets are view-independent and view-dependent. And \\(\\dagger\\) denotes that models are trained on full train dataset. Although our model is trained on mini train dataset (approximately \\(20\\%\\) of the full data), but it still surpasses previous methods trained on the full train dataset." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.334, + 0.482, + 0.621 + ], + "angle": 0, + "content": "As shown in Tab. 1, Proxy Transformation achieves a notable \\(7.49\\%\\) and \\(4.60\\%\\) improvement over the previous strongest baseline, EmbodiedScan, on the Overall@0.25 and Overall@0.50. Although only trained on the mini dataset, our method even surpasses the baseline trained on the full dataset. Through deformable point clustering, our model focuses on the most crucial target regions in the scene, reducing the extra computation overhead caused by redundant point clouds and improving efficiency. Additionally, a grid prior preserves essential original spatial information, mitigating early training instability. Recognizing that text information provides global positional relationships among different submanifolds and image information offers local semantic details within each submanifold, we designed generalized proxy attention to guide local transformations of the selected point cloud submanifolds. These transformations optimize local point cloud structures for each submanifold, ultimately providing higher-quality data for subsequent feature extraction and fusion." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.623, + 0.483, + 0.775 + ], + "angle": 0, + "content": "In summary, Proxy Transformation consistently outperforms the previous state-of-the-art across multiple evaluation metrics, including easy and hard samples as well as view-independent and view-dependent tasks. These consistent improvements across diverse metrics highlight not only the robustness and generalizability of our approach for 3D visual grounding tasks but also its adaptability to complex scenes and dynamic environments, making it an effective solution for advancing multimodal grounding capabilities in real-world embodied AI applications." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.787, + 0.295, + 0.803 + ], + "angle": 0, + "content": "4.2. Analysis Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Ablation on Proposed Modules. We conducted ablation studies on each module to verify their effectiveness as shown in Tab. 2. To ensure fair comparisons, the baseline is enhanced with several modules described in the implementation details. First, we introduce Proxy Transformation without deformable point clustering, resulting in a" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.332, + 0.9, + 0.424 + ], + "angle": 0, + "content": "
Grid PriorOffsetsPTEasyHardOverall
37.0530.6036.53
✓40.3932.6039.76
✓✓40.5932.1839.91
✓✓✓41.6634.3841.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.435, + 0.907, + 0.478 + ], + "angle": 0, + "content": "Table 2. Ablation of Proposed Modules. 'PT' represents 'Proxy Transformation'. The reported values are mAP for predictions greater than \\(25\\%\\) IoU." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.493, + 0.895, + 0.555 + ], + "angle": 0, + "content": "
AttnFLOPs#ParamsEasyHardOverall
Vanilla8.36G2.52M40.7133.6540.14
Proxy4.97G2.71M41.6634.3841.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.565, + 0.907, + 0.636 + ], + "angle": 0, + "content": "Table 3. Ablation on Proxy Attention. Here, we compare the vanilla self-attention block with our Proxy Block. The FLOPs and parameters are computed over 3 transformer blocks with cluster features as input. We use a grid size of 12 and a drop radio of 0.6. The reported values are mAP for predictions greater than \\(25\\%\\) IoU." + }, + { + "type": "table", + "bbox": [ + 0.577, + 0.651, + 0.845, + 0.743 + ], + "angle": 0, + "content": "
Grid SizeEasyHardOverall
w/o40.5932.1839.91
1040.9432.8140.29
1241.6634.3841.08
1441.1134.2840.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.753, + 0.906, + 0.782 + ], + "angle": 0, + "content": "Table 4. Ablation on the size of Grid Prior. The reported values are mAP for predictions greater than \\(25\\%\\) IoU." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.903 + ], + "angle": 0, + "content": "substantial improvement of \\(3.23\\%\\), which demonstrates the effectiveness and necessity of our multimodal point cloud enhancement. Then, we add deformable offsets, yielding an additional improvement on easy samples, indicating that offsets effectively guide cluster centers toward target regions. Finally, we incorporate grid prior, which improves" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24588" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.154, + 0.089, + 0.86, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.36, + 0.908, + 0.389 + ], + "angle": 0, + "content": "Figure 3. Visualization of ground truth and predictions. Ground truth boxes are shown in green, baseline in red, and ProxyTransformation's predictions in violet." + }, + { + "type": "table", + "bbox": [ + 0.163, + 0.405, + 0.413, + 0.497 + ], + "angle": 0, + "content": "
LayersEasyHardOverall
141.6034.0740.99
241.5731.9740.79
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" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.508, + 0.483, + 0.537 + ], + "angle": 0, + "content": "Table 5. Ablation on the number of Proxy Layers. The reported values are mAP for predictions greater than \\(25\\%\\) IoU." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.562, + 0.483, + 0.623 + ], + "angle": 0, + "content": "training stability and achieves an increase of \\(2.20\\%\\) on hard samples. This result shows that the grid prior mitigates the randomness of offsets in the early stages of training, preserving essential scene information for the model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.626, + 0.483, + 0.792 + ], + "angle": 0, + "content": "Ablation on Proxy Attention. We validate the effectiveness and efficiency of proxy attention by comparing the vanilla attention block with the proxy block. The input cluster features are aligned across both blocks. As discussed in Sec. 3.2, the number of proxy tokens is significantly smaller than the input sequence length. This reduction in proxy tokens compresses redundancy within the attention module, enhancing computational efficiency, which aligns with our experiment results. As shown in Tab. 3, our approach achieves higher performance than vanilla attention, while reducing the computation overhead by \\(40.6\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Ablation on Main Hyperparameters. Then, we ablate several hyperparameters in deformable point clustering and proxy transformation. As shown in Tab. 4, the size of the grid prior also influences performance by reducing instability during the early training stages, which can result from the randomness of the initial transformations. As shown in Tab. 5, we conduct several experiments to determine the" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.409, + 0.907, + 0.469 + ], + "angle": 0, + "content": "optimal layers of our proxy attention block for efficient learning. Based on these findings, we selected the optimal hyperparameters for our experiments. Moreover, further ablation studies are given in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.489, + 0.816, + 0.505 + ], + "angle": 0, + "content": "4.3. Qualitative Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.907, + 0.636 + ], + "angle": 0, + "content": "With our deformable point clustering and Proxy Transformation, the point cloud structure in target regions is optimized, providing higher-quality data for subsequent feature learning and fusion. As shown in Fig. 3, reference objects in these regions are small and difficult to distinguish, but with the enhanced manifold structure, our model effectively captures the relationships between target and reference objects, achieving improved grounding performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.66, + 0.634, + 0.675 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.9 + ], + "angle": 0, + "content": "In this work, we propose Proxy Transformation, a real-time multimodal point cloud enhancement model, to address issues of geometric loss and unexpected noise in 3D points within ego-centric 3D visual grounding. This approach yields a high-quality point cloud structure for feature learning. Extensive experiments show that our model not only outperforms all existing methods but also improves the computational efficiency of attention modules, setting a new SOTA on the EmbodiedScan benchmark. These results demonstrate the effectiveness and robustness of using multimodal information for real-time point cloud enhancement in ego-centric 3D visual grounding, offering fresh insights for advancing embodied AI and enabling human-computer interaction in real-world environments." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24589" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.162 + ], + "angle": 0, + "content": "The work is supported in part by the National Natural Science Foundation of China under Grant U24B2017, and Beijing Natural Science Foundation under Grant QY24257." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.173, + 0.188, + 0.189 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.199, + 0.484, + 0.282 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. 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In ICLR, 2021. 5" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24592" + } + ] +] \ No newline at end of file diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_origin.pdf b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..63e7a0ebbbbb3a640300fee27af3b42f16d4a05f --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/4b7e6ed5-1e73-47b0-831f-cd411124477b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cf392d2adcf533defd7e49753769fb1f323d73e085a9337895d947e9004a4da4 +size 8024270 diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/full.md b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8904b4911a7bf4955fb51869651fa4ab0fbbb807 --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/full.md @@ -0,0 +1,362 @@ +# ProxyTransformation: Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding + +Qihang Peng + +Henry Zheng + +Gao Huang* + +Tsinghua University + +# Abstract + +Embodied intelligence requires agents to interact with 3D environments in real time based on language instructions. A foundational task in this domain is ego-centric 3D visual grounding. However, the point clouds rendered from RGB-D images retain a large amount of redundant background data and inherent noise, both of which can interfere with the manifold structure of the target regions. Existing point cloud enhancement methods often require a tedious process to improve the manifold, which is not suitable for real-time tasks. We propose Proxy Transformation suitable for multimodal task to efficiently improve the point cloud manifold. Our method first leverages Deformable Point Clustering to identify the point cloud sub-manifolds in target regions. Then, we propose a Proxy Attention module that utilizes multimodal proxies to guide point cloud transformation. Built upon Proxy Attention, we design a submanifold transformation generation module where textual information globally guides translation vectors for different submanifolds, optimizing relative spatial relationships of target regions. Simultaneously, image information guides linear transformations within each submanifold, refining the local point cloud manifold of target regions. Extensive experiments demonstrate that Proxy Transformation significantly outperforms all existing methods, achieving an impressive improvement of $7.49\%$ on easy targets and $4.60\%$ on hard targets, while reducing the computational overhead of attention blocks by $40.6\%$ . These results establish a new SOTA in ego-centric 3D visual grounding, showcasing the effectiveness and robustness of our approach. + +# 1. Introduction + +In recent years, the field of embodied AI has gained increasing attention, spurred by 3D visual grounding benchmarks [1, 5, 46] that have led to a surge of research [16, 20, + +23, 46, 51, 57, 63]. The 3D visual grounding task, which involves locating target objects in real-world 3D environments based on natural language descriptions, is a core perception capability for embodied agents. This ability is crucial in enabling agents to interpret and interact with their surroundings via language, which supports applications in robotics and human-computer interaction. + +Despite these advancements, several significant challenges continue to hinder the performance of 3D visual grounding systems. One key challenge is the limited perception of embodied agents, who rely on ego-centric observations from multiple viewpoints, often lacking a holistic, scene-level understanding. While some methods attempt to improve scene-level perception using preconstructed 3D point clouds [16, 20, 23, 51, 57, 63], following previous 3D perception approaches [24, 50], they are impractical in real-world applications where comprehensive scene-level information is not readily available. + +In response, EmbodiedScan [46] was introduced, utilizing multi-view ego-centric RGB-D scans to enable models to process scenes directly from sparse, partial viewpoints. Previous methods[46, 65, 66, 70] decouple the encoding of RGB images and depth-reconstructed point clouds from ego-centric perspectives to extract both semantic and geometric information, which are then projected into 3D space using intrinsic and extrinsic matrices to form a semantically enriched point cloud for bounding box regression. While effective, these methods overlook the noise, such as errors in depth on non-lambertian surfaces, captured by the depth sensors [21, 22, 41] that causes suboptimal performance. Consequently, critical geometric details of corresponding target objects are lost, potentially distorting their original manifold and further compromising the model's grounding performance. Moreover, a substantial portion of the sampled points represents background regions, leading to a diminished density of foreground object points. + +In light of such critical challenges, previous works have focused on improving point cloud structure such as point cloud denoising [10, 11, 45] or completion methods [2, 26, + +![](images/8b33eed93fe1c9240c69a03169c95d1f4471ed714f23876a99405a029b0bf579.jpg) +Figure 1. Illustration of our main idea and SOTA results. Ground truth and reference boxes are shown in green and purple respectively. Circular regions represent 3D areas where point cloud enhancement is applied. Black areas indicate regions that do not contribute to grounding performance and would increase unnecessary computation overhead. Traditional single-modality point cloud guidance would enhance these redundant areas. Red regions highlight areas where multimodal-guided point cloud enhancement is efficiently applied. Text modality, containing global relative position information among different critical objects, guides translation vectors for these region, while image modality, with local fine-grained semantic details, guides transformation matrices within each target regions. Our model achieves better results with reduced computation, about which details are in Tabs. 1 and 3. + +![](images/d06c6cf044d438239d5d4c9b01dbbf95fc3e30d35cfbbf8a5a335eed5934cc2e.jpg) + +60, 61]. However, these methods often require extensive preprocessing the point cloud data, making them unsuitable for real-time ego-centric 3D visual grounding. Moreover, these methods rely on traditional statistical [43] methods or learning-based methods [31, 37] to enhance the point cloud structure in single modality, which cannot fully utilize the multimodal information available in our task. + +Given the limitations of the above methods in ego-centric 3D visual grounding, we propose Proxy Transformation, which enhances point cloud manifolds before feature learning. This approach effectively reduces redundant computation in background point cloud regions and fully leverages the available multimodal information in current context to optimize the submanifolds of target regions. Notably, our method does not require pre-trained offline reconstruction of scene-level point clouds, making it better suited for real-time ego-centric 3D visual grounding task. + +Specifically, to generate transformations for point cloud submanifolds, reference points are first initialized as a uniform 3D grid for different scenes. Motivated by the success of deformable offsets in 2D domain [9, 52], a 3D offset network then takes the initial point cloud clusters centered on these reference points as input, producing offsets for each reference cluster center. In this way, these deformable cluster centers shift toward critical regions. Subsequently, they serve as cluster centers in a succeeding stage to select candidate submanifolds on the original point cloud for further transformations. For each submanifold, we employ a novel generalized attention mechanism, Proxy Attention, to learn the corresponding transformation matrixes and translation vectors. Specific proxy tokens can be selected based on task requirements (e.g. downsampling points after pooling, + +multi-view image features or textual features). + +In the context of online point cloud submanifold enhancement, we utilize text and image features as proxy tokens to guide submanifold transformations. In this approach, text information provides global positional relationships among different submanifolds, while image information offers local semantic details within each submanifold, as illustrated in Fig. 1. Leveraging these designs, our method supplies the subsequent 3D backbone with a higher-quality point cloud manifold, thereby enhancing the model's effectiveness and robustness. + +In summary, our contributions are as follows. (1) We propose Proxy Transformation, enabling multimodal point cloud augmentation in the context of 3D visual grounding. (2) To obtain more desirable submanifolds for target regions, we design deformable point clustering, utilizing a 3D offset network to generate flexible and adaptive deformable clusters suited to diverse scenes. (3) We introduce a generalized proxy attention mechanism, allowing the selection of different proxy tokens based on task requirements, achieving linear computational complexity. (4) Our model significantly outperforms all existing methods, achieving an impressive improvement of $7.49\%$ on easy targets and $4.60\%$ on hard targets, while reducing the computational overhead of attention blocks by $40.6\%$ , establishing a new SOTA in ego-centric 3D visual grounding. + +# 2. Related Works + +3D Visual Grounding. 3D visual grounding integrates multimodal data to localize target objects in 3D point clouds and it has gained significant attention in recent + +years [12, 14, 47]. 3D visual grounding methods are divided into one-stage and two-stage architectures. One-stage approaches [15, 18, 27, 30] fuse textual and visual features to generate predictions in a single step, enabling end-to-end optimization and faster inference. However, they may struggle with complex scene layouts due to the absence of explicit object proposal refinement. In contrast, two-stage approaches [1, 4, 16, 20, 49, 58] follow a sequential process: they first utilize pre-trained object detectors [24, 49] to generate object proposals, which are subsequently matched with the linguistic input to identify the most likely target. This separation of detection and grounding allows for more precise alignment of visual and textual features, enhancing accuracy, particularly in complex scenes, but at the cost of increased computational overhead and inference time. + +Recent studies [4, 20, 23, 38, 40] have explored transformer-based structures for 3D visual grounding. BUTD-DETR [23] incorporates outputs from pre-trained detection networks, including predicted bounding boxes and their corresponding class labels, as additional inputs. Multi-View Transformer [20] projects the 3D scene into a multiview space to learn robust feature representations. MiKASA Transformer [4] integrates a scene-aware object encoder and an multi-key-anchor technique, enhancing object recognition accuracy and understanding of spatial relationships. In our paper, we focus on the more challenging one-stage methods with transformer modules. + +Point Cloud Enhancement. 3D point clouds provide rich geometric information and dense semantic details, playing a critical role in various domains [46, 54, 56, 60]. However, their inherent sparsity and irregularity limit model performance, and the deficiencies of existing sensors exacerbate issues such as high noise levels, sparsity, and incomplete structures in point clouds [32, 68]. These challenges make 3D point cloud augmentation a critical and challenging problem [35]. Traditional point cloud enhancement methods are often based on interpolation and optimization techniques [43], but their computational and memory overhead limits their applicability to large-scale datasets. Current deep learning-based point cloud augmentation methods can be broadly categorized into three main approaches: point cloud denoising, completion, and upsampling. + +Point cloud denoising [6, 10, 11, 45, 64] can eliminate noise in the point cloud while approximating and preserving the underlying surface geometry information and semantic details. Point cloud completion focuses mainly on completion for objects [7, 26, 60, 61] and scenes [48, 53, 55, 62]. And point cloud upsampling [13, 25, 28, 39, 59] aims to improve the resolution of point clouds while maintaining the integrity of the original geometric structure. + +However, these methods are still confined to a single point cloud modality and are not well-suited for tasks with high real-time requirements. In the context of ego-centric + +3D visual grounding, multimodal information is available. We leverage both textual and visual modalities as guidance to transform point cloud sub-manifolds. This approach enables simultaneous point cloud denoising and densification, providing higher-quality data for subsequent processing. Additionally, our method is designed with efficiency in mind, ensuring it meets the task's real-time requirements. + +# 3. Methodology + +In this section, we will introduce our network design. Firstly, we will give a brief introduction of the entire pipeline and what our module does in Sec. 3.1. Then, we introduce our effective yet efficient Proxy Attention in Sec. 3.2 and how deformable offsets are generated for reference points in Sec. 3.3. Finally, details of Proxy Transformation will be described in Sec. 3.4. + +# 3.1. Overall Structure + +We improve upon the previous SOTA in ego-centric 3D visual grounding [46]. Here we simply review the overall structure. First, the input RGB-D images from each view is transformed into a partial point cloud, which is then integrated into a holistic 3D point cloud $P \in \mathbb{R}^{N \times 3}$ using global alignment matrices, thereby preserving geometric details. Next, multi-scale image and point features $\{\mathcal{F}_{\mathrm{img}}^s\}_{s=1}^S \in \mathbb{R}^{V \times H_s \times W_s \times C_s}$ , $\{\mathcal{F}_{\mathrm{point}}^s\}_{s=1}^S \in \mathbb{R}^{N \times C_s}$ , and text features $\mathcal{T} \in \mathbb{R}^{L \times C}$ are learned by respective backbone. Here, $N$ is the total number of points sampled from all perspective views $V$ , $S$ is the number of scale for the encoded feature maps and $L$ is the length of text sequence. The point features are then projected onto the 2D feature planes using intrinsic and extrinsic matrices to get semantic information. Further, they are concatenated to form sparse fusion features $\{\mathcal{F}_{\mathrm{fusion}}^s\}_{s=1}^S \in \mathbb{R}^{N \times 2C_s}$ . Finally, they are fed into a DETR-like decoder and then finish 9-degree-of-freedom bounding box regression. + +However, due to the large number of points in the depth-reconstructed point cloud and computational limitations, only a sparse subset (about $2\%$ ) is sampled, resulting in a negative influence on the point cloud manifold. Due to the varying manifold structures in different local regions of scene-level point clouds, applying a global transformation to the entire point cloud is infeasible. To address this issue, we introduce Proxy Transformation to modify point cloud submanifolds with Proxy Attention, providing richer geometric information for subsequent feature learning. + +# 3.2. Proxy Attention + +For simplicity, we use following formulation to represent Softmax attention: + +$$ +O = \sigma (Q K ^ {T}) V \triangleq \operatorname {A t t n} (Q, K, V) \tag {1} +$$ + +![](images/0f66e98551b6939bc3fe7c4ab248f9d50f6b5baef917da8560802ec209287109.jpg) +(a) Overall framework of Proxy Transformation + +![](images/5d7d18f69d70dca8c2dbb9bac57eece4061aed3ebdf126cb272a3fa61cb095ef.jpg) +(b) Deformable Offset Network + +![](images/7c3267cb4ec5f681e01698228b7659c04ba348839f9dcb7ae97356fd3593ef6a.jpg) +(c) Proxy Attention of Proxy Block +Figure 2. (a) shows the overall framework of Proxy Transformation. For simplicity, $\dagger$ indicates that a 2D grid is used to represent the 3D spatial grid, with generated 3D offsets also expressed as 2D vectors for clarity. The Grid Prior spans the entire space, and we illustrate it with only four reference points for clearer visualization. In Proxy Transformation module, $\mathcal{M}$ and $\mathcal{T}$ are sets of transformation matrices and translation vectors for all clusters. (b) details the structure of our deformable offset network, and indicates the input and output shapes, where $M$ represents the number of clusters and $K$ represents the number of points per cluster. (c) illustrates the information flow in proxy attention. This module combines with FFN and skip connection in a standard Transformer architecture to form the Proxy Block. + +where $Q, K, V \in \mathbb{R}^{N \times C}$ denote query, key and value matrices and $\sigma(\cdot)$ represents Softmax function. And our proxy attention consists of three components as follows. + +$$ +\begin{array}{l} O ^ {\mathrm {P}} = \operatorname {P r o x y A t t n} (Q, K, V, P) \\ = \sigma (Q P ^ {T}) \sigma (P K ^ {T}) V \\ = \operatorname {A t t n} (Q, P, \operatorname {A t t n} (P, K, V)). \tag {2} \\ \end{array} +$$ + +$$ +\begin{array}{c} \hline \text {P r o x y C o m p r e s s i o n} \\ \hline \end{array} +$$ + +$$ +\text {P r o x y B r o a d c a s t} +$$ + +where $P\in \mathbb{R}^{n\times C}$ is our proxy tokens. + +Proxy Compression. Previous works [17, 33] have shown significant redundancy in query-key similarity computations within self-attention. To address this, we first compress the attention feature space using proxy tokens, whose number is substantially smaller than $N$ practically. This approach significantly alleviates computational overhead while preserving representational capacity, as shown + +in Tab. 3. Specifically, we use proxy tokens as queries to compute similarity with initial keys, subsequently aggregating original values to obtain a compressed proxy value representation $V^{\mathrm{P}}$ with reduced redundancy. + +Proxy Broadcast. Subsequently, we treat proxy tokens $P$ and proxy values $V^{\mathrm{P}}$ as keys and values for a second softmax operation with the original queries, allowing proxy features to be broadcast globally. This design preserves global contextual representation while reducing complexity to a linear scale. In practice, proxy tokens are selected based on the model's representational needs (e.g. downsampling points after pooting, multi-view image features or textual features). In these contexts, $n$ is much smaller than $N$ . Thus, this approach achieves generalized attention with a linear complexity of $\mathcal{O}(Nnd)$ relative to the number of input features $N$ , balancing computational efficiency with high representational capacity as shown in Tab. 3. + +Proxy Bias. Additionally, to compensate for the lack of po + +sitional information and the diversity of features, we introduce a novel proxy bias. To minimize parameter overhead, we merge two low-dimensional subspaces into a higher-dimensional space through a union operation of linear space. Specifically, we define two sets of low-dimensional learnable parameters, representing two subspaces $V_{c}$ and $V_{r}$ within feature space $V$ that satisfy $V = V_{c} \cup V_{r}$ . After broadcasting these two parameter sets, they match the original feature dimensionality, enriching the feature space with positional information, and guiding Proxy Attention to focus on diverse regions. + +# 3.3. Deformable Point Clustering + +To transform submanifolds, it is essential first to obtain suitable clusters. Motivated by [9, 19, 52, 71], we design a deformable clustering approach to identify optimal cluster center locations, capturing the desired target submanifolds. + +Grid Prior. As mentioned in Sec. 3.1, the randomly sampled sparse point cloud has already lost a significant amount of geometric information. To compensate for this loss, we first generate a 3D uniform grid and use its grid centers as reference points for the initial clustering: + +$$ +\begin{array}{l} \mathcal {Q} \triangleq \left\{q _ {(i, j, k)} \right\} _ {i, j, k = 1} ^ {x _ {s}, y _ {s}, z _ {s}} \sim U \left[ \mathcal {C} _ {\min }, \mathcal {C} _ {\max } \right], \\ \mathcal {N} _ {(i, j, k)} \triangleq \{p _ {l} ^ {i, j, k} \} _ {l = 1} ^ {m} = \gamma (\mathcal {Q} _ {(i, j, k)}, \{p _ {l} \} _ {l = 1} ^ {N}), \tag {3} \\ \end{array} +$$ + +where reference points $\mathcal{Q}$ are also the initial cluster centers. $U$ is a uniform distribution. $\mathcal{C}$ is the 3D coordinate of points. $p_l^{i,j,k}$ is a specific point in corresponding cluster $\mathcal{N}_{(i,j,k)}$ and $\gamma$ is clustering function, e.g. ball query or kNN. $N$ and $m$ are respective numbers of point cloud and local cluster. + +To simplify, we regard $\mathcal{N}_{(i,j,k)}$ as $\mathcal{N}_t$ , where $t \in [0, n-1]$ , where $n = x_s \times y_s \times z_s$ and $x_s, y_s, z_s$ are predefined as hyperparameter. Experimentally, we find that this approach does not affect performance, but provides greater stability in the training process compared to stochastic sampling. + +Deformable Offsets. To increase the diversity of submanifold selection, an offset network outputs the offset values for reference points respectively, allowing them to shift toward more relevant surrounding regions based on the current submanifold structure. Considering that each reference point covers a local $s$ ball region ( $s$ is the largest value for offset), the offset network is able to percept local features to learn reasonable offsets. In addition, we also provide global information to further enhance offset generation. + +$$ +\begin{array}{l} \hat {q} _ {t} = q _ {t} + \Gamma_ {\mathrm {o f f s e t}} (\mathcal {N} _ {t}), \\ \hat {\mathcal {N}} _ {t} = \gamma (\hat {q} _ {t}, \{p _ {l} \} _ {l = 1} ^ {N}), \tag {4} \\ \end{array} +$$ + +where $\Gamma_{\mathrm{offset}}(\cdot)$ is our offset network. $\hat{q}_t \in \hat{\mathcal{Q}}$ is a new cluster center and $\hat{\mathcal{N}}_t$ is a new neighborhood. + +Specifically, for $\mathcal{N}_t$ , we first concatenate the relative coordinates of sub-points with respect to the center and their + +global coordinates. It's then passed through $1 \times 1$ Conv2D and ReLU activation to extract point-wise features. We apply average pooling to obtain high-dimensional local-global features for each cluster, which are then fed into another $1 \times 1$ convolution to generate the final offsets, as shown in Fig. 2. Notably, we set the bias of the $1 \times 1$ convolution to zero to avoid introducing additional perturbations. Finally, we discard some clusters according to a predefined drop ratio $\beta$ with a certain sampling method (e.g. random sampling or FPS), allowing us to obtain a more diverse neighborhood based on the new cluster centers. + +# 3.4. Proxy Transformation + +For each submanifold, we leverage the Proxy Block to learn a unique manifold transformation. Any arbitrary transformation in 3D space can be decomposed into a linear transformation and a translation. Then, these transformations are applied to each deformable cluster. Details about the transformation generation module are described below. + +Proxy Block. Following the standard block design in Transformer architectures [42], we developed a Proxy Block based on proxy attention, aimed at cross-modal learning for subsequent manifold transformations. We denote $P_0$ and $F_0$ as a set of proxy tokens and cluster features. And $F_0$ is extracted by a simplified PointNet [34]. Then a transformer block comprises of proxy attention module and feedforward network: + +$$ +F = F _ {0} + B ^ {\mathrm {P}}, \tag {5} +$$ + +$$ +Q = F W _ {Q}, K = F W _ {K}, V = F W _ {V}, P = P _ {0} W _ {P}, \tag {6} +$$ + +$$ +O ^ {\mathrm {P}} = F + \operatorname {P r o x y A t t n} (Q, K, V, P), \tag {7} +$$ + +$$ +O = O ^ {\mathrm {P}} + \operatorname {F F N} \left(O ^ {\mathrm {P}}\right), \tag {8} +$$ + +where $B^{\mathrm{P}}$ is our proxy bias introduced in Sec. 3.2. $W_{Q}, W_{K}, W_{V}$ are projections for query, key and value. ProxyAttn(·) is a proxy attention module in Eq. (2). FFN(·) is a position-wise feedforward network. + +In the following sections, for simplicity, we use + +$$ +O = \operatorname {P r o x y B l o c k} (F, P), \tag {9} +$$ + +to represent the basic proxy block (Eqs. (5) to (8)). + +Text Guided Translation. In ego-centric 3D visual grounding, the input text contains global relative positional information between the target object and other reference objects, while the remaining parts naturally correspond to background point clouds. Therefore, text features can effectively guide the model in learning translation vectors that establish spatial relationships between various submanifolds, thereby enhancing the global relational information embedded within the point cloud structure. Specifically, we leverage text features as proxies within the Proxy Block, allowing it to generate text-guided point cloud features that ultimately yield accurate and context-aware final translation + +vectors for more precise grounding results. + +$$ +F ^ {l + 1} = \operatorname {P r o x y B l o c k} \left(F ^ {l}, P _ {T}\right), l = 0,.., L - 1, \tag {10} +$$ + +$$ +T = F ^ {L} U _ {\text {t e x t}}, \tag {11} +$$ + +where $P_{T}$ are text features $\mathcal{F}_{\mathrm{text}}\in \mathbb{R}^{S\times C}$ . $L$ is number of layers and $U_{\mathrm{text}}$ is a fully connected layer to generate final translation vectors $T\in \mathbb{R}^{n\times 3}$ . + +Image Guided Transformation. The input multi-view image contains rich fine-grained semantic information, compensating for the contextual loss caused by point cloud downsampling. Multi-view images provide pose information of the target object from various perspectives, guiding the model to learn internal transformations of each subpoints relative to the cluster center. Thus, we use pooled image features as proxies in the Proxy Block to generate reshaped image-guided point cloud features, which in turn yield the linear transformations for each submanifold: + +$$ +F ^ {l + 1} = \operatorname {P r o x y B l o c k} \left(F ^ {l}, P _ {I}\right), l = 0,.., L - 1, \tag {12} +$$ + +$$ +M = F ^ {L} U _ {\text {i m a g e}}, \tag {13} +$$ + +where $P_{I}\in \mathbb{R}^{V\times C}$ are pooled image features from an additional attention pooling layer. And $L$ is the number of layers and $U_{\mathrm{image}}$ is a fully connected layer to generate final transformation matrices $M\in \mathbb{R}^{n\times 3\times 3}$ . + +Submanifold Reshape. Once the transformation matrix, containing fine-grained semantic information from the image, and the translation vectors, encompassing precise global relative information from the text, are obtained, we can apply a Proxy Transformation to each submanifold and finally get a diverse enhanced point cloud manifold. To represent this process, we use concise set operations: + +$$ +\hat {\mathcal {P}} = \mathcal {M} \odot \mathcal {P} \oplus \mathcal {T}, \tag {14} +$$ + +where $\mathcal{M}$ and $\mathcal{T}$ are sets of transformation matrices and translation vectors for all clusters. $\mathcal{P}$ is a union set of submanifolds of different neighborhoods $\{\mathcal{N}_i\}_{i = 1}^n$ , namely a subset of original point cloud. $\odot$ and $\oplus$ represent elementwise multiplication and addition for sets. + +Equivalently, for a specific submanifold: + +$$ +\hat {P} _ {i} = P _ {i} M _ {i} ^ {T} + T _ {i}, \tag {15} +$$ + +where $P_{i}\in \mathcal{P}\cap \mathbb{R}^{m\times 3}$ represent sub-points in $\mathcal{N}_i$ . $M_{i}\in$ $\mathcal{M}\cap \mathbb{R}^{3\times 3}$ and $T_{i}\in \mathcal{T}\cap \mathbb{R}^{3}$ are the specific transformation matrix and translation vector for this submanifold. + +Finally, we replace the corresponding parts of the original point cloud with transformed submanifolds to obtain final enhanced point cloud, consisting of rich diversity in manifold structure, which is then fed into 3D backbone during training, enabling efficient multimodal-guided point cloud manifold enhancements. + +# 4. Experiments + +Dataset and Benchmark. The EmbodiedScan dataset [46] used in our experiments is a large-scale, multi-modal, egocentric resource tailored for comprehensive 3D scene understanding. It comprises 5,185 scene scans from widely-used datasets like ScanNet [8], 3RScan [44], and Matterport3D [3]. This diverse dataset offers a rich foundation for 3D visual grounding, covering a broader range of scenes than previous datasets. The training set includes 801,711 language prompts, while the validation set contains 168,322 prompts, making EmbodiedScan notably larger and more challenging, thus providing a rigorous benchmark for egocentric 3D visual grounding tasks. + +Experimental Settings. Due to limited resources, we train on the official mini dataset. Despite this, our model outperforms the official baseline trained on the full training set, as shown in Tab. 1. For analysis experiments in Sec. 4.2, we also use the mini training and validation sets available through the official EmbodiedScan release [46]. + +Our reported accuracy uses the official IoU metric, focusing on cases where IoU exceeds $25\%$ and $50\%$ . We also assess model performance on both "Easy" and "Hard" scenes, where a "Hard" scene contains three or more target objects of the same category. The "View-Dependent" and "View-Independent" metrics further test the model's spatial reasoning by evaluating performance with and without perspective-specific descriptions. + +Implementation Details. This work builds upon the strong baseline from EmbodiedScan for ego-centric 3D visual grounding. We applied several techniques to enhance the original baseline. First, we replace the RoBERTa language encoder [29] with the CLIP encoder [36] to achieve superior alignment between language and vision. Additionally, we incorporate Class-Balanced Grouping and Sampling (CBGS) [67] during pretraining to address data imbalance and enhance detection accuracy across rare and common object categories. We follow EmbodiedScan's approach by using pretrained visual encoders. Finally, we also adopt text augmented by LLM to provide richer semantic context when training, proposed by [65]. Moreover, our Proxy Transformation is trained using the AdamW optimizer with a learning rate of 5e-4, weight decay of 5e-4, and a batch size of 48. Training spans 12 epochs, with the learning rate reduced by 0.1 at epochs 8 and 11. + +# 4.1. Main Results + +We evaluate the 3D visual grounding performance of our proposed method, Proxy Transformation, with results presented in Tab. 1, comparing it against established SOTA methods from the dataset benchmark. In addition, the upper methods with $\dagger$ are trained on the full dataset, while the lower methods are trained on a mini dataset, approximately $20\%$ of the full dataset. + +
MethodEasy AP25Hard AP25Indep Dep AP25Overall AP25Easy AP50Hard AP50Indep Dep AP50Overall AP50
ScanRefer† [5]13.789.1213.4410.7712.85---
BUTD-DETR† [23]23.1218.2322.4720.9822.14---
L3Det† [69]24.0118.3423.5921.2223.07---
EmbodiedScan†39.8231.0240.3038.4839.1018.7914.9318.03
EmbodiedScan [46]33.8730.4933.5533.6133.5914.5812.4113.92
DenseG [65]40.1734.3838.7940.1839.7018.5215.8817.47
ProxyTransformation41.6634.3841.5740.8141.0819.4314.0918.65
+ +As shown in Tab. 1, Proxy Transformation achieves a notable $7.49\%$ and $4.60\%$ improvement over the previous strongest baseline, EmbodiedScan, on the Overall@0.25 and Overall@0.50. Although only trained on the mini dataset, our method even surpasses the baseline trained on the full dataset. Through deformable point clustering, our model focuses on the most crucial target regions in the scene, reducing the extra computation overhead caused by redundant point clouds and improving efficiency. Additionally, a grid prior preserves essential original spatial information, mitigating early training instability. Recognizing that text information provides global positional relationships among different submanifolds and image information offers local semantic details within each submanifold, we designed generalized proxy attention to guide local transformations of the selected point cloud submanifolds. These transformations optimize local point cloud structures for each submanifold, ultimately providing higher-quality data for subsequent feature extraction and fusion. + +In summary, Proxy Transformation consistently outperforms the previous state-of-the-art across multiple evaluation metrics, including easy and hard samples as well as view-independent and view-dependent tasks. These consistent improvements across diverse metrics highlight not only the robustness and generalizability of our approach for 3D visual grounding tasks but also its adaptability to complex scenes and dynamic environments, making it an effective solution for advancing multimodal grounding capabilities in real-world embodied AI applications. + +# 4.2. Analysis Experiments + +Ablation on Proposed Modules. We conducted ablation studies on each module to verify their effectiveness as shown in Tab. 2. To ensure fair comparisons, the baseline is enhanced with several modules described in the implementation details. First, we introduce Proxy Transformation without deformable point clustering, resulting in a + +Table 1. Main Results on the official validation set. The table displays accuracy performance considering instances where IoU exceeds $25\%$ and $50\%$ under different circumstances as mentioned in Sec. 4. 'Indep' and 'Dep' mean the targets are view-independent and view-dependent. And $\dagger$ denotes that models are trained on full train dataset. Although our model is trained on mini train dataset (approximately $20\%$ of the full data), but it still surpasses previous methods trained on the full train dataset. + +
Grid PriorOffsetsPTEasyHardOverall
37.0530.6036.53
✓40.3932.6039.76
✓✓40.5932.1839.91
✓✓✓41.6634.3841.08
+ +Table 2. Ablation of Proposed Modules. 'PT' represents 'Proxy Transformation'. The reported values are mAP for predictions greater than $25\%$ IoU. + +
AttnFLOPs#ParamsEasyHardOverall
Vanilla8.36G2.52M40.7133.6540.14
Proxy4.97G2.71M41.6634.3841.08
+ +Table 3. Ablation on Proxy Attention. Here, we compare the vanilla self-attention block with our Proxy Block. The FLOPs and parameters are computed over 3 transformer blocks with cluster features as input. We use a grid size of 12 and a drop radio of 0.6. The reported values are mAP for predictions greater than $25\%$ IoU. + +
Grid SizeEasyHardOverall
w/o40.5932.1839.91
1040.9432.8140.29
1241.6634.3841.08
1441.1134.2840.56
+ +Table 4. Ablation on the size of Grid Prior. The reported values are mAP for predictions greater than $25\%$ IoU. + +substantial improvement of $3.23\%$ , which demonstrates the effectiveness and necessity of our multimodal point cloud enhancement. Then, we add deformable offsets, yielding an additional improvement on easy samples, indicating that offsets effectively guide cluster centers toward target regions. Finally, we incorporate grid prior, which improves + +![](images/8de7be3e9c60e296a5e84c3eb8ed8f3d25f5ca81b327d4cb11d2a974ceac7d37.jpg) +Figure 3. Visualization of ground truth and predictions. Ground truth boxes are shown in green, baseline in red, and ProxyTransformation's predictions in violet. + +
LayersEasyHardOverall
141.6034.0740.99
241.5731.9740.79
341.6634.3841.08
441.7231.5540.90
+ +Table 5. Ablation on the number of Proxy Layers. The reported values are mAP for predictions greater than $25\%$ IoU. + +training stability and achieves an increase of $2.20\%$ on hard samples. This result shows that the grid prior mitigates the randomness of offsets in the early stages of training, preserving essential scene information for the model. + +Ablation on Proxy Attention. We validate the effectiveness and efficiency of proxy attention by comparing the vanilla attention block with the proxy block. The input cluster features are aligned across both blocks. As discussed in Sec. 3.2, the number of proxy tokens is significantly smaller than the input sequence length. This reduction in proxy tokens compresses redundancy within the attention module, enhancing computational efficiency, which aligns with our experiment results. As shown in Tab. 3, our approach achieves higher performance than vanilla attention, while reducing the computation overhead by $40.6\%$ . + +Ablation on Main Hyperparameters. Then, we ablate several hyperparameters in deformable point clustering and proxy transformation. As shown in Tab. 4, the size of the grid prior also influences performance by reducing instability during the early training stages, which can result from the randomness of the initial transformations. As shown in Tab. 5, we conduct several experiments to determine the + +optimal layers of our proxy attention block for efficient learning. Based on these findings, we selected the optimal hyperparameters for our experiments. Moreover, further ablation studies are given in the supplementary material. + +# 4.3. Qualitative Results and Discussion + +With our deformable point clustering and Proxy Transformation, the point cloud structure in target regions is optimized, providing higher-quality data for subsequent feature learning and fusion. As shown in Fig. 3, reference objects in these regions are small and difficult to distinguish, but with the enhanced manifold structure, our model effectively captures the relationships between target and reference objects, achieving improved grounding performance. + +# 5. Conclusion + +In this work, we propose Proxy Transformation, a real-time multimodal point cloud enhancement model, to address issues of geometric loss and unexpected noise in 3D points within ego-centric 3D visual grounding. This approach yields a high-quality point cloud structure for feature learning. Extensive experiments show that our model not only outperforms all existing methods but also improves the computational efficiency of attention modules, setting a new SOTA on the EmbodiedScan benchmark. These results demonstrate the effectiveness and robustness of using multimodal information for real-time point cloud enhancement in ego-centric 3D visual grounding, offering fresh insights for advancing embodied AI and enabling human-computer interaction in real-world environments. + +# Acknowledgement + +The work is supported in part by the National Natural Science Foundation of China under Grant U24B2017, and Beijing Natural Science Foundation under Grant QY24257. + +# References + +[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. Referit3d: Neural listeners for fine-grained 3d object identification in real-world scenes. 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Denseg: Alleviating vision-language feature sparsity in multi-view 3d visual grounding. 2024. 1, 6, 7 +[66] Henry Zheng, Hao Shi, Qihang Peng, Yong Xien Chng, Rui Huang, Yepeng Weng, Gao Huang, et al. Densegrounding: Improving dense language-vision semantics for ego-centric 3d visual grounding. In The Thirteenth International Conference on Learning Representations, 2025. 1 + +[67] Benjin Zhu, Zhengkai Jiang, Xiangxin Zhou, Zeming Li, and Gang Yu. Class-balanced grouping and sampling for point cloud 3d object detection. arXiv preprint arXiv:1908.09492, 2019. 6 +[68] Chen Zhu, Jianyu Yang, Zhanpeng Shao, and Chunping Liu. Vision based hand gesture recognition using 3d shape context. IEEE/CAA Journal of Automatica Sinica, 8(9):1600-1613, 2019. 3 +[69] Chenming Zhu, Wenwei Zhang, Tai Wang, Xihui Liu, and Kai Chen. Object2scene: Putting objects in context for open-vocabulary 3d detection, 2023. 7 +[70] Chenming Zhu, Tai Wang, Wenwei Zhang, Kai Chen, and Xihui Liu. 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In ICLR, 2021. 5 \ No newline at end of file diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/images.zip b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6e9945d8e6fdd5a1497f3ffc36da0169a65298f5 --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fe8abfebee7a4d008c83aeaccd6ceef767f36fdbc71b576c742956c3c6672dd4 +size 512402 diff --git a/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/layout.json b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0f36989d5eb319e375392e5450298aa86cf64b40 --- /dev/null +++ b/2025/ProxyTransformation_ Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding/layout.json @@ -0,0 +1,9470 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 130, + 103, + 481, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 103, + 481, + 140 + ], + "spans": [ + { + "bbox": [ + 130, + 103, + 481, + 140 + ], + "type": "text", + "content": "ProxyTransformation: Preshaping Point Cloud Manifold With Proxy Attention For 3D Visual Grounding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 154, + 162, + 220, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 154, + 162, + 220, + 176 + ], + "spans": [ + { + "bbox": [ + 154, + 162, + 220, + 176 + ], + "type": "text", + "content": "Qihang Peng" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 274, + 162, + 340, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 274, + 162, + 340, + 176 + ], + "spans": [ + { + "bbox": [ + 274, + 162, + 340, + 176 + ], + "type": "text", + "content": "Henry Zheng" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 394, + 162, + 456, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 162, + 456, + 176 + ], + "spans": [ + { + "bbox": [ + 394, + 162, + 456, + 176 + ], + "type": "text", + "content": "Gao Huang*" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 257, + 189, + 358, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 257, + 189, + 358, + 204 + ], + "spans": [ + { + "bbox": [ + 257, + 189, + 358, + 204 + ], + "type": "text", + "content": "Tsinghua University" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "spans": [ + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "text", + "content": "Embodied intelligence requires agents to interact with 3D environments in real time based on language instructions. A foundational task in this domain is ego-centric 3D visual grounding. However, the point clouds rendered from RGB-D images retain a large amount of redundant background data and inherent noise, both of which can interfere with the manifold structure of the target regions. Existing point cloud enhancement methods often require a tedious process to improve the manifold, which is not suitable for real-time tasks. We propose Proxy Transformation suitable for multimodal task to efficiently improve the point cloud manifold. Our method first leverages Deformable Point Clustering to identify the point cloud sub-manifolds in target regions. Then, we propose a Proxy Attention module that utilizes multimodal proxies to guide point cloud transformation. Built upon Proxy Attention, we design a submanifold transformation generation module where textual information globally guides translation vectors for different submanifolds, optimizing relative spatial relationships of target regions. Simultaneously, image information guides linear transformations within each submanifold, refining the local point cloud manifold of target regions. Extensive experiments demonstrate that Proxy Transformation significantly outperforms all existing methods, achieving an impressive improvement of " + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "inline_equation", + "content": "7.49\\%" + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "text", + "content": " on easy targets and " + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "inline_equation", + "content": "4.60\\%" + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "text", + "content": " on hard targets, while reducing the computational overhead of attention blocks by " + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "inline_equation", + "content": "40.6\\%" + }, + { + "bbox": [ + 54, + 270, + 297, + 619 + ], + "type": "text", + "content": ". These results establish a new SOTA in ego-centric 3D visual grounding, showcasing the effectiveness and robustness of our approach." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "spans": [ + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 659, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 296, + 696 + ], + "type": "text", + "content": "In recent years, the field of embodied AI has gained increasing attention, spurred by 3D visual grounding benchmarks [1, 5, 46] that have led to a surge of research [16, 20," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 246, + 555, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 246, + 555, + 329 + ], + "spans": [ + { + "bbox": [ + 313, + 246, + 555, + 329 + ], + "type": "text", + "content": "23, 46, 51, 57, 63]. The 3D visual grounding task, which involves locating target objects in real-world 3D environments based on natural language descriptions, is a core perception capability for embodied agents. This ability is crucial in enabling agents to interpret and interact with their surroundings via language, which supports applications in robotics and human-computer interaction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 330, + 556, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 330, + 556, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 556, + 461 + ], + "type": "text", + "content": "Despite these advancements, several significant challenges continue to hinder the performance of 3D visual grounding systems. One key challenge is the limited perception of embodied agents, who rely on ego-centric observations from multiple viewpoints, often lacking a holistic, scene-level understanding. While some methods attempt to improve scene-level perception using preconstructed 3D point clouds [16, 20, 23, 51, 57, 63], following previous 3D perception approaches [24, 50], they are impractical in real-world applications where comprehensive scene-level information is not readily available." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 462, + 556, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 556, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 556, + 677 + ], + "type": "text", + "content": "In response, EmbodiedScan [46] was introduced, utilizing multi-view ego-centric RGB-D scans to enable models to process scenes directly from sparse, partial viewpoints. Previous methods[46, 65, 66, 70] decouple the encoding of RGB images and depth-reconstructed point clouds from ego-centric perspectives to extract both semantic and geometric information, which are then projected into 3D space using intrinsic and extrinsic matrices to form a semantically enriched point cloud for bounding box regression. While effective, these methods overlook the noise, such as errors in depth on non-lambertian surfaces, captured by the depth sensors [21, 22, 41] that causes suboptimal performance. Consequently, critical geometric details of corresponding target objects are lost, potentially distorting their original manifold and further compromising the model's grounding performance. Moreover, a substantial portion of the sampled points represents background regions, leading to a diminished density of foreground object points." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "In light of such critical challenges, previous works have focused on improving point cloud structure such as point cloud denoising [10, 11, 45] or completion methods [2, 26," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 147, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 147, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 147, + 713 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24582" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 400, + 223 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 400, + 223 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 400, + 223 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 400, + 223 + ], + "type": "image", + "image_path": "8b33eed93fe1c9240c69a03169c95d1f4471ed714f23876a99405a029b0bf579.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 231, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 54, + 231, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 54, + 231, + 555, + 308 + ], + "type": "text", + "content": "Figure 1. Illustration of our main idea and SOTA results. Ground truth and reference boxes are shown in green and purple respectively. Circular regions represent 3D areas where point cloud enhancement is applied. Black areas indicate regions that do not contribute to grounding performance and would increase unnecessary computation overhead. Traditional single-modality point cloud guidance would enhance these redundant areas. Red regions highlight areas where multimodal-guided point cloud enhancement is efficiently applied. Text modality, containing global relative position information among different critical objects, guides translation vectors for these region, while image modality, with local fine-grained semantic details, guides transformation matrices within each target regions. Our model achieves better results with reduced computation, about which details are in Tabs. 1 and 3." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 416, + 74, + 545, + 223 + ], + "blocks": [ + { + "bbox": [ + 416, + 74, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 416, + 74, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 416, + 74, + 545, + 223 + ], + "type": "image", + "image_path": "d06c6cf044d438239d5d4c9b01dbbf95fc3e30d35cfbbf8a5a335eed5934cc2e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 330, + 294, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 330, + 294, + 413 + ], + "spans": [ + { + "bbox": [ + 54, + 330, + 294, + 413 + ], + "type": "text", + "content": "60, 61]. However, these methods often require extensive preprocessing the point cloud data, making them unsuitable for real-time ego-centric 3D visual grounding. Moreover, these methods rely on traditional statistical [43] methods or learning-based methods [31, 37] to enhance the point cloud structure in single modality, which cannot fully utilize the multimodal information available in our task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 414, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 414, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 54, + 414, + 295, + 533 + ], + "type": "text", + "content": "Given the limitations of the above methods in ego-centric 3D visual grounding, we propose Proxy Transformation, which enhances point cloud manifolds before feature learning. This approach effectively reduces redundant computation in background point cloud regions and fully leverages the available multimodal information in current context to optimize the submanifolds of target regions. Notably, our method does not require pre-trained offline reconstruction of scene-level point clouds, making it better suited for real-time ego-centric 3D visual grounding task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "content": "Specifically, to generate transformations for point cloud submanifolds, reference points are first initialized as a uniform 3D grid for different scenes. Motivated by the success of deformable offsets in 2D domain [9, 52], a 3D offset network then takes the initial point cloud clusters centered on these reference points as input, producing offsets for each reference cluster center. In this way, these deformable cluster centers shift toward critical regions. Subsequently, they serve as cluster centers in a succeeding stage to select candidate submanifolds on the original point cloud for further transformations. For each submanifold, we employ a novel generalized attention mechanism, Proxy Attention, to learn the corresponding transformation matrixes and translation vectors. Specific proxy tokens can be selected based on task requirements (e.g. downsampling points after pooling," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 330, + 501, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 330, + 501, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 501, + 342 + ], + "type": "text", + "content": "multi-view image features or textual features)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 342, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 461 + ], + "type": "text", + "content": "In the context of online point cloud submanifold enhancement, we utilize text and image features as proxy tokens to guide submanifold transformations. In this approach, text information provides global positional relationships among different submanifolds, while image information offers local semantic details within each submanifold, as illustrated in Fig. 1. Leveraging these designs, our method supplies the subsequent 3D backbone with a higher-quality point cloud manifold, thereby enhancing the model's effectiveness and robustness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "text", + "content": "In summary, our contributions are as follows. (1) We propose Proxy Transformation, enabling multimodal point cloud augmentation in the context of 3D visual grounding. (2) To obtain more desirable submanifolds for target regions, we design deformable point clustering, utilizing a 3D offset network to generate flexible and adaptive deformable clusters suited to diverse scenes. (3) We introduce a generalized proxy attention mechanism, allowing the selection of different proxy tokens based on task requirements, achieving linear computational complexity. (4) Our model significantly outperforms all existing methods, achieving an impressive improvement of " + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "inline_equation", + "content": "7.49\\%" + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "text", + "content": " on easy targets and " + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "inline_equation", + "content": "4.60\\%" + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "text", + "content": " on hard targets, while reducing the computational overhead of attention blocks by " + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "inline_equation", + "content": "40.6\\%" + }, + { + "bbox": [ + 313, + 464, + 556, + 643 + ], + "type": "text", + "content": ", establishing a new SOTA in ego-centric 3D visual grounding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 656, + 406, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 656, + 406, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 656, + 406, + 669 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "3D Visual Grounding. 3D visual grounding integrates multimodal data to localize target objects in 3D point clouds and it has gained significant attention in recent" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24583" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "type": "text", + "content": "years [12, 14, 47]. 3D visual grounding methods are divided into one-stage and two-stage architectures. One-stage approaches [15, 18, 27, 30] fuse textual and visual features to generate predictions in a single step, enabling end-to-end optimization and faster inference. However, they may struggle with complex scene layouts due to the absence of explicit object proposal refinement. In contrast, two-stage approaches [1, 4, 16, 20, 49, 58] follow a sequential process: they first utilize pre-trained object detectors [24, 49] to generate object proposals, which are subsequently matched with the linguistic input to identify the most likely target. This separation of detection and grounding allows for more precise alignment of visual and textual features, enhancing accuracy, particularly in complex scenes, but at the cost of increased computational overhead and inference time." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 253, + 294, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 294, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 294, + 396 + ], + "type": "text", + "content": "Recent studies [4, 20, 23, 38, 40] have explored transformer-based structures for 3D visual grounding. BUTD-DETR [23] incorporates outputs from pre-trained detection networks, including predicted bounding boxes and their corresponding class labels, as additional inputs. Multi-View Transformer [20] projects the 3D scene into a multiview space to learn robust feature representations. MiKASA Transformer [4] integrates a scene-aware object encoder and an multi-key-anchor technique, enhancing object recognition accuracy and understanding of spatial relationships. In our paper, we focus on the more challenging one-stage methods with transformer modules." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 399, + 294, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 294, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 294, + 579 + ], + "type": "text", + "content": "Point Cloud Enhancement. 3D point clouds provide rich geometric information and dense semantic details, playing a critical role in various domains [46, 54, 56, 60]. However, their inherent sparsity and irregularity limit model performance, and the deficiencies of existing sensors exacerbate issues such as high noise levels, sparsity, and incomplete structures in point clouds [32, 68]. These challenges make 3D point cloud augmentation a critical and challenging problem [35]. Traditional point cloud enhancement methods are often based on interpolation and optimization techniques [43], but their computational and memory overhead limits their applicability to large-scale datasets. Current deep learning-based point cloud augmentation methods can be broadly categorized into three main approaches: point cloud denoising, completion, and upsampling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 580, + 294, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 294, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 294, + 675 + ], + "type": "text", + "content": "Point cloud denoising [6, 10, 11, 45, 64] can eliminate noise in the point cloud while approximating and preserving the underlying surface geometry information and semantic details. Point cloud completion focuses mainly on completion for objects [7, 26, 60, 61] and scenes [48, 53, 55, 62]. And point cloud upsampling [13, 25, 28, 39, 59] aims to improve the resolution of point clouds while maintaining the integrity of the original geometric structure." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 294, + 713 + ], + "type": "text", + "content": "However, these methods are still confined to a single point cloud modality and are not well-suited for tasks with high real-time requirements. In the context of ego-centric" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "3D visual grounding, multimodal information is available. We leverage both textual and visual modalities as guidance to transform point cloud sub-manifolds. This approach enables simultaneous point cloud denoising and densification, providing higher-quality data for subsequent processing. Additionally, our method is designed with efficiency in mind, ensuring it meets the task's real-time requirements." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 168, + 397, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 397, + 182 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 397, + 182 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 190, + 553, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 553, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 553, + 273 + ], + "type": "text", + "content": "In this section, we will introduce our network design. Firstly, we will give a brief introduction of the entire pipeline and what our module does in Sec. 3.1. Then, we introduce our effective yet efficient Proxy Attention in Sec. 3.2 and how deformable offsets are generated for reference points in Sec. 3.3. Finally, details of Proxy Transformation will be described in Sec. 3.4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 283, + 420, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 283, + 420, + 295 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 420, + 295 + ], + "type": "text", + "content": "3.1. Overall Structure" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": "We improve upon the previous SOTA in ego-centric 3D visual grounding [46]. Here we simply review the overall structure. First, the input RGB-D images from each view is transformed into a partial point cloud, which is then integrated into a holistic 3D point cloud " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": " using global alignment matrices, thereby preserving geometric details. Next, multi-scale image and point features " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_{\\mathrm{img}}^s\\}_{s=1}^S \\in \\mathbb{R}^{V \\times H_s \\times W_s \\times C_s}" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_{\\mathrm{point}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times C_s}" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": ", and text features " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{T} \\in \\mathbb{R}^{L \\times C}" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": " are learned by respective backbone. Here, " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": " is the total number of points sampled from all perspective views " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": " is the number of scale for the encoded feature maps and " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": " is the length of text sequence. The point features are then projected onto the 2D feature planes using intrinsic and extrinsic matrices to get semantic information. Further, they are concatenated to form sparse fusion features " + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_{\\mathrm{fusion}}^s\\}_{s=1}^S \\in \\mathbb{R}^{N \\times 2C_s}" + }, + { + "bbox": [ + 313, + 301, + 553, + 518 + ], + "type": "text", + "content": ". Finally, they are fed into a DETR-like decoder and then finish 9-degree-of-freedom bounding box regression." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 519, + 554, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 519, + 554, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 519, + 554, + 639 + ], + "type": "text", + "content": "However, due to the large number of points in the depth-reconstructed point cloud and computational limitations, only a sparse subset (about " + }, + { + "bbox": [ + 313, + 519, + 554, + 639 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 313, + 519, + 554, + 639 + ], + "type": "text", + "content": ") is sampled, resulting in a negative influence on the point cloud manifold. Due to the varying manifold structures in different local regions of scene-level point clouds, applying a global transformation to the entire point cloud is infeasible. To address this issue, we introduce Proxy Transformation to modify point cloud submanifolds with Proxy Attention, providing richer geometric information for subsequent feature learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 648, + 411, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 411, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 411, + 661 + ], + "type": "text", + "content": "3.2. Proxy Attention" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 666, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 553, + 689 + ], + "type": "text", + "content": "For simplicity, we use following formulation to represent Softmax attention:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 361, + 700, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 700, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 361, + 700, + 553, + 715 + ], + "type": "interline_equation", + "content": "O = \\sigma (Q K ^ {T}) V \\triangleq \\operatorname {A t t n} (Q, K, V) \\tag {1}", + "image_path": "379f7d9099f8740174afa07e087462053f0e5d6a9fcb06b26facf4c185d4411e.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24584" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 68, + 539, + 248 + ], + "blocks": [ + { + "bbox": [ + 72, + 68, + 539, + 248 + ], + "lines": [ + { + "bbox": [ + 72, + 68, + 539, + 248 + ], + "spans": [ + { + "bbox": [ + 72, + 68, + 539, + 248 + ], + "type": "image", + "image_path": "0f66e98551b6939bc3fe7c4ab248f9d50f6b5baef917da8560802ec209287109.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 252, + 347, + 261 + ], + "lines": [ + { + "bbox": [ + 212, + 252, + 347, + 261 + ], + "spans": [ + { + "bbox": [ + 212, + 252, + 347, + 261 + ], + "type": "text", + "content": "(a) Overall framework of Proxy Transformation" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 57, + 268, + 255, + 384 + ], + "blocks": [ + { + "bbox": [ + 57, + 268, + 255, + 384 + ], + "lines": [ + { + "bbox": [ + 57, + 268, + 255, + 384 + ], + "spans": [ + { + "bbox": [ + 57, + 268, + 255, + 384 + ], + "type": "image", + "image_path": "5d7d18f69d70dca8c2dbb9bac57eece4061aed3ebdf126cb272a3fa61cb095ef.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 386, + 179, + 394 + ], + "lines": [ + { + "bbox": [ + 89, + 386, + 179, + 394 + ], + "spans": [ + { + "bbox": [ + 89, + 386, + 179, + 394 + ], + "type": "text", + "content": "(b) Deformable Offset Network" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 268, + 268, + 535, + 384 + ], + "blocks": [ + { + "bbox": [ + 268, + 268, + 535, + 384 + ], + "lines": [ + { + "bbox": [ + 268, + 268, + 535, + 384 + ], + "spans": [ + { + "bbox": [ + 268, + 268, + 535, + 384 + ], + "type": "image", + "image_path": "7c3267cb4ec5f681e01698228b7659c04ba348839f9dcb7ae97356fd3593ef6a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 355, + 386, + 454, + 394 + ], + "lines": [ + { + "bbox": [ + 355, + 386, + 454, + 394 + ], + "spans": [ + { + "bbox": [ + 355, + 386, + 454, + 394 + ], + "type": "text", + "content": "(c) Proxy Attention of Proxy Block" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "lines": [ + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": "Figure 2. (a) shows the overall framework of Proxy Transformation. For simplicity, " + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": " indicates that a 2D grid is used to represent the 3D spatial grid, with generated 3D offsets also expressed as 2D vectors for clarity. The Grid Prior spans the entire space, and we illustrate it with only four reference points for clearer visualization. In Proxy Transformation module, " + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": " are sets of transformation matrices and translation vectors for all clusters. (b) details the structure of our deformable offset network, and indicates the input and output shapes, where " + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": " represents the number of clusters and " + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 404, + 555, + 472 + ], + "type": "text", + "content": " represents the number of points per cluster. (c) illustrates the information flow in proxy attention. This module combines with FFN and skip connection in a standard Transformer architecture to form the Proxy Block." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "inline_equation", + "content": "Q, K, V \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "text", + "content": " denote query, key and value matrices and " + }, + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 55, + 491, + 295, + 528 + ], + "type": "text", + "content": " represents Softmax function. And our proxy attention consists of three components as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 97, + 533, + 295, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 533, + 295, + 578 + ], + "spans": [ + { + "bbox": [ + 97, + 533, + 295, + 578 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} O ^ {\\mathrm {P}} = \\operatorname {P r o x y A t t n} (Q, K, V, P) \\\\ = \\sigma (Q P ^ {T}) \\sigma (P K ^ {T}) V \\\\ = \\operatorname {A t t n} (Q, P, \\operatorname {A t t n} (P, K, V)). \\tag {2} \\\\ \\end{array}", + "image_path": "dc8761aaa02c2a5237c06bc90aeaf8a2a03627376b0a5d54f396bcd20fbff3fe.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 159, + 580, + 250, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 580, + 250, + 594 + ], + "spans": [ + { + "bbox": [ + 159, + 580, + 250, + 594 + ], + "type": "interline_equation", + "content": "\\begin{array}{c} \\hline \\text {P r o x y C o m p r e s s i o n} \\\\ \\hline \\end{array}", + "image_path": "8c56c41574cc481a089b2c5e8f95f743eaea0bc98e676299490f77a1d95b6d48.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 158, + 601, + 218, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 158, + 601, + 218, + 609 + ], + "spans": [ + { + "bbox": [ + 158, + 601, + 218, + 609 + ], + "type": "interline_equation", + "content": "\\text {P r o x y B r o a d c a s t}", + "image_path": "b699827851a98b085aa47412d2b086c8f08ae3b34660eda97a9bb1530b9a34cc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 616, + 212, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 616, + 212, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 616, + 212, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 616, + 212, + 629 + ], + "type": "inline_equation", + "content": "P\\in \\mathbb{R}^{n\\times C}" + }, + { + "bbox": [ + 55, + 616, + 212, + 629 + ], + "type": "text", + "content": " is our proxy tokens." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": "Proxy Compression. Previous works [17, 33] have shown significant redundancy in query-key similarity computations within self-attention. To address this, we first compress the attention feature space using proxy tokens, whose number is substantially smaller than " + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": " practically. This approach significantly alleviates computational overhead while preserving representational capacity, as shown" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 492, + 555, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 555, + 539 + ], + "type": "text", + "content": "in Tab. 3. Specifically, we use proxy tokens as queries to compute similarity with initial keys, subsequently aggregating original values to obtain a compressed proxy value representation " + }, + { + "bbox": [ + 313, + 492, + 555, + 539 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{P}}" + }, + { + "bbox": [ + 313, + 492, + 555, + 539 + ], + "type": "text", + "content": " with reduced redundancy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": "Proxy Broadcast. Subsequently, we treat proxy tokens " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": " and proxy values " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{P}}" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": " as keys and values for a second softmax operation with the original queries, allowing proxy features to be broadcast globally. This design preserves global contextual representation while reducing complexity to a linear scale. In practice, proxy tokens are selected based on the model's representational needs (e.g. downsampling points after pooting, multi-view image features or textual features). In these contexts, " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": " is much smaller than " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": ". Thus, this approach achieves generalized attention with a linear complexity of " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(Nnd)" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": " relative to the number of input features " + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 542, + 555, + 698 + ], + "type": "text", + "content": ", balancing computational efficiency with high representational capacity as shown in Tab. 3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "type": "text", + "content": "Proxy Bias. Additionally, to compensate for the lack of po" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24585" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "content": "sitional information and the diversity of features, we introduce a novel proxy bias. To minimize parameter overhead, we merge two low-dimensional subspaces into a higher-dimensional space through a union operation of linear space. Specifically, we define two sets of low-dimensional learnable parameters, representing two subspaces " + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "inline_equation", + "content": "V_{c}" + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "inline_equation", + "content": "V_{r}" + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "content": " within feature space " + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "content": " that satisfy " + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "inline_equation", + "content": "V = V_{c} \\cup V_{r}" + }, + { + "bbox": [ + 55, + 72, + 296, + 204 + ], + "type": "text", + "content": ". After broadcasting these two parameter sets, they match the original feature dimensionality, enriching the feature space with positional information, and guiding Proxy Attention to focus on diverse regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 212, + 214, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 212, + 214, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 214, + 224 + ], + "type": "text", + "content": "3.3. Deformable Point Clustering" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 228, + 296, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 296, + 277 + ], + "type": "text", + "content": "To transform submanifolds, it is essential first to obtain suitable clusters. Motivated by [9, 19, 52, 71], we design a deformable clustering approach to identify optimal cluster center locations, capturing the desired target submanifolds." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 277, + 296, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 277, + 296, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 296, + 337 + ], + "type": "text", + "content": "Grid Prior. As mentioned in Sec. 3.1, the randomly sampled sparse point cloud has already lost a significant amount of geometric information. To compensate for this loss, we first generate a 3D uniform grid and use its grid centers as reference points for the initial clustering:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 346, + 294, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 346, + 294, + 379 + ], + "spans": [ + { + "bbox": [ + 70, + 346, + 294, + 379 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {Q} \\triangleq \\left\\{q _ {(i, j, k)} \\right\\} _ {i, j, k = 1} ^ {x _ {s}, y _ {s}, z _ {s}} \\sim U \\left[ \\mathcal {C} _ {\\min }, \\mathcal {C} _ {\\max } \\right], \\\\ \\mathcal {N} _ {(i, j, k)} \\triangleq \\{p _ {l} ^ {i, j, k} \\} _ {l = 1} ^ {m} = \\gamma (\\mathcal {Q} _ {(i, j, k)}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {3} \\\\ \\end{array}", + "image_path": "5c936471af1c147a7c11125579d3be6838c96734e2832cf6705117d29e4a7d6b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": "where reference points " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " are also the initial cluster centers. " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " is a uniform distribution. " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " is the 3D coordinate of points. " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "p_l^{i,j,k}" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " is a specific point in corresponding cluster " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{(i,j,k)}" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " is clustering function, e.g. ball query or kNN. " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 387, + 296, + 446 + ], + "type": "text", + "content": " are respective numbers of point cloud and local cluster." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": "To simplify, we regard " + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{(i,j,k)}" + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "inline_equation", + "content": "t \\in [0, n-1]" + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "inline_equation", + "content": "n = x_s \\times y_s \\times z_s" + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "inline_equation", + "content": "x_s, y_s, z_s" + }, + { + "bbox": [ + 55, + 447, + 296, + 506 + ], + "type": "text", + "content": " are predefined as hyperparameter. Experimentally, we find that this approach does not affect performance, but provides greater stability in the training process compared to stochastic sampling." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "text", + "content": "Deformable Offsets. To increase the diversity of submanifold selection, an offset network outputs the offset values for reference points respectively, allowing them to shift toward more relevant surrounding regions based on the current submanifold structure. Considering that each reference point covers a local " + }, + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "text", + "content": " ball region (" + }, + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 507, + 296, + 615 + ], + "type": "text", + "content": " is the largest value for offset), the offset network is able to percept local features to learn reasonable offsets. In addition, we also provide global information to further enhance offset generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 126, + 624, + 294, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 624, + 294, + 654 + ], + "spans": [ + { + "bbox": [ + 126, + 624, + 294, + 654 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {q} _ {t} = q _ {t} + \\Gamma_ {\\mathrm {o f f s e t}} (\\mathcal {N} _ {t}), \\\\ \\hat {\\mathcal {N}} _ {t} = \\gamma (\\hat {q} _ {t}, \\{p _ {l} \\} _ {l = 1} ^ {N}), \\tag {4} \\\\ \\end{array}", + "image_path": "b5c8a405fca33aeff4f88dde651656d305b84b0f25f1b6a6cc461ff80037fe10.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\Gamma_{\\mathrm{offset}}(\\cdot)" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": " is our offset network. " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\hat{q}_t \\in \\hat{\\mathcal{Q}}" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": " is a new cluster center and " + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{N}}_t" + }, + { + "bbox": [ + 55, + 665, + 295, + 689 + ], + "type": "text", + "content": " is a new neighborhood." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Specifically, for " + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": ", we first concatenate the relative coordinates of sub-points with respect to the center and their" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": "global coordinates. It's then passed through " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " Conv2D and ReLU activation to extract point-wise features. We apply average pooling to obtain high-dimensional local-global features for each cluster, which are then fed into another " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " convolution to generate the final offsets, as shown in Fig. 2. Notably, we set the bias of the " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " convolution to zero to avoid introducing additional perturbations. Finally, we discard some clusters according to a predefined drop ratio " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " with a certain sampling method (e.g. random sampling or FPS), allowing us to obtain a more diverse neighborhood based on the new cluster centers." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 210, + 441, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 441, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 441, + 222 + ], + "type": "text", + "content": "3.4. Proxy Transformation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 228, + 554, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 554, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 554, + 299 + ], + "type": "text", + "content": "For each submanifold, we leverage the Proxy Block to learn a unique manifold transformation. Any arbitrary transformation in 3D space can be decomposed into a linear transformation and a translation. Then, these transformations are applied to each deformable cluster. Details about the transformation generation module are described below." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "text", + "content": "Proxy Block. Following the standard block design in Transformer architectures [42], we developed a Proxy Block based on proxy attention, aimed at cross-modal learning for subsequent manifold transformations. We denote " + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "inline_equation", + "content": "P_0" + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "inline_equation", + "content": "F_0" + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "text", + "content": " as a set of proxy tokens and cluster features. And " + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "inline_equation", + "content": "F_0" + }, + { + "bbox": [ + 313, + 300, + 555, + 394 + ], + "type": "text", + "content": " is extracted by a simplified PointNet [34]. Then a transformer block comprises of proxy attention module and feedforward network:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 402, + 401, + 553, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 401, + 553, + 415 + ], + "spans": [ + { + "bbox": [ + 402, + 401, + 553, + 415 + ], + "type": "interline_equation", + "content": "F = F _ {0} + B ^ {\\mathrm {P}}, \\tag {5}", + "image_path": "22435c4e2c863086347d1966e98a455c7bcee5527e86628503ddde99ffd97a3c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 422, + 553, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 422, + 553, + 434 + ], + "spans": [ + { + "bbox": [ + 326, + 422, + 553, + 434 + ], + "type": "interline_equation", + "content": "Q = F W _ {Q}, K = F W _ {K}, V = F W _ {V}, P = P _ {0} W _ {P}, \\tag {6}", + "image_path": "95f7861d7c9cb5c0da98df856e39f2dff7e51f1688232edff550246df4127662.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 359, + 437, + 553, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 437, + 553, + 451 + ], + "spans": [ + { + "bbox": [ + 359, + 437, + 553, + 451 + ], + "type": "interline_equation", + "content": "O ^ {\\mathrm {P}} = F + \\operatorname {P r o x y A t t n} (Q, K, V, P), \\tag {7}", + "image_path": "5ff391ab9aba7ec70c0a070da61eac380f101e98da7b0ebff06f71573e9f92c7.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 387, + 453, + 553, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 453, + 553, + 467 + ], + "spans": [ + { + "bbox": [ + 387, + 453, + 553, + 467 + ], + "type": "interline_equation", + "content": "O = O ^ {\\mathrm {P}} + \\operatorname {F F N} \\left(O ^ {\\mathrm {P}}\\right), \\tag {8}", + "image_path": "85b78950be32d8a0fcc7090a609cccda2394f000a982fb080f5f60c493172a09.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "inline_equation", + "content": "B^{\\mathrm{P}}" + }, + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "text", + "content": " is our proxy bias introduced in Sec. 3.2. " + }, + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "inline_equation", + "content": "W_{Q}, W_{K}, W_{V}" + }, + { + "bbox": [ + 313, + 471, + 554, + 519 + ], + "type": "text", + "content": " are projections for query, key and value. ProxyAttn(·) is a proxy attention module in Eq. (2). FFN(·) is a position-wise feedforward network." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 326, + 519, + 518, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 519, + 518, + 531 + ], + "spans": [ + { + "bbox": [ + 326, + 519, + 518, + 531 + ], + "type": "text", + "content": "In the following sections, for simplicity, we use" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 382, + 539, + 553, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 539, + 553, + 551 + ], + "spans": [ + { + "bbox": [ + 382, + 539, + 553, + 551 + ], + "type": "interline_equation", + "content": "O = \\operatorname {P r o x y B l o c k} (F, P), \\tag {9}", + "image_path": "718051572c7b45cfcfdf0bbe3699f7d585d43c540d5455c27f0cfef8235f1408.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 558, + 520, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 520, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 520, + 569 + ], + "type": "text", + "content": "to represent the basic proxy block (Eqs. (5) to (8))." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "Text Guided Translation. In ego-centric 3D visual grounding, the input text contains global relative positional information between the target object and other reference objects, while the remaining parts naturally correspond to background point clouds. Therefore, text features can effectively guide the model in learning translation vectors that establish spatial relationships between various submanifolds, thereby enhancing the global relational information embedded within the point cloud structure. Specifically, we leverage text features as proxies within the Proxy Block, allowing it to generate text-guided point cloud features that ultimately yield accurate and context-aware final translation" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24586" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 230, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 230, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 230, + 84 + ], + "type": "text", + "content": "vectors for more precise grounding results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 72, + 92, + 294, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 92, + 294, + 106 + ], + "spans": [ + { + "bbox": [ + 72, + 92, + 294, + 106 + ], + "type": "interline_equation", + "content": "F ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {T}\\right), l = 0,.., L - 1, \\tag {10}", + "image_path": "b4dfc366f6c2e8e016db54a90fbdc92d4697a08555278e158e012222d3ddd4cb.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 144, + 114, + 294, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 114, + 294, + 129 + ], + "spans": [ + { + "bbox": [ + 144, + 114, + 294, + 129 + ], + "type": "interline_equation", + "content": "T = F ^ {L} U _ {\\text {t e x t}}, \\tag {11}", + "image_path": "dae26ff97a05cf8334ce8b56c4c374492471fb248b6973b49baeefe6f7b66371.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "inline_equation", + "content": "P_{T}" + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": " are text features " + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{text}}\\in \\mathbb{R}^{S\\times C}" + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": " is number of layers and " + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "inline_equation", + "content": "U_{\\mathrm{text}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": " is a fully connected layer to generate final translation vectors " + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "inline_equation", + "content": "T\\in \\mathbb{R}^{n\\times 3}" + }, + { + "bbox": [ + 55, + 133, + 295, + 169 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 170, + 296, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 170, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 170, + 296, + 289 + ], + "type": "text", + "content": "Image Guided Transformation. The input multi-view image contains rich fine-grained semantic information, compensating for the contextual loss caused by point cloud downsampling. Multi-view images provide pose information of the target object from various perspectives, guiding the model to learn internal transformations of each subpoints relative to the cluster center. Thus, we use pooled image features as proxies in the Proxy Block to generate reshaped image-guided point cloud features, which in turn yield the linear transformations for each submanifold:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 298, + 295, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 298, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 73, + 298, + 295, + 312 + ], + "type": "interline_equation", + "content": "F ^ {l + 1} = \\operatorname {P r o x y B l o c k} \\left(F ^ {l}, P _ {I}\\right), l = 0,.., L - 1, \\tag {12}", + "image_path": "b5875a45428ce9bf7c05030bbba996b9c0197cd5d09e941a24185cd017909d10.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 140, + 319, + 294, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 319, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 140, + 319, + 294, + 335 + ], + "type": "interline_equation", + "content": "M = F ^ {L} U _ {\\text {i m a g e}}, \\tag {13}", + "image_path": "430f4b2ff2150de375453d1ad1363c68c1faae78c0974affcb34b526d9379351.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "inline_equation", + "content": "P_{I}\\in \\mathbb{R}^{V\\times C}" + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "content": " are pooled image features from an additional attention pooling layer. And " + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "content": " is the number of layers and " + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "inline_equation", + "content": "U_{\\mathrm{image}}" + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "content": " is a fully connected layer to generate final transformation matrices " + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "inline_equation", + "content": "M\\in \\mathbb{R}^{n\\times 3\\times 3}" + }, + { + "bbox": [ + 55, + 338, + 295, + 386 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 471 + ], + "type": "text", + "content": "Submanifold Reshape. Once the transformation matrix, containing fine-grained semantic information from the image, and the translation vectors, encompassing precise global relative information from the text, are obtained, we can apply a Proxy Transformation to each submanifold and finally get a diverse enhanced point cloud manifold. To represent this process, we use concise set operations:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 130, + 479, + 294, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 479, + 294, + 493 + ], + "spans": [ + { + "bbox": [ + 130, + 479, + 294, + 493 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {P}} = \\mathcal {M} \\odot \\mathcal {P} \\oplus \\mathcal {T}, \\tag {14}", + "image_path": "3cb9e1f29125d3cdd80ad14969dccc71168f22fc1a3a33d9c89624ad3f375dd5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " are sets of transformation matrices and translation vectors for all clusters. " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " is a union set of submanifolds of different neighborhoods " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}_i\\}_{i = 1}^n" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " , namely a subset of original point cloud. " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 55, + 502, + 295, + 561 + ], + "type": "text", + "content": " represent elementwise multiplication and addition for sets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 562, + 233, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 562, + 233, + 574 + ], + "spans": [ + { + "bbox": [ + 67, + 562, + 233, + 574 + ], + "type": "text", + "content": "Equivalently, for a specific submanifold:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 137, + 582, + 294, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 582, + 294, + 597 + ], + "spans": [ + { + "bbox": [ + 137, + 582, + 294, + 597 + ], + "type": "interline_equation", + "content": "\\hat {P} _ {i} = P _ {i} M _ {i} ^ {T} + T _ {i}, \\tag {15}", + "image_path": "c28f06e422c234284cf39f1329409a81b54eaea6d2ed233484ad49d96b34b750.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "P_{i}\\in \\mathcal{P}\\cap \\mathbb{R}^{m\\times 3}" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " represent sub-points in " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "M_{i}\\in" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{M}\\cap \\mathbb{R}^{3\\times 3}" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "T_{i}\\in \\mathcal{T}\\cap \\mathbb{R}^{3}" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " are the specific transformation matrix and translation vector for this submanifold." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "type": "text", + "content": "Finally, we replace the corresponding parts of the original point cloud with transformed submanifolds to obtain final enhanced point cloud, consisting of rich diversity in manifold structure, which is then fed into 3D backbone during training, enabling efficient multimodal-guided point cloud manifold enhancements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 72, + 395, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 395, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 395, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 91, + 553, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 235 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 235 + ], + "type": "text", + "content": "Dataset and Benchmark. The EmbodiedScan dataset [46] used in our experiments is a large-scale, multi-modal, egocentric resource tailored for comprehensive 3D scene understanding. It comprises 5,185 scene scans from widely-used datasets like ScanNet [8], 3RScan [44], and Matterport3D [3]. This diverse dataset offers a rich foundation for 3D visual grounding, covering a broader range of scenes than previous datasets. The training set includes 801,711 language prompts, while the validation set contains 168,322 prompts, making EmbodiedScan notably larger and more challenging, thus providing a rigorous benchmark for egocentric 3D visual grounding tasks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 235, + 553, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 235, + 553, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 235, + 553, + 306 + ], + "type": "text", + "content": "Experimental Settings. Due to limited resources, we train on the official mini dataset. Despite this, our model outperforms the official baseline trained on the full training set, as shown in Tab. 1. For analysis experiments in Sec. 4.2, we also use the mini training and validation sets available through the official EmbodiedScan release [46]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "text", + "content": "Our reported accuracy uses the official IoU metric, focusing on cases where IoU exceeds " + }, + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 307, + 554, + 402 + ], + "type": "text", + "content": ". We also assess model performance on both \"Easy\" and \"Hard\" scenes, where a \"Hard\" scene contains three or more target objects of the same category. The \"View-Dependent\" and \"View-Independent\" metrics further test the model's spatial reasoning by evaluating performance with and without perspective-specific descriptions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 402, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 554, + 605 + ], + "type": "text", + "content": "Implementation Details. This work builds upon the strong baseline from EmbodiedScan for ego-centric 3D visual grounding. We applied several techniques to enhance the original baseline. First, we replace the RoBERTa language encoder [29] with the CLIP encoder [36] to achieve superior alignment between language and vision. Additionally, we incorporate Class-Balanced Grouping and Sampling (CBGS) [67] during pretraining to address data imbalance and enhance detection accuracy across rare and common object categories. We follow EmbodiedScan's approach by using pretrained visual encoders. Finally, we also adopt text augmented by LLM to provide richer semantic context when training, proposed by [65]. Moreover, our Proxy Transformation is trained using the AdamW optimizer with a learning rate of 5e-4, weight decay of 5e-4, and a batch size of 48. Training spans 12 epochs, with the learning rate reduced by 0.1 at epochs 8 and 11." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 612, + 399, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 612, + 399, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 612, + 399, + 624 + ], + "type": "text", + "content": "4.1. Main Results" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "text", + "content": "We evaluate the 3D visual grounding performance of our proposed method, Proxy Transformation, with results presented in Tab. 1, comparing it against established SOTA methods from the dataset benchmark. In addition, the upper methods with " + }, + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "text", + "content": " are trained on the full dataset, while the lower methods are trained on a mini dataset, approximately " + }, + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 629, + 553, + 712 + ], + "type": "text", + "content": " of the full dataset." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24587" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 89, + 70, + 523, + 191 + ], + "blocks": [ + { + "bbox": [ + 89, + 70, + 523, + 191 + ], + "lines": [ + { + "bbox": [ + 89, + 70, + 523, + 191 + ], + "spans": [ + { + "bbox": [ + 89, + 70, + 523, + 191 + ], + "type": "table", + "html": "
MethodEasy AP25Hard AP25Indep Dep AP25Overall AP25Easy AP50Hard AP50Indep Dep AP50Overall AP50
ScanRefer† [5]13.789.1213.4410.7712.85---
BUTD-DETR† [23]23.1218.2322.4720.9822.14---
L3Det† [69]24.0118.3423.5921.2223.07---
EmbodiedScan†39.8231.0240.3038.4839.1018.7914.9318.03
EmbodiedScan [46]33.8730.4933.5533.6133.5914.5812.4113.92
DenseG [65]40.1734.3838.7940.1839.7018.5215.8817.47
ProxyTransformation41.6634.3841.5740.8141.0819.4314.0918.65
", + "image_path": "a266bfe2a283caea7627c001d9844239e7e3580c77387db31d735a487800e7be.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "spans": [ + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "text", + "content": "As shown in Tab. 1, Proxy Transformation achieves a notable " + }, + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "inline_equation", + "content": "7.49\\%" + }, + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "inline_equation", + "content": "4.60\\%" + }, + { + "bbox": [ + 54, + 264, + 294, + 491 + ], + "type": "text", + "content": " improvement over the previous strongest baseline, EmbodiedScan, on the Overall@0.25 and Overall@0.50. Although only trained on the mini dataset, our method even surpasses the baseline trained on the full dataset. Through deformable point clustering, our model focuses on the most crucial target regions in the scene, reducing the extra computation overhead caused by redundant point clouds and improving efficiency. Additionally, a grid prior preserves essential original spatial information, mitigating early training instability. Recognizing that text information provides global positional relationships among different submanifolds and image information offers local semantic details within each submanifold, we designed generalized proxy attention to guide local transformations of the selected point cloud submanifolds. These transformations optimize local point cloud structures for each submanifold, ultimately providing higher-quality data for subsequent feature extraction and fusion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 493, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 493, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 493, + 295, + 613 + ], + "type": "text", + "content": "In summary, Proxy Transformation consistently outperforms the previous state-of-the-art across multiple evaluation metrics, including easy and hard samples as well as view-independent and view-dependent tasks. These consistent improvements across diverse metrics highlight not only the robustness and generalizability of our approach for 3D visual grounding tasks but also its adaptability to complex scenes and dynamic environments, making it an effective solution for advancing multimodal grounding capabilities in real-world embodied AI applications." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "type": "text", + "content": "4.2. Analysis Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "Ablation on Proposed Modules. We conducted ablation studies on each module to verify their effectiveness as shown in Tab. 2. To ensure fair comparisons, the baseline is enhanced with several modules described in the implementation details. First, we introduce Proxy Transformation without deformable point clustering, resulting in a" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 319, + 262, + 550, + 335 + ], + "blocks": [ + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "lines": [ + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "spans": [ + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "text", + "content": "Table 1. Main Results on the official validation set. The table displays accuracy performance considering instances where IoU exceeds " + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "text", + "content": " under different circumstances as mentioned in Sec. 4. 'Indep' and 'Dep' mean the targets are view-independent and view-dependent. And " + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "text", + "content": " denotes that models are trained on full train dataset. Although our model is trained on mini train dataset (approximately " + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 55, + 200, + 555, + 244 + ], + "type": "text", + "content": " of the full data), but it still surpasses previous methods trained on the full train dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 262, + 550, + 335 + ], + "lines": [ + { + "bbox": [ + 319, + 262, + 550, + 335 + ], + "spans": [ + { + "bbox": [ + 319, + 262, + 550, + 335 + ], + "type": "table", + "html": "
Grid PriorOffsetsPTEasyHardOverall
37.0530.6036.53
✓40.3932.6039.76
✓✓40.5932.1839.91
✓✓✓41.6634.3841.08
", + "image_path": "f3881558a7730385f3f9cc1068231a414cec31d31cec9550e91167845bbaef0f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 321, + 390, + 547, + 439 + ], + "blocks": [ + { + "bbox": [ + 313, + 344, + 555, + 378 + ], + "lines": [ + { + "bbox": [ + 313, + 344, + 555, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 555, + 378 + ], + "type": "text", + "content": "Table 2. Ablation of Proposed Modules. 'PT' represents 'Proxy Transformation'. The reported values are mAP for predictions greater than " + }, + { + "bbox": [ + 313, + 344, + 555, + 378 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 313, + 344, + 555, + 378 + ], + "type": "text", + "content": " IoU." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 390, + 547, + 439 + ], + "lines": [ + { + "bbox": [ + 321, + 390, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 321, + 390, + 547, + 439 + ], + "type": "table", + "html": "
AttnFLOPs#ParamsEasyHardOverall
Vanilla8.36G2.52M40.7133.6540.14
Proxy4.97G2.71M41.6634.3841.08
", + "image_path": "b53803725ee41e2906334e46ed83a84c17b85e4e821528b68a57d464ab11820a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 353, + 515, + 517, + 588 + ], + "blocks": [ + { + "bbox": [ + 313, + 447, + 555, + 503 + ], + "lines": [ + { + "bbox": [ + 313, + 447, + 555, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 555, + 503 + ], + "type": "text", + "content": "Table 3. Ablation on Proxy Attention. Here, we compare the vanilla self-attention block with our Proxy Block. The FLOPs and parameters are computed over 3 transformer blocks with cluster features as input. We use a grid size of 12 and a drop radio of 0.6. The reported values are mAP for predictions greater than " + }, + { + "bbox": [ + 313, + 447, + 555, + 503 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 313, + 447, + 555, + 503 + ], + "type": "text", + "content": " IoU." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 353, + 515, + 517, + 588 + ], + "lines": [ + { + "bbox": [ + 353, + 515, + 517, + 588 + ], + "spans": [ + { + "bbox": [ + 353, + 515, + 517, + 588 + ], + "type": "table", + "html": "
Grid SizeEasyHardOverall
w/o40.5932.1839.91
1040.9432.8140.29
1241.6634.3841.08
1441.1134.2840.56
", + "image_path": "55ca8e69c429e181002f1ad5ce943278af20567722a552c4fafe487fe725fd6f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 596, + 554, + 619 + ], + "lines": [ + { + "bbox": [ + 313, + 596, + 554, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 596, + 554, + 619 + ], + "type": "text", + "content": "Table 4. Ablation on the size of Grid Prior. The reported values are mAP for predictions greater than " + }, + { + "bbox": [ + 313, + 596, + 554, + 619 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 313, + 596, + 554, + 619 + ], + "type": "text", + "content": " IoU." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "content": "substantial improvement of " + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "inline_equation", + "content": "3.23\\%" + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "content": ", which demonstrates the effectiveness and necessity of our multimodal point cloud enhancement. Then, we add deformable offsets, yielding an additional improvement on easy samples, indicating that offsets effectively guide cluster centers toward target regions. Finally, we incorporate grid prior, which improves" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24588" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 94, + 70, + 526, + 274 + ], + "blocks": [ + { + "bbox": [ + 94, + 70, + 526, + 274 + ], + "lines": [ + { + "bbox": [ + 94, + 70, + 526, + 274 + ], + "spans": [ + { + "bbox": [ + 94, + 70, + 526, + 274 + ], + "type": "image", + "image_path": "8de7be3e9c60e296a5e84c3eb8ed8f3d25f5ca81b327d4cb11d2a974ceac7d37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 285, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 55, + 285, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 555, + 308 + ], + "type": "text", + "content": "Figure 3. Visualization of ground truth and predictions. Ground truth boxes are shown in green, baseline in red, and ProxyTransformation's predictions in violet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 99, + 320, + 252, + 393 + ], + "blocks": [ + { + "bbox": [ + 99, + 320, + 252, + 393 + ], + "lines": [ + { + "bbox": [ + 99, + 320, + 252, + 393 + ], + "spans": [ + { + "bbox": [ + 99, + 320, + 252, + 393 + ], + "type": "table", + "html": "
LayersEasyHardOverall
141.6034.0740.99
241.5731.9740.79
341.6634.3841.08
441.7231.5540.90
", + "image_path": "67f50c3b96060e4b47da9e54602eca39cee7a17b9b4fe1535d27a6e1074bddf1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 402, + 295, + 425 + ], + "lines": [ + { + "bbox": [ + 55, + 402, + 295, + 425 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 295, + 425 + ], + "type": "text", + "content": "Table 5. Ablation on the number of Proxy Layers. The reported values are mAP for predictions greater than " + }, + { + "bbox": [ + 55, + 402, + 295, + 425 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 55, + 402, + 295, + 425 + ], + "type": "text", + "content": " IoU." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 445, + 295, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 295, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 295, + 493 + ], + "type": "text", + "content": "training stability and achieves an increase of " + }, + { + "bbox": [ + 55, + 445, + 295, + 493 + ], + "type": "inline_equation", + "content": "2.20\\%" + }, + { + "bbox": [ + 55, + 445, + 295, + 493 + ], + "type": "text", + "content": " on hard samples. This result shows that the grid prior mitigates the randomness of offsets in the early stages of training, preserving essential scene information for the model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 495, + 295, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 295, + 627 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 295, + 627 + ], + "type": "text", + "content": "Ablation on Proxy Attention. We validate the effectiveness and efficiency of proxy attention by comparing the vanilla attention block with the proxy block. The input cluster features are aligned across both blocks. As discussed in Sec. 3.2, the number of proxy tokens is significantly smaller than the input sequence length. This reduction in proxy tokens compresses redundancy within the attention module, enhancing computational efficiency, which aligns with our experiment results. As shown in Tab. 3, our approach achieves higher performance than vanilla attention, while reducing the computation overhead by " + }, + { + "bbox": [ + 55, + 495, + 295, + 627 + ], + "type": "inline_equation", + "content": "40.6\\%" + }, + { + "bbox": [ + 55, + 495, + 295, + 627 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Ablation on Main Hyperparameters. Then, we ablate several hyperparameters in deformable point clustering and proxy transformation. As shown in Tab. 4, the size of the grid prior also influences performance by reducing instability during the early training stages, which can result from the randomness of the initial transformations. As shown in Tab. 5, we conduct several experiments to determine the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 323, + 555, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 555, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 555, + 371 + ], + "type": "text", + "content": "optimal layers of our proxy attention block for efficient learning. Based on these findings, we selected the optimal hyperparameters for our experiments. Moreover, further ablation studies are given in the supplementary material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 387, + 499, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 499, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 499, + 399 + ], + "type": "text", + "content": "4.3. Qualitative Results and Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 407, + 555, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 503 + ], + "type": "text", + "content": "With our deformable point clustering and Proxy Transformation, the point cloud structure in target regions is optimized, providing higher-quality data for subsequent feature learning and fusion. As shown in Fig. 3, reference objects in these regions are small and difficult to distinguish, but with the enhanced manifold structure, our model effectively captures the relationships between target and reference objects, achieving improved grounding performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 522, + 388, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 388, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 388, + 534 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 546, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 555, + 712 + ], + "type": "text", + "content": "In this work, we propose Proxy Transformation, a real-time multimodal point cloud enhancement model, to address issues of geometric loss and unexpected noise in 3D points within ego-centric 3D visual grounding. This approach yields a high-quality point cloud structure for feature learning. Extensive experiments show that our model not only outperforms all existing methods but also improves the computational efficiency of attention modules, setting a new SOTA on the EmbodiedScan benchmark. These results demonstrate the effectiveness and robustness of using multimodal information for real-time point cloud enhancement in ego-centric 3D visual grounding, offering fresh insights for advancing embodied AI and enabling human-computer interaction in real-world environments." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24589" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 128 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 128 + ], + "type": "text", + "content": "The work is supported in part by the National Natural Science Foundation of China under Grant U24B2017, and Beijing Natural Science Foundation under Grant QY24257." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "spans": [ + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 157, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "spans": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. 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In ICLR, 2021. 5" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24592" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_content_list.json b/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..059693918f2f872e727c32e28a5894fe8f11d450 --- /dev/null +++ b/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_content_list.json @@ -0,0 +1,1509 @@ +[ + { + "type": "text", + "text": "Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection", + "text_level": 1, + "bbox": [ + 122, + 130, + 875, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ting Li $^{1}$ , Mao Ye $^{1*}$ , Tianwen Wu $^{1}$ , Nianxin Li $^{1}$ , Shuaifeng Li $^{1}$ , Song Tang $^{2}$ , and Luping Ji $^{1}$ $^{1}$ University of Electronic Science and Technology of China \n $^{2}$ University of Shanghai for Science and Technology", + "bbox": [ + 135, + 179, + 857, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lting1103@gmail.com, cvlab.uestc@gmail.com", + "bbox": [ + 308, + 236, + 683, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thermal object detection is a critical task in various fields, such as surveillance and autonomous driving. Current state-of-the-art (SOTA) models always leverage a prior Thermal-To-Visible (T2V) translation model to obtain visible spectrum information, followed by a cross-modality aggregation module to fuse information from both modalities. However, this fusion approach does not fully exploit the complementary visible spectrum information beneficial for thermal detection. To address this issue, we propose a novel cross-modal fusion method called Pseudo Visible Feature Fine-Grained Fusion (PFGF). Specifically, a graph is constructed with nodes generated from multi-level thermal features and pseudo-visual latent features produced by the T2V model. Each level of features corresponds to a subgraph. An Inter-Mamba block is proposed to perform cross-modality fusion between nodes at the lowest level; while a Cascade Knowledge Integration (CKI) strategy is used to fuse low-level fused information to high-level subgraphs in a cascade manner. After several iterations of graph node updating, each subgraph outputs an aggregated feature to the detection head respectively. Unlike previous cross-modal fusion methods, our approach explicitly models high-level relationships between cross-modal data, effectively fusing different granularity information. Experimental results demonstrate that our method achieves SOTA detection performance. Code is available at https://github.com/liting1018/PFGF.", + "bbox": [ + 86, + 318, + 485, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 742, + 220, + 757 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object detection is critical in computer vision, with applications in autonomous driving and video surveillance [27]. While most methods rely on visible spectrum images, they often struggle in adverse conditions like nighttime, fog, or snow. In contrast, thermal spectrum images offer robustness in challenging environments [13], but they may falter in the daytime due to limited texture detail. Both visible-", + "bbox": [ + 89, + 767, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/58bcf8f9f51cd5387bee19dab540b69f8302e97d1b428858add2456ed14b0db5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 287, + 931, + 410 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1af7d47aa4ad8ba3036fc5a578bf357cce731796779777b10aa862f60184de68.jpg", + "image_caption": [ + "Figure 1. Comparison between previous attention-based method and our method. (a) An attention-based module combines channel and spatial attention to augment the modality-translation awareness of detection. (b) Our method employs a Graph-Mamba Fusion module to integrate cross-modality knowledge in a cascade manner with different granularity." + ], + "image_footnote": [], + "bbox": [ + 516, + 415, + 931, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "only and thermal-only approaches face limitations by solely relying on one spectrum, and lacking complementary data. As a result, multi-spectral (visible and thermal) object detection [8, 25, 52] have gained popularity. However, these approaches require paired visible and thermal images for both training and inference, increasing hardware costs and complexity. Furthermore, the need for precise alignment between modalities further limits practical deployment [5]. Consequently, there is growing interest in visible knowledge assistance methods that utilize paired visible-thermal images for training and solely thermal images for testing.", + "bbox": [ + 509, + 654, + 906, + 820 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visible knowledge-assisted thermal pedestrian detection methods can be categorized into two routes: data enhancement and cross-modal transfer. The route of data enhancement [2] employs generative models to adapt visible images to the thermal domain like domain adaptation [26, 29], us", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The corresponding author.", + "bbox": [ + 107, + 887, + 256, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6710", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing them during training to mitigate the limitations caused by relying solely on thermal data during testing. However, the generated thermal images may be unreliable, potentially degrading the performance of thermal pedestrian detectors. Another route is based on cross-modal transfer, which can be further divided into two approaches. The first approach, feature domain transformation [45], utilizes an auxiliary network to convert thermal features into visible ones. However, this process demands substantial computation and large models to maintain feature quality in high-dimensional spaces. The second approach, image domain transformation [44], employs a generative model to directly convert thermal images into visible ones. The transformed visible images are then fused with the original thermal images, as illustrated in Fig.1(a).", + "bbox": [ + 89, + 90, + 480, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While image domain transformation methods have attained the state-of-the-art performance in thermal object detection, they still face obstacles related to occlusions and visible image noise. This limitation primarily stems from the inherent unreliability of visible images generated from thermal data, which can introduce noise that adversely affects detection accuracy. Furthermore, these approaches often neglect the fine-grained multimodal knowledge relationships between pseudo-visible and thermal data. As a result, effectively harnessing the complementary nature of thermal and visible information to resolve ambiguities in complex scenes remains a significant challenge. Fortunately, Graph Neural Networks (GNNs) offer a promising alternative for modeling and reasoning about relationships [30]. This motivates us to utilize graph structures for enabling interactions among features at various granularities. Such an approach ensures comprehensive utilization of information between low-level features to high-level semantics, leading to richer and more nuanced cross-modal integration. However, the flexible flow of information between nodes may introduce redundancy or irrelevant data, potentially hindering detection performance. To address this, we incorporate Mamba's selection mechanism [53] to effectively filter out unimportant information in the long-range context, which is particularly crucial for thermal feature maps that often contain noise and lack texture details. Furthermore, by iteratively updating node features based on neighborhood nodes, it can minimize the impact of less relevant nodes, thereby enhancing feature fusion and representation.", + "bbox": [ + 91, + 321, + 482, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the above analysis, as illustrated in Fig. 1(b), we propose a novel cross-modal fusion method, dubbed as Pseudo Visible Feature Fine-Grained Fusion (PFGF). First, we obtain the visible features using the Pearl-GAN method [37], which are referred to as generative features. To fuse these generative features, we introduce the Graph-Mamba Fusion module. Specially, a graph is constructed that consists of multiple subgraphs, where each subgraph corresponds to either the generative feature or the output features", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "from different levels of the detector backbone (referred to as discriminative features). The node features in each subgraph represent multi-level information, corresponding to different feature levels. For graph computation, we propose the Inter-Mamba block and Cascade Knowledge Integration (CKI) strategy, which facilitate efficient knowledge fusion and propagation across subgraphs. The Inter-Mamba block is introduced to fuse the nodes of subgraphs between the generative feature and the low-level discriminative feature, here the $c^3$ feature from CSPDarknet [1]. Then, a Cascade Knowledge Integration (CKI) strategy is proposed to propagate the knowledge from the low-level subgraph to the high-level subgraph in a cascade manner. During this cascading process, node features are updated using the Gate Recurrent Unit (GRU) method [9], while the VMamba block further refines these features across subgraphs.", + "bbox": [ + 511, + 90, + 903, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows: (1) We are the first to employ pseudo visible feature fine-grained fusion method for thermal object detection. The information interaction ability of graph at different granularities and the information selection and enhancement ability of Mamba have been fully utilized. (2) An Inter-Mamba block is proposed to facilitate cross-modality fusion between generative and discriminative node features. Additionally, the cascade knowledge integration strategy aggregates knowledge from low-level to high-level feature subgraphs avoiding tedious computation. (3) Experiments conducted on public FLIR, LLVIP, and Autonomous Vehicles datasets demonstrate significant advantages over the state-of-the-art (SOTA) thermal object detection methods.", + "bbox": [ + 511, + 335, + 903, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 561, + 653, + 577 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Thermal Object Detection", + "text_level": 1, + "bbox": [ + 511, + 589, + 750, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thermal object detection is crucial in low-light environments and privacy-sensitive scenarios. Existing approaches can be categorized into direct reconstruction and visible knowledge assistance. In the direct reconstruction approach, the methods [21, 22, 38] focus on designing networks to extract discriminative features by leveraging the intrinsic characteristics of thermal images. For example, GPCAnet [48] predicts object positions in the image to allocate more ROIs to the predicted areas. The Visible knowledge assistance methods can be further divided into data augmentation and cross-modal transfer. The data augmentation works [2, 20] use GANs to convert visible images into thermal images, mixing them to enhance detector robustness. In the cross-modal transfer approach, the works try to generate pseudo visual images or features. For example, TIRDet [44] uses Pearl-GAN for image translation. Xie et al [45] use a hallucination network to learn visible features from thermal images. All methods lack in-depth research on pseudo-visible information fusion.", + "bbox": [ + 511, + 613, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6711", + "bbox": [ + 482, + 945, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Graph Based Cross Modality Fusion", + "text_level": 1, + "bbox": [ + 89, + 90, + 406, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent years, graph-based approaches have gained significant traction in computer vision applications [36]. Typically, graph operates as message-passing algorithms, where node representations are iteratively updated based on their neighbors through a differentiable aggregation function [34]. This makes graph particularly valuable in multisource data fusion. For instance, Cai et al. [3] used a graph-attention mechanism to fuse embeddings from different feature extractors, while Li et al. [24] proposed an interactive GNN-based architecture to facilitate cross-modality fusion. Our work is closely related latter work that utilizes graph structures to explicitly model and reason about different granularity information interactions between complementary data sources. However, our approach uniquely incorporates Mamba's selection mechanism to strengthen graph node representations, effectively minimizing the impact of unimportant nodes at each step of hidden state computation.", + "bbox": [ + 89, + 112, + 483, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Mamba Based Cross Modality Fusion", + "text_level": 1, + "bbox": [ + 89, + 378, + 416, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since its inception for linear-time sequence modeling in natural language processing, Mamba [14] has rapidly been adapted for various applications in computer vision. For example, VMamba [35] leverages a four-way scanning algorithm to advance object detection and segmentation beyond the capabilities of the Swin Transformer. Mamba has already been used in cross-modality fusion. Xie et al. [46] leveraged Mamba for dynamic feature enhancement in multimodal image fusion. Pan-Mamba [15] is developed to facilitate efficient cross-modal information exchange and fusion. The Fusion-Mamba block [10] is introduced to mitigate disparities between cross-modal features and enhance the consistency of fused feature representations. Additionally, Li et al. [23] proposed cross-modality fusion-Mamba, coupled with weather removal techniques, to improve detection accuracy under adverse weather conditions. Distinct from prior research, our work pioneers the integration of the Mamba architecture into graph representations for thermal object detection tasks, significantly enhancing graph embeddings and processing capabilities.", + "bbox": [ + 89, + 398, + 483, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 89, + 715, + 225, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Statement", + "text_level": 1, + "bbox": [ + 89, + 739, + 274, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose the training dataset $D_{s} = \\{X^{t},X^{v}\\}$ , where the thermal image set $X^{t} = \\{x_{s_{i}}^{t}\\}_{i = 1}^{N_{st}}$ with labels $\\{y_{s_i}^t\\}_{i = 1}^{N_{st}}$ and the unpaired visible image set $X^{v} = \\{x_{s_{i}}^{v}\\}_{i = 1}^{N_{sv}}$ . $N_{st}$ and $N_{sv}$ denote the cardinality of the thermal image set and visible image set respectively. The test dataset $D_{t} = \\{x_{t_{i}}^{t}\\}_{i = 1}^{N_{t}}$ be exclusively composed of thermal images, where $N^t$ represents the number of thermal images in the test dataset. Our objective is to compensate for visible knowledge while using solely thermal images as the input at the test stage,", + "bbox": [ + 89, + 762, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and fully leverage information from both modalities to develop robust representations at the training stage.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Fig. 2(a) illustrates the proposed Pseudo Visible Feature Fine-Grained Fusion (PFGF) framework, which uses the single-stage detector YOLOX [12] as the baseline model. Both training and testing are conducted exclusively with thermal images. Specifically, we first train Pearl-GAN as a prior thermal-to-visible (T2V) translation model $\\Phi$ , which is trained on both thermal and visible modalities, to convert thermal image $x^t$ into daytime visible image $x^v$ , thereby incorporating valuable visible information from the unpaired set $X^v$ . This process is described as follows:", + "bbox": [ + 511, + 121, + 906, + 272 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ x ^ {v}, z ] = \\Phi (x ^ {t}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 279, + 903, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x^{t} \\in \\mathbb{R}^{H \\times W \\times 1}$ and $x^{v} \\in \\mathbb{R}^{H \\times W \\times 3}$ . $\\Phi(x^{t})$ comprises a convolution-based encoder $z = \\varepsilon(x^{t})$ and a decoder $x^{v} = \\mu(z)$ . The latent T2V code $z \\in \\mathbb{R}^{h_{z} \\times w_{z} \\times c_{z}}$ is considered as generative feature.", + "bbox": [ + 511, + 301, + 903, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CSPDarknet is employed as the backbone $\\mathcal{F}$ to extract multi-level features $c^3, c^4$ and $c^5$ from the concatenated images $x^t$ and $x^v$ as follows,", + "bbox": [ + 511, + 364, + 903, + 410 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ c ^ {3}, c ^ {4}, c ^ {5} \\right] = \\mathcal {F} \\left(\\operatorname {c o n c a t} \\left(x ^ {t}, x ^ {v}\\right)\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 417, + 903, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A VMamba [35] block $\\mathcal{M}$ then refines these features:", + "bbox": [ + 511, + 441, + 867, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {i} = \\mathcal {M} ^ {i} \\left(c ^ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 464, + 903, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for $i \\in \\{3,4,5\\}$ . The output features $f^i \\in R^{h \\times w \\times c}$ are considered as discriminative features. We refer to this process as the VMamba-based Multi-level feature Enhancement (MEM). Here, a VMamba block is utilized to learn global relationships and contextual information from two modalities, thereby enhancing the model's representational capacity. Additionally, due to Mamba's input-dependent mechanism and various hardware-optimized techniques, it excels in long-range modeling with reduced computational cost compared to Transformers.", + "bbox": [ + 511, + 489, + 905, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To better integrate the generated visible features, we propose a novel Graph-Mamba Fusion (GMF) module $\\mathcal{G}$ . This approach effectively combines generative feature $z$ with discriminative features $f_{i}$ as follows,", + "bbox": [ + 511, + 642, + 905, + 702 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ g ^ {3}, g ^ {4}, g ^ {5} \\right] = \\mathcal {G} \\left(f ^ {3}, f ^ {4}, f ^ {5}, z\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 708, + 903, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graph-Mamba Fusion (GMF) module, as a key contribution, goes beyond simple attention by establishing high-level relationships. It first fuses generative feature $z$ with the discriminate feature $f^3$ and then performs high-level fusion from $f^3$ to $f^5$ , which will be introduced later.", + "bbox": [ + 511, + 734, + 905, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Subsequently, the features $f^i$ and $g^i$ are combined using residual connections and a Neck module $\\Phi$ to obtain the output features $f^{i'} = \\Phi (f^i + g^i)$ , where $i \\in \\{3, 4, 5\\}$ . Finally, the Decoupled Detection Head $\\mathcal{H}$ [12] is employed to obtain the detection result based on $f^{i'}$ . The model is trained using the standard detection loss $L_{d}(\\mathcal{H}(f^{3'}, f^{4'}, f^{5'}, y_{s_i}^t))$ .", + "bbox": [ + 511, + 810, + 905, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6712", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bef22e91b37620cb3327916041c00ae8d2d5337a5a13ab67a3ebc7cda5d53109.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 116, + 88, + 880, + 268 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/874c38a39bf8f360c1526cb641989e0fdac7f8ca00018af058d7817eb0f72e03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 116, + 271, + 880, + 353 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0057ff9040ce5b042438dece57b1c480ad3e0189a88f04a95f72de9aa5c09b0b.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed PFGF method. (a) The framework of the PFGF, with our modules highlighted in the purple box. (b) The Graph-Mamba Fusion Module constructs the graph structure for both discriminative and generative features, with leader nodes guiding the flow of information between graphs. (c) The Inter-Mamba Module facilitates interactions between different modalities. (d) The VMamba Module updates nodes within the same modality." + ], + "image_footnote": [], + "bbox": [ + 116, + 356, + 880, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Pseudo Visible Feature Fine-Grained Fusion", + "text_level": 1, + "bbox": [ + 89, + 532, + 465, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For further integrating the generative feature $z$ , a straightforward attention-based fusion approach, as used in [44], can be employed. However, this method has limitations in effectively capturing high-level relationships among the features. Additionally, it struggles to capture essential visual information due to the unreliability of the generated visible images, which often introduces a substantial amount of irrelevant information. To overcome these challenges, we introduce the Graph-Mamba Fusion (GMF) module as shown in Fig. 2(b). Graph structure is employed to establish more compensated relationships between different level features, which Mamba is adapted to capture long-range dependencies with less computational complexity.", + "bbox": [ + 89, + 561, + 483, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To avoid getting lost in details, let's first briefly introduce the process. (1) Graph construction. The features $f^3$ , $f^4$ , $f^5$ , and $z$ are down-and-up sampled to different copies as graph nodes. Graph edges are constructed by computing similarity between nodes, and message passing is performed by aggregating features from neighboring nodes. (2) Graph computation. An Inter-Mamba block is proposed to facilitate fusion between the nodes produced by latent feature $z$ and discriminative feature $f^3$ respectively as illus-", + "bbox": [ + 89, + 763, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "trated in Fig. 2 (c). The GRU algorithm is used to update graph nodes, ensuring effective information propagation. Subsequently, a VMamba block is used to further refine the node feature. The output $g^3$ is formed by merging the node features of $f^3$ and is then multiplied with the nodes derived from $f^4$ , enabling the fusion of information across different levels. The output $g^4$ and $g^5$ are obtained by merging the node features from $f^4$ and $f^5$ , respectively.", + "bbox": [ + 511, + 532, + 906, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1. Graph construction", + "text_level": 1, + "bbox": [ + 511, + 666, + 696, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this part, we will introduce how to construct a graph $\\Psi = (U,E)$ based on the features $f$ and $z$ . This structure is inspired by the method [24], which effectively models the relationships and dependencies among features extracted from different levels or modalities. The graph structure is designed to ensure that the fusion of these features is contextually relevant, thereby enhancing the accuracy and robustness of the representations used for detection.", + "bbox": [ + 511, + 686, + 906, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Node generation. Given the generative feature $z$ and discriminative feature $f$ , two types of nodes are generated. To capture multi-level information and enhance feature diversity, we make replicas of different granularities of the corresponding features as graph nodes. Specifically, pyramid pooling, convolution, and upsampling operations are ap-", + "bbox": [ + 511, + 810, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6713", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "plied to both generative feature $z$ and discriminate feature $f$ , which can be formally computed as follows:", + "bbox": [ + 89, + 90, + 482, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {j} ^ {i} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} \\left(f ^ {i}\\right)\\right)\\right), z _ {j} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} (z)\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 128, + 482, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the operator $\\mathcal{P}_j(\\cdot)$ pools the given feature to various sizes according to the scale setting $j$ , a $1 \\times 1$ convolution is applied to reduce the dimension of the pooled representation, and $Up$ operator, using bi-linear interpolation, up-samples the feature maps to match the original size. For each $f^i$ and $z$ , there are $n$ node features $f_j^i \\in R^{h \\times w \\times c'}$ for $j \\in \\{1, \\dots, n\\}$ and $z_j \\in R^{h \\times w \\times c'}$ . Here $n = 3$ . Note that $z$ has only one scale and shares the same shape as $f^3$ .", + "bbox": [ + 89, + 156, + 483, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Edge generation. The edges play a crucial aspect, as it facilitates the propagation of information between nodes. Here, we only compute intra-edges, i.e., the edges connect the nodes produced by the same feature. Since our goal is to incorporate the information from the generative feature $z$ into the discriminative feature $f$ , there is no need to construct additional edges between the nodes produced by the generative feature. Specifically, for the feature $f^i$ , the intra-edge $e_{j,k}^i$ is computed as", + "bbox": [ + 89, + 281, + 483, + 417 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne _ {j, k} ^ {i} = \\operatorname {C o n v} \\left(f _ {j} ^ {i} - f _ {k} ^ {i}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 426, + 482, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Conv(\\cdot)$ is used to learn relationships between nodes. The term $f_{j}^{i} - f_{k}^{i}$ represents the difference between the node features $f_{j}^{i}$ and $f_{k}^{i}$ . This highlights the relative disparity between nodes, following the approach outlined in [43]. Based on our edge computation method, we have formed four subgraphs, which are constructed by graph nodes formed by the features $z, f^{3}, f^{4}$ , and $f^{5}$ , respectively. Here the edges between the subgraphs of different discriminative features are not computed to avoid tedious computation. Instead, we introduce a new leader node to aggregate subgraph node features, and then pass the aggregated feature to the next subgraph from $f^{3}$ to $f^{5}$ .", + "bbox": [ + 89, + 453, + 483, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Message Passing. In each subgraph composed of discriminative features, every node aggregates feature messages from all its neighboring nodes. For the node $f_{j}^{i}$ , at $l - 1$ message passing, denoted as $m_{j}^{i,l - 1}$ , is computed as", + "bbox": [ + 89, + 637, + 483, + 702 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nm _ {j} ^ {i, l - 1} = \\sum_ {k \\in \\mathcal {N} (j)} \\operatorname {S i g m o i d} \\left(e _ {k, j} ^ {i, l - 1}\\right) \\cdot f _ {k} ^ {i, l - 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 710, + 482, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Sigmoid(\\cdot)$ function is utilized to calculate the link weight between nodes.", + "bbox": [ + 89, + 753, + 482, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2. Graph computation", + "text_level": 1, + "bbox": [ + 89, + 791, + 274, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Graph-based cross-modality information fusion consists of two key components: cross-modality fusion through the Inter-Mamba block and knowledge integration via GRU and VMamba.", + "bbox": [ + 89, + 809, + 483, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross modality fusion by Inter-Mamba block. For fusing the node features $z_{j}$ and $f_{j}^{3}$ , instead of transformer-based", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "route, we proposed a Mamba-based block. As shown in Fig. 2(c), the node features $f_{j}^{3}$ and $z_{j}$ are first projected into the hidden state space followed by a VMamba block, and a gating operation is then employed to facilitate the interaction between these two types of hidden state features.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, the node features $f_{j}^{3}$ and $z_{j}$ are first flattened to form the input token sequences $T_{j}^{3}$ and $T_{j}$ , each with dimensions $B \\times N \\times C$ , where $B$ , $N$ , and $C$ denote the batch size, sequence length, and number of channels, respectively. These sequences are then normalized by a normalization layer. Next, the normalized sequences $T_{j}^{3}$ and $T_{j}$ are projected into the hidden state space respectively through linear layers, convolution, and SSM, resulting in the hidden state features $\\hat{f}_{j}^{3}$ and $\\hat{z}_{j}$ . Simultaneously, the normalized sequence $T_{j}^{3}$ is also projected through linear layers with SiLU activation to obtain the gating weight $r$ . It is used for hidden state feature fusion as follows,", + "bbox": [ + 511, + 167, + 906, + 351 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {j} ^ {3} = \\mathcal {R} \\left(\\mathcal {Y} \\left(\\left(\\hat {z} _ {j} + \\hat {f} _ {j} ^ {3}\\right) \\odot r\\right) + f _ {j} ^ {3}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 366, + 903, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ represents element-wise multiplication. The operator $\\mathcal{V}$ denotes the projection operation with a linear transformation, while $\\mathcal{R}$ refers to the reshaping operation.", + "bbox": [ + 511, + 401, + 903, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cascade Knowledge Integration (CKI) strategy. Existing studies [11] have demonstrated that deep and shallow features exhibit complementary characteristics: deep features capture high-level semantic information, while shallow features retain rich spatial details. Leveraging multilevel features is therefore advantageous for enhancing detection performance. As we stated before, a leader node is proposed to convey low-level fused information to high-level subgraph in a cascade manner.", + "bbox": [ + 511, + 446, + 905, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first apply a GRU-based update method [9] to enhance the nodes' ability to capture complex feature interactions and retain relevant information from neighboring nodes. After $l-1$ message passing, the node feature $f_{j}^{i}$ is updated by $\\mathcal{U}_{GRU}(f_{j}^{i}, m_{j}^{i,l-1})$ (See the Appendix for a detailed description of $\\mathcal{U}_{GRU}$ ).", + "bbox": [ + 511, + 585, + 905, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A leader node feature $g^i$ at the $i$ -th scale is computed as", + "bbox": [ + 532, + 681, + 901, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng ^ {i} = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(\\mathcal {M} \\left(f _ {1} ^ {i}\\right), \\dots , \\mathcal {M} \\left(f _ {n} ^ {i}\\right)\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 710, + 903, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{M}$ denotes a VMamba block as mentioned before.", + "bbox": [ + 511, + 744, + 892, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The leader node $g^i$ conveys knowledge to the subsequent subgraph nodes as follows,", + "bbox": [ + 511, + 761, + 903, + 791 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {j} ^ {i + 1} = f _ {j} ^ {i + 1} \\odot \\mathcal {A} (g ^ {i}) + f _ {j} ^ {i + 1}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 805, + 903, + 827 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{A}$ represents an attention operation, which is computed via global average pooling followed by a Sigmoid activation. Since the last subgraph does not contribute to knowledge transmission, the scale $i$ is set to 3 and 4.", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6714", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 89, + 222, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 89, + 114, + 297, + 132 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. To evaluate our method, we conduct experiments on the FLIR-aligned dataset [49], LLVIP dataset [18], and Autonomous Vehicles dataset [42]. (1) The FLIR dataset originally presented challenges due to unaligned thermal-visible image pairs. Therefore, we utilize the aligned version, consisting of 5,142 thermal-visible image pairs, with 4,129 pairs for training and 1,013 for testing. This dataset includes three object categories: \"person,\" \"car,\" and \"bicycle\". (2) The LLVIP dataset is collected in very dark environments. It comprises 15488 aligned image pairs, with 12,025 pairs used for training and 3,463 pairs for testing. This dataset focuses on a single object class: \"person\". (3) The Autonomous Vehicles dataset comprises 6,009 paired images for training and 1,503 for testing, covering five categories: \"bike\", \"car\", \"car_stop\", \"color_cone\", and \"person\". Compared to the FLIR and LLVIP datasets, the scenes in this dataset are more complex.", + "bbox": [ + 89, + 138, + 482, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We evaluate our method using standard object detection metrics [31], including mean Average Precision (mAP), mAP50, and mAP75. The mAP metric represents the average AP over IoU thresholds ranging from 0.50 to 0.95, with an interval of 0.05. The mAP50 and mAP75 metrics correspond to the AP values at IoU thresholds of 0.50 and 0.75, respectively. Higher values for these metrics indicate better performance.", + "bbox": [ + 89, + 396, + 482, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We utilize a pre-trained model on the COCO dataset and implement our approach using the MMDetection toolbox [6], a widely adopted framework for object detection. The network is trained using the SGD optimizer with a batch size of 4 and an initial learning rate of 5e-4. The input image size is set to $640 \\times 640$ for the FLIR, LLVIP, and Autonomous Vehicles datasets, with the training conducted over 8 epochs. The training process is conducted in two stages. In the first stage, the Pearl-GAN module is trained. In the second stage, with the parameters of the Pearl-GAN module fixed, the backbone, VMamba, Graph-Mamba Fusion (GMF) module, neck, and detection head are trained. For the GMF module, the number of graph nodes $n$ is set to 3, and the number of message-passing iterations $L$ is also set to 3. The cascade quantities of VMamba and Inter-Mamba blocks are each configured to 2. Details on hyper-parameter sensitivity are provided in the Appendix. To ensure reproducibility, all experiments are conducted with a random seed set to 0.", + "bbox": [ + 89, + 517, + 482, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 89, + 816, + 454, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. We compare the proposed PFGF method with both mono-modality (thermal) and multispectral (visible + thermal) methods. The mono-modality methods include Faster RCNN [41], SSD [33], RetinaNet", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0e116b0be64d19a93663f15f7669f11d2f154d5764864cb0795e8f8ec6fbbb5d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5074.432.537.6
SSD [33]TVGG1665.522.429.6
RetinaNet [32]TResNet5064.520.328.3
YOLOv3 [40]TDarknet5373.631.336.8
YOLOX-L [12]TCSPD5378.139.442.6
IAH [45]TDarknet5376.4--
DIP [17]TResNet5077.3--
TIRDet [44]TCSPD5381.441.144.3
IDA [28]TCSPD5381.143.446.3
PFGF (Ours)TCSPD5384.844.647.1
CFR_3 [49]V+TVGG1672.4--
GAFF [50]V+TResNet1872.932.937.5
YOLOFusion [39]V+TVGG1676.6-39.8
CMX [51]V+TSwinT82.237.142.3
IGT [7]V+TSwinT85.036.943.6
DATFF [16]V+TResNet5080.2--
RSDet [52]V+TResNet5081.1-41.1
Fusion-Mamba [10]V+TCSPD5384.9-47.0
", + "bbox": [ + 516, + 89, + 903, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparisons on FLIR dataset in terms of MAP. The best results are highlighted in bold.", + "bbox": [ + 511, + 388, + 906, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[32], YOLOv3 [40], YOLOX-L [12], IAH [45], DIP [17], TIRDet [44] and IDA [28]. These methods utilize paired visible and thermal images for training, but only thermal images for testing. In contrast, the multispectral methods include CFR_3 [49], GAFF [50], YOLOFusion [39], CMX [51], IGT [7], DATFF [16], RSDet [52], YOLOv5-VT [19], DM-Fusion [47], and Fusion-Mamba [10]. These methods employ paired visible and thermal images for both training and testing. The results presented in the tables are cited from the respective papers.", + "bbox": [ + 511, + 445, + 906, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. The quantitative comparison results are presented in Tables 1, 2, and 3. Our method achieves the state-of-the-art (SOTA) performance among mono-modality (thermal) methods on the FLIR, LLVIP, and Autonomous Vehicles datasets. On the FLIR dataset, our approach outperforms the recent TIRDet and IDA methods, achieving mAP gains of $2.8\\%$ and $0.8\\%$ , respectively, along with mAP50 improvements of $3.4\\%$ and $3.7\\%$ . For a fair comparison of the LLVIP dataset, we reproduced the TIRDet method using a Pearl-GAN model trained on the LLVIP dataset, referred to as TIRDet*. Similarly, our method denoted as PFGF*, utilizes this same Pearl-GAN model. Additionally, to facilitate comparison with the original results reported in the TIRDet paper, we also use a Pearl-GAN model trained on the FLIR dataset. The results demonstrate that our proposed method consistently achieves superior performance in both sets of comparisons: between TIRDet and PFGF, as well as between TIRDet* and PFGF*. On the more complex Autonomous Vehicles dataset, our method surpasses the IDA method, with mAP50 increas", + "bbox": [ + 511, + 599, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6715", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/918fb33aba375de687537c65f1a702856c437a55c4e21ef216cd9bc31003d29f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5096.168.561.1
SSD [33]TVGG1690.257.953.5
RetinaNet [32]TResNet5093.749.350.9
YOLOv3 [40]TDarknet5389.753.452.8
YOLOX-L [12]TCSPD5395.272.763.6
TIRDet [44]TCSPD5396.373.164.2
TIRDet* [44]TCSPD5396.874.765.2
PFGF (Ours)TCSPD5396.677.966.8
PFGF* (Ours)TCSPD5396.978.467.3
DM-Fusion [47]V+TCSPD5388.1-53.1
YOLOv5-VT [19]V+TCSPD5395.871.462.3
RSDet [52]V+TResNet5095.8-61.3
Fusion-Mamba [10]V+TCSPD5397.0-64.3
", + "bbox": [ + 91, + 88, + 480, + 308 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d8ca998c299d1777431f531808405f0721660beea15f4c21cb78bab11117dbfb.jpg", + "table_caption": [ + "Table 2. Comparisons on LLVIP dataset in terms of MAP." + ], + "table_footnote": [], + "table_body": "
MethodsDataBackbonemAP50mAP75mAP
YOLOv3 [40]TDarknet5371.929.934.6
FasterRCNN [41]TResNet5072.539.839.9
CascadeRCNN [4]TResNet5072.942.742.2
YOLOX-L [12]TCSPD5372.340.640.6
IDA [28]TCSPD5373.143.843.1
PFGF (Ours)TCSPD5378.846.645.9
", + "bbox": [ + 94, + 349, + 478, + 463 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing by $5.7\\%$ , mAP75 rising by $2.8\\%$ , and overall mAP improving by $2.8\\%$ . Moreover, our method outperforms most multispectral methods in detection performance, achieving the highest mAP and mAP75, and the second-best mAP50 on both FLIR and LLVIP datasets. These results indicate that the combination of the T2V model and the proposed PFGF approach effectively enhances thermal detection performance with valuable visible information.", + "bbox": [ + 89, + 513, + 482, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also conduct a visual comparison between the proposed PFGF method, and the publicly method TIRDet. Our method significantly improves the detection performance of thermal images (See the Appendix).", + "bbox": [ + 89, + 637, + 483, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Further Analysis", + "text_level": 1, + "bbox": [ + 89, + 710, + 256, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation studies. Our framework comprises T2V translation model Pearl-GAN, VMamba-based Multi-level Feature Enhancement (MEM) block, and Graph-Mamba Fusion (GMF) module, which includes both the Inter-Mamba block and CKI strategy. To assess the contribution of each component, we performed ablation studies on the FLIR, LLVIP, and Autonomous Vehicles datasets. There are several variants: 'w/o Pearl-GAN' refers to the exclusion of visible information with only thermal image input; 'w/o MEM' denotes the detector backbone features are not enhanced by MEM block; 'w/o GMF' means the enhanced", + "bbox": [ + 89, + 734, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/55c198c2a8f9a450e3863204ed283e5fdbfc7fbe5e2ed1da9a000e42cc1784e0.jpg", + "table_caption": [ + "Table 3. Comparisons on AV dataset in terms of MAP. AV: Autonomous Vehicles dataset." + ], + "table_footnote": [], + "table_body": "
MethodmAP
FLIRLLVIPAV
w/o PearlGAN45.265.044.4
w/o MEM46.066.145.4
w/o GMF45.665.644.3
w/o Inter-Mamba (GMF)45.966.245.1
w/o CKI (GMF)46.166.445.3
PFGF47.167.345.9
", + "bbox": [ + 545, + 88, + 874, + 220 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study on FLIR, LLVIP, and AV datasets.", + "bbox": [ + 535, + 232, + 880, + 246 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "features will be passed directly to the detector head; 'w/o Inter-Mamba' implies that generative features $z$ are not fused with discriminative features $f^3$ ; while 'w/o CKI' does not integrate features from $f^3$ to $f^5$ .", + "bbox": [ + 511, + 260, + 903, + 320 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4 demonstrates that each component positively contributes to performance. Removing Pearl-GAN prevents the incorporation of visible information, leading to a substantial performance decline on the FLIR and LLVIP datasets and the second-largest performance drop on the Autonomous Vehicles dataset. The absence of MEM affects performance differently across datasets, suggesting its role in refining and enhancing coarse fusion features. Excluding the GMF module reduces mAP by $1.5\\%$ on the FLIR dataset, $1.7\\%$ on the LLVIP dataset, and $1.6\\%$ on the Autonomous Vehicles dataset, underscoring its importance in integrating generated visible and thermal information. Furthermore, ablation analysis on the GMF module reveals that the Inter-Mamba block has a more significant impact than the CKI block, indicating that the Inter-Mamba block can effectively filter redundant visible information while preserving information beneficial for thermal detection.", + "bbox": [ + 511, + 321, + 906, + 579 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of different fusion methods. To validate the superiority of our proposed fusion module, we conduct further experiments comparing it with various fusion strategies, including addition, concatenation, CMA [44], MMFT [45], GIM [24] and FMB [10]. The CMA method employs Convolutional Block Attention Module (CBAM) to generate attention maps; the MMFT leverages a Transformer-based architecture to perform fusion based on varying illumination conditions; GIM utilizes graph neural networks to handle cross-modal interactions through features; while the FMB method, rooted in the Mamba architecture, is specifically designed for multispectral detection tasks.", + "bbox": [ + 511, + 580, + 905, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 5, our method outperforms all other strategies. Specifically, CMA method is relatively simplistic and fails to effectively capture visible information beneficial for thermal detection; in contrast to the MMFT method, our approach eliminates the dependency on an additional illumination-aware module. The FMB method has achieved superior performance in multispectral tasks, it does not adapt well to our specific problem due to the unreliability of the generated visible information. The GIM", + "bbox": [ + 511, + 763, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6716", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e4361c04b61f50207d3efc8d4f3dcaf2b89c2dcbb94b37cc7cc05c1bcfc41639.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFLIRLLVIPAV
mAPmAP50mAPmAP50mAPmAP50
Add42.677.561.795.240.473.9
Concat43.779.963.394.842.474.7
CMA[44]44.381.464.696.343.976.5
MMFT[45]44.682.165.195.244.176.8
GIM[24]46.081.866.396.244.874.5
FMB[10]45.782.465.996.344.277.0
GMF (Ours)47.184.867.396.945.978.8
", + "bbox": [ + 106, + 88, + 470, + 234 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2209585bd115945c83294bc686c93cb51c6229132f131af9c1e4dc339fdb97f1.jpg", + "table_caption": [ + "Table 5. Comparison of different fusion methods." + ], + "table_footnote": [], + "table_body": "
MethodmAPmAP50FLOPS(G)↓Param(M)↓
GMTF46.282.7604.171.8
PFGF47.184.8409.066.9
", + "bbox": [ + 106, + 276, + 468, + 334 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Comparisons of VMamba and Transformer based methods on the FLIR dataset.", + "bbox": [ + 89, + 344, + 482, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "method introduces redundant information when facilitating interactions among features at various granularities. While our GMF method outperforms the FMB fusion method which depends exclusively on Mamba. These results indicate that the Graph-Mamba-based architecture facilitates a more explicit and robust integration of thermal and pseudovisible information.", + "bbox": [ + 89, + 385, + 483, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effectiveness of using VMamba block. An efficiency analysis is conducted to evaluate Mamba block compared with Transformer block. For a fair comparison, all VMamba blocks are replaced with Transformer blocks, resulting in a new method designated as GMTF. Specifically, the VMamba block is substituted with a self-attention block, and the Inter-Mamba block is replaced with a cross-attention block. As shown in Table 6, our PFGF method surpasses GMTF with a $0.9\\%$ increase in mAP and a $2.1\\%$ gain in mAP50. Additionally, PFGF demonstrates parameter efficiency by reducing the parameter count by 4.93M and decreasing FLOPs from 604.1 GFLOPs to 409.0 GFLOPs. These findings highlight that the VMamba block not only effectively suppresses redundant features and captures complementary cross-modal information but also achieves superior computational efficiency.", + "bbox": [ + 89, + 492, + 483, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effectiveness of using leader nodes. To incorporate the generative feature $z$ into the multi-level discriminative features, we utilize leader nodes to guide information transfer from the low-level subgraph to the high-level subgraph. To verify the effectiveness of leader nodes, we compare our method with an approach that lacks leader nodes on FLIR and LLVIP datasets. Without leader nodes, the next high-level features don't receive the previous low-level features, which ignore the integration from $f^3$ to $f^5$ . With ground truth serving as a labeled reference, Fig. 3 clearly shows that without the assistance of leader nodes, the object", + "bbox": [ + 89, + 734, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9641115da26912c51349bc58bd466e1bb7eaabced5a26086c511f2c50a922cc.jpg", + "image_caption": [ + "Figure 3. Effectiveness of using leader nodes. The first two rows present samples from FLIR dataset, and the last two rows present samples from LLVIP dataset. Red, blue, and green boxes denote the detected objects \"person\", \"car\", and \"bicycle\", respectively." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 903, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "confidence is significantly lower and there are more occurrences of false detections. This indicates that our method effectively leverages the features delivered by leader nodes across subgraphs, integrating both high-level semantics and low-level local details to build a more robust representation.", + "bbox": [ + 511, + 465, + 906, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 563, + 633, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a novel cross-modal fusion method, termed Pseudo Visible Feature Fine-Grained Fusion (PFGF), for thermal object detection. The PFGF framework begins by constructing a graph which consists of several subgraphs. Each subgraph is generated from different level output features from the backbone or synthetic visible feature. An Inter-Mamba block is then employed to facilitate cross-modality feature association between generative and discriminative node features. Additionally, we introduce a Cascade Knowledge Integration strategy to propagate knowledge hierarchically from lower-level to higher-level subgraphs. In the process, VMamba is employed to further refine features. Extensive experiments demonstrate that our method achieves the SOTA performance.", + "bbox": [ + 511, + 592, + 906, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by the National Natural Science Foundation of China (62276048, 62476169), Chengdu Science and Technology Projects (2023-YF06-00009-HZ) and Postdoctoral Fellowship Program of CPSF (GZC20233323).", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6717", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. Yolov4: Optimal speed and accuracy of object detection, 2020. 2", + "[2] Francesco Bongini, Lorenzo Berlincioni, Marco Bertini, and Alberto Del Bimbo. Partially fake it till you make it: Mixing real and fake thermal images for improved object detection. 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Vision mamba: Efficient visual representation learning with bidirectional state space model, 2024. 2" + ], + "bbox": [ + 516, + 92, + 903, + 878 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6719", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_model.json b/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8c3acfe4d9c0cbfe252df95fc9615f29258b8a8f --- /dev/null +++ b/2025/Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection/6a6b4e19-6c9a-4a0e-90ee-27b158772a20_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.131, + 0.877, + 0.154 + ], + "angle": 0, + "content": "Pseudo Visible Feature Fine-Grained Fusion for Thermal Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.18, + 0.858, + 0.235 + ], + "angle": 0, + "content": "Ting Li\\(^{1}\\), Mao Ye\\(^{1*}\\), Tianwen Wu\\(^{1}\\), Nianxin Li\\(^{1}\\), Shuaifeng Li\\(^{1}\\), Song Tang\\(^{2}\\), and Luping Ji\\(^{1}\\) \n\\(^{1}\\) University of Electronic Science and Technology of China \n\\(^{2}\\) University of Shanghai for Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.309, + 0.237, + 0.684, + 0.251 + ], + "angle": 0, + "content": "lting1103@gmail.com, cvlab.uestc@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.319, + 0.486, + 0.728 + ], + "angle": 0, + "content": "Thermal object detection is a critical task in various fields, such as surveillance and autonomous driving. Current state-of-the-art (SOTA) models always leverage a prior Thermal-To-Visible (T2V) translation model to obtain visible spectrum information, followed by a cross-modality aggregation module to fuse information from both modalities. However, this fusion approach does not fully exploit the complementary visible spectrum information beneficial for thermal detection. To address this issue, we propose a novel cross-modal fusion method called Pseudo Visible Feature Fine-Grained Fusion (PFGF). Specifically, a graph is constructed with nodes generated from multi-level thermal features and pseudo-visual latent features produced by the T2V model. Each level of features corresponds to a subgraph. An Inter-Mamba block is proposed to perform cross-modality fusion between nodes at the lowest level; while a Cascade Knowledge Integration (CKI) strategy is used to fuse low-level fused information to high-level subgraphs in a cascade manner. After several iterations of graph node updating, each subgraph outputs an aggregated feature to the detection head respectively. Unlike previous cross-modal fusion methods, our approach explicitly models high-level relationships between cross-modal data, effectively fusing different granularity information. Experimental results demonstrate that our method achieves SOTA detection performance. Code is available at https://github.com/liting1018/PFGF." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.743, + 0.222, + 0.758 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.768, + 0.485, + 0.875 + ], + "angle": 0, + "content": "Object detection is critical in computer vision, with applications in autonomous driving and video surveillance [27]. While most methods rely on visible spectrum images, they often struggle in adverse conditions like nighttime, fog, or snow. In contrast, thermal spectrum images offer robustness in challenging environments [13], but they may falter in the daytime due to limited texture detail. Both visible-" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.288, + 0.933, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.416, + 0.933, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.552, + 0.908, + 0.636 + ], + "angle": 0, + "content": "Figure 1. Comparison between previous attention-based method and our method. (a) An attention-based module combines channel and spatial attention to augment the modality-translation awareness of detection. (b) Our method employs a Graph-Mamba Fusion module to integrate cross-modality knowledge in a cascade manner with different granularity." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.655, + 0.907, + 0.821 + ], + "angle": 0, + "content": "only and thermal-only approaches face limitations by solely relying on one spectrum, and lacking complementary data. As a result, multi-spectral (visible and thermal) object detection [8, 25, 52] have gained popularity. However, these approaches require paired visible and thermal images for both training and inference, increasing hardware costs and complexity. Furthermore, the need for precise alignment between modalities further limits practical deployment [5]. Consequently, there is growing interest in visible knowledge assistance methods that utilize paired visible-thermal images for training and solely thermal images for testing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Visible knowledge-assisted thermal pedestrian detection methods can be categorized into two routes: data enhancement and cross-modal transfer. The route of data enhancement [2] employs generative models to adapt visible images to the thermal domain like domain adaptation [26, 29], us" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.888, + 0.258, + 0.901 + ], + "angle": 0, + "content": "*The corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6710" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.318 + ], + "angle": 0, + "content": "ing them during training to mitigate the limitations caused by relying solely on thermal data during testing. However, the generated thermal images may be unreliable, potentially degrading the performance of thermal pedestrian detectors. Another route is based on cross-modal transfer, which can be further divided into two approaches. The first approach, feature domain transformation [45], utilizes an auxiliary network to convert thermal features into visible ones. However, this process demands substantial computation and large models to maintain feature quality in high-dimensional spaces. The second approach, image domain transformation [44], employs a generative model to directly convert thermal images into visible ones. The transformed visible images are then fused with the original thermal images, as illustrated in Fig.1(a)." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.322, + 0.483, + 0.761 + ], + "angle": 0, + "content": "While image domain transformation methods have attained the state-of-the-art performance in thermal object detection, they still face obstacles related to occlusions and visible image noise. This limitation primarily stems from the inherent unreliability of visible images generated from thermal data, which can introduce noise that adversely affects detection accuracy. Furthermore, these approaches often neglect the fine-grained multimodal knowledge relationships between pseudo-visible and thermal data. As a result, effectively harnessing the complementary nature of thermal and visible information to resolve ambiguities in complex scenes remains a significant challenge. Fortunately, Graph Neural Networks (GNNs) offer a promising alternative for modeling and reasoning about relationships [30]. This motivates us to utilize graph structures for enabling interactions among features at various granularities. Such an approach ensures comprehensive utilization of information between low-level features to high-level semantics, leading to richer and more nuanced cross-modal integration. However, the flexible flow of information between nodes may introduce redundancy or irrelevant data, potentially hindering detection performance. To address this, we incorporate Mamba's selection mechanism [53] to effectively filter out unimportant information in the long-range context, which is particularly crucial for thermal feature maps that often contain noise and lack texture details. Furthermore, by iteratively updating node features based on neighborhood nodes, it can minimize the impact of less relevant nodes, thereby enhancing feature fusion and representation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Based on the above analysis, as illustrated in Fig. 1(b), we propose a novel cross-modal fusion method, dubbed as Pseudo Visible Feature Fine-Grained Fusion (PFGF). First, we obtain the visible features using the Pearl-GAN method [37], which are referred to as generative features. To fuse these generative features, we introduce the Graph-Mamba Fusion module. Specially, a graph is constructed that consists of multiple subgraphs, where each subgraph corresponds to either the generative feature or the output features" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.333 + ], + "angle": 0, + "content": "from different levels of the detector backbone (referred to as discriminative features). The node features in each subgraph represent multi-level information, corresponding to different feature levels. For graph computation, we propose the Inter-Mamba block and Cascade Knowledge Integration (CKI) strategy, which facilitate efficient knowledge fusion and propagation across subgraphs. The Inter-Mamba block is introduced to fuse the nodes of subgraphs between the generative feature and the low-level discriminative feature, here the \\( c^3 \\) feature from CSPDarknet [1]. Then, a Cascade Knowledge Integration (CKI) strategy is proposed to propagate the knowledge from the low-level subgraph to the high-level subgraph in a cascade manner. During this cascading process, node features are updated using the Gate Recurrent Unit (GRU) method [9], while the VMamba block further refines these features across subgraphs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.336, + 0.905, + 0.547 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows: (1) We are the first to employ pseudo visible feature fine-grained fusion method for thermal object detection. The information interaction ability of graph at different granularities and the information selection and enhancement ability of Mamba have been fully utilized. (2) An Inter-Mamba block is proposed to facilitate cross-modality fusion between generative and discriminative node features. Additionally, the cascade knowledge integration strategy aggregates knowledge from low-level to high-level feature subgraphs avoiding tedious computation. (3) Experiments conducted on public FLIR, LLVIP, and Autonomous Vehicles datasets demonstrate significant advantages over the state-of-the-art (SOTA) thermal object detection methods." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.562, + 0.655, + 0.578 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.59, + 0.75, + 0.605 + ], + "angle": 0, + "content": "2.1. Thermal Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Thermal object detection is crucial in low-light environments and privacy-sensitive scenarios. Existing approaches can be categorized into direct reconstruction and visible knowledge assistance. In the direct reconstruction approach, the methods [21, 22, 38] focus on designing networks to extract discriminative features by leveraging the intrinsic characteristics of thermal images. For example, GPCAnet [48] predicts object positions in the image to allocate more ROIs to the predicted areas. The Visible knowledge assistance methods can be further divided into data augmentation and cross-modal transfer. The data augmentation works [2, 20] use GANs to convert visible images into thermal images, mixing them to enhance detector robustness. In the cross-modal transfer approach, the works try to generate pseudo visual images or features. For example, TIRDet [44] uses Pearl-GAN for image translation. Xie et al [45] use a hallucination network to learn visible features from thermal images. All methods lack in-depth research on pseudo-visible information fusion." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.513, + 0.957 + ], + "angle": 0, + "content": "6711" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.408, + 0.108 + ], + "angle": 0, + "content": "2.2. Graph Based Cross Modality Fusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.371 + ], + "angle": 0, + "content": "In recent years, graph-based approaches have gained significant traction in computer vision applications [36]. Typically, graph operates as message-passing algorithms, where node representations are iteratively updated based on their neighbors through a differentiable aggregation function [34]. This makes graph particularly valuable in multisource data fusion. For instance, Cai et al. [3] used a graph-attention mechanism to fuse embeddings from different feature extractors, while Li et al. [24] proposed an interactive GNN-based architecture to facilitate cross-modality fusion. Our work is closely related latter work that utilizes graph structures to explicitly model and reason about different granularity information interactions between complementary data sources. However, our approach uniquely incorporates Mamba's selection mechanism to strengthen graph node representations, effectively minimizing the impact of unimportant nodes at each step of hidden state computation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.379, + 0.417, + 0.395 + ], + "angle": 0, + "content": "2.3. Mamba Based Cross Modality Fusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.4, + 0.484, + 0.705 + ], + "angle": 0, + "content": "Since its inception for linear-time sequence modeling in natural language processing, Mamba [14] has rapidly been adapted for various applications in computer vision. For example, VMamba [35] leverages a four-way scanning algorithm to advance object detection and segmentation beyond the capabilities of the Swin Transformer. Mamba has already been used in cross-modality fusion. Xie et al. [46] leveraged Mamba for dynamic feature enhancement in multimodal image fusion. Pan-Mamba [15] is developed to facilitate efficient cross-modal information exchange and fusion. The Fusion-Mamba block [10] is introduced to mitigate disparities between cross-modal features and enhance the consistency of fused feature representations. Additionally, Li et al. [23] proposed cross-modality fusion-Mamba, coupled with weather removal techniques, to improve detection accuracy under adverse weather conditions. Distinct from prior research, our work pioneers the integration of the Mamba architecture into graph representations for thermal object detection tasks, significantly enhancing graph embeddings and processing capabilities." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.716, + 0.226, + 0.733 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.741, + 0.276, + 0.756 + ], + "angle": 0, + "content": "3.1. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.763, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Suppose the training dataset \\(D_{s} = \\{X^{t},X^{v}\\}\\), where the thermal image set \\(X^{t} = \\{x_{s_{i}}^{t}\\}_{i = 1}^{N_{st}}\\) with labels \\(\\{y_{s_i}^t\\}_{i = 1}^{N_{st}}\\) and the unpaired visible image set \\(X^{v} = \\{x_{s_{i}}^{v}\\}_{i = 1}^{N_{sv}}\\). \\(N_{st}\\) and \\(N_{sv}\\) denote the cardinality of the thermal image set and visible image set respectively. The test dataset \\(D_{t} = \\{x_{t_{i}}^{t}\\}_{i = 1}^{N_{t}}\\) be exclusively composed of thermal images, where \\(N^t\\) represents the number of thermal images in the test dataset. Our objective is to compensate for visible knowledge while using solely thermal images as the input at the test stage," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "and fully leverage information from both modalities to develop robust representations at the training stage." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.122, + 0.907, + 0.273 + ], + "angle": 0, + "content": "Overview. Fig. 2(a) illustrates the proposed Pseudo Visible Feature Fine-Grained Fusion (PFGF) framework, which uses the single-stage detector YOLOX [12] as the baseline model. Both training and testing are conducted exclusively with thermal images. Specifically, we first train Pearl-GAN as a prior thermal-to-visible (T2V) translation model \\(\\Phi\\), which is trained on both thermal and visible modalities, to convert thermal image \\(x^t\\) into daytime visible image \\(x^v\\), thereby incorporating valuable visible information from the unpaired set \\(X^v\\). This process is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.28, + 0.905, + 0.298 + ], + "angle": 0, + "content": "\\[\n[ x ^ {v}, z ] = \\Phi (x ^ {t}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.303, + 0.905, + 0.365 + ], + "angle": 0, + "content": "where \\(x^{t} \\in \\mathbb{R}^{H \\times W \\times 1}\\) and \\(x^{v} \\in \\mathbb{R}^{H \\times W \\times 3}\\). \\(\\Phi(x^{t})\\) comprises a convolution-based encoder \\(z = \\varepsilon(x^{t})\\) and a decoder \\(x^{v} = \\mu(z)\\). The latent T2V code \\(z \\in \\mathbb{R}^{h_{z} \\times w_{z} \\times c_{z}}\\) is considered as generative feature." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.365, + 0.905, + 0.411 + ], + "angle": 0, + "content": "CSPDarknet is employed as the backbone \\(\\mathcal{F}\\) to extract multi-level features \\(c^3, c^4\\) and \\(c^5\\) from the concatenated images \\(x^t\\) and \\(x^v\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.418, + 0.905, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\left[ c ^ {3}, c ^ {4}, c ^ {5} \\right] = \\mathcal {F} \\left(\\operatorname {c o n c a t} \\left(x ^ {t}, x ^ {v}\\right)\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.443, + 0.869, + 0.457 + ], + "angle": 0, + "content": "A VMamba [35] block \\(\\mathcal{M}\\) then refines these features:" + }, + { + "type": "equation", + "bbox": [ + 0.662, + 0.465, + 0.905, + 0.483 + ], + "angle": 0, + "content": "\\[\nf ^ {i} = \\mathcal {M} ^ {i} \\left(c ^ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.49, + 0.906, + 0.642 + ], + "angle": 0, + "content": "for \\( i \\in \\{3,4,5\\} \\). The output features \\( f^i \\in R^{h \\times w \\times c} \\) are considered as discriminative features. We refer to this process as the VMamba-based Multi-level feature Enhancement (MEM). Here, a VMamba block is utilized to learn global relationships and contextual information from two modalities, thereby enhancing the model's representational capacity. Additionally, due to Mamba's input-dependent mechanism and various hardware-optimized techniques, it excels in long-range modeling with reduced computational cost compared to Transformers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.906, + 0.703 + ], + "angle": 0, + "content": "To better integrate the generated visible features, we propose a novel Graph-Mamba Fusion (GMF) module \\(\\mathcal{G}\\). This approach effectively combines generative feature \\(z\\) with discriminative features \\(f_{i}\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.709, + 0.905, + 0.729 + ], + "angle": 0, + "content": "\\[\n\\left[ g ^ {3}, g ^ {4}, g ^ {5} \\right] = \\mathcal {G} \\left(f ^ {3}, f ^ {4}, f ^ {5}, z\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.906, + 0.81 + ], + "angle": 0, + "content": "Graph-Mamba Fusion (GMF) module, as a key contribution, goes beyond simple attention by establishing high-level relationships. It first fuses generative feature \\( z \\) with the discriminate feature \\( f^3 \\) and then performs high-level fusion from \\( f^3 \\) to \\( f^5 \\), which will be introduced later." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Subsequently, the features \\( f^i \\) and \\( g^i \\) are combined using residual connections and a Neck module \\( \\Phi \\) to obtain the output features \\( f^{i'} = \\Phi (f^i + g^i) \\), where \\( i \\in \\{3, 4, 5\\} \\). Finally, the Decoupled Detection Head \\( \\mathcal{H} \\) [12] is employed to obtain the detection result based on \\( f^{i'} \\). The model is trained using the standard detection loss \\( L_{d}(\\mathcal{H}(f^{3'}, f^{4'}, f^{5'}, y_{s_i}^t)) \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6712" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.089, + 0.882, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.272, + 0.882, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.357, + 0.882, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.464, + 0.907, + 0.522 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed PFGF method. (a) The framework of the PFGF, with our modules highlighted in the purple box. (b) The Graph-Mamba Fusion Module constructs the graph structure for both discriminative and generative features, with leader nodes guiding the flow of information between graphs. (c) The Inter-Mamba Module facilitates interactions between different modalities. (d) The VMamba Module updates nodes within the same modality." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.533, + 0.467, + 0.549 + ], + "angle": 0, + "content": "3.2. Pseudo Visible Feature Fine-Grained Fusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.562, + 0.484, + 0.76 + ], + "angle": 0, + "content": "For further integrating the generative feature \\( z \\), a straightforward attention-based fusion approach, as used in [44], can be employed. However, this method has limitations in effectively capturing high-level relationships among the features. Additionally, it struggles to capture essential visual information due to the unreliability of the generated visible images, which often introduces a substantial amount of irrelevant information. To overcome these challenges, we introduce the Graph-Mamba Fusion (GMF) module as shown in Fig. 2(b). Graph structure is employed to establish more compensated relationships between different level features, which Mamba is adapted to capture long-range dependencies with less computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.903 + ], + "angle": 0, + "content": "To avoid getting lost in details, let's first briefly introduce the process. (1) Graph construction. The features \\( f^3 \\), \\( f^4 \\), \\( f^5 \\), and \\( z \\) are down-and-up sampled to different copies as graph nodes. Graph edges are constructed by computing similarity between nodes, and message passing is performed by aggregating features from neighboring nodes. (2) Graph computation. An Inter-Mamba block is proposed to facilitate fusion between the nodes produced by latent feature \\( z \\) and discriminative feature \\( f^3 \\) respectively as illus-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.534, + 0.907, + 0.657 + ], + "angle": 0, + "content": "trated in Fig. 2 (c). The GRU algorithm is used to update graph nodes, ensuring effective information propagation. Subsequently, a VMamba block is used to further refine the node feature. The output \\( g^3 \\) is formed by merging the node features of \\( f^3 \\) and is then multiplied with the nodes derived from \\( f^4 \\), enabling the fusion of information across different levels. The output \\( g^4 \\) and \\( g^5 \\) are obtained by merging the node features from \\( f^4 \\) and \\( f^5 \\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.667, + 0.697, + 0.683 + ], + "angle": 0, + "content": "3.2.1. Graph construction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.688, + 0.907, + 0.809 + ], + "angle": 0, + "content": "In this part, we will introduce how to construct a graph \\(\\Psi = (U,E)\\) based on the features \\(f\\) and \\(z\\). This structure is inspired by the method [24], which effectively models the relationships and dependencies among features extracted from different levels or modalities. The graph structure is designed to ensure that the fusion of these features is contextually relevant, thereby enhancing the accuracy and robustness of the representations used for detection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Node generation. Given the generative feature \\( z \\) and discriminative feature \\( f \\), two types of nodes are generated. To capture multi-level information and enhance feature diversity, we make replicas of different granularities of the corresponding features as graph nodes. Specifically, pyramid pooling, convolution, and upsampling operations are ap-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6713" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.123 + ], + "angle": 0, + "content": "plied to both generative feature \\(z\\) and discriminate feature \\(f\\), which can be formally computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.13, + 0.483, + 0.15 + ], + "angle": 0, + "content": "\\[\nf _ {j} ^ {i} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} \\left(f ^ {i}\\right)\\right)\\right), z _ {j} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} (z)\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.157, + 0.484, + 0.281 + ], + "angle": 0, + "content": "where the operator \\(\\mathcal{P}_j(\\cdot)\\) pools the given feature to various sizes according to the scale setting \\(j\\), a \\(1 \\times 1\\) convolution is applied to reduce the dimension of the pooled representation, and \\(Up\\) operator, using bi-linear interpolation, up-samples the feature maps to match the original size. For each \\(f^i\\) and \\(z\\), there are \\(n\\) node features \\(f_j^i \\in R^{h \\times w \\times c'}\\) for \\(j \\in \\{1, \\dots, n\\}\\) and \\(z_j \\in R^{h \\times w \\times c'}\\). Here \\(n = 3\\). Note that \\(z\\) has only one scale and shares the same shape as \\(f^3\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.282, + 0.484, + 0.419 + ], + "angle": 0, + "content": "Edge generation. The edges play a crucial aspect, as it facilitates the propagation of information between nodes. Here, we only compute intra-edges, i.e., the edges connect the nodes produced by the same feature. Since our goal is to incorporate the information from the generative feature \\( z \\) into the discriminative feature \\( f \\), there is no need to construct additional edges between the nodes produced by the generative feature. Specifically, for the feature \\( f^i \\), the intra-edge \\( e_{j,k}^i \\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.427, + 0.483, + 0.448 + ], + "angle": 0, + "content": "\\[\ne _ {j, k} ^ {i} = \\operatorname {C o n v} \\left(f _ {j} ^ {i} - f _ {k} ^ {i}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.454, + 0.484, + 0.637 + ], + "angle": 0, + "content": "where \\( Conv(\\cdot) \\) is used to learn relationships between nodes. The term \\( f_{j}^{i} - f_{k}^{i} \\) represents the difference between the node features \\( f_{j}^{i} \\) and \\( f_{k}^{i} \\). This highlights the relative disparity between nodes, following the approach outlined in [43]. Based on our edge computation method, we have formed four subgraphs, which are constructed by graph nodes formed by the features \\( z, f^{3}, f^{4} \\), and \\( f^{5} \\), respectively. Here the edges between the subgraphs of different discriminative features are not computed to avoid tedious computation. Instead, we introduce a new leader node to aggregate subgraph node features, and then pass the aggregated feature to the next subgraph from \\( f^{3} \\) to \\( f^{5} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.484, + 0.703 + ], + "angle": 0, + "content": "Message Passing. In each subgraph composed of discriminative features, every node aggregates feature messages from all its neighboring nodes. For the node \\( f_{j}^{i} \\), at \\( l - 1 \\) message passing, denoted as \\( m_{j}^{i,l - 1} \\), is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.711, + 0.483, + 0.747 + ], + "angle": 0, + "content": "\\[\nm _ {j} ^ {i, l - 1} = \\sum_ {k \\in \\mathcal {N} (j)} \\operatorname {S i g m o i d} \\left(e _ {k, j} ^ {i, l - 1}\\right) \\cdot f _ {k} ^ {i, l - 1}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.755, + 0.483, + 0.785 + ], + "angle": 0, + "content": "where \\( Sigmoid(\\cdot) \\) function is utilized to calculate the link weight between nodes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.792, + 0.276, + 0.807 + ], + "angle": 0, + "content": "3.2.2. Graph computation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.869 + ], + "angle": 0, + "content": "Graph-based cross-modality information fusion consists of two key components: cross-modality fusion through the Inter-Mamba block and knowledge integration via GRU and VMamba." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Cross modality fusion by Inter-Mamba block. For fusing the node features \\( z_{j} \\) and \\( f_{j}^{3} \\), instead of transformer-based" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "route, we proposed a Mamba-based block. As shown in Fig. 2(c), the node features \\( f_{j}^{3} \\) and \\( z_{j} \\) are first projected into the hidden state space followed by a VMamba block, and a gating operation is then employed to facilitate the interaction between these two types of hidden state features." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.169, + 0.907, + 0.352 + ], + "angle": 0, + "content": "Specifically, the node features \\( f_{j}^{3} \\) and \\( z_{j} \\) are first flattened to form the input token sequences \\( T_{j}^{3} \\) and \\( T_{j} \\), each with dimensions \\( B \\times N \\times C \\), where \\( B \\), \\( N \\), and \\( C \\) denote the batch size, sequence length, and number of channels, respectively. These sequences are then normalized by a normalization layer. Next, the normalized sequences \\( T_{j}^{3} \\) and \\( T_{j} \\) are projected into the hidden state space respectively through linear layers, convolution, and SSM, resulting in the hidden state features \\( \\hat{f}_{j}^{3} \\) and \\( \\hat{z}_{j} \\). Simultaneously, the normalized sequence \\( T_{j}^{3} \\) is also projected through linear layers with SiLU activation to obtain the gating weight \\( r \\). It is used for hidden state feature fusion as follows," + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.367, + 0.905, + 0.389 + ], + "angle": 0, + "content": "\\[\nf _ {j} ^ {3} = \\mathcal {R} \\left(\\mathcal {Y} \\left(\\left(\\hat {z} _ {j} + \\hat {f} _ {j} ^ {3}\\right) \\odot r\\right) + f _ {j} ^ {3}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.402, + 0.905, + 0.447 + ], + "angle": 0, + "content": "where \\(\\odot\\) represents element-wise multiplication. The operator \\(\\mathcal{V}\\) denotes the projection operation with a linear transformation, while \\(\\mathcal{R}\\) refers to the reshaping operation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.906, + 0.584 + ], + "angle": 0, + "content": "Cascade Knowledge Integration (CKI) strategy. Existing studies [11] have demonstrated that deep and shallow features exhibit complementary characteristics: deep features capture high-level semantic information, while shallow features retain rich spatial details. Leveraging multilevel features is therefore advantageous for enhancing detection performance. As we stated before, a leader node is proposed to convey low-level fused information to high-level subgraph in a cascade manner." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.906, + 0.68 + ], + "angle": 0, + "content": "We first apply a GRU-based update method [9] to enhance the nodes' ability to capture complex feature interactions and retain relevant information from neighboring nodes. After \\(l-1\\) message passing, the node feature \\(f_{j}^{i}\\) is updated by \\(\\mathcal{U}_{GRU}(f_{j}^{i}, m_{j}^{i,l-1})\\) (See the Appendix for a detailed description of \\(\\mathcal{U}_{GRU}\\))." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.682, + 0.903, + 0.699 + ], + "angle": 0, + "content": "A leader node feature \\(g^i\\) at the \\(i\\)-th scale is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.712, + 0.905, + 0.731 + ], + "angle": 0, + "content": "\\[\ng ^ {i} = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(\\mathcal {M} \\left(f _ {1} ^ {i}\\right), \\dots , \\mathcal {M} \\left(f _ {n} ^ {i}\\right)\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.746, + 0.893, + 0.76 + ], + "angle": 0, + "content": "where \\(\\mathcal{M}\\) denotes a VMamba block as mentioned before." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.762, + 0.905, + 0.792 + ], + "angle": 0, + "content": "The leader node \\(g^i\\) conveys knowledge to the subsequent subgraph nodes as follows," + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.806, + 0.905, + 0.828 + ], + "angle": 0, + "content": "\\[\nf _ {j} ^ {i + 1} = f _ {j} ^ {i + 1} \\odot \\mathcal {A} (g ^ {i}) + f _ {j} ^ {i + 1}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}\\) represents an attention operation, which is computed via global average pooling followed by a Sigmoid activation. Since the last subgraph does not contribute to knowledge transmission, the scale \\(i\\) is set to 3 and 4." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6714" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.223, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.115, + 0.298, + 0.133 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.139, + 0.483, + 0.395 + ], + "angle": 0, + "content": "Datasets. To evaluate our method, we conduct experiments on the FLIR-aligned dataset [49], LLVIP dataset [18], and Autonomous Vehicles dataset [42]. (1) The FLIR dataset originally presented challenges due to unaligned thermal-visible image pairs. Therefore, we utilize the aligned version, consisting of 5,142 thermal-visible image pairs, with 4,129 pairs for training and 1,013 for testing. This dataset includes three object categories: \"person,\" \"car,\" and \"bicycle\". (2) The LLVIP dataset is collected in very dark environments. It comprises 15488 aligned image pairs, with 12,025 pairs used for training and 3,463 pairs for testing. This dataset focuses on a single object class: \"person\". (3) The Autonomous Vehicles dataset comprises 6,009 paired images for training and 1,503 for testing, covering five categories: \"bike\", \"car\", \"car_stop\", \"color_cone\", and \"person\". Compared to the FLIR and LLVIP datasets, the scenes in this dataset are more complex." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.483, + 0.518 + ], + "angle": 0, + "content": "Evaluation Metrics. We evaluate our method using standard object detection metrics [31], including mean Average Precision (mAP), mAP50, and mAP75. The mAP metric represents the average AP over IoU thresholds ranging from 0.50 to 0.95, with an interval of 0.05. The mAP50 and mAP75 metrics correspond to the AP values at IoU thresholds of 0.50 and 0.75, respectively. Higher values for these metrics indicate better performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.518, + 0.483, + 0.806 + ], + "angle": 0, + "content": "Implementation Details. We utilize a pre-trained model on the COCO dataset and implement our approach using the MMDetection toolbox [6], a widely adopted framework for object detection. The network is trained using the SGD optimizer with a batch size of 4 and an initial learning rate of 5e-4. The input image size is set to \\(640 \\times 640\\) for the FLIR, LLVIP, and Autonomous Vehicles datasets, with the training conducted over 8 epochs. The training process is conducted in two stages. In the first stage, the Pearl-GAN module is trained. In the second stage, with the parameters of the Pearl-GAN module fixed, the backbone, VMamba, Graph-Mamba Fusion (GMF) module, neck, and detection head are trained. For the GMF module, the number of graph nodes \\(n\\) is set to 3, and the number of message-passing iterations \\(L\\) is also set to 3. The cascade quantities of VMamba and Inter-Mamba blocks are each configured to 2. Details on hyper-parameter sensitivity are provided in the Appendix. To ensure reproducibility, all experiments are conducted with a random seed set to 0." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.818, + 0.455, + 0.835 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Compared methods. We compare the proposed PFGF method with both mono-modality (thermal) and multispectral (visible + thermal) methods. The mono-modality methods include Faster RCNN [41], SSD [33], RetinaNet" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.09, + 0.905, + 0.38 + ], + "angle": 0, + "content": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5074.432.537.6
SSD [33]TVGG1665.522.429.6
RetinaNet [32]TResNet5064.520.328.3
YOLOv3 [40]TDarknet5373.631.336.8
YOLOX-L [12]TCSPD5378.139.442.6
IAH [45]TDarknet5376.4--
DIP [17]TResNet5077.3--
TIRDet [44]TCSPD5381.441.144.3
IDA [28]TCSPD5381.143.446.3
PFGF (Ours)TCSPD5384.844.647.1
CFR_3 [49]V+TVGG1672.4--
GAFF [50]V+TResNet1872.932.937.5
YOLOFusion [39]V+TVGG1676.6-39.8
CMX [51]V+TSwinT82.237.142.3
IGT [7]V+TSwinT85.036.943.6
DATFF [16]V+TResNet5080.2--
RSDet [52]V+TResNet5081.1-41.1
Fusion-Mamba [10]V+TCSPD5384.9-47.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.389, + 0.907, + 0.418 + ], + "angle": 0, + "content": "Table 1. Comparisons on FLIR dataset in terms of MAP. The best results are highlighted in bold." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.446, + 0.907, + 0.599 + ], + "angle": 0, + "content": "[32], YOLOv3 [40], YOLOX-L [12], IAH [45], DIP [17], TIRDet [44] and IDA [28]. These methods utilize paired visible and thermal images for training, but only thermal images for testing. In contrast, the multispectral methods include CFR_3 [49], GAFF [50], YOLOFusion [39], CMX [51], IGT [7], DATFF [16], RSDet [52], YOLOv5-VT [19], DM-Fusion [47], and Fusion-Mamba [10]. These methods employ paired visible and thermal images for both training and testing. The results presented in the tables are cited from the respective papers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.6, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Quantitative comparison. The quantitative comparison results are presented in Tables 1, 2, and 3. Our method achieves the state-of-the-art (SOTA) performance among mono-modality (thermal) methods on the FLIR, LLVIP, and Autonomous Vehicles datasets. On the FLIR dataset, our approach outperforms the recent TIRDet and IDA methods, achieving mAP gains of \\(2.8\\%\\) and \\(0.8\\%\\), respectively, along with mAP50 improvements of \\(3.4\\%\\) and \\(3.7\\%\\). For a fair comparison of the LLVIP dataset, we reproduced the TIRDet method using a Pearl-GAN model trained on the LLVIP dataset, referred to as TIRDet*. Similarly, our method denoted as PFGF*, utilizes this same Pearl-GAN model. Additionally, to facilitate comparison with the original results reported in the TIRDet paper, we also use a Pearl-GAN model trained on the FLIR dataset. The results demonstrate that our proposed method consistently achieves superior performance in both sets of comparisons: between TIRDet and PFGF, as well as between TIRDet* and PFGF*. On the more complex Autonomous Vehicles dataset, our method surpasses the IDA method, with mAP50 increas" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6715" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.482, + 0.309 + ], + "angle": 0, + "content": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5096.168.561.1
SSD [33]TVGG1690.257.953.5
RetinaNet [32]TResNet5093.749.350.9
YOLOv3 [40]TDarknet5389.753.452.8
YOLOX-L [12]TCSPD5395.272.763.6
TIRDet [44]TCSPD5396.373.164.2
TIRDet* [44]TCSPD5396.874.765.2
PFGF (Ours)TCSPD5396.677.966.8
PFGF* (Ours)TCSPD5396.978.467.3
DM-Fusion [47]V+TCSPD5388.1-53.1
YOLOv5-VT [19]V+TCSPD5395.871.462.3
RSDet [52]V+TResNet5095.8-61.3
Fusion-Mamba [10]V+TCSPD5397.0-64.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.32, + 0.458, + 0.334 + ], + "angle": 0, + "content": "Table 2. Comparisons on LLVIP dataset in terms of MAP." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.35, + 0.48, + 0.464 + ], + "angle": 0, + "content": "
MethodsDataBackbonemAP50mAP75mAP
YOLOv3 [40]TDarknet5371.929.934.6
FasterRCNN [41]TResNet5072.539.839.9
CascadeRCNN [4]TResNet5072.942.742.2
YOLOX-L [12]TCSPD5372.340.640.6
IDA [28]TCSPD5373.143.843.1
PFGF (Ours)TCSPD5378.846.645.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.475, + 0.483, + 0.503 + ], + "angle": 0, + "content": "Table 3. Comparisons on AV dataset in terms of MAP. AV: Autonomous Vehicles dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.515, + 0.483, + 0.636 + ], + "angle": 0, + "content": "ing by \\(5.7\\%\\), mAP75 rising by \\(2.8\\%\\), and overall mAP improving by \\(2.8\\%\\). Moreover, our method outperforms most multispectral methods in detection performance, achieving the highest mAP and mAP75, and the second-best mAP50 on both FLIR and LLVIP datasets. These results indicate that the combination of the T2V model and the proposed PFGF approach effectively enhances thermal detection performance with valuable visible information." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.484, + 0.699 + ], + "angle": 0, + "content": "We also conduct a visual comparison between the proposed PFGF method, and the publicly method TIRDet. Our method significantly improves the detection performance of thermal images (See the Appendix)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.712, + 0.258, + 0.727 + ], + "angle": 0, + "content": "4.3. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Ablation studies. Our framework comprises T2V translation model Pearl-GAN, VMamba-based Multi-level Feature Enhancement (MEM) block, and Graph-Mamba Fusion (GMF) module, which includes both the Inter-Mamba block and CKI strategy. To assess the contribution of each component, we performed ablation studies on the FLIR, LLVIP, and Autonomous Vehicles datasets. There are several variants: 'w/o Pearl-GAN' refers to the exclusion of visible information with only thermal image input; 'w/o MEM' denotes the detector backbone features are not enhanced by MEM block; 'w/o GMF' means the enhanced" + }, + { + "type": "table", + "bbox": [ + 0.547, + 0.089, + 0.875, + 0.222 + ], + "angle": 0, + "content": "
MethodmAP
FLIRLLVIPAV
w/o PearlGAN45.265.044.4
w/o MEM46.066.145.4
w/o GMF45.665.644.3
w/o Inter-Mamba (GMF)45.966.245.1
w/o CKI (GMF)46.166.445.3
PFGF47.167.345.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.233, + 0.882, + 0.247 + ], + "angle": 0, + "content": "Table 4. Ablation study on FLIR, LLVIP, and AV datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.261, + 0.905, + 0.321 + ], + "angle": 0, + "content": "features will be passed directly to the detector head; 'w/o Inter-Mamba' implies that generative features \\( z \\) are not fused with discriminative features \\( f^3 \\); while 'w/o CKI' does not integrate features from \\( f^3 \\) to \\( f^5 \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.323, + 0.907, + 0.58 + ], + "angle": 0, + "content": "Table 4 demonstrates that each component positively contributes to performance. Removing Pearl-GAN prevents the incorporation of visible information, leading to a substantial performance decline on the FLIR and LLVIP datasets and the second-largest performance drop on the Autonomous Vehicles dataset. The absence of MEM affects performance differently across datasets, suggesting its role in refining and enhancing coarse fusion features. Excluding the GMF module reduces mAP by \\(1.5\\%\\) on the FLIR dataset, \\(1.7\\%\\) on the LLVIP dataset, and \\(1.6\\%\\) on the Autonomous Vehicles dataset, underscoring its importance in integrating generated visible and thermal information. Furthermore, ablation analysis on the GMF module reveals that the Inter-Mamba block has a more significant impact than the CKI block, indicating that the Inter-Mamba block can effectively filter redundant visible information while preserving information beneficial for thermal detection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.906, + 0.763 + ], + "angle": 0, + "content": "Comparison of different fusion methods. To validate the superiority of our proposed fusion module, we conduct further experiments comparing it with various fusion strategies, including addition, concatenation, CMA [44], MMFT [45], GIM [24] and FMB [10]. The CMA method employs Convolutional Block Attention Module (CBAM) to generate attention maps; the MMFT leverages a Transformer-based architecture to perform fusion based on varying illumination conditions; GIM utilizes graph neural networks to handle cross-modal interactions through features; while the FMB method, rooted in the Mamba architecture, is specifically designed for multispectral detection tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 5, our method outperforms all other strategies. Specifically, CMA method is relatively simplistic and fails to effectively capture visible information beneficial for thermal detection; in contrast to the MMFT method, our approach eliminates the dependency on an additional illumination-aware module. The FMB method has achieved superior performance in multispectral tasks, it does not adapt well to our specific problem due to the unreliability of the generated visible information. The GIM" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6716" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.472, + 0.235 + ], + "angle": 0, + "content": "
MethodFLIRLLVIPAV
mAPmAP50mAPmAP50mAPmAP50
Add42.677.561.795.240.473.9
Concat43.779.963.394.842.474.7
CMA[44]44.381.464.696.343.976.5
MMFT[45]44.682.165.195.244.176.8
GIM[24]46.081.866.396.244.874.5
FMB[10]45.782.465.996.344.277.0
GMF (Ours)47.184.867.396.945.978.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.247, + 0.434, + 0.26 + ], + "angle": 0, + "content": "Table 5. Comparison of different fusion methods." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.277, + 0.47, + 0.335 + ], + "angle": 0, + "content": "
MethodmAPmAP50FLOPS(G)↓Param(M)↓
GMTF46.282.7604.171.8
PFGF47.184.8409.066.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.345, + 0.483, + 0.372 + ], + "angle": 0, + "content": "Table 6. Comparisons of VMamba and Transformer based methods on the FLIR dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.386, + 0.484, + 0.492 + ], + "angle": 0, + "content": "method introduces redundant information when facilitating interactions among features at various granularities. While our GMF method outperforms the FMB fusion method which depends exclusively on Mamba. These results indicate that the Graph-Mamba-based architecture facilitates a more explicit and robust integration of thermal and pseudovisible information." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.493, + 0.484, + 0.734 + ], + "angle": 0, + "content": "The effectiveness of using VMamba block. An efficiency analysis is conducted to evaluate Mamba block compared with Transformer block. For a fair comparison, all VMamba blocks are replaced with Transformer blocks, resulting in a new method designated as GMTF. Specifically, the VMamba block is substituted with a self-attention block, and the Inter-Mamba block is replaced with a cross-attention block. As shown in Table 6, our PFGF method surpasses GMTF with a \\(0.9\\%\\) increase in mAP and a \\(2.1\\%\\) gain in mAP50. Additionally, PFGF demonstrates parameter efficiency by reducing the parameter count by 4.93M and decreasing FLOPs from 604.1 GFLOPs to 409.0 GFLOPs. These findings highlight that the VMamba block not only effectively suppresses redundant features and captures complementary cross-modal information but also achieves superior computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The effectiveness of using leader nodes. To incorporate the generative feature \\( z \\) into the multi-level discriminative features, we utilize leader nodes to guide information transfer from the low-level subgraph to the high-level subgraph. To verify the effectiveness of leader nodes, we compare our method with an approach that lacks leader nodes on FLIR and LLVIP datasets. Without leader nodes, the next high-level features don't receive the previous low-level features, which ignore the integration from \\( f^3 \\) to \\( f^5 \\). With ground truth serving as a labeled reference, Fig. 3 clearly shows that without the assistance of leader nodes, the object" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.905, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.394, + 0.907, + 0.451 + ], + "angle": 0, + "content": "Figure 3. Effectiveness of using leader nodes. The first two rows present samples from FLIR dataset, and the last two rows present samples from LLVIP dataset. Red, blue, and green boxes denote the detected objects \"person\", \"car\", and \"bicycle\", respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.907, + 0.542 + ], + "angle": 0, + "content": "confidence is significantly lower and there are more occurrences of false detections. This indicates that our method effectively leverages the features delivered by leader nodes across subgraphs, integrating both high-level semantics and low-level local details to build a more robust representation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.564, + 0.634, + 0.58 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.907, + 0.803 + ], + "angle": 0, + "content": "In this paper, we proposed a novel cross-modal fusion method, termed Pseudo Visible Feature Fine-Grained Fusion (PFGF), for thermal object detection. The PFGF framework begins by constructing a graph which consists of several subgraphs. Each subgraph is generated from different level output features from the backbone or synthetic visible feature. An Inter-Mamba block is then employed to facilitate cross-modality feature association between generative and discriminative node features. Additionally, we introduce a Cascade Knowledge Integration strategy to propagate knowledge hierarchically from lower-level to higher-level subgraphs. In the process, VMamba is employed to further refine features. Extensive experiments demonstrate that our method achieves the SOTA performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by the National Natural Science Foundation of China (62276048, 62476169), Chengdu Science and Technology Projects (2023-YF06-00009-HZ) and Postdoctoral Fellowship Program of CPSF (GZC20233323)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6717" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.156 + ], + "angle": 0, + "content": "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. 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Current state-of-the-art (SOTA) models always leverage a prior Thermal-To-Visible (T2V) translation model to obtain visible spectrum information, followed by a cross-modality aggregation module to fuse information from both modalities. However, this fusion approach does not fully exploit the complementary visible spectrum information beneficial for thermal detection. To address this issue, we propose a novel cross-modal fusion method called Pseudo Visible Feature Fine-Grained Fusion (PFGF). Specifically, a graph is constructed with nodes generated from multi-level thermal features and pseudo-visual latent features produced by the T2V model. Each level of features corresponds to a subgraph. An Inter-Mamba block is proposed to perform cross-modality fusion between nodes at the lowest level; while a Cascade Knowledge Integration (CKI) strategy is used to fuse low-level fused information to high-level subgraphs in a cascade manner. After several iterations of graph node updating, each subgraph outputs an aggregated feature to the detection head respectively. Unlike previous cross-modal fusion methods, our approach explicitly models high-level relationships between cross-modal data, effectively fusing different granularity information. Experimental results demonstrate that our method achieves SOTA detection performance. Code is available at https://github.com/liting1018/PFGF. + +# 1. Introduction + +Object detection is critical in computer vision, with applications in autonomous driving and video surveillance [27]. While most methods rely on visible spectrum images, they often struggle in adverse conditions like nighttime, fog, or snow. In contrast, thermal spectrum images offer robustness in challenging environments [13], but they may falter in the daytime due to limited texture detail. Both visible- + +![](images/58bcf8f9f51cd5387bee19dab540b69f8302e97d1b428858add2456ed14b0db5.jpg) + +![](images/1af7d47aa4ad8ba3036fc5a578bf357cce731796779777b10aa862f60184de68.jpg) +Figure 1. Comparison between previous attention-based method and our method. (a) An attention-based module combines channel and spatial attention to augment the modality-translation awareness of detection. (b) Our method employs a Graph-Mamba Fusion module to integrate cross-modality knowledge in a cascade manner with different granularity. + +only and thermal-only approaches face limitations by solely relying on one spectrum, and lacking complementary data. As a result, multi-spectral (visible and thermal) object detection [8, 25, 52] have gained popularity. However, these approaches require paired visible and thermal images for both training and inference, increasing hardware costs and complexity. Furthermore, the need for precise alignment between modalities further limits practical deployment [5]. Consequently, there is growing interest in visible knowledge assistance methods that utilize paired visible-thermal images for training and solely thermal images for testing. + +Visible knowledge-assisted thermal pedestrian detection methods can be categorized into two routes: data enhancement and cross-modal transfer. The route of data enhancement [2] employs generative models to adapt visible images to the thermal domain like domain adaptation [26, 29], us + +ing them during training to mitigate the limitations caused by relying solely on thermal data during testing. However, the generated thermal images may be unreliable, potentially degrading the performance of thermal pedestrian detectors. Another route is based on cross-modal transfer, which can be further divided into two approaches. The first approach, feature domain transformation [45], utilizes an auxiliary network to convert thermal features into visible ones. However, this process demands substantial computation and large models to maintain feature quality in high-dimensional spaces. The second approach, image domain transformation [44], employs a generative model to directly convert thermal images into visible ones. The transformed visible images are then fused with the original thermal images, as illustrated in Fig.1(a). + +While image domain transformation methods have attained the state-of-the-art performance in thermal object detection, they still face obstacles related to occlusions and visible image noise. This limitation primarily stems from the inherent unreliability of visible images generated from thermal data, which can introduce noise that adversely affects detection accuracy. Furthermore, these approaches often neglect the fine-grained multimodal knowledge relationships between pseudo-visible and thermal data. As a result, effectively harnessing the complementary nature of thermal and visible information to resolve ambiguities in complex scenes remains a significant challenge. Fortunately, Graph Neural Networks (GNNs) offer a promising alternative for modeling and reasoning about relationships [30]. This motivates us to utilize graph structures for enabling interactions among features at various granularities. Such an approach ensures comprehensive utilization of information between low-level features to high-level semantics, leading to richer and more nuanced cross-modal integration. However, the flexible flow of information between nodes may introduce redundancy or irrelevant data, potentially hindering detection performance. To address this, we incorporate Mamba's selection mechanism [53] to effectively filter out unimportant information in the long-range context, which is particularly crucial for thermal feature maps that often contain noise and lack texture details. Furthermore, by iteratively updating node features based on neighborhood nodes, it can minimize the impact of less relevant nodes, thereby enhancing feature fusion and representation. + +Based on the above analysis, as illustrated in Fig. 1(b), we propose a novel cross-modal fusion method, dubbed as Pseudo Visible Feature Fine-Grained Fusion (PFGF). First, we obtain the visible features using the Pearl-GAN method [37], which are referred to as generative features. To fuse these generative features, we introduce the Graph-Mamba Fusion module. Specially, a graph is constructed that consists of multiple subgraphs, where each subgraph corresponds to either the generative feature or the output features + +from different levels of the detector backbone (referred to as discriminative features). The node features in each subgraph represent multi-level information, corresponding to different feature levels. For graph computation, we propose the Inter-Mamba block and Cascade Knowledge Integration (CKI) strategy, which facilitate efficient knowledge fusion and propagation across subgraphs. The Inter-Mamba block is introduced to fuse the nodes of subgraphs between the generative feature and the low-level discriminative feature, here the $c^3$ feature from CSPDarknet [1]. Then, a Cascade Knowledge Integration (CKI) strategy is proposed to propagate the knowledge from the low-level subgraph to the high-level subgraph in a cascade manner. During this cascading process, node features are updated using the Gate Recurrent Unit (GRU) method [9], while the VMamba block further refines these features across subgraphs. + +Our contributions can be summarized as follows: (1) We are the first to employ pseudo visible feature fine-grained fusion method for thermal object detection. The information interaction ability of graph at different granularities and the information selection and enhancement ability of Mamba have been fully utilized. (2) An Inter-Mamba block is proposed to facilitate cross-modality fusion between generative and discriminative node features. Additionally, the cascade knowledge integration strategy aggregates knowledge from low-level to high-level feature subgraphs avoiding tedious computation. (3) Experiments conducted on public FLIR, LLVIP, and Autonomous Vehicles datasets demonstrate significant advantages over the state-of-the-art (SOTA) thermal object detection methods. + +# 2. Related Work + +# 2.1. Thermal Object Detection + +Thermal object detection is crucial in low-light environments and privacy-sensitive scenarios. Existing approaches can be categorized into direct reconstruction and visible knowledge assistance. In the direct reconstruction approach, the methods [21, 22, 38] focus on designing networks to extract discriminative features by leveraging the intrinsic characteristics of thermal images. For example, GPCAnet [48] predicts object positions in the image to allocate more ROIs to the predicted areas. The Visible knowledge assistance methods can be further divided into data augmentation and cross-modal transfer. The data augmentation works [2, 20] use GANs to convert visible images into thermal images, mixing them to enhance detector robustness. In the cross-modal transfer approach, the works try to generate pseudo visual images or features. For example, TIRDet [44] uses Pearl-GAN for image translation. Xie et al [45] use a hallucination network to learn visible features from thermal images. All methods lack in-depth research on pseudo-visible information fusion. + +# 2.2. Graph Based Cross Modality Fusion + +In recent years, graph-based approaches have gained significant traction in computer vision applications [36]. Typically, graph operates as message-passing algorithms, where node representations are iteratively updated based on their neighbors through a differentiable aggregation function [34]. This makes graph particularly valuable in multisource data fusion. For instance, Cai et al. [3] used a graph-attention mechanism to fuse embeddings from different feature extractors, while Li et al. [24] proposed an interactive GNN-based architecture to facilitate cross-modality fusion. Our work is closely related latter work that utilizes graph structures to explicitly model and reason about different granularity information interactions between complementary data sources. However, our approach uniquely incorporates Mamba's selection mechanism to strengthen graph node representations, effectively minimizing the impact of unimportant nodes at each step of hidden state computation. + +# 2.3. Mamba Based Cross Modality Fusion + +Since its inception for linear-time sequence modeling in natural language processing, Mamba [14] has rapidly been adapted for various applications in computer vision. For example, VMamba [35] leverages a four-way scanning algorithm to advance object detection and segmentation beyond the capabilities of the Swin Transformer. Mamba has already been used in cross-modality fusion. Xie et al. [46] leveraged Mamba for dynamic feature enhancement in multimodal image fusion. Pan-Mamba [15] is developed to facilitate efficient cross-modal information exchange and fusion. The Fusion-Mamba block [10] is introduced to mitigate disparities between cross-modal features and enhance the consistency of fused feature representations. Additionally, Li et al. [23] proposed cross-modality fusion-Mamba, coupled with weather removal techniques, to improve detection accuracy under adverse weather conditions. Distinct from prior research, our work pioneers the integration of the Mamba architecture into graph representations for thermal object detection tasks, significantly enhancing graph embeddings and processing capabilities. + +# 3. Methodology + +# 3.1. Problem Statement + +Suppose the training dataset $D_{s} = \{X^{t},X^{v}\}$ , where the thermal image set $X^{t} = \{x_{s_{i}}^{t}\}_{i = 1}^{N_{st}}$ with labels $\{y_{s_i}^t\}_{i = 1}^{N_{st}}$ and the unpaired visible image set $X^{v} = \{x_{s_{i}}^{v}\}_{i = 1}^{N_{sv}}$ . $N_{st}$ and $N_{sv}$ denote the cardinality of the thermal image set and visible image set respectively. The test dataset $D_{t} = \{x_{t_{i}}^{t}\}_{i = 1}^{N_{t}}$ be exclusively composed of thermal images, where $N^t$ represents the number of thermal images in the test dataset. Our objective is to compensate for visible knowledge while using solely thermal images as the input at the test stage, + +and fully leverage information from both modalities to develop robust representations at the training stage. + +Overview. Fig. 2(a) illustrates the proposed Pseudo Visible Feature Fine-Grained Fusion (PFGF) framework, which uses the single-stage detector YOLOX [12] as the baseline model. Both training and testing are conducted exclusively with thermal images. Specifically, we first train Pearl-GAN as a prior thermal-to-visible (T2V) translation model $\Phi$ , which is trained on both thermal and visible modalities, to convert thermal image $x^t$ into daytime visible image $x^v$ , thereby incorporating valuable visible information from the unpaired set $X^v$ . This process is described as follows: + +$$ +[ x ^ {v}, z ] = \Phi (x ^ {t}), \tag {1} +$$ + +where $x^{t} \in \mathbb{R}^{H \times W \times 1}$ and $x^{v} \in \mathbb{R}^{H \times W \times 3}$ . $\Phi(x^{t})$ comprises a convolution-based encoder $z = \varepsilon(x^{t})$ and a decoder $x^{v} = \mu(z)$ . The latent T2V code $z \in \mathbb{R}^{h_{z} \times w_{z} \times c_{z}}$ is considered as generative feature. + +CSPDarknet is employed as the backbone $\mathcal{F}$ to extract multi-level features $c^3, c^4$ and $c^5$ from the concatenated images $x^t$ and $x^v$ as follows, + +$$ +\left[ c ^ {3}, c ^ {4}, c ^ {5} \right] = \mathcal {F} \left(\operatorname {c o n c a t} \left(x ^ {t}, x ^ {v}\right)\right). \tag {2} +$$ + +A VMamba [35] block $\mathcal{M}$ then refines these features: + +$$ +f ^ {i} = \mathcal {M} ^ {i} \left(c ^ {i}\right), \tag {3} +$$ + +for $i \in \{3,4,5\}$ . The output features $f^i \in R^{h \times w \times c}$ are considered as discriminative features. We refer to this process as the VMamba-based Multi-level feature Enhancement (MEM). Here, a VMamba block is utilized to learn global relationships and contextual information from two modalities, thereby enhancing the model's representational capacity. Additionally, due to Mamba's input-dependent mechanism and various hardware-optimized techniques, it excels in long-range modeling with reduced computational cost compared to Transformers. + +To better integrate the generated visible features, we propose a novel Graph-Mamba Fusion (GMF) module $\mathcal{G}$ . This approach effectively combines generative feature $z$ with discriminative features $f_{i}$ as follows, + +$$ +\left[ g ^ {3}, g ^ {4}, g ^ {5} \right] = \mathcal {G} \left(f ^ {3}, f ^ {4}, f ^ {5}, z\right). \tag {4} +$$ + +Graph-Mamba Fusion (GMF) module, as a key contribution, goes beyond simple attention by establishing high-level relationships. It first fuses generative feature $z$ with the discriminate feature $f^3$ and then performs high-level fusion from $f^3$ to $f^5$ , which will be introduced later. + +Subsequently, the features $f^i$ and $g^i$ are combined using residual connections and a Neck module $\Phi$ to obtain the output features $f^{i'} = \Phi (f^i + g^i)$ , where $i \in \{3, 4, 5\}$ . Finally, the Decoupled Detection Head $\mathcal{H}$ [12] is employed to obtain the detection result based on $f^{i'}$ . The model is trained using the standard detection loss $L_{d}(\mathcal{H}(f^{3'}, f^{4'}, f^{5'}, y_{s_i}^t))$ . + +![](images/bef22e91b37620cb3327916041c00ae8d2d5337a5a13ab67a3ebc7cda5d53109.jpg) + +![](images/874c38a39bf8f360c1526cb641989e0fdac7f8ca00018af058d7817eb0f72e03.jpg) + +![](images/0057ff9040ce5b042438dece57b1c480ad3e0189a88f04a95f72de9aa5c09b0b.jpg) +Figure 2. Overview of the proposed PFGF method. (a) The framework of the PFGF, with our modules highlighted in the purple box. (b) The Graph-Mamba Fusion Module constructs the graph structure for both discriminative and generative features, with leader nodes guiding the flow of information between graphs. (c) The Inter-Mamba Module facilitates interactions between different modalities. (d) The VMamba Module updates nodes within the same modality. + +# 3.2. Pseudo Visible Feature Fine-Grained Fusion + +For further integrating the generative feature $z$ , a straightforward attention-based fusion approach, as used in [44], can be employed. However, this method has limitations in effectively capturing high-level relationships among the features. Additionally, it struggles to capture essential visual information due to the unreliability of the generated visible images, which often introduces a substantial amount of irrelevant information. To overcome these challenges, we introduce the Graph-Mamba Fusion (GMF) module as shown in Fig. 2(b). Graph structure is employed to establish more compensated relationships between different level features, which Mamba is adapted to capture long-range dependencies with less computational complexity. + +To avoid getting lost in details, let's first briefly introduce the process. (1) Graph construction. The features $f^3$ , $f^4$ , $f^5$ , and $z$ are down-and-up sampled to different copies as graph nodes. Graph edges are constructed by computing similarity between nodes, and message passing is performed by aggregating features from neighboring nodes. (2) Graph computation. An Inter-Mamba block is proposed to facilitate fusion between the nodes produced by latent feature $z$ and discriminative feature $f^3$ respectively as illus- + +trated in Fig. 2 (c). The GRU algorithm is used to update graph nodes, ensuring effective information propagation. Subsequently, a VMamba block is used to further refine the node feature. The output $g^3$ is formed by merging the node features of $f^3$ and is then multiplied with the nodes derived from $f^4$ , enabling the fusion of information across different levels. The output $g^4$ and $g^5$ are obtained by merging the node features from $f^4$ and $f^5$ , respectively. + +# 3.2.1. Graph construction + +In this part, we will introduce how to construct a graph $\Psi = (U,E)$ based on the features $f$ and $z$ . This structure is inspired by the method [24], which effectively models the relationships and dependencies among features extracted from different levels or modalities. The graph structure is designed to ensure that the fusion of these features is contextually relevant, thereby enhancing the accuracy and robustness of the representations used for detection. + +Node generation. Given the generative feature $z$ and discriminative feature $f$ , two types of nodes are generated. To capture multi-level information and enhance feature diversity, we make replicas of different granularities of the corresponding features as graph nodes. Specifically, pyramid pooling, convolution, and upsampling operations are ap- + +plied to both generative feature $z$ and discriminate feature $f$ , which can be formally computed as follows: + +$$ +f _ {j} ^ {i} = U p \left(\operatorname {C o n v} \left(\mathcal {P} _ {j} \left(f ^ {i}\right)\right)\right), z _ {j} = U p \left(\operatorname {C o n v} \left(\mathcal {P} _ {j} (z)\right)\right), \tag {5} +$$ + +where the operator $\mathcal{P}_j(\cdot)$ pools the given feature to various sizes according to the scale setting $j$ , a $1 \times 1$ convolution is applied to reduce the dimension of the pooled representation, and $Up$ operator, using bi-linear interpolation, up-samples the feature maps to match the original size. For each $f^i$ and $z$ , there are $n$ node features $f_j^i \in R^{h \times w \times c'}$ for $j \in \{1, \dots, n\}$ and $z_j \in R^{h \times w \times c'}$ . Here $n = 3$ . Note that $z$ has only one scale and shares the same shape as $f^3$ . + +Edge generation. The edges play a crucial aspect, as it facilitates the propagation of information between nodes. Here, we only compute intra-edges, i.e., the edges connect the nodes produced by the same feature. Since our goal is to incorporate the information from the generative feature $z$ into the discriminative feature $f$ , there is no need to construct additional edges between the nodes produced by the generative feature. Specifically, for the feature $f^i$ , the intra-edge $e_{j,k}^i$ is computed as + +$$ +e _ {j, k} ^ {i} = \operatorname {C o n v} \left(f _ {j} ^ {i} - f _ {k} ^ {i}\right), \tag {6} +$$ + +where $Conv(\cdot)$ is used to learn relationships between nodes. The term $f_{j}^{i} - f_{k}^{i}$ represents the difference between the node features $f_{j}^{i}$ and $f_{k}^{i}$ . This highlights the relative disparity between nodes, following the approach outlined in [43]. Based on our edge computation method, we have formed four subgraphs, which are constructed by graph nodes formed by the features $z, f^{3}, f^{4}$ , and $f^{5}$ , respectively. Here the edges between the subgraphs of different discriminative features are not computed to avoid tedious computation. Instead, we introduce a new leader node to aggregate subgraph node features, and then pass the aggregated feature to the next subgraph from $f^{3}$ to $f^{5}$ . + +Message Passing. In each subgraph composed of discriminative features, every node aggregates feature messages from all its neighboring nodes. For the node $f_{j}^{i}$ , at $l - 1$ message passing, denoted as $m_{j}^{i,l - 1}$ , is computed as + +$$ +m _ {j} ^ {i, l - 1} = \sum_ {k \in \mathcal {N} (j)} \operatorname {S i g m o i d} \left(e _ {k, j} ^ {i, l - 1}\right) \cdot f _ {k} ^ {i, l - 1}, \tag {7} +$$ + +where $Sigmoid(\cdot)$ function is utilized to calculate the link weight between nodes. + +# 3.2.2. Graph computation + +Graph-based cross-modality information fusion consists of two key components: cross-modality fusion through the Inter-Mamba block and knowledge integration via GRU and VMamba. + +Cross modality fusion by Inter-Mamba block. For fusing the node features $z_{j}$ and $f_{j}^{3}$ , instead of transformer-based + +route, we proposed a Mamba-based block. As shown in Fig. 2(c), the node features $f_{j}^{3}$ and $z_{j}$ are first projected into the hidden state space followed by a VMamba block, and a gating operation is then employed to facilitate the interaction between these two types of hidden state features. + +Specifically, the node features $f_{j}^{3}$ and $z_{j}$ are first flattened to form the input token sequences $T_{j}^{3}$ and $T_{j}$ , each with dimensions $B \times N \times C$ , where $B$ , $N$ , and $C$ denote the batch size, sequence length, and number of channels, respectively. These sequences are then normalized by a normalization layer. Next, the normalized sequences $T_{j}^{3}$ and $T_{j}$ are projected into the hidden state space respectively through linear layers, convolution, and SSM, resulting in the hidden state features $\hat{f}_{j}^{3}$ and $\hat{z}_{j}$ . Simultaneously, the normalized sequence $T_{j}^{3}$ is also projected through linear layers with SiLU activation to obtain the gating weight $r$ . It is used for hidden state feature fusion as follows, + +$$ +f _ {j} ^ {3} = \mathcal {R} \left(\mathcal {Y} \left(\left(\hat {z} _ {j} + \hat {f} _ {j} ^ {3}\right) \odot r\right) + f _ {j} ^ {3}\right), \tag {8} +$$ + +where $\odot$ represents element-wise multiplication. The operator $\mathcal{V}$ denotes the projection operation with a linear transformation, while $\mathcal{R}$ refers to the reshaping operation. + +Cascade Knowledge Integration (CKI) strategy. Existing studies [11] have demonstrated that deep and shallow features exhibit complementary characteristics: deep features capture high-level semantic information, while shallow features retain rich spatial details. Leveraging multilevel features is therefore advantageous for enhancing detection performance. As we stated before, a leader node is proposed to convey low-level fused information to high-level subgraph in a cascade manner. + +We first apply a GRU-based update method [9] to enhance the nodes' ability to capture complex feature interactions and retain relevant information from neighboring nodes. After $l-1$ message passing, the node feature $f_{j}^{i}$ is updated by $\mathcal{U}_{GRU}(f_{j}^{i}, m_{j}^{i,l-1})$ (See the Appendix for a detailed description of $\mathcal{U}_{GRU}$ ). + +A leader node feature $g^i$ at the $i$ -th scale is computed as + +$$ +g ^ {i} = \operatorname {C o n v} \left(\operatorname {C o n c a t} \left(\mathcal {M} \left(f _ {1} ^ {i}\right), \dots , \mathcal {M} \left(f _ {n} ^ {i}\right)\right)\right), \tag {9} +$$ + +where $\mathcal{M}$ denotes a VMamba block as mentioned before. + +The leader node $g^i$ conveys knowledge to the subsequent subgraph nodes as follows, + +$$ +f _ {j} ^ {i + 1} = f _ {j} ^ {i + 1} \odot \mathcal {A} (g ^ {i}) + f _ {j} ^ {i + 1}, \tag {10} +$$ + +where $\mathcal{A}$ represents an attention operation, which is computed via global average pooling followed by a Sigmoid activation. Since the last subgraph does not contribute to knowledge transmission, the scale $i$ is set to 3 and 4. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. To evaluate our method, we conduct experiments on the FLIR-aligned dataset [49], LLVIP dataset [18], and Autonomous Vehicles dataset [42]. (1) The FLIR dataset originally presented challenges due to unaligned thermal-visible image pairs. Therefore, we utilize the aligned version, consisting of 5,142 thermal-visible image pairs, with 4,129 pairs for training and 1,013 for testing. This dataset includes three object categories: "person," "car," and "bicycle". (2) The LLVIP dataset is collected in very dark environments. It comprises 15488 aligned image pairs, with 12,025 pairs used for training and 3,463 pairs for testing. This dataset focuses on a single object class: "person". (3) The Autonomous Vehicles dataset comprises 6,009 paired images for training and 1,503 for testing, covering five categories: "bike", "car", "car_stop", "color_cone", and "person". Compared to the FLIR and LLVIP datasets, the scenes in this dataset are more complex. + +Evaluation Metrics. We evaluate our method using standard object detection metrics [31], including mean Average Precision (mAP), mAP50, and mAP75. The mAP metric represents the average AP over IoU thresholds ranging from 0.50 to 0.95, with an interval of 0.05. The mAP50 and mAP75 metrics correspond to the AP values at IoU thresholds of 0.50 and 0.75, respectively. Higher values for these metrics indicate better performance. + +Implementation Details. We utilize a pre-trained model on the COCO dataset and implement our approach using the MMDetection toolbox [6], a widely adopted framework for object detection. The network is trained using the SGD optimizer with a batch size of 4 and an initial learning rate of 5e-4. The input image size is set to $640 \times 640$ for the FLIR, LLVIP, and Autonomous Vehicles datasets, with the training conducted over 8 epochs. The training process is conducted in two stages. In the first stage, the Pearl-GAN module is trained. In the second stage, with the parameters of the Pearl-GAN module fixed, the backbone, VMamba, Graph-Mamba Fusion (GMF) module, neck, and detection head are trained. For the GMF module, the number of graph nodes $n$ is set to 3, and the number of message-passing iterations $L$ is also set to 3. The cascade quantities of VMamba and Inter-Mamba blocks are each configured to 2. Details on hyper-parameter sensitivity are provided in the Appendix. To ensure reproducibility, all experiments are conducted with a random seed set to 0. + +# 4.2. Comparison with State-of-the-art Methods + +Compared methods. We compare the proposed PFGF method with both mono-modality (thermal) and multispectral (visible + thermal) methods. The mono-modality methods include Faster RCNN [41], SSD [33], RetinaNet + +
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5074.432.537.6
SSD [33]TVGG1665.522.429.6
RetinaNet [32]TResNet5064.520.328.3
YOLOv3 [40]TDarknet5373.631.336.8
YOLOX-L [12]TCSPD5378.139.442.6
IAH [45]TDarknet5376.4--
DIP [17]TResNet5077.3--
TIRDet [44]TCSPD5381.441.144.3
IDA [28]TCSPD5381.143.446.3
PFGF (Ours)TCSPD5384.844.647.1
CFR_3 [49]V+TVGG1672.4--
GAFF [50]V+TResNet1872.932.937.5
YOLOFusion [39]V+TVGG1676.6-39.8
CMX [51]V+TSwinT82.237.142.3
IGT [7]V+TSwinT85.036.943.6
DATFF [16]V+TResNet5080.2--
RSDet [52]V+TResNet5081.1-41.1
Fusion-Mamba [10]V+TCSPD5384.9-47.0
+ +Table 1. Comparisons on FLIR dataset in terms of MAP. The best results are highlighted in bold. + +[32], YOLOv3 [40], YOLOX-L [12], IAH [45], DIP [17], TIRDet [44] and IDA [28]. These methods utilize paired visible and thermal images for training, but only thermal images for testing. In contrast, the multispectral methods include CFR_3 [49], GAFF [50], YOLOFusion [39], CMX [51], IGT [7], DATFF [16], RSDet [52], YOLOv5-VT [19], DM-Fusion [47], and Fusion-Mamba [10]. These methods employ paired visible and thermal images for both training and testing. The results presented in the tables are cited from the respective papers. + +Quantitative comparison. The quantitative comparison results are presented in Tables 1, 2, and 3. Our method achieves the state-of-the-art (SOTA) performance among mono-modality (thermal) methods on the FLIR, LLVIP, and Autonomous Vehicles datasets. On the FLIR dataset, our approach outperforms the recent TIRDet and IDA methods, achieving mAP gains of $2.8\%$ and $0.8\%$ , respectively, along with mAP50 improvements of $3.4\%$ and $3.7\%$ . For a fair comparison of the LLVIP dataset, we reproduced the TIRDet method using a Pearl-GAN model trained on the LLVIP dataset, referred to as TIRDet*. Similarly, our method denoted as PFGF*, utilizes this same Pearl-GAN model. Additionally, to facilitate comparison with the original results reported in the TIRDet paper, we also use a Pearl-GAN model trained on the FLIR dataset. The results demonstrate that our proposed method consistently achieves superior performance in both sets of comparisons: between TIRDet and PFGF, as well as between TIRDet* and PFGF*. On the more complex Autonomous Vehicles dataset, our method surpasses the IDA method, with mAP50 increas + +
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5096.168.561.1
SSD [33]TVGG1690.257.953.5
RetinaNet [32]TResNet5093.749.350.9
YOLOv3 [40]TDarknet5389.753.452.8
YOLOX-L [12]TCSPD5395.272.763.6
TIRDet [44]TCSPD5396.373.164.2
TIRDet* [44]TCSPD5396.874.765.2
PFGF (Ours)TCSPD5396.677.966.8
PFGF* (Ours)TCSPD5396.978.467.3
DM-Fusion [47]V+TCSPD5388.1-53.1
YOLOv5-VT [19]V+TCSPD5395.871.462.3
RSDet [52]V+TResNet5095.8-61.3
Fusion-Mamba [10]V+TCSPD5397.0-64.3
+ +Table 2. Comparisons on LLVIP dataset in terms of MAP. + +
MethodsDataBackbonemAP50mAP75mAP
YOLOv3 [40]TDarknet5371.929.934.6
FasterRCNN [41]TResNet5072.539.839.9
CascadeRCNN [4]TResNet5072.942.742.2
YOLOX-L [12]TCSPD5372.340.640.6
IDA [28]TCSPD5373.143.843.1
PFGF (Ours)TCSPD5378.846.645.9
+ +ing by $5.7\%$ , mAP75 rising by $2.8\%$ , and overall mAP improving by $2.8\%$ . Moreover, our method outperforms most multispectral methods in detection performance, achieving the highest mAP and mAP75, and the second-best mAP50 on both FLIR and LLVIP datasets. These results indicate that the combination of the T2V model and the proposed PFGF approach effectively enhances thermal detection performance with valuable visible information. + +We also conduct a visual comparison between the proposed PFGF method, and the publicly method TIRDet. Our method significantly improves the detection performance of thermal images (See the Appendix). + +# 4.3. Further Analysis + +Ablation studies. Our framework comprises T2V translation model Pearl-GAN, VMamba-based Multi-level Feature Enhancement (MEM) block, and Graph-Mamba Fusion (GMF) module, which includes both the Inter-Mamba block and CKI strategy. To assess the contribution of each component, we performed ablation studies on the FLIR, LLVIP, and Autonomous Vehicles datasets. There are several variants: 'w/o Pearl-GAN' refers to the exclusion of visible information with only thermal image input; 'w/o MEM' denotes the detector backbone features are not enhanced by MEM block; 'w/o GMF' means the enhanced + +Table 3. Comparisons on AV dataset in terms of MAP. AV: Autonomous Vehicles dataset. + +
MethodmAP
FLIRLLVIPAV
w/o PearlGAN45.265.044.4
w/o MEM46.066.145.4
w/o GMF45.665.644.3
w/o Inter-Mamba (GMF)45.966.245.1
w/o CKI (GMF)46.166.445.3
PFGF47.167.345.9
+ +Table 4. Ablation study on FLIR, LLVIP, and AV datasets. + +features will be passed directly to the detector head; 'w/o Inter-Mamba' implies that generative features $z$ are not fused with discriminative features $f^3$ ; while 'w/o CKI' does not integrate features from $f^3$ to $f^5$ . + +Table 4 demonstrates that each component positively contributes to performance. Removing Pearl-GAN prevents the incorporation of visible information, leading to a substantial performance decline on the FLIR and LLVIP datasets and the second-largest performance drop on the Autonomous Vehicles dataset. The absence of MEM affects performance differently across datasets, suggesting its role in refining and enhancing coarse fusion features. Excluding the GMF module reduces mAP by $1.5\%$ on the FLIR dataset, $1.7\%$ on the LLVIP dataset, and $1.6\%$ on the Autonomous Vehicles dataset, underscoring its importance in integrating generated visible and thermal information. Furthermore, ablation analysis on the GMF module reveals that the Inter-Mamba block has a more significant impact than the CKI block, indicating that the Inter-Mamba block can effectively filter redundant visible information while preserving information beneficial for thermal detection. + +Comparison of different fusion methods. To validate the superiority of our proposed fusion module, we conduct further experiments comparing it with various fusion strategies, including addition, concatenation, CMA [44], MMFT [45], GIM [24] and FMB [10]. The CMA method employs Convolutional Block Attention Module (CBAM) to generate attention maps; the MMFT leverages a Transformer-based architecture to perform fusion based on varying illumination conditions; GIM utilizes graph neural networks to handle cross-modal interactions through features; while the FMB method, rooted in the Mamba architecture, is specifically designed for multispectral detection tasks. + +As shown in Table 5, our method outperforms all other strategies. Specifically, CMA method is relatively simplistic and fails to effectively capture visible information beneficial for thermal detection; in contrast to the MMFT method, our approach eliminates the dependency on an additional illumination-aware module. The FMB method has achieved superior performance in multispectral tasks, it does not adapt well to our specific problem due to the unreliability of the generated visible information. The GIM + +
MethodFLIRLLVIPAV
mAPmAP50mAPmAP50mAPmAP50
Add42.677.561.795.240.473.9
Concat43.779.963.394.842.474.7
CMA[44]44.381.464.696.343.976.5
MMFT[45]44.682.165.195.244.176.8
GIM[24]46.081.866.396.244.874.5
FMB[10]45.782.465.996.344.277.0
GMF (Ours)47.184.867.396.945.978.8
+ +Table 5. Comparison of different fusion methods. + +
MethodmAPmAP50FLOPS(G)↓Param(M)↓
GMTF46.282.7604.171.8
PFGF47.184.8409.066.9
+ +Table 6. Comparisons of VMamba and Transformer based methods on the FLIR dataset. + +method introduces redundant information when facilitating interactions among features at various granularities. While our GMF method outperforms the FMB fusion method which depends exclusively on Mamba. These results indicate that the Graph-Mamba-based architecture facilitates a more explicit and robust integration of thermal and pseudovisible information. + +The effectiveness of using VMamba block. An efficiency analysis is conducted to evaluate Mamba block compared with Transformer block. For a fair comparison, all VMamba blocks are replaced with Transformer blocks, resulting in a new method designated as GMTF. Specifically, the VMamba block is substituted with a self-attention block, and the Inter-Mamba block is replaced with a cross-attention block. As shown in Table 6, our PFGF method surpasses GMTF with a $0.9\%$ increase in mAP and a $2.1\%$ gain in mAP50. Additionally, PFGF demonstrates parameter efficiency by reducing the parameter count by 4.93M and decreasing FLOPs from 604.1 GFLOPs to 409.0 GFLOPs. These findings highlight that the VMamba block not only effectively suppresses redundant features and captures complementary cross-modal information but also achieves superior computational efficiency. + +The effectiveness of using leader nodes. To incorporate the generative feature $z$ into the multi-level discriminative features, we utilize leader nodes to guide information transfer from the low-level subgraph to the high-level subgraph. To verify the effectiveness of leader nodes, we compare our method with an approach that lacks leader nodes on FLIR and LLVIP datasets. Without leader nodes, the next high-level features don't receive the previous low-level features, which ignore the integration from $f^3$ to $f^5$ . With ground truth serving as a labeled reference, Fig. 3 clearly shows that without the assistance of leader nodes, the object + +![](images/e9641115da26912c51349bc58bd466e1bb7eaabced5a26086c511f2c50a922cc.jpg) +Figure 3. Effectiveness of using leader nodes. The first two rows present samples from FLIR dataset, and the last two rows present samples from LLVIP dataset. Red, blue, and green boxes denote the detected objects "person", "car", and "bicycle", respectively. + +confidence is significantly lower and there are more occurrences of false detections. This indicates that our method effectively leverages the features delivered by leader nodes across subgraphs, integrating both high-level semantics and low-level local details to build a more robust representation. + +# 5. Conclusion + +In this paper, we proposed a novel cross-modal fusion method, termed Pseudo Visible Feature Fine-Grained Fusion (PFGF), for thermal object detection. The PFGF framework begins by constructing a graph which consists of several subgraphs. Each subgraph is generated from different level output features from the backbone or synthetic visible feature. An Inter-Mamba block is then employed to facilitate cross-modality feature association between generative and discriminative node features. Additionally, we introduce a Cascade Knowledge Integration strategy to propagate knowledge hierarchically from lower-level to higher-level subgraphs. In the process, VMamba is employed to further refine features. Extensive experiments demonstrate that our method achieves the SOTA performance. + +Acknowledgement. This work was supported by the National Natural Science Foundation of China (62276048, 62476169), Chengdu Science and Technology Projects (2023-YF06-00009-HZ) and Postdoctoral Fellowship Program of CPSF (GZC20233323). + +# References + +[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. 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Current state-of-the-art (SOTA) models always leverage a prior Thermal-To-Visible (T2V) translation model to obtain visible spectrum information, followed by a cross-modality aggregation module to fuse information from both modalities. However, this fusion approach does not fully exploit the complementary visible spectrum information beneficial for thermal detection. To address this issue, we propose a novel cross-modal fusion method called Pseudo Visible Feature Fine-Grained Fusion (PFGF). Specifically, a graph is constructed with nodes generated from multi-level thermal features and pseudo-visual latent features produced by the T2V model. Each level of features corresponds to a subgraph. An Inter-Mamba block is proposed to perform cross-modality fusion between nodes at the lowest level; while a Cascade Knowledge Integration (CKI) strategy is used to fuse low-level fused information to high-level subgraphs in a cascade manner. 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Comparison between previous attention-based method and our method. (a) An attention-based module combines channel and spatial attention to augment the modality-translation awareness of detection. (b) Our method employs a Graph-Mamba Fusion module to integrate cross-modality knowledge in a cascade manner with different granularity." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 518, + 555, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 518, + 555, + 650 + ], + "spans": [ + { + "bbox": [ + 312, + 518, + 555, + 650 + ], + "type": "text", + "content": "only and thermal-only approaches face limitations by solely relying on one spectrum, and lacking complementary data. As a result, multi-spectral (visible and thermal) object detection [8, 25, 52] have gained popularity. 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The route of data enhancement [2] employs generative models to adapt visible images to the thermal domain like domain adaptation [26, 29], us" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 703, + 157, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 703, + 157, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 703, + 157, + 713 + ], + "type": "text", + "content": "*The corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6710" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 251 + ], + "type": "text", + "content": "ing them during training to mitigate the limitations caused by relying solely on thermal data during testing. However, the generated thermal images may be unreliable, potentially degrading the performance of thermal pedestrian detectors. Another route is based on cross-modal transfer, which can be further divided into two approaches. The first approach, feature domain transformation [45], utilizes an auxiliary network to convert thermal features into visible ones. However, this process demands substantial computation and large models to maintain feature quality in high-dimensional spaces. The second approach, image domain transformation [44], employs a generative model to directly convert thermal images into visible ones. The transformed visible images are then fused with the original thermal images, as illustrated in Fig.1(a)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 255, + 295, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 255, + 295, + 602 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 295, + 602 + ], + "type": "text", + "content": "While image domain transformation methods have attained the state-of-the-art performance in thermal object detection, they still face obstacles related to occlusions and visible image noise. This limitation primarily stems from the inherent unreliability of visible images generated from thermal data, which can introduce noise that adversely affects detection accuracy. Furthermore, these approaches often neglect the fine-grained multimodal knowledge relationships between pseudo-visible and thermal data. As a result, effectively harnessing the complementary nature of thermal and visible information to resolve ambiguities in complex scenes remains a significant challenge. Fortunately, Graph Neural Networks (GNNs) offer a promising alternative for modeling and reasoning about relationships [30]. This motivates us to utilize graph structures for enabling interactions among features at various granularities. Such an approach ensures comprehensive utilization of information between low-level features to high-level semantics, leading to richer and more nuanced cross-modal integration. However, the flexible flow of information between nodes may introduce redundancy or irrelevant data, potentially hindering detection performance. To address this, we incorporate Mamba's selection mechanism [53] to effectively filter out unimportant information in the long-range context, which is particularly crucial for thermal feature maps that often contain noise and lack texture details. Furthermore, by iteratively updating node features based on neighborhood nodes, it can minimize the impact of less relevant nodes, thereby enhancing feature fusion and representation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Based on the above analysis, as illustrated in Fig. 1(b), we propose a novel cross-modal fusion method, dubbed as Pseudo Visible Feature Fine-Grained Fusion (PFGF). First, we obtain the visible features using the Pearl-GAN method [37], which are referred to as generative features. To fuse these generative features, we introduce the Graph-Mamba Fusion module. Specially, a graph is constructed that consists of multiple subgraphs, where each subgraph corresponds to either the generative feature or the output features" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "text", + "content": "from different levels of the detector backbone (referred to as discriminative features). The node features in each subgraph represent multi-level information, corresponding to different feature levels. For graph computation, we propose the Inter-Mamba block and Cascade Knowledge Integration (CKI) strategy, which facilitate efficient knowledge fusion and propagation across subgraphs. The Inter-Mamba block is introduced to fuse the nodes of subgraphs between the generative feature and the low-level discriminative feature, here the " + }, + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "inline_equation", + "content": "c^3" + }, + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "text", + "content": " feature from CSPDarknet [1]. Then, a Cascade Knowledge Integration (CKI) strategy is proposed to propagate the knowledge from the low-level subgraph to the high-level subgraph in a cascade manner. During this cascading process, node features are updated using the Gate Recurrent Unit (GRU) method [9], while the VMamba block further refines these features across subgraphs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 266, + 553, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 553, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 553, + 433 + ], + "type": "text", + "content": "Our contributions can be summarized as follows: (1) We are the first to employ pseudo visible feature fine-grained fusion method for thermal object detection. The information interaction ability of graph at different granularities and the information selection and enhancement ability of Mamba have been fully utilized. (2) An Inter-Mamba block is proposed to facilitate cross-modality fusion between generative and discriminative node features. Additionally, the cascade knowledge integration strategy aggregates knowledge from low-level to high-level feature subgraphs avoiding tedious computation. (3) Experiments conducted on public FLIR, LLVIP, and Autonomous Vehicles datasets demonstrate significant advantages over the state-of-the-art (SOTA) thermal object detection methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 445, + 400, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 445, + 400, + 457 + ], + "spans": [ + { + "bbox": [ + 314, + 445, + 400, + 457 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 467, + 459, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 459, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 459, + 479 + ], + "type": "text", + "content": "2.1. Thermal Object Detection" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "type": "text", + "content": "Thermal object detection is crucial in low-light environments and privacy-sensitive scenarios. Existing approaches can be categorized into direct reconstruction and visible knowledge assistance. In the direct reconstruction approach, the methods [21, 22, 38] focus on designing networks to extract discriminative features by leveraging the intrinsic characteristics of thermal images. For example, GPCAnet [48] predicts object positions in the image to allocate more ROIs to the predicted areas. The Visible knowledge assistance methods can be further divided into data augmentation and cross-modal transfer. The data augmentation works [2, 20] use GANs to convert visible images into thermal images, mixing them to enhance detector robustness. In the cross-modal transfer approach, the works try to generate pseudo visual images or features. For example, TIRDet [44] uses Pearl-GAN for image translation. Xie et al [45] use a hallucination network to learn visible features from thermal images. All methods lack in-depth research on pseudo-visible information fusion." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 313, + 757 + ], + "type": "text", + "content": "6711" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 249, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 249, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 249, + 85 + ], + "type": "text", + "content": "2.2. Graph Based Cross Modality Fusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 293 + ], + "type": "text", + "content": "In recent years, graph-based approaches have gained significant traction in computer vision applications [36]. Typically, graph operates as message-passing algorithms, where node representations are iteratively updated based on their neighbors through a differentiable aggregation function [34]. This makes graph particularly valuable in multisource data fusion. For instance, Cai et al. [3] used a graph-attention mechanism to fuse embeddings from different feature extractors, while Li et al. [24] proposed an interactive GNN-based architecture to facilitate cross-modality fusion. Our work is closely related latter work that utilizes graph structures to explicitly model and reason about different granularity information interactions between complementary data sources. However, our approach uniquely incorporates Mamba's selection mechanism to strengthen graph node representations, effectively minimizing the impact of unimportant nodes at each step of hidden state computation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 300, + 255, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 255, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 255, + 312 + ], + "type": "text", + "content": "2.3. Mamba Based Cross Modality Fusion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 316, + 296, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 296, + 558 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 296, + 558 + ], + "type": "text", + "content": "Since its inception for linear-time sequence modeling in natural language processing, Mamba [14] has rapidly been adapted for various applications in computer vision. For example, VMamba [35] leverages a four-way scanning algorithm to advance object detection and segmentation beyond the capabilities of the Swin Transformer. Mamba has already been used in cross-modality fusion. Xie et al. [46] leveraged Mamba for dynamic feature enhancement in multimodal image fusion. Pan-Mamba [15] is developed to facilitate efficient cross-modal information exchange and fusion. The Fusion-Mamba block [10] is introduced to mitigate disparities between cross-modal features and enhance the consistency of fused feature representations. Additionally, Li et al. [23] proposed cross-modality fusion-Mamba, coupled with weather removal techniques, to improve detection accuracy under adverse weather conditions. Distinct from prior research, our work pioneers the integration of the Mamba architecture into graph representations for thermal object detection tasks, significantly enhancing graph embeddings and processing capabilities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 567, + 138, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 138, + 580 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 138, + 580 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 586, + 168, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 168, + 598 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 168, + 598 + ], + "type": "text", + "content": "3.1. Problem Statement" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": "Suppose the training dataset " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "D_{s} = \\{X^{t},X^{v}\\}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": ", where the thermal image set " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "X^{t} = \\{x_{s_{i}}^{t}\\}_{i = 1}^{N_{st}}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " with labels " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{y_{s_i}^t\\}_{i = 1}^{N_{st}}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " and the unpaired visible image set " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "X^{v} = \\{x_{s_{i}}^{v}\\}_{i = 1}^{N_{sv}}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "N_{st}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "N_{sv}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " denote the cardinality of the thermal image set and visible image set respectively. The test dataset " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "D_{t} = \\{x_{t_{i}}^{t}\\}_{i = 1}^{N_{t}}" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " be exclusively composed of thermal images, where " + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "inline_equation", + "content": "N^t" + }, + { + "bbox": [ + 55, + 604, + 296, + 715 + ], + "type": "text", + "content": " represents the number of thermal images in the test dataset. Our objective is to compensate for visible knowledge while using solely thermal images as the input at the test stage," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "and fully leverage information from both modalities to develop robust representations at the training stage." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "content": "Overview. Fig. 2(a) illustrates the proposed Pseudo Visible Feature Fine-Grained Fusion (PFGF) framework, which uses the single-stage detector YOLOX [12] as the baseline model. Both training and testing are conducted exclusively with thermal images. Specifically, we first train Pearl-GAN as a prior thermal-to-visible (T2V) translation model " + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "content": ", which is trained on both thermal and visible modalities, to convert thermal image " + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "content": " into daytime visible image " + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "inline_equation", + "content": "x^v" + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "content": ", thereby incorporating valuable visible information from the unpaired set " + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 313, + 96, + 555, + 216 + ], + "type": "text", + "content": ". This process is described as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 399, + 221, + 553, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 221, + 553, + 236 + ], + "spans": [ + { + "bbox": [ + 399, + 221, + 553, + 236 + ], + "type": "interline_equation", + "content": "[ x ^ {v}, z ] = \\Phi (x ^ {t}), \\tag {1}", + "image_path": "578bbc550e7c54c71029f7f3b6580fe6eff8075e8ad7e7f5cba8fbc4f612a71c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "x^{t} \\in \\mathbb{R}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "x^{v} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "\\Phi(x^{t})" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": " comprises a convolution-based encoder " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "z = \\varepsilon(x^{t})" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": " and a decoder " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "x^{v} = \\mu(z)" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": ". The latent T2V code " + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^{h_{z} \\times w_{z} \\times c_{z}}" + }, + { + "bbox": [ + 313, + 239, + 553, + 289 + ], + "type": "text", + "content": " is considered as generative feature." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": "CSPDarknet is employed as the backbone " + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": " to extract multi-level features " + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "inline_equation", + "content": "c^3, c^4" + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "inline_equation", + "content": "c^5" + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": " from the concatenated images " + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "inline_equation", + "content": "x^v" + }, + { + "bbox": [ + 313, + 289, + 553, + 325 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 366, + 331, + 553, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 331, + 553, + 345 + ], + "spans": [ + { + "bbox": [ + 366, + 331, + 553, + 345 + ], + "type": "interline_equation", + "content": "\\left[ c ^ {3}, c ^ {4}, c ^ {5} \\right] = \\mathcal {F} \\left(\\operatorname {c o n c a t} \\left(x ^ {t}, x ^ {v}\\right)\\right). \\tag {2}", + "image_path": "d70bbcf486b8fb7088cd40ab63eaf38c0794458ed68fcc194cc0613395ec0f16.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 350, + 531, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 531, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 531, + 361 + ], + "type": "text", + "content": "A VMamba [35] block " + }, + { + "bbox": [ + 313, + 350, + 531, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 350, + 531, + 361 + ], + "type": "text", + "content": " then refines these features:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 405, + 368, + 553, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 368, + 553, + 382 + ], + "spans": [ + { + "bbox": [ + 405, + 368, + 553, + 382 + ], + "type": "interline_equation", + "content": "f ^ {i} = \\mathcal {M} ^ {i} \\left(c ^ {i}\\right), \\tag {3}", + "image_path": "ed7fcc815bedb688a2e2465c15c13933f486dcdda1942ef79f023960c9a5061d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "inline_equation", + "content": "i \\in \\{3,4,5\\}" + }, + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "text", + "content": ". The output features " + }, + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "inline_equation", + "content": "f^i \\in R^{h \\times w \\times c}" + }, + { + "bbox": [ + 313, + 388, + 554, + 508 + ], + "type": "text", + "content": " are considered as discriminative features. We refer to this process as the VMamba-based Multi-level feature Enhancement (MEM). Here, a VMamba block is utilized to learn global relationships and contextual information from two modalities, thereby enhancing the model's representational capacity. Additionally, due to Mamba's input-dependent mechanism and various hardware-optimized techniques, it excels in long-range modeling with reduced computational cost compared to Transformers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "text", + "content": "To better integrate the generated visible features, we propose a novel Graph-Mamba Fusion (GMF) module " + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "text", + "content": ". This approach effectively combines generative feature " + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "text", + "content": " with discriminative features " + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 313, + 509, + 554, + 556 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 370, + 561, + 553, + 577 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 561, + 553, + 577 + ], + "spans": [ + { + "bbox": [ + 370, + 561, + 553, + 577 + ], + "type": "interline_equation", + "content": "\\left[ g ^ {3}, g ^ {4}, g ^ {5} \\right] = \\mathcal {G} \\left(f ^ {3}, f ^ {4}, f ^ {5}, z\\right). \\tag {4}", + "image_path": "fa2ca2f8b6b7d90567e2307f4fadd7c4c9c14beaf3c21f9b3b31344430a2e854.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "content": "Graph-Mamba Fusion (GMF) module, as a key contribution, goes beyond simple attention by establishing high-level relationships. It first fuses generative feature " + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "content": " with the discriminate feature " + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "content": " and then performs high-level fusion from " + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "inline_equation", + "content": "f^5" + }, + { + "bbox": [ + 313, + 582, + 554, + 641 + ], + "type": "text", + "content": ", which will be introduced later." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": "Subsequently, the features " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "f^i" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "g^i" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": " are combined using residual connections and a Neck module " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": " to obtain the output features " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "f^{i'} = \\Phi (f^i + g^i)" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "i \\in \\{3, 4, 5\\}" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ". Finally, the Decoupled Detection Head " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": " [12] is employed to obtain the detection result based on " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "f^{i'}" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ". The model is trained using the standard detection loss " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "L_{d}(\\mathcal{H}(f^{3'}, f^{4'}, f^{5'}, y_{s_i}^t))" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6712" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 70, + 539, + 213 + ], + "blocks": [ + { + "bbox": [ + 71, + 70, + 539, + 213 + ], + "lines": [ + { + "bbox": [ + 71, + 70, + 539, + 213 + ], + "spans": [ + { + "bbox": [ + 71, + 70, + 539, + 213 + ], + "type": "image", + "image_path": "bef22e91b37620cb3327916041c00ae8d2d5337a5a13ab67a3ebc7cda5d53109.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 71, + 215, + 539, + 280 + ], + "blocks": [ + { + "bbox": [ + 71, + 215, + 539, + 280 + ], + "lines": [ + { + "bbox": [ + 71, + 215, + 539, + 280 + ], + "spans": [ + { + "bbox": [ + 71, + 215, + 539, + 280 + ], + "type": "image", + "image_path": "874c38a39bf8f360c1526cb641989e0fdac7f8ca00018af058d7817eb0f72e03.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 71, + 282, + 539, + 357 + ], + "blocks": [ + { + "bbox": [ + 71, + 282, + 539, + 357 + ], + "lines": [ + { + "bbox": [ + 71, + 282, + 539, + 357 + ], + "spans": [ + { + "bbox": [ + 71, + 282, + 539, + 357 + ], + "type": "image", + "image_path": "0057ff9040ce5b042438dece57b1c480ad3e0189a88f04a95f72de9aa5c09b0b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 367, + 555, + 413 + ], + "lines": [ + { + "bbox": [ + 55, + 367, + 555, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 367, + 555, + 413 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed PFGF method. (a) The framework of the PFGF, with our modules highlighted in the purple box. (b) The Graph-Mamba Fusion Module constructs the graph structure for both discriminative and generative features, with leader nodes guiding the flow of information between graphs. (c) The Inter-Mamba Module facilitates interactions between different modalities. (d) The VMamba Module updates nodes within the same modality." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 422, + 285, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 285, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 285, + 434 + ], + "type": "text", + "content": "3.2. Pseudo Visible Feature Fine-Grained Fusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 445, + 296, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 296, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 296, + 601 + ], + "type": "text", + "content": "For further integrating the generative feature " + }, + { + "bbox": [ + 55, + 445, + 296, + 601 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 445, + 296, + 601 + ], + "type": "text", + "content": ", a straightforward attention-based fusion approach, as used in [44], can be employed. However, this method has limitations in effectively capturing high-level relationships among the features. Additionally, it struggles to capture essential visual information due to the unreliability of the generated visible images, which often introduces a substantial amount of irrelevant information. To overcome these challenges, we introduce the Graph-Mamba Fusion (GMF) module as shown in Fig. 2(b). Graph structure is employed to establish more compensated relationships between different level features, which Mamba is adapted to capture long-range dependencies with less computational complexity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": "To avoid getting lost in details, let's first briefly introduce the process. (1) Graph construction. The features " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "f^4" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "f^5" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " are down-and-up sampled to different copies as graph nodes. Graph edges are constructed by computing similarity between nodes, and message passing is performed by aggregating features from neighboring nodes. (2) Graph computation. An Inter-Mamba block is proposed to facilitate fusion between the nodes produced by latent feature " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " and discriminative feature " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " respectively as illus-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": "trated in Fig. 2 (c). The GRU algorithm is used to update graph nodes, ensuring effective information propagation. Subsequently, a VMamba block is used to further refine the node feature. The output " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "g^3" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": " is formed by merging the node features of " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": " and is then multiplied with the nodes derived from " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "f^4" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": ", enabling the fusion of information across different levels. The output " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "g^4" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "g^5" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": " are obtained by merging the node features from " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "f^4" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "inline_equation", + "content": "f^5" + }, + { + "bbox": [ + 313, + 422, + 555, + 520 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 528, + 426, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 426, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 426, + 540 + ], + "type": "text", + "content": "3.2.1. Graph construction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "content": "In this part, we will introduce how to construct a graph " + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\Psi = (U,E)" + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "content": " based on the features " + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "content": ". This structure is inspired by the method [24], which effectively models the relationships and dependencies among features extracted from different levels or modalities. The graph structure is designed to ensure that the fusion of these features is contextually relevant, thereby enhancing the accuracy and robustness of the representations used for detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": "Node generation. Given the generative feature " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": " and discriminative feature " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": ", two types of nodes are generated. To capture multi-level information and enhance feature diversity, we make replicas of different granularities of the corresponding features as graph nodes. Specifically, pyramid pooling, convolution, and upsampling operations are ap-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6713" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "content": "plied to both generative feature " + }, + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "content": " and discriminate feature " + }, + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "content": ", which can be formally computed as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 64, + 102, + 295, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 102, + 295, + 118 + ], + "spans": [ + { + "bbox": [ + 64, + 102, + 295, + 118 + ], + "type": "interline_equation", + "content": "f _ {j} ^ {i} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} \\left(f ^ {i}\\right)\\right)\\right), z _ {j} = U p \\left(\\operatorname {C o n v} \\left(\\mathcal {P} _ {j} (z)\\right)\\right), \\tag {5}", + "image_path": "7e12e35521f071aead90dc5dfc8b6874b3369e4689d4dde1040c8cba046de565.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": "where the operator " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_j(\\cdot)" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " pools the given feature to various sizes according to the scale setting " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": ", a " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " convolution is applied to reduce the dimension of the pooled representation, and " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "Up" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " operator, using bi-linear interpolation, up-samples the feature maps to match the original size. For each " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "f^i" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": ", there are " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " node features " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "f_j^i \\in R^{h \\times w \\times c'}" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "j \\in \\{1, \\dots, n\\}" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "z_j \\in R^{h \\times w \\times c'}" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "n = 3" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": " has only one scale and shares the same shape as " + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 55, + 124, + 296, + 222 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": "Edge generation. The edges play a crucial aspect, as it facilitates the propagation of information between nodes. Here, we only compute intra-edges, i.e., the edges connect the nodes produced by the same feature. Since our goal is to incorporate the information from the generative feature " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " into the discriminative feature " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": ", there is no need to construct additional edges between the nodes produced by the generative feature. Specifically, for the feature " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "f^i" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": ", the intra-edge " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "e_{j,k}^i" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 338, + 295, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 338, + 295, + 354 + ], + "spans": [ + { + "bbox": [ + 126, + 338, + 295, + 354 + ], + "type": "interline_equation", + "content": "e _ {j, k} ^ {i} = \\operatorname {C o n v} \\left(f _ {j} ^ {i} - f _ {k} ^ {i}\\right), \\tag {6}", + "image_path": "37e4be4c237e0a0dec9d236d6f265ded3802a9f0fd328e3a39d986c7bea98813.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "Conv(\\cdot)" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": " is used to learn relationships between nodes. The term " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f_{j}^{i} - f_{k}^{i}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": " represents the difference between the node features " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f_{j}^{i}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f_{k}^{i}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": ". This highlights the relative disparity between nodes, following the approach outlined in [43]. Based on our edge computation method, we have formed four subgraphs, which are constructed by graph nodes formed by the features " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "z, f^{3}, f^{4}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f^{5}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": ", respectively. Here the edges between the subgraphs of different discriminative features are not computed to avoid tedious computation. Instead, we introduce a new leader node to aggregate subgraph node features, and then pass the aggregated feature to the next subgraph from " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f^{3}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "inline_equation", + "content": "f^{5}" + }, + { + "bbox": [ + 55, + 359, + 296, + 504 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "text", + "content": "Message Passing. In each subgraph composed of discriminative features, every node aggregates feature messages from all its neighboring nodes. For the node " + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "inline_equation", + "content": "f_{j}^{i}" + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "text", + "content": ", at " + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "inline_equation", + "content": "l - 1" + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "text", + "content": " message passing, denoted as " + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "inline_equation", + "content": "m_{j}^{i,l - 1}" + }, + { + "bbox": [ + 55, + 505, + 296, + 556 + ], + "type": "text", + "content": ", is computed as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 87, + 563, + 295, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 563, + 295, + 591 + ], + "spans": [ + { + "bbox": [ + 87, + 563, + 295, + 591 + ], + "type": "interline_equation", + "content": "m _ {j} ^ {i, l - 1} = \\sum_ {k \\in \\mathcal {N} (j)} \\operatorname {S i g m o i d} \\left(e _ {k, j} ^ {i, l - 1}\\right) \\cdot f _ {k} ^ {i, l - 1}, \\tag {7}", + "image_path": "d9f83e8d2ab6d0ede1f1d632d93e9b93d54bdf5767dbec3e42a39626226234e7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 597, + 295, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 295, + 621 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 295, + 621 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 597, + 295, + 621 + ], + "type": "inline_equation", + "content": "Sigmoid(\\cdot)" + }, + { + "bbox": [ + 55, + 597, + 295, + 621 + ], + "type": "text", + "content": " function is utilized to calculate the link weight between nodes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 627, + 168, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 627, + 168, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 627, + 168, + 639 + ], + "type": "text", + "content": "3.2.2. Graph computation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 641, + 296, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 688 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 688 + ], + "type": "text", + "content": "Graph-based cross-modality information fusion consists of two key components: cross-modality fusion through the Inter-Mamba block and knowledge integration via GRU and VMamba." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Cross modality fusion by Inter-Mamba block. For fusing the node features " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "z_{j}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "f_{j}^{3}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": ", instead of transformer-based" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "route, we proposed a Mamba-based block. As shown in Fig. 2(c), the node features " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "f_{j}^{3}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "z_{j}" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " are first projected into the hidden state space followed by a VMamba block, and a gating operation is then employed to facilitate the interaction between these two types of hidden state features." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": "Specifically, the node features " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "f_{j}^{3}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "z_{j}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " are first flattened to form the input token sequences " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "T_{j}^{3}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "T_{j}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ", each with dimensions " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "B \\times N \\times C" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " denote the batch size, sequence length, and number of channels, respectively. These sequences are then normalized by a normalization layer. Next, the normalized sequences " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "T_{j}^{3}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "T_{j}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " are projected into the hidden state space respectively through linear layers, convolution, and SSM, resulting in the hidden state features " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "\\hat{f}_{j}^{3}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "\\hat{z}_{j}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ". Simultaneously, the normalized sequence " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "T_{j}^{3}" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": " is also projected through linear layers with SiLU activation to obtain the gating weight " + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 133, + 555, + 278 + ], + "type": "text", + "content": ". It is used for hidden state feature fusion as follows," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 290, + 553, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 290, + 553, + 308 + ], + "spans": [ + { + "bbox": [ + 364, + 290, + 553, + 308 + ], + "type": "interline_equation", + "content": "f _ {j} ^ {3} = \\mathcal {R} \\left(\\mathcal {Y} \\left(\\left(\\hat {z} _ {j} + \\hat {f} _ {j} ^ {3}\\right) \\odot r\\right) + f _ {j} ^ {3}\\right), \\tag {8}", + "image_path": "1ca488529b80b0e7e72cf5cf697d0d9b57c42ce3799758eb18ec1f331c85c869.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "text", + "content": " represents element-wise multiplication. The operator " + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "text", + "content": " denotes the projection operation with a linear transformation, while " + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 318, + 553, + 354 + ], + "type": "text", + "content": " refers to the reshaping operation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 354, + 554, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 462 + ], + "type": "text", + "content": "Cascade Knowledge Integration (CKI) strategy. Existing studies [11] have demonstrated that deep and shallow features exhibit complementary characteristics: deep features capture high-level semantic information, while shallow features retain rich spatial details. Leveraging multilevel features is therefore advantageous for enhancing detection performance. As we stated before, a leader node is proposed to convey low-level fused information to high-level subgraph in a cascade manner." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "content": "We first apply a GRU-based update method [9] to enhance the nodes' ability to capture complex feature interactions and retain relevant information from neighboring nodes. After " + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "inline_equation", + "content": "l-1" + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "content": " message passing, the node feature " + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "inline_equation", + "content": "f_{j}^{i}" + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "content": " is updated by " + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{GRU}(f_{j}^{i}, m_{j}^{i,l-1})" + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "content": " (See the Appendix for a detailed description of " + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{GRU}" + }, + { + "bbox": [ + 313, + 464, + 554, + 538 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "spans": [ + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "text", + "content": "A leader node feature " + }, + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "inline_equation", + "content": "g^i" + }, + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 326, + 540, + 552, + 553 + ], + "type": "text", + "content": "-th scale is computed as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 342, + 563, + 553, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 563, + 553, + 578 + ], + "spans": [ + { + "bbox": [ + 342, + 563, + 553, + 578 + ], + "type": "interline_equation", + "content": "g ^ {i} = \\operatorname {C o n v} \\left(\\operatorname {C o n c a t} \\left(\\mathcal {M} \\left(f _ {1} ^ {i}\\right), \\dots , \\mathcal {M} \\left(f _ {n} ^ {i}\\right)\\right)\\right), \\tag {9}", + "image_path": "ed74fff0a25be8bffa80fadbe975be1e07909172423969ae488d2cd148766822.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 590, + 546, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 546, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 546, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 590, + 546, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 590, + 546, + 601 + ], + "type": "text", + "content": " denotes a VMamba block as mentioned before." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 603, + 553, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 553, + 627 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 553, + 627 + ], + "type": "text", + "content": "The leader node " + }, + { + "bbox": [ + 313, + 603, + 553, + 627 + ], + "type": "inline_equation", + "content": "g^i" + }, + { + "bbox": [ + 313, + 603, + 553, + 627 + ], + "type": "text", + "content": " conveys knowledge to the subsequent subgraph nodes as follows," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 370, + 638, + 553, + 655 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 638, + 553, + 655 + ], + "spans": [ + { + "bbox": [ + 370, + 638, + 553, + 655 + ], + "type": "interline_equation", + "content": "f _ {j} ^ {i + 1} = f _ {j} ^ {i + 1} \\odot \\mathcal {A} (g ^ {i}) + f _ {j} ^ {i + 1}, \\tag {10}", + "image_path": "1a27c27eca43d2a22e52a1b17095c3d4bab8803bb7dcf78203c42a35c0381911.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " represents an attention operation, which is computed via global average pooling followed by a Sigmoid activation. Since the last subgraph does not contribute to knowledge transmission, the scale " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " is set to 3 and 4." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6714" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 136, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 136, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 136, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 182, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 182, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 182, + 105 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 110, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 110, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 295, + 312 + ], + "type": "text", + "content": "Datasets. To evaluate our method, we conduct experiments on the FLIR-aligned dataset [49], LLVIP dataset [18], and Autonomous Vehicles dataset [42]. (1) The FLIR dataset originally presented challenges due to unaligned thermal-visible image pairs. Therefore, we utilize the aligned version, consisting of 5,142 thermal-visible image pairs, with 4,129 pairs for training and 1,013 for testing. This dataset includes three object categories: \"person,\" \"car,\" and \"bicycle\". (2) The LLVIP dataset is collected in very dark environments. It comprises 15488 aligned image pairs, with 12,025 pairs used for training and 3,463 pairs for testing. This dataset focuses on a single object class: \"person\". (3) The Autonomous Vehicles dataset comprises 6,009 paired images for training and 1,503 for testing, covering five categories: \"bike\", \"car\", \"car_stop\", \"color_cone\", and \"person\". Compared to the FLIR and LLVIP datasets, the scenes in this dataset are more complex." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 314, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 295, + 410 + ], + "type": "text", + "content": "Evaluation Metrics. We evaluate our method using standard object detection metrics [31], including mean Average Precision (mAP), mAP50, and mAP75. The mAP metric represents the average AP over IoU thresholds ranging from 0.50 to 0.95, with an interval of 0.05. The mAP50 and mAP75 metrics correspond to the AP values at IoU thresholds of 0.50 and 0.75, respectively. Higher values for these metrics indicate better performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "text", + "content": "Implementation Details. We utilize a pre-trained model on the COCO dataset and implement our approach using the MMDetection toolbox [6], a widely adopted framework for object detection. The network is trained using the SGD optimizer with a batch size of 4 and an initial learning rate of 5e-4. The input image size is set to " + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "inline_equation", + "content": "640 \\times 640" + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "text", + "content": " for the FLIR, LLVIP, and Autonomous Vehicles datasets, with the training conducted over 8 epochs. The training process is conducted in two stages. In the first stage, the Pearl-GAN module is trained. In the second stage, with the parameters of the Pearl-GAN module fixed, the backbone, VMamba, Graph-Mamba Fusion (GMF) module, neck, and detection head are trained. For the GMF module, the number of graph nodes " + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "text", + "content": " is set to 3, and the number of message-passing iterations " + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 410, + 295, + 638 + ], + "type": "text", + "content": " is also set to 3. The cascade quantities of VMamba and Inter-Mamba blocks are each configured to 2. Details on hyper-parameter sensitivity are provided in the Appendix. To ensure reproducibility, all experiments are conducted with a random seed set to 0." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 647, + 278, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 278, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 278, + 661 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "Compared methods. We compare the proposed PFGF method with both mono-modality (thermal) and multispectral (visible + thermal) methods. The mono-modality methods include Faster RCNN [41], SSD [33], RetinaNet" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 316, + 71, + 553, + 300 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 553, + 300 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 553, + 300 + ], + "type": "table", + "html": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5074.432.537.6
SSD [33]TVGG1665.522.429.6
RetinaNet [32]TResNet5064.520.328.3
YOLOv3 [40]TDarknet5373.631.336.8
YOLOX-L [12]TCSPD5378.139.442.6
IAH [45]TDarknet5376.4--
DIP [17]TResNet5077.3--
TIRDet [44]TCSPD5381.441.144.3
IDA [28]TCSPD5381.143.446.3
PFGF (Ours)TCSPD5384.844.647.1
CFR_3 [49]V+TVGG1672.4--
GAFF [50]V+TResNet1872.932.937.5
YOLOFusion [39]V+TVGG1676.6-39.8
CMX [51]V+TSwinT82.237.142.3
IGT [7]V+TSwinT85.036.943.6
DATFF [16]V+TResNet5080.2--
RSDet [52]V+TResNet5081.1-41.1
Fusion-Mamba [10]V+TCSPD5384.9-47.0
", + "image_path": "0e116b0be64d19a93663f15f7669f11d2f154d5764864cb0795e8f8ec6fbbb5d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 308, + 555, + 331 + ], + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 331 + ], + "type": "text", + "content": "Table 1. Comparisons on FLIR dataset in terms of MAP. The best results are highlighted in bold." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 353, + 555, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 555, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 555, + 474 + ], + "type": "text", + "content": "[32], YOLOv3 [40], YOLOX-L [12], IAH [45], DIP [17], TIRDet [44] and IDA [28]. These methods utilize paired visible and thermal images for training, but only thermal images for testing. In contrast, the multispectral methods include CFR_3 [49], GAFF [50], YOLOFusion [39], CMX [51], IGT [7], DATFF [16], RSDet [52], YOLOv5-VT [19], DM-Fusion [47], and Fusion-Mamba [10]. These methods employ paired visible and thermal images for both training and testing. The results presented in the tables are cited from the respective papers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "content": "Quantitative comparison. The quantitative comparison results are presented in Tables 1, 2, and 3. Our method achieves the state-of-the-art (SOTA) performance among mono-modality (thermal) methods on the FLIR, LLVIP, and Autonomous Vehicles datasets. On the FLIR dataset, our approach outperforms the recent TIRDet and IDA methods, achieving mAP gains of " + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "content": ", respectively, along with mAP50 improvements of " + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 313, + 475, + 556, + 714 + ], + "type": "text", + "content": ". For a fair comparison of the LLVIP dataset, we reproduced the TIRDet method using a Pearl-GAN model trained on the LLVIP dataset, referred to as TIRDet*. Similarly, our method denoted as PFGF*, utilizes this same Pearl-GAN model. Additionally, to facilitate comparison with the original results reported in the TIRDet paper, we also use a Pearl-GAN model trained on the FLIR dataset. The results demonstrate that our proposed method consistently achieves superior performance in both sets of comparisons: between TIRDet and PFGF, as well as between TIRDet* and PFGF*. On the more complex Autonomous Vehicles dataset, our method surpasses the IDA method, with mAP50 increas" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6715" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 294, + 244 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 294, + 244 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 294, + 244 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 294, + 244 + ], + "type": "table", + "html": "
MethodsDataBackbonemAP50mAP75mAP
Faster RCNN [41]TResNet5096.168.561.1
SSD [33]TVGG1690.257.953.5
RetinaNet [32]TResNet5093.749.350.9
YOLOv3 [40]TDarknet5389.753.452.8
YOLOX-L [12]TCSPD5395.272.763.6
TIRDet [44]TCSPD5396.373.164.2
TIRDet* [44]TCSPD5396.874.765.2
PFGF (Ours)TCSPD5396.677.966.8
PFGF* (Ours)TCSPD5396.978.467.3
DM-Fusion [47]V+TCSPD5388.1-53.1
YOLOv5-VT [19]V+TCSPD5395.871.462.3
RSDet [52]V+TResNet5095.8-61.3
Fusion-Mamba [10]V+TCSPD5397.0-64.3
", + "image_path": "918fb33aba375de687537c65f1a702856c437a55c4e21ef216cd9bc31003d29f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 277, + 293, + 367 + ], + "blocks": [ + { + "bbox": [ + 69, + 253, + 280, + 264 + ], + "lines": [ + { + "bbox": [ + 69, + 253, + 280, + 264 + ], + "spans": [ + { + "bbox": [ + 69, + 253, + 280, + 264 + ], + "type": "text", + "content": "Table 2. Comparisons on LLVIP dataset in terms of MAP." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 277, + 293, + 367 + ], + "lines": [ + { + "bbox": [ + 58, + 277, + 293, + 367 + ], + "spans": [ + { + "bbox": [ + 58, + 277, + 293, + 367 + ], + "type": "table", + "html": "
MethodsDataBackbonemAP50mAP75mAP
YOLOv3 [40]TDarknet5371.929.934.6
FasterRCNN [41]TResNet5072.539.839.9
CascadeRCNN [4]TResNet5072.942.742.2
YOLOX-L [12]TCSPD5372.340.640.6
IDA [28]TCSPD5373.143.843.1
PFGF (Ours)TCSPD5378.846.645.9
", + "image_path": "d8ca998c299d1777431f531808405f0721660beea15f4c21cb78bab11117dbfb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "text", + "content": "ing by " + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "text", + "content": ", mAP75 rising by " + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "text", + "content": ", and overall mAP improving by " + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 55, + 407, + 295, + 503 + ], + "type": "text", + "content": ". Moreover, our method outperforms most multispectral methods in detection performance, achieving the highest mAP and mAP75, and the second-best mAP50 on both FLIR and LLVIP datasets. These results indicate that the combination of the T2V model and the proposed PFGF approach effectively enhances thermal detection performance with valuable visible information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 505, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 296, + 553 + ], + "type": "text", + "content": "We also conduct a visual comparison between the proposed PFGF method, and the publicly method TIRDet. Our method significantly improves the detection performance of thermal images (See the Appendix)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 563, + 157, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 157, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 157, + 575 + ], + "type": "text", + "content": "4.3. Further Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "content": "Ablation studies. Our framework comprises T2V translation model Pearl-GAN, VMamba-based Multi-level Feature Enhancement (MEM) block, and Graph-Mamba Fusion (GMF) module, which includes both the Inter-Mamba block and CKI strategy. To assess the contribution of each component, we performed ablation studies on the FLIR, LLVIP, and Autonomous Vehicles datasets. There are several variants: 'w/o Pearl-GAN' refers to the exclusion of visible information with only thermal image input; 'w/o MEM' denotes the detector backbone features are not enhanced by MEM block; 'w/o GMF' means the enhanced" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 334, + 70, + 535, + 175 + ], + "blocks": [ + { + "bbox": [ + 55, + 376, + 295, + 398 + ], + "lines": [ + { + "bbox": [ + 55, + 376, + 295, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 295, + 398 + ], + "type": "text", + "content": "Table 3. Comparisons on AV dataset in terms of MAP. AV: Autonomous Vehicles dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 70, + 535, + 175 + ], + "lines": [ + { + "bbox": [ + 334, + 70, + 535, + 175 + ], + "spans": [ + { + "bbox": [ + 334, + 70, + 535, + 175 + ], + "type": "table", + "html": "
MethodmAP
FLIRLLVIPAV
w/o PearlGAN45.265.044.4
w/o MEM46.066.145.4
w/o GMF45.665.644.3
w/o Inter-Mamba (GMF)45.966.245.1
w/o CKI (GMF)46.166.445.3
PFGF47.167.345.9
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Ablation study on FLIR, LLVIP, and AV datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "spans": [ + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "content": "features will be passed directly to the detector head; 'w/o Inter-Mamba' implies that generative features " + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "content": " are not fused with discriminative features " + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "content": "; while 'w/o CKI' does not integrate features from " + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "inline_equation", + "content": "f^5" + }, + { + "bbox": [ + 313, + 206, + 553, + 254 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "text", + "content": "Table 4 demonstrates that each component positively contributes to performance. Removing Pearl-GAN prevents the incorporation of visible information, leading to a substantial performance decline on the FLIR and LLVIP datasets and the second-largest performance drop on the Autonomous Vehicles dataset. The absence of MEM affects performance differently across datasets, suggesting its role in refining and enhancing coarse fusion features. Excluding the GMF module reduces mAP by " + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "text", + "content": " on the FLIR dataset, " + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "text", + "content": " on the LLVIP dataset, and " + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 313, + 255, + 555, + 459 + ], + "type": "text", + "content": " on the Autonomous Vehicles dataset, underscoring its importance in integrating generated visible and thermal information. Furthermore, ablation analysis on the GMF module reveals that the Inter-Mamba block has a more significant impact than the CKI block, indicating that the Inter-Mamba block can effectively filter redundant visible information while preserving information beneficial for thermal detection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 460, + 554, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 604 + ], + "type": "text", + "content": "Comparison of different fusion methods. To validate the superiority of our proposed fusion module, we conduct further experiments comparing it with various fusion strategies, including addition, concatenation, CMA [44], MMFT [45], GIM [24] and FMB [10]. The CMA method employs Convolutional Block Attention Module (CBAM) to generate attention maps; the MMFT leverages a Transformer-based architecture to perform fusion based on varying illumination conditions; GIM utilizes graph neural networks to handle cross-modal interactions through features; while the FMB method, rooted in the Mamba architecture, is specifically designed for multispectral detection tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": "As shown in Table 5, our method outperforms all other strategies. Specifically, CMA method is relatively simplistic and fails to effectively capture visible information beneficial for thermal detection; in contrast to the MMFT method, our approach eliminates the dependency on an additional illumination-aware module. The FMB method has achieved superior performance in multispectral tasks, it does not adapt well to our specific problem due to the unreliability of the generated visible information. The GIM" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6716" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 288, + 186 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 288, + 186 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 288, + 186 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 288, + 186 + ], + "type": "table", + "html": "
MethodFLIRLLVIPAV
mAPmAP50mAPmAP50mAPmAP50
Add42.677.561.795.240.473.9
Concat43.779.963.394.842.474.7
CMA[44]44.381.464.696.343.976.5
MMFT[45]44.682.165.195.244.176.8
GIM[24]46.081.866.396.244.874.5
FMB[10]45.782.465.996.344.277.0
GMF (Ours)47.184.867.396.945.978.8
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MethodmAPmAP50FLOPS(G)↓Param(M)↓
GMTF46.282.7604.171.8
PFGF47.184.8409.066.9
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These results indicate that the Graph-Mamba-based architecture facilitates a more explicit and robust integration of thermal and pseudovisible information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "text", + "content": "The effectiveness of using VMamba block. An efficiency analysis is conducted to evaluate Mamba block compared with Transformer block. For a fair comparison, all VMamba blocks are replaced with Transformer blocks, resulting in a new method designated as GMTF. Specifically, the VMamba block is substituted with a self-attention block, and the Inter-Mamba block is replaced with a cross-attention block. As shown in Table 6, our PFGF method surpasses GMTF with a " + }, + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "text", + "content": " increase in mAP and a " + }, + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 55, + 390, + 296, + 581 + ], + "type": "text", + "content": " gain in mAP50. Additionally, PFGF demonstrates parameter efficiency by reducing the parameter count by 4.93M and decreasing FLOPs from 604.1 GFLOPs to 409.0 GFLOPs. These findings highlight that the VMamba block not only effectively suppresses redundant features and captures complementary cross-modal information but also achieves superior computational efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": "The effectiveness of using leader nodes. To incorporate the generative feature " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " into the multi-level discriminative features, we utilize leader nodes to guide information transfer from the low-level subgraph to the high-level subgraph. To verify the effectiveness of leader nodes, we compare our method with an approach that lacks leader nodes on FLIR and LLVIP datasets. Without leader nodes, the next high-level features don't receive the previous low-level features, which ignore the integration from " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "f^3" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "f^5" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ". With ground truth serving as a labeled reference, Fig. 3 clearly shows that without the assistance of leader nodes, the object" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 553, + 305 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 305 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 305 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 305 + ], + "type": "image", + "image_path": "e9641115da26912c51349bc58bd466e1bb7eaabced5a26086c511f2c50a922cc.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "type": "text", + "content": "Figure 3. Effectiveness of using leader nodes. The first two rows present samples from FLIR dataset, and the last two rows present samples from LLVIP dataset. Red, blue, and green boxes denote the detected objects \"person\", \"car\", and \"bicycle\", respectively." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 369, + 555, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 429 + ], + "type": "text", + "content": "confidence is significantly lower and there are more occurrences of false detections. This indicates that our method effectively leverages the features delivered by leader nodes across subgraphs, integrating both high-level semantics and low-level local details to build a more robust representation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 446, + 388, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 446, + 388, + 459 + ], + "spans": [ + { + "bbox": [ + 314, + 446, + 388, + 459 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 469, + 555, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 555, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 555, + 635 + ], + "type": "text", + "content": "In this paper, we proposed a novel cross-modal fusion method, termed Pseudo Visible Feature Fine-Grained Fusion (PFGF), for thermal object detection. The PFGF framework begins by constructing a graph which consists of several subgraphs. Each subgraph is generated from different level output features from the backbone or synthetic visible feature. An Inter-Mamba block is then employed to facilitate cross-modality feature association between generative and discriminative node features. Additionally, we introduce a Cascade Knowledge Integration strategy to propagate knowledge hierarchically from lower-level to higher-level subgraphs. In the process, VMamba is employed to further refine features. Extensive experiments demonstrate that our method achieves the SOTA performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by the National Natural Science Foundation of China (62276048, 62476169), Chengdu Science and Technology Projects (2023-YF06-00009-HZ) and Postdoctoral Fellowship Program of CPSF (GZC20233323)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6717" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "text", + "content": "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. 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Vision mamba: Efficient visual representation learning with bidirectional state space model, 2024. 2" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6719" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_content_list.json b/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8823cd62995db015e75c780b279727a8c4c071ce --- /dev/null +++ b/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_content_list.json @@ -0,0 +1,1431 @@ +[ + { + "type": "text", + "text": "Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction", + "text_level": 1, + "bbox": [ + 230, + 130, + 767, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dong Li $^{1}$ , Wenqi Zhong $^{2*}$ , Wei Yu $^{1}$ , Yingwei Pan $^{1}$ , Dingwen Zhang $^{2}$ , Ting Yao $^{1}$ , Junwei Han $^{2}$ , and Tao Mei $^{1}$", + "bbox": [ + 222, + 202, + 774, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 HiDream.ai Inc.", + "bbox": [ + 267, + 239, + 377, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Northwest Polytechnical University, Xi'an, China", + "bbox": [ + 421, + 239, + 728, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lidong@hidream.ai, wenqizhong@mail.nwpu.edu.cn, {yuwei, pandy}@hidream.ai", + "bbox": [ + 176, + 258, + 820, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhangdingwen2006yyyy@gmail.com, tiyao@hidream.ai, junweihan2010@gmail.com", + "bbox": [ + 179, + 277, + 818, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tmei@hidream.ai", + "bbox": [ + 428, + 295, + 562, + 308 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 344, + 326, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video virtual try-on aims to seamlessly dress a subject in a video with a specific garment. The primary challenge involves preserving the visual authenticity of the garment while dynamically adapting to the pose and physique of the subject. While existing methods have predominantly focused on image-based virtual try-on, extending these techniques directly to videos often results in temporal inconsistencies. Most current video virtual try-on approaches alleviate this challenge by incorporating temporal modules, yet still overlook the critical spatiotemporal pose interactions between human and garment. Effective pose interactions in videos should not only consider spatial alignment between human and garment poses in each frame but also account for the temporal dynamics of human poses throughout the entire video. With such motivation, we propose a new framework, namely Dynamic Pose Interaction Diffusion Models (DPIDM), to leverage diffusion models to delve into dynamic pose interactions for video virtual try-on. Technically, DPIDM introduces a skeleton-based pose adapter to integrate synchronized human and garment poses into the denoising network. A hierarchical attention module is then exquisitely designed to model intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware spatial and temporal attention mechanisms. Moreover, DPIDM capitalizes on a temporal regularized attention loss between consecutive frames to enhance temporal consistency. Extensive experiments conducted on VITON-HD, VVT and ViViD datasets demonstrate the superiority of our DPIDM against the baseline methods. Notably, DPIDM achieves VFID score of 0.506 on VVT dataset, leading to $60.5\\%$ improvement over the state-of-the-art GPD-VVTO approach.", + "bbox": [ + 86, + 377, + 485, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4b7fb5f9df07272c629b1bf8ffc3b5296feeeb926a403fbe3c9297e00854895f.jpg", + "image_caption": [ + "Figure 1. Given a garment and a person video, DPIDM generates a lifelike video that preserves the visual authenticity of the garment while adapting to the individual's pose and physique." + ], + "image_footnote": [], + "bbox": [ + 545, + 354, + 880, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 556, + 643, + 570 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative models have made tremendous progress in recent years, with wide-ranging applications across various fields, including computer vision [9, 36, 59], computer graphics [6, 13], aesthetic design [35], and medical research [18]. Virtual try-on is a quintessential generative task that aims to synthesize a lifelike image/video of the specific person wearing the provided garment. By harnessing the powerful generative capacities of diffusion models, this field has emerged as a promising domain with versatile applications in immersive e-commerce and short-form video platforms.", + "bbox": [ + 509, + 582, + 906, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior research mainly focused on image-based virtual try-on. The earlier approaches typically build on Generative Adversarial Networks (GANs) [7, 19, 39, 45], incorporating a warping module alongside a try-on generator. The warping module deforms clothing to align with the human body, and then the warped garment is fused with the person image through the try-on generator. However, in light of the recent emergence of UNet-based Latent Diffusion Models (LDMs) [5, 8, 50, 56, 62], researchers have progressively directed their focus towards these innovative models. A diffusion-based try-on network combines the warping and blending", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution. This work was performed at HiDream.ai.", + "bbox": [ + 114, + 886, + 447, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22648", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "processes into a unified operation of cross-attention without explicit segregation. By employing pre-trained text-to-image weights, these diffusion approaches demonstrate superior fidelity compared to their GAN-based counterparts.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, researchers have endeavored to replicate the success of image try-on within the realm of video. One direct approach involves applying image try-on techniques to process videos frame by frame. However, this method often results in notable inter-frame inconsistencies. To address this challenge, various specialized designs have been explored for video virtual try-on [10, 26, 28, 61]. These approaches commonly integrate optical flow prediction modules to warp frames produced by the try-on generator. Despite reasonable performance, GAN-based methods encounter difficulties in handling garment-person misalignment, particularly when faced with inaccurate warping flow estimations. To harness the capabilities of pretrained image-based diffusion models, TunnelTry-on [51] and ViViD [12] utilize a pre-trained inpainting U-Net as the primary branch and integrate a reference U-Net to capture detailed clothing features. They enhance temporal consistency by incorporating standard temporal attention after each stage of the main U-Net. GPD-VVTO [46] takes a step further by integrating garment features into temporal attention, enabling the model to better preserve fidelity to the garment during temporal modeling. Despite showing promise, these methods struggle to maintain both visual integrity and motion consistency simultaneously, particularly when there is a significant stylistic gap between the garment being tried on and the original one. To alleviate these issues, we argue that two key ingredients should be taken into account. One is spatial alignment between human and garment poses within each frame. Such alignment is essential for virtual try-on as it ensures that clothing adapts appropriately to factors like coverage and wrinkles based on the individual's posture. The other is the temporal dynamics of human poses across the entire video. A comprehensive understanding of this long-term interaction is paramount for upholding temporal coherence, given that human movements naturally progress as a continuum of interconnected poses.", + "bbox": [ + 91, + 154, + 485, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By consolidating the idea of modeling both spatial and temporal pose interactions in a video, we novelly present Dynamic Pose Interaction Diffusion Models (DPIDM) for boosting video virtual try-on. Specifically, DPIDM employs a dual-branch architecture, where the Main U-Net conducts denoising processes on the video, while the Garment U-Net extracts intricate details from the garment image and integrates them into the Main U-Net. This architecture facilitates a holistic understanding of the relationship between humans and garments within a unified feature space. To effectively leverage the spatiotemporal pose interactions in videos, we introduce a skeleton-based pose adapter that seamlessly integrates synchronized human and", + "bbox": [ + 89, + 704, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "garment poses into the Main U-Net. With the adapter, we present a hierarchical attention module comprising four key components: a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block. The pose-aware spatial attention block plays a crucial role in capturing intricate intra-frame human-garment pose interactions, while the pose-aware temporal attention block models the long-term dynamics of human poses across frames. Moreover, a temporal regularized attention loss is defined on consecutive frames to ensure temporal coherence. As a result, our DPIDM excels in generating videos with meticulously aligned garment details and enhanced temporal stability.", + "bbox": [ + 511, + 90, + 903, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contribution of this work is the proposal of Dynamic Pose Interaction Diffusion Models that facilitate the video virtual try-on (VVTON) task. This also leads to the elegant view of how a diffusion model should be designed for excavating the pose-focused prior knowledge (e.g., spatial pose alignment and temporal pose dynamics) tailored to VVTON, and how to improve diffusion process with these amplified pose-focused guidance. Through an extensive set of experiments on VITON-HD, VVT, and ViViD datasets, DPIPM consistently achieves superior results over state-of-the-art methods in both image and video virtual try-on tasks.", + "bbox": [ + 511, + 287, + 903, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 511, + 472, + 663, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image-based Virtual Try-on", + "text_level": 1, + "bbox": [ + 511, + 498, + 764, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The development of image-based virtual try-on is largely inspired by the success of GANs [15], leading to pioneering works such as [7, 11, 19, 31, 33, 45]. A standard GAN-based virtual try-on framework typically adheres to a two-stage paradigm. The initial stage involves an image warping process, such as Thin Plate Spline (TPS) warping [19], which aligns the garment with the target individual's body. In the second stage, a GAN-based try-on generator merges the warped attire with the target individual's clothing-agnostic representation to produce authentic try-on outcomes. However, these methods heavily rely on the warping module to preserve garment details and often suffer from performance degradation due to inaccurate warping.", + "bbox": [ + 511, + 521, + 903, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, with the powerful generative capabilities of Latent Diffusion Models (LDMs), many diffusion-based models have been introduced to generate more realistic virtual try-on results [5, 44, 52, 54, 56, 62]. TryOnDiffusion [62] was the first to propose a dual U-Net architecture that simultaneously preserves garment details and implicitly warps the garment to match the target pose. StableVITON [56] introduced a zero cross-attention block to learn the semantic correspondence between the garment and the target person. Wear-any-way [5] utilized a sparse point control method to align person and garment features in feature space. MMTryon [57] presented a multi-modal, multi", + "bbox": [ + 511, + 719, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22649", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a1b9dce895c76998357be45785afb8f4cd657730040a812ca3b05b776cd2007b.jpg", + "image_caption": [ + "Figure 2. (a) Overall architecture of DPIDM. DPIDM employs a dual-branch architecture. The main U-Net processes a concatenated input comprising the noisy latent of the video, the latent of the cloth-agnostic video, and the cloth-agnostic mask sequence. The garment U-Net extracts fine-grained garment features, which are subsequently integrated into the main U-Net. The pose estimator is utilized to extract aligned human and garment poses, which are then fed into the attention modules of the main U-Net to guide the diffusion process. The VAE is not shown for clarity. (b) Detailed illustration of the proposed pose-aware attention module within the main U-Net. The module comprises pose-aware spatial attention, temporal-shift attention, cross-attention, and pose-aware temporal attention. The pose embeddings are seamlessly integrated into the attention module through a specialized pose adapter. (better viewed in color)" + ], + "image_footnote": [], + "bbox": [ + 112, + 93, + 669, + 349 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6d6bc78bf275bd216cafe75ac1ee557bd4869c7a082904da1f27c54158881fcb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 673, + 93, + 880, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "garment virtual try-on approach that combines text and multiple reference images to create a multimodal embedding as a condition to control the diffusion model. IDM [8] proposed a RefNet-style architecture to align the feature space between garment and person. Although these diffusion-based methods have achieved high-fidelity results in single-image inference, their application to video virtual try-on reveals a crucial limitation: the oversight of inter-frame relationships. This deficiency results in notable inter-frame inconsistencies, ultimately yielding unsatisfactory outcomes.", + "bbox": [ + 88, + 459, + 483, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Video-based Virtual Try-on", + "text_level": 1, + "bbox": [ + 89, + 621, + 338, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent studies, researchers have aimed to expand the capabilities of image-based try-on approaches into video applications. A key issue in video generation is inter-frame inconsistency. ClothFormer [26] leverages optical flow in the warping and blending processes to achieve temporal smoothing. Recently, diffusion-based video virtual try-on methods have been introduced to generate more realistic results [12, 21, 46, 51, 60]. For instance, TunnelTry-on [51] proposed a focus-tunnel method that crops the human image according to the pose map, aligning the try-on image to accommodate scenarios where the person is off-center in the frame. VTON-DiT [60] introduced a DiT architecture compatible with OpenSora, where the clothing-agnostic human image is provided via ControlNet. WildVidFit [21] proposed an image-based diffusion model and used video MAE to update the intermediate representations of the diffusion process to improve frame consistency. ViViD [12]", + "bbox": [ + 89, + 643, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "introduced a large-scale video try-on dataset and proposed an additional reference-based U-Net. GPD-VVTON [46] went a step further by integrating garment features into temporal attention to generate spatio-temporally consistent results. While these explorations of video try-on make steady advancements, they currently struggle to accurately capture the dynamic interaction between clothing and the human body in real-world scenarios. Our method employs a hierarchical attention module to capture the critical spatiotemporal pose interactions between the human and the garment.", + "bbox": [ + 511, + 459, + 906, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 511, + 627, + 648, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we present Dynamic Pose Interaction Diffusion Models (DPIDM), a pioneering framework based on latent diffusion models designed to enhance the VVTON task. The complete architecture is depicted in Figure 2 (a). This section begins with a brief introduction to Stable Diffusion [39] in Section 3.1 to lay the groundwork for subsequent discussions. Subsequently, we offer a comprehensive overview of DPIDM in Section 3.2, and delve into the specific design details in Section 3.3-3.5. Finally, we encapsulate our training and inference strategies in Section 3.6.", + "bbox": [ + 511, + 652, + 906, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 816, + 642, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stable Diffusion (SD) stands out as one of the most prevalent latent diffusion models within the community. It leverages a variational autoencoder (VAE) architecture, comprising an encoder $\\mathcal{E}$ and a decoder $\\mathcal{D}$ , to facilitate image rep", + "bbox": [ + 511, + 839, + 905, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22650", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "resentations in the latent space. Additionally, a U-Net [40] $\\epsilon_{\\theta}$ is trained to denoise a Gaussian noise $\\epsilon$ with a conditioning input encoded by a CLIP text encoder [37] $\\tau_{\\theta}$ . Given an image $\\mathbf{x}$ and a text prompt $\\mathbf{y}$ , the denoising U-Net $\\epsilon_{\\theta}$ undergoes training by minimizing the loss function:", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})) \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 172, + 480, + 203 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ denotes the time step of the forward diffusion process, and $\\mathbf{z}_t$ is the noisy latent constructed by adding Gaussian noise $\\epsilon \\sim \\mathcal{N}(0,1)$ to the encoded image $\\mathcal{E}(\\mathbf{x})$ . During the inference stage, $\\mathbf{z}_t$ is randomly sampled from a Gaussian distribution and iteratively denoised to derive $\\mathbf{z}_0$ following a predefined sampling schedule [23, 41]. Finally, the latent decoder $\\mathcal{D}$ decodes $\\mathbf{z}_0$ back into the image space.", + "bbox": [ + 89, + 204, + 483, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 89, + 319, + 200, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall architecture of DPIDM is depicted in Fig. 2. DPIDM takes a reference garment image $\\pmb{G} \\in \\mathbb{R}^{3 \\times H \\times W}$ and a source human video $\\pmb{I}_S \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}$ as input, where $H$ and $W$ represent the height and width of each frame, and $T$ signifies the video length. Its objective is to generate a realistic video $\\hat{\\pmb{I}} \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}$ showing the individual in $\\pmb{I}_S$ adorned in the garment $\\pmb{G}$ .", + "bbox": [ + 89, + 340, + 482, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We approach the video virtual try-on as a video inpainting challenge, aimed at integrating the garment onto clothing-agnostic areas. To achieve this, DPIDM employs a dual-branch architecture. The main U-Net is the inpainting model initialized with the pre-trained weights from SD. It takes in a 9-channel tensor comprising 4 channels for the noisy latent of the video, 4 channels for the clothing-agnostic video latent, and 1 channel for the binary agnostic mask sequence. In contrast to the original SD model, which utilizes text embeddings to guide the diffusion process, we have substituted these embeddings with image embeddings derived from a CLIP image encoder representing the garment image. While the CLIP image embedding effectively captures the overall colors and textures of the garment, it may not retain finer details. To address this, we also use a Garment U-Net to extract detailed garment features. The Garment U-Net follows a standard text-to-image diffusion model with a 4-channel input. This dual-branch architecture has proven to be effective by previous works [12, 46, 51].", + "bbox": [ + 89, + 446, + 482, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further enhance the generation, we incorporate human and garment poses as supplementary guidance to refine the diffusion process. We develop a light-weight pose encoder to extract features of the pose maps and a pose adapter to inject these features into the attention modules of the main U-Net. The human/garment pose maps are derived from the input video/image with pose estimator.", + "bbox": [ + 89, + 734, + 482, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pose Estimator", + "text_level": 1, + "bbox": [ + 89, + 848, + 243, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We directly employ DW-Pose [53] to estimate human poses $P_{h}$ from video frames. However, there is a lack of an open-", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/869db8ec1e0cbba932b5ca4ec03ae3bd51cc706d13162a512814997a7d2ce1d6.jpg", + "image_caption": [ + "Figure 3. Visualization of predicted human and garment poses." + ], + "image_footnote": [], + "bbox": [ + 524, + 89, + 880, + 155 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "source garment pose estimator currently. To establish alignment between human and garment poses, we train a garment pose estimator to predict a set of landmarks $P_{g}$ that correspond to various parts of the human pose $P_{h}$ . The ground truth of $P_{g}$ is labeled manually, with the number of landmarks varying based on the garment types. For instance, in upper clothing, $|P_{g}| = 9$ , encompassing landmarks such as the neck, shoulders, elbows, wrists, and hips. These landmarks serve as explicit indicators of the alignment between human and garment poses, and therefore can be used as guidance to improve the diffusion process. The visualization of human and garment poses is shown in Fig. 3.", + "bbox": [ + 511, + 181, + 903, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Dynamic Pose Interaction", + "text_level": 1, + "bbox": [ + 511, + 372, + 748, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To facilitate the dynamic pose interaction, we propose a hierarchical attention module consisting of a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block.", + "bbox": [ + 511, + 393, + 903, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pose-aware Spatial Attention (PASA). To capture intricate intra-frame human-garment pose interactions, we inject the features of human and garment poses into the spatial attention layer. In our baseline, the human feature map $\\mathbf{f}_h$ from the main U-Net is concatenated with the corresponding garment feature map $\\mathbf{f}_g$ from the garment U-Net to jointly compute self-attention, which is computed as:", + "bbox": [ + 511, + 455, + 905, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f}), \\psi_ {k} (\\mathbf {f}), \\psi_ {v} (\\mathbf {f})\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 571, + 903, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{f} = [\\mathbf{f}_h,\\mathbf{f}_g]$ is the concatenation of human feature map and garment feature map in the spatial dimension, and $\\psi_q,\\psi_k,\\psi_v$ are linear projections. Afterward, only the half feature from the main U-Net undergoes further computation. This attention layer enables garment features extracted by the garment U-Net to be integrated into the main U-Net.", + "bbox": [ + 511, + 599, + 905, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enable the correspondence control with pose guidance, we modify this attention layer by adding the pose embeddings of the human and garment. Formally, given the human pose embedding $\\mathbf{p}_h$ and garment pose embedding $\\mathbf{p}_g$ extracted from the pose encoder, we first concatenate them in spatial dimension $\\mathbf{p} = [\\mathbf{p}_h,\\mathbf{p}_g]$ . Then we utilize a pose adapter to project $\\mathbf{p}$ into the diffusion feature space. The pose adapter employs two fully connected (FC) layers with an intermediate activation layer. The first FC layer maps the input to a lower-dimensional space, while the second FC layer maps it back to the original dimensional. The pose adapter can be written as:", + "bbox": [ + 511, + 691, + 905, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA d p t (\\mathbf {p}) = \\mathbf {W} _ {u p} (G E L U (\\mathbf {W} _ {d o w n} (\\mathbf {p}))), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 883, + 903, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22651", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_{up}$ and $\\mathbf{W}_{down}$ are the learnable weight matrix. To preserve the original feature space of diffusion models, we initialize $\\mathbf{W}_{up}$ with zeros. Subsequently, we add the diffusion feature $\\mathbf{f}$ and the adapter embedding $Adpt(\\mathbf{p})$ together and feed them into the self-attention mechanism, leading to the revised form of Eq. 2:", + "bbox": [ + 89, + 90, + 480, + 170 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {k} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {v} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p}))\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 175, + 482, + 190 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, when integrating the garment feature into the main U-Net, the feature aggregation process takes into account the alignment of human and garment poses. This implicit consideration results in the garment being deformed to better fit the natural pose of the person.", + "bbox": [ + 89, + 196, + 480, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Existing PoseGuider-style methods [24, 46, 51] typically achieve pose control by directly adding processed human pose images and noisy latents as inputs to the first layer of the diffusion network, without incorporating pose information into the attention modules. In contrast, our PASA introduces pose information into each layer's attention modules through a pose adapter, enabling more precise and varying degrees of pose control. Moreover, besides human poses, we further inject garment poses into PASA, thus achieving intricate intra-frame human-garment pose alignment.", + "bbox": [ + 89, + 272, + 482, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal-shift Attention (TSA). In the original SD model, the attention block of the U-Net solely focuses on self-attention within individual frames, overlooking valuable information across frames. Current VVTON techniques predominantly integrate a temporal attention layer at each stage to capture temporal dependencies among video frames. Nevertheless, this approach can introduce a covariate shift in the feature space, potentially undermining the model's generative capacity [58]. While a direct remedy could involve joint space-time 3D attention, this method escalates the complexity of attention calculations quadratically. Drawing inspiration from prior works [1, 32, 49], a novel approach involves employing temporal shift operations that utilize a 2D module to amalgamate spatial and temporal information by incorporating neighboring frame data into the current frame. Specifically, in addition to examining tokens within the present frame, a patch-level shifting operation transpires along the temporal dimension, transferring tokens from the preceding $L$ frames to the current frame, thereby constructing a novel latent feature frame. We concatenate the latent feature of the current frame $\\mathbf{h}$ with the temporally shifted latent feature $\\mathbf{h}_{shift}$ in the spatial dimension, thus establishing keys and values for subsequent self-attention mechanisms. The temporal-shift attention can be formally written as:", + "bbox": [ + 89, + 422, + 482, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {h}} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {h}), \\psi_ {k} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right), \\psi_ {v} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right). \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 810, + 482, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It notably reduces the computational load when juxtaposed with 3D attention. Furthermore, it empowers the model to discern short-term relationships between adjacent frames, enhancing temporal coherence during video generation.", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross-Attention (CA). In contrast to the original SD model, which employs text embeddings to steer the diffusion process with cross-attention, we have replaced these embeddings with garment image embeddings generated from a CLIP image encoder. These embeddings encapsulate comprehensive global information like color and style, which serve as a valuable supplement to the detailed appearance characteristics provided by the Garment U-Net.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pose-aware Temporal Attention (PATA). Although TSA can effectively capture short-term relationships between adjacent frames, it fails to consider the long-term temporal dynamics across the entire video. Previous studies [12, 17, 24] have introduced a plug-and-play motion module with temporal attention to enhance video smoothness. However, these approaches overlook the dynamic changes in human poses, which are crucial for the VVTON task where garment appearance must adapt to individual poses. To address this limitation, we propose a pose-aware temporal attention. Similar to PASA, our method involves feeding the human pose embedding $\\mathbf{p}_h$ into a pose adapter. This adapted embedding is then element-wise added to the output feature of the cross-attention block, followed by standard temporal attention. Our experiments have demonstrated that this straightforward strategy significantly improves video continuity and enhances the realism of clothing dynamics in motion, as shown in Fig. 5.", + "bbox": [ + 511, + 212, + 903, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Temporal Regularized Attention Loss", + "text_level": 1, + "bbox": [ + 511, + 491, + 836, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generally, SD is merely optimized with the mean-squared loss defined in Eq. 1, which treats all regions of the synthesized video equally without emphasizing temporal consistency. Inspired by the idea that self-attention maps within diffusion models capture the structural essence of generated content [3, 25, 29, 42], we employ the temporal regularized attention loss. This loss function is designed to minimize variations in self-attention maps across successive frames:", + "bbox": [ + 511, + 512, + 905, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T R A}} = \\sum_ {i} ^ {N} \\sum_ {j = 2} ^ {T} \\gamma_ {i} \\left| \\mathcal {A} _ {i} ^ {(j)} - \\mathcal {A} _ {i} ^ {(j - 1)} \\right|, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 640, + 903, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{A}_i^{(j)}$ represents the self-attention map of the PASA block in the $i$ -th layer on $j$ -th frame. Specifically, We calculate $L_{TRA}$ only on the last two decoder layers in the main U-Net, with $\\gamma_i = 0.5$ in our context.", + "bbox": [ + 511, + 683, + 903, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Training and Inference", + "text_level": 1, + "bbox": [ + 511, + 753, + 725, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Strategy. Different from previous multi-stage training approaches [46, 51], we employ a single-stage training strategy. The loss function is defined as follows:", + "bbox": [ + 511, + 773, + 903, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {L D M} + \\lambda \\mathcal {L} _ {T R A}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 835, + 903, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is the hyper-parameter used to balance the MSE loss and the proposed TRA loss. When training with image datasets, the TSA and PATA blocks are omitted. As for", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22652", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "video datasets, we implement an image-video joint training strategy. Initially, we randomly pick $B$ videos from the dataset and extract a single frame randomly from each video for training. At this stage, solely the PASA and CA modules undergo training. Subsequently, in the following phase, another set of $B$ videos is randomly chosen and a sequence of $T$ consecutive frames is extracted from each video for training purposes. Here, the training focuses exclusively on the TSA and PATA modules. This process repeats iteratively until the training concludes. Here, $B$ represents the batch size, and $T$ symbolizes the length of video clips. This training methodology effectively reduces the GPU memory requirements and enhances the speed of convergence.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To tackle discontinuous pose sequences, we also implement a condition dropping strategy during training. Specifically, each pose keypoint has a 0.05 probability of being dropped. When a keypoint of the current frame is dropped, the model is forced to refer to the poses of adjacent frames to infer the correct pose of the current frame. This strategy not only enhances the model's robustness to pose estimation methods but also improves temporal consistency.", + "bbox": [ + 89, + 287, + 480, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference Strategy. To improve temporal coherence and smoothness in long videos, we follow [12, 46] and implement a sliding window approach during inference. It involves dividing the long video into overlapping segments of a specified length $T$ and conducting inference on each segment. For overlapping frames, the ultimate output is derived by averaging the results obtained from each inference.", + "bbox": [ + 89, + 410, + 480, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 534, + 220, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 559, + 191, + 573 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Video Virtual Try-On. We empirically verify and analyze the effectiveness of our DPIDM on two popular video virtual try-on datasets, VVT [10] and ViViD [12]. The VVT dataset contains 791 video clips with a resolution of 256 $\\times$ 192. Following the official settings[10, 51], we partition it into a training set of 661 clips and a test set of 130 clips. However, the VVT dataset exhibits limited diversity in terms of garment varieties and human actions. ViViD, a recent and challenging dataset, includes 9,700 video-image pairs at a resolution of $832 \\times 624$ . It classifies garments into three categories: upper-body, lower-body, and dresses. The dataset is divided into 7,759 videos for training and 1,941 videos for testing. It is worth noting that due to inaccuracies in the provided cloth-agnostic masks for individuals in a back-facing posture, we excluded video segments depicting such scenarios from the original footage. Consequently, only the remaining segments were utilized for testing.", + "bbox": [ + 89, + 582, + 482, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image Virtual Try-On. To further validate the effectiveness of our method, we carried out additional experiments on the widely recognized image-based virtual try-on dataset, VITON-HD [7]. This dataset comprises 13,679", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d20f7746754db60cf4fa13690f173eb77f7b760e5f3d9bc36f0ec4342f4813be.jpg", + "table_caption": [ + "Table 1. Comparison results on the VVT dataset. $\\mathrm{VFID}_I$ and $\\mathrm{VFID}_R$ represent $\\mathrm{VFID}_{I3D}$ and $\\mathrm{VFID}_{ResNeXt}$ respectively. $\\uparrow$ denotes higher is better, while $\\downarrow$ indicates lower is better." + ], + "table_footnote": [], + "table_body": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
CP-VTON [45]0.4590.5356.36112.10
FW-GAN [10]0.6750.2838.01912.15
PBAFN [14]0.8700.1574.5168.690
ClothFormer [26]0.9210.0813.9675.048
LaDI-VTON [34]0.8780.1905.880-
StableVITON [56]0.8760.0764.0215.076
TunnelTry-on [51]0.9130.0543.3454.614
ViViD [12]0.9490.0683.4055.074
VITON-DiT [60]0.8960.0802.4980.187
GPD-VVTO [46]0.9280.0561.280-
DPIDM (Ours)0.9300.0410.5060.047
", + "bbox": [ + 517, + 142, + 893, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "pairs of upper-body model and garment images, out of which 2,032 pairs were specifically reserved for testing.", + "bbox": [ + 511, + 349, + 903, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. For image datasets, we use Structural Similarity (SSIM) [47] and Learned Perceptual Image Patch Similarity (LPIPS) [55] to measure the similarity between the generated image and the ground-truth. Additionally, Fréchet Inception Distance(FID) [22] and Kernel Inception Distance(KID) [2] are employed to measure the quality and realism of the generated images. For video datasets, we further utilize Video Fréchet Inception Distance (VFID) [43] to evaluate spatiotemporal consistency. Two CNN backbones, I3D [4] and 3D-ResNeXt101 [20], are adopted as feature extractors for VFID.", + "bbox": [ + 511, + 380, + 905, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 556, + 730, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We initialize the main U-Net with the pre-trained SD v1.5 inpainting model and the garment U-Net with SD v1.5. The pose estimator is trained offline using YOLOv8 [38]. The pose encoder incorporates four convolutional layers to align the pose image with the noise latent at the same resolution. During training, all data is resized to a uniform resolution of $512 \\times 384$ . To improve model resilience, we employ data augmentation by randomly flipping images horizontally with a $50\\%$ probability. We utilize the Adam optimizer [27] with a consistent learning rate of $2 \\times 10^{-5}$ . All the experiments are conducted using 16 NVIDIA A100 GPUs. Sequences of 24 frames are sampled, and the batch size $B$ is set to 32. The model is trained for 80,000 iterations. The hyper-parameter $\\lambda$ is set to $10^{-3}$ for video datasets and 0 for image datasets. During inference, we utilize the DDIM [41] sampler and set the classifier-free guidance scale to 1.5.", + "bbox": [ + 511, + 579, + 905, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.Quantitative Results", + "text_level": 1, + "bbox": [ + 511, + 832, + 705, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Video Virtual Try-On. We compare our DPIDM with a series of state-of-the-art virtual try-on methods, which can be grouped into two directions: GAN-based methods", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22653", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e982f54b36171c44b36062be50a2d1f040d52e3db4779f2f255b5ff272cad56f.jpg", + "table_caption": [ + "Table 2. Comparison results on the ViViD dataset." + ], + "table_footnote": [], + "table_body": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
LaDI-VTON [34]0.8240.1648.2831.185
CAT-DM [54]0.8260.1629.3542.139
ViViD [12]0.8460.1181.8940.870
DPIDM (Ours)0.8830.0810.4880.090
", + "bbox": [ + 99, + 114, + 468, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e7e2becbc46670532a32a16664a3db8af762c1dc6ce827f417efe3e417bd94a8.jpg", + "table_caption": [ + "Table 3. Quantitative results of image-based virtual try-on task on the VITON-HD dataset. $\\mathrm{FID}_u / \\mathrm{KID}_u$ stands for the FID/KID score in unpaired setting. Note that the KID score is multiplied by 1000." + ], + "table_footnote": [], + "table_body": "
MethodSSIM↑LPIPS↓FIDu↓KIDu↓
VITON-HD [7]0.8620.11712.123.23
HR-VITON [30]0.8760.09612.313.81
GP-VTON [48]0.8900.0859.821.42
LaDI-VTON [34]0.8750.0919.321.55
WearAnyWay [5]0.8770.0788.160.78
DCI-VTON [16]0.8900.0728.770.89
StableVITON [56]0.8780.0759.431.54
CAT-DM [54]0.8770.0808.931.37
IDM [8]0.8810.0788.600.55
GPD-VVTO [46]0.8910.0708.570.78
DPIDM (Ours)0.8930.0678.150.32
", + "bbox": [ + 99, + 260, + 468, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "[10, 14, 26, 45] and Diffusion-based methods [12, 34, 46, 51, 54, 56, 60]. Table 1 summarizes the performance comparisons on the VVT dataset. Notably, our DPIDM consistently outperforms other state-of-the-art methods across LPIPS and VFID metrics. Although ViViD [12] attains a higher SSIM score, its advantage is expected due to the utilization of a significantly larger volume of high-resolution videos during training, approximately six times more than the VVT dataset. Despite this, our DPIDM notably surpasses ViViD in the VFID metric, showcasing substantial enhancements in video coherence while preserving garment visual authenticity. ClothFormer improves FW-GAN by introducing an appearance-flow tracking module to ensure temporal consistency in garment warping. TunnelTry-on and ViViD further boost the performances by leveraging the capabilities of pre-trained diffusion models. Additionally, GPD-VVTO introduces garment-aware temporal attention to enhance temporal consistency, leading to a clear VFID score boost. However, existing approaches often neglect crucial spatiotemporal pose interactions between individuals and garments. In contrast, our DPIDM effectively models both intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware attention mechanisms, leading to superior results in the VVTON task. Specifically, our DPIDM achieves a $\\mathrm{VFID}_I$ score of 0.506, marking a substantial $60.5\\%$ relative improvement over the top competitor GPD-VVTO. Note that GPD-VVTO employs SD v2.1 for model initialization, whereas we choose SD v1.5 for fewer parameters.", + "bbox": [ + 89, + 462, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d2ecb45cdfd86fa2e1368630fb003dd58f92ba506159068f7a5955ba0a23c986.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison on the ViViD dataset. Our DPIDM excels in seamlessly integrating the garment with the wearer and maintaining the visual integrity of the garment." + ], + "image_footnote": [], + "bbox": [ + 522, + 92, + 897, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 presents performance comparisons on the ViViD dataset. As observed with VVT, DPIDM consistently outperforms other VVTON methods across all metrics. which again evinces the pivotal merit of the pose-aware guidance for preserving spatiotemporal consistency in the generated videos. Particularly, DPIDM demonstrates a substantial relative improvement of $74.2\\%$ over ViViD in $\\mathrm{VFID}_I$", + "bbox": [ + 511, + 429, + 906, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image Virtual Try-On. Table 3 displays the quantitative results on the VITON-HD [7]. Following the official settings, we utilize SSIM and LPIPS metrics for the paired setting, and FID and KID for the unpaired setting. Our DPIDM consistently outperforms other methods across all metrics, showcasing its ability to produce authentic and lifelike images while maintaining the integrity of the initial garment structure. It is noteworthy that diffusion-based approaches exhibit lower FID and KID scores compared to GAN-based methods, suggesting that diffusion models excel in generating images with heightened fidelity.", + "bbox": [ + 511, + 535, + 908, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 712, + 694, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct qualitative analysis from two aspects: visual authenticity of the garment and temporal consistency. When evaluating visual authenticity, we compare results from several virtual try-on methods using individual video frames, as illustrated in Figure 4. In the first row, LaDI-VTON and CAT-DM change the style of the target garment and introduce color discrepancies. While ViViD achieves a natural fit, it struggles to maintain the original patterns, leading to their displacement on the garment. In contrast, our method excels in seamlessly blending the garment with the wearer while preserving intricate fabric patterns. Moving", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22654", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c38118303f52f5ea54d65bd8c7305c41fa89baf7b6146cc26931c3619e3bc97d.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on the ViViD dataset. Our DPIDM maintains temporal consistency even during substantial movements." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 883, + 353 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f7b900e79d5c8e4cf8e08eaed38c7ed5a3dc74210c493bee8b746eed0a5272e8.jpg", + "table_caption": [ + "Table 4. Performance contribution of each component in DPIDM." + ], + "table_footnote": [], + "table_body": "
idPAATSATRASSIM↑LPIPS↓VFIDI↓VFIDR↓
(a)XXX0.8930.0843.4512.435
(b)✓XX0.9250.0501.0680.153
(c)✓✓X0.9290.0430.7210.075
(d)✓✓✓0.9300.0410.5060.047
", + "bbox": [ + 94, + 404, + 473, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to the second row with a pair of striped shorts, competitors maintain the garment's style but exhibit noticeable artifacts around the legs. Conversely, our method adeptly addresses these issues by naturally supplementing missing skin tones while upholding the garment's visual integrity. This trend continues in the subsequent example with a dress in the third row, highlighting the effectiveness of DPIDM. To further evaluate temporal consistency, we extract four frames at equal intervals from the generated video and present them in Fig. 5. While ViViD achieves a natural fit in individual frames, it struggles to maintain garment details and temporal consistency across frames, especially during person movements. In contrast, our DPIDM consistently delivers high-quality results that preserve garment details and ensure temporal consistency without introducing artifacts, even during actions involving significant movements.", + "bbox": [ + 88, + 503, + 482, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 757, + 254, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we analyze the impact of each design element within DPIDM on the overall performance using the VVT dataset. As shown in Table 4, the proposed elements are denoted as follows: PAA refers to pose-aware attention, TSA to temporal-shift attention, and TRA to temporal regularized attention loss. We start with a basic model (a) that directly inserts standard temporal attention after each stage of the main U-Net. Subsequently, in (b), we substitute the", + "bbox": [ + 89, + 780, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "standard spatial/temporal attention with our proposed pose-aware spatial/temporal attention. Notably, the introduction of $PAA$ yields a significant performance enhancement over (a), surpassing even the state-of-the-art methods detailed in Table 1. This not only validates the efficacy of our proposed pose-aware spatial/temporal attention but also underscores the critical role of integrating spatiotemporal pose interactions into the VVTON task. Furthermore, we introduce the temporal-shift attention and the temporal regularized attention loss in (c) and (d) respectively. While TSA and TRA did not result in significant enhancements in the SSIM and LPIPS metrics, they notably improved the VFID metric, highlighting their effectiveness in enhancing video consistency. Collectively, the innovative modules introduced in DPIDM enhance the visual integrity of the garment and improve the temporal consistency of the generated videos.", + "bbox": [ + 511, + 380, + 906, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 633, + 633, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have presented Dynamic Pose Interaction Diffusion Models (DPIDM), a novel approach that capitalizes on spatial and temporal pose interactions to enhance video virtual try-on. Particularly, we study the problem from the viewpoint of employing intra-frame human-garment pose interactions and long-term human pose dynamics across frames. To verify our claim, we develop a hierarchical pose-aware attention module to integrate human and garment pose features into spatial and temporal attention, enhancing the temporal coherence of the generated videos while preserving the visual fidelity of the garments. Additionally, a new temporal regularized attention loss is devised to bolster consistency across successive frames. Through extensive experiments, we demonstrate that our DPIDM surpasses existing state-of-the-art methods on image-based and video-based virtual try-on datasets.", + "bbox": [ + 511, + 659, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22655", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the Beijing Municipal Science and Technology Project No. Z241100001324002 and Beijing Nova Program No. 20240484681.", + "bbox": [ + 89, + 113, + 485, + 157 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 183, + 187, + 199 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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In CVPR, 2023. 1, 2" + ], + "bbox": [ + 516, + 90, + 903, + 883 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22657", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_model.json b/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b7594e406d1b1ba04f7b48965ce693a8efd10ced --- /dev/null +++ b/2025/Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction/0dbff5db-f8cb-4f92-8abf-9eb7e5e15468_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.232, + 0.131, + 0.768, + 0.175 + ], + "angle": 0, + "content": "Pursuing Temporal-Consistent Video Virtual Try-On via Dynamic Pose Interaction" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.203, + 0.775, + 0.24 + ], + "angle": 0, + "content": "Dong Li\\(^{1}\\), Wenqi Zhong\\(^{2*}\\), Wei Yu\\(^{1}\\), Yingwei Pan\\(^{1}\\), Dingwen Zhang\\(^{2}\\), Ting Yao\\(^{1}\\), Junwei Han\\(^{2}\\), and Tao Mei\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.241, + 0.379, + 0.255 + ], + "angle": 0, + "content": "1 HiDream.ai Inc." + }, + { + "type": "text", + "bbox": [ + 0.422, + 0.241, + 0.73, + 0.257 + ], + "angle": 0, + "content": "\\(^{2}\\) Northwest Polytechnical University, Xi'an, China" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.26, + 0.821, + 0.275 + ], + "angle": 0, + "content": "lidong@hidream.ai, wenqizhong@mail.nwpu.edu.cn, {yuwei, pandy}@hidream.ai" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.278, + 0.819, + 0.293 + ], + "angle": 0, + "content": "zhangdingwen2006yyyy@gmail.com, tiyao@hidream.ai, junweihan2010@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.429, + 0.296, + 0.563, + 0.309 + ], + "angle": 0, + "content": "tmei@hidream.ai" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.345, + 0.327, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.378, + 0.486, + 0.862 + ], + "angle": 0, + "content": "Video virtual try-on aims to seamlessly dress a subject in a video with a specific garment. The primary challenge involves preserving the visual authenticity of the garment while dynamically adapting to the pose and physique of the subject. While existing methods have predominantly focused on image-based virtual try-on, extending these techniques directly to videos often results in temporal inconsistencies. Most current video virtual try-on approaches alleviate this challenge by incorporating temporal modules, yet still overlook the critical spatiotemporal pose interactions between human and garment. Effective pose interactions in videos should not only consider spatial alignment between human and garment poses in each frame but also account for the temporal dynamics of human poses throughout the entire video. With such motivation, we propose a new framework, namely Dynamic Pose Interaction Diffusion Models (DPIDM), to leverage diffusion models to delve into dynamic pose interactions for video virtual try-on. Technically, DPIDM introduces a skeleton-based pose adapter to integrate synchronized human and garment poses into the denoising network. A hierarchical attention module is then exquisitely designed to model intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware spatial and temporal attention mechanisms. Moreover, DPIDM capitalizes on a temporal regularized attention loss between consecutive frames to enhance temporal consistency. Extensive experiments conducted on VITON-HD, VVT and ViViD datasets demonstrate the superiority of our DPIDM against the baseline methods. Notably, DPIDM achieves VFID score of 0.506 on VVT dataset, leading to \\(60.5\\%\\) improvement over the state-of-the-art GPD-VVTO approach." + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.356, + 0.882, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.505, + 0.908, + 0.547 + ], + "angle": 0, + "content": "Figure 1. Given a garment and a person video, DPIDM generates a lifelike video that preserves the visual authenticity of the garment while adapting to the individual's pose and physique." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.557, + 0.645, + 0.571 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.583, + 0.907, + 0.734 + ], + "angle": 0, + "content": "Generative models have made tremendous progress in recent years, with wide-ranging applications across various fields, including computer vision [9, 36, 59], computer graphics [6, 13], aesthetic design [35], and medical research [18]. Virtual try-on is a quintessential generative task that aims to synthesize a lifelike image/video of the specific person wearing the provided garment. By harnessing the powerful generative capacities of diffusion models, this field has emerged as a promising domain with versatile applications in immersive e-commerce and short-form video platforms." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Prior research mainly focused on image-based virtual try-on. The earlier approaches typically build on Generative Adversarial Networks (GANs) [7, 19, 39, 45], incorporating a warping module alongside a try-on generator. The warping module deforms clothing to align with the human body, and then the warped garment is fused with the person image through the try-on generator. However, in light of the recent emergence of UNet-based Latent Diffusion Models (LDMs) [5, 8, 50, 56, 62], researchers have progressively directed their focus towards these innovative models. A diffusion-based try-on network combines the warping and blending" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.887, + 0.448, + 0.9 + ], + "angle": 0, + "content": "* Equal contribution. This work was performed at HiDream.ai." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22648" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "processes into a unified operation of cross-attention without explicit segregation. By employing pre-trained text-to-image weights, these diffusion approaches demonstrate superior fidelity compared to their GAN-based counterparts." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.155, + 0.486, + 0.701 + ], + "angle": 0, + "content": "In recent years, researchers have endeavored to replicate the success of image try-on within the realm of video. One direct approach involves applying image try-on techniques to process videos frame by frame. However, this method often results in notable inter-frame inconsistencies. To address this challenge, various specialized designs have been explored for video virtual try-on [10, 26, 28, 61]. These approaches commonly integrate optical flow prediction modules to warp frames produced by the try-on generator. Despite reasonable performance, GAN-based methods encounter difficulties in handling garment-person misalignment, particularly when faced with inaccurate warping flow estimations. To harness the capabilities of pretrained image-based diffusion models, TunnelTry-on [51] and ViViD [12] utilize a pre-trained inpainting U-Net as the primary branch and integrate a reference U-Net to capture detailed clothing features. They enhance temporal consistency by incorporating standard temporal attention after each stage of the main U-Net. GPD-VVTO [46] takes a step further by integrating garment features into temporal attention, enabling the model to better preserve fidelity to the garment during temporal modeling. Despite showing promise, these methods struggle to maintain both visual integrity and motion consistency simultaneously, particularly when there is a significant stylistic gap between the garment being tried on and the original one. To alleviate these issues, we argue that two key ingredients should be taken into account. One is spatial alignment between human and garment poses within each frame. Such alignment is essential for virtual try-on as it ensures that clothing adapts appropriately to factors like coverage and wrinkles based on the individual's posture. The other is the temporal dynamics of human poses across the entire video. A comprehensive understanding of this long-term interaction is paramount for upholding temporal coherence, given that human movements naturally progress as a continuum of interconnected poses." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.901 + ], + "angle": 0, + "content": "By consolidating the idea of modeling both spatial and temporal pose interactions in a video, we novelly present Dynamic Pose Interaction Diffusion Models (DPIDM) for boosting video virtual try-on. Specifically, DPIDM employs a dual-branch architecture, where the Main U-Net conducts denoising processes on the video, while the Garment U-Net extracts intricate details from the garment image and integrates them into the Main U-Net. This architecture facilitates a holistic understanding of the relationship between humans and garments within a unified feature space. To effectively leverage the spatiotemporal pose interactions in videos, we introduce a skeleton-based pose adapter that seamlessly integrates synchronized human and" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.288 + ], + "angle": 0, + "content": "garment poses into the Main U-Net. With the adapter, we present a hierarchical attention module comprising four key components: a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block. The pose-aware spatial attention block plays a crucial role in capturing intricate intra-frame human-garment pose interactions, while the pose-aware temporal attention block models the long-term dynamics of human poses across frames. Moreover, a temporal regularized attention loss is defined on consecutive frames to ensure temporal coherence. As a result, our DPIDM excels in generating videos with meticulously aligned garment details and enhanced temporal stability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.289, + 0.905, + 0.456 + ], + "angle": 0, + "content": "The main contribution of this work is the proposal of Dynamic Pose Interaction Diffusion Models that facilitate the video virtual try-on (VVTON) task. This also leads to the elegant view of how a diffusion model should be designed for excavating the pose-focused prior knowledge (e.g., spatial pose alignment and temporal pose dynamics) tailored to VVTON, and how to improve diffusion process with these amplified pose-focused guidance. Through an extensive set of experiments on VITON-HD, VVT, and ViViD datasets, DPIPM consistently achieves superior results over state-of-the-art methods in both image and video virtual try-on tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.473, + 0.665, + 0.488 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.499, + 0.766, + 0.515 + ], + "angle": 0, + "content": "2.1. Image-based Virtual Try-on" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.522, + 0.905, + 0.719 + ], + "angle": 0, + "content": "The development of image-based virtual try-on is largely inspired by the success of GANs [15], leading to pioneering works such as [7, 11, 19, 31, 33, 45]. A standard GAN-based virtual try-on framework typically adheres to a two-stage paradigm. The initial stage involves an image warping process, such as Thin Plate Spline (TPS) warping [19], which aligns the garment with the target individual's body. In the second stage, a GAN-based try-on generator merges the warped attire with the target individual's clothing-agnostic representation to produce authentic try-on outcomes. However, these methods heavily rely on the warping module to preserve garment details and often suffer from performance degradation due to inaccurate warping." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Recently, with the powerful generative capabilities of Latent Diffusion Models (LDMs), many diffusion-based models have been introduced to generate more realistic virtual try-on results [5, 44, 52, 54, 56, 62]. TryOnDiffusion [62] was the first to propose a dual U-Net architecture that simultaneously preserves garment details and implicitly warps the garment to match the target pose. StableVITON [56] introduced a zero cross-attention block to learn the semantic correspondence between the garment and the target person. Wear-any-way [5] utilized a sparse point control method to align person and garment features in feature space. MMTryon [57] presented a multi-modal, multi" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22649" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.094, + 0.671, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.674, + 0.094, + 0.882, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.352, + 0.908, + 0.451 + ], + "angle": 0, + "content": "Figure 2. (a) Overall architecture of DPIDM. DPIDM employs a dual-branch architecture. The main U-Net processes a concatenated input comprising the noisy latent of the video, the latent of the cloth-agnostic video, and the cloth-agnostic mask sequence. The garment U-Net extracts fine-grained garment features, which are subsequently integrated into the main U-Net. The pose estimator is utilized to extract aligned human and garment poses, which are then fed into the attention modules of the main U-Net to guide the diffusion process. The VAE is not shown for clarity. (b) Detailed illustration of the proposed pose-aware attention module within the main U-Net. The module comprises pose-aware spatial attention, temporal-shift attention, cross-attention, and pose-aware temporal attention. The pose embeddings are seamlessly integrated into the attention module through a specialized pose adapter. (better viewed in color)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.46, + 0.484, + 0.611 + ], + "angle": 0, + "content": "garment virtual try-on approach that combines text and multiple reference images to create a multimodal embedding as a condition to control the diffusion model. IDM [8] proposed a RefNet-style architecture to align the feature space between garment and person. Although these diffusion-based methods have achieved high-fidelity results in single-image inference, their application to video virtual try-on reveals a crucial limitation: the oversight of inter-frame relationships. This deficiency results in notable inter-frame inconsistencies, ultimately yielding unsatisfactory outcomes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.622, + 0.339, + 0.639 + ], + "angle": 0, + "content": "2.2. Video-based Virtual Try-on" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In recent studies, researchers have aimed to expand the capabilities of image-based try-on approaches into video applications. A key issue in video generation is inter-frame inconsistency. ClothFormer [26] leverages optical flow in the warping and blending processes to achieve temporal smoothing. Recently, diffusion-based video virtual try-on methods have been introduced to generate more realistic results [12, 21, 46, 51, 60]. For instance, TunnelTry-on [51] proposed a focus-tunnel method that crops the human image according to the pose map, aligning the try-on image to accommodate scenarios where the person is off-center in the frame. VTON-DiT [60] introduced a DiT architecture compatible with OpenSora, where the clothing-agnostic human image is provided via ControlNet. WildVidFit [21] proposed an image-based diffusion model and used video MAE to update the intermediate representations of the diffusion process to improve frame consistency. ViViD [12]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.907, + 0.612 + ], + "angle": 0, + "content": "introduced a large-scale video try-on dataset and proposed an additional reference-based U-Net. GPD-VVTON [46] went a step further by integrating garment features into temporal attention to generate spatio-temporally consistent results. While these explorations of video try-on make steady advancements, they currently struggle to accurately capture the dynamic interaction between clothing and the human body in real-world scenarios. Our method employs a hierarchical attention module to capture the critical spatiotemporal pose interactions between the human and the garment." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.628, + 0.649, + 0.644 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.654, + 0.907, + 0.806 + ], + "angle": 0, + "content": "In this paper, we present Dynamic Pose Interaction Diffusion Models (DPIDM), a pioneering framework based on latent diffusion models designed to enhance the VVTON task. The complete architecture is depicted in Figure 2 (a). This section begins with a brief introduction to Stable Diffusion [39] in Section 3.1 to lay the groundwork for subsequent discussions. Subsequently, we offer a comprehensive overview of DPIDM in Section 3.2, and delve into the specific design details in Section 3.3-3.5. Finally, we encapsulate our training and inference strategies in Section 3.6." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.818, + 0.643, + 0.834 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Stable Diffusion (SD) stands out as one of the most prevalent latent diffusion models within the community. It leverages a variational autoencoder (VAE) architecture, comprising an encoder \\(\\mathcal{E}\\) and a decoder \\(\\mathcal{D}\\), to facilitate image rep" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22650" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "resentations in the latent space. Additionally, a U-Net [40] \\(\\epsilon_{\\theta}\\) is trained to denoise a Gaussian noise \\(\\epsilon\\) with a conditioning input encoded by a CLIP text encoder [37] \\(\\tau_{\\theta}\\). Given an image \\(\\mathbf{x}\\) and a text prompt \\(\\mathbf{y}\\), the denoising U-Net \\(\\epsilon_{\\theta}\\) undergoes training by minimizing the loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.173, + 0.482, + 0.204 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})) \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.205, + 0.484, + 0.311 + ], + "angle": 0, + "content": "where \\(t\\) denotes the time step of the forward diffusion process, and \\(\\mathbf{z}_t\\) is the noisy latent constructed by adding Gaussian noise \\(\\epsilon \\sim \\mathcal{N}(0,1)\\) to the encoded image \\(\\mathcal{E}(\\mathbf{x})\\). During the inference stage, \\(\\mathbf{z}_t\\) is randomly sampled from a Gaussian distribution and iteratively denoised to derive \\(\\mathbf{z}_0\\) following a predefined sampling schedule [23, 41]. Finally, the latent decoder \\(\\mathcal{D}\\) decodes \\(\\mathbf{z}_0\\) back into the image space." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.32, + 0.202, + 0.334 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.341, + 0.483, + 0.447 + ], + "angle": 0, + "content": "The overall architecture of DPIDM is depicted in Fig. 2. DPIDM takes a reference garment image \\( \\pmb{G} \\in \\mathbb{R}^{3 \\times H \\times W} \\) and a source human video \\( \\pmb{I}_S \\in \\mathbb{R}^{T \\times 3 \\times H \\times W} \\) as input, where \\( H \\) and \\( W \\) represent the height and width of each frame, and \\( T \\) signifies the video length. Its objective is to generate a realistic video \\( \\hat{\\pmb{I}} \\in \\mathbb{R}^{T \\times 3 \\times H \\times W} \\) showing the individual in \\( \\pmb{I}_S \\) adorned in the garment \\( \\pmb{G} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.483, + 0.734 + ], + "angle": 0, + "content": "We approach the video virtual try-on as a video inpainting challenge, aimed at integrating the garment onto clothing-agnostic areas. To achieve this, DPIDM employs a dual-branch architecture. The main U-Net is the inpainting model initialized with the pre-trained weights from SD. It takes in a 9-channel tensor comprising 4 channels for the noisy latent of the video, 4 channels for the clothing-agnostic video latent, and 1 channel for the binary agnostic mask sequence. In contrast to the original SD model, which utilizes text embeddings to guide the diffusion process, we have substituted these embeddings with image embeddings derived from a CLIP image encoder representing the garment image. While the CLIP image embedding effectively captures the overall colors and textures of the garment, it may not retain finer details. To address this, we also use a Garment U-Net to extract detailed garment features. The Garment U-Net follows a standard text-to-image diffusion model with a 4-channel input. This dual-branch architecture has proven to be effective by previous works [12, 46, 51]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.84 + ], + "angle": 0, + "content": "To further enhance the generation, we incorporate human and garment poses as supplementary guidance to refine the diffusion process. We develop a light-weight pose encoder to extract features of the pose maps and a pose adapter to inject these features into the attention modules of the main U-Net. The human/garment pose maps are derived from the input video/image with pose estimator." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.245, + 0.863 + ], + "angle": 0, + "content": "3.3. Pose Estimator" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We directly employ DW-Pose [53] to estimate human poses \\( P_{h} \\) from video frames. However, there is a lack of an open-" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.09, + 0.882, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.158, + 0.896, + 0.173 + ], + "angle": 0, + "content": "Figure 3. Visualization of predicted human and garment poses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.905, + 0.364 + ], + "angle": 0, + "content": "source garment pose estimator currently. To establish alignment between human and garment poses, we train a garment pose estimator to predict a set of landmarks \\( P_{g} \\) that correspond to various parts of the human pose \\( P_{h} \\). The ground truth of \\( P_{g} \\) is labeled manually, with the number of landmarks varying based on the garment types. For instance, in upper clothing, \\( |P_{g}| = 9 \\), encompassing landmarks such as the neck, shoulders, elbows, wrists, and hips. These landmarks serve as explicit indicators of the alignment between human and garment poses, and therefore can be used as guidance to improve the diffusion process. The visualization of human and garment poses is shown in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.373, + 0.749, + 0.389 + ], + "angle": 0, + "content": "3.4. Dynamic Pose Interaction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.395, + 0.905, + 0.456 + ], + "angle": 0, + "content": "To facilitate the dynamic pose interaction, we propose a hierarchical attention module consisting of a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.456, + 0.906, + 0.562 + ], + "angle": 0, + "content": "Pose-aware Spatial Attention (PASA). To capture intricate intra-frame human-garment pose interactions, we inject the features of human and garment poses into the spatial attention layer. In our baseline, the human feature map \\(\\mathbf{f}_h\\) from the main U-Net is concatenated with the corresponding garment feature map \\(\\mathbf{f}_g\\) from the garment U-Net to jointly compute self-attention, which is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.573, + 0.905, + 0.591 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f}), \\psi_ {k} (\\mathbf {f}), \\psi_ {v} (\\mathbf {f})\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.601, + 0.906, + 0.692 + ], + "angle": 0, + "content": "where \\(\\mathbf{f} = [\\mathbf{f}_h,\\mathbf{f}_g]\\) is the concatenation of human feature map and garment feature map in the spatial dimension, and \\(\\psi_q,\\psi_k,\\psi_v\\) are linear projections. Afterward, only the half feature from the main U-Net undergoes further computation. This attention layer enables garment features extracted by the garment U-Net to be integrated into the main U-Net." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.692, + 0.906, + 0.873 + ], + "angle": 0, + "content": "To enable the correspondence control with pose guidance, we modify this attention layer by adding the pose embeddings of the human and garment. Formally, given the human pose embedding \\(\\mathbf{p}_h\\) and garment pose embedding \\(\\mathbf{p}_g\\) extracted from the pose encoder, we first concatenate them in spatial dimension \\(\\mathbf{p} = [\\mathbf{p}_h,\\mathbf{p}_g]\\). Then we utilize a pose adapter to project \\(\\mathbf{p}\\) into the diffusion feature space. The pose adapter employs two fully connected (FC) layers with an intermediate activation layer. The first FC layer maps the input to a lower-dimensional space, while the second FC layer maps it back to the original dimensional. The pose adapter can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.885, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\nA d p t (\\mathbf {p}) = \\mathbf {W} _ {u p} (G E L U (\\mathbf {W} _ {d o w n} (\\mathbf {p}))), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22651" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.171 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_{up}\\) and \\(\\mathbf{W}_{down}\\) are the learnable weight matrix. To preserve the original feature space of diffusion models, we initialize \\(\\mathbf{W}_{up}\\) with zeros. Subsequently, we add the diffusion feature \\(\\mathbf{f}\\) and the adapter embedding \\(Adpt(\\mathbf{p})\\) together and feed them into the self-attention mechanism, leading to the revised form of Eq. 2:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.176, + 0.483, + 0.191 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {k} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {v} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p}))\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.197, + 0.482, + 0.272 + ], + "angle": 0, + "content": "In this way, when integrating the garment feature into the main U-Net, the feature aggregation process takes into account the alignment of human and garment poses. This implicit consideration results in the garment being deformed to better fit the natural pose of the person." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.273, + 0.483, + 0.424 + ], + "angle": 0, + "content": "Existing PoseGuider-style methods [24, 46, 51] typically achieve pose control by directly adding processed human pose images and noisy latents as inputs to the first layer of the diffusion network, without incorporating pose information into the attention modules. In contrast, our PASA introduces pose information into each layer's attention modules through a pose adapter, enabling more precise and varying degrees of pose control. Moreover, besides human poses, we further inject garment poses into PASA, thus achieving intricate intra-frame human-garment pose alignment." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.483, + 0.802 + ], + "angle": 0, + "content": "Temporal-shift Attention (TSA). In the original SD model, the attention block of the U-Net solely focuses on self-attention within individual frames, overlooking valuable information across frames. Current VVTON techniques predominantly integrate a temporal attention layer at each stage to capture temporal dependencies among video frames. Nevertheless, this approach can introduce a covariate shift in the feature space, potentially undermining the model's generative capacity [58]. While a direct remedy could involve joint space-time 3D attention, this method escalates the complexity of attention calculations quadratically. Drawing inspiration from prior works [1, 32, 49], a novel approach involves employing temporal shift operations that utilize a 2D module to amalgamate spatial and temporal information by incorporating neighboring frame data into the current frame. Specifically, in addition to examining tokens within the present frame, a patch-level shifting operation transpires along the temporal dimension, transferring tokens from the preceding \\(L\\) frames to the current frame, thereby constructing a novel latent feature frame. We concatenate the latent feature of the current frame \\(\\mathbf{h}\\) with the temporally shifted latent feature \\(\\mathbf{h}_{shift}\\) in the spatial dimension, thus establishing keys and values for subsequent self-attention mechanisms. The temporal-shift attention can be formally written as:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.811, + 0.483, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {h}} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {h}), \\psi_ {k} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right), \\psi_ {v} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right). \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "It notably reduces the computational load when juxtaposed with 3D attention. Furthermore, it empowers the model to discern short-term relationships between adjacent frames, enhancing temporal coherence during video generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "Cross-Attention (CA). In contrast to the original SD model, which employs text embeddings to steer the diffusion process with cross-attention, we have replaced these embeddings with garment image embeddings generated from a CLIP image encoder. These embeddings encapsulate comprehensive global information like color and style, which serve as a valuable supplement to the detailed appearance characteristics provided by the Garment U-Net." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.213, + 0.905, + 0.485 + ], + "angle": 0, + "content": "Pose-aware Temporal Attention (PATA). Although TSA can effectively capture short-term relationships between adjacent frames, it fails to consider the long-term temporal dynamics across the entire video. Previous studies [12, 17, 24] have introduced a plug-and-play motion module with temporal attention to enhance video smoothness. However, these approaches overlook the dynamic changes in human poses, which are crucial for the VVTON task where garment appearance must adapt to individual poses. To address this limitation, we propose a pose-aware temporal attention. Similar to PASA, our method involves feeding the human pose embedding \\(\\mathbf{p}_h\\) into a pose adapter. This adapted embedding is then element-wise added to the output feature of the cross-attention block, followed by standard temporal attention. Our experiments have demonstrated that this straightforward strategy significantly improves video continuity and enhances the realism of clothing dynamics in motion, as shown in Fig. 5." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.492, + 0.838, + 0.507 + ], + "angle": 0, + "content": "3.5. Temporal Regularized Attention Loss" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.513, + 0.906, + 0.635 + ], + "angle": 0, + "content": "Generally, SD is merely optimized with the mean-squared loss defined in Eq. 1, which treats all regions of the synthesized video equally without emphasizing temporal consistency. Inspired by the idea that self-attention maps within diffusion models capture the structural essence of generated content [3, 25, 29, 42], we employ the temporal regularized attention loss. This loss function is designed to minimize variations in self-attention maps across successive frames:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.641, + 0.905, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {T R A}} = \\sum_ {i} ^ {N} \\sum_ {j = 2} ^ {T} \\gamma_ {i} \\left| \\mathcal {A} _ {i} ^ {(j)} - \\mathcal {A} _ {i} ^ {(j - 1)} \\right|, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.684, + 0.905, + 0.747 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}_i^{(j)}\\) represents the self-attention map of the PASA block in the \\(i\\)-th layer on \\(j\\)-th frame. Specifically, We calculate \\(L_{TRA}\\) only on the last two decoder layers in the main U-Net, with \\(\\gamma_i = 0.5\\) in our context." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.754, + 0.727, + 0.769 + ], + "angle": 0, + "content": "3.6. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.905, + 0.822 + ], + "angle": 0, + "content": "Training Strategy. Different from previous multi-stage training approaches [46, 51], we employ a single-stage training strategy. The loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.836, + 0.905, + 0.852 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {L D M} + \\lambda \\mathcal {L} _ {T R A}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the hyper-parameter used to balance the MSE loss and the proposed TRA loss. When training with image datasets, the TSA and PATA blocks are omitted. As for" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22652" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "video datasets, we implement an image-video joint training strategy. Initially, we randomly pick \\( B \\) videos from the dataset and extract a single frame randomly from each video for training. At this stage, solely the PASA and CA modules undergo training. Subsequently, in the following phase, another set of \\( B \\) videos is randomly chosen and a sequence of \\( T \\) consecutive frames is extracted from each video for training purposes. Here, the training focuses exclusively on the TSA and PATA modules. This process repeats iteratively until the training concludes. Here, \\( B \\) represents the batch size, and \\( T \\) symbolizes the length of video clips. This training methodology effectively reduces the GPU memory requirements and enhances the speed of convergence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.482, + 0.41 + ], + "angle": 0, + "content": "To tackle discontinuous pose sequences, we also implement a condition dropping strategy during training. Specifically, each pose keypoint has a 0.05 probability of being dropped. When a keypoint of the current frame is dropped, the model is forced to refer to the poses of adjacent frames to infer the correct pose of the current frame. This strategy not only enhances the model's robustness to pose estimation methods but also improves temporal consistency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.411, + 0.482, + 0.516 + ], + "angle": 0, + "content": "Inference Strategy. To improve temporal coherence and smoothness in long videos, we follow [12, 46] and implement a sliding window approach during inference. It involves dividing the long video into overlapping segments of a specified length \\( T \\) and conducting inference on each segment. For overlapping frames, the ultimate output is derived by averaging the results obtained from each inference." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.535, + 0.222, + 0.551 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.56, + 0.192, + 0.574 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Video Virtual Try-On. We empirically verify and analyze the effectiveness of our DPIDM on two popular video virtual try-on datasets, VVT [10] and ViViD [12]. The VVT dataset contains 791 video clips with a resolution of 256 \\(\\times\\) 192. Following the official settings[10, 51], we partition it into a training set of 661 clips and a test set of 130 clips. However, the VVT dataset exhibits limited diversity in terms of garment varieties and human actions. ViViD, a recent and challenging dataset, includes 9,700 video-image pairs at a resolution of \\(832 \\times 624\\). It classifies garments into three categories: upper-body, lower-body, and dresses. The dataset is divided into 7,759 videos for training and 1,941 videos for testing. It is worth noting that due to inaccuracies in the provided cloth-agnostic masks for individuals in a back-facing posture, we excluded video segments depicting such scenarios from the original footage. Consequently, only the remaining segments were utilized for testing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Image Virtual Try-On. To further validate the effectiveness of our method, we carried out additional experiments on the widely recognized image-based virtual try-on dataset, VITON-HD [7]. This dataset comprises 13,679" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.905, + 0.132 + ], + "angle": 0, + "content": "Table 1. Comparison results on the VVT dataset. \\(\\mathrm{VFID}_I\\) and \\(\\mathrm{VFID}_R\\) represent \\(\\mathrm{VFID}_{I3D}\\) and \\(\\mathrm{VFID}_{ResNeXt}\\) respectively. \\(\\uparrow\\) denotes higher is better, while \\(\\downarrow\\) indicates lower is better." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.143, + 0.895, + 0.332 + ], + "angle": 0, + "content": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
CP-VTON [45]0.4590.5356.36112.10
FW-GAN [10]0.6750.2838.01912.15
PBAFN [14]0.8700.1574.5168.690
ClothFormer [26]0.9210.0813.9675.048
LaDI-VTON [34]0.8780.1905.880-
StableVITON [56]0.8760.0764.0215.076
TunnelTry-on [51]0.9130.0543.3454.614
ViViD [12]0.9490.0683.4055.074
VITON-DiT [60]0.8960.0802.4980.187
GPD-VVTO [46]0.9280.0561.280-
DPIDM (Ours)0.9300.0410.5060.047
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.905, + 0.379 + ], + "angle": 0, + "content": "pairs of upper-body model and garment images, out of which 2,032 pairs were specifically reserved for testing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.906, + 0.547 + ], + "angle": 0, + "content": "Evaluation Metrics. For image datasets, we use Structural Similarity (SSIM) [47] and Learned Perceptual Image Patch Similarity (LPIPS) [55] to measure the similarity between the generated image and the ground-truth. Additionally, Fréchet Inception Distance(FID) [22] and Kernel Inception Distance(KID) [2] are employed to measure the quality and realism of the generated images. For video datasets, we further utilize Video Fréchet Inception Distance (VFID) [43] to evaluate spatiotemporal consistency. Two CNN backbones, I3D [4] and 3D-ResNeXt101 [20], are adopted as feature extractors for VFID." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.558, + 0.731, + 0.573 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.906, + 0.822 + ], + "angle": 0, + "content": "We initialize the main U-Net with the pre-trained SD v1.5 inpainting model and the garment U-Net with SD v1.5. The pose estimator is trained offline using YOLOv8 [38]. The pose encoder incorporates four convolutional layers to align the pose image with the noise latent at the same resolution. During training, all data is resized to a uniform resolution of \\(512 \\times 384\\). To improve model resilience, we employ data augmentation by randomly flipping images horizontally with a \\(50\\%\\) probability. We utilize the Adam optimizer [27] with a consistent learning rate of \\(2 \\times 10^{-5}\\). All the experiments are conducted using 16 NVIDIA A100 GPUs. Sequences of 24 frames are sampled, and the batch size \\(B\\) is set to 32. The model is trained for 80,000 iterations. The hyper-parameter \\(\\lambda\\) is set to \\(10^{-3}\\) for video datasets and 0 for image datasets. During inference, we utilize the DDIM [41] sampler and set the classifier-free guidance scale to 1.5." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.707, + 0.849 + ], + "angle": 0, + "content": "4.3.Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Video Virtual Try-On. We compare our DPIDM with a series of state-of-the-art virtual try-on methods, which can be grouped into two directions: GAN-based methods" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22653" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.138, + 0.09, + 0.437, + 0.104 + ], + "angle": 0, + "content": "Table 2. Comparison results on the ViViD dataset." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.116, + 0.47, + 0.201 + ], + "angle": 0, + "content": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
LaDI-VTON [34]0.8240.1648.2831.185
CAT-DM [54]0.8260.1629.3542.139
ViViD [12]0.8460.1181.8940.870
DPIDM (Ours)0.8830.0810.4880.090
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.207, + 0.483, + 0.25 + ], + "angle": 0, + "content": "Table 3. Quantitative results of image-based virtual try-on task on the VITON-HD dataset. \\(\\mathrm{FID}_u / \\mathrm{KID}_u\\) stands for the FID/KID score in unpaired setting. Note that the KID score is multiplied by 1000." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.261, + 0.469, + 0.449 + ], + "angle": 0, + "content": "
MethodSSIM↑LPIPS↓FIDu↓KIDu↓
VITON-HD [7]0.8620.11712.123.23
HR-VITON [30]0.8760.09612.313.81
GP-VTON [48]0.8900.0859.821.42
LaDI-VTON [34]0.8750.0919.321.55
WearAnyWay [5]0.8770.0788.160.78
DCI-VTON [16]0.8900.0728.770.89
StableVITON [56]0.8780.0759.431.54
CAT-DM [54]0.8770.0808.931.37
IDM [8]0.8810.0788.600.55
GPD-VVTO [46]0.8910.0708.570.78
DPIDM (Ours)0.8930.0678.150.32
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.484, + 0.901 + ], + "angle": 0, + "content": "[10, 14, 26, 45] and Diffusion-based methods [12, 34, 46, 51, 54, 56, 60]. Table 1 summarizes the performance comparisons on the VVT dataset. Notably, our DPIDM consistently outperforms other state-of-the-art methods across LPIPS and VFID metrics. Although ViViD [12] attains a higher SSIM score, its advantage is expected due to the utilization of a significantly larger volume of high-resolution videos during training, approximately six times more than the VVT dataset. Despite this, our DPIDM notably surpasses ViViD in the VFID metric, showcasing substantial enhancements in video coherence while preserving garment visual authenticity. ClothFormer improves FW-GAN by introducing an appearance-flow tracking module to ensure temporal consistency in garment warping. TunnelTry-on and ViViD further boost the performances by leveraging the capabilities of pre-trained diffusion models. Additionally, GPD-VVTO introduces garment-aware temporal attention to enhance temporal consistency, leading to a clear VFID score boost. However, existing approaches often neglect crucial spatiotemporal pose interactions between individuals and garments. In contrast, our DPIDM effectively models both intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware attention mechanisms, leading to superior results in the VVTON task. Specifically, our DPIDM achieves a \\(\\mathrm{VFID}_I\\) score of 0.506, marking a substantial \\(60.5\\%\\) relative improvement over the top competitor GPD-VVTO. Note that GPD-VVTO employs SD v2.1 for model initialization, whereas we choose SD v1.5 for fewer parameters." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.093, + 0.898, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.369, + 0.907, + 0.412 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison on the ViViD dataset. Our DPIDM excels in seamlessly integrating the garment with the wearer and maintaining the visual integrity of the garment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.43, + 0.907, + 0.534 + ], + "angle": 0, + "content": "Table 2 presents performance comparisons on the ViViD dataset. As observed with VVT, DPIDM consistently outperforms other VVTON methods across all metrics. which again evinces the pivotal merit of the pose-aware guidance for preserving spatiotemporal consistency in the generated videos. Particularly, DPIDM demonstrates a substantial relative improvement of \\(74.2\\%\\) over ViViD in \\(\\mathrm{VFID}_I\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.536, + 0.909, + 0.703 + ], + "angle": 0, + "content": "Image Virtual Try-On. Table 3 displays the quantitative results on the VITON-HD [7]. Following the official settings, we utilize SSIM and LPIPS metrics for the paired setting, and FID and KID for the unpaired setting. Our DPIDM consistently outperforms other methods across all metrics, showcasing its ability to produce authentic and lifelike images while maintaining the integrity of the initial garment structure. It is noteworthy that diffusion-based approaches exhibit lower FID and KID scores compared to GAN-based methods, suggesting that diffusion models excel in generating images with heightened fidelity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.696, + 0.728 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We conduct qualitative analysis from two aspects: visual authenticity of the garment and temporal consistency. When evaluating visual authenticity, we compare results from several virtual try-on methods using individual video frames, as illustrated in Figure 4. In the first row, LaDI-VTON and CAT-DM change the style of the target garment and introduce color discrepancies. While ViViD achieves a natural fit, it struggles to maintain the original patterns, leading to their displacement on the garment. In contrast, our method excels in seamlessly blending the garment with the wearer while preserving intricate fabric patterns. Moving" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22654" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.885, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.354, + 0.904, + 0.368 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on the ViViD dataset. Our DPIDM maintains temporal consistency even during substantial movements." + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.379, + 0.482, + 0.394 + ], + "angle": 0, + "content": "Table 4. Performance contribution of each component in DPIDM." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.405, + 0.475, + 0.488 + ], + "angle": 0, + "content": "
idPAATSATRASSIM↑LPIPS↓VFIDI↓VFIDR↓
(a)XXX0.8930.0843.4512.435
(b)✓XX0.9250.0501.0680.153
(c)✓✓X0.9290.0430.7210.075
(d)✓✓✓0.9300.0410.5060.047
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.505, + 0.483, + 0.746 + ], + "angle": 0, + "content": "to the second row with a pair of striped shorts, competitors maintain the garment's style but exhibit noticeable artifacts around the legs. Conversely, our method adeptly addresses these issues by naturally supplementing missing skin tones while upholding the garment's visual integrity. This trend continues in the subsequent example with a dress in the third row, highlighting the effectiveness of DPIDM. To further evaluate temporal consistency, we extract four frames at equal intervals from the generated video and present them in Fig. 5. While ViViD achieves a natural fit in individual frames, it struggles to maintain garment details and temporal consistency across frames, especially during person movements. In contrast, our DPIDM consistently delivers high-quality results that preserve garment details and ensure temporal consistency without introducing artifacts, even during actions involving significant movements." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.758, + 0.255, + 0.772 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this study, we analyze the impact of each design element within DPIDM on the overall performance using the VVT dataset. As shown in Table 4, the proposed elements are denoted as follows: PAA refers to pose-aware attention, TSA to temporal-shift attention, and TRA to temporal regularized attention loss. We start with a basic model (a) that directly inserts standard temporal attention after each stage of the main U-Net. Subsequently, in (b), we substitute the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.907, + 0.624 + ], + "angle": 0, + "content": "standard spatial/temporal attention with our proposed pose-aware spatial/temporal attention. Notably, the introduction of \\( PAA \\) yields a significant performance enhancement over (a), surpassing even the state-of-the-art methods detailed in Table 1. This not only validates the efficacy of our proposed pose-aware spatial/temporal attention but also underscores the critical role of integrating spatiotemporal pose interactions into the VVTON task. Furthermore, we introduce the temporal-shift attention and the temporal regularized attention loss in (c) and (d) respectively. While TSA and TRA did not result in significant enhancements in the SSIM and LPIPS metrics, they notably improved the VFID metric, highlighting their effectiveness in enhancing video consistency. Collectively, the innovative modules introduced in DPIDM enhance the visual integrity of the garment and improve the temporal consistency of the generated videos." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.634, + 0.634, + 0.65 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this work, we have presented Dynamic Pose Interaction Diffusion Models (DPIDM), a novel approach that capitalizes on spatial and temporal pose interactions to enhance video virtual try-on. Particularly, we study the problem from the viewpoint of employing intra-frame human-garment pose interactions and long-term human pose dynamics across frames. To verify our claim, we develop a hierarchical pose-aware attention module to integrate human and garment pose features into spatial and temporal attention, enhancing the temporal coherence of the generated videos while preserving the visual fidelity of the garments. Additionally, a new temporal regularized attention loss is devised to bolster consistency across successive frames. Through extensive experiments, we demonstrate that our DPIDM surpasses existing state-of-the-art methods on image-based and video-based virtual try-on datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22655" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.114, + 0.486, + 0.158 + ], + "angle": 0, + "content": "This work was supported in part by the Beijing Municipal Science and Technology Project No. Z241100001324002 and Beijing Nova Program No. 20240484681." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.184, + 0.188, + 0.2 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.21, + 0.484, + 0.265 + ], + "angle": 0, + "content": "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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The primary challenge involves preserving the visual authenticity of the garment while dynamically adapting to the pose and physique of the subject. While existing methods have predominantly focused on image-based virtual try-on, extending these techniques directly to videos often results in temporal inconsistencies. Most current video virtual try-on approaches alleviate this challenge by incorporating temporal modules, yet still overlook the critical spatiotemporal pose interactions between human and garment. Effective pose interactions in videos should not only consider spatial alignment between human and garment poses in each frame but also account for the temporal dynamics of human poses throughout the entire video. With such motivation, we propose a new framework, namely Dynamic Pose Interaction Diffusion Models (DPIDM), to leverage diffusion models to delve into dynamic pose interactions for video virtual try-on. Technically, DPIDM introduces a skeleton-based pose adapter to integrate synchronized human and garment poses into the denoising network. A hierarchical attention module is then exquisitely designed to model intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware spatial and temporal attention mechanisms. Moreover, DPIDM capitalizes on a temporal regularized attention loss between consecutive frames to enhance temporal consistency. Extensive experiments conducted on VITON-HD, VVT and ViViD datasets demonstrate the superiority of our DPIDM against the baseline methods. Notably, DPIDM achieves VFID score of 0.506 on VVT dataset, leading to $60.5\%$ improvement over the state-of-the-art GPD-VVTO approach. + +![](images/4b7fb5f9df07272c629b1bf8ffc3b5296feeeb926a403fbe3c9297e00854895f.jpg) +Figure 1. Given a garment and a person video, DPIDM generates a lifelike video that preserves the visual authenticity of the garment while adapting to the individual's pose and physique. + +# 1. Introduction + +Generative models have made tremendous progress in recent years, with wide-ranging applications across various fields, including computer vision [9, 36, 59], computer graphics [6, 13], aesthetic design [35], and medical research [18]. Virtual try-on is a quintessential generative task that aims to synthesize a lifelike image/video of the specific person wearing the provided garment. By harnessing the powerful generative capacities of diffusion models, this field has emerged as a promising domain with versatile applications in immersive e-commerce and short-form video platforms. + +Prior research mainly focused on image-based virtual try-on. The earlier approaches typically build on Generative Adversarial Networks (GANs) [7, 19, 39, 45], incorporating a warping module alongside a try-on generator. The warping module deforms clothing to align with the human body, and then the warped garment is fused with the person image through the try-on generator. However, in light of the recent emergence of UNet-based Latent Diffusion Models (LDMs) [5, 8, 50, 56, 62], researchers have progressively directed their focus towards these innovative models. A diffusion-based try-on network combines the warping and blending + +processes into a unified operation of cross-attention without explicit segregation. By employing pre-trained text-to-image weights, these diffusion approaches demonstrate superior fidelity compared to their GAN-based counterparts. + +In recent years, researchers have endeavored to replicate the success of image try-on within the realm of video. One direct approach involves applying image try-on techniques to process videos frame by frame. However, this method often results in notable inter-frame inconsistencies. To address this challenge, various specialized designs have been explored for video virtual try-on [10, 26, 28, 61]. These approaches commonly integrate optical flow prediction modules to warp frames produced by the try-on generator. Despite reasonable performance, GAN-based methods encounter difficulties in handling garment-person misalignment, particularly when faced with inaccurate warping flow estimations. To harness the capabilities of pretrained image-based diffusion models, TunnelTry-on [51] and ViViD [12] utilize a pre-trained inpainting U-Net as the primary branch and integrate a reference U-Net to capture detailed clothing features. They enhance temporal consistency by incorporating standard temporal attention after each stage of the main U-Net. GPD-VVTO [46] takes a step further by integrating garment features into temporal attention, enabling the model to better preserve fidelity to the garment during temporal modeling. Despite showing promise, these methods struggle to maintain both visual integrity and motion consistency simultaneously, particularly when there is a significant stylistic gap between the garment being tried on and the original one. To alleviate these issues, we argue that two key ingredients should be taken into account. One is spatial alignment between human and garment poses within each frame. Such alignment is essential for virtual try-on as it ensures that clothing adapts appropriately to factors like coverage and wrinkles based on the individual's posture. The other is the temporal dynamics of human poses across the entire video. A comprehensive understanding of this long-term interaction is paramount for upholding temporal coherence, given that human movements naturally progress as a continuum of interconnected poses. + +By consolidating the idea of modeling both spatial and temporal pose interactions in a video, we novelly present Dynamic Pose Interaction Diffusion Models (DPIDM) for boosting video virtual try-on. Specifically, DPIDM employs a dual-branch architecture, where the Main U-Net conducts denoising processes on the video, while the Garment U-Net extracts intricate details from the garment image and integrates them into the Main U-Net. This architecture facilitates a holistic understanding of the relationship between humans and garments within a unified feature space. To effectively leverage the spatiotemporal pose interactions in videos, we introduce a skeleton-based pose adapter that seamlessly integrates synchronized human and + +garment poses into the Main U-Net. With the adapter, we present a hierarchical attention module comprising four key components: a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block. The pose-aware spatial attention block plays a crucial role in capturing intricate intra-frame human-garment pose interactions, while the pose-aware temporal attention block models the long-term dynamics of human poses across frames. Moreover, a temporal regularized attention loss is defined on consecutive frames to ensure temporal coherence. As a result, our DPIDM excels in generating videos with meticulously aligned garment details and enhanced temporal stability. + +The main contribution of this work is the proposal of Dynamic Pose Interaction Diffusion Models that facilitate the video virtual try-on (VVTON) task. This also leads to the elegant view of how a diffusion model should be designed for excavating the pose-focused prior knowledge (e.g., spatial pose alignment and temporal pose dynamics) tailored to VVTON, and how to improve diffusion process with these amplified pose-focused guidance. Through an extensive set of experiments on VITON-HD, VVT, and ViViD datasets, DPIPM consistently achieves superior results over state-of-the-art methods in both image and video virtual try-on tasks. + +# 2. Related Works + +# 2.1. Image-based Virtual Try-on + +The development of image-based virtual try-on is largely inspired by the success of GANs [15], leading to pioneering works such as [7, 11, 19, 31, 33, 45]. A standard GAN-based virtual try-on framework typically adheres to a two-stage paradigm. The initial stage involves an image warping process, such as Thin Plate Spline (TPS) warping [19], which aligns the garment with the target individual's body. In the second stage, a GAN-based try-on generator merges the warped attire with the target individual's clothing-agnostic representation to produce authentic try-on outcomes. However, these methods heavily rely on the warping module to preserve garment details and often suffer from performance degradation due to inaccurate warping. + +Recently, with the powerful generative capabilities of Latent Diffusion Models (LDMs), many diffusion-based models have been introduced to generate more realistic virtual try-on results [5, 44, 52, 54, 56, 62]. TryOnDiffusion [62] was the first to propose a dual U-Net architecture that simultaneously preserves garment details and implicitly warps the garment to match the target pose. StableVITON [56] introduced a zero cross-attention block to learn the semantic correspondence between the garment and the target person. Wear-any-way [5] utilized a sparse point control method to align person and garment features in feature space. MMTryon [57] presented a multi-modal, multi + +![](images/a1b9dce895c76998357be45785afb8f4cd657730040a812ca3b05b776cd2007b.jpg) +Figure 2. (a) Overall architecture of DPIDM. DPIDM employs a dual-branch architecture. The main U-Net processes a concatenated input comprising the noisy latent of the video, the latent of the cloth-agnostic video, and the cloth-agnostic mask sequence. The garment U-Net extracts fine-grained garment features, which are subsequently integrated into the main U-Net. The pose estimator is utilized to extract aligned human and garment poses, which are then fed into the attention modules of the main U-Net to guide the diffusion process. The VAE is not shown for clarity. (b) Detailed illustration of the proposed pose-aware attention module within the main U-Net. The module comprises pose-aware spatial attention, temporal-shift attention, cross-attention, and pose-aware temporal attention. The pose embeddings are seamlessly integrated into the attention module through a specialized pose adapter. (better viewed in color) + +![](images/6d6bc78bf275bd216cafe75ac1ee557bd4869c7a082904da1f27c54158881fcb.jpg) + +garment virtual try-on approach that combines text and multiple reference images to create a multimodal embedding as a condition to control the diffusion model. IDM [8] proposed a RefNet-style architecture to align the feature space between garment and person. Although these diffusion-based methods have achieved high-fidelity results in single-image inference, their application to video virtual try-on reveals a crucial limitation: the oversight of inter-frame relationships. This deficiency results in notable inter-frame inconsistencies, ultimately yielding unsatisfactory outcomes. + +# 2.2. Video-based Virtual Try-on + +In recent studies, researchers have aimed to expand the capabilities of image-based try-on approaches into video applications. A key issue in video generation is inter-frame inconsistency. ClothFormer [26] leverages optical flow in the warping and blending processes to achieve temporal smoothing. Recently, diffusion-based video virtual try-on methods have been introduced to generate more realistic results [12, 21, 46, 51, 60]. For instance, TunnelTry-on [51] proposed a focus-tunnel method that crops the human image according to the pose map, aligning the try-on image to accommodate scenarios where the person is off-center in the frame. VTON-DiT [60] introduced a DiT architecture compatible with OpenSora, where the clothing-agnostic human image is provided via ControlNet. WildVidFit [21] proposed an image-based diffusion model and used video MAE to update the intermediate representations of the diffusion process to improve frame consistency. ViViD [12] + +introduced a large-scale video try-on dataset and proposed an additional reference-based U-Net. GPD-VVTON [46] went a step further by integrating garment features into temporal attention to generate spatio-temporally consistent results. While these explorations of video try-on make steady advancements, they currently struggle to accurately capture the dynamic interaction between clothing and the human body in real-world scenarios. Our method employs a hierarchical attention module to capture the critical spatiotemporal pose interactions between the human and the garment. + +# 3. Methodology + +In this paper, we present Dynamic Pose Interaction Diffusion Models (DPIDM), a pioneering framework based on latent diffusion models designed to enhance the VVTON task. The complete architecture is depicted in Figure 2 (a). This section begins with a brief introduction to Stable Diffusion [39] in Section 3.1 to lay the groundwork for subsequent discussions. Subsequently, we offer a comprehensive overview of DPIDM in Section 3.2, and delve into the specific design details in Section 3.3-3.5. Finally, we encapsulate our training and inference strategies in Section 3.6. + +# 3.1. Preliminary + +Stable Diffusion (SD) stands out as one of the most prevalent latent diffusion models within the community. It leverages a variational autoencoder (VAE) architecture, comprising an encoder $\mathcal{E}$ and a decoder $\mathcal{D}$ , to facilitate image rep + +resentations in the latent space. Additionally, a U-Net [40] $\epsilon_{\theta}$ is trained to denoise a Gaussian noise $\epsilon$ with a conditioning input encoded by a CLIP text encoder [37] $\tau_{\theta}$ . Given an image $\mathbf{x}$ and a text prompt $\mathbf{y}$ , the denoising U-Net $\epsilon_{\theta}$ undergoes training by minimizing the loss function: + +$$ +\mathcal {L} _ {L D M} = \mathbb {E} _ {\mathcal {E} (\mathbf {x}), \mathbf {y}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, t, \tau_ {\theta} (\mathbf {y})) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $t$ denotes the time step of the forward diffusion process, and $\mathbf{z}_t$ is the noisy latent constructed by adding Gaussian noise $\epsilon \sim \mathcal{N}(0,1)$ to the encoded image $\mathcal{E}(\mathbf{x})$ . During the inference stage, $\mathbf{z}_t$ is randomly sampled from a Gaussian distribution and iteratively denoised to derive $\mathbf{z}_0$ following a predefined sampling schedule [23, 41]. Finally, the latent decoder $\mathcal{D}$ decodes $\mathbf{z}_0$ back into the image space. + +# 3.2. Overview + +The overall architecture of DPIDM is depicted in Fig. 2. DPIDM takes a reference garment image $\pmb{G} \in \mathbb{R}^{3 \times H \times W}$ and a source human video $\pmb{I}_S \in \mathbb{R}^{T \times 3 \times H \times W}$ as input, where $H$ and $W$ represent the height and width of each frame, and $T$ signifies the video length. Its objective is to generate a realistic video $\hat{\pmb{I}} \in \mathbb{R}^{T \times 3 \times H \times W}$ showing the individual in $\pmb{I}_S$ adorned in the garment $\pmb{G}$ . + +We approach the video virtual try-on as a video inpainting challenge, aimed at integrating the garment onto clothing-agnostic areas. To achieve this, DPIDM employs a dual-branch architecture. The main U-Net is the inpainting model initialized with the pre-trained weights from SD. It takes in a 9-channel tensor comprising 4 channels for the noisy latent of the video, 4 channels for the clothing-agnostic video latent, and 1 channel for the binary agnostic mask sequence. In contrast to the original SD model, which utilizes text embeddings to guide the diffusion process, we have substituted these embeddings with image embeddings derived from a CLIP image encoder representing the garment image. While the CLIP image embedding effectively captures the overall colors and textures of the garment, it may not retain finer details. To address this, we also use a Garment U-Net to extract detailed garment features. The Garment U-Net follows a standard text-to-image diffusion model with a 4-channel input. This dual-branch architecture has proven to be effective by previous works [12, 46, 51]. + +To further enhance the generation, we incorporate human and garment poses as supplementary guidance to refine the diffusion process. We develop a light-weight pose encoder to extract features of the pose maps and a pose adapter to inject these features into the attention modules of the main U-Net. The human/garment pose maps are derived from the input video/image with pose estimator. + +# 3.3. Pose Estimator + +We directly employ DW-Pose [53] to estimate human poses $P_{h}$ from video frames. However, there is a lack of an open- + +![](images/869db8ec1e0cbba932b5ca4ec03ae3bd51cc706d13162a512814997a7d2ce1d6.jpg) +Figure 3. Visualization of predicted human and garment poses. + +source garment pose estimator currently. To establish alignment between human and garment poses, we train a garment pose estimator to predict a set of landmarks $P_{g}$ that correspond to various parts of the human pose $P_{h}$ . The ground truth of $P_{g}$ is labeled manually, with the number of landmarks varying based on the garment types. For instance, in upper clothing, $|P_{g}| = 9$ , encompassing landmarks such as the neck, shoulders, elbows, wrists, and hips. These landmarks serve as explicit indicators of the alignment between human and garment poses, and therefore can be used as guidance to improve the diffusion process. The visualization of human and garment poses is shown in Fig. 3. + +# 3.4. Dynamic Pose Interaction + +To facilitate the dynamic pose interaction, we propose a hierarchical attention module consisting of a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block. + +Pose-aware Spatial Attention (PASA). To capture intricate intra-frame human-garment pose interactions, we inject the features of human and garment poses into the spatial attention layer. In our baseline, the human feature map $\mathbf{f}_h$ from the main U-Net is concatenated with the corresponding garment feature map $\mathbf{f}_g$ from the garment U-Net to jointly compute self-attention, which is computed as: + +$$ +\boldsymbol {h} = \operatorname {A t t n} \left(\psi_ {q} (\mathbf {f}), \psi_ {k} (\mathbf {f}), \psi_ {v} (\mathbf {f})\right), \tag {2} +$$ + +where $\mathbf{f} = [\mathbf{f}_h,\mathbf{f}_g]$ is the concatenation of human feature map and garment feature map in the spatial dimension, and $\psi_q,\psi_k,\psi_v$ are linear projections. Afterward, only the half feature from the main U-Net undergoes further computation. This attention layer enables garment features extracted by the garment U-Net to be integrated into the main U-Net. + +To enable the correspondence control with pose guidance, we modify this attention layer by adding the pose embeddings of the human and garment. Formally, given the human pose embedding $\mathbf{p}_h$ and garment pose embedding $\mathbf{p}_g$ extracted from the pose encoder, we first concatenate them in spatial dimension $\mathbf{p} = [\mathbf{p}_h,\mathbf{p}_g]$ . Then we utilize a pose adapter to project $\mathbf{p}$ into the diffusion feature space. The pose adapter employs two fully connected (FC) layers with an intermediate activation layer. The first FC layer maps the input to a lower-dimensional space, while the second FC layer maps it back to the original dimensional. The pose adapter can be written as: + +$$ +A d p t (\mathbf {p}) = \mathbf {W} _ {u p} (G E L U (\mathbf {W} _ {d o w n} (\mathbf {p}))), \tag {3} +$$ + +where $\mathbf{W}_{up}$ and $\mathbf{W}_{down}$ are the learnable weight matrix. To preserve the original feature space of diffusion models, we initialize $\mathbf{W}_{up}$ with zeros. Subsequently, we add the diffusion feature $\mathbf{f}$ and the adapter embedding $Adpt(\mathbf{p})$ together and feed them into the self-attention mechanism, leading to the revised form of Eq. 2: + +$$ +\boldsymbol {h} = \operatorname {A t t n} \left(\psi_ {q} (\mathbf {f} + \operatorname {A d p t} (\mathbf {p})) , \psi_ {k} (\mathbf {f} + \operatorname {A d p t} (\mathbf {p})) , \psi_ {v} (\mathbf {f} + \operatorname {A d p t} (\mathbf {p}))\right). \tag {4} +$$ + +In this way, when integrating the garment feature into the main U-Net, the feature aggregation process takes into account the alignment of human and garment poses. This implicit consideration results in the garment being deformed to better fit the natural pose of the person. + +Existing PoseGuider-style methods [24, 46, 51] typically achieve pose control by directly adding processed human pose images and noisy latents as inputs to the first layer of the diffusion network, without incorporating pose information into the attention modules. In contrast, our PASA introduces pose information into each layer's attention modules through a pose adapter, enabling more precise and varying degrees of pose control. Moreover, besides human poses, we further inject garment poses into PASA, thus achieving intricate intra-frame human-garment pose alignment. + +Temporal-shift Attention (TSA). In the original SD model, the attention block of the U-Net solely focuses on self-attention within individual frames, overlooking valuable information across frames. Current VVTON techniques predominantly integrate a temporal attention layer at each stage to capture temporal dependencies among video frames. Nevertheless, this approach can introduce a covariate shift in the feature space, potentially undermining the model's generative capacity [58]. While a direct remedy could involve joint space-time 3D attention, this method escalates the complexity of attention calculations quadratically. Drawing inspiration from prior works [1, 32, 49], a novel approach involves employing temporal shift operations that utilize a 2D module to amalgamate spatial and temporal information by incorporating neighboring frame data into the current frame. Specifically, in addition to examining tokens within the present frame, a patch-level shifting operation transpires along the temporal dimension, transferring tokens from the preceding $L$ frames to the current frame, thereby constructing a novel latent feature frame. We concatenate the latent feature of the current frame $\mathbf{h}$ with the temporally shifted latent feature $\mathbf{h}_{shift}$ in the spatial dimension, thus establishing keys and values for subsequent self-attention mechanisms. The temporal-shift attention can be formally written as: + +$$ +\hat {\boldsymbol {h}} = \operatorname {A t t n} \left(\psi_ {q} (\mathbf {h}), \psi_ {k} \left(\left[ \mathbf {h}, \mathbf {h} _ {\text {s h i f t}} \right]\right), \psi_ {v} \left(\left[ \mathbf {h}, \mathbf {h} _ {\text {s h i f t}} \right]\right). \right. \tag {5} +$$ + +It notably reduces the computational load when juxtaposed with 3D attention. Furthermore, it empowers the model to discern short-term relationships between adjacent frames, enhancing temporal coherence during video generation. + +Cross-Attention (CA). In contrast to the original SD model, which employs text embeddings to steer the diffusion process with cross-attention, we have replaced these embeddings with garment image embeddings generated from a CLIP image encoder. These embeddings encapsulate comprehensive global information like color and style, which serve as a valuable supplement to the detailed appearance characteristics provided by the Garment U-Net. + +Pose-aware Temporal Attention (PATA). Although TSA can effectively capture short-term relationships between adjacent frames, it fails to consider the long-term temporal dynamics across the entire video. Previous studies [12, 17, 24] have introduced a plug-and-play motion module with temporal attention to enhance video smoothness. However, these approaches overlook the dynamic changes in human poses, which are crucial for the VVTON task where garment appearance must adapt to individual poses. To address this limitation, we propose a pose-aware temporal attention. Similar to PASA, our method involves feeding the human pose embedding $\mathbf{p}_h$ into a pose adapter. This adapted embedding is then element-wise added to the output feature of the cross-attention block, followed by standard temporal attention. Our experiments have demonstrated that this straightforward strategy significantly improves video continuity and enhances the realism of clothing dynamics in motion, as shown in Fig. 5. + +# 3.5. Temporal Regularized Attention Loss + +Generally, SD is merely optimized with the mean-squared loss defined in Eq. 1, which treats all regions of the synthesized video equally without emphasizing temporal consistency. Inspired by the idea that self-attention maps within diffusion models capture the structural essence of generated content [3, 25, 29, 42], we employ the temporal regularized attention loss. This loss function is designed to minimize variations in self-attention maps across successive frames: + +$$ +\mathcal {L} _ {\mathrm {T R A}} = \sum_ {i} ^ {N} \sum_ {j = 2} ^ {T} \gamma_ {i} \left| \mathcal {A} _ {i} ^ {(j)} - \mathcal {A} _ {i} ^ {(j - 1)} \right|, \tag {6} +$$ + +where $\mathcal{A}_i^{(j)}$ represents the self-attention map of the PASA block in the $i$ -th layer on $j$ -th frame. Specifically, We calculate $L_{TRA}$ only on the last two decoder layers in the main U-Net, with $\gamma_i = 0.5$ in our context. + +# 3.6. Training and Inference + +Training Strategy. Different from previous multi-stage training approaches [46, 51], we employ a single-stage training strategy. The loss function is defined as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {L D M} + \lambda \mathcal {L} _ {T R A}, \tag {7} +$$ + +where $\lambda$ is the hyper-parameter used to balance the MSE loss and the proposed TRA loss. When training with image datasets, the TSA and PATA blocks are omitted. As for + +video datasets, we implement an image-video joint training strategy. Initially, we randomly pick $B$ videos from the dataset and extract a single frame randomly from each video for training. At this stage, solely the PASA and CA modules undergo training. Subsequently, in the following phase, another set of $B$ videos is randomly chosen and a sequence of $T$ consecutive frames is extracted from each video for training purposes. Here, the training focuses exclusively on the TSA and PATA modules. This process repeats iteratively until the training concludes. Here, $B$ represents the batch size, and $T$ symbolizes the length of video clips. This training methodology effectively reduces the GPU memory requirements and enhances the speed of convergence. + +To tackle discontinuous pose sequences, we also implement a condition dropping strategy during training. Specifically, each pose keypoint has a 0.05 probability of being dropped. When a keypoint of the current frame is dropped, the model is forced to refer to the poses of adjacent frames to infer the correct pose of the current frame. This strategy not only enhances the model's robustness to pose estimation methods but also improves temporal consistency. + +Inference Strategy. To improve temporal coherence and smoothness in long videos, we follow [12, 46] and implement a sliding window approach during inference. It involves dividing the long video into overlapping segments of a specified length $T$ and conducting inference on each segment. For overlapping frames, the ultimate output is derived by averaging the results obtained from each inference. + +# 4. Experiments + +# 4.1. Datasets + +Video Virtual Try-On. We empirically verify and analyze the effectiveness of our DPIDM on two popular video virtual try-on datasets, VVT [10] and ViViD [12]. The VVT dataset contains 791 video clips with a resolution of 256 $\times$ 192. Following the official settings[10, 51], we partition it into a training set of 661 clips and a test set of 130 clips. However, the VVT dataset exhibits limited diversity in terms of garment varieties and human actions. ViViD, a recent and challenging dataset, includes 9,700 video-image pairs at a resolution of $832 \times 624$ . It classifies garments into three categories: upper-body, lower-body, and dresses. The dataset is divided into 7,759 videos for training and 1,941 videos for testing. It is worth noting that due to inaccuracies in the provided cloth-agnostic masks for individuals in a back-facing posture, we excluded video segments depicting such scenarios from the original footage. Consequently, only the remaining segments were utilized for testing. + +Image Virtual Try-On. To further validate the effectiveness of our method, we carried out additional experiments on the widely recognized image-based virtual try-on dataset, VITON-HD [7]. This dataset comprises 13,679 + +Table 1. Comparison results on the VVT dataset. $\mathrm{VFID}_I$ and $\mathrm{VFID}_R$ represent $\mathrm{VFID}_{I3D}$ and $\mathrm{VFID}_{ResNeXt}$ respectively. $\uparrow$ denotes higher is better, while $\downarrow$ indicates lower is better. + +
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
CP-VTON [45]0.4590.5356.36112.10
FW-GAN [10]0.6750.2838.01912.15
PBAFN [14]0.8700.1574.5168.690
ClothFormer [26]0.9210.0813.9675.048
LaDI-VTON [34]0.8780.1905.880-
StableVITON [56]0.8760.0764.0215.076
TunnelTry-on [51]0.9130.0543.3454.614
ViViD [12]0.9490.0683.4055.074
VITON-DiT [60]0.8960.0802.4980.187
GPD-VVTO [46]0.9280.0561.280-
DPIDM (Ours)0.9300.0410.5060.047
+ +pairs of upper-body model and garment images, out of which 2,032 pairs were specifically reserved for testing. + +Evaluation Metrics. For image datasets, we use Structural Similarity (SSIM) [47] and Learned Perceptual Image Patch Similarity (LPIPS) [55] to measure the similarity between the generated image and the ground-truth. Additionally, Fréchet Inception Distance(FID) [22] and Kernel Inception Distance(KID) [2] are employed to measure the quality and realism of the generated images. For video datasets, we further utilize Video Fréchet Inception Distance (VFID) [43] to evaluate spatiotemporal consistency. Two CNN backbones, I3D [4] and 3D-ResNeXt101 [20], are adopted as feature extractors for VFID. + +# 4.2. Implementation Details + +We initialize the main U-Net with the pre-trained SD v1.5 inpainting model and the garment U-Net with SD v1.5. The pose estimator is trained offline using YOLOv8 [38]. The pose encoder incorporates four convolutional layers to align the pose image with the noise latent at the same resolution. During training, all data is resized to a uniform resolution of $512 \times 384$ . To improve model resilience, we employ data augmentation by randomly flipping images horizontally with a $50\%$ probability. We utilize the Adam optimizer [27] with a consistent learning rate of $2 \times 10^{-5}$ . All the experiments are conducted using 16 NVIDIA A100 GPUs. Sequences of 24 frames are sampled, and the batch size $B$ is set to 32. The model is trained for 80,000 iterations. The hyper-parameter $\lambda$ is set to $10^{-3}$ for video datasets and 0 for image datasets. During inference, we utilize the DDIM [41] sampler and set the classifier-free guidance scale to 1.5. + +# 4.3.Quantitative Results + +Video Virtual Try-On. We compare our DPIDM with a series of state-of-the-art virtual try-on methods, which can be grouped into two directions: GAN-based methods + +Table 2. Comparison results on the ViViD dataset. + +
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
LaDI-VTON [34]0.8240.1648.2831.185
CAT-DM [54]0.8260.1629.3542.139
ViViD [12]0.8460.1181.8940.870
DPIDM (Ours)0.8830.0810.4880.090
+ +Table 3. Quantitative results of image-based virtual try-on task on the VITON-HD dataset. $\mathrm{FID}_u / \mathrm{KID}_u$ stands for the FID/KID score in unpaired setting. Note that the KID score is multiplied by 1000. + +
MethodSSIM↑LPIPS↓FIDu↓KIDu↓
VITON-HD [7]0.8620.11712.123.23
HR-VITON [30]0.8760.09612.313.81
GP-VTON [48]0.8900.0859.821.42
LaDI-VTON [34]0.8750.0919.321.55
WearAnyWay [5]0.8770.0788.160.78
DCI-VTON [16]0.8900.0728.770.89
StableVITON [56]0.8780.0759.431.54
CAT-DM [54]0.8770.0808.931.37
IDM [8]0.8810.0788.600.55
GPD-VVTO [46]0.8910.0708.570.78
DPIDM (Ours)0.8930.0678.150.32
+ +[10, 14, 26, 45] and Diffusion-based methods [12, 34, 46, 51, 54, 56, 60]. Table 1 summarizes the performance comparisons on the VVT dataset. Notably, our DPIDM consistently outperforms other state-of-the-art methods across LPIPS and VFID metrics. Although ViViD [12] attains a higher SSIM score, its advantage is expected due to the utilization of a significantly larger volume of high-resolution videos during training, approximately six times more than the VVT dataset. Despite this, our DPIDM notably surpasses ViViD in the VFID metric, showcasing substantial enhancements in video coherence while preserving garment visual authenticity. ClothFormer improves FW-GAN by introducing an appearance-flow tracking module to ensure temporal consistency in garment warping. TunnelTry-on and ViViD further boost the performances by leveraging the capabilities of pre-trained diffusion models. Additionally, GPD-VVTO introduces garment-aware temporal attention to enhance temporal consistency, leading to a clear VFID score boost. However, existing approaches often neglect crucial spatiotemporal pose interactions between individuals and garments. In contrast, our DPIDM effectively models both intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware attention mechanisms, leading to superior results in the VVTON task. Specifically, our DPIDM achieves a $\mathrm{VFID}_I$ score of 0.506, marking a substantial $60.5\%$ relative improvement over the top competitor GPD-VVTO. Note that GPD-VVTO employs SD v2.1 for model initialization, whereas we choose SD v1.5 for fewer parameters. + +![](images/d2ecb45cdfd86fa2e1368630fb003dd58f92ba506159068f7a5955ba0a23c986.jpg) +Figure 4. Qualitative comparison on the ViViD dataset. Our DPIDM excels in seamlessly integrating the garment with the wearer and maintaining the visual integrity of the garment. + +Table 2 presents performance comparisons on the ViViD dataset. As observed with VVT, DPIDM consistently outperforms other VVTON methods across all metrics. which again evinces the pivotal merit of the pose-aware guidance for preserving spatiotemporal consistency in the generated videos. Particularly, DPIDM demonstrates a substantial relative improvement of $74.2\%$ over ViViD in $\mathrm{VFID}_I$ + +Image Virtual Try-On. Table 3 displays the quantitative results on the VITON-HD [7]. Following the official settings, we utilize SSIM and LPIPS metrics for the paired setting, and FID and KID for the unpaired setting. Our DPIDM consistently outperforms other methods across all metrics, showcasing its ability to produce authentic and lifelike images while maintaining the integrity of the initial garment structure. It is noteworthy that diffusion-based approaches exhibit lower FID and KID scores compared to GAN-based methods, suggesting that diffusion models excel in generating images with heightened fidelity. + +# 4.4. Qualitative Results + +We conduct qualitative analysis from two aspects: visual authenticity of the garment and temporal consistency. When evaluating visual authenticity, we compare results from several virtual try-on methods using individual video frames, as illustrated in Figure 4. In the first row, LaDI-VTON and CAT-DM change the style of the target garment and introduce color discrepancies. While ViViD achieves a natural fit, it struggles to maintain the original patterns, leading to their displacement on the garment. In contrast, our method excels in seamlessly blending the garment with the wearer while preserving intricate fabric patterns. Moving + +![](images/c38118303f52f5ea54d65bd8c7305c41fa89baf7b6146cc26931c3619e3bc97d.jpg) +Figure 5. Qualitative comparison on the ViViD dataset. Our DPIDM maintains temporal consistency even during substantial movements. + +Table 4. Performance contribution of each component in DPIDM. + +
idPAATSATRASSIM↑LPIPS↓VFIDI↓VFIDR↓
(a)XXX0.8930.0843.4512.435
(b)✓XX0.9250.0501.0680.153
(c)✓✓X0.9290.0430.7210.075
(d)✓✓✓0.9300.0410.5060.047
+ +to the second row with a pair of striped shorts, competitors maintain the garment's style but exhibit noticeable artifacts around the legs. Conversely, our method adeptly addresses these issues by naturally supplementing missing skin tones while upholding the garment's visual integrity. This trend continues in the subsequent example with a dress in the third row, highlighting the effectiveness of DPIDM. To further evaluate temporal consistency, we extract four frames at equal intervals from the generated video and present them in Fig. 5. While ViViD achieves a natural fit in individual frames, it struggles to maintain garment details and temporal consistency across frames, especially during person movements. In contrast, our DPIDM consistently delivers high-quality results that preserve garment details and ensure temporal consistency without introducing artifacts, even during actions involving significant movements. + +# 4.5. Ablation Studies + +In this study, we analyze the impact of each design element within DPIDM on the overall performance using the VVT dataset. As shown in Table 4, the proposed elements are denoted as follows: PAA refers to pose-aware attention, TSA to temporal-shift attention, and TRA to temporal regularized attention loss. We start with a basic model (a) that directly inserts standard temporal attention after each stage of the main U-Net. Subsequently, in (b), we substitute the + +standard spatial/temporal attention with our proposed pose-aware spatial/temporal attention. Notably, the introduction of $PAA$ yields a significant performance enhancement over (a), surpassing even the state-of-the-art methods detailed in Table 1. This not only validates the efficacy of our proposed pose-aware spatial/temporal attention but also underscores the critical role of integrating spatiotemporal pose interactions into the VVTON task. Furthermore, we introduce the temporal-shift attention and the temporal regularized attention loss in (c) and (d) respectively. While TSA and TRA did not result in significant enhancements in the SSIM and LPIPS metrics, they notably improved the VFID metric, highlighting their effectiveness in enhancing video consistency. Collectively, the innovative modules introduced in DPIDM enhance the visual integrity of the garment and improve the temporal consistency of the generated videos. + +# 5. Conclusion + +In this work, we have presented Dynamic Pose Interaction Diffusion Models (DPIDM), a novel approach that capitalizes on spatial and temporal pose interactions to enhance video virtual try-on. Particularly, we study the problem from the viewpoint of employing intra-frame human-garment pose interactions and long-term human pose dynamics across frames. To verify our claim, we develop a hierarchical pose-aware attention module to integrate human and garment pose features into spatial and temporal attention, enhancing the temporal coherence of the generated videos while preserving the visual fidelity of the garments. Additionally, a new temporal regularized attention loss is devised to bolster consistency across successive frames. Through extensive experiments, we demonstrate that our DPIDM surpasses existing state-of-the-art methods on image-based and video-based virtual try-on datasets. + +# Acknowledgments + +This work was supported in part by the Beijing Municipal Science and Technology Project No. Z241100001324002 and Beijing Nova Program No. 20240484681. + +# References + +[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 273, + 200, + 285 + ], + "spans": [ + { + "bbox": [ + 151, + 273, + 200, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 299, + 297, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 299, + 297, + 682 + ], + "spans": [ + { + "bbox": [ + 53, + 299, + 297, + 682 + ], + "type": "text", + "content": "Video virtual try-on aims to seamlessly dress a subject in a video with a specific garment. The primary challenge involves preserving the visual authenticity of the garment while dynamically adapting to the pose and physique of the subject. While existing methods have predominantly focused on image-based virtual try-on, extending these techniques directly to videos often results in temporal inconsistencies. Most current video virtual try-on approaches alleviate this challenge by incorporating temporal modules, yet still overlook the critical spatiotemporal pose interactions between human and garment. Effective pose interactions in videos should not only consider spatial alignment between human and garment poses in each frame but also account for the temporal dynamics of human poses throughout the entire video. With such motivation, we propose a new framework, namely Dynamic Pose Interaction Diffusion Models (DPIDM), to leverage diffusion models to delve into dynamic pose interactions for video virtual try-on. Technically, DPIDM introduces a skeleton-based pose adapter to integrate synchronized human and garment poses into the denoising network. A hierarchical attention module is then exquisitely designed to model intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware spatial and temporal attention mechanisms. Moreover, DPIDM capitalizes on a temporal regularized attention loss between consecutive frames to enhance temporal consistency. Extensive experiments conducted on VITON-HD, VVT and ViViD datasets demonstrate the superiority of our DPIDM against the baseline methods. Notably, DPIDM achieves VFID score of 0.506 on VVT dataset, leading to " + }, + { + "bbox": [ + 53, + 299, + 297, + 682 + ], + "type": "inline_equation", + "content": "60.5\\%" + }, + { + "bbox": [ + 53, + 299, + 297, + 682 + ], + "type": "text", + "content": " improvement over the state-of-the-art GPD-VVTO approach." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 334, + 281, + 539, + 395 + ], + "blocks": [ + { + "bbox": [ + 334, + 281, + 539, + 395 + ], + "lines": [ + { + "bbox": [ + 334, + 281, + 539, + 395 + ], + "spans": [ + { + "bbox": [ + 334, + 281, + 539, + 395 + ], + "type": "image", + "image_path": "4b7fb5f9df07272c629b1bf8ffc3b5296feeeb926a403fbe3c9297e00854895f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 399, + 555, + 433 + ], + "lines": [ + { + "bbox": [ + 313, + 399, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 555, + 433 + ], + "type": "text", + "content": "Figure 1. Given a garment and a person video, DPIDM generates a lifelike video that preserves the visual authenticity of the garment while adapting to the individual's pose and physique." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 441, + 394, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 441, + 394, + 452 + ], + "spans": [ + { + "bbox": [ + 314, + 441, + 394, + 452 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 461, + 555, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 461, + 555, + 581 + ], + "spans": [ + { + "bbox": [ + 312, + 461, + 555, + 581 + ], + "type": "text", + "content": "Generative models have made tremendous progress in recent years, with wide-ranging applications across various fields, including computer vision [9, 36, 59], computer graphics [6, 13], aesthetic design [35], and medical research [18]. Virtual try-on is a quintessential generative task that aims to synthesize a lifelike image/video of the specific person wearing the provided garment. By harnessing the powerful generative capacities of diffusion models, this field has emerged as a promising domain with versatile applications in immersive e-commerce and short-form video platforms." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "Prior research mainly focused on image-based virtual try-on. The earlier approaches typically build on Generative Adversarial Networks (GANs) [7, 19, 39, 45], incorporating a warping module alongside a try-on generator. The warping module deforms clothing to align with the human body, and then the warped garment is fused with the person image through the try-on generator. However, in light of the recent emergence of UNet-based Latent Diffusion Models (LDMs) [5, 8, 50, 56, 62], researchers have progressively directed their focus towards these innovative models. A diffusion-based try-on network combines the warping and blending" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 274, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 274, + 712 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 274, + 712 + ], + "type": "text", + "content": "* Equal contribution. This work was performed at HiDream.ai." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22648" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "processes into a unified operation of cross-attention without explicit segregation. By employing pre-trained text-to-image weights, these diffusion approaches demonstrate superior fidelity compared to their GAN-based counterparts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 122, + 297, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 122, + 297, + 555 + ], + "spans": [ + { + "bbox": [ + 56, + 122, + 297, + 555 + ], + "type": "text", + "content": "In recent years, researchers have endeavored to replicate the success of image try-on within the realm of video. One direct approach involves applying image try-on techniques to process videos frame by frame. However, this method often results in notable inter-frame inconsistencies. To address this challenge, various specialized designs have been explored for video virtual try-on [10, 26, 28, 61]. These approaches commonly integrate optical flow prediction modules to warp frames produced by the try-on generator. Despite reasonable performance, GAN-based methods encounter difficulties in handling garment-person misalignment, particularly when faced with inaccurate warping flow estimations. To harness the capabilities of pretrained image-based diffusion models, TunnelTry-on [51] and ViViD [12] utilize a pre-trained inpainting U-Net as the primary branch and integrate a reference U-Net to capture detailed clothing features. They enhance temporal consistency by incorporating standard temporal attention after each stage of the main U-Net. GPD-VVTO [46] takes a step further by integrating garment features into temporal attention, enabling the model to better preserve fidelity to the garment during temporal modeling. Despite showing promise, these methods struggle to maintain both visual integrity and motion consistency simultaneously, particularly when there is a significant stylistic gap between the garment being tried on and the original one. To alleviate these issues, we argue that two key ingredients should be taken into account. One is spatial alignment between human and garment poses within each frame. Such alignment is essential for virtual try-on as it ensures that clothing adapts appropriately to factors like coverage and wrinkles based on the individual's posture. The other is the temporal dynamics of human poses across the entire video. A comprehensive understanding of this long-term interaction is paramount for upholding temporal coherence, given that human movements naturally progress as a continuum of interconnected poses." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": "By consolidating the idea of modeling both spatial and temporal pose interactions in a video, we novelly present Dynamic Pose Interaction Diffusion Models (DPIDM) for boosting video virtual try-on. Specifically, DPIDM employs a dual-branch architecture, where the Main U-Net conducts denoising processes on the video, while the Garment U-Net extracts intricate details from the garment image and integrates them into the Main U-Net. This architecture facilitates a holistic understanding of the relationship between humans and garments within a unified feature space. To effectively leverage the spatiotemporal pose interactions in videos, we introduce a skeleton-based pose adapter that seamlessly integrates synchronized human and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "content": "garment poses into the Main U-Net. With the adapter, we present a hierarchical attention module comprising four key components: a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block. The pose-aware spatial attention block plays a crucial role in capturing intricate intra-frame human-garment pose interactions, while the pose-aware temporal attention block models the long-term dynamics of human poses across frames. Moreover, a temporal regularized attention loss is defined on consecutive frames to ensure temporal coherence. As a result, our DPIDM excels in generating videos with meticulously aligned garment details and enhanced temporal stability." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 228, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 361 + ], + "type": "text", + "content": "The main contribution of this work is the proposal of Dynamic Pose Interaction Diffusion Models that facilitate the video virtual try-on (VVTON) task. This also leads to the elegant view of how a diffusion model should be designed for excavating the pose-focused prior knowledge (e.g., spatial pose alignment and temporal pose dynamics) tailored to VVTON, and how to improve diffusion process with these amplified pose-focused guidance. Through an extensive set of experiments on VITON-HD, VVT, and ViViD datasets, DPIPM consistently achieves superior results over state-of-the-art methods in both image and video virtual try-on tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 374, + 406, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 406, + 386 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 406, + 386 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 395, + 468, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 468, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 468, + 407 + ], + "type": "text", + "content": "2.1. Image-based Virtual Try-on" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 413, + 553, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 553, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 553, + 569 + ], + "type": "text", + "content": "The development of image-based virtual try-on is largely inspired by the success of GANs [15], leading to pioneering works such as [7, 11, 19, 31, 33, 45]. A standard GAN-based virtual try-on framework typically adheres to a two-stage paradigm. The initial stage involves an image warping process, such as Thin Plate Spline (TPS) warping [19], which aligns the garment with the target individual's body. In the second stage, a GAN-based try-on generator merges the warped attire with the target individual's clothing-agnostic representation to produce authentic try-on outcomes. However, these methods heavily rely on the warping module to preserve garment details and often suffer from performance degradation due to inaccurate warping." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "content": "Recently, with the powerful generative capabilities of Latent Diffusion Models (LDMs), many diffusion-based models have been introduced to generate more realistic virtual try-on results [5, 44, 52, 54, 56, 62]. TryOnDiffusion [62] was the first to propose a dual U-Net architecture that simultaneously preserves garment details and implicitly warps the garment to match the target pose. StableVITON [56] introduced a zero cross-attention block to learn the semantic correspondence between the garment and the target person. Wear-any-way [5] utilized a sparse point control method to align person and garment features in feature space. MMTryon [57] presented a multi-modal, multi" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22649" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 74, + 410, + 277 + ], + "blocks": [ + { + "bbox": [ + 69, + 74, + 410, + 277 + ], + "lines": [ + { + "bbox": [ + 69, + 74, + 410, + 277 + ], + "spans": [ + { + "bbox": [ + 69, + 74, + 410, + 277 + ], + "type": "image", + "image_path": "a1b9dce895c76998357be45785afb8f4cd657730040a812ca3b05b776cd2007b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 278, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 54, + 278, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 54, + 278, + 555, + 357 + ], + "type": "text", + "content": "Figure 2. (a) Overall architecture of DPIDM. DPIDM employs a dual-branch architecture. The main U-Net processes a concatenated input comprising the noisy latent of the video, the latent of the cloth-agnostic video, and the cloth-agnostic mask sequence. The garment U-Net extracts fine-grained garment features, which are subsequently integrated into the main U-Net. The pose estimator is utilized to extract aligned human and garment poses, which are then fed into the attention modules of the main U-Net to guide the diffusion process. The VAE is not shown for clarity. (b) Detailed illustration of the proposed pose-aware attention module within the main U-Net. The module comprises pose-aware spatial attention, temporal-shift attention, cross-attention, and pose-aware temporal attention. The pose embeddings are seamlessly integrated into the attention module through a specialized pose adapter. (better viewed in color)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 412, + 74, + 539, + 277 + ], + "blocks": [ + { + "bbox": [ + 412, + 74, + 539, + 277 + ], + "lines": [ + { + "bbox": [ + 412, + 74, + 539, + 277 + ], + "spans": [ + { + "bbox": [ + 412, + 74, + 539, + 277 + ], + "type": "image", + "image_path": "6d6bc78bf275bd216cafe75ac1ee557bd4869c7a082904da1f27c54158881fcb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 364, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 364, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 54, + 364, + 296, + 483 + ], + "type": "text", + "content": "garment virtual try-on approach that combines text and multiple reference images to create a multimodal embedding as a condition to control the diffusion model. IDM [8] proposed a RefNet-style architecture to align the feature space between garment and person. Although these diffusion-based methods have achieved high-fidelity results in single-image inference, their application to video virtual try-on reveals a crucial limitation: the oversight of inter-frame relationships. This deficiency results in notable inter-frame inconsistencies, ultimately yielding unsatisfactory outcomes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 492, + 207, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 492, + 207, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 492, + 207, + 506 + ], + "type": "text", + "content": "2.2. Video-based Virtual Try-on" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 714 + ], + "type": "text", + "content": "In recent studies, researchers have aimed to expand the capabilities of image-based try-on approaches into video applications. A key issue in video generation is inter-frame inconsistency. ClothFormer [26] leverages optical flow in the warping and blending processes to achieve temporal smoothing. Recently, diffusion-based video virtual try-on methods have been introduced to generate more realistic results [12, 21, 46, 51, 60]. For instance, TunnelTry-on [51] proposed a focus-tunnel method that crops the human image according to the pose map, aligning the try-on image to accommodate scenarios where the person is off-center in the frame. VTON-DiT [60] introduced a DiT architecture compatible with OpenSora, where the clothing-agnostic human image is provided via ControlNet. WildVidFit [21] proposed an image-based diffusion model and used video MAE to update the intermediate representations of the diffusion process to improve frame consistency. ViViD [12]" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 364, + 555, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 555, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 555, + 484 + ], + "type": "text", + "content": "introduced a large-scale video try-on dataset and proposed an additional reference-based U-Net. GPD-VVTON [46] went a step further by integrating garment features into temporal attention to generate spatio-temporally consistent results. While these explorations of video try-on make steady advancements, they currently struggle to accurately capture the dynamic interaction between clothing and the human body in real-world scenarios. Our method employs a hierarchical attention module to capture the critical spatiotemporal pose interactions between the human and the garment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 497, + 397, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 397, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 397, + 510 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 517, + 555, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 555, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 555, + 638 + ], + "type": "text", + "content": "In this paper, we present Dynamic Pose Interaction Diffusion Models (DPIDM), a pioneering framework based on latent diffusion models designed to enhance the VVTON task. The complete architecture is depicted in Figure 2 (a). This section begins with a brief introduction to Stable Diffusion [39] in Section 3.1 to lay the groundwork for subsequent discussions. Subsequently, we offer a comprehensive overview of DPIDM in Section 3.2, and delve into the specific design details in Section 3.3-3.5. Finally, we encapsulate our training and inference strategies in Section 3.6." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 647, + 393, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 393, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 393, + 660 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "content": "Stable Diffusion (SD) stands out as one of the most prevalent latent diffusion models within the community. It leverages a variational autoencoder (VAE) architecture, comprising an encoder " + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "content": " and a decoder " + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "content": ", to facilitate image rep" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22650" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "resentations in the latent space. Additionally, a U-Net [40] " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " is trained to denoise a Gaussian noise " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " with a conditioning input encoded by a CLIP text encoder [37] " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": ". Given an image " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " and a text prompt " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": ", the denoising U-Net " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " undergoes training by minimizing the loss function:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 64, + 137, + 294, + 161 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 137, + 294, + 161 + ], + "spans": [ + { + "bbox": [ + 64, + 137, + 294, + 161 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})) \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "54888ccb79192cb76f981c05da3251bd6704bbc6e7130e52237ad59c79a8d908.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " denotes the time step of the forward diffusion process, and " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " is the noisy latent constructed by adding Gaussian noise " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " to the encoded image " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": ". During the inference stage, " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " is randomly sampled from a Gaussian distribution and iteratively denoised to derive " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " following a predefined sampling schedule [23, 41]. Finally, the latent decoder " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " decodes " + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 55, + 162, + 296, + 246 + ], + "type": "text", + "content": " back into the image space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 253, + 123, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 123, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 123, + 264 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": "The overall architecture of DPIDM is depicted in Fig. 2. DPIDM takes a reference garment image " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\pmb{G} \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " and a source human video " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\pmb{I}_S \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " as input, where " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " represent the height and width of each frame, and " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " signifies the video length. Its objective is to generate a realistic video " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{I}} \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " showing the individual in " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\pmb{I}_S" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": " adorned in the garment " + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "inline_equation", + "content": "\\pmb{G}" + }, + { + "bbox": [ + 55, + 270, + 295, + 354 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 354, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 581 + ], + "type": "text", + "content": "We approach the video virtual try-on as a video inpainting challenge, aimed at integrating the garment onto clothing-agnostic areas. To achieve this, DPIDM employs a dual-branch architecture. The main U-Net is the inpainting model initialized with the pre-trained weights from SD. It takes in a 9-channel tensor comprising 4 channels for the noisy latent of the video, 4 channels for the clothing-agnostic video latent, and 1 channel for the binary agnostic mask sequence. In contrast to the original SD model, which utilizes text embeddings to guide the diffusion process, we have substituted these embeddings with image embeddings derived from a CLIP image encoder representing the garment image. While the CLIP image embedding effectively captures the overall colors and textures of the garment, it may not retain finer details. To address this, we also use a Garment U-Net to extract detailed garment features. The Garment U-Net follows a standard text-to-image diffusion model with a 4-channel input. This dual-branch architecture has proven to be effective by previous works [12, 46, 51]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 665 + ], + "type": "text", + "content": "To further enhance the generation, we incorporate human and garment poses as supplementary guidance to refine the diffusion process. We develop a light-weight pose encoder to extract features of the pose maps and a pose adapter to inject these features into the attention modules of the main U-Net. The human/garment pose maps are derived from the input video/image with pose estimator." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 672, + 149, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 149, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 149, + 683 + ], + "type": "text", + "content": "3.3. Pose Estimator" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "We directly employ DW-Pose [53] to estimate human poses " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "P_{h}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": " from video frames. However, there is a lack of an open-" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 71, + 539, + 123 + ], + "blocks": [ + { + "bbox": [ + 321, + 71, + 539, + 123 + ], + "lines": [ + { + "bbox": [ + 321, + 71, + 539, + 123 + ], + "spans": [ + { + "bbox": [ + 321, + 71, + 539, + 123 + ], + "type": "image", + "image_path": "869db8ec1e0cbba932b5ca4ec03ae3bd51cc706d13162a512814997a7d2ce1d6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 125, + 548, + 137 + ], + "lines": [ + { + "bbox": [ + 319, + 125, + 548, + 137 + ], + "spans": [ + { + "bbox": [ + 319, + 125, + 548, + 137 + ], + "type": "text", + "content": "Figure 3. Visualization of predicted human and garment poses." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "content": "source garment pose estimator currently. To establish alignment between human and garment poses, we train a garment pose estimator to predict a set of landmarks " + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "inline_equation", + "content": "P_{g}" + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "content": " that correspond to various parts of the human pose " + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "inline_equation", + "content": "P_{h}" + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "content": ". The ground truth of " + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "inline_equation", + "content": "P_{g}" + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "content": " is labeled manually, with the number of landmarks varying based on the garment types. For instance, in upper clothing, " + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "inline_equation", + "content": "|P_{g}| = 9" + }, + { + "bbox": [ + 313, + 144, + 553, + 288 + ], + "type": "text", + "content": ", encompassing landmarks such as the neck, shoulders, elbows, wrists, and hips. These landmarks serve as explicit indicators of the alignment between human and garment poses, and therefore can be used as guidance to improve the diffusion process. The visualization of human and garment poses is shown in Fig. 3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 295, + 458, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 295, + 458, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 458, + 308 + ], + "type": "text", + "content": "3.4. Dynamic Pose Interaction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 312, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 553, + 361 + ], + "type": "text", + "content": "To facilitate the dynamic pose interaction, we propose a hierarchical attention module consisting of a pose-aware spatial attention block, a temporal-shift attention block, a cross-attention block, and a pose-aware temporal attention block." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "text", + "content": "Pose-aware Spatial Attention (PASA). To capture intricate intra-frame human-garment pose interactions, we inject the features of human and garment poses into the spatial attention layer. In our baseline, the human feature map " + }, + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h" + }, + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "text", + "content": " from the main U-Net is concatenated with the corresponding garment feature map " + }, + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_g" + }, + { + "bbox": [ + 313, + 361, + 554, + 445 + ], + "type": "text", + "content": " from the garment U-Net to jointly compute self-attention, which is computed as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 368, + 453, + 553, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 453, + 553, + 468 + ], + "spans": [ + { + "bbox": [ + 368, + 453, + 553, + 468 + ], + "type": "interline_equation", + "content": "\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f}), \\psi_ {k} (\\mathbf {f}), \\psi_ {v} (\\mathbf {f})\\right), \\tag {2}", + "image_path": "319f4fe53bf58a5b2d0a80825365de09df62faa30fd5ac8eb8c40dfca3c4907b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{f} = [\\mathbf{f}_h,\\mathbf{f}_g]" + }, + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "text", + "content": " is the concatenation of human feature map and garment feature map in the spatial dimension, and " + }, + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "inline_equation", + "content": "\\psi_q,\\psi_k,\\psi_v" + }, + { + "bbox": [ + 313, + 475, + 554, + 548 + ], + "type": "text", + "content": " are linear projections. Afterward, only the half feature from the main U-Net undergoes further computation. This attention layer enables garment features extracted by the garment U-Net to be integrated into the main U-Net." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "content": "To enable the correspondence control with pose guidance, we modify this attention layer by adding the pose embeddings of the human and garment. Formally, given the human pose embedding " + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_h" + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "content": " and garment pose embedding " + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_g" + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "content": " extracted from the pose encoder, we first concatenate them in spatial dimension " + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = [\\mathbf{p}_h,\\mathbf{p}_g]" + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "content": ". Then we utilize a pose adapter to project " + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 313, + 548, + 554, + 691 + ], + "type": "text", + "content": " into the diffusion feature space. The pose adapter employs two fully connected (FC) layers with an intermediate activation layer. The first FC layer maps the input to a lower-dimensional space, while the second FC layer maps it back to the original dimensional. The pose adapter can be written as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 353, + 700, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 700, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 353, + 700, + 553, + 715 + ], + "type": "interline_equation", + "content": "A d p t (\\mathbf {p}) = \\mathbf {W} _ {u p} (G E L U (\\mathbf {W} _ {d o w n} (\\mathbf {p}))), \\tag {3}", + "image_path": "b27a5690689ff78c7d094474de0e19c0b6f3433898c283a2b9097822e37817e1.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22651" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{up}" + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{down}" + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": " are the learnable weight matrix. To preserve the original feature space of diffusion models, we initialize " + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{up}" + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": " with zeros. Subsequently, we add the diffusion feature " + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": " and the adapter embedding " + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "inline_equation", + "content": "Adpt(\\mathbf{p})" + }, + { + "bbox": [ + 55, + 72, + 294, + 135 + ], + "type": "text", + "content": " together and feed them into the self-attention mechanism, leading to the revised form of Eq. 2:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 139, + 295, + 151 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 139, + 295, + 151 + ], + "spans": [ + { + "bbox": [ + 59, + 139, + 295, + 151 + ], + "type": "interline_equation", + "content": "\\boldsymbol {h} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {k} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p})) , \\psi_ {v} (\\mathbf {f} + \\operatorname {A d p t} (\\mathbf {p}))\\right). \\tag {4}", + "image_path": "ed46ff348115b5abc0d716e793b8d2c7e3a0b1cc6bdfb1e86dd152c544a109a0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 156, + 294, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 156, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 55, + 156, + 294, + 215 + ], + "type": "text", + "content": "In this way, when integrating the garment feature into the main U-Net, the feature aggregation process takes into account the alignment of human and garment poses. This implicit consideration results in the garment being deformed to better fit the natural pose of the person." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 216, + 295, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 216, + 295, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 295, + 335 + ], + "type": "text", + "content": "Existing PoseGuider-style methods [24, 46, 51] typically achieve pose control by directly adding processed human pose images and noisy latents as inputs to the first layer of the diffusion network, without incorporating pose information into the attention modules. In contrast, our PASA introduces pose information into each layer's attention modules through a pose adapter, enabling more precise and varying degrees of pose control. Moreover, besides human poses, we further inject garment poses into PASA, thus achieving intricate intra-frame human-garment pose alignment." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "text", + "content": "Temporal-shift Attention (TSA). In the original SD model, the attention block of the U-Net solely focuses on self-attention within individual frames, overlooking valuable information across frames. Current VVTON techniques predominantly integrate a temporal attention layer at each stage to capture temporal dependencies among video frames. Nevertheless, this approach can introduce a covariate shift in the feature space, potentially undermining the model's generative capacity [58]. While a direct remedy could involve joint space-time 3D attention, this method escalates the complexity of attention calculations quadratically. Drawing inspiration from prior works [1, 32, 49], a novel approach involves employing temporal shift operations that utilize a 2D module to amalgamate spatial and temporal information by incorporating neighboring frame data into the current frame. Specifically, in addition to examining tokens within the present frame, a patch-level shifting operation transpires along the temporal dimension, transferring tokens from the preceding " + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "text", + "content": " frames to the current frame, thereby constructing a novel latent feature frame. We concatenate the latent feature of the current frame " + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "text", + "content": " with the temporally shifted latent feature " + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{shift}" + }, + { + "bbox": [ + 55, + 335, + 295, + 635 + ], + "type": "text", + "content": " in the spatial dimension, thus establishing keys and values for subsequent self-attention mechanisms. The temporal-shift attention can be formally written as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 642, + 295, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 642, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 67, + 642, + 295, + 658 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {h}} = \\operatorname {A t t n} \\left(\\psi_ {q} (\\mathbf {h}), \\psi_ {k} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right), \\psi_ {v} \\left(\\left[ \\mathbf {h}, \\mathbf {h} _ {\\text {s h i f t}} \\right]\\right). \\right. \\tag {5}", + "image_path": "1e92067542e7b1bcae834f2475ec91305479c4abbff8c5e9049e75439556ebac.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "It notably reduces the computational load when juxtaposed with 3D attention. Furthermore, it empowers the model to discern short-term relationships between adjacent frames, enhancing temporal coherence during video generation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "Cross-Attention (CA). In contrast to the original SD model, which employs text embeddings to steer the diffusion process with cross-attention, we have replaced these embeddings with garment image embeddings generated from a CLIP image encoder. These embeddings encapsulate comprehensive global information like color and style, which serve as a valuable supplement to the detailed appearance characteristics provided by the Garment U-Net." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 168, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 384 + ], + "type": "text", + "content": "Pose-aware Temporal Attention (PATA). Although TSA can effectively capture short-term relationships between adjacent frames, it fails to consider the long-term temporal dynamics across the entire video. Previous studies [12, 17, 24] have introduced a plug-and-play motion module with temporal attention to enhance video smoothness. However, these approaches overlook the dynamic changes in human poses, which are crucial for the VVTON task where garment appearance must adapt to individual poses. To address this limitation, we propose a pose-aware temporal attention. Similar to PASA, our method involves feeding the human pose embedding " + }, + { + "bbox": [ + 313, + 168, + 553, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_h" + }, + { + "bbox": [ + 313, + 168, + 553, + 384 + ], + "type": "text", + "content": " into a pose adapter. This adapted embedding is then element-wise added to the output feature of the cross-attention block, followed by standard temporal attention. Our experiments have demonstrated that this straightforward strategy significantly improves video continuity and enhances the realism of clothing dynamics in motion, as shown in Fig. 5." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 389, + 512, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 512, + 401 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 512, + 401 + ], + "type": "text", + "content": "3.5. Temporal Regularized Attention Loss" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 406, + 554, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 406, + 554, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 406, + 554, + 502 + ], + "type": "text", + "content": "Generally, SD is merely optimized with the mean-squared loss defined in Eq. 1, which treats all regions of the synthesized video equally without emphasizing temporal consistency. Inspired by the idea that self-attention maps within diffusion models capture the structural essence of generated content [3, 25, 29, 42], we employ the temporal regularized attention loss. This loss function is designed to minimize variations in self-attention maps across successive frames:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 361, + 507, + 553, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 507, + 553, + 541 + ], + "spans": [ + { + "bbox": [ + 361, + 507, + 553, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {T R A}} = \\sum_ {i} ^ {N} \\sum_ {j = 2} ^ {T} \\gamma_ {i} \\left| \\mathcal {A} _ {i} ^ {(j)} - \\mathcal {A} _ {i} ^ {(j - 1)} \\right|, \\tag {6}", + "image_path": "3d16c5baf307892a292db9eca023d31619b3f1d91333d56beae98f13f80610f2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_i^{(j)}" + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": " represents the self-attention map of the PASA block in the " + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": "-th layer on " + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": "-th frame. Specifically, We calculate " + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "inline_equation", + "content": "L_{TRA}" + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": " only on the last two decoder layers in the main U-Net, with " + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "inline_equation", + "content": "\\gamma_i = 0.5" + }, + { + "bbox": [ + 313, + 541, + 553, + 591 + ], + "type": "text", + "content": " in our context." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 597, + 444, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 597, + 444, + 609 + ], + "spans": [ + { + "bbox": [ + 313, + 597, + 444, + 609 + ], + "type": "text", + "content": "3.6. Training and Inference" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 613, + 553, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 553, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 553, + 651 + ], + "type": "text", + "content": "Training Strategy. Different from previous multi-stage training approaches [46, 51], we employ a single-stage training strategy. The loss function is defined as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 385, + 662, + 553, + 674 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 662, + 553, + 674 + ], + "spans": [ + { + "bbox": [ + 385, + 662, + 553, + 674 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {L D M} + \\lambda \\mathcal {L} _ {T R A}, \\tag {7}", + "image_path": "3872f6beab2f5e7a839ba54a5bbf778408d72d19d12b33347a0bbaa78bbc506e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": " is the hyper-parameter used to balance the MSE loss and the proposed TRA loss. When training with image datasets, the TSA and PATA blocks are omitted. As for" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22652" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": "video datasets, we implement an image-video joint training strategy. Initially, we randomly pick " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " videos from the dataset and extract a single frame randomly from each video for training. At this stage, solely the PASA and CA modules undergo training. Subsequently, in the following phase, another set of " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " videos is randomly chosen and a sequence of " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " consecutive frames is extracted from each video for training purposes. Here, the training focuses exclusively on the TSA and PATA modules. This process repeats iteratively until the training concludes. Here, " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " represents the batch size, and " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " symbolizes the length of video clips. This training methodology effectively reduces the GPU memory requirements and enhances the speed of convergence." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 228, + 294, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 294, + 324 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 294, + 324 + ], + "type": "text", + "content": "To tackle discontinuous pose sequences, we also implement a condition dropping strategy during training. Specifically, each pose keypoint has a 0.05 probability of being dropped. When a keypoint of the current frame is dropped, the model is forced to refer to the poses of adjacent frames to infer the correct pose of the current frame. This strategy not only enhances the model's robustness to pose estimation methods but also improves temporal consistency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 325, + 294, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 325, + 294, + 408 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 294, + 408 + ], + "type": "text", + "content": "Inference Strategy. To improve temporal coherence and smoothness in long videos, we follow [12, 46] and implement a sliding window approach during inference. It involves dividing the long video into overlapping segments of a specified length " + }, + { + "bbox": [ + 55, + 325, + 294, + 408 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 325, + 294, + 408 + ], + "type": "text", + "content": " and conducting inference on each segment. For overlapping frames, the ultimate output is derived by averaging the results obtained from each inference." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 423, + 135, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 135, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 135, + 436 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 443, + 117, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 117, + 454 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 117, + 454 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "text", + "content": "Video Virtual Try-On. We empirically verify and analyze the effectiveness of our DPIDM on two popular video virtual try-on datasets, VVT [10] and ViViD [12]. The VVT dataset contains 791 video clips with a resolution of 256 " + }, + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "text", + "content": " 192. Following the official settings[10, 51], we partition it into a training set of 661 clips and a test set of 130 clips. However, the VVT dataset exhibits limited diversity in terms of garment varieties and human actions. ViViD, a recent and challenging dataset, includes 9,700 video-image pairs at a resolution of " + }, + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "inline_equation", + "content": "832 \\times 624" + }, + { + "bbox": [ + 55, + 461, + 295, + 665 + ], + "type": "text", + "content": ". It classifies garments into three categories: upper-body, lower-body, and dresses. The dataset is divided into 7,759 videos for training and 1,941 videos for testing. It is worth noting that due to inaccuracies in the provided cloth-agnostic masks for individuals in a back-facing posture, we excluded video segments depicting such scenarios from the original footage. Consequently, only the remaining segments were utilized for testing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Image Virtual Try-On. To further validate the effectiveness of our method, we carried out additional experiments on the widely recognized image-based virtual try-on dataset, VITON-HD [7]. This dataset comprises 13,679" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 113, + 547, + 262 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": "Table 1. Comparison results on the VVT dataset. " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_I" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_R" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " represent " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_{I3D}" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_{ResNeXt}" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " respectively. " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " denotes higher is better, while " + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 313, + 71, + 553, + 104 + ], + "type": "text", + "content": " indicates lower is better." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 113, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 317, + 113, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 317, + 113, + 547, + 262 + ], + "type": "table", + "html": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
CP-VTON [45]0.4590.5356.36112.10
FW-GAN [10]0.6750.2838.01912.15
PBAFN [14]0.8700.1574.5168.690
ClothFormer [26]0.9210.0813.9675.048
LaDI-VTON [34]0.8780.1905.880-
StableVITON [56]0.8760.0764.0215.076
TunnelTry-on [51]0.9130.0543.3454.614
ViViD [12]0.9490.0683.4055.074
VITON-DiT [60]0.8960.0802.4980.187
GPD-VVTO [46]0.9280.0561.280-
DPIDM (Ours)0.9300.0410.5060.047
", + "image_path": "d20f7746754db60cf4fa13690f173eb77f7b760e5f3d9bc36f0ec4342f4813be.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 277, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 553, + 300 + ], + "type": "text", + "content": "pairs of upper-body model and garment images, out of which 2,032 pairs were specifically reserved for testing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 301, + 554, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 554, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 554, + 433 + ], + "type": "text", + "content": "Evaluation Metrics. For image datasets, we use Structural Similarity (SSIM) [47] and Learned Perceptual Image Patch Similarity (LPIPS) [55] to measure the similarity between the generated image and the ground-truth. Additionally, Fréchet Inception Distance(FID) [22] and Kernel Inception Distance(KID) [2] are employed to measure the quality and realism of the generated images. For video datasets, we further utilize Video Fréchet Inception Distance (VFID) [43] to evaluate spatiotemporal consistency. Two CNN backbones, I3D [4] and 3D-ResNeXt101 [20], are adopted as feature extractors for VFID." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 441, + 447, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 447, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 447, + 453 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": "We initialize the main U-Net with the pre-trained SD v1.5 inpainting model and the garment U-Net with SD v1.5. The pose estimator is trained offline using YOLOv8 [38]. The pose encoder incorporates four convolutional layers to align the pose image with the noise latent at the same resolution. During training, all data is resized to a uniform resolution of " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "512 \\times 384" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": ". To improve model resilience, we employ data augmentation by randomly flipping images horizontally with a " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": " probability. We utilize the Adam optimizer [27] with a consistent learning rate of " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-5}" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": ". All the experiments are conducted using 16 NVIDIA A100 GPUs. Sequences of 24 frames are sampled, and the batch size " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": " is set to 32. The model is trained for 80,000 iterations. The hyper-parameter " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 313, + 459, + 554, + 651 + ], + "type": "text", + "content": " for video datasets and 0 for image datasets. During inference, we utilize the DDIM [41] sampler and set the classifier-free guidance scale to 1.5." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 659, + 432, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 432, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 432, + 672 + ], + "type": "text", + "content": "4.3.Quantitative Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "Video Virtual Try-On. We compare our DPIDM with a series of state-of-the-art virtual try-on methods, which can be grouped into two directions: GAN-based methods" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22653" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 91, + 287, + 159 + ], + "blocks": [ + { + "bbox": [ + 84, + 71, + 267, + 82 + ], + "lines": [ + { + "bbox": [ + 84, + 71, + 267, + 82 + ], + "spans": [ + { + "bbox": [ + 84, + 71, + 267, + 82 + ], + "type": "text", + "content": "Table 2. Comparison results on the ViViD dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 91, + 287, + 159 + ], + "lines": [ + { + "bbox": [ + 61, + 91, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 287, + 159 + ], + "type": "table", + "html": "
MethodSSIM↑LPIPS↓VFID1↓VFIDR↓
LaDI-VTON [34]0.8240.1648.2831.185
CAT-DM [54]0.8260.1629.3542.139
ViViD [12]0.8460.1181.8940.870
DPIDM (Ours)0.8830.0810.4880.090
", + "image_path": "e982f54b36171c44b36062be50a2d1f040d52e3db4779f2f255b5ff272cad56f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 61, + 206, + 287, + 355 + ], + "blocks": [ + { + "bbox": [ + 55, + 163, + 295, + 198 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 295, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 295, + 198 + ], + "type": "text", + "content": "Table 3. Quantitative results of image-based virtual try-on task on the VITON-HD dataset. " + }, + { + "bbox": [ + 55, + 163, + 295, + 198 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_u / \\mathrm{KID}_u" + }, + { + "bbox": [ + 55, + 163, + 295, + 198 + ], + "type": "text", + "content": " stands for the FID/KID score in unpaired setting. Note that the KID score is multiplied by 1000." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 206, + 287, + 355 + ], + "lines": [ + { + "bbox": [ + 61, + 206, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 61, + 206, + 287, + 355 + ], + "type": "table", + "html": "
MethodSSIM↑LPIPS↓FIDu↓KIDu↓
VITON-HD [7]0.8620.11712.123.23
HR-VITON [30]0.8760.09612.313.81
GP-VTON [48]0.8900.0859.821.42
LaDI-VTON [34]0.8750.0919.321.55
WearAnyWay [5]0.8770.0788.160.78
DCI-VTON [16]0.8900.0728.770.89
StableVITON [56]0.8780.0759.431.54
CAT-DM [54]0.8770.0808.931.37
IDM [8]0.8810.0788.600.55
GPD-VVTO [46]0.8910.0708.570.78
DPIDM (Ours)0.8930.0678.150.32
", + "image_path": "e7e2becbc46670532a32a16664a3db8af762c1dc6ce827f417efe3e417bd94a8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "content": "[10, 14, 26, 45] and Diffusion-based methods [12, 34, 46, 51, 54, 56, 60]. Table 1 summarizes the performance comparisons on the VVT dataset. Notably, our DPIDM consistently outperforms other state-of-the-art methods across LPIPS and VFID metrics. Although ViViD [12] attains a higher SSIM score, its advantage is expected due to the utilization of a significantly larger volume of high-resolution videos during training, approximately six times more than the VVT dataset. Despite this, our DPIDM notably surpasses ViViD in the VFID metric, showcasing substantial enhancements in video coherence while preserving garment visual authenticity. ClothFormer improves FW-GAN by introducing an appearance-flow tracking module to ensure temporal consistency in garment warping. TunnelTry-on and ViViD further boost the performances by leveraging the capabilities of pre-trained diffusion models. Additionally, GPD-VVTO introduces garment-aware temporal attention to enhance temporal consistency, leading to a clear VFID score boost. However, existing approaches often neglect crucial spatiotemporal pose interactions between individuals and garments. In contrast, our DPIDM effectively models both intra-frame human-garment pose interactions and long-term human pose dynamics across frames through pose-aware attention mechanisms, leading to superior results in the VVTON task. Specifically, our DPIDM achieves a " + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_I" + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "content": " score of 0.506, marking a substantial " + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "inline_equation", + "content": "60.5\\%" + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "content": " relative improvement over the top competitor GPD-VVTO. Note that GPD-VVTO employs SD v2.1 for model initialization, whereas we choose SD v1.5 for fewer parameters." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 320, + 73, + 549, + 289 + ], + "blocks": [ + { + "bbox": [ + 320, + 73, + 549, + 289 + ], + "lines": [ + { + "bbox": [ + 320, + 73, + 549, + 289 + ], + "spans": [ + { + "bbox": [ + 320, + 73, + 549, + 289 + ], + "type": "image", + "image_path": "d2ecb45cdfd86fa2e1368630fb003dd58f92ba506159068f7a5955ba0a23c986.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 292, + 555, + 326 + ], + "lines": [ + { + "bbox": [ + 313, + 292, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 555, + 326 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison on the ViViD dataset. Our DPIDM excels in seamlessly integrating the garment with the wearer and maintaining the visual integrity of the garment." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "type": "text", + "content": "Table 2 presents performance comparisons on the ViViD dataset. As observed with VVT, DPIDM consistently outperforms other VVTON methods across all metrics. which again evinces the pivotal merit of the pose-aware guidance for preserving spatiotemporal consistency in the generated videos. Particularly, DPIDM demonstrates a substantial relative improvement of " + }, + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "type": "inline_equation", + "content": "74.2\\%" + }, + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "type": "text", + "content": " over ViViD in " + }, + { + "bbox": [ + 313, + 340, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\mathrm{VFID}_I" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 424, + 556, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 424, + 556, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 424, + 556, + 556 + ], + "type": "text", + "content": "Image Virtual Try-On. Table 3 displays the quantitative results on the VITON-HD [7]. Following the official settings, we utilize SSIM and LPIPS metrics for the paired setting, and FID and KID for the unpaired setting. Our DPIDM consistently outperforms other methods across all metrics, showcasing its ability to produce authentic and lifelike images while maintaining the integrity of the initial garment structure. It is noteworthy that diffusion-based approaches exhibit lower FID and KID scores compared to GAN-based methods, suggesting that diffusion models excel in generating images with heightened fidelity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 564, + 425, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 425, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 425, + 576 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "We conduct qualitative analysis from two aspects: visual authenticity of the garment and temporal consistency. When evaluating visual authenticity, we compare results from several virtual try-on methods using individual video frames, as illustrated in Figure 4. In the first row, LaDI-VTON and CAT-DM change the style of the target garment and introduce color discrepancies. While ViViD achieves a natural fit, it struggles to maintain the original patterns, leading to their displacement on the garment. In contrast, our method excels in seamlessly blending the garment with the wearer while preserving intricate fabric patterns. Moving" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22654" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 541, + 280 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 541, + 280 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 541, + 280 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 541, + 280 + ], + "type": "image", + "image_path": "c38118303f52f5ea54d65bd8c7305c41fa89baf7b6146cc26931c3619e3bc97d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 280, + 553, + 291 + ], + "lines": [ + { + "bbox": [ + 56, + 280, + 553, + 291 + ], + "spans": [ + { + "bbox": [ + 56, + 280, + 553, + 291 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on the ViViD dataset. Our DPIDM maintains temporal consistency even during substantial movements." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 320, + 290, + 386 + ], + "blocks": [ + { + "bbox": [ + 56, + 300, + 294, + 312 + ], + "lines": [ + { + "bbox": [ + 56, + 300, + 294, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 300, + 294, + 312 + ], + "type": "text", + "content": "Table 4. Performance contribution of each component in DPIDM." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 320, + 290, + 386 + ], + "lines": [ + { + "bbox": [ + 58, + 320, + 290, + 386 + ], + "spans": [ + { + "bbox": [ + 58, + 320, + 290, + 386 + ], + "type": "table", + "html": "
idPAATSATRASSIM↑LPIPS↓VFIDI↓VFIDR↓
(a)XXX0.8930.0843.4512.435
(b)✓XX0.9250.0501.0680.153
(c)✓✓X0.9290.0430.7210.075
(d)✓✓✓0.9300.0410.5060.047
", + "image_path": "f7b900e79d5c8e4cf8e08eaed38c7ed5a3dc74210c493bee8b746eed0a5272e8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 399, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 399, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 54, + 399, + 295, + 590 + ], + "type": "text", + "content": "to the second row with a pair of striped shorts, competitors maintain the garment's style but exhibit noticeable artifacts around the legs. Conversely, our method adeptly addresses these issues by naturally supplementing missing skin tones while upholding the garment's visual integrity. This trend continues in the subsequent example with a dress in the third row, highlighting the effectiveness of DPIDM. To further evaluate temporal consistency, we extract four frames at equal intervals from the generated video and present them in Fig. 5. While ViViD achieves a natural fit in individual frames, it struggles to maintain garment details and temporal consistency across frames, especially during person movements. In contrast, our DPIDM consistently delivers high-quality results that preserve garment details and ensure temporal consistency without introducing artifacts, even during actions involving significant movements." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 600, + 156, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 156, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 156, + 611 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "content": "In this study, we analyze the impact of each design element within DPIDM on the overall performance using the VVT dataset. As shown in Table 4, the proposed elements are denoted as follows: PAA refers to pose-aware attention, TSA to temporal-shift attention, and TRA to temporal regularized attention loss. We start with a basic model (a) that directly inserts standard temporal attention after each stage of the main U-Net. Subsequently, in (b), we substitute the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 301, + 555, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 494 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 494 + ], + "type": "text", + "content": "standard spatial/temporal attention with our proposed pose-aware spatial/temporal attention. Notably, the introduction of " + }, + { + "bbox": [ + 313, + 301, + 555, + 494 + ], + "type": "inline_equation", + "content": "PAA" + }, + { + "bbox": [ + 313, + 301, + 555, + 494 + ], + "type": "text", + "content": " yields a significant performance enhancement over (a), surpassing even the state-of-the-art methods detailed in Table 1. This not only validates the efficacy of our proposed pose-aware spatial/temporal attention but also underscores the critical role of integrating spatiotemporal pose interactions into the VVTON task. Furthermore, we introduce the temporal-shift attention and the temporal regularized attention loss in (c) and (d) respectively. While TSA and TRA did not result in significant enhancements in the SSIM and LPIPS metrics, they notably improved the VFID metric, highlighting their effectiveness in enhancing video consistency. Collectively, the innovative modules introduced in DPIDM enhance the visual integrity of the garment and improve the temporal consistency of the generated videos." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": "In this work, we have presented Dynamic Pose Interaction Diffusion Models (DPIDM), a novel approach that capitalizes on spatial and temporal pose interactions to enhance video virtual try-on. Particularly, we study the problem from the viewpoint of employing intra-frame human-garment pose interactions and long-term human pose dynamics across frames. To verify our claim, we develop a hierarchical pose-aware attention module to integrate human and garment pose features into spatial and temporal attention, enhancing the temporal coherence of the generated videos while preserving the visual fidelity of the garments. Additionally, a new temporal regularized attention loss is devised to bolster consistency across successive frames. Through extensive experiments, we demonstrate that our DPIDM surpasses existing state-of-the-art methods on image-based and video-based virtual try-on datasets." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22655" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "type": "text", + "content": "This work was supported in part by the Beijing Municipal Science and Technology Project No. Z241100001324002 and Beijing Nova Program No. 20240484681." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "spans": [ + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 166, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 166, + 296, + 209 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 166, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 61, + 166, + 296, + 209 + ], + "type": "text", + "content": "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Unlike traditional CAD model retrieval, shape programs allow reasoning about semantic parameters, editing, and a low memory footprint. Despite their potential, shape programs for 3D scene understanding have been largely overlooked. Our key contribution is enabling gradient-based optimization by parsing shape programs, or more precisely procedural models designed in Blender, into efficient PyTorch code. While there are many possible applications of our PyTorchGeoNodes, we show that a combination of PyTorchGeoNodes with genetic algorithm is a method of choice to optimize both discrete and continuous shape program parameters for 3D reconstruction and understanding of 3D object parameters. Our modular framework can be further integrated with other reconstruction algorithms, and we demonstrate one such integration to enable procedural Gaussian splattig. Our experiments on the ScanNet dataset show that our method achieves accurate reconstructions while enabling, until now, unseen level of 3D scene understanding.", + "bbox": [ + 89, + 347, + 485, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 693, + 220, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Various 3D object representations have already been considered for 3D scene understanding: voxels [21, 31], meshes [11, 38], SDFs [25], NeRFs [5], Gaussian Splatting [34], exemplars from a shape database [3]. SDFs, NeRFs, or Gaussian Splatting generalize to shapes unseen during training but produce artifacts for example when parts of the object are occluded in scenes captured \"in the wild\". Their memory footprint can also become large. Using exemplars guarantees that the retrieved shapes look good as they are created by human designers, however the database may not contain shapes similar to the target object.", + "bbox": [ + 89, + 719, + 482, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we investigate the use of interpretable", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shape programs to represent objects. Shape programs are a form of procedural modeling [10] introduced in [35] for representing 3D objects. While shape programs have already been considered for 3D scene understanding [27, 32], their use in this context remains largely unexplored. As shown in Figure 1, our method can be used to accurately retrieve geometry and 3D parameters of target objects, together with its texture even in presence of partial occlusions.", + "bbox": [ + 511, + 318, + 903, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shape programs can be seen as computational graphs of parametrized geometric operations that generate various 3D shapes from an object category given input shape parameters, such as object dimensions as well as \"semantic\" properties like existence of armrest or backrest in case of chairs. Multiple similar parts, for example the legs of a chair or the shelves of a bookshelves—are obtained by first generating a single instance, duplicating it and applying geometric transformations such as rotations and translations as needed.", + "bbox": [ + 511, + 439, + 905, + 574 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to this procedural modeling approach, shape programs generate shapes that remain appealing and that can fit many different instances. Alongside being interpretable, the shapes they generate are editable in an intuitive manner and have a very small memory footprint. In fact, they are already a popular tool for building reconstruction [19, 24, 37, 39] and the interest around shape programs for objects is growing [15, 16, 27, 35]. Blender [8] already provides support for them. A research challenge targeting reconstruction of walls, doors, and windows using such structured languages was organized by Meta in $2024^{1}$ .", + "bbox": [ + 511, + 575, + 905, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recovering parameters of a shape program from an image is however challenging. Typically, a shape generated by a shape program depends on a number of parameters. Some parameters such as the width and height of the objects take continuous values but other parameters take only discrete values, e.g. the number of shelves in a bookshelf.", + "bbox": [ + 511, + 742, + 903, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Optimizing on these parameters turns out to be tricky: For example, changing the number of shelves from 5 to 6", + "bbox": [ + 511, + 834, + 903, + 864 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "[https://eval.ai/web/challenges/challenge-page/2115/overview (Accessed: November 2024)]", + "bbox": [ + 511, + 875, + 903, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16283", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/80770942641ffe2de892d7429e97f61d72a0fdae7264d5705582bad38f157eec.jpg", + "image_caption": [ + "Jointly recovered geometry and parameters of target objects from RGB-D scans" + ], + "image_footnote": [], + "bbox": [ + 174, + 88, + 830, + 310 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/229ebaedaf2d7d0343c40def75a5d4a9b5aa00d622157f0092caa42308a2da96.jpg", + "image_caption": [ + "Views of Target object" + ], + "image_footnote": [], + "bbox": [ + 189, + 327, + 352, + 425 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e4725d16ccfda5844f61f37fd05e144977d82643473a1f3aa4f5dd472a1c7216.jpg", + "image_caption": [ + "Recovered Gaussians" + ], + "image_footnote": [], + "bbox": [ + 374, + 327, + 488, + 424 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8665358bc796bf429eabb5cb9a35d18e0bfd18170fee97961b7710372dbe7e91.jpg", + "image_caption": [ + "Procedural Gaussians editing", + "Figure 1. Our PyTorchGeoNodes is a framework that enables differentiable shape programs for 3D reconstruction. Our semantically-rich reconstructions of 3D objects from RGB-D scans enable understanding of important metric parameters of individual parts for different objects. These parameters are physically bound to the 3D reconstruction as PyTorchGeoNodes enables flow of gradients from the generated shape to the parameters of the object. Our PyTorchGeoNodes is modular, e.g. we can use it to enable procedural modeling for Gaussian splatting. In the example, our method recovers Gaussians for the target sofa and 'clones' all details from the visible armrest to the occluded armrest in the scene. Our integration enables procedural editing of Gaussians and we can alter shape parameters to edit the reconstruction: e.g. by extending or shrinking width of the seat, removing backrest, left armrest, changing height of the backrest and depth of the seat etc." + ], + "image_footnote": [], + "bbox": [ + 532, + 327, + 810, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "changes significantly the shape and appearance of a bookshelf. There have been a few attempts in the computer vision community to use procedural shapes [27, 32]. In [27] the authors train a neural network to predict the parameters of a shape program. While this method shows impressive results using synthetic data, we show in Section 5.3 that on real data such an approach fails to generalize well, due to the lack of real world image data annotated with shape parameters. Using synthetically generated data to train such models also performs very badly: While shape programs capture very well the global structure of objects, they do not represent details. As a result, the model can hardly generalize from synthetic images to real ones. In comparison, our proposed method utilizes an objective function which is not based on learning and does not need training data, hence it is able to generalize well to real world scenarios.", + "bbox": [ + 88, + 566, + 482, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce three main contributions which enable the estimation of shape programs' parameters from images:", + "bbox": [ + 89, + 810, + 482, + 840 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our first contribution is a 'compiler' that generates PyTorch [26] code for a shape program, which can be defined in Blender for example. This code generates 3D shapes that are differentiable with respect to the continuous parameters", + "bbox": [ + 89, + 840, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and can therefore be used easily with 3D reconstruction algorithms to optimize the continuous parameters.", + "bbox": [ + 511, + 566, + 903, + 597 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Second, we contribute a method to obtain efficiently and reliably all shape program parameters from RGB-D scans: While our compiler can be used to optimize over the continuous parameters, the challenge of estimating the discrete parameters remains. We propose to adapt methods based on genetic algorithms to our problem of jointly optimizing the continuous and the discrete parameters of a shape program.", + "- Our third contribution is an extension of shape programs to capture fine details and appearance of objects. We do this by augmenting our programs with Gaussians. Once we retrieved the shape parameters, we initialize our procedural Gaussians over the primitives and optimize them as in Gaussian splatting [17]. The key difference with regular Gaussian Splatting is that our Gaussians are constrained by the procedural model: The Gaussians sampled on 'cloned' base primitives are tied together. e.g. as the legs of a chair are 'clones' of the same base primitives, the occluded part of a leg can still be recovered if it is visible for another leg." + ], + "bbox": [ + 511, + 598, + 905, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our method on both synthetic and real scenes. In addition to the usual metrics, we also evaluate", + "bbox": [ + 511, + 869, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16284", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "how well we reconstruct the shape program continuous and discrete parameters. Because existing datasets are not annotated with the value of these parameters, we manually annotated 176 objects.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, our main contribution is a general tool to create PyTorch code from Blender shape programs. In addition, we provide a method for estimating the parameters of shape programs from views together with the poses of the objects. Our PyTorchGeoNodes is a modular tool and it can be extended to novel use cases in 3D scene understanding. The source code is available to the general public.", + "bbox": [ + 89, + 154, + 480, + 260 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 281, + 232, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the field of retrieving 3D models for objects from images is very large, we focus here only on methods that can provide a light CAD model designed for specific categories: 3D model retrieval methods and Shape Programs.", + "bbox": [ + 89, + 309, + 480, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. 3D Model Retrieval", + "text_level": 1, + "bbox": [ + 89, + 387, + 277, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D model retrieval aims to retrieve a CAD model from a database of objects, such as the ShapeNet dataset [6], that maximizes some scoring function which is typically based on an input 3D representation or a single or multiple input images.", + "bbox": [ + 89, + 412, + 480, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some methods approach CAD model retrieval as a classification problem [3, 23]. For a given input a neural network can be trained to predict a probability distribution over all models in the database. However, these direct approaches do not scale well to large object databases such as the ShapeNet database. Another popular approach is computing a similarity metric between synthetic objects and real inputs. There are several possible ways of computing such metrics. It is possible to render an image from a synthetic object, and then for a synthetic-real image pair, we can compute and compare image descriptors [2, 13, 22] or encode images into embedding vector representations and calculate the similarity in the embedding space [20].", + "bbox": [ + 89, + 489, + 482, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While such approaches have displayed promising results, one clear limitation is expressiveness of the database of objects. In fact, even with large databases of objects, in practice we often encounter objects in real scenes that are not represented in the database, or we might encounter modified or articulated objects. For example, we can modify seat height, arm rest and back support position of a work chair but the object in the database appears in the default setting which will introduce errors during retrieval. While it is possible to perform mesh refinement and deformation [4, 14, 33], these approaches typically introduce artifacts and deformations in the reconstruction and the final object shape might not be representative of the actual object category after refinement.", + "bbox": [ + 89, + 688, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Shape Programs", + "text_level": 1, + "bbox": [ + 513, + 90, + 678, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Procedural modelling is an attractive way of generating 3D shapes in computer graphics, and as such it is an interesting feature of different 3D modelling software. In general, procedural modelling is a family of techniques that generate 3D content by abiding to a set of rules. A variety of methods were proposed that combine procedural modeling with machine learning approaches, summarized in detail in [30]. For example, [35] introduced a procedural language that enables the generation of a variety of shapes in form of so-called shape programs. In [35], shape programs are written in Domain Specific Language (DSL) for shapes with two types of statements. \"Draw\" statements describes shape primitive, such as cuboid or a cylinder, together with its geometric and semantic properties. \"For\" statements represent loops of sub-programs including parameters that indicate how the sub-program should be repeatedly executed.", + "bbox": [ + 511, + 112, + 903, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[35] also showed that it is possible to learn to infer shape programs that describe input 3D shapes. However, as it is based on basic geometric primitives, it becomes difficult to model more complex geometries, and resulting shapes can be non-representative of the target category. Other methods suffer from the same limitations [15, 16].", + "bbox": [ + 511, + 356, + 903, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GeoCode [27] recently introduced hand-designed shape programs as a mapping between 3D shapes of a specific object category and human-interpretable parameter space. The language used for developing shape programs is based on the geometry node feature of Blender, an open-source modeling software, which, in contrast to [35], allows designing of more expressive shape programs that can represent and interpolate between a variety of shapes by simply modifying human-interpretable program's parameters.", + "bbox": [ + 511, + 448, + 903, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some nodes define a shape primitive or pre-designed more complex shapes, e.g., chair seat or chair leg. Other nodes represent geometric transformations on individual shapes, or how two shapes should be connected, e.g., legs should always be connected to the bottom of the seat. There are nodes representing mathematical operations such as addition and multiplication, and there are nodes that are used to replicate specific shapes, e.g., in case of chair legs we can add a replicator node to create four instances of a chair leg of the same shape. There are also nodes that serve as control statements, e.g., it is possible to switch between a four-legged chair and a one-legged chair. A pre-defined set of input program's parameters allow non-expert user to easily control shape-generation process. [27] also showed that it is possible to learn the mapping from input point clouds of 3D shapes, or a sketch, to program's parameters.", + "bbox": [ + 511, + 585, + 903, + 827 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. PyTorchGeoNodes", + "text_level": 1, + "bbox": [ + 513, + 844, + 692, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we discuss shape programs and how they can be beneficial for tasks in 3D scene understanding. We", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16285", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d7c1dfe342c447bb538967e6268c53959d58a9d875ad6c34b75647b5138f58d6.jpg", + "image_caption": [ + "Figure 2. A procedural model in Blender generating dividing boards of a cabinet. The computational graph is designed and visualized in Blender using Geometry Nodes feature. Underneath, we show how we abstract the different nodes using PyTorch tensors and PyTorch3D meshes. The input node takes input parameters, here {Width: 0.5, Dividing Board Thickness: 0.04, Height: 0.6, Number of Dividing Boards: 5, Board Thickness: 0.04} and feeds them to a series of operations. The blue nodes are arithmetic and concatenation nodes, which transform input parameters and feed the results to geometry nodes, in green. In this example, we generate a cuboid mesh and instantiate a line of points which generates the final geometry for dividing boards. In practice, this shape program is part of a larger shape program for modeling cabinets." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 867, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "then describe our framework for enabling efficient gradient-based optimization for shape programs and, in addition, allowing to translate shape programs designed in Blender to PyTorch code to enable differentiable optimization. In Section 4, we explain how our framework can be applied for reconstructing 3D objects from images.", + "bbox": [ + 89, + 483, + 482, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We consider shape programs as defined in Blender, i.e., as a computational graph that computes 3D shapes given a number of input parameters. Such graphs contain nodes of different types; in our framework, we currently consider the following node types:", + "bbox": [ + 89, + 579, + 482, + 654 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An 'Input' node contains input parameters of the shape programs and their value ranges. We consider floating, integer, and boolean values;", + "- A 'Math' node performs mathematical operations on its input (addition, subtraction, multiplication, division, and comparison);", + "- A 'Switch' node switches between two inputs conditioned on a boolean input;", + "- A 'Combine' node concatenates three input values into a 3D vector;", + "- A 'Primitive' node creates a geometric primitive, e.g., a cuboid or a cylinder;", + "- A 'Transform' node applies scaling, rotation, and translation to the input geometry;", + "- 'Mesh Line' node creates a tensor of 3D points on a line from input vectors that define the start location and the" + ], + "bbox": [ + 91, + 659, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "offset of the line, and an integer that defines the number of points to be generated;", + "bbox": [ + 527, + 483, + 903, + 513 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A 'Points on instances' node clones input geometry at given input 3D points;", + "- A 'Join geometry' node merges geometries;", + "- An 'Output geometry node' generates the final mesh for the shape." + ], + "bbox": [ + 513, + 513, + 903, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that for example, the Transform node depends on continuous, the Points on instances node on integer, and the Switch node on boolean.", + "bbox": [ + 511, + 602, + 903, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our framework provides differentiable computational nodes that reimplement the functionalities of the individual geometry nodes in Blender as we show in Figure 2. More exactly, for every node type in Blender, we implement a corresponding node type with the same functionalities using PyTorch, or PyTorch3D [29] in case of geometric operations. In practice, we designed shape programs directly using the Blender interface. Given a shape program created in Blender, our parser generates a differentiable PyTorch-GeoNodes code. We can then use this code in PyTorch in an optimization procedure where we fit shape parameters to generate a shape consistent with the input scene.", + "bbox": [ + 511, + 661, + 906, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the supplementary material, we detail our design choices and technical details which make our implementation computationally efficient.", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16286", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4ab110ea511650d4681465f874960f68071790893c7e1e7c4825a6ff86194d70.jpg", + "image_caption": [ + "Figure 3. Fitting shape parameters with PyTorchGeoNodes. At every iteration, our genetic algorithm generates individuals of shape parameters and object poses. We parse 3D shapes from individual parameters using PyTorchGeoNodes and perform shape parameter optimization based on loss that evaluates how well the shape fits the input scene. In the next iteration, the optimized set of individuals is used to update the pool of individuals based on selection of the fittest principle." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 473, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Search Algorithm", + "text_level": 1, + "bbox": [ + 89, + 339, + 264, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We leverage our PyTorchGeoNodes framework to retrieve shape parameters and geometry of a target object in an RGB-D scan. We look for shape parameters $\\mathcal{P}^*$ by minimizing an objective function that encourages the shape to fit the point cloud reconstructed from the images while lying on the floor:", + "bbox": [ + 89, + 364, + 483, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} (\\mathcal {P}) = \\lambda_ {\\mathrm {C D}} \\mathcal {L} _ {\\mathrm {C D}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})) + \\lambda_ {\\mathrm {G}} \\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) + \\\\ \\lambda_ {\\mathrm {F l}} \\mathcal {L} _ {\\mathrm {F l}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P}))). \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 465, + 480, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{\\mathrm{CD}}(\\mathrm{PC}, \\mathrm{Sh}(\\mathcal{P}))$ measures the single-direction chamfer distance between PC, the point cloud reconstructed from the depth maps and object masks, and $\\mathrm{Sh}(\\mathcal{P})$ , the shape generated by the shape program. We follow pre-processing from [1] which relies on sparse point cloud instance segmentation of the object and use a segmentation model [18] on images to obtain the object masks. We then back-project these masks to obtain a dense target point cloud. $\\mathcal{L}_{\\mathrm{G}}(\\mathrm{G}, \\mathrm{Sh}(\\mathcal{P}))$ penalizes occlusions in the scene caused by $\\mathrm{Sh}(\\mathcal{P})$ . G is an occlusion grid obtained by densely sampling 3D points along rays between the camera and surfaces for different views:", + "bbox": [ + 89, + 510, + 483, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) = \\sum_ {p \\in \\operatorname {S h} (\\mathcal {P})} \\left\\{ \\begin{array}{l l} \\vec {\\mathrm {C D}} (p, \\mathrm {P C}) & \\text {i f} \\mathrm {G} (p) \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 698, + 483, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\vec{\\mathrm{CD}}$ ( $p, \\mathrm{PC}$ ) is the distance of point $p$ to PC. $\\mathbf{G}(p) = \\vec{\\mathbf{CD}}$ ( $p, \\mathrm{PC}$ ) < $\\omega$ determines whether $p$ is on grid G. We set threshold $\\omega = 5cm$ in our experiments. Since G is generated using input views for the scene, this loss does not penalize points that are occluded in the scene, similar to render-and-compare objectives. The term $\\mathcal{L}_{\\mathrm{Fl}}$ simply enforces the objects to stay on the floor plane:", + "bbox": [ + 89, + 753, + 483, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {F l}} \\left(\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})\\right) = | \\mathrm {F l} (\\mathrm {P C}) - \\mathrm {F l} (\\operatorname {S h} (\\mathcal {P})) | _ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 880, + 482, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{Fl}(\\mathrm{PC})$ returns the height of the lowest point in PC, and $\\operatorname{Fl}(\\operatorname{Sh}(\\mathcal{P}))$ similarly determines the lowest point of shape $\\operatorname{Sh}(\\mathcal{P})$ . We set weights of individual loss terms to $\\lambda_{\\mathrm{CD}} = 1$ , $\\lambda_{\\mathrm{G}} = 0.5$ , $\\lambda_{\\mathrm{Fl}} = 0.01$ in our experiments. Parameters $\\mathcal{P}$ include the object pose in addition to the shape program parameters. We initialize the translation based on an initial estimate of the object center which is refined during search. We constrain the rotation to be around the vertical axis only.", + "bbox": [ + 511, + 90, + 905, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use our PyTorchGeoNodes framework to compute $\\mathrm{Sh}(\\mathcal{P})$ . Thanks to this framework, PyTorch can compute the derivatives of $\\mathrm{Sh}(\\mathcal{P})$ and thus the derivatives of $\\mathcal{L}$ with respect to the continuous parameters in $\\mathcal{P}$ . However, some parameters in $\\mathcal{P}$ are discrete, i.e., integers or booleans. Therefore, we cannot optimize $\\mathcal{L}$ using a simple gradient descent. Also, $\\mathcal{L}$ has no special form that we can exploit to optimize it.", + "bbox": [ + 511, + 228, + 905, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To solve this problem, we propose to resort to genetic algorithms to optimize the parameters and combine it with gradient descent to further refine the continuous parameters.", + "bbox": [ + 511, + 349, + 906, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Shape Parameter Search", + "text_level": 1, + "bbox": [ + 511, + 407, + 741, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A genetic algorithm is a stochastic optimization algorithm that iteratively applies random manipulations of high-dimensional search parameters to identify the most promising complex search subspaces, subject to an objective function. In contrast to gradient-based techniques, it can optimize discrete and continuous values and the objective function can be very general and non-differentiable.", + "bbox": [ + 511, + 430, + 905, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The algorithm starts by randomly generating instances of parameter values $\\mathcal{P}$ , individuals, that form an initial set called population of search parameters. Every iteration has three phases: crossover and mutation for exploring search subspaces, and selection for exploiting the most promising subspaces. Crossover randomly selects pairs of individuals, parents, and mixes them by combining the individual parameters to create a new offspring. Therefore, an offspring lies in the search subspace at intersection of parents' search spaces. Mutation then randomly alters offsprings' parameters to further explore this subspace. Selection evaluates the quality of the population, and based on survival of the fittest strategy, it takes the best performing individuals to form the population for the next iteration. Further details and hyperparameters are given in the supplementary material.", + "bbox": [ + 511, + 537, + 906, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our adaptation of genetic algorithms to our problem is described in details in the supplementary material. The main points are given below. We generate an initial population by randomly generating instances of all program's parameters $\\mathcal{P}$ representing individuals in the population. We draw random values from the empirical distributions of the parameters. The crossover operation generates offspring $P_{1,2}$ from a pair of parents $\\mathcal{P}_1$ , $\\mathcal{P}_2$ . Mutation varies depending on the parameter type. For discrete parameter $d \\in \\mathcal{P}_D$", + "bbox": [ + 511, + 765, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16287", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we adapt its value $v_{d}$ :", + "bbox": [ + 89, + 90, + 236, + 106 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nv _ {d} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {d} & \\text {w i t h p r o b a b i l i t y} P _ {m} \\\\ v _ {d} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 117, + 480, + 157 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where operator $\\in_R$ randomly selects value $v$ from the set of valid discrete values $\\nu_{p}$ . $P_{m}$ is a hyper-parameter that defines the probability of mutating parameter values. In case of a continuous parameter $c\\in \\mathcal{P}_C$ , we adapt its value $v_{c}$ as:", + "bbox": [ + 89, + 169, + 482, + 229 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nv _ {c} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\cdot P _ {m} \\\\ v _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\\\ v _ {c} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 241, + 482, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{V}_c$ is a discretisation of values for parameter $c$ that we further discuss in the supplementary. $\\mathcal{N}(0,\\sigma)$ is normal distribution with mean value set to 0 and standard deviation $\\sigma$ . Finally, we evaluate offsprings, append them to the current population and we select the best individuals based on a score function, in our case negative of objective in Equation 1, to form the population for the next iteration.", + "bbox": [ + 89, + 308, + 483, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimization step. Using PyTorchGeoNodes, during the selection phase of every iteration, we perform a gradient-based optimization to further refine values of continuous shape parameters of individuals before selecting the population for next iteration. After a specified number of iterations the search concludes and we return shape parameters of the best performing individual.", + "bbox": [ + 89, + 414, + 483, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Integrating Gaussians Splats", + "text_level": 1, + "bbox": [ + 89, + 530, + 346, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Shape programs explicitly capture symmetries and similarities between repeated structures, while this aspect is lacking in many representations for 3D reconstruction. On the other hand, earlier shape programs do not capture well details and appearance.", + "bbox": [ + 89, + 551, + 482, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we show we enable procedural Gaussian splats by integrating them within shape programs and our PyTorchGeoNodes framework. This allows us to capture fine details of objects while keeping the advantages of shape programs. First, we explain how we augment the primitives with 'Gaussian primitives' while keeping the graph of PyTorchGeoNodes differentiable, and then, we introduce our render-and-compare objective function.", + "bbox": [ + 89, + 628, + 482, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Extending PyTorchGeoNodes with Gaussian primitives. To enable integration of our procedural graph to support Gaussian splats, we extend the nodes creating mesh primitives to also create trainable Gaussian parameters. We subsample the primitives meshes into many triangles and create Gaussians from these triangles. We initialize the Gaussians means, scales, and quaternions to fit the mesh triangles as we show in Figure 4. Their colors are initialized based on the closest 3D point in the scan. Their opacities are fixed to a high value. As with other primitives,", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6eeee1e0ddbb1b11fe12002e08cd994b46ccd9aaac55137b1c9bc07fd7a91907.jpg", + "image_caption": [ + "Figure 4. We integrate Gaussians directly into shape programs and PyTorchGeoNodes, to have the advantages of both procedural models and Gaussian splatting." + ], + "image_footnote": [], + "bbox": [ + 560, + 87, + 859, + 189 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the graph transforms the Gaussians to form a complete set of Gaussians, some of them sharing parameters due to the cloning in the graph.", + "bbox": [ + 511, + 247, + 903, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimizing the Gaussians. We noticed that it is more robust to, rather than jointly, first estimate the shape parameters and then optimize the Gaussians. Given a set of optimal shape parameters $\\mathcal{P}$ , we minimize the render-and compare loss as in other Gaussian splatting works, by rendering the Gaussians $\\mathcal{G}(\\mathcal{P})$ into scene views [12, 17, 40]:", + "bbox": [ + 511, + 292, + 905, + 383 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}} + \\mathcal {L} _ {\\text {r e g}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 393, + 903, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{RGB}}$ and $\\mathcal{L}_{\\mathrm{D}}$ are standard losses on color and depth consistency used in Gaussian splatting literature [7, 36, 40].", + "bbox": [ + 511, + 419, + 903, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{\\mathcal{P}} = \\mathrm{CD}(\\mathrm{Sh}(\\mathcal{P}),\\mathcal{G}(\\mathcal{P}))$ measures the consistency between the shape parameters and the Gaussians by relying on the chamfer distance. $\\mathcal{L}_{\\mathrm{reg}}$ is a regularizer term:", + "bbox": [ + 511, + 450, + 903, + 496 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {3} | M (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\lambda_ {4} | S (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 505, + 903, + 523 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {5} \\sum_ {G \\in \\mathcal {G} (\\mathcal {P})} \\operatorname {V a r} (C (G) |, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 526, + 903, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to enforce mean offsets $M(\\mathcal{G}(\\mathcal{P}))$ and scales offsets $S(\\mathcal{G}(\\mathcal{P}))$ of Gaussians to be small and the colors of the Gaussians on the same primitive $C(G)$ to remain close to each other. We set $\\lambda_1 = 0.1, \\lambda_2 = 0.1, \\lambda_3 = 100, \\lambda_4 = 10.00, \\lambda_5 = 1$ in our experiments. In addition, we observed that optimizing object Gaussians and background Gaussians jointly at the same time, with loss for background locations set to $\\lambda_{bgd}(\\mathcal{L}_{\\mathrm{RGB}} + \\lambda_1\\mathcal{L}_{\\mathrm{D}})$ and $\\lambda_{bgd} = 0.5$ ensures that object Gaussians remain consistent around edges.", + "bbox": [ + 511, + 569, + 905, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Validation", + "text_level": 1, + "bbox": [ + 511, + 717, + 625, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate our PyTorchGeoNodes framework and our optimization method on three common furniture categories: Sofa, with 18 parameters, Chair with 20, and Table, with 10, for which we created shape programs in Blender. We designed our shape programs to capture interpretable object structures that are relevant for objects in ScanNet, allowing unseen-before reasoning about high-level object parameters. More details are provided in the supplementary material.", + "bbox": [ + 511, + 742, + 905, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method jointly estimates the pose and shape parameters of the object. The orientation is defined as the rotation", + "bbox": [ + 511, + 871, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16288", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "around the up-axis as done in to [1], which is sufficient for indoor scenes.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We validate our method on object shape reconstruction for real world scenes from the ScanNet dataset [9]. ScanNet is a challenging dataset of indoor environment RGB-D scans: Furniture is only partially visible and highly occluded, and depth maps are incomplete due to missing sensor values—this happens for dark and reflective materials, for example. We manually annotated 176 objects for Sofa, Chair, and Table. We also provide additional results on automatically generated synthetic scenes in the supplementary material including an additional object category.", + "bbox": [ + 89, + 119, + 483, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Evaluation Criteria", + "text_level": 1, + "bbox": [ + 89, + 272, + 277, + 286 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation of shape parameters. Each object category has properties which are an important aspect of the reconstruction. This is neglected by current state-of-the-art methods. Our approach integrates these properties as shape parameters into the reconstruction and we evaluate them by comparing the reconstructed and ground truth parameters of the target objects. For the experiments with ScanNet, we manually annotated all relevant objects with shape parameters.", + "bbox": [ + 89, + 292, + 482, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data pre-processing. We assume that for the target object in the RGB-D scan, we have an initial estimate for the 3D center of the target object, here we follow preprocessing from [1]. Then, we estimate 2D segmentation masks of the object used to generate dense point clouds in the objective function in Equation (1).", + "bbox": [ + 89, + 409, + 483, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Search Baseline Details", + "text_level": 1, + "bbox": [ + 89, + 503, + 305, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In our evaluations of our search algorithm, we compare results of our genetic algorithm to two baselines:", + "bbox": [ + 89, + 523, + 482, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- GeoCode [27] introduces a supervised learning method based on an encoder-decoder architecture that takes a target point cloud as input and outputs a value for target program parameters. We use DGCNN [28] as encoder, and the resulting embedding of size 128 is shared between separate decoders that predict values for program parameters. More precisely, we use three feed-forward layers per parameter, each of size 256. For discrete parameters, we add a classification head as the output layer with number of outputs matching the number of different discrete values. For continuous parameters, we simply regress the output value. Finally, we perform gradient descent that further refines predictions by passing predicted parameter values to PyTorchGeoNodes and optimizing the objective function. We train it by randomly generating 10000 instances of ground truth shape program parameters and rotations and then generating synthetic point clouds from these parameters using PyTorchGeoNodes.", + "bbox": [ + 91, + 555, + 482, + 814 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Our implementation of coordinate descent iteratively optimizes individual parameters of the shape program. First, we initialize the estimate of parameters randomly. Then, at every iteration, we take the current estimate and replace value of the selected parameter by all valid discrete values and calculate the objective term. In case of", + "bbox": [ + 91, + 814, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cfd22c17674680e246b13a3db78986e0cad7200fb7b119add10b75fafc26a4c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 526, + 89, + 898, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8b65aa4e3f76d5fad28475adce1b6ac54e877e575f9e96162c16e76ed5e81e63.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 526, + 164, + 898, + 238 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ed32c9270f8a4574715d073c33fb0de87624c5494901ca944a61a9ceab345bc.jpg", + "image_caption": [ + "Figure 5. Shape from recovered object parameters aligns very well with the target object also when projected into sampled images of the scene. In the first row, we reconstruct a variety of chairs along with many detailed parameters including seat thickness, thickness and offsets of side and front/back support legs, existence of different semantic elements like 'star-shaped' legs and its exact rotation. In the second row, we correctly estimate shape of table top and its measurements, including width, depth and thickness, parameters of table legs, and existence of middle shelf including its offset from the bottom. In the third row we reconstruct parameters of 'L-element' of sofa including its depth and width, existence and size of legs, and existence of individual armrests, backrest, and the corresponding measurements. We show more results in the supplementary material." + ], + "image_footnote": [], + "bbox": [ + 524, + 241, + 898, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "continuous values we first discretize them as we explain in the supplementary. In case this improves the objective, we update the current estimate. Finally, we perform gradient descent that further refines the current estimate by passing it to PyTorchGeoNodes and optimizing the objective function. We repeat the process for all different parameters and loop 3 times which approximately matches the execution time of our genetic algorithm.", + "bbox": [ + 527, + 551, + 906, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Validation on the ScanNet Dataset", + "text_level": 1, + "bbox": [ + 511, + 676, + 812, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our approach on challenging real-world scenarios on validation scenes from ScanNet [9], which provides RGB-D scans of indoor scenes. We selected a subset of object instances from the Scannotate dataset [1] for which we manually annotated 57 sofas, 52 chairs, and 67 tables.", + "bbox": [ + 511, + 698, + 905, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 evaluates the quality for object parameters reconstruction for the 'table' category and general reconstruction quality across different categories. We report the numbers for 'chair' and 'sofa' in the supplementary material. We measure the classification accuracy for discrete parameteres and absolute difference for continuous parameters.", + "bbox": [ + 511, + 771, + 905, + 856 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We observe that the supervised learning method from [27], trained on synthetic data, generalises poorly to the scene from ScanNet, while coordinate descent baseline", + "bbox": [ + 511, + 857, + 905, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16289", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cb3d084733a59ed79032e5b85ecc1fd2ecdd150601ca21b0097987cb349467b6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ParameterModel from [27] w\\o refinementModel from [27] w\\o refinementCD w\\o refinementCD w\\o refinementGenetic w\\o refinementGenetic
Continuous ParametersWidth [cm]0.740.220.210.210.150.08
Height [cm]0.340.140.150.150.120.06
Depth [cm]0.40.20.220.220.130.08
Mid Leg X Scale0.190.130.160.140.10.07
Mid Leg Y Scale0.160.140.110.110.080.08
Legs Offset Y0.350.340.370.370.310.27
Legs Offset X0.320.320.360.360.150.13
Legs Scale Y0.170.150.180.190.130.1
Mid Board Z Scale0.210.180.180.180.170.14
Cabinet Width Scale0.150.10.150.110.10.05
Top Thickness [cm]0.030.030.020.020.020.02
Legs Size [cm]0.030.030.030.030.010.01
Discrete P:Top ShapeClassification Accuracy for Table ()
Legs Type0.780.780.720.720.940.94
Has Cabinet Leg0.390.390.60.580.780.78
Has Mid Board0.710.710.570.550.780.86
0.710.710.550.490.760.76
Chamfer distance [m] Abs. rotation error [rad]Reconstruction quality across all categories ()
0.520.210.160.160.140.11
0.450.120.130.110.080.06
", + "bbox": [ + 122, + 88, + 874, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Quantitative results of shape program parameters between different baselines for category Table, and general reconstruction metrics across all categories. We observe that GeoCode [27] performs worst due to the domain gap, but the optimization helps improve the performance. Coordinate Descent (CD) does better but is prone to local minima. Genetic algorithm outperforms other baselines by a significant margin.", + "bbox": [ + 88, + 457, + 906, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is prone to local minima. Our genetic algorithm performs very well across all metrics except for parameters defining very small details. Visually, the models recovered by our method are comparable in quality to the ground truth and we confirm the benefits of our refinement procedure. Figure 5 and Figure 6 show some qualitative results. In the supplementary we show additional results, and include a downstream application for point cloud segmentation based on our reconstructions.", + "bbox": [ + 88, + 536, + 480, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 686, + 209, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our code is publicly available and we hope this will encourage other researchers to develop the field and further extend possibilities with PyTorchGeoNodes. While shape programs are an attractive representation of objects, there are indeed still many things to develop: e.g. extensions to consider deformable and articulated objects and to integrate textures. Modularity of PyTorchGeoNodes enables integrations with other types of 3D representation, as we demonstrate with our integration of Gaussian Splatting. Moreover, differentiable rendering of PyTorchGeoNodes enables development of deep learning methods for creating shape programs from images in a self-supervised way. Finally, a major limitation is that our shape programs need to be de", + "bbox": [ + 88, + 712, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b348e0ac8ebc3dbb7f2c76d2360469dee827f4314ba1ec5e6cc8b6ea559c0781.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 553, + 534, + 647, + 590 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3c0d22fd298af7e184212eafe8a41d4f08d48a4c96f783e69d9020e4f2344c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 553, + 592, + 647, + 648 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3151cb23ef2768ce77fe883de212c43f2585e19b58fad6ac70c45fc0266f52ac.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 553, + 651, + 647, + 705 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/585ccc93522a48f56ac7737bf2a0524821cd2297b29980c5e91da7faf8af6e9f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 534, + 741, + 590 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/510d592bd3d2328274253fb15eb0c5f6a50c966146cc43b4c8808d2601864042.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 592, + 741, + 648 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c2c30f1f685406a4f6ba7b4b834232759067a9d513533810d3cc9c3d191adb29.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 647, + 651, + 741, + 705 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ba237cd9b99fae90506d8620afad4b90064afed4920a17cb5a44d6d89ca9c64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 536, + 846, + 590 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d1b9fe4bd7803eaf38a3a1eb9f756dcc1c7d2807160f4fad385de164f8cdda3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 593, + 861, + 648 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bf75121d42a0f9c23e83480204ea91417ff9b9b757c9f7eab5757671ab76a1ec.jpg", + "image_caption": [ + "(c)", + "Figure 6. (a) We overlay shape reconstructed using our retrieved shape parameters with the image and (b) compare it to the ground truth. (c) Our integration of Gaussians into PyTorchGeoNodes enables appealing 3D reconstructions." + ], + "image_footnote": [], + "bbox": [ + 774, + 652, + 846, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "signed by humans for different categories which can lead to limited expressiveness when applying our approach in the wild. Learning shape program designs from database of shapes would make our method easily applicable to novel categories.", + "bbox": [ + 511, + 797, + 906, + 869 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16290", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This project was funded by the European Union (ERC Advanced Grant explorer Funding ID #101097259). This work was performed using HPC resources from GENCI-IDRIS (Grant 2024-AD010615585).", + "bbox": [ + 89, + 116, + 483, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 194, + 187, + 210 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Stefan Ainetter, Sinisa Stekovic, Friedrich Fraundorfer, and Vincent Lepetit. 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As-Rigid-as-Possible Surface Modeling. In Symposium on Geometry Processing, 2007.", + "[34] Stanislaw Szymanowicz, Christian Rupprecht, and Andrea Vedaldi. Splatter Image: Ultra-Fast Single-View 3D Reconstruction. arXiv Preprint, 2023.", + "[35] Yonglong Tian, Andrew Luo, Xingyuan Sun, Kevin Ellis, William T Freeman, Joshua B Tenenbaum, and Jiajun Wu. Learning to Infer and Execute 3D Shape Programs. International Conference for Learning Representations, 2019.", + "[36] Matias Turkulainen, Xuqian Ren, Iaroslav Melekhov, Otto Seiskari, Esa Rahtu, and Juho Kannala. DN-Splatter: Depth and Normal Priors for Gaussian Splatting and Meshing. arXiv preprint arXiv:2403.17822, 2024.", + "[37] Beatrice Vaienti, Rémi Petitpierre, Isabella di Lenardo, and Frédéric Kaplan. Machine-Learning-Enhanced Procedural Modeling for 4D Historical Cities Reconstruction. Remote Sensing, 15(13), 2023.", + "[38] Nanyang Wang, Yinda Zhang, Zhuwen Li, Yanwei Fu, Wei Liu, and Yu-Gang Jiang. Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images. In European Conference on Computer Vision, 2018.", + "[39] Peter Wonka, Michael Wimmer, François Sillion, and William Ribarsky. Instant Architecture. ACM Transactions on Graphics (TOG), 2003.", + "[40] Tong Wu, Yu-Jie Yuan, Ling-Xiao Zhang, Jie Yang, Yan-Pei Cao, Ling-Qi Yan, and Lin Gao. Recent Advances in 3D Gaussian Splatting. Computational Visual Media, 2024." + ], + "bbox": [ + 91, + 92, + 480, + 800 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16292", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_model.json b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..33979230855dfb3df9cba8f0cac94e6b201ec5d4 --- /dev/null +++ b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_model.json @@ -0,0 +1,2244 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.124, + 0.13, + 0.877, + 0.175 + ], + "angle": 0, + "content": "PyTorchGeoNodes: Enabling Differentiable Shape Programs for 3D Shape Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.203, + 0.899, + 0.221 + ], + "angle": 0, + "content": "Sinisa Stekovic\\(^{1,2}\\) Arslan Artykov\\(^{1}\\) Stefan Ainetter\\(^{2}\\) Mattia D'Urso\\(^{2}\\) Friedrich Fraundorfer\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.223, + 0.707, + 0.239 + ], + "angle": 0, + "content": "1 LIGM, École des Ponts et Chaussees, IP Paris, CNRS, France" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.24, + 0.753, + 0.257 + ], + "angle": 0, + "content": "2 Inst. for Computer Graphics and Vision, Graz Univ. of Technology, Austria" + }, + { + "type": "text", + "bbox": [ + 0.281, + 0.268, + 0.71, + 0.282 + ], + "angle": 0, + "content": "Project page: vvenom.github.io/pytorchgeonodes" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.317, + 0.327, + 0.334 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.348, + 0.486, + 0.667 + ], + "angle": 0, + "content": "We propose PyTorchGeoNodes, a differentiable module for reconstructing 3D objects and their parameters from images using interpretable shape programs. Unlike traditional CAD model retrieval, shape programs allow reasoning about semantic parameters, editing, and a low memory footprint. Despite their potential, shape programs for 3D scene understanding have been largely overlooked. Our key contribution is enabling gradient-based optimization by parsing shape programs, or more precisely procedural models designed in Blender, into efficient PyTorch code. While there are many possible applications of our PyTorchGeoNodes, we show that a combination of PyTorchGeoNodes with genetic algorithm is a method of choice to optimize both discrete and continuous shape program parameters for 3D reconstruction and understanding of 3D object parameters. Our modular framework can be further integrated with other reconstruction algorithms, and we demonstrate one such integration to enable procedural Gaussian splattig. Our experiments on the ScanNet dataset show that our method achieves accurate reconstructions while enabling, until now, unseen level of 3D scene understanding." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.694, + 0.222, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.886 + ], + "angle": 0, + "content": "Various 3D object representations have already been considered for 3D scene understanding: voxels [21, 31], meshes [11, 38], SDFs [25], NeRFs [5], Gaussian Splatting [34], exemplars from a shape database [3]. SDFs, NeRFs, or Gaussian Splatting generalize to shapes unseen during training but produce artifacts for example when parts of the object are occluded in scenes captured \"in the wild\". Their memory footprint can also become large. Using exemplars guarantees that the retrieved shapes look good as they are created by human designers, however the database may not contain shapes similar to the target object." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this paper, we investigate the use of interpretable" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.319, + 0.905, + 0.439 + ], + "angle": 0, + "content": "shape programs to represent objects. Shape programs are a form of procedural modeling [10] introduced in [35] for representing 3D objects. While shape programs have already been considered for 3D scene understanding [27, 32], their use in this context remains largely unexplored. As shown in Figure 1, our method can be used to accurately retrieve geometry and 3D parameters of target objects, together with its texture even in presence of partial occlusions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.44, + 0.906, + 0.575 + ], + "angle": 0, + "content": "Shape programs can be seen as computational graphs of parametrized geometric operations that generate various 3D shapes from an object category given input shape parameters, such as object dimensions as well as \"semantic\" properties like existence of armrest or backrest in case of chairs. Multiple similar parts, for example the legs of a chair or the shelves of a bookshelves—are obtained by first generating a single instance, duplicating it and applying geometric transformations such as rotations and translations as needed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.577, + 0.906, + 0.743 + ], + "angle": 0, + "content": "Thanks to this procedural modeling approach, shape programs generate shapes that remain appealing and that can fit many different instances. Alongside being interpretable, the shapes they generate are editable in an intuitive manner and have a very small memory footprint. In fact, they are already a popular tool for building reconstruction [19, 24, 37, 39] and the interest around shape programs for objects is growing [15, 16, 27, 35]. Blender [8] already provides support for them. A research challenge targeting reconstruction of walls, doors, and windows using such structured languages was organized by Meta in \\(2024^{1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.743, + 0.905, + 0.834 + ], + "angle": 0, + "content": "Recovering parameters of a shape program from an image is however challenging. Typically, a shape generated by a shape program depends on a number of parameters. Some parameters such as the width and height of the objects take continuous values but other parameters take only discrete values, e.g. the number of shelves in a bookshelf." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.835, + 0.905, + 0.865 + ], + "angle": 0, + "content": "Optimizing on these parameters turns out to be tricky: For example, changing the number of shelves from 5 to 6" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.905, + 0.901 + ], + "angle": 0, + "content": "[https://eval.ai/web/challenges/challenge-page/2115/overview (Accessed: November 2024)]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16283" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.175, + 0.089, + 0.831, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.314, + 0.738, + 0.327 + ], + "angle": 0, + "content": "Jointly recovered geometry and parameters of target objects from RGB-D scans" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.328, + 0.353, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.429, + 0.34, + 0.442 + ], + "angle": 0, + "content": "Views of Target object" + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.328, + 0.49, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.429, + 0.497, + 0.44 + ], + "angle": 0, + "content": "Recovered Gaussians" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.328, + 0.811, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.583, + 0.429, + 0.758, + 0.442 + ], + "angle": 0, + "content": "Procedural Gaussians editing" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.455, + 0.907, + 0.553 + ], + "angle": 0, + "content": "Figure 1. Our PyTorchGeoNodes is a framework that enables differentiable shape programs for 3D reconstruction. Our semantically-rich reconstructions of 3D objects from RGB-D scans enable understanding of important metric parameters of individual parts for different objects. These parameters are physically bound to the 3D reconstruction as PyTorchGeoNodes enables flow of gradients from the generated shape to the parameters of the object. Our PyTorchGeoNodes is modular, e.g. we can use it to enable procedural modeling for Gaussian splatting. In the example, our method recovers Gaussians for the target sofa and 'clones' all details from the visible armrest to the occluded armrest in the scene. Our integration enables procedural editing of Gaussians and we can alter shape parameters to edit the reconstruction: e.g. by extending or shrinking width of the seat, removing backrest, left armrest, changing height of the backrest and depth of the seat etc." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.568, + 0.483, + 0.809 + ], + "angle": 0, + "content": "changes significantly the shape and appearance of a bookshelf. There have been a few attempts in the computer vision community to use procedural shapes [27, 32]. In [27] the authors train a neural network to predict the parameters of a shape program. While this method shows impressive results using synthetic data, we show in Section 5.3 that on real data such an approach fails to generalize well, due to the lack of real world image data annotated with shape parameters. Using synthetically generated data to train such models also performs very badly: While shape programs capture very well the global structure of objects, they do not represent details. As a result, the model can hardly generalize from synthetic images to real ones. In comparison, our proposed method utilizes an objective function which is not based on learning and does not need training data, hence it is able to generalize well to real world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.841 + ], + "angle": 0, + "content": "We introduce three main contributions which enable the estimation of shape programs' parameters from images:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- Our first contribution is a 'compiler' that generates PyTorch [26] code for a shape program, which can be defined in Blender for example. This code generates 3D shapes that are differentiable with respect to the continuous parameters" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.905, + 0.598 + ], + "angle": 0, + "content": "and can therefore be used easily with 3D reconstruction algorithms to optimize the continuous parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.906, + 0.703 + ], + "angle": 0, + "content": "- Second, we contribute a method to obtain efficiently and reliably all shape program parameters from RGB-D scans: While our compiler can be used to optimize over the continuous parameters, the challenge of estimating the discrete parameters remains. We propose to adapt methods based on genetic algorithms to our problem of jointly optimizing the continuous and the discrete parameters of a shape program." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.906, + 0.87 + ], + "angle": 0, + "content": "- Our third contribution is an extension of shape programs to capture fine details and appearance of objects. We do this by augmenting our programs with Gaussians. Once we retrieved the shape parameters, we initialize our procedural Gaussians over the primitives and optimize them as in Gaussian splatting [17]. The key difference with regular Gaussian Splatting is that our Gaussians are constrained by the procedural model: The Gaussians sampled on 'cloned' base primitives are tied together. e.g. as the legs of a chair are 'clones' of the same base primitives, the occluded part of a leg can still be recovered if it is visible for another leg." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.599, + 0.906, + 0.87 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.9 + ], + "angle": 0, + "content": "We evaluate our method on both synthetic and real scenes. In addition to the usual metrics, we also evaluate" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16284" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "how well we reconstruct the shape program continuous and discrete parameters. Because existing datasets are not annotated with the value of these parameters, we manually annotated 176 objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.155, + 0.482, + 0.261 + ], + "angle": 0, + "content": "In summary, our main contribution is a general tool to create PyTorch code from Blender shape programs. In addition, we provide a method for estimating the parameters of shape programs from views together with the poses of the objects. Our PyTorchGeoNodes is a modular tool and it can be extended to novel use cases in 3D scene understanding. The source code is available to the general public." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.282, + 0.233, + 0.298 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.31, + 0.482, + 0.371 + ], + "angle": 0, + "content": "Since the field of retrieving 3D models for objects from images is very large, we focus here only on methods that can provide a light CAD model designed for specific categories: 3D model retrieval methods and Shape Programs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.388, + 0.279, + 0.403 + ], + "angle": 0, + "content": "2.1. 3D Model Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.413, + 0.482, + 0.488 + ], + "angle": 0, + "content": "3D model retrieval aims to retrieve a CAD model from a database of objects, such as the ShapeNet dataset [6], that maximizes some scoring function which is typically based on an input 3D representation or a single or multiple input images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.491, + 0.483, + 0.687 + ], + "angle": 0, + "content": "Some methods approach CAD model retrieval as a classification problem [3, 23]. For a given input a neural network can be trained to predict a probability distribution over all models in the database. However, these direct approaches do not scale well to large object databases such as the ShapeNet database. Another popular approach is computing a similarity metric between synthetic objects and real inputs. There are several possible ways of computing such metrics. It is possible to render an image from a synthetic object, and then for a synthetic-real image pair, we can compute and compare image descriptors [2, 13, 22] or encode images into embedding vector representations and calculate the similarity in the embedding space [20]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "While such approaches have displayed promising results, one clear limitation is expressiveness of the database of objects. In fact, even with large databases of objects, in practice we often encounter objects in real scenes that are not represented in the database, or we might encounter modified or articulated objects. For example, we can modify seat height, arm rest and back support position of a work chair but the object in the database appears in the default setting which will introduce errors during retrieval. While it is possible to perform mesh refinement and deformation [4, 14, 33], these approaches typically introduce artifacts and deformations in the reconstruction and the final object shape might not be representative of the actual object category after refinement." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.679, + 0.108 + ], + "angle": 0, + "content": "2.2. Shape Programs" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.113, + 0.905, + 0.355 + ], + "angle": 0, + "content": "Procedural modelling is an attractive way of generating 3D shapes in computer graphics, and as such it is an interesting feature of different 3D modelling software. In general, procedural modelling is a family of techniques that generate 3D content by abiding to a set of rules. A variety of methods were proposed that combine procedural modeling with machine learning approaches, summarized in detail in [30]. For example, [35] introduced a procedural language that enables the generation of a variety of shapes in form of so-called shape programs. In [35], shape programs are written in Domain Specific Language (DSL) for shapes with two types of statements. \"Draw\" statements describes shape primitive, such as cuboid or a cylinder, together with its geometric and semantic properties. \"For\" statements represent loops of sub-programs including parameters that indicate how the sub-program should be repeatedly executed." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.357, + 0.905, + 0.447 + ], + "angle": 0, + "content": "[35] also showed that it is possible to learn to infer shape programs that describe input 3D shapes. However, as it is based on basic geometric primitives, it becomes difficult to model more complex geometries, and resulting shapes can be non-representative of the target category. Other methods suffer from the same limitations [15, 16]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.449, + 0.905, + 0.585 + ], + "angle": 0, + "content": "GeoCode [27] recently introduced hand-designed shape programs as a mapping between 3D shapes of a specific object category and human-interpretable parameter space. The language used for developing shape programs is based on the geometry node feature of Blender, an open-source modeling software, which, in contrast to [35], allows designing of more expressive shape programs that can represent and interpolate between a variety of shapes by simply modifying human-interpretable program's parameters." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.586, + 0.905, + 0.828 + ], + "angle": 0, + "content": "Some nodes define a shape primitive or pre-designed more complex shapes, e.g., chair seat or chair leg. Other nodes represent geometric transformations on individual shapes, or how two shapes should be connected, e.g., legs should always be connected to the bottom of the seat. There are nodes representing mathematical operations such as addition and multiplication, and there are nodes that are used to replicate specific shapes, e.g., in case of chair legs we can add a replicator node to create four instances of a chair leg of the same shape. There are also nodes that serve as control statements, e.g., it is possible to switch between a four-legged chair and a one-legged chair. A pre-defined set of input program's parameters allow non-expert user to easily control shape-generation process. [27] also showed that it is possible to learn the mapping from input point clouds of 3D shapes, or a sketch, to program's parameters." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.845, + 0.694, + 0.861 + ], + "angle": 0, + "content": "3. PyTorchGeoNodes" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In this section, we discuss shape programs and how they can be beneficial for tasks in 3D scene understanding. We" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "16285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.868, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.36, + 0.908, + 0.457 + ], + "angle": 0, + "content": "Figure 2. A procedural model in Blender generating dividing boards of a cabinet. The computational graph is designed and visualized in Blender using Geometry Nodes feature. Underneath, we show how we abstract the different nodes using PyTorch tensors and PyTorch3D meshes. The input node takes input parameters, here {Width: 0.5, Dividing Board Thickness: 0.04, Height: 0.6, Number of Dividing Boards: 5, Board Thickness: 0.04} and feeds them to a series of operations. The blue nodes are arithmetic and concatenation nodes, which transform input parameters and feed the results to geometry nodes, in green. In this example, we generate a cuboid mesh and instantiate a line of points which generates the final geometry for dividing boards. In practice, this shape program is part of a larger shape program for modeling cabinets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.484, + 0.483, + 0.576 + ], + "angle": 0, + "content": "then describe our framework for enabling efficient gradient-based optimization for shape programs and, in addition, allowing to translate shape programs designed in Blender to PyTorch code to enable differentiable optimization. In Section 4, we explain how our framework can be applied for reconstructing 3D objects from images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.483, + 0.655 + ], + "angle": 0, + "content": "We consider shape programs as defined in Blender, i.e., as a computational graph that computes 3D shapes given a number of input parameters. Such graphs contain nodes of different types; in our framework, we currently consider the following node types:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.66, + 0.483, + 0.704 + ], + "angle": 0, + "content": "- An 'Input' node contains input parameters of the shape programs and their value ranges. We consider floating, integer, and boolean values;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.705, + 0.483, + 0.749 + ], + "angle": 0, + "content": "- A 'Math' node performs mathematical operations on its input (addition, subtraction, multiplication, division, and comparison);" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.75, + 0.483, + 0.779 + ], + "angle": 0, + "content": "- A 'Switch' node switches between two inputs conditioned on a boolean input;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.781, + 0.483, + 0.809 + ], + "angle": 0, + "content": "- A 'Combine' node concatenates three input values into a 3D vector;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.811, + 0.483, + 0.841 + ], + "angle": 0, + "content": "- A 'Primitive' node creates a geometric primitive, e.g., a cuboid or a cylinder;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.841, + 0.483, + 0.871 + ], + "angle": 0, + "content": "- A 'Transform' node applies scaling, rotation, and translation to the input geometry;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- 'Mesh Line' node creates a tensor of 3D points on a line from input vectors that define the start location and the" + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.66, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.484, + 0.905, + 0.514 + ], + "angle": 0, + "content": "offset of the line, and an integer that defines the number of points to be generated;" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.515, + 0.905, + 0.544 + ], + "angle": 0, + "content": "- A 'Points on instances' node clones input geometry at given input 3D points;" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.545, + 0.821, + 0.559 + ], + "angle": 0, + "content": "- A 'Join geometry' node merges geometries;" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.56, + 0.905, + 0.589 + ], + "angle": 0, + "content": "- An 'Output geometry node' generates the final mesh for the shape." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.515, + 0.905, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.603, + 0.905, + 0.647 + ], + "angle": 0, + "content": "Note that for example, the Transform node depends on continuous, the Points on instances node on integer, and the Switch node on boolean." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.662, + 0.907, + 0.844 + ], + "angle": 0, + "content": "Our framework provides differentiable computational nodes that reimplement the functionalities of the individual geometry nodes in Blender as we show in Figure 2. More exactly, for every node type in Blender, we implement a corresponding node type with the same functionalities using PyTorch, or PyTorch3D [29] in case of geometric operations. In practice, we designed shape programs directly using the Blender interface. Given a shape program created in Blender, our parser generates a differentiable PyTorch-GeoNodes code. We can then use this code in PyTorch in an optimization procedure where we fit shape parameters to generate a shape consistent with the input scene." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In the supplementary material, we detail our design choices and technical details which make our implementation computationally efficient." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16286" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.475, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.204, + 0.485, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Fitting shape parameters with PyTorchGeoNodes. At every iteration, our genetic algorithm generates individuals of shape parameters and object poses. We parse 3D shapes from individual parameters using PyTorchGeoNodes and perform shape parameter optimization based on loss that evaluates how well the shape fits the input scene. In the next iteration, the optimized set of individuals is used to update the pool of individuals based on selection of the fittest principle." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.34, + 0.266, + 0.358 + ], + "angle": 0, + "content": "4. Search Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.365, + 0.484, + 0.456 + ], + "angle": 0, + "content": "We leverage our PyTorchGeoNodes framework to retrieve shape parameters and geometry of a target object in an RGB-D scan. We look for shape parameters \\(\\mathcal{P}^*\\) by minimizing an objective function that encourages the shape to fit the point cloud reconstructed from the images while lying on the floor:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.466, + 0.482, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} (\\mathcal {P}) = \\lambda_ {\\mathrm {C D}} \\mathcal {L} _ {\\mathrm {C D}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})) + \\lambda_ {\\mathrm {G}} \\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) + \\\\ \\lambda_ {\\mathrm {F l}} \\mathcal {L} _ {\\mathrm {F l}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P}))). \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.511, + 0.484, + 0.692 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{\\mathrm{CD}}(\\mathrm{PC}, \\mathrm{Sh}(\\mathcal{P}))\\) measures the single-direction chamfer distance between PC, the point cloud reconstructed from the depth maps and object masks, and \\(\\mathrm{Sh}(\\mathcal{P})\\), the shape generated by the shape program. We follow pre-processing from [1] which relies on sparse point cloud instance segmentation of the object and use a segmentation model [18] on images to obtain the object masks. We then back-project these masks to obtain a dense target point cloud. \\(\\mathcal{L}_{\\mathrm{G}}(\\mathrm{G}, \\mathrm{Sh}(\\mathcal{P}))\\) penalizes occlusions in the scene caused by \\(\\mathrm{Sh}(\\mathcal{P})\\). G is an occlusion grid obtained by densely sampling 3D points along rays between the camera and surfaces for different views:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.699, + 0.484, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) = \\sum_ {p \\in \\operatorname {S h} (\\mathcal {P})} \\left\\{ \\begin{array}{l l} \\vec {\\mathrm {C D}} (p, \\mathrm {P C}) & \\text {i f} \\mathrm {G} (p) \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.755, + 0.484, + 0.871 + ], + "angle": 0, + "content": "where \\(\\vec{\\mathrm{CD}}\\) (\\(p, \\mathrm{PC}\\)) is the distance of point \\(p\\) to PC. \\(\\mathbf{G}(p) = \\vec{\\mathbf{CD}}\\) (\\(p, \\mathrm{PC}\\)) < \\(\\omega\\) determines whether \\(p\\) is on grid G. We set threshold \\(\\omega = 5cm\\) in our experiments. Since G is generated using input views for the scene, this loss does not penalize points that are occluded in the scene, similar to render-and-compare objectives. The term \\(\\mathcal{L}_{\\mathrm{Fl}}\\) simply enforces the objects to stay on the floor plane:" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.881, + 0.483, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {F l}} \\left(\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})\\right) = | \\mathrm {F l} (\\mathrm {P C}) - \\mathrm {F l} (\\operatorname {S h} (\\mathcal {P})) | _ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.228 + ], + "angle": 0, + "content": "where \\(\\operatorname{Fl}(\\mathrm{PC})\\) returns the height of the lowest point in PC, and \\(\\operatorname{Fl}(\\operatorname{Sh}(\\mathcal{P}))\\) similarly determines the lowest point of shape \\(\\operatorname{Sh}(\\mathcal{P})\\). We set weights of individual loss terms to \\(\\lambda_{\\mathrm{CD}} = 1\\), \\(\\lambda_{\\mathrm{G}} = 0.5\\), \\(\\lambda_{\\mathrm{Fl}} = 0.01\\) in our experiments. Parameters \\(\\mathcal{P}\\) include the object pose in addition to the shape program parameters. We initialize the translation based on an initial estimate of the object center which is refined during search. We constrain the rotation to be around the vertical axis only." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.229, + 0.906, + 0.348 + ], + "angle": 0, + "content": "We use our PyTorchGeoNodes framework to compute \\(\\mathrm{Sh}(\\mathcal{P})\\). Thanks to this framework, PyTorch can compute the derivatives of \\(\\mathrm{Sh}(\\mathcal{P})\\) and thus the derivatives of \\(\\mathcal{L}\\) with respect to the continuous parameters in \\(\\mathcal{P}\\). However, some parameters in \\(\\mathcal{P}\\) are discrete, i.e., integers or booleans. Therefore, we cannot optimize \\(\\mathcal{L}\\) using a simple gradient descent. Also, \\(\\mathcal{L}\\) has no special form that we can exploit to optimize it." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.907, + 0.397 + ], + "angle": 0, + "content": "To solve this problem, we propose to resort to genetic algorithms to optimize the parameters and combine it with gradient descent to further refine the continuous parameters." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.408, + 0.742, + 0.424 + ], + "angle": 0, + "content": "4.1. Shape Parameter Search" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.906, + 0.537 + ], + "angle": 0, + "content": "A genetic algorithm is a stochastic optimization algorithm that iteratively applies random manipulations of high-dimensional search parameters to identify the most promising complex search subspaces, subject to an objective function. In contrast to gradient-based techniques, it can optimize discrete and continuous values and the objective function can be very general and non-differentiable." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.538, + 0.907, + 0.765 + ], + "angle": 0, + "content": "The algorithm starts by randomly generating instances of parameter values \\(\\mathcal{P}\\), individuals, that form an initial set called population of search parameters. Every iteration has three phases: crossover and mutation for exploring search subspaces, and selection for exploiting the most promising subspaces. Crossover randomly selects pairs of individuals, parents, and mixes them by combining the individual parameters to create a new offspring. Therefore, an offspring lies in the search subspace at intersection of parents' search spaces. Mutation then randomly alters offsprings' parameters to further explore this subspace. Selection evaluates the quality of the population, and based on survival of the fittest strategy, it takes the best performing individuals to form the population for the next iteration. Further details and hyperparameters are given in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Our adaptation of genetic algorithms to our problem is described in details in the supplementary material. The main points are given below. We generate an initial population by randomly generating instances of all program's parameters \\(\\mathcal{P}\\) representing individuals in the population. We draw random values from the empirical distributions of the parameters. The crossover operation generates offspring \\(P_{1,2}\\) from a pair of parents \\(\\mathcal{P}_1\\), \\(\\mathcal{P}_2\\). Mutation varies depending on the parameter type. For discrete parameter \\(d \\in \\mathcal{P}_D\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16287" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.238, + 0.107 + ], + "angle": 0, + "content": "we adapt its value \\( v_{d} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.118, + 0.482, + 0.159 + ], + "angle": 0, + "content": "\\[\nv _ {d} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {d} & \\text {w i t h p r o b a b i l i t y} P _ {m} \\\\ v _ {d} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.17, + 0.483, + 0.231 + ], + "angle": 0, + "content": "where operator \\(\\in_R\\) randomly selects value \\(v\\) from the set of valid discrete values \\(\\nu_{p}\\). \\(P_{m}\\) is a hyper-parameter that defines the probability of mutating parameter values. In case of a continuous parameter \\(c\\in \\mathcal{P}_C\\), we adapt its value \\(v_{c}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.242, + 0.483, + 0.297 + ], + "angle": 0, + "content": "\\[\nv _ {c} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\cdot P _ {m} \\\\ v _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\\\ v _ {c} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.309, + 0.484, + 0.414 + ], + "angle": 0, + "content": "where \\(\\mathcal{V}_c\\) is a discretisation of values for parameter \\(c\\) that we further discuss in the supplementary. \\(\\mathcal{N}(0,\\sigma)\\) is normal distribution with mean value set to 0 and standard deviation \\(\\sigma\\). Finally, we evaluate offsprings, append them to the current population and we select the best individuals based on a score function, in our case negative of objective in Equation 1, to form the population for the next iteration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.415, + 0.484, + 0.522 + ], + "angle": 0, + "content": "Optimization step. Using PyTorchGeoNodes, during the selection phase of every iteration, we perform a gradient-based optimization to further refine values of continuous shape parameters of individuals before selecting the population for next iteration. After a specified number of iterations the search concludes and we return shape parameters of the best performing individual." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.531, + 0.348, + 0.547 + ], + "angle": 0, + "content": "4.2. Integrating Gaussians Splats" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.483, + 0.629 + ], + "angle": 0, + "content": "Shape programs explicitly capture symmetries and similarities between repeated structures, while this aspect is lacking in many representations for 3D reconstruction. On the other hand, earlier shape programs do not capture well details and appearance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.483, + 0.749 + ], + "angle": 0, + "content": "In this section, we show we enable procedural Gaussian splats by integrating them within shape programs and our PyTorchGeoNodes framework. This allows us to capture fine details of objects while keeping the advantages of shape programs. First, we explain how we augment the primitives with 'Gaussian primitives' while keeping the graph of PyTorchGeoNodes differentiable, and then, we introduce our render-and-compare objective function." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Extending PyTorchGeoNodes with Gaussian primitives. To enable integration of our procedural graph to support Gaussian splats, we extend the nodes creating mesh primitives to also create trainable Gaussian parameters. We subsample the primitives meshes into many triangles and create Gaussians from these triangles. We initialize the Gaussians means, scales, and quaternions to fit the mesh triangles as we show in Figure 4. Their colors are initialized based on the closest 3D point in the scan. Their opacities are fixed to a high value. As with other primitives," + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.088, + 0.86, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.195, + 0.906, + 0.238 + ], + "angle": 0, + "content": "Figure 4. We integrate Gaussians directly into shape programs and PyTorchGeoNodes, to have the advantages of both procedural models and Gaussian splatting." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.248, + 0.905, + 0.293 + ], + "angle": 0, + "content": "the graph transforms the Gaussians to form a complete set of Gaussians, some of them sharing parameters due to the cloning in the graph." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.294, + 0.906, + 0.385 + ], + "angle": 0, + "content": "Optimizing the Gaussians. We noticed that it is more robust to, rather than jointly, first estimate the shape parameters and then optimize the Gaussians. Given a set of optimal shape parameters \\(\\mathcal{P}\\), we minimize the render-and compare loss as in other Gaussian splatting works, by rendering the Gaussians \\(\\mathcal{G}(\\mathcal{P})\\) into scene views [12, 17, 40]:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.395, + 0.905, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}} + \\mathcal {L} _ {\\text {r e g}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.42, + 0.905, + 0.451 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{RGB}}\\) and \\(\\mathcal{L}_{\\mathrm{D}}\\) are standard losses on color and depth consistency used in Gaussian splatting literature [7, 36, 40]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.451, + 0.905, + 0.497 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{\\mathcal{P}} = \\mathrm{CD}(\\mathrm{Sh}(\\mathcal{P}),\\mathcal{G}(\\mathcal{P}))\\) measures the consistency between the shape parameters and the Gaussians by relying on the chamfer distance. \\(\\mathcal{L}_{\\mathrm{reg}}\\) is a regularizer term:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.506, + 0.905, + 0.524 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {3} | M (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\lambda_ {4} | S (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.527, + 0.905, + 0.56 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {5} \\sum_ {G \\in \\mathcal {G} (\\mathcal {P})} \\operatorname {V a r} (C (G) |, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.57, + 0.906, + 0.707 + ], + "angle": 0, + "content": "to enforce mean offsets \\( M(\\mathcal{G}(\\mathcal{P})) \\) and scales offsets \\( S(\\mathcal{G}(\\mathcal{P})) \\) of Gaussians to be small and the colors of the Gaussians on the same primitive \\( C(G) \\) to remain close to each other. We set \\( \\lambda_1 = 0.1, \\lambda_2 = 0.1, \\lambda_3 = 100, \\lambda_4 = 10.00, \\lambda_5 = 1 \\) in our experiments. In addition, we observed that optimizing object Gaussians and background Gaussians jointly at the same time, with loss for background locations set to \\( \\lambda_{bgd}(\\mathcal{L}_{\\mathrm{RGB}} + \\lambda_1\\mathcal{L}_{\\mathrm{D}}) \\) and \\( \\lambda_{bgd} = 0.5 \\) ensures that object Gaussians remain consistent around edges." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.718, + 0.627, + 0.734 + ], + "angle": 0, + "content": "5. Validation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.743, + 0.906, + 0.87 + ], + "angle": 0, + "content": "We validate our PyTorchGeoNodes framework and our optimization method on three common furniture categories: Sofa, with 18 parameters, Chair with 20, and Table, with 10, for which we created shape programs in Blender. We designed our shape programs to capture interpretable object structures that are relevant for objects in ScanNet, allowing unseen-before reasoning about high-level object parameters. More details are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.872, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Our method jointly estimates the pose and shape parameters of the object. The orientation is defined as the rotation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16288" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.12 + ], + "angle": 0, + "content": "around the up-axis as done in to [1], which is sufficient for indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.121, + 0.484, + 0.265 + ], + "angle": 0, + "content": "We validate our method on object shape reconstruction for real world scenes from the ScanNet dataset [9]. ScanNet is a challenging dataset of indoor environment RGB-D scans: Furniture is only partially visible and highly occluded, and depth maps are incomplete due to missing sensor values—this happens for dark and reflective materials, for example. We manually annotated 176 objects for Sofa, Chair, and Table. We also provide additional results on automatically generated synthetic scenes in the supplementary material including an additional object category." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.273, + 0.279, + 0.287 + ], + "angle": 0, + "content": "5.1. Evaluation Criteria" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.294, + 0.483, + 0.409 + ], + "angle": 0, + "content": "Evaluation of shape parameters. Each object category has properties which are an important aspect of the reconstruction. This is neglected by current state-of-the-art methods. Our approach integrates these properties as shape parameters into the reconstruction and we evaluate them by comparing the reconstructed and ground truth parameters of the target objects. For the experiments with ScanNet, we manually annotated all relevant objects with shape parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.496 + ], + "angle": 0, + "content": "Data pre-processing. We assume that for the target object in the RGB-D scan, we have an initial estimate for the 3D center of the target object, here we follow preprocessing from [1]. Then, we estimate 2D segmentation masks of the object used to generate dense point clouds in the objective function in Equation (1)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.504, + 0.307, + 0.518 + ], + "angle": 0, + "content": "5.2. Search Baseline Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.525, + 0.483, + 0.554 + ], + "angle": 0, + "content": "In our evaluations of our search algorithm, we compare results of our genetic algorithm to two baselines:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.556, + 0.483, + 0.815 + ], + "angle": 0, + "content": "- GeoCode [27] introduces a supervised learning method based on an encoder-decoder architecture that takes a target point cloud as input and outputs a value for target program parameters. We use DGCNN [28] as encoder, and the resulting embedding of size 128 is shared between separate decoders that predict values for program parameters. More precisely, we use three feed-forward layers per parameter, each of size 256. For discrete parameters, we add a classification head as the output layer with number of outputs matching the number of different discrete values. For continuous parameters, we simply regress the output value. Finally, we perform gradient descent that further refines predictions by passing predicted parameter values to PyTorchGeoNodes and optimizing the objective function. We train it by randomly generating 10000 instances of ground truth shape program parameters and rotations and then generating synthetic point clouds from these parameters using PyTorchGeoNodes." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.815, + 0.484, + 0.901 + ], + "angle": 0, + "content": "- Our implementation of coordinate descent iteratively optimizes individual parameters of the shape program. First, we initialize the estimate of parameters randomly. Then, at every iteration, we take the current estimate and replace value of the selected parameter by all valid discrete values and calculate the objective term. In case of" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.09, + 0.9, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.165, + 0.9, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.242, + 0.9, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.331, + 0.907, + 0.525 + ], + "angle": 0, + "content": "Figure 5. Shape from recovered object parameters aligns very well with the target object also when projected into sampled images of the scene. In the first row, we reconstruct a variety of chairs along with many detailed parameters including seat thickness, thickness and offsets of side and front/back support legs, existence of different semantic elements like 'star-shaped' legs and its exact rotation. In the second row, we correctly estimate shape of table top and its measurements, including width, depth and thickness, parameters of table legs, and existence of middle shelf including its offset from the bottom. In the third row we reconstruct parameters of 'L-element' of sofa including its depth and width, existence and size of legs, and existence of individual armrests, backrest, and the corresponding measurements. We show more results in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.553, + 0.907, + 0.669 + ], + "angle": 0, + "content": "continuous values we first discretize them as we explain in the supplementary. In case this improves the objective, we update the current estimate. Finally, we perform gradient descent that further refines the current estimate by passing it to PyTorchGeoNodes and optimizing the objective function. We repeat the process for all different parameters and loop 3 times which approximately matches the execution time of our genetic algorithm." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.678, + 0.813, + 0.693 + ], + "angle": 0, + "content": "5.3. Validation on the ScanNet Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.699, + 0.906, + 0.771 + ], + "angle": 0, + "content": "We evaluate our approach on challenging real-world scenarios on validation scenes from ScanNet [9], which provides RGB-D scans of indoor scenes. We selected a subset of object instances from the Scannotate dataset [1] for which we manually annotated 57 sofas, 52 chairs, and 67 tables." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.772, + 0.906, + 0.857 + ], + "angle": 0, + "content": "Table 1 evaluates the quality for object parameters reconstruction for the 'table' category and general reconstruction quality across different categories. We report the numbers for 'chair' and 'sofa' in the supplementary material. We measure the classification accuracy for discrete parameteres and absolute difference for continuous parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.858, + 0.906, + 0.9 + ], + "angle": 0, + "content": "We observe that the supervised learning method from [27], trained on synthetic data, generalises poorly to the scene from ScanNet, while coordinate descent baseline" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16289" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.124, + 0.089, + 0.875, + 0.449 + ], + "angle": 0, + "content": "
ParameterModel from [27] w\\o refinementModel from [27] w\\o refinementCD w\\o refinementCD w\\o refinementGenetic w\\o refinementGenetic
Continuous ParametersWidth [cm]0.740.220.210.210.150.08
Height [cm]0.340.140.150.150.120.06
Depth [cm]0.40.20.220.220.130.08
Mid Leg X Scale0.190.130.160.140.10.07
Mid Leg Y Scale0.160.140.110.110.080.08
Legs Offset Y0.350.340.370.370.310.27
Legs Offset X0.320.320.360.360.150.13
Legs Scale Y0.170.150.180.190.130.1
Mid Board Z Scale0.210.180.180.180.170.14
Cabinet Width Scale0.150.10.150.110.10.05
Top Thickness [cm]0.030.030.020.020.020.02
Legs Size [cm]0.030.030.030.030.010.01
Discrete P:Top ShapeClassification Accuracy for Table ()
Legs Type0.780.780.720.720.940.94
Has Cabinet Leg0.390.390.60.580.780.78
Has Mid Board0.710.710.570.550.780.86
0.710.710.550.490.760.76
Chamfer distance [m] Abs. rotation error [rad]Reconstruction quality across all categories ()
0.520.210.160.160.140.11
0.450.120.130.110.080.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.089, + 0.458, + 0.908, + 0.515 + ], + "angle": 0, + "content": "Table 1. Quantitative results of shape program parameters between different baselines for category Table, and general reconstruction metrics across all categories. We observe that GeoCode [27] performs worst due to the domain gap, but the optimization helps improve the performance. Coordinate Descent (CD) does better but is prone to local minima. Genetic algorithm outperforms other baselines by a significant margin." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.537, + 0.482, + 0.668 + ], + "angle": 0, + "content": "is prone to local minima. Our genetic algorithm performs very well across all metrics except for parameters defining very small details. Visually, the models recovered by our method are comparable in quality to the ground truth and we confirm the benefits of our refinement procedure. Figure 5 and Figure 6 show some qualitative results. In the supplementary we show additional results, and include a downstream application for point cloud segmentation based on our reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.687, + 0.21, + 0.702 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.713, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Our code is publicly available and we hope this will encourage other researchers to develop the field and further extend possibilities with PyTorchGeoNodes. While shape programs are an attractive representation of objects, there are indeed still many things to develop: e.g. extensions to consider deformable and articulated objects and to integrate textures. Modularity of PyTorchGeoNodes enables integrations with other types of 3D representation, as we demonstrate with our integration of Gaussian Splatting. Moreover, differentiable rendering of PyTorchGeoNodes enables development of deep learning methods for creating shape programs from images in a self-supervised way. Finally, a major limitation is that our shape programs need to be de" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.535, + 0.648, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.593, + 0.648, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.652, + 0.648, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.59, + 0.711, + 0.611, + 0.725 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.535, + 0.743, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.593, + 0.743, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.652, + 0.742, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.711, + 0.696, + 0.724 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.537, + 0.847, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.594, + 0.862, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.653, + 0.848, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.711, + 0.824, + 0.725 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.727, + 0.908, + 0.783 + ], + "angle": 0, + "content": "Figure 6. (a) We overlay shape reconstructed using our retrieved shape parameters with the image and (b) compare it to the ground truth. (c) Our integration of Gaussians into PyTorchGeoNodes enables appealing 3D reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.799, + 0.907, + 0.871 + ], + "angle": 0, + "content": "signed by humans for different categories which can lead to limited expressiveness when applying our approach in the wild. Learning shape program designs from database of shapes would make our method easily applicable to novel categories." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16290" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.117, + 0.484, + 0.178 + ], + "angle": 0, + "content": "This project was funded by the European Union (ERC Advanced Grant explorer Funding ID #101097259). This work was performed using HPC resources from GENCI-IDRIS (Grant 2024-AD010615585)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.195, + 0.188, + 0.211 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.221, + 0.484, + 0.275 + ], + "angle": 0, + "content": "[1] Stefan Ainetter, Sinisa Stekovic, Friedrich Fraundorfer, and Vincent Lepetit. 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Computational Visual Media, 2024." + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16292" + } + ] +] \ No newline at end of file diff --git a/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_origin.pdf b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e3217c1e53a2f316f03e2814dea8d2c7249f99ed --- /dev/null +++ b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/795f18d0-96c4-47cf-9ef2-701d590c4ab0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a42ff659d908ba3309c1b9db0ca971680c13d1adcf397efcba08d6ad2903a90d +size 6218228 diff --git a/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/full.md b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..41b630a8c2dde3699c9c48c53550d31f912ca4e8 --- /dev/null +++ b/2025/PyTorchGeoNodes_ Enabling Differentiable Shape Programs for 3D Shape Reconstruction/full.md @@ -0,0 +1,322 @@ +# PyTorchGeoNodes: Enabling Differentiable Shape Programs for 3D Shape Reconstruction + +Sinisa Stekovic $^{1,2}$ Arslan Artykov $^{1}$ Stefan Ainetter $^{2}$ Mattia D'Urso $^{2}$ Friedrich Fraundorfer $^{2}$ + +1 LIGM, École des Ponts et Chaussees, IP Paris, CNRS, France + +2 Inst. for Computer Graphics and Vision, Graz Univ. of Technology, Austria + +Project page: vvenom.github.io/pytorchgeonodes + +# Abstract + +We propose PyTorchGeoNodes, a differentiable module for reconstructing 3D objects and their parameters from images using interpretable shape programs. Unlike traditional CAD model retrieval, shape programs allow reasoning about semantic parameters, editing, and a low memory footprint. Despite their potential, shape programs for 3D scene understanding have been largely overlooked. Our key contribution is enabling gradient-based optimization by parsing shape programs, or more precisely procedural models designed in Blender, into efficient PyTorch code. While there are many possible applications of our PyTorchGeoNodes, we show that a combination of PyTorchGeoNodes with genetic algorithm is a method of choice to optimize both discrete and continuous shape program parameters for 3D reconstruction and understanding of 3D object parameters. Our modular framework can be further integrated with other reconstruction algorithms, and we demonstrate one such integration to enable procedural Gaussian splattig. Our experiments on the ScanNet dataset show that our method achieves accurate reconstructions while enabling, until now, unseen level of 3D scene understanding. + +# 1. Introduction + +Various 3D object representations have already been considered for 3D scene understanding: voxels [21, 31], meshes [11, 38], SDFs [25], NeRFs [5], Gaussian Splatting [34], exemplars from a shape database [3]. SDFs, NeRFs, or Gaussian Splatting generalize to shapes unseen during training but produce artifacts for example when parts of the object are occluded in scenes captured "in the wild". Their memory footprint can also become large. Using exemplars guarantees that the retrieved shapes look good as they are created by human designers, however the database may not contain shapes similar to the target object. + +In this paper, we investigate the use of interpretable + +shape programs to represent objects. Shape programs are a form of procedural modeling [10] introduced in [35] for representing 3D objects. While shape programs have already been considered for 3D scene understanding [27, 32], their use in this context remains largely unexplored. As shown in Figure 1, our method can be used to accurately retrieve geometry and 3D parameters of target objects, together with its texture even in presence of partial occlusions. + +Shape programs can be seen as computational graphs of parametrized geometric operations that generate various 3D shapes from an object category given input shape parameters, such as object dimensions as well as "semantic" properties like existence of armrest or backrest in case of chairs. Multiple similar parts, for example the legs of a chair or the shelves of a bookshelves—are obtained by first generating a single instance, duplicating it and applying geometric transformations such as rotations and translations as needed. + +Thanks to this procedural modeling approach, shape programs generate shapes that remain appealing and that can fit many different instances. Alongside being interpretable, the shapes they generate are editable in an intuitive manner and have a very small memory footprint. In fact, they are already a popular tool for building reconstruction [19, 24, 37, 39] and the interest around shape programs for objects is growing [15, 16, 27, 35]. Blender [8] already provides support for them. A research challenge targeting reconstruction of walls, doors, and windows using such structured languages was organized by Meta in $2024^{1}$ . + +Recovering parameters of a shape program from an image is however challenging. Typically, a shape generated by a shape program depends on a number of parameters. Some parameters such as the width and height of the objects take continuous values but other parameters take only discrete values, e.g. the number of shelves in a bookshelf. + +Optimizing on these parameters turns out to be tricky: For example, changing the number of shelves from 5 to 6 + +![](images/80770942641ffe2de892d7429e97f61d72a0fdae7264d5705582bad38f157eec.jpg) +Jointly recovered geometry and parameters of target objects from RGB-D scans + +![](images/229ebaedaf2d7d0343c40def75a5d4a9b5aa00d622157f0092caa42308a2da96.jpg) +Views of Target object + +![](images/e4725d16ccfda5844f61f37fd05e144977d82643473a1f3aa4f5dd472a1c7216.jpg) +Recovered Gaussians + +![](images/8665358bc796bf429eabb5cb9a35d18e0bfd18170fee97961b7710372dbe7e91.jpg) +Procedural Gaussians editing +Figure 1. Our PyTorchGeoNodes is a framework that enables differentiable shape programs for 3D reconstruction. Our semantically-rich reconstructions of 3D objects from RGB-D scans enable understanding of important metric parameters of individual parts for different objects. These parameters are physically bound to the 3D reconstruction as PyTorchGeoNodes enables flow of gradients from the generated shape to the parameters of the object. Our PyTorchGeoNodes is modular, e.g. we can use it to enable procedural modeling for Gaussian splatting. In the example, our method recovers Gaussians for the target sofa and 'clones' all details from the visible armrest to the occluded armrest in the scene. Our integration enables procedural editing of Gaussians and we can alter shape parameters to edit the reconstruction: e.g. by extending or shrinking width of the seat, removing backrest, left armrest, changing height of the backrest and depth of the seat etc. + +changes significantly the shape and appearance of a bookshelf. There have been a few attempts in the computer vision community to use procedural shapes [27, 32]. In [27] the authors train a neural network to predict the parameters of a shape program. While this method shows impressive results using synthetic data, we show in Section 5.3 that on real data such an approach fails to generalize well, due to the lack of real world image data annotated with shape parameters. Using synthetically generated data to train such models also performs very badly: While shape programs capture very well the global structure of objects, they do not represent details. As a result, the model can hardly generalize from synthetic images to real ones. In comparison, our proposed method utilizes an objective function which is not based on learning and does not need training data, hence it is able to generalize well to real world scenarios. + +We introduce three main contributions which enable the estimation of shape programs' parameters from images: + +- Our first contribution is a 'compiler' that generates PyTorch [26] code for a shape program, which can be defined in Blender for example. This code generates 3D shapes that are differentiable with respect to the continuous parameters + +and can therefore be used easily with 3D reconstruction algorithms to optimize the continuous parameters. + +- Second, we contribute a method to obtain efficiently and reliably all shape program parameters from RGB-D scans: While our compiler can be used to optimize over the continuous parameters, the challenge of estimating the discrete parameters remains. We propose to adapt methods based on genetic algorithms to our problem of jointly optimizing the continuous and the discrete parameters of a shape program. +- Our third contribution is an extension of shape programs to capture fine details and appearance of objects. We do this by augmenting our programs with Gaussians. Once we retrieved the shape parameters, we initialize our procedural Gaussians over the primitives and optimize them as in Gaussian splatting [17]. The key difference with regular Gaussian Splatting is that our Gaussians are constrained by the procedural model: The Gaussians sampled on 'cloned' base primitives are tied together. e.g. as the legs of a chair are 'clones' of the same base primitives, the occluded part of a leg can still be recovered if it is visible for another leg. + +We evaluate our method on both synthetic and real scenes. In addition to the usual metrics, we also evaluate + +how well we reconstruct the shape program continuous and discrete parameters. Because existing datasets are not annotated with the value of these parameters, we manually annotated 176 objects. + +In summary, our main contribution is a general tool to create PyTorch code from Blender shape programs. In addition, we provide a method for estimating the parameters of shape programs from views together with the poses of the objects. Our PyTorchGeoNodes is a modular tool and it can be extended to novel use cases in 3D scene understanding. The source code is available to the general public. + +# 2. Related Work + +Since the field of retrieving 3D models for objects from images is very large, we focus here only on methods that can provide a light CAD model designed for specific categories: 3D model retrieval methods and Shape Programs. + +# 2.1. 3D Model Retrieval + +3D model retrieval aims to retrieve a CAD model from a database of objects, such as the ShapeNet dataset [6], that maximizes some scoring function which is typically based on an input 3D representation or a single or multiple input images. + +Some methods approach CAD model retrieval as a classification problem [3, 23]. For a given input a neural network can be trained to predict a probability distribution over all models in the database. However, these direct approaches do not scale well to large object databases such as the ShapeNet database. Another popular approach is computing a similarity metric between synthetic objects and real inputs. There are several possible ways of computing such metrics. It is possible to render an image from a synthetic object, and then for a synthetic-real image pair, we can compute and compare image descriptors [2, 13, 22] or encode images into embedding vector representations and calculate the similarity in the embedding space [20]. + +While such approaches have displayed promising results, one clear limitation is expressiveness of the database of objects. In fact, even with large databases of objects, in practice we often encounter objects in real scenes that are not represented in the database, or we might encounter modified or articulated objects. For example, we can modify seat height, arm rest and back support position of a work chair but the object in the database appears in the default setting which will introduce errors during retrieval. While it is possible to perform mesh refinement and deformation [4, 14, 33], these approaches typically introduce artifacts and deformations in the reconstruction and the final object shape might not be representative of the actual object category after refinement. + +# 2.2. Shape Programs + +Procedural modelling is an attractive way of generating 3D shapes in computer graphics, and as such it is an interesting feature of different 3D modelling software. In general, procedural modelling is a family of techniques that generate 3D content by abiding to a set of rules. A variety of methods were proposed that combine procedural modeling with machine learning approaches, summarized in detail in [30]. For example, [35] introduced a procedural language that enables the generation of a variety of shapes in form of so-called shape programs. In [35], shape programs are written in Domain Specific Language (DSL) for shapes with two types of statements. "Draw" statements describes shape primitive, such as cuboid or a cylinder, together with its geometric and semantic properties. "For" statements represent loops of sub-programs including parameters that indicate how the sub-program should be repeatedly executed. + +[35] also showed that it is possible to learn to infer shape programs that describe input 3D shapes. However, as it is based on basic geometric primitives, it becomes difficult to model more complex geometries, and resulting shapes can be non-representative of the target category. Other methods suffer from the same limitations [15, 16]. + +GeoCode [27] recently introduced hand-designed shape programs as a mapping between 3D shapes of a specific object category and human-interpretable parameter space. The language used for developing shape programs is based on the geometry node feature of Blender, an open-source modeling software, which, in contrast to [35], allows designing of more expressive shape programs that can represent and interpolate between a variety of shapes by simply modifying human-interpretable program's parameters. + +Some nodes define a shape primitive or pre-designed more complex shapes, e.g., chair seat or chair leg. Other nodes represent geometric transformations on individual shapes, or how two shapes should be connected, e.g., legs should always be connected to the bottom of the seat. There are nodes representing mathematical operations such as addition and multiplication, and there are nodes that are used to replicate specific shapes, e.g., in case of chair legs we can add a replicator node to create four instances of a chair leg of the same shape. There are also nodes that serve as control statements, e.g., it is possible to switch between a four-legged chair and a one-legged chair. A pre-defined set of input program's parameters allow non-expert user to easily control shape-generation process. [27] also showed that it is possible to learn the mapping from input point clouds of 3D shapes, or a sketch, to program's parameters. + +# 3. PyTorchGeoNodes + +In this section, we discuss shape programs and how they can be beneficial for tasks in 3D scene understanding. We + +![](images/d7c1dfe342c447bb538967e6268c53959d58a9d875ad6c34b75647b5138f58d6.jpg) +Figure 2. A procedural model in Blender generating dividing boards of a cabinet. The computational graph is designed and visualized in Blender using Geometry Nodes feature. Underneath, we show how we abstract the different nodes using PyTorch tensors and PyTorch3D meshes. The input node takes input parameters, here {Width: 0.5, Dividing Board Thickness: 0.04, Height: 0.6, Number of Dividing Boards: 5, Board Thickness: 0.04} and feeds them to a series of operations. The blue nodes are arithmetic and concatenation nodes, which transform input parameters and feed the results to geometry nodes, in green. In this example, we generate a cuboid mesh and instantiate a line of points which generates the final geometry for dividing boards. In practice, this shape program is part of a larger shape program for modeling cabinets. + +then describe our framework for enabling efficient gradient-based optimization for shape programs and, in addition, allowing to translate shape programs designed in Blender to PyTorch code to enable differentiable optimization. In Section 4, we explain how our framework can be applied for reconstructing 3D objects from images. + +We consider shape programs as defined in Blender, i.e., as a computational graph that computes 3D shapes given a number of input parameters. Such graphs contain nodes of different types; in our framework, we currently consider the following node types: + +- An 'Input' node contains input parameters of the shape programs and their value ranges. We consider floating, integer, and boolean values; +- A 'Math' node performs mathematical operations on its input (addition, subtraction, multiplication, division, and comparison); +- A 'Switch' node switches between two inputs conditioned on a boolean input; +- A 'Combine' node concatenates three input values into a 3D vector; +- A 'Primitive' node creates a geometric primitive, e.g., a cuboid or a cylinder; +- A 'Transform' node applies scaling, rotation, and translation to the input geometry; +- 'Mesh Line' node creates a tensor of 3D points on a line from input vectors that define the start location and the + +offset of the line, and an integer that defines the number of points to be generated; + +- A 'Points on instances' node clones input geometry at given input 3D points; +- A 'Join geometry' node merges geometries; +- An 'Output geometry node' generates the final mesh for the shape. + +Note that for example, the Transform node depends on continuous, the Points on instances node on integer, and the Switch node on boolean. + +Our framework provides differentiable computational nodes that reimplement the functionalities of the individual geometry nodes in Blender as we show in Figure 2. More exactly, for every node type in Blender, we implement a corresponding node type with the same functionalities using PyTorch, or PyTorch3D [29] in case of geometric operations. In practice, we designed shape programs directly using the Blender interface. Given a shape program created in Blender, our parser generates a differentiable PyTorch-GeoNodes code. We can then use this code in PyTorch in an optimization procedure where we fit shape parameters to generate a shape consistent with the input scene. + +In the supplementary material, we detail our design choices and technical details which make our implementation computationally efficient. + +![](images/4ab110ea511650d4681465f874960f68071790893c7e1e7c4825a6ff86194d70.jpg) +Figure 3. Fitting shape parameters with PyTorchGeoNodes. At every iteration, our genetic algorithm generates individuals of shape parameters and object poses. We parse 3D shapes from individual parameters using PyTorchGeoNodes and perform shape parameter optimization based on loss that evaluates how well the shape fits the input scene. In the next iteration, the optimized set of individuals is used to update the pool of individuals based on selection of the fittest principle. + +# 4. Search Algorithm + +We leverage our PyTorchGeoNodes framework to retrieve shape parameters and geometry of a target object in an RGB-D scan. We look for shape parameters $\mathcal{P}^*$ by minimizing an objective function that encourages the shape to fit the point cloud reconstructed from the images while lying on the floor: + +$$ +\begin{array}{l} \mathcal {L} (\mathcal {P}) = \lambda_ {\mathrm {C D}} \mathcal {L} _ {\mathrm {C D}} (\mathrm {P C}, \operatorname {S h} (\mathcal {P})) + \lambda_ {\mathrm {G}} \mathcal {L} _ {\mathrm {G}} (\mathrm {G}, \operatorname {S h} (\mathcal {P})) + \\ \lambda_ {\mathrm {F l}} \mathcal {L} _ {\mathrm {F l}} (\mathrm {P C}, \operatorname {S h} (\mathcal {P}))). \tag {1} \\ \end{array} +$$ + +$\mathcal{L}_{\mathrm{CD}}(\mathrm{PC}, \mathrm{Sh}(\mathcal{P}))$ measures the single-direction chamfer distance between PC, the point cloud reconstructed from the depth maps and object masks, and $\mathrm{Sh}(\mathcal{P})$ , the shape generated by the shape program. We follow pre-processing from [1] which relies on sparse point cloud instance segmentation of the object and use a segmentation model [18] on images to obtain the object masks. We then back-project these masks to obtain a dense target point cloud. $\mathcal{L}_{\mathrm{G}}(\mathrm{G}, \mathrm{Sh}(\mathcal{P}))$ penalizes occlusions in the scene caused by $\mathrm{Sh}(\mathcal{P})$ . G is an occlusion grid obtained by densely sampling 3D points along rays between the camera and surfaces for different views: + +$$ +\mathcal {L} _ {\mathrm {G}} (\mathrm {G}, \operatorname {S h} (\mathcal {P})) = \sum_ {p \in \operatorname {S h} (\mathcal {P})} \left\{ \begin{array}{l l} \vec {\mathrm {C D}} (p, \mathrm {P C}) & \text {i f} \mathrm {G} (p) \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {2} +$$ + +where $\vec{\mathrm{CD}}$ ( $p, \mathrm{PC}$ ) is the distance of point $p$ to PC. $\mathbf{G}(p) = \vec{\mathbf{CD}}$ ( $p, \mathrm{PC}$ ) < $\omega$ determines whether $p$ is on grid G. We set threshold $\omega = 5cm$ in our experiments. Since G is generated using input views for the scene, this loss does not penalize points that are occluded in the scene, similar to render-and-compare objectives. The term $\mathcal{L}_{\mathrm{Fl}}$ simply enforces the objects to stay on the floor plane: + +$$ +\mathcal {L} _ {\mathrm {F l}} \left(\mathrm {P C}, \operatorname {S h} (\mathcal {P})\right) = | \mathrm {F l} (\mathrm {P C}) - \mathrm {F l} (\operatorname {S h} (\mathcal {P})) | _ {2}, \tag {3} +$$ + +where $\operatorname{Fl}(\mathrm{PC})$ returns the height of the lowest point in PC, and $\operatorname{Fl}(\operatorname{Sh}(\mathcal{P}))$ similarly determines the lowest point of shape $\operatorname{Sh}(\mathcal{P})$ . We set weights of individual loss terms to $\lambda_{\mathrm{CD}} = 1$ , $\lambda_{\mathrm{G}} = 0.5$ , $\lambda_{\mathrm{Fl}} = 0.01$ in our experiments. Parameters $\mathcal{P}$ include the object pose in addition to the shape program parameters. We initialize the translation based on an initial estimate of the object center which is refined during search. We constrain the rotation to be around the vertical axis only. + +We use our PyTorchGeoNodes framework to compute $\mathrm{Sh}(\mathcal{P})$ . Thanks to this framework, PyTorch can compute the derivatives of $\mathrm{Sh}(\mathcal{P})$ and thus the derivatives of $\mathcal{L}$ with respect to the continuous parameters in $\mathcal{P}$ . However, some parameters in $\mathcal{P}$ are discrete, i.e., integers or booleans. Therefore, we cannot optimize $\mathcal{L}$ using a simple gradient descent. Also, $\mathcal{L}$ has no special form that we can exploit to optimize it. + +To solve this problem, we propose to resort to genetic algorithms to optimize the parameters and combine it with gradient descent to further refine the continuous parameters. + +# 4.1. Shape Parameter Search + +A genetic algorithm is a stochastic optimization algorithm that iteratively applies random manipulations of high-dimensional search parameters to identify the most promising complex search subspaces, subject to an objective function. In contrast to gradient-based techniques, it can optimize discrete and continuous values and the objective function can be very general and non-differentiable. + +The algorithm starts by randomly generating instances of parameter values $\mathcal{P}$ , individuals, that form an initial set called population of search parameters. Every iteration has three phases: crossover and mutation for exploring search subspaces, and selection for exploiting the most promising subspaces. Crossover randomly selects pairs of individuals, parents, and mixes them by combining the individual parameters to create a new offspring. Therefore, an offspring lies in the search subspace at intersection of parents' search spaces. Mutation then randomly alters offsprings' parameters to further explore this subspace. Selection evaluates the quality of the population, and based on survival of the fittest strategy, it takes the best performing individuals to form the population for the next iteration. Further details and hyperparameters are given in the supplementary material. + +Our adaptation of genetic algorithms to our problem is described in details in the supplementary material. The main points are given below. We generate an initial population by randomly generating instances of all program's parameters $\mathcal{P}$ representing individuals in the population. We draw random values from the empirical distributions of the parameters. The crossover operation generates offspring $P_{1,2}$ from a pair of parents $\mathcal{P}_1$ , $\mathcal{P}_2$ . Mutation varies depending on the parameter type. For discrete parameter $d \in \mathcal{P}_D$ + +we adapt its value $v_{d}$ : + +$$ +v _ {d} \leftarrow \left\{ \begin{array}{l l} v _ {s} \in_ {R} \mathcal {V} _ {d} & \text {w i t h p r o b a b i l i t y} P _ {m} \\ v _ {d} & \text {o t h e r w i s e ,} \end{array} \right. \tag {4} +$$ + +where operator $\in_R$ randomly selects value $v$ from the set of valid discrete values $\nu_{p}$ . $P_{m}$ is a hyper-parameter that defines the probability of mutating parameter values. In case of a continuous parameter $c\in \mathcal{P}_C$ , we adapt its value $v_{c}$ as: + +$$ +v _ {c} \leftarrow \left\{ \begin{array}{l l} v _ {s} \in_ {R} \mathcal {V} _ {c} + \mathcal {N} (0, \sigma) & \text {w i t h p r o b .} P _ {m} \cdot P _ {m} \\ v _ {c} + \mathcal {N} (0, \sigma) & \text {w i t h p r o b .} P _ {m} \\ v _ {c} & \text {o t h e r w i s e ,} \end{array} \right. \tag {5} +$$ + +where $\mathcal{V}_c$ is a discretisation of values for parameter $c$ that we further discuss in the supplementary. $\mathcal{N}(0,\sigma)$ is normal distribution with mean value set to 0 and standard deviation $\sigma$ . Finally, we evaluate offsprings, append them to the current population and we select the best individuals based on a score function, in our case negative of objective in Equation 1, to form the population for the next iteration. + +Optimization step. Using PyTorchGeoNodes, during the selection phase of every iteration, we perform a gradient-based optimization to further refine values of continuous shape parameters of individuals before selecting the population for next iteration. After a specified number of iterations the search concludes and we return shape parameters of the best performing individual. + +# 4.2. Integrating Gaussians Splats + +Shape programs explicitly capture symmetries and similarities between repeated structures, while this aspect is lacking in many representations for 3D reconstruction. On the other hand, earlier shape programs do not capture well details and appearance. + +In this section, we show we enable procedural Gaussian splats by integrating them within shape programs and our PyTorchGeoNodes framework. This allows us to capture fine details of objects while keeping the advantages of shape programs. First, we explain how we augment the primitives with 'Gaussian primitives' while keeping the graph of PyTorchGeoNodes differentiable, and then, we introduce our render-and-compare objective function. + +Extending PyTorchGeoNodes with Gaussian primitives. To enable integration of our procedural graph to support Gaussian splats, we extend the nodes creating mesh primitives to also create trainable Gaussian parameters. We subsample the primitives meshes into many triangles and create Gaussians from these triangles. We initialize the Gaussians means, scales, and quaternions to fit the mesh triangles as we show in Figure 4. Their colors are initialized based on the closest 3D point in the scan. Their opacities are fixed to a high value. As with other primitives, + +![](images/6eeee1e0ddbb1b11fe12002e08cd994b46ccd9aaac55137b1c9bc07fd7a91907.jpg) +Figure 4. We integrate Gaussians directly into shape programs and PyTorchGeoNodes, to have the advantages of both procedural models and Gaussian splatting. + +the graph transforms the Gaussians to form a complete set of Gaussians, some of them sharing parameters due to the cloning in the graph. + +Optimizing the Gaussians. We noticed that it is more robust to, rather than jointly, first estimate the shape parameters and then optimize the Gaussians. Given a set of optimal shape parameters $\mathcal{P}$ , we minimize the render-and compare loss as in other Gaussian splatting works, by rendering the Gaussians $\mathcal{G}(\mathcal{P})$ into scene views [12, 17, 40]: + +$$ +\mathcal {L} _ {\mathrm {R G B}} + \lambda_ {1} \mathcal {L} _ {\mathrm {D}} + \lambda_ {2} \mathcal {L} _ {\mathcal {P}} + \mathcal {L} _ {\text {r e g}}, \tag {6} +$$ + +where $\mathcal{L}_{\mathrm{RGB}}$ and $\mathcal{L}_{\mathrm{D}}$ are standard losses on color and depth consistency used in Gaussian splatting literature [7, 36, 40]. + +$\mathcal{L}_{\mathcal{P}} = \mathrm{CD}(\mathrm{Sh}(\mathcal{P}),\mathcal{G}(\mathcal{P}))$ measures the consistency between the shape parameters and the Gaussians by relying on the chamfer distance. $\mathcal{L}_{\mathrm{reg}}$ is a regularizer term: + +$$ +\mathcal {L} _ {\text {r e g}} = \lambda_ {3} | M (\mathcal {G} (\mathcal {P})) | _ {2} + \lambda_ {4} | S (\mathcal {G} (\mathcal {P})) | _ {2} + \tag {7} +$$ + +$$ +\lambda_ {5} \sum_ {G \in \mathcal {G} (\mathcal {P})} \operatorname {V a r} (C (G) |, \tag {8} +$$ + +to enforce mean offsets $M(\mathcal{G}(\mathcal{P}))$ and scales offsets $S(\mathcal{G}(\mathcal{P}))$ of Gaussians to be small and the colors of the Gaussians on the same primitive $C(G)$ to remain close to each other. We set $\lambda_1 = 0.1, \lambda_2 = 0.1, \lambda_3 = 100, \lambda_4 = 10.00, \lambda_5 = 1$ in our experiments. In addition, we observed that optimizing object Gaussians and background Gaussians jointly at the same time, with loss for background locations set to $\lambda_{bgd}(\mathcal{L}_{\mathrm{RGB}} + \lambda_1\mathcal{L}_{\mathrm{D}})$ and $\lambda_{bgd} = 0.5$ ensures that object Gaussians remain consistent around edges. + +# 5. Validation + +We validate our PyTorchGeoNodes framework and our optimization method on three common furniture categories: Sofa, with 18 parameters, Chair with 20, and Table, with 10, for which we created shape programs in Blender. We designed our shape programs to capture interpretable object structures that are relevant for objects in ScanNet, allowing unseen-before reasoning about high-level object parameters. More details are provided in the supplementary material. + +Our method jointly estimates the pose and shape parameters of the object. The orientation is defined as the rotation + +around the up-axis as done in to [1], which is sufficient for indoor scenes. + +We validate our method on object shape reconstruction for real world scenes from the ScanNet dataset [9]. ScanNet is a challenging dataset of indoor environment RGB-D scans: Furniture is only partially visible and highly occluded, and depth maps are incomplete due to missing sensor values—this happens for dark and reflective materials, for example. We manually annotated 176 objects for Sofa, Chair, and Table. We also provide additional results on automatically generated synthetic scenes in the supplementary material including an additional object category. + +# 5.1. Evaluation Criteria + +Evaluation of shape parameters. Each object category has properties which are an important aspect of the reconstruction. This is neglected by current state-of-the-art methods. Our approach integrates these properties as shape parameters into the reconstruction and we evaluate them by comparing the reconstructed and ground truth parameters of the target objects. For the experiments with ScanNet, we manually annotated all relevant objects with shape parameters. + +Data pre-processing. We assume that for the target object in the RGB-D scan, we have an initial estimate for the 3D center of the target object, here we follow preprocessing from [1]. Then, we estimate 2D segmentation masks of the object used to generate dense point clouds in the objective function in Equation (1). + +# 5.2. Search Baseline Details + +In our evaluations of our search algorithm, we compare results of our genetic algorithm to two baselines: + +- GeoCode [27] introduces a supervised learning method based on an encoder-decoder architecture that takes a target point cloud as input and outputs a value for target program parameters. We use DGCNN [28] as encoder, and the resulting embedding of size 128 is shared between separate decoders that predict values for program parameters. More precisely, we use three feed-forward layers per parameter, each of size 256. For discrete parameters, we add a classification head as the output layer with number of outputs matching the number of different discrete values. For continuous parameters, we simply regress the output value. Finally, we perform gradient descent that further refines predictions by passing predicted parameter values to PyTorchGeoNodes and optimizing the objective function. We train it by randomly generating 10000 instances of ground truth shape program parameters and rotations and then generating synthetic point clouds from these parameters using PyTorchGeoNodes. + +- Our implementation of coordinate descent iteratively optimizes individual parameters of the shape program. First, we initialize the estimate of parameters randomly. Then, at every iteration, we take the current estimate and replace value of the selected parameter by all valid discrete values and calculate the objective term. In case of + +![](images/cfd22c17674680e246b13a3db78986e0cad7200fb7b119add10b75fafc26a4c0.jpg) + +![](images/8b65aa4e3f76d5fad28475adce1b6ac54e877e575f9e96162c16e76ed5e81e63.jpg) + +![](images/5ed32c9270f8a4574715d073c33fb0de87624c5494901ca944a61a9ceab345bc.jpg) +Figure 5. Shape from recovered object parameters aligns very well with the target object also when projected into sampled images of the scene. In the first row, we reconstruct a variety of chairs along with many detailed parameters including seat thickness, thickness and offsets of side and front/back support legs, existence of different semantic elements like 'star-shaped' legs and its exact rotation. In the second row, we correctly estimate shape of table top and its measurements, including width, depth and thickness, parameters of table legs, and existence of middle shelf including its offset from the bottom. In the third row we reconstruct parameters of 'L-element' of sofa including its depth and width, existence and size of legs, and existence of individual armrests, backrest, and the corresponding measurements. We show more results in the supplementary material. + +continuous values we first discretize them as we explain in the supplementary. In case this improves the objective, we update the current estimate. Finally, we perform gradient descent that further refines the current estimate by passing it to PyTorchGeoNodes and optimizing the objective function. We repeat the process for all different parameters and loop 3 times which approximately matches the execution time of our genetic algorithm. + +# 5.3. Validation on the ScanNet Dataset + +We evaluate our approach on challenging real-world scenarios on validation scenes from ScanNet [9], which provides RGB-D scans of indoor scenes. We selected a subset of object instances from the Scannotate dataset [1] for which we manually annotated 57 sofas, 52 chairs, and 67 tables. + +Table 1 evaluates the quality for object parameters reconstruction for the 'table' category and general reconstruction quality across different categories. We report the numbers for 'chair' and 'sofa' in the supplementary material. We measure the classification accuracy for discrete parameteres and absolute difference for continuous parameters. + +We observe that the supervised learning method from [27], trained on synthetic data, generalises poorly to the scene from ScanNet, while coordinate descent baseline + +
ParameterModel from [27] w\o refinementModel from [27] w\o refinementCD w\o refinementCD w\o refinementGenetic w\o refinementGenetic
Continuous ParametersWidth [cm]0.740.220.210.210.150.08
Height [cm]0.340.140.150.150.120.06
Depth [cm]0.40.20.220.220.130.08
Mid Leg X Scale0.190.130.160.140.10.07
Mid Leg Y Scale0.160.140.110.110.080.08
Legs Offset Y0.350.340.370.370.310.27
Legs Offset X0.320.320.360.360.150.13
Legs Scale Y0.170.150.180.190.130.1
Mid Board Z Scale0.210.180.180.180.170.14
Cabinet Width Scale0.150.10.150.110.10.05
Top Thickness [cm]0.030.030.020.020.020.02
Legs Size [cm]0.030.030.030.030.010.01
Discrete P:Top ShapeClassification Accuracy for Table ()
Legs Type0.780.780.720.720.940.94
Has Cabinet Leg0.390.390.60.580.780.78
Has Mid Board0.710.710.570.550.780.86
0.710.710.550.490.760.76
Chamfer distance [m] Abs. rotation error [rad]Reconstruction quality across all categories ()
0.520.210.160.160.140.11
0.450.120.130.110.080.06
+ +Table 1. Quantitative results of shape program parameters between different baselines for category Table, and general reconstruction metrics across all categories. We observe that GeoCode [27] performs worst due to the domain gap, but the optimization helps improve the performance. Coordinate Descent (CD) does better but is prone to local minima. Genetic algorithm outperforms other baselines by a significant margin. + +is prone to local minima. Our genetic algorithm performs very well across all metrics except for parameters defining very small details. Visually, the models recovered by our method are comparable in quality to the ground truth and we confirm the benefits of our refinement procedure. Figure 5 and Figure 6 show some qualitative results. In the supplementary we show additional results, and include a downstream application for point cloud segmentation based on our reconstructions. + +# 6. Conclusion + +Our code is publicly available and we hope this will encourage other researchers to develop the field and further extend possibilities with PyTorchGeoNodes. While shape programs are an attractive representation of objects, there are indeed still many things to develop: e.g. extensions to consider deformable and articulated objects and to integrate textures. Modularity of PyTorchGeoNodes enables integrations with other types of 3D representation, as we demonstrate with our integration of Gaussian Splatting. Moreover, differentiable rendering of PyTorchGeoNodes enables development of deep learning methods for creating shape programs from images in a self-supervised way. Finally, a major limitation is that our shape programs need to be de + +![](images/b348e0ac8ebc3dbb7f2c76d2360469dee827f4314ba1ec5e6cc8b6ea559c0781.jpg) + +![](images/e3c0d22fd298af7e184212eafe8a41d4f08d48a4c96f783e69d9020e4f2344c9.jpg) + +![](images/3151cb23ef2768ce77fe883de212c43f2585e19b58fad6ac70c45fc0266f52ac.jpg) +(a) + +![](images/585ccc93522a48f56ac7737bf2a0524821cd2297b29980c5e91da7faf8af6e9f.jpg) + +![](images/510d592bd3d2328274253fb15eb0c5f6a50c966146cc43b4c8808d2601864042.jpg) + +![](images/c2c30f1f685406a4f6ba7b4b834232759067a9d513533810d3cc9c3d191adb29.jpg) +(b) + +![](images/6ba237cd9b99fae90506d8620afad4b90064afed4920a17cb5a44d6d89ca9c64.jpg) + +![](images/5d1b9fe4bd7803eaf38a3a1eb9f756dcc1c7d2807160f4fad385de164f8cdda3.jpg) + +![](images/bf75121d42a0f9c23e83480204ea91417ff9b9b757c9f7eab5757671ab76a1ec.jpg) +(c) +Figure 6. (a) We overlay shape reconstructed using our retrieved shape parameters with the image and (b) compare it to the ground truth. (c) Our integration of Gaussians into PyTorchGeoNodes enables appealing 3D reconstructions. + +signed by humans for different categories which can lead to limited expressiveness when applying our approach in the wild. Learning shape program designs from database of shapes would make our method easily applicable to novel categories. + +# Acknowledgement + +This project was funded by the European Union (ERC Advanced Grant explorer Funding ID #101097259). This work was performed using HPC resources from GENCI-IDRIS (Grant 2024-AD010615585). + +# References + +[1] Stefan Ainetter, Sinisa Stekovic, Friedrich Fraundorfer, and Vincent Lepetit. HOC-Search: Efficient CAD Model and Pose Retrieval from RGB-D Scans. International Conference on 3D Vision, 2024. +[2] Mathieu Aubry and Bryan C Russell. Understanding Deep Features with Computer-Generated Imagery. 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In Conference on Computer Vision and Pattern Recognition, 2016. +[23] Roozbeh Mottaghi, Yu Xiang, and Silvio Savarese. A Coarse-to-Fine Model for 3D Pose Estimation and SubCategory Recognition. In Conference on Computer Vision and Pattern Recognition, 2015. +[24] Pascal Müller, Peter Wonka, Simon Haegler, Andreas Ulmer, and Luc Van Gool. Procedural Modeling of Buildings. In ACM SIGGRAPH 2006 Papers, 2006. +[25] Jeong Joon Park, Peter Florence, Julian Straub, Richard A. Newcombe, and Steven J. Lovegrove. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation. In Conference on Computer Vision and Pattern Recognition, 2019. +[26] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. 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In Conference on Computer Vision and Pattern Recognition, 2018. +[32] Loic Simon, Olivier Teboul, Panagiotis Koutsourakis, and Nikos Paragios. Random Exploration of the Procedural Space for Single-View 3D Modeling of Buildings. International Journal of Computer Vision, 2011. +[33] Olga Sorkine and Marc Alexa. As-Rigid-as-Possible Surface Modeling. In Symposium on Geometry Processing, 2007. +[34] Stanislaw Szymanowicz, Christian Rupprecht, and Andrea Vedaldi. Splatter Image: Ultra-Fast Single-View 3D Reconstruction. arXiv Preprint, 2023. +[35] Yonglong Tian, Andrew Luo, Xingyuan Sun, Kevin Ellis, William T Freeman, Joshua B Tenenbaum, and Jiajun Wu. Learning to Infer and Execute 3D Shape Programs. International Conference for Learning Representations, 2019. +[36] Matias Turkulainen, Xuqian Ren, Iaroslav Melekhov, Otto Seiskari, Esa Rahtu, and Juho Kannala. DN-Splatter: Depth and Normal Priors for Gaussian Splatting and Meshing. arXiv preprint arXiv:2403.17822, 2024. +[37] Beatrice Vaienti, Rémi Petitpierre, Isabella di Lenardo, and Frédéric Kaplan. Machine-Learning-Enhanced Procedural Modeling for 4D Historical Cities Reconstruction. Remote Sensing, 15(13), 2023. +[38] Nanyang Wang, Yinda Zhang, Zhuwen Li, Yanwei Fu, Wei Liu, and Yu-Gang Jiang. Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images. In European Conference on Computer Vision, 2018. +[39] Peter Wonka, Michael Wimmer, François Sillion, and William Ribarsky. Instant Architecture. ACM Transactions on Graphics (TOG), 2003. +[40] Tong Wu, Yu-Jie Yuan, Ling-Xiao Zhang, Jie Yang, Yan-Pei Cao, Ling-Qi Yan, and Lin Gao. Recent Advances in 3D Gaussian Splatting. 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Unlike traditional CAD model retrieval, shape programs allow reasoning about semantic parameters, editing, and a low memory footprint. Despite their potential, shape programs for 3D scene understanding have been largely overlooked. Our key contribution is enabling gradient-based optimization by parsing shape programs, or more precisely procedural models designed in Blender, into efficient PyTorch code. While there are many possible applications of our PyTorchGeoNodes, we show that a combination of PyTorchGeoNodes with genetic algorithm is a method of choice to optimize both discrete and continuous shape program parameters for 3D reconstruction and understanding of 3D object parameters. Our modular framework can be further integrated with other reconstruction algorithms, and we demonstrate one such integration to enable procedural Gaussian splattig. Our experiments on the ScanNet dataset show that our method achieves accurate reconstructions while enabling, until now, unseen level of 3D scene understanding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 549, + 135, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 549, + 135, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 549, + 135, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 570, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 701 + ], + "type": "text", + "content": "Various 3D object representations have already been considered for 3D scene understanding: voxels [21, 31], meshes [11, 38], SDFs [25], NeRFs [5], Gaussian Splatting [34], exemplars from a shape database [3]. SDFs, NeRFs, or Gaussian Splatting generalize to shapes unseen during training but produce artifacts for example when parts of the object are occluded in scenes captured \"in the wild\". Their memory footprint can also become large. Using exemplars guarantees that the retrieved shapes look good as they are created by human designers, however the database may not contain shapes similar to the target object." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "In this paper, we investigate the use of interpretable" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 252, + 553, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 553, + 347 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 553, + 347 + ], + "type": "text", + "content": "shape programs to represent objects. Shape programs are a form of procedural modeling [10] introduced in [35] for representing 3D objects. While shape programs have already been considered for 3D scene understanding [27, 32], their use in this context remains largely unexplored. As shown in Figure 1, our method can be used to accurately retrieve geometry and 3D parameters of target objects, together with its texture even in presence of partial occlusions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 348, + 554, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 554, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 554, + 455 + ], + "type": "text", + "content": "Shape programs can be seen as computational graphs of parametrized geometric operations that generate various 3D shapes from an object category given input shape parameters, such as object dimensions as well as \"semantic\" properties like existence of armrest or backrest in case of chairs. Multiple similar parts, for example the legs of a chair or the shelves of a bookshelves—are obtained by first generating a single instance, duplicating it and applying geometric transformations such as rotations and translations as needed." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 456, + 554, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 554, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 554, + 588 + ], + "type": "text", + "content": "Thanks to this procedural modeling approach, shape programs generate shapes that remain appealing and that can fit many different instances. Alongside being interpretable, the shapes they generate are editable in an intuitive manner and have a very small memory footprint. In fact, they are already a popular tool for building reconstruction [19, 24, 37, 39] and the interest around shape programs for objects is growing [15, 16, 27, 35]. Blender [8] already provides support for them. A research challenge targeting reconstruction of walls, doors, and windows using such structured languages was organized by Meta in " + }, + { + "bbox": [ + 313, + 456, + 554, + 588 + ], + "type": "inline_equation", + "content": "2024^{1}" + }, + { + "bbox": [ + 313, + 456, + 554, + 588 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 588, + 553, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 553, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 553, + 660 + ], + "type": "text", + "content": "Recovering parameters of a shape program from an image is however challenging. Typically, a shape generated by a shape program depends on a number of parameters. Some parameters such as the width and height of the objects take continuous values but other parameters take only discrete values, e.g. the number of shelves in a bookshelf." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 661, + 553, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 661, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 661, + 553, + 685 + ], + "type": "text", + "content": "Optimizing on these parameters turns out to be tricky: For example, changing the number of shelves from 5 to 6" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "text", + "content": "[https://eval.ai/web/challenges/challenge-page/2115/overview (Accessed: November 2024)]" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16283" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 70, + 508, + 246 + ], + "blocks": [ + { + "bbox": [ + 107, + 70, + 508, + 246 + ], + "lines": [ + { + "bbox": [ + 107, + 70, + 508, + 246 + ], + "spans": [ + { + "bbox": [ + 107, + 70, + 508, + 246 + ], + "type": "image", + "image_path": "80770942641ffe2de892d7429e97f61d72a0fdae7264d5705582bad38f157eec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 248, + 451, + 258 + ], + "lines": [ + { + "bbox": [ + 162, + 248, + 451, + 258 + ], + "spans": [ + { + "bbox": [ + 162, + 248, + 451, + 258 + ], + "type": "text", + "content": "Jointly recovered geometry and parameters of target objects from RGB-D scans" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 116, + 259, + 216, + 337 + ], + "blocks": [ + { + "bbox": [ + 116, + 259, + 216, + 337 + ], + "lines": [ + { + "bbox": [ + 116, + 259, + 216, + 337 + ], + "spans": [ + { + "bbox": [ + 116, + 259, + 216, + 337 + ], + "type": "image", + "image_path": "229ebaedaf2d7d0343c40def75a5d4a9b5aa00d622157f0092caa42308a2da96.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 339, + 208, + 350 + ], + "lines": [ + { + "bbox": [ + 124, + 339, + 208, + 350 + ], + "spans": [ + { + "bbox": [ + 124, + 339, + 208, + 350 + ], + "type": "text", + "content": "Views of Target object" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 229, + 259, + 299, + 336 + ], + "blocks": [ + { + "bbox": [ + 229, + 259, + 299, + 336 + ], + "lines": [ + { + "bbox": [ + 229, + 259, + 299, + 336 + ], + "spans": [ + { + "bbox": [ + 229, + 259, + 299, + 336 + ], + "type": "image", + "image_path": "e4725d16ccfda5844f61f37fd05e144977d82643473a1f3aa4f5dd472a1c7216.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 225, + 339, + 304, + 348 + ], + "lines": [ + { + "bbox": [ + 225, + 339, + 304, + 348 + ], + "spans": [ + { + "bbox": [ + 225, + 339, + 304, + 348 + ], + "type": "text", + "content": "Recovered Gaussians" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 326, + 259, + 496, + 337 + ], + "blocks": [ + { + "bbox": [ + 326, + 259, + 496, + 337 + ], + "lines": [ + { + "bbox": [ + 326, + 259, + 496, + 337 + ], + "spans": [ + { + "bbox": [ + 326, + 259, + 496, + 337 + ], + "type": "image", + "image_path": "8665358bc796bf429eabb5cb9a35d18e0bfd18170fee97961b7710372dbe7e91.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 356, + 339, + 463, + 350 + ], + "lines": [ + { + "bbox": [ + 356, + 339, + 463, + 350 + ], + "spans": [ + { + "bbox": [ + 356, + 339, + 463, + 350 + ], + "type": "text", + "content": "Procedural Gaussians editing" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 360, + 555, + 437 + ], + "lines": [ + { + "bbox": [ + 55, + 360, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 555, + 437 + ], + "type": "text", + "content": "Figure 1. Our PyTorchGeoNodes is a framework that enables differentiable shape programs for 3D reconstruction. Our semantically-rich reconstructions of 3D objects from RGB-D scans enable understanding of important metric parameters of individual parts for different objects. These parameters are physically bound to the 3D reconstruction as PyTorchGeoNodes enables flow of gradients from the generated shape to the parameters of the object. Our PyTorchGeoNodes is modular, e.g. we can use it to enable procedural modeling for Gaussian splatting. In the example, our method recovers Gaussians for the target sofa and 'clones' all details from the visible armrest to the occluded armrest in the scene. Our integration enables procedural editing of Gaussians and we can alter shape parameters to edit the reconstruction: e.g. by extending or shrinking width of the seat, removing backrest, left armrest, changing height of the backrest and depth of the seat etc." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "text", + "content": "changes significantly the shape and appearance of a bookshelf. There have been a few attempts in the computer vision community to use procedural shapes [27, 32]. In [27] the authors train a neural network to predict the parameters of a shape program. While this method shows impressive results using synthetic data, we show in Section 5.3 that on real data such an approach fails to generalize well, due to the lack of real world image data annotated with shape parameters. Using synthetically generated data to train such models also performs very badly: While shape programs capture very well the global structure of objects, they do not represent details. As a result, the model can hardly generalize from synthetic images to real ones. In comparison, our proposed method utilizes an objective function which is not based on learning and does not need training data, hence it is able to generalize well to real world scenarios." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 642, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 666 + ], + "type": "text", + "content": "We introduce three main contributions which enable the estimation of shape programs' parameters from images:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 666, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 295, + 713 + ], + "type": "text", + "content": "- Our first contribution is a 'compiler' that generates PyTorch [26] code for a shape program, which can be defined in Blender for example. This code generates 3D shapes that are differentiable with respect to the continuous parameters" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 449, + 553, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 553, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 553, + 473 + ], + "type": "text", + "content": "and can therefore be used easily with 3D reconstruction algorithms to optimize the continuous parameters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 474, + 554, + 689 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 313, + 474, + 554, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 554, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 554, + 556 + ], + "type": "text", + "content": "- Second, we contribute a method to obtain efficiently and reliably all shape program parameters from RGB-D scans: While our compiler can be used to optimize over the continuous parameters, the challenge of estimating the discrete parameters remains. We propose to adapt methods based on genetic algorithms to our problem of jointly optimizing the continuous and the discrete parameters of a shape program." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 557, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 554, + 689 + ], + "type": "text", + "content": "- Our third contribution is an extension of shape programs to capture fine details and appearance of objects. We do this by augmenting our programs with Gaussians. Once we retrieved the shape parameters, we initialize our procedural Gaussians over the primitives and optimize them as in Gaussian splatting [17]. The key difference with regular Gaussian Splatting is that our Gaussians are constrained by the procedural model: The Gaussians sampled on 'cloned' base primitives are tied together. e.g. as the legs of a chair are 'clones' of the same base primitives, the occluded part of a leg can still be recovered if it is visible for another leg." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 689, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 712 + ], + "type": "text", + "content": "We evaluate our method on both synthetic and real scenes. In addition to the usual metrics, we also evaluate" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16284" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "how well we reconstruct the shape program continuous and discrete parameters. Because existing datasets are not annotated with the value of these parameters, we manually annotated 176 objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 122, + 294, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 122, + 294, + 206 + ], + "spans": [ + { + "bbox": [ + 55, + 122, + 294, + 206 + ], + "type": "text", + "content": "In summary, our main contribution is a general tool to create PyTorch code from Blender shape programs. In addition, we provide a method for estimating the parameters of shape programs from views together with the poses of the objects. Our PyTorchGeoNodes is a modular tool and it can be extended to novel use cases in 3D scene understanding. The source code is available to the general public." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 223, + 142, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 142, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 142, + 236 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 245, + 294, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 245, + 294, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 294, + 293 + ], + "type": "text", + "content": "Since the field of retrieving 3D models for objects from images is very large, we focus here only on methods that can provide a light CAD model designed for specific categories: 3D model retrieval methods and Shape Programs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 307, + 170, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 307, + 170, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 307, + 170, + 319 + ], + "type": "text", + "content": "2.1. 3D Model Retrieval" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 327, + 294, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 294, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 294, + 386 + ], + "type": "text", + "content": "3D model retrieval aims to retrieve a CAD model from a database of objects, such as the ShapeNet dataset [6], that maximizes some scoring function which is typically based on an input 3D representation or a single or multiple input images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 388, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 544 + ], + "type": "text", + "content": "Some methods approach CAD model retrieval as a classification problem [3, 23]. For a given input a neural network can be trained to predict a probability distribution over all models in the database. However, these direct approaches do not scale well to large object databases such as the ShapeNet database. Another popular approach is computing a similarity metric between synthetic objects and real inputs. There are several possible ways of computing such metrics. It is possible to render an image from a synthetic object, and then for a synthetic-real image pair, we can compute and compare image descriptors [2, 13, 22] or encode images into embedding vector representations and calculate the similarity in the embedding space [20]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "content": "While such approaches have displayed promising results, one clear limitation is expressiveness of the database of objects. In fact, even with large databases of objects, in practice we often encounter objects in real scenes that are not represented in the database, or we might encounter modified or articulated objects. For example, we can modify seat height, arm rest and back support position of a work chair but the object in the database appears in the default setting which will introduce errors during retrieval. While it is possible to perform mesh refinement and deformation [4, 14, 33], these approaches typically introduce artifacts and deformations in the reconstruction and the final object shape might not be representative of the actual object category after refinement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 72, + 415, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 415, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 415, + 85 + ], + "type": "text", + "content": "2.2. Shape Programs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 89, + 553, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 553, + 281 + ], + "type": "text", + "content": "Procedural modelling is an attractive way of generating 3D shapes in computer graphics, and as such it is an interesting feature of different 3D modelling software. In general, procedural modelling is a family of techniques that generate 3D content by abiding to a set of rules. A variety of methods were proposed that combine procedural modeling with machine learning approaches, summarized in detail in [30]. For example, [35] introduced a procedural language that enables the generation of a variety of shapes in form of so-called shape programs. In [35], shape programs are written in Domain Specific Language (DSL) for shapes with two types of statements. \"Draw\" statements describes shape primitive, such as cuboid or a cylinder, together with its geometric and semantic properties. \"For\" statements represent loops of sub-programs including parameters that indicate how the sub-program should be repeatedly executed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 282, + 553, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 553, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 553, + 354 + ], + "type": "text", + "content": "[35] also showed that it is possible to learn to infer shape programs that describe input 3D shapes. However, as it is based on basic geometric primitives, it becomes difficult to model more complex geometries, and resulting shapes can be non-representative of the target category. Other methods suffer from the same limitations [15, 16]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 355, + 553, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 355, + 553, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 355, + 553, + 463 + ], + "type": "text", + "content": "GeoCode [27] recently introduced hand-designed shape programs as a mapping between 3D shapes of a specific object category and human-interpretable parameter space. The language used for developing shape programs is based on the geometry node feature of Blender, an open-source modeling software, which, in contrast to [35], allows designing of more expressive shape programs that can represent and interpolate between a variety of shapes by simply modifying human-interpretable program's parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 464, + 553, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 553, + 655 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 553, + 655 + ], + "type": "text", + "content": "Some nodes define a shape primitive or pre-designed more complex shapes, e.g., chair seat or chair leg. Other nodes represent geometric transformations on individual shapes, or how two shapes should be connected, e.g., legs should always be connected to the bottom of the seat. There are nodes representing mathematical operations such as addition and multiplication, and there are nodes that are used to replicate specific shapes, e.g., in case of chair legs we can add a replicator node to create four instances of a chair leg of the same shape. There are also nodes that serve as control statements, e.g., it is possible to switch between a four-legged chair and a one-legged chair. A pre-defined set of input program's parameters allow non-expert user to easily control shape-generation process. [27] also showed that it is possible to learn the mapping from input point clouds of 3D shapes, or a sketch, to program's parameters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 669, + 424, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 669, + 424, + 681 + ], + "spans": [ + { + "bbox": [ + 314, + 669, + 424, + 681 + ], + "type": "text", + "content": "3. PyTorchGeoNodes" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "In this section, we discuss shape programs and how they can be beneficial for tasks in 3D scene understanding. We" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16285" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 531, + 277 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 531, + 277 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 531, + 277 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 531, + 277 + ], + "type": "image", + "image_path": "d7c1dfe342c447bb538967e6268c53959d58a9d875ad6c34b75647b5138f58d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 285, + 555, + 361 + ], + "lines": [ + { + "bbox": [ + 55, + 285, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 555, + 361 + ], + "type": "text", + "content": "Figure 2. A procedural model in Blender generating dividing boards of a cabinet. The computational graph is designed and visualized in Blender using Geometry Nodes feature. Underneath, we show how we abstract the different nodes using PyTorch tensors and PyTorch3D meshes. The input node takes input parameters, here {Width: 0.5, Dividing Board Thickness: 0.04, Height: 0.6, Number of Dividing Boards: 5, Board Thickness: 0.04} and feeds them to a series of operations. The blue nodes are arithmetic and concatenation nodes, which transform input parameters and feed the results to geometry nodes, in green. In this example, we generate a cuboid mesh and instantiate a line of points which generates the final geometry for dividing boards. In practice, this shape program is part of a larger shape program for modeling cabinets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 383, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 383, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 295, + 456 + ], + "type": "text", + "content": "then describe our framework for enabling efficient gradient-based optimization for shape programs and, in addition, allowing to translate shape programs designed in Blender to PyTorch code to enable differentiable optimization. In Section 4, we explain how our framework can be applied for reconstructing 3D objects from images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 459, + 295, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 518 + ], + "type": "text", + "content": "We consider shape programs as defined in Blender, i.e., as a computational graph that computes 3D shapes given a number of input parameters. Such graphs contain nodes of different types; in our framework, we currently consider the following node types:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 522, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 56, + 522, + 295, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 522, + 295, + 557 + ], + "spans": [ + { + "bbox": [ + 56, + 522, + 295, + 557 + ], + "type": "text", + "content": "- An 'Input' node contains input parameters of the shape programs and their value ranges. We consider floating, integer, and boolean values;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 558, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 558, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 56, + 558, + 295, + 593 + ], + "type": "text", + "content": "- A 'Math' node performs mathematical operations on its input (addition, subtraction, multiplication, division, and comparison);" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 594, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 594, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 56, + 594, + 295, + 616 + ], + "type": "text", + "content": "- A 'Switch' node switches between two inputs conditioned on a boolean input;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 618, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 618, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 56, + 618, + 295, + 640 + ], + "type": "text", + "content": "- A 'Combine' node concatenates three input values into a 3D vector;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 642, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 642, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 56, + 642, + 295, + 666 + ], + "type": "text", + "content": "- A 'Primitive' node creates a geometric primitive, e.g., a cuboid or a cylinder;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 666, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 666, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 56, + 666, + 295, + 689 + ], + "type": "text", + "content": "- A 'Transform' node applies scaling, rotation, and translation to the input geometry;" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 689, + 295, + 713 + ], + "type": "text", + "content": "- 'Mesh Line' node creates a tensor of 3D points on a line from input vectors that define the start location and the" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 383, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 383, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 323, + 383, + 553, + 407 + ], + "type": "text", + "content": "offset of the line, and an integer that defines the number of points to be generated;" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 407, + 553, + 466 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 314, + 407, + 553, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 407, + 553, + 430 + ], + "spans": [ + { + "bbox": [ + 314, + 407, + 553, + 430 + ], + "type": "text", + "content": "- A 'Points on instances' node clones input geometry at given input 3D points;" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 431, + 502, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 431, + 502, + 442 + ], + "spans": [ + { + "bbox": [ + 314, + 431, + 502, + 442 + ], + "type": "text", + "content": "- A 'Join geometry' node merges geometries;" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 443, + 553, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 443, + 553, + 466 + ], + "spans": [ + { + "bbox": [ + 314, + 443, + 553, + 466 + ], + "type": "text", + "content": "- An 'Output geometry node' generates the final mesh for the shape." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 477, + 553, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 553, + 512 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 553, + 512 + ], + "type": "text", + "content": "Note that for example, the Transform node depends on continuous, the Points on instances node on integer, and the Switch node on boolean." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 524, + 555, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 524, + 555, + 668 + ], + "spans": [ + { + "bbox": [ + 313, + 524, + 555, + 668 + ], + "type": "text", + "content": "Our framework provides differentiable computational nodes that reimplement the functionalities of the individual geometry nodes in Blender as we show in Figure 2. More exactly, for every node type in Blender, we implement a corresponding node type with the same functionalities using PyTorch, or PyTorch3D [29] in case of geometric operations. In practice, we designed shape programs directly using the Blender interface. Given a shape program created in Blender, our parser generates a differentiable PyTorch-GeoNodes code. We can then use this code in PyTorch in an optimization procedure where we fit shape parameters to generate a shape consistent with the input scene." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "In the supplementary material, we detail our design choices and technical details which make our implementation computationally efficient." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16286" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 290, + 150 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 290, + 150 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 290, + 150 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 290, + 150 + ], + "type": "image", + "image_path": "4ab110ea511650d4681465f874960f68071790893c7e1e7c4825a6ff86194d70.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 161, + 296, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 161, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 161, + 296, + 251 + ], + "type": "text", + "content": "Figure 3. Fitting shape parameters with PyTorchGeoNodes. At every iteration, our genetic algorithm generates individuals of shape parameters and object poses. We parse 3D shapes from individual parameters using PyTorchGeoNodes and perform shape parameter optimization based on loss that evaluates how well the shape fits the input scene. In the next iteration, the optimized set of individuals is used to update the pool of individuals based on selection of the fittest principle." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 269, + 162, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 269, + 162, + 283 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 162, + 283 + ], + "type": "text", + "content": "4. Search Algorithm" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": "We leverage our PyTorchGeoNodes framework to retrieve shape parameters and geometry of a target object in an RGB-D scan. We look for shape parameters " + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^*" + }, + { + "bbox": [ + 55, + 289, + 296, + 361 + ], + "type": "text", + "content": " by minimizing an objective function that encourages the shape to fit the point cloud reconstructed from the images while lying on the floor:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 369, + 294, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 369, + 294, + 397 + ], + "spans": [ + { + "bbox": [ + 70, + 369, + 294, + 397 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} (\\mathcal {P}) = \\lambda_ {\\mathrm {C D}} \\mathcal {L} _ {\\mathrm {C D}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})) + \\lambda_ {\\mathrm {G}} \\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) + \\\\ \\lambda_ {\\mathrm {F l}} \\mathcal {L} _ {\\mathrm {F l}} (\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P}))). \\tag {1} \\\\ \\end{array}", + "image_path": "1ca09bf920b1aee30b5d31a368cb29fb082e83b4b02417bb784eca9dd0fa15de.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CD}}(\\mathrm{PC}, \\mathrm{Sh}(\\mathcal{P}))" + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "text", + "content": " measures the single-direction chamfer distance between PC, the point cloud reconstructed from the depth maps and object masks, and " + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathrm{Sh}(\\mathcal{P})" + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "text", + "content": ", the shape generated by the shape program. We follow pre-processing from [1] which relies on sparse point cloud instance segmentation of the object and use a segmentation model [18] on images to obtain the object masks. We then back-project these masks to obtain a dense target point cloud. " + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{G}}(\\mathrm{G}, \\mathrm{Sh}(\\mathcal{P}))" + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "text", + "content": " penalizes occlusions in the scene caused by " + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathrm{Sh}(\\mathcal{P})" + }, + { + "bbox": [ + 55, + 404, + 296, + 548 + ], + "type": "text", + "content": ". G is an occlusion grid obtained by densely sampling 3D points along rays between the camera and surfaces for different views:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 553, + 296, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 553, + 296, + 588 + ], + "spans": [ + { + "bbox": [ + 63, + 553, + 296, + 588 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {G}} (\\mathrm {G}, \\operatorname {S h} (\\mathcal {P})) = \\sum_ {p \\in \\operatorname {S h} (\\mathcal {P})} \\left\\{ \\begin{array}{l l} \\vec {\\mathrm {C D}} (p, \\mathrm {P C}) & \\text {i f} \\mathrm {G} (p) \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {2}", + "image_path": "ad8ab9884d5e4c7d36211e448f2a8d6e9771ef03a72a982412d61ea632d5e3df.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "\\vec{\\mathrm{CD}}" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "p, \\mathrm{PC}" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": ") is the distance of point " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " to PC. " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{G}(p) = \\vec{\\mathbf{CD}}" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "p, \\mathrm{PC}" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": ") < " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " determines whether " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " is on grid G. We set threshold " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "\\omega = 5cm" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " in our experiments. Since G is generated using input views for the scene, this loss does not penalize points that are occluded in the scene, similar to render-and-compare objectives. The term " + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Fl}}" + }, + { + "bbox": [ + 55, + 597, + 296, + 689 + ], + "type": "text", + "content": " simply enforces the objects to stay on the floor plane:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 697, + 295, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 697, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 85, + 697, + 295, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {F l}} \\left(\\mathrm {P C}, \\operatorname {S h} (\\mathcal {P})\\right) = | \\mathrm {F l} (\\mathrm {P C}) - \\mathrm {F l} (\\operatorname {S h} (\\mathcal {P})) | _ {2}, \\tag {3}", + "image_path": "a7c68df4daf15840dc324acb5c4d8a861fc6144f60b185abc67b8d3622595fa4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\operatorname{Fl}(\\mathrm{PC})" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": " returns the height of the lowest point in PC, and " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\operatorname{Fl}(\\operatorname{Sh}(\\mathcal{P}))" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": " similarly determines the lowest point of shape " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\operatorname{Sh}(\\mathcal{P})" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": ". We set weights of individual loss terms to " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{CD}} = 1" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{G}} = 0.5" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{Fl}} = 0.01" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": " in our experiments. Parameters " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": " include the object pose in addition to the shape program parameters. We initialize the translation based on an initial estimate of the object center which is refined during search. We constrain the rotation to be around the vertical axis only." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": "We use our PyTorchGeoNodes framework to compute " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{Sh}(\\mathcal{P})" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": ". Thanks to this framework, PyTorch can compute the derivatives of " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{Sh}(\\mathcal{P})" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": " and thus the derivatives of " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": " with respect to the continuous parameters in " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": ". However, some parameters in " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": " are discrete, i.e., integers or booleans. Therefore, we cannot optimize " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": " using a simple gradient descent. Also, " + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 181, + 554, + 275 + ], + "type": "text", + "content": " has no special form that we can exploit to optimize it." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "type": "text", + "content": "To solve this problem, we propose to resort to genetic algorithms to optimize the parameters and combine it with gradient descent to further refine the continuous parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 323, + 454, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 454, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 454, + 335 + ], + "type": "text", + "content": "4.1. Shape Parameter Search" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 341, + 554, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 554, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 554, + 425 + ], + "type": "text", + "content": "A genetic algorithm is a stochastic optimization algorithm that iteratively applies random manipulations of high-dimensional search parameters to identify the most promising complex search subspaces, subject to an objective function. In contrast to gradient-based techniques, it can optimize discrete and continuous values and the objective function can be very general and non-differentiable." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 426, + 555, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 605 + ], + "type": "text", + "content": "The algorithm starts by randomly generating instances of parameter values " + }, + { + "bbox": [ + 313, + 426, + 555, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 426, + 555, + 605 + ], + "type": "text", + "content": ", individuals, that form an initial set called population of search parameters. Every iteration has three phases: crossover and mutation for exploring search subspaces, and selection for exploiting the most promising subspaces. Crossover randomly selects pairs of individuals, parents, and mixes them by combining the individual parameters to create a new offspring. Therefore, an offspring lies in the search subspace at intersection of parents' search spaces. Mutation then randomly alters offsprings' parameters to further explore this subspace. Selection evaluates the quality of the population, and based on survival of the fittest strategy, it takes the best performing individuals to form the population for the next iteration. Further details and hyperparameters are given in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": "Our adaptation of genetic algorithms to our problem is described in details in the supplementary material. The main points are given below. We generate an initial population by randomly generating instances of all program's parameters " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": " representing individuals in the population. We draw random values from the empirical distributions of the parameters. The crossover operation generates offspring " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "P_{1,2}" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": " from a pair of parents " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_1" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_2" + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "text", + "content": ". Mutation varies depending on the parameter type. For discrete parameter " + }, + { + "bbox": [ + 313, + 606, + 556, + 715 + ], + "type": "inline_equation", + "content": "d \\in \\mathcal{P}_D" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16287" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 145, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 145, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 145, + 84 + ], + "type": "text", + "content": "we adapt its value " + }, + { + "bbox": [ + 55, + 72, + 145, + 84 + ], + "type": "inline_equation", + "content": "v_{d}" + }, + { + "bbox": [ + 55, + 72, + 145, + 84 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 93, + 294, + 125 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 93, + 294, + 125 + ], + "spans": [ + { + "bbox": [ + 86, + 93, + 294, + 125 + ], + "type": "interline_equation", + "content": "v _ {d} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {d} & \\text {w i t h p r o b a b i l i t y} P _ {m} \\\\ v _ {d} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}", + "image_path": "1c453e2e0aafb942bfe2109d61b4c6d07cbf170d281c39622453074c6792f8fe.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "spans": [ + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": "where operator " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "\\in_R" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": " randomly selects value " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": " from the set of valid discrete values " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "\\nu_{p}" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "P_{m}" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": " is a hyper-parameter that defines the probability of mutating parameter values. In case of a continuous parameter " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "c\\in \\mathcal{P}_C" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": ", we adapt its value " + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "inline_equation", + "content": "v_{c}" + }, + { + "bbox": [ + 55, + 134, + 295, + 182 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 191, + 295, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 191, + 295, + 235 + ], + "spans": [ + { + "bbox": [ + 64, + 191, + 295, + 235 + ], + "type": "interline_equation", + "content": "v _ {c} \\leftarrow \\left\\{ \\begin{array}{l l} v _ {s} \\in_ {R} \\mathcal {V} _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\cdot P _ {m} \\\\ v _ {c} + \\mathcal {N} (0, \\sigma) & \\text {w i t h p r o b .} P _ {m} \\\\ v _ {c} & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}", + "image_path": "f5cee1765e2cd7a6adb4b65d6e95498f9b2c22c9f29cda195acc3210363cca64.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_c" + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "content": " is a discretisation of values for parameter " + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "content": " that we further discuss in the supplementary. " + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\sigma)" + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "content": " is normal distribution with mean value set to 0 and standard deviation " + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 244, + 296, + 327 + ], + "type": "text", + "content": ". Finally, we evaluate offsprings, append them to the current population and we select the best individuals based on a score function, in our case negative of objective in Equation 1, to form the population for the next iteration." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 328, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 328, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 328, + 296, + 413 + ], + "type": "text", + "content": "Optimization step. Using PyTorchGeoNodes, during the selection phase of every iteration, we perform a gradient-based optimization to further refine values of continuous shape parameters of individuals before selecting the population for next iteration. After a specified number of iterations the search concludes and we return shape parameters of the best performing individual." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 420, + 212, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 212, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 212, + 433 + ], + "type": "text", + "content": "4.2. Integrating Gaussians Splats" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 437, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 498 + ], + "type": "text", + "content": "Shape programs explicitly capture symmetries and similarities between repeated structures, while this aspect is lacking in many representations for 3D reconstruction. On the other hand, earlier shape programs do not capture well details and appearance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 498, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 593 + ], + "type": "text", + "content": "In this section, we show we enable procedural Gaussian splats by integrating them within shape programs and our PyTorchGeoNodes framework. This allows us to capture fine details of objects while keeping the advantages of shape programs. First, we explain how we augment the primitives with 'Gaussian primitives' while keeping the graph of PyTorchGeoNodes differentiable, and then, we introduce our render-and-compare objective function." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "Extending PyTorchGeoNodes with Gaussian primitives. To enable integration of our procedural graph to support Gaussian splats, we extend the nodes creating mesh primitives to also create trainable Gaussian parameters. We subsample the primitives meshes into many triangles and create Gaussians from these triangles. We initialize the Gaussians means, scales, and quaternions to fit the mesh triangles as we show in Figure 4. Their colors are initialized based on the closest 3D point in the scan. Their opacities are fixed to a high value. As with other primitives," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 343, + 69, + 526, + 150 + ], + "blocks": [ + { + "bbox": [ + 343, + 69, + 526, + 150 + ], + "lines": [ + { + "bbox": [ + 343, + 69, + 526, + 150 + ], + "spans": [ + { + "bbox": [ + 343, + 69, + 526, + 150 + ], + "type": "image", + "image_path": "6eeee1e0ddbb1b11fe12002e08cd994b46ccd9aaac55137b1c9bc07fd7a91907.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 154, + 554, + 188 + ], + "lines": [ + { + "bbox": [ + 313, + 154, + 554, + 188 + ], + "spans": [ + { + "bbox": [ + 313, + 154, + 554, + 188 + ], + "type": "text", + "content": "Figure 4. We integrate Gaussians directly into shape programs and PyTorchGeoNodes, to have the advantages of both procedural models and Gaussian splatting." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 196, + 553, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 196, + 553, + 232 + ], + "spans": [ + { + "bbox": [ + 313, + 196, + 553, + 232 + ], + "type": "text", + "content": "the graph transforms the Gaussians to form a complete set of Gaussians, some of them sharing parameters due to the cloning in the graph." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": "Optimizing the Gaussians. We noticed that it is more robust to, rather than jointly, first estimate the shape parameters and then optimize the Gaussians. Given a set of optimal shape parameters " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": ", we minimize the render-and compare loss as in other Gaussian splatting works, by rendering the Gaussians " + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathcal{P})" + }, + { + "bbox": [ + 313, + 232, + 554, + 304 + ], + "type": "text", + "content": " into scene views [12, 17, 40]:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 369, + 312, + 553, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 312, + 553, + 326 + ], + "spans": [ + { + "bbox": [ + 369, + 312, + 553, + 326 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}} + \\mathcal {L} _ {\\text {r e g}}, \\tag {6}", + "image_path": "b5d4a349659732911b0e57fc0b9ad20fd95dad592814a01fe83cc3798f3d8de0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RGB}}" + }, + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{D}}" + }, + { + "bbox": [ + 313, + 332, + 553, + 357 + ], + "type": "text", + "content": " are standard losses on color and depth consistency used in Gaussian splatting literature [7, 36, 40]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}} = \\mathrm{CD}(\\mathrm{Sh}(\\mathcal{P}),\\mathcal{G}(\\mathcal{P}))" + }, + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "type": "text", + "content": " measures the consistency between the shape parameters and the Gaussians by relying on the chamfer distance. " + }, + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 313, + 357, + 553, + 393 + ], + "type": "text", + "content": " is a regularizer term:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 350, + 400, + 553, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 400, + 553, + 415 + ], + "spans": [ + { + "bbox": [ + 350, + 400, + 553, + 415 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {3} | M (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\lambda_ {4} | S (\\mathcal {G} (\\mathcal {P})) | _ {2} + \\tag {7}", + "image_path": "c7abf9b855f9afdd849339585e8e18b99c64562bdf8777cd48eb8554406826f2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 377, + 417, + 553, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 417, + 553, + 443 + ], + "spans": [ + { + "bbox": [ + 377, + 417, + 553, + 443 + ], + "type": "interline_equation", + "content": "\\lambda_ {5} \\sum_ {G \\in \\mathcal {G} (\\mathcal {P})} \\operatorname {V a r} (C (G) |, \\tag {8}", + "image_path": "d39ca4ebfa36072ff1df6b54bffeb8d4dd7d2add39b9627bc5a1252541b0ed3d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": "to enforce mean offsets " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "M(\\mathcal{G}(\\mathcal{P}))" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " and scales offsets " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "S(\\mathcal{G}(\\mathcal{P}))" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " of Gaussians to be small and the colors of the Gaussians on the same primitive " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "C(G)" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " to remain close to each other. We set " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 0.1, \\lambda_2 = 0.1, \\lambda_3 = 100, \\lambda_4 = 10.00, \\lambda_5 = 1" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " in our experiments. In addition, we observed that optimizing object Gaussians and background Gaussians jointly at the same time, with loss for background locations set to " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "\\lambda_{bgd}(\\mathcal{L}_{\\mathrm{RGB}} + \\lambda_1\\mathcal{L}_{\\mathrm{D}})" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "inline_equation", + "content": "\\lambda_{bgd} = 0.5" + }, + { + "bbox": [ + 313, + 451, + 554, + 559 + ], + "type": "text", + "content": " ensures that object Gaussians remain consistent around edges." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 568, + 383, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 383, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 383, + 581 + ], + "type": "text", + "content": "5. Validation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 588, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 554, + 689 + ], + "type": "text", + "content": "We validate our PyTorchGeoNodes framework and our optimization method on three common furniture categories: Sofa, with 18 parameters, Chair with 20, and Table, with 10, for which we created shape programs in Blender. We designed our shape programs to capture interpretable object structures that are relevant for objects in ScanNet, allowing unseen-before reasoning about high-level object parameters. More details are provided in the supplementary material." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 690, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 690, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 690, + 554, + 713 + ], + "type": "text", + "content": "Our method jointly estimates the pose and shape parameters of the object. The orientation is defined as the rotation" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16288" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "around the up-axis as done in to [1], which is sufficient for indoor scenes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 95, + 296, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 95, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 55, + 95, + 296, + 209 + ], + "type": "text", + "content": "We validate our method on object shape reconstruction for real world scenes from the ScanNet dataset [9]. ScanNet is a challenging dataset of indoor environment RGB-D scans: Furniture is only partially visible and highly occluded, and depth maps are incomplete due to missing sensor values—this happens for dark and reflective materials, for example. We manually annotated 176 objects for Sofa, Chair, and Table. We also provide additional results on automatically generated synthetic scenes in the supplementary material including an additional object category." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 216, + 170, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 216, + 170, + 227 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 170, + 227 + ], + "type": "text", + "content": "5.1. Evaluation Criteria" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 232, + 295, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 232, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 295, + 323 + ], + "type": "text", + "content": "Evaluation of shape parameters. Each object category has properties which are an important aspect of the reconstruction. This is neglected by current state-of-the-art methods. Our approach integrates these properties as shape parameters into the reconstruction and we evaluate them by comparing the reconstructed and ground truth parameters of the target objects. For the experiments with ScanNet, we manually annotated all relevant objects with shape parameters." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 324, + 296, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 392 + ], + "type": "text", + "content": "Data pre-processing. We assume that for the target object in the RGB-D scan, we have an initial estimate for the 3D center of the target object, here we follow preprocessing from [1]. Then, we estimate 2D segmentation masks of the object used to generate dense point clouds in the objective function in Equation (1)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 399, + 187, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 187, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 187, + 410 + ], + "type": "text", + "content": "5.2. Search Baseline Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 415, + 295, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 295, + 438 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 295, + 438 + ], + "type": "text", + "content": "In our evaluations of our search algorithm, we compare results of our genetic algorithm to two baselines:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 440, + 295, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 440, + 295, + 645 + ], + "spans": [ + { + "bbox": [ + 56, + 440, + 295, + 645 + ], + "type": "text", + "content": "- GeoCode [27] introduces a supervised learning method based on an encoder-decoder architecture that takes a target point cloud as input and outputs a value for target program parameters. We use DGCNN [28] as encoder, and the resulting embedding of size 128 is shared between separate decoders that predict values for program parameters. More precisely, we use three feed-forward layers per parameter, each of size 256. For discrete parameters, we add a classification head as the output layer with number of outputs matching the number of different discrete values. For continuous parameters, we simply regress the output value. Finally, we perform gradient descent that further refines predictions by passing predicted parameter values to PyTorchGeoNodes and optimizing the objective function. We train it by randomly generating 10000 instances of ground truth shape program parameters and rotations and then generating synthetic point clouds from these parameters using PyTorchGeoNodes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 645, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 645, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 645, + 296, + 713 + ], + "type": "text", + "content": "- Our implementation of coordinate descent iteratively optimizes individual parameters of the shape program. First, we initialize the estimate of parameters randomly. Then, at every iteration, we take the current estimate and replace value of the selected parameter by all valid discrete values and calculate the objective term. In case of" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 322, + 71, + 550, + 129 + ], + "blocks": [ + { + "bbox": [ + 322, + 71, + 550, + 129 + ], + "lines": [ + { + "bbox": [ + 322, + 71, + 550, + 129 + ], + "spans": [ + { + "bbox": [ + 322, + 71, + 550, + 129 + ], + "type": "image", + "image_path": "cfd22c17674680e246b13a3db78986e0cad7200fb7b119add10b75fafc26a4c0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 322, + 130, + 550, + 189 + ], + "blocks": [ + { + "bbox": [ + 322, + 130, + 550, + 189 + ], + "lines": [ + { + "bbox": [ + 322, + 130, + 550, + 189 + ], + "spans": [ + { + "bbox": [ + 322, + 130, + 550, + 189 + ], + "type": "image", + "image_path": "8b65aa4e3f76d5fad28475adce1b6ac54e877e575f9e96162c16e76ed5e81e63.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 321, + 191, + 550, + 249 + ], + "blocks": [ + { + "bbox": [ + 321, + 191, + 550, + 249 + ], + "lines": [ + { + "bbox": [ + 321, + 191, + 550, + 249 + ], + "spans": [ + { + "bbox": [ + 321, + 191, + 550, + 249 + ], + "type": "image", + "image_path": "5ed32c9270f8a4574715d073c33fb0de87624c5494901ca944a61a9ceab345bc.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 262, + 555, + 415 + ], + "lines": [ + { + "bbox": [ + 313, + 262, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 555, + 415 + ], + "type": "text", + "content": "Figure 5. Shape from recovered object parameters aligns very well with the target object also when projected into sampled images of the scene. In the first row, we reconstruct a variety of chairs along with many detailed parameters including seat thickness, thickness and offsets of side and front/back support legs, existence of different semantic elements like 'star-shaped' legs and its exact rotation. In the second row, we correctly estimate shape of table top and its measurements, including width, depth and thickness, parameters of table legs, and existence of middle shelf including its offset from the bottom. In the third row we reconstruct parameters of 'L-element' of sofa including its depth and width, existence and size of legs, and existence of individual armrests, backrest, and the corresponding measurements. We show more results in the supplementary material." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 437, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 437, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 323, + 437, + 555, + 529 + ], + "type": "text", + "content": "continuous values we first discretize them as we explain in the supplementary. In case this improves the objective, we update the current estimate. Finally, we perform gradient descent that further refines the current estimate by passing it to PyTorchGeoNodes and optimizing the objective function. We repeat the process for all different parameters and loop 3 times which approximately matches the execution time of our genetic algorithm." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 536, + 497, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 497, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 497, + 548 + ], + "type": "text", + "content": "5.3. Validation on the ScanNet Dataset" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 553, + 554, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 553, + 554, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 553, + 554, + 610 + ], + "type": "text", + "content": "We evaluate our approach on challenging real-world scenarios on validation scenes from ScanNet [9], which provides RGB-D scans of indoor scenes. We selected a subset of object instances from the Scannotate dataset [1] for which we manually annotated 57 sofas, 52 chairs, and 67 tables." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 611, + 554, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 554, + 678 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 554, + 678 + ], + "type": "text", + "content": "Table 1 evaluates the quality for object parameters reconstruction for the 'table' category and general reconstruction quality across different categories. We report the numbers for 'chair' and 'sofa' in the supplementary material. We measure the classification accuracy for discrete parameteres and absolute difference for continuous parameters." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 679, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 679, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 679, + 554, + 712 + ], + "type": "text", + "content": "We observe that the supervised learning method from [27], trained on synthetic data, generalises poorly to the scene from ScanNet, while coordinate descent baseline" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16289" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 535, + 355 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 535, + 355 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 535, + 355 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 535, + 355 + ], + "type": "table", + "html": "
ParameterModel from [27] w\\o refinementModel from [27] w\\o refinementCD w\\o refinementCD w\\o refinementGenetic w\\o refinementGenetic
Continuous ParametersWidth [cm]0.740.220.210.210.150.08
Height [cm]0.340.140.150.150.120.06
Depth [cm]0.40.20.220.220.130.08
Mid Leg X Scale0.190.130.160.140.10.07
Mid Leg Y Scale0.160.140.110.110.080.08
Legs Offset Y0.350.340.370.370.310.27
Legs Offset X0.320.320.360.360.150.13
Legs Scale Y0.170.150.180.190.130.1
Mid Board Z Scale0.210.180.180.180.170.14
Cabinet Width Scale0.150.10.150.110.10.05
Top Thickness [cm]0.030.030.020.020.020.02
Legs Size [cm]0.030.030.030.030.010.01
Discrete P:Top ShapeClassification Accuracy for Table ()
Legs Type0.780.780.720.720.940.94
Has Cabinet Leg0.390.390.60.580.780.78
Has Mid Board0.710.710.570.550.780.86
0.710.710.550.490.760.76
Chamfer distance [m] Abs. rotation error [rad]Reconstruction quality across all categories ()
0.520.210.160.160.140.11
0.450.120.130.110.080.06
", + "image_path": "cb3d084733a59ed79032e5b85ecc1fd2ecdd150601ca21b0097987cb349467b6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 362, + 555, + 407 + ], + "lines": [ + { + "bbox": [ + 54, + 362, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 54, + 362, + 555, + 407 + ], + "type": "text", + "content": "Table 1. Quantitative results of shape program parameters between different baselines for category Table, and general reconstruction metrics across all categories. We observe that GeoCode [27] performs worst due to the domain gap, but the optimization helps improve the performance. Coordinate Descent (CD) does better but is prone to local minima. Genetic algorithm outperforms other baselines by a significant margin." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 425, + 294, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 425, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 425, + 294, + 529 + ], + "type": "text", + "content": "is prone to local minima. Our genetic algorithm performs very well across all metrics except for parameters defining very small details. Visually, the models recovered by our method are comparable in quality to the ground truth and we confirm the benefits of our refinement procedure. Figure 5 and Figure 6 show some qualitative results. In the supplementary we show additional results, and include a downstream application for point cloud segmentation based on our reconstructions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 544, + 128, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 128, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 128, + 555 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 564, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 564, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 564, + 295, + 713 + ], + "type": "text", + "content": "Our code is publicly available and we hope this will encourage other researchers to develop the field and further extend possibilities with PyTorchGeoNodes. While shape programs are an attractive representation of objects, there are indeed still many things to develop: e.g. extensions to consider deformable and articulated objects and to integrate textures. Modularity of PyTorchGeoNodes enables integrations with other types of 3D representation, as we demonstrate with our integration of Gaussian Splatting. Moreover, differentiable rendering of PyTorchGeoNodes enables development of deep learning methods for creating shape programs from images in a self-supervised way. 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(a) We overlay shape reconstructed using our retrieved shape parameters with the image and (b) compare it to the ground truth. (c) Our integration of Gaussians into PyTorchGeoNodes enables appealing 3D reconstructions." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 632, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 555, + 689 + ], + "type": "text", + "content": "signed by humans for different categories which can lead to limited expressiveness when applying our approach in the wild. Learning shape program designs from database of shapes would make our method easily applicable to novel categories." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16290" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 296, + 140 + ], + "type": "text", + "content": "This project was funded by the European Union (ERC Advanced Grant explorer Funding ID #101097259). 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Computational Visual Media, 2024." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16292" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_content_list.json b/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..66fb243f65470b746f35b959281e46564b62365f --- /dev/null +++ b/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_content_list.json @@ -0,0 +1,1794 @@ +[ + { + "type": "text", + "text": "Q-Bench-Video: Benchmark the Video Quality Understanding of LMMs", + "text_level": 1, + "bbox": [ + 133, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zicheng Zhang $^{1*}$ , Ziheng Jia $^{1*}$ , Haoning Wu $^{2\\dagger}$ , Chunyi Li $^{1}$ , Zijian Chen $^{1}$ , Yingjie Zhou $^{1}$ , Wei Sun $^{1}$ , Xiaohong Liu $^{1}$ , Xiongkuo Min $^{1\\dagger}$ , Weisi Lin $^{2}$ , and Guangtao Zhai $^{1\\dagger}$ $^{1}$ Shanghai Jiaotong University, $^{2}$ Nanyang Technological University", + "bbox": [ + 145, + 179, + 849, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "*First Authors, †Corresponding Authors https://github.com/Q-Future/Q-Bench-Video", + "bbox": [ + 313, + 236, + 679, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 304, + 326, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rising interest in research on Large Multi-modal Models (LMMs) for video understanding, many studies have emphasized general video comprehension capabilities, neglecting the systematic exploration into video quality understanding. To address this oversight, we introduce Q-Bench-Video in this paper, a new benchmark specifically designed to evaluate LMMs' proficiency in discerning video quality. a) To ensure video source diversity, Q-Bench-Video encompasses videos from natural scenes, AI-generated content (AIGC), and computer graphics (CG). b) Building on the traditional multiple-choice questions format with the Yes-or-No and What-How categories, we include Open-ended questions to better evaluate complex scenarios. Additionally, we incorporate the video pair quality comparison question to enhance comprehensiveness. c) Beyond the traditional Technical, Aesthetic, and Temporal distortions, we have expanded our evaluation aspects to include the dimension of AIGC distortions, which addresses the increasing demand for video generation. Finally, we collect a total of 2,378 question-answer pairs and test them on 12 open-source & 5 proprietary LMMs. Our findings indicate that while LMMs have a foundational understanding of perceptual video quality, their performance remains incomplete and imprecise, with a notable discrepancy compared to the performance of human beings. Through Q-Bench-Video, we seek to catalyze community interest, stimulate further research, and unlock the untapped potential of LMMs to close the gap in video quality understanding.", + "bbox": [ + 89, + 338, + 485, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 797, + 220, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As the field of artificial intelligence (AI) continues to evolve, Large Multi-modal Models (LMMs) [4, 16, 19, 50, 51] are progressively utilized in high-level video understanding tasks. These models have shown remarkable capabilities in analyzing and interpreting the semantic content of", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "videos, such as classifying objects, identifying actions, and recognizing events. However, the aspect of video quality, which is vital for optimizing compression and transmission systems, enhancing viewer experience, and establishing standards for high-quality video generation, has received less attention. Although numerous LMM video benchmarks[8, 10, 23] have been developed to assess the semantic understanding of videos by LMMs comprehensively, benchmarks systematically targeting video quality are still lacking. Additionally, while semantic understanding is closely linked to high-level video information, the perception and understanding of low-level information are crucial in video quality [5, 25] as well.", + "bbox": [ + 511, + 305, + 906, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this gap, we introduce Q-Bench-Video, a novel benchmark specifically designed to systematically evaluate the video quality understanding of LMMs. As illustrated in Fig. 1, our benchmark encompasses a wide range of video content, including natural scenes, AI-generated content (AIGC), and computer graphics (CG), ensuring diversity in video sources. In addition, to maintain a reasonable distribution of source video quality, we employ uniform sampling from video datasets that contain subjective quality annotations. This approach guarantees comprehensive coverage of the quality spectrum while avoiding imbalanced quality distributions. Moreover, we extend beyond traditional video evaluations by incorporating both multiple-choice questions (MCQs) and open-ended questions. This enables a more thorough analysis of LMMs' ability to discern video quality across diverse scenarios. We further introduce a new evaluation dimension specifically tailored to assess distortions related to AIGC, which are increasingly prominent in video generation tasks. Recognizing the importance of quality comparison settings in real-world applications, such as camera parameter optimization and AIGC video generation, we further incorporate video pairs to facilitate quality comparison assessment as well. In total, we collect 1800 videos and annotated 2,378 question-answer pairs for validation, creating a robust framework for systematic evaluation on video quality understanding.", + "bbox": [ + 511, + 508, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3229", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/49212cba749d85d0982fa30e92ed050f1353de4a77333a2c7277c300f82cf5ed.jpg", + "image_caption": [ + "Figure 1. The construction overview of the proposed Q-Bench-Video. To ensure diversity in video content, we collect natural scenes, AIGC, and CG videos from video quality assessment datasets as depicted in (a). To achieve a balanced quality distribution among the sampled videos, we employ uniform sampling for quality control. As indicated in (c-1) and (c-2), we utilize three types of questions (Yes-or-No, What-How, Open-ended) and address a comprehensive range of quality concerns including Technical, Aesthetic, Temporal, and AIGC distortions. Additionally, we incorporate the video pairs comparison task to enhance the comprehensiveness of the benchmark." + ], + "image_footnote": [], + "bbox": [ + 194, + 87, + 803, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through the rigorous experiment, we demonstrate that while LMMs show promise in video quality assessment, their performance lags significantly behind human-level understanding. By offering a systematic and thorough evaluation of LMMs' video quality perception, Q-Bench-Video aims to foster research in this underexplored area and push the boundaries of LMM capabilities on video quality understanding. Our contributions can be summarized as follows:", + "bbox": [ + 89, + 469, + 482, + 590 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to assess the video quality understanding capabilities of LMMs. This benchmark includes a diverse collection of source videos and ensures a balanced quality distribution, complemented by human-crafted question-answer annotations.", + "- Our evaluation framework spans four key quality dimensions: Technical, Aesthetic, Temporal, and AIGC distortions, which offers a holistic evaluation approach to video quality assessment. Uniquely, Q-Bench-Video enhances its utility by introducing the task of video pairs comparison, which sets it apart from existing video benchmarks.", + "- We conduct a comprehensive evaluation using both proprietary and open-source LMMs to measure their effectiveness in understanding video quality. The results expose notable deficiencies in current LMMs, while also shedding light on performance variations across different quality dimensions. These findings provide critical insights and suggest promising directions for future enhancements in the field of video quality understanding." + ], + "bbox": [ + 89, + 595, + 482, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 468, + 663, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Video LMMs and Benchmarks", + "text_level": 1, + "bbox": [ + 511, + 494, + 785, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The rapid advancement of Large Multi-modal Models (LMMs) in recent years [4, 28-30, 52, 56, 67] has showcased their remarkable perception and cognitive abilities across various multimodal benchmarks for images [9, 33, 35, 47, 62]. As development progresses, the focus of visual analysis has gradually shifted from images to videos. Early efforts [22, 27, 31, 50] aimed at unlocking the video understanding potential of LMMs have yielded promising results. However, initial video-based benchmarks [24, 34, 41] typically concentrated on specific aspects of video comprehension, falling short of fully capturing the performance of these models due to limitations such as a lack of diversity in video types and inadequate coverage of temporal dynamics. In response, recent video benchmarks [8, 10] have moved toward a more comprehensive evaluation of LMMs. Nonetheless, these efforts focus on high-level semantic understanding without systematic exploration of video quality.", + "bbox": [ + 511, + 517, + 906, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Video Quality Assessment", + "text_level": 1, + "bbox": [ + 511, + 786, + 750, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Quality Assessment (VQA) is a task aimed at quantifying video scores based on visual quality. Initially, early VQA methods employ hand-crafted features extracted from videos and regress the features into quality scores [17, 20, 26, 40, 58, 64, 65]. With the emergence of deep neural networks, a shift occurs as numerous methods adopted deep", + "bbox": [ + 511, + 810, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3230", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/131b6371b83ab8872d999dbfe8136d5ee280d48fc2aa42f7a4afd25cf6535347.jpg", + "table_caption": [ + "Table 1. Overview of the diverse video source datasets in the Q-Bench-Video. We consider various video content types, including natural scenes, AIGC, and CG videos. The term 'MOS' denotes that the videos are annotated via Mean Opinion Scores under ITU standards [1]. We have conducted uniform sampling based on their quality labels to ensure a balanced quality distribution." + ], + "table_footnote": [], + "table_body": "
Video TypeVideo Source DatasetMOSQuality ConcernsSampled SizeFull Dataset Size
Natural (1000)LSVQ [54]✓Spatial & Temporal60039K
MaxWell [46]✓Spatial & Temporal & Aesthetic3504.5K
WaterlooSQoE-III [6]✓Quality-of-Experience20450
WaterlooSQoE-IV [7]✓Quality-of-Experience301,350
AIGC (600)T2VQA-DB [17]✓Quality & Text Alignment20010K
VideoFeedback [13]×Quality & Text Alignment40037.6K
CG (200)LIVE-YT-Gaming [55]✓Visual Quality200600
", + "bbox": [ + 91, + 135, + 903, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "learning techniques for VQA tasks [18, 21, 38, 42]. As the field progresses, newer methods begin incorporating considerations for both temporal dynamics and aesthetic qualities, leading to a more holistic approach to video quality analysis [3, 12, 43, 45, 59]. Moreover, the evolution of large-scale models has further revolutionized VQA methodologies. Many recent approaches have redefined the traditional quality assessment process into a quality question-answering format [11, 15, 48, 60, 63]. This adaptation leverages the substantial prior knowledge embedded in large models to enhance the precision of quality quantification [61]. Despite these technological advances, VQA still grapples with challenges in providing interpretable quality scores and deepening the understanding of how models perceive and analyze video quality more comprehensively.", + "bbox": [ + 88, + 253, + 480, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Benchmark Construction", + "text_level": 1, + "bbox": [ + 89, + 492, + 328, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Benchmark Principle", + "text_level": 1, + "bbox": [ + 89, + 516, + 290, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Q-Bench-Video is designed based on three guiding principles: (1) It encompasses a broad spectrum of video content, including natural scenes, AIGC, and CG videos. (2) It ensures a comprehensive and representative sampling process across a wide quality range, enhancing the benchmark's overall effectiveness. (3) It primarily focuses on the aspects of video quality that significantly influence the viewing experience, including technical, aesthetic, temporal, and AIGC distortions. This significantly differs from other video benchmarks that prioritize semantic understanding. Additionally, the video pair quality comparison is integrated to address the challenges associated with comparing video quality. The overall construction process can be clearly overviewed in Fig. 1.", + "bbox": [ + 89, + 537, + 482, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Source Videos Collection", + "text_level": 1, + "bbox": [ + 89, + 757, + 316, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Table 1, the source videos are primarily gathered from video quality assessment datasets. We selected videos from these datasets for two main reasons: (1) These datasets have inherently considered the diversity of quality features during video selection; (2) These datasets possess quality annotations that adhere to ITU standards [1] (with the exception of VideoFeedback), which allow us to accurately and authentically sample videos.", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our sampling method primarily employs a uniform approach, extracting videos evenly from each dataset based on the quality range. Moreover, considering the current popularity of AIGC and CG videos, we have also incorporated a selection of these video types. (More details in the Supp.)", + "bbox": [ + 511, + 253, + 906, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Benchmark Designs", + "text_level": 1, + "bbox": [ + 511, + 339, + 702, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we provide a detailed description of the design of Q-Bench-Video. In this benchmark, the metastructure tuple $(\\mathrm{V},\\mathbb{Q},\\mathbb{A},\\mathbb{C})$ of each data item can be decomposed into several components: the video object V (which can be a single video or a pair of videos), the video quality query $\\mathbb{Q}$ , the set of possible answers A, and the correct answer C. The question samples are listed in Fig. 2.", + "bbox": [ + 511, + 359, + 905, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.1. Question Types", + "text_level": 1, + "bbox": [ + 511, + 474, + 666, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "I) Yes-or-No Questions. The basic Yes-or-No questions are designed to prompt LMMs to make binary judgments on video quality queries, typically limited to the answers Yes or No. To address the potential bias in LMMs that may skew towards yes responses, we employ an annotation adjustment process, which modifies the questions and correct answers if necessary (based on the Yes-or-No ratio). This process ensures that the distribution of correct answers, either Yes or No, remains balanced at about $50\\%:50\\%$ ratio in the end. This balanced approach allows for a more accurate assessment of LMMs' performance on Yes-or-No questions. II) What-How Questions. The What-How questions are commonly utilized in benchmarks for LMMs. The What questions focus on identifying specific distortions (e.g., What is the most apparent distortion in this video?). On the other hand, the How questions are employed to distinguish the finer details of distortion levels (e.g., How is the overall clarity of this video?). Including both What and How questions allows Q-Bench-Video to thoroughly and meticulously evaluate LMMs' ability on identifying video distortions and evaluating the distortion levels.", + "bbox": [ + 511, + 493, + 906, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "III) Open-ended Questions. It's important to note that the two types of questions previously mentioned require LMMs to select the correct answer from a predefined set. However, in many real-world scenarios, Open-ended Questions, which do not restrict responses to a predefined set, are often more necessary and challenging for LMMs (e.g., What", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3231", + "bbox": [ + 482, + 944, + 511, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Yes-or-No", + "text_level": 1, + "bbox": [ + 166, + 104, + 184, + 162 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4e1dafae2a53d12b2460431ec69a4c3f2477118643a23a6ba12692870b3b1d61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 101, + 483, + 160 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: Does the fabric in this video exhibit good clarity and proper lighting?", + "bbox": [ + 192, + 161, + 449, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A. Yes", + "bbox": [ + 192, + 186, + 251, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "B. No", + "bbox": [ + 313, + 186, + 348, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "What-How", + "text_level": 1, + "bbox": [ + 501, + 101, + 517, + 162 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e1f62e085d2bdf24ac361cf221aff90aa980e7d3a18e1fd70cd5b35d1fe0e1ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 102, + 816, + 160 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q: What quality issues do not exist in this video?", + "A. None of the options B. Blurriness", + "C. Overexposure D. Underexposure" + ], + "bbox": [ + 521, + 161, + 802, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Open-ended", + "text_level": 1, + "bbox": [ + 171, + 202, + 187, + 271 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f7faefb28ec5588951fcb482518a2325a2811be29aaea00c347144c228be4a8d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 203, + 816, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: Why is it difficult for viewers to identify the dish the man is cooking in the video?", + "bbox": [ + 192, + 268, + 683, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Open-ended Response: The video has severe compression blur and block artifacts, significantly reducing the discernibility of objects in the video.", + "bbox": [ + 192, + 281, + 785, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(a) Question Type", + "text_level": 1, + "bbox": [ + 431, + 316, + 560, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Technical", + "text_level": 1, + "bbox": [ + 168, + 342, + 184, + 393 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0e597968c4e1f7dd36861b9bdcc5b399ae273d0bfd01ecbe64dce082a1a9a961.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 337, + 483, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: As the camera moves away in this video, is there a noticeable increase in the clarity of the person's face?", + "bbox": [ + 192, + 398, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "A. No", + "B. Yes" + ], + "bbox": [ + 192, + 436, + 236, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal", + "text_level": 1, + "bbox": [ + 168, + 459, + 184, + 508 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c8f8fefd1c1da1386506db86f85fa7612664991c9dbb34d01990fbe2e31d7755.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 191, + 460, + 486, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: Does this video have severe camera shake?", + "bbox": [ + 196, + 520, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "A. No", + "B. Yes" + ], + "bbox": [ + 197, + 532, + 241, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Aesthetic", + "text_level": 1, + "bbox": [ + 490, + 338, + 506, + 392 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ee6edd4d27097cb1e69945ec3c75031ad03dcaccb5d7ce361bbc6c5e28e6e7d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 338, + 802, + 388 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q: what feelings does this video evoke?", + "Open-ended Response: This video depicts a castle in a unnatural and twisted jungle, where the plants have bizarre, sharp structures and dull colors. The atmosphere is eerie and terrifying, creating a sense of horror" + ], + "bbox": [ + 511, + 391, + 820, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "AIGC", + "text_level": 1, + "bbox": [ + 493, + 474, + 509, + 503 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c014e3070272177d3bf155e730e17f63be7213b6c3266b7fbf1f53abd3ec5e13.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 460, + 803, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: What is the most impactual quality issue of this video?", + "bbox": [ + 514, + 520, + 836, + 530 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "A. Noise", + "C. Blurriness" + ], + "bbox": [ + 514, + 532, + 593, + 556 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "B. Incorrect human structure", + "D. Overexposure" + ], + "bbox": [ + 635, + 532, + 810, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(b) Quality Concern", + "text_level": 1, + "bbox": [ + 426, + 561, + 571, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Global", + "text_level": 1, + "bbox": [ + 166, + 598, + 184, + 633 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ec92803065c6fe205b78d15a0ddd5b9d4c6f6f61e08bde74d5f3666fe346df0f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 587, + 485, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: How is the overall lighting level in this game video?", + "bbox": [ + 191, + 646, + 493, + 657 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "A. Very poor", + "C. Average" + ], + "bbox": [ + 191, + 659, + 261, + 683 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "B. Poor", + "D. Good" + ], + "bbox": [ + 334, + 659, + 377, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Joint", + "text_level": 1, + "bbox": [ + 165, + 698, + 183, + 727 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/30d454897ba18a168f5a1b91325a7f4bafc851082e165ad5493fe506f9f2b994.jpg", + "image_caption": [ + "Figure 2. The visualization samples from Q-Bench-Video, with the question-answer content most representative of each subcategory being underlined. It is important to note that, regarding quality concerns, a single question-answer annotation may not only focus on one distortion dimension. Therefore, the distortion visualization examples shown in (b) primarily highlight instances that are most closely aligned with the mentioned distortion types." + ], + "image_footnote": [], + "bbox": [ + 189, + 686, + 485, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: Are both videos primarily in cold colors?", + "bbox": [ + 200, + 744, + 444, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compare", + "text_level": 1, + "bbox": [ + 168, + 767, + 184, + 819 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c5d78593dcf3d6c0c606d5d76913a91ddafd2553c5f4fee7b87dca9c0d7370f9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 191, + 761, + 486, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: Is the exposure of the first video more balanced than", + "bbox": [ + 199, + 821, + 532, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5", + "text_level": 1, + "bbox": [ + 493, + 707, + 511, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Referring", + "text_level": 1, + "bbox": [ + 500, + 589, + 514, + 642 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/237481856f8363e477745139de9dbd98d80c519f4f82e73230e9076e0c5b9b2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 587, + 813, + 645 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q: Is the main character in this game video rendered in high details but with relatively low clarity?", + "A. Yes" + ], + "bbox": [ + 522, + 648, + 818, + 684 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6be3ff884f68d079cf9305a8516f9601ce6a8b5909d6f2ebe985b74a0539c34d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 686, + 813, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A. Yes", + "bbox": [ + 521, + 744, + 557, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "B. No", + "bbox": [ + 669, + 746, + 720, + 756 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/32091bbc093ec6593e35f02cccb503bca1b6ab9f5acdbefaa7ceda4fd937ac7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 761, + 813, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A. No B. Yes", + "bbox": [ + 665, + 821, + 772, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(c) Single Video vs. Video Pairs", + "text_level": 1, + "bbox": [ + 395, + 845, + 622, + 861 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3232", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are the possible factors that lead to the low clarity of this video? Please list and explain.). By adopting this form of questioning, we can better assess an LMM's ability to perceive video quality in real-world conditions.", + "bbox": [ + 89, + 90, + 482, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2. Quality Concerns", + "text_level": 1, + "bbox": [ + 89, + 159, + 261, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It's important to recognize that video quality can be influenced by multiple factors on some occasions. Therefore, a query tuple $(\\mathrm{V},\\mathrm{Q},\\mathrm{A},\\mathrm{C})$ does not need to be restricted to a single concern. It can address multiple concerns simultaneously. For instance, the question Is this video clear and well-composed? can be seen as evaluating both technical and aesthetic quality understanding.", + "bbox": [ + 89, + 178, + 482, + 282 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "I) Technical Distortions. Technical distortions refer to the low-level degradation in video quality that arises from the limitations of recording, compression, and transmission [37, 54]. These distortions often include artifacts such as blurring, noise, compression artifact, exposure, etc., which are directly tied to the technical processes used in video production and delivery. The CG-specific distortions related to geometry and texture are taken into consideration.", + "II) Aesthetic Distortions. Aesthetic distortions involve deviations from the intended visual style, artistic design, or creative intent that negatively affect the viewer's perception of the video [14, 44]. These distortions can include aspects such as confusing color, poor composition, lighting inconsistencies, or distracting elements that reduce the overall aesthetic appeal. Unlike technical distortions, aesthetic distortions are subjective and might be affected by viewer preference, cultural context, or artistic norms." + ], + "bbox": [ + 89, + 284, + 482, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "III) Temporal Distortions. Temporal distortions are related to the degradation of visual quality over time, impacting the fluidity and consistency of the video [36]. These distortions manifest as issues like screen shake, flickering, motion inconsistency, frame drops, and stuttering that result from unstable shooting devices, dramatically changing lighting conditions, and unstable bitrate environments [46]. Such disruptions hinder the viewer's natural perception of the video, leading to a disjointed and unpleasant viewing experience, especially in live-streaming scenarios.", + "bbox": [ + 89, + 541, + 482, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "IV) AIGC Distortions. AIGC distortions pertain to imperfections and unnaturalness specifically arising from the generation of video content through AI models [32, 61]. These distortions may include unnatural textures, inconsistent lighting, uncanny facial features, or unrealistic object behavior that result from limitations or biases in the training data, model architecture, or generative process. These distortions are unique to AI-generated content and require specialized evaluation metrics that consider both the technical and perceptual quality aspects.", + "bbox": [ + 89, + 691, + 482, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3. Single Videos & Video Pairs", + "text_level": 1, + "bbox": [ + 89, + 851, + 333, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Accurately comparing and jointly analyzing the quality of video pairs is sometimes more crucial than assessing the", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3f334b3ac00be8d23553e4e8bc98550a22921b8fe7d4a6a165dae9d87050a0b0.jpg", + "image_caption": [ + "(a) Annotation GUI for single videos of Q-Bench-Video." + ], + "image_footnote": [], + "bbox": [ + 521, + 89, + 910, + 178 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eab9b8817af0798538f50eb836fe01b6501ca11d061219ed2b4a0b3dcb56cc5e.jpg", + "image_caption": [ + "(b) Annotation GUI for video pairs of Q-Bench-Video.", + "Figure 3. Illustration of the annotation GUIs for Q-Bench-Video. (a) shows the interface for annotating single videos, where the annotator can select the question type and play the videos using the Video Play button. The annotator can also switch to the next and previous annotation with the Next and Previous buttons. (b) presents the interface for annotating video pairs. When the annotator presses the Video Play button, the video pairs are played sequentially, with a five-second gray screen serving as an interval between the two videos." + ], + "image_footnote": [], + "bbox": [ + 521, + 193, + 910, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "quality of a single video, especially in scenarios such as performance tests in video compression and quality control in video generation (In which it is more important to find out Which video is better in visual quality and why?) [49, 66]. Therefore, in Q-Bench-Video, we include video quality queries for both single videos and video pairs.", + "bbox": [ + 511, + 470, + 906, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1) Single Videos. Queries related to single videos can primarily be categorized into two types: a) Global perception, which involves questions about the overall visual quality of the video, such as How is the overall contrast of this video? b) Referring perception, which focuses on the visual quality of specific elements within the video, like querying What is the most apparent distortion when the player strikes the ball? Through these approaches, we aim to comprehensively evaluate the LMMs' ability to perceive both the overall and localized aspects of video quality.", + "bbox": [ + 511, + 564, + 908, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "II) Video Pairs. Firstly, to ensure that the comparison of video pairs is clear and meaningful, comparisons are only made between videos from the same source, such as videos from natural sources being paired together while CG videos and AIGC videos are not being paired. There are mainly two types of video pair categories: a) Joint analysis, which involves understanding the shared quality features of the video pairs, for example, such as asking Are both videos blurry? b) Comparative analysis, which involves comparing the quality dimension across two videos, such as How does the level of brightness in the first video compare to that in the second one? It is important to note", + "bbox": [ + 511, + 719, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3233", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8ec1451ad71d55a9769b3dfcbba26607309af2914313e044d5d5d70ba4818e32.jpg", + "image_caption": [ + "(a) Overall performance on Q-Bench-Video." + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 488, + 371 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6a784e6997abe34e6b511c01dace16c2b2cc4bb8b2ceb740a1d0aa466ad59670.jpg", + "image_caption": [ + "(b) Subcategory performance on Q-Bench-Video.", + "Figure 4. A concise summary of the LMMs' performance on Q-Bench-Video. (a) provides a comparison detailing the overall performance of humans and 17 selected LMMs, including both proprietary and open-source models. (b) illustrates a radar chart that outlines the performance of the top-2 proprietary LMMs (GPT-4o & Gemini 1.5 Pro) and open-source LMMs (mPLUG-Owl3 & LLaVA-OneVision) across various subcategories within Q-Bench-Video." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 898, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that we further categorize comparisons based on the difference in quality labels of the videos involved into coarse-grain (with relatively more significant visual quality differences) and fine-grain (with relatively minor visual quality differences) comparisons. (More details in the Supp.)", + "bbox": [ + 88, + 484, + 482, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.4. Questions & Answers Annotation", + "text_level": 1, + "bbox": [ + 89, + 565, + 372, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The annotation process of Q-Bench-Video is conducted in a well-controlled laboratory environment. A total of 8 experts are employed and trained to ensure the consistency of the annotations. The experts are required to watch the videos in their entirety before making annotations. Each annotated question-answer pair is then reviewed by at least three other experts to ensure its validity and accuracy.", + "bbox": [ + 88, + 584, + 482, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Benchmark Setting & Evaluation", + "text_level": 1, + "bbox": [ + 89, + 696, + 383, + 713 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unless specifically stated otherwise, for Video LMMs we typically analyze by uniformly sampling 16 frames from the video, while for Image LMMs, the sampling is reduced to 8 frames. It's worth noting that if the LMMs are not compatible with the specified number of sampling frames (e.g. if they cannot support up to 8-frame input), we will use the official default settings for testing. For Yes-or-No and What-How questions, if the LMMs can accurately respond with the options, we directly record the accuracy of the responses as results. If the LMMs cannot provide option-based answers, we implement a GPT-assisted evaluation strategy to help judge the accuracy of the answers. For Open-ended", + "bbox": [ + 88, + 719, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "questions, since the answers are open-ended and cannot be directly quantified for accuracy, we also employ the GPT-assisted evaluation strategy. This involves GPT scoring the responses based on their accuracy, completeness, and relevance compared to the annotated answer.", + "bbox": [ + 511, + 484, + 906, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Results of Q-Bench-Video", + "text_level": 1, + "bbox": [ + 511, + 599, + 754, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 511, + 633, + 714, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LMMs Participants. A total of 17 LMMs (12 Open-source LMMs and 5 Proprietary LMMs) are included for validation, which includes a) 3 Open-source Image LMMs: LLaVA-Next [30], LLaVA-v1.5 [28], and mPLUG-Owl2 [53]; b) 9 Open-source Video LMMs: mPLUG-Owl3 [51], LLaVA-OneVision [19], InternVL-Chat [4], VILA1.5 [16], PLLaVA [50], LLaVA-Next-Video [57], ST-LLM [31], Video-LLaVA [27], and VideoChat2 [22]; c) 5 Proprietary LMMs: Gemini 1.5 Flash, Gemini 1.5 Pro [39], GPT-4o mini, GPT-4o, and GPT-4 Turbo [2].", + "bbox": [ + 511, + 664, + 906, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Subsets Split. The Q-Bench-Video is divided into test (1,186 question-answer items) and dev (1,192 question-answer items) subsets. The correct answers will be released and proprietary for the dev and test subsets. All discussions and analyses are based on the test subset.", + "bbox": [ + 511, + 824, + 908, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3234", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c75f255fbe0a30741193f9b17ad793c5454b7e6620e35c4c739fead3f32472f6.jpg", + "table_caption": [ + "Table 2. Results on the test subset for the video quality perception ability of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively. The Open-ended questions are excluded for Random guess. (Performance of the test subset is in the Supp.)" + ], + "table_footnote": [], + "table_body": "
Sub-categoriesQuestion TypesQuality ConcernsOverall↑
LMM (LLM)Yes-or-No↑What-How↑Open-ended↑Tech.↑Aes.↑Temp.↑AIGC↑
Random guess w/o Open-ended50.00%25.00%/37.10%37.31%37.25%37.22%37.79%
Human86.57%81.00%77.11%79.22%80.23%82.72%86.21%81.56%
Open-source Image LMMs
LLaVA-Next (Mistral-7B)62.83%45.14%33.69%46.38%57.86%47.84%48.46%47.52%
LLaVA-v1.5 (Vicuna-v1.5-13B)52.98%46.44%37.01%45.77%58.12%45.30%46.48%45.64%
mPLUG-Owl2 (LLaMA2-7B)59.19%39.07%31.19%42.07%52.38%41.71%39.37%43.43%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)60.48%56.39%39.48%52.68%58.31%52.05%43.49%52.39%
LLaVA-OneVision (Qwen2-7B)61.34%53.88%39.15%49.35%64.15%50.68%44.30%51.70%
InternVL-Chat (Vicuna-7B)66.02%52.13%33.93%48.42%52.73%50.59%53.12%51.11%
VILA1.5 (LLaMA3-8B)61.95%46.00%39.60%47.85%57.85%45.65%42.57%49.41%
PLLAVA (Mistral-7B)65.63%52.33%32.23%49.69%61.32%50.96%53.64%50.39%
LLaVA-Next-Video (Mistral-7B)61.34%45.95%38.10%49.03%60.94%46.97%49.40%48.69%
ST-LLM (Vicuna-v1.1-7B)44.63%28.50%32.78%34.99%46.11%34.28%34.02%35.42%
Video-LLaVA (Vicuna-v1.5-7B)64.67%40.79%29.11%43.25%54.04%42.38%42.76%43.49%
VideoChat2 (Mistral-7B)56.09%29.98%34.99%39.26%50.02%38.25%35.88%40.56%
Proprietary LMMs
Gemini 1.5 Flash65.48%56.79%47.51%54.11%66.58%53.51%50.22%56.78%
Gemini 1.5 Pro65.42%62.35%47.57%56.80%69.61%53.38%53.26%58.63%
GPT-4o mini62.95%50.93%42.10%49.38%60.90%48.43%41.71%52.20%
GPT-4o67.48%58.79%49.25%56.01%58.57%65.39%52.22%58.70%
GPT-4 Turbo66.93%58.33%40.15%54.23%66.23%54.00%52.04%56.36%
", + "bbox": [ + 89, + 132, + 906, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Findings", + "text_level": 1, + "bbox": [ + 89, + 452, + 194, + 468 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The overall performance and subcategory comparisons (human vs. top-performing LMMs) on Q-Bench-Video can be quickly glanced at Fig. 4. Detailed performance across the subcategories for each LMM are shown in Table 2 (Question Types & Quality Concerns) and Table 3 (Single Videos vs. Video Pairs) respectively. The findings are organized as follows:", + "bbox": [ + 89, + 476, + 482, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "1) General Performance. Human>Proprietary LMMs>Open-source LMMs>Random guess. From the performance results presented in Table 2, we observe that nearly all LMMs significantly outperform random guess, demonstrating their basic capability to understand video quality. Among the open-source LMMs, the recently released mPLUG-Owl3 achieves the highest overall performance at $52.39\\%$ , even slightly surpassing GPT-4o mini $(52.20\\%)$ , followed closely by LLaVA-OneVision $(51.70\\%)$ and InternVL-Chat $(51.11\\%)$ . Image LMMs deliver moderate performance. Although they outperform some Video LMMs, the gap between them and the latest Video LMMs is still notable. Benefiting from larger training datasets and more parameters, proprietary LMMs (except GPT-4o mini) outperform all open-source models. However, even the best-performing model, GPT-4o, which achieved an overall performance of $58.70\\%$ , still lags behind human performance by $22.86\\%$ . This gap highlights that, despite the advancements in current state-of-the-art LMMs on video general understanding, there remains a significant need for improvement in video quality understanding ability.", + "bbox": [ + 89, + 583, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "2) Question Types. Open-ended questions are more challenging for LMMs. From Table 2, a discernible hierarchy in task difficulty for video quality assessment emerges for both humans and LMMs, arranged as follows: Open-ended $>$ What-How $>$ Yes-or-No. It is crucial to highlight that while humans exhibit a performance decline in Open-ended tasks by approximately $9.46\\%$ compared to Yes-or-No tasks, and about $3.89\\%$ compared to What-How tasks, these reductions are markedly less pronounced than those observed in LMMs for the Open-ended questions. This disparity underscores a significant proficiency gap between LMMs' capability in handling straightforward, closed-form questions and their effectiveness in navigating the complexities of real-world problem-solving on open-ended questions, particularly in the context of video quality evaluation.", + "bbox": [ + 511, + 452, + 906, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3) Quality Concerns. LMMs exhibit unbalanced performance across different types of distortions. From Table 2, it is evident that humans are particularly good at identifying AIGC distortions, while LMMs demonstrate stronger performance in detecting Aesthetic distortions. This distinction likely stems from the inherent sensitivity of humans to the conspicuous unnaturalness of AIGC distortions, which readily draws human attention. In contrast, Aesthetic distortions, which often involve high-level semantic nuances, align more closely with the training contexts of LMMs, enabling them to excel in this area. However, LMMs face challenges with AIGC distortions due to insufficient exposure to such anomalies during their pretraining phases, specific architectural constraints, and imperfections", + "bbox": [ + 511, + 688, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3235", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/70cd380eab22623a5c2847c8b09d9c22dbf9b39968c28aea7a314b7519024cb3.jpg", + "table_caption": [ + "Table 3. Results on the test subset for the video quality perception ability across single videos and video pairs of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively." + ], + "table_footnote": [], + "table_body": "
Sub-categoriesSingle VideosVideo Pairs
LMM (LLM)Global↑Referring↑Overall↑Joint↑Compare -fine↑Compare -coarse↑Overall↑
Random guess w/o Open-ended36.49%38.61%37.71%40.56%37.94%36.83%38.00%
Human78.87%80.43%79.65%84.90%87.34%89.11%87.56%
LLaVA-Next (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
LLaVA-v1.5 (Vicuna-v1.5-13B)47.99%51.94%50.10%27.72%34.60%42.12%36.42%
mPLUG-Owl2 (LLaMA2-7B)46.86%43.51%45.07%51.49%37.10%40.28%43.69%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)52.46%50.60%51.47%48.03%54.90%59.20%55.31%
LLaVA-OneVision (Qwen2-7B)51.56%48.43%49.89%53.48%58.10%63.36%59.41%
InternVL-Chat (Vicuna-7B)51.15%51.86%51.52%48.85%51.10%49.20%49.79%
VILA1.5 (LLaMA3-8B)52.35%47.37%49.69%56.11%45.40%48.04%48.84%
PLLAVA (Mistral-7B)51.44%55.49%53.60%40.36%50.40%54.16%49.90%
LLaVA-Next-Video (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
ST-LLM (Vicuna-v1.1-7B)36.54%36.49%36.51%28.03%36.80%32.08%32.87%
Video-LLaVA (Vicuna-v1.5-7B)45.46%44.67%45.04%49.36%42.00%43.00%44.01%
VideoChat2 (Mistral-7B)43.52%38.27%40.72%57.23%44.40%41.64%45.93%
Proprietary LMMs
Gemini 1.5 Flash58.00%53.18%55.43%46.59%65.30%68.84%62.77%
Gemini 1.5 Pro52.36%61.41%57.19%45.43%65.30%72.00%63.55%
GPT-4o mini52.67%48.96%50.69%44.00%60.50%63.88%58.02%
GPT-4o58.75%54.18%56.31%46.93%67.30%69.24%63.80%
GPT-4 Turbo57.36%52.80%54.93%46.13%62.50%64.80%59.84%
", + "bbox": [ + 89, + 118, + 906, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in the generation process. In the case of proprietary LMMs, their performance on Technical and Temporal distortions appear comparably consistent, indicating a uniform capability in recognizing these two types of distortions. Nonetheless, across all four subcategories, LMMs exhibit a notable performance disparity compared to humans, with varying degrees of accuracy among the different types of distortions. This variability highlights the need for significant enhancements in LMMs' abilities to accurately understand and interpret various distortion types.", + "bbox": [ + 88, + 446, + 480, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4) Single Videos vs. Video Pairs. LMMs demonstrate superior capabilities in comparing video quality. From Table 3, we observe that for single videos, LMMs achieve similar performance in Global and Referring quality perception (except for Gemini 1.5 Pro), without any significant trend of the performance for one subcategory over the other. This suggests that LMMs have comparable abilities in perceiving both Global video quality and Referring video quality. In terms of comparison, however, LMMs clearly outperform their performance on single video analysis and joint analysis. Notably, LMMs perform significantly better in the Compare-coarse subcategory, where video pairs have more pronounced quality differences, than in the Compare-fine subcategory. This highlights that LMMs are more adept at comparing video quality than analyzing the quality of single videos. This advantage in comparative assessment can be attributed to the inherent clarity in pairwise comparisons, which provide explicit contrasts, as opposed to the more ambiguous nature of evaluating a single video. Both humans and LMMs exhibit enhanced performance in com", + "bbox": [ + 88, + 598, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "parative tasks. Although there is still a significant accuracy gap between LMMs and humans, LMMs show promising potential as effective tools for comparing video quality.", + "bbox": [ + 511, + 446, + 906, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 511, + 503, + 635, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1) Subjectivity can not be fully avoided in annotations for aspects like aesthetics. 2) As video generation advances, new models may show different distortions, which might potentially make parts of Q-Bench-Video outdated.", + "bbox": [ + 511, + 529, + 906, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 603, + 633, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to evaluate Large Multi-modal Models' (LMMs) understanding of video quality. Our benchmark includes a diverse range of video types, questions that challenge multiple aspects of video quality, and a holistic evaluation framework encompassing Technical, Aesthetic, Temporal, and AIGC distortions. Through extensive experimentation with 17 open-source and proprietary LMMs, we find that while LMMs show promise in discerning video quality, their performance remains significantly below human-level understanding, especially when addressing Open-ended questions and AIGC-specific distortions. These findings highlight the current limitations of LMMs in video quality perception and underscore the need for further advancements in this area. By offering Q-Bench-Video, we aim to stimulate future research and drive improvements in the field, bridging the gap between LMM and human video quality understanding.", + "bbox": [ + 509, + 628, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3236", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 91, + 90, + 240, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The work was supported in part by the National Natural Science Foundation of China under Grant (623B2073, 62301310), the Ministry of Education, Singapore, under the funding of MOE-T2EP20123-0006, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426.", + "bbox": [ + 89, + 114, + 483, + 204 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 217, + 187, + 233 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Recommendation 500-10: Methodology for the subjective assessment of the quality of television pictures. 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Apollo: An exploration of video understanding in large multimodal models. arXiv preprint arXiv:2412.10360, 2024. 2" + ], + "bbox": [ + 516, + 92, + 903, + 387 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3239", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_model.json b/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b735811759f67c4c8ab04d1d59bed461a1ea7ede --- /dev/null +++ b/2025/Q-Bench-Video_ Benchmark the Video Quality Understanding of LMMs/f97aa133-81bf-4c87-9369-c5d1f7aad162_model.json @@ -0,0 +1,2741 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.135, + 0.131, + 0.865, + 0.153 + ], + "angle": 0, + "content": "Q-Bench-Video: Benchmark the Video Quality Understanding of LMMs" + }, + { + "type": "text", + "bbox": [ + 0.147, + 0.18, + 0.851, + 0.235 + ], + "angle": 0, + "content": "Zicheng Zhang\\(^{1*}\\), Ziheng Jia\\(^{1*}\\), Haoning Wu\\(^{2\\dagger}\\), Chunyi Li\\(^{1}\\), Zijian Chen\\(^{1}\\), Yingjie Zhou\\(^{1}\\), Wei Sun\\(^{1}\\), Xiaohong Liu\\(^{1}\\), Xiongkuo Min\\(^{1\\dagger}\\), Weisi Lin\\(^{2}\\), and Guangtao Zhai\\(^{1\\dagger}\\) \n\\(^{1}\\)Shanghai Jiaotong University, \\(^{2}\\)Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.315, + 0.237, + 0.681, + 0.27 + ], + "angle": 0, + "content": "*First Authors, †Corresponding Authors https://github.com/Q-Future/Q-Bench-Video" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.305, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.339, + 0.486, + 0.764 + ], + "angle": 0, + "content": "With the rising interest in research on Large Multi-modal Models (LMMs) for video understanding, many studies have emphasized general video comprehension capabilities, neglecting the systematic exploration into video quality understanding. To address this oversight, we introduce Q-Bench-Video in this paper, a new benchmark specifically designed to evaluate LMMs' proficiency in discerning video quality. a) To ensure video source diversity, Q-Bench-Video encompasses videos from natural scenes, AI-generated content (AIGC), and computer graphics (CG). b) Building on the traditional multiple-choice questions format with the Yes-or-No and What-How categories, we include Open-ended questions to better evaluate complex scenarios. Additionally, we incorporate the video pair quality comparison question to enhance comprehensiveness. c) Beyond the traditional Technical, Aesthetic, and Temporal distortions, we have expanded our evaluation aspects to include the dimension of AIGC distortions, which addresses the increasing demand for video generation. Finally, we collect a total of 2,378 question-answer pairs and test them on 12 open-source & 5 proprietary LMMs. Our findings indicate that while LMMs have a foundational understanding of perceptual video quality, their performance remains incomplete and imprecise, with a notable discrepancy compared to the performance of human beings. Through Q-Bench-Video, we seek to catalyze community interest, stimulate further research, and unlock the untapped potential of LMMs to close the gap in video quality understanding." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.798, + 0.222, + 0.813 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.485, + 0.903 + ], + "angle": 0, + "content": "As the field of artificial intelligence (AI) continues to evolve, Large Multi-modal Models (LMMs) [4, 16, 19, 50, 51] are progressively utilized in high-level video understanding tasks. These models have shown remarkable capabilities in analyzing and interpreting the semantic content of" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.306, + 0.908, + 0.504 + ], + "angle": 0, + "content": "videos, such as classifying objects, identifying actions, and recognizing events. However, the aspect of video quality, which is vital for optimizing compression and transmission systems, enhancing viewer experience, and establishing standards for high-quality video generation, has received less attention. Although numerous LMM video benchmarks[8, 10, 23] have been developed to assess the semantic understanding of videos by LMMs comprehensively, benchmarks systematically targeting video quality are still lacking. Additionally, while semantic understanding is closely linked to high-level video information, the perception and understanding of low-level information are crucial in video quality [5, 25] as well." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.909, + 0.903 + ], + "angle": 0, + "content": "To address this gap, we introduce Q-Bench-Video, a novel benchmark specifically designed to systematically evaluate the video quality understanding of LMMs. As illustrated in Fig. 1, our benchmark encompasses a wide range of video content, including natural scenes, AI-generated content (AIGC), and computer graphics (CG), ensuring diversity in video sources. In addition, to maintain a reasonable distribution of source video quality, we employ uniform sampling from video datasets that contain subjective quality annotations. This approach guarantees comprehensive coverage of the quality spectrum while avoiding imbalanced quality distributions. Moreover, we extend beyond traditional video evaluations by incorporating both multiple-choice questions (MCQs) and open-ended questions. This enables a more thorough analysis of LMMs' ability to discern video quality across diverse scenarios. We further introduce a new evaluation dimension specifically tailored to assess distortions related to AIGC, which are increasingly prominent in video generation tasks. Recognizing the importance of quality comparison settings in real-world applications, such as camera parameter optimization and AIGC video generation, we further incorporate video pairs to facilitate quality comparison assessment as well. In total, we collect 1800 videos and annotated 2,378 question-answer pairs for validation, creating a robust framework for systematic evaluation on video quality understanding." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3229" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.195, + 0.088, + 0.805, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.388, + 0.908, + 0.459 + ], + "angle": 0, + "content": "Figure 1. The construction overview of the proposed Q-Bench-Video. To ensure diversity in video content, we collect natural scenes, AIGC, and CG videos from video quality assessment datasets as depicted in (a). To achieve a balanced quality distribution among the sampled videos, we employ uniform sampling for quality control. As indicated in (c-1) and (c-2), we utilize three types of questions (Yes-or-No, What-How, Open-ended) and address a comprehensive range of quality concerns including Technical, Aesthetic, Temporal, and AIGC distortions. Additionally, we incorporate the video pairs comparison task to enhance the comprehensiveness of the benchmark." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.47, + 0.483, + 0.592 + ], + "angle": 0, + "content": "Through the rigorous experiment, we demonstrate that while LMMs show promise in video quality assessment, their performance lags significantly behind human-level understanding. By offering a systematic and thorough evaluation of LMMs' video quality perception, Q-Bench-Video aims to foster research in this underexplored area and push the boundaries of LMM capabilities on video quality understanding. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.597, + 0.483, + 0.687 + ], + "angle": 0, + "content": "- We introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to assess the video quality understanding capabilities of LMMs. This benchmark includes a diverse collection of source videos and ensures a balanced quality distribution, complemented by human-crafted question-answer annotations." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.687, + 0.483, + 0.777 + ], + "angle": 0, + "content": "- Our evaluation framework spans four key quality dimensions: Technical, Aesthetic, Temporal, and AIGC distortions, which offers a holistic evaluation approach to video quality assessment. Uniquely, Q-Bench-Video enhances its utility by introducing the task of video pairs comparison, which sets it apart from existing video benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.779, + 0.483, + 0.899 + ], + "angle": 0, + "content": "- We conduct a comprehensive evaluation using both proprietary and open-source LMMs to measure their effectiveness in understanding video quality. The results expose notable deficiencies in current LMMs, while also shedding light on performance variations across different quality dimensions. These findings provide critical insights and suggest promising directions for future enhancements in the field of video quality understanding." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.597, + 0.483, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.469, + 0.665, + 0.485 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.495, + 0.787, + 0.51 + ], + "angle": 0, + "content": "2.1. Video LMMs and Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.907, + 0.775 + ], + "angle": 0, + "content": "The rapid advancement of Large Multi-modal Models (LMMs) in recent years [4, 28-30, 52, 56, 67] has showcased their remarkable perception and cognitive abilities across various multimodal benchmarks for images [9, 33, 35, 47, 62]. As development progresses, the focus of visual analysis has gradually shifted from images to videos. Early efforts [22, 27, 31, 50] aimed at unlocking the video understanding potential of LMMs have yielded promising results. However, initial video-based benchmarks [24, 34, 41] typically concentrated on specific aspects of video comprehension, falling short of fully capturing the performance of these models due to limitations such as a lack of diversity in video types and inadequate coverage of temporal dynamics. In response, recent video benchmarks [8, 10] have moved toward a more comprehensive evaluation of LMMs. Nonetheless, these efforts focus on high-level semantic understanding without systematic exploration of video quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.787, + 0.75, + 0.803 + ], + "angle": 0, + "content": "2.2. Video Quality Assessment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Video Quality Assessment (VQA) is a task aimed at quantifying video scores based on visual quality. Initially, early VQA methods employ hand-crafted features extracted from videos and regress the features into quality scores [17, 20, 26, 40, 58, 64, 65]. With the emergence of deep neural networks, a shift occurs as numerous methods adopted deep" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3230" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.133 + ], + "angle": 0, + "content": "Table 1. Overview of the diverse video source datasets in the Q-Bench-Video. We consider various video content types, including natural scenes, AIGC, and CG videos. The term 'MOS' denotes that the videos are annotated via Mean Opinion Scores under ITU standards [1]. We have conducted uniform sampling based on their quality labels to ensure a balanced quality distribution." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.136, + 0.905, + 0.243 + ], + "angle": 0, + "content": "
Video TypeVideo Source DatasetMOSQuality ConcernsSampled SizeFull Dataset Size
Natural (1000)LSVQ [54]✓Spatial & Temporal60039K
MaxWell [46]✓Spatial & Temporal & Aesthetic3504.5K
WaterlooSQoE-III [6]✓Quality-of-Experience20450
WaterlooSQoE-IV [7]✓Quality-of-Experience301,350
AIGC (600)T2VQA-DB [17]✓Quality & Text Alignment20010K
VideoFeedback [13]×Quality & Text Alignment40037.6K
CG (200)LIVE-YT-Gaming [55]✓Visual Quality200600
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.254, + 0.482, + 0.482 + ], + "angle": 0, + "content": "learning techniques for VQA tasks [18, 21, 38, 42]. As the field progresses, newer methods begin incorporating considerations for both temporal dynamics and aesthetic qualities, leading to a more holistic approach to video quality analysis [3, 12, 43, 45, 59]. Moreover, the evolution of large-scale models has further revolutionized VQA methodologies. Many recent approaches have redefined the traditional quality assessment process into a quality question-answering format [11, 15, 48, 60, 63]. This adaptation leverages the substantial prior knowledge embedded in large models to enhance the precision of quality quantification [61]. Despite these technological advances, VQA still grapples with challenges in providing interpretable quality scores and deepening the understanding of how models perceive and analyze video quality more comprehensively." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.493, + 0.329, + 0.509 + ], + "angle": 0, + "content": "3. Benchmark Construction" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.517, + 0.292, + 0.534 + ], + "angle": 0, + "content": "3.1. Benchmark Principle" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.483, + 0.751 + ], + "angle": 0, + "content": "The Q-Bench-Video is designed based on three guiding principles: (1) It encompasses a broad spectrum of video content, including natural scenes, AIGC, and CG videos. (2) It ensures a comprehensive and representative sampling process across a wide quality range, enhancing the benchmark's overall effectiveness. (3) It primarily focuses on the aspects of video quality that significantly influence the viewing experience, including technical, aesthetic, temporal, and AIGC distortions. This significantly differs from other video benchmarks that prioritize semantic understanding. Additionally, the video pair quality comparison is integrated to address the challenges associated with comparing video quality. The overall construction process can be clearly overviewed in Fig. 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.758, + 0.318, + 0.773 + ], + "angle": 0, + "content": "3.2. Source Videos Collection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "As shown in Table 1, the source videos are primarily gathered from video quality assessment datasets. We selected videos from these datasets for two main reasons: (1) These datasets have inherently considered the diversity of quality features during video selection; (2) These datasets possess quality annotations that adhere to ITU standards [1] (with the exception of VideoFeedback), which allow us to accurately and authentically sample videos." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.255, + 0.907, + 0.332 + ], + "angle": 0, + "content": "Our sampling method primarily employs a uniform approach, extracting videos evenly from each dataset based on the quality range. Moreover, considering the current popularity of AIGC and CG videos, we have also incorporated a selection of these video types. (More details in the Supp.)" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.34, + 0.704, + 0.357 + ], + "angle": 0, + "content": "3.3. Benchmark Designs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.361, + 0.906, + 0.468 + ], + "angle": 0, + "content": "In this section, we provide a detailed description of the design of Q-Bench-Video. In this benchmark, the metastructure tuple \\((\\mathrm{V},\\mathbb{Q},\\mathbb{A},\\mathbb{C})\\) of each data item can be decomposed into several components: the video object V (which can be a single video or a pair of videos), the video quality query \\(\\mathbb{Q}\\), the set of possible answers A, and the correct answer C. The question samples are listed in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.475, + 0.668, + 0.491 + ], + "angle": 0, + "content": "3.3.1. Question Types" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.81 + ], + "angle": 0, + "content": "I) Yes-or-No Questions. The basic Yes-or-No questions are designed to prompt LMMs to make binary judgments on video quality queries, typically limited to the answers Yes or No. To address the potential bias in LMMs that may skew towards yes responses, we employ an annotation adjustment process, which modifies the questions and correct answers if necessary (based on the Yes-or-No ratio). This process ensures that the distribution of correct answers, either Yes or No, remains balanced at about \\(50\\%:50\\%\\) ratio in the end. This balanced approach allows for a more accurate assessment of LMMs' performance on Yes-or-No questions. II) What-How Questions. The What-How questions are commonly utilized in benchmarks for LMMs. The What questions focus on identifying specific distortions (e.g., What is the most apparent distortion in this video?). On the other hand, the How questions are employed to distinguish the finer details of distortion levels (e.g., How is the overall clarity of this video?). Including both What and How questions allows Q-Bench-Video to thoroughly and meticulously evaluate LMMs' ability on identifying video distortions and evaluating the distortion levels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "III) Open-ended Questions. It's important to note that the two types of questions previously mentioned require LMMs to select the correct answer from a predefined set. However, in many real-world scenarios, Open-ended Questions, which do not restrict responses to a predefined set, are often more necessary and challenging for LMMs (e.g., What" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.513, + 0.957 + ], + "angle": 0, + "content": "3231" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.167, + 0.105, + 0.186, + 0.163 + ], + "angle": 270, + "content": "Yes-or-No" + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.102, + 0.484, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.162, + 0.45, + 0.187 + ], + "angle": 0, + "content": "Q: Does the fabric in this video exhibit good clarity and proper lighting?" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.188, + 0.252, + 0.2 + ], + "angle": 0, + "content": "A. Yes" + }, + { + "type": "text", + "bbox": [ + 0.315, + 0.188, + 0.349, + 0.2 + ], + "angle": 0, + "content": "B. No" + }, + { + "type": "title", + "bbox": [ + 0.503, + 0.102, + 0.518, + 0.163 + ], + "angle": 270, + "content": "What-How" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.103, + 0.817, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.162, + 0.803, + 0.173 + ], + "angle": 0, + "content": "Q: What quality issues do not exist in this video?" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.175, + 0.741, + 0.185 + ], + "angle": 0, + "content": "A. None of the options B. Blurriness" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.187, + 0.767, + 0.198 + ], + "angle": 0, + "content": "C. Overexposure D. Underexposure" + }, + { + "type": "list", + "bbox": [ + 0.522, + 0.162, + 0.803, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.203, + 0.188, + 0.272 + ], + "angle": 270, + "content": "Open-ended" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.204, + 0.818, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.269, + 0.684, + 0.281 + ], + "angle": 0, + "content": "Q: Why is it difficult for viewers to identify the dish the man is cooking in the video?" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.282, + 0.787, + 0.306 + ], + "angle": 0, + "content": "Open-ended Response: The video has severe compression blur and block artifacts, significantly reducing the discernibility of objects in the video." + }, + { + "type": "title", + "bbox": [ + 0.433, + 0.317, + 0.562, + 0.332 + ], + "angle": 0, + "content": "(a) Question Type" + }, + { + "type": "title", + "bbox": [ + 0.169, + 0.343, + 0.186, + 0.394 + ], + "angle": 270, + "content": "Technical" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.338, + 0.485, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.399, + 0.469, + 0.435 + ], + "angle": 0, + "content": "Q: As the camera moves away in this video, is there a noticeable increase in the clarity of the person's face?" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.438, + 0.234, + 0.447 + ], + "angle": 0, + "content": "A. No" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.451, + 0.238, + 0.46 + ], + "angle": 0, + "content": "B. Yes" + }, + { + "type": "list", + "bbox": [ + 0.194, + 0.438, + 0.238, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.169, + 0.46, + 0.186, + 0.51 + ], + "angle": 270, + "content": "Temporal" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.461, + 0.487, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.521, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Q: Does this video have severe camera shake?" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.533, + 0.238, + 0.541 + ], + "angle": 0, + "content": "A. No" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.545, + 0.242, + 0.556 + ], + "angle": 0, + "content": "B. Yes" + }, + { + "type": "list", + "bbox": [ + 0.199, + 0.533, + 0.242, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.491, + 0.339, + 0.507, + 0.393 + ], + "angle": 270, + "content": "Aesthetic" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.339, + 0.803, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.392, + 0.741, + 0.404 + ], + "angle": 0, + "content": "Q: what feelings does this video evoke?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.405, + 0.821, + 0.455 + ], + "angle": 0, + "content": "Open-ended Response: This video depicts a castle in a unnatural and twisted jungle, where the plants have bizarre, sharp structures and dull colors. The atmosphere is eerie and terrifying, creating a sense of horror" + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.392, + 0.821, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.495, + 0.476, + 0.51, + 0.505 + ], + "angle": 270, + "content": "AIGC" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.461, + 0.805, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.521, + 0.838, + 0.531 + ], + "angle": 0, + "content": "Q: What is the most impactual quality issue of this video?" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.533, + 0.571, + 0.544 + ], + "angle": 0, + "content": "A. Noise" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.546, + 0.594, + 0.557 + ], + "angle": 0, + "content": "C. Blurriness" + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.533, + 0.594, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.636, + 0.534, + 0.811, + 0.544 + ], + "angle": 0, + "content": "B. Incorrect human structure" + }, + { + "type": "text", + "bbox": [ + 0.637, + 0.546, + 0.735, + 0.557 + ], + "angle": 0, + "content": "D. Overexposure" + }, + { + "type": "list", + "bbox": [ + 0.636, + 0.534, + 0.811, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.427, + 0.563, + 0.573, + 0.578 + ], + "angle": 0, + "content": "(b) Quality Concern" + }, + { + "type": "title", + "bbox": [ + 0.168, + 0.599, + 0.185, + 0.634 + ], + "angle": 270, + "content": "Global" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.588, + 0.486, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.647, + 0.495, + 0.659 + ], + "angle": 0, + "content": "Q: How is the overall lighting level in this game video?" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.66, + 0.262, + 0.671 + ], + "angle": 0, + "content": "A. Very poor" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.673, + 0.262, + 0.684 + ], + "angle": 0, + "content": "C. Average" + }, + { + "type": "list", + "bbox": [ + 0.192, + 0.66, + 0.262, + 0.684 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.336, + 0.66, + 0.379, + 0.669 + ], + "angle": 0, + "content": "B. Poor" + }, + { + "type": "text", + "bbox": [ + 0.335, + 0.672, + 0.379, + 0.684 + ], + "angle": 0, + "content": "D. Good" + }, + { + "type": "list", + "bbox": [ + 0.335, + 0.66, + 0.379, + 0.684 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.699, + 0.184, + 0.728 + ], + "angle": 270, + "content": "Joint" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.687, + 0.486, + 0.744 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.746, + 0.446, + 0.758 + ], + "angle": 0, + "content": "Q: Are both videos primarily in cold colors?" + }, + { + "type": "title", + "bbox": [ + 0.169, + 0.768, + 0.186, + 0.82 + ], + "angle": 270, + "content": "Compare" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.762, + 0.487, + 0.82 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.822, + 0.533, + 0.834 + ], + "angle": 0, + "content": "Q: Is the exposure of the first video more balanced than" + }, + { + "type": "title", + "bbox": [ + 0.495, + 0.708, + 0.512, + 0.724 + ], + "angle": 270, + "content": "5" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.516, + 0.643 + ], + "angle": 270, + "content": "Referring" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.588, + 0.814, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.649, + 0.82, + 0.672 + ], + "angle": 0, + "content": "Q: Is the main character in this game video rendered in high details but with relatively low clarity?" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.673, + 0.574, + 0.685 + ], + "angle": 0, + "content": "A. Yes" + }, + { + "type": "list", + "bbox": [ + 0.523, + 0.649, + 0.82, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.687, + 0.814, + 0.744 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.746, + 0.558, + 0.757 + ], + "angle": 0, + "content": "A. Yes" + }, + { + "type": "text", + "bbox": [ + 0.67, + 0.747, + 0.721, + 0.757 + ], + "angle": 0, + "content": "B. No" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.762, + 0.814, + 0.82 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.666, + 0.823, + 0.774, + 0.834 + ], + "angle": 0, + "content": "A. No B. Yes" + }, + { + "type": "title", + "bbox": [ + 0.397, + 0.847, + 0.624, + 0.862 + ], + "angle": 0, + "content": "(c) Single Video vs. Video Pairs" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.873, + 0.907, + 0.93 + ], + "angle": 0, + "content": "Figure 2. The visualization samples from Q-Bench-Video, with the question-answer content most representative of each subcategory being underlined. It is important to note that, regarding quality concerns, a single question-answer annotation may not only focus on one distortion dimension. Therefore, the distortion visualization examples shown in (b) primarily highlight instances that are most closely aligned with the mentioned distortion types." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3232" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.152 + ], + "angle": 0, + "content": "are the possible factors that lead to the low clarity of this video? Please list and explain.). By adopting this form of questioning, we can better assess an LMM's ability to perceive video quality in real-world conditions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.16, + 0.262, + 0.175 + ], + "angle": 0, + "content": "3.3.2. Quality Concerns" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.179, + 0.483, + 0.284 + ], + "angle": 0, + "content": "It's important to recognize that video quality can be influenced by multiple factors on some occasions. Therefore, a query tuple \\((\\mathrm{V},\\mathrm{Q},\\mathrm{A},\\mathrm{C})\\) does not need to be restricted to a single concern. It can address multiple concerns simultaneously. For instance, the question Is this video clear and well-composed? can be seen as evaluating both technical and aesthetic quality understanding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.285, + 0.483, + 0.405 + ], + "angle": 0, + "content": "I) Technical Distortions. Technical distortions refer to the low-level degradation in video quality that arises from the limitations of recording, compression, and transmission [37, 54]. These distortions often include artifacts such as blurring, noise, compression artifact, exposure, etc., which are directly tied to the technical processes used in video production and delivery. The CG-specific distortions related to geometry and texture are taken into consideration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.406, + 0.483, + 0.541 + ], + "angle": 0, + "content": "II) Aesthetic Distortions. Aesthetic distortions involve deviations from the intended visual style, artistic design, or creative intent that negatively affect the viewer's perception of the video [14, 44]. These distortions can include aspects such as confusing color, poor composition, lighting inconsistencies, or distracting elements that reduce the overall aesthetic appeal. Unlike technical distortions, aesthetic distortions are subjective and might be affected by viewer preference, cultural context, or artistic norms." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.285, + 0.483, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.542, + 0.483, + 0.692 + ], + "angle": 0, + "content": "III) Temporal Distortions. Temporal distortions are related to the degradation of visual quality over time, impacting the fluidity and consistency of the video [36]. These distortions manifest as issues like screen shake, flickering, motion inconsistency, frame drops, and stuttering that result from unstable shooting devices, dramatically changing lighting conditions, and unstable bitrate environments [46]. Such disruptions hinder the viewer's natural perception of the video, leading to a disjointed and unpleasant viewing experience, especially in live-streaming scenarios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.693, + 0.483, + 0.844 + ], + "angle": 0, + "content": "IV) AIGC Distortions. AIGC distortions pertain to imperfections and unnaturalness specifically arising from the generation of video content through AI models [32, 61]. These distortions may include unnatural textures, inconsistent lighting, uncanny facial features, or unrealistic object behavior that result from limitations or biases in the training data, model architecture, or generative process. These distortions are unique to AI-generated content and require specialized evaluation metrics that consider both the technical and perceptual quality aspects." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.852, + 0.334, + 0.867 + ], + "angle": 0, + "content": "3.3.3. Single Videos & Video Pairs" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Accurately comparing and jointly analyzing the quality of video pairs is sometimes more crucial than assessing the" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.09, + 0.911, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.181, + 0.865, + 0.193 + ], + "angle": 0, + "content": "(a) Annotation GUI for single videos of Q-Bench-Video." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.194, + 0.911, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.288, + 0.86, + 0.3 + ], + "angle": 0, + "content": "(b) Annotation GUI for video pairs of Q-Bench-Video." + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.312, + 0.907, + 0.436 + ], + "angle": 0, + "content": "Figure 3. Illustration of the annotation GUIs for Q-Bench-Video. (a) shows the interface for annotating single videos, where the annotator can select the question type and play the videos using the Video Play button. The annotator can also switch to the next and previous annotation with the Next and Previous buttons. (b) presents the interface for annotating video pairs. When the annotator presses the Video Play button, the video pairs are played sequentially, with a five-second gray screen serving as an interval between the two videos." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.471, + 0.907, + 0.563 + ], + "angle": 0, + "content": "quality of a single video, especially in scenarios such as performance tests in video compression and quality control in video generation (In which it is more important to find out Which video is better in visual quality and why?) [49, 66]. Therefore, in Q-Bench-Video, we include video quality queries for both single videos and video pairs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.565, + 0.909, + 0.717 + ], + "angle": 0, + "content": "1) Single Videos. Queries related to single videos can primarily be categorized into two types: a) Global perception, which involves questions about the overall visual quality of the video, such as How is the overall contrast of this video? b) Referring perception, which focuses on the visual quality of specific elements within the video, like querying What is the most apparent distortion when the player strikes the ball? Through these approaches, we aim to comprehensively evaluate the LMMs' ability to perceive both the overall and localized aspects of video quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.901 + ], + "angle": 0, + "content": "II) Video Pairs. Firstly, to ensure that the comparison of video pairs is clear and meaningful, comparisons are only made between videos from the same source, such as videos from natural sources being paired together while CG videos and AIGC videos are not being paired. There are mainly two types of video pair categories: a) Joint analysis, which involves understanding the shared quality features of the video pairs, for example, such as asking Are both videos blurry? b) Comparative analysis, which involves comparing the quality dimension across two videos, such as How does the level of brightness in the first video compare to that in the second one? It is important to note" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3233" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.49, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.378, + 0.414, + 0.391 + ], + "angle": 0, + "content": "(a) Overall performance on Q-Bench-Video." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.9, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.378, + 0.839, + 0.391 + ], + "angle": 0, + "content": "(b) Subcategory performance on Q-Bench-Video." + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.402, + 0.908, + 0.459 + ], + "angle": 0, + "content": "Figure 4. A concise summary of the LMMs' performance on Q-Bench-Video. (a) provides a comparison detailing the overall performance of humans and 17 selected LMMs, including both proprietary and open-source models. (b) illustrates a radar chart that outlines the performance of the top-2 proprietary LMMs (GPT-4o & Gemini 1.5 Pro) and open-source LMMs (mPLUG-Owl3 & LLaVA-OneVision) across various subcategories within Q-Bench-Video." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.485, + 0.483, + 0.561 + ], + "angle": 0, + "content": "that we further categorize comparisons based on the difference in quality labels of the videos involved into coarse-grain (with relatively more significant visual quality differences) and fine-grain (with relatively minor visual quality differences) comparisons. (More details in the Supp.)" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.566, + 0.373, + 0.58 + ], + "angle": 0, + "content": "3.3.4. Questions & Answers Annotation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.585, + 0.483, + 0.691 + ], + "angle": 0, + "content": "The annotation process of Q-Bench-Video is conducted in a well-controlled laboratory environment. A total of 8 experts are employed and trained to ensure the consistency of the annotations. The experts are required to watch the videos in their entirety before making annotations. Each annotated question-answer pair is then reviewed by at least three other experts to ensure its validity and accuracy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.698, + 0.384, + 0.714 + ], + "angle": 0, + "content": "3.4. Benchmark Setting & Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.72, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Unless specifically stated otherwise, for Video LMMs we typically analyze by uniformly sampling 16 frames from the video, while for Image LMMs, the sampling is reduced to 8 frames. It's worth noting that if the LMMs are not compatible with the specified number of sampling frames (e.g. if they cannot support up to 8-frame input), we will use the official default settings for testing. For Yes-or-No and What-How questions, if the LMMs can accurately respond with the options, we directly record the accuracy of the responses as results. If the LMMs cannot provide option-based answers, we implement a GPT-assisted evaluation strategy to help judge the accuracy of the answers. For Open-ended" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.485, + 0.907, + 0.561 + ], + "angle": 0, + "content": "questions, since the answers are open-ended and cannot be directly quantified for accuracy, we also employ the GPT-assisted evaluation strategy. This involves GPT scoring the responses based on their accuracy, completeness, and relevance compared to the annotated answer." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.601, + 0.756, + 0.618 + ], + "angle": 0, + "content": "4. Results of Q-Bench-Video" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.635, + 0.715, + 0.651 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.665, + 0.907, + 0.817 + ], + "angle": 0, + "content": "LMMs Participants. A total of 17 LMMs (12 Open-source LMMs and 5 Proprietary LMMs) are included for validation, which includes a) 3 Open-source Image LMMs: LLaVA-Next [30], LLaVA-v1.5 [28], and mPLUG-Owl2 [53]; b) 9 Open-source Video LMMs: mPLUG-Owl3 [51], LLaVA-OneVision [19], InternVL-Chat [4], VILA1.5 [16], PLLaVA [50], LLaVA-Next-Video [57], ST-LLM [31], Video-LLaVA [27], and VideoChat2 [22]; c) 5 Proprietary LMMs: Gemini 1.5 Flash, Gemini 1.5 Pro [39], GPT-4o mini, GPT-4o, and GPT-4 Turbo [2]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Subsets Split. The Q-Bench-Video is divided into test (1,186 question-answer items) and dev (1,192 question-answer items) subsets. The correct answers will be released and proprietary for the dev and test subsets. All discussions and analyses are based on the test subset." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3234" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.131 + ], + "angle": 0, + "content": "Table 2. Results on the test subset for the video quality perception ability of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively. The Open-ended questions are excluded for Random guess. (Performance of the test subset is in the Supp.)" + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.133, + 0.907, + 0.435 + ], + "angle": 0, + "content": "
Sub-categoriesQuestion TypesQuality ConcernsOverall↑
LMM (LLM)Yes-or-No↑What-How↑Open-ended↑Tech.↑Aes.↑Temp.↑AIGC↑
Random guess w/o Open-ended50.00%25.00%/37.10%37.31%37.25%37.22%37.79%
Human86.57%81.00%77.11%79.22%80.23%82.72%86.21%81.56%
Open-source Image LMMs
LLaVA-Next (Mistral-7B)62.83%45.14%33.69%46.38%57.86%47.84%48.46%47.52%
LLaVA-v1.5 (Vicuna-v1.5-13B)52.98%46.44%37.01%45.77%58.12%45.30%46.48%45.64%
mPLUG-Owl2 (LLaMA2-7B)59.19%39.07%31.19%42.07%52.38%41.71%39.37%43.43%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)60.48%56.39%39.48%52.68%58.31%52.05%43.49%52.39%
LLaVA-OneVision (Qwen2-7B)61.34%53.88%39.15%49.35%64.15%50.68%44.30%51.70%
InternVL-Chat (Vicuna-7B)66.02%52.13%33.93%48.42%52.73%50.59%53.12%51.11%
VILA1.5 (LLaMA3-8B)61.95%46.00%39.60%47.85%57.85%45.65%42.57%49.41%
PLLAVA (Mistral-7B)65.63%52.33%32.23%49.69%61.32%50.96%53.64%50.39%
LLaVA-Next-Video (Mistral-7B)61.34%45.95%38.10%49.03%60.94%46.97%49.40%48.69%
ST-LLM (Vicuna-v1.1-7B)44.63%28.50%32.78%34.99%46.11%34.28%34.02%35.42%
Video-LLaVA (Vicuna-v1.5-7B)64.67%40.79%29.11%43.25%54.04%42.38%42.76%43.49%
VideoChat2 (Mistral-7B)56.09%29.98%34.99%39.26%50.02%38.25%35.88%40.56%
Proprietary LMMs
Gemini 1.5 Flash65.48%56.79%47.51%54.11%66.58%53.51%50.22%56.78%
Gemini 1.5 Pro65.42%62.35%47.57%56.80%69.61%53.38%53.26%58.63%
GPT-4o mini62.95%50.93%42.10%49.38%60.90%48.43%41.71%52.20%
GPT-4o67.48%58.79%49.25%56.01%58.57%65.39%52.22%58.70%
GPT-4 Turbo66.93%58.33%40.15%54.23%66.23%54.00%52.04%56.36%
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.453, + 0.196, + 0.469 + ], + "angle": 0, + "content": "4.2. Findings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.477, + 0.483, + 0.583 + ], + "angle": 0, + "content": "The overall performance and subcategory comparisons (human vs. top-performing LMMs) on Q-Bench-Video can be quickly glanced at Fig. 4. Detailed performance across the subcategories for each LMM are shown in Table 2 (Question Types & Quality Concerns) and Table 3 (Single Videos vs. Video Pairs) respectively. The findings are organized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.483, + 0.903 + ], + "angle": 0, + "content": "1) General Performance. Human>Proprietary LMMs>Open-source LMMs>Random guess. From the performance results presented in Table 2, we observe that nearly all LMMs significantly outperform random guess, demonstrating their basic capability to understand video quality. Among the open-source LMMs, the recently released mPLUG-Owl3 achieves the highest overall performance at \\(52.39\\%\\), even slightly surpassing GPT-4o mini \\((52.20\\%)\\), followed closely by LLaVA-OneVision \\((51.70\\%)\\) and InternVL-Chat \\((51.11\\%)\\). Image LMMs deliver moderate performance. Although they outperform some Video LMMs, the gap between them and the latest Video LMMs is still notable. Benefiting from larger training datasets and more parameters, proprietary LMMs (except GPT-4o mini) outperform all open-source models. However, even the best-performing model, GPT-4o, which achieved an overall performance of \\(58.70\\%\\), still lags behind human performance by \\(22.86\\%\\). This gap highlights that, despite the advancements in current state-of-the-art LMMs on video general understanding, there remains a significant need for improvement in video quality understanding ability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.453, + 0.907, + 0.681 + ], + "angle": 0, + "content": "2) Question Types. Open-ended questions are more challenging for LMMs. From Table 2, a discernible hierarchy in task difficulty for video quality assessment emerges for both humans and LMMs, arranged as follows: Open-ended \\(>\\) What-How \\(>\\) Yes-or-No. It is crucial to highlight that while humans exhibit a performance decline in Open-ended tasks by approximately \\(9.46\\%\\) compared to Yes-or-No tasks, and about \\(3.89\\%\\) compared to What-How tasks, these reductions are markedly less pronounced than those observed in LMMs for the Open-ended questions. This disparity underscores a significant proficiency gap between LMMs' capability in handling straightforward, closed-form questions and their effectiveness in navigating the complexities of real-world problem-solving on open-ended questions, particularly in the context of video quality evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.909, + 0.903 + ], + "angle": 0, + "content": "3) Quality Concerns. LMMs exhibit unbalanced performance across different types of distortions. From Table 2, it is evident that humans are particularly good at identifying AIGC distortions, while LMMs demonstrate stronger performance in detecting Aesthetic distortions. This distinction likely stems from the inherent sensitivity of humans to the conspicuous unnaturalness of AIGC distortions, which readily draws human attention. In contrast, Aesthetic distortions, which often involve high-level semantic nuances, align more closely with the training contexts of LMMs, enabling them to excel in this area. However, LMMs face challenges with AIGC distortions due to insufficient exposure to such anomalies during their pretraining phases, specific architectural constraints, and imperfections" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3235" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.118 + ], + "angle": 0, + "content": "Table 3. Results on the test subset for the video quality perception ability across single videos and video pairs of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.119, + 0.907, + 0.428 + ], + "angle": 0, + "content": "
Sub-categoriesSingle VideosVideo Pairs
LMM (LLM)Global↑Referring↑Overall↑Joint↑Compare -fine↑Compare -coarse↑Overall↑
Random guess w/o Open-ended36.49%38.61%37.71%40.56%37.94%36.83%38.00%
Human78.87%80.43%79.65%84.90%87.34%89.11%87.56%
LLaVA-Next (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
LLaVA-v1.5 (Vicuna-v1.5-13B)47.99%51.94%50.10%27.72%34.60%42.12%36.42%
mPLUG-Owl2 (LLaMA2-7B)46.86%43.51%45.07%51.49%37.10%40.28%43.69%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)52.46%50.60%51.47%48.03%54.90%59.20%55.31%
LLaVA-OneVision (Qwen2-7B)51.56%48.43%49.89%53.48%58.10%63.36%59.41%
InternVL-Chat (Vicuna-7B)51.15%51.86%51.52%48.85%51.10%49.20%49.79%
VILA1.5 (LLaMA3-8B)52.35%47.37%49.69%56.11%45.40%48.04%48.84%
PLLAVA (Mistral-7B)51.44%55.49%53.60%40.36%50.40%54.16%49.90%
LLaVA-Next-Video (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
ST-LLM (Vicuna-v1.1-7B)36.54%36.49%36.51%28.03%36.80%32.08%32.87%
Video-LLaVA (Vicuna-v1.5-7B)45.46%44.67%45.04%49.36%42.00%43.00%44.01%
VideoChat2 (Mistral-7B)43.52%38.27%40.72%57.23%44.40%41.64%45.93%
Proprietary LMMs
Gemini 1.5 Flash58.00%53.18%55.43%46.59%65.30%68.84%62.77%
Gemini 1.5 Pro52.36%61.41%57.19%45.43%65.30%72.00%63.55%
GPT-4o mini52.67%48.96%50.69%44.00%60.50%63.88%58.02%
GPT-4o58.75%54.18%56.31%46.93%67.30%69.24%63.80%
GPT-4 Turbo57.36%52.80%54.93%46.13%62.50%64.80%59.84%
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.447, + 0.482, + 0.599 + ], + "angle": 0, + "content": "in the generation process. In the case of proprietary LMMs, their performance on Technical and Temporal distortions appear comparably consistent, indicating a uniform capability in recognizing these two types of distortions. Nonetheless, across all four subcategories, LMMs exhibit a notable performance disparity compared to humans, with varying degrees of accuracy among the different types of distortions. This variability highlights the need for significant enhancements in LMMs' abilities to accurately understand and interpret various distortion types." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.599, + 0.483, + 0.901 + ], + "angle": 0, + "content": "4) Single Videos vs. Video Pairs. LMMs demonstrate superior capabilities in comparing video quality. From Table 3, we observe that for single videos, LMMs achieve similar performance in Global and Referring quality perception (except for Gemini 1.5 Pro), without any significant trend of the performance for one subcategory over the other. This suggests that LMMs have comparable abilities in perceiving both Global video quality and Referring video quality. In terms of comparison, however, LMMs clearly outperform their performance on single video analysis and joint analysis. Notably, LMMs perform significantly better in the Compare-coarse subcategory, where video pairs have more pronounced quality differences, than in the Compare-fine subcategory. This highlights that LMMs are more adept at comparing video quality than analyzing the quality of single videos. This advantage in comparative assessment can be attributed to the inherent clarity in pairwise comparisons, which provide explicit contrasts, as opposed to the more ambiguous nature of evaluating a single video. Both humans and LMMs exhibit enhanced performance in com" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.447, + 0.907, + 0.493 + ], + "angle": 0, + "content": "parative tasks. Although there is still a significant accuracy gap between LMMs and humans, LMMs show promising potential as effective tools for comparing video quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.505, + 0.637, + 0.521 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.53, + 0.907, + 0.592 + ], + "angle": 0, + "content": "1) Subjectivity can not be fully avoided in annotations for aspects like aesthetics. 2) As video generation advances, new models may show different distortions, which might potentially make parts of Q-Bench-Video outdated." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.634, + 0.62 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.629, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In this paper, we introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to evaluate Large Multi-modal Models' (LMMs) understanding of video quality. Our benchmark includes a diverse range of video types, questions that challenge multiple aspects of video quality, and a holistic evaluation framework encompassing Technical, Aesthetic, Temporal, and AIGC distortions. Through extensive experimentation with 17 open-source and proprietary LMMs, we find that while LMMs show promise in discerning video quality, their performance remains significantly below human-level understanding, especially when addressing Open-ended questions and AIGC-specific distortions. These findings highlight the current limitations of LMMs in video quality perception and underscore the need for further advancements in this area. By offering Q-Bench-Video, we aim to stimulate future research and drive improvements in the field, bridging the gap between LMM and human video quality understanding." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3236" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.241, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.205 + ], + "angle": 0, + "content": "The work was supported in part by the National Natural Science Foundation of China under Grant (623B2073, 62301310), the Ministry of Education, Singapore, under the funding of MOE-T2EP20123-0006, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.218, + 0.188, + 0.234 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.244, + 0.481, + 0.285 + ], + "angle": 0, + "content": "[1] Recommendation 500-10: Methodology for the subjective assessment of the quality of television pictures. 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To address this oversight, we introduce Q-Bench-Video in this paper, a new benchmark specifically designed to evaluate LMMs' proficiency in discerning video quality. a) To ensure video source diversity, Q-Bench-Video encompasses videos from natural scenes, AI-generated content (AIGC), and computer graphics (CG). b) Building on the traditional multiple-choice questions format with the Yes-or-No and What-How categories, we include Open-ended questions to better evaluate complex scenarios. Additionally, we incorporate the video pair quality comparison question to enhance comprehensiveness. c) Beyond the traditional Technical, Aesthetic, and Temporal distortions, we have expanded our evaluation aspects to include the dimension of AIGC distortions, which addresses the increasing demand for video generation. Finally, we collect a total of 2,378 question-answer pairs and test them on 12 open-source & 5 proprietary LMMs. Our findings indicate that while LMMs have a foundational understanding of perceptual video quality, their performance remains incomplete and imprecise, with a notable discrepancy compared to the performance of human beings. Through Q-Bench-Video, we seek to catalyze community interest, stimulate further research, and unlock the untapped potential of LMMs to close the gap in video quality understanding. + +# 1. Introduction + +As the field of artificial intelligence (AI) continues to evolve, Large Multi-modal Models (LMMs) [4, 16, 19, 50, 51] are progressively utilized in high-level video understanding tasks. These models have shown remarkable capabilities in analyzing and interpreting the semantic content of + +videos, such as classifying objects, identifying actions, and recognizing events. However, the aspect of video quality, which is vital for optimizing compression and transmission systems, enhancing viewer experience, and establishing standards for high-quality video generation, has received less attention. Although numerous LMM video benchmarks[8, 10, 23] have been developed to assess the semantic understanding of videos by LMMs comprehensively, benchmarks systematically targeting video quality are still lacking. Additionally, while semantic understanding is closely linked to high-level video information, the perception and understanding of low-level information are crucial in video quality [5, 25] as well. + +To address this gap, we introduce Q-Bench-Video, a novel benchmark specifically designed to systematically evaluate the video quality understanding of LMMs. As illustrated in Fig. 1, our benchmark encompasses a wide range of video content, including natural scenes, AI-generated content (AIGC), and computer graphics (CG), ensuring diversity in video sources. In addition, to maintain a reasonable distribution of source video quality, we employ uniform sampling from video datasets that contain subjective quality annotations. This approach guarantees comprehensive coverage of the quality spectrum while avoiding imbalanced quality distributions. Moreover, we extend beyond traditional video evaluations by incorporating both multiple-choice questions (MCQs) and open-ended questions. This enables a more thorough analysis of LMMs' ability to discern video quality across diverse scenarios. We further introduce a new evaluation dimension specifically tailored to assess distortions related to AIGC, which are increasingly prominent in video generation tasks. Recognizing the importance of quality comparison settings in real-world applications, such as camera parameter optimization and AIGC video generation, we further incorporate video pairs to facilitate quality comparison assessment as well. In total, we collect 1800 videos and annotated 2,378 question-answer pairs for validation, creating a robust framework for systematic evaluation on video quality understanding. + +![](images/49212cba749d85d0982fa30e92ed050f1353de4a77333a2c7277c300f82cf5ed.jpg) +Figure 1. The construction overview of the proposed Q-Bench-Video. To ensure diversity in video content, we collect natural scenes, AIGC, and CG videos from video quality assessment datasets as depicted in (a). To achieve a balanced quality distribution among the sampled videos, we employ uniform sampling for quality control. As indicated in (c-1) and (c-2), we utilize three types of questions (Yes-or-No, What-How, Open-ended) and address a comprehensive range of quality concerns including Technical, Aesthetic, Temporal, and AIGC distortions. Additionally, we incorporate the video pairs comparison task to enhance the comprehensiveness of the benchmark. + +Through the rigorous experiment, we demonstrate that while LMMs show promise in video quality assessment, their performance lags significantly behind human-level understanding. By offering a systematic and thorough evaluation of LMMs' video quality perception, Q-Bench-Video aims to foster research in this underexplored area and push the boundaries of LMM capabilities on video quality understanding. Our contributions can be summarized as follows: + +- We introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to assess the video quality understanding capabilities of LMMs. This benchmark includes a diverse collection of source videos and ensures a balanced quality distribution, complemented by human-crafted question-answer annotations. +- Our evaluation framework spans four key quality dimensions: Technical, Aesthetic, Temporal, and AIGC distortions, which offers a holistic evaluation approach to video quality assessment. Uniquely, Q-Bench-Video enhances its utility by introducing the task of video pairs comparison, which sets it apart from existing video benchmarks. +- We conduct a comprehensive evaluation using both proprietary and open-source LMMs to measure their effectiveness in understanding video quality. The results expose notable deficiencies in current LMMs, while also shedding light on performance variations across different quality dimensions. These findings provide critical insights and suggest promising directions for future enhancements in the field of video quality understanding. + +# 2. Related Works + +# 2.1. Video LMMs and Benchmarks + +The rapid advancement of Large Multi-modal Models (LMMs) in recent years [4, 28-30, 52, 56, 67] has showcased their remarkable perception and cognitive abilities across various multimodal benchmarks for images [9, 33, 35, 47, 62]. As development progresses, the focus of visual analysis has gradually shifted from images to videos. Early efforts [22, 27, 31, 50] aimed at unlocking the video understanding potential of LMMs have yielded promising results. However, initial video-based benchmarks [24, 34, 41] typically concentrated on specific aspects of video comprehension, falling short of fully capturing the performance of these models due to limitations such as a lack of diversity in video types and inadequate coverage of temporal dynamics. In response, recent video benchmarks [8, 10] have moved toward a more comprehensive evaluation of LMMs. Nonetheless, these efforts focus on high-level semantic understanding without systematic exploration of video quality. + +# 2.2. Video Quality Assessment + +Video Quality Assessment (VQA) is a task aimed at quantifying video scores based on visual quality. Initially, early VQA methods employ hand-crafted features extracted from videos and regress the features into quality scores [17, 20, 26, 40, 58, 64, 65]. With the emergence of deep neural networks, a shift occurs as numerous methods adopted deep + +Table 1. Overview of the diverse video source datasets in the Q-Bench-Video. We consider various video content types, including natural scenes, AIGC, and CG videos. The term 'MOS' denotes that the videos are annotated via Mean Opinion Scores under ITU standards [1]. We have conducted uniform sampling based on their quality labels to ensure a balanced quality distribution. + +
Video TypeVideo Source DatasetMOSQuality ConcernsSampled SizeFull Dataset Size
Natural (1000)LSVQ [54]✓Spatial & Temporal60039K
MaxWell [46]✓Spatial & Temporal & Aesthetic3504.5K
WaterlooSQoE-III [6]✓Quality-of-Experience20450
WaterlooSQoE-IV [7]✓Quality-of-Experience301,350
AIGC (600)T2VQA-DB [17]✓Quality & Text Alignment20010K
VideoFeedback [13]×Quality & Text Alignment40037.6K
CG (200)LIVE-YT-Gaming [55]✓Visual Quality200600
+ +learning techniques for VQA tasks [18, 21, 38, 42]. As the field progresses, newer methods begin incorporating considerations for both temporal dynamics and aesthetic qualities, leading to a more holistic approach to video quality analysis [3, 12, 43, 45, 59]. Moreover, the evolution of large-scale models has further revolutionized VQA methodologies. Many recent approaches have redefined the traditional quality assessment process into a quality question-answering format [11, 15, 48, 60, 63]. This adaptation leverages the substantial prior knowledge embedded in large models to enhance the precision of quality quantification [61]. Despite these technological advances, VQA still grapples with challenges in providing interpretable quality scores and deepening the understanding of how models perceive and analyze video quality more comprehensively. + +# 3. Benchmark Construction + +# 3.1. Benchmark Principle + +The Q-Bench-Video is designed based on three guiding principles: (1) It encompasses a broad spectrum of video content, including natural scenes, AIGC, and CG videos. (2) It ensures a comprehensive and representative sampling process across a wide quality range, enhancing the benchmark's overall effectiveness. (3) It primarily focuses on the aspects of video quality that significantly influence the viewing experience, including technical, aesthetic, temporal, and AIGC distortions. This significantly differs from other video benchmarks that prioritize semantic understanding. Additionally, the video pair quality comparison is integrated to address the challenges associated with comparing video quality. The overall construction process can be clearly overviewed in Fig. 1. + +# 3.2. Source Videos Collection + +As shown in Table 1, the source videos are primarily gathered from video quality assessment datasets. We selected videos from these datasets for two main reasons: (1) These datasets have inherently considered the diversity of quality features during video selection; (2) These datasets possess quality annotations that adhere to ITU standards [1] (with the exception of VideoFeedback), which allow us to accurately and authentically sample videos. + +Our sampling method primarily employs a uniform approach, extracting videos evenly from each dataset based on the quality range. Moreover, considering the current popularity of AIGC and CG videos, we have also incorporated a selection of these video types. (More details in the Supp.) + +# 3.3. Benchmark Designs + +In this section, we provide a detailed description of the design of Q-Bench-Video. In this benchmark, the metastructure tuple $(\mathrm{V},\mathbb{Q},\mathbb{A},\mathbb{C})$ of each data item can be decomposed into several components: the video object V (which can be a single video or a pair of videos), the video quality query $\mathbb{Q}$ , the set of possible answers A, and the correct answer C. The question samples are listed in Fig. 2. + +# 3.3.1. Question Types + +I) Yes-or-No Questions. The basic Yes-or-No questions are designed to prompt LMMs to make binary judgments on video quality queries, typically limited to the answers Yes or No. To address the potential bias in LMMs that may skew towards yes responses, we employ an annotation adjustment process, which modifies the questions and correct answers if necessary (based on the Yes-or-No ratio). This process ensures that the distribution of correct answers, either Yes or No, remains balanced at about $50\%:50\%$ ratio in the end. This balanced approach allows for a more accurate assessment of LMMs' performance on Yes-or-No questions. II) What-How Questions. The What-How questions are commonly utilized in benchmarks for LMMs. The What questions focus on identifying specific distortions (e.g., What is the most apparent distortion in this video?). On the other hand, the How questions are employed to distinguish the finer details of distortion levels (e.g., How is the overall clarity of this video?). Including both What and How questions allows Q-Bench-Video to thoroughly and meticulously evaluate LMMs' ability on identifying video distortions and evaluating the distortion levels. + +III) Open-ended Questions. It's important to note that the two types of questions previously mentioned require LMMs to select the correct answer from a predefined set. However, in many real-world scenarios, Open-ended Questions, which do not restrict responses to a predefined set, are often more necessary and challenging for LMMs (e.g., What + +# Yes-or-No + +![](images/4e1dafae2a53d12b2460431ec69a4c3f2477118643a23a6ba12692870b3b1d61.jpg) + +Q: Does the fabric in this video exhibit good clarity and proper lighting? + +A. Yes + +B. No + +# What-How + +![](images/e1f62e085d2bdf24ac361cf221aff90aa980e7d3a18e1fd70cd5b35d1fe0e1ed.jpg) + +Q: What quality issues do not exist in this video? +A. None of the options B. Blurriness +C. Overexposure D. Underexposure + +# Open-ended + +![](images/f7faefb28ec5588951fcb482518a2325a2811be29aaea00c347144c228be4a8d.jpg) + +Q: Why is it difficult for viewers to identify the dish the man is cooking in the video? + +Open-ended Response: The video has severe compression blur and block artifacts, significantly reducing the discernibility of objects in the video. + +# (a) Question Type + +# Technical + +![](images/0e597968c4e1f7dd36861b9bdcc5b399ae273d0bfd01ecbe64dce082a1a9a961.jpg) + +Q: As the camera moves away in this video, is there a noticeable increase in the clarity of the person's face? + +A. No +B. Yes + +# Temporal + +![](images/c8f8fefd1c1da1386506db86f85fa7612664991c9dbb34d01990fbe2e31d7755.jpg) + +Q: Does this video have severe camera shake? + +A. No +B. Yes + +# Aesthetic + +![](images/ee6edd4d27097cb1e69945ec3c75031ad03dcaccb5d7ce361bbc6c5e28e6e7d6.jpg) + +Q: what feelings does this video evoke? +Open-ended Response: This video depicts a castle in a unnatural and twisted jungle, where the plants have bizarre, sharp structures and dull colors. The atmosphere is eerie and terrifying, creating a sense of horror + +# AIGC + +![](images/c014e3070272177d3bf155e730e17f63be7213b6c3266b7fbf1f53abd3ec5e13.jpg) + +Q: What is the most impactual quality issue of this video? + +A. Noise +C. Blurriness + +B. Incorrect human structure +D. Overexposure + +# (b) Quality Concern + +# Global + +![](images/ec92803065c6fe205b78d15a0ddd5b9d4c6f6f61e08bde74d5f3666fe346df0f.jpg) + +Q: How is the overall lighting level in this game video? + +A. Very poor +C. Average + +B. Poor +D. Good + +# Joint + +![](images/30d454897ba18a168f5a1b91325a7f4bafc851082e165ad5493fe506f9f2b994.jpg) +Figure 2. The visualization samples from Q-Bench-Video, with the question-answer content most representative of each subcategory being underlined. It is important to note that, regarding quality concerns, a single question-answer annotation may not only focus on one distortion dimension. Therefore, the distortion visualization examples shown in (b) primarily highlight instances that are most closely aligned with the mentioned distortion types. + +Q: Are both videos primarily in cold colors? + +# Compare + +![](images/c5d78593dcf3d6c0c606d5d76913a91ddafd2553c5f4fee7b87dca9c0d7370f9.jpg) + +Q: Is the exposure of the first video more balanced than + +# 5 + +# Referring + +![](images/237481856f8363e477745139de9dbd98d80c519f4f82e73230e9076e0c5b9b2e.jpg) + +Q: Is the main character in this game video rendered in high details but with relatively low clarity? +A. Yes + +![](images/6be3ff884f68d079cf9305a8516f9601ce6a8b5909d6f2ebe985b74a0539c34d.jpg) + +A. Yes + +B. No + +![](images/32091bbc093ec6593e35f02cccb503bca1b6ab9f5acdbefaa7ceda4fd937ac7b.jpg) + +A. No B. Yes + +# (c) Single Video vs. Video Pairs + +are the possible factors that lead to the low clarity of this video? Please list and explain.). By adopting this form of questioning, we can better assess an LMM's ability to perceive video quality in real-world conditions. + +# 3.3.2. Quality Concerns + +It's important to recognize that video quality can be influenced by multiple factors on some occasions. Therefore, a query tuple $(\mathrm{V},\mathrm{Q},\mathrm{A},\mathrm{C})$ does not need to be restricted to a single concern. It can address multiple concerns simultaneously. For instance, the question Is this video clear and well-composed? can be seen as evaluating both technical and aesthetic quality understanding. + +I) Technical Distortions. Technical distortions refer to the low-level degradation in video quality that arises from the limitations of recording, compression, and transmission [37, 54]. These distortions often include artifacts such as blurring, noise, compression artifact, exposure, etc., which are directly tied to the technical processes used in video production and delivery. The CG-specific distortions related to geometry and texture are taken into consideration. +II) Aesthetic Distortions. Aesthetic distortions involve deviations from the intended visual style, artistic design, or creative intent that negatively affect the viewer's perception of the video [14, 44]. These distortions can include aspects such as confusing color, poor composition, lighting inconsistencies, or distracting elements that reduce the overall aesthetic appeal. Unlike technical distortions, aesthetic distortions are subjective and might be affected by viewer preference, cultural context, or artistic norms. + +III) Temporal Distortions. Temporal distortions are related to the degradation of visual quality over time, impacting the fluidity and consistency of the video [36]. These distortions manifest as issues like screen shake, flickering, motion inconsistency, frame drops, and stuttering that result from unstable shooting devices, dramatically changing lighting conditions, and unstable bitrate environments [46]. Such disruptions hinder the viewer's natural perception of the video, leading to a disjointed and unpleasant viewing experience, especially in live-streaming scenarios. + +IV) AIGC Distortions. AIGC distortions pertain to imperfections and unnaturalness specifically arising from the generation of video content through AI models [32, 61]. These distortions may include unnatural textures, inconsistent lighting, uncanny facial features, or unrealistic object behavior that result from limitations or biases in the training data, model architecture, or generative process. These distortions are unique to AI-generated content and require specialized evaluation metrics that consider both the technical and perceptual quality aspects. + +# 3.3.3. Single Videos & Video Pairs + +Accurately comparing and jointly analyzing the quality of video pairs is sometimes more crucial than assessing the + +![](images/3f334b3ac00be8d23553e4e8bc98550a22921b8fe7d4a6a165dae9d87050a0b0.jpg) +(a) Annotation GUI for single videos of Q-Bench-Video. + +![](images/eab9b8817af0798538f50eb836fe01b6501ca11d061219ed2b4a0b3dcb56cc5e.jpg) +(b) Annotation GUI for video pairs of Q-Bench-Video. +Figure 3. Illustration of the annotation GUIs for Q-Bench-Video. (a) shows the interface for annotating single videos, where the annotator can select the question type and play the videos using the Video Play button. The annotator can also switch to the next and previous annotation with the Next and Previous buttons. (b) presents the interface for annotating video pairs. When the annotator presses the Video Play button, the video pairs are played sequentially, with a five-second gray screen serving as an interval between the two videos. + +quality of a single video, especially in scenarios such as performance tests in video compression and quality control in video generation (In which it is more important to find out Which video is better in visual quality and why?) [49, 66]. Therefore, in Q-Bench-Video, we include video quality queries for both single videos and video pairs. + +1) Single Videos. Queries related to single videos can primarily be categorized into two types: a) Global perception, which involves questions about the overall visual quality of the video, such as How is the overall contrast of this video? b) Referring perception, which focuses on the visual quality of specific elements within the video, like querying What is the most apparent distortion when the player strikes the ball? Through these approaches, we aim to comprehensively evaluate the LMMs' ability to perceive both the overall and localized aspects of video quality. + +II) Video Pairs. Firstly, to ensure that the comparison of video pairs is clear and meaningful, comparisons are only made between videos from the same source, such as videos from natural sources being paired together while CG videos and AIGC videos are not being paired. There are mainly two types of video pair categories: a) Joint analysis, which involves understanding the shared quality features of the video pairs, for example, such as asking Are both videos blurry? b) Comparative analysis, which involves comparing the quality dimension across two videos, such as How does the level of brightness in the first video compare to that in the second one? It is important to note + +![](images/8ec1451ad71d55a9769b3dfcbba26607309af2914313e044d5d5d70ba4818e32.jpg) +(a) Overall performance on Q-Bench-Video. + +![](images/6a784e6997abe34e6b511c01dace16c2b2cc4bb8b2ceb740a1d0aa466ad59670.jpg) +(b) Subcategory performance on Q-Bench-Video. +Figure 4. A concise summary of the LMMs' performance on Q-Bench-Video. (a) provides a comparison detailing the overall performance of humans and 17 selected LMMs, including both proprietary and open-source models. (b) illustrates a radar chart that outlines the performance of the top-2 proprietary LMMs (GPT-4o & Gemini 1.5 Pro) and open-source LMMs (mPLUG-Owl3 & LLaVA-OneVision) across various subcategories within Q-Bench-Video. + +that we further categorize comparisons based on the difference in quality labels of the videos involved into coarse-grain (with relatively more significant visual quality differences) and fine-grain (with relatively minor visual quality differences) comparisons. (More details in the Supp.) + +# 3.3.4. Questions & Answers Annotation + +The annotation process of Q-Bench-Video is conducted in a well-controlled laboratory environment. A total of 8 experts are employed and trained to ensure the consistency of the annotations. The experts are required to watch the videos in their entirety before making annotations. Each annotated question-answer pair is then reviewed by at least three other experts to ensure its validity and accuracy. + +# 3.4. Benchmark Setting & Evaluation + +Unless specifically stated otherwise, for Video LMMs we typically analyze by uniformly sampling 16 frames from the video, while for Image LMMs, the sampling is reduced to 8 frames. It's worth noting that if the LMMs are not compatible with the specified number of sampling frames (e.g. if they cannot support up to 8-frame input), we will use the official default settings for testing. For Yes-or-No and What-How questions, if the LMMs can accurately respond with the options, we directly record the accuracy of the responses as results. If the LMMs cannot provide option-based answers, we implement a GPT-assisted evaluation strategy to help judge the accuracy of the answers. For Open-ended + +questions, since the answers are open-ended and cannot be directly quantified for accuracy, we also employ the GPT-assisted evaluation strategy. This involves GPT scoring the responses based on their accuracy, completeness, and relevance compared to the annotated answer. + +# 4. Results of Q-Bench-Video + +# 4.1. Experimental Setting + +LMMs Participants. A total of 17 LMMs (12 Open-source LMMs and 5 Proprietary LMMs) are included for validation, which includes a) 3 Open-source Image LMMs: LLaVA-Next [30], LLaVA-v1.5 [28], and mPLUG-Owl2 [53]; b) 9 Open-source Video LMMs: mPLUG-Owl3 [51], LLaVA-OneVision [19], InternVL-Chat [4], VILA1.5 [16], PLLaVA [50], LLaVA-Next-Video [57], ST-LLM [31], Video-LLaVA [27], and VideoChat2 [22]; c) 5 Proprietary LMMs: Gemini 1.5 Flash, Gemini 1.5 Pro [39], GPT-4o mini, GPT-4o, and GPT-4 Turbo [2]. + +Subsets Split. The Q-Bench-Video is divided into test (1,186 question-answer items) and dev (1,192 question-answer items) subsets. The correct answers will be released and proprietary for the dev and test subsets. All discussions and analyses are based on the test subset. + +Table 2. Results on the test subset for the video quality perception ability of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively. The Open-ended questions are excluded for Random guess. (Performance of the test subset is in the Supp.) + +
Sub-categoriesQuestion TypesQuality ConcernsOverall↑
LMM (LLM)Yes-or-No↑What-How↑Open-ended↑Tech.↑Aes.↑Temp.↑AIGC↑
Random guess w/o Open-ended50.00%25.00%/37.10%37.31%37.25%37.22%37.79%
Human86.57%81.00%77.11%79.22%80.23%82.72%86.21%81.56%
Open-source Image LMMs
LLaVA-Next (Mistral-7B)62.83%45.14%33.69%46.38%57.86%47.84%48.46%47.52%
LLaVA-v1.5 (Vicuna-v1.5-13B)52.98%46.44%37.01%45.77%58.12%45.30%46.48%45.64%
mPLUG-Owl2 (LLaMA2-7B)59.19%39.07%31.19%42.07%52.38%41.71%39.37%43.43%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)60.48%56.39%39.48%52.68%58.31%52.05%43.49%52.39%
LLaVA-OneVision (Qwen2-7B)61.34%53.88%39.15%49.35%64.15%50.68%44.30%51.70%
InternVL-Chat (Vicuna-7B)66.02%52.13%33.93%48.42%52.73%50.59%53.12%51.11%
VILA1.5 (LLaMA3-8B)61.95%46.00%39.60%47.85%57.85%45.65%42.57%49.41%
PLLAVA (Mistral-7B)65.63%52.33%32.23%49.69%61.32%50.96%53.64%50.39%
LLaVA-Next-Video (Mistral-7B)61.34%45.95%38.10%49.03%60.94%46.97%49.40%48.69%
ST-LLM (Vicuna-v1.1-7B)44.63%28.50%32.78%34.99%46.11%34.28%34.02%35.42%
Video-LLaVA (Vicuna-v1.5-7B)64.67%40.79%29.11%43.25%54.04%42.38%42.76%43.49%
VideoChat2 (Mistral-7B)56.09%29.98%34.99%39.26%50.02%38.25%35.88%40.56%
Proprietary LMMs
Gemini 1.5 Flash65.48%56.79%47.51%54.11%66.58%53.51%50.22%56.78%
Gemini 1.5 Pro65.42%62.35%47.57%56.80%69.61%53.38%53.26%58.63%
GPT-4o mini62.95%50.93%42.10%49.38%60.90%48.43%41.71%52.20%
GPT-4o67.48%58.79%49.25%56.01%58.57%65.39%52.22%58.70%
GPT-4 Turbo66.93%58.33%40.15%54.23%66.23%54.00%52.04%56.36%
+ +# 4.2. Findings + +The overall performance and subcategory comparisons (human vs. top-performing LMMs) on Q-Bench-Video can be quickly glanced at Fig. 4. Detailed performance across the subcategories for each LMM are shown in Table 2 (Question Types & Quality Concerns) and Table 3 (Single Videos vs. Video Pairs) respectively. The findings are organized as follows: + +1) General Performance. Human>Proprietary LMMs>Open-source LMMs>Random guess. From the performance results presented in Table 2, we observe that nearly all LMMs significantly outperform random guess, demonstrating their basic capability to understand video quality. Among the open-source LMMs, the recently released mPLUG-Owl3 achieves the highest overall performance at $52.39\%$ , even slightly surpassing GPT-4o mini $(52.20\%)$ , followed closely by LLaVA-OneVision $(51.70\%)$ and InternVL-Chat $(51.11\%)$ . Image LMMs deliver moderate performance. Although they outperform some Video LMMs, the gap between them and the latest Video LMMs is still notable. Benefiting from larger training datasets and more parameters, proprietary LMMs (except GPT-4o mini) outperform all open-source models. However, even the best-performing model, GPT-4o, which achieved an overall performance of $58.70\%$ , still lags behind human performance by $22.86\%$ . This gap highlights that, despite the advancements in current state-of-the-art LMMs on video general understanding, there remains a significant need for improvement in video quality understanding ability. + +2) Question Types. Open-ended questions are more challenging for LMMs. From Table 2, a discernible hierarchy in task difficulty for video quality assessment emerges for both humans and LMMs, arranged as follows: Open-ended $>$ What-How $>$ Yes-or-No. It is crucial to highlight that while humans exhibit a performance decline in Open-ended tasks by approximately $9.46\%$ compared to Yes-or-No tasks, and about $3.89\%$ compared to What-How tasks, these reductions are markedly less pronounced than those observed in LMMs for the Open-ended questions. This disparity underscores a significant proficiency gap between LMMs' capability in handling straightforward, closed-form questions and their effectiveness in navigating the complexities of real-world problem-solving on open-ended questions, particularly in the context of video quality evaluation. + +3) Quality Concerns. LMMs exhibit unbalanced performance across different types of distortions. From Table 2, it is evident that humans are particularly good at identifying AIGC distortions, while LMMs demonstrate stronger performance in detecting Aesthetic distortions. This distinction likely stems from the inherent sensitivity of humans to the conspicuous unnaturalness of AIGC distortions, which readily draws human attention. In contrast, Aesthetic distortions, which often involve high-level semantic nuances, align more closely with the training contexts of LMMs, enabling them to excel in this area. However, LMMs face challenges with AIGC distortions due to insufficient exposure to such anomalies during their pretraining phases, specific architectural constraints, and imperfections + +Table 3. Results on the test subset for the video quality perception ability across single videos and video pairs of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively. + +
Sub-categoriesSingle VideosVideo Pairs
LMM (LLM)Global↑Referring↑Overall↑Joint↑Compare -fine↑Compare -coarse↑Overall↑
Random guess w/o Open-ended36.49%38.61%37.71%40.56%37.94%36.83%38.00%
Human78.87%80.43%79.65%84.90%87.34%89.11%87.56%
LLaVA-Next (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
LLaVA-v1.5 (Vicuna-v1.5-13B)47.99%51.94%50.10%27.72%34.60%42.12%36.42%
mPLUG-Owl2 (LLaMA2-7B)46.86%43.51%45.07%51.49%37.10%40.28%43.69%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)52.46%50.60%51.47%48.03%54.90%59.20%55.31%
LLaVA-OneVision (Qwen2-7B)51.56%48.43%49.89%53.48%58.10%63.36%59.41%
InternVL-Chat (Vicuna-7B)51.15%51.86%51.52%48.85%51.10%49.20%49.79%
VILA1.5 (LLaMA3-8B)52.35%47.37%49.69%56.11%45.40%48.04%48.84%
PLLAVA (Mistral-7B)51.44%55.49%53.60%40.36%50.40%54.16%49.90%
LLaVA-Next-Video (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
ST-LLM (Vicuna-v1.1-7B)36.54%36.49%36.51%28.03%36.80%32.08%32.87%
Video-LLaVA (Vicuna-v1.5-7B)45.46%44.67%45.04%49.36%42.00%43.00%44.01%
VideoChat2 (Mistral-7B)43.52%38.27%40.72%57.23%44.40%41.64%45.93%
Proprietary LMMs
Gemini 1.5 Flash58.00%53.18%55.43%46.59%65.30%68.84%62.77%
Gemini 1.5 Pro52.36%61.41%57.19%45.43%65.30%72.00%63.55%
GPT-4o mini52.67%48.96%50.69%44.00%60.50%63.88%58.02%
GPT-4o58.75%54.18%56.31%46.93%67.30%69.24%63.80%
GPT-4 Turbo57.36%52.80%54.93%46.13%62.50%64.80%59.84%
+ +in the generation process. In the case of proprietary LMMs, their performance on Technical and Temporal distortions appear comparably consistent, indicating a uniform capability in recognizing these two types of distortions. Nonetheless, across all four subcategories, LMMs exhibit a notable performance disparity compared to humans, with varying degrees of accuracy among the different types of distortions. This variability highlights the need for significant enhancements in LMMs' abilities to accurately understand and interpret various distortion types. + +4) Single Videos vs. Video Pairs. LMMs demonstrate superior capabilities in comparing video quality. From Table 3, we observe that for single videos, LMMs achieve similar performance in Global and Referring quality perception (except for Gemini 1.5 Pro), without any significant trend of the performance for one subcategory over the other. This suggests that LMMs have comparable abilities in perceiving both Global video quality and Referring video quality. In terms of comparison, however, LMMs clearly outperform their performance on single video analysis and joint analysis. Notably, LMMs perform significantly better in the Compare-coarse subcategory, where video pairs have more pronounced quality differences, than in the Compare-fine subcategory. This highlights that LMMs are more adept at comparing video quality than analyzing the quality of single videos. This advantage in comparative assessment can be attributed to the inherent clarity in pairwise comparisons, which provide explicit contrasts, as opposed to the more ambiguous nature of evaluating a single video. Both humans and LMMs exhibit enhanced performance in com + +parative tasks. Although there is still a significant accuracy gap between LMMs and humans, LMMs show promising potential as effective tools for comparing video quality. + +# 5. Limitations + +1) Subjectivity can not be fully avoided in annotations for aspects like aesthetics. 2) As video generation advances, new models may show different distortions, which might potentially make parts of Q-Bench-Video outdated. + +# 6. Conclusion + +In this paper, we introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to evaluate Large Multi-modal Models' (LMMs) understanding of video quality. Our benchmark includes a diverse range of video types, questions that challenge multiple aspects of video quality, and a holistic evaluation framework encompassing Technical, Aesthetic, Temporal, and AIGC distortions. Through extensive experimentation with 17 open-source and proprietary LMMs, we find that while LMMs show promise in discerning video quality, their performance remains significantly below human-level understanding, especially when addressing Open-ended questions and AIGC-specific distortions. These findings highlight the current limitations of LMMs in video quality perception and underscore the need for further advancements in this area. By offering Q-Bench-Video, we aim to stimulate future research and drive improvements in the field, bridging the gap between LMM and human video quality understanding. + +# Acknowledgment + +The work was supported in part by the National Natural Science Foundation of China under Grant (623B2073, 62301310), the Ministry of Education, Singapore, under the funding of MOE-T2EP20123-0006, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426. + +# References + +[1] Recommendation 500-10: Methodology for the subjective assessment of the quality of television pictures. ITU-R Rec. BT.500, 2000. 3 +[2] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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A comprehensive study of multimodal large language models for image quality assessment. arXiv preprint arXiv:2403.10854, 2024. 5 +[50] Lin Xu, Yilin Zhao, Daquan Zhou, Zhijie Lin, See Kiong Ng, and Jiashi Feng. Pllava: Parameter-free llava extension from images to videos for video dense captioning, 2024. 1, 2, 6 +[51] Jiabo Ye, Haiyang Xu, Haowei Liu, Anwen Hu, Ming Yan, Qi Qian, Ji Zhang, Fei Huang, and Jingren Zhou. mplug-owl3: Towards long image-sequence understanding + +in multi-modal large language models. arXiv preprint arXiv:2408.04840, 2024.1,6 +[52] Qinghao Ye, Haiyang Xu, Guohai Xu, Jiabo Ye, Ming Yan, Yiyang Zhou, Junyang Wang, Anwen Hu, Pengcheng Shi, Yaya Shi, Chaoya Jiang, Chenliang Li, Yuanhong Xu, Hehong Chen, Junfeng Tian, Qian Qi, Ji Zhang, and Fei Huang. mPLUG-Owl: Modularization empowers large language models with multimodality. 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Q-boost: On visual quality assessment ability of low-level multi-modality foundation models. In 2024 IEEE International Conference on Multimedia and Expo Workshops (ICMEW), pages 1-6. IEEE, 2024. 3 +[61] Zicheng Zhang, Haoning Wu, Chunyi Li, Yingjie Zhou, Wei Sun, Xiongkuo Min, Zijian Chen, Xiaohong Liu, Weisi Lin, and Guangtao Zhai. A-bench: Are lmm masters at evaluating ai-generated images? arXiv preprint arXiv:2406.03070, 2024. 3, 5 +[62] Zicheng Zhang, Haoning Wu, Erli Zhang, Guangtao Zhai, and Weisi Lin. A benchmark for multi-modal foundation models on low-level vision: from single images to pairs. CoRR, abs/2402.07116, 2024. 2 +[63] Zicheng Zhang, Haoning Wu, Yingjie Zhou, Chunyi Li, Wei Sun, Chaofeng Chen, Xiongkuo Min, Xiaohong Liu, Weisi + +Lin, and Guangtao Zhai. Lmm-pcqa: Assisting point cloud quality assessment with lmm. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 7783-7792, 2024. 3 +[64] Qi Zheng, Zhengzhong Tu, Xiaoyang Zeng, Alan C Bovik, and Yibo Fan. A completely blind video quality evaluator. IEEE Signal Processing Letters, 29:2228-2232, 2022. 2 +[65] Xunchu Zhou, Xiaohong Liu, Yunlong Dong, Tengchuan Kou, Yixuan Gao, Zicheng Zhang, Chunyi Li, Haoning Wu, and Guangtao Zhai. Light-vqa+: A video quality assessment model for exposure correction with vision-language guidance. arXiv preprint arXiv:2405.03333, 2024. 2 +[66] Hanwei Zhu, Xiangjie Sui, Baoliang Chen, Xuelin Liu, Peilin Chen, Yuming Fang, and Shiqi Wang. 2AFC prompting of large multimodal models for image quality assessment. CoRR, abs/2402.01162, 2024. 5 +[67] Orr Zohar, Xiaohan Wang, Yann Dubois, Nikhil Mehta, Tong Xiao, Philippe Hansen-Estruch, Licheng Yu, Xiaofang Wang, Felix Juefei-Xu, Ning Zhang, et al. 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To address this oversight, we introduce Q-Bench-Video in this paper, a new benchmark specifically designed to evaluate LMMs' proficiency in discerning video quality. a) To ensure video source diversity, Q-Bench-Video encompasses videos from natural scenes, AI-generated content (AIGC), and computer graphics (CG). b) Building on the traditional multiple-choice questions format with the Yes-or-No and What-How categories, we include Open-ended questions to better evaluate complex scenarios. Additionally, we incorporate the video pair quality comparison question to enhance comprehensiveness. c) Beyond the traditional Technical, Aesthetic, and Temporal distortions, we have expanded our evaluation aspects to include the dimension of AIGC distortions, which addresses the increasing demand for video generation. Finally, we collect a total of 2,378 question-answer pairs and test them on 12 open-source & 5 proprietary LMMs. Our findings indicate that while LMMs have a foundational understanding of perceptual video quality, their performance remains incomplete and imprecise, with a notable discrepancy compared to the performance of human beings. Through Q-Bench-Video, we seek to catalyze community interest, stimulate further research, and unlock the untapped potential of LMMs to close the gap in video quality understanding." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 632, + 135, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 632, + 135, + 643 + ], + "spans": [ + { + "bbox": [ + 56, + 632, + 135, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "As the field of artificial intelligence (AI) continues to evolve, Large Multi-modal Models (LMMs) [4, 16, 19, 50, 51] are progressively utilized in high-level video understanding tasks. These models have shown remarkable capabilities in analyzing and interpreting the semantic content of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 242, + 555, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 242, + 555, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 242, + 555, + 399 + ], + "type": "text", + "content": "videos, such as classifying objects, identifying actions, and recognizing events. However, the aspect of video quality, which is vital for optimizing compression and transmission systems, enhancing viewer experience, and establishing standards for high-quality video generation, has received less attention. Although numerous LMM video benchmarks[8, 10, 23] have been developed to assess the semantic understanding of videos by LMMs comprehensively, benchmarks systematically targeting video quality are still lacking. Additionally, while semantic understanding is closely linked to high-level video information, the perception and understanding of low-level information are crucial in video quality [5, 25] as well." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 403, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 556, + 715 + ], + "type": "text", + "content": "To address this gap, we introduce Q-Bench-Video, a novel benchmark specifically designed to systematically evaluate the video quality understanding of LMMs. As illustrated in Fig. 1, our benchmark encompasses a wide range of video content, including natural scenes, AI-generated content (AIGC), and computer graphics (CG), ensuring diversity in video sources. In addition, to maintain a reasonable distribution of source video quality, we employ uniform sampling from video datasets that contain subjective quality annotations. This approach guarantees comprehensive coverage of the quality spectrum while avoiding imbalanced quality distributions. Moreover, we extend beyond traditional video evaluations by incorporating both multiple-choice questions (MCQs) and open-ended questions. This enables a more thorough analysis of LMMs' ability to discern video quality across diverse scenarios. We further introduce a new evaluation dimension specifically tailored to assess distortions related to AIGC, which are increasingly prominent in video generation tasks. Recognizing the importance of quality comparison settings in real-world applications, such as camera parameter optimization and AIGC video generation, we further incorporate video pairs to facilitate quality comparison assessment as well. In total, we collect 1800 videos and annotated 2,378 question-answer pairs for validation, creating a robust framework for systematic evaluation on video quality understanding." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3229" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 119, + 69, + 492, + 299 + ], + "blocks": [ + { + "bbox": [ + 119, + 69, + 492, + 299 + ], + "lines": [ + { + "bbox": [ + 119, + 69, + 492, + 299 + ], + "spans": [ + { + "bbox": [ + 119, + 69, + 492, + 299 + ], + "type": "image", + "image_path": "49212cba749d85d0982fa30e92ed050f1353de4a77333a2c7277c300f82cf5ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 307, + 555, + 363 + ], + "lines": [ + { + "bbox": [ + 54, + 307, + 555, + 363 + ], + "spans": [ + { + "bbox": [ + 54, + 307, + 555, + 363 + ], + "type": "text", + "content": "Figure 1. The construction overview of the proposed Q-Bench-Video. To ensure diversity in video content, we collect natural scenes, AIGC, and CG videos from video quality assessment datasets as depicted in (a). To achieve a balanced quality distribution among the sampled videos, we employ uniform sampling for quality control. As indicated in (c-1) and (c-2), we utilize three types of questions (Yes-or-No, What-How, Open-ended) and address a comprehensive range of quality concerns including Technical, Aesthetic, Temporal, and AIGC distortions. Additionally, we incorporate the video pairs comparison task to enhance the comprehensiveness of the benchmark." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 372, + 295, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 372, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 372, + 295, + 468 + ], + "type": "text", + "content": "Through the rigorous experiment, we demonstrate that while LMMs show promise in video quality assessment, their performance lags significantly behind human-level understanding. By offering a systematic and thorough evaluation of LMMs' video quality perception, Q-Bench-Video aims to foster research in this underexplored area and push the boundaries of LMM capabilities on video quality understanding. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 472, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "text", + "content": "- We introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to assess the video quality understanding capabilities of LMMs. This benchmark includes a diverse collection of source videos and ensures a balanced quality distribution, complemented by human-crafted question-answer annotations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 544, + 295, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 615 + ], + "type": "text", + "content": "- Our evaluation framework spans four key quality dimensions: Technical, Aesthetic, Temporal, and AIGC distortions, which offers a holistic evaluation approach to video quality assessment. Uniquely, Q-Bench-Video enhances its utility by introducing the task of video pairs comparison, which sets it apart from existing video benchmarks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 616, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 616, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 616, + 295, + 712 + ], + "type": "text", + "content": "- We conduct a comprehensive evaluation using both proprietary and open-source LMMs to measure their effectiveness in understanding video quality. The results expose notable deficiencies in current LMMs, while also shedding light on performance variations across different quality dimensions. These findings provide critical insights and suggest promising directions for future enhancements in the field of video quality understanding." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 371, + 406, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 371, + 406, + 384 + ], + "spans": [ + { + "bbox": [ + 314, + 371, + 406, + 384 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 392, + 481, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 481, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 481, + 403 + ], + "type": "text", + "content": "2.1. Video LMMs and Benchmarks" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 410, + 555, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 555, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 555, + 613 + ], + "type": "text", + "content": "The rapid advancement of Large Multi-modal Models (LMMs) in recent years [4, 28-30, 52, 56, 67] has showcased their remarkable perception and cognitive abilities across various multimodal benchmarks for images [9, 33, 35, 47, 62]. As development progresses, the focus of visual analysis has gradually shifted from images to videos. Early efforts [22, 27, 31, 50] aimed at unlocking the video understanding potential of LMMs have yielded promising results. However, initial video-based benchmarks [24, 34, 41] typically concentrated on specific aspects of video comprehension, falling short of fully capturing the performance of these models due to limitations such as a lack of diversity in video types and inadequate coverage of temporal dynamics. In response, recent video benchmarks [8, 10] have moved toward a more comprehensive evaluation of LMMs. Nonetheless, these efforts focus on high-level semantic understanding without systematic exploration of video quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 623, + 459, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 623, + 459, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 623, + 459, + 635 + ], + "type": "text", + "content": "2.2. Video Quality Assessment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "Video Quality Assessment (VQA) is a task aimed at quantifying video scores based on visual quality. Initially, early VQA methods employ hand-crafted features extracted from videos and regress the features into quality scores [17, 20, 26, 40, 58, 64, 65]. With the emergence of deep neural networks, a shift occurs as numerous methods adopted deep" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3230" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 107, + 553, + 192 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "type": "text", + "content": "Table 1. Overview of the diverse video source datasets in the Q-Bench-Video. We consider various video content types, including natural scenes, AIGC, and CG videos. The term 'MOS' denotes that the videos are annotated via Mean Opinion Scores under ITU standards [1]. We have conducted uniform sampling based on their quality labels to ensure a balanced quality distribution." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 107, + 553, + 192 + ], + "lines": [ + { + "bbox": [ + 56, + 107, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 56, + 107, + 553, + 192 + ], + "type": "table", + "html": "
Video TypeVideo Source DatasetMOSQuality ConcernsSampled SizeFull Dataset Size
Natural (1000)LSVQ [54]✓Spatial & Temporal60039K
MaxWell [46]✓Spatial & Temporal & Aesthetic3504.5K
WaterlooSQoE-III [6]✓Quality-of-Experience20450
WaterlooSQoE-IV [7]✓Quality-of-Experience301,350
AIGC (600)T2VQA-DB [17]✓Quality & Text Alignment20010K
VideoFeedback [13]×Quality & Text Alignment40037.6K
CG (200)LIVE-YT-Gaming [55]✓Visual Quality200600
", + "image_path": "131b6371b83ab8872d999dbfe8136d5ee280d48fc2aa42f7a4afd25cf6535347.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 201, + 294, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 201, + 294, + 381 + ], + "spans": [ + { + "bbox": [ + 54, + 201, + 294, + 381 + ], + "type": "text", + "content": "learning techniques for VQA tasks [18, 21, 38, 42]. As the field progresses, newer methods begin incorporating considerations for both temporal dynamics and aesthetic qualities, leading to a more holistic approach to video quality analysis [3, 12, 43, 45, 59]. Moreover, the evolution of large-scale models has further revolutionized VQA methodologies. Many recent approaches have redefined the traditional quality assessment process into a quality question-answering format [11, 15, 48, 60, 63]. This adaptation leverages the substantial prior knowledge embedded in large models to enhance the precision of quality quantification [61]. Despite these technological advances, VQA still grapples with challenges in providing interpretable quality scores and deepening the understanding of how models perceive and analyze video quality more comprehensively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 390, + 201, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 390, + 201, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 390, + 201, + 403 + ], + "type": "text", + "content": "3. Benchmark Construction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 409, + 178, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 409, + 178, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 178, + 422 + ], + "type": "text", + "content": "3.1. Benchmark Principle" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 426, + 295, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 594 + ], + "type": "text", + "content": "The Q-Bench-Video is designed based on three guiding principles: (1) It encompasses a broad spectrum of video content, including natural scenes, AIGC, and CG videos. (2) It ensures a comprehensive and representative sampling process across a wide quality range, enhancing the benchmark's overall effectiveness. (3) It primarily focuses on the aspects of video quality that significantly influence the viewing experience, including technical, aesthetic, temporal, and AIGC distortions. This significantly differs from other video benchmarks that prioritize semantic understanding. Additionally, the video pair quality comparison is integrated to address the challenges associated with comparing video quality. The overall construction process can be clearly overviewed in Fig. 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 600, + 194, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 194, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 194, + 612 + ], + "type": "text", + "content": "3.2. Source Videos Collection" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": "As shown in Table 1, the source videos are primarily gathered from video quality assessment datasets. We selected videos from these datasets for two main reasons: (1) These datasets have inherently considered the diversity of quality features during video selection; (2) These datasets possess quality annotations that adhere to ITU standards [1] (with the exception of VideoFeedback), which allow us to accurately and authentically sample videos." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 201, + 555, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 555, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 555, + 262 + ], + "type": "text", + "content": "Our sampling method primarily employs a uniform approach, extracting videos evenly from each dataset based on the quality range. Moreover, considering the current popularity of AIGC and CG videos, we have also incorporated a selection of these video types. (More details in the Supp.)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 269, + 430, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 430, + 282 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 430, + 282 + ], + "type": "text", + "content": "3.3. Benchmark Designs" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "text", + "content": "In this section, we provide a detailed description of the design of Q-Bench-Video. In this benchmark, the metastructure tuple " + }, + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "inline_equation", + "content": "(\\mathrm{V},\\mathbb{Q},\\mathbb{A},\\mathbb{C})" + }, + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "text", + "content": " of each data item can be decomposed into several components: the video object V (which can be a single video or a pair of videos), the video quality query " + }, + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}" + }, + { + "bbox": [ + 313, + 285, + 554, + 370 + ], + "type": "text", + "content": ", the set of possible answers A, and the correct answer C. The question samples are listed in Fig. 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 376, + 408, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 408, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 408, + 388 + ], + "type": "text", + "content": "3.3.1. Question Types" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 391, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 641 + ], + "type": "text", + "content": "I) Yes-or-No Questions. The basic Yes-or-No questions are designed to prompt LMMs to make binary judgments on video quality queries, typically limited to the answers Yes or No. To address the potential bias in LMMs that may skew towards yes responses, we employ an annotation adjustment process, which modifies the questions and correct answers if necessary (based on the Yes-or-No ratio). This process ensures that the distribution of correct answers, either Yes or No, remains balanced at about " + }, + { + "bbox": [ + 313, + 391, + 555, + 641 + ], + "type": "inline_equation", + "content": "50\\%:50\\%" + }, + { + "bbox": [ + 313, + 391, + 555, + 641 + ], + "type": "text", + "content": " ratio in the end. This balanced approach allows for a more accurate assessment of LMMs' performance on Yes-or-No questions. II) What-How Questions. The What-How questions are commonly utilized in benchmarks for LMMs. The What questions focus on identifying specific distortions (e.g., What is the most apparent distortion in this video?). On the other hand, the How questions are employed to distinguish the finer details of distortion levels (e.g., How is the overall clarity of this video?). Including both What and How questions allows Q-Bench-Video to thoroughly and meticulously evaluate LMMs' ability on identifying video distortions and evaluating the distortion levels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "III) Open-ended Questions. It's important to note that the two types of questions previously mentioned require LMMs to select the correct answer from a predefined set. However, in many real-world scenarios, Open-ended Questions, which do not restrict responses to a predefined set, are often more necessary and challenging for LMMs (e.g., What" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "type": "text", + "content": "3231" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 102, + 83, + 113, + 129 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 102, + 83, + 113, + 129 + ], + "spans": [ + { + "bbox": [ + 102, + 83, + 113, + 129 + ], + "type": "text", + "content": "Yes-or-No" + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 116, + 80, + 296, + 127 + ], + "blocks": [ + { + "bbox": [ + 116, + 80, + 296, + 127 + ], + "lines": [ + { + "bbox": [ + 116, + 80, + 296, + 127 + ], + "spans": [ + { + "bbox": [ + 116, + 80, + 296, + 127 + ], + "type": "image", + "image_path": "4e1dafae2a53d12b2460431ec69a4c3f2477118643a23a6ba12692870b3b1d61.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 118, + 128, + 275, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 128, + 275, + 148 + ], + "spans": [ + { + "bbox": [ + 118, + 128, + 275, + 148 + ], + "type": "text", + "content": "Q: Does the fabric in this video exhibit good clarity and proper lighting?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 118, + 148, + 154, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 148, + 154, + 158 + ], + "spans": [ + { + "bbox": [ + 118, + 148, + 154, + 158 + ], + "type": "text", + "content": "A. 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None of the options B. Blurriness" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 319, + 148, + 469, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 148, + 469, + 156 + ], + "spans": [ + { + "bbox": [ + 319, + 148, + 469, + 156 + ], + "type": "text", + "content": "C. Overexposure D. 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Yes" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 103, + 364, + 113, + 403 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 103, + 364, + 113, + 403 + ], + "spans": [ + { + "bbox": [ + 103, + 364, + 113, + 403 + ], + "type": "text", + "content": "Temporal" + } + ] + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 117, + 365, + 298, + 410 + ], + "blocks": [ + { + "bbox": [ + 117, + 365, + 298, + 410 + ], + "lines": [ + { + "bbox": [ + 117, + 365, + 298, + 410 + ], + "spans": [ + { + "bbox": [ + 117, + 365, + 298, + 410 + ], + "type": "image", + "image_path": "c8f8fefd1c1da1386506db86f85fa7612664991c9dbb34d01990fbe2e31d7755.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 120, + 412, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 412, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 120, + 412, + 287, + 419 + ], + "type": "text", + "content": "Q: Does this video have severe camera shake?" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 121, + 422, + 148, + 440 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 121, + 422, + 145, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 422, + 145, + 428 + ], + "spans": [ + { + "bbox": [ + 121, + 422, + 145, + 428 + ], + "type": "text", + "content": "A. 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Yes" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 300, + 268, + 310, + 311 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 300, + 268, + 310, + 311 + ], + "spans": [ + { + "bbox": [ + 300, + 268, + 310, + 311 + ], + "type": "text", + "content": "Aesthetic" + } + ] + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 313, + 268, + 491, + 308 + ], + "blocks": [ + { + "bbox": [ + 313, + 268, + 491, + 308 + ], + "lines": [ + { + "bbox": [ + 313, + 268, + 491, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 491, + 308 + ], + "type": "image", + "image_path": "ee6edd4d27097cb1e69945ec3c75031ad03dcaccb5d7ce361bbc6c5e28e6e7d6.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 310, + 502, + 360 + ], + "type": "list", + "angle": 0, + "index": 32, + "blocks": [ + { + "bbox": [ + 313, + 310, + 453, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 453, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 453, + 319 + ], + "type": "text", + "content": "Q: what feelings does this video evoke?" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 320, + 502, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 502, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 502, + 360 + ], + "type": "text", + "content": "Open-ended Response: This video depicts a castle in a unnatural and twisted jungle, where the plants have bizarre, sharp structures and dull colors. The atmosphere is eerie and terrifying, creating a sense of horror" + } + ] + } + ], + "index": 31 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 302, + 376, + 312, + 399 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 302, + 376, + 312, + 399 + ], + "spans": [ + { + "bbox": [ + 302, + 376, + 312, + 399 + ], + "type": "text", + "content": "AIGC" + } + ] + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 313, + 365, + 492, + 411 + ], + "blocks": [ + { + "bbox": [ + 313, + 365, + 492, + 411 + ], + "lines": [ + { + "bbox": [ + 313, + 365, + 492, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 492, + 411 + ], + "type": "image", + "image_path": "c014e3070272177d3bf155e730e17f63be7213b6c3266b7fbf1f53abd3ec5e13.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + } + ], + "index": 34 + }, + { + "bbox": [ + 315, + 412, + 512, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 412, + 512, + 420 + ], + "spans": [ + { + "bbox": [ + 315, + 412, + 512, + 420 + ], + "type": "text", + "content": "Q: What is the most impactual quality issue of this video?" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 315, + 422, + 363, + 441 + ], + "type": "list", + "angle": 0, + "index": 38, + "blocks": [ + { + "bbox": [ + 315, + 422, + 349, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 422, + 349, + 430 + ], + "spans": [ + { + "bbox": [ + 315, + 422, + 349, + 430 + ], + "type": "text", + "content": "A. Noise" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 315, + 432, + 363, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 432, + 363, + 441 + ], + "spans": [ + { + "bbox": [ + 315, + 432, + 363, + 441 + ], + "type": "text", + "content": "C. Blurriness" + } + ] + } + ], + "index": 37 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 389, + 422, + 496, + 441 + ], + "type": "list", + "angle": 0, + "index": 41, + "blocks": [ + { + "bbox": [ + 389, + 422, + 496, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 422, + 496, + 430 + ], + "spans": [ + { + "bbox": [ + 389, + 422, + 496, + 430 + ], + "type": "text", + "content": "B. Incorrect human structure" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 389, + 432, + 449, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 432, + 449, + 441 + ], + "spans": [ + { + "bbox": [ + 389, + 432, + 449, + 441 + ], + "type": "text", + "content": "D. 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Good" + } + ] + } + ], + "index": 50 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 101, + 553, + 112, + 576 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 101, + 553, + 112, + 576 + ], + "spans": [ + { + "bbox": [ + 101, + 553, + 112, + 576 + ], + "type": "text", + "content": "Joint" + } + ] + } + ], + "index": 52 + }, + { + "type": "image", + "bbox": [ + 116, + 544, + 297, + 589 + ], + "blocks": [ + { + "bbox": [ + 116, + 544, + 297, + 589 + ], + "lines": [ + { + "bbox": [ + 116, + 544, + 297, + 589 + ], + "spans": [ + { + "bbox": [ + 116, + 544, + 297, + 589 + ], + "type": "image", + "image_path": "30d454897ba18a168f5a1b91325a7f4bafc851082e165ad5493fe506f9f2b994.jpg" + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 691, + 555, + 736 + ], + "lines": [ + { + "bbox": [ + 55, + 691, + 555, + 736 + ], + "spans": [ + { + "bbox": [ + 55, + 691, + 555, + 736 + ], + "type": "text", + "content": "Figure 2. The visualization samples from Q-Bench-Video, with the question-answer content most representative of each subcategory being underlined. It is important to note that, regarding quality concerns, a single question-answer annotation may not only focus on one distortion dimension. Therefore, the distortion visualization examples shown in (b) primarily highlight instances that are most closely aligned with the mentioned distortion types." + } + ] + } + ], + "index": 70, + "angle": 0, + "type": "image_caption" + } + ], + "index": 53 + }, + { + "bbox": [ + 123, + 590, + 272, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 590, + 272, + 600 + ], + "spans": [ + { + "bbox": [ + 123, + 590, + 272, + 600 + ], + "type": "text", + "content": "Q: Are both videos primarily in cold colors?" + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 103, + 608, + 113, + 649 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 103, + 608, + 113, + 649 + ], + "spans": [ + { + "bbox": [ + 103, + 608, + 113, + 649 + ], + "type": "text", + "content": "Compare" + } + ] + } + ], + "index": 55 + }, + { + "type": "image", + "bbox": [ + 117, + 603, + 298, + 649 + ], + "blocks": [ + { + "bbox": [ + 117, + 603, + 298, + 649 + ], + "lines": [ + { + "bbox": [ + 117, + 603, + 298, + 649 + ], + "spans": [ + { + "bbox": [ + 117, + 603, + 298, + 649 + ], + "type": "image", + "image_path": "c5d78593dcf3d6c0c606d5d76913a91ddafd2553c5f4fee7b87dca9c0d7370f9.jpg" + } + ] + } + ], + "index": 56, + "angle": 0, + "type": "image_body" + } + ], + "index": 56 + }, + { + "bbox": [ + 122, + 651, + 326, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 651, + 326, + 660 + ], + "spans": [ + { + "bbox": [ + 122, + 651, + 326, + 660 + ], + "type": "text", + "content": "Q: Is the exposure of the first video more balanced than" + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 302, + 560, + 313, + 573 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 302, + 560, + 313, + 573 + ], + "spans": [ + { + "bbox": [ + 302, + 560, + 313, + 573 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 306, + 467, + 315, + 509 + ], + "type": "title", + "angle": 270, + "lines": [ + { + "bbox": [ + 306, + 467, + 315, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 315, + 509 + ], + "type": "text", + "content": "Referring" + } + ] + } + ], + "index": 59 + }, + { + "type": "image", + "bbox": [ + 318, + 465, + 498, + 511 + ], + "blocks": [ + { + "bbox": [ + 318, + 465, + 498, + 511 + ], + "lines": [ + { + "bbox": [ + 318, + 465, + 498, + 511 + ], + "spans": [ + { + "bbox": [ + 318, + 465, + 498, + 511 + ], + "type": "image", + "image_path": "237481856f8363e477745139de9dbd98d80c519f4f82e73230e9076e0c5b9b2e.jpg" + } + ] + } + ], + "index": 60, + "angle": 0, + "type": "image_body" + } + ], + "index": 60 + }, + { + "bbox": [ + 320, + 514, + 501, + 542 + ], + "type": "list", + "angle": 0, + "index": 63, + "blocks": [ + { + "bbox": [ + 320, + 514, + 501, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 514, + 501, + 532 + ], + "spans": [ + { + "bbox": [ + 320, + 514, + 501, + 532 + ], + "type": "text", + "content": "Q: Is the main character in this game video rendered in high details but with relatively low clarity?" + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 320, + 533, + 351, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 533, + 351, + 542 + ], + "spans": [ + { + "bbox": [ + 320, + 533, + 351, + 542 + ], + "type": "text", + "content": "A. 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No" + } + ] + } + ], + "index": 66 + }, + { + "type": "image", + "bbox": [ + 318, + 603, + 498, + 649 + ], + "blocks": [ + { + "bbox": [ + 318, + 603, + 498, + 649 + ], + "lines": [ + { + "bbox": [ + 318, + 603, + 498, + 649 + ], + "spans": [ + { + "bbox": [ + 318, + 603, + 498, + 649 + ], + "type": "image", + "image_path": "32091bbc093ec6593e35f02cccb503bca1b6ab9f5acdbefaa7ceda4fd937ac7b.jpg" + } + ] + } + ], + "index": 67, + "angle": 0, + "type": "image_body" + } + ], + "index": 67 + }, + { + "bbox": [ + 407, + 651, + 473, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 407, + 651, + 473, + 660 + ], + "spans": [ + { + "bbox": [ + 407, + 651, + 473, + 660 + ], + "type": "text", + "content": "A. No B. Yes" + } + ] + } + ], + "index": 68 + }, + { + "bbox": [ + 242, + 670, + 381, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 242, + 670, + 381, + 682 + ], + "spans": [ + { + "bbox": [ + 242, + 670, + 381, + 682 + ], + "type": "text", + "content": "(c) Single Video vs. Video Pairs" + } + ] + } + ], + "index": 69 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3232" + } + ] + } + ], + "index": 71 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": "are the possible factors that lead to the low clarity of this video? Please list and explain.). By adopting this form of questioning, we can better assess an LMM's ability to perceive video quality in real-world conditions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 126, + 160, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 126, + 160, + 138 + ], + "spans": [ + { + "bbox": [ + 55, + 126, + 160, + 138 + ], + "type": "text", + "content": "3.3.2. Quality Concerns" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 141, + 295, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 141, + 295, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 141, + 295, + 224 + ], + "type": "text", + "content": "It's important to recognize that video quality can be influenced by multiple factors on some occasions. Therefore, a query tuple " + }, + { + "bbox": [ + 55, + 141, + 295, + 224 + ], + "type": "inline_equation", + "content": "(\\mathrm{V},\\mathrm{Q},\\mathrm{A},\\mathrm{C})" + }, + { + "bbox": [ + 55, + 141, + 295, + 224 + ], + "type": "text", + "content": " does not need to be restricted to a single concern. It can address multiple concerns simultaneously. For instance, the question Is this video clear and well-composed? can be seen as evaluating both technical and aesthetic quality understanding." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 225, + 295, + 428 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 225, + 295, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 225, + 295, + 320 + ], + "spans": [ + { + "bbox": [ + 55, + 225, + 295, + 320 + ], + "type": "text", + "content": "I) Technical Distortions. Technical distortions refer to the low-level degradation in video quality that arises from the limitations of recording, compression, and transmission [37, 54]. These distortions often include artifacts such as blurring, noise, compression artifact, exposure, etc., which are directly tied to the technical processes used in video production and delivery. The CG-specific distortions related to geometry and texture are taken into consideration." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 321, + 295, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 321, + 295, + 428 + ], + "spans": [ + { + "bbox": [ + 55, + 321, + 295, + 428 + ], + "type": "text", + "content": "II) Aesthetic Distortions. Aesthetic distortions involve deviations from the intended visual style, artistic design, or creative intent that negatively affect the viewer's perception of the video [14, 44]. These distortions can include aspects such as confusing color, poor composition, lighting inconsistencies, or distracting elements that reduce the overall aesthetic appeal. Unlike technical distortions, aesthetic distortions are subjective and might be affected by viewer preference, cultural context, or artistic norms." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 429, + 295, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 429, + 295, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 429, + 295, + 548 + ], + "type": "text", + "content": "III) Temporal Distortions. Temporal distortions are related to the degradation of visual quality over time, impacting the fluidity and consistency of the video [36]. These distortions manifest as issues like screen shake, flickering, motion inconsistency, frame drops, and stuttering that result from unstable shooting devices, dramatically changing lighting conditions, and unstable bitrate environments [46]. Such disruptions hinder the viewer's natural perception of the video, leading to a disjointed and unpleasant viewing experience, especially in live-streaming scenarios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "type": "text", + "content": "IV) AIGC Distortions. AIGC distortions pertain to imperfections and unnaturalness specifically arising from the generation of video content through AI models [32, 61]. These distortions may include unnatural textures, inconsistent lighting, uncanny facial features, or unrealistic object behavior that result from limitations or biases in the training data, model architecture, or generative process. These distortions are unique to AI-generated content and require specialized evaluation metrics that consider both the technical and perceptual quality aspects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 674, + 204, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 204, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 204, + 686 + ], + "type": "text", + "content": "3.3.3. Single Videos & Video Pairs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Accurately comparing and jointly analyzing the quality of video pairs is sometimes more crucial than assessing the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 319, + 71, + 557, + 141 + ], + "blocks": [ + { + "bbox": [ + 319, + 71, + 557, + 141 + ], + "lines": [ + { + "bbox": [ + 319, + 71, + 557, + 141 + ], + "spans": [ + { + "bbox": [ + 319, + 71, + 557, + 141 + ], + "type": "image", + "image_path": "3f334b3ac00be8d23553e4e8bc98550a22921b8fe7d4a6a165dae9d87050a0b0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 143, + 529, + 152 + ], + "lines": [ + { + "bbox": [ + 345, + 143, + 529, + 152 + ], + "spans": [ + { + "bbox": [ + 345, + 143, + 529, + 152 + ], + "type": "text", + "content": "(a) Annotation GUI for single videos of Q-Bench-Video." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 319, + 153, + 557, + 225 + ], + "blocks": [ + { + "bbox": [ + 319, + 153, + 557, + 225 + ], + "lines": [ + { + "bbox": [ + 319, + 153, + 557, + 225 + ], + "spans": [ + { + "bbox": [ + 319, + 153, + 557, + 225 + ], + "type": "image", + "image_path": "eab9b8817af0798538f50eb836fe01b6501ca11d061219ed2b4a0b3dcb56cc5e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 347, + 228, + 526, + 237 + ], + "lines": [ + { + "bbox": [ + 347, + 228, + 526, + 237 + ], + "spans": [ + { + "bbox": [ + 347, + 228, + 526, + 237 + ], + "type": "text", + "content": "(b) Annotation GUI for video pairs of Q-Bench-Video." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 247, + 555, + 345 + ], + "lines": [ + { + "bbox": [ + 313, + 247, + 555, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 555, + 345 + ], + "type": "text", + "content": "Figure 3. Illustration of the annotation GUIs for Q-Bench-Video. (a) shows the interface for annotating single videos, where the annotator can select the question type and play the videos using the Video Play button. The annotator can also switch to the next and previous annotation with the Next and Previous buttons. (b) presents the interface for annotating video pairs. When the annotator presses the Video Play button, the video pairs are played sequentially, with a five-second gray screen serving as an interval between the two videos." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 373, + 555, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 555, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 555, + 445 + ], + "type": "text", + "content": "quality of a single video, especially in scenarios such as performance tests in video compression and quality control in video generation (In which it is more important to find out Which video is better in visual quality and why?) [49, 66]. Therefore, in Q-Bench-Video, we include video quality queries for both single videos and video pairs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 447, + 556, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 556, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 556, + 567 + ], + "type": "text", + "content": "1) Single Videos. Queries related to single videos can primarily be categorized into two types: a) Global perception, which involves questions about the overall visual quality of the video, such as How is the overall contrast of this video? b) Referring perception, which focuses on the visual quality of specific elements within the video, like querying What is the most apparent distortion when the player strikes the ball? Through these approaches, we aim to comprehensively evaluate the LMMs' ability to perceive both the overall and localized aspects of video quality." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 570, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 713 + ], + "type": "text", + "content": "II) Video Pairs. Firstly, to ensure that the comparison of video pairs is clear and meaningful, comparisons are only made between videos from the same source, such as videos from natural sources being paired together while CG videos and AIGC videos are not being paired. There are mainly two types of video pair categories: a) Joint analysis, which involves understanding the shared quality features of the video pairs, for example, such as asking Are both videos blurry? b) Comparative analysis, which involves comparing the quality dimension across two videos, such as How does the level of brightness in the first video compare to that in the second one? It is important to note" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3233" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 71, + 299, + 294 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 299, + 294 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 299, + 294 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 299, + 294 + ], + "type": "image", + "image_path": "8ec1451ad71d55a9769b3dfcbba26607309af2914313e044d5d5d70ba4818e32.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 299, + 253, + 309 + ], + "lines": [ + { + "bbox": [ + 107, + 299, + 253, + 309 + ], + "spans": [ + { + "bbox": [ + 107, + 299, + 253, + 309 + ], + "type": "text", + "content": "(a) Overall performance on Q-Bench-Video." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 550, + 295 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 550, + 295 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 550, + 295 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 550, + 295 + ], + "type": "image", + "image_path": "6a784e6997abe34e6b511c01dace16c2b2cc4bb8b2ceb740a1d0aa466ad59670.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 299, + 513, + 309 + ], + "lines": [ + { + "bbox": [ + 351, + 299, + 513, + 309 + ], + "spans": [ + { + "bbox": [ + 351, + 299, + 513, + 309 + ], + "type": "text", + "content": "(b) Subcategory performance on Q-Bench-Video." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 318, + 555, + 363 + ], + "lines": [ + { + "bbox": [ + 54, + 318, + 555, + 363 + ], + "spans": [ + { + "bbox": [ + 54, + 318, + 555, + 363 + ], + "type": "text", + "content": "Figure 4. A concise summary of the LMMs' performance on Q-Bench-Video. (a) provides a comparison detailing the overall performance of humans and 17 selected LMMs, including both proprietary and open-source models. (b) illustrates a radar chart that outlines the performance of the top-2 proprietary LMMs (GPT-4o & Gemini 1.5 Pro) and open-source LMMs (mPLUG-Owl3 & LLaVA-OneVision) across various subcategories within Q-Bench-Video." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 384, + 295, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 384, + 295, + 444 + ], + "spans": [ + { + "bbox": [ + 54, + 384, + 295, + 444 + ], + "type": "text", + "content": "that we further categorize comparisons based on the difference in quality labels of the videos involved into coarse-grain (with relatively more significant visual quality differences) and fine-grain (with relatively minor visual quality differences) comparisons. (More details in the Supp.)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 448, + 228, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 228, + 459 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 228, + 459 + ], + "type": "text", + "content": "3.3.4. Questions & Answers Annotation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 463, + 295, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 463, + 295, + 547 + ], + "spans": [ + { + "bbox": [ + 54, + 463, + 295, + 547 + ], + "type": "text", + "content": "The annotation process of Q-Bench-Video is conducted in a well-controlled laboratory environment. A total of 8 experts are employed and trained to ensure the consistency of the annotations. The experts are required to watch the videos in their entirety before making annotations. Each annotated question-answer pair is then reviewed by at least three other experts to ensure its validity and accuracy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 552, + 235, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 235, + 565 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 235, + 565 + ], + "type": "text", + "content": "3.4. Benchmark Setting & Evaluation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 570, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 570, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 570, + 295, + 713 + ], + "type": "text", + "content": "Unless specifically stated otherwise, for Video LMMs we typically analyze by uniformly sampling 16 frames from the video, while for Image LMMs, the sampling is reduced to 8 frames. It's worth noting that if the LMMs are not compatible with the specified number of sampling frames (e.g. if they cannot support up to 8-frame input), we will use the official default settings for testing. For Yes-or-No and What-How questions, if the LMMs can accurately respond with the options, we directly record the accuracy of the responses as results. If the LMMs cannot provide option-based answers, we implement a GPT-assisted evaluation strategy to help judge the accuracy of the answers. For Open-ended" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 384, + 555, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 444 + ], + "type": "text", + "content": "questions, since the answers are open-ended and cannot be directly quantified for accuracy, we also employ the GPT-assisted evaluation strategy. This involves GPT scoring the responses based on their accuracy, completeness, and relevance compared to the annotated answer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 475, + 462, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 462, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 462, + 489 + ], + "type": "text", + "content": "4. Results of Q-Bench-Video" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 502, + 437, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 437, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 437, + 515 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 526, + 555, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 555, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 555, + 647 + ], + "type": "text", + "content": "LMMs Participants. A total of 17 LMMs (12 Open-source LMMs and 5 Proprietary LMMs) are included for validation, which includes a) 3 Open-source Image LMMs: LLaVA-Next [30], LLaVA-v1.5 [28], and mPLUG-Owl2 [53]; b) 9 Open-source Video LMMs: mPLUG-Owl3 [51], LLaVA-OneVision [19], InternVL-Chat [4], VILA1.5 [16], PLLaVA [50], LLaVA-Next-Video [57], ST-LLM [31], Video-LLaVA [27], and VideoChat2 [22]; c) 5 Proprietary LMMs: Gemini 1.5 Flash, Gemini 1.5 Pro [39], GPT-4o mini, GPT-4o, and GPT-4 Turbo [2]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 653, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 713 + ], + "type": "text", + "content": "Subsets Split. The Q-Bench-Video is divided into test (1,186 question-answer items) and dev (1,192 question-answer items) subsets. The correct answers will be released and proprietary for the dev and test subsets. All discussions and analyses are based on the test subset." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3234" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 105, + 555, + 344 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "type": "text", + "content": "Table 2. Results on the test subset for the video quality perception ability of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively. The Open-ended questions are excluded for Random guess. (Performance of the test subset is in the Supp.)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 105, + 555, + 344 + ], + "lines": [ + { + "bbox": [ + 55, + 105, + 555, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 105, + 555, + 344 + ], + "type": "table", + "html": "
Sub-categoriesQuestion TypesQuality ConcernsOverall↑
LMM (LLM)Yes-or-No↑What-How↑Open-ended↑Tech.↑Aes.↑Temp.↑AIGC↑
Random guess w/o Open-ended50.00%25.00%/37.10%37.31%37.25%37.22%37.79%
Human86.57%81.00%77.11%79.22%80.23%82.72%86.21%81.56%
Open-source Image LMMs
LLaVA-Next (Mistral-7B)62.83%45.14%33.69%46.38%57.86%47.84%48.46%47.52%
LLaVA-v1.5 (Vicuna-v1.5-13B)52.98%46.44%37.01%45.77%58.12%45.30%46.48%45.64%
mPLUG-Owl2 (LLaMA2-7B)59.19%39.07%31.19%42.07%52.38%41.71%39.37%43.43%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)60.48%56.39%39.48%52.68%58.31%52.05%43.49%52.39%
LLaVA-OneVision (Qwen2-7B)61.34%53.88%39.15%49.35%64.15%50.68%44.30%51.70%
InternVL-Chat (Vicuna-7B)66.02%52.13%33.93%48.42%52.73%50.59%53.12%51.11%
VILA1.5 (LLaMA3-8B)61.95%46.00%39.60%47.85%57.85%45.65%42.57%49.41%
PLLAVA (Mistral-7B)65.63%52.33%32.23%49.69%61.32%50.96%53.64%50.39%
LLaVA-Next-Video (Mistral-7B)61.34%45.95%38.10%49.03%60.94%46.97%49.40%48.69%
ST-LLM (Vicuna-v1.1-7B)44.63%28.50%32.78%34.99%46.11%34.28%34.02%35.42%
Video-LLaVA (Vicuna-v1.5-7B)64.67%40.79%29.11%43.25%54.04%42.38%42.76%43.49%
VideoChat2 (Mistral-7B)56.09%29.98%34.99%39.26%50.02%38.25%35.88%40.56%
Proprietary LMMs
Gemini 1.5 Flash65.48%56.79%47.51%54.11%66.58%53.51%50.22%56.78%
Gemini 1.5 Pro65.42%62.35%47.57%56.80%69.61%53.38%53.26%58.63%
GPT-4o mini62.95%50.93%42.10%49.38%60.90%48.43%41.71%52.20%
GPT-4o67.48%58.79%49.25%56.01%58.57%65.39%52.22%58.70%
GPT-4 Turbo66.93%58.33%40.15%54.23%66.23%54.00%52.04%56.36%
", + "image_path": "c75f255fbe0a30741193f9b17ad793c5454b7e6620e35c4c739fead3f32472f6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 358, + 119, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 358, + 119, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 119, + 371 + ], + "type": "text", + "content": "4.2. Findings" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 377, + 295, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 295, + 461 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 295, + 461 + ], + "type": "text", + "content": "The overall performance and subcategory comparisons (human vs. top-performing LMMs) on Q-Bench-Video can be quickly glanced at Fig. 4. Detailed performance across the subcategories for each LMM are shown in Table 2 (Question Types & Quality Concerns) and Table 3 (Single Videos vs. Video Pairs) respectively. The findings are organized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": "1) General Performance. Human>Proprietary LMMs>Open-source LMMs>Random guess. From the performance results presented in Table 2, we observe that nearly all LMMs significantly outperform random guess, demonstrating their basic capability to understand video quality. Among the open-source LMMs, the recently released mPLUG-Owl3 achieves the highest overall performance at " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "52.39\\%" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": ", even slightly surpassing GPT-4o mini " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "(52.20\\%)" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": ", followed closely by LLaVA-OneVision " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "(51.70\\%)" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": " and InternVL-Chat " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "(51.11\\%)" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": ". Image LMMs deliver moderate performance. Although they outperform some Video LMMs, the gap between them and the latest Video LMMs is still notable. Benefiting from larger training datasets and more parameters, proprietary LMMs (except GPT-4o mini) outperform all open-source models. However, even the best-performing model, GPT-4o, which achieved an overall performance of " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "58.70\\%" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": ", still lags behind human performance by " + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "inline_equation", + "content": "22.86\\%" + }, + { + "bbox": [ + 55, + 462, + 295, + 715 + ], + "type": "text", + "content": ". This gap highlights that, despite the advancements in current state-of-the-art LMMs on video general understanding, there remains a significant need for improvement in video quality understanding ability." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "content": "2) Question Types. Open-ended questions are more challenging for LMMs. From Table 2, a discernible hierarchy in task difficulty for video quality assessment emerges for both humans and LMMs, arranged as follows: Open-ended " + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "inline_equation", + "content": ">" + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "content": " What-How " + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "inline_equation", + "content": ">" + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "content": " Yes-or-No. It is crucial to highlight that while humans exhibit a performance decline in Open-ended tasks by approximately " + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "inline_equation", + "content": "9.46\\%" + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "content": " compared to Yes-or-No tasks, and about " + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "inline_equation", + "content": "3.89\\%" + }, + { + "bbox": [ + 313, + 358, + 555, + 539 + ], + "type": "text", + "content": " compared to What-How tasks, these reductions are markedly less pronounced than those observed in LMMs for the Open-ended questions. This disparity underscores a significant proficiency gap between LMMs' capability in handling straightforward, closed-form questions and their effectiveness in navigating the complexities of real-world problem-solving on open-ended questions, particularly in the context of video quality evaluation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "type": "text", + "content": "3) Quality Concerns. LMMs exhibit unbalanced performance across different types of distortions. From Table 2, it is evident that humans are particularly good at identifying AIGC distortions, while LMMs demonstrate stronger performance in detecting Aesthetic distortions. This distinction likely stems from the inherent sensitivity of humans to the conspicuous unnaturalness of AIGC distortions, which readily draws human attention. In contrast, Aesthetic distortions, which often involve high-level semantic nuances, align more closely with the training contexts of LMMs, enabling them to excel in this area. However, LMMs face challenges with AIGC distortions due to insufficient exposure to such anomalies during their pretraining phases, specific architectural constraints, and imperfections" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3235" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 94, + 555, + 338 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": "Table 3. Results on the test subset for the video quality perception ability across single videos and video pairs of LMMs. The best performance is marked in bold and the second performance is underlined for Open-source and Proprietary LMMs respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 94, + 555, + 338 + ], + "lines": [ + { + "bbox": [ + 55, + 94, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 94, + 555, + 338 + ], + "type": "table", + "html": "
Sub-categoriesSingle VideosVideo Pairs
LMM (LLM)Global↑Referring↑Overall↑Joint↑Compare -fine↑Compare -coarse↑Overall↑
Random guess w/o Open-ended36.49%38.61%37.71%40.56%37.94%36.83%38.00%
Human78.87%80.43%79.65%84.90%87.34%89.11%87.56%
LLaVA-Next (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
LLaVA-v1.5 (Vicuna-v1.5-13B)47.99%51.94%50.10%27.72%34.60%42.12%36.42%
mPLUG-Owl2 (LLaMA2-7B)46.86%43.51%45.07%51.49%37.10%40.28%43.69%
Open-source Video LMMs
mPLUG-Owl3 (Qwen2-7B)52.46%50.60%51.47%48.03%54.90%59.20%55.31%
LLaVA-OneVision (Qwen2-7B)51.56%48.43%49.89%53.48%58.10%63.36%59.41%
InternVL-Chat (Vicuna-7B)51.15%51.86%51.52%48.85%51.10%49.20%49.79%
VILA1.5 (LLaMA3-8B)52.35%47.37%49.69%56.11%45.40%48.04%48.84%
PLLAVA (Mistral-7B)51.44%55.49%53.60%40.36%50.40%54.16%49.90%
LLaVA-Next-Video (Mistral-7B)51.33%50.20%50.73%38.03%48.00%42.48%43.46%
ST-LLM (Vicuna-v1.1-7B)36.54%36.49%36.51%28.03%36.80%32.08%32.87%
Video-LLaVA (Vicuna-v1.5-7B)45.46%44.67%45.04%49.36%42.00%43.00%44.01%
VideoChat2 (Mistral-7B)43.52%38.27%40.72%57.23%44.40%41.64%45.93%
Proprietary LMMs
Gemini 1.5 Flash58.00%53.18%55.43%46.59%65.30%68.84%62.77%
Gemini 1.5 Pro52.36%61.41%57.19%45.43%65.30%72.00%63.55%
GPT-4o mini52.67%48.96%50.69%44.00%60.50%63.88%58.02%
GPT-4o58.75%54.18%56.31%46.93%67.30%69.24%63.80%
GPT-4 Turbo57.36%52.80%54.93%46.13%62.50%64.80%59.84%
", + "image_path": "70cd380eab22623a5c2847c8b09d9c22dbf9b39968c28aea7a314b7519024cb3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 354, + 294, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 354, + 294, + 474 + ], + "spans": [ + { + "bbox": [ + 54, + 354, + 294, + 474 + ], + "type": "text", + "content": "in the generation process. In the case of proprietary LMMs, their performance on Technical and Temporal distortions appear comparably consistent, indicating a uniform capability in recognizing these two types of distortions. Nonetheless, across all four subcategories, LMMs exhibit a notable performance disparity compared to humans, with varying degrees of accuracy among the different types of distortions. This variability highlights the need for significant enhancements in LMMs' abilities to accurately understand and interpret various distortion types." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 474, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 474, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 474, + 295, + 713 + ], + "type": "text", + "content": "4) Single Videos vs. Video Pairs. LMMs demonstrate superior capabilities in comparing video quality. From Table 3, we observe that for single videos, LMMs achieve similar performance in Global and Referring quality perception (except for Gemini 1.5 Pro), without any significant trend of the performance for one subcategory over the other. This suggests that LMMs have comparable abilities in perceiving both Global video quality and Referring video quality. In terms of comparison, however, LMMs clearly outperform their performance on single video analysis and joint analysis. Notably, LMMs perform significantly better in the Compare-coarse subcategory, where video pairs have more pronounced quality differences, than in the Compare-fine subcategory. This highlights that LMMs are more adept at comparing video quality than analyzing the quality of single videos. This advantage in comparative assessment can be attributed to the inherent clarity in pairwise comparisons, which provide explicit contrasts, as opposed to the more ambiguous nature of evaluating a single video. Both humans and LMMs exhibit enhanced performance in com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "type": "text", + "content": "parative tasks. Although there is still a significant accuracy gap between LMMs and humans, LMMs show promising potential as effective tools for comparing video quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 399, + 389, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 389, + 412 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 389, + 412 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 419, + 555, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 555, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 555, + 468 + ], + "type": "text", + "content": "1) Subjectivity can not be fully avoided in annotations for aspects like aesthetics. 2) As video generation advances, new models may show different distortions, which might potentially make parts of Q-Bench-Video outdated." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 498, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 498, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 498, + 556, + 715 + ], + "type": "text", + "content": "In this paper, we introduce Q-Bench-Video, the first comprehensive benchmark explicitly designed to evaluate Large Multi-modal Models' (LMMs) understanding of video quality. Our benchmark includes a diverse range of video types, questions that challenge multiple aspects of video quality, and a holistic evaluation framework encompassing Technical, Aesthetic, Temporal, and AIGC distortions. Through extensive experimentation with 17 open-source and proprietary LMMs, we find that while LMMs show promise in discerning video quality, their performance remains significantly below human-level understanding, especially when addressing Open-ended questions and AIGC-specific distortions. These findings highlight the current limitations of LMMs in video quality perception and underscore the need for further advancements in this area. By offering Q-Bench-Video, we aim to stimulate future research and drive improvements in the field, bridging the gap between LMM and human video quality understanding." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3236" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "type": "text", + "content": "The work was supported in part by the National Natural Science Foundation of China under Grant (623B2073, 62301310), the Ministry of Education, Singapore, under the funding of MOE-T2EP20123-0006, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "spans": [ + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 193, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 193, + 294, + 225 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 193, + 294, + 225 + ], + "spans": [ + { + "bbox": [ + 61, + 193, + 294, + 225 + ], + "type": "text", + "content": "[1] Recommendation 500-10: Methodology for the subjective assessment of the quality of television pictures. 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However, despite their impressive capabilities, the substantial computational costs of these large-scale models pose significant challenges for real-world deployment. Post-Training Quantization (PTQ) emerges as a promising solution, enabling model compression and accelerated inference for pretrained models, without the costly retraining. However, research on DiT quantization remains sparse, and existing PTQ frameworks, primarily designed for traditional diffusion models, tend to suffer from biased quantization, leading to notable performance degradation. In this work, we identify that DiTs typically exhibit significant spatial variance in both weights and activations, along with temporal variance in activations. To address these issues, we propose Q-DiT, a novel approach that seamlessly integrates two key techniques: automatic quantization granularity allocation to handle the significant variance of weights and activations across input channels, and sample-wise dynamic activation quantization to adaptively capture activation changes across both timesteps and samples. Extensive experiments conducted on ImageNet and VBench demonstrate the effectiveness of the proposed Q-DiT. Specifically, when quantizing DiT-XL/2 to W6A8 on ImageNet $(256\\times 256)$ , Q-DiT achieves a remarkable reduction in FID by 1.09 compared to the baseline. Under the more challenging W4A8 setting, it maintains high fidelity in image and video generation, establishing a new benchmark for efficient, high-quality quantization in DiTs.", + "bbox": [ + 89, + 318, + 485, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 818, + 220, + 832 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models [6, 16, 26, 32] have emerged as a powerful base model for various tasks, ranging from computer", + "bbox": [ + 89, + 844, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vision, natural language processing, multi-modal modeling, etc. The architectural design of diffusion models has evolved significantly. Traditionally, these models employed UNet [28] architecture due to their efficiency in managing hierarchical feature representations. However, recent advances have shifted the focus towards diffusion transformers (DiTs) [27], and notable examples, including Stable Diffusion 3 [8] and Sora [4], have demonstrated its superior performance and scalability for complex generative tasks.", + "bbox": [ + 511, + 287, + 906, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite their success, a significant limitation of DiTs lies in their inherently high latency in the inference. The iterative denoising process, although effective, requires numerous sampling steps, making real-time or large-scale applications computationally intensive. Model quantization offers a particularly promising avenue to reduce inference latency, and Post Training Quantization (PTQ) is particularly appealing for large models as it eliminates the need for retraining. However, the application of quantization techniques to transformer-based diffusion models remains limited. Existing quantization methods for diffusion models [12, 13, 30] primarily focus on UNet architecture and heavily rely on reconstruction-based methods, challenging to scale to large models [21, 25].", + "bbox": [ + 511, + 426, + 908, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we propose a customized quantization method for DiTs. To achieve this, we first explore the distinct characteristics of DiT models and identify two key issues in DiT quantization: significant variance of weights and activations across input channels and varying activations across different timesteps. Therefore, we propose Q-DiT, consisting of a fine-grained group quantization strategy and a dynamic activation quantization strategy. These two designs address the aforementioned challenges individually and collaboratively contribute to the proposed quantization framework (see Fig. 1).", + "bbox": [ + 511, + 641, + 908, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In particular, for the first challenge, a promising solution is group quantization [23, 40] which can manage high-magnitude values at the group level. However, we observe the non-monotonicity in group sizes, e.g., reducing group size (increasing group number) does not always lead to better performance. Consequently, we employ an evolution-", + "bbox": [ + 511, + 810, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28306", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8ba232458c181f61a64d5aa55aa7f84d4a4a61e4bd166bef56dc6c384821c7e3.jpg", + "image_caption": [ + "Figure 1. Overview of the proposed Q-DiT. The weights and activations within each layer are quantized with the same group size. Group size configurations allocated for each layer are based on the evolutionary search results, which are guided by the FID/FVD score between the real samples and samples generated by the quantized model. The activations are dynamically quantized during runtime." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 885, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ary search algorithm to configure group sizes for quantization across different model layers. This method utilizes the Fréchet Inception Distance (FID) and Fréchet Video Distance (FVD) as metrics to directly correlate the quantization effects with the visual quality of generated samples, enabling a more targeted and effective quantization strategy. The evolutionary approach not only identifies the optimal group sizes but also ensures that the quantization process adheres to predefined computational constraints, effectively balancing performance with efficiency.", + "bbox": [ + 88, + 424, + 480, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second challenge, varying activations across timesteps, highlights that quantization parameters calibrated at specific timesteps often fail to generalize across all timesteps. To address this variability, Q-DiT adopts a sample-wise dynamic activation quantization mechanism, which adapts with sample granularity to the changing distribution of activations throughout the diffusion process. This approach significantly reduces quantization error by adjusting quantization parameters on-the-fly, ensuring high-quality image/video generation with minimal overhead.", + "bbox": [ + 89, + 578, + 482, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 107, + 731, + 447, + 744 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce Q-DiT, an accurate PTQ method designed for DiTs. This method employs fine-grained group quantization to effectively manage input channel variance in both weights and activations, and it adopts sample-wise dynamic activation quantization to adapt to activation variations across different timesteps and samples.", + "- We identify that the default group size configuration is sub-optimal and propose an evolutionary search strategy to optimize group size allocation, which enhances the efficiency and efficacy of the quantization process." + ], + "bbox": [ + 89, + 748, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments on ImageNet and VBench demonstrate that Q-DiT achieves lossless compression under a W6A8 configuration and minimal degradation under W4A8 for image and video generation, highlighting its superior performance.", + "bbox": [ + 513, + 424, + 906, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 512, + 653, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model quantization. Model quantization is a widely used technique to reduce the model size and accelerate its inference speed by converting the model's weights and activations from high-precision floating-point numbers to lower-precision numbers. There are two primary approaches to quantization: Quantization-Aware Training (QAT) [2, 5, 9] and Post-Training Quantization (PTQ) [21, 25]. QAT integrates the quantization process directly into the fine-tuning phase, leveraging STE [1] to simultaneously optimize quantizer parameters and model parameters during fine-tuning. This approach restores the model's performance degradation caused by quantization. However, QAT is resource-intensive because it necessitates fine-tuning the model on the original training dataset. In contrast, PTQ is far more efficient and practical, as it does not require model retraining. PTQ operates by utilizing a small calibration dataset to adjust the quantization parameters for weights and activations, facilitating significant model compression with minimal effort. Although PTQ is highly efficient, it can result in significant performance degradation when applied to low-bit quantization. Reconstruction-based method [21, 25] tries to minimize performance degradation by reducing the reconstruction error of each layer or each block. Although the reconstruction-based method performs well in CNN, they", + "bbox": [ + 511, + 537, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28307", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "are not easy to scale up to a large model.", + "bbox": [ + 89, + 90, + 359, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization of transformers. Quantization of transformers has been extensively researched in the contexts of both Vision Transformers (ViTs) and Large Language Models (LLMs). Specifically, PTQ4ViT [39] proposed the twin uniform quantizer to handle the special distributions of post-softmax and post-GELU activations. RepQ-ViT [22] used scale reparameterization to reduce the quantization error of activations. For LLM, weight-only quantization quantizes the weight to reduce the heavy memory movements to achieve better inference efficiency. GPTQ [10] reduced the bit-width to 4 bits per weight based on approximate second-order information with weight-only quantization. AWQ [23] proposed activation-aware weight quantization to reduce the quantization error of salient weight. On the other hand, weight-activation quantization further enhances inference efficiency by quantizing both weight and activation but has to face activation outliers. LLM.int8() [7] reduces the effect of outliers by keeping them in FP16 with mixed-precision computations. Outlier Suppression [35] reduces the quantization error of activations by using the non-scaling LayerNorm. However, these quantization techniques may not be directly applied to DiTs, due to their diffusion model characteristics.", + "bbox": [ + 89, + 106, + 483, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization of diffusion models. Diffusion models tend to have a slow inference speed due to the large number of sampling steps required. Consequently, some recent studies have focused on accelerating these models through quantization techniques. PTQ4DM [30] and Q-diffusion [20] discover activation variance across different denoising steps and adopt reconstruction-based methods for quantization. PTQD [13] finds the correlation between the quantization noise and model output and proposes variance schedule calibration to rectify the uncorrelated part. TDQ [31] utilizes an MLP layer to estimate the activation quantization parameters for each step. TMPQ-DM [33] further reduces the sequence length of timestep along with the quantization to reduce the overall costs. PTQ4DiT [36] introduces a PTQ method tailored for Diffusion Transformers, addressing challenges like extreme channel magnitudes and temporal activation variability using Channel-wise Salience Balancing (CSB) and Spearman's $\\rho$ -guided Salience Calibration (SSC), while achieving W4A8 quantization. Comparison table of PTQ methods for diffusion models can be found in the supplementary materials. These methods are unable to handle simultaneously the characteristics of the transformer architecture and the dynamics of activation during denoising process, leading to significant performance drops.", + "bbox": [ + 89, + 454, + 483, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Observations of DiT Quantization", + "text_level": 1, + "bbox": [ + 89, + 844, + 398, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We find directly applying recent UNet-based quantization methods to quantize DiTs will lead to significant perfor", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/56fcc118ba3e243ec54de1bdf6b54ee5ac74f379aefc67c7b9aaf36c622a3cd5.jpg", + "image_caption": [ + "(a) Weight distribution" + ], + "image_footnote": [], + "bbox": [ + 527, + 99, + 650, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/61476ed5356a5a7a00860ffd6c47684c899ae1b2aa003dae932688300582547d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 99, + 777, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9b06358e12dd14e4e02a95a5fedbae79030dc2a548cc00fd7a084e6f921b0a38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 782, + 99, + 903, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/abc490331d84ba7678fade15ad5172266af3ddff8af7f0917d2f6418ae452779.jpg", + "image_caption": [ + "(b) Activation distribution" + ], + "image_footnote": [], + "bbox": [ + 527, + 215, + 648, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/34c00deaa09cfd531fec1b77594226e5c6aacca2795354d2203c9291e61d1d7e.jpg", + "image_caption": [ + "Figure 2. Distributions of weights and activations in different layers of DiT-XL/2. The red peaks indicate higher values, while the blue areas represent lower values." + ], + "image_footnote": [], + "bbox": [ + 653, + 215, + 777, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/831ec507620b42bcc4a816955e4f1dd191d35892a1809f30f4fd87a6326d39ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 782, + 215, + 906, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mance degradation. To understand the underlying reasons, we explore the distinct characteristics of DiT models, particularly how they differ from UNet-based architectures in terms of weight and activation distributions.", + "bbox": [ + 511, + 402, + 903, + 463 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Observation 1: DiTs exhibit significant variance of weights and activations across input channels. As shown in Fig. 2a, the variance of weights and activations across input channels is much more significant than the output channels. This variance substantially affects quantization since common methods typically apply channel-wise quantization along the output channel for diffusion models [13, 30]. Besides, we also find outliers persist in specific channels of the activation, as shown in Fig. 2b. This suggests that, if we continue to use tensor-wise quantization, these outliers will significantly impact the quantization parameters, resulting in substantial quantization errors for non-outliers.", + "bbox": [ + 511, + 465, + 905, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Observation 2: Significant distribution shift of activations across timesteps. We observe that the distribution of activations in DiT models undergoes significant changes at different timesteps during the denoising process, as demonstrated in Fig. 3 and Fig. 4. Further, we discovered that this temporal shift also exhibits significant variability across different samples. The relevant experimental results are presented in the supplementary materials.", + "bbox": [ + 511, + 646, + 905, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 784, + 638, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use uniform quantization to quantize both weights and activations in this work, as it is more hardware-friendly [11, 19]. Particularly, uniform quantization divides the range of floating-point values into equally spaced intervals, and each interval is mapped to a discrete value. The uniform quantization function $Q$ that quantize input floating-point tensor", + "bbox": [ + 511, + 810, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28308", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9ec77b6571d217b06cb45ea71b43c087a0c1cc61b4ece03b8fd5fec3e67e530a.jpg", + "image_caption": [ + "Figure 3. Box plot showing the distribution of activation values across various timesteps (from 50 to 0) for the DiT-XL/2 model when generating one image from ImageNet at $256 \\times 256$ resolution.." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 480, + 189 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b47f3b99b034b37f957959805ad1af41e486e77b9e808468b34330a4d9b24a16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 273, + 287, + 372 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ccd99c2201626f426c5104301df2c78f5e4a896a7964979fa79f95aab806008f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 273, + 480, + 372 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a0743d833622abc53caa848a3bfec91d31f12c617b9347548c3be526a38f636c.jpg", + "image_caption": [ + "Figure 4. Standard deviation of activations in MLP and attention layers across different blocks over 50 timesteps for DiT-XL/2 when generating one image from ImageNet at $256 \\times 256$ resolution." + ], + "image_footnote": [], + "bbox": [ + 94, + 373, + 287, + 470 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/21babe4695157e0bcec82da16a8f44d855dbfc1bf598f90ddcc4afbf83bddbb1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 373, + 480, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{x}$ into $b$ bit integer tensor $\\hat{\\mathbf{x}}$ can be expressed as:", + "bbox": [ + 89, + 569, + 413, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = Q (\\mathbf {x}; b) = s \\cdot \\left(\\operatorname {c l i p} \\left(\\left\\lfloor \\frac {\\mathbf {x}}{s} \\right\\rfloor + Z, 0, 2 ^ {b} - 1\\right) - Z\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 595, + 482, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s = \\frac{\\max(\\mathbf{x}) - \\min(\\mathbf{x})}{2^b - 1}$ and $Z = -\\left\\lfloor \\frac{\\min(\\mathbf{x})}{s} \\right\\rfloor$ . Here, $\\lfloor \\cdot \\rceil$ is the round operation, $s$ is the scaling factor and $Z$ denotes the zero point.", + "bbox": [ + 89, + 633, + 483, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Method: Q-DiT", + "text_level": 1, + "bbox": [ + 89, + 703, + 248, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 1, the proposed Q-DiT involves two novel designs, including automatic quantization granularity allocation and dynamic activation quantization. Here we introduce them in the following parts.", + "bbox": [ + 89, + 729, + 483, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Automatic Quantization Granularity Allocation", + "text_level": 1, + "bbox": [ + 89, + 801, + 483, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Base solution. A straightforward solution to deal with the input channel-wise variance, as highlighted in observation 1, is to apply input channel-wise quantization, using different quantization parameters for each channel. However,", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/27b7df83a10252cfd75bd4da37018f75b7e73a74f8dfa4f29a25e3fe4d7c740c.jpg", + "table_caption": [ + "Table 1. Quantization results with varying group sizes on ImageNet $256 \\times 256$ and $512 \\times 512$ ." + ], + "table_footnote": [], + "table_body": "
256×256512×512
GroupFID ↓sFID ↓GroupFID ↓sFID ↓
28825.1128.5428827.2428.16
12817.8720.4512822.7824.31
9619.9721.429620.7621.97
6417.6420.916420.9022.58
3216.4519.343219.6721.57
", + "bbox": [ + 553, + 128, + 864, + 236 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "this approach compromises computational efficiency during hardware deployment, as it prevents the full utilization of low-precision computation due to the need for repeated intermediate rescaling [3, 38].", + "bbox": [ + 511, + 246, + 906, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fine-grained group quantization. As discussed in recent LLM quantization work [23, 40], a compromise approach between input channel-wise quantization and tensor quantization is the group quantization. As shown in Fig. 1, the weight and activation matrices are divided into groups, and then we perform quantization for each group separately. Specifically, consider a matrix multiplication $\\mathbf{Y} = \\mathbf{X}\\mathbf{W}$ in a linear layer, where $\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{\\mathrm{in}}}$ and $\\mathbf{W} \\in \\mathbb{R}^{d_{\\mathrm{in}} \\times d_{\\mathrm{out}}}$ . The quantized value for each output element can be obtained by:", + "bbox": [ + 511, + 306, + 906, + 444 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {Y}} _ {i, j} = \\sum_ {k = 0} ^ {d _ {\\mathrm {i n}}} \\hat {\\mathbf {X}} _ {i, k} \\hat {\\mathbf {W}} _ {k, j} (2) \\\\ = \\sum_ {u = 0} ^ {d _ {\\mathrm {i n}} / g _ {l l} - 1} \\sum_ {v = 0} ^ {g _ {l l}} Q _ {u} ^ {\\mathbf {X}} \\left(\\mathbf {X} _ {i, u g _ {l l} + v}\\right) Q _ {u} ^ {\\mathbf {W}} \\left(\\mathbf {W} _ {u g _ {l l} + v, j}\\right), (3) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 455, + 906, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g_{ll}$ denotes the group size.", + "bbox": [ + 511, + 554, + 732, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Non-monotonicity in quantization group selection. Ideally, we can improve model performance by reducing the group size (i.e., increase the group number) because finer-grained quantization reduces quantization error. However, as shown in Tab. 1, smaller group sizes do not always improve results, demonstrating the existence of non-monotonicity in quantization groups. For instance, when the group size reduces from 128 to 96, the FID increases by about $11.8\\%$ , from 17.87 to 19.97, indicating a degradation in the quality of generated images. This suggests that there is an optimal group size configuration that can achieve better quantization effects with the same average group size or achieve the same quantization results with a larger average group size. Additionally, the sensitivity of each layer in the model varies. By assigning different group sizes to different layers, we can achieve high efficiency and quality in both model performance and image generation.", + "bbox": [ + 511, + 568, + 906, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Automatic group allocation. The main challenge in group size allocation is identifying its impact on generation performance. Previous works on mixed precision quantization focus on identifying sensitivity indicators [21, 34] for each layer, such as the MSE between the quantized layer and the", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28309", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "full precision layer, and then transforming this into an integer linear programming (ILP) problem for optimization. However, we find that a smaller MSE does not necessarily correspond to a reduced performance degradation for DiT quantization, indicating that the previous methods may be ineffective.", + "bbox": [ + 89, + 90, + 480, + 180 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To this end, we directly use the FID as our metric for image generation, defined as follows:", + "bbox": [ + 89, + 181, + 482, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\mathbf {g}) = \\operatorname {F I D} \\left(R, G _ {\\mathbf {g}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 220, + 482, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, for video generation models, we use the FVD as our metric:", + "bbox": [ + 89, + 246, + 482, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\mathbf {g}) = \\operatorname {F V D} \\left(R, G _ {\\mathbf {g}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 276, + 482, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{g} = \\{g_1, g_2, \\dots, g_N\\}$ is the layer-wise group size configuration and $N$ is the number of quantized layers. $R$ and $G_{\\mathbf{g}}$ denote the real samples and the samples generated by the quantized model, respectively. We then employ an evolutionary algorithm to optimize the following objective function:", + "bbox": [ + 89, + 297, + 483, + 386 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} ^ {*} = \\underset {\\mathbf {g}} {\\arg \\min } L (\\mathbf {g}), \\text {s . t .} B (\\mathbf {g}) \\leq N _ {\\text {b i t o p s}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 396, + 482, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $B(\\cdot)$ is the measurement of bit-operations (BitOps), and $N_{\\text{bitops}}$ is the predefined threshold.", + "bbox": [ + 89, + 430, + 482, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This approach allows us to better capture the nuanced impacts of group size on quantization performance, leading to improved outcomes in both efficiency and image quality. The algorithm is located in Alg. 1.", + "bbox": [ + 89, + 460, + 483, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Sample-wise Dynamic Activation Quantization", + "text_level": 1, + "bbox": [ + 89, + 529, + 482, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In UNet-based diffusion quantization, previous studies either allocate a set of quantization parameters for all activations at each timestep [12] or design a multi-layer perceptron (MLP) [31] to predict quantization parameters based on the timestep. However, due to observation 2, these methods are not compatible with our fine-grained quantization because assigning quantization parameters to each group at every timestep results in considerable memory overheads. Specifically, for a sampler with 50 timesteps, the memory overhead could reach up to $39\\%$ of the full-precision model's size.", + "bbox": [ + 89, + 551, + 482, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the recent work in LLM optimization [37], we design an on-the-fly dynamic quantization approach for activations. Specifically, during inference, the quantization parameters for each group of the activations are calculated based on their min-max values. For a given sample $i$ at timestep $t$ , the quantization parameters for the activation $\\mathbf{x}_{i,t}$ can be expressed as:", + "bbox": [ + 89, + 717, + 483, + 823 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i, t} = \\frac {\\operatorname* {m a x} \\left(\\mathbf {x} _ {i , t}\\right) - \\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{2 ^ {b} - 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 830, + 482, + 862 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {i, t} = - \\left\\lfloor \\frac {\\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{s _ {i , t}} \\right\\rceil . \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 864, + 482, + 897 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Automatic quantization granularity allocation of Q-DiT" + ], + "code_body": "Input: Group size search space $S_{g}$ ; number of layers $L$ ; population size $N_{p}$ ; iterations $N_{iter}$ ; mutation probability $p$ ; Constraint $N_{bitops}$ \nInitialize population $\\mathcal{P} = \\{\\mathbf{g}^j\\}_{j=1}^{N_p}$ , where each element in configuration $\\mathbf{g}^j \\in \\mathbb{R}^L$ is randomly selected from $S_{g}$ ; Initialize TopK candidate set $S_{TopK} = \\emptyset$ ; \nfor $t = 1,2,\\ldots,N_{iter}$ do \nfor $i = 1,2,\\ldots,N_p$ do \nCalculate FID (or FVD) for each configuration $\\mathbf{g}^j$ based on Eq. 4 (or Eq. 5); Update $S_{TopK}$ with $K$ configurations, according to ranked FID (or FVD) scores; \nClear population $\\mathcal{P} = \\emptyset$ ; \nrepeat \n $\\mathbf{g}_{cross} = \\text{CrossOver}(S_{TopK})$ with probability $1 - p$ ; \nAppend $\\mathbf{g}_{cross}$ to $\\mathcal{P}$ if $B(\\mathbf{g}_{cross}) < N_{bitops}$ ; \nuntil $|\\mathcal{P}| = N_p/2$ ; \nrepeat \n $\\mathbf{g}_{mutate} = \\text{Mutate}(S_{TopK})$ with probability $p$ ; \nAppend $\\mathbf{g}_{mutate}$ to $\\mathcal{P}$ if $B(\\mathbf{g}_{mutate}) < N_{bitops}$ ; \nuntil $|\\mathcal{P}| = N_p$ ; \nGet the best group size configuration $\\mathbf{g}^{\\text{best}}$ , and use it to quantize the model; \nreturn quantized model", + "bbox": [ + 522, + 126, + 883, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, we integrate the dynamic quantization with min-max computation into the prior operator, which can benefit from the operator fusion and the overhead becomes negligible compared to the costly matrix multiplications in transformer blocks. A detailed analysis is provided in the supplementary materials.", + "bbox": [ + 511, + 594, + 906, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 513, + 700, + 645, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 513, + 726, + 702, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image generation. We first evaluate our Q-DiT on the image generation task, closely following the evaluation setting used in DiT [27]. We use the pre-trained DiT-XL/2 models with image resolutions of $256 \\times 256$ and $512 \\times 512$ , converting them to FP16 as our full precision baseline model. For fast and accurate sampling, we adopt the DDIM sampler [32] with 50 and 100 sampling steps. Performance is also evaluated both with and without classifier-free guidance [15]. Note that \"cfg\" denotes the classifier-free guidance scale. We sample 10K images for both ImageNet", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28310", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c04b8bb046db4f1bea78d74ef4217ef265454a24f23f7edb5cdbd389652b792e.jpg", + "table_caption": [ + "Table 2. Results on image generation. We show the quantization results of DiT-XL/2 on ImageNet ${256} \\times {256}$ and ${512} \\times {512}$ . 'W/A' indicates the bit-width of weight and activation, respectively." + ], + "table_footnote": [], + "table_body": "
ModelBit-width (W/A)MethodSize (MB)FID ↓sFID ↓IS ↑Precision ↑
DiT-XL/2\n256×256\n(steps = 100)16/16FP134912.4019.11116.680.6605
6/8PTQ4DM50817.8625.3392.240.6077
RepQ-ViT50827.7420.9163.410.5600
TFMQ-DM50822.3327.4472.740.5869
PTQ4DiT50815.2121.34105.030.6440
G4W+P4A52016.7224.61100.090.6123
Ours51812.2118.48117.750.6631
4/8PTQ4DM339213.6685.113.260.0839
RepQ-ViT339224.1481.243.250.0373
TFMQ-DM339143.4761.095.610.0497
PTQ4DiT33928.9034.5665.730.4931
G4W+P4A35125.4825.5773.460.5392
Ours34715.7619.8498.780.6395
DiT-XL/2\n256×256\nsteps = 100\ncfg = 1.5)16/16FP13495.3117.61245.850.8077
6/8PTQ4DM5088.4125.56196.730.7622
RepQ-ViT50810.7718.53163.110.7264
TFMQ-DM5088.8723.52194.080.7737
PTQ4DiT5085.3418.48209.900.8047
G4W+P4A5206.4119.52225.480.7705
Ours5185.3217.40243.950.8044
4/8PTQ4DM339215.6886.633.240.0741
RepQ-ViT339226.6077.933.610.0337
TFMQ-DM339141.9056.016.240.0439
PTQ4DiT3397.7522.01190.380.7292
G4W+P4A3517.6620.76193.760.7261
Ours3476.4018.60211.720.7609
DiT-XL/2\n512×512\nSteps = 50\ncfg = 1.5)16/16FP13496.2718.45204.470.8343
6/8PTQ4DM5089.8426.57164.910.8215
RepQ-ViT5088.3019.19158.800.8153
TFMQ-DM5088.3417.94162.160.8262
PTQ4DiT5087.6918.86178.340.8121
G4W+P4A5207.2819.62185.920.8143
Ours5176.2418.36202.480.8341
4/8PTQ4DM33988.4550.8026.790.3206
RepQ-ViT33979.6949.7629.460.3413
TFMQ-DM33954.6144.2758.770.4215
PTQ4DiT33911.6922.86117.340.7121
G4W+P4A3519.9820.76156.070.7840
Ours3477.8219.60174.180.8127
", + "bbox": [ + 205, + 123, + 792, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$256 \\times 256$ and ImageNet $512 \\times 512$ in each setting, and employ four metrics in our experiments, including Fréchet Inception Distance (FID) [14], spatial FID (sFID) [29], Inception Score (IS), and Precision.", + "bbox": [ + 89, + 690, + 482, + 751 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Video generation. We also evaluate Q-DiT on video generation, with the STDiT3 model from the Open-Sora project [41]. Specifically, we sample five 2-second videos for each prompt in the VBench prompt suite [18] using a 30-step rectified flow scheduler with a CFG scale of 7.0. The results are assessed across 16 dimensions provided by VBench.", + "bbox": [ + 89, + 755, + 482, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare Q-DiT with five strong baselines:", + "bbox": [ + 89, + 849, + 473, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1) PTQ4DM [30]: A method specifically designed for UNet-based diffusion models, focusing on calibration of", + "bbox": [ + 91, + 869, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "activations.", + "bbox": [ + 535, + 691, + 614, + 703 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2) RepQ-ViT [22]: A technique developed for the quantization of ViTs, aiming to reduce quantization errors in transformer activations.", + "3) TFMQ-DM [17]: A PTQ framework specifically developed for diffusion models to preserve temporal features during quantization.", + "4) PTQ4DiT [36]: A tailored PTQ approach for DiTs that addresses the quantization challenges through CSB and SSC.", + "5) G4W+P4A: A robust baseline we build in this work for both video and image generation tasks, utilizing GPTQ [10] for weight quantization and PTQ4DM for" + ], + "bbox": [ + 513, + 705, + 903, + 886 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28311", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/37409a49908db81050f7b9d453d7d5b51fd7ffdd6d6dc5007030f73681c84ca2.jpg", + "table_caption": [ + "Table 3. Results on video generation. We show the quantization results of STDiT3 on VBench. Higher metrics indicate better performance." + ], + "table_footnote": [], + "table_body": "
MethodBit-width (W/A)Subject ConsistencyOverall ConsistencyTemporal StyleAppearance StyleSceneSpatial RelationshipColorHuman Action
FP16/160.95220.26670.25070.23520.40940.34410.78640.8680
G4W+P4A4/80.94440.26280.24890.23440.39240.32650.76570.8600
Ours4/80.94980.26630.25110.23460.38710.38100.79470.8620
MethodBit-width (W/A)Multiple ObjectsObject ClassImaging QualityAesthetic QualityDynamic DegreeMotion SmoothnessTemporal FlickeringBackground Consistency
FP16/160.41430.83830.58290.51730.61390.98550.99170.9678
G4W+P4A4/80.35400.82250.57300.50180.56390.98490.98950.9651
Ours4/80.39040.84750.58120.51600.61670.98590.99150.9687
", + "bbox": [ + 120, + 109, + 874, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "activation quantization.", + "bbox": [ + 114, + 292, + 267, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Others. Q-DiT applies asymmetric quantization for both weights and activations, and uses GPTQ [10] for weight quantization. A default group size of 128 is adopted, with optimal group size allocation for each layer determined through evolutionary search. The search space for group size $S_{g}$ is {32, 64, 128, 192, 288}. Note that the group size for weights and activations within the same layer should be the same. For the evaluation metric during the search process, we compute the FID using 500 images and the FVD using 100 videos. These sample sizes were empirically chosen to ensure a strong correlation with the final metric evaluations.", + "bbox": [ + 93, + 309, + 480, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Main Results", + "text_level": 1, + "bbox": [ + 93, + 500, + 227, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image generation results. The quantitative results for image generation are shown in Tab. 2. Specifically, in experiments conducted on ImageNet at a resolution of $256 \\times 256$ , the PTQ4DM, RepQ-ViT, TFMQ-DM, PTQ4DiT and G4W+P4A methods exhibit significant performance degradation at a bit-width of W6A8. In contrast, Q-DiT shows marked improvements over PTQ4DM under the W6A8 setting, effectively minimizing the impact of quantization. Notably, Q-DiT is closely aligned with the full-precision configuration, achieving an FID of 12.21 and an IS of 117.75. These results highlight the effectiveness of our method in achieving near-lossless compression in the W6A8 quantization setting. When the bit-width is reduced to W4A8, the performance disparities among the methods become more pronounced. In particular, the other five baselines have severe performance degradation, while our method substantially outperforms them, dramatically reducing quantization loss with an FID of 15.76 and an IS of 98.78. This demonstrates a significant preservation of quality and diversity at lower bit-widths, highlighting the robustness of our approach under stringent quantization constraints. Across varying steps (100 and 50) and classifier-free guidance scales, our method consistently shows superior performance, closely emulating the full-precision model metrics. The evaluation on the ImageNet $512 \\times 512$", + "bbox": [ + 93, + 523, + 480, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dataset demonstrates consistent trends with the $256 \\times 256$ dataset, indicating that Q-DiT can also perform well in high-resolution image generation. Visual demonstrations in Fig. 5 further illustrate that our method maintains superior image generation quality compared to the baseline.", + "bbox": [ + 516, + 292, + 903, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Video generation results. Tab. 3 shows the results for video generation. Under a stringent W4A8 quantization setting, our method consistently outperforms G4W+P4A in 15 out of 16 metrics, exhibiting minimal degradation compared to the full-precision model. This indicates that our method performs well in terms of preserving video quality and maintaining video-condition consistency.", + "bbox": [ + 516, + 369, + 903, + 473 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 516, + 484, + 674, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of each proposed component, we conduct ablation studies on ImageNet $256 \\times 256$ with the DiT-XL/2 model. The sampling steps and classifier-free guidance scale are set to 100 and 1.5, as detailed in Tab. 4.", + "bbox": [ + 516, + 507, + 903, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Incremental analysis of Q-DiT. We begin our assessment with a round-to-nearest (RTN) baseline, which simply rounds weights and activations to the nearest available quantization level. Under the W4A8 configuration, RTN demonstrates significantly low performance across all metrics. Enhancing RTN by adjusting the quantization granularity to a group size of 128 markedly improves the results. The introduction of dynamic activation quantization led to a significant boost in generation quality, evidenced by an FID of 6.64, an sFID of 19.29, and an IS of 211.27. By further incorporating group size allocation, our approach achieves an impressive FID of 6.40, approaching the performance of the full-precision model.", + "bbox": [ + 516, + 568, + 903, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons of dynamic activation quantization methods. We also conducted experiments on activation quantization, as shown in Tab. 5. Both TFMQ-DM and our method are quantized to W16A8 to isolate and compare the impact of activation quantization on overall performance. Our method achieves an FID of 5.34, demonstrating a significant improvement over TFMQ-DM, which has an FID of 7.74. This highlights the effectiveness of our sample-aware dynamic activation quantization in maintaining model ac", + "bbox": [ + 516, + 763, + 903, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28312", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/775c6332e170a304b83042cb1ff3f103b16ee57399fd622c6db3e4a2dcc6f177.jpg", + "image_caption": [ + "Ours G4W+P4A", + "a) Castle", + "Figure 5. Qualitative results. Samples generated by G4W+P4A (one of our baselines) and Q-DiT with W4A8 on ImageNet $256 \\times 256$ and ImageNet $512 \\times 512$ . For each example (a-e), the image generated by G4W+P4A shows notable artifacts and distortions. In contrast, our method produces cleaner and more realistic images, with better preservation of textures." + ], + "image_footnote": [], + "bbox": [ + 120, + 108, + 215, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f088d25b5aa532e8733c90e8c98bf3ffec3defc9ab89a4720eb5dc39d63a1baf.jpg", + "image_caption": [ + "b) Daisy" + ], + "image_footnote": [], + "bbox": [ + 222, + 108, + 318, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f7b89679512ab3afb23f779fc606b69c6590aa5ed98d43aed49ff34449831d6.jpg", + "image_caption": [ + "c) Husky" + ], + "image_footnote": [], + "bbox": [ + 325, + 109, + 419, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/330cb177c68319ebc7a689638bc8a5e5b15c18aaac91928ecfac176845631f99.jpg", + "image_caption": [ + "d) Bubble" + ], + "image_footnote": [], + "bbox": [ + 424, + 109, + 519, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa743c4b7c307782822470000eace49cdb629cd73a972087c17566a8b057c53a.jpg", + "image_caption": [ + "$\\mathrm{G4W + P4A}$", + "e) Arctic fox" + ], + "image_footnote": [], + "bbox": [ + 534, + 109, + 718, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1168257f263958d885773425dfca6a0a4231e5c017b1dc80f381c411ea75d19a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 720, + 109, + 903, + 253 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/36f8eed58596d1e0de2909193acbe4a76076f0ce2e19f266a483b6e476718a84.jpg", + "table_caption": [ + "Table 4. Incremental analysis of individual components in our proposed method under the W4A8 setting." + ], + "table_footnote": [], + "table_body": "
FID ↓sFID ↓IS ↑
FP (W16A16)5.3117.61245.85
W4A8 RTN225.5088.542.96
+ Group size 12813.7727.41146.93
+ Sample-wise Dynamic activation quantization6.6419.29211.27
+ Automatic quantization granularity allocation6.4018.60211.72
", + "bbox": [ + 94, + 383, + 483, + 520 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/825db0cf95b87b86333204250632e0da1cc54ad4fcf2e50e291107a475056189.jpg", + "table_caption": [ + "Table 5. Comparisons of dynamic activation quantization methods with W16A8 setting. TFMQ-DM is a method for timestep-aware activation quantization, whereas our approach is both timestep-wise and sample-wise." + ], + "table_footnote": [], + "table_body": "
MethodFID ↓sFID ↓IS ↑Precision↑
FP (W16A16)5.3117.61245.850.8077
TFMQ-DM7.7419.23204.560.7765
Ours5.3417.44245.240.8048
", + "bbox": [ + 102, + 592, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "curacy while reducing performance degradation compared to TFMQ-DM.", + "bbox": [ + 89, + 689, + 482, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparisons of search methods. Furthermore, we also evaluate the effectiveness of the proposed search method (Alg. 1) used in group quantization and show the results in Tab. 6. We can find the proposed method significantly performs better than ILP method [24], Hessian-based search method [21], and the baseline, which demonstrates the effectiveness the our method.", + "bbox": [ + 89, + 720, + 482, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 843, + 209, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our study presents Q-DiT, a novel post-training quantization framework designed for DiTs. To address the signifi", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1afb0794a2a4d07ba33aecf71a95cbfb5de7f02139e50dd7474dcc5eb37663a1.jpg", + "table_caption": [ + "Table 6. Comparisons of the proposed search method and potential counterparts." + ], + "table_footnote": [], + "table_body": "
Search methodFID ↓sFID ↓IS ↑Precision↑
Group size = 1286.6419.29211.270.7548
ILP6.7119.20205.540.7538
Hessian-based7.3819.41197.480.7385
Ours6.4018.60211.720.7609
", + "bbox": [ + 516, + 383, + 898, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cant spatial variance of weights and activations in input channels, we introduced an automatic quantization granularity allocation method. Furthermore, to manage variations in activation ranges across different timesteps, we implemented dynamic activation quantization that adaptively adjusts quantization parameters during runtime. Extensive experiments have underscored the effectiveness of our approach, showcasing its superiority over existing baselines. Notably, even when quantizing the model to W4A8 on the ImageNet $256 \\times 256$ dataset, the FID increased by only 1.09.", + "bbox": [ + 511, + 493, + 906, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. One of the primary limitations of the current Q-DiT approach is its reliance on evolutionary algorithms to determine the optimal group size configuration for quantization. This process is computationally expensive and time-consuming, increasing the overall cost and duration of optimization. We plan to optimize this part in the future work.", + "bbox": [ + 511, + 646, + 908, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 513, + 768, + 681, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by National Key Research and Development Project of China (Grant No. 2023YFF0905502), National Natural Science Foundation of China (Grant No. 92467204, 62472249, and 62402264), and Shenzhen Science and Technology Program (Grant No. JCYJ20220818101014030 and KJZD20240903102300001).", + "bbox": [ + 511, + 794, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28313", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Open-sora: Democratizing efficient video production for all, 2024. 6" + ], + "bbox": [ + 516, + 90, + 903, + 217 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28315", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_model.json b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1efb2ad7ed6559fd6f2ba6653e3cba64be03b6c8 --- /dev/null +++ b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.865, + 0.153 + ], + "angle": 0, + "content": "Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.179, + 0.852, + 0.216 + ], + "angle": 0, + "content": "Lei Chen\\(^{1}\\) Yuan Meng\\(^{1,*}\\) Chen Tang\\(^{1,2}\\) Xinzhu Ma\\(^{2}\\) Jingyan Jiang\\(^{3}\\) Xin Wang\\(^{1}\\) Zhi Wang\\(^{1,*}\\) Wenwu Zhu\\(^{1,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.217, + 0.761, + 0.253 + ], + "angle": 0, + "content": "\\(^{1}\\)Tsinghua University \\(^{2}\\)MMLab, CUHK \\(^{3}\\)Shenzhen Technology University https://q-dit.github.io" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.319, + 0.486, + 0.789 + ], + "angle": 0, + "content": "Recent advancements in diffusion models, particularly the architectural transformation from UNet-based models to Diffusion Transformers (DiTs), significantly improve the quality and scalability of image and video generation. However, despite their impressive capabilities, the substantial computational costs of these large-scale models pose significant challenges for real-world deployment. Post-Training Quantization (PTQ) emerges as a promising solution, enabling model compression and accelerated inference for pretrained models, without the costly retraining. However, research on DiT quantization remains sparse, and existing PTQ frameworks, primarily designed for traditional diffusion models, tend to suffer from biased quantization, leading to notable performance degradation. In this work, we identify that DiTs typically exhibit significant spatial variance in both weights and activations, along with temporal variance in activations. To address these issues, we propose Q-DiT, a novel approach that seamlessly integrates two key techniques: automatic quantization granularity allocation to handle the significant variance of weights and activations across input channels, and sample-wise dynamic activation quantization to adaptively capture activation changes across both timesteps and samples. Extensive experiments conducted on ImageNet and VBench demonstrate the effectiveness of the proposed Q-DiT. Specifically, when quantizing DiT-XL/2 to W6A8 on ImageNet \\((256\\times 256)\\), Q-DiT achieves a remarkable reduction in FID by 1.09 compared to the baseline. Under the more challenging W4A8 setting, it maintains high fidelity in image and video generation, establishing a new benchmark for efficient, high-quality quantization in DiTs." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.819, + 0.222, + 0.833 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.845, + 0.484, + 0.875 + ], + "angle": 0, + "content": "Diffusion models [6, 16, 26, 32] have emerged as a powerful base model for various tasks, ranging from computer" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.908, + 0.426 + ], + "angle": 0, + "content": "vision, natural language processing, multi-modal modeling, etc. The architectural design of diffusion models has evolved significantly. Traditionally, these models employed UNet [28] architecture due to their efficiency in managing hierarchical feature representations. However, recent advances have shifted the focus towards diffusion transformers (DiTs) [27], and notable examples, including Stable Diffusion 3 [8] and Sora [4], have demonstrated its superior performance and scalability for complex generative tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.427, + 0.909, + 0.639 + ], + "angle": 0, + "content": "Despite their success, a significant limitation of DiTs lies in their inherently high latency in the inference. The iterative denoising process, although effective, requires numerous sampling steps, making real-time or large-scale applications computationally intensive. Model quantization offers a particularly promising avenue to reduce inference latency, and Post Training Quantization (PTQ) is particularly appealing for large models as it eliminates the need for retraining. However, the application of quantization techniques to transformer-based diffusion models remains limited. Existing quantization methods for diffusion models [12, 13, 30] primarily focus on UNet architecture and heavily rely on reconstruction-based methods, challenging to scale to large models [21, 25]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.642, + 0.909, + 0.808 + ], + "angle": 0, + "content": "In this work, we propose a customized quantization method for DiTs. To achieve this, we first explore the distinct characteristics of DiT models and identify two key issues in DiT quantization: significant variance of weights and activations across input channels and varying activations across different timesteps. Therefore, we propose Q-DiT, consisting of a fine-grained group quantization strategy and a dynamic activation quantization strategy. These two designs address the aforementioned challenges individually and collaboratively contribute to the proposed quantization framework (see Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In particular, for the first challenge, a promising solution is group quantization [23, 40] which can manage high-magnitude values at the group level. However, we observe the non-monotonicity in group sizes, e.g., reducing group size (increasing group number) does not always lead to better performance. Consequently, we employ an evolution-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.887, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.356, + 0.908, + 0.4 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed Q-DiT. The weights and activations within each layer are quantized with the same group size. Group size configurations allocated for each layer are based on the evolutionary search results, which are guided by the FID/FVD score between the real samples and samples generated by the quantized model. The activations are dynamically quantized during runtime." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.425, + 0.482, + 0.576 + ], + "angle": 0, + "content": "ary search algorithm to configure group sizes for quantization across different model layers. This method utilizes the Fréchet Inception Distance (FID) and Fréchet Video Distance (FVD) as metrics to directly correlate the quantization effects with the visual quality of generated samples, enabling a more targeted and effective quantization strategy. The evolutionary approach not only identifies the optimal group sizes but also ensures that the quantization process adheres to predefined computational constraints, effectively balancing performance with efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.579, + 0.483, + 0.73 + ], + "angle": 0, + "content": "The second challenge, varying activations across timesteps, highlights that quantization parameters calibrated at specific timesteps often fail to generalize across all timesteps. To address this variability, Q-DiT adopts a sample-wise dynamic activation quantization mechanism, which adapts with sample granularity to the changing distribution of activations throughout the diffusion process. This approach significantly reduces quantization error by adjusting quantization parameters on-the-fly, ensuring high-quality image/video generation with minimal overhead." + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.732, + 0.449, + 0.746 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.749, + 0.483, + 0.839 + ], + "angle": 0, + "content": "- We introduce Q-DiT, an accurate PTQ method designed for DiTs. This method employs fine-grained group quantization to effectively manage input channel variance in both weights and activations, and it adopts sample-wise dynamic activation quantization to adapt to activation variations across different timesteps and samples." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "- We identify that the default group size configuration is sub-optimal and propose an evolutionary search strategy to optimize group size allocation, which enhances the efficiency and efficacy of the quantization process." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.749, + 0.484, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.425, + 0.907, + 0.502 + ], + "angle": 0, + "content": "- Extensive experiments on ImageNet and VBench demonstrate that Q-DiT achieves lossless compression under a W6A8 configuration and minimal degradation under W4A8 for image and video generation, highlighting its superior performance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.513, + 0.655, + 0.529 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.539, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Model quantization. Model quantization is a widely used technique to reduce the model size and accelerate its inference speed by converting the model's weights and activations from high-precision floating-point numbers to lower-precision numbers. There are two primary approaches to quantization: Quantization-Aware Training (QAT) [2, 5, 9] and Post-Training Quantization (PTQ) [21, 25]. QAT integrates the quantization process directly into the fine-tuning phase, leveraging STE [1] to simultaneously optimize quantizer parameters and model parameters during fine-tuning. This approach restores the model's performance degradation caused by quantization. However, QAT is resource-intensive because it necessitates fine-tuning the model on the original training dataset. In contrast, PTQ is far more efficient and practical, as it does not require model retraining. PTQ operates by utilizing a small calibration dataset to adjust the quantization parameters for weights and activations, facilitating significant model compression with minimal effort. Although PTQ is highly efficient, it can result in significant performance degradation when applied to low-bit quantization. Reconstruction-based method [21, 25] tries to minimize performance degradation by reducing the reconstruction error of each layer or each block. Although the reconstruction-based method performs well in CNN, they" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28307" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.36, + 0.106 + ], + "angle": 0, + "content": "are not easy to scale up to a large model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.107, + 0.484, + 0.452 + ], + "angle": 0, + "content": "Quantization of transformers. Quantization of transformers has been extensively researched in the contexts of both Vision Transformers (ViTs) and Large Language Models (LLMs). Specifically, PTQ4ViT [39] proposed the twin uniform quantizer to handle the special distributions of post-softmax and post-GELU activations. RepQ-ViT [22] used scale reparameterization to reduce the quantization error of activations. For LLM, weight-only quantization quantizes the weight to reduce the heavy memory movements to achieve better inference efficiency. GPTQ [10] reduced the bit-width to 4 bits per weight based on approximate second-order information with weight-only quantization. AWQ [23] proposed activation-aware weight quantization to reduce the quantization error of salient weight. On the other hand, weight-activation quantization further enhances inference efficiency by quantizing both weight and activation but has to face activation outliers. LLM.int8() [7] reduces the effect of outliers by keeping them in FP16 with mixed-precision computations. Outlier Suppression [35] reduces the quantization error of activations by using the non-scaling LayerNorm. However, these quantization techniques may not be directly applied to DiTs, due to their diffusion model characteristics." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.455, + 0.484, + 0.833 + ], + "angle": 0, + "content": "Quantization of diffusion models. Diffusion models tend to have a slow inference speed due to the large number of sampling steps required. Consequently, some recent studies have focused on accelerating these models through quantization techniques. PTQ4DM [30] and Q-diffusion [20] discover activation variance across different denoising steps and adopt reconstruction-based methods for quantization. PTQD [13] finds the correlation between the quantization noise and model output and proposes variance schedule calibration to rectify the uncorrelated part. TDQ [31] utilizes an MLP layer to estimate the activation quantization parameters for each step. TMPQ-DM [33] further reduces the sequence length of timestep along with the quantization to reduce the overall costs. PTQ4DiT [36] introduces a PTQ method tailored for Diffusion Transformers, addressing challenges like extreme channel magnitudes and temporal activation variability using Channel-wise Salience Balancing (CSB) and Spearman's \\(\\rho\\)-guided Salience Calibration (SSC), while achieving W4A8 quantization. Comparison table of PTQ methods for diffusion models can be found in the supplementary materials. These methods are unable to handle simultaneously the characteristics of the transformer architecture and the dynamics of activation during denoising process, leading to significant performance drops." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.4, + 0.863 + ], + "angle": 0, + "content": "3. Observations of DiT Quantization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We find directly applying recent UNet-based quantization methods to quantize DiTs will lead to significant perfor" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.1, + 0.651, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.1, + 0.778, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.1, + 0.905, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.193, + 0.773, + 0.205 + ], + "angle": 0, + "content": "(a) Weight distribution" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.217, + 0.65, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.216, + 0.779, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.216, + 0.907, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.31, + 0.782, + 0.321 + ], + "angle": 0, + "content": "(b) Activation distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.334, + 0.907, + 0.376 + ], + "angle": 0, + "content": "Figure 2. Distributions of weights and activations in different layers of DiT-XL/2. The red peaks indicate higher values, while the blue areas represent lower values." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.404, + 0.905, + 0.464 + ], + "angle": 0, + "content": "mance degradation. To understand the underlying reasons, we explore the distinct characteristics of DiT models, particularly how they differ from UNet-based architectures in terms of weight and activation distributions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.906, + 0.646 + ], + "angle": 0, + "content": "Observation 1: DiTs exhibit significant variance of weights and activations across input channels. As shown in Fig. 2a, the variance of weights and activations across input channels is much more significant than the output channels. This variance substantially affects quantization since common methods typically apply channel-wise quantization along the output channel for diffusion models [13, 30]. Besides, we also find outliers persist in specific channels of the activation, as shown in Fig. 2b. This suggests that, if we continue to use tensor-wise quantization, these outliers will significantly impact the quantization parameters, resulting in substantial quantization errors for non-outliers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.906, + 0.769 + ], + "angle": 0, + "content": "Observation 2: Significant distribution shift of activations across timesteps. We observe that the distribution of activations in DiT models undergoes significant changes at different timesteps during the denoising process, as demonstrated in Fig. 3 and Fig. 4. Further, we discovered that this temporal shift also exhibits significant variability across different samples. The relevant experimental results are presented in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.785, + 0.64, + 0.802 + ], + "angle": 0, + "content": "4. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.902 + ], + "angle": 0, + "content": "We use uniform quantization to quantize both weights and activations in this work, as it is more hardware-friendly [11, 19]. Particularly, uniform quantization divides the range of floating-point values into equally spaced intervals, and each interval is mapped to a discrete value. The uniform quantization function \\( Q \\) that quantize input floating-point tensor" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28308" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.482, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.202, + 0.485, + 0.256 + ], + "angle": 0, + "content": "Figure 3. Box plot showing the distribution of activation values across various timesteps (from 50 to 0) for the DiT-XL/2 model when generating one image from ImageNet at \\(256 \\times 256\\) resolution.." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.274, + 0.289, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.275, + 0.482, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.374, + 0.289, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.374, + 0.482, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.485, + 0.484, + 0.541 + ], + "angle": 0, + "content": "Figure 4. Standard deviation of activations in MLP and attention layers across different blocks over 50 timesteps for DiT-XL/2 when generating one image from ImageNet at \\(256 \\times 256\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.57, + 0.414, + 0.586 + ], + "angle": 0, + "content": "\\(\\mathbf{x}\\) into \\(b\\) bit integer tensor \\(\\hat{\\mathbf{x}}\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.596, + 0.483, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = Q (\\mathbf {x}; b) = s \\cdot \\left(\\operatorname {c l i p} \\left(\\left\\lfloor \\frac {\\mathbf {x}}{s} \\right\\rfloor + Z, 0, 2 ^ {b} - 1\\right) - Z\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.635, + 0.484, + 0.689 + ], + "angle": 0, + "content": "where \\( s = \\frac{\\max(\\mathbf{x}) - \\min(\\mathbf{x})}{2^b - 1} \\) and \\( Z = -\\left\\lfloor \\frac{\\min(\\mathbf{x})}{s} \\right\\rfloor \\). Here, \\( \\lfloor \\cdot \\rceil \\) is the round operation, \\( s \\) is the scaling factor and \\( Z \\) denotes the zero point." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.704, + 0.249, + 0.722 + ], + "angle": 0, + "content": "5. Method: Q-DiT" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.73, + 0.484, + 0.792 + ], + "angle": 0, + "content": "As shown in Fig. 1, the proposed Q-DiT involves two novel designs, including automatic quantization granularity allocation and dynamic activation quantization. Here we introduce them in the following parts." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.803, + 0.484, + 0.833 + ], + "angle": 0, + "content": "5.1. Automatic Quantization Granularity Allocation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Base solution. A straightforward solution to deal with the input channel-wise variance, as highlighted in observation 1, is to apply input channel-wise quantization, using different quantization parameters for each channel. However," + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.907, + 0.119 + ], + "angle": 0, + "content": "Table 1. Quantization results with varying group sizes on ImageNet \\(256 \\times 256\\) and \\(512 \\times 512\\)." + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.129, + 0.866, + 0.237 + ], + "angle": 0, + "content": "
256×256512×512
GroupFID ↓sFID ↓GroupFID ↓sFID ↓
28825.1128.5428827.2428.16
12817.8720.4512822.7824.31
9619.9721.429620.7621.97
6417.6420.916420.9022.58
3216.4519.343219.6721.57
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.247, + 0.907, + 0.307 + ], + "angle": 0, + "content": "this approach compromises computational efficiency during hardware deployment, as it prevents the full utilization of low-precision computation due to the need for repeated intermediate rescaling [3, 38]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.308, + 0.908, + 0.445 + ], + "angle": 0, + "content": "Fine-grained group quantization. As discussed in recent LLM quantization work [23, 40], a compromise approach between input channel-wise quantization and tensor quantization is the group quantization. As shown in Fig. 1, the weight and activation matrices are divided into groups, and then we perform quantization for each group separately. Specifically, consider a matrix multiplication \\(\\mathbf{Y} = \\mathbf{X}\\mathbf{W}\\) in a linear layer, where \\(\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{\\mathrm{in}}}\\) and \\(\\mathbf{W} \\in \\mathbb{R}^{d_{\\mathrm{in}} \\times d_{\\mathrm{out}}}\\). The quantized value for each output element can be obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.456, + 0.907, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {Y}} _ {i, j} = \\sum_ {k = 0} ^ {d _ {\\mathrm {i n}}} \\hat {\\mathbf {X}} _ {i, k} \\hat {\\mathbf {W}} _ {k, j} (2) \\\\ = \\sum_ {u = 0} ^ {d _ {\\mathrm {i n}} / g _ {l l} - 1} \\sum_ {v = 0} ^ {g _ {l l}} Q _ {u} ^ {\\mathbf {X}} \\left(\\mathbf {X} _ {i, u g _ {l l} + v}\\right) Q _ {u} ^ {\\mathbf {W}} \\left(\\mathbf {W} _ {u g _ {l l} + v, j}\\right), (3) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.555, + 0.733, + 0.569 + ], + "angle": 0, + "content": "where \\(g_{ll}\\) denotes the group size." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.907, + 0.827 + ], + "angle": 0, + "content": "Non-monotonicity in quantization group selection. Ideally, we can improve model performance by reducing the group size (i.e., increase the group number) because finer-grained quantization reduces quantization error. However, as shown in Tab. 1, smaller group sizes do not always improve results, demonstrating the existence of non-monotonicity in quantization groups. For instance, when the group size reduces from 128 to 96, the FID increases by about \\(11.8\\%\\), from 17.87 to 19.97, indicating a degradation in the quality of generated images. This suggests that there is an optimal group size configuration that can achieve better quantization effects with the same average group size or achieve the same quantization results with a larger average group size. Additionally, the sensitivity of each layer in the model varies. By assigning different group sizes to different layers, we can achieve high efficiency and quality in both model performance and image generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Automatic group allocation. The main challenge in group size allocation is identifying its impact on generation performance. Previous works on mixed precision quantization focus on identifying sensitivity indicators [21, 34] for each layer, such as the MSE between the quantized layer and the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28309" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.181 + ], + "angle": 0, + "content": "full precision layer, and then transforming this into an integer linear programming (ILP) problem for optimization. However, we find that a smaller MSE does not necessarily correspond to a reduced performance degradation for DiT quantization, indicating that the previous methods may be ineffective." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.182, + 0.483, + 0.213 + ], + "angle": 0, + "content": "To this end, we directly use the FID as our metric for image generation, defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.221, + 0.483, + 0.24 + ], + "angle": 0, + "content": "\\[\nL (\\mathbf {g}) = \\operatorname {F I D} \\left(R, G _ {\\mathbf {g}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.247, + 0.483, + 0.275 + ], + "angle": 0, + "content": "Similarly, for video generation models, we use the FVD as our metric:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.277, + 0.483, + 0.294 + ], + "angle": 0, + "content": "\\[\nL (\\mathbf {g}) = \\operatorname {F V D} \\left(R, G _ {\\mathbf {g}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.298, + 0.484, + 0.387 + ], + "angle": 0, + "content": "where \\(\\mathbf{g} = \\{g_1, g_2, \\dots, g_N\\}\\) is the layer-wise group size configuration and \\(N\\) is the number of quantized layers. \\(R\\) and \\(G_{\\mathbf{g}}\\) denote the real samples and the samples generated by the quantized model, respectively. We then employ an evolutionary algorithm to optimize the following objective function:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.397, + 0.483, + 0.423 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} ^ {*} = \\underset {\\mathbf {g}} {\\arg \\min } L (\\mathbf {g}), \\text {s . t .} B (\\mathbf {g}) \\leq N _ {\\text {b i t o p s}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.483, + 0.461 + ], + "angle": 0, + "content": "where \\(B(\\cdot)\\) is the measurement of bit-operations (BitOps), and \\(N_{\\text{bitops}}\\) is the predefined threshold." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.484, + 0.522 + ], + "angle": 0, + "content": "This approach allows us to better capture the nuanced impacts of group size on quantization performance, leading to improved outcomes in both efficiency and image quality. The algorithm is located in Alg. 1." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.53, + 0.483, + 0.546 + ], + "angle": 0, + "content": "5.2. Sample-wise Dynamic Activation Quantization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.483, + 0.717 + ], + "angle": 0, + "content": "In UNet-based diffusion quantization, previous studies either allocate a set of quantization parameters for all activations at each timestep [12] or design a multi-layer perceptron (MLP) [31] to predict quantization parameters based on the timestep. However, due to observation 2, these methods are not compatible with our fine-grained quantization because assigning quantization parameters to each group at every timestep results in considerable memory overheads. Specifically, for a sampler with 50 timesteps, the memory overhead could reach up to \\(39\\%\\) of the full-precision model's size." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.484, + 0.824 + ], + "angle": 0, + "content": "Inspired by the recent work in LLM optimization [37], we design an on-the-fly dynamic quantization approach for activations. Specifically, during inference, the quantization parameters for each group of the activations are calculated based on their min-max values. For a given sample \\(i\\) at timestep \\(t\\), the quantization parameters for the activation \\(\\mathbf{x}_{i,t}\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.832, + 0.483, + 0.863 + ], + "angle": 0, + "content": "\\[\ns _ {i, t} = \\frac {\\operatorname* {m a x} \\left(\\mathbf {x} _ {i , t}\\right) - \\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{2 ^ {b} - 1}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.865, + 0.483, + 0.898 + ], + "angle": 0, + "content": "\\[\nZ _ {i, t} = - \\left\\lfloor \\frac {\\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{s _ {i , t}} \\right\\rceil . \\tag {8}\n\\]" + }, + { + "type": "code_caption", + "bbox": [ + 0.523, + 0.095, + 0.862, + 0.125 + ], + "angle": 0, + "content": "Algorithm 1: Automatic quantization granularity allocation of Q-DiT" + }, + { + "type": "algorithm", + "bbox": [ + 0.524, + 0.127, + 0.884, + 0.563 + ], + "angle": 0, + "content": "Input: Group size search space \\(S_{g}\\); number of layers \\(L\\); population size \\(N_{p}\\); iterations \\(N_{iter}\\); mutation probability \\(p\\); Constraint \\(N_{bitops}\\) \nInitialize population \\(\\mathcal{P} = \\{\\mathbf{g}^j\\}_{j=1}^{N_p}\\), where each element in configuration \\(\\mathbf{g}^j \\in \\mathbb{R}^L\\) is randomly selected from \\(S_{g}\\); Initialize TopK candidate set \\(S_{TopK} = \\emptyset\\); \nfor \\(t = 1,2,\\ldots,N_{iter}\\) do \nfor \\(i = 1,2,\\ldots,N_p\\) do \nCalculate FID (or FVD) for each configuration \\(\\mathbf{g}^j\\) based on Eq. 4 (or Eq. 5); Update \\(S_{TopK}\\) with \\(K\\) configurations, according to ranked FID (or FVD) scores; \nClear population \\(\\mathcal{P} = \\emptyset\\); \nrepeat \n\\(\\mathbf{g}_{cross} = \\text{CrossOver}(S_{TopK})\\) with probability \\(1 - p\\); \nAppend \\(\\mathbf{g}_{cross}\\) to \\(\\mathcal{P}\\) if \\(B(\\mathbf{g}_{cross}) < N_{bitops}\\); \nuntil \\(|\\mathcal{P}| = N_p/2\\); \nrepeat \n\\(\\mathbf{g}_{mutate} = \\text{Mutate}(S_{TopK})\\) with probability \\(p\\); \nAppend \\(\\mathbf{g}_{mutate}\\) to \\(\\mathcal{P}\\) if \\(B(\\mathbf{g}_{mutate}) < N_{bitops}\\); \nuntil \\(|\\mathcal{P}| = N_p\\); \nGet the best group size configuration \\(\\mathbf{g}^{\\text{best}}\\), and use it to quantize the model; \nreturn quantized model" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.907, + 0.687 + ], + "angle": 0, + "content": "Furthermore, we integrate the dynamic quantization with min-max computation into the prior operator, which can benefit from the operator fusion and the overhead becomes negligible compared to the costly matrix multiplications in transformer blocks. A detailed analysis is provided in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.702, + 0.646, + 0.719 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.727, + 0.704, + 0.744 + ], + "angle": 0, + "content": "6.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Image generation. We first evaluate our Q-DiT on the image generation task, closely following the evaluation setting used in DiT [27]. We use the pre-trained DiT-XL/2 models with image resolutions of \\(256 \\times 256\\) and \\(512 \\times 512\\), converting them to FP16 as our full precision baseline model. For fast and accurate sampling, we adopt the DDIM sampler [32] with 50 and 100 sampling steps. Performance is also evaluated both with and without classifier-free guidance [15]. Note that \"cfg\" denotes the classifier-free guidance scale. We sample 10K images for both ImageNet" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28310" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 2. Results on image generation. We show the quantization results of DiT-XL/2 on ImageNet \\( {256} \\times {256} \\) and \\( {512} \\times {512} \\) . 'W/A' indicates the bit-width of weight and activation, respectively." + }, + { + "type": "table", + "bbox": [ + 0.207, + 0.124, + 0.794, + 0.668 + ], + "angle": 0, + "content": "
ModelBit-width (W/A)MethodSize (MB)FID ↓sFID ↓IS ↑Precision ↑
DiT-XL/2\n256×256\n(steps = 100)16/16FP134912.4019.11116.680.6605
6/8PTQ4DM50817.8625.3392.240.6077
RepQ-ViT50827.7420.9163.410.5600
TFMQ-DM50822.3327.4472.740.5869
PTQ4DiT50815.2121.34105.030.6440
G4W+P4A52016.7224.61100.090.6123
Ours51812.2118.48117.750.6631
4/8PTQ4DM339213.6685.113.260.0839
RepQ-ViT339224.1481.243.250.0373
TFMQ-DM339143.4761.095.610.0497
PTQ4DiT33928.9034.5665.730.4931
G4W+P4A35125.4825.5773.460.5392
Ours34715.7619.8498.780.6395
DiT-XL/2\n256×256\nsteps = 100\ncfg = 1.5)16/16FP13495.3117.61245.850.8077
6/8PTQ4DM5088.4125.56196.730.7622
RepQ-ViT50810.7718.53163.110.7264
TFMQ-DM5088.8723.52194.080.7737
PTQ4DiT5085.3418.48209.900.8047
G4W+P4A5206.4119.52225.480.7705
Ours5185.3217.40243.950.8044
4/8PTQ4DM339215.6886.633.240.0741
RepQ-ViT339226.6077.933.610.0337
TFMQ-DM339141.9056.016.240.0439
PTQ4DiT3397.7522.01190.380.7292
G4W+P4A3517.6620.76193.760.7261
Ours3476.4018.60211.720.7609
DiT-XL/2\n512×512\nSteps = 50\ncfg = 1.5)16/16FP13496.2718.45204.470.8343
6/8PTQ4DM5089.8426.57164.910.8215
RepQ-ViT5088.3019.19158.800.8153
TFMQ-DM5088.3417.94162.160.8262
PTQ4DiT5087.6918.86178.340.8121
G4W+P4A5207.2819.62185.920.8143
Ours5176.2418.36202.480.8341
4/8PTQ4DM33988.4550.8026.790.3206
RepQ-ViT33979.6949.7629.460.3413
TFMQ-DM33954.6144.2758.770.4215
PTQ4DiT33911.6922.86117.340.7121
G4W+P4A3519.9820.76156.070.7840
Ours3477.8219.60174.180.8127
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.691, + 0.483, + 0.752 + ], + "angle": 0, + "content": "\\(256 \\times 256\\) and ImageNet \\(512 \\times 512\\) in each setting, and employ four metrics in our experiments, including Fréchet Inception Distance (FID) [14], spatial FID (sFID) [29], Inception Score (IS), and Precision." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.756, + 0.483, + 0.848 + ], + "angle": 0, + "content": "Video generation. We also evaluate Q-DiT on video generation, with the STDiT3 model from the Open-Sora project [41]. Specifically, we sample five 2-second videos for each prompt in the VBench prompt suite [18] using a 30-step rectified flow scheduler with a CFG scale of 7.0. The results are assessed across 16 dimensions provided by VBench." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.851, + 0.474, + 0.867 + ], + "angle": 0, + "content": "Baselines. We compare Q-DiT with five strong baselines:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "1) PTQ4DM [30]: A method specifically designed for UNet-based diffusion models, focusing on calibration of" + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.692, + 0.615, + 0.704 + ], + "angle": 0, + "content": "activations." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.706, + 0.905, + 0.749 + ], + "angle": 0, + "content": "2) RepQ-ViT [22]: A technique developed for the quantization of ViTs, aiming to reduce quantization errors in transformer activations." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.751, + 0.905, + 0.796 + ], + "angle": 0, + "content": "3) TFMQ-DM [17]: A PTQ framework specifically developed for diffusion models to preserve temporal features during quantization." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.797, + 0.905, + 0.84 + ], + "angle": 0, + "content": "4) PTQ4DiT [36]: A tailored PTQ approach for DiTs that addresses the quantization challenges through CSB and SSC." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.842, + 0.905, + 0.887 + ], + "angle": 0, + "content": "5) G4W+P4A: A robust baseline we build in this work for both video and image generation tasks, utilizing GPTQ [10] for weight quantization and PTQ4DM for" + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.706, + 0.905, + 0.887 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28311" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.09, + 0.904, + 0.104 + ], + "angle": 0, + "content": "Table 3. Results on video generation. We show the quantization results of STDiT3 on VBench. Higher metrics indicate better performance." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.111, + 0.875, + 0.279 + ], + "angle": 0, + "content": "
MethodBit-width (W/A)Subject ConsistencyOverall ConsistencyTemporal StyleAppearance StyleSceneSpatial RelationshipColorHuman Action
FP16/160.95220.26670.25070.23520.40940.34410.78640.8680
G4W+P4A4/80.94440.26280.24890.23440.39240.32650.76570.8600
Ours4/80.94980.26630.25110.23460.38710.38100.79470.8620
MethodBit-width (W/A)Multiple ObjectsObject ClassImaging QualityAesthetic QualityDynamic DegreeMotion SmoothnessTemporal FlickeringBackground Consistency
FP16/160.41430.83830.58290.51730.61390.98550.99170.9678
G4W+P4A4/80.35400.82250.57300.50180.56390.98490.98950.9651
Ours4/80.39040.84750.58120.51600.61670.98590.99150.9687
" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.294, + 0.269, + 0.308 + ], + "angle": 0, + "content": "activation quantization." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.31, + 0.482, + 0.489 + ], + "angle": 0, + "content": "Others. Q-DiT applies asymmetric quantization for both weights and activations, and uses GPTQ [10] for weight quantization. A default group size of 128 is adopted, with optimal group size allocation for each layer determined through evolutionary search. The search space for group size \\( S_{g} \\) is {32, 64, 128, 192, 288}. Note that the group size for weights and activations within the same layer should be the same. For the evaluation metric during the search process, we compute the FID using 500 images and the FVD using 100 videos. These sample sizes were empirically chosen to ensure a strong correlation with the final metric evaluations." + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.501, + 0.228, + 0.516 + ], + "angle": 0, + "content": "6.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.524, + 0.482, + 0.9 + ], + "angle": 0, + "content": "Image generation results. The quantitative results for image generation are shown in Tab. 2. Specifically, in experiments conducted on ImageNet at a resolution of \\(256 \\times 256\\), the PTQ4DM, RepQ-ViT, TFMQ-DM, PTQ4DiT and G4W+P4A methods exhibit significant performance degradation at a bit-width of W6A8. In contrast, Q-DiT shows marked improvements over PTQ4DM under the W6A8 setting, effectively minimizing the impact of quantization. Notably, Q-DiT is closely aligned with the full-precision configuration, achieving an FID of 12.21 and an IS of 117.75. These results highlight the effectiveness of our method in achieving near-lossless compression in the W6A8 quantization setting. When the bit-width is reduced to W4A8, the performance disparities among the methods become more pronounced. In particular, the other five baselines have severe performance degradation, while our method substantially outperforms them, dramatically reducing quantization loss with an FID of 15.76 and an IS of 98.78. This demonstrates a significant preservation of quality and diversity at lower bit-widths, highlighting the robustness of our approach under stringent quantization constraints. Across varying steps (100 and 50) and classifier-free guidance scales, our method consistently shows superior performance, closely emulating the full-precision model metrics. The evaluation on the ImageNet \\(512 \\times 512\\)" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.294, + 0.905, + 0.368 + ], + "angle": 0, + "content": "dataset demonstrates consistent trends with the \\(256 \\times 256\\) dataset, indicating that Q-DiT can also perform well in high-resolution image generation. Visual demonstrations in Fig. 5 further illustrate that our method maintains superior image generation quality compared to the baseline." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.37, + 0.905, + 0.474 + ], + "angle": 0, + "content": "Video generation results. Tab. 3 shows the results for video generation. Under a stringent W4A8 quantization setting, our method consistently outperforms G4W+P4A in 15 out of 16 metrics, exhibiting minimal degradation compared to the full-precision model. This indicates that our method performs well in terms of preserving video quality and maintaining video-condition consistency." + }, + { + "type": "title", + "bbox": [ + 0.517, + 0.485, + 0.676, + 0.5 + ], + "angle": 0, + "content": "6.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.508, + 0.905, + 0.568 + ], + "angle": 0, + "content": "To evaluate the effectiveness of each proposed component, we conduct ablation studies on ImageNet \\(256 \\times 256\\) with the DiT-XL/2 model. The sampling steps and classifier-free guidance scale are set to 100 and 1.5, as detailed in Tab. 4." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.569, + 0.905, + 0.763 + ], + "angle": 0, + "content": "Incremental analysis of Q-DiT. We begin our assessment with a round-to-nearest (RTN) baseline, which simply rounds weights and activations to the nearest available quantization level. Under the W4A8 configuration, RTN demonstrates significantly low performance across all metrics. Enhancing RTN by adjusting the quantization granularity to a group size of 128 markedly improves the results. The introduction of dynamic activation quantization led to a significant boost in generation quality, evidenced by an FID of 6.64, an sFID of 19.29, and an IS of 211.27. By further incorporating group size allocation, our approach achieves an impressive FID of 6.40, approaching the performance of the full-precision model." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.765, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Comparisons of dynamic activation quantization methods. We also conducted experiments on activation quantization, as shown in Tab. 5. Both TFMQ-DM and our method are quantized to W16A8 to isolate and compare the impact of activation quantization on overall performance. Our method achieves an FID of 5.34, demonstrating a significant improvement over TFMQ-DM, which has an FID of 7.74. This highlights the effectiveness of our sample-aware dynamic activation quantization in maintaining model ac" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28312" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.114, + 0.117, + 0.23 + ], + "angle": 270, + "content": "Ours G4W+P4A" + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.109, + 0.216, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.258, + 0.194, + 0.27 + ], + "angle": 0, + "content": "a) Castle" + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.109, + 0.319, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.257, + 0.296, + 0.271 + ], + "angle": 0, + "content": "b) Daisy" + }, + { + "type": "image", + "bbox": [ + 0.326, + 0.11, + 0.42, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.339, + 0.258, + 0.399, + 0.272 + ], + "angle": 0, + "content": "c) Husky" + }, + { + "type": "image", + "bbox": [ + 0.425, + 0.11, + 0.52, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.438, + 0.257, + 0.502, + 0.271 + ], + "angle": 0, + "content": "d) Bubble" + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.096, + 0.663, + 0.108 + ], + "angle": 0, + "content": "\\(\\mathrm{G4W + P4A}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.097, + 0.828, + 0.108 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.11, + 0.72, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.258, + 0.76, + 0.27 + ], + "angle": 0, + "content": "e) Arctic fox" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.11, + 0.905, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.29, + 0.908, + 0.334 + ], + "angle": 0, + "content": "Figure 5. Qualitative results. Samples generated by G4W+P4A (one of our baselines) and Q-DiT with W4A8 on ImageNet \\(256 \\times 256\\) and ImageNet \\(512 \\times 512\\). For each example (a-e), the image generated by G4W+P4A shows notable artifacts and distortions. In contrast, our method produces cleaner and more realistic images, with better preservation of textures." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.346, + 0.483, + 0.374 + ], + "angle": 0, + "content": "Table 4. Incremental analysis of individual components in our proposed method under the W4A8 setting." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.385, + 0.484, + 0.521 + ], + "angle": 0, + "content": "
FID ↓sFID ↓IS ↑
FP (W16A16)5.3117.61245.85
W4A8 RTN225.5088.542.96
+ Group size 12813.7727.41146.93
+ Sample-wise Dynamic activation quantization6.6419.29211.27
+ Automatic quantization granularity allocation6.4018.60211.72
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.526, + 0.484, + 0.584 + ], + "angle": 0, + "content": "Table 5. Comparisons of dynamic activation quantization methods with W16A8 setting. TFMQ-DM is a method for timestep-aware activation quantization, whereas our approach is both timestep-wise and sample-wise." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.593, + 0.469, + 0.673 + ], + "angle": 0, + "content": "
MethodFID ↓sFID ↓IS ↑Precision↑
FP (W16A16)5.3117.61245.850.8077
TFMQ-DM7.7419.23204.560.7765
Ours5.3417.44245.240.8048
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.719 + ], + "angle": 0, + "content": "curacy while reducing performance degradation compared to TFMQ-DM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.721, + 0.483, + 0.826 + ], + "angle": 0, + "content": "Comparisons of search methods. Furthermore, we also evaluate the effectiveness of the proposed search method (Alg. 1) used in group quantization and show the results in Tab. 6. We can find the proposed method significantly performs better than ILP method [24], Hessian-based search method [21], and the baseline, which demonstrates the effectiveness the our method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.844, + 0.21, + 0.86 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Our study presents Q-DiT, a novel post-training quantization framework designed for DiTs. To address the signifi" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.346, + 0.907, + 0.374 + ], + "angle": 0, + "content": "Table 6. Comparisons of the proposed search method and potential counterparts." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.385, + 0.9, + 0.478 + ], + "angle": 0, + "content": "
Search methodFID ↓sFID ↓IS ↑Precision↑
Group size = 1286.6419.29211.270.7548
ILP6.7119.20205.540.7538
Hessian-based7.3819.41197.480.7385
Ours6.4018.60211.720.7609
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.646 + ], + "angle": 0, + "content": "cant spatial variance of weights and activations in input channels, we introduced an automatic quantization granularity allocation method. Furthermore, to manage variations in activation ranges across different timesteps, we implemented dynamic activation quantization that adaptively adjusts quantization parameters during runtime. Extensive experiments have underscored the effectiveness of our approach, showcasing its superiority over existing baselines. Notably, even when quantizing the model to W4A8 on the ImageNet \\(256 \\times 256\\) dataset, the FID increased by only 1.09." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.909, + 0.752 + ], + "angle": 0, + "content": "Limitations and future work. One of the primary limitations of the current Q-DiT approach is its reliance on evolutionary algorithms to determine the optimal group size configuration for quantization. This process is computationally expensive and time-consuming, increasing the overall cost and duration of optimization. We plan to optimize this part in the future work." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.769, + 0.682, + 0.787 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.901 + ], + "angle": 0, + "content": "This work is supported by National Key Research and Development Project of China (Grant No. 2023YFF0905502), National Natural Science Foundation of China (Grant No. 92467204, 62472249, and 62402264), and Shenzhen Science and Technology Program (Grant No. JCYJ20220818101014030 and KJZD20240903102300001)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28313" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Open-sora: Democratizing efficient video production for all, 2024. 6" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.905, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "28315" + } + ] +] \ No newline at end of file diff --git a/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_origin.pdf b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..60d877e0db2afd9aebdf6141d300e909f279acea --- /dev/null +++ b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/5289ce42-2d7e-4bc4-96f9-cf1d2e0175bf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b82b32ccca780944d86e717ee1551ee67779a49eaf55eb409950cefb4715e34b +size 4652756 diff --git a/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/full.md b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..16653be48fca27efff899eae0481f8ad669ebdb9 --- /dev/null +++ b/2025/Q-DiT_ Accurate Post-Training Quantization for Diffusion Transformers/full.md @@ -0,0 +1,333 @@ +# Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers + +Lei Chen $^{1}$ Yuan Meng $^{1,*}$ Chen Tang $^{1,2}$ Xinzhu Ma $^{2}$ Jingyan Jiang $^{3}$ Xin Wang $^{1}$ Zhi Wang $^{1,*}$ Wenwu Zhu $^{1,*}$ + +$^{1}$ Tsinghua University $^{2}$ MMLab, CUHK $^{3}$ Shenzhen Technology University https://q-dit.github.io + +# Abstract + +Recent advancements in diffusion models, particularly the architectural transformation from UNet-based models to Diffusion Transformers (DiTs), significantly improve the quality and scalability of image and video generation. However, despite their impressive capabilities, the substantial computational costs of these large-scale models pose significant challenges for real-world deployment. Post-Training Quantization (PTQ) emerges as a promising solution, enabling model compression and accelerated inference for pretrained models, without the costly retraining. However, research on DiT quantization remains sparse, and existing PTQ frameworks, primarily designed for traditional diffusion models, tend to suffer from biased quantization, leading to notable performance degradation. In this work, we identify that DiTs typically exhibit significant spatial variance in both weights and activations, along with temporal variance in activations. To address these issues, we propose Q-DiT, a novel approach that seamlessly integrates two key techniques: automatic quantization granularity allocation to handle the significant variance of weights and activations across input channels, and sample-wise dynamic activation quantization to adaptively capture activation changes across both timesteps and samples. Extensive experiments conducted on ImageNet and VBench demonstrate the effectiveness of the proposed Q-DiT. Specifically, when quantizing DiT-XL/2 to W6A8 on ImageNet $(256\times 256)$ , Q-DiT achieves a remarkable reduction in FID by 1.09 compared to the baseline. Under the more challenging W4A8 setting, it maintains high fidelity in image and video generation, establishing a new benchmark for efficient, high-quality quantization in DiTs. + +# 1. Introduction + +Diffusion models [6, 16, 26, 32] have emerged as a powerful base model for various tasks, ranging from computer + +vision, natural language processing, multi-modal modeling, etc. The architectural design of diffusion models has evolved significantly. Traditionally, these models employed UNet [28] architecture due to their efficiency in managing hierarchical feature representations. However, recent advances have shifted the focus towards diffusion transformers (DiTs) [27], and notable examples, including Stable Diffusion 3 [8] and Sora [4], have demonstrated its superior performance and scalability for complex generative tasks. + +Despite their success, a significant limitation of DiTs lies in their inherently high latency in the inference. The iterative denoising process, although effective, requires numerous sampling steps, making real-time or large-scale applications computationally intensive. Model quantization offers a particularly promising avenue to reduce inference latency, and Post Training Quantization (PTQ) is particularly appealing for large models as it eliminates the need for retraining. However, the application of quantization techniques to transformer-based diffusion models remains limited. Existing quantization methods for diffusion models [12, 13, 30] primarily focus on UNet architecture and heavily rely on reconstruction-based methods, challenging to scale to large models [21, 25]. + +In this work, we propose a customized quantization method for DiTs. To achieve this, we first explore the distinct characteristics of DiT models and identify two key issues in DiT quantization: significant variance of weights and activations across input channels and varying activations across different timesteps. Therefore, we propose Q-DiT, consisting of a fine-grained group quantization strategy and a dynamic activation quantization strategy. These two designs address the aforementioned challenges individually and collaboratively contribute to the proposed quantization framework (see Fig. 1). + +In particular, for the first challenge, a promising solution is group quantization [23, 40] which can manage high-magnitude values at the group level. However, we observe the non-monotonicity in group sizes, e.g., reducing group size (increasing group number) does not always lead to better performance. Consequently, we employ an evolution- + +![](images/8ba232458c181f61a64d5aa55aa7f84d4a4a61e4bd166bef56dc6c384821c7e3.jpg) +Figure 1. Overview of the proposed Q-DiT. The weights and activations within each layer are quantized with the same group size. Group size configurations allocated for each layer are based on the evolutionary search results, which are guided by the FID/FVD score between the real samples and samples generated by the quantized model. The activations are dynamically quantized during runtime. + +ary search algorithm to configure group sizes for quantization across different model layers. This method utilizes the Fréchet Inception Distance (FID) and Fréchet Video Distance (FVD) as metrics to directly correlate the quantization effects with the visual quality of generated samples, enabling a more targeted and effective quantization strategy. The evolutionary approach not only identifies the optimal group sizes but also ensures that the quantization process adheres to predefined computational constraints, effectively balancing performance with efficiency. + +The second challenge, varying activations across timesteps, highlights that quantization parameters calibrated at specific timesteps often fail to generalize across all timesteps. To address this variability, Q-DiT adopts a sample-wise dynamic activation quantization mechanism, which adapts with sample granularity to the changing distribution of activations throughout the diffusion process. This approach significantly reduces quantization error by adjusting quantization parameters on-the-fly, ensuring high-quality image/video generation with minimal overhead. + +In summary, our main contributions are as follows: + +- We introduce Q-DiT, an accurate PTQ method designed for DiTs. This method employs fine-grained group quantization to effectively manage input channel variance in both weights and activations, and it adopts sample-wise dynamic activation quantization to adapt to activation variations across different timesteps and samples. +- We identify that the default group size configuration is sub-optimal and propose an evolutionary search strategy to optimize group size allocation, which enhances the efficiency and efficacy of the quantization process. + +- Extensive experiments on ImageNet and VBench demonstrate that Q-DiT achieves lossless compression under a W6A8 configuration and minimal degradation under W4A8 for image and video generation, highlighting its superior performance. + +# 2. Related Work + +Model quantization. Model quantization is a widely used technique to reduce the model size and accelerate its inference speed by converting the model's weights and activations from high-precision floating-point numbers to lower-precision numbers. There are two primary approaches to quantization: Quantization-Aware Training (QAT) [2, 5, 9] and Post-Training Quantization (PTQ) [21, 25]. QAT integrates the quantization process directly into the fine-tuning phase, leveraging STE [1] to simultaneously optimize quantizer parameters and model parameters during fine-tuning. This approach restores the model's performance degradation caused by quantization. However, QAT is resource-intensive because it necessitates fine-tuning the model on the original training dataset. In contrast, PTQ is far more efficient and practical, as it does not require model retraining. PTQ operates by utilizing a small calibration dataset to adjust the quantization parameters for weights and activations, facilitating significant model compression with minimal effort. Although PTQ is highly efficient, it can result in significant performance degradation when applied to low-bit quantization. Reconstruction-based method [21, 25] tries to minimize performance degradation by reducing the reconstruction error of each layer or each block. Although the reconstruction-based method performs well in CNN, they + +are not easy to scale up to a large model. + +Quantization of transformers. Quantization of transformers has been extensively researched in the contexts of both Vision Transformers (ViTs) and Large Language Models (LLMs). Specifically, PTQ4ViT [39] proposed the twin uniform quantizer to handle the special distributions of post-softmax and post-GELU activations. RepQ-ViT [22] used scale reparameterization to reduce the quantization error of activations. For LLM, weight-only quantization quantizes the weight to reduce the heavy memory movements to achieve better inference efficiency. GPTQ [10] reduced the bit-width to 4 bits per weight based on approximate second-order information with weight-only quantization. AWQ [23] proposed activation-aware weight quantization to reduce the quantization error of salient weight. On the other hand, weight-activation quantization further enhances inference efficiency by quantizing both weight and activation but has to face activation outliers. LLM.int8() [7] reduces the effect of outliers by keeping them in FP16 with mixed-precision computations. Outlier Suppression [35] reduces the quantization error of activations by using the non-scaling LayerNorm. However, these quantization techniques may not be directly applied to DiTs, due to their diffusion model characteristics. + +Quantization of diffusion models. Diffusion models tend to have a slow inference speed due to the large number of sampling steps required. Consequently, some recent studies have focused on accelerating these models through quantization techniques. PTQ4DM [30] and Q-diffusion [20] discover activation variance across different denoising steps and adopt reconstruction-based methods for quantization. PTQD [13] finds the correlation between the quantization noise and model output and proposes variance schedule calibration to rectify the uncorrelated part. TDQ [31] utilizes an MLP layer to estimate the activation quantization parameters for each step. TMPQ-DM [33] further reduces the sequence length of timestep along with the quantization to reduce the overall costs. PTQ4DiT [36] introduces a PTQ method tailored for Diffusion Transformers, addressing challenges like extreme channel magnitudes and temporal activation variability using Channel-wise Salience Balancing (CSB) and Spearman's $\rho$ -guided Salience Calibration (SSC), while achieving W4A8 quantization. Comparison table of PTQ methods for diffusion models can be found in the supplementary materials. These methods are unable to handle simultaneously the characteristics of the transformer architecture and the dynamics of activation during denoising process, leading to significant performance drops. + +# 3. Observations of DiT Quantization + +We find directly applying recent UNet-based quantization methods to quantize DiTs will lead to significant perfor + +![](images/56fcc118ba3e243ec54de1bdf6b54ee5ac74f379aefc67c7b9aaf36c622a3cd5.jpg) +(a) Weight distribution + +![](images/61476ed5356a5a7a00860ffd6c47684c899ae1b2aa003dae932688300582547d.jpg) + +![](images/9b06358e12dd14e4e02a95a5fedbae79030dc2a548cc00fd7a084e6f921b0a38.jpg) + +![](images/abc490331d84ba7678fade15ad5172266af3ddff8af7f0917d2f6418ae452779.jpg) +(b) Activation distribution + +![](images/34c00deaa09cfd531fec1b77594226e5c6aacca2795354d2203c9291e61d1d7e.jpg) +Figure 2. Distributions of weights and activations in different layers of DiT-XL/2. The red peaks indicate higher values, while the blue areas represent lower values. + +![](images/831ec507620b42bcc4a816955e4f1dd191d35892a1809f30f4fd87a6326d39ea.jpg) + +mance degradation. To understand the underlying reasons, we explore the distinct characteristics of DiT models, particularly how they differ from UNet-based architectures in terms of weight and activation distributions. + +Observation 1: DiTs exhibit significant variance of weights and activations across input channels. As shown in Fig. 2a, the variance of weights and activations across input channels is much more significant than the output channels. This variance substantially affects quantization since common methods typically apply channel-wise quantization along the output channel for diffusion models [13, 30]. Besides, we also find outliers persist in specific channels of the activation, as shown in Fig. 2b. This suggests that, if we continue to use tensor-wise quantization, these outliers will significantly impact the quantization parameters, resulting in substantial quantization errors for non-outliers. + +Observation 2: Significant distribution shift of activations across timesteps. We observe that the distribution of activations in DiT models undergoes significant changes at different timesteps during the denoising process, as demonstrated in Fig. 3 and Fig. 4. Further, we discovered that this temporal shift also exhibits significant variability across different samples. The relevant experimental results are presented in the supplementary materials. + +# 4. Preliminary + +We use uniform quantization to quantize both weights and activations in this work, as it is more hardware-friendly [11, 19]. Particularly, uniform quantization divides the range of floating-point values into equally spaced intervals, and each interval is mapped to a discrete value. The uniform quantization function $Q$ that quantize input floating-point tensor + +![](images/9ec77b6571d217b06cb45ea71b43c087a0c1cc61b4ece03b8fd5fec3e67e530a.jpg) +Figure 3. Box plot showing the distribution of activation values across various timesteps (from 50 to 0) for the DiT-XL/2 model when generating one image from ImageNet at $256 \times 256$ resolution.. + +![](images/b47f3b99b034b37f957959805ad1af41e486e77b9e808468b34330a4d9b24a16.jpg) + +![](images/ccd99c2201626f426c5104301df2c78f5e4a896a7964979fa79f95aab806008f.jpg) + +![](images/a0743d833622abc53caa848a3bfec91d31f12c617b9347548c3be526a38f636c.jpg) +Figure 4. Standard deviation of activations in MLP and attention layers across different blocks over 50 timesteps for DiT-XL/2 when generating one image from ImageNet at $256 \times 256$ resolution. + +![](images/21babe4695157e0bcec82da16a8f44d855dbfc1bf598f90ddcc4afbf83bddbb1.jpg) + +$\mathbf{x}$ into $b$ bit integer tensor $\hat{\mathbf{x}}$ can be expressed as: + +$$ +\hat {\mathbf {x}} = Q (\mathbf {x}; b) = s \cdot \left(\operatorname {c l i p} \left(\left\lfloor \frac {\mathbf {x}}{s} \right\rfloor + Z, 0, 2 ^ {b} - 1\right) - Z\right), \tag {1} +$$ + +where $s = \frac{\max(\mathbf{x}) - \min(\mathbf{x})}{2^b - 1}$ and $Z = -\left\lfloor \frac{\min(\mathbf{x})}{s} \right\rfloor$ . Here, $\lfloor \cdot \rceil$ is the round operation, $s$ is the scaling factor and $Z$ denotes the zero point. + +# 5. Method: Q-DiT + +As shown in Fig. 1, the proposed Q-DiT involves two novel designs, including automatic quantization granularity allocation and dynamic activation quantization. Here we introduce them in the following parts. + +# 5.1. Automatic Quantization Granularity Allocation + +Base solution. A straightforward solution to deal with the input channel-wise variance, as highlighted in observation 1, is to apply input channel-wise quantization, using different quantization parameters for each channel. However, + +Table 1. Quantization results with varying group sizes on ImageNet $256 \times 256$ and $512 \times 512$ . + +
256×256512×512
GroupFID ↓sFID ↓GroupFID ↓sFID ↓
28825.1128.5428827.2428.16
12817.8720.4512822.7824.31
9619.9721.429620.7621.97
6417.6420.916420.9022.58
3216.4519.343219.6721.57
+ +this approach compromises computational efficiency during hardware deployment, as it prevents the full utilization of low-precision computation due to the need for repeated intermediate rescaling [3, 38]. + +Fine-grained group quantization. As discussed in recent LLM quantization work [23, 40], a compromise approach between input channel-wise quantization and tensor quantization is the group quantization. As shown in Fig. 1, the weight and activation matrices are divided into groups, and then we perform quantization for each group separately. Specifically, consider a matrix multiplication $\mathbf{Y} = \mathbf{X}\mathbf{W}$ in a linear layer, where $\mathbf{X} \in \mathbb{R}^{n \times d_{\mathrm{in}}}$ and $\mathbf{W} \in \mathbb{R}^{d_{\mathrm{in}} \times d_{\mathrm{out}}}$ . The quantized value for each output element can be obtained by: + +$$ +\begin{array}{l} \hat {\mathbf {Y}} _ {i, j} = \sum_ {k = 0} ^ {d _ {\mathrm {i n}}} \hat {\mathbf {X}} _ {i, k} \hat {\mathbf {W}} _ {k, j} (2) \\ = \sum_ {u = 0} ^ {d _ {\mathrm {i n}} / g _ {l l} - 1} \sum_ {v = 0} ^ {g _ {l l}} Q _ {u} ^ {\mathbf {X}} \left(\mathbf {X} _ {i, u g _ {l l} + v}\right) Q _ {u} ^ {\mathbf {W}} \left(\mathbf {W} _ {u g _ {l l} + v, j}\right), (3) \\ \end{array} +$$ + +where $g_{ll}$ denotes the group size. + +Non-monotonicity in quantization group selection. Ideally, we can improve model performance by reducing the group size (i.e., increase the group number) because finer-grained quantization reduces quantization error. However, as shown in Tab. 1, smaller group sizes do not always improve results, demonstrating the existence of non-monotonicity in quantization groups. For instance, when the group size reduces from 128 to 96, the FID increases by about $11.8\%$ , from 17.87 to 19.97, indicating a degradation in the quality of generated images. This suggests that there is an optimal group size configuration that can achieve better quantization effects with the same average group size or achieve the same quantization results with a larger average group size. Additionally, the sensitivity of each layer in the model varies. By assigning different group sizes to different layers, we can achieve high efficiency and quality in both model performance and image generation. + +Automatic group allocation. The main challenge in group size allocation is identifying its impact on generation performance. Previous works on mixed precision quantization focus on identifying sensitivity indicators [21, 34] for each layer, such as the MSE between the quantized layer and the + +full precision layer, and then transforming this into an integer linear programming (ILP) problem for optimization. However, we find that a smaller MSE does not necessarily correspond to a reduced performance degradation for DiT quantization, indicating that the previous methods may be ineffective. + +To this end, we directly use the FID as our metric for image generation, defined as follows: + +$$ +L (\mathbf {g}) = \operatorname {F I D} \left(R, G _ {\mathbf {g}}\right). \tag {4} +$$ + +Similarly, for video generation models, we use the FVD as our metric: + +$$ +L (\mathbf {g}) = \operatorname {F V D} \left(R, G _ {\mathbf {g}}\right), \tag {5} +$$ + +where $\mathbf{g} = \{g_1, g_2, \dots, g_N\}$ is the layer-wise group size configuration and $N$ is the number of quantized layers. $R$ and $G_{\mathbf{g}}$ denote the real samples and the samples generated by the quantized model, respectively. We then employ an evolutionary algorithm to optimize the following objective function: + +$$ +\mathbf {g} ^ {*} = \underset {\mathbf {g}} {\arg \min } L (\mathbf {g}), \text {s . t .} B (\mathbf {g}) \leq N _ {\text {b i t o p s}}, \tag {6} +$$ + +where $B(\cdot)$ is the measurement of bit-operations (BitOps), and $N_{\text{bitops}}$ is the predefined threshold. + +This approach allows us to better capture the nuanced impacts of group size on quantization performance, leading to improved outcomes in both efficiency and image quality. The algorithm is located in Alg. 1. + +# 5.2. Sample-wise Dynamic Activation Quantization + +In UNet-based diffusion quantization, previous studies either allocate a set of quantization parameters for all activations at each timestep [12] or design a multi-layer perceptron (MLP) [31] to predict quantization parameters based on the timestep. However, due to observation 2, these methods are not compatible with our fine-grained quantization because assigning quantization parameters to each group at every timestep results in considerable memory overheads. Specifically, for a sampler with 50 timesteps, the memory overhead could reach up to $39\%$ of the full-precision model's size. + +Inspired by the recent work in LLM optimization [37], we design an on-the-fly dynamic quantization approach for activations. Specifically, during inference, the quantization parameters for each group of the activations are calculated based on their min-max values. For a given sample $i$ at timestep $t$ , the quantization parameters for the activation $\mathbf{x}_{i,t}$ can be expressed as: + +$$ +s _ {i, t} = \frac {\operatorname* {m a x} \left(\mathbf {x} _ {i , t}\right) - \operatorname* {m i n} \left(\mathbf {x} _ {i , t}\right)}{2 ^ {b} - 1}, \tag {7} +$$ + +$$ +Z _ {i, t} = - \left\lfloor \frac {\operatorname* {m i n} \left(\mathbf {x} _ {i , t}\right)}{s _ {i , t}} \right\rceil . \tag {8} +$$ + +Algorithm 1: Automatic quantization granularity allocation of Q-DiT +Input: Group size search space $S_{g}$ ; number of layers $L$ ; population size $N_{p}$ ; iterations $N_{iter}$ ; mutation probability $p$ ; Constraint $N_{bitops}$ +Initialize population $\mathcal{P} = \{\mathbf{g}^j\}_{j=1}^{N_p}$ , where each element in configuration $\mathbf{g}^j \in \mathbb{R}^L$ is randomly selected from $S_{g}$ ; Initialize TopK candidate set $S_{TopK} = \emptyset$ ; +for $t = 1,2,\ldots,N_{iter}$ do +for $i = 1,2,\ldots,N_p$ do +Calculate FID (or FVD) for each configuration $\mathbf{g}^j$ based on Eq. 4 (or Eq. 5); Update $S_{TopK}$ with $K$ configurations, according to ranked FID (or FVD) scores; +Clear population $\mathcal{P} = \emptyset$ ; +repeat + $\mathbf{g}_{cross} = \text{CrossOver}(S_{TopK})$ with probability $1 - p$ ; +Append $\mathbf{g}_{cross}$ to $\mathcal{P}$ if $B(\mathbf{g}_{cross}) < N_{bitops}$ ; +until $|\mathcal{P}| = N_p/2$ ; +repeat + $\mathbf{g}_{mutate} = \text{Mutate}(S_{TopK})$ with probability $p$ ; +Append $\mathbf{g}_{mutate}$ to $\mathcal{P}$ if $B(\mathbf{g}_{mutate}) < N_{bitops}$ ; +until $|\mathcal{P}| = N_p$ ; +Get the best group size configuration $\mathbf{g}^{\text{best}}$ , and use it to quantize the model; +return quantized model + +Furthermore, we integrate the dynamic quantization with min-max computation into the prior operator, which can benefit from the operator fusion and the overhead becomes negligible compared to the costly matrix multiplications in transformer blocks. A detailed analysis is provided in the supplementary materials. + +# 6. Experiments + +# 6.1. Experimental Setup + +Image generation. We first evaluate our Q-DiT on the image generation task, closely following the evaluation setting used in DiT [27]. We use the pre-trained DiT-XL/2 models with image resolutions of $256 \times 256$ and $512 \times 512$ , converting them to FP16 as our full precision baseline model. For fast and accurate sampling, we adopt the DDIM sampler [32] with 50 and 100 sampling steps. Performance is also evaluated both with and without classifier-free guidance [15]. Note that "cfg" denotes the classifier-free guidance scale. We sample 10K images for both ImageNet + +Table 2. Results on image generation. We show the quantization results of DiT-XL/2 on ImageNet ${256} \times {256}$ and ${512} \times {512}$ . 'W/A' indicates the bit-width of weight and activation, respectively. + +
ModelBit-width (W/A)MethodSize (MB)FID ↓sFID ↓IS ↑Precision ↑
DiT-XL/2 +256×256 +(steps = 100)16/16FP134912.4019.11116.680.6605
6/8PTQ4DM50817.8625.3392.240.6077
RepQ-ViT50827.7420.9163.410.5600
TFMQ-DM50822.3327.4472.740.5869
PTQ4DiT50815.2121.34105.030.6440
G4W+P4A52016.7224.61100.090.6123
Ours51812.2118.48117.750.6631
4/8PTQ4DM339213.6685.113.260.0839
RepQ-ViT339224.1481.243.250.0373
TFMQ-DM339143.4761.095.610.0497
PTQ4DiT33928.9034.5665.730.4931
G4W+P4A35125.4825.5773.460.5392
Ours34715.7619.8498.780.6395
DiT-XL/2 +256×256 +steps = 100 +cfg = 1.5)16/16FP13495.3117.61245.850.8077
6/8PTQ4DM5088.4125.56196.730.7622
RepQ-ViT50810.7718.53163.110.7264
TFMQ-DM5088.8723.52194.080.7737
PTQ4DiT5085.3418.48209.900.8047
G4W+P4A5206.4119.52225.480.7705
Ours5185.3217.40243.950.8044
4/8PTQ4DM339215.6886.633.240.0741
RepQ-ViT339226.6077.933.610.0337
TFMQ-DM339141.9056.016.240.0439
PTQ4DiT3397.7522.01190.380.7292
G4W+P4A3517.6620.76193.760.7261
Ours3476.4018.60211.720.7609
DiT-XL/2 +512×512 +Steps = 50 +cfg = 1.5)16/16FP13496.2718.45204.470.8343
6/8PTQ4DM5089.8426.57164.910.8215
RepQ-ViT5088.3019.19158.800.8153
TFMQ-DM5088.3417.94162.160.8262
PTQ4DiT5087.6918.86178.340.8121
G4W+P4A5207.2819.62185.920.8143
Ours5176.2418.36202.480.8341
4/8PTQ4DM33988.4550.8026.790.3206
RepQ-ViT33979.6949.7629.460.3413
TFMQ-DM33954.6144.2758.770.4215
PTQ4DiT33911.6922.86117.340.7121
G4W+P4A3519.9820.76156.070.7840
Ours3477.8219.60174.180.8127
+ +$256 \times 256$ and ImageNet $512 \times 512$ in each setting, and employ four metrics in our experiments, including Fréchet Inception Distance (FID) [14], spatial FID (sFID) [29], Inception Score (IS), and Precision. + +Video generation. We also evaluate Q-DiT on video generation, with the STDiT3 model from the Open-Sora project [41]. Specifically, we sample five 2-second videos for each prompt in the VBench prompt suite [18] using a 30-step rectified flow scheduler with a CFG scale of 7.0. The results are assessed across 16 dimensions provided by VBench. + +Baselines. We compare Q-DiT with five strong baselines: + +1) PTQ4DM [30]: A method specifically designed for UNet-based diffusion models, focusing on calibration of + +activations. + +2) RepQ-ViT [22]: A technique developed for the quantization of ViTs, aiming to reduce quantization errors in transformer activations. +3) TFMQ-DM [17]: A PTQ framework specifically developed for diffusion models to preserve temporal features during quantization. +4) PTQ4DiT [36]: A tailored PTQ approach for DiTs that addresses the quantization challenges through CSB and SSC. +5) G4W+P4A: A robust baseline we build in this work for both video and image generation tasks, utilizing GPTQ [10] for weight quantization and PTQ4DM for + +Table 3. Results on video generation. We show the quantization results of STDiT3 on VBench. Higher metrics indicate better performance. + +
MethodBit-width (W/A)Subject ConsistencyOverall ConsistencyTemporal StyleAppearance StyleSceneSpatial RelationshipColorHuman Action
FP16/160.95220.26670.25070.23520.40940.34410.78640.8680
G4W+P4A4/80.94440.26280.24890.23440.39240.32650.76570.8600
Ours4/80.94980.26630.25110.23460.38710.38100.79470.8620
MethodBit-width (W/A)Multiple ObjectsObject ClassImaging QualityAesthetic QualityDynamic DegreeMotion SmoothnessTemporal FlickeringBackground Consistency
FP16/160.41430.83830.58290.51730.61390.98550.99170.9678
G4W+P4A4/80.35400.82250.57300.50180.56390.98490.98950.9651
Ours4/80.39040.84750.58120.51600.61670.98590.99150.9687
+ +activation quantization. + +Others. Q-DiT applies asymmetric quantization for both weights and activations, and uses GPTQ [10] for weight quantization. A default group size of 128 is adopted, with optimal group size allocation for each layer determined through evolutionary search. The search space for group size $S_{g}$ is {32, 64, 128, 192, 288}. Note that the group size for weights and activations within the same layer should be the same. For the evaluation metric during the search process, we compute the FID using 500 images and the FVD using 100 videos. These sample sizes were empirically chosen to ensure a strong correlation with the final metric evaluations. + +# 6.2. Main Results + +Image generation results. The quantitative results for image generation are shown in Tab. 2. Specifically, in experiments conducted on ImageNet at a resolution of $256 \times 256$ , the PTQ4DM, RepQ-ViT, TFMQ-DM, PTQ4DiT and G4W+P4A methods exhibit significant performance degradation at a bit-width of W6A8. In contrast, Q-DiT shows marked improvements over PTQ4DM under the W6A8 setting, effectively minimizing the impact of quantization. Notably, Q-DiT is closely aligned with the full-precision configuration, achieving an FID of 12.21 and an IS of 117.75. These results highlight the effectiveness of our method in achieving near-lossless compression in the W6A8 quantization setting. When the bit-width is reduced to W4A8, the performance disparities among the methods become more pronounced. In particular, the other five baselines have severe performance degradation, while our method substantially outperforms them, dramatically reducing quantization loss with an FID of 15.76 and an IS of 98.78. This demonstrates a significant preservation of quality and diversity at lower bit-widths, highlighting the robustness of our approach under stringent quantization constraints. Across varying steps (100 and 50) and classifier-free guidance scales, our method consistently shows superior performance, closely emulating the full-precision model metrics. The evaluation on the ImageNet $512 \times 512$ + +dataset demonstrates consistent trends with the $256 \times 256$ dataset, indicating that Q-DiT can also perform well in high-resolution image generation. Visual demonstrations in Fig. 5 further illustrate that our method maintains superior image generation quality compared to the baseline. + +Video generation results. Tab. 3 shows the results for video generation. Under a stringent W4A8 quantization setting, our method consistently outperforms G4W+P4A in 15 out of 16 metrics, exhibiting minimal degradation compared to the full-precision model. This indicates that our method performs well in terms of preserving video quality and maintaining video-condition consistency. + +# 6.3. Ablation Studies + +To evaluate the effectiveness of each proposed component, we conduct ablation studies on ImageNet $256 \times 256$ with the DiT-XL/2 model. The sampling steps and classifier-free guidance scale are set to 100 and 1.5, as detailed in Tab. 4. + +Incremental analysis of Q-DiT. We begin our assessment with a round-to-nearest (RTN) baseline, which simply rounds weights and activations to the nearest available quantization level. Under the W4A8 configuration, RTN demonstrates significantly low performance across all metrics. Enhancing RTN by adjusting the quantization granularity to a group size of 128 markedly improves the results. The introduction of dynamic activation quantization led to a significant boost in generation quality, evidenced by an FID of 6.64, an sFID of 19.29, and an IS of 211.27. By further incorporating group size allocation, our approach achieves an impressive FID of 6.40, approaching the performance of the full-precision model. + +Comparisons of dynamic activation quantization methods. We also conducted experiments on activation quantization, as shown in Tab. 5. Both TFMQ-DM and our method are quantized to W16A8 to isolate and compare the impact of activation quantization on overall performance. Our method achieves an FID of 5.34, demonstrating a significant improvement over TFMQ-DM, which has an FID of 7.74. This highlights the effectiveness of our sample-aware dynamic activation quantization in maintaining model ac + +![](images/775c6332e170a304b83042cb1ff3f103b16ee57399fd622c6db3e4a2dcc6f177.jpg) +Ours G4W+P4A +a) Castle +Figure 5. Qualitative results. Samples generated by G4W+P4A (one of our baselines) and Q-DiT with W4A8 on ImageNet $256 \times 256$ and ImageNet $512 \times 512$ . For each example (a-e), the image generated by G4W+P4A shows notable artifacts and distortions. In contrast, our method produces cleaner and more realistic images, with better preservation of textures. + +![](images/f088d25b5aa532e8733c90e8c98bf3ffec3defc9ab89a4720eb5dc39d63a1baf.jpg) +b) Daisy + +![](images/3f7b89679512ab3afb23f779fc606b69c6590aa5ed98d43aed49ff34449831d6.jpg) +c) Husky + +![](images/330cb177c68319ebc7a689638bc8a5e5b15c18aaac91928ecfac176845631f99.jpg) +d) Bubble + +![](images/aa743c4b7c307782822470000eace49cdb629cd73a972087c17566a8b057c53a.jpg) +$\mathrm{G4W + P4A}$ +e) Arctic fox + +![](images/1168257f263958d885773425dfca6a0a4231e5c017b1dc80f381c411ea75d19a.jpg) +Ours + +Table 4. Incremental analysis of individual components in our proposed method under the W4A8 setting. + +
FID ↓sFID ↓IS ↑
FP (W16A16)5.3117.61245.85
W4A8 RTN225.5088.542.96
+ Group size 12813.7727.41146.93
+ Sample-wise Dynamic activation quantization6.6419.29211.27
+ Automatic quantization granularity allocation6.4018.60211.72
+ +Table 5. Comparisons of dynamic activation quantization methods with W16A8 setting. TFMQ-DM is a method for timestep-aware activation quantization, whereas our approach is both timestep-wise and sample-wise. + +
MethodFID ↓sFID ↓IS ↑Precision↑
FP (W16A16)5.3117.61245.850.8077
TFMQ-DM7.7419.23204.560.7765
Ours5.3417.44245.240.8048
+ +curacy while reducing performance degradation compared to TFMQ-DM. + +Comparisons of search methods. Furthermore, we also evaluate the effectiveness of the proposed search method (Alg. 1) used in group quantization and show the results in Tab. 6. We can find the proposed method significantly performs better than ILP method [24], Hessian-based search method [21], and the baseline, which demonstrates the effectiveness the our method. + +# 7. Conclusion + +Our study presents Q-DiT, a novel post-training quantization framework designed for DiTs. To address the signifi + +Table 6. Comparisons of the proposed search method and potential counterparts. + +
Search methodFID ↓sFID ↓IS ↑Precision↑
Group size = 1286.6419.29211.270.7548
ILP6.7119.20205.540.7538
Hessian-based7.3819.41197.480.7385
Ours6.4018.60211.720.7609
+ +cant spatial variance of weights and activations in input channels, we introduced an automatic quantization granularity allocation method. Furthermore, to manage variations in activation ranges across different timesteps, we implemented dynamic activation quantization that adaptively adjusts quantization parameters during runtime. Extensive experiments have underscored the effectiveness of our approach, showcasing its superiority over existing baselines. Notably, even when quantizing the model to W4A8 on the ImageNet $256 \times 256$ dataset, the FID increased by only 1.09. + +Limitations and future work. One of the primary limitations of the current Q-DiT approach is its reliance on evolutionary algorithms to determine the optimal group size configuration for quantization. This process is computationally expensive and time-consuming, increasing the overall cost and duration of optimization. We plan to optimize this part in the future work. + +# Acknowledgements + +This work is supported by National Key Research and Development Project of China (Grant No. 2023YFF0905502), National Natural Science Foundation of China (Grant No. 92467204, 62472249, and 62402264), and Shenzhen Science and Technology Program (Grant No. JCYJ20220818101014030 and KJZD20240903102300001). + +# References + +[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint arXiv:1308.3432, 2013. 2 +[2] Yash Bhalgat, Jinwon Lee, Markus Nagel, Tijmen Blankevoort, and Nojun Kwak. Lsq+: Improving low-bit quantization through learnable offsets and better initialization. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops, pages 696-697, 2020. 2 +[3] Yelysei Bondarenko, Markus Nagel, and Tijmen Blankevoort. 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Zeroquant-fp: A leap forward in lms post-training w4a8 quantization using floating-point formats. arXiv preprint arXiv:2307.09782, 2023.5 +[38] Guangxuan Xiao, Ji Lin, Mickael Seznec, Hao Wu, Julien Demouth, and Song Han. SmoothQuant: Accurate and efficient post-training quantization for large language models. In Proceedings of the 40th International Conference on Machine Learning, 2023. 4 +[39] Zhihang Yuan, Chenhao Xue, Yiqi Chen, Qiang Wu, and Guangyu Sun. Ptq4vit: Post-training quantization for vision transformers with twin uniform quantization. In European conference on computer vision, pages 191-207. Springer, 2022. 3 + +[40] Yilong Zhao, Chien-Yu Lin, Kan Zhu, Zihao Ye, Lequn Chen, Size Zheng, Luis Ceze, Arvind Krishnamurthy, Tianqi Chen, and Baris Kasikci. Atom: Low-bit quantization for efficient and accurate llm serving. Proceedings of Machine Learning and Systems, 6:196-209, 2024. 1, 4 +[41] Zangwei Zheng, Xiangyu Peng, Tianji Yang, Chenhui Shen, Shenggui Li, Hongxin Liu, Yukun Zhou, Tianyi Li, and Yang You. 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However, despite their impressive capabilities, the substantial computational costs of these large-scale models pose significant challenges for real-world deployment. Post-Training Quantization (PTQ) emerges as a promising solution, enabling model compression and accelerated inference for pretrained models, without the costly retraining. However, research on DiT quantization remains sparse, and existing PTQ frameworks, primarily designed for traditional diffusion models, tend to suffer from biased quantization, leading to notable performance degradation. In this work, we identify that DiTs typically exhibit significant spatial variance in both weights and activations, along with temporal variance in activations. To address these issues, we propose Q-DiT, a novel approach that seamlessly integrates two key techniques: automatic quantization granularity allocation to handle the significant variance of weights and activations across input channels, and sample-wise dynamic activation quantization to adaptively capture activation changes across both timesteps and samples. Extensive experiments conducted on ImageNet and VBench demonstrate the effectiveness of the proposed Q-DiT. Specifically, when quantizing DiT-XL/2 to W6A8 on ImageNet " + }, + { + "bbox": [ + 55, + 252, + 297, + 624 + ], + "type": "inline_equation", + "content": "(256\\times 256)" + }, + { + "bbox": [ + 55, + 252, + 297, + 624 + ], + "type": "text", + "content": ", Q-DiT achieves a remarkable reduction in FID by 1.09 compared to the baseline. Under the more challenging W4A8 setting, it maintains high fidelity in image and video generation, establishing a new benchmark for efficient, high-quality quantization in DiTs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 648, + 135, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 648, + 135, + 659 + ], + "spans": [ + { + "bbox": [ + 56, + 648, + 135, + 659 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 296, + 693 + ], + "type": "text", + "content": "Diffusion models [6, 16, 26, 32] have emerged as a powerful base model for various tasks, ranging from computer" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 228, + 555, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 555, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 555, + 337 + ], + "type": "text", + "content": "vision, natural language processing, multi-modal modeling, etc. The architectural design of diffusion models has evolved significantly. Traditionally, these models employed UNet [28] architecture due to their efficiency in managing hierarchical feature representations. However, recent advances have shifted the focus towards diffusion transformers (DiTs) [27], and notable examples, including Stable Diffusion 3 [8] and Sora [4], have demonstrated its superior performance and scalability for complex generative tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 338, + 556, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 556, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 556, + 506 + ], + "type": "text", + "content": "Despite their success, a significant limitation of DiTs lies in their inherently high latency in the inference. The iterative denoising process, although effective, requires numerous sampling steps, making real-time or large-scale applications computationally intensive. Model quantization offers a particularly promising avenue to reduce inference latency, and Post Training Quantization (PTQ) is particularly appealing for large models as it eliminates the need for retraining. However, the application of quantization techniques to transformer-based diffusion models remains limited. Existing quantization methods for diffusion models [12, 13, 30] primarily focus on UNet architecture and heavily rely on reconstruction-based methods, challenging to scale to large models [21, 25]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 508, + 556, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 508, + 556, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 508, + 556, + 639 + ], + "type": "text", + "content": "In this work, we propose a customized quantization method for DiTs. To achieve this, we first explore the distinct characteristics of DiT models and identify two key issues in DiT quantization: significant variance of weights and activations across input channels and varying activations across different timesteps. Therefore, we propose Q-DiT, consisting of a fine-grained group quantization strategy and a dynamic activation quantization strategy. These two designs address the aforementioned challenges individually and collaboratively contribute to the proposed quantization framework (see Fig. 1)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": "In particular, for the first challenge, a promising solution is group quantization [23, 40] which can manage high-magnitude values at the group level. However, we observe the non-monotonicity in group sizes, e.g., reducing group size (increasing group number) does not always lead to better performance. Consequently, we employ an evolution-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28306" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 542, + 270 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 542, + 270 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 542, + 270 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 542, + 270 + ], + "type": "image", + "image_path": "8ba232458c181f61a64d5aa55aa7f84d4a4a61e4bd166bef56dc6c384821c7e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 281, + 555, + 316 + ], + "lines": [ + { + "bbox": [ + 54, + 281, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 54, + 281, + 555, + 316 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed Q-DiT. The weights and activations within each layer are quantized with the same group size. Group size configurations allocated for each layer are based on the evolutionary search results, which are guided by the FID/FVD score between the real samples and samples generated by the quantized model. The activations are dynamically quantized during runtime." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 336, + 294, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 336, + 294, + 456 + ], + "spans": [ + { + "bbox": [ + 54, + 336, + 294, + 456 + ], + "type": "text", + "content": "ary search algorithm to configure group sizes for quantization across different model layers. This method utilizes the Fréchet Inception Distance (FID) and Fréchet Video Distance (FVD) as metrics to directly correlate the quantization effects with the visual quality of generated samples, enabling a more targeted and effective quantization strategy. The evolutionary approach not only identifies the optimal group sizes but also ensures that the quantization process adheres to predefined computational constraints, effectively balancing performance with efficiency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 458, + 295, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 295, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 295, + 578 + ], + "type": "text", + "content": "The second challenge, varying activations across timesteps, highlights that quantization parameters calibrated at specific timesteps often fail to generalize across all timesteps. To address this variability, Q-DiT adopts a sample-wise dynamic activation quantization mechanism, which adapts with sample granularity to the changing distribution of activations throughout the diffusion process. This approach significantly reduces quantization error by adjusting quantization parameters on-the-fly, ensuring high-quality image/video generation with minimal overhead." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 579, + 274, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 579, + 274, + 590 + ], + "spans": [ + { + "bbox": [ + 66, + 579, + 274, + 590 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 593, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 593, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 593, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 593, + 295, + 664 + ], + "type": "text", + "content": "- We introduce Q-DiT, an accurate PTQ method designed for DiTs. This method employs fine-grained group quantization to effectively manage input channel variance in both weights and activations, and it adopts sample-wise dynamic activation quantization to adapt to activation variations across different timesteps and samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "- We identify that the default group size configuration is sub-optimal and propose an evolutionary search strategy to optimize group size allocation, which enhances the efficiency and efficacy of the quantization process." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 336, + 555, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 336, + 555, + 397 + ], + "spans": [ + { + "bbox": [ + 314, + 336, + 555, + 397 + ], + "type": "text", + "content": "- Extensive experiments on ImageNet and VBench demonstrate that Q-DiT achieves lossless compression under a W6A8 configuration and minimal degradation under W4A8 for image and video generation, highlighting its superior performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 406, + 400, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 406, + 400, + 418 + ], + "spans": [ + { + "bbox": [ + 314, + 406, + 400, + 418 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 426, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 715 + ], + "type": "text", + "content": "Model quantization. Model quantization is a widely used technique to reduce the model size and accelerate its inference speed by converting the model's weights and activations from high-precision floating-point numbers to lower-precision numbers. There are two primary approaches to quantization: Quantization-Aware Training (QAT) [2, 5, 9] and Post-Training Quantization (PTQ) [21, 25]. QAT integrates the quantization process directly into the fine-tuning phase, leveraging STE [1] to simultaneously optimize quantizer parameters and model parameters during fine-tuning. This approach restores the model's performance degradation caused by quantization. However, QAT is resource-intensive because it necessitates fine-tuning the model on the original training dataset. In contrast, PTQ is far more efficient and practical, as it does not require model retraining. PTQ operates by utilizing a small calibration dataset to adjust the quantization parameters for weights and activations, facilitating significant model compression with minimal effort. Although PTQ is highly efficient, it can result in significant performance degradation when applied to low-bit quantization. Reconstruction-based method [21, 25] tries to minimize performance degradation by reducing the reconstruction error of each layer or each block. Although the reconstruction-based method performs well in CNN, they" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28307" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 220, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 220, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 220, + 83 + ], + "type": "text", + "content": "are not easy to scale up to a large model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 84, + 296, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 84, + 296, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 84, + 296, + 357 + ], + "type": "text", + "content": "Quantization of transformers. Quantization of transformers has been extensively researched in the contexts of both Vision Transformers (ViTs) and Large Language Models (LLMs). Specifically, PTQ4ViT [39] proposed the twin uniform quantizer to handle the special distributions of post-softmax and post-GELU activations. RepQ-ViT [22] used scale reparameterization to reduce the quantization error of activations. For LLM, weight-only quantization quantizes the weight to reduce the heavy memory movements to achieve better inference efficiency. GPTQ [10] reduced the bit-width to 4 bits per weight based on approximate second-order information with weight-only quantization. AWQ [23] proposed activation-aware weight quantization to reduce the quantization error of salient weight. On the other hand, weight-activation quantization further enhances inference efficiency by quantizing both weight and activation but has to face activation outliers. LLM.int8() [7] reduces the effect of outliers by keeping them in FP16 with mixed-precision computations. Outlier Suppression [35] reduces the quantization error of activations by using the non-scaling LayerNorm. However, these quantization techniques may not be directly applied to DiTs, due to their diffusion model characteristics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 360, + 296, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 296, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 296, + 659 + ], + "type": "text", + "content": "Quantization of diffusion models. Diffusion models tend to have a slow inference speed due to the large number of sampling steps required. Consequently, some recent studies have focused on accelerating these models through quantization techniques. PTQ4DM [30] and Q-diffusion [20] discover activation variance across different denoising steps and adopt reconstruction-based methods for quantization. PTQD [13] finds the correlation between the quantization noise and model output and proposes variance schedule calibration to rectify the uncorrelated part. TDQ [31] utilizes an MLP layer to estimate the activation quantization parameters for each step. TMPQ-DM [33] further reduces the sequence length of timestep along with the quantization to reduce the overall costs. PTQ4DiT [36] introduces a PTQ method tailored for Diffusion Transformers, addressing challenges like extreme channel magnitudes and temporal activation variability using Channel-wise Salience Balancing (CSB) and Spearman's " + }, + { + "bbox": [ + 55, + 360, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 55, + 360, + 296, + 659 + ], + "type": "text", + "content": "-guided Salience Calibration (SSC), while achieving W4A8 quantization. Comparison table of PTQ methods for diffusion models can be found in the supplementary materials. These methods are unable to handle simultaneously the characteristics of the transformer architecture and the dynamics of activation during denoising process, leading to significant performance drops." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "type": "text", + "content": "3. Observations of DiT Quantization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "We find directly applying recent UNet-based quantization methods to quantize DiTs will lead to significant perfor" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 323, + 79, + 398, + 151 + ], + "blocks": [ + { + "bbox": [ + 323, + 79, + 398, + 151 + ], + "lines": [ + { + "bbox": [ + 323, + 79, + 398, + 151 + ], + "spans": [ + { + "bbox": [ + 323, + 79, + 398, + 151 + ], + "type": "image", + "image_path": "56fcc118ba3e243ec54de1bdf6b54ee5ac74f379aefc67c7b9aaf36c622a3cd5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 152, + 473, + 162 + ], + "lines": [ + { + "bbox": [ + 397, + 152, + 473, + 162 + ], + "spans": [ + { + "bbox": [ + 397, + 152, + 473, + 162 + ], + "type": "text", + "content": "(a) Weight distribution" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 400, + 79, + 476, + 151 + ], + "blocks": [ + { + "bbox": [ + 400, + 79, + 476, + 151 + ], + "lines": [ + { + "bbox": [ + 400, + 79, + 476, + 151 + ], + "spans": [ + { + "bbox": [ + 400, + 79, + 476, + 151 + ], + "type": "image", + "image_path": "61476ed5356a5a7a00860ffd6c47684c899ae1b2aa003dae932688300582547d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 479, + 79, + 553, + 151 + ], + "blocks": [ + { + "bbox": [ + 479, + 79, + 553, + 151 + ], + "lines": [ + { + "bbox": [ + 479, + 79, + 553, + 151 + ], + "spans": [ + { + "bbox": [ + 479, + 79, + 553, + 151 + ], + "type": "image", + "image_path": "9b06358e12dd14e4e02a95a5fedbae79030dc2a548cc00fd7a084e6f921b0a38.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 323, + 171, + 397, + 243 + ], + "blocks": [ + { + "bbox": [ + 323, + 171, + 397, + 243 + ], + "lines": [ + { + "bbox": [ + 323, + 171, + 397, + 243 + ], + "spans": [ + { + "bbox": [ + 323, + 171, + 397, + 243 + ], + "type": "image", + "image_path": "abc490331d84ba7678fade15ad5172266af3ddff8af7f0917d2f6418ae452779.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 391, + 245, + 478, + 254 + ], + "lines": [ + { + "bbox": [ + 391, + 245, + 478, + 254 + ], + "spans": [ + { + "bbox": [ + 391, + 245, + 478, + 254 + ], + "type": "text", + "content": "(b) Activation distribution" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 400, + 171, + 476, + 243 + ], + "blocks": [ + { + "bbox": [ + 400, + 171, + 476, + 243 + ], + "lines": [ + { + "bbox": [ + 400, + 171, + 476, + 243 + ], + "spans": [ + { + "bbox": [ + 400, + 171, + 476, + 243 + ], + "type": "image", + "image_path": "34c00deaa09cfd531fec1b77594226e5c6aacca2795354d2203c9291e61d1d7e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 264, + 555, + 297 + ], + "lines": [ + { + "bbox": [ + 313, + 264, + 555, + 297 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 555, + 297 + ], + "type": "text", + "content": "Figure 2. Distributions of weights and activations in different layers of DiT-XL/2. The red peaks indicate higher values, while the blue areas represent lower values." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 479, + 171, + 555, + 243 + ], + "blocks": [ + { + "bbox": [ + 479, + 171, + 555, + 243 + ], + "lines": [ + { + "bbox": [ + 479, + 171, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 479, + 171, + 555, + 243 + ], + "type": "image", + "image_path": "831ec507620b42bcc4a816955e4f1dd191d35892a1809f30f4fd87a6326d39ea.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 319, + 553, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 553, + 367 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 553, + 367 + ], + "type": "text", + "content": "mance degradation. To understand the underlying reasons, we explore the distinct characteristics of DiT models, particularly how they differ from UNet-based architectures in terms of weight and activation distributions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 369, + 554, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 554, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 554, + 511 + ], + "type": "text", + "content": "Observation 1: DiTs exhibit significant variance of weights and activations across input channels. As shown in Fig. 2a, the variance of weights and activations across input channels is much more significant than the output channels. This variance substantially affects quantization since common methods typically apply channel-wise quantization along the output channel for diffusion models [13, 30]. Besides, we also find outliers persist in specific channels of the activation, as shown in Fig. 2b. This suggests that, if we continue to use tensor-wise quantization, these outliers will significantly impact the quantization parameters, resulting in substantial quantization errors for non-outliers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 512, + 554, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 554, + 609 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 554, + 609 + ], + "type": "text", + "content": "Observation 2: Significant distribution shift of activations across timesteps. We observe that the distribution of activations in DiT models undergoes significant changes at different timesteps during the denoising process, as demonstrated in Fig. 3 and Fig. 4. Further, we discovered that this temporal shift also exhibits significant variability across different samples. The relevant experimental results are presented in the supplementary materials." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 621, + 391, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 621, + 391, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 621, + 391, + 635 + ], + "type": "text", + "content": "4. Preliminary" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "text", + "content": "We use uniform quantization to quantize both weights and activations in this work, as it is more hardware-friendly [11, 19]. Particularly, uniform quantization divides the range of floating-point values into equally spaced intervals, and each interval is mapped to a discrete value. The uniform quantization function " + }, + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "text", + "content": " that quantize input floating-point tensor" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28308" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 294, + 150 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 294, + 150 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 294, + 150 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 294, + 150 + ], + "type": "image", + "image_path": "9ec77b6571d217b06cb45ea71b43c087a0c1cc61b4ece03b8fd5fec3e67e530a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 159, + 296, + 202 + ], + "lines": [ + { + "bbox": [ + 55, + 159, + 296, + 202 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 296, + 202 + ], + "type": "text", + "content": "Figure 3. Box plot showing the distribution of activation values across various timesteps (from 50 to 0) for the DiT-XL/2 model when generating one image from ImageNet at " + }, + { + "bbox": [ + 55, + 159, + 296, + 202 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 159, + 296, + 202 + ], + "type": "text", + "content": " resolution.." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 217, + 176, + 295 + ], + "blocks": [ + { + "bbox": [ + 58, + 217, + 176, + 295 + ], + "lines": [ + { + "bbox": [ + 58, + 217, + 176, + 295 + ], + "spans": [ + { + "bbox": [ + 58, + 217, + 176, + 295 + ], + "type": "image", + "image_path": "b47f3b99b034b37f957959805ad1af41e486e77b9e808468b34330a4d9b24a16.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 176, + 217, + 294, + 295 + ], + "blocks": [ + { + "bbox": [ + 176, + 217, + 294, + 295 + ], + "lines": [ + { + "bbox": [ + 176, + 217, + 294, + 295 + ], + "spans": [ + { + "bbox": [ + 176, + 217, + 294, + 295 + ], + "type": "image", + "image_path": "ccd99c2201626f426c5104301df2c78f5e4a896a7964979fa79f95aab806008f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 296, + 176, + 373 + ], + "blocks": [ + { + "bbox": [ + 58, + 296, + 176, + 373 + ], + "lines": [ + { + "bbox": [ + 58, + 296, + 176, + 373 + ], + "spans": [ + { + "bbox": [ + 58, + 296, + 176, + 373 + ], + "type": "image", + "image_path": "a0743d833622abc53caa848a3bfec91d31f12c617b9347548c3be526a38f636c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 384, + 296, + 428 + ], + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 428 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 428 + ], + "type": "text", + "content": "Figure 4. Standard deviation of activations in MLP and attention layers across different blocks over 50 timesteps for DiT-XL/2 when generating one image from ImageNet at " + }, + { + "bbox": [ + 55, + 384, + 296, + 428 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 384, + 296, + 428 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 176, + 296, + 294, + 373 + ], + "blocks": [ + { + "bbox": [ + 176, + 296, + 294, + 373 + ], + "lines": [ + { + "bbox": [ + 176, + 296, + 294, + 373 + ], + "spans": [ + { + "bbox": [ + 176, + 296, + 294, + 373 + ], + "type": "image", + "image_path": "21babe4695157e0bcec82da16a8f44d855dbfc1bf598f90ddcc4afbf83bddbb1.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "text", + "content": " bit integer tensor " + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 55, + 451, + 253, + 464 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 65, + 472, + 295, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 472, + 295, + 493 + ], + "spans": [ + { + "bbox": [ + 65, + 472, + 295, + 493 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = Q (\\mathbf {x}; b) = s \\cdot \\left(\\operatorname {c l i p} \\left(\\left\\lfloor \\frac {\\mathbf {x}}{s} \\right\\rfloor + Z, 0, 2 ^ {b} - 1\\right) - Z\\right), \\tag {1}", + "image_path": "955cc3820964a57c036a18701320f264681b479523a6854bb34296890b6c53aa.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "inline_equation", + "content": "s = \\frac{\\max(\\mathbf{x}) - \\min(\\mathbf{x})}{2^b - 1}" + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "inline_equation", + "content": "Z = -\\left\\lfloor \\frac{\\min(\\mathbf{x})}{s} \\right\\rfloor" + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "inline_equation", + "content": "\\lfloor \\cdot \\rceil" + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": " is the round operation, " + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": " is the scaling factor and " + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 55, + 502, + 296, + 545 + ], + "type": "text", + "content": " denotes the zero point." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 557, + 152, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 152, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 152, + 571 + ], + "type": "text", + "content": "5. Method: Q-DiT" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 578, + 296, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 296, + 627 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 296, + 627 + ], + "type": "text", + "content": "As shown in Fig. 1, the proposed Q-DiT involves two novel designs, including automatic quantization granularity allocation and dynamic activation quantization. Here we introduce them in the following parts." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 635, + 296, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 296, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 296, + 659 + ], + "type": "text", + "content": "5.1. Automatic Quantization Granularity Allocation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Base solution. A straightforward solution to deal with the input channel-wise variance, as highlighted in observation 1, is to apply input channel-wise quantization, using different quantization parameters for each channel. However," + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 339, + 102, + 529, + 187 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "type": "text", + "content": "Table 1. Quantization results with varying group sizes on ImageNet " + }, + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 71, + 555, + 94 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 339, + 102, + 529, + 187 + ], + "lines": [ + { + "bbox": [ + 339, + 102, + 529, + 187 + ], + "spans": [ + { + "bbox": [ + 339, + 102, + 529, + 187 + ], + "type": "table", + "html": "
256×256512×512
GroupFID ↓sFID ↓GroupFID ↓sFID ↓
28825.1128.5428827.2428.16
12817.8720.4512822.7824.31
9619.9721.429620.7621.97
6417.6420.916420.9022.58
3216.4519.343219.6721.57
", + "image_path": "27b7df83a10252cfd75bd4da37018f75b7e73a74f8dfa4f29a25e3fe4d7c740c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 195, + 555, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 195, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 195, + 555, + 243 + ], + "type": "text", + "content": "this approach compromises computational efficiency during hardware deployment, as it prevents the full utilization of low-precision computation due to the need for repeated intermediate rescaling [3, 38]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "text", + "content": "Fine-grained group quantization. As discussed in recent LLM quantization work [23, 40], a compromise approach between input channel-wise quantization and tensor quantization is the group quantization. As shown in Fig. 1, the weight and activation matrices are divided into groups, and then we perform quantization for each group separately. Specifically, consider a matrix multiplication " + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = \\mathbf{X}\\mathbf{W}" + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "text", + "content": " in a linear layer, where " + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{n \\times d_{\\mathrm{in}}}" + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{d_{\\mathrm{in}} \\times d_{\\mathrm{out}}}" + }, + { + "bbox": [ + 313, + 243, + 555, + 352 + ], + "type": "text", + "content": ". The quantized value for each output element can be obtained by:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 319, + 361, + 555, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 361, + 555, + 430 + ], + "spans": [ + { + "bbox": [ + 319, + 361, + 555, + 430 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathbf {Y}} _ {i, j} = \\sum_ {k = 0} ^ {d _ {\\mathrm {i n}}} \\hat {\\mathbf {X}} _ {i, k} \\hat {\\mathbf {W}} _ {k, j} (2) \\\\ = \\sum_ {u = 0} ^ {d _ {\\mathrm {i n}} / g _ {l l} - 1} \\sum_ {v = 0} ^ {g _ {l l}} Q _ {u} ^ {\\mathbf {X}} \\left(\\mathbf {X} _ {i, u g _ {l l} + v}\\right) Q _ {u} ^ {\\mathbf {W}} \\left(\\mathbf {W} _ {u g _ {l l} + v, j}\\right), (3) \\\\ \\end{array}", + "image_path": "d88a4a15a8adcf64a6761d365ebd46ac6c436f556203fdd35dde3e1c38b07f30.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 439, + 448, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 439, + 448, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 439, + 448, + 450 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 439, + 448, + 450 + ], + "type": "inline_equation", + "content": "g_{ll}" + }, + { + "bbox": [ + 313, + 439, + 448, + 450 + ], + "type": "text", + "content": " denotes the group size." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 450, + 555, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 654 + ], + "type": "text", + "content": "Non-monotonicity in quantization group selection. Ideally, we can improve model performance by reducing the group size (i.e., increase the group number) because finer-grained quantization reduces quantization error. However, as shown in Tab. 1, smaller group sizes do not always improve results, demonstrating the existence of non-monotonicity in quantization groups. For instance, when the group size reduces from 128 to 96, the FID increases by about " + }, + { + "bbox": [ + 313, + 450, + 555, + 654 + ], + "type": "inline_equation", + "content": "11.8\\%" + }, + { + "bbox": [ + 313, + 450, + 555, + 654 + ], + "type": "text", + "content": ", from 17.87 to 19.97, indicating a degradation in the quality of generated images. This suggests that there is an optimal group size configuration that can achieve better quantization effects with the same average group size or achieve the same quantization results with a larger average group size. Additionally, the sensitivity of each layer in the model varies. By assigning different group sizes to different layers, we can achieve high efficiency and quality in both model performance and image generation." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "Automatic group allocation. The main challenge in group size allocation is identifying its impact on generation performance. Previous works on mixed precision quantization focus on identifying sensitivity indicators [21, 34] for each layer, such as the MSE between the quantized layer and the" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28309" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "content": "full precision layer, and then transforming this into an integer linear programming (ILP) problem for optimization. However, we find that a smaller MSE does not necessarily correspond to a reduced performance degradation for DiT quantization, indicating that the previous methods may be ineffective." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": "To this end, we directly use the FID as our metric for image generation, defined as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 131, + 175, + 295, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 175, + 295, + 190 + ], + "spans": [ + { + "bbox": [ + 131, + 175, + 295, + 190 + ], + "type": "interline_equation", + "content": "L (\\mathbf {g}) = \\operatorname {F I D} \\left(R, G _ {\\mathbf {g}}\\right). \\tag {4}", + "image_path": "a549be659b78958f95dc69e3346d59f3d1f146b2c5e34b69638563646127bf0b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "type": "text", + "content": "Similarly, for video generation models, we use the FVD as our metric:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 219, + 295, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 219, + 295, + 232 + ], + "spans": [ + { + "bbox": [ + 129, + 219, + 295, + 232 + ], + "type": "interline_equation", + "content": "L (\\mathbf {g}) = \\operatorname {F V D} \\left(R, G _ {\\mathbf {g}}\\right), \\tag {5}", + "image_path": "4bad95e9c9975aa8fcd08d5fad3fd316650b85522d95502c66b3cdfdb140e842.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = \\{g_1, g_2, \\dots, g_N\\}" + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "content": " is the layer-wise group size configuration and " + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "content": " is the number of quantized layers. " + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "inline_equation", + "content": "G_{\\mathbf{g}}" + }, + { + "bbox": [ + 55, + 236, + 296, + 306 + ], + "type": "text", + "content": " denote the real samples and the samples generated by the quantized model, respectively. We then employ an evolutionary algorithm to optimize the following objective function:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 88, + 314, + 295, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 314, + 295, + 335 + ], + "spans": [ + { + "bbox": [ + 88, + 314, + 295, + 335 + ], + "type": "interline_equation", + "content": "\\mathbf {g} ^ {*} = \\underset {\\mathbf {g}} {\\arg \\min } L (\\mathbf {g}), \\text {s . t .} B (\\mathbf {g}) \\leq N _ {\\text {b i t o p s}}, \\tag {6}", + "image_path": "f691ee12618ffd40a37b41fa924d8701355a7b19c25b690daf8dfa99b270d456.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "inline_equation", + "content": "B(\\cdot)" + }, + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "text", + "content": " is the measurement of bit-operations (BitOps), and " + }, + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "inline_equation", + "content": "N_{\\text{bitops}}" + }, + { + "bbox": [ + 55, + 341, + 295, + 365 + ], + "type": "text", + "content": " is the predefined threshold." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 365, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 296, + 413 + ], + "type": "text", + "content": "This approach allows us to better capture the nuanced impacts of group size on quantization performance, leading to improved outcomes in both efficiency and image quality. The algorithm is located in Alg. 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 419, + 295, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 295, + 432 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 295, + 432 + ], + "type": "text", + "content": "5.2. Sample-wise Dynamic Activation Quantization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 437, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 567 + ], + "type": "text", + "content": "In UNet-based diffusion quantization, previous studies either allocate a set of quantization parameters for all activations at each timestep [12] or design a multi-layer perceptron (MLP) [31] to predict quantization parameters based on the timestep. However, due to observation 2, these methods are not compatible with our fine-grained quantization because assigning quantization parameters to each group at every timestep results in considerable memory overheads. Specifically, for a sampler with 50 timesteps, the memory overhead could reach up to " + }, + { + "bbox": [ + 55, + 437, + 295, + 567 + ], + "type": "inline_equation", + "content": "39\\%" + }, + { + "bbox": [ + 55, + 437, + 295, + 567 + ], + "type": "text", + "content": " of the full-precision model's size." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "text", + "content": "Inspired by the recent work in LLM optimization [37], we design an on-the-fly dynamic quantization approach for activations. Specifically, during inference, the quantization parameters for each group of the activations are calculated based on their min-max values. For a given sample " + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "text", + "content": ", the quantization parameters for the activation " + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,t}" + }, + { + "bbox": [ + 55, + 568, + 296, + 652 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 112, + 658, + 295, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 658, + 295, + 683 + ], + "spans": [ + { + "bbox": [ + 112, + 658, + 295, + 683 + ], + "type": "interline_equation", + "content": "s _ {i, t} = \\frac {\\operatorname* {m a x} \\left(\\mathbf {x} _ {i , t}\\right) - \\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{2 ^ {b} - 1}, \\tag {7}", + "image_path": "09d9c5824c5dd90aa518414a6ad687910008f13ded6436381f5136430dc61fdd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 111, + 685, + 295, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 685, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 111, + 685, + 295, + 711 + ], + "type": "interline_equation", + "content": "Z _ {i, t} = - \\left\\lfloor \\frac {\\operatorname* {m i n} \\left(\\mathbf {x} _ {i , t}\\right)}{s _ {i , t}} \\right\\rceil . \\tag {8}", + "image_path": "77d23cdfa325db07538e0071be740529f746df25a954d44cc0d98fd88390c57e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "type": "code", + "bbox": [ + 320, + 100, + 541, + 445 + ], + "blocks": [ + { + "bbox": [ + 320, + 75, + 527, + 99 + ], + "lines": [ + { + "bbox": [ + 320, + 75, + 527, + 99 + ], + "spans": [ + { + "bbox": [ + 320, + 75, + 527, + 99 + ], + "type": "text", + "content": "Algorithm 1: Automatic quantization granularity allocation of Q-DiT" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "lines": [ + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "spans": [ + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "Input: Group size search space " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "S_{g}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; number of layers " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; population size " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; iterations " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "N_{iter}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; mutation probability " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; Constraint " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "N_{bitops}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " \nInitialize population " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{\\mathbf{g}^j\\}_{j=1}^{N_p}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": ", where each element in configuration " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^j \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " is randomly selected from " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "S_{g}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; Initialize TopK candidate set " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "S_{TopK} = \\emptyset" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nfor " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "t = 1,2,\\ldots,N_{iter}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " do \nfor " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "i = 1,2,\\ldots,N_p" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " do \nCalculate FID (or FVD) for each configuration " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^j" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " based on Eq. 4 (or Eq. 5); Update " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "S_{TopK}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " configurations, according to ranked FID (or FVD) scores; \nClear population " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\emptyset" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nrepeat \n" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{cross} = \\text{CrossOver}(S_{TopK})" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " with probability " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "1 - p" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nAppend " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{cross}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "B(\\mathbf{g}_{cross}) < N_{bitops}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nuntil " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "|\\mathcal{P}| = N_p/2" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nrepeat \n" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{mutate} = \\text{Mutate}(S_{TopK})" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " with probability " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nAppend " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{mutate}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "B(\\mathbf{g}_{mutate}) < N_{bitops}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nuntil " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "|\\mathcal{P}| = N_p" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": "; \nGet the best group size configuration " + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^{\\text{best}}" + }, + { + "bbox": [ + 320, + 100, + 541, + 445 + ], + "type": "text", + "content": ", and use it to quantize the model; \nreturn quantized model" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 471, + 555, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 555, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 555, + 544 + ], + "type": "text", + "content": "Furthermore, we integrate the dynamic quantization with min-max computation into the prior operator, which can benefit from the operator fusion and the overhead becomes negligible compared to the costly matrix multiplications in transformer blocks. A detailed analysis is provided in the supplementary materials." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 555, + 395, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 555, + 395, + 569 + ], + "spans": [ + { + "bbox": [ + 314, + 555, + 395, + 569 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 575, + 430, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 575, + 430, + 589 + ], + "spans": [ + { + "bbox": [ + 314, + 575, + 430, + 589 + ], + "type": "text", + "content": "6.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "Image generation. We first evaluate our Q-DiT on the image generation task, closely following the evaluation setting used in DiT [27]. We use the pre-trained DiT-XL/2 models with image resolutions of " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": ", converting them to FP16 as our full precision baseline model. For fast and accurate sampling, we adopt the DDIM sampler [32] with 50 and 100 sampling steps. Performance is also evaluated both with and without classifier-free guidance [15]. Note that \"cfg\" denotes the classifier-free guidance scale. We sample 10K images for both ImageNet" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28310" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 126, + 98, + 485, + 529 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 2. Results on image generation. We show the quantization results of DiT-XL/2 on ImageNet " + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "inline_equation", + "content": "{512} \\times {512}" + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": " . 'W/A' indicates the bit-width of weight and activation, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 126, + 98, + 485, + 529 + ], + "lines": [ + { + "bbox": [ + 126, + 98, + 485, + 529 + ], + "spans": [ + { + "bbox": [ + 126, + 98, + 485, + 529 + ], + "type": "table", + "html": "
ModelBit-width (W/A)MethodSize (MB)FID ↓sFID ↓IS ↑Precision ↑
DiT-XL/2\n256×256\n(steps = 100)16/16FP134912.4019.11116.680.6605
6/8PTQ4DM50817.8625.3392.240.6077
RepQ-ViT50827.7420.9163.410.5600
TFMQ-DM50822.3327.4472.740.5869
PTQ4DiT50815.2121.34105.030.6440
G4W+P4A52016.7224.61100.090.6123
Ours51812.2118.48117.750.6631
4/8PTQ4DM339213.6685.113.260.0839
RepQ-ViT339224.1481.243.250.0373
TFMQ-DM339143.4761.095.610.0497
PTQ4DiT33928.9034.5665.730.4931
G4W+P4A35125.4825.5773.460.5392
Ours34715.7619.8498.780.6395
DiT-XL/2\n256×256\nsteps = 100\ncfg = 1.5)16/16FP13495.3117.61245.850.8077
6/8PTQ4DM5088.4125.56196.730.7622
RepQ-ViT50810.7718.53163.110.7264
TFMQ-DM5088.8723.52194.080.7737
PTQ4DiT5085.3418.48209.900.8047
G4W+P4A5206.4119.52225.480.7705
Ours5185.3217.40243.950.8044
4/8PTQ4DM339215.6886.633.240.0741
RepQ-ViT339226.6077.933.610.0337
TFMQ-DM339141.9056.016.240.0439
PTQ4DiT3397.7522.01190.380.7292
G4W+P4A3517.6620.76193.760.7261
Ours3476.4018.60211.720.7609
DiT-XL/2\n512×512\nSteps = 50\ncfg = 1.5)16/16FP13496.2718.45204.470.8343
6/8PTQ4DM5089.8426.57164.910.8215
RepQ-ViT5088.3019.19158.800.8153
TFMQ-DM5088.3417.94162.160.8262
PTQ4DiT5087.6918.86178.340.8121
G4W+P4A5207.2819.62185.920.8143
Ours5176.2418.36202.480.8341
4/8PTQ4DM33988.4550.8026.790.3206
RepQ-ViT33979.6949.7629.460.3413
TFMQ-DM33954.6144.2758.770.4215
PTQ4DiT33911.6922.86117.340.7121
G4W+P4A3519.9820.76156.070.7840
Ours3477.8219.60174.180.8127
", + "image_path": "c04b8bb046db4f1bea78d74ef4217ef265454a24f23f7edb5cdbd389652b792e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "spans": [ + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "type": "text", + "content": " and ImageNet " + }, + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 547, + 295, + 595 + ], + "type": "text", + "content": " in each setting, and employ four metrics in our experiments, including Fréchet Inception Distance (FID) [14], spatial FID (sFID) [29], Inception Score (IS), and Precision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 598, + 295, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 295, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 295, + 671 + ], + "type": "text", + "content": "Video generation. We also evaluate Q-DiT on video generation, with the STDiT3 model from the Open-Sora project [41]. Specifically, we sample five 2-second videos for each prompt in the VBench prompt suite [18] using a 30-step rectified flow scheduler with a CFG scale of 7.0. The results are assessed across 16 dimensions provided by VBench." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 673, + 290, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 673, + 290, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 290, + 686 + ], + "type": "text", + "content": "Baselines. We compare Q-DiT with five strong baselines:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 689, + 296, + 714 + ], + "type": "text", + "content": "1) PTQ4DM [30]: A method specifically designed for UNet-based diffusion models, focusing on calibration of" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 328, + 548, + 376, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 548, + 376, + 557 + ], + "spans": [ + { + "bbox": [ + 328, + 548, + 376, + 557 + ], + "type": "text", + "content": "activations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 559, + 553, + 702 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 314, + 559, + 553, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 559, + 553, + 593 + ], + "spans": [ + { + "bbox": [ + 314, + 559, + 553, + 593 + ], + "type": "text", + "content": "2) RepQ-ViT [22]: A technique developed for the quantization of ViTs, aiming to reduce quantization errors in transformer activations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 594, + 553, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 594, + 553, + 630 + ], + "spans": [ + { + "bbox": [ + 314, + 594, + 553, + 630 + ], + "type": "text", + "content": "3) TFMQ-DM [17]: A PTQ framework specifically developed for diffusion models to preserve temporal features during quantization." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 631, + 553, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 631, + 553, + 665 + ], + "spans": [ + { + "bbox": [ + 314, + 631, + 553, + 665 + ], + "type": "text", + "content": "4) PTQ4DiT [36]: A tailored PTQ approach for DiTs that addresses the quantization challenges through CSB and SSC." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 666, + 553, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 666, + 553, + 702 + ], + "spans": [ + { + "bbox": [ + 314, + 666, + 553, + 702 + ], + "type": "text", + "content": "5) G4W+P4A: A robust baseline we build in this work for both video and image generation tasks, utilizing GPTQ [10] for weight quantization and PTQ4DM for" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28311" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 87, + 535, + 220 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 553, + 82 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 553, + 82 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 553, + 82 + ], + "type": "text", + "content": "Table 3. Results on video generation. We show the quantization results of STDiT3 on VBench. Higher metrics indicate better performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 87, + 535, + 220 + ], + "lines": [ + { + "bbox": [ + 74, + 87, + 535, + 220 + ], + "spans": [ + { + "bbox": [ + 74, + 87, + 535, + 220 + ], + "type": "table", + "html": "
MethodBit-width (W/A)Subject ConsistencyOverall ConsistencyTemporal StyleAppearance StyleSceneSpatial RelationshipColorHuman Action
FP16/160.95220.26670.25070.23520.40940.34410.78640.8680
G4W+P4A4/80.94440.26280.24890.23440.39240.32650.76570.8600
Ours4/80.94980.26630.25110.23460.38710.38100.79470.8620
MethodBit-width (W/A)Multiple ObjectsObject ClassImaging QualityAesthetic QualityDynamic DegreeMotion SmoothnessTemporal FlickeringBackground Consistency
FP16/160.41430.83830.58290.51730.61390.98550.99170.9678
G4W+P4A4/80.35400.82250.57300.50180.56390.98490.98950.9651
Ours4/80.39040.84750.58120.51600.61670.98590.99150.9687
", + "image_path": "37409a49908db81050f7b9d453d7d5b51fd7ffdd6d6dc5007030f73681c84ca2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 232, + 164, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 232, + 164, + 243 + ], + "spans": [ + { + "bbox": [ + 70, + 232, + 164, + 243 + ], + "type": "text", + "content": "activation quantization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 245, + 294, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 245, + 294, + 387 + ], + "spans": [ + { + "bbox": [ + 57, + 245, + 294, + 387 + ], + "type": "text", + "content": "Others. Q-DiT applies asymmetric quantization for both weights and activations, and uses GPTQ [10] for weight quantization. A default group size of 128 is adopted, with optimal group size allocation for each layer determined through evolutionary search. The search space for group size " + }, + { + "bbox": [ + 57, + 245, + 294, + 387 + ], + "type": "inline_equation", + "content": "S_{g}" + }, + { + "bbox": [ + 57, + 245, + 294, + 387 + ], + "type": "text", + "content": " is {32, 64, 128, 192, 288}. Note that the group size for weights and activations within the same layer should be the same. For the evaluation metric during the search process, we compute the FID using 500 images and the FVD using 100 videos. These sample sizes were empirically chosen to ensure a strong correlation with the final metric evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 396, + 139, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 396, + 139, + 408 + ], + "spans": [ + { + "bbox": [ + 57, + 396, + 139, + 408 + ], + "type": "text", + "content": "6.2. Main Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "type": "text", + "content": "Image generation results. The quantitative results for image generation are shown in Tab. 2. Specifically, in experiments conducted on ImageNet at a resolution of " + }, + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "type": "text", + "content": ", the PTQ4DM, RepQ-ViT, TFMQ-DM, PTQ4DiT and G4W+P4A methods exhibit significant performance degradation at a bit-width of W6A8. In contrast, Q-DiT shows marked improvements over PTQ4DM under the W6A8 setting, effectively minimizing the impact of quantization. Notably, Q-DiT is closely aligned with the full-precision configuration, achieving an FID of 12.21 and an IS of 117.75. These results highlight the effectiveness of our method in achieving near-lossless compression in the W6A8 quantization setting. When the bit-width is reduced to W4A8, the performance disparities among the methods become more pronounced. In particular, the other five baselines have severe performance degradation, while our method substantially outperforms them, dramatically reducing quantization loss with an FID of 15.76 and an IS of 98.78. This demonstrates a significant preservation of quality and diversity at lower bit-widths, highlighting the robustness of our approach under stringent quantization constraints. Across varying steps (100 and 50) and classifier-free guidance scales, our method consistently shows superior performance, closely emulating the full-precision model metrics. The evaluation on the ImageNet " + }, + { + "bbox": [ + 57, + 415, + 294, + 712 + ], + "type": "inline_equation", + "content": "512 \\times 512" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 232, + 553, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 232, + 553, + 291 + ], + "spans": [ + { + "bbox": [ + 316, + 232, + 553, + 291 + ], + "type": "text", + "content": "dataset demonstrates consistent trends with the " + }, + { + "bbox": [ + 316, + 232, + 553, + 291 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 316, + 232, + 553, + 291 + ], + "type": "text", + "content": " dataset, indicating that Q-DiT can also perform well in high-resolution image generation. Visual demonstrations in Fig. 5 further illustrate that our method maintains superior image generation quality compared to the baseline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 293, + 553, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 293, + 553, + 375 + ], + "spans": [ + { + "bbox": [ + 316, + 293, + 553, + 375 + ], + "type": "text", + "content": "Video generation results. Tab. 3 shows the results for video generation. Under a stringent W4A8 quantization setting, our method consistently outperforms G4W+P4A in 15 out of 16 metrics, exhibiting minimal degradation compared to the full-precision model. This indicates that our method performs well in terms of preserving video quality and maintaining video-condition consistency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 316, + 384, + 413, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 384, + 413, + 396 + ], + "spans": [ + { + "bbox": [ + 316, + 384, + 413, + 396 + ], + "type": "text", + "content": "6.3. Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 402, + 553, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 402, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 316, + 402, + 553, + 449 + ], + "type": "text", + "content": "To evaluate the effectiveness of each proposed component, we conduct ablation studies on ImageNet " + }, + { + "bbox": [ + 316, + 402, + 553, + 449 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 316, + 402, + 553, + 449 + ], + "type": "text", + "content": " with the DiT-XL/2 model. The sampling steps and classifier-free guidance scale are set to 100 and 1.5, as detailed in Tab. 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 450, + 553, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 450, + 553, + 604 + ], + "spans": [ + { + "bbox": [ + 316, + 450, + 553, + 604 + ], + "type": "text", + "content": "Incremental analysis of Q-DiT. We begin our assessment with a round-to-nearest (RTN) baseline, which simply rounds weights and activations to the nearest available quantization level. Under the W4A8 configuration, RTN demonstrates significantly low performance across all metrics. Enhancing RTN by adjusting the quantization granularity to a group size of 128 markedly improves the results. The introduction of dynamic activation quantization led to a significant boost in generation quality, evidenced by an FID of 6.64, an sFID of 19.29, and an IS of 211.27. By further incorporating group size allocation, our approach achieves an impressive FID of 6.40, approaching the performance of the full-precision model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 316, + 605, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 605, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 316, + 605, + 553, + 712 + ], + "type": "text", + "content": "Comparisons of dynamic activation quantization methods. We also conducted experiments on activation quantization, as shown in Tab. 5. Both TFMQ-DM and our method are quantized to W16A8 to isolate and compare the impact of activation quantization on overall performance. Our method achieves an FID of 5.34, demonstrating a significant improvement over TFMQ-DM, which has an FID of 7.74. This highlights the effectiveness of our sample-aware dynamic activation quantization in maintaining model ac" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28312" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 86, + 132, + 201 + ], + "blocks": [ + { + "bbox": [ + 61, + 90, + 71, + 182 + ], + "lines": [ + { + "bbox": [ + 61, + 90, + 71, + 182 + ], + "spans": [ + { + "bbox": [ + 61, + 90, + 71, + 182 + ], + "type": "text", + "content": "Ours G4W+P4A" + } + ] + } + ], + "index": 0, + "angle": 270, + "type": "image_caption" + }, + { + "bbox": [ + 74, + 86, + 132, + 201 + ], + "lines": [ + { + "bbox": [ + 74, + 86, + 132, + 201 + ], + "spans": [ + { + "bbox": [ + 74, + 86, + 132, + 201 + ], + "type": "image", + "image_path": "775c6332e170a304b83042cb1ff3f103b16ee57399fd622c6db3e4a2dcc6f177.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 204, + 118, + 213 + ], + "lines": [ + { + "bbox": [ + 83, + 204, + 118, + 213 + ], + "spans": [ + { + "bbox": [ + 83, + 204, + 118, + 213 + ], + "type": "text", + "content": "a) Castle" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "lines": [ + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "type": "text", + "content": "Figure 5. Qualitative results. Samples generated by G4W+P4A (one of our baselines) and Q-DiT with W4A8 on ImageNet " + }, + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "type": "text", + "content": " and ImageNet " + }, + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 229, + 555, + 264 + ], + "type": "text", + "content": ". For each example (a-e), the image generated by G4W+P4A shows notable artifacts and distortions. 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Incremental analysis of individual components in our proposed method under the W4A8 setting." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 304, + 296, + 412 + ], + "lines": [ + { + "bbox": [ + 58, + 304, + 296, + 412 + ], + "spans": [ + { + "bbox": [ + 58, + 304, + 296, + 412 + ], + "type": "table", + "html": "
FID ↓sFID ↓IS ↑
FP (W16A16)5.3117.61245.85
W4A8 RTN225.5088.542.96
+ Group size 12813.7727.41146.93
+ Sample-wise Dynamic activation quantization6.6419.29211.27
+ Automatic quantization granularity allocation6.4018.60211.72
", + "image_path": "36f8eed58596d1e0de2909193acbe4a76076f0ce2e19f266a483b6e476718a84.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 63, + 469, + 287, + 533 + ], + "blocks": [ + { + "bbox": [ + 55, + 416, + 296, + 462 + ], + "lines": [ + { + "bbox": [ + 55, + 416, + 296, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 416, + 296, + 462 + ], + "type": "text", + "content": "Table 5. Comparisons of dynamic activation quantization methods with W16A8 setting. TFMQ-DM is a method for timestep-aware activation quantization, whereas our approach is both timestep-wise and sample-wise." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 469, + 287, + 533 + ], + "lines": [ + { + "bbox": [ + 63, + 469, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 63, + 469, + 287, + 533 + ], + "type": "table", + "html": "
MethodFID ↓sFID ↓IS ↑Precision↑
FP (W16A16)5.3117.61245.850.8077
TFMQ-DM7.7419.23204.560.7765
Ours5.3417.44245.240.8048
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Search methodFID ↓sFID ↓IS ↑Precision↑
Group size = 1286.6419.29211.270.7548
ILP6.7119.20205.540.7538
Hessian-based7.3819.41197.480.7385
Ours6.4018.60211.720.7609
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Notably, even when quantizing the model to W4A8 on the ImageNet " + }, + { + "bbox": [ + 313, + 391, + 555, + 511 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 391, + 555, + 511 + ], + "type": "text", + "content": " dataset, the FID increased by only 1.09." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 512, + 556, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 556, + 595 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 556, + 595 + ], + "type": "text", + "content": "Limitations and future work. One of the primary limitations of the current Q-DiT approach is its reliance on evolutionary algorithms to determine the optimal group size configuration for quantization. This process is computationally expensive and time-consuming, increasing the overall cost and duration of optimization. We plan to optimize this part in the future work." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 314, + 609, + 417, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 609, + 417, + 623 + ], + "spans": [ + { + "bbox": [ + 314, + 609, + 417, + 623 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 629, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 713 + ], + "type": "text", + "content": "This work is supported by National Key Research and Development Project of China (Grant No. 2023YFF0905502), National Natural Science Foundation of China (Grant No. 92467204, 62472249, and 62402264), and Shenzhen Science and Technology Program (Grant No. JCYJ20220818101014030 and KJZD20240903102300001)." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28313" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Open-sora: Democratizing efficient video production for all, 2024. 6" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28315" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_content_list.json b/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a8628332f696f665157c16a295f03a93e7c139f3 --- /dev/null +++ b/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_content_list.json @@ -0,0 +1,1548 @@ +[ + { + "type": "text", + "text": "Q-Eval-100K: Evaluating Visual Quality and Alignment Level for Text-to-Vision Content", + "text_level": 1, + "bbox": [ + 184, + 128, + 816, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zicheng Zhang $^{1}$ Tengchuan Kou $^{1}$ Shushi Wang $^{1}$ Chunyi Li $^{1}$ Wei Sun $^{1}$ Wei Wang $^{2}$ Xiaoyu Li $^{2}$ Zongyu Wang $^{2}$ Xuezhi Cao $^{2}$ Xiongkuo Min $^{1}$ Xiaohong Liu $^{1\\dagger}$ Guangtao Zhai $^{1}$ Shanghai Jiao Tong University ${}^{2}$ Meituan", + "bbox": [ + 212, + 202, + 782, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 308, + 326, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Evaluating text-to-vision content hinges on two crucial aspects: visual quality and alignment. While significant progress has been made in developing objective models to assess these dimensions, the performance of such models heavily relies on the scale and quality of human annotations. According to Scaling Law, increasing the number of human-labeled instances follows a predictable pattern that enhances the performance of evaluation models. Therefore, we introduce a comprehensive dataset designed to Evaluate Visual quality and Alignment Level for text-to-vision content (Q-EVAL-100K), featuring the largest collection of human-labeled Mean Opinion Scores (MOS) for the mentioned two aspects. The Q-EVAL-100K dataset encompasses both text-to-image and text-to-video models, with 960K human annotations specifically focused on visual quality and alignment for 100K instances (60K images and 40K videos). Leveraging this dataset with context prompt, we propose Q-Eval-Score, a unified model capable of evaluating both visual quality and alignment with special improvements for handling long-text prompt alignment. Experimental results indicate that the proposed Q-Eval-Score achieves superior performance on both visual quality and alignment, with strong generalization capabilities across other benchmarks. These findings highlight the significant value of the Q-EVAL-100K dataset. Data and codes will be available at https://github.com/zzc-1998/QEval.", + "bbox": [ + 89, + 340, + 483, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 776, + 220, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid advancement of generative AI, millions of text-to-image and text-to-video content are being generated daily across various platforms [25, 56], applied in industrial production or directly used by consumers. However, due to current technological limitations, text-to-vision con", + "bbox": [ + 89, + 801, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/edb458ae9ef8368e4fd927a8a6da84767788b9dd7f7357536a821b5b7f4eb7ac.jpg", + "image_caption": [ + "Figure 1. Illustration of the unified evaluation dimensions of Q-Eval-100K. We focus on visual quality (including all factors that may impact the viewing experience) and alignment level, which measures the accuracy of the generated content to the prompt." + ], + "image_footnote": [], + "bbox": [ + 545, + 309, + 870, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tent often falls short of being perfect upon generation and cannot be immediately deployed [34, 36, 40], which usually requires expert evaluation, editing, and fine-tuning. As a result, numerous efforts have been made to develop automated methods for evaluating text-to-vision content, aiming to control the quality of generation and guide the necessary optimizations effectively [13, 26, 27, 29, 40, 60–63, 65, 70, 72]. Through extensive theoretical and experimental analy-", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 107, + 886, + 238, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10621", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/d920fd1f53c0deb66aa14068882d0fa026cf7fc238aa8cbced1613e2aae7d620.jpg", + "table_caption": [ + "Table 1. A brief comparison of the latest text-to-vision evaluation datasets (I. for image, V. for video). For Annotation Type, SBS (side-by-side) and MOS (mean-opinion-score) refer to selecting the preferred instance from a pair of instances and assigning an average absolute score to a single instance respectively. For Rating Concerns, Overall indicates assigning scores from a holistic perspective while $\\checkmark$ denotes assigning separate scores to quality or alignment. For Number, Ins. and Ann. stand for the number of instances and human annotations respectively." + ], + "table_footnote": [], + "table_body": "
DatasetYearContentAnnotation Type (Single/Pair)Evaluation ConcernNumber Ins./Ann.
QualityAlignment
Pick-a-pic [27]2023I.SBSOverall1M/500K
ImageReward [65]2023I.SBSOverall68k/137k
HPDv2 [63]2023I.SBSOverall430k/645K
AGIQA-3k [34]2023I.MOS✓✓3K/81K
AIGCIA2023 [58]2023I.MOS✓✓2K/17K
PKU-AIGIA-4k [67]2024I.MOS✓✓4K/84K
AIGIA-20k [35]2024I.MOSOverall20K/420K
RichHF [39]2024I.MOS✓✓18K/54K
VideoFeedback [19]2024V.MOS✓✓37.6K/37.6K
T2VQA-DB [28]2024V.MOSOverall10K/27K
GenAI-Bench [33]2024I.&V.1-5 Likert ScaleOverall9.6K/9.6K
Q-Eval-100K (Ours)2024I.&V.MOS✓✓100K/960K
", + "bbox": [ + 91, + 218, + 483, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sis, the evaluation of text-to-vision content can be primarily divided into two dimensions [41, 64, 65, 73, 76]: Visual Quality (the perceived quality of the visual content, which can be simply understood as how good it looks) and Alignment level (the consistency between text and vision, which can be interpreted as how accurate the generation is).", + "bbox": [ + 89, + 369, + 482, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To meet the need for evaluation, many text-to-vision evaluation datasets have been proposed, along with corresponding evaluation algorithms [11, 12, 19, 19, 24, 28, 33-35, 39, 41, 58, 67, 71, 74, 75]. However, these efforts face the following significant limitations: 1) The key evaluation dimensions for text-to-vision content are often not systematically captured. Some datasets propose too many dimensions, adding unnecessary complexity to the evaluation process. The practical applicability of these dimensions can be narrow or lead to redundancy. 2) Most text-to-vision evaluation datasets fail to disentangle visual quality and alignment. These datasets either focus solely on alignment or visual quality, or merge both dimensions into a single score, leading to results that are often incomplete and ambiguous, making it challenging to address specific evaluation needs. 3) The scale of these datasets remains insufficient. With the rise of Large Multimodal Models (LMMs), which have demonstrated strong capabilities in visual and textual understanding, researchers are increasingly leveraging them for text-to-vision evaluation. However, current dataset sizes remain inadequate to fully unlock the potential of LMM-based models [76], conceivably restricting their applicability and generalization in real-world scenarios.", + "bbox": [ + 89, + 462, + 482, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we present Q-Eval-100K, which, to the best of our knowledge, is the largest text-to-vision evaluation dataset with Mean Opinion Scores (MOSs), comprising 100K instances (including 60K generated images & 40K generated videos). A brief comparison of Q-Eval-100K and previous text-to-vision eval", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "uation datasets is illustrated in Table 1. We manually gather prompts from existing benchmarks and create diverse prompts that focus on three key aspects: entity generation, entity attribute generation, and interaction capability. The instances in Q-Eval-100K are then generated from a diverse range of generative models, both open-source and closed-source, to ensure high diversity. We implement a rigorous, scientifically grounded subjective evaluation process using a Sample & Scrutinize strategy, focusing on both visual quality and alignment level for each of the 100K instances, yielding a total of high-quality 960K human annotations.", + "bbox": [ + 511, + 90, + 903, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Building on the proposed Q-Eval-100K, we propose Q-Eval-Score, a unified evaluation framework capable of assessing both visual quality and alignment, providing separate scores for each dimension. We first adapt Q-Eval-100K into a Supervised Fine-Tuning (SFT) dataset optimized for injecting knowledge into LMMs. Scores are transformed into adjective-based ratings, then reformulated within a well-guided context-prompt format. Specifically, for visual quality, we guide the model to identify positive and negative visual impacts, evaluate the intensity of these impacts, and make a balanced judgment. For alignment, we guide the model to perceive the overall situation, examine details, and reach a balanced judgment. The fine-tuning process is then supervised by a combined CE and MSE loss. During inference, the final score is computed as a weighted average based on the probability of each rating token. Notably, in handling long-prompt alignment, we observed that direct alignment assessment often yields low scores due to oversimplification. To address this, we propose a Vague-to-Specific strategy, where a long prompt is converted into a vague version retaining only core information and multiple prompts with specific details. These prompts are evaluated separately and the alignment scores are combined to the final score. Our contributions can be summarized as follows:", + "bbox": [ + 511, + 268, + 906, + 630 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present Q-Eval-100K, the largest text-to-vision evaluation dataset with MOSs, comprising 100K instances from various generative models. We employ a scientifically grounded evaluation methodology, using a Sample & Scrutinize strategy to collect 960K human annotations focusing on visual quality and alignment.", + "- We propose Q-Eval-Score, a unified evaluation framework capable of independently assessing visual quality and alignment, providing separate scores for each dimension. Specifically, we adapt Q-Eval-100K into an SFT dataset with adjective-based ratings in a structured context-prompt format for enhancing the visual quality and alignment evaluation capabilities of LMMs.", + "- To improve alignment evaluation for long prompts, we introduce a Vague-to-Specific strategy, which separates prompts into core and detailed variants, yielding a more accurate alignment score through weighted averaging." + ], + "bbox": [ + 514, + 641, + 903, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10622", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 91, + 89, + 240, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Benchmarks for Text-to-Vision Evaluation", + "text_level": 1, + "bbox": [ + 89, + 117, + 450, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Early text-to-vision benchmarks largely depend on multimodal datasets labeled with captions [10, 22, 43]. However, with increasing recognition of human feedback's value [14, 23, 76], many benchmarks begin to employ human annotations. Common annotation methods include SBS (side-by-side) and MOS (mean opinion score) [49, 68]. SBS requires selecting a preferred instance from a pair, while MOS assigns a score to a single instance. SBS is generally easier for human subjects and more precise, but MOS is more versatile and broadly applicable to various situations [6, 32].", + "bbox": [ + 89, + 143, + 483, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-vision evaluation dimensions [41, 73] can be categorized into visual quality and alignment. While some benchmarks [11, 12, 19, 24] treat aspects like naturalness, aesthetics, and temporal consistency as distinct dimensions, we view these as components of visual quality since they collectively influence the quality of experience (QoE) for viewers. Early benchmarks [34, 35, 58, 67] for generated images comprehensively address both visual quality and alignment for evaluation. RichHF [39] enhances these evaluations by incorporating subjective scores, heatmaps, and misalignment tokens. For video, VideoFeedback [19] introduces five dimensions of quality and alignment, while T2VQA-DB [28] focuses primarily on visual quality. Further, GenAI-Bench [33] evaluates alignment for both generated images and generated videos. The proposed Q-Eval-100K dataset offers a unified text-to-vision evaluation framework, significantly increasing dataset scale and diversity, making it distinct from prior benchmarks.", + "bbox": [ + 89, + 297, + 483, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Metric for Text-to-Vision Evaluation", + "text_level": 1, + "bbox": [ + 89, + 587, + 406, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous evaluation methods separately focus on either visual quality or alignment. Perceptual methods assess the visual quality of generated content, utilizing traditional scores like IS [52], FID [21], and LPIPS [69] with pretrained neural networks. Recently, data-driven models [34] trained on specialized datasets have further advanced perceptual score prediction. Additionally, methods such as CLIP-IQA [57] and Q-Align [62] leverage text prompts to enhance perceptual alignment. Alignment methods, integrating both text and vision modalities, initially use CLIP-Score [20] due to its ease of application. To address more complex prompts, some approaches [27, 63, 65] incorporate human feedback to improve evaluation accuracy. Given the powerful interpretative capabilities of LMMs, recent work [13, 26, 29, 40, 70] has begun to apply these models to alignment assessments. Most existing models evaluate either perceptual quality or alignment exclusively. The proposed Q-Eval-Score addresses this gap by offering decoupled scores for both perceptual quality and alignment.", + "bbox": [ + 89, + 613, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d00cbcf089f2da000b26a669464fb8b3f547426aff33b7e9d8994df2ff0a2768.jpg", + "image_caption": [ + "Figure 2. Illustration of the Sample and Scrutinize quality control strategy for annotations in Q-Eval-100K. We randomly select a sample of 5K instances from the full dataset, which are then reviewed by experts to establish golden scores. A batch of annotations is approved only if the scores of the sampled instances show a high correlation with these expert-assigned golden scores." + ], + "image_footnote": [], + "bbox": [ + 553, + 89, + 867, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Q-Eval-100K Construction", + "text_level": 1, + "bbox": [ + 513, + 378, + 764, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Basic Principles", + "text_level": 1, + "bbox": [ + 513, + 404, + 671, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The construction process of Q-Eval-100K is illustrated in Fig. 3. We follow these guiding principles: 1) Ensuring diversity in generated content by collecting a wide range of prompts and using multiple generative models; 2) Ensuring annotation quality through carefully designed experimental settings and standards to achieve the highest accuracy; 3) Ensuring effective learning, through adapting the data for LMM suitability by transforming both visual quality and alignment scores into a context-aware SFT dataset.", + "bbox": [ + 511, + 428, + 906, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Sources Collection", + "text_level": 1, + "bbox": [ + 513, + 574, + 692, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt Designing. The prompt design focuses on three main aspects: Entity Generation, Entity Attribute Generation, and Interaction Capability. 1) Entity generation targets the primary entities (people, objects, etc.) to be generated. 2) Entity attribute generation emphasizes the attributes (clothing, color, material, etc.) of the entities. 3) Interaction capability focuses on the interactions between the generated entities and other entities or the background, such as their spatial relationships and actions. Following the outlines mentioned above, we manually create a portion of the prompts and extract some from existing datasets [33, 46].", + "bbox": [ + 511, + 598, + 906, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generation Models. We utilize multiple popular text-to-image and text-to-video models to ensure diversity, which include FLUX [30], Lumina-T2X [17], PixArt [9], Stable Diffusion 3 [3], Stable Diffusion XL [50], DALL-E 3 [47], Wanx [15], Midjourney [44], Hunyuan-DiT [38], Kolors [54], ERNIE-ViLG [16], CogVideoX [66], Runway GEN-2 [18], Runway GEN-3 [51], Latte [42], Kling [53], Dreamina [8], Luma [1], PixVerse [2], Pika [31], Stable Video Diffusion [7], Vidu [55].", + "bbox": [ + 511, + 765, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10623", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bfa9e0925b787e3463079c31ef131d339345223b4920fdc44c25ee0a73cfa136.jpg", + "image_caption": [ + "Figure 3. Overview of the Q-Eval-100K construction process. We design a wide range of prompts and employ various text-to-vision models to generate diverse content. Subjective evaluations are then conducted to rate the visual quality and alignment of these generated instances. The resulting scores form the SFT dataset, which can help inject corresponding knowledge into LMMs." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 346, + 309 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ed5657f5a42e2a5dc799860bc70c301c7c6630409c672829db1eae3fb8d7f1d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 89, + 635, + 309 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a1edd7e9cd78560fccf5a1532f7f19bbf76ff9e8f26fab474814c74caefbd498.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 90, + 897, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Subjective Experiment", + "text_level": 1, + "bbox": [ + 89, + 391, + 302, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the large scale of Q-Eval-100K, we develop rigorous experimental protocols to ensure the highest possible accuracy in our annotations. To facilitate this, we establish a well-controlled indoor experimental environment, where more than 200 human subjects are recruited to participate in the annotation. To ensure the accuracy of annotations is not compromised by individual cognitive differences or annotator fatigue, we propose a Sample & Scrutinize data control strategy as shown in Fig. 2. The strategy includes two steps: 1) First, we randomly sample 5,000 instances from the entire dataset. We then organize experts with rich experience to discuss and score these instances, leading to the establishment of golden scores for both visual quality and alignment. These golden scores remain hidden for all subsequent experimental subjects. 2) Next, we provide human annotators with comprehensive training before they begin the annotation process. After each batch, we gather the scores for instances that have golden scores and compare them with these golden scores, calculating the correlation values (SRCC-rank similarity). Only batches with an SRCC above 0.8 are accepted, otherwise, they are rejected.", + "bbox": [ + 88, + 415, + 483, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, we split Q-Eval-100K into training and testing sets in an 80:20 ratio. Each instance in the training set has at least three annotations, while each instance in the testing set has a minimum of twelve annotations to ensure accuracy. This process results in a total of over 960K annotations, calculated as follows: 80K (training instances) x 2 (visual quality & alignment) x 3 (minimum annotation number) + 20K (training instances) x 2 (visual quality & alignment) x 12 (minimum annotation number) = 960K annotations. Finally, we calculate the average of the multiple annotations to derive the score for each instance.", + "bbox": [ + 89, + 734, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Statistical Analysis", + "text_level": 1, + "bbox": [ + 513, + 391, + 694, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The distributions of MOSs for visual quality and alignment are exhibited in Fig. 4 respectively, which reveal several key insights. In general, there are substantial differences among generation models in both visual quality and alignment, with their distributions displaying significant inconsistencies, indicating varied performance across different generation prompts. 1) For image alignment, distributions are generally skewed higher, suggesting that models perform relatively well in aligning images, though multiple peaks in the 4-5 and 2-3 score ranges indicate some fluctuation in performance. 2) In video alignment, model performance varies more markedly, with most scores concentrated between 2 and 4, highlighting the need for improvement in alignment in video generation. 3) Visual quality for images scores noticeably lower than image alignment, indicating that generation models perform significantly worse in visual quality. Furthermore, the wider distribution spread in image visual quality suggests greater variance and instability across models. 4) Similarly, video visual quality scores are lower than alignment scores, highlighting a consistent underperformance in visual quality. Interestingly, models such as Kling, Dreamina, Luma, PixVerse, and Pika exhibit similar distributions for alignment and visual quality, indicating consistent capability across both aspects. However, this consistency is not observed across all models.", + "bbox": [ + 511, + 415, + 906, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, the findings above highlight a notable disparity in that visual quality generally falls behind alignment. This gap likely stems from the current emphasis on alignment optimization, which is also relatively easier to improve, whereas visual quality has received less focus. This analysis underscores the importance of Q-Eval-100K as a comprehensive benchmark for evaluating both dimensions.", + "bbox": [ + 511, + 794, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10624", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/868b3b0a0196b8fab8bb19d8e29a9f703adcfd0fe0ed01a44b85f63d88381eee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 90, + 493, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/31eb319bda4ca5c23fae2bcdaf5eef3328911ab680c9f7f7f057aa7aff4eed4c.jpg", + "image_caption": [ + "(b) Video Alignment" + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 879, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/13ade1db97feb245fb068571b7d359659d11239699a102d0ba99f3463e72c69c.jpg", + "image_caption": [ + "(a) Image Alignment", + "(c) Image Visual Quality" + ], + "image_footnote": [], + "bbox": [ + 117, + 224, + 493, + 337 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b0b710acf65d2c5262715d1ecdf0d4df9936593eb632caefd507a4db37b2a244.jpg", + "image_caption": [ + "(d) Video Visual Quality", + "Figure 4. MOS distributions for the visual quality and alignment of generated images and videos in the Q-Eval-100K dataset respectively." + ], + "image_footnote": [], + "bbox": [ + 504, + 227, + 879, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Q-Eval-Score", + "text_level": 1, + "bbox": [ + 89, + 401, + 228, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Unified Pipeline for Decoupled Evaluation", + "text_level": 1, + "bbox": [ + 89, + 426, + 449, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although the evaluation of visual quality and alignment are two relatively independent tasks, we leverage the adaptability and extensive prior knowledge of LMMs to propose a unified model, Q-Eval-Score, that addresses both visual quality and alignment level evaluation within a single framework. Specifically, we convert the human-labeled MOS from the Q-Eval-100K dataset for both visual quality and alignment levels into a fixed-prompt format, creating a mixed SFT dataset. We then fine-tune the LMM, enabling it to evaluate both visual quality and alignment levels.", + "bbox": [ + 89, + 450, + 483, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. How to Teach LMMs to Evaluate", + "text_level": 1, + "bbox": [ + 89, + 611, + 382, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Context Prompt", + "text_level": 1, + "bbox": [ + 89, + 633, + 259, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In previous work using prompts with LMMs for evaluation, the questions are often straightforward and simple, such as 'Can you evaluate the quality of the image?' (Q-Align [62]) or 'Does this figure show [Prompt]? Please answer yes or no.' (VQAScore [40]). However, this simplicity may lead to confusion for the model, as the prompts may not be specific enough to guide a more detailed or accurate evaluation.", + "bbox": [ + 89, + 657, + 482, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the chain-of-thought (CoT [59]) concept and given that humans undergo a reasoning process when evaluating visual quality and alignment, we propose a Context-Prompt format to construct our SFT dataset. For the visual quality task, the human evaluation process can be summarized as first identifying both positive and negative quality factors, then measuring these factors, and finally weighing them to reach a conclusion. Based on this process, we design the following prompt structure:", + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Context Prompt for Visual Quality", + "text_level": 1, + "bbox": [ + 513, + 402, + 759, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "# User: Suppose you are an expert in evaluating the visual quality of AI-generated image/video. First, identify any visual distortions and positive visual appeal regarding low-level features and aesthetics. Next, assess the severity of distortions and their impact on the viewing experience, noting whether they are subtle or distracting, and evaluate how the positive features enhance the visual appeal, considering their strength and contribution to the overall aesthetics. Finally, balance the identified distortions against the positive aspects and give your rating on the visual quality. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad).", + "bbox": [ + 511, + 420, + 906, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the alignment task, the human evaluation process involves observing whether the overall content generally aligns with the text, followed by a more detailed comparison, and finally a comprehensive evaluation for conclusion:", + "bbox": [ + 511, + 637, + 905, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Context Prompt for Visual Quality", + "text_level": 1, + "bbox": [ + 511, + 699, + 759, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "# User: Suppose you are an expert in evaluating alignment between the text prompt and the AI-generated image/video. Begin by considering whether the overall concept of the prompt is captured in the image/video. Then, examine the specific details, such as the presence of key objects, their attributes, and relationships. Check if the visual content accurately reflects these aspects. Finally, give your alignment rating considering both overall and detailed accuracy. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad).", + "bbox": [ + 511, + 717, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10625", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c012a1b87628a1fe21a919634134272466e72d18892c926c1717820e29b00ea8.jpg", + "image_caption": [ + "Figure 5. The pipeline of the proposed Q-Eval-Score model involves multiple stages. First, the Q-Eval-100K SFT dataset is used to train the LMM on visual quality and alignment knowledge. Then, context prompts are applied to guide the LMM towards generating more detailed and accurate outputs. Finally, the rating token probabilities are converted into predicted scores. Additionally, long prompt alignment is achieved through a Vague-to-Specific strategy to further refine the model's responses." + ], + "image_footnote": [], + "bbox": [ + 114, + 87, + 883, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 'Translating' MOS into Ratings", + "text_level": 1, + "bbox": [ + 89, + 373, + 369, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is well established that discrete adjective ratings are easier for LMMs to interpret compared to numerical scores [62, 72]. Since MOS in Q-Eval-100K is labeled in absolute terms, we can easily map MOS to the corresponding rating:", + "bbox": [ + 89, + 398, + 483, + 463 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nR (s) = r _ {i} \\text {i f} m + \\frac {i - 1}{5} \\times (M - m) < s \\leq m + \\frac {i}{5} \\times (M - m), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 473, + 480, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\{r_i|_{i = 1\\sim 5}\\} = \\{Bad,Poor,Fair,Good,Excellent\\}$", + "bbox": [ + 101, + 505, + 455, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $m = 1$ and $M = 5$ (score range bound of Q-Eval-100K), $R(s)$ indicates the mapped rating of MOS value $s$ .", + "bbox": [ + 89, + 535, + 483, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Model Architecture", + "text_level": 1, + "bbox": [ + 89, + 579, + 277, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Using the constructed SFT dataset with the question-answer pairs as described, we select Qwen-VL [5] as the LMM model (Qwen2-VL-7B-Instruct) for training, which has demonstrated strong visual understanding capabilities for both images and videos. For video processing, each video is converted into a sequence of images at a rate of one frame per second, which is then fed into the model as the input. The scoring computation method is detailed as follows. For the rating token, we first calculate the model output probabilities $p_j$ for each of the five rating terms {Excellent, Good, Fair, Poor, Bad}, where $j \\in \\{1, 2, 3, 4, 5\\}$ . Then we define the final predicted rating $\\hat{r}$ as the weighted average of these probabilities:", + "bbox": [ + 89, + 604, + 483, + 801 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {r} = \\sum_ {j = 1} ^ {5} p _ {j} \\cdot w _ {j}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 814, + 483, + 858 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $w_{j}$ is the numerical weight assigned to each rating (e.g., $w_{j} = \\{1,0.75,0.5,0.25,0\\}$ for Excellent to Bad).", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Loss Function", + "text_level": 1, + "bbox": [ + 513, + 372, + 660, + 387 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The loss function for the model consists of two parts: Cross-Entropy (CE) Loss and Mean Squared Error (MSE) Loss. The CE Loss can assist the LMM in learning the general question-answer format and necessary knowledge. Meanwhile, the MSE Loss refines the score prediction accuracy. The CE Loss for question-answer pairs is defined as:", + "bbox": [ + 511, + 396, + 906, + 488 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C E} = - \\sum_ {i = 1} ^ {N} y _ {i} \\cdot \\log \\left(p _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 497, + 906, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $y_{i}$ is the one-hot encoded vector representing the true label for instance $i$ , and $p_{i}$ is the predicted probability vector for the answer tokens. The MSE Loss can then be given by:", + "bbox": [ + 511, + 547, + 906, + 595 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M S E} = \\left(\\hat {r} - r _ {\\mathrm {M O S}}\\right) ^ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 603, + 906, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{r}$ and $r_{\\mathrm{MOS}}$ represent the predicted scores and the MOS labels respectively. The total loss $\\mathcal{L}$ is a weighted sum of the CE Loss and MSE Loss:", + "bbox": [ + 511, + 632, + 905, + 678 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\alpha_ {1} \\cdot \\mathcal {L} _ {C E} + \\beta_ {1} \\cdot \\mathcal {L} _ {M S E}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 689, + 903, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha_{1}$ and $\\beta_{1}$ (default set as $1\\& 1$ ) are weight parameters controlling the contribution of each loss term.", + "bbox": [ + 511, + 717, + 905, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Handling Long Prompt Alignment", + "text_level": 1, + "bbox": [ + 511, + 756, + 815, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During inference, we observe that the trained LMM tends to undervalue alignment when handling long prompts (more than 25 words). This is partly because long prompts are underrepresented in the training data, leading to insufficient training. More importantly, the LMM acts as a strict evaluator, often penalizing significant points for inconsistencies that may seem minor to humans. These small discrepancies occur more frequently with long prompts. To manage this", + "bbox": [ + 511, + 779, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10626", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/70c39ee643de592e929e042c19d1cc44556bda901b06a6412dd8b3c809e8180d.jpg", + "image_caption": [ + "Generated Image", + "Original Long Prompt", + "Figure 6. An example of the Vague-to-Specific strategy. The original long prompt is divided by the LLM (QwenLM [4]) into a Vague Prompt and several Specific Prompts. The alignment score is first calculated separately for each part, then combined using weighted averaging to form the final score." + ], + "image_footnote": [], + "bbox": [ + 114, + 107, + 267, + 224 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A new Chinese style painting, a group of animals are having a meeting, the owl is sitting in the leader's position and speaking, they are all wearing clothes with futuristic designs, and the picture should have a sense of technology.", + "bbox": [ + 282, + 108, + 454, + 223 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62e7a80e8eac99f65dbdd31692230e6861027a9228781e5c480ba047955e6c7b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Vague PromptIn a futuristic Chinese-style painting, an owl leads a tech-themed animal meeting. 4 A_v=4
Specific Prompts-A group of animals are depicted in a meeting. 5
-The owl is the leader, sitting in the center, speaking. 51/n ∑i=1n As_i = 13/3
Final Align. 0.5*4+0.5*4.33 = 4.17-Each animal wears futuristic clothing, adding a tech flair to the scene.3
", + "bbox": [ + 109, + 232, + 464, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "issue, we propose a Vague-to-Specific strategy. We use an additional LLM (QwenLM [4]) to summarize long prompts, retaining only the core features while filtering out details, producing a concise Vague Prompt. Then, we split the long prompt into Specific Prompts (no more than three), each maintaining full details but avoiding redundancy:", + "bbox": [ + 89, + 434, + 483, + 526 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\left(P _ {v}, \\left\\{P _ {s _ {1}}, \\dots , P _ {s _ {n}} \\right\\}\\right) = \\mathcal {V S} \\left(P _ {L o n g}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 541, + 482, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $P_{v}$ represents the Vague Prompt, $\\{P_{S_1},\\dots ,P_{S_n}\\}$ stands for the set of Specific Prompts, $\\mathcal{VS}(\\cdot)$ indicates the prompt split function, and $P_{Long}$ is the original long prompt. For the Vague Prompt, we calculate alignment in the usual way. However, directly asking for consistency with the Specific Prompts is not appropriate since each one addresses only part of the vision content. Drawing inspiration from the VQAScore [40] approach, we modify the question to a softer format, such as 'Does the image/video show [Prompt]?' to evaluate alignment (measuring as the logit probability of answering 'Yes') for each Specific Prompts. Finally, we combine the results from both the Vague Prompt and Specific Prompt using a weighted approach to calculate the final alignment score:", + "bbox": [ + 89, + 573, + 483, + 785 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {f} = \\alpha_ {2} \\mathcal {A} _ {v} + \\beta_ {2} \\left(\\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {A} _ {s _ {i}}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 800, + 482, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\mathcal{A}_f, \\mathcal{A}_v,$ and $\\mathcal{A}_{s_i}$ are the alignment scores for the final evaluation, vague prompt, and $i$ -th specific prompt. $\\alpha_{2}$ and $\\beta_{2}$ (0.5 & 0.5 as default) are weight parameters.", + "bbox": [ + 89, + 854, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f7f2512ef22d09c3b61f14334a12b8ba03c7c9de58710e0106ede4137aa7b0c3.jpg", + "table_caption": [ + "Table 2. Performance comparison on the visual quality aspect of Q-Eval-100K. Best in bold, second underlined." + ], + "table_footnote": [], + "table_body": "
Model\n(Visual\nQuality)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE0.2390.2380.8290.758-0.057-0.074-0.333-0.241
CLIP-IQA0.3340.3240.6000.6850.1940.1750.0950.076
Q-Align0.5870.5780.7140.9140.5000.5020.7620.762
IPCE0.5500.5600.9330.9370.2990.3020.4760.568
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.814
", + "bbox": [ + 514, + 121, + 906, + 222 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/821ab9cc6cf30f345fe07877a08d74e48f865801d898148e305ddd2d9f9bfbf5.jpg", + "table_caption": [ + "Table 3. Performance comparison on the alignment aspect of Q-Eval-100K. Considering that CLIPScore, BLIP2Score, and VQAScore are popular zero-shot alignment evaluation metrics, we provide the corresponding performance with the official default weight as well (marked with *)." + ], + "table_footnote": [], + "table_body": "
Model (Align-ment)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
CLIPScore*0.2450.2520.6170.6850.1860.2190.5180.500
BLIP2Score*0.2970.3300.7640.8350.2180.2500.2950.296
VQAScore*0.5490.4680.3850.5550.4330.4320.4330.351
CLIPScore0.7680.7400.9580.9560.4310.4430.5190.509
BLIP2Score0.7660.7430.9330.9340.4830.4880.5120.481
ImageReward0.7620.7320.9250.9550.4720.4850.3750.362
Q-Eval-Score0.8220.8020.9640.9690.6070.6340.6480.605
", + "bbox": [ + 514, + 297, + 906, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 511, + 434, + 638, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 511, + 460, + 702, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training & Evaluation. The Qwen2-VL-7B-Instruct [5] serves as the backbone LMM for Q-Eval-Score. All visual quality and alignment data from images and videos are combined for training. Training is conducted on 8 A100 GPUs for one epoch by default. For evaluation metrics, we use SRCC and PLCC, which measure the rank and linear correlation between predicted scores and MOSs. We propose evaluations at the Instance-level and Model-level which assess accuracy in ranking specific generated instances and generative models based on overall performance.", + "bbox": [ + 511, + 484, + 906, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Competitors. Few models can simultaneously predict both visual quality and alignment. Thus we selected task-specific competitors for each sub-task: For visual quality, we include NIQE [45], CLIP-IQA [57], Q-Align [62], and IPCE [48] (the top method from the 'NTIRE 2024 Quality Assessment of AI-Generated Content Challenge' [41]). For alignment, we choose CLIPScore [20], BLIP2Score [37], ImageReward [65] and VQAScore [40] as the competitors. All models are trained and tested using their default recommended parameters and the corresponding train-test sets of the Q-Eval-100K dataset unless specified.", + "bbox": [ + 511, + 637, + 908, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Discussion & General Findings", + "text_level": 1, + "bbox": [ + 511, + 815, + 790, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The general performance on the visual quality and alignment is exhibited in Table 2 and Table 3, from which we can draw several conclusions: 1) For visual quality, The proposed Q-Eval-Score outperforms all competitors, achiev-", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10627", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/35e80da09de7286c309f68fdf34027588d50de88c256210c009007f2a331c0bf.jpg", + "table_caption": [ + "Table 4. Ablation Study of Q-Eval-Score." + ], + "table_footnote": [], + "table_body": "
ModelQ-Eval-Image (Quality)Q-Eval-Video (Quality)Q-Eval-Image (Alignment)Q-Eval-Video (Alignment)
Instance-levelModel-levelInstance-levelModel-levelInstance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
w/o SFT Training0.0710.0960.2570.1360.0180.0080.2620.3140.5290.4230.5600.7050.4640.4370.5670.478
w/o Context Prompt0.5040.5090.6000.7560.5980.5910.5710.6380.8050.7760.9600.9630.5880.5970.6010.602
w/o CE Loss0.6520.6220.9320.9100.2470.2490.0710.2390.8040.7760.9480.9610.6040.6260.6420.593
w/o MSE Loss0.6650.6730.9330.9410.5950.5830.6900.7120.7950.7630.9540.9580.5800.6050.6240.599
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.8140.8220.8020.9640.9690.6070.6340.6480.605
", + "bbox": [ + 91, + 107, + 903, + 196 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a6fd853166bbe222072116d413868c2922c3255c3bb9aaf0eeeb8766682f880a.jpg", + "table_caption": [ + "Table 5. Performance comparison on the alignment aspect of Q-Eval-100K on the long prompt subset, where w/o V2S and w V2S represents the proposed Q-Eval-Score model with and without the Vague-to-Specific strategy respectively." + ], + "table_footnote": [], + "table_body": "
Model\n(Align-ment)Q-Eval-Image (Long)Q-Eval-Video (Long)
Instance-levelInstance-level
SRCCPLCCSRCCPLCC
CLIPScore0.5330.5470.3590.367
BLIP2Score0.6200.6360.3920.395
VQAScore0.4320.3250.3440.350
w/o V2S0.5910.5990.4800.470
w V2S0.6200.6230.5170.512
", + "bbox": [ + 91, + 262, + 482, + 353 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ed6008abf06a9b7907295e6241dd25a3ca04dadf5ed136432c49975029ff6f6f.jpg", + "table_caption": [ + "Table 6. Cross-dataset validation performance on GenAI-Bench. The Q-Eval-Score is trained on the Q-Eval-100K and then validated on GenAI-Bench. * indicates using default weight." + ], + "table_footnote": [], + "table_body": "
Model\n(Alignment)GenAI-Bench (Image)GenAI-Bench (Video)
SRCCPLCCSRCCPLCC
CLIPScore*0.1740.1690.2690.269
BLIP2Score*0.2210.2090.2890.275
VQAScore*0.5560.5020.5270.505
CLIPScore0.6810.6700.6100.628
BLIP2Score0.6870.6790.6790.705
ImageReward0.6640.6560.6630.684
Q-Eval-Score0.7570.7470.7170.714
", + "bbox": [ + 91, + 412, + 482, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing the best performance overall. The decline in video performance is likely due to the 1fps frame sampling method, which causes a loss of temporal information, leading to inaccurate estimations. Despite this, at the instance-level, Q-Eval-Score still leads the second-best competitor (Q-Align) by $10\\%$ on video instance-level SRCC. 2) For alignment, Q-Eval-Score also demonstrates a significant lead in alignment, outperforming competitors by $6\\%$ in image instance-level SRCC and $12\\%$ in video instance-level SRCC. Additionally, the substantial performance improvements seen in the trained competitors suggest that Q-Eval-100K provides valuable knowledge for alignment evaluation. 3) In comparison to alignment, Q-Eval-Score's performance in visual quality is notably lower, indicating that predicting visual quality is more challenging. This is likely because alignment evaluation is more straightforward and objective, while visual quality perception is more complex and subjective, making it harder to assess. Overall, the proposed Q-Eval-Score exhibits exceptional potential in both visual quality and alignment, achieving over 0.94 performance at the image model-level, closely aligning with human evaluations. This strong performance not only highlights the robustness of the model but also underscores its promising ability to serve as an effective evaluation metric.", + "bbox": [ + 88, + 537, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Further Experiments", + "text_level": 1, + "bbox": [ + 511, + 204, + 714, + 219 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "I) Ablation Study. We conduct a detailed ablation study to assess the contribution of proposed strategies and CE/MSE loss. The results are presented in Table 4. It is clear that each of the strategies we proposed and both CE/MSE loss make a significant contribution to the final outcome.", + "bbox": [ + 511, + 228, + 903, + 304 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "II) Long Prompt. To test the Vague-to-Specific strategy for long prompt alignment, we select a subset of 5,000 instances from Q-Eval-100K that contain long prompts (over 25 words) for testing, performance shown in Table 5. Due to the limited data size, we present only the instance-level performance. The results clearly show that the Vague-to-Specific strategy significantly improves performance, indicating the effectiveness of handling long prompt alignment.", + "bbox": [ + 511, + 306, + 903, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "III) Cross-dataset Validation. To demonstrate the value of the Q-Eval-100K dataset, we conduct a cross-dataset validation, with performance results shown in Table 6. It is important to note that instances generated from prompts in GenAI-Bench are excluded from this validation. The results clearly show that models trained on Q-Eval-100K significantly outperform the current state-of-the-art VQAScore on GenAI-Bench by a large margin, providing strong evidence of the generalization value of the Q-Eval-100K dataset.", + "bbox": [ + 511, + 429, + 905, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 585, + 633, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, we introduce Q-Eval-100K, the largest text-to-vision evaluation dataset to date, featuring 100K instances and 960K human annotations for assessing visual quality and alignment. We also present Q-Eval-Score, a unified evaluation framework that leverages this dataset to provide separate scores for each dimension. Experimental results show that Q-Eval-Score outperforms existing methods, demonstrating its potential for more reliable, comprehensive assessments of text-to-vision models. Looking ahead, we hope this work can lay a strong foundation for further advancements in text-to-vision model promotion and real-world evaluation applications.", + "bbox": [ + 511, + 612, + 905, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 511, + 813, + 665, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The work was supported in part by the National Natural Science Foundation of China under Grant 62301310, Grant 623B2073, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426.", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10628", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Luma AI. 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Gpt-4v (ision) as a generalist evaluator for vision-language tasks. arXiv preprint arXiv:2311.01361, 2023. 1, 3", + "[71] Zicheng Zhang, Ziheng Jia, Haoning Wu, Chunyi Li, Zijian Chen, Yingjie Zhou, Wei Sun, Xiaohong Liu, Xiongkuo Min, Weisi Lin, et al. Q-bench-video: Benchmarking the video quality understanding of Imms. arXiv preprint arXiv:2409.20063, 2024. 2", + "[72] Zicheng Zhang, Haoning Wu, Zhongpeng Ji, Chunyi Li, Erli Zhang, Wei Sun, Xiaohong Liu, Xiongkuo Min, Fengyu Sun, Shangling Jui, et al. Q-boost: On visual quality assessment ability of low-level multi-modality foundation models. In 2024 IEEE International Conference on Multimedia and Expo Workshops (ICMEW), pages 1-6. IEEE, 2024. 1, 6", + "[73] Zicheng Zhang, Haoning Wu, Chunyi Li, Yingjie Zhou, Wei Sun, Xiongkuo Min, Zijian Chen, Xiaohong Liu, Weisi Lin, and Guangtao Zhai. 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Quality assessment in the era of large models: A survey. arXiv preprint arXiv:2409.00031, 2024. 2, 3" + ], + "bbox": [ + 516, + 90, + 903, + 837 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10631", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_model.json b/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed5c9527d8c5e46b9a46a41e5ad1830616a5053b --- /dev/null +++ b/2025/Q-Eval-100K_ Evaluating Visual Quality and Alignment Level for Text-to-Vision Content/4ac7661d-7792-4463-bffb-e8cb82d66bee_model.json @@ -0,0 +1,2444 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.186, + 0.13, + 0.817, + 0.175 + ], + "angle": 0, + "content": "Q-Eval-100K: Evaluating Visual Quality and Alignment Level for Text-to-Vision Content" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.203, + 0.784, + 0.277 + ], + "angle": 0, + "content": "Zicheng Zhang\\(^{1}\\) Tengchuan Kou\\(^{1}\\) Shushi Wang\\(^{1}\\) Chunyi Li\\(^{1}\\) Wei Sun\\(^{1}\\) Wei Wang\\(^{2}\\) Xiaoyu Li\\(^{2}\\) Zongyu Wang\\(^{2}\\) Xuezhi Cao\\(^{2}\\) Xiongkuo Min\\(^{1}\\) Xiaohong Liu\\(^{1\\dagger}\\) Guangtao Zhai\\(^{1}\\) Shanghai Jiao Tong University \\({}^{2}\\)Meituan" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.309, + 0.327, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.341, + 0.485, + 0.749 + ], + "angle": 0, + "content": "Evaluating text-to-vision content hinges on two crucial aspects: visual quality and alignment. While significant progress has been made in developing objective models to assess these dimensions, the performance of such models heavily relies on the scale and quality of human annotations. According to Scaling Law, increasing the number of human-labeled instances follows a predictable pattern that enhances the performance of evaluation models. Therefore, we introduce a comprehensive dataset designed to Evaluate Visual quality and Alignment Level for text-to-vision content (Q-EVAL-100K), featuring the largest collection of human-labeled Mean Opinion Scores (MOS) for the mentioned two aspects. The Q-EVAL-100K dataset encompasses both text-to-image and text-to-video models, with 960K human annotations specifically focused on visual quality and alignment for 100K instances (60K images and 40K videos). Leveraging this dataset with context prompt, we propose Q-Eval-Score, a unified model capable of evaluating both visual quality and alignment with special improvements for handling long-text prompt alignment. Experimental results indicate that the proposed Q-Eval-Score achieves superior performance on both visual quality and alignment, with strong generalization capabilities across other benchmarks. These findings highlight the significant value of the Q-EVAL-100K dataset. Data and codes will be available at https://github.com/zzc-1998/QEval." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.777, + 0.222, + 0.793 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.802, + 0.484, + 0.879 + ], + "angle": 0, + "content": "With the rapid advancement of generative AI, millions of text-to-image and text-to-video content are being generated daily across various platforms [25, 56], applied in industrial production or directly used by consumers. However, due to current technological limitations, text-to-vision con" + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.31, + 0.871, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.708, + 0.908, + 0.765 + ], + "angle": 0, + "content": "Figure 1. Illustration of the unified evaluation dimensions of Q-Eval-100K. We focus on visual quality (including all factors that may impact the viewing experience) and alignment level, which measures the accuracy of the generated content to the prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "tent often falls short of being perfect upon generation and cannot be immediately deployed [34, 36, 40], which usually requires expert evaluation, editing, and fine-tuning. As a result, numerous efforts have been made to develop automated methods for evaluating text-to-vision content, aiming to control the quality of generation and guide the necessary optimizations effectively [13, 26, 27, 29, 40, 60–63, 65, 70, 72]. Through extensive theoretical and experimental analy-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.24, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10621" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.483, + 0.215 + ], + "angle": 0, + "content": "Table 1. A brief comparison of the latest text-to-vision evaluation datasets (I. for image, V. for video). For Annotation Type, SBS (side-by-side) and MOS (mean-opinion-score) refer to selecting the preferred instance from a pair of instances and assigning an average absolute score to a single instance respectively. For Rating Concerns, Overall indicates assigning scores from a holistic perspective while \\(\\checkmark\\) denotes assigning separate scores to quality or alignment. For Number, Ins. and Ann. stand for the number of instances and human annotations respectively." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.219, + 0.485, + 0.356 + ], + "angle": 0, + "content": "
DatasetYearContentAnnotation Type (Single/Pair)Evaluation ConcernNumber Ins./Ann.
QualityAlignment
Pick-a-pic [27]2023I.SBSOverall1M/500K
ImageReward [65]2023I.SBSOverall68k/137k
HPDv2 [63]2023I.SBSOverall430k/645K
AGIQA-3k [34]2023I.MOS✓✓3K/81K
AIGCIA2023 [58]2023I.MOS✓✓2K/17K
PKU-AIGIA-4k [67]2024I.MOS✓✓4K/84K
AIGIA-20k [35]2024I.MOSOverall20K/420K
RichHF [39]2024I.MOS✓✓18K/54K
VideoFeedback [19]2024V.MOS✓✓37.6K/37.6K
T2VQA-DB [28]2024V.MOSOverall10K/27K
GenAI-Bench [33]2024I.&V.1-5 Likert ScaleOverall9.6K/9.6K
Q-Eval-100K (Ours)2024I.&V.MOS✓✓100K/960K
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.371, + 0.483, + 0.462 + ], + "angle": 0, + "content": "sis, the evaluation of text-to-vision content can be primarily divided into two dimensions [41, 64, 65, 73, 76]: Visual Quality (the perceived quality of the visual content, which can be simply understood as how good it looks) and Alignment level (the consistency between text and vision, which can be interpreted as how accurate the generation is)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.809 + ], + "angle": 0, + "content": "To meet the need for evaluation, many text-to-vision evaluation datasets have been proposed, along with corresponding evaluation algorithms [11, 12, 19, 19, 24, 28, 33-35, 39, 41, 58, 67, 71, 74, 75]. However, these efforts face the following significant limitations: 1) The key evaluation dimensions for text-to-vision content are often not systematically captured. Some datasets propose too many dimensions, adding unnecessary complexity to the evaluation process. The practical applicability of these dimensions can be narrow or lead to redundancy. 2) Most text-to-vision evaluation datasets fail to disentangle visual quality and alignment. These datasets either focus solely on alignment or visual quality, or merge both dimensions into a single score, leading to results that are often incomplete and ambiguous, making it challenging to address specific evaluation needs. 3) The scale of these datasets remains insufficient. With the rise of Large Multimodal Models (LMMs), which have demonstrated strong capabilities in visual and textual understanding, researchers are increasingly leveraging them for text-to-vision evaluation. However, current dataset sizes remain inadequate to fully unlock the potential of LMM-based models [76], conceivably restricting their applicability and generalization in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "To address these challenges, we present Q-Eval-100K, which, to the best of our knowledge, is the largest text-to-vision evaluation dataset with Mean Opinion Scores (MOSs), comprising 100K instances (including 60K generated images & 40K generated videos). A brief comparison of Q-Eval-100K and previous text-to-vision eval" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.259 + ], + "angle": 0, + "content": "uation datasets is illustrated in Table 1. We manually gather prompts from existing benchmarks and create diverse prompts that focus on three key aspects: entity generation, entity attribute generation, and interaction capability. The instances in Q-Eval-100K are then generated from a diverse range of generative models, both open-source and closed-source, to ensure high diversity. We implement a rigorous, scientifically grounded subjective evaluation process using a Sample & Scrutinize strategy, focusing on both visual quality and alignment level for each of the 100K instances, yielding a total of high-quality 960K human annotations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.269, + 0.907, + 0.631 + ], + "angle": 0, + "content": "Building on the proposed Q-Eval-100K, we propose Q-Eval-Score, a unified evaluation framework capable of assessing both visual quality and alignment, providing separate scores for each dimension. We first adapt Q-Eval-100K into a Supervised Fine-Tuning (SFT) dataset optimized for injecting knowledge into LMMs. Scores are transformed into adjective-based ratings, then reformulated within a well-guided context-prompt format. Specifically, for visual quality, we guide the model to identify positive and negative visual impacts, evaluate the intensity of these impacts, and make a balanced judgment. For alignment, we guide the model to perceive the overall situation, examine details, and reach a balanced judgment. The fine-tuning process is then supervised by a combined CE and MSE loss. During inference, the final score is computed as a weighted average based on the probability of each rating token. Notably, in handling long-prompt alignment, we observed that direct alignment assessment often yields low scores due to oversimplification. To address this, we propose a Vague-to-Specific strategy, where a long prompt is converted into a vague version retaining only core information and multiple prompts with specific details. These prompts are evaluated separately and the alignment scores are combined to the final score. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.642, + 0.905, + 0.732 + ], + "angle": 0, + "content": "- We present Q-Eval-100K, the largest text-to-vision evaluation dataset with MOSs, comprising 100K instances from various generative models. We employ a scientifically grounded evaluation methodology, using a Sample & Scrutinize strategy to collect 960K human annotations focusing on visual quality and alignment." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.733, + 0.905, + 0.837 + ], + "angle": 0, + "content": "- We propose Q-Eval-Score, a unified evaluation framework capable of independently assessing visual quality and alignment, providing separate scores for each dimension. Specifically, we adapt Q-Eval-100K into an SFT dataset with adjective-based ratings in a structured context-prompt format for enhancing the visual quality and alignment evaluation capabilities of LMMs." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.838, + 0.905, + 0.898 + ], + "angle": 0, + "content": "- To improve alignment evaluation for long prompts, we introduce a Vague-to-Specific strategy, which separates prompts into core and detailed variants, yielding a more accurate alignment score through weighted averaging." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.642, + 0.905, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10622" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.241, + 0.106 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.118, + 0.452, + 0.133 + ], + "angle": 0, + "content": "2.1. Benchmarks for Text-to-Vision Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.144, + 0.484, + 0.295 + ], + "angle": 0, + "content": "Early text-to-vision benchmarks largely depend on multimodal datasets labeled with captions [10, 22, 43]. However, with increasing recognition of human feedback's value [14, 23, 76], many benchmarks begin to employ human annotations. Common annotation methods include SBS (side-by-side) and MOS (mean opinion score) [49, 68]. SBS requires selecting a preferred instance from a pair, while MOS assigns a score to a single instance. SBS is generally easier for human subjects and more precise, but MOS is more versatile and broadly applicable to various situations [6, 32]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.298, + 0.484, + 0.57 + ], + "angle": 0, + "content": "Text-to-vision evaluation dimensions [41, 73] can be categorized into visual quality and alignment. While some benchmarks [11, 12, 19, 24] treat aspects like naturalness, aesthetics, and temporal consistency as distinct dimensions, we view these as components of visual quality since they collectively influence the quality of experience (QoE) for viewers. Early benchmarks [34, 35, 58, 67] for generated images comprehensively address both visual quality and alignment for evaluation. RichHF [39] enhances these evaluations by incorporating subjective scores, heatmaps, and misalignment tokens. For video, VideoFeedback [19] introduces five dimensions of quality and alignment, while T2VQA-DB [28] focuses primarily on visual quality. Further, GenAI-Bench [33] evaluates alignment for both generated images and generated videos. The proposed Q-Eval-100K dataset offers a unified text-to-vision evaluation framework, significantly increasing dataset scale and diversity, making it distinct from prior benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.588, + 0.407, + 0.603 + ], + "angle": 0, + "content": "2.2. Metric for Text-to-Vision Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Previous evaluation methods separately focus on either visual quality or alignment. Perceptual methods assess the visual quality of generated content, utilizing traditional scores like IS [52], FID [21], and LPIPS [69] with pretrained neural networks. Recently, data-driven models [34] trained on specialized datasets have further advanced perceptual score prediction. Additionally, methods such as CLIP-IQA [57] and Q-Align [62] leverage text prompts to enhance perceptual alignment. Alignment methods, integrating both text and vision modalities, initially use CLIP-Score [20] due to its ease of application. To address more complex prompts, some approaches [27, 63, 65] incorporate human feedback to improve evaluation accuracy. Given the powerful interpretative capabilities of LMMs, recent work [13, 26, 29, 40, 70] has begun to apply these models to alignment assessments. Most existing models evaluate either perceptual quality or alignment exclusively. The proposed Q-Eval-Score addresses this gap by offering decoupled scores for both perceptual quality and alignment." + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.09, + 0.868, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.286, + 0.907, + 0.37 + ], + "angle": 0, + "content": "Figure 2. Illustration of the Sample and Scrutinize quality control strategy for annotations in Q-Eval-100K. We randomly select a sample of 5K instances from the full dataset, which are then reviewed by experts to establish golden scores. A batch of annotations is approved only if the scores of the sampled instances show a high correlation with these expert-assigned golden scores." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.38, + 0.766, + 0.397 + ], + "angle": 0, + "content": "3. Q-Eval-100K Construction" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.405, + 0.673, + 0.421 + ], + "angle": 0, + "content": "3.1. Basic Principles" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.907, + 0.565 + ], + "angle": 0, + "content": "The construction process of Q-Eval-100K is illustrated in Fig. 3. We follow these guiding principles: 1) Ensuring diversity in generated content by collecting a wide range of prompts and using multiple generative models; 2) Ensuring annotation quality through carefully designed experimental settings and standards to achieve the highest accuracy; 3) Ensuring effective learning, through adapting the data for LMM suitability by transforming both visual quality and alignment scores into a context-aware SFT dataset." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.575, + 0.693, + 0.59 + ], + "angle": 0, + "content": "3.2. Sources Collection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.765 + ], + "angle": 0, + "content": "Prompt Designing. The prompt design focuses on three main aspects: Entity Generation, Entity Attribute Generation, and Interaction Capability. 1) Entity generation targets the primary entities (people, objects, etc.) to be generated. 2) Entity attribute generation emphasizes the attributes (clothing, color, material, etc.) of the entities. 3) Interaction capability focuses on the interactions between the generated entities and other entities or the background, such as their spatial relationships and actions. Following the outlines mentioned above, we manually create a portion of the prompts and extract some from existing datasets [33, 46]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Generation Models. We utilize multiple popular text-to-image and text-to-video models to ensure diversity, which include FLUX [30], Lumina-T2X [17], PixArt [9], Stable Diffusion 3 [3], Stable Diffusion XL [50], DALL-E 3 [47], Wanx [15], Midjourney [44], Hunyuan-DiT [38], Kolors [54], ERNIE-ViLG [16], CogVideoX [66], Runway GEN-2 [18], Runway GEN-3 [51], Latte [42], Kling [53], Dreamina [8], Luma [1], PixVerse [2], Pika [31], Stable Video Diffusion [7], Vidu [55]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10623" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.347, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.09, + 0.637, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.091, + 0.898, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.323, + 0.908, + 0.366 + ], + "angle": 0, + "content": "Figure 3. Overview of the Q-Eval-100K construction process. We design a wide range of prompts and employ various text-to-vision models to generate diverse content. Subjective evaluations are then conducted to rate the visual quality and alignment of these generated instances. The resulting scores form the SFT dataset, which can help inject corresponding knowledge into LMMs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.392, + 0.303, + 0.407 + ], + "angle": 0, + "content": "3.3. Subjective Experiment" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.416, + 0.484, + 0.734 + ], + "angle": 0, + "content": "Given the large scale of Q-Eval-100K, we develop rigorous experimental protocols to ensure the highest possible accuracy in our annotations. To facilitate this, we establish a well-controlled indoor experimental environment, where more than 200 human subjects are recruited to participate in the annotation. To ensure the accuracy of annotations is not compromised by individual cognitive differences or annotator fatigue, we propose a Sample & Scrutinize data control strategy as shown in Fig. 2. The strategy includes two steps: 1) First, we randomly sample 5,000 instances from the entire dataset. We then organize experts with rich experience to discuss and score these instances, leading to the establishment of golden scores for both visual quality and alignment. These golden scores remain hidden for all subsequent experimental subjects. 2) Next, we provide human annotators with comprehensive training before they begin the annotation process. After each batch, we gather the scores for instances that have golden scores and compare them with these golden scores, calculating the correlation values (SRCC-rank similarity). Only batches with an SRCC above 0.8 are accepted, otherwise, they are rejected." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Additionally, we split Q-Eval-100K into training and testing sets in an 80:20 ratio. Each instance in the training set has at least three annotations, while each instance in the testing set has a minimum of twelve annotations to ensure accuracy. This process results in a total of over 960K annotations, calculated as follows: 80K (training instances) x 2 (visual quality & alignment) x 3 (minimum annotation number) + 20K (training instances) x 2 (visual quality & alignment) x 12 (minimum annotation number) = 960K annotations. Finally, we calculate the average of the multiple annotations to derive the score for each instance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.392, + 0.696, + 0.407 + ], + "angle": 0, + "content": "3.4. Statistical Analysis" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.416, + 0.907, + 0.793 + ], + "angle": 0, + "content": "The distributions of MOSs for visual quality and alignment are exhibited in Fig. 4 respectively, which reveal several key insights. In general, there are substantial differences among generation models in both visual quality and alignment, with their distributions displaying significant inconsistencies, indicating varied performance across different generation prompts. 1) For image alignment, distributions are generally skewed higher, suggesting that models perform relatively well in aligning images, though multiple peaks in the 4-5 and 2-3 score ranges indicate some fluctuation in performance. 2) In video alignment, model performance varies more markedly, with most scores concentrated between 2 and 4, highlighting the need for improvement in alignment in video generation. 3) Visual quality for images scores noticeably lower than image alignment, indicating that generation models perform significantly worse in visual quality. Furthermore, the wider distribution spread in image visual quality suggests greater variance and instability across models. 4) Similarly, video visual quality scores are lower than alignment scores, highlighting a consistent underperformance in visual quality. Interestingly, models such as Kling, Dreamina, Luma, PixVerse, and Pika exhibit similar distributions for alignment and visual quality, indicating consistent capability across both aspects. However, this consistency is not observed across all models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Overall, the findings above highlight a notable disparity in that visual quality generally falls behind alignment. This gap likely stems from the current emphasis on alignment optimization, which is also relatively easier to improve, whereas visual quality has received less focus. This analysis underscores the importance of Q-Eval-100K as a comprehensive benchmark for evaluating both dimensions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10624" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.092, + 0.495, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.251, + 0.211, + 0.364, + 0.223 + ], + "angle": 0, + "content": "(a) Image Alignment" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.093, + 0.88, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.211, + 0.747, + 0.223 + ], + "angle": 0, + "content": "(b) Video Alignment" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.226, + 0.495, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.346, + 0.373, + 0.358 + ], + "angle": 0, + "content": "(c) Image Visual Quality" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.228, + 0.88, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.345, + 0.756, + 0.358 + ], + "angle": 0, + "content": "(d) Video Visual Quality" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.37, + 0.905, + 0.385 + ], + "angle": 0, + "content": "Figure 4. MOS distributions for the visual quality and alignment of generated images and videos in the Q-Eval-100K dataset respectively." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.402, + 0.229, + 0.418 + ], + "angle": 0, + "content": "4. Q-Eval-Score" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.427, + 0.45, + 0.443 + ], + "angle": 0, + "content": "4.1. Unified Pipeline for Decoupled Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.451, + 0.484, + 0.603 + ], + "angle": 0, + "content": "Although the evaluation of visual quality and alignment are two relatively independent tasks, we leverage the adaptability and extensive prior knowledge of LMMs to propose a unified model, Q-Eval-Score, that addresses both visual quality and alignment level evaluation within a single framework. Specifically, we convert the human-labeled MOS from the Q-Eval-100K dataset for both visual quality and alignment levels into a fixed-prompt format, creating a mixed SFT dataset. We then fine-tune the LMM, enabling it to evaluate both visual quality and alignment levels." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.612, + 0.383, + 0.627 + ], + "angle": 0, + "content": "4.2. How to Teach LMMs to Evaluate" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.635, + 0.26, + 0.65 + ], + "angle": 0, + "content": "4.2.1 Context Prompt" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.764 + ], + "angle": 0, + "content": "In previous work using prompts with LMMs for evaluation, the questions are often straightforward and simple, such as 'Can you evaluate the quality of the image?' (Q-Align [62]) or 'Does this figure show [Prompt]? Please answer yes or no.' (VQAScore [40]). However, this simplicity may lead to confusion for the model, as the prompts may not be specific enough to guide a more detailed or accurate evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Inspired by the chain-of-thought (CoT [59]) concept and given that humans undergo a reasoning process when evaluating visual quality and alignment, we propose a Context-Prompt format to construct our SFT dataset. For the visual quality task, the human evaluation process can be summarized as first identifying both positive and negative quality factors, then measuring these factors, and finally weighing them to reach a conclusion. Based on this process, we design the following prompt structure:" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.403, + 0.761, + 0.419 + ], + "angle": 0, + "content": "Context Prompt for Visual Quality" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.421, + 0.907, + 0.635 + ], + "angle": 0, + "content": "# User: Suppose you are an expert in evaluating the visual quality of AI-generated image/video. First, identify any visual distortions and positive visual appeal regarding low-level features and aesthetics. Next, assess the severity of distortions and their impact on the viewing experience, noting whether they are subtle or distracting, and evaluate how the positive features enhance the visual appeal, considering their strength and contribution to the overall aesthetics. Finally, balance the identified distortions against the positive aspects and give your rating on the visual quality. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.638, + 0.906, + 0.698 + ], + "angle": 0, + "content": "For the alignment task, the human evaluation process involves observing whether the overall content generally aligns with the text, followed by a more detailed comparison, and finally a comprehensive evaluation for conclusion:" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.7, + 0.761, + 0.716 + ], + "angle": 0, + "content": "Context Prompt for Visual Quality" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.907, + 0.901 + ], + "angle": 0, + "content": "# User: Suppose you are an expert in evaluating alignment between the text prompt and the AI-generated image/video. Begin by considering whether the overall concept of the prompt is captured in the image/video. Then, examine the specific details, such as the presence of key objects, their attributes, and relationships. Check if the visual content accurately reflects these aspects. Finally, give your alignment rating considering both overall and detailed accuracy. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10625" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.088, + 0.885, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.291, + 0.908, + 0.351 + ], + "angle": 0, + "content": "Figure 5. The pipeline of the proposed Q-Eval-Score model involves multiple stages. First, the Q-Eval-100K SFT dataset is used to train the LMM on visual quality and alignment knowledge. Then, context prompts are applied to guide the LMM towards generating more detailed and accurate outputs. Finally, the rating token probabilities are converted into predicted scores. Additionally, long prompt alignment is achieved through a Vague-to-Specific strategy to further refine the model's responses." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.374, + 0.37, + 0.391 + ], + "angle": 0, + "content": "4.2.2 'Translating' MOS into Ratings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.4, + 0.484, + 0.464 + ], + "angle": 0, + "content": "It is well established that discrete adjective ratings are easier for LMMs to interpret compared to numerical scores [62, 72]. Since MOS in Q-Eval-100K is labeled in absolute terms, we can easily map MOS to the corresponding rating:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.474, + 0.482, + 0.506 + ], + "angle": 0, + "content": "\\[\nR (s) = r _ {i} \\text {i f} m + \\frac {i - 1}{5} \\times (M - m) < s \\leq m + \\frac {i}{5} \\times (M - m), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.506, + 0.456, + 0.524 + ], + "angle": 0, + "content": "\\(\\{r_i|_{i = 1\\sim 5}\\} = \\{Bad,Poor,Fair,Good,Excellent\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.536, + 0.484, + 0.569 + ], + "angle": 0, + "content": "where \\(m = 1\\) and \\(M = 5\\) (score range bound of Q-Eval-100K), \\(R(s)\\) indicates the mapped rating of MOS value \\(s\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.58, + 0.279, + 0.595 + ], + "angle": 0, + "content": "4.3. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.605, + 0.484, + 0.803 + ], + "angle": 0, + "content": "Using the constructed SFT dataset with the question-answer pairs as described, we select Qwen-VL [5] as the LMM model (Qwen2-VL-7B-Instruct) for training, which has demonstrated strong visual understanding capabilities for both images and videos. For video processing, each video is converted into a sequence of images at a rate of one frame per second, which is then fed into the model as the input. The scoring computation method is detailed as follows. For the rating token, we first calculate the model output probabilities \\( p_j \\) for each of the five rating terms {Excellent, Good, Fair, Poor, Bad}, where \\( j \\in \\{1, 2, 3, 4, 5\\} \\). Then we define the final predicted rating \\( \\hat{r} \\) as the weighted average of these probabilities:" + }, + { + "type": "equation", + "bbox": [ + 0.23, + 0.815, + 0.484, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\hat {r} = \\sum_ {j = 1} ^ {5} p _ {j} \\cdot w _ {j}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.485, + 0.903 + ], + "angle": 0, + "content": "where \\( w_{j} \\) is the numerical weight assigned to each rating (e.g., \\( w_{j} = \\{1,0.75,0.5,0.25,0\\} \\) for Excellent to Bad)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.373, + 0.661, + 0.388 + ], + "angle": 0, + "content": "4.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.397, + 0.907, + 0.489 + ], + "angle": 0, + "content": "The loss function for the model consists of two parts: Cross-Entropy (CE) Loss and Mean Squared Error (MSE) Loss. The CE Loss can assist the LMM in learning the general question-answer format and necessary knowledge. Meanwhile, the MSE Loss refines the score prediction accuracy. The CE Loss for question-answer pairs is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.498, + 0.907, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C E} = - \\sum_ {i = 1} ^ {N} y _ {i} \\cdot \\log \\left(p _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.549, + 0.907, + 0.596 + ], + "angle": 0, + "content": "where \\( y_{i} \\) is the one-hot encoded vector representing the true label for instance \\( i \\), and \\( p_{i} \\) is the predicted probability vector for the answer tokens. The MSE Loss can then be given by:" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.604, + 0.907, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M S E} = \\left(\\hat {r} - r _ {\\mathrm {M O S}}\\right) ^ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.633, + 0.906, + 0.679 + ], + "angle": 0, + "content": "where \\(\\hat{r}\\) and \\(r_{\\mathrm{MOS}}\\) represent the predicted scores and the MOS labels respectively. The total loss \\(\\mathcal{L}\\) is a weighted sum of the CE Loss and MSE Loss:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.69, + 0.905, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\alpha_ {1} \\cdot \\mathcal {L} _ {C E} + \\beta_ {1} \\cdot \\mathcal {L} _ {M S E}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.906, + 0.748 + ], + "angle": 0, + "content": "where \\(\\alpha_{1}\\) and \\(\\beta_{1}\\) (default set as \\(1\\& 1\\) ) are weight parameters controlling the contribution of each loss term." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.757, + 0.816, + 0.774 + ], + "angle": 0, + "content": "4.5. Handling Long Prompt Alignment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.903 + ], + "angle": 0, + "content": "During inference, we observe that the trained LMM tends to undervalue alignment when handling long prompts (more than 25 words). This is partly because long prompts are underrepresented in the training data, leading to insufficient training. More importantly, the LMM acts as a strict evaluator, often penalizing significant points for inconsistencies that may seem minor to humans. These small discrepancies occur more frequently with long prompts. To manage this" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10626" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.092, + 0.238, + 0.105 + ], + "angle": 0, + "content": "Generated Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.304, + 0.092, + 0.435, + 0.105 + ], + "angle": 0, + "content": "Original Long Prompt" + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.108, + 0.268, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.109, + 0.455, + 0.224 + ], + "angle": 0, + "content": "A new Chinese style painting, a group of animals are having a meeting, the owl is sitting in the leader's position and speaking, they are all wearing clothes with futuristic designs, and the picture should have a sense of technology." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.233, + 0.465, + 0.337 + ], + "angle": 0, + "content": "
Vague PromptIn a futuristic Chinese-style painting, an owl leads a tech-themed animal meeting. 4 A_v=4
Specific Prompts-A group of animals are depicted in a meeting. 5
-The owl is the leader, sitting in the center, speaking. 51/n ∑i=1n As_i = 13/3
Final Align. 0.5*4+0.5*4.33 = 4.17-Each animal wears futuristic clothing, adding a tech flair to the scene.3
" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.35, + 0.483, + 0.42 + ], + "angle": 0, + "content": "Figure 6. An example of the Vague-to-Specific strategy. The original long prompt is divided by the LLM (QwenLM [4]) into a Vague Prompt and several Specific Prompts. The alignment score is first calculated separately for each part, then combined using weighted averaging to form the final score." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.435, + 0.484, + 0.527 + ], + "angle": 0, + "content": "issue, we propose a Vague-to-Specific strategy. We use an additional LLM (QwenLM [4]) to summarize long prompts, retaining only the core features while filtering out details, producing a concise Vague Prompt. Then, we split the long prompt into Specific Prompts (no more than three), each maintaining full details but avoiding redundancy:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.542, + 0.483, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\left(P _ {v}, \\left\\{P _ {s _ {1}}, \\dots , P _ {s _ {n}} \\right\\}\\right) = \\mathcal {V S} \\left(P _ {L o n g}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.574, + 0.484, + 0.786 + ], + "angle": 0, + "content": "where \\(P_{v}\\) represents the Vague Prompt, \\(\\{P_{S_1},\\dots ,P_{S_n}\\}\\) stands for the set of Specific Prompts, \\(\\mathcal{VS}(\\cdot)\\) indicates the prompt split function, and \\(P_{Long}\\) is the original long prompt. For the Vague Prompt, we calculate alignment in the usual way. However, directly asking for consistency with the Specific Prompts is not appropriate since each one addresses only part of the vision content. Drawing inspiration from the VQAScore [40] approach, we modify the question to a softer format, such as 'Does the image/video show [Prompt]?' to evaluate alignment (measuring as the logit probability of answering 'Yes') for each Specific Prompts. Finally, we combine the results from both the Vague Prompt and Specific Prompt using a weighted approach to calculate the final alignment score:" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.801, + 0.483, + 0.842 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} _ {f} = \\alpha_ {2} \\mathcal {A} _ {v} + \\beta_ {2} \\left(\\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {A} _ {s _ {i}}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}_f, \\mathcal{A}_v,\\) and \\(\\mathcal{A}_{s_i}\\) are the alignment scores for the final evaluation, vague prompt, and \\(i\\)-th specific prompt. \\(\\alpha_{2}\\) and \\(\\beta_{2}\\) (0.5 & 0.5 as default) are weight parameters." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.907, + 0.118 + ], + "angle": 0, + "content": "Table 2. Performance comparison on the visual quality aspect of Q-Eval-100K. Best in bold, second underlined." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.122, + 0.907, + 0.223 + ], + "angle": 0, + "content": "
Model\n(Visual\nQuality)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE0.2390.2380.8290.758-0.057-0.074-0.333-0.241
CLIP-IQA0.3340.3240.6000.6850.1940.1750.0950.076
Q-Align0.5870.5780.7140.9140.5000.5020.7620.762
IPCE0.5500.5600.9330.9370.2990.3020.4760.568
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.814
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.224, + 0.907, + 0.295 + ], + "angle": 0, + "content": "Table 3. Performance comparison on the alignment aspect of Q-Eval-100K. Considering that CLIPScore, BLIP2Score, and VQAScore are popular zero-shot alignment evaluation metrics, we provide the corresponding performance with the official default weight as well (marked with *)." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.298, + 0.907, + 0.424 + ], + "angle": 0, + "content": "
Model (Align-ment)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
CLIPScore*0.2450.2520.6170.6850.1860.2190.5180.500
BLIP2Score*0.2970.3300.7640.8350.2180.2500.2950.296
VQAScore*0.5490.4680.3850.5550.4330.4320.4330.351
CLIPScore0.7680.7400.9580.9560.4310.4430.5190.509
BLIP2Score0.7660.7430.9330.9340.4830.4880.5120.481
ImageReward0.7620.7320.9250.9550.4720.4850.3750.362
Q-Eval-Score0.8220.8020.9640.9690.6070.6340.6480.605
" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.435, + 0.64, + 0.453 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.461, + 0.704, + 0.478 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.485, + 0.907, + 0.636 + ], + "angle": 0, + "content": "Training & Evaluation. The Qwen2-VL-7B-Instruct [5] serves as the backbone LMM for Q-Eval-Score. All visual quality and alignment data from images and videos are combined for training. Training is conducted on 8 A100 GPUs for one epoch by default. For evaluation metrics, we use SRCC and PLCC, which measure the rank and linear correlation between predicted scores and MOSs. We propose evaluations at the Instance-level and Model-level which assess accuracy in ranking specific generated instances and generative models based on overall performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.638, + 0.909, + 0.804 + ], + "angle": 0, + "content": "Competitors. Few models can simultaneously predict both visual quality and alignment. Thus we selected task-specific competitors for each sub-task: For visual quality, we include NIQE [45], CLIP-IQA [57], Q-Align [62], and IPCE [48] (the top method from the 'NTIRE 2024 Quality Assessment of AI-Generated Content Challenge' [41]). For alignment, we choose CLIPScore [20], BLIP2Score [37], ImageReward [65] and VQAScore [40] as the competitors. All models are trained and tested using their default recommended parameters and the corresponding train-test sets of the Q-Eval-100K dataset unless specified." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.816, + 0.791, + 0.833 + ], + "angle": 0, + "content": "5.2. Discussion & General Findings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.903 + ], + "angle": 0, + "content": "The general performance on the visual quality and alignment is exhibited in Table 2 and Table 3, from which we can draw several conclusions: 1) For visual quality, The proposed Q-Eval-Score outperforms all competitors, achiev-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10627" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.372, + 0.09, + 0.624, + 0.104 + ], + "angle": 0, + "content": "Table 4. Ablation Study of Q-Eval-Score." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.108, + 0.905, + 0.198 + ], + "angle": 0, + "content": "
ModelQ-Eval-Image (Quality)Q-Eval-Video (Quality)Q-Eval-Image (Alignment)Q-Eval-Video (Alignment)
Instance-levelModel-levelInstance-levelModel-levelInstance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
w/o SFT Training0.0710.0960.2570.1360.0180.0080.2620.3140.5290.4230.5600.7050.4640.4370.5670.478
w/o Context Prompt0.5040.5090.6000.7560.5980.5910.5710.6380.8050.7760.9600.9630.5880.5970.6010.602
w/o CE Loss0.6520.6220.9320.9100.2470.2490.0710.2390.8040.7760.9480.9610.6040.6260.6420.593
w/o MSE Loss0.6650.6730.9330.9410.5950.5830.6900.7120.7950.7630.9540.9580.5800.6050.6240.599
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.8140.8220.8020.9640.9690.6070.6340.6480.605
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.203, + 0.483, + 0.259 + ], + "angle": 0, + "content": "Table 5. Performance comparison on the alignment aspect of Q-Eval-100K on the long prompt subset, where w/o V2S and w V2S represents the proposed Q-Eval-Score model with and without the Vague-to-Specific strategy respectively." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.263, + 0.483, + 0.354 + ], + "angle": 0, + "content": "
Model\n(Align-ment)Q-Eval-Image (Long)Q-Eval-Video (Long)
Instance-levelInstance-level
SRCCPLCCSRCCPLCC
CLIPScore0.5330.5470.3590.367
BLIP2Score0.6200.6360.3920.395
VQAScore0.4320.3250.3440.350
w/o V2S0.5910.5990.4800.470
w V2S0.6200.6230.5170.512
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.369, + 0.483, + 0.412 + ], + "angle": 0, + "content": "Table 6. Cross-dataset validation performance on GenAI-Bench. The Q-Eval-Score is trained on the Q-Eval-100K and then validated on GenAI-Bench. * indicates using default weight." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.414, + 0.483, + 0.512 + ], + "angle": 0, + "content": "
Model\n(Alignment)GenAI-Bench (Image)GenAI-Bench (Video)
SRCCPLCCSRCCPLCC
CLIPScore*0.1740.1690.2690.269
BLIP2Score*0.2210.2090.2890.275
VQAScore*0.5560.5020.5270.505
CLIPScore0.6810.6700.6100.628
BLIP2Score0.6870.6790.6790.705
ImageReward0.6640.6560.6630.684
Q-Eval-Score0.7570.7470.7170.714
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.539, + 0.483, + 0.901 + ], + "angle": 0, + "content": "ing the best performance overall. The decline in video performance is likely due to the 1fps frame sampling method, which causes a loss of temporal information, leading to inaccurate estimations. Despite this, at the instance-level, Q-Eval-Score still leads the second-best competitor (Q-Align) by \\(10\\%\\) on video instance-level SRCC. 2) For alignment, Q-Eval-Score also demonstrates a significant lead in alignment, outperforming competitors by \\(6\\%\\) in image instance-level SRCC and \\(12\\%\\) in video instance-level SRCC. Additionally, the substantial performance improvements seen in the trained competitors suggest that Q-Eval-100K provides valuable knowledge for alignment evaluation. 3) In comparison to alignment, Q-Eval-Score's performance in visual quality is notably lower, indicating that predicting visual quality is more challenging. This is likely because alignment evaluation is more straightforward and objective, while visual quality perception is more complex and subjective, making it harder to assess. Overall, the proposed Q-Eval-Score exhibits exceptional potential in both visual quality and alignment, achieving over 0.94 performance at the image model-level, closely aligning with human evaluations. This strong performance not only highlights the robustness of the model but also underscores its promising ability to serve as an effective evaluation metric." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.205, + 0.715, + 0.22 + ], + "angle": 0, + "content": "5.3. Further Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.229, + 0.905, + 0.305 + ], + "angle": 0, + "content": "I) Ablation Study. We conduct a detailed ablation study to assess the contribution of proposed strategies and CE/MSE loss. The results are presented in Table 4. It is clear that each of the strategies we proposed and both CE/MSE loss make a significant contribution to the final outcome." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.307, + 0.905, + 0.428 + ], + "angle": 0, + "content": "II) Long Prompt. To test the Vague-to-Specific strategy for long prompt alignment, we select a subset of 5,000 instances from Q-Eval-100K that contain long prompts (over 25 words) for testing, performance shown in Table 5. Due to the limited data size, we present only the instance-level performance. The results clearly show that the Vague-to-Specific strategy significantly improves performance, indicating the effectiveness of handling long prompt alignment." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.43, + 0.906, + 0.566 + ], + "angle": 0, + "content": "III) Cross-dataset Validation. To demonstrate the value of the Q-Eval-100K dataset, we conduct a cross-dataset validation, with performance results shown in Table 6. It is important to note that instances generated from prompts in GenAI-Bench are excluded from this validation. The results clearly show that models trained on Q-Eval-100K significantly outperform the current state-of-the-art VQAScore on GenAI-Bench by a large margin, providing strong evidence of the generalization value of the Q-Eval-100K dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.586, + 0.634, + 0.601 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.906, + 0.794 + ], + "angle": 0, + "content": "In conclusion, we introduce Q-Eval-100K, the largest text-to-vision evaluation dataset to date, featuring 100K instances and 960K human annotations for assessing visual quality and alignment. We also present Q-Eval-Score, a unified evaluation framework that leverages this dataset to provide separate scores for each dimension. Experimental results show that Q-Eval-Score outperforms existing methods, demonstrating its potential for more reliable, comprehensive assessments of text-to-vision models. Looking ahead, we hope this work can lay a strong foundation for further advancements in text-to-vision model promotion and real-world evaluation applications." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.814, + 0.666, + 0.83 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The work was supported in part by the National Natural Science Foundation of China under Grant 62301310, Grant 623B2073, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10628" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.156 + ], + "angle": 0, + "content": "[1] Luma AI. 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While significant progress has been made in developing objective models to assess these dimensions, the performance of such models heavily relies on the scale and quality of human annotations. According to Scaling Law, increasing the number of human-labeled instances follows a predictable pattern that enhances the performance of evaluation models. Therefore, we introduce a comprehensive dataset designed to Evaluate Visual quality and Alignment Level for text-to-vision content (Q-EVAL-100K), featuring the largest collection of human-labeled Mean Opinion Scores (MOS) for the mentioned two aspects. The Q-EVAL-100K dataset encompasses both text-to-image and text-to-video models, with 960K human annotations specifically focused on visual quality and alignment for 100K instances (60K images and 40K videos). Leveraging this dataset with context prompt, we propose Q-Eval-Score, a unified model capable of evaluating both visual quality and alignment with special improvements for handling long-text prompt alignment. Experimental results indicate that the proposed Q-Eval-Score achieves superior performance on both visual quality and alignment, with strong generalization capabilities across other benchmarks. These findings highlight the significant value of the Q-EVAL-100K dataset. Data and codes will be available at https://github.com/zzc-1998/QEval. + +# 1. Introduction + +With the rapid advancement of generative AI, millions of text-to-image and text-to-video content are being generated daily across various platforms [25, 56], applied in industrial production or directly used by consumers. However, due to current technological limitations, text-to-vision con + +![](images/edb458ae9ef8368e4fd927a8a6da84767788b9dd7f7357536a821b5b7f4eb7ac.jpg) +Figure 1. Illustration of the unified evaluation dimensions of Q-Eval-100K. We focus on visual quality (including all factors that may impact the viewing experience) and alignment level, which measures the accuracy of the generated content to the prompt. + +tent often falls short of being perfect upon generation and cannot be immediately deployed [34, 36, 40], which usually requires expert evaluation, editing, and fine-tuning. As a result, numerous efforts have been made to develop automated methods for evaluating text-to-vision content, aiming to control the quality of generation and guide the necessary optimizations effectively [13, 26, 27, 29, 40, 60–63, 65, 70, 72]. Through extensive theoretical and experimental analy- + +Table 1. A brief comparison of the latest text-to-vision evaluation datasets (I. for image, V. for video). For Annotation Type, SBS (side-by-side) and MOS (mean-opinion-score) refer to selecting the preferred instance from a pair of instances and assigning an average absolute score to a single instance respectively. For Rating Concerns, Overall indicates assigning scores from a holistic perspective while $\checkmark$ denotes assigning separate scores to quality or alignment. For Number, Ins. and Ann. stand for the number of instances and human annotations respectively. + +
DatasetYearContentAnnotation Type (Single/Pair)Evaluation ConcernNumber Ins./Ann.
QualityAlignment
Pick-a-pic [27]2023I.SBSOverall1M/500K
ImageReward [65]2023I.SBSOverall68k/137k
HPDv2 [63]2023I.SBSOverall430k/645K
AGIQA-3k [34]2023I.MOS✓✓3K/81K
AIGCIA2023 [58]2023I.MOS✓✓2K/17K
PKU-AIGIA-4k [67]2024I.MOS✓✓4K/84K
AIGIA-20k [35]2024I.MOSOverall20K/420K
RichHF [39]2024I.MOS✓✓18K/54K
VideoFeedback [19]2024V.MOS✓✓37.6K/37.6K
T2VQA-DB [28]2024V.MOSOverall10K/27K
GenAI-Bench [33]2024I.&V.1-5 Likert ScaleOverall9.6K/9.6K
Q-Eval-100K (Ours)2024I.&V.MOS✓✓100K/960K
+ +sis, the evaluation of text-to-vision content can be primarily divided into two dimensions [41, 64, 65, 73, 76]: Visual Quality (the perceived quality of the visual content, which can be simply understood as how good it looks) and Alignment level (the consistency between text and vision, which can be interpreted as how accurate the generation is). + +To meet the need for evaluation, many text-to-vision evaluation datasets have been proposed, along with corresponding evaluation algorithms [11, 12, 19, 19, 24, 28, 33-35, 39, 41, 58, 67, 71, 74, 75]. However, these efforts face the following significant limitations: 1) The key evaluation dimensions for text-to-vision content are often not systematically captured. Some datasets propose too many dimensions, adding unnecessary complexity to the evaluation process. The practical applicability of these dimensions can be narrow or lead to redundancy. 2) Most text-to-vision evaluation datasets fail to disentangle visual quality and alignment. These datasets either focus solely on alignment or visual quality, or merge both dimensions into a single score, leading to results that are often incomplete and ambiguous, making it challenging to address specific evaluation needs. 3) The scale of these datasets remains insufficient. With the rise of Large Multimodal Models (LMMs), which have demonstrated strong capabilities in visual and textual understanding, researchers are increasingly leveraging them for text-to-vision evaluation. However, current dataset sizes remain inadequate to fully unlock the potential of LMM-based models [76], conceivably restricting their applicability and generalization in real-world scenarios. + +To address these challenges, we present Q-Eval-100K, which, to the best of our knowledge, is the largest text-to-vision evaluation dataset with Mean Opinion Scores (MOSs), comprising 100K instances (including 60K generated images & 40K generated videos). A brief comparison of Q-Eval-100K and previous text-to-vision eval + +uation datasets is illustrated in Table 1. We manually gather prompts from existing benchmarks and create diverse prompts that focus on three key aspects: entity generation, entity attribute generation, and interaction capability. The instances in Q-Eval-100K are then generated from a diverse range of generative models, both open-source and closed-source, to ensure high diversity. We implement a rigorous, scientifically grounded subjective evaluation process using a Sample & Scrutinize strategy, focusing on both visual quality and alignment level for each of the 100K instances, yielding a total of high-quality 960K human annotations. + +Building on the proposed Q-Eval-100K, we propose Q-Eval-Score, a unified evaluation framework capable of assessing both visual quality and alignment, providing separate scores for each dimension. We first adapt Q-Eval-100K into a Supervised Fine-Tuning (SFT) dataset optimized for injecting knowledge into LMMs. Scores are transformed into adjective-based ratings, then reformulated within a well-guided context-prompt format. Specifically, for visual quality, we guide the model to identify positive and negative visual impacts, evaluate the intensity of these impacts, and make a balanced judgment. For alignment, we guide the model to perceive the overall situation, examine details, and reach a balanced judgment. The fine-tuning process is then supervised by a combined CE and MSE loss. During inference, the final score is computed as a weighted average based on the probability of each rating token. Notably, in handling long-prompt alignment, we observed that direct alignment assessment often yields low scores due to oversimplification. To address this, we propose a Vague-to-Specific strategy, where a long prompt is converted into a vague version retaining only core information and multiple prompts with specific details. These prompts are evaluated separately and the alignment scores are combined to the final score. Our contributions can be summarized as follows: + +- We present Q-Eval-100K, the largest text-to-vision evaluation dataset with MOSs, comprising 100K instances from various generative models. We employ a scientifically grounded evaluation methodology, using a Sample & Scrutinize strategy to collect 960K human annotations focusing on visual quality and alignment. +- We propose Q-Eval-Score, a unified evaluation framework capable of independently assessing visual quality and alignment, providing separate scores for each dimension. Specifically, we adapt Q-Eval-100K into an SFT dataset with adjective-based ratings in a structured context-prompt format for enhancing the visual quality and alignment evaluation capabilities of LMMs. +- To improve alignment evaluation for long prompts, we introduce a Vague-to-Specific strategy, which separates prompts into core and detailed variants, yielding a more accurate alignment score through weighted averaging. + +# 2. Related Works + +# 2.1. Benchmarks for Text-to-Vision Evaluation + +Early text-to-vision benchmarks largely depend on multimodal datasets labeled with captions [10, 22, 43]. However, with increasing recognition of human feedback's value [14, 23, 76], many benchmarks begin to employ human annotations. Common annotation methods include SBS (side-by-side) and MOS (mean opinion score) [49, 68]. SBS requires selecting a preferred instance from a pair, while MOS assigns a score to a single instance. SBS is generally easier for human subjects and more precise, but MOS is more versatile and broadly applicable to various situations [6, 32]. + +Text-to-vision evaluation dimensions [41, 73] can be categorized into visual quality and alignment. While some benchmarks [11, 12, 19, 24] treat aspects like naturalness, aesthetics, and temporal consistency as distinct dimensions, we view these as components of visual quality since they collectively influence the quality of experience (QoE) for viewers. Early benchmarks [34, 35, 58, 67] for generated images comprehensively address both visual quality and alignment for evaluation. RichHF [39] enhances these evaluations by incorporating subjective scores, heatmaps, and misalignment tokens. For video, VideoFeedback [19] introduces five dimensions of quality and alignment, while T2VQA-DB [28] focuses primarily on visual quality. Further, GenAI-Bench [33] evaluates alignment for both generated images and generated videos. The proposed Q-Eval-100K dataset offers a unified text-to-vision evaluation framework, significantly increasing dataset scale and diversity, making it distinct from prior benchmarks. + +# 2.2. Metric for Text-to-Vision Evaluation + +Previous evaluation methods separately focus on either visual quality or alignment. Perceptual methods assess the visual quality of generated content, utilizing traditional scores like IS [52], FID [21], and LPIPS [69] with pretrained neural networks. Recently, data-driven models [34] trained on specialized datasets have further advanced perceptual score prediction. Additionally, methods such as CLIP-IQA [57] and Q-Align [62] leverage text prompts to enhance perceptual alignment. Alignment methods, integrating both text and vision modalities, initially use CLIP-Score [20] due to its ease of application. To address more complex prompts, some approaches [27, 63, 65] incorporate human feedback to improve evaluation accuracy. Given the powerful interpretative capabilities of LMMs, recent work [13, 26, 29, 40, 70] has begun to apply these models to alignment assessments. Most existing models evaluate either perceptual quality or alignment exclusively. The proposed Q-Eval-Score addresses this gap by offering decoupled scores for both perceptual quality and alignment. + +![](images/d00cbcf089f2da000b26a669464fb8b3f547426aff33b7e9d8994df2ff0a2768.jpg) +Figure 2. Illustration of the Sample and Scrutinize quality control strategy for annotations in Q-Eval-100K. We randomly select a sample of 5K instances from the full dataset, which are then reviewed by experts to establish golden scores. A batch of annotations is approved only if the scores of the sampled instances show a high correlation with these expert-assigned golden scores. + +# 3. Q-Eval-100K Construction + +# 3.1. Basic Principles + +The construction process of Q-Eval-100K is illustrated in Fig. 3. We follow these guiding principles: 1) Ensuring diversity in generated content by collecting a wide range of prompts and using multiple generative models; 2) Ensuring annotation quality through carefully designed experimental settings and standards to achieve the highest accuracy; 3) Ensuring effective learning, through adapting the data for LMM suitability by transforming both visual quality and alignment scores into a context-aware SFT dataset. + +# 3.2. Sources Collection + +Prompt Designing. The prompt design focuses on three main aspects: Entity Generation, Entity Attribute Generation, and Interaction Capability. 1) Entity generation targets the primary entities (people, objects, etc.) to be generated. 2) Entity attribute generation emphasizes the attributes (clothing, color, material, etc.) of the entities. 3) Interaction capability focuses on the interactions between the generated entities and other entities or the background, such as their spatial relationships and actions. Following the outlines mentioned above, we manually create a portion of the prompts and extract some from existing datasets [33, 46]. + +Generation Models. We utilize multiple popular text-to-image and text-to-video models to ensure diversity, which include FLUX [30], Lumina-T2X [17], PixArt [9], Stable Diffusion 3 [3], Stable Diffusion XL [50], DALL-E 3 [47], Wanx [15], Midjourney [44], Hunyuan-DiT [38], Kolors [54], ERNIE-ViLG [16], CogVideoX [66], Runway GEN-2 [18], Runway GEN-3 [51], Latte [42], Kling [53], Dreamina [8], Luma [1], PixVerse [2], Pika [31], Stable Video Diffusion [7], Vidu [55]. + +![](images/bfa9e0925b787e3463079c31ef131d339345223b4920fdc44c25ee0a73cfa136.jpg) +Figure 3. Overview of the Q-Eval-100K construction process. We design a wide range of prompts and employ various text-to-vision models to generate diverse content. Subjective evaluations are then conducted to rate the visual quality and alignment of these generated instances. The resulting scores form the SFT dataset, which can help inject corresponding knowledge into LMMs. + +![](images/ed5657f5a42e2a5dc799860bc70c301c7c6630409c672829db1eae3fb8d7f1d1.jpg) + +![](images/a1edd7e9cd78560fccf5a1532f7f19bbf76ff9e8f26fab474814c74caefbd498.jpg) + +# 3.3. Subjective Experiment + +Given the large scale of Q-Eval-100K, we develop rigorous experimental protocols to ensure the highest possible accuracy in our annotations. To facilitate this, we establish a well-controlled indoor experimental environment, where more than 200 human subjects are recruited to participate in the annotation. To ensure the accuracy of annotations is not compromised by individual cognitive differences or annotator fatigue, we propose a Sample & Scrutinize data control strategy as shown in Fig. 2. The strategy includes two steps: 1) First, we randomly sample 5,000 instances from the entire dataset. We then organize experts with rich experience to discuss and score these instances, leading to the establishment of golden scores for both visual quality and alignment. These golden scores remain hidden for all subsequent experimental subjects. 2) Next, we provide human annotators with comprehensive training before they begin the annotation process. After each batch, we gather the scores for instances that have golden scores and compare them with these golden scores, calculating the correlation values (SRCC-rank similarity). Only batches with an SRCC above 0.8 are accepted, otherwise, they are rejected. + +Additionally, we split Q-Eval-100K into training and testing sets in an 80:20 ratio. Each instance in the training set has at least three annotations, while each instance in the testing set has a minimum of twelve annotations to ensure accuracy. This process results in a total of over 960K annotations, calculated as follows: 80K (training instances) x 2 (visual quality & alignment) x 3 (minimum annotation number) + 20K (training instances) x 2 (visual quality & alignment) x 12 (minimum annotation number) = 960K annotations. Finally, we calculate the average of the multiple annotations to derive the score for each instance. + +# 3.4. Statistical Analysis + +The distributions of MOSs for visual quality and alignment are exhibited in Fig. 4 respectively, which reveal several key insights. In general, there are substantial differences among generation models in both visual quality and alignment, with their distributions displaying significant inconsistencies, indicating varied performance across different generation prompts. 1) For image alignment, distributions are generally skewed higher, suggesting that models perform relatively well in aligning images, though multiple peaks in the 4-5 and 2-3 score ranges indicate some fluctuation in performance. 2) In video alignment, model performance varies more markedly, with most scores concentrated between 2 and 4, highlighting the need for improvement in alignment in video generation. 3) Visual quality for images scores noticeably lower than image alignment, indicating that generation models perform significantly worse in visual quality. Furthermore, the wider distribution spread in image visual quality suggests greater variance and instability across models. 4) Similarly, video visual quality scores are lower than alignment scores, highlighting a consistent underperformance in visual quality. Interestingly, models such as Kling, Dreamina, Luma, PixVerse, and Pika exhibit similar distributions for alignment and visual quality, indicating consistent capability across both aspects. However, this consistency is not observed across all models. + +Overall, the findings above highlight a notable disparity in that visual quality generally falls behind alignment. This gap likely stems from the current emphasis on alignment optimization, which is also relatively easier to improve, whereas visual quality has received less focus. This analysis underscores the importance of Q-Eval-100K as a comprehensive benchmark for evaluating both dimensions. + +![](images/868b3b0a0196b8fab8bb19d8e29a9f703adcfd0fe0ed01a44b85f63d88381eee.jpg) + +![](images/31eb319bda4ca5c23fae2bcdaf5eef3328911ab680c9f7f7f057aa7aff4eed4c.jpg) +(b) Video Alignment + +![](images/13ade1db97feb245fb068571b7d359659d11239699a102d0ba99f3463e72c69c.jpg) +(a) Image Alignment +(c) Image Visual Quality + +![](images/b0b710acf65d2c5262715d1ecdf0d4df9936593eb632caefd507a4db37b2a244.jpg) +(d) Video Visual Quality +Figure 4. MOS distributions for the visual quality and alignment of generated images and videos in the Q-Eval-100K dataset respectively. + +# 4. Q-Eval-Score + +# 4.1. Unified Pipeline for Decoupled Evaluation + +Although the evaluation of visual quality and alignment are two relatively independent tasks, we leverage the adaptability and extensive prior knowledge of LMMs to propose a unified model, Q-Eval-Score, that addresses both visual quality and alignment level evaluation within a single framework. Specifically, we convert the human-labeled MOS from the Q-Eval-100K dataset for both visual quality and alignment levels into a fixed-prompt format, creating a mixed SFT dataset. We then fine-tune the LMM, enabling it to evaluate both visual quality and alignment levels. + +# 4.2. How to Teach LMMs to Evaluate + +# 4.2.1 Context Prompt + +In previous work using prompts with LMMs for evaluation, the questions are often straightforward and simple, such as 'Can you evaluate the quality of the image?' (Q-Align [62]) or 'Does this figure show [Prompt]? Please answer yes or no.' (VQAScore [40]). However, this simplicity may lead to confusion for the model, as the prompts may not be specific enough to guide a more detailed or accurate evaluation. + +Inspired by the chain-of-thought (CoT [59]) concept and given that humans undergo a reasoning process when evaluating visual quality and alignment, we propose a Context-Prompt format to construct our SFT dataset. For the visual quality task, the human evaluation process can be summarized as first identifying both positive and negative quality factors, then measuring these factors, and finally weighing them to reach a conclusion. Based on this process, we design the following prompt structure: + +# Context Prompt for Visual Quality + +# User: Suppose you are an expert in evaluating the visual quality of AI-generated image/video. First, identify any visual distortions and positive visual appeal regarding low-level features and aesthetics. Next, assess the severity of distortions and their impact on the viewing experience, noting whether they are subtle or distracting, and evaluate how the positive features enhance the visual appeal, considering their strength and contribution to the overall aesthetics. Finally, balance the identified distortions against the positive aspects and give your rating on the visual quality. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad). + +For the alignment task, the human evaluation process involves observing whether the overall content generally aligns with the text, followed by a more detailed comparison, and finally a comprehensive evaluation for conclusion: + +# Context Prompt for Visual Quality + +# User: Suppose you are an expert in evaluating alignment between the text prompt and the AI-generated image/video. Begin by considering whether the overall concept of the prompt is captured in the image/video. Then, examine the specific details, such as the presence of key objects, their attributes, and relationships. Check if the visual content accurately reflects these aspects. Finally, give your alignment rating considering both overall and detailed accuracy. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad). + +![](images/c012a1b87628a1fe21a919634134272466e72d18892c926c1717820e29b00ea8.jpg) +Figure 5. The pipeline of the proposed Q-Eval-Score model involves multiple stages. First, the Q-Eval-100K SFT dataset is used to train the LMM on visual quality and alignment knowledge. Then, context prompts are applied to guide the LMM towards generating more detailed and accurate outputs. Finally, the rating token probabilities are converted into predicted scores. Additionally, long prompt alignment is achieved through a Vague-to-Specific strategy to further refine the model's responses. + +# 4.2.2 'Translating' MOS into Ratings + +It is well established that discrete adjective ratings are easier for LMMs to interpret compared to numerical scores [62, 72]. Since MOS in Q-Eval-100K is labeled in absolute terms, we can easily map MOS to the corresponding rating: + +$$ +R (s) = r _ {i} \text {i f} m + \frac {i - 1}{5} \times (M - m) < s \leq m + \frac {i}{5} \times (M - m), \tag {1} +$$ + +$\{r_i|_{i = 1\sim 5}\} = \{Bad,Poor,Fair,Good,Excellent\}$ + +where $m = 1$ and $M = 5$ (score range bound of Q-Eval-100K), $R(s)$ indicates the mapped rating of MOS value $s$ . + +# 4.3. Model Architecture + +Using the constructed SFT dataset with the question-answer pairs as described, we select Qwen-VL [5] as the LMM model (Qwen2-VL-7B-Instruct) for training, which has demonstrated strong visual understanding capabilities for both images and videos. For video processing, each video is converted into a sequence of images at a rate of one frame per second, which is then fed into the model as the input. The scoring computation method is detailed as follows. For the rating token, we first calculate the model output probabilities $p_j$ for each of the five rating terms {Excellent, Good, Fair, Poor, Bad}, where $j \in \{1, 2, 3, 4, 5\}$ . Then we define the final predicted rating $\hat{r}$ as the weighted average of these probabilities: + +$$ +\hat {r} = \sum_ {j = 1} ^ {5} p _ {j} \cdot w _ {j}, \tag {2} +$$ + +where $w_{j}$ is the numerical weight assigned to each rating (e.g., $w_{j} = \{1,0.75,0.5,0.25,0\}$ for Excellent to Bad). + +# 4.4. Loss Function + +The loss function for the model consists of two parts: Cross-Entropy (CE) Loss and Mean Squared Error (MSE) Loss. The CE Loss can assist the LMM in learning the general question-answer format and necessary knowledge. Meanwhile, the MSE Loss refines the score prediction accuracy. The CE Loss for question-answer pairs is defined as: + +$$ +\mathcal {L} _ {C E} = - \sum_ {i = 1} ^ {N} y _ {i} \cdot \log \left(p _ {i}\right), \tag {3} +$$ + +where $y_{i}$ is the one-hot encoded vector representing the true label for instance $i$ , and $p_{i}$ is the predicted probability vector for the answer tokens. The MSE Loss can then be given by: + +$$ +\mathcal {L} _ {M S E} = \left(\hat {r} - r _ {\mathrm {M O S}}\right) ^ {2}, \tag {4} +$$ + +where $\hat{r}$ and $r_{\mathrm{MOS}}$ represent the predicted scores and the MOS labels respectively. The total loss $\mathcal{L}$ is a weighted sum of the CE Loss and MSE Loss: + +$$ +\mathcal {L} = \alpha_ {1} \cdot \mathcal {L} _ {C E} + \beta_ {1} \cdot \mathcal {L} _ {M S E}, \tag {5} +$$ + +where $\alpha_{1}$ and $\beta_{1}$ (default set as $1\& 1$ ) are weight parameters controlling the contribution of each loss term. + +# 4.5. Handling Long Prompt Alignment + +During inference, we observe that the trained LMM tends to undervalue alignment when handling long prompts (more than 25 words). This is partly because long prompts are underrepresented in the training data, leading to insufficient training. More importantly, the LMM acts as a strict evaluator, often penalizing significant points for inconsistencies that may seem minor to humans. These small discrepancies occur more frequently with long prompts. To manage this + +![](images/70c39ee643de592e929e042c19d1cc44556bda901b06a6412dd8b3c809e8180d.jpg) +Generated Image +Original Long Prompt +Figure 6. An example of the Vague-to-Specific strategy. The original long prompt is divided by the LLM (QwenLM [4]) into a Vague Prompt and several Specific Prompts. The alignment score is first calculated separately for each part, then combined using weighted averaging to form the final score. + +A new Chinese style painting, a group of animals are having a meeting, the owl is sitting in the leader's position and speaking, they are all wearing clothes with futuristic designs, and the picture should have a sense of technology. + +
Vague PromptIn a futuristic Chinese-style painting, an owl leads a tech-themed animal meeting. 4 A_v=4
Specific Prompts-A group of animals are depicted in a meeting. 5
-The owl is the leader, sitting in the center, speaking. 51/n ∑i=1n As_i = 13/3
Final Align. 0.5*4+0.5*4.33 = 4.17-Each animal wears futuristic clothing, adding a tech flair to the scene.3
+ +issue, we propose a Vague-to-Specific strategy. We use an additional LLM (QwenLM [4]) to summarize long prompts, retaining only the core features while filtering out details, producing a concise Vague Prompt. Then, we split the long prompt into Specific Prompts (no more than three), each maintaining full details but avoiding redundancy: + +$$ +\left(P _ {v}, \left\{P _ {s _ {1}}, \dots , P _ {s _ {n}} \right\}\right) = \mathcal {V S} \left(P _ {L o n g}\right), \tag {6} +$$ + +where $P_{v}$ represents the Vague Prompt, $\{P_{S_1},\dots ,P_{S_n}\}$ stands for the set of Specific Prompts, $\mathcal{VS}(\cdot)$ indicates the prompt split function, and $P_{Long}$ is the original long prompt. For the Vague Prompt, we calculate alignment in the usual way. However, directly asking for consistency with the Specific Prompts is not appropriate since each one addresses only part of the vision content. Drawing inspiration from the VQAScore [40] approach, we modify the question to a softer format, such as 'Does the image/video show [Prompt]?' to evaluate alignment (measuring as the logit probability of answering 'Yes') for each Specific Prompts. Finally, we combine the results from both the Vague Prompt and Specific Prompt using a weighted approach to calculate the final alignment score: + +$$ +\mathcal {A} _ {f} = \alpha_ {2} \mathcal {A} _ {v} + \beta_ {2} \left(\frac {1}{n} \sum_ {i = 1} ^ {n} \mathcal {A} _ {s _ {i}}\right), \tag {7} +$$ + +where $\mathcal{A}_f, \mathcal{A}_v,$ and $\mathcal{A}_{s_i}$ are the alignment scores for the final evaluation, vague prompt, and $i$ -th specific prompt. $\alpha_{2}$ and $\beta_{2}$ (0.5 & 0.5 as default) are weight parameters. + +Table 2. Performance comparison on the visual quality aspect of Q-Eval-100K. Best in bold, second underlined. + +
Model +(Visual +Quality)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE0.2390.2380.8290.758-0.057-0.074-0.333-0.241
CLIP-IQA0.3340.3240.6000.6850.1940.1750.0950.076
Q-Align0.5870.5780.7140.9140.5000.5020.7620.762
IPCE0.5500.5600.9330.9370.2990.3020.4760.568
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.814
+ +Table 3. Performance comparison on the alignment aspect of Q-Eval-100K. Considering that CLIPScore, BLIP2Score, and VQAScore are popular zero-shot alignment evaluation metrics, we provide the corresponding performance with the official default weight as well (marked with *). + +
Model (Align-ment)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
CLIPScore*0.2450.2520.6170.6850.1860.2190.5180.500
BLIP2Score*0.2970.3300.7640.8350.2180.2500.2950.296
VQAScore*0.5490.4680.3850.5550.4330.4320.4330.351
CLIPScore0.7680.7400.9580.9560.4310.4430.5190.509
BLIP2Score0.7660.7430.9330.9340.4830.4880.5120.481
ImageReward0.7620.7320.9250.9550.4720.4850.3750.362
Q-Eval-Score0.8220.8020.9640.9690.6070.6340.6480.605
+ +# 5. Experiment + +# 5.1. Experimental Setup + +Training & Evaluation. The Qwen2-VL-7B-Instruct [5] serves as the backbone LMM for Q-Eval-Score. All visual quality and alignment data from images and videos are combined for training. Training is conducted on 8 A100 GPUs for one epoch by default. For evaluation metrics, we use SRCC and PLCC, which measure the rank and linear correlation between predicted scores and MOSs. We propose evaluations at the Instance-level and Model-level which assess accuracy in ranking specific generated instances and generative models based on overall performance. + +Competitors. Few models can simultaneously predict both visual quality and alignment. Thus we selected task-specific competitors for each sub-task: For visual quality, we include NIQE [45], CLIP-IQA [57], Q-Align [62], and IPCE [48] (the top method from the 'NTIRE 2024 Quality Assessment of AI-Generated Content Challenge' [41]). For alignment, we choose CLIPScore [20], BLIP2Score [37], ImageReward [65] and VQAScore [40] as the competitors. All models are trained and tested using their default recommended parameters and the corresponding train-test sets of the Q-Eval-100K dataset unless specified. + +# 5.2. Discussion & General Findings + +The general performance on the visual quality and alignment is exhibited in Table 2 and Table 3, from which we can draw several conclusions: 1) For visual quality, The proposed Q-Eval-Score outperforms all competitors, achiev- + +Table 4. Ablation Study of Q-Eval-Score. + +
ModelQ-Eval-Image (Quality)Q-Eval-Video (Quality)Q-Eval-Image (Alignment)Q-Eval-Video (Alignment)
Instance-levelModel-levelInstance-levelModel-levelInstance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
w/o SFT Training0.0710.0960.2570.1360.0180.0080.2620.3140.5290.4230.5600.7050.4640.4370.5670.478
w/o Context Prompt0.5040.5090.6000.7560.5980.5910.5710.6380.8050.7760.9600.9630.5880.5970.6010.602
w/o CE Loss0.6520.6220.9320.9100.2470.2490.0710.2390.8040.7760.9480.9610.6040.6260.6420.593
w/o MSE Loss0.6650.6730.9330.9410.5950.5830.6900.7120.7950.7630.9540.9580.5800.6050.6240.599
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.8140.8220.8020.9640.9690.6070.6340.6480.605
+ +Table 5. Performance comparison on the alignment aspect of Q-Eval-100K on the long prompt subset, where w/o V2S and w V2S represents the proposed Q-Eval-Score model with and without the Vague-to-Specific strategy respectively. + +
Model +(Align-ment)Q-Eval-Image (Long)Q-Eval-Video (Long)
Instance-levelInstance-level
SRCCPLCCSRCCPLCC
CLIPScore0.5330.5470.3590.367
BLIP2Score0.6200.6360.3920.395
VQAScore0.4320.3250.3440.350
w/o V2S0.5910.5990.4800.470
w V2S0.6200.6230.5170.512
+ +Table 6. Cross-dataset validation performance on GenAI-Bench. The Q-Eval-Score is trained on the Q-Eval-100K and then validated on GenAI-Bench. * indicates using default weight. + +
Model +(Alignment)GenAI-Bench (Image)GenAI-Bench (Video)
SRCCPLCCSRCCPLCC
CLIPScore*0.1740.1690.2690.269
BLIP2Score*0.2210.2090.2890.275
VQAScore*0.5560.5020.5270.505
CLIPScore0.6810.6700.6100.628
BLIP2Score0.6870.6790.6790.705
ImageReward0.6640.6560.6630.684
Q-Eval-Score0.7570.7470.7170.714
+ +ing the best performance overall. The decline in video performance is likely due to the 1fps frame sampling method, which causes a loss of temporal information, leading to inaccurate estimations. Despite this, at the instance-level, Q-Eval-Score still leads the second-best competitor (Q-Align) by $10\%$ on video instance-level SRCC. 2) For alignment, Q-Eval-Score also demonstrates a significant lead in alignment, outperforming competitors by $6\%$ in image instance-level SRCC and $12\%$ in video instance-level SRCC. Additionally, the substantial performance improvements seen in the trained competitors suggest that Q-Eval-100K provides valuable knowledge for alignment evaluation. 3) In comparison to alignment, Q-Eval-Score's performance in visual quality is notably lower, indicating that predicting visual quality is more challenging. This is likely because alignment evaluation is more straightforward and objective, while visual quality perception is more complex and subjective, making it harder to assess. Overall, the proposed Q-Eval-Score exhibits exceptional potential in both visual quality and alignment, achieving over 0.94 performance at the image model-level, closely aligning with human evaluations. This strong performance not only highlights the robustness of the model but also underscores its promising ability to serve as an effective evaluation metric. + +# 5.3. Further Experiments + +I) Ablation Study. We conduct a detailed ablation study to assess the contribution of proposed strategies and CE/MSE loss. The results are presented in Table 4. It is clear that each of the strategies we proposed and both CE/MSE loss make a significant contribution to the final outcome. + +II) Long Prompt. To test the Vague-to-Specific strategy for long prompt alignment, we select a subset of 5,000 instances from Q-Eval-100K that contain long prompts (over 25 words) for testing, performance shown in Table 5. Due to the limited data size, we present only the instance-level performance. The results clearly show that the Vague-to-Specific strategy significantly improves performance, indicating the effectiveness of handling long prompt alignment. + +III) Cross-dataset Validation. To demonstrate the value of the Q-Eval-100K dataset, we conduct a cross-dataset validation, with performance results shown in Table 6. It is important to note that instances generated from prompts in GenAI-Bench are excluded from this validation. The results clearly show that models trained on Q-Eval-100K significantly outperform the current state-of-the-art VQAScore on GenAI-Bench by a large margin, providing strong evidence of the generalization value of the Q-Eval-100K dataset. + +# 6. Conclusion + +In conclusion, we introduce Q-Eval-100K, the largest text-to-vision evaluation dataset to date, featuring 100K instances and 960K human annotations for assessing visual quality and alignment. We also present Q-Eval-Score, a unified evaluation framework that leverages this dataset to provide separate scores for each dimension. Experimental results show that Q-Eval-Score outperforms existing methods, demonstrating its potential for more reliable, comprehensive assessments of text-to-vision models. Looking ahead, we hope this work can lay a strong foundation for further advancements in text-to-vision model promotion and real-world evaluation applications. + +# Acknowledgment + +The work was supported in part by the National Natural Science Foundation of China under Grant 62301310, Grant 623B2073, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426. + +# References + +[1] Luma AI. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 635, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 296, + 696 + ], + "type": "text", + "content": "With the rapid advancement of generative AI, millions of text-to-image and text-to-video content are being generated daily across various platforms [25, 56], applied in industrial production or directly used by consumers. However, due to current technological limitations, text-to-vision con" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 334, + 245, + 533, + 550 + ], + "blocks": [ + { + "bbox": [ + 334, + 245, + 533, + 550 + ], + "lines": [ + { + "bbox": [ + 334, + 245, + 533, + 550 + ], + "spans": [ + { + "bbox": [ + 334, + 245, + 533, + 550 + ], + "type": "image", + "image_path": "edb458ae9ef8368e4fd927a8a6da84767788b9dd7f7357536a821b5b7f4eb7ac.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 560, + 555, + 605 + ], + "lines": [ + { + "bbox": [ + 313, + 560, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 555, + 605 + ], + "type": "text", + "content": "Figure 1. Illustration of the unified evaluation dimensions of Q-Eval-100K. We focus on visual quality (including all factors that may impact the viewing experience) and alignment level, which measures the accuracy of the generated content to the prompt." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "tent often falls short of being perfect upon generation and cannot be immediately deployed [34, 36, 40], which usually requires expert evaluation, editing, and fine-tuning. As a result, numerous efforts have been made to develop automated methods for evaluating text-to-vision content, aiming to control the quality of generation and guide the necessary optimizations effectively [13, 26, 27, 29, 40, 60–63, 65, 70, 72]. Through extensive theoretical and experimental analy-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 146, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 146, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 146, + 713 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10621" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 173, + 296, + 281 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 295, + 170 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 295, + 170 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 295, + 170 + ], + "type": "text", + "content": "Table 1. A brief comparison of the latest text-to-vision evaluation datasets (I. for image, V. for video). For Annotation Type, SBS (side-by-side) and MOS (mean-opinion-score) refer to selecting the preferred instance from a pair of instances and assigning an average absolute score to a single instance respectively. For Rating Concerns, Overall indicates assigning scores from a holistic perspective while " + }, + { + "bbox": [ + 55, + 70, + 295, + 170 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 55, + 70, + 295, + 170 + ], + "type": "text", + "content": " denotes assigning separate scores to quality or alignment. For Number, Ins. and Ann. stand for the number of instances and human annotations respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 173, + 296, + 281 + ], + "lines": [ + { + "bbox": [ + 56, + 173, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 56, + 173, + 296, + 281 + ], + "type": "table", + "html": "
DatasetYearContentAnnotation Type (Single/Pair)Evaluation ConcernNumber Ins./Ann.
QualityAlignment
Pick-a-pic [27]2023I.SBSOverall1M/500K
ImageReward [65]2023I.SBSOverall68k/137k
HPDv2 [63]2023I.SBSOverall430k/645K
AGIQA-3k [34]2023I.MOS✓✓3K/81K
AIGCIA2023 [58]2023I.MOS✓✓2K/17K
PKU-AIGIA-4k [67]2024I.MOS✓✓4K/84K
AIGIA-20k [35]2024I.MOSOverall20K/420K
RichHF [39]2024I.MOS✓✓18K/54K
VideoFeedback [19]2024V.MOS✓✓37.6K/37.6K
T2VQA-DB [28]2024V.MOSOverall10K/27K
GenAI-Bench [33]2024I.&V.1-5 Likert ScaleOverall9.6K/9.6K
Q-Eval-100K (Ours)2024I.&V.MOS✓✓100K/960K
", + "image_path": "d920fd1f53c0deb66aa14068882d0fa026cf7fc238aa8cbced1613e2aae7d620.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 293, + 295, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 295, + 365 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 295, + 365 + ], + "type": "text", + "content": "sis, the evaluation of text-to-vision content can be primarily divided into two dimensions [41, 64, 65, 73, 76]: Visual Quality (the perceived quality of the visual content, which can be simply understood as how good it looks) and Alignment level (the consistency between text and vision, which can be interpreted as how accurate the generation is)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 366, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 640 + ], + "type": "text", + "content": "To meet the need for evaluation, many text-to-vision evaluation datasets have been proposed, along with corresponding evaluation algorithms [11, 12, 19, 19, 24, 28, 33-35, 39, 41, 58, 67, 71, 74, 75]. However, these efforts face the following significant limitations: 1) The key evaluation dimensions for text-to-vision content are often not systematically captured. Some datasets propose too many dimensions, adding unnecessary complexity to the evaluation process. The practical applicability of these dimensions can be narrow or lead to redundancy. 2) Most text-to-vision evaluation datasets fail to disentangle visual quality and alignment. These datasets either focus solely on alignment or visual quality, or merge both dimensions into a single score, leading to results that are often incomplete and ambiguous, making it challenging to address specific evaluation needs. 3) The scale of these datasets remains insufficient. With the rise of Large Multimodal Models (LMMs), which have demonstrated strong capabilities in visual and textual understanding, researchers are increasingly leveraging them for text-to-vision evaluation. However, current dataset sizes remain inadequate to fully unlock the potential of LMM-based models [76], conceivably restricting their applicability and generalization in real-world scenarios." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "To address these challenges, we present Q-Eval-100K, which, to the best of our knowledge, is the largest text-to-vision evaluation dataset with Mean Opinion Scores (MOSs), comprising 100K instances (including 60K generated images & 40K generated videos). A brief comparison of Q-Eval-100K and previous text-to-vision eval" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": "uation datasets is illustrated in Table 1. We manually gather prompts from existing benchmarks and create diverse prompts that focus on three key aspects: entity generation, entity attribute generation, and interaction capability. The instances in Q-Eval-100K are then generated from a diverse range of generative models, both open-source and closed-source, to ensure high diversity. We implement a rigorous, scientifically grounded subjective evaluation process using a Sample & Scrutinize strategy, focusing on both visual quality and alignment level for each of the 100K instances, yielding a total of high-quality 960K human annotations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 213, + 555, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 499 + ], + "type": "text", + "content": "Building on the proposed Q-Eval-100K, we propose Q-Eval-Score, a unified evaluation framework capable of assessing both visual quality and alignment, providing separate scores for each dimension. We first adapt Q-Eval-100K into a Supervised Fine-Tuning (SFT) dataset optimized for injecting knowledge into LMMs. Scores are transformed into adjective-based ratings, then reformulated within a well-guided context-prompt format. Specifically, for visual quality, we guide the model to identify positive and negative visual impacts, evaluate the intensity of these impacts, and make a balanced judgment. For alignment, we guide the model to perceive the overall situation, examine details, and reach a balanced judgment. The fine-tuning process is then supervised by a combined CE and MSE loss. During inference, the final score is computed as a weighted average based on the probability of each rating token. Notably, in handling long-prompt alignment, we observed that direct alignment assessment often yields low scores due to oversimplification. To address this, we propose a Vague-to-Specific strategy, where a long prompt is converted into a vague version retaining only core information and multiple prompts with specific details. These prompts are evaluated separately and the alignment scores are combined to the final score. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 508, + 553, + 711 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 315, + 508, + 553, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 508, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 315, + 508, + 553, + 579 + ], + "type": "text", + "content": "- We present Q-Eval-100K, the largest text-to-vision evaluation dataset with MOSs, comprising 100K instances from various generative models. We employ a scientifically grounded evaluation methodology, using a Sample & Scrutinize strategy to collect 960K human annotations focusing on visual quality and alignment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 580, + 553, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 580, + 553, + 662 + ], + "spans": [ + { + "bbox": [ + 315, + 580, + 553, + 662 + ], + "type": "text", + "content": "- We propose Q-Eval-Score, a unified evaluation framework capable of independently assessing visual quality and alignment, providing separate scores for each dimension. Specifically, we adapt Q-Eval-100K into an SFT dataset with adjective-based ratings in a structured context-prompt format for enhancing the visual quality and alignment evaluation capabilities of LMMs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 663, + 553, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 663, + 553, + 711 + ], + "spans": [ + { + "bbox": [ + 315, + 663, + 553, + 711 + ], + "type": "text", + "content": "- To improve alignment evaluation for long prompts, we introduce a Vague-to-Specific strategy, which separates prompts into core and detailed variants, yielding a more accurate alignment score through weighted averaging." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10622" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 93, + 276, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 93, + 276, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 93, + 276, + 105 + ], + "type": "text", + "content": "2.1. Benchmarks for Text-to-Vision Evaluation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 114, + 296, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 114, + 296, + 233 + ], + "spans": [ + { + "bbox": [ + 55, + 114, + 296, + 233 + ], + "type": "text", + "content": "Early text-to-vision benchmarks largely depend on multimodal datasets labeled with captions [10, 22, 43]. However, with increasing recognition of human feedback's value [14, 23, 76], many benchmarks begin to employ human annotations. Common annotation methods include SBS (side-by-side) and MOS (mean opinion score) [49, 68]. SBS requires selecting a preferred instance from a pair, while MOS assigns a score to a single instance. SBS is generally easier for human subjects and more precise, but MOS is more versatile and broadly applicable to various situations [6, 32]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 236, + 296, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 451 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 451 + ], + "type": "text", + "content": "Text-to-vision evaluation dimensions [41, 73] can be categorized into visual quality and alignment. While some benchmarks [11, 12, 19, 24] treat aspects like naturalness, aesthetics, and temporal consistency as distinct dimensions, we view these as components of visual quality since they collectively influence the quality of experience (QoE) for viewers. Early benchmarks [34, 35, 58, 67] for generated images comprehensively address both visual quality and alignment for evaluation. RichHF [39] enhances these evaluations by incorporating subjective scores, heatmaps, and misalignment tokens. For video, VideoFeedback [19] introduces five dimensions of quality and alignment, while T2VQA-DB [28] focuses primarily on visual quality. Further, GenAI-Bench [33] evaluates alignment for both generated images and generated videos. The proposed Q-Eval-100K dataset offers a unified text-to-vision evaluation framework, significantly increasing dataset scale and diversity, making it distinct from prior benchmarks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 465, + 249, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 249, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 249, + 477 + ], + "type": "text", + "content": "2.2. Metric for Text-to-Vision Evaluation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": "Previous evaluation methods separately focus on either visual quality or alignment. Perceptual methods assess the visual quality of generated content, utilizing traditional scores like IS [52], FID [21], and LPIPS [69] with pretrained neural networks. Recently, data-driven models [34] trained on specialized datasets have further advanced perceptual score prediction. Additionally, methods such as CLIP-IQA [57] and Q-Align [62] leverage text prompts to enhance perceptual alignment. Alignment methods, integrating both text and vision modalities, initially use CLIP-Score [20] due to its ease of application. To address more complex prompts, some approaches [27, 63, 65] incorporate human feedback to improve evaluation accuracy. Given the powerful interpretative capabilities of LMMs, recent work [13, 26, 29, 40, 70] has begun to apply these models to alignment assessments. Most existing models evaluate either perceptual quality or alignment exclusively. The proposed Q-Eval-Score addresses this gap by offering decoupled scores for both perceptual quality and alignment." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 339, + 71, + 531, + 217 + ], + "blocks": [ + { + "bbox": [ + 339, + 71, + 531, + 217 + ], + "lines": [ + { + "bbox": [ + 339, + 71, + 531, + 217 + ], + "spans": [ + { + "bbox": [ + 339, + 71, + 531, + 217 + ], + "type": "image", + "image_path": "d00cbcf089f2da000b26a669464fb8b3f547426aff33b7e9d8994df2ff0a2768.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 226, + 555, + 293 + ], + "lines": [ + { + "bbox": [ + 313, + 226, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 226, + 555, + 293 + ], + "type": "text", + "content": "Figure 2. Illustration of the Sample and Scrutinize quality control strategy for annotations in Q-Eval-100K. We randomly select a sample of 5K instances from the full dataset, which are then reviewed by experts to establish golden scores. A batch of annotations is approved only if the scores of the sampled instances show a high correlation with these expert-assigned golden scores." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 300, + 468, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 300, + 468, + 314 + ], + "spans": [ + { + "bbox": [ + 314, + 300, + 468, + 314 + ], + "type": "text", + "content": "3. Q-Eval-100K Construction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 320, + 411, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 320, + 411, + 333 + ], + "spans": [ + { + "bbox": [ + 314, + 320, + 411, + 333 + ], + "type": "text", + "content": "3.1. Basic Principles" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 339, + 555, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 555, + 447 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 555, + 447 + ], + "type": "text", + "content": "The construction process of Q-Eval-100K is illustrated in Fig. 3. We follow these guiding principles: 1) Ensuring diversity in generated content by collecting a wide range of prompts and using multiple generative models; 2) Ensuring annotation quality through carefully designed experimental settings and standards to achieve the highest accuracy; 3) Ensuring effective learning, through adapting the data for LMM suitability by transforming both visual quality and alignment scores into a context-aware SFT dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 455, + 424, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 455, + 424, + 467 + ], + "spans": [ + { + "bbox": [ + 314, + 455, + 424, + 467 + ], + "type": "text", + "content": "3.2. Sources Collection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 474, + 555, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 605 + ], + "type": "text", + "content": "Prompt Designing. The prompt design focuses on three main aspects: Entity Generation, Entity Attribute Generation, and Interaction Capability. 1) Entity generation targets the primary entities (people, objects, etc.) to be generated. 2) Entity attribute generation emphasizes the attributes (clothing, color, material, etc.) of the entities. 3) Interaction capability focuses on the interactions between the generated entities and other entities or the background, such as their spatial relationships and actions. Following the outlines mentioned above, we manually create a portion of the prompts and extract some from existing datasets [33, 46]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 606, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 556, + 714 + ], + "type": "text", + "content": "Generation Models. We utilize multiple popular text-to-image and text-to-video models to ensure diversity, which include FLUX [30], Lumina-T2X [17], PixArt [9], Stable Diffusion 3 [3], Stable Diffusion XL [50], DALL-E 3 [47], Wanx [15], Midjourney [44], Hunyuan-DiT [38], Kolors [54], ERNIE-ViLG [16], CogVideoX [66], Runway GEN-2 [18], Runway GEN-3 [51], Latte [42], Kling [53], Dreamina [8], Luma [1], PixVerse [2], Pika [31], Stable Video Diffusion [7], Vidu [55]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10623" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 212, + 245 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 212, + 245 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 212, + 245 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 212, + 245 + ], + "type": "image", + "image_path": "bfa9e0925b787e3463079c31ef131d339345223b4920fdc44c25ee0a73cfa136.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 255, + 555, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 255, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 555, + 289 + ], + "type": "text", + "content": "Figure 3. Overview of the Q-Eval-100K construction process. We design a wide range of prompts and employ various text-to-vision models to generate diverse content. Subjective evaluations are then conducted to rate the visual quality and alignment of these generated instances. The resulting scores form the SFT dataset, which can help inject corresponding knowledge into LMMs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 221, + 71, + 389, + 245 + ], + "blocks": [ + { + "bbox": [ + 221, + 71, + 389, + 245 + ], + "lines": [ + { + "bbox": [ + 221, + 71, + 389, + 245 + ], + "spans": [ + { + "bbox": [ + 221, + 71, + 389, + 245 + ], + "type": "image", + "image_path": "ed5657f5a42e2a5dc799860bc70c301c7c6630409c672829db1eae3fb8d7f1d1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 391, + 72, + 549, + 244 + ], + "blocks": [ + { + "bbox": [ + 391, + 72, + 549, + 244 + ], + "lines": [ + { + "bbox": [ + 391, + 72, + 549, + 244 + ], + "spans": [ + { + "bbox": [ + 391, + 72, + 549, + 244 + ], + "type": "image", + "image_path": "a1edd7e9cd78560fccf5a1532f7f19bbf76ff9e8f26fab474814c74caefbd498.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 310, + 185, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 310, + 185, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 310, + 185, + 322 + ], + "type": "text", + "content": "3.3. Subjective Experiment" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 329, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 329, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 54, + 329, + 296, + 581 + ], + "type": "text", + "content": "Given the large scale of Q-Eval-100K, we develop rigorous experimental protocols to ensure the highest possible accuracy in our annotations. To facilitate this, we establish a well-controlled indoor experimental environment, where more than 200 human subjects are recruited to participate in the annotation. To ensure the accuracy of annotations is not compromised by individual cognitive differences or annotator fatigue, we propose a Sample & Scrutinize data control strategy as shown in Fig. 2. The strategy includes two steps: 1) First, we randomly sample 5,000 instances from the entire dataset. We then organize experts with rich experience to discuss and score these instances, leading to the establishment of golden scores for both visual quality and alignment. These golden scores remain hidden for all subsequent experimental subjects. 2) Next, we provide human annotators with comprehensive training before they begin the annotation process. After each batch, we gather the scores for instances that have golden scores and compare them with these golden scores, calculating the correlation values (SRCC-rank similarity). Only batches with an SRCC above 0.8 are accepted, otherwise, they are rejected." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "type": "text", + "content": "Additionally, we split Q-Eval-100K into training and testing sets in an 80:20 ratio. Each instance in the training set has at least three annotations, while each instance in the testing set has a minimum of twelve annotations to ensure accuracy. This process results in a total of over 960K annotations, calculated as follows: 80K (training instances) x 2 (visual quality & alignment) x 3 (minimum annotation number) + 20K (training instances) x 2 (visual quality & alignment) x 12 (minimum annotation number) = 960K annotations. Finally, we calculate the average of the multiple annotations to derive the score for each instance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 310, + 425, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 310, + 425, + 322 + ], + "spans": [ + { + "bbox": [ + 314, + 310, + 425, + 322 + ], + "type": "text", + "content": "3.4. Statistical Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 329, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 329, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 329, + 555, + 628 + ], + "type": "text", + "content": "The distributions of MOSs for visual quality and alignment are exhibited in Fig. 4 respectively, which reveal several key insights. In general, there are substantial differences among generation models in both visual quality and alignment, with their distributions displaying significant inconsistencies, indicating varied performance across different generation prompts. 1) For image alignment, distributions are generally skewed higher, suggesting that models perform relatively well in aligning images, though multiple peaks in the 4-5 and 2-3 score ranges indicate some fluctuation in performance. 2) In video alignment, model performance varies more markedly, with most scores concentrated between 2 and 4, highlighting the need for improvement in alignment in video generation. 3) Visual quality for images scores noticeably lower than image alignment, indicating that generation models perform significantly worse in visual quality. Furthermore, the wider distribution spread in image visual quality suggests greater variance and instability across models. 4) Similarly, video visual quality scores are lower than alignment scores, highlighting a consistent underperformance in visual quality. Interestingly, models such as Kling, Dreamina, Luma, PixVerse, and Pika exhibit similar distributions for alignment and visual quality, indicating consistent capability across both aspects. However, this consistency is not observed across all models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "type": "text", + "content": "Overall, the findings above highlight a notable disparity in that visual quality generally falls behind alignment. This gap likely stems from the current emphasis on alignment optimization, which is also relatively easier to improve, whereas visual quality has received less focus. This analysis underscores the importance of Q-Eval-100K as a comprehensive benchmark for evaluating both dimensions." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10624" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 72, + 302, + 159 + ], + "blocks": [ + { + "bbox": [ + 73, + 72, + 302, + 159 + ], + "lines": [ + { + "bbox": [ + 73, + 72, + 302, + 159 + ], + "spans": [ + { + "bbox": [ + 73, + 72, + 302, + 159 + ], + "type": "image", + "image_path": "868b3b0a0196b8fab8bb19d8e29a9f703adcfd0fe0ed01a44b85f63d88381eee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 538, + 159 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 538, + 159 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 538, + 159 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 538, + 159 + ], + "type": "image", + "image_path": "31eb319bda4ca5c23fae2bcdaf5eef3328911ab680c9f7f7f057aa7aff4eed4c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 389, + 167, + 457, + 176 + ], + "lines": [ + { + "bbox": [ + 389, + 167, + 457, + 176 + ], + "spans": [ + { + "bbox": [ + 389, + 167, + 457, + 176 + ], + "type": "text", + "content": "(b) Video Alignment" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 72, + 178, + 302, + 267 + ], + "blocks": [ + { + "bbox": [ + 153, + 167, + 222, + 176 + ], + "lines": [ + { + "bbox": [ + 153, + 167, + 222, + 176 + ], + "spans": [ + { + "bbox": [ + 153, + 167, + 222, + 176 + ], + "type": "text", + "content": "(a) Image Alignment" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 72, + 178, + 302, + 267 + ], + "lines": [ + { + "bbox": [ + 72, + 178, + 302, + 267 + ], + "spans": [ + { + "bbox": [ + 72, + 178, + 302, + 267 + ], + "type": "image", + "image_path": "13ade1db97feb245fb068571b7d359659d11239699a102d0ba99f3463e72c69c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 147, + 274, + 228, + 283 + ], + "lines": [ + { + "bbox": [ + 147, + 274, + 228, + 283 + ], + "spans": [ + { + "bbox": [ + 147, + 274, + 228, + 283 + ], + "type": "text", + "content": "(c) Image Visual Quality" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 309, + 180, + 538, + 266 + ], + "blocks": [ + { + "bbox": [ + 309, + 180, + 538, + 266 + ], + "lines": [ + { + "bbox": [ + 309, + 180, + 538, + 266 + ], + "spans": [ + { + "bbox": [ + 309, + 180, + 538, + 266 + ], + "type": "image", + "image_path": "b0b710acf65d2c5262715d1ecdf0d4df9936593eb632caefd507a4db37b2a244.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 273, + 462, + 283 + ], + "lines": [ + { + "bbox": [ + 383, + 273, + 462, + 283 + ], + "spans": [ + { + "bbox": [ + 383, + 273, + 462, + 283 + ], + "type": "text", + "content": "(d) Video Visual Quality" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 293, + 553, + 304 + ], + "lines": [ + { + "bbox": [ + 55, + 293, + 553, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 553, + 304 + ], + "type": "text", + "content": "Figure 4. MOS distributions for the visual quality and alignment of generated images and videos in the Q-Eval-100K dataset respectively." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 318, + 140, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 140, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 140, + 331 + ], + "type": "text", + "content": "4. Q-Eval-Score" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 338, + 275, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 275, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 275, + 350 + ], + "type": "text", + "content": "4.1. Unified Pipeline for Decoupled Evaluation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 357, + 296, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 477 + ], + "type": "text", + "content": "Although the evaluation of visual quality and alignment are two relatively independent tasks, we leverage the adaptability and extensive prior knowledge of LMMs to propose a unified model, Q-Eval-Score, that addresses both visual quality and alignment level evaluation within a single framework. Specifically, we convert the human-labeled MOS from the Q-Eval-100K dataset for both visual quality and alignment levels into a fixed-prompt format, creating a mixed SFT dataset. We then fine-tune the LMM, enabling it to evaluate both visual quality and alignment levels." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 484, + 234, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 234, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 234, + 496 + ], + "type": "text", + "content": "4.2. How to Teach LMMs to Evaluate" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 502, + 159, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 159, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 159, + 514 + ], + "type": "text", + "content": "4.2.1 Context Prompt" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "type": "text", + "content": "In previous work using prompts with LMMs for evaluation, the questions are often straightforward and simple, such as 'Can you evaluate the quality of the image?' (Q-Align [62]) or 'Does this figure show [Prompt]? Please answer yes or no.' (VQAScore [40]). However, this simplicity may lead to confusion for the model, as the prompts may not be specific enough to guide a more detailed or accurate evaluation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": "Inspired by the chain-of-thought (CoT [59]) concept and given that humans undergo a reasoning process when evaluating visual quality and alignment, we propose a Context-Prompt format to construct our SFT dataset. For the visual quality task, the human evaluation process can be summarized as first identifying both positive and negative quality factors, then measuring these factors, and finally weighing them to reach a conclusion. Based on this process, we design the following prompt structure:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 319, + 465, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 319, + 465, + 331 + ], + "spans": [ + { + "bbox": [ + 314, + 319, + 465, + 331 + ], + "type": "text", + "content": "Context Prompt for Visual Quality" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 333, + 555, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 333, + 555, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 333, + 555, + 502 + ], + "type": "text", + "content": "# User: Suppose you are an expert in evaluating the visual quality of AI-generated image/video. First, identify any visual distortions and positive visual appeal regarding low-level features and aesthetics. Next, assess the severity of distortions and their impact on the viewing experience, noting whether they are subtle or distracting, and evaluate how the positive features enhance the visual appeal, considering their strength and contribution to the overall aesthetics. Finally, balance the identified distortions against the positive aspects and give your rating on the visual quality. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 505, + 554, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 505, + 554, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 505, + 554, + 552 + ], + "type": "text", + "content": "For the alignment task, the human evaluation process involves observing whether the overall content generally aligns with the text, followed by a more detailed comparison, and finally a comprehensive evaluation for conclusion:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 554, + 465, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 465, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 465, + 567 + ], + "type": "text", + "content": "Context Prompt for Visual Quality" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 568, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 555, + 713 + ], + "type": "text", + "content": "# User: Suppose you are an expert in evaluating alignment between the text prompt and the AI-generated image/video. Begin by considering whether the overall concept of the prompt is captured in the image/video. Then, examine the specific details, such as the presence of key objects, their attributes, and relationships. Check if the visual content accurately reflects these aspects. Finally, give your alignment rating considering both overall and detailed accuracy. Your rating should be chosen from the following five categories: [Excellent, Good, Fair, Poor, and Bad]. For this image/video [Image/Frames], the text prompt is [Prompt]. # Answer: [Rating] (Excellent, Good, Fair, Poor, Bad)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10625" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 69, + 541, + 222 + ], + "blocks": [ + { + "bbox": [ + 70, + 69, + 541, + 222 + ], + "lines": [ + { + "bbox": [ + 70, + 69, + 541, + 222 + ], + "spans": [ + { + "bbox": [ + 70, + 69, + 541, + 222 + ], + "type": "image", + "image_path": "c012a1b87628a1fe21a919634134272466e72d18892c926c1717820e29b00ea8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 230, + 555, + 277 + ], + "lines": [ + { + "bbox": [ + 54, + 230, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 54, + 230, + 555, + 277 + ], + "type": "text", + "content": "Figure 5. The pipeline of the proposed Q-Eval-Score model involves multiple stages. First, the Q-Eval-100K SFT dataset is used to train the LMM on visual quality and alignment knowledge. Then, context prompts are applied to guide the LMM towards generating more detailed and accurate outputs. Finally, the rating token probabilities are converted into predicted scores. Additionally, long prompt alignment is achieved through a Vague-to-Specific strategy to further refine the model's responses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 296, + 226, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 296, + 226, + 309 + ], + "spans": [ + { + "bbox": [ + 55, + 296, + 226, + 309 + ], + "type": "text", + "content": "4.2.2 'Translating' MOS into Ratings" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 316, + 296, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 296, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 296, + 367 + ], + "type": "text", + "content": "It is well established that discrete adjective ratings are easier for LMMs to interpret compared to numerical scores [62, 72]. Since MOS in Q-Eval-100K is labeled in absolute terms, we can easily map MOS to the corresponding rating:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 375, + 294, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 375, + 294, + 400 + ], + "spans": [ + { + "bbox": [ + 61, + 375, + 294, + 400 + ], + "type": "interline_equation", + "content": "R (s) = r _ {i} \\text {i f} m + \\frac {i - 1}{5} \\times (M - m) < s \\leq m + \\frac {i}{5} \\times (M - m), \\tag {1}", + "image_path": "4a9e127f10db886bf21acff966e406a59c5a2224546220057b19a98762e97d9f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 400, + 279, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 400, + 279, + 415 + ], + "spans": [ + { + "bbox": [ + 62, + 400, + 279, + 415 + ], + "type": "inline_equation", + "content": "\\{r_i|_{i = 1\\sim 5}\\} = \\{Bad,Poor,Fair,Good,Excellent\\}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "spans": [ + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "inline_equation", + "content": "m = 1" + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "inline_equation", + "content": "M = 5" + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "content": " (score range bound of Q-Eval-100K), " + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "inline_equation", + "content": "R(s)" + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "content": " indicates the mapped rating of MOS value " + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 424, + 296, + 450 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 459, + 170, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 170, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 170, + 471 + ], + "type": "text", + "content": "4.3. Model Architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "text", + "content": "Using the constructed SFT dataset with the question-answer pairs as described, we select Qwen-VL [5] as the LMM model (Qwen2-VL-7B-Instruct) for training, which has demonstrated strong visual understanding capabilities for both images and videos. For video processing, each video is converted into a sequence of images at a rate of one frame per second, which is then fed into the model as the input. The scoring computation method is detailed as follows. For the rating token, we first calculate the model output probabilities " + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "text", + "content": " for each of the five rating terms {Excellent, Good, Fair, Poor, Bad}, where " + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "inline_equation", + "content": "j \\in \\{1, 2, 3, 4, 5\\}" + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "text", + "content": ". Then we define the final predicted rating " + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\hat{r}" + }, + { + "bbox": [ + 55, + 479, + 296, + 635 + ], + "type": "text", + "content": " as the weighted average of these probabilities:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 140, + 645, + 296, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 645, + 296, + 680 + ], + "spans": [ + { + "bbox": [ + 140, + 645, + 296, + 680 + ], + "type": "interline_equation", + "content": "\\hat {r} = \\sum_ {j = 1} ^ {5} p _ {j} \\cdot w _ {j}, \\tag {2}", + "image_path": "40534b958f74a288893fd8819402439df451f7a4cd6ad9f0034d6f76859119bd.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "w_{j}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " is the numerical weight assigned to each rating (e.g., " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "w_{j} = \\{1,0.75,0.5,0.25,0\\}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " for Excellent to Bad)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 295, + 404, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 295, + 404, + 307 + ], + "spans": [ + { + "bbox": [ + 314, + 295, + 404, + 307 + ], + "type": "text", + "content": "4.4. Loss Function" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 314, + 555, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 314, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 314, + 555, + 387 + ], + "type": "text", + "content": "The loss function for the model consists of two parts: Cross-Entropy (CE) Loss and Mean Squared Error (MSE) Loss. The CE Loss can assist the LMM in learning the general question-answer format and necessary knowledge. Meanwhile, the MSE Loss refines the score prediction accuracy. The CE Loss for question-answer pairs is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 379, + 394, + 555, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 394, + 555, + 427 + ], + "spans": [ + { + "bbox": [ + 379, + 394, + 555, + 427 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C E} = - \\sum_ {i = 1} ^ {N} y _ {i} \\cdot \\log \\left(p _ {i}\\right), \\tag {3}", + "image_path": "b9d35c7219d84138f16afec68ed0585147eb6e02cc274681ea37772be5b83193.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "text", + "content": " is the one-hot encoded vector representing the true label for instance " + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 313, + 434, + 555, + 472 + ], + "type": "text", + "content": " is the predicted probability vector for the answer tokens. The MSE Loss can then be given by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 386, + 478, + 555, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 478, + 555, + 493 + ], + "spans": [ + { + "bbox": [ + 386, + 478, + 555, + 493 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M S E} = \\left(\\hat {r} - r _ {\\mathrm {M O S}}\\right) ^ {2}, \\tag {4}", + "image_path": "1751fd54a714595a1cfcee2a2f6efde230bf4dd771182c281b6b02dd914d60c9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "inline_equation", + "content": "\\hat{r}" + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{MOS}}" + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "text", + "content": " represent the predicted scores and the MOS labels respectively. The total loss " + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 501, + 554, + 537 + ], + "type": "text", + "content": " is a weighted sum of the CE Loss and MSE Loss:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 373, + 546, + 553, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 546, + 553, + 559 + ], + "spans": [ + { + "bbox": [ + 373, + 546, + 553, + 559 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\alpha_ {1} \\cdot \\mathcal {L} _ {C E} + \\beta_ {1} \\cdot \\mathcal {L} _ {M S E}, \\tag {5}", + "image_path": "0cc7bb8b9fb8d0abb6456ce5581cbbab3017e95749714dafb875f506d506f361.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "inline_equation", + "content": "\\beta_{1}" + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "text", + "content": " (default set as " + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "inline_equation", + "content": "1\\& 1" + }, + { + "bbox": [ + 313, + 568, + 554, + 592 + ], + "type": "text", + "content": " ) are weight parameters controlling the contribution of each loss term." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 599, + 499, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 499, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 499, + 613 + ], + "type": "text", + "content": "4.5. Handling Long Prompt Alignment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "content": "During inference, we observe that the trained LMM tends to undervalue alignment when handling long prompts (more than 25 words). This is partly because long prompts are underrepresented in the training data, leading to insufficient training. More importantly, the LMM acts as a strict evaluator, often penalizing significant points for inconsistencies that may seem minor to humans. These small discrepancies occur more frequently with long prompts. To manage this" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10626" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 85, + 164, + 178 + ], + "blocks": [ + { + "bbox": [ + 81, + 72, + 145, + 83 + ], + "lines": [ + { + "bbox": [ + 81, + 72, + 145, + 83 + ], + "spans": [ + { + "bbox": [ + 81, + 72, + 145, + 83 + ], + "type": "text", + "content": "Generated Image" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 186, + 72, + 266, + 83 + ], + "lines": [ + { + "bbox": [ + 186, + 72, + 266, + 83 + ], + "spans": [ + { + "bbox": [ + 186, + 72, + 266, + 83 + ], + "type": "text", + "content": "Original Long Prompt" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 70, + 85, + 164, + 178 + ], + "lines": [ + { + "bbox": [ + 70, + 85, + 164, + 178 + ], + "spans": [ + { + "bbox": [ + 70, + 85, + 164, + 178 + ], + "type": "image", + "image_path": "70c39ee643de592e929e042c19d1cc44556bda901b06a6412dd8b3c809e8180d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 277, + 295, + 332 + ], + "lines": [ + { + "bbox": [ + 55, + 277, + 295, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 295, + 332 + ], + "type": "text", + "content": "Figure 6. An example of the Vague-to-Specific strategy. The original long prompt is divided by the LLM (QwenLM [4]) into a Vague Prompt and several Specific Prompts. The alignment score is first calculated separately for each part, then combined using weighted averaging to form the final score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 173, + 86, + 278, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 86, + 278, + 177 + ], + "spans": [ + { + "bbox": [ + 173, + 86, + 278, + 177 + ], + "type": "text", + "content": "A new Chinese style painting, a group of animals are having a meeting, the owl is sitting in the leader's position and speaking, they are all wearing clothes with futuristic designs, and the picture should have a sense of technology." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 67, + 184, + 284, + 266 + ], + "blocks": [ + { + "bbox": [ + 67, + 184, + 284, + 266 + ], + "lines": [ + { + "bbox": [ + 67, + 184, + 284, + 266 + ], + "spans": [ + { + "bbox": [ + 67, + 184, + 284, + 266 + ], + "type": "table", + "html": "
Vague PromptIn a futuristic Chinese-style painting, an owl leads a tech-themed animal meeting. 4 A_v=4
Specific Prompts-A group of animals are depicted in a meeting. 5
-The owl is the leader, sitting in the center, speaking. 51/n ∑i=1n As_i = 13/3
Final Align. 0.5*4+0.5*4.33 = 4.17-Each animal wears futuristic clothing, adding a tech flair to the scene.3
", + "image_path": "62e7a80e8eac99f65dbdd31692230e6861027a9228781e5c480ba047955e6c7b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 344, + 296, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 344, + 296, + 417 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 296, + 417 + ], + "type": "text", + "content": "issue, we propose a Vague-to-Specific strategy. We use an additional LLM (QwenLM [4]) to summarize long prompts, retaining only the core features while filtering out details, producing a concise Vague Prompt. Then, we split the long prompt into Specific Prompts (no more than three), each maintaining full details but avoiding redundancy:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 429, + 295, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 429, + 295, + 444 + ], + "spans": [ + { + "bbox": [ + 99, + 429, + 295, + 444 + ], + "type": "interline_equation", + "content": "\\left(P _ {v}, \\left\\{P _ {s _ {1}}, \\dots , P _ {s _ {n}} \\right\\}\\right) = \\mathcal {V S} \\left(P _ {L o n g}\\right), \\tag {6}", + "image_path": "7db133d137e0c1d4128775cf5a3e7b90ce53628d87d30d365c4fe0c7abb4087e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "spans": [ + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "inline_equation", + "content": "P_{v}" + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "content": " represents the Vague Prompt, " + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "inline_equation", + "content": "\\{P_{S_1},\\dots ,P_{S_n}\\}" + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "content": " stands for the set of Specific Prompts, " + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{VS}(\\cdot)" + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "content": " indicates the prompt split function, and " + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "inline_equation", + "content": "P_{Long}" + }, + { + "bbox": [ + 55, + 454, + 296, + 622 + ], + "type": "text", + "content": " is the original long prompt. For the Vague Prompt, we calculate alignment in the usual way. However, directly asking for consistency with the Specific Prompts is not appropriate since each one addresses only part of the vision content. Drawing inspiration from the VQAScore [40] approach, we modify the question to a softer format, such as 'Does the image/video show [Prompt]?' to evaluate alignment (measuring as the logit probability of answering 'Yes') for each Specific Prompts. Finally, we combine the results from both the Vague Prompt and Specific Prompt using a weighted approach to calculate the final alignment score:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 634, + 295, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 634, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 295, + 666 + ], + "type": "interline_equation", + "content": "\\mathcal {A} _ {f} = \\alpha_ {2} \\mathcal {A} _ {v} + \\beta_ {2} \\left(\\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {A} _ {s _ {i}}\\right), \\tag {7}", + "image_path": "962f3fec784f96e006e435426118db55775e1db858225a0dc417344fb7da8320.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_f, \\mathcal{A}_v," + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{s_i}" + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": " are the alignment scores for the final evaluation, vague prompt, and " + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": "-th specific prompt. " + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\beta_{2}" + }, + { + "bbox": [ + 55, + 677, + 295, + 715 + ], + "type": "text", + "content": " (0.5 & 0.5 as default) are weight parameters." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 96, + 555, + 176 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "type": "text", + "content": "Table 2. Performance comparison on the visual quality aspect of Q-Eval-100K. Best in bold, second underlined." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 96, + 555, + 176 + ], + "lines": [ + { + "bbox": [ + 315, + 96, + 555, + 176 + ], + "spans": [ + { + "bbox": [ + 315, + 96, + 555, + 176 + ], + "type": "table", + "html": "
Model\n(Visual\nQuality)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE0.2390.2380.8290.758-0.057-0.074-0.333-0.241
CLIP-IQA0.3340.3240.6000.6850.1940.1750.0950.076
Q-Align0.5870.5780.7140.9140.5000.5020.7620.762
IPCE0.5500.5600.9330.9370.2990.3020.4760.568
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.814
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Model (Align-ment)Q-Eval-ImageQ-Eval-Video
Instance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
CLIPScore*0.2450.2520.6170.6850.1860.2190.5180.500
BLIP2Score*0.2970.3300.7640.8350.2180.2500.2950.296
VQAScore*0.5490.4680.3850.5550.4330.4320.4330.351
CLIPScore0.7680.7400.9580.9560.4310.4430.5190.509
BLIP2Score0.7660.7430.9330.9340.4830.4880.5120.481
ImageReward0.7620.7320.9250.9550.4720.4850.3750.362
Q-Eval-Score0.8220.8020.9640.9690.6070.6340.6480.605
", + "image_path": "821ab9cc6cf30f345fe07877a08d74e48f865801d898148e305ddd2d9f9bfbf5.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 344, + 391, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 391, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 391, + 358 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 365, + 430, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 430, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 430, + 378 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 384, + 555, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 503 + ], + "type": "text", + "content": "Training & Evaluation. The Qwen2-VL-7B-Instruct [5] serves as the backbone LMM for Q-Eval-Score. All visual quality and alignment data from images and videos are combined for training. Training is conducted on 8 A100 GPUs for one epoch by default. For evaluation metrics, we use SRCC and PLCC, which measure the rank and linear correlation between predicted scores and MOSs. We propose evaluations at the Instance-level and Model-level which assess accuracy in ranking specific generated instances and generative models based on overall performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 505, + 556, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 505, + 556, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 505, + 556, + 636 + ], + "type": "text", + "content": "Competitors. Few models can simultaneously predict both visual quality and alignment. Thus we selected task-specific competitors for each sub-task: For visual quality, we include NIQE [45], CLIP-IQA [57], Q-Align [62], and IPCE [48] (the top method from the 'NTIRE 2024 Quality Assessment of AI-Generated Content Challenge' [41]). For alignment, we choose CLIPScore [20], BLIP2Score [37], ImageReward [65] and VQAScore [40] as the competitors. All models are trained and tested using their default recommended parameters and the corresponding train-test sets of the Q-Eval-100K dataset unless specified." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 646, + 484, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 646, + 484, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 646, + 484, + 659 + ], + "type": "text", + "content": "5.2. Discussion & General Findings" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "The general performance on the visual quality and alignment is exhibited in Table 2 and Table 3, from which we can draw several conclusions: 1) For visual quality, The proposed Q-Eval-Score outperforms all competitors, achiev-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10627" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 85, + 553, + 156 + ], + "blocks": [ + { + "bbox": [ + 227, + 71, + 381, + 82 + ], + "lines": [ + { + "bbox": [ + 227, + 71, + 381, + 82 + ], + "spans": [ + { + "bbox": [ + 227, + 71, + 381, + 82 + ], + "type": "text", + "content": "Table 4. Ablation Study of Q-Eval-Score." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 85, + 553, + 156 + ], + "lines": [ + { + "bbox": [ + 56, + 85, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 56, + 85, + 553, + 156 + ], + "type": "table", + "html": "
ModelQ-Eval-Image (Quality)Q-Eval-Video (Quality)Q-Eval-Image (Alignment)Q-Eval-Video (Alignment)
Instance-levelModel-levelInstance-levelModel-levelInstance-levelModel-levelInstance-levelModel-level
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
w/o SFT Training0.0710.0960.2570.1360.0180.0080.2620.3140.5290.4230.5600.7050.4640.4370.5670.478
w/o Context Prompt0.5040.5090.6000.7560.5980.5910.5710.6380.8050.7760.9600.9630.5880.5970.6010.602
w/o CE Loss0.6520.6220.9320.9100.2470.2490.0710.2390.8040.7760.9480.9610.6040.6260.6420.593
w/o MSE Loss0.6650.6730.9330.9410.5950.5830.6900.7120.7950.7630.9540.9580.5800.6050.6240.599
Q-Eval-Score0.7320.7310.9430.9490.6010.6090.7620.8140.8220.8020.9640.9690.6070.6340.6480.605
", + "image_path": "35e80da09de7286c309f68fdf34027588d50de88c256210c009007f2a331c0bf.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 208, + 295, + 280 + ], + "blocks": [ + { + "bbox": [ + 55, + 160, + 295, + 205 + ], + "lines": [ + { + "bbox": [ + 55, + 160, + 295, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 160, + 295, + 205 + ], + "type": "text", + "content": "Table 5. Performance comparison on the alignment aspect of Q-Eval-100K on the long prompt subset, where w/o V2S and w V2S represents the proposed Q-Eval-Score model with and without the Vague-to-Specific strategy respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 208, + 295, + 280 + ], + "lines": [ + { + "bbox": [ + 56, + 208, + 295, + 280 + ], + "spans": [ + { + "bbox": [ + 56, + 208, + 295, + 280 + ], + "type": "table", + "html": "
Model\n(Align-ment)Q-Eval-Image (Long)Q-Eval-Video (Long)
Instance-levelInstance-level
SRCCPLCCSRCCPLCC
CLIPScore0.5330.5470.3590.367
BLIP2Score0.6200.6360.3920.395
VQAScore0.4320.3250.3440.350
w/o V2S0.5910.5990.4800.470
w V2S0.6200.6230.5170.512
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Model\n(Alignment)GenAI-Bench (Image)GenAI-Bench (Video)
SRCCPLCCSRCCPLCC
CLIPScore*0.1740.1690.2690.269
BLIP2Score*0.2210.2090.2890.275
VQAScore*0.5560.5020.5270.505
CLIPScore0.6810.6700.6100.628
BLIP2Score0.6870.6790.6790.705
ImageReward0.6640.6560.6630.684
Q-Eval-Score0.7570.7470.7170.714
", + "image_path": "ed6008abf06a9b7907295e6241dd25a3ca04dadf5ed136432c49975029ff6f6f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "text", + "content": "ing the best performance overall. The decline in video performance is likely due to the 1fps frame sampling method, which causes a loss of temporal information, leading to inaccurate estimations. Despite this, at the instance-level, Q-Eval-Score still leads the second-best competitor (Q-Align) by " + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "text", + "content": " on video instance-level SRCC. 2) For alignment, Q-Eval-Score also demonstrates a significant lead in alignment, outperforming competitors by " + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "text", + "content": " in image instance-level SRCC and " + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 54, + 426, + 295, + 713 + ], + "type": "text", + "content": " in video instance-level SRCC. Additionally, the substantial performance improvements seen in the trained competitors suggest that Q-Eval-100K provides valuable knowledge for alignment evaluation. 3) In comparison to alignment, Q-Eval-Score's performance in visual quality is notably lower, indicating that predicting visual quality is more challenging. This is likely because alignment evaluation is more straightforward and objective, while visual quality perception is more complex and subjective, making it harder to assess. Overall, the proposed Q-Eval-Score exhibits exceptional potential in both visual quality and alignment, achieving over 0.94 performance at the image model-level, closely aligning with human evaluations. This strong performance not only highlights the robustness of the model but also underscores its promising ability to serve as an effective evaluation metric." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 162, + 437, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 162, + 437, + 174 + ], + "spans": [ + { + "bbox": [ + 313, + 162, + 437, + 174 + ], + "type": "text", + "content": "5.3. Further Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 181, + 553, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 181, + 553, + 241 + ], + "spans": [ + { + "bbox": [ + 313, + 181, + 553, + 241 + ], + "type": "text", + "content": "I) Ablation Study. We conduct a detailed ablation study to assess the contribution of proposed strategies and CE/MSE loss. The results are presented in Table 4. It is clear that each of the strategies we proposed and both CE/MSE loss make a significant contribution to the final outcome." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 243, + 553, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 553, + 338 + ], + "type": "text", + "content": "II) Long Prompt. To test the Vague-to-Specific strategy for long prompt alignment, we select a subset of 5,000 instances from Q-Eval-100K that contain long prompts (over 25 words) for testing, performance shown in Table 5. Due to the limited data size, we present only the instance-level performance. The results clearly show that the Vague-to-Specific strategy significantly improves performance, indicating the effectiveness of handling long prompt alignment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 340, + 554, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 340, + 554, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 340, + 554, + 448 + ], + "type": "text", + "content": "III) Cross-dataset Validation. To demonstrate the value of the Q-Eval-100K dataset, we conduct a cross-dataset validation, with performance results shown in Table 6. It is important to note that instances generated from prompts in GenAI-Bench are excluded from this validation. The results clearly show that models trained on Q-Eval-100K significantly outperform the current state-of-the-art VQAScore on GenAI-Bench by a large margin, providing strong evidence of the generalization value of the Q-Eval-100K dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 464, + 388, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 388, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 388, + 475 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 485, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 554, + 628 + ], + "type": "text", + "content": "In conclusion, we introduce Q-Eval-100K, the largest text-to-vision evaluation dataset to date, featuring 100K instances and 960K human annotations for assessing visual quality and alignment. We also present Q-Eval-Score, a unified evaluation framework that leverages this dataset to provide separate scores for each dimension. Experimental results show that Q-Eval-Score outperforms existing methods, demonstrating its potential for more reliable, comprehensive assessments of text-to-vision models. Looking ahead, we hope this work can lay a strong foundation for further advancements in text-to-vision model promotion and real-world evaluation applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 644, + 407, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 644, + 407, + 657 + ], + "spans": [ + { + "bbox": [ + 313, + 644, + 407, + 657 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "The work was supported in part by the National Natural Science Foundation of China under Grant 62301310, Grant 623B2073, and in part by Sichuan Science and Technology Program under Grant 2024NSFSC1426." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "10628" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "text", + "content": "[1] Luma AI. 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Ltd. $^{3}$ Technische Universität München", + "bbox": [ + 204, + 244, + 764, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 316, + 313, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we address the challenge of adaptive pediatric Left Ventricular Ejection Fraction (LVEF) assessment. While Test-time Training (TTT) approaches show promise for this task, they suffer from two significant limitations. Existing TTT works are primarily designed for classification tasks rather than continuous value regression, and they lack mechanisms to handle the quasi-periodic nature of cardiac signals. To tackle these issues, we propose a novel Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART) framework. In the training stage, the proposed Quasi-Period Network decomposes the echocardiogram into periodic and aperiodic components within latent space by combining parameterized helix trajectories with Neural Controlled Differential Equations. During inference, our framework further employs a variance minimization strategy across image augmentations that simulate common quality issues in echocardiogram acquisition, along with differential adaptation rates for periodic and aperiodic components. Theoretical analysis is provided to demonstrate that our variance minimization objective effectively bounds the regression error under mild conditions. Furthermore, extensive experiments across three pediatric age groups demonstrate that Q-PART not only significantly outperforms existing approaches in pediatric LVEF prediction, but also exhibits strong clinical screening capability with high mAUROC scores (up to 0.9747) and maintains gender-fair performance across all metrics, validating its robustness and practical utility in pediatric echocardiography analysis. The project can be found in Q-PART.", + "bbox": [ + 75, + 348, + 472, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 818, + 209, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Evaluation of Left Ventricular Ejection Fraction (LVEF) for pediatric patients plays a vital role in early diagnosis of con", + "bbox": [ + 75, + 843, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "genital and acquired heart disease [31]. Echocardiography, recognized for its noninvasive nature and safety, has become the standard modality for LVEF evaluation [3, 26]. Although recent deep learning models [13, 16, 21] have shown promising results in adult LVEF assessment, their direct application to pediatric cases is problematic due to fundamental differences in cardiac imaging. As demonstrated in Figure 1 (a), pediatric patients exhibit considerable anatomical and physiological variations, including distinct differences in heart size, shape, and rate across different age groups [7]. Moreover, acquiring pediatric echocardiogram data is inherently challenging. Young children often exhibit difficulty cooperating during examinations, and ethical considerations limit unnecessary medical procedures, resulting in significant inter-observer variability and scarcity of labeled data for training.", + "bbox": [ + 500, + 316, + 893, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Test-time training (TTT) emerges as a promising paradigm to address these challenges by enabling model adaptation to distribution shifts during inference [15, 32]. TTT can enable model adaptation to each specific patient case during inference, without requiring access to training data or labels [28, 29], making it particularly valuable for pediatric LVEF assessment. This patient-specific adaptation naturally handles diverse pediatric cases without the necessity for extensive training echocardiograms, while also accommodating diverse anatomical variations and ensuring data privacy.", + "bbox": [ + 496, + 563, + 893, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the regression of pediatric LVEF presents unique challenges for direct application of TTT in this area. Firstly, existing TTT methods such as entropy minimization [33, 36, 39, 40], primarily designed for classification tasks with discrete decision boundaries [28, 29, 32], are not well suited for LVEF prediction, which is essentially a continuous value regression task. This challenge is further complicated by the quality issues in echocardiogram acquisition, as shown in Figure 1 (a), where varying acoustic shadow, probe positions, and speckle noise significantly impact regression accuracy, necessitating specialized self", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors: Haoliang Li.", + "bbox": [ + 94, + 886, + 297, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15560", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e7599e4e2365862e1fc9eebaf36a7b85439ccac7e595ba2645745fd26add4103.jpg", + "image_caption": [ + "Figure 1. (a) Adult and Pediatric Echocardiogram Visualization. These two kinds of echocardiograms exhibit anatomical and physiological variations, including distinct differences in heart size and shape. Moreover, We demonstrate two quality issues, i.e., acoustic shadow and speckle noise. (b) Quasi-Period Signal. Electrocardiogram (ECG) signals can be decomposed into periodic components originating from regular cardiac cycles and aperiodic components induced by physiological variations and noise." + ], + "image_footnote": [], + "bbox": [ + 91, + 92, + 460, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "supervised algorithms for stable predictions. Secondly, the inherent complexity of cardiac activities in echocardiograms introduces additional challenges. As illustrated by the Electrocardiogram (ECG) signal example in Figure 1 (b), cardiac activities demonstrate a characteristic duality, comprising periodic components from regular cardiac cycles and aperiodic components from physiological variations, collectively forming quasi-periodic signals [1, 2, 14]. While periodic cardiac patterns remain relatively consistent across age groups, pediatric cases exhibit significant aperiodic variations due to diverse heart sizes and irregular activities. Leveraging this quasi-periodic nature for test-time training in echocardiogram analysis thus presents a promising yet unexplored research direction.", + "bbox": [ + 75, + 520, + 468, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose a novel test-time training framework, named Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART), tailored for pediatric LVEF regression with two key innovations: (1) a Quasi-Period Network that explicitly disentangles echocardiogram features into periodic and aperiodic components in latent space, and (2) a specialized variance minimization strategy across augmented samples for continuous value regression. Specifically, the Quasi-Period Network is composed of a latent period encoder that captures fundamental cardiac cycles through a parameterized helix trajectory, and", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a Neural Controlled Differential Equations (Neural CDE) to represent aperiodic dynamics. This decomposition enables more nuanced feature extraction and adaptation. During test time, we augment test samples with carefully designed augmentation that simulate common quality issues in echocardiogram acquisition, such as acoustic shadows and speckle noise. Then, we introduce a variance minimization objective that minimizes prediction discrepancy across these augmented views, along with a differential adaptation scheme that employs distinct learning rates for periodic and aperiodic components. This design ensures stable regression predictions while effectively handling domain shifts. Furthermore, we provide theoretical guarantees demonstrating that our variance minimization approach effectively bounds the regression error. Extensive experiments demonstrate that our method achieves superior performance compared to existing approaches. Our contributions can be summarized as follows:", + "bbox": [ + 496, + 90, + 890, + 361 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Q-PART, a novel test-time training framework for pediatric LVEF regression. To the best of our knowledge, this represents the first efforts to leverage quasi-periodic properties for test-time training in echocardiogram analysis.", + "- We introduce two key technical innovations: a Quasi-Period Network that explicitly disentangles periodic and aperiodic components of echocardiogram, and a variance minimization strategy with theoretical guarantees on regression error bounds.", + "- We conduct comprehensive experiments, demonstrating that Q-PART achieves state-of-the-art performance in pediatric LVEF prediction, exhibits strong clinical screening capability, and maintains gender-fair performance. Additional ablation studies validate the effectiveness of each proposed component." + ], + "bbox": [ + 500, + 366, + 890, + 608 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 625, + 640, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Automated Echocardiogram Analysis", + "text_level": 1, + "bbox": [ + 500, + 648, + 823, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Left Ventricular Segmentation. Echocardiography is essential for cardiovascular diagnosis and treatment planning [5, 12, 17]. EchoNet-Dynamic [26] pioneered large-scale echocardiogram video analysis using deep learning framework for left ventricular segmentation in adult patients. This sparked numerous developments in echocardiogram analysis [9, 37, 38]. Through the quantification of left ventricular masks across consecutive frames, the LVEF can be calculated.", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LVEF regression. Beyond these segmentation-based approaches, several works have explored end-to-end frameworks for direct LVEF prediction [5, 12, 19, 26]. Recently, Echo_CLIP [4] train a large vision-language foundation model for echocardiogram with 1,032,975 cardiac ultrasound videos and corresponding expert text. However,", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15561", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "these methods, primarily designed for adult echocardiograms, often struggle with pediatric cases due to significant anatomical variations.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quasi-period Property. Cardiac activities exhibit quasi-periodic characteristics, combining regular cardiac cycles with aperiodic physiological variations. While existing methods have explored quasi-periodic signal processing for one-dimensional signals like ECG [1, 14, 30], their direct application to high-dimensional spatio-temporal echocardiograms remains challenging. Different from these work, we propose a novel framework that performs quasi-periodic decomposition in the latent space for echocardiogram.", + "bbox": [ + 75, + 136, + 468, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Test-time Training", + "text_level": 1, + "bbox": [ + 76, + 282, + 256, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Models often experience significant performance degradation when deployed on test data that differs from the training distribution [27]. To address this distribution shift problem, Test-time Training (TTT) has emerged as a promising paradigm that enables models to adapt dynamically during inference [28, 29, 32].", + "bbox": [ + 75, + 306, + 468, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Researchers have employed a self-supervised auxiliary task [8, 10, 18, 23, 34] to adapt to distribution shifts encountered during test time, from rotation prediction [34] and masked autoencoding [8] to contrastive learning [18] and normalizing flows [23]. Unlike these general methods, we propose a nuanced domain-specific self-supervised strategy that leverages echocardiogram quality variations through targeted augmentations.", + "bbox": [ + 75, + 398, + 468, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another mainstream approach uses entropy minimization during inference, pioneered by Tent [36], which introduced adaptive updates to normalization layers through the mechanism of entropy minimization. This framework has inspired a multitude of subsequent studies [22, 33, 39-41] that enhance adaptation capabilities via various refinements to the entropy-based objective. Nevertheless, these approaches predominantly target classification tasks, presenting inherent limitations for regression problems, as regression models generate continuous numerical predictions rather than discrete probability distributions required for entropy computation.", + "bbox": [ + 75, + 520, + 468, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Q-PART Framework", + "text_level": 1, + "bbox": [ + 76, + 715, + 277, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Statement", + "text_level": 1, + "bbox": [ + 76, + 741, + 263, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{D}_{train} = \\{(x_i, y_i)\\}_{i=1}^N$ denote the training dataset, where $x_i$ represents an echocardiogram sequence with temporal frames and spatial dimensions, and $y_i$ is the corresponding LVEF value. During training, we learn a regression model that maps echocardiogram sequences to LVEF values. The objective of test-time training is to adapt the model for domain-shifted test samples $x_{test} \\in \\mathcal{P}_{test}$ , $\\mathcal{P}_{test} \\neq \\mathcal{P}_{train}$ , using self-supervised adaptation objective that does not require ground truth labels. In TTT, the train-", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing data are unavailable and the training pipeline cannot be modified.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 500, + 130, + 609, + 143 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Figure 2 and Figure 3, our Q-PART framework consists of a Quasi-Period Network and Variance Minimization during testing time. Given an input sequence $\\pmb{x}$ , the encoder extracts initial features $\\pmb{z}$ , which are decomposed into periodic components $\\hat{\\pmb{z}}^{period}$ through parameterized helix trajectory and aperiodic components $\\hat{\\pmb{z}}^{aperiod}$ captured by Neural CDEs. During training, the model is optimized with regression loss $\\mathcal{L}_{reg}$ and reconstruction loss $\\mathcal{L}_{rec}$ . At test time, we optimize the model through variance minimization loss $\\mathcal{L}_{var}$ and reconstruction loss $\\mathcal{L}_{rec}$ using multiple augmented views, with different learning rates for periodic and aperiodic components. Detailed information on important components is provided below.", + "bbox": [ + 498, + 152, + 890, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Quasi-Period Network", + "text_level": 1, + "bbox": [ + 500, + 359, + 709, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quasi-Period Network addresses the fundamental challenge of disentangling periodic cardiac motion from patient-specific variations in echocardiogram analysis. It decomposes echocardiogram in the latent space through a nuanced architecture with physiologically-informed priors. Notably, during the test phase, this dual representation allows for adaptive optimization with different learning rates for periodic and aperiodic components, facilitating more effective model adaptation to individual cases.", + "bbox": [ + 498, + 381, + 890, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent Period Encoder. The latent period encoder architecturally embeds the intrinsic periodicity of cardiac motion into the feature space. Given the initial feature representation $\\mathbf{z}$ , we employ specialized projection head $p$ to compute four fundamental components, frequency $f$ , phase shift $\\phi$ , static offset $b$ , and velocity $v$ . This parameterization process can be formalized as", + "bbox": [ + 498, + 517, + 890, + 623 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {f}, \\phi , \\boldsymbol {b}, \\boldsymbol {v} = p (\\boldsymbol {z}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 633, + 890, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f, \\phi, b, v \\in \\mathbb{R}^{c \\times h \\times w}$ represents the global periodic characteristics for sequence $x$ , maintaining $c$ latent channels and spatial dimensions $h \\times w$ to preserve spatial structures. To explicitly represent the periodicity, we define a parameterized helix trajectory function $g(\\cdot)$ in multidimensional space, motivated by the physiological nature of cardiac motion that exhibits spiral-like patterns through combined rotational and translational movements:", + "bbox": [ + 498, + 660, + 890, + 781 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\boldsymbol {z}} _ {t} ^ {\\text {p e r i o d}} = g (t) = \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ \\begin{array}{l} - \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ + \\sin (2 \\pi (\\boldsymbol {f} t - \\phi)) + \\boldsymbol {v} t + \\boldsymbol {b}. \\end{array} \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 789, + 890, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{z}_t^{period} \\in \\mathbb{R}^{c \\times h \\times w}$ represents the period component in time $t$ . The sinusoidal terms capture the intrinsic periodicity of cardiac motion, while the linear term $vt + b$ accounts for long-term translational movements. This formulation", + "bbox": [ + 498, + 838, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15562", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/48c287a2ae8824cadeb6430f87a5cad0cda85081cf6ebe3393eca55787a4d2d2.jpg", + "image_caption": [ + "Figure 2. Overview of Q-PART Framework. The Quasi-Period Network decomposes input echocardiogram sequences into periodic and aperiodic components. The periodic component is modeled through a parameterized helix trajectory with frequency $f$ , phase shift $\\phi$ , offset $b$ , and velocity $v$ . The aperiodic component is captured by Neural CDE. The model is jointly optimized with regression loss $\\mathcal{L}_{reg}$ for LVEF prediction and reconstruction loss $\\mathcal{L}_{rec}$ for feature learning." + ], + "image_footnote": [], + "bbox": [ + 84, + 98, + 883, + 324 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/afd30d48078896288152220afd8dfad7aef356a45064a26ee9dc27f6a00b86ec.jpg", + "image_caption": [ + "Figure 3. Variance Minimization during Test. we generate multiple augmented views of the test sequence through domain-specific transformations. The model adapts to each test case by minimizing prediction variance $\\mathcal{L}_{var}$ across augmented views and maintaining reconstruction consistency $\\mathcal{L}_{rec}$ with different learning rates applied to periodic and aperiodic components.", + "Fig. 1. Differences between discrete state transitions and continuous state transitions" + ], + "image_footnote": [ + "(a) Discrete State Transition", + "(b) Continuous State Transition" + ], + "bbox": [ + 86, + 428, + 457, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "creates a helix trajectory that naturally integrates both cyclic cardiac motion and progressive physiological dynamics.", + "bbox": [ + 75, + 684, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latent Aperiodic Encoder. To capture the inherent non-periodic variations in cardiac motion, we design a latent aperiodic encoder that explicitly models these irregular components. The aperiodic features are obtained as the residual between the initial representation and the periodic component: $z' = z - \\hat{z}^{period}$ . While traditional RNNs could potentially model temporal variations, Neural CDEs offer these crucial advantages for our task: 1) they naturally handle irregular representation in echocardiogram sequences, (2) they learn continuous-time dynamics from discretely sampled observations, which is better aligned with physiological processes.", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formally, given the aperiodic component $z'$ , we first construct a continuous path $V(t)$ through natural cubic spline [20] to controlled differential equations, $V(t) = \\mathrm{CubicSpline}(z_t')$ , where $z_t'$ represents the aperiodic component $z'$ at time $t$ . The spline ensures smooth transitions between discrete observations while preserving the underlying temporal structure. The evolution of the aperiodic representation is then governed by the controlled differential equation, $d\\hat{z}_t^{aperiod} = f_\\theta(\\hat{z}_t^{aperiod}, t)dV(t)$ , where $f_\\theta$ is implemented as a neural network that learns the mapping between the current state and its differential elements. The final aperiodic representation at time $T$ is obtained through integration,", + "bbox": [ + 496, + 424, + 892, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {z}} _ {T} ^ {\\text {a p e r i o d}} = \\boldsymbol {z} _ {0} ^ {\\prime} + \\int_ {0} ^ {T} f _ {\\theta} \\left(\\hat {\\boldsymbol {z}} _ {t} ^ {\\text {a p e r i o d}}, t\\right) d \\boldsymbol {V} (t), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 628, + 890, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_0'$ serves as the initial condition. The neural CDE network is optimized using the CDE solver [11], which compute the gradients via the adjoint method.", + "bbox": [ + 496, + 672, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The decomposition provides a foundation for our test-time training strategy, where periodic and aperiodic components can be optimized with different learning dynamics. Empirically, we find that this architecture achieves superior performance in capturing complex cardiac motions, as demonstrated in our ablation studies §4.3.", + "bbox": [ + 496, + 718, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Variance Minimization", + "text_level": 1, + "bbox": [ + 500, + 816, + 712, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the domain shift challenge during testing, we propose a theoretically-grounded self-supervised strategy that combines test-time augmentation with variance minimization. Our key insight is that while echocardiographic", + "bbox": [ + 496, + 839, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15563", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "acquisitions may vary in quality and appearance, the underlying cardiac function remains consistent across different views of the same sequence.", + "bbox": [ + 76, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Domain-Specific Augmentation. For each test sequence $\\boldsymbol{x}_{test}$ , we generate $K$ augmented versions through a carefully curated augmentation pipeline:", + "bbox": [ + 76, + 137, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {x} _ {\\text {t e s t}} ^ {k} \\right\\} _ {k = 1} ^ {K} = \\mathcal {T} _ {\\text {a u g}} (\\boldsymbol {x} _ {\\text {t e s t}}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 191, + 468, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{T}_{\\text{aug}}$ comprises three categories of domain-specific augmentations. Beyond conventional image augmentations, we introduce three ultrasound-specific transformations: gamma correction to simulate varying image contrast settings, speckle noise injection to mimic acoustic interference patterns, and elastic deformation to account for cardiac tissue deformation during acquisition. These domain-specific augmentations are specifically designed to simulate real-world variations in echocardiographic acquisition while preserving the underlying cardiac motion patterns essential for LVEF assessment.", + "bbox": [ + 75, + 222, + 468, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Variance-Based Adaptation. Then, we minimizes the prediction variance across augmented samples. The variance loss $\\mathcal{L}_{var}$ is computed as:", + "bbox": [ + 76, + 388, + 468, + 434 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v a r} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\hat {y} _ {k} - \\bar {y}\\right) ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 446, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{y}_k$ represents the prediction for the $k$ -th augmented sequence and $\\bar{y}$ denotes the mean prediction across all augmentations. This formulation encourages the model to learn invariant features that are robust to acquisition-specific variations while remaining sensitive to true cardiac function changes. We provide theoretical analysis in Section 3.6 demonstrating that minimizing this variance effectively bounds the adaptation error under mild conditions.", + "bbox": [ + 75, + 498, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Optimization", + "text_level": 1, + "bbox": [ + 76, + 628, + 215, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our optimization strategy consists of two phases: training time and testing time. The overall pipeline is summarized in Appendix Algorithm 1.", + "bbox": [ + 75, + 652, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training time. During the training phase, our model employs a multi-objective learning strategy combining regression and reconstruction objectives:", + "bbox": [ + 75, + 698, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 756, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reconstruction loss ensures that both periodic and aperiodic components collectively preserve the essential information of the input sequence.", + "bbox": [ + 75, + 784, + 468, + 829 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\left\\| \\boldsymbol {x} - \\operatorname {D e c} \\left(\\hat {\\boldsymbol {z}} ^ {\\text {p e r i o d}} + \\hat {\\boldsymbol {z}} ^ {\\text {a p e r i o d}}\\right) \\right\\| _ {2} ^ {2} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 839, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{Dec}(\\cdot)$ denotes the decoder network. For LVEF prediction, we aggregate the combined latent representation", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "through Global Average Pooling (GAP) followed by a Multiple Layer Perceptron (MLP), $\\hat{y} = \\mathrm{MLP}(\\hat{z}^{period} + \\hat{z}^{aperiod})$ . The regression loss is defined as:", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} = \\| \\hat {y} - y \\| _ {2} ^ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 143, + 890, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through this joint optimization, our model learns to decompose the echocardiogram into meaningful periodic and aperiodic representation while maintaining accurate LVEF predictions.", + "bbox": [ + 496, + 169, + 890, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Testing Time. The overall test optimization objective combines this variance minimization with reconstruction consistency", + "bbox": [ + 496, + 229, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t e s t}} = \\mathcal {L} _ {\\text {v a r}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 275, + 890, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During testing time, we only update the batch normalization (BN) parameters in our network [34], which has been shown to be effective for test-time training while maintaining model stability. Given the inherent differences between periodic and aperiodic cardiac components, we employ different learning rates for their respective BN parameters. The periodic components, which capture the fundamental cardiac cycles, require more conservative updates to maintain temporal consistency. Therefore, we use a smaller learning rate for BN layers in the latent period encoder. In contrast, the aperiodic components, representing physiological variations and acquisition-specific features, benefit from more aggressive adaptation.", + "bbox": [ + 496, + 295, + 890, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Theoretical Analysis", + "text_level": 1, + "bbox": [ + 498, + 500, + 692, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To theoretically justify the effectiveness of our test-time training strategy, we establish the relationship between prediction variance and regression error. Our theoretical framework demonstrates how variance minimization across augmented samples inherently reduces the model's prediction error.", + "bbox": [ + 496, + 523, + 890, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assumption 1 (Unbiased Augmentation) The expected prediction over augmentations equals the ground truth $LVEF$ : $\\mathbb{E}_{\\mathcal{T}_{a u q}}[\\hat{y}_k] = y$", + "bbox": [ + 496, + 614, + 890, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This assumption is grounded in the design of our augmentation strategy $\\mathcal{T}_{\\text{aug}}$ , which simulates acquisition-specific variations (e.g., speckle noise, gamma correction) while preserving the underlying cardiac motion patterns that determine LVEF. These perturbations affect image quality but do not alter the fundamental cardiac functional measurements.", + "bbox": [ + 496, + 659, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assumption 2 (Augmentation Independence) The predictions from different augmented samples are independently distributed, with zero cross-covariance: $\\mathrm{Cov}_{\\mathcal{T}_{a u g}}(\\hat{y}_k,\\hat{y}_j) = 0$ for $k\\neq j$", + "bbox": [ + 496, + 765, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This assumption reflects our augmentation design principle where each transformation introduces independent variations. The independence is achieved through combining multiple orthogonal perturbation types, ensuring minimal correlation between augmented samples.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15564", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c777534c8b3ac3ff0785a7957fe9c7f67472ce81ec3ae23834af96fc82b9bee8.jpg", + "table_caption": [ + "Table 1. Dataset Statistics. Demographic and clinical characteristics across age groups. The statistics show substantial differences in sample sizes (ranging from 831 to 7465), with notably fewer samples in younger age groups due to the inherent challenges in pediatric data collection." + ], + "table_footnote": [], + "table_body": "
StatisticsPre-schoolSchool-ageAdolescenceAdult
#Samples8319141,5397,465
Age2 ± 19 ± 215 ± 270 ± 22
Female (%)404 (49%)371 (41%)617 (40%)3662 (49%)
LVEF (%)59.6 ± 12.862.0 ± 9.261.0 ± 9.855.8 ± 12.4
", + "bbox": [ + 78, + 169, + 467, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 1 Consider a test sample $\\mathbf{x}_{test}$ with ground truth label $y$ , and its $K$ augmented versions $\\{\\mathbf{x}_{test}^k\\}_{k=1}^K$ generated by $\\mathcal{T}_{aug}$ . Under Assumptions 1 and 2, the expected regression loss $\\mathbb{E}[L_{reg}] = \\mathbb{E}[(\\hat{y} - y)^2]$ is upper bounded by:", + "bbox": [ + 75, + 268, + 468, + 345 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} [ L _ {r e g} ] \\leq \\frac {2 \\mathbb {E} [ L _ {v a r} ]}{K}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 345, + 468, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L_{var}$ is the variance loss defined in Equation 5.", + "bbox": [ + 76, + 381, + 434, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proof uses standard techniques in optimization, and is left for the Appendix A. This theoretical result provides a justification for our test-time training strategy. Minimizing the variance loss directly leads to a reduction in the expected regression error, with the bound becoming tighter as we increase the number of augmentations $K$ .", + "bbox": [ + 75, + 397, + 468, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 503, + 202, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 76, + 527, + 253, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Metrics. We evaluate Q-PART using two benchmark datasets of apical-4-chamber echocardiogram videos collected from EchoNet-Dynamic [25] and EchoNet-Pediatric [31]. Following clinical standards, we stratify the data into four age cohorts: pre-school (ages 0-5), school-age (ages 6-11), adolescence (ages 12-18), and adult (ages $>18$ ). The detailed statistics of each cohort are summarized in Table 1. We train the model on the adult cohort and assess its performance through test-time training on pre-school, school-age, and adolescence cohorts respectively. For evaluation metrics, we adopt three widely-used metrics to comprehensively evaluate the LVEF prediction performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Moreover, we evaluate the model's clinical screening capability through mean Area Under the Receiver Operating Characteristic curve (mAUROC) analysis at multiple LVEF thresholds (35%, 40%, 45%, and 50%). More details please refer to Appendix C.1.", + "bbox": [ + 75, + 551, + 468, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We adopt R3D Network [35] as the backbone encoder. The projection head contains four groups, with each group consisting of two $1 \\times 1$ convolutional layers ( $512 \\rightarrow 64 \\rightarrow 64$ ) with batch normalization and ReLU", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "activation. The decoder uses five transposed convolutional layers for reconstruction. In training stage, The model is optimized using SGD with momentum 0.9 and weight decay 1e-4, with a linear warmup for the first 10 epochs followed by cosine annealing for the remaining 35 epochs. During test-time training, we employ both general augmentations (rotation, flips, grid distortion, Gaussian blur) and ultrasound-specific transformations (speckle noise, gamma correction, acoustic shadow). We apply different learning rates to periodic (1e-5) and aperiodic (1e-3) components, while maintaining a base learning rate of 1e-4 for other parameters. The value K is 8. All experiments are conducted on a single NVIDIA A100 80GB GPU.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 498, + 299, + 864, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We comprehensively evaluate Q-PART against seven representative methods spanning three methodological categories, i.e., segmentation-based approaches, vision-language models, and end-to-end regression methods, as mentioned in §2.1. Three key findings emerge from our experiments:", + "bbox": [ + 496, + 323, + 890, + 412 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) Superior Performance. As shown in Table 2, our method achieves consistent improvements across all metrics and age groups, with particularly notable gains in the challenging Pre-School cohort (MAE: 7.235, MAPE: 0.1611, RMSE: 9.290). This demonstrates Q-PART's robust adaptation capability and its effectiveness in handling the unique challenges of pediatric echocardiography.", + "2) Clinical Screening Capability. Beyond regression metrics, we evaluate our model's clinical utility through ROC analysis at multiple LVEF thresholds in Figure 4. The high mAUROC scores have significant clinical implications: the enhanced sensitivity ensures reliable detection of cardiac dysfunction cases requiring immediate intervention, while the improved specificity reduces unnecessary follow-up examinations, thereby optimizing healthcare resource allocation and minimizing patient anxiety. Q-PART achieves remarkable mAUROC scores of 0.9362, 0.9747, and 0.9083 for Pre-School, School Age, and Adolescence cohorts, respectively, substantially outperforming other TTA methods. This superior performance validates the effectiveness of our echocardiogram-specific framework.", + "3) Segmentation vs End-to-End Approaches. As discussed in §2.1, while lots of methods rely on left ventricular segmentation to derive LVEF values, recent end-to-end approaches directly predict LVEF. Our experimental results in Table 2 strongly support the superiority of end-to-end approaches. Despite advances in segmentation accuracy with methods like EchoNet and MemSAM, their LVEF estimation performance (MAE > 17.94) lags significantly behind end-to-end approaches (MAE < 9.114). This substantial performance gap suggests that accurate segmentation does not necessarily translate to precise LVEF estimation, as the" + ], + "bbox": [ + 496, + 415, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15565", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/96cdaeae1d45edba340f8c3d0a7821a7bd901f5dd761fb4ab54cd2cb3a98a9e6.jpg", + "table_caption": [ + "Table 2. Comparison with State-of-the-Art Methods. We benchmark Q-PART against representative approaches spanning three methodological categories: segmentation-based methods (Seg-Based), vision-language models (VLM), and end-to-end regression approaches (E2E). Our method demonstrates superior adaptation capability and robustness across age groups, particularly in challenging scenarios with younger patients. All results are reported with four significant digits. Bold numbers indicate the best performance." + ], + "table_footnote": [], + "table_body": "
TypeApproachPre-SchoolSchool AgeAdolescence
MAEMAPERMSEMAEMAPERMSEMAEMAPERMSE
Seg-BasedEchoNet [26] (Nature 2020)20.900.473026.1417.860.340321.9719.640.376123.90
MemSAM [6] (CVPR 2024)17.940.367521.9718.350.321621.7618.710.324922.26
VLMEchoCLIP [4] (Nature Med. 2024)11.560.203514.189.3030.160411.718.4960.152110.93
E2ESource-only9.1140.175910.868.4250.146910.038.6360.154910.53
TTT++ [18] (NeurIPS 2022)8.0530.166910.017.4300.13169.0967.6160.14169.601
Clust3 [10] (CVPR 2023)9.2920.185211.237.8920.13939.4248.2160.15099.995
NC-TTT [24] (CVPR 2024)8.3520.180010.457.2850.13258.9627.4220.14089.347
Q-PART (Ours)7.2350.16119.2906.7060.12448.4326.9800.13448.950
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ROC Analysis at Multiple Clinical Thresholds. Please zoom in for better view. Receiver Operating Characteristic (ROC) curves for LVEF regression with four clinically significant thresholds: $35\\%$ (blue), $40\\%$ (green), $45\\%$ (red), and $50\\%$ (cyan). These thresholds represent different degrees of cardiac dysfunction severity. The x-axis shows 1-specificity (false positive rate) and the y-axis shows sensitivity (true positive rate). The mAuroC is shown in gray box. A high mAuroC value indicates strong clinical reliability. Higher sensitivity ensures early detection of cardiac dysfunction, while higher specificity reduces unnecessary follow-up examinations and patient anxiety, collectively supporting more accurate clinical decision-making and resource allocation." + ], + "image_footnote": [], + "bbox": [ + 83, + 494, + 207, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5f2a583f2e531e436ee43b638648ab18160a87da9eb7fa90ca2b1ccc8970e0b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 494, + 320, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e7e45486e61e0535d5174b6758762f1cfbca2fe4d80ec6c5845c5189027614e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 494, + 431, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fec9ac5470e1d9698b8ea4a88f3b64587ae7f465e9ab1cbdda6ed6343235674.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 433, + 494, + 542, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4164e0b2eea17298501a591ed8815df04f07b7fb64e71d4b81d8ad36b2d7e5d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 545, + 494, + 653, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ea738242af349c6b313708c628c61335e68fca17e3548ad61959b5e82c711521.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 494, + 766, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/52cf57d72f9c55958c26587be4cec0aaae291b2651d8b35bbe22bdb43b7e0a84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 771, + 494, + 883, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "latter requires capturing complex temporal dynamics and subtle motion patterns that may be lost in the intermediate segmentation step.", + "bbox": [ + 75, + 722, + 470, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 784, + 230, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct comprehensive ablation studies to evaluate the contribution of each key component in Q-PART, i.e., Quasi-Period Network (QP-Net), Learning Rate Strategy (LR), and Variance Minimization (VM). Table 3 presents the results on the Pre-School cohort. Several observations can be drawn from the ablation results: (1) The Quasi-Period Net", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "work alone yields substantial improvements (MAE: 7.949), demonstrating the effectiveness of disentangling periodic and aperiodic components during test-time training. (2) When combining QP-Net with VM, we observe a notable performance gain (MAE: 7.283), validating our hypothesis that variance minimization across augmented views effectively guides model adaptation. (3) The differential learning rate strategy further refines the adaptation process, with our full model achieving the best performance (MAE: 7.235). This suggests that applying different learning rates to periodic and aperiodic components helps maintain stable car", + "bbox": [ + 496, + 722, + 893, + 890 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15566", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc4757dbde6bb5a94cc1397b5ea9a07f703fa64a7801d563c9afa9926b9c7e13.jpg", + "table_caption": [ + "Table 3. Ablation Study of Key Components. Analysis of three key components: QP-Net (Quasi-Period Network), LR (Learning Rate Strategy), and VM (Variance Minimization). We presents the results on Pre-School cohort here, which demonstrates the effectiveness of each component. Complete results across all age cohorts are presented in Appendix Table 4." + ], + "table_footnote": [], + "table_body": "
QP-NetLRVMMAEMAPERMSE
8.1290.168110.09
✓7.9490.16669.909
✓✓7.9090.16569.878
✓7.8420.16409.714
✓✓7.2830.16199.307
✓✓✓7.2350.16119.290
", + "bbox": [ + 81, + 183, + 467, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ad437852703e71ebe437fd0060b0f966069695224124eb1bcae6cfcc8c4d9d6.jpg", + "image_caption": [ + "Figure 5. Impact of $K$ Augmentation Number on Model Performance. The plot shows how performance varies with different numbers of augmentation number across three age cohorts." + ], + "image_footnote": [], + "bbox": [ + 122, + 316, + 423, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "diac cycle patterns while allowing flexible adaptation to patient-specific variations.", + "bbox": [ + 75, + 574, + 468, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Analysis", + "text_level": 1, + "bbox": [ + 76, + 618, + 181, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Augmentation Number $K$ . We investigate how the number of augmented views $K$ in variance minimization affects model performance. As shown in Figure 5, larger $K$ values generally lead to better performance across all age cohorts. Notably, when $K = 2$ , the model performs worse than the baseline without variance minimization, with MAE increasing from 7.909 to 8.036 in the Pre-School cohort. This deterioration can be attributed to the insufficient number of samples for reliable variance estimation, resulting in unstable optimization signals during test-time adaptation. While further increasing $K$ to 32 continues to yield marginal improvements, it significantly increases computational overhead during inference. Balancing performance gains against computational efficiency, we choose $K = 8$ as our default setting for all main experiments.", + "bbox": [ + 75, + 642, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Gender-fair Performance. To assess potential gender bias, we conduct a comprehensive analysis comparing model per", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/802150e0437b9fafcb327671d6ff78d9d844320adc3f518c761727027b0eca59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 90, + 647, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/356b82242284a5a9537ca05cef4d7353b212f4711775da05030b01b307eda979.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 90, + 761, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ceaa2efafa0a9dcfcff946f0b6caa0d85be1f2c252c7e0fe28cfcbb9f3e7b4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 90, + 872, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9bb00021b608468943982f43780c2a533b8b036963e427dbd11b72999b5f5290.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 193, + 647, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c2abf8d1978bbedffca7f69ef2c80915219374093edaacdb8ecd77a47f4718fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 193, + 761, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8105cd6e5687569fbddce1a89f9c161fa2492c61eaacdeae3156dc78ee7d3162.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 193, + 872, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d0ea52627dd1c37c80e17ae77f5420817c2cfdd2f993c95fd109d78e96d0542b.jpg", + "image_caption": [ + "Figure 6. Gender Bias Analysis Across Age Cohorts. Box plots comparing model performance between male and female subjects across three age cohorts using three metrics. Each subplot shows the distribution of performance metrics for both genders, with p-values from Mann-Whitney U tests. The absence of statistically significant differences $(p > 0.05)$ in eight out of nine comparisons demonstrates the model's gender-fair adaptation capability." + ], + "image_footnote": [], + "bbox": [ + 517, + 294, + 647, + 392 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9fce9c645374471c74fc40679063e126e5085efbc7108c91196a288f9a95c8ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 294, + 761, + 392 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fbfe5f28495ca13d66c259ad5c4bf189a5e47e73c66ca422cb9766a2172ef708.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 294, + 872, + 392 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance between male and female subjects across all age cohorts and metrics, as visualized in Figure 6. Statistical analysis reveals no significant differences $(\\mathrm{p} > 0.05$ in eight out of nine comparisons) between gender groups across all evaluation metrics (MAE, MAPE, RMSE) and age cohorts. This gender-fair performance demonstrates that QPART maintains consistent reliability regardless of gender, which is crucial for ensuring equitable healthcare delivery and maintaining diagnostic consistency across diverse patient populations.", + "bbox": [ + 496, + 530, + 890, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 694, + 617, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present Q-PART, a novel test-time training framework specifically designed for pediatric LVEF regression. By explicitly disentangling periodic cardiac motion from patient-specific variations through our Quasi-Period Network, and employing a theoretically-grounded variance minimization strategy, Q-PART effectively addresses the unique challenges in pediatric echocardiography. Extensive experiments demonstrate that our method significantly outperforms existing approaches across different age groups and evaluation metrics. Q-PART advances the field of automated cardiac function assessment and shows promise for improving clinical workflow in pediatric cardiology.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15567", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 78, + 90, + 235, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), the Hong Kong Research Grants Council (Projects 21200522 and 11204821), DON-RMG 9229106 and a grant from the Institute of Digital Medicine of City University of Hong Kong.", + "bbox": [ + 76, + 114, + 468, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 220, + 173, + 237 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Luis Enrique Avendaño, Luis David Avendaño-Valencia, Edilson Delgado-Trejos, and David Cuesta-Frau. 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Delta: degradation-free fully test-time adaptation. arXiv preprint arXiv:2301.13018, 2023. 3" + ], + "bbox": [ + 501, + 92, + 890, + 627 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15569", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_model.json b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0d3363edbe5c28796fdefb212cc3bd12b88e4e5a --- /dev/null +++ b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.13, + 0.856, + 0.177 + ], + "angle": 0, + "content": "Q-PART: Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.203, + 0.721, + 0.24 + ], + "angle": 0, + "content": "Jie Liu\\(^{1}\\), Tiexin Qin\\(^{1}\\), Hui Liu\\(^{1}\\), Yilei Shi\\(^{2,3}\\), Lichao Mou\\(^{2,3}\\), Xiao Xiang Zhu\\(^{3}\\), Shiqi Wang\\(^{1}\\), and Haoliang Li\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.245, + 0.766, + 0.282 + ], + "angle": 0, + "content": "\\(^{1}\\)City University of Hong Kong \\(^{2}\\)MedAI Technology (Wuxi) Co. Ltd. \\(^{3}\\)Technische Universität München" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.317, + 0.314, + 0.332 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.789 + ], + "angle": 0, + "content": "In this work, we address the challenge of adaptive pediatric Left Ventricular Ejection Fraction (LVEF) assessment. While Test-time Training (TTT) approaches show promise for this task, they suffer from two significant limitations. Existing TTT works are primarily designed for classification tasks rather than continuous value regression, and they lack mechanisms to handle the quasi-periodic nature of cardiac signals. To tackle these issues, we propose a novel Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART) framework. In the training stage, the proposed Quasi-Period Network decomposes the echocardiogram into periodic and aperiodic components within latent space by combining parameterized helix trajectories with Neural Controlled Differential Equations. During inference, our framework further employs a variance minimization strategy across image augmentations that simulate common quality issues in echocardiogram acquisition, along with differential adaptation rates for periodic and aperiodic components. Theoretical analysis is provided to demonstrate that our variance minimization objective effectively bounds the regression error under mild conditions. Furthermore, extensive experiments across three pediatric age groups demonstrate that Q-PART not only significantly outperforms existing approaches in pediatric LVEF prediction, but also exhibits strong clinical screening capability with high mAUROC scores (up to 0.9747) and maintains gender-fair performance across all metrics, validating its robustness and practical utility in pediatric echocardiography analysis. The project can be found in Q-PART." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.819, + 0.21, + 0.834 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.844, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Evaluation of Left Ventricular Ejection Fraction (LVEF) for pediatric patients plays a vital role in early diagnosis of con" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.318, + 0.895, + 0.56 + ], + "angle": 0, + "content": "genital and acquired heart disease [31]. Echocardiography, recognized for its noninvasive nature and safety, has become the standard modality for LVEF evaluation [3, 26]. Although recent deep learning models [13, 16, 21] have shown promising results in adult LVEF assessment, their direct application to pediatric cases is problematic due to fundamental differences in cardiac imaging. As demonstrated in Figure 1 (a), pediatric patients exhibit considerable anatomical and physiological variations, including distinct differences in heart size, shape, and rate across different age groups [7]. Moreover, acquiring pediatric echocardiogram data is inherently challenging. Young children often exhibit difficulty cooperating during examinations, and ethical considerations limit unnecessary medical procedures, resulting in significant inter-observer variability and scarcity of labeled data for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Test-time training (TTT) emerges as a promising paradigm to address these challenges by enabling model adaptation to distribution shifts during inference [15, 32]. TTT can enable model adaptation to each specific patient case during inference, without requiring access to training data or labels [28, 29], making it particularly valuable for pediatric LVEF assessment. This patient-specific adaptation naturally handles diverse pediatric cases without the necessity for extensive training echocardiograms, while also accommodating diverse anatomical variations and ensuring data privacy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "However, the regression of pediatric LVEF presents unique challenges for direct application of TTT in this area. Firstly, existing TTT methods such as entropy minimization [33, 36, 39, 40], primarily designed for classification tasks with discrete decision boundaries [28, 29, 32], are not well suited for LVEF prediction, which is essentially a continuous value regression task. This challenge is further complicated by the quality issues in echocardiogram acquisition, as shown in Figure 1 (a), where varying acoustic shadow, probe positions, and speckle noise significantly impact regression accuracy, necessitating specialized self" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.298, + 0.901 + ], + "angle": 0, + "content": "*Corresponding authors: Haoliang Li." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15560" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.093, + 0.462, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.487 + ], + "angle": 0, + "content": "Figure 1. (a) Adult and Pediatric Echocardiogram Visualization. These two kinds of echocardiograms exhibit anatomical and physiological variations, including distinct differences in heart size and shape. Moreover, We demonstrate two quality issues, i.e., acoustic shadow and speckle noise. (b) Quasi-Period Signal. Electrocardiogram (ECG) signals can be decomposed into periodic components originating from regular cardiac cycles and aperiodic components induced by physiological variations and noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.732 + ], + "angle": 0, + "content": "supervised algorithms for stable predictions. Secondly, the inherent complexity of cardiac activities in echocardiograms introduces additional challenges. As illustrated by the Electrocardiogram (ECG) signal example in Figure 1 (b), cardiac activities demonstrate a characteristic duality, comprising periodic components from regular cardiac cycles and aperiodic components from physiological variations, collectively forming quasi-periodic signals [1, 2, 14]. While periodic cardiac patterns remain relatively consistent across age groups, pediatric cases exhibit significant aperiodic variations due to diverse heart sizes and irregular activities. Leveraging this quasi-periodic nature for test-time training in echocardiogram analysis thus presents a promising yet unexplored research direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To address these challenges, we propose a novel test-time training framework, named Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART), tailored for pediatric LVEF regression with two key innovations: (1) a Quasi-Period Network that explicitly disentangles echocardiogram features into periodic and aperiodic components in latent space, and (2) a specialized variance minimization strategy across augmented samples for continuous value regression. Specifically, the Quasi-Period Network is composed of a latent period encoder that captures fundamental cardiac cycles through a parameterized helix trajectory, and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.362 + ], + "angle": 0, + "content": "a Neural Controlled Differential Equations (Neural CDE) to represent aperiodic dynamics. This decomposition enables more nuanced feature extraction and adaptation. During test time, we augment test samples with carefully designed augmentation that simulate common quality issues in echocardiogram acquisition, such as acoustic shadows and speckle noise. Then, we introduce a variance minimization objective that minimizes prediction discrepancy across these augmented views, along with a differential adaptation scheme that employs distinct learning rates for periodic and aperiodic components. This design ensures stable regression predictions while effectively handling domain shifts. Furthermore, we provide theoretical guarantees demonstrating that our variance minimization approach effectively bounds the regression error. Extensive experiments demonstrate that our method achieves superior performance compared to existing approaches. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.367, + 0.892, + 0.442 + ], + "angle": 0, + "content": "- We propose Q-PART, a novel test-time training framework for pediatric LVEF regression. To the best of our knowledge, this represents the first efforts to leverage quasi-periodic properties for test-time training in echocardiogram analysis." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.443, + 0.892, + 0.517 + ], + "angle": 0, + "content": "- We introduce two key technical innovations: a Quasi-Period Network that explicitly disentangles periodic and aperiodic components of echocardiogram, and a variance minimization strategy with theoretical guarantees on regression error bounds." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.519, + 0.892, + 0.609 + ], + "angle": 0, + "content": "- We conduct comprehensive experiments, demonstrating that Q-PART achieves state-of-the-art performance in pediatric LVEF prediction, exhibits strong clinical screening capability, and maintains gender-fair performance. Additional ablation studies validate the effectiveness of each proposed component." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.367, + 0.892, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.641, + 0.64 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.824, + 0.667 + ], + "angle": 0, + "content": "2.1. Automated Echocardiogram Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Left Ventricular Segmentation. Echocardiography is essential for cardiovascular diagnosis and treatment planning [5, 12, 17]. EchoNet-Dynamic [26] pioneered large-scale echocardiogram video analysis using deep learning framework for left ventricular segmentation in adult patients. This sparked numerous developments in echocardiogram analysis [9, 37, 38]. Through the quantification of left ventricular masks across consecutive frames, the LVEF can be calculated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "LVEF regression. Beyond these segmentation-based approaches, several works have explored end-to-end frameworks for direct LVEF prediction [5, 12, 19, 26]. Recently, Echo_CLIP [4] train a large vision-language foundation model for echocardiogram with 1,032,975 cardiac ultrasound videos and corresponding expert text. However," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15561" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "these methods, primarily designed for adult echocardiograms, often struggle with pediatric cases due to significant anatomical variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.274 + ], + "angle": 0, + "content": "Quasi-period Property. Cardiac activities exhibit quasi-periodic characteristics, combining regular cardiac cycles with aperiodic physiological variations. While existing methods have explored quasi-periodic signal processing for one-dimensional signals like ECG [1, 14, 30], their direct application to high-dimensional spatio-temporal echocardiograms remains challenging. Different from these work, we propose a novel framework that performs quasi-periodic decomposition in the latent space for echocardiogram." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.284, + 0.258, + 0.301 + ], + "angle": 0, + "content": "2.2. Test-time Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.469, + 0.398 + ], + "angle": 0, + "content": "Models often experience significant performance degradation when deployed on test data that differs from the training distribution [27]. To address this distribution shift problem, Test-time Training (TTT) has emerged as a promising paradigm that enables models to adapt dynamically during inference [28, 29, 32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.469, + 0.52 + ], + "angle": 0, + "content": "Researchers have employed a self-supervised auxiliary task [8, 10, 18, 23, 34] to adapt to distribution shifts encountered during test time, from rotation prediction [34] and masked autoencoding [8] to contrastive learning [18] and normalizing flows [23]. Unlike these general methods, we propose a nuanced domain-specific self-supervised strategy that leverages echocardiogram quality variations through targeted augmentations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.469, + 0.702 + ], + "angle": 0, + "content": "Another mainstream approach uses entropy minimization during inference, pioneered by Tent [36], which introduced adaptive updates to normalization layers through the mechanism of entropy minimization. This framework has inspired a multitude of subsequent studies [22, 33, 39-41] that enhance adaptation capabilities via various refinements to the entropy-based objective. Nevertheless, these approaches predominantly target classification tasks, presenting inherent limitations for regression problems, as regression models generate continuous numerical predictions rather than discrete probability distributions required for entropy computation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.716, + 0.279, + 0.733 + ], + "angle": 0, + "content": "3. Q-PART Framework" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.264, + 0.756 + ], + "angle": 0, + "content": "3.1. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Let \\(\\mathcal{D}_{train} = \\{(x_i, y_i)\\}_{i=1}^N\\) denote the training dataset, where \\(x_i\\) represents an echocardiogram sequence with temporal frames and spatial dimensions, and \\(y_i\\) is the corresponding LVEF value. During training, we learn a regression model that maps echocardiogram sequences to LVEF values. The objective of test-time training is to adapt the model for domain-shifted test samples \\(x_{test} \\in \\mathcal{P}_{test}\\), \\(\\mathcal{P}_{test} \\neq \\mathcal{P}_{train}\\), using self-supervised adaptation objective that does not require ground truth labels. In TTT, the train-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "ing data are unavailable and the training pipeline cannot be modified." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.131, + 0.611, + 0.145 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.154, + 0.892, + 0.35 + ], + "angle": 0, + "content": "As illustrated in Figure 2 and Figure 3, our Q-PART framework consists of a Quasi-Period Network and Variance Minimization during testing time. Given an input sequence \\( \\pmb{x} \\), the encoder extracts initial features \\( \\pmb{z} \\), which are decomposed into periodic components \\( \\hat{\\pmb{z}}^{period} \\) through parameterized helix trajectory and aperiodic components \\( \\hat{\\pmb{z}}^{aperiod} \\) captured by Neural CDEs. During training, the model is optimized with regression loss \\( \\mathcal{L}_{reg} \\) and reconstruction loss \\( \\mathcal{L}_{rec} \\). At test time, we optimize the model through variance minimization loss \\( \\mathcal{L}_{var} \\) and reconstruction loss \\( \\mathcal{L}_{rec} \\) using multiple augmented views, with different learning rates for periodic and aperiodic components. Detailed information on important components is provided below." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.36, + 0.71, + 0.375 + ], + "angle": 0, + "content": "3.3. Quasi-Period Network" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Quasi-Period Network addresses the fundamental challenge of disentangling periodic cardiac motion from patient-specific variations in echocardiogram analysis. It decomposes echocardiogram in the latent space through a nuanced architecture with physiologically-informed priors. Notably, during the test phase, this dual representation allows for adaptive optimization with different learning rates for periodic and aperiodic components, facilitating more effective model adaptation to individual cases." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.518, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Latent Period Encoder. The latent period encoder architecturally embeds the intrinsic periodicity of cardiac motion into the feature space. Given the initial feature representation \\( \\mathbf{z} \\), we employ specialized projection head \\( p \\) to compute four fundamental components, frequency \\( f \\), phase shift \\( \\phi \\), static offset \\( b \\), and velocity \\( v \\). This parameterization process can be formalized as" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.635, + 0.892, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {f}, \\phi , \\boldsymbol {b}, \\boldsymbol {v} = p (\\boldsymbol {z}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.661, + 0.892, + 0.782 + ], + "angle": 0, + "content": "where \\( f, \\phi, b, v \\in \\mathbb{R}^{c \\times h \\times w} \\) represents the global periodic characteristics for sequence \\( x \\), maintaining \\( c \\) latent channels and spatial dimensions \\( h \\times w \\) to preserve spatial structures. To explicitly represent the periodicity, we define a parameterized helix trajectory function \\( g(\\cdot) \\) in multidimensional space, motivated by the physiological nature of cardiac motion that exhibits spiral-like patterns through combined rotational and translational movements:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.79, + 0.891, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\boldsymbol {z}} _ {t} ^ {\\text {p e r i o d}} = g (t) = \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ \\begin{array}{l} - \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ + \\sin (2 \\pi (\\boldsymbol {f} t - \\phi)) + \\boldsymbol {v} t + \\boldsymbol {b}. \\end{array} \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.839, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\hat{z}_t^{period} \\in \\mathbb{R}^{c \\times h \\times w}\\) represents the period component in time \\(t\\). The sinusoidal terms capture the intrinsic periodicity of cardiac motion, while the linear term \\(vt + b\\) accounts for long-term translational movements. This formulation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15562" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.099, + 0.885, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.893, + 0.399 + ], + "angle": 0, + "content": "Figure 2. Overview of Q-PART Framework. The Quasi-Period Network decomposes input echocardiogram sequences into periodic and aperiodic components. The periodic component is modeled through a parameterized helix trajectory with frequency \\( f \\), phase shift \\( \\phi \\), offset \\( b \\), and velocity \\( v \\). The aperiodic component is captured by Neural CDE. The model is jointly optimized with regression loss \\( \\mathcal{L}_{reg} \\) for LVEF prediction and reconstruction loss \\( \\mathcal{L}_{rec} \\) for feature learning." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.429, + 0.459, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Figure 3. Variance Minimization during Test. we generate multiple augmented views of the test sequence through domain-specific transformations. The model adapts to each test case by minimizing prediction variance \\(\\mathcal{L}_{var}\\) across augmented views and maintaining reconstruction consistency \\(\\mathcal{L}_{rec}\\) with different learning rates applied to periodic and aperiodic components." + }, + { + "type": "image_footnote", + "bbox": [ + 0.225, + 0.657, + 0.307, + 0.664 + ], + "angle": 0, + "content": "(a) Discrete State Transition" + }, + { + "type": "image_footnote", + "bbox": [ + 0.356, + 0.657, + 0.446, + 0.664 + ], + "angle": 0, + "content": "(b) Continuous State Transition" + }, + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.671, + 0.482, + 0.679 + ], + "angle": 0, + "content": "Fig. 1. Differences between discrete state transitions and continuous state transitions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.716 + ], + "angle": 0, + "content": "creates a helix trajectory that naturally integrates both cyclic cardiac motion and progressive physiological dynamics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Latent Aperiodic Encoder. To capture the inherent non-periodic variations in cardiac motion, we design a latent aperiodic encoder that explicitly models these irregular components. The aperiodic features are obtained as the residual between the initial representation and the periodic component: \\( z' = z - \\hat{z}^{period} \\). While traditional RNNs could potentially model temporal variations, Neural CDEs offer these crucial advantages for our task: 1) they naturally handle irregular representation in echocardiogram sequences, (2) they learn continuous-time dynamics from discretely sampled observations, which is better aligned with physiological processes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.893, + 0.621 + ], + "angle": 0, + "content": "Formally, given the aperiodic component \\( z' \\), we first construct a continuous path \\( V(t) \\) through natural cubic spline [20] to controlled differential equations, \\( V(t) = \\mathrm{CubicSpline}(z_t') \\), where \\( z_t' \\) represents the aperiodic component \\( z' \\) at time \\( t \\). The spline ensures smooth transitions between discrete observations while preserving the underlying temporal structure. The evolution of the aperiodic representation is then governed by the controlled differential equation, \\( d\\hat{z}_t^{aperiod} = f_\\theta(\\hat{z}_t^{aperiod}, t)dV(t) \\), where \\( f_\\theta \\) is implemented as a neural network that learns the mapping between the current state and its differential elements. The final aperiodic representation at time \\( T \\) is obtained through integration," + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.629, + 0.892, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {z}} _ {T} ^ {\\text {a p e r i o d}} = \\boldsymbol {z} _ {0} ^ {\\prime} + \\int_ {0} ^ {T} f _ {\\theta} \\left(\\hat {\\boldsymbol {z}} _ {t} ^ {\\text {a p e r i o d}}, t\\right) d \\boldsymbol {V} (t), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.718 + ], + "angle": 0, + "content": "where \\( z_0' \\) serves as the initial condition. The neural CDE network is optimized using the CDE solver [11], which compute the gradients via the adjoint method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The decomposition provides a foundation for our test-time training strategy, where periodic and aperiodic components can be optimized with different learning dynamics. Empirically, we find that this architecture achieves superior performance in capturing complex cardiac motions, as demonstrated in our ablation studies §4.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.714, + 0.832 + ], + "angle": 0, + "content": "3.4. Variance Minimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.902 + ], + "angle": 0, + "content": "To address the domain shift challenge during testing, we propose a theoretically-grounded self-supervised strategy that combines test-time augmentation with variance minimization. Our key insight is that while echocardiographic" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15563" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "acquisitions may vary in quality and appearance, the underlying cardiac function remains consistent across different views of the same sequence." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.138, + 0.47, + 0.183 + ], + "angle": 0, + "content": "Domain-Specific Augmentation. For each test sequence \\( \\boldsymbol{x}_{test} \\), we generate \\( K \\) augmented versions through a carefully curated augmentation pipeline:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.193, + 0.47, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {x} _ {\\text {t e s t}} ^ {k} \\right\\} _ {k = 1} ^ {K} = \\mathcal {T} _ {\\text {a u g}} (\\boldsymbol {x} _ {\\text {t e s t}}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.469, + 0.388 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}_{\\text{aug}}\\) comprises three categories of domain-specific augmentations. Beyond conventional image augmentations, we introduce three ultrasound-specific transformations: gamma correction to simulate varying image contrast settings, speckle noise injection to mimic acoustic interference patterns, and elastic deformation to account for cardiac tissue deformation during acquisition. These domain-specific augmentations are specifically designed to simulate real-world variations in echocardiographic acquisition while preserving the underlying cardiac motion patterns essential for LVEF assessment." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.39, + 0.469, + 0.435 + ], + "angle": 0, + "content": "Variance-Based Adaptation. Then, we minimizes the prediction variance across augmented samples. The variance loss \\(\\mathcal{L}_{var}\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.447, + 0.469, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v a r} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\hat {y} _ {k} - \\bar {y}\\right) ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.469, + 0.62 + ], + "angle": 0, + "content": "where \\(\\hat{y}_k\\) represents the prediction for the \\(k\\)-th augmented sequence and \\(\\bar{y}\\) denotes the mean prediction across all augmentations. This formulation encourages the model to learn invariant features that are robust to acquisition-specific variations while remaining sensitive to true cardiac function changes. We provide theoretical analysis in Section 3.6 demonstrating that minimizing this variance effectively bounds the adaptation error under mild conditions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.629, + 0.217, + 0.645 + ], + "angle": 0, + "content": "3.5. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.469, + 0.698 + ], + "angle": 0, + "content": "Our optimization strategy consists of two phases: training time and testing time. The overall pipeline is summarized in Appendix Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.469, + 0.743 + ], + "angle": 0, + "content": "Training time. During the training phase, our model employs a multi-objective learning strategy combining regression and reconstruction objectives:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.757, + 0.469, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.785, + 0.469, + 0.83 + ], + "angle": 0, + "content": "The reconstruction loss ensures that both periodic and aperiodic components collectively preserve the essential information of the input sequence." + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.84, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\left\\| \\boldsymbol {x} - \\operatorname {D e c} \\left(\\hat {\\boldsymbol {z}} ^ {\\text {p e r i o d}} + \\hat {\\boldsymbol {z}} ^ {\\text {a p e r i o d}}\\right) \\right\\| _ {2} ^ {2} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathrm{Dec}(\\cdot)\\) denotes the decoder network. For LVEF prediction, we aggregate the combined latent representation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "through Global Average Pooling (GAP) followed by a Multiple Layer Perceptron (MLP), \\(\\hat{y} = \\mathrm{MLP}(\\hat{z}^{period} + \\hat{z}^{aperiod})\\). The regression loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.144, + 0.892, + 0.163 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} = \\| \\hat {y} - y \\| _ {2} ^ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.892, + 0.229 + ], + "angle": 0, + "content": "Through this joint optimization, our model learns to decompose the echocardiogram into meaningful periodic and aperiodic representation while maintaining accurate LVEF predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Testing Time. The overall test optimization objective combines this variance minimization with reconstruction consistency" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.276, + 0.892, + 0.291 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t e s t}} = \\mathcal {L} _ {\\text {v a r}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.493 + ], + "angle": 0, + "content": "During testing time, we only update the batch normalization (BN) parameters in our network [34], which has been shown to be effective for test-time training while maintaining model stability. Given the inherent differences between periodic and aperiodic cardiac components, we employ different learning rates for their respective BN parameters. The periodic components, which capture the fundamental cardiac cycles, require more conservative updates to maintain temporal consistency. Therefore, we use a smaller learning rate for BN layers in the latent period encoder. In contrast, the aperiodic components, representing physiological variations and acquisition-specific features, benefit from more aggressive adaptation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.5, + 0.694, + 0.516 + ], + "angle": 0, + "content": "3.6. Theoretical Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.613 + ], + "angle": 0, + "content": "To theoretically justify the effectiveness of our test-time training strategy, we establish the relationship between prediction variance and regression error. Our theoretical framework demonstrates how variance minimization across augmented samples inherently reduces the model's prediction error." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.892, + 0.66 + ], + "angle": 0, + "content": "Assumption 1 (Unbiased Augmentation) The expected prediction over augmentations equals the ground truth \\(LVEF\\): \\(\\mathbb{E}_{\\mathcal{T}_{a u q}}[\\hat{y}_k] = y\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.764 + ], + "angle": 0, + "content": "This assumption is grounded in the design of our augmentation strategy \\(\\mathcal{T}_{\\text{aug}}\\), which simulates acquisition-specific variations (e.g., speckle noise, gamma correction) while preserving the underlying cardiac motion patterns that determine LVEF. These perturbations affect image quality but do not alter the fundamental cardiac functional measurements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.892, + 0.826 + ], + "angle": 0, + "content": "Assumption 2 (Augmentation Independence) The predictions from different augmented samples are independently distributed, with zero cross-covariance: \\(\\mathrm{Cov}_{\\mathcal{T}_{a u g}}(\\hat{y}_k,\\hat{y}_j) = 0\\) for \\(k\\neq j\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This assumption reflects our augmentation design principle where each transformation introduces independent variations. The independence is achieved through combining multiple orthogonal perturbation types, ensuring minimal correlation between augmented samples." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15564" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.16 + ], + "angle": 0, + "content": "Table 1. Dataset Statistics. Demographic and clinical characteristics across age groups. The statistics show substantial differences in sample sizes (ranging from 831 to 7465), with notably fewer samples in younger age groups due to the inherent challenges in pediatric data collection." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.17, + 0.468, + 0.246 + ], + "angle": 0, + "content": "
StatisticsPre-schoolSchool-ageAdolescenceAdult
#Samples8319141,5397,465
Age2 ± 19 ± 215 ± 270 ± 22
Female (%)404 (49%)371 (41%)617 (40%)3662 (49%)
LVEF (%)59.6 ± 12.862.0 ± 9.261.0 ± 9.855.8 ± 12.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.47, + 0.346 + ], + "angle": 0, + "content": "Theorem 1 Consider a test sample \\( \\mathbf{x}_{test} \\) with ground truth label \\( y \\), and its \\( K \\) augmented versions \\( \\{\\mathbf{x}_{test}^k\\}_{k=1}^K \\) generated by \\( \\mathcal{T}_{aug} \\). Under Assumptions 1 and 2, the expected regression loss \\( \\mathbb{E}[L_{reg}] = \\mathbb{E}[(\\hat{y} - y)^2] \\) is upper bounded by:" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.346, + 0.469, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} [ L _ {r e g} ] \\leq \\frac {2 \\mathbb {E} [ L _ {v a r} ]}{K}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.382, + 0.435, + 0.398 + ], + "angle": 0, + "content": "where \\(L_{var}\\) is the variance loss defined in Equation 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.47, + 0.489 + ], + "angle": 0, + "content": "The proof uses standard techniques in optimization, and is left for the Appendix A. This theoretical result provides a justification for our test-time training strategy. Minimizing the variance loss directly leads to a reduction in the expected regression error, with the bound becoming tighter as we increase the number of augmentations \\( K \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.504, + 0.203, + 0.521 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.529, + 0.254, + 0.545 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Dataset and Metrics. We evaluate Q-PART using two benchmark datasets of apical-4-chamber echocardiogram videos collected from EchoNet-Dynamic [25] and EchoNet-Pediatric [31]. Following clinical standards, we stratify the data into four age cohorts: pre-school (ages 0-5), school-age (ages 6-11), adolescence (ages 12-18), and adult (ages \\(>18\\)). The detailed statistics of each cohort are summarized in Table 1. We train the model on the adult cohort and assess its performance through test-time training on pre-school, school-age, and adolescence cohorts respectively. For evaluation metrics, we adopt three widely-used metrics to comprehensively evaluate the LVEF prediction performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Moreover, we evaluate the model's clinical screening capability through mean Area Under the Receiver Operating Characteristic curve (mAUROC) analysis at multiple LVEF thresholds (35%, 40%, 45%, and 50%). More details please refer to Appendix C.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation. We adopt R3D Network [35] as the backbone encoder. The projection head contains four groups, with each group consisting of two \\(1 \\times 1\\) convolutional layers (\\(512 \\rightarrow 64 \\rightarrow 64\\)) with batch normalization and ReLU" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "activation. The decoder uses five transposed convolutional layers for reconstruction. In training stage, The model is optimized using SGD with momentum 0.9 and weight decay 1e-4, with a linear warmup for the first 10 epochs followed by cosine annealing for the remaining 35 epochs. During test-time training, we employ both general augmentations (rotation, flips, grid distortion, Gaussian blur) and ultrasound-specific transformations (speckle noise, gamma correction, acoustic shadow). We apply different learning rates to periodic (1e-5) and aperiodic (1e-3) components, while maintaining a base learning rate of 1e-4 for other parameters. The value K is 8. All experiments are conducted on a single NVIDIA A100 80GB GPU." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.3, + 0.866, + 0.317 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.414 + ], + "angle": 0, + "content": "We comprehensively evaluate Q-PART against seven representative methods spanning three methodological categories, i.e., segmentation-based approaches, vision-language models, and end-to-end regression methods, as mentioned in §2.1. Three key findings emerge from our experiments:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.522 + ], + "angle": 0, + "content": "1) Superior Performance. As shown in Table 2, our method achieves consistent improvements across all metrics and age groups, with particularly notable gains in the challenging Pre-School cohort (MAE: 7.235, MAPE: 0.1611, RMSE: 9.290). This demonstrates Q-PART's robust adaptation capability and its effectiveness in handling the unique challenges of pediatric echocardiography." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.734 + ], + "angle": 0, + "content": "2) Clinical Screening Capability. Beyond regression metrics, we evaluate our model's clinical utility through ROC analysis at multiple LVEF thresholds in Figure 4. The high mAUROC scores have significant clinical implications: the enhanced sensitivity ensures reliable detection of cardiac dysfunction cases requiring immediate intervention, while the improved specificity reduces unnecessary follow-up examinations, thereby optimizing healthcare resource allocation and minimizing patient anxiety. Q-PART achieves remarkable mAUROC scores of 0.9362, 0.9747, and 0.9083 for Pre-School, School Age, and Adolescence cohorts, respectively, substantially outperforming other TTA methods. This superior performance validates the effectiveness of our echocardiogram-specific framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3) Segmentation vs End-to-End Approaches. As discussed in §2.1, while lots of methods rely on left ventricular segmentation to derive LVEF values, recent end-to-end approaches directly predict LVEF. Our experimental results in Table 2 strongly support the superiority of end-to-end approaches. Despite advances in segmentation accuracy with methods like EchoNet and MemSAM, their LVEF estimation performance (MAE > 17.94) lags significantly behind end-to-end approaches (MAE < 9.114). This substantial performance gap suggests that accurate segmentation does not necessarily translate to precise LVEF estimation, as the" + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15565" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.149 + ], + "angle": 0, + "content": "Table 2. Comparison with State-of-the-Art Methods. We benchmark Q-PART against representative approaches spanning three methodological categories: segmentation-based methods (Seg-Based), vision-language models (VLM), and end-to-end regression approaches (E2E). Our method demonstrates superior adaptation capability and robustness across age groups, particularly in challenging scenarios with younger patients. All results are reported with four significant digits. Bold numbers indicate the best performance." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.156, + 0.891, + 0.304 + ], + "angle": 0, + "content": "
TypeApproachPre-SchoolSchool AgeAdolescence
MAEMAPERMSEMAEMAPERMSEMAEMAPERMSE
Seg-BasedEchoNet [26] (Nature 2020)20.900.473026.1417.860.340321.9719.640.376123.90
MemSAM [6] (CVPR 2024)17.940.367521.9718.350.321621.7618.710.324922.26
VLMEchoCLIP [4] (Nature Med. 2024)11.560.203514.189.3030.160411.718.4960.152110.93
E2ESource-only9.1140.175910.868.4250.146910.038.6360.154910.53
TTT++ [18] (NeurIPS 2022)8.0530.166910.017.4300.13169.0967.6160.14169.601
Clust3 [10] (CVPR 2023)9.2920.185211.237.8920.13939.4248.2160.15099.995
NC-TTT [24] (CVPR 2024)8.3520.180010.457.2850.13258.9627.4220.14089.347
Q-PART (Ours)7.2350.16119.2906.7060.12448.4326.9800.13448.950
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ROC Analysis at Multiple Clinical Thresholds. Please zoom in for better view. Receiver Operating Characteristic (ROC) curves for LVEF regression with four clinically significant thresholds: \\(35\\%\\) (blue), \\(40\\%\\) (green), \\(45\\%\\) (red), and \\(50\\%\\) (cyan). These thresholds represent different degrees of cardiac dysfunction severity. The x-axis shows 1-specificity (false positive rate) and the y-axis shows sensitivity (true positive rate). The mAuroC is shown in gray box. A high mAuroC value indicates strong clinical reliability. Higher sensitivity ensures early detection of cardiac dysfunction, while higher specificity reduces unnecessary follow-up examinations and patient anxiety, collectively supporting more accurate clinical decision-making and resource allocation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.471, + 0.768 + ], + "angle": 0, + "content": "latter requires capturing complex temporal dynamics and subtle motion patterns that may be lost in the intermediate segmentation step." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.231, + 0.801 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We conduct comprehensive ablation studies to evaluate the contribution of each key component in Q-PART, i.e., Quasi-Period Network (QP-Net), Learning Rate Strategy (LR), and Variance Minimization (VM). Table 3 presents the results on the Pre-School cohort. Several observations can be drawn from the ablation results: (1) The Quasi-Period Net" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.895, + 0.891 + ], + "angle": 0, + "content": "work alone yields substantial improvements (MAE: 7.949), demonstrating the effectiveness of disentangling periodic and aperiodic components during test-time training. (2) When combining QP-Net with VM, we observe a notable performance gain (MAE: 7.283), validating our hypothesis that variance minimization across augmented views effectively guides model adaptation. (3) The differential learning rate strategy further refines the adaptation process, with our full model achieving the best performance (MAE: 7.235). This suggests that applying different learning rates to periodic and aperiodic components helps maintain stable car" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15566" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.175 + ], + "angle": 0, + "content": "Table 3. Ablation Study of Key Components. Analysis of three key components: QP-Net (Quasi-Period Network), LR (Learning Rate Strategy), and VM (Variance Minimization). We presents the results on Pre-School cohort here, which demonstrates the effectiveness of each component. Complete results across all age cohorts are presented in Appendix Table 4." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.184, + 0.468, + 0.302 + ], + "angle": 0, + "content": "
QP-NetLRVMMAEMAPERMSE
8.1290.168110.09
✓7.9490.16669.909
✓✓7.9090.16569.878
✓7.8420.16409.714
✓✓7.2830.16199.307
✓✓✓7.2350.16119.290
" + }, + { + "type": "image", + "bbox": [ + 0.124, + 0.318, + 0.424, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.504, + 0.471, + 0.547 + ], + "angle": 0, + "content": "Figure 5. Impact of \\( K \\) Augmentation Number on Model Performance. The plot shows how performance varies with different numbers of augmentation number across three age cohorts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.606 + ], + "angle": 0, + "content": "diac cycle patterns while allowing flexible adaptation to patient-specific variations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.182, + 0.635 + ], + "angle": 0, + "content": "4.4. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Impact of Augmentation Number \\( K \\). We investigate how the number of augmented views \\( K \\) in variance minimization affects model performance. As shown in Figure 5, larger \\( K \\) values generally lead to better performance across all age cohorts. Notably, when \\( K = 2 \\), the model performs worse than the baseline without variance minimization, with MAE increasing from 7.909 to 8.036 in the Pre-School cohort. This deterioration can be attributed to the insufficient number of samples for reliable variance estimation, resulting in unstable optimization signals during test-time adaptation. While further increasing \\( K \\) to 32 continues to yield marginal improvements, it significantly increases computational overhead during inference. Balancing performance gains against computational efficiency, we choose \\( K = 8 \\) as our default setting for all main experiments." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Gender-fair Performance. To assess potential gender bias, we conduct a comprehensive analysis comparing model per" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.092, + 0.648, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.092, + 0.762, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.092, + 0.874, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.194, + 0.648, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.194, + 0.762, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.194, + 0.874, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.295, + 0.648, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.295, + 0.762, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.295, + 0.874, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.408, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Figure 6. Gender Bias Analysis Across Age Cohorts. Box plots comparing model performance between male and female subjects across three age cohorts using three metrics. Each subplot shows the distribution of performance metrics for both genders, with p-values from Mann-Whitney U tests. The absence of statistically significant differences \\((p > 0.05)\\) in eight out of nine comparisons demonstrates the model's gender-fair adaptation capability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.682 + ], + "angle": 0, + "content": "formance between male and female subjects across all age cohorts and metrics, as visualized in Figure 6. Statistical analysis reveals no significant differences \\((\\mathrm{p} > 0.05\\) in eight out of nine comparisons) between gender groups across all evaluation metrics (MAE, MAPE, RMSE) and age cohorts. This gender-fair performance demonstrates that QPART maintains consistent reliability regardless of gender, which is crucial for ensuring equitable healthcare delivery and maintaining diagnostic consistency across diverse patient populations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.619, + 0.71 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We present Q-PART, a novel test-time training framework specifically designed for pediatric LVEF regression. By explicitly disentangling periodic cardiac motion from patient-specific variations through our Quasi-Period Network, and employing a theoretically-grounded variance minimization strategy, Q-PART effectively addresses the unique challenges in pediatric echocardiography. Extensive experiments demonstrate that our method significantly outperforms existing approaches across different age groups and evaluation metrics. Q-PART advances the field of automated cardiac function assessment and shows promise for improving clinical workflow in pediatric cardiology." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15567" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.091, + 0.236, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.47, + 0.207 + ], + "angle": 0, + "content": "This work is supported by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), the Hong Kong Research Grants Council (Projects 21200522 and 11204821), DON-RMG 9229106 and a grant from the Institute of Digital Medicine of City University of Hong Kong." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.222, + 0.174, + 0.238 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.247, + 0.47, + 0.316 + ], + "angle": 0, + "content": "[1] Luis Enrique Avendaño, Luis David Avendaño-Valencia, Edilson Delgado-Trejos, and David Cuesta-Frau. 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Delta: degradation-free fully test-time adaptation. arXiv preprint arXiv:2301.13018, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15569" + } + ] +] \ No newline at end of file diff --git a/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_origin.pdf b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e32a8db6d811837eb027d4ba6b320e7bc3a46c2a --- /dev/null +++ b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/9b3ea12c-1e95-4e84-9ddd-5170e5c7771b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:72bf8d349d097c2cff4aec118adced6169f4f53b815b1ea2c2b5b21d131c3fab +size 2763068 diff --git a/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/full.md b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/full.md new file mode 100644 index 0000000000000000000000000000000000000000..294174eec90e920169ba31ca1158173955171f6a --- /dev/null +++ b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/full.md @@ -0,0 +1,354 @@ +# Q-PART: Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression + +Jie Liu $^{1}$ , Tiexin Qin $^{1}$ , Hui Liu $^{1}$ , Yilei Shi $^{2,3}$ , Lichao Mou $^{2,3}$ , Xiao Xiang Zhu $^{3}$ , Shiqi Wang $^{1}$ , and Haoliang Li $^{1*}$ + +$^{1}$ City University of Hong Kong $^{2}$ MedAI Technology (Wuxi) Co. Ltd. $^{3}$ Technische Universität München + +# Abstract + +In this work, we address the challenge of adaptive pediatric Left Ventricular Ejection Fraction (LVEF) assessment. While Test-time Training (TTT) approaches show promise for this task, they suffer from two significant limitations. Existing TTT works are primarily designed for classification tasks rather than continuous value regression, and they lack mechanisms to handle the quasi-periodic nature of cardiac signals. To tackle these issues, we propose a novel Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART) framework. In the training stage, the proposed Quasi-Period Network decomposes the echocardiogram into periodic and aperiodic components within latent space by combining parameterized helix trajectories with Neural Controlled Differential Equations. During inference, our framework further employs a variance minimization strategy across image augmentations that simulate common quality issues in echocardiogram acquisition, along with differential adaptation rates for periodic and aperiodic components. Theoretical analysis is provided to demonstrate that our variance minimization objective effectively bounds the regression error under mild conditions. Furthermore, extensive experiments across three pediatric age groups demonstrate that Q-PART not only significantly outperforms existing approaches in pediatric LVEF prediction, but also exhibits strong clinical screening capability with high mAUROC scores (up to 0.9747) and maintains gender-fair performance across all metrics, validating its robustness and practical utility in pediatric echocardiography analysis. The project can be found in Q-PART. + +# 1. Introduction + +Evaluation of Left Ventricular Ejection Fraction (LVEF) for pediatric patients plays a vital role in early diagnosis of con + +genital and acquired heart disease [31]. Echocardiography, recognized for its noninvasive nature and safety, has become the standard modality for LVEF evaluation [3, 26]. Although recent deep learning models [13, 16, 21] have shown promising results in adult LVEF assessment, their direct application to pediatric cases is problematic due to fundamental differences in cardiac imaging. As demonstrated in Figure 1 (a), pediatric patients exhibit considerable anatomical and physiological variations, including distinct differences in heart size, shape, and rate across different age groups [7]. Moreover, acquiring pediatric echocardiogram data is inherently challenging. Young children often exhibit difficulty cooperating during examinations, and ethical considerations limit unnecessary medical procedures, resulting in significant inter-observer variability and scarcity of labeled data for training. + +Test-time training (TTT) emerges as a promising paradigm to address these challenges by enabling model adaptation to distribution shifts during inference [15, 32]. TTT can enable model adaptation to each specific patient case during inference, without requiring access to training data or labels [28, 29], making it particularly valuable for pediatric LVEF assessment. This patient-specific adaptation naturally handles diverse pediatric cases without the necessity for extensive training echocardiograms, while also accommodating diverse anatomical variations and ensuring data privacy. + +However, the regression of pediatric LVEF presents unique challenges for direct application of TTT in this area. Firstly, existing TTT methods such as entropy minimization [33, 36, 39, 40], primarily designed for classification tasks with discrete decision boundaries [28, 29, 32], are not well suited for LVEF prediction, which is essentially a continuous value regression task. This challenge is further complicated by the quality issues in echocardiogram acquisition, as shown in Figure 1 (a), where varying acoustic shadow, probe positions, and speckle noise significantly impact regression accuracy, necessitating specialized self + +![](images/e7599e4e2365862e1fc9eebaf36a7b85439ccac7e595ba2645745fd26add4103.jpg) +Figure 1. (a) Adult and Pediatric Echocardiogram Visualization. These two kinds of echocardiograms exhibit anatomical and physiological variations, including distinct differences in heart size and shape. Moreover, We demonstrate two quality issues, i.e., acoustic shadow and speckle noise. (b) Quasi-Period Signal. Electrocardiogram (ECG) signals can be decomposed into periodic components originating from regular cardiac cycles and aperiodic components induced by physiological variations and noise. + +supervised algorithms for stable predictions. Secondly, the inherent complexity of cardiac activities in echocardiograms introduces additional challenges. As illustrated by the Electrocardiogram (ECG) signal example in Figure 1 (b), cardiac activities demonstrate a characteristic duality, comprising periodic components from regular cardiac cycles and aperiodic components from physiological variations, collectively forming quasi-periodic signals [1, 2, 14]. While periodic cardiac patterns remain relatively consistent across age groups, pediatric cases exhibit significant aperiodic variations due to diverse heart sizes and irregular activities. Leveraging this quasi-periodic nature for test-time training in echocardiogram analysis thus presents a promising yet unexplored research direction. + +To address these challenges, we propose a novel test-time training framework, named Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART), tailored for pediatric LVEF regression with two key innovations: (1) a Quasi-Period Network that explicitly disentangles echocardiogram features into periodic and aperiodic components in latent space, and (2) a specialized variance minimization strategy across augmented samples for continuous value regression. Specifically, the Quasi-Period Network is composed of a latent period encoder that captures fundamental cardiac cycles through a parameterized helix trajectory, and + +a Neural Controlled Differential Equations (Neural CDE) to represent aperiodic dynamics. This decomposition enables more nuanced feature extraction and adaptation. During test time, we augment test samples with carefully designed augmentation that simulate common quality issues in echocardiogram acquisition, such as acoustic shadows and speckle noise. Then, we introduce a variance minimization objective that minimizes prediction discrepancy across these augmented views, along with a differential adaptation scheme that employs distinct learning rates for periodic and aperiodic components. This design ensures stable regression predictions while effectively handling domain shifts. Furthermore, we provide theoretical guarantees demonstrating that our variance minimization approach effectively bounds the regression error. Extensive experiments demonstrate that our method achieves superior performance compared to existing approaches. Our contributions can be summarized as follows: + +- We propose Q-PART, a novel test-time training framework for pediatric LVEF regression. To the best of our knowledge, this represents the first efforts to leverage quasi-periodic properties for test-time training in echocardiogram analysis. +- We introduce two key technical innovations: a Quasi-Period Network that explicitly disentangles periodic and aperiodic components of echocardiogram, and a variance minimization strategy with theoretical guarantees on regression error bounds. +- We conduct comprehensive experiments, demonstrating that Q-PART achieves state-of-the-art performance in pediatric LVEF prediction, exhibits strong clinical screening capability, and maintains gender-fair performance. Additional ablation studies validate the effectiveness of each proposed component. + +# 2. Related Work + +# 2.1. Automated Echocardiogram Analysis + +Left Ventricular Segmentation. Echocardiography is essential for cardiovascular diagnosis and treatment planning [5, 12, 17]. EchoNet-Dynamic [26] pioneered large-scale echocardiogram video analysis using deep learning framework for left ventricular segmentation in adult patients. This sparked numerous developments in echocardiogram analysis [9, 37, 38]. Through the quantification of left ventricular masks across consecutive frames, the LVEF can be calculated. + +LVEF regression. Beyond these segmentation-based approaches, several works have explored end-to-end frameworks for direct LVEF prediction [5, 12, 19, 26]. Recently, Echo_CLIP [4] train a large vision-language foundation model for echocardiogram with 1,032,975 cardiac ultrasound videos and corresponding expert text. However, + +these methods, primarily designed for adult echocardiograms, often struggle with pediatric cases due to significant anatomical variations. + +Quasi-period Property. Cardiac activities exhibit quasi-periodic characteristics, combining regular cardiac cycles with aperiodic physiological variations. While existing methods have explored quasi-periodic signal processing for one-dimensional signals like ECG [1, 14, 30], their direct application to high-dimensional spatio-temporal echocardiograms remains challenging. Different from these work, we propose a novel framework that performs quasi-periodic decomposition in the latent space for echocardiogram. + +# 2.2. Test-time Training + +Models often experience significant performance degradation when deployed on test data that differs from the training distribution [27]. To address this distribution shift problem, Test-time Training (TTT) has emerged as a promising paradigm that enables models to adapt dynamically during inference [28, 29, 32]. + +Researchers have employed a self-supervised auxiliary task [8, 10, 18, 23, 34] to adapt to distribution shifts encountered during test time, from rotation prediction [34] and masked autoencoding [8] to contrastive learning [18] and normalizing flows [23]. Unlike these general methods, we propose a nuanced domain-specific self-supervised strategy that leverages echocardiogram quality variations through targeted augmentations. + +Another mainstream approach uses entropy minimization during inference, pioneered by Tent [36], which introduced adaptive updates to normalization layers through the mechanism of entropy minimization. This framework has inspired a multitude of subsequent studies [22, 33, 39-41] that enhance adaptation capabilities via various refinements to the entropy-based objective. Nevertheless, these approaches predominantly target classification tasks, presenting inherent limitations for regression problems, as regression models generate continuous numerical predictions rather than discrete probability distributions required for entropy computation. + +# 3. Q-PART Framework + +# 3.1. Problem Statement + +Let $\mathcal{D}_{train} = \{(x_i, y_i)\}_{i=1}^N$ denote the training dataset, where $x_i$ represents an echocardiogram sequence with temporal frames and spatial dimensions, and $y_i$ is the corresponding LVEF value. During training, we learn a regression model that maps echocardiogram sequences to LVEF values. The objective of test-time training is to adapt the model for domain-shifted test samples $x_{test} \in \mathcal{P}_{test}$ , $\mathcal{P}_{test} \neq \mathcal{P}_{train}$ , using self-supervised adaptation objective that does not require ground truth labels. In TTT, the train- + +ing data are unavailable and the training pipeline cannot be modified. + +# 3.2. Overview + +As illustrated in Figure 2 and Figure 3, our Q-PART framework consists of a Quasi-Period Network and Variance Minimization during testing time. Given an input sequence $\pmb{x}$ , the encoder extracts initial features $\pmb{z}$ , which are decomposed into periodic components $\hat{\pmb{z}}^{period}$ through parameterized helix trajectory and aperiodic components $\hat{\pmb{z}}^{aperiod}$ captured by Neural CDEs. During training, the model is optimized with regression loss $\mathcal{L}_{reg}$ and reconstruction loss $\mathcal{L}_{rec}$ . At test time, we optimize the model through variance minimization loss $\mathcal{L}_{var}$ and reconstruction loss $\mathcal{L}_{rec}$ using multiple augmented views, with different learning rates for periodic and aperiodic components. Detailed information on important components is provided below. + +# 3.3. Quasi-Period Network + +Quasi-Period Network addresses the fundamental challenge of disentangling periodic cardiac motion from patient-specific variations in echocardiogram analysis. It decomposes echocardiogram in the latent space through a nuanced architecture with physiologically-informed priors. Notably, during the test phase, this dual representation allows for adaptive optimization with different learning rates for periodic and aperiodic components, facilitating more effective model adaptation to individual cases. + +Latent Period Encoder. The latent period encoder architecturally embeds the intrinsic periodicity of cardiac motion into the feature space. Given the initial feature representation $\mathbf{z}$ , we employ specialized projection head $p$ to compute four fundamental components, frequency $f$ , phase shift $\phi$ , static offset $b$ , and velocity $v$ . This parameterization process can be formalized as + +$$ +\boldsymbol {f}, \phi , \boldsymbol {b}, \boldsymbol {v} = p (\boldsymbol {z}), \tag {1} +$$ + +where $f, \phi, b, v \in \mathbb{R}^{c \times h \times w}$ represents the global periodic characteristics for sequence $x$ , maintaining $c$ latent channels and spatial dimensions $h \times w$ to preserve spatial structures. To explicitly represent the periodicity, we define a parameterized helix trajectory function $g(\cdot)$ in multidimensional space, motivated by the physiological nature of cardiac motion that exhibits spiral-like patterns through combined rotational and translational movements: + +$$ +\begin{array}{l} \hat {\boldsymbol {z}} _ {t} ^ {\text {p e r i o d}} = g (t) = \cos (2 \pi (\boldsymbol {f} t - \phi)) \\ \begin{array}{l} - \cos (2 \pi (\boldsymbol {f} t - \phi)) \\ + \sin (2 \pi (\boldsymbol {f} t - \phi)) + \boldsymbol {v} t + \boldsymbol {b}. \end{array} \tag {2} \\ \end{array} +$$ + +where $\hat{z}_t^{period} \in \mathbb{R}^{c \times h \times w}$ represents the period component in time $t$ . The sinusoidal terms capture the intrinsic periodicity of cardiac motion, while the linear term $vt + b$ accounts for long-term translational movements. This formulation + +![](images/48c287a2ae8824cadeb6430f87a5cad0cda85081cf6ebe3393eca55787a4d2d2.jpg) +Figure 2. Overview of Q-PART Framework. The Quasi-Period Network decomposes input echocardiogram sequences into periodic and aperiodic components. The periodic component is modeled through a parameterized helix trajectory with frequency $f$ , phase shift $\phi$ , offset $b$ , and velocity $v$ . The aperiodic component is captured by Neural CDE. The model is jointly optimized with regression loss $\mathcal{L}_{reg}$ for LVEF prediction and reconstruction loss $\mathcal{L}_{rec}$ for feature learning. + +Figure 3. Variance Minimization during Test. we generate multiple augmented views of the test sequence through domain-specific transformations. The model adapts to each test case by minimizing prediction variance $\mathcal{L}_{var}$ across augmented views and maintaining reconstruction consistency $\mathcal{L}_{rec}$ with different learning rates applied to periodic and aperiodic components. +Fig. 1. Differences between discrete state transitions and continuous state transitions +![](images/afd30d48078896288152220afd8dfad7aef356a45064a26ee9dc27f6a00b86ec.jpg) +(a) Discrete State Transition +(b) Continuous State Transition + +creates a helix trajectory that naturally integrates both cyclic cardiac motion and progressive physiological dynamics. + +Latent Aperiodic Encoder. To capture the inherent non-periodic variations in cardiac motion, we design a latent aperiodic encoder that explicitly models these irregular components. The aperiodic features are obtained as the residual between the initial representation and the periodic component: $z' = z - \hat{z}^{period}$ . While traditional RNNs could potentially model temporal variations, Neural CDEs offer these crucial advantages for our task: 1) they naturally handle irregular representation in echocardiogram sequences, (2) they learn continuous-time dynamics from discretely sampled observations, which is better aligned with physiological processes. + +Formally, given the aperiodic component $z'$ , we first construct a continuous path $V(t)$ through natural cubic spline [20] to controlled differential equations, $V(t) = \mathrm{CubicSpline}(z_t')$ , where $z_t'$ represents the aperiodic component $z'$ at time $t$ . The spline ensures smooth transitions between discrete observations while preserving the underlying temporal structure. The evolution of the aperiodic representation is then governed by the controlled differential equation, $d\hat{z}_t^{aperiod} = f_\theta(\hat{z}_t^{aperiod}, t)dV(t)$ , where $f_\theta$ is implemented as a neural network that learns the mapping between the current state and its differential elements. The final aperiodic representation at time $T$ is obtained through integration, + +$$ +\hat {\boldsymbol {z}} _ {T} ^ {\text {a p e r i o d}} = \boldsymbol {z} _ {0} ^ {\prime} + \int_ {0} ^ {T} f _ {\theta} \left(\hat {\boldsymbol {z}} _ {t} ^ {\text {a p e r i o d}}, t\right) d \boldsymbol {V} (t), \tag {3} +$$ + +where $z_0'$ serves as the initial condition. The neural CDE network is optimized using the CDE solver [11], which compute the gradients via the adjoint method. + +The decomposition provides a foundation for our test-time training strategy, where periodic and aperiodic components can be optimized with different learning dynamics. Empirically, we find that this architecture achieves superior performance in capturing complex cardiac motions, as demonstrated in our ablation studies §4.3. + +# 3.4. Variance Minimization + +To address the domain shift challenge during testing, we propose a theoretically-grounded self-supervised strategy that combines test-time augmentation with variance minimization. Our key insight is that while echocardiographic + +acquisitions may vary in quality and appearance, the underlying cardiac function remains consistent across different views of the same sequence. + +Domain-Specific Augmentation. For each test sequence $\boldsymbol{x}_{test}$ , we generate $K$ augmented versions through a carefully curated augmentation pipeline: + +$$ +\left\{\boldsymbol {x} _ {\text {t e s t}} ^ {k} \right\} _ {k = 1} ^ {K} = \mathcal {T} _ {\text {a u g}} (\boldsymbol {x} _ {\text {t e s t}}), \tag {4} +$$ + +where $\mathcal{T}_{\text{aug}}$ comprises three categories of domain-specific augmentations. Beyond conventional image augmentations, we introduce three ultrasound-specific transformations: gamma correction to simulate varying image contrast settings, speckle noise injection to mimic acoustic interference patterns, and elastic deformation to account for cardiac tissue deformation during acquisition. These domain-specific augmentations are specifically designed to simulate real-world variations in echocardiographic acquisition while preserving the underlying cardiac motion patterns essential for LVEF assessment. + +Variance-Based Adaptation. Then, we minimizes the prediction variance across augmented samples. The variance loss $\mathcal{L}_{var}$ is computed as: + +$$ +\mathcal {L} _ {v a r} = \frac {1}{K} \sum_ {k = 1} ^ {K} \left(\hat {y} _ {k} - \bar {y}\right) ^ {2}, \tag {5} +$$ + +where $\hat{y}_k$ represents the prediction for the $k$ -th augmented sequence and $\bar{y}$ denotes the mean prediction across all augmentations. This formulation encourages the model to learn invariant features that are robust to acquisition-specific variations while remaining sensitive to true cardiac function changes. We provide theoretical analysis in Section 3.6 demonstrating that minimizing this variance effectively bounds the adaptation error under mild conditions. + +# 3.5. Optimization + +Our optimization strategy consists of two phases: training time and testing time. The overall pipeline is summarized in Appendix Algorithm 1. + +Training time. During the training phase, our model employs a multi-objective learning strategy combining regression and reconstruction objectives: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e g}} + \mathcal {L} _ {\text {r e c}}. \tag {6} +$$ + +The reconstruction loss ensures that both periodic and aperiodic components collectively preserve the essential information of the input sequence. + +$$ +\mathcal {L} _ {r e c} = \left\| \boldsymbol {x} - \operatorname {D e c} \left(\hat {\boldsymbol {z}} ^ {\text {p e r i o d}} + \hat {\boldsymbol {z}} ^ {\text {a p e r i o d}}\right) \right\| _ {2} ^ {2} \tag {7} +$$ + +where $\mathrm{Dec}(\cdot)$ denotes the decoder network. For LVEF prediction, we aggregate the combined latent representation + +through Global Average Pooling (GAP) followed by a Multiple Layer Perceptron (MLP), $\hat{y} = \mathrm{MLP}(\hat{z}^{period} + \hat{z}^{aperiod})$ . The regression loss is defined as: + +$$ +\mathcal {L} _ {r e g} = \| \hat {y} - y \| _ {2} ^ {2}, \tag {8} +$$ + +Through this joint optimization, our model learns to decompose the echocardiogram into meaningful periodic and aperiodic representation while maintaining accurate LVEF predictions. + +Testing Time. The overall test optimization objective combines this variance minimization with reconstruction consistency + +$$ +\mathcal {L} _ {\text {t e s t}} = \mathcal {L} _ {\text {v a r}} + \mathcal {L} _ {\text {r e c}}. \tag {9} +$$ + +During testing time, we only update the batch normalization (BN) parameters in our network [34], which has been shown to be effective for test-time training while maintaining model stability. Given the inherent differences between periodic and aperiodic cardiac components, we employ different learning rates for their respective BN parameters. The periodic components, which capture the fundamental cardiac cycles, require more conservative updates to maintain temporal consistency. Therefore, we use a smaller learning rate for BN layers in the latent period encoder. In contrast, the aperiodic components, representing physiological variations and acquisition-specific features, benefit from more aggressive adaptation. + +# 3.6. Theoretical Analysis + +To theoretically justify the effectiveness of our test-time training strategy, we establish the relationship between prediction variance and regression error. Our theoretical framework demonstrates how variance minimization across augmented samples inherently reduces the model's prediction error. + +Assumption 1 (Unbiased Augmentation) The expected prediction over augmentations equals the ground truth $LVEF$ : $\mathbb{E}_{\mathcal{T}_{a u q}}[\hat{y}_k] = y$ + +This assumption is grounded in the design of our augmentation strategy $\mathcal{T}_{\text{aug}}$ , which simulates acquisition-specific variations (e.g., speckle noise, gamma correction) while preserving the underlying cardiac motion patterns that determine LVEF. These perturbations affect image quality but do not alter the fundamental cardiac functional measurements. + +Assumption 2 (Augmentation Independence) The predictions from different augmented samples are independently distributed, with zero cross-covariance: $\mathrm{Cov}_{\mathcal{T}_{a u g}}(\hat{y}_k,\hat{y}_j) = 0$ for $k\neq j$ + +This assumption reflects our augmentation design principle where each transformation introduces independent variations. The independence is achieved through combining multiple orthogonal perturbation types, ensuring minimal correlation between augmented samples. + +Table 1. Dataset Statistics. Demographic and clinical characteristics across age groups. The statistics show substantial differences in sample sizes (ranging from 831 to 7465), with notably fewer samples in younger age groups due to the inherent challenges in pediatric data collection. + +
StatisticsPre-schoolSchool-ageAdolescenceAdult
#Samples8319141,5397,465
Age2 ± 19 ± 215 ± 270 ± 22
Female (%)404 (49%)371 (41%)617 (40%)3662 (49%)
LVEF (%)59.6 ± 12.862.0 ± 9.261.0 ± 9.855.8 ± 12.4
+ +Theorem 1 Consider a test sample $\mathbf{x}_{test}$ with ground truth label $y$ , and its $K$ augmented versions $\{\mathbf{x}_{test}^k\}_{k=1}^K$ generated by $\mathcal{T}_{aug}$ . Under Assumptions 1 and 2, the expected regression loss $\mathbb{E}[L_{reg}] = \mathbb{E}[(\hat{y} - y)^2]$ is upper bounded by: + +$$ +\mathbb {E} [ L _ {r e g} ] \leq \frac {2 \mathbb {E} [ L _ {v a r} ]}{K}, \tag {10} +$$ + +where $L_{var}$ is the variance loss defined in Equation 5. + +The proof uses standard techniques in optimization, and is left for the Appendix A. This theoretical result provides a justification for our test-time training strategy. Minimizing the variance loss directly leads to a reduction in the expected regression error, with the bound becoming tighter as we increase the number of augmentations $K$ . + +# 4. Experiment + +# 4.1. Experiment Setup + +Dataset and Metrics. We evaluate Q-PART using two benchmark datasets of apical-4-chamber echocardiogram videos collected from EchoNet-Dynamic [25] and EchoNet-Pediatric [31]. Following clinical standards, we stratify the data into four age cohorts: pre-school (ages 0-5), school-age (ages 6-11), adolescence (ages 12-18), and adult (ages $>18$ ). The detailed statistics of each cohort are summarized in Table 1. We train the model on the adult cohort and assess its performance through test-time training on pre-school, school-age, and adolescence cohorts respectively. For evaluation metrics, we adopt three widely-used metrics to comprehensively evaluate the LVEF prediction performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Moreover, we evaluate the model's clinical screening capability through mean Area Under the Receiver Operating Characteristic curve (mAUROC) analysis at multiple LVEF thresholds (35%, 40%, 45%, and 50%). More details please refer to Appendix C.1. + +Implementation. We adopt R3D Network [35] as the backbone encoder. The projection head contains four groups, with each group consisting of two $1 \times 1$ convolutional layers ( $512 \rightarrow 64 \rightarrow 64$ ) with batch normalization and ReLU + +activation. The decoder uses five transposed convolutional layers for reconstruction. In training stage, The model is optimized using SGD with momentum 0.9 and weight decay 1e-4, with a linear warmup for the first 10 epochs followed by cosine annealing for the remaining 35 epochs. During test-time training, we employ both general augmentations (rotation, flips, grid distortion, Gaussian blur) and ultrasound-specific transformations (speckle noise, gamma correction, acoustic shadow). We apply different learning rates to periodic (1e-5) and aperiodic (1e-3) components, while maintaining a base learning rate of 1e-4 for other parameters. The value K is 8. All experiments are conducted on a single NVIDIA A100 80GB GPU. + +# 4.2. Comparison with State-of-the-art Methods + +We comprehensively evaluate Q-PART against seven representative methods spanning three methodological categories, i.e., segmentation-based approaches, vision-language models, and end-to-end regression methods, as mentioned in §2.1. Three key findings emerge from our experiments: + +1) Superior Performance. As shown in Table 2, our method achieves consistent improvements across all metrics and age groups, with particularly notable gains in the challenging Pre-School cohort (MAE: 7.235, MAPE: 0.1611, RMSE: 9.290). This demonstrates Q-PART's robust adaptation capability and its effectiveness in handling the unique challenges of pediatric echocardiography. +2) Clinical Screening Capability. Beyond regression metrics, we evaluate our model's clinical utility through ROC analysis at multiple LVEF thresholds in Figure 4. The high mAUROC scores have significant clinical implications: the enhanced sensitivity ensures reliable detection of cardiac dysfunction cases requiring immediate intervention, while the improved specificity reduces unnecessary follow-up examinations, thereby optimizing healthcare resource allocation and minimizing patient anxiety. Q-PART achieves remarkable mAUROC scores of 0.9362, 0.9747, and 0.9083 for Pre-School, School Age, and Adolescence cohorts, respectively, substantially outperforming other TTA methods. This superior performance validates the effectiveness of our echocardiogram-specific framework. +3) Segmentation vs End-to-End Approaches. As discussed in §2.1, while lots of methods rely on left ventricular segmentation to derive LVEF values, recent end-to-end approaches directly predict LVEF. Our experimental results in Table 2 strongly support the superiority of end-to-end approaches. Despite advances in segmentation accuracy with methods like EchoNet and MemSAM, their LVEF estimation performance (MAE > 17.94) lags significantly behind end-to-end approaches (MAE < 9.114). This substantial performance gap suggests that accurate segmentation does not necessarily translate to precise LVEF estimation, as the + +Table 2. Comparison with State-of-the-Art Methods. We benchmark Q-PART against representative approaches spanning three methodological categories: segmentation-based methods (Seg-Based), vision-language models (VLM), and end-to-end regression approaches (E2E). Our method demonstrates superior adaptation capability and robustness across age groups, particularly in challenging scenarios with younger patients. All results are reported with four significant digits. Bold numbers indicate the best performance. + +
TypeApproachPre-SchoolSchool AgeAdolescence
MAEMAPERMSEMAEMAPERMSEMAEMAPERMSE
Seg-BasedEchoNet [26] (Nature 2020)20.900.473026.1417.860.340321.9719.640.376123.90
MemSAM [6] (CVPR 2024)17.940.367521.9718.350.321621.7618.710.324922.26
VLMEchoCLIP [4] (Nature Med. 2024)11.560.203514.189.3030.160411.718.4960.152110.93
E2ESource-only9.1140.175910.868.4250.146910.038.6360.154910.53
TTT++ [18] (NeurIPS 2022)8.0530.166910.017.4300.13169.0967.6160.14169.601
Clust3 [10] (CVPR 2023)9.2920.185211.237.8920.13939.4248.2160.15099.995
NC-TTT [24] (CVPR 2024)8.3520.180010.457.2850.13258.9627.4220.14089.347
Q-PART (Ours)7.2350.16119.2906.7060.12448.4326.9800.13448.950
+ +![](images/cb5577d8545b728210fcde3ddaf2100a94e820ac3077a331faa9bf3c396ecd09.jpg) + +![](images/2ba720424fa05acb42ed9d1034b1844fdb506473c745f02fdf1e49c5dc54a842.jpg) + +![](images/666e4817ee78d5767cc9735284049fc537a2757794488d5b79592156616c29b3.jpg) + +![](images/364d3450d9cd7158c268fe5a4d7707578802b4789c15386f8635cf6995068e81.jpg) + +![](images/18d510b939f8a1356fe967fb3a52f806a82763928617ae758eddc6f3ae3d0102.jpg) + +![](images/2f4b775c53eecd94abb16811b15b93ceb0cccb2bbfb08d28028a5458a00c8699.jpg) + +![](images/9aa79e25b4f2e471cc8a67970316c1df8ba5aadd58c71d5a87bc0834c216bbe8.jpg) + +![](images/68698ab1fa78575eb4e231ebd19a3d798f36ff26bab7a4a19e787db19ef876fa.jpg) + +![](images/b2014fa4f4da0eece19d7f40eb51cc168a8f0d3aaa9924558d979112f23124e9.jpg) + +![](images/423f089d62f184a49615a5345afa422ed5276b4d31e15b99273bf9dcd0c4c1b1.jpg) + +![](images/4f7f9b684c23c72d34ffe70cc8b29b480fb2d3d1ac58fbec08201deccd80ced3.jpg) + +![](images/fbfaa2b8a8095503fd763ad4b05503203b030b0be28c8357495d17bf8f5f0ae5.jpg) + +![](images/718bc83c070b1778df29345c4cf589ca6c312ef5208e2ea74f6336f18663be4c.jpg) + +![](images/187e75af6798a2b47f15bc89ffaf92b1250b1467505af47f89fe5c56ef1ecd52.jpg) + +![](images/9dbb766442d6d7875a2cd69b40c2da9deac3def766ffc4a678ed7e365fc7cc9e.jpg) +Figure 4. ROC Analysis at Multiple Clinical Thresholds. Please zoom in for better view. Receiver Operating Characteristic (ROC) curves for LVEF regression with four clinically significant thresholds: $35\%$ (blue), $40\%$ (green), $45\%$ (red), and $50\%$ (cyan). These thresholds represent different degrees of cardiac dysfunction severity. The x-axis shows 1-specificity (false positive rate) and the y-axis shows sensitivity (true positive rate). The mAuroC is shown in gray box. A high mAuroC value indicates strong clinical reliability. Higher sensitivity ensures early detection of cardiac dysfunction, while higher specificity reduces unnecessary follow-up examinations and patient anxiety, collectively supporting more accurate clinical decision-making and resource allocation. + +![](images/5f2a583f2e531e436ee43b638648ab18160a87da9eb7fa90ca2b1ccc8970e0b6.jpg) + +![](images/6e7e45486e61e0535d5174b6758762f1cfbca2fe4d80ec6c5845c5189027614e.jpg) + +![](images/2fec9ac5470e1d9698b8ea4a88f3b64587ae7f465e9ab1cbdda6ed6343235674.jpg) + +![](images/4164e0b2eea17298501a591ed8815df04f07b7fb64e71d4b81d8ad36b2d7e5d6.jpg) + +![](images/ea738242af349c6b313708c628c61335e68fca17e3548ad61959b5e82c711521.jpg) + +![](images/52cf57d72f9c55958c26587be4cec0aaae291b2651d8b35bbe22bdb43b7e0a84.jpg) + +latter requires capturing complex temporal dynamics and subtle motion patterns that may be lost in the intermediate segmentation step. + +# 4.3. Ablation Study + +We conduct comprehensive ablation studies to evaluate the contribution of each key component in Q-PART, i.e., Quasi-Period Network (QP-Net), Learning Rate Strategy (LR), and Variance Minimization (VM). Table 3 presents the results on the Pre-School cohort. Several observations can be drawn from the ablation results: (1) The Quasi-Period Net + +work alone yields substantial improvements (MAE: 7.949), demonstrating the effectiveness of disentangling periodic and aperiodic components during test-time training. (2) When combining QP-Net with VM, we observe a notable performance gain (MAE: 7.283), validating our hypothesis that variance minimization across augmented views effectively guides model adaptation. (3) The differential learning rate strategy further refines the adaptation process, with our full model achieving the best performance (MAE: 7.235). This suggests that applying different learning rates to periodic and aperiodic components helps maintain stable car + +Table 3. Ablation Study of Key Components. Analysis of three key components: QP-Net (Quasi-Period Network), LR (Learning Rate Strategy), and VM (Variance Minimization). We presents the results on Pre-School cohort here, which demonstrates the effectiveness of each component. Complete results across all age cohorts are presented in Appendix Table 4. + +
QP-NetLRVMMAEMAPERMSE
8.1290.168110.09
✓7.9490.16669.909
✓✓7.9090.16569.878
✓7.8420.16409.714
✓✓7.2830.16199.307
✓✓✓7.2350.16119.290
+ +![](images/5ad437852703e71ebe437fd0060b0f966069695224124eb1bcae6cfcc8c4d9d6.jpg) +Figure 5. Impact of $K$ Augmentation Number on Model Performance. The plot shows how performance varies with different numbers of augmentation number across three age cohorts. + +diac cycle patterns while allowing flexible adaptation to patient-specific variations. + +# 4.4. Analysis + +Impact of Augmentation Number $K$ . We investigate how the number of augmented views $K$ in variance minimization affects model performance. As shown in Figure 5, larger $K$ values generally lead to better performance across all age cohorts. Notably, when $K = 2$ , the model performs worse than the baseline without variance minimization, with MAE increasing from 7.909 to 8.036 in the Pre-School cohort. This deterioration can be attributed to the insufficient number of samples for reliable variance estimation, resulting in unstable optimization signals during test-time adaptation. While further increasing $K$ to 32 continues to yield marginal improvements, it significantly increases computational overhead during inference. Balancing performance gains against computational efficiency, we choose $K = 8$ as our default setting for all main experiments. + +Gender-fair Performance. To assess potential gender bias, we conduct a comprehensive analysis comparing model per + +![](images/802150e0437b9fafcb327671d6ff78d9d844320adc3f518c761727027b0eca59.jpg) + +![](images/356b82242284a5a9537ca05cef4d7353b212f4711775da05030b01b307eda979.jpg) + +![](images/8ceaa2efafa0a9dcfcff946f0b6caa0d85be1f2c252c7e0fe28cfcbb9f3e7b4f.jpg) + +![](images/9bb00021b608468943982f43780c2a533b8b036963e427dbd11b72999b5f5290.jpg) + +![](images/c2abf8d1978bbedffca7f69ef2c80915219374093edaacdb8ecd77a47f4718fc.jpg) + +![](images/8105cd6e5687569fbddce1a89f9c161fa2492c61eaacdeae3156dc78ee7d3162.jpg) + +![](images/d0ea52627dd1c37c80e17ae77f5420817c2cfdd2f993c95fd109d78e96d0542b.jpg) +Figure 6. Gender Bias Analysis Across Age Cohorts. Box plots comparing model performance between male and female subjects across three age cohorts using three metrics. Each subplot shows the distribution of performance metrics for both genders, with p-values from Mann-Whitney U tests. The absence of statistically significant differences $(p > 0.05)$ in eight out of nine comparisons demonstrates the model's gender-fair adaptation capability. + +![](images/9fce9c645374471c74fc40679063e126e5085efbc7108c91196a288f9a95c8ee.jpg) + +![](images/fbfe5f28495ca13d66c259ad5c4bf189a5e47e73c66ca422cb9766a2172ef708.jpg) + +formance between male and female subjects across all age cohorts and metrics, as visualized in Figure 6. Statistical analysis reveals no significant differences $(\mathrm{p} > 0.05$ in eight out of nine comparisons) between gender groups across all evaluation metrics (MAE, MAPE, RMSE) and age cohorts. This gender-fair performance demonstrates that QPART maintains consistent reliability regardless of gender, which is crucial for ensuring equitable healthcare delivery and maintaining diagnostic consistency across diverse patient populations. + +# 5. Conclusion + +We present Q-PART, a novel test-time training framework specifically designed for pediatric LVEF regression. By explicitly disentangling periodic cardiac motion from patient-specific variations through our Quasi-Period Network, and employing a theoretically-grounded variance minimization strategy, Q-PART effectively addresses the unique challenges in pediatric echocardiography. Extensive experiments demonstrate that our method significantly outperforms existing approaches across different age groups and evaluation metrics. Q-PART advances the field of automated cardiac function assessment and shows promise for improving clinical workflow in pediatric cardiology. + +# Acknowledgments + +This work is supported by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), the Hong Kong Research Grants Council (Projects 21200522 and 11204821), DON-RMG 9229106 and a grant from the Institute of Digital Medicine of City University of Hong Kong. + +# References + +[1] Luis Enrique Avendaño, Luis David Avendaño-Valencia, Edilson Delgado-Trejos, and David Cuesta-Frau. State space model-based harmonic decomposition of pseudo-periodic non-stationary multivariate signals. Signal Processing, 213: 109192, 2023. 2, 3 +[2] Goutam Chakraborty, Takuya Kamiyama, Hideyuki Takahashi, and Tetsuo Kinoshita. An efficient anomaly detection in quasi-periodic time series data—a case study with ecg. In Time Series Analysis and Forecasting: Selected Contributions from ITISE 2017, pages 147–157. 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Delta: degradation-free fully test-time adaptation. arXiv preprint arXiv:2301.13018, 2023. 3 \ No newline at end of file diff --git a/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/images.zip b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..33fa995f67ee3ffba7281d09c9d1c74ba7352ebe --- /dev/null +++ b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:42f4d94f8a7d313c9370ff0e6925b26864649225c439ad3e1aba423fba9da31d +size 532868 diff --git a/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/layout.json b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b650f92dddc68da32c52b89b4c91c71a24ecb62c --- /dev/null +++ b/2025/Q-PART_ Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression/layout.json @@ -0,0 +1,9348 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "spans": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "type": "text", + "content": "Q-PART: Quasi-Periodic Adaptive Regression with Test-time Training for Pediatric Left Ventricular Ejection Fraction Regression" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "spans": [ + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": "Jie Liu" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Tiexin Qin" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Hui Liu" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Yilei Shi" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Lichao Mou" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Xiao Xiang Zhu" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", Shiqi Wang" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "text", + "content": ", and Haoliang Li" + }, + { + "bbox": [ + 150, + 160, + 441, + 190 + ], + "type": "inline_equation", + "content": "^{1*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "spans": [ + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "text", + "content": "City University of Hong Kong " + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "text", + "content": "MedAI Technology (Wuxi) Co. Ltd. " + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 125, + 194, + 468, + 223 + ], + "type": "text", + "content": "Technische Universität München" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 276, + 289, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 624 + ], + "type": "text", + "content": "In this work, we address the challenge of adaptive pediatric Left Ventricular Ejection Fraction (LVEF) assessment. While Test-time Training (TTT) approaches show promise for this task, they suffer from two significant limitations. Existing TTT works are primarily designed for classification tasks rather than continuous value regression, and they lack mechanisms to handle the quasi-periodic nature of cardiac signals. To tackle these issues, we propose a novel Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART) framework. In the training stage, the proposed Quasi-Period Network decomposes the echocardiogram into periodic and aperiodic components within latent space by combining parameterized helix trajectories with Neural Controlled Differential Equations. During inference, our framework further employs a variance minimization strategy across image augmentations that simulate common quality issues in echocardiogram acquisition, along with differential adaptation rates for periodic and aperiodic components. Theoretical analysis is provided to demonstrate that our variance minimization objective effectively bounds the regression error under mild conditions. Furthermore, extensive experiments across three pediatric age groups demonstrate that Q-PART not only significantly outperforms existing approaches in pediatric LVEF prediction, but also exhibits strong clinical screening capability with high mAUROC scores (up to 0.9747) and maintains gender-fair performance across all metrics, validating its robustness and practical utility in pediatric echocardiography analysis. The project can be found in Q-PART." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 648, + 128, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 648, + 128, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 648, + 128, + 660 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 668, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 668, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 668, + 288, + 693 + ], + "type": "text", + "content": "Evaluation of Left Ventricular Ejection Fraction (LVEF) for pediatric patients plays a vital role in early diagnosis of con" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 251, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 547, + 443 + ], + "type": "text", + "content": "genital and acquired heart disease [31]. Echocardiography, recognized for its noninvasive nature and safety, has become the standard modality for LVEF evaluation [3, 26]. Although recent deep learning models [13, 16, 21] have shown promising results in adult LVEF assessment, their direct application to pediatric cases is problematic due to fundamental differences in cardiac imaging. As demonstrated in Figure 1 (a), pediatric patients exhibit considerable anatomical and physiological variations, including distinct differences in heart size, shape, and rate across different age groups [7]. Moreover, acquiring pediatric echocardiogram data is inherently challenging. Young children often exhibit difficulty cooperating during examinations, and ethical considerations limit unnecessary medical procedures, resulting in significant inter-observer variability and scarcity of labeled data for training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 446, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 547, + 579 + ], + "type": "text", + "content": "Test-time training (TTT) emerges as a promising paradigm to address these challenges by enabling model adaptation to distribution shifts during inference [15, 32]. TTT can enable model adaptation to each specific patient case during inference, without requiring access to training data or labels [28, 29], making it particularly valuable for pediatric LVEF assessment. This patient-specific adaptation naturally handles diverse pediatric cases without the necessity for extensive training echocardiograms, while also accommodating diverse anatomical variations and ensuring data privacy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "However, the regression of pediatric LVEF presents unique challenges for direct application of TTT in this area. Firstly, existing TTT methods such as entropy minimization [33, 36, 39, 40], primarily designed for classification tasks with discrete decision boundaries [28, 29, 32], are not well suited for LVEF prediction, which is essentially a continuous value regression task. This challenge is further complicated by the quality issues in echocardiogram acquisition, as shown in Figure 1 (a), where varying acoustic shadow, probe positions, and speckle noise significantly impact regression accuracy, necessitating specialized self" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 182, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 182, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 182, + 713 + ], + "type": "text", + "content": "*Corresponding authors: Haoliang Li." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15560" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 73, + 282, + 285 + ], + "blocks": [ + { + "bbox": [ + 56, + 73, + 282, + 285 + ], + "lines": [ + { + "bbox": [ + 56, + 73, + 282, + 285 + ], + "spans": [ + { + "bbox": [ + 56, + 73, + 282, + 285 + ], + "type": "image", + "image_path": "e7599e4e2365862e1fc9eebaf36a7b85439ccac7e595ba2645745fd26add4103.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 297, + 287, + 385 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 385 + ], + "type": "text", + "content": "Figure 1. (a) Adult and Pediatric Echocardiogram Visualization. These two kinds of echocardiograms exhibit anatomical and physiological variations, including distinct differences in heart size and shape. Moreover, We demonstrate two quality issues, i.e., acoustic shadow and speckle noise. (b) Quasi-Period Signal. Electrocardiogram (ECG) signals can be decomposed into periodic components originating from regular cardiac cycles and aperiodic components induced by physiological variations and noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "type": "text", + "content": "supervised algorithms for stable predictions. Secondly, the inherent complexity of cardiac activities in echocardiograms introduces additional challenges. As illustrated by the Electrocardiogram (ECG) signal example in Figure 1 (b), cardiac activities demonstrate a characteristic duality, comprising periodic components from regular cardiac cycles and aperiodic components from physiological variations, collectively forming quasi-periodic signals [1, 2, 14]. While periodic cardiac patterns remain relatively consistent across age groups, pediatric cases exhibit significant aperiodic variations due to diverse heart sizes and irregular activities. Leveraging this quasi-periodic nature for test-time training in echocardiogram analysis thus presents a promising yet unexplored research direction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "To address these challenges, we propose a novel test-time training framework, named Quasi-Periodic Adaptive Regression with Test-time Training (Q-PART), tailored for pediatric LVEF regression with two key innovations: (1) a Quasi-Period Network that explicitly disentangles echocardiogram features into periodic and aperiodic components in latent space, and (2) a specialized variance minimization strategy across augmented samples for continuous value regression. Specifically, the Quasi-Period Network is composed of a latent period encoder that captures fundamental cardiac cycles through a parameterized helix trajectory, and" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 286 + ], + "type": "text", + "content": "a Neural Controlled Differential Equations (Neural CDE) to represent aperiodic dynamics. This decomposition enables more nuanced feature extraction and adaptation. During test time, we augment test samples with carefully designed augmentation that simulate common quality issues in echocardiogram acquisition, such as acoustic shadows and speckle noise. Then, we introduce a variance minimization objective that minimizes prediction discrepancy across these augmented views, along with a differential adaptation scheme that employs distinct learning rates for periodic and aperiodic components. This design ensures stable regression predictions while effectively handling domain shifts. Furthermore, we provide theoretical guarantees demonstrating that our variance minimization approach effectively bounds the regression error. Extensive experiments demonstrate that our method achieves superior performance compared to existing approaches. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 290, + 545, + 482 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 290, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 290, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 290, + 545, + 350 + ], + "type": "text", + "content": "- We propose Q-PART, a novel test-time training framework for pediatric LVEF regression. To the best of our knowledge, this represents the first efforts to leverage quasi-periodic properties for test-time training in echocardiogram analysis." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 350, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 545, + 409 + ], + "type": "text", + "content": "- We introduce two key technical innovations: a Quasi-Period Network that explicitly disentangles periodic and aperiodic components of echocardiogram, and a variance minimization strategy with theoretical guarantees on regression error bounds." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 411, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 545, + 482 + ], + "type": "text", + "content": "- We conduct comprehensive experiments, demonstrating that Q-PART achieves state-of-the-art performance in pediatric LVEF prediction, exhibits strong clinical screening capability, and maintains gender-fair performance. Additional ablation studies validate the effectiveness of each proposed component." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "type": "text", + "content": "2.1. Automated Echocardiogram Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "Left Ventricular Segmentation. Echocardiography is essential for cardiovascular diagnosis and treatment planning [5, 12, 17]. EchoNet-Dynamic [26] pioneered large-scale echocardiogram video analysis using deep learning framework for left ventricular segmentation in adult patients. This sparked numerous developments in echocardiogram analysis [9, 37, 38]. Through the quantification of left ventricular masks across consecutive frames, the LVEF can be calculated." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "LVEF regression. Beyond these segmentation-based approaches, several works have explored end-to-end frameworks for direct LVEF prediction [5, 12, 19, 26]. Recently, Echo_CLIP [4] train a large vision-language foundation model for echocardiogram with 1,032,975 cardiac ultrasound videos and corresponding expert text. However," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15561" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "these methods, primarily designed for adult echocardiograms, often struggle with pediatric cases due to significant anatomical variations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 217 + ], + "type": "text", + "content": "Quasi-period Property. Cardiac activities exhibit quasi-periodic characteristics, combining regular cardiac cycles with aperiodic physiological variations. While existing methods have explored quasi-periodic signal processing for one-dimensional signals like ECG [1, 14, 30], their direct application to high-dimensional spatio-temporal echocardiograms remains challenging. Different from these work, we propose a novel framework that performs quasi-periodic decomposition in the latent space for echocardiogram." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 224, + 157, + 238 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 157, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 157, + 238 + ], + "type": "text", + "content": "2.2. Test-time Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 315 + ], + "type": "text", + "content": "Models often experience significant performance degradation when deployed on test data that differs from the training distribution [27]. To address this distribution shift problem, Test-time Training (TTT) has emerged as a promising paradigm that enables models to adapt dynamically during inference [28, 29, 32]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "type": "text", + "content": "Researchers have employed a self-supervised auxiliary task [8, 10, 18, 23, 34] to adapt to distribution shifts encountered during test time, from rotation prediction [34] and masked autoencoding [8] to contrastive learning [18] and normalizing flows [23]. Unlike these general methods, we propose a nuanced domain-specific self-supervised strategy that leverages echocardiogram quality variations through targeted augmentations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 412, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 555 + ], + "type": "text", + "content": "Another mainstream approach uses entropy minimization during inference, pioneered by Tent [36], which introduced adaptive updates to normalization layers through the mechanism of entropy minimization. This framework has inspired a multitude of subsequent studies [22, 33, 39-41] that enhance adaptation capabilities via various refinements to the entropy-based objective. Nevertheless, these approaches predominantly target classification tasks, presenting inherent limitations for regression problems, as regression models generate continuous numerical predictions rather than discrete probability distributions required for entropy computation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 567, + 170, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 170, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 170, + 580 + ], + "type": "text", + "content": "3. Q-PART Framework" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 161, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 161, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 161, + 598 + ], + "type": "text", + "content": "3.1. Problem Statement" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{train} = \\{(x_i, y_i)\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " denote the training dataset, where " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " represents an echocardiogram sequence with temporal frames and spatial dimensions, and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is the corresponding LVEF value. During training, we learn a regression model that maps echocardiogram sequences to LVEF values. The objective of test-time training is to adapt the model for domain-shifted test samples " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_{test} \\in \\mathcal{P}_{test}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{test} \\neq \\mathcal{P}_{train}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", using self-supervised adaptation objective that does not require ground truth labels. In TTT, the train-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "ing data are unavailable and the training pipeline cannot be modified." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 103, + 373, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 103, + 373, + 114 + ], + "spans": [ + { + "bbox": [ + 306, + 103, + 373, + 114 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": "As illustrated in Figure 2 and Figure 3, our Q-PART framework consists of a Quasi-Period Network and Variance Minimization during testing time. Given an input sequence " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": ", the encoder extracts initial features " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": ", which are decomposed into periodic components " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{z}}^{period}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": " through parameterized helix trajectory and aperiodic components " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{z}}^{aperiod}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": " captured by Neural CDEs. During training, the model is optimized with regression loss " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": " and reconstruction loss " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": ". At test time, we optimize the model through variance minimization loss " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{var}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": " and reconstruction loss " + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 305, + 121, + 545, + 277 + ], + "type": "text", + "content": " using multiple augmented views, with different learning rates for periodic and aperiodic components. Detailed information on important components is provided below." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 285, + 434, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 434, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 434, + 297 + ], + "type": "text", + "content": "3.3. Quasi-Period Network" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 302, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 410 + ], + "type": "text", + "content": "Quasi-Period Network addresses the fundamental challenge of disentangling periodic cardiac motion from patient-specific variations in echocardiogram analysis. It decomposes echocardiogram in the latent space through a nuanced architecture with physiologically-informed priors. Notably, during the test phase, this dual representation allows for adaptive optimization with different learning rates for periodic and aperiodic components, facilitating more effective model adaptation to individual cases." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": "Latent Period Encoder. The latent period encoder architecturally embeds the intrinsic periodicity of cardiac motion into the feature space. Given the initial feature representation " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": ", we employ specialized projection head " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": " to compute four fundamental components, frequency " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": ", phase shift " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": ", static offset " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": ", and velocity " + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 410, + 545, + 494 + ], + "type": "text", + "content": ". This parameterization process can be formalized as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 387, + 502, + 545, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 502, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 387, + 502, + 545, + 516 + ], + "type": "interline_equation", + "content": "\\boldsymbol {f}, \\phi , \\boldsymbol {b}, \\boldsymbol {v} = p (\\boldsymbol {z}), \\tag {1}", + "image_path": "ac8abcd741052bf4809e00e237838aed0131260e0317365ccba79face63c61bd.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "f, \\phi, b, v \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": " represents the global periodic characteristics for sequence " + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": ", maintaining " + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": " latent channels and spatial dimensions " + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": " to preserve spatial structures. To explicitly represent the periodicity, we define a parameterized helix trajectory function " + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 305, + 523, + 545, + 619 + ], + "type": "text", + "content": " in multidimensional space, motivated by the physiological nature of cardiac motion that exhibits spiral-like patterns through combined rotational and translational movements:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 625, + 545, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 625, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 332, + 625, + 545, + 654 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\boldsymbol {z}} _ {t} ^ {\\text {p e r i o d}} = g (t) = \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ \\begin{array}{l} - \\cos (2 \\pi (\\boldsymbol {f} t - \\phi)) \\\\ + \\sin (2 \\pi (\\boldsymbol {f} t - \\phi)) + \\boldsymbol {v} t + \\boldsymbol {b}. \\end{array} \\tag {2} \\\\ \\end{array}", + "image_path": "2c039a2688c193146547ad45c7128c2aefa327ef3f1ad46101e9f7223d15dc4f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{z}_t^{period} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "text", + "content": " represents the period component in time " + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "text", + "content": ". The sinusoidal terms capture the intrinsic periodicity of cardiac motion, while the linear term " + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "vt + b" + }, + { + "bbox": [ + 305, + 664, + 545, + 713 + ], + "type": "text", + "content": " accounts for long-term translational movements. This formulation" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15562" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 78, + 541, + 257 + ], + "blocks": [ + { + "bbox": [ + 52, + 78, + 541, + 257 + ], + "lines": [ + { + "bbox": [ + 52, + 78, + 541, + 257 + ], + "spans": [ + { + "bbox": [ + 52, + 78, + 541, + 257 + ], + "type": "image", + "image_path": "48c287a2ae8824cadeb6430f87a5cad0cda85081cf6ebe3393eca55787a4d2d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": "Figure 2. Overview of Q-PART Framework. The Quasi-Period Network decomposes input echocardiogram sequences into periodic and aperiodic components. The periodic component is modeled through a parameterized helix trajectory with frequency " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": ", phase shift " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": ", offset " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": ", and velocity " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": ". The aperiodic component is captured by Neural CDE. The model is jointly optimized with regression loss " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": " for LVEF prediction and reconstruction loss " + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 46, + 270, + 546, + 316 + ], + "type": "text", + "content": " for feature learning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 339, + 280, + 438 + ], + "blocks": [ + { + "bbox": [ + 53, + 339, + 280, + 438 + ], + "lines": [ + { + "bbox": [ + 53, + 339, + 280, + 438 + ], + "spans": [ + { + "bbox": [ + 53, + 339, + 280, + 438 + ], + "type": "image", + "image_path": "afd30d48078896288152220afd8dfad7aef356a45064a26ee9dc27f6a00b86ec.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "type": "text", + "content": "Figure 3. Variance Minimization during Test. we generate multiple augmented views of the test sequence through domain-specific transformations. The model adapts to each test case by minimizing prediction variance " + }, + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{var}" + }, + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "type": "text", + "content": " across augmented views and maintaining reconstruction consistency " + }, + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 46, + 448, + 287, + 515 + ], + "type": "text", + "content": " with different learning rates applied to periodic and aperiodic components." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 137, + 520, + 187, + 525 + ], + "lines": [ + { + "bbox": [ + 137, + 520, + 187, + 525 + ], + "spans": [ + { + "bbox": [ + 137, + 520, + 187, + 525 + ], + "type": "text", + "content": "(a) Discrete State Transition" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 217, + 520, + 272, + 525 + ], + "lines": [ + { + "bbox": [ + 217, + 520, + 272, + 525 + ], + "spans": [ + { + "bbox": [ + 217, + 520, + 272, + 525 + ], + "type": "text", + "content": "(b) Continuous State Transition" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 107, + 531, + 294, + 537 + ], + "lines": [ + { + "bbox": [ + 107, + 531, + 294, + 537 + ], + "spans": [ + { + "bbox": [ + 107, + 531, + 294, + 537 + ], + "type": "text", + "content": "Fig. 1. Differences between discrete state transitions and continuous state transitions" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": "creates a helix trajectory that naturally integrates both cyclic cardiac motion and progressive physiological dynamics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": "Latent Aperiodic Encoder. To capture the inherent non-periodic variations in cardiac motion, we design a latent aperiodic encoder that explicitly models these irregular components. The aperiodic features are obtained as the residual between the initial representation and the periodic component: " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "z' = z - \\hat{z}^{period}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": ". While traditional RNNs could potentially model temporal variations, Neural CDEs offer these crucial advantages for our task: 1) they naturally handle irregular representation in echocardiogram sequences, (2) they learn continuous-time dynamics from discretely sampled observations, which is better aligned with physiological processes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": "Formally, given the aperiodic component " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "z'" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": ", we first construct a continuous path " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "V(t)" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": " through natural cubic spline [20] to controlled differential equations, " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "V(t) = \\mathrm{CubicSpline}(z_t')" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "z_t'" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": " represents the aperiodic component " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "z'" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": ". The spline ensures smooth transitions between discrete observations while preserving the underlying temporal structure. The evolution of the aperiodic representation is then governed by the controlled differential equation, " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "d\\hat{z}_t^{aperiod} = f_\\theta(\\hat{z}_t^{aperiod}, t)dV(t)" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "f_\\theta" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": " is implemented as a neural network that learns the mapping between the current state and its differential elements. The final aperiodic representation at time " + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 336, + 546, + 491 + ], + "type": "text", + "content": " is obtained through integration," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 336, + 498, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 498, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 336, + 498, + 545, + 526 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {z}} _ {T} ^ {\\text {a p e r i o d}} = \\boldsymbol {z} _ {0} ^ {\\prime} + \\int_ {0} ^ {T} f _ {\\theta} \\left(\\hat {\\boldsymbol {z}} _ {t} ^ {\\text {a p e r i o d}}, t\\right) d \\boldsymbol {V} (t), \\tag {3}", + "image_path": "806ba8c67a99b82bc0010717de03feb0d1a6e55415a84cef8801a0a3e5dc3603.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "z_0'" + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": " serves as the initial condition. The neural CDE network is optimized using the CDE solver [11], which compute the gradients via the adjoint method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 569, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 640 + ], + "type": "text", + "content": "The decomposition provides a foundation for our test-time training strategy, where periodic and aperiodic components can be optimized with different learning dynamics. Empirically, we find that this architecture achieves superior performance in capturing complex cardiac motions, as demonstrated in our ablation studies §4.3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 647, + 436, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 436, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 436, + 658 + ], + "type": "text", + "content": "3.4. Variance Minimization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": "To address the domain shift challenge during testing, we propose a theoretically-grounded self-supervised strategy that combines test-time augmentation with variance minimization. Our key insight is that while echocardiographic" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15563" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": "acquisitions may vary in quality and appearance, the underlying cardiac function remains consistent across different views of the same sequence." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "text", + "content": "Domain-Specific Augmentation. For each test sequence " + }, + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{test}" + }, + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 109, + 287, + 144 + ], + "type": "text", + "content": " augmented versions through a carefully curated augmentation pipeline:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 111, + 152, + 287, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 152, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 111, + 152, + 287, + 168 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {x} _ {\\text {t e s t}} ^ {k} \\right\\} _ {k = 1} ^ {K} = \\mathcal {T} _ {\\text {a u g}} (\\boldsymbol {x} _ {\\text {t e s t}}), \\tag {4}", + "image_path": "8657b6dd709e1d9818455ea1c60c8c3f43dd4ec9520f49866ecd65457a916c8a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 176, + 287, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 287, + 307 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 176, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\text{aug}}" + }, + { + "bbox": [ + 46, + 176, + 287, + 307 + ], + "type": "text", + "content": " comprises three categories of domain-specific augmentations. Beyond conventional image augmentations, we introduce three ultrasound-specific transformations: gamma correction to simulate varying image contrast settings, speckle noise injection to mimic acoustic interference patterns, and elastic deformation to account for cardiac tissue deformation during acquisition. These domain-specific augmentations are specifically designed to simulate real-world variations in echocardiographic acquisition while preserving the underlying cardiac motion patterns essential for LVEF assessment." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 308, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 287, + 344 + ], + "type": "text", + "content": "Variance-Based Adaptation. Then, we minimizes the prediction variance across augmented samples. The variance loss " + }, + { + "bbox": [ + 47, + 308, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{var}" + }, + { + "bbox": [ + 47, + 308, + 287, + 344 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 354, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 354, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 113, + 354, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v a r} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\hat {y} _ {k} - \\bar {y}\\right) ^ {2}, \\tag {5}", + "image_path": "cafea244b772f656b6e314f272d6bbaadd9766fb85c1768b4b39f381323356bc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\hat{y}_k" + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "text", + "content": " represents the prediction for the " + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "text", + "content": "-th augmented sequence and " + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 46, + 395, + 287, + 491 + ], + "type": "text", + "content": " denotes the mean prediction across all augmentations. This formulation encourages the model to learn invariant features that are robust to acquisition-specific variations while remaining sensitive to true cardiac function changes. We provide theoretical analysis in Section 3.6 demonstrating that minimizing this variance effectively bounds the adaptation error under mild conditions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 498, + 132, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 132, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 132, + 510 + ], + "type": "text", + "content": "3.5. Optimization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 517, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 552 + ], + "type": "text", + "content": "Our optimization strategy consists of two phases: training time and testing time. The overall pipeline is summarized in Appendix Algorithm 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 553, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 588 + ], + "type": "text", + "content": "Training time. During the training phase, our model employs a multi-objective learning strategy combining regression and reconstruction objectives:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 120, + 599, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 599, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 120, + 599, + 287, + 612 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {6}", + "image_path": "5e31234efd3f08b7b54a98806fb62c561dc47067b5d5e769ff1bacff72f54379.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 621, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 621, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 621, + 287, + 657 + ], + "type": "text", + "content": "The reconstruction loss ensures that both periodic and aperiodic components collectively preserve the essential information of the input sequence." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 83, + 665, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 665, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 83, + 665, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\left\\| \\boldsymbol {x} - \\operatorname {D e c} \\left(\\hat {\\boldsymbol {z}} ^ {\\text {p e r i o d}} + \\hat {\\boldsymbol {z}} ^ {\\text {a p e r i o d}}\\right) \\right\\| _ {2} ^ {2} \\tag {7}", + "image_path": "f8c9ed6857f00eb8ecbd5b0e9e628f77f71ace114507e96d6bfb793cf2bd1cce.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Dec}(\\cdot)" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " denotes the decoder network. For LVEF prediction, we aggregate the combined latent representation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "through Global Average Pooling (GAP) followed by a Multiple Layer Perceptron (MLP), " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\mathrm{MLP}(\\hat{z}^{period} + \\hat{z}^{aperiod})" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": ". The regression loss is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 388, + 114, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 114, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 388, + 114, + 545, + 129 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} = \\| \\hat {y} - y \\| _ {2} ^ {2}, \\tag {8}", + "image_path": "0d6ee0a59cd6bdf6a726ce4a3363dcc4e4f1a2e053c4563c15d57c66f3b21f90.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 134, + 545, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 545, + 181 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 545, + 181 + ], + "type": "text", + "content": "Through this joint optimization, our model learns to decompose the echocardiogram into meaningful periodic and aperiodic representation while maintaining accurate LVEF predictions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 182, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 217 + ], + "type": "text", + "content": "Testing Time. The overall test optimization objective combines this variance minimization with reconstruction consistency" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 380, + 218, + 545, + 230 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 218, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 380, + 218, + 545, + 230 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t e s t}} = \\mathcal {L} _ {\\text {v a r}} + \\mathcal {L} _ {\\text {r e c}}. \\tag {9}", + "image_path": "cdf9d6d14803c51e77aa5c5a4b084250ebb56cfc3045d22dd937646963f3d0c1.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 234, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 390 + ], + "type": "text", + "content": "During testing time, we only update the batch normalization (BN) parameters in our network [34], which has been shown to be effective for test-time training while maintaining model stability. Given the inherent differences between periodic and aperiodic cardiac components, we employ different learning rates for their respective BN parameters. The periodic components, which capture the fundamental cardiac cycles, require more conservative updates to maintain temporal consistency. Therefore, we use a smaller learning rate for BN layers in the latent period encoder. In contrast, the aperiodic components, representing physiological variations and acquisition-specific features, benefit from more aggressive adaptation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "type": "text", + "content": "3.6. Theoretical Analysis" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 415, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 485 + ], + "type": "text", + "content": "To theoretically justify the effectiveness of our test-time training strategy, we establish the relationship between prediction variance and regression error. Our theoretical framework demonstrates how variance minimization across augmented samples inherently reduces the model's prediction error." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "type": "text", + "content": "Assumption 1 (Unbiased Augmentation) The expected prediction over augmentations equals the ground truth " + }, + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "type": "inline_equation", + "content": "LVEF" + }, + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 487, + 545, + 522 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{\\mathcal{T}_{a u q}}[\\hat{y}_k] = y" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 522, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 605 + ], + "type": "text", + "content": "This assumption is grounded in the design of our augmentation strategy " + }, + { + "bbox": [ + 304, + 522, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\text{aug}}" + }, + { + "bbox": [ + 304, + 522, + 545, + 605 + ], + "type": "text", + "content": ", which simulates acquisition-specific variations (e.g., speckle noise, gamma correction) while preserving the underlying cardiac motion patterns that determine LVEF. These perturbations affect image quality but do not alter the fundamental cardiac functional measurements." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "type": "text", + "content": "Assumption 2 (Augmentation Independence) The predictions from different augmented samples are independently distributed, with zero cross-covariance: " + }, + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{Cov}_{\\mathcal{T}_{a u g}}(\\hat{y}_k,\\hat{y}_j) = 0" + }, + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 606, + 545, + 654 + ], + "type": "inline_equation", + "content": "k\\neq j" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "This assumption reflects our augmentation design principle where each transformation introduces independent variations. The independence is achieved through combining multiple orthogonal perturbation types, ensuring minimal correlation between augmented samples." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15564" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 134, + 286, + 194 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "type": "text", + "content": "Table 1. Dataset Statistics. Demographic and clinical characteristics across age groups. The statistics show substantial differences in sample sizes (ranging from 831 to 7465), with notably fewer samples in younger age groups due to the inherent challenges in pediatric data collection." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 134, + 286, + 194 + ], + "lines": [ + { + "bbox": [ + 48, + 134, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 48, + 134, + 286, + 194 + ], + "type": "table", + "html": "
StatisticsPre-schoolSchool-ageAdolescenceAdult
#Samples8319141,5397,465
Age2 ± 19 ± 215 ± 270 ± 22
Female (%)404 (49%)371 (41%)617 (40%)3662 (49%)
LVEF (%)59.6 ± 12.862.0 ± 9.261.0 ± 9.855.8 ± 12.4
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Under Assumptions 1 and 2, the expected regression loss " + }, + { + "bbox": [ + 46, + 213, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[L_{reg}] = \\mathbb{E}[(\\hat{y} - y)^2]" + }, + { + "bbox": [ + 46, + 213, + 287, + 274 + ], + "type": "text", + "content": " is upper bounded by:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 121, + 274, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 274, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 121, + 274, + 287, + 298 + ], + "type": "interline_equation", + "content": "\\mathbb {E} [ L _ {r e g} ] \\leq \\frac {2 \\mathbb {E} [ L _ {v a r} ]}{K}, \\tag {10}", + "image_path": "9e1e597105e29eec008d1f182f8cee337ac5644c7fa28ae01873088df45641f5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 302, + 266, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 302, + 266, + 315 + ], + "spans": [ + { + "bbox": [ + 47, + 302, + 266, + 315 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 302, + 266, + 315 + ], + "type": "inline_equation", + "content": "L_{var}" + }, + { + "bbox": [ + 47, + 302, + 266, + 315 + ], + "type": "text", + "content": " is the variance loss defined in Equation 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": "The proof uses standard techniques in optimization, and is left for the Appendix A. This theoretical result provides a justification for our test-time training strategy. Minimizing the variance loss directly leads to a reduction in the expected regression error, with the bound becoming tighter as we increase the number of augmentations " + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 124, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 124, + 412 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 124, + 412 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 418, + 155, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 155, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 155, + 431 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 437, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 665 + ], + "type": "text", + "content": "Dataset and Metrics. We evaluate Q-PART using two benchmark datasets of apical-4-chamber echocardiogram videos collected from EchoNet-Dynamic [25] and EchoNet-Pediatric [31]. Following clinical standards, we stratify the data into four age cohorts: pre-school (ages 0-5), school-age (ages 6-11), adolescence (ages 12-18), and adult (ages " + }, + { + "bbox": [ + 46, + 437, + 287, + 665 + ], + "type": "inline_equation", + "content": ">18" + }, + { + "bbox": [ + 46, + 437, + 287, + 665 + ], + "type": "text", + "content": "). The detailed statistics of each cohort are summarized in Table 1. We train the model on the adult cohort and assess its performance through test-time training on pre-school, school-age, and adolescence cohorts respectively. For evaluation metrics, we adopt three widely-used metrics to comprehensively evaluate the LVEF prediction performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Moreover, we evaluate the model's clinical screening capability through mean Area Under the Receiver Operating Characteristic curve (mAUROC) analysis at multiple LVEF thresholds (35%, 40%, 45%, and 50%). More details please refer to Appendix C.1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Implementation. We adopt R3D Network [35] as the backbone encoder. The projection head contains four groups, with each group consisting of two " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " convolutional layers (" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "512 \\rightarrow 64 \\rightarrow 64" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": ") with batch normalization and ReLU" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "activation. The decoder uses five transposed convolutional layers for reconstruction. In training stage, The model is optimized using SGD with momentum 0.9 and weight decay 1e-4, with a linear warmup for the first 10 epochs followed by cosine annealing for the remaining 35 epochs. During test-time training, we employ both general augmentations (rotation, flips, grid distortion, Gaussian blur) and ultrasound-specific transformations (speckle noise, gamma correction, acoustic shadow). We apply different learning rates to periodic (1e-5) and aperiodic (1e-3) components, while maintaining a base learning rate of 1e-4 for other parameters. The value K is 8. All experiments are conducted on a single NVIDIA A100 80GB GPU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 237, + 529, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 529, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 529, + 251 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 256, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 327 + ], + "type": "text", + "content": "We comprehensively evaluate Q-PART against seven representative methods spanning three methodological categories, i.e., segmentation-based approaches, vision-language models, and end-to-end regression methods, as mentioned in §2.1. Three key findings emerge from our experiments:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 329, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 305, + 329, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 413 + ], + "type": "text", + "content": "1) Superior Performance. As shown in Table 2, our method achieves consistent improvements across all metrics and age groups, with particularly notable gains in the challenging Pre-School cohort (MAE: 7.235, MAPE: 0.1611, RMSE: 9.290). This demonstrates Q-PART's robust adaptation capability and its effectiveness in handling the unique challenges of pediatric echocardiography." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 413, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 581 + ], + "type": "text", + "content": "2) Clinical Screening Capability. Beyond regression metrics, we evaluate our model's clinical utility through ROC analysis at multiple LVEF thresholds in Figure 4. The high mAUROC scores have significant clinical implications: the enhanced sensitivity ensures reliable detection of cardiac dysfunction cases requiring immediate intervention, while the improved specificity reduces unnecessary follow-up examinations, thereby optimizing healthcare resource allocation and minimizing patient anxiety. Q-PART achieves remarkable mAUROC scores of 0.9362, 0.9747, and 0.9083 for Pre-School, School Age, and Adolescence cohorts, respectively, substantially outperforming other TTA methods. This superior performance validates the effectiveness of our echocardiogram-specific framework." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "3) Segmentation vs End-to-End Approaches. As discussed in §2.1, while lots of methods rely on left ventricular segmentation to derive LVEF values, recent end-to-end approaches directly predict LVEF. Our experimental results in Table 2 strongly support the superiority of end-to-end approaches. Despite advances in segmentation accuracy with methods like EchoNet and MemSAM, their LVEF estimation performance (MAE > 17.94) lags significantly behind end-to-end approaches (MAE < 9.114). This substantial performance gap suggests that accurate segmentation does not necessarily translate to precise LVEF estimation, as the" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15565" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 123, + 545, + 240 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 118 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 118 + ], + "type": "text", + "content": "Table 2. Comparison with State-of-the-Art Methods. We benchmark Q-PART against representative approaches spanning three methodological categories: segmentation-based methods (Seg-Based), vision-language models (VLM), and end-to-end regression approaches (E2E). Our method demonstrates superior adaptation capability and robustness across age groups, particularly in challenging scenarios with younger patients. All results are reported with four significant digits. Bold numbers indicate the best performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 123, + 545, + 240 + ], + "lines": [ + { + "bbox": [ + 49, + 123, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 49, + 123, + 545, + 240 + ], + "type": "table", + "html": "
TypeApproachPre-SchoolSchool AgeAdolescence
MAEMAPERMSEMAEMAPERMSEMAEMAPERMSE
Seg-BasedEchoNet [26] (Nature 2020)20.900.473026.1417.860.340321.9719.640.376123.90
MemSAM [6] (CVPR 2024)17.940.367521.9718.350.321621.7618.710.324922.26
VLMEchoCLIP [4] (Nature Med. 2024)11.560.203514.189.3030.160411.718.4960.152110.93
E2ESource-only9.1140.175910.868.4250.146910.038.6360.154910.53
TTT++ [18] (NeurIPS 2022)8.0530.166910.017.4300.13169.0967.6160.14169.601
Clust3 [10] (CVPR 2023)9.2920.185211.237.8920.13939.4248.2160.15099.995
NC-TTT [24] (CVPR 2024)8.3520.180010.457.2850.13258.9627.4220.14089.347
Q-PART (Ours)7.2350.16119.2906.7060.12448.4326.9800.13448.950
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ROC Analysis at Multiple Clinical Thresholds. Please zoom in for better view. Receiver Operating Characteristic (ROC) curves for LVEF regression with four clinically significant thresholds: " + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "text", + "content": " (blue), " + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "text", + "content": " (green), " + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "text", + "content": " (red), and " + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 482, + 548, + 553 + ], + "type": "text", + "content": " (cyan). These thresholds represent different degrees of cardiac dysfunction severity. The x-axis shows 1-specificity (false positive rate) and the y-axis shows sensitivity (true positive rate). The mAuroC is shown in gray box. A high mAuroC value indicates strong clinical reliability. Higher sensitivity ensures early detection of cardiac dysfunction, while higher specificity reduces unnecessary follow-up examinations and patient anxiety, collectively supporting more accurate clinical decision-making and resource allocation." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 129, + 392, + 196, + 470 + ], + "blocks": [ + { + "bbox": [ + 129, + 392, + 196, + 470 + ], + "lines": [ + { + "bbox": [ + 129, + 392, + 196, + 470 + ], + "spans": [ + { + "bbox": [ + 129, + 392, + 196, + 470 + ], + "type": "image", + "image_path": "5f2a583f2e531e436ee43b638648ab18160a87da9eb7fa90ca2b1ccc8970e0b6.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 197, + 392, + 264, + 470 + ], + "blocks": [ + { + "bbox": [ + 197, + 392, + 264, + 470 + ], + "lines": [ + { + "bbox": [ + 197, + 392, + 264, + 470 + ], + "spans": [ + { + "bbox": [ + 197, + 392, + 264, + 470 + ], + "type": "image", + "image_path": "6e7e45486e61e0535d5174b6758762f1cfbca2fe4d80ec6c5845c5189027614e.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 265, + 392, + 332, + 470 + ], + "blocks": [ + { + "bbox": [ + 265, + 392, + 332, + 470 + ], + "lines": [ + { + "bbox": [ + 265, + 392, + 332, + 470 + ], + "spans": [ + { + "bbox": [ + 265, + 392, + 332, + 470 + ], + "type": "image", + "image_path": "2fec9ac5470e1d9698b8ea4a88f3b64587ae7f465e9ab1cbdda6ed6343235674.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 334, + 392, + 400, + 470 + ], + "blocks": [ + { + "bbox": [ + 334, + 392, + 400, + 470 + ], + "lines": [ + { + "bbox": [ + 334, + 392, + 400, + 470 + ], + "spans": [ + { + "bbox": [ + 334, + 392, + 400, + 470 + ], + "type": "image", + "image_path": "4164e0b2eea17298501a591ed8815df04f07b7fb64e71d4b81d8ad36b2d7e5d6.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 402, + 392, + 469, + 470 + ], + "blocks": [ + { + "bbox": [ + 402, + 392, + 469, + 470 + ], + "lines": [ + { + "bbox": [ + 402, + 392, + 469, + 470 + ], + "spans": [ + { + "bbox": [ + 402, + 392, + 469, + 470 + ], + "type": "image", + "image_path": "ea738242af349c6b313708c628c61335e68fca17e3548ad61959b5e82c711521.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 472, + 392, + 541, + 470 + ], + "blocks": [ + { + "bbox": [ + 472, + 392, + 541, + 470 + ], + "lines": [ + { + "bbox": [ + 472, + 392, + 541, + 470 + ], + "spans": [ + { + "bbox": [ + 472, + 392, + 541, + 470 + ], + "type": "image", + "image_path": "52cf57d72f9c55958c26587be4cec0aaae291b2651d8b35bbe22bdb43b7e0a84.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 572, + 288, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 288, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 288, + 608 + ], + "type": "text", + "content": "latter requires capturing complex temporal dynamics and subtle motion patterns that may be lost in the intermediate segmentation step." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 621, + 141, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 141, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 141, + 634 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "We conduct comprehensive ablation studies to evaluate the contribution of each key component in Q-PART, i.e., Quasi-Period Network (QP-Net), Learning Rate Strategy (LR), and Variance Minimization (VM). Table 3 presents the results on the Pre-School cohort. Several observations can be drawn from the ablation results: (1) The Quasi-Period Net" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 572, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 705 + ], + "type": "text", + "content": "work alone yields substantial improvements (MAE: 7.949), demonstrating the effectiveness of disentangling periodic and aperiodic components during test-time training. (2) When combining QP-Net with VM, we observe a notable performance gain (MAE: 7.283), validating our hypothesis that variance minimization across augmented views effectively guides model adaptation. (3) The differential learning rate strategy further refines the adaptation process, with our full model achieving the best performance (MAE: 7.235). This suggests that applying different learning rates to periodic and aperiodic components helps maintain stable car" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15566" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 145, + 286, + 239 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 138 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 138 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 138 + ], + "type": "text", + "content": "Table 3. Ablation Study of Key Components. Analysis of three key components: QP-Net (Quasi-Period Network), LR (Learning Rate Strategy), and VM (Variance Minimization). We presents the results on Pre-School cohort here, which demonstrates the effectiveness of each component. Complete results across all age cohorts are presented in Appendix Table 4." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 145, + 286, + 239 + ], + "lines": [ + { + "bbox": [ + 50, + 145, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 50, + 145, + 286, + 239 + ], + "type": "table", + "html": "
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Impact of " + }, + { + "bbox": [ + 46, + 399, + 288, + 433 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 399, + 288, + 433 + ], + "type": "text", + "content": " Augmentation Number on Model Performance. The plot shows how performance varies with different numbers of augmentation number across three age cohorts." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 455, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 479 + ], + "type": "text", + "content": "diac cycle patterns while allowing flexible adaptation to patient-specific variations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 490, + 111, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 111, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 111, + 502 + ], + "type": "text", + "content": "4.4. Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": "Impact of Augmentation Number " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": ". We investigate how the number of augmented views " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": " in variance minimization affects model performance. As shown in Figure 5, larger " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": " values generally lead to better performance across all age cohorts. Notably, when " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": ", the model performs worse than the baseline without variance minimization, with MAE increasing from 7.909 to 8.036 in the Pre-School cohort. This deterioration can be attributed to the insufficient number of samples for reliable variance estimation, resulting in unstable optimization signals during test-time adaptation. While further increasing " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": " to 32 continues to yield marginal improvements, it significantly increases computational overhead during inference. Balancing performance gains against computational efficiency, we choose " + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "inline_equation", + "content": "K = 8" + }, + { + "bbox": [ + 46, + 509, + 287, + 688 + ], + "type": "text", + "content": " as our default setting for all main experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Gender-fair Performance. To assess potential gender bias, we conduct a comprehensive analysis comparing model per" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 396, + 150 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 396, + 150 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 396, + 150 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 396, + 150 + ], + "type": "image", + "image_path": "802150e0437b9fafcb327671d6ff78d9d844320adc3f518c761727027b0eca59.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 400, + 72, + 466, + 150 + ], + "blocks": [ + { + "bbox": [ + 400, + 72, + 466, + 150 + ], + "lines": [ + { + "bbox": [ + 400, + 72, + 466, + 150 + ], + "spans": [ + { + "bbox": [ + 400, + 72, + 466, + 150 + ], + "type": "image", + "image_path": "356b82242284a5a9537ca05cef4d7353b212f4711775da05030b01b307eda979.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 469, + 72, + 534, + 149 + ], + "blocks": [ + { + "bbox": [ + 469, + 72, + 534, + 149 + ], + "lines": [ + { + "bbox": [ + 469, + 72, + 534, + 149 + ], + "spans": [ + { + "bbox": [ + 469, + 72, + 534, + 149 + ], + "type": "image", + "image_path": "8ceaa2efafa0a9dcfcff946f0b6caa0d85be1f2c252c7e0fe28cfcbb9f3e7b4f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 153, + 396, + 232 + ], + "blocks": [ + { + "bbox": [ + 317, + 153, + 396, + 232 + ], + "lines": [ + { + "bbox": [ + 317, + 153, + 396, + 232 + ], + "spans": [ + { + "bbox": [ + 317, + 153, + 396, + 232 + ], + "type": "image", + "image_path": "9bb00021b608468943982f43780c2a533b8b036963e427dbd11b72999b5f5290.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 399, + 153, + 466, + 232 + ], + "blocks": [ + { + "bbox": [ + 399, + 153, + 466, + 232 + ], + "lines": [ + { + "bbox": [ + 399, + 153, + 466, + 232 + ], + "spans": [ + { + "bbox": [ + 399, + 153, + 466, + 232 + ], + "type": "image", + "image_path": "c2abf8d1978bbedffca7f69ef2c80915219374093edaacdb8ecd77a47f4718fc.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 469, + 153, + 534, + 232 + ], + "blocks": [ + { + "bbox": [ + 469, + 153, + 534, + 232 + ], + "lines": [ + { + "bbox": [ + 469, + 153, + 534, + 232 + ], + "spans": [ + { + "bbox": [ + 469, + 153, + 534, + 232 + ], + "type": "image", + "image_path": "8105cd6e5687569fbddce1a89f9c161fa2492c61eaacdeae3156dc78ee7d3162.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 233, + 396, + 311 + ], + "blocks": [ + { + "bbox": [ + 317, + 233, + 396, + 311 + ], + "lines": [ + { + "bbox": [ + 317, + 233, + 396, + 311 + ], + "spans": [ + { + "bbox": [ + 317, + 233, + 396, + 311 + ], + "type": "image", + "image_path": "d0ea52627dd1c37c80e17ae77f5420817c2cfdd2f993c95fd109d78e96d0542b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 323, + 545, + 400 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 545, + 400 + ], + "type": "text", + "content": "Figure 6. Gender Bias Analysis Across Age Cohorts. Box plots comparing model performance between male and female subjects across three age cohorts using three metrics. Each subplot shows the distribution of performance metrics for both genders, with p-values from Mann-Whitney U tests. The absence of statistically significant differences " + }, + { + "bbox": [ + 305, + 323, + 545, + 400 + ], + "type": "inline_equation", + "content": "(p > 0.05)" + }, + { + "bbox": [ + 305, + 323, + 545, + 400 + ], + "type": "text", + "content": " in eight out of nine comparisons demonstrates the model's gender-fair adaptation capability." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 400, + 233, + 466, + 311 + ], + "blocks": [ + { + "bbox": [ + 400, + 233, + 466, + 311 + ], + "lines": [ + { + "bbox": [ + 400, + 233, + 466, + 311 + ], + "spans": [ + { + "bbox": [ + 400, + 233, + 466, + 311 + ], + "type": "image", + "image_path": "9fce9c645374471c74fc40679063e126e5085efbc7108c91196a288f9a95c8ee.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 469, + 233, + 534, + 311 + ], + "blocks": [ + { + "bbox": [ + 469, + 233, + 534, + 311 + ], + "lines": [ + { + "bbox": [ + 469, + 233, + 534, + 311 + ], + "spans": [ + { + "bbox": [ + 469, + 233, + 534, + 311 + ], + "type": "image", + "image_path": "fbfe5f28495ca13d66c259ad5c4bf189a5e47e73c66ca422cb9766a2172ef708.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 420, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 540 + ], + "type": "text", + "content": "formance between male and female subjects across all age cohorts and metrics, as visualized in Figure 6. Statistical analysis reveals no significant differences " + }, + { + "bbox": [ + 304, + 420, + 545, + 540 + ], + "type": "inline_equation", + "content": "(\\mathrm{p} > 0.05" + }, + { + "bbox": [ + 304, + 420, + 545, + 540 + ], + "type": "text", + "content": " in eight out of nine comparisons) between gender groups across all evaluation metrics (MAE, MAPE, RMSE) and age cohorts. This gender-fair performance demonstrates that QPART maintains consistent reliability regardless of gender, which is crucial for ensuring equitable healthcare delivery and maintaining diagnostic consistency across diverse patient populations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We present Q-PART, a novel test-time training framework specifically designed for pediatric LVEF regression. By explicitly disentangling periodic cardiac motion from patient-specific variations through our Quasi-Period Network, and employing a theoretically-grounded variance minimization strategy, Q-PART effectively addresses the unique challenges in pediatric echocardiography. Extensive experiments demonstrate that our method significantly outperforms existing approaches across different age groups and evaluation metrics. Q-PART advances the field of automated cardiac function assessment and shows promise for improving clinical workflow in pediatric cardiology." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15567" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 144, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 144, + 85 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 144, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 163 + ], + "type": "text", + "content": "This work is supported by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), the Hong Kong Research Grants Council (Projects 21200522 and 11204821), DON-RMG 9229106 and a grant from the Institute of Digital Medicine of City University of Hong Kong." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 175, + 106, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 175, + 106, + 188 + ], + "spans": [ + { + "bbox": [ + 48, + 175, + 106, + 188 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 195, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 195, + 287, + 250 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 195, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 53, + 195, + 287, + 250 + ], + "type": "text", + "content": "[1] Luis Enrique Avendaño, Luis David Avendaño-Valencia, Edilson Delgado-Trejos, and David Cuesta-Frau. 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The primary challenge lies in effectively extracting useful information while mitigating the impact of high-frequency noise. Most existing methods rely on frame-by-frame fusion, which often struggles to distinguish informative subpixels from noise, leading to suboptimal performance. To address these limitations, we introduce a novel Query Mamba Burst Super-Resolution (QMambaBSR) network. Specifically, we observe that subpixels have consistent spatial distribution while noise appears randomly. Considering the entire burst sequence during fusion allows for more reliable extraction of consistent subpixels and better suppression of noise outliers. Based on this, a Query State Space Model (QSSM) is proposed for both inter-frame querying and intra-frame scanning, enabling a more efficient fusion of useful subpixels. Additionally, to overcome the limitations of static upsampling methods that often result in over-smoothing, we propose an Adaptive Upsampling (AdaUp) module that dynamically adjusts the upsampling kernel to suit the characteristics of different burst scenes, achieving superior detail reconstruction. Extensive experiments on four benchmark datasets—spanning both synthetic and real-world images—demonstrate that QMambaBSR outperforms existing state-of-the-art methods.", + "bbox": [ + 89, + 300, + 483, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 723, + 220, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, with the continuous development of smartphones, overcoming the limitations of smartphone sensors and lenses to reconstruct high-quality, high-resolution (HR) images has become a research hotspot. Benefited from the development of deep learning, single image superresolution (SISR) [9, 19, 33, 34, 50, 53] has achieved re", + "bbox": [ + 89, + 750, + 482, + 840 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4af320378dd6d5a44f706fe5449b96754e04c8d60ddf7b76e443de1d09a307e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 267, + 895, + 362 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99feba807c7e0c0a5dc213a889eab31927ce24fd032ba278e06f9337782d1dd1.jpg", + "image_caption": [ + "(a) Existing Methods", + "Figure 1. The concat and frame-by-frame operations in existing methods struggle to efficiently extract sub-pixels and suppress noise, leading to remaining artifacts and over-smoothed details, as shown in (a). We observe that noise randomly appears on several frames, while effective sub-pixels have consistent intensity at corresponding positions in all frames, as shown in (c). Based on this, a novel inter-frame query and intra-frame scanning-based QMambaBSR is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously, as shown in (b)." + ], + "image_footnote": [], + "bbox": [ + 517, + 375, + 895, + 520 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "markable progress, but the performance is still limited by the finite information provided by a single image. Consequently, numerous researchers are dedicating their efforts to burst super-resolution (BurstSR), which aims to leverage the rich sub-pixel details provided by a sequence of burst low-resolution images captured by hand-tremor and camera/object motions to overcome the limitations of SISR, achieving substantial advancements [7, 23, 24, 36, 43].", + "bbox": [ + 511, + 686, + 906, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In BurstSR, the first image is the super-resolution frame, denoted as the base frame, while the remaining images, referred to as current frames, supply sub-pixel information for producing a high-quality HR image. The pipeline of most existing BurstSR approaches can be mainly categorized: alignment, fusion, and upsampling. Firstly, due to", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Yang Wang and Renjing Pei are the corresponding authors. † These authors contributed equally to this work. ‡Long Peng is the project leader. This work was finished during Xin Di and Long Peng in the internship of Huawei Noah.", + "bbox": [ + 89, + 851, + 482, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23080", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the misalignment caused by hand-tremor, alignment methods [1, 11, 29, 45] are employed to align the current frames with the target base frame. Then, the primary challenge lies in extracting sub-pixel information from the current frames that match the content of the base frame while concurrently suppressing high-frequency random noise. Previous methods, such as weighted-based multi-frame fusion [1, 2], obtain residuals by subtracting each current frame from the base frame and utilizing simple weighting techniques to fuse obtained residual information. Although easy to perform, these methods neglect the inter-frame relationship among multi-frames, failing to extract sub-pixels that better match the base frame and are susceptible to interference from noise in RAW images. To enhance inter-frame relationships, BIPNet [11] proposes channel shuffling of multiframe features to improve information flow between different frames. Consequently, recent state-of-the-art methods, such as GMTNet [12, 28, 31], propose using crossattention, explicitly employing the base frame as a query to retrieve and capture feature differences from the current frame pixel-to-pixel to extract sub-pixel information. RBSR [46] utilize RNNs [25] for frame-by-frame feature fusion, as shown in Figure 1 (a). The aforementioned methods extract sub-pixel information and denoise in a frame-by-frame manner or implement sub-pixel extraction and denoising through separate modules. However, these methods overlook the distinct characteristics between sub-pixels and noise, making it challenging to capture useful sub-pixels from noise and leading to artifacts and over-smoothed details.", + "bbox": [ + 93, + 90, + 480, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After fusion, adaptively learning high-resolution mappings from the extracted and fused features remains a paramount challenge in BurstSR. The existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], primarily utilize static interpolation, transposed convolution [14], or pixel shuffle [38] for static upsampling. Nevertheless, these approaches make it difficult to adaptively perceive the variations in sub-pixel distribution across different scenes by employing static upsampling methods, resulting in the inability to utilize the spatial arrangement of sub-pixels to accurately reconstruct high-quality, high-resolution (HR) images.", + "bbox": [ + 93, + 549, + 480, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we propose a novel Query Mamba Burst Super-Resolution (QMambaBSR) network, which integrates a novel Query State Space Model (QSSM) and an Adaptive Up-sampling module (AdaUp) to reconstruct high-quality high-resolution images from burst lowresolution images. Specifically, QSSM is first proposed to efficiently extract the sub-pixels in both inter-frame and intra-frame while mitigating noise interference. In particular, QSSM retrieves information across current frames for the base frame by modifying control matrix $B$ and discretization step size $\\Delta$ in the state space function, as shown", + "bbox": [ + 93, + 734, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in Figure 1 (b). QSSM synchronously performs inter-frame querying and intra-frame scanning, comprehensively considering both inter-frame and intra-frame information to achieve integrated sub-pixel extraction and noise suppression. AdaUp is proposed to perceive the spatial distribution of sub-pixel information and subsequently adaptively adjust the upsampling kernel to enhance the reconstruction of high-quality HR images across diverse burst LR scenarios. Furthermore, to comprehensively fuse sub-pixels with different scales, the Multi-scale Fusion Module is proposed to combine channel Transformer and local CNN, as well as horizontal and vertical global Mamba, to fuse sub-pixel information of different scales. Extensive experiments on four popular synthetic and real-world benchmarks demonstrate that our method achieves a new state-of-the-art, delivering superior visual results.", + "bbox": [ + 516, + 90, + 903, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions can be summarized as follows:", + "bbox": [ + 532, + 333, + 856, + 345 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel inter-frame query and intra-frame scanning-based Query State Space Model (QSSM) is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously.", + "- We propose a novel Adaptive Up-sampling module, designed respectively for adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst LR scenarios, and for the fusion of sub-pixels across different scales.", + "- Our proposed method achieves new state-of-the-art (SOTA) performance on the four popular public synthetic and real benchmarks, demonstrating the superiority and practicability of our method." + ], + "bbox": [ + 513, + 348, + 903, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 516, + 558, + 653, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review Multi-Frame SuperResolution and State Space Models. More comprehensive surveys are provided in [3, 48].", + "bbox": [ + 516, + 584, + 903, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-Frame Super-Resolution. With the rapid development of deep learning in recent years [15, 18, 26, 41], deep-learning-based single image super-resolution (SISR) achieves significant breakthroughs [6, 47, 49, 51]. However, due to the limited information provided by a single image, the performance of SISR is significantly constrained [27, 39, 42, 52]. Therefore, Multi-Frame Super-Resolution (MFSR) is proposed to overcome the limitations of SISR by leveraging the useful sub-pixel information contained in multiple low-resolution images, achieving superior high-resolution reconstruction. In particular, DBSR [1] proposes using optical flow methods to explicitly align multiple low-resolution images and then fuse their features through attention weights. MFIR [2] utilizes optical flow for feature warping and proposes a deep reparametrization of the classical MAP formulation for multi-frame image restoration. BIPNet [11] proposes a pseudo-burst fusion strategy by fusing temporal features channel-by-channel,", + "bbox": [ + 516, + 628, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23081", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "enabling frequent inter-frame interaction. Burstormer [12] leverages multi-scale local and non-local features for alignment and employs neighborhood interaction for further inter-frame feature fusion. RBSR [46] utilizes recurrent neural networks for progressive feature aggregation. However, most of these methods mainly use frame-by-frame approaches or pairwise interactions, either failing to explicitly extract sub-pixel information from the current frames or only querying the current frame point-by-point from the base frame. This makes it difficult for them to effectively extract sub-pixel details while suppressing noise interference. To address these limitations, we propose Query Mamba Burst Super-Resolution (QMambaBSR), which allows the base frame to simultaneously query inter-frame and intra-frame information to extract sub-pixel details embedded in structured regions while also suppressing noise interference.", + "bbox": [ + 89, + 90, + 480, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "State Space Models. State Space Models (SSMs) originated in the 1960s in control systems [20], where they are used for modeling continuous signal input systems. Recently, advancements in SSMs have led to their application in computer vision [5, 13, 32, 56]. Notably, Visual Mamba introduced a residual VSS module and developed four scanning directions for visual images, achieving superior performance compared to ViT [10] while maintaining lower model complexity, thereby attracting significant attention [16, 22, 35, 40, 44, 54]. QueryMamba [55] is proposed to apply SSM to video action forecasting tasks. MambaIR [16] is the first to employ SSMs in image restoration, enhancing efficiency and global perceptual capabilities. However, there remains potential for further exploration of SSMs in BurstSR. Therefore, we propose a novel Query-based State Space Model designed to efficiently extract sub-pixel information for BurstSR.", + "bbox": [ + 89, + 348, + 482, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 623, + 181, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 89, + 648, + 200, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a sequence of input low-resolution (LR) images, denoted as $\\{x_{i}\\}_{i = 1}^{N}$ , where $N$ represents the number of burst LR frames. Following [1], we denote the first image as the base frame for super-resolution, while the other LR frames are used to provide rich sub-pixel information and are referred to as current frames. BurstSR can be defined as utilizing the sub-pixel information extracted from the current frames to supplement the base frame, generating a high-quality, high-resolution RGB image $I_{HR}$ with a superresolution factor of $s$ .", + "bbox": [ + 89, + 672, + 482, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve this goal, we propose QMambaBSR for burst image super-resolution, as illustrated in Figure 2. First, we use alignment block [12] to align the current images to the spatial position of the base frame. Next, we introduce a novel Query State Space Model (QSSM) designed to query", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sub-pixel information from the current images and mitigate noise interference in both inter-frame and intra-frame manner. Additionally, we present a novel Adaptive Up-sampling (AdaUp) module, which facilitates adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst images. Finally, a new Multi-scale Fusion Module is incorporated to fuse sub-pixel information across different scales. Next, we provide a detailed explanation of each component.", + "bbox": [ + 511, + 90, + 906, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Query State Space Model", + "text_level": 1, + "bbox": [ + 511, + 238, + 745, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considering that burst RAW images often contain high-frequency random noise and the sub-pixel information to be extracted typically shares a similar distribution with the base frame, it is crucial for the BurstSR task to utilize the base frame to uncover the rich sub-pixel information contained in the current frames for super-resolution, while simultaneously suppressing noise. Existing methods [1, 11, 12, 45, 46] simply concatenate multi-frame information but fail to precisely extract sub-pixel information from the current frames using the base frame, resulting in a scarcity of sub-pixel details and consequently making it difficult to reconstruct fine details. Moreover, while some existing approaches attempt to use cross-attention [31], utilizing the base frame as the query for sub-pixels extraction, such frame-by-frame methods struggle to suppress noise interference and are plagued by high computational complexity. This often results in the presence of noise and the introduction of artifacts. Therefore, we propose the Query State Space Model (QSSM), which enables the base frame to efficiently query all current frames simultaneously in both intra-frame and inter-frame manners. By leveraging the consistent distribution of sub-pixels and the inconsistent distribution of noise, our QSSM can simultaneously query multiple images to extract the necessary sub-pixel information while effectively suppressing random noise.", + "bbox": [ + 511, + 261, + 906, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, let's briefly review the State Space Model (SSM). The latest advances in structured state space sequence models (S4) are largely inspired by continuous linear time-invariant (LTI) systems, which map input $x(t)$ to output $y(t)$ through an implicit latent state $h(t) \\in \\mathbb{R}^N$ [16]. This system can be represented as a linear ordinary differential equation (ODE):", + "bbox": [ + 511, + 638, + 906, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\dot {h} (t) = A h (t) + B x (t), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 758, + 903, + 782 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny (t) = C h (t) + D x (t),\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 779, + 790, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $N$ is the state size, $A \\in \\mathbb{R}^{N \\times N}$ , $B \\in \\mathbb{R}^{N \\times 1}$ , $C \\in \\mathbb{R}^{1 \\times N}$ , and $D \\in \\mathbb{R}$ . Discretized using a zero-order hold as follows:", + "bbox": [ + 511, + 806, + 906, + 853 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {A} = \\exp (\\Delta A), \\\\ - \\end{array} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 864, + 903, + 890 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{B}} = (\\Delta A) ^ {- 1} (\\exp (\\Delta A) - I) \\Delta B,\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 887, + 825, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23082", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e60171a60c6c90a522cea2c63295c4ab321aff8eec7b846d02a6b150dba9431c.jpg", + "image_caption": [ + "Figure 2. The overall framework of our proposed QMambaBSR, primarily includes the novel Query State Space Model (QSSM), Multiscale Fusion Module (MSFM), and the Adaptive Up-sampling Module (AdaUp)." + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 906, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the discretization, the discretized version of Eq. (1) with step size $\\Delta$ can be rewritten as:", + "bbox": [ + 89, + 462, + 482, + 493 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {k} = \\bar {A} h _ {k - 1} + \\bar {B} x _ {k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 501, + 480, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {k} = C h _ {k} + D x _ {k},\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 522, + 343, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At this point, the LTI system's input parameter matrices are static. Therefore, recent work [16] makes $B$ , $C$ , and $\\Delta$ depend on the input. Recent research suggests that since the $A$ matrix is a HIPPO matrix and $\\Delta$ represents the step size, $\\exp(\\Delta A)$ can be viewed as forget gate and input gate [17], which modulates the influence of the input on the state.", + "bbox": [ + 89, + 547, + 482, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, traditional SSM lacks the multi-frame querying capabilities that are crucial for BurstSR tasks. Therefore, we propose a QSSM to enable the base frame to gate the output of the current frames, thereby allowing the base frame to perform information queries on the current frames to obtain the sub-pixels while eliminating noise, as illustrated in Figure 1. Specifically, we let the current frames drive the state changes, with the base frame gating the influence of the current frames on the state through $B$ and $\\Delta$ . As shown in Figure 2 (a), the corresponding formulas are as follows:", + "bbox": [ + 89, + 638, + 482, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\left(\\bar {A} _ {\\text {b a s e} _ {t}}\\right) h _ {t - 1} + \\left(\\bar {B} _ {\\text {b a s e} _ {t}}\\right) x _ {\\text {c u r} _ {t}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 809, + 480, + 834 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {t} = C h _ {t} + D x _ {\\mathrm {c u r} _ {t}},\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 830, + 308, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering that noise may exist at certain locations in the base frame and is randomly distributed at the same locations in other current frames, we concatenate the base", + "bbox": [ + 89, + 854, + 482, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "frame with other current frames to initially reduce random noise in the original base frame and achieve preliminary feature fusion. Specifically, the concatenated features are processed by an MLP layer and finally projected back to the channel dimension of the original base frame, using it as the new base frame. Then the base frame is transformed through a learnable linear layer to generate $\\Delta_{\\mathrm{base}_t}$ and $B_{\\mathrm{base}_t}$ , and these are then used in the discretization formula from Eq. (2) to obtain $\\overline{A}_{\\mathrm{base}_t}$ and $\\overline{B}_{\\mathrm{base}_t}$ . The current frames are processed through another linear layer to obtain $x_{\\mathrm{cur}_t}$ , where $t$ indicates the positional relationship after flattening the base frame and current frames.", + "bbox": [ + 511, + 462, + 906, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Utilizing Eq. (2), the zero-order hold and discretization can be expanded as follows:", + "bbox": [ + 511, + 643, + 905, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 678, + 906, + 724 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} y _ {t} = C \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}} \\tag {6} \\\\ + D x _ {\\mathrm {c u r} _ {2}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 729, + 905, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{f}$ represents the functions of $\\Delta$ and $B$ corresponding to the zero-order hold of $B$ , as follows:", + "bbox": [ + 511, + 796, + 905, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {t}}\\right) = \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) ^ {- 1} \\left(\\exp \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) - I\\right) \\Delta_ {\\text {b a s e} _ {t}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 832, + 903, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, in the State Space Model, the input $x_{t}$ at time $t$ is influenced by the control matrix $B$ , which in turn affects the change in state $h$ . In the discretized state space,", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23083", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/996149ebb5329f6b0eb7dd933df3d6bcdc878a5c8980b82be96deba3cf6d4be1.jpg", + "image_caption": [ + "Figure 3. Illustrative comparison between the proposed QSSM and existing cross-attention mechanisms." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 480, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the discretization step size $\\Delta$ represents the time $x_{t}$ acts on the state. In QSSM, we desire the base frame to act as a gate controlling the influence of the current frames on the state, thereby affecting the output. Thus, we generate $\\mathrm{base}_t$ and $\\Delta$ by the base frame through a linear layer. To exploit the differences in sub-pixels and noise distribution characteristics across multiple frames, we merge current features into the channel dim. Subsequently, all current features are projected into a unified set of merged current features through a linear layer. This allows the base feature to query all current features at once, thereby achieving multi-frame joint denoising. Additionally, as Eq. (5) and (6), when the flattened base feature $f_{\\mathrm{base}_t}$ queries the current features at other times $f_{\\mathrm{cur}_j}$ , $f_{\\mathrm{base}_t}$ modulates and guides $f_{\\mathrm{base}_j}$ to query $f_{\\mathrm{cur}_j}$ through the forget gate and input gate $\\exp (\\Delta_{\\mathrm{base}_t}A)$ , ultimately feeding back to the output at time $t$ . This enhances the interaction between $f_{\\mathrm{base}_t}$ and its neighboring base features as well as current features. Due to the characteristics of the matrix $A$ , the influence of $f_{\\mathrm{base}_t}$ in guiding the query of $f_{\\mathrm{base}_j}$ gradually decreases with their distance in the sequence, forming a progressively diminishing receptive field. This prevents $f_{\\mathrm{base}_t}$ from overly focusing on spatially distant information, thereby enhancing neighborhood interactions. Since each query by the base feature simultaneously queries all current features, the base feature can better perceive sub-pixel information consistently distributed across frames, suppressing random noise. We modify the RSSB block [16] by integrating our proposed QSSM with four scanning directions and using channel attention to enhance channel interaction.", + "bbox": [ + 91, + 311, + 483, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Discussion To clarify the differences between the proposed QSSM and existing cross-attention methods, we conduct a detailed analysis along with a schematic comparison. As shown in Figure 3 (a), the cross-attention method uses serialized base feature tokens at position $t$ as the $\\mathrm{Q}$ matrix, querying with all position tokens of the current features as the $\\mathrm{K}$ matrix to extract sub-pixel information. In contrast, our QSSM, as shown in Figure 3 (b), not only extracts sub-pixel information from the current features to the base fea", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ture but also facilitates information interaction within the base feature. It simultaneously retrieves corresponding current feature tokens from other position tokens in the serialized base feature, thereby achieving joint multi-position sub-pixel information retrieval and noise suppression between the base feature and current features.", + "bbox": [ + 511, + 90, + 905, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Multi-Scale Fusion Module", + "text_level": 1, + "bbox": [ + 511, + 190, + 759, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering the presence of sub-pixel information across various scales within the intricate details of images, we propose a novel Multi-scale Fusion Module (MSFM). This module is designed to effectively integrate multi-scale subpixel information from the current frames, thereby enhancing the capability for detailed image reconstruction. The MSFM comprises three distinct branches: a Convolutional Neural Network (CNN), a State Space Model (SSM) with diverse scanning orientations, and a channel Transformer. To begin with, a $3 \\times 3$ convolution is utilized for the fusion of local sub-pixel features. The SSM is introduced to efficiently learn and integrate sub-pixel features along both horizontal and vertical axes. Furthermore, considering the attenuation characteristics of the A matrix within the SSM when dealing with long-range perception, we concurrently employ a Transformer block to augment the network's proficiency in capturing global information. The mathematical formulation of the MSFM is as follows:", + "bbox": [ + 511, + 212, + 906, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny = w _ {1} \\cdot \\operatorname {C N N} (x) + w _ {2} \\cdot \\operatorname {S S M} (x) + w _ {3} \\cdot \\operatorname {T r a n s f o r m e r} (x) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 494, + 906, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{i}$ represents the balancing factors. $x$ and $y$ represent the input feature and output feature, respectively.", + "bbox": [ + 511, + 522, + 906, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Adaptive Up-sampling Module", + "text_level": 1, + "bbox": [ + 511, + 561, + 785, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the aforementioned processes, the sub-pixel structural information from burst LR images is extracted and distributed in the feature space. The next critical challenge is to utilize this valuable sub-pixel information to adaptively upsample the image resolution and incorporate sub-pixel details into the high-resolution image. Existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], simply employ interpolation, transposed convolution, or pixel shuffle techniques for resolution upsampling. However, these methods lack the capability to perceive the distribution of sub-pixels in the feature space, leading to an inability to adaptively reconstruct fine details. Therefore, we introduce a novel Adaptive Up-sampling (AdaUp) module that perceives the distribution of sub-pixels in the spatial domain and adaptively adjusts the up-sampling kernel, thereby achieving higher-quality image detail, as shown in Figure 2 (b). Specifically, we first adaptively perceive the distribution of sub-pixels $L \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times 1 \\times 1}$ from the input features $X \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times H \\times W}$ by adaptive pooling. We then perform sequence feature interaction on $L$ to obtain the output channel feature distribution sequence $L_1 \\in \\mathbb{R}^{B \\times C_{\\mathrm{out}} \\times 1 \\times 1}$ . Sub", + "bbox": [ + 511, + 583, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23084", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sequentially, we apply both the input distribution sequence and the output distribution sequence to the upsampling transposed convolution kernel $W \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times C_{\\mathrm{out}} \\times 3 \\times 3}$ using broadcasting, thereby endowing the kernel with feature perception capability. Finally, we obtain the high-resolution output through the upsampling transposed convolution kernel. The corresponding formulas are as follows:", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = \\text {A d a p t i v e P o o l i n g} (X) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 203, + 482, + 219 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {1} = \\operatorname {C o n v} _ {1 \\times 1} (L) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 224, + 480, + 241 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nW _ {f} = (W \\odot L) \\odot L _ {1} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 244, + 482, + 261 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ny = \\operatorname {T r a n s - C o n v} \\left(W _ {f}, X\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 263, + 482, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\odot$ represents element-wise multiplication. Thus, AdaUp can leverage the underlying content information from input frames at different channels and utilize it to get better performance than the mainstream up-sampling operations, pixel shuffle, or interpolations [4, 37].", + "bbox": [ + 89, + 284, + 483, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments and Analysis", + "text_level": 1, + "bbox": [ + 89, + 369, + 334, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 89, + 395, + 297, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We evaluate the effectiveness of our proposed method on four public burst image superresolution benchmarks, encompassing both synthetic and real datasets: synthetic BurstSR [1], Real BurstSR [1], RealBSR-RAW [45], and RealBSR-RGB [45]. To ensure fairness, we follow [12] for training and evaluation. More details of datasets and data processing can be found in Appendix A section. Following [12], we train the model from scratch on the synthetic BurstSR dataset for 300 epochs, using the AdamW optimizer with parameters $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999$ . We employ a cosine annealing strategy to gradually decrease the learning rate from $3\\times 10^{-4}$ to $10^{-6}$ and set the training patch size to $48\\times 48$ . For the Real BurstSR dataset, we follow [1] to fine-tune the model pretrained on synthetic BurstSR for 60 epochs, maintaining the same training setting as the synthetic BurstSR but adjusting the learning rate to $1\\times 10^{-6}$ and the training patch size to $56\\times 56$ . For the RealBSR-RAW and RealBSR-RGB datasets, we follow [45] to train from scratch for 100 epochs, using the same training setting as the synthetic BurstSR, with a training patch size of $80\\times 80$ . We set the batch size to 8, and the burst size to 14, and all experiments are conducted on 8 V100 GPUs.", + "bbox": [ + 89, + 417, + 483, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric. Following previous works [1, 45], we use reference metrics to evaluate performance, including PSNR and SSIM.", + "bbox": [ + 89, + 763, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. To comprehensively demonstrate the superiority of our proposed method, we compare our QMambaBSR with ten classic and state-of-the-art (SOTA) BurstSR approaches HighRes-net [8], DBSR [1], LKR [21], MFIR [2], BIPNet [11], AFCNet [30], FBAnet [45], Burstormer [12], RBSR [46], GMTNet [31].", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative and Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 90, + 830, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on the Synthetic BurstSR dataset. As shown in Table 1, our method outperforms existing BurstSR methods, achieving the best performance. For example, compared to the existing SOTA method, Burstormer, our method achieves a $0.29\\mathrm{dB}$ improvement in PSNR. Furthermore, to further demonstrate the visual superiority of our method, we present a visual comparison with existing methods in Figure 4. We can observe that the RAW low-resolution images exhibit significant noise and severe detail loss, as illustrated in the window area of Figure 4. Compared to existing methods, our method demonstrates superior performance in reconstructing textures and details in the window area. Additionally, in the green stripes region at the bottom of Figure 4, the substantial noise in the base frame leads existing methods to leave artifacts. However, our method more effectively distinguishes between noise and sub-pixels, producing more detailed, artifact-free high-resolution images, thereby demonstrating the visual superiority of our method.", + "bbox": [ + 511, + 112, + 903, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on RealBSR-RGB and RealBSR-RAW. As shown in Table 2, our method consistently outperforms existing methods on these two real benchmarks, achieving the best performance. For RealBSR-RAW, our method surpasses FBANet and Burstormer in PSNR and linear-PSNR by $0.268\\mathrm{dB}$ and $0.258\\mathrm{dB}$ , respectively. For RealBSR-RGB, our method surpasses FBANet and Burstormer in PSNR by $0.204\\mathrm{dB}$ . Furthermore, as shown in Figure 5, the results demonstrate the superior performance of our method in detail reconstruction and artifact suppression. This validates the effectiveness of our method in real-world scenarios, highlighting its superiority and practicality. More results on Real BurstSR and qualitative results will be presented in the appendix.", + "bbox": [ + 511, + 385, + 905, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 606, + 666, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness and superiority of the proposed modules, we conduct a series of ablation experiments. Specifically, we incrementally integrate the proposed modules into the baseline network. For rapid evaluation, we train our model on the synthetic dataset for 100 epochs. From Table 3, we observe that the introduction of the MSFM module, which enhances the network's multiscale perception and fully integrates sub-pixel information from different frames, significantly improves performance by 1.34 dB in PSNR. Furthermore, the addition of the QSSM, which extracts sub-pixels from the current frames that match the content of the base frame while suppressing noise, leads to an additional performance gain of 0.72 dB in PSNR. Finally, incorporating the proposed Adaptive Up-sampling module, which better adapts the up-sampling kernel according to the scene, thereby generating high-resolution images with richer details, results in a further improvement of 0.26 dB. These results indicate that the pro", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23085", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4c2387762618e17b5576c5f5b4a51915d16725cd0e462c9cf5f1b998a585fb50.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BicubicHighRes-netDBSRLKRMFIRBIPNetAFCNetFBAnetGMTNetRBSRBurstormerOurs
PSNR↑36.1737.4540.7641.4541.5641.9342.2142.2342.3642.4442.8343.12
SSIM↑0.910.920.960.950.960.960.960.970.960.970.970.97
", + "bbox": [ + 96, + 89, + 903, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c720215ff483f423f83b6f1cfb8696a6e1dcbd1f4d2d5a83ae8d97309fa0ce21.jpg", + "image_caption": [ + "Figure 4. Visual comparison results with different methods on SyntheticBurst datasets for $\\times 4$ BurstSR." + ], + "image_footnote": [], + "bbox": [ + 91, + 185, + 903, + 440 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5bae37df9159f006147c8ca3fe020e4ea40ddf2f704755bbac47720cc4a4ff1f.jpg", + "table_caption": [ + "Table 1. Performance comparison of existing methods on Synthetic BurstSR dataset for $\\times 4$ BurstSR." + ], + "table_footnote": [], + "table_body": "
MethodRealBSR-RAWRealBSR-RGB
PSNR↑SSIM↑L-PSNR↑PSNR↑SSIM↑
DBSR20.9060.63530.48430.7150.899
MFIR21.5620.63830.97930.8950.899
BSRT22.5790.62230.82930.7820.900
BIPNet22.8960.64131.31130.6550.892
FBANet23.4230.67732.25631.0120.898
Burstormer27.2900.81632.53331.1970.907
Ours27.5580.82032.79131.4010.908
", + "bbox": [ + 96, + 489, + 475, + 656 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "posed modules significantly enhance burst super-resolution performance.", + "bbox": [ + 89, + 729, + 482, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Existing Modules. To verify the effectiveness of proposed module, we replaced it with existing fusion and up-sampling modules. To effectively represent the performance of various methods while also considering training time, we train for 100 epochs on the synthetic dataset. As shown in Table 4, in the fusion stage, compared to PBFF [11] or NRFE [12], our QSSM and MSFM modules are able to better exploit the inter-frame consistency of sub-pixel distribution while denoising, resulting in", + "bbox": [ + 88, + 763, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d7d370e4aeb6de60a36e90bc4085af564a5ef2fdb381fd62abb4f66dc3ec1c36.jpg", + "table_caption": [ + "Table 2. Performance comparison of existing methods on RealBSR-RGB and RealBSR-RAW datasets for $\\times 4$ BurstSR." + ], + "table_footnote": [], + "table_body": "
QSSMMSFMAdaUpPSNR↑SSIM↑
×××39.810.93
×✓×41.150.94
✓✓×41.870.96
✓✓✓42.130.96
", + "bbox": [ + 516, + 489, + 898, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation experiment on proposed core modules.", + "bbox": [ + 537, + 592, + 877, + 607 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PSNR improvements of 1.56 dB and 0.41 dB, respectively. In contrast to static upsampling like pixel shuffle and transposed convolution, our AdaUp module enhances the network's ability to perceive scene-specific sub-pixel distributions, leading to a PSNR improvement of 0.16 dB.", + "bbox": [ + 511, + 640, + 903, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation about MSFM. To validate the effectiveness of different branches within the proposed MSFM, we conducted ablation experiments with various internal branch setting. The experimental results are shown in Table 5. To minimize training time while ensuring experimental validity, the ablation experiments were conducted on a synthetic dataset and trained for 100 epochs. As shown in the table, we use only the convolution in the MSFM module as the baseline. Adding the transformer module resulted in a PSNR increase of $0.39\\mathrm{dB}$ . When the transformer was replaced with SSM, the PSNR improved by $0.44\\mathrm{dB}$ compared to using only the conv method. Under our proposed", + "bbox": [ + 511, + 719, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23086", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36f9b19c16b2751da3bb40f93c3c978ca13499ba0378649f71e4db3bd1c41093.jpg", + "image_caption": [ + "Base frame" + ], + "image_footnote": [], + "bbox": [ + 93, + 87, + 207, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/276f9e2792f69034366bc192f024dca131030e0668b65e728e75d321cca21607.jpg", + "image_caption": [ + "DBSR" + ], + "image_footnote": [], + "bbox": [ + 210, + 87, + 323, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ce575c281f01f9328fd39050b8526fb19975bdab7ee9dd113b4c34aa0a3d8b9.jpg", + "image_caption": [ + "MFIR" + ], + "image_footnote": [], + "bbox": [ + 326, + 87, + 439, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a2ef664901149353271a234b44b9f7858855663725fbf7c332a40e774985cd2.jpg", + "image_caption": [ + "BIPNet" + ], + "image_footnote": [], + "bbox": [ + 441, + 87, + 555, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2a238e248bf82d6736b0a3f0cfc3e9648eb675b64ccd0eb2490a124891656d6.jpg", + "image_caption": [ + "Burstomer" + ], + "image_footnote": [], + "bbox": [ + 557, + 87, + 671, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7f66e730c5bd8c2c0b7c549da4aceee9477d29fa0418321004d56ecd555f325b.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 674, + 87, + 789, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa62d775277509aa33a491bff134ba30340b7eb6d729f15fbb263dc6dbc7df80.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 790, + 87, + 905, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/88240037ed5f132da88424335868ec71de1b314d3dce160234ba13e5790c0566.jpg", + "image_caption": [ + "Figure 5. Visual comparison results with different methods on RealBSR-RGB dataset for $\\times 4$ BurstSR.", + "Figure 6. User study of reconstructed real HR images." + ], + "image_footnote": [], + "bbox": [ + 93, + 279, + 478, + 460 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9769796b5fbbe8bb79fcefdb2b9991d1ebf6102fd94fdbf1f321687c031ca37f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Process StageMethodsPSNR↑SSIM↑
FusionConcat39.850.93
PBFF [11]40.570.94
NRFE [12]41.720.96
Ours42.130.96
Up-samplerPixelshuffle41.890.96
Transposed conv41.970.96
Ours42.130.96
", + "bbox": [ + 93, + 500, + 478, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MSFM, the PSNR increased by 0.56 dB, clearly demonstrating the effectiveness of both the SSM and transformer branches in the MSFM.", + "bbox": [ + 89, + 696, + 483, + 743 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. User study", + "text_level": 1, + "bbox": [ + 89, + 756, + 210, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To effectively illustrate the superiority of our proposed method in reconstructing visually pleasing images, we conducted a user study involving 10 real burst images selected from well-established benchmarks. Twenty volunteers participated in this study, tasked with rating the similarity and quality between each reconstructed image and the ground truth (GT). They used a detailed scale ranging from 0, indicating visually unsatisfactory and completely dissimilar", + "bbox": [ + 89, + 779, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d8ade884c675a118f55b3f3bcaed7ed05ce50c40e10797df848225ca67a44fb9.jpg", + "table_caption": [ + "Table 4. Comparison with existing modules on fusion and upsampling process stage." + ], + "table_footnote": [], + "table_body": "
ConvTransformerSSMPSNR↑SSIM↑
✓××41.570.95
✓✓×41.960.96
✓×✓42.010.96
✓✓✓42.130.96
", + "bbox": [ + 527, + 277, + 888, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation studies on our proposed MSFM.", + "bbox": [ + 557, + 381, + 859, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "images, to 10, representing visually satisfactory and highly similar images. We then meticulously aggregated the scores from all volunteers, and the results are depicted in Figure 6. When compared to existing methods such as Burstormer and BIPNet, our proposed method stands out by adaptively extracting sub-pixels to achieve superior visual effects. This approach earned our method the highest average score of 8.56, underscoring its effectiveness.", + "bbox": [ + 511, + 412, + 906, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 553, + 633, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a novel approach called QMambaBSR for burst image super-resolution. Based on the structural consistency of sub-pixels and the inconsistency of random noise, we propose a novel Query State Space Model to efficiently query sub-pixel information embedded in current frames through an intra- and inter-frame multi-frame joint query approach while suppressing noise interference. We introduce a Multi-scale Fusion Module for information on sub-pixels across different scales. Additionally, a novel Adaptive Up-sampling module is proposed to perceive the spatial arrangement of sub-pixel information in various burst scenarios for adaptive up-sampling and detail reconstruction. Extensive experiments on four public synthetic and real benchmarks demonstrate that our method surpasses existing methods, achieving state-of-the-art performance while presenting the best visual quality.", + "bbox": [ + 511, + 580, + 906, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 511, + 843, + 692, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the Natural Science Foundation of China under Grants 62225207,62436008 and 62206262.", + "bbox": [ + 511, + 869, + 905, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23087", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Goutam Bhat, Martin Danelljan, Luc Van Gool, and Radu Timofte. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1874-1883, 2016. 2" + ], + "bbox": [ + 91, + 90, + 480, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[39] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. 2", + "[40] Yujin Tang, Peijie Dong, Zhenheng Tang, Xiaowen Chu, and Junwei Liang. Vmrnn: Integrating vision mamba and lstm for efficient and accurate spatiotemporal forecasting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5663-5673, 2024. 3", + "[41] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017. 2", + "[42] Jianyi Wang, Zongsheng Yue, Shangchen Zhou, Kelvin CK Chan, and Chen Change Loy. 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Rbsr: Efficient and flexible recurrent network for burst super-resolution. In Chinese Conference on Pattern Recognition and Computer Vision (PRCV), pages 65-78. Springer, 2023. 2, 3, 6", + "[47] Rongyuan Wu, Tao Yang, Lingchen Sun, Zhengqiang Zhang, Shuai Li, and Lei Zhang. Seesr: Towards semantics-aware real-world image super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 25456-25467, 2024. 2", + "[48] Rui Xu, Shu Yang, Yihui Wang, Bo Du, and Hao Chen. A survey on vision mamba: Models, applications and challenges. arXiv preprint arXiv:2404.18861, 2024. 2", + "[49] Fuzhi Yang, Huan Yang, Jianlong Fu, Hongtao Lu, and Baining Guo. Learning texture transformer network for image super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5791-5800, 2020. 2", + "[50] Jianchao Yang, John Wright, Thomas S Huang, and Yi Ma. Image super-resolution via sparse representation. IEEE transactions on image processing, 19(11):2861-2873, 2010. 1", + "[51] Zongsheng Yue, Jianyi Wang, and Chen Change Loy. Reshift: Efficient diffusion model for image superresolution by residual shifting. Advances in Neural Information Processing Systems, 36, 2024. 2", + "[52] Kai Zhang, Luc Van Gool, and Radu Timofte. Deep unfolding network for image super-resolution. In Proceedings of" + ], + "bbox": [ + 516, + 92, + 906, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23089", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "the IEEE/CVF conference on computer vision and pattern recognition, pages 3217-3226, 2020. 2", + "[53] Yulun Zhang, Yapeng Tian, Yu Kong, Bineng Zhong, and Yun Fu. Residual dense network for image super-resolution. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2472-2481, 2018. 1", + "[54] Zou Zhen, Yu Hu, and Zhao Feng. Freqmamba: Viewing mamba from a frequency perspective for image deraining. arXiv preprint arXiv:2404.09476, 2024. 3", + "[55] Zeyun Zhong, Manuel Martin, Frederik Diederichs, and Juergen Beyerer. Querymamba: A mamba-based encoder-decoder architecture with a statistical verb-noun interaction module for video action forecasting@ ego4d long-term action anticipation challenge 2024. arXiv preprint arXiv:2407.04184, 2024. 3, 4", + "[56] Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, and Xinggang Wang. Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 3" + ], + "bbox": [ + 91, + 90, + 482, + 359 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23090", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_model.json b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c5b2c7aa705a9bc17f4c94d0c2209fdb2122e2ee --- /dev/null +++ b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_model.json @@ -0,0 +1,2257 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.131, + 0.887, + 0.154 + ], + "angle": 0, + "content": "QMambaBSR: Burst Image Super-Resolution with Query State Space Model" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.18, + 0.951, + 0.217 + ], + "angle": 0, + "content": "Xin Di\\(^{1\\dagger}\\), Long Peng\\(^{1\\dagger,\\ddagger}\\), Peizhe Xia\\(^{1}\\), Wenbo Li\\(^{2}\\), Renjing Pei\\(^{2*}\\), Yang Cao\\(^{1}\\), Yang Wang\\(^{1,3*}\\), Zheng-Jun Zha\\(^{1}\\) \n\\(^{1}\\)University of Science and Technology of China, \\(^{2}\\)Huawei Noah's Ark Lab, \\(^{3}\\)Chang'an University" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.219, + 0.87, + 0.234 + ], + "angle": 0, + "content": "{dx9826, longp2001}@mail.ustc.edu.cn, peirenjing@huawei.com, ywang120@chd.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.301, + 0.485, + 0.694 + ], + "angle": 0, + "content": "Burst super-resolution (BurstSR) aims to reconstruct high-resolution images by fusing subpixel details from multiple low-resolution burst frames. The primary challenge lies in effectively extracting useful information while mitigating the impact of high-frequency noise. Most existing methods rely on frame-by-frame fusion, which often struggles to distinguish informative subpixels from noise, leading to suboptimal performance. To address these limitations, we introduce a novel Query Mamba Burst Super-Resolution (QMambaBSR) network. Specifically, we observe that subpixels have consistent spatial distribution while noise appears randomly. Considering the entire burst sequence during fusion allows for more reliable extraction of consistent subpixels and better suppression of noise outliers. Based on this, a Query State Space Model (QSSM) is proposed for both inter-frame querying and intra-frame scanning, enabling a more efficient fusion of useful subpixels. Additionally, to overcome the limitations of static upsampling methods that often result in over-smoothing, we propose an Adaptive Upsampling (AdaUp) module that dynamically adjusts the upsampling kernel to suit the characteristics of different burst scenes, achieving superior detail reconstruction. Extensive experiments on four benchmark datasets—spanning both synthetic and real-world images—demonstrate that QMambaBSR outperforms existing state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.724, + 0.222, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.841 + ], + "angle": 0, + "content": "In recent years, with the continuous development of smartphones, overcoming the limitations of smartphone sensors and lenses to reconstruct high-quality, high-resolution (HR) images has become a research hotspot. Benefited from the development of deep learning, single image superresolution (SISR) [9, 19, 33, 34, 50, 53] has achieved re" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.268, + 0.897, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.364, + 0.756, + 0.375 + ], + "angle": 0, + "content": "(a) Existing Methods" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.375, + 0.896, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.533, + 0.907, + 0.659 + ], + "angle": 0, + "content": "Figure 1. The concat and frame-by-frame operations in existing methods struggle to efficiently extract sub-pixels and suppress noise, leading to remaining artifacts and over-smoothed details, as shown in (a). We observe that noise randomly appears on several frames, while effective sub-pixels have consistent intensity at corresponding positions in all frames, as shown in (c). Based on this, a novel inter-frame query and intra-frame scanning-based QMambaBSR is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously, as shown in (b)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.688, + 0.907, + 0.809 + ], + "angle": 0, + "content": "markable progress, but the performance is still limited by the finite information provided by a single image. Consequently, numerous researchers are dedicating their efforts to burst super-resolution (BurstSR), which aims to leverage the rich sub-pixel details provided by a sequence of burst low-resolution images captured by hand-tremor and camera/object motions to overcome the limitations of SISR, achieving substantial advancements [7, 23, 24, 36, 43]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "In BurstSR, the first image is the super-resolution frame, denoted as the base frame, while the remaining images, referred to as current frames, supply sub-pixel information for producing a high-quality HR image. The pipeline of most existing BurstSR approaches can be mainly categorized: alignment, fusion, and upsampling. Firstly, due to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.852, + 0.483, + 0.9 + ], + "angle": 0, + "content": "*Yang Wang and Renjing Pei are the corresponding authors. † These authors contributed equally to this work. ‡Long Peng is the project leader. This work was finished during Xin Di and Long Peng in the internship of Huawei Noah." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23080" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.543 + ], + "angle": 0, + "content": "the misalignment caused by hand-tremor, alignment methods [1, 11, 29, 45] are employed to align the current frames with the target base frame. Then, the primary challenge lies in extracting sub-pixel information from the current frames that match the content of the base frame while concurrently suppressing high-frequency random noise. Previous methods, such as weighted-based multi-frame fusion [1, 2], obtain residuals by subtracting each current frame from the base frame and utilizing simple weighting techniques to fuse obtained residual information. Although easy to perform, these methods neglect the inter-frame relationship among multi-frames, failing to extract sub-pixels that better match the base frame and are susceptible to interference from noise in RAW images. To enhance inter-frame relationships, BIPNet [11] proposes channel shuffling of multiframe features to improve information flow between different frames. Consequently, recent state-of-the-art methods, such as GMTNet [12, 28, 31], propose using crossattention, explicitly employing the base frame as a query to retrieve and capture feature differences from the current frame pixel-to-pixel to extract sub-pixel information. RBSR [46] utilize RNNs [25] for frame-by-frame feature fusion, as shown in Figure 1 (a). The aforementioned methods extract sub-pixel information and denoise in a frame-by-frame manner or implement sub-pixel extraction and denoising through separate modules. However, these methods overlook the distinct characteristics between sub-pixels and noise, making it challenging to capture useful sub-pixels from noise and leading to artifacts and over-smoothed details." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.55, + 0.482, + 0.73 + ], + "angle": 0, + "content": "After fusion, adaptively learning high-resolution mappings from the extracted and fused features remains a paramount challenge in BurstSR. The existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], primarily utilize static interpolation, transposed convolution [14], or pixel shuffle [38] for static upsampling. Nevertheless, these approaches make it difficult to adaptively perceive the variations in sub-pixel distribution across different scenes by employing static upsampling methods, resulting in the inability to utilize the spatial arrangement of sub-pixels to accurately reconstruct high-quality, high-resolution (HR) images." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.736, + 0.482, + 0.9 + ], + "angle": 0, + "content": "To address these issues, we propose a novel Query Mamba Burst Super-Resolution (QMambaBSR) network, which integrates a novel Query State Space Model (QSSM) and an Adaptive Up-sampling module (AdaUp) to reconstruct high-quality high-resolution images from burst lowresolution images. Specifically, QSSM is first proposed to efficiently extract the sub-pixels in both inter-frame and intra-frame while mitigating noise interference. In particular, QSSM retrieves information across current frames for the base frame by modifying control matrix \\(B\\) and discretization step size \\(\\Delta\\) in the state space function, as shown" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.092, + 0.905, + 0.332 + ], + "angle": 0, + "content": "in Figure 1 (b). QSSM synchronously performs inter-frame querying and intra-frame scanning, comprehensively considering both inter-frame and intra-frame information to achieve integrated sub-pixel extraction and noise suppression. AdaUp is proposed to perceive the spatial distribution of sub-pixel information and subsequently adaptively adjust the upsampling kernel to enhance the reconstruction of high-quality HR images across diverse burst LR scenarios. Furthermore, to comprehensively fuse sub-pixels with different scales, the Multi-scale Fusion Module is proposed to combine channel Transformer and local CNN, as well as horizontal and vertical global Mamba, to fuse sub-pixel information of different scales. Extensive experiments on four popular synthetic and real-world benchmarks demonstrate that our method achieves a new state-of-the-art, delivering superior visual results." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.334, + 0.857, + 0.347 + ], + "angle": 0, + "content": "The contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.349, + 0.905, + 0.408 + ], + "angle": 0, + "content": "- A novel inter-frame query and intra-frame scanning-based Query State Space Model (QSSM) is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.409, + 0.905, + 0.482 + ], + "angle": 0, + "content": "- We propose a novel Adaptive Up-sampling module, designed respectively for adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst LR scenarios, and for the fusion of sub-pixels across different scales." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.484, + 0.905, + 0.544 + ], + "angle": 0, + "content": "- Our proposed method achieves new state-of-the-art (SOTA) performance on the four popular public synthetic and real benchmarks, demonstrating the superiority and practicability of our method." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.349, + 0.905, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.517, + 0.559, + 0.654, + 0.573 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.585, + 0.905, + 0.628 + ], + "angle": 0, + "content": "In this section, we briefly review Multi-Frame SuperResolution and State Space Models. More comprehensive surveys are provided in [3, 48]." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.63, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Multi-Frame Super-Resolution. With the rapid development of deep learning in recent years [15, 18, 26, 41], deep-learning-based single image super-resolution (SISR) achieves significant breakthroughs [6, 47, 49, 51]. However, due to the limited information provided by a single image, the performance of SISR is significantly constrained [27, 39, 42, 52]. Therefore, Multi-Frame Super-Resolution (MFSR) is proposed to overcome the limitations of SISR by leveraging the useful sub-pixel information contained in multiple low-resolution images, achieving superior high-resolution reconstruction. In particular, DBSR [1] proposes using optical flow methods to explicitly align multiple low-resolution images and then fuse their features through attention weights. MFIR [2] utilizes optical flow for feature warping and proposes a deep reparametrization of the classical MAP formulation for multi-frame image restoration. BIPNet [11] proposes a pseudo-burst fusion strategy by fusing temporal features channel-by-channel," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23081" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.346 + ], + "angle": 0, + "content": "enabling frequent inter-frame interaction. Burstormer [12] leverages multi-scale local and non-local features for alignment and employs neighborhood interaction for further inter-frame feature fusion. RBSR [46] utilizes recurrent neural networks for progressive feature aggregation. However, most of these methods mainly use frame-by-frame approaches or pairwise interactions, either failing to explicitly extract sub-pixel information from the current frames or only querying the current frame point-by-point from the base frame. This makes it difficult for them to effectively extract sub-pixel details while suppressing noise interference. To address these limitations, we propose Query Mamba Burst Super-Resolution (QMambaBSR), which allows the base frame to simultaneously query inter-frame and intra-frame information to extract sub-pixel details embedded in structured regions while also suppressing noise interference." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.349, + 0.483, + 0.606 + ], + "angle": 0, + "content": "State Space Models. State Space Models (SSMs) originated in the 1960s in control systems [20], where they are used for modeling continuous signal input systems. Recently, advancements in SSMs have led to their application in computer vision [5, 13, 32, 56]. Notably, Visual Mamba introduced a residual VSS module and developed four scanning directions for visual images, achieving superior performance compared to ViT [10] while maintaining lower model complexity, thereby attracting significant attention [16, 22, 35, 40, 44, 54]. QueryMamba [55] is proposed to apply SSM to video action forecasting tasks. MambaIR [16] is the first to employ SSMs in image restoration, enhancing efficiency and global perceptual capabilities. However, there remains potential for further exploration of SSMs in BurstSR. Therefore, we propose a novel Query-based State Space Model designed to efficiently extract sub-pixel information for BurstSR." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.624, + 0.182, + 0.639 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.65, + 0.201, + 0.665 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.673, + 0.483, + 0.822 + ], + "angle": 0, + "content": "Given a sequence of input low-resolution (LR) images, denoted as \\(\\{x_{i}\\}_{i = 1}^{N}\\), where \\(N\\) represents the number of burst LR frames. Following [1], we denote the first image as the base frame for super-resolution, while the other LR frames are used to provide rich sub-pixel information and are referred to as current frames. BurstSR can be defined as utilizing the sub-pixel information extracted from the current frames to supplement the base frame, generating a high-quality, high-resolution RGB image \\(I_{HR}\\) with a superresolution factor of \\(s\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "To achieve this goal, we propose QMambaBSR for burst image super-resolution, as illustrated in Figure 2. First, we use alignment block [12] to align the current images to the spatial position of the base frame. Next, we introduce a novel Query State Space Model (QSSM) designed to query" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.228 + ], + "angle": 0, + "content": "sub-pixel information from the current images and mitigate noise interference in both inter-frame and intra-frame manner. Additionally, we present a novel Adaptive Up-sampling (AdaUp) module, which facilitates adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst images. Finally, a new Multi-scale Fusion Module is incorporated to fuse sub-pixel information across different scales. Next, we provide a detailed explanation of each component." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.239, + 0.746, + 0.256 + ], + "angle": 0, + "content": "3.2. Query State Space Model" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.262, + 0.907, + 0.639 + ], + "angle": 0, + "content": "Considering that burst RAW images often contain high-frequency random noise and the sub-pixel information to be extracted typically shares a similar distribution with the base frame, it is crucial for the BurstSR task to utilize the base frame to uncover the rich sub-pixel information contained in the current frames for super-resolution, while simultaneously suppressing noise. Existing methods [1, 11, 12, 45, 46] simply concatenate multi-frame information but fail to precisely extract sub-pixel information from the current frames using the base frame, resulting in a scarcity of sub-pixel details and consequently making it difficult to reconstruct fine details. Moreover, while some existing approaches attempt to use cross-attention [31], utilizing the base frame as the query for sub-pixels extraction, such frame-by-frame methods struggle to suppress noise interference and are plagued by high computational complexity. This often results in the presence of noise and the introduction of artifacts. Therefore, we propose the Query State Space Model (QSSM), which enables the base frame to efficiently query all current frames simultaneously in both intra-frame and inter-frame manners. By leveraging the consistent distribution of sub-pixels and the inconsistent distribution of noise, our QSSM can simultaneously query multiple images to extract the necessary sub-pixel information while effectively suppressing random noise." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.64, + 0.907, + 0.746 + ], + "angle": 0, + "content": "First, let's briefly review the State Space Model (SSM). The latest advances in structured state space sequence models (S4) are largely inspired by continuous linear time-invariant (LTI) systems, which map input \\( x(t) \\) to output \\( y(t) \\) through an implicit latent state \\( h(t) \\in \\mathbb{R}^N \\) [16]. This system can be represented as a linear ordinary differential equation (ODE):" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.759, + 0.905, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\dot {h} (t) = A h (t) + B x (t), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.78, + 0.792, + 0.795 + ], + "angle": 0, + "content": "\\[\ny (t) = C h (t) + D x (t),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.808, + 0.907, + 0.854 + ], + "angle": 0, + "content": "where \\(N\\) is the state size, \\(A \\in \\mathbb{R}^{N \\times N}\\), \\(B \\in \\mathbb{R}^{N \\times 1}\\), \\(C \\in \\mathbb{R}^{1 \\times N}\\), and \\(D \\in \\mathbb{R}\\). Discretized using a zero-order hold as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.865, + 0.905, + 0.891 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {A} = \\exp (\\Delta A), \\\\ - \\end{array} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.888, + 0.826, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\overline {{B}} = (\\Delta A) ^ {- 1} (\\exp (\\Delta A) - I) \\Delta B,\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23082" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.907, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.408, + 0.907, + 0.438 + ], + "angle": 0, + "content": "Figure 2. The overall framework of our proposed QMambaBSR, primarily includes the novel Query State Space Model (QSSM), Multiscale Fusion Module (MSFM), and the Adaptive Up-sampling Module (AdaUp)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.494 + ], + "angle": 0, + "content": "After the discretization, the discretized version of Eq. (1) with step size \\(\\Delta\\) can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.502, + 0.482, + 0.527 + ], + "angle": 0, + "content": "\\[\nh _ {k} = \\bar {A} h _ {k - 1} + \\bar {B} x _ {k}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.523, + 0.344, + 0.539 + ], + "angle": 0, + "content": "\\[\ny _ {k} = C h _ {k} + D x _ {k},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.483, + 0.638 + ], + "angle": 0, + "content": "At this point, the LTI system's input parameter matrices are static. Therefore, recent work [16] makes \\( B \\), \\( C \\), and \\( \\Delta \\) depend on the input. Recent research suggests that since the \\( A \\) matrix is a HIPPO matrix and \\( \\Delta \\) represents the step size, \\( \\exp(\\Delta A) \\) can be viewed as forget gate and input gate [17], which modulates the influence of the input on the state." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.639, + 0.483, + 0.803 + ], + "angle": 0, + "content": "However, traditional SSM lacks the multi-frame querying capabilities that are crucial for BurstSR tasks. Therefore, we propose a QSSM to enable the base frame to gate the output of the current frames, thereby allowing the base frame to perform information queries on the current frames to obtain the sub-pixels while eliminating noise, as illustrated in Figure 1. Specifically, we let the current frames drive the state changes, with the base frame gating the influence of the current frames on the state through \\( B \\) and \\( \\Delta \\). As shown in Figure 2 (a), the corresponding formulas are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.81, + 0.482, + 0.835 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\left(\\bar {A} _ {\\text {b a s e} _ {t}}\\right) h _ {t - 1} + \\left(\\bar {B} _ {\\text {b a s e} _ {t}}\\right) x _ {\\text {c u r} _ {t}}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.832, + 0.309, + 0.847 + ], + "angle": 0, + "content": "\\[\ny _ {t} = C h _ {t} + D x _ {\\mathrm {c u r} _ {t}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.9 + ], + "angle": 0, + "content": "Considering that noise may exist at certain locations in the base frame and is randomly distributed at the same locations in other current frames, we concatenate the base" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.907, + 0.644 + ], + "angle": 0, + "content": "frame with other current frames to initially reduce random noise in the original base frame and achieve preliminary feature fusion. Specifically, the concatenated features are processed by an MLP layer and finally projected back to the channel dimension of the original base frame, using it as the new base frame. Then the base frame is transformed through a learnable linear layer to generate \\(\\Delta_{\\mathrm{base}_t}\\) and \\(B_{\\mathrm{base}_t}\\), and these are then used in the discretization formula from Eq. (2) to obtain \\(\\overline{A}_{\\mathrm{base}_t}\\) and \\(\\overline{B}_{\\mathrm{base}_t}\\). The current frames are processed through another linear layer to obtain \\(x_{\\mathrm{cur}_t}\\), where \\(t\\) indicates the positional relationship after flattening the base frame and current frames." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.906, + 0.674 + ], + "angle": 0, + "content": "Utilizing Eq. (2), the zero-order hold and discretization can be expanded as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.679, + 0.907, + 0.726 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.73, + 0.906, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} y _ {t} = C \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}} \\tag {6} \\\\ + D x _ {\\mathrm {c u r} _ {2}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.797, + 0.906, + 0.827 + ], + "angle": 0, + "content": "where \\(\\tilde{f}\\) represents the functions of \\(\\Delta\\) and \\(B\\) corresponding to the zero-order hold of \\(B\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.833, + 0.905, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {t}}\\right) = \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) ^ {- 1} \\left(\\exp \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) - I\\right) \\Delta_ {\\text {b a s e} _ {t}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Specifically, in the State Space Model, the input \\( x_{t} \\) at time \\( t \\) is influenced by the control matrix \\( B \\), which in turn affects the change in state \\( h \\). In the discretized state space," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23083" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.482, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.254, + 0.483, + 0.283 + ], + "angle": 0, + "content": "Figure 3. Illustrative comparison between the proposed QSSM and existing cross-attention mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.312, + 0.485, + 0.763 + ], + "angle": 0, + "content": "the discretization step size \\(\\Delta\\) represents the time \\(x_{t}\\) acts on the state. In QSSM, we desire the base frame to act as a gate controlling the influence of the current frames on the state, thereby affecting the output. Thus, we generate \\(\\mathrm{base}_t\\) and \\(\\Delta\\) by the base frame through a linear layer. To exploit the differences in sub-pixels and noise distribution characteristics across multiple frames, we merge current features into the channel dim. Subsequently, all current features are projected into a unified set of merged current features through a linear layer. This allows the base feature to query all current features at once, thereby achieving multi-frame joint denoising. Additionally, as Eq. (5) and (6), when the flattened base feature \\(f_{\\mathrm{base}_t}\\) queries the current features at other times \\(f_{\\mathrm{cur}_j}\\), \\(f_{\\mathrm{base}_t}\\) modulates and guides \\(f_{\\mathrm{base}_j}\\) to query \\(f_{\\mathrm{cur}_j}\\) through the forget gate and input gate \\(\\exp (\\Delta_{\\mathrm{base}_t}A)\\), ultimately feeding back to the output at time \\(t\\). This enhances the interaction between \\(f_{\\mathrm{base}_t}\\) and its neighboring base features as well as current features. Due to the characteristics of the matrix \\(A\\), the influence of \\(f_{\\mathrm{base}_t}\\) in guiding the query of \\(f_{\\mathrm{base}_j}\\) gradually decreases with their distance in the sequence, forming a progressively diminishing receptive field. This prevents \\(f_{\\mathrm{base}_t}\\) from overly focusing on spatially distant information, thereby enhancing neighborhood interactions. Since each query by the base feature simultaneously queries all current features, the base feature can better perceive sub-pixel information consistently distributed across frames, suppressing random noise. We modify the RSSB block [16] by integrating our proposed QSSM with four scanning directions and using channel attention to enhance channel interaction." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Discussion To clarify the differences between the proposed QSSM and existing cross-attention methods, we conduct a detailed analysis along with a schematic comparison. As shown in Figure 3 (a), the cross-attention method uses serialized base feature tokens at position \\( t \\) as the \\( \\mathrm{Q} \\) matrix, querying with all position tokens of the current features as the \\( \\mathrm{K} \\) matrix to extract sub-pixel information. In contrast, our QSSM, as shown in Figure 3 (b), not only extracts sub-pixel information from the current features to the base fea" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.182 + ], + "angle": 0, + "content": "ture but also facilitates information interaction within the base feature. It simultaneously retrieves corresponding current feature tokens from other position tokens in the serialized base feature, thereby achieving joint multi-position sub-pixel information retrieval and noise suppression between the base feature and current features." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.191, + 0.761, + 0.206 + ], + "angle": 0, + "content": "3.3. Multi-Scale Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.213, + 0.907, + 0.485 + ], + "angle": 0, + "content": "Considering the presence of sub-pixel information across various scales within the intricate details of images, we propose a novel Multi-scale Fusion Module (MSFM). This module is designed to effectively integrate multi-scale subpixel information from the current frames, thereby enhancing the capability for detailed image reconstruction. The MSFM comprises three distinct branches: a Convolutional Neural Network (CNN), a State Space Model (SSM) with diverse scanning orientations, and a channel Transformer. To begin with, a \\(3 \\times 3\\) convolution is utilized for the fusion of local sub-pixel features. The SSM is introduced to efficiently learn and integrate sub-pixel features along both horizontal and vertical axes. Furthermore, considering the attenuation characteristics of the A matrix within the SSM when dealing with long-range perception, we concurrently employ a Transformer block to augment the network's proficiency in capturing global information. The mathematical formulation of the MSFM is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.496, + 0.907, + 0.513 + ], + "angle": 0, + "content": "\\[\ny = w _ {1} \\cdot \\operatorname {C N N} (x) + w _ {2} \\cdot \\operatorname {S S M} (x) + w _ {3} \\cdot \\operatorname {T r a n s f o r m e r} (x) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.523, + 0.907, + 0.553 + ], + "angle": 0, + "content": "where \\(w_{i}\\) represents the balancing factors. \\(x\\) and \\(y\\) represent the input feature and output feature, respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.562, + 0.787, + 0.579 + ], + "angle": 0, + "content": "3.4. Adaptive Up-sampling Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.909, + 0.903 + ], + "angle": 0, + "content": "After the aforementioned processes, the sub-pixel structural information from burst LR images is extracted and distributed in the feature space. The next critical challenge is to utilize this valuable sub-pixel information to adaptively upsample the image resolution and incorporate sub-pixel details into the high-resolution image. Existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], simply employ interpolation, transposed convolution, or pixel shuffle techniques for resolution upsampling. However, these methods lack the capability to perceive the distribution of sub-pixels in the feature space, leading to an inability to adaptively reconstruct fine details. Therefore, we introduce a novel Adaptive Up-sampling (AdaUp) module that perceives the distribution of sub-pixels in the spatial domain and adaptively adjusts the up-sampling kernel, thereby achieving higher-quality image detail, as shown in Figure 2 (b). Specifically, we first adaptively perceive the distribution of sub-pixels \\( L \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times 1 \\times 1} \\) from the input features \\( X \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times H \\times W} \\) by adaptive pooling. We then perform sequence feature interaction on \\( L \\) to obtain the output channel feature distribution sequence \\( L_1 \\in \\mathbb{R}^{B \\times C_{\\mathrm{out}} \\times 1 \\times 1} \\). Sub" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23084" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "sequentially, we apply both the input distribution sequence and the output distribution sequence to the upsampling transposed convolution kernel \\( W \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times C_{\\mathrm{out}} \\times 3 \\times 3} \\) using broadcasting, thereby endowing the kernel with feature perception capability. Finally, we obtain the high-resolution output through the upsampling transposed convolution kernel. The corresponding formulas are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.204, + 0.483, + 0.22 + ], + "angle": 0, + "content": "\\[\nL = \\text {A d a p t i v e P o o l i n g} (X) \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.226, + 0.482, + 0.242 + ], + "angle": 0, + "content": "\\[\nL _ {1} = \\operatorname {C o n v} _ {1 \\times 1} (L) \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.246, + 0.483, + 0.262 + ], + "angle": 0, + "content": "\\[\nW _ {f} = (W \\odot L) \\odot L _ {1} \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.265, + 0.483, + 0.281 + ], + "angle": 0, + "content": "\\[\ny = \\operatorname {T r a n s - C o n v} \\left(W _ {f}, X\\right) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.285, + 0.484, + 0.361 + ], + "angle": 0, + "content": "where \\(\\odot\\) represents element-wise multiplication. Thus, AdaUp can leverage the underlying content information from input frames at different channels and utilize it to get better performance than the mainstream up-sampling operations, pixel shuffle, or interpolations [4, 37]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.371, + 0.336, + 0.389 + ], + "angle": 0, + "content": "4. Experiments and Analysis" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.396, + 0.299, + 0.412 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.418, + 0.484, + 0.764 + ], + "angle": 0, + "content": "Implementation details. We evaluate the effectiveness of our proposed method on four public burst image superresolution benchmarks, encompassing both synthetic and real datasets: synthetic BurstSR [1], Real BurstSR [1], RealBSR-RAW [45], and RealBSR-RGB [45]. To ensure fairness, we follow [12] for training and evaluation. More details of datasets and data processing can be found in Appendix A section. Following [12], we train the model from scratch on the synthetic BurstSR dataset for 300 epochs, using the AdamW optimizer with parameters \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999\\). We employ a cosine annealing strategy to gradually decrease the learning rate from \\(3\\times 10^{-4}\\) to \\(10^{-6}\\) and set the training patch size to \\(48\\times 48\\). For the Real BurstSR dataset, we follow [1] to fine-tune the model pretrained on synthetic BurstSR for 60 epochs, maintaining the same training setting as the synthetic BurstSR but adjusting the learning rate to \\(1\\times 10^{-6}\\) and the training patch size to \\(56\\times 56\\). For the RealBSR-RAW and RealBSR-RGB datasets, we follow [45] to train from scratch for 100 epochs, using the same training setting as the synthetic BurstSR, with a training patch size of \\(80\\times 80\\). We set the batch size to 8, and the burst size to 14, and all experiments are conducted on 8 V100 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Metric. Following previous works [1, 45], we use reference metrics to evaluate performance, including PSNR and SSIM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Compared methods. To comprehensively demonstrate the superiority of our proposed method, we compare our QMambaBSR with ten classic and state-of-the-art (SOTA) BurstSR approaches HighRes-net [8], DBSR [1], LKR [21], MFIR [2], BIPNet [11], AFCNet [30], FBAnet [45], Burstormer [12], RBSR [46], GMTNet [31]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.091, + 0.831, + 0.107 + ], + "angle": 0, + "content": "4.2. Quantitative and Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.113, + 0.905, + 0.385 + ], + "angle": 0, + "content": "Results on the Synthetic BurstSR dataset. As shown in Table 1, our method outperforms existing BurstSR methods, achieving the best performance. For example, compared to the existing SOTA method, Burstormer, our method achieves a \\(0.29\\mathrm{dB}\\) improvement in PSNR. Furthermore, to further demonstrate the visual superiority of our method, we present a visual comparison with existing methods in Figure 4. We can observe that the RAW low-resolution images exhibit significant noise and severe detail loss, as illustrated in the window area of Figure 4. Compared to existing methods, our method demonstrates superior performance in reconstructing textures and details in the window area. Additionally, in the green stripes region at the bottom of Figure 4, the substantial noise in the base frame leads existing methods to leave artifacts. However, our method more effectively distinguishes between noise and sub-pixels, producing more detailed, artifact-free high-resolution images, thereby demonstrating the visual superiority of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.386, + 0.906, + 0.597 + ], + "angle": 0, + "content": "Results on RealBSR-RGB and RealBSR-RAW. As shown in Table 2, our method consistently outperforms existing methods on these two real benchmarks, achieving the best performance. For RealBSR-RAW, our method surpasses FBANet and Burstormer in PSNR and linear-PSNR by \\(0.268\\mathrm{dB}\\) and \\(0.258\\mathrm{dB}\\), respectively. For RealBSR-RGB, our method surpasses FBANet and Burstormer in PSNR by \\(0.204\\mathrm{dB}\\). Furthermore, as shown in Figure 5, the results demonstrate the superior performance of our method in detail reconstruction and artifact suppression. This validates the effectiveness of our method in real-world scenarios, highlighting its superiority and practicality. More results on Real BurstSR and qualitative results will be presented in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.607, + 0.667, + 0.623 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "To demonstrate the effectiveness and superiority of the proposed modules, we conduct a series of ablation experiments. Specifically, we incrementally integrate the proposed modules into the baseline network. For rapid evaluation, we train our model on the synthetic dataset for 100 epochs. From Table 3, we observe that the introduction of the MSFM module, which enhances the network's multiscale perception and fully integrates sub-pixel information from different frames, significantly improves performance by 1.34 dB in PSNR. Furthermore, the addition of the QSSM, which extracts sub-pixels from the current frames that match the content of the base frame while suppressing noise, leads to an additional performance gain of 0.72 dB in PSNR. Finally, incorporating the proposed Adaptive Up-sampling module, which better adapts the up-sampling kernel according to the scene, thereby generating high-resolution images with richer details, results in a further improvement of 0.26 dB. These results indicate that the pro" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23085" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.09, + 0.905, + 0.149 + ], + "angle": 0, + "content": "
BicubicHighRes-netDBSRLKRMFIRBIPNetAFCNetFBAnetGMTNetRBSRBurstormerOurs
PSNR↑36.1737.4540.7641.4541.5641.9342.2142.2342.3642.4442.8343.12
SSIM↑0.910.920.960.950.960.960.960.970.960.970.970.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.2, + 0.159, + 0.796, + 0.173 + ], + "angle": 0, + "content": "Table 1. Performance comparison of existing methods on Synthetic BurstSR dataset for \\( \\times 4 \\) BurstSR." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.186, + 0.905, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.453, + 0.8, + 0.467 + ], + "angle": 0, + "content": "Figure 4. Visual comparison results with different methods on SyntheticBurst datasets for \\(\\times 4\\) BurstSR." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.491, + 0.477, + 0.657 + ], + "angle": 0, + "content": "
MethodRealBSR-RAWRealBSR-RGB
PSNR↑SSIM↑L-PSNR↑PSNR↑SSIM↑
DBSR20.9060.63530.48430.7150.899
MFIR21.5620.63830.97930.8950.899
BSRT22.5790.62230.82930.7820.900
BIPNet22.8960.64131.31130.6550.892
FBANet23.4230.67732.25631.0120.898
Burstormer27.2900.81632.53331.1970.907
Ours27.5580.82032.79131.4010.908
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.667, + 0.483, + 0.695 + ], + "angle": 0, + "content": "Table 2. Performance comparison of existing methods on RealBSR-RGB and RealBSR-RAW datasets for \\(\\times 4\\) BurstSR." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.731, + 0.483, + 0.761 + ], + "angle": 0, + "content": "posed modules significantly enhance burst super-resolution performance." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Comparison with Existing Modules. To verify the effectiveness of proposed module, we replaced it with existing fusion and up-sampling modules. To effectively represent the performance of various methods while also considering training time, we train for 100 epochs on the synthetic dataset. As shown in Table 4, in the fusion stage, compared to PBFF [11] or NRFE [12], our QSSM and MSFM modules are able to better exploit the inter-frame consistency of sub-pixel distribution while denoising, resulting in" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.491, + 0.9, + 0.584 + ], + "angle": 0, + "content": "
QSSMMSFMAdaUpPSNR↑SSIM↑
×××39.810.93
×✓×41.150.94
✓✓×41.870.96
✓✓✓42.130.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.539, + 0.593, + 0.879, + 0.608 + ], + "angle": 0, + "content": "Table 3. Ablation experiment on proposed core modules." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.641, + 0.905, + 0.716 + ], + "angle": 0, + "content": "PSNR improvements of 1.56 dB and 0.41 dB, respectively. In contrast to static upsampling like pixel shuffle and transposed convolution, our AdaUp module enhances the network's ability to perceive scene-specific sub-pixel distributions, leading to a PSNR improvement of 0.16 dB." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Evaluation about MSFM. To validate the effectiveness of different branches within the proposed MSFM, we conducted ablation experiments with various internal branch setting. The experimental results are shown in Table 5. To minimize training time while ensuring experimental validity, the ablation experiments were conducted on a synthetic dataset and trained for 100 epochs. As shown in the table, we use only the convolution in the MSFM module as the baseline. Adding the transformer module resulted in a PSNR increase of \\(0.39\\mathrm{dB}\\). When the transformer was replaced with SSM, the PSNR improved by \\(0.44\\mathrm{dB}\\) compared to using only the conv method. Under our proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23086" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.209, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.215, + 0.191, + 0.228 + ], + "angle": 0, + "content": "Base frame" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.088, + 0.324, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.242, + 0.215, + 0.288, + 0.228 + ], + "angle": 0, + "content": "DBSR" + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.088, + 0.44, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.215, + 0.406, + 0.228 + ], + "angle": 0, + "content": "MFIR" + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.088, + 0.556, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.471, + 0.215, + 0.525, + 0.228 + ], + "angle": 0, + "content": "BIPNet" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.088, + 0.672, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.215, + 0.655, + 0.228 + ], + "angle": 0, + "content": "Burstomer" + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.088, + 0.79, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.215, + 0.75, + 0.228 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.088, + 0.906, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.215, + 0.896, + 0.228 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.196, + 0.244, + 0.8, + 0.259 + ], + "angle": 0, + "content": "Figure 5. Visual comparison results with different methods on RealBSR-RGB dataset for \\(\\times 4\\) BurstSR." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.28, + 0.48, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.47, + 0.447, + 0.485 + ], + "angle": 0, + "content": "Figure 6. User study of reconstructed real HR images." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.501, + 0.48, + 0.646 + ], + "angle": 0, + "content": "
Process StageMethodsPSNR↑SSIM↑
FusionConcat39.850.93
PBFF [11]40.570.94
NRFE [12]41.720.96
Ours42.130.96
Up-samplerPixelshuffle41.890.96
Transposed conv41.970.96
Ours42.130.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.656, + 0.483, + 0.684 + ], + "angle": 0, + "content": "Table 4. Comparison with existing modules on fusion and upsampling process stage." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.484, + 0.744 + ], + "angle": 0, + "content": "MSFM, the PSNR increased by 0.56 dB, clearly demonstrating the effectiveness of both the SSM and transformer branches in the MSFM." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.757, + 0.212, + 0.773 + ], + "angle": 0, + "content": "4.4. User study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To effectively illustrate the superiority of our proposed method in reconstructing visually pleasing images, we conducted a user study involving 10 real burst images selected from well-established benchmarks. Twenty volunteers participated in this study, tasked with rating the similarity and quality between each reconstructed image and the ground truth (GT). They used a detailed scale ranging from 0, indicating visually unsatisfactory and completely dissimilar" + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.279, + 0.89, + 0.372 + ], + "angle": 0, + "content": "
ConvTransformerSSMPSNR↑SSIM↑
✓××41.570.95
✓✓×41.960.96
✓×✓42.010.96
✓✓✓42.130.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.382, + 0.86, + 0.397 + ], + "angle": 0, + "content": "Table 5. Ablation studies on our proposed MSFM." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.907, + 0.534 + ], + "angle": 0, + "content": "images, to 10, representing visually satisfactory and highly similar images. We then meticulously aggregated the scores from all volunteers, and the results are depicted in Figure 6. When compared to existing methods such as Burstormer and BIPNet, our proposed method stands out by adaptively extracting sub-pixels to achieve superior visual effects. This approach earned our method the highest average score of 8.56, underscoring its effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.554, + 0.634, + 0.57 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.907, + 0.825 + ], + "angle": 0, + "content": "In this paper, we introduce a novel approach called QMambaBSR for burst image super-resolution. Based on the structural consistency of sub-pixels and the inconsistency of random noise, we propose a novel Query State Space Model to efficiently query sub-pixel information embedded in current frames through an intra- and inter-frame multi-frame joint query approach while suppressing noise interference. We introduce a Multi-scale Fusion Module for information on sub-pixels across different scales. Additionally, a novel Adaptive Up-sampling module is proposed to perceive the spatial arrangement of sub-pixel information in various burst scenarios for adaptive up-sampling and detail reconstruction. Extensive experiments on four public synthetic and real benchmarks demonstrate that our method surpasses existing methods, achieving state-of-the-art performance while presenting the best visual quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.844, + 0.693, + 0.861 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.9 + ], + "angle": 0, + "content": "This work was supported by the Natural Science Foundation of China under Grants 62225207,62436008 and 62206262." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23087" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.486, + 0.171 + ], + "angle": 0, + "content": "[1] Goutam Bhat, Martin Danelljan, Luc Van Gool, and Radu Timofte. 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Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 3" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.483, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23090" + } + ] +] \ No newline at end of file diff --git a/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_origin.pdf b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8352a86d442c0fd65742c1a509c3f2dbf3f32210 --- /dev/null +++ b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/ccb55e80-eeaa-40e8-8e8b-d128ea3974f0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ac3172edf80c006d28ddeda8033c271db5971cbaee94276c8c4cb2ca6237d059 +size 4468997 diff --git a/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/full.md b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/full.md new file mode 100644 index 0000000000000000000000000000000000000000..df1b2e7180dc22714110846449402999e4984c7c --- /dev/null +++ b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/full.md @@ -0,0 +1,328 @@ +# QMambaBSR: Burst Image Super-Resolution with Query State Space Model + +Xin Di $^{1\dagger}$ , Long Peng $^{1\dagger,\ddagger}$ , Peizhe Xia $^{1}$ , Wenbo Li $^{2}$ , Renjing Pei $^{2*}$ , Yang Cao $^{1}$ , Yang Wang $^{1,3*}$ , Zheng-Jun Zha $^{1}$ $^{1}$ University of Science and Technology of China, $^{2}$ Huawei Noah's Ark Lab, $^{3}$ Chang'an University + +{dx9826, longp2001}@mail.ustc.edu.cn, peirenjing@huawei.com, ywang120@chd.edu.cn + +# Abstract + +Burst super-resolution (BurstSR) aims to reconstruct high-resolution images by fusing subpixel details from multiple low-resolution burst frames. The primary challenge lies in effectively extracting useful information while mitigating the impact of high-frequency noise. Most existing methods rely on frame-by-frame fusion, which often struggles to distinguish informative subpixels from noise, leading to suboptimal performance. To address these limitations, we introduce a novel Query Mamba Burst Super-Resolution (QMambaBSR) network. Specifically, we observe that subpixels have consistent spatial distribution while noise appears randomly. Considering the entire burst sequence during fusion allows for more reliable extraction of consistent subpixels and better suppression of noise outliers. Based on this, a Query State Space Model (QSSM) is proposed for both inter-frame querying and intra-frame scanning, enabling a more efficient fusion of useful subpixels. Additionally, to overcome the limitations of static upsampling methods that often result in over-smoothing, we propose an Adaptive Upsampling (AdaUp) module that dynamically adjusts the upsampling kernel to suit the characteristics of different burst scenes, achieving superior detail reconstruction. Extensive experiments on four benchmark datasets—spanning both synthetic and real-world images—demonstrate that QMambaBSR outperforms existing state-of-the-art methods. + +# 1. Introduction + +In recent years, with the continuous development of smartphones, overcoming the limitations of smartphone sensors and lenses to reconstruct high-quality, high-resolution (HR) images has become a research hotspot. Benefited from the development of deep learning, single image superresolution (SISR) [9, 19, 33, 34, 50, 53] has achieved re + +![](images/4af320378dd6d5a44f706fe5449b96754e04c8d60ddf7b76e443de1d09a307e0.jpg) + +![](images/99feba807c7e0c0a5dc213a889eab31927ce24fd032ba278e06f9337782d1dd1.jpg) +(a) Existing Methods +Figure 1. The concat and frame-by-frame operations in existing methods struggle to efficiently extract sub-pixels and suppress noise, leading to remaining artifacts and over-smoothed details, as shown in (a). We observe that noise randomly appears on several frames, while effective sub-pixels have consistent intensity at corresponding positions in all frames, as shown in (c). Based on this, a novel inter-frame query and intra-frame scanning-based QMambaBSR is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously, as shown in (b). + +markable progress, but the performance is still limited by the finite information provided by a single image. Consequently, numerous researchers are dedicating their efforts to burst super-resolution (BurstSR), which aims to leverage the rich sub-pixel details provided by a sequence of burst low-resolution images captured by hand-tremor and camera/object motions to overcome the limitations of SISR, achieving substantial advancements [7, 23, 24, 36, 43]. + +In BurstSR, the first image is the super-resolution frame, denoted as the base frame, while the remaining images, referred to as current frames, supply sub-pixel information for producing a high-quality HR image. The pipeline of most existing BurstSR approaches can be mainly categorized: alignment, fusion, and upsampling. Firstly, due to + +the misalignment caused by hand-tremor, alignment methods [1, 11, 29, 45] are employed to align the current frames with the target base frame. Then, the primary challenge lies in extracting sub-pixel information from the current frames that match the content of the base frame while concurrently suppressing high-frequency random noise. Previous methods, such as weighted-based multi-frame fusion [1, 2], obtain residuals by subtracting each current frame from the base frame and utilizing simple weighting techniques to fuse obtained residual information. Although easy to perform, these methods neglect the inter-frame relationship among multi-frames, failing to extract sub-pixels that better match the base frame and are susceptible to interference from noise in RAW images. To enhance inter-frame relationships, BIPNet [11] proposes channel shuffling of multiframe features to improve information flow between different frames. Consequently, recent state-of-the-art methods, such as GMTNet [12, 28, 31], propose using crossattention, explicitly employing the base frame as a query to retrieve and capture feature differences from the current frame pixel-to-pixel to extract sub-pixel information. RBSR [46] utilize RNNs [25] for frame-by-frame feature fusion, as shown in Figure 1 (a). The aforementioned methods extract sub-pixel information and denoise in a frame-by-frame manner or implement sub-pixel extraction and denoising through separate modules. However, these methods overlook the distinct characteristics between sub-pixels and noise, making it challenging to capture useful sub-pixels from noise and leading to artifacts and over-smoothed details. + +After fusion, adaptively learning high-resolution mappings from the extracted and fused features remains a paramount challenge in BurstSR. The existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], primarily utilize static interpolation, transposed convolution [14], or pixel shuffle [38] for static upsampling. Nevertheless, these approaches make it difficult to adaptively perceive the variations in sub-pixel distribution across different scenes by employing static upsampling methods, resulting in the inability to utilize the spatial arrangement of sub-pixels to accurately reconstruct high-quality, high-resolution (HR) images. + +To address these issues, we propose a novel Query Mamba Burst Super-Resolution (QMambaBSR) network, which integrates a novel Query State Space Model (QSSM) and an Adaptive Up-sampling module (AdaUp) to reconstruct high-quality high-resolution images from burst lowresolution images. Specifically, QSSM is first proposed to efficiently extract the sub-pixels in both inter-frame and intra-frame while mitigating noise interference. In particular, QSSM retrieves information across current frames for the base frame by modifying control matrix $B$ and discretization step size $\Delta$ in the state space function, as shown + +in Figure 1 (b). QSSM synchronously performs inter-frame querying and intra-frame scanning, comprehensively considering both inter-frame and intra-frame information to achieve integrated sub-pixel extraction and noise suppression. AdaUp is proposed to perceive the spatial distribution of sub-pixel information and subsequently adaptively adjust the upsampling kernel to enhance the reconstruction of high-quality HR images across diverse burst LR scenarios. Furthermore, to comprehensively fuse sub-pixels with different scales, the Multi-scale Fusion Module is proposed to combine channel Transformer and local CNN, as well as horizontal and vertical global Mamba, to fuse sub-pixel information of different scales. Extensive experiments on four popular synthetic and real-world benchmarks demonstrate that our method achieves a new state-of-the-art, delivering superior visual results. + +The contributions can be summarized as follows: + +- A novel inter-frame query and intra-frame scanning-based Query State Space Model (QSSM) is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously. +- We propose a novel Adaptive Up-sampling module, designed respectively for adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst LR scenarios, and for the fusion of sub-pixels across different scales. +- Our proposed method achieves new state-of-the-art (SOTA) performance on the four popular public synthetic and real benchmarks, demonstrating the superiority and practicability of our method. + +# 2. Related Work + +In this section, we briefly review Multi-Frame SuperResolution and State Space Models. More comprehensive surveys are provided in [3, 48]. + +Multi-Frame Super-Resolution. With the rapid development of deep learning in recent years [15, 18, 26, 41], deep-learning-based single image super-resolution (SISR) achieves significant breakthroughs [6, 47, 49, 51]. However, due to the limited information provided by a single image, the performance of SISR is significantly constrained [27, 39, 42, 52]. Therefore, Multi-Frame Super-Resolution (MFSR) is proposed to overcome the limitations of SISR by leveraging the useful sub-pixel information contained in multiple low-resolution images, achieving superior high-resolution reconstruction. In particular, DBSR [1] proposes using optical flow methods to explicitly align multiple low-resolution images and then fuse their features through attention weights. MFIR [2] utilizes optical flow for feature warping and proposes a deep reparametrization of the classical MAP formulation for multi-frame image restoration. BIPNet [11] proposes a pseudo-burst fusion strategy by fusing temporal features channel-by-channel, + +enabling frequent inter-frame interaction. Burstormer [12] leverages multi-scale local and non-local features for alignment and employs neighborhood interaction for further inter-frame feature fusion. RBSR [46] utilizes recurrent neural networks for progressive feature aggregation. However, most of these methods mainly use frame-by-frame approaches or pairwise interactions, either failing to explicitly extract sub-pixel information from the current frames or only querying the current frame point-by-point from the base frame. This makes it difficult for them to effectively extract sub-pixel details while suppressing noise interference. To address these limitations, we propose Query Mamba Burst Super-Resolution (QMambaBSR), which allows the base frame to simultaneously query inter-frame and intra-frame information to extract sub-pixel details embedded in structured regions while also suppressing noise interference. + +State Space Models. State Space Models (SSMs) originated in the 1960s in control systems [20], where they are used for modeling continuous signal input systems. Recently, advancements in SSMs have led to their application in computer vision [5, 13, 32, 56]. Notably, Visual Mamba introduced a residual VSS module and developed four scanning directions for visual images, achieving superior performance compared to ViT [10] while maintaining lower model complexity, thereby attracting significant attention [16, 22, 35, 40, 44, 54]. QueryMamba [55] is proposed to apply SSM to video action forecasting tasks. MambaIR [16] is the first to employ SSMs in image restoration, enhancing efficiency and global perceptual capabilities. However, there remains potential for further exploration of SSMs in BurstSR. Therefore, we propose a novel Query-based State Space Model designed to efficiently extract sub-pixel information for BurstSR. + +# 3. Method + +# 3.1. Overview + +Given a sequence of input low-resolution (LR) images, denoted as $\{x_{i}\}_{i = 1}^{N}$ , where $N$ represents the number of burst LR frames. Following [1], we denote the first image as the base frame for super-resolution, while the other LR frames are used to provide rich sub-pixel information and are referred to as current frames. BurstSR can be defined as utilizing the sub-pixel information extracted from the current frames to supplement the base frame, generating a high-quality, high-resolution RGB image $I_{HR}$ with a superresolution factor of $s$ . + +To achieve this goal, we propose QMambaBSR for burst image super-resolution, as illustrated in Figure 2. First, we use alignment block [12] to align the current images to the spatial position of the base frame. Next, we introduce a novel Query State Space Model (QSSM) designed to query + +sub-pixel information from the current images and mitigate noise interference in both inter-frame and intra-frame manner. Additionally, we present a novel Adaptive Up-sampling (AdaUp) module, which facilitates adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst images. Finally, a new Multi-scale Fusion Module is incorporated to fuse sub-pixel information across different scales. Next, we provide a detailed explanation of each component. + +# 3.2. Query State Space Model + +Considering that burst RAW images often contain high-frequency random noise and the sub-pixel information to be extracted typically shares a similar distribution with the base frame, it is crucial for the BurstSR task to utilize the base frame to uncover the rich sub-pixel information contained in the current frames for super-resolution, while simultaneously suppressing noise. Existing methods [1, 11, 12, 45, 46] simply concatenate multi-frame information but fail to precisely extract sub-pixel information from the current frames using the base frame, resulting in a scarcity of sub-pixel details and consequently making it difficult to reconstruct fine details. Moreover, while some existing approaches attempt to use cross-attention [31], utilizing the base frame as the query for sub-pixels extraction, such frame-by-frame methods struggle to suppress noise interference and are plagued by high computational complexity. This often results in the presence of noise and the introduction of artifacts. Therefore, we propose the Query State Space Model (QSSM), which enables the base frame to efficiently query all current frames simultaneously in both intra-frame and inter-frame manners. By leveraging the consistent distribution of sub-pixels and the inconsistent distribution of noise, our QSSM can simultaneously query multiple images to extract the necessary sub-pixel information while effectively suppressing random noise. + +First, let's briefly review the State Space Model (SSM). The latest advances in structured state space sequence models (S4) are largely inspired by continuous linear time-invariant (LTI) systems, which map input $x(t)$ to output $y(t)$ through an implicit latent state $h(t) \in \mathbb{R}^N$ [16]. This system can be represented as a linear ordinary differential equation (ODE): + +$$ +\dot {h} (t) = A h (t) + B x (t), \tag {1} +$$ + +$$ +y (t) = C h (t) + D x (t), +$$ + +where $N$ is the state size, $A \in \mathbb{R}^{N \times N}$ , $B \in \mathbb{R}^{N \times 1}$ , $C \in \mathbb{R}^{1 \times N}$ , and $D \in \mathbb{R}$ . Discretized using a zero-order hold as follows: + +$$ +\begin{array}{l} \bar {A} = \exp (\Delta A), \\ - \end{array} \tag {2} +$$ + +$$ +\overline {{B}} = (\Delta A) ^ {- 1} (\exp (\Delta A) - I) \Delta B, +$$ + +![](images/e60171a60c6c90a522cea2c63295c4ab321aff8eec7b846d02a6b150dba9431c.jpg) +Figure 2. The overall framework of our proposed QMambaBSR, primarily includes the novel Query State Space Model (QSSM), Multiscale Fusion Module (MSFM), and the Adaptive Up-sampling Module (AdaUp). + +After the discretization, the discretized version of Eq. (1) with step size $\Delta$ can be rewritten as: + +$$ +h _ {k} = \bar {A} h _ {k - 1} + \bar {B} x _ {k}, \tag {3} +$$ + +$$ +y _ {k} = C h _ {k} + D x _ {k}, +$$ + +At this point, the LTI system's input parameter matrices are static. Therefore, recent work [16] makes $B$ , $C$ , and $\Delta$ depend on the input. Recent research suggests that since the $A$ matrix is a HIPPO matrix and $\Delta$ represents the step size, $\exp(\Delta A)$ can be viewed as forget gate and input gate [17], which modulates the influence of the input on the state. + +However, traditional SSM lacks the multi-frame querying capabilities that are crucial for BurstSR tasks. Therefore, we propose a QSSM to enable the base frame to gate the output of the current frames, thereby allowing the base frame to perform information queries on the current frames to obtain the sub-pixels while eliminating noise, as illustrated in Figure 1. Specifically, we let the current frames drive the state changes, with the base frame gating the influence of the current frames on the state through $B$ and $\Delta$ . As shown in Figure 2 (a), the corresponding formulas are as follows: + +$$ +h _ {t} = \left(\bar {A} _ {\text {b a s e} _ {t}}\right) h _ {t - 1} + \left(\bar {B} _ {\text {b a s e} _ {t}}\right) x _ {\text {c u r} _ {t}}, \tag {4} +$$ + +$$ +y _ {t} = C h _ {t} + D x _ {\mathrm {c u r} _ {t}}, +$$ + +Considering that noise may exist at certain locations in the base frame and is randomly distributed at the same locations in other current frames, we concatenate the base + +frame with other current frames to initially reduce random noise in the original base frame and achieve preliminary feature fusion. Specifically, the concatenated features are processed by an MLP layer and finally projected back to the channel dimension of the original base frame, using it as the new base frame. Then the base frame is transformed through a learnable linear layer to generate $\Delta_{\mathrm{base}_t}$ and $B_{\mathrm{base}_t}$ , and these are then used in the discretization formula from Eq. (2) to obtain $\overline{A}_{\mathrm{base}_t}$ and $\overline{B}_{\mathrm{base}_t}$ . The current frames are processed through another linear layer to obtain $x_{\mathrm{cur}_t}$ , where $t$ indicates the positional relationship after flattening the base frame and current frames. + +Utilizing Eq. (2), the zero-order hold and discretization can be expanded as follows: + +$$ +h _ {t} = \sum_ {j = 0} ^ {t} \left[ \prod_ {i = j + 1} ^ {t} \exp \left(\Delta_ {\text {b a s e} _ {i}} A\right) \right] \tilde {f} \left(\Delta_ {\text {b a s e} _ {j}}\right) B _ {\text {b a s e} _ {j}} x _ {\text {c u r} _ {j}}, \tag {5} +$$ + +$$ +\begin{array}{l} y _ {t} = C \sum_ {j = 0} ^ {t} \left[ \prod_ {i = j + 1} ^ {t} \exp \left(\Delta_ {\text {b a s e} _ {i}} A\right) \right] \tilde {f} \left(\Delta_ {\text {b a s e} _ {j}}\right) B _ {\text {b a s e} _ {j}} x _ {\text {c u r} _ {j}} \tag {6} \\ + D x _ {\mathrm {c u r} _ {2}}, \\ \end{array} +$$ + +where $\tilde{f}$ represents the functions of $\Delta$ and $B$ corresponding to the zero-order hold of $B$ , as follows: + +$$ +\tilde {f} \left(\Delta_ {\text {b a s e} _ {t}}\right) = \left(\Delta_ {\text {b a s e} _ {t}} A\right) ^ {- 1} \left(\exp \left(\Delta_ {\text {b a s e} _ {t}} A\right) - I\right) \Delta_ {\text {b a s e} _ {t}}. \tag {7} +$$ + +Specifically, in the State Space Model, the input $x_{t}$ at time $t$ is influenced by the control matrix $B$ , which in turn affects the change in state $h$ . In the discretized state space, + +![](images/996149ebb5329f6b0eb7dd933df3d6bcdc878a5c8980b82be96deba3cf6d4be1.jpg) +Figure 3. Illustrative comparison between the proposed QSSM and existing cross-attention mechanisms. + +the discretization step size $\Delta$ represents the time $x_{t}$ acts on the state. In QSSM, we desire the base frame to act as a gate controlling the influence of the current frames on the state, thereby affecting the output. Thus, we generate $\mathrm{base}_t$ and $\Delta$ by the base frame through a linear layer. To exploit the differences in sub-pixels and noise distribution characteristics across multiple frames, we merge current features into the channel dim. Subsequently, all current features are projected into a unified set of merged current features through a linear layer. This allows the base feature to query all current features at once, thereby achieving multi-frame joint denoising. Additionally, as Eq. (5) and (6), when the flattened base feature $f_{\mathrm{base}_t}$ queries the current features at other times $f_{\mathrm{cur}_j}$ , $f_{\mathrm{base}_t}$ modulates and guides $f_{\mathrm{base}_j}$ to query $f_{\mathrm{cur}_j}$ through the forget gate and input gate $\exp (\Delta_{\mathrm{base}_t}A)$ , ultimately feeding back to the output at time $t$ . This enhances the interaction between $f_{\mathrm{base}_t}$ and its neighboring base features as well as current features. Due to the characteristics of the matrix $A$ , the influence of $f_{\mathrm{base}_t}$ in guiding the query of $f_{\mathrm{base}_j}$ gradually decreases with their distance in the sequence, forming a progressively diminishing receptive field. This prevents $f_{\mathrm{base}_t}$ from overly focusing on spatially distant information, thereby enhancing neighborhood interactions. Since each query by the base feature simultaneously queries all current features, the base feature can better perceive sub-pixel information consistently distributed across frames, suppressing random noise. We modify the RSSB block [16] by integrating our proposed QSSM with four scanning directions and using channel attention to enhance channel interaction. + +Discussion To clarify the differences between the proposed QSSM and existing cross-attention methods, we conduct a detailed analysis along with a schematic comparison. As shown in Figure 3 (a), the cross-attention method uses serialized base feature tokens at position $t$ as the $\mathrm{Q}$ matrix, querying with all position tokens of the current features as the $\mathrm{K}$ matrix to extract sub-pixel information. In contrast, our QSSM, as shown in Figure 3 (b), not only extracts sub-pixel information from the current features to the base fea + +ture but also facilitates information interaction within the base feature. It simultaneously retrieves corresponding current feature tokens from other position tokens in the serialized base feature, thereby achieving joint multi-position sub-pixel information retrieval and noise suppression between the base feature and current features. + +# 3.3. Multi-Scale Fusion Module + +Considering the presence of sub-pixel information across various scales within the intricate details of images, we propose a novel Multi-scale Fusion Module (MSFM). This module is designed to effectively integrate multi-scale subpixel information from the current frames, thereby enhancing the capability for detailed image reconstruction. The MSFM comprises three distinct branches: a Convolutional Neural Network (CNN), a State Space Model (SSM) with diverse scanning orientations, and a channel Transformer. To begin with, a $3 \times 3$ convolution is utilized for the fusion of local sub-pixel features. The SSM is introduced to efficiently learn and integrate sub-pixel features along both horizontal and vertical axes. Furthermore, considering the attenuation characteristics of the A matrix within the SSM when dealing with long-range perception, we concurrently employ a Transformer block to augment the network's proficiency in capturing global information. The mathematical formulation of the MSFM is as follows: + +$$ +y = w _ {1} \cdot \operatorname {C N N} (x) + w _ {2} \cdot \operatorname {S S M} (x) + w _ {3} \cdot \operatorname {T r a n s f o r m e r} (x) \tag {8} +$$ + +where $w_{i}$ represents the balancing factors. $x$ and $y$ represent the input feature and output feature, respectively. + +# 3.4. Adaptive Up-sampling Module + +After the aforementioned processes, the sub-pixel structural information from burst LR images is extracted and distributed in the feature space. The next critical challenge is to utilize this valuable sub-pixel information to adaptively upsample the image resolution and incorporate sub-pixel details into the high-resolution image. Existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], simply employ interpolation, transposed convolution, or pixel shuffle techniques for resolution upsampling. However, these methods lack the capability to perceive the distribution of sub-pixels in the feature space, leading to an inability to adaptively reconstruct fine details. Therefore, we introduce a novel Adaptive Up-sampling (AdaUp) module that perceives the distribution of sub-pixels in the spatial domain and adaptively adjusts the up-sampling kernel, thereby achieving higher-quality image detail, as shown in Figure 2 (b). Specifically, we first adaptively perceive the distribution of sub-pixels $L \in \mathbb{R}^{B \times C_{\mathrm{in}} \times 1 \times 1}$ from the input features $X \in \mathbb{R}^{B \times C_{\mathrm{in}} \times H \times W}$ by adaptive pooling. We then perform sequence feature interaction on $L$ to obtain the output channel feature distribution sequence $L_1 \in \mathbb{R}^{B \times C_{\mathrm{out}} \times 1 \times 1}$ . Sub + +sequentially, we apply both the input distribution sequence and the output distribution sequence to the upsampling transposed convolution kernel $W \in \mathbb{R}^{B \times C_{\mathrm{in}} \times C_{\mathrm{out}} \times 3 \times 3}$ using broadcasting, thereby endowing the kernel with feature perception capability. Finally, we obtain the high-resolution output through the upsampling transposed convolution kernel. The corresponding formulas are as follows: + +$$ +L = \text {A d a p t i v e P o o l i n g} (X) \tag {9} +$$ + +$$ +L _ {1} = \operatorname {C o n v} _ {1 \times 1} (L) \tag {10} +$$ + +$$ +W _ {f} = (W \odot L) \odot L _ {1} \tag {11} +$$ + +$$ +y = \operatorname {T r a n s - C o n v} \left(W _ {f}, X\right) \tag {12} +$$ + +where $\odot$ represents element-wise multiplication. Thus, AdaUp can leverage the underlying content information from input frames at different channels and utilize it to get better performance than the mainstream up-sampling operations, pixel shuffle, or interpolations [4, 37]. + +# 4. Experiments and Analysis + +# 4.1. Experimental Settings + +Implementation details. We evaluate the effectiveness of our proposed method on four public burst image superresolution benchmarks, encompassing both synthetic and real datasets: synthetic BurstSR [1], Real BurstSR [1], RealBSR-RAW [45], and RealBSR-RGB [45]. To ensure fairness, we follow [12] for training and evaluation. More details of datasets and data processing can be found in Appendix A section. Following [12], we train the model from scratch on the synthetic BurstSR dataset for 300 epochs, using the AdamW optimizer with parameters $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ . We employ a cosine annealing strategy to gradually decrease the learning rate from $3\times 10^{-4}$ to $10^{-6}$ and set the training patch size to $48\times 48$ . For the Real BurstSR dataset, we follow [1] to fine-tune the model pretrained on synthetic BurstSR for 60 epochs, maintaining the same training setting as the synthetic BurstSR but adjusting the learning rate to $1\times 10^{-6}$ and the training patch size to $56\times 56$ . For the RealBSR-RAW and RealBSR-RGB datasets, we follow [45] to train from scratch for 100 epochs, using the same training setting as the synthetic BurstSR, with a training patch size of $80\times 80$ . We set the batch size to 8, and the burst size to 14, and all experiments are conducted on 8 V100 GPUs. + +Metric. Following previous works [1, 45], we use reference metrics to evaluate performance, including PSNR and SSIM. + +Compared methods. To comprehensively demonstrate the superiority of our proposed method, we compare our QMambaBSR with ten classic and state-of-the-art (SOTA) BurstSR approaches HighRes-net [8], DBSR [1], LKR [21], MFIR [2], BIPNet [11], AFCNet [30], FBAnet [45], Burstormer [12], RBSR [46], GMTNet [31]. + +# 4.2. Quantitative and Qualitative Results + +Results on the Synthetic BurstSR dataset. As shown in Table 1, our method outperforms existing BurstSR methods, achieving the best performance. For example, compared to the existing SOTA method, Burstormer, our method achieves a $0.29\mathrm{dB}$ improvement in PSNR. Furthermore, to further demonstrate the visual superiority of our method, we present a visual comparison with existing methods in Figure 4. We can observe that the RAW low-resolution images exhibit significant noise and severe detail loss, as illustrated in the window area of Figure 4. Compared to existing methods, our method demonstrates superior performance in reconstructing textures and details in the window area. Additionally, in the green stripes region at the bottom of Figure 4, the substantial noise in the base frame leads existing methods to leave artifacts. However, our method more effectively distinguishes between noise and sub-pixels, producing more detailed, artifact-free high-resolution images, thereby demonstrating the visual superiority of our method. + +Results on RealBSR-RGB and RealBSR-RAW. As shown in Table 2, our method consistently outperforms existing methods on these two real benchmarks, achieving the best performance. For RealBSR-RAW, our method surpasses FBANet and Burstormer in PSNR and linear-PSNR by $0.268\mathrm{dB}$ and $0.258\mathrm{dB}$ , respectively. For RealBSR-RGB, our method surpasses FBANet and Burstormer in PSNR by $0.204\mathrm{dB}$ . Furthermore, as shown in Figure 5, the results demonstrate the superior performance of our method in detail reconstruction and artifact suppression. This validates the effectiveness of our method in real-world scenarios, highlighting its superiority and practicality. More results on Real BurstSR and qualitative results will be presented in the appendix. + +# 4.3. Ablation Study + +To demonstrate the effectiveness and superiority of the proposed modules, we conduct a series of ablation experiments. Specifically, we incrementally integrate the proposed modules into the baseline network. For rapid evaluation, we train our model on the synthetic dataset for 100 epochs. From Table 3, we observe that the introduction of the MSFM module, which enhances the network's multiscale perception and fully integrates sub-pixel information from different frames, significantly improves performance by 1.34 dB in PSNR. Furthermore, the addition of the QSSM, which extracts sub-pixels from the current frames that match the content of the base frame while suppressing noise, leads to an additional performance gain of 0.72 dB in PSNR. Finally, incorporating the proposed Adaptive Up-sampling module, which better adapts the up-sampling kernel according to the scene, thereby generating high-resolution images with richer details, results in a further improvement of 0.26 dB. These results indicate that the pro + +
BicubicHighRes-netDBSRLKRMFIRBIPNetAFCNetFBAnetGMTNetRBSRBurstormerOurs
PSNR↑36.1737.4540.7641.4541.5641.9342.2142.2342.3642.4442.8343.12
SSIM↑0.910.920.960.950.960.960.960.970.960.970.970.97
+ +![](images/c720215ff483f423f83b6f1cfb8696a6e1dcbd1f4d2d5a83ae8d97309fa0ce21.jpg) +Figure 4. Visual comparison results with different methods on SyntheticBurst datasets for $\times 4$ BurstSR. + +Table 1. Performance comparison of existing methods on Synthetic BurstSR dataset for $\times 4$ BurstSR. + +
MethodRealBSR-RAWRealBSR-RGB
PSNR↑SSIM↑L-PSNR↑PSNR↑SSIM↑
DBSR20.9060.63530.48430.7150.899
MFIR21.5620.63830.97930.8950.899
BSRT22.5790.62230.82930.7820.900
BIPNet22.8960.64131.31130.6550.892
FBANet23.4230.67732.25631.0120.898
Burstormer27.2900.81632.53331.1970.907
Ours27.5580.82032.79131.4010.908
+ +posed modules significantly enhance burst super-resolution performance. + +Comparison with Existing Modules. To verify the effectiveness of proposed module, we replaced it with existing fusion and up-sampling modules. To effectively represent the performance of various methods while also considering training time, we train for 100 epochs on the synthetic dataset. As shown in Table 4, in the fusion stage, compared to PBFF [11] or NRFE [12], our QSSM and MSFM modules are able to better exploit the inter-frame consistency of sub-pixel distribution while denoising, resulting in + +Table 2. Performance comparison of existing methods on RealBSR-RGB and RealBSR-RAW datasets for $\times 4$ BurstSR. + +
QSSMMSFMAdaUpPSNR↑SSIM↑
×××39.810.93
×✓×41.150.94
✓✓×41.870.96
✓✓✓42.130.96
+ +Table 3. Ablation experiment on proposed core modules. + +PSNR improvements of 1.56 dB and 0.41 dB, respectively. In contrast to static upsampling like pixel shuffle and transposed convolution, our AdaUp module enhances the network's ability to perceive scene-specific sub-pixel distributions, leading to a PSNR improvement of 0.16 dB. + +Evaluation about MSFM. To validate the effectiveness of different branches within the proposed MSFM, we conducted ablation experiments with various internal branch setting. The experimental results are shown in Table 5. To minimize training time while ensuring experimental validity, the ablation experiments were conducted on a synthetic dataset and trained for 100 epochs. As shown in the table, we use only the convolution in the MSFM module as the baseline. Adding the transformer module resulted in a PSNR increase of $0.39\mathrm{dB}$ . When the transformer was replaced with SSM, the PSNR improved by $0.44\mathrm{dB}$ compared to using only the conv method. Under our proposed + +![](images/36f9b19c16b2751da3bb40f93c3c978ca13499ba0378649f71e4db3bd1c41093.jpg) +Base frame + +![](images/276f9e2792f69034366bc192f024dca131030e0668b65e728e75d321cca21607.jpg) +DBSR + +![](images/3ce575c281f01f9328fd39050b8526fb19975bdab7ee9dd113b4c34aa0a3d8b9.jpg) +MFIR + +![](images/1a2ef664901149353271a234b44b9f7858855663725fbf7c332a40e774985cd2.jpg) +BIPNet + +![](images/a2a238e248bf82d6736b0a3f0cfc3e9648eb675b64ccd0eb2490a124891656d6.jpg) +Burstomer + +![](images/7f66e730c5bd8c2c0b7c549da4aceee9477d29fa0418321004d56ecd555f325b.jpg) +Ours + +![](images/aa62d775277509aa33a491bff134ba30340b7eb6d729f15fbb263dc6dbc7df80.jpg) +Ground Truth + +![](images/88240037ed5f132da88424335868ec71de1b314d3dce160234ba13e5790c0566.jpg) +Figure 5. Visual comparison results with different methods on RealBSR-RGB dataset for $\times 4$ BurstSR. +Figure 6. User study of reconstructed real HR images. + +
Process StageMethodsPSNR↑SSIM↑
FusionConcat39.850.93
PBFF [11]40.570.94
NRFE [12]41.720.96
Ours42.130.96
Up-samplerPixelshuffle41.890.96
Transposed conv41.970.96
Ours42.130.96
+ +MSFM, the PSNR increased by 0.56 dB, clearly demonstrating the effectiveness of both the SSM and transformer branches in the MSFM. + +# 4.4. User study + +To effectively illustrate the superiority of our proposed method in reconstructing visually pleasing images, we conducted a user study involving 10 real burst images selected from well-established benchmarks. Twenty volunteers participated in this study, tasked with rating the similarity and quality between each reconstructed image and the ground truth (GT). They used a detailed scale ranging from 0, indicating visually unsatisfactory and completely dissimilar + +Table 4. Comparison with existing modules on fusion and upsampling process stage. + +
ConvTransformerSSMPSNR↑SSIM↑
✓××41.570.95
✓✓×41.960.96
✓×✓42.010.96
✓✓✓42.130.96
+ +Table 5. Ablation studies on our proposed MSFM. + +images, to 10, representing visually satisfactory and highly similar images. We then meticulously aggregated the scores from all volunteers, and the results are depicted in Figure 6. When compared to existing methods such as Burstormer and BIPNet, our proposed method stands out by adaptively extracting sub-pixels to achieve superior visual effects. This approach earned our method the highest average score of 8.56, underscoring its effectiveness. + +# 5. Conclusion + +In this paper, we introduce a novel approach called QMambaBSR for burst image super-resolution. Based on the structural consistency of sub-pixels and the inconsistency of random noise, we propose a novel Query State Space Model to efficiently query sub-pixel information embedded in current frames through an intra- and inter-frame multi-frame joint query approach while suppressing noise interference. We introduce a Multi-scale Fusion Module for information on sub-pixels across different scales. Additionally, a novel Adaptive Up-sampling module is proposed to perceive the spatial arrangement of sub-pixel information in various burst scenarios for adaptive up-sampling and detail reconstruction. Extensive experiments on four public synthetic and real benchmarks demonstrate that our method surpasses existing methods, achieving state-of-the-art performance while presenting the best visual quality. + +# 6. Acknowledgments + +This work was supported by the Natural Science Foundation of China under Grants 62225207,62436008 and 62206262. + +# References + +[1] Goutam Bhat, Martin Danelljan, Luc Van Gool, and Radu Timofte. Deep burst super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9209-9218, 2021. 2, 3, 6 +[2] Goutam Bhat, Martin Danelljan, Fisher Yu, Luc Van Gool, and Radu Timofte. 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Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 3 \ No newline at end of file diff --git a/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/images.zip b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..42873680493327857e956dedf723fad91570bb63 --- /dev/null +++ b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7eb6d5defedd6610f598554fa26418a4742c93930cfc971f99351136c57775fe +size 655506 diff --git a/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/layout.json b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f1802df99b507e9206f026d12c00b3f8c42671e8 --- /dev/null +++ b/2025/QMambaBSR_ Burst Image Super-Resolution with Query State Space Model/layout.json @@ -0,0 +1,8839 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 67, + 103, + 542, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 103, + 542, + 121 + ], + "spans": [ + { + "bbox": [ + 67, + 103, + 542, + 121 + ], + "type": "text", + "content": "QMambaBSR: Burst Image Super-Resolution with Query State Space Model" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "spans": [ + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": "Xin Di" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Long Peng" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1\\dagger,\\ddagger}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Peizhe Xia" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Wenbo Li" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Renjing Pei" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Yang Cao" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Yang Wang" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1,3*}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": ", Zheng-Jun Zha" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": "University of Science and Technology of China, " + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": "Huawei Noah's Ark Lab, " + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 61, + 142, + 582, + 171 + ], + "type": "text", + "content": "Chang'an University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 173, + 532, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 173, + 532, + 185 + ], + "spans": [ + { + "bbox": [ + 110, + 173, + 532, + 185 + ], + "type": "text", + "content": "{dx9826, longp2001}@mail.ustc.edu.cn, peirenjing@huawei.com, ywang120@chd.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "spans": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 238, + 296, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 238, + 296, + 549 + ], + "spans": [ + { + "bbox": [ + 55, + 238, + 296, + 549 + ], + "type": "text", + "content": "Burst super-resolution (BurstSR) aims to reconstruct high-resolution images by fusing subpixel details from multiple low-resolution burst frames. The primary challenge lies in effectively extracting useful information while mitigating the impact of high-frequency noise. Most existing methods rely on frame-by-frame fusion, which often struggles to distinguish informative subpixels from noise, leading to suboptimal performance. To address these limitations, we introduce a novel Query Mamba Burst Super-Resolution (QMambaBSR) network. Specifically, we observe that subpixels have consistent spatial distribution while noise appears randomly. Considering the entire burst sequence during fusion allows for more reliable extraction of consistent subpixels and better suppression of noise outliers. Based on this, a Query State Space Model (QSSM) is proposed for both inter-frame querying and intra-frame scanning, enabling a more efficient fusion of useful subpixels. Additionally, to overcome the limitations of static upsampling methods that often result in over-smoothing, we propose an Adaptive Upsampling (AdaUp) module that dynamically adjusts the upsampling kernel to suit the characteristics of different burst scenes, achieving superior detail reconstruction. Extensive experiments on four benchmark datasets—spanning both synthetic and real-world images—demonstrate that QMambaBSR outperforms existing state-of-the-art methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 573, + 135, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 573, + 135, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 573, + 135, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 594, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 666 + ], + "type": "text", + "content": "In recent years, with the continuous development of smartphones, overcoming the limitations of smartphone sensors and lenses to reconstruct high-quality, high-resolution (HR) images has become a research hotspot. Benefited from the development of deep learning, single image superresolution (SISR) [9, 19, 33, 34, 50, 53] has achieved re" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 320, + 212, + 548, + 287 + ], + "blocks": [ + { + "bbox": [ + 320, + 212, + 548, + 287 + ], + "lines": [ + { + "bbox": [ + 320, + 212, + 548, + 287 + ], + "spans": [ + { + "bbox": [ + 320, + 212, + 548, + 287 + ], + "type": "image", + "image_path": "4af320378dd6d5a44f706fe5449b96754e04c8d60ddf7b76e443de1d09a307e0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 297, + 548, + 412 + ], + "blocks": [ + { + "bbox": [ + 406, + 288, + 462, + 297 + ], + "lines": [ + { + "bbox": [ + 406, + 288, + 462, + 297 + ], + "spans": [ + { + "bbox": [ + 406, + 288, + 462, + 297 + ], + "type": "text", + "content": "(a) Existing Methods" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 297, + 548, + 412 + ], + "lines": [ + { + "bbox": [ + 317, + 297, + 548, + 412 + ], + "spans": [ + { + "bbox": [ + 317, + 297, + 548, + 412 + ], + "type": "image", + "image_path": "99feba807c7e0c0a5dc213a889eab31927ce24fd032ba278e06f9337782d1dd1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 422, + 555, + 521 + ], + "lines": [ + { + "bbox": [ + 313, + 422, + 555, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 555, + 521 + ], + "type": "text", + "content": "Figure 1. The concat and frame-by-frame operations in existing methods struggle to efficiently extract sub-pixels and suppress noise, leading to remaining artifacts and over-smoothed details, as shown in (a). We observe that noise randomly appears on several frames, while effective sub-pixels have consistent intensity at corresponding positions in all frames, as shown in (c). Based on this, a novel inter-frame query and intra-frame scanning-based QMambaBSR is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously, as shown in (b)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 555, + 640 + ], + "type": "text", + "content": "markable progress, but the performance is still limited by the finite information provided by a single image. Consequently, numerous researchers are dedicating their efforts to burst super-resolution (BurstSR), which aims to leverage the rich sub-pixel details provided by a sequence of burst low-resolution images captured by hand-tremor and camera/object motions to overcome the limitations of SISR, achieving substantial advancements [7, 23, 24, 36, 43]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "In BurstSR, the first image is the super-resolution frame, denoted as the base frame, while the remaining images, referred to as current frames, supply sub-pixel information for producing a high-quality HR image. The pipeline of most existing BurstSR approaches can be mainly categorized: alignment, fusion, and upsampling. Firstly, due to" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 674, + 295, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 295, + 712 + ], + "type": "text", + "content": "*Yang Wang and Renjing Pei are the corresponding authors. † These authors contributed equally to this work. ‡Long Peng is the project leader. This work was finished during Xin Di and Long Peng in the internship of Huawei Noah." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23080" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 430 + ], + "type": "text", + "content": "the misalignment caused by hand-tremor, alignment methods [1, 11, 29, 45] are employed to align the current frames with the target base frame. Then, the primary challenge lies in extracting sub-pixel information from the current frames that match the content of the base frame while concurrently suppressing high-frequency random noise. Previous methods, such as weighted-based multi-frame fusion [1, 2], obtain residuals by subtracting each current frame from the base frame and utilizing simple weighting techniques to fuse obtained residual information. Although easy to perform, these methods neglect the inter-frame relationship among multi-frames, failing to extract sub-pixels that better match the base frame and are susceptible to interference from noise in RAW images. To enhance inter-frame relationships, BIPNet [11] proposes channel shuffling of multiframe features to improve information flow between different frames. Consequently, recent state-of-the-art methods, such as GMTNet [12, 28, 31], propose using crossattention, explicitly employing the base frame as a query to retrieve and capture feature differences from the current frame pixel-to-pixel to extract sub-pixel information. RBSR [46] utilize RNNs [25] for frame-by-frame feature fusion, as shown in Figure 1 (a). The aforementioned methods extract sub-pixel information and denoise in a frame-by-frame manner or implement sub-pixel extraction and denoising through separate modules. However, these methods overlook the distinct characteristics between sub-pixels and noise, making it challenging to capture useful sub-pixels from noise and leading to artifacts and over-smoothed details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 435, + 294, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 435, + 294, + 578 + ], + "spans": [ + { + "bbox": [ + 57, + 435, + 294, + 578 + ], + "type": "text", + "content": "After fusion, adaptively learning high-resolution mappings from the extracted and fused features remains a paramount challenge in BurstSR. The existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], primarily utilize static interpolation, transposed convolution [14], or pixel shuffle [38] for static upsampling. Nevertheless, these approaches make it difficult to adaptively perceive the variations in sub-pixel distribution across different scenes by employing static upsampling methods, resulting in the inability to utilize the spatial arrangement of sub-pixels to accurately reconstruct high-quality, high-resolution (HR) images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "text", + "content": "To address these issues, we propose a novel Query Mamba Burst Super-Resolution (QMambaBSR) network, which integrates a novel Query State Space Model (QSSM) and an Adaptive Up-sampling module (AdaUp) to reconstruct high-quality high-resolution images from burst lowresolution images. Specifically, QSSM is first proposed to efficiently extract the sub-pixels in both inter-frame and intra-frame while mitigating noise interference. In particular, QSSM retrieves information across current frames for the base frame by modifying control matrix " + }, + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "text", + "content": " and discretization step size " + }, + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 57, + 582, + 294, + 712 + ], + "type": "text", + "content": " in the state space function, as shown" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 316, + 72, + 553, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 72, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 553, + 262 + ], + "type": "text", + "content": "in Figure 1 (b). QSSM synchronously performs inter-frame querying and intra-frame scanning, comprehensively considering both inter-frame and intra-frame information to achieve integrated sub-pixel extraction and noise suppression. AdaUp is proposed to perceive the spatial distribution of sub-pixel information and subsequently adaptively adjust the upsampling kernel to enhance the reconstruction of high-quality HR images across diverse burst LR scenarios. Furthermore, to comprehensively fuse sub-pixels with different scales, the Multi-scale Fusion Module is proposed to combine channel Transformer and local CNN, as well as horizontal and vertical global Mamba, to fuse sub-pixel information of different scales. Extensive experiments on four popular synthetic and real-world benchmarks demonstrate that our method achieves a new state-of-the-art, delivering superior visual results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 326, + 264, + 524, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 264, + 524, + 274 + ], + "spans": [ + { + "bbox": [ + 326, + 264, + 524, + 274 + ], + "type": "text", + "content": "The contributions can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 276, + 553, + 430 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 276, + 553, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 276, + 553, + 323 + ], + "spans": [ + { + "bbox": [ + 314, + 276, + 553, + 323 + ], + "type": "text", + "content": "- A novel inter-frame query and intra-frame scanning-based Query State Space Model (QSSM) is proposed to extract more accurate sub-pixels while mitigating noise interference simultaneously." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 323, + 553, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 323, + 553, + 381 + ], + "spans": [ + { + "bbox": [ + 314, + 323, + 553, + 381 + ], + "type": "text", + "content": "- We propose a novel Adaptive Up-sampling module, designed respectively for adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst LR scenarios, and for the fusion of sub-pixels across different scales." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 383, + 553, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 383, + 553, + 430 + ], + "spans": [ + { + "bbox": [ + 314, + 383, + 553, + 430 + ], + "type": "text", + "content": "- Our proposed method achieves new state-of-the-art (SOTA) performance on the four popular public synthetic and real benchmarks, demonstrating the superiority and practicability of our method." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 316, + 442, + 400, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 442, + 400, + 453 + ], + "spans": [ + { + "bbox": [ + 316, + 442, + 400, + 453 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 463, + 553, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 463, + 553, + 497 + ], + "spans": [ + { + "bbox": [ + 316, + 463, + 553, + 497 + ], + "type": "text", + "content": "In this section, we briefly review Multi-Frame SuperResolution and State Space Models. More comprehensive surveys are provided in [3, 48]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 316, + 498, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 498, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 316, + 498, + 553, + 712 + ], + "type": "text", + "content": "Multi-Frame Super-Resolution. With the rapid development of deep learning in recent years [15, 18, 26, 41], deep-learning-based single image super-resolution (SISR) achieves significant breakthroughs [6, 47, 49, 51]. However, due to the limited information provided by a single image, the performance of SISR is significantly constrained [27, 39, 42, 52]. Therefore, Multi-Frame Super-Resolution (MFSR) is proposed to overcome the limitations of SISR by leveraging the useful sub-pixel information contained in multiple low-resolution images, achieving superior high-resolution reconstruction. In particular, DBSR [1] proposes using optical flow methods to explicitly align multiple low-resolution images and then fuse their features through attention weights. MFIR [2] utilizes optical flow for feature warping and proposes a deep reparametrization of the classical MAP formulation for multi-frame image restoration. BIPNet [11] proposes a pseudo-burst fusion strategy by fusing temporal features channel-by-channel," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23081" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 274 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 274 + ], + "type": "text", + "content": "enabling frequent inter-frame interaction. Burstormer [12] leverages multi-scale local and non-local features for alignment and employs neighborhood interaction for further inter-frame feature fusion. RBSR [46] utilizes recurrent neural networks for progressive feature aggregation. However, most of these methods mainly use frame-by-frame approaches or pairwise interactions, either failing to explicitly extract sub-pixel information from the current frames or only querying the current frame point-by-point from the base frame. This makes it difficult for them to effectively extract sub-pixel details while suppressing noise interference. To address these limitations, we propose Query Mamba Burst Super-Resolution (QMambaBSR), which allows the base frame to simultaneously query inter-frame and intra-frame information to extract sub-pixel details embedded in structured regions while also suppressing noise interference." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 276, + 295, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 276, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 276, + 295, + 479 + ], + "type": "text", + "content": "State Space Models. State Space Models (SSMs) originated in the 1960s in control systems [20], where they are used for modeling continuous signal input systems. Recently, advancements in SSMs have led to their application in computer vision [5, 13, 32, 56]. Notably, Visual Mamba introduced a residual VSS module and developed four scanning directions for visual images, achieving superior performance compared to ViT [10] while maintaining lower model complexity, thereby attracting significant attention [16, 22, 35, 40, 44, 54]. QueryMamba [55] is proposed to apply SSM to video action forecasting tasks. MambaIR [16] is the first to employ SSMs in image restoration, enhancing efficiency and global perceptual capabilities. However, there remains potential for further exploration of SSMs in BurstSR. Therefore, we propose a novel Query-based State Space Model designed to efficiently extract sub-pixel information for BurstSR." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 494, + 111, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 111, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 111, + 506 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 514, + 123, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 123, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 123, + 526 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "content": "Given a sequence of input low-resolution (LR) images, denoted as " + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "inline_equation", + "content": "\\{x_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "content": " represents the number of burst LR frames. Following [1], we denote the first image as the base frame for super-resolution, while the other LR frames are used to provide rich sub-pixel information and are referred to as current frames. BurstSR can be defined as utilizing the sub-pixel information extracted from the current frames to supplement the base frame, generating a high-quality, high-resolution RGB image " + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "inline_equation", + "content": "I_{HR}" + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "content": " with a superresolution factor of " + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 533, + 295, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "To achieve this goal, we propose QMambaBSR for burst image super-resolution, as illustrated in Figure 2. First, we use alignment block [12] to align the current images to the spatial position of the base frame. Next, we introduce a novel Query State Space Model (QSSM) designed to query" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": "sub-pixel information from the current images and mitigate noise interference in both inter-frame and intra-frame manner. Additionally, we present a novel Adaptive Up-sampling (AdaUp) module, which facilitates adaptive up-sampling based on the spatial arrangement of sub-pixel information in various burst images. Finally, a new Multi-scale Fusion Module is incorporated to fuse sub-pixel information across different scales. Next, we provide a detailed explanation of each component." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 189, + 456, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 189, + 456, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 189, + 456, + 202 + ], + "type": "text", + "content": "3.2. Query State Space Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 207, + 555, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 207, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 555, + 506 + ], + "type": "text", + "content": "Considering that burst RAW images often contain high-frequency random noise and the sub-pixel information to be extracted typically shares a similar distribution with the base frame, it is crucial for the BurstSR task to utilize the base frame to uncover the rich sub-pixel information contained in the current frames for super-resolution, while simultaneously suppressing noise. Existing methods [1, 11, 12, 45, 46] simply concatenate multi-frame information but fail to precisely extract sub-pixel information from the current frames using the base frame, resulting in a scarcity of sub-pixel details and consequently making it difficult to reconstruct fine details. Moreover, while some existing approaches attempt to use cross-attention [31], utilizing the base frame as the query for sub-pixels extraction, such frame-by-frame methods struggle to suppress noise interference and are plagued by high computational complexity. This often results in the presence of noise and the introduction of artifacts. Therefore, we propose the Query State Space Model (QSSM), which enables the base frame to efficiently query all current frames simultaneously in both intra-frame and inter-frame manners. By leveraging the consistent distribution of sub-pixels and the inconsistent distribution of noise, our QSSM can simultaneously query multiple images to extract the necessary sub-pixel information while effectively suppressing random noise." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "text", + "content": "First, let's briefly review the State Space Model (SSM). The latest advances in structured state space sequence models (S4) are largely inspired by continuous linear time-invariant (LTI) systems, which map input " + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "inline_equation", + "content": "x(t)" + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "text", + "content": " to output " + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "inline_equation", + "content": "y(t)" + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "text", + "content": " through an implicit latent state " + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "inline_equation", + "content": "h(t) \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 313, + 506, + 555, + 590 + ], + "type": "text", + "content": " [16]. This system can be represented as a linear ordinary differential equation (ODE):" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 384, + 601, + 553, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 601, + 553, + 620 + ], + "spans": [ + { + "bbox": [ + 384, + 601, + 553, + 620 + ], + "type": "interline_equation", + "content": "\\dot {h} (t) = A h (t) + B x (t), \\tag {1}", + "image_path": "c91cde5274042bc5835e2216b44aaf17407da749e8cef6a372f2ad50eae6ddc2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 386, + 617, + 484, + 629 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 617, + 484, + 629 + ], + "spans": [ + { + "bbox": [ + 386, + 617, + 484, + 629 + ], + "type": "interline_equation", + "content": "y (t) = C h (t) + D x (t),", + "image_path": "dd77375f25490cac16a5fc7c5c71d44b620fa33d8a0f50bb445b5c0ff5f39046.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": " is the state size, " + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{N \\times 1}" + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "inline_equation", + "content": "C \\in \\mathbb{R}^{1 \\times N}" + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "inline_equation", + "content": "D \\in \\mathbb{R}" + }, + { + "bbox": [ + 313, + 639, + 555, + 676 + ], + "type": "text", + "content": ". Discretized using a zero-order hold as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 363, + 685, + 553, + 705 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 685, + 553, + 705 + ], + "spans": [ + { + "bbox": [ + 363, + 685, + 553, + 705 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {A} = \\exp (\\Delta A), \\\\ - \\end{array} \\tag {2}", + "image_path": "0920935f2ea41dadc5313936fbd6cc5f4c5e4e3f50e1126b7ceacd91fa53c0fa.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 703, + 505, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 703, + 505, + 715 + ], + "spans": [ + { + "bbox": [ + 364, + 703, + 505, + 715 + ], + "type": "interline_equation", + "content": "\\overline {{B}} = (\\Delta A) ^ {- 1} (\\exp (\\Delta A) - I) \\Delta B,", + "image_path": "a8281f255650bf60fa3865e279bf2b2872a93b0194b55145e52283dee4fb3f1a.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23082" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 555, + 312 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 555, + 312 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 555, + 312 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 555, + 312 + ], + "type": "image", + "image_path": "e60171a60c6c90a522cea2c63295c4ab321aff8eec7b846d02a6b150dba9431c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 323, + 555, + 346 + ], + "lines": [ + { + "bbox": [ + 55, + 323, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 323, + 555, + 346 + ], + "type": "text", + "content": "Figure 2. The overall framework of our proposed QMambaBSR, primarily includes the novel Query State Space Model (QSSM), Multiscale Fusion Module (MSFM), and the Adaptive Up-sampling Module (AdaUp)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 366, + 295, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 391 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 391 + ], + "type": "text", + "content": "After the discretization, the discretized version of Eq. (1) with step size " + }, + { + "bbox": [ + 55, + 366, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 55, + 366, + 295, + 391 + ], + "type": "text", + "content": " can be rewritten as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 130, + 397, + 294, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 397, + 294, + 417 + ], + "spans": [ + { + "bbox": [ + 130, + 397, + 294, + 417 + ], + "type": "interline_equation", + "content": "h _ {k} = \\bar {A} h _ {k - 1} + \\bar {B} x _ {k}, \\tag {3}", + "image_path": "19b724faed1f277d874b21ace61e23a5728632d67f51bc16fdfd666d1956c57d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 414, + 210, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 414, + 210, + 426 + ], + "spans": [ + { + "bbox": [ + 133, + 414, + 210, + 426 + ], + "type": "interline_equation", + "content": "y _ {k} = C h _ {k} + D x _ {k},", + "image_path": "2105c34445890428c91d0cf924e3835e7e599edf849ea1bc167106515e507efe.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": "At this point, the LTI system's input parameter matrices are static. Therefore, recent work [16] makes " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": " depend on the input. Recent research suggests that since the " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": " matrix is a HIPPO matrix and " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": " represents the step size, " + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "inline_equation", + "content": "\\exp(\\Delta A)" + }, + { + "bbox": [ + 55, + 434, + 295, + 505 + ], + "type": "text", + "content": " can be viewed as forget gate and input gate [17], which modulates the influence of the input on the state." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "text", + "content": "However, traditional SSM lacks the multi-frame querying capabilities that are crucial for BurstSR tasks. Therefore, we propose a QSSM to enable the base frame to gate the output of the current frames, thereby allowing the base frame to perform information queries on the current frames to obtain the sub-pixels while eliminating noise, as illustrated in Figure 1. Specifically, we let the current frames drive the state changes, with the base frame gating the influence of the current frames on the state through " + }, + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 55, + 506, + 295, + 635 + ], + "type": "text", + "content": ". As shown in Figure 2 (a), the corresponding formulas are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 641, + 294, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 641, + 294, + 661 + ], + "spans": [ + { + "bbox": [ + 104, + 641, + 294, + 661 + ], + "type": "interline_equation", + "content": "h _ {t} = \\left(\\bar {A} _ {\\text {b a s e} _ {t}}\\right) h _ {t - 1} + \\left(\\bar {B} _ {\\text {b a s e} _ {t}}\\right) x _ {\\text {c u r} _ {t}}, \\tag {4}", + "image_path": "8df17c628d70c3365502c50234d0a925323e2501a0d6592ed3e20d5068d6b8d5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 658, + 189, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 658, + 189, + 670 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 189, + 670 + ], + "type": "interline_equation", + "content": "y _ {t} = C h _ {t} + D x _ {\\mathrm {c u r} _ {t}},", + "image_path": "86701e5e08a61217200cf39664d8037561e792a50035b4d08affbc8d298c56d7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 712 + ], + "type": "text", + "content": "Considering that noise may exist at certain locations in the base frame and is randomly distributed at the same locations in other current frames, we concatenate the base" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": "frame with other current frames to initially reduce random noise in the original base frame and achieve preliminary feature fusion. Specifically, the concatenated features are processed by an MLP layer and finally projected back to the channel dimension of the original base frame, using it as the new base frame. Then the base frame is transformed through a learnable linear layer to generate " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "B_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": ", and these are then used in the discretization formula from Eq. (2) to obtain " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "\\overline{A}_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "\\overline{B}_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": ". The current frames are processed through another linear layer to obtain " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{cur}_t}" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": " indicates the positional relationship after flattening the base frame and current frames." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 510, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 533 + ], + "type": "text", + "content": "Utilizing Eq. (2), the zero-order hold and discretization can be expanded as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 319, + 537, + 555, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 537, + 555, + 574 + ], + "spans": [ + { + "bbox": [ + 319, + 537, + 555, + 574 + ], + "type": "interline_equation", + "content": "h _ {t} = \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}}, \\tag {5}", + "image_path": "6393b83fc9cd75960f7ccc8b949c01c212cc80dcae37806a64547ec666cfc734.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 578, + 554, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 578, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 319, + 578, + 554, + 628 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} y _ {t} = C \\sum_ {j = 0} ^ {t} \\left[ \\prod_ {i = j + 1} ^ {t} \\exp \\left(\\Delta_ {\\text {b a s e} _ {i}} A\\right) \\right] \\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {j}}\\right) B _ {\\text {b a s e} _ {j}} x _ {\\text {c u r} _ {j}} \\tag {6} \\\\ + D x _ {\\mathrm {c u r} _ {2}}, \\\\ \\end{array}", + "image_path": "f2194c68cd7825bcce61da678e7dc3057e61f3128c5c34f1f4aea0d1582c0213.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "inline_equation", + "content": "\\tilde{f}" + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "content": " represents the functions of " + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "content": " corresponding to the zero-order hold of " + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 631, + 554, + 654 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 319, + 659, + 553, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 659, + 553, + 673 + ], + "spans": [ + { + "bbox": [ + 319, + 659, + 553, + 673 + ], + "type": "interline_equation", + "content": "\\tilde {f} \\left(\\Delta_ {\\text {b a s e} _ {t}}\\right) = \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) ^ {- 1} \\left(\\exp \\left(\\Delta_ {\\text {b a s e} _ {t}} A\\right) - I\\right) \\Delta_ {\\text {b a s e} _ {t}}. \\tag {7}", + "image_path": "39dea7cbad2c299ebbaf9863652c75d5cf721efe6c720801aa170ea7f0c880c1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Specifically, in the State Space Model, the input " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": " is influenced by the control matrix " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": ", which in turn affects the change in state " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": ". In the discretized state space," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23083" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 294, + 193 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 294, + 193 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 294, + 193 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 294, + 193 + ], + "type": "image", + "image_path": "996149ebb5329f6b0eb7dd933df3d6bcdc878a5c8980b82be96deba3cf6d4be1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "lines": [ + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "type": "text", + "content": "Figure 3. Illustrative comparison between the proposed QSSM and existing cross-attention mechanisms." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "spans": [ + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": "the discretization step size " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " represents the time " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " acts on the state. In QSSM, we desire the base frame to act as a gate controlling the influence of the current frames on the state, thereby affecting the output. Thus, we generate " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "\\mathrm{base}_t" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " by the base frame through a linear layer. To exploit the differences in sub-pixels and noise distribution characteristics across multiple frames, we merge current features into the channel dim. Subsequently, all current features are projected into a unified set of merged current features through a linear layer. This allows the base feature to query all current features at once, thereby achieving multi-frame joint denoising. Additionally, as Eq. (5) and (6), when the flattened base feature " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " queries the current features at other times " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cur}_j}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " modulates and guides " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_j}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " to query " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cur}_j}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " through the forget gate and input gate " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "\\exp (\\Delta_{\\mathrm{base}_t}A)" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": ", ultimately feeding back to the output at time " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": ". This enhances the interaction between " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " and its neighboring base features as well as current features. Due to the characteristics of the matrix " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": ", the influence of " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " in guiding the query of " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_j}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " gradually decreases with their distance in the sequence, forming a progressively diminishing receptive field. This prevents " + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{base}_t}" + }, + { + "bbox": [ + 56, + 247, + 296, + 604 + ], + "type": "text", + "content": " from overly focusing on spatially distant information, thereby enhancing neighborhood interactions. Since each query by the base feature simultaneously queries all current features, the base feature can better perceive sub-pixel information consistently distributed across frames, suppressing random noise. We modify the RSSB block [16] by integrating our proposed QSSM with four scanning directions and using channel attention to enhance channel interaction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Discussion To clarify the differences between the proposed QSSM and existing cross-attention methods, we conduct a detailed analysis along with a schematic comparison. As shown in Figure 3 (a), the cross-attention method uses serialized base feature tokens at position " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Q}" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " matrix, querying with all position tokens of the current features as the " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{K}" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " matrix to extract sub-pixel information. In contrast, our QSSM, as shown in Figure 3 (b), not only extracts sub-pixel information from the current features to the base fea" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": "ture but also facilitates information interaction within the base feature. It simultaneously retrieves corresponding current feature tokens from other position tokens in the serialized base feature, thereby achieving joint multi-position sub-pixel information retrieval and noise suppression between the base feature and current features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 151, + 465, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 151, + 465, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 465, + 163 + ], + "type": "text", + "content": "3.3. Multi-Scale Fusion Module" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 168, + 555, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 555, + 384 + ], + "type": "text", + "content": "Considering the presence of sub-pixel information across various scales within the intricate details of images, we propose a novel Multi-scale Fusion Module (MSFM). This module is designed to effectively integrate multi-scale subpixel information from the current frames, thereby enhancing the capability for detailed image reconstruction. The MSFM comprises three distinct branches: a Convolutional Neural Network (CNN), a State Space Model (SSM) with diverse scanning orientations, and a channel Transformer. To begin with, a " + }, + { + "bbox": [ + 313, + 168, + 555, + 384 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 168, + 555, + 384 + ], + "type": "text", + "content": " convolution is utilized for the fusion of local sub-pixel features. The SSM is introduced to efficiently learn and integrate sub-pixel features along both horizontal and vertical axes. Furthermore, considering the attenuation characteristics of the A matrix within the SSM when dealing with long-range perception, we concurrently employ a Transformer block to augment the network's proficiency in capturing global information. The mathematical formulation of the MSFM is as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 392, + 555, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 392, + 555, + 406 + ], + "spans": [ + { + "bbox": [ + 318, + 392, + 555, + 406 + ], + "type": "interline_equation", + "content": "y = w _ {1} \\cdot \\operatorname {C N N} (x) + w _ {2} \\cdot \\operatorname {S S M} (x) + w _ {3} \\cdot \\operatorname {T r a n s f o r m e r} (x) \\tag {8}", + "image_path": "de36d8ce6ca6a3ae5a19d25cd50690a1346c05a8ea4a7ff6d06ec7032b6d85d1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "text", + "content": " represents the balancing factors. " + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 414, + 555, + 437 + ], + "type": "text", + "content": " represent the input feature and output feature, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 445, + 481, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 481, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 481, + 458 + ], + "type": "text", + "content": "3.4. Adaptive Up-sampling Module" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": "After the aforementioned processes, the sub-pixel structural information from burst LR images is extracted and distributed in the feature space. The next critical challenge is to utilize this valuable sub-pixel information to adaptively upsample the image resolution and incorporate sub-pixel details into the high-resolution image. Existing state-of-the-art methods, such as Burstormer [12] and BIPNet [11], simply employ interpolation, transposed convolution, or pixel shuffle techniques for resolution upsampling. However, these methods lack the capability to perceive the distribution of sub-pixels in the feature space, leading to an inability to adaptively reconstruct fine details. Therefore, we introduce a novel Adaptive Up-sampling (AdaUp) module that perceives the distribution of sub-pixels in the spatial domain and adaptively adjusts the up-sampling kernel, thereby achieving higher-quality image detail, as shown in Figure 2 (b). Specifically, we first adaptively perceive the distribution of sub-pixels " + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "inline_equation", + "content": "L \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times 1 \\times 1}" + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": " from the input features " + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times H \\times W}" + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": " by adaptive pooling. We then perform sequence feature interaction on " + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": " to obtain the output channel feature distribution sequence " + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "inline_equation", + "content": "L_1 \\in \\mathbb{R}^{B \\times C_{\\mathrm{out}} \\times 1 \\times 1}" + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": ". Sub" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23084" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "sequentially, we apply both the input distribution sequence and the output distribution sequence to the upsampling transposed convolution kernel " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{B \\times C_{\\mathrm{in}} \\times C_{\\mathrm{out}} \\times 3 \\times 3}" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " using broadcasting, thereby endowing the kernel with feature perception capability. Finally, we obtain the high-resolution output through the upsampling transposed convolution kernel. The corresponding formulas are as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 122, + 161, + 295, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 161, + 295, + 174 + ], + "spans": [ + { + "bbox": [ + 122, + 161, + 295, + 174 + ], + "type": "interline_equation", + "content": "L = \\text {A d a p t i v e P o o l i n g} (X) \\tag {9}", + "image_path": "45048a2384824259c0b05a6d8498a73139f6a2351cdf1deacf9c16f1911bc531.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 137, + 178, + 294, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 178, + 294, + 191 + ], + "spans": [ + { + "bbox": [ + 137, + 178, + 294, + 191 + ], + "type": "interline_equation", + "content": "L _ {1} = \\operatorname {C o n v} _ {1 \\times 1} (L) \\tag {10}", + "image_path": "a7da42c5d8f49f7a95a22871a902bb1f5667381b6290fedbb79a74d3d4b0b9d7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 194, + 295, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 194, + 295, + 207 + ], + "spans": [ + { + "bbox": [ + 129, + 194, + 295, + 207 + ], + "type": "interline_equation", + "content": "W _ {f} = (W \\odot L) \\odot L _ {1} \\tag {11}", + "image_path": "f2a8df3e03001eecb7aad54c60429bb3dd2c23c47229d4d36848da281ce032cc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 209, + 295, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 209, + 295, + 222 + ], + "spans": [ + { + "bbox": [ + 123, + 209, + 295, + 222 + ], + "type": "interline_equation", + "content": "y = \\operatorname {T r a n s - C o n v} \\left(W _ {f}, X\\right) \\tag {12}", + "image_path": "da70ada02003be1c1a21f5f435a6603997a0c62e7d5c97cf7fde53801fed4e08.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 225, + 296, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 225, + 296, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 225, + 296, + 285 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 225, + 296, + 285 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 225, + 296, + 285 + ], + "type": "text", + "content": " represents element-wise multiplication. Thus, AdaUp can leverage the underlying content information from input frames at different channels and utilize it to get better performance than the mainstream up-sampling operations, pixel shuffle, or interpolations [4, 37]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 293, + 205, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 205, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 205, + 308 + ], + "type": "text", + "content": "4. Experiments and Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 313, + 182, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 182, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 182, + 326 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": "Implementation details. We evaluate the effectiveness of our proposed method on four public burst image superresolution benchmarks, encompassing both synthetic and real datasets: synthetic BurstSR [1], Real BurstSR [1], RealBSR-RAW [45], and RealBSR-RGB [45]. To ensure fairness, we follow [12] for training and evaluation. More details of datasets and data processing can be found in Appendix A section. Following [12], we train the model from scratch on the synthetic BurstSR dataset for 300 epochs, using the AdamW optimizer with parameters " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": ". We employ a cosine annealing strategy to gradually decrease the learning rate from " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "3\\times 10^{-4}" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "10^{-6}" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": " and set the training patch size to " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "48\\times 48" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": ". For the Real BurstSR dataset, we follow [1] to fine-tune the model pretrained on synthetic BurstSR for 60 epochs, maintaining the same training setting as the synthetic BurstSR but adjusting the learning rate to " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "1\\times 10^{-6}" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": " and the training patch size to " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "56\\times 56" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": ". For the RealBSR-RAW and RealBSR-RGB datasets, we follow [45] to train from scratch for 100 epochs, using the same training setting as the synthetic BurstSR, with a training patch size of " + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "inline_equation", + "content": "80\\times 80" + }, + { + "bbox": [ + 55, + 331, + 296, + 605 + ], + "type": "text", + "content": ". We set the batch size to 8, and the burst size to 14, and all experiments are conducted on 8 V100 GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": "Metric. Following previous works [1, 45], we use reference metrics to evaluate performance, including PSNR and SSIM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Compared methods. To comprehensively demonstrate the superiority of our proposed method, we compare our QMambaBSR with ten classic and state-of-the-art (SOTA) BurstSR approaches HighRes-net [8], DBSR [1], LKR [21], MFIR [2], BIPNet [11], AFCNet [30], FBAnet [45], Burstormer [12], RBSR [46], GMTNet [31]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 508, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 508, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 508, + 84 + ], + "type": "text", + "content": "4.2. Quantitative and Qualitative Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 89, + 553, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 553, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 553, + 304 + ], + "type": "text", + "content": "Results on the Synthetic BurstSR dataset. As shown in Table 1, our method outperforms existing BurstSR methods, achieving the best performance. For example, compared to the existing SOTA method, Burstormer, our method achieves a " + }, + { + "bbox": [ + 313, + 89, + 553, + 304 + ], + "type": "inline_equation", + "content": "0.29\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 89, + 553, + 304 + ], + "type": "text", + "content": " improvement in PSNR. Furthermore, to further demonstrate the visual superiority of our method, we present a visual comparison with existing methods in Figure 4. We can observe that the RAW low-resolution images exhibit significant noise and severe detail loss, as illustrated in the window area of Figure 4. Compared to existing methods, our method demonstrates superior performance in reconstructing textures and details in the window area. Additionally, in the green stripes region at the bottom of Figure 4, the substantial noise in the base frame leads existing methods to leave artifacts. However, our method more effectively distinguishes between noise and sub-pixels, producing more detailed, artifact-free high-resolution images, thereby demonstrating the visual superiority of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "text", + "content": "Results on RealBSR-RGB and RealBSR-RAW. As shown in Table 2, our method consistently outperforms existing methods on these two real benchmarks, achieving the best performance. For RealBSR-RAW, our method surpasses FBANet and Burstormer in PSNR and linear-PSNR by " + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "inline_equation", + "content": "0.268\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "inline_equation", + "content": "0.258\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "text", + "content": ", respectively. For RealBSR-RGB, our method surpasses FBANet and Burstormer in PSNR by " + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "inline_equation", + "content": "0.204\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 305, + 554, + 472 + ], + "type": "text", + "content": ". Furthermore, as shown in Figure 5, the results demonstrate the superior performance of our method in detail reconstruction and artifact suppression. This validates the effectiveness of our method in real-world scenarios, highlighting its superiority and practicality. More results on Real BurstSR and qualitative results will be presented in the appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 480, + 408, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 408, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 408, + 493 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "To demonstrate the effectiveness and superiority of the proposed modules, we conduct a series of ablation experiments. Specifically, we incrementally integrate the proposed modules into the baseline network. For rapid evaluation, we train our model on the synthetic dataset for 100 epochs. From Table 3, we observe that the introduction of the MSFM module, which enhances the network's multiscale perception and fully integrates sub-pixel information from different frames, significantly improves performance by 1.34 dB in PSNR. Furthermore, the addition of the QSSM, which extracts sub-pixels from the current frames that match the content of the base frame while suppressing noise, leads to an additional performance gain of 0.72 dB in PSNR. Finally, incorporating the proposed Adaptive Up-sampling module, which better adapts the up-sampling kernel according to the scene, thereby generating high-resolution images with richer details, results in a further improvement of 0.26 dB. These results indicate that the pro" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23085" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 71, + 553, + 118 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 553, + 118 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 553, + 118 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 553, + 118 + ], + "type": "table", + "html": "
BicubicHighRes-netDBSRLKRMFIRBIPNetAFCNetFBAnetGMTNetRBSRBurstormerOurs
PSNR↑36.1737.4540.7641.4541.5641.9342.2142.2342.3642.4442.8343.12
SSIM↑0.910.920.960.950.960.960.960.970.960.970.970.97
", + "image_path": "4c2387762618e17b5576c5f5b4a51915d16725cd0e462c9cf5f1b998a585fb50.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 147, + 553, + 349 + ], + "blocks": [ + { + "bbox": [ + 56, + 147, + 553, + 349 + ], + "lines": [ + { + "bbox": [ + 56, + 147, + 553, + 349 + ], + "spans": [ + { + "bbox": [ + 56, + 147, + 553, + 349 + ], + "type": "image", + "image_path": "c720215ff483f423f83b6f1cfb8696a6e1dcbd1f4d2d5a83ae8d97309fa0ce21.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 118, + 358, + 489, + 369 + ], + "lines": [ + { + "bbox": [ + 118, + 358, + 489, + 369 + ], + "spans": [ + { + "bbox": [ + 118, + 358, + 489, + 369 + ], + "type": "text", + "content": "Figure 4. Visual comparison results with different methods on SyntheticBurst datasets for " + }, + { + "bbox": [ + 118, + 358, + 489, + 369 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 118, + 358, + 489, + 369 + ], + "type": "text", + "content": " BurstSR." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 59, + 388, + 291, + 520 + ], + "blocks": [ + { + "bbox": [ + 122, + 125, + 487, + 137 + ], + "lines": [ + { + "bbox": [ + 122, + 125, + 487, + 137 + ], + "spans": [ + { + "bbox": [ + 122, + 125, + 487, + 137 + ], + "type": "text", + "content": "Table 1. Performance comparison of existing methods on Synthetic BurstSR dataset for " + }, + { + "bbox": [ + 122, + 125, + 487, + 137 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 122, + 125, + 487, + 137 + ], + "type": "text", + "content": " BurstSR." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 388, + 291, + 520 + ], + "lines": [ + { + "bbox": [ + 59, + 388, + 291, + 520 + ], + "spans": [ + { + "bbox": [ + 59, + 388, + 291, + 520 + ], + "type": "table", + "html": "
MethodRealBSR-RAWRealBSR-RGB
PSNR↑SSIM↑L-PSNR↑PSNR↑SSIM↑
DBSR20.9060.63530.48430.7150.899
MFIR21.5620.63830.97930.8950.899
BSRT22.5790.62230.82930.7820.900
BIPNet22.8960.64131.31130.6550.892
FBANet23.4230.67732.25631.0120.898
Burstormer27.2900.81632.53331.1970.907
Ours27.5580.82032.79131.4010.908
", + "image_path": "5bae37df9159f006147c8ca3fe020e4ea40ddf2f704755bbac47720cc4a4ff1f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 578, + 295, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 602 + ], + "type": "text", + "content": "posed modules significantly enhance burst super-resolution performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": "Comparison with Existing Modules. To verify the effectiveness of proposed module, we replaced it with existing fusion and up-sampling modules. To effectively represent the performance of various methods while also considering training time, we train for 100 epochs on the synthetic dataset. As shown in Table 4, in the fusion stage, compared to PBFF [11] or NRFE [12], our QSSM and MSFM modules are able to better exploit the inter-frame consistency of sub-pixel distribution while denoising, resulting in" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 316, + 388, + 550, + 462 + ], + "blocks": [ + { + "bbox": [ + 55, + 528, + 295, + 550 + ], + "lines": [ + { + "bbox": [ + 55, + 528, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 295, + 550 + ], + "type": "text", + "content": "Table 2. Performance comparison of existing methods on RealBSR-RGB and RealBSR-RAW datasets for " + }, + { + "bbox": [ + 55, + 528, + 295, + 550 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 55, + 528, + 295, + 550 + ], + "type": "text", + "content": " BurstSR." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 388, + 550, + 462 + ], + "lines": [ + { + "bbox": [ + 316, + 388, + 550, + 462 + ], + "spans": [ + { + "bbox": [ + 316, + 388, + 550, + 462 + ], + "type": "table", + "html": "
QSSMMSFMAdaUpPSNR↑SSIM↑
×××39.810.93
×✓×41.150.94
✓✓×41.870.96
✓✓✓42.130.96
", + "image_path": "d7d370e4aeb6de60a36e90bc4085af564a5ef2fdb381fd62abb4f66dc3ec1c36.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 329, + 469, + 537, + 481 + ], + "lines": [ + { + "bbox": [ + 329, + 469, + 537, + 481 + ], + "spans": [ + { + "bbox": [ + 329, + 469, + 537, + 481 + ], + "type": "text", + "content": "Table 3. Ablation experiment on proposed core modules." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 507, + 553, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 507, + 553, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 507, + 553, + 567 + ], + "type": "text", + "content": "PSNR improvements of 1.56 dB and 0.41 dB, respectively. In contrast to static upsampling like pixel shuffle and transposed convolution, our AdaUp module enhances the network's ability to perceive scene-specific sub-pixel distributions, leading to a PSNR improvement of 0.16 dB." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "content": "Evaluation about MSFM. To validate the effectiveness of different branches within the proposed MSFM, we conducted ablation experiments with various internal branch setting. The experimental results are shown in Table 5. To minimize training time while ensuring experimental validity, the ablation experiments were conducted on a synthetic dataset and trained for 100 epochs. As shown in the table, we use only the convolution in the MSFM module as the baseline. Adding the transformer module resulted in a PSNR increase of " + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "inline_equation", + "content": "0.39\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "content": ". When the transformer was replaced with SSM, the PSNR improved by " + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "inline_equation", + "content": "0.44\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "content": " compared to using only the conv method. 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User study of reconstructed real HR images." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 57, + 396, + 293, + 511 + ], + "blocks": [ + { + "bbox": [ + 57, + 396, + 293, + 511 + ], + "lines": [ + { + "bbox": [ + 57, + 396, + 293, + 511 + ], + "spans": [ + { + "bbox": [ + 57, + 396, + 293, + 511 + ], + "type": "table", + "html": "
Process StageMethodsPSNR↑SSIM↑
FusionConcat39.850.93
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NRFE [12]41.720.96
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ConvTransformerSSMPSNR↑SSIM↑
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✓✓×41.960.96
✓×✓42.010.96
✓✓✓42.130.96
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When compared to existing methods such as Burstormer and BIPNet, our proposed method stands out by adaptively extracting sub-pixels to achieve superior visual effects. This approach earned our method the highest average score of 8.56, underscoring its effectiveness." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 314, + 438, + 388, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 438, + 388, + 451 + ], + "spans": [ + { + "bbox": [ + 314, + 438, + 388, + 451 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 460, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 555, + 653 + ], + "type": "text", + "content": "In this paper, we introduce a novel approach called QMambaBSR for burst image super-resolution. Based on the structural consistency of sub-pixels and the inconsistency of random noise, we propose a novel Query State Space Model to efficiently query sub-pixel information embedded in current frames through an intra- and inter-frame multi-frame joint query approach while suppressing noise interference. We introduce a Multi-scale Fusion Module for information on sub-pixels across different scales. Additionally, a novel Adaptive Up-sampling module is proposed to perceive the spatial arrangement of sub-pixel information in various burst scenarios for adaptive up-sampling and detail reconstruction. Extensive experiments on four public synthetic and real benchmarks demonstrate that our method surpasses existing methods, achieving state-of-the-art performance while presenting the best visual quality." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 668, + 424, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 668, + 424, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 668, + 424, + 681 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 689, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 712 + ], + "type": "text", + "content": "This work was supported by the Natural Science Foundation of China under Grants 62225207,62436008 and 62206262." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23087" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 297, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 297, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 297, + 135 + ], + "type": "text", + "content": "[1] Goutam Bhat, Martin Danelljan, Luc Van Gool, and Radu Timofte. 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Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 3" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23090" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_content_list.json b/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..05080d0f6b25708dc9434699119a284874a0e01f --- /dev/null +++ b/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_content_list.json @@ -0,0 +1,2040 @@ +[ + { + "type": "text", + "text": "QuCOOP: A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers", + "text_level": 1, + "bbox": [ + 187, + 130, + 810, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Natacha Kuete Meli1 Vladislav Golyanik2 \n1University of Siegen", + "bbox": [ + 109, + 202, + 473, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "www.vsa.informatik.uni-siegen.de", + "bbox": [ + 200, + 242, + 486, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Marcel Seelbach Benkner", + "bbox": [ + 500, + 202, + 714, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Michael Moeller1", + "bbox": [ + 743, + 202, + 883, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ MPI for Informatics, SIC", + "bbox": [ + 504, + 220, + 715, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://4dqv.mpi-inf.mpg.de", + "bbox": [ + 545, + 242, + 789, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained Binary Optimisation (QUBO) problems, which severely limits their applicability. This paper proposes a new way to overcome this limitation and introduces QuCOOP, an optimisation framework extending the scope of AQC to composite and binary parametrised, possibly non-quadratic problems. The key idea of QuCOOP is to iteratively approximate the original objective function by a sequel of local (intermediate) QUBO forms, whose binary parameters can be sampled on AQC devices. We experiment with quadratic assignment problems, shape matching and point set registration without knowing the correspondences in advance. Our approach achieves state-of-the-art results across multiple instances of tested problems1.", + "bbox": [ + 88, + 321, + 485, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 625, + 220, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adiabatic Quantum Computing (AQC) has become a promising approach for solving combinatorial optimisation problems in different fields of science including computer vision [3, 46, 48, 70]. AQC leverages principles of quantum mechanics to explore optimisation landscapes in a way that classical methods cannot do, allowing them to tunnel through energy barriers and escape local minima. Unfortunately, current AQC devices such as D-Wave's machines, also referred to as Quantum Annealers, are restricted to Quadratic Unconstrained Binary Optimisation (QUBO) problems. Any deviations from the QUBO form—e.g., when the objective function is non-quadratic or quadratic in a non-linear function of the binary variables—makes the potential benefits of AQCs not directly accessible. At the same time, many computer vision problems re", + "bbox": [ + 89, + 650, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b0c56ab4c8dc7d9d3a2fd41f38a65e0c5f2f2f0853735c7d4fe57189d22c038b.jpg", + "image_caption": [ + "(a) Minimise $f(g(x))$" + ], + "image_footnote": [], + "bbox": [ + 553, + 282, + 647, + 333 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/388f5b446bcaa926e3c5fea9ef749ddfb54d484a49a4be5d66f5411564795a60.jpg", + "image_caption": [ + "$f$ quadratic in $g(x)$ .. $\\checkmark$", + "$f$ quadratic in $g^t (x)$ .. $\\checkmark$" + ], + "image_footnote": [], + "bbox": [ + 669, + 282, + 779, + 333 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33ea57dc6c07a2cbaf09a7eca47e4c4ebc2d56c99b51c03d2a72878f2151eca6.jpg", + "image_caption": [ + "Minimise $f(g^{t}(x):= g$", + "$\\langle x^t\\rangle +\\langle \\nabla g(x^t),x - x^t\\rangle)$" + ], + "image_footnote": [], + "bbox": [ + 785, + 281, + 880, + 333 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d5892642eae230fddb6145f9320117cb948c345c65183c2e9abb2ad385b2e7f5.jpg", + "image_caption": [ + "$x$ binary: $\\checkmark$ , $g$ linear in $x$ : $\\times$", + "Initial", + "(b) Rigid point sets registration." + ], + "image_footnote": [], + "bbox": [ + 529, + 393, + 616, + 463 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/709c8775af2b0646617a90a5ee3d89316720ff00c9c37fdc0684ce5f1588f5a2.jpg", + "image_caption": [ + "AQC: Not a QUBO !!!", + "Result" + ], + "image_footnote": [], + "bbox": [ + 622, + 397, + 710, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/346b15731605c7fff983d55a0a7a9a9932728e33895b076d286eb31f05a91736.jpg", + "image_caption": [ + "ary: $\\checkmark$ $g^{t}$ linear in $x$ : $\\checkmark$", + "AQC: $\\checkmark$ Iteratively solve QUBOs !!!", + "Reference", + "(c) Shape matching on FAUST.", + "Figure 1. (a) Our QuCOOP framework for solving composite and binary-parametrised problems using Adiabatic Quantum Computing (AQC). Some qualitative results are shown for: (b) Point set registration without known correspondences; (c) Mesh alignment problems. Our general approach is competitive with specialised existing quantum and classical methods; it is compatible with quantum annealers and classical simulated annealing solvers." + ], + "image_footnote": [], + "bbox": [ + 732, + 383, + 808, + 473 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "quire non-quadratic objectives to obtain accurate solutions. Motivated by the tangible implications for computer vision of the restriction of the current AQC generation to QUBOs, we develop a new AQC-based optimisation method that can handle a certain type of non-quadratic objective functions.", + "bbox": [ + 511, + 623, + 906, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We consider the general problem", + "bbox": [ + 532, + 699, + 754, + 714 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {s \\in \\mathcal {S}} {\\arg \\min } f (s) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 724, + 906, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of optimising a function $f: S \\to \\mathbb{R}$ over a feasible set $S \\subsetneq \\mathbb{R}^n$ . Moreover, we assume $S$ to be parameterizable by elements of a set $\\mathcal{X} \\subset \\mathbb{R}^k$ via a smooth function $g: \\mathcal{X} \\to S$ allowing to rewrite Problem (1) in a composite form as", + "bbox": [ + 511, + 760, + 906, + 821 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } f (g (x)). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 647, + 833, + 906, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "If $\\mathcal{X} = \\mathbb{R}^k$ , Problem (2) describes an unconstrained problem and can be solved locally, or even globally (for $f \\circ g$", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 0, + 810, + 18 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 722, + 30 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 754, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1project page: https://4dqv.mpi-inf.mpg.de/QuCOOP/", + "bbox": [ + 107, + 886, + 465, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11395", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "convex in $x$ ) using gradient-based methods. If $\\mathcal{X}\\subsetneq \\mathbb{R}^k$ Problem (2) becomes a constrained optimisation problem. If $\\mathcal{X}$ is further non-convex, as e.g., the set $\\mathbb{B}^k\\coloneqq \\{0,1\\} ^k$ of binary vectors of length $k$ , Problem (2) is generally $\\mathcal{NP}$ - hard [52] and, very often, can be solved only approximately.", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gradient descent [54, 56] is perhaps the most simple algorithm for solving Problem (2) when $\\mathcal{X} = \\mathbb{R}^k$ . It is an iterative method, where at each iteration $t$ , a local model $f^t$ of $f$ is constructed around the current iterate $x^t$ to identify a descent direction for updating $x^t$ . For constrained problems, one typically turns to iterative projection or additional penalty terms to ensure that all iterates $x^t$ remain feasible. Examples of such techniques include: Gradient projection methods [7] that project the iterates of gradient descent onto $\\mathcal{X}$ ; interior-point methods [60] that minimize an augmented objective function where a so-called barrier function penalizes non-feasible iterates; feasible direction methods [59], e.g., Frank-Wolfe [28], that compute a feasible descent direction by solving an easier constrained problem and then update the iterate accordingly.", + "bbox": [ + 89, + 167, + 482, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One of the strengths of AQC is its natural ability to optimize over discrete binary variables, whereas classical methods often resort to relaxations. To leverage this, we present QuCOOP (Quantum Framework for Composite and Binary-Parametrised OPoptimisation Problems), a general framework to solve (2) on AQCs. We are concerned with the case when $\\mathcal{X} = \\mathbb{B}^k \\coloneqq \\{0,1\\}^k$ and $f$ is a quadratic function in $g(x)$ . The key idea is to iteratively minimize a 1D cut of $f$ at a current linear Taylor approximation of $g$ : At iteration $t$ , we approximate $f$ through a local model $f^t$ by linearising the inner function $g$ around the current iterate $x^t$ . Since $f$ is quadratic in $g(x)$ and $x$ binary, the resulting sub-objectives are QUBO problems for which modern quantum annealers provide an exciting new way to sample possible low-energy states. As a result, our proposed optimisation does not require descent directions or step sizes in the usual sense as classical methods do, but directly targets a state $x^{t + 1}$ minimising $f^t$ . See Fig. 1-(a) for an overview.", + "bbox": [ + 89, + 395, + 482, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Applications. Our configuration of Problem (2) is common in computer vision. Applications we are interested in this work include the Quadratic Assignment Problem (QAP, [45]), a reputed $\\mathcal{NP}$ -hard problem that aims to optimize a quadratic function over the set of permutation matrices. QAP models many real-life problems such as graph matching [5, 6], travelling salesman [30], facility location [45], or scheduling problems [32], to name just a few. Moreover, we show in further application examples how to solve mesh alignment [6] and rigid point set registration without input correspondences [49] with QuCOOP. See Fig. 1-(b, c) for representative results.", + "bbox": [ + 89, + 685, + 482, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. Our primary technical contributions are:", + "bbox": [ + 89, + 885, + 475, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- QuCOOP, a new general framework for solving composite and binary-parametrised problems on AQCs (Sec. 4);", + "- An iterative scheme to construct and solve QUBO problems that locally approximate the original, perhaps nonquadratic objective function;", + "- Applications of QuCOOP to a variety of computer vision problems including QAP, shape alignment and point set registration (Secs. 5 and 6). For correspondence problems, we introduce a binary parametrisation of permutation matrices fitting in the proposed QuCOOP framework. We experimentally validated the algorithm, first with simulated annealing and achieving state-of-the-art results for several considered problems (Secs. 7.1 to 7.3); then on real D-Wave quantum annealers and improving the dimensionality of solvable permutation-related problems compared to previous quantum-compatible approaches (Sec. 7.4)." + ], + "bbox": [ + 511, + 90, + 906, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 344, + 653, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Classical Optimisation Theory. A binary optimisation technique related to ours is the quadratisation of pseudo-Boolean functions [36, 47]. Pseudo-Boolean functions are functions that can be written uniquely as a multi-linear polynomial of binary variables, with QUBOs being a particular types of those with degrees not exceeding two. Quadratisation techniques [12, 47, 63] can be generally used to reduce the degree of higher-order polynomials to two in order to obtain a QUBO form. However, they often require auxiliary variables, which increases the problem size and can be costly for actual AQC devices. In contrast, QuCOOP does not require additional variables. Moreover, it is not restricted to polynomials, but could also be applied to any function as long as it fits in our composite form, see Eq. (6).", + "bbox": [ + 511, + 369, + 903, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Next, our proposed QuCOOP technique falls into the class of composite optimisation methods [31, 43, 58]. These approaches leverage the composite form of optimisation problem (2) to derive easy-to-solve sub-problems that return better local optima of the original problem. An incomplete list of example applications of composite optimisation problems in computer vision include super-resolution from raw time-of-flight data [31], image and point set registration [50], shape matching [6, 16, 74]. Composite optimisation is classically well studied for continuous problems [22, 31, 43, 58]. This work explores similar techniques for the discrete case, especially to leverage AQC-based optimisation. Hence, in a broad sense, this work improves our understanding of how AQCs can be used for optimising non-quadratic objectives.", + "bbox": [ + 511, + 580, + 903, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quantum-enhanced Computer Vision (QeCV). In computer vision, AQCs have been used to solve problems such as matching involving optimising over permutation matrices [5, 6, 9]; object tracking [78] by optimising binary assignments between observations and a set of tracks; or", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11396", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "clustering [79] by sampling multiple binary assignments of a sample set to models its posterior distribution. Several other approaches [8, 33, 49, 68, 69] were focused on registering point sets. A feature shared by all above-mentioned methods is the construction of QUBO problems with binary solution parametrisation that suit quantum annealers.", + "bbox": [ + 88, + 90, + 480, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Remark. QeCV methods relying on gate-based quantum computing remain substantially less explored than AQCs [61], and many works in this domain are theoretical, heavily use simulators and are at the intersection with quantum machine learning [18, 35, 44]. One of the reasons is that quantum annealing can be considered the most advanced quantum computing technology nowadays, while fault-tolerant quantum computers that could be useful in computer vision are under development [1].", + "bbox": [ + 89, + 181, + 482, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The IQT Approach [49]. The most closely related work to ours is the iterative quantum transformation (IQT) approach of Kuete Meli et al. [49]. IQT iteratively finds rotation matrices $R$ aligning two point sets using AQC. Since rotations can be parametrised by non-redundant parameters $v$ (e.g., a rotation angle in 2D and rotation angle and axis in 3D), the original constrained problem on rotation matrices is cast in Ref. [49] into an unconstrained optimisation problem over rotation parameters. Specifically, IQT iteratively linearizes $R$ around a current rotation parameter as $R(v) = R(v^t) + \\langle \\nabla R(v^t), v - v^t \\rangle + \\mathcal{O}(\\|v - v^t\\|^2)$ and uses an AQC to sample, in each iteration, a binary representation of $v$ minimising a target function quadratic in $R(v)$ . Hence, the IQT approach can be interpreted as a special case of QuCOOP, i.e., a more general optimisation technique relying on AQC as will become apparent from Sec. 4.", + "bbox": [ + 91, + 335, + 483, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 89, + 588, + 218, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As our method is designed for AQC devices, we briefly revise their principles. We also review classical composite optimisation, which QuCOOP builds upon. For a detailed introduction to quantum computing and numerical optimisation, see Ref. [20, 55, 71] and [54, 56], respectively.", + "bbox": [ + 89, + 614, + 482, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Adiabatic Quantum Computing", + "text_level": 1, + "bbox": [ + 89, + 696, + 372, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adiabatic Quantum Computing (AQC) is a model of quantum computation which is polynomially equivalent to the circuit model [2]. Quantum annealers (QAs) are experimental realisations of the AQC paradigm that do not perfectly fulfill the adiabaticity condition [3, 20, 38, 48]. They provide a meta-heuristic for finding globally-optimal solutions to combinatorial optimisation problems relying on the evolution of a quantum-mechanical system driven by quantum fluctuations. Usually they optimize QUBO objectives, i.e., problems of the form", + "bbox": [ + 89, + 719, + 482, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\quad \\langle x, \\mathbf {Q} x + \\mathbf {c} \\rangle , \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 877, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\langle \\cdot, \\cdot \\rangle$ is the standard inner product in $\\mathbb{R}^k$ , $\\mathbf{Q}$ a symmetric matrix, and $\\mathbf{c}$ a vector. QUBO problems are $\\mathcal{NP}$ -hard in general, and solving them on a QA is of high practical interest. Casting computer vision problems to QUBO forms can be challenging and has become an active research area [6, 9, 79]. While QUBOs can be optimised with classical optimisation techniques such as Simulated Annealing (SA) [41], QA is expected to offer substantial advantages over SA in certain cases [20, 21].", + "bbox": [ + 511, + 90, + 903, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In QA, the provided QUBO problem is converted to the corresponding physical Ising Hamiltonian $\\mathbf{H}_p$ . The mapping is such that the ground state of $\\mathbf{H}_p$ , i.e. the spin configuration of the physical system achieving the minimal energy value, encodes the solution of the QUBO. To obtain the ground state of $\\mathbf{H}_p$ , the system evolves according to a time-dependent Hamiltonian $\\mathbf{H}(t)$ changing from the initial Hamiltonian $\\mathbf{H}_i$ (with a known ground state) to $\\mathbf{H}_p$ , e.g. in the way that $\\mathbf{H}(t) = (1 - \\frac{t}{T})\\mathbf{H}_i + t\\mathbf{H}_p$ for $t \\in [0,T]$ . If the system transitions according to the adiabatic theorem of quantum mechanics [11, 37, 39] it stays always in a ground state. One of the conditions is a slow-enough transition, e.g. a one that is inversely proportional to the squared minimum (over all instantaneous $t$ ) spectral gap of $\\mathbf{H}$ . In practice, modern experimental realisations of AQCs are non-adiabatic and return ground states with probabilities $\\ll 1.0$ . To increase the probability of finding the ground state at least once, annealing is repeated multiple times.", + "bbox": [ + 511, + 227, + 906, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Composite Optimisation", + "text_level": 1, + "bbox": [ + 511, + 508, + 736, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Iterative methods [54, 56] solve Problem (2) by repeatedly minimising a local model $f^t$ built upon the actual iterate $x^t$ :", + "bbox": [ + 511, + 530, + 903, + 561 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {t + 1} := \\underset {x \\in \\mathcal {X}} {\\arg \\min } f ^ {t} (x), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 574, + 903, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the local model $f^t$ should have some nice properties such as convexity or separability making it easier to solve.", + "bbox": [ + 511, + 607, + 903, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In composite optimisation, also known as 'prox-linear' or 'prox-descent' [22, 31, 43, 58], the idea is to exploit the underlying composite nature of the objective function in Problem (2) to derive a local model that, still being easier to solve, approximates the original landscape more faithfully. Two approaches to achieve this are to either approximate the outer function $f$ [31], or linearize the inner function $g$ [22, 43, 58]. In the later case, the local model reads", + "bbox": [ + 511, + 638, + 905, + 758 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {t} (x) := f \\left(g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle\\right) + \\frac {1}{2 \\alpha^ {t}} \\| x - x ^ {t} \\| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 768, + 903, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $\\alpha^t$ being the step size that prevents $x^{t + 1}$ to deviate too much from $x^t$ , point around which the approximation is more reliable. It is shown in Ref. [58] that for a convex and coercive $f$ and under the Kurdyka-Lojasiewicz property, the iterates $(x^{t})_{t = 1}^{\\infty}$ for the model Eq. (5) converge", + "bbox": [ + 511, + 824, + 903, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11397", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to a critical point, i.e. a minimizer of $f$ . We build on this later approximation, i.e. the linearisation of the inner function $g$ , to derive QUBOs for AQC, as we consider that the outer function $f$ is quadratic in $g(x)$ .", + "bbox": [ + 89, + 90, + 483, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. The Proposed QuCOOP Iteration", + "text_level": 1, + "bbox": [ + 89, + 165, + 398, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section describes our general QuCOOP framework, followed by its applications in Sec. 5 and Sec. 6. Proofs of all Lemmas are given in Appendix A.", + "bbox": [ + 89, + 190, + 483, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "QuCOOP is an optimisation algorithm for composite optimisation problems of the form (2), where $f$ is quadratic in $g(x)$ , that iteratively uses AQC. The function $g: \\mathbb{R}^k \\to \\mathbb{R}^n$ is a smooth function such that $S = \\operatorname{Im}_g(\\mathbb{B}^k) := \\{g(x): x \\in \\mathbb{B}^k\\}$ , hence, $g$ parametrizes the feasible domain $S \\subsetneq \\mathbb{R}^n$ of the original Problem (1) by elements of the set $\\mathcal{X} := \\mathbb{B}^k$ . For convenience, we write Problem (1) as", + "bbox": [ + 89, + 236, + 483, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf (g (x)) = \\langle g (x), \\mathbf {Q} g (x) + \\mathbf {c} \\rangle , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 368, + 483, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for a given matrix $\\mathbf{Q} \\in \\mathbb{R}^{n \\times n}$ and a vector $\\mathbf{c} \\in \\mathbb{R}^n$ .", + "bbox": [ + 89, + 396, + 429, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that for Problem (1), we are only interested in values of $g$ on $\\mathbb{B}^k$ . However, from a theoretical point of view, our algorithm involves a Taylor approximation of $g$ , requiring $g$ to be smooth as described above. Such a $g$ is far from being unique. Moreover, in addition to $S = \\operatorname{Im}_g(\\mathbb{B}^k)$ , the gradient of $g$ can take any value by design. Thus, from a practical point of view, this function $g$ should model a \"reasonable\" or \"natural\" smooth parametrisation of $S$ .", + "bbox": [ + 89, + 411, + 483, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A high-level description of the algorithm is provided in Algorithm 1. Next, we analyse its different steps.", + "bbox": [ + 89, + 532, + 483, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1: QuCOOP Iteration", + "text_level": 1, + "bbox": [ + 107, + 575, + 344, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initialize $x^0$ and repeat for $t = 0,1,2,\\ldots$", + "bbox": [ + 107, + 599, + 383, + 616 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} g ^ {t} (x) := g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle (7) \\\\ x ^ {t + 1} \\leftarrow \\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\left\\{f ^ {t} (x) := f \\left(g ^ {t} (x)\\right) \\right\\} (8) \\\\ \\begin{array}{l l} \\text {s . t .} & g ^ {t} (x) \\in \\mathcal {S} \\end{array} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 626, + 465, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Return $g(x^{t + 1})$ .", + "bbox": [ + 112, + 705, + 220, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first step is the familiar choice of the starting point $x^0$ . This can be a vector based on prior knowledge, the result of a previous optimisation, or any random point. As will be discussed later in Lemma 1, QuCOOP converges globally, but not necessarily to the global optimum. Hence, different $x^0$ can lead to different results.", + "bbox": [ + 89, + 734, + 483, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a subsequent loop, at each iteration $t$ , the inner function $g$ is linearised around the current iterate $x^t$ using first-order Taylor expansion, Eq. (7), and the next iterate $x^{t + 1}$ is computed by solving the minimisation Problem (8). Evaluated on the hyperplane $g^{t}(x)$ , $f$ results in a", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$k$ -dimensional quadratic function $f^t$ in variable $x$ . In cases where the parametrisation $g^t(x)$ differs substantially from the parametrisation $g(x)$ , to guarantee a monotone decrease of the objective values, it might also be necessary to include a step $x^{t+1} = g^{-1}(g^t(\\tilde{x}^{t+1}))$ , with $\\tilde{x}$ being the output of Problem (8).", + "bbox": [ + 511, + 90, + 905, + 180 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 1 provides a visual intuition of the constructed local model $f^t$ . Next, we ensure the compatibility of Problem (8) with quantum annealers (see Sec. 3.1) through a QUBO formulation.", + "bbox": [ + 511, + 181, + 905, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Unconstrained Part of Problem (8). The objective function of the minimisation in Problem (8) is already in an AQC-compatible form. At iteration $t$ , we solve the QUBO", + "bbox": [ + 511, + 265, + 905, + 311 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle x, \\mathbf {Q} ^ {t} x + \\mathbf {c} ^ {t} \\right\\rangle , \\text {w i t h} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 321, + 905, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} ^ {t} := \\nabla g \\left(x ^ {t}\\right) \\mathbf {Q} \\nabla g \\left(x ^ {t}\\right) ^ {\\top}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 378, + 905, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} ^ {t} := \\nabla g (x ^ {t}) \\left(\\mathbf {c} + 2 \\mathbf {Q} \\left(g (x ^ {t}) - \\nabla g (x ^ {t}) ^ {\\top} x ^ {t}\\right)\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 401, + 905, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is because the local model $f^t$ now becomes quadratic in the binary variable $x$ . Details on the derivation of this QUBO problem can be found in Appendix B.", + "bbox": [ + 511, + 446, + 905, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Meeting the Constraint of Problem (8). In classical optimisation when $\\mathcal{X}$ is convex, cf. Eq. (5), the damping term factored to the step size ensures that $g(x)$ or $x$ remains close to $g(x^t)$ or $x^t$ . This is reminiscent of trust-region methods requiring that the local model $f^t$ trustfully approximates $f$ , which happens in a close neighborhood of $x^t$ .", + "bbox": [ + 511, + 515, + 905, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our case, $\\mathcal{X}$ is discrete, but the quantum annealer can essentially navigate the complete $\\mathcal{X}$ domain, allowing us to explore solutions beyond the trust region. At the same time, as required in Problem (8), we have to guarantee that $g^{t}(x)\\in S$ ; or, more generally, to replace it with a nearby feasible point with the objective value not much worse than the linearised estimate $f(g^{t}(x))$ . As the whole QuCOOP iteration should be carried out by AQC, ensuring this feasibility amounts to designing a penalty term in the form of a quadratic function in $g^{t}(x)$ . Depending on the form of $S$ , this may, or may not, be easy computationally. The yet resulting objective function is a standard QUBO problem that can run on AQC. We refer to Secs. 5 and 6 for exemplary penalty functions on two computer vision problems, namely graph or shape matching and point set registration.", + "bbox": [ + 511, + 606, + 905, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Convergence Analysis. While QuCOOP does not guarantee global convergence, it, at least, monotonically decreases the objective function values as stated next:", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11398", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 1. The series $(f(g(x^{t})))_{t\\in \\mathbb{N}}$ generated by Algorithm 1 with reparametrisation, or without and under assumptions found in Appendix A, monotonically decreases.", + "bbox": [ + 89, + 90, + 483, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Graph Matching and QAP with QuCOOP", + "text_level": 1, + "bbox": [ + 89, + 148, + 470, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section shows an application of QuCOOP to graph matching and quadratic assignment problems (QAP).", + "bbox": [ + 89, + 174, + 482, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A general graph matching problem of size $n \\in \\mathbb{N}$ can be written in matrix form as", + "bbox": [ + 89, + 204, + 483, + 233 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } \\| \\mathbf {A P} - \\mathbf {P B} \\| _ {F} ^ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 241, + 482, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{A}$ and $\\mathbf{B}$ are given $n\\times n$ symmetric matrices and $\\Pi_{n}$ is the set of all $n\\times n$ permutation matrices [16]. Equivalently, by assuming the constraint $\\mathbf{P}\\in \\Pi_n$ to be always held and ignoring resulting constant terms, Eq. (12) becomes", + "bbox": [ + 89, + 275, + 483, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } - \\left\\langle \\mathbf {A P}, \\mathbf {P B} \\right\\rangle_ {F}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 343, + 482, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Quadratic Assignment Problem (QAP) aims to maximize (13). To apply QuCOOP to (13), we need to parametrisse the permutation matrix $\\mathbf{P}$ using binary variables:", + "bbox": [ + 89, + 375, + 483, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 2. Let $((a,b), a,b = 1,\\dots,n, a < b)$ , with cardinality $k := n(n - 1)/2$ , be the tuple of all 2-cycles permuting $a$ and $b$ , and $\\mathbf{T}_i$ the matrix representation of the $i$ -th cycle. Any permutation matrix can be parametrised with a length- $k$ binary vector $x := (x_1, \\ldots, x_k)$ via the function", + "bbox": [ + 89, + 443, + 483, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P}: \\mathbb {B} ^ {k} \\to \\Pi_ {n}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 540, + 202, + 558 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx \\mapsto \\mathbf {P} (x) := \\prod_ {i = 1} ^ {k} \\mathbf {P} _ {i} \\left(x _ {i}\\right), \\quad \\mathbf {P} _ {i} \\left(x _ {i}\\right) := \\mathbf {T} _ {i} ^ {x _ {i}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 561, + 482, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{T}_i^{x_i}$ is $\\mathbf{T}_i$ if $x_{i} = 1$ and the identity $\\mathbf{I}_{n\\times n}$ otherwise.", + "bbox": [ + 89, + 609, + 478, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we construct out of $\\mathbf{P}$ from Eq. (14) a smooth function $g$ to be used in QuCOOP. A natural choice is to design, for each $\\mathbf{P}_i$ from Eq. (14), a smooth function defined through $\\mathbf{P}_i(x_i) = x_i(\\mathbf{T}_i - \\mathbf{I}_n) + \\mathbf{I}_n$ for $x_i\\in \\mathbb{R}$ which makes $\\mathbf{P}_i$ and thus $\\mathbf{P}$ differentiable with respect to $x_{i}$ and thus $x$ . Now letting $g(x)\\coloneqq \\mathbf{p}(x)\\coloneqq \\operatorname {vec}(\\mathbf{P}(x))$ be the vector formed by the rows of $\\mathbf{P}(x)$ , we propose to solve Problem (13) using Algorithm 1 by solving at each iteration $t$ the sub-problem", + "bbox": [ + 89, + 632, + 483, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\left\\langle g ^ {t} (x), \\mathbf {Q} g ^ {t} (x) \\right\\rangle , \\quad \\mathbf {Q} := \\alpha \\mathbf {I} _ {n \\times n} - \\mathbf {A} \\otimes \\mathbf {B}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 775, + 482, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g^{t}(x) = \\mathbf{p}^{t}(x) = \\mathbf{p}(x^{t}) + \\langle \\nabla \\mathbf{p}(x^{t}), x - x^{t} \\rangle$ . The term $\\alpha \\mathbf{I}_{n \\times n}$ is, for some $\\alpha \\in \\mathbb{R}_+$ , the penalty added to enforce $\\mathbf{p}^t(x) \\in \\Pi_n$ as required by QuCOOP. In the next paragraph, we justify why our penalty term effectively penalizes non-feasible solutions. Finally, the optimisation follows Algorithm 1 with $x \\in \\mathcal{X} = \\mathbb{B}^k$ .", + "bbox": [ + 89, + 808, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the Penalty Term of the Permutation Constraint. We next show why minimising $\\alpha \\| \\mathbf{p}^t (x)\\| _2^2$ effectively constrains the result of the minimisation step in (15) to lie in the set $\\Pi_{n}$ of permutation matrices. At iteration $t$ , we have", + "bbox": [ + 511, + 90, + 905, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} ^ {t} (x) = \\mathbf {p} \\left(x ^ {t}\\right) + \\left\\langle \\nabla \\mathbf {p} \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle , \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 157, + 903, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which each row of $\\nabla \\mathbf{p}(x^t)$ , that is, each partial derivative of $\\mathbf{p}$ (cf. Eq. (42) in the supplement), contains exactly two 1 and two $-1$ entries. A following nice property of QuCOOP is that its iterates $\\mathbf{P}^t(x)$ partially satisfy the permutation matrix constraint in the sense that their rows and columns sum up to ones, as stated in Lemma 3.", + "bbox": [ + 511, + 181, + 906, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 3. All the iterates $\\mathbf{P}^t (x)$ computed by Algorithm 1 for $\\mathbf{P}(x)$ from Eq. (14) fulfill $\\mathbf{P}^t (x)\\in X,\\forall x\\in \\mathbb{B}^k$ , where", + "bbox": [ + 511, + 279, + 905, + 311 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nX := \\left\\{\\mathbf {M} \\in \\mathbb {Z} ^ {n \\times n} \\Bigg | \\sum_ {i = 1} ^ {n} \\mathbf {M} _ {i j} = \\sum_ {j = 1} ^ {n} \\mathbf {M} _ {i j} = 1, \\forall i j \\right\\}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 316, + 903, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As a consequence of Lemma 3, $n \\leq \\| \\mathbf{p}^t(x) \\|_2^2$ holds so that minimising $\\| \\mathbf{p}^t(x) \\|_2^2$ enforces $\\mathbf{P}^t(x) \\in \\Pi_n$ as desired.", + "bbox": [ + 511, + 359, + 905, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Point Set Registration with QuCOOP", + "text_level": 1, + "bbox": [ + 511, + 402, + 852, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We next apply QuCOOP to point set registration. Given a reference set $\\mathbf{X} := (x_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}$ and a template set $\\mathbf{Y} := (y_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}$ , our goal is to determine the best rotation $\\mathbf{R} \\in \\mathrm{SO}(d)$ and the best permutation $\\mathbf{P} \\in \\Pi_n$ that jointly transform the template set and find correspondences with the reference set. Concretely, we aim to solve", + "bbox": [ + 511, + 428, + 905, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {R} \\in \\operatorname {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } \\| \\mathbf {X P} - \\mathbf {R Y} \\| _ {F} ^ {2}. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 525, + 903, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By assuming the constraints $\\mathbf{R} \\in \\mathrm{SO}(d)$ and $\\mathbf{P} \\in \\Pi_n$ to be always fulfilled and discarding resulting constant terms, we retrieve the problem formulation:", + "bbox": [ + 511, + 560, + 905, + 604 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {R} \\in \\mathrm {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } - \\left\\langle \\mathbf {X P}, \\mathbf {R Y} \\right\\rangle_ {F}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 613, + 903, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As required by Algorithm 1, we need to binary-parametrisse $\\mathbf{R}$ and $\\mathbf{P}$ . For $\\mathbf{P}$ , we use the parametrisation from Lemma 2, again with a total of $k_{p} \\coloneqq n(n - 1)/2$ binary parameters. For $\\mathbf{R}$ , we follow Ref. [33, 49] and write $\\mathbf{R}$ using the exponential mapping from the orthogonal Lie algebra to its group, as a function $\\mathbf{R}(y) = \\exp(\\mathbf{M}(y))$ , where $\\mathbf{M}$ is a skew-symmetric matrix depending on the rotation parameter $y \\in \\mathbb{R}^k$ , with $k_{r} \\coloneqq d(d - 1)/2$ .", + "bbox": [ + 511, + 646, + 905, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By flattening the optimisation variables $\\mathbf{R}(y)$ and $\\mathbf{P}(x)$ as $\\mathbf{r}(y) := \\operatorname{vec}(\\mathbf{R}(y))$ and $\\mathbf{p}(x) := \\operatorname{vec}(\\mathbf{P}(x))$ our optimisation sub-problem in the QuCOOP iteration $t$ becomes", + "bbox": [ + 511, + 767, + 905, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {(x, y) \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle g ^ {t} (x, y), \\mathbf {Q} g ^ {t} (x, y) \\right\\rangle , \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 834, + 903, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} := \\left( \\begin{array}{c c} \\alpha \\mathbf {I} _ {n \\times n} & - \\frac {1}{2} \\mathbf {X} \\otimes \\mathbf {Y} \\\\ - \\frac {1}{2} (\\mathbf {X} \\otimes \\mathbf {Y}) ^ {\\top} & \\beta \\mathbf {I} _ {d \\times d} \\end{array} \\right), \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 864, + 903, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11399", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g^{t}(x,y) \\coloneqq (\\mathbf{p}^{t}(x),\\mathbf{r}^{t}(y))$ with the linearisation $\\mathbf{p}^t (x) = \\mathbf{p}(x^t) + \\langle \\nabla \\mathbf{p}(x^t),x - x^t\\rangle$ for the permutation and $\\mathbf{r}^t (y) = \\mathbf{r}(y^t) + \\langle \\nabla \\mathbf{r}(y^t),y - y^t\\rangle$ for the rotation. The term $\\alpha \\mathbf{I}_{n\\times n}$ ensures that the iterate $\\mathbf{P}^t (x)$ is a valid permutation matrix, and $\\beta \\mathbf{I}_{d\\times d}$ that $\\mathbf{R}^t (y)$ approaches an orthonormal matrix. The optimisation now follows Alg. 1 in which the permutation variable $x$ lies in $\\mathbb{B}^k$ , and, as in Ref. [49], we binarize the rotation variable $y$ by considering its flexible $m$ -bits discretisation over a tunable interval, leading to $y\\in \\mathbb{B}^{m\\cdot k}$ . In total, $(x,y)$ is a binary vector in $\\mathbb{B}^{k + m\\cdot k}$ .", + "bbox": [ + 89, + 90, + 483, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7. Experimental Evaluation", + "text_level": 1, + "bbox": [ + 89, + 253, + 326, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform numerical experiments on QAP, shape matching and point set registration problems. Secs. 7.1 to 7.3 report results of our method when optimised using Simulated Annealing (SA) on classical hardware, and Sec. 7.4 reports results of the same experiments using real D-Wave Quantum Annealer (QA). Details about the used datasets and benchmark methods are discussed in the corresponding sections. SA, along with the preparation of couplings and biases of QuCOOP for the quantum annealer, is carried out on a conventional computer (AMD Ryzen 95900X 12-Core Processor CPU with 128GB RAM).", + "bbox": [ + 89, + 279, + 483, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Penalty Factors. Similar to many other AQC methods dealing with constrained problems [5, 9, 46], our approach is not exempt from the choice of the penalty factors $\\alpha$ in (15), and $\\alpha$ and $\\beta$ in (21). The penalty factors should be large enough to enforce the constraint while not significantly worsening the dynamic range of the resulting problem Hamiltonian, which otherwise could lead to incorrect solutions of the QUBO problem on the quantum annealer [51]. In our experiments, we set the penalty factors for QAP and point set registration by grid search on smaller problems, which is a widely used approach in the field [9, 27]. In the following, $\\alpha$ is set for QAPs to the lowest eigenvalue for $\\mathbf{A} \\otimes \\mathbf{B}$ ; for shape matching problems, $\\alpha$ is ten times the lowest eigenvalue of $\\mathbf{A} \\otimes \\mathbf{B}$ ; and in point set registration, $\\alpha$ equals $\\|\\mathbf{X}\\|_F^2$ and $\\beta$ equals $0.1 \\cdot \\|\\mathbf{Y}\\|_F^2$ .", + "bbox": [ + 89, + 463, + 483, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7.1. Quadratic Assignment Problems (QAP)", + "text_level": 1, + "bbox": [ + 89, + 696, + 431, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To benchmark our method on QAP, we consider the Fast Approximate Quadratic programming for graph matching (FAQ) [75] and the 2-OPT method [19] as classical competitors, and Q-Match [6] as an AQC-compatible competitor. Implementations for FAQ and 2-OPT are provided within Python's Scipy-library, and our method as well as Q-Match are optimised using the SA implementation provided by D-Wave. Q-Match's source code is publicly available [4]. A technical comparison between QuCOOP and Q-Match can be found in Appendix C.", + "bbox": [ + 89, + 719, + 482, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report results on the QAPLIB dataset [15] for all instances with problem size $n \\leq 50$ , 72 in total. Details", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/005cd46a6d293e8bdf5bc59898c63729f5961938724e6f34b9ca1a3ca0b74205.jpg", + "image_caption": [ + "Figure 2. Benchmark results on QAPLIB [15]. We plot the percentage energy error for all considered problem instances (note the means over all instances reported in the legend) and provide their runtimes. Our method clearly outperforms its competitors." + ], + "image_footnote": [], + "bbox": [ + 521, + 73, + 898, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on those problem instances, along with calculated objective values, are provided in the supplement, Tab. III. Fig. 2 shows the relative errors of the computed objective values w.r.t. optimal ones. Overall, our method consistently outperforms both classical and quantum competitors and has the smallest confidence intervals. Our method and Q-Match exhibit higher runtimes compared to FAQ and 2-Opt for almost all $n$ . This can be explained by the fact that Q-Match solves smaller problems but requires a lot of iterations ( $\\approx 800$ for $n = 50$ ), while QuCOOP solves larger problems in much fewer iterations ( $\\approx 5$ for $n = 50$ ).", + "bbox": [ + 511, + 347, + 906, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7.2. Shape Matching", + "text_level": 1, + "bbox": [ + 511, + 527, + 676, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We match pairs $(\\mathcal{U},\\mathcal{V})$ of reduced meshes from the FAUST dataset [10], with 502 vertices each following Seelbach Benkner et al. [6]. We follow Ref. [6] in several further design choices. Due to the high problem dimensionality, we break down each problem into carefully selected sub-problems solved iteratively. An initial registration based on descriptor similarities is first calculated using linear assignment. Subsequently, in each iteration and for each vertex $u\\in \\mathcal{U}$ , we compute the contribution $\\sum_{v\\in \\mathcal{V}}\\mathbf{Q}_{u\\cdot n + \\mathbf{P}u,v\\cdot n + \\mathbf{P}v}$ to the objective function, where $\\mathbf{P}$ is the current solution. The $n = 40$ vertices with the highest mismatch scores on both meshes are selected as sub-meshes and registered using either our QuCOOP or Q-Match [6] to enhance registration. We repeat until the set of worst vertices converges.", + "bbox": [ + 511, + 550, + 906, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The evaluation metric is the common Princeton benchmark protocol [40] which calculates for each $u \\in \\mathcal{U}$ the geodesic distance between the computed and the optimal vertex assignment of $u$ , normalised by the diameter of $\\mathcal{V}$ . We report cumulative geodesic errors, i.e. the percentage of assignments with error bellow incremental thresholds.", + "bbox": [ + 511, + 777, + 908, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 3 displays some qualitative registration results and Fig. 4 presents the function value decrease over the iter-", + "bbox": [ + 511, + 869, + 908, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11400", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8ca7948b8d6571bc9b24aea8313d1074cb247c21dc044c30932545892b8c1f2e.jpg", + "image_caption": [ + "Figure 3. Registration results on FAUST [10]. The proposed approach performs at least as well as Q-Match [6]; see circled areas." + ], + "image_footnote": [], + "bbox": [ + 98, + 95, + 480, + 303 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e116b9b7e45d9bc1d46054bb9a85306951c31e411edc21bb7bdec470b2502c1d.jpg", + "image_caption": [ + "Figure 5. Registration results on 2D and 3D point sets with different $n$ . Grey lines show correspondences between reference (olive) and template (blue) points. With up to a few correspondence errors, our method performs well on both isomorphic (left to vertical line) and non-isomorphic shapes (right to vertical line). CPD performs better on isomorphic shapes than on non-isomorphic shapes." + ], + "image_footnote": [], + "bbox": [ + 96, + 359, + 478, + 450 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b50a9efd78c3d5cb0b52b28193e3a55be5f09145424c3a7f6392164e85e0b795.jpg", + "image_caption": [ + "Figure 4. Energy decrease and geodesic errors, averaged on ten instances of FAUST [10] in each pose category. The mean geodesic error for both methods is given in the legend of the plot. The proposed method performs slightly better than Q-Match [6]." + ], + "image_footnote": [], + "bbox": [ + 96, + 455, + 477, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ations as well as the cumulative geodesic errors. Failure cases are discussed in Appendix E. Our general QuCOOP framework clearly matches the accuracy of the previous specialised Q-Match method. It reduces the mean geodesic error by about 0.01, as it can achieve better results on the sub-problems (see Appendix C). This selection of worst vertices, however, also worsens the performance of both methods, preventing them from matching the results of recent classical state-of-the-art methods [64, 65, 80].", + "bbox": [ + 89, + 641, + 483, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "7.3. Point Set Registration", + "text_level": 1, + "bbox": [ + 89, + 787, + 294, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform experiments on 2D and 3D point set registration. In 2D, points were picked on fish images, and in 3D they were generated from geometrical curves. The number of points varies from $n = 20$ to $n = 40$ . We benchmark QuCOOP against the classical rigid CPD algorithm [53] implemented within the pycpd package [29]. Quantum com", + "bbox": [ + 89, + 809, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d5e7c17ab26db552ab91e7a94299376af64f587dfcb52b700e0a428d7a11de52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 92, + 895, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a5f519f7e51049e13af6f1e7dfa914ad1c6fa36138e16fdd5ed4861a2c5a449.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 229, + 895, + 366 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e86a73e4d4f1a93603f15b0849a0b94b3bd3f34287e8d7168195fb278556e10a.jpg", + "image_caption": [ + "Figure 6. Varying rotation angle in the point sets registration experiment. Both CPD and our method show difficulties to register the points for a rotation angle exceeding $90^{\\circ}$ in 2D and $45^{\\circ}$ in 3D." + ], + "image_footnote": [], + "bbox": [ + 519, + 479, + 890, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "petitor methods that would have been IQT [49] and QA [33] cannot handle registration without correspondences.", + "bbox": [ + 511, + 642, + 905, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 shows our registration results. Left to the vertical line in the figure are point sets that are isomorphic up to the rotation and permutation, Right are cases where, additionally, the sets are non-isomorphic and/or have different number of points. In the later case, we zero-pad the set with the lowest cardinality to match the other. We use $k_{r} = 10$ variables for the rotation parameter and perform 15 iterations on each problem instance. We see that QuCOOP's computed correspondences are overall correct, so that a reasonable transformation of the template set can still be found. CPD shows difficulties in registering non-isomorphic sets.", + "bbox": [ + 511, + 672, + 905, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 6, we show registration performances, averaged over ten random problem instances of size $n = 10$ , for both methods, while varying the rotation angle. The larger the rotation angle, the harder the registration for both methods.", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11401", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e342bb5bb4106eecf85ab78726254c10d7d83d429cfc1f9e8197c79071bf751b.jpg", + "image_caption": [ + "Figure 7. D-Wave results for 5 randomly generated QAP instances for $n = 3, 5, 7, 9, 12, 15$ . Left are returned energy function values, 0 being the best. Right is the validness $|n - \\| \\mathbf{P} \\|_F^2|$ of returned matrices, 0 indicating a valid permutation matrix. Up to $n \\approx 12$ , D-Wave finds valid permutation matrices, and often optimal ones." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 472, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7.4. Experiments on D-Wave Machines", + "text_level": 1, + "bbox": [ + 89, + 275, + 392, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We now execute QuCOOP on a real quantum device, D-Wave Advantage 6.4 accessed through the Leap API [23-25]. Advantage has $>5000$ physical qubits connected in the Pegasus topology. However, due to the connectivity pattern of the physical qubits which induces chains in the problem embedding, it is estimated that it can solve problems of about 180 fully connected logical variables, limiting our experiments to problems of sizes $n \\approx 15$ ; see also Appendix G.", + "bbox": [ + 89, + 297, + 483, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "QAP. On D-Wave, we solve 5 randomly generated QAP instances for $n = 3, 5, 7, 9, 12, 15$ . The entries of matrix A are $\\mathbf{A}_{ij} = \\| x_i - x_j\\|_2$ for standard and normally distributed $\\{x_i \\in \\mathbb{R}^2\\}_{i=1}^n$ , and B equals $\\mathbf{P}^\\top \\mathbf{A}\\mathbf{P}$ such that, according to Eq. (12), the optimal function value is 0. Each iteration of the algorithm is executed with the default annealing time of $20\\mu s$ and 50 sample reads. We investigate, whether the last computed matrices (i.e. $\\mathbf{P} = \\mathbf{P}^t(x^{t+1})$ ) are valid permutation matrices² and plot their function values. We compare against the SA implementation and Q-Match (with QA).", + "bbox": [ + 89, + 436, + 483, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our results are reported in Fig. 7. Up to $n \\approx 12$ , QuCOOP QA finds valid permutation matrices, but returns higher objective values compared to QuCOOP SA and Q-Match QA. As $n$ becomes large, QuCOOP QA tends to compute non-valid matrices. QuCOOP QA took about $5 \\times$ less runtime than Q-Match QA on one problem instance, including overheads such as minor embedding and access. Compared to previous works [5, 77] which reasonably—i.e. by returning valid permutation matrices—solved only problems of size $n = 3,4$ on D-Wave machines, we consider QuCOOP as an improvement of the state-of-the-art.", + "bbox": [ + 89, + 588, + 482, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Point Set Registration. We perform point set registration on D-Wave for five randomly generated problem instances for $n = 3,5,7,9,12,15$ in each set. The results are reported in Fig. 8. Qualitative results can be found in Appendix F. We see that QuCOOP can register the points without correspondences up to $n = 5$ , improving previous work [49] in which correspondences are known beforehand.", + "bbox": [ + 89, + 772, + 482, + 878 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/943996b037c9b64773c2de143be761d602c5dc230b7b6131c7434987c3514e49.jpg", + "image_caption": [ + "Figure 8. D-Wave results for five randomly generated point sets registrations for $n = 3,5,7,9,12,15$ . In line with the QAP experiment, D-Wave successfully registers small problem instances." + ], + "image_footnote": [], + "bbox": [ + 516, + 92, + 893, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 511, + 252, + 764, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The experiments reveal several features of QuCOOP: First, its ability to handle problems involving permutation problems; second, its versatility and compatibility with continuous problems such as point set registration without correspondences, which previous techniques [6, 33, 49] are not able to address. Moreover, QuCOOP supports optimisation over permutation matrices up to size $n = 12$ using the chosen parametrisation on D-Wave annealers.", + "bbox": [ + 511, + 277, + 905, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Approximation Accuracy. As for many first-order methods, the linearisation $g^t$ of the inner function $g$ is both the key and the bottleneck of QuCOOP. It may not always provide accurate approximations for highly non-linear $g$ and lead to suboptimal solutions as observed in the tests.", + "bbox": [ + 511, + 424, + 905, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scalability and Scaling. The space complexity of our permutation parameterisation scales quadratically with $n$ , making it difficult to solve large problems on D-Wave, as complex embeddings increase the chain break probability.", + "bbox": [ + 511, + 523, + 905, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "9. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 602, + 633, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented QuCOOP, a framework for solving composite, binary-parametrised and possibly non-quadratic problems using AQC. This represents a new class of problems solvable on AQC previously restricted to QUBO forms. QuCOOP solves a sequence of QUBO forms approximating the original objective function, which facilitates the non-intuitive and challenging task of handcrafting QUBOs for the aforementioned problem types. We show that our single framework can effectively be applied to several computer vision problems. Namely, we address QAP and shape matching problems, outperforming the previous specialised quantum-enhanced Q-Match method by $5\\%$ on QAP and 0.01 on shape matching. For the first time, an AQC-compatible method for rigid point set registration is shown not to require input correspondences and match the accuracy of the classical CPD algorithm on tested problems. We hope this work inspires future exploration of new methods for other CV problems within the proposed framework.", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "Note that $\\mathbf{P}^t (x^{t + 1})$ may be non-valid, but $\\mathbf{P}(x^{t + 1})$ is always valid.", + "bbox": [ + 107, + 885, + 480, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11402", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 534951134.", + "bbox": [ + 89, + 113, + 485, + 157 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 183, + 187, + 199 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rajeev Acharya et al. 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In Computer Vision and Pattern Recognition (CVPR), 2025. 7" + ], + "bbox": [ + 91, + 92, + 480, + 643 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11405", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_model.json b/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..528fa0e4b6ecbf7330dbbe60810aae2ab457a2b2 --- /dev/null +++ b/2025/QuCOOP_ A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers/c311c3bc-3c21-4b1a-a4f8-f00774ef973f_model.json @@ -0,0 +1,3016 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.723, + 0.031 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.032, + 0.755, + 0.047 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.188, + 0.131, + 0.812, + 0.175 + ], + "angle": 0, + "content": "QuCOOP: A Versatile Framework for Solving Composite and Binary-Parametrised Problems on Quantum Annealers" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.203, + 0.474, + 0.24 + ], + "angle": 0, + "content": "Natacha Kuete Meli1 Vladislav Golyanik2 \n1University of Siegen" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.243, + 0.488, + 0.256 + ], + "angle": 0, + "content": "www.vsa.informatik.uni-siegen.de" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.203, + 0.715, + 0.22 + ], + "angle": 0, + "content": "Marcel Seelbach Benkner" + }, + { + "type": "text", + "bbox": [ + 0.744, + 0.203, + 0.885, + 0.22 + ], + "angle": 0, + "content": "Michael Moeller1" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.222, + 0.717, + 0.238 + ], + "angle": 0, + "content": "\\(^{2}\\)MPI for Informatics, SIC" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.243, + 0.79, + 0.257 + ], + "angle": 0, + "content": "https://4dqv.mpi-inf.mpg.de" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.323, + 0.486, + 0.596 + ], + "angle": 0, + "content": "There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained Binary Optimisation (QUBO) problems, which severely limits their applicability. This paper proposes a new way to overcome this limitation and introduces QuCOOP, an optimisation framework extending the scope of AQC to composite and binary parametrised, possibly non-quadratic problems. The key idea of QuCOOP is to iteratively approximate the original objective function by a sequel of local (intermediate) QUBO forms, whose binary parameters can be sampled on AQC devices. We experiment with quadratic assignment problems, shape matching and point set registration without knowing the correspondences in advance. Our approach achieves state-of-the-art results across multiple instances of tested problems1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.625, + 0.222, + 0.64 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.651, + 0.485, + 0.877 + ], + "angle": 0, + "content": "Adiabatic Quantum Computing (AQC) has become a promising approach for solving combinatorial optimisation problems in different fields of science including computer vision [3, 46, 48, 70]. AQC leverages principles of quantum mechanics to explore optimisation landscapes in a way that classical methods cannot do, allowing them to tunnel through energy barriers and escape local minima. Unfortunately, current AQC devices such as D-Wave's machines, also referred to as Quantum Annealers, are restricted to Quadratic Unconstrained Binary Optimisation (QUBO) problems. Any deviations from the QUBO form—e.g., when the objective function is non-quadratic or quadratic in a non-linear function of the binary variables—makes the potential benefits of AQCs not directly accessible. At the same time, many computer vision problems re" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.283, + 0.648, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.337, + 0.648, + 0.348 + ], + "angle": 0, + "content": "(a) Minimise \\( f(g(x)) \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.348, + 0.658, + 0.358 + ], + "angle": 0, + "content": "\\(f\\) quadratic in \\(g(x)\\) .. \\(\\checkmark\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.358, + 0.668, + 0.369 + ], + "angle": 0, + "content": "\\(x\\) binary: \\(\\checkmark\\), \\(g\\) linear in \\(x\\): \\(\\times\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.369, + 0.666, + 0.379 + ], + "angle": 0, + "content": "AQC: Not a QUBO !!!" + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.283, + 0.781, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.336, + 0.78, + 0.348 + ], + "angle": 0, + "content": "Minimise \\(f(g^{t}(x):= g\\)" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.282, + 0.882, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.336, + 0.891, + 0.348 + ], + "angle": 0, + "content": "\\(\\langle x^t\\rangle +\\langle \\nabla g(x^t),x - x^t\\rangle)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.348, + 0.839, + 0.359 + ], + "angle": 0, + "content": "\\(f\\) quadratic in \\(g^t (x)\\) .. \\(\\checkmark\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.737, + 0.359, + 0.852, + 0.369 + ], + "angle": 0, + "content": "ary: \\(\\checkmark\\) \\(g^{t}\\) linear in \\(x\\): \\(\\checkmark\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.369, + 0.875, + 0.38 + ], + "angle": 0, + "content": "AQC: \\(\\checkmark\\) Iteratively solve QUBOs !!!" + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.394, + 0.617, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.471, + 0.594, + 0.481 + ], + "angle": 0, + "content": "Initial" + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.483, + 0.693, + 0.494 + ], + "angle": 0, + "content": "(b) Rigid point sets registration." + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.398, + 0.711, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.471, + 0.684, + 0.48 + ], + "angle": 0, + "content": "Result" + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.385, + 0.809, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.751, + 0.474, + 0.794, + 0.482 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.483, + 0.881, + 0.494 + ], + "angle": 0, + "content": "(c) Shape matching on FAUST." + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.5, + 0.907, + 0.598 + ], + "angle": 0, + "content": "Figure 1. (a) Our QuCOOP framework for solving composite and binary-parametrised problems using Adiabatic Quantum Computing (AQC). Some qualitative results are shown for: (b) Point set registration without known correspondences; (c) Mesh alignment problems. Our general approach is competitive with specialised existing quantum and classical methods; it is compatible with quantum annealers and classical simulated annealing solvers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.624, + 0.907, + 0.699 + ], + "angle": 0, + "content": "quire non-quadratic objectives to obtain accurate solutions. Motivated by the tangible implications for computer vision of the restriction of the current AQC generation to QUBOs, we develop a new AQC-based optimisation method that can handle a certain type of non-quadratic objective functions." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.7, + 0.755, + 0.715 + ], + "angle": 0, + "content": "We consider the general problem" + }, + { + "type": "equation", + "bbox": [ + 0.662, + 0.726, + 0.907, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\underset {s \\in \\mathcal {S}} {\\arg \\min } f (s) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.761, + 0.907, + 0.822 + ], + "angle": 0, + "content": "of optimising a function \\( f: S \\to \\mathbb{R} \\) over a feasible set \\( S \\subsetneq \\mathbb{R}^n \\). Moreover, we assume \\( S \\) to be parameterizable by elements of a set \\( \\mathcal{X} \\subset \\mathbb{R}^k \\) via a smooth function \\( g: \\mathcal{X} \\to S \\) allowing to rewrite Problem (1) in a composite form as" + }, + { + "type": "equation", + "bbox": [ + 0.648, + 0.834, + 0.907, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } f (g (x)). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.87, + 0.907, + 0.903 + ], + "angle": 0, + "content": "If \\(\\mathcal{X} = \\mathbb{R}^k\\), Problem (2) describes an unconstrained problem and can be solved locally, or even globally (for \\(f \\circ g\\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.466, + 0.902 + ], + "angle": 0, + "content": "1project page: https://4dqv.mpi-inf.mpg.de/QuCOOP/" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11395" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.168 + ], + "angle": 0, + "content": "convex in \\(x\\) ) using gradient-based methods. If \\(\\mathcal{X}\\subsetneq \\mathbb{R}^k\\) Problem (2) becomes a constrained optimisation problem. If \\(\\mathcal{X}\\) is further non-convex, as e.g., the set \\(\\mathbb{B}^k\\coloneqq \\{0,1\\} ^k\\) of binary vectors of length \\(k\\) , Problem (2) is generally \\(\\mathcal{NP}\\) - hard [52] and, very often, can be solved only approximately." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.169, + 0.483, + 0.395 + ], + "angle": 0, + "content": "Gradient descent [54, 56] is perhaps the most simple algorithm for solving Problem (2) when \\(\\mathcal{X} = \\mathbb{R}^k\\). It is an iterative method, where at each iteration \\(t\\), a local model \\(f^t\\) of \\(f\\) is constructed around the current iterate \\(x^t\\) to identify a descent direction for updating \\(x^t\\). For constrained problems, one typically turns to iterative projection or additional penalty terms to ensure that all iterates \\(x^t\\) remain feasible. Examples of such techniques include: Gradient projection methods [7] that project the iterates of gradient descent onto \\(\\mathcal{X}\\); interior-point methods [60] that minimize an augmented objective function where a so-called barrier function penalizes non-feasible iterates; feasible direction methods [59], e.g., Frank-Wolfe [28], that compute a feasible descent direction by solving an easier constrained problem and then update the iterate accordingly." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.396, + 0.483, + 0.668 + ], + "angle": 0, + "content": "One of the strengths of AQC is its natural ability to optimize over discrete binary variables, whereas classical methods often resort to relaxations. To leverage this, we present QuCOOP (Quantum Framework for Composite and Binary-Parametrised OPoptimisation Problems), a general framework to solve (2) on AQCs. We are concerned with the case when \\(\\mathcal{X} = \\mathbb{B}^k \\coloneqq \\{0,1\\}^k\\) and \\(f\\) is a quadratic function in \\(g(x)\\). The key idea is to iteratively minimize a 1D cut of \\(f\\) at a current linear Taylor approximation of \\(g\\): At iteration \\(t\\), we approximate \\(f\\) through a local model \\(f^t\\) by linearising the inner function \\(g\\) around the current iterate \\(x^t\\). Since \\(f\\) is quadratic in \\(g(x)\\) and \\(x\\) binary, the resulting sub-objectives are QUBO problems for which modern quantum annealers provide an exciting new way to sample possible low-energy states. As a result, our proposed optimisation does not require descent directions or step sizes in the usual sense as classical methods do, but directly targets a state \\(x^{t + 1}\\) minimising \\(f^t\\). See Fig. 1-(a) for an overview." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.686, + 0.483, + 0.867 + ], + "angle": 0, + "content": "Applications. Our configuration of Problem (2) is common in computer vision. Applications we are interested in this work include the Quadratic Assignment Problem (QAP, [45]), a reputed \\(\\mathcal{NP}\\)-hard problem that aims to optimize a quadratic function over the set of permutation matrices. QAP models many real-life problems such as graph matching [5, 6], travelling salesman [30], facility location [45], or scheduling problems [32], to name just a few. Moreover, we show in further application examples how to solve mesh alignment [6] and rigid point set registration without input correspondences [49] with QuCOOP. See Fig. 1-(b, c) for representative results." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.476, + 0.901 + ], + "angle": 0, + "content": "Contributions. Our primary technical contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "- QuCOOP, a new general framework for solving composite and binary-parametrised problems on AQCs (Sec. 4);" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.122, + 0.905, + 0.166 + ], + "angle": 0, + "content": "- An iterative scheme to construct and solve QUBO problems that locally approximate the original, perhaps nonquadratic objective function;" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.168, + 0.907, + 0.334 + ], + "angle": 0, + "content": "- Applications of QuCOOP to a variety of computer vision problems including QAP, shape alignment and point set registration (Secs. 5 and 6). For correspondence problems, we introduce a binary parametrisation of permutation matrices fitting in the proposed QuCOOP framework. We experimentally validated the algorithm, first with simulated annealing and achieving state-of-the-art results for several considered problems (Secs. 7.1 to 7.3); then on real D-Wave quantum annealers and improving the dimensionality of solvable permutation-related problems compared to previous quantum-compatible approaches (Sec. 7.4)." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.345, + 0.655, + 0.36 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.37, + 0.905, + 0.581 + ], + "angle": 0, + "content": "Classical Optimisation Theory. A binary optimisation technique related to ours is the quadratisation of pseudo-Boolean functions [36, 47]. Pseudo-Boolean functions are functions that can be written uniquely as a multi-linear polynomial of binary variables, with QUBOs being a particular types of those with degrees not exceeding two. Quadratisation techniques [12, 47, 63] can be generally used to reduce the degree of higher-order polynomials to two in order to obtain a QUBO form. However, they often require auxiliary variables, which increases the problem size and can be costly for actual AQC devices. In contrast, QuCOOP does not require additional variables. Moreover, it is not restricted to polynomials, but could also be applied to any function as long as it fits in our composite form, see Eq. (6)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.905, + 0.807 + ], + "angle": 0, + "content": "Next, our proposed QuCOOP technique falls into the class of composite optimisation methods [31, 43, 58]. These approaches leverage the composite form of optimisation problem (2) to derive easy-to-solve sub-problems that return better local optima of the original problem. An incomplete list of example applications of composite optimisation problems in computer vision include super-resolution from raw time-of-flight data [31], image and point set registration [50], shape matching [6, 16, 74]. Composite optimisation is classically well studied for continuous problems [22, 31, 43, 58]. This work explores similar techniques for the discrete case, especially to leverage AQC-based optimisation. Hence, in a broad sense, this work improves our understanding of how AQCs can be used for optimising non-quadratic objectives." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Quantum-enhanced Computer Vision (QeCV). In computer vision, AQCs have been used to solve problems such as matching involving optimising over permutation matrices [5, 6, 9]; object tracking [78] by optimising binary assignments between observations and a set of tracks; or" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11396" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "clustering [79] by sampling multiple binary assignments of a sample set to models its posterior distribution. Several other approaches [8, 33, 49, 68, 69] were focused on registering point sets. A feature shared by all above-mentioned methods is the construction of QUBO problems with binary solution parametrisation that suit quantum annealers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.183, + 0.483, + 0.318 + ], + "angle": 0, + "content": "Remark. QeCV methods relying on gate-based quantum computing remain substantially less explored than AQCs [61], and many works in this domain are theoretical, heavily use simulators and are at the intersection with quantum machine learning [18, 35, 44]. One of the reasons is that quantum annealing can be considered the most advanced quantum computing technology nowadays, while fault-tolerant quantum computers that could be useful in computer vision are under development [1]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.336, + 0.485, + 0.578 + ], + "angle": 0, + "content": "The IQT Approach [49]. The most closely related work to ours is the iterative quantum transformation (IQT) approach of Kuete Meli et al. [49]. IQT iteratively finds rotation matrices \\( R \\) aligning two point sets using AQC. Since rotations can be parametrised by non-redundant parameters \\( v \\) (e.g., a rotation angle in 2D and rotation angle and axis in 3D), the original constrained problem on rotation matrices is cast in Ref. [49] into an unconstrained optimisation problem over rotation parameters. Specifically, IQT iteratively linearizes \\( R \\) around a current rotation parameter as \\( R(v) = R(v^t) + \\langle \\nabla R(v^t), v - v^t \\rangle + \\mathcal{O}(\\|v - v^t\\|^2) \\) and uses an AQC to sample, in each iteration, a binary representation of \\( v \\) minimising a target function quadratic in \\( R(v) \\). Hence, the IQT approach can be interpreted as a special case of QuCOOP, i.e., a more general optimisation technique relying on AQC as will become apparent from Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.589, + 0.22, + 0.606 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.615, + 0.483, + 0.691 + ], + "angle": 0, + "content": "As our method is designed for AQC devices, we briefly revise their principles. We also review classical composite optimisation, which QuCOOP builds upon. For a detailed introduction to quantum computing and numerical optimisation, see Ref. [20, 55, 71] and [54, 56], respectively." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.698, + 0.373, + 0.714 + ], + "angle": 0, + "content": "3.1. Adiabatic Quantum Computing" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Adiabatic Quantum Computing (AQC) is a model of quantum computation which is polynomially equivalent to the circuit model [2]. Quantum annealers (QAs) are experimental realisations of the AQC paradigm that do not perfectly fulfill the adiabaticity condition [3, 20, 38, 48]. They provide a meta-heuristic for finding globally-optimal solutions to combinatorial optimisation problems relying on the evolution of a quantum-mechanical system driven by quantum fluctuations. Usually they optimize QUBO objectives, i.e., problems of the form" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.878, + 0.483, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\quad \\langle x, \\mathbf {Q} x + \\mathbf {c} \\rangle , \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.227 + ], + "angle": 0, + "content": "where \\(\\langle \\cdot, \\cdot \\rangle\\) is the standard inner product in \\(\\mathbb{R}^k\\), \\(\\mathbf{Q}\\) a symmetric matrix, and \\(\\mathbf{c}\\) a vector. QUBO problems are \\(\\mathcal{NP}\\)-hard in general, and solving them on a QA is of high practical interest. Casting computer vision problems to QUBO forms can be challenging and has become an active research area [6, 9, 79]. While QUBOs can be optimised with classical optimisation techniques such as Simulated Annealing (SA) [41], QA is expected to offer substantial advantages over SA in certain cases [20, 21]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.907, + 0.5 + ], + "angle": 0, + "content": "In QA, the provided QUBO problem is converted to the corresponding physical Ising Hamiltonian \\(\\mathbf{H}_p\\). The mapping is such that the ground state of \\(\\mathbf{H}_p\\), i.e. the spin configuration of the physical system achieving the minimal energy value, encodes the solution of the QUBO. To obtain the ground state of \\(\\mathbf{H}_p\\), the system evolves according to a time-dependent Hamiltonian \\(\\mathbf{H}(t)\\) changing from the initial Hamiltonian \\(\\mathbf{H}_i\\) (with a known ground state) to \\(\\mathbf{H}_p\\), e.g. in the way that \\(\\mathbf{H}(t) = (1 - \\frac{t}{T})\\mathbf{H}_i + t\\mathbf{H}_p\\) for \\(t \\in [0,T]\\). If the system transitions according to the adiabatic theorem of quantum mechanics [11, 37, 39] it stays always in a ground state. One of the conditions is a slow-enough transition, e.g. a one that is inversely proportional to the squared minimum (over all instantaneous \\(t\\)) spectral gap of \\(\\mathbf{H}\\). In practice, modern experimental realisations of AQCs are non-adiabatic and return ground states with probabilities \\(\\ll 1.0\\). To increase the probability of finding the ground state at least once, annealing is repeated multiple times." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.509, + 0.738, + 0.525 + ], + "angle": 0, + "content": "3.2. Composite Optimisation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.531, + 0.905, + 0.562 + ], + "angle": 0, + "content": "Iterative methods [54, 56] solve Problem (2) by repeatedly minimising a local model \\( f^t \\) built upon the actual iterate \\( x^t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.575, + 0.905, + 0.6 + ], + "angle": 0, + "content": "\\[\nx ^ {t + 1} := \\underset {x \\in \\mathcal {X}} {\\arg \\min } f ^ {t} (x), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.904, + 0.638 + ], + "angle": 0, + "content": "where the local model \\( f^t \\) should have some nice properties such as convexity or separability making it easier to solve." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.639, + 0.906, + 0.759 + ], + "angle": 0, + "content": "In composite optimisation, also known as 'prox-linear' or 'prox-descent' [22, 31, 43, 58], the idea is to exploit the underlying composite nature of the objective function in Problem (2) to derive a local model that, still being easier to solve, approximates the original landscape more faithfully. Two approaches to achieve this are to either approximate the outer function \\( f \\) [31], or linearize the inner function \\( g \\) [22, 43, 58]. In the later case, the local model reads" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.769, + 0.905, + 0.812 + ], + "angle": 0, + "content": "\\[\nf ^ {t} (x) := f \\left(g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle\\right) + \\frac {1}{2 \\alpha^ {t}} \\| x - x ^ {t} \\| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.905, + 0.902 + ], + "angle": 0, + "content": "with \\(\\alpha^t\\) being the step size that prevents \\(x^{t + 1}\\) to deviate too much from \\(x^t\\), point around which the approximation is more reliable. It is shown in Ref. [58] that for a convex and coercive \\(f\\) and under the Kurdyka-Lojasiewicz property, the iterates \\((x^{t})_{t = 1}^{\\infty}\\) for the model Eq. (5) converge" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11397" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.155 + ], + "angle": 0, + "content": "to a critical point, i.e. a minimizer of \\( f \\). We build on this later approximation, i.e. the linearisation of the inner function \\( g \\), to derive QUBOs for AQC, as we consider that the outer function \\( f \\) is quadratic in \\( g(x) \\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.166, + 0.4, + 0.183 + ], + "angle": 0, + "content": "4. The Proposed QuCOOP Iteration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.191, + 0.484, + 0.236 + ], + "angle": 0, + "content": "This section describes our general QuCOOP framework, followed by its applications in Sec. 5 and Sec. 6. Proofs of all Lemmas are given in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.237, + 0.484, + 0.356 + ], + "angle": 0, + "content": "QuCOOP is an optimisation algorithm for composite optimisation problems of the form (2), where \\( f \\) is quadratic in \\( g(x) \\), that iteratively uses AQC. The function \\( g: \\mathbb{R}^k \\to \\mathbb{R}^n \\) is a smooth function such that \\( S = \\operatorname{Im}_g(\\mathbb{B}^k) := \\{g(x): x \\in \\mathbb{B}^k\\} \\), hence, \\( g \\) parametrizes the feasible domain \\( S \\subsetneq \\mathbb{R}^n \\) of the original Problem (1) by elements of the set \\( \\mathcal{X} := \\mathbb{B}^k \\). For convenience, we write Problem (1) as" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.369, + 0.484, + 0.387 + ], + "angle": 0, + "content": "\\[\nf (g (x)) = \\langle g (x), \\mathbf {Q} g (x) + \\mathbf {c} \\rangle , \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.431, + 0.412 + ], + "angle": 0, + "content": "for a given matrix \\(\\mathbf{Q} \\in \\mathbb{R}^{n \\times n}\\) and a vector \\(\\mathbf{c} \\in \\mathbb{R}^n\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.412, + 0.484, + 0.533 + ], + "angle": 0, + "content": "Note that for Problem (1), we are only interested in values of \\( g \\) on \\( \\mathbb{B}^k \\). However, from a theoretical point of view, our algorithm involves a Taylor approximation of \\( g \\), requiring \\( g \\) to be smooth as described above. Such a \\( g \\) is far from being unique. Moreover, in addition to \\( S = \\operatorname{Im}_g(\\mathbb{B}^k) \\), the gradient of \\( g \\) can take any value by design. Thus, from a practical point of view, this function \\( g \\) should model a \"reasonable\" or \"natural\" smooth parametrisation of \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.484, + 0.564 + ], + "angle": 0, + "content": "A high-level description of the algorithm is provided in Algorithm 1. Next, we analyse its different steps." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.576, + 0.345, + 0.592 + ], + "angle": 0, + "content": "Algorithm 1: QuCOOP Iteration" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.601, + 0.384, + 0.617 + ], + "angle": 0, + "content": "Initialize \\(x^0\\) and repeat for \\(t = 0,1,2,\\ldots\\)" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.627, + 0.466, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} g ^ {t} (x) := g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle (7) \\\\ x ^ {t + 1} \\leftarrow \\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\left\\{f ^ {t} (x) := f \\left(g ^ {t} (x)\\right) \\right\\} (8) \\\\ \\begin{array}{l l} \\text {s . t .} & g ^ {t} (x) \\in \\mathcal {S} \\end{array} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.706, + 0.222, + 0.722 + ], + "angle": 0, + "content": "Return \\( g(x^{t + 1}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.825 + ], + "angle": 0, + "content": "The first step is the familiar choice of the starting point \\( x^0 \\). This can be a vector based on prior knowledge, the result of a previous optimisation, or any random point. As will be discussed later in Lemma 1, QuCOOP converges globally, but not necessarily to the global optimum. Hence, different \\( x^0 \\) can lead to different results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In a subsequent loop, at each iteration \\( t \\), the inner function \\( g \\) is linearised around the current iterate \\( x^t \\) using first-order Taylor expansion, Eq. (7), and the next iterate \\( x^{t + 1} \\) is computed by solving the minimisation Problem (8). Evaluated on the hyperplane \\( g^{t}(x) \\), \\( f \\) results in a" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.181 + ], + "angle": 0, + "content": "\\(k\\)-dimensional quadratic function \\(f^t\\) in variable \\(x\\). In cases where the parametrisation \\(g^t(x)\\) differs substantially from the parametrisation \\(g(x)\\), to guarantee a monotone decrease of the objective values, it might also be necessary to include a step \\(x^{t+1} = g^{-1}(g^t(\\tilde{x}^{t+1}))\\), with \\(\\tilde{x}\\) being the output of Problem (8)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.183, + 0.906, + 0.243 + ], + "angle": 0, + "content": "Fig. 1 provides a visual intuition of the constructed local model \\( f^t \\). Next, we ensure the compatibility of Problem (8) with quantum annealers (see Sec. 3.1) through a QUBO formulation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.266, + 0.906, + 0.312 + ], + "angle": 0, + "content": "The Unconstrained Part of Problem (8). The objective function of the minimisation in Problem (8) is already in an AQC-compatible form. At iteration \\( t \\), we solve the QUBO" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.323, + 0.906, + 0.35 + ], + "angle": 0, + "content": "\\[\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle x, \\mathbf {Q} ^ {t} x + \\mathbf {c} ^ {t} \\right\\rangle , \\text {w i t h} \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.38, + 0.906, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} ^ {t} := \\nabla g \\left(x ^ {t}\\right) \\mathbf {Q} \\nabla g \\left(x ^ {t}\\right) ^ {\\top}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.402, + 0.906, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} ^ {t} := \\nabla g (x ^ {t}) \\left(\\mathbf {c} + 2 \\mathbf {Q} \\left(g (x ^ {t}) - \\nabla g (x ^ {t}) ^ {\\top} x ^ {t}\\right)\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.906, + 0.495 + ], + "angle": 0, + "content": "This is because the local model \\( f^t \\) now becomes quadratic in the binary variable \\( x \\). Details on the derivation of this QUBO problem can be found in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.906, + 0.606 + ], + "angle": 0, + "content": "Meeting the Constraint of Problem (8). In classical optimisation when \\(\\mathcal{X}\\) is convex, cf. Eq. (5), the damping term factored to the step size ensures that \\(g(x)\\) or \\(x\\) remains close to \\(g(x^t)\\) or \\(x^t\\). This is reminiscent of trust-region methods requiring that the local model \\(f^t\\) trustfully approximates \\(f\\), which happens in a close neighborhood of \\(x^t\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.607, + 0.906, + 0.835 + ], + "angle": 0, + "content": "In our case, \\(\\mathcal{X}\\) is discrete, but the quantum annealer can essentially navigate the complete \\(\\mathcal{X}\\) domain, allowing us to explore solutions beyond the trust region. At the same time, as required in Problem (8), we have to guarantee that \\(g^{t}(x)\\in S\\); or, more generally, to replace it with a nearby feasible point with the objective value not much worse than the linearised estimate \\(f(g^{t}(x))\\). As the whole QuCOOP iteration should be carried out by AQC, ensuring this feasibility amounts to designing a penalty term in the form of a quadratic function in \\(g^{t}(x)\\). Depending on the form of \\(S\\), this may, or may not, be easy computationally. The yet resulting objective function is a standard QUBO problem that can run on AQC. We refer to Secs. 5 and 6 for exemplary penalty functions on two computer vision problems, namely graph or shape matching and point set registration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Convergence Analysis. While QuCOOP does not guarantee global convergence, it, at least, monotonically decreases the objective function values as stated next:" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11398" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.138 + ], + "angle": 0, + "content": "Lemma 1. The series \\((f(g(x^{t})))_{t\\in \\mathbb{N}}\\) generated by Algorithm 1 with reparametrisation, or without and under assumptions found in Appendix A, monotonically decreases." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.149, + 0.471, + 0.167 + ], + "angle": 0, + "content": "5. Graph Matching and QAP with QuCOOP" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.175, + 0.483, + 0.205 + ], + "angle": 0, + "content": "This section shows an application of QuCOOP to graph matching and quadratic assignment problems (QAP)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.205, + 0.484, + 0.234 + ], + "angle": 0, + "content": "A general graph matching problem of size \\( n \\in \\mathbb{N} \\) can be written in matrix form as" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.242, + 0.483, + 0.269 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } \\| \\mathbf {A P} - \\mathbf {P B} \\| _ {F} ^ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.276, + 0.484, + 0.336 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}\\) and \\(\\mathbf{B}\\) are given \\(n\\times n\\) symmetric matrices and \\(\\Pi_{n}\\) is the set of all \\(n\\times n\\) permutation matrices [16]. Equivalently, by assuming the constraint \\(\\mathbf{P}\\in \\Pi_n\\) to be always held and ignoring resulting constant terms, Eq. (12) becomes" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.344, + 0.483, + 0.369 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } - \\left\\langle \\mathbf {A P}, \\mathbf {P B} \\right\\rangle_ {F}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.376, + 0.484, + 0.435 + ], + "angle": 0, + "content": "The Quadratic Assignment Problem (QAP) aims to maximize (13). To apply QuCOOP to (13), we need to parametrisse the permutation matrix \\(\\mathbf{P}\\) using binary variables:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.484, + 0.52 + ], + "angle": 0, + "content": "Lemma 2. Let \\(((a,b), a,b = 1,\\dots,n, a < b)\\), with cardinality \\(k := n(n - 1)/2\\), be the tuple of all 2-cycles permuting \\(a\\) and \\(b\\), and \\(\\mathbf{T}_i\\) the matrix representation of the \\(i\\)-th cycle. Any permutation matrix can be parametrised with a length-\\(k\\) binary vector \\(x := (x_1, \\ldots, x_k)\\) via the function" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.541, + 0.203, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P}: \\mathbb {B} ^ {k} \\to \\Pi_ {n}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.563, + 0.483, + 0.604 + ], + "angle": 0, + "content": "\\[\nx \\mapsto \\mathbf {P} (x) := \\prod_ {i = 1} ^ {k} \\mathbf {P} _ {i} \\left(x _ {i}\\right), \\quad \\mathbf {P} _ {i} \\left(x _ {i}\\right) := \\mathbf {T} _ {i} ^ {x _ {i}}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.611, + 0.48, + 0.628 + ], + "angle": 0, + "content": "where \\(\\mathbf{T}_i^{x_i}\\) is \\(\\mathbf{T}_i\\) if \\(x_{i} = 1\\) and the identity \\(\\mathbf{I}_{n\\times n}\\) otherwise." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.633, + 0.484, + 0.77 + ], + "angle": 0, + "content": "Next, we construct out of \\(\\mathbf{P}\\) from Eq. (14) a smooth function \\(g\\) to be used in QuCOOP. A natural choice is to design, for each \\(\\mathbf{P}_i\\) from Eq. (14), a smooth function defined through \\(\\mathbf{P}_i(x_i) = x_i(\\mathbf{T}_i - \\mathbf{I}_n) + \\mathbf{I}_n\\) for \\(x_i\\in \\mathbb{R}\\) which makes \\(\\mathbf{P}_i\\) and thus \\(\\mathbf{P}\\) differentiable with respect to \\(x_{i}\\) and thus \\(x\\). Now letting \\(g(x)\\coloneqq \\mathbf{p}(x)\\coloneqq \\operatorname {vec}(\\mathbf{P}(x))\\) be the vector formed by the rows of \\(\\mathbf{P}(x)\\), we propose to solve Problem (13) using Algorithm 1 by solving at each iteration \\(t\\) the sub-problem" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.776, + 0.483, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\left\\langle g ^ {t} (x), \\mathbf {Q} g ^ {t} (x) \\right\\rangle , \\quad \\mathbf {Q} := \\alpha \\mathbf {I} _ {n \\times n} - \\mathbf {A} \\otimes \\mathbf {B}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.809, + 0.484, + 0.901 + ], + "angle": 0, + "content": "where \\( g^{t}(x) = \\mathbf{p}^{t}(x) = \\mathbf{p}(x^{t}) + \\langle \\nabla \\mathbf{p}(x^{t}), x - x^{t} \\rangle \\). The term \\( \\alpha \\mathbf{I}_{n \\times n} \\) is, for some \\( \\alpha \\in \\mathbb{R}_+ \\), the penalty added to enforce \\( \\mathbf{p}^t(x) \\in \\Pi_n \\) as required by QuCOOP. In the next paragraph, we justify why our penalty term effectively penalizes non-feasible solutions. Finally, the optimisation follows Algorithm 1 with \\( x \\in \\mathcal{X} = \\mathbb{B}^k \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.152 + ], + "angle": 0, + "content": "On the Penalty Term of the Permutation Constraint. We next show why minimising \\(\\alpha \\| \\mathbf{p}^t (x)\\| _2^2\\) effectively constrains the result of the minimisation step in (15) to lie in the set \\(\\Pi_{n}\\) of permutation matrices. At iteration \\(t\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.159, + 0.905, + 0.177 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} ^ {t} (x) = \\mathbf {p} \\left(x ^ {t}\\right) + \\left\\langle \\nabla \\mathbf {p} \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle , \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.907, + 0.273 + ], + "angle": 0, + "content": "in which each row of \\(\\nabla \\mathbf{p}(x^t)\\), that is, each partial derivative of \\(\\mathbf{p}\\) (cf. Eq. (42) in the supplement), contains exactly two 1 and two \\(-1\\) entries. A following nice property of QuCOOP is that its iterates \\(\\mathbf{P}^t(x)\\) partially satisfy the permutation matrix constraint in the sense that their rows and columns sum up to ones, as stated in Lemma 3." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.28, + 0.906, + 0.312 + ], + "angle": 0, + "content": "Lemma 3. All the iterates \\(\\mathbf{P}^t (x)\\) computed by Algorithm 1 for \\(\\mathbf{P}(x)\\) from Eq. (14) fulfill \\(\\mathbf{P}^t (x)\\in X,\\forall x\\in \\mathbb{B}^k\\) , where" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.317, + 0.905, + 0.355 + ], + "angle": 0, + "content": "\\[\nX := \\left\\{\\mathbf {M} \\in \\mathbb {Z} ^ {n \\times n} \\Bigg | \\sum_ {i = 1} ^ {n} \\mathbf {M} _ {i j} = \\sum_ {j = 1} ^ {n} \\mathbf {M} _ {i j} = 1, \\forall i j \\right\\}. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.361, + 0.906, + 0.393 + ], + "angle": 0, + "content": "As a consequence of Lemma 3, \\(n \\leq \\| \\mathbf{p}^t(x) \\|_2^2\\) holds so that minimising \\(\\| \\mathbf{p}^t(x) \\|_2^2\\) enforces \\(\\mathbf{P}^t(x) \\in \\Pi_n\\) as desired." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.403, + 0.854, + 0.421 + ], + "angle": 0, + "content": "6. Point Set Registration with QuCOOP" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.906, + 0.52 + ], + "angle": 0, + "content": "We next apply QuCOOP to point set registration. Given a reference set \\(\\mathbf{X} := (x_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}\\) and a template set \\(\\mathbf{Y} := (y_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}\\), our goal is to determine the best rotation \\(\\mathbf{R} \\in \\mathrm{SO}(d)\\) and the best permutation \\(\\mathbf{P} \\in \\Pi_n\\) that jointly transform the template set and find correspondences with the reference set. Concretely, we aim to solve" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.526, + 0.905, + 0.554 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {R} \\in \\operatorname {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } \\| \\mathbf {X P} - \\mathbf {R Y} \\| _ {F} ^ {2}. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.561, + 0.906, + 0.606 + ], + "angle": 0, + "content": "By assuming the constraints \\(\\mathbf{R} \\in \\mathrm{SO}(d)\\) and \\(\\mathbf{P} \\in \\Pi_n\\) to be always fulfilled and discarding resulting constant terms, we retrieve the problem formulation:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.614, + 0.905, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {R} \\in \\mathrm {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } - \\left\\langle \\mathbf {X P}, \\mathbf {R Y} \\right\\rangle_ {F}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.906, + 0.767 + ], + "angle": 0, + "content": "As required by Algorithm 1, we need to binary-parametrisse \\(\\mathbf{R}\\) and \\(\\mathbf{P}\\). For \\(\\mathbf{P}\\), we use the parametrisation from Lemma 2, again with a total of \\(k_{p} \\coloneqq n(n - 1)/2\\) binary parameters. For \\(\\mathbf{R}\\), we follow Ref. [33, 49] and write \\(\\mathbf{R}\\) using the exponential mapping from the orthogonal Lie algebra to its group, as a function \\(\\mathbf{R}(y) = \\exp(\\mathbf{M}(y))\\), where \\(\\mathbf{M}\\) is a skew-symmetric matrix depending on the rotation parameter \\(y \\in \\mathbb{R}^k\\), with \\(k_{r} \\coloneqq d(d - 1)/2\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.768, + 0.906, + 0.813 + ], + "angle": 0, + "content": "By flattening the optimisation variables \\(\\mathbf{R}(y)\\) and \\(\\mathbf{P}(x)\\) as \\(\\mathbf{r}(y) := \\operatorname{vec}(\\mathbf{R}(y))\\) and \\(\\mathbf{p}(x) := \\operatorname{vec}(\\mathbf{P}(x))\\) our optimisation sub-problem in the QuCOOP iteration \\(t\\) becomes" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.835, + 0.905, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\underset {(x, y) \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle g ^ {t} (x, y), \\mathbf {Q} g ^ {t} (x, y) \\right\\rangle , \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.865, + 0.905, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} := \\left( \\begin{array}{c c} \\alpha \\mathbf {I} _ {n \\times n} & - \\frac {1}{2} \\mathbf {X} \\otimes \\mathbf {Y} \\\\ - \\frac {1}{2} (\\mathbf {X} \\otimes \\mathbf {Y}) ^ {\\top} & \\beta \\mathbf {I} _ {d \\times d} \\end{array} \\right), \\tag {21}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11399" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.244 + ], + "angle": 0, + "content": "where \\( g^{t}(x,y) \\coloneqq (\\mathbf{p}^{t}(x),\\mathbf{r}^{t}(y)) \\) with the linearisation \\( \\mathbf{p}^t (x) = \\mathbf{p}(x^t) + \\langle \\nabla \\mathbf{p}(x^t),x - x^t\\rangle \\) for the permutation and \\( \\mathbf{r}^t (y) = \\mathbf{r}(y^t) + \\langle \\nabla \\mathbf{r}(y^t),y - y^t\\rangle \\) for the rotation. The term \\( \\alpha \\mathbf{I}_{n\\times n} \\) ensures that the iterate \\( \\mathbf{P}^t (x) \\) is a valid permutation matrix, and \\( \\beta \\mathbf{I}_{d\\times d} \\) that \\( \\mathbf{R}^t (y) \\) approaches an orthonormal matrix. The optimisation now follows Alg. 1 in which the permutation variable \\( x \\) lies in \\( \\mathbb{B}^k \\), and, as in Ref. [49], we binarize the rotation variable \\( y \\) by considering its flexible \\( m \\)-bits discretisation over a tunable interval, leading to \\( y\\in \\mathbb{B}^{m\\cdot k} \\). In total, \\( (x,y) \\) is a binary vector in \\( \\mathbb{B}^{k + m\\cdot k} \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.255, + 0.327, + 0.272 + ], + "angle": 0, + "content": "7. Experimental Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.484, + 0.446 + ], + "angle": 0, + "content": "We perform numerical experiments on QAP, shape matching and point set registration problems. Secs. 7.1 to 7.3 report results of our method when optimised using Simulated Annealing (SA) on classical hardware, and Sec. 7.4 reports results of the same experiments using real D-Wave Quantum Annealer (QA). Details about the used datasets and benchmark methods are discussed in the corresponding sections. SA, along with the preparation of couplings and biases of QuCOOP for the quantum annealer, is carried out on a conventional computer (AMD Ryzen 95900X 12-Core Processor CPU with 128GB RAM)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.464, + 0.484, + 0.692 + ], + "angle": 0, + "content": "Penalty Factors. Similar to many other AQC methods dealing with constrained problems [5, 9, 46], our approach is not exempt from the choice of the penalty factors \\(\\alpha\\) in (15), and \\(\\alpha\\) and \\(\\beta\\) in (21). The penalty factors should be large enough to enforce the constraint while not significantly worsening the dynamic range of the resulting problem Hamiltonian, which otherwise could lead to incorrect solutions of the QUBO problem on the quantum annealer [51]. In our experiments, we set the penalty factors for QAP and point set registration by grid search on smaller problems, which is a widely used approach in the field [9, 27]. In the following, \\(\\alpha\\) is set for QAPs to the lowest eigenvalue for \\(\\mathbf{A} \\otimes \\mathbf{B}\\); for shape matching problems, \\(\\alpha\\) is ten times the lowest eigenvalue of \\(\\mathbf{A} \\otimes \\mathbf{B}\\); and in point set registration, \\(\\alpha\\) equals \\(\\|\\mathbf{X}\\|_F^2\\) and \\(\\beta\\) equals \\(0.1 \\cdot \\|\\mathbf{Y}\\|_F^2\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.698, + 0.433, + 0.715 + ], + "angle": 0, + "content": "7.1. Quadratic Assignment Problems (QAP)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.87 + ], + "angle": 0, + "content": "To benchmark our method on QAP, we consider the Fast Approximate Quadratic programming for graph matching (FAQ) [75] and the 2-OPT method [19] as classical competitors, and Q-Match [6] as an AQC-compatible competitor. Implementations for FAQ and 2-OPT are provided within Python's Scipy-library, and our method as well as Q-Match are optimised using the SA implementation provided by D-Wave. Q-Match's source code is publicly available [4]. A technical comparison between QuCOOP and Q-Match can be found in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We report results on the QAPLIB dataset [15] for all instances with problem size \\( n \\leq 50 \\), 72 in total. Details" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.074, + 0.9, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.262, + 0.907, + 0.319 + ], + "angle": 0, + "content": "Figure 2. Benchmark results on QAPLIB [15]. We plot the percentage energy error for all considered problem instances (note the means over all instances reported in the legend) and provide their runtimes. Our method clearly outperforms its competitors." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.348, + 0.907, + 0.515 + ], + "angle": 0, + "content": "on those problem instances, along with calculated objective values, are provided in the supplement, Tab. III. Fig. 2 shows the relative errors of the computed objective values w.r.t. optimal ones. Overall, our method consistently outperforms both classical and quantum competitors and has the smallest confidence intervals. Our method and Q-Match exhibit higher runtimes compared to FAQ and 2-Opt for almost all \\( n \\). This can be explained by the fact that Q-Match solves smaller problems but requires a lot of iterations (\\( \\approx 800 \\) for \\( n = 50 \\)), while QuCOOP solves larger problems in much fewer iterations (\\( \\approx 5 \\) for \\( n = 50 \\))." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.528, + 0.677, + 0.544 + ], + "angle": 0, + "content": "7.2. Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.551, + 0.907, + 0.777 + ], + "angle": 0, + "content": "We match pairs \\((\\mathcal{U},\\mathcal{V})\\) of reduced meshes from the FAUST dataset [10], with 502 vertices each following Seelbach Benkner et al. [6]. We follow Ref. [6] in several further design choices. Due to the high problem dimensionality, we break down each problem into carefully selected sub-problems solved iteratively. An initial registration based on descriptor similarities is first calculated using linear assignment. Subsequently, in each iteration and for each vertex \\(u\\in \\mathcal{U}\\), we compute the contribution \\(\\sum_{v\\in \\mathcal{V}}\\mathbf{Q}_{u\\cdot n + \\mathbf{P}u,v\\cdot n + \\mathbf{P}v}\\) to the objective function, where \\(\\mathbf{P}\\) is the current solution. The \\(n = 40\\) vertices with the highest mismatch scores on both meshes are selected as sub-meshes and registered using either our QuCOOP or Q-Match [6] to enhance registration. We repeat until the set of worst vertices converges." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.779, + 0.909, + 0.869 + ], + "angle": 0, + "content": "The evaluation metric is the common Princeton benchmark protocol [40] which calculates for each \\( u \\in \\mathcal{U} \\) the geodesic distance between the computed and the optimal vertex assignment of \\( u \\), normalised by the diameter of \\( \\mathcal{V} \\). We report cumulative geodesic errors, i.e. the percentage of assignments with error bellow incremental thresholds." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Fig. 3 displays some qualitative registration results and Fig. 4 presents the function value decrease over the iter-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11400" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.096, + 0.481, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.314, + 0.484, + 0.344 + ], + "angle": 0, + "content": "Figure 3. Registration results on FAUST [10]. The proposed approach performs at least as well as Q-Match [6]; see circled areas." + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.36, + 0.48, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.457, + 0.478, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.56, + 0.483, + 0.618 + ], + "angle": 0, + "content": "Figure 4. Energy decrease and geodesic errors, averaged on ten instances of FAUST [10] in each pose category. The mean geodesic error for both methods is given in the legend of the plot. The proposed method performs slightly better than Q-Match [6]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.642, + 0.484, + 0.779 + ], + "angle": 0, + "content": "ations as well as the cumulative geodesic errors. Failure cases are discussed in Appendix E. Our general QuCOOP framework clearly matches the accuracy of the previous specialised Q-Match method. It reduces the mean geodesic error by about 0.01, as it can achieve better results on the sub-problems (see Appendix C). This selection of worst vertices, however, also worsens the performance of both methods, preventing them from matching the results of recent classical state-of-the-art methods [64, 65, 80]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.295, + 0.804 + ], + "angle": 0, + "content": "7.3. Point Set Registration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We perform experiments on 2D and 3D point set registration. In 2D, points were picked on fish images, and in 3D they were generated from geometrical curves. The number of points varies from \\( n = 20 \\) to \\( n = 40 \\). We benchmark QuCOOP against the classical rigid CPD algorithm [53] implemented within the pycpd package [29]. Quantum com" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.897, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.231, + 0.896, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.379, + 0.907, + 0.465 + ], + "angle": 0, + "content": "Figure 5. Registration results on 2D and 3D point sets with different \\( n \\). Grey lines show correspondences between reference (olive) and template (blue) points. With up to a few correspondence errors, our method performs well on both isomorphic (left to vertical line) and non-isomorphic shapes (right to vertical line). CPD performs better on isomorphic shapes than on non-isomorphic shapes." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.48, + 0.891, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.574, + 0.906, + 0.616 + ], + "angle": 0, + "content": "Figure 6. Varying rotation angle in the point sets registration experiment. Both CPD and our method show difficulties to register the points for a rotation angle exceeding \\(90^{\\circ}\\) in 2D and \\(45^{\\circ}\\) in 3D." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.906, + 0.673 + ], + "angle": 0, + "content": "petitor methods that would have been IQT [49] and QA [33] cannot handle registration without correspondences." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Fig. 5 shows our registration results. Left to the vertical line in the figure are point sets that are isomorphic up to the rotation and permutation, Right are cases where, additionally, the sets are non-isomorphic and/or have different number of points. In the later case, we zero-pad the set with the lowest cardinality to match the other. We use \\( k_{r} = 10 \\) variables for the rotation parameter and perform 15 iterations on each problem instance. We see that QuCOOP's computed correspondences are overall correct, so that a reasonable transformation of the template set can still be found. CPD shows difficulties in registering non-isomorphic sets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In Fig. 6, we show registration performances, averaged over ten random problem instances of size \\( n = 10 \\), for both methods, while varying the rotation angle. The larger the rotation angle, the harder the registration for both methods." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11401" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.092, + 0.473, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.182, + 0.483, + 0.252 + ], + "angle": 0, + "content": "Figure 7. D-Wave results for 5 randomly generated QAP instances for \\( n = 3, 5, 7, 9, 12, 15 \\). Left are returned energy function values, 0 being the best. Right is the validness \\( |n - \\| \\mathbf{P} \\|_F^2| \\) of returned matrices, 0 indicating a valid permutation matrix. Up to \\( n \\approx 12 \\), D-Wave finds valid permutation matrices, and often optimal ones." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.276, + 0.393, + 0.293 + ], + "angle": 0, + "content": "7.4. Experiments on D-Wave Machines" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.298, + 0.484, + 0.42 + ], + "angle": 0, + "content": "We now execute QuCOOP on a real quantum device, D-Wave Advantage 6.4 accessed through the Leap API [23-25]. Advantage has \\(>5000\\) physical qubits connected in the Pegasus topology. However, due to the connectivity pattern of the physical qubits which induces chains in the problem embedding, it is estimated that it can solve problems of about 180 fully connected logical variables, limiting our experiments to problems of sizes \\(n \\approx 15\\); see also Appendix G." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.438, + 0.484, + 0.589 + ], + "angle": 0, + "content": "QAP. On D-Wave, we solve 5 randomly generated QAP instances for \\( n = 3, 5, 7, 9, 12, 15 \\). The entries of matrix A are \\( \\mathbf{A}_{ij} = \\| x_i - x_j\\|_2 \\) for standard and normally distributed \\( \\{x_i \\in \\mathbb{R}^2\\}_{i=1}^n \\), and B equals \\( \\mathbf{P}^\\top \\mathbf{A}\\mathbf{P} \\) such that, according to Eq. (12), the optimal function value is 0. Each iteration of the algorithm is executed with the default annealing time of \\( 20\\mu s \\) and 50 sample reads. We investigate, whether the last computed matrices (i.e. \\( \\mathbf{P} = \\mathbf{P}^t(x^{t+1}) \\)) are valid permutation matrices² and plot their function values. We compare against the SA implementation and Q-Match (with QA)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.589, + 0.483, + 0.755 + ], + "angle": 0, + "content": "Our results are reported in Fig. 7. Up to \\( n \\approx 12 \\), QuCOOP QA finds valid permutation matrices, but returns higher objective values compared to QuCOOP SA and Q-Match QA. As \\( n \\) becomes large, QuCOOP QA tends to compute non-valid matrices. QuCOOP QA took about \\( 5 \\times \\) less runtime than Q-Match QA on one problem instance, including overheads such as minor embedding and access. Compared to previous works [5, 77] which reasonably—i.e. by returning valid permutation matrices—solved only problems of size \\( n = 3,4 \\) on D-Wave machines, we consider QuCOOP as an improvement of the state-of-the-art." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.773, + 0.483, + 0.879 + ], + "angle": 0, + "content": "Point Set Registration. We perform point set registration on D-Wave for five randomly generated problem instances for \\( n = 3,5,7,9,12,15 \\) in each set. The results are reported in Fig. 8. Qualitative results can be found in Appendix F. We see that QuCOOP can register the points without correspondences up to \\( n = 5 \\), improving previous work [49] in which correspondences are known beforehand." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.093, + 0.895, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.183, + 0.905, + 0.226 + ], + "angle": 0, + "content": "Figure 8. D-Wave results for five randomly generated point sets registrations for \\( n = 3,5,7,9,12,15 \\). In line with the QAP experiment, D-Wave successfully registers small problem instances." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.253, + 0.766, + 0.269 + ], + "angle": 0, + "content": "8. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.279, + 0.906, + 0.4 + ], + "angle": 0, + "content": "The experiments reveal several features of QuCOOP: First, its ability to handle problems involving permutation problems; second, its versatility and compatibility with continuous problems such as point set registration without correspondences, which previous techniques [6, 33, 49] are not able to address. Moreover, QuCOOP supports optimisation over permutation matrices up to size \\( n = 12 \\) using the chosen parametrisation on D-Wave annealers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.425, + 0.906, + 0.501 + ], + "angle": 0, + "content": "Approximation Accuracy. As for many first-order methods, the linearisation \\( g^t \\) of the inner function \\( g \\) is both the key and the bottleneck of QuCOOP. It may not always provide accurate approximations for highly non-linear \\( g \\) and lead to suboptimal solutions as observed in the tests." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.525, + 0.906, + 0.587 + ], + "angle": 0, + "content": "Scalability and Scaling. The space complexity of our permutation parameterisation scales quadratically with \\( n \\), making it difficult to solve large problems on D-Wave, as complex embeddings increase the chain break probability." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.603, + 0.634, + 0.618 + ], + "angle": 0, + "content": "9. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We have presented QuCOOP, a framework for solving composite, binary-parametrised and possibly non-quadratic problems using AQC. This represents a new class of problems solvable on AQC previously restricted to QUBO forms. QuCOOP solves a sequence of QUBO forms approximating the original objective function, which facilitates the non-intuitive and challenging task of handcrafting QUBOs for the aforementioned problem types. We show that our single framework can effectively be applied to several computer vision problems. Namely, we address QAP and shape matching problems, outperforming the previous specialised quantum-enhanced Q-Match method by \\(5\\%\\) on QAP and 0.01 on shape matching. For the first time, an AQC-compatible method for rigid point set registration is shown not to require input correspondences and match the accuracy of the classical CPD algorithm on tested problems. We hope this work inspires future exploration of new methods for other CV problems within the proposed framework." + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.886, + 0.481, + 0.901 + ], + "angle": 0, + "content": "Note that \\(\\mathbf{P}^t (x^{t + 1})\\) may be non-valid, but \\(\\mathbf{P}(x^{t + 1})\\) is always valid." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11402" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.114, + 0.486, + 0.158 + ], + "angle": 0, + "content": "This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 534951134." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.184, + 0.188, + 0.2 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.209, + 0.484, + 0.236 + ], + "angle": 0, + "content": "[1] Rajeev Acharya et al. 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Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained Binary Optimisation (QUBO) problems, which severely limits their applicability. This paper proposes a new way to overcome this limitation and introduces QuCOOP, an optimisation framework extending the scope of AQC to composite and binary parametrised, possibly non-quadratic problems. The key idea of QuCOOP is to iteratively approximate the original objective function by a sequel of local (intermediate) QUBO forms, whose binary parameters can be sampled on AQC devices. We experiment with quadratic assignment problems, shape matching and point set registration without knowing the correspondences in advance. Our approach achieves state-of-the-art results across multiple instances of tested problems1. + +# 1. Introduction + +Adiabatic Quantum Computing (AQC) has become a promising approach for solving combinatorial optimisation problems in different fields of science including computer vision [3, 46, 48, 70]. AQC leverages principles of quantum mechanics to explore optimisation landscapes in a way that classical methods cannot do, allowing them to tunnel through energy barriers and escape local minima. Unfortunately, current AQC devices such as D-Wave's machines, also referred to as Quantum Annealers, are restricted to Quadratic Unconstrained Binary Optimisation (QUBO) problems. Any deviations from the QUBO form—e.g., when the objective function is non-quadratic or quadratic in a non-linear function of the binary variables—makes the potential benefits of AQCs not directly accessible. At the same time, many computer vision problems re + +![](images/b0c56ab4c8dc7d9d3a2fd41f38a65e0c5f2f2f0853735c7d4fe57189d22c038b.jpg) +(a) Minimise $f(g(x))$ + +![](images/388f5b446bcaa926e3c5fea9ef749ddfb54d484a49a4be5d66f5411564795a60.jpg) +$f$ quadratic in $g(x)$ .. $\checkmark$ +$f$ quadratic in $g^t (x)$ .. $\checkmark$ + +![](images/33ea57dc6c07a2cbaf09a7eca47e4c4ebc2d56c99b51c03d2a72878f2151eca6.jpg) +Minimise $f(g^{t}(x):= g$ +$\langle x^t\rangle +\langle \nabla g(x^t),x - x^t\rangle)$ + +![](images/d5892642eae230fddb6145f9320117cb948c345c65183c2e9abb2ad385b2e7f5.jpg) +$x$ binary: $\checkmark$ , $g$ linear in $x$ : $\times$ +Initial +(b) Rigid point sets registration. + +![](images/709c8775af2b0646617a90a5ee3d89316720ff00c9c37fdc0684ce5f1588f5a2.jpg) +AQC: Not a QUBO !!! +Result + +![](images/346b15731605c7fff983d55a0a7a9a9932728e33895b076d286eb31f05a91736.jpg) +ary: $\checkmark$ $g^{t}$ linear in $x$ : $\checkmark$ +AQC: $\checkmark$ Iteratively solve QUBOs !!! +Reference +(c) Shape matching on FAUST. +Figure 1. (a) Our QuCOOP framework for solving composite and binary-parametrised problems using Adiabatic Quantum Computing (AQC). Some qualitative results are shown for: (b) Point set registration without known correspondences; (c) Mesh alignment problems. Our general approach is competitive with specialised existing quantum and classical methods; it is compatible with quantum annealers and classical simulated annealing solvers. + +quire non-quadratic objectives to obtain accurate solutions. Motivated by the tangible implications for computer vision of the restriction of the current AQC generation to QUBOs, we develop a new AQC-based optimisation method that can handle a certain type of non-quadratic objective functions. + +We consider the general problem + +$$ +\underset {s \in \mathcal {S}} {\arg \min } f (s) \tag {1} +$$ + +of optimising a function $f: S \to \mathbb{R}$ over a feasible set $S \subsetneq \mathbb{R}^n$ . Moreover, we assume $S$ to be parameterizable by elements of a set $\mathcal{X} \subset \mathbb{R}^k$ via a smooth function $g: \mathcal{X} \to S$ allowing to rewrite Problem (1) in a composite form as + +$$ +\underset {x \in \mathcal {X}} {\arg \min } f (g (x)). \tag {2} +$$ + +If $\mathcal{X} = \mathbb{R}^k$ , Problem (2) describes an unconstrained problem and can be solved locally, or even globally (for $f \circ g$ + +convex in $x$ ) using gradient-based methods. If $\mathcal{X}\subsetneq \mathbb{R}^k$ Problem (2) becomes a constrained optimisation problem. If $\mathcal{X}$ is further non-convex, as e.g., the set $\mathbb{B}^k\coloneqq \{0,1\} ^k$ of binary vectors of length $k$ , Problem (2) is generally $\mathcal{NP}$ - hard [52] and, very often, can be solved only approximately. + +Gradient descent [54, 56] is perhaps the most simple algorithm for solving Problem (2) when $\mathcal{X} = \mathbb{R}^k$ . It is an iterative method, where at each iteration $t$ , a local model $f^t$ of $f$ is constructed around the current iterate $x^t$ to identify a descent direction for updating $x^t$ . For constrained problems, one typically turns to iterative projection or additional penalty terms to ensure that all iterates $x^t$ remain feasible. Examples of such techniques include: Gradient projection methods [7] that project the iterates of gradient descent onto $\mathcal{X}$ ; interior-point methods [60] that minimize an augmented objective function where a so-called barrier function penalizes non-feasible iterates; feasible direction methods [59], e.g., Frank-Wolfe [28], that compute a feasible descent direction by solving an easier constrained problem and then update the iterate accordingly. + +One of the strengths of AQC is its natural ability to optimize over discrete binary variables, whereas classical methods often resort to relaxations. To leverage this, we present QuCOOP (Quantum Framework for Composite and Binary-Parametrised OPoptimisation Problems), a general framework to solve (2) on AQCs. We are concerned with the case when $\mathcal{X} = \mathbb{B}^k \coloneqq \{0,1\}^k$ and $f$ is a quadratic function in $g(x)$ . The key idea is to iteratively minimize a 1D cut of $f$ at a current linear Taylor approximation of $g$ : At iteration $t$ , we approximate $f$ through a local model $f^t$ by linearising the inner function $g$ around the current iterate $x^t$ . Since $f$ is quadratic in $g(x)$ and $x$ binary, the resulting sub-objectives are QUBO problems for which modern quantum annealers provide an exciting new way to sample possible low-energy states. As a result, our proposed optimisation does not require descent directions or step sizes in the usual sense as classical methods do, but directly targets a state $x^{t + 1}$ minimising $f^t$ . See Fig. 1-(a) for an overview. + +Applications. Our configuration of Problem (2) is common in computer vision. Applications we are interested in this work include the Quadratic Assignment Problem (QAP, [45]), a reputed $\mathcal{NP}$ -hard problem that aims to optimize a quadratic function over the set of permutation matrices. QAP models many real-life problems such as graph matching [5, 6], travelling salesman [30], facility location [45], or scheduling problems [32], to name just a few. Moreover, we show in further application examples how to solve mesh alignment [6] and rigid point set registration without input correspondences [49] with QuCOOP. See Fig. 1-(b, c) for representative results. + +Contributions. Our primary technical contributions are: + +- QuCOOP, a new general framework for solving composite and binary-parametrised problems on AQCs (Sec. 4); +- An iterative scheme to construct and solve QUBO problems that locally approximate the original, perhaps nonquadratic objective function; +- Applications of QuCOOP to a variety of computer vision problems including QAP, shape alignment and point set registration (Secs. 5 and 6). For correspondence problems, we introduce a binary parametrisation of permutation matrices fitting in the proposed QuCOOP framework. We experimentally validated the algorithm, first with simulated annealing and achieving state-of-the-art results for several considered problems (Secs. 7.1 to 7.3); then on real D-Wave quantum annealers and improving the dimensionality of solvable permutation-related problems compared to previous quantum-compatible approaches (Sec. 7.4). + +# 2. Related Work + +Classical Optimisation Theory. A binary optimisation technique related to ours is the quadratisation of pseudo-Boolean functions [36, 47]. Pseudo-Boolean functions are functions that can be written uniquely as a multi-linear polynomial of binary variables, with QUBOs being a particular types of those with degrees not exceeding two. Quadratisation techniques [12, 47, 63] can be generally used to reduce the degree of higher-order polynomials to two in order to obtain a QUBO form. However, they often require auxiliary variables, which increases the problem size and can be costly for actual AQC devices. In contrast, QuCOOP does not require additional variables. Moreover, it is not restricted to polynomials, but could also be applied to any function as long as it fits in our composite form, see Eq. (6). + +Next, our proposed QuCOOP technique falls into the class of composite optimisation methods [31, 43, 58]. These approaches leverage the composite form of optimisation problem (2) to derive easy-to-solve sub-problems that return better local optima of the original problem. An incomplete list of example applications of composite optimisation problems in computer vision include super-resolution from raw time-of-flight data [31], image and point set registration [50], shape matching [6, 16, 74]. Composite optimisation is classically well studied for continuous problems [22, 31, 43, 58]. This work explores similar techniques for the discrete case, especially to leverage AQC-based optimisation. Hence, in a broad sense, this work improves our understanding of how AQCs can be used for optimising non-quadratic objectives. + +Quantum-enhanced Computer Vision (QeCV). In computer vision, AQCs have been used to solve problems such as matching involving optimising over permutation matrices [5, 6, 9]; object tracking [78] by optimising binary assignments between observations and a set of tracks; or + +clustering [79] by sampling multiple binary assignments of a sample set to models its posterior distribution. Several other approaches [8, 33, 49, 68, 69] were focused on registering point sets. A feature shared by all above-mentioned methods is the construction of QUBO problems with binary solution parametrisation that suit quantum annealers. + +Remark. QeCV methods relying on gate-based quantum computing remain substantially less explored than AQCs [61], and many works in this domain are theoretical, heavily use simulators and are at the intersection with quantum machine learning [18, 35, 44]. One of the reasons is that quantum annealing can be considered the most advanced quantum computing technology nowadays, while fault-tolerant quantum computers that could be useful in computer vision are under development [1]. + +The IQT Approach [49]. The most closely related work to ours is the iterative quantum transformation (IQT) approach of Kuete Meli et al. [49]. IQT iteratively finds rotation matrices $R$ aligning two point sets using AQC. Since rotations can be parametrised by non-redundant parameters $v$ (e.g., a rotation angle in 2D and rotation angle and axis in 3D), the original constrained problem on rotation matrices is cast in Ref. [49] into an unconstrained optimisation problem over rotation parameters. Specifically, IQT iteratively linearizes $R$ around a current rotation parameter as $R(v) = R(v^t) + \langle \nabla R(v^t), v - v^t \rangle + \mathcal{O}(\|v - v^t\|^2)$ and uses an AQC to sample, in each iteration, a binary representation of $v$ minimising a target function quadratic in $R(v)$ . Hence, the IQT approach can be interpreted as a special case of QuCOOP, i.e., a more general optimisation technique relying on AQC as will become apparent from Sec. 4. + +# 3. Background + +As our method is designed for AQC devices, we briefly revise their principles. We also review classical composite optimisation, which QuCOOP builds upon. For a detailed introduction to quantum computing and numerical optimisation, see Ref. [20, 55, 71] and [54, 56], respectively. + +# 3.1. Adiabatic Quantum Computing + +Adiabatic Quantum Computing (AQC) is a model of quantum computation which is polynomially equivalent to the circuit model [2]. Quantum annealers (QAs) are experimental realisations of the AQC paradigm that do not perfectly fulfill the adiabaticity condition [3, 20, 38, 48]. They provide a meta-heuristic for finding globally-optimal solutions to combinatorial optimisation problems relying on the evolution of a quantum-mechanical system driven by quantum fluctuations. Usually they optimize QUBO objectives, i.e., problems of the form + +$$ +\underset {x \in \mathbb {B} ^ {k}} {\arg \min } \quad \langle x, \mathbf {Q} x + \mathbf {c} \rangle , \tag {3} +$$ + +where $\langle \cdot, \cdot \rangle$ is the standard inner product in $\mathbb{R}^k$ , $\mathbf{Q}$ a symmetric matrix, and $\mathbf{c}$ a vector. QUBO problems are $\mathcal{NP}$ -hard in general, and solving them on a QA is of high practical interest. Casting computer vision problems to QUBO forms can be challenging and has become an active research area [6, 9, 79]. While QUBOs can be optimised with classical optimisation techniques such as Simulated Annealing (SA) [41], QA is expected to offer substantial advantages over SA in certain cases [20, 21]. + +In QA, the provided QUBO problem is converted to the corresponding physical Ising Hamiltonian $\mathbf{H}_p$ . The mapping is such that the ground state of $\mathbf{H}_p$ , i.e. the spin configuration of the physical system achieving the minimal energy value, encodes the solution of the QUBO. To obtain the ground state of $\mathbf{H}_p$ , the system evolves according to a time-dependent Hamiltonian $\mathbf{H}(t)$ changing from the initial Hamiltonian $\mathbf{H}_i$ (with a known ground state) to $\mathbf{H}_p$ , e.g. in the way that $\mathbf{H}(t) = (1 - \frac{t}{T})\mathbf{H}_i + t\mathbf{H}_p$ for $t \in [0,T]$ . If the system transitions according to the adiabatic theorem of quantum mechanics [11, 37, 39] it stays always in a ground state. One of the conditions is a slow-enough transition, e.g. a one that is inversely proportional to the squared minimum (over all instantaneous $t$ ) spectral gap of $\mathbf{H}$ . In practice, modern experimental realisations of AQCs are non-adiabatic and return ground states with probabilities $\ll 1.0$ . To increase the probability of finding the ground state at least once, annealing is repeated multiple times. + +# 3.2. Composite Optimisation + +Iterative methods [54, 56] solve Problem (2) by repeatedly minimising a local model $f^t$ built upon the actual iterate $x^t$ : + +$$ +x ^ {t + 1} := \underset {x \in \mathcal {X}} {\arg \min } f ^ {t} (x), \tag {4} +$$ + +where the local model $f^t$ should have some nice properties such as convexity or separability making it easier to solve. + +In composite optimisation, also known as 'prox-linear' or 'prox-descent' [22, 31, 43, 58], the idea is to exploit the underlying composite nature of the objective function in Problem (2) to derive a local model that, still being easier to solve, approximates the original landscape more faithfully. Two approaches to achieve this are to either approximate the outer function $f$ [31], or linearize the inner function $g$ [22, 43, 58]. In the later case, the local model reads + +$$ +f ^ {t} (x) := f \left(g \left(x ^ {t}\right) + \left\langle \nabla g \left(x ^ {t}\right), x - x ^ {t} \right\rangle\right) + \frac {1}{2 \alpha^ {t}} \| x - x ^ {t} \| _ {2} ^ {2}, \tag {5} +$$ + +with $\alpha^t$ being the step size that prevents $x^{t + 1}$ to deviate too much from $x^t$ , point around which the approximation is more reliable. It is shown in Ref. [58] that for a convex and coercive $f$ and under the Kurdyka-Lojasiewicz property, the iterates $(x^{t})_{t = 1}^{\infty}$ for the model Eq. (5) converge + +to a critical point, i.e. a minimizer of $f$ . We build on this later approximation, i.e. the linearisation of the inner function $g$ , to derive QUBOs for AQC, as we consider that the outer function $f$ is quadratic in $g(x)$ . + +# 4. The Proposed QuCOOP Iteration + +This section describes our general QuCOOP framework, followed by its applications in Sec. 5 and Sec. 6. Proofs of all Lemmas are given in Appendix A. + +QuCOOP is an optimisation algorithm for composite optimisation problems of the form (2), where $f$ is quadratic in $g(x)$ , that iteratively uses AQC. The function $g: \mathbb{R}^k \to \mathbb{R}^n$ is a smooth function such that $S = \operatorname{Im}_g(\mathbb{B}^k) := \{g(x): x \in \mathbb{B}^k\}$ , hence, $g$ parametrizes the feasible domain $S \subsetneq \mathbb{R}^n$ of the original Problem (1) by elements of the set $\mathcal{X} := \mathbb{B}^k$ . For convenience, we write Problem (1) as + +$$ +f (g (x)) = \langle g (x), \mathbf {Q} g (x) + \mathbf {c} \rangle , \tag {6} +$$ + +for a given matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ and a vector $\mathbf{c} \in \mathbb{R}^n$ . + +Note that for Problem (1), we are only interested in values of $g$ on $\mathbb{B}^k$ . However, from a theoretical point of view, our algorithm involves a Taylor approximation of $g$ , requiring $g$ to be smooth as described above. Such a $g$ is far from being unique. Moreover, in addition to $S = \operatorname{Im}_g(\mathbb{B}^k)$ , the gradient of $g$ can take any value by design. Thus, from a practical point of view, this function $g$ should model a "reasonable" or "natural" smooth parametrisation of $S$ . + +A high-level description of the algorithm is provided in Algorithm 1. Next, we analyse its different steps. + +# Algorithm 1: QuCOOP Iteration + +Initialize $x^0$ and repeat for $t = 0,1,2,\ldots$ + +$$ +\begin{array}{l} g ^ {t} (x) := g \left(x ^ {t}\right) + \left\langle \nabla g \left(x ^ {t}\right), x - x ^ {t} \right\rangle (7) \\ x ^ {t + 1} \leftarrow \underset {x \in \mathbb {B} ^ {k}} {\arg \min } \left\{f ^ {t} (x) := f \left(g ^ {t} (x)\right) \right\} (8) \\ \begin{array}{l l} \text {s . t .} & g ^ {t} (x) \in \mathcal {S} \end{array} \\ \end{array} +$$ + +Return $g(x^{t + 1})$ . + +The first step is the familiar choice of the starting point $x^0$ . This can be a vector based on prior knowledge, the result of a previous optimisation, or any random point. As will be discussed later in Lemma 1, QuCOOP converges globally, but not necessarily to the global optimum. Hence, different $x^0$ can lead to different results. + +In a subsequent loop, at each iteration $t$ , the inner function $g$ is linearised around the current iterate $x^t$ using first-order Taylor expansion, Eq. (7), and the next iterate $x^{t + 1}$ is computed by solving the minimisation Problem (8). Evaluated on the hyperplane $g^{t}(x)$ , $f$ results in a + +$k$ -dimensional quadratic function $f^t$ in variable $x$ . In cases where the parametrisation $g^t(x)$ differs substantially from the parametrisation $g(x)$ , to guarantee a monotone decrease of the objective values, it might also be necessary to include a step $x^{t+1} = g^{-1}(g^t(\tilde{x}^{t+1}))$ , with $\tilde{x}$ being the output of Problem (8). + +Fig. 1 provides a visual intuition of the constructed local model $f^t$ . Next, we ensure the compatibility of Problem (8) with quantum annealers (see Sec. 3.1) through a QUBO formulation. + +The Unconstrained Part of Problem (8). The objective function of the minimisation in Problem (8) is already in an AQC-compatible form. At iteration $t$ , we solve the QUBO + +$$ +\underset {x \in \mathcal {X}} {\arg \min } \quad \left\langle x, \mathbf {Q} ^ {t} x + \mathbf {c} ^ {t} \right\rangle , \text {w i t h} \tag {9} +$$ + +$$ +\mathbf {Q} ^ {t} := \nabla g \left(x ^ {t}\right) \mathbf {Q} \nabla g \left(x ^ {t}\right) ^ {\top}, \tag {10} +$$ + +$$ +\mathbf {c} ^ {t} := \nabla g (x ^ {t}) \left(\mathbf {c} + 2 \mathbf {Q} \left(g (x ^ {t}) - \nabla g (x ^ {t}) ^ {\top} x ^ {t}\right)\right). \tag {11} +$$ + +This is because the local model $f^t$ now becomes quadratic in the binary variable $x$ . Details on the derivation of this QUBO problem can be found in Appendix B. + +Meeting the Constraint of Problem (8). In classical optimisation when $\mathcal{X}$ is convex, cf. Eq. (5), the damping term factored to the step size ensures that $g(x)$ or $x$ remains close to $g(x^t)$ or $x^t$ . This is reminiscent of trust-region methods requiring that the local model $f^t$ trustfully approximates $f$ , which happens in a close neighborhood of $x^t$ . + +In our case, $\mathcal{X}$ is discrete, but the quantum annealer can essentially navigate the complete $\mathcal{X}$ domain, allowing us to explore solutions beyond the trust region. At the same time, as required in Problem (8), we have to guarantee that $g^{t}(x)\in S$ ; or, more generally, to replace it with a nearby feasible point with the objective value not much worse than the linearised estimate $f(g^{t}(x))$ . As the whole QuCOOP iteration should be carried out by AQC, ensuring this feasibility amounts to designing a penalty term in the form of a quadratic function in $g^{t}(x)$ . Depending on the form of $S$ , this may, or may not, be easy computationally. The yet resulting objective function is a standard QUBO problem that can run on AQC. We refer to Secs. 5 and 6 for exemplary penalty functions on two computer vision problems, namely graph or shape matching and point set registration. + +Convergence Analysis. While QuCOOP does not guarantee global convergence, it, at least, monotonically decreases the objective function values as stated next: + +Lemma 1. The series $(f(g(x^{t})))_{t\in \mathbb{N}}$ generated by Algorithm 1 with reparametrisation, or without and under assumptions found in Appendix A, monotonically decreases. + +# 5. Graph Matching and QAP with QuCOOP + +This section shows an application of QuCOOP to graph matching and quadratic assignment problems (QAP). + +A general graph matching problem of size $n \in \mathbb{N}$ can be written in matrix form as + +$$ +\underset {\mathbf {P} \in \Pi_ {n}} {\arg \min } \| \mathbf {A P} - \mathbf {P B} \| _ {F} ^ {2}, \tag {12} +$$ + +where $\mathbf{A}$ and $\mathbf{B}$ are given $n\times n$ symmetric matrices and $\Pi_{n}$ is the set of all $n\times n$ permutation matrices [16]. Equivalently, by assuming the constraint $\mathbf{P}\in \Pi_n$ to be always held and ignoring resulting constant terms, Eq. (12) becomes + +$$ +\underset {\mathbf {P} \in \Pi_ {n}} {\arg \min } - \left\langle \mathbf {A P}, \mathbf {P B} \right\rangle_ {F}. \tag {13} +$$ + +The Quadratic Assignment Problem (QAP) aims to maximize (13). To apply QuCOOP to (13), we need to parametrisse the permutation matrix $\mathbf{P}$ using binary variables: + +Lemma 2. Let $((a,b), a,b = 1,\dots,n, a < b)$ , with cardinality $k := n(n - 1)/2$ , be the tuple of all 2-cycles permuting $a$ and $b$ , and $\mathbf{T}_i$ the matrix representation of the $i$ -th cycle. Any permutation matrix can be parametrised with a length- $k$ binary vector $x := (x_1, \ldots, x_k)$ via the function + +$$ +\mathbf {P}: \mathbb {B} ^ {k} \to \Pi_ {n} +$$ + +$$ +x \mapsto \mathbf {P} (x) := \prod_ {i = 1} ^ {k} \mathbf {P} _ {i} \left(x _ {i}\right), \quad \mathbf {P} _ {i} \left(x _ {i}\right) := \mathbf {T} _ {i} ^ {x _ {i}}, \tag {14} +$$ + +where $\mathbf{T}_i^{x_i}$ is $\mathbf{T}_i$ if $x_{i} = 1$ and the identity $\mathbf{I}_{n\times n}$ otherwise. + +Next, we construct out of $\mathbf{P}$ from Eq. (14) a smooth function $g$ to be used in QuCOOP. A natural choice is to design, for each $\mathbf{P}_i$ from Eq. (14), a smooth function defined through $\mathbf{P}_i(x_i) = x_i(\mathbf{T}_i - \mathbf{I}_n) + \mathbf{I}_n$ for $x_i\in \mathbb{R}$ which makes $\mathbf{P}_i$ and thus $\mathbf{P}$ differentiable with respect to $x_{i}$ and thus $x$ . Now letting $g(x)\coloneqq \mathbf{p}(x)\coloneqq \operatorname {vec}(\mathbf{P}(x))$ be the vector formed by the rows of $\mathbf{P}(x)$ , we propose to solve Problem (13) using Algorithm 1 by solving at each iteration $t$ the sub-problem + +$$ +\underset {x \in \mathcal {X}} {\arg \min } \left\langle g ^ {t} (x), \mathbf {Q} g ^ {t} (x) \right\rangle , \quad \mathbf {Q} := \alpha \mathbf {I} _ {n \times n} - \mathbf {A} \otimes \mathbf {B}, \tag {15} +$$ + +where $g^{t}(x) = \mathbf{p}^{t}(x) = \mathbf{p}(x^{t}) + \langle \nabla \mathbf{p}(x^{t}), x - x^{t} \rangle$ . The term $\alpha \mathbf{I}_{n \times n}$ is, for some $\alpha \in \mathbb{R}_+$ , the penalty added to enforce $\mathbf{p}^t(x) \in \Pi_n$ as required by QuCOOP. In the next paragraph, we justify why our penalty term effectively penalizes non-feasible solutions. Finally, the optimisation follows Algorithm 1 with $x \in \mathcal{X} = \mathbb{B}^k$ . + +On the Penalty Term of the Permutation Constraint. We next show why minimising $\alpha \| \mathbf{p}^t (x)\| _2^2$ effectively constrains the result of the minimisation step in (15) to lie in the set $\Pi_{n}$ of permutation matrices. At iteration $t$ , we have + +$$ +\mathbf {p} ^ {t} (x) = \mathbf {p} \left(x ^ {t}\right) + \left\langle \nabla \mathbf {p} \left(x ^ {t}\right), x - x ^ {t} \right\rangle , \tag {16} +$$ + +in which each row of $\nabla \mathbf{p}(x^t)$ , that is, each partial derivative of $\mathbf{p}$ (cf. Eq. (42) in the supplement), contains exactly two 1 and two $-1$ entries. A following nice property of QuCOOP is that its iterates $\mathbf{P}^t(x)$ partially satisfy the permutation matrix constraint in the sense that their rows and columns sum up to ones, as stated in Lemma 3. + +Lemma 3. All the iterates $\mathbf{P}^t (x)$ computed by Algorithm 1 for $\mathbf{P}(x)$ from Eq. (14) fulfill $\mathbf{P}^t (x)\in X,\forall x\in \mathbb{B}^k$ , where + +$$ +X := \left\{\mathbf {M} \in \mathbb {Z} ^ {n \times n} \Bigg | \sum_ {i = 1} ^ {n} \mathbf {M} _ {i j} = \sum_ {j = 1} ^ {n} \mathbf {M} _ {i j} = 1, \forall i j \right\}. \tag {17} +$$ + +As a consequence of Lemma 3, $n \leq \| \mathbf{p}^t(x) \|_2^2$ holds so that minimising $\| \mathbf{p}^t(x) \|_2^2$ enforces $\mathbf{P}^t(x) \in \Pi_n$ as desired. + +# 6. Point Set Registration with QuCOOP + +We next apply QuCOOP to point set registration. Given a reference set $\mathbf{X} := (x_i)_{i=1}^n \in \mathbb{R}^{d \times n}$ and a template set $\mathbf{Y} := (y_i)_{i=1}^n \in \mathbb{R}^{d \times n}$ , our goal is to determine the best rotation $\mathbf{R} \in \mathrm{SO}(d)$ and the best permutation $\mathbf{P} \in \Pi_n$ that jointly transform the template set and find correspondences with the reference set. Concretely, we aim to solve + +$$ +\underset {\mathbf {R} \in \operatorname {S O} (d), \mathbf {P} \in \Pi} {\arg \min } \| \mathbf {X P} - \mathbf {R Y} \| _ {F} ^ {2}. \tag {18} +$$ + +By assuming the constraints $\mathbf{R} \in \mathrm{SO}(d)$ and $\mathbf{P} \in \Pi_n$ to be always fulfilled and discarding resulting constant terms, we retrieve the problem formulation: + +$$ +\underset {\mathbf {R} \in \mathrm {S O} (d), \mathbf {P} \in \Pi} {\arg \min } - \left\langle \mathbf {X P}, \mathbf {R Y} \right\rangle_ {F}. \tag {19} +$$ + +As required by Algorithm 1, we need to binary-parametrisse $\mathbf{R}$ and $\mathbf{P}$ . For $\mathbf{P}$ , we use the parametrisation from Lemma 2, again with a total of $k_{p} \coloneqq n(n - 1)/2$ binary parameters. For $\mathbf{R}$ , we follow Ref. [33, 49] and write $\mathbf{R}$ using the exponential mapping from the orthogonal Lie algebra to its group, as a function $\mathbf{R}(y) = \exp(\mathbf{M}(y))$ , where $\mathbf{M}$ is a skew-symmetric matrix depending on the rotation parameter $y \in \mathbb{R}^k$ , with $k_{r} \coloneqq d(d - 1)/2$ . + +By flattening the optimisation variables $\mathbf{R}(y)$ and $\mathbf{P}(x)$ as $\mathbf{r}(y) := \operatorname{vec}(\mathbf{R}(y))$ and $\mathbf{p}(x) := \operatorname{vec}(\mathbf{P}(x))$ our optimisation sub-problem in the QuCOOP iteration $t$ becomes + +$$ +\underset {(x, y) \in \mathcal {X}} {\arg \min } \quad \left\langle g ^ {t} (x, y), \mathbf {Q} g ^ {t} (x, y) \right\rangle , \tag {20} +$$ + +$$ +\mathbf {Q} := \left( \begin{array}{c c} \alpha \mathbf {I} _ {n \times n} & - \frac {1}{2} \mathbf {X} \otimes \mathbf {Y} \\ - \frac {1}{2} (\mathbf {X} \otimes \mathbf {Y}) ^ {\top} & \beta \mathbf {I} _ {d \times d} \end{array} \right), \tag {21} +$$ + +where $g^{t}(x,y) \coloneqq (\mathbf{p}^{t}(x),\mathbf{r}^{t}(y))$ with the linearisation $\mathbf{p}^t (x) = \mathbf{p}(x^t) + \langle \nabla \mathbf{p}(x^t),x - x^t\rangle$ for the permutation and $\mathbf{r}^t (y) = \mathbf{r}(y^t) + \langle \nabla \mathbf{r}(y^t),y - y^t\rangle$ for the rotation. The term $\alpha \mathbf{I}_{n\times n}$ ensures that the iterate $\mathbf{P}^t (x)$ is a valid permutation matrix, and $\beta \mathbf{I}_{d\times d}$ that $\mathbf{R}^t (y)$ approaches an orthonormal matrix. The optimisation now follows Alg. 1 in which the permutation variable $x$ lies in $\mathbb{B}^k$ , and, as in Ref. [49], we binarize the rotation variable $y$ by considering its flexible $m$ -bits discretisation over a tunable interval, leading to $y\in \mathbb{B}^{m\cdot k}$ . In total, $(x,y)$ is a binary vector in $\mathbb{B}^{k + m\cdot k}$ . + +# 7. Experimental Evaluation + +We perform numerical experiments on QAP, shape matching and point set registration problems. Secs. 7.1 to 7.3 report results of our method when optimised using Simulated Annealing (SA) on classical hardware, and Sec. 7.4 reports results of the same experiments using real D-Wave Quantum Annealer (QA). Details about the used datasets and benchmark methods are discussed in the corresponding sections. SA, along with the preparation of couplings and biases of QuCOOP for the quantum annealer, is carried out on a conventional computer (AMD Ryzen 95900X 12-Core Processor CPU with 128GB RAM). + +Penalty Factors. Similar to many other AQC methods dealing with constrained problems [5, 9, 46], our approach is not exempt from the choice of the penalty factors $\alpha$ in (15), and $\alpha$ and $\beta$ in (21). The penalty factors should be large enough to enforce the constraint while not significantly worsening the dynamic range of the resulting problem Hamiltonian, which otherwise could lead to incorrect solutions of the QUBO problem on the quantum annealer [51]. In our experiments, we set the penalty factors for QAP and point set registration by grid search on smaller problems, which is a widely used approach in the field [9, 27]. In the following, $\alpha$ is set for QAPs to the lowest eigenvalue for $\mathbf{A} \otimes \mathbf{B}$ ; for shape matching problems, $\alpha$ is ten times the lowest eigenvalue of $\mathbf{A} \otimes \mathbf{B}$ ; and in point set registration, $\alpha$ equals $\|\mathbf{X}\|_F^2$ and $\beta$ equals $0.1 \cdot \|\mathbf{Y}\|_F^2$ . + +# 7.1. Quadratic Assignment Problems (QAP) + +To benchmark our method on QAP, we consider the Fast Approximate Quadratic programming for graph matching (FAQ) [75] and the 2-OPT method [19] as classical competitors, and Q-Match [6] as an AQC-compatible competitor. Implementations for FAQ and 2-OPT are provided within Python's Scipy-library, and our method as well as Q-Match are optimised using the SA implementation provided by D-Wave. Q-Match's source code is publicly available [4]. A technical comparison between QuCOOP and Q-Match can be found in Appendix C. + +We report results on the QAPLIB dataset [15] for all instances with problem size $n \leq 50$ , 72 in total. Details + +![](images/005cd46a6d293e8bdf5bc59898c63729f5961938724e6f34b9ca1a3ca0b74205.jpg) +Figure 2. Benchmark results on QAPLIB [15]. We plot the percentage energy error for all considered problem instances (note the means over all instances reported in the legend) and provide their runtimes. Our method clearly outperforms its competitors. + +on those problem instances, along with calculated objective values, are provided in the supplement, Tab. III. Fig. 2 shows the relative errors of the computed objective values w.r.t. optimal ones. Overall, our method consistently outperforms both classical and quantum competitors and has the smallest confidence intervals. Our method and Q-Match exhibit higher runtimes compared to FAQ and 2-Opt for almost all $n$ . This can be explained by the fact that Q-Match solves smaller problems but requires a lot of iterations ( $\approx 800$ for $n = 50$ ), while QuCOOP solves larger problems in much fewer iterations ( $\approx 5$ for $n = 50$ ). + +# 7.2. Shape Matching + +We match pairs $(\mathcal{U},\mathcal{V})$ of reduced meshes from the FAUST dataset [10], with 502 vertices each following Seelbach Benkner et al. [6]. We follow Ref. [6] in several further design choices. Due to the high problem dimensionality, we break down each problem into carefully selected sub-problems solved iteratively. An initial registration based on descriptor similarities is first calculated using linear assignment. Subsequently, in each iteration and for each vertex $u\in \mathcal{U}$ , we compute the contribution $\sum_{v\in \mathcal{V}}\mathbf{Q}_{u\cdot n + \mathbf{P}u,v\cdot n + \mathbf{P}v}$ to the objective function, where $\mathbf{P}$ is the current solution. The $n = 40$ vertices with the highest mismatch scores on both meshes are selected as sub-meshes and registered using either our QuCOOP or Q-Match [6] to enhance registration. We repeat until the set of worst vertices converges. + +The evaluation metric is the common Princeton benchmark protocol [40] which calculates for each $u \in \mathcal{U}$ the geodesic distance between the computed and the optimal vertex assignment of $u$ , normalised by the diameter of $\mathcal{V}$ . We report cumulative geodesic errors, i.e. the percentage of assignments with error bellow incremental thresholds. + +Fig. 3 displays some qualitative registration results and Fig. 4 presents the function value decrease over the iter- + +![](images/8ca7948b8d6571bc9b24aea8313d1074cb247c21dc044c30932545892b8c1f2e.jpg) +Figure 3. Registration results on FAUST [10]. The proposed approach performs at least as well as Q-Match [6]; see circled areas. + +![](images/e116b9b7e45d9bc1d46054bb9a85306951c31e411edc21bb7bdec470b2502c1d.jpg) +Figure 5. Registration results on 2D and 3D point sets with different $n$ . Grey lines show correspondences between reference (olive) and template (blue) points. With up to a few correspondence errors, our method performs well on both isomorphic (left to vertical line) and non-isomorphic shapes (right to vertical line). CPD performs better on isomorphic shapes than on non-isomorphic shapes. + +![](images/b50a9efd78c3d5cb0b52b28193e3a55be5f09145424c3a7f6392164e85e0b795.jpg) +Figure 4. Energy decrease and geodesic errors, averaged on ten instances of FAUST [10] in each pose category. The mean geodesic error for both methods is given in the legend of the plot. The proposed method performs slightly better than Q-Match [6]. + +ations as well as the cumulative geodesic errors. Failure cases are discussed in Appendix E. Our general QuCOOP framework clearly matches the accuracy of the previous specialised Q-Match method. It reduces the mean geodesic error by about 0.01, as it can achieve better results on the sub-problems (see Appendix C). This selection of worst vertices, however, also worsens the performance of both methods, preventing them from matching the results of recent classical state-of-the-art methods [64, 65, 80]. + +# 7.3. Point Set Registration + +We perform experiments on 2D and 3D point set registration. In 2D, points were picked on fish images, and in 3D they were generated from geometrical curves. The number of points varies from $n = 20$ to $n = 40$ . We benchmark QuCOOP against the classical rigid CPD algorithm [53] implemented within the pycpd package [29]. Quantum com + +![](images/d5e7c17ab26db552ab91e7a94299376af64f587dfcb52b700e0a428d7a11de52.jpg) + +![](images/8a5f519f7e51049e13af6f1e7dfa914ad1c6fa36138e16fdd5ed4861a2c5a449.jpg) + +![](images/e86a73e4d4f1a93603f15b0849a0b94b3bd3f34287e8d7168195fb278556e10a.jpg) +Figure 6. Varying rotation angle in the point sets registration experiment. Both CPD and our method show difficulties to register the points for a rotation angle exceeding $90^{\circ}$ in 2D and $45^{\circ}$ in 3D. + +petitor methods that would have been IQT [49] and QA [33] cannot handle registration without correspondences. + +Fig. 5 shows our registration results. Left to the vertical line in the figure are point sets that are isomorphic up to the rotation and permutation, Right are cases where, additionally, the sets are non-isomorphic and/or have different number of points. In the later case, we zero-pad the set with the lowest cardinality to match the other. We use $k_{r} = 10$ variables for the rotation parameter and perform 15 iterations on each problem instance. We see that QuCOOP's computed correspondences are overall correct, so that a reasonable transformation of the template set can still be found. CPD shows difficulties in registering non-isomorphic sets. + +In Fig. 6, we show registration performances, averaged over ten random problem instances of size $n = 10$ , for both methods, while varying the rotation angle. The larger the rotation angle, the harder the registration for both methods. + +![](images/e342bb5bb4106eecf85ab78726254c10d7d83d429cfc1f9e8197c79071bf751b.jpg) +Figure 7. D-Wave results for 5 randomly generated QAP instances for $n = 3, 5, 7, 9, 12, 15$ . Left are returned energy function values, 0 being the best. Right is the validness $|n - \| \mathbf{P} \|_F^2|$ of returned matrices, 0 indicating a valid permutation matrix. Up to $n \approx 12$ , D-Wave finds valid permutation matrices, and often optimal ones. + +# 7.4. Experiments on D-Wave Machines + +We now execute QuCOOP on a real quantum device, D-Wave Advantage 6.4 accessed through the Leap API [23-25]. Advantage has $>5000$ physical qubits connected in the Pegasus topology. However, due to the connectivity pattern of the physical qubits which induces chains in the problem embedding, it is estimated that it can solve problems of about 180 fully connected logical variables, limiting our experiments to problems of sizes $n \approx 15$ ; see also Appendix G. + +QAP. On D-Wave, we solve 5 randomly generated QAP instances for $n = 3, 5, 7, 9, 12, 15$ . The entries of matrix A are $\mathbf{A}_{ij} = \| x_i - x_j\|_2$ for standard and normally distributed $\{x_i \in \mathbb{R}^2\}_{i=1}^n$ , and B equals $\mathbf{P}^\top \mathbf{A}\mathbf{P}$ such that, according to Eq. (12), the optimal function value is 0. Each iteration of the algorithm is executed with the default annealing time of $20\mu s$ and 50 sample reads. We investigate, whether the last computed matrices (i.e. $\mathbf{P} = \mathbf{P}^t(x^{t+1})$ ) are valid permutation matrices² and plot their function values. We compare against the SA implementation and Q-Match (with QA). + +Our results are reported in Fig. 7. Up to $n \approx 12$ , QuCOOP QA finds valid permutation matrices, but returns higher objective values compared to QuCOOP SA and Q-Match QA. As $n$ becomes large, QuCOOP QA tends to compute non-valid matrices. QuCOOP QA took about $5 \times$ less runtime than Q-Match QA on one problem instance, including overheads such as minor embedding and access. Compared to previous works [5, 77] which reasonably—i.e. by returning valid permutation matrices—solved only problems of size $n = 3,4$ on D-Wave machines, we consider QuCOOP as an improvement of the state-of-the-art. + +Point Set Registration. We perform point set registration on D-Wave for five randomly generated problem instances for $n = 3,5,7,9,12,15$ in each set. The results are reported in Fig. 8. Qualitative results can be found in Appendix F. We see that QuCOOP can register the points without correspondences up to $n = 5$ , improving previous work [49] in which correspondences are known beforehand. + +![](images/943996b037c9b64773c2de143be761d602c5dc230b7b6131c7434987c3514e49.jpg) +Figure 8. D-Wave results for five randomly generated point sets registrations for $n = 3,5,7,9,12,15$ . In line with the QAP experiment, D-Wave successfully registers small problem instances. + +# 8. Discussion and Limitations + +The experiments reveal several features of QuCOOP: First, its ability to handle problems involving permutation problems; second, its versatility and compatibility with continuous problems such as point set registration without correspondences, which previous techniques [6, 33, 49] are not able to address. Moreover, QuCOOP supports optimisation over permutation matrices up to size $n = 12$ using the chosen parametrisation on D-Wave annealers. + +Approximation Accuracy. As for many first-order methods, the linearisation $g^t$ of the inner function $g$ is both the key and the bottleneck of QuCOOP. It may not always provide accurate approximations for highly non-linear $g$ and lead to suboptimal solutions as observed in the tests. + +Scalability and Scaling. The space complexity of our permutation parameterisation scales quadratically with $n$ , making it difficult to solve large problems on D-Wave, as complex embeddings increase the chain break probability. + +# 9. Conclusion + +We have presented QuCOOP, a framework for solving composite, binary-parametrised and possibly non-quadratic problems using AQC. This represents a new class of problems solvable on AQC previously restricted to QUBO forms. QuCOOP solves a sequence of QUBO forms approximating the original objective function, which facilitates the non-intuitive and challenging task of handcrafting QUBOs for the aforementioned problem types. We show that our single framework can effectively be applied to several computer vision problems. Namely, we address QAP and shape matching problems, outperforming the previous specialised quantum-enhanced Q-Match method by $5\%$ on QAP and 0.01 on shape matching. For the first time, an AQC-compatible method for rigid point set registration is shown not to require input correspondences and match the accuracy of the classical CPD algorithm on tested problems. We hope this work inspires future exploration of new methods for other CV problems within the proposed framework. + +# Acknowledgements + +This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 534951134. + +# References + +[1] Rajeev Acharya et al. 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(a) Our QuCOOP framework for solving composite and binary-parametrised problems using Adiabatic Quantum Computing (AQC). Some qualitative results are shown for: (b) Point set registration without known correspondences; (c) Mesh alignment problems. Our general approach is competitive with specialised existing quantum and classical methods; it is compatible with quantum annealers and classical simulated annealing solvers." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 494, + 555, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 555, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 555, + 553 + ], + "type": "text", + "content": "quire non-quadratic objectives to obtain accurate solutions. Motivated by the tangible implications for computer vision of the restriction of the current AQC generation to QUBOs, we develop a new AQC-based optimisation method that can handle a certain type of non-quadratic objective functions." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 326, + 554, + 462, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 554, + 462, + 566 + ], + "spans": [ + { + "bbox": [ + 326, + 554, + 462, + 566 + ], + "type": "text", + "content": "We consider the general problem" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 405, + 574, + 555, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 574, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 405, + 574, + 555, + 594 + ], + "type": "interline_equation", + "content": "\\underset {s \\in \\mathcal {S}} {\\arg \\min } f (s) \\tag {1}", + "image_path": "4a3e34e72e6e36af57b145a5c8ca2d68c7b739f1053ad3edb1716c708b24bb5a.jpg" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "text", + "content": "of optimising a function " + }, + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "inline_equation", + "content": "f: S \\to \\mathbb{R}" + }, + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "text", + "content": " over a feasible set " + }, + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "inline_equation", + "content": "S \\subsetneq \\mathbb{R}^n" + }, + { + "bbox": [ + 313, + 602, + 555, + 651 + ], + "type": "text", + "content": ". 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If " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{X}\\subsetneq \\mathbb{R}^k" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " Problem (2) becomes a constrained optimisation problem. If " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " is further non-convex, as e.g., the set " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathbb{B}^k\\coloneqq \\{0,1\\} ^k" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " of binary vectors of length " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " , Problem (2) is generally " + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{NP}" + }, + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": " - hard [52] and, very often, can be solved only approximately." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": "Gradient descent [54, 56] is perhaps the most simple algorithm for solving Problem (2) when " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\mathbb{R}^k" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": ". It is an iterative method, where at each iteration " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": ", a local model " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": " is constructed around the current iterate " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": " to identify a descent direction for updating " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": ". For constrained problems, one typically turns to iterative projection or additional penalty terms to ensure that all iterates " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": " remain feasible. Examples of such techniques include: Gradient projection methods [7] that project the iterates of gradient descent onto " + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 55, + 133, + 295, + 312 + ], + "type": "text", + "content": "; interior-point methods [60] that minimize an augmented objective function where a so-called barrier function penalizes non-feasible iterates; feasible direction methods [59], e.g., Frank-Wolfe [28], that compute a feasible descent direction by solving an easier constrained problem and then update the iterate accordingly." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": "One of the strengths of AQC is its natural ability to optimize over discrete binary variables, whereas classical methods often resort to relaxations. To leverage this, we present QuCOOP (Quantum Framework for Composite and Binary-Parametrised OPoptimisation Problems), a general framework to solve (2) on AQCs. We are concerned with the case when " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\mathbb{B}^k \\coloneqq \\{0,1\\}^k" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " is a quadratic function in " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": ". The key idea is to iteratively minimize a 1D cut of " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " at a current linear Taylor approximation of " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": ": At iteration " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": ", we approximate " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " through a local model " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " by linearising the inner function " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " around the current iterate " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " is quadratic in " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " binary, the resulting sub-objectives are QUBO problems for which modern quantum annealers provide an exciting new way to sample possible low-energy states. As a result, our proposed optimisation does not require descent directions or step sizes in the usual sense as classical methods do, but directly targets a state " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "x^{t + 1}" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": " minimising " + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 55, + 313, + 295, + 529 + ], + "type": "text", + "content": ". See Fig. 1-(a) for an overview." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 543, + 295, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 543, + 295, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 543, + 295, + 686 + ], + "type": "text", + "content": "Applications. Our configuration of Problem (2) is common in computer vision. Applications we are interested in this work include the Quadratic Assignment Problem (QAP, [45]), a reputed " + }, + { + "bbox": [ + 55, + 543, + 295, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{NP}" + }, + { + "bbox": [ + 55, + 543, + 295, + 686 + ], + "type": "text", + "content": "-hard problem that aims to optimize a quadratic function over the set of permutation matrices. QAP models many real-life problems such as graph matching [5, 6], travelling salesman [30], facility location [45], or scheduling problems [32], to name just a few. Moreover, we show in further application examples how to solve mesh alignment [6] and rigid point set registration without input correspondences [49] with QuCOOP. See Fig. 1-(b, c) for representative results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 701, + 291, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 291, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 291, + 713 + ], + "type": "text", + "content": "Contributions. Our primary technical contributions are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 264 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 95 + ], + "type": "text", + "content": "- QuCOOP, a new general framework for solving composite and binary-parametrised problems on AQCs (Sec. 4);" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 96, + 553, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 131 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 131 + ], + "type": "text", + "content": "- An iterative scheme to construct and solve QUBO problems that locally approximate the original, perhaps nonquadratic objective function;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 133, + 555, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 264 + ], + "type": "text", + "content": "- Applications of QuCOOP to a variety of computer vision problems including QAP, shape alignment and point set registration (Secs. 5 and 6). For correspondence problems, we introduce a binary parametrisation of permutation matrices fitting in the proposed QuCOOP framework. We experimentally validated the algorithm, first with simulated annealing and achieving state-of-the-art results for several considered problems (Secs. 7.1 to 7.3); then on real D-Wave quantum annealers and improving the dimensionality of solvable permutation-related problems compared to previous quantum-compatible approaches (Sec. 7.4)." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 273, + 400, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 273, + 400, + 285 + ], + "spans": [ + { + "bbox": [ + 314, + 273, + 400, + 285 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 293, + 553, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 553, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 553, + 460 + ], + "type": "text", + "content": "Classical Optimisation Theory. A binary optimisation technique related to ours is the quadratisation of pseudo-Boolean functions [36, 47]. Pseudo-Boolean functions are functions that can be written uniquely as a multi-linear polynomial of binary variables, with QUBOs being a particular types of those with degrees not exceeding two. Quadratisation techniques [12, 47, 63] can be generally used to reduce the degree of higher-order polynomials to two in order to obtain a QUBO form. However, they often require auxiliary variables, which increases the problem size and can be costly for actual AQC devices. In contrast, QuCOOP does not require additional variables. Moreover, it is not restricted to polynomials, but could also be applied to any function as long as it fits in our composite form, see Eq. (6)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 460, + 553, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 553, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 553, + 639 + ], + "type": "text", + "content": "Next, our proposed QuCOOP technique falls into the class of composite optimisation methods [31, 43, 58]. These approaches leverage the composite form of optimisation problem (2) to derive easy-to-solve sub-problems that return better local optima of the original problem. An incomplete list of example applications of composite optimisation problems in computer vision include super-resolution from raw time-of-flight data [31], image and point set registration [50], shape matching [6, 16, 74]. Composite optimisation is classically well studied for continuous problems [22, 31, 43, 58]. This work explores similar techniques for the discrete case, especially to leverage AQC-based optimisation. Hence, in a broad sense, this work improves our understanding of how AQCs can be used for optimising non-quadratic objectives." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "Quantum-enhanced Computer Vision (QeCV). In computer vision, AQCs have been used to solve problems such as matching involving optimising over permutation matrices [5, 6, 9]; object tracking [78] by optimising binary assignments between observations and a set of tracks; or" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11396" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "type": "text", + "content": "clustering [79] by sampling multiple binary assignments of a sample set to models its posterior distribution. Several other approaches [8, 33, 49, 68, 69] were focused on registering point sets. A feature shared by all above-mentioned methods is the construction of QUBO problems with binary solution parametrisation that suit quantum annealers." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 295, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 251 + ], + "type": "text", + "content": "Remark. QeCV methods relying on gate-based quantum computing remain substantially less explored than AQCs [61], and many works in this domain are theoretical, heavily use simulators and are at the intersection with quantum machine learning [18, 35, 44]. One of the reasons is that quantum annealing can be considered the most advanced quantum computing technology nowadays, while fault-tolerant quantum computers that could be useful in computer vision are under development [1]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "spans": [ + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": "The IQT Approach [49]. The most closely related work to ours is the iterative quantum transformation (IQT) approach of Kuete Meli et al. [49]. IQT iteratively finds rotation matrices " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": " aligning two point sets using AQC. Since rotations can be parametrised by non-redundant parameters " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": " (e.g., a rotation angle in 2D and rotation angle and axis in 3D), the original constrained problem on rotation matrices is cast in Ref. [49] into an unconstrained optimisation problem over rotation parameters. Specifically, IQT iteratively linearizes " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": " around a current rotation parameter as " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "R(v) = R(v^t) + \\langle \\nabla R(v^t), v - v^t \\rangle + \\mathcal{O}(\\|v - v^t\\|^2)" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": " and uses an AQC to sample, in each iteration, a binary representation of " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": " minimising a target function quadratic in " + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "inline_equation", + "content": "R(v)" + }, + { + "bbox": [ + 56, + 266, + 296, + 457 + ], + "type": "text", + "content": ". Hence, the IQT approach can be interpreted as a special case of QuCOOP, i.e., a more general optimisation technique relying on AQC as will become apparent from Sec. 4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 466, + 134, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 466, + 134, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 466, + 134, + 479 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 487, + 295, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 295, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 295, + 547 + ], + "type": "text", + "content": "As our method is designed for AQC devices, we briefly revise their principles. We also review classical composite optimisation, which QuCOOP builds upon. For a detailed introduction to quantum computing and numerical optimisation, see Ref. [20, 55, 71] and [54, 56], respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 552, + 228, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 228, + 565 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 228, + 565 + ], + "type": "text", + "content": "3.1. Adiabatic Quantum Computing" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "type": "text", + "content": "Adiabatic Quantum Computing (AQC) is a model of quantum computation which is polynomially equivalent to the circuit model [2]. Quantum annealers (QAs) are experimental realisations of the AQC paradigm that do not perfectly fulfill the adiabaticity condition [3, 20, 38, 48]. They provide a meta-heuristic for finding globally-optimal solutions to combinatorial optimisation problems relying on the evolution of a quantum-mechanical system driven by quantum fluctuations. Usually they optimize QUBO objectives, i.e., problems of the form" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 124, + 695, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 695, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 124, + 695, + 295, + 715 + ], + "type": "interline_equation", + "content": "\\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\quad \\langle x, \\mathbf {Q} x + \\mathbf {c} \\rangle , \\tag {3}", + "image_path": "5bfeb43cf82e333d2c4681939a64571c40360ef1bb6f0f42593826a152d7855c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "inline_equation", + "content": "\\langle \\cdot, \\cdot \\rangle" + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": " is the standard inner product in " + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^k" + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": " a symmetric matrix, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": " a vector. QUBO problems are " + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "inline_equation", + "content": "\\mathcal{NP}" + }, + { + "bbox": [ + 313, + 72, + 553, + 179 + ], + "type": "text", + "content": "-hard in general, and solving them on a QA is of high practical interest. Casting computer vision problems to QUBO forms can be challenging and has become an active research area [6, 9, 79]. While QUBOs can be optimised with classical optimisation techniques such as Simulated Annealing (SA) [41], QA is expected to offer substantial advantages over SA in certain cases [20, 21]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": "In QA, the provided QUBO problem is converted to the corresponding physical Ising Hamiltonian " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_p" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ". The mapping is such that the ground state of " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_p" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ", i.e. the spin configuration of the physical system achieving the minimal energy value, encodes the solution of the QUBO. To obtain the ground state of " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_p" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ", the system evolves according to a time-dependent Hamiltonian " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}(t)" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": " changing from the initial Hamiltonian " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_i" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": " (with a known ground state) to " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_p" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ", e.g. in the way that " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}(t) = (1 - \\frac{t}{T})\\mathbf{H}_i + t\\mathbf{H}_p" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ". If the system transitions according to the adiabatic theorem of quantum mechanics [11, 37, 39] it stays always in a ground state. One of the conditions is a slow-enough transition, e.g. a one that is inversely proportional to the squared minimum (over all instantaneous " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ") spectral gap of " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ". In practice, modern experimental realisations of AQCs are non-adiabatic and return ground states with probabilities " + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\ll 1.0" + }, + { + "bbox": [ + 313, + 180, + 555, + 396 + ], + "type": "text", + "content": ". To increase the probability of finding the ground state at least once, annealing is repeated multiple times." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 403, + 451, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 451, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 451, + 415 + ], + "type": "text", + "content": "3.2. Composite Optimisation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "text", + "content": "Iterative methods [54, 56] solve Problem (2) by repeatedly minimising a local model " + }, + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "text", + "content": " built upon the actual iterate " + }, + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 420, + 553, + 445 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 379, + 455, + 553, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 455, + 553, + 475 + ], + "spans": [ + { + "bbox": [ + 379, + 455, + 553, + 475 + ], + "type": "interline_equation", + "content": "x ^ {t + 1} := \\underset {x \\in \\mathcal {X}} {\\arg \\min } f ^ {t} (x), \\tag {4}", + "image_path": "dde941cc58f03b229db8cd368d9a0e8859b3c1c9f8cce89da43483e48b71dd27.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 481, + 553, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 553, + 505 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 553, + 505 + ], + "type": "text", + "content": "where the local model " + }, + { + "bbox": [ + 313, + 481, + 553, + 505 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 481, + 553, + 505 + ], + "type": "text", + "content": " should have some nice properties such as convexity or separability making it easier to solve." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "text", + "content": "In composite optimisation, also known as 'prox-linear' or 'prox-descent' [22, 31, 43, 58], the idea is to exploit the underlying composite nature of the objective function in Problem (2) to derive a local model that, still being easier to solve, approximates the original landscape more faithfully. Two approaches to achieve this are to either approximate the outer function " + }, + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "text", + "content": " [31], or linearize the inner function " + }, + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 506, + 554, + 601 + ], + "type": "text", + "content": " [22, 43, 58]. In the later case, the local model reads" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 609, + 553, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 609, + 553, + 643 + ], + "spans": [ + { + "bbox": [ + 315, + 609, + 553, + 643 + ], + "type": "interline_equation", + "content": "f ^ {t} (x) := f \\left(g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle\\right) + \\frac {1}{2 \\alpha^ {t}} \\| x - x ^ {t} \\| _ {2} ^ {2}, \\tag {5}", + "image_path": "058214b8d46150fca9614f113aff2a452d060e9aef5310442ae7282162ac7636.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "inline_equation", + "content": "\\alpha^t" + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": " being the step size that prevents " + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "inline_equation", + "content": "x^{t + 1}" + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": " to deviate too much from " + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": ", point around which the approximation is more reliable. It is shown in Ref. [58] that for a convex and coercive " + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": " and under the Kurdyka-Lojasiewicz property, the iterates " + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "inline_equation", + "content": "(x^{t})_{t = 1}^{\\infty}" + }, + { + "bbox": [ + 313, + 653, + 553, + 714 + ], + "type": "text", + "content": " for the model Eq. (5) converge" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11397" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": "to a critical point, i.e. a minimizer of " + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": ". We build on this later approximation, i.e. the linearisation of the inner function " + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": ", to derive QUBOs for AQC, as we consider that the outer function " + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": " is quadratic in " + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 131, + 244, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 131, + 244, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 131, + 244, + 144 + ], + "type": "text", + "content": "4. The Proposed QuCOOP Iteration" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 151, + 296, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 151, + 296, + 186 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 296, + 186 + ], + "type": "text", + "content": "This section describes our general QuCOOP framework, followed by its applications in Sec. 5 and Sec. 6. Proofs of all Lemmas are given in Appendix A." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": "QuCOOP is an optimisation algorithm for composite optimisation problems of the form (2), where " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": " is quadratic in " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": ", that iteratively uses AQC. The function " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "g: \\mathbb{R}^k \\to \\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": " is a smooth function such that " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "S = \\operatorname{Im}_g(\\mathbb{B}^k) := \\{g(x): x \\in \\mathbb{B}^k\\}" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": ", hence, " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": " parametrizes the feasible domain " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "S \\subsetneq \\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": " of the original Problem (1) by elements of the set " + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{X} := \\mathbb{B}^k" + }, + { + "bbox": [ + 55, + 187, + 296, + 281 + ], + "type": "text", + "content": ". For convenience, we write Problem (1) as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 292, + 296, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 292, + 296, + 306 + ], + "spans": [ + { + "bbox": [ + 111, + 292, + 296, + 306 + ], + "type": "interline_equation", + "content": "f (g (x)) = \\langle g (x), \\mathbf {Q} g (x) + \\mathbf {c} \\rangle , \\tag {6}", + "image_path": "543e5c6db147550278bbac12f4fc95ae4ce696014a8c7da8c1778568e44e9ba1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "text", + "content": "for a given matrix " + }, + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "text", + "content": " and a vector " + }, + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 314, + 263, + 326 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": "Note that for Problem (1), we are only interested in values of " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "\\mathbb{B}^k" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": ". However, from a theoretical point of view, our algorithm involves a Taylor approximation of " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": ", requiring " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": " to be smooth as described above. Such a " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": " is far from being unique. Moreover, in addition to " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "S = \\operatorname{Im}_g(\\mathbb{B}^k)" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": ", the gradient of " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": " can take any value by design. Thus, from a practical point of view, this function " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": " should model a \"reasonable\" or \"natural\" smooth parametrisation of " + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 326, + 296, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 422, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 446 + ], + "type": "text", + "content": "A high-level description of the algorithm is provided in Algorithm 1. Next, we analyse its different steps." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 456, + 211, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 456, + 211, + 468 + ], + "spans": [ + { + "bbox": [ + 66, + 456, + 211, + 468 + ], + "type": "text", + "content": "Algorithm 1: QuCOOP Iteration" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "spans": [ + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "type": "text", + "content": "Initialize " + }, + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "type": "inline_equation", + "content": "x^0" + }, + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "type": "text", + "content": " and repeat for " + }, + { + "bbox": [ + 66, + 475, + 235, + 488 + ], + "type": "inline_equation", + "content": "t = 0,1,2,\\ldots" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 496, + 285, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 496, + 285, + 550 + ], + "spans": [ + { + "bbox": [ + 93, + 496, + 285, + 550 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} g ^ {t} (x) := g \\left(x ^ {t}\\right) + \\left\\langle \\nabla g \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle (7) \\\\ x ^ {t + 1} \\leftarrow \\underset {x \\in \\mathbb {B} ^ {k}} {\\arg \\min } \\left\\{f ^ {t} (x) := f \\left(g ^ {t} (x)\\right) \\right\\} (8) \\\\ \\begin{array}{l l} \\text {s . t .} & g ^ {t} (x) \\in \\mathcal {S} \\end{array} \\\\ \\end{array}", + "image_path": "b9b0d5f067d9a975d245edc4dd7b64c51cc954522c0cccee62ac1057fba3a12d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 559, + 135, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 559, + 135, + 571 + ], + "spans": [ + { + "bbox": [ + 69, + 559, + 135, + 571 + ], + "type": "text", + "content": "Return " + }, + { + "bbox": [ + 69, + 559, + 135, + 571 + ], + "type": "inline_equation", + "content": "g(x^{t + 1})" + }, + { + "bbox": [ + 69, + 559, + 135, + 571 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": "The first step is the familiar choice of the starting point " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "x^0" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": ". This can be a vector based on prior knowledge, the result of a previous optimisation, or any random point. As will be discussed later in Lemma 1, QuCOOP converges globally, but not necessarily to the global optimum. Hence, different " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "x^0" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " can lead to different results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "In a subsequent loop, at each iteration " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": ", the inner function " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " is linearised around the current iterate " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " using first-order Taylor expansion, Eq. (7), and the next iterate " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "x^{t + 1}" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " is computed by solving the minimisation Problem (8). Evaluated on the hyperplane " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "g^{t}(x)" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " results in a" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": "-dimensional quadratic function " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": " in variable " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": ". In cases where the parametrisation " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "g^t(x)" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": " differs substantially from the parametrisation " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": ", to guarantee a monotone decrease of the objective values, it might also be necessary to include a step " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "x^{t+1} = g^{-1}(g^t(\\tilde{x}^{t+1}))" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 313, + 72, + 554, + 143 + ], + "type": "text", + "content": " being the output of Problem (8)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 144, + 554, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 554, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 554, + 192 + ], + "type": "text", + "content": "Fig. 1 provides a visual intuition of the constructed local model " + }, + { + "bbox": [ + 313, + 144, + 554, + 192 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 144, + 554, + 192 + ], + "type": "text", + "content": ". Next, we ensure the compatibility of Problem (8) with quantum annealers (see Sec. 3.1) through a QUBO formulation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 210, + 554, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 554, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 554, + 247 + ], + "type": "text", + "content": "The Unconstrained Part of Problem (8). The objective function of the minimisation in Problem (8) is already in an AQC-compatible form. At iteration " + }, + { + "bbox": [ + 313, + 210, + 554, + 247 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 210, + 554, + 247 + ], + "type": "text", + "content": ", we solve the QUBO" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 367, + 255, + 554, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 255, + 554, + 277 + ], + "spans": [ + { + "bbox": [ + 367, + 255, + 554, + 277 + ], + "type": "interline_equation", + "content": "\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle x, \\mathbf {Q} ^ {t} x + \\mathbf {c} ^ {t} \\right\\rangle , \\text {w i t h} \\tag {9}", + "image_path": "3824411dc20fa30abbfde6249b3ff9f554ea675e8568ca7783221039ec2b105a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 323, + 300, + 554, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 300, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 323, + 300, + 554, + 316 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} ^ {t} := \\nabla g \\left(x ^ {t}\\right) \\mathbf {Q} \\nabla g \\left(x ^ {t}\\right) ^ {\\top}, \\tag {10}", + "image_path": "b36f1c68e3a00a48f5e32002816da46a5fa7de6d2d5566d56aada3e5c0576d96.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 324, + 318, + 554, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 318, + 554, + 345 + ], + "spans": [ + { + "bbox": [ + 324, + 318, + 554, + 345 + ], + "type": "interline_equation", + "content": "\\mathbf {c} ^ {t} := \\nabla g (x ^ {t}) \\left(\\mathbf {c} + 2 \\mathbf {Q} \\left(g (x ^ {t}) - \\nabla g (x ^ {t}) ^ {\\top} x ^ {t}\\right)\\right). \\tag {11}", + "image_path": "7949ced2597ea7f5911efffb0927978a26afdc4db39625e72279a3263fb202a8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "text", + "content": "This is because the local model " + }, + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "text", + "content": " now becomes quadratic in the binary variable " + }, + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 354, + 554, + 392 + ], + "type": "text", + "content": ". Details on the derivation of this QUBO problem can be found in Appendix B." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": "Meeting the Constraint of Problem (8). In classical optimisation when " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": " is convex, cf. Eq. (5), the damping term factored to the step size ensures that " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": " remains close to " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "g(x^t)" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": ". This is reminiscent of trust-region methods requiring that the local model " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "f^t" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": " trustfully approximates " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": ", which happens in a close neighborhood of " + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": "In our case, " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": " is discrete, but the quantum annealer can essentially navigate the complete " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": " domain, allowing us to explore solutions beyond the trust region. At the same time, as required in Problem (8), we have to guarantee that " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "g^{t}(x)\\in S" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": "; or, more generally, to replace it with a nearby feasible point with the objective value not much worse than the linearised estimate " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "f(g^{t}(x))" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": ". As the whole QuCOOP iteration should be carried out by AQC, ensuring this feasibility amounts to designing a penalty term in the form of a quadratic function in " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "g^{t}(x)" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": ". Depending on the form of " + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 480, + 554, + 661 + ], + "type": "text", + "content": ", this may, or may not, be easy computationally. The yet resulting objective function is a standard QUBO problem that can run on AQC. We refer to Secs. 5 and 6 for exemplary penalty functions on two computer vision problems, namely graph or shape matching and point set registration." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Convergence Analysis. While QuCOOP does not guarantee global convergence, it, at least, monotonically decreases the objective function values as stated next:" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11398" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": "Lemma 1. The series " + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "inline_equation", + "content": "(f(g(x^{t})))_{t\\in \\mathbb{N}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": " generated by Algorithm 1 with reparametrisation, or without and under assumptions found in Appendix A, monotonically decreases." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 118, + 288, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 118, + 288, + 132 + ], + "spans": [ + { + "bbox": [ + 55, + 118, + 288, + 132 + ], + "type": "text", + "content": "5. Graph Matching and QAP with QuCOOP" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 138, + 295, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 138, + 295, + 162 + ], + "spans": [ + { + "bbox": [ + 55, + 138, + 295, + 162 + ], + "type": "text", + "content": "This section shows an application of QuCOOP to graph matching and quadratic assignment problems (QAP)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 162, + 296, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 296, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 296, + 185 + ], + "type": "text", + "content": "A general graph matching problem of size " + }, + { + "bbox": [ + 55, + 162, + 296, + 185 + ], + "type": "inline_equation", + "content": "n \\in \\mathbb{N}" + }, + { + "bbox": [ + 55, + 162, + 296, + 185 + ], + "type": "text", + "content": " can be written in matrix form as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 119, + 191, + 295, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 191, + 295, + 213 + ], + "spans": [ + { + "bbox": [ + 119, + 191, + 295, + 213 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } \\| \\mathbf {A P} - \\mathbf {P B} \\| _ {F} ^ {2}, \\tag {12}", + "image_path": "9381a5a671682d128f7a880bbf4cb1f09d8e584beb28164c79302e4c2b4e138a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " are given " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "n\\times n" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " symmetric matrices and " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\Pi_{n}" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " is the set of all " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "n\\times n" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " permutation matrices [16]. Equivalently, by assuming the constraint " + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{P}\\in \\Pi_n" + }, + { + "bbox": [ + 55, + 218, + 296, + 266 + ], + "type": "text", + "content": " to be always held and ignoring resulting constant terms, Eq. (12) becomes" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 272, + 295, + 292 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 272, + 295, + 292 + ], + "spans": [ + { + "bbox": [ + 118, + 272, + 295, + 292 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {P} \\in \\Pi_ {n}} {\\arg \\min } - \\left\\langle \\mathbf {A P}, \\mathbf {P B} \\right\\rangle_ {F}. \\tag {13}", + "image_path": "388177dff0d241152d434c0624d6e6e44a20bd4a81f5e6b25fed074341b5dc79.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 297, + 296, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 296, + 344 + ], + "type": "text", + "content": "The Quadratic Assignment Problem (QAP) aims to maximize (13). To apply QuCOOP to (13), we need to parametrisse the permutation matrix " + }, + { + "bbox": [ + 55, + 297, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 297, + 296, + 344 + ], + "type": "text", + "content": " using binary variables:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": "Lemma 2. Let " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "((a,b), a,b = 1,\\dots,n, a < b)" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": ", with cardinality " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "k := n(n - 1)/2" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": ", be the tuple of all 2-cycles permuting " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": " the matrix representation of the " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": "-th cycle. Any permutation matrix can be parametrised with a length-" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": " binary vector " + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "inline_equation", + "content": "x := (x_1, \\ldots, x_k)" + }, + { + "bbox": [ + 55, + 351, + 296, + 411 + ], + "type": "text", + "content": " via the function" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 65, + 428, + 124, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 428, + 124, + 442 + ], + "spans": [ + { + "bbox": [ + 65, + 428, + 124, + 442 + ], + "type": "interline_equation", + "content": "\\mathbf {P}: \\mathbb {B} ^ {k} \\to \\Pi_ {n}", + "image_path": "a0516ab29b2a01eddb75d1c63da1de4d59cba5c62bae19e421d549f2678ec1d8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 86, + 445, + 295, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 445, + 295, + 478 + ], + "spans": [ + { + "bbox": [ + 86, + 445, + 295, + 478 + ], + "type": "interline_equation", + "content": "x \\mapsto \\mathbf {P} (x) := \\prod_ {i = 1} ^ {k} \\mathbf {P} _ {i} \\left(x _ {i}\\right), \\quad \\mathbf {P} _ {i} \\left(x _ {i}\\right) := \\mathbf {T} _ {i} ^ {x _ {i}}, \\tag {14}", + "image_path": "80b0706f6fc15afabdfcc7a0862c2785d0b70e565dad01328ece9279efebc600.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i^{x_i}" + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "inline_equation", + "content": "x_{i} = 1" + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "content": " and the identity " + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{n\\times n}" + }, + { + "bbox": [ + 55, + 483, + 293, + 497 + ], + "type": "text", + "content": " otherwise." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": "Next, we construct out of " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " from Eq. (14) a smooth function " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " to be used in QuCOOP. A natural choice is to design, for each " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " from Eq. (14), a smooth function defined through " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i(x_i) = x_i(\\mathbf{T}_i - \\mathbf{I}_n) + \\mathbf{I}_n" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "x_i\\in \\mathbb{R}" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " which makes " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " and thus " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " differentiable with respect to " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " and thus " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": ". Now letting " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "g(x)\\coloneqq \\mathbf{p}(x)\\coloneqq \\operatorname {vec}(\\mathbf{P}(x))" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " be the vector formed by the rows of " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{P}(x)" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": ", we propose to solve Problem (13) using Algorithm 1 by solving at each iteration " + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 501, + 296, + 609 + ], + "type": "text", + "content": " the sub-problem" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 60, + 614, + 295, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 614, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 60, + 614, + 295, + 635 + ], + "type": "interline_equation", + "content": "\\underset {x \\in \\mathcal {X}} {\\arg \\min } \\left\\langle g ^ {t} (x), \\mathbf {Q} g ^ {t} (x) \\right\\rangle , \\quad \\mathbf {Q} := \\alpha \\mathbf {I} _ {n \\times n} - \\mathbf {A} \\otimes \\mathbf {B}, \\tag {15}", + "image_path": "8d4df95f219146fda6b4cf6549fe27841c48430da3ff1e571a84097938108657.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "inline_equation", + "content": "g^{t}(x) = \\mathbf{p}^{t}(x) = \\mathbf{p}(x^{t}) + \\langle \\nabla \\mathbf{p}(x^{t}), x - x^{t} \\rangle" + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": ". The term " + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\alpha \\mathbf{I}_{n \\times n}" + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": " is, for some " + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": ", the penalty added to enforce " + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^t(x) \\in \\Pi_n" + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": " as required by QuCOOP. In the next paragraph, we justify why our penalty term effectively penalizes non-feasible solutions. Finally, the optimisation follows Algorithm 1 with " + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X} = \\mathbb{B}^k" + }, + { + "bbox": [ + 55, + 640, + 296, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": "On the Penalty Term of the Permutation Constraint. We next show why minimising " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "\\alpha \\| \\mathbf{p}^t (x)\\| _2^2" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": " effectively constrains the result of the minimisation step in (15) to lie in the set " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "\\Pi_{n}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": " of permutation matrices. At iteration " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 358, + 125, + 553, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 125, + 553, + 140 + ], + "spans": [ + { + "bbox": [ + 358, + 125, + 553, + 140 + ], + "type": "interline_equation", + "content": "\\mathbf {p} ^ {t} (x) = \\mathbf {p} \\left(x ^ {t}\\right) + \\left\\langle \\nabla \\mathbf {p} \\left(x ^ {t}\\right), x - x ^ {t} \\right\\rangle , \\tag {16}", + "image_path": "12cbefaf5ca56d881ad2e4a22823a76405355147d86514d75fe11fb5255e8a78.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "content": "in which each row of " + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\nabla \\mathbf{p}(x^t)" + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "content": ", that is, each partial derivative of " + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "content": " (cf. Eq. (42) in the supplement), contains exactly two 1 and two " + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "content": " entries. A following nice property of QuCOOP is that its iterates " + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t(x)" + }, + { + "bbox": [ + 313, + 144, + 555, + 216 + ], + "type": "text", + "content": " partially satisfy the permutation matrix constraint in the sense that their rows and columns sum up to ones, as stated in Lemma 3." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "text", + "content": "Lemma 3. All the iterates " + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t (x)" + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "text", + "content": " computed by Algorithm 1 for " + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\mathbf{P}(x)" + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "text", + "content": " from Eq. (14) fulfill " + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t (x)\\in X,\\forall x\\in \\mathbb{B}^k" + }, + { + "bbox": [ + 313, + 221, + 554, + 247 + ], + "type": "text", + "content": " , where" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 324, + 251, + 553, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 251, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 324, + 251, + 553, + 281 + ], + "type": "interline_equation", + "content": "X := \\left\\{\\mathbf {M} \\in \\mathbb {Z} ^ {n \\times n} \\Bigg | \\sum_ {i = 1} ^ {n} \\mathbf {M} _ {i j} = \\sum_ {j = 1} ^ {n} \\mathbf {M} _ {i j} = 1, \\forall i j \\right\\}. \\tag {17}", + "image_path": "d5dbca160c1266776a25404164e3b917a45414f365a16f0fddb932fdc25499e9.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "text", + "content": "As a consequence of Lemma 3, " + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "inline_equation", + "content": "n \\leq \\| \\mathbf{p}^t(x) \\|_2^2" + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "text", + "content": " holds so that minimising " + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{p}^t(x) \\|_2^2" + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "text", + "content": " enforces " + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t(x) \\in \\Pi_n" + }, + { + "bbox": [ + 313, + 285, + 554, + 311 + ], + "type": "text", + "content": " as desired." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 319, + 522, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 522, + 333 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 522, + 333 + ], + "type": "text", + "content": "6. Point Set Registration with QuCOOP" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "content": "We next apply QuCOOP to point set registration. Given a reference set " + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{X} := (x_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}" + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "content": " and a template set " + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} := (y_i)_{i=1}^n \\in \\mathbb{R}^{d \\times n}" + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "content": ", our goal is to determine the best rotation " + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in \\mathrm{SO}(d)" + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "content": " and the best permutation " + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\Pi_n" + }, + { + "bbox": [ + 313, + 339, + 554, + 411 + ], + "type": "text", + "content": " that jointly transform the template set and find correspondences with the reference set. Concretely, we aim to solve" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 365, + 416, + 553, + 438 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 416, + 553, + 438 + ], + "spans": [ + { + "bbox": [ + 365, + 416, + 553, + 438 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {R} \\in \\operatorname {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } \\| \\mathbf {X P} - \\mathbf {R Y} \\| _ {F} ^ {2}. \\tag {18}", + "image_path": "39ff268bb3e9cd7de61fa68e3f7a9f6f6186358119651d2cadf209b68bef0648.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "text", + "content": "By assuming the constraints " + }, + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in \\mathrm{SO}(d)" + }, + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\Pi_n" + }, + { + "bbox": [ + 313, + 444, + 554, + 479 + ], + "type": "text", + "content": " to be always fulfilled and discarding resulting constant terms, we retrieve the problem formulation:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 365, + 486, + 553, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 486, + 553, + 507 + ], + "spans": [ + { + "bbox": [ + 365, + 486, + 553, + 507 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {R} \\in \\mathrm {S O} (d), \\mathbf {P} \\in \\Pi} {\\arg \\min } - \\left\\langle \\mathbf {X P}, \\mathbf {R Y} \\right\\rangle_ {F}. \\tag {19}", + "image_path": "75618c88be84162f65f1cfabc6bc00cbe9e48e21ac7875e26c28a20cdac2c266.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": "As required by Algorithm 1, we need to binary-parametrisse " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": ", we use the parametrisation from Lemma 2, again with a total of " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "k_{p} \\coloneqq n(n - 1)/2" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": " binary parameters. For " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": ", we follow Ref. [33, 49] and write " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": " using the exponential mapping from the orthogonal Lie algebra to its group, as a function " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{R}(y) = \\exp(\\mathbf{M}(y))" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": " is a skew-symmetric matrix depending on the rotation parameter " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^k" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "inline_equation", + "content": "k_{r} \\coloneqq d(d - 1)/2" + }, + { + "bbox": [ + 313, + 512, + 554, + 607 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": "By flattening the optimisation variables " + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{R}(y)" + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{P}(x)" + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(y) := \\operatorname{vec}(\\mathbf{R}(y))" + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{p}(x) := \\operatorname{vec}(\\mathbf{P}(x))" + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": " our optimisation sub-problem in the QuCOOP iteration " + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 608, + 554, + 643 + ], + "type": "text", + "content": " becomes" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 378, + 661, + 553, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 661, + 553, + 682 + ], + "spans": [ + { + "bbox": [ + 378, + 661, + 553, + 682 + ], + "type": "interline_equation", + "content": "\\underset {(x, y) \\in \\mathcal {X}} {\\arg \\min } \\quad \\left\\langle g ^ {t} (x, y), \\mathbf {Q} g ^ {t} (x, y) \\right\\rangle , \\tag {20}", + "image_path": "381b7966f5f2253f92dead6f3422d4b8bd6e1ec226b06819ef914dfb78611f44.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 354, + 685, + 553, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 685, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 354, + 685, + 553, + 712 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} := \\left( \\begin{array}{c c} \\alpha \\mathbf {I} _ {n \\times n} & - \\frac {1}{2} \\mathbf {X} \\otimes \\mathbf {Y} \\\\ - \\frac {1}{2} (\\mathbf {X} \\otimes \\mathbf {Y}) ^ {\\top} & \\beta \\mathbf {I} _ {d \\times d} \\end{array} \\right), \\tag {21}", + "image_path": "a980b1a66bcffd293ca3e0764c8619edf981713d066519425c9fbcc4402ee459.jpg" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11399" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "g^{t}(x,y) \\coloneqq (\\mathbf{p}^{t}(x),\\mathbf{r}^{t}(y))" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " with the linearisation " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^t (x) = \\mathbf{p}(x^t) + \\langle \\nabla \\mathbf{p}(x^t),x - x^t\\rangle" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " for the permutation and " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{r}^t (y) = \\mathbf{r}(y^t) + \\langle \\nabla \\mathbf{r}(y^t),y - y^t\\rangle" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " for the rotation. The term " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\alpha \\mathbf{I}_{n\\times n}" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " ensures that the iterate " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t (x)" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " is a valid permutation matrix, and " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\beta \\mathbf{I}_{d\\times d}" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " that " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^t (y)" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " approaches an orthonormal matrix. The optimisation now follows Alg. 1 in which the permutation variable " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " lies in " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbb{B}^k" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": ", and, as in Ref. [49], we binarize the rotation variable " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " by considering its flexible " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": "-bits discretisation over a tunable interval, leading to " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "y\\in \\mathbb{B}^{m\\cdot k}" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": ". In total, " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": " is a binary vector in " + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "inline_equation", + "content": "\\mathbb{B}^{k + m\\cdot k}" + }, + { + "bbox": [ + 55, + 72, + 296, + 193 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 201, + 200, + 215 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 201, + 200, + 215 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 200, + 215 + ], + "type": "text", + "content": "7. Experimental Evaluation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 221, + 296, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 296, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 296, + 353 + ], + "type": "text", + "content": "We perform numerical experiments on QAP, shape matching and point set registration problems. Secs. 7.1 to 7.3 report results of our method when optimised using Simulated Annealing (SA) on classical hardware, and Sec. 7.4 reports results of the same experiments using real D-Wave Quantum Annealer (QA). Details about the used datasets and benchmark methods are discussed in the corresponding sections. SA, along with the preparation of couplings and biases of QuCOOP for the quantum annealer, is carried out on a conventional computer (AMD Ryzen 95900X 12-Core Processor CPU with 128GB RAM)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": "Penalty Factors. Similar to many other AQC methods dealing with constrained problems [5, 9, 46], our approach is not exempt from the choice of the penalty factors " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " in (15), and " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " in (21). The penalty factors should be large enough to enforce the constraint while not significantly worsening the dynamic range of the resulting problem Hamiltonian, which otherwise could lead to incorrect solutions of the QUBO problem on the quantum annealer [51]. In our experiments, we set the penalty factors for QAP and point set registration by grid search on smaller problems, which is a widely used approach in the field [9, 27]. In the following, " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " is set for QAPs to the lowest eigenvalue for " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\otimes \\mathbf{B}" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": "; for shape matching problems, " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " is ten times the lowest eigenvalue of " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\otimes \\mathbf{B}" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": "; and in point set registration, " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\|\\mathbf{X}\\|_F^2" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "inline_equation", + "content": "0.1 \\cdot \\|\\mathbf{Y}\\|_F^2" + }, + { + "bbox": [ + 55, + 367, + 296, + 548 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 552, + 264, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 264, + 566 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 264, + 566 + ], + "type": "text", + "content": "7.1. Quadratic Assignment Problems (QAP)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 689 + ], + "type": "text", + "content": "To benchmark our method on QAP, we consider the Fast Approximate Quadratic programming for graph matching (FAQ) [75] and the 2-OPT method [19] as classical competitors, and Q-Match [6] as an AQC-compatible competitor. Implementations for FAQ and 2-OPT are provided within Python's Scipy-library, and our method as well as Q-Match are optimised using the SA implementation provided by D-Wave. Q-Match's source code is publicly available [4]. A technical comparison between QuCOOP and Q-Match can be found in Appendix C." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "We report results on the QAPLIB dataset [15] for all instances with problem size " + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "inline_equation", + "content": "n \\leq 50" + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": ", 72 in total. Details" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 58, + 550, + 201 + ], + "blocks": [ + { + "bbox": [ + 319, + 58, + 550, + 201 + ], + "lines": [ + { + "bbox": [ + 319, + 58, + 550, + 201 + ], + "spans": [ + { + "bbox": [ + 319, + 58, + 550, + 201 + ], + "type": "image", + "image_path": "005cd46a6d293e8bdf5bc59898c63729f5961938724e6f34b9ca1a3ca0b74205.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "lines": [ + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "type": "text", + "content": "Figure 2. Benchmark results on QAPLIB [15]. We plot the percentage energy error for all considered problem instances (note the means over all instances reported in the legend) and provide their runtimes. Our method clearly outperforms its competitors." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": "on those problem instances, along with calculated objective values, are provided in the supplement, Tab. III. Fig. 2 shows the relative errors of the computed objective values w.r.t. optimal ones. Overall, our method consistently outperforms both classical and quantum competitors and has the smallest confidence intervals. Our method and Q-Match exhibit higher runtimes compared to FAQ and 2-Opt for almost all " + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": ". This can be explained by the fact that Q-Match solves smaller problems but requires a lot of iterations (" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\approx 800" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "inline_equation", + "content": "n = 50" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": "), while QuCOOP solves larger problems in much fewer iterations (" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\approx 5" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "inline_equation", + "content": "n = 50" + }, + { + "bbox": [ + 313, + 275, + 555, + 407 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 418, + 414, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 414, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 414, + 430 + ], + "type": "text", + "content": "7.2. Shape Matching" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": "We match pairs " + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "inline_equation", + "content": "(\\mathcal{U},\\mathcal{V})" + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": " of reduced meshes from the FAUST dataset [10], with 502 vertices each following Seelbach Benkner et al. [6]. We follow Ref. [6] in several further design choices. Due to the high problem dimensionality, we break down each problem into carefully selected sub-problems solved iteratively. An initial registration based on descriptor similarities is first calculated using linear assignment. Subsequently, in each iteration and for each vertex " + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "inline_equation", + "content": "u\\in \\mathcal{U}" + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": ", we compute the contribution " + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\sum_{v\\in \\mathcal{V}}\\mathbf{Q}_{u\\cdot n + \\mathbf{P}u,v\\cdot n + \\mathbf{P}v}" + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": " to the objective function, where " + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": " is the current solution. The " + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "inline_equation", + "content": "n = 40" + }, + { + "bbox": [ + 313, + 436, + 555, + 615 + ], + "type": "text", + "content": " vertices with the highest mismatch scores on both meshes are selected as sub-meshes and registered using either our QuCOOP or Q-Match [6] to enhance registration. We repeat until the set of worst vertices converges." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "text", + "content": "The evaluation metric is the common Princeton benchmark protocol [40] which calculates for each " + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "inline_equation", + "content": "u \\in \\mathcal{U}" + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "text", + "content": " the geodesic distance between the computed and the optimal vertex assignment of " + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "text", + "content": ", normalised by the diameter of " + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 616, + 556, + 688 + ], + "type": "text", + "content": ". We report cumulative geodesic errors, i.e. the percentage of assignments with error bellow incremental thresholds." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 689, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 713 + ], + "type": "text", + "content": "Fig. 3 displays some qualitative registration results and Fig. 4 presents the function value decrease over the iter-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11400" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 76, + 294, + 240 + ], + "blocks": [ + { + "bbox": [ + 60, + 76, + 294, + 240 + ], + "lines": [ + { + "bbox": [ + 60, + 76, + 294, + 240 + ], + "spans": [ + { + "bbox": [ + 60, + 76, + 294, + 240 + ], + "type": "image", + "image_path": "8ca7948b8d6571bc9b24aea8313d1074cb247c21dc044c30932545892b8c1f2e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 248, + 296, + 272 + ], + "lines": [ + { + "bbox": [ + 55, + 248, + 296, + 272 + ], + "spans": [ + { + "bbox": [ + 55, + 248, + 296, + 272 + ], + "type": "text", + "content": "Figure 3. Registration results on FAUST [10]. The proposed approach performs at least as well as Q-Match [6]; see circled areas." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 285, + 293, + 357 + ], + "blocks": [ + { + "bbox": [ + 59, + 285, + 293, + 357 + ], + "lines": [ + { + "bbox": [ + 59, + 285, + 293, + 357 + ], + "spans": [ + { + "bbox": [ + 59, + 285, + 293, + 357 + ], + "type": "image", + "image_path": "e116b9b7e45d9bc1d46054bb9a85306951c31e411edc21bb7bdec470b2502c1d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 300, + 555, + 368 + ], + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 368 + ], + "type": "text", + "content": "Figure 5. Registration results on 2D and 3D point sets with different " + }, + { + "bbox": [ + 313, + 300, + 555, + 368 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 300, + 555, + 368 + ], + "type": "text", + "content": ". Grey lines show correspondences between reference (olive) and template (blue) points. With up to a few correspondence errors, our method performs well on both isomorphic (left to vertical line) and non-isomorphic shapes (right to vertical line). CPD performs better on isomorphic shapes than on non-isomorphic shapes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 59, + 361, + 292, + 434 + ], + "blocks": [ + { + "bbox": [ + 59, + 361, + 292, + 434 + ], + "lines": [ + { + "bbox": [ + 59, + 361, + 292, + 434 + ], + "spans": [ + { + "bbox": [ + 59, + 361, + 292, + 434 + ], + "type": "image", + "image_path": "b50a9efd78c3d5cb0b52b28193e3a55be5f09145424c3a7f6392164e85e0b795.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 443, + 295, + 489 + ], + "lines": [ + { + "bbox": [ + 55, + 443, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 295, + 489 + ], + "type": "text", + "content": "Figure 4. Energy decrease and geodesic errors, averaged on ten instances of FAUST [10] in each pose category. The mean geodesic error for both methods is given in the legend of the plot. The proposed method performs slightly better than Q-Match [6]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 508, + 296, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 296, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 296, + 616 + ], + "type": "text", + "content": "ations as well as the cumulative geodesic errors. Failure cases are discussed in Appendix E. Our general QuCOOP framework clearly matches the accuracy of the previous specialised Q-Match method. It reduces the mean geodesic error by about 0.01, as it can achieve better results on the sub-problems (see Appendix C). This selection of worst vertices, however, also worsens the performance of both methods, preventing them from matching the results of recent classical state-of-the-art methods [64, 65, 80]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 624, + 180, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 180, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 180, + 636 + ], + "type": "text", + "content": "7.3. Point Set Registration" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "content": "We perform experiments on 2D and 3D point set registration. In 2D, points were picked on fish images, and in 3D they were generated from geometrical curves. The number of points varies from " + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "inline_equation", + "content": "n = 20" + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "inline_equation", + "content": "n = 40" + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "content": ". We benchmark QuCOOP against the classical rigid CPD algorithm [53] implemented within the pycpd package [29]. Quantum com" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 548, + 178 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 548, + 178 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 548, + 178 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 548, + 178 + ], + "type": "image", + "image_path": "d5e7c17ab26db552ab91e7a94299376af64f587dfcb52b700e0a428d7a11de52.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 182, + 548, + 290 + ], + "blocks": [ + { + "bbox": [ + 317, + 182, + 548, + 290 + ], + "lines": [ + { + "bbox": [ + 317, + 182, + 548, + 290 + ], + "spans": [ + { + "bbox": [ + 317, + 182, + 548, + 290 + ], + "type": "image", + "image_path": "8a5f519f7e51049e13af6f1e7dfa914ad1c6fa36138e16fdd5ed4861a2c5a449.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 380, + 545, + 452 + ], + "blocks": [ + { + "bbox": [ + 318, + 380, + 545, + 452 + ], + "lines": [ + { + "bbox": [ + 318, + 380, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 318, + 380, + 545, + 452 + ], + "type": "image", + "image_path": "e86a73e4d4f1a93603f15b0849a0b94b3bd3f34287e8d7168195fb278556e10a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "lines": [ + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "spans": [ + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "type": "text", + "content": "Figure 6. Varying rotation angle in the point sets registration experiment. Both CPD and our method show difficulties to register the points for a rotation angle exceeding " + }, + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "type": "text", + "content": " in 2D and " + }, + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 313, + 454, + 554, + 487 + ], + "type": "text", + "content": " in 3D." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 509, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 554, + 533 + ], + "type": "text", + "content": "petitor methods that would have been IQT [49] and QA [33] cannot handle registration without correspondences." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 554, + 665 + ], + "type": "text", + "content": "Fig. 5 shows our registration results. Left to the vertical line in the figure are point sets that are isomorphic up to the rotation and permutation, Right are cases where, additionally, the sets are non-isomorphic and/or have different number of points. In the later case, we zero-pad the set with the lowest cardinality to match the other. We use " + }, + { + "bbox": [ + 313, + 533, + 554, + 665 + ], + "type": "inline_equation", + "content": "k_{r} = 10" + }, + { + "bbox": [ + 313, + 533, + 554, + 665 + ], + "type": "text", + "content": " variables for the rotation parameter and perform 15 iterations on each problem instance. We see that QuCOOP's computed correspondences are overall correct, so that a reasonable transformation of the template set can still be found. CPD shows difficulties in registering non-isomorphic sets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "In Fig. 6, we show registration performances, averaged over ten random problem instances of size " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "n = 10" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": ", for both methods, while varying the rotation angle. The larger the rotation angle, the harder the registration for both methods." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11401" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 289, + 141 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 289, + 141 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 289, + 141 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 289, + 141 + ], + "type": "image", + "image_path": "e342bb5bb4106eecf85ab78726254c10d7d83d429cfc1f9e8197c79071bf751b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "text", + "content": "Figure 7. D-Wave results for 5 randomly generated QAP instances for " + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "inline_equation", + "content": "n = 3, 5, 7, 9, 12, 15" + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "text", + "content": ". Left are returned energy function values, 0 being the best. Right is the validness " + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "inline_equation", + "content": "|n - \\| \\mathbf{P} \\|_F^2|" + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "text", + "content": " of returned matrices, 0 indicating a valid permutation matrix. Up to " + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "inline_equation", + "content": "n \\approx 12" + }, + { + "bbox": [ + 55, + 144, + 295, + 199 + ], + "type": "text", + "content": ", D-Wave finds valid permutation matrices, and often optimal ones." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 218, + 240, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 218, + 240, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 240, + 232 + ], + "type": "text", + "content": "7.4. Experiments on D-Wave Machines" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "text", + "content": "We now execute QuCOOP on a real quantum device, D-Wave Advantage 6.4 accessed through the Leap API [23-25]. Advantage has " + }, + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "inline_equation", + "content": ">5000" + }, + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "text", + "content": " physical qubits connected in the Pegasus topology. However, due to the connectivity pattern of the physical qubits which induces chains in the problem embedding, it is estimated that it can solve problems of about 180 fully connected logical variables, limiting our experiments to problems of sizes " + }, + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "inline_equation", + "content": "n \\approx 15" + }, + { + "bbox": [ + 55, + 236, + 296, + 332 + ], + "type": "text", + "content": "; see also Appendix G." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": "QAP. On D-Wave, we solve 5 randomly generated QAP instances for " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "n = 3, 5, 7, 9, 12, 15" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": ". The entries of matrix A are " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ij} = \\| x_i - x_j\\|_2" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": " for standard and normally distributed " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\{x_i \\in \\mathbb{R}^2\\}_{i=1}^n" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": ", and B equals " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^\\top \\mathbf{A}\\mathbf{P}" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": " such that, according to Eq. (12), the optimal function value is 0. Each iteration of the algorithm is executed with the default annealing time of " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "20\\mu s" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": " and 50 sample reads. We investigate, whether the last computed matrices (i.e. " + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\mathbf{P}^t(x^{t+1})" + }, + { + "bbox": [ + 55, + 346, + 296, + 466 + ], + "type": "text", + "content": ") are valid permutation matrices² and plot their function values. We compare against the SA implementation and Q-Match (with QA)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "content": "Our results are reported in Fig. 7. Up to " + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "n \\approx 12" + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "content": ", QuCOOP QA finds valid permutation matrices, but returns higher objective values compared to QuCOOP SA and Q-Match QA. As " + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "content": " becomes large, QuCOOP QA tends to compute non-valid matrices. QuCOOP QA took about " + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "content": " less runtime than Q-Match QA on one problem instance, including overheads such as minor embedding and access. Compared to previous works [5, 77] which reasonably—i.e. by returning valid permutation matrices—solved only problems of size " + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "n = 3,4" + }, + { + "bbox": [ + 55, + 466, + 295, + 597 + ], + "type": "text", + "content": " on D-Wave machines, we consider QuCOOP as an improvement of the state-of-the-art." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "text", + "content": "Point Set Registration. We perform point set registration on D-Wave for five randomly generated problem instances for " + }, + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "inline_equation", + "content": "n = 3,5,7,9,12,15" + }, + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "text", + "content": " in each set. The results are reported in Fig. 8. Qualitative results can be found in Appendix F. We see that QuCOOP can register the points without correspondences up to " + }, + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "inline_equation", + "content": "n = 5" + }, + { + "bbox": [ + 55, + 612, + 295, + 696 + ], + "type": "text", + "content": ", improving previous work [49] in which correspondences are known beforehand." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 316, + 73, + 547, + 141 + ], + "blocks": [ + { + "bbox": [ + 316, + 73, + 547, + 141 + ], + "lines": [ + { + "bbox": [ + 316, + 73, + 547, + 141 + ], + "spans": [ + { + "bbox": [ + 316, + 73, + 547, + 141 + ], + "type": "image", + "image_path": "943996b037c9b64773c2de143be761d602c5dc230b7b6131c7434987c3514e49.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 144, + 553, + 178 + ], + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 178 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 178 + ], + "type": "text", + "content": "Figure 8. D-Wave results for five randomly generated point sets registrations for " + }, + { + "bbox": [ + 313, + 144, + 553, + 178 + ], + "type": "inline_equation", + "content": "n = 3,5,7,9,12,15" + }, + { + "bbox": [ + 313, + 144, + 553, + 178 + ], + "type": "text", + "content": ". In line with the QAP experiment, D-Wave successfully registers small problem instances." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 200, + 468, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 200, + 468, + 213 + ], + "spans": [ + { + "bbox": [ + 313, + 200, + 468, + 213 + ], + "type": "text", + "content": "8. Discussion and Limitations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": "The experiments reveal several features of QuCOOP: First, its ability to handle problems involving permutation problems; second, its versatility and compatibility with continuous problems such as point set registration without correspondences, which previous techniques [6, 33, 49] are not able to address. Moreover, QuCOOP supports optimisation over permutation matrices up to size " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "n = 12" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " using the chosen parametrisation on D-Wave annealers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "text", + "content": "Approximation Accuracy. As for many first-order methods, the linearisation " + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "inline_equation", + "content": "g^t" + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "text", + "content": " of the inner function " + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "text", + "content": " is both the key and the bottleneck of QuCOOP. It may not always provide accurate approximations for highly non-linear " + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 336, + 554, + 396 + ], + "type": "text", + "content": " and lead to suboptimal solutions as observed in the tests." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 415, + 554, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 554, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 554, + 464 + ], + "type": "text", + "content": "Scalability and Scaling. The space complexity of our permutation parameterisation scales quadratically with " + }, + { + "bbox": [ + 313, + 415, + 554, + 464 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 415, + 554, + 464 + ], + "type": "text", + "content": ", making it difficult to solve large problems on D-Wave, as complex embeddings increase the chain break probability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 477, + 388, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 388, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 388, + 489 + ], + "type": "text", + "content": "9. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "We have presented QuCOOP, a framework for solving composite, binary-parametrised and possibly non-quadratic problems using AQC. This represents a new class of problems solvable on AQC previously restricted to QUBO forms. QuCOOP solves a sequence of QUBO forms approximating the original objective function, which facilitates the non-intuitive and challenging task of handcrafting QUBOs for the aforementioned problem types. We show that our single framework can effectively be applied to several computer vision problems. Namely, we address QAP and shape matching problems, outperforming the previous specialised quantum-enhanced Q-Match method by " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " on QAP and 0.01 on shape matching. For the first time, an AQC-compatible method for rigid point set registration is shown not to require input correspondences and match the accuracy of the classical CPD algorithm on tested problems. We hope this work inspires future exploration of new methods for other CV problems within the proposed framework." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t (x^{t + 1})" + }, + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "text", + "content": " may be non-valid, but " + }, + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}(x^{t + 1})" + }, + { + "bbox": [ + 66, + 701, + 294, + 713 + ], + "type": "text", + "content": " is always valid." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11402" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 297, + 125 + ], + "type": "text", + "content": "This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 534951134." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "spans": [ + { + "bbox": [ + 56, + 145, + 115, + 158 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 165, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 61, + 165, + 296, + 186 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 165, + 296, + 186 + ], + "spans": [ + { + "bbox": [ + 61, + 165, + 296, + 186 + ], + "type": "text", + "content": "[1] Rajeev Acharya et al. 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In Computer Vision and Pattern Recognition (CVPR), 2025. 7" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11405" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_content_list.json b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3b4dcf530cc85d6d9c85ae9386c1af006c6187be --- /dev/null +++ b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_content_list.json @@ -0,0 +1,1686 @@ +[ + { + "type": "text", + "text": "Quad-Pixel Image Defocus Deblurring: A New Benchmark and Model", + "text_level": 1, + "bbox": [ + 143, + 130, + 852, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hang Chen $^{1}$ Yin Xie $^{1}$ Xiaoxiu Peng $^{1}$ Lihu Sun $^{1}$ Wenkai Su $^{1}$ Xiaodong Yang $^{2}$ Chengming Liu $^{2}$ $^{1}$ OMNIVISION, Wuhan, China $^{2}$ OMNIVISION, Santa Clara, CA", + "bbox": [ + 109, + 179, + 887, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 251, + 326, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Defocus deblurring is a challenging task due to the spatially varying blur. Recent works have shown impressive results in data-driven approaches using dual-pixel (DP) sensors. Quad-pixel (QP) sensors represent an advanced evolution of DP sensors, providing four distinct sub-aperture views in contrast to only two views offered by DP sensors. However, research on QP-based defocus deblurring is scarce. In this paper, we propose a novel end-to-end learning-based approach for defocus deblurring that leverages QP data. To achieve this, we design a QP defocus and all-in-focus image pair acquisition method and provide a QP Defocus Deblurring (QPDD) dataset containing 4,935 image pairs. We then introduce a Local-gate assisted Mamba Network (LMNet), which includes a two-branch encoder and a Simple Fusion Module (SFM) to fully utilize features of sub-aperture views. In particular, our LMNet incorporates a Local-gate assisted Mamba Block (LAMB) that mitigates local pixel forgetting and channel redundancy within Mamba, and effectively captures global and local dependencies. By extending the defocus deblurring task from a DP-based to a QP-based approach, we demonstrate significant improvements in restoring sharp images. Comprehensive experimental evaluations further indicate that our approach outperforms state-of-the-art methods.", + "bbox": [ + 89, + 282, + 483, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 676, + 220, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Defocus blur occurs in scene regions captured outside the camera's depth of field (DoF) [1-3]. Restoring an all-in-focus image from a defocused image is challenging due to the spatially varying point spread functions (PSFs) [6, 20, 38, 40, 46], which are not only scene depth dependent, but also vary based on intrinsic camera parameters [2].", + "bbox": [ + 89, + 703, + 482, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, researchers have addressed this challenge by developing end-to-end deep neural networks that leverage dual-pixel (DP) data [1-3, 21, 24, 29, 47, 48, 53]. The first DP Defocus Deblurring (DPDD) [1] dataset, captured sequentially with various aperture sizes using a Canon 5D DSLR camera, is widely utilized. Quad-pixel (QP) sensors [28, 39] represent a significant advancement over DP", + "bbox": [ + 89, + 795, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/df0bbb8480e387dca510af644d9edbe112145d763170083d6b6e671eca7bfc0e.jpg", + "image_caption": [ + "Figure 1. Characteristics of DP and QP sensors. The light rays from different parts of the main lens fall on each DP unit or QP unit. A DP unit has two photodiodes under a single microlens, producing two sub-aperture views, while a QP unit has four photodiodes, producing four sub-aperture views. Different views of DP or QP data exhibit different PSFs with directional characteristics, leading to disparity between the sub-aperture views. The disparity $d$ is correlated with the amount of defocus blur $b$ [1, 12]: $d = \\alpha * b \\approx \\alpha \\frac{Lf}{1 - f / D_f} \\left( \\frac{1}{D_f} - \\frac{1}{D} \\right)$ , where $\\alpha$ is a constant of proportionality, $L$ is the diameter of the aperture, $f$ is the focal length, $D_f$ is the focus distance, and $D$ is the depth. DP sensors provide disparity in only a single direction, whereas QP sensors can provide disparity in two directions." + ], + "image_footnote": [], + "bbox": [ + 540, + 251, + 879, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sensors and have gained widespread adoption in smartphones due to their superior Phase Detection Auto Focus (PDAF) performance. As indicated in Fig. 1, by utilizing four photodiodes under each microlens instead of two photodiodes, a QP sensor captures more light signal aspects, enhancing disparity detection [44] accuracy and providing more reliable guidance for defocus deblurring.", + "bbox": [ + 511, + 732, + 906, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, to the best of our knowledge, research on QP-based defocus deblurring is limited, primarily due to the lack of relevant dataset. Most QP sensors on smartphones have a fixed aperture size, making it difficult to adopt the", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5709", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "data acquisition method used in DPDD, which involves adjusting the aperture size. In contrast, we adjust the voice coil motors (VCMs) [17] of the QP sensor to change the focus distance, and acquire defocus and all-in-focus image pairs. However, this process induces a zoom-like effect [17]. To overcome this, we use the Enhanced Correlation Coefficient (ECC) [11] alignment algorithm. Furthermore, we propose an open-source QP defocus deblurring (QPDD) dataset. This dataset primarily includes RAW images that are linear with respect to the scene's physical light [4, 23], and also provides sRGB images for the convenience of researchers.", + "bbox": [ + 89, + 90, + 480, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modern deep learning models, such as CNNs [1-3, 50, 51] and Transformers [18, 22, 42, 52], have continuously improved state-of-the-art (SOTA) performance. CNNs have efficient parallel convolutions but limited receptive fields. In contrast, Transformers can model long-range dependencies but face quadratic computational complexity. Recently, state space models (SSMs) [13, 14, 36], particularly Mamba [13], have emerged as backbones due to their ability to capture long-range dependencies with linear complexity. Nevertheless, Mamba's recursive image sequence processing tends to cause local pixel forgetting, and the abundance of hidden states in the state space equation can lead to channel redundancy [15, 35, 55]. These factors impede the learning of local context, thereby resulting in poor performance when applying Mamba directly.", + "bbox": [ + 89, + 273, + 482, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Considering the multi-subaperture view characteristics of QP data and the critical role of efficient global and local dependencies in the defocus deblurring task, we propose the Local-gate assisted Mamba Network (LMNet) with several key components. Our LMNet employs an encoder-decoder architecture with a two-branch encoder that leverages information from different sub-aperture views, and incorporates a Simple Fusion Module (SFM) for effective feature integration from these two branches. Furthermore, instead of solely employing Mamba, we devise an effective Local-gate assisted Mamba Block (LAMB), which includes a parallel Vision State Space Module (VSSM) and Local Gate Module (LGM). By integrating the features from VSSM and LGM using learnable weights, the LAMB enables a more enhanced capture of global and local dependencies. To demonstrate the effectiveness of our LMNet, we first train it on the DPDD dataset, achieving SOTA performance. We then validate the performance of our QP-based deblurring approach and its advantages over DP-based approaches. In summary, our contributions are as follows:", + "bbox": [ + 89, + 501, + 482, + 801 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A QP defocus deblurring (QPDD) dataset, which consists of 4,935 defocus and all-in-focus image pairs, available in both RAW and sRGB formats.", + "- A novel network LMNet for defocus deblurring, which fully utilizes information from the sub-aperture views of QP/DP images and enables effective capture of global and" + ], + "bbox": [ + 89, + 804, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "local dependencies.", + "bbox": [ + 527, + 90, + 658, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments evaluate our QP-based deblurring approach and its advantages over the DP-based methods.", + "bbox": [ + 511, + 109, + 903, + 138 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 154, + 653, + 169 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Defocus Deblurring", + "text_level": 1, + "bbox": [ + 511, + 179, + 700, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In learning-based defocus deblurring methods, Abdullah et al. [1] are the first to propose DPDNet for addressing defocus deblurring on DP images, and they also release a defocus deblurring dataset, named DPDD, based on the DP camera. Since then, an increasing number of defocus deblurring studies have been conducted based on this dataset. Existing DP-based defocus deblurring methods fall into two main categories: those that directly process DP data pairs and those that rely on disparity information.", + "bbox": [ + 511, + 200, + 903, + 337 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the first category of methods, Abdullah et al. [2] propose the network RDPD with convolutional LSTM units and a synthetic dataset to improve performance. Son et al. [37] propose an effective way to iteratively learn deblur kernels for different feature channels with the shape attention mechanism. Ruan et al. [31] use the DPDD and LFOF datasets and introduce filter dynamic networks. General restoration networks such as MIRNetV2 [49], Restormer [52], GRL [22], and LaKDNet [32] also fit into this category. Moreover, these studies show that two-view inputs outperform single-view inputs in defocus deblurring. For the second category of methods, Liang et al. [24] use the translating disk proposed by Abhijith et al. [30] to estimate a four-layer defocus mask by a four-branch network. Yang et al. [48] estimate defocus disparity only in feature space without explicitly showing a defocus map. Subsequently, Yang et al. [47] propose a new framework that leverages the capabilities of language-image pre-training framework (CLIP) for blur map estimation by designing an image-text format. These methods require additional data or modules to obtain the disparity from DP data to aid in restoring an all-in-focus image.", + "bbox": [ + 511, + 338, + 903, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our LMNet is specifically designed for both DP and QP defocus deblurring tasks. Unlike the above two categories of methods, we introduce a two-branch encoder and a SFM to effectively integrate information from different sub-aperture views.", + "bbox": [ + 511, + 670, + 903, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Visual State Space Models", + "text_level": 1, + "bbox": [ + 511, + 756, + 751, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SSMs [13, 14, 36] have garnered increasing attention from researchers due to their ability to capture long-range dependencies with linear complexity. S4 [14] is the first structured SSM to introduce a diagonal structure and combine it with a diagonal plus low-rank approach. Subsequently, S5 [36] proposes the diagonal SSM approximation and computes recurrently using a parallel scan. Building on these gains, Mamba [13] integrates SSM with the", + "bbox": [ + 511, + 779, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5710", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "MLP block of Transformer and introduces a selection scanning mechanism within SSM to filter out irrelevant information for long-sequence modeling. However, the standard Mamba primarily focuses on unidirectional sequential data and cannot handle image data lacking specific directionality. To tackle this challenge, VMamba [25] and Vision Mamba [55] transform arbitrary visual images into ordered sequences and introduce a multiple scanning module that traverses the image space domain to tackle image classification and segmentation. Nevertheless, these multiple scanning Mamba modules still face certain challenges in low-level vision tasks, such as local pixel forgetting and channel redundancy. To address these issues, MambaIR [15], MMA [8], VmambaIR [35], and CU-Mamba [10] introduce the channel attention (CA) mechanism [54] for local modeling. Although the widely used CA mechanism can explore inter-channel relationships, it lacks explicit consideration of spatially-varying contents. In this context, we design an effective LAMB, featuring parallel VSSM and LGM. Unlike previous works that commonly use the CA mechanism, LGM combines CA and spatial attention (SA) [43] mechanisms through gate computation, thereby effectively enhancing local dependencies.", + "bbox": [ + 89, + 90, + 483, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. QPDD Dataset Collection", + "text_level": 1, + "bbox": [ + 89, + 452, + 328, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "QP sensors have found widespread applications in smartphones [28, 39], and most QP sensors are equipped with fixed aperture size, making it difficult to adopt data acquisition method like DPDD, which involves adjusting the aperture size. In this section, we design an alternative alignment-based approach to generate high-quality defocused and all-in-focus RAW image pairs using a QP sensor.", + "bbox": [ + 89, + 477, + 482, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Nearly all smartphone cameras use VCMs to focus [17]. VCMs control the movement of the camera lens, thereby changing the focus distance. As illustrated in Fig. 2a, we use the QP sensor to capture a static planar scene and control the VCMs in fixed steps to obtain a series of RAW images with varying amounts of blur. Then we employ the Contrast Detection Auto Focus (CDAF) algorithm to select the sharpest image as the in-focus target, and the others are considered as defocus images. Figure 2b demonstrates our QP data post-process pipeline. To reduce the impact of noise while maintaining the correlation between disparity and blur, we apply two-pixel averaging both vertically and horizontally within the same color channel to produce four-view images: left (L), right (R), top (T), and bottom (B). Additionally, we apply adjacent four-pixel averaging to produce a reference center (C) view. However, a noticeable zoom-like effect (a kind of misalignment) [17] arises between the defocus C image $I_{dc}$ and the in-focus C image $I_{ic}$ . Defocus effects violate the brightness constancy assumption of corresponding points or regions [11], thereby posing significant challenges for alignment methods based on fea", + "bbox": [ + 89, + 584, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cb7acc5cbb36e2539e5603f1bf13073fc7e5877a226772a747f65419827db51b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 88, + 898, + 176 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d8946d172ceddc74c624255e7603cb26d36929fb3e9030b658fba9d0d25f1c78.jpg", + "image_caption": [ + "(a) Capture sequence frames.", + "(b) Post-process of frames.", + "Figure 2. QPDD dataset generation pipeline: (a) Capture sequence frames with QP sensor. (b) Post-process of frames, we first adopt pixel average to generate five-view images: left (L), right (R), top (T), bottom (B) and center (C), and then utilize ECC alignment to mitigate the zoom-like effect between $I_{dc}$ and $I_{ic}$ ." + ], + "image_footnote": [], + "bbox": [ + 514, + 191, + 897, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ture point matching and optical flow. To mitigate the zoom-like effect, we introduce similarity-based ECC [11], which is well-suited for aligning planar defocus and in-focus images. Given $I_{dc}$ and $I_{ic}$ as inputs, the aligned in-focus C image $I_{ac}$ can be defined as follows:", + "bbox": [ + 511, + 434, + 906, + 511 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI _ {a c} = \\operatorname {W a r p} \\left(I _ {i c}, E C C \\left(I _ {d c}, I _ {i c}\\right)\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 518, + 906, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ECC algorithm operates on the mean values of the Gb and Gr channels from both $I_{dc}$ and $I_{ic}$ to calculate the affine transformation matrix. This affine transformation matrix is subsequently warped to each color channel of the $I_{ic}$ to obtain a well-aligned, sharp $I_{ac}$ . Our original defocus five-view images and target image $I_{ac}$ have a resolution of $4096 \\times 3072$ pixels. During alignment, we crop the central regions based on specific scenes, resulting in sizes of $2160 \\times 1280$ , $1280 \\times 1792$ , and $1080 \\times 1280$ pixels.", + "bbox": [ + 511, + 545, + 908, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, our dataset comprises 200 indoor scenes and 4,935 pairs. We divide the dataset into 3,735 pairs training, 600 pairs validation, and 600 pairs testing sets. Furthermore, we provide an additional 100 full-resolution images, both indoor and outdoor with multi-depth, to test generalization performance. Additionally, to obtain training data in sRGB format, we perform Image Signal Processing (ISP) on the L, R, T, B, and C views of defocused images, as well as the target images $I_{ac}$ . More information about the QPDD dataset can be found in supplementary material.", + "bbox": [ + 511, + 681, + 908, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 844, + 604, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to present an effective method to achieve high-quality defocus deblurring for both QP and DP data. In this", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5711", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/78ef9b91b7ea380b3bc64f2609ba81f9175a7d87911712e8dd31290809dc6067.jpg", + "image_caption": [ + "Figure 3. The overall network architecture of our LMNet. LMNet consists of a two-branch encoder which is designed to extract deep features from different sub-aperture views. Between the two branches, each level has a SFM (Fig. 4a) to fuse the two-branch features and pass them to the corresponding level in the decoder. To capture effective global and local dependencies in the defocus deblurring task, we propose LAMB (Fig. 4a)." + ], + "image_footnote": [], + "bbox": [ + 112, + 87, + 883, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5a913ad62c060493a8b2f3d733c5e990afa67fae9ae3eec197d9f87f9bd6ee06.jpg", + "image_caption": [ + "(a) LAMB and SFM" + ], + "image_footnote": [], + "bbox": [ + 112, + 343, + 460, + 526 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fd4b480a5dc6a6041aaf384c71360e2dabbb72ef9f7e33d14fb4a9205f91aec6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 545, + 460, + 612 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3281e34f91f390df1b512ff05f69b7b27d7920617e4d10d12062a628e0a53ac5.jpg", + "image_caption": [ + "(b) VSSM", + "(c) LGM", + "Figure 4. Details of the network structure: (a)The structures of LAMB and SFM. (b)The structure of VSSM. (c)The structure of LGM." + ], + "image_footnote": [], + "bbox": [ + 102, + 628, + 464, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "section, we first outline the overall pipeline of our Local-gate assisted Mamba Network (LMNet), and then we dive into its components by explaining: the Simple Fusion Module (SFM), the Local-gate assisted Mamba Block (LAMB), the Vision State Space Module (VSSM), and the Local Gate Module (LGM).", + "bbox": [ + 89, + 810, + 483, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Overall Pipeline", + "text_level": 1, + "bbox": [ + 511, + 345, + 673, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3, LMNet adopts a three-level encoder-decoder architecture with skip connections. Two branches in the encoder are designed to extract deep features from different views. At each level, a SFM is used to fuse the features from the two branches and pass them to the corresponding level in the decoder. The decoder aims to predict the latent all-in-focus image. To be specific, given an input image $I \\in \\mathbb{R}^{H \\times W \\times n}$ of one encoder, LMNet firstly applies a $3 \\times 3$ convolution to extract low-level features $X_0 \\in \\mathbb{R}^{H \\times W \\times M}$ . Here $H$ , $W$ and $n$ are the image height, width and channel number, respectively. $M$ is the number of feature channels. Next, these shallow features $X_0$ pass through a three-level encoder-decoder and are transformed into deep features $X_l \\in \\mathbb{R}^{\\frac{H}{2^{l-1}} \\times \\frac{W}{2^{l-1}} \\times 2^{l-1}M}$ , where $l \\in \\{1,2,3\\}$ indicates stage level. Each level of encoder and decoder is composed of $N$ LAMBs, where $N \\in \\{N_1, N_2, N_3\\}$ . At the third level, following the third SFM, there is a feature enhancement module consisting of $N_4$ LAMBs. For feature downsampling and upsampling, we apply pixel-unshuffle and pixel-shuffle operations [34], respectively. Finally, applying a $3 \\times 3$ convolution and adding skip connection from the input center image $I_C$ , we obtain the sharp image $I_S$ .", + "bbox": [ + 511, + 368, + 906, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For DP data, the left view $I_{L}$ and the right view $I_{R}$ are input into the two-branch encoder with shared parameters separately. For QP data, the left view $I_{L}$ and the right view $I_{R}$ are concatenated, as well as the top view $I_{T}$ and the bottom view $I_{B}$ . Each concatenated pair is then fed separately into the two-branch encoder without shared parameters. The entire pipeline can be expressed as:", + "bbox": [ + 511, + 704, + 908, + 810 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {S} = I _ {C} + L M N e t \\left(I _ {L}, I _ {R}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 821, + 903, + 838 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {S} = I _ {C} + L M N e t \\left(C A T \\left(I _ {L}, I _ {R}\\right), C A T \\left(I _ {T}, I _ {B}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 840, + 903, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $CAT(\\cdot, \\cdot)$ indicates concatenation. Equation (2) and Eq. (3) demonstrate the deblurring processes for DP", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5712", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and QP data, respectively.", + "bbox": [ + 89, + 90, + 264, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We optimize the proposed network LMNet with the following loss function [5, 9]:", + "bbox": [ + 89, + 106, + 482, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sqrt {\\left\\| I _ {S} - I _ {G} \\right\\| ^ {2} + \\epsilon^ {2}} + \\lambda \\| \\mathcal {F} (I _ {S}) - \\mathcal {F} (I _ {G}) \\| _ {1}, \\quad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 111, + 147, + 482, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I_G$ is the ground-truth image, $\\mathcal{F}$ is the Fourier transform. We set $\\epsilon = 10^{-3}$ and $\\lambda = 0.1$ in the experiments.", + "bbox": [ + 89, + 181, + 482, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Simple Fusion Module", + "text_level": 1, + "bbox": [ + 89, + 220, + 300, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The SFM is responsible for fusing the outputs from the two-branch encoder and passing them to the corresponding decoder stage for reconstruction. Depth-wise convolution (DWConv) and point-wise convolution play a crucial role in facilitating interactive information across spatial and channel dimensions [32, 52]. Inspired by these, our SFM also primarily adopts these two types of convolutional layers. As shown in Fig. 4a, given that the outputs of the $l$ -th stage of the two-branch encoder are $X_{1}$ , $X_{2} \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}$ , we first concatenate $X_{1}$ and $X_{2}$ to get $X_{3}$ , and use a $7 \\times 7$ DWConv for effective local features encoding followed by GELU [16] activation function. Then, a residual connection is applied. Finally, a $1 \\times 1$ convolution is employed to aggregate pixel-wise cross-channel context and reduce the channel numbers. The output $Y \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}$ of the SFM can be expressed as:", + "bbox": [ + 89, + 242, + 483, + 489 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {3} = C A T \\left(X _ {1}, X _ {2}\\right), \\\\ Y = \\operatorname {C o n v} _ {1 \\times 1} (G E L U (D W C o n v _ {7 \\times 7} (X _ {3})) + X _ {3}). \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 501, + 480, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Local-gate assisted Mamba Block", + "text_level": 1, + "bbox": [ + 89, + 546, + 383, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the defocus deblurring task, both global and local representations are crucial. The motivation behind the LAMB design is to explore Mamba to capture long-range dependencies with linear complexity and to design a LGM to obtain effective local connectivities, thereby reducing local pixel forgetting and channel redundancy of Mamba. As indicated in Fig. 4a, LAMB mainly follows the novel LayerNorm-Attention-LayerNorm-MLP flow [8, 15, 52]. We replace the Attention with a parallel VSSM and LGM structure. Furthermore, the direct fusion of different level features (global and local) inevitably leads to confused and conflicting representations [45]. To this end, we introduce two learnable scale factors $\\alpha \\in \\mathbb{R}^M$ and $\\beta \\in \\mathbb{R}^M$ to adaptively integrate global and local representations. Given that the input deep feature of LAMB is $X_0 \\in \\mathbb{R}^{H \\times W \\times M}$ , the output $Y \\in \\mathbb{R}^{H \\times W \\times M}$ can be formulated as:", + "bbox": [ + 89, + 568, + 483, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {1} = L N \\left(X _ {0}\\right), \\\\ X _ {2} = X _ {0} + V S S M \\left(X _ {1}\\right) \\cdot \\alpha + L G M \\left(X _ {1}\\right) \\cdot \\beta , \\tag {6} \\\\ Y = X _ {2} + M L P \\left(L N \\left(X _ {2}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 820, + 482, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $LN$ indicates Layer Norm.", + "bbox": [ + 89, + 885, + 315, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Vision State Space Module", + "text_level": 1, + "bbox": [ + 513, + 90, + 756, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The standard Mamba block is designed for the 1-D sequence, which is not suitable for vision tasks requiring spatial-aware understanding [15, 25, 55]. VSSM [55], which uses a ViT-like architecture and incorporates bidirectional Mamba blocks, can efficiently compress visual representations and meet the demands of global representations in defocus deblurring. As illustrated in Fig. 4b, following the reference [55], we first transform the input 2D feature $X_0 \\in \\mathbb{R}^{H \\times W \\times M}$ into a flattened sequence of non-overlapping patches $X_p \\in \\mathbb{R}^{J \\times (P \\times P \\times M)}$ , where $M$ is the number of channels, $J$ is the number of patches and $P$ is the patch size. Then, we linearly project $X_p$ to a vector of size $Z$ and add position embeddings $E_{pos} \\in \\mathbb{R}^{(J + 1) \\times Z}$ to obtain the token sequence $X_s$ . In VSSM, the input token sequence $X_s$ is first normalized and then linearly projected to the $X_a$ and $X_b$ . Then, we process the $X_a$ from the forward and backward directions. For each direction, we apply the 1-D convolution and the SSM to get $Y_f$ and $Y_b$ , respectively. The $Y_f$ and $Y_b$ are then gated by the $X_b$ followed by SiLU [33] and added together to get the output token sequence $Y_s$ . Finally we transpose the token sequence $Y_s$ to 2D feature $Y \\in \\mathbb{R}^{H \\times W \\times M}$ . This VSSM can be defined as:", + "bbox": [ + 511, + 114, + 906, + 448 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {s} = E m b e d d e d P a t c h e s \\left(X _ {0}\\right), \\\\ X _ {a}, X _ {b} = \\operatorname {L i n e a r} \\left(L N \\left(X _ {s}\\right)\\right), \\\\ Y _ {f} = S S M _ {F o r w a r d} \\left(\\operatorname {C o n v 1} d _ {F o r w a r d} \\left(X _ {a}\\right)\\right), \\\\ Y _ {b} = S S M _ {\\text {B a c k w a r d}} \\left(\\operatorname {C o n v 1 d} _ {\\text {B a c k w a r d}} \\left(X _ {a}\\right)\\right), \\tag {7} \\\\ Y _ {s} = \\operatorname {L i n e a r} ^ {T} \\left(Y _ {f} \\odot X _ {b} + Y _ {b} \\odot X _ {b}\\right) + X _ {s}, \\\\ Y = \\operatorname {T r a n s p o s e} \\left(Y _ {s}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 469, + 903, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Local Gate Module", + "text_level": 1, + "bbox": [ + 513, + 603, + 697, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Current methods [8, 10, 15, 41, 50] often utilize channel attention (CA) [54] and spatial attention (SA) [43] mechanisms to introduce critical locality for improved performance. Drawing inspiration from these approaches, we creatively propose the LGM to learn a comprehensive local context. As shown in Fig. 4c, the input features $X_0 \\in \\mathbb{R}^{H \\times W \\times M}$ are first passed through a $1 \\times 1$ convolution to expand the channel dimension to $2M$ . This is followed by $3 \\times 3$ DWConv to encode channel-wise spatial context, and then the features are split into two halves along the channel dimension, obtaining inputs $X_1$ and $X_2$ for two branch. In the first branch, CA mechanism is used to exploit the interchannel relationships of the convolutional feature maps. In the second branch, SA mechanism captures the interspatial dependencies. Unlike simple concatenation in [50], the output features from the two branches are further enhanced using a gating mechanism [7]. Finally, the gating features are passed through a $1 \\times 1$ convolution to output", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5713", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$Y\\in \\mathbb{R}^{H\\times W\\times M}$ . The entire LGM can be expressed as:", + "bbox": [ + 89, + 89, + 452, + 107 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX _ {1}, X _ {2} = \\operatorname {C h u n k} \\left(\\operatorname {D W C o n v} _ {3 \\times 3} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(X _ {0}\\right)\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 117, + 480, + 138 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nY = \\operatorname {C o n v} _ {1 \\times 1} (C A (X _ {1}) \\odot S A (X _ {2})),\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 137, + 357, + 152 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $Chunk$ represents splitting the features into two halves along the channel dimension and $\\odot$ denotes the Hadamard product.", + "bbox": [ + 89, + 164, + 482, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 223, + 295, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we present the experimental results, structured into three key components for a comprehensive evaluation. Firstly, we evaluate the efficacy of our LMNet by training it on the DPDD dataset and benchmarking its performance against SOTA methods on the associated test set. Next, we train on our proposed QPDD dataset to assess and confirm the feasibility of the QP-based approach, highlighting its advantages over the DP-based method. Finally, we perform ablation studies to further analyze the impact of individual model components.", + "bbox": [ + 89, + 248, + 483, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 409, + 279, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We utilize the AdamW optimizer [27] with momentum $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ , weight decay 1e-4. The learning rate starts from 1e-4 and gradually approaches 1e-7 using the cosine annealing strategy [26]. We follow a similar training strategy as proposed in [52] where the patch size progressively increases [128, 160, 192, 256, 320, 384] and the batch size decreases [18, 12, 8, 4, 2, 2] at iterations [90k, 150k, 210k, 270k, 330k, 390k]. More training details are provided in the supplementary material.", + "bbox": [ + 89, + 431, + 483, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We utilize Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Mean Absolute Error (MAE) as our evaluation metrics. We also provide the number of parameters and FLOPs with image size at $1120 \\times 1680$ for researchers' reference.", + "bbox": [ + 89, + 566, + 483, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparisons with State-of-the-Art", + "text_level": 1, + "bbox": [ + 89, + 652, + 393, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Defocus Deblurring on DPDD. We first provide defocus deblurring results on the DPDD [1] dataset. The comparisons among different methods are shown in Tab. 1 and Fig. 5. The metrics for UFormer [42], BaMBNet [24], K3DN [48], and LDP [47] are derived from their respective published papers, while the metrics and qualitative results for the other methods are obtained from the authors' official implementations. Table 1 presents the quantitative comparisons on the DPDD dataset and shows that our proposed method substantially outperforms existing baseline methods. For instance, compared with the Transformer-based method Restormer [52] and the large kernel-based method LaKDNet [32], our method achieves a significant performance boost of $0.59\\mathrm{dB}$ and $0.36\\mathrm{dB}$ , respectively, while maintaining only $69.58\\%$ and $47.32\\%$ of the parameters.", + "bbox": [ + 89, + 672, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared with the disparity-based approach K3DN [48], our method outperforms by 0.19 dB. To the best of our knowledge, LDP [47] is the first to innovatively introduce the language-image pre-training framework (CLIP) for defocus deblurring and achieve excellent results. Notably, our model achieves a 0.01 dB improvement in PSNR and a 0.005 improvement in SSIM using only 18.18M parameters, whereas LDP uses 19.60M parameters and relies on CLIP with 88M parameters. Figure 5 shows the corresponding qualitative results. It is noticeable that our method effectively removes spatially varying defocus blur, producing sharper images compared to publicly available approaches.", + "bbox": [ + 511, + 90, + 903, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Defocus Deblurring on QPDD. For the QPDD dataset, we evaluate the defocus deblurring performance using both two-view (L/R) and four-view (L/R and T/B) inputs on the RAW format dataset with our LMNet. The two-view (L/R) inputs are similar to those used in DP data. Since there is a lack of publicly available open-source code for K3DN [48] and LDP [47], we select six other classic defocus deblurring methods, DPDNet [1], UFormer [42], MIRNetV2 [49], DRBNet [31], Restormer [52] and LaKDNet [32], as references. We retrain these six methods using the sRGB images in the QPDD dataset following their own setups, and provide our training results on sRGB as a reference. Our metric evaluation is conducted in the sRGB format. Table 2 indicates that, within the LMNet framework, four-view inputs enhance PSNR by $0.27\\mathrm{dB}$ for RAW and $0.39\\mathrm{dB}$ for sRGB, compared to two-view inputs. When the inputs are limited to two views, our LMNet substantially outperforms SOTA methods Restormer [52] and LaKDNet [32]. Figure 6 further shows that our QP-based method is more effective than DP-based methods qualitatively, particularly in handling texture details (see the first and second rows of Fig. 6). This is attributed to the robustness of four-view disparity estimation, which is correlated to the amount of defocus blur. Notably, despite the QPDD dataset primarily consisting of indoor planar data, our approach exhibits robust performance in multi-depth and outdoor scenarios (see the third and fourth rows of Fig. 6).", + "bbox": [ + 511, + 273, + 906, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 694, + 666, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform ablations on different components of our LMNet on the DPDD dataset.", + "bbox": [ + 511, + 717, + 903, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Two-branch Encoder. We adopt a two-branch encoder with shared weights to separately extract information from different views. As shown in Tab. 3, compared to a single encoder architecture, the two-branch encoder approach only increases the parameter count by $0.29\\mathrm{M}$ and achieves a $0.29\\mathrm{dB}$ improvement in PSNR.", + "bbox": [ + 511, + 748, + 903, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of SFM. In this paper, we propose a two-branch encoder with SFM. Compared to a simple add operation between the two-branch encoder, SFM adds only 0.29M parameters and achieves a 0.15 dB PSNR improvement.", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5714", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4ecfeb7c0684cf0502607242dad886e259405524bd6f506c77efe7559e8f0c9e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodIndoor ScenesOutdoor ScenesCombinedParams (M)FLOPs (G)
PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓
DPDNet [1]27.480.8490.02922.900.7260.05225.130.7860.04131.033150
RDPD [2]28.100.8430.02722.820.7040.05325.390.7720.04024.28901
UFormer [42]28.230.8600.02623.100.7280.05125.650.7950.03950.882482
IFAN [19]28.660.8680.02523.460.7430.04925.990.8040.03710.48794
MIRNetV2 [49]28.960.8810.02423.590.7530.04926.200.8160.0375.864045
DRBNet [31]29.060.8730.02423.730.7520.04826.330.8110.03611.691273
BaMBNet [24]28.600.8720.02624.300.7720.04526.400.8210.0364.501804
Restormer [52]29.480.8950.02323.970.7730.04726.660.8330.03526.134458
LaKDNet [32]29.680.8890.02324.230.7770.04626.890.8320.03538.425168
K3DN [48]29.870.8900.02224.370.7800.04627.060.8350.03415.903352
LDP [47]29.880.8960.02024.730.7860.03727.240.8400.02819.60-
Ours30.080.8980.02224.570.7950.04427.250.8450.03318.183227
", + "bbox": [ + 114, + 88, + 883, + 280 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/efb582ac06a327db81b1d6760a9b543eb88579459b9f981aaa2cb733bbf21f35.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 91, + 329, + 176, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2f5c55e8e1588469c4e1d9352b4aa44a266ead748b8feab902b51c6bd0235d7.jpg", + "image_caption": [ + "Blurred Image" + ], + "image_footnote": [], + "bbox": [ + 183, + 329, + 267, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d425d3572cf6a0ce414f33e8df08f97ac136e40938cb3663d0646627a1af248.jpg", + "image_caption": [ + "RDPD[2]" + ], + "image_footnote": [], + "bbox": [ + 272, + 329, + 357, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/381b3d0e6045435b557760fce51db1d473e5db19191b31006cb2e2d460240bea.jpg", + "image_caption": [ + "IFAN[19]" + ], + "image_footnote": [], + "bbox": [ + 364, + 329, + 447, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51e3654d9059171fb8c15366cfee7b3718b578a1250f447880107c46b82eab20.jpg", + "image_caption": [ + "MIRNetV2[49]", + "Figure 5. Qualitative comparisons on the DPDD dataset. Our LMNet effectively removes defocus blur and restores more details." + ], + "image_footnote": [], + "bbox": [ + 454, + 329, + 539, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a8780e7de99bde640da29bb3a83ec05315eb6e6407907bf1b6831f14493c8dde.jpg", + "image_caption": [ + "Restormer[52]" + ], + "image_footnote": [], + "bbox": [ + 545, + 329, + 630, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6fc1f39fbd19644f44f136d90fb105f88e00b746bfe0dacf86afaf6d26674b15.jpg", + "image_caption": [ + "LaKDNet[32]" + ], + "image_footnote": [], + "bbox": [ + 635, + 329, + 718, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/937b333963b7ed405280b1563fd49b049765ab2288869cad093c0715d8e7469f.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 723, + 329, + 810, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fed19e4b9c81d95d6b303dc643ada9eb32d3925a3afb2673d7fef92dbfccc535.jpg", + "image_caption": [ + "Sharp Image" + ], + "image_footnote": [], + "bbox": [ + 816, + 329, + 901, + 503 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/eab5da307bb31cca2188777cc604c145305066f0e5963c85a639236aa67bc2e2.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons on the DPDD dataset. All the networks use DP images as input. The best and second best results are highlighted and underlined." + ], + "table_footnote": [], + "table_body": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)FLOPs (G)
DPDNetD [1]33.240.8980.014331.033150
UFormerD [42]33.630.9000.013250.882482
MIRNetV2D [49]33.860.9050.01355.864045
DRBNetD [31]34.180.9070.012911.691273
RestormerD [52]34.360.9180.012426.134458
LaKDNetD [32]34.640.9240.012138.425168
OursD (sRGB)36.250.9160.010918.183227
OursQ (sRGB)36.640.9200.010423.863231
OursD36.480.9260.010218.183221
OursQ36.750.9280.009923.863224
", + "bbox": [ + 94, + 569, + 480, + 705 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8c5fb9d437920aee3e4214b8b0b24d65a331a3e866c93a10ef724f0e59df8579.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on the QPDD dataset. Suffix D indicates two-view (L/R) inputs, and suffix Q indicates four-view (L/R and T/B) inputs." + ], + "table_footnote": [], + "table_body": "
Encoder ModePSNR ↑SSIM ↑MAE ↓Params (M)
single26.960.8400.03517.89
two-branch27.250.8450.03318.18
", + "bbox": [ + 94, + 773, + 480, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation experiments for different encoder modes.", + "bbox": [ + 109, + 840, + 462, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of LAMB. As the core component, the LAMB can improve VSSM with LGM. In this section, we ablate different components of the LAMB. The results, presented in Tab. 4, indicate that (a) directly using the VSSM is not good enough since it lacks local connectivity. (b) and (c) show that using only the channel attention block (CAB) [8] or LGM does not yield satisfactory performance because they lack global dependencies. However, LGM outperforms the CAB, achieving a $0.03\\mathrm{dB}$ improvement in PSNR. (d) shows that combining VSSM and CAB significantly improves performance. (e) further boosts the PSNR to 27.25 dB when LGM replaces CAB. The above experiments show that both global and local representations are crucial for defocus deblurring and validate the effectiveness of our proposed LAMB.", + "bbox": [ + 511, + 571, + 906, + 799 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "What's more, we visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and the overall LAMB, as shown in Fig. 7. For input images with varying degrees of blur, the VSSM module, benefiting from long-range dependencies, pays more attention to regions with higher blur levels, while the LGM demonstrates its po", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5715", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/15a16581e967515f6c1961f9e60211edcaceab83950b5e69bed8e0dd690f035d.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 205, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ab018eaff40c4f16866329ba7f4fa313938f42e2e12bdfc9324e673d85f7e984.jpg", + "image_caption": [ + "Blurred Image" + ], + "image_footnote": [], + "bbox": [ + 207, + 88, + 321, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e2114bd3a71221f539a756d6b3195b58b0ae869e765ef9f7db95f4172d4d7417.jpg", + "image_caption": [ + "$\\mathrm{Restormer}_D[52]$" + ], + "image_footnote": [], + "bbox": [ + 323, + 88, + 437, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6346849abf7637dba0127ab371f47bc940f2a5d212d83f73b7254a2e323adecf.jpg", + "image_caption": [ + "LaKDNetD[32]" + ], + "image_footnote": [], + "bbox": [ + 439, + 88, + 553, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63d69edbc9db266e37e3e4121430350155d4f89afe876103b57bd100bfe5ac5d.jpg", + "image_caption": [ + "Ours", + "Figure 6. Qualitative comparisons on the QPDD dataset. The suffix D indicates two-view (L/R) inputs, and the suffix Q indicates four-view (L/R and T/B) inputs. The test images in the first and second rows are planar indoor test scenes, while the third and fourth rows are multi-depth test scenes." + ], + "image_footnote": [], + "bbox": [ + 555, + 88, + 669, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed556171dcc042dbe66d29246b7453b5a58de0e76af1f133b1c108797d1232e2.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 669, + 88, + 785, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a0cab1e96a552fb5a7ea63b6bcbcb58723efcce1effefd6874b0188539e0e47.jpg", + "image_caption": [ + "Sharp Image" + ], + "image_footnote": [], + "bbox": [ + 787, + 88, + 901, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tential in restoring details. The weighted combination of VSSM and LGM forms the final LAMB, which further distinguishes between blurred and detailed regions, guiding the decoder for deblurring.", + "bbox": [ + 89, + 445, + 482, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Generalization Ability. To evaluate generalization, Restormer [52], LaKDNet [32], and our LMNet are trained on the DPDD dataset and tested on the QPDD dataset using two-view sRGB data as inputs. The weights of Restormer and LaKDNet are obtained from the authors' official implementations. Table 5 shows that our LMNet has better generalization ability compared to Restormer and LaKDNet.", + "bbox": [ + 89, + 506, + 483, + 612 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/36626747a7dd18a03bcdbf52871d23a73b45c464e3c05d3f1ddb652155d9873c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
VSSMCABLGM
(a)√26.770.8360.03515.33
(b)√26.760.8340.03613.84
(c)√26.790.8330.03511.36
(d)√√26.950.8390.03519.30
(e)√√27.250.8450.03318.18
", + "bbox": [ + 94, + 625, + 480, + 720 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f7432bd6504c65177e33a979d0e9665caa6c889542b0764222f47d9a5ce4306a.jpg", + "image_caption": [ + "(a) Input", + "Figure 7. Visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and LAMB." + ], + "image_footnote": [], + "bbox": [ + 91, + 773, + 189, + 825 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd24d81c59a03b54e7d24d526e431554c886e85452cd7fa158e2fb66814e5dbd.jpg", + "image_caption": [ + "(b) VSSM" + ], + "image_footnote": [], + "bbox": [ + 189, + 773, + 287, + 825 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cef8e04a0a2ad1492abdcd1f8fd4f35692f35e5e98b0f187c753a3fe3edc96f3.jpg", + "image_caption": [ + "(c) LGM" + ], + "image_footnote": [], + "bbox": [ + 289, + 773, + 383, + 825 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11d9e1219eae373cb11660f9f31bdf12fc1b0c64ccb0c0029708e890d123aaa7.jpg", + "image_caption": [ + "(d) LAMB" + ], + "image_footnote": [], + "bbox": [ + 385, + 773, + 480, + 825 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7178d1b963320df28c47fe603071719a1798d96361fd633ea7d50271e113ef3b.jpg", + "table_caption": [ + "Table 4. Ablation experiments for different designs of LAMB." + ], + "table_footnote": [], + "table_body": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
Restormer [52]29.530.8500.028226.13
LaKDNet [32]29.530.7760.026138.42
Ours30.370.8460.024718.18
", + "bbox": [ + 519, + 441, + 901, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Experiments for model generalization.", + "bbox": [ + 568, + 522, + 849, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 580, + 633, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a comprehensive solution for defocus deblurring based on QP data, encompassing both a novel dataset and a SOTA model. Notably, our LMNet achieves excellent performance on both the DPDD dataset and our proposed QPDD dataset. Considering the multisubaperture view characteristics of QP data, we design a two-branch encoder architecture with SFM for feature fusion. Additionally, we introduce a LAMB to mitigate local pixel forgetting and channel redundancy within Mamba. Extensive comparisons and ablation studies demonstrate the effectiveness of our method.", + "bbox": [ + 511, + 614, + 906, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. Although we have proposed a new QPDD dataset, it mainly consists of planar indoor scenes. We will continue to collect more diverse QPDD data, particularly datasets that span a wider range of DoF scenarios. Additionally, we will design a less computationally complex network for mobile devices or embedded systems, while maintaining performance.", + "bbox": [ + 511, + 787, + 908, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5716", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdullah Abuolaim and Michael S. Brown. 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IEEE, 2022. 1" + ], + "bbox": [ + 516, + 92, + 903, + 901 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5718", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[54] Yulun Zhang, Kunpeng Li, Kai Li, Lichen Wang, Bineng Zhong, and Yun Fu. Image super-resolution using very deep residual channel attention networks. In Computer Vision - ECCV 2018, pages 294-310. Springer, 2018. 3, 5", + "[55] Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, and Xinggang Wang. Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 2, 3, 5" + ], + "bbox": [ + 91, + 92, + 480, + 204 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5719", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_model.json b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_model.json new file mode 100644 index 0000000000000000000000000000000000000000..107749bfcac7afa027b707d8e09eef8f288a49f2 --- /dev/null +++ b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/c721a9dd-029d-4470-b5ba-1f618e42b739_model.json @@ -0,0 +1,2521 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.854, + 0.153 + ], + "angle": 0, + "content": "Quad-Pixel Image Defocus Deblurring: A New Benchmark and Model" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.18, + 0.888, + 0.217 + ], + "angle": 0, + "content": "Hang Chen\\(^{1}\\) Yin Xie\\(^{1}\\) Xiaoxiu Peng\\(^{1}\\) Lihu Sun\\(^{1}\\) Wenkai Su\\(^{1}\\) Xiaodong Yang\\(^{2}\\) Chengming Liu\\(^{2}\\) \\(^{1}\\)OMNIVISION, Wuhan, China \\(^{2}\\)OMNIVISION, Santa Clara, CA" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.252, + 0.327, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.284, + 0.485, + 0.649 + ], + "angle": 0, + "content": "Defocus deblurring is a challenging task due to the spatially varying blur. Recent works have shown impressive results in data-driven approaches using dual-pixel (DP) sensors. Quad-pixel (QP) sensors represent an advanced evolution of DP sensors, providing four distinct sub-aperture views in contrast to only two views offered by DP sensors. However, research on QP-based defocus deblurring is scarce. In this paper, we propose a novel end-to-end learning-based approach for defocus deblurring that leverages QP data. To achieve this, we design a QP defocus and all-in-focus image pair acquisition method and provide a QP Defocus Deblurring (QPDD) dataset containing 4,935 image pairs. We then introduce a Local-gate assisted Mamba Network (LMNet), which includes a two-branch encoder and a Simple Fusion Module (SFM) to fully utilize features of sub-aperture views. In particular, our LMNet incorporates a Local-gate assisted Mamba Block (LAMB) that mitigates local pixel forgetting and channel redundancy within Mamba, and effectively captures global and local dependencies. By extending the defocus deblurring task from a DP-based to a QP-based approach, we demonstrate significant improvements in restoring sharp images. Comprehensive experimental evaluations further indicate that our approach outperforms state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.678, + 0.222, + 0.693 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.483, + 0.795 + ], + "angle": 0, + "content": "Defocus blur occurs in scene regions captured outside the camera's depth of field (DoF) [1-3]. Restoring an all-in-focus image from a defocused image is challenging due to the spatially varying point spread functions (PSFs) [6, 20, 38, 40, 46], which are not only scene depth dependent, but also vary based on intrinsic camera parameters [2]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Recently, researchers have addressed this challenge by developing end-to-end deep neural networks that leverage dual-pixel (DP) data [1-3, 21, 24, 29, 47, 48, 53]. The first DP Defocus Deblurring (DPDD) [1] dataset, captured sequentially with various aperture sizes using a Canon 5D DSLR camera, is widely utilized. Quad-pixel (QP) sensors [28, 39] represent a significant advancement over DP" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.252, + 0.88, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.509, + 0.908, + 0.703 + ], + "angle": 0, + "content": "Figure 1. Characteristics of DP and QP sensors. The light rays from different parts of the main lens fall on each DP unit or QP unit. A DP unit has two photodiodes under a single microlens, producing two sub-aperture views, while a QP unit has four photodiodes, producing four sub-aperture views. Different views of DP or QP data exhibit different PSFs with directional characteristics, leading to disparity between the sub-aperture views. The disparity \\( d \\) is correlated with the amount of defocus blur \\( b \\) [1, 12]: \\( d = \\alpha * b \\approx \\alpha \\frac{Lf}{1 - f / D_f} \\left( \\frac{1}{D_f} - \\frac{1}{D} \\right) \\), where \\( \\alpha \\) is a constant of proportionality, \\( L \\) is the diameter of the aperture, \\( f \\) is the focal length, \\( D_f \\) is the focus distance, and \\( D \\) is the depth. DP sensors provide disparity in only a single direction, whereas QP sensors can provide disparity in two directions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.907, + 0.838 + ], + "angle": 0, + "content": "sensors and have gained widespread adoption in smartphones due to their superior Phase Detection Auto Focus (PDAF) performance. As indicated in Fig. 1, by utilizing four photodiodes under each microlens instead of two photodiodes, a QP sensor captures more light signal aspects, enhancing disparity detection [44] accuracy and providing more reliable guidance for defocus deblurring." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "However, to the best of our knowledge, research on QP-based defocus deblurring is limited, primarily due to the lack of relevant dataset. Most QP sensors on smartphones have a fixed aperture size, making it difficult to adopt the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5709" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.272 + ], + "angle": 0, + "content": "data acquisition method used in DPDD, which involves adjusting the aperture size. In contrast, we adjust the voice coil motors (VCMs) [17] of the QP sensor to change the focus distance, and acquire defocus and all-in-focus image pairs. However, this process induces a zoom-like effect [17]. To overcome this, we use the Enhanced Correlation Coefficient (ECC) [11] alignment algorithm. Furthermore, we propose an open-source QP defocus deblurring (QPDD) dataset. This dataset primarily includes RAW images that are linear with respect to the scene's physical light [4, 23], and also provides sRGB images for the convenience of researchers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.274, + 0.483, + 0.501 + ], + "angle": 0, + "content": "Modern deep learning models, such as CNNs [1-3, 50, 51] and Transformers [18, 22, 42, 52], have continuously improved state-of-the-art (SOTA) performance. CNNs have efficient parallel convolutions but limited receptive fields. In contrast, Transformers can model long-range dependencies but face quadratic computational complexity. Recently, state space models (SSMs) [13, 14, 36], particularly Mamba [13], have emerged as backbones due to their ability to capture long-range dependencies with linear complexity. Nevertheless, Mamba's recursive image sequence processing tends to cause local pixel forgetting, and the abundance of hidden states in the state space equation can lead to channel redundancy [15, 35, 55]. These factors impede the learning of local context, thereby resulting in poor performance when applying Mamba directly." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.502, + 0.483, + 0.803 + ], + "angle": 0, + "content": "Considering the multi-subaperture view characteristics of QP data and the critical role of efficient global and local dependencies in the defocus deblurring task, we propose the Local-gate assisted Mamba Network (LMNet) with several key components. Our LMNet employs an encoder-decoder architecture with a two-branch encoder that leverages information from different sub-aperture views, and incorporates a Simple Fusion Module (SFM) for effective feature integration from these two branches. Furthermore, instead of solely employing Mamba, we devise an effective Local-gate assisted Mamba Block (LAMB), which includes a parallel Vision State Space Module (VSSM) and Local Gate Module (LGM). By integrating the features from VSSM and LGM using learnable weights, the LAMB enables a more enhanced capture of global and local dependencies. To demonstrate the effectiveness of our LMNet, we first train it on the DPDD dataset, achieving SOTA performance. We then validate the performance of our QP-based deblurring approach and its advantages over DP-based approaches. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.805, + 0.483, + 0.849 + ], + "angle": 0, + "content": "- A QP defocus deblurring (QPDD) dataset, which consists of 4,935 defocus and all-in-focus image pairs, available in both RAW and sRGB formats." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "- A novel network LMNet for defocus deblurring, which fully utilizes information from the sub-aperture views of QP/DP images and enables effective capture of global and" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.805, + 0.484, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.092, + 0.66, + 0.106 + ], + "angle": 0, + "content": "local dependencies." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.11, + 0.905, + 0.14 + ], + "angle": 0, + "content": "- Extensive experiments evaluate our QP-based deblurring approach and its advantages over the DP-based methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.155, + 0.655, + 0.17 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.18, + 0.702, + 0.196 + ], + "angle": 0, + "content": "2.1. Defocus Deblurring" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.202, + 0.905, + 0.338 + ], + "angle": 0, + "content": "In learning-based defocus deblurring methods, Abdullah et al. [1] are the first to propose DPDNet for addressing defocus deblurring on DP images, and they also release a defocus deblurring dataset, named DPDD, based on the DP camera. Since then, an increasing number of defocus deblurring studies have been conducted based on this dataset. Existing DP-based defocus deblurring methods fall into two main categories: those that directly process DP data pairs and those that rely on disparity information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.339, + 0.905, + 0.67 + ], + "angle": 0, + "content": "For the first category of methods, Abdullah et al. [2] propose the network RDPD with convolutional LSTM units and a synthetic dataset to improve performance. Son et al. [37] propose an effective way to iteratively learn deblur kernels for different feature channels with the shape attention mechanism. Ruan et al. [31] use the DPDD and LFOF datasets and introduce filter dynamic networks. General restoration networks such as MIRNetV2 [49], Restormer [52], GRL [22], and LaKDNet [32] also fit into this category. Moreover, these studies show that two-view inputs outperform single-view inputs in defocus deblurring. For the second category of methods, Liang et al. [24] use the translating disk proposed by Abhijith et al. [30] to estimate a four-layer defocus mask by a four-branch network. Yang et al. [48] estimate defocus disparity only in feature space without explicitly showing a defocus map. Subsequently, Yang et al. [47] propose a new framework that leverages the capabilities of language-image pre-training framework (CLIP) for blur map estimation by designing an image-text format. These methods require additional data or modules to obtain the disparity from DP data to aid in restoring an all-in-focus image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.905, + 0.747 + ], + "angle": 0, + "content": "Our LMNet is specifically designed for both DP and QP defocus deblurring tasks. Unlike the above two categories of methods, we introduce a two-branch encoder and a SFM to effectively integrate information from different sub-aperture views." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.757, + 0.753, + 0.773 + ], + "angle": 0, + "content": "2.2. Visual State Space Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.905, + 0.901 + ], + "angle": 0, + "content": "SSMs [13, 14, 36] have garnered increasing attention from researchers due to their ability to capture long-range dependencies with linear complexity. S4 [14] is the first structured SSM to introduce a diagonal structure and combine it with a diagonal plus low-rank approach. Subsequently, S5 [36] proposes the diagonal SSM approximation and computes recurrently using a parallel scan. Building on these gains, Mamba [13] integrates SSM with the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5710" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.44 + ], + "angle": 0, + "content": "MLP block of Transformer and introduces a selection scanning mechanism within SSM to filter out irrelevant information for long-sequence modeling. However, the standard Mamba primarily focuses on unidirectional sequential data and cannot handle image data lacking specific directionality. To tackle this challenge, VMamba [25] and Vision Mamba [55] transform arbitrary visual images into ordered sequences and introduce a multiple scanning module that traverses the image space domain to tackle image classification and segmentation. Nevertheless, these multiple scanning Mamba modules still face certain challenges in low-level vision tasks, such as local pixel forgetting and channel redundancy. To address these issues, MambaIR [15], MMA [8], VmambaIR [35], and CU-Mamba [10] introduce the channel attention (CA) mechanism [54] for local modeling. Although the widely used CA mechanism can explore inter-channel relationships, it lacks explicit consideration of spatially-varying contents. In this context, we design an effective LAMB, featuring parallel VSSM and LGM. Unlike previous works that commonly use the CA mechanism, LGM combines CA and spatial attention (SA) [43] mechanisms through gate computation, thereby effectively enhancing local dependencies." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.453, + 0.33, + 0.47 + ], + "angle": 0, + "content": "3. QPDD Dataset Collection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.478, + 0.483, + 0.584 + ], + "angle": 0, + "content": "QP sensors have found widespread applications in smartphones [28, 39], and most QP sensors are equipped with fixed aperture size, making it difficult to adopt data acquisition method like DPDD, which involves adjusting the aperture size. In this section, we design an alternative alignment-based approach to generate high-quality defocused and all-in-focus RAW image pairs using a QP sensor." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Nearly all smartphone cameras use VCMs to focus [17]. VCMs control the movement of the camera lens, thereby changing the focus distance. As illustrated in Fig. 2a, we use the QP sensor to capture a static planar scene and control the VCMs in fixed steps to obtain a series of RAW images with varying amounts of blur. Then we employ the Contrast Detection Auto Focus (CDAF) algorithm to select the sharpest image as the in-focus target, and the others are considered as defocus images. Figure 2b demonstrates our QP data post-process pipeline. To reduce the impact of noise while maintaining the correlation between disparity and blur, we apply two-pixel averaging both vertically and horizontally within the same color channel to produce four-view images: left (L), right (R), top (T), and bottom (B). Additionally, we apply adjacent four-pixel averaging to produce a reference center (C) view. However, a noticeable zoom-like effect (a kind of misalignment) [17] arises between the defocus C image \\( I_{dc} \\) and the in-focus C image \\( I_{ic} \\). Defocus effects violate the brightness constancy assumption of corresponding points or regions [11], thereby posing significant challenges for alignment methods based on fea" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.9, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.18, + 0.788, + 0.192 + ], + "angle": 0, + "content": "(a) Capture sequence frames." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.193, + 0.898, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.316, + 0.782, + 0.328 + ], + "angle": 0, + "content": "(b) Post-process of frames." + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.34, + 0.907, + 0.41 + ], + "angle": 0, + "content": "Figure 2. QPDD dataset generation pipeline: (a) Capture sequence frames with QP sensor. (b) Post-process of frames, we first adopt pixel average to generate five-view images: left (L), right (R), top (T), bottom (B) and center (C), and then utilize ECC alignment to mitigate the zoom-like effect between \\( I_{dc} \\) and \\( I_{ic} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.907, + 0.512 + ], + "angle": 0, + "content": "ture point matching and optical flow. To mitigate the zoom-like effect, we introduce similarity-based ECC [11], which is well-suited for aligning planar defocus and in-focus images. Given \\( I_{dc} \\) and \\( I_{ic} \\) as inputs, the aligned in-focus C image \\( I_{ac} \\) can be defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.52, + 0.907, + 0.538 + ], + "angle": 0, + "content": "\\[\nI _ {a c} = \\operatorname {W a r p} \\left(I _ {i c}, E C C \\left(I _ {d c}, I _ {i c}\\right)\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.546, + 0.909, + 0.682 + ], + "angle": 0, + "content": "The ECC algorithm operates on the mean values of the Gb and Gr channels from both \\( I_{dc} \\) and \\( I_{ic} \\) to calculate the affine transformation matrix. This affine transformation matrix is subsequently warped to each color channel of the \\( I_{ic} \\) to obtain a well-aligned, sharp \\( I_{ac} \\). Our original defocus five-view images and target image \\( I_{ac} \\) have a resolution of \\( 4096 \\times 3072 \\) pixels. During alignment, we crop the central regions based on specific scenes, resulting in sizes of \\( 2160 \\times 1280 \\), \\( 1280 \\times 1792 \\), and \\( 1080 \\times 1280 \\) pixels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.683, + 0.909, + 0.834 + ], + "angle": 0, + "content": "In summary, our dataset comprises 200 indoor scenes and 4,935 pairs. We divide the dataset into 3,735 pairs training, 600 pairs validation, and 600 pairs testing sets. Furthermore, we provide an additional 100 full-resolution images, both indoor and outdoor with multi-depth, to test generalization performance. Additionally, to obtain training data in sRGB format, we perform Image Signal Processing (ISP) on the L, R, T, B, and C views of defocused images, as well as the target images \\( I_{ac} \\). More information about the QPDD dataset can be found in supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.845, + 0.605, + 0.86 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Our goal is to present an effective method to achieve high-quality defocus deblurring for both QP and DP data. In this" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5711" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.088, + 0.885, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.265, + 0.908, + 0.322 + ], + "angle": 0, + "content": "Figure 3. The overall network architecture of our LMNet. LMNet consists of a two-branch encoder which is designed to extract deep features from different sub-aperture views. Between the two branches, each level has a SFM (Fig. 4a) to fuse the two-branch features and pass them to the corresponding level in the decoder. To capture effective global and local dependencies in the defocus deblurring task, we propose LAMB (Fig. 4a)." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.344, + 0.462, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.233, + 0.533, + 0.343, + 0.544 + ], + "angle": 0, + "content": "(a) LAMB and SFM" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.546, + 0.462, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.617, + 0.317, + 0.628 + ], + "angle": 0, + "content": "(b) VSSM" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.63, + 0.465, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.712, + 0.312, + 0.724 + ], + "angle": 0, + "content": "(c) LGM" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.737, + 0.486, + 0.778 + ], + "angle": 0, + "content": "Figure 4. Details of the network structure: (a)The structures of LAMB and SFM. (b)The structure of VSSM. (c)The structure of LGM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.485, + 0.9 + ], + "angle": 0, + "content": "section, we first outline the overall pipeline of our Local-gate assisted Mamba Network (LMNet), and then we dive into its components by explaining: the Simple Fusion Module (SFM), the Local-gate assisted Mamba Block (LAMB), the Vision State Space Module (VSSM), and the Local Gate Module (LGM)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.347, + 0.674, + 0.364 + ], + "angle": 0, + "content": "4.1. Overall Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.369, + 0.907, + 0.705 + ], + "angle": 0, + "content": "As shown in Fig. 3, LMNet adopts a three-level encoder-decoder architecture with skip connections. Two branches in the encoder are designed to extract deep features from different views. At each level, a SFM is used to fuse the features from the two branches and pass them to the corresponding level in the decoder. The decoder aims to predict the latent all-in-focus image. To be specific, given an input image \\( I \\in \\mathbb{R}^{H \\times W \\times n} \\) of one encoder, LMNet firstly applies a \\( 3 \\times 3 \\) convolution to extract low-level features \\( X_0 \\in \\mathbb{R}^{H \\times W \\times M} \\). Here \\( H \\), \\( W \\) and \\( n \\) are the image height, width and channel number, respectively. \\( M \\) is the number of feature channels. Next, these shallow features \\( X_0 \\) pass through a three-level encoder-decoder and are transformed into deep features \\( X_l \\in \\mathbb{R}^{\\frac{H}{2^{l-1}} \\times \\frac{W}{2^{l-1}} \\times 2^{l-1}M} \\), where \\( l \\in \\{1,2,3\\} \\) indicates stage level. Each level of encoder and decoder is composed of \\( N \\) LAMBs, where \\( N \\in \\{N_1, N_2, N_3\\} \\). At the third level, following the third SFM, there is a feature enhancement module consisting of \\( N_4 \\) LAMBs. For feature downsampling and upsampling, we apply pixel-unshuffle and pixel-shuffle operations [34], respectively. Finally, applying a \\( 3 \\times 3 \\) convolution and adding skip connection from the input center image \\( I_C \\), we obtain the sharp image \\( I_S \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.811 + ], + "angle": 0, + "content": "For DP data, the left view \\( I_{L} \\) and the right view \\( I_{R} \\) are input into the two-branch encoder with shared parameters separately. For QP data, the left view \\( I_{L} \\) and the right view \\( I_{R} \\) are concatenated, as well as the top view \\( I_{T} \\) and the bottom view \\( I_{B} \\). Each concatenated pair is then fed separately into the two-branch encoder without shared parameters. The entire pipeline can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.823, + 0.905, + 0.839 + ], + "angle": 0, + "content": "\\[\nI _ {S} = I _ {C} + L M N e t \\left(I _ {L}, I _ {R}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.842, + 0.905, + 0.859 + ], + "angle": 0, + "content": "\\[\nI _ {S} = I _ {C} + L M N e t \\left(C A T \\left(I _ {L}, I _ {R}\\right), C A T \\left(I _ {T}, I _ {B}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.902 + ], + "angle": 0, + "content": "where \\(CAT(\\cdot, \\cdot)\\) indicates concatenation. Equation (2) and Eq. (3) demonstrate the deblurring processes for DP" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5712" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.265, + 0.106 + ], + "angle": 0, + "content": "and QP data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.107, + 0.483, + 0.137 + ], + "angle": 0, + "content": "We optimize the proposed network LMNet with the following loss function [5, 9]:" + }, + { + "type": "equation", + "bbox": [ + 0.112, + 0.148, + 0.483, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sqrt {\\left\\| I _ {S} - I _ {G} \\right\\| ^ {2} + \\epsilon^ {2}} + \\lambda \\| \\mathcal {F} (I _ {S}) - \\mathcal {F} (I _ {G}) \\| _ {1}, \\quad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.182, + 0.483, + 0.213 + ], + "angle": 0, + "content": "where \\(I_G\\) is the ground-truth image, \\(\\mathcal{F}\\) is the Fourier transform. We set \\(\\epsilon = 10^{-3}\\) and \\(\\lambda = 0.1\\) in the experiments." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.221, + 0.301, + 0.237 + ], + "angle": 0, + "content": "4.2. Simple Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.243, + 0.484, + 0.491 + ], + "angle": 0, + "content": "The SFM is responsible for fusing the outputs from the two-branch encoder and passing them to the corresponding decoder stage for reconstruction. Depth-wise convolution (DWConv) and point-wise convolution play a crucial role in facilitating interactive information across spatial and channel dimensions [32, 52]. Inspired by these, our SFM also primarily adopts these two types of convolutional layers. As shown in Fig. 4a, given that the outputs of the \\(l\\)-th stage of the two-branch encoder are \\(X_{1}\\), \\(X_{2} \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}\\), we first concatenate \\(X_{1}\\) and \\(X_{2}\\) to get \\(X_{3}\\), and use a \\(7 \\times 7\\) DWConv for effective local features encoding followed by GELU [16] activation function. Then, a residual connection is applied. Finally, a \\(1 \\times 1\\) convolution is employed to aggregate pixel-wise cross-channel context and reduce the channel numbers. The output \\(Y \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}\\) of the SFM can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.502, + 0.482, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {3} = C A T \\left(X _ {1}, X _ {2}\\right), \\\\ Y = \\operatorname {C o n v} _ {1 \\times 1} (G E L U (D W C o n v _ {7 \\times 7} (X _ {3})) + X _ {3}). \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.547, + 0.384, + 0.563 + ], + "angle": 0, + "content": "4.3. Local-gate assisted Mamba Block" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.484, + 0.812 + ], + "angle": 0, + "content": "For the defocus deblurring task, both global and local representations are crucial. The motivation behind the LAMB design is to explore Mamba to capture long-range dependencies with linear complexity and to design a LGM to obtain effective local connectivities, thereby reducing local pixel forgetting and channel redundancy of Mamba. As indicated in Fig. 4a, LAMB mainly follows the novel LayerNorm-Attention-LayerNorm-MLP flow [8, 15, 52]. We replace the Attention with a parallel VSSM and LGM structure. Furthermore, the direct fusion of different level features (global and local) inevitably leads to confused and conflicting representations [45]. To this end, we introduce two learnable scale factors \\(\\alpha \\in \\mathbb{R}^M\\) and \\(\\beta \\in \\mathbb{R}^M\\) to adaptively integrate global and local representations. Given that the input deep feature of LAMB is \\(X_0 \\in \\mathbb{R}^{H \\times W \\times M}\\), the output \\(Y \\in \\mathbb{R}^{H \\times W \\times M}\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.821, + 0.483, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {1} = L N \\left(X _ {0}\\right), \\\\ X _ {2} = X _ {0} + V S S M \\left(X _ {1}\\right) \\cdot \\alpha + L G M \\left(X _ {1}\\right) \\cdot \\beta , \\tag {6} \\\\ Y = X _ {2} + M L P \\left(L N \\left(X _ {2}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.316, + 0.901 + ], + "angle": 0, + "content": "where \\(LN\\) indicates Layer Norm." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.757, + 0.108 + ], + "angle": 0, + "content": "4.4. Vision State Space Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.907, + 0.449 + ], + "angle": 0, + "content": "The standard Mamba block is designed for the 1-D sequence, which is not suitable for vision tasks requiring spatial-aware understanding [15, 25, 55]. VSSM [55], which uses a ViT-like architecture and incorporates bidirectional Mamba blocks, can efficiently compress visual representations and meet the demands of global representations in defocus deblurring. As illustrated in Fig. 4b, following the reference [55], we first transform the input 2D feature \\(X_0 \\in \\mathbb{R}^{H \\times W \\times M}\\) into a flattened sequence of non-overlapping patches \\(X_p \\in \\mathbb{R}^{J \\times (P \\times P \\times M)}\\), where \\(M\\) is the number of channels, \\(J\\) is the number of patches and \\(P\\) is the patch size. Then, we linearly project \\(X_p\\) to a vector of size \\(Z\\) and add position embeddings \\(E_{pos} \\in \\mathbb{R}^{(J + 1) \\times Z}\\) to obtain the token sequence \\(X_s\\). In VSSM, the input token sequence \\(X_s\\) is first normalized and then linearly projected to the \\(X_a\\) and \\(X_b\\). Then, we process the \\(X_a\\) from the forward and backward directions. For each direction, we apply the 1-D convolution and the SSM to get \\(Y_f\\) and \\(Y_b\\), respectively. The \\(Y_f\\) and \\(Y_b\\) are then gated by the \\(X_b\\) followed by SiLU [33] and added together to get the output token sequence \\(Y_s\\). Finally we transpose the token sequence \\(Y_s\\) to 2D feature \\(Y \\in \\mathbb{R}^{H \\times W \\times M}\\). This VSSM can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.47, + 0.905, + 0.584 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {s} = E m b e d d e d P a t c h e s \\left(X _ {0}\\right), \\\\ X _ {a}, X _ {b} = \\operatorname {L i n e a r} \\left(L N \\left(X _ {s}\\right)\\right), \\\\ Y _ {f} = S S M _ {F o r w a r d} \\left(\\operatorname {C o n v 1} d _ {F o r w a r d} \\left(X _ {a}\\right)\\right), \\\\ Y _ {b} = S S M _ {\\text {B a c k w a r d}} \\left(\\operatorname {C o n v 1 d} _ {\\text {B a c k w a r d}} \\left(X _ {a}\\right)\\right), \\tag {7} \\\\ Y _ {s} = \\operatorname {L i n e a r} ^ {T} \\left(Y _ {f} \\odot X _ {b} + Y _ {b} \\odot X _ {b}\\right) + X _ {s}, \\\\ Y = \\operatorname {T r a n s p o s e} \\left(Y _ {s}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.604, + 0.698, + 0.618 + ], + "angle": 0, + "content": "4.5. Local Gate Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Current methods [8, 10, 15, 41, 50] often utilize channel attention (CA) [54] and spatial attention (SA) [43] mechanisms to introduce critical locality for improved performance. Drawing inspiration from these approaches, we creatively propose the LGM to learn a comprehensive local context. As shown in Fig. 4c, the input features \\(X_0 \\in \\mathbb{R}^{H \\times W \\times M}\\) are first passed through a \\(1 \\times 1\\) convolution to expand the channel dimension to \\(2M\\). This is followed by \\(3 \\times 3\\) DWConv to encode channel-wise spatial context, and then the features are split into two halves along the channel dimension, obtaining inputs \\(X_1\\) and \\(X_2\\) for two branch. In the first branch, CA mechanism is used to exploit the interchannel relationships of the convolutional feature maps. In the second branch, SA mechanism captures the interspatial dependencies. Unlike simple concatenation in [50], the output features from the two branches are further enhanced using a gating mechanism [7]. Finally, the gating features are passed through a \\(1 \\times 1\\) convolution to output" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5713" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.09, + 0.454, + 0.108 + ], + "angle": 0, + "content": "\\(Y\\in \\mathbb{R}^{H\\times W\\times M}\\) . The entire LGM can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.118, + 0.481, + 0.14 + ], + "angle": 0, + "content": "\\[\nX _ {1}, X _ {2} = \\operatorname {C h u n k} \\left(\\operatorname {D W C o n v} _ {3 \\times 3} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(X _ {0}\\right)\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.138, + 0.358, + 0.153 + ], + "angle": 0, + "content": "\\[\nY = \\operatorname {C o n v} _ {1 \\times 1} (C A (X _ {1}) \\odot S A (X _ {2})),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.165, + 0.483, + 0.21 + ], + "angle": 0, + "content": "where \\(Chunk\\) represents splitting the features into two halves along the channel dimension and \\(\\odot\\) denotes the Hadamard product." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.224, + 0.296, + 0.24 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.249, + 0.484, + 0.4 + ], + "angle": 0, + "content": "In this section, we present the experimental results, structured into three key components for a comprehensive evaluation. Firstly, we evaluate the efficacy of our LMNet by training it on the DPDD dataset and benchmarking its performance against SOTA methods on the associated test set. Next, we train on our proposed QPDD dataset to assess and confirm the feasibility of the QP-based approach, highlighting its advantages over the DP-based method. Finally, we perform ablation studies to further analyze the impact of individual model components." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.41, + 0.281, + 0.426 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.432, + 0.484, + 0.567 + ], + "angle": 0, + "content": "Implementation Details. We utilize the AdamW optimizer [27] with momentum \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\), weight decay 1e-4. The learning rate starts from 1e-4 and gradually approaches 1e-7 using the cosine annealing strategy [26]. We follow a similar training strategy as proposed in [52] where the patch size progressively increases [128, 160, 192, 256, 320, 384] and the batch size decreases [18, 12, 8, 4, 2, 2] at iterations [90k, 150k, 210k, 270k, 330k, 390k]. More training details are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.568, + 0.484, + 0.643 + ], + "angle": 0, + "content": "Evaluation Metrics. We utilize Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Mean Absolute Error (MAE) as our evaluation metrics. We also provide the number of parameters and FLOPs with image size at \\(1120 \\times 1680\\) for researchers' reference." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.653, + 0.395, + 0.669 + ], + "angle": 0, + "content": "5.2. Comparisons with State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Defocus Deblurring on DPDD. We first provide defocus deblurring results on the DPDD [1] dataset. The comparisons among different methods are shown in Tab. 1 and Fig. 5. The metrics for UFormer [42], BaMBNet [24], K3DN [48], and LDP [47] are derived from their respective published papers, while the metrics and qualitative results for the other methods are obtained from the authors' official implementations. Table 1 presents the quantitative comparisons on the DPDD dataset and shows that our proposed method substantially outperforms existing baseline methods. For instance, compared with the Transformer-based method Restormer [52] and the large kernel-based method LaKDNet [32], our method achieves a significant performance boost of \\(0.59\\mathrm{dB}\\) and \\(0.36\\mathrm{dB}\\), respectively, while maintaining only \\(69.58\\%\\) and \\(47.32\\%\\) of the parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.273 + ], + "angle": 0, + "content": "Compared with the disparity-based approach K3DN [48], our method outperforms by 0.19 dB. To the best of our knowledge, LDP [47] is the first to innovatively introduce the language-image pre-training framework (CLIP) for defocus deblurring and achieve excellent results. Notably, our model achieves a 0.01 dB improvement in PSNR and a 0.005 improvement in SSIM using only 18.18M parameters, whereas LDP uses 19.60M parameters and relies on CLIP with 88M parameters. Figure 5 shows the corresponding qualitative results. It is noticeable that our method effectively removes spatially varying defocus blur, producing sharper images compared to publicly available approaches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.274, + 0.907, + 0.682 + ], + "angle": 0, + "content": "Defocus Deblurring on QPDD. For the QPDD dataset, we evaluate the defocus deblurring performance using both two-view (L/R) and four-view (L/R and T/B) inputs on the RAW format dataset with our LMNet. The two-view (L/R) inputs are similar to those used in DP data. Since there is a lack of publicly available open-source code for K3DN [48] and LDP [47], we select six other classic defocus deblurring methods, DPDNet [1], UFormer [42], MIRNetV2 [49], DRBNet [31], Restormer [52] and LaKDNet [32], as references. We retrain these six methods using the sRGB images in the QPDD dataset following their own setups, and provide our training results on sRGB as a reference. Our metric evaluation is conducted in the sRGB format. Table 2 indicates that, within the LMNet framework, four-view inputs enhance PSNR by \\(0.27\\mathrm{dB}\\) for RAW and \\(0.39\\mathrm{dB}\\) for sRGB, compared to two-view inputs. When the inputs are limited to two views, our LMNet substantially outperforms SOTA methods Restormer [52] and LaKDNet [32]. Figure 6 further shows that our QP-based method is more effective than DP-based methods qualitatively, particularly in handling texture details (see the first and second rows of Fig. 6). This is attributed to the robustness of four-view disparity estimation, which is correlated to the amount of defocus blur. Notably, despite the QPDD dataset primarily consisting of indoor planar data, our approach exhibits robust performance in multi-depth and outdoor scenarios (see the third and fourth rows of Fig. 6)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.695, + 0.667, + 0.71 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.904, + 0.746 + ], + "angle": 0, + "content": "We perform ablations on different components of our LMNet on the DPDD dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.905, + 0.839 + ], + "angle": 0, + "content": "Effect of Two-branch Encoder. We adopt a two-branch encoder with shared weights to separately extract information from different views. As shown in Tab. 3, compared to a single encoder architecture, the two-branch encoder approach only increases the parameter count by \\(0.29\\mathrm{M}\\) and achieves a \\(0.29\\mathrm{dB}\\) improvement in PSNR." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Effect of SFM. In this paper, we propose a two-branch encoder with SFM. Compared to a simple add operation between the two-branch encoder, SFM adds only 0.29M parameters and achieves a 0.15 dB PSNR improvement." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5714" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.116, + 0.089, + 0.885, + 0.281 + ], + "angle": 0, + "content": "
MethodIndoor ScenesOutdoor ScenesCombinedParams (M)FLOPs (G)
PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓
DPDNet [1]27.480.8490.02922.900.7260.05225.130.7860.04131.033150
RDPD [2]28.100.8430.02722.820.7040.05325.390.7720.04024.28901
UFormer [42]28.230.8600.02623.100.7280.05125.650.7950.03950.882482
IFAN [19]28.660.8680.02523.460.7430.04925.990.8040.03710.48794
MIRNetV2 [49]28.960.8810.02423.590.7530.04926.200.8160.0375.864045
DRBNet [31]29.060.8730.02423.730.7520.04826.330.8110.03611.691273
BaMBNet [24]28.600.8720.02624.300.7720.04526.400.8210.0364.501804
Restormer [52]29.480.8950.02323.970.7730.04726.660.8330.03526.134458
LaKDNet [32]29.680.8890.02324.230.7770.04626.890.8320.03538.425168
K3DN [48]29.870.8900.02224.370.7800.04627.060.8350.03415.903352
LDP [47]29.880.8960.02024.730.7860.03727.240.8400.02819.60-
Ours30.080.8980.02224.570.7950.04427.250.8450.03318.183227
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.289, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on the DPDD dataset. All the networks use DP images as input. The best and second best results are highlighted and underlined." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.33, + 0.177, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.122, + 0.51, + 0.153, + 0.521 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.33, + 0.268, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.509, + 0.268, + 0.522 + ], + "angle": 0, + "content": "Blurred Image" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.33, + 0.359, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.509, + 0.345, + 0.521 + ], + "angle": 0, + "content": "RDPD[2]" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.33, + 0.448, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.381, + 0.509, + 0.434, + 0.521 + ], + "angle": 0, + "content": "IFAN[19]" + }, + { + "type": "image", + "bbox": [ + 0.455, + 0.33, + 0.54, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.457, + 0.509, + 0.541, + 0.521 + ], + "angle": 0, + "content": "MIRNetV2[49]" + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.33, + 0.631, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.509, + 0.629, + 0.521 + ], + "angle": 0, + "content": "Restormer[52]" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.33, + 0.72, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.509, + 0.718, + 0.521 + ], + "angle": 0, + "content": "LaKDNet[32]" + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.33, + 0.811, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.756, + 0.509, + 0.786, + 0.52 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.818, + 0.33, + 0.902, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.827, + 0.509, + 0.896, + 0.522 + ], + "angle": 0, + "content": "Sharp Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.532, + 0.877, + 0.547 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons on the DPDD dataset. Our LMNet effectively removes defocus blur and restores more details." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.57, + 0.481, + 0.706 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)FLOPs (G)
DPDNetD [1]33.240.8980.014331.033150
UFormerD [42]33.630.9000.013250.882482
MIRNetV2D [49]33.860.9050.01355.864045
DRBNetD [31]34.180.9070.012911.691273
RestormerD [52]34.360.9180.012426.134458
LaKDNetD [32]34.640.9240.012138.425168
OursD (sRGB)36.250.9160.010918.183227
OursQ (sRGB)36.640.9200.010423.863231
OursD36.480.9260.010218.183221
OursQ36.750.9280.009923.863224
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.716, + 0.483, + 0.759 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on the QPDD dataset. Suffix D indicates two-view (L/R) inputs, and suffix Q indicates four-view (L/R and T/B) inputs." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.775, + 0.481, + 0.831 + ], + "angle": 0, + "content": "
Encoder ModePSNR ↑SSIM ↑MAE ↓Params (M)
single26.960.8400.03517.89
two-branch27.250.8450.03318.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.11, + 0.842, + 0.463, + 0.856 + ], + "angle": 0, + "content": "Table 3. Ablation experiments for different encoder modes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.573, + 0.907, + 0.8 + ], + "angle": 0, + "content": "Effect of LAMB. As the core component, the LAMB can improve VSSM with LGM. In this section, we ablate different components of the LAMB. The results, presented in Tab. 4, indicate that (a) directly using the VSSM is not good enough since it lacks local connectivity. (b) and (c) show that using only the channel attention block (CAB) [8] or LGM does not yield satisfactory performance because they lack global dependencies. However, LGM outperforms the CAB, achieving a \\(0.03\\mathrm{dB}\\) improvement in PSNR. (d) shows that combining VSSM and CAB significantly improves performance. (e) further boosts the PSNR to 27.25 dB when LGM replaces CAB. The above experiments show that both global and local representations are crucial for defocus deblurring and validate the effectiveness of our proposed LAMB." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "What's more, we visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and the overall LAMB, as shown in Fig. 7. For input images with varying degrees of blur, the VSSM module, benefiting from long-range dependencies, pays more attention to regions with higher blur levels, while the LGM demonstrates its po" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5715" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.207, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.353, + 0.166, + 0.365 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.208, + 0.089, + 0.322, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.353, + 0.306, + 0.365 + ], + "angle": 0, + "content": "Blurred Image" + }, + { + "type": "image", + "bbox": [ + 0.325, + 0.089, + 0.439, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.339, + 0.353, + 0.428, + 0.365 + ], + "angle": 0, + "content": "\\(\\mathrm{Restormer}_D[52]\\)" + }, + { + "type": "image", + "bbox": [ + 0.441, + 0.089, + 0.554, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.456, + 0.353, + 0.542, + 0.365 + ], + "angle": 0, + "content": "LaKDNetD[32]" + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.089, + 0.67, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.353, + 0.635, + 0.366 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.089, + 0.786, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.353, + 0.75, + 0.366 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.089, + 0.902, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.353, + 0.882, + 0.366 + ], + "angle": 0, + "content": "Sharp Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.377, + 0.908, + 0.419 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons on the QPDD dataset. The suffix D indicates two-view (L/R) inputs, and the suffix Q indicates four-view (L/R and T/B) inputs. The test images in the first and second rows are planar indoor test scenes, while the third and fourth rows are multi-depth test scenes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.446, + 0.483, + 0.506 + ], + "angle": 0, + "content": "tential in restoring details. The weighted combination of VSSM and LGM forms the final LAMB, which further distinguishes between blurred and detailed regions, guiding the decoder for deblurring." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.507, + 0.484, + 0.613 + ], + "angle": 0, + "content": "Generalization Ability. To evaluate generalization, Restormer [52], LaKDNet [32], and our LMNet are trained on the DPDD dataset and tested on the QPDD dataset using two-view sRGB data as inputs. The weights of Restormer and LaKDNet are obtained from the authors' official implementations. Table 5 shows that our LMNet has better generalization ability compared to Restormer and LaKDNet." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.625, + 0.481, + 0.722 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
VSSMCABLGM
(a)√26.770.8360.03515.33
(b)√26.760.8340.03613.84
(c)√26.790.8330.03511.36
(d)√√26.950.8390.03519.30
(e)√√27.250.8450.03318.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.101, + 0.732, + 0.472, + 0.746 + ], + "angle": 0, + "content": "Table 4. Ablation experiments for different designs of LAMB." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.775, + 0.19, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.829, + 0.166, + 0.841 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.775, + 0.288, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.211, + 0.829, + 0.267, + 0.84 + ], + "angle": 0, + "content": "(b) VSSM" + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.775, + 0.385, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.829, + 0.361, + 0.84 + ], + "angle": 0, + "content": "(c) LGM" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.775, + 0.482, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.829, + 0.462, + 0.84 + ], + "angle": 0, + "content": "(d) LAMB" + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.853, + 0.483, + 0.881 + ], + "angle": 0, + "content": "Figure 7. Visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and LAMB." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.443, + 0.903, + 0.513 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
Restormer [52]29.530.8500.028226.13
LaKDNet [32]29.530.7760.026138.42
Ours30.370.8460.024718.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.569, + 0.523, + 0.851, + 0.537 + ], + "angle": 0, + "content": "Table 5. Experiments for model generalization." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.581, + 0.634, + 0.597 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.615, + 0.907, + 0.78 + ], + "angle": 0, + "content": "In this paper, we present a comprehensive solution for defocus deblurring based on QP data, encompassing both a novel dataset and a SOTA model. Notably, our LMNet achieves excellent performance on both the DPDD dataset and our proposed QPDD dataset. Considering the multisubaperture view characteristics of QP data, we design a two-branch encoder architecture with SFM for feature fusion. Additionally, we introduce a LAMB to mitigate local pixel forgetting and channel redundancy within Mamba. Extensive comparisons and ablation studies demonstrate the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.789, + 0.909, + 0.888 + ], + "angle": 0, + "content": "Limitations and future work. Although we have proposed a new QPDD dataset, it mainly consists of planar indoor scenes. We will continue to collect more diverse QPDD data, particularly datasets that span a wider range of DoF scenarios. Additionally, we will design a less computationally complex network for mobile devices or embedded systems, while maintaining performance." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5716" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.157 + ], + "angle": 0, + "content": "[1] Abdullah Abuolaim and Michael S. Brown. 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Recent works have shown impressive results in data-driven approaches using dual-pixel (DP) sensors. Quad-pixel (QP) sensors represent an advanced evolution of DP sensors, providing four distinct sub-aperture views in contrast to only two views offered by DP sensors. However, research on QP-based defocus deblurring is scarce. In this paper, we propose a novel end-to-end learning-based approach for defocus deblurring that leverages QP data. To achieve this, we design a QP defocus and all-in-focus image pair acquisition method and provide a QP Defocus Deblurring (QPDD) dataset containing 4,935 image pairs. We then introduce a Local-gate assisted Mamba Network (LMNet), which includes a two-branch encoder and a Simple Fusion Module (SFM) to fully utilize features of sub-aperture views. In particular, our LMNet incorporates a Local-gate assisted Mamba Block (LAMB) that mitigates local pixel forgetting and channel redundancy within Mamba, and effectively captures global and local dependencies. By extending the defocus deblurring task from a DP-based to a QP-based approach, we demonstrate significant improvements in restoring sharp images. Comprehensive experimental evaluations further indicate that our approach outperforms state-of-the-art methods. + +# 1. Introduction + +Defocus blur occurs in scene regions captured outside the camera's depth of field (DoF) [1-3]. Restoring an all-in-focus image from a defocused image is challenging due to the spatially varying point spread functions (PSFs) [6, 20, 38, 40, 46], which are not only scene depth dependent, but also vary based on intrinsic camera parameters [2]. + +Recently, researchers have addressed this challenge by developing end-to-end deep neural networks that leverage dual-pixel (DP) data [1-3, 21, 24, 29, 47, 48, 53]. The first DP Defocus Deblurring (DPDD) [1] dataset, captured sequentially with various aperture sizes using a Canon 5D DSLR camera, is widely utilized. Quad-pixel (QP) sensors [28, 39] represent a significant advancement over DP + +![](images/df0bbb8480e387dca510af644d9edbe112145d763170083d6b6e671eca7bfc0e.jpg) +Figure 1. Characteristics of DP and QP sensors. The light rays from different parts of the main lens fall on each DP unit or QP unit. A DP unit has two photodiodes under a single microlens, producing two sub-aperture views, while a QP unit has four photodiodes, producing four sub-aperture views. Different views of DP or QP data exhibit different PSFs with directional characteristics, leading to disparity between the sub-aperture views. The disparity $d$ is correlated with the amount of defocus blur $b$ [1, 12]: $d = \alpha * b \approx \alpha \frac{Lf}{1 - f / D_f} \left( \frac{1}{D_f} - \frac{1}{D} \right)$ , where $\alpha$ is a constant of proportionality, $L$ is the diameter of the aperture, $f$ is the focal length, $D_f$ is the focus distance, and $D$ is the depth. DP sensors provide disparity in only a single direction, whereas QP sensors can provide disparity in two directions. + +sensors and have gained widespread adoption in smartphones due to their superior Phase Detection Auto Focus (PDAF) performance. As indicated in Fig. 1, by utilizing four photodiodes under each microlens instead of two photodiodes, a QP sensor captures more light signal aspects, enhancing disparity detection [44] accuracy and providing more reliable guidance for defocus deblurring. + +However, to the best of our knowledge, research on QP-based defocus deblurring is limited, primarily due to the lack of relevant dataset. Most QP sensors on smartphones have a fixed aperture size, making it difficult to adopt the + +data acquisition method used in DPDD, which involves adjusting the aperture size. In contrast, we adjust the voice coil motors (VCMs) [17] of the QP sensor to change the focus distance, and acquire defocus and all-in-focus image pairs. However, this process induces a zoom-like effect [17]. To overcome this, we use the Enhanced Correlation Coefficient (ECC) [11] alignment algorithm. Furthermore, we propose an open-source QP defocus deblurring (QPDD) dataset. This dataset primarily includes RAW images that are linear with respect to the scene's physical light [4, 23], and also provides sRGB images for the convenience of researchers. + +Modern deep learning models, such as CNNs [1-3, 50, 51] and Transformers [18, 22, 42, 52], have continuously improved state-of-the-art (SOTA) performance. CNNs have efficient parallel convolutions but limited receptive fields. In contrast, Transformers can model long-range dependencies but face quadratic computational complexity. Recently, state space models (SSMs) [13, 14, 36], particularly Mamba [13], have emerged as backbones due to their ability to capture long-range dependencies with linear complexity. Nevertheless, Mamba's recursive image sequence processing tends to cause local pixel forgetting, and the abundance of hidden states in the state space equation can lead to channel redundancy [15, 35, 55]. These factors impede the learning of local context, thereby resulting in poor performance when applying Mamba directly. + +Considering the multi-subaperture view characteristics of QP data and the critical role of efficient global and local dependencies in the defocus deblurring task, we propose the Local-gate assisted Mamba Network (LMNet) with several key components. Our LMNet employs an encoder-decoder architecture with a two-branch encoder that leverages information from different sub-aperture views, and incorporates a Simple Fusion Module (SFM) for effective feature integration from these two branches. Furthermore, instead of solely employing Mamba, we devise an effective Local-gate assisted Mamba Block (LAMB), which includes a parallel Vision State Space Module (VSSM) and Local Gate Module (LGM). By integrating the features from VSSM and LGM using learnable weights, the LAMB enables a more enhanced capture of global and local dependencies. To demonstrate the effectiveness of our LMNet, we first train it on the DPDD dataset, achieving SOTA performance. We then validate the performance of our QP-based deblurring approach and its advantages over DP-based approaches. In summary, our contributions are as follows: + +- A QP defocus deblurring (QPDD) dataset, which consists of 4,935 defocus and all-in-focus image pairs, available in both RAW and sRGB formats. +- A novel network LMNet for defocus deblurring, which fully utilizes information from the sub-aperture views of QP/DP images and enables effective capture of global and + +local dependencies. + +- Extensive experiments evaluate our QP-based deblurring approach and its advantages over the DP-based methods. + +# 2. Related Work + +# 2.1. Defocus Deblurring + +In learning-based defocus deblurring methods, Abdullah et al. [1] are the first to propose DPDNet for addressing defocus deblurring on DP images, and they also release a defocus deblurring dataset, named DPDD, based on the DP camera. Since then, an increasing number of defocus deblurring studies have been conducted based on this dataset. Existing DP-based defocus deblurring methods fall into two main categories: those that directly process DP data pairs and those that rely on disparity information. + +For the first category of methods, Abdullah et al. [2] propose the network RDPD with convolutional LSTM units and a synthetic dataset to improve performance. Son et al. [37] propose an effective way to iteratively learn deblur kernels for different feature channels with the shape attention mechanism. Ruan et al. [31] use the DPDD and LFOF datasets and introduce filter dynamic networks. General restoration networks such as MIRNetV2 [49], Restormer [52], GRL [22], and LaKDNet [32] also fit into this category. Moreover, these studies show that two-view inputs outperform single-view inputs in defocus deblurring. For the second category of methods, Liang et al. [24] use the translating disk proposed by Abhijith et al. [30] to estimate a four-layer defocus mask by a four-branch network. Yang et al. [48] estimate defocus disparity only in feature space without explicitly showing a defocus map. Subsequently, Yang et al. [47] propose a new framework that leverages the capabilities of language-image pre-training framework (CLIP) for blur map estimation by designing an image-text format. These methods require additional data or modules to obtain the disparity from DP data to aid in restoring an all-in-focus image. + +Our LMNet is specifically designed for both DP and QP defocus deblurring tasks. Unlike the above two categories of methods, we introduce a two-branch encoder and a SFM to effectively integrate information from different sub-aperture views. + +# 2.2. Visual State Space Models + +SSMs [13, 14, 36] have garnered increasing attention from researchers due to their ability to capture long-range dependencies with linear complexity. S4 [14] is the first structured SSM to introduce a diagonal structure and combine it with a diagonal plus low-rank approach. Subsequently, S5 [36] proposes the diagonal SSM approximation and computes recurrently using a parallel scan. Building on these gains, Mamba [13] integrates SSM with the + +MLP block of Transformer and introduces a selection scanning mechanism within SSM to filter out irrelevant information for long-sequence modeling. However, the standard Mamba primarily focuses on unidirectional sequential data and cannot handle image data lacking specific directionality. To tackle this challenge, VMamba [25] and Vision Mamba [55] transform arbitrary visual images into ordered sequences and introduce a multiple scanning module that traverses the image space domain to tackle image classification and segmentation. Nevertheless, these multiple scanning Mamba modules still face certain challenges in low-level vision tasks, such as local pixel forgetting and channel redundancy. To address these issues, MambaIR [15], MMA [8], VmambaIR [35], and CU-Mamba [10] introduce the channel attention (CA) mechanism [54] for local modeling. Although the widely used CA mechanism can explore inter-channel relationships, it lacks explicit consideration of spatially-varying contents. In this context, we design an effective LAMB, featuring parallel VSSM and LGM. Unlike previous works that commonly use the CA mechanism, LGM combines CA and spatial attention (SA) [43] mechanisms through gate computation, thereby effectively enhancing local dependencies. + +# 3. QPDD Dataset Collection + +QP sensors have found widespread applications in smartphones [28, 39], and most QP sensors are equipped with fixed aperture size, making it difficult to adopt data acquisition method like DPDD, which involves adjusting the aperture size. In this section, we design an alternative alignment-based approach to generate high-quality defocused and all-in-focus RAW image pairs using a QP sensor. + +Nearly all smartphone cameras use VCMs to focus [17]. VCMs control the movement of the camera lens, thereby changing the focus distance. As illustrated in Fig. 2a, we use the QP sensor to capture a static planar scene and control the VCMs in fixed steps to obtain a series of RAW images with varying amounts of blur. Then we employ the Contrast Detection Auto Focus (CDAF) algorithm to select the sharpest image as the in-focus target, and the others are considered as defocus images. Figure 2b demonstrates our QP data post-process pipeline. To reduce the impact of noise while maintaining the correlation between disparity and blur, we apply two-pixel averaging both vertically and horizontally within the same color channel to produce four-view images: left (L), right (R), top (T), and bottom (B). Additionally, we apply adjacent four-pixel averaging to produce a reference center (C) view. However, a noticeable zoom-like effect (a kind of misalignment) [17] arises between the defocus C image $I_{dc}$ and the in-focus C image $I_{ic}$ . Defocus effects violate the brightness constancy assumption of corresponding points or regions [11], thereby posing significant challenges for alignment methods based on fea + +![](images/cb7acc5cbb36e2539e5603f1bf13073fc7e5877a226772a747f65419827db51b.jpg) + +![](images/d8946d172ceddc74c624255e7603cb26d36929fb3e9030b658fba9d0d25f1c78.jpg) +(a) Capture sequence frames. +(b) Post-process of frames. +Figure 2. QPDD dataset generation pipeline: (a) Capture sequence frames with QP sensor. (b) Post-process of frames, we first adopt pixel average to generate five-view images: left (L), right (R), top (T), bottom (B) and center (C), and then utilize ECC alignment to mitigate the zoom-like effect between $I_{dc}$ and $I_{ic}$ . + +ture point matching and optical flow. To mitigate the zoom-like effect, we introduce similarity-based ECC [11], which is well-suited for aligning planar defocus and in-focus images. Given $I_{dc}$ and $I_{ic}$ as inputs, the aligned in-focus C image $I_{ac}$ can be defined as follows: + +$$ +I _ {a c} = \operatorname {W a r p} \left(I _ {i c}, E C C \left(I _ {d c}, I _ {i c}\right)\right). \tag {1} +$$ + +The ECC algorithm operates on the mean values of the Gb and Gr channels from both $I_{dc}$ and $I_{ic}$ to calculate the affine transformation matrix. This affine transformation matrix is subsequently warped to each color channel of the $I_{ic}$ to obtain a well-aligned, sharp $I_{ac}$ . Our original defocus five-view images and target image $I_{ac}$ have a resolution of $4096 \times 3072$ pixels. During alignment, we crop the central regions based on specific scenes, resulting in sizes of $2160 \times 1280$ , $1280 \times 1792$ , and $1080 \times 1280$ pixels. + +In summary, our dataset comprises 200 indoor scenes and 4,935 pairs. We divide the dataset into 3,735 pairs training, 600 pairs validation, and 600 pairs testing sets. Furthermore, we provide an additional 100 full-resolution images, both indoor and outdoor with multi-depth, to test generalization performance. Additionally, to obtain training data in sRGB format, we perform Image Signal Processing (ISP) on the L, R, T, B, and C views of defocused images, as well as the target images $I_{ac}$ . More information about the QPDD dataset can be found in supplementary material. + +# 4. Method + +Our goal is to present an effective method to achieve high-quality defocus deblurring for both QP and DP data. In this + +![](images/78ef9b91b7ea380b3bc64f2609ba81f9175a7d87911712e8dd31290809dc6067.jpg) +Figure 3. The overall network architecture of our LMNet. LMNet consists of a two-branch encoder which is designed to extract deep features from different sub-aperture views. Between the two branches, each level has a SFM (Fig. 4a) to fuse the two-branch features and pass them to the corresponding level in the decoder. To capture effective global and local dependencies in the defocus deblurring task, we propose LAMB (Fig. 4a). + +![](images/5a913ad62c060493a8b2f3d733c5e990afa67fae9ae3eec197d9f87f9bd6ee06.jpg) +(a) LAMB and SFM + +![](images/fd4b480a5dc6a6041aaf384c71360e2dabbb72ef9f7e33d14fb4a9205f91aec6.jpg) + +![](images/3281e34f91f390df1b512ff05f69b7b27d7920617e4d10d12062a628e0a53ac5.jpg) +(b) VSSM +(c) LGM +Figure 4. Details of the network structure: (a)The structures of LAMB and SFM. (b)The structure of VSSM. (c)The structure of LGM. + +section, we first outline the overall pipeline of our Local-gate assisted Mamba Network (LMNet), and then we dive into its components by explaining: the Simple Fusion Module (SFM), the Local-gate assisted Mamba Block (LAMB), the Vision State Space Module (VSSM), and the Local Gate Module (LGM). + +# 4.1. Overall Pipeline + +As shown in Fig. 3, LMNet adopts a three-level encoder-decoder architecture with skip connections. Two branches in the encoder are designed to extract deep features from different views. At each level, a SFM is used to fuse the features from the two branches and pass them to the corresponding level in the decoder. The decoder aims to predict the latent all-in-focus image. To be specific, given an input image $I \in \mathbb{R}^{H \times W \times n}$ of one encoder, LMNet firstly applies a $3 \times 3$ convolution to extract low-level features $X_0 \in \mathbb{R}^{H \times W \times M}$ . Here $H$ , $W$ and $n$ are the image height, width and channel number, respectively. $M$ is the number of feature channels. Next, these shallow features $X_0$ pass through a three-level encoder-decoder and are transformed into deep features $X_l \in \mathbb{R}^{\frac{H}{2^{l-1}} \times \frac{W}{2^{l-1}} \times 2^{l-1}M}$ , where $l \in \{1,2,3\}$ indicates stage level. Each level of encoder and decoder is composed of $N$ LAMBs, where $N \in \{N_1, N_2, N_3\}$ . At the third level, following the third SFM, there is a feature enhancement module consisting of $N_4$ LAMBs. For feature downsampling and upsampling, we apply pixel-unshuffle and pixel-shuffle operations [34], respectively. Finally, applying a $3 \times 3$ convolution and adding skip connection from the input center image $I_C$ , we obtain the sharp image $I_S$ . + +For DP data, the left view $I_{L}$ and the right view $I_{R}$ are input into the two-branch encoder with shared parameters separately. For QP data, the left view $I_{L}$ and the right view $I_{R}$ are concatenated, as well as the top view $I_{T}$ and the bottom view $I_{B}$ . Each concatenated pair is then fed separately into the two-branch encoder without shared parameters. The entire pipeline can be expressed as: + +$$ +I _ {S} = I _ {C} + L M N e t \left(I _ {L}, I _ {R}\right), \tag {2} +$$ + +$$ +I _ {S} = I _ {C} + L M N e t \left(C A T \left(I _ {L}, I _ {R}\right), C A T \left(I _ {T}, I _ {B}\right)\right), \tag {3} +$$ + +where $CAT(\cdot, \cdot)$ indicates concatenation. Equation (2) and Eq. (3) demonstrate the deblurring processes for DP + +and QP data, respectively. + +We optimize the proposed network LMNet with the following loss function [5, 9]: + +$$ +\mathcal {L} = \sqrt {\left\| I _ {S} - I _ {G} \right\| ^ {2} + \epsilon^ {2}} + \lambda \| \mathcal {F} (I _ {S}) - \mathcal {F} (I _ {G}) \| _ {1}, \quad (4) +$$ + +where $I_G$ is the ground-truth image, $\mathcal{F}$ is the Fourier transform. We set $\epsilon = 10^{-3}$ and $\lambda = 0.1$ in the experiments. + +# 4.2. Simple Fusion Module + +The SFM is responsible for fusing the outputs from the two-branch encoder and passing them to the corresponding decoder stage for reconstruction. Depth-wise convolution (DWConv) and point-wise convolution play a crucial role in facilitating interactive information across spatial and channel dimensions [32, 52]. Inspired by these, our SFM also primarily adopts these two types of convolutional layers. As shown in Fig. 4a, given that the outputs of the $l$ -th stage of the two-branch encoder are $X_{1}$ , $X_{2} \in \mathbb{R}^{\frac{H}{2^{l - 1}} \times \frac{W}{2^{l - 1}} \times 2^{l - 1}M}$ , we first concatenate $X_{1}$ and $X_{2}$ to get $X_{3}$ , and use a $7 \times 7$ DWConv for effective local features encoding followed by GELU [16] activation function. Then, a residual connection is applied. Finally, a $1 \times 1$ convolution is employed to aggregate pixel-wise cross-channel context and reduce the channel numbers. The output $Y \in \mathbb{R}^{\frac{H}{2^{l - 1}} \times \frac{W}{2^{l - 1}} \times 2^{l - 1}M}$ of the SFM can be expressed as: + +$$ +\begin{array}{l} X _ {3} = C A T \left(X _ {1}, X _ {2}\right), \\ Y = \operatorname {C o n v} _ {1 \times 1} (G E L U (D W C o n v _ {7 \times 7} (X _ {3})) + X _ {3}). \tag {5} \\ \end{array} +$$ + +# 4.3. Local-gate assisted Mamba Block + +For the defocus deblurring task, both global and local representations are crucial. The motivation behind the LAMB design is to explore Mamba to capture long-range dependencies with linear complexity and to design a LGM to obtain effective local connectivities, thereby reducing local pixel forgetting and channel redundancy of Mamba. As indicated in Fig. 4a, LAMB mainly follows the novel LayerNorm-Attention-LayerNorm-MLP flow [8, 15, 52]. We replace the Attention with a parallel VSSM and LGM structure. Furthermore, the direct fusion of different level features (global and local) inevitably leads to confused and conflicting representations [45]. To this end, we introduce two learnable scale factors $\alpha \in \mathbb{R}^M$ and $\beta \in \mathbb{R}^M$ to adaptively integrate global and local representations. Given that the input deep feature of LAMB is $X_0 \in \mathbb{R}^{H \times W \times M}$ , the output $Y \in \mathbb{R}^{H \times W \times M}$ can be formulated as: + +$$ +\begin{array}{l} X _ {1} = L N \left(X _ {0}\right), \\ X _ {2} = X _ {0} + V S S M \left(X _ {1}\right) \cdot \alpha + L G M \left(X _ {1}\right) \cdot \beta , \tag {6} \\ Y = X _ {2} + M L P \left(L N \left(X _ {2}\right)\right), \\ \end{array} +$$ + +where $LN$ indicates Layer Norm. + +# 4.4. Vision State Space Module + +The standard Mamba block is designed for the 1-D sequence, which is not suitable for vision tasks requiring spatial-aware understanding [15, 25, 55]. VSSM [55], which uses a ViT-like architecture and incorporates bidirectional Mamba blocks, can efficiently compress visual representations and meet the demands of global representations in defocus deblurring. As illustrated in Fig. 4b, following the reference [55], we first transform the input 2D feature $X_0 \in \mathbb{R}^{H \times W \times M}$ into a flattened sequence of non-overlapping patches $X_p \in \mathbb{R}^{J \times (P \times P \times M)}$ , where $M$ is the number of channels, $J$ is the number of patches and $P$ is the patch size. Then, we linearly project $X_p$ to a vector of size $Z$ and add position embeddings $E_{pos} \in \mathbb{R}^{(J + 1) \times Z}$ to obtain the token sequence $X_s$ . In VSSM, the input token sequence $X_s$ is first normalized and then linearly projected to the $X_a$ and $X_b$ . Then, we process the $X_a$ from the forward and backward directions. For each direction, we apply the 1-D convolution and the SSM to get $Y_f$ and $Y_b$ , respectively. The $Y_f$ and $Y_b$ are then gated by the $X_b$ followed by SiLU [33] and added together to get the output token sequence $Y_s$ . Finally we transpose the token sequence $Y_s$ to 2D feature $Y \in \mathbb{R}^{H \times W \times M}$ . This VSSM can be defined as: + +$$ +\begin{array}{l} X _ {s} = E m b e d d e d P a t c h e s \left(X _ {0}\right), \\ X _ {a}, X _ {b} = \operatorname {L i n e a r} \left(L N \left(X _ {s}\right)\right), \\ Y _ {f} = S S M _ {F o r w a r d} \left(\operatorname {C o n v 1} d _ {F o r w a r d} \left(X _ {a}\right)\right), \\ Y _ {b} = S S M _ {\text {B a c k w a r d}} \left(\operatorname {C o n v 1 d} _ {\text {B a c k w a r d}} \left(X _ {a}\right)\right), \tag {7} \\ Y _ {s} = \operatorname {L i n e a r} ^ {T} \left(Y _ {f} \odot X _ {b} + Y _ {b} \odot X _ {b}\right) + X _ {s}, \\ Y = \operatorname {T r a n s p o s e} \left(Y _ {s}\right). \\ \end{array} +$$ + +# 4.5. Local Gate Module + +Current methods [8, 10, 15, 41, 50] often utilize channel attention (CA) [54] and spatial attention (SA) [43] mechanisms to introduce critical locality for improved performance. Drawing inspiration from these approaches, we creatively propose the LGM to learn a comprehensive local context. As shown in Fig. 4c, the input features $X_0 \in \mathbb{R}^{H \times W \times M}$ are first passed through a $1 \times 1$ convolution to expand the channel dimension to $2M$ . This is followed by $3 \times 3$ DWConv to encode channel-wise spatial context, and then the features are split into two halves along the channel dimension, obtaining inputs $X_1$ and $X_2$ for two branch. In the first branch, CA mechanism is used to exploit the interchannel relationships of the convolutional feature maps. In the second branch, SA mechanism captures the interspatial dependencies. Unlike simple concatenation in [50], the output features from the two branches are further enhanced using a gating mechanism [7]. Finally, the gating features are passed through a $1 \times 1$ convolution to output + +$Y\in \mathbb{R}^{H\times W\times M}$ . The entire LGM can be expressed as: + +$$ +X _ {1}, X _ {2} = \operatorname {C h u n k} \left(\operatorname {D W C o n v} _ {3 \times 3} \left(\operatorname {C o n v} _ {1 \times 1} \left(X _ {0}\right)\right)\right), \tag {8} +$$ + +$$ +Y = \operatorname {C o n v} _ {1 \times 1} (C A (X _ {1}) \odot S A (X _ {2})), +$$ + +where $Chunk$ represents splitting the features into two halves along the channel dimension and $\odot$ denotes the Hadamard product. + +# 5. Experimental Results + +In this section, we present the experimental results, structured into three key components for a comprehensive evaluation. Firstly, we evaluate the efficacy of our LMNet by training it on the DPDD dataset and benchmarking its performance against SOTA methods on the associated test set. Next, we train on our proposed QPDD dataset to assess and confirm the feasibility of the QP-based approach, highlighting its advantages over the DP-based method. Finally, we perform ablation studies to further analyze the impact of individual model components. + +# 5.1. Experimental Setup + +Implementation Details. We utilize the AdamW optimizer [27] with momentum $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , weight decay 1e-4. The learning rate starts from 1e-4 and gradually approaches 1e-7 using the cosine annealing strategy [26]. We follow a similar training strategy as proposed in [52] where the patch size progressively increases [128, 160, 192, 256, 320, 384] and the batch size decreases [18, 12, 8, 4, 2, 2] at iterations [90k, 150k, 210k, 270k, 330k, 390k]. More training details are provided in the supplementary material. + +Evaluation Metrics. We utilize Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Mean Absolute Error (MAE) as our evaluation metrics. We also provide the number of parameters and FLOPs with image size at $1120 \times 1680$ for researchers' reference. + +# 5.2. Comparisons with State-of-the-Art + +Defocus Deblurring on DPDD. We first provide defocus deblurring results on the DPDD [1] dataset. The comparisons among different methods are shown in Tab. 1 and Fig. 5. The metrics for UFormer [42], BaMBNet [24], K3DN [48], and LDP [47] are derived from their respective published papers, while the metrics and qualitative results for the other methods are obtained from the authors' official implementations. Table 1 presents the quantitative comparisons on the DPDD dataset and shows that our proposed method substantially outperforms existing baseline methods. For instance, compared with the Transformer-based method Restormer [52] and the large kernel-based method LaKDNet [32], our method achieves a significant performance boost of $0.59\mathrm{dB}$ and $0.36\mathrm{dB}$ , respectively, while maintaining only $69.58\%$ and $47.32\%$ of the parameters. + +Compared with the disparity-based approach K3DN [48], our method outperforms by 0.19 dB. To the best of our knowledge, LDP [47] is the first to innovatively introduce the language-image pre-training framework (CLIP) for defocus deblurring and achieve excellent results. Notably, our model achieves a 0.01 dB improvement in PSNR and a 0.005 improvement in SSIM using only 18.18M parameters, whereas LDP uses 19.60M parameters and relies on CLIP with 88M parameters. Figure 5 shows the corresponding qualitative results. It is noticeable that our method effectively removes spatially varying defocus blur, producing sharper images compared to publicly available approaches. + +Defocus Deblurring on QPDD. For the QPDD dataset, we evaluate the defocus deblurring performance using both two-view (L/R) and four-view (L/R and T/B) inputs on the RAW format dataset with our LMNet. The two-view (L/R) inputs are similar to those used in DP data. Since there is a lack of publicly available open-source code for K3DN [48] and LDP [47], we select six other classic defocus deblurring methods, DPDNet [1], UFormer [42], MIRNetV2 [49], DRBNet [31], Restormer [52] and LaKDNet [32], as references. We retrain these six methods using the sRGB images in the QPDD dataset following their own setups, and provide our training results on sRGB as a reference. Our metric evaluation is conducted in the sRGB format. Table 2 indicates that, within the LMNet framework, four-view inputs enhance PSNR by $0.27\mathrm{dB}$ for RAW and $0.39\mathrm{dB}$ for sRGB, compared to two-view inputs. When the inputs are limited to two views, our LMNet substantially outperforms SOTA methods Restormer [52] and LaKDNet [32]. Figure 6 further shows that our QP-based method is more effective than DP-based methods qualitatively, particularly in handling texture details (see the first and second rows of Fig. 6). This is attributed to the robustness of four-view disparity estimation, which is correlated to the amount of defocus blur. Notably, despite the QPDD dataset primarily consisting of indoor planar data, our approach exhibits robust performance in multi-depth and outdoor scenarios (see the third and fourth rows of Fig. 6). + +# 5.3. Ablation Study + +We perform ablations on different components of our LMNet on the DPDD dataset. + +Effect of Two-branch Encoder. We adopt a two-branch encoder with shared weights to separately extract information from different views. As shown in Tab. 3, compared to a single encoder architecture, the two-branch encoder approach only increases the parameter count by $0.29\mathrm{M}$ and achieves a $0.29\mathrm{dB}$ improvement in PSNR. + +Effect of SFM. In this paper, we propose a two-branch encoder with SFM. Compared to a simple add operation between the two-branch encoder, SFM adds only 0.29M parameters and achieves a 0.15 dB PSNR improvement. + +
MethodIndoor ScenesOutdoor ScenesCombinedParams (M)FLOPs (G)
PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓
DPDNet [1]27.480.8490.02922.900.7260.05225.130.7860.04131.033150
RDPD [2]28.100.8430.02722.820.7040.05325.390.7720.04024.28901
UFormer [42]28.230.8600.02623.100.7280.05125.650.7950.03950.882482
IFAN [19]28.660.8680.02523.460.7430.04925.990.8040.03710.48794
MIRNetV2 [49]28.960.8810.02423.590.7530.04926.200.8160.0375.864045
DRBNet [31]29.060.8730.02423.730.7520.04826.330.8110.03611.691273
BaMBNet [24]28.600.8720.02624.300.7720.04526.400.8210.0364.501804
Restormer [52]29.480.8950.02323.970.7730.04726.660.8330.03526.134458
LaKDNet [32]29.680.8890.02324.230.7770.04626.890.8320.03538.425168
K3DN [48]29.870.8900.02224.370.7800.04627.060.8350.03415.903352
LDP [47]29.880.8960.02024.730.7860.03727.240.8400.02819.60-
Ours30.080.8980.02224.570.7950.04427.250.8450.03318.183227
+ +![](images/efb582ac06a327db81b1d6760a9b543eb88579459b9f981aaa2cb733bbf21f35.jpg) +Input + +![](images/c2f5c55e8e1588469c4e1d9352b4aa44a266ead748b8feab902b51c6bd0235d7.jpg) +Blurred Image + +![](images/8d425d3572cf6a0ce414f33e8df08f97ac136e40938cb3663d0646627a1af248.jpg) +RDPD[2] + +![](images/381b3d0e6045435b557760fce51db1d473e5db19191b31006cb2e2d460240bea.jpg) +IFAN[19] + +![](images/51e3654d9059171fb8c15366cfee7b3718b578a1250f447880107c46b82eab20.jpg) +MIRNetV2[49] +Figure 5. Qualitative comparisons on the DPDD dataset. Our LMNet effectively removes defocus blur and restores more details. + +![](images/a8780e7de99bde640da29bb3a83ec05315eb6e6407907bf1b6831f14493c8dde.jpg) +Restormer[52] + +![](images/6fc1f39fbd19644f44f136d90fb105f88e00b746bfe0dacf86afaf6d26674b15.jpg) +LaKDNet[32] + +![](images/937b333963b7ed405280b1563fd49b049765ab2288869cad093c0715d8e7469f.jpg) +Ours + +![](images/fed19e4b9c81d95d6b303dc643ada9eb32d3925a3afb2673d7fef92dbfccc535.jpg) +Sharp Image + +Table 1. Quantitative comparisons on the DPDD dataset. All the networks use DP images as input. The best and second best results are highlighted and underlined. + +
MethodPSNR ↑SSIM ↑MAE ↓Params (M)FLOPs (G)
DPDNetD [1]33.240.8980.014331.033150
UFormerD [42]33.630.9000.013250.882482
MIRNetV2D [49]33.860.9050.01355.864045
DRBNetD [31]34.180.9070.012911.691273
RestormerD [52]34.360.9180.012426.134458
LaKDNetD [32]34.640.9240.012138.425168
OursD (sRGB)36.250.9160.010918.183227
OursQ (sRGB)36.640.9200.010423.863231
OursD36.480.9260.010218.183221
OursQ36.750.9280.009923.863224
+ +Table 2. Quantitative comparisons on the QPDD dataset. Suffix D indicates two-view (L/R) inputs, and suffix Q indicates four-view (L/R and T/B) inputs. + +
Encoder ModePSNR ↑SSIM ↑MAE ↓Params (M)
single26.960.8400.03517.89
two-branch27.250.8450.03318.18
+ +Table 3. Ablation experiments for different encoder modes. + +Effect of LAMB. As the core component, the LAMB can improve VSSM with LGM. In this section, we ablate different components of the LAMB. The results, presented in Tab. 4, indicate that (a) directly using the VSSM is not good enough since it lacks local connectivity. (b) and (c) show that using only the channel attention block (CAB) [8] or LGM does not yield satisfactory performance because they lack global dependencies. However, LGM outperforms the CAB, achieving a $0.03\mathrm{dB}$ improvement in PSNR. (d) shows that combining VSSM and CAB significantly improves performance. (e) further boosts the PSNR to 27.25 dB when LGM replaces CAB. The above experiments show that both global and local representations are crucial for defocus deblurring and validate the effectiveness of our proposed LAMB. + +What's more, we visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and the overall LAMB, as shown in Fig. 7. For input images with varying degrees of blur, the VSSM module, benefiting from long-range dependencies, pays more attention to regions with higher blur levels, while the LGM demonstrates its po + +![](images/15a16581e967515f6c1961f9e60211edcaceab83950b5e69bed8e0dd690f035d.jpg) +Input + +![](images/ab018eaff40c4f16866329ba7f4fa313938f42e2e12bdfc9324e673d85f7e984.jpg) +Blurred Image + +![](images/e2114bd3a71221f539a756d6b3195b58b0ae869e765ef9f7db95f4172d4d7417.jpg) +$\mathrm{Restormer}_D[52]$ + +![](images/6346849abf7637dba0127ab371f47bc940f2a5d212d83f73b7254a2e323adecf.jpg) +LaKDNetD[32] + +![](images/63d69edbc9db266e37e3e4121430350155d4f89afe876103b57bd100bfe5ac5d.jpg) +Ours +Figure 6. Qualitative comparisons on the QPDD dataset. The suffix D indicates two-view (L/R) inputs, and the suffix Q indicates four-view (L/R and T/B) inputs. The test images in the first and second rows are planar indoor test scenes, while the third and fourth rows are multi-depth test scenes. + +![](images/ed556171dcc042dbe66d29246b7453b5a58de0e76af1f133b1c108797d1232e2.jpg) +Ours + +![](images/5a0cab1e96a552fb5a7ea63b6bcbcb58723efcce1effefd6874b0188539e0e47.jpg) +Sharp Image + +tential in restoring details. The weighted combination of VSSM and LGM forms the final LAMB, which further distinguishes between blurred and detailed regions, guiding the decoder for deblurring. + +Generalization Ability. To evaluate generalization, Restormer [52], LaKDNet [32], and our LMNet are trained on the DPDD dataset and tested on the QPDD dataset using two-view sRGB data as inputs. The weights of Restormer and LaKDNet are obtained from the authors' official implementations. Table 5 shows that our LMNet has better generalization ability compared to Restormer and LaKDNet. + +
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
VSSMCABLGM
(a)√26.770.8360.03515.33
(b)√26.760.8340.03613.84
(c)√26.790.8330.03511.36
(d)√√26.950.8390.03519.30
(e)√√27.250.8450.03318.18
+ +![](images/f7432bd6504c65177e33a979d0e9665caa6c889542b0764222f47d9a5ce4306a.jpg) +(a) Input +Figure 7. Visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and LAMB. + +![](images/cd24d81c59a03b54e7d24d526e431554c886e85452cd7fa158e2fb66814e5dbd.jpg) +(b) VSSM + +![](images/cef8e04a0a2ad1492abdcd1f8fd4f35692f35e5e98b0f187c753a3fe3edc96f3.jpg) +(c) LGM + +![](images/11d9e1219eae373cb11660f9f31bdf12fc1b0c64ccb0c0029708e890d123aaa7.jpg) +(d) LAMB + +Table 4. Ablation experiments for different designs of LAMB. + +
MethodPSNR ↑SSIM ↑MAE ↓Params (M)
Restormer [52]29.530.8500.028226.13
LaKDNet [32]29.530.7760.026138.42
Ours30.370.8460.024718.18
+ +Table 5. Experiments for model generalization. + +# 6. Conclusion + +In this paper, we present a comprehensive solution for defocus deblurring based on QP data, encompassing both a novel dataset and a SOTA model. Notably, our LMNet achieves excellent performance on both the DPDD dataset and our proposed QPDD dataset. Considering the multisubaperture view characteristics of QP data, we design a two-branch encoder architecture with SFM for feature fusion. Additionally, we introduce a LAMB to mitigate local pixel forgetting and channel redundancy within Mamba. Extensive comparisons and ablation studies demonstrate the effectiveness of our method. + +Limitations and future work. Although we have proposed a new QPDD dataset, it mainly consists of planar indoor scenes. We will continue to collect more diverse QPDD data, particularly datasets that span a wider range of DoF scenarios. 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Learning enriched features for real image restoration and enhancement. In European Conference on Computer Vision. Springer, 2020. 2, 5 +[51] Syed Waqas Zamir, Aditya Arora, Salman H. Khan, Munawar Hayat, Fahad Shahbaz Khan, Ming-Hsuan Yang, and Ling Shao. Multi-stage progressive image restoration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 14821-14831. IEEE, 2021. 2 +[52] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image restoration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5728-5739, 2022. 2, 5, 6, 7, 8 +[53] Dafeng Zhang and Xiaobing Wang. Dynamic multi-scale network for dual-pixel images defocus deblurring with transformer. In Proceedings of IEEE/CVF International Conference on Multimedia and Expo, pages 1-6. 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Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024. 2, 3, 5 \ No newline at end of file diff --git a/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/images.zip b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..678e2460ef4850f1e5a73e42b8caac090b82ee6b --- /dev/null +++ b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:111f3744743818f1398c68e8829541f232bf84ebcb8739c9a43d39cea3c86e44 +size 688286 diff --git a/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/layout.json b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe2a93a0242e418a76a7339d81149ee60c02fb3 --- /dev/null +++ b/2025/Quad-Pixel Image Defocus Deblurring_ A New Benchmark and Model/layout.json @@ -0,0 +1,10342 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "type": "text", + "content": "Quad-Pixel Image Defocus Deblurring: A New Benchmark and Model" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "spans": [ + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": "Hang Chen" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Yin Xie" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Xiaoxiu Peng" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Lihu Sun" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Wenkai Su" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Xiaodong Yang" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": " Chengming Liu" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": "OMNIVISION, Wuhan, China " + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 67, + 142, + 543, + 171 + ], + "type": "text", + "content": "OMNIVISION, Santa Clara, CA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "spans": [ + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 224, + 296, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 224, + 296, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 224, + 296, + 514 + ], + "type": "text", + "content": "Defocus deblurring is a challenging task due to the spatially varying blur. Recent works have shown impressive results in data-driven approaches using dual-pixel (DP) sensors. Quad-pixel (QP) sensors represent an advanced evolution of DP sensors, providing four distinct sub-aperture views in contrast to only two views offered by DP sensors. However, research on QP-based defocus deblurring is scarce. In this paper, we propose a novel end-to-end learning-based approach for defocus deblurring that leverages QP data. To achieve this, we design a QP defocus and all-in-focus image pair acquisition method and provide a QP Defocus Deblurring (QPDD) dataset containing 4,935 image pairs. We then introduce a Local-gate assisted Mamba Network (LMNet), which includes a two-branch encoder and a Simple Fusion Module (SFM) to fully utilize features of sub-aperture views. In particular, our LMNet incorporates a Local-gate assisted Mamba Block (LAMB) that mitigates local pixel forgetting and channel redundancy within Mamba, and effectively captures global and local dependencies. By extending the defocus deblurring task from a DP-based to a QP-based approach, we demonstrate significant improvements in restoring sharp images. Comprehensive experimental evaluations further indicate that our approach outperforms state-of-the-art methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 536, + 135, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 536, + 135, + 548 + ], + "spans": [ + { + "bbox": [ + 56, + 536, + 135, + 548 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 557, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 295, + 629 + ], + "type": "text", + "content": "Defocus blur occurs in scene regions captured outside the camera's depth of field (DoF) [1-3]. Restoring an all-in-focus image from a defocused image is challenging due to the spatially varying point spread functions (PSFs) [6, 20, 38, 40, 46], which are not only scene depth dependent, but also vary based on intrinsic camera parameters [2]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "content": "Recently, researchers have addressed this challenge by developing end-to-end deep neural networks that leverage dual-pixel (DP) data [1-3, 21, 24, 29, 47, 48, 53]. The first DP Defocus Deblurring (DPDD) [1] dataset, captured sequentially with various aperture sizes using a Canon 5D DSLR camera, is widely utilized. Quad-pixel (QP) sensors [28, 39] represent a significant advancement over DP" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 199, + 538, + 393 + ], + "blocks": [ + { + "bbox": [ + 331, + 199, + 538, + 393 + ], + "lines": [ + { + "bbox": [ + 331, + 199, + 538, + 393 + ], + "spans": [ + { + "bbox": [ + 331, + 199, + 538, + 393 + ], + "type": "image", + "image_path": "df0bbb8480e387dca510af644d9edbe112145d763170083d6b6e671eca7bfc0e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": "Figure 1. Characteristics of DP and QP sensors. The light rays from different parts of the main lens fall on each DP unit or QP unit. A DP unit has two photodiodes under a single microlens, producing two sub-aperture views, while a QP unit has four photodiodes, producing four sub-aperture views. Different views of DP or QP data exhibit different PSFs with directional characteristics, leading to disparity between the sub-aperture views. The disparity " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is correlated with the amount of defocus blur " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " [1, 12]: " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "d = \\alpha * b \\approx \\alpha \\frac{Lf}{1 - f / D_f} \\left( \\frac{1}{D_f} - \\frac{1}{D} \\right)" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is a constant of proportionality, " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is the diameter of the aperture, " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is the focal length, " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "D_f" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is the focus distance, and " + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 403, + 555, + 556 + ], + "type": "text", + "content": " is the depth. DP sensors provide disparity in only a single direction, whereas QP sensors can provide disparity in two directions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 580, + 555, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 555, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 555, + 663 + ], + "type": "text", + "content": "sensors and have gained widespread adoption in smartphones due to their superior Phase Detection Auto Focus (PDAF) performance. As indicated in Fig. 1, by utilizing four photodiodes under each microlens instead of two photodiodes, a QP sensor captures more light signal aspects, enhancing disparity detection [44] accuracy and providing more reliable guidance for defocus deblurring." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "However, to the best of our knowledge, research on QP-based defocus deblurring is limited, primarily due to the lack of relevant dataset. Most QP sensors on smartphones have a fixed aperture size, making it difficult to adopt the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5709" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 215 + ], + "type": "text", + "content": "data acquisition method used in DPDD, which involves adjusting the aperture size. In contrast, we adjust the voice coil motors (VCMs) [17] of the QP sensor to change the focus distance, and acquire defocus and all-in-focus image pairs. However, this process induces a zoom-like effect [17]. To overcome this, we use the Enhanced Correlation Coefficient (ECC) [11] alignment algorithm. Furthermore, we propose an open-source QP defocus deblurring (QPDD) dataset. This dataset primarily includes RAW images that are linear with respect to the scene's physical light [4, 23], and also provides sRGB images for the convenience of researchers." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 217, + 295, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 295, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 295, + 396 + ], + "type": "text", + "content": "Modern deep learning models, such as CNNs [1-3, 50, 51] and Transformers [18, 22, 42, 52], have continuously improved state-of-the-art (SOTA) performance. CNNs have efficient parallel convolutions but limited receptive fields. In contrast, Transformers can model long-range dependencies but face quadratic computational complexity. Recently, state space models (SSMs) [13, 14, 36], particularly Mamba [13], have emerged as backbones due to their ability to capture long-range dependencies with linear complexity. Nevertheless, Mamba's recursive image sequence processing tends to cause local pixel forgetting, and the abundance of hidden states in the state space equation can lead to channel redundancy [15, 35, 55]. These factors impede the learning of local context, thereby resulting in poor performance when applying Mamba directly." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 397, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 397, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 397, + 295, + 635 + ], + "type": "text", + "content": "Considering the multi-subaperture view characteristics of QP data and the critical role of efficient global and local dependencies in the defocus deblurring task, we propose the Local-gate assisted Mamba Network (LMNet) with several key components. Our LMNet employs an encoder-decoder architecture with a two-branch encoder that leverages information from different sub-aperture views, and incorporates a Simple Fusion Module (SFM) for effective feature integration from these two branches. Furthermore, instead of solely employing Mamba, we devise an effective Local-gate assisted Mamba Block (LAMB), which includes a parallel Vision State Space Module (VSSM) and Local Gate Module (LGM). By integrating the features from VSSM and LGM using learnable weights, the LAMB enables a more enhanced capture of global and local dependencies. To demonstrate the effectiveness of our LMNet, we first train it on the DPDD dataset, achieving SOTA performance. We then validate the performance of our QP-based deblurring approach and its advantages over DP-based approaches. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 637, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 637, + 295, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 637, + 295, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 637, + 295, + 672 + ], + "type": "text", + "content": "- A QP defocus deblurring (QPDD) dataset, which consists of 4,935 defocus and all-in-focus image pairs, available in both RAW and sRGB formats." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "- A novel network LMNet for defocus deblurring, which fully utilizes information from the sub-aperture views of QP/DP images and enables effective capture of global and" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 72, + 403, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 72, + 403, + 83 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 403, + 83 + ], + "type": "text", + "content": "local dependencies." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 87, + 553, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 87, + 553, + 110 + ], + "spans": [ + { + "bbox": [ + 313, + 87, + 553, + 110 + ], + "type": "text", + "content": "- Extensive experiments evaluate our QP-based deblurring approach and its advantages over the DP-based methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 122, + 400, + 134 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 122, + 400, + 134 + ], + "spans": [ + { + "bbox": [ + 313, + 122, + 400, + 134 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 142, + 429, + 155 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 142, + 429, + 155 + ], + "spans": [ + { + "bbox": [ + 313, + 142, + 429, + 155 + ], + "type": "text", + "content": "2.1. Defocus Deblurring" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 159, + 553, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 553, + 267 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 553, + 267 + ], + "type": "text", + "content": "In learning-based defocus deblurring methods, Abdullah et al. [1] are the first to propose DPDNet for addressing defocus deblurring on DP images, and they also release a defocus deblurring dataset, named DPDD, based on the DP camera. Since then, an increasing number of defocus deblurring studies have been conducted based on this dataset. Existing DP-based defocus deblurring methods fall into two main categories: those that directly process DP data pairs and those that rely on disparity information." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 268, + 553, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 268, + 553, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 553, + 530 + ], + "type": "text", + "content": "For the first category of methods, Abdullah et al. [2] propose the network RDPD with convolutional LSTM units and a synthetic dataset to improve performance. Son et al. [37] propose an effective way to iteratively learn deblur kernels for different feature channels with the shape attention mechanism. Ruan et al. [31] use the DPDD and LFOF datasets and introduce filter dynamic networks. General restoration networks such as MIRNetV2 [49], Restormer [52], GRL [22], and LaKDNet [32] also fit into this category. Moreover, these studies show that two-view inputs outperform single-view inputs in defocus deblurring. For the second category of methods, Liang et al. [24] use the translating disk proposed by Abhijith et al. [30] to estimate a four-layer defocus mask by a four-branch network. Yang et al. [48] estimate defocus disparity only in feature space without explicitly showing a defocus map. Subsequently, Yang et al. [47] propose a new framework that leverages the capabilities of language-image pre-training framework (CLIP) for blur map estimation by designing an image-text format. These methods require additional data or modules to obtain the disparity from DP data to aid in restoring an all-in-focus image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 531, + 553, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 553, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 553, + 591 + ], + "type": "text", + "content": "Our LMNet is specifically designed for both DP and QP defocus deblurring tasks. Unlike the above two categories of methods, we introduce a two-branch encoder and a SFM to effectively integrate information from different sub-aperture views." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 599, + 460, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 460, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 460, + 612 + ], + "type": "text", + "content": "2.2. Visual State Space Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 553, + 713 + ], + "type": "text", + "content": "SSMs [13, 14, 36] have garnered increasing attention from researchers due to their ability to capture long-range dependencies with linear complexity. S4 [14] is the first structured SSM to introduce a diagonal structure and combine it with a diagonal plus low-rank approach. Subsequently, S5 [36] proposes the diagonal SSM approximation and computes recurrently using a parallel scan. Building on these gains, Mamba [13] integrates SSM with the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5710" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "type": "text", + "content": "MLP block of Transformer and introduces a selection scanning mechanism within SSM to filter out irrelevant information for long-sequence modeling. However, the standard Mamba primarily focuses on unidirectional sequential data and cannot handle image data lacking specific directionality. To tackle this challenge, VMamba [25] and Vision Mamba [55] transform arbitrary visual images into ordered sequences and introduce a multiple scanning module that traverses the image space domain to tackle image classification and segmentation. Nevertheless, these multiple scanning Mamba modules still face certain challenges in low-level vision tasks, such as local pixel forgetting and channel redundancy. To address these issues, MambaIR [15], MMA [8], VmambaIR [35], and CU-Mamba [10] introduce the channel attention (CA) mechanism [54] for local modeling. Although the widely used CA mechanism can explore inter-channel relationships, it lacks explicit consideration of spatially-varying contents. In this context, we design an effective LAMB, featuring parallel VSSM and LGM. Unlike previous works that commonly use the CA mechanism, LGM combines CA and spatial attention (SA) [43] mechanisms through gate computation, thereby effectively enhancing local dependencies." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 358, + 201, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 358, + 201, + 372 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 201, + 372 + ], + "type": "text", + "content": "3. QPDD Dataset Collection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 378, + 295, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 295, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 295, + 462 + ], + "type": "text", + "content": "QP sensors have found widespread applications in smartphones [28, 39], and most QP sensors are equipped with fixed aperture size, making it difficult to adopt data acquisition method like DPDD, which involves adjusting the aperture size. In this section, we design an alternative alignment-based approach to generate high-quality defocused and all-in-focus RAW image pairs using a QP sensor." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": "Nearly all smartphone cameras use VCMs to focus [17]. VCMs control the movement of the camera lens, thereby changing the focus distance. As illustrated in Fig. 2a, we use the QP sensor to capture a static planar scene and control the VCMs in fixed steps to obtain a series of RAW images with varying amounts of blur. Then we employ the Contrast Detection Auto Focus (CDAF) algorithm to select the sharpest image as the in-focus target, and the others are considered as defocus images. Figure 2b demonstrates our QP data post-process pipeline. To reduce the impact of noise while maintaining the correlation between disparity and blur, we apply two-pixel averaging both vertically and horizontally within the same color channel to produce four-view images: left (L), right (R), top (T), and bottom (B). Additionally, we apply adjacent four-pixel averaging to produce a reference center (C) view. However, a noticeable zoom-like effect (a kind of misalignment) [17] arises between the defocus C image " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "I_{dc}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": " and the in-focus C image " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "I_{ic}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ". Defocus effects violate the brightness constancy assumption of corresponding points or regions [11], thereby posing significant challenges for alignment methods based on fea" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 550, + 140 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 550, + 140 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 550, + 140 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 550, + 140 + ], + "type": "image", + "image_path": "cb7acc5cbb36e2539e5603f1bf13073fc7e5877a226772a747f65419827db51b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 315, + 152, + 549, + 249 + ], + "blocks": [ + { + "bbox": [ + 388, + 142, + 482, + 152 + ], + "lines": [ + { + "bbox": [ + 388, + 142, + 482, + 152 + ], + "spans": [ + { + "bbox": [ + 388, + 142, + 482, + 152 + ], + "type": "text", + "content": "(a) Capture sequence frames." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 152, + 549, + 249 + ], + "lines": [ + { + "bbox": [ + 315, + 152, + 549, + 249 + ], + "spans": [ + { + "bbox": [ + 315, + 152, + 549, + 249 + ], + "type": "image", + "image_path": "d8946d172ceddc74c624255e7603cb26d36929fb3e9030b658fba9d0d25f1c78.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 250, + 478, + 259 + ], + "lines": [ + { + "bbox": [ + 390, + 250, + 478, + 259 + ], + "spans": [ + { + "bbox": [ + 390, + 250, + 478, + 259 + ], + "type": "text", + "content": "(b) Post-process of frames." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "lines": [ + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "type": "text", + "content": "Figure 2. QPDD dataset generation pipeline: (a) Capture sequence frames with QP sensor. (b) Post-process of frames, we first adopt pixel average to generate five-view images: left (L), right (R), top (T), bottom (B) and center (C), and then utilize ECC alignment to mitigate the zoom-like effect between " + }, + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "type": "inline_equation", + "content": "I_{dc}" + }, + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "type": "inline_equation", + "content": "I_{ic}" + }, + { + "bbox": [ + 313, + 269, + 555, + 324 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "text", + "content": "ture point matching and optical flow. To mitigate the zoom-like effect, we introduce similarity-based ECC [11], which is well-suited for aligning planar defocus and in-focus images. Given " + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "inline_equation", + "content": "I_{dc}" + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "inline_equation", + "content": "I_{ic}" + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "text", + "content": " as inputs, the aligned in-focus C image " + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "inline_equation", + "content": "I_{ac}" + }, + { + "bbox": [ + 313, + 344, + 555, + 405 + ], + "type": "text", + "content": " can be defined as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 363, + 411, + 555, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 411, + 555, + 426 + ], + "spans": [ + { + "bbox": [ + 363, + 411, + 555, + 426 + ], + "type": "interline_equation", + "content": "I _ {a c} = \\operatorname {W a r p} \\left(I _ {i c}, E C C \\left(I _ {d c}, I _ {i c}\\right)\\right). \\tag {1}", + "image_path": "9bf00a926ff033c2d799dfe06c3efce66b270def5c9a98c70d93badf20737f5f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": "The ECC algorithm operates on the mean values of the Gb and Gr channels from both " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "I_{dc}" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "I_{ic}" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " to calculate the affine transformation matrix. This affine transformation matrix is subsequently warped to each color channel of the " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "I_{ic}" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " to obtain a well-aligned, sharp " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "I_{ac}" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": ". Our original defocus five-view images and target image " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "I_{ac}" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " have a resolution of " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "4096 \\times 3072" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " pixels. During alignment, we crop the central regions based on specific scenes, resulting in sizes of " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "2160 \\times 1280" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "1280 \\times 1792" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "inline_equation", + "content": "1080 \\times 1280" + }, + { + "bbox": [ + 313, + 432, + 556, + 540 + ], + "type": "text", + "content": " pixels." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 540, + 556, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 556, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 556, + 660 + ], + "type": "text", + "content": "In summary, our dataset comprises 200 indoor scenes and 4,935 pairs. We divide the dataset into 3,735 pairs training, 600 pairs validation, and 600 pairs testing sets. Furthermore, we provide an additional 100 full-resolution images, both indoor and outdoor with multi-depth, to test generalization performance. Additionally, to obtain training data in sRGB format, we perform Image Signal Processing (ISP) on the L, R, T, B, and C views of defocused images, as well as the target images " + }, + { + "bbox": [ + 313, + 540, + 556, + 660 + ], + "type": "inline_equation", + "content": "I_{ac}" + }, + { + "bbox": [ + 313, + 540, + 556, + 660 + ], + "type": "text", + "content": ". More information about the QPDD dataset can be found in supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 669, + 370, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 370, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 370, + 681 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Our goal is to present an effective method to achieve high-quality defocus deblurring for both QP and DP data. In this" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5711" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 69, + 541, + 201 + ], + "blocks": [ + { + "bbox": [ + 69, + 69, + 541, + 201 + ], + "lines": [ + { + "bbox": [ + 69, + 69, + 541, + 201 + ], + "spans": [ + { + "bbox": [ + 69, + 69, + 541, + 201 + ], + "type": "image", + "image_path": "78ef9b91b7ea380b3bc64f2609ba81f9175a7d87911712e8dd31290809dc6067.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 209, + 555, + 255 + ], + "lines": [ + { + "bbox": [ + 54, + 209, + 555, + 255 + ], + "spans": [ + { + "bbox": [ + 54, + 209, + 555, + 255 + ], + "type": "text", + "content": "Figure 3. The overall network architecture of our LMNet. LMNet consists of a two-branch encoder which is designed to extract deep features from different sub-aperture views. Between the two branches, each level has a SFM (Fig. 4a) to fuse the two-branch features and pass them to the corresponding level in the decoder. To capture effective global and local dependencies in the defocus deblurring task, we propose LAMB (Fig. 4a)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 272, + 282, + 417 + ], + "blocks": [ + { + "bbox": [ + 69, + 272, + 282, + 417 + ], + "lines": [ + { + "bbox": [ + 69, + 272, + 282, + 417 + ], + "spans": [ + { + "bbox": [ + 69, + 272, + 282, + 417 + ], + "type": "image", + "image_path": "5a913ad62c060493a8b2f3d733c5e990afa67fae9ae3eec197d9f87f9bd6ee06.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 142, + 422, + 209, + 430 + ], + "lines": [ + { + "bbox": [ + 142, + 422, + 209, + 430 + ], + "spans": [ + { + "bbox": [ + 142, + 422, + 209, + 430 + ], + "type": "text", + "content": "(a) LAMB and SFM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 63, + 432, + 282, + 485 + ], + "blocks": [ + { + "bbox": [ + 63, + 432, + 282, + 485 + ], + "lines": [ + { + "bbox": [ + 63, + 432, + 282, + 485 + ], + "spans": [ + { + "bbox": [ + 63, + 432, + 282, + 485 + ], + "type": "image", + "image_path": "fd4b480a5dc6a6041aaf384c71360e2dabbb72ef9f7e33d14fb4a9205f91aec6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 63, + 498, + 284, + 561 + ], + "blocks": [ + { + "bbox": [ + 158, + 488, + 194, + 497 + ], + "lines": [ + { + "bbox": [ + 158, + 488, + 194, + 497 + ], + "spans": [ + { + "bbox": [ + 158, + 488, + 194, + 497 + ], + "type": "text", + "content": "(b) VSSM" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 63, + 498, + 284, + 561 + ], + "lines": [ + { + "bbox": [ + 63, + 498, + 284, + 561 + ], + "spans": [ + { + "bbox": [ + 63, + 498, + 284, + 561 + ], + "type": "image", + "image_path": "3281e34f91f390df1b512ff05f69b7b27d7920617e4d10d12062a628e0a53ac5.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 563, + 190, + 573 + ], + "lines": [ + { + "bbox": [ + 160, + 563, + 190, + 573 + ], + "spans": [ + { + "bbox": [ + 160, + 563, + 190, + 573 + ], + "type": "text", + "content": "(c) LGM" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 583, + 297, + 616 + ], + "lines": [ + { + "bbox": [ + 55, + 583, + 297, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 583, + 297, + 616 + ], + "type": "text", + "content": "Figure 4. Details of the network structure: (a)The structures of LAMB and SFM. (b)The structure of VSSM. (c)The structure of LGM." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 712 + ], + "type": "text", + "content": "section, we first outline the overall pipeline of our Local-gate assisted Mamba Network (LMNet), and then we dive into its components by explaining: the Simple Fusion Module (SFM), the Local-gate assisted Mamba Block (LAMB), the Vision State Space Module (VSSM), and the Local Gate Module (LGM)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 274, + 412, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 412, + 288 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 412, + 288 + ], + "type": "text", + "content": "4.1. Overall Pipeline" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": "As shown in Fig. 3, LMNet adopts a three-level encoder-decoder architecture with skip connections. Two branches in the encoder are designed to extract deep features from different views. At each level, a SFM is used to fuse the features from the two branches and pass them to the corresponding level in the decoder. The decoder aims to predict the latent all-in-focus image. To be specific, given an input image " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times n}" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " of one encoder, LMNet firstly applies a " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " convolution to extract low-level features " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "X_0 \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " are the image height, width and channel number, respectively. " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " is the number of feature channels. Next, these shallow features " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " pass through a three-level encoder-decoder and are transformed into deep features " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "X_l \\in \\mathbb{R}^{\\frac{H}{2^{l-1}} \\times \\frac{W}{2^{l-1}} \\times 2^{l-1}M}" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "l \\in \\{1,2,3\\}" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " indicates stage level. Each level of encoder and decoder is composed of " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " LAMBs, where " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "N \\in \\{N_1, N_2, N_3\\}" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": ". At the third level, following the third SFM, there is a feature enhancement module consisting of " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "N_4" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " LAMBs. For feature downsampling and upsampling, we apply pixel-unshuffle and pixel-shuffle operations [34], respectively. Finally, applying a " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": " convolution and adding skip connection from the input center image " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "I_C" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": ", we obtain the sharp image " + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "inline_equation", + "content": "I_S" + }, + { + "bbox": [ + 313, + 292, + 555, + 558 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": "For DP data, the left view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{L}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": " and the right view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{R}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": " are input into the two-branch encoder with shared parameters separately. For QP data, the left view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{L}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": " and the right view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{R}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": " are concatenated, as well as the top view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{T}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": " and the bottom view " + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "inline_equation", + "content": "I_{B}" + }, + { + "bbox": [ + 313, + 558, + 556, + 642 + ], + "type": "text", + "content": ". Each concatenated pair is then fed separately into the two-branch encoder without shared parameters. The entire pipeline can be expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 651, + 553, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 651, + 553, + 664 + ], + "spans": [ + { + "bbox": [ + 321, + 651, + 553, + 664 + ], + "type": "interline_equation", + "content": "I _ {S} = I _ {C} + L M N e t \\left(I _ {L}, I _ {R}\\right), \\tag {2}", + "image_path": "e9dde7f0dfb780f4feb74227ae69e081ca8bbe7fcf106d91aaddcf375fce7537.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 322, + 666, + 553, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 666, + 553, + 680 + ], + "spans": [ + { + "bbox": [ + 322, + 666, + 553, + 680 + ], + "type": "interline_equation", + "content": "I _ {S} = I _ {C} + L M N e t \\left(C A T \\left(I _ {L}, I _ {R}\\right), C A T \\left(I _ {T}, I _ {B}\\right)\\right), \\tag {3}", + "image_path": "45650fb1d2328e2873f57960a07a95b146222e84e0153117acbbf1bc2ba6eb21.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "CAT(\\cdot, \\cdot)" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " indicates concatenation. Equation (2) and Eq. (3) demonstrate the deblurring processes for DP" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5712" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 162, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 162, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 162, + 83 + ], + "type": "text", + "content": "and QP data, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 84, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 84, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 84, + 295, + 108 + ], + "type": "text", + "content": "We optimize the proposed network LMNet with the following loss function [5, 9]:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 117, + 295, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 117, + 295, + 137 + ], + "spans": [ + { + "bbox": [ + 68, + 117, + 295, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sqrt {\\left\\| I _ {S} - I _ {G} \\right\\| ^ {2} + \\epsilon^ {2}} + \\lambda \\| \\mathcal {F} (I _ {S}) - \\mathcal {F} (I _ {G}) \\| _ {1}, \\quad (4)", + "image_path": "61f9a5eb0fdb5fc48760618ef3bde4beb06e1d7269ff1c14b2acda09db976e02.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "inline_equation", + "content": "I_G" + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": " is the ground-truth image, " + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": " is the Fourier transform. We set " + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-3}" + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 55, + 144, + 295, + 168 + ], + "type": "text", + "content": " in the experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 175, + 184, + 187 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 184, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 184, + 187 + ], + "type": "text", + "content": "4.2. Simple Fusion Module" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "spans": [ + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": "The SFM is responsible for fusing the outputs from the two-branch encoder and passing them to the corresponding decoder stage for reconstruction. Depth-wise convolution (DWConv) and point-wise convolution play a crucial role in facilitating interactive information across spatial and channel dimensions [32, 52]. Inspired by these, our SFM also primarily adopts these two types of convolutional layers. As shown in Fig. 4a, given that the outputs of the " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": "-th stage of the two-branch encoder are " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "X_{1}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "X_{2} \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": ", we first concatenate " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "X_{1}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "X_{2}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "X_{3}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": ", and use a " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": " DWConv for effective local features encoding followed by GELU [16] activation function. Then, a residual connection is applied. Finally, a " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": " convolution is employed to aggregate pixel-wise cross-channel context and reduce the channel numbers. The output " + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{\\frac{H}{2^{l - 1}} \\times \\frac{W}{2^{l - 1}} \\times 2^{l - 1}M}" + }, + { + "bbox": [ + 55, + 192, + 296, + 388 + ], + "type": "text", + "content": " of the SFM can be expressed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 397, + 294, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 397, + 294, + 425 + ], + "spans": [ + { + "bbox": [ + 62, + 397, + 294, + 425 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {3} = C A T \\left(X _ {1}, X _ {2}\\right), \\\\ Y = \\operatorname {C o n v} _ {1 \\times 1} (G E L U (D W C o n v _ {7 \\times 7} (X _ {3})) + X _ {3}). \\tag {5} \\\\ \\end{array}", + "image_path": "bc2397ce84b7920a11bd522dcce875b46c110c7a1b3814bfccda910371cdb2fb.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 433, + 235, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 433, + 235, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 433, + 235, + 445 + ], + "type": "text", + "content": "4.3. Local-gate assisted Mamba Block" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "content": "For the defocus deblurring task, both global and local representations are crucial. The motivation behind the LAMB design is to explore Mamba to capture long-range dependencies with linear complexity and to design a LGM to obtain effective local connectivities, thereby reducing local pixel forgetting and channel redundancy of Mamba. As indicated in Fig. 4a, LAMB mainly follows the novel LayerNorm-Attention-LayerNorm-MLP flow [8, 15, 52]. We replace the Attention with a parallel VSSM and LGM structure. Furthermore, the direct fusion of different level features (global and local) inevitably leads to confused and conflicting representations [45]. To this end, we introduce two learnable scale factors " + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\mathbb{R}^M" + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^M" + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "content": " to adaptively integrate global and local representations. Given that the input deep feature of LAMB is " + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "inline_equation", + "content": "X_0 \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "content": ", the output " + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 55, + 450, + 296, + 643 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 71, + 650, + 295, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 650, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 71, + 650, + 295, + 693 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {1} = L N \\left(X _ {0}\\right), \\\\ X _ {2} = X _ {0} + V S S M \\left(X _ {1}\\right) \\cdot \\alpha + L G M \\left(X _ {1}\\right) \\cdot \\beta , \\tag {6} \\\\ Y = X _ {2} + M L P \\left(L N \\left(X _ {2}\\right)\\right), \\\\ \\end{array}", + "image_path": "a15b1e12b5afce43ef2b96713994ab814461f76592ffabb6e1f963b1e1233731.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 701, + 193, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 193, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 193, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 701, + 193, + 713 + ], + "type": "inline_equation", + "content": "LN" + }, + { + "bbox": [ + 55, + 701, + 193, + 713 + ], + "type": "text", + "content": " indicates Layer Norm." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 72, + 463, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 463, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 463, + 85 + ], + "type": "text", + "content": "4.4. Vision State Space Module" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": "The standard Mamba block is designed for the 1-D sequence, which is not suitable for vision tasks requiring spatial-aware understanding [15, 25, 55]. VSSM [55], which uses a ViT-like architecture and incorporates bidirectional Mamba blocks, can efficiently compress visual representations and meet the demands of global representations in defocus deblurring. As illustrated in Fig. 4b, following the reference [55], we first transform the input 2D feature " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_0 \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " into a flattened sequence of non-overlapping patches " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_p \\in \\mathbb{R}^{J \\times (P \\times P \\times M)}" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " is the number of channels, " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " is the number of patches and " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " is the patch size. Then, we linearly project " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_p" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " to a vector of size " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " and add position embeddings " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "E_{pos} \\in \\mathbb{R}^{(J + 1) \\times Z}" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " to obtain the token sequence " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_s" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ". In VSSM, the input token sequence " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_s" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " is first normalized and then linearly projected to the " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_a" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_b" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ". Then, we process the " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_a" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " from the forward and backward directions. For each direction, we apply the 1-D convolution and the SSM to get " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_f" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_b" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ", respectively. The " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_f" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_b" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " are then gated by the " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "X_b" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " followed by SiLU [33] and added together to get the output token sequence " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_s" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ". Finally we transpose the token sequence " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y_s" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": " to 2D feature " + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 313, + 91, + 555, + 355 + ], + "type": "text", + "content": ". This VSSM can be defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 338, + 372, + 553, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 372, + 553, + 462 + ], + "spans": [ + { + "bbox": [ + 338, + 372, + 553, + 462 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {s} = E m b e d d e d P a t c h e s \\left(X _ {0}\\right), \\\\ X _ {a}, X _ {b} = \\operatorname {L i n e a r} \\left(L N \\left(X _ {s}\\right)\\right), \\\\ Y _ {f} = S S M _ {F o r w a r d} \\left(\\operatorname {C o n v 1} d _ {F o r w a r d} \\left(X _ {a}\\right)\\right), \\\\ Y _ {b} = S S M _ {\\text {B a c k w a r d}} \\left(\\operatorname {C o n v 1 d} _ {\\text {B a c k w a r d}} \\left(X _ {a}\\right)\\right), \\tag {7} \\\\ Y _ {s} = \\operatorname {L i n e a r} ^ {T} \\left(Y _ {f} \\odot X _ {b} + Y _ {b} \\odot X _ {b}\\right) + X _ {s}, \\\\ Y = \\operatorname {T r a n s p o s e} \\left(Y _ {s}\\right). \\\\ \\end{array}", + "image_path": "3c18f31818084d28dc2319fcc6f38ddbbfcceaa73228dcd179eeebe0ad371d8a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 478, + 427, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 478, + 427, + 489 + ], + "spans": [ + { + "bbox": [ + 314, + 478, + 427, + 489 + ], + "type": "text", + "content": "4.5. Local Gate Module" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "Current methods [8, 10, 15, 41, 50] often utilize channel attention (CA) [54] and spatial attention (SA) [43] mechanisms to introduce critical locality for improved performance. Drawing inspiration from these approaches, we creatively propose the LGM to learn a comprehensive local context. As shown in Fig. 4c, the input features " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "X_0 \\in \\mathbb{R}^{H \\times W \\times M}" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " are first passed through a " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " convolution to expand the channel dimension to " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "2M" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": ". This is followed by " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " DWConv to encode channel-wise spatial context, and then the features are split into two halves along the channel dimension, obtaining inputs " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "X_1" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "X_2" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " for two branch. In the first branch, CA mechanism is used to exploit the interchannel relationships of the convolutional feature maps. In the second branch, SA mechanism captures the interspatial dependencies. Unlike simple concatenation in [50], the output features from the two branches are further enhanced using a gating mechanism [7]. Finally, the gating features are passed through a " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " convolution to output" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5713" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 277, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 277, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 277, + 85 + ], + "type": "inline_equation", + "content": "Y\\in \\mathbb{R}^{H\\times W\\times M}" + }, + { + "bbox": [ + 55, + 71, + 277, + 85 + ], + "type": "text", + "content": " . The entire LGM can be expressed as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 93, + 294, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 93, + 294, + 110 + ], + "spans": [ + { + "bbox": [ + 63, + 93, + 294, + 110 + ], + "type": "interline_equation", + "content": "X _ {1}, X _ {2} = \\operatorname {C h u n k} \\left(\\operatorname {D W C o n v} _ {3 \\times 3} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(X _ {0}\\right)\\right)\\right), \\tag {8}", + "image_path": "724bd47a4c16b24bf4d74c9dd02eb8a11d91cc4eb95595305231f927c635e6fc.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 109, + 219, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 109, + 219, + 121 + ], + "spans": [ + { + "bbox": [ + 63, + 109, + 219, + 121 + ], + "type": "interline_equation", + "content": "Y = \\operatorname {C o n v} _ {1 \\times 1} (C A (X _ {1}) \\odot S A (X _ {2})),", + "image_path": "26afa0da0d7dc3e207546794801614eb09b2a4014660f9800d187e299dcf383d.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "spans": [ + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "inline_equation", + "content": "Chunk" + }, + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "text", + "content": " represents splitting the features into two halves along the channel dimension and " + }, + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 130, + 295, + 166 + ], + "type": "text", + "content": " denotes the Hadamard product." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 177, + 181, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 177, + 181, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 177, + 181, + 190 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 197, + 296, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 197, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 197, + 296, + 316 + ], + "type": "text", + "content": "In this section, we present the experimental results, structured into three key components for a comprehensive evaluation. Firstly, we evaluate the efficacy of our LMNet by training it on the DPDD dataset and benchmarking its performance against SOTA methods on the associated test set. Next, we train on our proposed QPDD dataset to assess and confirm the feasibility of the QP-based approach, highlighting its advantages over the DP-based method. Finally, we perform ablation studies to further analyze the impact of individual model components." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 324, + 171, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 171, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 171, + 337 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "text", + "content": "Implementation Details. We utilize the AdamW optimizer [27] with momentum " + }, + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 55, + 342, + 296, + 449 + ], + "type": "text", + "content": ", weight decay 1e-4. The learning rate starts from 1e-4 and gradually approaches 1e-7 using the cosine annealing strategy [26]. We follow a similar training strategy as proposed in [52] where the patch size progressively increases [128, 160, 192, 256, 320, 384] and the batch size decreases [18, 12, 8, 4, 2, 2] at iterations [90k, 150k, 210k, 270k, 330k, 390k]. More training details are provided in the supplementary material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "text", + "content": "Evaluation Metrics. We utilize Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Mean Absolute Error (MAE) as our evaluation metrics. We also provide the number of parameters and FLOPs with image size at " + }, + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "inline_equation", + "content": "1120 \\times 1680" + }, + { + "bbox": [ + 55, + 449, + 296, + 509 + ], + "type": "text", + "content": " for researchers' reference." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 517, + 241, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 241, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 241, + 529 + ], + "type": "text", + "content": "5.2. Comparisons with State-of-the-Art" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "content": "Defocus Deblurring on DPDD. We first provide defocus deblurring results on the DPDD [1] dataset. The comparisons among different methods are shown in Tab. 1 and Fig. 5. The metrics for UFormer [42], BaMBNet [24], K3DN [48], and LDP [47] are derived from their respective published papers, while the metrics and qualitative results for the other methods are obtained from the authors' official implementations. Table 1 presents the quantitative comparisons on the DPDD dataset and shows that our proposed method substantially outperforms existing baseline methods. For instance, compared with the Transformer-based method Restormer [52] and the large kernel-based method LaKDNet [32], our method achieves a significant performance boost of " + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "inline_equation", + "content": "0.59\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "inline_equation", + "content": "0.36\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "content": ", respectively, while maintaining only " + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "inline_equation", + "content": "69.58\\%" + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "inline_equation", + "content": "47.32\\%" + }, + { + "bbox": [ + 55, + 533, + 295, + 713 + ], + "type": "text", + "content": " of the parameters." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 216 + ], + "type": "text", + "content": "Compared with the disparity-based approach K3DN [48], our method outperforms by 0.19 dB. To the best of our knowledge, LDP [47] is the first to innovatively introduce the language-image pre-training framework (CLIP) for defocus deblurring and achieve excellent results. Notably, our model achieves a 0.01 dB improvement in PSNR and a 0.005 improvement in SSIM using only 18.18M parameters, whereas LDP uses 19.60M parameters and relies on CLIP with 88M parameters. Figure 5 shows the corresponding qualitative results. It is noticeable that our method effectively removes spatially varying defocus blur, producing sharper images compared to publicly available approaches." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "text", + "content": "Defocus Deblurring on QPDD. For the QPDD dataset, we evaluate the defocus deblurring performance using both two-view (L/R) and four-view (L/R and T/B) inputs on the RAW format dataset with our LMNet. The two-view (L/R) inputs are similar to those used in DP data. Since there is a lack of publicly available open-source code for K3DN [48] and LDP [47], we select six other classic defocus deblurring methods, DPDNet [1], UFormer [42], MIRNetV2 [49], DRBNet [31], Restormer [52] and LaKDNet [32], as references. We retrain these six methods using the sRGB images in the QPDD dataset following their own setups, and provide our training results on sRGB as a reference. Our metric evaluation is conducted in the sRGB format. Table 2 indicates that, within the LMNet framework, four-view inputs enhance PSNR by " + }, + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "inline_equation", + "content": "0.27\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "text", + "content": " for RAW and " + }, + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "inline_equation", + "content": "0.39\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 217, + 555, + 540 + ], + "type": "text", + "content": " for sRGB, compared to two-view inputs. When the inputs are limited to two views, our LMNet substantially outperforms SOTA methods Restormer [52] and LaKDNet [32]. Figure 6 further shows that our QP-based method is more effective than DP-based methods qualitatively, particularly in handling texture details (see the first and second rows of Fig. 6). This is attributed to the robustness of four-view disparity estimation, which is correlated to the amount of defocus blur. Notably, despite the QPDD dataset primarily consisting of indoor planar data, our approach exhibits robust performance in multi-depth and outdoor scenarios (see the third and fourth rows of Fig. 6)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 550, + 408, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 408, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 408, + 562 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 568, + 553, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 553, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 553, + 590 + ], + "type": "text", + "content": "We perform ablations on different components of our LMNet on the DPDD dataset." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "text", + "content": "Effect of Two-branch Encoder. We adopt a two-branch encoder with shared weights to separately extract information from different views. As shown in Tab. 3, compared to a single encoder architecture, the two-branch encoder approach only increases the parameter count by " + }, + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "inline_equation", + "content": "0.29\\mathrm{M}" + }, + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "text", + "content": " and achieves a " + }, + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "inline_equation", + "content": "0.29\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 593, + 553, + 664 + ], + "type": "text", + "content": " improvement in PSNR." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Effect of SFM. In this paper, we propose a two-branch encoder with SFM. Compared to a simple add operation between the two-branch encoder, SFM adds only 0.29M parameters and achieves a 0.15 dB PSNR improvement." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5714" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 541, + 222 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 541, + 222 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 541, + 222 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 541, + 222 + ], + "type": "table", + "html": "
MethodIndoor ScenesOutdoor ScenesCombinedParams (M)FLOPs (G)
PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓PSNR ↑SSIM ↑MAE ↓
DPDNet [1]27.480.8490.02922.900.7260.05225.130.7860.04131.033150
RDPD [2]28.100.8430.02722.820.7040.05325.390.7720.04024.28901
UFormer [42]28.230.8600.02623.100.7280.05125.650.7950.03950.882482
IFAN [19]28.660.8680.02523.460.7430.04925.990.8040.03710.48794
MIRNetV2 [49]28.960.8810.02423.590.7530.04926.200.8160.0375.864045
DRBNet [31]29.060.8730.02423.730.7520.04826.330.8110.03611.691273
BaMBNet [24]28.600.8720.02624.300.7720.04526.400.8210.0364.501804
Restormer [52]29.480.8950.02323.970.7730.04726.660.8330.03526.134458
LaKDNet [32]29.680.8890.02324.230.7770.04626.890.8320.03538.425168
K3DN [48]29.870.8900.02224.370.7800.04627.060.8350.03415.903352
LDP [47]29.880.8960.02024.730.7860.03727.240.8400.02819.60-
Ours30.080.8980.02224.570.7950.04427.250.8450.03318.183227
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Qualitative comparisons on the DPDD dataset. Our LMNet effectively removes defocus blur and restores more details." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 334, + 261, + 386, + 399 + ], + "blocks": [ + { + "bbox": [ + 334, + 261, + 386, + 399 + ], + "lines": [ + { + "bbox": [ + 334, + 261, + 386, + 399 + ], + "spans": [ + { + "bbox": [ + 334, + 261, + 386, + 399 + ], + "type": "image", + "image_path": "a8780e7de99bde640da29bb3a83ec05315eb6e6407907bf1b6831f14493c8dde.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 403, + 384, + 412 + ], + "lines": [ + { + "bbox": [ + 337, + 403, + 384, + 412 + ], + "spans": [ + { + "bbox": [ + 337, + 403, + 384, + 412 + ], + "type": "text", + "content": "Restormer[52]" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 389, + 261, + 440, + 399 + ], + "blocks": [ + { + "bbox": [ + 389, + 261, + 440, + 399 + ], + "lines": [ + { + "bbox": [ + 389, + 261, + 440, + 399 + ], + "spans": [ + { + "bbox": [ + 389, + 261, + 440, + 399 + ], + "type": "image", + "image_path": "6fc1f39fbd19644f44f136d90fb105f88e00b746bfe0dacf86afaf6d26674b15.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 403, + 439, + 412 + ], + "lines": [ + { + "bbox": [ + 392, + 403, + 439, + 412 + ], + "spans": [ + { + "bbox": [ + 392, + 403, + 439, + 412 + ], + "type": "text", + "content": "LaKDNet[32]" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 443, + 261, + 496, + 399 + ], + "blocks": [ + { + "bbox": [ + 443, + 261, + 496, + 399 + ], + "lines": [ + { + "bbox": [ + 443, + 261, + 496, + 399 + ], + "spans": [ + { + "bbox": [ + 443, + 261, + 496, + 399 + ], + "type": "image", + "image_path": "937b333963b7ed405280b1563fd49b049765ab2288869cad093c0715d8e7469f.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 462, + 403, + 481, + 411 + ], + "lines": [ + { + "bbox": [ + 462, + 403, + 481, + 411 + ], + "spans": [ + { + "bbox": [ + 462, + 403, + 481, + 411 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 500, + 261, + 552, + 399 + ], + "blocks": [ + { + "bbox": [ + 500, + 261, + 552, + 399 + ], + "lines": [ + { + "bbox": [ + 500, + 261, + 552, + 399 + ], + "spans": [ + { + "bbox": [ + 500, + 261, + 552, + 399 + ], + "type": "image", + "image_path": "fed19e4b9c81d95d6b303dc643ada9eb32d3925a3afb2673d7fef92dbfccc535.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 506, + 403, + 548, + 413 + ], + "lines": [ + { + "bbox": [ + 506, + 403, + 548, + 413 + ], + "spans": [ + { + "bbox": [ + 506, + 403, + 548, + 413 + ], + "type": "text", + "content": "Sharp Image" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 58, + 451, + 294, + 559 + ], + "blocks": [ + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on the DPDD dataset. All the networks use DP images as input. The best and second best results are highlighted and underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 451, + 294, + 559 + ], + "lines": [ + { + "bbox": [ + 58, + 451, + 294, + 559 + ], + "spans": [ + { + "bbox": [ + 58, + 451, + 294, + 559 + ], + "type": "table", + "html": "
MethodPSNR ↑SSIM ↑MAE ↓Params (M)FLOPs (G)
DPDNetD [1]33.240.8980.014331.033150
UFormerD [42]33.630.9000.013250.882482
MIRNetV2D [49]33.860.9050.01355.864045
DRBNetD [31]34.180.9070.012911.691273
RestormerD [52]34.360.9180.012426.134458
LaKDNetD [32]34.640.9240.012138.425168
OursD (sRGB)36.250.9160.010918.183227
OursQ (sRGB)36.640.9200.010423.863231
OursD36.480.9260.010218.183221
OursQ36.750.9280.009923.863224
", + "image_path": "eab5da307bb31cca2188777cc604c145305066f0e5963c85a639236aa67bc2e2.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 58, + 613, + 294, + 658 + ], + "blocks": [ + { + "bbox": [ + 55, + 567, + 295, + 601 + ], + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 601 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on the QPDD dataset. Suffix D indicates two-view (L/R) inputs, and suffix Q indicates four-view (L/R and T/B) inputs." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 613, + 294, + 658 + ], + "lines": [ + { + "bbox": [ + 58, + 613, + 294, + 658 + ], + "spans": [ + { + "bbox": [ + 58, + 613, + 294, + 658 + ], + "type": "table", + "html": "
Encoder ModePSNR ↑SSIM ↑MAE ↓Params (M)
single26.960.8400.03517.89
two-branch27.250.8450.03318.18
", + "image_path": "8c5fb9d437920aee3e4214b8b0b24d65a331a3e866c93a10ef724f0e59df8579.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 67, + 666, + 283, + 677 + ], + "lines": [ + { + "bbox": [ + 67, + 666, + 283, + 677 + ], + "spans": [ + { + "bbox": [ + 67, + 666, + 283, + 677 + ], + "type": "text", + "content": "Table 3. Ablation experiments for different encoder modes." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 453, + 555, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 633 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 633 + ], + "type": "text", + "content": "Effect of LAMB. As the core component, the LAMB can improve VSSM with LGM. In this section, we ablate different components of the LAMB. The results, presented in Tab. 4, indicate that (a) directly using the VSSM is not good enough since it lacks local connectivity. (b) and (c) show that using only the channel attention block (CAB) [8] or LGM does not yield satisfactory performance because they lack global dependencies. However, LGM outperforms the CAB, achieving a " + }, + { + "bbox": [ + 313, + 453, + 555, + 633 + ], + "type": "inline_equation", + "content": "0.03\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 453, + 555, + 633 + ], + "type": "text", + "content": " improvement in PSNR. (d) shows that combining VSSM and CAB significantly improves performance. (e) further boosts the PSNR to 27.25 dB when LGM replaces CAB. The above experiments show that both global and local representations are crucial for defocus deblurring and validate the effectiveness of our proposed LAMB." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": "What's more, we visualize the fourth encoder feature maps of the main modules: VSSM, LGM, and the overall LAMB, as shown in Fig. 7. For input images with varying degrees of blur, the VSSM module, benefiting from long-range dependencies, pays more attention to regions with higher blur levels, while the LGM demonstrates its po" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5715" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 126, + 277 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 126, + 277 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 126, + 277 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 126, + 277 + ], + "type": "image", + "image_path": "15a16581e967515f6c1961f9e60211edcaceab83950b5e69bed8e0dd690f035d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 279, + 101, + 289 + ], + "lines": [ + { + "bbox": [ + 83, + 279, + 101, + 289 + ], + "spans": [ + { + "bbox": [ + 83, + 279, + 101, + 289 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 127, + 70, + 197, + 277 + ], + "blocks": [ + { + "bbox": [ + 127, + 70, + 197, + 277 + ], + "lines": [ + { + "bbox": [ + 127, + 70, + 197, + 277 + ], + "spans": [ + { + "bbox": [ + 127, + 70, + 197, + 277 + ], + "type": "image", + "image_path": "ab018eaff40c4f16866329ba7f4fa313938f42e2e12bdfc9324e673d85f7e984.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 139, + 279, + 187, + 289 + ], + "lines": [ + { + "bbox": [ + 139, + 279, + 187, + 289 + ], + "spans": [ + { + "bbox": [ + 139, + 279, + 187, + 289 + ], + "type": "text", + "content": "Blurred Image" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 198, + 70, + 268, + 277 + ], + "blocks": [ + { + "bbox": [ + 198, + 70, + 268, + 277 + ], + "lines": [ + { + "bbox": [ + 198, + 70, + 268, + 277 + ], + "spans": [ + { + "bbox": [ + 198, + 70, + 268, + 277 + ], + "type": "image", + "image_path": "e2114bd3a71221f539a756d6b3195b58b0ae869e765ef9f7db95f4172d4d7417.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 207, + 279, + 261, + 289 + ], + "lines": [ + { + "bbox": [ + 207, + 279, + 261, + 289 + ], + "spans": [ + { + "bbox": [ + 207, + 279, + 261, + 289 + ], + "type": "inline_equation", + "content": "\\mathrm{Restormer}_D[52]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 269, + 70, + 339, + 277 + ], + "blocks": [ + { + "bbox": [ + 269, + 70, + 339, + 277 + ], + "lines": [ + { + "bbox": [ + 269, + 70, + 339, + 277 + ], + "spans": [ + { + "bbox": [ + 269, + 70, + 339, + 277 + ], + "type": "image", + "image_path": "6346849abf7637dba0127ab371f47bc940f2a5d212d83f73b7254a2e323adecf.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 279, + 279, + 331, + 289 + ], + "lines": [ + { + "bbox": [ + 279, + 279, + 331, + 289 + ], + "spans": [ + { + "bbox": [ + 279, + 279, + 331, + 289 + ], + "type": "text", + "content": "LaKDNetD[32]" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 340, + 70, + 410, + 277 + ], + "blocks": [ + { + "bbox": [ + 340, + 70, + 410, + 277 + ], + "lines": [ + { + "bbox": [ + 340, + 70, + 410, + 277 + ], + "spans": [ + { + "bbox": [ + 340, + 70, + 410, + 277 + ], + "type": "image", + "image_path": "63d69edbc9db266e37e3e4121430350155d4f89afe876103b57bd100bfe5ac5d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 364, + 279, + 388, + 289 + ], + "lines": [ + { + "bbox": [ + 364, + 279, + 388, + 289 + ], + "spans": [ + { + "bbox": [ + 364, + 279, + 388, + 289 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 298, + 555, + 331 + ], + "lines": [ + { + "bbox": [ + 55, + 298, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 298, + 555, + 331 + ], + "type": "text", + "content": "Figure 6. Qualitative comparisons on the QPDD dataset. The suffix D indicates two-view (L/R) inputs, and the suffix Q indicates four-view (L/R and T/B) inputs. The test images in the first and second rows are planar indoor test scenes, while the third and fourth rows are multi-depth test scenes." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 410, + 70, + 481, + 277 + ], + "blocks": [ + { + "bbox": [ + 410, + 70, + 481, + 277 + ], + "lines": [ + { + "bbox": [ + 410, + 70, + 481, + 277 + ], + "spans": [ + { + "bbox": [ + 410, + 70, + 481, + 277 + ], + "type": "image", + "image_path": "ed556171dcc042dbe66d29246b7453b5a58de0e76af1f133b1c108797d1232e2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 279, + 459, + 289 + ], + "lines": [ + { + "bbox": [ + 435, + 279, + 459, + 289 + ], + "spans": [ + { + "bbox": [ + 435, + 279, + 459, + 289 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 482, + 70, + 552, + 277 + ], + "blocks": [ + { + "bbox": [ + 482, + 70, + 552, + 277 + ], + "lines": [ + { + "bbox": [ + 482, + 70, + 552, + 277 + ], + "spans": [ + { + "bbox": [ + 482, + 70, + 552, + 277 + ], + "type": "image", + "image_path": "5a0cab1e96a552fb5a7ea63b6bcbcb58723efcce1effefd6874b0188539e0e47.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 497, + 279, + 539, + 289 + ], + "lines": [ + { + "bbox": [ + 497, + 279, + 539, + 289 + ], + "spans": [ + { + "bbox": [ + 497, + 279, + 539, + 289 + ], + "type": "text", + "content": "Sharp Image" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 353, + 295, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 353, + 295, + 400 + ], + "spans": [ + { + "bbox": [ + 55, + 353, + 295, + 400 + ], + "type": "text", + "content": "tential in restoring details. The weighted combination of VSSM and LGM forms the final LAMB, which further distinguishes between blurred and detailed regions, guiding the decoder for deblurring." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 401, + 296, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 296, + 485 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 296, + 485 + ], + "type": "text", + "content": "Generalization Ability. To evaluate generalization, Restormer [52], LaKDNet [32], and our LMNet are trained on the DPDD dataset and tested on the QPDD dataset using two-view sRGB data as inputs. The weights of Restormer and LaKDNet are obtained from the authors' official implementations. Table 5 shows that our LMNet has better generalization ability compared to Restormer and LaKDNet." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 58, + 495, + 294, + 571 + ], + "blocks": [ + { + "bbox": [ + 58, + 495, + 294, + 571 + ], + "lines": [ + { + "bbox": [ + 58, + 495, + 294, + 571 + ], + "spans": [ + { + "bbox": [ + 58, + 495, + 294, + 571 + ], + "type": "table", + "html": "
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VSSMCABLGM
(a)√26.770.8360.03515.33
(b)√26.760.8340.03613.84
(c)√26.790.8330.03511.36
(d)√√26.950.8390.03519.30
(e)√√27.250.8450.03318.18
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MethodPSNR ↑SSIM ↑MAE ↓Params (M)
Restormer [52]29.530.8500.028226.13
LaKDNet [32]29.530.7760.026138.42
Ours30.370.8460.024718.18
", + "image_path": "7178d1b963320df28c47fe603071719a1798d96361fd633ea7d50271e113ef3b.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "table_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 348, + 414, + 520, + 425 + ], + "lines": [ + { + "bbox": [ + 348, + 414, + 520, + 425 + ], + "spans": [ + { + "bbox": [ + 348, + 414, + 520, + 425 + ], + "type": "text", + "content": "Table 5. Experiments for model generalization." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 314, + 460, + 388, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 460, + 388, + 472 + ], + "spans": [ + { + "bbox": [ + 314, + 460, + 388, + 472 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 487, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 555, + 617 + ], + "type": "text", + "content": "In this paper, we present a comprehensive solution for defocus deblurring based on QP data, encompassing both a novel dataset and a SOTA model. Notably, our LMNet achieves excellent performance on both the DPDD dataset and our proposed QPDD dataset. Considering the multisubaperture view characteristics of QP data, we design a two-branch encoder architecture with SFM for feature fusion. Additionally, we introduce a LAMB to mitigate local pixel forgetting and channel redundancy within Mamba. Extensive comparisons and ablation studies demonstrate the effectiveness of our method." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 624, + 556, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 556, + 703 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 556, + 703 + ], + "type": "text", + "content": "Limitations and future work. Although we have proposed a new QPDD dataset, it mainly consists of planar indoor scenes. We will continue to collect more diverse QPDD data, particularly datasets that span a wider range of DoF scenarios. Additionally, we will design a less computationally complex network for mobile devices or embedded systems, while maintaining performance." + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5716" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 124 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 124 + ], + "type": "text", + "content": "[1] Abdullah Abuolaim and Michael S. Brown. Defocus deblurring using dual-pixel data. In European Conference on Computer Vision, pages 111-126. Springer, 2020. 1, 2, 6, 7" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 125, + 295, + 179 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 125, + 295, + 179 + ], + "spans": [ + { + "bbox": [ + 61, + 125, + 295, + 179 + ], + "type": "text", + "content": "[2] Abdullah Abuolaim, Mauricio Delbracio, Damien Kelly, Michael S Brown, and Peyman Milanfar. Learning to reduce defocus blur by realistically modeling dual-pixel data. 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We present Quaffure, a real-time quasi-static neural hair simulator, which produces naturally draped hair in only a few milliseconds on commodity hardware, taking the hairstyle, body shape and pose into account. Our method scales to predicting the drape of 1000 hair grooms in just 0.3 seconds. Quaffure is trained using a physics-based self-supervised loss, eliminating the need for simulated training data that is costly and cumbersome to obtain. We show that our method works for a wide variety of body shapes and poses with a range of hairstyles varying from straight to curly, short to long." + ], + "image_footnote": [], + "bbox": [ + 119, + 260, + 869, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 633, + 326, + 647 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Realistic hair motion is crucial for high-quality avatars, but it is often limited by the computational resources available for real-time applications. To address this challenge, we propose a novel neural approach to predict physically plausible hair deformations that generalizes to various body poses, shapes, and hairstyles. Our model is trained using a self-supervised loss, eliminating the need for expensive data generation and storage. We demonstrate our method's effectiveness through numerous results across a wide range of pose and shape variations, showcasing its robust generalization capabilities and temporally smooth results. Our approach is highly suitable for real-time applications with an inference time of only a few milliseconds on consumer hardware and its ability to scale to predicting the drape of 1000 grooms in 0.3 seconds.", + "bbox": [ + 88, + 667, + 485, + 893 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 633, + 643, + 647 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hair is a crucial aspect of realistic avatars, playing a vital role in real-time applications such as games and telepresence, as well as offline generation of digital characters for film. Over the past decades, computer graphics research has devoted significant attention to the topic of hair, in order to create believable and engaging virtual characters. Hair modeling is a complex process that involves multiple stages, including grooming, simulation, and rendering. Previous research has explored various approaches to hair motion modeling, including physics-based simulations [7, 15, 43] and data-driven methods [11, 39, 40]. However, hair remains a challenging phenomenon to model due to the high number of degrees of freedom required to represent a full head of hair, which typically consists of hundreds of thousands of strands. To make hair motion modeling more tractable, it is common practice to model a full groom with a", + "bbox": [ + 511, + 659, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "239", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "limited number of strands, often referred to as guide strands. This approach involves modeling a subset of strands to represent the full groom, and then recovering the full resolution hair groom from these guide strands for rendering [13].", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Simulating the dynamics of hair motions has received significant attention in the field. Several approaches have been developed to model the behavior of hair strands ranging from efficient mass-spring systems [33] to rod models [2, 21, 38] able to model bending and twisting, producing complex coiling motions to volumetric approaches [1, 26, 29]. Despite impressive visual results, these models still require large computational resources making them ill-suited for real-time applications. Many advances in the field of physics-based simulation has resulted in efficient algorithms that are able to exploit parallelism of GPU hardware, resulting in real-time simulations [5, 25, 27]. However, these still require dedicated hardware resources [7, 43] and compute time might vary based on the resolution and number of the hair strands as well as the number of collisions occurring in the scene. Additionally, physics-based simulation can often be unstable and require significant parameter tuning, often leading to unpredictable or undesirable results. To address this, subspace simulation has been applied to hair dynamics but this remains limited to models that overfit to a single groom only [6]. Learned simulators [24, 51] have shown promise for modeling real-time hair dynamics but require large data sets, which are cumbersome to obtain. In general, supervised learning requires training data, which needs to be generated using physics-based simulation. This is both expensive in terms of time and storage required but also requires expert knowledge and access to specialized tools to produce. There is no publicly available data set that could be leveraged.", + "bbox": [ + 91, + 154, + 485, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel and efficient neural hair simulation approach to model hair quasi-statics. Our method leverages a learning-based method to predict physically plausible hair deformations, while also generalizing to various body poses and shapes. We opted for training in a self-supervised manner, eliminating the need for expensive data generation and storage. Our approach achieves an inference performance of just a few milliseconds on standard consumer hardware, without requiring elaborate code optimizations or specialized hardware features. In contrast to physics-based simulation methods, the inference time of our approach is fixed and is independent of the number of strands in the groom or number of collisions in the scene. Our results are stable and the method scales to predicting hundreds of groom simultaneously at interactive rates. In summary, our contributions are", + "bbox": [ + 89, + 595, + 482, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- A hair decomposition strategy consisting of a hair pose module and a learned corrector, which enables the use of an efficient neural decoder able to produce quasi-static hair results in milliseconds and scales to running a thou", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sand grooms at interactive rates.", + "bbox": [ + 527, + 92, + 743, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We are the first to propose a self-supervised learning approach for hair that completely eliminates the necessity of computing and storing large amounts training data, which would require expert knowledge and access to specialized tools to produce.", + "- A modified formulation of the Cosserat energy for modeling hair. Our formulation is efficient in its evaluation and we demonstrate that it is well-suited for neural network training. Our proposed model is able to preserve hair strand shape for a wide range of hairstyles including very curly hair.", + "- We demonstrate how a single trained network efficiently models different hairstyles, generalizing to body poses and shapes." + ], + "bbox": [ + 511, + 106, + 903, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 513, + 330, + 651, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Strand-based Hair Reconstruction. In recent years there has been significant progress in hair reconstruction research. Recovering hair strands has been especially sought after, since hair reconstructed as strands can easily be integrated into existing game engines, to be animated and rendered with physics-based simulation and rendering. Neural Strands [31] represent the hair groom as a neural texture on the head scalp, where each texel feature can be decoded into an explicit strand. This representation was later trained on a dataset of synthetic grooms, to provide prior for strand-based hair fitting to multi-view images [36]. Zhou et al. [52] proposes a prior-free reconstruction approach. It was extended to support text-guided hair generation in HAAR [37]. The fitting quality was further improved in [23, 45, 48] by additionally decoding Gaussian splats [18] along the strands, representing hair appearance. Instead of requiring multi-view capture, several works explored strand-based hair reconstruction from a dynamic monocular video [46] or just a single image [44, 50], where volumetric 3D hair orientations were used to model hair geometry. To achieve the highest reconstruction quality, Shen et al. [35] captured volumetric CT scans to reconstruct strand-based grooms.", + "bbox": [ + 511, + 356, + 906, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based Hair Models. To either accelerate or improve the realism of physics-based simulation or rendering methods, many learning-based hair models have been introduced. Wang et al. [40] use a hybrid representation, with volumetric primitives aligned along guide strands to model hair appearance under motion. To simplify fitting to real observations, Wang et al. [39] used a mixture of volumetric primitives that jointly represent hair geometry and appearance. A unified latent representation for diverse hairstyles has been explored in [12, 51], where explicit strand geometry is encoded into a latent space using a variational autoencoder (VAE) [51] or a generative adversarial network (GAN) [12], enabling hair generation and interpolation across hairstyles. To accelerate hair simulation, Guan", + "bbox": [ + 511, + 689, + 908, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "240", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e4e8b800fa9fb3b13c9e1441e5668b1904cfb07dd113cae244ae3333450f975a.jpg", + "image_caption": [ + "Figure 2. Quaffure Overview: Our method takes a code as input, consisting of a latent code for the rest hair shape, body shape parameters, and full skeleton pose. The output is naturally draped hair produced as the sum of posed hair given the body pose and shape parameters, combined with learned corrections which are produced by the groom deformation decoder. We train our method in two stages: i) an autoencoder is trained on all hairstyles to obtain a groom latent code, and ii) the groom deformation decoder is trained in a physics-based self-supervised fashion. The hair strands are encoded in a 2D texture representation (left) where strands are encoded in the pixel in which the root particle is located. The figure shows how the 3D scalp geometry (bottom) is mapped to a high dimensional 2D texture map (top)." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 897, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "et al. [11] proposed a multi-linear model for representing hair dynamics, and Lyu et al. [24] introduced a neural upsampler to efficiently convert a low number of guide strands into dense hair.", + "bbox": [ + 88, + 349, + 480, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Physics-based Hair Models. Realistic hair simulation [41, 42] has been an active area of research in computer graphics for decades. To achieve high-fidelity results, it is necessary to simulate every individual strand and their interactions with each other. Common elastic models used for strand-based hair include mass-spring models [33] and elastic rods [2, 21, 38]. In addition, complex hair-hair interactions such as self-collision [26] and friction forces [17] are also important for realistic behavior. Several reduced models have been developed to lower the computational budget for real-time hair simulation. One idea is to simulate the hair as layered elastic bodies [4, 47], while another suggests representing a group of hairs as strips [19, 20]. The most popular approach is to simulate a subset of the overall hair as guide strands and interpolate between the guides for individual strand detail [6, 13]. Hu et al. [14] propose a method to automatically determine simulation parameters from video footage.", + "bbox": [ + 93, + 412, + 482, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Physics-based Self-supervised Learning. Data-driven methods have been successful in the field of simulation [9, 30, 49]. However, data-driven methods do not ensure that the simulated system adheres to physical constraints, which can result in non-physical states. To address this, researchers have proposed incorporating physics energy loss directly into the training process to eliminate the need for generating large amounts of data and to enable better generalization. Physics-based self-supervised methods have shown promise in learning a reduced latent space for quasi-static states of rigid motion [34] and cloth drapes [8], which has been expanded to dynamic motions of cloth [3, 10, 16, 32]. However, there is limited research on hair simulation. The neural simulator of GroomGen [51]", + "bbox": [ + 89, + 689, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "only demonstrated hair deformation for varying gravity directions, while our method is the first to apply a physics-supervised method for hair that generalizes to full motions and incorporates collision under different poses and body shapes.", + "bbox": [ + 511, + 349, + 906, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 511, + 436, + 648, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach shown in Figure 2, enables real-time estimation of posed quasi-static hair $\\mathbf{x}_{\\mathrm{hair}}$ based on hairstyle, body shape and pose. We achieve this by splitting the problem at hand in two parts. First, a simple and efficient groom transformation model transforms the hair groom rigidly with body pose and shape variations expressed as $\\mathbf{x}_{\\mathrm{posed}}$ . Second, to model the groom specific pose and shape dependent variations $\\mathbf{x}_{\\mathrm{deformation}}$ , we train a network to produce deformation fields, which when added to the posed hair, result in a physically plausible quasi-static drape that takes physical effects such as gravity and collisions into account. The final hair drape is simply obtained as $\\mathbf{x}_{\\mathrm{hair}} = \\mathbf{x}_{\\mathrm{posed}} + \\mathbf{x}_{\\mathrm{deformation}}$ .", + "bbox": [ + 511, + 462, + 908, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Representation", + "text_level": 1, + "bbox": [ + 511, + 651, + 666, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We encode all hair geometry into a texture based representation based on the UV map of the scalp geometry as shown in the left of Figure 2. Where a hair strand root particle falls into a pixel in the map, we encode a high dimensional feature, which represents the strand geometry. For a texture with height and width $T$ and a groom with $N$ vertices per strand, the encoding is of dimension $\\mathbb{R}^{T\\times T\\times N\\times 3}$ .", + "bbox": [ + 511, + 674, + 906, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Body Model: Our body model consists of body geometry rigged with a skeleton model, which enables the body geometry to change pose using linear blend skinning. The skeleton pose is represented using a set of pose parameters $\\theta \\in \\mathbb{R}^{81}$ . To model variations in body shape, we leverage a statistical body model. This model has been constructed from a large data set of human body scans, to which our body geometry has been registered. Body shape variations", + "bbox": [ + 511, + 780, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "241", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/408364c7d6dd40cd3212852b7a790691224bd851140480cbf1cda69674453424.jpg", + "image_caption": [ + "Figure 3. Pose & Shape-based Deformations: Example of posed groom (top) which accounts for rigid rotations and translations of the rest shape only and the combined posed groom with learned deformations (bottom), which accounts for physical effects such as strand material model, gravity and collisions. Despite body intersections incurred by the rigid transformation applied by the groom transformation module, our proposed network resolves all collisions with the body after applying the learned deformations (bottom). Note the significant change resulting in a natural drape." + ], + "image_footnote": [], + "bbox": [ + 93, + 89, + 483, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are modeled as variations on top of an average shape and are parameterized using body shape coefficients $\\beta \\in \\mathbb{R}^{10}$ .", + "bbox": [ + 89, + 421, + 483, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Groom Autoencoder", + "text_level": 1, + "bbox": [ + 89, + 468, + 284, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leverage an autoencoder to obtain a compact representation for all the different grooms in their rest shape. This model is trained separately and produces compact latent codes in $\\mathbb{R}^{16}$ to distinguish different hairstyles. The autoencoder input and output are grooms encoded on the scalp as high dimensional texture maps. The autoencoder structure is made up of 2D convolutional down and up sampling layers for the encoder and decoder respectively. Once the groom autoencoder is fully-trained, we discard its decoder since we are only interested in the latent groom codes produced by the encoder. The weights of the encoder are frozen for the follow-up training of the groom deformation decoder discussed in Section 3.4.", + "bbox": [ + 89, + 494, + 483, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pose-based Groom Transformation", + "text_level": 1, + "bbox": [ + 89, + 708, + 395, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our pose-based transformation module rigidly transforms the groom in rest shape to account for any rotation and translation changes of the head motion based on the skeleton pose. Every individual hair strand is attached to a scalp triangle at the root. Given the rest configuration, we compute a local coordinate system based on the triangle edges and compute embedding of the hair strand vertices in this local axis. This allows us to efficiently update the strand geometry to move rigidly with the head motion and shape deformations. The top row of Figure 3 shows example results of the pose-based groom transformation.", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Groom Deformation Decoder", + "text_level": 1, + "bbox": [ + 513, + 90, + 774, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the pose-based transformation moves the groom rigidly with the scalp, accounting for global rotation and translation effects, it does not include any deformation as a result of varying external forces resulting from changing body pose and shape. The pose-dependent draping effects are accounted for by the groom deformation decoder that produces deformations that, when added to the transformation module's output, produce a physical drape that reacts naturally to gravity and collisions with the underlying body. This module is implemented using a 2D convolutional neural network that takes a vector in $\\mathbb{R}^{107}$ , which encodes the groom latent code, the body shape parameters and the body pose parameters. This input vector is transformed by the network into a texture map of dimension $\\mathbb{R}^{T\\times T\\times N\\times 3}$ , which encodes the displacements for the vertices along the hair strands. This decoder is trained using a self-supervised loss. Visual results of adding posed based correctives to the rigid groom transformation are shown in Figure 3.", + "bbox": [ + 511, + 114, + 906, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Physics-Based Self-Supervision", + "text_level": 1, + "bbox": [ + 511, + 400, + 790, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We formulate a physics-based loss in order to guide the network to produce physically plausible quasi-static drapes for different grooms under different pose and body variations without the need to pre-compute any simulation data. The proposed loss function is designed to capture the different components that enable the hair to settle in a physically plausible way. This includes the elastic potential of the strands, which limits stretching, bending and twisting of the individual strands, the gravitational pull, the collisions with the underlying body, and the collisions between the hair strands themselves. Additionally, we add a pose regularizer to produce smoothly varying results for smoothly varying skeleton motion sequences. Thus the total consist of the following terms:", + "bbox": [ + 511, + 424, + 908, + 636 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {b o d y - c o l l i s i o n}} \\\\ + \\mathcal {L} _ {\\text {s e l f - c o l l i s i o n}} + \\mathcal {L} _ {\\text {p o s e - r e g}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 640, + 851, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(1)", + "bbox": [ + 883, + 650, + 903, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "**Elastic Potentials:** The elastic potentials allow hair deformation while preserving the length and curvature of each strand. To better preserve the natural curliness of a hairstyle, We first incorporated the Cosserat rod model [21] into our system by introducing additional orientation information (stored as unit quaternions $q = (q_0, \\mathbf{q}^T)^T \\in \\mathbb{H}$ with the scalar part $q_0$ and the vector part $\\mathbf{q}$ ) for each hair segment and optimizing for the additional orientation offsets. Our elastic potential is in the form:", + "bbox": [ + 511, + 678, + 906, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} + \\mathcal {L} _ {\\text {b e n d - t w i s t}} + \\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 818, + 903, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the Cosserat stretch-shear energy:", + "bbox": [ + 513, + 849, + 782, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} \\mathrm {k} _ {\\text {s t r e t c h - s h e a r}} \\boldsymbol {\\Gamma} ^ {T} \\boldsymbol {\\Gamma}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 866, + 903, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "242", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is computed from the discrete stretch-shear strain measure $\\Gamma = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\Im (q_i\\mathbf{e}_3\\bar{q}_i)$ for a hair segment $i$ , with rest length $l_{\\mathrm{rest}}$ , end points $\\mathbf{x}_{i + 1}$ and $\\mathbf{x}_i$ , orientation $q_{i}$ and fixed coordinate basis $\\{\\mathbf{e}_1,\\mathbf{e}_2,\\mathbf{e}_3\\}$ , where $\\Im ()$ is the imaginary part of the quaternion product. Similarly, the Cosserat bend-twist energy:", + "bbox": [ + 89, + 90, + 483, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b e n d}, \\text {t w i s t}} = \\frac {1}{2} \\sum_ {\\text {e d g e p a i r s}} \\mathrm {k} _ {\\text {b e n d}, \\text {t w i s t}} \\boldsymbol {\\Omega} ^ {T} \\boldsymbol {\\Omega}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 184, + 483, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is computed from the discrete bend-twist strain measure $\\Omega = \\frac{2}{l_{\\mathrm{rest}}} (\\Im (\\bar{q}_i q_{i + 1}) - \\Im (\\bar{q}_i^0 q_{i + 1}^0))$ for each consecutive hair orientation pair $q_{i}$ and $q_{i + 1}$ , with rest orientations $q_{i}^{0}$ and $q_{i + 1}^{0}$ . An additional unit quaternion constraint is needed for correct bend-twist strain measure, this is enforced for each orientation $q$ :", + "bbox": [ + 89, + 224, + 483, + 316 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {u n i t - q u a t e r n i o n}} (| | q | | - 1) ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 319, + 482, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although this full Cosserat rod model, which optimizes for both position and orientation offsets, can enable realistic modeling of hair, we observed impractically slow training times and in combination with slow convergence, this approach was deemed infeasible. Instead, we propose an alternative formulation, which optimizes for position offsets only with the following modified Cosserat potential:", + "bbox": [ + 89, + 358, + 483, + 464 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {C o s s e r a t}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {C o s s e r a t}} \\tilde {\\Gamma} ^ {T} \\tilde {\\Gamma}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 467, + 482, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\mathbf{d}_3$ , with $\\mathbf{d}_3$ being the unit director along the edge, computed from the rigidly transformed groom. As the modified Cosserat potential penalizes stretching and shearing simultaneously, we observed that hair would become overly rigid when a large stiffness value $\\mathrm{k_{COSERAT}}$ is used (which is common as hair is almost inextensible). Therefore, to relax $\\mathrm{k_{COSERAT}}$ for more natural hair deformation, we model resistance to stretching explicitly by adding a Hookean potential to penalize the length $l$ of each hair segment to be close to $l_{\\mathrm{rest}}$ :", + "bbox": [ + 89, + 508, + 483, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t r e t c h}} = \\frac {k _ {\\text {s t r e t c h}}}{2} \\sum_ {\\text {e d g e s}} \\left(l - l _ {\\text {r e s t}}\\right) ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 664, + 482, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Alternatively, one can choose to use the potential that penalizes shearing only: $\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l} -\\mathbf{d}_3$ , with $l$ being the segment length. In practice, we observed similar results from both potentials. Our final elastic potential include only two terms and we observe orders of magnitude faster training time when compared with the full Cosserat rod model", + "bbox": [ + 89, + 703, + 483, + 792 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h}} + \\mathcal {L} _ {\\text {C o s s e r a t}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 797, + 482, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gravity: The gravity potential is modeled using the potential energy of the hair nodes with positions $\\mathbf{x}$ as:", + "bbox": [ + 89, + 818, + 482, + 848 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g r a v i t y}} = \\sum_ {\\text {v e r t i c e s}} - m \\mathbf {g} ^ {\\top} \\mathbf {x}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 851, + 482, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{g}$ is the gravitational acceleration and $m$ is the parti", + "bbox": [ + 89, + 885, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cle point mass.", + "bbox": [ + 511, + 92, + 616, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Body Collision: To prevent the hair strands from intersecting with the body geometry, we implement a vertex-triangle based collision model to maintain a minimal distance $D$ between the predicted hair and the outward facing side of the body geometry. We exploit the face normal information to ensure the collision response is pointing outwards of the body. The loss is formulated as follows:", + "bbox": [ + 511, + 106, + 906, + 210 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b o d y ＿ c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {b c}} \\sum_ {\\text {v e r t i c e s}} \\max (D - d (\\mathbf {x}), 0) ^ {3}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 215, + 906, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d$ computes the signed distance along the body triangle normal direction and $\\mathsf{k}_{\\mathrm{bc}}$ is the collision stiffness. Body triangle normals are facing outwards by convention.", + "bbox": [ + 511, + 250, + 905, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-Collision: Inspired by work on volumetric methods for hair [1, 26, 29], we model hair self-collisions using Smoothed Particle Hydrodynamics (SPH) density estimation. Our energy potential is designed to push vertices apart when they exceed the reference density computed from the rest shape in a smooth and differentiable way:", + "bbox": [ + 511, + 294, + 906, + 385 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e l f . c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {s c}} \\sum_ {\\text {v e r t i c e s}} \\max \\left(\\rho (\\mathbf {x}) - \\rho_ {\\text {r e s t}}, 0\\right) ^ {3}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 388, + 905, + 421 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\rho (\\mathbf {x}) = \\sum_ {j} m _ {j} W \\left(\\left\\| \\mathbf {x} - \\mathbf {x} _ {j} \\right\\|, h\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 422, + 905, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "using the smoothing kernel proposed by Bando et al. [1]:", + "bbox": [ + 511, + 460, + 888, + 477 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nW (r, h) = \\left\\{ \\begin{array}{l l} 4 - 6 \\left(\\frac {r}{h}\\right) ^ {2} + 3 \\left(\\frac {r}{h}\\right) ^ {3} & 0 \\leq r \\leq h \\\\ \\left(2 - \\frac {r}{h}\\right) ^ {3} & h \\leq r \\leq 2 h \\\\ 0 & 2 h \\leq r \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 479, + 903, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\rho_{\\mathrm{rest}}$ is the density computed from the rest groom and $h$ is the SPH smoothing length.", + "bbox": [ + 511, + 540, + 905, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pose Regularization: We add a final loss to encourage the groom deformation decoder to predict smoothly varying deformations for smoothly varying input pose signals. During training, for every randomly sampled pose from our motion capture data set, we include $N_{\\mathrm{pose\\_reg}}$ continuous frames and penalize the difference with respect to the average deformation in predicted outputs for consecutive frames as:", + "bbox": [ + 511, + 570, + 905, + 675 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p o s e} \\cdot \\text {r e g}} = k _ {p r} \\sum_ {i = 0} ^ {N _ {\\text {p o s e} \\cdot \\text {r e g}}} | | \\bar {\\mathbf {x}} _ {\\text {d e f o r m a t i o n}} - \\mathbf {x} _ {\\text {d e f o r m a t i o n}} ^ {i} | | ^ {2} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 679, + 903, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{x}}_{\\mathrm{deformation}}$ is the average of $\\mathbf{x}_{\\mathrm{deformation}}^i$ over all $N_{\\mathrm{pose\\_reg}}$ continuous frames per randomly selected pose.", + "bbox": [ + 511, + 726, + 905, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 768, + 645, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset: We train our networks using the CT-groom data set [35] complemented with additional grooms made by technical artists to showcase a wider variety of hairstyles. Our method is capable of simulating.", + "bbox": [ + 511, + 794, + 905, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics: To evaluate our approach we opted for three key metrics: i) the length preservation of the hair strands measured on the segment lengths, ii) the percentage of intersec", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "243", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/765d3efa720f56644b269112c8217ab8d995423b8ce0125e9474ef7539a81e6e.jpg", + "image_caption": [ + "Figure 4. Modeling Diverse Hairstyles: We showcase the versatility of our method in modeling the quasi-static behavior of a plethora of hairstyles and lengths for different body shapes and poses where all results are obtained using the same settings without any manual parameter tuning. Our results cover short/medium/long hair, with various levels of curliness, including straight, wavy, curly, and kinky." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 906, + 292 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1dc02333ddb41dfc439ccf2446bdd24c691753669a82b2699cf70d145fd39433.jpg", + "image_caption": [ + "Figure 5. Resolving Collisions: Our method is conditioned on the body shape parameters, enabling it to efficiently resolve collisions with body shape variations. Here we show a static pose and groom under quasi-statically draped under varying body shapes." + ], + "image_footnote": [], + "bbox": [ + 91, + 366, + 482, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tions between the hair and the body, and iii) the preservation of the hair shape measured from the segment orientations.", + "bbox": [ + 89, + 530, + 482, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines: We compare our method against two optimization-based approaches (Adam, L-BFGS) and one simulation (XPBD [25]) baseline. We additionally compare to a recent related work GroomGen [51], which presented a neural quasi-static simulator using supervised training. GroomGen only showed results for varying gravity directions for a single fixed pose and shape, whereas our method generalizes to different shapes and poses. All images show the predicted strands directly without any hair interpolation to provide a fair assessment. When rendering hair for the final application, hair interpolation [13] can be leveraged to obtain the full set of hair strands.", + "bbox": [ + 89, + 564, + 482, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: In all of our results, strands consist of $N = 24$ vertices, which are encoded into $64 \\times 64$ texture maps. This choice of texture dimensions provides us with the ability to model several thousands of hair strands, which is sufficient for guide hair simulation. We implement our method with PyTorch [28], with training and inference measurements performed on an AMD Ryzen Threadripper PRO 3975WX CPU and a single NVIDIA RTX A6000 GPU. We refer the reader to the supplementary material for additional details.", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Qualitative Comparisons", + "text_level": 1, + "bbox": [ + 511, + 368, + 741, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Body Pose and Shape Generalization: Our deformation decoder network is able to ingest body shape parameters directly and effectively learns to adapt the deformations of the hair strands to produce intersection free results for a large variety of body shapes. Figure 4 showcases a large sample of pose variations for a diverse set of grooms while in Figure 5 we demonstrate body shape generalization. Implausible deformations are possible when deforming the body in non-physical ways, e.g. when bending the neck backwards beyond limits feasible in real-life and thus absent from our training data set.", + "bbox": [ + 511, + 392, + 906, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Temporal Stability: Our method demonstrates excellent temporal stability in its predictions when the pose parameters are smoothly varied. This is evident in Figure 6, where the hair smoothly slides over the shoulder as the head turns, avoiding any self-penetration with the body. The supplemental material shows video results.", + "bbox": [ + 511, + 559, + 906, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Groom Generalization: We prioritize real-time performance for our approach, therefore opting for a smaller network structure that enables real-time inference results. We show that our model can handle at least 10 distinct grooms. In the supplemental material, we demonstrate that the network already shows some generalization properties for unseen grooms when they are similar to the training set.", + "bbox": [ + 511, + 651, + 905, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Comparisons", + "text_level": 1, + "bbox": [ + 511, + 770, + 751, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons: The quantitative results are listed in Table 1. As expected, directly modifying the simulated hair positions, either using Adam, L-BFGS or XPBD simulation to minimize the loss produces the highest quality results but at a high computational cost. Neural methods like GroomGen and ours are orders of magnitude faster. Our method produces significantly better quantitative results when com", + "bbox": [ + 511, + 794, + 905, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "244", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/30ed7d84f703e61ffb6ca6d3479877ecab7ce834a3f76601e0c5acfdfac42564.jpg", + "table_caption": [ + "Table 1. Quantitative Comparisons. We compare our method to several optimization and simulation baselines as well as related work. Our method displays comparable metrics to directly optimizing for the positions but does so orders of magnitude faster. Compared to the state-of-the-art method GroomGen, our method produces better quality metrics while being generalizable to body shape and pose, with comparable compute performance, providing the best trade-off between speed and quality. Gravity potentials are provided for reference." + ], + "table_footnote": [], + "table_body": "
Method(↓) Time (↓) % body in secondsIntersectionLength (↓) Orientation PreservationOrientation PotentialGravity Potential
Adam179.380.22103.5376.153011.33
L-BFGS281.180.2289.5370.223047.53
XPBD (GPU) [25]63.260.0157.9618.103507.53
GroomGen [51]0.002490.391319.741281.963889.78
Ours0.002860.26175.42286.133399.95
", + "bbox": [ + 89, + 223, + 486, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/829d556dc1f5131a4015b5490075b9c01bffb6665f085d0b459de3936d1ba57c.jpg", + "image_caption": [ + "Figure 6. Temporal Stability: To demonstrate how predicted results are smoothly varying with pose changes, we gradually modify the neck rotation. Starting from looking to the right to looking left. Note how the results are smoothly varying where every pose produces a natural drape. Note especially the hair sliding over the shoulders with minimal body intersections." + ], + "image_footnote": [], + "bbox": [ + 91, + 345, + 483, + 441 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be5c07deb8a48ec2aefbf9f4f3b558d08743c3848c61842cb612a4e2ecabb05f.jpg", + "image_caption": [ + "Quaffure" + ], + "image_footnote": [], + "bbox": [ + 94, + 549, + 189, + 625 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/731a957535f3637331d407bde1c04c0770e119e224b1f4f6e88478f5c6e78801.jpg", + "image_caption": [ + "Adam" + ], + "image_footnote": [], + "bbox": [ + 191, + 549, + 287, + 625 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8220902cbd6a87cc3c881ec7470c140a4ef7a4e550d9c031a1d5c48b8f77888.jpg", + "image_caption": [ + "L-BFGS", + "Figure 7. Qualitative Comparisons: Our method produces visually comparable results to directly minimizing the energies or to quasi-static simulation with XPBD while being orders of magnitude faster at inference by memorizing body pose and shape dependent groom deformations." + ], + "image_footnote": [], + "bbox": [ + 287, + 549, + 383, + 625 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc628280e2e724ddec160d93085aa07485cd88f1ca3acd50b2ea96dcf81823da.jpg", + "image_caption": [ + "XPBD" + ], + "image_footnote": [], + "bbox": [ + 385, + 549, + 480, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pared to GroomGen at preserving strand lengths as well as the preservation of the hair shape measured from the segment orientations. Furthermore, it is important to note that, unlike GroomGen, our method handles arbitrary motion and generalizes to body shape. Figure 8 shows that GroomGen results display frequent intersections of the hair strands with the body. These results demonstrate that our method provides the best trade-offs in terms of performance and quantitative results with the significant added benefit that we do not require any simulated training data.", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/85f70c115d6ce3e0216583a4dc6648317572468c508532caeba7cdc58760f655.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 88, + 903, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/24fc831fc786f964f16c3bcf81cfd1eba5e46f93530f05ff30c4c30ebf9b41fa.jpg", + "image_caption": [ + "Figure 8. Comparisons with GroomGen: We compare our results (bottom) to those obtained with the neural simulator proposed in GroomGen [51] (top). The inset figure highlights that GroomGen produces results where strands intersect with the head geometry. In contrast, our method produces much fewer body-collisions producing better visual results. See the supplemental video for the full animated comparison." + ], + "image_footnote": [], + "bbox": [ + 516, + 193, + 903, + 296 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adam & L-BFGS - Energy Minimization: We compare against quasi-static simulation results by minimizing the loss energy with respect to the hair vertex positions directly using Adam and L-BFGS. The results are computed with the highest learning rate that produces stable results. The use of L-BFGS in simulation research has been applied for generating simulations at interactive rates [22]. Visual results in Figure 7 show that our method is visually comparable with the quasi-static energy minimization results, but at real-time rates that are independent of groom resolution. This demonstrates that our method is highly effective at learning the mapping that positions deformed hair vertices near the energy minimum.", + "bbox": [ + 511, + 426, + 906, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "XPBD - Physics-based Simulation: The XPBD method [25] effectively exploits GPU parallelism, which results in fast computation times. Simulation has been the de facto solution to hair animation for years due to the high realism, albeit at a high computational cost. Additionally, time integration of the system can often lead to instabilities, which will result in failures or undesirable results. In contrast, our method does not display any time integration instabilities. In our comparison, we model hair using the same energy as described in Subsection 3.5. To obtain quasi-static simulation results, we reset the velocities for each time step in the XPBD simulation loop, before applying gravity. We integrate the positions and use 10000 iterations to minimize the loss. We run 30 time steps to obtain results close to convergence.", + "bbox": [ + 511, + 626, + 908, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "GroomGen: We additionally compare our method to GroomGen [51]. Code is not publicly available so we compare to our own re-implementation. Instead of train", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "245", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a382d4552855119937471fea77f44515d46b7120534d23a52a1a2a002d9b34bf.jpg", + "image_caption": [ + "Figure 9. Performance & Scaling: Our method takes less than 3 ms on average to predict a single groom and the time complexity scales linearly with the number of grooms. The method is able to predict a thousand hairstyles in 0.3 seconds." + ], + "image_footnote": [], + "bbox": [ + 60, + 89, + 472, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed38f364795c1b4950dabc54931157d29dc90373cca2101348f39d714c7674c7.jpg", + "image_caption": [ + "Groom Rest Shape", + "Figure 10. Ablation Study: We perform an ablation of our proposed optimization-friendly Cosserat model against the commonly used mass-spring energy for modeling hair. Our model excels at maintaining the desired hairstyle whereas the mass-spring model struggles with maintaining curliness and volume." + ], + "image_footnote": [], + "bbox": [ + 94, + 303, + 222, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0af1a3b283fd4bd4339e952fc43376a1ebc311a538d816db0259d109ba70e3e8.jpg", + "image_caption": [ + "Mass-Spring Energy" + ], + "image_footnote": [], + "bbox": [ + 222, + 303, + 349, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/84fb876b729b262d78995bb23da258e3f70c0b563c2242cceaedb312e0e2cf24.jpg", + "image_caption": [ + "Cosserat Energy (ours)" + ], + "image_footnote": [], + "bbox": [ + 352, + 303, + 478, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing the neural simulator with different gravity directions, we stochastically sample 1000 body poses with different neck rotations within 30 degrees along $(x,y,z)$ axes, and run quasi-static hair simulation to obtain the training data. In Figure 8 provides a qualitative comparison between our approach and GroomGen for a groom that consists of 1919 strands. Both methods provide visually pleasing results but our approach results in significantly fewer intersections of hair with the body. This is highlighted in the inset figure where you can see several hair strands intersect for GroomGen whereas ours remains intersection free.", + "bbox": [ + 88, + 518, + 482, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Performance", + "text_level": 1, + "bbox": [ + 89, + 694, + 225, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Predicting a single groom takes $2.86\\mathrm{ms}$ and predicting a thousand at once requires 0.3 seconds. The performance is independent of the number of strands due to the fixed size of the representation. Performance for a varying number of groom and pose variations is shown in Figure 9. Strand count for the varying grooms used in training varies between 1500 and 2500.", + "bbox": [ + 89, + 715, + 482, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablations & Discussion", + "text_level": 1, + "bbox": [ + 89, + 832, + 305, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We perform an ablation experiment on the importance of our proposed Cosserat energy. Figure 10 shows that our model is highly effective at maintaining hairstyle and curli", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a229e7dd445386b96d46de5d7b5dae76c93a5f6746f91bc268df2f5845ecf25d.jpg", + "image_caption": [ + "Figure 11. Ablation Study on Cosserat stiffness: Results obtained by varying the Cosserat stiffness in our proposed physics-based loss that enables artistic control. A higher stiffness results in strands that maintain their rest shape better (left) compared to a lower value (right). The images are mirrored and a few strand hair tip locations are highlighted for an easier comparison." + ], + "image_footnote": [], + "bbox": [ + 535, + 88, + 885, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ness. We compare our results to those using a mass-spring energy [33]. Our model maintains the intended hairstyle well without manual intervention whereas the mass-spring model requires extensive parameter tuning to obtain satisfactory results and the hair still falls mostly flat under gravity. Our model provides artistic control by manipulating the stiffness parameters. Figure 11 demonstrates the effect of varying material stiffness.", + "bbox": [ + 511, + 362, + 905, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Future Work: Our pose-based groom transformation module can produce hair where strands are partially initialized inside the body. A better model which results in fewer intersections would make it easier for the model to learn the required deformations. Nonetheless, we observe that our network is able to robustly handle this. Current results use a single set of physical parameters for the hair material properties. This shows that parameter tuning is not required to produce visually pleasing results. However, we plan to condition the network on material parameters to enable artistic control at inference.", + "bbox": [ + 511, + 482, + 905, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 662, + 633, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present the first self-supervised neural approach to real-time quasi-static hair simulation. Our method enables efficient drape generation for various hairstyles on different body poses and shapes, which varies smoothly with pose variations. Our model leverages a hair deformation decomposition based on a transformation module and a learned deformation decoder, which is trained using self-supervision. We demonstrate complex behavior such as hair sliding over shoulders, maintaining complex hairstyles such as curly grooms and natural draping results due to the effects of gravity. To validate the method, we demonstrate that our decoder is effective and efficient at posing hair strands near the quasi-static energy minimum with better qualitative and quantitative results compared to related work.", + "bbox": [ + 511, + 689, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "246", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yosuke Bando, Bing-Yu Chen, and Tomoyuki Nishita. 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ACM Transactions on Graphics, 2024. 2" + ], + "bbox": [ + 91, + 90, + 483, + 628 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "249", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_model.json b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed0d422e7fdd675e41e55387a8bbff3598d5e85c --- /dev/null +++ b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_model.json @@ -0,0 +1,2301 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.131, + 0.795, + 0.152 + ], + "angle": 0, + "content": "Quaffure: Real-Time Quasi-Static Neural Hair Simulation" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.181, + 0.773, + 0.218 + ], + "angle": 0, + "content": "Tuur Stuyck* Gene Wei-Chin Lin* Egor Larionov Hsiao-yu Chen\nAljaz Bozic Nikolaos Sarafianos Doug Roble" + }, + { + "type": "text", + "bbox": [ + 0.437, + 0.219, + 0.562, + 0.234 + ], + "angle": 0, + "content": "Meta Reality Labs" + }, + { + "type": "text", + "bbox": [ + 0.429, + 0.236, + 0.566, + 0.251 + ], + "angle": 0, + "content": "*equal contributions" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.261, + 0.87, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.556, + 0.908, + 0.626 + ], + "angle": 0, + "content": "Figure 1. We present Quaffure, a real-time quasi-static neural hair simulator, which produces naturally draped hair in only a few milliseconds on commodity hardware, taking the hairstyle, body shape and pose into account. Our method scales to predicting the drape of 1000 hair grooms in just 0.3 seconds. Quaffure is trained using a physics-based self-supervised loss, eliminating the need for simulated training data that is costly and cumbersome to obtain. We show that our method works for a wide variety of body shapes and poses with a range of hairstyles varying from straight to curly, short to long." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.634, + 0.327, + 0.648 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.668, + 0.486, + 0.895 + ], + "angle": 0, + "content": "Realistic hair motion is crucial for high-quality avatars, but it is often limited by the computational resources available for real-time applications. To address this challenge, we propose a novel neural approach to predict physically plausible hair deformations that generalizes to various body poses, shapes, and hairstyles. Our model is trained using a self-supervised loss, eliminating the need for expensive data generation and storage. We demonstrate our method's effectiveness through numerous results across a wide range of pose and shape variations, showcasing its robust generalization capabilities and temporally smooth results. Our approach is highly suitable for real-time applications with an inference time of only a few milliseconds on consumer hardware and its ability to scale to predicting the drape of 1000 grooms in 0.3 seconds." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.634, + 0.645, + 0.648 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Hair is a crucial aspect of realistic avatars, playing a vital role in real-time applications such as games and telepresence, as well as offline generation of digital characters for film. Over the past decades, computer graphics research has devoted significant attention to the topic of hair, in order to create believable and engaging virtual characters. Hair modeling is a complex process that involves multiple stages, including grooming, simulation, and rendering. Previous research has explored various approaches to hair motion modeling, including physics-based simulations [7, 15, 43] and data-driven methods [11, 39, 40]. However, hair remains a challenging phenomenon to model due to the high number of degrees of freedom required to represent a full head of hair, which typically consists of hundreds of thousands of strands. To make hair motion modeling more tractable, it is common practice to model a full groom with a" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "239" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "limited number of strands, often referred to as guide strands. This approach involves modeling a subset of strands to represent the full groom, and then recovering the full resolution hair groom from these guide strands for rendering [13]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.155, + 0.486, + 0.593 + ], + "angle": 0, + "content": "Simulating the dynamics of hair motions has received significant attention in the field. Several approaches have been developed to model the behavior of hair strands ranging from efficient mass-spring systems [33] to rod models [2, 21, 38] able to model bending and twisting, producing complex coiling motions to volumetric approaches [1, 26, 29]. Despite impressive visual results, these models still require large computational resources making them ill-suited for real-time applications. Many advances in the field of physics-based simulation has resulted in efficient algorithms that are able to exploit parallelism of GPU hardware, resulting in real-time simulations [5, 25, 27]. However, these still require dedicated hardware resources [7, 43] and compute time might vary based on the resolution and number of the hair strands as well as the number of collisions occurring in the scene. Additionally, physics-based simulation can often be unstable and require significant parameter tuning, often leading to unpredictable or undesirable results. To address this, subspace simulation has been applied to hair dynamics but this remains limited to models that overfit to a single groom only [6]. Learned simulators [24, 51] have shown promise for modeling real-time hair dynamics but require large data sets, which are cumbersome to obtain. In general, supervised learning requires training data, which needs to be generated using physics-based simulation. This is both expensive in terms of time and storage required but also requires expert knowledge and access to specialized tools to produce. There is no publicly available data set that could be leveraged." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.483, + 0.837 + ], + "angle": 0, + "content": "In this paper, we propose a novel and efficient neural hair simulation approach to model hair quasi-statics. Our method leverages a learning-based method to predict physically plausible hair deformations, while also generalizing to various body poses and shapes. We opted for training in a self-supervised manner, eliminating the need for expensive data generation and storage. Our approach achieves an inference performance of just a few milliseconds on standard consumer hardware, without requiring elaborate code optimizations or specialized hardware features. In contrast to physics-based simulation methods, the inference time of our approach is fixed and is independent of the number of strands in the groom or number of collisions in the scene. Our results are stable and the method scales to predicting hundreds of groom simultaneously at interactive rates. In summary, our contributions are" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- A hair decomposition strategy consisting of a hair pose module and a learned corrector, which enables the use of an efficient neural decoder able to produce quasi-static hair results in milliseconds and scales to running a thou" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.093, + 0.744, + 0.106 + ], + "angle": 0, + "content": "sand grooms at interactive rates." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.107, + 0.905, + 0.181 + ], + "angle": 0, + "content": "- We are the first to propose a self-supervised learning approach for hair that completely eliminates the necessity of computing and storing large amounts training data, which would require expert knowledge and access to specialized tools to produce." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.183, + 0.905, + 0.272 + ], + "angle": 0, + "content": "- A modified formulation of the Cosserat energy for modeling hair. Our formulation is efficient in its evaluation and we demonstrate that it is well-suited for neural network training. Our proposed model is able to preserve hair strand shape for a wide range of hairstyles including very curly hair." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.273, + 0.905, + 0.318 + ], + "angle": 0, + "content": "- We demonstrate how a single trained network efficiently models different hairstyles, generalizing to body poses and shapes." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.107, + 0.905, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.332, + 0.652, + 0.348 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.907, + 0.689 + ], + "angle": 0, + "content": "Strand-based Hair Reconstruction. In recent years there has been significant progress in hair reconstruction research. Recovering hair strands has been especially sought after, since hair reconstructed as strands can easily be integrated into existing game engines, to be animated and rendered with physics-based simulation and rendering. Neural Strands [31] represent the hair groom as a neural texture on the head scalp, where each texel feature can be decoded into an explicit strand. This representation was later trained on a dataset of synthetic grooms, to provide prior for strand-based hair fitting to multi-view images [36]. Zhou et al. [52] proposes a prior-free reconstruction approach. It was extended to support text-guided hair generation in HAAR [37]. The fitting quality was further improved in [23, 45, 48] by additionally decoding Gaussian splats [18] along the strands, representing hair appearance. Instead of requiring multi-view capture, several works explored strand-based hair reconstruction from a dynamic monocular video [46] or just a single image [44, 50], where volumetric 3D hair orientations were used to model hair geometry. To achieve the highest reconstruction quality, Shen et al. [35] captured volumetric CT scans to reconstruct strand-based grooms." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Learning-based Hair Models. To either accelerate or improve the realism of physics-based simulation or rendering methods, many learning-based hair models have been introduced. Wang et al. [40] use a hybrid representation, with volumetric primitives aligned along guide strands to model hair appearance under motion. To simplify fitting to real observations, Wang et al. [39] used a mixture of volumetric primitives that jointly represent hair geometry and appearance. A unified latent representation for diverse hairstyles has been explored in [12, 51], where explicit strand geometry is encoded into a latent space using a variational autoencoder (VAE) [51] or a generative adversarial network (GAN) [12], enabling hair generation and interpolation across hairstyles. To accelerate hair simulation, Guan" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.513, + 0.957 + ], + "angle": 0, + "content": "240" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.898, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.247, + 0.908, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Quaffure Overview: Our method takes a code as input, consisting of a latent code for the rest hair shape, body shape parameters, and full skeleton pose. The output is naturally draped hair produced as the sum of posed hair given the body pose and shape parameters, combined with learned corrections which are produced by the groom deformation decoder. We train our method in two stages: i) an autoencoder is trained on all hairstyles to obtain a groom latent code, and ii) the groom deformation decoder is trained in a physics-based self-supervised fashion. The hair strands are encoded in a 2D texture representation (left) where strands are encoded in the pixel in which the root particle is located. The figure shows how the 3D scalp geometry (bottom) is mapped to a high dimensional 2D texture map (top)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.35, + 0.482, + 0.412 + ], + "angle": 0, + "content": "et al. [11] proposed a multi-linear model for representing hair dynamics, and Lyu et al. [24] introduced a neural upsampler to efficiently convert a low number of guide strands into dense hair." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.414, + 0.483, + 0.686 + ], + "angle": 0, + "content": "Physics-based Hair Models. Realistic hair simulation [41, 42] has been an active area of research in computer graphics for decades. To achieve high-fidelity results, it is necessary to simulate every individual strand and their interactions with each other. Common elastic models used for strand-based hair include mass-spring models [33] and elastic rods [2, 21, 38]. In addition, complex hair-hair interactions such as self-collision [26] and friction forces [17] are also important for realistic behavior. Several reduced models have been developed to lower the computational budget for real-time hair simulation. One idea is to simulate the hair as layered elastic bodies [4, 47], while another suggests representing a group of hairs as strips [19, 20]. The most popular approach is to simulate a subset of the overall hair as guide strands and interpolate between the guides for individual strand detail [6, 13]. Hu et al. [14] propose a method to automatically determine simulation parameters from video footage." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Physics-based Self-supervised Learning. Data-driven methods have been successful in the field of simulation [9, 30, 49]. However, data-driven methods do not ensure that the simulated system adheres to physical constraints, which can result in non-physical states. To address this, researchers have proposed incorporating physics energy loss directly into the training process to eliminate the need for generating large amounts of data and to enable better generalization. Physics-based self-supervised methods have shown promise in learning a reduced latent space for quasi-static states of rigid motion [34] and cloth drapes [8], which has been expanded to dynamic motions of cloth [3, 10, 16, 32]. However, there is limited research on hair simulation. The neural simulator of GroomGen [51]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.907, + 0.427 + ], + "angle": 0, + "content": "only demonstrated hair deformation for varying gravity directions, while our method is the first to apply a physics-supervised method for hair that generalizes to full motions and incorporates collision under different poses and body shapes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.438, + 0.649, + 0.455 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.909, + 0.646 + ], + "angle": 0, + "content": "Our approach shown in Figure 2, enables real-time estimation of posed quasi-static hair \\(\\mathbf{x}_{\\mathrm{hair}}\\) based on hairstyle, body shape and pose. We achieve this by splitting the problem at hand in two parts. First, a simple and efficient groom transformation model transforms the hair groom rigidly with body pose and shape variations expressed as \\(\\mathbf{x}_{\\mathrm{posed}}\\). Second, to model the groom specific pose and shape dependent variations \\(\\mathbf{x}_{\\mathrm{deformation}}\\), we train a network to produce deformation fields, which when added to the posed hair, result in a physically plausible quasi-static drape that takes physical effects such as gravity and collisions into account. The final hair drape is simply obtained as \\(\\mathbf{x}_{\\mathrm{hair}} = \\mathbf{x}_{\\mathrm{posed}} + \\mathbf{x}_{\\mathrm{deformation}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.652, + 0.667, + 0.667 + ], + "angle": 0, + "content": "3.1. Representation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.78 + ], + "angle": 0, + "content": "We encode all hair geometry into a texture based representation based on the UV map of the scalp geometry as shown in the left of Figure 2. Where a hair strand root particle falls into a pixel in the map, we encode a high dimensional feature, which represents the strand geometry. For a texture with height and width \\( T \\) and a groom with \\( N \\) vertices per strand, the encoding is of dimension \\( \\mathbb{R}^{T\\times T\\times N\\times 3} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Body Model: Our body model consists of body geometry rigged with a skeleton model, which enables the body geometry to change pose using linear blend skinning. The skeleton pose is represented using a set of pose parameters \\(\\theta \\in \\mathbb{R}^{81}\\). To model variations in body shape, we leverage a statistical body model. This model has been constructed from a large data set of human body scans, to which our body geometry has been registered. Body shape variations" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "241" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.09, + 0.485, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.272, + 0.485, + 0.399 + ], + "angle": 0, + "content": "Figure 3. Pose & Shape-based Deformations: Example of posed groom (top) which accounts for rigid rotations and translations of the rest shape only and the combined posed groom with learned deformations (bottom), which accounts for physical effects such as strand material model, gravity and collisions. Despite body intersections incurred by the rigid transformation applied by the groom transformation module, our proposed network resolves all collisions with the body after applying the learned deformations (bottom). Note the significant change resulting in a natural drape." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.422, + 0.484, + 0.455 + ], + "angle": 0, + "content": "are modeled as variations on top of an average shape and are parameterized using body shape coefficients \\(\\beta \\in \\mathbb{R}^{10}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.469, + 0.285, + 0.485 + ], + "angle": 0, + "content": "3.2. Groom Autoencoder" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.495, + 0.484, + 0.691 + ], + "angle": 0, + "content": "We leverage an autoencoder to obtain a compact representation for all the different grooms in their rest shape. This model is trained separately and produces compact latent codes in \\(\\mathbb{R}^{16}\\) to distinguish different hairstyles. The autoencoder input and output are grooms encoded on the scalp as high dimensional texture maps. The autoencoder structure is made up of 2D convolutional down and up sampling layers for the encoder and decoder respectively. Once the groom autoencoder is fully-trained, we discard its decoder since we are only interested in the latent groom codes produced by the encoder. The weights of the encoder are frozen for the follow-up training of the groom deformation decoder discussed in Section 3.4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.709, + 0.396, + 0.725 + ], + "angle": 0, + "content": "3.3. Pose-based Groom Transformation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Our pose-based transformation module rigidly transforms the groom in rest shape to account for any rotation and translation changes of the head motion based on the skeleton pose. Every individual hair strand is attached to a scalp triangle at the root. Given the rest configuration, we compute a local coordinate system based on the triangle edges and compute embedding of the hair strand vertices in this local axis. This allows us to efficiently update the strand geometry to move rigidly with the head motion and shape deformations. The top row of Figure 3 shows example results of the pose-based groom transformation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.776, + 0.107 + ], + "angle": 0, + "content": "3.4. Groom Deformation Decoder" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.907, + 0.389 + ], + "angle": 0, + "content": "While the pose-based transformation moves the groom rigidly with the scalp, accounting for global rotation and translation effects, it does not include any deformation as a result of varying external forces resulting from changing body pose and shape. The pose-dependent draping effects are accounted for by the groom deformation decoder that produces deformations that, when added to the transformation module's output, produce a physical drape that reacts naturally to gravity and collisions with the underlying body. This module is implemented using a 2D convolutional neural network that takes a vector in \\(\\mathbb{R}^{107}\\), which encodes the groom latent code, the body shape parameters and the body pose parameters. This input vector is transformed by the network into a texture map of dimension \\(\\mathbb{R}^{T\\times T\\times N\\times 3}\\), which encodes the displacements for the vertices along the hair strands. This decoder is trained using a self-supervised loss. Visual results of adding posed based correctives to the rigid groom transformation are shown in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.401, + 0.792, + 0.418 + ], + "angle": 0, + "content": "3.5. Physics-Based Self-Supervision" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.425, + 0.909, + 0.637 + ], + "angle": 0, + "content": "We formulate a physics-based loss in order to guide the network to produce physically plausible quasi-static drapes for different grooms under different pose and body variations without the need to pre-compute any simulation data. The proposed loss function is designed to capture the different components that enable the hair to settle in a physically plausible way. This includes the elastic potential of the strands, which limits stretching, bending and twisting of the individual strands, the gravitational pull, the collisions with the underlying body, and the collisions between the hair strands themselves. Additionally, we add a pose regularizer to produce smoothly varying results for smoothly varying skeleton motion sequences. Thus the total consist of the following terms:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.641, + 0.852, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {b o d y - c o l l i s i o n}} \\\\ + \\mathcal {L} _ {\\text {s e l f - c o l l i s i o n}} + \\mathcal {L} _ {\\text {p o s e - r e g}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.884, + 0.651, + 0.905, + 0.665 + ], + "angle": 0, + "content": "(1)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.679, + 0.907, + 0.815 + ], + "angle": 0, + "content": "**Elastic Potentials:** The elastic potentials allow hair deformation while preserving the length and curvature of each strand. To better preserve the natural curliness of a hairstyle, We first incorporated the Cosserat rod model [21] into our system by introducing additional orientation information (stored as unit quaternions \\( q = (q_0, \\mathbf{q}^T)^T \\in \\mathbb{H} \\) with the scalar part \\( q_0 \\) and the vector part \\( \\mathbf{q} \\)) for each hair segment and optimizing for the additional orientation offsets. Our elastic potential is in the form:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.819, + 0.905, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} + \\mathcal {L} _ {\\text {b e n d - t w i s t}} + \\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.85, + 0.783, + 0.865 + ], + "angle": 0, + "content": "where the Cosserat stretch-shear energy:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.867, + 0.905, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} \\mathrm {k} _ {\\text {s t r e t c h - s h e a r}} \\boldsymbol {\\Gamma} ^ {T} \\boldsymbol {\\Gamma}, \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "242" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.182 + ], + "angle": 0, + "content": "is computed from the discrete stretch-shear strain measure \\(\\Gamma = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\Im (q_i\\mathbf{e}_3\\bar{q}_i)\\) for a hair segment \\(i\\), with rest length \\(l_{\\mathrm{rest}}\\), end points \\(\\mathbf{x}_{i + 1}\\) and \\(\\mathbf{x}_i\\), orientation \\(q_{i}\\) and fixed coordinate basis \\(\\{\\mathbf{e}_1,\\mathbf{e}_2,\\mathbf{e}_3\\}\\), where \\(\\Im ()\\) is the imaginary part of the quaternion product. Similarly, the Cosserat bend-twist energy:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.185, + 0.484, + 0.222 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b e n d}, \\text {t w i s t}} = \\frac {1}{2} \\sum_ {\\text {e d g e p a i r s}} \\mathrm {k} _ {\\text {b e n d}, \\text {t w i s t}} \\boldsymbol {\\Omega} ^ {T} \\boldsymbol {\\Omega}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.225, + 0.484, + 0.317 + ], + "angle": 0, + "content": "is computed from the discrete bend-twist strain measure \\(\\Omega = \\frac{2}{l_{\\mathrm{rest}}} (\\Im (\\bar{q}_i q_{i + 1}) - \\Im (\\bar{q}_i^0 q_{i + 1}^0))\\) for each consecutive hair orientation pair \\(q_{i}\\) and \\(q_{i + 1}\\), with rest orientations \\(q_{i}^{0}\\) and \\(q_{i + 1}^{0}\\). An additional unit quaternion constraint is needed for correct bend-twist strain measure, this is enforced for each orientation \\(q\\):" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.32, + 0.483, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {u n i t - q u a t e r n i o n}} (| | q | | - 1) ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.359, + 0.484, + 0.465 + ], + "angle": 0, + "content": "Although this full Cosserat rod model, which optimizes for both position and orientation offsets, can enable realistic modeling of hair, we observed impractically slow training times and in combination with slow convergence, this approach was deemed infeasible. Instead, we propose an alternative formulation, which optimizes for position offsets only with the following modified Cosserat potential:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.468, + 0.483, + 0.505 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {C o s s e r a t}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {C o s s e r a t}} \\tilde {\\Gamma} ^ {T} \\tilde {\\Gamma}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.509, + 0.484, + 0.661 + ], + "angle": 0, + "content": "where \\(\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\mathbf{d}_3\\), with \\(\\mathbf{d}_3\\) being the unit director along the edge, computed from the rigidly transformed groom. As the modified Cosserat potential penalizes stretching and shearing simultaneously, we observed that hair would become overly rigid when a large stiffness value \\(\\mathrm{k_{COSERAT}}\\) is used (which is common as hair is almost inextensible). Therefore, to relax \\(\\mathrm{k_{COSERAT}}\\) for more natural hair deformation, we model resistance to stretching explicitly by adding a Hookean potential to penalize the length \\(l\\) of each hair segment to be close to \\(l_{\\mathrm{rest}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.665, + 0.483, + 0.702 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t r e t c h}} = \\frac {k _ {\\text {s t r e t c h}}}{2} \\sum_ {\\text {e d g e s}} \\left(l - l _ {\\text {r e s t}}\\right) ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.794 + ], + "angle": 0, + "content": "Alternatively, one can choose to use the potential that penalizes shearing only: \\(\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l} -\\mathbf{d}_3\\), with \\(l\\) being the segment length. In practice, we observed similar results from both potentials. Our final elastic potential include only two terms and we observe orders of magnitude faster training time when compared with the full Cosserat rod model" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.799, + 0.483, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h}} + \\mathcal {L} _ {\\text {C o s s e r a t}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.819, + 0.483, + 0.849 + ], + "angle": 0, + "content": "Gravity: The gravity potential is modeled using the potential energy of the hair nodes with positions \\(\\mathbf{x}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.852, + 0.483, + 0.884 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g r a v i t y}} = \\sum_ {\\text {v e r t i c e s}} - m \\mathbf {g} ^ {\\top} \\mathbf {x}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{g}\\) is the gravitational acceleration and \\(m\\) is the parti" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.093, + 0.617, + 0.106 + ], + "angle": 0, + "content": "cle point mass." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.107, + 0.907, + 0.212 + ], + "angle": 0, + "content": "Body Collision: To prevent the hair strands from intersecting with the body geometry, we implement a vertex-triangle based collision model to maintain a minimal distance \\(D\\) between the predicted hair and the outward facing side of the body geometry. We exploit the face normal information to ensure the collision response is pointing outwards of the body. The loss is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.216, + 0.907, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b o d y ＿ c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {b c}} \\sum_ {\\text {v e r t i c e s}} \\max (D - d (\\mathbf {x}), 0) ^ {3}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.25, + 0.906, + 0.295 + ], + "angle": 0, + "content": "where \\(d\\) computes the signed distance along the body triangle normal direction and \\(\\mathsf{k}_{\\mathrm{bc}}\\) is the collision stiffness. Body triangle normals are facing outwards by convention." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.295, + 0.907, + 0.386 + ], + "angle": 0, + "content": "Self-Collision: Inspired by work on volumetric methods for hair [1, 26, 29], we model hair self-collisions using Smoothed Particle Hydrodynamics (SPH) density estimation. Our energy potential is designed to push vertices apart when they exceed the reference density computed from the rest shape in a smooth and differentiable way:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.389, + 0.906, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e l f . c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {s c}} \\sum_ {\\text {v e r t i c e s}} \\max \\left(\\rho (\\mathbf {x}) - \\rho_ {\\text {r e s t}}, 0\\right) ^ {3}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.424, + 0.906, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\rho (\\mathbf {x}) = \\sum_ {j} m _ {j} W \\left(\\left\\| \\mathbf {x} - \\mathbf {x} _ {j} \\right\\|, h\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.462, + 0.89, + 0.478 + ], + "angle": 0, + "content": "using the smoothing kernel proposed by Bando et al. [1]:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.48, + 0.905, + 0.538 + ], + "angle": 0, + "content": "\\[\nW (r, h) = \\left\\{ \\begin{array}{l l} 4 - 6 \\left(\\frac {r}{h}\\right) ^ {2} + 3 \\left(\\frac {r}{h}\\right) ^ {3} & 0 \\leq r \\leq h \\\\ \\left(2 - \\frac {r}{h}\\right) ^ {3} & h \\leq r \\leq 2 h \\\\ 0 & 2 h \\leq r \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.541, + 0.906, + 0.571 + ], + "angle": 0, + "content": "where \\(\\rho_{\\mathrm{rest}}\\) is the density computed from the rest groom and \\(h\\) is the SPH smoothing length." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.571, + 0.906, + 0.676 + ], + "angle": 0, + "content": "Pose Regularization: We add a final loss to encourage the groom deformation decoder to predict smoothly varying deformations for smoothly varying input pose signals. During training, for every randomly sampled pose from our motion capture data set, we include \\( N_{\\mathrm{pose\\_reg}} \\) continuous frames and penalize the difference with respect to the average deformation in predicted outputs for consecutive frames as:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.68, + 0.905, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p o s e} \\cdot \\text {r e g}} = k _ {p r} \\sum_ {i = 0} ^ {N _ {\\text {p o s e} \\cdot \\text {r e g}}} | | \\bar {\\mathbf {x}} _ {\\text {d e f o r m a t i o n}} - \\mathbf {x} _ {\\text {d e f o r m a t i o n}} ^ {i} | | ^ {2} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.727, + 0.906, + 0.758 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{x}}_{\\mathrm{deformation}}\\) is the average of \\(\\mathbf{x}_{\\mathrm{deformation}}^i\\) over all \\(N_{\\mathrm{pose\\_reg}}\\) continuous frames per randomly selected pose." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.77, + 0.646, + 0.788 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.856 + ], + "angle": 0, + "content": "Dataset: We train our networks using the CT-groom data set [35] complemented with additional grooms made by technical artists to showcase a wider variety of hairstyles. Our method is capable of simulating." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Metrics: To evaluate our approach we opted for three key metrics: i) the length preservation of the hair strands measured on the segment lengths, ii) the percentage of intersec" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "243" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.907, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.302, + 0.908, + 0.345 + ], + "angle": 0, + "content": "Figure 4. Modeling Diverse Hairstyles: We showcase the versatility of our method in modeling the quasi-static behavior of a plethora of hairstyles and lengths for different body shapes and poses where all results are obtained using the same settings without any manual parameter tuning. Our results cover short/medium/long hair, with various levels of curliness, including straight, wavy, curly, and kinky." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.367, + 0.483, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.447, + 0.483, + 0.504 + ], + "angle": 0, + "content": "Figure 5. Resolving Collisions: Our method is conditioned on the body shape parameters, enabling it to efficiently resolve collisions with body shape variations. Here we show a static pose and groom under quasi-statically draped under varying body shapes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.531, + 0.483, + 0.561 + ], + "angle": 0, + "content": "tions between the hair and the body, and iii) the preservation of the hair shape measured from the segment orientations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.483, + 0.746 + ], + "angle": 0, + "content": "Baselines: We compare our method against two optimization-based approaches (Adam, L-BFGS) and one simulation (XPBD [25]) baseline. We additionally compare to a recent related work GroomGen [51], which presented a neural quasi-static simulator using supervised training. GroomGen only showed results for varying gravity directions for a single fixed pose and shape, whereas our method generalizes to different shapes and poses. All images show the predicted strands directly without any hair interpolation to provide a fair assessment. When rendering hair for the final application, hair interpolation [13] can be leveraged to obtain the full set of hair strands." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Implementation Details: In all of our results, strands consist of \\(N = 24\\) vertices, which are encoded into \\(64 \\times 64\\) texture maps. This choice of texture dimensions provides us with the ability to model several thousands of hair strands, which is sufficient for guide hair simulation. We implement our method with PyTorch [28], with training and inference measurements performed on an AMD Ryzen Threadripper PRO 3975WX CPU and a single NVIDIA RTX A6000 GPU. We refer the reader to the supplementary material for additional details." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.369, + 0.742, + 0.385 + ], + "angle": 0, + "content": "4.1. Qualitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.393, + 0.907, + 0.558 + ], + "angle": 0, + "content": "Body Pose and Shape Generalization: Our deformation decoder network is able to ingest body shape parameters directly and effectively learns to adapt the deformations of the hair strands to produce intersection free results for a large variety of body shapes. Figure 4 showcases a large sample of pose variations for a diverse set of grooms while in Figure 5 we demonstrate body shape generalization. Implausible deformations are possible when deforming the body in non-physical ways, e.g. when bending the neck backwards beyond limits feasible in real-life and thus absent from our training data set." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.56, + 0.907, + 0.65 + ], + "angle": 0, + "content": "Temporal Stability: Our method demonstrates excellent temporal stability in its predictions when the pose parameters are smoothly varied. This is evident in Figure 6, where the hair smoothly slides over the shoulder as the head turns, avoiding any self-penetration with the body. The supplemental material shows video results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.652, + 0.906, + 0.759 + ], + "angle": 0, + "content": "Groom Generalization: We prioritize real-time performance for our approach, therefore opting for a smaller network structure that enables real-time inference results. We show that our model can handle at least 10 distinct grooms. In the supplemental material, we demonstrate that the network already shows some generalization properties for unseen grooms when they are similar to the training set." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.771, + 0.753, + 0.788 + ], + "angle": 0, + "content": "4.2. Quantitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Comparisons: The quantitative results are listed in Table 1. As expected, directly modifying the simulated hair positions, either using Adam, L-BFGS or XPBD simulation to minimize the loss produces the highest quality results but at a high computational cost. Neural methods like GroomGen and ours are orders of magnitude faster. Our method produces significantly better quantitative results when com" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "244" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.483, + 0.213 + ], + "angle": 0, + "content": "Table 1. Quantitative Comparisons. We compare our method to several optimization and simulation baselines as well as related work. Our method displays comparable metrics to directly optimizing for the positions but does so orders of magnitude faster. Compared to the state-of-the-art method GroomGen, our method produces better quality metrics while being generalizable to body shape and pose, with comparable compute performance, providing the best trade-off between speed and quality. Gravity potentials are provided for reference." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.224, + 0.487, + 0.332 + ], + "angle": 0, + "content": "
Method(↓) Time (↓) % body in secondsIntersectionLength (↓) Orientation PreservationOrientation PotentialGravity Potential
Adam179.380.22103.5376.153011.33
L-BFGS281.180.2289.5370.223047.53
XPBD (GPU) [25]63.260.0157.9618.103507.53
GroomGen [51]0.002490.391319.741281.963889.78
Ours0.002860.26175.42286.133399.95
" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.346, + 0.484, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.536 + ], + "angle": 0, + "content": "Figure 6. Temporal Stability: To demonstrate how predicted results are smoothly varying with pose changes, we gradually modify the neck rotation. Starting from looking to the right to looking left. Note how the results are smoothly varying where every pose produces a natural drape. Note especially the hair sliding over the shoulders with minimal body intersections." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.55, + 0.191, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.103, + 0.627, + 0.176, + 0.641 + ], + "angle": 0, + "content": "Quaffure" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.55, + 0.288, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.627, + 0.262, + 0.64 + ], + "angle": 0, + "content": "Adam" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.55, + 0.385, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.303, + 0.627, + 0.361, + 0.64 + ], + "angle": 0, + "content": "L-BFGS" + }, + { + "type": "image", + "bbox": [ + 0.386, + 0.55, + 0.481, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.627, + 0.454, + 0.64 + ], + "angle": 0, + "content": "XPBD" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.652, + 0.484, + 0.722 + ], + "angle": 0, + "content": "Figure 7. Qualitative Comparisons: Our method produces visually comparable results to directly minimizing the energies or to quasi-static simulation with XPBD while being orders of magnitude faster at inference by memorizing body pose and shape dependent groom deformations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "pared to GroomGen at preserving strand lengths as well as the preservation of the hair shape measured from the segment orientations. Furthermore, it is important to note that, unlike GroomGen, our method handles arbitrary motion and generalizes to body shape. Figure 8 shows that GroomGen results display frequent intersections of the hair strands with the body. These results demonstrate that our method provides the best trade-offs in terms of performance and quantitative results with the significant added benefit that we do not require any simulated training data." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.905, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.194, + 0.905, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.308, + 0.907, + 0.406 + ], + "angle": 0, + "content": "Figure 8. Comparisons with GroomGen: We compare our results (bottom) to those obtained with the neural simulator proposed in GroomGen [51] (top). The inset figure highlights that GroomGen produces results where strands intersect with the head geometry. In contrast, our method produces much fewer body-collisions producing better visual results. See the supplemental video for the full animated comparison." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.907, + 0.625 + ], + "angle": 0, + "content": "Adam & L-BFGS - Energy Minimization: We compare against quasi-static simulation results by minimizing the loss energy with respect to the hair vertex positions directly using Adam and L-BFGS. The results are computed with the highest learning rate that produces stable results. The use of L-BFGS in simulation research has been applied for generating simulations at interactive rates [22]. Visual results in Figure 7 show that our method is visually comparable with the quasi-static energy minimization results, but at real-time rates that are independent of groom resolution. This demonstrates that our method is highly effective at learning the mapping that positions deformed hair vertices near the energy minimum." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.909, + 0.853 + ], + "angle": 0, + "content": "XPBD - Physics-based Simulation: The XPBD method [25] effectively exploits GPU parallelism, which results in fast computation times. Simulation has been the de facto solution to hair animation for years due to the high realism, albeit at a high computational cost. Additionally, time integration of the system can often lead to instabilities, which will result in failures or undesirable results. In contrast, our method does not display any time integration instabilities. In our comparison, we model hair using the same energy as described in Subsection 3.5. To obtain quasi-static simulation results, we reset the velocities for each time step in the XPBD simulation loop, before applying gravity. We integrate the positions and use 10000 iterations to minimize the loss. We run 30 time steps to obtain results close to convergence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "GroomGen: We additionally compare our method to GroomGen [51]. Code is not publicly available so we compare to our own re-implementation. Instead of train" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "245" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.062, + 0.09, + 0.473, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.235, + 0.483, + 0.293 + ], + "angle": 0, + "content": "Figure 9. Performance & Scaling: Our method takes less than 3 ms on average to predict a single groom and the time complexity scales linearly with the number of grooms. The method is able to predict a thousand hairstyles in 0.3 seconds." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.304, + 0.223, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.4, + 0.207, + 0.41 + ], + "angle": 0, + "content": "Groom Rest Shape" + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.304, + 0.351, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.4, + 0.342, + 0.411 + ], + "angle": 0, + "content": "Mass-Spring Energy" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.304, + 0.479, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.4, + 0.477, + 0.411 + ], + "angle": 0, + "content": "Cosserat Energy (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.424, + 0.483, + 0.493 + ], + "angle": 0, + "content": "Figure 10. Ablation Study: We perform an ablation of our proposed optimization-friendly Cosserat model against the commonly used mass-spring energy for modeling hair. Our model excels at maintaining the desired hairstyle whereas the mass-spring model struggles with maintaining curliness and volume." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.519, + 0.483, + 0.685 + ], + "angle": 0, + "content": "ing the neural simulator with different gravity directions, we stochastically sample 1000 body poses with different neck rotations within 30 degrees along \\((x,y,z)\\) axes, and run quasi-static hair simulation to obtain the training data. In Figure 8 provides a qualitative comparison between our approach and GroomGen for a groom that consists of 1919 strands. Both methods provide visually pleasing results but our approach results in significantly fewer intersections of hair with the body. This is highlighted in the inset figure where you can see several hair strands intersect for GroomGen whereas ours remains intersection free." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.695, + 0.227, + 0.709 + ], + "angle": 0, + "content": "4.3. Performance" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.483, + 0.822 + ], + "angle": 0, + "content": "Predicting a single groom takes \\(2.86\\mathrm{ms}\\) and predicting a thousand at once requires 0.3 seconds. The performance is independent of the number of strands due to the fixed size of the representation. Performance for a varying number of groom and pose variations is shown in Figure 9. Strand count for the varying grooms used in training varies between 1500 and 2500." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.833, + 0.307, + 0.848 + ], + "angle": 0, + "content": "4.4. Ablations & Discussion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We perform an ablation experiment on the importance of our proposed Cosserat energy. Figure 10 shows that our model is highly effective at maintaining hairstyle and curli" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.089, + 0.887, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.253, + 0.906, + 0.336 + ], + "angle": 0, + "content": "Figure 11. Ablation Study on Cosserat stiffness: Results obtained by varying the Cosserat stiffness in our proposed physics-based loss that enables artistic control. A higher stiffness results in strands that maintain their rest shape better (left) compared to a lower value (right). The images are mirrored and a few strand hair tip locations are highlighted for an easier comparison." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.363, + 0.906, + 0.483 + ], + "angle": 0, + "content": "ness. We compare our results to those using a mass-spring energy [33]. Our model maintains the intended hairstyle well without manual intervention whereas the mass-spring model requires extensive parameter tuning to obtain satisfactory results and the hair still falls mostly flat under gravity. Our model provides artistic control by manipulating the stiffness parameters. Figure 11 demonstrates the effect of varying material stiffness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.483, + 0.906, + 0.649 + ], + "angle": 0, + "content": "Limitations and Future Work: Our pose-based groom transformation module can produce hair where strands are partially initialized inside the body. A better model which results in fewer intersections would make it easier for the model to learn the required deformations. Nonetheless, we observe that our network is able to robustly handle this. Current results use a single set of physical parameters for the hair material properties. This shows that parameter tuning is not required to produce visually pleasing results. However, we plan to condition the network on material parameters to enable artistic control at inference." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.664, + 0.634, + 0.68 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We present the first self-supervised neural approach to real-time quasi-static hair simulation. Our method enables efficient drape generation for various hairstyles on different body poses and shapes, which varies smoothly with pose variations. Our model leverages a hair deformation decomposition based on a transformation module and a learned deformation decoder, which is trained using self-supervision. We demonstrate complex behavior such as hair sliding over shoulders, maintaining complex hairstyles such as curly grooms and natural draping results due to the effects of gravity. To validate the method, we demonstrate that our decoder is effective and efficient at posing hair strands near the quasi-static energy minimum with better qualitative and quantitative results compared to related work." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "246" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.176 + ], + "angle": 0, + "content": "[1] Yosuke Bando, Bing-Yu Chen, and Tomoyuki Nishita. 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ACM Transactions on Graphics, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.091, + 0.484, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "249" + } + ] +] \ No newline at end of file diff --git a/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_origin.pdf b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..224b63791477182f16396ebfceaa3a3658d7ceb3 --- /dev/null +++ b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/40107a29-fe45-40f8-a607-7d120945adc2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f53292fe81c866fb757f03cfa56fd495fc9f6e9d7143c90ebedc1b5e70cc8879 +size 9595758 diff --git a/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/full.md b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d47ebb3da1e99107ee49d9aef8c3106fcde41e3f --- /dev/null +++ b/2025/Quaffure_ Real-Time Quasi-Static Neural Hair Simulation/full.md @@ -0,0 +1,333 @@ +# Quaffure: Real-Time Quasi-Static Neural Hair Simulation + +Tuur Stuyck* Gene Wei-Chin Lin* Egor Larionov Hsiao-yu Chen +Aljaz Bozic Nikolaos Sarafianos Doug Roble + +Meta Reality Labs + +*equal contributions + +![](images/ae9b2779b4a61ef01c6d713a012ab307287a8ec93e6d809d2135584953a24330.jpg) +Figure 1. We present Quaffure, a real-time quasi-static neural hair simulator, which produces naturally draped hair in only a few milliseconds on commodity hardware, taking the hairstyle, body shape and pose into account. Our method scales to predicting the drape of 1000 hair grooms in just 0.3 seconds. Quaffure is trained using a physics-based self-supervised loss, eliminating the need for simulated training data that is costly and cumbersome to obtain. We show that our method works for a wide variety of body shapes and poses with a range of hairstyles varying from straight to curly, short to long. + +# Abstract + +Realistic hair motion is crucial for high-quality avatars, but it is often limited by the computational resources available for real-time applications. To address this challenge, we propose a novel neural approach to predict physically plausible hair deformations that generalizes to various body poses, shapes, and hairstyles. Our model is trained using a self-supervised loss, eliminating the need for expensive data generation and storage. We demonstrate our method's effectiveness through numerous results across a wide range of pose and shape variations, showcasing its robust generalization capabilities and temporally smooth results. Our approach is highly suitable for real-time applications with an inference time of only a few milliseconds on consumer hardware and its ability to scale to predicting the drape of 1000 grooms in 0.3 seconds. + +# 1. Introduction + +Hair is a crucial aspect of realistic avatars, playing a vital role in real-time applications such as games and telepresence, as well as offline generation of digital characters for film. Over the past decades, computer graphics research has devoted significant attention to the topic of hair, in order to create believable and engaging virtual characters. Hair modeling is a complex process that involves multiple stages, including grooming, simulation, and rendering. Previous research has explored various approaches to hair motion modeling, including physics-based simulations [7, 15, 43] and data-driven methods [11, 39, 40]. However, hair remains a challenging phenomenon to model due to the high number of degrees of freedom required to represent a full head of hair, which typically consists of hundreds of thousands of strands. To make hair motion modeling more tractable, it is common practice to model a full groom with a + +limited number of strands, often referred to as guide strands. This approach involves modeling a subset of strands to represent the full groom, and then recovering the full resolution hair groom from these guide strands for rendering [13]. + +Simulating the dynamics of hair motions has received significant attention in the field. Several approaches have been developed to model the behavior of hair strands ranging from efficient mass-spring systems [33] to rod models [2, 21, 38] able to model bending and twisting, producing complex coiling motions to volumetric approaches [1, 26, 29]. Despite impressive visual results, these models still require large computational resources making them ill-suited for real-time applications. Many advances in the field of physics-based simulation has resulted in efficient algorithms that are able to exploit parallelism of GPU hardware, resulting in real-time simulations [5, 25, 27]. However, these still require dedicated hardware resources [7, 43] and compute time might vary based on the resolution and number of the hair strands as well as the number of collisions occurring in the scene. Additionally, physics-based simulation can often be unstable and require significant parameter tuning, often leading to unpredictable or undesirable results. To address this, subspace simulation has been applied to hair dynamics but this remains limited to models that overfit to a single groom only [6]. Learned simulators [24, 51] have shown promise for modeling real-time hair dynamics but require large data sets, which are cumbersome to obtain. In general, supervised learning requires training data, which needs to be generated using physics-based simulation. This is both expensive in terms of time and storage required but also requires expert knowledge and access to specialized tools to produce. There is no publicly available data set that could be leveraged. + +In this paper, we propose a novel and efficient neural hair simulation approach to model hair quasi-statics. Our method leverages a learning-based method to predict physically plausible hair deformations, while also generalizing to various body poses and shapes. We opted for training in a self-supervised manner, eliminating the need for expensive data generation and storage. Our approach achieves an inference performance of just a few milliseconds on standard consumer hardware, without requiring elaborate code optimizations or specialized hardware features. In contrast to physics-based simulation methods, the inference time of our approach is fixed and is independent of the number of strands in the groom or number of collisions in the scene. Our results are stable and the method scales to predicting hundreds of groom simultaneously at interactive rates. In summary, our contributions are + +- A hair decomposition strategy consisting of a hair pose module and a learned corrector, which enables the use of an efficient neural decoder able to produce quasi-static hair results in milliseconds and scales to running a thou + +sand grooms at interactive rates. + +- We are the first to propose a self-supervised learning approach for hair that completely eliminates the necessity of computing and storing large amounts training data, which would require expert knowledge and access to specialized tools to produce. +- A modified formulation of the Cosserat energy for modeling hair. Our formulation is efficient in its evaluation and we demonstrate that it is well-suited for neural network training. Our proposed model is able to preserve hair strand shape for a wide range of hairstyles including very curly hair. +- We demonstrate how a single trained network efficiently models different hairstyles, generalizing to body poses and shapes. + +# 2. Related work + +Strand-based Hair Reconstruction. In recent years there has been significant progress in hair reconstruction research. Recovering hair strands has been especially sought after, since hair reconstructed as strands can easily be integrated into existing game engines, to be animated and rendered with physics-based simulation and rendering. Neural Strands [31] represent the hair groom as a neural texture on the head scalp, where each texel feature can be decoded into an explicit strand. This representation was later trained on a dataset of synthetic grooms, to provide prior for strand-based hair fitting to multi-view images [36]. Zhou et al. [52] proposes a prior-free reconstruction approach. It was extended to support text-guided hair generation in HAAR [37]. The fitting quality was further improved in [23, 45, 48] by additionally decoding Gaussian splats [18] along the strands, representing hair appearance. Instead of requiring multi-view capture, several works explored strand-based hair reconstruction from a dynamic monocular video [46] or just a single image [44, 50], where volumetric 3D hair orientations were used to model hair geometry. To achieve the highest reconstruction quality, Shen et al. [35] captured volumetric CT scans to reconstruct strand-based grooms. + +Learning-based Hair Models. To either accelerate or improve the realism of physics-based simulation or rendering methods, many learning-based hair models have been introduced. Wang et al. [40] use a hybrid representation, with volumetric primitives aligned along guide strands to model hair appearance under motion. To simplify fitting to real observations, Wang et al. [39] used a mixture of volumetric primitives that jointly represent hair geometry and appearance. A unified latent representation for diverse hairstyles has been explored in [12, 51], where explicit strand geometry is encoded into a latent space using a variational autoencoder (VAE) [51] or a generative adversarial network (GAN) [12], enabling hair generation and interpolation across hairstyles. To accelerate hair simulation, Guan + +![](images/e4e8b800fa9fb3b13c9e1441e5668b1904cfb07dd113cae244ae3333450f975a.jpg) +Figure 2. Quaffure Overview: Our method takes a code as input, consisting of a latent code for the rest hair shape, body shape parameters, and full skeleton pose. The output is naturally draped hair produced as the sum of posed hair given the body pose and shape parameters, combined with learned corrections which are produced by the groom deformation decoder. We train our method in two stages: i) an autoencoder is trained on all hairstyles to obtain a groom latent code, and ii) the groom deformation decoder is trained in a physics-based self-supervised fashion. The hair strands are encoded in a 2D texture representation (left) where strands are encoded in the pixel in which the root particle is located. The figure shows how the 3D scalp geometry (bottom) is mapped to a high dimensional 2D texture map (top). + +et al. [11] proposed a multi-linear model for representing hair dynamics, and Lyu et al. [24] introduced a neural upsampler to efficiently convert a low number of guide strands into dense hair. + +Physics-based Hair Models. Realistic hair simulation [41, 42] has been an active area of research in computer graphics for decades. To achieve high-fidelity results, it is necessary to simulate every individual strand and their interactions with each other. Common elastic models used for strand-based hair include mass-spring models [33] and elastic rods [2, 21, 38]. In addition, complex hair-hair interactions such as self-collision [26] and friction forces [17] are also important for realistic behavior. Several reduced models have been developed to lower the computational budget for real-time hair simulation. One idea is to simulate the hair as layered elastic bodies [4, 47], while another suggests representing a group of hairs as strips [19, 20]. The most popular approach is to simulate a subset of the overall hair as guide strands and interpolate between the guides for individual strand detail [6, 13]. Hu et al. [14] propose a method to automatically determine simulation parameters from video footage. + +Physics-based Self-supervised Learning. Data-driven methods have been successful in the field of simulation [9, 30, 49]. However, data-driven methods do not ensure that the simulated system adheres to physical constraints, which can result in non-physical states. To address this, researchers have proposed incorporating physics energy loss directly into the training process to eliminate the need for generating large amounts of data and to enable better generalization. Physics-based self-supervised methods have shown promise in learning a reduced latent space for quasi-static states of rigid motion [34] and cloth drapes [8], which has been expanded to dynamic motions of cloth [3, 10, 16, 32]. However, there is limited research on hair simulation. The neural simulator of GroomGen [51] + +only demonstrated hair deformation for varying gravity directions, while our method is the first to apply a physics-supervised method for hair that generalizes to full motions and incorporates collision under different poses and body shapes. + +# 3. Methodology + +Our approach shown in Figure 2, enables real-time estimation of posed quasi-static hair $\mathbf{x}_{\mathrm{hair}}$ based on hairstyle, body shape and pose. We achieve this by splitting the problem at hand in two parts. First, a simple and efficient groom transformation model transforms the hair groom rigidly with body pose and shape variations expressed as $\mathbf{x}_{\mathrm{posed}}$ . Second, to model the groom specific pose and shape dependent variations $\mathbf{x}_{\mathrm{deformation}}$ , we train a network to produce deformation fields, which when added to the posed hair, result in a physically plausible quasi-static drape that takes physical effects such as gravity and collisions into account. The final hair drape is simply obtained as $\mathbf{x}_{\mathrm{hair}} = \mathbf{x}_{\mathrm{posed}} + \mathbf{x}_{\mathrm{deformation}}$ . + +# 3.1. Representation + +We encode all hair geometry into a texture based representation based on the UV map of the scalp geometry as shown in the left of Figure 2. Where a hair strand root particle falls into a pixel in the map, we encode a high dimensional feature, which represents the strand geometry. For a texture with height and width $T$ and a groom with $N$ vertices per strand, the encoding is of dimension $\mathbb{R}^{T\times T\times N\times 3}$ . + +Body Model: Our body model consists of body geometry rigged with a skeleton model, which enables the body geometry to change pose using linear blend skinning. The skeleton pose is represented using a set of pose parameters $\theta \in \mathbb{R}^{81}$ . To model variations in body shape, we leverage a statistical body model. This model has been constructed from a large data set of human body scans, to which our body geometry has been registered. Body shape variations + +![](images/408364c7d6dd40cd3212852b7a790691224bd851140480cbf1cda69674453424.jpg) +Figure 3. Pose & Shape-based Deformations: Example of posed groom (top) which accounts for rigid rotations and translations of the rest shape only and the combined posed groom with learned deformations (bottom), which accounts for physical effects such as strand material model, gravity and collisions. Despite body intersections incurred by the rigid transformation applied by the groom transformation module, our proposed network resolves all collisions with the body after applying the learned deformations (bottom). Note the significant change resulting in a natural drape. + +are modeled as variations on top of an average shape and are parameterized using body shape coefficients $\beta \in \mathbb{R}^{10}$ . + +# 3.2. Groom Autoencoder + +We leverage an autoencoder to obtain a compact representation for all the different grooms in their rest shape. This model is trained separately and produces compact latent codes in $\mathbb{R}^{16}$ to distinguish different hairstyles. The autoencoder input and output are grooms encoded on the scalp as high dimensional texture maps. The autoencoder structure is made up of 2D convolutional down and up sampling layers for the encoder and decoder respectively. Once the groom autoencoder is fully-trained, we discard its decoder since we are only interested in the latent groom codes produced by the encoder. The weights of the encoder are frozen for the follow-up training of the groom deformation decoder discussed in Section 3.4. + +# 3.3. Pose-based Groom Transformation + +Our pose-based transformation module rigidly transforms the groom in rest shape to account for any rotation and translation changes of the head motion based on the skeleton pose. Every individual hair strand is attached to a scalp triangle at the root. Given the rest configuration, we compute a local coordinate system based on the triangle edges and compute embedding of the hair strand vertices in this local axis. This allows us to efficiently update the strand geometry to move rigidly with the head motion and shape deformations. The top row of Figure 3 shows example results of the pose-based groom transformation. + +# 3.4. Groom Deformation Decoder + +While the pose-based transformation moves the groom rigidly with the scalp, accounting for global rotation and translation effects, it does not include any deformation as a result of varying external forces resulting from changing body pose and shape. The pose-dependent draping effects are accounted for by the groom deformation decoder that produces deformations that, when added to the transformation module's output, produce a physical drape that reacts naturally to gravity and collisions with the underlying body. This module is implemented using a 2D convolutional neural network that takes a vector in $\mathbb{R}^{107}$ , which encodes the groom latent code, the body shape parameters and the body pose parameters. This input vector is transformed by the network into a texture map of dimension $\mathbb{R}^{T\times T\times N\times 3}$ , which encodes the displacements for the vertices along the hair strands. This decoder is trained using a self-supervised loss. Visual results of adding posed based correctives to the rigid groom transformation are shown in Figure 3. + +# 3.5. Physics-Based Self-Supervision + +We formulate a physics-based loss in order to guide the network to produce physically plausible quasi-static drapes for different grooms under different pose and body variations without the need to pre-compute any simulation data. The proposed loss function is designed to capture the different components that enable the hair to settle in a physically plausible way. This includes the elastic potential of the strands, which limits stretching, bending and twisting of the individual strands, the gravitational pull, the collisions with the underlying body, and the collisions between the hair strands themselves. Additionally, we add a pose regularizer to produce smoothly varying results for smoothly varying skeleton motion sequences. Thus the total consist of the following terms: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\text {e l a s t i c - p o t e n t i a l}} + \mathcal {L} _ {\text {g r a v i t y}} + \mathcal {L} _ {\text {b o d y - c o l l i s i o n}} \\ + \mathcal {L} _ {\text {s e l f - c o l l i s i o n}} + \mathcal {L} _ {\text {p o s e - r e g}} \\ \end{array} +$$ + +(1) + +**Elastic Potentials:** The elastic potentials allow hair deformation while preserving the length and curvature of each strand. To better preserve the natural curliness of a hairstyle, We first incorporated the Cosserat rod model [21] into our system by introducing additional orientation information (stored as unit quaternions $q = (q_0, \mathbf{q}^T)^T \in \mathbb{H}$ with the scalar part $q_0$ and the vector part $\mathbf{q}$ ) for each hair segment and optimizing for the additional orientation offsets. Our elastic potential is in the form: + +$$ +\mathcal {L} _ {\text {e l a s t i c - p o t e n t i a l}} = \mathcal {L} _ {\text {s t r e t c h - s h e a r}} + \mathcal {L} _ {\text {b e n d - t w i s t}} + \mathcal {L} _ {\text {u n i t - q u a t e r n i o n}}, \tag {2} +$$ + +where the Cosserat stretch-shear energy: + +$$ +\mathcal {L} _ {\text {s t r e t c h - s h e a r}} = \frac {1}{2} \sum_ {\text {e d g e s}} \mathrm {k} _ {\text {s t r e t c h - s h e a r}} \boldsymbol {\Gamma} ^ {T} \boldsymbol {\Gamma}, \tag {3} +$$ + +is computed from the discrete stretch-shear strain measure $\Gamma = \frac{\mathbf{x}_{i + 1} - \mathbf{x}_i}{l_{\mathrm{rest}}} - \Im (q_i\mathbf{e}_3\bar{q}_i)$ for a hair segment $i$ , with rest length $l_{\mathrm{rest}}$ , end points $\mathbf{x}_{i + 1}$ and $\mathbf{x}_i$ , orientation $q_{i}$ and fixed coordinate basis $\{\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3\}$ , where $\Im ()$ is the imaginary part of the quaternion product. Similarly, the Cosserat bend-twist energy: + +$$ +\mathcal {L} _ {\text {b e n d}, \text {t w i s t}} = \frac {1}{2} \sum_ {\text {e d g e p a i r s}} \mathrm {k} _ {\text {b e n d}, \text {t w i s t}} \boldsymbol {\Omega} ^ {T} \boldsymbol {\Omega}, \tag {4} +$$ + +is computed from the discrete bend-twist strain measure $\Omega = \frac{2}{l_{\mathrm{rest}}} (\Im (\bar{q}_i q_{i + 1}) - \Im (\bar{q}_i^0 q_{i + 1}^0))$ for each consecutive hair orientation pair $q_{i}$ and $q_{i + 1}$ , with rest orientations $q_{i}^{0}$ and $q_{i + 1}^{0}$ . An additional unit quaternion constraint is needed for correct bend-twist strain measure, this is enforced for each orientation $q$ : + +$$ +\mathcal {L} _ {\text {u n i t - q u a t e r n i o n}} = \frac {1}{2} \sum_ {\text {e d g e s}} k _ {\text {u n i t - q u a t e r n i o n}} (| | q | | - 1) ^ {2}. \tag {5} +$$ + +Although this full Cosserat rod model, which optimizes for both position and orientation offsets, can enable realistic modeling of hair, we observed impractically slow training times and in combination with slow convergence, this approach was deemed infeasible. Instead, we propose an alternative formulation, which optimizes for position offsets only with the following modified Cosserat potential: + +$$ +\mathcal {L} _ {\text {C o s s e r a t}} = \frac {1}{2} \sum_ {\text {e d g e s}} k _ {\text {C o s s e r a t}} \tilde {\Gamma} ^ {T} \tilde {\Gamma}, \tag {6} +$$ + +where $\tilde{\Gamma} = \frac{\mathbf{x}_{i + 1} - \mathbf{x}_i}{l_{\mathrm{rest}}} - \mathbf{d}_3$ , with $\mathbf{d}_3$ being the unit director along the edge, computed from the rigidly transformed groom. As the modified Cosserat potential penalizes stretching and shearing simultaneously, we observed that hair would become overly rigid when a large stiffness value $\mathrm{k_{COSERAT}}$ is used (which is common as hair is almost inextensible). Therefore, to relax $\mathrm{k_{COSERAT}}$ for more natural hair deformation, we model resistance to stretching explicitly by adding a Hookean potential to penalize the length $l$ of each hair segment to be close to $l_{\mathrm{rest}}$ : + +$$ +\mathcal {L} _ {\text {s t r e t c h}} = \frac {k _ {\text {s t r e t c h}}}{2} \sum_ {\text {e d g e s}} \left(l - l _ {\text {r e s t}}\right) ^ {2}. \tag {7} +$$ + +Alternatively, one can choose to use the potential that penalizes shearing only: $\tilde{\Gamma} = \frac{\mathbf{x}_{i + 1} - \mathbf{x}_i}{l} -\mathbf{d}_3$ , with $l$ being the segment length. In practice, we observed similar results from both potentials. Our final elastic potential include only two terms and we observe orders of magnitude faster training time when compared with the full Cosserat rod model + +$$ +\mathcal {L} _ {\text {e l a s t i c - p o t e n t i a l}} = \mathcal {L} _ {\text {s t r e t c h}} + \mathcal {L} _ {\text {C o s s e r a t}}. \tag {8} +$$ + +Gravity: The gravity potential is modeled using the potential energy of the hair nodes with positions $\mathbf{x}$ as: + +$$ +\mathcal {L} _ {\text {g r a v i t y}} = \sum_ {\text {v e r t i c e s}} - m \mathbf {g} ^ {\top} \mathbf {x}, \tag {9} +$$ + +where $\mathbf{g}$ is the gravitational acceleration and $m$ is the parti + +cle point mass. + +Body Collision: To prevent the hair strands from intersecting with the body geometry, we implement a vertex-triangle based collision model to maintain a minimal distance $D$ between the predicted hair and the outward facing side of the body geometry. We exploit the face normal information to ensure the collision response is pointing outwards of the body. The loss is formulated as follows: + +$$ +\mathcal {L} _ {\text {b o d y ＿ c o l l i s i o n}} = \mathrm {k} _ {\mathrm {b c}} \sum_ {\text {v e r t i c e s}} \max (D - d (\mathbf {x}), 0) ^ {3}, \tag {10} +$$ + +where $d$ computes the signed distance along the body triangle normal direction and $\mathsf{k}_{\mathrm{bc}}$ is the collision stiffness. Body triangle normals are facing outwards by convention. + +Self-Collision: Inspired by work on volumetric methods for hair [1, 26, 29], we model hair self-collisions using Smoothed Particle Hydrodynamics (SPH) density estimation. Our energy potential is designed to push vertices apart when they exceed the reference density computed from the rest shape in a smooth and differentiable way: + +$$ +\mathcal {L} _ {\text {s e l f . c o l l i s i o n}} = \mathrm {k} _ {\mathrm {s c}} \sum_ {\text {v e r t i c e s}} \max \left(\rho (\mathbf {x}) - \rho_ {\text {r e s t}}, 0\right) ^ {3}, \tag {11} +$$ + +$$ +\rho (\mathbf {x}) = \sum_ {j} m _ {j} W \left(\left\| \mathbf {x} - \mathbf {x} _ {j} \right\|, h\right), \tag {12} +$$ + +using the smoothing kernel proposed by Bando et al. [1]: + +$$ +W (r, h) = \left\{ \begin{array}{l l} 4 - 6 \left(\frac {r}{h}\right) ^ {2} + 3 \left(\frac {r}{h}\right) ^ {3} & 0 \leq r \leq h \\ \left(2 - \frac {r}{h}\right) ^ {3} & h \leq r \leq 2 h \\ 0 & 2 h \leq r \end{array} \right. \tag {13} +$$ + +where $\rho_{\mathrm{rest}}$ is the density computed from the rest groom and $h$ is the SPH smoothing length. + +Pose Regularization: We add a final loss to encourage the groom deformation decoder to predict smoothly varying deformations for smoothly varying input pose signals. During training, for every randomly sampled pose from our motion capture data set, we include $N_{\mathrm{pose\_reg}}$ continuous frames and penalize the difference with respect to the average deformation in predicted outputs for consecutive frames as: + +$$ +\mathcal {L} _ {\text {p o s e} \cdot \text {r e g}} = k _ {p r} \sum_ {i = 0} ^ {N _ {\text {p o s e} \cdot \text {r e g}}} | | \bar {\mathbf {x}} _ {\text {d e f o r m a t i o n}} - \mathbf {x} _ {\text {d e f o r m a t i o n}} ^ {i} | | ^ {2} \tag {14} +$$ + +where $\bar{\mathbf{x}}_{\mathrm{deformation}}$ is the average of $\mathbf{x}_{\mathrm{deformation}}^i$ over all $N_{\mathrm{pose\_reg}}$ continuous frames per randomly selected pose. + +# 4. Experiments + +Dataset: We train our networks using the CT-groom data set [35] complemented with additional grooms made by technical artists to showcase a wider variety of hairstyles. Our method is capable of simulating. + +Metrics: To evaluate our approach we opted for three key metrics: i) the length preservation of the hair strands measured on the segment lengths, ii) the percentage of intersec + +![](images/765d3efa720f56644b269112c8217ab8d995423b8ce0125e9474ef7539a81e6e.jpg) +Figure 4. Modeling Diverse Hairstyles: We showcase the versatility of our method in modeling the quasi-static behavior of a plethora of hairstyles and lengths for different body shapes and poses where all results are obtained using the same settings without any manual parameter tuning. Our results cover short/medium/long hair, with various levels of curliness, including straight, wavy, curly, and kinky. + +![](images/1dc02333ddb41dfc439ccf2446bdd24c691753669a82b2699cf70d145fd39433.jpg) +Figure 5. Resolving Collisions: Our method is conditioned on the body shape parameters, enabling it to efficiently resolve collisions with body shape variations. Here we show a static pose and groom under quasi-statically draped under varying body shapes. + +tions between the hair and the body, and iii) the preservation of the hair shape measured from the segment orientations. + +Baselines: We compare our method against two optimization-based approaches (Adam, L-BFGS) and one simulation (XPBD [25]) baseline. We additionally compare to a recent related work GroomGen [51], which presented a neural quasi-static simulator using supervised training. GroomGen only showed results for varying gravity directions for a single fixed pose and shape, whereas our method generalizes to different shapes and poses. All images show the predicted strands directly without any hair interpolation to provide a fair assessment. When rendering hair for the final application, hair interpolation [13] can be leveraged to obtain the full set of hair strands. + +Implementation Details: In all of our results, strands consist of $N = 24$ vertices, which are encoded into $64 \times 64$ texture maps. This choice of texture dimensions provides us with the ability to model several thousands of hair strands, which is sufficient for guide hair simulation. We implement our method with PyTorch [28], with training and inference measurements performed on an AMD Ryzen Threadripper PRO 3975WX CPU and a single NVIDIA RTX A6000 GPU. We refer the reader to the supplementary material for additional details. + +# 4.1. Qualitative Comparisons + +Body Pose and Shape Generalization: Our deformation decoder network is able to ingest body shape parameters directly and effectively learns to adapt the deformations of the hair strands to produce intersection free results for a large variety of body shapes. Figure 4 showcases a large sample of pose variations for a diverse set of grooms while in Figure 5 we demonstrate body shape generalization. Implausible deformations are possible when deforming the body in non-physical ways, e.g. when bending the neck backwards beyond limits feasible in real-life and thus absent from our training data set. + +Temporal Stability: Our method demonstrates excellent temporal stability in its predictions when the pose parameters are smoothly varied. This is evident in Figure 6, where the hair smoothly slides over the shoulder as the head turns, avoiding any self-penetration with the body. The supplemental material shows video results. + +Groom Generalization: We prioritize real-time performance for our approach, therefore opting for a smaller network structure that enables real-time inference results. We show that our model can handle at least 10 distinct grooms. In the supplemental material, we demonstrate that the network already shows some generalization properties for unseen grooms when they are similar to the training set. + +# 4.2. Quantitative Comparisons + +Comparisons: The quantitative results are listed in Table 1. As expected, directly modifying the simulated hair positions, either using Adam, L-BFGS or XPBD simulation to minimize the loss produces the highest quality results but at a high computational cost. Neural methods like GroomGen and ours are orders of magnitude faster. Our method produces significantly better quantitative results when com + +Table 1. Quantitative Comparisons. We compare our method to several optimization and simulation baselines as well as related work. Our method displays comparable metrics to directly optimizing for the positions but does so orders of magnitude faster. Compared to the state-of-the-art method GroomGen, our method produces better quality metrics while being generalizable to body shape and pose, with comparable compute performance, providing the best trade-off between speed and quality. Gravity potentials are provided for reference. + +
Method(↓) Time (↓) % body in secondsIntersectionLength (↓) Orientation PreservationOrientation PotentialGravity Potential
Adam179.380.22103.5376.153011.33
L-BFGS281.180.2289.5370.223047.53
XPBD (GPU) [25]63.260.0157.9618.103507.53
GroomGen [51]0.002490.391319.741281.963889.78
Ours0.002860.26175.42286.133399.95
+ +![](images/829d556dc1f5131a4015b5490075b9c01bffb6665f085d0b459de3936d1ba57c.jpg) +Figure 6. Temporal Stability: To demonstrate how predicted results are smoothly varying with pose changes, we gradually modify the neck rotation. Starting from looking to the right to looking left. Note how the results are smoothly varying where every pose produces a natural drape. Note especially the hair sliding over the shoulders with minimal body intersections. + +![](images/be5c07deb8a48ec2aefbf9f4f3b558d08743c3848c61842cb612a4e2ecabb05f.jpg) +Quaffure + +![](images/731a957535f3637331d407bde1c04c0770e119e224b1f4f6e88478f5c6e78801.jpg) +Adam + +![](images/e8220902cbd6a87cc3c881ec7470c140a4ef7a4e550d9c031a1d5c48b8f77888.jpg) +L-BFGS +Figure 7. Qualitative Comparisons: Our method produces visually comparable results to directly minimizing the energies or to quasi-static simulation with XPBD while being orders of magnitude faster at inference by memorizing body pose and shape dependent groom deformations. + +![](images/fc628280e2e724ddec160d93085aa07485cd88f1ca3acd50b2ea96dcf81823da.jpg) +XPBD + +pared to GroomGen at preserving strand lengths as well as the preservation of the hair shape measured from the segment orientations. Furthermore, it is important to note that, unlike GroomGen, our method handles arbitrary motion and generalizes to body shape. Figure 8 shows that GroomGen results display frequent intersections of the hair strands with the body. These results demonstrate that our method provides the best trade-offs in terms of performance and quantitative results with the significant added benefit that we do not require any simulated training data. + +![](images/85f70c115d6ce3e0216583a4dc6648317572468c508532caeba7cdc58760f655.jpg) + +![](images/24fc831fc786f964f16c3bcf81cfd1eba5e46f93530f05ff30c4c30ebf9b41fa.jpg) +Figure 8. Comparisons with GroomGen: We compare our results (bottom) to those obtained with the neural simulator proposed in GroomGen [51] (top). The inset figure highlights that GroomGen produces results where strands intersect with the head geometry. In contrast, our method produces much fewer body-collisions producing better visual results. See the supplemental video for the full animated comparison. + +Adam & L-BFGS - Energy Minimization: We compare against quasi-static simulation results by minimizing the loss energy with respect to the hair vertex positions directly using Adam and L-BFGS. The results are computed with the highest learning rate that produces stable results. The use of L-BFGS in simulation research has been applied for generating simulations at interactive rates [22]. Visual results in Figure 7 show that our method is visually comparable with the quasi-static energy minimization results, but at real-time rates that are independent of groom resolution. This demonstrates that our method is highly effective at learning the mapping that positions deformed hair vertices near the energy minimum. + +XPBD - Physics-based Simulation: The XPBD method [25] effectively exploits GPU parallelism, which results in fast computation times. Simulation has been the de facto solution to hair animation for years due to the high realism, albeit at a high computational cost. Additionally, time integration of the system can often lead to instabilities, which will result in failures or undesirable results. In contrast, our method does not display any time integration instabilities. In our comparison, we model hair using the same energy as described in Subsection 3.5. To obtain quasi-static simulation results, we reset the velocities for each time step in the XPBD simulation loop, before applying gravity. We integrate the positions and use 10000 iterations to minimize the loss. We run 30 time steps to obtain results close to convergence. + +GroomGen: We additionally compare our method to GroomGen [51]. Code is not publicly available so we compare to our own re-implementation. Instead of train + +![](images/a382d4552855119937471fea77f44515d46b7120534d23a52a1a2a002d9b34bf.jpg) +Figure 9. Performance & Scaling: Our method takes less than 3 ms on average to predict a single groom and the time complexity scales linearly with the number of grooms. The method is able to predict a thousand hairstyles in 0.3 seconds. + +![](images/ed38f364795c1b4950dabc54931157d29dc90373cca2101348f39d714c7674c7.jpg) +Groom Rest Shape +Figure 10. Ablation Study: We perform an ablation of our proposed optimization-friendly Cosserat model against the commonly used mass-spring energy for modeling hair. Our model excels at maintaining the desired hairstyle whereas the mass-spring model struggles with maintaining curliness and volume. + +![](images/0af1a3b283fd4bd4339e952fc43376a1ebc311a538d816db0259d109ba70e3e8.jpg) +Mass-Spring Energy + +![](images/84fb876b729b262d78995bb23da258e3f70c0b563c2242cceaedb312e0e2cf24.jpg) +Cosserat Energy (ours) + +ing the neural simulator with different gravity directions, we stochastically sample 1000 body poses with different neck rotations within 30 degrees along $(x,y,z)$ axes, and run quasi-static hair simulation to obtain the training data. In Figure 8 provides a qualitative comparison between our approach and GroomGen for a groom that consists of 1919 strands. Both methods provide visually pleasing results but our approach results in significantly fewer intersections of hair with the body. This is highlighted in the inset figure where you can see several hair strands intersect for GroomGen whereas ours remains intersection free. + +# 4.3. Performance + +Predicting a single groom takes $2.86\mathrm{ms}$ and predicting a thousand at once requires 0.3 seconds. The performance is independent of the number of strands due to the fixed size of the representation. Performance for a varying number of groom and pose variations is shown in Figure 9. Strand count for the varying grooms used in training varies between 1500 and 2500. + +# 4.4. Ablations & Discussion + +We perform an ablation experiment on the importance of our proposed Cosserat energy. Figure 10 shows that our model is highly effective at maintaining hairstyle and curli + +![](images/a229e7dd445386b96d46de5d7b5dae76c93a5f6746f91bc268df2f5845ecf25d.jpg) +Figure 11. Ablation Study on Cosserat stiffness: Results obtained by varying the Cosserat stiffness in our proposed physics-based loss that enables artistic control. A higher stiffness results in strands that maintain their rest shape better (left) compared to a lower value (right). The images are mirrored and a few strand hair tip locations are highlighted for an easier comparison. + +ness. We compare our results to those using a mass-spring energy [33]. Our model maintains the intended hairstyle well without manual intervention whereas the mass-spring model requires extensive parameter tuning to obtain satisfactory results and the hair still falls mostly flat under gravity. Our model provides artistic control by manipulating the stiffness parameters. Figure 11 demonstrates the effect of varying material stiffness. + +Limitations and Future Work: Our pose-based groom transformation module can produce hair where strands are partially initialized inside the body. A better model which results in fewer intersections would make it easier for the model to learn the required deformations. Nonetheless, we observe that our network is able to robustly handle this. Current results use a single set of physical parameters for the hair material properties. This shows that parameter tuning is not required to produce visually pleasing results. However, we plan to condition the network on material parameters to enable artistic control at inference. + +# 5. Conclusion + +We present the first self-supervised neural approach to real-time quasi-static hair simulation. Our method enables efficient drape generation for various hairstyles on different body poses and shapes, which varies smoothly with pose variations. Our model leverages a hair deformation decomposition based on a transformation module and a learned deformation decoder, which is trained using self-supervision. We demonstrate complex behavior such as hair sliding over shoulders, maintaining complex hairstyles such as curly grooms and natural draping results due to the effects of gravity. To validate the method, we demonstrate that our decoder is effective and efficient at posing hair strands near the quasi-static energy minimum with better qualitative and quantitative results compared to related work. + +# References + +[1] Yosuke Bando, Bing-Yu Chen, and Tomoyuki Nishita. Animating hair with loosely connected particles. In Computer Graphics Forum, pages 411-418. Wiley Online Library, 2003. 2, 5 +[2] Miklos Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. Discrete elastic rods. In ACM SIGGRAPH 2008 Papers. 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We present Quaffure, a real-time quasi-static neural hair simulator, which produces naturally draped hair in only a few milliseconds on commodity hardware, taking the hairstyle, body shape and pose into account. Our method scales to predicting the drape of 1000 hair grooms in just 0.3 seconds. Quaffure is trained using a physics-based self-supervised loss, eliminating the need for simulated training data that is costly and cumbersome to obtain. We show that our method works for a wide variety of body shapes and poses with a range of hairstyles varying from straight to curly, short to long." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 151, + 502, + 200, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 502, + 200, + 513 + ], + "spans": [ + { + "bbox": [ + 151, + 502, + 200, + 513 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 529, + 297, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 529, + 297, + 708 + ], + "spans": [ + { + "bbox": [ + 54, + 529, + 297, + 708 + ], + "type": "text", + "content": "Realistic hair motion is crucial for high-quality avatars, but it is often limited by the computational resources available for real-time applications. To address this challenge, we propose a novel neural approach to predict physically plausible hair deformations that generalizes to various body poses, shapes, and hairstyles. Our model is trained using a self-supervised loss, eliminating the need for expensive data generation and storage. We demonstrate our method's effectiveness through numerous results across a wide range of pose and shape variations, showcasing its robust generalization capabilities and temporally smooth results. Our approach is highly suitable for real-time applications with an inference time of only a few milliseconds on consumer hardware and its ability to scale to predicting the drape of 1000 grooms in 0.3 seconds." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 502, + 394, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 502, + 394, + 513 + ], + "spans": [ + { + "bbox": [ + 315, + 502, + 394, + 513 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": "Hair is a crucial aspect of realistic avatars, playing a vital role in real-time applications such as games and telepresence, as well as offline generation of digital characters for film. Over the past decades, computer graphics research has devoted significant attention to the topic of hair, in order to create believable and engaging virtual characters. Hair modeling is a complex process that involves multiple stages, including grooming, simulation, and rendering. Previous research has explored various approaches to hair motion modeling, including physics-based simulations [7, 15, 43] and data-driven methods [11, 39, 40]. However, hair remains a challenging phenomenon to model due to the high number of degrees of freedom required to represent a full head of hair, which typically consists of hundreds of thousands of strands. To make hair motion modeling more tractable, it is common practice to model a full groom with a" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "239" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "limited number of strands, often referred to as guide strands. This approach involves modeling a subset of strands to represent the full groom, and then recovering the full resolution hair groom from these guide strands for rendering [13]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 122, + 297, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 122, + 297, + 469 + ], + "spans": [ + { + "bbox": [ + 56, + 122, + 297, + 469 + ], + "type": "text", + "content": "Simulating the dynamics of hair motions has received significant attention in the field. Several approaches have been developed to model the behavior of hair strands ranging from efficient mass-spring systems [33] to rod models [2, 21, 38] able to model bending and twisting, producing complex coiling motions to volumetric approaches [1, 26, 29]. Despite impressive visual results, these models still require large computational resources making them ill-suited for real-time applications. Many advances in the field of physics-based simulation has resulted in efficient algorithms that are able to exploit parallelism of GPU hardware, resulting in real-time simulations [5, 25, 27]. However, these still require dedicated hardware resources [7, 43] and compute time might vary based on the resolution and number of the hair strands as well as the number of collisions occurring in the scene. Additionally, physics-based simulation can often be unstable and require significant parameter tuning, often leading to unpredictable or undesirable results. To address this, subspace simulation has been applied to hair dynamics but this remains limited to models that overfit to a single groom only [6]. Learned simulators [24, 51] have shown promise for modeling real-time hair dynamics but require large data sets, which are cumbersome to obtain. In general, supervised learning requires training data, which needs to be generated using physics-based simulation. This is both expensive in terms of time and storage required but also requires expert knowledge and access to specialized tools to produce. There is no publicly available data set that could be leveraged." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 472, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 295, + 662 + ], + "type": "text", + "content": "In this paper, we propose a novel and efficient neural hair simulation approach to model hair quasi-statics. Our method leverages a learning-based method to predict physically plausible hair deformations, while also generalizing to various body poses and shapes. We opted for training in a self-supervised manner, eliminating the need for expensive data generation and storage. Our approach achieves an inference performance of just a few milliseconds on standard consumer hardware, without requiring elaborate code optimizations or specialized hardware features. In contrast to physics-based simulation methods, the inference time of our approach is fixed and is independent of the number of strands in the groom or number of collisions in the scene. Our results are stable and the method scales to predicting hundreds of groom simultaneously at interactive rates. In summary, our contributions are" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "- A hair decomposition strategy consisting of a hair pose module and a learned corrector, which enables the use of an efficient neural decoder able to produce quasi-static hair results in milliseconds and scales to running a thou" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 323, + 73, + 455, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 73, + 455, + 83 + ], + "spans": [ + { + "bbox": [ + 323, + 73, + 455, + 83 + ], + "type": "text", + "content": "sand grooms at interactive rates." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 84, + 553, + 251 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 84, + 553, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 84, + 553, + 143 + ], + "spans": [ + { + "bbox": [ + 314, + 84, + 553, + 143 + ], + "type": "text", + "content": "- We are the first to propose a self-supervised learning approach for hair that completely eliminates the necessity of computing and storing large amounts training data, which would require expert knowledge and access to specialized tools to produce." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 144, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 215 + ], + "type": "text", + "content": "- A modified formulation of the Cosserat energy for modeling hair. Our formulation is efficient in its evaluation and we demonstrate that it is well-suited for neural network training. Our proposed model is able to preserve hair strand shape for a wide range of hairstyles including very curly hair." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 216, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 216, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 216, + 553, + 251 + ], + "type": "text", + "content": "- We demonstrate how a single trained network efficiently models different hairstyles, generalizing to body poses and shapes." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 262, + 399, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 262, + 399, + 275 + ], + "spans": [ + { + "bbox": [ + 314, + 262, + 399, + 275 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 282, + 555, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 555, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 555, + 545 + ], + "type": "text", + "content": "Strand-based Hair Reconstruction. In recent years there has been significant progress in hair reconstruction research. Recovering hair strands has been especially sought after, since hair reconstructed as strands can easily be integrated into existing game engines, to be animated and rendered with physics-based simulation and rendering. Neural Strands [31] represent the hair groom as a neural texture on the head scalp, where each texel feature can be decoded into an explicit strand. This representation was later trained on a dataset of synthetic grooms, to provide prior for strand-based hair fitting to multi-view images [36]. Zhou et al. [52] proposes a prior-free reconstruction approach. It was extended to support text-guided hair generation in HAAR [37]. The fitting quality was further improved in [23, 45, 48] by additionally decoding Gaussian splats [18] along the strands, representing hair appearance. Instead of requiring multi-view capture, several works explored strand-based hair reconstruction from a dynamic monocular video [46] or just a single image [44, 50], where volumetric 3D hair orientations were used to model hair geometry. To achieve the highest reconstruction quality, Shen et al. [35] captured volumetric CT scans to reconstruct strand-based grooms." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "type": "text", + "content": "Learning-based Hair Models. To either accelerate or improve the realism of physics-based simulation or rendering methods, many learning-based hair models have been introduced. Wang et al. [40] use a hybrid representation, with volumetric primitives aligned along guide strands to model hair appearance under motion. To simplify fitting to real observations, Wang et al. [39] used a mixture of volumetric primitives that jointly represent hair geometry and appearance. A unified latent representation for diverse hairstyles has been explored in [12, 51], where explicit strand geometry is encoded into a latent space using a variational autoencoder (VAE) [51] or a generative adversarial network (GAN) [12], enabling hair generation and interpolation across hairstyles. To accelerate hair simulation, Guan" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "240" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 549, + 186 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 549, + 186 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 549, + 186 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 549, + 186 + ], + "type": "image", + "image_path": "e4e8b800fa9fb3b13c9e1441e5668b1904cfb07dd113cae244ae3333450f975a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 195, + 555, + 262 + ], + "lines": [ + { + "bbox": [ + 54, + 195, + 555, + 262 + ], + "spans": [ + { + "bbox": [ + 54, + 195, + 555, + 262 + ], + "type": "text", + "content": "Figure 2. Quaffure Overview: Our method takes a code as input, consisting of a latent code for the rest hair shape, body shape parameters, and full skeleton pose. The output is naturally draped hair produced as the sum of posed hair given the body pose and shape parameters, combined with learned corrections which are produced by the groom deformation decoder. We train our method in two stages: i) an autoencoder is trained on all hairstyles to obtain a groom latent code, and ii) the groom deformation decoder is trained in a physics-based self-supervised fashion. The hair strands are encoded in a 2D texture representation (left) where strands are encoded in the pixel in which the root particle is located. The figure shows how the 3D scalp geometry (bottom) is mapped to a high dimensional 2D texture map (top)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 277, + 294, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 277, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 54, + 277, + 294, + 326 + ], + "type": "text", + "content": "et al. [11] proposed a multi-linear model for representing hair dynamics, and Lyu et al. [24] introduced a neural upsampler to efficiently convert a low number of guide strands into dense hair." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 327, + 295, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 327, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 57, + 327, + 295, + 543 + ], + "type": "text", + "content": "Physics-based Hair Models. Realistic hair simulation [41, 42] has been an active area of research in computer graphics for decades. To achieve high-fidelity results, it is necessary to simulate every individual strand and their interactions with each other. Common elastic models used for strand-based hair include mass-spring models [33] and elastic rods [2, 21, 38]. In addition, complex hair-hair interactions such as self-collision [26] and friction forces [17] are also important for realistic behavior. Several reduced models have been developed to lower the computational budget for real-time hair simulation. One idea is to simulate the hair as layered elastic bodies [4, 47], while another suggests representing a group of hairs as strips [19, 20]. The most popular approach is to simulate a subset of the overall hair as guide strands and interpolate between the guides for individual strand detail [6, 13]. Hu et al. [14] propose a method to automatically determine simulation parameters from video footage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "type": "text", + "content": "Physics-based Self-supervised Learning. Data-driven methods have been successful in the field of simulation [9, 30, 49]. However, data-driven methods do not ensure that the simulated system adheres to physical constraints, which can result in non-physical states. To address this, researchers have proposed incorporating physics energy loss directly into the training process to eliminate the need for generating large amounts of data and to enable better generalization. Physics-based self-supervised methods have shown promise in learning a reduced latent space for quasi-static states of rigid motion [34] and cloth drapes [8], which has been expanded to dynamic motions of cloth [3, 10, 16, 32]. However, there is limited research on hair simulation. The neural simulator of GroomGen [51]" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 277, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 338 + ], + "type": "text", + "content": "only demonstrated hair deformation for varying gravity directions, while our method is the first to apply a physics-supervised method for hair that generalizes to full motions and incorporates collision under different poses and body shapes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 346, + 397, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 397, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 397, + 360 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "content": "Our approach shown in Figure 2, enables real-time estimation of posed quasi-static hair " + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{hair}}" + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "content": " based on hairstyle, body shape and pose. We achieve this by splitting the problem at hand in two parts. First, a simple and efficient groom transformation model transforms the hair groom rigidly with body pose and shape variations expressed as " + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{posed}}" + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "content": ". Second, to model the groom specific pose and shape dependent variations " + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{deformation}}" + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "content": ", we train a network to produce deformation fields, which when added to the posed hair, result in a physically plausible quasi-static drape that takes physical effects such as gravity and collisions into account. The final hair drape is simply obtained as " + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{hair}} = \\mathbf{x}_{\\mathrm{posed}} + \\mathbf{x}_{\\mathrm{deformation}}" + }, + { + "bbox": [ + 313, + 366, + 556, + 511 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 516, + 408, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 408, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 408, + 528 + ], + "type": "text", + "content": "3.1. Representation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "text", + "content": "We encode all hair geometry into a texture based representation based on the UV map of the scalp geometry as shown in the left of Figure 2. Where a hair strand root particle falls into a pixel in the map, we encode a high dimensional feature, which represents the strand geometry. For a texture with height and width " + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "text", + "content": " and a groom with " + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "text", + "content": " vertices per strand, the encoding is of dimension " + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{T\\times T\\times N\\times 3}" + }, + { + "bbox": [ + 313, + 534, + 555, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": "Body Model: Our body model consists of body geometry rigged with a skeleton model, which enables the body geometry to change pose using linear blend skinning. The skeleton pose is represented using a set of pose parameters " + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{81}" + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": ". To model variations in body shape, we leverage a statistical body model. This model has been constructed from a large data set of human body scans, to which our body geometry has been registered. Body shape variations" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "241" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 71, + 296, + 209 + ], + "blocks": [ + { + "bbox": [ + 57, + 71, + 296, + 209 + ], + "lines": [ + { + "bbox": [ + 57, + 71, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 57, + 71, + 296, + 209 + ], + "type": "image", + "image_path": "408364c7d6dd40cd3212852b7a790691224bd851140480cbf1cda69674453424.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 215, + 296, + 316 + ], + "lines": [ + { + "bbox": [ + 55, + 215, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 215, + 296, + 316 + ], + "type": "text", + "content": "Figure 3. Pose & Shape-based Deformations: Example of posed groom (top) which accounts for rigid rotations and translations of the rest shape only and the combined posed groom with learned deformations (bottom), which accounts for physical effects such as strand material model, gravity and collisions. Despite body intersections incurred by the rigid transformation applied by the groom transformation module, our proposed network resolves all collisions with the body after applying the learned deformations (bottom). Note the significant change resulting in a natural drape." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 334, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 296, + 360 + ], + "type": "text", + "content": "are modeled as variations on top of an average shape and are parameterized using body shape coefficients " + }, + { + "bbox": [ + 55, + 334, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 55, + 334, + 296, + 360 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 371, + 174, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 174, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 174, + 384 + ], + "type": "text", + "content": "3.2. Groom Autoencoder" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 392, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 392, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 392, + 296, + 547 + ], + "type": "text", + "content": "We leverage an autoencoder to obtain a compact representation for all the different grooms in their rest shape. This model is trained separately and produces compact latent codes in " + }, + { + "bbox": [ + 55, + 392, + 296, + 547 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{16}" + }, + { + "bbox": [ + 55, + 392, + 296, + 547 + ], + "type": "text", + "content": " to distinguish different hairstyles. The autoencoder input and output are grooms encoded on the scalp as high dimensional texture maps. The autoencoder structure is made up of 2D convolutional down and up sampling layers for the encoder and decoder respectively. Once the groom autoencoder is fully-trained, we discard its decoder since we are only interested in the latent groom codes produced by the encoder. The weights of the encoder are frozen for the follow-up training of the groom deformation decoder discussed in Section 3.4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 561, + 242, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 242, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 242, + 574 + ], + "type": "text", + "content": "3.3. Pose-based Groom Transformation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "Our pose-based transformation module rigidly transforms the groom in rest shape to account for any rotation and translation changes of the head motion based on the skeleton pose. Every individual hair strand is attached to a scalp triangle at the root. Given the rest configuration, we compute a local coordinate system based on the triangle edges and compute embedding of the hair strand vertices in this local axis. This allows us to efficiently update the strand geometry to move rigidly with the head motion and shape deformations. The top row of Figure 3 shows example results of the pose-based groom transformation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 72, + 474, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 474, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 474, + 84 + ], + "type": "text", + "content": "3.4. Groom Deformation Decoder" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "text", + "content": "While the pose-based transformation moves the groom rigidly with the scalp, accounting for global rotation and translation effects, it does not include any deformation as a result of varying external forces resulting from changing body pose and shape. The pose-dependent draping effects are accounted for by the groom deformation decoder that produces deformations that, when added to the transformation module's output, produce a physical drape that reacts naturally to gravity and collisions with the underlying body. This module is implemented using a 2D convolutional neural network that takes a vector in " + }, + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{107}" + }, + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "text", + "content": ", which encodes the groom latent code, the body shape parameters and the body pose parameters. This input vector is transformed by the network into a texture map of dimension " + }, + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{T\\times T\\times N\\times 3}" + }, + { + "bbox": [ + 313, + 91, + 555, + 308 + ], + "type": "text", + "content": ", which encodes the displacements for the vertices along the hair strands. This decoder is trained using a self-supervised loss. Visual results of adding posed based correctives to the rigid groom transformation are shown in Figure 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 317, + 484, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 317, + 484, + 331 + ], + "spans": [ + { + "bbox": [ + 313, + 317, + 484, + 331 + ], + "type": "text", + "content": "3.5. Physics-Based Self-Supervision" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 336, + 556, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 336, + 556, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 336, + 556, + 504 + ], + "type": "text", + "content": "We formulate a physics-based loss in order to guide the network to produce physically plausible quasi-static drapes for different grooms under different pose and body variations without the need to pre-compute any simulation data. The proposed loss function is designed to capture the different components that enable the hair to settle in a physically plausible way. This includes the elastic potential of the strands, which limits stretching, bending and twisting of the individual strands, the gravitational pull, the collisions with the underlying body, and the collisions between the hair strands themselves. Additionally, we add a pose regularizer to produce smoothly varying results for smoothly varying skeleton motion sequences. Thus the total consist of the following terms:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 507, + 521, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 507, + 521, + 536 + ], + "spans": [ + { + "bbox": [ + 347, + 507, + 521, + 536 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {b o d y - c o l l i s i o n}} \\\\ + \\mathcal {L} _ {\\text {s e l f - c o l l i s i o n}} + \\mathcal {L} _ {\\text {p o s e - r e g}} \\\\ \\end{array}", + "image_path": "d8ef9e4226f6f035017981360750b6631cafa82744f968642f009db330f37ec9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 541, + 515, + 553, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 541, + 515, + 553, + 526 + ], + "spans": [ + { + "bbox": [ + 541, + 515, + 553, + 526 + ], + "type": "text", + "content": "(1)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "text", + "content": "**Elastic Potentials:** The elastic potentials allow hair deformation while preserving the length and curvature of each strand. To better preserve the natural curliness of a hairstyle, We first incorporated the Cosserat rod model [21] into our system by introducing additional orientation information (stored as unit quaternions " + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "inline_equation", + "content": "q = (q_0, \\mathbf{q}^T)^T \\in \\mathbb{H}" + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "text", + "content": " with the scalar part " + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "inline_equation", + "content": "q_0" + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "text", + "content": " and the vector part " + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 313, + 537, + 555, + 645 + ], + "type": "text", + "content": ") for each hair segment and optimizing for the additional orientation offsets. Our elastic potential is in the form:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 648, + 553, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 648, + 553, + 671 + ], + "spans": [ + { + "bbox": [ + 315, + 648, + 553, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} + \\mathcal {L} _ {\\text {b e n d - t w i s t}} + \\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}}, \\tag {2}", + "image_path": "5026202a52abee4b9c9154ba1ab593e1bc4cb03d927ade5346cbaab42a0df833.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 673, + 479, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 673, + 479, + 685 + ], + "spans": [ + { + "bbox": [ + 314, + 673, + 479, + 685 + ], + "type": "text", + "content": "where the Cosserat stretch-shear energy:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 358, + 686, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 686, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 358, + 686, + 553, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t r e t c h - s h e a r}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} \\mathrm {k} _ {\\text {s t r e t c h - s h e a r}} \\boldsymbol {\\Gamma} ^ {T} \\boldsymbol {\\Gamma}, \\tag {3}", + "image_path": "947c8e28fb6bf47efdc5275aa2413545449a3fb36ed73dffb40e6a0892148272.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "242" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": "is computed from the discrete stretch-shear strain measure " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\Gamma = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\Im (q_i\\mathbf{e}_3\\bar{q}_i)" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " for a hair segment " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": ", with rest length " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{rest}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": ", end points " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i + 1}" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": ", orientation " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " and fixed coordinate basis " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{e}_1,\\mathbf{e}_2,\\mathbf{e}_3\\}" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\Im ()" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " is the imaginary part of the quaternion product. Similarly, the Cosserat bend-twist energy:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 146, + 296, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 146, + 296, + 175 + ], + "spans": [ + { + "bbox": [ + 97, + 146, + 296, + 175 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b e n d}, \\text {t w i s t}} = \\frac {1}{2} \\sum_ {\\text {e d g e p a i r s}} \\mathrm {k} _ {\\text {b e n d}, \\text {t w i s t}} \\boldsymbol {\\Omega} ^ {T} \\boldsymbol {\\Omega}, \\tag {4}", + "image_path": "0b6e6988cbbb531fff7ea795bd37bbe97d4b72cdc082201dfa880b204102d19b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": "is computed from the discrete bend-twist strain measure " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\Omega = \\frac{2}{l_{\\mathrm{rest}}} (\\Im (\\bar{q}_i q_{i + 1}) - \\Im (\\bar{q}_i^0 q_{i + 1}^0))" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": " for each consecutive hair orientation pair " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "q_{i + 1}" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": ", with rest orientations " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "q_{i}^{0}" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "q_{i + 1}^{0}" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": ". An additional unit quaternion constraint is needed for correct bend-twist strain measure, this is enforced for each orientation " + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 178, + 296, + 251 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 253, + 295, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 253, + 295, + 281 + ], + "spans": [ + { + "bbox": [ + 80, + 253, + 295, + 281 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {u n i t - q u a t e r n i o n}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {u n i t - q u a t e r n i o n}} (| | q | | - 1) ^ {2}. \\tag {5}", + "image_path": "95695040051b8d583833f28b43bb5ed19d7147b3884190c5d81a972cdc2a1bd9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 284, + 296, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 284, + 296, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 284, + 296, + 368 + ], + "type": "text", + "content": "Although this full Cosserat rod model, which optimizes for both position and orientation offsets, can enable realistic modeling of hair, we observed impractically slow training times and in combination with slow convergence, this approach was deemed infeasible. Instead, we propose an alternative formulation, which optimizes for position offsets only with the following modified Cosserat potential:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 370, + 295, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 370, + 295, + 399 + ], + "spans": [ + { + "bbox": [ + 111, + 370, + 295, + 399 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {C o s s e r a t}} = \\frac {1}{2} \\sum_ {\\text {e d g e s}} k _ {\\text {C o s s e r a t}} \\tilde {\\Gamma} ^ {T} \\tilde {\\Gamma}, \\tag {6}", + "image_path": "d0ea4af53ba82199c7a97f6b670afcb0629817f4161f172676fac5f4803c6cd0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l_{\\mathrm{rest}}} - \\mathbf{d}_3" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_3" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": " being the unit director along the edge, computed from the rigidly transformed groom. As the modified Cosserat potential penalizes stretching and shearing simultaneously, we observed that hair would become overly rigid when a large stiffness value " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "\\mathrm{k_{COSERAT}}" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": " is used (which is common as hair is almost inextensible). Therefore, to relax " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "\\mathrm{k_{COSERAT}}" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": " for more natural hair deformation, we model resistance to stretching explicitly by adding a Hookean potential to penalize the length " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": " of each hair segment to be close to " + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{rest}}" + }, + { + "bbox": [ + 55, + 403, + 296, + 523 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 526, + 295, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 526, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 110, + 526, + 295, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t r e t c h}} = \\frac {k _ {\\text {s t r e t c h}}}{2} \\sum_ {\\text {e d g e s}} \\left(l - l _ {\\text {r e s t}}\\right) ^ {2}. \\tag {7}", + "image_path": "c85a0d1087d6947c2fa0cc812be3a6aa7c97b4cdeaf6de068fd07f7e19458784.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "text", + "content": "Alternatively, one can choose to use the potential that penalizes shearing only: " + }, + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "inline_equation", + "content": "\\tilde{\\Gamma} = \\frac{\\mathbf{x}_{i + 1} - \\mathbf{x}_i}{l} -\\mathbf{d}_3" + }, + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 557, + 296, + 628 + ], + "type": "text", + "content": " being the segment length. In practice, we observed similar results from both potentials. Our final elastic potential include only two terms and we observe orders of magnitude faster training time when compared with the full Cosserat rod model" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 632, + 295, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 632, + 295, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 295, + 645 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e l a s t i c - p o t e n t i a l}} = \\mathcal {L} _ {\\text {s t r e t c h}} + \\mathcal {L} _ {\\text {C o s s e r a t}}. \\tag {8}", + "image_path": "e9675cbb0f382d59ac3afb47e2e7b47adb886c394479d70d35966e7c22b7b5b9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 648, + 295, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 648, + 295, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 648, + 295, + 672 + ], + "type": "text", + "content": "Gravity: The gravity potential is modeled using the potential energy of the hair nodes with positions " + }, + { + "bbox": [ + 55, + 648, + 295, + 672 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 648, + 295, + 672 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 123, + 674, + 295, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 674, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 123, + 674, + 295, + 700 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g r a v i t y}} = \\sum_ {\\text {v e r t i c e s}} - m \\mathbf {g} ^ {\\top} \\mathbf {x}, \\tag {9}", + "image_path": "4c7c9bcf71af11f4ce2ccb3291702467e92ac216e7f36f584c9bcecbe8f841ed.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": " is the gravitational acceleration and " + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": " is the parti" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 73, + 377, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 73, + 377, + 83 + ], + "spans": [ + { + "bbox": [ + 313, + 73, + 377, + 83 + ], + "type": "text", + "content": "cle point mass." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 84, + 555, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 555, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 555, + 167 + ], + "type": "text", + "content": "Body Collision: To prevent the hair strands from intersecting with the body geometry, we implement a vertex-triangle based collision model to maintain a minimal distance " + }, + { + "bbox": [ + 313, + 84, + 555, + 167 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 84, + 555, + 167 + ], + "type": "text", + "content": " between the predicted hair and the outward facing side of the body geometry. We exploit the face normal information to ensure the collision response is pointing outwards of the body. The loss is formulated as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 171, + 555, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 171, + 555, + 196 + ], + "spans": [ + { + "bbox": [ + 330, + 171, + 555, + 196 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b o d y ＿ c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {b c}} \\sum_ {\\text {v e r t i c e s}} \\max (D - d (\\mathbf {x}), 0) ^ {3}, \\tag {10}", + "image_path": "aeec262d71fc4de0a399f613c477317f7e93a5a6abaeaaef56f8c06379484cae.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "text", + "content": " computes the signed distance along the body triangle normal direction and " + }, + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "inline_equation", + "content": "\\mathsf{k}_{\\mathrm{bc}}" + }, + { + "bbox": [ + 313, + 198, + 554, + 233 + ], + "type": "text", + "content": " is the collision stiffness. Body triangle normals are facing outwards by convention." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 233, + 555, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 233, + 555, + 305 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 555, + 305 + ], + "type": "text", + "content": "Self-Collision: Inspired by work on volumetric methods for hair [1, 26, 29], we model hair self-collisions using Smoothed Particle Hydrodynamics (SPH) density estimation. Our energy potential is designed to push vertices apart when they exceed the reference density computed from the rest shape in a smooth and differentiable way:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 331, + 308, + 554, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 308, + 554, + 334 + ], + "spans": [ + { + "bbox": [ + 331, + 308, + 554, + 334 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e l f . c o l l i s i o n}} = \\mathrm {k} _ {\\mathrm {s c}} \\sum_ {\\text {v e r t i c e s}} \\max \\left(\\rho (\\mathbf {x}) - \\rho_ {\\text {r e s t}}, 0\\right) ^ {3}, \\tag {11}", + "image_path": "11dc34a371462c5c97e82b7196bd730e1c1bb24a0ea1ede5248bd976c25ba90f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 364, + 335, + 554, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 335, + 554, + 361 + ], + "spans": [ + { + "bbox": [ + 364, + 335, + 554, + 361 + ], + "type": "interline_equation", + "content": "\\rho (\\mathbf {x}) = \\sum_ {j} m _ {j} W \\left(\\left\\| \\mathbf {x} - \\mathbf {x} _ {j} \\right\\|, h\\right), \\tag {12}", + "image_path": "f6645ec59f462cbce18957499777fb8e83ce376d1c6ea729d41cbd31503c46c9.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 365, + 544, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 544, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 544, + 378 + ], + "type": "text", + "content": "using the smoothing kernel proposed by Bando et al. [1]:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 323, + 380, + 553, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 380, + 553, + 426 + ], + "spans": [ + { + "bbox": [ + 323, + 380, + 553, + 426 + ], + "type": "interline_equation", + "content": "W (r, h) = \\left\\{ \\begin{array}{l l} 4 - 6 \\left(\\frac {r}{h}\\right) ^ {2} + 3 \\left(\\frac {r}{h}\\right) ^ {3} & 0 \\leq r \\leq h \\\\ \\left(2 - \\frac {r}{h}\\right) ^ {3} & h \\leq r \\leq 2 h \\\\ 0 & 2 h \\leq r \\end{array} \\right. \\tag {13}", + "image_path": "1cc1f1841682dac4aef216aa2740c4a3021dde3272eff0c67db205e6ab85ec29.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{rest}}" + }, + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "text", + "content": " is the density computed from the rest groom and " + }, + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 428, + 554, + 452 + ], + "type": "text", + "content": " is the SPH smoothing length." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 452, + 554, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 452, + 554, + 535 + ], + "spans": [ + { + "bbox": [ + 313, + 452, + 554, + 535 + ], + "type": "text", + "content": "Pose Regularization: We add a final loss to encourage the groom deformation decoder to predict smoothly varying deformations for smoothly varying input pose signals. During training, for every randomly sampled pose from our motion capture data set, we include " + }, + { + "bbox": [ + 313, + 452, + 554, + 535 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{pose\\_reg}}" + }, + { + "bbox": [ + 313, + 452, + 554, + 535 + ], + "type": "text", + "content": " continuous frames and penalize the difference with respect to the average deformation in predicted outputs for consecutive frames as:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 326, + 538, + 553, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 538, + 553, + 572 + ], + "spans": [ + { + "bbox": [ + 326, + 538, + 553, + 572 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p o s e} \\cdot \\text {r e g}} = k _ {p r} \\sum_ {i = 0} ^ {N _ {\\text {p o s e} \\cdot \\text {r e g}}} | | \\bar {\\mathbf {x}} _ {\\text {d e f o r m a t i o n}} - \\mathbf {x} _ {\\text {d e f o r m a t i o n}} ^ {i} | | ^ {2} \\tag {14}", + "image_path": "92aa95b85bf38cb74af416748b157bbaa4734040562099b29fe10f337500fd1c.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{x}}_{\\mathrm{deformation}}" + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "text", + "content": " is the average of " + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{deformation}}^i" + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "text", + "content": " over all " + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{pose\\_reg}}" + }, + { + "bbox": [ + 313, + 575, + 554, + 600 + ], + "type": "text", + "content": " continuous frames per randomly selected pose." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 609, + 395, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 609, + 395, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 609, + 395, + 624 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 629, + 554, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 677 + ], + "type": "text", + "content": "Dataset: We train our networks using the CT-groom data set [35] complemented with additional grooms made by technical artists to showcase a wider variety of hairstyles. Our method is capable of simulating." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Metrics: To evaluate our approach we opted for three key metrics: i) the length preservation of the hair strands measured on the segment lengths, ii) the percentage of intersec" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "243" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 555, + 232 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 232 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 232 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 232 + ], + "type": "image", + "image_path": "765d3efa720f56644b269112c8217ab8d995423b8ce0125e9474ef7539a81e6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 239, + 555, + 273 + ], + "lines": [ + { + "bbox": [ + 55, + 239, + 555, + 273 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 555, + 273 + ], + "type": "text", + "content": "Figure 4. Modeling Diverse Hairstyles: We showcase the versatility of our method in modeling the quasi-static behavior of a plethora of hairstyles and lengths for different body shapes and poses where all results are obtained using the same settings without any manual parameter tuning. Our results cover short/medium/long hair, with various levels of curliness, including straight, wavy, curly, and kinky." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 290, + 295, + 346 + ], + "blocks": [ + { + "bbox": [ + 56, + 290, + 295, + 346 + ], + "lines": [ + { + "bbox": [ + 56, + 290, + 295, + 346 + ], + "spans": [ + { + "bbox": [ + 56, + 290, + 295, + 346 + ], + "type": "image", + "image_path": "1dc02333ddb41dfc439ccf2446bdd24c691753669a82b2699cf70d145fd39433.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 354, + 295, + 399 + ], + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 399 + ], + "type": "text", + "content": "Figure 5. Resolving Collisions: Our method is conditioned on the body shape parameters, enabling it to efficiently resolve collisions with body shape variations. Here we show a static pose and groom under quasi-statically draped under varying body shapes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 420, + 295, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 295, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 295, + 444 + ], + "type": "text", + "content": "tions between the hair and the body, and iii) the preservation of the hair shape measured from the segment orientations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 447, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 295, + 590 + ], + "type": "text", + "content": "Baselines: We compare our method against two optimization-based approaches (Adam, L-BFGS) and one simulation (XPBD [25]) baseline. We additionally compare to a recent related work GroomGen [51], which presented a neural quasi-static simulator using supervised training. GroomGen only showed results for varying gravity directions for a single fixed pose and shape, whereas our method generalizes to different shapes and poses. All images show the predicted strands directly without any hair interpolation to provide a fair assessment. When rendering hair for the final application, hair interpolation [13] can be leveraged to obtain the full set of hair strands." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "Implementation Details: In all of our results, strands consist of " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "N = 24" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " vertices, which are encoded into " + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": " texture maps. This choice of texture dimensions provides us with the ability to model several thousands of hair strands, which is sufficient for guide hair simulation. We implement our method with PyTorch [28], with training and inference measurements performed on an AMD Ryzen Threadripper PRO 3975WX CPU and a single NVIDIA RTX A6000 GPU. We refer the reader to the supplementary material for additional details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 292, + 454, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 292, + 454, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 454, + 304 + ], + "type": "text", + "content": "4.1. Qualitative Comparisons" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 311, + 555, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 311, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 311, + 555, + 441 + ], + "type": "text", + "content": "Body Pose and Shape Generalization: Our deformation decoder network is able to ingest body shape parameters directly and effectively learns to adapt the deformations of the hair strands to produce intersection free results for a large variety of body shapes. Figure 4 showcases a large sample of pose variations for a diverse set of grooms while in Figure 5 we demonstrate body shape generalization. Implausible deformations are possible when deforming the body in non-physical ways, e.g. when bending the neck backwards beyond limits feasible in real-life and thus absent from our training data set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 443, + 555, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 555, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 555, + 514 + ], + "type": "text", + "content": "Temporal Stability: Our method demonstrates excellent temporal stability in its predictions when the pose parameters are smoothly varied. This is evident in Figure 6, where the hair smoothly slides over the shoulder as the head turns, avoiding any self-penetration with the body. The supplemental material shows video results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 516, + 554, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 554, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 554, + 601 + ], + "type": "text", + "content": "Groom Generalization: We prioritize real-time performance for our approach, therefore opting for a smaller network structure that enables real-time inference results. We show that our model can handle at least 10 distinct grooms. In the supplemental material, we demonstrate that the network already shows some generalization properties for unseen grooms when they are similar to the training set." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 610, + 460, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 610, + 460, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 610, + 460, + 624 + ], + "type": "text", + "content": "4.2. Quantitative Comparisons" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": "Comparisons: The quantitative results are listed in Table 1. As expected, directly modifying the simulated hair positions, either using Adam, L-BFGS or XPBD simulation to minimize the loss produces the highest quality results but at a high computational cost. Neural methods like GroomGen and ours are orders of magnitude faster. Our method produces significantly better quantitative results when com" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "244" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 177, + 298, + 262 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 295, + 168 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 295, + 168 + ], + "type": "text", + "content": "Table 1. Quantitative Comparisons. We compare our method to several optimization and simulation baselines as well as related work. Our method displays comparable metrics to directly optimizing for the positions but does so orders of magnitude faster. Compared to the state-of-the-art method GroomGen, our method produces better quality metrics while being generalizable to body shape and pose, with comparable compute performance, providing the best trade-off between speed and quality. Gravity potentials are provided for reference." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 177, + 298, + 262 + ], + "lines": [ + { + "bbox": [ + 55, + 177, + 298, + 262 + ], + "spans": [ + { + "bbox": [ + 55, + 177, + 298, + 262 + ], + "type": "table", + "html": "
Method(↓) Time (↓) % body in secondsIntersectionLength (↓) Orientation PreservationOrientation PotentialGravity Potential
Adam179.380.22103.5376.153011.33
L-BFGS281.180.2289.5370.223047.53
XPBD (GPU) [25]63.260.0157.9618.103507.53
GroomGen [51]0.002490.391319.741281.963889.78
Ours0.002860.26175.42286.133399.95
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Starting from looking to the right to looking left. Note how the results are smoothly varying where every pose produces a natural drape. Note especially the hair sliding over the shoulders with minimal body intersections." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 58, + 435, + 116, + 495 + ], + "blocks": [ + { + "bbox": [ + 58, + 435, + 116, + 495 + ], + "lines": [ + { + "bbox": [ + 58, + 435, + 116, + 495 + ], + "spans": [ + { + "bbox": [ + 58, + 435, + 116, + 495 + ], + "type": "image", + "image_path": "be5c07deb8a48ec2aefbf9f4f3b558d08743c3848c61842cb612a4e2ecabb05f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 496, + 107, + 507 + ], + "lines": [ + { + "bbox": [ + 63, + 496, + 107, + 507 + ], + "spans": [ + { + "bbox": [ + 63, + 496, + 107, + 507 + ], + "type": "text", + "content": "Quaffure" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 117, + 435, + 176, + 495 + ], + "blocks": [ + { + "bbox": [ + 117, + 435, + 176, + 495 + ], + "lines": [ + { + "bbox": [ + 117, + 435, + 176, + 495 + ], + "spans": [ + { + "bbox": [ + 117, + 435, + 176, + 495 + ], + "type": "image", + "image_path": "731a957535f3637331d407bde1c04c0770e119e224b1f4f6e88478f5c6e78801.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 130, + 496, + 160, + 506 + ], + "lines": [ + { + "bbox": [ + 130, + 496, + 160, + 506 + ], + "spans": [ + { + "bbox": [ + 130, + 496, + 160, + 506 + ], + "type": "text", + "content": "Adam" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 176, + 435, + 235, + 495 + ], + "blocks": [ + { + "bbox": [ + 176, + 435, + 235, + 495 + ], + "lines": [ + { + "bbox": [ + 176, + 435, + 235, + 495 + ], + "spans": [ + { + "bbox": [ + 176, + 435, + 235, + 495 + ], + "type": "image", + "image_path": "e8220902cbd6a87cc3c881ec7470c140a4ef7a4e550d9c031a1d5c48b8f77888.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 185, + 496, + 220, + 506 + ], + "lines": [ + { + "bbox": [ + 185, + 496, + 220, + 506 + ], + "spans": [ + { + "bbox": [ + 185, + 496, + 220, + 506 + ], + "type": "text", + "content": "L-BFGS" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 516, + 296, + 571 + ], + "lines": [ + { + "bbox": [ + 55, + 516, + 296, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 516, + 296, + 571 + ], + "type": "text", + "content": "Figure 7. Qualitative Comparisons: Our method produces visually comparable results to directly minimizing the energies or to quasi-static simulation with XPBD while being orders of magnitude faster at inference by memorizing body pose and shape dependent groom deformations." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 236, + 435, + 294, + 495 + ], + "blocks": [ + { + "bbox": [ + 236, + 435, + 294, + 495 + ], + "lines": [ + { + "bbox": [ + 236, + 435, + 294, + 495 + ], + "spans": [ + { + "bbox": [ + 236, + 435, + 294, + 495 + ], + "type": "image", + "image_path": "fc628280e2e724ddec160d93085aa07485cd88f1ca3acd50b2ea96dcf81823da.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 496, + 277, + 506 + ], + "lines": [ + { + "bbox": [ + 249, + 496, + 277, + 506 + ], + "spans": [ + { + "bbox": [ + 249, + 496, + 277, + 506 + ], + "type": "text", + "content": "XPBD" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "pared to GroomGen at preserving strand lengths as well as the preservation of the hair shape measured from the segment orientations. Furthermore, it is important to note that, unlike GroomGen, our method handles arbitrary motion and generalizes to body shape. Figure 8 shows that GroomGen results display frequent intersections of the hair strands with the body. These results demonstrate that our method provides the best trade-offs in terms of performance and quantitative results with the significant added benefit that we do not require any simulated training data." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 553, + 152 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 553, + 152 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 553, + 152 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 553, + 152 + ], + "type": "image", + "image_path": "85f70c115d6ce3e0216583a4dc6648317572468c508532caeba7cdc58760f655.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 316, + 153, + 553, + 235 + ], + "blocks": [ + { + "bbox": [ + 316, + 153, + 553, + 235 + ], + "lines": [ + { + "bbox": [ + 316, + 153, + 553, + 235 + ], + "spans": [ + { + "bbox": [ + 316, + 153, + 553, + 235 + ], + "type": "image", + "image_path": "24fc831fc786f964f16c3bcf81cfd1eba5e46f93530f05ff30c4c30ebf9b41fa.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 243, + 555, + 321 + ], + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 321 + ], + "type": "text", + "content": "Figure 8. Comparisons with GroomGen: We compare our results (bottom) to those obtained with the neural simulator proposed in GroomGen [51] (top). The inset figure highlights that GroomGen produces results where strands intersect with the head geometry. In contrast, our method produces much fewer body-collisions producing better visual results. See the supplemental video for the full animated comparison." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 338, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 555, + 495 + ], + "type": "text", + "content": "Adam & L-BFGS - Energy Minimization: We compare against quasi-static simulation results by minimizing the loss energy with respect to the hair vertex positions directly using Adam and L-BFGS. The results are computed with the highest learning rate that produces stable results. The use of L-BFGS in simulation research has been applied for generating simulations at interactive rates [22]. Visual results in Figure 7 show that our method is visually comparable with the quasi-static energy minimization results, but at real-time rates that are independent of groom resolution. This demonstrates that our method is highly effective at learning the mapping that positions deformed hair vertices near the energy minimum." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 496, + 556, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 556, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 556, + 675 + ], + "type": "text", + "content": "XPBD - Physics-based Simulation: The XPBD method [25] effectively exploits GPU parallelism, which results in fast computation times. Simulation has been the de facto solution to hair animation for years due to the high realism, albeit at a high computational cost. Additionally, time integration of the system can often lead to instabilities, which will result in failures or undesirable results. In contrast, our method does not display any time integration instabilities. In our comparison, we model hair using the same energy as described in Subsection 3.5. To obtain quasi-static simulation results, we reset the velocities for each time step in the XPBD simulation loop, before applying gravity. We integrate the positions and use 10000 iterations to minimize the loss. We run 30 time steps to obtain results close to convergence." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "GroomGen: We additionally compare our method to GroomGen [51]. Code is not publicly available so we compare to our own re-implementation. Instead of train" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "245" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 37, + 71, + 289, + 175 + ], + "blocks": [ + { + "bbox": [ + 37, + 71, + 289, + 175 + ], + "lines": [ + { + "bbox": [ + 37, + 71, + 289, + 175 + ], + "spans": [ + { + "bbox": [ + 37, + 71, + 289, + 175 + ], + "type": "image", + "image_path": "a382d4552855119937471fea77f44515d46b7120534d23a52a1a2a002d9b34bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 186, + 295, + 232 + ], + "lines": [ + { + "bbox": [ + 55, + 186, + 295, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 295, + 232 + ], + "type": "text", + "content": "Figure 9. Performance & Scaling: Our method takes less than 3 ms on average to predict a single groom and the time complexity scales linearly with the number of grooms. The method is able to predict a thousand hairstyles in 0.3 seconds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 240, + 136, + 316 + ], + "blocks": [ + { + "bbox": [ + 58, + 240, + 136, + 316 + ], + "lines": [ + { + "bbox": [ + 58, + 240, + 136, + 316 + ], + "spans": [ + { + "bbox": [ + 58, + 240, + 136, + 316 + ], + "type": "image", + "image_path": "ed38f364795c1b4950dabc54931157d29dc90373cca2101348f39d714c7674c7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 316, + 126, + 324 + ], + "lines": [ + { + "bbox": [ + 65, + 316, + 126, + 324 + ], + "spans": [ + { + "bbox": [ + 65, + 316, + 126, + 324 + ], + "type": "text", + "content": "Groom Rest Shape" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 335, + 295, + 390 + ], + "lines": [ + { + "bbox": [ + 55, + 335, + 295, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 295, + 390 + ], + "type": "text", + "content": "Figure 10. Ablation Study: We perform an ablation of our proposed optimization-friendly Cosserat model against the commonly used mass-spring energy for modeling hair. Our model excels at maintaining the desired hairstyle whereas the mass-spring model struggles with maintaining curliness and volume." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 136, + 240, + 214, + 314 + ], + "blocks": [ + { + "bbox": [ + 136, + 240, + 214, + 314 + ], + "lines": [ + { + "bbox": [ + 136, + 240, + 214, + 314 + ], + "spans": [ + { + "bbox": [ + 136, + 240, + 214, + 314 + ], + "type": "image", + "image_path": "0af1a3b283fd4bd4339e952fc43376a1ebc311a538d816db0259d109ba70e3e8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 144, + 316, + 209, + 325 + ], + "lines": [ + { + "bbox": [ + 144, + 316, + 209, + 325 + ], + "spans": [ + { + "bbox": [ + 144, + 316, + 209, + 325 + ], + "type": "text", + "content": "Mass-Spring Energy" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 216, + 240, + 293, + 314 + ], + "blocks": [ + { + "bbox": [ + 216, + 240, + 293, + 314 + ], + "lines": [ + { + "bbox": [ + 216, + 240, + 293, + 314 + ], + "spans": [ + { + "bbox": [ + 216, + 240, + 293, + 314 + ], + "type": "image", + "image_path": "84fb876b729b262d78995bb23da258e3f70c0b563c2242cceaedb312e0e2cf24.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 217, + 316, + 291, + 325 + ], + "lines": [ + { + "bbox": [ + 217, + 316, + 291, + 325 + ], + "spans": [ + { + "bbox": [ + 217, + 316, + 291, + 325 + ], + "type": "text", + "content": "Cosserat Energy (ours)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 411, + 295, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 411, + 295, + 542 + ], + "spans": [ + { + "bbox": [ + 54, + 411, + 295, + 542 + ], + "type": "text", + "content": "ing the neural simulator with different gravity directions, we stochastically sample 1000 body poses with different neck rotations within 30 degrees along " + }, + { + "bbox": [ + 54, + 411, + 295, + 542 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 54, + 411, + 295, + 542 + ], + "type": "text", + "content": " axes, and run quasi-static hair simulation to obtain the training data. In Figure 8 provides a qualitative comparison between our approach and GroomGen for a groom that consists of 1919 strands. Both methods provide visually pleasing results but our approach results in significantly fewer intersections of hair with the body. This is highlighted in the inset figure where you can see several hair strands intersect for GroomGen whereas ours remains intersection free." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 550, + 138, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 550, + 138, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 550, + 138, + 561 + ], + "type": "text", + "content": "4.3. Performance" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "content": "Predicting a single groom takes " + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "inline_equation", + "content": "2.86\\mathrm{ms}" + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "content": " and predicting a thousand at once requires 0.3 seconds. The performance is independent of the number of strands due to the fixed size of the representation. Performance for a varying number of groom and pose variations is shown in Figure 9. Strand count for the varying grooms used in training varies between 1500 and 2500." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 659, + 187, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 187, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 187, + 671 + ], + "type": "text", + "content": "4.4. Ablations & Discussion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "We perform an ablation experiment on the importance of our proposed Cosserat energy. Figure 10 shows that our model is highly effective at maintaining hairstyle and curli" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 328, + 70, + 542, + 192 + ], + "blocks": [ + { + "bbox": [ + 328, + 70, + 542, + 192 + ], + "lines": [ + { + "bbox": [ + 328, + 70, + 542, + 192 + ], + "spans": [ + { + "bbox": [ + 328, + 70, + 542, + 192 + ], + "type": "image", + "image_path": "a229e7dd445386b96d46de5d7b5dae76c93a5f6746f91bc268df2f5845ecf25d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 200, + 554, + 266 + ], + "lines": [ + { + "bbox": [ + 313, + 200, + 554, + 266 + ], + "spans": [ + { + "bbox": [ + 313, + 200, + 554, + 266 + ], + "type": "text", + "content": "Figure 11. Ablation Study on Cosserat stiffness: Results obtained by varying the Cosserat stiffness in our proposed physics-based loss that enables artistic control. A higher stiffness results in strands that maintain their rest shape better (left) compared to a lower value (right). The images are mirrored and a few strand hair tip locations are highlighted for an easier comparison." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 287, + 554, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 287, + 554, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 287, + 554, + 382 + ], + "type": "text", + "content": "ness. We compare our results to those using a mass-spring energy [33]. Our model maintains the intended hairstyle well without manual intervention whereas the mass-spring model requires extensive parameter tuning to obtain satisfactory results and the hair still falls mostly flat under gravity. Our model provides artistic control by manipulating the stiffness parameters. Figure 11 demonstrates the effect of varying material stiffness." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 382, + 554, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 382, + 554, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 382, + 554, + 514 + ], + "type": "text", + "content": "Limitations and Future Work: Our pose-based groom transformation module can produce hair where strands are partially initialized inside the body. A better model which results in fewer intersections would make it easier for the model to learn the required deformations. Nonetheless, we observe that our network is able to robustly handle this. Current results use a single set of physical parameters for the hair material properties. This shows that parameter tuning is not required to produce visually pleasing results. However, we plan to condition the network on material parameters to enable artistic control at inference." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 525, + 388, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 525, + 388, + 538 + ], + "spans": [ + { + "bbox": [ + 314, + 525, + 388, + 538 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "content": "We present the first self-supervised neural approach to real-time quasi-static hair simulation. Our method enables efficient drape generation for various hairstyles on different body poses and shapes, which varies smoothly with pose variations. Our model leverages a hair deformation decomposition based on a transformation module and a learned deformation decoder, which is trained using self-supervision. We demonstrate complex behavior such as hair sliding over shoulders, maintaining complex hairstyles such as curly grooms and natural draping results due to the effects of gravity. To validate the method, we demonstrate that our decoder is effective and efficient at posing hair strands near the quasi-static energy minimum with better qualitative and quantitative results compared to related work." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "246" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 139 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 139 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 139 + ], + "type": "text", + "content": "[1] Yosuke Bando, Bing-Yu Chen, and Tomoyuki Nishita. 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Network quantization, as a standard compression and acceleration technique, reduces storage costs and enables potential inference acceleration by discretizing network weights and activations into a finite set of integer values. However, current quantization methods are often complex and sensitive, requiring extensive task-specific hyperparameters, where even a single misconfiguration can impair model performance, limiting generality across different models and tasks. In this paper, we propose Quantization without Tears (QwT), a method that simultaneously achieves quantization speed, accuracy, simplicity, and generality. The key insight of QwT is to incorporate a lightweight additional structure into the quantized network to mitigate information loss during quantization. This structure consists solely of a small set of linear layers, keeping the method simple and efficient. More importantly, it provides a closed-form solution, allowing us to improve accuracy effortlessly under 2 minutes. Extensive experiments across various vision, language, and multimodal tasks demonstrate that QwT is both highly effective and versatile. In fact, our approach offers a robust solution for network quantization that combines simplicity, accuracy, and adaptability, which provides new insights for the design of novel quantization paradigms.", + "bbox": [ + 89, + 318, + 485, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 757, + 220, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Along with their extraordinary breakthroughs in various vision [18], language [10] and multimodal [41] tasks, deep neural networks [11, 17] also exhibit ferocious greed for various resources: compute, GPU memory, bandwidth, storage, energy, etc. Hence, compressing and accelerating deep nets have not only attracted interests in academia, but", + "bbox": [ + 89, + 782, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "are also an urgent need in real-world deployments and applications.", + "bbox": [ + 511, + 287, + 903, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among various research efforts in this direction, network quantization [28] is arguably the most practical one. Different from unstructured pruning [16], it is well supported by existing hardware. Compared to structured pruning [19, 22], its compression ratio is higher and its loss is relatively smaller. For example, the INT8 quantization of both FP32 weights and activations leads to roughly $4 \\times$ reduction in network size and $4 \\times$ speedup with almost zero accuracy loss in many applications [26], which far exceeds structured pruning. Existing methods are often categorized as Post-Training Quantization (PTQ) [27, 31, 32, 37, 46, 52] or Quantization-Aware Training (QAT) [13, 21, 25, 33, 54], where the difference is whether training is required ('no' for PTQ and 'yes' for QAT).", + "bbox": [ + 511, + 319, + 906, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Quantization, however, is not as perfect as it seems to be. There are also obvious drawbacks and pitfalls in existing quantization methods.", + "bbox": [ + 511, + 532, + 905, + 577 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The speed-accuracy dilemma: PTQ can be thousands of times faster than QAT during the quantization process, but QAT may well be 10 percentage points higher than PTQ in accuracy during inference.", + "- Complexity: Quantization methods are often delicate and tricky. They often have tons of hyperparameters to tune for each specific task, and even one improperly set hyperparameter value may ruin the quantized model.", + "- Missing generality: Relevant to their complexities, an existing method is often geared toward a specific model and/or task. Different models/tasks require different quantization methods." + ], + "bbox": [ + 513, + 579, + 905, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given the status quo, at this moment it does not seem unreasonable to treat the act of network quantization as an art rather than an established engineering tool.", + "bbox": [ + 511, + 762, + 905, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a Quantization without Tears (QwT) method to address these drawbacks, which achieves quantization speed, accuracy, simplicity and generality simultaneously.", + "bbox": [ + 511, + 809, + 903, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The key to achieve these goals simultaneously is to slightly change the quantization paradigm. Suppose a net", + "bbox": [ + 511, + 869, + 903, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{*}$ J. Wu is the corresponding author.", + "bbox": [ + 107, + 886, + 297, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4462", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "work $M$ has the network structure $S$ and parameters $\\theta$ . Current quantization methods will quantize it into a model $M^{\\mathbb{Z}}$ with the same structure $S(S^{\\mathbb{Z}} = S)$ and quantized parameters $\\theta^{\\mathbb{Z}}$ in the integer format.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key argument is that the quantized structure does not need to be strictly $S$ . In our QwT, it becomes $S \\cup S_{c}$ , where some extra modules $S_{c}$ are added to the network structure to compensate for the information loss due to quantized parameters and activations. The extra $S_{c}$ thus help us achieve high accuracy.", + "bbox": [ + 89, + 152, + 480, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "$S_{c}$ does lead to extra overheads. But, it is also obvious that so long as the size and computation of $S_{c}$ is small or even negligible when compared to $S^{\\mathbb{Z}}$ , we achieve both speed and accuracy. In our QwT, $S_{c}$ has very simple structures: only few linear layers, which renders it both simple and general.", + "bbox": [ + 89, + 244, + 480, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To be more specific, the parameters in $S_{c}$ can be set in closed-form with a small calibration set, which in almost all cases leads to significantly higher accuracy than PTQ methods.", + "bbox": [ + 89, + 335, + 480, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, the contributions of this paper are:", + "bbox": [ + 109, + 398, + 413, + 412 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Proposing a new paradigm for network quantization by lifting the restriction that the quantized network structure $S^{\\mathbb{Z}}$ has to be exactly the same as that of the original network structure $S$ .", + "- Proposing QwT, a simple and general quantization method without tears in this new paradigm. QwT achieves speed, accuracy, simplicity and generality simultaneously." + ], + "bbox": [ + 91, + 415, + 480, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments have been carried out, which show that QwT has the following properties:", + "bbox": [ + 89, + 537, + 480, + 566 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Fast and accurate. For example, QwT quantizes a ViT network in roughly 2 minutes. During inference, its throughput is almost the same as models quantized by existing quantization methods. QwT is significantly more accurate than existing PTQ methods even without any back-propagation. On top of that, if higher accuracy is requested, QwT requires only 1 epoch of training to approach the accuracy of QAT methods. In contrast, QAT often requires a large number of epochs (e.g., 200 epochs).", + "- Simple. There is zero (0) hyperparameters to tune, and the parameters in $S_{c}$ can be found in closed-form.", + "- General. Exactly the same QwT method has been successfully applied to various networks and applications, including both CNNs [17] and Transformers (ViT [11] and Swin [34]), object recognition, detection (with both Mask R-CNN [18] and DETR [4]) and segmentation, multimodal models (CLIP [41]), generative models (DiT [40]), and large language models (LLaMA [12]).", + "- Practical. In addition to quantizing to low-bits in simulators, the same QwT method can quantize a model that is able to run directly on GPUs with minimum ef" + ], + "bbox": [ + 91, + 569, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "forts (i.e., quantization 'without tears'): Simply obtain $\\theta^{\\mathbb{Z}}$ using TensorRT, then add $S_{c}$ using QwT. The resulting quantized model is then ready to be deployed on GPUs that support quantized fix-point inference.", + "bbox": [ + 524, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 165, + 653, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Network quantization [28] aims to reduce the bit-width of weights and activations, enabling the quantized model to be stored more efficiently and to perform faster inference with suitable hardware support. The fundamental principle of network quantization involves approximating full-precision weights and activations by mapping them to a finite set of discrete values, which are subsequently used in forward model computations (i.e., in inference).", + "bbox": [ + 511, + 190, + 903, + 310 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One line of research focuses on quantization-aware training (QAT) [13, 21, 25, 33], which integrates quantization into the training process using back-propagation, where the straight-through estimator [1] is commonly employed to approximate gradients for non-differentiable rounding functions.", + "bbox": [ + 511, + 311, + 903, + 400 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of research concentrates on post-training quantization (PTQ) [14, 27, 31, 52], which converts a fully trained full-precision model into low-bit format using a small set of calibration samples. AdaRound [38] proposed an adaptive weight-rounding mechanism. BRECQ [24] leveraged block reconstruction for quantization, utilizing the Fisher Information Matrix to guide the process. QDrop [50] randomly dropped the quantization of activations during quantization to achieve flatness of the low-bit model.", + "bbox": [ + 511, + 402, + 903, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While these methods [24, 38, 50] have proven effective on ResNet [17] backbones, applying them directly to ViT [11] often degrades recognition accuracy since the intrinsic structure of the softmax attention is incompatible with these methods. This poses new challenges to design general PTQ methods for the Transformer architecture.", + "bbox": [ + 511, + 553, + 903, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this issue, [35] introduced a ranking loss designed to preserve the relative order between quantized and non-quantized attention scores. PTQ4ViT [52] proposed twin uniform quantization for shifted activations and a Hessian-guided metric to generate scaling factors. RepQViT [27] decoupled quantization and inference, employing distinct quantizers to enable precise quantization while simultaneously ensuring efficient inference. IGQ-ViT [37] introduced instance-aware group quantization for ViT to dynamically allocate channels of activation maps to different quantization groups. GPTQ [14] introduced a one-shot weight quantization technique that exploits approximate second-order information.", + "bbox": [ + 511, + 643, + 905, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from all of these methods, we propose a new quantization paradigm that introduces a lightweight module to compensate for the information loss caused by quantization. This new paradigm allows our method to be", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4463", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "seamlessly integrated with any state-of-the-art quantization methods as a plugin in a completely black-box fashion. Experiments demonstrate that our method is highly compatible with various PTQ approaches, enabling effortless improvements in recognition accuracy within just 2 minutes.", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 180, + 181, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 205, + 230, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start by outlining key concepts and notations related to network quantization. Given a quantization bit-width $b$ , the quantization function $Q(\\cdot | b): \\mathbb{R} \\to \\mathbb{Z}$ maps a floating-point number $x$ (e.g., weight or activation) into its corresponding fixed-point representation $x^{\\mathbb{Z}}$ encoded by $b$ bits. Among various quantization approaches, uniform quantization is particularly favored thanks to its simplicity and compatibility with hardware deployment. The uniform quantization procedure is formalized as:", + "bbox": [ + 89, + 227, + 483, + 363 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {\\mathbb {Z}} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 375, + 482, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $s \\in \\mathbb{R}^+$ represents the quantization scale, and $z \\in \\mathbb{Z}$ denotes the zero-point offset. These parameters are determined as follows:", + "bbox": [ + 89, + 412, + 483, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns = \\frac {\\operatorname* {m a x} (x) - \\operatorname* {m i n} (x)}{2 ^ {b} - 1}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 465, + 482, + 496 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz = \\operatorname {c l i p} \\left(\\lfloor - \\frac {\\min (x)}{s} \\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 500, + 482, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In these equations, $\\lfloor .\\rfloor$ denotes the rounding function, and the $\\operatorname{clip}(\\cdot ,a,b)$ operation constrains the input value into the range $[a,b]$ . The reconstructed quantized output can then be formulated as:", + "bbox": [ + 89, + 542, + 483, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = s \\times \\left(x ^ {\\mathbb {Z}} - z\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 602, + 480, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Beyond the naive uniform quantizer, a range of more sophisticated quantization techniques [27, 38, 51, 52] have been proposed and extensively studied by the community. In the literature, quantization methods typically quantize both the model weights and activations.", + "bbox": [ + 89, + 627, + 483, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization significantly reduces the storage requirements by enabling models to be stored in lower bit formats. Additionally, thanks to hardware support for integer-only computations, operations involving the quantized representations $x^{\\mathbb{Z}}$ , such as matrix multiplications between quantized weights and activations, can be performed with substantial improvements in computational efficiency.", + "bbox": [ + 89, + 703, + 483, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Compensation: The Key Insight", + "text_level": 1, + "bbox": [ + 89, + 816, + 375, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "But, obviously there is significant information loss between $x$ and $x^{\\mathbb{Z}}$ , and it grows very fast when many layers of computation and quantization are stacked together. To recover from the resulting accuracy loss, QAT methods resort to", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "many epochs of training, which leads to the speed-accuracy dilemma and complex, ad hoc quantization methods.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a model $M = (S, \\theta)$ , where $S$ and $\\theta$ denote its structure and weights, respectively, existing quantization techniques transform $M$ into a quantized version $M^{\\mathbb{Z}} = (S^{\\mathbb{Z}}, \\theta^{\\mathbb{Z}})$ , which maintains the same network structure (i.e., $S = S^{\\mathbb{Z}}$ ) while modifying the original parameters $\\theta$ to their quantized counterparts $\\theta^{\\mathbb{Z}}$ .", + "bbox": [ + 511, + 122, + 905, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our key insight is to challenge this structural rigidity: the quantized model does not necessarily need to retain the exactly same structural configuration, i.e., it is legitimate to allow $S^{\\mathbb{Z}} \\neq S$ . We argue that some extra modules $S_{c}$ can be added to the quantized model, such that its structure $S^{\\mathbb{Z}} = S \\cup S_{c}$ . The extra modules in $S_{c}$ can compensate for the information loss caused by quantization.", + "bbox": [ + 511, + 213, + 905, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More specifically, modern deep nets typically compose of many blocks, e.g., bottleneck blocks in ResNet [17] or Transformer blocks in ViT [11]. Let $l_{i}$ denote the $i$ -th block in a model, and let $x_{i} \\in \\mathbb{R}^{d_{in}}$ and $y_{i} \\in \\mathbb{R}^{d_{out}}$ be the input and output of this block $l_{i}$ , respectively, such that $y_{i} = l_{i}(x_{i})$ . We argue that we can add a compensation module $c_{i}$ for this block. Then, $S_{c} = \\bigcup_{i} c_{i}$ .", + "bbox": [ + 511, + 319, + 905, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For notational simplicity, we omit the subscript $i$ from now on, i.e., we represent a block as $y = l(x)$ and the compensation module is simply denoted as $c$ . After quantization, the input activations and weights of the block $l$ are modified into the quantized version $x^{\\mathbb{Z}}$ and $l^{\\mathbb{Z}}$ , respectively. The quantized computation becomes $y^{\\mathbb{Z}} = l^{\\mathbb{Z}}(x^{\\mathbb{Z}})$ .", + "bbox": [ + 511, + 426, + 903, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Clearly, there is information loss in all 3 quantization pairs: $l \\mapsto l^{\\mathbb{Z}}$ , $x \\mapsto x^{\\mathbb{Z}}$ and $y \\mapsto y^{\\mathbb{Z}}$ . What is intriguing is that the information loss is obviously highly non-linear in all 3 pairs. To implement the compensation idea, we have to answer the following questions:", + "bbox": [ + 511, + 517, + 905, + 593 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. How to measure the information losses in all 3 pairs that interplay with each other in a complex manner?", + "2. How to design the compensation module $c$ that accounts for these highly non-linear information losses?" + ], + "bbox": [ + 511, + 593, + 905, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. QwT: Quantization without Tears", + "text_level": 1, + "bbox": [ + 511, + 665, + 808, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a QwT (quantization without tears) method, which answers both questions in the simplest possible form.", + "bbox": [ + 511, + 686, + 903, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, the information loss is measured by $\\| y - y^{\\mathbb{Z}}\\| ^2$ . Because $y$ is the output of $l$ , it naturally takes care of information losses in $x^{\\mathbb{Z}}$ and $l^{\\mathbb{Z}}$ when $y^{\\mathbb{Z}} = y$ , intuitively there is absolutely zero information loss even if $x\\neq x^{\\mathbb{Z}}$ and $l\\neq l^{\\mathbb{Z}}$ . Note that $\\| y - y^{\\mathbb{Z}}\\|^{2}$ also accounts for cumulative information losses. That is, in the $i$ -th block, $c_{i}$ compensates information losses accumulated in all previous blocks that have not yet been corrected by $c_{1},c_{2},\\ldots ,c_{i - 1}$ .", + "bbox": [ + 511, + 718, + 905, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Second, because of this cumulative nature of our choice, in QwT we choose to implement $c$ (with the index $i$ omitted) as a simple linear layer. Although it is impossible to accurately compensate the non-linear information loss in", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4464", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8a03c144eadd23deea77c72632f8303f6001806202afce6c88c3c3cd4f0b78ae.jpg", + "image_caption": [ + "Figure 1. Illustration of QwT in one block. QwT adds a simple linear layer to any model block, compensating for information loss using the block input $x^{\\mathbb{Z}}$ . This approach is straightforward and compatible with almost all types of backbones [11, 17, 34]." + ], + "image_footnote": [], + "bbox": [ + 116, + 90, + 460, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "one block via a linear layer, we have many chances to repeatedly apply linear corrections. The entire compensation formed by all extra modules is in fact non-linear because it interacts with the quantized network in every block.", + "bbox": [ + 89, + 268, + 483, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To be concrete, we define $c(x) = Wx + b$ and then", + "bbox": [ + 109, + 329, + 452, + 343 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {\\mathrm {Q w T}} = l ^ {\\mathbb {Z}} \\left(x ^ {\\mathbb {Z}}\\right) + c \\left(x ^ {\\mathbb {Z}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 352, + 482, + 371 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W \\in \\mathbb{R}^{d_{out} \\times d_{in}}$ and $b \\in \\mathbb{R}^{d_{out}}$ are the weight matrix and bias vector of the linear layer $c$ , respectively. The QwT structure is illustrated in Figure 1.", + "bbox": [ + 89, + 378, + 483, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These choices are deliberate. They not only make QwT conceptually the simplest, but also ensures a closed-form solution. To minimize the difference between $y$ and $y^{\\mathbb{Z}}$ , we select a small set of training examples (512 images) from the training set. Using these samples, QwT collects all inputs for the block $l^{\\mathbb{Z}}$ to form a matrix $X^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{in} \\times N}$ , where $N$ is the total number of features or tokens. We feed $X^{\\mathbb{Z}}$ into the quantized block $l^{\\mathbb{Z}}$ to obtain $Y^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{out} \\times N}$ . Next, we feed $X^{\\mathbb{Z}}$ into the non-quantized block $l$ to obtain $Y \\in \\mathbb{R}^{d_{out} \\times N}$ . Correspondingly, $Y$ contains output of the matching block in the original model.", + "bbox": [ + 89, + 426, + 483, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our task is then to estimate $Y - Y^{\\mathbb{Z}}$ using $X^{\\mathbb{Z}}$ . This is a classic linear regression problem, and has a closed-form solution:", + "bbox": [ + 89, + 590, + 483, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW ^ {*} = \\left(Y - Y ^ {\\mathbb {Z}}\\right) X ^ {\\mathbb {Z} ^ {\\top}} \\left(X ^ {\\mathbb {Z}} X ^ {\\mathbb {Z} ^ {\\top}}\\right) ^ {- 1}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 643, + 482, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Equation 6, to simplify the solution, the bias $b$ is absorbed into $W$ and a row vector of $\\mathbf{1}^{\\top}$ are concatenated to $X^{\\mathbb{Z}}$ . It is worth mentioning that theoretically QwT will not make the quantized network getting worse—by setting $W$ and $b$ to all zeros, QwT will not alter the quantized network.", + "bbox": [ + 89, + 674, + 482, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that after the QwT module for $l^{\\mathbb{Z}}$ is inserted, the compensation in the next block depends on all the previous QwT modules. Consequently, the information loss from $y$ to $y^{\\mathbb{Z}}$ is gradually compensated block by block, allowing $c$ to account for the accumulated loss from all preceding blocks that remain uncorrected.", + "bbox": [ + 89, + 750, + 482, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our experiments, we observed that the coefficient of determination $(R^2)$ [43] for a small subset $(< 5\\%)$ of QwT modules was notably low, adversely hurting recognition accuracy. Consequently, we apply the initialization using", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Equation 6 only when $R^2 > 0$ ; Otherwise, the $W$ and $b$ of the QwT module are set to zero.", + "bbox": [ + 511, + 90, + 906, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the QwT method has a simple pipeline: first quantize a model $M$ using any PTQ method, then add the compensation module $c_{i}$ to every block $i$ and set the parameters in $c_{i}$ using Equation 6.", + "bbox": [ + 511, + 121, + 903, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A notable advantage of QwT lies in its inherent simplicity. This simplicity ensures that the initialization process of QwT modules is highly efficient, which requires roughly 2 minutes in practice to compensate for the information loss during quantization, thereby enhancing recognition accuracy. Experimental results demonstrated that QwT exhibits significant versatility and efficiency across various vision and language tasks.", + "bbox": [ + 511, + 181, + 906, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 316, + 645, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we begin by evaluating our QwT method on a range of discriminative tasks, including image classification, object detection, instance segmentation, and multimodal recognition. Subsequently, we extend our analysis to generative tasks, such as image generation using diffusion models [40] and text generation with large language models [12].", + "bbox": [ + 511, + 340, + 905, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experiments on Image Classification", + "text_level": 1, + "bbox": [ + 511, + 455, + 831, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Settings. We evaluated our method on image classification tasks using the ImageNet dataset [8], leveraging various backbone architectures including ViT [11], DeiT [48], Swin [34], and ResNet [17]. We randomly sampled 512 images from the training set to initialize the parameters of the QwT modules using Equation 6. In all networks, the affine transformation matrix $W$ in QwT is implemented in FP16 format to reduce model size. In ResNet, $W$ is further simplified as a group-wise convolution using a kernel size of 1 and 64 channels per group, achieving additional efficiency in storage and computation. Note that a group-wise convolution is still a linear operator, which can be perfectly encoded by the pair $(W, b)$ . Other details were consistent with prior work [27]. Please refer to the appendix for more information.", + "bbox": [ + 511, + 477, + 906, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Results on different backbones. Table 1 summarizes the quantization results when applying QwT across different backbone architectures. Specifically, we selected RepQViT [27] and Percentile [23] as the baseline methods for the Transformer family [11, 34, 48] and ResNet [17], respectively. The results show that incorporating the QwT module consistently boosts the recognition accuracy, leading to an average increase of approximately $2.6\\%$ , and even up to $5\\%$ for 4-bit quantization, highlighting that QwT is particularly effective for low-bit scenarios. Additionally, after the QwT modules are integrated, the accuracy in 6-bit quantization cases aligns closely with prior state-of-the-art approaches [37, 46].", + "bbox": [ + 511, + 704, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4465", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/7ee27db430841755c2ad954181a40a57493683bed2f460980ed99a18822b1dd1.jpg", + "table_caption": [ + "Table 1. Quantization results on the ImageNet dataset [8]. #Bits' indicates the bit-width of weights/activations. 'Size' (MB) represents the storage cost of the model on the hard disk. * denotes QwT modules and classification head are finetuned for one epoch. † indicates that the previous state-of-the-art results are directly sourced from the papers [37, 46] due to the unavailability of their official code implementations." + ], + "table_footnote": [], + "table_body": "
NetworkMethod#BitsSizeTop-1
DeiT-TFull-precision32/3222.972.2
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-62.5
RepQ-ViT [27]4/43.358.2
RepQ-ViT + QwT4/44.261.4
RepQ-ViT + QwT*4/44.264.8
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-71.2
RepQ-ViT [27]6/64.671.0
RepQ-ViT + QwT6/65.571.2
RepQ-ViT + QwT*6/65.571.6
Swin-TFull-precision32/32113.281.4
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-77.8
RepQ-ViT [27]4/414.973.0
RepQ-ViT + QwT4/419.275.5
RepQ-ViT + QwT*4/419.279.3
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-80.9
RepQ-ViT [27]6/621.780.6
RepQ-ViT + QwT6/626.080.7
RepQ-ViT + QwT*6/626.080.9
ViT-BFull-precision32/32346.384.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-79.3
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
RepQ-ViT + QwT*4/459.178.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-83.8
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
RepQ-ViT + QwT*6/680.484.0
ResNet-50Full-precision32/32102.276.6
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]4/4-75.4
Percentile[23]4/414.068.4
Percentile + QwT4/416.074.5
Percentile + QwT*4/416.075.8
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]6/6--
Percentile[23]6/619.976.0
Percentile + QwT6/621.976.8
Percentile + QwT*6/621.976.8
", + "bbox": [ + 94, + 196, + 478, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The potential of our QwT method can be further unlocked through finetuning. By jointly optimizing the QwT modules and the classification head for only one (1) additional epoch (results marked with *), more gains in accuracy are achieved, enabling our method to surpass previous state-of-the-art results in nearly all cases.", + "bbox": [ + 89, + 758, + 482, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These results are even closer to those produced by QAT methods, which typically require extensive training (e.g., 200 epochs). In contrast, our $\\mathrm{QwT^{*}}$ achieves similar per", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cfc4f4d6e6b1b666b2f9b4bf4f8c8826868f1617c86f82ca31b5926cf0cc4f16.jpg", + "table_caption": [ + "Table 2. Results of 8-bit quantization, using tensor-wise Percentile [23] as the baseline PTQ method. 'Latency' (ms) is measured on a single RTX 3090 GPU with a batch size of 64, utilizing Nvidia's TensorRT [39] toolkit for deployment." + ], + "table_footnote": [], + "table_body": "
NetworkMethodSizeLatencyTop-1
DeiT-TFull-precision22.911.672.2
Percentile [23]5.92.871.2
Percentile + QwT6.83.271.5
Swin-TFull-precision113.234.581.4
Percentile [23]28.69.580.8
Percentile + QwT32.910.981.0
Swin-SFull-precision198.461.083.2
Percentile [23]50.116.082.1
Percentile + QwT58.017.983.0
ViT-SFull-precision88.228.381.4
Percentile [23]22.55.879.2
Percentile + QwT26.06.680.1
ViT-BFull-precision346.385.384.5
Percentile [23]87.415.575.8
Percentile + QwT101.617.582.8
", + "bbox": [ + 522, + 156, + 895, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "formance with only one epoch of finetuning. Our approach not only substantially improves training efficiency but also keeps the backbone parameters unchanged, making it more suitable for hardware deployment.", + "bbox": [ + 511, + 416, + 906, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Table 2, we additionally report the inference latency of different models directly deployed on a GPU. Compared to full-precision models, naive quantized models achieve an average reduction of $77\\%$ in inference latency and $75\\%$ in model size. When QwT modules are incorporated, these reductions slightly decrease to $74\\%$ and $71\\%$ , respectively, with an overhead of only $3\\%$ . This minimal additional cost is offset by an average 1.9 percentage points improvement in recognition accuracy, demonstrating the strong practicality of the QwT method.", + "bbox": [ + 511, + 477, + 908, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results across various PTQ methods. We extended our experiments to evaluate the versatility of QwT by applying it to various PTQ methods. As shown in Table 3, we integrated QwT into PTQ4ViT [52], RepQ-ViT [27], and Percentile [23], using ViT-B as the backbone.", + "bbox": [ + 511, + 628, + 906, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observe that QwT consistently enhances top-1 accuracy across all baseline PTQ methods. Notably, in 4-bit scenarios, PTQ4ViT demonstrates an improvement of approximately $40\\%$ , while RepQ-ViT shows an $8\\%$ increase. Compared to modern PTQ methods [27, 37, 52], which often involve complex and tedious procedures, our method demonstrates high simplicity and, most importantly, is compatible with all these approaches, too. The significant improvement in accuracy narrows the performance gap between different PTQ methods, and offers new insights into the design of new paradigms for network quantization.", + "bbox": [ + 511, + 704, + 908, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Extension to QAT methods. We further investigated the potential of adapting QwT to QAT methods. Specifically,", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4466", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/fcfd630e8d1fde077e719862a64cd4581e532462707777f31b1e1774cab9f1eb.jpg", + "table_caption": [ + "Table 3. Quantization results among different PTQ methods on the ImageNet dataset [8] using ViT-B [11] as the backbone." + ], + "table_footnote": [], + "table_body": "
Method#BitsSizeTop-1
Full-precision32/32346.384.5
PTQ4ViT [52]4/444.930.7
PTQ4ViT+QwT4/459.170.0
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
Percentile [23]6/666.256.7
Percentile+QwT6/680.479.8
PTQ4ViT [52]6/666.281.7
PTQ4ViT+QwT6/680.483.2
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
Percentile [23]8/887.475.8
Percentile+QwT8/8101.682.8
", + "bbox": [ + 138, + 128, + 433, + 335 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e188dcfb04510d07a21d95e5d8ff1829d2c8bf070dda8fdf40afa55e552e94a.jpg", + "table_caption": [ + "Table 4. Quantization results of applying QwT finetuning schema on QAT methods." + ], + "table_footnote": [], + "table_body": "
NetworkMethod#BitsTop-1
DeiT-SQ-ViT [25]2/272.1
Q-ViT + QwT*2/272.5
Q-ViT [25]3/379.0
Q-ViT + QwT*3/379.1
", + "bbox": [ + 140, + 386, + 433, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we applied QwT modules to QAT models after completing QAT training to assess whether QwT can further enhance recognition accuracy.", + "bbox": [ + 89, + 491, + 482, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We preliminarily found that for QAT models, the initialization process described by Equation 6 is no longer effective. Applying it directly to QAT models significantly degrades accuracy. We attribute this to the fact that, unlike full-precision models, the optimization state of a QAT-trained model is sufficiently converged, resulting in almost no information loss from $y$ to $y^{\\mathbb{Z}}$ . In fact, $y^{\\mathbb{Z}}$ may even outperform $y$ , as QAT models sometimes surpass their full-precision counterparts in evaluation accuracy.", + "bbox": [ + 88, + 537, + 482, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To integrate QwT into QAT methods, we therefore initialize $W$ and $b$ to zero as a compromise. We then explore whether fine-tuning QwT can still improve recognition accuracy. For this study, we use Q-ViT [25], a representative QAT method for ViT backbones, as the baseline. The results in Table 4 demonstrate that, even without using the initialization from Equation 6, fine-tuning the QwT modules consistently enhances QAT models, confirming the generalizability of our approach.", + "bbox": [ + 88, + 672, + 482, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiments on Object Detection & Instance Segmentation", + "text_level": 1, + "bbox": [ + 89, + 818, + 483, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We evaluated our method on object detection and instance segmentation tasks using the COCO 2017 [30] dataset. ResNet50 [17] with DETR [4], Swin-S [34] with", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mask R-CNN [18], and Swin-S/B [34] with Cascade Mask R-CNN [3] were used as detectors. The evaluation metric was Average Precision (AP). Similar to image classification, we randomly selected 512 images from the training set to initialize the QwT weights and biases. For ResNet, the QwT was implemented using group-wise convolution with a kernel size of 1 and 64 channels per group to balance model size and AP. For DETR, we used MinMax as the PTQ baseline, a classic method that quantizes the model based on the range between the minimum and maximum values of weights or activations. For the other detectors, RepQViT [27] was chosen as the baseline PTQ method.", + "bbox": [ + 511, + 90, + 903, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main results. Table 5 presents the results of applying QwT to object detection and instance segmentation tasks. We observe that QwT consistently enhances both $\\mathrm{AP^{box}}$ and $\\mathrm{AP^{mask}}$ across all cases without finetuning, achieving an average improvement of $0.4\\%$ with individual gains ranging from $0.1\\%$ to $0.7\\%$ . The consistent improvement underscores the robustness of our method for both object detection and instance segmentation tasks. Notably, in certain 6-bit scenarios, such as on Cascade Mask R-CNN, QwT even achieves AP comparable to full-precision models.", + "bbox": [ + 511, + 273, + 903, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, a clear trend emerges where the AP gains introduced by QwT increases along with model size. For instance, in $\\mathrm{AP^{box}}$ , the average improvement achieved by QwT rises from $0.3\\%$ in ResNet-50+DETR to $0.5\\%$ in Swin-B+Cascade Mask R-CNN, indicating the method's enhanced effectiveness in larger models.", + "bbox": [ + 511, + 425, + 903, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared to full-precision models, baseline PTQ methods yield an average storage reduction of approximately $80\\%$ . The introduction of QwT modules slightly reduces this savings to around $78\\%$ $(-2\\%)$ , which demonstrates that QwT enhances AP metrics with negligible overhead.", + "bbox": [ + 511, + 516, + 906, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Experiments on Multimodal Recognition", + "text_level": 1, + "bbox": [ + 511, + 604, + 864, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We conducted experiments using OpenAI's CLIP model [41]. Known for its exceptional zero-shot performance on the ImageNet [8] classification task, CLIP serves as an ideal benchmark for assessing the effectiveness on multimodal recognition tasks. We selected the variant of CLIP that includes a ViT-B/32 [11] as the visual encoder and a 12-block Transformer [49] as the text encoder. Since, to the best of our knowledge, no publicly available PTQ implementation exists for CLIP, we developed a baseline using RepQ-ViT [27]. We randomly selected 512 image-text pairs from the training data, both for PTQ model calibration and QwT initialization. Thanks to the simplicity and efficiency of our method, it achieved significant improvements under 30 seconds, as detailed in Table 6.", + "bbox": [ + 511, + 627, + 905, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main results. We conducted experiments with two quantization strategies: quantizing 1) only the visual encoder and 2) both visual and text encoders. As shown in Table 6, baseline PTQ methods showed significant drop in top-", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4467", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/13954f56b49f0562ddd122b4b95ca89428cbc7cb5dba7bfcb2637786cda592fb.jpg", + "table_caption": [ + "Table 5. Quantization results on the COCO dataset [8]. We use box average precision $(\\mathrm{AP}^{\\mathrm{box}})$ and mask average precision $(\\mathrm{AP}^{\\mathrm{mask}})$ to assess object detection and instance segmentation accuracy, respectively." + ], + "table_footnote": [], + "table_body": "
NetworkMethod#BitsSizeAPboxAPmask
ResNet-50 + DETRFull-precision32/32164.542.0-
MinMax6/647.439.5-
MinMax + QwT6/649.440.0-
MinMax8/856.441.6-
MinMax + QwT8/858.441.7-
Swin-S + Mask R-CNNFull-precision32/32276.548.543.3
RepQ-ViT [27]4/436.142.640.0
RepQ-ViT + QwT4/444.043.140.4
RepQ-ViT [27]6/653.347.642.9
RepQ-ViT + QwT6/661.248.043.1
Swin-S + Cascade Mask R-CNNFull-precision32/32427.851.945.0
RepQ-ViT [27]4/456.949.343.1
RepQ-ViT + QwT4/464.849.943.4
RepQ-ViT [27]6/683.451.444.6
RepQ-ViT + QwT6/691.351.744.8
Swin-B + Cascade Mask R-CNNFull-precision32/32579.951.945.0
RepQ-ViT [27]4/476.149.343.1
RepQ-ViT + QwT4/490.150.043.7
RepQ-ViT [27]6/6112.151.544.8
RepQ-ViT + QwT6/6126.151.845.0
", + "bbox": [ + 98, + 155, + 475, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "1 accuracy compared to their full-precision counterparts, struggling to effectively represent a low-bit CLIP model. The reduction in performance is especially obvious when both the visual and text encoders are quantized.", + "bbox": [ + 89, + 486, + 482, + 546 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In contrast, our QwT method enhanced top-1 accuracy across all cases, significantly bridging the accuracy gap between low-bit and full-precision models. Specifically, in vision-only quantization, QwT increased top-1 accuracy by an average of $0.6\\%$ , with only a modest $4\\%$ increase in model size compared to baseline PTQ methods.", + "bbox": [ + 89, + 547, + 482, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When both the visual and text encoders are quantized, baseline PTQ methods exhibited an average accuracy drop of $29.2\\%$ . In contrast, QwT provided a significant accuracy improvement, with an average increase of $14.8\\%$ . These findings highlight QwT's effectiveness in preserving high accuracy while substantially reducing model size for multimodal recognition tasks.", + "bbox": [ + 89, + 638, + 482, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Experiments on Image Generation", + "text_level": 1, + "bbox": [ + 89, + 757, + 393, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "QwT has also demonstrated efficacy in generative models, notably enhancing the performance of quantized diffusion models. Unlike classifiers or detectors, which require a single forward pass, diffusion models involve multiple forward passes to generate the final images, presenting a unique prototype. Under these circumstances, QwT has proven itself highly effective, underscoring its general applicability and robustness.", + "bbox": [ + 89, + 779, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aca11c3e0548fc77403c363416ee709f5f9d40d2a8a5502e748480a2264dfa0a.jpg", + "table_caption": [ + "Table 6. Quantization results of CLIP for zero-shot classification tasks on ImageNet. The 'Quant Setup' column differentiates between two strategies: quantizing only the vision encoder and quantizing both the vision and text encoders concurrently." + ], + "table_footnote": [], + "table_body": "
Quant SetupMethod#BitsSize (MB)Top-1
VisionFull-precision32/32607.263.4
RepQ-ViT [27]6/6323.559.2
RepQ-ViT + QwT6/6336.860.3
RepQ-ViT [27]8/8345.362.9
RepQ-ViT + QwT8/8359.563.0
Vision & TextFull-precision32/32607.263.4
RepQ-ViT [27]6/6200.829.8
RepQ-ViT + QwT6/6221.343.5
RepQ-ViT [27]8/8232.138.7
RepQ-ViT + QwT8/8252.654.6
", + "bbox": [ + 517, + 155, + 901, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Settings. For our experiments, we selected the influential DiT [40] (Diffusion Transformer) architecture, following the experimental setup of Q-DiT [5]. Specifically, we employed pretrained DiT-XL/2 models at a resolution of $256 \\times 256$ . For rapid and precise sampling, we utilized the DDIM sampler with 50 sampling steps and applied classifier-free guidance (cfg) of 1.5, abbreviated as DiT-XL/2 (steps = 50, CFG = 1.5). Our experiments included two quantization configurations: W8A8 and W4A8. Additional results involving various model sizes, steps, and CFG values are available in the appendix.", + "bbox": [ + 511, + 349, + 906, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We applied QwT directly to the quantized diffusion model using Q-DiT. A key consideration is that the model performs $T$ forward passes per inference, with notable variation in the activation distribution and range across steps. A key assumption is that quantization error is primarily dependent on the input $x$ , with minimal influence from elements like the time step or class condition. Accordingly, we set $t = 0$ to initialize the compensation module. The results are presented in Table 7.", + "bbox": [ + 511, + 517, + 908, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main results. Our method was compared with three representative quantization techniques: RepQ-ViT, GPTQ and Q-DiT designed for diffusion models. For both W8A8 and W4A8 settings, QwT significantly enhanced the performance of the quantized models, yielding improvements of 0.10 and 0.69 in FID, which illustrates the efficacy of QwT with minimal increase in model size.", + "bbox": [ + 511, + 656, + 908, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We visualize the images generated by our model alongside those from compared models in Figure 2. The three rows represent the original images, quantized images with Q-DiT, and quantized images with QwT, respectively. All models are based on DiT-XL/2 (steps $= 50$ , $\\mathrm{cfg} = 1.5$ ). To enable a fair comparison, we ensure that the initial Gaussian noise and the noise added during inference are identical across all methods. The images produced by our method show a closer visual resemblance to the original model,", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4468", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45c730c8370f8d3c5774d66020f043555f34dcd073648450c890ad38aa9b309c.jpg", + "image_caption": [ + "Figure 2. Qualitative visualization results of quantizing DiT-XL/2." + ], + "image_footnote": [], + "bbox": [ + 158, + 94, + 841, + 282 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/79f4bcae5d0984bbef64e212baa0cda187c0085408d79e9a0520f79e11b859c9.jpg", + "table_caption": [ + "Table 7. Quantitative results of quantizing DiT-XL/2. $\\downarrow$ (↑) means smaller (larger) is better." + ], + "table_footnote": [], + "table_body": "
Method#BitsSize (MB)FID (↓)IS (↑)
Full-precision16/1613495.32236.17
RepQ-ViT8/86775.46234.74
GPTQ8/86905.90218.90
Q-DiT8/86835.45236.52
Q-DiT + QwT8/87075.35236.91
RepQ-ViT4/8339319.682.20
GPTQ4/83519.94166.35
Q-DiT4/83476.75208.38
Q-DiT + QwT4/83616.06215.70
", + "bbox": [ + 107, + 376, + 464, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "which aligns with the quantitative results.", + "bbox": [ + 89, + 582, + 367, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Experiments on Large Language Models", + "text_level": 1, + "bbox": [ + 89, + 606, + 439, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Settings. We evaluated our framework on the LLaMA3-8B [12] model. For PTQ methods, we adopted GPTQ [14] with INT4 weight quantization. Our approach is also compatible with other PTQ methods such as AWQ [29] and SPQR [9]. We conducted a group-wise asymmetric quantization with a group size of 128 and apply activation reordering. In particular, GPTQ take 128 samples from the C4 dataset as calibration sets, and each sample is 2048 tokens long. We use the same calibration set when performing QwT after GPTQ algorithm.", + "bbox": [ + 88, + 628, + 482, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation metrics. Following the settings of GPTQ, we evaluated the perplexity on the WikiText2 [47] and C4 [42] datasets. We further assessed the zero-shot commonsense question answering (QA) ability on eight tasks covering SIQA [45], HellaSwag [53], PIQA [2], Wino-Grande [44], ARC [7], BoolQ [6], and OpenBookQA [36]. We also evaluated both the zero-shot and five-shot performance of the LLMs on Massively Multitask Language Un", + "bbox": [ + 88, + 779, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ef3b1ab12fabb7ab8f65e6c4b4f99e811089f542e9e79dc7e09eda4bccddac74.jpg", + "table_caption": [ + "Table 8. Quantization results among WikiText2, C4 and eight zero-shot commonsense QA datasets using LLaMA3-8B as the backbone. $\\downarrow (\\uparrow)$ means smaller (larger) is better." + ], + "table_footnote": [], + "table_body": "
Method#BitsSize (GB)W2 (↓)C4 (↓)QA. Avg (↑)
Full-precision1616.066.248.9666.10
GPTQ45.736.659.4464.90
GPTQ + QwT46.806.639.3865.18
", + "bbox": [ + 514, + 388, + 906, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "derstanding (MMLU) benchmark [20]. It consists of 57 language tasks including humanities, STEM, social science, etc. We adopted lm-eval-harness [15] to produce the accuracy results.", + "bbox": [ + 511, + 483, + 906, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. Table 8 summarizes the perplexity in WikiText2, C4 and the average accuracy in eight common sense reasoning datasets. More results are shown in the appendix. Note that we abbreviate WikiText2 to W2. As the results show, our optimized models will not overfit the calibration dataset and consistently outperform the original PTQ models. These results reveal the effectiveness of our QwT.", + "bbox": [ + 511, + 544, + 906, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 664, + 640, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed Quantization without Tears (QwT), a novel approach that incorporates a lightweight structure into quantized models to compensate for the information loss during network quantization. The QwT modules, implemented as a tiny set of linear layers and seamlessly integrated into backbone blocks, achieved accuracy, simplicity, and generality simultaneously. Notably, QwT provides a closed-form solution to complete the compensation process in under 2 minutes and enables effortless integration with existing quantization techniques. Extensive experiments demonstrated QwT's exceptional effectiveness and versatility across a wide range of tasks, models, and quantization methods, advancing a streamlined and flexible paradigm for network quantization.", + "bbox": [ + 509, + 688, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4469", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was partly supported by the National Natural Science Foundation of China under Grant 62276123.", + "bbox": [ + 89, + 114, + 483, + 143 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "J.W. designed the compensation insight and the QwT framework mathematically. M.F. made them into algorithms and codes that work well in practice, and carried out the main empirical validations. H.Y., J.S. and J.Z. carried out experiments and validations on LLM, AIGC and multimodal tasks, respectively. K.Z. engaged in discussions. All authors contributed to paper writing.", + "bbox": [ + 89, + 146, + 483, + 252 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 266, + 187, + 281 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv:1308.3432, 2013. 2", + "[2] Yonatan Bisk, Rowan Zellers, Ronan Le Bras, Jianfeng Gao, and Yejin Choi. Piaq: Reasoning about physical commonsense in natural language. In AAAI Conference on Artificial Intelligence, pages 7432-7439, 2020. 8", + "[3] Zhaowei Cai and Nuno Vasconcelos. Cascade R-CNN: Delving into high quality object detection. 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HellaSwag: Can a machine really finish" + ], + "bbox": [ + 516, + 90, + 903, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4471", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "your sentence? In Annual Meeting of the Association for Computational Linguistics, page 4791-4800, 2019. 8", + "[54] Ke Zhu, Yin-Yin He, and Jianxin Wu. Quantized feature distillation for network quantization. In AAAI Conference on Artificial Intelligence, pages 11452-11460, 2023. 1" + ], + "bbox": [ + 91, + 90, + 483, + 162 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4472", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Quantization without Tears/7acb9c84-5b2e-438a-8a19-e3c09310038a_model.json b/2025/Quantization without Tears/7acb9c84-5b2e-438a-8a19-e3c09310038a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d821663904d1fcd879d9da04cd6d352262a741f4 --- /dev/null +++ b/2025/Quantization without Tears/7acb9c84-5b2e-438a-8a19-e3c09310038a_model.json @@ -0,0 +1,2433 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.359, + 0.131, + 0.64, + 0.152 + ], + "angle": 0, + "content": "Quantization without Tears" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.181, + 0.832, + 0.234 + ], + "angle": 0, + "content": "Minghao Fu Hao Yu Jie Shao Junjie Zhou Ke Zhu Jianxin Wu* National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.237, + 0.802, + 0.253 + ], + "angle": 0, + "content": "{fumh, yuh, shaoj, zhoujj, zhuk}@lamda.nju.edu.cn, wujx2001@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.319, + 0.486, + 0.729 + ], + "angle": 0, + "content": "Deep neural networks, while achieving remarkable success across diverse tasks, demand significant resources, including computation, GPU memory, bandwidth, storage, and energy. Network quantization, as a standard compression and acceleration technique, reduces storage costs and enables potential inference acceleration by discretizing network weights and activations into a finite set of integer values. However, current quantization methods are often complex and sensitive, requiring extensive task-specific hyperparameters, where even a single misconfiguration can impair model performance, limiting generality across different models and tasks. In this paper, we propose Quantization without Tears (QwT), a method that simultaneously achieves quantization speed, accuracy, simplicity, and generality. The key insight of QwT is to incorporate a lightweight additional structure into the quantized network to mitigate information loss during quantization. This structure consists solely of a small set of linear layers, keeping the method simple and efficient. More importantly, it provides a closed-form solution, allowing us to improve accuracy effortlessly under 2 minutes. Extensive experiments across various vision, language, and multimodal tasks demonstrate that QwT is both highly effective and versatile. In fact, our approach offers a robust solution for network quantization that combines simplicity, accuracy, and adaptability, which provides new insights for the design of novel quantization paradigms." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.758, + 0.222, + 0.773 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.784, + 0.485, + 0.875 + ], + "angle": 0, + "content": "Along with their extraordinary breakthroughs in various vision [18], language [10] and multimodal [41] tasks, deep neural networks [11, 17] also exhibit ferocious greed for various resources: compute, GPU memory, bandwidth, storage, energy, etc. Hence, compressing and accelerating deep nets have not only attracted interests in academia, but" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.318 + ], + "angle": 0, + "content": "are also an urgent need in real-world deployments and applications." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.32, + 0.907, + 0.532 + ], + "angle": 0, + "content": "Among various research efforts in this direction, network quantization [28] is arguably the most practical one. Different from unstructured pruning [16], it is well supported by existing hardware. Compared to structured pruning [19, 22], its compression ratio is higher and its loss is relatively smaller. For example, the INT8 quantization of both FP32 weights and activations leads to roughly \\(4 \\times\\) reduction in network size and \\(4 \\times\\) speedup with almost zero accuracy loss in many applications [26], which far exceeds structured pruning. Existing methods are often categorized as Post-Training Quantization (PTQ) [27, 31, 32, 37, 46, 52] or Quantization-Aware Training (QAT) [13, 21, 25, 33, 54], where the difference is whether training is required ('no' for PTQ and 'yes' for QAT)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.533, + 0.906, + 0.578 + ], + "angle": 0, + "content": "Quantization, however, is not as perfect as it seems to be. There are also obvious drawbacks and pitfalls in existing quantization methods." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.58, + 0.906, + 0.64 + ], + "angle": 0, + "content": "- The speed-accuracy dilemma: PTQ can be thousands of times faster than QAT during the quantization process, but QAT may well be 10 percentage points higher than PTQ in accuracy during inference." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.64, + 0.906, + 0.7 + ], + "angle": 0, + "content": "- Complexity: Quantization methods are often delicate and tricky. They often have tons of hyperparameters to tune for each specific task, and even one improperly set hyperparameter value may ruin the quantized model." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.7, + 0.906, + 0.76 + ], + "angle": 0, + "content": "- Missing generality: Relevant to their complexities, an existing method is often geared toward a specific model and/or task. Different models/tasks require different quantization methods." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.58, + 0.906, + 0.76 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.763, + 0.906, + 0.808 + ], + "angle": 0, + "content": "Given the status quo, at this moment it does not seem unreasonable to treat the act of network quantization as an art rather than an established engineering tool." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.905, + 0.869 + ], + "angle": 0, + "content": "In this paper, we propose a Quantization without Tears (QwT) method to address these drawbacks, which achieves quantization speed, accuracy, simplicity and generality simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.902 + ], + "angle": 0, + "content": "The key to achieve these goals simultaneously is to slightly change the quantization paradigm. Suppose a net" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.298, + 0.901 + ], + "angle": 0, + "content": "\\(^{*}\\)J. Wu is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4462" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "work \\(M\\) has the network structure \\(S\\) and parameters \\(\\theta\\). Current quantization methods will quantize it into a model \\(M^{\\mathbb{Z}}\\) with the same structure \\(S(S^{\\mathbb{Z}} = S)\\) and quantized parameters \\(\\theta^{\\mathbb{Z}}\\) in the integer format." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.482, + 0.244 + ], + "angle": 0, + "content": "Our key argument is that the quantized structure does not need to be strictly \\( S \\). In our QwT, it becomes \\( S \\cup S_{c} \\), where some extra modules \\( S_{c} \\) are added to the network structure to compensate for the information loss due to quantized parameters and activations. The extra \\( S_{c} \\) thus help us achieve high accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.245, + 0.482, + 0.336 + ], + "angle": 0, + "content": "\\(S_{c}\\) does lead to extra overheads. But, it is also obvious that so long as the size and computation of \\(S_{c}\\) is small or even negligible when compared to \\(S^{\\mathbb{Z}}\\), we achieve both speed and accuracy. In our QwT, \\(S_{c}\\) has very simple structures: only few linear layers, which renders it both simple and general." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.337, + 0.482, + 0.397 + ], + "angle": 0, + "content": "To be more specific, the parameters in \\( S_{c} \\) can be set in closed-form with a small calibration set, which in almost all cases leads to significantly higher accuracy than PTQ methods." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.399, + 0.415, + 0.414 + ], + "angle": 0, + "content": "To sum up, the contributions of this paper are:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.416, + 0.481, + 0.475 + ], + "angle": 0, + "content": "- Proposing a new paradigm for network quantization by lifting the restriction that the quantized network structure \\( S^{\\mathbb{Z}} \\) has to be exactly the same as that of the original network structure \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.476, + 0.482, + 0.536 + ], + "angle": 0, + "content": "- Proposing QwT, a simple and general quantization method without tears in this new paradigm. QwT achieves speed, accuracy, simplicity and generality simultaneously." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.416, + 0.482, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.538, + 0.482, + 0.568 + ], + "angle": 0, + "content": "Extensive experiments have been carried out, which show that QwT has the following properties:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.57, + 0.483, + 0.719 + ], + "angle": 0, + "content": "- Fast and accurate. For example, QwT quantizes a ViT network in roughly 2 minutes. During inference, its throughput is almost the same as models quantized by existing quantization methods. QwT is significantly more accurate than existing PTQ methods even without any back-propagation. On top of that, if higher accuracy is requested, QwT requires only 1 epoch of training to approach the accuracy of QAT methods. In contrast, QAT often requires a large number of epochs (e.g., 200 epochs)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.72, + 0.483, + 0.75 + ], + "angle": 0, + "content": "- Simple. There is zero (0) hyperparameters to tune, and the parameters in \\( S_{c} \\) can be found in closed-form." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.751, + 0.483, + 0.856 + ], + "angle": 0, + "content": "- General. Exactly the same QwT method has been successfully applied to various networks and applications, including both CNNs [17] and Transformers (ViT [11] and Swin [34]), object recognition, detection (with both Mask R-CNN [18] and DETR [4]) and segmentation, multimodal models (CLIP [41]), generative models (DiT [40]), and large language models (LLaMA [12])." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- Practical. In addition to quantizing to low-bits in simulators, the same QwT method can quantize a model that is able to run directly on GPUs with minimum ef" + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.57, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.091, + 0.905, + 0.152 + ], + "angle": 0, + "content": "forts (i.e., quantization 'without tears'): Simply obtain \\(\\theta^{\\mathbb{Z}}\\) using TensorRT, then add \\(S_{c}\\) using QwT. The resulting quantized model is then ready to be deployed on GPUs that support quantized fix-point inference." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.166, + 0.655, + 0.181 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.191, + 0.905, + 0.311 + ], + "angle": 0, + "content": "Network quantization [28] aims to reduce the bit-width of weights and activations, enabling the quantized model to be stored more efficiently and to perform faster inference with suitable hardware support. The fundamental principle of network quantization involves approximating full-precision weights and activations by mapping them to a finite set of discrete values, which are subsequently used in forward model computations (i.e., in inference)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.312, + 0.905, + 0.401 + ], + "angle": 0, + "content": "One line of research focuses on quantization-aware training (QAT) [13, 21, 25, 33], which integrates quantization into the training process using back-propagation, where the straight-through estimator [1] is commonly employed to approximate gradients for non-differentiable rounding functions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.403, + 0.905, + 0.552 + ], + "angle": 0, + "content": "Another line of research concentrates on post-training quantization (PTQ) [14, 27, 31, 52], which converts a fully trained full-precision model into low-bit format using a small set of calibration samples. AdaRound [38] proposed an adaptive weight-rounding mechanism. BRECQ [24] leveraged block reconstruction for quantization, utilizing the Fisher Information Matrix to guide the process. QDrop [50] randomly dropped the quantization of activations during quantization to achieve flatness of the low-bit model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.905, + 0.644 + ], + "angle": 0, + "content": "While these methods [24, 38, 50] have proven effective on ResNet [17] backbones, applying them directly to ViT [11] often degrades recognition accuracy since the intrinsic structure of the softmax attention is incompatible with these methods. This poses new challenges to design general PTQ methods for the Transformer architecture." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.906, + 0.839 + ], + "angle": 0, + "content": "To address this issue, [35] introduced a ranking loss designed to preserve the relative order between quantized and non-quantized attention scores. PTQ4ViT [52] proposed twin uniform quantization for shifted activations and a Hessian-guided metric to generate scaling factors. RepQViT [27] decoupled quantization and inference, employing distinct quantizers to enable precise quantization while simultaneously ensuring efficient inference. IGQ-ViT [37] introduced instance-aware group quantization for ViT to dynamically allocate channels of activation maps to different quantization groups. GPTQ [14] introduced a one-shot weight quantization technique that exploits approximate second-order information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Different from all of these methods, we propose a new quantization paradigm that introduces a lightweight module to compensate for the information loss caused by quantization. This new paradigm allows our method to be" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4463" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "seamlessly integrated with any state-of-the-art quantization methods as a plugin in a completely black-box fashion. Experiments demonstrate that our method is highly compatible with various PTQ approaches, enabling effortless improvements in recognition accuracy within just 2 minutes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.181, + 0.182, + 0.197 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.206, + 0.232, + 0.221 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.228, + 0.484, + 0.364 + ], + "angle": 0, + "content": "We start by outlining key concepts and notations related to network quantization. Given a quantization bit-width \\( b \\), the quantization function \\( Q(\\cdot | b): \\mathbb{R} \\to \\mathbb{Z} \\) maps a floating-point number \\( x \\) (e.g., weight or activation) into its corresponding fixed-point representation \\( x^{\\mathbb{Z}} \\) encoded by \\( b \\) bits. Among various quantization approaches, uniform quantization is particularly favored thanks to its simplicity and compatibility with hardware deployment. The uniform quantization procedure is formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.375, + 0.483, + 0.402 + ], + "angle": 0, + "content": "\\[\nx ^ {\\mathbb {Z}} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.413, + 0.484, + 0.457 + ], + "angle": 0, + "content": "in which \\( s \\in \\mathbb{R}^+ \\) represents the quantization scale, and \\( z \\in \\mathbb{Z} \\) denotes the zero-point offset. These parameters are determined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.467, + 0.483, + 0.497 + ], + "angle": 0, + "content": "\\[\ns = \\frac {\\operatorname* {m a x} (x) - \\operatorname* {m i n} (x)}{2 ^ {b} - 1}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.5, + 0.483, + 0.533 + ], + "angle": 0, + "content": "\\[\nz = \\operatorname {c l i p} \\left(\\lfloor - \\frac {\\min (x)}{s} \\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.544, + 0.484, + 0.603 + ], + "angle": 0, + "content": "In these equations, \\(\\lfloor .\\rfloor\\) denotes the rounding function, and the \\(\\operatorname{clip}(\\cdot ,a,b)\\) operation constrains the input value into the range \\([a,b]\\). The reconstructed quantized output can then be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.603, + 0.482, + 0.621 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = s \\times \\left(x ^ {\\mathbb {Z}} - z\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.628, + 0.484, + 0.703 + ], + "angle": 0, + "content": "Beyond the naive uniform quantizer, a range of more sophisticated quantization techniques [27, 38, 51, 52] have been proposed and extensively studied by the community. In the literature, quantization methods typically quantize both the model weights and activations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.809 + ], + "angle": 0, + "content": "Quantization significantly reduces the storage requirements by enabling models to be stored in lower bit formats. Additionally, thanks to hardware support for integer-only computations, operations involving the quantized representations \\( x^{\\mathbb{Z}} \\), such as matrix multiplications between quantized weights and activations, can be performed with substantial improvements in computational efficiency." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.376, + 0.835 + ], + "angle": 0, + "content": "3.2. Compensation: The Key Insight" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "But, obviously there is significant information loss between \\( x \\) and \\( x^{\\mathbb{Z}} \\), and it grows very fast when many layers of computation and quantization are stacked together. To recover from the resulting accuracy loss, QAT methods resort to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "many epochs of training, which leads to the speed-accuracy dilemma and complex, ad hoc quantization methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.123, + 0.906, + 0.213 + ], + "angle": 0, + "content": "Given a model \\( M = (S, \\theta) \\), where \\( S \\) and \\( \\theta \\) denote its structure and weights, respectively, existing quantization techniques transform \\( M \\) into a quantized version \\( M^{\\mathbb{Z}} = (S^{\\mathbb{Z}}, \\theta^{\\mathbb{Z}}) \\), which maintains the same network structure (i.e., \\( S = S^{\\mathbb{Z}} \\)) while modifying the original parameters \\( \\theta \\) to their quantized counterparts \\( \\theta^{\\mathbb{Z}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.214, + 0.906, + 0.32 + ], + "angle": 0, + "content": "Our key insight is to challenge this structural rigidity: the quantized model does not necessarily need to retain the exactly same structural configuration, i.e., it is legitimate to allow \\( S^{\\mathbb{Z}} \\neq S \\). We argue that some extra modules \\( S_{c} \\) can be added to the quantized model, such that its structure \\( S^{\\mathbb{Z}} = S \\cup S_{c} \\). The extra modules in \\( S_{c} \\) can compensate for the information loss caused by quantization." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.32, + 0.906, + 0.427 + ], + "angle": 0, + "content": "More specifically, modern deep nets typically compose of many blocks, e.g., bottleneck blocks in ResNet [17] or Transformer blocks in ViT [11]. Let \\( l_{i} \\) denote the \\( i \\)-th block in a model, and let \\( x_{i} \\in \\mathbb{R}^{d_{in}} \\) and \\( y_{i} \\in \\mathbb{R}^{d_{out}} \\) be the input and output of this block \\( l_{i} \\), respectively, such that \\( y_{i} = l_{i}(x_{i}) \\). We argue that we can add a compensation module \\( c_{i} \\) for this block. Then, \\( S_{c} = \\bigcup_{i} c_{i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.427, + 0.905, + 0.517 + ], + "angle": 0, + "content": "For notational simplicity, we omit the subscript \\(i\\) from now on, i.e., we represent a block as \\(y = l(x)\\) and the compensation module is simply denoted as \\(c\\). After quantization, the input activations and weights of the block \\(l\\) are modified into the quantized version \\(x^{\\mathbb{Z}}\\) and \\(l^{\\mathbb{Z}}\\), respectively. The quantized computation becomes \\(y^{\\mathbb{Z}} = l^{\\mathbb{Z}}(x^{\\mathbb{Z}})\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.518, + 0.906, + 0.594 + ], + "angle": 0, + "content": "Clearly, there is information loss in all 3 quantization pairs: \\( l \\mapsto l^{\\mathbb{Z}} \\), \\( x \\mapsto x^{\\mathbb{Z}} \\) and \\( y \\mapsto y^{\\mathbb{Z}} \\). What is intriguing is that the information loss is obviously highly non-linear in all 3 pairs. To implement the compensation idea, we have to answer the following questions:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.594, + 0.906, + 0.625 + ], + "angle": 0, + "content": "1. How to measure the information losses in all 3 pairs that interplay with each other in a complex manner?" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.625, + 0.905, + 0.655 + ], + "angle": 0, + "content": "2. How to design the compensation module \\( c \\) that accounts for these highly non-linear information losses?" + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.594, + 0.906, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.666, + 0.81, + 0.682 + ], + "angle": 0, + "content": "3.3. QwT: Quantization without Tears" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.688, + 0.905, + 0.719 + ], + "angle": 0, + "content": "We propose a QwT (quantization without tears) method, which answers both questions in the simplest possible form." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.719, + 0.906, + 0.84 + ], + "angle": 0, + "content": "First, the information loss is measured by \\( \\| y - y^{\\mathbb{Z}}\\| ^2 \\). Because \\( y \\) is the output of \\( l \\), it naturally takes care of information losses in \\( x^{\\mathbb{Z}} \\) and \\( l^{\\mathbb{Z}} \\) when \\( y^{\\mathbb{Z}} = y \\), intuitively there is absolutely zero information loss even if \\( x\\neq x^{\\mathbb{Z}} \\) and \\( l\\neq l^{\\mathbb{Z}} \\). Note that \\( \\| y - y^{\\mathbb{Z}}\\|^{2} \\) also accounts for cumulative information losses. That is, in the \\( i \\)-th block, \\( c_{i} \\) compensates information losses accumulated in all previous blocks that have not yet been corrected by \\( c_{1},c_{2},\\ldots ,c_{i - 1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Second, because of this cumulative nature of our choice, in QwT we choose to implement \\( c \\) (with the index \\( i \\) omitted) as a simple linear layer. Although it is impossible to accurately compensate the non-linear information loss in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4464" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.092, + 0.462, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.187, + 0.483, + 0.245 + ], + "angle": 0, + "content": "Figure 1. Illustration of QwT in one block. QwT adds a simple linear layer to any model block, compensating for information loss using the block input \\( x^{\\mathbb{Z}} \\). This approach is straightforward and compatible with almost all types of backbones [11, 17, 34]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.269, + 0.484, + 0.329 + ], + "angle": 0, + "content": "one block via a linear layer, we have many chances to repeatedly apply linear corrections. The entire compensation formed by all extra modules is in fact non-linear because it interacts with the quantized network in every block." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.33, + 0.453, + 0.344 + ], + "angle": 0, + "content": "To be concrete, we define \\( c(x) = Wx + b \\) and then" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.353, + 0.483, + 0.372 + ], + "angle": 0, + "content": "\\[\ny ^ {\\mathrm {Q w T}} = l ^ {\\mathbb {Z}} \\left(x ^ {\\mathbb {Z}}\\right) + c \\left(x ^ {\\mathbb {Z}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.38, + 0.484, + 0.426 + ], + "angle": 0, + "content": "where \\( W \\in \\mathbb{R}^{d_{out} \\times d_{in}} \\) and \\( b \\in \\mathbb{R}^{d_{out}} \\) are the weight matrix and bias vector of the linear layer \\( c \\), respectively. The QwT structure is illustrated in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.484, + 0.591 + ], + "angle": 0, + "content": "These choices are deliberate. They not only make QwT conceptually the simplest, but also ensures a closed-form solution. To minimize the difference between \\(y\\) and \\(y^{\\mathbb{Z}}\\), we select a small set of training examples (512 images) from the training set. Using these samples, QwT collects all inputs for the block \\(l^{\\mathbb{Z}}\\) to form a matrix \\(X^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{in} \\times N}\\), where \\(N\\) is the total number of features or tokens. We feed \\(X^{\\mathbb{Z}}\\) into the quantized block \\(l^{\\mathbb{Z}}\\) to obtain \\(Y^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{out} \\times N}\\). Next, we feed \\(X^{\\mathbb{Z}}\\) into the non-quantized block \\(l\\) to obtain \\(Y \\in \\mathbb{R}^{d_{out} \\times N}\\). Correspondingly, \\(Y\\) contains output of the matching block in the original model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.592, + 0.484, + 0.636 + ], + "angle": 0, + "content": "Our task is then to estimate \\( Y - Y^{\\mathbb{Z}} \\) using \\( X^{\\mathbb{Z}} \\). This is a classic linear regression problem, and has a closed-form solution:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.644, + 0.483, + 0.667 + ], + "angle": 0, + "content": "\\[\nW ^ {*} = \\left(Y - Y ^ {\\mathbb {Z}}\\right) X ^ {\\mathbb {Z} ^ {\\top}} \\left(X ^ {\\mathbb {Z}} X ^ {\\mathbb {Z} ^ {\\top}}\\right) ^ {- 1}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.749 + ], + "angle": 0, + "content": "In Equation 6, to simplify the solution, the bias \\( b \\) is absorbed into \\( W \\) and a row vector of \\( \\mathbf{1}^{\\top} \\) are concatenated to \\( X^{\\mathbb{Z}} \\). It is worth mentioning that theoretically QwT will not make the quantized network getting worse—by setting \\( W \\) and \\( b \\) to all zeros, QwT will not alter the quantized network." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.839 + ], + "angle": 0, + "content": "Note that after the QwT module for \\(l^{\\mathbb{Z}}\\) is inserted, the compensation in the next block depends on all the previous QwT modules. Consequently, the information loss from \\(y\\) to \\(y^{\\mathbb{Z}}\\) is gradually compensated block by block, allowing \\(c\\) to account for the accumulated loss from all preceding blocks that remain uncorrected." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In our experiments, we observed that the coefficient of determination \\((R^2)\\) [43] for a small subset \\((< 5\\%)\\) of QwT modules was notably low, adversely hurting recognition accuracy. Consequently, we apply the initialization using" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.121 + ], + "angle": 0, + "content": "Equation 6 only when \\( R^2 > 0 \\); Otherwise, the \\( W \\) and \\( b \\) of the QwT module are set to zero." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.122, + 0.905, + 0.182 + ], + "angle": 0, + "content": "Finally, the QwT method has a simple pipeline: first quantize a model \\(M\\) using any PTQ method, then add the compensation module \\(c_{i}\\) to every block \\(i\\) and set the parameters in \\(c_{i}\\) using Equation 6." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.907, + 0.303 + ], + "angle": 0, + "content": "A notable advantage of QwT lies in its inherent simplicity. This simplicity ensures that the initialization process of QwT modules is highly efficient, which requires roughly 2 minutes in practice to compensate for the information loss during quantization, thereby enhancing recognition accuracy. Experimental results demonstrated that QwT exhibits significant versatility and efficiency across various vision and language tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.317, + 0.646, + 0.334 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.342, + 0.906, + 0.448 + ], + "angle": 0, + "content": "In this section, we begin by evaluating our QwT method on a range of discriminative tasks, including image classification, object detection, instance segmentation, and multimodal recognition. Subsequently, we extend our analysis to generative tasks, such as image generation using diffusion models [40] and text generation with large language models [12]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.456, + 0.833, + 0.472 + ], + "angle": 0, + "content": "4.1. Experiments on Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.907, + 0.703 + ], + "angle": 0, + "content": "Settings. We evaluated our method on image classification tasks using the ImageNet dataset [8], leveraging various backbone architectures including ViT [11], DeiT [48], Swin [34], and ResNet [17]. We randomly sampled 512 images from the training set to initialize the parameters of the QwT modules using Equation 6. In all networks, the affine transformation matrix \\( W \\) in QwT is implemented in FP16 format to reduce model size. In ResNet, \\( W \\) is further simplified as a group-wise convolution using a kernel size of 1 and 64 channels per group, achieving additional efficiency in storage and computation. Note that a group-wise convolution is still a linear operator, which can be perfectly encoded by the pair \\( (W, b) \\). Other details were consistent with prior work [27]. Please refer to the appendix for more information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Results on different backbones. Table 1 summarizes the quantization results when applying QwT across different backbone architectures. Specifically, we selected RepQViT [27] and Percentile [23] as the baseline methods for the Transformer family [11, 34, 48] and ResNet [17], respectively. The results show that incorporating the QwT module consistently boosts the recognition accuracy, leading to an average increase of approximately \\(2.6\\%\\), and even up to \\(5\\%\\) for 4-bit quantization, highlighting that QwT is particularly effective for low-bit scenarios. Additionally, after the QwT modules are integrated, the accuracy in 6-bit quantization cases aligns closely with prior state-of-the-art approaches [37, 46]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4465" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.483, + 0.187 + ], + "angle": 0, + "content": "Table 1. Quantization results on the ImageNet dataset [8]. #Bits' indicates the bit-width of weights/activations. 'Size' (MB) represents the storage cost of the model on the hard disk. * denotes QwT modules and classification head are finetuned for one epoch. † indicates that the previous state-of-the-art results are directly sourced from the papers [37, 46] due to the unavailability of their official code implementations." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.197, + 0.479, + 0.727 + ], + "angle": 0, + "content": "
NetworkMethod#BitsSizeTop-1
DeiT-TFull-precision32/3222.972.2
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-62.5
RepQ-ViT [27]4/43.358.2
RepQ-ViT + QwT4/44.261.4
RepQ-ViT + QwT*4/44.264.8
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-71.2
RepQ-ViT [27]6/64.671.0
RepQ-ViT + QwT6/65.571.2
RepQ-ViT + QwT*6/65.571.6
Swin-TFull-precision32/32113.281.4
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-77.8
RepQ-ViT [27]4/414.973.0
RepQ-ViT + QwT4/419.275.5
RepQ-ViT + QwT*4/419.279.3
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-80.9
RepQ-ViT [27]6/621.780.6
RepQ-ViT + QwT6/626.080.7
RepQ-ViT + QwT*6/626.080.9
ViT-BFull-precision32/32346.384.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-79.3
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
RepQ-ViT + QwT*4/459.178.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-83.8
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
RepQ-ViT + QwT*6/680.484.0
ResNet-50Full-precision32/32102.276.6
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]4/4-75.4
Percentile[23]4/414.068.4
Percentile + QwT4/416.074.5
Percentile + QwT*4/416.075.8
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]6/6--
Percentile[23]6/619.976.0
Percentile + QwT6/621.976.8
Percentile + QwT*6/621.976.8
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.76, + 0.483, + 0.852 + ], + "angle": 0, + "content": "The potential of our QwT method can be further unlocked through finetuning. By jointly optimizing the QwT modules and the classification head for only one (1) additional epoch (results marked with *), more gains in accuracy are achieved, enabling our method to surpass previous state-of-the-art results in nearly all cases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.903 + ], + "angle": 0, + "content": "These results are even closer to those produced by QAT methods, which typically require extensive training (e.g., 200 epochs). In contrast, our \\(\\mathrm{QwT^{*}}\\) achieves similar per" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.148 + ], + "angle": 0, + "content": "Table 2. Results of 8-bit quantization, using tensor-wise Percentile [23] as the baseline PTQ method. 'Latency' (ms) is measured on a single RTX 3090 GPU with a batch size of 64, utilizing Nvidia's TensorRT [39] toolkit for deployment." + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.157, + 0.897, + 0.391 + ], + "angle": 0, + "content": "
NetworkMethodSizeLatencyTop-1
DeiT-TFull-precision22.911.672.2
Percentile [23]5.92.871.2
Percentile + QwT6.83.271.5
Swin-TFull-precision113.234.581.4
Percentile [23]28.69.580.8
Percentile + QwT32.910.981.0
Swin-SFull-precision198.461.083.2
Percentile [23]50.116.082.1
Percentile + QwT58.017.983.0
ViT-SFull-precision88.228.381.4
Percentile [23]22.55.879.2
Percentile + QwT26.06.680.1
ViT-BFull-precision346.385.384.5
Percentile [23]87.415.575.8
Percentile + QwT101.617.582.8
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.417, + 0.907, + 0.478 + ], + "angle": 0, + "content": "formance with only one epoch of finetuning. Our approach not only substantially improves training efficiency but also keeps the backbone parameters unchanged, making it more suitable for hardware deployment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.909, + 0.628 + ], + "angle": 0, + "content": "In Table 2, we additionally report the inference latency of different models directly deployed on a GPU. Compared to full-precision models, naive quantized models achieve an average reduction of \\(77\\%\\) in inference latency and \\(75\\%\\) in model size. When QwT modules are incorporated, these reductions slightly decrease to \\(74\\%\\) and \\(71\\%\\), respectively, with an overhead of only \\(3\\%\\). This minimal additional cost is offset by an average 1.9 percentage points improvement in recognition accuracy, demonstrating the strong practicality of the QwT method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.704 + ], + "angle": 0, + "content": "Results across various PTQ methods. We extended our experiments to evaluate the versatility of QwT by applying it to various PTQ methods. As shown in Table 3, we integrated QwT into PTQ4ViT [52], RepQ-ViT [27], and Percentile [23], using ViT-B as the backbone." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.87 + ], + "angle": 0, + "content": "We observe that QwT consistently enhances top-1 accuracy across all baseline PTQ methods. Notably, in 4-bit scenarios, PTQ4ViT demonstrates an improvement of approximately \\(40\\%\\), while RepQ-ViT shows an \\(8\\%\\) increase. Compared to modern PTQ methods [27, 37, 52], which often involve complex and tedious procedures, our method demonstrates high simplicity and, most importantly, is compatible with all these approaches, too. The significant improvement in accuracy narrows the performance gap between different PTQ methods, and offers new insights into the design of new paradigms for network quantization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Extension to QAT methods. We further investigated the potential of adapting QwT to QAT methods. Specifically," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "4466" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.486, + 0.12 + ], + "angle": 0, + "content": "Table 3. Quantization results among different PTQ methods on the ImageNet dataset [8] using ViT-B [11] as the backbone." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.129, + 0.434, + 0.337 + ], + "angle": 0, + "content": "
Method#BitsSizeTop-1
Full-precision32/32346.384.5
PTQ4ViT [52]4/444.930.7
PTQ4ViT+QwT4/459.170.0
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
Percentile [23]6/666.256.7
Percentile+QwT6/680.479.8
PTQ4ViT [52]6/666.281.7
PTQ4ViT+QwT6/680.483.2
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
Percentile [23]8/887.475.8
Percentile+QwT8/8101.682.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.348, + 0.485, + 0.378 + ], + "angle": 0, + "content": "Table 4. Quantization results of applying QwT finetuning schema on QAT methods." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.387, + 0.434, + 0.469 + ], + "angle": 0, + "content": "
NetworkMethod#BitsTop-1
DeiT-SQ-ViT [25]2/272.1
Q-ViT + QwT*2/272.5
Q-ViT [25]3/379.0
Q-ViT + QwT*3/379.1
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.483, + 0.538 + ], + "angle": 0, + "content": "we applied QwT modules to QAT models after completing QAT training to assess whether QwT can further enhance recognition accuracy." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.538, + 0.483, + 0.674 + ], + "angle": 0, + "content": "We preliminarily found that for QAT models, the initialization process described by Equation 6 is no longer effective. Applying it directly to QAT models significantly degrades accuracy. We attribute this to the fact that, unlike full-precision models, the optimization state of a QAT-trained model is sufficiently converged, resulting in almost no information loss from \\( y \\) to \\( y^{\\mathbb{Z}} \\). In fact, \\( y^{\\mathbb{Z}} \\) may even outperform \\( y \\), as QAT models sometimes surpass their full-precision counterparts in evaluation accuracy." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.673, + 0.483, + 0.81 + ], + "angle": 0, + "content": "To integrate QwT into QAT methods, we therefore initialize \\( W \\) and \\( b \\) to zero as a compromise. We then explore whether fine-tuning QwT can still improve recognition accuracy. For this study, we use Q-ViT [25], a representative QAT method for ViT backbones, as the baseline. The results in Table 4 demonstrate that, even without using the initialization from Equation 6, fine-tuning the QwT modules consistently enhances QAT models, confirming the generalizability of our approach." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.819, + 0.485, + 0.851 + ], + "angle": 0, + "content": "4.2. Experiments on Object Detection & Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Settings. We evaluated our method on object detection and instance segmentation tasks using the COCO 2017 [30] dataset. ResNet50 [17] with DETR [4], Swin-S [34] with" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.272 + ], + "angle": 0, + "content": "Mask R-CNN [18], and Swin-S/B [34] with Cascade Mask R-CNN [3] were used as detectors. The evaluation metric was Average Precision (AP). Similar to image classification, we randomly selected 512 images from the training set to initialize the QwT weights and biases. For ResNet, the QwT was implemented using group-wise convolution with a kernel size of 1 and 64 channels per group to balance model size and AP. For DETR, we used MinMax as the PTQ baseline, a classic method that quantizes the model based on the range between the minimum and maximum values of weights or activations. For the other detectors, RepQViT [27] was chosen as the baseline PTQ method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.274, + 0.905, + 0.426 + ], + "angle": 0, + "content": "Main results. Table 5 presents the results of applying QwT to object detection and instance segmentation tasks. We observe that QwT consistently enhances both \\(\\mathrm{AP^{box}}\\) and \\(\\mathrm{AP^{mask}}\\) across all cases without finetuning, achieving an average improvement of \\(0.4\\%\\) with individual gains ranging from \\(0.1\\%\\) to \\(0.7\\%\\). The consistent improvement underscores the robustness of our method for both object detection and instance segmentation tasks. Notably, in certain 6-bit scenarios, such as on Cascade Mask R-CNN, QwT even achieves AP comparable to full-precision models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.426, + 0.905, + 0.517 + ], + "angle": 0, + "content": "Additionally, a clear trend emerges where the AP gains introduced by QwT increases along with model size. For instance, in \\(\\mathrm{AP^{box}}\\), the average improvement achieved by QwT rises from \\(0.3\\%\\) in ResNet-50+DETR to \\(0.5\\%\\) in Swin-B+Cascade Mask R-CNN, indicating the method's enhanced effectiveness in larger models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.517, + 0.907, + 0.594 + ], + "angle": 0, + "content": "Compared to full-precision models, baseline PTQ methods yield an average storage reduction of approximately \\(80\\%\\). The introduction of QwT modules slightly reduces this savings to around \\(78\\%\\) \\((-2\\%)\\), which demonstrates that QwT enhances AP metrics with negligible overhead." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.605, + 0.866, + 0.623 + ], + "angle": 0, + "content": "4.3. Experiments on Multimodal Recognition" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.906, + 0.839 + ], + "angle": 0, + "content": "Settings. We conducted experiments using OpenAI's CLIP model [41]. Known for its exceptional zero-shot performance on the ImageNet [8] classification task, CLIP serves as an ideal benchmark for assessing the effectiveness on multimodal recognition tasks. We selected the variant of CLIP that includes a ViT-B/32 [11] as the visual encoder and a 12-block Transformer [49] as the text encoder. Since, to the best of our knowledge, no publicly available PTQ implementation exists for CLIP, we developed a baseline using RepQ-ViT [27]. We randomly selected 512 image-text pairs from the training data, both for PTQ model calibration and QwT initialization. Thanks to the simplicity and efficiency of our method, it achieved significant improvements under 30 seconds, as detailed in Table 6." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Main results. We conducted experiments with two quantization strategies: quantizing 1) only the visual encoder and 2) both visual and text encoders. As shown in Table 6, baseline PTQ methods showed significant drop in top-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4467" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.486, + 0.148 + ], + "angle": 0, + "content": "Table 5. Quantization results on the COCO dataset [8]. We use box average precision \\((\\mathrm{AP}^{\\mathrm{box}})\\) and mask average precision \\((\\mathrm{AP}^{\\mathrm{mask}})\\) to assess object detection and instance segmentation accuracy, respectively." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.156, + 0.477, + 0.461 + ], + "angle": 0, + "content": "
NetworkMethod#BitsSizeAPboxAPmask
ResNet-50 + DETRFull-precision32/32164.542.0-
MinMax6/647.439.5-
MinMax + QwT6/649.440.0-
MinMax8/856.441.6-
MinMax + QwT8/858.441.7-
Swin-S + Mask R-CNNFull-precision32/32276.548.543.3
RepQ-ViT [27]4/436.142.640.0
RepQ-ViT + QwT4/444.043.140.4
RepQ-ViT [27]6/653.347.642.9
RepQ-ViT + QwT6/661.248.043.1
Swin-S + Cascade Mask R-CNNFull-precision32/32427.851.945.0
RepQ-ViT [27]4/456.949.343.1
RepQ-ViT + QwT4/464.849.943.4
RepQ-ViT [27]6/683.451.444.6
RepQ-ViT + QwT6/691.351.744.8
Swin-B + Cascade Mask R-CNNFull-precision32/32579.951.945.0
RepQ-ViT [27]4/476.149.343.1
RepQ-ViT + QwT4/490.150.043.7
RepQ-ViT [27]6/6112.151.544.8
RepQ-ViT + QwT6/6126.151.845.0
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.547 + ], + "angle": 0, + "content": "1 accuracy compared to their full-precision counterparts, struggling to effectively represent a low-bit CLIP model. The reduction in performance is especially obvious when both the visual and text encoders are quantized." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.483, + 0.639 + ], + "angle": 0, + "content": "In contrast, our QwT method enhanced top-1 accuracy across all cases, significantly bridging the accuracy gap between low-bit and full-precision models. Specifically, in vision-only quantization, QwT increased top-1 accuracy by an average of \\(0.6\\%\\), with only a modest \\(4\\%\\) increase in model size compared to baseline PTQ methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.64, + 0.483, + 0.746 + ], + "angle": 0, + "content": "When both the visual and text encoders are quantized, baseline PTQ methods exhibited an average accuracy drop of \\(29.2\\%\\). In contrast, QwT provided a significant accuracy improvement, with an average increase of \\(14.8\\%\\). These findings highlight QwT's effectiveness in preserving high accuracy while substantially reducing model size for multimodal recognition tasks." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.758, + 0.395, + 0.775 + ], + "angle": 0, + "content": "4.4. Experiments on Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.901 + ], + "angle": 0, + "content": "QwT has also demonstrated efficacy in generative models, notably enhancing the performance of quantized diffusion models. Unlike classifiers or detectors, which require a single forward pass, diffusion models involve multiple forward passes to generate the final images, presenting a unique prototype. Under these circumstances, QwT has proven itself highly effective, underscoring its general applicability and robustness." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.148 + ], + "angle": 0, + "content": "Table 6. Quantization results of CLIP for zero-shot classification tasks on ImageNet. The 'Quant Setup' column differentiates between two strategies: quantizing only the vision encoder and quantizing both the vision and text encoders concurrently." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.156, + 0.902, + 0.322 + ], + "angle": 0, + "content": "
Quant SetupMethod#BitsSize (MB)Top-1
VisionFull-precision32/32607.263.4
RepQ-ViT [27]6/6323.559.2
RepQ-ViT + QwT6/6336.860.3
RepQ-ViT [27]8/8345.362.9
RepQ-ViT + QwT8/8359.563.0
Vision & TextFull-precision32/32607.263.4
RepQ-ViT [27]6/6200.829.8
RepQ-ViT + QwT6/6221.343.5
RepQ-ViT [27]8/8232.138.7
RepQ-ViT + QwT8/8252.654.6
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.907, + 0.517 + ], + "angle": 0, + "content": "Settings. For our experiments, we selected the influential DiT [40] (Diffusion Transformer) architecture, following the experimental setup of Q-DiT [5]. Specifically, we employed pretrained DiT-XL/2 models at a resolution of \\(256 \\times 256\\). For rapid and precise sampling, we utilized the DDIM sampler with 50 sampling steps and applied classifier-free guidance (cfg) of 1.5, abbreviated as DiT-XL/2 (steps = 50, CFG = 1.5). Our experiments included two quantization configurations: W8A8 and W4A8. Additional results involving various model sizes, steps, and CFG values are available in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.909, + 0.655 + ], + "angle": 0, + "content": "We applied QwT directly to the quantized diffusion model using Q-DiT. A key consideration is that the model performs \\( T \\) forward passes per inference, with notable variation in the activation distribution and range across steps. A key assumption is that quantization error is primarily dependent on the input \\( x \\), with minimal influence from elements like the time step or class condition. Accordingly, we set \\( t = 0 \\) to initialize the compensation module. The results are presented in Table 7." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.657, + 0.909, + 0.763 + ], + "angle": 0, + "content": "Main results. Our method was compared with three representative quantization techniques: RepQ-ViT, GPTQ and Q-DiT designed for diffusion models. For both W8A8 and W4A8 settings, QwT significantly enhanced the performance of the quantized models, yielding improvements of 0.10 and 0.69 in FID, which illustrates the efficacy of QwT with minimal increase in model size." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We visualize the images generated by our model alongside those from compared models in Figure 2. The three rows represent the original images, quantized images with Q-DiT, and quantized images with QwT, respectively. All models are based on DiT-XL/2 (steps \\(= 50\\), \\(\\mathrm{cfg} = 1.5\\)). To enable a fair comparison, we ensure that the initial Gaussian noise and the noise added during inference are identical across all methods. The images produced by our method show a closer visual resemblance to the original model," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "4468" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.159, + 0.095, + 0.842, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.299, + 0.696, + 0.314 + ], + "angle": 0, + "content": "Figure 2. Qualitative visualization results of quantizing DiT-XL/2." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.338, + 0.483, + 0.366 + ], + "angle": 0, + "content": "Table 7. Quantitative results of quantizing DiT-XL/2. \\( \\downarrow \\) (↑) means smaller (larger) is better." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.377, + 0.465, + 0.558 + ], + "angle": 0, + "content": "
Method#BitsSize (MB)FID (↓)IS (↑)
Full-precision16/1613495.32236.17
RepQ-ViT8/86775.46234.74
GPTQ8/86905.90218.90
Q-DiT8/86835.45236.52
Q-DiT + QwT8/87075.35236.91
RepQ-ViT4/8339319.682.20
GPTQ4/83519.94166.35
Q-DiT4/83476.75208.38
Q-DiT + QwT4/83616.06215.70
" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.583, + 0.368, + 0.598 + ], + "angle": 0, + "content": "which aligns with the quantitative results." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.607, + 0.441, + 0.623 + ], + "angle": 0, + "content": "4.5. Experiments on Large Language Models" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.629, + 0.483, + 0.78 + ], + "angle": 0, + "content": "Settings. We evaluated our framework on the LLaMA3-8B [12] model. For PTQ methods, we adopted GPTQ [14] with INT4 weight quantization. Our approach is also compatible with other PTQ methods such as AWQ [29] and SPQR [9]. We conducted a group-wise asymmetric quantization with a group size of 128 and apply activation reordering. In particular, GPTQ take 128 samples from the C4 dataset as calibration sets, and each sample is 2048 tokens long. We use the same calibration set when performing QwT after GPTQ algorithm." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. Following the settings of GPTQ, we evaluated the perplexity on the WikiText2 [47] and C4 [42] datasets. We further assessed the zero-shot commonsense question answering (QA) ability on eight tasks covering SIQA [45], HellaSwag [53], PIQA [2], Wino-Grande [44], ARC [7], BoolQ [6], and OpenBookQA [36]. We also evaluated both the zero-shot and five-shot performance of the LLMs on Massively Multitask Language Un" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.338, + 0.907, + 0.381 + ], + "angle": 0, + "content": "Table 8. Quantization results among WikiText2, C4 and eight zero-shot commonsense QA datasets using LLaMA3-8B as the backbone. \\(\\downarrow (\\uparrow)\\) means smaller (larger) is better." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.39, + 0.907, + 0.459 + ], + "angle": 0, + "content": "
Method#BitsSize (GB)W2 (↓)C4 (↓)QA. Avg (↑)
Full-precision1616.066.248.9666.10
GPTQ45.736.659.4464.90
GPTQ + QwT46.806.639.3865.18
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.484, + 0.907, + 0.545 + ], + "angle": 0, + "content": "derstanding (MMLU) benchmark [20]. It consists of 57 language tasks including humanities, STEM, social science, etc. We adopted lm-eval-harness [15] to produce the accuracy results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.907, + 0.651 + ], + "angle": 0, + "content": "Results. Table 8 summarizes the perplexity in WikiText2, C4 and the average accuracy in eight common sense reasoning datasets. More results are shown in the appendix. Note that we abbreviate WikiText2 to W2. As the results show, our optimized models will not overfit the calibration dataset and consistently outperform the original PTQ models. These results reveal the effectiveness of our QwT." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.665, + 0.642, + 0.68 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.689, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this paper, we proposed Quantization without Tears (QwT), a novel approach that incorporates a lightweight structure into quantized models to compensate for the information loss during network quantization. The QwT modules, implemented as a tiny set of linear layers and seamlessly integrated into backbone blocks, achieved accuracy, simplicity, and generality simultaneously. Notably, QwT provides a closed-form solution to complete the compensation process in under 2 minutes and enables effortless integration with existing quantization techniques. Extensive experiments demonstrated QwT's exceptional effectiveness and versatility across a wide range of tasks, models, and quantization methods, advancing a streamlined and flexible paradigm for network quantization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4469" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.484, + 0.145 + ], + "angle": 0, + "content": "This research was partly supported by the National Natural Science Foundation of China under Grant 62276123." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.147, + 0.484, + 0.253 + ], + "angle": 0, + "content": "J.W. designed the compensation insight and the QwT framework mathematically. M.F. made them into algorithms and codes that work well in practice, and carried out the main empirical validations. H.Y., J.S. and J.Z. carried out experiments and validations on LLM, AIGC and multimodal tasks, respectively. K.Z. engaged in discussions. All authors contributed to paper writing." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.267, + 0.188, + 0.282 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.291, + 0.484, + 0.332 + ], + "angle": 0, + "content": "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv:1308.3432, 2013. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.335, + 0.484, + 0.389 + ], + "angle": 0, + "content": "[2] Yonatan Bisk, Rowan Zellers, Ronan Le Bras, Jianfeng Gao, and Yejin Choi. Piaq: Reasoning about physical commonsense in natural language. 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Network quantization, as a standard compression and acceleration technique, reduces storage costs and enables potential inference acceleration by discretizing network weights and activations into a finite set of integer values. However, current quantization methods are often complex and sensitive, requiring extensive task-specific hyperparameters, where even a single misconfiguration can impair model performance, limiting generality across different models and tasks. In this paper, we propose Quantization without Tears (QwT), a method that simultaneously achieves quantization speed, accuracy, simplicity, and generality. The key insight of QwT is to incorporate a lightweight additional structure into the quantized network to mitigate information loss during quantization. This structure consists solely of a small set of linear layers, keeping the method simple and efficient. More importantly, it provides a closed-form solution, allowing us to improve accuracy effortlessly under 2 minutes. Extensive experiments across various vision, language, and multimodal tasks demonstrate that QwT is both highly effective and versatile. In fact, our approach offers a robust solution for network quantization that combines simplicity, accuracy, and adaptability, which provides new insights for the design of novel quantization paradigms. + +# 1. Introduction + +Along with their extraordinary breakthroughs in various vision [18], language [10] and multimodal [41] tasks, deep neural networks [11, 17] also exhibit ferocious greed for various resources: compute, GPU memory, bandwidth, storage, energy, etc. Hence, compressing and accelerating deep nets have not only attracted interests in academia, but + +are also an urgent need in real-world deployments and applications. + +Among various research efforts in this direction, network quantization [28] is arguably the most practical one. Different from unstructured pruning [16], it is well supported by existing hardware. Compared to structured pruning [19, 22], its compression ratio is higher and its loss is relatively smaller. For example, the INT8 quantization of both FP32 weights and activations leads to roughly $4 \times$ reduction in network size and $4 \times$ speedup with almost zero accuracy loss in many applications [26], which far exceeds structured pruning. Existing methods are often categorized as Post-Training Quantization (PTQ) [27, 31, 32, 37, 46, 52] or Quantization-Aware Training (QAT) [13, 21, 25, 33, 54], where the difference is whether training is required ('no' for PTQ and 'yes' for QAT). + +Quantization, however, is not as perfect as it seems to be. There are also obvious drawbacks and pitfalls in existing quantization methods. + +- The speed-accuracy dilemma: PTQ can be thousands of times faster than QAT during the quantization process, but QAT may well be 10 percentage points higher than PTQ in accuracy during inference. +- Complexity: Quantization methods are often delicate and tricky. They often have tons of hyperparameters to tune for each specific task, and even one improperly set hyperparameter value may ruin the quantized model. +- Missing generality: Relevant to their complexities, an existing method is often geared toward a specific model and/or task. Different models/tasks require different quantization methods. + +Given the status quo, at this moment it does not seem unreasonable to treat the act of network quantization as an art rather than an established engineering tool. + +In this paper, we propose a Quantization without Tears (QwT) method to address these drawbacks, which achieves quantization speed, accuracy, simplicity and generality simultaneously. + +The key to achieve these goals simultaneously is to slightly change the quantization paradigm. Suppose a net + +work $M$ has the network structure $S$ and parameters $\theta$ . Current quantization methods will quantize it into a model $M^{\mathbb{Z}}$ with the same structure $S(S^{\mathbb{Z}} = S)$ and quantized parameters $\theta^{\mathbb{Z}}$ in the integer format. + +Our key argument is that the quantized structure does not need to be strictly $S$ . In our QwT, it becomes $S \cup S_{c}$ , where some extra modules $S_{c}$ are added to the network structure to compensate for the information loss due to quantized parameters and activations. The extra $S_{c}$ thus help us achieve high accuracy. + +$S_{c}$ does lead to extra overheads. But, it is also obvious that so long as the size and computation of $S_{c}$ is small or even negligible when compared to $S^{\mathbb{Z}}$ , we achieve both speed and accuracy. In our QwT, $S_{c}$ has very simple structures: only few linear layers, which renders it both simple and general. + +To be more specific, the parameters in $S_{c}$ can be set in closed-form with a small calibration set, which in almost all cases leads to significantly higher accuracy than PTQ methods. + +To sum up, the contributions of this paper are: + +- Proposing a new paradigm for network quantization by lifting the restriction that the quantized network structure $S^{\mathbb{Z}}$ has to be exactly the same as that of the original network structure $S$ . +- Proposing QwT, a simple and general quantization method without tears in this new paradigm. QwT achieves speed, accuracy, simplicity and generality simultaneously. + +Extensive experiments have been carried out, which show that QwT has the following properties: + +- Fast and accurate. For example, QwT quantizes a ViT network in roughly 2 minutes. During inference, its throughput is almost the same as models quantized by existing quantization methods. QwT is significantly more accurate than existing PTQ methods even without any back-propagation. On top of that, if higher accuracy is requested, QwT requires only 1 epoch of training to approach the accuracy of QAT methods. In contrast, QAT often requires a large number of epochs (e.g., 200 epochs). +- Simple. There is zero (0) hyperparameters to tune, and the parameters in $S_{c}$ can be found in closed-form. +- General. Exactly the same QwT method has been successfully applied to various networks and applications, including both CNNs [17] and Transformers (ViT [11] and Swin [34]), object recognition, detection (with both Mask R-CNN [18] and DETR [4]) and segmentation, multimodal models (CLIP [41]), generative models (DiT [40]), and large language models (LLaMA [12]). +- Practical. In addition to quantizing to low-bits in simulators, the same QwT method can quantize a model that is able to run directly on GPUs with minimum ef + +forts (i.e., quantization 'without tears'): Simply obtain $\theta^{\mathbb{Z}}$ using TensorRT, then add $S_{c}$ using QwT. The resulting quantized model is then ready to be deployed on GPUs that support quantized fix-point inference. + +# 2. Related Work + +Network quantization [28] aims to reduce the bit-width of weights and activations, enabling the quantized model to be stored more efficiently and to perform faster inference with suitable hardware support. The fundamental principle of network quantization involves approximating full-precision weights and activations by mapping them to a finite set of discrete values, which are subsequently used in forward model computations (i.e., in inference). + +One line of research focuses on quantization-aware training (QAT) [13, 21, 25, 33], which integrates quantization into the training process using back-propagation, where the straight-through estimator [1] is commonly employed to approximate gradients for non-differentiable rounding functions. + +Another line of research concentrates on post-training quantization (PTQ) [14, 27, 31, 52], which converts a fully trained full-precision model into low-bit format using a small set of calibration samples. AdaRound [38] proposed an adaptive weight-rounding mechanism. BRECQ [24] leveraged block reconstruction for quantization, utilizing the Fisher Information Matrix to guide the process. QDrop [50] randomly dropped the quantization of activations during quantization to achieve flatness of the low-bit model. + +While these methods [24, 38, 50] have proven effective on ResNet [17] backbones, applying them directly to ViT [11] often degrades recognition accuracy since the intrinsic structure of the softmax attention is incompatible with these methods. This poses new challenges to design general PTQ methods for the Transformer architecture. + +To address this issue, [35] introduced a ranking loss designed to preserve the relative order between quantized and non-quantized attention scores. PTQ4ViT [52] proposed twin uniform quantization for shifted activations and a Hessian-guided metric to generate scaling factors. RepQViT [27] decoupled quantization and inference, employing distinct quantizers to enable precise quantization while simultaneously ensuring efficient inference. IGQ-ViT [37] introduced instance-aware group quantization for ViT to dynamically allocate channels of activation maps to different quantization groups. GPTQ [14] introduced a one-shot weight quantization technique that exploits approximate second-order information. + +Different from all of these methods, we propose a new quantization paradigm that introduces a lightweight module to compensate for the information loss caused by quantization. This new paradigm allows our method to be + +seamlessly integrated with any state-of-the-art quantization methods as a plugin in a completely black-box fashion. Experiments demonstrate that our method is highly compatible with various PTQ approaches, enabling effortless improvements in recognition accuracy within just 2 minutes. + +# 3. Method + +# 3.1. Preliminaries + +We start by outlining key concepts and notations related to network quantization. Given a quantization bit-width $b$ , the quantization function $Q(\cdot | b): \mathbb{R} \to \mathbb{Z}$ maps a floating-point number $x$ (e.g., weight or activation) into its corresponding fixed-point representation $x^{\mathbb{Z}}$ encoded by $b$ bits. Among various quantization approaches, uniform quantization is particularly favored thanks to its simplicity and compatibility with hardware deployment. The uniform quantization procedure is formalized as: + +$$ +x ^ {\mathbb {Z}} = \operatorname {c l i p} \left(\left\lfloor \frac {x}{s} \right\rceil + z, 0, 2 ^ {b} - 1\right), \tag {1} +$$ + +in which $s \in \mathbb{R}^+$ represents the quantization scale, and $z \in \mathbb{Z}$ denotes the zero-point offset. These parameters are determined as follows: + +$$ +s = \frac {\operatorname* {m a x} (x) - \operatorname* {m i n} (x)}{2 ^ {b} - 1}, \tag {2} +$$ + +$$ +z = \operatorname {c l i p} \left(\lfloor - \frac {\min (x)}{s} \rfloor , 0, 2 ^ {b} - 1\right). \tag {3} +$$ + +In these equations, $\lfloor .\rfloor$ denotes the rounding function, and the $\operatorname{clip}(\cdot ,a,b)$ operation constrains the input value into the range $[a,b]$ . The reconstructed quantized output can then be formulated as: + +$$ +\hat {x} = s \times \left(x ^ {\mathbb {Z}} - z\right). \tag {4} +$$ + +Beyond the naive uniform quantizer, a range of more sophisticated quantization techniques [27, 38, 51, 52] have been proposed and extensively studied by the community. In the literature, quantization methods typically quantize both the model weights and activations. + +Quantization significantly reduces the storage requirements by enabling models to be stored in lower bit formats. Additionally, thanks to hardware support for integer-only computations, operations involving the quantized representations $x^{\mathbb{Z}}$ , such as matrix multiplications between quantized weights and activations, can be performed with substantial improvements in computational efficiency. + +# 3.2. Compensation: The Key Insight + +But, obviously there is significant information loss between $x$ and $x^{\mathbb{Z}}$ , and it grows very fast when many layers of computation and quantization are stacked together. To recover from the resulting accuracy loss, QAT methods resort to + +many epochs of training, which leads to the speed-accuracy dilemma and complex, ad hoc quantization methods. + +Given a model $M = (S, \theta)$ , where $S$ and $\theta$ denote its structure and weights, respectively, existing quantization techniques transform $M$ into a quantized version $M^{\mathbb{Z}} = (S^{\mathbb{Z}}, \theta^{\mathbb{Z}})$ , which maintains the same network structure (i.e., $S = S^{\mathbb{Z}}$ ) while modifying the original parameters $\theta$ to their quantized counterparts $\theta^{\mathbb{Z}}$ . + +Our key insight is to challenge this structural rigidity: the quantized model does not necessarily need to retain the exactly same structural configuration, i.e., it is legitimate to allow $S^{\mathbb{Z}} \neq S$ . We argue that some extra modules $S_{c}$ can be added to the quantized model, such that its structure $S^{\mathbb{Z}} = S \cup S_{c}$ . The extra modules in $S_{c}$ can compensate for the information loss caused by quantization. + +More specifically, modern deep nets typically compose of many blocks, e.g., bottleneck blocks in ResNet [17] or Transformer blocks in ViT [11]. Let $l_{i}$ denote the $i$ -th block in a model, and let $x_{i} \in \mathbb{R}^{d_{in}}$ and $y_{i} \in \mathbb{R}^{d_{out}}$ be the input and output of this block $l_{i}$ , respectively, such that $y_{i} = l_{i}(x_{i})$ . We argue that we can add a compensation module $c_{i}$ for this block. Then, $S_{c} = \bigcup_{i} c_{i}$ . + +For notational simplicity, we omit the subscript $i$ from now on, i.e., we represent a block as $y = l(x)$ and the compensation module is simply denoted as $c$ . After quantization, the input activations and weights of the block $l$ are modified into the quantized version $x^{\mathbb{Z}}$ and $l^{\mathbb{Z}}$ , respectively. The quantized computation becomes $y^{\mathbb{Z}} = l^{\mathbb{Z}}(x^{\mathbb{Z}})$ . + +Clearly, there is information loss in all 3 quantization pairs: $l \mapsto l^{\mathbb{Z}}$ , $x \mapsto x^{\mathbb{Z}}$ and $y \mapsto y^{\mathbb{Z}}$ . What is intriguing is that the information loss is obviously highly non-linear in all 3 pairs. To implement the compensation idea, we have to answer the following questions: + +1. How to measure the information losses in all 3 pairs that interplay with each other in a complex manner? +2. How to design the compensation module $c$ that accounts for these highly non-linear information losses? + +# 3.3. QwT: Quantization without Tears + +We propose a QwT (quantization without tears) method, which answers both questions in the simplest possible form. + +First, the information loss is measured by $\| y - y^{\mathbb{Z}}\| ^2$ . Because $y$ is the output of $l$ , it naturally takes care of information losses in $x^{\mathbb{Z}}$ and $l^{\mathbb{Z}}$ when $y^{\mathbb{Z}} = y$ , intuitively there is absolutely zero information loss even if $x\neq x^{\mathbb{Z}}$ and $l\neq l^{\mathbb{Z}}$ . Note that $\| y - y^{\mathbb{Z}}\|^{2}$ also accounts for cumulative information losses. That is, in the $i$ -th block, $c_{i}$ compensates information losses accumulated in all previous blocks that have not yet been corrected by $c_{1},c_{2},\ldots ,c_{i - 1}$ . + +Second, because of this cumulative nature of our choice, in QwT we choose to implement $c$ (with the index $i$ omitted) as a simple linear layer. Although it is impossible to accurately compensate the non-linear information loss in + +![](images/8a03c144eadd23deea77c72632f8303f6001806202afce6c88c3c3cd4f0b78ae.jpg) +Figure 1. Illustration of QwT in one block. QwT adds a simple linear layer to any model block, compensating for information loss using the block input $x^{\mathbb{Z}}$ . This approach is straightforward and compatible with almost all types of backbones [11, 17, 34]. + +one block via a linear layer, we have many chances to repeatedly apply linear corrections. The entire compensation formed by all extra modules is in fact non-linear because it interacts with the quantized network in every block. + +To be concrete, we define $c(x) = Wx + b$ and then + +$$ +y ^ {\mathrm {Q w T}} = l ^ {\mathbb {Z}} \left(x ^ {\mathbb {Z}}\right) + c \left(x ^ {\mathbb {Z}}\right), \tag {5} +$$ + +where $W \in \mathbb{R}^{d_{out} \times d_{in}}$ and $b \in \mathbb{R}^{d_{out}}$ are the weight matrix and bias vector of the linear layer $c$ , respectively. The QwT structure is illustrated in Figure 1. + +These choices are deliberate. They not only make QwT conceptually the simplest, but also ensures a closed-form solution. To minimize the difference between $y$ and $y^{\mathbb{Z}}$ , we select a small set of training examples (512 images) from the training set. Using these samples, QwT collects all inputs for the block $l^{\mathbb{Z}}$ to form a matrix $X^{\mathbb{Z}} \in \mathbb{R}^{d_{in} \times N}$ , where $N$ is the total number of features or tokens. We feed $X^{\mathbb{Z}}$ into the quantized block $l^{\mathbb{Z}}$ to obtain $Y^{\mathbb{Z}} \in \mathbb{R}^{d_{out} \times N}$ . Next, we feed $X^{\mathbb{Z}}$ into the non-quantized block $l$ to obtain $Y \in \mathbb{R}^{d_{out} \times N}$ . Correspondingly, $Y$ contains output of the matching block in the original model. + +Our task is then to estimate $Y - Y^{\mathbb{Z}}$ using $X^{\mathbb{Z}}$ . This is a classic linear regression problem, and has a closed-form solution: + +$$ +W ^ {*} = \left(Y - Y ^ {\mathbb {Z}}\right) X ^ {\mathbb {Z} ^ {\top}} \left(X ^ {\mathbb {Z}} X ^ {\mathbb {Z} ^ {\top}}\right) ^ {- 1}. \tag {6} +$$ + +In Equation 6, to simplify the solution, the bias $b$ is absorbed into $W$ and a row vector of $\mathbf{1}^{\top}$ are concatenated to $X^{\mathbb{Z}}$ . It is worth mentioning that theoretically QwT will not make the quantized network getting worse—by setting $W$ and $b$ to all zeros, QwT will not alter the quantized network. + +Note that after the QwT module for $l^{\mathbb{Z}}$ is inserted, the compensation in the next block depends on all the previous QwT modules. Consequently, the information loss from $y$ to $y^{\mathbb{Z}}$ is gradually compensated block by block, allowing $c$ to account for the accumulated loss from all preceding blocks that remain uncorrected. + +In our experiments, we observed that the coefficient of determination $(R^2)$ [43] for a small subset $(< 5\%)$ of QwT modules was notably low, adversely hurting recognition accuracy. Consequently, we apply the initialization using + +Equation 6 only when $R^2 > 0$ ; Otherwise, the $W$ and $b$ of the QwT module are set to zero. + +Finally, the QwT method has a simple pipeline: first quantize a model $M$ using any PTQ method, then add the compensation module $c_{i}$ to every block $i$ and set the parameters in $c_{i}$ using Equation 6. + +A notable advantage of QwT lies in its inherent simplicity. This simplicity ensures that the initialization process of QwT modules is highly efficient, which requires roughly 2 minutes in practice to compensate for the information loss during quantization, thereby enhancing recognition accuracy. Experimental results demonstrated that QwT exhibits significant versatility and efficiency across various vision and language tasks. + +# 4. Experiments + +In this section, we begin by evaluating our QwT method on a range of discriminative tasks, including image classification, object detection, instance segmentation, and multimodal recognition. Subsequently, we extend our analysis to generative tasks, such as image generation using diffusion models [40] and text generation with large language models [12]. + +# 4.1. Experiments on Image Classification + +Settings. We evaluated our method on image classification tasks using the ImageNet dataset [8], leveraging various backbone architectures including ViT [11], DeiT [48], Swin [34], and ResNet [17]. We randomly sampled 512 images from the training set to initialize the parameters of the QwT modules using Equation 6. In all networks, the affine transformation matrix $W$ in QwT is implemented in FP16 format to reduce model size. In ResNet, $W$ is further simplified as a group-wise convolution using a kernel size of 1 and 64 channels per group, achieving additional efficiency in storage and computation. Note that a group-wise convolution is still a linear operator, which can be perfectly encoded by the pair $(W, b)$ . Other details were consistent with prior work [27]. Please refer to the appendix for more information. + +Results on different backbones. Table 1 summarizes the quantization results when applying QwT across different backbone architectures. Specifically, we selected RepQViT [27] and Percentile [23] as the baseline methods for the Transformer family [11, 34, 48] and ResNet [17], respectively. The results show that incorporating the QwT module consistently boosts the recognition accuracy, leading to an average increase of approximately $2.6\%$ , and even up to $5\%$ for 4-bit quantization, highlighting that QwT is particularly effective for low-bit scenarios. Additionally, after the QwT modules are integrated, the accuracy in 6-bit quantization cases aligns closely with prior state-of-the-art approaches [37, 46]. + +Table 1. Quantization results on the ImageNet dataset [8]. #Bits' indicates the bit-width of weights/activations. 'Size' (MB) represents the storage cost of the model on the hard disk. * denotes QwT modules and classification head are finetuned for one epoch. † indicates that the previous state-of-the-art results are directly sourced from the papers [37, 46] due to the unavailability of their official code implementations. + +
NetworkMethod#BitsSizeTop-1
DeiT-TFull-precision32/3222.972.2
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]4/4-62.5
RepQ-ViT [27]4/43.358.2
RepQ-ViT + QwT4/44.261.4
RepQ-ViT + QwT*4/44.264.8
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]6/6-71.2
RepQ-ViT [27]6/64.671.0
RepQ-ViT + QwT6/65.571.2
RepQ-ViT + QwT*6/65.571.6
Swin-TFull-precision32/32113.281.4
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]4/4-77.8
RepQ-ViT [27]4/414.973.0
RepQ-ViT + QwT4/419.275.5
RepQ-ViT + QwT*4/419.279.3
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]6/6-80.9
RepQ-ViT [27]6/621.780.6
RepQ-ViT + QwT6/626.080.7
RepQ-ViT + QwT*6/626.080.9
ViT-BFull-precision32/32346.384.5
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]4/4-79.3
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
RepQ-ViT + QwT*4/459.178.5
\( \overline{\text{IGQ-ViT}}^{\dagger} \) [37]6/6-83.8
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
RepQ-ViT + QwT*6/680.484.0
ResNet-50Full-precision32/32102.276.6
\( \overline{\text{CL-Calib}}^{\dagger} \) [46]4/4-75.4
Percentile[23]4/414.068.4
Percentile + QwT4/416.074.5
Percentile + QwT*4/416.075.8
\( \overline{\text{CL-Calib}}^{\dagger} \) [46]6/6--
Percentile[23]6/619.976.0
Percentile + QwT6/621.976.8
Percentile + QwT*6/621.976.8
+ +The potential of our QwT method can be further unlocked through finetuning. By jointly optimizing the QwT modules and the classification head for only one (1) additional epoch (results marked with *), more gains in accuracy are achieved, enabling our method to surpass previous state-of-the-art results in nearly all cases. + +These results are even closer to those produced by QAT methods, which typically require extensive training (e.g., 200 epochs). In contrast, our $\mathrm{QwT^{*}}$ achieves similar per + +Table 2. Results of 8-bit quantization, using tensor-wise Percentile [23] as the baseline PTQ method. 'Latency' (ms) is measured on a single RTX 3090 GPU with a batch size of 64, utilizing Nvidia's TensorRT [39] toolkit for deployment. + +
NetworkMethodSizeLatencyTop-1
DeiT-TFull-precision22.911.672.2
Percentile [23]5.92.871.2
Percentile + QwT6.83.271.5
Swin-TFull-precision113.234.581.4
Percentile [23]28.69.580.8
Percentile + QwT32.910.981.0
Swin-SFull-precision198.461.083.2
Percentile [23]50.116.082.1
Percentile + QwT58.017.983.0
ViT-SFull-precision88.228.381.4
Percentile [23]22.55.879.2
Percentile + QwT26.06.680.1
ViT-BFull-precision346.385.384.5
Percentile [23]87.415.575.8
Percentile + QwT101.617.582.8
+ +formance with only one epoch of finetuning. Our approach not only substantially improves training efficiency but also keeps the backbone parameters unchanged, making it more suitable for hardware deployment. + +In Table 2, we additionally report the inference latency of different models directly deployed on a GPU. Compared to full-precision models, naive quantized models achieve an average reduction of $77\%$ in inference latency and $75\%$ in model size. When QwT modules are incorporated, these reductions slightly decrease to $74\%$ and $71\%$ , respectively, with an overhead of only $3\%$ . This minimal additional cost is offset by an average 1.9 percentage points improvement in recognition accuracy, demonstrating the strong practicality of the QwT method. + +Results across various PTQ methods. We extended our experiments to evaluate the versatility of QwT by applying it to various PTQ methods. As shown in Table 3, we integrated QwT into PTQ4ViT [52], RepQ-ViT [27], and Percentile [23], using ViT-B as the backbone. + +We observe that QwT consistently enhances top-1 accuracy across all baseline PTQ methods. Notably, in 4-bit scenarios, PTQ4ViT demonstrates an improvement of approximately $40\%$ , while RepQ-ViT shows an $8\%$ increase. Compared to modern PTQ methods [27, 37, 52], which often involve complex and tedious procedures, our method demonstrates high simplicity and, most importantly, is compatible with all these approaches, too. The significant improvement in accuracy narrows the performance gap between different PTQ methods, and offers new insights into the design of new paradigms for network quantization. + +Extension to QAT methods. We further investigated the potential of adapting QwT to QAT methods. Specifically, + +Table 3. Quantization results among different PTQ methods on the ImageNet dataset [8] using ViT-B [11] as the backbone. + +
Method#BitsSizeTop-1
Full-precision32/32346.384.5
PTQ4ViT [52]4/444.930.7
PTQ4ViT+QwT4/459.170.0
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
Percentile [23]6/666.256.7
Percentile+QwT6/680.479.8
PTQ4ViT [52]6/666.281.7
PTQ4ViT+QwT6/680.483.2
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
Percentile [23]8/887.475.8
Percentile+QwT8/8101.682.8
+ +Table 4. Quantization results of applying QwT finetuning schema on QAT methods. + +
NetworkMethod#BitsTop-1
DeiT-SQ-ViT [25]2/272.1
Q-ViT + QwT*2/272.5
Q-ViT [25]3/379.0
Q-ViT + QwT*3/379.1
+ +we applied QwT modules to QAT models after completing QAT training to assess whether QwT can further enhance recognition accuracy. + +We preliminarily found that for QAT models, the initialization process described by Equation 6 is no longer effective. Applying it directly to QAT models significantly degrades accuracy. We attribute this to the fact that, unlike full-precision models, the optimization state of a QAT-trained model is sufficiently converged, resulting in almost no information loss from $y$ to $y^{\mathbb{Z}}$ . In fact, $y^{\mathbb{Z}}$ may even outperform $y$ , as QAT models sometimes surpass their full-precision counterparts in evaluation accuracy. + +To integrate QwT into QAT methods, we therefore initialize $W$ and $b$ to zero as a compromise. We then explore whether fine-tuning QwT can still improve recognition accuracy. For this study, we use Q-ViT [25], a representative QAT method for ViT backbones, as the baseline. The results in Table 4 demonstrate that, even without using the initialization from Equation 6, fine-tuning the QwT modules consistently enhances QAT models, confirming the generalizability of our approach. + +# 4.2. Experiments on Object Detection & Instance Segmentation + +Settings. We evaluated our method on object detection and instance segmentation tasks using the COCO 2017 [30] dataset. ResNet50 [17] with DETR [4], Swin-S [34] with + +Mask R-CNN [18], and Swin-S/B [34] with Cascade Mask R-CNN [3] were used as detectors. The evaluation metric was Average Precision (AP). Similar to image classification, we randomly selected 512 images from the training set to initialize the QwT weights and biases. For ResNet, the QwT was implemented using group-wise convolution with a kernel size of 1 and 64 channels per group to balance model size and AP. For DETR, we used MinMax as the PTQ baseline, a classic method that quantizes the model based on the range between the minimum and maximum values of weights or activations. For the other detectors, RepQViT [27] was chosen as the baseline PTQ method. + +Main results. Table 5 presents the results of applying QwT to object detection and instance segmentation tasks. We observe that QwT consistently enhances both $\mathrm{AP^{box}}$ and $\mathrm{AP^{mask}}$ across all cases without finetuning, achieving an average improvement of $0.4\%$ with individual gains ranging from $0.1\%$ to $0.7\%$ . The consistent improvement underscores the robustness of our method for both object detection and instance segmentation tasks. Notably, in certain 6-bit scenarios, such as on Cascade Mask R-CNN, QwT even achieves AP comparable to full-precision models. + +Additionally, a clear trend emerges where the AP gains introduced by QwT increases along with model size. For instance, in $\mathrm{AP^{box}}$ , the average improvement achieved by QwT rises from $0.3\%$ in ResNet-50+DETR to $0.5\%$ in Swin-B+Cascade Mask R-CNN, indicating the method's enhanced effectiveness in larger models. + +Compared to full-precision models, baseline PTQ methods yield an average storage reduction of approximately $80\%$ . The introduction of QwT modules slightly reduces this savings to around $78\%$ $(-2\%)$ , which demonstrates that QwT enhances AP metrics with negligible overhead. + +# 4.3. Experiments on Multimodal Recognition + +Settings. We conducted experiments using OpenAI's CLIP model [41]. Known for its exceptional zero-shot performance on the ImageNet [8] classification task, CLIP serves as an ideal benchmark for assessing the effectiveness on multimodal recognition tasks. We selected the variant of CLIP that includes a ViT-B/32 [11] as the visual encoder and a 12-block Transformer [49] as the text encoder. Since, to the best of our knowledge, no publicly available PTQ implementation exists for CLIP, we developed a baseline using RepQ-ViT [27]. We randomly selected 512 image-text pairs from the training data, both for PTQ model calibration and QwT initialization. Thanks to the simplicity and efficiency of our method, it achieved significant improvements under 30 seconds, as detailed in Table 6. + +Main results. We conducted experiments with two quantization strategies: quantizing 1) only the visual encoder and 2) both visual and text encoders. As shown in Table 6, baseline PTQ methods showed significant drop in top- + +Table 5. Quantization results on the COCO dataset [8]. We use box average precision $(\mathrm{AP}^{\mathrm{box}})$ and mask average precision $(\mathrm{AP}^{\mathrm{mask}})$ to assess object detection and instance segmentation accuracy, respectively. + +
NetworkMethod#BitsSizeAPboxAPmask
ResNet-50 + DETRFull-precision32/32164.542.0-
MinMax6/647.439.5-
MinMax + QwT6/649.440.0-
MinMax8/856.441.6-
MinMax + QwT8/858.441.7-
Swin-S + Mask R-CNNFull-precision32/32276.548.543.3
RepQ-ViT [27]4/436.142.640.0
RepQ-ViT + QwT4/444.043.140.4
RepQ-ViT [27]6/653.347.642.9
RepQ-ViT + QwT6/661.248.043.1
Swin-S + Cascade Mask R-CNNFull-precision32/32427.851.945.0
RepQ-ViT [27]4/456.949.343.1
RepQ-ViT + QwT4/464.849.943.4
RepQ-ViT [27]6/683.451.444.6
RepQ-ViT + QwT6/691.351.744.8
Swin-B + Cascade Mask R-CNNFull-precision32/32579.951.945.0
RepQ-ViT [27]4/476.149.343.1
RepQ-ViT + QwT4/490.150.043.7
RepQ-ViT [27]6/6112.151.544.8
RepQ-ViT + QwT6/6126.151.845.0
+ +1 accuracy compared to their full-precision counterparts, struggling to effectively represent a low-bit CLIP model. The reduction in performance is especially obvious when both the visual and text encoders are quantized. + +In contrast, our QwT method enhanced top-1 accuracy across all cases, significantly bridging the accuracy gap between low-bit and full-precision models. Specifically, in vision-only quantization, QwT increased top-1 accuracy by an average of $0.6\%$ , with only a modest $4\%$ increase in model size compared to baseline PTQ methods. + +When both the visual and text encoders are quantized, baseline PTQ methods exhibited an average accuracy drop of $29.2\%$ . In contrast, QwT provided a significant accuracy improvement, with an average increase of $14.8\%$ . These findings highlight QwT's effectiveness in preserving high accuracy while substantially reducing model size for multimodal recognition tasks. + +# 4.4. Experiments on Image Generation + +QwT has also demonstrated efficacy in generative models, notably enhancing the performance of quantized diffusion models. Unlike classifiers or detectors, which require a single forward pass, diffusion models involve multiple forward passes to generate the final images, presenting a unique prototype. Under these circumstances, QwT has proven itself highly effective, underscoring its general applicability and robustness. + +Table 6. Quantization results of CLIP for zero-shot classification tasks on ImageNet. The 'Quant Setup' column differentiates between two strategies: quantizing only the vision encoder and quantizing both the vision and text encoders concurrently. + +
Quant SetupMethod#BitsSize (MB)Top-1
VisionFull-precision32/32607.263.4
RepQ-ViT [27]6/6323.559.2
RepQ-ViT + QwT6/6336.860.3
RepQ-ViT [27]8/8345.362.9
RepQ-ViT + QwT8/8359.563.0
Vision & TextFull-precision32/32607.263.4
RepQ-ViT [27]6/6200.829.8
RepQ-ViT + QwT6/6221.343.5
RepQ-ViT [27]8/8232.138.7
RepQ-ViT + QwT8/8252.654.6
+ +Settings. For our experiments, we selected the influential DiT [40] (Diffusion Transformer) architecture, following the experimental setup of Q-DiT [5]. Specifically, we employed pretrained DiT-XL/2 models at a resolution of $256 \times 256$ . For rapid and precise sampling, we utilized the DDIM sampler with 50 sampling steps and applied classifier-free guidance (cfg) of 1.5, abbreviated as DiT-XL/2 (steps = 50, CFG = 1.5). Our experiments included two quantization configurations: W8A8 and W4A8. Additional results involving various model sizes, steps, and CFG values are available in the appendix. + +We applied QwT directly to the quantized diffusion model using Q-DiT. A key consideration is that the model performs $T$ forward passes per inference, with notable variation in the activation distribution and range across steps. A key assumption is that quantization error is primarily dependent on the input $x$ , with minimal influence from elements like the time step or class condition. Accordingly, we set $t = 0$ to initialize the compensation module. The results are presented in Table 7. + +Main results. Our method was compared with three representative quantization techniques: RepQ-ViT, GPTQ and Q-DiT designed for diffusion models. For both W8A8 and W4A8 settings, QwT significantly enhanced the performance of the quantized models, yielding improvements of 0.10 and 0.69 in FID, which illustrates the efficacy of QwT with minimal increase in model size. + +We visualize the images generated by our model alongside those from compared models in Figure 2. The three rows represent the original images, quantized images with Q-DiT, and quantized images with QwT, respectively. All models are based on DiT-XL/2 (steps $= 50$ , $\mathrm{cfg} = 1.5$ ). To enable a fair comparison, we ensure that the initial Gaussian noise and the noise added during inference are identical across all methods. The images produced by our method show a closer visual resemblance to the original model, + +![](images/45c730c8370f8d3c5774d66020f043555f34dcd073648450c890ad38aa9b309c.jpg) +Figure 2. Qualitative visualization results of quantizing DiT-XL/2. + +Table 7. Quantitative results of quantizing DiT-XL/2. $\downarrow$ (↑) means smaller (larger) is better. + +
Method#BitsSize (MB)FID (↓)IS (↑)
Full-precision16/1613495.32236.17
RepQ-ViT8/86775.46234.74
GPTQ8/86905.90218.90
Q-DiT8/86835.45236.52
Q-DiT + QwT8/87075.35236.91
RepQ-ViT4/8339319.682.20
GPTQ4/83519.94166.35
Q-DiT4/83476.75208.38
Q-DiT + QwT4/83616.06215.70
+ +which aligns with the quantitative results. + +# 4.5. Experiments on Large Language Models + +Settings. We evaluated our framework on the LLaMA3-8B [12] model. For PTQ methods, we adopted GPTQ [14] with INT4 weight quantization. Our approach is also compatible with other PTQ methods such as AWQ [29] and SPQR [9]. We conducted a group-wise asymmetric quantization with a group size of 128 and apply activation reordering. In particular, GPTQ take 128 samples from the C4 dataset as calibration sets, and each sample is 2048 tokens long. We use the same calibration set when performing QwT after GPTQ algorithm. + +Evaluation metrics. Following the settings of GPTQ, we evaluated the perplexity on the WikiText2 [47] and C4 [42] datasets. We further assessed the zero-shot commonsense question answering (QA) ability on eight tasks covering SIQA [45], HellaSwag [53], PIQA [2], Wino-Grande [44], ARC [7], BoolQ [6], and OpenBookQA [36]. We also evaluated both the zero-shot and five-shot performance of the LLMs on Massively Multitask Language Un + +Table 8. Quantization results among WikiText2, C4 and eight zero-shot commonsense QA datasets using LLaMA3-8B as the backbone. $\downarrow (\uparrow)$ means smaller (larger) is better. + +
Method#BitsSize (GB)W2 (↓)C4 (↓)QA. Avg (↑)
Full-precision1616.066.248.9666.10
GPTQ45.736.659.4464.90
GPTQ + QwT46.806.639.3865.18
+ +derstanding (MMLU) benchmark [20]. It consists of 57 language tasks including humanities, STEM, social science, etc. We adopted lm-eval-harness [15] to produce the accuracy results. + +Results. Table 8 summarizes the perplexity in WikiText2, C4 and the average accuracy in eight common sense reasoning datasets. More results are shown in the appendix. Note that we abbreviate WikiText2 to W2. As the results show, our optimized models will not overfit the calibration dataset and consistently outperform the original PTQ models. These results reveal the effectiveness of our QwT. + +# 5. Conclusions + +In this paper, we proposed Quantization without Tears (QwT), a novel approach that incorporates a lightweight structure into quantized models to compensate for the information loss during network quantization. The QwT modules, implemented as a tiny set of linear layers and seamlessly integrated into backbone blocks, achieved accuracy, simplicity, and generality simultaneously. Notably, QwT provides a closed-form solution to complete the compensation process in under 2 minutes and enables effortless integration with existing quantization techniques. Extensive experiments demonstrated QwT's exceptional effectiveness and versatility across a wide range of tasks, models, and quantization methods, advancing a streamlined and flexible paradigm for network quantization. + +# Acknowledgments + +This research was partly supported by the National Natural Science Foundation of China under Grant 62276123. + +J.W. designed the compensation insight and the QwT framework mathematically. M.F. made them into algorithms and codes that work well in practice, and carried out the main empirical validations. H.Y., J.S. and J.Z. carried out experiments and validations on LLM, AIGC and multimodal tasks, respectively. K.Z. engaged in discussions. All authors contributed to paper writing. + +# References + +[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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In AAAI Conference on Artificial Intelligence, pages 11452-11460, 2023. 1 \ No newline at end of file diff --git a/2025/Quantization without Tears/images.zip b/2025/Quantization without Tears/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..37a9839dcf1ff8a5bfdcf80b066f0c15c8e7c691 --- /dev/null +++ b/2025/Quantization without Tears/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e2acaa3c06f9eef6ee2ea9f4eaaf6aa3b5eebcf5399183e889a8d623c3a2df3e +size 557388 diff --git a/2025/Quantization without Tears/layout.json b/2025/Quantization without Tears/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d6607c0a83c9a0f48244229408e26729b676e5 --- /dev/null +++ b/2025/Quantization without Tears/layout.json @@ -0,0 +1,10547 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 219, + 103, + 391, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 219, + 103, + 391, + 120 + ], + "spans": [ + { + "bbox": [ + 219, + 103, + 391, + 120 + ], + "type": "text", + "content": "Quantization without Tears" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 143, + 509, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 143, + 509, + 185 + ], + "spans": [ + { + "bbox": [ + 100, + 143, + 509, + 185 + ], + "type": "text", + "content": "Minghao Fu Hao Yu Jie Shao Junjie Zhou Ke Zhu Jianxin Wu* National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 187, + 490, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 187, + 490, + 200 + ], + "spans": [ + { + "bbox": [ + 116, + 187, + 490, + 200 + ], + "type": "text", + "content": "{fumh, yuh, shaoj, zhoujj, zhuk}@lamda.nju.edu.cn, wujx2001@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "spans": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 252, + 297, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 252, + 297, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 252, + 297, + 577 + ], + "type": "text", + "content": "Deep neural networks, while achieving remarkable success across diverse tasks, demand significant resources, including computation, GPU memory, bandwidth, storage, and energy. Network quantization, as a standard compression and acceleration technique, reduces storage costs and enables potential inference acceleration by discretizing network weights and activations into a finite set of integer values. However, current quantization methods are often complex and sensitive, requiring extensive task-specific hyperparameters, where even a single misconfiguration can impair model performance, limiting generality across different models and tasks. In this paper, we propose Quantization without Tears (QwT), a method that simultaneously achieves quantization speed, accuracy, simplicity, and generality. The key insight of QwT is to incorporate a lightweight additional structure into the quantized network to mitigate information loss during quantization. This structure consists solely of a small set of linear layers, keeping the method simple and efficient. More importantly, it provides a closed-form solution, allowing us to improve accuracy effortlessly under 2 minutes. Extensive experiments across various vision, language, and multimodal tasks demonstrate that QwT is both highly effective and versatile. In fact, our approach offers a robust solution for network quantization that combines simplicity, accuracy, and adaptability, which provides new insights for the design of novel quantization paradigms." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 600, + 135, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 600, + 135, + 612 + ], + "spans": [ + { + "bbox": [ + 56, + 600, + 135, + 612 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 620, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 620, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 620, + 296, + 693 + ], + "type": "text", + "content": "Along with their extraordinary breakthroughs in various vision [18], language [10] and multimodal [41] tasks, deep neural networks [11, 17] also exhibit ferocious greed for various resources: compute, GPU memory, bandwidth, storage, energy, etc. Hence, compressing and accelerating deep nets have not only attracted interests in academia, but" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "type": "text", + "content": "are also an urgent need in real-world deployments and applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "text", + "content": "Among various research efforts in this direction, network quantization [28] is arguably the most practical one. Different from unstructured pruning [16], it is well supported by existing hardware. Compared to structured pruning [19, 22], its compression ratio is higher and its loss is relatively smaller. For example, the INT8 quantization of both FP32 weights and activations leads to roughly " + }, + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "text", + "content": " reduction in network size and " + }, + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 313, + 253, + 555, + 421 + ], + "type": "text", + "content": " speedup with almost zero accuracy loss in many applications [26], which far exceeds structured pruning. Existing methods are often categorized as Post-Training Quantization (PTQ) [27, 31, 32, 37, 46, 52] or Quantization-Aware Training (QAT) [13, 21, 25, 33, 54], where the difference is whether training is required ('no' for PTQ and 'yes' for QAT)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 422, + 554, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 554, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 554, + 457 + ], + "type": "text", + "content": "Quantization, however, is not as perfect as it seems to be. There are also obvious drawbacks and pitfalls in existing quantization methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 459, + 554, + 601 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 314, + 459, + 554, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 459, + 554, + 506 + ], + "spans": [ + { + "bbox": [ + 314, + 459, + 554, + 506 + ], + "type": "text", + "content": "- The speed-accuracy dilemma: PTQ can be thousands of times faster than QAT during the quantization process, but QAT may well be 10 percentage points higher than PTQ in accuracy during inference." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 506, + 554, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 506, + 554, + 554 + ], + "spans": [ + { + "bbox": [ + 314, + 506, + 554, + 554 + ], + "type": "text", + "content": "- Complexity: Quantization methods are often delicate and tricky. They often have tons of hyperparameters to tune for each specific task, and even one improperly set hyperparameter value may ruin the quantized model." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 554, + 554, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 554, + 554, + 601 + ], + "spans": [ + { + "bbox": [ + 314, + 554, + 554, + 601 + ], + "type": "text", + "content": "- Missing generality: Relevant to their complexities, an existing method is often geared toward a specific model and/or task. Different models/tasks require different quantization methods." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 604, + 554, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 554, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 554, + 639 + ], + "type": "text", + "content": "Given the status quo, at this moment it does not seem unreasonable to treat the act of network quantization as an art rather than an established engineering tool." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 641, + 553, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 553, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 553, + 688 + ], + "type": "text", + "content": "In this paper, we propose a Quantization without Tears (QwT) method to address these drawbacks, which achieves quantization speed, accuracy, simplicity and generality simultaneously." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "content": "The key to achieve these goals simultaneously is to slightly change the quantization paradigm. Suppose a net" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 182, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 182, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 182, + 713 + ], + "type": "inline_equation", + "content": "^{*}" + }, + { + "bbox": [ + 66, + 702, + 182, + 713 + ], + "type": "text", + "content": "J. Wu is the corresponding author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4462" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "work " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " has the network structure " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " and parameters " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": ". Current quantization methods will quantize it into a model " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "M^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " with the same structure " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "S(S^{\\mathbb{Z}} = S)" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " and quantized parameters " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\theta^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " in the integer format." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "content": "Our key argument is that the quantized structure does not need to be strictly " + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "content": ". In our QwT, it becomes " + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "inline_equation", + "content": "S \\cup S_{c}" + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "content": ", where some extra modules " + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "content": " are added to the network structure to compensate for the information loss due to quantized parameters and activations. The extra " + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 121, + 294, + 193 + ], + "type": "text", + "content": " thus help us achieve high accuracy." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "text", + "content": " does lead to extra overheads. But, it is also obvious that so long as the size and computation of " + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "text", + "content": " is small or even negligible when compared to " + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "inline_equation", + "content": "S^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "text", + "content": ", we achieve both speed and accuracy. In our QwT, " + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 194, + 294, + 266 + ], + "type": "text", + "content": " has very simple structures: only few linear layers, which renders it both simple and general." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 266, + 294, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 294, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 294, + 314 + ], + "type": "text", + "content": "To be more specific, the parameters in " + }, + { + "bbox": [ + 55, + 266, + 294, + 314 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 55, + 266, + 294, + 314 + ], + "type": "text", + "content": " can be set in closed-form with a small calibration set, which in almost all cases leads to significantly higher accuracy than PTQ methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 316, + 253, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 316, + 253, + 327 + ], + "spans": [ + { + "bbox": [ + 67, + 316, + 253, + 327 + ], + "type": "text", + "content": "To sum up, the contributions of this paper are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 329, + 294, + 424 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "spans": [ + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "text", + "content": "- Proposing a new paradigm for network quantization by lifting the restriction that the quantized network structure " + }, + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "inline_equation", + "content": "S^{\\mathbb{Z}}" + }, + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "text", + "content": " has to be exactly the same as that of the original network structure " + }, + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 56, + 329, + 294, + 376 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 376, + 294, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 376, + 294, + 424 + ], + "spans": [ + { + "bbox": [ + 56, + 376, + 294, + 424 + ], + "type": "text", + "content": "- Proposing QwT, a simple and general quantization method without tears in this new paradigm. QwT achieves speed, accuracy, simplicity and generality simultaneously." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 426, + 294, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 294, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 294, + 449 + ], + "type": "text", + "content": "Extensive experiments have been carried out, which show that QwT has the following properties:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 451, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 56, + 451, + 295, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 451, + 295, + 569 + ], + "spans": [ + { + "bbox": [ + 56, + 451, + 295, + 569 + ], + "type": "text", + "content": "- Fast and accurate. For example, QwT quantizes a ViT network in roughly 2 minutes. During inference, its throughput is almost the same as models quantized by existing quantization methods. QwT is significantly more accurate than existing PTQ methods even without any back-propagation. On top of that, if higher accuracy is requested, QwT requires only 1 epoch of training to approach the accuracy of QAT methods. In contrast, QAT often requires a large number of epochs (e.g., 200 epochs)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 570, + 295, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 570, + 295, + 594 + ], + "spans": [ + { + "bbox": [ + 56, + 570, + 295, + 594 + ], + "type": "text", + "content": "- Simple. There is zero (0) hyperparameters to tune, and the parameters in " + }, + { + "bbox": [ + 56, + 570, + 295, + 594 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 56, + 570, + 295, + 594 + ], + "type": "text", + "content": " can be found in closed-form." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 594, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 594, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 56, + 594, + 295, + 677 + ], + "type": "text", + "content": "- General. Exactly the same QwT method has been successfully applied to various networks and applications, including both CNNs [17] and Transformers (ViT [11] and Swin [34]), object recognition, detection (with both Mask R-CNN [18] and DETR [4]) and segmentation, multimodal models (CLIP [41]), generative models (DiT [40]), and large language models (LLaMA [12])." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 56, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 677, + 295, + 713 + ], + "type": "text", + "content": "- Practical. In addition to quantizing to low-bits in simulators, the same QwT method can quantize a model that is able to run directly on GPUs with minimum ef" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "content": "forts (i.e., quantization 'without tears'): Simply obtain " + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "\\theta^{\\mathbb{Z}}" + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "content": " using TensorRT, then add " + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "content": " using QwT. The resulting quantized model is then ready to be deployed on GPUs that support quantized fix-point inference." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 131, + 400, + 143 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 131, + 400, + 143 + ], + "spans": [ + { + "bbox": [ + 314, + 131, + 400, + 143 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 151, + 553, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 151, + 553, + 246 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 553, + 246 + ], + "type": "text", + "content": "Network quantization [28] aims to reduce the bit-width of weights and activations, enabling the quantized model to be stored more efficiently and to perform faster inference with suitable hardware support. The fundamental principle of network quantization involves approximating full-precision weights and activations by mapping them to a finite set of discrete values, which are subsequently used in forward model computations (i.e., in inference)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 247, + 553, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 247, + 553, + 317 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 553, + 317 + ], + "type": "text", + "content": "One line of research focuses on quantization-aware training (QAT) [13, 21, 25, 33], which integrates quantization into the training process using back-propagation, where the straight-through estimator [1] is commonly employed to approximate gradients for non-differentiable rounding functions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 319, + 553, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 553, + 437 + ], + "type": "text", + "content": "Another line of research concentrates on post-training quantization (PTQ) [14, 27, 31, 52], which converts a fully trained full-precision model into low-bit format using a small set of calibration samples. AdaRound [38] proposed an adaptive weight-rounding mechanism. BRECQ [24] leveraged block reconstruction for quantization, utilizing the Fisher Information Matrix to guide the process. QDrop [50] randomly dropped the quantization of activations during quantization to achieve flatness of the low-bit model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 438, + 553, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 553, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 553, + 510 + ], + "type": "text", + "content": "While these methods [24, 38, 50] have proven effective on ResNet [17] backbones, applying them directly to ViT [11] often degrades recognition accuracy since the intrinsic structure of the softmax attention is incompatible with these methods. This poses new challenges to design general PTQ methods for the Transformer architecture." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 510, + 554, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 664 + ], + "type": "text", + "content": "To address this issue, [35] introduced a ranking loss designed to preserve the relative order between quantized and non-quantized attention scores. PTQ4ViT [52] proposed twin uniform quantization for shifted activations and a Hessian-guided metric to generate scaling factors. RepQViT [27] decoupled quantization and inference, employing distinct quantizers to enable precise quantization while simultaneously ensuring efficient inference. IGQ-ViT [37] introduced instance-aware group quantization for ViT to dynamically allocate channels of activation maps to different quantization groups. GPTQ [14] introduced a one-shot weight quantization technique that exploits approximate second-order information." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Different from all of these methods, we propose a new quantization paradigm that introduces a lightweight module to compensate for the information loss caused by quantization. This new paradigm allows our method to be" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4463" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "seamlessly integrated with any state-of-the-art quantization methods as a plugin in a completely black-box fashion. Experiments demonstrate that our method is highly compatible with various PTQ approaches, enabling effortless improvements in recognition accuracy within just 2 minutes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 143, + 111, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 143, + 111, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 143, + 111, + 156 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 163, + 141, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 141, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 141, + 175 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "spans": [ + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": "We start by outlining key concepts and notations related to network quantization. Given a quantization bit-width " + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": ", the quantization function " + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "inline_equation", + "content": "Q(\\cdot | b): \\mathbb{R} \\to \\mathbb{Z}" + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": " maps a floating-point number " + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": " (e.g., weight or activation) into its corresponding fixed-point representation " + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": " encoded by " + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 180, + 296, + 288 + ], + "type": "text", + "content": " bits. Among various quantization approaches, uniform quantization is particularly favored thanks to its simplicity and compatibility with hardware deployment. The uniform quantization procedure is formalized as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 297, + 295, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 297, + 295, + 318 + ], + "spans": [ + { + "bbox": [ + 107, + 297, + 295, + 318 + ], + "type": "interline_equation", + "content": "x ^ {\\mathbb {Z}} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}", + "image_path": "7023ecf0c3cc00032ab75c58d8b4592a88510c7acf8264b24b16d0b8e9543a97.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}^+" + }, + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "text", + "content": " represents the quantization scale, and " + }, + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{Z}" + }, + { + "bbox": [ + 55, + 327, + 296, + 361 + ], + "type": "text", + "content": " denotes the zero-point offset. These parameters are determined as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 101, + 369, + 295, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 369, + 295, + 393 + ], + "spans": [ + { + "bbox": [ + 101, + 369, + 295, + 393 + ], + "type": "interline_equation", + "content": "s = \\frac {\\operatorname* {m a x} (x) - \\operatorname* {m i n} (x)}{2 ^ {b} - 1}, \\tag {2}", + "image_path": "c9e8f3918e01240395ffd320d7340a200a751b1f418c5aa4d0c5447732f77079.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 101, + 396, + 295, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 396, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 101, + 396, + 295, + 422 + ], + "type": "interline_equation", + "content": "z = \\operatorname {c l i p} \\left(\\lfloor - \\frac {\\min (x)}{s} \\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {3}", + "image_path": "1f51778259a821195cfde0ab142f40d489dd427b900291e3bf770f577d04ca9c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "text", + "content": "In these equations, " + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "inline_equation", + "content": "\\lfloor .\\rfloor" + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "text", + "content": " denotes the rounding function, and the " + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname{clip}(\\cdot ,a,b)" + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "text", + "content": " operation constrains the input value into the range " + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "inline_equation", + "content": "[a,b]" + }, + { + "bbox": [ + 55, + 430, + 296, + 477 + ], + "type": "text", + "content": ". The reconstructed quantized output can then be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 135, + 477, + 294, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 477, + 294, + 491 + ], + "spans": [ + { + "bbox": [ + 135, + 477, + 294, + 491 + ], + "type": "interline_equation", + "content": "\\hat {x} = s \\times \\left(x ^ {\\mathbb {Z}} - z\\right). \\tag {4}", + "image_path": "29001e0d3afd48eba702ea37022618328627e474a4b7d4da06ac144d594cdaf9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 497, + 296, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 497, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 497, + 296, + 556 + ], + "type": "text", + "content": "Beyond the naive uniform quantizer, a range of more sophisticated quantization techniques [27, 38, 51, 52] have been proposed and extensively studied by the community. In the literature, quantization methods typically quantize both the model weights and activations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 557, + 296, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 296, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 296, + 640 + ], + "type": "text", + "content": "Quantization significantly reduces the storage requirements by enabling models to be stored in lower bit formats. Additionally, thanks to hardware support for integer-only computations, operations involving the quantized representations " + }, + { + "bbox": [ + 55, + 557, + 296, + 640 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 557, + 296, + 640 + ], + "type": "text", + "content": ", such as matrix multiplications between quantized weights and activations, can be performed with substantial improvements in computational efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 647, + 230, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 230, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 230, + 661 + ], + "type": "text", + "content": "3.2. Compensation: The Key Insight" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "But, obviously there is significant information loss between " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": ", and it grows very fast when many layers of computation and quantization are stacked together. To recover from the resulting accuracy loss, QAT methods resort to" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "many epochs of training, which leads to the speed-accuracy dilemma and complex, ad hoc quantization methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "spans": [ + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": "Given a model " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "M = (S, \\theta)" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": " denote its structure and weights, respectively, existing quantization techniques transform " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": " into a quantized version " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "M^{\\mathbb{Z}} = (S^{\\mathbb{Z}}, \\theta^{\\mathbb{Z}})" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": ", which maintains the same network structure (i.e., " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "S = S^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": ") while modifying the original parameters " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": " to their quantized counterparts " + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "inline_equation", + "content": "\\theta^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 97, + 554, + 168 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "content": "Our key insight is to challenge this structural rigidity: the quantized model does not necessarily need to retain the exactly same structural configuration, i.e., it is legitimate to allow " + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "inline_equation", + "content": "S^{\\mathbb{Z}} \\neq S" + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "content": ". We argue that some extra modules " + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "content": " can be added to the quantized model, such that its structure " + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "inline_equation", + "content": "S^{\\mathbb{Z}} = S \\cup S_{c}" + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "content": ". The extra modules in " + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 313, + 169, + 554, + 253 + ], + "type": "text", + "content": " can compensate for the information loss caused by quantization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": "More specifically, modern deep nets typically compose of many blocks, e.g., bottleneck blocks in ResNet [17] or Transformer blocks in ViT [11]. Let " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": "-th block in a model, and let " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "x_{i} \\in \\mathbb{R}^{d_{in}}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "y_{i} \\in \\mathbb{R}^{d_{out}}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": " be the input and output of this block " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": ", respectively, such that " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "y_{i} = l_{i}(x_{i})" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": ". We argue that we can add a compensation module " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": " for this block. Then, " + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "inline_equation", + "content": "S_{c} = \\bigcup_{i} c_{i}" + }, + { + "bbox": [ + 313, + 253, + 554, + 338 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": "For notational simplicity, we omit the subscript " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": " from now on, i.e., we represent a block as " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "y = l(x)" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": " and the compensation module is simply denoted as " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": ". After quantization, the input activations and weights of the block " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": " are modified into the quantized version " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": ", respectively. The quantized computation becomes " + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}} = l^{\\mathbb{Z}}(x^{\\mathbb{Z}})" + }, + { + "bbox": [ + 313, + 338, + 553, + 409 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "text", + "content": "Clearly, there is information loss in all 3 quantization pairs: " + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "inline_equation", + "content": "l \\mapsto l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "inline_equation", + "content": "x \\mapsto x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "inline_equation", + "content": "y \\mapsto y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 410, + 554, + 470 + ], + "type": "text", + "content": ". What is intriguing is that the information loss is obviously highly non-linear in all 3 pairs. To implement the compensation idea, we have to answer the following questions:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 470, + 554, + 518 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 314, + 470, + 554, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 470, + 554, + 495 + ], + "spans": [ + { + "bbox": [ + 314, + 470, + 554, + 495 + ], + "type": "text", + "content": "1. How to measure the information losses in all 3 pairs that interplay with each other in a complex manner?" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 495, + 553, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 553, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 553, + 518 + ], + "type": "text", + "content": "2. How to design the compensation module " + }, + { + "bbox": [ + 313, + 495, + 553, + 518 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 495, + 553, + 518 + ], + "type": "text", + "content": " that accounts for these highly non-linear information losses?" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 527, + 495, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 527, + 495, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 527, + 495, + 540 + ], + "type": "text", + "content": "3.3. QwT: Quantization without Tears" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 544, + 553, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 553, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 553, + 569 + ], + "type": "text", + "content": "We propose a QwT (quantization without tears) method, which answers both questions in the simplest possible form." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": "First, the information loss is measured by " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\| y - y^{\\mathbb{Z}}\\| ^2" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": ". Because " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " is the output of " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": ", it naturally takes care of information losses in " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}} = y" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": ", intuitively there is absolutely zero information loss even if " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "x\\neq x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "l\\neq l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\| y - y^{\\mathbb{Z}}\\|^{2}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " also accounts for cumulative information losses. That is, in the " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": "-th block, " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " compensates information losses accumulated in all previous blocks that have not yet been corrected by " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "c_{1},c_{2},\\ldots ,c_{i - 1}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "Second, because of this cumulative nature of our choice, in QwT we choose to implement " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " (with the index " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " omitted) as a simple linear layer. Although it is impossible to accurately compensate the non-linear information loss in" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4464" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 72, + 282, + 137 + ], + "blocks": [ + { + "bbox": [ + 71, + 72, + 282, + 137 + ], + "lines": [ + { + "bbox": [ + 71, + 72, + 282, + 137 + ], + "spans": [ + { + "bbox": [ + 71, + 72, + 282, + 137 + ], + "type": "image", + "image_path": "8a03c144eadd23deea77c72632f8303f6001806202afce6c88c3c3cd4f0b78ae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 148, + 295, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 148, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 295, + 194 + ], + "type": "text", + "content": "Figure 1. Illustration of QwT in one block. QwT adds a simple linear layer to any model block, compensating for information loss using the block input " + }, + { + "bbox": [ + 55, + 148, + 295, + 194 + ], + "type": "inline_equation", + "content": "x^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 148, + 295, + 194 + ], + "type": "text", + "content": ". This approach is straightforward and compatible with almost all types of backbones [11, 17, 34]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 213, + 296, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 296, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 296, + 260 + ], + "type": "text", + "content": "one block via a linear layer, we have many chances to repeatedly apply linear corrections. The entire compensation formed by all extra modules is in fact non-linear because it interacts with the quantized network in every block." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 261, + 277, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 261, + 277, + 272 + ], + "spans": [ + { + "bbox": [ + 67, + 261, + 277, + 272 + ], + "type": "text", + "content": "To be concrete, we define " + }, + { + "bbox": [ + 67, + 261, + 277, + 272 + ], + "type": "inline_equation", + "content": "c(x) = Wx + b" + }, + { + "bbox": [ + 67, + 261, + 277, + 272 + ], + "type": "text", + "content": " and then" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 279, + 295, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 279, + 295, + 294 + ], + "spans": [ + { + "bbox": [ + 123, + 279, + 295, + 294 + ], + "type": "interline_equation", + "content": "y ^ {\\mathrm {Q w T}} = l ^ {\\mathbb {Z}} \\left(x ^ {\\mathbb {Z}}\\right) + c \\left(x ^ {\\mathbb {Z}}\\right), \\tag {5}", + "image_path": "74d6bb8d9ec6be8d2656f7065dc7fb3eea18ba56e81bc6b789d3f1204eef4ff2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{d_{out} \\times d_{in}}" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "b \\in \\mathbb{R}^{d_{out}}" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": " are the weight matrix and bias vector of the linear layer " + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 300, + 296, + 337 + ], + "type": "text", + "content": ", respectively. The QwT structure is illustrated in Figure 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": "These choices are deliberate. They not only make QwT conceptually the simplest, but also ensures a closed-form solution. To minimize the difference between " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": ", we select a small set of training examples (512 images) from the training set. Using these samples, QwT collects all inputs for the block " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " to form a matrix " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "X^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{in} \\times N}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " is the total number of features or tokens. We feed " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "X^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " into the quantized block " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "Y^{\\mathbb{Z}} \\in \\mathbb{R}^{d_{out} \\times N}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": ". Next, we feed " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "X^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " into the non-quantized block " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{d_{out} \\times N}" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": ". Correspondingly, " + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 338, + 296, + 468 + ], + "type": "text", + "content": " contains output of the matching block in the original model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "text", + "content": "Our task is then to estimate " + }, + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "inline_equation", + "content": "Y - Y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "inline_equation", + "content": "X^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 468, + 296, + 503 + ], + "type": "text", + "content": ". This is a classic linear regression problem, and has a closed-form solution:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 99, + 510, + 295, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 510, + 295, + 528 + ], + "spans": [ + { + "bbox": [ + 99, + 510, + 295, + 528 + ], + "type": "interline_equation", + "content": "W ^ {*} = \\left(Y - Y ^ {\\mathbb {Z}}\\right) X ^ {\\mathbb {Z} ^ {\\top}} \\left(X ^ {\\mathbb {Z}} X ^ {\\mathbb {Z} ^ {\\top}}\\right) ^ {- 1}. \\tag {6}", + "image_path": "41060a8d88f26bb195e39e2cd9bd63bdaef14437761afc0917d981f72e627a74.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": "In Equation 6, to simplify the solution, the bias " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": " is absorbed into " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": " and a row vector of " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{1}^{\\top}" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": " are concatenated to " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "X^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": ". It is worth mentioning that theoretically QwT will not make the quantized network getting worse—by setting " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 534, + 295, + 593 + ], + "type": "text", + "content": " to all zeros, QwT will not alter the quantized network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": "Note that after the QwT module for " + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "inline_equation", + "content": "l^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": " is inserted, the compensation in the next block depends on all the previous QwT modules. Consequently, the information loss from " + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": " is gradually compensated block by block, allowing " + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": " to account for the accumulated loss from all preceding blocks that remain uncorrected." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "In our experiments, we observed that the coefficient of determination " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "(R^2)" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " [43] for a small subset " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "(< 5\\%)" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " of QwT modules was notably low, adversely hurting recognition accuracy. Consequently, we apply the initialization using" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": "Equation 6 only when " + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "inline_equation", + "content": "R^2 > 0" + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": "; Otherwise, the " + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": " of the QwT module are set to zero." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": "Finally, the QwT method has a simple pipeline: first quantize a model " + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": " using any PTQ method, then add the compensation module " + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": " to every block " + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": " and set the parameters in " + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 313, + 96, + 553, + 144 + ], + "type": "text", + "content": " using Equation 6." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 144, + 555, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 555, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 555, + 239 + ], + "type": "text", + "content": "A notable advantage of QwT lies in its inherent simplicity. This simplicity ensures that the initialization process of QwT modules is highly efficient, which requires roughly 2 minutes in practice to compensate for the information loss during quantization, thereby enhancing recognition accuracy. Experimental results demonstrated that QwT exhibits significant versatility and efficiency across various vision and language tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 251, + 395, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 395, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 395, + 264 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 270, + 554, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 554, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 554, + 354 + ], + "type": "text", + "content": "In this section, we begin by evaluating our QwT method on a range of discriminative tasks, including image classification, object detection, instance segmentation, and multimodal recognition. Subsequently, we extend our analysis to generative tasks, such as image generation using diffusion models [40] and text generation with large language models [12]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 361, + 509, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 509, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 509, + 373 + ], + "type": "text", + "content": "4.1. Experiments on Image Classification" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "text", + "content": "Settings. We evaluated our method on image classification tasks using the ImageNet dataset [8], leveraging various backbone architectures including ViT [11], DeiT [48], Swin [34], and ResNet [17]. We randomly sampled 512 images from the training set to initialize the parameters of the QwT modules using Equation 6. In all networks, the affine transformation matrix " + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "text", + "content": " in QwT is implemented in FP16 format to reduce model size. In ResNet, " + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "text", + "content": " is further simplified as a group-wise convolution using a kernel size of 1 and 64 channels per group, achieving additional efficiency in storage and computation. Note that a group-wise convolution is still a linear operator, which can be perfectly encoded by the pair " + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "inline_equation", + "content": "(W, b)" + }, + { + "bbox": [ + 313, + 378, + 555, + 556 + ], + "type": "text", + "content": ". Other details were consistent with prior work [27]. Please refer to the appendix for more information." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "content": "Results on different backbones. Table 1 summarizes the quantization results when applying QwT across different backbone architectures. Specifically, we selected RepQViT [27] and Percentile [23] as the baseline methods for the Transformer family [11, 34, 48] and ResNet [17], respectively. The results show that incorporating the QwT module consistently boosts the recognition accuracy, leading to an average increase of approximately " + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "content": ", and even up to " + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "content": " for 4-bit quantization, highlighting that QwT is particularly effective for low-bit scenarios. Additionally, after the QwT modules are integrated, the accuracy in 6-bit quantization cases aligns closely with prior state-of-the-art approaches [37, 46]." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4465" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 156, + 293, + 575 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 295, + 148 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 295, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 295, + 148 + ], + "type": "text", + "content": "Table 1. Quantization results on the ImageNet dataset [8]. #Bits' indicates the bit-width of weights/activations. 'Size' (MB) represents the storage cost of the model on the hard disk. * denotes QwT modules and classification head are finetuned for one epoch. † indicates that the previous state-of-the-art results are directly sourced from the papers [37, 46] due to the unavailability of their official code implementations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 156, + 293, + 575 + ], + "lines": [ + { + "bbox": [ + 58, + 156, + 293, + 575 + ], + "spans": [ + { + "bbox": [ + 58, + 156, + 293, + 575 + ], + "type": "table", + "html": "
NetworkMethod#BitsSizeTop-1
DeiT-TFull-precision32/3222.972.2
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-62.5
RepQ-ViT [27]4/43.358.2
RepQ-ViT + QwT4/44.261.4
RepQ-ViT + QwT*4/44.264.8
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-71.2
RepQ-ViT [27]6/64.671.0
RepQ-ViT + QwT6/65.571.2
RepQ-ViT + QwT*6/65.571.6
Swin-TFull-precision32/32113.281.4
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-77.8
RepQ-ViT [27]4/414.973.0
RepQ-ViT + QwT4/419.275.5
RepQ-ViT + QwT*4/419.279.3
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-80.9
RepQ-ViT [27]6/621.780.6
RepQ-ViT + QwT6/626.080.7
RepQ-ViT + QwT*6/626.080.9
ViT-BFull-precision32/32346.384.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]4/4-79.3
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
RepQ-ViT + QwT*4/459.178.5
\\( \\overline{\\text{IGQ-ViT}}^{\\dagger} \\) [37]6/6-83.8
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
RepQ-ViT + QwT*6/680.484.0
ResNet-50Full-precision32/32102.276.6
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]4/4-75.4
Percentile[23]4/414.068.4
Percentile + QwT4/416.074.5
Percentile + QwT*4/416.075.8
\\( \\overline{\\text{CL-Calib}}^{\\dagger} \\) [46]6/6--
Percentile[23]6/619.976.0
Percentile + QwT6/621.976.8
Percentile + QwT*6/621.976.8
", + "image_path": "7ee27db430841755c2ad954181a40a57493683bed2f460980ed99a18822b1dd1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 601, + 295, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 601, + 295, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 601, + 295, + 674 + ], + "type": "text", + "content": "The potential of our QwT method can be further unlocked through finetuning. By jointly optimizing the QwT modules and the classification head for only one (1) additional epoch (results marked with *), more gains in accuracy are achieved, enabling our method to surpass previous state-of-the-art results in nearly all cases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "These results are even closer to those produced by QAT methods, which typically require extensive training (e.g., 200 epochs). In contrast, our " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{QwT^{*}}" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": " achieves similar per" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 320, + 124, + 548, + 309 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "type": "text", + "content": "Table 2. Results of 8-bit quantization, using tensor-wise Percentile [23] as the baseline PTQ method. 'Latency' (ms) is measured on a single RTX 3090 GPU with a batch size of 64, utilizing Nvidia's TensorRT [39] toolkit for deployment." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 124, + 548, + 309 + ], + "lines": [ + { + "bbox": [ + 320, + 124, + 548, + 309 + ], + "spans": [ + { + "bbox": [ + 320, + 124, + 548, + 309 + ], + "type": "table", + "html": "
NetworkMethodSizeLatencyTop-1
DeiT-TFull-precision22.911.672.2
Percentile [23]5.92.871.2
Percentile + QwT6.83.271.5
Swin-TFull-precision113.234.581.4
Percentile [23]28.69.580.8
Percentile + QwT32.910.981.0
Swin-SFull-precision198.461.083.2
Percentile [23]50.116.082.1
Percentile + QwT58.017.983.0
ViT-SFull-precision88.228.381.4
Percentile [23]22.55.879.2
Percentile + QwT26.06.680.1
ViT-BFull-precision346.385.384.5
Percentile [23]87.415.575.8
Percentile + QwT101.617.582.8
", + "image_path": "cfc4f4d6e6b1b666b2f9b4bf4f8c8826868f1617c86f82ca31b5926cf0cc4f16.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 330, + 555, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 330, + 555, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 555, + 378 + ], + "type": "text", + "content": "formance with only one epoch of finetuning. Our approach not only substantially improves training efficiency but also keeps the backbone parameters unchanged, making it more suitable for hardware deployment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": "In Table 2, we additionally report the inference latency of different models directly deployed on a GPU. Compared to full-precision models, naive quantized models achieve an average reduction of " + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "inline_equation", + "content": "77\\%" + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": " in inference latency and " + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": " in model size. When QwT modules are incorporated, these reductions slightly decrease to " + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "inline_equation", + "content": "74\\%" + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "inline_equation", + "content": "71\\%" + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": ", respectively, with an overhead of only " + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 313, + 378, + 556, + 497 + ], + "type": "text", + "content": ". This minimal additional cost is offset by an average 1.9 percentage points improvement in recognition accuracy, demonstrating the strong practicality of the QwT method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 498, + 555, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 557 + ], + "type": "text", + "content": "Results across various PTQ methods. We extended our experiments to evaluate the versatility of QwT by applying it to various PTQ methods. As shown in Table 3, we integrated QwT into PTQ4ViT [52], RepQ-ViT [27], and Percentile [23], using ViT-B as the backbone." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "text", + "content": "We observe that QwT consistently enhances top-1 accuracy across all baseline PTQ methods. Notably, in 4-bit scenarios, PTQ4ViT demonstrates an improvement of approximately " + }, + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "text", + "content": ", while RepQ-ViT shows an " + }, + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 313, + 558, + 556, + 689 + ], + "type": "text", + "content": " increase. Compared to modern PTQ methods [27, 37, 52], which often involve complex and tedious procedures, our method demonstrates high simplicity and, most importantly, is compatible with all these approaches, too. The significant improvement in accuracy narrows the performance gap between different PTQ methods, and offers new insights into the design of new paradigms for network quantization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Extension to QAT methods. We further investigated the potential of adapting QwT to QAT methods. Specifically," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4466" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 102, + 265, + 266 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "text", + "content": "Table 3. Quantization results among different PTQ methods on the ImageNet dataset [8] using ViT-B [11] as the backbone." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 102, + 265, + 266 + ], + "lines": [ + { + "bbox": [ + 85, + 102, + 265, + 266 + ], + "spans": [ + { + "bbox": [ + 85, + 102, + 265, + 266 + ], + "type": "table", + "html": "
Method#BitsSizeTop-1
Full-precision32/32346.384.5
PTQ4ViT [52]4/444.930.7
PTQ4ViT+QwT4/459.170.0
RepQ-ViT [27]4/444.968.5
RepQ-ViT + QwT4/459.176.3
Percentile [23]6/666.256.7
Percentile+QwT6/680.479.8
PTQ4ViT [52]6/666.281.7
PTQ4ViT+QwT6/680.483.2
RepQ-ViT [27]6/666.283.6
RepQ-ViT + QwT6/680.483.9
Percentile [23]8/887.475.8
Percentile+QwT8/8101.682.8
", + "image_path": "fcfd630e8d1fde077e719862a64cd4581e532462707777f31b1e1774cab9f1eb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 86, + 306, + 265, + 371 + ], + "blocks": [ + { + "bbox": [ + 55, + 275, + 296, + 299 + ], + "lines": [ + { + "bbox": [ + 55, + 275, + 296, + 299 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 296, + 299 + ], + "type": "text", + "content": "Table 4. Quantization results of applying QwT finetuning schema on QAT methods." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 306, + 265, + 371 + ], + "lines": [ + { + "bbox": [ + 86, + 306, + 265, + 371 + ], + "spans": [ + { + "bbox": [ + 86, + 306, + 265, + 371 + ], + "type": "table", + "html": "
NetworkMethod#BitsTop-1
DeiT-SQ-ViT [25]2/272.1
Q-ViT + QwT*2/272.5
Q-ViT [25]3/379.0
Q-ViT + QwT*3/379.1
", + "image_path": "1e188dcfb04510d07a21d95e5d8ff1829d2c8bf070dda8fdf40afa55e552e94a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 389, + 295, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 295, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 295, + 426 + ], + "type": "text", + "content": "we applied QwT modules to QAT models after completing QAT training to assess whether QwT can further enhance recognition accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "content": "We preliminarily found that for QAT models, the initialization process described by Equation 6 is no longer effective. Applying it directly to QAT models significantly degrades accuracy. We attribute this to the fact that, unlike full-precision models, the optimization state of a QAT-trained model is sufficiently converged, resulting in almost no information loss from " + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "content": ". In fact, " + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "inline_equation", + "content": "y^{\\mathbb{Z}}" + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "content": " may even outperform " + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 426, + 295, + 533 + ], + "type": "text", + "content": ", as QAT models sometimes surpass their full-precision counterparts in evaluation accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "text", + "content": "To integrate QwT into QAT methods, we therefore initialize " + }, + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 54, + 533, + 295, + 641 + ], + "type": "text", + "content": " to zero as a compromise. We then explore whether fine-tuning QwT can still improve recognition accuracy. For this study, we use Q-ViT [25], a representative QAT method for ViT backbones, as the baseline. The results in Table 4 demonstrate that, even without using the initialization from Equation 6, fine-tuning the QwT modules consistently enhances QAT models, confirming the generalizability of our approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 648, + 296, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 648, + 296, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 648, + 296, + 673 + ], + "type": "text", + "content": "4.2. Experiments on Object Detection & Instance Segmentation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "Settings. We evaluated our method on object detection and instance segmentation tasks using the COCO 2017 [30] dataset. ResNet50 [17] with DETR [4], Swin-S [34] with" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "content": "Mask R-CNN [18], and Swin-S/B [34] with Cascade Mask R-CNN [3] were used as detectors. The evaluation metric was Average Precision (AP). Similar to image classification, we randomly selected 512 images from the training set to initialize the QwT weights and biases. For ResNet, the QwT was implemented using group-wise convolution with a kernel size of 1 and 64 channels per group to balance model size and AP. For DETR, we used MinMax as the PTQ baseline, a classic method that quantizes the model based on the range between the minimum and maximum values of weights or activations. For the other detectors, RepQViT [27] was chosen as the baseline PTQ method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": "Main results. Table 5 presents the results of applying QwT to object detection and instance segmentation tasks. We observe that QwT consistently enhances both " + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{box}}" + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{mask}}" + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": " across all cases without finetuning, achieving an average improvement of " + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": " with individual gains ranging from " + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 313, + 217, + 553, + 337 + ], + "type": "text", + "content": ". The consistent improvement underscores the robustness of our method for both object detection and instance segmentation tasks. Notably, in certain 6-bit scenarios, such as on Cascade Mask R-CNN, QwT even achieves AP comparable to full-precision models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "text", + "content": "Additionally, a clear trend emerges where the AP gains introduced by QwT increases along with model size. For instance, in " + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{box}}" + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "text", + "content": ", the average improvement achieved by QwT rises from " + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "text", + "content": " in ResNet-50+DETR to " + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 313, + 337, + 553, + 409 + ], + "type": "text", + "content": " in Swin-B+Cascade Mask R-CNN, indicating the method's enhanced effectiveness in larger models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "text", + "content": "Compared to full-precision models, baseline PTQ methods yield an average storage reduction of approximately " + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "text", + "content": ". The introduction of QwT modules slightly reduces this savings to around " + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "inline_equation", + "content": "78\\%" + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "inline_equation", + "content": "(-2\\%)" + }, + { + "bbox": [ + 313, + 409, + 555, + 470 + ], + "type": "text", + "content": ", which demonstrates that QwT enhances AP metrics with negligible overhead." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 479, + 529, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 529, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 529, + 493 + ], + "type": "text", + "content": "4.3. Experiments on Multimodal Recognition" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 497, + 554, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 554, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 554, + 664 + ], + "type": "text", + "content": "Settings. We conducted experiments using OpenAI's CLIP model [41]. Known for its exceptional zero-shot performance on the ImageNet [8] classification task, CLIP serves as an ideal benchmark for assessing the effectiveness on multimodal recognition tasks. We selected the variant of CLIP that includes a ViT-B/32 [11] as the visual encoder and a 12-block Transformer [49] as the text encoder. Since, to the best of our knowledge, no publicly available PTQ implementation exists for CLIP, we developed a baseline using RepQ-ViT [27]. We randomly selected 512 image-text pairs from the training data, both for PTQ model calibration and QwT initialization. Thanks to the simplicity and efficiency of our method, it achieved significant improvements under 30 seconds, as detailed in Table 6." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Main results. We conducted experiments with two quantization strategies: quantizing 1) only the visual encoder and 2) both visual and text encoders. As shown in Table 6, baseline PTQ methods showed significant drop in top-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4467" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 123, + 291, + 365 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": "Table 5. Quantization results on the COCO dataset [8]. We use box average precision " + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}^{\\mathrm{box}})" + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": " and mask average precision " + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}^{\\mathrm{mask}})" + }, + { + "bbox": [ + 55, + 70, + 297, + 117 + ], + "type": "text", + "content": " to assess object detection and instance segmentation accuracy, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 123, + 291, + 365 + ], + "lines": [ + { + "bbox": [ + 60, + 123, + 291, + 365 + ], + "spans": [ + { + "bbox": [ + 60, + 123, + 291, + 365 + ], + "type": "table", + "html": "
NetworkMethod#BitsSizeAPboxAPmask
ResNet-50 + DETRFull-precision32/32164.542.0-
MinMax6/647.439.5-
MinMax + QwT6/649.440.0-
MinMax8/856.441.6-
MinMax + QwT8/858.441.7-
Swin-S + Mask R-CNNFull-precision32/32276.548.543.3
RepQ-ViT [27]4/436.142.640.0
RepQ-ViT + QwT4/444.043.140.4
RepQ-ViT [27]6/653.347.642.9
RepQ-ViT + QwT6/661.248.043.1
Swin-S + Cascade Mask R-CNNFull-precision32/32427.851.945.0
RepQ-ViT [27]4/456.949.343.1
RepQ-ViT + QwT4/464.849.943.4
RepQ-ViT [27]6/683.451.444.6
RepQ-ViT + QwT6/691.351.744.8
Swin-B + Cascade Mask R-CNNFull-precision32/32579.951.945.0
RepQ-ViT [27]4/476.149.343.1
RepQ-ViT + QwT4/490.150.043.7
RepQ-ViT [27]6/6112.151.544.8
RepQ-ViT + QwT6/6126.151.845.0
", + "image_path": "13954f56b49f0562ddd122b4b95ca89428cbc7cb5dba7bfcb2637786cda592fb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 385, + 295, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 433 + ], + "type": "text", + "content": "1 accuracy compared to their full-precision counterparts, struggling to effectively represent a low-bit CLIP model. The reduction in performance is especially obvious when both the visual and text encoders are quantized." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "text", + "content": "In contrast, our QwT method enhanced top-1 accuracy across all cases, significantly bridging the accuracy gap between low-bit and full-precision models. Specifically, in vision-only quantization, QwT increased top-1 accuracy by an average of " + }, + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "text", + "content": ", with only a modest " + }, + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 55, + 434, + 295, + 506 + ], + "type": "text", + "content": " increase in model size compared to baseline PTQ methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": "When both the visual and text encoders are quantized, baseline PTQ methods exhibited an average accuracy drop of " + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "inline_equation", + "content": "29.2\\%" + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": ". In contrast, QwT provided a significant accuracy improvement, with an average increase of " + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "inline_equation", + "content": "14.8\\%" + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": ". These findings highlight QwT's effectiveness in preserving high accuracy while substantially reducing model size for multimodal recognition tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 600, + 241, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 241, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 241, + 613 + ], + "type": "text", + "content": "4.4. Experiments on Image Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 713 + ], + "type": "text", + "content": "QwT has also demonstrated efficacy in generative models, notably enhancing the performance of quantized diffusion models. Unlike classifiers or detectors, which require a single forward pass, diffusion models involve multiple forward passes to generate the final images, presenting a unique prototype. Under these circumstances, QwT has proven itself highly effective, underscoring its general applicability and robustness." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 123, + 552, + 255 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 117 + ], + "type": "text", + "content": "Table 6. Quantization results of CLIP for zero-shot classification tasks on ImageNet. The 'Quant Setup' column differentiates between two strategies: quantizing only the vision encoder and quantizing both the vision and text encoders concurrently." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 123, + 552, + 255 + ], + "lines": [ + { + "bbox": [ + 317, + 123, + 552, + 255 + ], + "spans": [ + { + "bbox": [ + 317, + 123, + 552, + 255 + ], + "type": "table", + "html": "
Quant SetupMethod#BitsSize (MB)Top-1
VisionFull-precision32/32607.263.4
RepQ-ViT [27]6/6323.559.2
RepQ-ViT + QwT6/6336.860.3
RepQ-ViT [27]8/8345.362.9
RepQ-ViT + QwT8/8359.563.0
Vision & TextFull-precision32/32607.263.4
RepQ-ViT [27]6/6200.829.8
RepQ-ViT + QwT6/6221.343.5
RepQ-ViT [27]8/8232.138.7
RepQ-ViT + QwT8/8252.654.6
", + "image_path": "aca11c3e0548fc77403c363416ee709f5f9d40d2a8a5502e748480a2264dfa0a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 277, + 555, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 409 + ], + "type": "text", + "content": "Settings. For our experiments, we selected the influential DiT [40] (Diffusion Transformer) architecture, following the experimental setup of Q-DiT [5]. Specifically, we employed pretrained DiT-XL/2 models at a resolution of " + }, + { + "bbox": [ + 313, + 277, + 555, + 409 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 277, + 555, + 409 + ], + "type": "text", + "content": ". For rapid and precise sampling, we utilized the DDIM sampler with 50 sampling steps and applied classifier-free guidance (cfg) of 1.5, abbreviated as DiT-XL/2 (steps = 50, CFG = 1.5). Our experiments included two quantization configurations: W8A8 and W4A8. Additional results involving various model sizes, steps, and CFG values are available in the appendix." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "text", + "content": "We applied QwT directly to the quantized diffusion model using Q-DiT. A key consideration is that the model performs " + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "text", + "content": " forward passes per inference, with notable variation in the activation distribution and range across steps. A key assumption is that quantization error is primarily dependent on the input " + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "text", + "content": ", with minimal influence from elements like the time step or class condition. Accordingly, we set " + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 313, + 410, + 556, + 518 + ], + "type": "text", + "content": " to initialize the compensation module. The results are presented in Table 7." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 520, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 556, + 604 + ], + "type": "text", + "content": "Main results. Our method was compared with three representative quantization techniques: RepQ-ViT, GPTQ and Q-DiT designed for diffusion models. For both W8A8 and W4A8 settings, QwT significantly enhanced the performance of the quantized models, yielding improvements of 0.10 and 0.69 in FID, which illustrates the efficacy of QwT with minimal increase in model size." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "We visualize the images generated by our model alongside those from compared models in Figure 2. The three rows represent the original images, quantized images with Q-DiT, and quantized images with QwT, respectively. All models are based on DiT-XL/2 (steps " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "= 50" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{cfg} = 1.5" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "). To enable a fair comparison, we ensure that the initial Gaussian noise and the noise added during inference are identical across all methods. The images produced by our method show a closer visual resemblance to the original model," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4468" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 75, + 515, + 224 + ], + "blocks": [ + { + "bbox": [ + 97, + 75, + 515, + 224 + ], + "lines": [ + { + "bbox": [ + 97, + 75, + 515, + 224 + ], + "spans": [ + { + "bbox": [ + 97, + 75, + 515, + 224 + ], + "type": "image", + "image_path": "45c730c8370f8d3c5774d66020f043555f34dcd073648450c890ad38aa9b309c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 236, + 425, + 248 + ], + "lines": [ + { + "bbox": [ + 184, + 236, + 425, + 248 + ], + "spans": [ + { + "bbox": [ + 184, + 236, + 425, + 248 + ], + "type": "text", + "content": "Figure 2. Qualitative visualization results of quantizing DiT-XL/2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 66, + 298, + 284, + 441 + ], + "blocks": [ + { + "bbox": [ + 55, + 267, + 295, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 267, + 295, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 267, + 295, + 289 + ], + "type": "text", + "content": "Table 7. Quantitative results of quantizing DiT-XL/2. " + }, + { + "bbox": [ + 55, + 267, + 295, + 289 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 267, + 295, + 289 + ], + "type": "text", + "content": " (↑) means smaller (larger) is better." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 298, + 284, + 441 + ], + "lines": [ + { + "bbox": [ + 66, + 298, + 284, + 441 + ], + "spans": [ + { + "bbox": [ + 66, + 298, + 284, + 441 + ], + "type": "table", + "html": "
Method#BitsSize (MB)FID (↓)IS (↑)
Full-precision16/1613495.32236.17
RepQ-ViT8/86775.46234.74
GPTQ8/86905.90218.90
Q-DiT8/86835.45236.52
Q-DiT + QwT8/87075.35236.91
RepQ-ViT4/8339319.682.20
GPTQ4/83519.94166.35
Q-DiT4/83476.75208.38
Q-DiT + QwT4/83616.06215.70
", + "image_path": "79f4bcae5d0984bbef64e212baa0cda187c0085408d79e9a0520f79e11b859c9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 461, + 225, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 225, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 225, + 473 + ], + "type": "text", + "content": "which aligns with the quantitative results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 480, + 269, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 269, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 269, + 493 + ], + "type": "text", + "content": "4.5. Experiments on Large Language Models" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 498, + 295, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 498, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 54, + 498, + 295, + 617 + ], + "type": "text", + "content": "Settings. We evaluated our framework on the LLaMA3-8B [12] model. For PTQ methods, we adopted GPTQ [14] with INT4 weight quantization. Our approach is also compatible with other PTQ methods such as AWQ [29] and SPQR [9]. We conducted a group-wise asymmetric quantization with a group size of 128 and apply activation reordering. In particular, GPTQ take 128 samples from the C4 dataset as calibration sets, and each sample is 2048 tokens long. We use the same calibration set when performing QwT after GPTQ algorithm." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "content": "Evaluation metrics. Following the settings of GPTQ, we evaluated the perplexity on the WikiText2 [47] and C4 [42] datasets. We further assessed the zero-shot commonsense question answering (QA) ability on eight tasks covering SIQA [45], HellaSwag [53], PIQA [2], Wino-Grande [44], ARC [7], BoolQ [6], and OpenBookQA [36]. We also evaluated both the zero-shot and five-shot performance of the LLMs on Massively Multitask Language Un" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 308, + 555, + 363 + ], + "blocks": [ + { + "bbox": [ + 313, + 267, + 555, + 301 + ], + "lines": [ + { + "bbox": [ + 313, + 267, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 267, + 555, + 301 + ], + "type": "text", + "content": "Table 8. Quantization results among WikiText2, C4 and eight zero-shot commonsense QA datasets using LLaMA3-8B as the backbone. " + }, + { + "bbox": [ + 313, + 267, + 555, + 301 + ], + "type": "inline_equation", + "content": "\\downarrow (\\uparrow)" + }, + { + "bbox": [ + 313, + 267, + 555, + 301 + ], + "type": "text", + "content": " means smaller (larger) is better." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 308, + 555, + 363 + ], + "lines": [ + { + "bbox": [ + 315, + 308, + 555, + 363 + ], + "spans": [ + { + "bbox": [ + 315, + 308, + 555, + 363 + ], + "type": "table", + "html": "
Method#BitsSize (GB)W2 (↓)C4 (↓)QA. Avg (↑)
Full-precision1616.066.248.9666.10
GPTQ45.736.659.4464.90
GPTQ + QwT46.806.639.3865.18
", + "image_path": "ef3b1ab12fabb7ab8f65e6c4b4f99e811089f542e9e79dc7e09eda4bccddac74.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 383, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 555, + 431 + ], + "type": "text", + "content": "derstanding (MMLU) benchmark [20]. It consists of 57 language tasks including humanities, STEM, social science, etc. We adopted lm-eval-harness [15] to produce the accuracy results." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 431, + 555, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 515 + ], + "type": "text", + "content": "Results. Table 8 summarizes the perplexity in WikiText2, C4 and the average accuracy in eight common sense reasoning datasets. More results are shown in the appendix. Note that we abbreviate WikiText2 to W2. As the results show, our optimized models will not overfit the calibration dataset and consistently outperform the original PTQ models. These results reveal the effectiveness of our QwT." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 526, + 392, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 392, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 392, + 538 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 545, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 545, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 545, + 555, + 715 + ], + "type": "text", + "content": "In this paper, we proposed Quantization without Tears (QwT), a novel approach that incorporates a lightweight structure into quantized models to compensate for the information loss during network quantization. The QwT modules, implemented as a tiny set of linear layers and seamlessly integrated into backbone blocks, achieved accuracy, simplicity, and generality simultaneously. Notably, QwT provides a closed-form solution to complete the compensation process in under 2 minutes and enables effortless integration with existing quantization techniques. Extensive experiments demonstrated QwT's exceptional effectiveness and versatility across a wide range of tasks, models, and quantization methods, advancing a streamlined and flexible paradigm for network quantization." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4469" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 114 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 114 + ], + "type": "text", + "content": "This research was partly supported by the National Natural Science Foundation of China under Grant 62276123." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 116, + 296, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 116, + 296, + 200 + ], + "spans": [ + { + "bbox": [ + 55, + 116, + 296, + 200 + ], + "type": "text", + "content": "J.W. designed the compensation insight and the QwT framework mathematically. M.F. made them into algorithms and codes that work well in practice, and carried out the main empirical validations. H.Y., J.S. and J.Z. carried out experiments and validations on LLM, AIGC and multimodal tasks, respectively. K.Z. engaged in discussions. 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However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose Quart-Depth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth", + "bbox": [ + 89, + 393, + 485, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 818, + 220, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Monocular Depth Estimation (MDE) is a critical task in computer vision, essential for a wide range of applications", + "bbox": [ + 89, + 844, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/27a4440b701133d9e5301a2a2f232e4c92a81cd561616303da4cc024bef95b17.jpg", + "image_caption": [ + "Figure 1. Visualization of accuracy vs. latency on ASIC for monocular depth estimation models with different backbones." + ], + "image_footnote": [], + "bbox": [ + 514, + 359, + 906, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "including robotics [82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105]. The objective of MDE is to estimate depth information from a single image, making it particularly valuable for scenarios where stereo or multi-view depth sensors are impractical. Previously, depth estimation methods have been classified into three main approaches: learning metric depth [3, 89, 91, 99], learning relative depth [8, 9, 86, 87], and learning affine-invariant depth [54, 56, 93, 94, 105]. Among these, metric depth methods have demonstrated remarkable performance across benchmarks but often show limited generalizability to diverse, real-world images, which is compounded by variations in camera parameters between training and test sets.", + "bbox": [ + 509, + 598, + 908, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, inspired by the rise of \"foundation models\" [5, 107], a new wave of MDE models [4, 66, 90, 95] has been developed. These foundational MDE models exhibit superior generalization and robustness, effectively extending their applicability to in-the-wild images and accommodating a wide array of camera parameters. However, while these foundational MDE models achieve impressive performance,", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 109, + 886, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11448", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "they rely on sophisticated and computationally intensive algorithms. This reliance on complex architectures and operations significantly increases computational costs, making such models resource-heavy and challenging to deploy on edge devices or specialized hardware such as Application-Specific Integrated Circuits (ASICs) [35, 52, 81, 82]. The high computational demands also hinder real-time performance and scalability, which are critical for practical applications such as autonomous navigation [2], robotic perception [80], and augmented reality [68]. This constraint underscores the need for more efficient approaches that can maintain high accuracy while reducing computational overhead. Among common techniques like pruning [16, 64, 82, 106], knowledge distillation [18, 50], and architecture optimization [1, 37, 38, 63, 85, 101], which mainly reduce model complexity, quantization [11, 36, 46, 79] stands out for achieving both compactness and speed. Quantization [14, 39, 41, 84, 100] reduces weights and activations to lower bit-widths (e.g., 4-bit or 8-bit integers), minimizing model size while accelerating inference through optimized integer kernels specifically designed for edge devices. This dual benefit makes it ideal for deploying high-performing models on resource-limited edge hardware. Given the complexity of large foundational MDE models and their extensive datasets [31, 34, 98], we employ Post-Training Quantization (PTQ) [36, 41, 62, 100, 108] to facilitate efficient deployment without retraining.", + "bbox": [ + 93, + 90, + 483, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose QuartDepth, a post-training quantization framework designed for real-time depth estimation on edge devices. We begin by analyzing the outlier deviant distribution in MDE foundation models [90, 95]. Through an in-depth per-channel analysis of these abnormal distributions, we identify persistent extreme outliers in the depth decoders. To address this, we propose the LogNP polishing optimization method to smooth the outliers and transform the abnormal distribution into a more quantization-friendly, normalized distribution. Furthermore, to mitigate the loss from activation quantization, we employ a compensation algorithm that updates the weights to minimize the activation quantization error. Next we perform weight quantization with a weight reconstruction method that leverages gradients to minimize second-order weight quantization errors. Meanwhile, we design a novel flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, which enables direct processing of intermediate results and concurrent execution of computational tasks. In detail, we design specialized computation kernels for W4A4 and W4A8 configurations, which enables full utilization of external memory bandwidth. Also, we design a novel programmable vector computation array to support the proposed LogNP polishing optimization, effectively hiding its additional overhead.", + "bbox": [ + 93, + 503, + 483, + 880 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are outlined as follows,", + "bbox": [ + 112, + 886, + 465, + 898 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We observe a challenging outlier deviant distribution for activations and propose the LogNP polishing for activation quantization, which transforms these outliers into a quantization-friendly, normalized distribution.", + "2. For weight quantization, we first update the weights to compensate the error of activation quantization, and then quantize the updated weights with weight reconstruction to minimize the second-order weight quantization error.", + "3. We develop a novel flexible and programmable hardware accelerator on ASICs corresponding to our proposed quantization methods.", + "4. Comprehensive experiments confirm the effectiveness of our QuartDepth framework with superior accuracy, real-time inference and higher power efficiency on ASICs." + ], + "bbox": [ + 522, + 90, + 906, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 517, + 319, + 653, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Efficient Depth Estimation", + "text_level": 1, + "bbox": [ + 517, + 344, + 753, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth estimation from a single color image has been a prominent research focus in the field of computer vision for over a decade. This task plays a critical role in various applications, including robotic perception [12, 13, 82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105], all of which require rapid and accurate depth perception. The demand for real-time processing in these applications highlights the necessity for efficient model deployment. To meet these requirements, advanced optimization techniques such as pruning [16, 42, 65, 82, 104], knowledge distillation [18, 50], and architecture optimization [1, 88, 108] have been adopted to compress and accelerate the model. However, previous research has primarily focused on relatively smaller models, which, while effective, do not match the scale and capability of foundational MDE models [90, 95]. These modern foundational MDE models [4, 66] have gained significant attention for their ability to achieve state-of-the-art performance and generalize effectively across diverse real-world scenarios. By leveraging massive datasets and advanced architectures, these models provide robust depth estimation at the cost of increased computational complexity and larger model sizes. Thus, there is an urgent need for new model compression and acceleration techniques specifically designed to meet real-time requirements on resource-limited edge devices.", + "bbox": [ + 514, + 367, + 906, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Hardware Design", + "text_level": 1, + "bbox": [ + 517, + 757, + 683, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deploying large foundational models on edge devices presents significant challenges due to stringent constraints on computation and memory access [69]. To tackle these issues, various optimization techniques [59-62, 83, 102, 103, 108] have been explored to reduce model size and computational overhead. However, models subjected to such aggressive optimizations often fail to achieve peak performance on general-purpose CPUs and GPUs [96]. In contrast, ASICs,", + "bbox": [ + 514, + 780, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11449", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a00c83984be3fdd5ed0073252265194f954786873afc4fe01942b5fa9432f9ec.jpg", + "image_caption": [ + "Figure 2. Latency profiling for 3 different resolutions using Metric3D with ViT-Large backbone. Vector includes activation functions (e.g. ReLU) and element-wise addition and multiplication." + ], + "image_footnote": [], + "bbox": [ + 93, + 85, + 486, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "optimized for specific models and algorithms, offer significant performance and energy efficiency gains, making them ideal for deploying large foundational models on edge devices [22, 23, 43, 53, 78, 96]. Early work, such as TPU [28], DNA [72], and Eyeriss [10], significantly improved inference speed and energy efficiency by focusing on specialized hardware designs tailored to the needs of deep learning models. Recent works [29, 30, 49, 73, 74] have proposed dedicated hardware architectures in ASICs to accelerate neural network inference. These ASIC architectures have significantly improved inference latency and energy efficiency through solutions such as quantization, sparsity, data flow reconstruction, and algorithm-hardware co-design [40]. Thus, to maximize potential of large foundational models, the advantages offered by ASICs make them platform of choice.", + "bbox": [ + 88, + 289, + 486, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Analysis and Motivation", + "text_level": 1, + "bbox": [ + 89, + 532, + 321, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Latency Profiling", + "text_level": 1, + "bbox": [ + 89, + 556, + 261, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To optimize edge device inference, we first profile the Float32 model to identify the most time-consuming components for targeted optimization. In detail, we implement the Metric3D [95] model with ViT-Large [15] backbone on a hardware performance emulator with our ASIC design. The latency profiling results in Figure 2 show that the matrix multiplication and convolution operations dominate the inference time, while non-linear operations like softmax and layer normalization contribute minimally. The vector operations include activation functions such as SiLU, ReLU, and GeLU, as well as element-wise addition and multiplication, which also contribute minimally to the overall latency. This motivates our focus on quantization and ASIC design for linear and convolution layers, keeping non-linear operations in floating point to preserve accuracy.", + "bbox": [ + 88, + 579, + 486, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.Deviant Distribution", + "text_level": 1, + "bbox": [ + 89, + 816, + 285, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We investigate the deviant distribution in MDE models from a per-channel perspective. In Figure 3, we visualize the outliers across various channels of an activation in the decoder [55] of the Metric3D model on NYUv2 dataset. We", + "bbox": [ + 89, + 839, + 485, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e6521ca76e44b7f737bcd83cbe82ab27014c98ac8c84caa0ef8338c769c1a4a8.jpg", + "image_caption": [ + "Figure 3. Visualization of outliers in various channels at the decoder [55] of Metric3D model on NYUv2 dataset." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 905, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/09348e4c09371b3ad8b68cbd4659bc31ea9d369b66c817adc5b7a0415845a7d0.jpg", + "image_caption": [ + "Figure 4. Visualization for the activation data distribution of different channels in decoder with log frequency." + ], + "image_footnote": [], + "bbox": [ + 514, + 262, + 906, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "observe large amount of outliers and significant variability in outlier values across different channels, making per-tensor quantization challenging. This motivates the adoption of a per-channel quantization method to better handle these variations. However, for per-channel quantization, the presence of outliers that deviate significantly from the main data distribution, as shown in Figure 4, still leads to substantial quantization errors. Thus, smoothing these large outliers and integrating them into the main data distribution is crucial for maintaining model accuracy.", + "bbox": [ + 511, + 426, + 908, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Quantization Framework", + "text_level": 1, + "bbox": [ + 511, + 593, + 751, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first quantize the polished activations with LogNP polishing (Section 4.2). Then we update weights to compensate the loss of activation quantization (Section 4.3). Finally, we quantize updated weights (Section 4.4).", + "bbox": [ + 511, + 619, + 908, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 691, + 643, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization. We mainly adopt the hardware-efficient PTQ methods. For uniform quantization, the quantize and dequantize operations for $x$ can be defined as follows,", + "bbox": [ + 511, + 714, + 908, + 761 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z p, 0, 2 ^ {k} - 1\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 772, + 908, + 800 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = s \\cdot \\left(x _ {q} - z\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 814, + 908, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s$ represents the scale and $zp$ is the zero point. The operator $\\lfloor \\cdot \\rceil$ indicates rounding to the nearest integer, and the CLIP function constrains values that fall outside the range of a $k$ -bit integer.", + "bbox": [ + 511, + 840, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11450", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As for Log2 quantization, which is mainly used for post-softmax quantization, can be defined as follows,", + "bbox": [ + 89, + 90, + 485, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor - \\log_ {2} \\frac {x}{s} \\right\\rceil , 0, 2 ^ {k} - 1\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 132, + 483, + 161 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = s \\cdot 2 ^ {- x _ {q}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 240, + 174, + 483, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notations. The quantized layers (including both linear and convolutional layers) in the mode are indexed by $l$ , $1 \\leq l \\leq L$ . The weights in the $l^{th}$ layer are denoted by $\\mathbf{W}^{(l)}$ with its vectorized/flatened version $\\mathbf{w}^{(l)}$ . $\\mathbf{x}$ denotes its inputs.", + "bbox": [ + 89, + 199, + 483, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Activation Polishing", + "text_level": 1, + "bbox": [ + 89, + 271, + 282, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Building on analysis in Section 3.2, we propose LogNP polishing method to adaptively smooth the deviant distribution in decoders in per-channel prospective. For one activation $\\mathbf{x} \\in \\mathbb{R}^{n \\times d}$ where $n$ denotes the number of tokens and $d$ denotes the channel number, the LogNP polishing function $\\Phi(\\cdot, \\cdot)$ for each element $x$ of input $\\mathbf{x}$ is defined as follows,", + "bbox": [ + 89, + 294, + 483, + 385 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi (x, \\alpha) = \\operatorname {s i g n} (x) \\cdot \\left[ \\log_ {2} (| x | + \\alpha) - \\log_ {2} (\\alpha) \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 397, + 483, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{sign}(\\cdot)$ denotes the sign function, and $\\alpha$ is the polishing factor for one single channel.", + "bbox": [ + 89, + 426, + 483, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To reduce the quantization error in each channel, the polishing factor $\\alpha_{i}$ corresponding to the $i^{th}$ channel with activation $\\mathbf{x}_i$ (i.e., $\\mathbf{x} = [\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_d]$ ) is computed according to the given percentile $\\epsilon$ as follows,", + "bbox": [ + 89, + 458, + 483, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} = P _ {\\epsilon} \\left(\\mathbf {x} _ {i}\\right), i \\in \\{1, 2, 3, \\dots , d \\}, \\epsilon \\in (0, 1 0 0) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 532, + 483, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{\\epsilon}(\\cdot)$ denotes the $\\epsilon$ -th percentile function. We adopt uniform $\\epsilon$ equals to 95 as deviant activation distributions remain similar across different inputs. We provide the visualization of the polished activation in Figure 5. The polished activation colored in blue appears smoother compared to the original activation colored in red shown in Figure 4, making it more friendly for quantization. After polishing, we perform activation quantization with uniform quantization in Section 4.1. Following activation dequantization, we adopt reverse transformation (i.e., unpolishing) as follows,", + "bbox": [ + 89, + 561, + 483, + 712 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi^ {- 1} (\\hat {x}, \\alpha) = \\operatorname {s i g n} (\\hat {x}) \\cdot \\left[ 2 ^ {\\operatorname {s i g n} (\\hat {x}) \\cdot \\hat {x} + \\log_ {2} (\\alpha)} - \\alpha \\right] \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 724, + 483, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The latency overhead introduced by LogNP polishing and unpolishing is hidden by concurrent execution in our hardware design, which is further explained in Section 5.2.", + "bbox": [ + 89, + 760, + 485, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Activation Loss Compensation", + "text_level": 1, + "bbox": [ + 89, + 816, + 362, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The activation quantization introduces quantization errors. To mitigate this issue, before weight quantization, we first update all weights to compensate the loss of activation quantization. To save the computation cost, we address the problem", + "bbox": [ + 89, + 840, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/077c36dce931a03818627546c18f92c5213e4ce9cc8a4173f4d6ba27eb7fc150.jpg", + "image_caption": [ + "Figure 5. Visualization for the polished activation data distribution of different channels in decoder with log frequency." + ], + "image_footnote": [], + "bbox": [ + 514, + 87, + 905, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "layer by layer instead of for the whole model. The layer-wise compensation problem is formulated as the following,", + "bbox": [ + 511, + 248, + 905, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Delta \\mathbf {W}} \\| \\mathbf {W} \\mathbf {x} - (\\mathbf {W} + \\Delta \\mathbf {W}) \\hat {\\mathbf {x}} \\| _ {2} ^ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 287, + 906, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}$ and $\\mathbf{x}$ are the original weights and inputs of the layer. $\\hat{\\mathbf{x}}$ is the quantized inputs and we update the weights with $\\Delta \\mathbf{W}$ to compensate the activation quantization error, so that the layer outputs after activation quantization and weight compensation should be close to the original outputs.", + "bbox": [ + 511, + 321, + 906, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This problem can be solved by setting the gradients of the minimization objective to zero, as the following,", + "bbox": [ + 511, + 396, + 906, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\mathbf {W} \\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}} + \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} = 0. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 436, + 906, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The optimal solution can be obtained by", + "bbox": [ + 511, + 465, + 782, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\mathbf {W} ^ {*} = - \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} \\left(\\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}}\\right) ^ {- 1} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 489, + 906, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After activation quantization, we can update weights with the above $\\Delta \\mathbf{W}^*$ to compensate the activation quantization error. If $\\hat{\\mathbf{x}}\\hat{\\mathbf{x}}^{\\mathrm{T}}$ is not full rank with difficulties for matrix inversion, we adopt the dampening technique [21, 45]. Next, we quantize the updated weights under the quantized activations.", + "bbox": [ + 511, + 518, + 906, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Weight Reconstruction", + "text_level": 1, + "bbox": [ + 511, + 603, + 725, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Problem formulation. In quantization, the weights are modified and we would like to minimize the change of loss incurred by quantization to maintain the superior performance of the model. To quantitatively analyze the loss degradation by quantization, we approximate the loss degradation with Taylor expansion as the following,", + "bbox": [ + 511, + 625, + 906, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L (\\mathbf {w} + \\Delta \\mathbf {w}) - L (\\mathbf {w}) \\approx \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {g} _ {\\mathbf {w}} + \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\\\ \\approx \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 724, + 906, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{g}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}L$ represents the gradients and $\\mathbf{H}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}^{2}L$ denotes the Hessian matrix. $\\Delta \\mathbf{w}$ is the weight perturbation in this step. Here we use the vectorized/flatened version $\\mathbf{w}$ instead of the matrix version $\\mathbf{W}$ to obtain a scalar output. As the pre-trained model has been well trained and converged to a minimum, it is reasonable to assume the gradients to be 0. The complexity to obtain the full Hessian is very high", + "bbox": [ + 511, + 794, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11451", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and typically it is not possible to obtain the full Hessian due to computation and memory limitations. Specifically, $\\mathbf{H}_{\\mathbf{w}} \\in \\mathbb{R}^{B \\times B}$ where $B$ is the number of parameters in $\\mathbf{w}$ . The memory cost for $\\mathbf{H}_{\\mathbf{w}}$ is extremely heavy in LLMs with billions of parameters.", + "bbox": [ + 89, + 90, + 483, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Approximating Hessian. For a network trained with negative log-likelihood loss and a probabilistic model $p_{\\mathbf{w}}(y|x_s)$ under softmax, the Hessian is identical to the Fisher matrix:", + "bbox": [ + 89, + 166, + 485, + 208 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {H} _ {\\mathbf {w}} = \\mathbf {F} _ {\\mathbf {w}} = \\sum_ {s = 1} ^ {S} \\mathbb {E} _ {y \\sim p _ {\\mathbf {w}} (y | x _ {s})} [ \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} (y | x _ {s}) \\\\ \\left. \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} \\left(y \\mid x _ {s}\\right) ^ {T} \\right] \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 218, + 482, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S$ is the number of samples, and for each sample, it needs to compute the expectation over all categories. The complexity with the expectation is also high if there are too many categories. Thus, in practice, the empirical Fisher is commonly adopted to replace the expectation over $y$ with target label $y_{s}$ [33]. The dimension of $\\mathbf{F}_{\\mathbf{w}}$ is the same as $\\mathbf{H}_{\\mathbf{w}}$ with quadratic memory complexity to the number of parameters. To reduce the complexity, the empirical Fisher is computed by treating layers independently and the layer-wise empirical Fisher can be obtained as below [6, 44],", + "bbox": [ + 89, + 273, + 483, + 425 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {l} = \\mathbb {E} \\left[ \\left(\\mathbf {g} ^ {(l)} \\mathbf {g} ^ {(l), \\mathrm {T}}\\right) \\otimes \\left(\\hat {\\mathbf {x}} ^ {(l)} \\hat {\\mathbf {x}} ^ {(l), \\mathrm {T}}\\right) \\right], \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 436, + 483, + 464 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{x}}^{(l)}$ is the input activations and $\\mathbf{g}^{(l)}$ is the gradients of the $l^{th}$ layer. $\\otimes$ denotes Kronecker product. The expectation is taken with respect to data distribution over inputs.", + "bbox": [ + 89, + 474, + 483, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For two different layers (for example, the $i^{th}$ and the $j^{th}$ layers), their Fisher is often written as $\\mathbf{F}_{ij} = \\sum_{s=1}^{S} \\mathbb{E}\\left[\\nabla_{\\mathbf{w}^{(i)}} \\log p_{\\mathbf{w}}(y_s | x_s) \\nabla_{\\mathbf{w}^{(j)}} \\log p_{\\mathbf{w}}(y_s | x_s)^T\\right]$ ,", + "bbox": [ + 89, + 522, + 483, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which are often ignored to save computations. The Fisher for the whole model can be formulated as a block diagonal matrix $\\mathbf{F}_{\\mathbf{w}} = \\mathrm{diag}(\\mathbf{F}_1,\\mathbf{F}_2,\\dots ,\\mathbf{F}_L)$", + "bbox": [ + 89, + 571, + 483, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain the Fisher in practice, we adopt the KFAC approximation method [20, 44] as below,", + "bbox": [ + 89, + 616, + 483, + 646 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {l} = \\mathbf {G} _ {l} \\otimes \\mathbf {A} _ {l} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 659, + 482, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\mathbf {g} _ {s} ^ {(l)} \\mathbf {g} _ {s} ^ {(l), \\mathrm {T}} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 678, + 482, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\hat {\\mathbf {x}} _ {s} ^ {(l)} \\hat {\\mathbf {x}} _ {s} ^ {(l). \\mathrm {T}} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 712, + 482, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The KFAC approximation [25, 76] approximates an expectation of Kronecker products as a Kronecker product of two expectations $\\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}\\otimes \\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]\\approx \\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}]\\otimes$ $\\mathbb{E}[\\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]$ , where the activations and derivatives are assumed to be independent.", + "bbox": [ + 89, + 753, + 483, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimizing quantization parameters. Next we optimize the quantization parameters. Given our optimization loss in Equation (11), multiple optimization methods can be adopted such as STE [24] and AdaRound [46]. Due to its superior performance in PTQ, we use AdaRound [46] to learn the", + "bbox": [ + 89, + 830, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/84c4f3f019ba0ce28385fd4967e69731f144f201b00a624a71b577b9cf008c16.jpg", + "image_caption": [ + "Figure 6. The block diagram of the proposed hardware accelerator." + ], + "image_footnote": [], + "bbox": [ + 517, + 87, + 906, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "rounding parameter which decides rounding up or down. Formally, we minimize the following loss,", + "bbox": [ + 511, + 289, + 906, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {v}} \\sum_ {l = 1} ^ {L} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) ^ {\\mathrm {T}} \\mathbf {F} _ {l} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) + \\lambda h (\\mathbf {v}), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 325, + 906, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{v}$ denotes the rounding parameter which are used to construct the quantized weights $\\hat{\\mathbf{w}}^{(l)}$ . $h(\\mathbf{v})$ is a regularizer in AdaRound [46] with $\\lambda$ controlling its strength. More details about AdaRound are presented in Appendix 9. We only use a small calibration set (32 samples) sampled from the training dataset to calibrate the quantized model.", + "bbox": [ + 511, + 371, + 906, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Hardware Design", + "text_level": 1, + "bbox": [ + 511, + 474, + 684, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Top-Level Design", + "text_level": 1, + "bbox": [ + 511, + 500, + 683, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We design a flexible and programmable accelerator as shown in Figure 6. The Dispatch module fetches instructions via the AXI bus and distributes them to local Instruction FIFOs, while the Synchronize module controls the start and end of each module. Instruction FIFOs hold out-of-order instructions and are controlled by Synchronize module for execution. The Load and Store modules, functioning as the DMA, facilitate data transfer between off-chip memory (e.g., HBM or DDR) and local buffers. The Matrix Multiplication Unit (MMU) performs General Matrix Multiply (GeMM) and convolution when the Vector Compute Unit (VCU) handles nonlinear activation functions.", + "bbox": [ + 511, + 522, + 908, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. On-Chip Kernel Design", + "text_level": 1, + "bbox": [ + 511, + 712, + 732, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt a multiply-accumulate tree array to implement both matrix multiplication and convolution. For W4A4 and W4A8 configurations, we design specialized multipliers and adders to enhance computational efficiency and reduce chip area overhead. Additionally, the use of low-bit quantized matrices eases memory bandwidth demands during data transfer, allowing for full utilization of the external memory bandwidth. As for Float32, we implement IEEE 754 standard floating-point computation for fair comparison.", + "bbox": [ + 511, + 734, + 906, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Meanwhile, we propose a programmable vector computation array composed of multiple Floating-Point Units (FPU)", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11452", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8c21b2bbab0497ea6faa33eb0b8bf9e85c55959dd7225d8e5196529627540ccf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodW/ANYUv2 [47]KITTI [19]
AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓
ViT-Small Backbone
\\Float320.0870.9380.9900.9960.3310.0350.0740.9340.9840.9953.4030.043
OBS [17]W40.1070.8850.9850.9970.3910.0420.1220.8670.9730.9914.5080.058
minmax [27]W4A80.4530.4050.7020.8681.0670.1110.4560.1020.3290.57513.3550.159
ema [26]0.2570.5910.8590.9580.7930.0930.3120.3410.6320.80711.1020.139
percentile [11]0.1900.6350.9120.9810.7740.0770.2220.5520.8140.9188.9000.114
AdaRound [46]0.1340.7930.9670.9810.4710.0420.1280.8760.9530.9934.2360.051
BrecQ [36]0.1280.8170.9800.9960.4520.0400.1040.9000.9770.9933.9140.047
Ours0.1030.8990.9870.9960.3800.0420.0920.9160.9810.9953.6820.046
minmax [27]W4A41.2650.1300.2850.4772.5930.1600.5840.0540.1600.32115.8770.245
ema [26]0.3710.3590.3590.8411.2260.1460.6320.0220.0810.22816.2650.244
percentile [11]0.3570.3660.6590.8461.2230.1460.6460.0190.0640.19716.3840.244
AdaRound [46]0.2510.4590.8120.9360.8480.1030.5010.2390.3680.53814.3980.216
BrecQ [36]0.2170.5980.8840.9700.7240.0710.4050.2780.4930.63412.3370.184
Ours0.1330.8150.9650.9900.4530.0520.1970.5340.9370.9855.4290.059
ViT-Large Backbone
\\Float320.0670.9720.9930.9970.2620.0400.0540.9740.9950.9992.5050.032
OBS [17]W40.0700.9720.9940.9980.2670.0380.0600.9680.9950.9982.7480.034
minmax [27]W4A80.6710.2790.5470.7481.4480.1440.5460.0550.1720.38514.8410.202
ema [26]0.6570.2890.5590.7561.4250.1410.3940.2190.4810.68612.0850.169
percentile [11]0.4250.3490.7150.9071.0730.1060.1920.6450.8830.9496.9570.093
AdaRound [46]0.0840.9590.9910.9970.2760.0400.0570.9720.9950.9992.7690.034
BrecQ [36]0.0760.9670.9930.9970.2720.0390.0570.9710.9950.9992.7780.034
Ours0.0710.9700.9930.9970.2640.0360.0550.9730.9950.9992.5420.032
minmax [27]W4A42.2380.1160.2490.3915.7610.2610.5650.0630.1900.36315.6930.253
ema [26]1.0390.1740.3760.5782.1260.1570.5080.1230.2940.46015.2060.247
percentile [11]0.9200.2070.4280.6311.9150.1570.4920.1440.3170.48715.0120.244
AdaRound [46]0.5010.2590.5640.7821.4820.1450.4820.1720.3950.54113.7820.207
BrecQ [36]0.4690.3300.6090.8111.3230.1370.4340.1910.4070.59013.4620.192
Ours0.0970.9320.9930.9980.3270.0450.0700.9520.9930.9983.1040.038
", + "bbox": [ + 94, + 88, + 906, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Main results of Metric3D model with ViT-Small and ViT-Large backbone on NYUv2 and KITTI datasets. Results with ViT-Giant backbone is included in Table A1 at Appendix 10.", + "bbox": [ + 89, + 559, + 906, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in Vector Computing Unit (VCU). In the VCU, we design a programmable vector computation array composed of multiple FPU to enable more efficient computation. The FPU supports the Special Function Unit (SFU) through polynomial approximation [51], which achieves the computation of non-linear functions (e.g. $\\log_2$ and $\\exp$ ) within 3 to 5 clock cycles while maintaining ultra-high precision. For the activation polishing optimization discussed in Section 4.2, the FPU is further specifically designed to enhance execution efficiency. Compared to the NVIDIA GPU [48], the proposed SFU achieves nearly same accuracy, with only a 2 to 5 ULP (units in the last place) error. Meanwhile, the VCU supports multiple numerical format inputs, unifying them into Float32 for computation, and then converts these Float32 numbers into integers such as INT4 or INT8 as needed, which seamlessly integrates both floating-point and integer data types for efficient processing. Hence, the proposed quantization framework for MDE models with ac", + "bbox": [ + 88, + 613, + 485, + 888 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tivation polishing optimization is accurately and efficiently deployed on our hardware.", + "bbox": [ + 511, + 613, + 906, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Overlapped Computation Flow", + "text_level": 1, + "bbox": [ + 511, + 651, + 790, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our hardware architecture supports kernel fusion of on-chip matrix multiplication and vector computation, enabling intermediate results stored in local SRAM to be directly sent to the VCU for activation, quantization, or dequantization without being written back to DDR. By fusing these operations into a single flow, we minimize the latency introduced by multiple memory accesses. Also, this design reduces data transfer time and enhances the overall execution efficiency. Furthermore, our hardware is designed to be programmable with customized instructions, enabling the configuration of different computational tasks to be executed concurrently within an instruction cycle. This parallelism enables a substantial speedup in processing by allowing multiple operations to be pipelined, thereby reducing the total time needed to complete complex tasks. As shown in Figure 7, data trans", + "bbox": [ + 509, + 674, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11453", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ferring, matrix computation, and vector computation can be fully overlapped to improve execution efficiency. This concurrency ensures that no computational resource is idle and every cycle is utilized to its maximum potential, leading to a streamlined and optimized workflow. Therefore, the total on-device latency of the depth estimation model executed with our quantization framework is optimized through extensive operator fusion and concurrent execution.", + "bbox": [ + 89, + 90, + 480, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ee7b1aae37539988b3fce184a81a88dc6c84959de08d23fe8bca98f407e10a50.jpg", + "image_caption": [ + "Figure 7. The schematic of concurrent execution, where the computation of Matrix, Vector, Load and Store can execute parallel." + ], + "image_footnote": [], + "bbox": [ + 91, + 223, + 483, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 383, + 295, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 89, + 409, + 266, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We adopt Metric3D [95] with ViT-Small, ViT-Large, and ViT-Giant [15] backbones to present the main results and Depth Anything [90] with ViT-Large backbone to further verify the generalization across additional datasets. For a fair comparison, we adopt per-channel asymmetric quantization for both weights and activations in W4A8 and W4A4 configurations. We randomly sample 32 images as calibration set from the training sets of NYUv2 [47] for indoor scenes and KITTI [19] for outdoor scenes. The percentile $\\epsilon$ for the polishing factor is set to 95, and $\\alpha$ is then computed as the average value across the calibration samples. For activation loss compensation and weight reconstruction, we still use same 32 samples for the calibration. For gradient computation in weight reconstruction, we adopt batch size of 1, learning rate set to 4e-5, warm up of 0.2, weight decay of 0.01, drop rate of 0.5, and 20,000 iterations. For evaluation, we use NYUv2 [47], SUN RGB-D [67], iBims-1 [32], and HyperSim [58] for indoor scenes; and KITTI [19], vKITTI [7], and DIODE [75] for outdoor scenes. Absolute relative error (AbsRel), accuracy under threshold $(\\delta_i < 1.25^i, i = 1, 2, 3)$ , root mean squared error (RMSE), and metric-depth loss (Silog) metrics are employed in our evaluation results.", + "bbox": [ + 89, + 430, + 483, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Hardware Implementation", + "text_level": 1, + "bbox": [ + 89, + 772, + 333, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We implement our hardware in RTL and synthesis the design using Design Compiler [70] under a commercial 28nm CMOS technology. The frequency and area are tested by the Design Compiler and the power is tested by Prime Time [71] PX with synthesized netlist and dynamic simulation switch rate under different modes. After synthesis, based on the latency profiled by simulation and the frequency given by", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Design Compiler, we introduce a hardware performance emulator for latency test. The DDR is simulated by RTL, with a bandwidth of 19.2 GB/s.", + "bbox": [ + 511, + 90, + 906, + 136 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Depth Estimation Results", + "text_level": 1, + "bbox": [ + 511, + 146, + 746, + 162 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present the quantization results with W4A8 and W4A4 configurations using Metric3D [95] with ViT-Small and ViT-Large backbone on indoor dataset NYUv2 [47] and outdoor dataset KITTI [19] in Table 1. The results with ViT-Giant backbone are included in Table A1 at Appendix 10. Compared to conventional PTQ methods such as minmax [27], EMA [26], and percentile [11], our framework demonstrates significantly improved performance. Additionally, when benchmarked against other learning-based approaches including OBS [17], AdaRound [46], and BrecQ [36], our method also achieves superior results. Notably, for the ViT-Large backbone with W4A8 settings, our method maintains nearly lossless performance. In the W4A4 configuration, our approach shows a substantial performance advantage over other methods, validating the effectiveness of our proposed quantization framework. Meanwhile, we present results of Depth Anything model with ViT-Large backbone on various additional datasets [7, 32, 58, 67, 75] covering both indoor and outdoor scenes, as shown in Table 2. Our method, which applies quantization to both weights and activations, achieves performance comparable to OBS (a weight-only quantization method) across multiple datasets in W4A8 configuration, and outperforms the BrecQ for all configurations, showing the effectiveness of our proposed quantization method.", + "bbox": [ + 511, + 169, + 908, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.4. Latency Results on ASIC", + "text_level": 1, + "bbox": [ + 511, + 542, + 743, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present the latency results of Metric3D with detailed hardware resource utility in Table 3. The latency is tested with three different resolutions. The power is further normalized by the latency and computation cost (i.e., GMACs) for the energy efficiency. For three different configurations, the frequency are uniformly $1\\mathrm{GHz}$ . The silicon area that our design occupies on a chip for Float32, W4A8, and W4A4 is $29.22\\mathrm{mm}^2$ , $23.94\\mathrm{mm}^2$ , and $24.35\\mathrm{mm}^2$ , respectively. As shown in Table 3, our proposed method demonstrates superior performance with faster inference speed and higher power efficiency across various model scales and resolutions. Notably, for ViT-Small backbone at 256 resolution under W4A4 configuration, our method achieves up to 26 FPS, showing the real-time performance.", + "bbox": [ + 511, + 565, + 908, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.5. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 787, + 666, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We regulate the number of calibration samples to verify the effectiveness of our proposed method, and the results are shown in Figure 8. We observe that the model performance stabilizes when the number of calibration samples reaches 32 for both W4A4 and W4A8 configuration. Additionally, activation compensation proves crucial for the W4A4.", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11454", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0fe8a442b931d4b8901ac001b99a58f50342462c0faae28d48c635d6809e4a35.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
W/ADataset MethodNYUv2 [47]SUN RGB-D [67]iBims-1 [32]HyperSim [58]KITTI [19]vKITTI2 [19]DIODE Outdoor [75]
AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑
\\Float320.0560.9840.5000.6600.1500.7140.3280.5080.0460.9820.0840.9120.7990.289
W4OBS [17]0.0590.9810.5080.6260.1510.7180.3270.5010.0490.9800.0910.8930.7930.287
W4A8BrecQ [36]0.0990.9030.4890.6920.1830.5930.3770.3720.0510.9510.6060.1320.7990.010
Ours0.0580.9820.3940.7560.1570.7000.3220.5230.0600.9650.1080.8460.8320.298
W4A4BrecQ [36]0.3420.2960.3960.4160.4190.2220.7030.0470.3850.2350.7570.0090.7650.034
Ours0.0700.9720.4660.7420.1770.6150.3220.5120.0590.9350.1000.8820.7580.280
", + "bbox": [ + 94, + 88, + 906, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f963739287c9b0bdc178b8e460f5f0089933e7dc17526d982a4fcf67085390dc.jpg", + "table_caption": [ + "Table 2. Main results of Depth Anything model with ViT-Large backbone. The first four sets are indoor scenes, while the last three are outdoor scenes. Full detailed results are included in Table A2 at Appendix 10." + ], + "table_footnote": [], + "table_body": "
W / ASize (MB)Res.Latency (ms) ↓FPS ↑Power Eff. (GMAC/W) ↑
ViT-Small
Float32143.125676.8 (1×)13.02 (1×)85.6 (1×)
W4A817.8842.6 (1.8×)23.47 (1.8×)172.8 (2.0×)
W4A438.3 (2.0×)26.11 (2.0×)177.5 (2.1×)
Float32143.1512325.5 (1×)3.07 (1×)87.3 (1×)
W4A817.88159.0 (2.0×)6.29 (2.0×)200.1 (2.3×)
W4A4133.4 (2.4×)7.50 (2.4×)220.3 (2.5×)
Float32143.110242181.4 (1×)0.46 (1×)78.4 (1×)
W4A817.88836.8 (2.6×)1.20 (2.6×)228.9 (2.9×)
W4A4616.7 (3.5×)1.62 (3.5×)287.0 (3.7×)
ViT-Large
Float321572256584.1 (1×)1.71 (1×)118.2 (1×)
W4A8196.5223.5 (2.6×)4.47 (2.6×)331.1 (2.8×)
W4A4167.9 (3.5×)5.96 (3.5×)425.4 (3.6×)
Float3215725122214.5 (1×)0.45 (1×)126.4 (1×)
W4A8196.5798.4 (2.8×)1.25 (2.8×)392.5 (3.1×)
W4A4568.5 (3.9×)1.76 (3.9×)509.3 (4.0×)
Float321572102413297.1 (1×)0.08 (1×)126.9 (1×)
W4A8196.54228.3 (3.1×)0.24 (3.1×)446.8 (3.5×)
W4A42725.1 (4.9×)0.37 (4.9×)640.6 (5.0×)
", + "bbox": [ + 94, + 271, + 480, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. ASIC results of Metric3D with ViT-Small and ViT-Large. ViT-Giant results are shown in Table A3 at Appendix 10.", + "bbox": [ + 89, + 575, + 482, + 604 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/896dba8aa1482d1300b2f104974dbb65727bca6a90846d45ad53ed72bd6027bb.jpg", + "image_caption": [ + "Figure 8. Accuracy ablation for the number of calibration samples using ViT-Large backbone on NYUv2 dataset." + ], + "image_footnote": [], + "bbox": [ + 89, + 616, + 483, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further perform ablation study on hardware resources by varying the number of MMUs and VCUs (i.e., number of cores). The results of 2, 4 and 8 cores are presented in Figure 9. The results show that more cores lead to faster speed. Compared to the Float32 model, the quantized model", + "bbox": [ + 89, + 825, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11d8dc23b72083ff2c54d486cca624b5c1ebda24b626d61fda6d7d8d97af6731.jpg", + "image_caption": [ + "Figure 9. Latency ablation for different number of cores using ViT-Large backbone with 256x256 resolution." + ], + "image_footnote": [], + "bbox": [ + 513, + 268, + 906, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is not sensitive to the hardware resource and achieves high hardware efficiency.", + "bbox": [ + 511, + 481, + 906, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Meanwhile, we also visualize depth estimation results of Metric3D with ViT-Large backbone in Figure A1 at Appendix 11 compared with BrecQ [36] on NYUv2 [47] for indoor scene and KITTI [19] for outdoor scene. The visualizations verify the effectiveness of our methods on both indoor and outdoor scenes.", + "bbox": [ + 511, + 513, + 908, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 626, + 633, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose QuartDepth, a quantization framework for the real-time acceleration of MDE models on ASICs. We provide the LogNP polishing method to smooth the outliers in the decoder of MDE models, and provide the compensation method to mitigate the loss of activation quantization. We then introduce the weight reconstruction to reduce the weight quantization loss. Furthermore, we design a novel flexible and programmable hardware accelerator for our efficient deployment on ASICs. Experimental results verify the effectiveness of our proposed framework.", + "bbox": [ + 511, + 654, + 908, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgment", + "text_level": 1, + "bbox": [ + 511, + 827, + 684, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was mainly supported by Northeastern University and Nanjing University. This work was also supported by National Natural Science Foundation of China 62472104.", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11455", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ibraheem Alhashim and Peter Wonka. 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Pruning foundation models for high accuracy without retraining. In Findings of EMNLP 2024, pages 9681-9694. ACL, 2024. 2", + "bbox": [ + 516, + 92, + 905, + 148 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "11460", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2025/QuartDepth_ Post-Training Quantization for Real-Time Depth Estimation on the Edge/7bffb5f3-e473-422d-9ee3-fd3a6408a1a4_model.json b/2025/QuartDepth_ Post-Training Quantization for Real-Time Depth Estimation on the Edge/7bffb5f3-e473-422d-9ee3-fd3a6408a1a4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0a2eb1f0cabb58b1c2752437c03a546b1cd5df35 --- /dev/null +++ b/2025/QuartDepth_ Post-Training Quantization for Real-Time Depth Estimation on the Edge/7bffb5f3-e473-422d-9ee3-fd3a6408a1a4_model.json @@ -0,0 +1,3031 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.274, + 0.131, + 0.726, + 0.177 + ], + "angle": 0, + "content": "QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.203, + 0.816, + 0.293 + ], + "angle": 0, + "content": "Xuan Shen\\(^{1}\\), Weize Ma\\(^{2}\\), Jing Liu\\(^{3}\\), Changdi Yang\\(^{1}\\), Rui Ding\\(^{2}\\), Quanyi Wang\\(^{4}\\), Henghui Ding\\(^{5}\\), Wei Niu\\(^{6}\\), Yanzhi Wang\\(^{1}\\), Pu Zhao\\(^{1*}\\), Jun Lin\\(^{2*}\\), Jiuming Gu\\(^{7*}\\) \n\\(^{1}\\)Northeastern University, \\(^{2}\\)Nanjing University, \\(^{3}\\)Monash University, \\(^{4}\\)Nanjing University of Information Science and Technology, \\(^{5}\\)Fudan University, \\(^{6}\\)University of Georgia, \\(^{7}\\)Adobe Research" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.295, + 0.804, + 0.327 + ], + "angle": 0, + "content": "{shen.xu, yanz.wang, p.zhao}@northeastern.edu, weizema@smail.nju.edu.cn, jlin@nju.edu.cn, jigu@adobe.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.362, + 0.327, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.395, + 0.486, + 0.789 + ], + "angle": 0, + "content": "Monocular Depth Estimation (MDE) has emerged as a pivotal task in computer vision, supporting numerous real-world applications. However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose Quart-Depth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.819, + 0.222, + 0.835 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.845, + 0.485, + 0.877 + ], + "angle": 0, + "content": "Monocular Depth Estimation (MDE) is a critical task in computer vision, essential for a wide range of applications" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.361, + 0.907, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.543, + 0.909, + 0.573 + ], + "angle": 0, + "content": "Figure 1. Visualization of accuracy vs. latency on ASIC for monocular depth estimation models with different backbones." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.599, + 0.909, + 0.795 + ], + "angle": 0, + "content": "including robotics [82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105]. The objective of MDE is to estimate depth information from a single image, making it particularly valuable for scenarios where stereo or multi-view depth sensors are impractical. Previously, depth estimation methods have been classified into three main approaches: learning metric depth [3, 89, 91, 99], learning relative depth [8, 9, 86, 87], and learning affine-invariant depth [54, 56, 93, 94, 105]. Among these, metric depth methods have demonstrated remarkable performance across benchmarks but often show limited generalizability to diverse, real-world images, which is compounded by variations in camera parameters between training and test sets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recently, inspired by the rise of \"foundation models\" [5, 107], a new wave of MDE models [4, 66, 90, 95] has been developed. These foundational MDE models exhibit superior generalization and robustness, effectively extending their applicability to in-the-wild images and accommodating a wide array of camera parameters. However, while these foundational MDE models achieve impressive performance," + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.239, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11448" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.484, + 0.499 + ], + "angle": 0, + "content": "they rely on sophisticated and computationally intensive algorithms. This reliance on complex architectures and operations significantly increases computational costs, making such models resource-heavy and challenging to deploy on edge devices or specialized hardware such as Application-Specific Integrated Circuits (ASICs) [35, 52, 81, 82]. The high computational demands also hinder real-time performance and scalability, which are critical for practical applications such as autonomous navigation [2], robotic perception [80], and augmented reality [68]. This constraint underscores the need for more efficient approaches that can maintain high accuracy while reducing computational overhead. Among common techniques like pruning [16, 64, 82, 106], knowledge distillation [18, 50], and architecture optimization [1, 37, 38, 63, 85, 101], which mainly reduce model complexity, quantization [11, 36, 46, 79] stands out for achieving both compactness and speed. Quantization [14, 39, 41, 84, 100] reduces weights and activations to lower bit-widths (e.g., 4-bit or 8-bit integers), minimizing model size while accelerating inference through optimized integer kernels specifically designed for edge devices. This dual benefit makes it ideal for deploying high-performing models on resource-limited edge hardware. Given the complexity of large foundational MDE models and their extensive datasets [31, 34, 98], we employ Post-Training Quantization (PTQ) [36, 41, 62, 100, 108] to facilitate efficient deployment without retraining." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.505, + 0.484, + 0.881 + ], + "angle": 0, + "content": "In this paper, we propose QuartDepth, a post-training quantization framework designed for real-time depth estimation on edge devices. We begin by analyzing the outlier deviant distribution in MDE foundation models [90, 95]. Through an in-depth per-channel analysis of these abnormal distributions, we identify persistent extreme outliers in the depth decoders. To address this, we propose the LogNP polishing optimization method to smooth the outliers and transform the abnormal distribution into a more quantization-friendly, normalized distribution. Furthermore, to mitigate the loss from activation quantization, we employ a compensation algorithm that updates the weights to minimize the activation quantization error. Next we perform weight quantization with a weight reconstruction method that leverages gradients to minimize second-order weight quantization errors. Meanwhile, we design a novel flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, which enables direct processing of intermediate results and concurrent execution of computational tasks. In detail, we design specialized computation kernels for W4A4 and W4A8 configurations, which enables full utilization of external memory bandwidth. Also, we design a novel programmable vector computation array to support the proposed LogNP polishing optimization, effectively hiding its additional overhead." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.887, + 0.467, + 0.9 + ], + "angle": 0, + "content": "In summary, our contributions are outlined as follows," + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.092, + 0.907, + 0.151 + ], + "angle": 0, + "content": "1. We observe a challenging outlier deviant distribution for activations and propose the LogNP polishing for activation quantization, which transforms these outliers into a quantization-friendly, normalized distribution." + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.153, + 0.905, + 0.212 + ], + "angle": 0, + "content": "2. For weight quantization, we first update the weights to compensate the error of activation quantization, and then quantize the updated weights with weight reconstruction to minimize the second-order weight quantization error." + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.213, + 0.907, + 0.257 + ], + "angle": 0, + "content": "3. We develop a novel flexible and programmable hardware accelerator on ASICs corresponding to our proposed quantization methods." + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.258, + 0.907, + 0.303 + ], + "angle": 0, + "content": "4. Comprehensive experiments confirm the effectiveness of our QuartDepth framework with superior accuracy, real-time inference and higher power efficiency on ASICs." + }, + { + "type": "list", + "bbox": [ + 0.523, + 0.092, + 0.907, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.32, + 0.654, + 0.335 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.345, + 0.754, + 0.361 + ], + "angle": 0, + "content": "2.1. Efficient Depth Estimation" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.368, + 0.908, + 0.745 + ], + "angle": 0, + "content": "Depth estimation from a single color image has been a prominent research focus in the field of computer vision for over a decade. This task plays a critical role in various applications, including robotic perception [12, 13, 82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105], all of which require rapid and accurate depth perception. The demand for real-time processing in these applications highlights the necessity for efficient model deployment. To meet these requirements, advanced optimization techniques such as pruning [16, 42, 65, 82, 104], knowledge distillation [18, 50], and architecture optimization [1, 88, 108] have been adopted to compress and accelerate the model. However, previous research has primarily focused on relatively smaller models, which, while effective, do not match the scale and capability of foundational MDE models [90, 95]. These modern foundational MDE models [4, 66] have gained significant attention for their ability to achieve state-of-the-art performance and generalize effectively across diverse real-world scenarios. By leveraging massive datasets and advanced architectures, these models provide robust depth estimation at the cost of increased computational complexity and larger model sizes. Thus, there is an urgent need for new model compression and acceleration techniques specifically designed to meet real-time requirements on resource-limited edge devices." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.758, + 0.684, + 0.773 + ], + "angle": 0, + "content": "2.2. Hardware Design" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.781, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Deploying large foundational models on edge devices presents significant challenges due to stringent constraints on computation and memory access [69]. To tackle these issues, various optimization techniques [59-62, 83, 102, 103, 108] have been explored to reduce model size and computational overhead. However, models subjected to such aggressive optimizations often fail to achieve peak performance on general-purpose CPUs and GPUs [96]. In contrast, ASICs," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11449" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.087, + 0.488, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.22, + 0.489, + 0.264 + ], + "angle": 0, + "content": "Figure 2. Latency profiling for 3 different resolutions using Metric3D with ViT-Large backbone. Vector includes activation functions (e.g. ReLU) and element-wise addition and multiplication." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.29, + 0.487, + 0.518 + ], + "angle": 0, + "content": "optimized for specific models and algorithms, offer significant performance and energy efficiency gains, making them ideal for deploying large foundational models on edge devices [22, 23, 43, 53, 78, 96]. Early work, such as TPU [28], DNA [72], and Eyeriss [10], significantly improved inference speed and energy efficiency by focusing on specialized hardware designs tailored to the needs of deep learning models. Recent works [29, 30, 49, 73, 74] have proposed dedicated hardware architectures in ASICs to accelerate neural network inference. These ASIC architectures have significantly improved inference latency and energy efficiency through solutions such as quantization, sparsity, data flow reconstruction, and algorithm-hardware co-design [40]. Thus, to maximize potential of large foundational models, the advantages offered by ASICs make them platform of choice." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.533, + 0.322, + 0.55 + ], + "angle": 0, + "content": "3. Analysis and Motivation" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.558, + 0.263, + 0.574 + ], + "angle": 0, + "content": "3.1. Latency Profiling" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.58, + 0.487, + 0.807 + ], + "angle": 0, + "content": "To optimize edge device inference, we first profile the Float32 model to identify the most time-consuming components for targeted optimization. In detail, we implement the Metric3D [95] model with ViT-Large [15] backbone on a hardware performance emulator with our ASIC design. The latency profiling results in Figure 2 show that the matrix multiplication and convolution operations dominate the inference time, while non-linear operations like softmax and layer normalization contribute minimally. The vector operations include activation functions such as SiLU, ReLU, and GeLU, as well as element-wise addition and multiplication, which also contribute minimally to the overall latency. This motivates our focus on quantization and ASIC design for linear and convolution layers, keeping non-linear operations in floating point to preserve accuracy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.287, + 0.833 + ], + "angle": 0, + "content": "3.2.Deviant Distribution" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.486, + 0.902 + ], + "angle": 0, + "content": "We investigate the deviant distribution in MDE models from a per-channel perspective. In Figure 3, we visualize the outliers across various channels of an activation in the decoder [55] of the Metric3D model on NYUv2 dataset. We" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.906, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.22, + 0.909, + 0.248 + ], + "angle": 0, + "content": "Figure 3. Visualization of outliers in various channels at the decoder [55] of Metric3D model on NYUv2 dataset." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.263, + 0.907, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.37, + 0.909, + 0.4 + ], + "angle": 0, + "content": "Figure 4. Visualization for the activation data distribution of different channels in decoder with log frequency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.427, + 0.909, + 0.58 + ], + "angle": 0, + "content": "observe large amount of outliers and significant variability in outlier values across different channels, making per-tensor quantization challenging. This motivates the adoption of a per-channel quantization method to better handle these variations. However, for per-channel quantization, the presence of outliers that deviate significantly from the main data distribution, as shown in Figure 4, still leads to substantial quantization errors. Thus, smoothing these large outliers and integrating them into the main data distribution is crucial for maintaining model accuracy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.594, + 0.753, + 0.611 + ], + "angle": 0, + "content": "4. Quantization Framework" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.62, + 0.909, + 0.682 + ], + "angle": 0, + "content": "We first quantize the polished activations with LogNP polishing (Section 4.2). Then we update weights to compensate the loss of activation quantization (Section 4.3). Finally, we quantize updated weights (Section 4.4)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.693, + 0.644, + 0.71 + ], + "angle": 0, + "content": "4.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.909, + 0.762 + ], + "angle": 0, + "content": "Quantization. We mainly adopt the hardware-efficient PTQ methods. For uniform quantization, the quantize and dequantize operations for \\( x \\) can be defined as follows," + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.773, + 0.909, + 0.801 + ], + "angle": 0, + "content": "\\[\nx _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z p, 0, 2 ^ {k} - 1\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.815, + 0.909, + 0.833 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = s \\cdot \\left(x _ {q} - z\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.908, + 0.902 + ], + "angle": 0, + "content": "where \\( s \\) represents the scale and \\( zp \\) is the zero point. The operator \\( \\lfloor \\cdot \\rceil \\) indicates rounding to the nearest integer, and the CLIP function constrains values that fall outside the range of a \\( k \\)-bit integer." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11450" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.486, + 0.122 + ], + "angle": 0, + "content": "As for Log2 quantization, which is mainly used for post-softmax quantization, can be defined as follows," + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.133, + 0.484, + 0.162 + ], + "angle": 0, + "content": "\\[\nx _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor - \\log_ {2} \\frac {x}{s} \\right\\rceil , 0, 2 ^ {k} - 1\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.241, + 0.175, + 0.484, + 0.19 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = s \\cdot 2 ^ {- x _ {q}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.2, + 0.485, + 0.262 + ], + "angle": 0, + "content": "Notations. The quantized layers (including both linear and convolutional layers) in the mode are indexed by \\(l\\), \\(1 \\leq l \\leq L\\). The weights in the \\(l^{th}\\) layer are denoted by \\(\\mathbf{W}^{(l)}\\) with its vectorized/flatened version \\(\\mathbf{w}^{(l)}\\). \\(\\mathbf{x}\\) denotes its inputs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.272, + 0.284, + 0.287 + ], + "angle": 0, + "content": "4.2. Activation Polishing" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.295, + 0.485, + 0.386 + ], + "angle": 0, + "content": "Building on analysis in Section 3.2, we propose LogNP polishing method to adaptively smooth the deviant distribution in decoders in per-channel prospective. For one activation \\(\\mathbf{x} \\in \\mathbb{R}^{n \\times d}\\) where \\(n\\) denotes the number of tokens and \\(d\\) denotes the channel number, the LogNP polishing function \\(\\Phi(\\cdot, \\cdot)\\) for each element \\(x\\) of input \\(\\mathbf{x}\\) is defined as follows," + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.398, + 0.484, + 0.416 + ], + "angle": 0, + "content": "\\[\n\\Phi (x, \\alpha) = \\operatorname {s i g n} (x) \\cdot \\left[ \\log_ {2} (| x | + \\alpha) - \\log_ {2} (\\alpha) \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.428, + 0.484, + 0.457 + ], + "angle": 0, + "content": "where \\(\\mathrm{sign}(\\cdot)\\) denotes the sign function, and \\(\\alpha\\) is the polishing factor for one single channel." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.459, + 0.485, + 0.519 + ], + "angle": 0, + "content": "To reduce the quantization error in each channel, the polishing factor \\(\\alpha_{i}\\) corresponding to the \\(i^{th}\\) channel with activation \\(\\mathbf{x}_i\\) (i.e., \\(\\mathbf{x} = [\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_d]\\)) is computed according to the given percentile \\(\\epsilon\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.533, + 0.484, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} = P _ {\\epsilon} \\left(\\mathbf {x} _ {i}\\right), i \\in \\{1, 2, 3, \\dots , d \\}, \\epsilon \\in (0, 1 0 0) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.562, + 0.484, + 0.713 + ], + "angle": 0, + "content": "where \\( P_{\\epsilon}(\\cdot) \\) denotes the \\( \\epsilon \\)-th percentile function. We adopt uniform \\( \\epsilon \\) equals to 95 as deviant activation distributions remain similar across different inputs. We provide the visualization of the polished activation in Figure 5. The polished activation colored in blue appears smoother compared to the original activation colored in red shown in Figure 4, making it more friendly for quantization. After polishing, we perform activation quantization with uniform quantization in Section 4.1. Following activation dequantization, we adopt reverse transformation (i.e., unpolishing) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.725, + 0.484, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\Phi^ {- 1} (\\hat {x}, \\alpha) = \\operatorname {s i g n} (\\hat {x}) \\cdot \\left[ 2 ^ {\\operatorname {s i g n} (\\hat {x}) \\cdot \\hat {x} + \\log_ {2} (\\alpha)} - \\alpha \\right] \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.761, + 0.486, + 0.807 + ], + "angle": 0, + "content": "The latency overhead introduced by LogNP polishing and unpolishing is hidden by concurrent execution in our hardware design, which is further explained in Section 5.2." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.363, + 0.835 + ], + "angle": 0, + "content": "4.3. Activation Loss Compensation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.485, + 0.902 + ], + "angle": 0, + "content": "The activation quantization introduces quantization errors. To mitigate this issue, before weight quantization, we first update all weights to compensate the loss of activation quantization. To save the computation cost, we address the problem" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.088, + 0.906, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.195, + 0.906, + 0.223 + ], + "angle": 0, + "content": "Figure 5. Visualization for the polished activation data distribution of different channels in decoder with log frequency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.906, + 0.279 + ], + "angle": 0, + "content": "layer by layer instead of for the whole model. The layer-wise compensation problem is formulated as the following," + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.289, + 0.907, + 0.312 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Delta \\mathbf {W}} \\| \\mathbf {W} \\mathbf {x} - (\\mathbf {W} + \\Delta \\mathbf {W}) \\hat {\\mathbf {x}} \\| _ {2} ^ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.322, + 0.907, + 0.397 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}\\) and \\(\\mathbf{x}\\) are the original weights and inputs of the layer. \\(\\hat{\\mathbf{x}}\\) is the quantized inputs and we update the weights with \\(\\Delta \\mathbf{W}\\) to compensate the activation quantization error, so that the layer outputs after activation quantization and weight compensation should be close to the original outputs." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.397, + 0.907, + 0.427 + ], + "angle": 0, + "content": "This problem can be solved by setting the gradients of the minimization objective to zero, as the following," + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.437, + 0.907, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\Delta \\mathbf {W} \\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}} + \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} = 0. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.466, + 0.783, + 0.481 + ], + "angle": 0, + "content": "The optimal solution can be obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.49, + 0.907, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\Delta \\mathbf {W} ^ {*} = - \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} \\left(\\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}}\\right) ^ {- 1} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.907, + 0.595 + ], + "angle": 0, + "content": "After activation quantization, we can update weights with the above \\(\\Delta \\mathbf{W}^*\\) to compensate the activation quantization error. If \\(\\hat{\\mathbf{x}}\\hat{\\mathbf{x}}^{\\mathrm{T}}\\) is not full rank with difficulties for matrix inversion, we adopt the dampening technique [21, 45]. Next, we quantize the updated weights under the quantized activations." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.726, + 0.619 + ], + "angle": 0, + "content": "4.4. Weight Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.907, + 0.717 + ], + "angle": 0, + "content": "Problem formulation. In quantization, the weights are modified and we would like to minimize the change of loss incurred by quantization to maintain the superior performance of the model. To quantitatively analyze the loss degradation by quantization, we approximate the loss degradation with Taylor expansion as the following," + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.726, + 0.907, + 0.785 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L (\\mathbf {w} + \\Delta \\mathbf {w}) - L (\\mathbf {w}) \\approx \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {g} _ {\\mathbf {w}} + \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\\\ \\approx \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{g}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}L\\) represents the gradients and \\(\\mathbf{H}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}^{2}L\\) denotes the Hessian matrix. \\(\\Delta \\mathbf{w}\\) is the weight perturbation in this step. Here we use the vectorized/flatened version \\(\\mathbf{w}\\) instead of the matrix version \\(\\mathbf{W}\\) to obtain a scalar output. As the pre-trained model has been well trained and converged to a minimum, it is reasonable to assume the gradients to be 0. The complexity to obtain the full Hessian is very high" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11451" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.166 + ], + "angle": 0, + "content": "and typically it is not possible to obtain the full Hessian due to computation and memory limitations. Specifically, \\(\\mathbf{H}_{\\mathbf{w}} \\in \\mathbb{R}^{B \\times B}\\) where \\(B\\) is the number of parameters in \\(\\mathbf{w}\\). The memory cost for \\(\\mathbf{H}_{\\mathbf{w}}\\) is extremely heavy in LLMs with billions of parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.167, + 0.486, + 0.209 + ], + "angle": 0, + "content": "Approximating Hessian. For a network trained with negative log-likelihood loss and a probabilistic model \\( p_{\\mathbf{w}}(y|x_s) \\) under softmax, the Hessian is identical to the Fisher matrix:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.219, + 0.483, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {H} _ {\\mathbf {w}} = \\mathbf {F} _ {\\mathbf {w}} = \\sum_ {s = 1} ^ {S} \\mathbb {E} _ {y \\sim p _ {\\mathbf {w}} (y | x _ {s})} [ \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} (y | x _ {s}) \\\\ \\left. \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} \\left(y \\mid x _ {s}\\right) ^ {T} \\right] \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.274, + 0.485, + 0.426 + ], + "angle": 0, + "content": "where \\(S\\) is the number of samples, and for each sample, it needs to compute the expectation over all categories. The complexity with the expectation is also high if there are too many categories. Thus, in practice, the empirical Fisher is commonly adopted to replace the expectation over \\(y\\) with target label \\(y_{s}\\) [33]. The dimension of \\(\\mathbf{F}_{\\mathbf{w}}\\) is the same as \\(\\mathbf{H}_{\\mathbf{w}}\\) with quadratic memory complexity to the number of parameters. To reduce the complexity, the empirical Fisher is computed by treating layers independently and the layer-wise empirical Fisher can be obtained as below [6, 44]," + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.437, + 0.484, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {l} = \\mathbb {E} \\left[ \\left(\\mathbf {g} ^ {(l)} \\mathbf {g} ^ {(l), \\mathrm {T}}\\right) \\otimes \\left(\\hat {\\mathbf {x}} ^ {(l)} \\hat {\\mathbf {x}} ^ {(l), \\mathrm {T}}\\right) \\right], \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.484, + 0.522 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{x}}^{(l)}\\) is the input activations and \\(\\mathbf{g}^{(l)}\\) is the gradients of the \\(l^{th}\\) layer. \\(\\otimes\\) denotes Kronecker product. The expectation is taken with respect to data distribution over inputs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.523, + 0.484, + 0.572 + ], + "angle": 0, + "content": "For two different layers (for example, the \\(i^{th}\\) and the \\(j^{th}\\) layers), their Fisher is often written as \\(\\mathbf{F}_{ij} = \\sum_{s=1}^{S} \\mathbb{E}\\left[\\nabla_{\\mathbf{w}^{(i)}} \\log p_{\\mathbf{w}}(y_s | x_s) \\nabla_{\\mathbf{w}^{(j)}} \\log p_{\\mathbf{w}}(y_s | x_s)^T\\right]\\)," + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.572, + 0.484, + 0.616 + ], + "angle": 0, + "content": "which are often ignored to save computations. The Fisher for the whole model can be formulated as a block diagonal matrix \\(\\mathbf{F}_{\\mathbf{w}} = \\mathrm{diag}(\\mathbf{F}_1,\\mathbf{F}_2,\\dots ,\\mathbf{F}_L)\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.617, + 0.484, + 0.647 + ], + "angle": 0, + "content": "To obtain the Fisher in practice, we adopt the KFAC approximation method [20, 44] as below," + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.66, + 0.483, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {l} = \\mathbf {G} _ {l} \\otimes \\mathbf {A} _ {l} \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.679, + 0.483, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\mathbf {g} _ {s} ^ {(l)} \\mathbf {g} _ {s} ^ {(l), \\mathrm {T}} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.713, + 0.483, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\hat {\\mathbf {x}} _ {s} ^ {(l)} \\hat {\\mathbf {x}} _ {s} ^ {(l). \\mathrm {T}} \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.755, + 0.485, + 0.83 + ], + "angle": 0, + "content": "The KFAC approximation [25, 76] approximates an expectation of Kronecker products as a Kronecker product of two expectations \\(\\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}\\otimes \\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]\\approx \\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}]\\otimes\\) \\(\\mathbb{E}[\\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]\\), where the activations and derivatives are assumed to be independent." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.831, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Optimizing quantization parameters. Next we optimize the quantization parameters. Given our optimization loss in Equation (11), multiple optimization methods can be adopted such as STE [24] and AdaRound [46]. Due to its superior performance in PTQ, we use AdaRound [46] to learn the" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.088, + 0.907, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.25, + 0.907, + 0.265 + ], + "angle": 0, + "content": "Figure 6. The block diagram of the proposed hardware accelerator." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.908, + 0.32 + ], + "angle": 0, + "content": "rounding parameter which decides rounding up or down. Formally, we minimize the following loss," + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.327, + 0.907, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {v}} \\sum_ {l = 1} ^ {L} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) ^ {\\mathrm {T}} \\mathbf {F} _ {l} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) + \\lambda h (\\mathbf {v}), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.372, + 0.907, + 0.463 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}\\) denotes the rounding parameter which are used to construct the quantized weights \\(\\hat{\\mathbf{w}}^{(l)}\\). \\(h(\\mathbf{v})\\) is a regularizer in AdaRound [46] with \\(\\lambda\\) controlling its strength. More details about AdaRound are presented in Appendix 9. We only use a small calibration set (32 samples) sampled from the training dataset to calibrate the quantized model." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.476, + 0.686, + 0.493 + ], + "angle": 0, + "content": "5. Hardware Design" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.5, + 0.684, + 0.517 + ], + "angle": 0, + "content": "5.1. Top-Level Design" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.523, + 0.909, + 0.705 + ], + "angle": 0, + "content": "We design a flexible and programmable accelerator as shown in Figure 6. The Dispatch module fetches instructions via the AXI bus and distributes them to local Instruction FIFOs, while the Synchronize module controls the start and end of each module. Instruction FIFOs hold out-of-order instructions and are controlled by Synchronize module for execution. The Load and Store modules, functioning as the DMA, facilitate data transfer between off-chip memory (e.g., HBM or DDR) and local buffers. The Matrix Multiplication Unit (MMU) performs General Matrix Multiply (GeMM) and convolution when the Vector Compute Unit (VCU) handles nonlinear activation functions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.733, + 0.729 + ], + "angle": 0, + "content": "5.2. On-Chip Kernel Design" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.908, + 0.871 + ], + "angle": 0, + "content": "We adopt a multiply-accumulate tree array to implement both matrix multiplication and convolution. For W4A4 and W4A8 configurations, we design specialized multipliers and adders to enhance computational efficiency and reduce chip area overhead. Additionally, the use of low-bit quantized matrices eases memory bandwidth demands during data transfer, allowing for full utilization of the external memory bandwidth. As for Float32, we implement IEEE 754 standard floating-point computation for fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.901 + ], + "angle": 0, + "content": "Meanwhile, we propose a programmable vector computation array composed of multiple Floating-Point Units (FPU)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11452" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.907, + 0.551 + ], + "angle": 0, + "content": "
MethodW/ANYUv2 [47]KITTI [19]
AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓
ViT-Small Backbone
\\Float320.0870.9380.9900.9960.3310.0350.0740.9340.9840.9953.4030.043
OBS [17]W40.1070.8850.9850.9970.3910.0420.1220.8670.9730.9914.5080.058
minmax [27]W4A80.4530.4050.7020.8681.0670.1110.4560.1020.3290.57513.3550.159
ema [26]0.2570.5910.8590.9580.7930.0930.3120.3410.6320.80711.1020.139
percentile [11]0.1900.6350.9120.9810.7740.0770.2220.5520.8140.9188.9000.114
AdaRound [46]0.1340.7930.9670.9810.4710.0420.1280.8760.9530.9934.2360.051
BrecQ [36]0.1280.8170.9800.9960.4520.0400.1040.9000.9770.9933.9140.047
Ours0.1030.8990.9870.9960.3800.0420.0920.9160.9810.9953.6820.046
minmax [27]W4A41.2650.1300.2850.4772.5930.1600.5840.0540.1600.32115.8770.245
ema [26]0.3710.3590.3590.8411.2260.1460.6320.0220.0810.22816.2650.244
percentile [11]0.3570.3660.6590.8461.2230.1460.6460.0190.0640.19716.3840.244
AdaRound [46]0.2510.4590.8120.9360.8480.1030.5010.2390.3680.53814.3980.216
BrecQ [36]0.2170.5980.8840.9700.7240.0710.4050.2780.4930.63412.3370.184
Ours0.1330.8150.9650.9900.4530.0520.1970.5340.9370.9855.4290.059
ViT-Large Backbone
\\Float320.0670.9720.9930.9970.2620.0400.0540.9740.9950.9992.5050.032
OBS [17]W40.0700.9720.9940.9980.2670.0380.0600.9680.9950.9982.7480.034
minmax [27]W4A80.6710.2790.5470.7481.4480.1440.5460.0550.1720.38514.8410.202
ema [26]0.6570.2890.5590.7561.4250.1410.3940.2190.4810.68612.0850.169
percentile [11]0.4250.3490.7150.9071.0730.1060.1920.6450.8830.9496.9570.093
AdaRound [46]0.0840.9590.9910.9970.2760.0400.0570.9720.9950.9992.7690.034
BrecQ [36]0.0760.9670.9930.9970.2720.0390.0570.9710.9950.9992.7780.034
Ours0.0710.9700.9930.9970.2640.0360.0550.9730.9950.9992.5420.032
minmax [27]W4A42.2380.1160.2490.3915.7610.2610.5650.0630.1900.36315.6930.253
ema [26]1.0390.1740.3760.5782.1260.1570.5080.1230.2940.46015.2060.247
percentile [11]0.9200.2070.4280.6311.9150.1570.4920.1440.3170.48715.0120.244
AdaRound [46]0.5010.2590.5640.7821.4820.1450.4820.1720.3950.54113.7820.207
BrecQ [36]0.4690.3300.6090.8111.3230.1370.4340.1910.4070.59013.4620.192
Ours0.0970.9320.9930.9980.3270.0450.0700.9520.9930.9983.1040.038
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.56, + 0.907, + 0.589 + ], + "angle": 0, + "content": "Table 1. Main results of Metric3D model with ViT-Small and ViT-Large backbone on NYUv2 and KITTI datasets. Results with ViT-Giant backbone is included in Table A1 at Appendix 10." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.614, + 0.486, + 0.889 + ], + "angle": 0, + "content": "in Vector Computing Unit (VCU). In the VCU, we design a programmable vector computation array composed of multiple FPU to enable more efficient computation. The FPU supports the Special Function Unit (SFU) through polynomial approximation [51], which achieves the computation of non-linear functions (e.g. \\(\\log_2\\) and \\(\\exp\\)) within 3 to 5 clock cycles while maintaining ultra-high precision. For the activation polishing optimization discussed in Section 4.2, the FPU is further specifically designed to enhance execution efficiency. Compared to the NVIDIA GPU [48], the proposed SFU achieves nearly same accuracy, with only a 2 to 5 ULP (units in the last place) error. Meanwhile, the VCU supports multiple numerical format inputs, unifying them into Float32 for computation, and then converts these Float32 numbers into integers such as INT4 or INT8 as needed, which seamlessly integrates both floating-point and integer data types for efficient processing. Hence, the proposed quantization framework for MDE models with ac" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.644 + ], + "angle": 0, + "content": "tivation polishing optimization is accurately and efficiently deployed on our hardware." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.652, + 0.792, + 0.669 + ], + "angle": 0, + "content": "5.3. Overlapped Computation Flow" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Our hardware architecture supports kernel fusion of on-chip matrix multiplication and vector computation, enabling intermediate results stored in local SRAM to be directly sent to the VCU for activation, quantization, or dequantization without being written back to DDR. By fusing these operations into a single flow, we minimize the latency introduced by multiple memory accesses. Also, this design reduces data transfer time and enhances the overall execution efficiency. Furthermore, our hardware is designed to be programmable with customized instructions, enabling the configuration of different computational tasks to be executed concurrently within an instruction cycle. This parallelism enables a substantial speedup in processing by allowing multiple operations to be pipelined, thereby reducing the total time needed to complete complex tasks. As shown in Figure 7, data trans" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11453" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.212 + ], + "angle": 0, + "content": "ferring, matrix computation, and vector computation can be fully overlapped to improve execution efficiency. This concurrency ensures that no computational resource is idle and every cycle is utilized to its maximum potential, leading to a streamlined and optimized workflow. Therefore, the total on-device latency of the depth estimation model executed with our quantization framework is optimized through extensive operator fusion and concurrent execution." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.224, + 0.485, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.327, + 0.485, + 0.357 + ], + "angle": 0, + "content": "Figure 7. The schematic of concurrent execution, where the computation of Matrix, Vector, Load and Store can execute parallel." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.385, + 0.296, + 0.403 + ], + "angle": 0, + "content": "6. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.41, + 0.267, + 0.426 + ], + "angle": 0, + "content": "6.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.485, + 0.765 + ], + "angle": 0, + "content": "We adopt Metric3D [95] with ViT-Small, ViT-Large, and ViT-Giant [15] backbones to present the main results and Depth Anything [90] with ViT-Large backbone to further verify the generalization across additional datasets. For a fair comparison, we adopt per-channel asymmetric quantization for both weights and activations in W4A8 and W4A4 configurations. We randomly sample 32 images as calibration set from the training sets of NYUv2 [47] for indoor scenes and KITTI [19] for outdoor scenes. The percentile \\(\\epsilon\\) for the polishing factor is set to 95, and \\(\\alpha\\) is then computed as the average value across the calibration samples. For activation loss compensation and weight reconstruction, we still use same 32 samples for the calibration. For gradient computation in weight reconstruction, we adopt batch size of 1, learning rate set to 4e-5, warm up of 0.2, weight decay of 0.01, drop rate of 0.5, and 20,000 iterations. For evaluation, we use NYUv2 [47], SUN RGB-D [67], iBims-1 [32], and HyperSim [58] for indoor scenes; and KITTI [19], vKITTI [7], and DIODE [75] for outdoor scenes. Absolute relative error (AbsRel), accuracy under threshold \\((\\delta_i < 1.25^i, i = 1, 2, 3)\\), root mean squared error (RMSE), and metric-depth loss (Silog) metrics are employed in our evaluation results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.773, + 0.334, + 0.79 + ], + "angle": 0, + "content": "6.2. Hardware Implementation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We implement our hardware in RTL and synthesis the design using Design Compiler [70] under a commercial 28nm CMOS technology. The frequency and area are tested by the Design Compiler and the power is tested by Prime Time [71] PX with synthesized netlist and dynamic simulation switch rate under different modes. After synthesis, based on the latency profiled by simulation and the frequency given by" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.137 + ], + "angle": 0, + "content": "Design Compiler, we introduce a hardware performance emulator for latency test. The DDR is simulated by RTL, with a bandwidth of 19.2 GB/s." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.147, + 0.747, + 0.164 + ], + "angle": 0, + "content": "6.3. Depth Estimation Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.17, + 0.909, + 0.533 + ], + "angle": 0, + "content": "We present the quantization results with W4A8 and W4A4 configurations using Metric3D [95] with ViT-Small and ViT-Large backbone on indoor dataset NYUv2 [47] and outdoor dataset KITTI [19] in Table 1. The results with ViT-Giant backbone are included in Table A1 at Appendix 10. Compared to conventional PTQ methods such as minmax [27], EMA [26], and percentile [11], our framework demonstrates significantly improved performance. Additionally, when benchmarked against other learning-based approaches including OBS [17], AdaRound [46], and BrecQ [36], our method also achieves superior results. Notably, for the ViT-Large backbone with W4A8 settings, our method maintains nearly lossless performance. In the W4A4 configuration, our approach shows a substantial performance advantage over other methods, validating the effectiveness of our proposed quantization framework. Meanwhile, we present results of Depth Anything model with ViT-Large backbone on various additional datasets [7, 32, 58, 67, 75] covering both indoor and outdoor scenes, as shown in Table 2. Our method, which applies quantization to both weights and activations, achieves performance comparable to OBS (a weight-only quantization method) across multiple datasets in W4A8 configuration, and outperforms the BrecQ for all configurations, showing the effectiveness of our proposed quantization method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.543, + 0.744, + 0.559 + ], + "angle": 0, + "content": "6.4. Latency Results on ASIC" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.909, + 0.779 + ], + "angle": 0, + "content": "We present the latency results of Metric3D with detailed hardware resource utility in Table 3. The latency is tested with three different resolutions. The power is further normalized by the latency and computation cost (i.e., GMACs) for the energy efficiency. For three different configurations, the frequency are uniformly \\(1\\mathrm{GHz}\\). The silicon area that our design occupies on a chip for Float32, W4A8, and W4A4 is \\(29.22\\mathrm{mm}^2\\), \\(23.94\\mathrm{mm}^2\\), and \\(24.35\\mathrm{mm}^2\\), respectively. As shown in Table 3, our proposed method demonstrates superior performance with faster inference speed and higher power efficiency across various model scales and resolutions. Notably, for ViT-Small backbone at 256 resolution under W4A4 configuration, our method achieves up to 26 FPS, showing the real-time performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.667, + 0.804 + ], + "angle": 0, + "content": "6.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We regulate the number of calibration samples to verify the effectiveness of our proposed method, and the results are shown in Figure 8. We observe that the model performance stabilizes when the number of calibration samples reaches 32 for both W4A4 and W4A8 configuration. Additionally, activation compensation proves crucial for the W4A4." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11454" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.908, + 0.21 + ], + "angle": 0, + "content": "
W/ADataset MethodNYUv2 [47]SUN RGB-D [67]iBims-1 [32]HyperSim [58]KITTI [19]vKITTI2 [19]DIODE Outdoor [75]
AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑
\\Float320.0560.9840.5000.6600.1500.7140.3280.5080.0460.9820.0840.9120.7990.289
W4OBS [17]0.0590.9810.5080.6260.1510.7180.3270.5010.0490.9800.0910.8930.7930.287
W4A8BrecQ [36]0.0990.9030.4890.6920.1830.5930.3770.3720.0510.9510.6060.1320.7990.010
Ours0.0580.9820.3940.7560.1570.7000.3220.5230.0600.9650.1080.8460.8320.298
W4A4BrecQ [36]0.3420.2960.3960.4160.4190.2220.7030.0470.3850.2350.7570.0090.7650.034
Ours0.0700.9720.4660.7420.1770.6150.3220.5120.0590.9350.1000.8820.7580.280
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.219, + 0.908, + 0.248 + ], + "angle": 0, + "content": "Table 2. Main results of Depth Anything model with ViT-Large backbone. The first four sets are indoor scenes, while the last three are outdoor scenes. Full detailed results are included in Table A2 at Appendix 10." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.272, + 0.481, + 0.566 + ], + "angle": 0, + "content": "
W / ASize (MB)Res.Latency (ms) ↓FPS ↑Power Eff. (GMAC/W) ↑
ViT-Small
Float32143.125676.8 (1×)13.02 (1×)85.6 (1×)
W4A817.8842.6 (1.8×)23.47 (1.8×)172.8 (2.0×)
W4A438.3 (2.0×)26.11 (2.0×)177.5 (2.1×)
Float32143.1512325.5 (1×)3.07 (1×)87.3 (1×)
W4A817.88159.0 (2.0×)6.29 (2.0×)200.1 (2.3×)
W4A4133.4 (2.4×)7.50 (2.4×)220.3 (2.5×)
Float32143.110242181.4 (1×)0.46 (1×)78.4 (1×)
W4A817.88836.8 (2.6×)1.20 (2.6×)228.9 (2.9×)
W4A4616.7 (3.5×)1.62 (3.5×)287.0 (3.7×)
ViT-Large
Float321572256584.1 (1×)1.71 (1×)118.2 (1×)
W4A8196.5223.5 (2.6×)4.47 (2.6×)331.1 (2.8×)
W4A4167.9 (3.5×)5.96 (3.5×)425.4 (3.6×)
Float3215725122214.5 (1×)0.45 (1×)126.4 (1×)
W4A8196.5798.4 (2.8×)1.25 (2.8×)392.5 (3.1×)
W4A4568.5 (3.9×)1.76 (3.9×)509.3 (4.0×)
Float321572102413297.1 (1×)0.08 (1×)126.9 (1×)
W4A8196.54228.3 (3.1×)0.24 (3.1×)446.8 (3.5×)
W4A42725.1 (4.9×)0.37 (4.9×)640.6 (5.0×)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.577, + 0.483, + 0.606 + ], + "angle": 0, + "content": "Table 3. ASIC results of Metric3D with ViT-Small and ViT-Large. ViT-Giant results are shown in Table A3 at Appendix 10." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.617, + 0.485, + 0.761 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.77, + 0.483, + 0.8 + ], + "angle": 0, + "content": "Figure 8. Accuracy ablation for the number of calibration samples using ViT-Large backbone on NYUv2 dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We further perform ablation study on hardware resources by varying the number of MMUs and VCUs (i.e., number of cores). The results of 2, 4 and 8 cores are presented in Figure 9. The results show that more cores lead to faster speed. Compared to the Float32 model, the quantized model" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.27, + 0.907, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.422, + 0.907, + 0.451 + ], + "angle": 0, + "content": "Figure 9. Latency ablation for different number of cores using ViT-Large backbone with 256x256 resolution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.482, + 0.907, + 0.514 + ], + "angle": 0, + "content": "is not sensitive to the hardware resource and achieves high hardware efficiency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.909, + 0.605 + ], + "angle": 0, + "content": "Meanwhile, we also visualize depth estimation results of Metric3D with ViT-Large backbone in Figure A1 at Appendix 11 compared with BrecQ [36] on NYUv2 [47] for indoor scene and KITTI [19] for outdoor scene. The visualizations verify the effectiveness of our methods on both indoor and outdoor scenes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.627, + 0.634, + 0.643 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.655, + 0.909, + 0.807 + ], + "angle": 0, + "content": "In this paper, we propose QuartDepth, a quantization framework for the real-time acceleration of MDE models on ASICs. We provide the LogNP polishing method to smooth the outliers in the decoder of MDE models, and provide the compensation method to mitigate the loss of activation quantization. We then introduce the weight reconstruction to reduce the weight quantization loss. Furthermore, we design a novel flexible and programmable hardware accelerator for our efficient deployment on ASICs. Experimental results verify the effectiveness of our proposed framework." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.828, + 0.686, + 0.846 + ], + "angle": 0, + "content": "8. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "This work was mainly supported by Northeastern University and Nanjing University. This work was also supported by National Natural Science Foundation of China 62472104." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11455" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.115, + 0.486, + 0.156 + ], + "angle": 0, + "content": "[1] Ibraheem Alhashim and Peter Wonka. 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However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose Quart-Depth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth + +# 1. Introduction + +Monocular Depth Estimation (MDE) is a critical task in computer vision, essential for a wide range of applications + +![](images/27a4440b701133d9e5301a2a2f232e4c92a81cd561616303da4cc024bef95b17.jpg) +Figure 1. Visualization of accuracy vs. latency on ASIC for monocular depth estimation models with different backbones. + +including robotics [82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105]. The objective of MDE is to estimate depth information from a single image, making it particularly valuable for scenarios where stereo or multi-view depth sensors are impractical. Previously, depth estimation methods have been classified into three main approaches: learning metric depth [3, 89, 91, 99], learning relative depth [8, 9, 86, 87], and learning affine-invariant depth [54, 56, 93, 94, 105]. Among these, metric depth methods have demonstrated remarkable performance across benchmarks but often show limited generalizability to diverse, real-world images, which is compounded by variations in camera parameters between training and test sets. + +Recently, inspired by the rise of "foundation models" [5, 107], a new wave of MDE models [4, 66, 90, 95] has been developed. These foundational MDE models exhibit superior generalization and robustness, effectively extending their applicability to in-the-wild images and accommodating a wide array of camera parameters. However, while these foundational MDE models achieve impressive performance, + +they rely on sophisticated and computationally intensive algorithms. This reliance on complex architectures and operations significantly increases computational costs, making such models resource-heavy and challenging to deploy on edge devices or specialized hardware such as Application-Specific Integrated Circuits (ASICs) [35, 52, 81, 82]. The high computational demands also hinder real-time performance and scalability, which are critical for practical applications such as autonomous navigation [2], robotic perception [80], and augmented reality [68]. This constraint underscores the need for more efficient approaches that can maintain high accuracy while reducing computational overhead. Among common techniques like pruning [16, 64, 82, 106], knowledge distillation [18, 50], and architecture optimization [1, 37, 38, 63, 85, 101], which mainly reduce model complexity, quantization [11, 36, 46, 79] stands out for achieving both compactness and speed. Quantization [14, 39, 41, 84, 100] reduces weights and activations to lower bit-widths (e.g., 4-bit or 8-bit integers), minimizing model size while accelerating inference through optimized integer kernels specifically designed for edge devices. This dual benefit makes it ideal for deploying high-performing models on resource-limited edge hardware. Given the complexity of large foundational MDE models and their extensive datasets [31, 34, 98], we employ Post-Training Quantization (PTQ) [36, 41, 62, 100, 108] to facilitate efficient deployment without retraining. + +In this paper, we propose QuartDepth, a post-training quantization framework designed for real-time depth estimation on edge devices. We begin by analyzing the outlier deviant distribution in MDE foundation models [90, 95]. Through an in-depth per-channel analysis of these abnormal distributions, we identify persistent extreme outliers in the depth decoders. To address this, we propose the LogNP polishing optimization method to smooth the outliers and transform the abnormal distribution into a more quantization-friendly, normalized distribution. Furthermore, to mitigate the loss from activation quantization, we employ a compensation algorithm that updates the weights to minimize the activation quantization error. Next we perform weight quantization with a weight reconstruction method that leverages gradients to minimize second-order weight quantization errors. Meanwhile, we design a novel flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, which enables direct processing of intermediate results and concurrent execution of computational tasks. In detail, we design specialized computation kernels for W4A4 and W4A8 configurations, which enables full utilization of external memory bandwidth. Also, we design a novel programmable vector computation array to support the proposed LogNP polishing optimization, effectively hiding its additional overhead. + +In summary, our contributions are outlined as follows, + +1. We observe a challenging outlier deviant distribution for activations and propose the LogNP polishing for activation quantization, which transforms these outliers into a quantization-friendly, normalized distribution. +2. For weight quantization, we first update the weights to compensate the error of activation quantization, and then quantize the updated weights with weight reconstruction to minimize the second-order weight quantization error. +3. We develop a novel flexible and programmable hardware accelerator on ASICs corresponding to our proposed quantization methods. +4. Comprehensive experiments confirm the effectiveness of our QuartDepth framework with superior accuracy, real-time inference and higher power efficiency on ASICs. + +# 2. Related Work + +# 2.1. Efficient Depth Estimation + +Depth estimation from a single color image has been a prominent research focus in the field of computer vision for over a decade. This task plays a critical role in various applications, including robotic perception [12, 13, 82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105], all of which require rapid and accurate depth perception. The demand for real-time processing in these applications highlights the necessity for efficient model deployment. To meet these requirements, advanced optimization techniques such as pruning [16, 42, 65, 82, 104], knowledge distillation [18, 50], and architecture optimization [1, 88, 108] have been adopted to compress and accelerate the model. However, previous research has primarily focused on relatively smaller models, which, while effective, do not match the scale and capability of foundational MDE models [90, 95]. These modern foundational MDE models [4, 66] have gained significant attention for their ability to achieve state-of-the-art performance and generalize effectively across diverse real-world scenarios. By leveraging massive datasets and advanced architectures, these models provide robust depth estimation at the cost of increased computational complexity and larger model sizes. Thus, there is an urgent need for new model compression and acceleration techniques specifically designed to meet real-time requirements on resource-limited edge devices. + +# 2.2. Hardware Design + +Deploying large foundational models on edge devices presents significant challenges due to stringent constraints on computation and memory access [69]. To tackle these issues, various optimization techniques [59-62, 83, 102, 103, 108] have been explored to reduce model size and computational overhead. However, models subjected to such aggressive optimizations often fail to achieve peak performance on general-purpose CPUs and GPUs [96]. In contrast, ASICs, + +![](images/a00c83984be3fdd5ed0073252265194f954786873afc4fe01942b5fa9432f9ec.jpg) +Figure 2. Latency profiling for 3 different resolutions using Metric3D with ViT-Large backbone. Vector includes activation functions (e.g. ReLU) and element-wise addition and multiplication. + +optimized for specific models and algorithms, offer significant performance and energy efficiency gains, making them ideal for deploying large foundational models on edge devices [22, 23, 43, 53, 78, 96]. Early work, such as TPU [28], DNA [72], and Eyeriss [10], significantly improved inference speed and energy efficiency by focusing on specialized hardware designs tailored to the needs of deep learning models. Recent works [29, 30, 49, 73, 74] have proposed dedicated hardware architectures in ASICs to accelerate neural network inference. These ASIC architectures have significantly improved inference latency and energy efficiency through solutions such as quantization, sparsity, data flow reconstruction, and algorithm-hardware co-design [40]. Thus, to maximize potential of large foundational models, the advantages offered by ASICs make them platform of choice. + +# 3. Analysis and Motivation + +# 3.1. Latency Profiling + +To optimize edge device inference, we first profile the Float32 model to identify the most time-consuming components for targeted optimization. In detail, we implement the Metric3D [95] model with ViT-Large [15] backbone on a hardware performance emulator with our ASIC design. The latency profiling results in Figure 2 show that the matrix multiplication and convolution operations dominate the inference time, while non-linear operations like softmax and layer normalization contribute minimally. The vector operations include activation functions such as SiLU, ReLU, and GeLU, as well as element-wise addition and multiplication, which also contribute minimally to the overall latency. This motivates our focus on quantization and ASIC design for linear and convolution layers, keeping non-linear operations in floating point to preserve accuracy. + +# 3.2.Deviant Distribution + +We investigate the deviant distribution in MDE models from a per-channel perspective. In Figure 3, we visualize the outliers across various channels of an activation in the decoder [55] of the Metric3D model on NYUv2 dataset. We + +![](images/e6521ca76e44b7f737bcd83cbe82ab27014c98ac8c84caa0ef8338c769c1a4a8.jpg) +Figure 3. Visualization of outliers in various channels at the decoder [55] of Metric3D model on NYUv2 dataset. + +![](images/09348e4c09371b3ad8b68cbd4659bc31ea9d369b66c817adc5b7a0415845a7d0.jpg) +Figure 4. Visualization for the activation data distribution of different channels in decoder with log frequency. + +observe large amount of outliers and significant variability in outlier values across different channels, making per-tensor quantization challenging. This motivates the adoption of a per-channel quantization method to better handle these variations. However, for per-channel quantization, the presence of outliers that deviate significantly from the main data distribution, as shown in Figure 4, still leads to substantial quantization errors. Thus, smoothing these large outliers and integrating them into the main data distribution is crucial for maintaining model accuracy. + +# 4. Quantization Framework + +We first quantize the polished activations with LogNP polishing (Section 4.2). Then we update weights to compensate the loss of activation quantization (Section 4.3). Finally, we quantize updated weights (Section 4.4). + +# 4.1. Preliminary + +Quantization. We mainly adopt the hardware-efficient PTQ methods. For uniform quantization, the quantize and dequantize operations for $x$ can be defined as follows, + +$$ +x _ {q} = \operatorname {C L I P} \left(\left\lfloor \frac {x}{s} \right\rceil + z p, 0, 2 ^ {k} - 1\right), \tag {1} +$$ + +$$ +\hat {x} = s \cdot \left(x _ {q} - z\right), \tag {2} +$$ + +where $s$ represents the scale and $zp$ is the zero point. The operator $\lfloor \cdot \rceil$ indicates rounding to the nearest integer, and the CLIP function constrains values that fall outside the range of a $k$ -bit integer. + +As for Log2 quantization, which is mainly used for post-softmax quantization, can be defined as follows, + +$$ +x _ {q} = \operatorname {C L I P} \left(\left\lfloor - \log_ {2} \frac {x}{s} \right\rceil , 0, 2 ^ {k} - 1\right), \tag {3} +$$ + +$$ +\hat {x} = s \cdot 2 ^ {- x _ {q}}. \tag {4} +$$ + +Notations. The quantized layers (including both linear and convolutional layers) in the mode are indexed by $l$ , $1 \leq l \leq L$ . The weights in the $l^{th}$ layer are denoted by $\mathbf{W}^{(l)}$ with its vectorized/flatened version $\mathbf{w}^{(l)}$ . $\mathbf{x}$ denotes its inputs. + +# 4.2. Activation Polishing + +Building on analysis in Section 3.2, we propose LogNP polishing method to adaptively smooth the deviant distribution in decoders in per-channel prospective. For one activation $\mathbf{x} \in \mathbb{R}^{n \times d}$ where $n$ denotes the number of tokens and $d$ denotes the channel number, the LogNP polishing function $\Phi(\cdot, \cdot)$ for each element $x$ of input $\mathbf{x}$ is defined as follows, + +$$ +\Phi (x, \alpha) = \operatorname {s i g n} (x) \cdot \left[ \log_ {2} (| x | + \alpha) - \log_ {2} (\alpha) \right], \tag {5} +$$ + +where $\mathrm{sign}(\cdot)$ denotes the sign function, and $\alpha$ is the polishing factor for one single channel. + +To reduce the quantization error in each channel, the polishing factor $\alpha_{i}$ corresponding to the $i^{th}$ channel with activation $\mathbf{x}_i$ (i.e., $\mathbf{x} = [\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_d]$ ) is computed according to the given percentile $\epsilon$ as follows, + +$$ +\alpha_ {i} = P _ {\epsilon} \left(\mathbf {x} _ {i}\right), i \in \{1, 2, 3, \dots , d \}, \epsilon \in (0, 1 0 0) \tag {6} +$$ + +where $P_{\epsilon}(\cdot)$ denotes the $\epsilon$ -th percentile function. We adopt uniform $\epsilon$ equals to 95 as deviant activation distributions remain similar across different inputs. We provide the visualization of the polished activation in Figure 5. The polished activation colored in blue appears smoother compared to the original activation colored in red shown in Figure 4, making it more friendly for quantization. After polishing, we perform activation quantization with uniform quantization in Section 4.1. Following activation dequantization, we adopt reverse transformation (i.e., unpolishing) as follows, + +$$ +\Phi^ {- 1} (\hat {x}, \alpha) = \operatorname {s i g n} (\hat {x}) \cdot \left[ 2 ^ {\operatorname {s i g n} (\hat {x}) \cdot \hat {x} + \log_ {2} (\alpha)} - \alpha \right] \tag {7} +$$ + +The latency overhead introduced by LogNP polishing and unpolishing is hidden by concurrent execution in our hardware design, which is further explained in Section 5.2. + +# 4.3. Activation Loss Compensation + +The activation quantization introduces quantization errors. To mitigate this issue, before weight quantization, we first update all weights to compensate the loss of activation quantization. To save the computation cost, we address the problem + +![](images/077c36dce931a03818627546c18f92c5213e4ce9cc8a4173f4d6ba27eb7fc150.jpg) +Figure 5. Visualization for the polished activation data distribution of different channels in decoder with log frequency. + +layer by layer instead of for the whole model. The layer-wise compensation problem is formulated as the following, + +$$ +\min _ {\Delta \mathbf {W}} \| \mathbf {W} \mathbf {x} - (\mathbf {W} + \Delta \mathbf {W}) \hat {\mathbf {x}} \| _ {2} ^ {2} \tag {8} +$$ + +where $\mathbf{W}$ and $\mathbf{x}$ are the original weights and inputs of the layer. $\hat{\mathbf{x}}$ is the quantized inputs and we update the weights with $\Delta \mathbf{W}$ to compensate the activation quantization error, so that the layer outputs after activation quantization and weight compensation should be close to the original outputs. + +This problem can be solved by setting the gradients of the minimization objective to zero, as the following, + +$$ +\Delta \mathbf {W} \hat {\mathbf {x}} \hat {\mathbf {x}} ^ {\mathrm {T}} + \mathbf {W} (\mathbf {x} - \hat {\mathbf {x}}) \hat {\mathbf {x}} ^ {\mathrm {T}} = 0. \tag {9} +$$ + +The optimal solution can be obtained by + +$$ +\Delta \mathbf {W} ^ {*} = - \mathbf {W} (\mathbf {x} - \hat {\mathbf {x}}) \hat {\mathbf {x}} ^ {\mathrm {T}} \left(\hat {\mathbf {x}} \hat {\mathbf {x}} ^ {\mathrm {T}}\right) ^ {- 1} \tag {10} +$$ + +After activation quantization, we can update weights with the above $\Delta \mathbf{W}^*$ to compensate the activation quantization error. If $\hat{\mathbf{x}}\hat{\mathbf{x}}^{\mathrm{T}}$ is not full rank with difficulties for matrix inversion, we adopt the dampening technique [21, 45]. Next, we quantize the updated weights under the quantized activations. + +# 4.4. Weight Reconstruction + +Problem formulation. In quantization, the weights are modified and we would like to minimize the change of loss incurred by quantization to maintain the superior performance of the model. To quantitatively analyze the loss degradation by quantization, we approximate the loss degradation with Taylor expansion as the following, + +$$ +\begin{array}{l} L (\mathbf {w} + \Delta \mathbf {w}) - L (\mathbf {w}) \approx \Delta \mathbf {w} ^ {\mathrm {T}} \mathbf {g} _ {\mathbf {w}} + \frac {1}{2} \Delta \mathbf {w} ^ {\mathrm {T}} \mathbf {H} _ {\mathbf {w}} \Delta \mathbf {w}, \\ \approx \frac {1}{2} \Delta \mathbf {w} ^ {\mathrm {T}} \mathbf {H} _ {\mathbf {w}} \Delta \mathbf {w}, \tag {11} \\ \end{array} +$$ + +where $\mathbf{g}_{\mathbf{w}} = \nabla_{\mathbf{w}}L$ represents the gradients and $\mathbf{H}_{\mathbf{w}} = \nabla_{\mathbf{w}}^{2}L$ denotes the Hessian matrix. $\Delta \mathbf{w}$ is the weight perturbation in this step. Here we use the vectorized/flatened version $\mathbf{w}$ instead of the matrix version $\mathbf{W}$ to obtain a scalar output. As the pre-trained model has been well trained and converged to a minimum, it is reasonable to assume the gradients to be 0. The complexity to obtain the full Hessian is very high + +and typically it is not possible to obtain the full Hessian due to computation and memory limitations. Specifically, $\mathbf{H}_{\mathbf{w}} \in \mathbb{R}^{B \times B}$ where $B$ is the number of parameters in $\mathbf{w}$ . The memory cost for $\mathbf{H}_{\mathbf{w}}$ is extremely heavy in LLMs with billions of parameters. + +Approximating Hessian. For a network trained with negative log-likelihood loss and a probabilistic model $p_{\mathbf{w}}(y|x_s)$ under softmax, the Hessian is identical to the Fisher matrix: + +$$ +\begin{array}{l} \mathbf {H} _ {\mathbf {w}} = \mathbf {F} _ {\mathbf {w}} = \sum_ {s = 1} ^ {S} \mathbb {E} _ {y \sim p _ {\mathbf {w}} (y | x _ {s})} [ \nabla_ {\mathbf {w}} \log p _ {\mathbf {w}} (y | x _ {s}) \\ \left. \nabla_ {\mathbf {w}} \log p _ {\mathbf {w}} \left(y \mid x _ {s}\right) ^ {T} \right] \tag {12} \\ \end{array} +$$ + +where $S$ is the number of samples, and for each sample, it needs to compute the expectation over all categories. The complexity with the expectation is also high if there are too many categories. Thus, in practice, the empirical Fisher is commonly adopted to replace the expectation over $y$ with target label $y_{s}$ [33]. The dimension of $\mathbf{F}_{\mathbf{w}}$ is the same as $\mathbf{H}_{\mathbf{w}}$ with quadratic memory complexity to the number of parameters. To reduce the complexity, the empirical Fisher is computed by treating layers independently and the layer-wise empirical Fisher can be obtained as below [6, 44], + +$$ +\mathbf {F} _ {l} = \mathbb {E} \left[ \left(\mathbf {g} ^ {(l)} \mathbf {g} ^ {(l), \mathrm {T}}\right) \otimes \left(\hat {\mathbf {x}} ^ {(l)} \hat {\mathbf {x}} ^ {(l), \mathrm {T}}\right) \right], \tag {13} +$$ + +where $\hat{\mathbf{x}}^{(l)}$ is the input activations and $\mathbf{g}^{(l)}$ is the gradients of the $l^{th}$ layer. $\otimes$ denotes Kronecker product. The expectation is taken with respect to data distribution over inputs. + +For two different layers (for example, the $i^{th}$ and the $j^{th}$ layers), their Fisher is often written as $\mathbf{F}_{ij} = \sum_{s=1}^{S} \mathbb{E}\left[\nabla_{\mathbf{w}^{(i)}} \log p_{\mathbf{w}}(y_s | x_s) \nabla_{\mathbf{w}^{(j)}} \log p_{\mathbf{w}}(y_s | x_s)^T\right]$ , + +which are often ignored to save computations. The Fisher for the whole model can be formulated as a block diagonal matrix $\mathbf{F}_{\mathbf{w}} = \mathrm{diag}(\mathbf{F}_1,\mathbf{F}_2,\dots ,\mathbf{F}_L)$ + +To obtain the Fisher in practice, we adopt the KFAC approximation method [20, 44] as below, + +$$ +\mathbf {F} _ {l} = \mathbf {G} _ {l} \otimes \mathbf {A} _ {l} \tag {14} +$$ + +$$ +\mathbf {G} _ {l} = \frac {1}{\sqrt {S}} \sum_ {s = 1} ^ {S} \mathbf {g} _ {s} ^ {(l)} \mathbf {g} _ {s} ^ {(l), \mathrm {T}} \tag {15} +$$ + +$$ +\mathbf {A} _ {l} = \frac {1}{\sqrt {S}} \sum_ {s = 1} ^ {S} \hat {\mathbf {x}} _ {s} ^ {(l)} \hat {\mathbf {x}} _ {s} ^ {(l). \mathrm {T}} \tag {16} +$$ + +The KFAC approximation [25, 76] approximates an expectation of Kronecker products as a Kronecker product of two expectations $\mathbb{E}[\mathbf{g}^{(l)}\mathbf{g}^{(l),T}\otimes \hat{\mathbf{x}}^{(l)}\hat{\mathbf{x}}^{(l),T}]\approx \mathbb{E}[\mathbf{g}^{(l)}\mathbf{g}^{(l),T}]\otimes$ $\mathbb{E}[\hat{\mathbf{x}}^{(l)}\hat{\mathbf{x}}^{(l),T}]$ , where the activations and derivatives are assumed to be independent. + +Optimizing quantization parameters. Next we optimize the quantization parameters. Given our optimization loss in Equation (11), multiple optimization methods can be adopted such as STE [24] and AdaRound [46]. Due to its superior performance in PTQ, we use AdaRound [46] to learn the + +![](images/84c4f3f019ba0ce28385fd4967e69731f144f201b00a624a71b577b9cf008c16.jpg) +Figure 6. The block diagram of the proposed hardware accelerator. + +rounding parameter which decides rounding up or down. Formally, we minimize the following loss, + +$$ +\min _ {\mathbf {v}} \sum_ {l = 1} ^ {L} \left(\mathbf {w} ^ {(l)} - \hat {\mathbf {w}} ^ {(l)}\right) ^ {\mathrm {T}} \mathbf {F} _ {l} \left(\mathbf {w} ^ {(l)} - \hat {\mathbf {w}} ^ {(l)}\right) + \lambda h (\mathbf {v}), \tag {17} +$$ + +where $\mathbf{v}$ denotes the rounding parameter which are used to construct the quantized weights $\hat{\mathbf{w}}^{(l)}$ . $h(\mathbf{v})$ is a regularizer in AdaRound [46] with $\lambda$ controlling its strength. More details about AdaRound are presented in Appendix 9. We only use a small calibration set (32 samples) sampled from the training dataset to calibrate the quantized model. + +# 5. Hardware Design + +# 5.1. Top-Level Design + +We design a flexible and programmable accelerator as shown in Figure 6. The Dispatch module fetches instructions via the AXI bus and distributes them to local Instruction FIFOs, while the Synchronize module controls the start and end of each module. Instruction FIFOs hold out-of-order instructions and are controlled by Synchronize module for execution. The Load and Store modules, functioning as the DMA, facilitate data transfer between off-chip memory (e.g., HBM or DDR) and local buffers. The Matrix Multiplication Unit (MMU) performs General Matrix Multiply (GeMM) and convolution when the Vector Compute Unit (VCU) handles nonlinear activation functions. + +# 5.2. On-Chip Kernel Design + +We adopt a multiply-accumulate tree array to implement both matrix multiplication and convolution. For W4A4 and W4A8 configurations, we design specialized multipliers and adders to enhance computational efficiency and reduce chip area overhead. Additionally, the use of low-bit quantized matrices eases memory bandwidth demands during data transfer, allowing for full utilization of the external memory bandwidth. As for Float32, we implement IEEE 754 standard floating-point computation for fair comparison. + +Meanwhile, we propose a programmable vector computation array composed of multiple Floating-Point Units (FPU) + +
MethodW/ANYUv2 [47]KITTI [19]
AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓
ViT-Small Backbone
\Float320.0870.9380.9900.9960.3310.0350.0740.9340.9840.9953.4030.043
OBS [17]W40.1070.8850.9850.9970.3910.0420.1220.8670.9730.9914.5080.058
minmax [27]W4A80.4530.4050.7020.8681.0670.1110.4560.1020.3290.57513.3550.159
ema [26]0.2570.5910.8590.9580.7930.0930.3120.3410.6320.80711.1020.139
percentile [11]0.1900.6350.9120.9810.7740.0770.2220.5520.8140.9188.9000.114
AdaRound [46]0.1340.7930.9670.9810.4710.0420.1280.8760.9530.9934.2360.051
BrecQ [36]0.1280.8170.9800.9960.4520.0400.1040.9000.9770.9933.9140.047
Ours0.1030.8990.9870.9960.3800.0420.0920.9160.9810.9953.6820.046
minmax [27]W4A41.2650.1300.2850.4772.5930.1600.5840.0540.1600.32115.8770.245
ema [26]0.3710.3590.3590.8411.2260.1460.6320.0220.0810.22816.2650.244
percentile [11]0.3570.3660.6590.8461.2230.1460.6460.0190.0640.19716.3840.244
AdaRound [46]0.2510.4590.8120.9360.8480.1030.5010.2390.3680.53814.3980.216
BrecQ [36]0.2170.5980.8840.9700.7240.0710.4050.2780.4930.63412.3370.184
Ours0.1330.8150.9650.9900.4530.0520.1970.5340.9370.9855.4290.059
ViT-Large Backbone
\Float320.0670.9720.9930.9970.2620.0400.0540.9740.9950.9992.5050.032
OBS [17]W40.0700.9720.9940.9980.2670.0380.0600.9680.9950.9982.7480.034
minmax [27]W4A80.6710.2790.5470.7481.4480.1440.5460.0550.1720.38514.8410.202
ema [26]0.6570.2890.5590.7561.4250.1410.3940.2190.4810.68612.0850.169
percentile [11]0.4250.3490.7150.9071.0730.1060.1920.6450.8830.9496.9570.093
AdaRound [46]0.0840.9590.9910.9970.2760.0400.0570.9720.9950.9992.7690.034
BrecQ [36]0.0760.9670.9930.9970.2720.0390.0570.9710.9950.9992.7780.034
Ours0.0710.9700.9930.9970.2640.0360.0550.9730.9950.9992.5420.032
minmax [27]W4A42.2380.1160.2490.3915.7610.2610.5650.0630.1900.36315.6930.253
ema [26]1.0390.1740.3760.5782.1260.1570.5080.1230.2940.46015.2060.247
percentile [11]0.9200.2070.4280.6311.9150.1570.4920.1440.3170.48715.0120.244
AdaRound [46]0.5010.2590.5640.7821.4820.1450.4820.1720.3950.54113.7820.207
BrecQ [36]0.4690.3300.6090.8111.3230.1370.4340.1910.4070.59013.4620.192
Ours0.0970.9320.9930.9980.3270.0450.0700.9520.9930.9983.1040.038
+ +Table 1. Main results of Metric3D model with ViT-Small and ViT-Large backbone on NYUv2 and KITTI datasets. Results with ViT-Giant backbone is included in Table A1 at Appendix 10. + +in Vector Computing Unit (VCU). In the VCU, we design a programmable vector computation array composed of multiple FPU to enable more efficient computation. The FPU supports the Special Function Unit (SFU) through polynomial approximation [51], which achieves the computation of non-linear functions (e.g. $\log_2$ and $\exp$ ) within 3 to 5 clock cycles while maintaining ultra-high precision. For the activation polishing optimization discussed in Section 4.2, the FPU is further specifically designed to enhance execution efficiency. Compared to the NVIDIA GPU [48], the proposed SFU achieves nearly same accuracy, with only a 2 to 5 ULP (units in the last place) error. Meanwhile, the VCU supports multiple numerical format inputs, unifying them into Float32 for computation, and then converts these Float32 numbers into integers such as INT4 or INT8 as needed, which seamlessly integrates both floating-point and integer data types for efficient processing. Hence, the proposed quantization framework for MDE models with ac + +tivation polishing optimization is accurately and efficiently deployed on our hardware. + +# 5.3. Overlapped Computation Flow + +Our hardware architecture supports kernel fusion of on-chip matrix multiplication and vector computation, enabling intermediate results stored in local SRAM to be directly sent to the VCU for activation, quantization, or dequantization without being written back to DDR. By fusing these operations into a single flow, we minimize the latency introduced by multiple memory accesses. Also, this design reduces data transfer time and enhances the overall execution efficiency. Furthermore, our hardware is designed to be programmable with customized instructions, enabling the configuration of different computational tasks to be executed concurrently within an instruction cycle. This parallelism enables a substantial speedup in processing by allowing multiple operations to be pipelined, thereby reducing the total time needed to complete complex tasks. As shown in Figure 7, data trans + +ferring, matrix computation, and vector computation can be fully overlapped to improve execution efficiency. This concurrency ensures that no computational resource is idle and every cycle is utilized to its maximum potential, leading to a streamlined and optimized workflow. Therefore, the total on-device latency of the depth estimation model executed with our quantization framework is optimized through extensive operator fusion and concurrent execution. + +![](images/ee7b1aae37539988b3fce184a81a88dc6c84959de08d23fe8bca98f407e10a50.jpg) +Figure 7. The schematic of concurrent execution, where the computation of Matrix, Vector, Load and Store can execute parallel. + +# 6. Experimental Results + +# 6.1. Experiment Setup + +We adopt Metric3D [95] with ViT-Small, ViT-Large, and ViT-Giant [15] backbones to present the main results and Depth Anything [90] with ViT-Large backbone to further verify the generalization across additional datasets. For a fair comparison, we adopt per-channel asymmetric quantization for both weights and activations in W4A8 and W4A4 configurations. We randomly sample 32 images as calibration set from the training sets of NYUv2 [47] for indoor scenes and KITTI [19] for outdoor scenes. The percentile $\epsilon$ for the polishing factor is set to 95, and $\alpha$ is then computed as the average value across the calibration samples. For activation loss compensation and weight reconstruction, we still use same 32 samples for the calibration. For gradient computation in weight reconstruction, we adopt batch size of 1, learning rate set to 4e-5, warm up of 0.2, weight decay of 0.01, drop rate of 0.5, and 20,000 iterations. For evaluation, we use NYUv2 [47], SUN RGB-D [67], iBims-1 [32], and HyperSim [58] for indoor scenes; and KITTI [19], vKITTI [7], and DIODE [75] for outdoor scenes. Absolute relative error (AbsRel), accuracy under threshold $(\delta_i < 1.25^i, i = 1, 2, 3)$ , root mean squared error (RMSE), and metric-depth loss (Silog) metrics are employed in our evaluation results. + +# 6.2. Hardware Implementation + +We implement our hardware in RTL and synthesis the design using Design Compiler [70] under a commercial 28nm CMOS technology. The frequency and area are tested by the Design Compiler and the power is tested by Prime Time [71] PX with synthesized netlist and dynamic simulation switch rate under different modes. After synthesis, based on the latency profiled by simulation and the frequency given by + +Design Compiler, we introduce a hardware performance emulator for latency test. The DDR is simulated by RTL, with a bandwidth of 19.2 GB/s. + +# 6.3. Depth Estimation Results + +We present the quantization results with W4A8 and W4A4 configurations using Metric3D [95] with ViT-Small and ViT-Large backbone on indoor dataset NYUv2 [47] and outdoor dataset KITTI [19] in Table 1. The results with ViT-Giant backbone are included in Table A1 at Appendix 10. Compared to conventional PTQ methods such as minmax [27], EMA [26], and percentile [11], our framework demonstrates significantly improved performance. Additionally, when benchmarked against other learning-based approaches including OBS [17], AdaRound [46], and BrecQ [36], our method also achieves superior results. Notably, for the ViT-Large backbone with W4A8 settings, our method maintains nearly lossless performance. In the W4A4 configuration, our approach shows a substantial performance advantage over other methods, validating the effectiveness of our proposed quantization framework. Meanwhile, we present results of Depth Anything model with ViT-Large backbone on various additional datasets [7, 32, 58, 67, 75] covering both indoor and outdoor scenes, as shown in Table 2. Our method, which applies quantization to both weights and activations, achieves performance comparable to OBS (a weight-only quantization method) across multiple datasets in W4A8 configuration, and outperforms the BrecQ for all configurations, showing the effectiveness of our proposed quantization method. + +# 6.4. Latency Results on ASIC + +We present the latency results of Metric3D with detailed hardware resource utility in Table 3. The latency is tested with three different resolutions. The power is further normalized by the latency and computation cost (i.e., GMACs) for the energy efficiency. For three different configurations, the frequency are uniformly $1\mathrm{GHz}$ . The silicon area that our design occupies on a chip for Float32, W4A8, and W4A4 is $29.22\mathrm{mm}^2$ , $23.94\mathrm{mm}^2$ , and $24.35\mathrm{mm}^2$ , respectively. As shown in Table 3, our proposed method demonstrates superior performance with faster inference speed and higher power efficiency across various model scales and resolutions. Notably, for ViT-Small backbone at 256 resolution under W4A4 configuration, our method achieves up to 26 FPS, showing the real-time performance. + +# 6.5. Ablation Study + +We regulate the number of calibration samples to verify the effectiveness of our proposed method, and the results are shown in Figure 8. We observe that the model performance stabilizes when the number of calibration samples reaches 32 for both W4A4 and W4A8 configuration. Additionally, activation compensation proves crucial for the W4A4. + +
W/ADataset MethodNYUv2 [47]SUN RGB-D [67]iBims-1 [32]HyperSim [58]KITTI [19]vKITTI2 [19]DIODE Outdoor [75]
AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑
\Float320.0560.9840.5000.6600.1500.7140.3280.5080.0460.9820.0840.9120.7990.289
W4OBS [17]0.0590.9810.5080.6260.1510.7180.3270.5010.0490.9800.0910.8930.7930.287
W4A8BrecQ [36]0.0990.9030.4890.6920.1830.5930.3770.3720.0510.9510.6060.1320.7990.010
Ours0.0580.9820.3940.7560.1570.7000.3220.5230.0600.9650.1080.8460.8320.298
W4A4BrecQ [36]0.3420.2960.3960.4160.4190.2220.7030.0470.3850.2350.7570.0090.7650.034
Ours0.0700.9720.4660.7420.1770.6150.3220.5120.0590.9350.1000.8820.7580.280
+ +Table 2. Main results of Depth Anything model with ViT-Large backbone. The first four sets are indoor scenes, while the last three are outdoor scenes. Full detailed results are included in Table A2 at Appendix 10. + +
W / ASize (MB)Res.Latency (ms) ↓FPS ↑Power Eff. (GMAC/W) ↑
ViT-Small
Float32143.125676.8 (1×)13.02 (1×)85.6 (1×)
W4A817.8842.6 (1.8×)23.47 (1.8×)172.8 (2.0×)
W4A438.3 (2.0×)26.11 (2.0×)177.5 (2.1×)
Float32143.1512325.5 (1×)3.07 (1×)87.3 (1×)
W4A817.88159.0 (2.0×)6.29 (2.0×)200.1 (2.3×)
W4A4133.4 (2.4×)7.50 (2.4×)220.3 (2.5×)
Float32143.110242181.4 (1×)0.46 (1×)78.4 (1×)
W4A817.88836.8 (2.6×)1.20 (2.6×)228.9 (2.9×)
W4A4616.7 (3.5×)1.62 (3.5×)287.0 (3.7×)
ViT-Large
Float321572256584.1 (1×)1.71 (1×)118.2 (1×)
W4A8196.5223.5 (2.6×)4.47 (2.6×)331.1 (2.8×)
W4A4167.9 (3.5×)5.96 (3.5×)425.4 (3.6×)
Float3215725122214.5 (1×)0.45 (1×)126.4 (1×)
W4A8196.5798.4 (2.8×)1.25 (2.8×)392.5 (3.1×)
W4A4568.5 (3.9×)1.76 (3.9×)509.3 (4.0×)
Float321572102413297.1 (1×)0.08 (1×)126.9 (1×)
W4A8196.54228.3 (3.1×)0.24 (3.1×)446.8 (3.5×)
W4A42725.1 (4.9×)0.37 (4.9×)640.6 (5.0×)
+ +Table 3. ASIC results of Metric3D with ViT-Small and ViT-Large. ViT-Giant results are shown in Table A3 at Appendix 10. + +![](images/896dba8aa1482d1300b2f104974dbb65727bca6a90846d45ad53ed72bd6027bb.jpg) +Figure 8. Accuracy ablation for the number of calibration samples using ViT-Large backbone on NYUv2 dataset. + +We further perform ablation study on hardware resources by varying the number of MMUs and VCUs (i.e., number of cores). The results of 2, 4 and 8 cores are presented in Figure 9. The results show that more cores lead to faster speed. Compared to the Float32 model, the quantized model + +![](images/11d8dc23b72083ff2c54d486cca624b5c1ebda24b626d61fda6d7d8d97af6731.jpg) +Figure 9. Latency ablation for different number of cores using ViT-Large backbone with 256x256 resolution. + +is not sensitive to the hardware resource and achieves high hardware efficiency. + +Meanwhile, we also visualize depth estimation results of Metric3D with ViT-Large backbone in Figure A1 at Appendix 11 compared with BrecQ [36] on NYUv2 [47] for indoor scene and KITTI [19] for outdoor scene. The visualizations verify the effectiveness of our methods on both indoor and outdoor scenes. + +# 7. Conclusion + +In this paper, we propose QuartDepth, a quantization framework for the real-time acceleration of MDE models on ASICs. We provide the LogNP polishing method to smooth the outliers in the decoder of MDE models, and provide the compensation method to mitigate the loss of activation quantization. We then introduce the weight reconstruction to reduce the weight quantization loss. Furthermore, we design a novel flexible and programmable hardware accelerator for our efficient deployment on ASICs. Experimental results verify the effectiveness of our proposed framework. + +# 8. Acknowledgment + +This work was mainly supported by Northeastern University and Nanjing University. This work was also supported by National Natural Science Foundation of China 62472104. + +# References + +[1] Ibraheem Alhashim and Peter Wonka. High quality monocular depth estimation via transfer learning. arXiv e-prints, abs/1812.11941:arXiv:1812.11941, 2018. 2 +[2] Claudine Badue, Rănik Guidolini, Raphael Vivacqua Carneiro, Pedro Azevedo, Vinicius B Cardoso, Avelino Forechi, Luan Jesus, Rodrigo Berriel, Thiago M Paixao, Filipe Mutz, et al. Self-driving cars: A survey. Expert systems with applications, 165:113816, 2021. 2 +[3] Shariq Farooq Bhat, Ibraheem Alhashim, and Peter Wonka. Adabins: Depth estimation using adaptive bins. 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Ptq4vit: Post-training quantization framework for vision transformers with twin uniform quantization. arXiv preprint arXiv:2111.12293, 2021. 2 +[101] Zheng Zhan, Yifan Gong, Pu Zhao, Geng Yuan, et al. Achieving on-mobile real-time super-resolution with neural architecture and pruning search. In ICCV, pages 4821-4831, 2021. 2 +[102] Zheng Zhan, Zhenglun Kong, Yifan Gong, Yushu Wu, Zichong Meng, Hangyu Zheng, Xuan Shen, Stratis Ioannidis, Wei Niu, Pu Zhao, and Yanzhi Wang. Exploring token pruning in vision state space models. In NeurIPS, 2024. 2 +[103] Zheng Zhan, Yushu Wu, Yifan Gong, Zichong Meng, Zhenglun Kong, Changdi Yang, Geng Yuan, Pu Zhao, Wei Niu, and Yanzhi Wang. Fast and memory-efficient video diffusion using streamlined inference. In NeurIPS, 2024. 2 +[104] Zheng Zhan, Yushu Wu, Zhenglun Kong, Changdi Yang, Yifan Gong, Xuan Shen, Xue Lin, Pu Zhao, and Yanzhi Wang. Rethinking token reduction for state space models. In EMNLP, pages 1686-1697, Miami, Florida, USA, 2024. ACL. 2 +[105] Chi Zhang, Wei Yin, Billzb Wang, Gang Yu, Bin Fu, and Chunhua Shen. Hierarchical normalization for robust monocular depth estimation. Advances in Neural Information Processing Systems, 35:14128-14139, 2022. 1, 2 +[106] Yihua Zhang, Yuguang Yao, Parikshit Ram, Pu Zhao, Tianlong Chen, Mingyi Hong, Yanzhi Wang, and Sijia Liu. Advancing model pruning via bi-level optimization. Advances in Neural Information Processing Systems, 35:18309-18326, 2022. 2 +[107] Pu Zhao, Xuan Shen, Zhenglun Kong, Yixin Shen, Sung-En Chang, Timothy Rupprecht, Lei Lu, Enfu Nan, Changdi Yang, Yumei He, et al. Fully open source moxin-7b technical report. arXiv preprint arXiv:2412.06845, 2024. 1 + +[108] Pu Zhao, Fei Sun, Xuan Shen, Pinrui Yu, Zhenglun Kong, Yanzhi Wang, and Xue Lin. Pruning foundation models for high accuracy without retraining. In Findings of EMNLP 2024, pages 9681-9694. 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200, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 286, + 200, + 300 + ], + "spans": [ + { + "bbox": [ + 151, + 286, + 200, + 300 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 312, + 297, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 297, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 297, + 624 + ], + "type": "text", + "content": "Monocular Depth Estimation (MDE) has emerged as a pivotal task in computer vision, supporting numerous real-world applications. However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose Quart-Depth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 648, + 135, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 648, + 135, + 661 + ], + "spans": [ + { + "bbox": [ + 56, + 648, + 135, + 661 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 669, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 296, + 694 + ], + "type": "text", + "content": "Monocular Depth Estimation (MDE) is a critical task in computer vision, essential for a wide range of applications" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 285, + 555, + 422 + ], + "blocks": [ + { + "bbox": [ + 315, + 285, + 555, + 422 + ], + "lines": [ + { + "bbox": [ + 315, + 285, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 315, + 285, + 555, + 422 + ], + "type": "image", + "image_path": "27a4440b701133d9e5301a2a2f232e4c92a81cd561616303da4cc024bef95b17.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 430, + 556, + 453 + ], + "lines": [ + { + "bbox": [ + 313, + 430, + 556, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 556, + 453 + ], + "type": "text", + "content": "Figure 1. Visualization of accuracy vs. latency on ASIC for monocular depth estimation models with different backbones." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 474, + 556, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 474, + 556, + 629 + ], + "spans": [ + { + "bbox": [ + 312, + 474, + 556, + 629 + ], + "type": "text", + "content": "including robotics [82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105]. The objective of MDE is to estimate depth information from a single image, making it particularly valuable for scenarios where stereo or multi-view depth sensors are impractical. Previously, depth estimation methods have been classified into three main approaches: learning metric depth [3, 89, 91, 99], learning relative depth [8, 9, 86, 87], and learning affine-invariant depth [54, 56, 93, 94, 105]. Among these, metric depth methods have demonstrated remarkable performance across benchmarks but often show limited generalizability to diverse, real-world images, which is compounded by variations in camera parameters between training and test sets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "Recently, inspired by the rise of \"foundation models\" [5, 107], a new wave of MDE models [4, 66, 90, 95] has been developed. These foundational MDE models exhibit superior generalization and robustness, effectively extending their applicability to in-the-wild images and accommodating a wide array of camera parameters. However, while these foundational MDE models achieve impressive performance," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11448" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 296, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 296, + 395 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 296, + 395 + ], + "type": "text", + "content": "they rely on sophisticated and computationally intensive algorithms. This reliance on complex architectures and operations significantly increases computational costs, making such models resource-heavy and challenging to deploy on edge devices or specialized hardware such as Application-Specific Integrated Circuits (ASICs) [35, 52, 81, 82]. The high computational demands also hinder real-time performance and scalability, which are critical for practical applications such as autonomous navigation [2], robotic perception [80], and augmented reality [68]. This constraint underscores the need for more efficient approaches that can maintain high accuracy while reducing computational overhead. Among common techniques like pruning [16, 64, 82, 106], knowledge distillation [18, 50], and architecture optimization [1, 37, 38, 63, 85, 101], which mainly reduce model complexity, quantization [11, 36, 46, 79] stands out for achieving both compactness and speed. Quantization [14, 39, 41, 84, 100] reduces weights and activations to lower bit-widths (e.g., 4-bit or 8-bit integers), minimizing model size while accelerating inference through optimized integer kernels specifically designed for edge devices. This dual benefit makes it ideal for deploying high-performing models on resource-limited edge hardware. Given the complexity of large foundational MDE models and their extensive datasets [31, 34, 98], we employ Post-Training Quantization (PTQ) [36, 41, 62, 100, 108] to facilitate efficient deployment without retraining." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 399, + 296, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 399, + 296, + 697 + ], + "spans": [ + { + "bbox": [ + 57, + 399, + 296, + 697 + ], + "type": "text", + "content": "In this paper, we propose QuartDepth, a post-training quantization framework designed for real-time depth estimation on edge devices. We begin by analyzing the outlier deviant distribution in MDE foundation models [90, 95]. Through an in-depth per-channel analysis of these abnormal distributions, we identify persistent extreme outliers in the depth decoders. To address this, we propose the LogNP polishing optimization method to smooth the outliers and transform the abnormal distribution into a more quantization-friendly, normalized distribution. Furthermore, to mitigate the loss from activation quantization, we employ a compensation algorithm that updates the weights to minimize the activation quantization error. Next we perform weight quantization with a weight reconstruction method that leverages gradients to minimize second-order weight quantization errors. Meanwhile, we design a novel flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, which enables direct processing of intermediate results and concurrent execution of computational tasks. In detail, we design specialized computation kernels for W4A4 and W4A8 configurations, which enables full utilization of external memory bandwidth. Also, we design a novel programmable vector computation array to support the proposed LogNP polishing optimization, effectively hiding its additional overhead." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 702, + 285, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 702, + 285, + 712 + ], + "spans": [ + { + "bbox": [ + 69, + 702, + 285, + 712 + ], + "type": "text", + "content": "In summary, our contributions are outlined as follows," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 320, + 72, + 555, + 239 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 320, + 72, + 555, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 72, + 555, + 119 + ], + "spans": [ + { + "bbox": [ + 320, + 72, + 555, + 119 + ], + "type": "text", + "content": "1. We observe a challenging outlier deviant distribution for activations and propose the LogNP polishing for activation quantization, which transforms these outliers into a quantization-friendly, normalized distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 321, + 121, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 121, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 321, + 121, + 553, + 167 + ], + "type": "text", + "content": "2. For weight quantization, we first update the weights to compensate the error of activation quantization, and then quantize the updated weights with weight reconstruction to minimize the second-order weight quantization error." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 321, + 168, + 555, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 168, + 555, + 203 + ], + "spans": [ + { + "bbox": [ + 321, + 168, + 555, + 203 + ], + "type": "text", + "content": "3. We develop a novel flexible and programmable hardware accelerator on ASICs corresponding to our proposed quantization methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 321, + 204, + 555, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 204, + 555, + 239 + ], + "spans": [ + { + "bbox": [ + 321, + 204, + 555, + 239 + ], + "type": "text", + "content": "4. Comprehensive experiments confirm the effectiveness of our QuartDepth framework with superior accuracy, real-time inference and higher power efficiency on ASICs." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 253, + 400, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 253, + 400, + 265 + ], + "spans": [ + { + "bbox": [ + 317, + 253, + 400, + 265 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 273, + 461, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 273, + 461, + 285 + ], + "spans": [ + { + "bbox": [ + 317, + 273, + 461, + 285 + ], + "type": "text", + "content": "2.1. Efficient Depth Estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 291, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 291, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 315, + 291, + 555, + 590 + ], + "type": "text", + "content": "Depth estimation from a single color image has been a prominent research focus in the field of computer vision for over a decade. This task plays a critical role in various applications, including robotic perception [12, 13, 82], autonomous driving [77, 97], virtual reality [57], and 3D reconstruction [54, 92, 105], all of which require rapid and accurate depth perception. The demand for real-time processing in these applications highlights the necessity for efficient model deployment. To meet these requirements, advanced optimization techniques such as pruning [16, 42, 65, 82, 104], knowledge distillation [18, 50], and architecture optimization [1, 88, 108] have been adopted to compress and accelerate the model. However, previous research has primarily focused on relatively smaller models, which, while effective, do not match the scale and capability of foundational MDE models [90, 95]. These modern foundational MDE models [4, 66] have gained significant attention for their ability to achieve state-of-the-art performance and generalize effectively across diverse real-world scenarios. By leveraging massive datasets and advanced architectures, these models provide robust depth estimation at the cost of increased computational complexity and larger model sizes. Thus, there is an urgent need for new model compression and acceleration techniques specifically designed to meet real-time requirements on resource-limited edge devices." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 600, + 418, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 600, + 418, + 612 + ], + "spans": [ + { + "bbox": [ + 317, + 600, + 418, + 612 + ], + "type": "text", + "content": "2.2. Hardware Design" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 618, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 618, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 618, + 555, + 713 + ], + "type": "text", + "content": "Deploying large foundational models on edge devices presents significant challenges due to stringent constraints on computation and memory access [69]. To tackle these issues, various optimization techniques [59-62, 83, 102, 103, 108] have been explored to reduce model size and computational overhead. However, models subjected to such aggressive optimizations often fail to achieve peak performance on general-purpose CPUs and GPUs [96]. In contrast, ASICs," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11449" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 68, + 298, + 167 + ], + "blocks": [ + { + "bbox": [ + 57, + 68, + 298, + 167 + ], + "lines": [ + { + "bbox": [ + 57, + 68, + 298, + 167 + ], + "spans": [ + { + "bbox": [ + 57, + 68, + 298, + 167 + ], + "type": "image", + "image_path": "a00c83984be3fdd5ed0073252265194f954786873afc4fe01942b5fa9432f9ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 174, + 299, + 209 + ], + "lines": [ + { + "bbox": [ + 55, + 174, + 299, + 209 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 299, + 209 + ], + "type": "text", + "content": "Figure 2. Latency profiling for 3 different resolutions using Metric3D with ViT-Large backbone. Vector includes activation functions (e.g. ReLU) and element-wise addition and multiplication." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 229, + 298, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 229, + 298, + 410 + ], + "spans": [ + { + "bbox": [ + 54, + 229, + 298, + 410 + ], + "type": "text", + "content": "optimized for specific models and algorithms, offer significant performance and energy efficiency gains, making them ideal for deploying large foundational models on edge devices [22, 23, 43, 53, 78, 96]. Early work, such as TPU [28], DNA [72], and Eyeriss [10], significantly improved inference speed and energy efficiency by focusing on specialized hardware designs tailored to the needs of deep learning models. Recent works [29, 30, 49, 73, 74] have proposed dedicated hardware architectures in ASICs to accelerate neural network inference. These ASIC architectures have significantly improved inference latency and energy efficiency through solutions such as quantization, sparsity, data flow reconstruction, and algorithm-hardware co-design [40]. Thus, to maximize potential of large foundational models, the advantages offered by ASICs make them platform of choice." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 422, + 197, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 197, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 197, + 435 + ], + "type": "text", + "content": "3. Analysis and Motivation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 441, + 160, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 160, + 454 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 160, + 454 + ], + "type": "text", + "content": "3.1. Latency Profiling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 459, + 298, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 459, + 298, + 639 + ], + "spans": [ + { + "bbox": [ + 54, + 459, + 298, + 639 + ], + "type": "text", + "content": "To optimize edge device inference, we first profile the Float32 model to identify the most time-consuming components for targeted optimization. In detail, we implement the Metric3D [95] model with ViT-Large [15] backbone on a hardware performance emulator with our ASIC design. The latency profiling results in Figure 2 show that the matrix multiplication and convolution operations dominate the inference time, while non-linear operations like softmax and layer normalization contribute minimally. The vector operations include activation functions such as SiLU, ReLU, and GeLU, as well as element-wise addition and multiplication, which also contribute minimally to the overall latency. This motivates our focus on quantization and ASIC design for linear and convolution layers, keeping non-linear operations in floating point to preserve accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 647, + 175, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 175, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 175, + 659 + ], + "type": "text", + "content": "3.2.Deviant Distribution" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": "We investigate the deviant distribution in MDE models from a per-channel perspective. In Figure 3, we visualize the outliers across various channels of an activation in the decoder [55] of the Metric3D model on NYUv2 dataset. We" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 554, + 167 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 554, + 167 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 554, + 167 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 554, + 167 + ], + "type": "image", + "image_path": "e6521ca76e44b7f737bcd83cbe82ab27014c98ac8c84caa0ef8338c769c1a4a8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 174, + 556, + 196 + ], + "lines": [ + { + "bbox": [ + 313, + 174, + 556, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 174, + 556, + 196 + ], + "type": "text", + "content": "Figure 3. Visualization of outliers in various channels at the decoder [55] of Metric3D model on NYUv2 dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 208, + 555, + 286 + ], + "blocks": [ + { + "bbox": [ + 315, + 208, + 555, + 286 + ], + "lines": [ + { + "bbox": [ + 315, + 208, + 555, + 286 + ], + "spans": [ + { + "bbox": [ + 315, + 208, + 555, + 286 + ], + "type": "image", + "image_path": "09348e4c09371b3ad8b68cbd4659bc31ea9d369b66c817adc5b7a0415845a7d0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 293, + 556, + 316 + ], + "lines": [ + { + "bbox": [ + 313, + 293, + 556, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 556, + 316 + ], + "type": "text", + "content": "Figure 4. Visualization for the activation data distribution of different channels in decoder with log frequency." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 338, + 556, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 556, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 556, + 459 + ], + "type": "text", + "content": "observe large amount of outliers and significant variability in outlier values across different channels, making per-tensor quantization challenging. This motivates the adoption of a per-channel quantization method to better handle these variations. However, for per-channel quantization, the presence of outliers that deviate significantly from the main data distribution, as shown in Figure 4, still leads to substantial quantization errors. Thus, smoothing these large outliers and integrating them into the main data distribution is crucial for maintaining model accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 470, + 460, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 460, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 460, + 483 + ], + "type": "text", + "content": "4. Quantization Framework" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 491, + 556, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 556, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 556, + 540 + ], + "type": "text", + "content": "We first quantize the polished activations with LogNP polishing (Section 4.2). Then we update weights to compensate the loss of activation quantization (Section 4.3). Finally, we quantize updated weights (Section 4.4)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 548, + 394, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 394, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 394, + 562 + ], + "type": "text", + "content": "4.1. Preliminary" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 566, + 556, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 556, + 603 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 556, + 603 + ], + "type": "text", + "content": "Quantization. We mainly adopt the hardware-efficient PTQ methods. For uniform quantization, the quantize and dequantize operations for " + }, + { + "bbox": [ + 313, + 566, + 556, + 603 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 566, + 556, + 603 + ], + "type": "text", + "content": " can be defined as follows," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 359, + 612, + 556, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 612, + 556, + 634 + ], + "spans": [ + { + "bbox": [ + 359, + 612, + 556, + 634 + ], + "type": "interline_equation", + "content": "x _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z p, 0, 2 ^ {k} - 1\\right), \\tag {1}", + "image_path": "2e8ecd35844c763f1fa71449a7fccf05d72a436eddace72a86a0fe1aeab9839b.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 398, + 645, + 556, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 645, + 556, + 659 + ], + "spans": [ + { + "bbox": [ + 398, + 645, + 556, + 659 + ], + "type": "interline_equation", + "content": "\\hat {x} = s \\cdot \\left(x _ {q} - z\\right), \\tag {2}", + "image_path": "7430bc84976bd51af93fcc5abfca22ca6ce3d5621802e9e02f354227df522d36.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": " represents the scale and " + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "inline_equation", + "content": "zp" + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": " is the zero point. The operator " + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\lfloor \\cdot \\rceil" + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": " indicates rounding to the nearest integer, and the CLIP function constrains values that fall outside the range of a " + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": "-bit integer." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11450" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "type": "text", + "content": "As for Log2 quantization, which is mainly used for post-softmax quantization, can be defined as follows," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 105, + 296, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 105, + 296, + 128 + ], + "spans": [ + { + "bbox": [ + 97, + 105, + 296, + 128 + ], + "type": "interline_equation", + "content": "x _ {q} = \\operatorname {C L I P} \\left(\\left\\lfloor - \\log_ {2} \\frac {x}{s} \\right\\rceil , 0, 2 ^ {k} - 1\\right), \\tag {3}", + "image_path": "907dd5dc9417b9dc61724e3e75f1327b2a9b4d3b93f706e463d4fada698da877.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 147, + 138, + 296, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 138, + 296, + 150 + ], + "spans": [ + { + "bbox": [ + 147, + 138, + 296, + 150 + ], + "type": "interline_equation", + "content": "\\hat {x} = s \\cdot 2 ^ {- x _ {q}}. \\tag {4}", + "image_path": "152d701fb322e3d6b3438c3df26b1d2a95f093670b307de3545c00bf92293428.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": "Notations. The quantized layers (including both linear and convolutional layers) in the mode are indexed by " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "1 \\leq l \\leq L" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": ". The weights in the " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "l^{th}" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": " layer are denoted by " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(l)}" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": " with its vectorized/flatened version " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^{(l)}" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 158, + 296, + 207 + ], + "type": "text", + "content": " denotes its inputs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 215, + 173, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 215, + 173, + 227 + ], + "spans": [ + { + "bbox": [ + 55, + 215, + 173, + 227 + ], + "type": "text", + "content": "4.2. Activation Polishing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": "Building on analysis in Section 3.2, we propose LogNP polishing method to adaptively smooth the deviant distribution in decoders in per-channel prospective. For one activation " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{n \\times d}" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " denotes the number of tokens and " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " denotes the channel number, the LogNP polishing function " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot, \\cdot)" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " for each element " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " of input " + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 233, + 296, + 305 + ], + "type": "text", + "content": " is defined as follows," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 315, + 296, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 315, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 77, + 315, + 296, + 329 + ], + "type": "interline_equation", + "content": "\\Phi (x, \\alpha) = \\operatorname {s i g n} (x) \\cdot \\left[ \\log_ {2} (| x | + \\alpha) - \\log_ {2} (\\alpha) \\right], \\tag {5}", + "image_path": "cf0c7692bfd626279d4603ce79917084b021655f51733253daef97f3cef36f22.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}(\\cdot)" + }, + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "text", + "content": " denotes the sign function, and " + }, + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 338, + 296, + 361 + ], + "type": "text", + "content": " is the polishing factor for one single channel." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": "To reduce the quantization error in each channel, the polishing factor " + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": " corresponding to the " + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": " channel with activation " + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = [\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_d]" + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": ") is computed according to the given percentile " + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 363, + 296, + 411 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 422, + 296, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 422, + 296, + 435 + ], + "spans": [ + { + "bbox": [ + 82, + 422, + 296, + 435 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} = P _ {\\epsilon} \\left(\\mathbf {x} _ {i}\\right), i \\in \\{1, 2, 3, \\dots , d \\}, \\epsilon \\in (0, 1 0 0) \\tag {6}", + "image_path": "3e8b470e40b52f001d341362163745fc67f5e35e6a747aad7dbc63fb2fa78713.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "inline_equation", + "content": "P_{\\epsilon}(\\cdot)" + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "text", + "content": "-th percentile function. We adopt uniform " + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 445, + 296, + 564 + ], + "type": "text", + "content": " equals to 95 as deviant activation distributions remain similar across different inputs. We provide the visualization of the polished activation in Figure 5. The polished activation colored in blue appears smoother compared to the original activation colored in red shown in Figure 4, making it more friendly for quantization. After polishing, we perform activation quantization with uniform quantization in Section 4.1. Following activation dequantization, we adopt reverse transformation (i.e., unpolishing) as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 80, + 574, + 296, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 574, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 80, + 574, + 296, + 594 + ], + "type": "interline_equation", + "content": "\\Phi^ {- 1} (\\hat {x}, \\alpha) = \\operatorname {s i g n} (\\hat {x}) \\cdot \\left[ 2 ^ {\\operatorname {s i g n} (\\hat {x}) \\cdot \\hat {x} + \\log_ {2} (\\alpha)} - \\alpha \\right] \\tag {7}", + "image_path": "5c74e5131be1bd1dabf55949c005d7f91247a57abade1543876bec1d4222fb7a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 602, + 297, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 602, + 297, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 602, + 297, + 639 + ], + "type": "text", + "content": "The latency overhead introduced by LogNP polishing and unpolishing is hidden by concurrent execution in our hardware design, which is further explained in Section 5.2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 647, + 222, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 222, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 222, + 661 + ], + "type": "text", + "content": "4.3. Activation Loss Compensation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": "The activation quantization introduces quantization errors. To mitigate this issue, before weight quantization, we first update all weights to compensate the loss of activation quantization. To save the computation cost, we address the problem" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 315, + 69, + 554, + 148 + ], + "blocks": [ + { + "bbox": [ + 315, + 69, + 554, + 148 + ], + "lines": [ + { + "bbox": [ + 315, + 69, + 554, + 148 + ], + "spans": [ + { + "bbox": [ + 315, + 69, + 554, + 148 + ], + "type": "image", + "image_path": "077c36dce931a03818627546c18f92c5213e4ce9cc8a4173f4d6ba27eb7fc150.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 154, + 554, + 176 + ], + "lines": [ + { + "bbox": [ + 313, + 154, + 554, + 176 + ], + "spans": [ + { + "bbox": [ + 313, + 154, + 554, + 176 + ], + "type": "text", + "content": "Figure 5. Visualization for the polished activation data distribution of different channels in decoder with log frequency." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 197, + 554, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 554, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 554, + 220 + ], + "type": "text", + "content": "layer by layer instead of for the whole model. The layer-wise compensation problem is formulated as the following," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 371, + 228, + 555, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 228, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 371, + 228, + 555, + 247 + ], + "type": "interline_equation", + "content": "\\min _ {\\Delta \\mathbf {W}} \\| \\mathbf {W} \\mathbf {x} - (\\mathbf {W} + \\Delta \\mathbf {W}) \\hat {\\mathbf {x}} \\| _ {2} ^ {2} \\tag {8}", + "image_path": "db413c46ba7f27b166171663e23e7618118d7abb3a0c48c0d043b15fa6910129.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "content": " are the original weights and inputs of the layer. " + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "content": " is the quantized inputs and we update the weights with " + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{W}" + }, + { + "bbox": [ + 313, + 255, + 555, + 314 + ], + "type": "text", + "content": " to compensate the activation quantization error, so that the layer outputs after activation quantization and weight compensation should be close to the original outputs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 314, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 314, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 314, + 555, + 338 + ], + "type": "text", + "content": "This problem can be solved by setting the gradients of the minimization objective to zero, as the following," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 370, + 346, + 555, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 346, + 555, + 360 + ], + "spans": [ + { + "bbox": [ + 370, + 346, + 555, + 360 + ], + "type": "interline_equation", + "content": "\\Delta \\mathbf {W} \\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}} + \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} = 0. \\tag {9}", + "image_path": "22ebe844e3c682fc7b4cb0bfddb8c48c0b005a078cad4f60f517f268e51ed2c7.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 369, + 479, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 479, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 479, + 380 + ], + "type": "text", + "content": "The optimal solution can be obtained by" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 365, + 388, + 555, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 388, + 555, + 403 + ], + "spans": [ + { + "bbox": [ + 365, + 388, + 555, + 403 + ], + "type": "interline_equation", + "content": "\\Delta \\mathbf {W} ^ {*} = - \\mathbf {W} (\\mathbf {x} - \\hat {\\mathbf {x}}) \\hat {\\mathbf {x}} ^ {\\mathrm {T}} \\left(\\hat {\\mathbf {x}} \\hat {\\mathbf {x}} ^ {\\mathrm {T}}\\right) ^ {- 1} \\tag {10}", + "image_path": "2a50bce0cd7b40447d24ff60655658be6cc5430a403420176a46f61db0834398.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "text", + "content": "After activation quantization, we can update weights with the above " + }, + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{W}^*" + }, + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "text", + "content": " to compensate the activation quantization error. If " + }, + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}\\hat{\\mathbf{x}}^{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 411, + 555, + 471 + ], + "type": "text", + "content": " is not full rank with difficulties for matrix inversion, we adopt the dampening technique [21, 45]. Next, we quantize the updated weights under the quantized activations." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 478, + 444, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 444, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 444, + 490 + ], + "type": "text", + "content": "4.4. Weight Reconstruction" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 495, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 555, + 567 + ], + "type": "text", + "content": "Problem formulation. In quantization, the weights are modified and we would like to minimize the change of loss incurred by quantization to maintain the superior performance of the model. To quantitatively analyze the loss degradation by quantization, we approximate the loss degradation with Taylor expansion as the following," + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 326, + 574, + 555, + 621 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 574, + 555, + 621 + ], + "spans": [ + { + "bbox": [ + 326, + 574, + 555, + 621 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L (\\mathbf {w} + \\Delta \\mathbf {w}) - L (\\mathbf {w}) \\approx \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {g} _ {\\mathbf {w}} + \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\\\ \\approx \\frac {1}{2} \\Delta \\mathbf {w} ^ {\\mathrm {T}} \\mathbf {H} _ {\\mathbf {w}} \\Delta \\mathbf {w}, \\tag {11} \\\\ \\end{array}", + "image_path": "2d290799eb3d56d9175f059f00959826400b033c72d4b66d3c489cf9c68fd447.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}L" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " represents the gradients and " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{w}} = \\nabla_{\\mathbf{w}}^{2}L" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " denotes the Hessian matrix. " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{w}" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " is the weight perturbation in this step. Here we use the vectorized/flatened version " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " instead of the matrix version " + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "text", + "content": " to obtain a scalar output. As the pre-trained model has been well trained and converged to a minimum, it is reasonable to assume the gradients to be 0. The complexity to obtain the full Hessian is very high" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11451" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "content": "and typically it is not possible to obtain the full Hessian due to computation and memory limitations. Specifically, " + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{w}} \\in \\mathbb{R}^{B \\times B}" + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "content": " is the number of parameters in " + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "content": ". The memory cost for " + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{w}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 131 + ], + "type": "text", + "content": " is extremely heavy in LLMs with billions of parameters." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 132, + 297, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 132, + 297, + 165 + ], + "spans": [ + { + "bbox": [ + 55, + 132, + 297, + 165 + ], + "type": "text", + "content": "Approximating Hessian. For a network trained with negative log-likelihood loss and a probabilistic model " + }, + { + "bbox": [ + 55, + 132, + 297, + 165 + ], + "type": "inline_equation", + "content": "p_{\\mathbf{w}}(y|x_s)" + }, + { + "bbox": [ + 55, + 132, + 297, + 165 + ], + "type": "text", + "content": " under softmax, the Hessian is identical to the Fisher matrix:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 65, + 173, + 295, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 173, + 295, + 208 + ], + "spans": [ + { + "bbox": [ + 65, + 173, + 295, + 208 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {H} _ {\\mathbf {w}} = \\mathbf {F} _ {\\mathbf {w}} = \\sum_ {s = 1} ^ {S} \\mathbb {E} _ {y \\sim p _ {\\mathbf {w}} (y | x _ {s})} [ \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} (y | x _ {s}) \\\\ \\left. \\nabla_ {\\mathbf {w}} \\log p _ {\\mathbf {w}} \\left(y \\mid x _ {s}\\right) ^ {T} \\right] \\tag {12} \\\\ \\end{array}", + "image_path": "59274e6c26333c66447896aecc8d1a72e1faf3051b462b437d5fc1f7b70e9d89.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": " is the number of samples, and for each sample, it needs to compute the expectation over all categories. The complexity with the expectation is also high if there are too many categories. Thus, in practice, the empirical Fisher is commonly adopted to replace the expectation over " + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": " with target label " + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "inline_equation", + "content": "y_{s}" + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": " [33]. The dimension of " + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{w}}" + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": " is the same as " + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{w}}" + }, + { + "bbox": [ + 55, + 217, + 296, + 337 + ], + "type": "text", + "content": " with quadratic memory complexity to the number of parameters. To reduce the complexity, the empirical Fisher is computed by treating layers independently and the layer-wise empirical Fisher can be obtained as below [6, 44]," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 346, + 296, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 346, + 296, + 368 + ], + "spans": [ + { + "bbox": [ + 99, + 346, + 296, + 368 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {l} = \\mathbb {E} \\left[ \\left(\\mathbf {g} ^ {(l)} \\mathbf {g} ^ {(l), \\mathrm {T}}\\right) \\otimes \\left(\\hat {\\mathbf {x}} ^ {(l)} \\hat {\\mathbf {x}} ^ {(l), \\mathrm {T}}\\right) \\right], \\tag {13}", + "image_path": "ab09c6a2115d774ded308f53ae8efd27ee65c86d5792d26e81228098d8e5866c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}^{(l)}" + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "content": " is the input activations and " + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^{(l)}" + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "content": " is the gradients of the " + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "inline_equation", + "content": "l^{th}" + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "content": " layer. " + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 55, + 376, + 296, + 413 + ], + "type": "text", + "content": " denotes Kronecker product. The expectation is taken with respect to data distribution over inputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "text", + "content": "For two different layers (for example, the " + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "text", + "content": " layers), their Fisher is often written as " + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{ij} = \\sum_{s=1}^{S} \\mathbb{E}\\left[\\nabla_{\\mathbf{w}^{(i)}} \\log p_{\\mathbf{w}}(y_s | x_s) \\nabla_{\\mathbf{w}^{(j)}} \\log p_{\\mathbf{w}}(y_s | x_s)^T\\right]" + }, + { + "bbox": [ + 55, + 414, + 296, + 453 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "text", + "content": "which are often ignored to save computations. The Fisher for the whole model can be formulated as a block diagonal matrix " + }, + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{w}} = \\mathrm{diag}(\\mathbf{F}_1,\\mathbf{F}_2,\\dots ,\\mathbf{F}_L)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 488, + 296, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 488, + 296, + 512 + ], + "spans": [ + { + "bbox": [ + 55, + 488, + 296, + 512 + ], + "type": "text", + "content": "To obtain the Fisher in practice, we adopt the KFAC approximation method [20, 44] as below," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 118, + 522, + 295, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 522, + 295, + 536 + ], + "spans": [ + { + "bbox": [ + 118, + 522, + 295, + 536 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {l} = \\mathbf {G} _ {l} \\otimes \\mathbf {A} _ {l} \\tag {14}", + "image_path": "0b35b92f57f6fe68e046dd464e6831912b875dd335881ae91d2bfbf226bcf918.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 118, + 537, + 295, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 537, + 295, + 563 + ], + "spans": [ + { + "bbox": [ + 118, + 537, + 295, + 563 + ], + "type": "interline_equation", + "content": "\\mathbf {G} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\mathbf {g} _ {s} ^ {(l)} \\mathbf {g} _ {s} ^ {(l), \\mathrm {T}} \\tag {15}", + "image_path": "f5256d9fc5a2b564a599ba9126aa4e371c270595de6c92308bd930dc9911c0c9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 118, + 564, + 295, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 564, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 118, + 564, + 295, + 590 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {l} = \\frac {1}{\\sqrt {S}} \\sum_ {s = 1} ^ {S} \\hat {\\mathbf {x}} _ {s} ^ {(l)} \\hat {\\mathbf {x}} _ {s} ^ {(l). \\mathrm {T}} \\tag {16}", + "image_path": "a15f9dd0de0f9252bb554a3ec0d6fe245df324433e1f27e7344fb9efa7ac2912.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "type": "text", + "content": "The KFAC approximation [25, 76] approximates an expectation of Kronecker products as a Kronecker product of two expectations " + }, + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}\\otimes \\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]\\approx \\mathbb{E}[\\mathbf{g}^{(l)}\\mathbf{g}^{(l),T}]\\otimes" + }, + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[\\hat{\\mathbf{x}}^{(l)}\\hat{\\mathbf{x}}^{(l),T}]" + }, + { + "bbox": [ + 55, + 597, + 296, + 657 + ], + "type": "text", + "content": ", where the activations and derivatives are assumed to be independent." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 658, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 296, + 714 + ], + "type": "text", + "content": "Optimizing quantization parameters. Next we optimize the quantization parameters. Given our optimization loss in Equation (11), multiple optimization methods can be adopted such as STE [24] and AdaRound [46]. Due to its superior performance in PTQ, we use AdaRound [46] to learn the" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 69, + 555, + 191 + ], + "blocks": [ + { + "bbox": [ + 317, + 69, + 555, + 191 + ], + "lines": [ + { + "bbox": [ + 317, + 69, + 555, + 191 + ], + "spans": [ + { + "bbox": [ + 317, + 69, + 555, + 191 + ], + "type": "image", + "image_path": "84c4f3f019ba0ce28385fd4967e69731f144f201b00a624a71b577b9cf008c16.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 198, + 555, + 209 + ], + "lines": [ + { + "bbox": [ + 313, + 198, + 555, + 209 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 555, + 209 + ], + "type": "text", + "content": "Figure 6. The block diagram of the proposed hardware accelerator." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 229, + 555, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 253 + ], + "type": "text", + "content": "rounding parameter which decides rounding up or down. Formally, we minimize the following loss," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 258, + 555, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 258, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 326, + 258, + 555, + 289 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {v}} \\sum_ {l = 1} ^ {L} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) ^ {\\mathrm {T}} \\mathbf {F} _ {l} \\left(\\mathbf {w} ^ {(l)} - \\hat {\\mathbf {w}} ^ {(l)}\\right) + \\lambda h (\\mathbf {v}), \\tag {17}", + "image_path": "112c27e6cae37f5c6c19c11f0a54af77e5def24117de85396341a36b6475f092.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "content": " denotes the rounding parameter which are used to construct the quantized weights " + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}^{(l)}" + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "inline_equation", + "content": "h(\\mathbf{v})" + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "content": " is a regularizer in AdaRound [46] with " + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 294, + 555, + 366 + ], + "type": "text", + "content": " controlling its strength. More details about AdaRound are presented in Appendix 9. We only use a small calibration set (32 samples) sampled from the training dataset to calibrate the quantized model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 376, + 419, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 419, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 419, + 390 + ], + "type": "text", + "content": "5. Hardware Design" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 396, + 418, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 418, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 418, + 409 + ], + "type": "text", + "content": "5.1. Top-Level Design" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 414, + 556, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 414, + 556, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 414, + 556, + 558 + ], + "type": "text", + "content": "We design a flexible and programmable accelerator as shown in Figure 6. The Dispatch module fetches instructions via the AXI bus and distributes them to local Instruction FIFOs, while the Synchronize module controls the start and end of each module. Instruction FIFOs hold out-of-order instructions and are controlled by Synchronize module for execution. The Load and Store modules, functioning as the DMA, facilitate data transfer between off-chip memory (e.g., HBM or DDR) and local buffers. The Matrix Multiplication Unit (MMU) performs General Matrix Multiply (GeMM) and convolution when the Vector Compute Unit (VCU) handles nonlinear activation functions." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 564, + 448, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 448, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 448, + 577 + ], + "type": "text", + "content": "5.2. On-Chip Kernel Design" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 582, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 689 + ], + "type": "text", + "content": "We adopt a multiply-accumulate tree array to implement both matrix multiplication and convolution. For W4A4 and W4A8 configurations, we design specialized multipliers and adders to enhance computational efficiency and reduce chip area overhead. Additionally, the use of low-bit quantized matrices eases memory bandwidth demands during data transfer, allowing for full utilization of the external memory bandwidth. As for Float32, we implement IEEE 754 standard floating-point computation for fair comparison." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "Meanwhile, we propose a programmable vector computation array composed of multiple Floating-Point Units (FPU)" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11452" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 555, + 436 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 555, + 436 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 555, + 436 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 555, + 436 + ], + "type": "table", + "html": "
MethodW/ANYUv2 [47]KITTI [19]
AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓AbsRel ↓δ1↑δ2↑δ3↑RMSE ↓Silog ↓
ViT-Small Backbone
\\Float320.0870.9380.9900.9960.3310.0350.0740.9340.9840.9953.4030.043
OBS [17]W40.1070.8850.9850.9970.3910.0420.1220.8670.9730.9914.5080.058
minmax [27]W4A80.4530.4050.7020.8681.0670.1110.4560.1020.3290.57513.3550.159
ema [26]0.2570.5910.8590.9580.7930.0930.3120.3410.6320.80711.1020.139
percentile [11]0.1900.6350.9120.9810.7740.0770.2220.5520.8140.9188.9000.114
AdaRound [46]0.1340.7930.9670.9810.4710.0420.1280.8760.9530.9934.2360.051
BrecQ [36]0.1280.8170.9800.9960.4520.0400.1040.9000.9770.9933.9140.047
Ours0.1030.8990.9870.9960.3800.0420.0920.9160.9810.9953.6820.046
minmax [27]W4A41.2650.1300.2850.4772.5930.1600.5840.0540.1600.32115.8770.245
ema [26]0.3710.3590.3590.8411.2260.1460.6320.0220.0810.22816.2650.244
percentile [11]0.3570.3660.6590.8461.2230.1460.6460.0190.0640.19716.3840.244
AdaRound [46]0.2510.4590.8120.9360.8480.1030.5010.2390.3680.53814.3980.216
BrecQ [36]0.2170.5980.8840.9700.7240.0710.4050.2780.4930.63412.3370.184
Ours0.1330.8150.9650.9900.4530.0520.1970.5340.9370.9855.4290.059
ViT-Large Backbone
\\Float320.0670.9720.9930.9970.2620.0400.0540.9740.9950.9992.5050.032
OBS [17]W40.0700.9720.9940.9980.2670.0380.0600.9680.9950.9982.7480.034
minmax [27]W4A80.6710.2790.5470.7481.4480.1440.5460.0550.1720.38514.8410.202
ema [26]0.6570.2890.5590.7561.4250.1410.3940.2190.4810.68612.0850.169
percentile [11]0.4250.3490.7150.9071.0730.1060.1920.6450.8830.9496.9570.093
AdaRound [46]0.0840.9590.9910.9970.2760.0400.0570.9720.9950.9992.7690.034
BrecQ [36]0.0760.9670.9930.9970.2720.0390.0570.9710.9950.9992.7780.034
Ours0.0710.9700.9930.9970.2640.0360.0550.9730.9950.9992.5420.032
minmax [27]W4A42.2380.1160.2490.3915.7610.2610.5650.0630.1900.36315.6930.253
ema [26]1.0390.1740.3760.5782.1260.1570.5080.1230.2940.46015.2060.247
percentile [11]0.9200.2070.4280.6311.9150.1570.4920.1440.3170.48715.0120.244
AdaRound [46]0.5010.2590.5640.7821.4820.1450.4820.1720.3950.54113.7820.207
BrecQ [36]0.4690.3300.6090.8111.3230.1370.4340.1910.4070.59013.4620.192
Ours0.0970.9320.9930.9980.3270.0450.0700.9520.9930.9983.1040.038
", + "image_path": "8c21b2bbab0497ea6faa33eb0b8bf9e85c55959dd7225d8e5196529627540ccf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 443, + 555, + 466 + ], + "lines": [ + { + "bbox": [ + 55, + 443, + 555, + 466 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 555, + 466 + ], + "type": "text", + "content": "Table 1. Main results of Metric3D model with ViT-Small and ViT-Large backbone on NYUv2 and KITTI datasets. Results with ViT-Giant backbone is included in Table A1 at Appendix 10." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "spans": [ + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "text", + "content": "in Vector Computing Unit (VCU). In the VCU, we design a programmable vector computation array composed of multiple FPU to enable more efficient computation. The FPU supports the Special Function Unit (SFU) through polynomial approximation [51], which achieves the computation of non-linear functions (e.g. " + }, + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "inline_equation", + "content": "\\log_2" + }, + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "inline_equation", + "content": "\\exp" + }, + { + "bbox": [ + 54, + 486, + 297, + 704 + ], + "type": "text", + "content": ") within 3 to 5 clock cycles while maintaining ultra-high precision. For the activation polishing optimization discussed in Section 4.2, the FPU is further specifically designed to enhance execution efficiency. Compared to the NVIDIA GPU [48], the proposed SFU achieves nearly same accuracy, with only a 2 to 5 ULP (units in the last place) error. Meanwhile, the VCU supports multiple numerical format inputs, unifying them into Float32 for computation, and then converts these Float32 numbers into integers such as INT4 or INT8 as needed, which seamlessly integrates both floating-point and integer data types for efficient processing. Hence, the proposed quantization framework for MDE models with ac" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 486, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 510 + ], + "type": "text", + "content": "tivation polishing optimization is accurately and efficiently deployed on our hardware." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 516, + 484, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 484, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 484, + 529 + ], + "type": "text", + "content": "5.3. Overlapped Computation Flow" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 312, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 534, + 556, + 715 + ], + "type": "text", + "content": "Our hardware architecture supports kernel fusion of on-chip matrix multiplication and vector computation, enabling intermediate results stored in local SRAM to be directly sent to the VCU for activation, quantization, or dequantization without being written back to DDR. By fusing these operations into a single flow, we minimize the latency introduced by multiple memory accesses. Also, this design reduces data transfer time and enhances the overall execution efficiency. Furthermore, our hardware is designed to be programmable with customized instructions, enabling the configuration of different computational tasks to be executed concurrently within an instruction cycle. This parallelism enables a substantial speedup in processing by allowing multiple operations to be pipelined, thereby reducing the total time needed to complete complex tasks. As shown in Figure 7, data trans" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11453" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": "ferring, matrix computation, and vector computation can be fully overlapped to improve execution efficiency. This concurrency ensures that no computational resource is idle and every cycle is utilized to its maximum potential, leading to a streamlined and optimized workflow. Therefore, the total on-device latency of the depth estimation model executed with our quantization framework is optimized through extensive operator fusion and concurrent execution." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 177, + 296, + 251 + ], + "blocks": [ + { + "bbox": [ + 56, + 177, + 296, + 251 + ], + "lines": [ + { + "bbox": [ + 56, + 177, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 56, + 177, + 296, + 251 + ], + "type": "image", + "image_path": "ee7b1aae37539988b3fce184a81a88dc6c84959de08d23fe8bca98f407e10a50.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 258, + 296, + 282 + ], + "lines": [ + { + "bbox": [ + 55, + 258, + 296, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 258, + 296, + 282 + ], + "type": "text", + "content": "Figure 7. The schematic of concurrent execution, where the computation of Matrix, Vector, Load and Store can execute parallel." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 304, + 181, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 181, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 181, + 319 + ], + "type": "text", + "content": "6. Experimental Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 324, + 163, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 163, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 163, + 337 + ], + "type": "text", + "content": "6.1. Experiment Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "text", + "content": "We adopt Metric3D [95] with ViT-Small, ViT-Large, and ViT-Giant [15] backbones to present the main results and Depth Anything [90] with ViT-Large backbone to further verify the generalization across additional datasets. For a fair comparison, we adopt per-channel asymmetric quantization for both weights and activations in W4A8 and W4A4 configurations. We randomly sample 32 images as calibration set from the training sets of NYUv2 [47] for indoor scenes and KITTI [19] for outdoor scenes. The percentile " + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "text", + "content": " for the polishing factor is set to 95, and " + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "text", + "content": " is then computed as the average value across the calibration samples. For activation loss compensation and weight reconstruction, we still use same 32 samples for the calibration. For gradient computation in weight reconstruction, we adopt batch size of 1, learning rate set to 4e-5, warm up of 0.2, weight decay of 0.01, drop rate of 0.5, and 20,000 iterations. For evaluation, we use NYUv2 [47], SUN RGB-D [67], iBims-1 [32], and HyperSim [58] for indoor scenes; and KITTI [19], vKITTI [7], and DIODE [75] for outdoor scenes. Absolute relative error (AbsRel), accuracy under threshold " + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "inline_equation", + "content": "(\\delta_i < 1.25^i, i = 1, 2, 3)" + }, + { + "bbox": [ + 55, + 341, + 296, + 605 + ], + "type": "text", + "content": ", root mean squared error (RMSE), and metric-depth loss (Silog) metrics are employed in our evaluation results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 612, + 204, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 204, + 625 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 204, + 625 + ], + "type": "text", + "content": "6.2. Hardware Implementation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "We implement our hardware in RTL and synthesis the design using Design Compiler [70] under a commercial 28nm CMOS technology. The frequency and area are tested by the Design Compiler and the power is tested by Prime Time [71] PX with synthesized netlist and dynamic simulation switch rate under different modes. After synthesis, based on the latency profiled by simulation and the frequency given by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": "Design Compiler, we introduce a hardware performance emulator for latency test. The DDR is simulated by RTL, with a bandwidth of 19.2 GB/s." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 116, + 457, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 116, + 457, + 129 + ], + "spans": [ + { + "bbox": [ + 313, + 116, + 457, + 129 + ], + "type": "text", + "content": "6.3. Depth Estimation Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 134, + 556, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 134, + 556, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 556, + 422 + ], + "type": "text", + "content": "We present the quantization results with W4A8 and W4A4 configurations using Metric3D [95] with ViT-Small and ViT-Large backbone on indoor dataset NYUv2 [47] and outdoor dataset KITTI [19] in Table 1. The results with ViT-Giant backbone are included in Table A1 at Appendix 10. Compared to conventional PTQ methods such as minmax [27], EMA [26], and percentile [11], our framework demonstrates significantly improved performance. Additionally, when benchmarked against other learning-based approaches including OBS [17], AdaRound [46], and BrecQ [36], our method also achieves superior results. Notably, for the ViT-Large backbone with W4A8 settings, our method maintains nearly lossless performance. In the W4A4 configuration, our approach shows a substantial performance advantage over other methods, validating the effectiveness of our proposed quantization framework. Meanwhile, we present results of Depth Anything model with ViT-Large backbone on various additional datasets [7, 32, 58, 67, 75] covering both indoor and outdoor scenes, as shown in Table 2. Our method, which applies quantization to both weights and activations, achieves performance comparable to OBS (a weight-only quantization method) across multiple datasets in W4A8 configuration, and outperforms the BrecQ for all configurations, showing the effectiveness of our proposed quantization method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 430, + 455, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 455, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 455, + 442 + ], + "type": "text", + "content": "6.4. Latency Results on ASIC" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "content": "We present the latency results of Metric3D with detailed hardware resource utility in Table 3. The latency is tested with three different resolutions. The power is further normalized by the latency and computation cost (i.e., GMACs) for the energy efficiency. For three different configurations, the frequency are uniformly " + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "inline_equation", + "content": "1\\mathrm{GHz}" + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "content": ". The silicon area that our design occupies on a chip for Float32, W4A8, and W4A4 is " + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "inline_equation", + "content": "29.22\\mathrm{mm}^2" + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "inline_equation", + "content": "23.94\\mathrm{mm}^2" + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "inline_equation", + "content": "24.35\\mathrm{mm}^2" + }, + { + "bbox": [ + 313, + 448, + 556, + 616 + ], + "type": "text", + "content": ", respectively. As shown in Table 3, our proposed method demonstrates superior performance with faster inference speed and higher power efficiency across various model scales and resolutions. Notably, for ViT-Small backbone at 256 resolution under W4A4 configuration, our method achieves up to 26 FPS, showing the real-time performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 624, + 408, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 408, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 408, + 636 + ], + "type": "text", + "content": "6.5. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": "We regulate the number of calibration samples to verify the effectiveness of our proposed method, and the results are shown in Figure 8. We observe that the model performance stabilizes when the number of calibration samples reaches 32 for both W4A4 and W4A8 configuration. Additionally, activation compensation proves crucial for the W4A4." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11454" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 555, + 166 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 555, + 166 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 555, + 166 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 555, + 166 + ], + "type": "table", + "html": "
W/ADataset MethodNYUv2 [47]SUN RGB-D [67]iBims-1 [32]HyperSim [58]KITTI [19]vKITTI2 [19]DIODE Outdoor [75]
AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑AbsRel ↓δ1↑
\\Float320.0560.9840.5000.6600.1500.7140.3280.5080.0460.9820.0840.9120.7990.289
W4OBS [17]0.0590.9810.5080.6260.1510.7180.3270.5010.0490.9800.0910.8930.7930.287
W4A8BrecQ [36]0.0990.9030.4890.6920.1830.5930.3770.3720.0510.9510.6060.1320.7990.010
Ours0.0580.9820.3940.7560.1570.7000.3220.5230.0600.9650.1080.8460.8320.298
W4A4BrecQ [36]0.3420.2960.3960.4160.4190.2220.7030.0470.3850.2350.7570.0090.7650.034
Ours0.0700.9720.4660.7420.1770.6150.3220.5120.0590.9350.1000.8820.7580.280
", + "image_path": "0fe8a442b931d4b8901ac001b99a58f50342462c0faae28d48c635d6809e4a35.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 215, + 294, + 448 + ], + "blocks": [ + { + "bbox": [ + 55, + 173, + 555, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 173, + 555, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 555, + 196 + ], + "type": "text", + "content": "Table 2. Main results of Depth Anything model with ViT-Large backbone. The first four sets are indoor scenes, while the last three are outdoor scenes. Full detailed results are included in Table A2 at Appendix 10." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 215, + 294, + 448 + ], + "lines": [ + { + "bbox": [ + 58, + 215, + 294, + 448 + ], + "spans": [ + { + "bbox": [ + 58, + 215, + 294, + 448 + ], + "type": "table", + "html": "
W / ASize (MB)Res.Latency (ms) ↓FPS ↑Power Eff. (GMAC/W) ↑
ViT-Small
Float32143.125676.8 (1×)13.02 (1×)85.6 (1×)
W4A817.8842.6 (1.8×)23.47 (1.8×)172.8 (2.0×)
W4A438.3 (2.0×)26.11 (2.0×)177.5 (2.1×)
Float32143.1512325.5 (1×)3.07 (1×)87.3 (1×)
W4A817.88159.0 (2.0×)6.29 (2.0×)200.1 (2.3×)
W4A4133.4 (2.4×)7.50 (2.4×)220.3 (2.5×)
Float32143.110242181.4 (1×)0.46 (1×)78.4 (1×)
W4A817.88836.8 (2.6×)1.20 (2.6×)228.9 (2.9×)
W4A4616.7 (3.5×)1.62 (3.5×)287.0 (3.7×)
ViT-Large
Float321572256584.1 (1×)1.71 (1×)118.2 (1×)
W4A8196.5223.5 (2.6×)4.47 (2.6×)331.1 (2.8×)
W4A4167.9 (3.5×)5.96 (3.5×)425.4 (3.6×)
Float3215725122214.5 (1×)0.45 (1×)126.4 (1×)
W4A8196.5798.4 (2.8×)1.25 (2.8×)392.5 (3.1×)
W4A4568.5 (3.9×)1.76 (3.9×)509.3 (4.0×)
Float321572102413297.1 (1×)0.08 (1×)126.9 (1×)
W4A8196.54228.3 (3.1×)0.24 (3.1×)446.8 (3.5×)
W4A42725.1 (4.9×)0.37 (4.9×)640.6 (5.0×)
", + "image_path": "f963739287c9b0bdc178b8e460f5f0089933e7dc17526d982a4fcf67085390dc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 456, + 295, + 479 + ], + "lines": [ + { + "bbox": [ + 55, + 456, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 295, + 479 + ], + "type": "text", + "content": "Table 3. ASIC results of Metric3D with ViT-Small and ViT-Large. ViT-Giant results are shown in Table A3 at Appendix 10." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 55, + 488, + 296, + 602 + ], + "blocks": [ + { + "bbox": [ + 55, + 488, + 296, + 602 + ], + "lines": [ + { + "bbox": [ + 55, + 488, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 488, + 296, + 602 + ], + "type": "image", + "image_path": "896dba8aa1482d1300b2f104974dbb65727bca6a90846d45ad53ed72bd6027bb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 609, + 295, + 633 + ], + "lines": [ + { + "bbox": [ + 55, + 609, + 295, + 633 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 295, + 633 + ], + "type": "text", + "content": "Figure 8. Accuracy ablation for the number of calibration samples using ViT-Large backbone on NYUv2 dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": "We further perform ablation study on hardware resources by varying the number of MMUs and VCUs (i.e., number of cores). The results of 2, 4 and 8 cores are presented in Figure 9. The results show that more cores lead to faster speed. Compared to the Float32 model, the quantized model" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 314, + 213, + 555, + 327 + ], + "blocks": [ + { + "bbox": [ + 314, + 213, + 555, + 327 + ], + "lines": [ + { + "bbox": [ + 314, + 213, + 555, + 327 + ], + "spans": [ + { + "bbox": [ + 314, + 213, + 555, + 327 + ], + "type": "image", + "image_path": "11d8dc23b72083ff2c54d486cca624b5c1ebda24b626d61fda6d7d8d97af6731.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "type": "text", + "content": "Figure 9. Latency ablation for different number of cores using ViT-Large backbone with 256x256 resolution." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 381, + 555, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 555, + 407 + ], + "type": "text", + "content": "is not sensitive to the hardware resource and achieves high hardware efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 407, + 556, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 556, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 556, + 479 + ], + "type": "text", + "content": "Meanwhile, we also visualize depth estimation results of Metric3D with ViT-Large backbone in Figure A1 at Appendix 11 compared with BrecQ [36] on NYUv2 [47] for indoor scene and KITTI [19] for outdoor scene. The visualizations verify the effectiveness of our methods on both indoor and outdoor scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 496, + 388, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 388, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 388, + 509 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 518, + 556, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 518, + 556, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 518, + 556, + 639 + ], + "type": "text", + "content": "In this paper, we propose QuartDepth, a quantization framework for the real-time acceleration of MDE models on ASICs. We provide the LogNP polishing method to smooth the outliers in the decoder of MDE models, and provide the compensation method to mitigate the loss of activation quantization. We then introduce the weight reconstruction to reduce the weight quantization loss. Furthermore, we design a novel flexible and programmable hardware accelerator for our efficient deployment on ASICs. Experimental results verify the effectiveness of our proposed framework." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 655, + 419, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 655, + 419, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 655, + 419, + 670 + ], + "type": "text", + "content": "8. Acknowledgment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "This work was mainly supported by Northeastern University and Nanjing University. 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ACL, 2024. 2" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11460" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_content_list.json b/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ee1e66e7efe0e1f5e5260b3d7592a3feaf652315 --- /dev/null +++ b/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_content_list.json @@ -0,0 +1,1415 @@ +[ + { + "type": "text", + "text": "Query Efficient Black-Box Visual Prompting with Subspace Learning", + "text_level": 1, + "bbox": [ + 148, + 130, + 849, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhaogeng Liu $^{1,\\dagger}$ , Haozhen Zhang $^{1,\\dagger}$ , Hualin Zhang $^{2}$ , Xingchen Li $^{1}$ , Wanli Shi $^{1}$ , Bin Gu $^{1,*}$ , Yi Chang $^{1,3,*}$ $^{1}$ School of Artificial Intelligence, Jilin University, 2699 Qianjin Street, Changchun, China \n $^{2}$ Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE \n $^{3}$ Engineering Research Center of Knowledge-Driven Human-Machine Intelligence, MOE, China \n{zgliu20, haozhen23}@mails.jlu.edu.cn, zhanghualin98@gmail.com, xcli23@mails.jlu.edu.cn \n{wanlishi2, jsgubin} @ gmail.com, yichang@jlu.edu.cn", + "bbox": [ + 89, + 178, + 903, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 321, + 326, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Prompt Learning (VPL) has emerged as a powerful strategy for harnessing the capabilities of large-scale pretrained models (PTMs) to tackle specific downstream tasks. However, the opaque nature of PTMs in many real-world applications has led to a growing interest in gradient-free approaches within VPL. A significant challenge with existing black-box VPL methods lies in the high dimensionality of visual prompts, which necessitates considerable API queries for tuning, thereby impacting efficiency. To address this issue, we propose a novel query-efficient framework for black-box visual prompting, designed to generate input-dependent visual prompts efficiently for large-scale black-box PTMs. Our framework is built upon the insight of reparameterizing prompts using neural networks, improving the typical pretraining-fine-tuning paradigm through the subspace learning strategy to maximize efficiency and adaptability from both the perspective of initial weights and parameter dimensionality. This tuning intrinsically optimizes low-dimensional representations within the well-learned subspace, enabling the efficient adaptation of the network to downstream tasks. Our approach significantly reduces the necessity for substantial API queries to PTMs, presenting an efficient method for leveraging large-scale black-box PTMs in visual prompting tasks. Most experimental results across various benchmarks demonstrate the effectiveness of our method, showcasing substantial reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on downstream tasks.", + "bbox": [ + 88, + 353, + 485, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 806, + 220, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large pre-trained models (PTMs) have demonstrated remarkable effectiveness across a range of tasks in computer", + "bbox": [ + 89, + 832, + 485, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vision, as evidenced by numerous studies [1, 13, 14, 41]. Recently, researchers have drawn inspiration from the success of prompt learning in natural language processing [11, 22, 23, 33], leading to the innovative approach of visual prompt learning (VPL) [5, 6, 19]. This method involves training a global visual prompt, consisting of pixel-level modifications often represented as padding or patches, using a pre-trained visual model and task-specific downstream data. The integration of this visual prompt with any downstream test image facilitates model predictions. Recent studies have validated the efficacy of VPL, demonstrating its competitive advantage over traditional parameter fine-tuning methods across various applications.", + "bbox": [ + 511, + 323, + 906, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although VPL has demonstrated significant potential [5, 6, 19], its practical application encounters substantial barriers, especially when pre-trained models are only available through opaque black-box APIs or as proprietary software. To address this challenge, Oh et al. [27] introduce Blackbox Visual Prompting (BlackVIP), an innovative approach that facilitates effective transfer learning with pre-trained vision models without requiring direct access to their parameters. However, black-box VPL necessitates considerable API queries to PTMs, resulting in significant costs. Furthermore, the high dimensionality of continuous prompts poses challenges for black-box optimization algorithms, as these methods require a substantial number of queries to optimize prompts effectively in high-dimensional spaces. Therefore, improving performance with a limited number of queries is a key challenge in high-dimensional black-box VPL.", + "bbox": [ + 511, + 521, + 908, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the straightforward candidates for addressing the abovementioned challenge is to adopt the pre-training-finetuning paradigm typical of large language models (LLMs). Pre-training can yield high-quality initial weights, which in turn significantly reduces the number of API queries required during the fine-tuning phase of black-box VPL. Nevertheless, pre-training does not reduce the dimensionality of the tunable parameters, which can significantly impact the convergence rate of black-box optimization methods. Therefore,", + "bbox": [ + 511, + 763, + 910, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Co-first authors and are listed in random order.", + "bbox": [ + 112, + 875, + 367, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "\\*Co-corresponding author.", + "bbox": [ + 112, + 887, + 256, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4322", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f15a9cca6e98089374fe423498198f7a65b10399db7482da70eca9d18a701061.jpg", + "image_caption": [ + "Figure 1. An overview of white/black-box visual prompt approaches. VP suffers from requiring a huge memory capacity to optimize the parameters through backpropagation. BlackVIP enjoys the proficiency of parameter efficiency but still suffers from large query complexity. Our approach solves the above problems by utilizing the strategy of subspace learning, resulting in a parameter-efficient and query-efficient black-box visual prompt framework." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 483, + 200 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "if the parameter dimensionality can be reduced on the basis of pre-training, it could theoretically lead to a further reduction in API query costs.", + "bbox": [ + 88, + 353, + 485, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fortunately, recent studies proposed the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. This discovery facilitates the development of efficient optimization strategies that concentrate on this reduced-dimensional subspace. Based on this idea, Sun et al. [33] optimize a latent representation of the prompt in a dimensionality-reduced space, using a random low-rank matrix to map this optimized representation back into the original high-dimensional prompt space [31, 33, 36, 37]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research explores adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to yield optimal prompt configurations [37]. Such adaptive strategies could significantly enhance the efficiency and effectiveness of black-box prompt tuning by dynamically adjusting to the characteristics of the prompt's underlying data distribution.", + "bbox": [ + 91, + 400, + 483, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the above motivation, this paper introduces a novel framework for Black-box Visual Prompting that optimizes query efficiency. To address the identified limitations, our framework leverages intrinsic dimensionality [31, 33, 36, 37] by integrating pre-training with subspace learning to develop efficient black-box visual prompting, as shown in Figure 1. This process aims to identify and utilize low-dimensional subspaces based on pre-training, thereby maximizing efficiency and adaptability from both the initial weights and parameter dimensionality perspectives to satisfy a broad spectrum of applications. A significant advancement is our proposal of the subspace learning paradigm,", + "bbox": [ + 89, + 719, + 485, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which effectively addresses the challenges associated with learning subspaces in the black-box setting. Fine-tuning the low-dimensional representation of the prompt generation network's parameters within the subspace derived from this paradigm enables the generation of input-dependent visual prompts that are both effective and efficient across various downstream tasks.", + "bbox": [ + 511, + 90, + 905, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work are summarized as follows:", + "bbox": [ + 511, + 198, + 906, + 227 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- This paper proposes an efficient black-box visual prompting framework, which leverages pre-training and subspace learning strategy to significantly reduce the number of API queries, for generating task-specific visual prompts without relying on gradient-based methods.", + "- Our framework introduces a novel subspace learning paradigm that iteratively generates each column of the projection matrix, effectively addressing the difficulties of learning a high-quality subspace in the black-box setting.", + "- Our method adapts the PTM to downstream tasks with low query requirements. The experimental results demonstrate the superiority of our framework. Compared to methods that learn visual prompts directly in downstream tasks, our framework uses less than $5\\%$ of their API queries. Additionally, when compared to fine-tuning methods with the same pre-trained weights, our framework also reduces the API queries by one-third." + ], + "bbox": [ + 513, + 229, + 908, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 503, + 663, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Visual Prompt Learning", + "text_level": 1, + "bbox": [ + 513, + 530, + 736, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt learning [11, 22, 23, 33] has emerged as a significant approach in natural language processing for effectively adapting pre-trained LLMs for specific downstream tasks. This method involves the creation of a trainable, lightweight component that serves as an additional input (or prompt) to a static model. Inspired by its great success in natural language processing, VPL [2, 5, 6, 19] also starts emerging in the computer vision domain to adapt the large-scale upstream pre-trained visual models to various downstream tasks, such as image classification [2], vision-language modeling [42], etc. Specifically, Context Optimization (CoOp) [39] innovatively incorporates a continuous text prompt within the text encoder of a Vision-Language Model (VLM), thereby enhancing its interpretative and processing capabilities. Building on this framework, Conditional CoOp (CoCoOp) [38] further refines the approach by adapting CoOp into a version that is dependent on the input. Jia et al. [19] propose the Visual Prompt Tuning (VPT) that governs learnable visual tokens to the embedding layer or several encoder layers of Vision Transformer. Bahng et al. [2] explore a technique for learning pixel perturbations that are applied to a specific, constrained area of an input image. All these methods require accessibility of the model architecture and parameters.", + "bbox": [ + 511, + 553, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4323", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, in real-world applications, many AI systems are offered as APIs or proprietary software, where the specifics of their implementation or the full range of parameters are not disclosed due to commercial considerations. This limitation renders these approaches impractical for use in such contexts. To solve this problem, Oh et al. [27] propose BlackVIP, which efficiently adapts the PTMs without knowledge about model architectures and parameters. However, this approach usually requires a high number of queries, which can lead to significant economic costs. Therefore, it motivates us to investigate a query-efficient black-box visual prompting method.", + "bbox": [ + 89, + 90, + 483, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Black-box Optimization in Prompt Learning", + "text_level": 1, + "bbox": [ + 89, + 286, + 470, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, the widespread deployment of AI applications as APIs or proprietary software has necessitated the use of black-box optimization techniques in prompt learning. This is primarily due to the commercial practice of withholding detailed implementation details or full parameter configurations, which has significantly contributed to the success of these optimization methods. Specifically, Dao et al. [11] use the policy gradient method to search the discrete prompt for the pre-trained language model. They also observed that the conventional policy gradient suffers from high variance, which makes it challenging to converge in practice. Therefore, they adopted a variance-reduced policy gradient estimator to improve the performance [12, 40]. RLPrompt [10] uses reinforcement learning to optimize the discrete prompt for the pre-trained language model. BlackVIP [27] adopts the Simultaneous Perturbation Stochastic Approximation (SPSA) as a zeroth-order optimization (ZOO) algorithm with gradient correction to search the visual prompt for the large-scale pre-trained vision models. These methods often necessitate a substantial number of queries to achieve convergence, resulting in increased costs. However, all these methods need to solve a high-dimensional optimization problem, where the black-box methods are usually inefficient.", + "bbox": [ + 91, + 310, + 483, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fortunately, recent studies propose the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. Based on this idea, Black-Box Tuning (BBT) [33] and BBTv2 [32] use a random matrix sampled from a uniform distribution to project the high-dimensional continuous prompt into a low-dimensional subspace and optimize a latent representation in this subspace using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [16, 17]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research is required to explore adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to", + "bbox": [ + 89, + 659, + 485, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "yield optimal prompt configurations.", + "bbox": [ + 511, + 90, + 756, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 513, + 119, + 648, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the proposed framework for black-box visual prompt generation, which consists of subspace learning and visual prompt tuning. The overall process of the proposed framework is illustrated in Figure 2.", + "bbox": [ + 511, + 143, + 906, + 205 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Brief Review of Visual Prompt Reparameterization", + "text_level": 1, + "bbox": [ + 511, + 214, + 906, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by the great success of prompt learning in NLP, Oh et al. [27] propose an asymmetric autoencoder-style network that receives the original image and produces a corresponding visual prompt for each image.", + "bbox": [ + 511, + 251, + 906, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective function of VPL is to minimize the downstream task loss by adapting the frozen PTM via input space prompt optimization. Specifically, given a frozen prediction model $P_{\\theta}$ ( $\\theta$ denotes the model parameters) and the perturbed image $\\tilde{x}$ with prompt corresponding to the label $y$ , the learning objective of VPL is formulated as:", + "bbox": [ + 511, + 311, + 908, + 402 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\phi} {\\arg \\min } - \\log P _ {\\theta ; \\phi} (y | \\tilde {x}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 414, + 906, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of directly optimizing the visual prompts, where $\\phi$ is defined as the visual prompt, Oh et al. [27] introduce a reparameterization technique through a network they call the prompt generation network, denoted as $h_{\\phi}$ . This network is characterized by parameters $\\phi = \\{p, W\\} \\in \\mathbb{R}^{D}$ . To implement this concept, they develop a network akin to an autoencoder, named Coordinator. This network uniquely integrates a \"frozen\" encoder $f(\\cdot)$ , which leverages self-supervised learning (SSL) objectives for pre-training on the ImageNet dataset. Complementing the encoder is a lightweight, learnable decoder, parameterized by $W$ , designed to work in tandem with the encoded inputs. Leveraging the encoder pre-trained via self-supervised learning (SSL) methods significantly reduces the number of learnable parameters, and this encoder not only facilitates easier adoption by users in local settings but also maintains the integrity of realistic experimental conditions. Then, the process of constructing an image that incorporates a prompt proceeds as follows:", + "bbox": [ + 511, + 449, + 908, + 722 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} = \\operatorname {c l i p} (x + \\epsilon h _ {\\phi} (x)) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 734, + 906, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {\\phi} (x) = g _ {W} (f (x), p) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 753, + 906, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f(x)$ is the feature vector of $x$ from the frozen SSL encoder $f(\\cdot)$ , and $\\epsilon \\in [0,1]$ is a hyperparameter that controls the intensity of visual prompt. In addition, $p$ is a task-specific prompt trigger vector that is jointly optimized with the decoder parameter $W$ . The procedure involves concatenating the output $f(x)$ with the task-specific prompt trigger vector $p$ , followed by reshaping this combination into a three-dimensional feature map. This map is then inputted into", + "bbox": [ + 511, + 779, + 910, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4324", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/88402e17232d9611e90d6151b17fe1d7054fa30e616d747448d499ff54ccf736.jpg", + "image_caption": [ + "Figure 2. Framework overview of the proposed subspace learning based black-box visual prompt approach. Subspace Learning: learn the projection matrices $\\tilde{A}_p$ and $\\tilde{A}_W$ by generating each column iteratively and concatenating them with random orthogonal matrices for the extension. Visual Prompt Tuning: optimize low-dimensional representations of parameters within subspace represented by projection matrices $\\tilde{A}_p$ and $\\tilde{A}_W$ ." + ], + "image_footnote": [], + "bbox": [ + 130, + 89, + 867, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the convolutional decoder. Through this process, the semantically rich, instance-specific representation $f(x)$ and the task-specific prompt trigger vector $p$ are seamlessly integrated. This integration forms a coherent and effective visual prompt $h_{\\phi}(x)$ , tailored specifically for the given image.", + "bbox": [ + 88, + 520, + 483, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Upon employing the reparameterization technique, we can apply black-box optimization strategies to address the specified objective. Nonetheless, a critical consideration is that the dimensionality of the learnable parameter, $\\phi$ , may still be substantially large. This elevated dimensionality can adversely affect the optimization process, potentially resulting in suboptimal convergence rates and necessitating a high number of queries to reach a satisfactory solution. This situation motivates the development of a method characterized by a lower query requirement.", + "bbox": [ + 88, + 595, + 483, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Problem Reformulation", + "text_level": 1, + "bbox": [ + 89, + 753, + 310, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As mentioned above, the dimensionality of the target variable $\\phi$ , which we are interested in optimizing, can be very high, rendering derivative-free optimization intractable. Inspired by the low-dimensional intrinsic subspace method, we propose the learning objective of our method as follows:", + "bbox": [ + 89, + 775, + 485, + 852 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {z} {\\arg \\min } - \\log P _ {\\theta ; \\phi = A z + a _ {0}} (y | \\tilde {x}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 873, + 483, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z = \\{z_{p},z_{W}\\}$ denotes the low dimensional latent parameters of the prompt trigger and the learnable decoder, $A = \\{A_p,A_W\\}$ $(A_{p}\\in \\mathbb{R}^{D_{p}\\times d_{p}},A_{W}\\in \\mathbb{R}^{D_{W}\\times d_{W}}$ and $d_p,d_W\\ll D)$ is the projection matrix and $a_0 = \\{p_0,W_0\\}$ denotes the initial parameters. As mentioned above, since the choice of the random matrix $A$ highly affects the final performance, in this paper, we first propose our subspace learning method, and then based on this method we propose our visual prompt learning method.", + "bbox": [ + 511, + 520, + 906, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Subspace Learning for Visual Prompt Learning", + "text_level": 1, + "bbox": [ + 511, + 666, + 906, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Figure 2 and Algorithm 1, our framework performs subspace learning based on the pre-trained weights $p_0$ and $W_0$ to reduce the dimensionality of tunable parameters during the black-box visual prompt tuning phase.", + "bbox": [ + 511, + 688, + 906, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subspace Learning. The goal of subspace learning phase is to learn a low dimensional subspace $\\{\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d},\\tilde{A}_W\\in$ $\\mathbb{R}^{D_W\\times d}\\}$ for the trigger vector $p$ and the decoder parameterized by $W$ , which are spanned by $\\{p_1,\\dots ,p_d\\}$ and $\\{W_{1},\\ldots ,W_{d}\\}$ , respectively. In the initialization step, we choose random projection matrices $A_{p_1}\\in \\mathbb{R}^{D_p\\times d_p}$ and $A_{W_1}\\in \\mathbb{R}^{D_W\\times d_W}$ . Subsequently, we generate $\\{p_1,\\dots ,p_d\\}$ and $\\{W_1,\\dots ,W_d\\}$ iteratively by the following way: at the $i$ -th iteration, the optimization parameters $z_{p_i}$ and $z_{W_i}$ are obtained by solving problem (4) through Algorithm 2 and", + "bbox": [ + 511, + 750, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4325", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "compute $p_i = A_{p_i}z_{p_i}$ $W_{i} = A_{W_{i}}z_{W_{i}}$", + "bbox": [ + 89, + 90, + 344, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since we consider PTM as a black-box predictor, we have no access to the true gradient of the learnable parameters. We adopt the following zeroth-order gradient estimator for Algorithm 2:", + "bbox": [ + 89, + 107, + 483, + 166 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\nabla} F _ {S} (z) = \\frac {1}{n} \\sum_ {j = 1} ^ {n} \\frac {F _ {S} (z + \\mu \\mathrm {u} _ {j}) - F _ {S} (z - \\mu \\mathrm {u} _ {j})}{2 \\mu} \\mathrm {u} _ {j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 176, + 483, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathfrak{u}_j\\in \\mathbb{R}^{d_p + d_W}$ is distributed over $\\mathcal{N}(0,\\mathrm{I})$ $z\\in \\mathbb{R}^{d_p + d_W}$ is $(d_p + d_W)$ -dimensional learnable parameters and $F_{\\mathcal{S}}(z)$ denotes the objective function evaluated on a batch of samples $\\mathcal{S}$ , where the function value is computed through a forward pass of the model, as illustrated in Algorithm 3.", + "bbox": [ + 89, + 229, + 483, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The projection matrices $A_{p_{i + 1}}$ and $A_{W_{i + 1}}$ are generated manually such that $A_{p_{i + 1}}\\bot \\tilde{A}_p$ , $A_{W_{i + 1}}\\bot \\tilde{A}_W$ , where $\\tilde{A}_p = [p_1,\\dots ,p_i]$ and $\\tilde{A}_W = [W_1,\\dots ,W_i]$ . After $d$ iterations, the learned projection matrices are presented by $\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d}$ and $\\tilde{A}_W\\in \\mathbb{R}^{D_W\\times d}$ , in which each column is orthogonal to the others. As noted above, we have learned the intrinsic low dimensional subspace for learnable parameters. However, directly adapting it to specific downstream tasks with limited trainable parameters is still a challenge. To fill this gap, we first construct random orthogonal matrices $\\tilde{A}_p^\\prime \\in \\mathbb{R}^{D_p\\times d'}$ and $\\tilde{A}_W^\\prime \\in \\mathbb{R}^{D_W\\times d'}$ such that $\\tilde{A}_p^\\prime \\bot \\tilde{A}_p$ , $\\tilde{A}_W^\\prime \\bot \\tilde{A}_W$ . The final projection matrices are constructed by $\\tilde{A}_p = [\\tilde{A}_p,\\tilde{A}_p^{\\prime}]\\in \\mathbb{R}^{D_p\\times (d + d')}$ , $\\tilde{A}_W = [\\tilde{A}_W,\\tilde{A}_W^{\\prime}]\\in \\mathbb{R}^{D_W\\times (d + d')}$ . By doing so, we make a trade-off between the limitations of insufficient training with a reduced number of trainable parameters and the high pretrain computational cost of querying the full set of trainable parameters.", + "bbox": [ + 89, + 306, + 483, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Black-Box Visual Prompt Tuning. The goal of the black-box prompt tuning phase is to utilize the learned subspace for generating task-specific visual prompts. The optimization process resembles that of the subspace learning phase, with the only difference being in the projection matrices.", + "bbox": [ + 89, + 589, + 483, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 678, + 220, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first provide the experimental setup in Section 4.1. Then, we report the average test accuracy and the number of black-box PTM calls for our method and all baseline methods across 14 benchmarks in Section 4.2. Ablation studies are provided in Section 4.3.", + "bbox": [ + 89, + 703, + 483, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 787, + 279, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. To evaluate the effectiveness of our proposed method and to compare it with baseline methods, we conduct experiments on 14 widely used benchmarks that cover diverse visual domains: Caltech101 [15], OxfordPnts [28], StanfordCars [21], Flowers102 [26], Food101 [4], FGVCAircraft [24], SUN397 [35], DTD [8], SVHN [25], EuroSAT", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Subspace Learning based Algorithm", + "bbox": [ + 514, + 90, + 843, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: $\\tilde{A}_p = \\emptyset$ , $\\tilde{A}_W = \\emptyset$ , random projection $A_{p_1}$ chosen from normal distribution $\\mathcal{N}(\\mu_p,\\sigma_p)$ and $A_{W_1}$ chosen from normal distribution $\\mathcal{N}(\\mu_W,\\sigma_W)$ , initial pre-train prompt $p_0$ , initial pre-train weights of decoder $W_0$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\\phi = \\{z_p,z_W\\}$", + "bbox": [ + 516, + 111, + 906, + 204 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Subspace learning", + "2: for $i = 1, \\dots, d$ do", + "3: Obtain $z_{p_i}$ and $z_{W_i}$ by running Algorithm 2 with $A_{p_i}$ and $A_{W_i}$", + "4: Update $\\tilde{A}_p = \\mathrm{Concat}(\\tilde{A}_p, A_{p_i}z_{p_i})$", + "5: Construct $A_{p_{i + 1}}$ such that $A_{p_{i + 1}}\\perp \\dot{A}_p$", + "6: Update $\\tilde{A}_W = \\mathrm{Concat}(\\tilde{A}_W, A_{W_i} z_{W_i})$", + "7: Construct $A_{W_{i + 1}}$ such that $A_{W_{i + 1}}\\perp A_W$", + "8: end for", + "9: Construct random orthogonal matrix $\\tilde{A}_p^\\prime \\perp \\tilde{A}_p$", + "10: Update $\\dot{A}_p = \\mathrm{Concat}(\\dot{A}_p, \\dot{A}_p')$", + "11: Construct random orthogonal matrix $\\tilde{A}_W^{\\prime}\\perp \\tilde{A}_W$", + "12: Update $\\tilde{A}_W = \\mathrm{Concat}(\\tilde{A}_W, \\tilde{A}_W')$", + "13: Fine-tuning", + "14: Obtain $\\tilde{z}_p$ and $\\tilde{z}_W$ running Algorithm 2 with $\\tilde{A}_p$ and $\\tilde{A}_W$", + "15: Final trigger vector $p = p_0 + \\tilde{A}_p\\tilde{z}_p$", + "16: Final decoder parameters $W = W_{0} + \\tilde{A}_{W}\\tilde{z}_{W}$" + ], + "bbox": [ + 519, + 205, + 903, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 2 Optimization", + "bbox": [ + 514, + 511, + 692, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: dataset $D$ , projection matrices $A_{p}$ and $A_{W}$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\\phi = \\{z_p, z_W\\}$ , step size $\\eta$ , and training iteration $R$", + "bbox": [ + 516, + 530, + 906, + 590 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for $i = 1,\\dots,R$ do", + "2: Draw samples $\\mathcal{S}_i = \\{(x_1,y_1),\\ldots ,(x_m,y_m)\\}$", + "3: Sample $n$ random directions $\\mathrm{u}_j (j = 1 \\dots n)$ from a Gaussian distribution $\\mathcal{N}(0, \\mathrm{I})$", + "4: Get $\\hat{\\nabla} F_{\\mathcal{S}_i}(\\phi_i) = \\left\\{\\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_p^{(i)}\\right),\\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_W^{(i)}\\right)\\right\\}$ by (5) according to Algorithm 3", + "5: Update $z_{p}^{(i + 1)} = z_{p}^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_{i}}\\left(z_{p}^{(i)}\\right)$", + "6: Update $z_W^{(i + 1)} = z_W^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_W^{(i)}\\right)$", + "7: end for" + ], + "bbox": [ + 524, + 590, + 903, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "[18], Resisc45 [7], CLEVR [20], UCF101 [30], and ImageNet [9]. They require comprehending diverse visual semantics, including actions, textures, scenes, the number of objects, and fine-grained categories, to name a few.", + "bbox": [ + 511, + 779, + 906, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "**Baseline Methods.** We compare our proposed method with the following baselines: CLIP's Zero-shot Classifier (ZS) [29], which is based on the manual text prompt and is widely used for vision tasks including classification, detection, etc.", + "bbox": [ + 511, + 840, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4326", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6d85ce1c841c8f9effdf3237c25cb7558458ba159c28f37285a0fd09b917a673.jpg", + "table_caption": [ + "Table 1. Overall comparison on 14 benchmarks that require the comprehension of diverse visual semantics. We report the average test accuracy on 3 different seeds. The last column shows the count of benchmarks in which each method outperforms zero-shot performance. All results are obtained using the CLIP ViT-B/16." + ], + "table_footnote": [], + "table_body": "
MethodParamsSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.Win
ZS-18.948.389.058.144.124.893.385.967.570.765.514.762.666.757.9-
VP69.8k33.172.786.965.345.924.490.080.565.167.457.427.861.862.460.05
BAR37.6k33.676.289.367.946.024.993.784.568.371.862.827.864.866.162.711
BlackVIP9.92k42.771.989.564.644.524.793.486.269.070.565.634.065.267.063.512
BlackVIP-ft9.92k42.572.689.563.244.824.793.386.168.971.065.732.164.866.963.313
Ours0.15k43.072.389.363.044.724.793.386.269.070.965.632.964.766.963.313
", + "bbox": [ + 91, + 142, + 903, + 289 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8c8693a36047a131ae853417da98976a036d29b4a1ef797c2f8fccc67969d0a6.jpg", + "table_caption": [ + "Table 2. Comparison of the number of API queries on 14 benchmarks during training using early stopping strategy. Our method shows outstanding query efficiency. The unit of data in the table is ${1k}$ (one thousand)." + ], + "table_footnote": [], + "table_body": "
MethodSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.
VP44.036.032.0220.0173.3588.0435.0420672.0345.7659.240.7670.9548.5349.0
BAR13.016.046.4109.067.0345.6234.0259.2421.2234.6325.518.0316.7501.2207.7
BlackVIP48.341.328.0193.360.0168.0420.084.0540.0317.3501.740.3434.1579.7246.9
BlackVIP-ft3.51.69.96.410.022.69.730.012.08.819.41.720.319.812.6
Ours2.71.77.42.87.06.810.721.29.28.821.81.87.515.18.9
", + "bbox": [ + 91, + 342, + 903, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Algorithm 3 Loss $F_{S}(\\phi)$ calculation", + "text_level": 1, + "bbox": [ + 91, + 507, + 336, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Require: projection matrices $A_{p}$ and $A_{W}$ , initial pre-train prompt $p_0$ , initial pre-train weights of decoder $W_{0}$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\\phi = \\{z_p, z_W\\}$ , prompt intensity $\\epsilon$ , frozen prediction model $P_{\\theta}$ , loss function $L$ , a batch of samples $S = \\{(x_1, y_1), \\ldots, (x_m, y_m)\\}$", + "bbox": [ + 91, + 527, + 485, + 619 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Get trigger vector $p = A_{p}z_{p} + p_{0}$", + "2: Get decoder parameters $W = A_{W}z_{W} + W_{0}$" + ], + "bbox": [ + 101, + 619, + 411, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3: for $i = 1, \\dots, m$ do", + "bbox": [ + 101, + 648, + 246, + 662 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "4: $h_{\\phi}(x_i) = g_{\\phi}(f(x_i),p,W)$", + "5: $\\tilde{x}_i = \\operatorname{clip}(x_i + \\epsilon h_\\phi(x_i))$", + "6: $F_{x_i}(\\phi) = L(P_\\theta (\\tilde{x}_i),y_i)$", + "7: end for", + "8: $F_{\\mathcal{S}}(\\phi) = \\frac{1}{m}\\sum_{i = 1}^{m}F_{x_i}(\\phi)$" + ], + "bbox": [ + 101, + 662, + 320, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Black-box Adversarial Reprogramming (BAR) [34], which utilizes the zeroth-order optimizer and randomized gradient-free minimization algorithm for transfer learning of pretrained model to the medical image domain. Visual Prompting with SPSA-GC (VP) [3], which is the version that replaces the first-order optimizer in Visual Prompting with a zero-order optimizer named SPSA-GC [27]. Black-box visual prompting (BlackVIP) [27], which utilizes a neural", + "bbox": [ + 89, + 779, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "network to reparameterize the visual prompt for adapting to black-box optimization and optimizes tiny parameters with SPSA-GC.", + "bbox": [ + 511, + 507, + 906, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our method is implemented using pytorch1. We employ CLIP ViT-B/16 as the target black-box PTM and the manual text prompts are consistent with those used in [27]. For the encoder, we use ImageNet pre-trained vit-mae-base checkpoint from the HuggingFace. The experimental setup for all baselines and pre-train in our method follows the implementation details in [27]. During the subspace learning stage, the dimension of the learned subspace is set to 5, i.e., $d = 5$ . The default maximum iteration of the subspace learning and last stages is 500. Similar to the few-shot classification setting of [27], we use 16-shot training samples for the pre-train and subspace learning stage, 8-shot training samples for the last stage, and the full test set for evaluating the performance of methods by default.", + "bbox": [ + 511, + 551, + 908, + 765 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 511, + 775, + 653, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments to compare test accuracy and the number of black-box PTM queries against all baselines across 14 benchmarks. The pre-train parameters $p_0$ and $W_0$ are obtained by running the BlackVIP on the 16-shot training samples. In our method, subspace learning is con", + "bbox": [ + 511, + 799, + 906, + 875 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code is available at https://github.com/Peter777777/EffiBlackVip", + "bbox": [ + 531, + 886, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4327", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "duced on identical training samples as those used in the pre-train. Additionally, black-box visual prompt tuning is executed on the 8-shot training samples. Subsequently, for a fair comparison, we merge the two sets above of training samples for all baseline methods except ZS and train them on the merged training set. Specifically, to showcase the efficacy of our training methodology, we additionally present the fine-tuning results of BlackVIP (BlackVIP-ft) on the 8-shot training samples based on the pre-train parameters $p_0$ and $W_0$ . The results from the pre-train and subspace learning stage are applicable for reuse in practical applications. Therefore, we report the results of the black-box visual prompt tuning stage by default in this section.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Baselines. For all benchmarks, we conduct experiments on our method and all baselines using three different seeds and report the test accuracy in Table 1. It is crucial to emphasize that the number of trainable parameters in our method is significantly lower than that of baselines, excluding ZS. Our method outperforms the zero-shot classifier on 13 over 14 benchmarks. Compared to BAR and VP, our method surpasses them on half of the benchmarks. The test accuracy of BlackVIP does not show significant differences between the two training approaches, indicating that both training methods effectively utilize the two sets of training samples. As shown in Table 1, the performance among our method, BlackVIP, and BlackVIP-ft is comparable across various tasks. Our method achieves a similar effect in adjusting the attention of black-box PTM as BlackVIP, demonstrating superior performance compared to other baselines on various benchmarks.", + "bbox": [ + 91, + 291, + 486, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on the Number of API Queries. The number of queries to the black-box PTM is a crucial metric for evaluating black-box algorithms. Therefore, we perform the early stopping strategy for all methods except ZS and provide the API query counts for all benchmarks in Table 2. Benefiting from pre-train results and subspace learning, our method exhibits remarkably low query requirements on 14 benchmarks. Our method's API queries are significantly lower than those of BAR, VP, and BlackVIP, which lack the pre-train stage. The average API query counts of our method across the 14 benchmarks are $2.6\\%$ , $4.3\\%$ , and $3.6\\%$ of the corresponding averages of VP, BAR, and BlackVIP, respectively. This underscores the superiority of our subspace learning based method. In comparison to BlackVIP-ft, which fine-tunes based on the identical pre-train results, our method consistently sustains lower API query counts across 9 benchmarks while achieving comparable performance. Moreover, our method exhibits an average query count across all benchmarks that is $3.7\\mathrm{k}$ less than that of BlackVIP-ft, indicating the superiority of our method. We attribute this phenomenon to the fact that our method reduces the number of trainable parameters through the utilization of a low-dimensional subspace. This feature enables faster convergence during further", + "bbox": [ + 91, + 553, + 486, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "optimization based on pre-train results.", + "bbox": [ + 511, + 90, + 771, + 106 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 114, + 666, + 130 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we investigate the impacts of diverse components within our method and report the relevant results of the ablation study. Except for the explicitly mentioned settings, all experimental settings remain consistent with those employed in the experiments detailed in Table 1. For each ablation, we report the average results obtained from experiments conducted with three different seeds.", + "bbox": [ + 511, + 136, + 903, + 239 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Random Orthogonal Matrices. In the black-box visual prompt tuning stage of our method, an increased number of trainable parameters results in higher costs during the subspace learning stage. To strike a balance between preventing inadequate learning from the second training set and mitigating the excessively high costs of subspace learning, we incorporate the utilization of random orthogonal matrices to augment the trainable parameters. To examine their effects on performance, we consider the following two situations: (1) Remove random orthogonal vectors in projections $\\tilde{A}_p$ and $\\tilde{A}_W$ , i.e., ignore the steps in lines 9-12 of Algorithm 1; (2) Remove the subspace learning stage, i.e., construct $\\tilde{A}_p$ and $\\tilde{A}_W$ using random orthogonal vectors. The performance comparison of the above two situations with the original method is provided in Table 3. It can be observed that the performance of both situations has declined. This decline is particularly noticeable on the SVHN benchmark, with reductions of $1.9\\%$ and $2.1\\%$ , respectively, compared to the original method. This phenomenon confirms the following two points: (1) Augmenting the trainable parameters through random orthogonal matrices is advantageous for improved learning of information in the second training set; (2) Subspace learning establishes foundational performance for the black-box visual prompt tuning stage, a facet that cannot be entirely supplanted by the use of random orthogonal matrices.", + "bbox": [ + 511, + 242, + 908, + 632 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c4f80c01ebb2ca97e289f746ef540871544882eb167f398d8594fee08aa15627.jpg", + "table_caption": [ + "Table 3. Ablations of random orthogonal matrices in projections $\\tilde{A}_p$ and $\\tilde{A}_W$ on SVHN, EuroSAT, CLEVR benchmarks. We report the average test accuracy. The data in the initial two rows of the table correspond to situations 1 and 2, respectively." + ], + "table_footnote": [], + "table_body": "
MethodSVHNEuroSATCLEVR
Remove Random41.172.132.9
All Random40.972.132.5
Ours43.072.332.9
", + "bbox": [ + 553, + 710, + 867, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Pre-train. Pre-train is a crucial step in our method, serving as the foundation for both the subsequent subspace learning and black-box visual prompt tuning stages. As a result, it directly influences the performance of our framework. We remove the pre-train stage, i.e., remove the $p_0$ and $W_0$ and compare it with the original method to demonstrate its", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4328", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/685260cac9bfec8902349220b8bfb0cefd1229b2ab14feaaccd57ca91c5d8cd1.jpg", + "image_caption": [ + "Figure 3. Ablations of pre-train on 3 benchmarks. We report the average test accuracy. The initial two columns of the figure correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + ], + "image_footnote": [], + "bbox": [ + 119, + 93, + 377, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/88802802c4c55bd72357583b43f9579a074b9f18b724739286bfa3378fa1a657.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 93, + 630, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3a68124e2eaf9ae13f1639cad1a3dda5b09c944cccc2d01077ed7a8d04268d24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 93, + 880, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "effectiveness. With the adjustments mentioned above to the method, we provide two additional results: (1) Optimize the parameters in the low dimensional subspace with random projection matrices; (2) Optimize the parameters in the original space. To guarantee a fair comparison with consistent training data across all methods, the training samples used in the two experiments above are formed by merging the two training sets employed by the original method. As shown in Figure 3 and Table 4, the second method without pre-train requires an increased number of training epochs, specifically 2663, 2327, and 1420, to attain performance comparable to the original method. This observation indicates that pretrain is effective in reducing training costs while ensuring subsequent training maintains acceptable performance. Additionally, the test accuracy of optimizing parameters in the low-dimensional subspace is lower compared to optimizing in the original space. We attribute this phenomenon to the inherent limitation of the low dimensional subspace, which is more suitable for fine-tuning based on pre-train results rather than direct model training.", + "bbox": [ + 88, + 354, + 485, + 656 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/660d568d028d32f972d3c0fdaf38e9f8da81ba163d164e7b34f94efa655312d6.jpg", + "table_caption": [ + "Table 4. Ablations of pre-train on 3 benchmarks. We report the average training epochs. The initial two rows of the table correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + ], + "table_footnote": [], + "table_body": "
MethodSVHNEuroSATCLEVR
Low Dim Subspace460041333466
Original Space293325001600
Ours270173180
", + "bbox": [ + 122, + 738, + 452, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Low Dimensional Subspace. The utilization of the low dimensional subspace is intended to reduce the number of trainable parameters, with the primary goal of expediting convergence in the black-box visual prompt tuning stage.", + "bbox": [ + 89, + 839, + 485, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e1cd65b9ef1096a1e9724f0950157c88b894a0d46d3538a0a84d425717223f2c.jpg", + "table_caption": [ + "Table 5. Ablations of low dimensional subspace. We report the average of test accuracy and training epochs over 3 different seeds." + ], + "table_footnote": [], + "table_body": "
MethodSVHNEuroSATCLEVR
AccEpochAccEpochAccEpoch
Original Space43.745372.524033.0180
Ours43.027072.317332.9180
", + "bbox": [ + 514, + 391, + 903, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We optimize the parameters of the trigger vector and decoder based on the pre-train results in the original space rather than in the low-dimensional subspace. Table 5 confirms the effectiveness of low dimensional subspace in reducing training costs. In most cases, optimizing parameters in the original space necessitates a higher number of training epochs to achieve comparable test accuracy between the two methods. Specifically, our method reduces the training epochs by 183 on SVHN benchmark, from 453 to 270. This denotes that low dimensional subspaces enhance the query efficiency of the method.", + "bbox": [ + 511, + 500, + 908, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 678, + 633, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper outlines a novel VPL method that reduces reliance on extensive API queries, making the use of pretrained models (PTMs) for downstream tasks more accessible and efficient. By using the subspace learning strategy, our method can learn a visual prompt in a task-specific lower-dimensional subspace. By using this method, our method can significantly reduce the necessity for API queries of PTMs, showcasing an efficient method for leveraging the capabilities of large-scale models in visual prompting tasks. Our experiments demonstrate the efficacy of our method, showing significant reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on various tasks.", + "bbox": [ + 511, + 703, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4329", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 256, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 202, + 187, + 217 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mehmet Aygun, Yusuf Aytar, and Hazim Kemal Ekenel. Exploiting convolution filter patterns for transfer learning. 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Proceedings of the IEEE, 109(1):43-76, 2021. 2" + ], + "bbox": [ + 516, + 92, + 906, + 415 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4331", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_model.json b/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e843b21cf2da21eb9ad4b5b8ffaa3520fd14b24d --- /dev/null +++ b/2025/Query Efficient Black-Box Visual Prompting with Subspace Learning/a238a6bd-550a-424d-9ec1-def2baa9176b_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.131, + 0.851, + 0.154 + ], + "angle": 0, + "content": "Query Efficient Black-Box Visual Prompting with Subspace Learning" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.179, + 0.905, + 0.288 + ], + "angle": 0, + "content": "Zhaogeng Liu\\(^{1,\\dagger}\\), Haozhen Zhang\\(^{1,\\dagger}\\), Hualin Zhang\\(^{2}\\), Xingchen Li\\(^{1}\\), Wanli Shi\\(^{1}\\), Bin Gu\\(^{1,*}\\), Yi Chang\\(^{1,3,*}\\) \n\\(^{1}\\)School of Artificial Intelligence, Jilin University, 2699 Qianjin Street, Changchun, China \n\\(^{2}\\)Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE \n\\(^{3}\\)Engineering Research Center of Knowledge-Driven Human-Machine Intelligence, MOE, China \n{zgliu20, haozhen23}@mails.jlu.edu.cn, zhanghualin98@gmail.com, xcli23@mails.jlu.edu.cn \n{wanlishi2, jsgubin} @ gmail.com, yichang@jlu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.322, + 0.327, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.354, + 0.486, + 0.778 + ], + "angle": 0, + "content": "Visual Prompt Learning (VPL) has emerged as a powerful strategy for harnessing the capabilities of large-scale pretrained models (PTMs) to tackle specific downstream tasks. However, the opaque nature of PTMs in many real-world applications has led to a growing interest in gradient-free approaches within VPL. A significant challenge with existing black-box VPL methods lies in the high dimensionality of visual prompts, which necessitates considerable API queries for tuning, thereby impacting efficiency. To address this issue, we propose a novel query-efficient framework for black-box visual prompting, designed to generate input-dependent visual prompts efficiently for large-scale black-box PTMs. Our framework is built upon the insight of reparameterizing prompts using neural networks, improving the typical pretraining-fine-tuning paradigm through the subspace learning strategy to maximize efficiency and adaptability from both the perspective of initial weights and parameter dimensionality. This tuning intrinsically optimizes low-dimensional representations within the well-learned subspace, enabling the efficient adaptation of the network to downstream tasks. Our approach significantly reduces the necessity for substantial API queries to PTMs, presenting an efficient method for leveraging large-scale black-box PTMs in visual prompting tasks. Most experimental results across various benchmarks demonstrate the effectiveness of our method, showcasing substantial reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.808, + 0.222, + 0.823 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.833, + 0.486, + 0.865 + ], + "angle": 0, + "content": "Large pre-trained models (PTMs) have demonstrated remarkable effectiveness across a range of tasks in computer" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.908, + 0.52 + ], + "angle": 0, + "content": "vision, as evidenced by numerous studies [1, 13, 14, 41]. Recently, researchers have drawn inspiration from the success of prompt learning in natural language processing [11, 22, 23, 33], leading to the innovative approach of visual prompt learning (VPL) [5, 6, 19]. This method involves training a global visual prompt, consisting of pixel-level modifications often represented as padding or patches, using a pre-trained visual model and task-specific downstream data. The integration of this visual prompt with any downstream test image facilitates model predictions. Recent studies have validated the efficacy of VPL, demonstrating its competitive advantage over traditional parameter fine-tuning methods across various applications." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.522, + 0.909, + 0.763 + ], + "angle": 0, + "content": "Although VPL has demonstrated significant potential [5, 6, 19], its practical application encounters substantial barriers, especially when pre-trained models are only available through opaque black-box APIs or as proprietary software. To address this challenge, Oh et al. [27] introduce Blackbox Visual Prompting (BlackVIP), an innovative approach that facilitates effective transfer learning with pre-trained vision models without requiring direct access to their parameters. However, black-box VPL necessitates considerable API queries to PTMs, resulting in significant costs. Furthermore, the high dimensionality of continuous prompts poses challenges for black-box optimization algorithms, as these methods require a substantial number of queries to optimize prompts effectively in high-dimensional spaces. Therefore, improving performance with a limited number of queries is a key challenge in high-dimensional black-box VPL." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.911, + 0.903 + ], + "angle": 0, + "content": "One of the straightforward candidates for addressing the abovementioned challenge is to adopt the pre-training-finetuning paradigm typical of large language models (LLMs). Pre-training can yield high-quality initial weights, which in turn significantly reduces the number of API queries required during the fine-tuning phase of black-box VPL. Nevertheless, pre-training does not reduce the dimensionality of the tunable parameters, which can significantly impact the convergence rate of black-box optimization methods. Therefore," + }, + { + "type": "page_footnote", + "bbox": [ + 0.114, + 0.875, + 0.368, + 0.888 + ], + "angle": 0, + "content": "\\(\\dagger\\) Co-first authors and are listed in random order." + }, + { + "type": "page_footnote", + "bbox": [ + 0.114, + 0.888, + 0.258, + 0.901 + ], + "angle": 0, + "content": "\\*Co-corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.114, + 0.875, + 0.368, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4322" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.485, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.212, + 0.487, + 0.325 + ], + "angle": 0, + "content": "Figure 1. An overview of white/black-box visual prompt approaches. VP suffers from requiring a huge memory capacity to optimize the parameters through backpropagation. BlackVIP enjoys the proficiency of parameter efficiency but still suffers from large query complexity. Our approach solves the above problems by utilizing the strategy of subspace learning, resulting in a parameter-efficient and query-efficient black-box visual prompt framework." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.354, + 0.486, + 0.399 + ], + "angle": 0, + "content": "if the parameter dimensionality can be reduced on the basis of pre-training, it could theoretically lead to a further reduction in API query costs." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.401, + 0.485, + 0.718 + ], + "angle": 0, + "content": "Fortunately, recent studies proposed the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. This discovery facilitates the development of efficient optimization strategies that concentrate on this reduced-dimensional subspace. Based on this idea, Sun et al. [33] optimize a latent representation of the prompt in a dimensionality-reduced space, using a random low-rank matrix to map this optimized representation back into the original high-dimensional prompt space [31, 33, 36, 37]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research explores adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to yield optimal prompt configurations [37]. Such adaptive strategies could significantly enhance the efficiency and effectiveness of black-box prompt tuning by dynamically adjusting to the characteristics of the prompt's underlying data distribution." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Based on the above motivation, this paper introduces a novel framework for Black-box Visual Prompting that optimizes query efficiency. To address the identified limitations, our framework leverages intrinsic dimensionality [31, 33, 36, 37] by integrating pre-training with subspace learning to develop efficient black-box visual prompting, as shown in Figure 1. This process aims to identify and utilize low-dimensional subspaces based on pre-training, thereby maximizing efficiency and adaptability from both the initial weights and parameter dimensionality perspectives to satisfy a broad spectrum of applications. A significant advancement is our proposal of the subspace learning paradigm," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.198 + ], + "angle": 0, + "content": "which effectively addresses the challenges associated with learning subspaces in the black-box setting. Fine-tuning the low-dimensional representation of the prompt generation network's parameters within the subspace derived from this paradigm enables the generation of input-dependent visual prompts that are both effective and efficient across various downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.199, + 0.907, + 0.228 + ], + "angle": 0, + "content": "The main contributions of this work are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.23, + 0.907, + 0.306 + ], + "angle": 0, + "content": "- This paper proposes an efficient black-box visual prompting framework, which leverages pre-training and subspace learning strategy to significantly reduce the number of API queries, for generating task-specific visual prompts without relying on gradient-based methods." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.306, + 0.907, + 0.367 + ], + "angle": 0, + "content": "- Our framework introduces a novel subspace learning paradigm that iteratively generates each column of the projection matrix, effectively addressing the difficulties of learning a high-quality subspace in the black-box setting." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.367, + 0.909, + 0.487 + ], + "angle": 0, + "content": "- Our method adapts the PTM to downstream tasks with low query requirements. The experimental results demonstrate the superiority of our framework. Compared to methods that learn visual prompts directly in downstream tasks, our framework uses less than \\(5\\%\\) of their API queries. Additionally, when compared to fine-tuning methods with the same pre-trained weights, our framework also reduces the API queries by one-third." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.23, + 0.909, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.505, + 0.665, + 0.52 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.531, + 0.738, + 0.547 + ], + "angle": 0, + "content": "2.1. Visual Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Prompt learning [11, 22, 23, 33] has emerged as a significant approach in natural language processing for effectively adapting pre-trained LLMs for specific downstream tasks. This method involves the creation of a trainable, lightweight component that serves as an additional input (or prompt) to a static model. Inspired by its great success in natural language processing, VPL [2, 5, 6, 19] also starts emerging in the computer vision domain to adapt the large-scale upstream pre-trained visual models to various downstream tasks, such as image classification [2], vision-language modeling [42], etc. Specifically, Context Optimization (CoOp) [39] innovatively incorporates a continuous text prompt within the text encoder of a Vision-Language Model (VLM), thereby enhancing its interpretative and processing capabilities. Building on this framework, Conditional CoOp (CoCoOp) [38] further refines the approach by adapting CoOp into a version that is dependent on the input. Jia et al. [19] propose the Visual Prompt Tuning (VPT) that governs learnable visual tokens to the embedding layer or several encoder layers of Vision Transformer. Bahng et al. [2] explore a technique for learning pixel perturbations that are applied to a specific, constrained area of an input image. All these methods require accessibility of the model architecture and parameters." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4323" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.273 + ], + "angle": 0, + "content": "However, in real-world applications, many AI systems are offered as APIs or proprietary software, where the specifics of their implementation or the full range of parameters are not disclosed due to commercial considerations. This limitation renders these approaches impractical for use in such contexts. To solve this problem, Oh et al. [27] propose BlackVIP, which efficiently adapts the PTMs without knowledge about model architectures and parameters. However, this approach usually requires a high number of queries, which can lead to significant economic costs. Therefore, it motivates us to investigate a query-efficient black-box visual prompting method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.287, + 0.471, + 0.304 + ], + "angle": 0, + "content": "2.2. Black-box Optimization in Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.311, + 0.485, + 0.657 + ], + "angle": 0, + "content": "Recently, the widespread deployment of AI applications as APIs or proprietary software has necessitated the use of black-box optimization techniques in prompt learning. This is primarily due to the commercial practice of withholding detailed implementation details or full parameter configurations, which has significantly contributed to the success of these optimization methods. Specifically, Dao et al. [11] use the policy gradient method to search the discrete prompt for the pre-trained language model. They also observed that the conventional policy gradient suffers from high variance, which makes it challenging to converge in practice. Therefore, they adopted a variance-reduced policy gradient estimator to improve the performance [12, 40]. RLPrompt [10] uses reinforcement learning to optimize the discrete prompt for the pre-trained language model. BlackVIP [27] adopts the Simultaneous Perturbation Stochastic Approximation (SPSA) as a zeroth-order optimization (ZOO) algorithm with gradient correction to search the visual prompt for the large-scale pre-trained vision models. These methods often necessitate a substantial number of queries to achieve convergence, resulting in increased costs. However, all these methods need to solve a high-dimensional optimization problem, where the black-box methods are usually inefficient." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Fortunately, recent studies propose the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. Based on this idea, Black-Box Tuning (BBT) [33] and BBTv2 [32] use a random matrix sampled from a uniform distribution to project the high-dimensional continuous prompt into a low-dimensional subspace and optimize a latent representation in this subspace using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [16, 17]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research is required to explore adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.757, + 0.107 + ], + "angle": 0, + "content": "yield optimal prompt configurations." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.12, + 0.649, + 0.138 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.145, + 0.908, + 0.207 + ], + "angle": 0, + "content": "In this section, we introduce the proposed framework for black-box visual prompt generation, which consists of subspace learning and visual prompt tuning. The overall process of the proposed framework is illustrated in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.215, + 0.907, + 0.245 + ], + "angle": 0, + "content": "3.1. Brief Review of Visual Prompt Reparameterization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.252, + 0.907, + 0.313 + ], + "angle": 0, + "content": "Motivated by the great success of prompt learning in NLP, Oh et al. [27] propose an asymmetric autoencoder-style network that receives the original image and produces a corresponding visual prompt for each image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.313, + 0.909, + 0.404 + ], + "angle": 0, + "content": "The objective function of VPL is to minimize the downstream task loss by adapting the frozen PTM via input space prompt optimization. Specifically, given a frozen prediction model \\( P_{\\theta} \\) (\\( \\theta \\) denotes the model parameters) and the perturbed image \\( \\tilde{x} \\) with prompt corresponding to the label \\( y \\), the learning objective of VPL is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.415, + 0.907, + 0.44 + ], + "angle": 0, + "content": "\\[\n\\underset {\\phi} {\\arg \\min } - \\log P _ {\\theta ; \\phi} (y | \\tilde {x}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.45, + 0.909, + 0.723 + ], + "angle": 0, + "content": "Instead of directly optimizing the visual prompts, where \\(\\phi\\) is defined as the visual prompt, Oh et al. [27] introduce a reparameterization technique through a network they call the prompt generation network, denoted as \\(h_{\\phi}\\). This network is characterized by parameters \\(\\phi = \\{p, W\\} \\in \\mathbb{R}^{D}\\). To implement this concept, they develop a network akin to an autoencoder, named Coordinator. This network uniquely integrates a \"frozen\" encoder \\(f(\\cdot)\\), which leverages self-supervised learning (SSL) objectives for pre-training on the ImageNet dataset. Complementing the encoder is a lightweight, learnable decoder, parameterized by \\(W\\), designed to work in tandem with the encoded inputs. Leveraging the encoder pre-trained via self-supervised learning (SSL) methods significantly reduces the number of learnable parameters, and this encoder not only facilitates easier adoption by users in local settings but also maintains the integrity of realistic experimental conditions. Then, the process of constructing an image that incorporates a prompt proceeds as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.735, + 0.907, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} = \\operatorname {c l i p} (x + \\epsilon h _ {\\phi} (x)) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.754, + 0.907, + 0.769 + ], + "angle": 0, + "content": "\\[\nh _ {\\phi} (x) = g _ {W} (f (x), p) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.911, + 0.902 + ], + "angle": 0, + "content": "where \\( f(x) \\) is the feature vector of \\( x \\) from the frozen SSL encoder \\( f(\\cdot) \\), and \\( \\epsilon \\in [0,1] \\) is a hyperparameter that controls the intensity of visual prompt. In addition, \\( p \\) is a task-specific prompt trigger vector that is jointly optimized with the decoder parameter \\( W \\). The procedure involves concatenating the output \\( f(x) \\) with the task-specific prompt trigger vector \\( p \\), followed by reshaping this combination into a three-dimensional feature map. This map is then inputted into" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4324" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.09, + 0.868, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.438, + 0.908, + 0.496 + ], + "angle": 0, + "content": "Figure 2. Framework overview of the proposed subspace learning based black-box visual prompt approach. Subspace Learning: learn the projection matrices \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\) by generating each column iteratively and concatenating them with random orthogonal matrices for the extension. Visual Prompt Tuning: optimize low-dimensional representations of parameters within subspace represented by projection matrices \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.521, + 0.484, + 0.596 + ], + "angle": 0, + "content": "the convolutional decoder. Through this process, the semantically rich, instance-specific representation \\( f(x) \\) and the task-specific prompt trigger vector \\( p \\) are seamlessly integrated. This integration forms a coherent and effective visual prompt \\( h_{\\phi}(x) \\), tailored specifically for the given image." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.597, + 0.484, + 0.747 + ], + "angle": 0, + "content": "Upon employing the reparameterization technique, we can apply black-box optimization strategies to address the specified objective. Nonetheless, a critical consideration is that the dimensionality of the learnable parameter, \\(\\phi\\), may still be substantially large. This elevated dimensionality can adversely affect the optimization process, potentially resulting in suboptimal convergence rates and necessitating a high number of queries to reach a satisfactory solution. This situation motivates the development of a method characterized by a lower query requirement." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.755, + 0.312, + 0.769 + ], + "angle": 0, + "content": "3.2. Problem Reformulation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.776, + 0.486, + 0.853 + ], + "angle": 0, + "content": "As mentioned above, the dimensionality of the target variable \\(\\phi\\), which we are interested in optimizing, can be very high, rendering derivative-free optimization intractable. Inspired by the low-dimensional intrinsic subspace method, we propose the learning objective of our method as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.874, + 0.484, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\underset {z} {\\arg \\min } - \\log P _ {\\theta ; \\phi = A z + a _ {0}} (y | \\tilde {x}) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.521, + 0.907, + 0.657 + ], + "angle": 0, + "content": "where \\(z = \\{z_{p},z_{W}\\}\\) denotes the low dimensional latent parameters of the prompt trigger and the learnable decoder, \\(A = \\{A_p,A_W\\}\\) \\((A_{p}\\in \\mathbb{R}^{D_{p}\\times d_{p}},A_{W}\\in \\mathbb{R}^{D_{W}\\times d_{W}}\\) and \\(d_p,d_W\\ll D)\\) is the projection matrix and \\(a_0 = \\{p_0,W_0\\}\\) denotes the initial parameters. As mentioned above, since the choice of the random matrix \\(A\\) highly affects the final performance, in this paper, we first propose our subspace learning method, and then based on this method we propose our visual prompt learning method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.667, + 0.907, + 0.684 + ], + "angle": 0, + "content": "3.3. Subspace Learning for Visual Prompt Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.75 + ], + "angle": 0, + "content": "As illustrated in Figure 2 and Algorithm 1, our framework performs subspace learning based on the pre-trained weights \\( p_0 \\) and \\( W_0 \\) to reduce the dimensionality of tunable parameters during the black-box visual prompt tuning phase." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.75, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Subspace Learning. The goal of subspace learning phase is to learn a low dimensional subspace \\(\\{\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d},\\tilde{A}_W\\in\\) \\(\\mathbb{R}^{D_W\\times d}\\}\\) for the trigger vector \\(p\\) and the decoder parameterized by \\(W\\) , which are spanned by \\(\\{p_1,\\dots ,p_d\\}\\) and \\(\\{W_{1},\\ldots ,W_{d}\\}\\) , respectively. In the initialization step, we choose random projection matrices \\(A_{p_1}\\in \\mathbb{R}^{D_p\\times d_p}\\) and \\(A_{W_1}\\in \\mathbb{R}^{D_W\\times d_W}\\) . Subsequently, we generate \\(\\{p_1,\\dots ,p_d\\}\\) and \\(\\{W_1,\\dots ,W_d\\}\\) iteratively by the following way: at the \\(i\\) -th iteration, the optimization parameters \\(z_{p_i}\\) and \\(z_{W_i}\\) are obtained by solving problem (4) through Algorithm 2 and" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4325" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.346, + 0.108 + ], + "angle": 0, + "content": "compute \\(p_i = A_{p_i}z_{p_i}\\) \\(W_{i} = A_{W_{i}}z_{W_{i}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.108, + 0.484, + 0.167 + ], + "angle": 0, + "content": "Since we consider PTM as a black-box predictor, we have no access to the true gradient of the learnable parameters. We adopt the following zeroth-order gradient estimator for Algorithm 2:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.178, + 0.484, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\hat {\\nabla} F _ {S} (z) = \\frac {1}{n} \\sum_ {j = 1} ^ {n} \\frac {F _ {S} (z + \\mu \\mathrm {u} _ {j}) - F _ {S} (z - \\mu \\mathrm {u} _ {j})}{2 \\mu} \\mathrm {u} _ {j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.23, + 0.484, + 0.306 + ], + "angle": 0, + "content": "where \\(\\mathfrak{u}_j\\in \\mathbb{R}^{d_p + d_W}\\) is distributed over \\(\\mathcal{N}(0,\\mathrm{I})\\) \\(z\\in \\mathbb{R}^{d_p + d_W}\\) is \\((d_p + d_W)\\)-dimensional learnable parameters and \\(F_{\\mathcal{S}}(z)\\) denotes the objective function evaluated on a batch of samples \\(\\mathcal{S}\\), where the function value is computed through a forward pass of the model, as illustrated in Algorithm 3." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.307, + 0.485, + 0.589 + ], + "angle": 0, + "content": "The projection matrices \\(A_{p_{i + 1}}\\) and \\(A_{W_{i + 1}}\\) are generated manually such that \\(A_{p_{i + 1}}\\bot \\tilde{A}_p\\), \\(A_{W_{i + 1}}\\bot \\tilde{A}_W\\), where \\(\\tilde{A}_p = [p_1,\\dots ,p_i]\\) and \\(\\tilde{A}_W = [W_1,\\dots ,W_i]\\). After \\(d\\) iterations, the learned projection matrices are presented by \\(\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d}\\) and \\(\\tilde{A}_W\\in \\mathbb{R}^{D_W\\times d}\\), in which each column is orthogonal to the others. As noted above, we have learned the intrinsic low dimensional subspace for learnable parameters. However, directly adapting it to specific downstream tasks with limited trainable parameters is still a challenge. To fill this gap, we first construct random orthogonal matrices \\(\\tilde{A}_p^\\prime \\in \\mathbb{R}^{D_p\\times d'}\\) and \\(\\tilde{A}_W^\\prime \\in \\mathbb{R}^{D_W\\times d'}\\) such that \\(\\tilde{A}_p^\\prime \\bot \\tilde{A}_p\\), \\(\\tilde{A}_W^\\prime \\bot \\tilde{A}_W\\). The final projection matrices are constructed by \\(\\tilde{A}_p = [\\tilde{A}_p,\\tilde{A}_p^{\\prime}]\\in \\mathbb{R}^{D_p\\times (d + d')}\\), \\(\\tilde{A}_W = [\\tilde{A}_W,\\tilde{A}_W^{\\prime}]\\in \\mathbb{R}^{D_W\\times (d + d')}\\). By doing so, we make a trade-off between the limitations of insufficient training with a reduced number of trainable parameters and the high pretrain computational cost of querying the full set of trainable parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.59, + 0.484, + 0.665 + ], + "angle": 0, + "content": "Black-Box Visual Prompt Tuning. The goal of the black-box prompt tuning phase is to utilize the learned subspace for generating task-specific visual prompts. The optimization process resembles that of the subspace learning phase, with the only difference being in the projection matrices." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.679, + 0.222, + 0.696 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.484, + 0.779 + ], + "angle": 0, + "content": "We first provide the experimental setup in Section 4.1. Then, we report the average test accuracy and the number of black-box PTM calls for our method and all baseline methods across 14 benchmarks in Section 4.2. Ablation studies are provided in Section 4.3." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.281, + 0.805 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Datasets. To evaluate the effectiveness of our proposed method and to compare it with baseline methods, we conduct experiments on 14 widely used benchmarks that cover diverse visual domains: Caltech101 [15], OxfordPnts [28], StanfordCars [21], Flowers102 [26], Food101 [4], FGVCAircraft [24], SUN397 [35], DTD [8], SVHN [25], EuroSAT" + }, + { + "type": "code_caption", + "bbox": [ + 0.515, + 0.092, + 0.844, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Subspace Learning based Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.112, + 0.907, + 0.205 + ], + "angle": 0, + "content": "Require: \\(\\tilde{A}_p = \\emptyset\\), \\(\\tilde{A}_W = \\emptyset\\), random projection \\(A_{p_1}\\) chosen from normal distribution \\(\\mathcal{N}(\\mu_p,\\sigma_p)\\) and \\(A_{W_1}\\) chosen from normal distribution \\(\\mathcal{N}(\\mu_W,\\sigma_W)\\), initial pre-train prompt \\(p_0\\), initial pre-train weights of decoder \\(W_0\\), coordinator \\(h\\) with encoder \\(f\\) and prompt decoder \\(g\\), is parameterized by \\(\\phi = \\{z_p,z_W\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.206, + 0.674, + 0.219 + ], + "angle": 0, + "content": "1: Subspace learning" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.22, + 0.664, + 0.234 + ], + "angle": 0, + "content": "2: for \\( i = 1, \\dots, d \\) do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.235, + 0.905, + 0.265 + ], + "angle": 0, + "content": "3: Obtain \\( z_{p_i} \\) and \\( z_{W_i} \\) by running Algorithm 2 with \\( A_{p_i} \\) and \\( A_{W_i} \\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.266, + 0.799, + 0.282 + ], + "angle": 0, + "content": "4: Update \\(\\tilde{A}_p = \\mathrm{Concat}(\\tilde{A}_p, A_{p_i}z_{p_i})\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.283, + 0.824, + 0.299 + ], + "angle": 0, + "content": "5: Construct \\(A_{p_{i + 1}}\\) such that \\(A_{p_{i + 1}}\\perp \\dot{A}_p\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.299, + 0.824, + 0.316 + ], + "angle": 0, + "content": "6: Update \\(\\tilde{A}_W = \\mathrm{Concat}(\\tilde{A}_W, A_{W_i} z_{W_i})\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.316, + 0.841, + 0.331 + ], + "angle": 0, + "content": "7: Construct \\(A_{W_{i + 1}}\\) such that \\(A_{W_{i + 1}}\\perp A_W\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.332, + 0.596, + 0.342 + ], + "angle": 0, + "content": "8: end for" + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.343, + 0.85, + 0.362 + ], + "angle": 0, + "content": "9: Construct random orthogonal matrix \\(\\tilde{A}_p^\\prime \\perp \\tilde{A}_p\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.363, + 0.748, + 0.379 + ], + "angle": 0, + "content": "10: Update \\(\\dot{A}_p = \\mathrm{Concat}(\\dot{A}_p, \\dot{A}_p')\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.38, + 0.863, + 0.395 + ], + "angle": 0, + "content": "11: Construct random orthogonal matrix \\(\\tilde{A}_W^{\\prime}\\perp \\tilde{A}_W\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.395, + 0.77, + 0.412 + ], + "angle": 0, + "content": "12: Update \\(\\tilde{A}_W = \\mathrm{Concat}(\\tilde{A}_W, \\tilde{A}_W')\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.412, + 0.628, + 0.425 + ], + "angle": 0, + "content": "13: Fine-tuning" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.425, + 0.905, + 0.455 + ], + "angle": 0, + "content": "14: Obtain \\(\\tilde{z}_p\\) and \\(\\tilde{z}_W\\) running Algorithm 2 with \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.456, + 0.775, + 0.473 + ], + "angle": 0, + "content": "15: Final trigger vector \\( p = p_0 + \\tilde{A}_p\\tilde{z}_p \\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.473, + 0.845, + 0.489 + ], + "angle": 0, + "content": "16: Final decoder parameters \\( W = W_{0} + \\tilde{A}_{W}\\tilde{z}_{W} \\)" + }, + { + "type": "list", + "bbox": [ + 0.521, + 0.206, + 0.905, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "code_caption", + "bbox": [ + 0.515, + 0.512, + 0.693, + 0.527 + ], + "angle": 0, + "content": "Algorithm 2 Optimization" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.531, + 0.907, + 0.591 + ], + "angle": 0, + "content": "Require: dataset \\(D\\), projection matrices \\(A_{p}\\) and \\(A_{W}\\), coordinator \\(h\\) with encoder \\(f\\) and prompt decoder \\(g\\), is parameterized by \\(\\phi = \\{z_p, z_W\\}\\), step size \\(\\eta\\), and training iteration \\(R\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.592, + 0.668, + 0.605 + ], + "angle": 0, + "content": "1: for \\(i = 1,\\dots,R\\) do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.607, + 0.87, + 0.622 + ], + "angle": 0, + "content": "2: Draw samples \\(\\mathcal{S}_i = \\{(x_1,y_1),\\ldots ,(x_m,y_m)\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.623, + 0.905, + 0.651 + ], + "angle": 0, + "content": "3: Sample \\( n \\) random directions \\( \\mathrm{u}_j (j = 1 \\dots n) \\) from a Gaussian distribution \\( \\mathcal{N}(0, \\mathrm{I}) \\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.652, + 0.903, + 0.688 + ], + "angle": 0, + "content": "4: Get \\(\\hat{\\nabla} F_{\\mathcal{S}_i}(\\phi_i) = \\left\\{\\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_p^{(i)}\\right),\\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_W^{(i)}\\right)\\right\\}\\) by (5) according to Algorithm 3" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.689, + 0.818, + 0.712 + ], + "angle": 0, + "content": "5: Update \\( z_{p}^{(i + 1)} = z_{p}^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_{i}}\\left(z_{p}^{(i)}\\right) \\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.713, + 0.818, + 0.736 + ], + "angle": 0, + "content": "6: Update \\(z_W^{(i + 1)} = z_W^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_W^{(i)}\\right)\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.736, + 0.596, + 0.747 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "list", + "bbox": [ + 0.526, + 0.592, + 0.905, + 0.747 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.84 + ], + "angle": 0, + "content": "[18], Resisc45 [7], CLEVR [20], UCF101 [30], and ImageNet [9]. They require comprehending diverse visual semantics, including actions, textures, scenes, the number of objects, and fine-grained categories, to name a few." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.907, + 0.901 + ], + "angle": 0, + "content": "**Baseline Methods.** We compare our proposed method with the following baselines: CLIP's Zero-shot Classifier (ZS) [29], which is based on the manual text prompt and is widely used for vision tasks including classification, detection, etc." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4326" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.132 + ], + "angle": 0, + "content": "Table 1. Overall comparison on 14 benchmarks that require the comprehension of diverse visual semantics. We report the average test accuracy on 3 different seeds. The last column shows the count of benchmarks in which each method outperforms zero-shot performance. All results are obtained using the CLIP ViT-B/16." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.143, + 0.905, + 0.29 + ], + "angle": 0, + "content": "
MethodParamsSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.Win
ZS-18.948.389.058.144.124.893.385.967.570.765.514.762.666.757.9-
VP69.8k33.172.786.965.345.924.490.080.565.167.457.427.861.862.460.05
BAR37.6k33.676.289.367.946.024.993.784.568.371.862.827.864.866.162.711
BlackVIP9.92k42.771.989.564.644.524.793.486.269.070.565.634.065.267.063.512
BlackVIP-ft9.92k42.572.689.563.244.824.793.386.168.971.065.732.164.866.963.313
Ours0.15k43.072.389.363.044.724.793.386.269.070.965.632.964.766.963.313
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.304, + 0.908, + 0.334 + ], + "angle": 0, + "content": "Table 2. Comparison of the number of API queries on 14 benchmarks during training using early stopping strategy. Our method shows outstanding query efficiency. The unit of data in the table is \\( {1k} \\) (one thousand)." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.343, + 0.905, + 0.482 + ], + "angle": 0, + "content": "
MethodSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.
VP44.036.032.0220.0173.3588.0435.0420672.0345.7659.240.7670.9548.5349.0
BAR13.016.046.4109.067.0345.6234.0259.2421.2234.6325.518.0316.7501.2207.7
BlackVIP48.341.328.0193.360.0168.0420.084.0540.0317.3501.740.3434.1579.7246.9
BlackVIP-ft3.51.69.96.410.022.69.730.012.08.819.41.720.319.812.6
Ours2.71.77.42.87.06.810.721.29.28.821.81.87.515.18.9
" + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.508, + 0.338, + 0.524 + ], + "angle": 0, + "content": "Algorithm 3 Loss \\( F_{S}(\\phi) \\) calculation" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.528, + 0.486, + 0.62 + ], + "angle": 0, + "content": "Require: projection matrices \\( A_{p} \\) and \\( A_{W} \\), initial pre-train prompt \\( p_0 \\), initial pre-train weights of decoder \\( W_{0} \\), coordinator \\( h \\) with encoder \\( f \\) and prompt decoder \\( g \\), is parameterized by \\( \\phi = \\{z_p, z_W\\} \\), prompt intensity \\( \\epsilon \\), frozen prediction model \\( P_{\\theta} \\), loss function \\( L \\), a batch of samples \\( S = \\{(x_1, y_1), \\ldots, (x_m, y_m)\\} \\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.62, + 0.343, + 0.635 + ], + "angle": 0, + "content": "1: Get trigger vector \\( p = A_{p}z_{p} + p_{0} \\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.635, + 0.413, + 0.649 + ], + "angle": 0, + "content": "2: Get decoder parameters \\( W = A_{W}z_{W} + W_{0} \\)" + }, + { + "type": "list", + "bbox": [ + 0.102, + 0.62, + 0.413, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.65, + 0.248, + 0.663 + ], + "angle": 0, + "content": "3: for \\( i = 1, \\dots, m \\) do" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.664, + 0.321, + 0.68 + ], + "angle": 0, + "content": "4: \\(h_{\\phi}(x_i) = g_{\\phi}(f(x_i),p,W)\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.68, + 0.31, + 0.695 + ], + "angle": 0, + "content": "5: \\(\\tilde{x}_i = \\operatorname{clip}(x_i + \\epsilon h_\\phi(x_i))\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.695, + 0.304, + 0.71 + ], + "angle": 0, + "content": "6: \\(F_{x_i}(\\phi) = L(P_\\theta (\\tilde{x}_i),y_i)\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.711, + 0.174, + 0.722 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.723, + 0.293, + 0.742 + ], + "angle": 0, + "content": "8: \\(F_{\\mathcal{S}}(\\phi) = \\frac{1}{m}\\sum_{i = 1}^{m}F_{x_i}(\\phi)\\)" + }, + { + "type": "list", + "bbox": [ + 0.102, + 0.664, + 0.321, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.485, + 0.901 + ], + "angle": 0, + "content": "Black-box Adversarial Reprogramming (BAR) [34], which utilizes the zeroth-order optimizer and randomized gradient-free minimization algorithm for transfer learning of pretrained model to the medical image domain. Visual Prompting with SPSA-GC (VP) [3], which is the version that replaces the first-order optimizer in Visual Prompting with a zero-order optimizer named SPSA-GC [27]. Black-box visual prompting (BlackVIP) [27], which utilizes a neural" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.907, + 0.553 + ], + "angle": 0, + "content": "network to reparameterize the visual prompt for adapting to black-box optimization and optimizes tiny parameters with SPSA-GC." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.909, + 0.766 + ], + "angle": 0, + "content": "Implementation Details. Our method is implemented using pytorch1. We employ CLIP ViT-B/16 as the target black-box PTM and the manual text prompts are consistent with those used in [27]. For the encoder, we use ImageNet pre-trained vit-mae-base checkpoint from the HuggingFace. The experimental setup for all baselines and pre-train in our method follows the implementation details in [27]. During the subspace learning stage, the dimension of the learned subspace is set to 5, i.e., \\( d = 5 \\). The default maximum iteration of the subspace learning and last stages is 500. Similar to the few-shot classification setting of [27], we use 16-shot training samples for the pre-train and subspace learning stage, 8-shot training samples for the last stage, and the full test set for evaluating the performance of methods by default." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.776, + 0.655, + 0.792 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.8, + 0.908, + 0.876 + ], + "angle": 0, + "content": "We conduct experiments to compare test accuracy and the number of black-box PTM queries against all baselines across 14 benchmarks. The pre-train parameters \\( p_0 \\) and \\( W_0 \\) are obtained by running the BlackVIP on the 16-shot training samples. In our method, subspace learning is con" + }, + { + "type": "page_footnote", + "bbox": [ + 0.532, + 0.887, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Code is available at https://github.com/Peter777777/EffiBlackVip" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4327" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "duced on identical training samples as those used in the pre-train. Additionally, black-box visual prompt tuning is executed on the 8-shot training samples. Subsequently, for a fair comparison, we merge the two sets above of training samples for all baseline methods except ZS and train them on the merged training set. Specifically, to showcase the efficacy of our training methodology, we additionally present the fine-tuning results of BlackVIP (BlackVIP-ft) on the 8-shot training samples based on the pre-train parameters \\( p_0 \\) and \\( W_0 \\). The results from the pre-train and subspace learning stage are applicable for reuse in practical applications. Therefore, we report the results of the black-box visual prompt tuning stage by default in this section." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.292, + 0.487, + 0.549 + ], + "angle": 0, + "content": "Comparison with Baselines. For all benchmarks, we conduct experiments on our method and all baselines using three different seeds and report the test accuracy in Table 1. It is crucial to emphasize that the number of trainable parameters in our method is significantly lower than that of baselines, excluding ZS. Our method outperforms the zero-shot classifier on 13 over 14 benchmarks. Compared to BAR and VP, our method surpasses them on half of the benchmarks. The test accuracy of BlackVIP does not show significant differences between the two training approaches, indicating that both training methods effectively utilize the two sets of training samples. As shown in Table 1, the performance among our method, BlackVIP, and BlackVIP-ft is comparable across various tasks. Our method achieves a similar effect in adjusting the attention of black-box PTM as BlackVIP, demonstrating superior performance compared to other baselines on various benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.554, + 0.487, + 0.902 + ], + "angle": 0, + "content": "Comparison on the Number of API Queries. The number of queries to the black-box PTM is a crucial metric for evaluating black-box algorithms. Therefore, we perform the early stopping strategy for all methods except ZS and provide the API query counts for all benchmarks in Table 2. Benefiting from pre-train results and subspace learning, our method exhibits remarkably low query requirements on 14 benchmarks. Our method's API queries are significantly lower than those of BAR, VP, and BlackVIP, which lack the pre-train stage. The average API query counts of our method across the 14 benchmarks are \\(2.6\\%\\), \\(4.3\\%\\), and \\(3.6\\%\\) of the corresponding averages of VP, BAR, and BlackVIP, respectively. This underscores the superiority of our subspace learning based method. In comparison to BlackVIP-ft, which fine-tunes based on the identical pre-train results, our method consistently sustains lower API query counts across 9 benchmarks while achieving comparable performance. Moreover, our method exhibits an average query count across all benchmarks that is \\(3.7\\mathrm{k}\\) less than that of BlackVIP-ft, indicating the superiority of our method. We attribute this phenomenon to the fact that our method reduces the number of trainable parameters through the utilization of a low-dimensional subspace. This feature enables faster convergence during further" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.772, + 0.107 + ], + "angle": 0, + "content": "optimization based on pre-train results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.115, + 0.667, + 0.131 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.137, + 0.905, + 0.241 + ], + "angle": 0, + "content": "In this section, we investigate the impacts of diverse components within our method and report the relevant results of the ablation study. Except for the explicitly mentioned settings, all experimental settings remain consistent with those employed in the experiments detailed in Table 1. For each ablation, we report the average results obtained from experiments conducted with three different seeds." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.243, + 0.909, + 0.633 + ], + "angle": 0, + "content": "Effect of Random Orthogonal Matrices. In the black-box visual prompt tuning stage of our method, an increased number of trainable parameters results in higher costs during the subspace learning stage. To strike a balance between preventing inadequate learning from the second training set and mitigating the excessively high costs of subspace learning, we incorporate the utilization of random orthogonal matrices to augment the trainable parameters. To examine their effects on performance, we consider the following two situations: (1) Remove random orthogonal vectors in projections \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\), i.e., ignore the steps in lines 9-12 of Algorithm 1; (2) Remove the subspace learning stage, i.e., construct \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\) using random orthogonal vectors. The performance comparison of the above two situations with the original method is provided in Table 3. It can be observed that the performance of both situations has declined. This decline is particularly noticeable on the SVHN benchmark, with reductions of \\(1.9\\%\\) and \\(2.1\\%\\), respectively, compared to the original method. This phenomenon confirms the following two points: (1) Augmenting the trainable parameters through random orthogonal matrices is advantageous for improved learning of information in the second training set; (2) Subspace learning establishes foundational performance for the black-box visual prompt tuning stage, a facet that cannot be entirely supplanted by the use of random orthogonal matrices." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.644, + 0.907, + 0.701 + ], + "angle": 0, + "content": "Table 3. Ablations of random orthogonal matrices in projections \\(\\tilde{A}_p\\) and \\(\\tilde{A}_W\\) on SVHN, EuroSAT, CLEVR benchmarks. We report the average test accuracy. The data in the initial two rows of the table correspond to situations 1 and 2, respectively." + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.711, + 0.868, + 0.794 + ], + "angle": 0, + "content": "
MethodSVHNEuroSATCLEVR
Remove Random41.172.132.9
All Random40.972.132.5
Ours43.072.332.9
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Effect of Pre-train. Pre-train is a crucial step in our method, serving as the foundation for both the subsequent subspace learning and black-box visual prompt tuning stages. As a result, it directly influences the performance of our framework. We remove the pre-train stage, i.e., remove the \\( p_0 \\) and \\( W_0 \\) and compare it with the original method to demonstrate its" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4328" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.094, + 0.379, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.094, + 0.631, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.094, + 0.882, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.3, + 0.908, + 0.33 + ], + "angle": 0, + "content": "Figure 3. Ablations of pre-train on 3 benchmarks. We report the average test accuracy. The initial two columns of the figure correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.355, + 0.486, + 0.657 + ], + "angle": 0, + "content": "effectiveness. With the adjustments mentioned above to the method, we provide two additional results: (1) Optimize the parameters in the low dimensional subspace with random projection matrices; (2) Optimize the parameters in the original space. To guarantee a fair comparison with consistent training data across all methods, the training samples used in the two experiments above are formed by merging the two training sets employed by the original method. As shown in Figure 3 and Table 4, the second method without pre-train requires an increased number of training epochs, specifically 2663, 2327, and 1420, to attain performance comparable to the original method. This observation indicates that pretrain is effective in reducing training costs while ensuring subsequent training maintains acceptable performance. Additionally, the test accuracy of optimizing parameters in the low-dimensional subspace is lower compared to optimizing in the original space. We attribute this phenomenon to the inherent limitation of the low dimensional subspace, which is more suitable for fine-tuning based on pre-train results rather than direct model training." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.672, + 0.485, + 0.73 + ], + "angle": 0, + "content": "Table 4. Ablations of pre-train on 3 benchmarks. We report the average training epochs. The initial two rows of the table correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.739, + 0.454, + 0.824 + ], + "angle": 0, + "content": "
MethodSVHNEuroSATCLEVR
Low Dim Subspace460041333466
Original Space293325001600
Ours270173180
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Effect of Low Dimensional Subspace. The utilization of the low dimensional subspace is intended to reduce the number of trainable parameters, with the primary goal of expediting convergence in the black-box visual prompt tuning stage." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.353, + 0.907, + 0.381 + ], + "angle": 0, + "content": "Table 5. Ablations of low dimensional subspace. We report the average of test accuracy and training epochs over 3 different seeds." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.392, + 0.905, + 0.476 + ], + "angle": 0, + "content": "
MethodSVHNEuroSATCLEVR
AccEpochAccEpochAccEpoch
Original Space43.745372.524033.0180
Ours43.027072.317332.9180
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.5, + 0.909, + 0.665 + ], + "angle": 0, + "content": "We optimize the parameters of the trigger vector and decoder based on the pre-train results in the original space rather than in the low-dimensional subspace. Table 5 confirms the effectiveness of low dimensional subspace in reducing training costs. In most cases, optimizing parameters in the original space necessitates a higher number of training epochs to achieve comparable test accuracy between the two methods. Specifically, our method reduces the training epochs by 183 on SVHN benchmark, from 453 to 270. This denotes that low dimensional subspaces enhance the query efficiency of the method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.679, + 0.634, + 0.695 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.909, + 0.901 + ], + "angle": 0, + "content": "This paper outlines a novel VPL method that reduces reliance on extensive API queries, making the use of pretrained models (PTMs) for downstream tasks more accessible and efficient. By using the subspace learning strategy, our method can learn a visual prompt in a task-specific lower-dimensional subspace. By using this method, our method can significantly reduce the necessity for API queries of PTMs, showcasing an efficient method for leveraging the capabilities of large-scale models in visual prompting tasks. Our experiments demonstrate the efficacy of our method, showing significant reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on various tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4329" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.258, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.486, + 0.173 + ], + "angle": 0, + "content": "This work was supported by the National Key R&D Program of China under Grant No.2023YFF0905400 and National Natural Science Foundation of China through Grant No.U2341229." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.203, + 0.188, + 0.218 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.227, + 0.486, + 0.284 + ], + "angle": 0, + "content": "[1] Mehmet Aygun, Yusuf Aytar, and Hazim Kemal Ekenel. 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However, the opaque nature of PTMs in many real-world applications has led to a growing interest in gradient-free approaches within VPL. A significant challenge with existing black-box VPL methods lies in the high dimensionality of visual prompts, which necessitates considerable API queries for tuning, thereby impacting efficiency. To address this issue, we propose a novel query-efficient framework for black-box visual prompting, designed to generate input-dependent visual prompts efficiently for large-scale black-box PTMs. Our framework is built upon the insight of reparameterizing prompts using neural networks, improving the typical pretraining-fine-tuning paradigm through the subspace learning strategy to maximize efficiency and adaptability from both the perspective of initial weights and parameter dimensionality. This tuning intrinsically optimizes low-dimensional representations within the well-learned subspace, enabling the efficient adaptation of the network to downstream tasks. Our approach significantly reduces the necessity for substantial API queries to PTMs, presenting an efficient method for leveraging large-scale black-box PTMs in visual prompting tasks. Most experimental results across various benchmarks demonstrate the effectiveness of our method, showcasing substantial reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on downstream tasks. + +# 1. Introduction + +Large pre-trained models (PTMs) have demonstrated remarkable effectiveness across a range of tasks in computer + +vision, as evidenced by numerous studies [1, 13, 14, 41]. Recently, researchers have drawn inspiration from the success of prompt learning in natural language processing [11, 22, 23, 33], leading to the innovative approach of visual prompt learning (VPL) [5, 6, 19]. This method involves training a global visual prompt, consisting of pixel-level modifications often represented as padding or patches, using a pre-trained visual model and task-specific downstream data. The integration of this visual prompt with any downstream test image facilitates model predictions. Recent studies have validated the efficacy of VPL, demonstrating its competitive advantage over traditional parameter fine-tuning methods across various applications. + +Although VPL has demonstrated significant potential [5, 6, 19], its practical application encounters substantial barriers, especially when pre-trained models are only available through opaque black-box APIs or as proprietary software. To address this challenge, Oh et al. [27] introduce Blackbox Visual Prompting (BlackVIP), an innovative approach that facilitates effective transfer learning with pre-trained vision models without requiring direct access to their parameters. However, black-box VPL necessitates considerable API queries to PTMs, resulting in significant costs. Furthermore, the high dimensionality of continuous prompts poses challenges for black-box optimization algorithms, as these methods require a substantial number of queries to optimize prompts effectively in high-dimensional spaces. Therefore, improving performance with a limited number of queries is a key challenge in high-dimensional black-box VPL. + +One of the straightforward candidates for addressing the abovementioned challenge is to adopt the pre-training-finetuning paradigm typical of large language models (LLMs). Pre-training can yield high-quality initial weights, which in turn significantly reduces the number of API queries required during the fine-tuning phase of black-box VPL. Nevertheless, pre-training does not reduce the dimensionality of the tunable parameters, which can significantly impact the convergence rate of black-box optimization methods. Therefore, + +![](images/f15a9cca6e98089374fe423498198f7a65b10399db7482da70eca9d18a701061.jpg) +Figure 1. An overview of white/black-box visual prompt approaches. VP suffers from requiring a huge memory capacity to optimize the parameters through backpropagation. BlackVIP enjoys the proficiency of parameter efficiency but still suffers from large query complexity. Our approach solves the above problems by utilizing the strategy of subspace learning, resulting in a parameter-efficient and query-efficient black-box visual prompt framework. + +if the parameter dimensionality can be reduced on the basis of pre-training, it could theoretically lead to a further reduction in API query costs. + +Fortunately, recent studies proposed the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. This discovery facilitates the development of efficient optimization strategies that concentrate on this reduced-dimensional subspace. Based on this idea, Sun et al. [33] optimize a latent representation of the prompt in a dimensionality-reduced space, using a random low-rank matrix to map this optimized representation back into the original high-dimensional prompt space [31, 33, 36, 37]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research explores adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to yield optimal prompt configurations [37]. Such adaptive strategies could significantly enhance the efficiency and effectiveness of black-box prompt tuning by dynamically adjusting to the characteristics of the prompt's underlying data distribution. + +Based on the above motivation, this paper introduces a novel framework for Black-box Visual Prompting that optimizes query efficiency. To address the identified limitations, our framework leverages intrinsic dimensionality [31, 33, 36, 37] by integrating pre-training with subspace learning to develop efficient black-box visual prompting, as shown in Figure 1. This process aims to identify and utilize low-dimensional subspaces based on pre-training, thereby maximizing efficiency and adaptability from both the initial weights and parameter dimensionality perspectives to satisfy a broad spectrum of applications. A significant advancement is our proposal of the subspace learning paradigm, + +which effectively addresses the challenges associated with learning subspaces in the black-box setting. Fine-tuning the low-dimensional representation of the prompt generation network's parameters within the subspace derived from this paradigm enables the generation of input-dependent visual prompts that are both effective and efficient across various downstream tasks. + +The main contributions of this work are summarized as follows: + +- This paper proposes an efficient black-box visual prompting framework, which leverages pre-training and subspace learning strategy to significantly reduce the number of API queries, for generating task-specific visual prompts without relying on gradient-based methods. +- Our framework introduces a novel subspace learning paradigm that iteratively generates each column of the projection matrix, effectively addressing the difficulties of learning a high-quality subspace in the black-box setting. +- Our method adapts the PTM to downstream tasks with low query requirements. The experimental results demonstrate the superiority of our framework. Compared to methods that learn visual prompts directly in downstream tasks, our framework uses less than $5\%$ of their API queries. Additionally, when compared to fine-tuning methods with the same pre-trained weights, our framework also reduces the API queries by one-third. + +# 2. Related Works + +# 2.1. Visual Prompt Learning + +Prompt learning [11, 22, 23, 33] has emerged as a significant approach in natural language processing for effectively adapting pre-trained LLMs for specific downstream tasks. This method involves the creation of a trainable, lightweight component that serves as an additional input (or prompt) to a static model. Inspired by its great success in natural language processing, VPL [2, 5, 6, 19] also starts emerging in the computer vision domain to adapt the large-scale upstream pre-trained visual models to various downstream tasks, such as image classification [2], vision-language modeling [42], etc. Specifically, Context Optimization (CoOp) [39] innovatively incorporates a continuous text prompt within the text encoder of a Vision-Language Model (VLM), thereby enhancing its interpretative and processing capabilities. Building on this framework, Conditional CoOp (CoCoOp) [38] further refines the approach by adapting CoOp into a version that is dependent on the input. Jia et al. [19] propose the Visual Prompt Tuning (VPT) that governs learnable visual tokens to the embedding layer or several encoder layers of Vision Transformer. Bahng et al. [2] explore a technique for learning pixel perturbations that are applied to a specific, constrained area of an input image. All these methods require accessibility of the model architecture and parameters. + +However, in real-world applications, many AI systems are offered as APIs or proprietary software, where the specifics of their implementation or the full range of parameters are not disclosed due to commercial considerations. This limitation renders these approaches impractical for use in such contexts. To solve this problem, Oh et al. [27] propose BlackVIP, which efficiently adapts the PTMs without knowledge about model architectures and parameters. However, this approach usually requires a high number of queries, which can lead to significant economic costs. Therefore, it motivates us to investigate a query-efficient black-box visual prompting method. + +# 2.2. Black-box Optimization in Prompt Learning + +Recently, the widespread deployment of AI applications as APIs or proprietary software has necessitated the use of black-box optimization techniques in prompt learning. This is primarily due to the commercial practice of withholding detailed implementation details or full parameter configurations, which has significantly contributed to the success of these optimization methods. Specifically, Dao et al. [11] use the policy gradient method to search the discrete prompt for the pre-trained language model. They also observed that the conventional policy gradient suffers from high variance, which makes it challenging to converge in practice. Therefore, they adopted a variance-reduced policy gradient estimator to improve the performance [12, 40]. RLPrompt [10] uses reinforcement learning to optimize the discrete prompt for the pre-trained language model. BlackVIP [27] adopts the Simultaneous Perturbation Stochastic Approximation (SPSA) as a zeroth-order optimization (ZOO) algorithm with gradient correction to search the visual prompt for the large-scale pre-trained vision models. These methods often necessitate a substantial number of queries to achieve convergence, resulting in increased costs. However, all these methods need to solve a high-dimensional optimization problem, where the black-box methods are usually inefficient. + +Fortunately, recent studies propose the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. Based on this idea, Black-Box Tuning (BBT) [33] and BBTv2 [32] use a random matrix sampled from a uniform distribution to project the high-dimensional continuous prompt into a low-dimensional subspace and optimize a latent representation in this subspace using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [16, 17]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research is required to explore adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to + +yield optimal prompt configurations. + +# 3. Methodology + +In this section, we introduce the proposed framework for black-box visual prompt generation, which consists of subspace learning and visual prompt tuning. The overall process of the proposed framework is illustrated in Figure 2. + +# 3.1. Brief Review of Visual Prompt Reparameterization + +Motivated by the great success of prompt learning in NLP, Oh et al. [27] propose an asymmetric autoencoder-style network that receives the original image and produces a corresponding visual prompt for each image. + +The objective function of VPL is to minimize the downstream task loss by adapting the frozen PTM via input space prompt optimization. Specifically, given a frozen prediction model $P_{\theta}$ ( $\theta$ denotes the model parameters) and the perturbed image $\tilde{x}$ with prompt corresponding to the label $y$ , the learning objective of VPL is formulated as: + +$$ +\underset {\phi} {\arg \min } - \log P _ {\theta ; \phi} (y | \tilde {x}) \tag {1} +$$ + +Instead of directly optimizing the visual prompts, where $\phi$ is defined as the visual prompt, Oh et al. [27] introduce a reparameterization technique through a network they call the prompt generation network, denoted as $h_{\phi}$ . This network is characterized by parameters $\phi = \{p, W\} \in \mathbb{R}^{D}$ . To implement this concept, they develop a network akin to an autoencoder, named Coordinator. This network uniquely integrates a "frozen" encoder $f(\cdot)$ , which leverages self-supervised learning (SSL) objectives for pre-training on the ImageNet dataset. Complementing the encoder is a lightweight, learnable decoder, parameterized by $W$ , designed to work in tandem with the encoded inputs. Leveraging the encoder pre-trained via self-supervised learning (SSL) methods significantly reduces the number of learnable parameters, and this encoder not only facilitates easier adoption by users in local settings but also maintains the integrity of realistic experimental conditions. Then, the process of constructing an image that incorporates a prompt proceeds as follows: + +$$ +\tilde {x} = \operatorname {c l i p} (x + \epsilon h _ {\phi} (x)) \tag {2} +$$ + +$$ +h _ {\phi} (x) = g _ {W} (f (x), p) \tag {3} +$$ + +where $f(x)$ is the feature vector of $x$ from the frozen SSL encoder $f(\cdot)$ , and $\epsilon \in [0,1]$ is a hyperparameter that controls the intensity of visual prompt. In addition, $p$ is a task-specific prompt trigger vector that is jointly optimized with the decoder parameter $W$ . The procedure involves concatenating the output $f(x)$ with the task-specific prompt trigger vector $p$ , followed by reshaping this combination into a three-dimensional feature map. This map is then inputted into + +![](images/88402e17232d9611e90d6151b17fe1d7054fa30e616d747448d499ff54ccf736.jpg) +Figure 2. Framework overview of the proposed subspace learning based black-box visual prompt approach. Subspace Learning: learn the projection matrices $\tilde{A}_p$ and $\tilde{A}_W$ by generating each column iteratively and concatenating them with random orthogonal matrices for the extension. Visual Prompt Tuning: optimize low-dimensional representations of parameters within subspace represented by projection matrices $\tilde{A}_p$ and $\tilde{A}_W$ . + +the convolutional decoder. Through this process, the semantically rich, instance-specific representation $f(x)$ and the task-specific prompt trigger vector $p$ are seamlessly integrated. This integration forms a coherent and effective visual prompt $h_{\phi}(x)$ , tailored specifically for the given image. + +Upon employing the reparameterization technique, we can apply black-box optimization strategies to address the specified objective. Nonetheless, a critical consideration is that the dimensionality of the learnable parameter, $\phi$ , may still be substantially large. This elevated dimensionality can adversely affect the optimization process, potentially resulting in suboptimal convergence rates and necessitating a high number of queries to reach a satisfactory solution. This situation motivates the development of a method characterized by a lower query requirement. + +# 3.2. Problem Reformulation + +As mentioned above, the dimensionality of the target variable $\phi$ , which we are interested in optimizing, can be very high, rendering derivative-free optimization intractable. Inspired by the low-dimensional intrinsic subspace method, we propose the learning objective of our method as follows: + +$$ +\underset {z} {\arg \min } - \log P _ {\theta ; \phi = A z + a _ {0}} (y | \tilde {x}) \tag {4} +$$ + +where $z = \{z_{p},z_{W}\}$ denotes the low dimensional latent parameters of the prompt trigger and the learnable decoder, $A = \{A_p,A_W\}$ $(A_{p}\in \mathbb{R}^{D_{p}\times d_{p}},A_{W}\in \mathbb{R}^{D_{W}\times d_{W}}$ and $d_p,d_W\ll D)$ is the projection matrix and $a_0 = \{p_0,W_0\}$ denotes the initial parameters. As mentioned above, since the choice of the random matrix $A$ highly affects the final performance, in this paper, we first propose our subspace learning method, and then based on this method we propose our visual prompt learning method. + +# 3.3. Subspace Learning for Visual Prompt Learning + +As illustrated in Figure 2 and Algorithm 1, our framework performs subspace learning based on the pre-trained weights $p_0$ and $W_0$ to reduce the dimensionality of tunable parameters during the black-box visual prompt tuning phase. + +Subspace Learning. The goal of subspace learning phase is to learn a low dimensional subspace $\{\tilde{A}_p\in \mathbb{R}^{D_p\times d},\tilde{A}_W\in$ $\mathbb{R}^{D_W\times d}\}$ for the trigger vector $p$ and the decoder parameterized by $W$ , which are spanned by $\{p_1,\dots ,p_d\}$ and $\{W_{1},\ldots ,W_{d}\}$ , respectively. In the initialization step, we choose random projection matrices $A_{p_1}\in \mathbb{R}^{D_p\times d_p}$ and $A_{W_1}\in \mathbb{R}^{D_W\times d_W}$ . Subsequently, we generate $\{p_1,\dots ,p_d\}$ and $\{W_1,\dots ,W_d\}$ iteratively by the following way: at the $i$ -th iteration, the optimization parameters $z_{p_i}$ and $z_{W_i}$ are obtained by solving problem (4) through Algorithm 2 and + +compute $p_i = A_{p_i}z_{p_i}$ $W_{i} = A_{W_{i}}z_{W_{i}}$ + +Since we consider PTM as a black-box predictor, we have no access to the true gradient of the learnable parameters. We adopt the following zeroth-order gradient estimator for Algorithm 2: + +$$ +\hat {\nabla} F _ {S} (z) = \frac {1}{n} \sum_ {j = 1} ^ {n} \frac {F _ {S} (z + \mu \mathrm {u} _ {j}) - F _ {S} (z - \mu \mathrm {u} _ {j})}{2 \mu} \mathrm {u} _ {j}, \tag {5} +$$ + +where $\mathfrak{u}_j\in \mathbb{R}^{d_p + d_W}$ is distributed over $\mathcal{N}(0,\mathrm{I})$ $z\in \mathbb{R}^{d_p + d_W}$ is $(d_p + d_W)$ -dimensional learnable parameters and $F_{\mathcal{S}}(z)$ denotes the objective function evaluated on a batch of samples $\mathcal{S}$ , where the function value is computed through a forward pass of the model, as illustrated in Algorithm 3. + +The projection matrices $A_{p_{i + 1}}$ and $A_{W_{i + 1}}$ are generated manually such that $A_{p_{i + 1}}\bot \tilde{A}_p$ , $A_{W_{i + 1}}\bot \tilde{A}_W$ , where $\tilde{A}_p = [p_1,\dots ,p_i]$ and $\tilde{A}_W = [W_1,\dots ,W_i]$ . After $d$ iterations, the learned projection matrices are presented by $\tilde{A}_p\in \mathbb{R}^{D_p\times d}$ and $\tilde{A}_W\in \mathbb{R}^{D_W\times d}$ , in which each column is orthogonal to the others. As noted above, we have learned the intrinsic low dimensional subspace for learnable parameters. However, directly adapting it to specific downstream tasks with limited trainable parameters is still a challenge. To fill this gap, we first construct random orthogonal matrices $\tilde{A}_p^\prime \in \mathbb{R}^{D_p\times d'}$ and $\tilde{A}_W^\prime \in \mathbb{R}^{D_W\times d'}$ such that $\tilde{A}_p^\prime \bot \tilde{A}_p$ , $\tilde{A}_W^\prime \bot \tilde{A}_W$ . The final projection matrices are constructed by $\tilde{A}_p = [\tilde{A}_p,\tilde{A}_p^{\prime}]\in \mathbb{R}^{D_p\times (d + d')}$ , $\tilde{A}_W = [\tilde{A}_W,\tilde{A}_W^{\prime}]\in \mathbb{R}^{D_W\times (d + d')}$ . By doing so, we make a trade-off between the limitations of insufficient training with a reduced number of trainable parameters and the high pretrain computational cost of querying the full set of trainable parameters. + +Black-Box Visual Prompt Tuning. The goal of the black-box prompt tuning phase is to utilize the learned subspace for generating task-specific visual prompts. The optimization process resembles that of the subspace learning phase, with the only difference being in the projection matrices. + +# 4. Experiments + +We first provide the experimental setup in Section 4.1. Then, we report the average test accuracy and the number of black-box PTM calls for our method and all baseline methods across 14 benchmarks in Section 4.2. Ablation studies are provided in Section 4.3. + +# 4.1. Experimental Setup + +Datasets. To evaluate the effectiveness of our proposed method and to compare it with baseline methods, we conduct experiments on 14 widely used benchmarks that cover diverse visual domains: Caltech101 [15], OxfordPnts [28], StanfordCars [21], Flowers102 [26], Food101 [4], FGVCAircraft [24], SUN397 [35], DTD [8], SVHN [25], EuroSAT + +Algorithm 1 Subspace Learning based Algorithm + +Require: $\tilde{A}_p = \emptyset$ , $\tilde{A}_W = \emptyset$ , random projection $A_{p_1}$ chosen from normal distribution $\mathcal{N}(\mu_p,\sigma_p)$ and $A_{W_1}$ chosen from normal distribution $\mathcal{N}(\mu_W,\sigma_W)$ , initial pre-train prompt $p_0$ , initial pre-train weights of decoder $W_0$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\phi = \{z_p,z_W\}$ + +1: Subspace learning +2: for $i = 1, \dots, d$ do +3: Obtain $z_{p_i}$ and $z_{W_i}$ by running Algorithm 2 with $A_{p_i}$ and $A_{W_i}$ +4: Update $\tilde{A}_p = \mathrm{Concat}(\tilde{A}_p, A_{p_i}z_{p_i})$ +5: Construct $A_{p_{i + 1}}$ such that $A_{p_{i + 1}}\perp \dot{A}_p$ +6: Update $\tilde{A}_W = \mathrm{Concat}(\tilde{A}_W, A_{W_i} z_{W_i})$ +7: Construct $A_{W_{i + 1}}$ such that $A_{W_{i + 1}}\perp A_W$ +8: end for +9: Construct random orthogonal matrix $\tilde{A}_p^\prime \perp \tilde{A}_p$ +10: Update $\dot{A}_p = \mathrm{Concat}(\dot{A}_p, \dot{A}_p')$ +11: Construct random orthogonal matrix $\tilde{A}_W^{\prime}\perp \tilde{A}_W$ +12: Update $\tilde{A}_W = \mathrm{Concat}(\tilde{A}_W, \tilde{A}_W')$ +13: Fine-tuning +14: Obtain $\tilde{z}_p$ and $\tilde{z}_W$ running Algorithm 2 with $\tilde{A}_p$ and $\tilde{A}_W$ +15: Final trigger vector $p = p_0 + \tilde{A}_p\tilde{z}_p$ +16: Final decoder parameters $W = W_{0} + \tilde{A}_{W}\tilde{z}_{W}$ + +Algorithm 2 Optimization + +Require: dataset $D$ , projection matrices $A_{p}$ and $A_{W}$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\phi = \{z_p, z_W\}$ , step size $\eta$ , and training iteration $R$ + +1: for $i = 1,\dots,R$ do +2: Draw samples $\mathcal{S}_i = \{(x_1,y_1),\ldots ,(x_m,y_m)\}$ +3: Sample $n$ random directions $\mathrm{u}_j (j = 1 \dots n)$ from a Gaussian distribution $\mathcal{N}(0, \mathrm{I})$ +4: Get $\hat{\nabla} F_{\mathcal{S}_i}(\phi_i) = \left\{\hat{\nabla} F_{\mathcal{S}_i}\left(z_p^{(i)}\right),\hat{\nabla} F_{\mathcal{S}_i}\left(z_W^{(i)}\right)\right\}$ by (5) according to Algorithm 3 +5: Update $z_{p}^{(i + 1)} = z_{p}^{(i)} - \eta \hat{\nabla} F_{\mathcal{S}_{i}}\left(z_{p}^{(i)}\right)$ +6: Update $z_W^{(i + 1)} = z_W^{(i)} - \eta \hat{\nabla} F_{\mathcal{S}_i}\left(z_W^{(i)}\right)$ +7: end for + +[18], Resisc45 [7], CLEVR [20], UCF101 [30], and ImageNet [9]. They require comprehending diverse visual semantics, including actions, textures, scenes, the number of objects, and fine-grained categories, to name a few. + +**Baseline Methods.** We compare our proposed method with the following baselines: CLIP's Zero-shot Classifier (ZS) [29], which is based on the manual text prompt and is widely used for vision tasks including classification, detection, etc. + +Table 1. Overall comparison on 14 benchmarks that require the comprehension of diverse visual semantics. We report the average test accuracy on 3 different seeds. The last column shows the count of benchmarks in which each method outperforms zero-shot performance. All results are obtained using the CLIP ViT-B/16. + +
MethodParamsSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.Win
ZS-18.948.389.058.144.124.893.385.967.570.765.514.762.666.757.9-
VP69.8k33.172.786.965.345.924.490.080.565.167.457.427.861.862.460.05
BAR37.6k33.676.289.367.946.024.993.784.568.371.862.827.864.866.162.711
BlackVIP9.92k42.771.989.564.644.524.793.486.269.070.565.634.065.267.063.512
BlackVIP-ft9.92k42.572.689.563.244.824.793.386.168.971.065.732.164.866.963.313
Ours0.15k43.072.389.363.044.724.793.386.269.070.965.632.964.766.963.313
+ +Table 2. Comparison of the number of API queries on 14 benchmarks during training using early stopping strategy. Our method shows outstanding query efficiency. The unit of data in the table is ${1k}$ (one thousand). + +
MethodSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.
VP44.036.032.0220.0173.3588.0435.0420672.0345.7659.240.7670.9548.5349.0
BAR13.016.046.4109.067.0345.6234.0259.2421.2234.6325.518.0316.7501.2207.7
BlackVIP48.341.328.0193.360.0168.0420.084.0540.0317.3501.740.3434.1579.7246.9
BlackVIP-ft3.51.69.96.410.022.69.730.012.08.819.41.720.319.812.6
Ours2.71.77.42.87.06.810.721.29.28.821.81.87.515.18.9
+ +# Algorithm 3 Loss $F_{S}(\phi)$ calculation + +Require: projection matrices $A_{p}$ and $A_{W}$ , initial pre-train prompt $p_0$ , initial pre-train weights of decoder $W_{0}$ , coordinator $h$ with encoder $f$ and prompt decoder $g$ , is parameterized by $\phi = \{z_p, z_W\}$ , prompt intensity $\epsilon$ , frozen prediction model $P_{\theta}$ , loss function $L$ , a batch of samples $S = \{(x_1, y_1), \ldots, (x_m, y_m)\}$ + +1: Get trigger vector $p = A_{p}z_{p} + p_{0}$ +2: Get decoder parameters $W = A_{W}z_{W} + W_{0}$ + +3: for $i = 1, \dots, m$ do + +4: $h_{\phi}(x_i) = g_{\phi}(f(x_i),p,W)$ +5: $\tilde{x}_i = \operatorname{clip}(x_i + \epsilon h_\phi(x_i))$ +6: $F_{x_i}(\phi) = L(P_\theta (\tilde{x}_i),y_i)$ +7: end for +8: $F_{\mathcal{S}}(\phi) = \frac{1}{m}\sum_{i = 1}^{m}F_{x_i}(\phi)$ + +Black-box Adversarial Reprogramming (BAR) [34], which utilizes the zeroth-order optimizer and randomized gradient-free minimization algorithm for transfer learning of pretrained model to the medical image domain. Visual Prompting with SPSA-GC (VP) [3], which is the version that replaces the first-order optimizer in Visual Prompting with a zero-order optimizer named SPSA-GC [27]. Black-box visual prompting (BlackVIP) [27], which utilizes a neural + +network to reparameterize the visual prompt for adapting to black-box optimization and optimizes tiny parameters with SPSA-GC. + +Implementation Details. Our method is implemented using pytorch1. We employ CLIP ViT-B/16 as the target black-box PTM and the manual text prompts are consistent with those used in [27]. For the encoder, we use ImageNet pre-trained vit-mae-base checkpoint from the HuggingFace. The experimental setup for all baselines and pre-train in our method follows the implementation details in [27]. During the subspace learning stage, the dimension of the learned subspace is set to 5, i.e., $d = 5$ . The default maximum iteration of the subspace learning and last stages is 500. Similar to the few-shot classification setting of [27], we use 16-shot training samples for the pre-train and subspace learning stage, 8-shot training samples for the last stage, and the full test set for evaluating the performance of methods by default. + +# 4.2. Main Results + +We conduct experiments to compare test accuracy and the number of black-box PTM queries against all baselines across 14 benchmarks. The pre-train parameters $p_0$ and $W_0$ are obtained by running the BlackVIP on the 16-shot training samples. In our method, subspace learning is con + +duced on identical training samples as those used in the pre-train. Additionally, black-box visual prompt tuning is executed on the 8-shot training samples. Subsequently, for a fair comparison, we merge the two sets above of training samples for all baseline methods except ZS and train them on the merged training set. Specifically, to showcase the efficacy of our training methodology, we additionally present the fine-tuning results of BlackVIP (BlackVIP-ft) on the 8-shot training samples based on the pre-train parameters $p_0$ and $W_0$ . The results from the pre-train and subspace learning stage are applicable for reuse in practical applications. Therefore, we report the results of the black-box visual prompt tuning stage by default in this section. + +Comparison with Baselines. For all benchmarks, we conduct experiments on our method and all baselines using three different seeds and report the test accuracy in Table 1. It is crucial to emphasize that the number of trainable parameters in our method is significantly lower than that of baselines, excluding ZS. Our method outperforms the zero-shot classifier on 13 over 14 benchmarks. Compared to BAR and VP, our method surpasses them on half of the benchmarks. The test accuracy of BlackVIP does not show significant differences between the two training approaches, indicating that both training methods effectively utilize the two sets of training samples. As shown in Table 1, the performance among our method, BlackVIP, and BlackVIP-ft is comparable across various tasks. Our method achieves a similar effect in adjusting the attention of black-box PTM as BlackVIP, demonstrating superior performance compared to other baselines on various benchmarks. + +Comparison on the Number of API Queries. The number of queries to the black-box PTM is a crucial metric for evaluating black-box algorithms. Therefore, we perform the early stopping strategy for all methods except ZS and provide the API query counts for all benchmarks in Table 2. Benefiting from pre-train results and subspace learning, our method exhibits remarkably low query requirements on 14 benchmarks. Our method's API queries are significantly lower than those of BAR, VP, and BlackVIP, which lack the pre-train stage. The average API query counts of our method across the 14 benchmarks are $2.6\%$ , $4.3\%$ , and $3.6\%$ of the corresponding averages of VP, BAR, and BlackVIP, respectively. This underscores the superiority of our subspace learning based method. In comparison to BlackVIP-ft, which fine-tunes based on the identical pre-train results, our method consistently sustains lower API query counts across 9 benchmarks while achieving comparable performance. Moreover, our method exhibits an average query count across all benchmarks that is $3.7\mathrm{k}$ less than that of BlackVIP-ft, indicating the superiority of our method. We attribute this phenomenon to the fact that our method reduces the number of trainable parameters through the utilization of a low-dimensional subspace. This feature enables faster convergence during further + +optimization based on pre-train results. + +# 4.3. Ablation Study + +In this section, we investigate the impacts of diverse components within our method and report the relevant results of the ablation study. Except for the explicitly mentioned settings, all experimental settings remain consistent with those employed in the experiments detailed in Table 1. For each ablation, we report the average results obtained from experiments conducted with three different seeds. + +Effect of Random Orthogonal Matrices. In the black-box visual prompt tuning stage of our method, an increased number of trainable parameters results in higher costs during the subspace learning stage. To strike a balance between preventing inadequate learning from the second training set and mitigating the excessively high costs of subspace learning, we incorporate the utilization of random orthogonal matrices to augment the trainable parameters. To examine their effects on performance, we consider the following two situations: (1) Remove random orthogonal vectors in projections $\tilde{A}_p$ and $\tilde{A}_W$ , i.e., ignore the steps in lines 9-12 of Algorithm 1; (2) Remove the subspace learning stage, i.e., construct $\tilde{A}_p$ and $\tilde{A}_W$ using random orthogonal vectors. The performance comparison of the above two situations with the original method is provided in Table 3. It can be observed that the performance of both situations has declined. This decline is particularly noticeable on the SVHN benchmark, with reductions of $1.9\%$ and $2.1\%$ , respectively, compared to the original method. This phenomenon confirms the following two points: (1) Augmenting the trainable parameters through random orthogonal matrices is advantageous for improved learning of information in the second training set; (2) Subspace learning establishes foundational performance for the black-box visual prompt tuning stage, a facet that cannot be entirely supplanted by the use of random orthogonal matrices. + +Table 3. Ablations of random orthogonal matrices in projections $\tilde{A}_p$ and $\tilde{A}_W$ on SVHN, EuroSAT, CLEVR benchmarks. We report the average test accuracy. The data in the initial two rows of the table correspond to situations 1 and 2, respectively. + +
MethodSVHNEuroSATCLEVR
Remove Random41.172.132.9
All Random40.972.132.5
Ours43.072.332.9
+ +Effect of Pre-train. Pre-train is a crucial step in our method, serving as the foundation for both the subsequent subspace learning and black-box visual prompt tuning stages. As a result, it directly influences the performance of our framework. We remove the pre-train stage, i.e., remove the $p_0$ and $W_0$ and compare it with the original method to demonstrate its + +![](images/685260cac9bfec8902349220b8bfb0cefd1229b2ab14feaaccd57ca91c5d8cd1.jpg) +Figure 3. Ablations of pre-train on 3 benchmarks. We report the average test accuracy. The initial two columns of the figure correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train. + +![](images/88802802c4c55bd72357583b43f9579a074b9f18b724739286bfa3378fa1a657.jpg) + +![](images/3a68124e2eaf9ae13f1639cad1a3dda5b09c944cccc2d01077ed7a8d04268d24.jpg) + +effectiveness. With the adjustments mentioned above to the method, we provide two additional results: (1) Optimize the parameters in the low dimensional subspace with random projection matrices; (2) Optimize the parameters in the original space. To guarantee a fair comparison with consistent training data across all methods, the training samples used in the two experiments above are formed by merging the two training sets employed by the original method. As shown in Figure 3 and Table 4, the second method without pre-train requires an increased number of training epochs, specifically 2663, 2327, and 1420, to attain performance comparable to the original method. This observation indicates that pretrain is effective in reducing training costs while ensuring subsequent training maintains acceptable performance. Additionally, the test accuracy of optimizing parameters in the low-dimensional subspace is lower compared to optimizing in the original space. We attribute this phenomenon to the inherent limitation of the low dimensional subspace, which is more suitable for fine-tuning based on pre-train results rather than direct model training. + +Table 4. Ablations of pre-train on 3 benchmarks. We report the average training epochs. The initial two rows of the table correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train. + +
MethodSVHNEuroSATCLEVR
Low Dim Subspace460041333466
Original Space293325001600
Ours270173180
+ +Effect of Low Dimensional Subspace. The utilization of the low dimensional subspace is intended to reduce the number of trainable parameters, with the primary goal of expediting convergence in the black-box visual prompt tuning stage. + +Table 5. Ablations of low dimensional subspace. We report the average of test accuracy and training epochs over 3 different seeds. + +
MethodSVHNEuroSATCLEVR
AccEpochAccEpochAccEpoch
Original Space43.745372.524033.0180
Ours43.027072.317332.9180
+ +We optimize the parameters of the trigger vector and decoder based on the pre-train results in the original space rather than in the low-dimensional subspace. Table 5 confirms the effectiveness of low dimensional subspace in reducing training costs. In most cases, optimizing parameters in the original space necessitates a higher number of training epochs to achieve comparable test accuracy between the two methods. Specifically, our method reduces the training epochs by 183 on SVHN benchmark, from 453 to 270. This denotes that low dimensional subspaces enhance the query efficiency of the method. + +# 5. Conclusion + +This paper outlines a novel VPL method that reduces reliance on extensive API queries, making the use of pretrained models (PTMs) for downstream tasks more accessible and efficient. By using the subspace learning strategy, our method can learn a visual prompt in a task-specific lower-dimensional subspace. By using this method, our method can significantly reduce the necessity for API queries of PTMs, showcasing an efficient method for leveraging the capabilities of large-scale models in visual prompting tasks. Our experiments demonstrate the efficacy of our method, showing significant reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on various tasks. + +# Acknowledgements + +# References + +[1] Mehmet Aygun, Yusuf Aytar, and Hazim Kemal Ekenel. Exploiting convolution filter patterns for transfer learning. In Proceedings of the IEEE International Conference on Computer Vision Workshops, pages 2674-2680, 2017. 1 +[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models. arXiv preprint arXiv:2203.17274, 2022. 2 +[3] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. 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However, the opaque nature of PTMs in many real-world applications has led to a growing interest in gradient-free approaches within VPL. A significant challenge with existing black-box VPL methods lies in the high dimensionality of visual prompts, which necessitates considerable API queries for tuning, thereby impacting efficiency. To address this issue, we propose a novel query-efficient framework for black-box visual prompting, designed to generate input-dependent visual prompts efficiently for large-scale black-box PTMs. Our framework is built upon the insight of reparameterizing prompts using neural networks, improving the typical pretraining-fine-tuning paradigm through the subspace learning strategy to maximize efficiency and adaptability from both the perspective of initial weights and parameter dimensionality. This tuning intrinsically optimizes low-dimensional representations within the well-learned subspace, enabling the efficient adaptation of the network to downstream tasks. Our approach significantly reduces the necessity for substantial API queries to PTMs, presenting an efficient method for leveraging large-scale black-box PTMs in visual prompting tasks. Most experimental results across various benchmarks demonstrate the effectiveness of our method, showcasing substantial reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on downstream tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "spans": [ + { + "bbox": [ + 56, + 639, + 135, + 651 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 659, + 297, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 297, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 297, + 685 + ], + "type": "text", + "content": "Large pre-trained models (PTMs) have demonstrated remarkable effectiveness across a range of tasks in computer" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 256, + 555, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 411 + ], + "type": "text", + "content": "vision, as evidenced by numerous studies [1, 13, 14, 41]. Recently, researchers have drawn inspiration from the success of prompt learning in natural language processing [11, 22, 23, 33], leading to the innovative approach of visual prompt learning (VPL) [5, 6, 19]. This method involves training a global visual prompt, consisting of pixel-level modifications often represented as padding or patches, using a pre-trained visual model and task-specific downstream data. The integration of this visual prompt with any downstream test image facilitates model predictions. Recent studies have validated the efficacy of VPL, demonstrating its competitive advantage over traditional parameter fine-tuning methods across various applications." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 413, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 556, + 604 + ], + "type": "text", + "content": "Although VPL has demonstrated significant potential [5, 6, 19], its practical application encounters substantial barriers, especially when pre-trained models are only available through opaque black-box APIs or as proprietary software. To address this challenge, Oh et al. [27] introduce Blackbox Visual Prompting (BlackVIP), an innovative approach that facilitates effective transfer learning with pre-trained vision models without requiring direct access to their parameters. However, black-box VPL necessitates considerable API queries to PTMs, resulting in significant costs. Furthermore, the high dimensionality of continuous prompts poses challenges for black-box optimization algorithms, as these methods require a substantial number of queries to optimize prompts effectively in high-dimensional spaces. Therefore, improving performance with a limited number of queries is a key challenge in high-dimensional black-box VPL." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 557, + 715 + ], + "type": "text", + "content": "One of the straightforward candidates for addressing the abovementioned challenge is to adopt the pre-training-finetuning paradigm typical of large language models (LLMs). Pre-training can yield high-quality initial weights, which in turn significantly reduces the number of API queries required during the fine-tuning phase of black-box VPL. Nevertheless, pre-training does not reduce the dimensionality of the tunable parameters, which can significantly impact the convergence rate of black-box optimization methods. Therefore," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 693, + 225, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 693, + 225, + 703 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 225, + 703 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 69, + 693, + 225, + 703 + ], + "type": "text", + "content": " Co-first authors and are listed in random order." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 703, + 157, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 703, + 157, + 713 + ], + "spans": [ + { + "bbox": [ + 69, + 703, + 157, + 713 + ], + "type": "text", + "content": "\\*Co-corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4322" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 296, + 159 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 296, + 159 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 296, + 159 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 296, + 159 + ], + "type": "image", + "image_path": "f15a9cca6e98089374fe423498198f7a65b10399db7482da70eca9d18a701061.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 167, + 298, + 257 + ], + "lines": [ + { + "bbox": [ + 55, + 167, + 298, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 298, + 257 + ], + "type": "text", + "content": "Figure 1. An overview of white/black-box visual prompt approaches. VP suffers from requiring a huge memory capacity to optimize the parameters through backpropagation. BlackVIP enjoys the proficiency of parameter efficiency but still suffers from large query complexity. Our approach solves the above problems by utilizing the strategy of subspace learning, resulting in a parameter-efficient and query-efficient black-box visual prompt framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 280, + 297, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 280, + 297, + 316 + ], + "spans": [ + { + "bbox": [ + 54, + 280, + 297, + 316 + ], + "type": "text", + "content": "if the parameter dimensionality can be reduced on the basis of pre-training, it could theoretically lead to a further reduction in API query costs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 317, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 317, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 56, + 317, + 296, + 568 + ], + "type": "text", + "content": "Fortunately, recent studies proposed the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. This discovery facilitates the development of efficient optimization strategies that concentrate on this reduced-dimensional subspace. Based on this idea, Sun et al. [33] optimize a latent representation of the prompt in a dimensionality-reduced space, using a random low-rank matrix to map this optimized representation back into the original high-dimensional prompt space [31, 33, 36, 37]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research explores adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to yield optimal prompt configurations [37]. Such adaptive strategies could significantly enhance the efficiency and effectiveness of black-box prompt tuning by dynamically adjusting to the characteristics of the prompt's underlying data distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "type": "text", + "content": "Based on the above motivation, this paper introduces a novel framework for Black-box Visual Prompting that optimizes query efficiency. To address the identified limitations, our framework leverages intrinsic dimensionality [31, 33, 36, 37] by integrating pre-training with subspace learning to develop efficient black-box visual prompting, as shown in Figure 1. This process aims to identify and utilize low-dimensional subspaces based on pre-training, thereby maximizing efficiency and adaptability from both the initial weights and parameter dimensionality perspectives to satisfy a broad spectrum of applications. A significant advancement is our proposal of the subspace learning paradigm," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": "which effectively addresses the challenges associated with learning subspaces in the black-box setting. Fine-tuning the low-dimensional representation of the prompt generation network's parameters within the subspace derived from this paradigm enables the generation of input-dependent visual prompts that are both effective and efficient across various downstream tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 157, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 555, + 180 + ], + "type": "text", + "content": "The main contributions of this work are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 182, + 556, + 385 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 182, + 555, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 182, + 555, + 242 + ], + "spans": [ + { + "bbox": [ + 314, + 182, + 555, + 242 + ], + "type": "text", + "content": "- This paper proposes an efficient black-box visual prompting framework, which leverages pre-training and subspace learning strategy to significantly reduce the number of API queries, for generating task-specific visual prompts without relying on gradient-based methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 242, + 555, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 242, + 555, + 290 + ], + "spans": [ + { + "bbox": [ + 315, + 242, + 555, + 290 + ], + "type": "text", + "content": "- Our framework introduces a novel subspace learning paradigm that iteratively generates each column of the projection matrix, effectively addressing the difficulties of learning a high-quality subspace in the black-box setting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 290, + 556, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 290, + 556, + 385 + ], + "spans": [ + { + "bbox": [ + 315, + 290, + 556, + 385 + ], + "type": "text", + "content": "- Our method adapts the PTM to downstream tasks with low query requirements. The experimental results demonstrate the superiority of our framework. Compared to methods that learn visual prompts directly in downstream tasks, our framework uses less than " + }, + { + "bbox": [ + 315, + 290, + 556, + 385 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 315, + 290, + 556, + 385 + ], + "type": "text", + "content": " of their API queries. Additionally, when compared to fine-tuning methods with the same pre-trained weights, our framework also reduces the API queries by one-third." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 399, + 406, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 399, + 406, + 411 + ], + "spans": [ + { + "bbox": [ + 314, + 399, + 406, + 411 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 420, + 451, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 420, + 451, + 433 + ], + "spans": [ + { + "bbox": [ + 314, + 420, + 451, + 433 + ], + "type": "text", + "content": "2.1. Visual Prompt Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "content": "Prompt learning [11, 22, 23, 33] has emerged as a significant approach in natural language processing for effectively adapting pre-trained LLMs for specific downstream tasks. This method involves the creation of a trainable, lightweight component that serves as an additional input (or prompt) to a static model. Inspired by its great success in natural language processing, VPL [2, 5, 6, 19] also starts emerging in the computer vision domain to adapt the large-scale upstream pre-trained visual models to various downstream tasks, such as image classification [2], vision-language modeling [42], etc. Specifically, Context Optimization (CoOp) [39] innovatively incorporates a continuous text prompt within the text encoder of a Vision-Language Model (VLM), thereby enhancing its interpretative and processing capabilities. Building on this framework, Conditional CoOp (CoCoOp) [38] further refines the approach by adapting CoOp into a version that is dependent on the input. Jia et al. [19] propose the Visual Prompt Tuning (VPT) that governs learnable visual tokens to the embedding layer or several encoder layers of Vision Transformer. Bahng et al. [2] explore a technique for learning pixel perturbations that are applied to a specific, constrained area of an input image. All these methods require accessibility of the model architecture and parameters." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4323" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "content": "However, in real-world applications, many AI systems are offered as APIs or proprietary software, where the specifics of their implementation or the full range of parameters are not disclosed due to commercial considerations. This limitation renders these approaches impractical for use in such contexts. To solve this problem, Oh et al. [27] propose BlackVIP, which efficiently adapts the PTMs without knowledge about model architectures and parameters. However, this approach usually requires a high number of queries, which can lead to significant economic costs. Therefore, it motivates us to investigate a query-efficient black-box visual prompting method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 227, + 288, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 227, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 227, + 288, + 240 + ], + "type": "text", + "content": "2.2. Black-box Optimization in Prompt Learning" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 246, + 296, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 246, + 296, + 520 + ], + "spans": [ + { + "bbox": [ + 56, + 246, + 296, + 520 + ], + "type": "text", + "content": "Recently, the widespread deployment of AI applications as APIs or proprietary software has necessitated the use of black-box optimization techniques in prompt learning. This is primarily due to the commercial practice of withholding detailed implementation details or full parameter configurations, which has significantly contributed to the success of these optimization methods. Specifically, Dao et al. [11] use the policy gradient method to search the discrete prompt for the pre-trained language model. They also observed that the conventional policy gradient suffers from high variance, which makes it challenging to converge in practice. Therefore, they adopted a variance-reduced policy gradient estimator to improve the performance [12, 40]. RLPrompt [10] uses reinforcement learning to optimize the discrete prompt for the pre-trained language model. BlackVIP [27] adopts the Simultaneous Perturbation Stochastic Approximation (SPSA) as a zeroth-order optimization (ZOO) algorithm with gradient correction to search the visual prompt for the large-scale pre-trained vision models. These methods often necessitate a substantial number of queries to achieve convergence, resulting in increased costs. However, all these methods need to solve a high-dimensional optimization problem, where the black-box methods are usually inefficient." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 522, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 297, + 714 + ], + "type": "text", + "content": "Fortunately, recent studies propose the concept of intrinsic dimensionality, which is the effective dimensionality needed to capture the significant variance in prompts and is much lower than the embedding space's high dimensionality [33]. Based on this idea, Black-Box Tuning (BBT) [33] and BBTv2 [32] use a random matrix sampled from a uniform distribution to project the high-dimensional continuous prompt into a low-dimensional subspace and optimize a latent representation in this subspace using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [16, 17]. Nevertheless, the randomness of subspace selection, while reducing computational complexity, may introduce additional API calls and potentially impact the precision of prompt optimization. To mitigate these effects, further research is required to explore adaptive methods for subspace selection, prioritizing regions of the latent space that are more likely to" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 463, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 463, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 463, + 84 + ], + "type": "text", + "content": "yield optimal prompt configurations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "spans": [ + { + "bbox": [ + 314, + 95, + 397, + 109 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 114, + 555, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 114, + 555, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 114, + 555, + 163 + ], + "type": "text", + "content": "In this section, we introduce the proposed framework for black-box visual prompt generation, which consists of subspace learning and visual prompt tuning. The overall process of the proposed framework is illustrated in Figure 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 170, + 555, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 170, + 555, + 194 + ], + "spans": [ + { + "bbox": [ + 313, + 170, + 555, + 194 + ], + "type": "text", + "content": "3.1. Brief Review of Visual Prompt Reparameterization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 199, + 555, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 199, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 199, + 555, + 247 + ], + "type": "text", + "content": "Motivated by the great success of prompt learning in NLP, Oh et al. [27] propose an asymmetric autoencoder-style network that receives the original image and produces a corresponding visual prompt for each image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "content": "The objective function of VPL is to minimize the downstream task loss by adapting the frozen PTM via input space prompt optimization. Specifically, given a frozen prediction model " + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "inline_equation", + "content": "P_{\\theta}" + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "content": " denotes the model parameters) and the perturbed image " + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "content": " with prompt corresponding to the label " + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 247, + 556, + 319 + ], + "type": "text", + "content": ", the learning objective of VPL is formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 383, + 328, + 555, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 328, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 383, + 328, + 555, + 348 + ], + "type": "interline_equation", + "content": "\\underset {\\phi} {\\arg \\min } - \\log P _ {\\theta ; \\phi} (y | \\tilde {x}) \\tag {1}", + "image_path": "75874df4a4faabc31293669720169330d1f0af9ac9b4e65f7e3622e75aebfba4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": "Instead of directly optimizing the visual prompts, where " + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": " is defined as the visual prompt, Oh et al. [27] introduce a reparameterization technique through a network they call the prompt generation network, denoted as " + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": ". This network is characterized by parameters " + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\phi = \\{p, W\\} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": ". To implement this concept, they develop a network akin to an autoencoder, named Coordinator. This network uniquely integrates a \"frozen\" encoder " + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": ", which leverages self-supervised learning (SSL) objectives for pre-training on the ImageNet dataset. Complementing the encoder is a lightweight, learnable decoder, parameterized by " + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 356, + 556, + 572 + ], + "type": "text", + "content": ", designed to work in tandem with the encoded inputs. Leveraging the encoder pre-trained via self-supervised learning (SSL) methods significantly reduces the number of learnable parameters, and this encoder not only facilitates easier adoption by users in local settings but also maintains the integrity of realistic experimental conditions. Then, the process of constructing an image that incorporates a prompt proceeds as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 388, + 582, + 555, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 582, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 388, + 582, + 555, + 594 + ], + "type": "interline_equation", + "content": "\\tilde {x} = \\operatorname {c l i p} (x + \\epsilon h _ {\\phi} (x)) \\tag {2}", + "image_path": "b849ee3ce47688cdc55fce71a0f1c431ef461ca21981b906e725bb2eab73a058.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 388, + 597, + 555, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 597, + 555, + 609 + ], + "spans": [ + { + "bbox": [ + 388, + 597, + 555, + 609 + ], + "type": "interline_equation", + "content": "h _ {\\phi} (x) = g _ {W} (f (x), p) \\tag {3}", + "image_path": "d899c5aaa63a29d5c3c490e39b369b4f7333e3cddcc88c969b30a2ddfd7d801e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " is the feature vector of " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " from the frozen SSL encoder " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon \\in [0,1]" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " is a hyperparameter that controls the intensity of visual prompt. In addition, " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " is a task-specific prompt trigger vector that is jointly optimized with the decoder parameter " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": ". The procedure involves concatenating the output " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": " with the task-specific prompt trigger vector " + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 617, + 557, + 714 + ], + "type": "text", + "content": ", followed by reshaping this combination into a three-dimensional feature map. This map is then inputted into" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4324" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 71, + 531, + 337 + ], + "blocks": [ + { + "bbox": [ + 80, + 71, + 531, + 337 + ], + "lines": [ + { + "bbox": [ + 80, + 71, + 531, + 337 + ], + "spans": [ + { + "bbox": [ + 80, + 71, + 531, + 337 + ], + "type": "image", + "image_path": "88402e17232d9611e90d6151b17fe1d7054fa30e616d747448d499ff54ccf736.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "lines": [ + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "spans": [ + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "text", + "content": "Figure 2. Framework overview of the proposed subspace learning based black-box visual prompt approach. Subspace Learning: learn the projection matrices " + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p" + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W" + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "text", + "content": " by generating each column iteratively and concatenating them with random orthogonal matrices for the extension. Visual Prompt Tuning: optimize low-dimensional representations of parameters within subspace represented by projection matrices " + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p" + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W" + }, + { + "bbox": [ + 54, + 346, + 555, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "spans": [ + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "text", + "content": "the convolutional decoder. Through this process, the semantically rich, instance-specific representation " + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "text", + "content": " and the task-specific prompt trigger vector " + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "text", + "content": " are seamlessly integrated. This integration forms a coherent and effective visual prompt " + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "inline_equation", + "content": "h_{\\phi}(x)" + }, + { + "bbox": [ + 54, + 412, + 296, + 472 + ], + "type": "text", + "content": ", tailored specifically for the given image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 472, + 296, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 472, + 296, + 591 + ], + "spans": [ + { + "bbox": [ + 54, + 472, + 296, + 591 + ], + "type": "text", + "content": "Upon employing the reparameterization technique, we can apply black-box optimization strategies to address the specified objective. Nonetheless, a critical consideration is that the dimensionality of the learnable parameter, " + }, + { + "bbox": [ + 54, + 472, + 296, + 591 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 54, + 472, + 296, + 591 + ], + "type": "text", + "content": ", may still be substantially large. This elevated dimensionality can adversely affect the optimization process, potentially resulting in suboptimal convergence rates and necessitating a high number of queries to reach a satisfactory solution. This situation motivates the development of a method characterized by a lower query requirement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 597, + 190, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 190, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 190, + 609 + ], + "type": "text", + "content": "3.2. Problem Reformulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 614, + 297, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 614, + 297, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 614, + 297, + 675 + ], + "type": "text", + "content": "As mentioned above, the dimensionality of the target variable " + }, + { + "bbox": [ + 55, + 614, + 297, + 675 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 614, + 297, + 675 + ], + "type": "text", + "content": ", which we are interested in optimizing, can be very high, rendering derivative-free optimization intractable. Inspired by the low-dimensional intrinsic subspace method, we propose the learning objective of our method as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 110, + 692, + 296, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 692, + 296, + 711 + ], + "spans": [ + { + "bbox": [ + 110, + 692, + 296, + 711 + ], + "type": "interline_equation", + "content": "\\underset {z} {\\arg \\min } - \\log P _ {\\theta ; \\phi = A z + a _ {0}} (y | \\tilde {x}) \\tag {4}", + "image_path": "c24c37a4655033329a704a9fc12bd436f8f4845df21c88790a9453772cf6a5c1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "z = \\{z_{p},z_{W}\\}" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": " denotes the low dimensional latent parameters of the prompt trigger and the learnable decoder, " + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "A = \\{A_p,A_W\\}" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "(A_{p}\\in \\mathbb{R}^{D_{p}\\times d_{p}},A_{W}\\in \\mathbb{R}^{D_{W}\\times d_{W}}" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "d_p,d_W\\ll D)" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": " is the projection matrix and " + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "a_0 = \\{p_0,W_0\\}" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": " denotes the initial parameters. As mentioned above, since the choice of the random matrix " + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 412, + 555, + 520 + ], + "type": "text", + "content": " highly affects the final performance, in this paper, we first propose our subspace learning method, and then based on this method we propose our visual prompt learning method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 528, + 555, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 555, + 541 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 555, + 541 + ], + "type": "text", + "content": "3.3. Subspace Learning for Visual Prompt Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "text", + "content": "As illustrated in Figure 2 and Algorithm 1, our framework performs subspace learning based on the pre-trained weights " + }, + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "inline_equation", + "content": "W_0" + }, + { + "bbox": [ + 313, + 545, + 555, + 594 + ], + "type": "text", + "content": " to reduce the dimensionality of tunable parameters during the black-box visual prompt tuning phase." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": "Subspace Learning. The goal of subspace learning phase is to learn a low dimensional subspace " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d},\\tilde{A}_W\\in" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{D_W\\times d}\\}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " for the trigger vector " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " and the decoder parameterized by " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " , which are spanned by " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{p_1,\\dots ,p_d\\}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{W_{1},\\ldots ,W_{d}\\}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " , respectively. In the initialization step, we choose random projection matrices " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "A_{p_1}\\in \\mathbb{R}^{D_p\\times d_p}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "A_{W_1}\\in \\mathbb{R}^{D_W\\times d_W}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " . Subsequently, we generate " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{p_1,\\dots ,p_d\\}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{W_1,\\dots ,W_d\\}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " iteratively by the following way: at the " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " -th iteration, the optimization parameters " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "z_{p_i}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "inline_equation", + "content": "z_{W_i}" + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": " are obtained by solving problem (4) through Algorithm 2 and" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4325" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 211, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 211, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 211, + 85 + ], + "type": "text", + "content": "compute " + }, + { + "bbox": [ + 55, + 72, + 211, + 85 + ], + "type": "inline_equation", + "content": "p_i = A_{p_i}z_{p_i}" + }, + { + "bbox": [ + 55, + 72, + 211, + 85 + ], + "type": "inline_equation", + "content": "W_{i} = A_{W_{i}}z_{W_{i}}" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 85, + 296, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 85, + 296, + 132 + ], + "spans": [ + { + "bbox": [ + 55, + 85, + 296, + 132 + ], + "type": "text", + "content": "Since we consider PTM as a black-box predictor, we have no access to the true gradient of the learnable parameters. We adopt the following zeroth-order gradient estimator for Algorithm 2:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 65, + 140, + 296, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 140, + 296, + 172 + ], + "spans": [ + { + "bbox": [ + 65, + 140, + 296, + 172 + ], + "type": "interline_equation", + "content": "\\hat {\\nabla} F _ {S} (z) = \\frac {1}{n} \\sum_ {j = 1} ^ {n} \\frac {F _ {S} (z + \\mu \\mathrm {u} _ {j}) - F _ {S} (z - \\mu \\mathrm {u} _ {j})}{2 \\mu} \\mathrm {u} _ {j}, \\tag {5}", + "image_path": "d8b56b346d83152e5d35a1c458b6a2d407c7ed0c62862317c7cd6cc8eb5b2c95.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathfrak{u}_j\\in \\mathbb{R}^{d_p + d_W}" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": " is distributed over " + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\mathrm{I})" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "z\\in \\mathbb{R}^{d_p + d_W}" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "(d_p + d_W)" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": "-dimensional learnable parameters and " + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{S}}(z)" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": " denotes the objective function evaluated on a batch of samples " + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 55, + 182, + 296, + 242 + ], + "type": "text", + "content": ", where the function value is computed through a forward pass of the model, as illustrated in Algorithm 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": "The projection matrices " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "A_{p_{i + 1}}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "A_{W_{i + 1}}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " are generated manually such that " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "A_{p_{i + 1}}\\bot \\tilde{A}_p" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "A_{W_{i + 1}}\\bot \\tilde{A}_W" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p = [p_1,\\dots ,p_i]" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W = [W_1,\\dots ,W_i]" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ". After " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " iterations, the learned projection matrices are presented by " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p\\in \\mathbb{R}^{D_p\\times d}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W\\in \\mathbb{R}^{D_W\\times d}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ", in which each column is orthogonal to the others. As noted above, we have learned the intrinsic low dimensional subspace for learnable parameters. However, directly adapting it to specific downstream tasks with limited trainable parameters is still a challenge. To fill this gap, we first construct random orthogonal matrices " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p^\\prime \\in \\mathbb{R}^{D_p\\times d'}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W^\\prime \\in \\mathbb{R}^{D_W\\times d'}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p^\\prime \\bot \\tilde{A}_p" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W^\\prime \\bot \\tilde{A}_W" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ". The final projection matrices are constructed by " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p = [\\tilde{A}_p,\\tilde{A}_p^{\\prime}]\\in \\mathbb{R}^{D_p\\times (d + d')}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W = [\\tilde{A}_W,\\tilde{A}_W^{\\prime}]\\in \\mathbb{R}^{D_W\\times (d + d')}" + }, + { + "bbox": [ + 55, + 243, + 296, + 466 + ], + "type": "text", + "content": ". By doing so, we make a trade-off between the limitations of insufficient training with a reduced number of trainable parameters and the high pretrain computational cost of querying the full set of trainable parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 467, + 296, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 467, + 296, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 467, + 296, + 526 + ], + "type": "text", + "content": "Black-Box Visual Prompt Tuning. The goal of the black-box prompt tuning phase is to utilize the learned subspace for generating task-specific visual prompts. The optimization process resembles that of the subspace learning phase, with the only difference being in the projection matrices." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 537, + 135, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 537, + 135, + 551 + ], + "spans": [ + { + "bbox": [ + 55, + 537, + 135, + 551 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 557, + 296, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 296, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 296, + 616 + ], + "type": "text", + "content": "We first provide the experimental setup in Section 4.1. Then, we report the average test accuracy and the number of black-box PTM calls for our method and all baseline methods across 14 benchmarks in Section 4.2. Ablation studies are provided in Section 4.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 624, + 171, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 171, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 171, + 637 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "Datasets. To evaluate the effectiveness of our proposed method and to compare it with baseline methods, we conduct experiments on 14 widely used benchmarks that cover diverse visual domains: Caltech101 [15], OxfordPnts [28], StanfordCars [21], Flowers102 [26], Food101 [4], FGVCAircraft [24], SUN397 [35], DTD [8], SVHN [25], EuroSAT" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 72, + 516, + 83 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 72, + 516, + 83 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 516, + 83 + ], + "type": "text", + "content": "Algorithm 1 Subspace Learning based Algorithm" + } + ] + } + ], + "index": 10, + "type": "text" + }, + { + "bbox": [ + 316, + 88, + 555, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 88, + 555, + 162 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 555, + 162 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 316, + 88, + 555, + 162 + ], + "type": "inline_equation", + 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"inline_equation", + "content": "\\mathcal{S}_i = \\{(x_1,y_1),\\ldots ,(x_m,y_m)\\}" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "spans": [ + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "text", + "content": "3: Sample " + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "text", + "content": " random directions " + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "inline_equation", + "content": "\\mathrm{u}_j (j = 1 \\dots n)" + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "text", + "content": " from a Gaussian distribution " + }, + { + "bbox": [ + 321, + 493, + 553, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0, \\mathrm{I})" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 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"z_{p}^{(i + 1)} = z_{p}^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_{i}}\\left(z_{p}^{(i)}\\right)" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 321, + 564, + 500, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 564, + 500, + 582 + ], + "spans": [ + { + "bbox": [ + 321, + 564, + 500, + 582 + ], + "type": "text", + "content": "6: Update " + }, + { + "bbox": [ + 321, + 564, + 500, + 582 + ], + "type": "inline_equation", + "content": "z_W^{(i + 1)} = z_W^{(i)} - \\eta \\hat{\\nabla} F_{\\mathcal{S}_i}\\left(z_W^{(i)}\\right)" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 321, + 582, + 364, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 582, + 364, + 591 + ], + "spans": [ + { + "bbox": [ + 321, + 582, + 364, + 591 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 37 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 617, + 555, + 665 + ], + "type": "text", + "angle": 0, 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They require comprehending diverse visual semantics, including actions, textures, scenes, the number of objects, and fine-grained categories, to name a few." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "content": "**Baseline Methods.** We compare our proposed method with the following baselines: CLIP's Zero-shot Classifier (ZS) [29], which is based on the manual text prompt and is widely used for vision tasks including classification, detection, etc." + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4326" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 113, + 553, + 229 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 104 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 104 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 104 + ], + "type": "text", + "content": "Table 1. Overall comparison on 14 benchmarks that require the comprehension of diverse visual semantics. We report the average test accuracy on 3 different seeds. The last column shows the count of benchmarks in which each method outperforms zero-shot performance. All results are obtained using the CLIP ViT-B/16." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 113, + 553, + 229 + ], + "lines": [ + { + "bbox": [ + 56, + 113, + 553, + 229 + ], + "spans": [ + { + "bbox": [ + 56, + 113, + 553, + 229 + ], + "type": "table", + "html": "
MethodParamsSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.Win
ZS-18.948.389.058.144.124.893.385.967.570.765.514.762.666.757.9-
VP69.8k33.172.786.965.345.924.490.080.565.167.457.427.861.862.460.05
BAR37.6k33.676.289.367.946.024.993.784.568.371.862.827.864.866.162.711
BlackVIP9.92k42.771.989.564.644.524.793.486.269.070.565.634.065.267.063.512
BlackVIP-ft9.92k42.572.689.563.244.824.793.386.168.971.065.732.164.866.963.313
Ours0.15k43.072.389.363.044.724.793.386.269.070.965.632.964.766.963.313
", + "image_path": "6d85ce1c841c8f9effdf3237c25cb7558458ba159c28f37285a0fd09b917a673.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 271, + 553, + 381 + ], + "blocks": [ + { + "bbox": [ + 55, + 240, + 555, + 264 + ], + "lines": [ + { + "bbox": [ + 55, + 240, + 555, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 240, + 555, + 264 + ], + "type": "text", + "content": "Table 2. Comparison of the number of API queries on 14 benchmarks during training using early stopping strategy. Our method shows outstanding query efficiency. The unit of data in the table is " + }, + { + "bbox": [ + 55, + 240, + 555, + 264 + ], + "type": "inline_equation", + "content": "{1k}" + }, + { + "bbox": [ + 55, + 240, + 555, + 264 + ], + "type": "text", + "content": " (one thousand)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 271, + 553, + 381 + ], + "lines": [ + { + "bbox": [ + 56, + 271, + 553, + 381 + ], + "spans": [ + { + "bbox": [ + 56, + 271, + 553, + 381 + ], + "type": "table", + "html": "
MethodSVHNEuroSATPetsRESISCDTDAircraftCaltechFoodUCFFlowersCarsCLEVRSUNImageAvg.
VP44.036.032.0220.0173.3588.0435.0420672.0345.7659.240.7670.9548.5349.0
BAR13.016.046.4109.067.0345.6234.0259.2421.2234.6325.518.0316.7501.2207.7
BlackVIP48.341.328.0193.360.0168.0420.084.0540.0317.3501.740.3434.1579.7246.9
BlackVIP-ft3.51.69.96.410.022.69.730.012.08.819.41.720.319.812.6
Ours2.71.77.42.87.06.810.721.29.28.821.81.87.515.18.9
", + "image_path": "8c8693a36047a131ae853417da98976a036d29b4a1ef797c2f8fccc67969d0a6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 402, + 206, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 402, + 206, + 415 + ], + "spans": [ + { + "bbox": [ + 56, + 402, + 206, + 415 + ], + "type": "text", + "content": "Algorithm 3 Loss " + }, + { + "bbox": [ + 56, + 402, + 206, + 415 + ], + "type": "inline_equation", + "content": "F_{S}(\\phi)" + }, + { + "bbox": [ + 56, + 402, + 206, + 415 + ], + "type": "text", + "content": " calculation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "spans": [ + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "type": "text", + "content": "Require: projection matrices " + }, + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + 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"text", + "content": ", loss function " + }, + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "type": "text", + "content": ", a batch of samples " + }, + { + "bbox": [ + 56, + 418, + 297, + 491 + ], + "type": "inline_equation", + "content": "S = \\{(x_1, y_1), \\ldots, (x_m, y_m)\\}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 491, + 252, + 514 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 62, + 491, + 209, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 491, + 209, + 502 + ], + "spans": [ + { + "bbox": [ + 62, + 491, + 209, + 502 + ], + "type": "text", + "content": "1: Get trigger vector " + }, + { + "bbox": [ + 62, + 491, + 209, + 502 + ], + "type": "inline_equation", + "content": "p = A_{p}z_{p} + p_{0}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 62, + 502, + 252, + 514 + ], + "type": "text", + 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], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 62, + 550, + 186, + 562 + ], + "type": "inline_equation", + "content": "F_{x_i}(\\phi) = L(P_\\theta (\\tilde{x}_i),y_i)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 62, + 563, + 106, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 563, + 106, + 571 + ], + "spans": [ + { + "bbox": [ + 62, + 563, + 106, + 571 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 62, + 572, + 179, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 572, + 179, + 587 + ], + "spans": [ + { + "bbox": [ + 62, + 572, + 179, + 587 + ], + "type": "text", + "content": "8: " + }, + { + "bbox": [ + 62, + 572, + 179, + 587 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{S}}(\\phi) = \\frac{1}{m}\\sum_{i = 1}^{m}F_{x_i}(\\phi)" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "content": "Black-box Adversarial Reprogramming (BAR) [34], which utilizes the zeroth-order optimizer and randomized gradient-free minimization algorithm for transfer learning of pretrained model to the medical image domain. Visual Prompting with SPSA-GC (VP) [3], which is the version that replaces the first-order optimizer in Visual Prompting with a zero-order optimizer named SPSA-GC [27]. Black-box visual prompting (BlackVIP) [27], which utilizes a neural" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 402, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 555, + 437 + ], + "type": "text", + "content": "network to reparameterize the visual prompt for adapting to black-box optimization and optimizes tiny parameters with SPSA-GC." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 437, + 556, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 556, + 606 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 556, + 606 + ], + "type": "text", + "content": "Implementation Details. Our method is implemented using pytorch1. We employ CLIP ViT-B/16 as the target black-box PTM and the manual text prompts are consistent with those used in [27]. For the encoder, we use ImageNet pre-trained vit-mae-base checkpoint from the HuggingFace. The experimental setup for all baselines and pre-train in our method follows the implementation details in [27]. During the subspace learning stage, the dimension of the learned subspace is set to 5, i.e., " + }, + { + "bbox": [ + 313, + 437, + 556, + 606 + ], + "type": "inline_equation", + "content": "d = 5" + }, + { + "bbox": [ + 313, + 437, + 556, + 606 + ], + "type": "text", + "content": ". The default maximum iteration of the subspace learning and last stages is 500. Similar to the few-shot classification setting of [27], we use 16-shot training samples for the pre-train and subspace learning stage, 8-shot training samples for the last stage, and the full test set for evaluating the performance of methods by default." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 614, + 400, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 614, + 400, + 627 + ], + "spans": [ + { + "bbox": [ + 313, + 614, + 400, + 627 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "text", + "content": "We conduct experiments to compare test accuracy and the number of black-box PTM queries against all baselines across 14 benchmarks. The pre-train parameters " + }, + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "inline_equation", + "content": "W_0" + }, + { + "bbox": [ + 313, + 633, + 555, + 693 + ], + "type": "text", + "content": " are obtained by running the BlackVIP on the 16-shot training samples. In our method, subspace learning is con" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 325, + 702, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 702, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 325, + 702, + 545, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 325, + 702, + 545, + 713 + ], + "type": "text", + "content": "Code is available at https://github.com/Peter777777/EffiBlackVip" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4327" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": "duced on identical training samples as those used in the pre-train. Additionally, black-box visual prompt tuning is executed on the 8-shot training samples. Subsequently, for a fair comparison, we merge the two sets above of training samples for all baseline methods except ZS and train them on the merged training set. Specifically, to showcase the efficacy of our training methodology, we additionally present the fine-tuning results of BlackVIP (BlackVIP-ft) on the 8-shot training samples based on the pre-train parameters " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "inline_equation", + "content": "W_0" + }, + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": ". The results from the pre-train and subspace learning stage are applicable for reuse in practical applications. Therefore, we report the results of the black-box visual prompt tuning stage by default in this section." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 231, + 298, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 231, + 298, + 434 + ], + "spans": [ + { + "bbox": [ + 56, + 231, + 298, + 434 + ], + "type": "text", + "content": "Comparison with Baselines. For all benchmarks, we conduct experiments on our method and all baselines using three different seeds and report the test accuracy in Table 1. It is crucial to emphasize that the number of trainable parameters in our method is significantly lower than that of baselines, excluding ZS. Our method outperforms the zero-shot classifier on 13 over 14 benchmarks. Compared to BAR and VP, our method surpasses them on half of the benchmarks. The test accuracy of BlackVIP does not show significant differences between the two training approaches, indicating that both training methods effectively utilize the two sets of training samples. As shown in Table 1, the performance among our method, BlackVIP, and BlackVIP-ft is comparable across various tasks. Our method achieves a similar effect in adjusting the attention of black-box PTM as BlackVIP, demonstrating superior performance compared to other baselines on various benchmarks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "content": "Comparison on the Number of API Queries. The number of queries to the black-box PTM is a crucial metric for evaluating black-box algorithms. Therefore, we perform the early stopping strategy for all methods except ZS and provide the API query counts for all benchmarks in Table 2. Benefiting from pre-train results and subspace learning, our method exhibits remarkably low query requirements on 14 benchmarks. Our method's API queries are significantly lower than those of BAR, VP, and BlackVIP, which lack the pre-train stage. The average API query counts of our method across the 14 benchmarks are " + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "inline_equation", + "content": "4.3\\%" + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "content": " of the corresponding averages of VP, BAR, and BlackVIP, respectively. This underscores the superiority of our subspace learning based method. In comparison to BlackVIP-ft, which fine-tunes based on the identical pre-train results, our method consistently sustains lower API query counts across 9 benchmarks while achieving comparable performance. Moreover, our method exhibits an average query count across all benchmarks that is " + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "inline_equation", + "content": "3.7\\mathrm{k}" + }, + { + "bbox": [ + 56, + 438, + 298, + 714 + ], + "type": "text", + "content": " less than that of BlackVIP-ft, indicating the superiority of our method. We attribute this phenomenon to the fact that our method reduces the number of trainable parameters through the utilization of a low-dimensional subspace. This feature enables faster convergence during further" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 472, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 472, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 472, + 84 + ], + "type": "text", + "content": "optimization based on pre-train results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 91, + 408, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 408, + 103 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 408, + 103 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 108, + 553, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 108, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 108, + 553, + 190 + ], + "type": "text", + "content": "In this section, we investigate the impacts of diverse components within our method and report the relevant results of the ablation study. Except for the explicitly mentioned settings, all experimental settings remain consistent with those employed in the experiments detailed in Table 1. For each ablation, we report the average results obtained from experiments conducted with three different seeds." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": "Effect of Random Orthogonal Matrices. In the black-box visual prompt tuning stage of our method, an increased number of trainable parameters results in higher costs during the subspace learning stage. To strike a balance between preventing inadequate learning from the second training set and mitigating the excessively high costs of subspace learning, we incorporate the utilization of random orthogonal matrices to augment the trainable parameters. To examine their effects on performance, we consider the following two situations: (1) Remove random orthogonal vectors in projections " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": ", i.e., ignore the steps in lines 9-12 of Algorithm 1; (2) Remove the subspace learning stage, i.e., construct " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": " using random orthogonal vectors. The performance comparison of the above two situations with the original method is provided in Table 3. It can be observed that the performance of both situations has declined. This decline is particularly noticeable on the SVHN benchmark, with reductions of " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 313, + 192, + 556, + 501 + ], + "type": "text", + "content": ", respectively, compared to the original method. This phenomenon confirms the following two points: (1) Augmenting the trainable parameters through random orthogonal matrices is advantageous for improved learning of information in the second training set; (2) Subspace learning establishes foundational performance for the black-box visual prompt tuning stage, a facet that cannot be entirely supplanted by the use of random orthogonal matrices." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 339, + 563, + 531, + 628 + ], + "blocks": [ + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "type": "text", + "content": "Table 3. Ablations of random orthogonal matrices in projections " + }, + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "type": "inline_equation", + "content": "\\tilde{A}_p" + }, + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "type": "inline_equation", + "content": "\\tilde{A}_W" + }, + { + "bbox": [ + 313, + 510, + 555, + 555 + ], + "type": "text", + "content": " on SVHN, EuroSAT, CLEVR benchmarks. We report the average test accuracy. The data in the initial two rows of the table correspond to situations 1 and 2, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 339, + 563, + 531, + 628 + ], + "lines": [ + { + "bbox": [ + 339, + 563, + 531, + 628 + ], + "spans": [ + { + "bbox": [ + 339, + 563, + 531, + 628 + ], + "type": "table", + "html": "
MethodSVHNEuroSATCLEVR
Remove Random41.172.132.9
All Random40.972.132.5
Ours43.072.332.9
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We remove the pre-train stage, i.e., remove the " + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "inline_equation", + "content": "W_0" + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": " and compare it with the original method to demonstrate its" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4328" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 74, + 231, + 223 + ], + "blocks": [ + { + "bbox": [ + 73, + 74, + 231, + 223 + ], + "lines": [ + { + "bbox": [ + 73, + 74, + 231, + 223 + ], + "spans": [ + { + "bbox": [ + 73, + 74, + 231, + 223 + ], + "type": "image", + "image_path": "685260cac9bfec8902349220b8bfb0cefd1229b2ab14feaaccd57ca91c5d8cd1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 237, + 555, + 261 + ], + "lines": [ + { + "bbox": [ + 55, + 237, + 555, + 261 + ], + "spans": [ + { + "bbox": [ + 55, + 237, + 555, + 261 + ], + "type": "text", + "content": "Figure 3. Ablations of pre-train on 3 benchmarks. We report the average test accuracy. The initial two columns of the figure correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 236, + 74, + 386, + 223 + ], + "blocks": [ + { + "bbox": [ + 236, + 74, + 386, + 223 + ], + "lines": [ + { + "bbox": [ + 236, + 74, + 386, + 223 + ], + "spans": [ + { + "bbox": [ + 236, + 74, + 386, + 223 + ], + "type": "image", + "image_path": "88802802c4c55bd72357583b43f9579a074b9f18b724739286bfa3378fa1a657.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 391, + 74, + 539, + 223 + ], + "blocks": [ + { + "bbox": [ + 391, + 74, + 539, + 223 + ], + "lines": [ + { + "bbox": [ + 391, + 74, + 539, + 223 + ], + "spans": [ + { + "bbox": [ + 391, + 74, + 539, + 223 + ], + "type": "image", + "image_path": "3a68124e2eaf9ae13f1639cad1a3dda5b09c944cccc2d01077ed7a8d04268d24.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 281, + 297, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 281, + 297, + 520 + ], + "spans": [ + { + "bbox": [ + 54, + 281, + 297, + 520 + ], + "type": "text", + "content": "effectiveness. With the adjustments mentioned above to the method, we provide two additional results: (1) Optimize the parameters in the low dimensional subspace with random projection matrices; (2) Optimize the parameters in the original space. To guarantee a fair comparison with consistent training data across all methods, the training samples used in the two experiments above are formed by merging the two training sets employed by the original method. As shown in Figure 3 and Table 4, the second method without pre-train requires an increased number of training epochs, specifically 2663, 2327, and 1420, to attain performance comparable to the original method. This observation indicates that pretrain is effective in reducing training costs while ensuring subsequent training maintains acceptable performance. Additionally, the test accuracy of optimizing parameters in the low-dimensional subspace is lower compared to optimizing in the original space. We attribute this phenomenon to the inherent limitation of the low dimensional subspace, which is more suitable for fine-tuning based on pre-train results rather than direct model training." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 75, + 585, + 277, + 652 + ], + "blocks": [ + { + "bbox": [ + 55, + 532, + 296, + 578 + ], + "lines": [ + { + "bbox": [ + 55, + 532, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 296, + 578 + ], + "type": "text", + "content": "Table 4. Ablations of pre-train on 3 benchmarks. We report the average training epochs. The initial two rows of the table correspond to optimizing parameters in the low dimensional subspace and original space, respectively, after removing the pre-train." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 585, + 277, + 652 + ], + "lines": [ + { + "bbox": [ + 75, + 585, + 277, + 652 + ], + "spans": [ + { + "bbox": [ + 75, + 585, + 277, + 652 + ], + "type": "table", + "html": "
MethodSVHNEuroSATCLEVR
Low Dim Subspace460041333466
Original Space293325001600
Ours270173180
", + "image_path": "660d568d028d32f972d3c0fdaf38e9f8da81ba163d164e7b34f94efa655312d6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "type": "text", + "content": "Effect of Low Dimensional Subspace. The utilization of the low dimensional subspace is intended to reduce the number of trainable parameters, with the primary goal of expediting convergence in the black-box visual prompt tuning stage." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 310, + 553, + 376 + ], + "blocks": [ + { + "bbox": [ + 313, + 279, + 555, + 301 + ], + "lines": [ + { + "bbox": [ + 313, + 279, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 555, + 301 + ], + "type": "text", + "content": "Table 5. Ablations of low dimensional subspace. We report the average of test accuracy and training epochs over 3 different seeds." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 310, + 553, + 376 + ], + "lines": [ + { + "bbox": [ + 315, + 310, + 553, + 376 + ], + "spans": [ + { + "bbox": [ + 315, + 310, + 553, + 376 + ], + "type": "table", + "html": "
MethodSVHNEuroSATCLEVR
AccEpochAccEpochAccEpoch
Original Space43.745372.524033.0180
Ours43.027072.317332.9180
", + "image_path": "e1cd65b9ef1096a1e9724f0950157c88b894a0d46d3538a0a84d425717223f2c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 396, + 556, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 556, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 556, + 526 + ], + "type": "text", + "content": "We optimize the parameters of the trigger vector and decoder based on the pre-train results in the original space rather than in the low-dimensional subspace. Table 5 confirms the effectiveness of low dimensional subspace in reducing training costs. In most cases, optimizing parameters in the original space necessitates a higher number of training epochs to achieve comparable test accuracy between the two methods. Specifically, our method reduces the training epochs by 183 on SVHN benchmark, from 453 to 270. This denotes that low dimensional subspaces enhance the query efficiency of the method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 537, + 388, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 537, + 388, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 537, + 388, + 550 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "type": "text", + "content": "This paper outlines a novel VPL method that reduces reliance on extensive API queries, making the use of pretrained models (PTMs) for downstream tasks more accessible and efficient. By using the subspace learning strategy, our method can learn a visual prompt in a task-specific lower-dimensional subspace. By using this method, our method can significantly reduce the necessity for API queries of PTMs, showcasing an efficient method for leveraging the capabilities of large-scale models in visual prompting tasks. Our experiments demonstrate the efficacy of our method, showing significant reductions in the number of required API queries to PTMs while maintaining or even enhancing performance on various tasks." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4329" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 160, + 115, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 160, + 115, + 172 + ], + "spans": [ + { + "bbox": [ + 56, + 160, + 115, + 172 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 179, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 179, + 297, + 224 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 179, + 297, + 224 + ], + "spans": [ + { + "bbox": [ + 61, + 179, + 297, + 224 + ], + "type": "text", + "content": "[1] Mehmet Aygun, Yusuf Aytar, and Hazim Kemal Ekenel. 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Proceedings of the IEEE, 109(1):43-76, 2021. 2" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "4331" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_content_list.json b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9dd05afa5075c78b0fa098534e8ff6d0dd009c69 --- /dev/null +++ b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_content_list.json @@ -0,0 +1,1612 @@ +[ + { + "type": "text", + "text": "Question-Aware Gaussian Experts for Audio-Visual Question Answering", + "text_level": 1, + "bbox": [ + 133, + 130, + 867, + 156 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hongyeob Kim $^{1*}$ Inyoung Jung $^{1*}$ Dayoon Suh $^{2}$ Youjia Zhang $^{1}$ Sangmin Lee $^{1}$ Sungeun Hong $^{1\\dagger}$ Sungkyunkwan University $^{2}$ Purdue University", + "bbox": [ + 109, + 179, + 890, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 251, + 328, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Audio-Visual Question Answering (AVQA) requires not only question-based multimodal reasoning but also precise temporal grounding to capture subtle dynamics for accurate prediction. However, existing methods mainly use question information implicitly, limiting focus on question-specific details. Furthermore, most studies rely on uniform frame sampling, which can miss key question-relevant frames. Although recent Top-K frame selection methods aim to address this, their discrete nature still overlooks fine-grained temporal details. This paper proposes QA-TIGER, a novel framework that explicitly incorporates question information and models continuous temporal dynamics. Our key idea is to use Gaussian-based modeling to adaptively focus on both consecutive and non-consecutive frames based on the question, while explicitly injecting question information and applying progressive refinement. We leverage a Mixture of Experts (MoE) to flexibly implement multiple Gaussian models, activating temporal experts specifically tailored to the question. Extensive experiments on multiple AVQA benchmarks show that QA-TIGER consistently achieves state-of-the-art performance. Code is available at https://aim-skku.github.io/QA-TIGER/", + "bbox": [ + 88, + 282, + 483, + 614 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 643, + 223, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Audio-Visual Question Answering (AVQA) focuses on analyzing and interpreting both audio and visual cues to provide accurate answers to questions. Recent advancements in AVQA have focused on spatial and temporal grounding [3, 13, 16], parameter-efficient models [5, 24, 37], and bias adjustments [14, 28]. Despite promising results, many existing methods struggle to capture fine-grained, question-specific details and temporal cues essential for effective reasoning. We argue that two key considerations are critical for successful AVQA: (i) flexibly capturing and integrating question-relevant audio-visual cues across temporal contexts, and (ii) embedding question context explicitly within the audio-visual feature processing stages.", + "bbox": [ + 89, + 669, + 482, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48eec1312ee1d49f64d0ec517c880b548b4350cd512f74200338453b30a38613.jpg", + "image_caption": [ + "(a) An example of input frames, audio, and question" + ], + "image_footnote": [], + "bbox": [ + 517, + 250, + 906, + 329 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24399206b5e951723d86d3e4abf1dd98f057ff492e957e774b477295b2ceacb9.jpg", + "image_caption": [ + "(b) Uniform sampling" + ], + "image_footnote": [], + "bbox": [ + 516, + 343, + 905, + 414 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bda0be9add41f493a8640ca6fa6ca7b366bbd92e53038b3f63b5cfd0cdae272d.jpg", + "image_caption": [ + "(c) Top-K frame selection", + "(d) QA-TIGER", + "Figure 1. Sampling comparison for AVQA. (a) Input sample. (b) Uniform sampling treats all frames equally, ignoring question-specific context. (c) Top-k frame selection samples discrete frames based only on question-video similarity, often missing important contextual details. (d) Ours provides explicit temporal grounding for both audio and visual modalities, focusing on continuous, question-relevant segments with precise multimodal alignment." + ], + "image_footnote": [], + "bbox": [ + 516, + 431, + 905, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most AVQA methods use uniform sampling or discrete frame selection [16, 24, 37], often overlooking question-specific details. These methods treat frames equally missing important, question-relevant information in both audio and visual modalities. Recent approaches, such as PSTP [17] and TSPM [19], use Top-K frame selection to improve context relevance by aligning frames with the question. However, they select them based solely on visual cues, relying on discrete sampling that disrupts continuity by ignoring temporal cues. Additionally, this approach focuses mainly on visual alignment, missing crucial audio details.", + "bbox": [ + 509, + 686, + 906, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In terms of question integration, most AVQA models incorporate question information only at the final reasoning stage, typically by simple multiplication [12, 16, 19, 24].", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution.", + "bbox": [ + 107, + 875, + 222, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding Author.", + "bbox": [ + 109, + 887, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13681", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This late-stage integration limits the model's ability to encode question-specific features during intermediate steps, reducing the effectiveness of reasoning. Although several methods attempt to enhance reasoning by using question details in frame selection [17, 19], this is done indirectly, and they fail to explicitly embed question context within the audio-visual encoding pipeline. This limited approach restricts the model's ability to focus on relevant temporal cues progressively.", + "bbox": [ + 89, + 90, + 480, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose QA-TIGER (Question-Aware Temporal Integration of Gaussian Experts for Reasoning), as illustrated in Figure 1. To address issue $(i)$ , QA-TIGER introduces a multi-Gaussian weighting mechanism embedded within a Mixture of Experts (MoE) framework [32]. This approach assigns adaptive weights across both consecutive and non-consecutive temporal spans, thereby enabling the model to capture complex temporal dependencies more effectively. Gaussian experts are adaptively activated with well-positioned centers, reducing redundancy and simultaneously improving temporal alignment. In contrast to previous methods [17, 19], which strictly align audio cues with corresponding visual frames, QA-TIGER provides explicit temporal grounding for both audio and visual modalities independently. This allows for more accurate and robust alignment with the question-relevant segments.", + "bbox": [ + 91, + 236, + 483, + 478 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address issue (ii), QA-TIGER incorporates question information early in the process, creating question-aware features that permeate both the visual and audio modalities. By embedding question context directly into each modality's features, QA-TIGER aligns with the question context throughout the entire pipeline, unlike prior methods that add question information only at the final stage [16, 17, 19, 24]. This approach allows the model to progressively refine its focus based on the question, resulting in deeper and more explicit integration of question relevance. Ultimately, this approach enhances accuracy and contextual alignment across all reasoning stages.", + "bbox": [ + 89, + 486, + 482, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 109, + 676, + 434, + 691 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose QA-TIGER, a framework that adaptively models temporal dynamics using strategically positioned Gaussian experts, capturing question-relevant information across continuous temporal spans and adjusting segment importance.", + "- We introduce a question-aware attention mechanism that incorporates question context carefully in the audiovisual encoding process, enabling progressive refinement of temporal focus and more effective feature extraction.", + "- QA-TIGER achieves state-of-the-art performance across multiple benchmark datasets and provides an in-depth analysis of the impact of frame selection strategies, an area that has been previously underexplored in AVQA." + ], + "bbox": [ + 91, + 702, + 482, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 89, + 663, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Audio-Visual Question Answering (AVQA) has advanced with datasets like MUSIC-AVQA [16], AVQA [40], and Pano-AVQA [46], enabling fine-grained reasoning [18, 34]. Early works have implemented spatial-temporal groundings for fine-grained audio-visual scene understanding and reasoning [16, 40]. Recently, adapter-based architectures [5, 24, 37] have achieved impressive performance by leveraging frozen pretrained vision transformers for efficiency. COCA [14] and M2KVDG [25] achieve multimodal collaboration with causal graphs, enhancing the model's robustness. APL [23] introduced an object-aware approach that employs adaptive-positivity learning to align question-object and audio-object semantics. Building on prior work, this study focuses on two often underexplored aspects: explicitly integrating question information and an effective frame sampling strategy to enhance temporal reasoning.", + "bbox": [ + 511, + 114, + 906, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Question Awareness", + "text_level": 1, + "bbox": [ + 511, + 364, + 705, + 380 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent multimodal AVQA research, question-awareness [4, 21, 33, 41] has been recognized as crucial for aligning questions with visual and auditory features. However, most AVQA models [16, 23, 24] only incorporate question awareness at the final reasoning stage, which limits its impact throughout the entire process. Although several methods utilize question information for key-frame selection [17, 19], this is typically applied in an implicit manner, further constraining their reasoning capabilities. While models like QA-ViT [7] embed question information early in the encoding process, they primarily focus on interactions between frame tokens (i.e., patches) and the question within a single frame. In contrast, our approach explicitly embeds question information early in the process, selectively integrating modality-relevant details along the temporal axis. This ensures consistent alignment with the question context throughout the AVQA pipeline, allowing the model to progressively refine its focus on relevant temporal cues and improving the ability to leverage both visual and audio information.", + "bbox": [ + 511, + 387, + 908, + 689 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Temporal Grounding", + "text_level": 1, + "bbox": [ + 511, + 696, + 714, + 713 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Understanding and reasoning over extended audio or video, often containing redundant information, is a key challenge in QA. A critical task is localizing specific temporal segments that align with a natural language query, reducing redundancy. Temporal grounding focuses on accurately identifying these relevant moments. Many existing QA methods, such as proposal-based [36, 44, 47] or proposal-free [6, 20, 29, 45] models, like SMIN [35], optimize multilevel interactions between the question and video segments. However, these approaches often rely on predefined knowledge, adding computational overhead. To mitigate this, many AVQA models [16, 24, 37, 42] use uniform sam", + "bbox": [ + 511, + 719, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13682", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/80cc788101a103da54acb1f6532199decd7746b3321e5581d06a9f3f56fc1782.jpg", + "image_caption": [ + "Figure 2. Overview of QA-TIGER: Each modality is processed through its specific pretrained encoder for feature extraction. The Question-Aware Fusion module embeds question context early in the encoding process, enabling progressive refinement throughout the pipeline. The Temporal Integration of Gaussian Experts module independently applies multi-Gaussian weighting to both audio and visual modalities, capturing consecutive and non-consecutive temporal dependencies. Finally, Question-Guided Reasoning produces context-aware audio-visual features for accurate answer prediction." + ], + "image_footnote": [], + "bbox": [ + 143, + 88, + 869, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pling, which overlooks question-specific details and treats the temporal dimension as discrete. Recent studies [17, 19] attempt to select frames based on question relevance, yet they still treat the temporal dimension as discrete, limiting their ability to capture continuous video dynamics. In contrast, our approach embeds temporal dependencies using Gaussian distributions, enabling continuous modeling of question-relevant segments. This ensures precise alignment with both audio and visual modalities, improving temporal grounding and overall reasoning. By adapting to both consecutive and non-consecutive spans, QA-TIGER captures and utilizes relevant temporal information more effectively than methods that rely on discrete sampling.", + "bbox": [ + 88, + 500, + 480, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 708, + 181, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "QA-TIGER aims to dynamically weight temporal segments based on question relevance and explicitly integrate question context as shown in Figure 2.", + "bbox": [ + 89, + 733, + 482, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Input Representation", + "text_level": 1, + "bbox": [ + 89, + 787, + 290, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The input video sequence is split into $T$ non-overlapping $1s$ segments, each with paired audio and visual elements.", + "bbox": [ + 89, + 809, + 482, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Representation. Each visual segment is processed using a pretrained CLIP model [30]. The visual input is divided into $M$ patches per segment, with a special [CLS] token added at the beginning. Visual features are extracted", + "bbox": [ + 89, + 840, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in two forms: Frame-level features $\\mathbf{v} = \\{v^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}$ are obtained from the [CLS] token output for each segment $t$ . Patch-level features $\\mathbf{p} = \\{p^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times M' \\times D}$ are obtained by merging the $M$ patch tokens into $M'$ tokens per segment using Token Merging (ToMe) [2], providing more spatially detailed information.", + "bbox": [ + 511, + 498, + 906, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Audio Representation. For each segment $t$ , we extract audio features $a^t \\in \\mathbb{R}^D$ using a VGGish model [11] pretrained on AudioSet [8], following previous work. The complete set of audio features is $\\mathbf{a} = \\{a^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}$ .", + "bbox": [ + 511, + 590, + 905, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Question Representation. The input question is tokenized and processed using the CLIP text encoder. We extract sentence-level features $q_{s} \\in \\mathbb{R}^{D}$ from the [EOT] token. Additionally, we obtain word-level features $q_{w} \\in \\mathbb{R}^{N \\times D}$ by skipping CLIP's final projection layer, where $N$ is the number of tokens including padding.", + "bbox": [ + 511, + 652, + 905, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Question-Aware Fusion", + "text_level": 1, + "bbox": [ + 511, + 756, + 730, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For effective AVQA, our question-aware attention module explicitly injects question context into both the video and audio modalities. Our question-aware fusion module operates in two main stages. First, multi-head Self-Attention (SA) enhances internal relationships within each modality by using the same input for the query, key, and value. Then, each modality undergoes two rounds of multi-head Cross-Attention (CA): visual features v use audio features a as", + "bbox": [ + 511, + 779, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13683", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the key and value, with $\\mathbf{v}$ as the query, and then apply word-level question feature $q_{w}$ as the key and value to align with question information. Similarly, audio features a use visual features $\\mathbf{v}$ and question features $q_{w}$ sequentially as key and value, with a as the query. This dual CA application per modality enables explicit question-informed cross-modal interactions. Finally, the outputs from the SA and two CA layers are combined with residual connections to enhance temporal coherence and retain alignment with the question as follows:", + "bbox": [ + 89, + 90, + 483, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {q} = \\mathbf {v} + \\operatorname {S A} (\\mathbf {v}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {v}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {v}, q _ {w}, q _ {w}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 253, + 482, + 268 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {q} = \\mathbf {a} + \\operatorname {S A} (\\mathbf {a}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {a}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {a}, q _ {w}, q _ {w}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 273, + 482, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The result is two question-aligned multimodal features, $\\mathbf{v}_q = \\{v_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}$ for visual and $\\mathbf{a}_q = \\{a_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}$ for audio. Unlike prior approaches that integrate question information only in the final stages, our method introduces question context from the start, allowing QA-TIGER to dynamically refine focus on relevant temporal cues throughout AVQA processing.", + "bbox": [ + 89, + 299, + 483, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the question-aware visual features $\\mathbf{v}_q$ and audio features $\\mathbf{a}_q$ are obtained, we further refine the patch-level visual features to align finer spatial details with the question context. This refinement ensures that finer spatial details in the visual data align more closely with the question context embedded in the modality-specific features. The process is formulated as follows:", + "bbox": [ + 89, + 406, + 483, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {v} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {v} _ {q}, \\mathbf {p}, \\mathbf {p}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 523, + 482, + 540 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {a} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {a} _ {q}, \\mathbf {p}, \\mathbf {p}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 542, + 482, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Temporal Integration of Gaussian Experts", + "text_level": 1, + "bbox": [ + 89, + 568, + 452, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To capture temporal dependencies in the video, we leverage the Mixture of Experts (MoE) framework [32], integrating multiple Gaussian distributions across the timeline. This approach enables the model to focus on distinct temporal segments relevant to the question.", + "bbox": [ + 89, + 590, + 483, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gaussian Generation. To produce question-relevant Gaussian distributions, we first generate a condensed, question-focused representation for each modality. This process aligns the visual and audio features with the question, to capture the temporal relevance of frames in both modalities. Using a cross-attention mechanism, we apply the sentence-level question feature $q_{s}$ to the question-aware features $\\mathbf{v}_q$ and $\\mathbf{a}_q$ , yielding $D$ -dimensional aggregated representations for each modality:", + "bbox": [ + 89, + 666, + 483, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {v} _ {q}, \\mathbf {v} _ {q}\\right), \\quad \\mathbf {a} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {a} _ {q}, \\mathbf {a} _ {q}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 811, + 482, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast to prior work [39], which used a single Gaussian mask across the temporal domain, we generate multiple Gaussian distributions to capture a broader range of key frames, especially in cases where temporal variations", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are complex and challenging. The Gaussian distributions $\\mathbf{g} = \\{g^{i}\\}_{i = 1}^{E}$ represent distinct temporal segments relevant to the question, where $E$ is the total number of Gaussian experts (i.e., Gaussian distributions):", + "bbox": [ + 511, + 90, + 905, + 154 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} _ {v} = \\mathcal {N} \\big (\\mu_ {v} ^ {i}, (\\sigma_ {v} ^ {i}) ^ {2} \\big), \\quad \\mathbf {g} _ {a} = \\mathcal {N} \\big (\\mu_ {a} ^ {i}, (\\sigma_ {a} ^ {i}) ^ {2} \\big). \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 167, + 906, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\{\\mu^i\\}_{i=1}^E$ and $\\{\\sigma^i\\}_{i=1}^E$ denote the Gaussian centers and standard deviations, generated through a linear layer with an input dimension of $D$ and an output dimension of two. To minimize conflicts across time segments and enhance temporal focus, the Gaussian centers are distributed along the timeline, with a predicted offset by a linear layer added to the initial centers. This ensures that each expert mainly covers a distinct segment, aligning with question-relevant frames and reducing redundancy.", + "bbox": [ + 511, + 202, + 906, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Integrating Temporal Information. To selectively capture relevant segments over time, we adapt the MoE framework, which combines multiple specialized \"experts,\" each trained to focus on specific temporal patterns. Instead of selecting discrete experts, our model adjusts the influence of each expert based on their context-dependent weights. These experts act as Gaussian distributions along the timeline, providing soft masks that help capture temporal dependencies in alignment with the question.", + "bbox": [ + 511, + 340, + 905, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The router assigns routing values $\\mathbf{r}_v = \\{r_v^i\\}_{i=1}^E$ and $\\mathbf{r}_a = \\{r_a^i\\}_{i=1}^E$ for each expert based on the cross-attention outputs $\\mathbf{v}_q'$ and $\\mathbf{a}_q'$ , respectively:", + "bbox": [ + 511, + 477, + 905, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {r} _ {v} = \\operatorname {S o f t m a x} \\left(\\mathbf {v} _ {q} ^ {\\prime} \\cdot W\\right), \\quad \\mathbf {r} _ {a} = \\operatorname {S o f t m a x} \\left(\\mathbf {a} _ {q} ^ {\\prime} \\cdot W\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 539, + 905, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W \\in \\mathbb{R}^{D \\times E}$ is a learnable weight matrix that dynamically controls the influence of each expert. The resulting expert weights allow the model to emphasize question-relevant time segments more effectively. The outputs from all experts are then combined through a weighted summation, producing a temporally integrated representation that captures question-specific insights across frames. This integration is expressed as follows:", + "bbox": [ + 511, + 571, + 905, + 693 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {v} _ {p _ {v}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {v}), \\quad \\tilde {v} _ {p _ {a}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {a}), \\quad \\tilde {a} = \\mathcal {G} _ {a} (\\mathbf {a} _ {q}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 709, + 906, + 727 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\mathcal {G} _ {m} (x) = \\sum_ {i = 1} ^ {E} g _ {m} ^ {i} r _ {m} ^ {i} \\mathcal {E} _ {m} ^ {i} (x). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 728, + 905, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this setup, $\\mathcal{E}_m^i (x)$ represents the output of the $i$ -th expert for input $x$ . The temporal visual features $\\tilde{v}_{p_v} \\in \\mathbb{R}^D$ and $\\tilde{v}_{p_a} \\in \\mathbb{R}^D$ are derived by applying the experts to modality-specific patch features $\\mathbf{p}_v$ and $\\mathbf{p}_a$ , respectively. Similarly, the temporal audio feature $\\tilde{a} \\in \\mathbb{R}^D$ is obtained by applying experts to the question-aware audio feature $\\mathbf{a}_q$ . This arrangement allows the model to maintain temporal coherence, aligning with question-relevant segments and minimizing redundancy.", + "bbox": [ + 511, + 763, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13684", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Question-Guided Reasoning and Prediction", + "text_level": 1, + "bbox": [ + 89, + 90, + 460, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The question-guided reasoning module combines audio and visual features from the temporal integration module, allowing the model to evaluate each input's importance in relation to the question context. To ensure a balanced representation, we use averaged features as a residual connection, preventing over-reliance on any single input type. First, the final visual feature $F_{v} \\in \\mathbb{R}^{D}$ is obtained as follows:", + "bbox": [ + 89, + 112, + 483, + 218 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {v} = \\operatorname {A v g} \\left(\\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}}\\right) + \\mathrm {C A} \\left(q _ {s}, \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right], \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right]\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 224, + 482, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[\\cdot, \\cdot]$ denotes concatenation. This process yields a question-aligned visual feature that balances information across both temporal visual representations. Next, the final audio-visual representation $F_{va} \\in \\mathbb{R}^{D}$ is obtained by fusing the temporal audio feature $\\tilde{a}$ with $F_{v}$ as follows:", + "bbox": [ + 89, + 250, + 483, + 327 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {v a} = \\operatorname {A v g} \\left(\\tilde {a}, F _ {v}\\right) + \\operatorname {C A} \\left(q _ {s}, \\left[ \\tilde {a}, F _ {v} \\right], \\left[ \\tilde {a}, F _ {v} \\right]\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 334, + 482, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This step ensures that both audio and visual features contribute to the final representation in a question-aware manner. Finally, answer prediction is performed by applying a linear layer and a Softmax layer to $F_{va}$ yielding probabilities over $C$ answer choices. The model is trained using cross-entropy loss: $\\mathcal{L}_{qa} = -\\sum_{c=1}^{C} y_c \\log \\mathcal{P}_c$ , with the answer selected as the class with the highest probability.", + "bbox": [ + 89, + 359, + 483, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 477, + 223, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 501, + 192, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our experiments utilize the MUSIC-AVQA [16], MUSIC-AVQA-R [28], and MUSIC-AVQA-v2.0 [26] datasets. MUSIC-AVQA serves as a benchmark for audio-visual reasoning over 22 instruments, with questions spanning audio-only, visual-only, and audio-visual modalities, covering reasoning types like existence, location, and temporal aspects. MUSIC-AVQA-R focuses on rare and out-of-distribution samples to assess model robustness. MUSIC-AVQA-v2.0 addresses dataset biases by enhancing diversity in ensemble scenes and multi-instrument cases.", + "bbox": [ + 89, + 523, + 483, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 681, + 307, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The video is sampled at 1 fps, with audio features extracted using VGGish [11], while visual features and questions are processed using the CLIP-ViT-L/14 [30] model. Token reduction is applied to visual features using ToMe [2] technique. To ensure consistency, all features are linearly transformed to 512 dimensions. Further details on the feature extraction process are provided in the supplementary materials. We set the expert number to 7 and configure every attention module with 8 heads with 0.1 dropout probability. The model is trained with the Adam optimizer at an initial learning rate of 1e-4, which decays by a factor of 0.1 every 8 epochs. Training is conducted for 15 epochs with a batch size of 32 on a single NVIDIA RTX A6000.", + "bbox": [ + 89, + 704, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0010469d71b339917f48f3685292a2262eb068e49ba7c5f4e63607236a9f71fd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset# Videos# Train QA# Valid QA# Test QA
MUSIC-AVQA [16]9,28831,9044,5689,129
MUSIC-AVQA-R [28]9,288--211,572
MUSIC-AVQA-v2.0 [26]10,49237,4085,34610,819
", + "bbox": [ + 514, + 90, + 905, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Summary of MUSIC-AVQA, MUSIC-AVQA-R, and MUSIC-AVQA-v2.0 datasets with the number of QA pairs.", + "bbox": [ + 511, + 138, + 906, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Quantitative Results and Analysis", + "text_level": 1, + "bbox": [ + 511, + 186, + 808, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate our model's effectiveness, we compared QA-TIGER to existing AVQA methods on Audio (A-QA), Visual (V-QA), and Audio-Visual (AV-QA) tasks, considering both question types and overall averages. QA-TIGER was trained on the MUSIC-AVQA [16] training set and validated using its validation set for testing both MUSIC-AVQA [16] and MUSIC-AVQA-R [28]. For MUSIC-AVQA-v2.0 [26], QA-TIGER was trained on both the balanced and biased training sets and tested accordingly.", + "bbox": [ + 511, + 210, + 906, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MUSIC-AVQA. QA-TIGER achieves the highest performance among all models, with an overall accuracy $(77.62\\%)$ , surpassing the previous best method $(76.79\\%)$ , TSPM [19], in Table 2. Notably, our model shows strong performance in complex reasoning tasks, achieving $78.58\\%$ and $72.50\\%$ in AV-Counting and AV-Local categories respectively, surpassing previous methods.", + "bbox": [ + 511, + 347, + 905, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MUSIC-AVQA-R. Our method achieves $67.99\\%$ overall accuracy on the MUSIC-AVQA-R dataset across diverse question types, as shown in Table 3, without the need for explicit bias handling techniques. This balanced performance highlights QA-TIGER's strong temporal modeling and question-aware feature extraction capabilities.", + "bbox": [ + 511, + 455, + 906, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MUSIC-AVQA-v2.0. QA-TIGER consistently outperforms existing models [16, 24, 28] on the biased test set, regardless of the training set type (Table 4a). On the balanced test set (Table 4b), QA-TIGER trained on the balanced dataset achieves superior accuracy in both $A - QA$ (79.90%) and $V - QA$ (86.95%), surpassing LAST-Att in overall accuracy (75.44% vs. 76.43%). Notably, LAST-Att underperforms in $A - QA$ despite incorporating an additional audio encoder, Audio Spectrogram Transformer [9]. This highlights QA-TIGER's robustness across diverse evaluation settings.", + "bbox": [ + 511, + 546, + 906, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference Time. We compare inference time between TSPM and QA-TIGER under identical conditions, using the full pipeline setup with CLIP and VGGish. TSPM records 1.767 seconds, while QA-TIGER achieves a comparable time of 1.737 seconds. Despite processing full temporal information, QA-TIGER matches TSPM's efficiency—which selects Top-K frames—demonstrating its ability to handle temporal dynamics without added overhead.", + "bbox": [ + 511, + 698, + 905, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Qualitative Results of Temporal Gaussian", + "text_level": 1, + "bbox": [ + 511, + 832, + 867, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate whether QA-TIGER accurately identifies question-relevant temporal segments, we qualitatively analyze its performance in Figure 3. Notably, the audio Gaus", + "bbox": [ + 511, + 854, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13685", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/62a859c7bedf0ffec19b4ae87ba6ddbb33bc1188e1bb9349e5a9d6afa5d2dda8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompAvgCountLocalAvgExistCountLocalCompTempAvg
FCNLSTM [10]70.4566.2268.8863.8946.7455.2182.0159.3446.2862.1547.3360.0660.34
BiLSTM [38]70.3547.9262.0564.6464.3364.4878.3956.9145.8553.0949.7657.1059.92
HCAtn [27]70.2554.9164.5764.0566.3765.2279.1059.9749.5155.2556.4360.1962.30
MCAN [43]77.5055.2469.2571.5670.9371.2480.4064.9154.4857.2247.5761.5865.49
PSAC [22]75.6466.0672.0968.6469.7969.2277.5963.4255.0261.1759.4763.5266.54
HME [1]74.7663.5670.6167.9769.4668.7680.3063.1953.1862.6959.8364.0566.45
HCRN [15]68.5950.9262.0564.3961.8163.0854.4753.3841.5352.1147.6950.2655.73
AVSD [31]72.4161.9068.5267.3974.1970.8381.6163.8958.7961.5261.4165.4967.44
Pano-AVQA [46]74.3664.5670.7369.3975.6572.5681.2164.9159.3364.2263.2366.6468.93
ST-AVQA [16]78.1867.0574.0671.5676.3874.0081.8170.8064.5166.0163.2369.5471.52
COCA [14]79.3567.6875.4275.1075.4375.2383.5066.6369.7264.1265.5769.9672.33
PSTP-Net [17]73.9765.5970.9177.1577.3677.2676.1872.2371.8071.7969.0072.5773.52
LAVISH [24]82.0965.5675.9778.9881.4380.2281.7175.5166.1363.7767.9671.2674.46
APL [23]82.4070.7178.0976.5282.7479.6982.9973.2966.6864.7665.9570.9674.53
TSPM [19]84.0764.6576.9182.2984.9083.6182.1976.2171.8565.7671.1773.5176.79
QA-TIGER84.8667.8578.5883.9686.2985.1483.1078.5872.5063.9469.5973.7477.62
", + "bbox": [ + 91, + 90, + 906, + 300 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8ff6712261f6cc4842b0babcb2073c0d9104a8832fd5f73823cbc15a48a6a3d9.jpg", + "table_caption": [ + "Table 2. Experimental results (%) on the MUSIC-AVQA test set. The top-2 results are highlighted." + ], + "table_footnote": [], + "table_body": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompCountLocalExistCountLocalCompTemp
HTHTHTHTHTHTHTHTHT
FCNLSTM [10]66.2336.4864.7851.2461.755.3154.8651.0664.7678.5262.697.2346.6657.3043.1371.6737.0230.7854.12
BiLSTM [38]73.6846.3221.5177.5864.300.0053.9242.0187.5121.1462.852.1835.1643.7527.6174.3817.5831.3248.84
HCAtnn [27]61.6741.6359.0947.1456.529.2067.0153.1666.5761.1359.5312.4837.0542.4848.8160.1233.8239.2651.90
MCAN [43]75.0260.1658.8950.0964.5826.6966.4862.2551.2967.2964.7625.2846.1161.6150.5752.4034.6458.0557.27
PSAC [22]53.0156.6857.4148.1249.5526.4372.9660.6950.5655.5456.7019.5841.9852.3038.1358.9226.6846.2450.45
HME [1]62.6053.9554.9758.2950.9516.4673.2558.6065.7466.4963.1817.1833.7946.0353.2069.5733.9541.5753.66
HCRN [15]55.5353.3147.1732.4441.8723.5539.4051.2741.8165.4554.5819.5736.6242.7233.3336.8740.4744.1343.92
AVSD [31]54.0047.8460.6147.7960.3410.0774.7861.4366.2861.9846.218.0633.0040.3551.9866.0040.1441.5252.33
Pano-AVQA [46]50.5743.4550.7844.9347.2815.5067.1965.5152.3722.0452.2121.5244.3561.6945.6140.4935.0049.3347.40
ST-AVQA [16]56.4041.4862.2857.5959.8612.9463.3154.0073.3577.2648.318.4135.3540.4953.3062.4440.2538.1552.80
LAVISH [24]61.7343.9965.0660.3865.5311.1370.2164.7377.8379.4649.8814.8741.7641.2059.2665.1041.8446.2657.63
TSPM† [19]81.6571.8067.6649.5678.2947.5680.5873.1869.1582.7977.0938.6442.2457.3752.0768.8639.2349.3666.30
QA-TIGER82.6775.8271.7543.1181.3054.5984.7675.5972.8478.5676.7033.5548.2264.6537.5580.4736.8562.9667.99
", + "bbox": [ + 91, + 327, + 906, + 530 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ec9c22d54694cfdc235d02835bccd81ef58ed0af7ae81a9154d33369cf099a24.jpg", + "table_caption": [ + "Table 3. Experimental results (%) on the MUSIC-AVQA-R test set, with H and T representing performance on Head (frequent) and Tail (rare) answer categories, respectively. † indicates results reproduced using official codes." + ], + "table_footnote": [], + "table_body": "
TestTrainingMethodA-QAV-QAAV-QAAvg
(a) BiasBiasST-AVQA [16]76.8677.7069.5973.07
LAVISH [24]76.7380.9670.8074.59
QA-TIGER79.1384.8372.3776.93
BalanceST-AVQA [16]76.1877.2067.9671.92
LAVISH [24]75.5680.8369.2773.51
LAST [26]77.1082.9970.8675.24
LAST-Att [26]77.2983.4771.0575.45
QA-TIGER77.0785.9371.2076.57
", + "bbox": [ + 91, + 585, + 480, + 696 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eb35525dea91cfb4755f2bb55bf3b882d72aca1aa907717ee4b5de845582fddb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TestTrainingMethodA-QAV-QAAV-QAAvg
(b) BalanceBiasST-AVQA [16]73.3476.8264.5169.40
LAVISH [24]73.1479.7065.0170.39
QA-TIGER77.5784.8467.4373.91
BalanceST-AVQA [16]75.5077.6766.3271.02
LAVISH [24]76.1581.3268.2873.18
LAST [26]78.0883.2969.7274.85
LAST-Att [26]78.5684.0770.3075.44
QA-TIGER79.9086.9570.2276.43
", + "bbox": [ + 91, + 705, + 480, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Experimental results (\\%) on the MUSIC-AVQA-v2.0 for (a) bias and (b) balanced test sets. Each evaluation is conducted with models trained on bias and balanced training sets, respectively. The performance of other methods was referenced from the scores provided by MUSIC-AVQA-v2.0.", + "bbox": [ + 89, + 832, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sian aligns more with A-QA in Figure 3a, while the visual Gaussian is more prominent for V-QA in Figure 3b. For AV-QA, both modalities show similar Gaussian distributions in Figure 3c, demonstrating the model's adaptive focus based on question type. A detailed comparison with uniform sampling and Top-K selection is provided in the supplementary.", + "bbox": [ + 511, + 587, + 906, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Audio Question. QA-TIGER demonstrates its ability to handle temporal reasoning. For the question \"Is the tuba playing longer than the clarinet?\", QA-TIGER's audio Gaussian assigns high weights across the entire durations, effectively capturing the complete temporal spans essential for accurately comparing the two instruments in the question. The visual Gaussian similarly focuses on frames where the tuba and clarinet are actively played, supporting a robust comparison of their durations, as shown in Figure 3a.", + "bbox": [ + 511, + 683, + 908, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Question. Our method effectively integrates both visual and audio modalities to accurately count the saxophones, in Figure 3b. The visual Gaussian assigns higher weights to frames where all five saxophonists are clearly visible from the front, while frames with less distinct views,", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13686", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6b0c8f44a888a9a6b1a04e508955d957b1f98aeda081d966546251e122914fff.jpg", + "image_caption": [ + "(a) Audio Question" + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5706d3226506819465300768fe60c06b0b88a58d2c410a3a98c2ddbebe2ab2d8.jpg", + "image_caption": [ + "(b) Visual Question" + ], + "image_footnote": [], + "bbox": [ + 93, + 186, + 903, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fb4c2b28f989f0cdf3b77cdef41ca18a6ec46f66bc713ba301ee7937a97aa656.jpg", + "image_caption": [ + "(c) Audio-Visual Question" + ], + "image_footnote": [], + "bbox": [ + 94, + 284, + 903, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "such as side angles or wide shots, are assigned lower weights. Meanwhile, the audio Gaussian emphasizes moments when the sounds of all five saxophones overlap, focusing on their simultaneous performance. This integration allows the model to concentrate on the most critical visual and auditory cues to predict the accurate answer.", + "bbox": [ + 88, + 422, + 482, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Audio-Visual Question. The visual Gaussian effectively focuses on frames in the early part of the video where individual instrument appear, as well as frames where all three instruments are shown together. Correspondingly, the audio Gaussian emphasizes prominent instrument sounds. This complementary alignment enables QA-TIGER to integrate visual and auditory cues effectively, resulting in accurate identification of all instruments, as shown in Figure 3c.", + "bbox": [ + 88, + 513, + 482, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Visualization of Question-Aware Fusion", + "text_level": 1, + "bbox": [ + 89, + 648, + 429, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the effectiveness of our question-aware fusion module, we performed word-level visualizations. Additional examples are provided in the supplementary material.", + "bbox": [ + 89, + 671, + 482, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Are there saxophone and piano sound\": In the visual modality, attention initially focuses on \"piano,\" where visual cues are subtle, then shifts to the more distinct \"saxophone.\" In the audio modality, attention consistently highlights \"piano,\" compensating for the limited visual cues, while \"saxophone,\" is primarily processed visually. This shows how QA-TIGER adapts to question context, effectively distributing attention across both modalities.", + "bbox": [ + 89, + 717, + 482, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"How many sounding saxophone in the video\": In the visual modality, attention focuses on \"saxophone,\" aiding in counting. In the audio modality, attention highlights \"sounding,\" and \"saxophone,\" to capture the auditory cues", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a3504f0893ddc09702f7af0d15af5c70b9bb3010b24d5e577ebbc139bb37dc8.jpg", + "image_caption": [ + "Figure 3. Qualitative results by question type of the proposed QA-TIGER on the MUSIC-AVQA test set.", + "Figure 4. Question-aware attention for visual (upper) and audio (lower) fusion in response to two different questions for the same video and audio input. The attention intensity is indicated by the color scale on the right." + ], + "image_footnote": [], + "bbox": [ + 516, + 419, + 906, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "necessary for counting saxophone occurrences.", + "bbox": [ + 511, + 691, + 823, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "These results demonstrate how the question-aware fusion module dynamically adapts to different questions. By emphasizing question-relevant elements in both modalities, QA-TIGER progressively refines its focus, improving accuracy and ensuring alignment with task demands throughout the reasoning process.", + "bbox": [ + 511, + 707, + 905, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. In-depth Analysis", + "text_level": 1, + "bbox": [ + 511, + 809, + 687, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 830, + 666, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluated our proposed modules on MUSIC-AVQA (Table 5). The baseline model used uniform sampling and achieved reasonable accuracy. Adding the Gaussian Ex", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13687", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/86c1f811f47acfa598f7b1b5e253e0747be799a15de1c46316bf5b5aca3607ec.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Question-Aware FusionGaussian ExpertsA-QAV-QAAV-QAAvg
75.0581.7971.8275.04
✓77.5984.5672.3776.53
✓76.3582.7472.7876.05
✓✓78.5885.1473.7477.62
", + "bbox": [ + 91, + 89, + 482, + 170 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation study of the proposed framework.", + "bbox": [ + 130, + 181, + 441, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "perts module improved performance by enhancing temporal modeling through specialized experts. The Question-Aware Fusion module alone also contributed a notable improvement. Combining both modules led to the best performance, demonstrating the synergistic benefits of integrating question context early on. This integration enriches the temporal context for the Gaussian Experts module, highlighting the complementary strengths of both modules in enhancing temporal reasoning. Without Question-Aware Fusion, question features were incorporated only at the final stage, as in prior work [12, 16, 24]. For setups excluding Gaussian Experts, uniform sampling was applied.", + "bbox": [ + 88, + 215, + 482, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Frame Sampling", + "text_level": 1, + "bbox": [ + 89, + 406, + 256, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluated conventional sampling strategies and Gaussian modeling designs for AVQA tasks (Figure 5). Note that all experiments compare only the frame sampling part after applying the proposed Question-Aware Fusion.", + "bbox": [ + 89, + 429, + 482, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sampling-based Methods. Uniform sampling at fixed intervals was less effective due to its lack of focus on question-relevant frames. The Top-K method, using the frame selection module from TSPM [19], improved performance by selecting question-relevant frames but lacked comprehensive temporal context.", + "bbox": [ + 89, + 489, + 482, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Gaussian-based Methods. We explore various Gaussian-based methods to model temporal dependencies. Gaussian, a simple sum of Gaussians, shows similar performance to uniform sampling. Weighted-Gaussian introduces dynamic weighting but still struggles with overlap. By adding disjoint center constraints, Weighted-Gaussian (Disjoint Center) reduces redundancy and improves accuracy. Building on this, Gaussian Experts extends the Weighted-Gaussian (Disjoint Center) approach with a MoE framework, dynamically assigning specialized experts to distinct temporal segments, resulting in the highest accuracy.", + "bbox": [ + 89, + 580, + 482, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Selection of Experts", + "text_level": 1, + "bbox": [ + 89, + 757, + 279, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this analysis, we explored the impact of expert selection in the proposed MoE approach. The decision to activate all seven experts stems from the observed performance gains as more experts are used. Even with the fewest experts, the model outperforms the current state-of-the-art TSPM [19] $(76.79\\%)$ on the MUSIC-AVQA [16] dataset, as shown in Figure 6. Using all seven experts achieves the highest accuracy $(77.62\\%)$ , showcasing the superiority of QA-TIGER.", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/345240f7ebdf49a7fa052f0a8bc75649cc5880e83b06f162e48ecc0b18fe996b.jpg", + "image_caption": [ + "Figure 5. Comparison of temporal selection methods based on the number of criteria (Gaussian or K). Gaussian-based methods use a simple summation for temporal aggregation. \"W\" refers to \"Weighted sum,\" and \"D.C.\" stands for \"Disjoint Center.\"" + ], + "image_footnote": [], + "bbox": [ + 532, + 89, + 885, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c522af42b522b67c5cb4f5195d4b5dab1091d1808cbf8e0b41039de6c73feed6.jpg", + "image_caption": [ + "Figure 6. Impact of expert selection on Gaussian experts." + ], + "image_footnote": [], + "bbox": [ + 562, + 316, + 857, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 484, + 633, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced QA-TIGER, designed to overcome the limitations of prior methods in handling complex temporal dynamics and question-specific feature integration. By leveraging multi-Gaussian modeling within the MoE framework, QA-TIGER adaptively captures subtle temporal dependencies while minimizing redundancy through strategically positioned Gaussian centers. We also incorporate question context explicitly from the encoding stages, ensuring that question information is gradually refined throughout the processing pipeline. Extensive experiments demonstrate QA-TIGER's state-of-the-art performance on various datasets, highlighting its effectiveness in tackling the continuous temporal domain and complex AVQA challenges. Future work could explore adaptive expert selection mechanisms in MoE-based AVQA, tailored to different question types, to further enhance the model's generalizability.", + "bbox": [ + 511, + 513, + 906, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00211348). This research was partly supported by the MSIT(Ministry of Science, ICT), Korea, under the Global Research Support Program in the Digital Field program)(RS-2024-00425354) supervised by the IITP(Institute for Information & Communications Technology Planning & Evaluation).", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13688", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Chenyou Fan abd Xiaofan Zhang, Shu Zhang, Wensheng Wang, Chi Zhang, and Heng Huang. Heterogeneous memory enhanced multimodal attention model for video question answering. In CVPR, pages 1999-2007, 2019.", + "[2] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. 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In AAAI, pages 12870-12877, 2020." + ], + "bbox": [ + 91, + 92, + 482, + 883 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13690", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_model.json b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..54b885bd9a8b3dc8aa17cad642237a470abe642e --- /dev/null +++ b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.868, + 0.157 + ], + "angle": 0, + "content": "Question-Aware Gaussian Experts for Audio-Visual Question Answering" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.18, + 0.892, + 0.219 + ], + "angle": 0, + "content": "Hongyeob Kim\\(^{1*}\\) Inyoung Jung\\(^{1*}\\) Dayoon Suh\\(^{2}\\) Youjia Zhang\\(^{1}\\) Sangmin Lee\\(^{1}\\) Sungeun Hong\\(^{1\\dagger}\\) Sungkyunkwan University \\(^{2}\\)Purdue University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.252, + 0.329, + 0.269 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.284, + 0.485, + 0.616 + ], + "angle": 0, + "content": "Audio-Visual Question Answering (AVQA) requires not only question-based multimodal reasoning but also precise temporal grounding to capture subtle dynamics for accurate prediction. However, existing methods mainly use question information implicitly, limiting focus on question-specific details. Furthermore, most studies rely on uniform frame sampling, which can miss key question-relevant frames. Although recent Top-K frame selection methods aim to address this, their discrete nature still overlooks fine-grained temporal details. This paper proposes QA-TIGER, a novel framework that explicitly incorporates question information and models continuous temporal dynamics. Our key idea is to use Gaussian-based modeling to adaptively focus on both consecutive and non-consecutive frames based on the question, while explicitly injecting question information and applying progressive refinement. We leverage a Mixture of Experts (MoE) to flexibly implement multiple Gaussian models, activating temporal experts specifically tailored to the question. Extensive experiments on multiple AVQA benchmarks show that QA-TIGER consistently achieves state-of-the-art performance. Code is available at https://aim-skku.github.io/QA-TIGER/" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.644, + 0.224, + 0.66 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.866 + ], + "angle": 0, + "content": "Audio-Visual Question Answering (AVQA) focuses on analyzing and interpreting both audio and visual cues to provide accurate answers to questions. Recent advancements in AVQA have focused on spatial and temporal grounding [3, 13, 16], parameter-efficient models [5, 24, 37], and bias adjustments [14, 28]. Despite promising results, many existing methods struggle to capture fine-grained, question-specific details and temporal cues essential for effective reasoning. We argue that two key considerations are critical for successful AVQA: (i) flexibly capturing and integrating question-relevant audio-visual cues across temporal contexts, and (ii) embedding question context explicitly within the audio-visual feature processing stages." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.251, + 0.908, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.331, + 0.85, + 0.342 + ], + "angle": 0, + "content": "(a) An example of input frames, audio, and question" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.344, + 0.906, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.418, + 0.672, + 0.43 + ], + "angle": 0, + "content": "(b) Uniform sampling" + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.418, + 0.876, + 0.43 + ], + "angle": 0, + "content": "(c) Top-K frame selection" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.432, + 0.906, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.67, + 0.537, + 0.753, + 0.548 + ], + "angle": 0, + "content": "(d) QA-TIGER" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.561, + 0.907, + 0.659 + ], + "angle": 0, + "content": "Figure 1. Sampling comparison for AVQA. (a) Input sample. (b) Uniform sampling treats all frames equally, ignoring question-specific context. (c) Top-k frame selection samples discrete frames based only on question-video similarity, often missing important contextual details. (d) Ours provides explicit temporal grounding for both audio and visual modalities, focusing on continuous, question-relevant segments with precise multimodal alignment." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.688, + 0.907, + 0.854 + ], + "angle": 0, + "content": "Most AVQA methods use uniform sampling or discrete frame selection [16, 24, 37], often overlooking question-specific details. These methods treat frames equally missing important, question-relevant information in both audio and visual modalities. Recent approaches, such as PSTP [17] and TSPM [19], use Top-K frame selection to improve context relevance by aligning frames with the question. However, they select them based solely on visual cues, relying on discrete sampling that disrupts continuity by ignoring temporal cues. Additionally, this approach focuses mainly on visual alignment, missing crucial audio details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In terms of question integration, most AVQA models incorporate question information only at the final reasoning stage, typically by simple multiplication [12, 16, 19, 24]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.223, + 0.888 + ], + "angle": 0, + "content": "*Equal Contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.24, + 0.9 + ], + "angle": 0, + "content": "† Corresponding Author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.24, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13681" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.228 + ], + "angle": 0, + "content": "This late-stage integration limits the model's ability to encode question-specific features during intermediate steps, reducing the effectiveness of reasoning. Although several methods attempt to enhance reasoning by using question details in frame selection [17, 19], this is done indirectly, and they fail to explicitly embed question context within the audio-visual encoding pipeline. This limited approach restricts the model's ability to focus on relevant temporal cues progressively." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.237, + 0.485, + 0.479 + ], + "angle": 0, + "content": "In this paper, we propose QA-TIGER (Question-Aware Temporal Integration of Gaussian Experts for Reasoning), as illustrated in Figure 1. To address issue \\((i)\\), QA-TIGER introduces a multi-Gaussian weighting mechanism embedded within a Mixture of Experts (MoE) framework [32]. This approach assigns adaptive weights across both consecutive and non-consecutive temporal spans, thereby enabling the model to capture complex temporal dependencies more effectively. Gaussian experts are adaptively activated with well-positioned centers, reducing redundancy and simultaneously improving temporal alignment. In contrast to previous methods [17, 19], which strictly align audio cues with corresponding visual frames, QA-TIGER provides explicit temporal grounding for both audio and visual modalities independently. This allows for more accurate and robust alignment with the question-relevant segments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.669 + ], + "angle": 0, + "content": "To address issue (ii), QA-TIGER incorporates question information early in the process, creating question-aware features that permeate both the visual and audio modalities. By embedding question context directly into each modality's features, QA-TIGER aligns with the question context throughout the entire pipeline, unlike prior methods that add question information only at the final stage [16, 17, 19, 24]. This approach allows the model to progressively refine its focus based on the question, resulting in deeper and more explicit integration of question relevance. Ultimately, this approach enhances accuracy and contextual alignment across all reasoning stages." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.678, + 0.435, + 0.692 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.703, + 0.483, + 0.776 + ], + "angle": 0, + "content": "- We propose QA-TIGER, a framework that adaptively models temporal dynamics using strategically positioned Gaussian experts, capturing question-relevant information across continuous temporal spans and adjusting segment importance." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.778, + 0.483, + 0.837 + ], + "angle": 0, + "content": "- We introduce a question-aware attention mechanism that incorporates question context carefully in the audiovisual encoding process, enabling progressive refinement of temporal focus and more effective feature extraction." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.838, + 0.483, + 0.898 + ], + "angle": 0, + "content": "- QA-TIGER achieves state-of-the-art performance across multiple benchmark datasets and provides an in-depth analysis of the impact of frame selection strategies, an area that has been previously underexplored in AVQA." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.703, + 0.483, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.664, + 0.106 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.907, + 0.358 + ], + "angle": 0, + "content": "Audio-Visual Question Answering (AVQA) has advanced with datasets like MUSIC-AVQA [16], AVQA [40], and Pano-AVQA [46], enabling fine-grained reasoning [18, 34]. Early works have implemented spatial-temporal groundings for fine-grained audio-visual scene understanding and reasoning [16, 40]. Recently, adapter-based architectures [5, 24, 37] have achieved impressive performance by leveraging frozen pretrained vision transformers for efficiency. COCA [14] and M2KVDG [25] achieve multimodal collaboration with causal graphs, enhancing the model's robustness. APL [23] introduced an object-aware approach that employs adaptive-positivity learning to align question-object and audio-object semantics. Building on prior work, this study focuses on two often underexplored aspects: explicitly integrating question information and an effective frame sampling strategy to enhance temporal reasoning." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.366, + 0.706, + 0.381 + ], + "angle": 0, + "content": "2.1. Question Awareness" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.388, + 0.909, + 0.69 + ], + "angle": 0, + "content": "In recent multimodal AVQA research, question-awareness [4, 21, 33, 41] has been recognized as crucial for aligning questions with visual and auditory features. However, most AVQA models [16, 23, 24] only incorporate question awareness at the final reasoning stage, which limits its impact throughout the entire process. Although several methods utilize question information for key-frame selection [17, 19], this is typically applied in an implicit manner, further constraining their reasoning capabilities. While models like QA-ViT [7] embed question information early in the encoding process, they primarily focus on interactions between frame tokens (i.e., patches) and the question within a single frame. In contrast, our approach explicitly embeds question information early in the process, selectively integrating modality-relevant details along the temporal axis. This ensures consistent alignment with the question context throughout the AVQA pipeline, allowing the model to progressively refine its focus on relevant temporal cues and improving the ability to leverage both visual and audio information." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.698, + 0.715, + 0.714 + ], + "angle": 0, + "content": "2.2. Temporal Grounding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Understanding and reasoning over extended audio or video, often containing redundant information, is a key challenge in QA. A critical task is localizing specific temporal segments that align with a natural language query, reducing redundancy. Temporal grounding focuses on accurately identifying these relevant moments. Many existing QA methods, such as proposal-based [36, 44, 47] or proposal-free [6, 20, 29, 45] models, like SMIN [35], optimize multilevel interactions between the question and video segments. However, these approaches often rely on predefined knowledge, adding computational overhead. To mitigate this, many AVQA models [16, 24, 37, 42] use uniform sam" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13682" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.145, + 0.089, + 0.87, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.403, + 0.907, + 0.475 + ], + "angle": 0, + "content": "Figure 2. Overview of QA-TIGER: Each modality is processed through its specific pretrained encoder for feature extraction. The Question-Aware Fusion module embeds question context early in the encoding process, enabling progressive refinement throughout the pipeline. The Temporal Integration of Gaussian Experts module independently applies multi-Gaussian weighting to both audio and visual modalities, capturing consecutive and non-consecutive temporal dependencies. Finally, Question-Guided Reasoning produces context-aware audio-visual features for accurate answer prediction." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.5, + 0.482, + 0.697 + ], + "angle": 0, + "content": "pling, which overlooks question-specific details and treats the temporal dimension as discrete. Recent studies [17, 19] attempt to select frames based on question relevance, yet they still treat the temporal dimension as discrete, limiting their ability to capture continuous video dynamics. In contrast, our approach embeds temporal dependencies using Gaussian distributions, enabling continuous modeling of question-relevant segments. This ensures precise alignment with both audio and visual modalities, improving temporal grounding and overall reasoning. By adapting to both consecutive and non-consecutive spans, QA-TIGER captures and utilizes relevant temporal information more effectively than methods that rely on discrete sampling." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.709, + 0.182, + 0.724 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.78 + ], + "angle": 0, + "content": "QA-TIGER aims to dynamically weight temporal segments based on question relevance and explicitly integrate question context as shown in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.292, + 0.805 + ], + "angle": 0, + "content": "3.1. Input Representation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.483, + 0.841 + ], + "angle": 0, + "content": "The input video sequence is split into \\( T \\) non-overlapping \\( 1s \\) segments, each with paired audio and visual elements." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Visual Representation. Each visual segment is processed using a pretrained CLIP model [30]. The visual input is divided into \\(M\\) patches per segment, with a special [CLS] token added at the beginning. Visual features are extracted" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.499, + 0.907, + 0.59 + ], + "angle": 0, + "content": "in two forms: Frame-level features \\(\\mathbf{v} = \\{v^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}\\) are obtained from the [CLS] token output for each segment \\(t\\). Patch-level features \\(\\mathbf{p} = \\{p^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times M' \\times D}\\) are obtained by merging the \\(M\\) patch tokens into \\(M'\\) tokens per segment using Token Merging (ToMe) [2], providing more spatially detailed information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.592, + 0.906, + 0.654 + ], + "angle": 0, + "content": "Audio Representation. For each segment \\( t \\), we extract audio features \\( a^t \\in \\mathbb{R}^D \\) using a VGGish model [11] pretrained on AudioSet [8], following previous work. The complete set of audio features is \\( \\mathbf{a} = \\{a^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.653, + 0.906, + 0.745 + ], + "angle": 0, + "content": "Question Representation. The input question is tokenized and processed using the CLIP text encoder. We extract sentence-level features \\( q_{s} \\in \\mathbb{R}^{D} \\) from the [EOT] token. Additionally, we obtain word-level features \\( q_{w} \\in \\mathbb{R}^{N \\times D} \\) by skipping CLIP's final projection layer, where \\( N \\) is the number of tokens including padding." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.757, + 0.731, + 0.773 + ], + "angle": 0, + "content": "3.2. Question-Aware Fusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.901 + ], + "angle": 0, + "content": "For effective AVQA, our question-aware attention module explicitly injects question context into both the video and audio modalities. Our question-aware fusion module operates in two main stages. First, multi-head Self-Attention (SA) enhances internal relationships within each modality by using the same input for the query, key, and value. Then, each modality undergoes two rounds of multi-head Cross-Attention (CA): visual features v use audio features a as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13683" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.243 + ], + "angle": 0, + "content": "the key and value, with \\(\\mathbf{v}\\) as the query, and then apply word-level question feature \\(q_{w}\\) as the key and value to align with question information. Similarly, audio features a use visual features \\(\\mathbf{v}\\) and question features \\(q_{w}\\) sequentially as key and value, with a as the query. This dual CA application per modality enables explicit question-informed cross-modal interactions. Finally, the outputs from the SA and two CA layers are combined with residual connections to enhance temporal coherence and retain alignment with the question as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.255, + 0.483, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {q} = \\mathbf {v} + \\operatorname {S A} (\\mathbf {v}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {v}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {v}, q _ {w}, q _ {w}), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.274, + 0.483, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {q} = \\mathbf {a} + \\operatorname {S A} (\\mathbf {a}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {a}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {a}, q _ {w}, q _ {w}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.3, + 0.484, + 0.407 + ], + "angle": 0, + "content": "The result is two question-aligned multimodal features, \\(\\mathbf{v}_q = \\{v_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}\\) for visual and \\(\\mathbf{a}_q = \\{a_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}\\) for audio. Unlike prior approaches that integrate question information only in the final stages, our method introduces question context from the start, allowing QA-TIGER to dynamically refine focus on relevant temporal cues throughout AVQA processing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.407, + 0.484, + 0.512 + ], + "angle": 0, + "content": "Once the question-aware visual features \\(\\mathbf{v}_q\\) and audio features \\(\\mathbf{a}_q\\) are obtained, we further refine the patch-level visual features to align finer spatial details with the question context. This refinement ensures that finer spatial details in the visual data align more closely with the question context embedded in the modality-specific features. The process is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.524, + 0.483, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {v} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {v} _ {q}, \\mathbf {p}, \\mathbf {p}), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.543, + 0.483, + 0.56 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {a} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {a} _ {q}, \\mathbf {p}, \\mathbf {p}). \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.569, + 0.453, + 0.585 + ], + "angle": 0, + "content": "3.3. Temporal Integration of Gaussian Experts" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.591, + 0.484, + 0.667 + ], + "angle": 0, + "content": "To capture temporal dependencies in the video, we leverage the Mixture of Experts (MoE) framework [32], integrating multiple Gaussian distributions across the timeline. This approach enables the model to focus on distinct temporal segments relevant to the question." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.484, + 0.803 + ], + "angle": 0, + "content": "Gaussian Generation. To produce question-relevant Gaussian distributions, we first generate a condensed, question-focused representation for each modality. This process aligns the visual and audio features with the question, to capture the temporal relevance of frames in both modalities. Using a cross-attention mechanism, we apply the sentence-level question feature \\( q_{s} \\) to the question-aware features \\( \\mathbf{v}_q \\) and \\( \\mathbf{a}_q \\), yielding \\( D \\)-dimensional aggregated representations for each modality:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.813, + 0.483, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {v} _ {q}, \\mathbf {v} _ {q}\\right), \\quad \\mathbf {a} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {a} _ {q}, \\mathbf {a} _ {q}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In contrast to prior work [39], which used a single Gaussian mask across the temporal domain, we generate multiple Gaussian distributions to capture a broader range of key frames, especially in cases where temporal variations" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.155 + ], + "angle": 0, + "content": "are complex and challenging. The Gaussian distributions \\(\\mathbf{g} = \\{g^{i}\\}_{i = 1}^{E}\\) represent distinct temporal segments relevant to the question, where \\(E\\) is the total number of Gaussian experts (i.e., Gaussian distributions):" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.169, + 0.907, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} _ {v} = \\mathcal {N} \\big (\\mu_ {v} ^ {i}, (\\sigma_ {v} ^ {i}) ^ {2} \\big), \\quad \\mathbf {g} _ {a} = \\mathcal {N} \\big (\\mu_ {a} ^ {i}, (\\sigma_ {a} ^ {i}) ^ {2} \\big). \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.203, + 0.907, + 0.34 + ], + "angle": 0, + "content": "Here, \\(\\{\\mu^i\\}_{i=1}^E\\) and \\(\\{\\sigma^i\\}_{i=1}^E\\) denote the Gaussian centers and standard deviations, generated through a linear layer with an input dimension of \\(D\\) and an output dimension of two. To minimize conflicts across time segments and enhance temporal focus, the Gaussian centers are distributed along the timeline, with a predicted offset by a linear layer added to the initial centers. This ensures that each expert mainly covers a distinct segment, aligning with question-relevant frames and reducing redundancy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.341, + 0.906, + 0.477 + ], + "angle": 0, + "content": "Integrating Temporal Information. To selectively capture relevant segments over time, we adapt the MoE framework, which combines multiple specialized \"experts,\" each trained to focus on specific temporal patterns. Instead of selecting discrete experts, our model adjusts the influence of each expert based on their context-dependent weights. These experts act as Gaussian distributions along the timeline, providing soft masks that help capture temporal dependencies in alignment with the question." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.478, + 0.906, + 0.527 + ], + "angle": 0, + "content": "The router assigns routing values \\(\\mathbf{r}_v = \\{r_v^i\\}_{i=1}^E\\) and \\(\\mathbf{r}_a = \\{r_a^i\\}_{i=1}^E\\) for each expert based on the cross-attention outputs \\(\\mathbf{v}_q'\\) and \\(\\mathbf{a}_q'\\), respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.54, + 0.906, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathbf {r} _ {v} = \\operatorname {S o f t m a x} \\left(\\mathbf {v} _ {q} ^ {\\prime} \\cdot W\\right), \\quad \\mathbf {r} _ {a} = \\operatorname {S o f t m a x} \\left(\\mathbf {a} _ {q} ^ {\\prime} \\cdot W\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.572, + 0.906, + 0.694 + ], + "angle": 0, + "content": "where \\( W \\in \\mathbb{R}^{D \\times E} \\) is a learnable weight matrix that dynamically controls the influence of each expert. The resulting expert weights allow the model to emphasize question-relevant time segments more effectively. The outputs from all experts are then combined through a weighted summation, producing a temporally integrated representation that captures question-specific insights across frames. This integration is expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.71, + 0.907, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\tilde {v} _ {p _ {v}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {v}), \\quad \\tilde {v} _ {p _ {a}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {a}), \\quad \\tilde {a} = \\mathcal {G} _ {a} (\\mathbf {a} _ {q}), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.729, + 0.906, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\mathcal {G} _ {m} (x) = \\sum_ {i = 1} ^ {E} g _ {m} ^ {i} r _ {m} ^ {i} \\mathcal {E} _ {m} ^ {i} (x). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In this setup, \\(\\mathcal{E}_m^i (x)\\) represents the output of the \\(i\\)-th expert for input \\(x\\). The temporal visual features \\(\\tilde{v}_{p_v} \\in \\mathbb{R}^D\\) and \\(\\tilde{v}_{p_a} \\in \\mathbb{R}^D\\) are derived by applying the experts to modality-specific patch features \\(\\mathbf{p}_v\\) and \\(\\mathbf{p}_a\\), respectively. Similarly, the temporal audio feature \\(\\tilde{a} \\in \\mathbb{R}^D\\) is obtained by applying experts to the question-aware audio feature \\(\\mathbf{a}_q\\). This arrangement allows the model to maintain temporal coherence, aligning with question-relevant segments and minimizing redundancy." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13684" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.461, + 0.108 + ], + "angle": 0, + "content": "3.4. Question-Guided Reasoning and Prediction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.219 + ], + "angle": 0, + "content": "The question-guided reasoning module combines audio and visual features from the temporal integration module, allowing the model to evaluate each input's importance in relation to the question context. To ensure a balanced representation, we use averaged features as a residual connection, preventing over-reliance on any single input type. First, the final visual feature \\( F_{v} \\in \\mathbb{R}^{D} \\) is obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.226, + 0.483, + 0.245 + ], + "angle": 0, + "content": "\\[\nF _ {v} = \\operatorname {A v g} \\left(\\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}}\\right) + \\mathrm {C A} \\left(q _ {s}, \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right], \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right]\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.251, + 0.484, + 0.328 + ], + "angle": 0, + "content": "where \\([\\cdot, \\cdot]\\) denotes concatenation. This process yields a question-aligned visual feature that balances information across both temporal visual representations. Next, the final audio-visual representation \\(F_{va} \\in \\mathbb{R}^{D}\\) is obtained by fusing the temporal audio feature \\(\\tilde{a}\\) with \\(F_{v}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.335, + 0.483, + 0.353 + ], + "angle": 0, + "content": "\\[\nF _ {v a} = \\operatorname {A v g} \\left(\\tilde {a}, F _ {v}\\right) + \\operatorname {C A} \\left(q _ {s}, \\left[ \\tilde {a}, F _ {v} \\right], \\left[ \\tilde {a}, F _ {v} \\right]\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.36, + 0.484, + 0.466 + ], + "angle": 0, + "content": "This step ensures that both audio and visual features contribute to the final representation in a question-aware manner. Finally, answer prediction is performed by applying a linear layer and a Softmax layer to \\( F_{va} \\) yielding probabilities over \\( C \\) answer choices. The model is trained using cross-entropy loss: \\( \\mathcal{L}_{qa} = -\\sum_{c=1}^{C} y_c \\log \\mathcal{P}_c \\), with the answer selected as the class with the highest probability." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.478, + 0.224, + 0.495 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.502, + 0.194, + 0.517 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.524, + 0.484, + 0.675 + ], + "angle": 0, + "content": "Our experiments utilize the MUSIC-AVQA [16], MUSIC-AVQA-R [28], and MUSIC-AVQA-v2.0 [26] datasets. MUSIC-AVQA serves as a benchmark for audio-visual reasoning over 22 instruments, with questions spanning audio-only, visual-only, and audio-visual modalities, covering reasoning types like existence, location, and temporal aspects. MUSIC-AVQA-R focuses on rare and out-of-distribution samples to assess model robustness. MUSIC-AVQA-v2.0 addresses dataset biases by enhancing diversity in ensemble scenes and multi-instrument cases." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.683, + 0.308, + 0.699 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The video is sampled at 1 fps, with audio features extracted using VGGish [11], while visual features and questions are processed using the CLIP-ViT-L/14 [30] model. Token reduction is applied to visual features using ToMe [2] technique. To ensure consistency, all features are linearly transformed to 512 dimensions. Further details on the feature extraction process are provided in the supplementary materials. We set the expert number to 7 and configure every attention module with 8 heads with 0.1 dropout probability. The model is trained with the Adam optimizer at an initial learning rate of 1e-4, which decays by a factor of 0.1 every 8 epochs. Training is conducted for 15 epochs with a batch size of 32 on a single NVIDIA RTX A6000." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.091, + 0.906, + 0.136 + ], + "angle": 0, + "content": "
Dataset# Videos# Train QA# Valid QA# Test QA
MUSIC-AVQA [16]9,28831,9044,5689,129
MUSIC-AVQA-R [28]9,288--211,572
MUSIC-AVQA-v2.0 [26]10,49237,4085,34610,819
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.139, + 0.907, + 0.168 + ], + "angle": 0, + "content": "Table 1. Summary of MUSIC-AVQA, MUSIC-AVQA-R, and MUSIC-AVQA-v2.0 datasets with the number of QA pairs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.188, + 0.81, + 0.205 + ], + "angle": 0, + "content": "4.3. Quantitative Results and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.212, + 0.907, + 0.348 + ], + "angle": 0, + "content": "To evaluate our model's effectiveness, we compared QA-TIGER to existing AVQA methods on Audio (A-QA), Visual (V-QA), and Audio-Visual (AV-QA) tasks, considering both question types and overall averages. QA-TIGER was trained on the MUSIC-AVQA [16] training set and validated using its validation set for testing both MUSIC-AVQA [16] and MUSIC-AVQA-R [28]. For MUSIC-AVQA-v2.0 [26], QA-TIGER was trained on both the balanced and biased training sets and tested accordingly." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.348, + 0.906, + 0.456 + ], + "angle": 0, + "content": "MUSIC-AVQA. QA-TIGER achieves the highest performance among all models, with an overall accuracy \\((77.62\\%)\\), surpassing the previous best method \\((76.79\\%)\\), TSPM [19], in Table 2. Notably, our model shows strong performance in complex reasoning tasks, achieving \\(78.58\\%\\) and \\(72.50\\%\\) in AV-Counting and AV-Local categories respectively, surpassing previous methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.456, + 0.907, + 0.547 + ], + "angle": 0, + "content": "MUSIC-AVQA-R. Our method achieves \\(67.99\\%\\) overall accuracy on the MUSIC-AVQA-R dataset across diverse question types, as shown in Table 3, without the need for explicit bias handling techniques. This balanced performance highlights QA-TIGER's strong temporal modeling and question-aware feature extraction capabilities." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.547, + 0.907, + 0.699 + ], + "angle": 0, + "content": "MUSIC-AVQA-v2.0. QA-TIGER consistently outperforms existing models [16, 24, 28] on the biased test set, regardless of the training set type (Table 4a). On the balanced test set (Table 4b), QA-TIGER trained on the balanced dataset achieves superior accuracy in both \\( A - QA \\) (79.90%) and \\( V - QA \\) (86.95%), surpassing LAST-Att in overall accuracy (75.44% vs. 76.43%). Notably, LAST-Att underperforms in \\( A - QA \\) despite incorporating an additional audio encoder, Audio Spectrogram Transformer [9]. This highlights QA-TIGER's robustness across diverse evaluation settings." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.699, + 0.906, + 0.821 + ], + "angle": 0, + "content": "Inference Time. We compare inference time between TSPM and QA-TIGER under identical conditions, using the full pipeline setup with CLIP and VGGish. TSPM records 1.767 seconds, while QA-TIGER achieves a comparable time of 1.737 seconds. Despite processing full temporal information, QA-TIGER matches TSPM's efficiency—which selects Top-K frames—demonstrating its ability to handle temporal dynamics without added overhead." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.869, + 0.849 + ], + "angle": 0, + "content": "4.4. Qualitative Results of Temporal Gaussian" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.902 + ], + "angle": 0, + "content": "To evaluate whether QA-TIGER accurately identifies question-relevant temporal segments, we qualitatively analyze its performance in Figure 3. Notably, the audio Gaus" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13685" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.092, + 0.907, + 0.301 + ], + "angle": 0, + "content": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompAvgCountLocalAvgExistCountLocalCompTempAvg
FCNLSTM [10]70.4566.2268.8863.8946.7455.2182.0159.3446.2862.1547.3360.0660.34
BiLSTM [38]70.3547.9262.0564.6464.3364.4878.3956.9145.8553.0949.7657.1059.92
HCAtn [27]70.2554.9164.5764.0566.3765.2279.1059.9749.5155.2556.4360.1962.30
MCAN [43]77.5055.2469.2571.5670.9371.2480.4064.9154.4857.2247.5761.5865.49
PSAC [22]75.6466.0672.0968.6469.7969.2277.5963.4255.0261.1759.4763.5266.54
HME [1]74.7663.5670.6167.9769.4668.7680.3063.1953.1862.6959.8364.0566.45
HCRN [15]68.5950.9262.0564.3961.8163.0854.4753.3841.5352.1147.6950.2655.73
AVSD [31]72.4161.9068.5267.3974.1970.8381.6163.8958.7961.5261.4165.4967.44
Pano-AVQA [46]74.3664.5670.7369.3975.6572.5681.2164.9159.3364.2263.2366.6468.93
ST-AVQA [16]78.1867.0574.0671.5676.3874.0081.8170.8064.5166.0163.2369.5471.52
COCA [14]79.3567.6875.4275.1075.4375.2383.5066.6369.7264.1265.5769.9672.33
PSTP-Net [17]73.9765.5970.9177.1577.3677.2676.1872.2371.8071.7969.0072.5773.52
LAVISH [24]82.0965.5675.9778.9881.4380.2281.7175.5166.1363.7767.9671.2674.46
APL [23]82.4070.7178.0976.5282.7479.6982.9973.2966.6864.7665.9570.9674.53
TSPM [19]84.0764.6576.9182.2984.9083.6182.1976.2171.8565.7671.1773.5176.79
QA-TIGER84.8667.8578.5883.9686.2985.1483.1078.5872.5063.9469.5973.7477.62
" + }, + { + "type": "table_caption", + "bbox": [ + 0.205, + 0.307, + 0.793, + 0.322 + ], + "angle": 0, + "content": "Table 2. Experimental results (%) on the MUSIC-AVQA test set. The top-2 results are highlighted." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.328, + 0.907, + 0.531 + ], + "angle": 0, + "content": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompCountLocalExistCountLocalCompTemp
HTHTHTHTHTHTHTHTHT
FCNLSTM [10]66.2336.4864.7851.2461.755.3154.8651.0664.7678.5262.697.2346.6657.3043.1371.6737.0230.7854.12
BiLSTM [38]73.6846.3221.5177.5864.300.0053.9242.0187.5121.1462.852.1835.1643.7527.6174.3817.5831.3248.84
HCAtnn [27]61.6741.6359.0947.1456.529.2067.0153.1666.5761.1359.5312.4837.0542.4848.8160.1233.8239.2651.90
MCAN [43]75.0260.1658.8950.0964.5826.6966.4862.2551.2967.2964.7625.2846.1161.6150.5752.4034.6458.0557.27
PSAC [22]53.0156.6857.4148.1249.5526.4372.9660.6950.5655.5456.7019.5841.9852.3038.1358.9226.6846.2450.45
HME [1]62.6053.9554.9758.2950.9516.4673.2558.6065.7466.4963.1817.1833.7946.0353.2069.5733.9541.5753.66
HCRN [15]55.5353.3147.1732.4441.8723.5539.4051.2741.8165.4554.5819.5736.6242.7233.3336.8740.4744.1343.92
AVSD [31]54.0047.8460.6147.7960.3410.0774.7861.4366.2861.9846.218.0633.0040.3551.9866.0040.1441.5252.33
Pano-AVQA [46]50.5743.4550.7844.9347.2815.5067.1965.5152.3722.0452.2121.5244.3561.6945.6140.4935.0049.3347.40
ST-AVQA [16]56.4041.4862.2857.5959.8612.9463.3154.0073.3577.2648.318.4135.3540.4953.3062.4440.2538.1552.80
LAVISH [24]61.7343.9965.0660.3865.5311.1370.2164.7377.8379.4649.8814.8741.7641.2059.2665.1041.8446.2657.63
TSPM† [19]81.6571.8067.6649.5678.2947.5680.5873.1869.1582.7977.0938.6442.2457.3752.0768.8639.2349.3666.30
QA-TIGER82.6775.8271.7543.1181.3054.5984.7675.5972.8478.5676.7033.5548.2264.6537.5580.4736.8562.9667.99
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.54, + 0.907, + 0.57 + ], + "angle": 0, + "content": "Table 3. Experimental results (%) on the MUSIC-AVQA-R test set, with H and T representing performance on Head (frequent) and Tail (rare) answer categories, respectively. † indicates results reproduced using official codes." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.587, + 0.482, + 0.698 + ], + "angle": 0, + "content": "
TestTrainingMethodA-QAV-QAAV-QAAvg
(a) BiasBiasST-AVQA [16]76.8677.7069.5973.07
LAVISH [24]76.7380.9670.8074.59
QA-TIGER79.1384.8372.3776.93
BalanceST-AVQA [16]76.1877.2067.9671.92
LAVISH [24]75.5680.8369.2773.51
LAST [26]77.1082.9970.8675.24
LAST-Att [26]77.2983.4771.0575.45
QA-TIGER77.0785.9371.2076.57
" + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.707, + 0.482, + 0.818 + ], + "angle": 0, + "content": "
TestTrainingMethodA-QAV-QAAV-QAAvg
(b) BalanceBiasST-AVQA [16]73.3476.8264.5169.40
LAVISH [24]73.1479.7065.0170.39
QA-TIGER77.5784.8467.4373.91
BalanceST-AVQA [16]75.5077.6766.3271.02
LAVISH [24]76.1581.3268.2873.18
LAST [26]78.0883.2969.7274.85
LAST-Att [26]78.5684.0770.3075.44
QA-TIGER79.9086.9570.2276.43
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.833, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Table 4. Experimental results (\\%) on the MUSIC-AVQA-v2.0 for (a) bias and (b) balanced test sets. Each evaluation is conducted with models trained on bias and balanced training sets, respectively. The performance of other methods was referenced from the scores provided by MUSIC-AVQA-v2.0." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.588, + 0.907, + 0.68 + ], + "angle": 0, + "content": "sian aligns more with A-QA in Figure 3a, while the visual Gaussian is more prominent for V-QA in Figure 3b. For AV-QA, both modalities show similar Gaussian distributions in Figure 3c, demonstrating the model's adaptive focus based on question type. A detailed comparison with uniform sampling and Top-K selection is provided in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.684, + 0.909, + 0.821 + ], + "angle": 0, + "content": "Audio Question. QA-TIGER demonstrates its ability to handle temporal reasoning. For the question \"Is the tuba playing longer than the clarinet?\", QA-TIGER's audio Gaussian assigns high weights across the entire durations, effectively capturing the complete temporal spans essential for accurately comparing the two instruments in the question. The visual Gaussian similarly focuses on frames where the tuba and clarinet are actively played, supporting a robust comparison of their durations, as shown in Figure 3a." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Visual Question. Our method effectively integrates both visual and audio modalities to accurately count the saxophones, in Figure 3b. The visual Gaussian assigns higher weights to frames where all five saxophonists are clearly visible from the front, while frames with less distinct views," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13686" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.447, + 0.175, + 0.551, + 0.186 + ], + "angle": 0, + "content": "(a) Audio Question" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.187, + 0.905, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.447, + 0.271, + 0.551, + 0.283 + ], + "angle": 0, + "content": "(b) Visual Question" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.285, + 0.905, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.429, + 0.368, + 0.57, + 0.38 + ], + "angle": 0, + "content": "(c) Audio-Visual Question" + }, + { + "type": "image_caption", + "bbox": [ + 0.187, + 0.39, + 0.809, + 0.404 + ], + "angle": 0, + "content": "Figure 3. Qualitative results by question type of the proposed QA-TIGER on the MUSIC-AVQA test set." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.424, + 0.483, + 0.514 + ], + "angle": 0, + "content": "such as side angles or wide shots, are assigned lower weights. Meanwhile, the audio Gaussian emphasizes moments when the sounds of all five saxophones overlap, focusing on their simultaneous performance. This integration allows the model to concentrate on the most critical visual and auditory cues to predict the accurate answer." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.515, + 0.483, + 0.636 + ], + "angle": 0, + "content": "Audio-Visual Question. The visual Gaussian effectively focuses on frames in the early part of the video where individual instrument appear, as well as frames where all three instruments are shown together. Correspondingly, the audio Gaussian emphasizes prominent instrument sounds. This complementary alignment enables QA-TIGER to integrate visual and auditory cues effectively, resulting in accurate identification of all instruments, as shown in Figure 3c." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.649, + 0.431, + 0.665 + ], + "angle": 0, + "content": "4.5. Visualization of Question-Aware Fusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.717 + ], + "angle": 0, + "content": "To validate the effectiveness of our question-aware fusion module, we performed word-level visualizations. Additional examples are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.483, + 0.839 + ], + "angle": 0, + "content": "\"Are there saxophone and piano sound\": In the visual modality, attention initially focuses on \"piano,\" where visual cues are subtle, then shifts to the more distinct \"saxophone.\" In the audio modality, attention consistently highlights \"piano,\" compensating for the limited visual cues, while \"saxophone,\" is primarily processed visually. This shows how QA-TIGER adapts to question context, effectively distributing attention across both modalities." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "\"How many sounding saxophone in the video\": In the visual modality, attention focuses on \"saxophone,\" aiding in counting. In the audio modality, attention highlights \"sounding,\" and \"saxophone,\" to capture the auditory cues" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.42, + 0.907, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.627, + 0.907, + 0.683 + ], + "angle": 0, + "content": "Figure 4. Question-aware attention for visual (upper) and audio (lower) fusion in response to two different questions for the same video and audio input. The attention intensity is indicated by the color scale on the right." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.692, + 0.825, + 0.706 + ], + "angle": 0, + "content": "necessary for counting saxophone occurrences." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.906, + 0.799 + ], + "angle": 0, + "content": "These results demonstrate how the question-aware fusion module dynamically adapts to different questions. By emphasizing question-relevant elements in both modalities, QA-TIGER progressively refines its focus, improving accuracy and ensuring alignment with task demands throughout the reasoning process." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.81, + 0.688, + 0.827 + ], + "angle": 0, + "content": "5. In-depth Analysis" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.832, + 0.667, + 0.848 + ], + "angle": 0, + "content": "5.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We evaluated our proposed modules on MUSIC-AVQA (Table 5). The baseline model used uniform sampling and achieved reasonable accuracy. Adding the Gaussian Ex" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "13687" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.09, + 0.483, + 0.171 + ], + "angle": 0, + "content": "
Question-Aware FusionGaussian ExpertsA-QAV-QAAV-QAAvg
75.0581.7971.8275.04
✓77.5984.5672.3776.53
✓76.3582.7472.7876.05
✓✓78.5885.1473.7477.62
" + }, + { + "type": "table_caption", + "bbox": [ + 0.132, + 0.182, + 0.442, + 0.198 + ], + "angle": 0, + "content": "Table 5. Ablation study of the proposed framework." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.217, + 0.483, + 0.399 + ], + "angle": 0, + "content": "perts module improved performance by enhancing temporal modeling through specialized experts. The Question-Aware Fusion module alone also contributed a notable improvement. Combining both modules led to the best performance, demonstrating the synergistic benefits of integrating question context early on. This integration enriches the temporal context for the Gaussian Experts module, highlighting the complementary strengths of both modules in enhancing temporal reasoning. Without Question-Aware Fusion, question features were incorporated only at the final stage, as in prior work [12, 16, 24]. For setups excluding Gaussian Experts, uniform sampling was applied." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.407, + 0.258, + 0.423 + ], + "angle": 0, + "content": "5.2. Frame Sampling" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.43, + 0.483, + 0.49 + ], + "angle": 0, + "content": "We evaluated conventional sampling strategies and Gaussian modeling designs for AVQA tasks (Figure 5). Note that all experiments compare only the frame sampling part after applying the proposed Question-Aware Fusion." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.49, + 0.483, + 0.58 + ], + "angle": 0, + "content": "Sampling-based Methods. Uniform sampling at fixed intervals was less effective due to its lack of focus on question-relevant frames. The Top-K method, using the frame selection module from TSPM [19], improved performance by selecting question-relevant frames but lacked comprehensive temporal context." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.581, + 0.483, + 0.749 + ], + "angle": 0, + "content": "Gaussian-based Methods. We explore various Gaussian-based methods to model temporal dependencies. Gaussian, a simple sum of Gaussians, shows similar performance to uniform sampling. Weighted-Gaussian introduces dynamic weighting but still struggles with overlap. By adding disjoint center constraints, Weighted-Gaussian (Disjoint Center) reduces redundancy and improves accuracy. Building on this, Gaussian Experts extends the Weighted-Gaussian (Disjoint Center) approach with a MoE framework, dynamically assigning specialized experts to distinct temporal segments, resulting in the highest accuracy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.758, + 0.281, + 0.774 + ], + "angle": 0, + "content": "5.3. Selection of Experts" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "In this analysis, we explored the impact of expert selection in the proposed MoE approach. The decision to activate all seven experts stems from the observed performance gains as more experts are used. Even with the fewest experts, the model outperforms the current state-of-the-art TSPM [19] \\((76.79\\%)\\) on the MUSIC-AVQA [16] dataset, as shown in Figure 6. Using all seven experts achieves the highest accuracy \\((77.62\\%)\\), showcasing the superiority of QA-TIGER." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.09, + 0.887, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.247, + 0.908, + 0.304 + ], + "angle": 0, + "content": "Figure 5. Comparison of temporal selection methods based on the number of criteria (Gaussian or K). Gaussian-based methods use a simple summation for temporal aggregation. \"W\" refers to \"Weighted sum,\" and \"D.C.\" stands for \"Disjoint Center.\"" + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.317, + 0.859, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.446, + 0.88, + 0.461 + ], + "angle": 0, + "content": "Figure 6. Impact of expert selection on Gaussian experts." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.486, + 0.634, + 0.503 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.907, + 0.759 + ], + "angle": 0, + "content": "We have introduced QA-TIGER, designed to overcome the limitations of prior methods in handling complex temporal dynamics and question-specific feature integration. By leveraging multi-Gaussian modeling within the MoE framework, QA-TIGER adaptively captures subtle temporal dependencies while minimizing redundancy through strategically positioned Gaussian centers. We also incorporate question context explicitly from the encoding stages, ensuring that question information is gradually refined throughout the processing pipeline. Extensive experiments demonstrate QA-TIGER's state-of-the-art performance on various datasets, highlighting its effectiveness in tackling the continuous temporal domain and complex AVQA challenges. Future work could explore adaptive expert selection mechanisms in MoE-based AVQA, tailored to different question types, to further enhance the model's generalizability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement. This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00211348). This research was partly supported by the MSIT(Ministry of Science, ICT), Korea, under the Global Research Support Program in the Digital Field program)(RS-2024-00425354) supervised by the IITP(Institute for Information & Communications Technology Planning & Evaluation)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13688" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Chenyou Fan abd Xiaofan Zhang, Shu Zhang, Wensheng Wang, Chi Zhang, and Heng Huang. Heterogeneous memory enhanced multimodal attention model for video question answering. 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In AAAI, pages 12870-12877, 2020." + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.483, + 0.884 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13690" + } + ] +] \ No newline at end of file diff --git a/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_origin.pdf b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..fbc997e9c0302e44db75d244fdc610e898c7a491 --- /dev/null +++ b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/8c821211-5fd4-495c-9b23-97b0652c108a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f62a07b851cab4bac9a5c68ae05fbe7b6286c3d2c8dd204d0e79f51e5986d3fd +size 2544000 diff --git a/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/full.md b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1aa32bb6f2d52b2f79ae9b5181edd8d43251a63f --- /dev/null +++ b/2025/Question-Aware Gaussian Experts for Audio-Visual Question Answering/full.md @@ -0,0 +1,321 @@ +# Question-Aware Gaussian Experts for Audio-Visual Question Answering + +Hongyeob Kim $^{1*}$ Inyoung Jung $^{1*}$ Dayoon Suh $^{2}$ Youjia Zhang $^{1}$ Sangmin Lee $^{1}$ Sungeun Hong $^{1\dagger}$ Sungkyunkwan University $^{2}$ Purdue University + +# Abstract + +Audio-Visual Question Answering (AVQA) requires not only question-based multimodal reasoning but also precise temporal grounding to capture subtle dynamics for accurate prediction. However, existing methods mainly use question information implicitly, limiting focus on question-specific details. Furthermore, most studies rely on uniform frame sampling, which can miss key question-relevant frames. Although recent Top-K frame selection methods aim to address this, their discrete nature still overlooks fine-grained temporal details. This paper proposes QA-TIGER, a novel framework that explicitly incorporates question information and models continuous temporal dynamics. Our key idea is to use Gaussian-based modeling to adaptively focus on both consecutive and non-consecutive frames based on the question, while explicitly injecting question information and applying progressive refinement. We leverage a Mixture of Experts (MoE) to flexibly implement multiple Gaussian models, activating temporal experts specifically tailored to the question. Extensive experiments on multiple AVQA benchmarks show that QA-TIGER consistently achieves state-of-the-art performance. Code is available at https://aim-skku.github.io/QA-TIGER/ + +# 1. Introduction + +Audio-Visual Question Answering (AVQA) focuses on analyzing and interpreting both audio and visual cues to provide accurate answers to questions. Recent advancements in AVQA have focused on spatial and temporal grounding [3, 13, 16], parameter-efficient models [5, 24, 37], and bias adjustments [14, 28]. Despite promising results, many existing methods struggle to capture fine-grained, question-specific details and temporal cues essential for effective reasoning. We argue that two key considerations are critical for successful AVQA: (i) flexibly capturing and integrating question-relevant audio-visual cues across temporal contexts, and (ii) embedding question context explicitly within the audio-visual feature processing stages. + +![](images/48eec1312ee1d49f64d0ec517c880b548b4350cd512f74200338453b30a38613.jpg) +(a) An example of input frames, audio, and question + +![](images/24399206b5e951723d86d3e4abf1dd98f057ff492e957e774b477295b2ceacb9.jpg) +(b) Uniform sampling + +![](images/bda0be9add41f493a8640ca6fa6ca7b366bbd92e53038b3f63b5cfd0cdae272d.jpg) +(c) Top-K frame selection +(d) QA-TIGER +Figure 1. Sampling comparison for AVQA. (a) Input sample. (b) Uniform sampling treats all frames equally, ignoring question-specific context. (c) Top-k frame selection samples discrete frames based only on question-video similarity, often missing important contextual details. (d) Ours provides explicit temporal grounding for both audio and visual modalities, focusing on continuous, question-relevant segments with precise multimodal alignment. + +Most AVQA methods use uniform sampling or discrete frame selection [16, 24, 37], often overlooking question-specific details. These methods treat frames equally missing important, question-relevant information in both audio and visual modalities. Recent approaches, such as PSTP [17] and TSPM [19], use Top-K frame selection to improve context relevance by aligning frames with the question. However, they select them based solely on visual cues, relying on discrete sampling that disrupts continuity by ignoring temporal cues. Additionally, this approach focuses mainly on visual alignment, missing crucial audio details. + +In terms of question integration, most AVQA models incorporate question information only at the final reasoning stage, typically by simple multiplication [12, 16, 19, 24]. + +This late-stage integration limits the model's ability to encode question-specific features during intermediate steps, reducing the effectiveness of reasoning. Although several methods attempt to enhance reasoning by using question details in frame selection [17, 19], this is done indirectly, and they fail to explicitly embed question context within the audio-visual encoding pipeline. This limited approach restricts the model's ability to focus on relevant temporal cues progressively. + +In this paper, we propose QA-TIGER (Question-Aware Temporal Integration of Gaussian Experts for Reasoning), as illustrated in Figure 1. To address issue $(i)$ , QA-TIGER introduces a multi-Gaussian weighting mechanism embedded within a Mixture of Experts (MoE) framework [32]. This approach assigns adaptive weights across both consecutive and non-consecutive temporal spans, thereby enabling the model to capture complex temporal dependencies more effectively. Gaussian experts are adaptively activated with well-positioned centers, reducing redundancy and simultaneously improving temporal alignment. In contrast to previous methods [17, 19], which strictly align audio cues with corresponding visual frames, QA-TIGER provides explicit temporal grounding for both audio and visual modalities independently. This allows for more accurate and robust alignment with the question-relevant segments. + +To address issue (ii), QA-TIGER incorporates question information early in the process, creating question-aware features that permeate both the visual and audio modalities. By embedding question context directly into each modality's features, QA-TIGER aligns with the question context throughout the entire pipeline, unlike prior methods that add question information only at the final stage [16, 17, 19, 24]. This approach allows the model to progressively refine its focus based on the question, resulting in deeper and more explicit integration of question relevance. Ultimately, this approach enhances accuracy and contextual alignment across all reasoning stages. + +Our contributions can be summarized as follows: + +- We propose QA-TIGER, a framework that adaptively models temporal dynamics using strategically positioned Gaussian experts, capturing question-relevant information across continuous temporal spans and adjusting segment importance. +- We introduce a question-aware attention mechanism that incorporates question context carefully in the audiovisual encoding process, enabling progressive refinement of temporal focus and more effective feature extraction. +- QA-TIGER achieves state-of-the-art performance across multiple benchmark datasets and provides an in-depth analysis of the impact of frame selection strategies, an area that has been previously underexplored in AVQA. + +# 2. Related Works + +Audio-Visual Question Answering (AVQA) has advanced with datasets like MUSIC-AVQA [16], AVQA [40], and Pano-AVQA [46], enabling fine-grained reasoning [18, 34]. Early works have implemented spatial-temporal groundings for fine-grained audio-visual scene understanding and reasoning [16, 40]. Recently, adapter-based architectures [5, 24, 37] have achieved impressive performance by leveraging frozen pretrained vision transformers for efficiency. COCA [14] and M2KVDG [25] achieve multimodal collaboration with causal graphs, enhancing the model's robustness. APL [23] introduced an object-aware approach that employs adaptive-positivity learning to align question-object and audio-object semantics. Building on prior work, this study focuses on two often underexplored aspects: explicitly integrating question information and an effective frame sampling strategy to enhance temporal reasoning. + +# 2.1. Question Awareness + +In recent multimodal AVQA research, question-awareness [4, 21, 33, 41] has been recognized as crucial for aligning questions with visual and auditory features. However, most AVQA models [16, 23, 24] only incorporate question awareness at the final reasoning stage, which limits its impact throughout the entire process. Although several methods utilize question information for key-frame selection [17, 19], this is typically applied in an implicit manner, further constraining their reasoning capabilities. While models like QA-ViT [7] embed question information early in the encoding process, they primarily focus on interactions between frame tokens (i.e., patches) and the question within a single frame. In contrast, our approach explicitly embeds question information early in the process, selectively integrating modality-relevant details along the temporal axis. This ensures consistent alignment with the question context throughout the AVQA pipeline, allowing the model to progressively refine its focus on relevant temporal cues and improving the ability to leverage both visual and audio information. + +# 2.2. Temporal Grounding + +Understanding and reasoning over extended audio or video, often containing redundant information, is a key challenge in QA. A critical task is localizing specific temporal segments that align with a natural language query, reducing redundancy. Temporal grounding focuses on accurately identifying these relevant moments. Many existing QA methods, such as proposal-based [36, 44, 47] or proposal-free [6, 20, 29, 45] models, like SMIN [35], optimize multilevel interactions between the question and video segments. However, these approaches often rely on predefined knowledge, adding computational overhead. To mitigate this, many AVQA models [16, 24, 37, 42] use uniform sam + +![](images/80cc788101a103da54acb1f6532199decd7746b3321e5581d06a9f3f56fc1782.jpg) +Figure 2. Overview of QA-TIGER: Each modality is processed through its specific pretrained encoder for feature extraction. The Question-Aware Fusion module embeds question context early in the encoding process, enabling progressive refinement throughout the pipeline. The Temporal Integration of Gaussian Experts module independently applies multi-Gaussian weighting to both audio and visual modalities, capturing consecutive and non-consecutive temporal dependencies. Finally, Question-Guided Reasoning produces context-aware audio-visual features for accurate answer prediction. + +pling, which overlooks question-specific details and treats the temporal dimension as discrete. Recent studies [17, 19] attempt to select frames based on question relevance, yet they still treat the temporal dimension as discrete, limiting their ability to capture continuous video dynamics. In contrast, our approach embeds temporal dependencies using Gaussian distributions, enabling continuous modeling of question-relevant segments. This ensures precise alignment with both audio and visual modalities, improving temporal grounding and overall reasoning. By adapting to both consecutive and non-consecutive spans, QA-TIGER captures and utilizes relevant temporal information more effectively than methods that rely on discrete sampling. + +# 3. Method + +QA-TIGER aims to dynamically weight temporal segments based on question relevance and explicitly integrate question context as shown in Figure 2. + +# 3.1. Input Representation + +The input video sequence is split into $T$ non-overlapping $1s$ segments, each with paired audio and visual elements. + +Visual Representation. Each visual segment is processed using a pretrained CLIP model [30]. The visual input is divided into $M$ patches per segment, with a special [CLS] token added at the beginning. Visual features are extracted + +in two forms: Frame-level features $\mathbf{v} = \{v^t\}_{t=1}^T \in \mathbb{R}^{T \times D}$ are obtained from the [CLS] token output for each segment $t$ . Patch-level features $\mathbf{p} = \{p^t\}_{t=1}^T \in \mathbb{R}^{T \times M' \times D}$ are obtained by merging the $M$ patch tokens into $M'$ tokens per segment using Token Merging (ToMe) [2], providing more spatially detailed information. + +Audio Representation. For each segment $t$ , we extract audio features $a^t \in \mathbb{R}^D$ using a VGGish model [11] pretrained on AudioSet [8], following previous work. The complete set of audio features is $\mathbf{a} = \{a^t\}_{t=1}^T \in \mathbb{R}^{T \times D}$ . + +Question Representation. The input question is tokenized and processed using the CLIP text encoder. We extract sentence-level features $q_{s} \in \mathbb{R}^{D}$ from the [EOT] token. Additionally, we obtain word-level features $q_{w} \in \mathbb{R}^{N \times D}$ by skipping CLIP's final projection layer, where $N$ is the number of tokens including padding. + +# 3.2. Question-Aware Fusion + +For effective AVQA, our question-aware attention module explicitly injects question context into both the video and audio modalities. Our question-aware fusion module operates in two main stages. First, multi-head Self-Attention (SA) enhances internal relationships within each modality by using the same input for the query, key, and value. Then, each modality undergoes two rounds of multi-head Cross-Attention (CA): visual features v use audio features a as + +the key and value, with $\mathbf{v}$ as the query, and then apply word-level question feature $q_{w}$ as the key and value to align with question information. Similarly, audio features a use visual features $\mathbf{v}$ and question features $q_{w}$ sequentially as key and value, with a as the query. This dual CA application per modality enables explicit question-informed cross-modal interactions. Finally, the outputs from the SA and two CA layers are combined with residual connections to enhance temporal coherence and retain alignment with the question as follows: + +$$ +\mathbf {v} _ {q} = \mathbf {v} + \operatorname {S A} (\mathbf {v}, \mathbf {v}, \mathbf {v}) + \operatorname {C A} (\mathbf {v}, \mathbf {a}, \mathbf {a}) + \operatorname {C A} (\mathbf {v}, q _ {w}, q _ {w}), \tag {1} +$$ + +$$ +\mathbf {a} _ {q} = \mathbf {a} + \operatorname {S A} (\mathbf {a}, \mathbf {a}, \mathbf {a}) + \operatorname {C A} (\mathbf {a}, \mathbf {v}, \mathbf {v}) + \operatorname {C A} (\mathbf {a}, q _ {w}, q _ {w}). \tag {2} +$$ + +The result is two question-aligned multimodal features, $\mathbf{v}_q = \{v_q^t\}_{t=1}^T \in \mathbb{R}^{T \times D}$ for visual and $\mathbf{a}_q = \{a_q^t\}_{t=1}^T \in \mathbb{R}^{T \times D}$ for audio. Unlike prior approaches that integrate question information only in the final stages, our method introduces question context from the start, allowing QA-TIGER to dynamically refine focus on relevant temporal cues throughout AVQA processing. + +Once the question-aware visual features $\mathbf{v}_q$ and audio features $\mathbf{a}_q$ are obtained, we further refine the patch-level visual features to align finer spatial details with the question context. This refinement ensures that finer spatial details in the visual data align more closely with the question context embedded in the modality-specific features. The process is formulated as follows: + +$$ +\mathbf {p} _ {v} = \mathbf {p} + \operatorname {S A} (\mathbf {p}, \mathbf {p}, \mathbf {p}) + \operatorname {C A} (\mathbf {v} _ {q}, \mathbf {p}, \mathbf {p}), \tag {3} +$$ + +$$ +\mathbf {p} _ {a} = \mathbf {p} + \operatorname {S A} (\mathbf {p}, \mathbf {p}, \mathbf {p}) + \operatorname {C A} (\mathbf {a} _ {q}, \mathbf {p}, \mathbf {p}). \tag {4} +$$ + +# 3.3. Temporal Integration of Gaussian Experts + +To capture temporal dependencies in the video, we leverage the Mixture of Experts (MoE) framework [32], integrating multiple Gaussian distributions across the timeline. This approach enables the model to focus on distinct temporal segments relevant to the question. + +Gaussian Generation. To produce question-relevant Gaussian distributions, we first generate a condensed, question-focused representation for each modality. This process aligns the visual and audio features with the question, to capture the temporal relevance of frames in both modalities. Using a cross-attention mechanism, we apply the sentence-level question feature $q_{s}$ to the question-aware features $\mathbf{v}_q$ and $\mathbf{a}_q$ , yielding $D$ -dimensional aggregated representations for each modality: + +$$ +\mathbf {v} _ {q} ^ {\prime} = \operatorname {C A} \left(q _ {s}, \mathbf {v} _ {q}, \mathbf {v} _ {q}\right), \quad \mathbf {a} _ {q} ^ {\prime} = \operatorname {C A} \left(q _ {s}, \mathbf {a} _ {q}, \mathbf {a} _ {q}\right). \tag {5} +$$ + +In contrast to prior work [39], which used a single Gaussian mask across the temporal domain, we generate multiple Gaussian distributions to capture a broader range of key frames, especially in cases where temporal variations + +are complex and challenging. The Gaussian distributions $\mathbf{g} = \{g^{i}\}_{i = 1}^{E}$ represent distinct temporal segments relevant to the question, where $E$ is the total number of Gaussian experts (i.e., Gaussian distributions): + +$$ +\mathbf {g} _ {v} = \mathcal {N} \big (\mu_ {v} ^ {i}, (\sigma_ {v} ^ {i}) ^ {2} \big), \quad \mathbf {g} _ {a} = \mathcal {N} \big (\mu_ {a} ^ {i}, (\sigma_ {a} ^ {i}) ^ {2} \big). \qquad (6) +$$ + +Here, $\{\mu^i\}_{i=1}^E$ and $\{\sigma^i\}_{i=1}^E$ denote the Gaussian centers and standard deviations, generated through a linear layer with an input dimension of $D$ and an output dimension of two. To minimize conflicts across time segments and enhance temporal focus, the Gaussian centers are distributed along the timeline, with a predicted offset by a linear layer added to the initial centers. This ensures that each expert mainly covers a distinct segment, aligning with question-relevant frames and reducing redundancy. + +Integrating Temporal Information. To selectively capture relevant segments over time, we adapt the MoE framework, which combines multiple specialized "experts," each trained to focus on specific temporal patterns. Instead of selecting discrete experts, our model adjusts the influence of each expert based on their context-dependent weights. These experts act as Gaussian distributions along the timeline, providing soft masks that help capture temporal dependencies in alignment with the question. + +The router assigns routing values $\mathbf{r}_v = \{r_v^i\}_{i=1}^E$ and $\mathbf{r}_a = \{r_a^i\}_{i=1}^E$ for each expert based on the cross-attention outputs $\mathbf{v}_q'$ and $\mathbf{a}_q'$ , respectively: + +$$ +\mathbf {r} _ {v} = \operatorname {S o f t m a x} \left(\mathbf {v} _ {q} ^ {\prime} \cdot W\right), \quad \mathbf {r} _ {a} = \operatorname {S o f t m a x} \left(\mathbf {a} _ {q} ^ {\prime} \cdot W\right), \tag {7} +$$ + +where $W \in \mathbb{R}^{D \times E}$ is a learnable weight matrix that dynamically controls the influence of each expert. The resulting expert weights allow the model to emphasize question-relevant time segments more effectively. The outputs from all experts are then combined through a weighted summation, producing a temporally integrated representation that captures question-specific insights across frames. This integration is expressed as follows: + +$$ +\tilde {v} _ {p _ {v}} = \mathcal {G} _ {v} (\mathbf {p} _ {v}), \quad \tilde {v} _ {p _ {a}} = \mathcal {G} _ {v} (\mathbf {p} _ {a}), \quad \tilde {a} = \mathcal {G} _ {a} (\mathbf {a} _ {q}), \tag {8} +$$ + +$$ +\text {w h e r e} \mathcal {G} _ {m} (x) = \sum_ {i = 1} ^ {E} g _ {m} ^ {i} r _ {m} ^ {i} \mathcal {E} _ {m} ^ {i} (x). \tag {9} +$$ + +In this setup, $\mathcal{E}_m^i (x)$ represents the output of the $i$ -th expert for input $x$ . The temporal visual features $\tilde{v}_{p_v} \in \mathbb{R}^D$ and $\tilde{v}_{p_a} \in \mathbb{R}^D$ are derived by applying the experts to modality-specific patch features $\mathbf{p}_v$ and $\mathbf{p}_a$ , respectively. Similarly, the temporal audio feature $\tilde{a} \in \mathbb{R}^D$ is obtained by applying experts to the question-aware audio feature $\mathbf{a}_q$ . This arrangement allows the model to maintain temporal coherence, aligning with question-relevant segments and minimizing redundancy. + +# 3.4. Question-Guided Reasoning and Prediction + +The question-guided reasoning module combines audio and visual features from the temporal integration module, allowing the model to evaluate each input's importance in relation to the question context. To ensure a balanced representation, we use averaged features as a residual connection, preventing over-reliance on any single input type. First, the final visual feature $F_{v} \in \mathbb{R}^{D}$ is obtained as follows: + +$$ +F _ {v} = \operatorname {A v g} \left(\tilde {v} _ {p _ {a}}, \tilde {v} _ {p _ {v}}\right) + \mathrm {C A} \left(q _ {s}, \left[ \tilde {v} _ {p _ {a}}, \tilde {v} _ {p _ {v}} \right], \left[ \tilde {v} _ {p _ {a}}, \tilde {v} _ {p _ {v}} \right]\right), \tag {10} +$$ + +where $[\cdot, \cdot]$ denotes concatenation. This process yields a question-aligned visual feature that balances information across both temporal visual representations. Next, the final audio-visual representation $F_{va} \in \mathbb{R}^{D}$ is obtained by fusing the temporal audio feature $\tilde{a}$ with $F_{v}$ as follows: + +$$ +F _ {v a} = \operatorname {A v g} \left(\tilde {a}, F _ {v}\right) + \operatorname {C A} \left(q _ {s}, \left[ \tilde {a}, F _ {v} \right], \left[ \tilde {a}, F _ {v} \right]\right). \tag {11} +$$ + +This step ensures that both audio and visual features contribute to the final representation in a question-aware manner. Finally, answer prediction is performed by applying a linear layer and a Softmax layer to $F_{va}$ yielding probabilities over $C$ answer choices. The model is trained using cross-entropy loss: $\mathcal{L}_{qa} = -\sum_{c=1}^{C} y_c \log \mathcal{P}_c$ , with the answer selected as the class with the highest probability. + +# 4. Experiments + +# 4.1. Datasets + +Our experiments utilize the MUSIC-AVQA [16], MUSIC-AVQA-R [28], and MUSIC-AVQA-v2.0 [26] datasets. MUSIC-AVQA serves as a benchmark for audio-visual reasoning over 22 instruments, with questions spanning audio-only, visual-only, and audio-visual modalities, covering reasoning types like existence, location, and temporal aspects. MUSIC-AVQA-R focuses on rare and out-of-distribution samples to assess model robustness. MUSIC-AVQA-v2.0 addresses dataset biases by enhancing diversity in ensemble scenes and multi-instrument cases. + +# 4.2. Implementation Details + +The video is sampled at 1 fps, with audio features extracted using VGGish [11], while visual features and questions are processed using the CLIP-ViT-L/14 [30] model. Token reduction is applied to visual features using ToMe [2] technique. To ensure consistency, all features are linearly transformed to 512 dimensions. Further details on the feature extraction process are provided in the supplementary materials. We set the expert number to 7 and configure every attention module with 8 heads with 0.1 dropout probability. The model is trained with the Adam optimizer at an initial learning rate of 1e-4, which decays by a factor of 0.1 every 8 epochs. Training is conducted for 15 epochs with a batch size of 32 on a single NVIDIA RTX A6000. + +
Dataset# Videos# Train QA# Valid QA# Test QA
MUSIC-AVQA [16]9,28831,9044,5689,129
MUSIC-AVQA-R [28]9,288--211,572
MUSIC-AVQA-v2.0 [26]10,49237,4085,34610,819
+ +Table 1. Summary of MUSIC-AVQA, MUSIC-AVQA-R, and MUSIC-AVQA-v2.0 datasets with the number of QA pairs. + +# 4.3. Quantitative Results and Analysis + +To evaluate our model's effectiveness, we compared QA-TIGER to existing AVQA methods on Audio (A-QA), Visual (V-QA), and Audio-Visual (AV-QA) tasks, considering both question types and overall averages. QA-TIGER was trained on the MUSIC-AVQA [16] training set and validated using its validation set for testing both MUSIC-AVQA [16] and MUSIC-AVQA-R [28]. For MUSIC-AVQA-v2.0 [26], QA-TIGER was trained on both the balanced and biased training sets and tested accordingly. + +MUSIC-AVQA. QA-TIGER achieves the highest performance among all models, with an overall accuracy $(77.62\%)$ , surpassing the previous best method $(76.79\%)$ , TSPM [19], in Table 2. Notably, our model shows strong performance in complex reasoning tasks, achieving $78.58\%$ and $72.50\%$ in AV-Counting and AV-Local categories respectively, surpassing previous methods. + +MUSIC-AVQA-R. Our method achieves $67.99\%$ overall accuracy on the MUSIC-AVQA-R dataset across diverse question types, as shown in Table 3, without the need for explicit bias handling techniques. This balanced performance highlights QA-TIGER's strong temporal modeling and question-aware feature extraction capabilities. + +MUSIC-AVQA-v2.0. QA-TIGER consistently outperforms existing models [16, 24, 28] on the biased test set, regardless of the training set type (Table 4a). On the balanced test set (Table 4b), QA-TIGER trained on the balanced dataset achieves superior accuracy in both $A - QA$ (79.90%) and $V - QA$ (86.95%), surpassing LAST-Att in overall accuracy (75.44% vs. 76.43%). Notably, LAST-Att underperforms in $A - QA$ despite incorporating an additional audio encoder, Audio Spectrogram Transformer [9]. This highlights QA-TIGER's robustness across diverse evaluation settings. + +Inference Time. We compare inference time between TSPM and QA-TIGER under identical conditions, using the full pipeline setup with CLIP and VGGish. TSPM records 1.767 seconds, while QA-TIGER achieves a comparable time of 1.737 seconds. Despite processing full temporal information, QA-TIGER matches TSPM's efficiency—which selects Top-K frames—demonstrating its ability to handle temporal dynamics without added overhead. + +# 4.4. Qualitative Results of Temporal Gaussian + +To evaluate whether QA-TIGER accurately identifies question-relevant temporal segments, we qualitatively analyze its performance in Figure 3. Notably, the audio Gaus + +
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompAvgCountLocalAvgExistCountLocalCompTempAvg
FCNLSTM [10]70.4566.2268.8863.8946.7455.2182.0159.3446.2862.1547.3360.0660.34
BiLSTM [38]70.3547.9262.0564.6464.3364.4878.3956.9145.8553.0949.7657.1059.92
HCAtn [27]70.2554.9164.5764.0566.3765.2279.1059.9749.5155.2556.4360.1962.30
MCAN [43]77.5055.2469.2571.5670.9371.2480.4064.9154.4857.2247.5761.5865.49
PSAC [22]75.6466.0672.0968.6469.7969.2277.5963.4255.0261.1759.4763.5266.54
HME [1]74.7663.5670.6167.9769.4668.7680.3063.1953.1862.6959.8364.0566.45
HCRN [15]68.5950.9262.0564.3961.8163.0854.4753.3841.5352.1147.6950.2655.73
AVSD [31]72.4161.9068.5267.3974.1970.8381.6163.8958.7961.5261.4165.4967.44
Pano-AVQA [46]74.3664.5670.7369.3975.6572.5681.2164.9159.3364.2263.2366.6468.93
ST-AVQA [16]78.1867.0574.0671.5676.3874.0081.8170.8064.5166.0163.2369.5471.52
COCA [14]79.3567.6875.4275.1075.4375.2383.5066.6369.7264.1265.5769.9672.33
PSTP-Net [17]73.9765.5970.9177.1577.3677.2676.1872.2371.8071.7969.0072.5773.52
LAVISH [24]82.0965.5675.9778.9881.4380.2281.7175.5166.1363.7767.9671.2674.46
APL [23]82.4070.7178.0976.5282.7479.6982.9973.2966.6864.7665.9570.9674.53
TSPM [19]84.0764.6576.9182.2984.9083.6182.1976.2171.8565.7671.1773.5176.79
QA-TIGER84.8667.8578.5883.9686.2985.1483.1078.5872.5063.9469.5973.7477.62
+ +Table 2. Experimental results (%) on the MUSIC-AVQA test set. The top-2 results are highlighted. + +
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompCountLocalExistCountLocalCompTemp
HTHTHTHTHTHTHTHTHT
FCNLSTM [10]66.2336.4864.7851.2461.755.3154.8651.0664.7678.5262.697.2346.6657.3043.1371.6737.0230.7854.12
BiLSTM [38]73.6846.3221.5177.5864.300.0053.9242.0187.5121.1462.852.1835.1643.7527.6174.3817.5831.3248.84
HCAtnn [27]61.6741.6359.0947.1456.529.2067.0153.1666.5761.1359.5312.4837.0542.4848.8160.1233.8239.2651.90
MCAN [43]75.0260.1658.8950.0964.5826.6966.4862.2551.2967.2964.7625.2846.1161.6150.5752.4034.6458.0557.27
PSAC [22]53.0156.6857.4148.1249.5526.4372.9660.6950.5655.5456.7019.5841.9852.3038.1358.9226.6846.2450.45
HME [1]62.6053.9554.9758.2950.9516.4673.2558.6065.7466.4963.1817.1833.7946.0353.2069.5733.9541.5753.66
HCRN [15]55.5353.3147.1732.4441.8723.5539.4051.2741.8165.4554.5819.5736.6242.7233.3336.8740.4744.1343.92
AVSD [31]54.0047.8460.6147.7960.3410.0774.7861.4366.2861.9846.218.0633.0040.3551.9866.0040.1441.5252.33
Pano-AVQA [46]50.5743.4550.7844.9347.2815.5067.1965.5152.3722.0452.2121.5244.3561.6945.6140.4935.0049.3347.40
ST-AVQA [16]56.4041.4862.2857.5959.8612.9463.3154.0073.3577.2648.318.4135.3540.4953.3062.4440.2538.1552.80
LAVISH [24]61.7343.9965.0660.3865.5311.1370.2164.7377.8379.4649.8814.8741.7641.2059.2665.1041.8446.2657.63
TSPM† [19]81.6571.8067.6649.5678.2947.5680.5873.1869.1582.7977.0938.6442.2457.3752.0768.8639.2349.3666.30
QA-TIGER82.6775.8271.7543.1181.3054.5984.7675.5972.8478.5676.7033.5548.2264.6537.5580.4736.8562.9667.99
+ +Table 3. Experimental results (%) on the MUSIC-AVQA-R test set, with H and T representing performance on Head (frequent) and Tail (rare) answer categories, respectively. † indicates results reproduced using official codes. + +
TestTrainingMethodA-QAV-QAAV-QAAvg
(a) BiasBiasST-AVQA [16]76.8677.7069.5973.07
LAVISH [24]76.7380.9670.8074.59
QA-TIGER79.1384.8372.3776.93
BalanceST-AVQA [16]76.1877.2067.9671.92
LAVISH [24]75.5680.8369.2773.51
LAST [26]77.1082.9970.8675.24
LAST-Att [26]77.2983.4771.0575.45
QA-TIGER77.0785.9371.2076.57
+ +
TestTrainingMethodA-QAV-QAAV-QAAvg
(b) BalanceBiasST-AVQA [16]73.3476.8264.5169.40
LAVISH [24]73.1479.7065.0170.39
QA-TIGER77.5784.8467.4373.91
BalanceST-AVQA [16]75.5077.6766.3271.02
LAVISH [24]76.1581.3268.2873.18
LAST [26]78.0883.2969.7274.85
LAST-Att [26]78.5684.0770.3075.44
QA-TIGER79.9086.9570.2276.43
+ +Table 4. Experimental results (\%) on the MUSIC-AVQA-v2.0 for (a) bias and (b) balanced test sets. Each evaluation is conducted with models trained on bias and balanced training sets, respectively. The performance of other methods was referenced from the scores provided by MUSIC-AVQA-v2.0. + +sian aligns more with A-QA in Figure 3a, while the visual Gaussian is more prominent for V-QA in Figure 3b. For AV-QA, both modalities show similar Gaussian distributions in Figure 3c, demonstrating the model's adaptive focus based on question type. A detailed comparison with uniform sampling and Top-K selection is provided in the supplementary. + +Audio Question. QA-TIGER demonstrates its ability to handle temporal reasoning. For the question "Is the tuba playing longer than the clarinet?", QA-TIGER's audio Gaussian assigns high weights across the entire durations, effectively capturing the complete temporal spans essential for accurately comparing the two instruments in the question. The visual Gaussian similarly focuses on frames where the tuba and clarinet are actively played, supporting a robust comparison of their durations, as shown in Figure 3a. + +Visual Question. Our method effectively integrates both visual and audio modalities to accurately count the saxophones, in Figure 3b. The visual Gaussian assigns higher weights to frames where all five saxophonists are clearly visible from the front, while frames with less distinct views, + +![](images/6b0c8f44a888a9a6b1a04e508955d957b1f98aeda081d966546251e122914fff.jpg) +(a) Audio Question + +![](images/5706d3226506819465300768fe60c06b0b88a58d2c410a3a98c2ddbebe2ab2d8.jpg) +(b) Visual Question + +![](images/fb4c2b28f989f0cdf3b77cdef41ca18a6ec46f66bc713ba301ee7937a97aa656.jpg) +(c) Audio-Visual Question + +such as side angles or wide shots, are assigned lower weights. Meanwhile, the audio Gaussian emphasizes moments when the sounds of all five saxophones overlap, focusing on their simultaneous performance. This integration allows the model to concentrate on the most critical visual and auditory cues to predict the accurate answer. + +Audio-Visual Question. The visual Gaussian effectively focuses on frames in the early part of the video where individual instrument appear, as well as frames where all three instruments are shown together. Correspondingly, the audio Gaussian emphasizes prominent instrument sounds. This complementary alignment enables QA-TIGER to integrate visual and auditory cues effectively, resulting in accurate identification of all instruments, as shown in Figure 3c. + +# 4.5. Visualization of Question-Aware Fusion + +To validate the effectiveness of our question-aware fusion module, we performed word-level visualizations. Additional examples are provided in the supplementary material. + +"Are there saxophone and piano sound": In the visual modality, attention initially focuses on "piano," where visual cues are subtle, then shifts to the more distinct "saxophone." In the audio modality, attention consistently highlights "piano," compensating for the limited visual cues, while "saxophone," is primarily processed visually. This shows how QA-TIGER adapts to question context, effectively distributing attention across both modalities. + +"How many sounding saxophone in the video": In the visual modality, attention focuses on "saxophone," aiding in counting. In the audio modality, attention highlights "sounding," and "saxophone," to capture the auditory cues + +![](images/0a3504f0893ddc09702f7af0d15af5c70b9bb3010b24d5e577ebbc139bb37dc8.jpg) +Figure 3. Qualitative results by question type of the proposed QA-TIGER on the MUSIC-AVQA test set. +Figure 4. Question-aware attention for visual (upper) and audio (lower) fusion in response to two different questions for the same video and audio input. The attention intensity is indicated by the color scale on the right. + +necessary for counting saxophone occurrences. + +These results demonstrate how the question-aware fusion module dynamically adapts to different questions. By emphasizing question-relevant elements in both modalities, QA-TIGER progressively refines its focus, improving accuracy and ensuring alignment with task demands throughout the reasoning process. + +# 5. In-depth Analysis + +# 5.1. Ablation Study + +We evaluated our proposed modules on MUSIC-AVQA (Table 5). The baseline model used uniform sampling and achieved reasonable accuracy. Adding the Gaussian Ex + +
Question-Aware FusionGaussian ExpertsA-QAV-QAAV-QAAvg
75.0581.7971.8275.04
✓77.5984.5672.3776.53
✓76.3582.7472.7876.05
✓✓78.5885.1473.7477.62
+ +Table 5. Ablation study of the proposed framework. + +perts module improved performance by enhancing temporal modeling through specialized experts. The Question-Aware Fusion module alone also contributed a notable improvement. Combining both modules led to the best performance, demonstrating the synergistic benefits of integrating question context early on. This integration enriches the temporal context for the Gaussian Experts module, highlighting the complementary strengths of both modules in enhancing temporal reasoning. Without Question-Aware Fusion, question features were incorporated only at the final stage, as in prior work [12, 16, 24]. For setups excluding Gaussian Experts, uniform sampling was applied. + +# 5.2. Frame Sampling + +We evaluated conventional sampling strategies and Gaussian modeling designs for AVQA tasks (Figure 5). Note that all experiments compare only the frame sampling part after applying the proposed Question-Aware Fusion. + +Sampling-based Methods. Uniform sampling at fixed intervals was less effective due to its lack of focus on question-relevant frames. The Top-K method, using the frame selection module from TSPM [19], improved performance by selecting question-relevant frames but lacked comprehensive temporal context. + +Gaussian-based Methods. We explore various Gaussian-based methods to model temporal dependencies. Gaussian, a simple sum of Gaussians, shows similar performance to uniform sampling. Weighted-Gaussian introduces dynamic weighting but still struggles with overlap. By adding disjoint center constraints, Weighted-Gaussian (Disjoint Center) reduces redundancy and improves accuracy. Building on this, Gaussian Experts extends the Weighted-Gaussian (Disjoint Center) approach with a MoE framework, dynamically assigning specialized experts to distinct temporal segments, resulting in the highest accuracy. + +# 5.3. Selection of Experts + +In this analysis, we explored the impact of expert selection in the proposed MoE approach. The decision to activate all seven experts stems from the observed performance gains as more experts are used. Even with the fewest experts, the model outperforms the current state-of-the-art TSPM [19] $(76.79\%)$ on the MUSIC-AVQA [16] dataset, as shown in Figure 6. Using all seven experts achieves the highest accuracy $(77.62\%)$ , showcasing the superiority of QA-TIGER. + +![](images/345240f7ebdf49a7fa052f0a8bc75649cc5880e83b06f162e48ecc0b18fe996b.jpg) +Figure 5. Comparison of temporal selection methods based on the number of criteria (Gaussian or K). Gaussian-based methods use a simple summation for temporal aggregation. "W" refers to "Weighted sum," and "D.C." stands for "Disjoint Center." + +![](images/c522af42b522b67c5cb4f5195d4b5dab1091d1808cbf8e0b41039de6c73feed6.jpg) +Figure 6. Impact of expert selection on Gaussian experts. + +# 6. Conclusion + +We have introduced QA-TIGER, designed to overcome the limitations of prior methods in handling complex temporal dynamics and question-specific feature integration. By leveraging multi-Gaussian modeling within the MoE framework, QA-TIGER adaptively captures subtle temporal dependencies while minimizing redundancy through strategically positioned Gaussian centers. We also incorporate question context explicitly from the encoding stages, ensuring that question information is gradually refined throughout the processing pipeline. Extensive experiments demonstrate QA-TIGER's state-of-the-art performance on various datasets, highlighting its effectiveness in tackling the continuous temporal domain and complex AVQA challenges. Future work could explore adaptive expert selection mechanisms in MoE-based AVQA, tailored to different question types, to further enhance the model's generalizability. + +Acknowledgement. This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00211348). This research was partly supported by the MSIT(Ministry of Science, ICT), Korea, under the Global Research Support Program in the Digital Field program)(RS-2024-00425354) supervised by the IITP(Institute for Information & Communications Technology Planning & Evaluation). + +# References + +[1] Chenyou Fan abd Xiaofan Zhang, Shu Zhang, Wensheng Wang, Chi Zhang, and Heng Huang. Heterogeneous memory enhanced multimodal attention model for video question answering. In CVPR, pages 1999-2007, 2019. +[2] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. Token merging: Your ViT but faster. In ICLR, 2023. +[3] Sihan Chen, Xingjian He, Longteng Guo, Xinxin Zhu, Weining Wang, Jinhui Tang, and Jing Liu. 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Pano-avqa: Grounded audio-visual question answering on 360deg videos. In ICCV, pages 2031–2041, 2021. +[47] Songyang Zhang, Houwen Peng, Jianlong Fu, and Jiebo Luo. Learning 2d temporal adjacent networks for moment localization with natural language. 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However, existing methods mainly use question information implicitly, limiting focus on question-specific details. Furthermore, most studies rely on uniform frame sampling, which can miss key question-relevant frames. Although recent Top-K frame selection methods aim to address this, their discrete nature still overlooks fine-grained temporal details. This paper proposes QA-TIGER, a novel framework that explicitly incorporates question information and models continuous temporal dynamics. Our key idea is to use Gaussian-based modeling to adaptively focus on both consecutive and non-consecutive frames based on the question, while explicitly injecting question information and applying progressive refinement. We leverage a Mixture of Experts (MoE) to flexibly implement multiple Gaussian models, activating temporal experts specifically tailored to the question. Extensive experiments on multiple AVQA benchmarks show that QA-TIGER consistently achieves state-of-the-art performance. Code is available at https://aim-skku.github.io/QA-TIGER/" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 510, + 137, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 137, + 522 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 137, + 522 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 530, + 295, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 685 + ], + "type": "text", + "content": "Audio-Visual Question Answering (AVQA) focuses on analyzing and interpreting both audio and visual cues to provide accurate answers to questions. Recent advancements in AVQA have focused on spatial and temporal grounding [3, 13, 16], parameter-efficient models [5, 24, 37], and bias adjustments [14, 28]. Despite promising results, many existing methods struggle to capture fine-grained, question-specific details and temporal cues essential for effective reasoning. We argue that two key considerations are critical for successful AVQA: (i) flexibly capturing and integrating question-relevant audio-visual cues across temporal contexts, and (ii) embedding question context explicitly within the audio-visual feature processing stages." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 198, + 555, + 261 + ], + "blocks": [ + { + "bbox": [ + 317, + 198, + 555, + 261 + ], + "lines": [ + { + "bbox": [ + 317, + 198, + 555, + 261 + ], + "spans": [ + { + "bbox": [ + 317, + 198, + 555, + 261 + ], + "type": "image", + "image_path": "48eec1312ee1d49f64d0ec517c880b548b4350cd512f74200338453b30a38613.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 262, + 520, + 270 + ], + "lines": [ + { + "bbox": [ + 351, + 262, + 520, + 270 + ], + "spans": [ + { + "bbox": [ + 351, + 262, + 520, + 270 + ], + "type": "text", + "content": "(a) An example of input frames, audio, and question" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 272, + 554, + 328 + ], + "blocks": [ + { + "bbox": [ + 316, + 272, + 554, + 328 + ], + "lines": [ + { + "bbox": [ + 316, + 272, + 554, + 328 + ], + "spans": [ + { + "bbox": [ + 316, + 272, + 554, + 328 + ], + "type": "image", + "image_path": "24399206b5e951723d86d3e4abf1dd98f057ff492e957e774b477295b2ceacb9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 331, + 411, + 340 + ], + "lines": [ + { + "bbox": [ + 339, + 331, + 411, + 340 + ], + "spans": [ + { + "bbox": [ + 339, + 331, + 411, + 340 + ], + "type": "text", + "content": "(b) Uniform sampling" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 316, + 342, + 554, + 422 + ], + "blocks": [ + { + "bbox": [ + 452, + 331, + 536, + 340 + ], + "lines": [ + { + "bbox": [ + 452, + 331, + 536, + 340 + ], + "spans": [ + { + "bbox": [ + 452, + 331, + 536, + 340 + ], + "type": "text", + "content": "(c) Top-K frame selection" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 316, + 342, + 554, + 422 + ], + "lines": [ + { + "bbox": [ + 316, + 342, + 554, + 422 + ], + "spans": [ + { + "bbox": [ + 316, + 342, + 554, + 422 + ], + "type": "image", + "image_path": "bda0be9add41f493a8640ca6fa6ca7b366bbd92e53038b3f63b5cfd0cdae272d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 410, + 425, + 460, + 434 + ], + "lines": [ + { + "bbox": [ + 410, + 425, + 460, + 434 + ], + "spans": [ + { + "bbox": [ + 410, + 425, + 460, + 434 + ], + "type": "text", + "content": "(d) QA-TIGER" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 444, + 555, + 521 + ], + "lines": [ + { + "bbox": [ + 313, + 444, + 555, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 555, + 521 + ], + "type": "text", + "content": "Figure 1. Sampling comparison for AVQA. (a) Input sample. (b) Uniform sampling treats all frames equally, ignoring question-specific context. (c) Top-k frame selection samples discrete frames based only on question-video similarity, often missing important contextual details. (d) Ours provides explicit temporal grounding for both audio and visual modalities, focusing on continuous, question-relevant segments with precise multimodal alignment." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 544, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 544, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 312, + 544, + 555, + 676 + ], + "type": "text", + "content": "Most AVQA methods use uniform sampling or discrete frame selection [16, 24, 37], often overlooking question-specific details. These methods treat frames equally missing important, question-relevant information in both audio and visual modalities. Recent approaches, such as PSTP [17] and TSPM [19], use Top-K frame selection to improve context relevance by aligning frames with the question. However, they select them based solely on visual cues, relying on discrete sampling that disrupts continuity by ignoring temporal cues. Additionally, this approach focuses mainly on visual alignment, missing crucial audio details." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "In terms of question integration, most AVQA models incorporate question information only at the final reasoning stage, typically by simple multiplication [12, 16, 19, 24]." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 136, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 136, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 136, + 703 + ], + "type": "text", + "content": "*Equal Contribution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "text", + "content": "† Corresponding Author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13681" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "content": "This late-stage integration limits the model's ability to encode question-specific features during intermediate steps, reducing the effectiveness of reasoning. Although several methods attempt to enhance reasoning by using question details in frame selection [17, 19], this is done indirectly, and they fail to explicitly embed question context within the audio-visual encoding pipeline. This limited approach restricts the model's ability to focus on relevant temporal cues progressively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 187, + 296, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 187, + 296, + 379 + ], + "spans": [ + { + "bbox": [ + 56, + 187, + 296, + 379 + ], + "type": "text", + "content": "In this paper, we propose QA-TIGER (Question-Aware Temporal Integration of Gaussian Experts for Reasoning), as illustrated in Figure 1. To address issue " + }, + { + "bbox": [ + 56, + 187, + 296, + 379 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 56, + 187, + 296, + 379 + ], + "type": "text", + "content": ", QA-TIGER introduces a multi-Gaussian weighting mechanism embedded within a Mixture of Experts (MoE) framework [32]. This approach assigns adaptive weights across both consecutive and non-consecutive temporal spans, thereby enabling the model to capture complex temporal dependencies more effectively. Gaussian experts are adaptively activated with well-positioned centers, reducing redundancy and simultaneously improving temporal alignment. In contrast to previous methods [17, 19], which strictly align audio cues with corresponding visual frames, QA-TIGER provides explicit temporal grounding for both audio and visual modalities independently. This allows for more accurate and robust alignment with the question-relevant segments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 385, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 529 + ], + "type": "text", + "content": "To address issue (ii), QA-TIGER incorporates question information early in the process, creating question-aware features that permeate both the visual and audio modalities. By embedding question context directly into each modality's features, QA-TIGER aligns with the question context throughout the entire pipeline, unlike prior methods that add question information only at the final stage [16, 17, 19, 24]. This approach allows the model to progressively refine its focus based on the question, resulting in deeper and more explicit integration of question relevance. Ultimately, this approach enhances accuracy and contextual alignment across all reasoning stages." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 536, + 266, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 536, + 266, + 548 + ], + "spans": [ + { + "bbox": [ + 67, + 536, + 266, + 548 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 556, + 295, + 711 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 56, + 556, + 295, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 556, + 295, + 614 + ], + "spans": [ + { + "bbox": [ + 56, + 556, + 295, + 614 + ], + "type": "text", + "content": "- We propose QA-TIGER, a framework that adaptively models temporal dynamics using strategically positioned Gaussian experts, capturing question-relevant information across continuous temporal spans and adjusting segment importance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 616, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 616, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 56, + 616, + 295, + 662 + ], + "type": "text", + "content": "- We introduce a question-aware attention mechanism that incorporates question context carefully in the audiovisual encoding process, enabling progressive refinement of temporal focus and more effective feature extraction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 663, + 295, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 663, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 56, + 663, + 295, + 711 + ], + "type": "text", + "content": "- QA-TIGER achieves state-of-the-art performance across multiple benchmark datasets and provides an in-depth analysis of the impact of frame selection strategies, an area that has been previously underexplored in AVQA." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 406, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 406, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 406, + 83 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 91, + 555, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 283 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 283 + ], + "type": "text", + "content": "Audio-Visual Question Answering (AVQA) has advanced with datasets like MUSIC-AVQA [16], AVQA [40], and Pano-AVQA [46], enabling fine-grained reasoning [18, 34]. Early works have implemented spatial-temporal groundings for fine-grained audio-visual scene understanding and reasoning [16, 40]. Recently, adapter-based architectures [5, 24, 37] have achieved impressive performance by leveraging frozen pretrained vision transformers for efficiency. COCA [14] and M2KVDG [25] achieve multimodal collaboration with causal graphs, enhancing the model's robustness. APL [23] introduced an object-aware approach that employs adaptive-positivity learning to align question-object and audio-object semantics. Building on prior work, this study focuses on two often underexplored aspects: explicitly integrating question information and an effective frame sampling strategy to enhance temporal reasoning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 289, + 432, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 432, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 432, + 301 + ], + "type": "text", + "content": "2.1. Question Awareness" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 307, + 556, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 556, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 556, + 546 + ], + "type": "text", + "content": "In recent multimodal AVQA research, question-awareness [4, 21, 33, 41] has been recognized as crucial for aligning questions with visual and auditory features. However, most AVQA models [16, 23, 24] only incorporate question awareness at the final reasoning stage, which limits its impact throughout the entire process. Although several methods utilize question information for key-frame selection [17, 19], this is typically applied in an implicit manner, further constraining their reasoning capabilities. While models like QA-ViT [7] embed question information early in the encoding process, they primarily focus on interactions between frame tokens (i.e., patches) and the question within a single frame. In contrast, our approach explicitly embeds question information early in the process, selectively integrating modality-relevant details along the temporal axis. This ensures consistent alignment with the question context throughout the AVQA pipeline, allowing the model to progressively refine its focus on relevant temporal cues and improving the ability to leverage both visual and audio information." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 552, + 437, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 437, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 437, + 565 + ], + "type": "text", + "content": "2.2. Temporal Grounding" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 715 + ], + "type": "text", + "content": "Understanding and reasoning over extended audio or video, often containing redundant information, is a key challenge in QA. A critical task is localizing specific temporal segments that align with a natural language query, reducing redundancy. Temporal grounding focuses on accurately identifying these relevant moments. Many existing QA methods, such as proposal-based [36, 44, 47] or proposal-free [6, 20, 29, 45] models, like SMIN [35], optimize multilevel interactions between the question and video segments. However, these approaches often rely on predefined knowledge, adding computational overhead. To mitigate this, many AVQA models [16, 24, 37, 42] use uniform sam" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13682" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 88, + 70, + 532, + 305 + ], + "blocks": [ + { + "bbox": [ + 88, + 70, + 532, + 305 + ], + "lines": [ + { + "bbox": [ + 88, + 70, + 532, + 305 + ], + "spans": [ + { + "bbox": [ + 88, + 70, + 532, + 305 + ], + "type": "image", + "image_path": "80cc788101a103da54acb1f6532199decd7746b3321e5581d06a9f3f56fc1782.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 319, + 555, + 376 + ], + "lines": [ + { + "bbox": [ + 55, + 319, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 555, + 376 + ], + "type": "text", + "content": "Figure 2. Overview of QA-TIGER: Each modality is processed through its specific pretrained encoder for feature extraction. The Question-Aware Fusion module embeds question context early in the encoding process, enabling progressive refinement throughout the pipeline. The Temporal Integration of Gaussian Experts module independently applies multi-Gaussian weighting to both audio and visual modalities, capturing consecutive and non-consecutive temporal dependencies. Finally, Question-Guided Reasoning produces context-aware audio-visual features for accurate answer prediction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 396, + 294, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 396, + 294, + 552 + ], + "spans": [ + { + "bbox": [ + 54, + 396, + 294, + 552 + ], + "type": "text", + "content": "pling, which overlooks question-specific details and treats the temporal dimension as discrete. Recent studies [17, 19] attempt to select frames based on question relevance, yet they still treat the temporal dimension as discrete, limiting their ability to capture continuous video dynamics. In contrast, our approach embeds temporal dependencies using Gaussian distributions, enabling continuous modeling of question-relevant segments. This ensures precise alignment with both audio and visual modalities, improving temporal grounding and overall reasoning. By adapting to both consecutive and non-consecutive spans, QA-TIGER captures and utilizes relevant temporal information more effectively than methods that rely on discrete sampling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 561, + 111, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 111, + 573 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 111, + 573 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 581, + 295, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 617 + ], + "type": "text", + "content": "QA-TIGER aims to dynamically weight temporal segments based on question relevance and explicitly integrate question context as shown in Figure 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 624, + 178, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 178, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 178, + 637 + ], + "type": "text", + "content": "3.1. Input Representation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "content": "The input video sequence is split into " + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "content": " non-overlapping " + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "inline_equation", + "content": "1s" + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "content": " segments, each with paired audio and visual elements." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": "Visual Representation. Each visual segment is processed using a pretrained CLIP model [30]. The visual input is divided into " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": " patches per segment, with a special [CLS] token added at the beginning. Visual features are extracted" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": "in two forms: Frame-level features " + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{v} = \\{v^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": " are obtained from the [CLS] token output for each segment " + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": ". Patch-level features " + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = \\{p^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times M' \\times D}" + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": " are obtained by merging the " + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": " patch tokens into " + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 313, + 395, + 555, + 467 + ], + "type": "text", + "content": " tokens per segment using Token Merging (ToMe) [2], providing more spatially detailed information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "text", + "content": "Audio Representation. For each segment " + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "text", + "content": ", we extract audio features " + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "inline_equation", + "content": "a^t \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "text", + "content": " using a VGGish model [11] pretrained on AudioSet [8], following previous work. The complete set of audio features is " + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{a} = \\{a^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 313, + 468, + 554, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "text", + "content": "Question Representation. The input question is tokenized and processed using the CLIP text encoder. We extract sentence-level features " + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "inline_equation", + "content": "q_{s} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "text", + "content": " from the [EOT] token. Additionally, we obtain word-level features " + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "inline_equation", + "content": "q_{w} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "text", + "content": " by skipping CLIP's final projection layer, where " + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 517, + 554, + 590 + ], + "type": "text", + "content": " is the number of tokens including padding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 599, + 447, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 447, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 447, + 612 + ], + "type": "text", + "content": "3.2. Question-Aware Fusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": "For effective AVQA, our question-aware attention module explicitly injects question context into both the video and audio modalities. Our question-aware fusion module operates in two main stages. First, multi-head Self-Attention (SA) enhances internal relationships within each modality by using the same input for the query, key, and value. Then, each modality undergoes two rounds of multi-head Cross-Attention (CA): visual features v use audio features a as" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13683" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": "the key and value, with " + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": " as the query, and then apply word-level question feature " + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "inline_equation", + "content": "q_{w}" + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": " as the key and value to align with question information. Similarly, audio features a use visual features " + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": " and question features " + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "inline_equation", + "content": "q_{w}" + }, + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": " sequentially as key and value, with a as the query. This dual CA application per modality enables explicit question-informed cross-modal interactions. Finally, the outputs from the SA and two CA layers are combined with residual connections to enhance temporal coherence and retain alignment with the question as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 64, + 201, + 295, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 201, + 295, + 213 + ], + "spans": [ + { + "bbox": [ + 64, + 201, + 295, + 213 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {q} = \\mathbf {v} + \\operatorname {S A} (\\mathbf {v}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {v}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {v}, q _ {w}, q _ {w}), \\tag {1}", + "image_path": "806ac26deb40af898c070ade3aaa06cb68734a0d87eed736675479388c110400.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 217, + 295, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 217, + 295, + 228 + ], + "spans": [ + { + "bbox": [ + 66, + 217, + 295, + 228 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {q} = \\mathbf {a} + \\operatorname {S A} (\\mathbf {a}, \\mathbf {a}, \\mathbf {a}) + \\operatorname {C A} (\\mathbf {a}, \\mathbf {v}, \\mathbf {v}) + \\operatorname {C A} (\\mathbf {a}, q _ {w}, q _ {w}). \\tag {2}", + "image_path": "6e0f7382de97945cbd23e4a9cd97e11ce78c8cf39c40f4197b12057b40ffbe0e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "text", + "content": "The result is two question-aligned multimodal features, " + }, + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_q = \\{v_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "text", + "content": " for visual and " + }, + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_q = \\{a_q^t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 55, + 237, + 296, + 322 + ], + "type": "text", + "content": " for audio. Unlike prior approaches that integrate question information only in the final stages, our method introduces question context from the start, allowing QA-TIGER to dynamically refine focus on relevant temporal cues throughout AVQA processing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "text", + "content": "Once the question-aware visual features " + }, + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_q" + }, + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "text", + "content": " and audio features " + }, + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_q" + }, + { + "bbox": [ + 55, + 322, + 296, + 405 + ], + "type": "text", + "content": " are obtained, we further refine the patch-level visual features to align finer spatial details with the question context. This refinement ensures that finer spatial details in the visual data align more closely with the question context embedded in the modality-specific features. The process is formulated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 92, + 415, + 295, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 415, + 295, + 428 + ], + "spans": [ + { + "bbox": [ + 92, + 415, + 295, + 428 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {v} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {v} _ {q}, \\mathbf {p}, \\mathbf {p}), \\tag {3}", + "image_path": "4ce871eda0f95b126fdc6e375e30f53c1882864b4056378f99740c22ecc22af3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 430, + 295, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 430, + 295, + 443 + ], + "spans": [ + { + "bbox": [ + 94, + 430, + 295, + 443 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {a} = \\mathbf {p} + \\operatorname {S A} (\\mathbf {p}, \\mathbf {p}, \\mathbf {p}) + \\operatorname {C A} (\\mathbf {a} _ {q}, \\mathbf {p}, \\mathbf {p}). \\tag {4}", + "image_path": "3e3bb9bb3008d35235d546ea5b81f8e498930d0e768247d771084635ef484968.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 450, + 277, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 277, + 463 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 277, + 463 + ], + "type": "text", + "content": "3.3. Temporal Integration of Gaussian Experts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 468, + 296, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 296, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 296, + 528 + ], + "type": "text", + "content": "To capture temporal dependencies in the video, we leverage the Mixture of Experts (MoE) framework [32], integrating multiple Gaussian distributions across the timeline. This approach enables the model to focus on distinct temporal segments relevant to the question." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "content": "Gaussian Generation. To produce question-relevant Gaussian distributions, we first generate a condensed, question-focused representation for each modality. This process aligns the visual and audio features with the question, to capture the temporal relevance of frames in both modalities. Using a cross-attention mechanism, we apply the sentence-level question feature " + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "inline_equation", + "content": "q_{s}" + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "content": " to the question-aware features " + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_q" + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_q" + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "content": ", yielding " + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 528, + 296, + 635 + ], + "type": "text", + "content": "-dimensional aggregated representations for each modality:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 81, + 643, + 295, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 643, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 81, + 643, + 295, + 658 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {v} _ {q}, \\mathbf {v} _ {q}\\right), \\quad \\mathbf {a} _ {q} ^ {\\prime} = \\operatorname {C A} \\left(q _ {s}, \\mathbf {a} _ {q}, \\mathbf {a} _ {q}\\right). \\tag {5}", + "image_path": "2d34d267abf2eb467013fb1154cbaad5ac06673b6f2d669ad35f46023e7afaea.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "In contrast to prior work [39], which used a single Gaussian mask across the temporal domain, we generate multiple Gaussian distributions to capture a broader range of key frames, especially in cases where temporal variations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "text", + "content": "are complex and challenging. The Gaussian distributions " + }, + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = \\{g^{i}\\}_{i = 1}^{E}" + }, + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "text", + "content": " represent distinct temporal segments relevant to the question, where " + }, + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 72, + 554, + 122 + ], + "type": "text", + "content": " is the total number of Gaussian experts (i.e., Gaussian distributions):" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 344, + 133, + 555, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 133, + 555, + 148 + ], + "spans": [ + { + "bbox": [ + 344, + 133, + 555, + 148 + ], + "type": "interline_equation", + "content": "\\mathbf {g} _ {v} = \\mathcal {N} \\big (\\mu_ {v} ^ {i}, (\\sigma_ {v} ^ {i}) ^ {2} \\big), \\quad \\mathbf {g} _ {a} = \\mathcal {N} \\big (\\mu_ {a} ^ {i}, (\\sigma_ {a} ^ {i}) ^ {2} \\big). \\qquad (6)", + "image_path": "b8e6a77d942bccaf30e7d6239ebd3375efbbc7d47b9e1901f778b98a0cdc4c5d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "spans": [ + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "inline_equation", + "content": "\\{\\mu^i\\}_{i=1}^E" + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "inline_equation", + "content": "\\{\\sigma^i\\}_{i=1}^E" + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "text", + "content": " denote the Gaussian centers and standard deviations, generated through a linear layer with an input dimension of " + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 160, + 555, + 269 + ], + "type": "text", + "content": " and an output dimension of two. To minimize conflicts across time segments and enhance temporal focus, the Gaussian centers are distributed along the timeline, with a predicted offset by a linear layer added to the initial centers. This ensures that each expert mainly covers a distinct segment, aligning with question-relevant frames and reducing redundancy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 270, + 554, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 554, + 377 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 554, + 377 + ], + "type": "text", + "content": "Integrating Temporal Information. To selectively capture relevant segments over time, we adapt the MoE framework, which combines multiple specialized \"experts,\" each trained to focus on specific temporal patterns. Instead of selecting discrete experts, our model adjusts the influence of each expert based on their context-dependent weights. These experts act as Gaussian distributions along the timeline, providing soft masks that help capture temporal dependencies in alignment with the question." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "content": "The router assigns routing values " + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_v = \\{r_v^i\\}_{i=1}^E" + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_a = \\{r_a^i\\}_{i=1}^E" + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "content": " for each expert based on the cross-attention outputs " + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_q'" + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_q'" + }, + { + "bbox": [ + 313, + 378, + 554, + 417 + ], + "type": "text", + "content": ", respectively:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 323, + 427, + 554, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 427, + 554, + 442 + ], + "spans": [ + { + "bbox": [ + 323, + 427, + 554, + 442 + ], + "type": "interline_equation", + "content": "\\mathbf {r} _ {v} = \\operatorname {S o f t m a x} \\left(\\mathbf {v} _ {q} ^ {\\prime} \\cdot W\\right), \\quad \\mathbf {r} _ {a} = \\operatorname {S o f t m a x} \\left(\\mathbf {a} _ {q} ^ {\\prime} \\cdot W\\right), \\tag {7}", + "image_path": "1bf57dc4c01d2cd144d310b2876d9d7f1ca1044b7e0c6010e4b5eace8b21b962.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 453, + 554, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 554, + 549 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 554, + 549 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 453, + 554, + 549 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{D \\times E}" + }, + { + "bbox": [ + 313, + 453, + 554, + 549 + ], + "type": "text", + "content": " is a learnable weight matrix that dynamically controls the influence of each expert. The resulting expert weights allow the model to emphasize question-relevant time segments more effectively. The outputs from all experts are then combined through a weighted summation, producing a temporally integrated representation that captures question-specific insights across frames. This integration is expressed as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 330, + 562, + 555, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 562, + 555, + 576 + ], + "spans": [ + { + "bbox": [ + 330, + 562, + 555, + 576 + ], + "type": "interline_equation", + "content": "\\tilde {v} _ {p _ {v}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {v}), \\quad \\tilde {v} _ {p _ {a}} = \\mathcal {G} _ {v} (\\mathbf {p} _ {a}), \\quad \\tilde {a} = \\mathcal {G} _ {a} (\\mathbf {a} _ {q}), \\tag {8}", + "image_path": "65347e4ccb6b25685000809d2e9d9491de1485510d5d82974032d2f084274043.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 356, + 577, + 554, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 577, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 356, + 577, + 554, + 594 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\mathcal {G} _ {m} (x) = \\sum_ {i = 1} ^ {E} g _ {m} ^ {i} r _ {m} ^ {i} \\mathcal {E} _ {m} ^ {i} (x). \\tag {9}", + "image_path": "3cf5e1723cf9fe188482af9ee6a5848cf09cddee2b119a8f5d37e92dd605e276.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": "In this setup, " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_m^i (x)" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": " represents the output of the " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": "-th expert for input " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": ". The temporal visual features " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{v}_{p_v} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{v}_{p_a} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": " are derived by applying the experts to modality-specific patch features " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_v" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_a" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": ", respectively. Similarly, the temporal audio feature " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{a} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": " is obtained by applying experts to the question-aware audio feature " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_q" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": ". This arrangement allows the model to maintain temporal coherence, aligning with question-relevant segments and minimizing redundancy." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13684" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 282, + 85 + ], + "type": "text", + "content": "3.4. Question-Guided Reasoning and Prediction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 173 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 173 + ], + "type": "text", + "content": "The question-guided reasoning module combines audio and visual features from the temporal integration module, allowing the model to evaluate each input's importance in relation to the question context. To ensure a balanced representation, we use averaged features as a residual connection, preventing over-reliance on any single input type. First, the final visual feature " + }, + { + "bbox": [ + 55, + 89, + 296, + 173 + ], + "type": "inline_equation", + "content": "F_{v} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 55, + 89, + 296, + 173 + ], + "type": "text", + "content": " is obtained as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 178, + 295, + 194 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 178, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 61, + 178, + 295, + 194 + ], + "type": "interline_equation", + "content": "F _ {v} = \\operatorname {A v g} \\left(\\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}}\\right) + \\mathrm {C A} \\left(q _ {s}, \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right], \\left[ \\tilde {v} _ {p _ {a}}, \\tilde {v} _ {p _ {v}} \\right]\\right), \\tag {10}", + "image_path": "04d1373da78cb6af3838fda54021337812589e1217fef66ce9db2cc790e2df4c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "inline_equation", + "content": "[\\cdot, \\cdot]" + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "content": " denotes concatenation. This process yields a question-aligned visual feature that balances information across both temporal visual representations. Next, the final audio-visual representation " + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "inline_equation", + "content": "F_{va} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "content": " is obtained by fusing the temporal audio feature " + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "inline_equation", + "content": "\\tilde{a}" + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "inline_equation", + "content": "F_{v}" + }, + { + "bbox": [ + 55, + 198, + 296, + 259 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 74, + 265, + 295, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 265, + 295, + 279 + ], + "spans": [ + { + "bbox": [ + 74, + 265, + 295, + 279 + ], + "type": "interline_equation", + "content": "F _ {v a} = \\operatorname {A v g} \\left(\\tilde {a}, F _ {v}\\right) + \\operatorname {C A} \\left(q _ {s}, \\left[ \\tilde {a}, F _ {v} \\right], \\left[ \\tilde {a}, F _ {v} \\right]\\right). \\tag {11}", + "image_path": "99763ab41faca742488b79b3122cb2852b754c8b4d80791953be88aae9dddf46.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": "This step ensures that both audio and visual features contribute to the final representation in a question-aware manner. Finally, answer prediction is performed by applying a linear layer and a Softmax layer to " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "F_{va}" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " yielding probabilities over " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": " answer choices. The model is trained using cross-entropy loss: " + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{qa} = -\\sum_{c=1}^{C} y_c \\log \\mathcal{P}_c" + }, + { + "bbox": [ + 55, + 285, + 296, + 369 + ], + "type": "text", + "content": ", with the answer selected as the class with the highest probability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 137, + 392 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 397, + 118, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 397, + 118, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 397, + 118, + 409 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 415, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 296, + 534 + ], + "type": "text", + "content": "Our experiments utilize the MUSIC-AVQA [16], MUSIC-AVQA-R [28], and MUSIC-AVQA-v2.0 [26] datasets. MUSIC-AVQA serves as a benchmark for audio-visual reasoning over 22 instruments, with questions spanning audio-only, visual-only, and audio-visual modalities, covering reasoning types like existence, location, and temporal aspects. MUSIC-AVQA-R focuses on rare and out-of-distribution samples to assess model robustness. MUSIC-AVQA-v2.0 addresses dataset biases by enhancing diversity in ensemble scenes and multi-instrument cases." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 540, + 188, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 188, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 188, + 553 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": "The video is sampled at 1 fps, with audio features extracted using VGGish [11], while visual features and questions are processed using the CLIP-ViT-L/14 [30] model. Token reduction is applied to visual features using ToMe [2] technique. To ensure consistency, all features are linearly transformed to 512 dimensions. Further details on the feature extraction process are provided in the supplementary materials. We set the expert number to 7 and configure every attention module with 8 heads with 0.1 dropout probability. The model is trained with the Adam optimizer at an initial learning rate of 1e-4, which decays by a factor of 0.1 every 8 epochs. Training is conducted for 15 epochs with a batch size of 32 on a single NVIDIA RTX A6000." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 72, + 554, + 107 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 554, + 107 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 554, + 107 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 554, + 107 + ], + "type": "table", + "html": "
Dataset# Videos# Train QA# Valid QA# Test QA
MUSIC-AVQA [16]9,28831,9044,5689,129
MUSIC-AVQA-R [28]9,288--211,572
MUSIC-AVQA-v2.0 [26]10,49237,4085,34610,819
", + "image_path": "0010469d71b339917f48f3685292a2262eb068e49ba7c5f4e63607236a9f71fd.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 110, + 555, + 133 + ], + "lines": [ + { + "bbox": [ + 313, + 110, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 110, + 555, + 133 + ], + "type": "text", + "content": "Table 1. Summary of MUSIC-AVQA, MUSIC-AVQA-R, and MUSIC-AVQA-v2.0 datasets with the number of QA pairs." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 148, + 495, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 148, + 495, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 148, + 495, + 162 + ], + "type": "text", + "content": "4.3. Quantitative Results and Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 167, + 555, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 167, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 555, + 275 + ], + "type": "text", + "content": "To evaluate our model's effectiveness, we compared QA-TIGER to existing AVQA methods on Audio (A-QA), Visual (V-QA), and Audio-Visual (AV-QA) tasks, considering both question types and overall averages. QA-TIGER was trained on the MUSIC-AVQA [16] training set and validated using its validation set for testing both MUSIC-AVQA [16] and MUSIC-AVQA-R [28]. For MUSIC-AVQA-v2.0 [26], QA-TIGER was trained on both the balanced and biased training sets and tested accordingly." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "content": "MUSIC-AVQA. QA-TIGER achieves the highest performance among all models, with an overall accuracy " + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "inline_equation", + "content": "(77.62\\%)" + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "content": ", surpassing the previous best method " + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "inline_equation", + "content": "(76.79\\%)" + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "content": ", TSPM [19], in Table 2. Notably, our model shows strong performance in complex reasoning tasks, achieving " + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "inline_equation", + "content": "78.58\\%" + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "inline_equation", + "content": "72.50\\%" + }, + { + "bbox": [ + 313, + 275, + 554, + 361 + ], + "type": "text", + "content": " in AV-Counting and AV-Local categories respectively, surpassing previous methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 361, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 555, + 433 + ], + "type": "text", + "content": "MUSIC-AVQA-R. Our method achieves " + }, + { + "bbox": [ + 313, + 361, + 555, + 433 + ], + "type": "inline_equation", + "content": "67.99\\%" + }, + { + "bbox": [ + 313, + 361, + 555, + 433 + ], + "type": "text", + "content": " overall accuracy on the MUSIC-AVQA-R dataset across diverse question types, as shown in Table 3, without the need for explicit bias handling techniques. This balanced performance highlights QA-TIGER's strong temporal modeling and question-aware feature extraction capabilities." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "text", + "content": "MUSIC-AVQA-v2.0. QA-TIGER consistently outperforms existing models [16, 24, 28] on the biased test set, regardless of the training set type (Table 4a). On the balanced test set (Table 4b), QA-TIGER trained on the balanced dataset achieves superior accuracy in both " + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "inline_equation", + "content": "A - QA" + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "text", + "content": " (79.90%) and " + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "inline_equation", + "content": "V - QA" + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "text", + "content": " (86.95%), surpassing LAST-Att in overall accuracy (75.44% vs. 76.43%). Notably, LAST-Att underperforms in " + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "inline_equation", + "content": "A - QA" + }, + { + "bbox": [ + 313, + 433, + 555, + 553 + ], + "type": "text", + "content": " despite incorporating an additional audio encoder, Audio Spectrogram Transformer [9]. This highlights QA-TIGER's robustness across diverse evaluation settings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 553, + 554, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 553, + 554, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 553, + 554, + 650 + ], + "type": "text", + "content": "Inference Time. We compare inference time between TSPM and QA-TIGER under identical conditions, using the full pipeline setup with CLIP and VGGish. TSPM records 1.767 seconds, while QA-TIGER achieves a comparable time of 1.737 seconds. Despite processing full temporal information, QA-TIGER matches TSPM's efficiency—which selects Top-K frames—demonstrating its ability to handle temporal dynamics without added overhead." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 659, + 531, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 531, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 531, + 672 + ], + "type": "text", + "content": "4.4. Qualitative Results of Temporal Gaussian" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 714 + ], + "type": "text", + "content": "To evaluate whether QA-TIGER accurately identifies question-relevant temporal segments, we qualitatively analyze its performance in Figure 3. Notably, the audio Gaus" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13685" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 72, + 555, + 238 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 555, + 238 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 555, + 238 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 555, + 238 + ], + "type": "table", + "html": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompAvgCountLocalAvgExistCountLocalCompTempAvg
FCNLSTM [10]70.4566.2268.8863.8946.7455.2182.0159.3446.2862.1547.3360.0660.34
BiLSTM [38]70.3547.9262.0564.6464.3364.4878.3956.9145.8553.0949.7657.1059.92
HCAtn [27]70.2554.9164.5764.0566.3765.2279.1059.9749.5155.2556.4360.1962.30
MCAN [43]77.5055.2469.2571.5670.9371.2480.4064.9154.4857.2247.5761.5865.49
PSAC [22]75.6466.0672.0968.6469.7969.2277.5963.4255.0261.1759.4763.5266.54
HME [1]74.7663.5670.6167.9769.4668.7680.3063.1953.1862.6959.8364.0566.45
HCRN [15]68.5950.9262.0564.3961.8163.0854.4753.3841.5352.1147.6950.2655.73
AVSD [31]72.4161.9068.5267.3974.1970.8381.6163.8958.7961.5261.4165.4967.44
Pano-AVQA [46]74.3664.5670.7369.3975.6572.5681.2164.9159.3364.2263.2366.6468.93
ST-AVQA [16]78.1867.0574.0671.5676.3874.0081.8170.8064.5166.0163.2369.5471.52
COCA [14]79.3567.6875.4275.1075.4375.2383.5066.6369.7264.1265.5769.9672.33
PSTP-Net [17]73.9765.5970.9177.1577.3677.2676.1872.2371.8071.7969.0072.5773.52
LAVISH [24]82.0965.5675.9778.9881.4380.2281.7175.5166.1363.7767.9671.2674.46
APL [23]82.4070.7178.0976.5282.7479.6982.9973.2966.6864.7665.9570.9674.53
TSPM [19]84.0764.6576.9182.2984.9083.6182.1976.2171.8565.7671.1773.5176.79
QA-TIGER84.8667.8578.5883.9686.2985.1483.1078.5872.5063.9469.5973.7477.62
", + "image_path": "62a859c7bedf0ffec19b4ae87ba6ddbb33bc1188e1bb9349e5a9d6afa5d2dda8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 259, + 555, + 420 + ], + "blocks": [ + { + "bbox": [ + 125, + 243, + 485, + 255 + ], + "lines": [ + { + "bbox": [ + 125, + 243, + 485, + 255 + ], + "spans": [ + { + "bbox": [ + 125, + 243, + 485, + 255 + ], + "type": "text", + "content": "Table 2. Experimental results (%) on the MUSIC-AVQA test set. The top-2 results are highlighted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 259, + 555, + 420 + ], + "lines": [ + { + "bbox": [ + 56, + 259, + 555, + 420 + ], + "spans": [ + { + "bbox": [ + 56, + 259, + 555, + 420 + ], + "type": "table", + "html": "
MethodAudio QAVisual QAAudio-Visual QAAvg
CountCompCountLocalExistCountLocalCompTemp
HTHTHTHTHTHTHTHTHT
FCNLSTM [10]66.2336.4864.7851.2461.755.3154.8651.0664.7678.5262.697.2346.6657.3043.1371.6737.0230.7854.12
BiLSTM [38]73.6846.3221.5177.5864.300.0053.9242.0187.5121.1462.852.1835.1643.7527.6174.3817.5831.3248.84
HCAtnn [27]61.6741.6359.0947.1456.529.2067.0153.1666.5761.1359.5312.4837.0542.4848.8160.1233.8239.2651.90
MCAN [43]75.0260.1658.8950.0964.5826.6966.4862.2551.2967.2964.7625.2846.1161.6150.5752.4034.6458.0557.27
PSAC [22]53.0156.6857.4148.1249.5526.4372.9660.6950.5655.5456.7019.5841.9852.3038.1358.9226.6846.2450.45
HME [1]62.6053.9554.9758.2950.9516.4673.2558.6065.7466.4963.1817.1833.7946.0353.2069.5733.9541.5753.66
HCRN [15]55.5353.3147.1732.4441.8723.5539.4051.2741.8165.4554.5819.5736.6242.7233.3336.8740.4744.1343.92
AVSD [31]54.0047.8460.6147.7960.3410.0774.7861.4366.2861.9846.218.0633.0040.3551.9866.0040.1441.5252.33
Pano-AVQA [46]50.5743.4550.7844.9347.2815.5067.1965.5152.3722.0452.2121.5244.3561.6945.6140.4935.0049.3347.40
ST-AVQA [16]56.4041.4862.2857.5959.8612.9463.3154.0073.3577.2648.318.4135.3540.4953.3062.4440.2538.1552.80
LAVISH [24]61.7343.9965.0660.3865.5311.1370.2164.7377.8379.4649.8814.8741.7641.2059.2665.1041.8446.2657.63
TSPM† [19]81.6571.8067.6649.5678.2947.5680.5873.1869.1582.7977.0938.6442.2457.3752.0768.8639.2349.3666.30
QA-TIGER82.6775.8271.7543.1181.3054.5984.7675.5972.8478.5676.7033.5548.2264.6537.5580.4736.8562.9667.99
", + "image_path": "8ff6712261f6cc4842b0babcb2073c0d9104a8832fd5f73823cbc15a48a6a3d9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 56, + 464, + 294, + 552 + ], + "blocks": [ + { + "bbox": [ + 55, + 427, + 555, + 451 + ], + "lines": [ + { + "bbox": [ + 55, + 427, + 555, + 451 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 555, + 451 + ], + "type": "text", + "content": "Table 3. Experimental results (%) on the MUSIC-AVQA-R test set, with H and T representing performance on Head (frequent) and Tail (rare) answer categories, respectively. † indicates results reproduced using official codes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 464, + 294, + 552 + ], + "lines": [ + { + "bbox": [ + 56, + 464, + 294, + 552 + ], + "spans": [ + { + "bbox": [ + 56, + 464, + 294, + 552 + ], + "type": "table", + "html": "
TestTrainingMethodA-QAV-QAAV-QAAvg
(a) BiasBiasST-AVQA [16]76.8677.7069.5973.07
LAVISH [24]76.7380.9670.8074.59
QA-TIGER79.1384.8372.3776.93
BalanceST-AVQA [16]76.1877.2067.9671.92
LAVISH [24]75.5680.8369.2773.51
LAST [26]77.1082.9970.8675.24
LAST-Att [26]77.2983.4771.0575.45
QA-TIGER77.0785.9371.2076.57
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TestTrainingMethodA-QAV-QAAV-QAAvg
(b) BalanceBiasST-AVQA [16]73.3476.8264.5169.40
LAVISH [24]73.1479.7065.0170.39
QA-TIGER77.5784.8467.4373.91
BalanceST-AVQA [16]75.5077.6766.3271.02
LAVISH [24]76.1581.3268.2873.18
LAST [26]78.0883.2969.7274.85
LAST-Att [26]78.5684.0770.3075.44
QA-TIGER79.9086.9570.2276.43
", + "image_path": "eb35525dea91cfb4755f2bb55bf3b882d72aca1aa907717ee4b5de845582fddb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 659, + 296, + 715 + ], + "lines": [ + { + "bbox": [ + 55, + 659, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 296, + 715 + ], + "type": "text", + "content": "Table 4. Experimental results (\\%) on the MUSIC-AVQA-v2.0 for (a) bias and (b) balanced test sets. Each evaluation is conducted with models trained on bias and balanced training sets, respectively. The performance of other methods was referenced from the scores provided by MUSIC-AVQA-v2.0." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 465, + 555, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 465, + 555, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 465, + 555, + 538 + ], + "type": "text", + "content": "sian aligns more with A-QA in Figure 3a, while the visual Gaussian is more prominent for V-QA in Figure 3b. For AV-QA, both modalities show similar Gaussian distributions in Figure 3c, demonstrating the model's adaptive focus based on question type. A detailed comparison with uniform sampling and Top-K selection is provided in the supplementary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 541, + 556, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 541, + 556, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 541, + 556, + 650 + ], + "type": "text", + "content": "Audio Question. QA-TIGER demonstrates its ability to handle temporal reasoning. For the question \"Is the tuba playing longer than the clarinet?\", QA-TIGER's audio Gaussian assigns high weights across the entire durations, effectively capturing the complete temporal spans essential for accurately comparing the two instruments in the question. The visual Gaussian similarly focuses on frames where the tuba and clarinet are actively played, supporting a robust comparison of their durations, as shown in Figure 3a." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": "Visual Question. Our method effectively integrates both visual and audio modalities to accurately count the saxophones, in Figure 3b. The visual Gaussian assigns higher weights to frames where all five saxophonists are clearly visible from the front, while frames with less distinct views," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "13686" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 137 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 137 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 137 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 137 + ], + "type": "image", + "image_path": "6b0c8f44a888a9a6b1a04e508955d957b1f98aeda081d966546251e122914fff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 273, + 138, + 337, + 147 + ], + "lines": [ + { + "bbox": [ + 273, + 138, + 337, + 147 + ], + "spans": [ + { + "bbox": [ + 273, + 138, + 337, + 147 + ], + "type": "text", + "content": "(a) Audio Question" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 57, + 148, + 553, + 213 + ], + "blocks": [ + { + "bbox": [ + 57, + 148, + 553, + 213 + ], + "lines": [ + { + "bbox": [ + 57, + 148, + 553, + 213 + ], + "spans": [ + { + "bbox": [ + 57, + 148, + 553, + 213 + ], + "type": "image", + "image_path": "5706d3226506819465300768fe60c06b0b88a58d2c410a3a98c2ddbebe2ab2d8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 273, + 214, + 337, + 224 + ], + "lines": [ + { + "bbox": [ + 273, + 214, + 337, + 224 + ], + "spans": [ + { + "bbox": [ + 273, + 214, + 337, + 224 + ], + "type": "text", + "content": "(b) Visual Question" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 58, + 225, + 553, + 289 + ], + "blocks": [ + { + "bbox": [ + 58, + 225, + 553, + 289 + ], + "lines": [ + { + "bbox": [ + 58, + 225, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 58, + 225, + 553, + 289 + ], + "type": "image", + "image_path": "fb4c2b28f989f0cdf3b77cdef41ca18a6ec46f66bc713ba301ee7937a97aa656.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 262, + 291, + 348, + 300 + ], + "lines": [ + { + "bbox": [ + 262, + 291, + 348, + 300 + ], + "spans": [ + { + "bbox": [ + 262, + 291, + 348, + 300 + ], + "type": "text", + "content": "(c) Audio-Visual Question" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 335, + 295, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 335, + 295, + 407 + ], + "spans": [ + { + "bbox": [ + 54, + 335, + 295, + 407 + ], + "type": "text", + "content": "such as side angles or wide shots, are assigned lower weights. Meanwhile, the audio Gaussian emphasizes moments when the sounds of all five saxophones overlap, focusing on their simultaneous performance. This integration allows the model to concentrate on the most critical visual and auditory cues to predict the accurate answer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 407, + 295, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 407, + 295, + 503 + ], + "spans": [ + { + "bbox": [ + 54, + 407, + 295, + 503 + ], + "type": "text", + "content": "Audio-Visual Question. The visual Gaussian effectively focuses on frames in the early part of the video where individual instrument appear, as well as frames where all three instruments are shown together. Correspondingly, the audio Gaussian emphasizes prominent instrument sounds. This complementary alignment enables QA-TIGER to integrate visual and auditory cues effectively, resulting in accurate identification of all instruments, as shown in Figure 3c." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 514, + 263, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 263, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 263, + 526 + ], + "type": "text", + "content": "4.5. Visualization of Question-Aware Fusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "content": "To validate the effectiveness of our question-aware fusion module, we performed word-level visualizations. Additional examples are provided in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 568, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 295, + 664 + ], + "type": "text", + "content": "\"Are there saxophone and piano sound\": In the visual modality, attention initially focuses on \"piano,\" where visual cues are subtle, then shifts to the more distinct \"saxophone.\" In the audio modality, attention consistently highlights \"piano,\" compensating for the limited visual cues, while \"saxophone,\" is primarily processed visually. This shows how QA-TIGER adapts to question context, effectively distributing attention across both modalities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "\"How many sounding saxophone in the video\": In the visual modality, attention focuses on \"saxophone,\" aiding in counting. In the audio modality, attention highlights \"sounding,\" and \"saxophone,\" to capture the auditory cues" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 316, + 332, + 555, + 487 + ], + "blocks": [ + { + "bbox": [ + 114, + 308, + 495, + 319 + ], + "lines": [ + { + "bbox": [ + 114, + 308, + 495, + 319 + ], + "spans": [ + { + "bbox": [ + 114, + 308, + 495, + 319 + ], + "type": "text", + "content": "Figure 3. Qualitative results by question type of the proposed QA-TIGER on the MUSIC-AVQA test set." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 316, + 332, + 555, + 487 + ], + "lines": [ + { + "bbox": [ + 316, + 332, + 555, + 487 + ], + "spans": [ + { + "bbox": [ + 316, + 332, + 555, + 487 + ], + "type": "image", + "image_path": "0a3504f0893ddc09702f7af0d15af5c70b9bb3010b24d5e577ebbc139bb37dc8.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 496, + 555, + 540 + ], + "lines": [ + { + "bbox": [ + 313, + 496, + 555, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 555, + 540 + ], + "type": "text", + "content": "Figure 4. Question-aware attention for visual (upper) and audio (lower) fusion in response to two different questions for the same video and audio input. The attention intensity is indicated by the color scale on the right." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 548, + 504, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 504, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 504, + 559 + ], + "type": "text", + "content": "necessary for counting saxophone occurrences." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 560, + 554, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 554, + 632 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 554, + 632 + ], + "type": "text", + "content": "These results demonstrate how the question-aware fusion module dynamically adapts to different questions. By emphasizing question-relevant elements in both modalities, QA-TIGER progressively refines its focus, improving accuracy and ensuring alignment with task demands throughout the reasoning process." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 641, + 421, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 421, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 421, + 654 + ], + "type": "text", + "content": "5. In-depth Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 658, + 408, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 408, + 671 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 408, + 671 + ], + "type": "text", + "content": "5.1. Ablation Study" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "We evaluated our proposed modules on MUSIC-AVQA (Table 5). The baseline model used uniform sampling and achieved reasonable accuracy. Adding the Gaussian Ex" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13687" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 71, + 295, + 135 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 295, + 135 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 295, + 135 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 295, + 135 + ], + "type": "table", + "html": "
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", + "image_path": "86c1f811f47acfa598f7b1b5e253e0747be799a15de1c46316bf5b5aca3607ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 144, + 270, + 156 + ], + "lines": [ + { + "bbox": [ + 80, + 144, + 270, + 156 + ], + "spans": [ + { + "bbox": [ + 80, + 144, + 270, + 156 + ], + "type": "text", + "content": "Table 5. Ablation study of the proposed framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 171, + 295, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 171, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 54, + 171, + 295, + 316 + ], + "type": "text", + "content": "perts module improved performance by enhancing temporal modeling through specialized experts. The Question-Aware Fusion module alone also contributed a notable improvement. Combining both modules led to the best performance, demonstrating the synergistic benefits of integrating question context early on. This integration enriches the temporal context for the Gaussian Experts module, highlighting the complementary strengths of both modules in enhancing temporal reasoning. Without Question-Aware Fusion, question features were incorporated only at the final stage, as in prior work [12, 16, 24]. For setups excluding Gaussian Experts, uniform sampling was applied." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 322, + 157, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 322, + 157, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 157, + 335 + ], + "type": "text", + "content": "5.2. Frame Sampling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 340, + 295, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 340, + 295, + 388 + ], + "spans": [ + { + "bbox": [ + 55, + 340, + 295, + 388 + ], + "type": "text", + "content": "We evaluated conventional sampling strategies and Gaussian modeling designs for AVQA tasks (Figure 5). Note that all experiments compare only the frame sampling part after applying the proposed Question-Aware Fusion." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 388, + 295, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 459 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 459 + ], + "type": "text", + "content": "Sampling-based Methods. Uniform sampling at fixed intervals was less effective due to its lack of focus on question-relevant frames. The Top-K method, using the frame selection module from TSPM [19], improved performance by selecting question-relevant frames but lacked comprehensive temporal context." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 460, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 295, + 593 + ], + "type": "text", + "content": "Gaussian-based Methods. We explore various Gaussian-based methods to model temporal dependencies. Gaussian, a simple sum of Gaussians, shows similar performance to uniform sampling. Weighted-Gaussian introduces dynamic weighting but still struggles with overlap. By adding disjoint center constraints, Weighted-Gaussian (Disjoint Center) reduces redundancy and improves accuracy. Building on this, Gaussian Experts extends the Weighted-Gaussian (Disjoint Center) approach with a MoE framework, dynamically assigning specialized experts to distinct temporal segments, resulting in the highest accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 600, + 171, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 171, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 171, + 613 + ], + "type": "text", + "content": "5.3. Selection of Experts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": "In this analysis, we explored the impact of expert selection in the proposed MoE approach. The decision to activate all seven experts stems from the observed performance gains as more experts are used. Even with the fewest experts, the model outperforms the current state-of-the-art TSPM [19] " + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "inline_equation", + "content": "(76.79\\%)" + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": " on the MUSIC-AVQA [16] dataset, as shown in Figure 6. Using all seven experts achieves the highest accuracy " + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "inline_equation", + "content": "(77.62\\%)" + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": ", showcasing the superiority of QA-TIGER." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 326, + 71, + 542, + 188 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 542, + 188 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 542, + 188 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 542, + 188 + ], + "type": "image", + "image_path": "345240f7ebdf49a7fa052f0a8bc75649cc5880e83b06f162e48ecc0b18fe996b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 195, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 313, + 195, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 195, + 555, + 240 + ], + "type": "text", + "content": "Figure 5. Comparison of temporal selection methods based on the number of criteria (Gaussian or K). Gaussian-based methods use a simple summation for temporal aggregation. \"W\" refers to \"Weighted sum,\" and \"D.C.\" stands for \"Disjoint Center.\"" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 344, + 251, + 525, + 347 + ], + "blocks": [ + { + "bbox": [ + 344, + 251, + 525, + 347 + ], + "lines": [ + { + "bbox": [ + 344, + 251, + 525, + 347 + ], + "spans": [ + { + "bbox": [ + 344, + 251, + 525, + 347 + ], + "type": "image", + "image_path": "c522af42b522b67c5cb4f5195d4b5dab1091d1808cbf8e0b41039de6c73feed6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 353, + 538, + 365 + ], + "lines": [ + { + "bbox": [ + 329, + 353, + 538, + 365 + ], + "spans": [ + { + "bbox": [ + 329, + 353, + 538, + 365 + ], + "type": "text", + "content": "Figure 6. Impact of expert selection on Gaussian experts." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 384, + 388, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 384, + 388, + 398 + ], + "spans": [ + { + "bbox": [ + 314, + 384, + 388, + 398 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 407, + 555, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 601 + ], + "type": "text", + "content": "We have introduced QA-TIGER, designed to overcome the limitations of prior methods in handling complex temporal dynamics and question-specific feature integration. By leveraging multi-Gaussian modeling within the MoE framework, QA-TIGER adaptively captures subtle temporal dependencies while minimizing redundancy through strategically positioned Gaussian centers. We also incorporate question context explicitly from the encoding stages, ensuring that question information is gradually refined throughout the processing pipeline. Extensive experiments demonstrate QA-TIGER's state-of-the-art performance on various datasets, highlighting its effectiveness in tackling the continuous temporal domain and complex AVQA challenges. Future work could explore adaptive expert selection mechanisms in MoE-based AVQA, tailored to different question types, to further enhance the model's generalizability." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Acknowledgement. This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00211348). This research was partly supported by the MSIT(Ministry of Science, ICT), Korea, under the Global Research Support Program in the Digital Field program)(RS-2024-00425354) supervised by the IITP(Institute for Information & Communications Technology Planning & Evaluation)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13688" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Chenyou Fan abd Xiaofan Zhang, Shu Zhang, Wensheng Wang, Chi Zhang, and Heng Huang. 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In AAAI, pages 12870-12877, 2020." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13690" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_content_list.json b/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..45425526db408202671c1a5bdba162967b1c762e --- /dev/null +++ b/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_content_list.json @@ -0,0 +1,1668 @@ +[ + { + "type": "text", + "text": "R-SCoRe: Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization", + "text_level": 1, + "bbox": [ + 124, + 128, + 875, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xudong Jiang $^{1}$ Fangjinhua Wang $^{1*}$ Silvano Galliani $^{2}$ Christoph Vogel $^{2}$ Marc Pollefeys $^{1,2}$ $^{1}$ Department of Computer Science, ETH Zurich \n $^{2}$ Microsoft Spatial AI Lab, Zurich", + "bbox": [ + 112, + 200, + 883, + 257 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0f5d8c6828655ff0ad6f420d18cfb6e314fcaf59d6eac377a1a8a195fddc5701.jpg", + "image_caption": [ + "Figure 1. Robust Visual Localization with R-SCoRe. Left: Point cloud of Aachen reconstructed by R-SCoRe. Right: On the large-scale Aachen Day-Night dataset [53, 56] using only daytime training images, R-SCoRe achieves $64.3\\%$ accuracy under the $(0.25\\mathrm{m}, 2^{\\circ})$ threshold for nighttime query images. It outperforms all previous SCR methods (circles) by a large margin. With a small map size of only 47MB at a comparable accuracy, R-SCoRe is an attractive alternative to traditional methods (triangles)." + ], + "image_footnote": [], + "bbox": [ + 112, + 266, + 580, + 489 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/20fb06e95c80d98f4604111579162b4b5839caa4581013fca60c3a25bda18fff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 266, + 883, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 575, + 328, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning-based visual localization methods that use scene coordinate regression (SCR) offer the advantage of smaller map sizes. However, on datasets with complex illumination changes or image-level ambiguities, it remains a less robust alternative to feature matching methods. This work aims to close the gap. We introduce a covisibility graph-based global encoding learning and data augmentation strategy, along with a depth-adjusted reprojection loss to facilitate implicit triangulation. Additionally, we revisit the network architecture and local feature extraction module. Our method achieves state-of-the-art on challenging large-scale datasets without relying on network ensembles or 3D supervision. On Aachen Day-Night, we are $10 \\times$ more accurate than previous SCR methods with similar map sizes and require at least $5 \\times$ smaller map sizes than any other SCR method while still delivering superior accuracy. Code is available at: https://github.com/cvg/scrstudio.", + "bbox": [ + 89, + 608, + 485, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 575, + 643, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual localization is the task of estimating the 6-DoF pose of a camera in a known scene with a query image. It is a fundamental problem in computer vision, with applications in augmented reality, autonomous driving, and robotics.", + "bbox": [ + 511, + 604, + 906, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Classical feature matching methods [19, 50, 51, 55] have matured through years of research and now provide robust and accurate localization results. However, these methods typically require explicit 3D scene representations, where a large number of descriptors are stored, leading to substantial map sizes, especially for large-scale scenes. In contrast, pose regression [11, 30, 31, 44, 59, 65, 71, 73] and scene coordinate regression (SCR) [4-6, 8, 9, 21, 36, 68] aim to implicitly encode scene information in neural networks.", + "bbox": [ + 509, + 669, + 908, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SCR methods follow a structure-based paradigm similar to feature matching, i.e., estimating pose from 2D-3D correspondences but replacing explicit matching with regressing the correspondences directly. They are usually limited to small scenes [9] and have yet to match feature matching methods in terms of accuracy and robustness. Recent ad", + "bbox": [ + 511, + 809, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author (fangjinhua.wang@inf.ethz.ch).", + "bbox": [ + 107, + 887, + 460, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11536", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vances [68] extend SCR to large-scale scenes using a single model. However, its performance is still not on par with feature matching methods, especially in complex scenes with challenging illumination changes [53, 56].", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we conduct a detailed analysis of the design principles behind the SCR framework, including local and global encoding, network architecture, and training strategies. Based on this analysis, we propose to revisit SCR to enhance the robustness and accuracy of SCR methods for large-scale visual localization tasks. As shown in Fig. 1, our robust SCR (R-SCoRe) improves the night-time localization accuracy for SCR methods to $64.3\\%$ under the $(0.25\\mathrm{m}, 2^{\\circ})$ threshold on the Aachen Day-Night dataset, all with a map size of only 47MB. R-SCoRe significantly outperforms previous SCR methods and achieves accuracy comparable to feature matching techniques.", + "bbox": [ + 88, + 152, + 482, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Tab. 1 summarizes the practicability of R-SCoRe in complex large-scale scenes. While feature matching methods are also accurate, their map size can be prohibitively large, sometimes more than two orders of magnitude [19, 50, 51]. Compared to SCR methods with similarly small map sizes [9, 68], R-SCoRe is at least one order of magnitude more accurate. While we still clearly outperform other SCR methods, we maintain fast inference and significantly smaller map sizes – all without the need for scene-specific depth supervision. Our contributions are as follows.", + "bbox": [ + 89, + 335, + 482, + 486 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose learning a global encoding and performing data augmentation based on the可视ability graph. To address the ambiguity of image retrieval features in complex large-scale scenes, we used multiple global hypotheses during testing.", + "- To bias the network from neglecting near points, we introduce a depth-adjusted reprojection loss and show that this allows for accurate localization without scene-specific ground truth coordinate supervision.", + "- To our knowledge, R-SCoRe is the first attempt of an SCR approach to achieve state-of-the-art performance on complex large-scale scenes without using an ensemble of networks or 3D model supervision." + ], + "bbox": [ + 89, + 488, + 482, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 702, + 232, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Feature Matching. Most state-of-the-art visual localization methods rely on feature matching [19, 50, 51, 55]. These methods typically adopt a structure-based paradigm, establishing 2D-3D correspondences between keypoints in a query image and 3D points in a scene. Camera pose is solved with geometric constraints, often a Perspective-n-Point (PnP) solver [26, 47] within a RANSAC framework [2, 17, 25] to effectively manage outliers. These methods commonly construct a Structure-from-Motion (SfM) map of the scene, which contains both 3D points and their descriptors [19, 22, 24, 49, 58]. To efficiently establish 2D", + "bbox": [ + 89, + 734, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/58107c6dd74507dbf6a3dda162f229c62602593ed7c1a279a2ea8403dae136f9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSizeTimeAcc.w/o Depth
FM[19, 50, 51]X✓✓✓
PR[31]✓✓X✓
SCR[64]XX✓X
[5, 36, 70]X✓✓X
[4, 9, 68]✓✓X✓
R-SCoRe✓✓✓✓
", + "bbox": [ + 516, + 88, + 903, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Comparison with other methods on complex large-scale scenes [53, 56]. Feature matching (FM) methods are accurate but need a large map size. Pose regression (PR) methods are fast but less accurate. We maintain a small map size while achieving remarkable accuracy.", + "bbox": [ + 511, + 233, + 903, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D matches, they often follow a two-level approach [50]. First, potentially relevant database images are retrieved using image retrieval techniques [1, 48, 75]. This is followed by 2D-2D matching with the query image [39, 50, 51].", + "bbox": [ + 511, + 330, + 903, + 391 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, a significant limitation of these methods is the necessity to store all descriptor vectors of the 3D model, which can lead to storage challenges, particularly in large maps. To address this issue, various compression techniques have been proposed. These include reducing the number of 3D points [12, 13, 23, 37, 72] or compressing descriptors [20, 28, 29, 34, 40, 54, 67, 72]. Recently, several studies [46, 69, 74] have proposed alternative approaches that eliminate the need for explicit descriptor storage. Instead, these methods advocate for direct matching against geometric representations, such as point clouds or meshes.", + "bbox": [ + 511, + 391, + 905, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pose Regression. These methods [11, 30, 31, 44, 59, 65, 71, 73] directly estimates the camera pose of a query image with a neural network. However, they tend to struggle with generalization and often only achieve an accuracy similar to image retrieval methods [57].", + "bbox": [ + 511, + 561, + 905, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene Coordinate Regression. Following a similar structure-based localization paradigm as feature matching methods, SCR methods [4-9, 14, 15, 21, 36, 45, 60, 66, 68, 70] regress 2D-3D correspondences between the query image and the scene, and estimate the camera pose using geometric constraints. Though SCR methods are more accurate than pose regression methods, they usually still struggle with large-scale scenes [9].", + "bbox": [ + 511, + 643, + 905, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, several approaches have been proposed to improve the scalability and performance of SCR in large-scale scenes. These methods often rely on ground truth 3D coordinates and aim to handle large scenes by dividing them into smaller segments, such as spatial regions [5], voxels [64], or hierarchical clusters [36, 70]. Recent advancements have explored alternatives that do not require ground truth 3D supervision. For example, ACE [9] uses reprojection loss only for training. GLACE [68] further introduces a global", + "bbox": [ + 511, + 763, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11537", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c9d7b97356fe9828d3f6679a8464d9a0ffde448a8dce5fe916adfdbf5dc2dc2a.jpg", + "image_caption": [ + "Figure 2. R-SCoRe pipeline. (a) Following the SCR workflow in [68], we concatenate patch-level local encodings with image-level global encodings as input to a scene-specific MLP. (b) We learn contrastive global encodings from the可视ability graph using Node2Vec [27]. During training, global encodings are sampled from neighboring nodes for data augmentation. During inference, we retrieve global encodings from the $k$ nearest training images via NetVLAD [1] as hypotheses and select the one yielding the most RANSAC inliers. We enhance the SCR MLP with a refinement module and introduce a depth-adjusted reprojection loss to reduce bias toward distant points." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 911, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "encoding mechanism that eliminates the need for scene segmentation. Despite these improvements, these methods still encounter limitations under challenging conditions, such as significant changes in illumination.", + "bbox": [ + 88, + 321, + 480, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 398, + 181, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our Scene Coordinate Regression (SCR) workflow is depicted in Fig. 2a. During training, we have access to a可视ability graph to learn global encodings which are concatenated to the local encodings. During inference, we retrieve global encoding hypotheses from the $k$ nearest training images and predict 2D-3D correspondences: we run PnP for each hypothesis and select the one yielding the most RANSAC inliers. Fig. 2b illustrates our detailed R-SCoRe pipeline, where we split SCR into coarse and refinement blocks and introduce可视ibility-based global encoding and data augmentation techniques.", + "bbox": [ + 88, + 424, + 483, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 603, + 232, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Localization. Given a test image $I_{\\mathrm{test}}$ with known intrinsic $\\mathbf{K}_{\\mathrm{test}}$ , the goal is to estimate its extrinsic, i.e., the rigid transformation $[\\mathbb{R}_{\\mathrm{test}}|\\mathbf{t}_{\\mathrm{test}}]$ from world coordinate to camera coordinate. The scene is typically given by a set of training images $I_{\\mathrm{train}}$ with known ground truth poses $[\\mathbb{R}_{\\mathrm{train}}|\\mathbf{t}_{\\mathrm{train}}]$ and intrinsics $\\mathbf{K}_{\\mathrm{train}}$ .", + "bbox": [ + 89, + 631, + 483, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene Coordinate Regression. The SCR pipeline employs a neural network $f$ to directly regress the 3D coordinate $y = f(\\mathbf{F}(x))$ for each 2D keypoint $x$ with feature $\\mathbf{F}(x)$ . Without the need to store large point clouds with descriptors, SCR methods implicitly represent the scene with a neural network, which usually results in a smaller map size.", + "bbox": [ + 89, + 728, + 483, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scalable SCR without 3D ground truth. Recent advances [9, 68] allow SCR to scale to large scenes without scene-specific 3D supervision. To reduce ambiguities in large scenes, GLACE [68] (Fig. 2a) concatenates a local patch-level encoding with an image-level global encoding", + "bbox": [ + 88, + 824, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "as the keypoint feature $\\mathbf{F}(x)$ . The local encoder is a pretrained DSAC* [6] backbone, following [9]. The global encoder uses a pretrained image retrieval model [75] with Gaussian noise augmentation to prevent overfitting to trivial solutions, cf. [68]. To accelerate training, all features are precomputed and buffered in GPU memory, from which a random sample is drawn for each batch.", + "bbox": [ + 511, + 321, + 906, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Without ground truth scene coordinates, the output 3D point $y$ is reprojected with the ground truth pose $\\mathbb{R}, t$ and intrinsics $\\mathbb{K}$ , and compared to the keypoint location $x$ in 2D:", + "bbox": [ + 511, + 426, + 906, + 472 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ne _ {2} (x, y) = \\left\\| x - \\pi (\\mathrm {K} (\\mathrm {R} y + \\mathbf {t})) \\right\\| _ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 479, + 903, + 497 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pi$ converts homogeneous to Cartesian coordinates.", + "bbox": [ + 511, + 503, + 890, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of explicitly grouping corresponding observations into tracks, this underconstrained supervision is applied to each independent prediction. Prior works [45, 68] suggest that implicit triangulation can still occur as the network tends to produce similar outputs for similar inputs.", + "bbox": [ + 511, + 518, + 905, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reprojection error is fed into a dynamic robust loss, cf. ACE [9], to focus on points accurately regressed:", + "bbox": [ + 511, + 594, + 905, + 625 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {d y n a m i c}} \\left(e _ {2} (x, y)\\right) = \\tau (t) \\rho \\left(\\frac {e _ {2} (x , y)}{\\tau (t)}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 630, + 903, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where ACE [9] uses tanh as robust loss $(\\rho \\coloneqq \\tanh)$ . Based on the relative training time $t \\in [0,1]$ , the bandwidth $\\tau(t)$ is adjusted dynamically during training:", + "bbox": [ + 511, + 669, + 905, + 715 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tau (t) = \\sqrt {1 - t ^ {2}} \\tau_ {\\max } + \\tau_ {\\min }. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 722, + 903, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Keypoints $x$ whose regressed 3D point $y$ fall outside the valid frustum are penalized differently. Valid points are defined to lie within a valid depth range $[d_{\\min}, d_{\\max}]$ in front of the camera. Further, their reprojection error $e_2(x, y)$ must be smaller than a threshold $e_{\\max}$ . For invalid points, we penalize their distance to a pseudo ground truth point $\\bar{y}$ :", + "bbox": [ + 511, + 748, + 906, + 840 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {i n v a l i d}} (y) = \\left\\| y - \\bar {y} \\right\\| _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 847, + 903, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\bar{y}$ is computed by the inverse projection of the pixel $x$ using a fixed target depth $d_{\\mathrm{target}}$ .", + "bbox": [ + 511, + 869, + 905, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11538", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Network Architecture", + "text_level": 1, + "bbox": [ + 89, + 90, + 295, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the MLP architecture and position decoder from GLACE [68], scaling the network width with scene size. As illustrated in Fig. 2b, we also introduce a refinement module at the end of the network, which adjusts the final output $y$ by predicting an offset from the intermediate prediction $y_0$ . The coarse coordinate $y_0$ is reintroduced into the refinement module through positional encoding [43, 63] using sine and cosine functions with periods ranging from 0.5 to 2048, which is added to the intermediate feature. This empirically improves training stability and allows the network to achieve lower training reprojection errors more rapidly.", + "bbox": [ + 89, + 112, + 483, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Input Encoding", + "text_level": 1, + "bbox": [ + 89, + 287, + 248, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Analysis. In implicit triangulation, reprojection constraints are grouped based on input similarity. Therefore, the desired properties of input encodings are as follows: positive pairs observing the same points should produce similar features, while negative pairs observing distinct points should yield clearly distinguishable features. Additionally, it is preferable for the encodings to be low-dimensional to minimize memory requirements.", + "bbox": [ + 89, + 316, + 483, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local Encoding. At the local patch level, features should differentiate observations of the same point from those of different points. The requirement aligns with the properties of local descriptors used in traditional feature matching, suggesting that we can directly leverage their local feature extractors. We investigate pretrained feature extractors for both dense and sparse matching methods, such as LoFTR [62] and Dedode [24]. To lower memory consumption during training, we apply PCA to all the features from the training dataset, reducing their dimensionality while retaining most of the variance. We experimentally observe that reducing the dimensionality to 128 dimensions preserves over $90\\%$ of the variance on various datasets [35, 53, 56].", + "bbox": [ + 89, + 441, + 483, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Covisibility Graph Based Global Encoding. Image-level global features should distinguish between covisible and non-covisible image pairs, i.e. whether the images are viewing the same part of the scene, to resolve ambiguities in local encodings. Although global encodings with image-level receptive fields can help, they may still be insufficient to resolve ambiguities in complex environments, as shown in Fig. 3. This limitation can lead to imperfect grouping of reprojection constraints during training, thereby impairing the effectiveness of implicit triangulation. Furthermore, we point out that the learned SCR function may lack (Lipschitz) smoothness [32] w.r.t. the global encodings if adapted naively, e.g. minor variations in the global encoding can result in significant shifts in corresponding 3D points and consequently reduce generalization at test time.", + "bbox": [ + 89, + 657, + 482, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these issues, we propose to directly learn", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/254385d40b9454430dda83bf93dc38f7ac1cdf46f8b04762d2706ce692f8651d.jpg", + "image_caption": [ + "(a) Distribution of feature distance for covisible and non-covisible pairs." + ], + "image_footnote": [], + "bbox": [ + 531, + 94, + 712, + 195 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db873f8d30c79bca577c3e1e1fc17e15a2afdb3b61e50d40cd2dab7e81cb577e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 715, + 94, + 895, + 195 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb876650ac78bfd8a51e93d40f8c644ac09b855ac7dd86e51fe08e65999f933e.jpg", + "image_caption": [ + "(b) Precision Recall Curve of predicting covisibility by feature distance.", + "Figure 3. Comparison of global encodings. Aligning the learning of global encodings with the covisibility graph topology (Node2Vec [27]) helps distinguish covisible and non-covisible pairs (a) and predict covisibility by feature distance (b)." + ], + "image_footnote": [], + "bbox": [ + 570, + 223, + 849, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "embeddings aligned with the可视isibility graph's topology using Node2Vec [27], which samples sequences with weighted random walks and optimizes node embeddings with a Skip-gram [42] objective. For training images, the可视isibility graph is easily available. It can be estimated from the frustum overlap of ground truth poses (see the supplementary for more details). At test time, however,可视isibility information is unknown, so we propose generating multiple global encoding hypotheses by retrieving the nearest training images using NetVLAD [1] features. The global encoding of each retrieved image serves as a hypothesis, and we select the hypothesis yielding the maximum RANSAC inliers for the final localization result.", + "bbox": [ + 511, + 469, + 906, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This approach effectively decouples training-time and test-time ambiguities: during training, the network focuses on learning scene structure without ambiguity, while at test time, multiple hypotheses enable the resolution of complex, often multimodal ambiguities.", + "bbox": [ + 511, + 667, + 906, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Covisibility Graph Based Data Augmentation. Our Covisibility Graph Encoding effectively learns a low-ambiguity global encoding. However, data augmentation is still necessary to prevent the network from distinguishing covisible pairs based on distinct global encodings. Instead of simply adding isotropic Gaussian noise [68], we introduce a graph-based data augmentation strategy. In this approach, rather than applying isotropic noise, we randomly replace an image's global encoding with that of a neighboring image from the covisibility graph. Specifically, with probabil", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11539", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8de174b7d4c166b2a4cc92948f00b3621ebfd2e0c831eefd85d6d09657802bb4.jpg", + "image_caption": [ + "Figure 4. Statistics of reprojection error for points with different depths. The kernel density estimation (KDE) of reprojection error distribution conditioned on disparity from SCR models trained with various local encodings across different datasets. We observe that far points (low disparity) exhibit a lower reprojection error. (Detector-free LoFTR [62] with an $8 \\times$ downsampled output has a larger 2D keypoint error than Detector-based Dedode [24].)" + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 287, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/edf8201abec980d6d59aa69ff737e0bdc00eac5ff6f4cedfbfeac56066374ae0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 89, + 478, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ity $p = 0.5$ , the current image's global encoding is retained, while with probability $1 - p$ , it is replaced by the global encoding of a randomly sampled neighboring image.", + "bbox": [ + 89, + 349, + 483, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Output Supervision", + "text_level": 1, + "bbox": [ + 89, + 402, + 279, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Bias in Reprojection Loss. Fig. 4 displays statistics collected from training SCR models with various local encodings across different datasets. It indicates that points closer to the camera empirically exhibit higher reprojection errors compared to distant points, hence we observe a bias toward distant points. This bias is magnified by training with the robust loss Eq. (2), as the supervision signal tends to neglect (nearby) points with higher reprojection errors (cf. Fig. 5). Assuming the training time distribution of camera poses to be representative for testing, regressing near points fewer and less accurately during testing diminishes the positional localization accuracy. We conjecture that to facilitate implicit triangulation for near points, a higher reprojection error should be allowed to compensate for the reprojection of nearby points being more sensitive to pose variations and coordinate inaccuracies.", + "bbox": [ + 89, + 429, + 483, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Adjusted Reprojection Error. We propose normalizing the reprojection error in Eq. (1) based on the depth of the predicted scene coordinate. Specifically, the observation standard deviation, $\\sigma_{o}$ , is defined as:", + "bbox": [ + 89, + 676, + 483, + 737 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {o} = \\sqrt {\\left(\\frac {\\sigma_ {3}}{d}\\right) ^ {2} + \\sigma_ {2} ^ {2}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 744, + 482, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we denote the variance of the noise of the 2D observations by $\\sigma_2^2$ . The variance of the 3D prediction is denoted by $\\sigma_3^2$ and by $d$ the depth of the point. The reprojection error is then adjusted accordingly:", + "bbox": [ + 89, + 786, + 483, + 848 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne _ {3} (x, y) = \\frac {e _ {2} (x , y)}{\\sigma_ {o}} = \\frac {e _ {2} (x , y)}{\\sigma_ {2}} \\sqrt {\\frac {d ^ {2}}{d ^ {2} + \\left(\\frac {\\sigma_ {3}}{\\sigma_ {2}}\\right) ^ {2}}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 854, + 483, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Selective Application of Depth Adjustment. The bias towards distant points may sometimes actually be beneficial, as underconstrained points can be pushed farther along the ray, making them easier to identify as outliers during test time. Therefore, we apply our depth-adjusted reprojection loss only to the intermediate coarse scene coordinate output $y_0$ during training (Fig. 2b), and retain the original reprojection loss for the final output. To mitigate the concentration of the supervision signal on points with low projection error, we replace tanh with the Geman-McClure [3] robust loss function which has a heavier tail than tanh:", + "bbox": [ + 511, + 90, + 906, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\rho (x) = \\frac {9 x ^ {2}}{9 x ^ {2} + 4}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 265, + 906, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to guide the convergence of the regressed points, $y$ , by the intermediate output $y_{0}$ (affected by the normalized loss from Eq. (6)), we also apply a consistency loss at the beginning of the training:", + "bbox": [ + 511, + 306, + 906, + 369 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {c o n s i s t e n c y}} = \\lambda (t) | | y - y _ {0} | | _ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 380, + 906, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda (t)$ is a dynamic weight that decreases to 0 in a cosine schedule during the first $50\\%$ of training time.", + "bbox": [ + 511, + 409, + 905, + 439 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda (t) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} (1 + \\cos 2 \\pi t), & \\text {i f} t \\in [ 0, 0. 5 ] \\\\ 0, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 450, + 905, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t$ is the relative training time.", + "bbox": [ + 511, + 501, + 751, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optional Depth Supervision. When depth is available, we can also benefit from direct depth supervision. The depth does not need to be accurate since we mainly use the depth for initialization. Specifically, we simply replace the consistency loss between intermediate and final output in Eq. (8) with a ground truth coordinate supervision loss:", + "bbox": [ + 511, + 521, + 905, + 613 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {d e p t h}} = \\lambda (t) \\left(\\left\\| y - \\bar {y} \\right\\| _ {2} + \\left\\| y _ {0} - \\bar {y} \\right\\| _ {2}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 625, + 906, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{y}$ is the pseudo ground truth computed by the inverse projection of the pixel given the depth, pose, and intrinsic.", + "bbox": [ + 511, + 652, + 905, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 696, + 645, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 511, + 722, + 614, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the Aachen Day-Night [53, 56] and the Hyundai Department Store dataset [35] to evaluate R-SCoRe on complex large-scale indoor and outdoor scenes.", + "bbox": [ + 511, + 744, + 905, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Aachen Day-Night. It is a large-scale benchmark for outdoor visual localization, covering the historic inner city of Aachen, Germany, over an area of approximately $6 \\, km^2$ . It presents significant challenges due to varying illumination conditions, especially between day and night. The dataset includes 4,328 daytime images for training, along with 824 daytime query images and 98 nighttime query images.", + "bbox": [ + 511, + 794, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11540", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d228548c4af20e1a020864702184fd00a3051b48bf5d728bd93a093322e94d15.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodsw/o DepthSizeAachen DayAachen Night
HLoc+SPSG [19, 50, 51]Yes7.82GB89.695.498.886.793.9100
AS [55]Yes750MB85.392.297.939.849.064.3
Cascaded [16]Yes140MB76.788.695.833.748.062.2
QP+R.Sift [41]Yes30MB62.676.384.716.318.424.5
Squeezezer [72]Yes240MB75.589.796.250.067.378.6
PixLoc [52]Yes2.13GB64.369.377.451.155.167.3
Neumap [64]No1.26GB80.890.995.648.067.387.8
HSCNet [36]No213MB71.181.991.732.743.965.3
HSCNet++ [70]No274MB72.781.691.443.957.176.5
ESAC (×50) [5]No1.31GB42.659.675.56.110.218.4
ACE (×50) [9]Yes205MB6.917.250.00.01.05.1
GLACE [68]Yes27MB8.620.864.01.01.017.3
R-SCoRe (Dedode [24]) + DepthYes47MB74.886.996.464.389.896.9
No47MB79.088.596.466.389.896.9
", + "bbox": [ + 179, + 87, + 821, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Aachen Day-Night evaluation. The map size and percentages of query images within three thresholds: (0.25m, $2^{\\circ}$ ), (0.5m, $5^{\\circ}$ ), and (5m, $10^{\\circ}$ ) and are reported. We report our results with Dedode [24] local encoding and optional depth supervision. Feature matching (FM) methods [19, 50, 51] are more accurate, but the map size is large. R-SCoRe achieves comparable accuracy with a small map size.", + "bbox": [ + 89, + 330, + 906, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyundai Department Store. It is a large-scale indoor visual localization benchmark, covering three floors of a department store. Each floor consists of multiple sequences captured over four months, spanning an area of approximately $10,000~m^2$ . It presents challenges beyond its large scale, including dynamic objects, illumination changes, and textureless regions. B1 is particularly challenging as the training images are captured under low-lighting conditions, while the query images are brightly illuminated. The dataset includes 44,283 training images and 5,927 test images.", + "bbox": [ + 88, + 398, + 485, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Benchmark Results", + "text_level": 1, + "bbox": [ + 89, + 568, + 277, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Aachen Day-Night. As shown in Tab. 2, R-SCoRe enhances the performance of scene coordinate regression (SCR) based methods [5, 36, 68, 70], achieving competitive results with a single low-map-size model without the need for scene-specific depth supervision. While R-SCoRe is competitive with the best performing method, HLoc [19, 50, 51], we forfeit some ground at highest accuracy. However, R-SCoRe demands $170 \\times$ less memory to store the map. This huge gap could already render SCR based methods as an attractive alternative for some applications. Most other feature-based methods (FM) also deliver significantly larger maps. While delivering comparable performance for the Aachen Day dataset, they all fall behind R-SCoRe on the Aachen Night dataset. The only FM method [41] with a comparable map size is outperformed on all metrics, e.g. [41] is $4 - 5 \\times$ worse in accuracy on the night dataset. Compared to other SCR methods that work without depth supervision [9, 68] R-SCoRe is $10 \\times$ superior in accuracy. The so far most accurate SCR based method [64] produces large maps ( $27 \\times$ larger) and is prohibitively slow", + "bbox": [ + 91, + 598, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in inference. The next most accurate SCR method, [70] is outperformed by $46\\%$ at night and highest threshold, while R-SCoRe maintains a $6\\times$ smaller map size - without the need for depth supervision. We observe a small gain in performance if we utilize depth for supervision of R-SCoRe.", + "bbox": [ + 511, + 398, + 906, + 476 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyundai Department Store. R-SCoRe again significantly outperforms the SCR based methods [5, 68], including recent ensemble networks [5, 9], see Tab. 3. Compared to the state-of-the-art feature matching based localization [50] we achieve competitive results with a single low-map-size model and forfeit some ground at the highest accuracy threshold. However, our model is at least three orders of magnitude smaller for either feature [22, 49] incorporated into [50], which can be a valuable advantage in practice. Recall that depth supervision is not necessary for R-SCoRe, but if available, it can also enhance performance further. The B1 scene exhibits strong illumination changes and we observe significantly better performance when using local encodings from Dedode instead of LoFTR [62].", + "bbox": [ + 511, + 479, + 908, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 705, + 732, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Most hyperparameters follow default values [68] and extensive tuning is not performed, as we empirically find the approach remains robust within a reasonable range, apart from the trade-off between network size and performance.", + "bbox": [ + 511, + 728, + 906, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Input Encodings. For local encodings, we perform PCA to reduce their dimensionality to 128. The global encodings are represented in 256 dimensions, consistent with the $R^2$ Former [75] feature dimension used in GLACE [68] for fair comparison. We estimate the可视ability graph based on camera poses, using a weighted frustum overlap method (details provided in the supplementary materials), with a", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11541", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7982c0b01347b8f527ed1bbda4073562c70a51848096682dd30adb34b5ae83f3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDept. 1F TestDept. 4F TestDept. B1 Test
HLoc+D2-Net [22, 50](78.0 / 82.8 / 88.0) / 398GB(84.2 / 89.8 / 92.0) / 183GB(73.7 / 79.3 / 87.2) / 505GB
HLoc+R2D2 [49, 50](80.6 / 84.3 / 89.4) / 166GB(85.3 / 91.0 / 93.1) / 76GB(75.2 / 80.3 / 87.6) / 210GB
PoseNet [31](0.0 / 0.0 / 0.4) / 41MB(0.0 / 0.0 / 0.1) / 41MB(0.0 / 0.0 / 0.1) / 41MB
ESAC (×50) [5](43.3 / 66.3 / 77.0) / 1.4GB(45.2 / 62.5 / 73.1) / 1.4GB(3.5 / 8.2 / 12.6) / 1.4GB
ACE (×50) [9](14.1 / 54.4 / 75.5) / 205MB(27.3 / 70.9 / 84.1) / 205MB(2.7 / 14.4 / 29.3) / 205MB
GLACE [68](5.6 / 21.3 / 48.6) / 42MB(8.4 / 29.8 / 51.6) / 42MB(0.9 / 4.4 / 11.9) / 42MB
R-SCoRe (LoFTR* [62]) + Depth(63.2 / 82.4 / 92.4) / 127MB(62.2 / 82.7 / 90.9) / 50MB(26.9 / 50.7 / 69.6) / 130MB
(67.3 / 84.5 / 92.6) / 127MB(70.5 / 87.0 / 92.9) / 50MB(30.8 / 53.7 / 72.7) / 130MB
R-SCoRe (Dedode [24]) + Depth(61.4 / 80.2 / 90.9) / 127MB(60.2 / 79.3 / 87.9) / 50MB(60.1 / 77.3 / 89.6) / 130MB
(63.9 / 83.3 / 90.8) / 127MB(76.7 / 89.3 / 93.0) / 50MB(61.5 / 77.6 / 88.8) / 130MB
", + "bbox": [ + 98, + 87, + 898, + 260 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "maximum viewing frustum depth of $d_{\\mathrm{v}} = 50$ for outdoor scenes and $d_{\\mathrm{v}} = 8$ for indoor scenes.", + "bbox": [ + 89, + 339, + 482, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Output Supervision. The supervision uses a dynamic robust loss bandwidth strategy inspired by ACE [9]. For coarse intermediate outputs, the parameters, see Eq. (3), are set to $\\tau_{\\mathrm{min}} = 1$ and $\\tau_{\\mathrm{max}} = 50$ . In contrast, $\\tau_{\\mathrm{max}} = 25$ is used for the final output, which allows the refinement layer to focus on the most accurate predictions while the initial layers do not ignore the optimization of relatively inaccurate predictions. Fixing $\\sigma_{2} = 1$ in the depth-adjusted reprojection loss, Eq. (6), allows us to control the behavior by adjusting $\\tau$ and $\\frac{\\sigma_3}{\\sigma_2}$ . For indoor scenes, $\\sigma_{3} = 3$ is applied, while $\\sigma_{3} = 8$ is used for outdoor scenes to account for different scales. We perform optional depth supervision using depth images rendered from the 3D model for the Hyundai Department Store dataset and Multi-View Stereo depth maps for the Aachen Day-Night dataset.", + "bbox": [ + 88, + 376, + 482, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network Architecture. We adopt the MLP architecture and position decoder from GLACE [68] with expansion ratio $m = 2$ for the MLP, and 50 clusters for the position decoder. With MLP width $w = 256\\left\\lceil \\sqrt{n / 1000} \\right\\rceil$ for $n$ training images, we scale the parameter count proportionally.", + "bbox": [ + 89, + 609, + 482, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training. We found that adopting the optimization settings from ACE Zero [10] enhances both stability and convergence speed compared to the original ACE [9]. Specifically, we reduce the warmup ratio of the one-cycle learning rate schedule [61] from 0.25 to 0.04 and lower the peak learning rate from $5 \\times 10^{-3}$ to $3 \\times 10^{-3}$ . For our evaluation we adopt similar training parameters to GLACE [68], including a local feature buffer size of 128M, a large batch size of 320K and a training duration of 100k iterations.", + "bbox": [ + 89, + 696, + 482, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Testing. At test time, we retrieve the 10 nearest training images with NetVLAD [1]. The global encoding and retrieval features for training images are precomputed and compressed using Product Quantization [28]. For final pose", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c083a880a5c7401b43ed791d0be15a108358cda7672289de0239e53db66cf9a1.jpg", + "table_caption": [ + "Table 3. Hyundai Department Store Test Set evaluation. The percentages of query images within three thresholds: (0.1m, $1^{\\circ}$ ), (0.25m, $2^{\\circ}$ ), and (1m, $5^{\\circ}$ ) and the map size are reported. R-SCoRe achieves competitive accuracy with a small map size. *We use LoFTR [62] outdoor, trained on MegaDepth [38], instead of the indoor model trained on ScanNet [18] for the B1 scene with strong illumination change." + ], + "table_footnote": [], + "table_body": "
Dept. 1F ValDept. B1 Val
ACE [9]68.787.595.914.128.345.8
LoFTR* [62]72.388.795.529.451.369.6
Dedode [24]70.686.695.557.774.786.7
", + "bbox": [ + 514, + 335, + 915, + 402 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c2b89fefb51e44249dac67ad78cfa130116cd339e69db02d175cc2e75b071d82.jpg", + "table_caption": [ + "Table 4. Ablation study of local encoders. Accuracy at (0.1m, $1^{\\circ}$ ), (0.25m, $2^{\\circ}$ ), and (1m, $5^{\\circ}$ ) thresholds are reported. Utilizing pretrained, off-the-shelf feature extractors improves the performance, especially under challenging conditions (B1)." + ], + "table_footnote": [], + "table_body": "
Dept. 1F Val
R2Former [75] w/ Gaussian34.160.178.3
+ Multi Hypotheses42.174.592.2
+ Covis Augmentation62.083.894.8
+ Covis Encoding72.388.795.5
", + "bbox": [ + 529, + 481, + 888, + 563 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation study of global encodings. We experiment with using multiple hypotheses at test time, applying covisibility graph-based data augmentation during training, and learning global encodings directly from the covisibility graph. Accuracy at $(0.1\\mathrm{m},1^{\\circ})$ , $(0.25\\mathrm{m},2^{\\circ})$ , and $(1\\mathrm{m},5^{\\circ})$ thresholds.", + "bbox": [ + 511, + 571, + 906, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "estimation, we utilize PoseLib [33] with a maximum reprojection error of 10 pixels and up to 10,000 RANSAC iterations. On our PC (NVIDIA RTX 2080 GPU & Intel i7-9700K CPU), the average inference time for a $640 \\times 480$ query image is 140 to $270\\mathrm{ms}$ in total.", + "bbox": [ + 511, + 670, + 906, + 744 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Global: NetVLAD (20ms), Retrieval (<1ms)", + "- Local: LoFTR (7ms) or DeDoDe (50ms)", + "- MLP: $\\mathrm{w} = {768}\\left( {{70}\\mathrm{{ms}}}\\right)$ or ${1280}\\left( {{160}\\mathrm{{ms}}}\\right)$", + "- Pose Solving: 40ms" + ], + "bbox": [ + 513, + 746, + 826, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study Results", + "text_level": 1, + "bbox": [ + 511, + 816, + 725, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In our ablation studies, we investigate the impact of the different components in R-SCoRe. We evaluate on the validation split for the Hyundai Department Store dataset. Since the Aachen Day-Night dataset does not provide a validation", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11542", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a3d67b6380067cef3a2f3cda436b0986da32e1e0ffed27906e83de2fd6560439.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Aachen DayAachen Night
FM Covis75.487.695.864.389.895.9
Pose Covis74.886.996.464.389.896.9
", + "bbox": [ + 93, + 88, + 480, + 137 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/119521074115fe846eca3d3bd490199c37ee42e6a359c7066c1cd218f5ffd602.jpg", + "table_caption": [ + "Table 6. Ablation study of covisibility graph. Building the covisibility graph using frustum overlap performs similarly to utilizing feature matching. Accuracy at $(0.25\\mathrm{m}, 2^{\\circ})$ , $(0.5\\mathrm{m}, 5^{\\circ})$ , and $(5\\mathrm{m}, 10^{\\circ})$ thresholds." + ], + "table_footnote": [], + "table_body": "
SupervisionDept. 1F ValDept. 4F Val
Original62.382.293.759.182.297.6
Adjusted70.686.695.563.984.298.3
Depth76.888.195.668.584.998.5
", + "bbox": [ + 91, + 220, + 483, + 286 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Ablation study of supervision methods. Original refers to the original reprojection error supervision, Adjusted refers to our depth-adjusted reprojection error supervision, and Depth uses ground truth depth for supervision. Accuracy at (0.1m, $1^{\\circ}$ ), (0.25m, $2^{\\circ}$ ), and (1m, $5^{\\circ}$ ).", + "bbox": [ + 89, + 296, + 483, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "split, we evaluate on the test set.", + "bbox": [ + 89, + 396, + 307, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Local Encoding. As shown in Tab. 4, for large scale indoor scenes with small illumination changes, alternative off-the-shelf local feature extractors [24, 62] achieve similar or even superior performance compared to the original ACE [9]. Note that this finding contradicts earlier investigations [9] that prefer a specifically trained backbone in their work. Additionally, local descriptors trained on MegaDepth [38], especially Dedode [24], demonstrate greater robustness in scenes with significant illumination changes.", + "bbox": [ + 88, + 417, + 483, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Global Encoding. Retrieving global encodings from training images avoids the domain gap. Better retrieval method and multiple hypotheses verification can help resolve ambiguities. Without retraining (Tab. 5), utilizing multiple global hypotheses at test time (+ Multi Hypotheses) results in a direct performance improvement in complex scenes. The performance improves significantly, once we incorporate our可视ibility graph-based data augmentation during training. In particular, we replace isotropic Gaussian noise [68] with our more precise可视ibility-based technique (+ Covis Augmentation). Finally, learning the global encoding directly from the可视ibility graph (+ Covis Encoding) reduces the interference between non-covisible training images and thereby facilitates implicit triangulation, especially in indoor scenes with significant ambiguity.", + "bbox": [ + 89, + 560, + 482, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we also explore the effect of computing the可视ibility graph via feature matching [19, 51]. As shown in Tab. 6, using a more accurate graph yields no significant improvement, indicating that R-SCoRe is robust to the quality of the可视ibility graph. Therefore, our simple frustum overlap-based graph is sufficient for effective performance.", + "bbox": [ + 89, + 787, + 482, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Supervision. Our depth-adjusted supervision effectively", + "bbox": [ + 89, + 885, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2d5a77aa5e072b8bb430d0c96d47eb035ed10c8bbbe6c4661bd1144732635ff.jpg", + "image_caption": [ + "Figure 5. Ablation study of depth distribution after training with different supervision methods. Our depth-adjusted supervision matches the distribution of ground truth depth for supervision as compared to the original." + ], + "image_footnote": [], + "bbox": [ + 524, + 87, + 898, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mitigates the bias towards distant points and enhances the implicit triangulation of nearby points. As demonstrated in Fig. 5, depth-adjusted supervision significantly alters the depth distribution of predicted points, alleviating the previous ignorance of nearby points. This adjustment brings the distribution closer to that achieved with ground truth depth supervision, demonstrating a substantial reduction in the bias inherent in the original supervision approach.", + "bbox": [ + 511, + 330, + 906, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 7, we observe that depth-adjusted supervision also leads to notable improvements in localization accuracy, particularly under stricter thresholds, where accurate translation estimation relies heavily on near points. Even without ground truth depth supervision, depth-adjusted supervision enables the model to achieve competitive performance.", + "bbox": [ + 511, + 459, + 908, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 582, + 633, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we revisited scene coordinate regression (SCR) methods for robust visual localization in large-scale, complex environments. We analyzed the design principles of input encoding and training strategies, identifying several areas for enhancement. Our proposed R-SCoRe includes a covisibility graph-based global encoding learning and data augmentation strategy, a depth-adjusted reprojection loss to improve the implicit triangulation, and also other improvements including better architecture and local feature. Our contributions advance the state-of-the-art in SCR and demonstrate that SCR-based localization methods can achieve competitive performance in large-scale applications. While operating at comparably very small map sizes, R-SCoRe trails the state-of-the-art FM-based localization methods only at the strictest error thresholds. 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In CVPR, 2023, 2, 3, 6, 7" + ], + "bbox": [ + 91, + 92, + 480, + 628 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11546", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_model.json b/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_model.json new file mode 100644 index 0000000000000000000000000000000000000000..91ac281256a65c3db11148a883d30fbebc37cd5a --- /dev/null +++ b/2025/R-SCoRe_ Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization/de480991-e387-4648-af00-268474a4dd11_model.json @@ -0,0 +1,2532 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.13, + 0.877, + 0.175 + ], + "angle": 0, + "content": "R-SCoRe: Revisiting Scene Coordinate Regression for Robust Large-Scale Visual Localization" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.202, + 0.885, + 0.258 + ], + "angle": 0, + "content": "Xudong Jiang\\(^{1}\\) Fangjinhua Wang\\(^{1*}\\) Silvano Galliani\\(^{2}\\) Christoph Vogel\\(^{2}\\) Marc Pollefeys\\(^{1,2}\\) \n\\(^{1}\\)Department of Computer Science, ETH Zurich \n\\(^{2}\\)Microsoft Spatial AI Lab, Zurich" + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.267, + 0.581, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.267, + 0.885, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.501, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Figure 1. Robust Visual Localization with R-SCoRe. Left: Point cloud of Aachen reconstructed by R-SCoRe. Right: On the large-scale Aachen Day-Night dataset [53, 56] using only daytime training images, R-SCoRe achieves \\(64.3\\%\\) accuracy under the \\((0.25\\mathrm{m}, 2^{\\circ})\\) threshold for nighttime query images. It outperforms all previous SCR methods (circles) by a large margin. With a small map size of only 47MB at a comparable accuracy, R-SCoRe is an attractive alternative to traditional methods (triangles)." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.576, + 0.329, + 0.592 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.609, + 0.486, + 0.879 + ], + "angle": 0, + "content": "Learning-based visual localization methods that use scene coordinate regression (SCR) offer the advantage of smaller map sizes. However, on datasets with complex illumination changes or image-level ambiguities, it remains a less robust alternative to feature matching methods. This work aims to close the gap. We introduce a covisibility graph-based global encoding learning and data augmentation strategy, along with a depth-adjusted reprojection loss to facilitate implicit triangulation. Additionally, we revisit the network architecture and local feature extraction module. Our method achieves state-of-the-art on challenging large-scale datasets without relying on network ensembles or 3D supervision. On Aachen Day-Night, we are \\(10 \\times\\) more accurate than previous SCR methods with similar map sizes and require at least \\(5 \\times\\) smaller map sizes than any other SCR method while still delivering superior accuracy. Code is available at: https://github.com/cvg/scrstudio." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.576, + 0.645, + 0.592 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.606, + 0.907, + 0.667 + ], + "angle": 0, + "content": "Visual localization is the task of estimating the 6-DoF pose of a camera in a known scene with a query image. It is a fundamental problem in computer vision, with applications in augmented reality, autonomous driving, and robotics." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.67, + 0.909, + 0.807 + ], + "angle": 0, + "content": "Classical feature matching methods [19, 50, 51, 55] have matured through years of research and now provide robust and accurate localization results. However, these methods typically require explicit 3D scene representations, where a large number of descriptors are stored, leading to substantial map sizes, especially for large-scale scenes. In contrast, pose regression [11, 30, 31, 44, 59, 65, 71, 73] and scene coordinate regression (SCR) [4-6, 8, 9, 21, 36, 68] aim to implicitly encode scene information in neural networks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.901 + ], + "angle": 0, + "content": "SCR methods follow a structure-based paradigm similar to feature matching, i.e., estimating pose from 2D-3D correspondences but replacing explicit matching with regressing the correspondences directly. They are usually limited to small scenes [9] and have yet to match feature matching methods in terms of accuracy and robustness. Recent ad" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.888, + 0.461, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author (fangjinhua.wang@inf.ethz.ch)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11536" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "vances [68] extend SCR to large-scale scenes using a single model. However, its performance is still not on par with feature matching methods, especially in complex scenes with challenging illumination changes [53, 56]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.153, + 0.483, + 0.334 + ], + "angle": 0, + "content": "In this work, we conduct a detailed analysis of the design principles behind the SCR framework, including local and global encoding, network architecture, and training strategies. Based on this analysis, we propose to revisit SCR to enhance the robustness and accuracy of SCR methods for large-scale visual localization tasks. As shown in Fig. 1, our robust SCR (R-SCoRe) improves the night-time localization accuracy for SCR methods to \\(64.3\\%\\) under the \\((0.25\\mathrm{m}, 2^{\\circ})\\) threshold on the Aachen Day-Night dataset, all with a map size of only 47MB. R-SCoRe significantly outperforms previous SCR methods and achieves accuracy comparable to feature matching techniques." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.336, + 0.483, + 0.487 + ], + "angle": 0, + "content": "Tab. 1 summarizes the practicability of R-SCoRe in complex large-scale scenes. While feature matching methods are also accurate, their map size can be prohibitively large, sometimes more than two orders of magnitude [19, 50, 51]. Compared to SCR methods with similarly small map sizes [9, 68], R-SCoRe is at least one order of magnitude more accurate. While we still clearly outperform other SCR methods, we maintain fast inference and significantly smaller map sizes – all without the need for scene-specific depth supervision. Our contributions are as follows." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.489, + 0.483, + 0.564 + ], + "angle": 0, + "content": "- We propose learning a global encoding and performing data augmentation based on the可视ability graph. To address the ambiguity of image retrieval features in complex large-scale scenes, we used multiple global hypotheses during testing." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.565, + 0.483, + 0.623 + ], + "angle": 0, + "content": "- To bias the network from neglecting near points, we introduce a depth-adjusted reprojection loss and show that this allows for accurate localization without scene-specific ground truth coordinate supervision." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.624, + 0.483, + 0.685 + ], + "angle": 0, + "content": "- To our knowledge, R-SCoRe is the first attempt of an SCR approach to achieve state-of-the-art performance on complex large-scale scenes without using an ensemble of networks or 3D model supervision." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.489, + 0.483, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.703, + 0.233, + 0.719 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Feature Matching. Most state-of-the-art visual localization methods rely on feature matching [19, 50, 51, 55]. These methods typically adopt a structure-based paradigm, establishing 2D-3D correspondences between keypoints in a query image and 3D points in a scene. Camera pose is solved with geometric constraints, often a Perspective-n-Point (PnP) solver [26, 47] within a RANSAC framework [2, 17, 25] to effectively manage outliers. These methods commonly construct a Structure-from-Motion (SfM) map of the scene, which contains both 3D points and their descriptors [19, 22, 24, 49, 58]. To efficiently establish 2D" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.905, + 0.224 + ], + "angle": 0, + "content": "
MethodsSizeTimeAcc.w/o Depth
FM[19, 50, 51]X✓✓✓
PR[31]✓✓X✓
SCR[64]XX✓X
[5, 36, 70]X✓✓X
[4, 9, 68]✓✓X✓
R-SCoRe✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.234, + 0.905, + 0.304 + ], + "angle": 0, + "content": "Table 1. Comparison with other methods on complex large-scale scenes [53, 56]. Feature matching (FM) methods are accurate but need a large map size. Pose regression (PR) methods are fast but less accurate. We maintain a small map size while achieving remarkable accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.331, + 0.905, + 0.392 + ], + "angle": 0, + "content": "3D matches, they often follow a two-level approach [50]. First, potentially relevant database images are retrieved using image retrieval techniques [1, 48, 75]. This is followed by 2D-2D matching with the query image [39, 50, 51]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.392, + 0.906, + 0.558 + ], + "angle": 0, + "content": "However, a significant limitation of these methods is the necessity to store all descriptor vectors of the 3D model, which can lead to storage challenges, particularly in large maps. To address this issue, various compression techniques have been proposed. These include reducing the number of 3D points [12, 13, 23, 37, 72] or compressing descriptors [20, 28, 29, 34, 40, 54, 67, 72]. Recently, several studies [46, 69, 74] have proposed alternative approaches that eliminate the need for explicit descriptor storage. Instead, these methods advocate for direct matching against geometric representations, such as point clouds or meshes." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.563, + 0.906, + 0.639 + ], + "angle": 0, + "content": "Pose Regression. These methods [11, 30, 31, 44, 59, 65, 71, 73] directly estimates the camera pose of a query image with a neural network. However, they tend to struggle with generalization and often only achieve an accuracy similar to image retrieval methods [57]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.906, + 0.765 + ], + "angle": 0, + "content": "Scene Coordinate Regression. Following a similar structure-based localization paradigm as feature matching methods, SCR methods [4-9, 14, 15, 21, 36, 45, 60, 66, 68, 70] regress 2D-3D correspondences between the query image and the scene, and estimate the camera pose using geometric constraints. Though SCR methods are more accurate than pose regression methods, they usually still struggle with large-scale scenes [9]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Recently, several approaches have been proposed to improve the scalability and performance of SCR in large-scale scenes. These methods often rely on ground truth 3D coordinates and aim to handle large scenes by dividing them into smaller segments, such as spatial regions [5], voxels [64], or hierarchical clusters [36, 70]. Recent advancements have explored alternatives that do not require ground truth 3D supervision. For example, ACE [9] uses reprojection loss only for training. GLACE [68] further introduces a global" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11537" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.086, + 0.912, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.225, + 0.908, + 0.298 + ], + "angle": 0, + "content": "Figure 2. R-SCoRe pipeline. (a) Following the SCR workflow in [68], we concatenate patch-level local encodings with image-level global encodings as input to a scene-specific MLP. (b) We learn contrastive global encodings from the可视ability graph using Node2Vec [27]. During training, global encodings are sampled from neighboring nodes for data augmentation. During inference, we retrieve global encodings from the \\(k\\) nearest training images via NetVLAD [1] as hypotheses and select the one yielding the most RANSAC inliers. We enhance the SCR MLP with a refinement module and introduce a depth-adjusted reprojection loss to reduce bias toward distant points." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.322, + 0.482, + 0.385 + ], + "angle": 0, + "content": "encoding mechanism that eliminates the need for scene segmentation. Despite these improvements, these methods still encounter limitations under challenging conditions, such as significant changes in illumination." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.399, + 0.182, + 0.415 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.425, + 0.484, + 0.593 + ], + "angle": 0, + "content": "Our Scene Coordinate Regression (SCR) workflow is depicted in Fig. 2a. During training, we have access to a可视ability graph to learn global encodings which are concatenated to the local encodings. During inference, we retrieve global encoding hypotheses from the \\(k\\) nearest training images and predict 2D-3D correspondences: we run PnP for each hypothesis and select the one yielding the most RANSAC inliers. Fig. 2b illustrates our detailed R-SCoRe pipeline, where we split SCR into coarse and refinement blocks and introduce可视ibility-based global encoding and data augmentation techniques." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.604, + 0.233, + 0.619 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.632, + 0.484, + 0.725 + ], + "angle": 0, + "content": "Visual Localization. Given a test image \\( I_{\\mathrm{test}} \\) with known intrinsic \\( \\mathbf{K}_{\\mathrm{test}} \\), the goal is to estimate its extrinsic, i.e., the rigid transformation \\( [\\mathbb{R}_{\\mathrm{test}}|\\mathbf{t}_{\\mathrm{test}}] \\) from world coordinate to camera coordinate. The scene is typically given by a set of training images \\( I_{\\mathrm{train}} \\) with known ground truth poses \\( [\\mathbb{R}_{\\mathrm{train}}|\\mathbf{t}_{\\mathrm{train}}] \\) and intrinsics \\( \\mathbf{K}_{\\mathrm{train}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.729, + 0.484, + 0.821 + ], + "angle": 0, + "content": "Scene Coordinate Regression. The SCR pipeline employs a neural network \\( f \\) to directly regress the 3D coordinate \\( y = f(\\mathbf{F}(x)) \\) for each 2D keypoint \\( x \\) with feature \\( \\mathbf{F}(x) \\). Without the need to store large point clouds with descriptors, SCR methods implicitly represent the scene with a neural network, which usually results in a smaller map size." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Scalable SCR without 3D ground truth. Recent advances [9, 68] allow SCR to scale to large scenes without scene-specific 3D supervision. To reduce ambiguities in large scenes, GLACE [68] (Fig. 2a) concatenates a local patch-level encoding with an image-level global encoding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.322, + 0.907, + 0.427 + ], + "angle": 0, + "content": "as the keypoint feature \\(\\mathbf{F}(x)\\). The local encoder is a pretrained DSAC* [6] backbone, following [9]. The global encoder uses a pretrained image retrieval model [75] with Gaussian noise augmentation to prevent overfitting to trivial solutions, cf. [68]. To accelerate training, all features are precomputed and buffered in GPU memory, from which a random sample is drawn for each batch." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.427, + 0.907, + 0.473 + ], + "angle": 0, + "content": "Without ground truth scene coordinates, the output 3D point \\(y\\) is reprojected with the ground truth pose \\(\\mathbb{R}, t\\) and intrinsics \\(\\mathbb{K}\\), and compared to the keypoint location \\(x\\) in 2D:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.48, + 0.905, + 0.498 + ], + "angle": 0, + "content": "\\[\ne _ {2} (x, y) = \\left\\| x - \\pi (\\mathrm {K} (\\mathrm {R} y + \\mathbf {t})) \\right\\| _ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.505, + 0.892, + 0.519 + ], + "angle": 0, + "content": "where \\(\\pi\\) converts homogeneous to Cartesian coordinates." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.906, + 0.595 + ], + "angle": 0, + "content": "Instead of explicitly grouping corresponding observations into tracks, this underconstrained supervision is applied to each independent prediction. Prior works [45, 68] suggest that implicit triangulation can still occur as the network tends to produce similar outputs for similar inputs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.906, + 0.626 + ], + "angle": 0, + "content": "The reprojection error is fed into a dynamic robust loss, cf. ACE [9], to focus on points accurately regressed:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.631, + 0.905, + 0.665 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {d y n a m i c}} \\left(e _ {2} (x, y)\\right) = \\tau (t) \\rho \\left(\\frac {e _ {2} (x , y)}{\\tau (t)}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.67, + 0.906, + 0.717 + ], + "angle": 0, + "content": "where ACE [9] uses tanh as robust loss \\((\\rho \\coloneqq \\tanh)\\). Based on the relative training time \\(t \\in [0,1]\\), the bandwidth \\(\\tau(t)\\) is adjusted dynamically during training:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.723, + 0.905, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\tau (t) = \\sqrt {1 - t ^ {2}} \\tau_ {\\max } + \\tau_ {\\min }. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.907, + 0.841 + ], + "angle": 0, + "content": "Keypoints \\( x \\) whose regressed 3D point \\( y \\) fall outside the valid frustum are penalized differently. Valid points are defined to lie within a valid depth range \\( [d_{\\min}, d_{\\max}] \\) in front of the camera. Further, their reprojection error \\( e_2(x, y) \\) must be smaller than a threshold \\( e_{\\max} \\). For invalid points, we penalize their distance to a pseudo ground truth point \\( \\bar{y} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.848, + 0.905, + 0.865 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {i n v a l i d}} (y) = \\left\\| y - \\bar {y} \\right\\| _ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.903 + ], + "angle": 0, + "content": "where \\(\\bar{y}\\) is computed by the inverse projection of the pixel \\(x\\) using a fixed target depth \\(d_{\\mathrm{target}}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11538" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.296, + 0.105 + ], + "angle": 0, + "content": "3.2. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.281 + ], + "angle": 0, + "content": "We adopt the MLP architecture and position decoder from GLACE [68], scaling the network width with scene size. As illustrated in Fig. 2b, we also introduce a refinement module at the end of the network, which adjusts the final output \\( y \\) by predicting an offset from the intermediate prediction \\( y_0 \\). The coarse coordinate \\( y_0 \\) is reintroduced into the refinement module through positional encoding [43, 63] using sine and cosine functions with periods ranging from 0.5 to 2048, which is added to the intermediate feature. This empirically improves training stability and allows the network to achieve lower training reprojection errors more rapidly." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.289, + 0.249, + 0.308 + ], + "angle": 0, + "content": "3.3. Input Encoding" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.317, + 0.484, + 0.437 + ], + "angle": 0, + "content": "Analysis. In implicit triangulation, reprojection constraints are grouped based on input similarity. Therefore, the desired properties of input encodings are as follows: positive pairs observing the same points should produce similar features, while negative pairs observing distinct points should yield clearly distinguishable features. Additionally, it is preferable for the encodings to be low-dimensional to minimize memory requirements." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.443, + 0.484, + 0.655 + ], + "angle": 0, + "content": "Local Encoding. At the local patch level, features should differentiate observations of the same point from those of different points. The requirement aligns with the properties of local descriptors used in traditional feature matching, suggesting that we can directly leverage their local feature extractors. We investigate pretrained feature extractors for both dense and sparse matching methods, such as LoFTR [62] and Dedode [24]. To lower memory consumption during training, we apply PCA to all the features from the training dataset, reducing their dimensionality while retaining most of the variance. We experimentally observe that reducing the dimensionality to 128 dimensions preserves over \\(90\\%\\) of the variance on various datasets [35, 53, 56]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Covisibility Graph Based Global Encoding. Image-level global features should distinguish between covisible and non-covisible image pairs, i.e. whether the images are viewing the same part of the scene, to resolve ambiguities in local encodings. Although global encodings with image-level receptive fields can help, they may still be insufficient to resolve ambiguities in complex environments, as shown in Fig. 3. This limitation can lead to imperfect grouping of reprojection constraints during training, thereby impairing the effectiveness of implicit triangulation. Furthermore, we point out that the learned SCR function may lack (Lipschitz) smoothness [32] w.r.t. the global encodings if adapted naively, e.g. minor variations in the global encoding can result in significant shifts in corresponding 3D points and consequently reduce generalization at test time." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To address these issues, we propose to directly learn" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.095, + 0.713, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.716, + 0.095, + 0.897, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.205, + 0.9, + 0.218 + ], + "angle": 0, + "content": "(a) Distribution of feature distance for covisible and non-covisible pairs." + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.224, + 0.85, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.36, + 0.899, + 0.373 + ], + "angle": 0, + "content": "(b) Precision Recall Curve of predicting covisibility by feature distance." + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.385, + 0.907, + 0.442 + ], + "angle": 0, + "content": "Figure 3. Comparison of global encodings. Aligning the learning of global encodings with the covisibility graph topology (Node2Vec [27]) helps distinguish covisible and non-covisible pairs (a) and predict covisibility by feature distance (b)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.907, + 0.666 + ], + "angle": 0, + "content": "embeddings aligned with the可视isibility graph's topology using Node2Vec [27], which samples sequences with weighted random walks and optimizes node embeddings with a Skip-gram [42] objective. For training images, the可视isibility graph is easily available. It can be estimated from the frustum overlap of ground truth poses (see the supplementary for more details). At test time, however,可视isibility information is unknown, so we propose generating multiple global encoding hypotheses by retrieving the nearest training images using NetVLAD [1] features. The global encoding of each retrieved image serves as a hypothesis, and we select the hypothesis yielding the maximum RANSAC inliers for the final localization result." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.669, + 0.907, + 0.744 + ], + "angle": 0, + "content": "This approach effectively decouples training-time and test-time ambiguities: during training, the network focuses on learning scene structure without ambiguity, while at test time, multiple hypotheses enable the resolution of complex, often multimodal ambiguities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Covisibility Graph Based Data Augmentation. Our Covisibility Graph Encoding effectively learns a low-ambiguity global encoding. However, data augmentation is still necessary to prevent the network from distinguishing covisible pairs based on distinct global encodings. Instead of simply adding isotropic Gaussian noise [68], we introduce a graph-based data augmentation strategy. In this approach, rather than applying isotropic noise, we randomly replace an image's global encoding with that of a neighboring image from the covisibility graph. Specifically, with probabil" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11539" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.288, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.09, + 0.48, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.227, + 0.485, + 0.326 + ], + "angle": 0, + "content": "Figure 4. Statistics of reprojection error for points with different depths. The kernel density estimation (KDE) of reprojection error distribution conditioned on disparity from SCR models trained with various local encodings across different datasets. We observe that far points (low disparity) exhibit a lower reprojection error. (Detector-free LoFTR [62] with an \\(8 \\times\\) downsampled output has a larger 2D keypoint error than Detector-based Dedode [24].)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.35, + 0.484, + 0.397 + ], + "angle": 0, + "content": "ity \\( p = 0.5 \\), the current image's global encoding is retained, while with probability \\( 1 - p \\), it is replaced by the global encoding of a randomly sampled neighboring image." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.403, + 0.281, + 0.42 + ], + "angle": 0, + "content": "3.4. Output Supervision" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.43, + 0.484, + 0.672 + ], + "angle": 0, + "content": "Depth Bias in Reprojection Loss. Fig. 4 displays statistics collected from training SCR models with various local encodings across different datasets. It indicates that points closer to the camera empirically exhibit higher reprojection errors compared to distant points, hence we observe a bias toward distant points. This bias is magnified by training with the robust loss Eq. (2), as the supervision signal tends to neglect (nearby) points with higher reprojection errors (cf. Fig. 5). Assuming the training time distribution of camera poses to be representative for testing, regressing near points fewer and less accurately during testing diminishes the positional localization accuracy. We conjecture that to facilitate implicit triangulation for near points, a higher reprojection error should be allowed to compensate for the reprojection of nearby points being more sensitive to pose variations and coordinate inaccuracies." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.677, + 0.485, + 0.738 + ], + "angle": 0, + "content": "Depth Adjusted Reprojection Error. We propose normalizing the reprojection error in Eq. (1) based on the depth of the predicted scene coordinate. Specifically, the observation standard deviation, \\(\\sigma_{o}\\), is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.746, + 0.483, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {o} = \\sqrt {\\left(\\frac {\\sigma_ {3}}{d}\\right) ^ {2} + \\sigma_ {2} ^ {2}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.787, + 0.484, + 0.849 + ], + "angle": 0, + "content": "where we denote the variance of the noise of the 2D observations by \\(\\sigma_2^2\\). The variance of the 3D prediction is denoted by \\(\\sigma_3^2\\) and by \\(d\\) the depth of the point. The reprojection error is then adjusted accordingly:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.856, + 0.484, + 0.906 + ], + "angle": 0, + "content": "\\[\ne _ {3} (x, y) = \\frac {e _ {2} (x , y)}{\\sigma_ {o}} = \\frac {e _ {2} (x , y)}{\\sigma_ {2}} \\sqrt {\\frac {d ^ {2}}{d ^ {2} + \\left(\\frac {\\sigma_ {3}}{\\sigma_ {2}}\\right) ^ {2}}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.258 + ], + "angle": 0, + "content": "Selective Application of Depth Adjustment. The bias towards distant points may sometimes actually be beneficial, as underconstrained points can be pushed farther along the ray, making them easier to identify as outliers during test time. Therefore, we apply our depth-adjusted reprojection loss only to the intermediate coarse scene coordinate output \\( y_0 \\) during training (Fig. 2b), and retain the original reprojection loss for the final output. To mitigate the concentration of the supervision signal on points with low projection error, we replace tanh with the Geman-McClure [3] robust loss function which has a heavier tail than tanh:" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.266, + 0.907, + 0.3 + ], + "angle": 0, + "content": "\\[\n\\rho (x) = \\frac {9 x ^ {2}}{9 x ^ {2} + 4}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.308, + 0.907, + 0.37 + ], + "angle": 0, + "content": "In order to guide the convergence of the regressed points, \\(y\\), by the intermediate output \\(y_{0}\\) (affected by the normalized loss from Eq. (6)), we also apply a consistency loss at the beginning of the training:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.381, + 0.907, + 0.4 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {c o n s i s t e n c y}} = \\lambda (t) | | y - y _ {0} | | _ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.41, + 0.906, + 0.44 + ], + "angle": 0, + "content": "where \\(\\lambda (t)\\) is a dynamic weight that decreases to 0 in a cosine schedule during the first \\(50\\%\\) of training time." + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.451, + 0.906, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\lambda (t) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} (1 + \\cos 2 \\pi t), & \\text {i f} t \\in [ 0, 0. 5 ] \\\\ 0, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.502, + 0.753, + 0.517 + ], + "angle": 0, + "content": "where \\(t\\) is the relative training time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.522, + 0.906, + 0.614 + ], + "angle": 0, + "content": "Optional Depth Supervision. When depth is available, we can also benefit from direct depth supervision. The depth does not need to be accurate since we mainly use the depth for initialization. Specifically, we simply replace the consistency loss between intermediate and final output in Eq. (8) with a ground truth coordinate supervision loss:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.625, + 0.907, + 0.643 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {d e p t h}} = \\lambda (t) \\left(\\left\\| y - \\bar {y} \\right\\| _ {2} + \\left\\| y _ {0} - \\bar {y} \\right\\| _ {2}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.654, + 0.906, + 0.685 + ], + "angle": 0, + "content": "where \\(\\bar{y}\\) is the pseudo ground truth computed by the inverse projection of the pixel given the depth, pose, and intrinsic." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.698, + 0.646, + 0.715 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.723, + 0.616, + 0.737 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.745, + 0.906, + 0.79 + ], + "angle": 0, + "content": "We use the Aachen Day-Night [53, 56] and the Hyundai Department Store dataset [35] to evaluate R-SCoRe on complex large-scale indoor and outdoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Aachen Day-Night. It is a large-scale benchmark for outdoor visual localization, covering the historic inner city of Aachen, Germany, over an area of approximately \\(6 \\, km^2\\). It presents significant challenges due to varying illumination conditions, especially between day and night. The dataset includes 4,328 daytime images for training, along with 824 daytime query images and 98 nighttime query images." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11540" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.18, + 0.088, + 0.822, + 0.322 + ], + "angle": 0, + "content": "
Methodsw/o DepthSizeAachen DayAachen Night
HLoc+SPSG [19, 50, 51]Yes7.82GB89.695.498.886.793.9100
AS [55]Yes750MB85.392.297.939.849.064.3
Cascaded [16]Yes140MB76.788.695.833.748.062.2
QP+R.Sift [41]Yes30MB62.676.384.716.318.424.5
Squeezezer [72]Yes240MB75.589.796.250.067.378.6
PixLoc [52]Yes2.13GB64.369.377.451.155.167.3
Neumap [64]No1.26GB80.890.995.648.067.387.8
HSCNet [36]No213MB71.181.991.732.743.965.3
HSCNet++ [70]No274MB72.781.691.443.957.176.5
ESAC (×50) [5]No1.31GB42.659.675.56.110.218.4
ACE (×50) [9]Yes205MB6.917.250.00.01.05.1
GLACE [68]Yes27MB8.620.864.01.01.017.3
R-SCoRe (Dedode [24]) + DepthYes47MB74.886.996.464.389.896.9
No47MB79.088.596.466.389.896.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.331, + 0.907, + 0.377 + ], + "angle": 0, + "content": "Table 2. Aachen Day-Night evaluation. The map size and percentages of query images within three thresholds: (0.25m, \\(2^{\\circ}\\)), (0.5m, \\(5^{\\circ}\\)), and (5m, \\(10^{\\circ}\\)) and are reported. We report our results with Dedode [24] local encoding and optional depth supervision. Feature matching (FM) methods [19, 50, 51] are more accurate, but the map size is large. R-SCoRe achieves comparable accuracy with a small map size." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.4, + 0.486, + 0.554 + ], + "angle": 0, + "content": "Hyundai Department Store. It is a large-scale indoor visual localization benchmark, covering three floors of a department store. Each floor consists of multiple sequences captured over four months, spanning an area of approximately \\(10,000~m^2\\). It presents challenges beyond its large scale, including dynamic objects, illumination changes, and textureless regions. B1 is particularly challenging as the training images are captured under low-lighting conditions, while the query images are brightly illuminated. The dataset includes 44,283 training images and 5,927 test images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.569, + 0.279, + 0.584 + ], + "angle": 0, + "content": "4.2. Benchmark Results" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.599, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Aachen Day-Night. As shown in Tab. 2, R-SCoRe enhances the performance of scene coordinate regression (SCR) based methods [5, 36, 68, 70], achieving competitive results with a single low-map-size model without the need for scene-specific depth supervision. While R-SCoRe is competitive with the best performing method, HLoc [19, 50, 51], we forfeit some ground at highest accuracy. However, R-SCoRe demands \\(170 \\times\\) less memory to store the map. This huge gap could already render SCR based methods as an attractive alternative for some applications. Most other feature-based methods (FM) also deliver significantly larger maps. While delivering comparable performance for the Aachen Day dataset, they all fall behind R-SCoRe on the Aachen Night dataset. The only FM method [41] with a comparable map size is outperformed on all metrics, e.g. [41] is \\(4 - 5 \\times\\) worse in accuracy on the night dataset. Compared to other SCR methods that work without depth supervision [9, 68] R-SCoRe is \\(10 \\times\\) superior in accuracy. The so far most accurate SCR based method [64] produces large maps (\\(27 \\times\\) larger) and is prohibitively slow" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.4, + 0.907, + 0.477 + ], + "angle": 0, + "content": "in inference. The next most accurate SCR method, [70] is outperformed by \\(46\\%\\) at night and highest threshold, while R-SCoRe maintains a \\(6\\times\\) smaller map size - without the need for depth supervision. We observe a small gain in performance if we utilize depth for supervision of R-SCoRe." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.481, + 0.909, + 0.694 + ], + "angle": 0, + "content": "Hyundai Department Store. R-SCoRe again significantly outperforms the SCR based methods [5, 68], including recent ensemble networks [5, 9], see Tab. 3. Compared to the state-of-the-art feature matching based localization [50] we achieve competitive results with a single low-map-size model and forfeit some ground at the highest accuracy threshold. However, our model is at least three orders of magnitude smaller for either feature [22, 49] incorporated into [50], which can be a valuable advantage in practice. Recall that depth supervision is not necessary for R-SCoRe, but if available, it can also enhance performance further. The B1 scene exhibits strong illumination changes and we observe significantly better performance when using local encodings from Dedode instead of LoFTR [62]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.706, + 0.733, + 0.722 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.729, + 0.907, + 0.79 + ], + "angle": 0, + "content": "Most hyperparameters follow default values [68] and extensive tuning is not performed, as we empirically find the approach remains robust within a reasonable range, apart from the trade-off between network size and performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Input Encodings. For local encodings, we perform PCA to reduce their dimensionality to 128. The global encodings are represented in 256 dimensions, consistent with the \\( R^2 \\) Former [75] feature dimension used in GLACE [68] for fair comparison. We estimate the可视ability graph based on camera poses, using a weighted frustum overlap method (details provided in the supplementary materials), with a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11541" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.088, + 0.9, + 0.261 + ], + "angle": 0, + "content": "
MethodsDept. 1F TestDept. 4F TestDept. B1 Test
HLoc+D2-Net [22, 50](78.0 / 82.8 / 88.0) / 398GB(84.2 / 89.8 / 92.0) / 183GB(73.7 / 79.3 / 87.2) / 505GB
HLoc+R2D2 [49, 50](80.6 / 84.3 / 89.4) / 166GB(85.3 / 91.0 / 93.1) / 76GB(75.2 / 80.3 / 87.6) / 210GB
PoseNet [31](0.0 / 0.0 / 0.4) / 41MB(0.0 / 0.0 / 0.1) / 41MB(0.0 / 0.0 / 0.1) / 41MB
ESAC (×50) [5](43.3 / 66.3 / 77.0) / 1.4GB(45.2 / 62.5 / 73.1) / 1.4GB(3.5 / 8.2 / 12.6) / 1.4GB
ACE (×50) [9](14.1 / 54.4 / 75.5) / 205MB(27.3 / 70.9 / 84.1) / 205MB(2.7 / 14.4 / 29.3) / 205MB
GLACE [68](5.6 / 21.3 / 48.6) / 42MB(8.4 / 29.8 / 51.6) / 42MB(0.9 / 4.4 / 11.9) / 42MB
R-SCoRe (LoFTR* [62]) + Depth(63.2 / 82.4 / 92.4) / 127MB(62.2 / 82.7 / 90.9) / 50MB(26.9 / 50.7 / 69.6) / 130MB
(67.3 / 84.5 / 92.6) / 127MB(70.5 / 87.0 / 92.9) / 50MB(30.8 / 53.7 / 72.7) / 130MB
R-SCoRe (Dedode [24]) + Depth(61.4 / 80.2 / 90.9) / 127MB(60.2 / 79.3 / 87.9) / 50MB(60.1 / 77.3 / 89.6) / 130MB
(63.9 / 83.3 / 90.8) / 127MB(76.7 / 89.3 / 93.0) / 50MB(61.5 / 77.6 / 88.8) / 130MB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.271, + 0.907, + 0.315 + ], + "angle": 0, + "content": "Table 3. Hyundai Department Store Test Set evaluation. The percentages of query images within three thresholds: (0.1m, \\(1^{\\circ}\\)), (0.25m, \\(2^{\\circ}\\)), and (1m, \\(5^{\\circ}\\)) and the map size are reported. R-SCoRe achieves competitive accuracy with a small map size. *We use LoFTR [62] outdoor, trained on MegaDepth [38], instead of the indoor model trained on ScanNet [18] for the B1 scene with strong illumination change." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.34, + 0.483, + 0.371 + ], + "angle": 0, + "content": "maximum viewing frustum depth of \\( d_{\\mathrm{v}} = 50 \\) for outdoor scenes and \\( d_{\\mathrm{v}} = 8 \\) for indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.377, + 0.483, + 0.603 + ], + "angle": 0, + "content": "Output Supervision. The supervision uses a dynamic robust loss bandwidth strategy inspired by ACE [9]. For coarse intermediate outputs, the parameters, see Eq. (3), are set to \\(\\tau_{\\mathrm{min}} = 1\\) and \\(\\tau_{\\mathrm{max}} = 50\\). In contrast, \\(\\tau_{\\mathrm{max}} = 25\\) is used for the final output, which allows the refinement layer to focus on the most accurate predictions while the initial layers do not ignore the optimization of relatively inaccurate predictions. Fixing \\(\\sigma_{2} = 1\\) in the depth-adjusted reprojection loss, Eq. (6), allows us to control the behavior by adjusting \\(\\tau\\) and \\(\\frac{\\sigma_3}{\\sigma_2}\\). For indoor scenes, \\(\\sigma_{3} = 3\\) is applied, while \\(\\sigma_{3} = 8\\) is used for outdoor scenes to account for different scales. We perform optional depth supervision using depth images rendered from the 3D model for the Hyundai Department Store dataset and Multi-View Stereo depth maps for the Aachen Day-Night dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.483, + 0.693 + ], + "angle": 0, + "content": "Network Architecture. We adopt the MLP architecture and position decoder from GLACE [68] with expansion ratio \\( m = 2 \\) for the MLP, and 50 clusters for the position decoder. With MLP width \\( w = 256\\left\\lceil \\sqrt{n / 1000} \\right\\rceil \\) for \\( n \\) training images, we scale the parameter count proportionally." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.483, + 0.835 + ], + "angle": 0, + "content": "Training. We found that adopting the optimization settings from ACE Zero [10] enhances both stability and convergence speed compared to the original ACE [9]. Specifically, we reduce the warmup ratio of the one-cycle learning rate schedule [61] from 0.25 to 0.04 and lower the peak learning rate from \\(5 \\times 10^{-3}\\) to \\(3 \\times 10^{-3}\\). For our evaluation we adopt similar training parameters to GLACE [68], including a local feature buffer size of 128M, a large batch size of 320K and a training duration of 100k iterations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Testing. At test time, we retrieve the 10 nearest training images with NetVLAD [1]. The global encoding and retrieval features for training images are precomputed and compressed using Product Quantization [28]. For final pose" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.337, + 0.916, + 0.403 + ], + "angle": 0, + "content": "
Dept. 1F ValDept. B1 Val
ACE [9]68.787.595.914.128.345.8
LoFTR* [62]72.388.795.529.451.369.6
Dedode [24]70.686.695.557.774.786.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.412, + 0.907, + 0.469 + ], + "angle": 0, + "content": "Table 4. Ablation study of local encoders. Accuracy at (0.1m, \\(1^{\\circ}\\)), (0.25m, \\(2^{\\circ}\\)), and (1m, \\(5^{\\circ}\\)) thresholds are reported. Utilizing pretrained, off-the-shelf feature extractors improves the performance, especially under challenging conditions (B1)." + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.482, + 0.89, + 0.564 + ], + "angle": 0, + "content": "
Dept. 1F Val
R2Former [75] w/ Gaussian34.160.178.3
+ Multi Hypotheses42.174.592.2
+ Covis Augmentation62.083.894.8
+ Covis Encoding72.388.795.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.573, + 0.907, + 0.645 + ], + "angle": 0, + "content": "Table 5. Ablation study of global encodings. We experiment with using multiple hypotheses at test time, applying covisibility graph-based data augmentation during training, and learning global encodings directly from the covisibility graph. Accuracy at \\((0.1\\mathrm{m},1^{\\circ})\\), \\((0.25\\mathrm{m},2^{\\circ})\\), and \\((1\\mathrm{m},5^{\\circ})\\) thresholds." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.907, + 0.746 + ], + "angle": 0, + "content": "estimation, we utilize PoseLib [33] with a maximum reprojection error of 10 pixels and up to 10,000 RANSAC iterations. On our PC (NVIDIA RTX 2080 GPU & Intel i7-9700K CPU), the average inference time for a \\(640 \\times 480\\) query image is 140 to \\(270\\mathrm{ms}\\) in total." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.747, + 0.827, + 0.761 + ], + "angle": 0, + "content": "- Global: NetVLAD (20ms), Retrieval (<1ms)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.762, + 0.799, + 0.776 + ], + "angle": 0, + "content": "- Local: LoFTR (7ms) or DeDoDe (50ms)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.778, + 0.792, + 0.791 + ], + "angle": 0, + "content": "- MLP: \\( \\mathrm{w} = {768}\\left( {{70}\\mathrm{{ms}}}\\right) \\) or \\( {1280}\\left( {{160}\\mathrm{{ms}}}\\right) \\)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.793, + 0.663, + 0.807 + ], + "angle": 0, + "content": "- Pose Solving: 40ms" + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.747, + 0.827, + 0.807 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.818, + 0.727, + 0.834 + ], + "angle": 0, + "content": "4.4. Ablation Study Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In our ablation studies, we investigate the impact of the different components in R-SCoRe. We evaluate on the validation split for the Hyundai Department Store dataset. Since the Aachen Day-Night dataset does not provide a validation" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11542" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.138 + ], + "angle": 0, + "content": "
Aachen DayAachen Night
FM Covis75.487.695.864.389.895.9
Pose Covis74.886.996.464.389.896.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.149, + 0.483, + 0.204 + ], + "angle": 0, + "content": "Table 6. Ablation study of covisibility graph. Building the covisibility graph using frustum overlap performs similarly to utilizing feature matching. Accuracy at \\((0.25\\mathrm{m}, 2^{\\circ})\\), \\((0.5\\mathrm{m}, 5^{\\circ})\\), and \\((5\\mathrm{m}, 10^{\\circ})\\) thresholds." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.222, + 0.485, + 0.287 + ], + "angle": 0, + "content": "
SupervisionDept. 1F ValDept. 4F Val
Original62.382.293.759.182.297.6
Adjusted70.686.695.563.984.298.3
Depth76.888.195.668.584.998.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.297, + 0.484, + 0.366 + ], + "angle": 0, + "content": "Table 7. Ablation study of supervision methods. Original refers to the original reprojection error supervision, Adjusted refers to our depth-adjusted reprojection error supervision, and Depth uses ground truth depth for supervision. Accuracy at (0.1m, \\(1^{\\circ}\\)), (0.25m, \\(2^{\\circ}\\)), and (1m, \\(5^{\\circ}\\))." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.308, + 0.412 + ], + "angle": 0, + "content": "split, we evaluate on the test set." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.418, + 0.484, + 0.555 + ], + "angle": 0, + "content": "Local Encoding. As shown in Tab. 4, for large scale indoor scenes with small illumination changes, alternative off-the-shelf local feature extractors [24, 62] achieve similar or even superior performance compared to the original ACE [9]. Note that this finding contradicts earlier investigations [9] that prefer a specifically trained backbone in their work. Additionally, local descriptors trained on MegaDepth [38], especially Dedode [24], demonstrate greater robustness in scenes with significant illumination changes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.561, + 0.483, + 0.789 + ], + "angle": 0, + "content": "Global Encoding. Retrieving global encodings from training images avoids the domain gap. Better retrieval method and multiple hypotheses verification can help resolve ambiguities. Without retraining (Tab. 5), utilizing multiple global hypotheses at test time (+ Multi Hypotheses) results in a direct performance improvement in complex scenes. The performance improves significantly, once we incorporate our可视ibility graph-based data augmentation during training. In particular, we replace isotropic Gaussian noise [68] with our more precise可视ibility-based technique (+ Covis Augmentation). Finally, learning the global encoding directly from the可视ibility graph (+ Covis Encoding) reduces the interference between non-covisible training images and thereby facilitates implicit triangulation, especially in indoor scenes with significant ambiguity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.789, + 0.483, + 0.88 + ], + "angle": 0, + "content": "Finally, we also explore the effect of computing the可视ibility graph via feature matching [19, 51]. As shown in Tab. 6, using a more accurate graph yields no significant improvement, indicating that R-SCoRe is robust to the quality of the可视ibility graph. Therefore, our simple frustum overlap-based graph is sufficient for effective performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Supervision. Our depth-adjusted supervision effectively" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.088, + 0.9, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.237, + 0.907, + 0.294 + ], + "angle": 0, + "content": "Figure 5. Ablation study of depth distribution after training with different supervision methods. Our depth-adjusted supervision matches the distribution of ground truth depth for supervision as compared to the original." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.332, + 0.907, + 0.455 + ], + "angle": 0, + "content": "mitigates the bias towards distant points and enhances the implicit triangulation of nearby points. As demonstrated in Fig. 5, depth-adjusted supervision significantly alters the depth distribution of predicted points, alleviating the previous ignorance of nearby points. This adjustment brings the distribution closer to that achieved with ground truth depth supervision, demonstrating a substantial reduction in the bias inherent in the original supervision approach." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.909, + 0.551 + ], + "angle": 0, + "content": "In Tab. 7, we observe that depth-adjusted supervision also leads to notable improvements in localization accuracy, particularly under stricter thresholds, where accurate translation estimation relies heavily on near points. Even without ground truth depth supervision, depth-adjusted supervision enables the model to achieve competitive performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.583, + 0.634, + 0.599 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.901 + ], + "angle": 0, + "content": "In this work, we revisited scene coordinate regression (SCR) methods for robust visual localization in large-scale, complex environments. We analyzed the design principles of input encoding and training strategies, identifying several areas for enhancement. Our proposed R-SCoRe includes a covisibility graph-based global encoding learning and data augmentation strategy, a depth-adjusted reprojection loss to improve the implicit triangulation, and also other improvements including better architecture and local feature. Our contributions advance the state-of-the-art in SCR and demonstrate that SCR-based localization methods can achieve competitive performance in large-scale applications. While operating at comparably very small map sizes, R-SCoRe trails the state-of-the-art FM-based localization methods only at the strictest error thresholds. Although out-of-distribution generalization remains challenging, and gaps persist in handling extreme cases, given the relatively small history of SCR, we are positive the accuracy gap can be closed completely in the near future." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11543" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.483, + 0.156 + ], + "angle": 0, + "content": "[1] R. Arandjelović, P. Gronat, A. Torii, T. Pajdla, and J. Sivic. NetVLAD: CNN architecture for weakly supervised place recognition. In CVPR, 2016. 2, 3, 4, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.157, + 0.483, + 0.198 + ], + "angle": 0, + "content": "[2] Daniel Barath, Jana Noskova, Maksym Ivashechkin, and Jiri Matas. MAGSAC++, a fast, reliable and accurate robust estimator. 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Robust Visual Localization with R-SCoRe. Left: Point cloud of Aachen reconstructed by R-SCoRe. Right: On the large-scale Aachen Day-Night dataset [53, 56] using only daytime training images, R-SCoRe achieves $64.3\%$ accuracy under the $(0.25\mathrm{m}, 2^{\circ})$ threshold for nighttime query images. It outperforms all previous SCR methods (circles) by a large margin. With a small map size of only 47MB at a comparable accuracy, R-SCoRe is an attractive alternative to traditional methods (triangles). + +![](images/20fb06e95c80d98f4604111579162b4b5839caa4581013fca60c3a25bda18fff.jpg) + +# Abstract + +Learning-based visual localization methods that use scene coordinate regression (SCR) offer the advantage of smaller map sizes. However, on datasets with complex illumination changes or image-level ambiguities, it remains a less robust alternative to feature matching methods. This work aims to close the gap. We introduce a covisibility graph-based global encoding learning and data augmentation strategy, along with a depth-adjusted reprojection loss to facilitate implicit triangulation. Additionally, we revisit the network architecture and local feature extraction module. Our method achieves state-of-the-art on challenging large-scale datasets without relying on network ensembles or 3D supervision. On Aachen Day-Night, we are $10 \times$ more accurate than previous SCR methods with similar map sizes and require at least $5 \times$ smaller map sizes than any other SCR method while still delivering superior accuracy. Code is available at: https://github.com/cvg/scrstudio. + +# 1. Introduction + +Visual localization is the task of estimating the 6-DoF pose of a camera in a known scene with a query image. It is a fundamental problem in computer vision, with applications in augmented reality, autonomous driving, and robotics. + +Classical feature matching methods [19, 50, 51, 55] have matured through years of research and now provide robust and accurate localization results. However, these methods typically require explicit 3D scene representations, where a large number of descriptors are stored, leading to substantial map sizes, especially for large-scale scenes. In contrast, pose regression [11, 30, 31, 44, 59, 65, 71, 73] and scene coordinate regression (SCR) [4-6, 8, 9, 21, 36, 68] aim to implicitly encode scene information in neural networks. + +SCR methods follow a structure-based paradigm similar to feature matching, i.e., estimating pose from 2D-3D correspondences but replacing explicit matching with regressing the correspondences directly. They are usually limited to small scenes [9] and have yet to match feature matching methods in terms of accuracy and robustness. Recent ad + +vances [68] extend SCR to large-scale scenes using a single model. However, its performance is still not on par with feature matching methods, especially in complex scenes with challenging illumination changes [53, 56]. + +In this work, we conduct a detailed analysis of the design principles behind the SCR framework, including local and global encoding, network architecture, and training strategies. Based on this analysis, we propose to revisit SCR to enhance the robustness and accuracy of SCR methods for large-scale visual localization tasks. As shown in Fig. 1, our robust SCR (R-SCoRe) improves the night-time localization accuracy for SCR methods to $64.3\%$ under the $(0.25\mathrm{m}, 2^{\circ})$ threshold on the Aachen Day-Night dataset, all with a map size of only 47MB. R-SCoRe significantly outperforms previous SCR methods and achieves accuracy comparable to feature matching techniques. + +Tab. 1 summarizes the practicability of R-SCoRe in complex large-scale scenes. While feature matching methods are also accurate, their map size can be prohibitively large, sometimes more than two orders of magnitude [19, 50, 51]. Compared to SCR methods with similarly small map sizes [9, 68], R-SCoRe is at least one order of magnitude more accurate. While we still clearly outperform other SCR methods, we maintain fast inference and significantly smaller map sizes – all without the need for scene-specific depth supervision. Our contributions are as follows. + +- We propose learning a global encoding and performing data augmentation based on the可视ability graph. To address the ambiguity of image retrieval features in complex large-scale scenes, we used multiple global hypotheses during testing. +- To bias the network from neglecting near points, we introduce a depth-adjusted reprojection loss and show that this allows for accurate localization without scene-specific ground truth coordinate supervision. +- To our knowledge, R-SCoRe is the first attempt of an SCR approach to achieve state-of-the-art performance on complex large-scale scenes without using an ensemble of networks or 3D model supervision. + +# 2. Related Work + +Feature Matching. Most state-of-the-art visual localization methods rely on feature matching [19, 50, 51, 55]. These methods typically adopt a structure-based paradigm, establishing 2D-3D correspondences between keypoints in a query image and 3D points in a scene. Camera pose is solved with geometric constraints, often a Perspective-n-Point (PnP) solver [26, 47] within a RANSAC framework [2, 17, 25] to effectively manage outliers. These methods commonly construct a Structure-from-Motion (SfM) map of the scene, which contains both 3D points and their descriptors [19, 22, 24, 49, 58]. To efficiently establish 2D + +
MethodsSizeTimeAcc.w/o Depth
FM[19, 50, 51]X✓✓✓
PR[31]✓✓X✓
SCR[64]XX✓X
[5, 36, 70]X✓✓X
[4, 9, 68]✓✓X✓
R-SCoRe✓✓✓✓
+ +Table 1. Comparison with other methods on complex large-scale scenes [53, 56]. Feature matching (FM) methods are accurate but need a large map size. Pose regression (PR) methods are fast but less accurate. We maintain a small map size while achieving remarkable accuracy. + +3D matches, they often follow a two-level approach [50]. First, potentially relevant database images are retrieved using image retrieval techniques [1, 48, 75]. This is followed by 2D-2D matching with the query image [39, 50, 51]. + +However, a significant limitation of these methods is the necessity to store all descriptor vectors of the 3D model, which can lead to storage challenges, particularly in large maps. To address this issue, various compression techniques have been proposed. These include reducing the number of 3D points [12, 13, 23, 37, 72] or compressing descriptors [20, 28, 29, 34, 40, 54, 67, 72]. Recently, several studies [46, 69, 74] have proposed alternative approaches that eliminate the need for explicit descriptor storage. Instead, these methods advocate for direct matching against geometric representations, such as point clouds or meshes. + +Pose Regression. These methods [11, 30, 31, 44, 59, 65, 71, 73] directly estimates the camera pose of a query image with a neural network. However, they tend to struggle with generalization and often only achieve an accuracy similar to image retrieval methods [57]. + +Scene Coordinate Regression. Following a similar structure-based localization paradigm as feature matching methods, SCR methods [4-9, 14, 15, 21, 36, 45, 60, 66, 68, 70] regress 2D-3D correspondences between the query image and the scene, and estimate the camera pose using geometric constraints. Though SCR methods are more accurate than pose regression methods, they usually still struggle with large-scale scenes [9]. + +Recently, several approaches have been proposed to improve the scalability and performance of SCR in large-scale scenes. These methods often rely on ground truth 3D coordinates and aim to handle large scenes by dividing them into smaller segments, such as spatial regions [5], voxels [64], or hierarchical clusters [36, 70]. Recent advancements have explored alternatives that do not require ground truth 3D supervision. For example, ACE [9] uses reprojection loss only for training. GLACE [68] further introduces a global + +![](images/c9d7b97356fe9828d3f6679a8464d9a0ffde448a8dce5fe916adfdbf5dc2dc2a.jpg) +Figure 2. R-SCoRe pipeline. (a) Following the SCR workflow in [68], we concatenate patch-level local encodings with image-level global encodings as input to a scene-specific MLP. (b) We learn contrastive global encodings from the可视ability graph using Node2Vec [27]. During training, global encodings are sampled from neighboring nodes for data augmentation. During inference, we retrieve global encodings from the $k$ nearest training images via NetVLAD [1] as hypotheses and select the one yielding the most RANSAC inliers. We enhance the SCR MLP with a refinement module and introduce a depth-adjusted reprojection loss to reduce bias toward distant points. + +encoding mechanism that eliminates the need for scene segmentation. Despite these improvements, these methods still encounter limitations under challenging conditions, such as significant changes in illumination. + +# 3. Method + +Our Scene Coordinate Regression (SCR) workflow is depicted in Fig. 2a. During training, we have access to a可视ability graph to learn global encodings which are concatenated to the local encodings. During inference, we retrieve global encoding hypotheses from the $k$ nearest training images and predict 2D-3D correspondences: we run PnP for each hypothesis and select the one yielding the most RANSAC inliers. Fig. 2b illustrates our detailed R-SCoRe pipeline, where we split SCR into coarse and refinement blocks and introduce可视ibility-based global encoding and data augmentation techniques. + +# 3.1. Preliminaries + +Visual Localization. Given a test image $I_{\mathrm{test}}$ with known intrinsic $\mathbf{K}_{\mathrm{test}}$ , the goal is to estimate its extrinsic, i.e., the rigid transformation $[\mathbb{R}_{\mathrm{test}}|\mathbf{t}_{\mathrm{test}}]$ from world coordinate to camera coordinate. The scene is typically given by a set of training images $I_{\mathrm{train}}$ with known ground truth poses $[\mathbb{R}_{\mathrm{train}}|\mathbf{t}_{\mathrm{train}}]$ and intrinsics $\mathbf{K}_{\mathrm{train}}$ . + +Scene Coordinate Regression. The SCR pipeline employs a neural network $f$ to directly regress the 3D coordinate $y = f(\mathbf{F}(x))$ for each 2D keypoint $x$ with feature $\mathbf{F}(x)$ . Without the need to store large point clouds with descriptors, SCR methods implicitly represent the scene with a neural network, which usually results in a smaller map size. + +Scalable SCR without 3D ground truth. Recent advances [9, 68] allow SCR to scale to large scenes without scene-specific 3D supervision. To reduce ambiguities in large scenes, GLACE [68] (Fig. 2a) concatenates a local patch-level encoding with an image-level global encoding + +as the keypoint feature $\mathbf{F}(x)$ . The local encoder is a pretrained DSAC* [6] backbone, following [9]. The global encoder uses a pretrained image retrieval model [75] with Gaussian noise augmentation to prevent overfitting to trivial solutions, cf. [68]. To accelerate training, all features are precomputed and buffered in GPU memory, from which a random sample is drawn for each batch. + +Without ground truth scene coordinates, the output 3D point $y$ is reprojected with the ground truth pose $\mathbb{R}, t$ and intrinsics $\mathbb{K}$ , and compared to the keypoint location $x$ in 2D: + +$$ +e _ {2} (x, y) = \left\| x - \pi (\mathrm {K} (\mathrm {R} y + \mathbf {t})) \right\| _ {2}, \tag {1} +$$ + +where $\pi$ converts homogeneous to Cartesian coordinates. + +Instead of explicitly grouping corresponding observations into tracks, this underconstrained supervision is applied to each independent prediction. Prior works [45, 68] suggest that implicit triangulation can still occur as the network tends to produce similar outputs for similar inputs. + +The reprojection error is fed into a dynamic robust loss, cf. ACE [9], to focus on points accurately regressed: + +$$ +l _ {\text {d y n a m i c}} \left(e _ {2} (x, y)\right) = \tau (t) \rho \left(\frac {e _ {2} (x , y)}{\tau (t)}\right), \tag {2} +$$ + +where ACE [9] uses tanh as robust loss $(\rho \coloneqq \tanh)$ . Based on the relative training time $t \in [0,1]$ , the bandwidth $\tau(t)$ is adjusted dynamically during training: + +$$ +\tau (t) = \sqrt {1 - t ^ {2}} \tau_ {\max } + \tau_ {\min }. \tag {3} +$$ + +Keypoints $x$ whose regressed 3D point $y$ fall outside the valid frustum are penalized differently. Valid points are defined to lie within a valid depth range $[d_{\min}, d_{\max}]$ in front of the camera. Further, their reprojection error $e_2(x, y)$ must be smaller than a threshold $e_{\max}$ . For invalid points, we penalize their distance to a pseudo ground truth point $\bar{y}$ : + +$$ +l _ {\text {i n v a l i d}} (y) = \left\| y - \bar {y} \right\| _ {2}, \tag {4} +$$ + +where $\bar{y}$ is computed by the inverse projection of the pixel $x$ using a fixed target depth $d_{\mathrm{target}}$ . + +# 3.2. Network Architecture + +We adopt the MLP architecture and position decoder from GLACE [68], scaling the network width with scene size. As illustrated in Fig. 2b, we also introduce a refinement module at the end of the network, which adjusts the final output $y$ by predicting an offset from the intermediate prediction $y_0$ . The coarse coordinate $y_0$ is reintroduced into the refinement module through positional encoding [43, 63] using sine and cosine functions with periods ranging from 0.5 to 2048, which is added to the intermediate feature. This empirically improves training stability and allows the network to achieve lower training reprojection errors more rapidly. + +# 3.3. Input Encoding + +Analysis. In implicit triangulation, reprojection constraints are grouped based on input similarity. Therefore, the desired properties of input encodings are as follows: positive pairs observing the same points should produce similar features, while negative pairs observing distinct points should yield clearly distinguishable features. Additionally, it is preferable for the encodings to be low-dimensional to minimize memory requirements. + +Local Encoding. At the local patch level, features should differentiate observations of the same point from those of different points. The requirement aligns with the properties of local descriptors used in traditional feature matching, suggesting that we can directly leverage their local feature extractors. We investigate pretrained feature extractors for both dense and sparse matching methods, such as LoFTR [62] and Dedode [24]. To lower memory consumption during training, we apply PCA to all the features from the training dataset, reducing their dimensionality while retaining most of the variance. We experimentally observe that reducing the dimensionality to 128 dimensions preserves over $90\%$ of the variance on various datasets [35, 53, 56]. + +Covisibility Graph Based Global Encoding. Image-level global features should distinguish between covisible and non-covisible image pairs, i.e. whether the images are viewing the same part of the scene, to resolve ambiguities in local encodings. Although global encodings with image-level receptive fields can help, they may still be insufficient to resolve ambiguities in complex environments, as shown in Fig. 3. This limitation can lead to imperfect grouping of reprojection constraints during training, thereby impairing the effectiveness of implicit triangulation. Furthermore, we point out that the learned SCR function may lack (Lipschitz) smoothness [32] w.r.t. the global encodings if adapted naively, e.g. minor variations in the global encoding can result in significant shifts in corresponding 3D points and consequently reduce generalization at test time. + +To address these issues, we propose to directly learn + +![](images/254385d40b9454430dda83bf93dc38f7ac1cdf46f8b04762d2706ce692f8651d.jpg) +(a) Distribution of feature distance for covisible and non-covisible pairs. + +![](images/db873f8d30c79bca577c3e1e1fc17e15a2afdb3b61e50d40cd2dab7e81cb577e.jpg) + +![](images/eb876650ac78bfd8a51e93d40f8c644ac09b855ac7dd86e51fe08e65999f933e.jpg) +(b) Precision Recall Curve of predicting covisibility by feature distance. +Figure 3. Comparison of global encodings. Aligning the learning of global encodings with the covisibility graph topology (Node2Vec [27]) helps distinguish covisible and non-covisible pairs (a) and predict covisibility by feature distance (b). + +embeddings aligned with the可视isibility graph's topology using Node2Vec [27], which samples sequences with weighted random walks and optimizes node embeddings with a Skip-gram [42] objective. For training images, the可视isibility graph is easily available. It can be estimated from the frustum overlap of ground truth poses (see the supplementary for more details). At test time, however,可视isibility information is unknown, so we propose generating multiple global encoding hypotheses by retrieving the nearest training images using NetVLAD [1] features. The global encoding of each retrieved image serves as a hypothesis, and we select the hypothesis yielding the maximum RANSAC inliers for the final localization result. + +This approach effectively decouples training-time and test-time ambiguities: during training, the network focuses on learning scene structure without ambiguity, while at test time, multiple hypotheses enable the resolution of complex, often multimodal ambiguities. + +Covisibility Graph Based Data Augmentation. Our Covisibility Graph Encoding effectively learns a low-ambiguity global encoding. However, data augmentation is still necessary to prevent the network from distinguishing covisible pairs based on distinct global encodings. Instead of simply adding isotropic Gaussian noise [68], we introduce a graph-based data augmentation strategy. In this approach, rather than applying isotropic noise, we randomly replace an image's global encoding with that of a neighboring image from the covisibility graph. Specifically, with probabil + +![](images/8de174b7d4c166b2a4cc92948f00b3621ebfd2e0c831eefd85d6d09657802bb4.jpg) +Figure 4. Statistics of reprojection error for points with different depths. The kernel density estimation (KDE) of reprojection error distribution conditioned on disparity from SCR models trained with various local encodings across different datasets. We observe that far points (low disparity) exhibit a lower reprojection error. (Detector-free LoFTR [62] with an $8 \times$ downsampled output has a larger 2D keypoint error than Detector-based Dedode [24].) + +![](images/edf8201abec980d6d59aa69ff737e0bdc00eac5ff6f4cedfbfeac56066374ae0.jpg) + +ity $p = 0.5$ , the current image's global encoding is retained, while with probability $1 - p$ , it is replaced by the global encoding of a randomly sampled neighboring image. + +# 3.4. Output Supervision + +Depth Bias in Reprojection Loss. Fig. 4 displays statistics collected from training SCR models with various local encodings across different datasets. It indicates that points closer to the camera empirically exhibit higher reprojection errors compared to distant points, hence we observe a bias toward distant points. This bias is magnified by training with the robust loss Eq. (2), as the supervision signal tends to neglect (nearby) points with higher reprojection errors (cf. Fig. 5). Assuming the training time distribution of camera poses to be representative for testing, regressing near points fewer and less accurately during testing diminishes the positional localization accuracy. We conjecture that to facilitate implicit triangulation for near points, a higher reprojection error should be allowed to compensate for the reprojection of nearby points being more sensitive to pose variations and coordinate inaccuracies. + +Depth Adjusted Reprojection Error. We propose normalizing the reprojection error in Eq. (1) based on the depth of the predicted scene coordinate. Specifically, the observation standard deviation, $\sigma_{o}$ , is defined as: + +$$ +\sigma_ {o} = \sqrt {\left(\frac {\sigma_ {3}}{d}\right) ^ {2} + \sigma_ {2} ^ {2}}, \tag {5} +$$ + +where we denote the variance of the noise of the 2D observations by $\sigma_2^2$ . The variance of the 3D prediction is denoted by $\sigma_3^2$ and by $d$ the depth of the point. The reprojection error is then adjusted accordingly: + +$$ +e _ {3} (x, y) = \frac {e _ {2} (x , y)}{\sigma_ {o}} = \frac {e _ {2} (x , y)}{\sigma_ {2}} \sqrt {\frac {d ^ {2}}{d ^ {2} + \left(\frac {\sigma_ {3}}{\sigma_ {2}}\right) ^ {2}}}. \tag {6} +$$ + +Selective Application of Depth Adjustment. The bias towards distant points may sometimes actually be beneficial, as underconstrained points can be pushed farther along the ray, making them easier to identify as outliers during test time. Therefore, we apply our depth-adjusted reprojection loss only to the intermediate coarse scene coordinate output $y_0$ during training (Fig. 2b), and retain the original reprojection loss for the final output. To mitigate the concentration of the supervision signal on points with low projection error, we replace tanh with the Geman-McClure [3] robust loss function which has a heavier tail than tanh: + +$$ +\rho (x) = \frac {9 x ^ {2}}{9 x ^ {2} + 4}. \tag {7} +$$ + +In order to guide the convergence of the regressed points, $y$ , by the intermediate output $y_{0}$ (affected by the normalized loss from Eq. (6)), we also apply a consistency loss at the beginning of the training: + +$$ +l _ {\text {c o n s i s t e n c y}} = \lambda (t) | | y - y _ {0} | | _ {2}, \tag {8} +$$ + +where $\lambda (t)$ is a dynamic weight that decreases to 0 in a cosine schedule during the first $50\%$ of training time. + +$$ +\lambda (t) = \left\{ \begin{array}{l l} \frac {1}{2} (1 + \cos 2 \pi t), & \text {i f} t \in [ 0, 0. 5 ] \\ 0, & \text {o t h e r w i s e} \end{array} , \right. \tag {9} +$$ + +where $t$ is the relative training time. + +Optional Depth Supervision. When depth is available, we can also benefit from direct depth supervision. The depth does not need to be accurate since we mainly use the depth for initialization. Specifically, we simply replace the consistency loss between intermediate and final output in Eq. (8) with a ground truth coordinate supervision loss: + +$$ +l _ {\text {d e p t h}} = \lambda (t) \left(\left\| y - \bar {y} \right\| _ {2} + \left\| y _ {0} - \bar {y} \right\| _ {2}\right), \tag {10} +$$ + +where $\bar{y}$ is the pseudo ground truth computed by the inverse projection of the pixel given the depth, pose, and intrinsic. + +# 4. Experiments + +# 4.1. Datasets + +We use the Aachen Day-Night [53, 56] and the Hyundai Department Store dataset [35] to evaluate R-SCoRe on complex large-scale indoor and outdoor scenes. + +Aachen Day-Night. It is a large-scale benchmark for outdoor visual localization, covering the historic inner city of Aachen, Germany, over an area of approximately $6 \, km^2$ . It presents significant challenges due to varying illumination conditions, especially between day and night. The dataset includes 4,328 daytime images for training, along with 824 daytime query images and 98 nighttime query images. + +
Methodsw/o DepthSizeAachen DayAachen Night
HLoc+SPSG [19, 50, 51]Yes7.82GB89.695.498.886.793.9100
AS [55]Yes750MB85.392.297.939.849.064.3
Cascaded [16]Yes140MB76.788.695.833.748.062.2
QP+R.Sift [41]Yes30MB62.676.384.716.318.424.5
Squeezezer [72]Yes240MB75.589.796.250.067.378.6
PixLoc [52]Yes2.13GB64.369.377.451.155.167.3
Neumap [64]No1.26GB80.890.995.648.067.387.8
HSCNet [36]No213MB71.181.991.732.743.965.3
HSCNet++ [70]No274MB72.781.691.443.957.176.5
ESAC (×50) [5]No1.31GB42.659.675.56.110.218.4
ACE (×50) [9]Yes205MB6.917.250.00.01.05.1
GLACE [68]Yes27MB8.620.864.01.01.017.3
R-SCoRe (Dedode [24]) + DepthYes47MB74.886.996.464.389.896.9
No47MB79.088.596.466.389.896.9
+ +Table 2. Aachen Day-Night evaluation. The map size and percentages of query images within three thresholds: (0.25m, $2^{\circ}$ ), (0.5m, $5^{\circ}$ ), and (5m, $10^{\circ}$ ) and are reported. We report our results with Dedode [24] local encoding and optional depth supervision. Feature matching (FM) methods [19, 50, 51] are more accurate, but the map size is large. R-SCoRe achieves comparable accuracy with a small map size. + +Hyundai Department Store. It is a large-scale indoor visual localization benchmark, covering three floors of a department store. Each floor consists of multiple sequences captured over four months, spanning an area of approximately $10,000~m^2$ . It presents challenges beyond its large scale, including dynamic objects, illumination changes, and textureless regions. B1 is particularly challenging as the training images are captured under low-lighting conditions, while the query images are brightly illuminated. The dataset includes 44,283 training images and 5,927 test images. + +# 4.2. Benchmark Results + +Aachen Day-Night. As shown in Tab. 2, R-SCoRe enhances the performance of scene coordinate regression (SCR) based methods [5, 36, 68, 70], achieving competitive results with a single low-map-size model without the need for scene-specific depth supervision. While R-SCoRe is competitive with the best performing method, HLoc [19, 50, 51], we forfeit some ground at highest accuracy. However, R-SCoRe demands $170 \times$ less memory to store the map. This huge gap could already render SCR based methods as an attractive alternative for some applications. Most other feature-based methods (FM) also deliver significantly larger maps. While delivering comparable performance for the Aachen Day dataset, they all fall behind R-SCoRe on the Aachen Night dataset. The only FM method [41] with a comparable map size is outperformed on all metrics, e.g. [41] is $4 - 5 \times$ worse in accuracy on the night dataset. Compared to other SCR methods that work without depth supervision [9, 68] R-SCoRe is $10 \times$ superior in accuracy. The so far most accurate SCR based method [64] produces large maps ( $27 \times$ larger) and is prohibitively slow + +in inference. The next most accurate SCR method, [70] is outperformed by $46\%$ at night and highest threshold, while R-SCoRe maintains a $6\times$ smaller map size - without the need for depth supervision. We observe a small gain in performance if we utilize depth for supervision of R-SCoRe. + +Hyundai Department Store. R-SCoRe again significantly outperforms the SCR based methods [5, 68], including recent ensemble networks [5, 9], see Tab. 3. Compared to the state-of-the-art feature matching based localization [50] we achieve competitive results with a single low-map-size model and forfeit some ground at the highest accuracy threshold. However, our model is at least three orders of magnitude smaller for either feature [22, 49] incorporated into [50], which can be a valuable advantage in practice. Recall that depth supervision is not necessary for R-SCoRe, but if available, it can also enhance performance further. The B1 scene exhibits strong illumination changes and we observe significantly better performance when using local encodings from Dedode instead of LoFTR [62]. + +# 4.3. Implementation Details + +Most hyperparameters follow default values [68] and extensive tuning is not performed, as we empirically find the approach remains robust within a reasonable range, apart from the trade-off between network size and performance. + +Input Encodings. For local encodings, we perform PCA to reduce their dimensionality to 128. The global encodings are represented in 256 dimensions, consistent with the $R^2$ Former [75] feature dimension used in GLACE [68] for fair comparison. We estimate the可视ability graph based on camera poses, using a weighted frustum overlap method (details provided in the supplementary materials), with a + +
MethodsDept. 1F TestDept. 4F TestDept. B1 Test
HLoc+D2-Net [22, 50](78.0 / 82.8 / 88.0) / 398GB(84.2 / 89.8 / 92.0) / 183GB(73.7 / 79.3 / 87.2) / 505GB
HLoc+R2D2 [49, 50](80.6 / 84.3 / 89.4) / 166GB(85.3 / 91.0 / 93.1) / 76GB(75.2 / 80.3 / 87.6) / 210GB
PoseNet [31](0.0 / 0.0 / 0.4) / 41MB(0.0 / 0.0 / 0.1) / 41MB(0.0 / 0.0 / 0.1) / 41MB
ESAC (×50) [5](43.3 / 66.3 / 77.0) / 1.4GB(45.2 / 62.5 / 73.1) / 1.4GB(3.5 / 8.2 / 12.6) / 1.4GB
ACE (×50) [9](14.1 / 54.4 / 75.5) / 205MB(27.3 / 70.9 / 84.1) / 205MB(2.7 / 14.4 / 29.3) / 205MB
GLACE [68](5.6 / 21.3 / 48.6) / 42MB(8.4 / 29.8 / 51.6) / 42MB(0.9 / 4.4 / 11.9) / 42MB
R-SCoRe (LoFTR* [62]) + Depth(63.2 / 82.4 / 92.4) / 127MB(62.2 / 82.7 / 90.9) / 50MB(26.9 / 50.7 / 69.6) / 130MB
(67.3 / 84.5 / 92.6) / 127MB(70.5 / 87.0 / 92.9) / 50MB(30.8 / 53.7 / 72.7) / 130MB
R-SCoRe (Dedode [24]) + Depth(61.4 / 80.2 / 90.9) / 127MB(60.2 / 79.3 / 87.9) / 50MB(60.1 / 77.3 / 89.6) / 130MB
(63.9 / 83.3 / 90.8) / 127MB(76.7 / 89.3 / 93.0) / 50MB(61.5 / 77.6 / 88.8) / 130MB
+ +maximum viewing frustum depth of $d_{\mathrm{v}} = 50$ for outdoor scenes and $d_{\mathrm{v}} = 8$ for indoor scenes. + +Output Supervision. The supervision uses a dynamic robust loss bandwidth strategy inspired by ACE [9]. For coarse intermediate outputs, the parameters, see Eq. (3), are set to $\tau_{\mathrm{min}} = 1$ and $\tau_{\mathrm{max}} = 50$ . In contrast, $\tau_{\mathrm{max}} = 25$ is used for the final output, which allows the refinement layer to focus on the most accurate predictions while the initial layers do not ignore the optimization of relatively inaccurate predictions. Fixing $\sigma_{2} = 1$ in the depth-adjusted reprojection loss, Eq. (6), allows us to control the behavior by adjusting $\tau$ and $\frac{\sigma_3}{\sigma_2}$ . For indoor scenes, $\sigma_{3} = 3$ is applied, while $\sigma_{3} = 8$ is used for outdoor scenes to account for different scales. We perform optional depth supervision using depth images rendered from the 3D model for the Hyundai Department Store dataset and Multi-View Stereo depth maps for the Aachen Day-Night dataset. + +Network Architecture. We adopt the MLP architecture and position decoder from GLACE [68] with expansion ratio $m = 2$ for the MLP, and 50 clusters for the position decoder. With MLP width $w = 256\left\lceil \sqrt{n / 1000} \right\rceil$ for $n$ training images, we scale the parameter count proportionally. + +Training. We found that adopting the optimization settings from ACE Zero [10] enhances both stability and convergence speed compared to the original ACE [9]. Specifically, we reduce the warmup ratio of the one-cycle learning rate schedule [61] from 0.25 to 0.04 and lower the peak learning rate from $5 \times 10^{-3}$ to $3 \times 10^{-3}$ . For our evaluation we adopt similar training parameters to GLACE [68], including a local feature buffer size of 128M, a large batch size of 320K and a training duration of 100k iterations. + +Testing. At test time, we retrieve the 10 nearest training images with NetVLAD [1]. The global encoding and retrieval features for training images are precomputed and compressed using Product Quantization [28]. For final pose + +Table 3. Hyundai Department Store Test Set evaluation. The percentages of query images within three thresholds: (0.1m, $1^{\circ}$ ), (0.25m, $2^{\circ}$ ), and (1m, $5^{\circ}$ ) and the map size are reported. R-SCoRe achieves competitive accuracy with a small map size. *We use LoFTR [62] outdoor, trained on MegaDepth [38], instead of the indoor model trained on ScanNet [18] for the B1 scene with strong illumination change. + +
Dept. 1F ValDept. B1 Val
ACE [9]68.787.595.914.128.345.8
LoFTR* [62]72.388.795.529.451.369.6
Dedode [24]70.686.695.557.774.786.7
+ +Table 4. Ablation study of local encoders. Accuracy at (0.1m, $1^{\circ}$ ), (0.25m, $2^{\circ}$ ), and (1m, $5^{\circ}$ ) thresholds are reported. Utilizing pretrained, off-the-shelf feature extractors improves the performance, especially under challenging conditions (B1). + +
Dept. 1F Val
R2Former [75] w/ Gaussian34.160.178.3
+ Multi Hypotheses42.174.592.2
+ Covis Augmentation62.083.894.8
+ Covis Encoding72.388.795.5
+ +Table 5. Ablation study of global encodings. We experiment with using multiple hypotheses at test time, applying covisibility graph-based data augmentation during training, and learning global encodings directly from the covisibility graph. Accuracy at $(0.1\mathrm{m},1^{\circ})$ , $(0.25\mathrm{m},2^{\circ})$ , and $(1\mathrm{m},5^{\circ})$ thresholds. + +estimation, we utilize PoseLib [33] with a maximum reprojection error of 10 pixels and up to 10,000 RANSAC iterations. On our PC (NVIDIA RTX 2080 GPU & Intel i7-9700K CPU), the average inference time for a $640 \times 480$ query image is 140 to $270\mathrm{ms}$ in total. + +- Global: NetVLAD (20ms), Retrieval (<1ms) +- Local: LoFTR (7ms) or DeDoDe (50ms) +- MLP: $\mathrm{w} = {768}\left( {{70}\mathrm{{ms}}}\right)$ or ${1280}\left( {{160}\mathrm{{ms}}}\right)$ +- Pose Solving: 40ms + +# 4.4. Ablation Study Results + +In our ablation studies, we investigate the impact of the different components in R-SCoRe. We evaluate on the validation split for the Hyundai Department Store dataset. Since the Aachen Day-Night dataset does not provide a validation + +
Aachen DayAachen Night
FM Covis75.487.695.864.389.895.9
Pose Covis74.886.996.464.389.896.9
+ +Table 6. Ablation study of covisibility graph. Building the covisibility graph using frustum overlap performs similarly to utilizing feature matching. Accuracy at $(0.25\mathrm{m}, 2^{\circ})$ , $(0.5\mathrm{m}, 5^{\circ})$ , and $(5\mathrm{m}, 10^{\circ})$ thresholds. + +
SupervisionDept. 1F ValDept. 4F Val
Original62.382.293.759.182.297.6
Adjusted70.686.695.563.984.298.3
Depth76.888.195.668.584.998.5
+ +Table 7. Ablation study of supervision methods. Original refers to the original reprojection error supervision, Adjusted refers to our depth-adjusted reprojection error supervision, and Depth uses ground truth depth for supervision. Accuracy at (0.1m, $1^{\circ}$ ), (0.25m, $2^{\circ}$ ), and (1m, $5^{\circ}$ ). + +split, we evaluate on the test set. + +Local Encoding. As shown in Tab. 4, for large scale indoor scenes with small illumination changes, alternative off-the-shelf local feature extractors [24, 62] achieve similar or even superior performance compared to the original ACE [9]. Note that this finding contradicts earlier investigations [9] that prefer a specifically trained backbone in their work. Additionally, local descriptors trained on MegaDepth [38], especially Dedode [24], demonstrate greater robustness in scenes with significant illumination changes. + +Global Encoding. Retrieving global encodings from training images avoids the domain gap. Better retrieval method and multiple hypotheses verification can help resolve ambiguities. Without retraining (Tab. 5), utilizing multiple global hypotheses at test time (+ Multi Hypotheses) results in a direct performance improvement in complex scenes. The performance improves significantly, once we incorporate our可视ibility graph-based data augmentation during training. In particular, we replace isotropic Gaussian noise [68] with our more precise可视ibility-based technique (+ Covis Augmentation). Finally, learning the global encoding directly from the可视ibility graph (+ Covis Encoding) reduces the interference between non-covisible training images and thereby facilitates implicit triangulation, especially in indoor scenes with significant ambiguity. + +Finally, we also explore the effect of computing the可视ibility graph via feature matching [19, 51]. As shown in Tab. 6, using a more accurate graph yields no significant improvement, indicating that R-SCoRe is robust to the quality of the可视ibility graph. Therefore, our simple frustum overlap-based graph is sufficient for effective performance. + +Supervision. Our depth-adjusted supervision effectively + +![](images/a2d5a77aa5e072b8bb430d0c96d47eb035ed10c8bbbe6c4661bd1144732635ff.jpg) +Figure 5. Ablation study of depth distribution after training with different supervision methods. Our depth-adjusted supervision matches the distribution of ground truth depth for supervision as compared to the original. + +mitigates the bias towards distant points and enhances the implicit triangulation of nearby points. As demonstrated in Fig. 5, depth-adjusted supervision significantly alters the depth distribution of predicted points, alleviating the previous ignorance of nearby points. This adjustment brings the distribution closer to that achieved with ground truth depth supervision, demonstrating a substantial reduction in the bias inherent in the original supervision approach. + +In Tab. 7, we observe that depth-adjusted supervision also leads to notable improvements in localization accuracy, particularly under stricter thresholds, where accurate translation estimation relies heavily on near points. Even without ground truth depth supervision, depth-adjusted supervision enables the model to achieve competitive performance. + +# 5. Conclusion + +In this work, we revisited scene coordinate regression (SCR) methods for robust visual localization in large-scale, complex environments. We analyzed the design principles of input encoding and training strategies, identifying several areas for enhancement. Our proposed R-SCoRe includes a covisibility graph-based global encoding learning and data augmentation strategy, a depth-adjusted reprojection loss to improve the implicit triangulation, and also other improvements including better architecture and local feature. Our contributions advance the state-of-the-art in SCR and demonstrate that SCR-based localization methods can achieve competitive performance in large-scale applications. While operating at comparably very small map sizes, R-SCoRe trails the state-of-the-art FM-based localization methods only at the strictest error thresholds. Although out-of-distribution generalization remains challenging, and gaps persist in handling extreme cases, given the relatively small history of SCR, we are positive the accuracy gap can be closed completely in the near future. + +# References + +[1] R. Arandjelović, P. Gronat, A. Torii, T. Pajdla, and J. Sivic. NetVLAD: CNN architecture for weakly supervised place recognition. 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Robust Visual Localization with R-SCoRe. Left: Point cloud of Aachen reconstructed by R-SCoRe. Right: On the large-scale Aachen Day-Night dataset [53, 56] using only daytime training images, R-SCoRe achieves " + }, + { + "bbox": [ + 54, + 396, + 555, + 441 + ], + "type": "inline_equation", + "content": "64.3\\%" + }, + { + "bbox": [ + 54, + 396, + 555, + 441 + ], + "type": "text", + "content": " accuracy under the " + }, + { + "bbox": [ + 54, + 396, + 555, + 441 + ], + "type": "inline_equation", + "content": "(0.25\\mathrm{m}, 2^{\\circ})" + }, + { + "bbox": [ + 54, + 396, + 555, + 441 + ], + "type": "text", + "content": " threshold for nighttime query images. It outperforms all previous SCR methods (circles) by a large margin. With a small map size of only 47MB at a comparable accuracy, R-SCoRe is an attractive alternative to traditional methods (triangles)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 356, + 211, + 541, + 388 + ], + "blocks": [ + { + "bbox": [ + 356, + 211, + 541, + 388 + ], + "lines": [ + { + "bbox": [ + 356, + 211, + 541, + 388 + ], + "spans": [ + { + "bbox": [ + 356, + 211, + 541, + 388 + ], + "type": "image", + "image_path": "20fb06e95c80d98f4604111579162b4b5839caa4581013fca60c3a25bda18fff.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 456, + 201, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 456, + 201, + 468 + ], + "spans": [ + { + "bbox": [ + 151, + 456, + 201, + 468 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "text", + "content": "Learning-based visual localization methods that use scene coordinate regression (SCR) offer the advantage of smaller map sizes. However, on datasets with complex illumination changes or image-level ambiguities, it remains a less robust alternative to feature matching methods. This work aims to close the gap. We introduce a covisibility graph-based global encoding learning and data augmentation strategy, along with a depth-adjusted reprojection loss to facilitate implicit triangulation. Additionally, we revisit the network architecture and local feature extraction module. Our method achieves state-of-the-art on challenging large-scale datasets without relying on network ensembles or 3D supervision. On Aachen Day-Night, we are " + }, + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "text", + "content": " more accurate than previous SCR methods with similar map sizes and require at least " + }, + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 55, + 482, + 297, + 696 + ], + "type": "text", + "content": " smaller map sizes than any other SCR method while still delivering superior accuracy. Code is available at: https://github.com/cvg/scrstudio." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 456, + 394, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 456, + 394, + 468 + ], + "spans": [ + { + "bbox": [ + 315, + 456, + 394, + 468 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 479, + 555, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 555, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 555, + 528 + ], + "type": "text", + "content": "Visual localization is the task of estimating the 6-DoF pose of a camera in a known scene with a query image. It is a fundamental problem in computer vision, with applications in augmented reality, autonomous driving, and robotics." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 530, + 556, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 530, + 556, + 639 + ], + "spans": [ + { + "bbox": [ + 312, + 530, + 556, + 639 + ], + "type": "text", + "content": "Classical feature matching methods [19, 50, 51, 55] have matured through years of research and now provide robust and accurate localization results. However, these methods typically require explicit 3D scene representations, where a large number of descriptors are stored, leading to substantial map sizes, especially for large-scale scenes. In contrast, pose regression [11, 30, 31, 44, 59, 65, 71, 73] and scene coordinate regression (SCR) [4-6, 8, 9, 21, 36, 68] aim to implicitly encode scene information in neural networks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": "SCR methods follow a structure-based paradigm similar to feature matching, i.e., estimating pose from 2D-3D correspondences but replacing explicit matching with regressing the correspondences directly. They are usually limited to small scenes [9] and have yet to match feature matching methods in terms of accuracy and robustness. Recent ad" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 703, + 282, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 703, + 282, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 703, + 282, + 713 + ], + "type": "text", + "content": "*Corresponding author (fangjinhua.wang@inf.ethz.ch)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11536" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "vances [68] extend SCR to large-scale scenes using a single model. However, its performance is still not on par with feature matching methods, especially in complex scenes with challenging illumination changes [53, 56]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "spans": [ + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "text", + "content": "In this work, we conduct a detailed analysis of the design principles behind the SCR framework, including local and global encoding, network architecture, and training strategies. Based on this analysis, we propose to revisit SCR to enhance the robustness and accuracy of SCR methods for large-scale visual localization tasks. As shown in Fig. 1, our robust SCR (R-SCoRe) improves the night-time localization accuracy for SCR methods to " + }, + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "inline_equation", + "content": "64.3\\%" + }, + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "text", + "content": " under the " + }, + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "inline_equation", + "content": "(0.25\\mathrm{m}, 2^{\\circ})" + }, + { + "bbox": [ + 54, + 121, + 295, + 264 + ], + "type": "text", + "content": " threshold on the Aachen Day-Night dataset, all with a map size of only 47MB. R-SCoRe significantly outperforms previous SCR methods and achieves accuracy comparable to feature matching techniques." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 266, + 295, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 295, + 385 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 295, + 385 + ], + "type": "text", + "content": "Tab. 1 summarizes the practicability of R-SCoRe in complex large-scale scenes. While feature matching methods are also accurate, their map size can be prohibitively large, sometimes more than two orders of magnitude [19, 50, 51]. Compared to SCR methods with similarly small map sizes [9, 68], R-SCoRe is at least one order of magnitude more accurate. While we still clearly outperform other SCR methods, we maintain fast inference and significantly smaller map sizes – all without the need for scene-specific depth supervision. Our contributions are as follows." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 387, + 295, + 542 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 387, + 295, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 295, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 295, + 446 + ], + "type": "text", + "content": "- We propose learning a global encoding and performing data augmentation based on the可视ability graph. To address the ambiguity of image retrieval features in complex large-scale scenes, we used multiple global hypotheses during testing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 447, + 295, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 295, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 295, + 493 + ], + "type": "text", + "content": "- To bias the network from neglecting near points, we introduce a depth-adjusted reprojection loss and show that this allows for accurate localization without scene-specific ground truth coordinate supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 494, + 295, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 295, + 542 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 295, + 542 + ], + "type": "text", + "content": "- To our knowledge, R-SCoRe is the first attempt of an SCR approach to achieve state-of-the-art performance on complex large-scale scenes without using an ensemble of networks or 3D model supervision." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 556, + 142, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 142, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 142, + 569 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "content": "Feature Matching. Most state-of-the-art visual localization methods rely on feature matching [19, 50, 51, 55]. These methods typically adopt a structure-based paradigm, establishing 2D-3D correspondences between keypoints in a query image and 3D points in a scene. Camera pose is solved with geometric constraints, often a Perspective-n-Point (PnP) solver [26, 47] within a RANSAC framework [2, 17, 25] to effectively manage outliers. These methods commonly construct a Structure-from-Motion (SfM) map of the scene, which contains both 3D points and their descriptors [19, 22, 24, 49, 58]. To efficiently establish 2D" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 553, + 177 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 553, + 177 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 553, + 177 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 553, + 177 + ], + "type": "table", + "html": "
MethodsSizeTimeAcc.w/o Depth
FM[19, 50, 51]X✓✓✓
PR[31]✓✓X✓
SCR[64]XX✓X
[5, 36, 70]X✓✓X
[4, 9, 68]✓✓X✓
R-SCoRe✓✓✓✓
", + "image_path": "58107c6dd74507dbf6a3dda162f229c62602593ed7c1a279a2ea8403dae136f9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 185, + 553, + 240 + ], + "lines": [ + { + "bbox": [ + 313, + 185, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 185, + 553, + 240 + ], + "type": "text", + "content": "Table 1. Comparison with other methods on complex large-scale scenes [53, 56]. Feature matching (FM) methods are accurate but need a large map size. Pose regression (PR) methods are fast but less accurate. We maintain a small map size while achieving remarkable accuracy." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 262, + 553, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 553, + 310 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 553, + 310 + ], + "type": "text", + "content": "3D matches, they often follow a two-level approach [50]. First, potentially relevant database images are retrieved using image retrieval techniques [1, 48, 75]. This is followed by 2D-2D matching with the query image [39, 50, 51]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 310, + 554, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 554, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 554, + 441 + ], + "type": "text", + "content": "However, a significant limitation of these methods is the necessity to store all descriptor vectors of the 3D model, which can lead to storage challenges, particularly in large maps. To address this issue, various compression techniques have been proposed. These include reducing the number of 3D points [12, 13, 23, 37, 72] or compressing descriptors [20, 28, 29, 34, 40, 54, 67, 72]. Recently, several studies [46, 69, 74] have proposed alternative approaches that eliminate the need for explicit descriptor storage. Instead, these methods advocate for direct matching against geometric representations, such as point clouds or meshes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 445, + 554, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 554, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 554, + 506 + ], + "type": "text", + "content": "Pose Regression. These methods [11, 30, 31, 44, 59, 65, 71, 73] directly estimates the camera pose of a query image with a neural network. However, they tend to struggle with generalization and often only achieve an accuracy similar to image retrieval methods [57]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 510, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 605 + ], + "type": "text", + "content": "Scene Coordinate Regression. Following a similar structure-based localization paradigm as feature matching methods, SCR methods [4-9, 14, 15, 21, 36, 45, 60, 66, 68, 70] regress 2D-3D correspondences between the query image and the scene, and estimate the camera pose using geometric constraints. Though SCR methods are more accurate than pose regression methods, they usually still struggle with large-scale scenes [9]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": "Recently, several approaches have been proposed to improve the scalability and performance of SCR in large-scale scenes. These methods often rely on ground truth 3D coordinates and aim to handle large scenes by dividing them into smaller segments, such as spatial regions [5], voxels [64], or hierarchical clusters [36, 70]. Recent advancements have explored alternatives that do not require ground truth 3D supervision. For example, ACE [9] uses reprojection loss only for training. 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R-SCoRe pipeline. (a) Following the SCR workflow in [68], we concatenate patch-level local encodings with image-level global encodings as input to a scene-specific MLP. (b) We learn contrastive global encodings from the可视ability graph using Node2Vec [27]. During training, global encodings are sampled from neighboring nodes for data augmentation. During inference, we retrieve global encodings from the " + }, + { + "bbox": [ + 54, + 178, + 555, + 236 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 54, + 178, + 555, + 236 + ], + "type": "text", + "content": " nearest training images via NetVLAD [1] as hypotheses and select the one yielding the most RANSAC inliers. 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Fig. 2b illustrates our detailed R-SCoRe pipeline, where we split SCR into coarse and refinement blocks and introduce可视ibility-based global encoding and data augmentation techniques." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 478, + 142, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 478, + 142, + 490 + ], + "spans": [ + { + "bbox": [ + 55, + 478, + 142, + 490 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 500, + 296, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 500, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 500, + 296, + 574 + ], + "type": "text", + "content": "Visual Localization. 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Without the need to store large point clouds with descriptors, SCR methods implicitly represent the scene with a neural network, which usually results in a smaller map size." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 653, + 296, + 715 + ], + "type": "text", + "content": "Scalable SCR without 3D ground truth. Recent advances [9, 68] allow SCR to scale to large scenes without scene-specific 3D supervision. 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ACE [9], to focus on points accurately regressed:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 499, + 553, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 499, + 553, + 526 + ], + "spans": [ + { + "bbox": [ + 353, + 499, + 553, + 526 + ], + "type": "interline_equation", + "content": "l _ {\\text {d y n a m i c}} \\left(e _ {2} (x, y)\\right) = \\tau (t) \\rho \\left(\\frac {e _ {2} (x , y)}{\\tau (t)}\\right), \\tag {2}", + "image_path": "517da426503170fa244e6fa9770fbfd1a17e9081f2045d3133890bae0488871e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "text", + "content": "where ACE [9] uses tanh as robust loss " + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "inline_equation", + "content": "(\\rho \\coloneqq \\tanh)" + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "text", + "content": ". Based on the relative training time " + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "text", + "content": ", the bandwidth " + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "inline_equation", + "content": "\\tau(t)" + }, + { + "bbox": [ + 313, + 530, + 554, + 567 + ], + "type": "text", + "content": " is adjusted dynamically during training:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 373, + 572, + 553, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 572, + 553, + 588 + ], + "spans": [ + { + "bbox": [ + 373, + 572, + 553, + 588 + ], + "type": "interline_equation", + "content": "\\tau (t) = \\sqrt {1 - t ^ {2}} \\tau_ {\\max } + \\tau_ {\\min }. \\tag {3}", + "image_path": "55bddad1faacb547608a921ce244914a4b05c99138223a506478420e439aeb92.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": "Keypoints " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": " whose regressed 3D point " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": " fall outside the valid frustum are penalized differently. Valid points are defined to lie within a valid depth range " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "[d_{\\min}, d_{\\max}]" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": " in front of the camera. Further, their reprojection error " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "e_2(x, y)" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": " must be smaller than a threshold " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "e_{\\max}" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": ". For invalid points, we penalize their distance to a pseudo ground truth point " + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 593, + 555, + 666 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 387, + 671, + 553, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 671, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 387, + 671, + 553, + 685 + ], + "type": "interline_equation", + "content": "l _ {\\text {i n v a l i d}} (y) = \\left\\| y - \\bar {y} \\right\\| _ {2}, \\tag {4}", + "image_path": "18c06debe2bfe7cebac5358747a9c5d9a3ccfdde89997b08eee58df46a56bc48.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": " is computed by the inverse projection of the pixel " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": " using a fixed target depth " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{target}}" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11538" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 181, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 181, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 181, + 83 + ], + "type": "text", + "content": "3.2. Network Architecture" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "text", + "content": "We adopt the MLP architecture and position decoder from GLACE [68], scaling the network width with scene size. As illustrated in Fig. 2b, we also introduce a refinement module at the end of the network, which adjusts the final output " + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "text", + "content": " by predicting an offset from the intermediate prediction " + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "inline_equation", + "content": "y_0" + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "text", + "content": ". The coarse coordinate " + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "inline_equation", + "content": "y_0" + }, + { + "bbox": [ + 55, + 89, + 296, + 222 + ], + "type": "text", + "content": " is reintroduced into the refinement module through positional encoding [43, 63] using sine and cosine functions with periods ranging from 0.5 to 2048, which is added to the intermediate feature. This empirically improves training stability and allows the network to achieve lower training reprojection errors more rapidly." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 228, + 152, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 152, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 152, + 243 + ], + "type": "text", + "content": "3.3. Input Encoding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 251, + 296, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 346 + ], + "type": "text", + "content": "Analysis. In implicit triangulation, reprojection constraints are grouped based on input similarity. Therefore, the desired properties of input encodings are as follows: positive pairs observing the same points should produce similar features, while negative pairs observing distinct points should yield clearly distinguishable features. Additionally, it is preferable for the encodings to be low-dimensional to minimize memory requirements." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 350, + 296, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 296, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 296, + 518 + ], + "type": "text", + "content": "Local Encoding. At the local patch level, features should differentiate observations of the same point from those of different points. The requirement aligns with the properties of local descriptors used in traditional feature matching, suggesting that we can directly leverage their local feature extractors. We investigate pretrained feature extractors for both dense and sparse matching methods, such as LoFTR [62] and Dedode [24]. To lower memory consumption during training, we apply PCA to all the features from the training dataset, reducing their dimensionality while retaining most of the variance. We experimentally observe that reducing the dimensionality to 128 dimensions preserves over " + }, + { + "bbox": [ + 55, + 350, + 296, + 518 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 55, + 350, + 296, + 518 + ], + "type": "text", + "content": " of the variance on various datasets [35, 53, 56]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 521, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 700 + ], + "type": "text", + "content": "Covisibility Graph Based Global Encoding. Image-level global features should distinguish between covisible and non-covisible image pairs, i.e. whether the images are viewing the same part of the scene, to resolve ambiguities in local encodings. Although global encodings with image-level receptive fields can help, they may still be insufficient to resolve ambiguities in complex environments, as shown in Fig. 3. This limitation can lead to imperfect grouping of reprojection constraints during training, thereby impairing the effectiveness of implicit triangulation. Furthermore, we point out that the learned SCR function may lack (Lipschitz) smoothness [32] w.r.t. the global encodings if adapted naively, e.g. minor variations in the global encoding can result in significant shifts in corresponding 3D points and consequently reduce generalization at test time." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "To address these issues, we propose to directly learn" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 325, + 75, + 436, + 155 + ], + "blocks": [ + { + "bbox": [ + 325, + 75, + 436, + 155 + ], + "lines": [ + { + "bbox": [ + 325, + 75, + 436, + 155 + ], + "spans": [ + { + "bbox": [ + 325, + 75, + 436, + 155 + ], + "type": "image", + "image_path": "254385d40b9454430dda83bf93dc38f7ac1cdf46f8b04762d2706ce692f8651d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 162, + 550, + 172 + ], + "lines": [ + { + "bbox": [ + 318, + 162, + 550, + 172 + ], + "spans": [ + { + "bbox": [ + 318, + 162, + 550, + 172 + ], + "type": "text", + "content": "(a) Distribution of feature distance for covisible and non-covisible pairs." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 438, + 75, + 548, + 155 + ], + "blocks": [ + { + "bbox": [ + 438, + 75, + 548, + 155 + ], + "lines": [ + { + "bbox": [ + 438, + 75, + 548, + 155 + ], + "spans": [ + { + "bbox": [ + 438, + 75, + 548, + 155 + ], + "type": "image", + "image_path": "db873f8d30c79bca577c3e1e1fc17e15a2afdb3b61e50d40cd2dab7e81cb577e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 349, + 177, + 520, + 277 + ], + "blocks": [ + { + "bbox": [ + 349, + 177, + 520, + 277 + ], + "lines": [ + { + "bbox": [ + 349, + 177, + 520, + 277 + ], + "spans": [ + { + "bbox": [ + 349, + 177, + 520, + 277 + ], + "type": "image", + "image_path": "eb876650ac78bfd8a51e93d40f8c644ac09b855ac7dd86e51fe08e65999f933e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 285, + 550, + 295 + ], + "lines": [ + { + "bbox": [ + 318, + 285, + 550, + 295 + ], + "spans": [ + { + "bbox": [ + 318, + 285, + 550, + 295 + ], + "type": "text", + "content": "(b) Precision Recall Curve of predicting covisibility by feature distance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 304, + 555, + 350 + ], + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 350 + ], + "type": "text", + "content": "Figure 3. Comparison of global encodings. Aligning the learning of global encodings with the covisibility graph topology (Node2Vec [27]) helps distinguish covisible and non-covisible pairs (a) and predict covisibility by feature distance (b)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 372, + 555, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 555, + 527 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 555, + 527 + ], + "type": "text", + "content": "embeddings aligned with the可视isibility graph's topology using Node2Vec [27], which samples sequences with weighted random walks and optimizes node embeddings with a Skip-gram [42] objective. For training images, the可视isibility graph is easily available. It can be estimated from the frustum overlap of ground truth poses (see the supplementary for more details). At test time, however,可视isibility information is unknown, so we propose generating multiple global encoding hypotheses by retrieving the nearest training images using NetVLAD [1] features. The global encoding of each retrieved image serves as a hypothesis, and we select the hypothesis yielding the maximum RANSAC inliers for the final localization result." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 529, + 555, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 555, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 555, + 589 + ], + "type": "text", + "content": "This approach effectively decouples training-time and test-time ambiguities: during training, the network focuses on learning scene structure without ambiguity, while at test time, multiple hypotheses enable the resolution of complex, often multimodal ambiguities." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "Covisibility Graph Based Data Augmentation. Our Covisibility Graph Encoding effectively learns a low-ambiguity global encoding. However, data augmentation is still necessary to prevent the network from distinguishing covisible pairs based on distinct global encodings. Instead of simply adding isotropic Gaussian noise [68], we introduce a graph-based data augmentation strategy. In this approach, rather than applying isotropic noise, we randomly replace an image's global encoding with that of a neighboring image from the covisibility graph. Specifically, with probabil" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11539" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 176, + 169 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 176, + 169 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 176, + 169 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 176, + 169 + ], + "type": "image", + "image_path": "8de174b7d4c166b2a4cc92948f00b3621ebfd2e0c831eefd85d6d09657802bb4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 179, + 296, + 258 + ], + "lines": [ + { + "bbox": [ + 55, + 179, + 296, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 179, + 296, + 258 + ], + "type": "text", + "content": "Figure 4. Statistics of reprojection error for points with different depths. The kernel density estimation (KDE) of reprojection error distribution conditioned on disparity from SCR models trained with various local encodings across different datasets. We observe that far points (low disparity) exhibit a lower reprojection error. (Detector-free LoFTR [62] with an " + }, + { + "bbox": [ + 55, + 179, + 296, + 258 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 55, + 179, + 296, + 258 + ], + "type": "text", + "content": " downsampled output has a larger 2D keypoint error than Detector-based Dedode [24].)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 179, + 71, + 293, + 168 + ], + "blocks": [ + { + "bbox": [ + 179, + 71, + 293, + 168 + ], + "lines": [ + { + "bbox": [ + 179, + 71, + 293, + 168 + ], + "spans": [ + { + "bbox": [ + 179, + 71, + 293, + 168 + ], + "type": "image", + "image_path": "edf8201abec980d6d59aa69ff737e0bdc00eac5ff6f4cedfbfeac56066374ae0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "text", + "content": "ity " + }, + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "inline_equation", + "content": "p = 0.5" + }, + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "text", + "content": ", the current image's global encoding is retained, while with probability " + }, + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "inline_equation", + "content": "1 - p" + }, + { + "bbox": [ + 55, + 277, + 296, + 314 + ], + "type": "text", + "content": ", it is replaced by the global encoding of a randomly sampled neighboring image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 319, + 171, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 171, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 171, + 332 + ], + "type": "text", + "content": "3.4. Output Supervision" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 340, + 296, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 340, + 296, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 340, + 296, + 532 + ], + "type": "text", + "content": "Depth Bias in Reprojection Loss. Fig. 4 displays statistics collected from training SCR models with various local encodings across different datasets. It indicates that points closer to the camera empirically exhibit higher reprojection errors compared to distant points, hence we observe a bias toward distant points. This bias is magnified by training with the robust loss Eq. (2), as the supervision signal tends to neglect (nearby) points with higher reprojection errors (cf. Fig. 5). Assuming the training time distribution of camera poses to be representative for testing, regressing near points fewer and less accurately during testing diminishes the positional localization accuracy. We conjecture that to facilitate implicit triangulation for near points, a higher reprojection error should be allowed to compensate for the reprojection of nearby points being more sensitive to pose variations and coordinate inaccuracies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 536, + 296, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 296, + 584 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 296, + 584 + ], + "type": "text", + "content": "Depth Adjusted Reprojection Error. We propose normalizing the reprojection error in Eq. (1) based on the depth of the predicted scene coordinate. Specifically, the observation standard deviation, " + }, + { + "bbox": [ + 55, + 536, + 296, + 584 + ], + "type": "inline_equation", + "content": "\\sigma_{o}" + }, + { + "bbox": [ + 55, + 536, + 296, + 584 + ], + "type": "text", + "content": ", is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 590, + 295, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 590, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 129, + 590, + 295, + 617 + ], + "type": "interline_equation", + "content": "\\sigma_ {o} = \\sqrt {\\left(\\frac {\\sigma_ {3}}{d}\\right) ^ {2} + \\sigma_ {2} ^ {2}}, \\tag {5}", + "image_path": "138a961a94c70827ad1d99ab9b96d7629cce5fb50e1f96d3b53929ed7ece0d3a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "text", + "content": "where we denote the variance of the noise of the 2D observations by " + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "inline_equation", + "content": "\\sigma_2^2" + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "text", + "content": ". The variance of the 3D prediction is denoted by " + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "inline_equation", + "content": "\\sigma_3^2" + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "text", + "content": " and by " + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 623, + 296, + 672 + ], + "type": "text", + "content": " the depth of the point. The reprojection error is then adjusted accordingly:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 70, + 677, + 296, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 677, + 296, + 717 + ], + "spans": [ + { + "bbox": [ + 70, + 677, + 296, + 717 + ], + "type": "interline_equation", + "content": "e _ {3} (x, y) = \\frac {e _ {2} (x , y)}{\\sigma_ {o}} = \\frac {e _ {2} (x , y)}{\\sigma_ {2}} \\sqrt {\\frac {d ^ {2}}{d ^ {2} + \\left(\\frac {\\sigma_ {3}}{\\sigma_ {2}}\\right) ^ {2}}}. \\tag {6}", + "image_path": "f479c586adb33b70b503939d30c5f2dbeef7ef82c1eeec717f053360ce7fc155.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": "Selective Application of Depth Adjustment. The bias towards distant points may sometimes actually be beneficial, as underconstrained points can be pushed farther along the ray, making them easier to identify as outliers during test time. Therefore, we apply our depth-adjusted reprojection loss only to the intermediate coarse scene coordinate output " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "y_0" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " during training (Fig. 2b), and retain the original reprojection loss for the final output. To mitigate the concentration of the supervision signal on points with low projection error, we replace tanh with the Geman-McClure [3] robust loss function which has a heavier tail than tanh:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 397, + 210, + 555, + 237 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 210, + 555, + 237 + ], + "spans": [ + { + "bbox": [ + 397, + 210, + 555, + 237 + ], + "type": "interline_equation", + "content": "\\rho (x) = \\frac {9 x ^ {2}}{9 x ^ {2} + 4}. \\tag {7}", + "image_path": "1bcac29bec436dab3c82abf5374e8b48769c9b77cd0741635a3595f8da76bc3c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "text", + "content": "In order to guide the convergence of the regressed points, " + }, + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "text", + "content": ", by the intermediate output " + }, + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "inline_equation", + "content": "y_{0}" + }, + { + "bbox": [ + 313, + 243, + 555, + 293 + ], + "type": "text", + "content": " (affected by the normalized loss from Eq. (6)), we also apply a consistency loss at the beginning of the training:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 376, + 301, + 555, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 301, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 376, + 301, + 555, + 316 + ], + "type": "interline_equation", + "content": "l _ {\\text {c o n s i s t e n c y}} = \\lambda (t) | | y - y _ {0} | | _ {2}, \\tag {8}", + "image_path": "8a16abce72627c252beef45b94ec2f6b0c131d6bd921a73ffed24a16cff0c452.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "inline_equation", + "content": "\\lambda (t)" + }, + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "text", + "content": " is a dynamic weight that decreases to 0 in a cosine schedule during the first " + }, + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 324, + 554, + 348 + ], + "type": "text", + "content": " of training time." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 345, + 357, + 554, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 357, + 554, + 389 + ], + "spans": [ + { + "bbox": [ + 345, + 357, + 554, + 389 + ], + "type": "interline_equation", + "content": "\\lambda (t) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} (1 + \\cos 2 \\pi t), & \\text {i f} t \\in [ 0, 0. 5 ] \\\\ 0, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {9}", + "image_path": "b9df57bd299b006e5e1f78902fc42e104e8306bd686dcbe4f260298d65b9fb3c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 397, + 460, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 397, + 460, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 397, + 460, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 397, + 460, + 409 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 397, + 460, + 409 + ], + "type": "text", + "content": " is the relative training time." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 413, + 554, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 554, + 486 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 554, + 486 + ], + "type": "text", + "content": "Optional Depth Supervision. When depth is available, we can also benefit from direct depth supervision. The depth does not need to be accurate since we mainly use the depth for initialization. Specifically, we simply replace the consistency loss between intermediate and final output in Eq. (8) with a ground truth coordinate supervision loss:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 353, + 495, + 555, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 495, + 555, + 509 + ], + "spans": [ + { + "bbox": [ + 353, + 495, + 555, + 509 + ], + "type": "interline_equation", + "content": "l _ {\\text {d e p t h}} = \\lambda (t) \\left(\\left\\| y - \\bar {y} \\right\\| _ {2} + \\left\\| y _ {0} - \\bar {y} \\right\\| _ {2}\\right), \\tag {10}", + "image_path": "7721d6cb577b15ec41b4e008929b60de7791ee2c725403a932811e8a6a6bff18.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 517, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 554, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 517, + 554, + 542 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 517, + 554, + 542 + ], + "type": "text", + "content": " is the pseudo ground truth computed by the inverse projection of the pixel given the depth, pose, and intrinsic." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 552, + 395, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 395, + 566 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 395, + 566 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 572, + 376, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 572, + 376, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 572, + 376, + 583 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 590, + 554, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 554, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 554, + 625 + ], + "type": "text", + "content": "We use the Aachen Day-Night [53, 56] and the Hyundai Department Store dataset [35] to evaluate R-SCoRe on complex large-scale indoor and outdoor scenes." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": "Aachen Day-Night. It is a large-scale benchmark for outdoor visual localization, covering the historic inner city of Aachen, Germany, over an area of approximately " + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "inline_equation", + "content": "6 \\, km^2" + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": ". It presents significant challenges due to varying illumination conditions, especially between day and night. The dataset includes 4,328 daytime images for training, along with 824 daytime query images and 98 nighttime query images." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11540" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 110, + 69, + 503, + 255 + ], + "blocks": [ + { + "bbox": [ + 110, + 69, + 503, + 255 + ], + "lines": [ + { + "bbox": [ + 110, + 69, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 110, + 69, + 503, + 255 + ], + "type": "table", + "html": "
Methodsw/o DepthSizeAachen DayAachen Night
HLoc+SPSG [19, 50, 51]Yes7.82GB89.695.498.886.793.9100
AS [55]Yes750MB85.392.297.939.849.064.3
Cascaded [16]Yes140MB76.788.695.833.748.062.2
QP+R.Sift [41]Yes30MB62.676.384.716.318.424.5
Squeezezer [72]Yes240MB75.589.796.250.067.378.6
PixLoc [52]Yes2.13GB64.369.377.451.155.167.3
Neumap [64]No1.26GB80.890.995.648.067.387.8
HSCNet [36]No213MB71.181.991.732.743.965.3
HSCNet++ [70]No274MB72.781.691.443.957.176.5
ESAC (×50) [5]No1.31GB42.659.675.56.110.218.4
ACE (×50) [9]Yes205MB6.917.250.00.01.05.1
GLACE [68]Yes27MB8.620.864.01.01.017.3
R-SCoRe (Dedode [24]) + DepthYes47MB74.886.996.464.389.896.9
No47MB79.088.596.466.389.896.9
", + "image_path": "d228548c4af20e1a020864702184fd00a3051b48bf5d728bd93a093322e94d15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "lines": [ + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "text", + "content": "Table 2. Aachen Day-Night evaluation. The map size and percentages of query images within three thresholds: (0.25m, " + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "inline_equation", + "content": "2^{\\circ}" + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "text", + "content": "), (0.5m, " + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "inline_equation", + "content": "5^{\\circ}" + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "text", + "content": "), and (5m, " + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "inline_equation", + "content": "10^{\\circ}" + }, + { + "bbox": [ + 55, + 262, + 555, + 298 + ], + "type": "text", + "content": ") and are reported. We report our results with Dedode [24] local encoding and optional depth supervision. Feature matching (FM) methods [19, 50, 51] are more accurate, but the map size is large. R-SCoRe achieves comparable accuracy with a small map size." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 316, + 297, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 316, + 297, + 438 + ], + "spans": [ + { + "bbox": [ + 54, + 316, + 297, + 438 + ], + "type": "text", + "content": "Hyundai Department Store. It is a large-scale indoor visual localization benchmark, covering three floors of a department store. Each floor consists of multiple sequences captured over four months, spanning an area of approximately " + }, + { + "bbox": [ + 54, + 316, + 297, + 438 + ], + "type": "inline_equation", + "content": "10,000~m^2" + }, + { + "bbox": [ + 54, + 316, + 297, + 438 + ], + "type": "text", + "content": ". It presents challenges beyond its large scale, including dynamic objects, illumination changes, and textureless regions. B1 is particularly challenging as the training images are captured under low-lighting conditions, while the query images are brightly illuminated. The dataset includes 44,283 training images and 5,927 test images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 450, + 170, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 170, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 170, + 462 + ], + "type": "text", + "content": "4.2. Benchmark Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "content": "Aachen Day-Night. As shown in Tab. 2, R-SCoRe enhances the performance of scene coordinate regression (SCR) based methods [5, 36, 68, 70], achieving competitive results with a single low-map-size model without the need for scene-specific depth supervision. While R-SCoRe is competitive with the best performing method, HLoc [19, 50, 51], we forfeit some ground at highest accuracy. However, R-SCoRe demands " + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "inline_equation", + "content": "170 \\times" + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "content": " less memory to store the map. This huge gap could already render SCR based methods as an attractive alternative for some applications. Most other feature-based methods (FM) also deliver significantly larger maps. While delivering comparable performance for the Aachen Day dataset, they all fall behind R-SCoRe on the Aachen Night dataset. The only FM method [41] with a comparable map size is outperformed on all metrics, e.g. [41] is " + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "inline_equation", + "content": "4 - 5 \\times" + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "content": " worse in accuracy on the night dataset. Compared to other SCR methods that work without depth supervision [9, 68] R-SCoRe is " + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "content": " superior in accuracy. The so far most accurate SCR based method [64] produces large maps (" + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "inline_equation", + "content": "27 \\times" + }, + { + "bbox": [ + 56, + 474, + 296, + 715 + ], + "type": "text", + "content": " larger) and is prohibitively slow" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "text", + "content": "in inference. The next most accurate SCR method, [70] is outperformed by " + }, + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "inline_equation", + "content": "46\\%" + }, + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "text", + "content": " at night and highest threshold, while R-SCoRe maintains a " + }, + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "inline_equation", + "content": "6\\times" + }, + { + "bbox": [ + 313, + 316, + 555, + 377 + ], + "type": "text", + "content": " smaller map size - without the need for depth supervision. We observe a small gain in performance if we utilize depth for supervision of R-SCoRe." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 380, + 556, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 556, + 549 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 556, + 549 + ], + "type": "text", + "content": "Hyundai Department Store. R-SCoRe again significantly outperforms the SCR based methods [5, 68], including recent ensemble networks [5, 9], see Tab. 3. Compared to the state-of-the-art feature matching based localization [50] we achieve competitive results with a single low-map-size model and forfeit some ground at the highest accuracy threshold. However, our model is at least three orders of magnitude smaller for either feature [22, 49] incorporated into [50], which can be a valuable advantage in practice. Recall that depth supervision is not necessary for R-SCoRe, but if available, it can also enhance performance further. The B1 scene exhibits strong illumination changes and we observe significantly better performance when using local encodings from Dedode instead of LoFTR [62]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 559, + 448, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 448, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 448, + 571 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 577, + 555, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 577, + 555, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 577, + 555, + 625 + ], + "type": "text", + "content": "Most hyperparameters follow default values [68] and extensive tuning is not performed, as we empirically find the approach remains robust within a reasonable range, apart from the trade-off between network size and performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "Input Encodings. For local encodings, we perform PCA to reduce their dimensionality to 128. The global encodings are represented in 256 dimensions, consistent with the " + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": " Former [75] feature dimension used in GLACE [68] for fair comparison. We estimate the可视ability graph based on camera poses, using a weighted frustum overlap method (details provided in the supplementary materials), with a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11541" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 69, + 550, + 206 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 550, + 206 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 550, + 206 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 550, + 206 + ], + "type": "table", + "html": "
MethodsDept. 1F TestDept. 4F TestDept. B1 Test
HLoc+D2-Net [22, 50](78.0 / 82.8 / 88.0) / 398GB(84.2 / 89.8 / 92.0) / 183GB(73.7 / 79.3 / 87.2) / 505GB
HLoc+R2D2 [49, 50](80.6 / 84.3 / 89.4) / 166GB(85.3 / 91.0 / 93.1) / 76GB(75.2 / 80.3 / 87.6) / 210GB
PoseNet [31](0.0 / 0.0 / 0.4) / 41MB(0.0 / 0.0 / 0.1) / 41MB(0.0 / 0.0 / 0.1) / 41MB
ESAC (×50) [5](43.3 / 66.3 / 77.0) / 1.4GB(45.2 / 62.5 / 73.1) / 1.4GB(3.5 / 8.2 / 12.6) / 1.4GB
ACE (×50) [9](14.1 / 54.4 / 75.5) / 205MB(27.3 / 70.9 / 84.1) / 205MB(2.7 / 14.4 / 29.3) / 205MB
GLACE [68](5.6 / 21.3 / 48.6) / 42MB(8.4 / 29.8 / 51.6) / 42MB(0.9 / 4.4 / 11.9) / 42MB
R-SCoRe (LoFTR* [62]) + Depth(63.2 / 82.4 / 92.4) / 127MB(62.2 / 82.7 / 90.9) / 50MB(26.9 / 50.7 / 69.6) / 130MB
(67.3 / 84.5 / 92.6) / 127MB(70.5 / 87.0 / 92.9) / 50MB(30.8 / 53.7 / 72.7) / 130MB
R-SCoRe (Dedode [24]) + Depth(61.4 / 80.2 / 90.9) / 127MB(60.2 / 79.3 / 87.9) / 50MB(60.1 / 77.3 / 89.6) / 130MB
(63.9 / 83.3 / 90.8) / 127MB(76.7 / 89.3 / 93.0) / 50MB(61.5 / 77.6 / 88.8) / 130MB
", + "image_path": "7982c0b01347b8f527ed1bbda4073562c70a51848096682dd30adb34b5ae83f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "text", + "content": "maximum viewing frustum depth of " + }, + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{v}} = 50" + }, + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "text", + "content": " for outdoor scenes and " + }, + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{v}} = 8" + }, + { + "bbox": [ + 55, + 269, + 295, + 293 + ], + "type": "text", + "content": " for indoor scenes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "spans": [ + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": "Output Supervision. The supervision uses a dynamic robust loss bandwidth strategy inspired by ACE [9]. For coarse intermediate outputs, the parameters, see Eq. (3), are set to " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{min}} = 1" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{max}} = 50" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": ". In contrast, " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{max}} = 25" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " is used for the final output, which allows the refinement layer to focus on the most accurate predictions while the initial layers do not ignore the optimization of relatively inaccurate predictions. Fixing " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\sigma_{2} = 1" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " in the depth-adjusted reprojection loss, Eq. (6), allows us to control the behavior by adjusting " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\frac{\\sigma_3}{\\sigma_2}" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": ". For indoor scenes, " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\sigma_{3} = 3" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " is applied, while " + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "inline_equation", + "content": "\\sigma_{3} = 8" + }, + { + "bbox": [ + 54, + 298, + 295, + 477 + ], + "type": "text", + "content": " is used for outdoor scenes to account for different scales. We perform optional depth supervision using depth images rendered from the 3D model for the Hyundai Department Store dataset and Multi-View Stereo depth maps for the Aachen Day-Night dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "text", + "content": "Network Architecture. We adopt the MLP architecture and position decoder from GLACE [68] with expansion ratio " + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "inline_equation", + "content": "m = 2" + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "text", + "content": " for the MLP, and 50 clusters for the position decoder. With MLP width " + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "inline_equation", + "content": "w = 256\\left\\lceil \\sqrt{n / 1000} \\right\\rceil" + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 483, + 295, + 548 + ], + "type": "text", + "content": " training images, we scale the parameter count proportionally." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "content": "Training. We found that adopting the optimization settings from ACE Zero [10] enhances both stability and convergence speed compared to the original ACE [9]. Specifically, we reduce the warmup ratio of the one-cycle learning rate schedule [61] from 0.25 to 0.04 and lower the peak learning rate from " + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "inline_equation", + "content": "3 \\times 10^{-3}" + }, + { + "bbox": [ + 55, + 552, + 295, + 661 + ], + "type": "text", + "content": ". For our evaluation we adopt similar training parameters to GLACE [68], including a local feature buffer size of 128M, a large batch size of 320K and a training duration of 100k iterations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "Testing. At test time, we retrieve the 10 nearest training images with NetVLAD [1]. The global encoding and retrieval features for training images are precomputed and compressed using Product Quantization [28]. For final pose" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 315, + 266, + 560, + 319 + ], + "blocks": [ + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "lines": [ + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "spans": [ + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "text", + "content": "Table 3. Hyundai Department Store Test Set evaluation. The percentages of query images within three thresholds: (0.1m, " + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "text", + "content": "), (0.25m, " + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "inline_equation", + "content": "2^{\\circ}" + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "text", + "content": "), and (1m, " + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "inline_equation", + "content": "5^{\\circ}" + }, + { + "bbox": [ + 55, + 214, + 555, + 249 + ], + "type": "text", + "content": ") and the map size are reported. R-SCoRe achieves competitive accuracy with a small map size. *We use LoFTR [62] outdoor, trained on MegaDepth [38], instead of the indoor model trained on ScanNet [18] for the B1 scene with strong illumination change." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 266, + 560, + 319 + ], + "lines": [ + { + "bbox": [ + 315, + 266, + 560, + 319 + ], + "spans": [ + { + "bbox": [ + 315, + 266, + 560, + 319 + ], + "type": "table", + "html": "
Dept. 1F ValDept. B1 Val
ACE [9]68.787.595.914.128.345.8
LoFTR* [62]72.388.795.529.451.369.6
Dedode [24]70.686.695.557.774.786.7
", + "image_path": "c083a880a5c7401b43ed791d0be15a108358cda7672289de0239e53db66cf9a1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 324, + 381, + 544, + 446 + ], + "blocks": [ + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "lines": [ + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "text", + "content": "Table 4. Ablation study of local encoders. Accuracy at (0.1m, " + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "text", + "content": "), (0.25m, " + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "inline_equation", + "content": "2^{\\circ}" + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "text", + "content": "), and (1m, " + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "inline_equation", + "content": "5^{\\circ}" + }, + { + "bbox": [ + 313, + 326, + 555, + 371 + ], + "type": "text", + "content": ") thresholds are reported. Utilizing pretrained, off-the-shelf feature extractors improves the performance, especially under challenging conditions (B1)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 381, + 544, + 446 + ], + "lines": [ + { + "bbox": [ + 324, + 381, + 544, + 446 + ], + "spans": [ + { + "bbox": [ + 324, + 381, + 544, + 446 + ], + "type": "table", + "html": "
Dept. 1F Val
R2Former [75] w/ Gaussian34.160.178.3
+ Multi Hypotheses42.174.592.2
+ Covis Augmentation62.083.894.8
+ Covis Encoding72.388.795.5
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Accuracy at " + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "inline_equation", + "content": "(0.1\\mathrm{m},1^{\\circ})" + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "inline_equation", + "content": "(0.25\\mathrm{m},2^{\\circ})" + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "inline_equation", + "content": "(1\\mathrm{m},5^{\\circ})" + }, + { + "bbox": [ + 313, + 453, + 555, + 510 + ], + "type": "text", + "content": " thresholds." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "text", + "content": "estimation, we utilize PoseLib [33] with a maximum reprojection error of 10 pixels and up to 10,000 RANSAC iterations. On our PC (NVIDIA RTX 2080 GPU & Intel i7-9700K CPU), the average inference time for a " + }, + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "text", + "content": " query image is 140 to " + }, + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "inline_equation", + "content": "270\\mathrm{ms}" + }, + { + "bbox": [ + 313, + 531, + 555, + 590 + ], + "type": "text", + "content": " in total." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 591, + 506, + 639 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 314, + 591, + 506, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 591, + 506, + 602 + ], + "spans": [ + { + "bbox": [ + 314, + 591, + 506, + 602 + ], + "type": "text", + "content": "- Global: NetVLAD (20ms), Retrieval (<1ms)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 603, + 488, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 603, + 488, + 614 + ], + "spans": [ + { + "bbox": [ + 315, + 603, + 488, + 614 + ], + "type": "text", + "content": "- Local: LoFTR (7ms) or DeDoDe (50ms)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "spans": [ + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "type": "text", + "content": "- MLP: " + }, + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "type": "inline_equation", + "content": "\\mathrm{w} = {768}\\left( {{70}\\mathrm{{ms}}}\\right)" + }, + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 315, + 616, + 484, + 626 + ], + "type": "inline_equation", + "content": "{1280}\\left( {{160}\\mathrm{{ms}}}\\right)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 628, + 405, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 628, + 405, + 639 + ], + "spans": [ + { + "bbox": [ + 315, + 628, + 405, + 639 + ], + "type": "text", + "content": "- Pose Solving: 40ms" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 647, + 444, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 444, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 444, + 660 + ], + "type": "text", + "content": "4.4. Ablation Study Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "In our ablation studies, we investigate the impact of the different components in R-SCoRe. We evaluate on the validation split for the Hyundai Department Store dataset. Since the Aachen Day-Night dataset does not provide a validation" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11542" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 294, + 109 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 109 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 109 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 109 + ], + "type": "table", + "html": "
Aachen DayAachen Night
FM Covis75.487.695.864.389.895.9
Pose Covis74.886.996.464.389.896.9
", + "image_path": "a3d67b6380067cef3a2f3cda436b0986da32e1e0ffed27906e83de2fd6560439.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 175, + 296, + 227 + ], + "blocks": [ + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "lines": [ + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "spans": [ + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "text", + "content": "Table 6. Ablation study of covisibility graph. Building the covisibility graph using frustum overlap performs similarly to utilizing feature matching. Accuracy at " + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "inline_equation", + "content": "(0.25\\mathrm{m}, 2^{\\circ})" + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "inline_equation", + "content": "(0.5\\mathrm{m}, 5^{\\circ})" + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "inline_equation", + "content": "(5\\mathrm{m}, 10^{\\circ})" + }, + { + "bbox": [ + 55, + 118, + 295, + 161 + ], + "type": "text", + "content": " thresholds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 175, + 296, + 227 + ], + "lines": [ + { + "bbox": [ + 56, + 175, + 296, + 227 + ], + "spans": [ + { + "bbox": [ + 56, + 175, + 296, + 227 + ], + "type": "table", + "html": "
SupervisionDept. 1F ValDept. 4F Val
Original62.382.293.759.182.297.6
Adjusted70.686.695.563.984.298.3
Depth76.888.195.668.584.998.5
", + "image_path": "119521074115fe846eca3d3bd490199c37ee42e6a359c7066c1cd218f5ffd602.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "text", + "content": "Table 7. Ablation study of supervision methods. Original refers to the original reprojection error supervision, Adjusted refers to our depth-adjusted reprojection error supervision, and Depth uses ground truth depth for supervision. Accuracy at (0.1m, " + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "text", + "content": "), (0.25m, " + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "inline_equation", + "content": "2^{\\circ}" + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "text", + "content": "), and (1m, " + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "inline_equation", + "content": "5^{\\circ}" + }, + { + "bbox": [ + 55, + 235, + 296, + 289 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 314, + 188, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 188, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 188, + 326 + ], + "type": "text", + "content": "split, we evaluate on the test set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 331, + 296, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 331, + 296, + 439 + ], + "spans": [ + { + "bbox": [ + 54, + 331, + 296, + 439 + ], + "type": "text", + "content": "Local Encoding. As shown in Tab. 4, for large scale indoor scenes with small illumination changes, alternative off-the-shelf local feature extractors [24, 62] achieve similar or even superior performance compared to the original ACE [9]. Note that this finding contradicts earlier investigations [9] that prefer a specifically trained backbone in their work. Additionally, local descriptors trained on MegaDepth [38], especially Dedode [24], demonstrate greater robustness in scenes with significant illumination changes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 444, + 295, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 444, + 295, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 295, + 624 + ], + "type": "text", + "content": "Global Encoding. Retrieving global encodings from training images avoids the domain gap. Better retrieval method and multiple hypotheses verification can help resolve ambiguities. Without retraining (Tab. 5), utilizing multiple global hypotheses at test time (+ Multi Hypotheses) results in a direct performance improvement in complex scenes. The performance improves significantly, once we incorporate our可视ibility graph-based data augmentation during training. In particular, we replace isotropic Gaussian noise [68] with our more precise可视ibility-based technique (+ Covis Augmentation). Finally, learning the global encoding directly from the可视ibility graph (+ Covis Encoding) reduces the interference between non-covisible training images and thereby facilitates implicit triangulation, especially in indoor scenes with significant ambiguity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "type": "text", + "content": "Finally, we also explore the effect of computing the可视ibility graph via feature matching [19, 51]. As shown in Tab. 6, using a more accurate graph yields no significant improvement, indicating that R-SCoRe is robust to the quality of the可视ibility graph. Therefore, our simple frustum overlap-based graph is sufficient for effective performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": "Supervision. Our depth-adjusted supervision effectively" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 69, + 550, + 178 + ], + "blocks": [ + { + "bbox": [ + 321, + 69, + 550, + 178 + ], + "lines": [ + { + "bbox": [ + 321, + 69, + 550, + 178 + ], + "spans": [ + { + "bbox": [ + 321, + 69, + 550, + 178 + ], + "type": "image", + "image_path": "a2d5a77aa5e072b8bb430d0c96d47eb035ed10c8bbbe6c4661bd1144732635ff.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 187, + 555, + 232 + ], + "lines": [ + { + "bbox": [ + 313, + 187, + 555, + 232 + ], + "spans": [ + { + "bbox": [ + 313, + 187, + 555, + 232 + ], + "type": "text", + "content": "Figure 5. Ablation study of depth distribution after training with different supervision methods. Our depth-adjusted supervision matches the distribution of ground truth depth for supervision as compared to the original." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 262, + 555, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 555, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 555, + 360 + ], + "type": "text", + "content": "mitigates the bias towards distant points and enhances the implicit triangulation of nearby points. As demonstrated in Fig. 5, depth-adjusted supervision significantly alters the depth distribution of predicted points, alleviating the previous ignorance of nearby points. This adjustment brings the distribution closer to that achieved with ground truth depth supervision, demonstrating a substantial reduction in the bias inherent in the original supervision approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 364, + 556, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 556, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 556, + 436 + ], + "type": "text", + "content": "In Tab. 7, we observe that depth-adjusted supervision also leads to notable improvements in localization accuracy, particularly under stricter thresholds, where accurate translation estimation relies heavily on near points. Even without ground truth depth supervision, depth-adjusted supervision enables the model to achieve competitive performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 486, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 713 + ], + "type": "text", + "content": "In this work, we revisited scene coordinate regression (SCR) methods for robust visual localization in large-scale, complex environments. We analyzed the design principles of input encoding and training strategies, identifying several areas for enhancement. Our proposed R-SCoRe includes a covisibility graph-based global encoding learning and data augmentation strategy, a depth-adjusted reprojection loss to improve the implicit triangulation, and also other improvements including better architecture and local feature. Our contributions advance the state-of-the-art in SCR and demonstrate that SCR-based localization methods can achieve competitive performance in large-scale applications. While operating at comparably very small map sizes, R-SCoRe trails the state-of-the-art FM-based localization methods only at the strictest error thresholds. Although out-of-distribution generalization remains challenging, and gaps persist in handling extreme cases, given the relatively small history of SCR, we are positive the accuracy gap can be closed completely in the near future." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11543" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 295, + 123 + ], + "type": "text", + "content": "[1] R. 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In CVPR, 2023, 2, 3, 6, 7" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11546" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/R-TPT_ Improving Adversarial Robustness of Vision-Language Models through Test-Time Prompt Tuning/db61575c-1280-4b24-9ca2-b88169374737_content_list.json b/2025/R-TPT_ Improving Adversarial Robustness of Vision-Language Models through Test-Time Prompt Tuning/db61575c-1280-4b24-9ca2-b88169374737_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f503e1ff6501958d4313d5b64de48904a30f5bfc --- /dev/null +++ b/2025/R-TPT_ Improving Adversarial Robustness of Vision-Language Models through Test-Time Prompt Tuning/db61575c-1280-4b24-9ca2-b88169374737_content_list.json @@ -0,0 +1,1467 @@ +[ + { + "type": "text", + "text": "R-TPT: Improving Adversarial Robustness of Vision-Language Models through Test-Time Prompt Tuning", + "text_level": 1, + "bbox": [ + 98, + 128, + 898, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lijun Sheng $^{1,2}$ , Jian Liang $^{2,3*}$ , Zilei Wang $^{1}$ , Ran He $^{2,3}$", + "bbox": [ + 282, + 200, + 712, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 University of Science and Technology of China", + "bbox": [ + 305, + 220, + 692, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ NLPR & MAIS, Institute of Automation, Chinese Academy of Sciences", + "bbox": [ + 207, + 238, + 787, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 University of Chinese Academy of Sciences", + "bbox": [ + 316, + 256, + 679, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "slj0728@mail.ustc.edu.cn, liangjian92@gmail.com", + "bbox": [ + 289, + 277, + 707, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 325, + 326, + 342 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-language models (VLMs), such as CLIP, have gained significant popularity as foundation models, with numerous fine-tuning methods developed to enhance performance on downstream tasks. However, due to their inherent vulnerability and the common practice of selecting from a limited set of open-source models, VLMs suffer from a higher risk of adversarial attacks than traditional vision models. Existing defense techniques typically rely on adversarial fine-tuning during training, which requires labeled data and lacks of flexibility for downstream tasks. To address these limitations, we propose robust test-time prompt tuning (R-TPT), which mitigates the impact of adversarial attacks during the inference stage. We first reformulate the classic marginal entropy objective by eliminating the term that introduces conflicts under adversarial conditions, retaining only the pointwise entropy minimization. Furthermore, we introduce a plug-and-play reliability-based weighted ensembling strategy, which aggregates useful information from reliable augmented views to strengthen the defense. R-TPT enhances defense against adversarial attacks without requiring labeled training data while offering high flexibility for inference tasks. Extensive experiments on widely used benchmarks with various attacks demonstrate the effectiveness of R-TPT. The code is available in https://github.com/TomSheng21/R-TPT.", + "bbox": [ + 86, + 357, + 483, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 762, + 220, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-language models (VLMs) [5, 32, 56] are multimodal models pretrained on large-scale paired image-text data. Their powerful zero-shot inference capability and broad applicability across a range of downstream tasks have made them a foundational tool in the research community. CLIP [32], a milestone work, aligns features from the text and", + "bbox": [ + 89, + 787, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ad788afd1afe75fee6ff469ab54a42501346f8a4f64735828ee4a68ae1734c4b.jpg", + "image_caption": [ + "Training-time defense", + "Figure 1. Comparison between training-time and test-time defense for CLIP. Our test-time defense paradigm provides robust prediction as the conventional training-time methods and requires no annotated dataset or adversarial training." + ], + "image_footnote": [], + "bbox": [ + 519, + 343, + 702, + 575 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/091a5216fb1ebab89d11443ebf16c75cc7474d84303ea74b8984f7a64e9b8e66.jpg", + "image_caption": [ + "Test-time defense" + ], + "image_footnote": [], + "bbox": [ + 715, + 343, + 898, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "visual modalities using two specialized feature extractors trained with a contrastive loss function. Due to its concise architecture and impressive performance, CLIP has become the most widely used VLM across diverse research topics. For classification tasks, CLIP extracts features from both images and category descriptions, then chooses the category whose features exhibit the highest similarity to the image's feature representation. Beyond classification [47, 48, 60, 61], CLIP has been successfully applied to various vision tasks, such as semantic segmentation [36, 59], object detection [55, 58], and image clustering [3, 22].", + "bbox": [ + 511, + 684, + 906, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The impressive performance on downstream tasks and the broad range of applications of CLIP not only highlight its powerful capabilities but also expose it to potential vul", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*To whom correspondence should be addressed.", + "bbox": [ + 107, + 886, + 364, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "29958", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "nerabilities, particularly under adversarial attacks [19, 26]. While adversarial attacks and defenses [13, 24, 54] have been widely explored for conventional visual models, the situation for CLIP is more complex. The pre-training of CLIP requires the collection of vast amounts of image-text pairs and substantial computational resources that most deployers cannot afford. As a result, many deployers choose to adopt open-source versions of CLIP from a small range of candidates. This fact introduces a relatively high risk of adversarial attacks targeting CLIP-based applications.", + "bbox": [ + 89, + 90, + 480, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent works [21, 26] explore adversarial prompt tuning using annotated data to enhance the robustness of CLIP. However, their reliance on labeled data and limited flexibility across tasks pose challenges for real-world deployment. To address this, we choose to defend adversarial attacks in the inference stage, which is applicable across various scenarios and requires no labeled dataset or prior knowledge of the downstream task, as shown in Figure 1. Existing test-time adaptation methods [37, 53] primarily focus on improving accuracy for clean test samples, while overlooking the potential risks posed by adversarial attacks. Moreover, deploying defense at test time necessitates short inference time and avoiding using additional resources, such as large language models or diffusion models, to ensure versatility.", + "bbox": [ + 89, + 244, + 482, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above challenges and achieve successful defense against potential attacks, we propose robust test-time prompt tuning (R-TPT). First, we revisit and refine the widely used optimization objective for instance adaptation. Many previous works [37, 41], following MEMO [57], augment the test instance and aim to minimize marginal entropy, which is defined as the entropy of the mean prediction. We decompose marginal entropy into two components: a pointwise entropy term and the Kullback-Leibler (KL) divergence, which measures the divergence between predictions from each augmented view and the mean prediction. We observe that when adapting to adversarial examples with high-confidence inaccurate predictions, the KL divergence term tends to pull the augmented views toward the misleading mean prediction, which does not exist in the clean scenario. This meaningless operation introduces conflicts into the optimization process. To mitigate the influence of adversarial samples and preserve simplicity, we discard the KL divergence term, retaining only the pointwise entropy minimization for tuning textual prompts. This straightforward modification not only defends against adversarial attacks but also maintains clean performance.", + "bbox": [ + 89, + 459, + 482, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to effectively leverage knowledge from augmented views, we propose a reliability-based weighted ensembling strategy. To assign a larger weight to reliable augmented views during ensembling, we introduce a similarity-based metric to assess the reliability of samples. We hypothesize that samples with higher similarity to their neighbors are farther away from outliers and contain more reli", + "bbox": [ + 89, + 795, + 480, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "able information. Thus, we calculate the average similarity of each sample with its neighbors to estimate its reliability. Using this metric, outliers such as adversarial examples and noisy augmented views are assigned lower reliability scores, which means less participation in the ensembling. Finally, we obtain the final prediction by ensembling the individual model predictions, weighted according to their reliability. Extensive experiments on fine-grained classification benchmarks and distribution shift benchmarks validate the effectiveness of our method in both adaptation and defense against adversarial attacks. Our contributions are summarized as follows:", + "bbox": [ + 511, + 90, + 903, + 271 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose R-TPT, which is the first to explore test-time paradigms for defending against potential adversarial attacks in CLIP.", + "- We discard the KL divergence term from the marginal entropy objective to eliminate optimization conflicts and propose a reliability-based weighted ensembling strategy to integrate knowledge from reliable augmented views.", + "- Extensive experiments demonstrate the effectiveness of our method in both adaptation and adversarial defense." + ], + "bbox": [ + 511, + 273, + 903, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 426, + 653, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Adversarial Attack and Defense", + "text_level": 1, + "bbox": [ + 511, + 452, + 795, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A lot of research [13, 24, 42] has been devoted to studying neural network's vulnerability to adversarial noise. A pioneering work [42] introduces the concept of adversarial examples and finds small-amplitude noise that humans cannot recognize leads to misclassifications. Since then, a series of attack methods to generate adversarial samples [4, 8, 13, 24] have been proposed. FGSM [13] proposes to utilize the gradient sign to generate an adversarial example. Researchers [24] generate the adversarial noise by projected gradient descent (PGD) operation, which becomes the standard measurement of model robustness. Moreover, a variety of works explore adversarial attacks in many restricted conditions, ranging from one-pixel attack [40], universal perturbation [28] to more realistic black-box setting [2, 18].", + "bbox": [ + 511, + 474, + 903, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In parallel, numerous defense strategies [24, 35, 49, 54] have been proposed to mitigate adversarial attacks. Adversarial training [13, 24] improves the robustness of the model by incorporating the adversarial samples into the training set. TRADES [54] provides a theoretical analysis of adversarial error to trade adversarial robustness against accuracy. AWP [49] perturbs the model's weights with small adversarial noise during training to enhance robustness. Reconstruction [29, 34] with generative models [12, 38] is also a commonly used technique in test-time defense methods.", + "bbox": [ + 511, + 688, + 903, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As for the vison-language models, TeCoA [26] and APT [21] employ adversarial training to pretrained CLIP [32] to improve the adversarial robustness. However, their training-time solution requires an annotated dataset and lacks flexi", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "29959", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/508cfb088be62b610b921a96fd20e3149fdd0def5e4830eec3cc5176694d21a3.jpg", + "image_caption": [ + "Figure 2. The pipeline of R-TPT framework. Given an instance-level task, we deploy augmentation on the test image and build a classifier with CLIP's text branch. After selecting a low-entropy batch, R-TPT discards the KL divergence minimization term which potentially introduces conflicts in the marginal entropy [57] and optimizes textual prompts with pointwise entropy minimization. To effectively utilize the knowledge of the augmented views, R-TPT applies a reliability-based weighted ensembling mechanism in the final inference process." + ], + "image_footnote": [], + "bbox": [ + 120, + 95, + 880, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "bility across tasks. In this work, we choose to deploy adversarial defense in the test time that is more effective and flexible and can collaborate with their training-time defense.", + "bbox": [ + 88, + 473, + 482, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Test-Time Adaptation for VLMs", + "text_level": 1, + "bbox": [ + 89, + 530, + 377, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Test-time adaptation [23, 37, 51] aims to adapt pre-trained models to the test data at inference time to improve the performance further. According to the test data form, test-time adaptation is divided into streaming data adaptation [43, 45, 52] and single instance adaptation [37, 57], and our work focuses on the latter. Recent research [37, 41, 53] has been devoted to exploring the instance adaptation methods for VLMs [32, 46, 56]. TPT [37] employs the marginal entropy minimization to augmentation views of the test instance to correct the prediction. DiffTPT [11] utilizes the diffusion technique to obtain diverse views which is helpful for the adaptation. PromptAlign [1] aligns the statistics of the test instance and collected natural images to make the model's parameters adapt to test samples. To take advantage of more prompt templates [32], TPS [41] chooses to optimize feature shift and utilizes prompt ensembling for initialization. Moreover, researchers [53] propose a training-free adaptation method by ensembling the augmented views with the MeanShift algorithm [7].", + "bbox": [ + 88, + 551, + 482, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Besides accuracy, researchers [50] also focus on improving calibration performance through higher text feature dispersion. In this work, we first utilize the test-time paradigm to defend against adversarial attacks for CLIP due to its se", + "bbox": [ + 88, + 839, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vere vulnerability to adversarial examples.", + "bbox": [ + 513, + 473, + 795, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 513, + 506, + 648, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we improve CLIP's adversarial robustness through a test-time paradigm, motivated by its inherent vulnerabilities and the high resource demands of train-time defense methods. Our proposed robust test-time prompt tuning (R-TPT), as illustrated in Figure 2, requires no annotated data and is equipped with greater flexibility. In Sec. 3.1, we begin with reviewing the foundational concepts of CLIP and the test-time prompt tuning approach. We then introduce the two key components of R-TPT: pointwise entropy minimization in Sec. 3.2, and the reliability-based weighted ensembling strategy in Sec. 3.3.", + "bbox": [ + 511, + 532, + 906, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 710, + 643, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive language-image pre-training. CLIP is a popular language-vision model with a double-tower architecture, consisting of an image encoder $F(\\cdot)$ and a text encoder $G(\\cdot)$ . It is pretrained by the contrastive learning objective with a large amount of image-text pairs. Benefiting from rich pretraining knowledge, CLIP has a strong zero-shot generalization ability. Take a C-way classification task with class names $\\{t_c\\}_{c=1}^C$ as an example, CLIP obtains textual features $g_c$ by the text encoder $G(\\cdot)$ with a prompt template (e.g., \"a photo of a [\"]) and the class name $t_c$ as the input. Also, each test image $x_i$ queries the image encoder", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "29960", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to calculate the image feature $f_{i} = F(x_{i})$ . The probability that $x_{i}$ belongs to category $c$ is calculated by a softmax operation with the cosine similarity of those features:", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {c} \\left(x _ {i}\\right) = \\frac {\\exp \\left(\\cos \\left(f _ {i} , g _ {c}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {C} \\exp \\left(\\cos \\left(f _ {i} , g _ {j}\\right) / \\tau\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 147, + 482, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\cos(\\cdot)$ represents the cosine similarity operation and $\\tau$ refers to the temperature default set to 0.01.", + "bbox": [ + 89, + 196, + 483, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Test-time prompt tuning. Although CLIP exhibits strong classification performance, it is sensitive to distribution shifts. To address this issue, test-time prompt tuning (TPT) [37] improves the model's performance on individual test instances, without requiring additional training data for adaptation. During the test time, TPT deploys augmentation operations on the test instance $x_0$ to obtain augmented views $\\{x_i\\}_{i=1}^N$ and tunes the textual prompts with low-entropy views. The core objective of TPT is to minimize marginal entropy, which is formulated as:", + "bbox": [ + 89, + 227, + 483, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {m a r g i n a l}} = \\mathcal {H} (\\bar {p}) = \\mathcal {H} \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} p (x)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 388, + 482, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{H}(\\cdot)$ is the Shannon entropy and $\\mathcal{B}$ represents the sample set selected from all views $\\{x_{i}\\}_{i = 0}^{N}$ based on the low entropy. When augmentation provides valuable information, the classification boundary adapts according to the new prompt, leading to more accurate predictions.", + "bbox": [ + 89, + 438, + 483, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Refining Marginal Entropy Minimization", + "text_level": 1, + "bbox": [ + 89, + 523, + 444, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the optimization of a single test sample, marginal entropy is the default choice for both visual models [57] and multimodal models [37]. Minimizing marginal entropy $\\mathcal{H}(\\bar{p})$ encourages the model to produce a consistent output across a set of selected low-entropy augmented views $\\mathcal{B}$ . However, when the test sample is adversarially perturbed, it can easily be selected into the set $\\mathcal{B}$ . While random augmentations can weaken the adversarial noise, enforcing consistency across all augmented outputs may mislead the optimization. Since our goal is to utilize test time adaptation to strengthen the model's defense ability to adversarial examples, we propose refining the marginal entropy objective.", + "bbox": [ + 89, + 547, + 483, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We decompose the marginal entropy objective into two items as follows:", + "bbox": [ + 89, + 729, + 482, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {H} (\\bar {p}) = - \\sum_ {c = 1} ^ {C} \\bar {p} _ {c} \\log \\bar {p} _ {c} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\bar {p} _ {c} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(- \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log p _ {c} ^ {b} + \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\frac {p _ {c} ^ {b}}{\\bar {p} _ {c}}\\right) \\tag {3} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\mathcal {H} \\left(p ^ {b}\\right) + \\mathcal {K L} \\left(p ^ {b} \\| \\bar {p}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 768, + 482, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{H}(\\cdot)$ denotes the Shannon entropy, $\\mathcal{KL}(\\cdot\\|\\cdot)$ refers to Kullback-Leibler (KL) divergence. Eq. 3 shows that marginal entropy is a combination of a pointwise entropy term and a KL divergence term. Minimizing pointwise entropy helps move the classification boundary away from low-entropy points, which is the main composition of the marginal entropy. The KL divergence term, on the other hand, encourages consistent predictions across the augmented views. In the case of clean test samples, the differences between low-entropy augmented views are small, and the KL divergence term has a minimal effect. However, in adversarial scenarios, the mean prediction is distorted by the original perturbed sample, which differs significantly from the augmented views. As a result, enforcing consistency across the augmented views leads to conflicts and neglects the valuable information in these views.", + "bbox": [ + 511, + 90, + 903, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To improve performance under both clean and adversarial conditions, we discard the KL divergence term and focus solely on minimizing pointwise entropy, as follows:", + "bbox": [ + 511, + 333, + 903, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {m i n i m i z e} \\mathcal {L} _ {\\text {p o i n t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\mathcal {H} \\left(p ^ {b}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 385, + 903, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For clean test instances, minimizing pointwise entropy functions similarly to the original marginal entropy objective. Also, for adversarial examples, this approach focuses more on augmented views, which have relatively high entropy and information, and ignores the original adversarial inputs. Therefore, our objective can handle both natural conditions and adversarial attacks well.", + "bbox": [ + 511, + 433, + 905, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Reliability-based Weighted Ensembling", + "text_level": 1, + "bbox": [ + 511, + 546, + 852, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unsupervised prompt tuning typically makes no change to image features and a small adjustment to the classification boundary. For adversarial examples, it is challenging to correct incorrect predictions since their feature representations are far from the correct decision boundary. Fortunately, augmentation at the pixel level can help mitigate the adversarial noise, as it weakens the effect of perturbations. Thus, we can leverage diverse augmented views of the test image, which provide valuable knowledge. To integrate information from augmented views effectively and protect the ensembling from the noise of lower-quality views, we propose a reliability-based weighted ensembling mechanism.", + "bbox": [ + 511, + 568, + 905, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since augmentation inherently involves randomness (e.g., background areas left after cropping), we introduce a reliability metric to represent the quality of each augmented view. Reliability is defined as the similarity between the sample and its nearest neighbors. High reliability indicates that the sample is densely clustered in the feature space, containing useful information. Conversely, low reliability suggests that the sample is an outlier, likely containing augmentation or adversarial noise, and should be downweighted or ignored during ensembling.", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "29961", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4c6d656dd2e223bca7fc4682d411b888a5d284cdc193645fe1b2ed19a251bd0c.jpg", + "image_caption": [ + "(a) Weight value in ImageNet." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 357, + 247 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f31bcb3b85a6256805cad09131208167ef732f437fcd8c58222f5b1186f232ce.jpg", + "image_caption": [ + "(b) Weight value in ImageNet-A.", + "Figure 3. Visualization of assigned reliability-based weight value under (a) clean, (b) distribution shift, and (c) adversarial attack scenarios. The red and blue bars denote the weight value of the original test instance and its augmented views, respectively. The weight assigned to the clean instance is higher than under the distribution shift. The weight of the adversarial test sample is close to 0." + ], + "image_footnote": [], + "bbox": [ + 366, + 92, + 625, + 247 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/644fa76348add333fa4e25af039ff5c8df68020f291a452e19e61ab8f85c0c07.jpg", + "image_caption": [ + "(c) Weight value in ImageNet under attack." + ], + "image_footnote": [], + "bbox": [ + 635, + 92, + 893, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given an augmented batch, which includes the test image and its $N$ augmented views, we calculate the similarity matrix $\\{S_{i,j}\\}_{i,j=0}^{N}$ of the visual features $\\{f_i\\}_{i=0}^N$ :", + "bbox": [ + 89, + 343, + 482, + 391 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i, j} = \\cos \\left(f _ {i}, f _ {j}\\right), i, j = 0, 1, \\dots , N, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 401, + 482, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\text{con}(\\cdot, \\cdot)$ denotes the cosine similarity operation. The $i$ -th row of the matrix $S$ represents the similarity between $x_i$ and all samples in the batch. We then select the $K$ closest neighbor of $x_i$ (excluding $x_i$ itself) to form the neighboring set $\\mathcal{N}_i$ . The reliability of $x_i$ is calculated as the average similarity within the neighboring set $\\mathcal{N}_i$ :", + "bbox": [ + 89, + 431, + 483, + 521 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i} = \\frac {1}{K} \\sum_ {k \\in \\mathcal {N} _ {i}} \\cos \\left(f _ {i}, f _ {k}\\right), i = 0, 1, \\dots , N. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 532, + 482, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reliability score reflects the degree to which $x_{i}$ is surrounded by similar samples in the feature space.", + "bbox": [ + 89, + 582, + 482, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain the final prediction, we ensemble the predictions from all augmented views, weighted by their respective reliability scores. The weight assigned to each view is calculated by applying a softmax operation on the reliabilities $\\{r_i\\}_{i = 0}^N$ . This weight assignment mechanism is flexible and adapts well to various scenarios. We present the weight values for clean samples (ImageNet), samples with distribution shift (ImageNet-A), and adversarial samples (ImageNet) in Figure 3. As shown, clean samples are assigned higher weights, and the ensembling mechanism focuses on augmented views when the test instance shows significant distribution shifts from natural images. For adversarial samples, the weight assigned to the poisoned instance is close to zero, which indicates that our mechanism protects the ensembling process from being misled by adversarial noise. This approach not only improves the robustness of predictions on adversarial samples but also maintains strong performance on clean samples, thus enhancing the overall reliability of the inference process.", + "bbox": [ + 89, + 613, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 340, + 637, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 511, + 369, + 594, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. To evaluate our proposed test-time defense method for VLMs, we conduct experiments on eight fine-grained classification datasets. These databases cover general objects (Caltech101 [10]), animals (Pets [31]), plants (Flower102 [30]), vehicles (Cars [20], Aircraft [25]), textures (DTD [6]), satellite images (EuroSAT [14]), and actions from videos (UCF101 [39]). Moreover, we evaluate on ImageNet [9] and four ImageNet-out-of-distribution (OOD) benchmarks with distribution shift. ImageNet-A [17] contains 200 classes and 7,500 natural adversarial examples which are collected with adversarial filtration technique. ImageNet-V2 [33] consists of 10,000 natural images across 1,000 categories from a different source than ImageNet. ImageNet-R [16] is a dataset containing 30,000 images with various renditions, leading to different textures and local statistics from ImageNet. ImageNet-S [44] consists of 50,889 sketch-style images and shares the same category space with ImageNet. Since our method is to defend against potential adversarial attacks during the test time, we do not need access to the training set of the above datasets.", + "bbox": [ + 511, + 397, + 906, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. Since our task focuses on instance-level test-time adaptation, the model update and prediction of each test sample can not utilize the information of other samples. Following the previous works [37, 53], we report the average classification accuracy (Acc.) to measure the method's adaptation ability on clean samples. To evaluate the adversarial defense performance, we provide the average accuracy (Rob.) on adversarial examples generated by the PGD algorithm [24] with various noise radii. It is worth noting that the adversarial examples are calculated on CLIP before adaptation, which is more suitable for real-world applications since attackers rely on open-source models and have no idea about the victim model's algorithm.", + "bbox": [ + 511, + 704, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "29962", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6231aaab320800041f0224e0e68f4728b61c1d6982139f5af09d61d06ae2d929.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]85.92.683.50.055.70.061.70.015.715.740.40.823.70.058.90.053.22.4
Ensemble83.574.882.369.957.136.258.046.616.416.437.129.516.713.753.943.050.641.3
TPT [37]87.97.084.70.158.40.062.10.017.317.342.44.328.40.060.60.355.23.6
C-TPT [50]87.73.783.60.056.60.064.80.016.716.741.51.327.00.060.10.154.82.7
MTA [53]87.365.984.859.858.717.861.031.518.118.140.318.822.51.660.631.354.130.6
R-TPT86.779.884.674.258.142.960.651.917.517.541.333.521.215.959.750.953.745.8
", + "bbox": [ + 99, + 82, + 895, + 205 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a061a26b6edd6aa749453ab76f8f344a47650b870a54267ee6aac9b8914ea874.jpg", + "table_caption": [ + "Table 1. Results (%) of clean accuracy (Acc.) and adversarial accuracy (Rob.) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ResNet50 ( $\\epsilon = 1.0$ ). Best clean accuracies are (bold), best adversarial accuracies are (bold red)." + ], + "table_footnote": [], + "table_body": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]94.00.088.30.065.50.067.40.023.923.944.40.042.20.065.20.061.43.0
Ensemble91.974.786.251.265.726.065.936.323.423.443.225.128.22.263.030.658.433.7
TPT [37]94.10.087.40.066.50.069.10.023.423.446.90.042.60.067.90.062.22.9
C-TPT [50]93.90.088.20.065.80.069.60.023.923.945.90.042.30.065.50.061.93.0
MTA [53]94.372.188.051.867.718.567.427.925.025.046.516.242.51.267.527.562.330.0
R-TPT93.782.087.260.267.034.768.744.623.923.946.432.834.78.567.243.261.141.2
", + "bbox": [ + 99, + 252, + 895, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Results (%) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ViT-B/16 ( $\\epsilon = {4.0}$ ).", + "bbox": [ + 101, + 386, + 892, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare R-TPT on the above benchmarks with existing test-time adaptation methods for CLIP, including TPT [37], C-TPT [50], and MTA [53], as well as zero-shot prediction from CLIP [32]. Also, we regard Ensemble as an additional baseline method, which employs simple average operation on predictions of all augmented views. Note that both our method and the compared baseline methods rely only on CLIP and AugMix [15] augmentation, without any additional foundation models (e.g., LLM, diffusion models) or knowledge. All results of baselines are reproduced with the official code.", + "bbox": [ + 88, + 426, + 480, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For all experiments, we utilize official pre-trained CLIP-ResNet50 and CLIP-ViT-B/16 [32] as our base model. As for adversarial example generation, we utilize the PGD algorithm [24] with $\\epsilon = 1.0$ and 7 steps for ResNet, while $\\epsilon = 4.0$ and 100 steps for ViT. In the defense stage at test time, the parameter optimized in all experiments is a textual prompt with a context length of 4 and is initiated with \"a photo of a\". We adopt the Adam optimizer with weight decay and a single step. Following previous work [37], the learning rate is set to 0.005 and the augmented batch size is 64. All experiments use the PyTorch framework and run on RTX3090 GPUs.", + "bbox": [ + 88, + 594, + 482, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 787, + 292, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on fine-grained datasets. We evaluate the adaptation and adversarial defense ability of R-TPT on eight fine-grained benchmarks and report the results in Table 1. It is shown that CLIP with strong zero-shot generalization ability is suffering from the adversarial attack with a small radius. TPT can steadily improve the accuracy of clean im", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ages but has weak defense capability. We observe that methods with an ensembling strategy (e.g., Ensemble, MTA, R-TPT) achieve significantly better adversarial accuracy. In particular, R-TPT achieves a $45.8\\%$ of adversarial accuracy which outperforms all baseline methods. Besides the attractive defense performance, R-TPT also improves the clean accuracy of CLIP from $53.2\\%$ to $53.7\\%$ . In contrast, although Ensemble has strong defense capabilities, it suffers from negative transfer in the clean scenario.", + "bbox": [ + 511, + 426, + 905, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on ImageNet and ImageNet-OOD datasets. We provide the experiential results on ImageNet and four ImageNet-OOD datasets in Table 3. CLIP can overcome distribution shifts, but fails to defend against adversarial attacks. R-TPT performs the best in adversarial defense under both ImageNet and its related out-of-distribution benchmarks. Especially, R-TPT achieves an adversarial accuracy of $47.7\\%$ on ImageNet, $7.6\\%$ higher than the second-best method Ensemble, while CLIP's adversarial accuracy on this benchmark is $0.1\\%$ . Moreover, our method obtains a similar clean accuracy with TPT, indicating that R-TPT is also effective for distribution shifts.", + "bbox": [ + 511, + 566, + 905, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results of CLIP-ViT backbone. We evaluate our method on CLIP-ViT-B/16 [32] model and provide the results in Table 2. We observe that R-TPT outperforms all baseline methods regarding adversarial defense performance. However, the performance gain of all adaptation methods for clean samples is small, and R-TPT and the remaining two ensembling-based methods make weak negative transfers. This illustrates that the space for improvement of clean accuracy for strong pre-training models is small, and R-TPT can greatly enhance its weak robustness.", + "bbox": [ + 511, + 750, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "29963", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/40284b8c6049556689473b185f8fdacc58b0b091d05c19ac2735405ac8f7eec2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodImageNetImageNet-AImageNet-V2ImageNet-RImageNet-SAvg.
Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.
CLIP [32]58.20.121.80.051.50.156.10.833.30.544.20.3
Ensemble58.040.122.610.152.037.251.339.329.520.742.729.5
TPT [37]60.70.326.50.054.80.358.91.835.01.447.20.7
C-TPT [50]60.40.124.10.054.30.157.71.034.70.946.20.4
MTA [53]60.430.027.55.654.224.658.429.835.211.347.120.3
R-TPT60.947.728.414.454.941.657.646.934.026.247.135.4
", + "bbox": [ + 173, + 82, + 821, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/afc1fe676bd3f8c712f6e8a493b1c998abca99fd58ac27ba233a6b19b9c25c69.jpg", + "table_caption": [ + "Table 3. Results (\\%) of various adaptation methods on ImageNet and ImageNet-OD benchmarks with pre-trained CLIP-ResNet50. OOD Avg. refers to the average results among four ImageNet-OD benchmarks ( $\\epsilon = 1.0$ )." + ], + "table_footnote": [], + "table_body": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP-TeCoA [26]79.344.366.915.810.21.030.89.06.66.624.510.714.510.834.66.733.413.1
Ensemble72.755.159.938.95.62.726.616.04.24.223.516.212.511.026.414.028.919.8
TPT [37]79.352.765.227.49.62.027.912.36.76.725.514.612.211.234.910.232.717.1
C-TPT [50]79.847.366.119.510.61.329.410.76.46.426.212.413.011.136.48.133.514.6
MTA [53]79.755.766.231.29.02.529.114.06.56.524.413.513.311.234.612.532.918.4
R-TPT76.160.563.240.17.73.526.616.56.16.125.217.711.511.331.117.430.921.7
", + "bbox": [ + 91, + 253, + 903, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. More Analysis", + "text_level": 1, + "bbox": [ + 89, + 424, + 238, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results under robust-pretrained models. we report the results of deploying adaptation methods on CLIP-ViT-B/32 with TeCoA [26] robust pretrained models in Table 4. It is shown that TeCoA significantly improves the robustness of CLIP, and the defense effect against adversarial attacks can benefit from our method during the testing stage, which increases adversarial accuracy form $13.1\\%$ to $21.7\\%$ . At the same time, we also find that R-TPT's defense effect on the TeCoA pretrained model is weaker than the vanilla CLIP. The reason is that introducing adversarial learning during the training time decreases the clean accuracy, which is the upper bound of defense. Robust pre-trained models also generate more difficult adversarial examples.", + "bbox": [ + 88, + 446, + 482, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis under various attacks. To demonstrate the versatility, we investigate the defense performance of R-TPT and baseline methods under various attack methods. We employ CW [4], DeepFool [27], and FGSM [13] as new attacks and report the adversarial accuracy on three benchmarks in Table 5. It is shown that our method improves CLIP's defense capability under each attack, which is consistent with the trend of PGD. In particular, R-TPT has reached $51.8\\%$ adversarial accuracy on Flowers. The excellent defense performance among various attack methods proves the versatility of R-TPT.", + "bbox": [ + 88, + 643, + 482, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of inference efficiency. We study the inference efficiency of R-TPT. Experiments of training-time defense method APT and R-TPT on UCF101 are provided in Table 6. It is shown that R-TPT spends a certain amount of time on each test sample, which is different from training-time defense which spends a lot of resources at one time", + "bbox": [ + 88, + 809, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/91654abb14338195b0a5dd16fbd86eff3e4344d5fb41d4cc351e07ea3a9c1ee4.jpg", + "table_caption": [ + "Table 4. Results (%) of adaptation methods on fine-grained classification datasets with TeCoA pre-trained CLIP-ViT-B/32 ( $\\epsilon = {4.0}$ )." + ], + "table_footnote": [], + "table_body": "
MethodFlowersDTD
CWDFFGSMAvg.CWDFFGSMAvg.
CLIP [32]0.80.44.82.02.37.613.47.8
Ensemble50.152.246.649.731.132.929.731.2
TPT [37]13.810.814.212.921.324.422.222.6
C-TPT [50]6.65.56.26.111.915.817.515.1
MTA [53]34.535.436.635.523.623.523.923.7
R-TPT51.654.749.251.834.235.932.534.2
", + "bbox": [ + 514, + 417, + 903, + 540 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3e36086aca06f781f737941e018ea0ed3fd541f469921bdd9986e919f203425b.jpg", + "table_caption": [ + "Table 5. Adversarial accuracies $(\\%)$ of adaptation methods against different attacks on two fine-grained datasets (DF = DeepFool)." + ], + "table_footnote": [], + "table_body": "
MethodStageRunning timeRob.
APT+TeCoA (4shots)Training time208s/50epochs39.4
R-TPT (64 views)Test time0.58s/image41.0
R-TPT (32 views)Test time0.28s/image40.8
R-TPT (16 views)Test time0.20s/image40.0
", + "bbox": [ + 517, + 593, + 903, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Running time and adversarial accuracies $(\\%)$ of adaptation methods against adversarial attack on UCF101 dataset.", + "bbox": [ + 511, + 691, + 906, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "during training. Moreover, we find that inference can be accelerated by appropriately reducing the number of augmented views to obtain better real-time performance. When we choose to reduce the number of views from 64 to 16, the time required for each test sample is reduced to less than half of the original.", + "bbox": [ + 511, + 748, + 906, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis under different prompt templates. Since in the realistic scenario, the attacker can not access the prompts of the model textual branch, we evaluate the defense performance of the adversarial examples generated by", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "29964", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5dfc6035ec6ffb3e6986b3d000c76da21cfe6d76c6850aadb8c75e0fce263f41.jpg", + "image_caption": [ + "(a) Different prompt templates." + ], + "image_footnote": [], + "bbox": [ + 101, + 89, + 346, + 248 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4569975943b3d91c312854db7b3323db48455d7a277863128c9e55860016e4b4.jpg", + "image_caption": [ + "(b) Sensitivity of neighbor number.", + "Figure 4. Results of different prompt templates in adversarial examples generation, different neighbor numbers, and different choices of optimization parameters in DTD dataset (CLIP-ResNet50, $\\epsilon = 1.0$ )." + ], + "image_footnote": [], + "bbox": [ + 367, + 95, + 625, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3a30117983e83d34297680117fe998e1da2b3063a2d0d3c9e41ba544436d559c.jpg", + "image_caption": [ + "(c) Sensitivity of optimization parameters." + ], + "image_footnote": [], + "bbox": [ + 635, + 98, + 893, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "different prompt templates. The result of DTD benchmark with six textual templates is provided in Figure 4(a) (P0='a photo of a []', P1='a bad photo of the []', P2='a origami []', P3='a photo of the large []', P4='a toy []', P5='art of the []'). It is shown that CLIP is suffering from adversarial samples even if attackers use different prompt templates. Also, R-TPT outperforms all baseline methods under each template.", + "bbox": [ + 89, + 329, + 483, + 449 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of sensitivity of hyperparameters and optimization parameters. We study the impact of the neighbor number in calculating reliability and the optimization parameter to further demonstrate the effectiveness of R-TPT. We provide the results of R-TPT with different neighbor numbers (10, 15, 20, 25, 30) in Figure 4(b). The results demonstrate that R-TPT performs stable across different neighbor numbers in terms of both clean and adversarial accuracy. Please note that if the neighbor number equals to augmented batch size, it will assign all samples with equal weights and the reliability-based ensembling mechanism will degenerate into the vanilla ensembling. Besides, we report the results with different optimization parameters in Figure 4(c). Compared to other choices of the parameter space, optimizing textual prompts owns better defense and adaptation effects and fewer parameters, which make it always a popular solution for parameter-efficient fine-tuning.", + "bbox": [ + 89, + 452, + 483, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 724, + 243, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To study the contribution of terms in our method, we investigate the effectiveness of ensembling, reliability-based weighted mechanism, and pointwise entropy objective in R-TPT. The results of the ablation study are reported in Table 7. From the table, we find that entropy minimization focuses on enhancing the accuracy of adaptation on the clean samples and Slightly improves the defense performance on CLIP. However, When cooperating with weighted ensembling, the improvement of entropy minimization on both metrics is significant. The ensembling strategy greatly", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3e892f93b68592e03c45dd6f90444abc0c15d47031c233cbc6500939573a66e9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EnsembleWeightedEntMinFine-grainedImageNet-X
Acc.Rob.Acc.Rob.
XXX53.22.444.20.3
XX✓55.23.647.20.7
✓XX50.641.342.729.5
✓X✓53.344.346.734.2
✓✓X51.644.344.833.4
✓✓✓53.745.847.135.4
", + "bbox": [ + 517, + 315, + 901, + 449 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Ablation study. Clean and adversarial accuracies $(\\%)$ on fine-grained datasets and ImageNet dataset (CLIP-ResNet50).", + "bbox": [ + 511, + 459, + 906, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "strengthens the defense capabilities of the model, but it also reduces the adaptation performance on clean samples. The weighted mechanism gives reliable samples more important roles during prediction, further improving the defense capabilities and mitigating the clean performance drop.", + "bbox": [ + 511, + 513, + 906, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 603, + 633, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we for the first time explore the adversarial defense for CLIP with a test-time paradigm and propose robust test-time prompt tuning (R-TPT). We first review the classic test time adaptation method and decompose its marginal entropy objective into a pointwise entropy term and a KL divergence term. We find that minimizing KL divergence will introduce conflicts when meeting the adversarial test instance, thus we discard KL divergence terms and only optimize the textual prompt with the pointwise entropy. We also introduce a reliability-based weighted ensembling strategy to utilize knowledge of the augmented views, which contain more knowledge than the risky original input under adversarial attacks. Extensive results show that R-TPT achieves the best defense against various adversarial attacks among all baseline methods and maintains a clean adaptation performance. We believe that our work will provide a new perspective on the defense and shed light on the safety issues of VLMs.", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "29965", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was funded by the National Natural Science Foundation of China under Grants (62276256, U2441251) and the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). The authors would like to thank Professor Tan Tieniu for his valuable guidance and contribution to this work.", + "bbox": [ + 89, + 114, + 483, + 204 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 217, + 187, + 233 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jameel Abdul Samadh, Mohammad Hanan Gani, Noor Hussein, Muhammad Uzair Khattak, Muhammad Muzammal Naseer, Fahad Shahbaz Khan, and Salman H Khan. Align your prompts: Test-time prompting with distribution alignment for zero-shot generalization. In Proc. NeurIPS, 2024. 3", + "[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Proc. ECCV, 2020. 2", + "[3] Shaotian Cai, Liping Qiu, Xiaojun Chen, Qin Zhang, and Longteng Chen. Semantic-enhanced image clustering. In Proc. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.13, + 0.9, + 0.178 + ], + "angle": 0, + "content": "R-TPT: Improving Adversarial Robustness of Vision-Language Models through Test-Time Prompt Tuning" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.202, + 0.713, + 0.222 + ], + "angle": 0, + "content": "Lijun Sheng\\(^{1,2}\\), Jian Liang\\(^{2,3*}\\), Zilei Wang\\(^{1}\\), Ran He\\(^{2,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.306, + 0.222, + 0.693, + 0.239 + ], + "angle": 0, + "content": "1 University of Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.239, + 0.788, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\) NLPR & MAIS, Institute of Automation, Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.318, + 0.257, + 0.68, + 0.275 + ], + "angle": 0, + "content": "3 University of Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.278, + 0.708, + 0.292 + ], + "angle": 0, + "content": "slj0728@mail.ustc.edu.cn, liangjian92@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.327, + 0.327, + 0.343 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.358, + 0.485, + 0.736 + ], + "angle": 0, + "content": "Vision-language models (VLMs), such as CLIP, have gained significant popularity as foundation models, with numerous fine-tuning methods developed to enhance performance on downstream tasks. However, due to their inherent vulnerability and the common practice of selecting from a limited set of open-source models, VLMs suffer from a higher risk of adversarial attacks than traditional vision models. Existing defense techniques typically rely on adversarial fine-tuning during training, which requires labeled data and lacks of flexibility for downstream tasks. To address these limitations, we propose robust test-time prompt tuning (R-TPT), which mitigates the impact of adversarial attacks during the inference stage. We first reformulate the classic marginal entropy objective by eliminating the term that introduces conflicts under adversarial conditions, retaining only the pointwise entropy minimization. Furthermore, we introduce a plug-and-play reliability-based weighted ensembling strategy, which aggregates useful information from reliable augmented views to strengthen the defense. R-TPT enhances defense against adversarial attacks without requiring labeled training data while offering high flexibility for inference tasks. Extensive experiments on widely used benchmarks with various attacks demonstrate the effectiveness of R-TPT. The code is available in https://github.com/TomSheng21/R-TPT." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.763, + 0.222, + 0.779 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.788, + 0.484, + 0.88 + ], + "angle": 0, + "content": "Vision-language models (VLMs) [5, 32, 56] are multimodal models pretrained on large-scale paired image-text data. Their powerful zero-shot inference capability and broad applicability across a range of downstream tasks have made them a foundational tool in the research community. CLIP [32], a milestone work, aligns features from the text and" + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.328, + 0.671, + 0.342 + ], + "angle": 0, + "content": "Training-time defense" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.344, + 0.703, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.758, + 0.329, + 0.858, + 0.34 + ], + "angle": 0, + "content": "Test-time defense" + }, + { + "type": "image", + "bbox": [ + 0.717, + 0.344, + 0.9, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.594, + 0.907, + 0.651 + ], + "angle": 0, + "content": "Figure 1. Comparison between training-time and test-time defense for CLIP. Our test-time defense paradigm provides robust prediction as the conventional training-time methods and requires no annotated dataset or adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.685, + 0.907, + 0.852 + ], + "angle": 0, + "content": "visual modalities using two specialized feature extractors trained with a contrastive loss function. Due to its concise architecture and impressive performance, CLIP has become the most widely used VLM across diverse research topics. For classification tasks, CLIP extracts features from both images and category descriptions, then chooses the category whose features exhibit the highest similarity to the image's feature representation. Beyond classification [47, 48, 60, 61], CLIP has been successfully applied to various vision tasks, such as semantic segmentation [36, 59], object detection [55, 58], and image clustering [3, 22]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The impressive performance on downstream tasks and the broad range of applications of CLIP not only highlight its powerful capabilities but also expose it to potential vul" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.366, + 0.9 + ], + "angle": 0, + "content": "*To whom correspondence should be addressed." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "29958" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.243 + ], + "angle": 0, + "content": "nerabilities, particularly under adversarial attacks [19, 26]. While adversarial attacks and defenses [13, 24, 54] have been widely explored for conventional visual models, the situation for CLIP is more complex. The pre-training of CLIP requires the collection of vast amounts of image-text pairs and substantial computational resources that most deployers cannot afford. As a result, many deployers choose to adopt open-source versions of CLIP from a small range of candidates. This fact introduces a relatively high risk of adversarial attacks targeting CLIP-based applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.246, + 0.483, + 0.457 + ], + "angle": 0, + "content": "Recent works [21, 26] explore adversarial prompt tuning using annotated data to enhance the robustness of CLIP. However, their reliance on labeled data and limited flexibility across tasks pose challenges for real-world deployment. To address this, we choose to defend adversarial attacks in the inference stage, which is applicable across various scenarios and requires no labeled dataset or prior knowledge of the downstream task, as shown in Figure 1. Existing test-time adaptation methods [37, 53] primarily focus on improving accuracy for clean test samples, while overlooking the potential risks posed by adversarial attacks. Moreover, deploying defense at test time necessitates short inference time and avoiding using additional resources, such as large language models or diffusion models, to ensure versatility." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.46, + 0.483, + 0.793 + ], + "angle": 0, + "content": "To address the above challenges and achieve successful defense against potential attacks, we propose robust test-time prompt tuning (R-TPT). First, we revisit and refine the widely used optimization objective for instance adaptation. Many previous works [37, 41], following MEMO [57], augment the test instance and aim to minimize marginal entropy, which is defined as the entropy of the mean prediction. We decompose marginal entropy into two components: a pointwise entropy term and the Kullback-Leibler (KL) divergence, which measures the divergence between predictions from each augmented view and the mean prediction. We observe that when adapting to adversarial examples with high-confidence inaccurate predictions, the KL divergence term tends to pull the augmented views toward the misleading mean prediction, which does not exist in the clean scenario. This meaningless operation introduces conflicts into the optimization process. To mitigate the influence of adversarial samples and preserve simplicity, we discard the KL divergence term, retaining only the pointwise entropy minimization for tuning textual prompts. This straightforward modification not only defends against adversarial attacks but also maintains clean performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.482, + 0.901 + ], + "angle": 0, + "content": "In order to effectively leverage knowledge from augmented views, we propose a reliability-based weighted ensembling strategy. To assign a larger weight to reliable augmented views during ensembling, we introduce a similarity-based metric to assess the reliability of samples. We hypothesize that samples with higher similarity to their neighbors are farther away from outliers and contain more reli" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.272 + ], + "angle": 0, + "content": "able information. Thus, we calculate the average similarity of each sample with its neighbors to estimate its reliability. Using this metric, outliers such as adversarial examples and noisy augmented views are assigned lower reliability scores, which means less participation in the ensembling. Finally, we obtain the final prediction by ensembling the individual model predictions, weighted according to their reliability. Extensive experiments on fine-grained classification benchmarks and distribution shift benchmarks validate the effectiveness of our method in both adaptation and defense against adversarial attacks. Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.274, + 0.905, + 0.317 + ], + "angle": 0, + "content": "- We propose R-TPT, which is the first to explore test-time paradigms for defending against potential adversarial attacks in CLIP." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.319, + 0.905, + 0.379 + ], + "angle": 0, + "content": "- We discard the KL divergence term from the marginal entropy objective to eliminate optimization conflicts and propose a reliability-based weighted ensembling strategy to integrate knowledge from reliable augmented views." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.38, + 0.905, + 0.409 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the effectiveness of our method in both adaptation and adversarial defense." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.274, + 0.905, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.427, + 0.655, + 0.442 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.453, + 0.796, + 0.468 + ], + "angle": 0, + "content": "2.1. Adversarial Attack and Defense" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.476, + 0.905, + 0.687 + ], + "angle": 0, + "content": "A lot of research [13, 24, 42] has been devoted to studying neural network's vulnerability to adversarial noise. A pioneering work [42] introduces the concept of adversarial examples and finds small-amplitude noise that humans cannot recognize leads to misclassifications. Since then, a series of attack methods to generate adversarial samples [4, 8, 13, 24] have been proposed. FGSM [13] proposes to utilize the gradient sign to generate an adversarial example. Researchers [24] generate the adversarial noise by projected gradient descent (PGD) operation, which becomes the standard measurement of model robustness. Moreover, a variety of works explore adversarial attacks in many restricted conditions, ranging from one-pixel attack [40], universal perturbation [28] to more realistic black-box setting [2, 18]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.905, + 0.839 + ], + "angle": 0, + "content": "In parallel, numerous defense strategies [24, 35, 49, 54] have been proposed to mitigate adversarial attacks. Adversarial training [13, 24] improves the robustness of the model by incorporating the adversarial samples into the training set. TRADES [54] provides a theoretical analysis of adversarial error to trade adversarial robustness against accuracy. AWP [49] perturbs the model's weights with small adversarial noise during training to enhance robustness. Reconstruction [29, 34] with generative models [12, 38] is also a commonly used technique in test-time defense methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "As for the vison-language models, TeCoA [26] and APT [21] employ adversarial training to pretrained CLIP [32] to improve the adversarial robustness. However, their training-time solution requires an annotated dataset and lacks flexi" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29959" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.096, + 0.882, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.392, + 0.908, + 0.451 + ], + "angle": 0, + "content": "Figure 2. The pipeline of R-TPT framework. Given an instance-level task, we deploy augmentation on the test image and build a classifier with CLIP's text branch. After selecting a low-entropy batch, R-TPT discards the KL divergence minimization term which potentially introduces conflicts in the marginal entropy [57] and optimizes textual prompts with pointwise entropy minimization. To effectively utilize the knowledge of the augmented views, R-TPT applies a reliability-based weighted ensembling mechanism in the final inference process." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.474, + 0.483, + 0.522 + ], + "angle": 0, + "content": "bility across tasks. In this work, we choose to deploy adversarial defense in the test time that is more effective and flexible and can collaborate with their training-time defense." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.531, + 0.378, + 0.547 + ], + "angle": 0, + "content": "2.2. Test-Time Adaptation for VLMs" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.553, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Test-time adaptation [23, 37, 51] aims to adapt pre-trained models to the test data at inference time to improve the performance further. According to the test data form, test-time adaptation is divided into streaming data adaptation [43, 45, 52] and single instance adaptation [37, 57], and our work focuses on the latter. Recent research [37, 41, 53] has been devoted to exploring the instance adaptation methods for VLMs [32, 46, 56]. TPT [37] employs the marginal entropy minimization to augmentation views of the test instance to correct the prediction. DiffTPT [11] utilizes the diffusion technique to obtain diverse views which is helpful for the adaptation. PromptAlign [1] aligns the statistics of the test instance and collected natural images to make the model's parameters adapt to test samples. To take advantage of more prompt templates [32], TPS [41] chooses to optimize feature shift and utilizes prompt ensembling for initialization. Moreover, researchers [53] propose a training-free adaptation method by ensembling the augmented views with the MeanShift algorithm [7]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Besides accuracy, researchers [50] also focus on improving calibration performance through higher text feature dispersion. In this work, we first utilize the test-time paradigm to defend against adversarial attacks for CLIP due to its se" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.474, + 0.796, + 0.49 + ], + "angle": 0, + "content": "vere vulnerability to adversarial examples." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.507, + 0.649, + 0.525 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.533, + 0.907, + 0.701 + ], + "angle": 0, + "content": "In this paper, we improve CLIP's adversarial robustness through a test-time paradigm, motivated by its inherent vulnerabilities and the high resource demands of train-time defense methods. Our proposed robust test-time prompt tuning (R-TPT), as illustrated in Figure 2, requires no annotated data and is equipped with greater flexibility. In Sec. 3.1, we begin with reviewing the foundational concepts of CLIP and the test-time prompt tuning approach. We then introduce the two key components of R-TPT: pointwise entropy minimization in Sec. 3.2, and the reliability-based weighted ensembling strategy in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.712, + 0.644, + 0.728 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Contrastive language-image pre-training. CLIP is a popular language-vision model with a double-tower architecture, consisting of an image encoder \\( F(\\cdot) \\) and a text encoder \\( G(\\cdot) \\). It is pretrained by the contrastive learning objective with a large amount of image-text pairs. Benefiting from rich pretraining knowledge, CLIP has a strong zero-shot generalization ability. Take a C-way classification task with class names \\( \\{t_c\\}_{c=1}^C \\) as an example, CLIP obtains textual features \\( g_c \\) by the text encoder \\( G(\\cdot) \\) with a prompt template (e.g., \"a photo of a [\"]) and the class name \\( t_c \\) as the input. Also, each test image \\( x_i \\) queries the image encoder" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "29960" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "to calculate the image feature \\( f_{i} = F(x_{i}) \\). The probability that \\( x_{i} \\) belongs to category \\( c \\) is calculated by a softmax operation with the cosine similarity of those features:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.148, + 0.483, + 0.186 + ], + "angle": 0, + "content": "\\[\np _ {c} \\left(x _ {i}\\right) = \\frac {\\exp \\left(\\cos \\left(f _ {i} , g _ {c}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {C} \\exp \\left(\\cos \\left(f _ {i} , g _ {j}\\right) / \\tau\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.198, + 0.484, + 0.227 + ], + "angle": 0, + "content": "where \\( \\cos(\\cdot) \\) represents the cosine similarity operation and \\( \\tau \\) refers to the temperature default set to 0.01." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.228, + 0.484, + 0.38 + ], + "angle": 0, + "content": "Test-time prompt tuning. Although CLIP exhibits strong classification performance, it is sensitive to distribution shifts. To address this issue, test-time prompt tuning (TPT) [37] improves the model's performance on individual test instances, without requiring additional training data for adaptation. During the test time, TPT deploys augmentation operations on the test instance \\( x_0 \\) to obtain augmented views \\( \\{x_i\\}_{i=1}^N \\) and tunes the textual prompts with low-entropy views. The core objective of TPT is to minimize marginal entropy, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.39, + 0.483, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {m a r g i n a l}} = \\mathcal {H} (\\bar {p}) = \\mathcal {H} \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} p (x)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.439, + 0.484, + 0.515 + ], + "angle": 0, + "content": "where \\(\\mathcal{H}(\\cdot)\\) is the Shannon entropy and \\(\\mathcal{B}\\) represents the sample set selected from all views \\(\\{x_{i}\\}_{i = 0}^{N}\\) based on the low entropy. When augmentation provides valuable information, the classification boundary adapts according to the new prompt, leading to more accurate predictions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.525, + 0.445, + 0.542 + ], + "angle": 0, + "content": "3.2. Refining Marginal Entropy Minimization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.484, + 0.729 + ], + "angle": 0, + "content": "In the optimization of a single test sample, marginal entropy is the default choice for both visual models [57] and multimodal models [37]. Minimizing marginal entropy \\(\\mathcal{H}(\\bar{p})\\) encourages the model to produce a consistent output across a set of selected low-entropy augmented views \\(\\mathcal{B}\\). However, when the test sample is adversarially perturbed, it can easily be selected into the set \\(\\mathcal{B}\\). While random augmentations can weaken the adversarial noise, enforcing consistency across all augmented outputs may mislead the optimization. Since our goal is to utilize test time adaptation to strengthen the model's defense ability to adversarial examples, we propose refining the marginal entropy objective." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.73, + 0.483, + 0.759 + ], + "angle": 0, + "content": "We decompose the marginal entropy objective into two items as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.77, + 0.483, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {H} (\\bar {p}) = - \\sum_ {c = 1} ^ {C} \\bar {p} _ {c} \\log \\bar {p} _ {c} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\bar {p} _ {c} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(- \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log p _ {c} ^ {b} + \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\frac {p _ {c} ^ {b}}{\\bar {p} _ {c}}\\right) \\tag {3} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\mathcal {H} \\left(p ^ {b}\\right) + \\mathcal {K L} \\left(p ^ {b} \\| \\bar {p}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.332 + ], + "angle": 0, + "content": "where \\(\\mathcal{H}(\\cdot)\\) denotes the Shannon entropy, \\(\\mathcal{KL}(\\cdot\\|\\cdot)\\) refers to Kullback-Leibler (KL) divergence. Eq. 3 shows that marginal entropy is a combination of a pointwise entropy term and a KL divergence term. Minimizing pointwise entropy helps move the classification boundary away from low-entropy points, which is the main composition of the marginal entropy. The KL divergence term, on the other hand, encourages consistent predictions across the augmented views. In the case of clean test samples, the differences between low-entropy augmented views are small, and the KL divergence term has a minimal effect. However, in adversarial scenarios, the mean prediction is distorted by the original perturbed sample, which differs significantly from the augmented views. As a result, enforcing consistency across the augmented views leads to conflicts and neglects the valuable information in these views." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.334, + 0.905, + 0.379 + ], + "angle": 0, + "content": "To improve performance under both clean and adversarial conditions, we discard the KL divergence term and focus solely on minimizing pointwise entropy, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.386, + 0.905, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\text {m i n i m i z e} \\mathcal {L} _ {\\text {p o i n t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\mathcal {H} \\left(p ^ {b}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.434, + 0.906, + 0.538 + ], + "angle": 0, + "content": "For clean test instances, minimizing pointwise entropy functions similarly to the original marginal entropy objective. Also, for adversarial examples, this approach focuses more on augmented views, which have relatively high entropy and information, and ignores the original adversarial inputs. Therefore, our objective can handle both natural conditions and adversarial attacks well." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.547, + 0.854, + 0.564 + ], + "angle": 0, + "content": "3.3. Reliability-based Weighted Ensembling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.906, + 0.75 + ], + "angle": 0, + "content": "Unsupervised prompt tuning typically makes no change to image features and a small adjustment to the classification boundary. For adversarial examples, it is challenging to correct incorrect predictions since their feature representations are far from the correct decision boundary. Fortunately, augmentation at the pixel level can help mitigate the adversarial noise, as it weakens the effect of perturbations. Thus, we can leverage diverse augmented views of the test image, which provide valuable knowledge. To integrate information from augmented views effectively and protect the ensembling from the noise of lower-quality views, we propose a reliability-based weighted ensembling mechanism." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Since augmentation inherently involves randomness (e.g., background areas left after cropping), we introduce a reliability metric to represent the quality of each augmented view. Reliability is defined as the similarity between the sample and its nearest neighbors. High reliability indicates that the sample is densely clustered in the feature space, containing useful information. Conversely, low reliability suggests that the sample is an outlier, likely containing augmentation or adversarial noise, and should be downweighted or ignored during ensembling." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29961" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.359, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.251, + 0.319, + 0.264 + ], + "angle": 0, + "content": "(a) Weight value in ImageNet." + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.093, + 0.626, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.251, + 0.594, + 0.264 + ], + "angle": 0, + "content": "(b) Weight value in ImageNet-A." + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.093, + 0.895, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.251, + 0.892, + 0.264 + ], + "angle": 0, + "content": "(c) Weight value in ImageNet under attack." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.274, + 0.907, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Visualization of assigned reliability-based weight value under (a) clean, (b) distribution shift, and (c) adversarial attack scenarios. The red and blue bars denote the weight value of the original test instance and its augmented views, respectively. The weight assigned to the clean instance is higher than under the distribution shift. The weight of the adversarial test sample is close to 0." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.344, + 0.483, + 0.392 + ], + "angle": 0, + "content": "Given an augmented batch, which includes the test image and its \\(N\\) augmented views, we calculate the similarity matrix \\(\\{S_{i,j}\\}_{i,j=0}^{N}\\) of the visual features \\(\\{f_i\\}_{i=0}^N\\):" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.402, + 0.483, + 0.42 + ], + "angle": 0, + "content": "\\[\nS _ {i, j} = \\cos \\left(f _ {i}, f _ {j}\\right), i, j = 0, 1, \\dots , N, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.432, + 0.484, + 0.522 + ], + "angle": 0, + "content": "where \\( \\text{con}(\\cdot, \\cdot) \\) denotes the cosine similarity operation. The \\( i \\)-th row of the matrix \\( S \\) represents the similarity between \\( x_i \\) and all samples in the batch. We then select the \\( K \\) closest neighbor of \\( x_i \\) (excluding \\( x_i \\) itself) to form the neighboring set \\( \\mathcal{N}_i \\). The reliability of \\( x_i \\) is calculated as the average similarity within the neighboring set \\( \\mathcal{N}_i \\):" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.534, + 0.483, + 0.571 + ], + "angle": 0, + "content": "\\[\nr _ {i} = \\frac {1}{K} \\sum_ {k \\in \\mathcal {N} _ {i}} \\cos \\left(f _ {i}, f _ {k}\\right), i = 0, 1, \\dots , N. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.483, + 0.614 + ], + "angle": 0, + "content": "The reliability score reflects the degree to which \\( x_{i} \\) is surrounded by similar samples in the feature space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To obtain the final prediction, we ensemble the predictions from all augmented views, weighted by their respective reliability scores. The weight assigned to each view is calculated by applying a softmax operation on the reliabilities \\(\\{r_i\\}_{i = 0}^N\\). This weight assignment mechanism is flexible and adapts well to various scenarios. We present the weight values for clean samples (ImageNet), samples with distribution shift (ImageNet-A), and adversarial samples (ImageNet) in Figure 3. As shown, clean samples are assigned higher weights, and the ensembling mechanism focuses on augmented views when the test instance shows significant distribution shifts from natural images. For adversarial samples, the weight assigned to the poisoned instance is close to zero, which indicates that our mechanism protects the ensembling process from being misled by adversarial noise. This approach not only improves the robustness of predictions on adversarial samples but also maintains strong performance on clean samples, thus enhancing the overall reliability of the inference process." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.342, + 0.638, + 0.359 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.371, + 0.596, + 0.387 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.907, + 0.7 + ], + "angle": 0, + "content": "Datasets. To evaluate our proposed test-time defense method for VLMs, we conduct experiments on eight fine-grained classification datasets. These databases cover general objects (Caltech101 [10]), animals (Pets [31]), plants (Flower102 [30]), vehicles (Cars [20], Aircraft [25]), textures (DTD [6]), satellite images (EuroSAT [14]), and actions from videos (UCF101 [39]). Moreover, we evaluate on ImageNet [9] and four ImageNet-out-of-distribution (OOD) benchmarks with distribution shift. ImageNet-A [17] contains 200 classes and 7,500 natural adversarial examples which are collected with adversarial filtration technique. ImageNet-V2 [33] consists of 10,000 natural images across 1,000 categories from a different source than ImageNet. ImageNet-R [16] is a dataset containing 30,000 images with various renditions, leading to different textures and local statistics from ImageNet. ImageNet-S [44] consists of 50,889 sketch-style images and shares the same category space with ImageNet. Since our method is to defend against potential adversarial attacks during the test time, we do not need access to the training set of the above datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Evaluation metrics. Since our task focuses on instance-level test-time adaptation, the model update and prediction of each test sample can not utilize the information of other samples. Following the previous works [37, 53], we report the average classification accuracy (Acc.) to measure the method's adaptation ability on clean samples. To evaluate the adversarial defense performance, we provide the average accuracy (Rob.) on adversarial examples generated by the PGD algorithm [24] with various noise radii. It is worth noting that the adversarial examples are calculated on CLIP before adaptation, which is more suitable for real-world applications since attackers rely on open-source models and have no idea about the victim model's algorithm." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29962" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.083, + 0.897, + 0.207 + ], + "angle": 0, + "content": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]85.92.683.50.055.70.061.70.015.715.740.40.823.70.058.90.053.22.4
Ensemble83.574.882.369.957.136.258.046.616.416.437.129.516.713.753.943.050.641.3
TPT [37]87.97.084.70.158.40.062.10.017.317.342.44.328.40.060.60.355.23.6
C-TPT [50]87.73.783.60.056.60.064.80.016.716.741.51.327.00.060.10.154.82.7
MTA [53]87.365.984.859.858.717.861.031.518.118.140.318.822.51.660.631.354.130.6
R-TPT86.779.884.674.258.142.960.651.917.517.541.333.521.215.959.750.953.745.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.217, + 0.905, + 0.245 + ], + "angle": 0, + "content": "Table 1. Results (%) of clean accuracy (Acc.) and adversarial accuracy (Rob.) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ResNet50 (\\(\\epsilon = 1.0\\)). Best clean accuracies are (bold), best adversarial accuracies are (bold red)." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.253, + 0.897, + 0.377 + ], + "angle": 0, + "content": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]94.00.088.30.065.50.067.40.023.923.944.40.042.20.065.20.061.43.0
Ensemble91.974.786.251.265.726.065.936.323.423.443.225.128.22.263.030.658.433.7
TPT [37]94.10.087.40.066.50.069.10.023.423.446.90.042.60.067.90.062.22.9
C-TPT [50]93.90.088.20.065.80.069.60.023.923.945.90.042.30.065.50.061.93.0
MTA [53]94.372.188.051.867.718.567.427.925.025.046.516.242.51.267.527.562.330.0
R-TPT93.782.087.260.267.034.768.744.623.923.946.432.834.78.567.243.261.141.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.387, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Table 2. Results (%) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ViT-B/16 ( \\( \\epsilon = {4.0} \\) )." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.428, + 0.482, + 0.594 + ], + "angle": 0, + "content": "Baselines. We compare R-TPT on the above benchmarks with existing test-time adaptation methods for CLIP, including TPT [37], C-TPT [50], and MTA [53], as well as zero-shot prediction from CLIP [32]. Also, we regard Ensemble as an additional baseline method, which employs simple average operation on predictions of all augmented views. Note that both our method and the compared baseline methods rely only on CLIP and AugMix [15] augmentation, without any additional foundation models (e.g., LLM, diffusion models) or knowledge. All results of baselines are reproduced with the official code." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.595, + 0.483, + 0.777 + ], + "angle": 0, + "content": "Implementation details. For all experiments, we utilize official pre-trained CLIP-ResNet50 and CLIP-ViT-B/16 [32] as our base model. As for adversarial example generation, we utilize the PGD algorithm [24] with \\(\\epsilon = 1.0\\) and 7 steps for ResNet, while \\(\\epsilon = 4.0\\) and 100 steps for ViT. In the defense stage at test time, the parameter optimized in all experiments is a textual prompt with a context length of 4 and is initiated with \"a photo of a\". We adopt the Adam optimizer with weight decay and a single step. Following previous work [37], the learning rate is set to 0.005 and the augmented batch size is 64. All experiments use the PyTorch framework and run on RTX3090 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.788, + 0.294, + 0.803 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Results on fine-grained datasets. We evaluate the adaptation and adversarial defense ability of R-TPT on eight fine-grained benchmarks and report the results in Table 1. It is shown that CLIP with strong zero-shot generalization ability is suffering from the adversarial attack with a small radius. TPT can steadily improve the accuracy of clean im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.906, + 0.563 + ], + "angle": 0, + "content": "ages but has weak defense capability. We observe that methods with an ensembling strategy (e.g., Ensemble, MTA, R-TPT) achieve significantly better adversarial accuracy. In particular, R-TPT achieves a \\(45.8\\%\\) of adversarial accuracy which outperforms all baseline methods. Besides the attractive defense performance, R-TPT also improves the clean accuracy of CLIP from \\(53.2\\%\\) to \\(53.7\\%\\). In contrast, although Ensemble has strong defense capabilities, it suffers from negative transfer in the clean scenario." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.906, + 0.747 + ], + "angle": 0, + "content": "Results on ImageNet and ImageNet-OOD datasets. We provide the experiential results on ImageNet and four ImageNet-OOD datasets in Table 3. CLIP can overcome distribution shifts, but fails to defend against adversarial attacks. R-TPT performs the best in adversarial defense under both ImageNet and its related out-of-distribution benchmarks. Especially, R-TPT achieves an adversarial accuracy of \\(47.7\\%\\) on ImageNet, \\(7.6\\%\\) higher than the second-best method Ensemble, while CLIP's adversarial accuracy on this benchmark is \\(0.1\\%\\). Moreover, our method obtains a similar clean accuracy with TPT, indicating that R-TPT is also effective for distribution shifts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Results of CLIP-ViT backbone. We evaluate our method on CLIP-ViT-B/16 [32] model and provide the results in Table 2. We observe that R-TPT outperforms all baseline methods regarding adversarial defense performance. However, the performance gain of all adaptation methods for clean samples is small, and R-TPT and the remaining two ensembling-based methods make weak negative transfers. This illustrates that the space for improvement of clean accuracy for strong pre-training models is small, and R-TPT can greatly enhance its weak robustness." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "29963" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.174, + 0.083, + 0.822, + 0.207 + ], + "angle": 0, + "content": "
MethodImageNetImageNet-AImageNet-V2ImageNet-RImageNet-SAvg.
Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.
CLIP [32]58.20.121.80.051.50.156.10.833.30.544.20.3
Ensemble58.040.122.610.152.037.251.339.329.520.742.729.5
TPT [37]60.70.326.50.054.80.358.91.835.01.447.20.7
C-TPT [50]60.40.124.10.054.30.157.71.034.70.946.20.4
MTA [53]60.430.027.55.654.224.658.429.835.211.347.120.3
R-TPT60.947.728.414.454.941.657.646.934.026.247.135.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.218, + 0.905, + 0.247 + ], + "angle": 0, + "content": "Table 3. Results (\\%) of various adaptation methods on ImageNet and ImageNet-OD benchmarks with pre-trained CLIP-ResNet50. OOD Avg. refers to the average results among four ImageNet-OD benchmarks (\\(\\epsilon = 1.0\\))." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.254, + 0.905, + 0.376 + ], + "angle": 0, + "content": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP-TeCoA [26]79.344.366.915.810.21.030.89.06.66.624.510.714.510.834.66.733.413.1
Ensemble72.755.159.938.95.62.726.616.04.24.223.516.212.511.026.414.028.919.8
TPT [37]79.352.765.227.49.62.027.912.36.76.725.514.612.211.234.910.232.717.1
C-TPT [50]79.847.366.119.510.61.329.410.76.46.426.212.413.011.136.48.133.514.6
MTA [53]79.755.766.231.29.02.529.114.06.56.524.413.513.311.234.612.532.918.4
R-TPT76.160.563.240.17.73.526.616.56.16.125.217.711.511.331.117.430.921.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.385, + 0.893, + 0.4 + ], + "angle": 0, + "content": "Table 4. Results (%) of adaptation methods on fine-grained classification datasets with TeCoA pre-trained CLIP-ViT-B/32 ( \\( \\epsilon = {4.0} \\) )." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.425, + 0.24, + 0.442 + ], + "angle": 0, + "content": "4.3. More Analysis" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.448, + 0.483, + 0.644 + ], + "angle": 0, + "content": "Results under robust-pretrained models. we report the results of deploying adaptation methods on CLIP-ViT-B/32 with TeCoA [26] robust pretrained models in Table 4. It is shown that TeCoA significantly improves the robustness of CLIP, and the defense effect against adversarial attacks can benefit from our method during the testing stage, which increases adversarial accuracy form \\(13.1\\%\\) to \\(21.7\\%\\). At the same time, we also find that R-TPT's defense effect on the TeCoA pretrained model is weaker than the vanilla CLIP. The reason is that introducing adversarial learning during the training time decreases the clean accuracy, which is the upper bound of defense. Robust pre-trained models also generate more difficult adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.644, + 0.483, + 0.81 + ], + "angle": 0, + "content": "Analysis under various attacks. To demonstrate the versatility, we investigate the defense performance of R-TPT and baseline methods under various attack methods. We employ CW [4], DeepFool [27], and FGSM [13] as new attacks and report the adversarial accuracy on three benchmarks in Table 5. It is shown that our method improves CLIP's defense capability under each attack, which is consistent with the trend of PGD. In particular, R-TPT has reached \\(51.8\\%\\) adversarial accuracy on Flowers. The excellent defense performance among various attack methods proves the versatility of R-TPT." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.81, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Analysis of inference efficiency. We study the inference efficiency of R-TPT. Experiments of training-time defense method APT and R-TPT on UCF101 are provided in Table 6. It is shown that R-TPT spends a certain amount of time on each test sample, which is different from training-time defense which spends a lot of resources at one time" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.418, + 0.905, + 0.541 + ], + "angle": 0, + "content": "
MethodFlowersDTD
CWDFFGSMAvg.CWDFFGSMAvg.
CLIP [32]0.80.44.82.02.37.613.47.8
Ensemble50.152.246.649.731.132.929.731.2
TPT [37]13.810.814.212.921.324.422.222.6
C-TPT [50]6.65.56.26.111.915.817.515.1
MTA [53]34.535.436.635.523.623.523.923.7
R-TPT51.654.749.251.834.235.932.534.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.55, + 0.907, + 0.579 + ], + "angle": 0, + "content": "Table 5. Adversarial accuracies \\((\\%)\\) of adaptation methods against different attacks on two fine-grained datasets (DF = DeepFool)." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.594, + 0.905, + 0.683 + ], + "angle": 0, + "content": "
MethodStageRunning timeRob.
APT+TeCoA (4shots)Training time208s/50epochs39.4
R-TPT (64 views)Test time0.58s/image41.0
R-TPT (32 views)Test time0.28s/image40.8
R-TPT (16 views)Test time0.20s/image40.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.692, + 0.907, + 0.721 + ], + "angle": 0, + "content": "Table 6. Running time and adversarial accuracies \\((\\%)\\) of adaptation methods against adversarial attack on UCF101 dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.907, + 0.839 + ], + "angle": 0, + "content": "during training. Moreover, we find that inference can be accelerated by appropriately reducing the number of augmented views to obtain better real-time performance. When we choose to reduce the number of views from 64 to 16, the time required for each test sample is reduced to less than half of the original." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Analysis under different prompt templates. Since in the realistic scenario, the attacker can not access the prompts of the model textual branch, we evaluate the defense performance of the adversarial examples generated by" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "29964" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.347, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.251, + 0.321, + 0.265 + ], + "angle": 0, + "content": "(a) Different prompt templates." + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.096, + 0.627, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.251, + 0.602, + 0.265 + ], + "angle": 0, + "content": "(b) Sensitivity of neighbor number." + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.099, + 0.895, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.251, + 0.89, + 0.265 + ], + "angle": 0, + "content": "(c) Sensitivity of optimization parameters." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.275, + 0.908, + 0.304 + ], + "angle": 0, + "content": "Figure 4. Results of different prompt templates in adversarial examples generation, different neighbor numbers, and different choices of optimization parameters in DTD dataset (CLIP-ResNet50, \\(\\epsilon = 1.0\\))." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.33, + 0.484, + 0.45 + ], + "angle": 0, + "content": "different prompt templates. The result of DTD benchmark with six textual templates is provided in Figure 4(a) (P0='a photo of a []', P1='a bad photo of the []', P2='a origami []', P3='a photo of the large []', P4='a toy []', P5='art of the []'). It is shown that CLIP is suffering from adversarial samples even if attackers use different prompt templates. Also, R-TPT outperforms all baseline methods under each template." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.453, + 0.484, + 0.71 + ], + "angle": 0, + "content": "Analysis of sensitivity of hyperparameters and optimization parameters. We study the impact of the neighbor number in calculating reliability and the optimization parameter to further demonstrate the effectiveness of R-TPT. We provide the results of R-TPT with different neighbor numbers (10, 15, 20, 25, 30) in Figure 4(b). The results demonstrate that R-TPT performs stable across different neighbor numbers in terms of both clean and adversarial accuracy. Please note that if the neighbor number equals to augmented batch size, it will assign all samples with equal weights and the reliability-based ensembling mechanism will degenerate into the vanilla ensembling. Besides, we report the results with different optimization parameters in Figure 4(c). Compared to other choices of the parameter space, optimizing textual prompts owns better defense and adaptation effects and fewer parameters, which make it always a popular solution for parameter-efficient fine-tuning." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.726, + 0.245, + 0.743 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "To study the contribution of terms in our method, we investigate the effectiveness of ensembling, reliability-based weighted mechanism, and pointwise entropy objective in R-TPT. The results of the ablation study are reported in Table 7. From the table, we find that entropy minimization focuses on enhancing the accuracy of adaptation on the clean samples and Slightly improves the defense performance on CLIP. However, When cooperating with weighted ensembling, the improvement of entropy minimization on both metrics is significant. The ensembling strategy greatly" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.316, + 0.903, + 0.45 + ], + "angle": 0, + "content": "
EnsembleWeightedEntMinFine-grainedImageNet-X
Acc.Rob.Acc.Rob.
XXX53.22.444.20.3
XX✓55.23.647.20.7
✓XX50.641.342.729.5
✓X✓53.344.346.734.2
✓✓X51.644.344.833.4
✓✓✓53.745.847.135.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.46, + 0.907, + 0.489 + ], + "angle": 0, + "content": "Table 7. Ablation study. Clean and adversarial accuracies \\((\\%)\\) on fine-grained datasets and ImageNet dataset (CLIP-ResNet50)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.907, + 0.592 + ], + "angle": 0, + "content": "strengthens the defense capabilities of the model, but it also reduces the adaptation performance on clean samples. The weighted mechanism gives reliable samples more important roles during prediction, further improving the defense capabilities and mitigating the clean performance drop." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.634, + 0.62 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this paper, we for the first time explore the adversarial defense for CLIP with a test-time paradigm and propose robust test-time prompt tuning (R-TPT). We first review the classic test time adaptation method and decompose its marginal entropy objective into a pointwise entropy term and a KL divergence term. We find that minimizing KL divergence will introduce conflicts when meeting the adversarial test instance, thus we discard KL divergence terms and only optimize the textual prompt with the pointwise entropy. We also introduce a reliability-based weighted ensembling strategy to utilize knowledge of the augmented views, which contain more knowledge than the risky original input under adversarial attacks. Extensive results show that R-TPT achieves the best defense against various adversarial attacks among all baseline methods and maintains a clean adaptation performance. We believe that our work will provide a new perspective on the defense and shed light on the safety issues of VLMs." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29965" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.205 + ], + "angle": 0, + "content": "This work was funded by the National Natural Science Foundation of China under Grants (62276256, U2441251) and the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). The authors would like to thank Professor Tan Tieniu for his valuable guidance and contribution to this work." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.218, + 0.188, + 0.234 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.243, + 0.484, + 0.325 + ], + "angle": 0, + "content": "[1] Jameel Abdul Samadh, Mohammad Hanan Gani, Noor Hussein, Muhammad Uzair Khattak, Muhammad Muzammal Naseer, Fahad Shahbaz Khan, and Salman H Khan. Align your prompts: Test-time prompting with distribution alignment for zero-shot generalization. In Proc. NeurIPS, 2024. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.1, + 0.327, + 0.484, + 0.382 + ], + "angle": 0, + "content": "[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Proc. 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However, due to their inherent vulnerability and the common practice of selecting from a limited set of open-source models, VLMs suffer from a higher risk of adversarial attacks than traditional vision models. Existing defense techniques typically rely on adversarial fine-tuning during training, which requires labeled data and lacks of flexibility for downstream tasks. To address these limitations, we propose robust test-time prompt tuning (R-TPT), which mitigates the impact of adversarial attacks during the inference stage. We first reformulate the classic marginal entropy objective by eliminating the term that introduces conflicts under adversarial conditions, retaining only the pointwise entropy minimization. Furthermore, we introduce a plug-and-play reliability-based weighted ensembling strategy, which aggregates useful information from reliable augmented views to strengthen the defense. R-TPT enhances defense against adversarial attacks without requiring labeled training data while offering high flexibility for inference tasks. Extensive experiments on widely used benchmarks with various attacks demonstrate the effectiveness of R-TPT. The code is available in https://github.com/TomSheng21/R-TPT. + +# 1. Introduction + +Vision-language models (VLMs) [5, 32, 56] are multimodal models pretrained on large-scale paired image-text data. Their powerful zero-shot inference capability and broad applicability across a range of downstream tasks have made them a foundational tool in the research community. CLIP [32], a milestone work, aligns features from the text and + +![](images/ad788afd1afe75fee6ff469ab54a42501346f8a4f64735828ee4a68ae1734c4b.jpg) +Training-time defense +Figure 1. Comparison between training-time and test-time defense for CLIP. Our test-time defense paradigm provides robust prediction as the conventional training-time methods and requires no annotated dataset or adversarial training. + +![](images/091a5216fb1ebab89d11443ebf16c75cc7474d84303ea74b8984f7a64e9b8e66.jpg) +Test-time defense + +visual modalities using two specialized feature extractors trained with a contrastive loss function. Due to its concise architecture and impressive performance, CLIP has become the most widely used VLM across diverse research topics. For classification tasks, CLIP extracts features from both images and category descriptions, then chooses the category whose features exhibit the highest similarity to the image's feature representation. Beyond classification [47, 48, 60, 61], CLIP has been successfully applied to various vision tasks, such as semantic segmentation [36, 59], object detection [55, 58], and image clustering [3, 22]. + +The impressive performance on downstream tasks and the broad range of applications of CLIP not only highlight its powerful capabilities but also expose it to potential vul + +nerabilities, particularly under adversarial attacks [19, 26]. While adversarial attacks and defenses [13, 24, 54] have been widely explored for conventional visual models, the situation for CLIP is more complex. The pre-training of CLIP requires the collection of vast amounts of image-text pairs and substantial computational resources that most deployers cannot afford. As a result, many deployers choose to adopt open-source versions of CLIP from a small range of candidates. This fact introduces a relatively high risk of adversarial attacks targeting CLIP-based applications. + +Recent works [21, 26] explore adversarial prompt tuning using annotated data to enhance the robustness of CLIP. However, their reliance on labeled data and limited flexibility across tasks pose challenges for real-world deployment. To address this, we choose to defend adversarial attacks in the inference stage, which is applicable across various scenarios and requires no labeled dataset or prior knowledge of the downstream task, as shown in Figure 1. Existing test-time adaptation methods [37, 53] primarily focus on improving accuracy for clean test samples, while overlooking the potential risks posed by adversarial attacks. Moreover, deploying defense at test time necessitates short inference time and avoiding using additional resources, such as large language models or diffusion models, to ensure versatility. + +To address the above challenges and achieve successful defense against potential attacks, we propose robust test-time prompt tuning (R-TPT). First, we revisit and refine the widely used optimization objective for instance adaptation. Many previous works [37, 41], following MEMO [57], augment the test instance and aim to minimize marginal entropy, which is defined as the entropy of the mean prediction. We decompose marginal entropy into two components: a pointwise entropy term and the Kullback-Leibler (KL) divergence, which measures the divergence between predictions from each augmented view and the mean prediction. We observe that when adapting to adversarial examples with high-confidence inaccurate predictions, the KL divergence term tends to pull the augmented views toward the misleading mean prediction, which does not exist in the clean scenario. This meaningless operation introduces conflicts into the optimization process. To mitigate the influence of adversarial samples and preserve simplicity, we discard the KL divergence term, retaining only the pointwise entropy minimization for tuning textual prompts. This straightforward modification not only defends against adversarial attacks but also maintains clean performance. + +In order to effectively leverage knowledge from augmented views, we propose a reliability-based weighted ensembling strategy. To assign a larger weight to reliable augmented views during ensembling, we introduce a similarity-based metric to assess the reliability of samples. We hypothesize that samples with higher similarity to their neighbors are farther away from outliers and contain more reli + +able information. Thus, we calculate the average similarity of each sample with its neighbors to estimate its reliability. Using this metric, outliers such as adversarial examples and noisy augmented views are assigned lower reliability scores, which means less participation in the ensembling. Finally, we obtain the final prediction by ensembling the individual model predictions, weighted according to their reliability. Extensive experiments on fine-grained classification benchmarks and distribution shift benchmarks validate the effectiveness of our method in both adaptation and defense against adversarial attacks. Our contributions are summarized as follows: + +- We propose R-TPT, which is the first to explore test-time paradigms for defending against potential adversarial attacks in CLIP. +- We discard the KL divergence term from the marginal entropy objective to eliminate optimization conflicts and propose a reliability-based weighted ensembling strategy to integrate knowledge from reliable augmented views. +- Extensive experiments demonstrate the effectiveness of our method in both adaptation and adversarial defense. + +# 2. Related Work + +# 2.1. Adversarial Attack and Defense + +A lot of research [13, 24, 42] has been devoted to studying neural network's vulnerability to adversarial noise. A pioneering work [42] introduces the concept of adversarial examples and finds small-amplitude noise that humans cannot recognize leads to misclassifications. Since then, a series of attack methods to generate adversarial samples [4, 8, 13, 24] have been proposed. FGSM [13] proposes to utilize the gradient sign to generate an adversarial example. Researchers [24] generate the adversarial noise by projected gradient descent (PGD) operation, which becomes the standard measurement of model robustness. Moreover, a variety of works explore adversarial attacks in many restricted conditions, ranging from one-pixel attack [40], universal perturbation [28] to more realistic black-box setting [2, 18]. + +In parallel, numerous defense strategies [24, 35, 49, 54] have been proposed to mitigate adversarial attacks. Adversarial training [13, 24] improves the robustness of the model by incorporating the adversarial samples into the training set. TRADES [54] provides a theoretical analysis of adversarial error to trade adversarial robustness against accuracy. AWP [49] perturbs the model's weights with small adversarial noise during training to enhance robustness. Reconstruction [29, 34] with generative models [12, 38] is also a commonly used technique in test-time defense methods. + +As for the vison-language models, TeCoA [26] and APT [21] employ adversarial training to pretrained CLIP [32] to improve the adversarial robustness. However, their training-time solution requires an annotated dataset and lacks flexi + +![](images/508cfb088be62b610b921a96fd20e3149fdd0def5e4830eec3cc5176694d21a3.jpg) +Figure 2. The pipeline of R-TPT framework. Given an instance-level task, we deploy augmentation on the test image and build a classifier with CLIP's text branch. After selecting a low-entropy batch, R-TPT discards the KL divergence minimization term which potentially introduces conflicts in the marginal entropy [57] and optimizes textual prompts with pointwise entropy minimization. To effectively utilize the knowledge of the augmented views, R-TPT applies a reliability-based weighted ensembling mechanism in the final inference process. + +bility across tasks. In this work, we choose to deploy adversarial defense in the test time that is more effective and flexible and can collaborate with their training-time defense. + +# 2.2. Test-Time Adaptation for VLMs + +Test-time adaptation [23, 37, 51] aims to adapt pre-trained models to the test data at inference time to improve the performance further. According to the test data form, test-time adaptation is divided into streaming data adaptation [43, 45, 52] and single instance adaptation [37, 57], and our work focuses on the latter. Recent research [37, 41, 53] has been devoted to exploring the instance adaptation methods for VLMs [32, 46, 56]. TPT [37] employs the marginal entropy minimization to augmentation views of the test instance to correct the prediction. DiffTPT [11] utilizes the diffusion technique to obtain diverse views which is helpful for the adaptation. PromptAlign [1] aligns the statistics of the test instance and collected natural images to make the model's parameters adapt to test samples. To take advantage of more prompt templates [32], TPS [41] chooses to optimize feature shift and utilizes prompt ensembling for initialization. Moreover, researchers [53] propose a training-free adaptation method by ensembling the augmented views with the MeanShift algorithm [7]. + +Besides accuracy, researchers [50] also focus on improving calibration performance through higher text feature dispersion. In this work, we first utilize the test-time paradigm to defend against adversarial attacks for CLIP due to its se + +vere vulnerability to adversarial examples. + +# 3. Methodology + +In this paper, we improve CLIP's adversarial robustness through a test-time paradigm, motivated by its inherent vulnerabilities and the high resource demands of train-time defense methods. Our proposed robust test-time prompt tuning (R-TPT), as illustrated in Figure 2, requires no annotated data and is equipped with greater flexibility. In Sec. 3.1, we begin with reviewing the foundational concepts of CLIP and the test-time prompt tuning approach. We then introduce the two key components of R-TPT: pointwise entropy minimization in Sec. 3.2, and the reliability-based weighted ensembling strategy in Sec. 3.3. + +# 3.1. Preliminary + +Contrastive language-image pre-training. CLIP is a popular language-vision model with a double-tower architecture, consisting of an image encoder $F(\cdot)$ and a text encoder $G(\cdot)$ . It is pretrained by the contrastive learning objective with a large amount of image-text pairs. Benefiting from rich pretraining knowledge, CLIP has a strong zero-shot generalization ability. Take a C-way classification task with class names $\{t_c\}_{c=1}^C$ as an example, CLIP obtains textual features $g_c$ by the text encoder $G(\cdot)$ with a prompt template (e.g., "a photo of a ["]) and the class name $t_c$ as the input. Also, each test image $x_i$ queries the image encoder + +to calculate the image feature $f_{i} = F(x_{i})$ . The probability that $x_{i}$ belongs to category $c$ is calculated by a softmax operation with the cosine similarity of those features: + +$$ +p _ {c} \left(x _ {i}\right) = \frac {\exp \left(\cos \left(f _ {i} , g _ {c}\right) / \tau\right)}{\sum_ {j = 1} ^ {C} \exp \left(\cos \left(f _ {i} , g _ {j}\right) / \tau\right)}, \tag {1} +$$ + +where $\cos(\cdot)$ represents the cosine similarity operation and $\tau$ refers to the temperature default set to 0.01. + +Test-time prompt tuning. Although CLIP exhibits strong classification performance, it is sensitive to distribution shifts. To address this issue, test-time prompt tuning (TPT) [37] improves the model's performance on individual test instances, without requiring additional training data for adaptation. During the test time, TPT deploys augmentation operations on the test instance $x_0$ to obtain augmented views $\{x_i\}_{i=1}^N$ and tunes the textual prompts with low-entropy views. The core objective of TPT is to minimize marginal entropy, which is formulated as: + +$$ +\mathcal {L} _ {\text {m a r g i n a l}} = \mathcal {H} (\bar {p}) = \mathcal {H} \left(\frac {1}{| \mathcal {B} |} \sum_ {x \in \mathcal {B}} p (x)\right), \tag {2} +$$ + +where $\mathcal{H}(\cdot)$ is the Shannon entropy and $\mathcal{B}$ represents the sample set selected from all views $\{x_{i}\}_{i = 0}^{N}$ based on the low entropy. When augmentation provides valuable information, the classification boundary adapts according to the new prompt, leading to more accurate predictions. + +# 3.2. Refining Marginal Entropy Minimization + +In the optimization of a single test sample, marginal entropy is the default choice for both visual models [57] and multimodal models [37]. Minimizing marginal entropy $\mathcal{H}(\bar{p})$ encourages the model to produce a consistent output across a set of selected low-entropy augmented views $\mathcal{B}$ . However, when the test sample is adversarially perturbed, it can easily be selected into the set $\mathcal{B}$ . While random augmentations can weaken the adversarial noise, enforcing consistency across all augmented outputs may mislead the optimization. Since our goal is to utilize test time adaptation to strengthen the model's defense ability to adversarial examples, we propose refining the marginal entropy objective. + +We decompose the marginal entropy objective into two items as follows: + +$$ +\begin{array}{l} \mathcal {H} (\bar {p}) = - \sum_ {c = 1} ^ {C} \bar {p} _ {c} \log \bar {p} _ {c} = - \frac {1}{| \mathcal {B} |} \sum_ {b = 1} ^ {| \mathcal {B} |} \sum_ {c = 1} ^ {C} p _ {c} ^ {b} \log \bar {p} _ {c} \\ = \frac {1}{| \mathcal {B} |} \sum_ {b = 1} ^ {| \mathcal {B} |} \left(- \sum_ {c = 1} ^ {C} p _ {c} ^ {b} \log p _ {c} ^ {b} + \sum_ {c = 1} ^ {C} p _ {c} ^ {b} \log \frac {p _ {c} ^ {b}}{\bar {p} _ {c}}\right) \tag {3} \\ = \frac {1}{| \mathcal {B} |} \sum_ {b = 1} ^ {| \mathcal {B} |} \left(\mathcal {H} \left(p ^ {b}\right) + \mathcal {K L} \left(p ^ {b} \| \bar {p}\right)\right), \\ \end{array} +$$ + +where $\mathcal{H}(\cdot)$ denotes the Shannon entropy, $\mathcal{KL}(\cdot\|\cdot)$ refers to Kullback-Leibler (KL) divergence. Eq. 3 shows that marginal entropy is a combination of a pointwise entropy term and a KL divergence term. Minimizing pointwise entropy helps move the classification boundary away from low-entropy points, which is the main composition of the marginal entropy. The KL divergence term, on the other hand, encourages consistent predictions across the augmented views. In the case of clean test samples, the differences between low-entropy augmented views are small, and the KL divergence term has a minimal effect. However, in adversarial scenarios, the mean prediction is distorted by the original perturbed sample, which differs significantly from the augmented views. As a result, enforcing consistency across the augmented views leads to conflicts and neglects the valuable information in these views. + +To improve performance under both clean and adversarial conditions, we discard the KL divergence term and focus solely on minimizing pointwise entropy, as follows: + +$$ +\text {m i n i m i z e} \mathcal {L} _ {\text {p o i n t}} = \frac {1}{| \mathcal {B} |} \sum_ {b = 1} ^ {| \mathcal {B} |} \mathcal {H} \left(p ^ {b}\right). \tag {4} +$$ + +For clean test instances, minimizing pointwise entropy functions similarly to the original marginal entropy objective. Also, for adversarial examples, this approach focuses more on augmented views, which have relatively high entropy and information, and ignores the original adversarial inputs. Therefore, our objective can handle both natural conditions and adversarial attacks well. + +# 3.3. Reliability-based Weighted Ensembling + +Unsupervised prompt tuning typically makes no change to image features and a small adjustment to the classification boundary. For adversarial examples, it is challenging to correct incorrect predictions since their feature representations are far from the correct decision boundary. Fortunately, augmentation at the pixel level can help mitigate the adversarial noise, as it weakens the effect of perturbations. Thus, we can leverage diverse augmented views of the test image, which provide valuable knowledge. To integrate information from augmented views effectively and protect the ensembling from the noise of lower-quality views, we propose a reliability-based weighted ensembling mechanism. + +Since augmentation inherently involves randomness (e.g., background areas left after cropping), we introduce a reliability metric to represent the quality of each augmented view. Reliability is defined as the similarity between the sample and its nearest neighbors. High reliability indicates that the sample is densely clustered in the feature space, containing useful information. Conversely, low reliability suggests that the sample is an outlier, likely containing augmentation or adversarial noise, and should be downweighted or ignored during ensembling. + +![](images/4c6d656dd2e223bca7fc4682d411b888a5d284cdc193645fe1b2ed19a251bd0c.jpg) +(a) Weight value in ImageNet. + +![](images/f31bcb3b85a6256805cad09131208167ef732f437fcd8c58222f5b1186f232ce.jpg) +(b) Weight value in ImageNet-A. +Figure 3. Visualization of assigned reliability-based weight value under (a) clean, (b) distribution shift, and (c) adversarial attack scenarios. The red and blue bars denote the weight value of the original test instance and its augmented views, respectively. The weight assigned to the clean instance is higher than under the distribution shift. The weight of the adversarial test sample is close to 0. + +![](images/644fa76348add333fa4e25af039ff5c8df68020f291a452e19e61ab8f85c0c07.jpg) +(c) Weight value in ImageNet under attack. + +Given an augmented batch, which includes the test image and its $N$ augmented views, we calculate the similarity matrix $\{S_{i,j}\}_{i,j=0}^{N}$ of the visual features $\{f_i\}_{i=0}^N$ : + +$$ +S _ {i, j} = \cos \left(f _ {i}, f _ {j}\right), i, j = 0, 1, \dots , N, \tag {5} +$$ + +where $\text{con}(\cdot, \cdot)$ denotes the cosine similarity operation. The $i$ -th row of the matrix $S$ represents the similarity between $x_i$ and all samples in the batch. We then select the $K$ closest neighbor of $x_i$ (excluding $x_i$ itself) to form the neighboring set $\mathcal{N}_i$ . The reliability of $x_i$ is calculated as the average similarity within the neighboring set $\mathcal{N}_i$ : + +$$ +r _ {i} = \frac {1}{K} \sum_ {k \in \mathcal {N} _ {i}} \cos \left(f _ {i}, f _ {k}\right), i = 0, 1, \dots , N. \tag {6} +$$ + +The reliability score reflects the degree to which $x_{i}$ is surrounded by similar samples in the feature space. + +To obtain the final prediction, we ensemble the predictions from all augmented views, weighted by their respective reliability scores. The weight assigned to each view is calculated by applying a softmax operation on the reliabilities $\{r_i\}_{i = 0}^N$ . This weight assignment mechanism is flexible and adapts well to various scenarios. We present the weight values for clean samples (ImageNet), samples with distribution shift (ImageNet-A), and adversarial samples (ImageNet) in Figure 3. As shown, clean samples are assigned higher weights, and the ensembling mechanism focuses on augmented views when the test instance shows significant distribution shifts from natural images. For adversarial samples, the weight assigned to the poisoned instance is close to zero, which indicates that our mechanism protects the ensembling process from being misled by adversarial noise. This approach not only improves the robustness of predictions on adversarial samples but also maintains strong performance on clean samples, thus enhancing the overall reliability of the inference process. + +# 4. Experiment + +# 4.1. Setup + +Datasets. To evaluate our proposed test-time defense method for VLMs, we conduct experiments on eight fine-grained classification datasets. These databases cover general objects (Caltech101 [10]), animals (Pets [31]), plants (Flower102 [30]), vehicles (Cars [20], Aircraft [25]), textures (DTD [6]), satellite images (EuroSAT [14]), and actions from videos (UCF101 [39]). Moreover, we evaluate on ImageNet [9] and four ImageNet-out-of-distribution (OOD) benchmarks with distribution shift. ImageNet-A [17] contains 200 classes and 7,500 natural adversarial examples which are collected with adversarial filtration technique. ImageNet-V2 [33] consists of 10,000 natural images across 1,000 categories from a different source than ImageNet. ImageNet-R [16] is a dataset containing 30,000 images with various renditions, leading to different textures and local statistics from ImageNet. ImageNet-S [44] consists of 50,889 sketch-style images and shares the same category space with ImageNet. Since our method is to defend against potential adversarial attacks during the test time, we do not need access to the training set of the above datasets. + +Evaluation metrics. Since our task focuses on instance-level test-time adaptation, the model update and prediction of each test sample can not utilize the information of other samples. Following the previous works [37, 53], we report the average classification accuracy (Acc.) to measure the method's adaptation ability on clean samples. To evaluate the adversarial defense performance, we provide the average accuracy (Rob.) on adversarial examples generated by the PGD algorithm [24] with various noise radii. It is worth noting that the adversarial examples are calculated on CLIP before adaptation, which is more suitable for real-world applications since attackers rely on open-source models and have no idea about the victim model's algorithm. + +
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]85.92.683.50.055.70.061.70.015.715.740.40.823.70.058.90.053.22.4
Ensemble83.574.882.369.957.136.258.046.616.416.437.129.516.713.753.943.050.641.3
TPT [37]87.97.084.70.158.40.062.10.017.317.342.44.328.40.060.60.355.23.6
C-TPT [50]87.73.783.60.056.60.064.80.016.716.741.51.327.00.060.10.154.82.7
MTA [53]87.365.984.859.858.717.861.031.518.118.140.318.822.51.660.631.354.130.6
R-TPT86.779.884.674.258.142.960.651.917.517.541.333.521.215.959.750.953.745.8
+ +Table 1. Results (%) of clean accuracy (Acc.) and adversarial accuracy (Rob.) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ResNet50 ( $\epsilon = 1.0$ ). Best clean accuracies are (bold), best adversarial accuracies are (bold red). + +
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]94.00.088.30.065.50.067.40.023.923.944.40.042.20.065.20.061.43.0
Ensemble91.974.786.251.265.726.065.936.323.423.443.225.128.22.263.030.658.433.7
TPT [37]94.10.087.40.066.50.069.10.023.423.446.90.042.60.067.90.062.22.9
C-TPT [50]93.90.088.20.065.80.069.60.023.923.945.90.042.30.065.50.061.93.0
MTA [53]94.372.188.051.867.718.567.427.925.025.046.516.242.51.267.527.562.330.0
R-TPT93.782.087.260.267.034.768.744.623.923.946.432.834.78.567.243.261.141.2
+ +Table 2. Results (%) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ViT-B/16 ( $\epsilon = {4.0}$ ). + +Baselines. We compare R-TPT on the above benchmarks with existing test-time adaptation methods for CLIP, including TPT [37], C-TPT [50], and MTA [53], as well as zero-shot prediction from CLIP [32]. Also, we regard Ensemble as an additional baseline method, which employs simple average operation on predictions of all augmented views. Note that both our method and the compared baseline methods rely only on CLIP and AugMix [15] augmentation, without any additional foundation models (e.g., LLM, diffusion models) or knowledge. All results of baselines are reproduced with the official code. + +Implementation details. For all experiments, we utilize official pre-trained CLIP-ResNet50 and CLIP-ViT-B/16 [32] as our base model. As for adversarial example generation, we utilize the PGD algorithm [24] with $\epsilon = 1.0$ and 7 steps for ResNet, while $\epsilon = 4.0$ and 100 steps for ViT. In the defense stage at test time, the parameter optimized in all experiments is a textual prompt with a context length of 4 and is initiated with "a photo of a". We adopt the Adam optimizer with weight decay and a single step. Following previous work [37], the learning rate is set to 0.005 and the augmented batch size is 64. All experiments use the PyTorch framework and run on RTX3090 GPUs. + +# 4.2. Experimental Results + +Results on fine-grained datasets. We evaluate the adaptation and adversarial defense ability of R-TPT on eight fine-grained benchmarks and report the results in Table 1. It is shown that CLIP with strong zero-shot generalization ability is suffering from the adversarial attack with a small radius. TPT can steadily improve the accuracy of clean im + +ages but has weak defense capability. We observe that methods with an ensembling strategy (e.g., Ensemble, MTA, R-TPT) achieve significantly better adversarial accuracy. In particular, R-TPT achieves a $45.8\%$ of adversarial accuracy which outperforms all baseline methods. Besides the attractive defense performance, R-TPT also improves the clean accuracy of CLIP from $53.2\%$ to $53.7\%$ . In contrast, although Ensemble has strong defense capabilities, it suffers from negative transfer in the clean scenario. + +Results on ImageNet and ImageNet-OOD datasets. We provide the experiential results on ImageNet and four ImageNet-OOD datasets in Table 3. CLIP can overcome distribution shifts, but fails to defend against adversarial attacks. R-TPT performs the best in adversarial defense under both ImageNet and its related out-of-distribution benchmarks. Especially, R-TPT achieves an adversarial accuracy of $47.7\%$ on ImageNet, $7.6\%$ higher than the second-best method Ensemble, while CLIP's adversarial accuracy on this benchmark is $0.1\%$ . Moreover, our method obtains a similar clean accuracy with TPT, indicating that R-TPT is also effective for distribution shifts. + +Results of CLIP-ViT backbone. We evaluate our method on CLIP-ViT-B/16 [32] model and provide the results in Table 2. We observe that R-TPT outperforms all baseline methods regarding adversarial defense performance. However, the performance gain of all adaptation methods for clean samples is small, and R-TPT and the remaining two ensembling-based methods make weak negative transfers. This illustrates that the space for improvement of clean accuracy for strong pre-training models is small, and R-TPT can greatly enhance its weak robustness. + +
MethodImageNetImageNet-AImageNet-V2ImageNet-RImageNet-SAvg.
Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.
CLIP [32]58.20.121.80.051.50.156.10.833.30.544.20.3
Ensemble58.040.122.610.152.037.251.339.329.520.742.729.5
TPT [37]60.70.326.50.054.80.358.91.835.01.447.20.7
C-TPT [50]60.40.124.10.054.30.157.71.034.70.946.20.4
MTA [53]60.430.027.55.654.224.658.429.835.211.347.120.3
R-TPT60.947.728.414.454.941.657.646.934.026.247.135.4
+ +Table 3. Results (\%) of various adaptation methods on ImageNet and ImageNet-OD benchmarks with pre-trained CLIP-ResNet50. OOD Avg. refers to the average results among four ImageNet-OD benchmarks ( $\epsilon = 1.0$ ). + +
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP-TeCoA [26]79.344.366.915.810.21.030.89.06.66.624.510.714.510.834.66.733.413.1
Ensemble72.755.159.938.95.62.726.616.04.24.223.516.212.511.026.414.028.919.8
TPT [37]79.352.765.227.49.62.027.912.36.76.725.514.612.211.234.910.232.717.1
C-TPT [50]79.847.366.119.510.61.329.410.76.46.426.212.413.011.136.48.133.514.6
MTA [53]79.755.766.231.29.02.529.114.06.56.524.413.513.311.234.612.532.918.4
R-TPT76.160.563.240.17.73.526.616.56.16.125.217.711.511.331.117.430.921.7
+ +# 4.3. More Analysis + +Results under robust-pretrained models. we report the results of deploying adaptation methods on CLIP-ViT-B/32 with TeCoA [26] robust pretrained models in Table 4. It is shown that TeCoA significantly improves the robustness of CLIP, and the defense effect against adversarial attacks can benefit from our method during the testing stage, which increases adversarial accuracy form $13.1\%$ to $21.7\%$ . At the same time, we also find that R-TPT's defense effect on the TeCoA pretrained model is weaker than the vanilla CLIP. The reason is that introducing adversarial learning during the training time decreases the clean accuracy, which is the upper bound of defense. Robust pre-trained models also generate more difficult adversarial examples. + +Analysis under various attacks. To demonstrate the versatility, we investigate the defense performance of R-TPT and baseline methods under various attack methods. We employ CW [4], DeepFool [27], and FGSM [13] as new attacks and report the adversarial accuracy on three benchmarks in Table 5. It is shown that our method improves CLIP's defense capability under each attack, which is consistent with the trend of PGD. In particular, R-TPT has reached $51.8\%$ adversarial accuracy on Flowers. The excellent defense performance among various attack methods proves the versatility of R-TPT. + +Analysis of inference efficiency. We study the inference efficiency of R-TPT. Experiments of training-time defense method APT and R-TPT on UCF101 are provided in Table 6. It is shown that R-TPT spends a certain amount of time on each test sample, which is different from training-time defense which spends a lot of resources at one time + +Table 4. Results (%) of adaptation methods on fine-grained classification datasets with TeCoA pre-trained CLIP-ViT-B/32 ( $\epsilon = {4.0}$ ). + +
MethodFlowersDTD
CWDFFGSMAvg.CWDFFGSMAvg.
CLIP [32]0.80.44.82.02.37.613.47.8
Ensemble50.152.246.649.731.132.929.731.2
TPT [37]13.810.814.212.921.324.422.222.6
C-TPT [50]6.65.56.26.111.915.817.515.1
MTA [53]34.535.436.635.523.623.523.923.7
R-TPT51.654.749.251.834.235.932.534.2
+ +Table 5. Adversarial accuracies $(\%)$ of adaptation methods against different attacks on two fine-grained datasets (DF = DeepFool). + +
MethodStageRunning timeRob.
APT+TeCoA (4shots)Training time208s/50epochs39.4
R-TPT (64 views)Test time0.58s/image41.0
R-TPT (32 views)Test time0.28s/image40.8
R-TPT (16 views)Test time0.20s/image40.0
+ +Table 6. Running time and adversarial accuracies $(\%)$ of adaptation methods against adversarial attack on UCF101 dataset. + +during training. Moreover, we find that inference can be accelerated by appropriately reducing the number of augmented views to obtain better real-time performance. When we choose to reduce the number of views from 64 to 16, the time required for each test sample is reduced to less than half of the original. + +Analysis under different prompt templates. Since in the realistic scenario, the attacker can not access the prompts of the model textual branch, we evaluate the defense performance of the adversarial examples generated by + +![](images/5dfc6035ec6ffb3e6986b3d000c76da21cfe6d76c6850aadb8c75e0fce263f41.jpg) +(a) Different prompt templates. + +![](images/4569975943b3d91c312854db7b3323db48455d7a277863128c9e55860016e4b4.jpg) +(b) Sensitivity of neighbor number. +Figure 4. Results of different prompt templates in adversarial examples generation, different neighbor numbers, and different choices of optimization parameters in DTD dataset (CLIP-ResNet50, $\epsilon = 1.0$ ). + +![](images/3a30117983e83d34297680117fe998e1da2b3063a2d0d3c9e41ba544436d559c.jpg) +(c) Sensitivity of optimization parameters. + +different prompt templates. The result of DTD benchmark with six textual templates is provided in Figure 4(a) (P0='a photo of a []', P1='a bad photo of the []', P2='a origami []', P3='a photo of the large []', P4='a toy []', P5='art of the []'). It is shown that CLIP is suffering from adversarial samples even if attackers use different prompt templates. Also, R-TPT outperforms all baseline methods under each template. + +Analysis of sensitivity of hyperparameters and optimization parameters. We study the impact of the neighbor number in calculating reliability and the optimization parameter to further demonstrate the effectiveness of R-TPT. We provide the results of R-TPT with different neighbor numbers (10, 15, 20, 25, 30) in Figure 4(b). The results demonstrate that R-TPT performs stable across different neighbor numbers in terms of both clean and adversarial accuracy. Please note that if the neighbor number equals to augmented batch size, it will assign all samples with equal weights and the reliability-based ensembling mechanism will degenerate into the vanilla ensembling. Besides, we report the results with different optimization parameters in Figure 4(c). Compared to other choices of the parameter space, optimizing textual prompts owns better defense and adaptation effects and fewer parameters, which make it always a popular solution for parameter-efficient fine-tuning. + +# 4.4. Ablation Study + +To study the contribution of terms in our method, we investigate the effectiveness of ensembling, reliability-based weighted mechanism, and pointwise entropy objective in R-TPT. The results of the ablation study are reported in Table 7. From the table, we find that entropy minimization focuses on enhancing the accuracy of adaptation on the clean samples and Slightly improves the defense performance on CLIP. However, When cooperating with weighted ensembling, the improvement of entropy minimization on both metrics is significant. The ensembling strategy greatly + +
EnsembleWeightedEntMinFine-grainedImageNet-X
Acc.Rob.Acc.Rob.
XXX53.22.444.20.3
XX✓55.23.647.20.7
✓XX50.641.342.729.5
✓X✓53.344.346.734.2
✓✓X51.644.344.833.4
✓✓✓53.745.847.135.4
+ +Table 7. Ablation study. Clean and adversarial accuracies $(\%)$ on fine-grained datasets and ImageNet dataset (CLIP-ResNet50). + +strengthens the defense capabilities of the model, but it also reduces the adaptation performance on clean samples. The weighted mechanism gives reliable samples more important roles during prediction, further improving the defense capabilities and mitigating the clean performance drop. + +# 5. Conclusion + +In this paper, we for the first time explore the adversarial defense for CLIP with a test-time paradigm and propose robust test-time prompt tuning (R-TPT). We first review the classic test time adaptation method and decompose its marginal entropy objective into a pointwise entropy term and a KL divergence term. We find that minimizing KL divergence will introduce conflicts when meeting the adversarial test instance, thus we discard KL divergence terms and only optimize the textual prompt with the pointwise entropy. We also introduce a reliability-based weighted ensembling strategy to utilize knowledge of the augmented views, which contain more knowledge than the risky original input under adversarial attacks. Extensive results show that R-TPT achieves the best defense against various adversarial attacks among all baseline methods and maintains a clean adaptation performance. We believe that our work will provide a new perspective on the defense and shed light on the safety issues of VLMs. + +# Acknowledgements + +This work was funded by the National Natural Science Foundation of China under Grants (62276256, U2441251) and the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). The authors would like to thank Professor Tan Tieniu for his valuable guidance and contribution to this work. + +# References + +[1] Jameel Abdul Samadh, Mohammad Hanan Gani, Noor Hussein, Muhammad Uzair Khattak, Muhammad Muzammal Naseer, Fahad Shahbaz Khan, and Salman H Khan. 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However, due to their inherent vulnerability and the common practice of selecting from a limited set of open-source models, VLMs suffer from a higher risk of adversarial attacks than traditional vision models. Existing defense techniques typically rely on adversarial fine-tuning during training, which requires labeled data and lacks of flexibility for downstream tasks. To address these limitations, we propose robust test-time prompt tuning (R-TPT), which mitigates the impact of adversarial attacks during the inference stage. We first reformulate the classic marginal entropy objective by eliminating the term that introduces conflicts under adversarial conditions, retaining only the pointwise entropy minimization. Furthermore, we introduce a plug-and-play reliability-based weighted ensembling strategy, which aggregates useful information from reliable augmented views to strengthen the defense. 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Our test-time defense paradigm provides robust prediction as the conventional training-time methods and requires no annotated dataset or adversarial training." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 438, + 272, + 550, + 456 + ], + "blocks": [ + { + "bbox": [ + 463, + 260, + 525, + 269 + ], + "lines": [ + { + "bbox": [ + 463, + 260, + 525, + 269 + ], + "spans": [ + { + "bbox": [ + 463, + 260, + 525, + 269 + ], + "type": "text", + "content": "Test-time defense" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 438, + 272, + 550, + 456 + ], + "lines": [ + { + "bbox": [ + 438, + 272, + 550, + 456 + ], + "spans": [ + { + "bbox": [ + 438, + 272, + 550, + 456 + ], + "type": "image", + "image_path": "091a5216fb1ebab89d11443ebf16c75cc7474d84303ea74b8984f7a64e9b8e66.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 542, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 555, + 674 + ], + "type": "text", + "content": "visual modalities using two specialized feature extractors trained with a contrastive loss function. Due to its concise architecture and impressive performance, CLIP has become the most widely used VLM across diverse research topics. For classification tasks, CLIP extracts features from both images and category descriptions, then chooses the category whose features exhibit the highest similarity to the image's feature representation. Beyond classification [47, 48, 60, 61], CLIP has been successfully applied to various vision tasks, such as semantic segmentation [36, 59], object detection [55, 58], and image clustering [3, 22]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "The impressive performance on downstream tasks and the broad range of applications of CLIP not only highlight its powerful capabilities but also expose it to potential vul" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 223, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 223, + 712 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 223, + 712 + ], + "type": "text", + "content": "*To whom correspondence should be addressed." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "29958" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 192 + ], + "type": "text", + "content": "nerabilities, particularly under adversarial attacks [19, 26]. While adversarial attacks and defenses [13, 24, 54] have been widely explored for conventional visual models, the situation for CLIP is more complex. The pre-training of CLIP requires the collection of vast amounts of image-text pairs and substantial computational resources that most deployers cannot afford. As a result, many deployers choose to adopt open-source versions of CLIP from a small range of candidates. This fact introduces a relatively high risk of adversarial attacks targeting CLIP-based applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 194, + 295, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 295, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 295, + 361 + ], + "type": "text", + "content": "Recent works [21, 26] explore adversarial prompt tuning using annotated data to enhance the robustness of CLIP. However, their reliance on labeled data and limited flexibility across tasks pose challenges for real-world deployment. To address this, we choose to defend adversarial attacks in the inference stage, which is applicable across various scenarios and requires no labeled dataset or prior knowledge of the downstream task, as shown in Figure 1. Existing test-time adaptation methods [37, 53] primarily focus on improving accuracy for clean test samples, while overlooking the potential risks posed by adversarial attacks. Moreover, deploying defense at test time necessitates short inference time and avoiding using additional resources, such as large language models or diffusion models, to ensure versatility." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 364, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 364, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 364, + 295, + 628 + ], + "type": "text", + "content": "To address the above challenges and achieve successful defense against potential attacks, we propose robust test-time prompt tuning (R-TPT). First, we revisit and refine the widely used optimization objective for instance adaptation. Many previous works [37, 41], following MEMO [57], augment the test instance and aim to minimize marginal entropy, which is defined as the entropy of the mean prediction. We decompose marginal entropy into two components: a pointwise entropy term and the Kullback-Leibler (KL) divergence, which measures the divergence between predictions from each augmented view and the mean prediction. We observe that when adapting to adversarial examples with high-confidence inaccurate predictions, the KL divergence term tends to pull the augmented views toward the misleading mean prediction, which does not exist in the clean scenario. This meaningless operation introduces conflicts into the optimization process. To mitigate the influence of adversarial samples and preserve simplicity, we discard the KL divergence term, retaining only the pointwise entropy minimization for tuning textual prompts. This straightforward modification not only defends against adversarial attacks but also maintains clean performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 630, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 294, + 713 + ], + "type": "text", + "content": "In order to effectively leverage knowledge from augmented views, we propose a reliability-based weighted ensembling strategy. To assign a larger weight to reliable augmented views during ensembling, we introduce a similarity-based metric to assess the reliability of samples. We hypothesize that samples with higher similarity to their neighbors are farther away from outliers and contain more reli" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "content": "able information. Thus, we calculate the average similarity of each sample with its neighbors to estimate its reliability. Using this metric, outliers such as adversarial examples and noisy augmented views are assigned lower reliability scores, which means less participation in the ensembling. Finally, we obtain the final prediction by ensembling the individual model predictions, weighted according to their reliability. Extensive experiments on fine-grained classification benchmarks and distribution shift benchmarks validate the effectiveness of our method in both adaptation and defense against adversarial attacks. Our contributions are summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 217, + 553, + 323 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 217, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 217, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 314, + 217, + 553, + 251 + ], + "type": "text", + "content": "- We propose R-TPT, which is the first to explore test-time paradigms for defending against potential adversarial attacks in CLIP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 252, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 553, + 300 + ], + "type": "text", + "content": "- We discard the KL divergence term from the marginal entropy objective to eliminate optimization conflicts and propose a reliability-based weighted ensembling strategy to integrate knowledge from reliable augmented views." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 300, + 553, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 553, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 553, + 323 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the effectiveness of our method in both adaptation and adversarial defense." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 338, + 400, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 338, + 400, + 350 + ], + "spans": [ + { + "bbox": [ + 314, + 338, + 400, + 350 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 358, + 487, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 487, + 370 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 487, + 370 + ], + "type": "text", + "content": "2.1. Adversarial Attack and Defense" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 376, + 553, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 553, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 553, + 544 + ], + "type": "text", + "content": "A lot of research [13, 24, 42] has been devoted to studying neural network's vulnerability to adversarial noise. A pioneering work [42] introduces the concept of adversarial examples and finds small-amplitude noise that humans cannot recognize leads to misclassifications. Since then, a series of attack methods to generate adversarial samples [4, 8, 13, 24] have been proposed. FGSM [13] proposes to utilize the gradient sign to generate an adversarial example. Researchers [24] generate the adversarial noise by projected gradient descent (PGD) operation, which becomes the standard measurement of model robustness. Moreover, a variety of works explore adversarial attacks in many restricted conditions, ranging from one-pixel attack [40], universal perturbation [28] to more realistic black-box setting [2, 18]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 545, + 553, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 553, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 553, + 664 + ], + "type": "text", + "content": "In parallel, numerous defense strategies [24, 35, 49, 54] have been proposed to mitigate adversarial attacks. Adversarial training [13, 24] improves the robustness of the model by incorporating the adversarial samples into the training set. TRADES [54] provides a theoretical analysis of adversarial error to trade adversarial robustness against accuracy. AWP [49] perturbs the model's weights with small adversarial noise during training to enhance robustness. Reconstruction [29, 34] with generative models [12, 38] is also a commonly used technique in test-time defense methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "As for the vison-language models, TeCoA [26] and APT [21] employ adversarial training to pretrained CLIP [32] to improve the adversarial robustness. However, their training-time solution requires an annotated dataset and lacks flexi" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29959" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 76, + 539, + 301 + ], + "blocks": [ + { + "bbox": [ + 74, + 76, + 539, + 301 + ], + "lines": [ + { + "bbox": [ + 74, + 76, + 539, + 301 + ], + "spans": [ + { + "bbox": [ + 74, + 76, + 539, + 301 + ], + "type": "image", + "image_path": "508cfb088be62b610b921a96fd20e3149fdd0def5e4830eec3cc5176694d21a3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 310, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 54, + 310, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 54, + 310, + 555, + 357 + ], + "type": "text", + "content": "Figure 2. The pipeline of R-TPT framework. Given an instance-level task, we deploy augmentation on the test image and build a classifier with CLIP's text branch. After selecting a low-entropy batch, R-TPT discards the KL divergence minimization term which potentially introduces conflicts in the marginal entropy [57] and optimizes textual prompts with pointwise entropy minimization. To effectively utilize the knowledge of the augmented views, R-TPT applies a reliability-based weighted ensembling mechanism in the final inference process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 375, + 295, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 375, + 295, + 413 + ], + "spans": [ + { + "bbox": [ + 54, + 375, + 295, + 413 + ], + "type": "text", + "content": "bility across tasks. In this work, we choose to deploy adversarial defense in the test time that is more effective and flexible and can collaborate with their training-time defense." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 420, + 231, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 231, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 231, + 433 + ], + "type": "text", + "content": "2.2. Test-Time Adaptation for VLMs" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 437, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 665 + ], + "type": "text", + "content": "Test-time adaptation [23, 37, 51] aims to adapt pre-trained models to the test data at inference time to improve the performance further. According to the test data form, test-time adaptation is divided into streaming data adaptation [43, 45, 52] and single instance adaptation [37, 57], and our work focuses on the latter. Recent research [37, 41, 53] has been devoted to exploring the instance adaptation methods for VLMs [32, 46, 56]. TPT [37] employs the marginal entropy minimization to augmentation views of the test instance to correct the prediction. DiffTPT [11] utilizes the diffusion technique to obtain diverse views which is helpful for the adaptation. PromptAlign [1] aligns the statistics of the test instance and collected natural images to make the model's parameters adapt to test samples. To take advantage of more prompt templates [32], TPS [41] chooses to optimize feature shift and utilizes prompt ensembling for initialization. Moreover, researchers [53] propose a training-free adaptation method by ensembling the augmented views with the MeanShift algorithm [7]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 665, + 295, + 713 + ], + "type": "text", + "content": "Besides accuracy, researchers [50] also focus on improving calibration performance through higher text feature dispersion. In this work, we first utilize the test-time paradigm to defend against adversarial attacks for CLIP due to its se" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 375, + 487, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 375, + 487, + 388 + ], + "spans": [ + { + "bbox": [ + 314, + 375, + 487, + 388 + ], + "type": "text", + "content": "vere vulnerability to adversarial examples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 401, + 397, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 401, + 397, + 415 + ], + "spans": [ + { + "bbox": [ + 314, + 401, + 397, + 415 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 422, + 555, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 555, + 555 + ], + "type": "text", + "content": "In this paper, we improve CLIP's adversarial robustness through a test-time paradigm, motivated by its inherent vulnerabilities and the high resource demands of train-time defense methods. Our proposed robust test-time prompt tuning (R-TPT), as illustrated in Figure 2, requires no annotated data and is equipped with greater flexibility. In Sec. 3.1, we begin with reviewing the foundational concepts of CLIP and the test-time prompt tuning approach. We then introduce the two key components of R-TPT: pointwise entropy minimization in Sec. 3.2, and the reliability-based weighted ensembling strategy in Sec. 3.3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 563, + 394, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 394, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 394, + 576 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "Contrastive language-image pre-training. CLIP is a popular language-vision model with a double-tower architecture, consisting of an image encoder " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "G(\\cdot)" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": ". It is pretrained by the contrastive learning objective with a large amount of image-text pairs. Benefiting from rich pretraining knowledge, CLIP has a strong zero-shot generalization ability. Take a C-way classification task with class names " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{t_c\\}_{c=1}^C" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " as an example, CLIP obtains textual features " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "g_c" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " by the text encoder " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "G(\\cdot)" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " with a prompt template (e.g., \"a photo of a [\"]) and the class name " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " as the input. Also, each test image " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " queries the image encoder" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29960" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "to calculate the image feature " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "f_{i} = F(x_{i})" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": ". The probability that " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " belongs to category " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " is calculated by a softmax operation with the cosine similarity of those features:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 117, + 295, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 117, + 295, + 147 + ], + "spans": [ + { + "bbox": [ + 99, + 117, + 295, + 147 + ], + "type": "interline_equation", + "content": "p _ {c} \\left(x _ {i}\\right) = \\frac {\\exp \\left(\\cos \\left(f _ {i} , g _ {c}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {C} \\exp \\left(\\cos \\left(f _ {i} , g _ {j}\\right) / \\tau\\right)}, \\tag {1}", + "image_path": "0be4d683fc54b45c33ea62e260b94f682d7279d46255ddfbc1dda4bdba66e443.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "inline_equation", + "content": "\\cos(\\cdot)" + }, + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "text", + "content": " represents the cosine similarity operation and " + }, + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 156, + 296, + 179 + ], + "type": "text", + "content": " refers to the temperature default set to 0.01." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "text", + "content": "Test-time prompt tuning. Although CLIP exhibits strong classification performance, it is sensitive to distribution shifts. To address this issue, test-time prompt tuning (TPT) [37] improves the model's performance on individual test instances, without requiring additional training data for adaptation. During the test time, TPT deploys augmentation operations on the test instance " + }, + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "text", + "content": " to obtain augmented views " + }, + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^N" + }, + { + "bbox": [ + 55, + 180, + 296, + 300 + ], + "type": "text", + "content": " and tunes the textual prompts with low-entropy views. The core objective of TPT is to minimize marginal entropy, which is formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 308, + 295, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 308, + 295, + 338 + ], + "spans": [ + { + "bbox": [ + 91, + 308, + 295, + 338 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {m a r g i n a l}} = \\mathcal {H} (\\bar {p}) = \\mathcal {H} \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} p (x)\\right), \\tag {2}", + "image_path": "b853d961466d93cacfac5084d23bc08acefbaddb4d7e093bab7b749cd77dafcf.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot)" + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "text", + "content": " is the Shannon entropy and " + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "text", + "content": " represents the sample set selected from all views " + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "inline_equation", + "content": "\\{x_{i}\\}_{i = 0}^{N}" + }, + { + "bbox": [ + 55, + 347, + 296, + 407 + ], + "type": "text", + "content": " based on the low entropy. When augmentation provides valuable information, the classification boundary adapts according to the new prompt, leading to more accurate predictions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 415, + 272, + 429 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 272, + 429 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 272, + 429 + ], + "type": "text", + "content": "3.2. Refining Marginal Entropy Minimization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "text", + "content": "In the optimization of a single test sample, marginal entropy is the default choice for both visual models [57] and multimodal models [37]. Minimizing marginal entropy " + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\bar{p})" + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "text", + "content": " encourages the model to produce a consistent output across a set of selected low-entropy augmented views " + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "text", + "content": ". However, when the test sample is adversarially perturbed, it can easily be selected into the set " + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 434, + 296, + 577 + ], + "type": "text", + "content": ". While random augmentations can weaken the adversarial noise, enforcing consistency across all augmented outputs may mislead the optimization. Since our goal is to utilize test time adaptation to strengthen the model's defense ability to adversarial examples, we propose refining the marginal entropy objective." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 578, + 295, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 601 + ], + "type": "text", + "content": "We decompose the marginal entropy objective into two items as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 66, + 609, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 609, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 66, + 609, + 295, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {H} (\\bar {p}) = - \\sum_ {c = 1} ^ {C} \\bar {p} _ {c} \\log \\bar {p} _ {c} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\bar {p} _ {c} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(- \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log p _ {c} ^ {b} + \\sum_ {c = 1} ^ {C} p _ {c} ^ {b} \\log \\frac {p _ {c} ^ {b}}{\\bar {p} _ {c}}\\right) \\tag {3} \\\\ = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\mathcal {H} \\left(p ^ {b}\\right) + \\mathcal {K L} \\left(p ^ {b} \\| \\bar {p}\\right)\\right), \\\\ \\end{array}", + "image_path": "eea9f634ea75ef85a2ca145b3e62254b02b1fc1486e38d5b09f5ce691355fc64.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "text", + "content": " denotes the Shannon entropy, " + }, + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}(\\cdot\\|\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 262 + ], + "type": "text", + "content": " refers to Kullback-Leibler (KL) divergence. Eq. 3 shows that marginal entropy is a combination of a pointwise entropy term and a KL divergence term. Minimizing pointwise entropy helps move the classification boundary away from low-entropy points, which is the main composition of the marginal entropy. The KL divergence term, on the other hand, encourages consistent predictions across the augmented views. In the case of clean test samples, the differences between low-entropy augmented views are small, and the KL divergence term has a minimal effect. However, in adversarial scenarios, the mean prediction is distorted by the original perturbed sample, which differs significantly from the augmented views. As a result, enforcing consistency across the augmented views leads to conflicts and neglects the valuable information in these views." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "type": "text", + "content": "To improve performance under both clean and adversarial conditions, we discard the KL divergence term and focus solely on minimizing pointwise entropy, as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 359, + 305, + 553, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 305, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 359, + 305, + 553, + 338 + ], + "type": "interline_equation", + "content": "\\text {m i n i m i z e} \\mathcal {L} _ {\\text {p o i n t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {b = 1} ^ {| \\mathcal {B} |} \\mathcal {H} \\left(p ^ {b}\\right). \\tag {4}", + "image_path": "411eacc5ee03932dd686e6d71c87e0629e3a42f194b29a7590c3cb5a2a8a70c8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 343, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 343, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 343, + 554, + 426 + ], + "type": "text", + "content": "For clean test instances, minimizing pointwise entropy functions similarly to the original marginal entropy objective. Also, for adversarial examples, this approach focuses more on augmented views, which have relatively high entropy and information, and ignores the original adversarial inputs. Therefore, our objective can handle both natural conditions and adversarial attacks well." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 433, + 522, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 522, + 446 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 522, + 446 + ], + "type": "text", + "content": "3.3. Reliability-based Weighted Ensembling" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 450, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 554, + 594 + ], + "type": "text", + "content": "Unsupervised prompt tuning typically makes no change to image features and a small adjustment to the classification boundary. For adversarial examples, it is challenging to correct incorrect predictions since their feature representations are far from the correct decision boundary. Fortunately, augmentation at the pixel level can help mitigate the adversarial noise, as it weakens the effect of perturbations. Thus, we can leverage diverse augmented views of the test image, which provide valuable knowledge. To integrate information from augmented views effectively and protect the ensembling from the noise of lower-quality views, we propose a reliability-based weighted ensembling mechanism." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "Since augmentation inherently involves randomness (e.g., background areas left after cropping), we introduce a reliability metric to represent the quality of each augmented view. Reliability is defined as the similarity between the sample and its nearest neighbors. High reliability indicates that the sample is densely clustered in the feature space, containing useful information. Conversely, low reliability suggests that the sample is an outlier, likely containing augmentation or adversarial noise, and should be downweighted or ignored during ensembling." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29961" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 219, + 196 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 219, + 196 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 219, + 196 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 219, + 196 + ], + "type": "image", + "image_path": "4c6d656dd2e223bca7fc4682d411b888a5d284cdc193645fe1b2ed19a251bd0c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 198, + 195, + 209 + ], + "lines": [ + { + "bbox": [ + 84, + 198, + 195, + 209 + ], + "spans": [ + { + "bbox": [ + 84, + 198, + 195, + 209 + ], + "type": "text", + "content": "(a) Weight value in ImageNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 224, + 73, + 383, + 196 + ], + "blocks": [ + { + "bbox": [ + 224, + 73, + 383, + 196 + ], + "lines": [ + { + "bbox": [ + 224, + 73, + 383, + 196 + ], + "spans": [ + { + "bbox": [ + 224, + 73, + 383, + 196 + ], + "type": "image", + "image_path": "f31bcb3b85a6256805cad09131208167ef732f437fcd8c58222f5b1186f232ce.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 244, + 198, + 363, + 209 + ], + "lines": [ + { + "bbox": [ + 244, + 198, + 363, + 209 + ], + "spans": [ + { + "bbox": [ + 244, + 198, + 363, + 209 + ], + "type": "text", + "content": "(b) Weight value in ImageNet-A." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "type": "text", + "content": "Figure 3. Visualization of assigned reliability-based weight value under (a) clean, (b) distribution shift, and (c) adversarial attack scenarios. The red and blue bars denote the weight value of the original test instance and its augmented views, respectively. The weight assigned to the clean instance is higher than under the distribution shift. The weight of the adversarial test sample is close to 0." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 389, + 73, + 547, + 196 + ], + "blocks": [ + { + "bbox": [ + 389, + 73, + 547, + 196 + ], + "lines": [ + { + "bbox": [ + 389, + 73, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 389, + 73, + 547, + 196 + ], + "type": "image", + "image_path": "644fa76348add333fa4e25af039ff5c8df68020f291a452e19e61ab8f85c0c07.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 198, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 390, + 198, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 390, + 198, + 545, + 209 + ], + "type": "text", + "content": "(c) Weight value in ImageNet under attack." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "spans": [ + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "text", + "content": "Given an augmented batch, which includes the test image and its " + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "text", + "content": " augmented views, we calculate the similarity matrix " + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "inline_equation", + "content": "\\{S_{i,j}\\}_{i,j=0}^{N}" + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "text", + "content": " of the visual features " + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "inline_equation", + "content": "\\{f_i\\}_{i=0}^N" + }, + { + "bbox": [ + 55, + 272, + 295, + 310 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 97, + 318, + 295, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 318, + 295, + 332 + ], + "spans": [ + { + "bbox": [ + 97, + 318, + 295, + 332 + ], + "type": "interline_equation", + "content": "S _ {i, j} = \\cos \\left(f _ {i}, f _ {j}\\right), i, j = 0, 1, \\dots , N, \\tag {5}", + "image_path": "9d46182fb828458033e5e86d9a3890cd4b4f8f19760244fe0eddc0b8b0ed3233.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\text{con}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " denotes the cosine similarity operation. The " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": "-th row of the matrix " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " represents the similarity between " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " and all samples in the batch. We then select the " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " closest neighbor of " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " (excluding " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " itself) to form the neighboring set " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": ". The reliability of " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": " is calculated as the average similarity within the neighboring set " + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 55, + 342, + 296, + 413 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 422, + 295, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 422, + 295, + 452 + ], + "spans": [ + { + "bbox": [ + 87, + 422, + 295, + 452 + ], + "type": "interline_equation", + "content": "r _ {i} = \\frac {1}{K} \\sum_ {k \\in \\mathcal {N} _ {i}} \\cos \\left(f _ {i}, f _ {k}\\right), i = 0, 1, \\dots , N. \\tag {6}", + "image_path": "09f1682fa67199a8c3ce8b2f159c67f15ec32a6e1d8e6a35a919f59f167e03e4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 461, + 295, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 295, + 486 + ], + "type": "text", + "content": "The reliability score reflects the degree to which " + }, + { + "bbox": [ + 55, + 461, + 295, + 486 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 55, + 461, + 295, + 486 + ], + "type": "text", + "content": " is surrounded by similar samples in the feature space." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": "To obtain the final prediction, we ensemble the predictions from all augmented views, weighted by their respective reliability scores. The weight assigned to each view is calculated by applying a softmax operation on the reliabilities " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\{r_i\\}_{i = 0}^N" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": ". This weight assignment mechanism is flexible and adapts well to various scenarios. We present the weight values for clean samples (ImageNet), samples with distribution shift (ImageNet-A), and adversarial samples (ImageNet) in Figure 3. As shown, clean samples are assigned higher weights, and the ensembling mechanism focuses on augmented views when the test instance shows significant distribution shifts from natural images. For adversarial samples, the weight assigned to the poisoned instance is close to zero, which indicates that our mechanism protects the ensembling process from being misled by adversarial noise. This approach not only improves the robustness of predictions on adversarial samples but also maintains strong performance on clean samples, thus enhancing the overall reliability of the inference process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 270, + 390, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 390, + 284 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 390, + 284 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 293, + 364, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 364, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 364, + 306 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 315, + 555, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 555, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 555, + 554 + ], + "type": "text", + "content": "Datasets. To evaluate our proposed test-time defense method for VLMs, we conduct experiments on eight fine-grained classification datasets. These databases cover general objects (Caltech101 [10]), animals (Pets [31]), plants (Flower102 [30]), vehicles (Cars [20], Aircraft [25]), textures (DTD [6]), satellite images (EuroSAT [14]), and actions from videos (UCF101 [39]). Moreover, we evaluate on ImageNet [9] and four ImageNet-out-of-distribution (OOD) benchmarks with distribution shift. ImageNet-A [17] contains 200 classes and 7,500 natural adversarial examples which are collected with adversarial filtration technique. ImageNet-V2 [33] consists of 10,000 natural images across 1,000 categories from a different source than ImageNet. ImageNet-R [16] is a dataset containing 30,000 images with various renditions, leading to different textures and local statistics from ImageNet. ImageNet-S [44] consists of 50,889 sketch-style images and shares the same category space with ImageNet. Since our method is to defend against potential adversarial attacks during the test time, we do not need access to the training set of the above datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 713 + ], + "type": "text", + "content": "Evaluation metrics. Since our task focuses on instance-level test-time adaptation, the model update and prediction of each test sample can not utilize the information of other samples. Following the previous works [37, 53], we report the average classification accuracy (Acc.) to measure the method's adaptation ability on clean samples. To evaluate the adversarial defense performance, we provide the average accuracy (Rob.) on adversarial examples generated by the PGD algorithm [24] with various noise radii. It is worth noting that the adversarial examples are calculated on CLIP before adaptation, which is more suitable for real-world applications since attackers rely on open-source models and have no idea about the victim model's algorithm." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29962" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 65, + 548, + 163 + ], + "blocks": [ + { + "bbox": [ + 61, + 65, + 548, + 163 + ], + "lines": [ + { + "bbox": [ + 61, + 65, + 548, + 163 + ], + "spans": [ + { + "bbox": [ + 61, + 65, + 548, + 163 + ], + "type": "table", + "html": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]85.92.683.50.055.70.061.70.015.715.740.40.823.70.058.90.053.22.4
Ensemble83.574.882.369.957.136.258.046.616.416.437.129.516.713.753.943.050.641.3
TPT [37]87.97.084.70.158.40.062.10.017.317.342.44.328.40.060.60.355.23.6
C-TPT [50]87.73.783.60.056.60.064.80.016.716.741.51.327.00.060.10.154.82.7
MTA [53]87.365.984.859.858.717.861.031.518.118.140.318.822.51.660.631.354.130.6
R-TPT86.779.884.674.258.142.960.651.917.517.541.333.521.215.959.750.953.745.8
", + "image_path": "6231aaab320800041f0224e0e68f4728b61c1d6982139f5af09d61d06ae2d929.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 61, + 200, + 548, + 298 + ], + "blocks": [ + { + "bbox": [ + 55, + 171, + 553, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 171, + 553, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 553, + 194 + ], + "type": "text", + "content": "Table 1. Results (%) of clean accuracy (Acc.) and adversarial accuracy (Rob.) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ResNet50 (" + }, + { + "bbox": [ + 55, + 171, + 553, + 194 + ], + "type": "inline_equation", + "content": "\\epsilon = 1.0" + }, + { + "bbox": [ + 55, + 171, + 553, + 194 + ], + "type": "text", + "content": "). Best clean accuracies are (bold), best adversarial accuracies are (bold red)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 200, + 548, + 298 + ], + "lines": [ + { + "bbox": [ + 61, + 200, + 548, + 298 + ], + "spans": [ + { + "bbox": [ + 61, + 200, + 548, + 298 + ], + "type": "table", + "html": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP [32]94.00.088.30.065.50.067.40.023.923.944.40.042.20.065.20.061.43.0
Ensemble91.974.786.251.265.726.065.936.323.423.443.225.128.22.263.030.658.433.7
TPT [37]94.10.087.40.066.50.069.10.023.423.446.90.042.60.067.90.062.22.9
C-TPT [50]93.90.088.20.065.80.069.60.023.923.945.90.042.30.065.50.061.93.0
MTA [53]94.372.188.051.867.718.567.427.925.025.046.516.242.51.267.527.562.330.0
R-TPT93.782.087.260.267.034.768.744.623.923.946.432.834.78.567.243.261.141.2
", + "image_path": "a061a26b6edd6aa749453ab76f8f344a47650b870a54267ee6aac9b8914ea874.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 306, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 62, + 306, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 62, + 306, + 546, + 319 + ], + "type": "text", + "content": "Table 2. Results (%) of various adaptation methods on fine-grained classification datasets with pre-trained CLIP-ViT-B/16 ( " + }, + { + "bbox": [ + 62, + 306, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\epsilon = {4.0}" + }, + { + "bbox": [ + 62, + 306, + 546, + 319 + ], + "type": "text", + "content": " )." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 338, + 294, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 338, + 294, + 470 + ], + "spans": [ + { + "bbox": [ + 54, + 338, + 294, + 470 + ], + "type": "text", + "content": "Baselines. We compare R-TPT on the above benchmarks with existing test-time adaptation methods for CLIP, including TPT [37], C-TPT [50], and MTA [53], as well as zero-shot prediction from CLIP [32]. Also, we regard Ensemble as an additional baseline method, which employs simple average operation on predictions of all augmented views. Note that both our method and the compared baseline methods rely only on CLIP and AugMix [15] augmentation, without any additional foundation models (e.g., LLM, diffusion models) or knowledge. All results of baselines are reproduced with the official code." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "spans": [ + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "text", + "content": "Implementation details. For all experiments, we utilize official pre-trained CLIP-ResNet50 and CLIP-ViT-B/16 [32] as our base model. As for adversarial example generation, we utilize the PGD algorithm [24] with " + }, + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "inline_equation", + "content": "\\epsilon = 1.0" + }, + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "text", + "content": " and 7 steps for ResNet, while " + }, + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "inline_equation", + "content": "\\epsilon = 4.0" + }, + { + "bbox": [ + 54, + 471, + 295, + 615 + ], + "type": "text", + "content": " and 100 steps for ViT. In the defense stage at test time, the parameter optimized in all experiments is a textual prompt with a context length of 4 and is initiated with \"a photo of a\". We adopt the Adam optimizer with weight decay and a single step. Following previous work [37], the learning rate is set to 0.005 and the augmented batch size is 64. All experiments use the PyTorch framework and run on RTX3090 GPUs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 624, + 179, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 179, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 179, + 635 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "Results on fine-grained datasets. We evaluate the adaptation and adversarial defense ability of R-TPT on eight fine-grained benchmarks and report the results in Table 1. It is shown that CLIP with strong zero-shot generalization ability is suffering from the adversarial attack with a small radius. TPT can steadily improve the accuracy of clean im" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "text", + "content": "ages but has weak defense capability. We observe that methods with an ensembling strategy (e.g., Ensemble, MTA, R-TPT) achieve significantly better adversarial accuracy. In particular, R-TPT achieves a " + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "inline_equation", + "content": "45.8\\%" + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "text", + "content": " of adversarial accuracy which outperforms all baseline methods. Besides the attractive defense performance, R-TPT also improves the clean accuracy of CLIP from " + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "inline_equation", + "content": "53.2\\%" + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "inline_equation", + "content": "53.7\\%" + }, + { + "bbox": [ + 313, + 338, + 554, + 445 + ], + "type": "text", + "content": ". In contrast, although Ensemble has strong defense capabilities, it suffers from negative transfer in the clean scenario." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "text", + "content": "Results on ImageNet and ImageNet-OOD datasets. We provide the experiential results on ImageNet and four ImageNet-OOD datasets in Table 3. CLIP can overcome distribution shifts, but fails to defend against adversarial attacks. R-TPT performs the best in adversarial defense under both ImageNet and its related out-of-distribution benchmarks. Especially, R-TPT achieves an adversarial accuracy of " + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "inline_equation", + "content": "47.7\\%" + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "text", + "content": " on ImageNet, " + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "inline_equation", + "content": "7.6\\%" + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "text", + "content": " higher than the second-best method Ensemble, while CLIP's adversarial accuracy on this benchmark is " + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 313, + 449, + 554, + 591 + ], + "type": "text", + "content": ". Moreover, our method obtains a similar clean accuracy with TPT, indicating that R-TPT is also effective for distribution shifts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": "Results of CLIP-ViT backbone. We evaluate our method on CLIP-ViT-B/16 [32] model and provide the results in Table 2. We observe that R-TPT outperforms all baseline methods regarding adversarial defense performance. However, the performance gain of all adaptation methods for clean samples is small, and R-TPT and the remaining two ensembling-based methods make weak negative transfers. This illustrates that the space for improvement of clean accuracy for strong pre-training models is small, and R-TPT can greatly enhance its weak robustness." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "29963" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 65, + 503, + 163 + ], + "blocks": [ + { + "bbox": [ + 106, + 65, + 503, + 163 + ], + "lines": [ + { + "bbox": [ + 106, + 65, + 503, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 65, + 503, + 163 + ], + "type": "table", + "html": "
MethodImageNetImageNet-AImageNet-V2ImageNet-RImageNet-SAvg.
Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.Acc.Rob.
CLIP [32]58.20.121.80.051.50.156.10.833.30.544.20.3
Ensemble58.040.122.610.152.037.251.339.329.520.742.729.5
TPT [37]60.70.326.50.054.80.358.91.835.01.447.20.7
C-TPT [50]60.40.124.10.054.30.157.71.034.70.946.20.4
MTA [53]60.430.027.55.654.224.658.429.835.211.347.120.3
R-TPT60.947.728.414.454.941.657.646.934.026.247.135.4
", + "image_path": "40284b8c6049556689473b185f8fdacc58b0b091d05c19ac2735405ac8f7eec2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 201, + 553, + 297 + ], + "blocks": [ + { + "bbox": [ + 55, + 172, + 553, + 195 + ], + "lines": [ + { + "bbox": [ + 55, + 172, + 553, + 195 + ], + "spans": [ + { + "bbox": [ + 55, + 172, + 553, + 195 + ], + "type": "text", + "content": "Table 3. Results (\\%) of various adaptation methods on ImageNet and ImageNet-OD benchmarks with pre-trained CLIP-ResNet50. OOD Avg. refers to the average results among four ImageNet-OD benchmarks (" + }, + { + "bbox": [ + 55, + 172, + 553, + 195 + ], + "type": "inline_equation", + "content": "\\epsilon = 1.0" + }, + { + "bbox": [ + 55, + 172, + 553, + 195 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 201, + 553, + 297 + ], + "lines": [ + { + "bbox": [ + 56, + 201, + 553, + 297 + ], + "spans": [ + { + "bbox": [ + 56, + 201, + 553, + 297 + ], + "type": "table", + "html": "
MethodCaltech101 Acc.Rob.Pets Acc.Rob.Cars Acc.Rob.Flower102 Acc.Rob.Aircraft Acc.Rob.DTD Acc.Rob.EuroSAT Acc.Rob.UCF101 Acc.Rob.Avg. Acc.Rob.
CLIP-TeCoA [26]79.344.366.915.810.21.030.89.06.66.624.510.714.510.834.66.733.413.1
Ensemble72.755.159.938.95.62.726.616.04.24.223.516.212.511.026.414.028.919.8
TPT [37]79.352.765.227.49.62.027.912.36.76.725.514.612.211.234.910.232.717.1
C-TPT [50]79.847.366.119.510.61.329.410.76.46.426.212.413.011.136.48.133.514.6
MTA [53]79.755.766.231.29.02.529.114.06.56.524.413.513.311.234.612.532.918.4
R-TPT76.160.563.240.17.73.526.616.56.16.125.217.711.511.331.117.430.921.7
", + "image_path": "afc1fe676bd3f8c712f6e8a493b1c998abca99fd58ac27ba233a6b19b9c25c69.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 336, + 146, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 336, + 146, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 336, + 146, + 350 + ], + "type": "text", + "content": "4.3. More Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "text", + "content": "Results under robust-pretrained models. we report the results of deploying adaptation methods on CLIP-ViT-B/32 with TeCoA [26] robust pretrained models in Table 4. It is shown that TeCoA significantly improves the robustness of CLIP, and the defense effect against adversarial attacks can benefit from our method during the testing stage, which increases adversarial accuracy form " + }, + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "inline_equation", + "content": "13.1\\%" + }, + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "inline_equation", + "content": "21.7\\%" + }, + { + "bbox": [ + 54, + 354, + 295, + 510 + ], + "type": "text", + "content": ". At the same time, we also find that R-TPT's defense effect on the TeCoA pretrained model is weaker than the vanilla CLIP. The reason is that introducing adversarial learning during the training time decreases the clean accuracy, which is the upper bound of defense. Robust pre-trained models also generate more difficult adversarial examples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "text", + "content": "Analysis under various attacks. To demonstrate the versatility, we investigate the defense performance of R-TPT and baseline methods under various attack methods. We employ CW [4], DeepFool [27], and FGSM [13] as new attacks and report the adversarial accuracy on three benchmarks in Table 5. It is shown that our method improves CLIP's defense capability under each attack, which is consistent with the trend of PGD. In particular, R-TPT has reached " + }, + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "inline_equation", + "content": "51.8\\%" + }, + { + "bbox": [ + 54, + 510, + 295, + 641 + ], + "type": "text", + "content": " adversarial accuracy on Flowers. The excellent defense performance among various attack methods proves the versatility of R-TPT." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 641, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 641, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 641, + 295, + 713 + ], + "type": "text", + "content": "Analysis of inference efficiency. We study the inference efficiency of R-TPT. Experiments of training-time defense method APT and R-TPT on UCF101 are provided in Table 6. It is shown that R-TPT spends a certain amount of time on each test sample, which is different from training-time defense which spends a lot of resources at one time" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 331, + 553, + 428 + ], + "blocks": [ + { + "bbox": [ + 63, + 304, + 546, + 316 + ], + "lines": [ + { + "bbox": [ + 63, + 304, + 546, + 316 + ], + "spans": [ + { + "bbox": [ + 63, + 304, + 546, + 316 + ], + "type": "text", + "content": "Table 4. Results (%) of adaptation methods on fine-grained classification datasets with TeCoA pre-trained CLIP-ViT-B/32 ( " + }, + { + "bbox": [ + 63, + 304, + 546, + 316 + ], + "type": "inline_equation", + "content": "\\epsilon = {4.0}" + }, + { + "bbox": [ + 63, + 304, + 546, + 316 + ], + "type": "text", + "content": " )." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 331, + 553, + 428 + ], + "lines": [ + { + "bbox": [ + 315, + 331, + 553, + 428 + ], + "spans": [ + { + "bbox": [ + 315, + 331, + 553, + 428 + ], + "type": "table", + "html": "
MethodFlowersDTD
CWDFFGSMAvg.CWDFFGSMAvg.
CLIP [32]0.80.44.82.02.37.613.47.8
Ensemble50.152.246.649.731.132.929.731.2
TPT [37]13.810.814.212.921.324.422.222.6
C-TPT [50]6.65.56.26.111.915.817.515.1
MTA [53]34.535.436.635.523.623.523.923.7
R-TPT51.654.749.251.834.235.932.534.2
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MethodStageRunning timeRob.
APT+TeCoA (4shots)Training time208s/50epochs39.4
R-TPT (64 views)Test time0.58s/image41.0
R-TPT (32 views)Test time0.28s/image40.8
R-TPT (16 views)Test time0.20s/image40.0
", + "image_path": "3e36086aca06f781f737941e018ea0ed3fd541f469921bdd9986e919f203425b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 548, + 555, + 571 + ], + "lines": [ + { + "bbox": [ + 313, + 548, + 555, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 555, + 571 + ], + "type": "text", + "content": "Table 6. Running time and adversarial accuracies " + }, + { + "bbox": [ + 313, + 548, + 555, + 571 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 313, + 548, + 555, + 571 + ], + "type": "text", + "content": " of adaptation methods against adversarial attack on UCF101 dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 593, + 555, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 555, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 555, + 664 + ], + "type": "text", + "content": "during training. Moreover, we find that inference can be accelerated by appropriately reducing the number of augmented views to obtain better real-time performance. When we choose to reduce the number of views from 64 to 16, the time required for each test sample is reduced to less than half of the original." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Analysis under different prompt templates. Since in the realistic scenario, the attacker can not access the prompts of the model textual branch, we evaluate the defense performance of the adversarial examples generated by" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29964" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 71, + 212, + 197 + ], + "blocks": [ + { + "bbox": [ + 62, + 71, + 212, + 197 + ], + "lines": [ + { + "bbox": [ + 62, + 71, + 212, + 197 + ], + "spans": [ + { + "bbox": [ + 62, + 71, + 212, + 197 + ], + "type": "image", + "image_path": "5dfc6035ec6ffb3e6986b3d000c76da21cfe6d76c6850aadb8c75e0fce263f41.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 198, + 196, + 209 + ], + "lines": [ + { + "bbox": [ + 83, + 198, + 196, + 209 + ], + "spans": [ + { + "bbox": [ + 83, + 198, + 196, + 209 + ], + "type": "text", + "content": "(a) Different prompt templates." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 225, + 76, + 383, + 196 + ], + "blocks": [ + { + "bbox": [ + 225, + 76, + 383, + 196 + ], + "lines": [ + { + "bbox": [ + 225, + 76, + 383, + 196 + ], + "spans": [ + { + "bbox": [ + 225, + 76, + 383, + 196 + ], + "type": "image", + "image_path": "4569975943b3d91c312854db7b3323db48455d7a277863128c9e55860016e4b4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 239, + 198, + 368, + 209 + ], + "lines": [ + { + "bbox": [ + 239, + 198, + 368, + 209 + ], + "spans": [ + { + "bbox": [ + 239, + 198, + 368, + 209 + ], + "type": "text", + "content": "(b) Sensitivity of neighbor number." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "type": "text", + "content": "Figure 4. Results of different prompt templates in adversarial examples generation, different neighbor numbers, and different choices of optimization parameters in DTD dataset (CLIP-ResNet50, " + }, + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon = 1.0" + }, + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 389, + 78, + 547, + 196 + ], + "blocks": [ + { + "bbox": [ + 389, + 78, + 547, + 196 + ], + "lines": [ + { + "bbox": [ + 389, + 78, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 389, + 78, + 547, + 196 + ], + "type": "image", + "image_path": "3a30117983e83d34297680117fe998e1da2b3063a2d0d3c9e41ba544436d559c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 391, + 198, + 544, + 209 + ], + "lines": [ + { + "bbox": [ + 391, + 198, + 544, + 209 + ], + "spans": [ + { + "bbox": [ + 391, + 198, + 544, + 209 + ], + "type": "text", + "content": "(c) Sensitivity of optimization parameters." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 261, + 296, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 261, + 296, + 356 + ], + "spans": [ + { + "bbox": [ + 55, + 261, + 296, + 356 + ], + "type": "text", + "content": "different prompt templates. The result of DTD benchmark with six textual templates is provided in Figure 4(a) (P0='a photo of a []', P1='a bad photo of the []', P2='a origami []', P3='a photo of the large []', P4='a toy []', P5='art of the []'). It is shown that CLIP is suffering from adversarial samples even if attackers use different prompt templates. Also, R-TPT outperforms all baseline methods under each template." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 358, + 296, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 358, + 296, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 296, + 562 + ], + "type": "text", + "content": "Analysis of sensitivity of hyperparameters and optimization parameters. We study the impact of the neighbor number in calculating reliability and the optimization parameter to further demonstrate the effectiveness of R-TPT. We provide the results of R-TPT with different neighbor numbers (10, 15, 20, 25, 30) in Figure 4(b). The results demonstrate that R-TPT performs stable across different neighbor numbers in terms of both clean and adversarial accuracy. Please note that if the neighbor number equals to augmented batch size, it will assign all samples with equal weights and the reliability-based ensembling mechanism will degenerate into the vanilla ensembling. Besides, we report the results with different optimization parameters in Figure 4(c). Compared to other choices of the parameter space, optimizing textual prompts owns better defense and adaptation effects and fewer parameters, which make it always a popular solution for parameter-efficient fine-tuning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 574, + 149, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 149, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 149, + 588 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "To study the contribution of terms in our method, we investigate the effectiveness of ensembling, reliability-based weighted mechanism, and pointwise entropy objective in R-TPT. The results of the ablation study are reported in Table 7. From the table, we find that entropy minimization focuses on enhancing the accuracy of adaptation on the clean samples and Slightly improves the defense performance on CLIP. However, When cooperating with weighted ensembling, the improvement of entropy minimization on both metrics is significant. The ensembling strategy greatly" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 317, + 250, + 552, + 356 + ], + "blocks": [ + { + "bbox": [ + 317, + 250, + 552, + 356 + ], + "lines": [ + { + "bbox": [ + 317, + 250, + 552, + 356 + ], + "spans": [ + { + "bbox": [ + 317, + 250, + 552, + 356 + ], + "type": "table", + "html": "
EnsembleWeightedEntMinFine-grainedImageNet-X
Acc.Rob.Acc.Rob.
XXX53.22.444.20.3
XX✓55.23.647.20.7
✓XX50.641.342.729.5
✓X✓53.344.346.734.2
✓✓X51.644.344.833.4
✓✓✓53.745.847.135.4
", + "image_path": "3e892f93b68592e03c45dd6f90444abc0c15d47031c233cbc6500939573a66e9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 364, + 555, + 387 + ], + "lines": [ + { + "bbox": [ + 313, + 364, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 555, + 387 + ], + "type": "text", + "content": "Table 7. Ablation study. Clean and adversarial accuracies " + }, + { + "bbox": [ + 313, + 364, + 555, + 387 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 313, + 364, + 555, + 387 + ], + "type": "text", + "content": " on fine-grained datasets and ImageNet dataset (CLIP-ResNet50)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 407, + 555, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 468 + ], + "type": "text", + "content": "strengthens the defense capabilities of the model, but it also reduces the adaptation performance on clean samples. The weighted mechanism gives reliable samples more important roles during prediction, further improving the defense capabilities and mitigating the clean performance drop." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 388, + 491 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "In this paper, we for the first time explore the adversarial defense for CLIP with a test-time paradigm and propose robust test-time prompt tuning (R-TPT). We first review the classic test time adaptation method and decompose its marginal entropy objective into a pointwise entropy term and a KL divergence term. We find that minimizing KL divergence will introduce conflicts when meeting the adversarial test instance, thus we discard KL divergence terms and only optimize the textual prompt with the pointwise entropy. We also introduce a reliability-based weighted ensembling strategy to utilize knowledge of the augmented views, which contain more knowledge than the risky original input under adversarial attacks. Extensive results show that R-TPT achieves the best defense against various adversarial attacks among all baseline methods and maintains a clean adaptation performance. We believe that our work will provide a new perspective on the defense and shed light on the safety issues of VLMs." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29965" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 162 + ], + "type": "text", + "content": "This work was funded by the National Natural Science Foundation of China under Grants (62276256, U2441251) and the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). The authors would like to thank Professor Tan Tieniu for his valuable guidance and contribution to this work." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "spans": [ + { + "bbox": [ + 56, + 172, + 115, + 185 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 192, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 192, + 296, + 257 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 192, + 296, + 257 + ], + "spans": [ + { + "bbox": [ + 61, + 192, + 296, + 257 + ], + "type": "text", + "content": "[1] Jameel Abdul Samadh, Mohammad Hanan Gani, Noor Hussein, Muhammad Uzair Khattak, Muhammad Muzammal Naseer, Fahad Shahbaz Khan, and Salman H Khan. 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While LLMs excel as the robot's \"brain\" for high-level planning, they face challenges in directly controlling the \"body\" by generating precise low-level actions. This limitation arises from LLMs' strength in high-level conceptual understanding but their inability to handle spatial perception effectively, restricting their potential in embodied tasks. To address this, we bridge the gap by enabling LLMs to not only comprehend complex instructions but also produce actionable, low-level plans. We introduce Room to Chessboard (R2C), a novel semantic representation that maps environmental states onto a grid-based chessboard, empowering LLMs to generate specific low-level coordinates and guide the robot in a manner akin to playing a game of chess. To further enhance decision-making, we propose the Chain-of-Thought Decision (CoT-D) paradigm, which improves LLMs' interpretability and context-awareness in spatial reasoning. By jointly training LLMs for high-level task decomposition and low-level action generation, we create a unified \"brain-body\" system capable of handling complex, free-form instructions while producing precise low-level actions, allowing the robot to flexibly control its movements and adapt to varying tasks. We validate R2C using both fine-tuned open-source LLMs and GPT-4, demonstrating effectiveness on the challenging ALFRED benchmark. Results show that with our R2C framework, LLMs can effectively act as low-level planners, generalizing across diverse settings and open-vocabulary robotic tasks. The code and demonstrations are available at: https://vipl-vsu.github.io/Room2Chessboard.", + "bbox": [ + 88, + 359, + 485, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 843, + 220, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The pursuit of general embodied agents focuses on developing robust systems capable of understanding natural lan", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33e7777691d95406c21223740585b937fe4302af0be7e17fef1223ad15dc1970.jpg", + "image_caption": [ + "Figure 1. Comparison of LLM as a high-level versus low-level planner for the task of \"heating eggs\". High-level planner provides subgoals while low-level planner directly provides exact path." + ], + "image_footnote": [], + "bbox": [ + 521, + 327, + 906, + 522 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "guage commands to meet diverse human requirements. Traditional robotic learning methods have succeeded in executing complex tasks but struggle to generalize to new environments or tasks due to their reliance on task-specific training and rigid planning. Recently, Large Language Models (LLMs) have emerged as promising embodied agents.", + "bbox": [ + 511, + 595, + 906, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several pioneering works [8, 13, 14, 37] have explored LLMs as the \"brain\" of embodied systems, leveraging their strong generalization to manage diverse tasks effectively. However, most LLM-based agents [1, 13, 37] focus mainly on high-level task planning, decomposing tasks like \"bring me an egg\" into subgoals (e.g., \"go to egg\") $\\rightarrow$ \"take it back\"). The execution of these subgoals is still delegated to low-level policy networks [5, 16, 18] or deterministic algorithms [7, 31]. While LLMs have extensive world knowledge, they lack spatial awareness of real environments, making it difficult to predict if these plans can be grounded to the physical world accurately. This often leads to frequent re-planning [1, 37], reducing efficiency and success rates, thereby limiting the potential of LLMs as embodied", + "bbox": [ + 511, + 688, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19456", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "agents in real-world applications.", + "bbox": [ + 89, + 90, + 313, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The primary barrier [37, 44] to unlocking the full potential of LLMs lies in the ineffective communication between the LLM (the \"brain\") and the robot (the \"body\"). The robot struggles to convey the updated spatial information about environment, leaving the LLM without a basis for decision-making. As a result, the LLM can only generate high-level subgoal plans, while controlling the robot's movements relies on external navigation APIs. To overcome this challenge, a \"common language\" is needed — a platform that delivers sufficient environmental states, empowering the LLM to generate precise low-level action plans and directly control the robot.", + "bbox": [ + 89, + 108, + 483, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose a novel Room to Chessboard (R2C) framework, which realizes a unified \"brain-body\" system that integrates high-level task understanding with direct low-level action decisions. As shown in Fig. 1, R2C utilizes a grid-based chessboard as an effective communication platform between the robot and the LLM. On one side, the robot can continuously map its observations onto the chessboard, which contains essential information while avoiding information overload. On the other side, the LLM is unlocked as a low-level action planner, directly guiding the robot \"moves\" on the chessboard to complete the task. Specifically, the LLM decomposes long-horizon tasks into sub-goals, which are then addressed through precise low-level planning. At this stage, an Environment Filter maintains task-aware environmental states on a compact chessboard. Since the chessboard grid size is calibrated to match the robot's step length, the LLM can perform low-level planning on the chessboard by predicting the robot's next position. Additionally, the Chain-of-Thought Decision (CoT-D) paradigm is proposed to enhance LLM's spatial reasoning and decision-making capabilities.", + "bbox": [ + 91, + 291, + 483, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To construct a chessboard representation that fully captures the complex environmental states while remaining manageable for LLMs, we introduce an Environment Filter to abstract the environment states. Initially, new observations are converted into a detailed 2D semantic map. However, such a high-dimensional representation can overwhelm LLMs. To mitigate this, we apply kernel filters to down-sample the map, then flatten it into a 2D chessboard, organized according to the priority of the current subgoal. The object occupancy on the chessboard is further abstracted into object coordinate sets. This representation strikes a balance between semantic richness and simplicity, effectively capturing critical information such as object semantics, object size and scene layout, while enabling efficient low-level action planning.", + "bbox": [ + 89, + 611, + 483, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In R2C framework, LLM needs robust long-context understanding capabilities to comprehend the object coordinate sets and spatial reasoning abilities for low-level planning. Despite advancements in LLM capabilities, achiev-", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing this remains a huge challenge. To enhance LLM's low-level action planning abilities, we design a fine-tuning paradigm and formalize the CoT-D fine-tuning task. CoT-D comprises four subtasks: key information extraction, direction determination, target prediction, and selection analysis. LLM is required to link these subtasks together into a coherent logical chain [42]. These tasks can not only strengthen the long-context understanding of LLM but also enhance its spatial reasoning to generate more interpretable low-level plans.", + "bbox": [ + 511, + 90, + 903, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our R2C framework on the challenging ALFRED [34] benchmark, which features a diverse set of long-horizon tasks. We test both GPT and fine-tuned open-source LLMs using our novel CoT-D. R2C achieves state-of-the-art (SoTA) performance among LLM-based methods. Additionally, LLMs trained with CoT-D exhibit strong spatial reasoning and action planning capabilities. Our LLM-based low-level action planner also demonstrates impressive generalization across open-vocabulary tasks and real-world deployment, highlighting the versatility and robustness of the R2C framework in various application scenarios.", + "bbox": [ + 511, + 242, + 906, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper are as follows:", + "bbox": [ + 532, + 409, + 874, + 424 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Room to Chessboard (R2C), a unified \"brain-body\" system that enables LLMs to simultaneously understand free-form instructions and generate specific, environment-aware low-level actions.", + "- We develop the Chain-of-Thought Decision (CoT-D) fine-tuning mechanism, which enhances the spatial reasoning capabilities of LLMs, leading to a significant improvement of $11.37\\%$ .", + "- We achieve SoTA performance among LLM-based methods using limited robotic data and demonstrate strong generalization to unseen environments, including real-world scenarios." + ], + "bbox": [ + 511, + 425, + 903, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 511, + 609, + 663, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Task Planning In Robotics", + "text_level": 1, + "bbox": [ + 511, + 635, + 754, + 651 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Task planning in robotics [28, 34] involves generating a sequence of actions for robots to execute in the environments to achieve a specific goal. In real-world applications, the instructions are typically complex, resulting in long-horizon tasks that encompass a variety of embodied activities, such as navigation [2, 9] and object interaction [20]. Early approaches [27, 38] simply integrate visual and textual inputs to generate contextually appropriate action sequences. Besides, one widely used approach is reinforcement learning (RL) [11, 24, 39, 41]. Although the above methods have good performance on some specific tasks, they are trained end-to-end using expert trajectories and low-level instructions, resulting in poor generalization to unknown environments [19, 25, 37].", + "bbox": [ + 511, + 657, + 906, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, some approaches [3, 15, 19, 23, 25] suggest explicitly breaking down the complex task into mul", + "bbox": [ + 511, + 869, + 903, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19457", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tiple functional modules. FILM [25] proposes a framework with four submodules including language processing, semantic mapping, semantic search and deterministic policy. ThinkBot [23] presents an additional object localizer based on multimodal transformers to predict the position of target objects. Though they provide more interpretable frameworks, each of their modules need to be fine-tuned with corresponding data, which make them struggle in adapting to novel robotic tasks.", + "bbox": [ + 89, + 90, + 480, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Task planning with LLMs", + "text_level": 1, + "bbox": [ + 89, + 234, + 326, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address the above generalization challenges, incorporating Large Language Models (LLMs) into robotic task planning presents a promising pathway [1, 10, 13, 14]. Early attempts [13] adopt LLMs to help with free-form human instruction following by decomposing the task into reasonable subgoals. However, due to LLM's inability to perceive the complex physical world, the generated goals often fail to execute in the environments [1].", + "bbox": [ + 89, + 256, + 482, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent research has delved into integrating environmental states to ground the output of the LLM-based planner. LM-Nav [32] leverages a pre-trained Vision-Language Model (VLM) to generate captions of viewpoints and ground them with landmarks to enhance the executability of navigation plan. Additionally, structured representations such as object-centric scene graphs and topology graphs [6, 10, 29, 46] are commonly employed to improve the LLM's comprehension of relationships among objects and the overall room layout within the environments. Beyond directly translating visual feedback into inputs for LLMs, Say-Can [1] trained a vision-based value function to judge the affordance of the LLM's plan in the environments. Furthermore, some other works [21, 35] involve text-form Planning Domain Definition Language (PDDL) descriptions of scenes, which are easier for LLMs to handle.", + "bbox": [ + 89, + 378, + 482, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although the above works address some cases where LLM-generated plans are not executable, they all use LLMs solely as high-level planners. Most works still rely on low-level controllers to translate these high-level plans into executable action sequences. Some recent works [12, 33, 47] train end-to-end models to directly map robot observations to actions on large amounts of robotic trajectory data to achieve generalization. Unlike these approaches, we unlock LLMs to function as both high-level and low-level planners by introducing an interpretable textual representation of the environment.", + "bbox": [ + 89, + 619, + 482, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 89, + 790, + 189, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to unlock LLMs as low-level action planners that can directly guide robots to solve long-horizon tasks. We first introduce our newly designed Room to Chessboard framework in Sec. 3.1, and then illustrate the Chain-of-Thought Decision (CoT-D) fine-tuning task formulation in Sec. 3.2.", + "bbox": [ + 89, + 809, + 482, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Room to Chessboard", + "text_level": 1, + "bbox": [ + 513, + 90, + 710, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce the Room to Chessboard (R2C) framework (Fig. 2), which enables LLMs to perform both High-Level Planning (HLP) and Low-Level Planning (LLP) within a unified framework. First, the LLM conducts HLP, processing step-by-step instructions into a sequence of subgoals. Each subgoal is then handled at the LLP stage. At each timestep, an egocentric RGB-D image is processed by an Environment Filter to generate a chessboard abstraction. The updated chessboard is subsequently converted into object occupancy coordinates, which are fed to the LLM. Acting like a chess player, the LLM predicts the robot's next move on the chessboard, guiding it to navigate or interact with the environment.", + "bbox": [ + 511, + 113, + 906, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1. High-Level Planning (HLP)", + "text_level": 1, + "bbox": [ + 511, + 319, + 751, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At the beginning of an episode, the LLM processes the natural language instruction $L$ into a sequence of high-level subgoals, denoted as $\\mathcal{G} = [G_1, G_2, \\dots, G_K]$ . Each subgoal $G_k$ is a tuple (Action, Object), where Action $\\in A_H$ is a primitive action chosen from the set of navigation action (GOTO) or interaction actions (e.g., PICKUP, PUT). The Object refers to the semantic class of the interacted object (e.g., SAFE, CD). These subgoals are executed sequentially during the LLP stage.", + "bbox": [ + 511, + 339, + 906, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.2. Environment Filter", + "text_level": 1, + "bbox": [ + 511, + 486, + 692, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the environment is partially observed, the agent has never explored the entire environment and must construct a map based on its own observations online. At each timestep, the Environment Filter $F(o_{t}, G_{k})$ takes the new observation $o_{t}$ as input to filter out the goal-related environment information conditioned on the current subgoal $G_{k}$ . This filtered information is then added to a dynamically updated semantic chessboard $\\mathcal{B}$ to represent the current state of the environment. The computation of $F$ involves two parts: semantic mapping and chessboard building.", + "bbox": [ + 511, + 506, + 906, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic mapping. We first build an online semantic map of the room, inspired by prior work [25]. At each timestep $t$ , the agent receives an egocentric RGB-D observation $o_{t} = I_{rgb}, I_{dpt}$ . An off-the-shelf instance segmentation model processes $I_{rgb}$ , and, combined with $I_{dpt}$ , the observation is converted into a point cloud, with each point labeled with predicted semantic categories. This 3D point cloud is then voxelized and flattened along the Z-axis to form the 2D semantic map $\\mathcal{M}$ . The resulting semantic map is represented as $(C + 2) \\times M \\times M$ binary grid, where $C$ is the number of object categories, and two additional channels denote obstacles and explored areas in each cell. Here, $M$ represents the map resolution.", + "bbox": [ + 511, + 657, + 906, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Chessboard building. We further abstract the semantic map into a compact chessboard, i.e., map to chessboard $(M2C)$ . The $M2C$ function consists of two cascaded kernels.", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19458", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cd851cc741c27a4a9b736a0e86d20f655dc9f2675fb7d12603da851066e62a89.jpg", + "image_caption": [ + "Figure 2. Overview of R2C framework: The LLM begins by generating high-level subgoals for the task. For each subgoal, the environment filter translates RGB-D observations into an updated grid-based chessboard representation of the environments. The LLM then uses chain-of-thought analysis to integrate this chessboard representation along with game rules, determining the next optimal position, which is finally converted into executable robot actions." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 903, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first kernel is a dilation kernel $\\mathcal{K}_{dila}$ , designed to prevent collisions between the agent and obstacles. Similar to the dilation algorithm in image processing [30], it expands all occupied pixels of obstacles (including objects) outward by $\\delta$ in the map. The second kernel is a max pooling kernel $\\mathcal{K}_{pool}$ , which performs max pooling on the map. Then, the map is down-sampled from size $M$ to size $W$ , where $W = \\left\\lceil \\frac{M}{\\omega} \\right\\rceil$ and $\\omega$ is the grid size, calibrated to match the length of the agent's step.", + "bbox": [ + 88, + 450, + 480, + 587 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we aggregate this map with multiple object layers into a unified single-layer chessboard. To address the many-to-one projection problem, where overlapping objects might appear in the same grid, e.g., \"apples on a table\", we introduce a Goal-aware Aggregate function $\\mathcal{A}(\\cdot)$ . This function prioritizes both the relevance to the current subgoal, i.e., the target object Object in current subgoal $G_{k}$ , and the size of the object. The most relevant and smallest objects are placed at the top layer, and then we merge object layers from bottom to top to produce the final chessboard. The overall formulation of the $M2C$ is:", + "bbox": [ + 88, + 588, + 482, + 753 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM 2 C = \\mathcal {A} \\circ \\mathcal {K} _ {d i l a} \\circ \\mathcal {K} _ {p o o l} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 758, + 482, + 781 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} = M 2 C (\\mathcal {M}, G _ {k}).\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 779, + 333, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.3. Low-Level Planning (LLP)", + "text_level": 1, + "bbox": [ + 89, + 805, + 323, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The chessboard filtered out from the Environment Filter provides compact yet sufficient environmental state information for LLM. We then simulate a \"chess game\" between the LLM and the robot to perform low-level planning. The LLP task is formulated as a single-step generation task for", + "bbox": [ + 88, + 824, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the LLM. As shown in Fig. 2, various state information is collected, including current subgoal $G_{k}$ , chessboard state $\\mathcal{U}$ , action history $\\mathcal{Q}$ and game rules $R$ . Our prompt system $\\mathcal{P}$ organizes such data and feeds them into the LLM to generate the next position prediction $w$ . Note that LLP is invoked only for navigation subgoals, as interaction subgoals in ALFRED can be handled by predefined low-level actions once the agent reaches the visible range of the target object.", + "bbox": [ + 511, + 450, + 906, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Chessboard state. To translate the chessboard state for the LLM, we convert it into textual object occupancy coordinate sets. The chessboard coordinate system originates from the upper left corner, with the X-axis pointing down and the Y-axis to the right. For each object on the chessboard, we gather a set of occupancy coordinates $\\mathcal{U}_t^c = \\{x_i,y_i\\}$ , where $c\\in [1,C + 2]$ and $x_{i},y_{i}\\in [1,W]$ . The initial agent position $w_{0}$ is predefined in the benchmark.", + "bbox": [ + 511, + 575, + 905, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Game rules. To assist the LLM in planning, we define key game rules $R$ : 1) Basic inputs, including chessboard dimensions $W$ , maximum steps $T$ , and maximum errors $E$ ; 2) Action space, simplified to adjacent grids in four directions (up, down, left, right), i.e., the robot is only allowed to move 1 block at a time, due to the limited spatial reasoning ability of current LLMs; 3) Collision rules, where grids occupied by objects or obstacles are considered illegal moves.", + "bbox": [ + 511, + 715, + 905, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Action history. We maintain a queue $\\mathcal{Q}$ with a fixed length $\\tau$ to store recent successful movement coordinates, providing the LLM with contextual information about previous actions. At each step $t$ , the prompt system combines", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19459", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "all such information and feeds them to the LLM, which simulates a chess player to decide the next move. The LLP models a policy $\\pi$ , defined as:", + "bbox": [ + 89, + 90, + 483, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {t} = \\pi (\\mathcal {P} (G _ {k}, \\mathcal {U} _ {t}, R, \\mathcal {Q} _ {t})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 138, + 482, + 156 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $u_{t} = (x_{t},y_{t})$ is the predicted next position on the chessboard. According to the defined action space, the available next positions are restricted to the adjacent grids in four directions $x_{t + 1}\\in [x_t - 1,x_t + 1]$ and $y_{t + 1}\\in [y_t - 1,y_t + 1]$ , with $x_{t + 1},y_{t + 1}\\in [1,W]$ .", + "bbox": [ + 89, + 162, + 483, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the chessboard grid size is calibrated to match the robot's step length, the predicted adjacency target position $u_{t}$ can be directly converted to a sequence of executable low-level actions $\\mathbf{a} = \\{a_{i}\\}$ , $a_{i} \\in \\mathbf{A}_{\\text{nav}}$ in the real-world environments. For example, in the ALFRED benchmark, $\\mathbf{A}_{\\text{nav}}$ includes (MoveForward, 0.25m), (TurnLeft, 90°) and, (TurnRight, 90°). Based on the predicted target position, the movement in any of the four directions can be converted into the corresponding action sequence (e.g., TurnLeft and MoveForward to move to the left adjacent grid). Additionally, if the output $w_{t}$ is within the visible range of the target object Object in the current subgoal, the system moves on to the next subgoal. See more details of the R2C framework in the pseudocode provided in the supplementary materials.", + "bbox": [ + 89, + 239, + 483, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Chain-of-Thought Fine-tuning Paradigm", + "text_level": 1, + "bbox": [ + 89, + 476, + 441, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To improve the decision-making capabilities of LLMs in our chess game, we introduce an interpretable fine-tuning paradigm with two core features: 1) simultaneous training of high-level task decomposition and low-level Chain of Thought Decision (CoT-D) tasks, enabling the integration of High-Level Planning (HLP) and Low-Level Planning (LLP) within a single LLM, and 2) structuring the CoT-D process into four distinct parts to enhance the LLM's comprehension of game rules and spatial reasoning.", + "bbox": [ + 89, + 498, + 483, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.1. Joint Training of HLP and LLP", + "text_level": 1, + "bbox": [ + 89, + 642, + 359, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Long-horizon planning often involves compositional tasks that require hierarchical planning capabilities. Therefore, rather than only exploiting the LLM as a high-level planner or training an end-to-end low-level action generation model, we jointly train the model on both HLP and LLP tasks simultaneously. Given the data imbalance between HLP and LLP, we apply data balancing techniques to ensure the model effectively learns skills at both levels.", + "bbox": [ + 89, + 661, + 483, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2. Chain of Thought Decision (CoT-D)", + "text_level": 1, + "bbox": [ + 89, + 790, + 385, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM should thoroughly comprehend our chessboard coordinate system and predict the next position based on the semantic information of the chessboard and its inherent common sense. For the given prompt $\\mathcal{P}$ with chessboard state $\\mathcal{U}$ , the LLM needs to generate answer sentence $S$ (including next position $w$ ) with probabilistic language model $p_{LM}$ . If", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM is asked to directly provide coordinates, this process can be formalized as:", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathcal {S} \\mid \\mathcal {P}) = \\prod_ {i = 1} ^ {| \\mathcal {S} |} p _ {L M} \\left(s _ {i} \\mid \\mathcal {P}, s _ {< i}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 114, + 903, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, such a complex task is much more challenging than the task decomposition. This requires the LLMs have strong capabilities in long-text comprehension and spatial reasoning. However, the current models are not particularly skilled in these abilities. Consequently, we design the Chain of Thought Decision (CoT-D) tasks to strengthen LLM's rationale $\\mathcal{R}$ in these aspects. The task consists of four subtasks, requiring LLMs to output the result of key information extraction $\\mathcal{R}_E$ , direction judgment $\\mathcal{R}_D$ , target prediction $\\mathcal{R}_T$ , and selection analysis $\\mathcal{R}_S$ , respectively. We link these sub-tasks sequentially in natural language to construct a coherent logical chain. The entire task can be represented as:", + "bbox": [ + 511, + 164, + 906, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\cdot p (\\mathcal {S} \\mid \\mathcal {P}) = p (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) \\cdot p (\\mathcal {R} \\mid \\mathcal {P}) \\\\ p (\\mathcal {R} \\mid \\mathcal {P}) = \\prod_ {r _ {i} \\in \\left\\{\\mathcal {R} _ {E}, \\mathcal {R} _ {D}, \\mathcal {R} _ {T}, \\mathcal {R} _ {S} \\right\\}} p _ {L M} \\left(r _ {i} \\mid \\mathcal {P}, r _ {< i}\\right) \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 354, + 903, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) = \\prod_ {j = 1} ^ {| \\mathcal {S} |} p _ {L M} (s _ {i} \\mid \\mathcal {P}, \\mathcal {R}, s _ {< j})\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 411, + 803, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The specific content of the four sub-tasks will be introduced below. Examples can be found in Fig. 2, with details available in the supplementary materials.", + "bbox": [ + 511, + 462, + 905, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Key information extraction. Due to the intricate information contained within the chessboard, when textualized, it becomes a lengthy document with substantial information. Considering that LLM often encounters issues such as context loss when comprehending long texts, this task is designed to train LLM in processing task-related long texts and extracting key information. This task requires LLM to extract relevant information about the current coordinates and target objects based on the chessboard information inputs. The form used in data annotation is as follows: The current position of the agent is [COORDS], and the target is [OBJECT NAME], which is located at [COORDS SET].", + "bbox": [ + 511, + 508, + 905, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Direction judgment. The conversion from a chessboard grid image to text is based on a two-dimensional Cartesian coordinate system, and all spatial relationship understanding relies on a good coordinate system understanding. Despite providing clear instructions to establish the coordinate system using prompts like Establish a coordinate system with the top-left grid as (1,1), experiments have shown that the LLM still frequently misunderstands the setup. This could be attributed to the length of the text and the scarcity of spatial reasoning tasks incorporated during the pre-training of contemporary LLM. To ensure LLM's accurate comprehension", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19460", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6e752921d4c9fe7994951f63db8f1349c5558856b92b9675f4dd7f02d8ba860a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTraining ModeVal SeenVal UnseenΔ SR ↑Δ GC ↑
SR ↑GC ↑SR ↑GC ↑
Specialists, only for ALFRED tasks
E.T. [27]from scratch46.5952.927.3220.87-39.27-32.05
HiTUT [45]from scratch25.2434.8512.4423.71-12.80-11.14
M-TRACK [36]from scratch26.7033.2117.2928.98-9.41-4.23
FILM [25]from scratch24.6337.2020.1032.45-4.53-4.75
LEBP [22]from scratch27.6335.7622.3629.58-5.27-6.18
Generalists, based on LLMs
SayCan [1]few-shot12.3024.529.8822.54-2.42-1.98
LLM-P (GPT) [37]1few-shot16.4530.1115.3629.88-1.09-0.23
R2C-GPT-4 (ours)zero-shot20.0028.4624.0028.24+4.00-0.22
R2C-Llama-7B (ours)fine-tune20.8329.6018.9929.69-1.84+0.09
R2C-Mistral-7B (ours)fine-tune22.3132.4022.3531.97+0.04-0.43
", + "bbox": [ + 99, + 89, + 584, + 261 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7ad85f7ae661cde6fafb79c7b5422a3e27e507b9942d6d0a734c8ac1087b752c.jpg", + "table_caption": [ + "Table 1. Main results on the ALFRED benchmark. SR and GC are short for success rate and goal-conditioned success rate. $\\Delta$ SR and $\\Delta$ GC represent the performance drops in generalizing from the seen to the unseen environments." + ], + "table_footnote": [], + "table_body": "
Task TypeVal SeenVal Unseen
SRGCSRGC
Overall48.1855.1353.3358.18
Examine75.8679.3183.3387.96
Pick & Place69.5769.5763.3363.33
Stack & Place29.0337.0045.4546.46
Clean & Place63.8973.8738.8950.45
Cool & Place36.8449.6061.1169.23
Heat & Place23.5341.3828.5741.13
Pick 2 & Place33.3354.4137.5053.70
", + "bbox": [ + 609, + 88, + 883, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the chessboard coordinate system, this task requires LLM to judge the direction between the target and the current coordinates. The format employed in data annotation is as follows: the target is at..., which is on the [DIRECTION] of the agent.", + "bbox": [ + 89, + 321, + 480, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Target prediction. The locations where different categories of objects appear often have priors. For example, sofas are likely to appear opposite the television. Therefore, we aim to enable LLM to develop the capability of predicting target locations. This can minimize the ineffective or inefficient exploration process for the robot to find target objects, thereby improving the efficiency of the system in accomplishing embodied tasks. The expression utilized in data annotation is: Based on the chessboard analysis, the target is likely located near [COORDS].", + "bbox": [ + 88, + 398, + 482, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Selection analysis. Based on the above comprehension, we require the LLM to further analyze all potential next positions according to the chessboard rules. During this analysis, the LLM evaluates each possible move, providing a rationale for each choice. The specific format used in the annotation is: [COORDS]: This position is on the [DIRECTION] of the agent, [Reason]. The [Reason] component is generated by GPT-4 based on the agent's current state and the relationship between the chosen position and the correct orientation. For instance: Objects in this direction have already been discovered; we should head to areas that have not been explored.", + "bbox": [ + 89, + 566, + 482, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These four sub-tasks comprehensively enhance the understanding of chessboard and spatial reasoning ability of the LLMs from different perspectives.", + "bbox": [ + 89, + 763, + 483, + 810 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 89, + 827, + 207, + 842 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 89, + 847, + 282, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benchmark. We evaluate our method on the challenging ALFRED [34] benchmark, which features long-horizon", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2be91cc0f55fea700b5ccd577e6c9f39c27506ce242700b6ac1190170b5973ad.jpg", + "table_caption": [ + "Table 2. Performance of R2C on different tasks. The R2C model excels in \"Examine\" tasks, but faces challenges in complex \"Heat & Place\" tasks, where the \"HeatObject\" subgoal alone involves seven interactive steps, increasing the risk of error accumulation." + ], + "table_footnote": [], + "table_body": "
MethodVal SeenVal Unseen
SRGCSRGC
Base Model (R2C-Mistral-7B)22.3132.4022.3531.97
+ GT Seg.37.9245.8335.2443.88
+ GT Seg., GT Goal48.1855.1353.3358.18
+ GT Seg., GT Goal, - SA45.9751.7547.4553.03
+ GT Seg., GT Goal, - CoT41.2249.3541.9647.88
", + "bbox": [ + 535, + 319, + 885, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation of R2C. \"GT Seg.\" represents the model using ground-truth segmentation. \"GT Goal\" represents using ground-truth subgoals. \"- SA\" is the model without Selection Analysis part of CoT. \"- CoT\" is the model without all CoT tasks.", + "bbox": [ + 511, + 426, + 905, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tasks (7 types in total) involving both navigation and interaction across 207 unique environments and 115 different object types. In our experiments, we adhere to the benchmark's settings, including low-level action space, maximum agent steps, and failure limits.", + "bbox": [ + 511, + 502, + 903, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Chessboard settings. The physical room size $D$ is set to $16m$ , which is the approximate maximum room size, and the grid size $\\omega$ corresponds to the agent's step length, $0.25m$ . Thus, the size of the semantic map and the chessboard is $M = 320$ and $W = 64$ separately. However, to represent more complex environments, one can choose a more fine-grained chessboard. We demonstrate this through a simple experiment in the supplementary materials.", + "bbox": [ + 511, + 579, + 905, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model settings. For the zero-shot R2C, we use the public GPT-4-turbo API [26] without any in-context examples. Considering the testing cost, we randomly sample a subset of size 100 covering all 7 types of tasks strictly according to the task distribution of ALFRED. We collected a total of 264,915 data samples for fine-tuning, including 70,000 samples for the Task Decomposition tasks and 194,915 samples for the CoT-D tasks. All data collection was based solely on the training set of ALFRED. During training,", + "bbox": [ + 511, + 700, + 905, + 838 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "For a fair comparison, we test the performance of the GPT-4 version of LLM-P on the same selected subset as ours, achieving an SR of $16.21\\%$ on seen scenes. Since this work solely employs LLMs for task decomposition, the performance is only slightly different when compared to using GPT-3.", + "bbox": [ + 511, + 849, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19461", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e4436f41a48d7d371afd859dc4cad439b08c812e31d4757a1ba7f128ab69b883.jpg", + "image_caption": [ + "Figure 3. Case study of R2C with Mistral model: The model completes an \"Examine\" task in 31 steps (top) but fails to locate the small target object, a bowl, during a \"Clean & Place\" task in a more complex environment (bottom)." + ], + "image_footnote": [], + "bbox": [ + 212, + 88, + 782, + 334 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we conduct full-parameter fine-tuning on both the Mistral-7B-Instruct-v0.2 model [17] and the Llama-7B-Chat model [40] using all the data. Both models were trained for only one epoch. We conduct all fine-tuning experiments using 4 NVIDIA H100 GPUs, and all evaluations are performed on 4 NVIDIA A40 GPUs.", + "bbox": [ + 89, + 377, + 483, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 89, + 481, + 230, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 1 presents the evaluation results on the validation set of ALFRED. We compare our R2C framework with both traditional robotic learning methods (specialists) and LLM-based approaches (generalists). R2C achieves state-of-the-art performance among LLM-based methods, with the Mistral-7B excelling in seen environments and GPT-4 in unseen environments.", + "bbox": [ + 89, + 503, + 483, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared to SayCan [1] and LLM-P [37], which use LLMs only for high-level planning, R2C integrates high-level and low-level planning, offering a more efficient, end-to-end solution. LLM-P requires 100 instruction-plan pairs for training, while R2C operates in a zero-shot setting without examples. Our CoT-D paradigm enables GPT to analyze the chessboard state comprehensively, improving decision interpretability and efficiency.", + "bbox": [ + 89, + 611, + 483, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "R2C fine-tuned on open-sourced LLMs achieves competitive results, with $2.31\\%$ improvement in the seen split and $1.65\\%$ drop in the unseen split compared to R2C-GPT-4. This highlights GPT-4's superior generalization to unseen environments. However, with our carefully designed fine-tuning tasks, R2C implemented on much smaller models like LLaMA and Mistral, can still deliver performance comparable to GPT-4. This demonstrates the effectiveness and efficiency of our fine-tuning approach.", + "bbox": [ + 89, + 733, + 482, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, R2C fine-tuned on collected data performs comparably to specialist models like FILM [25] and LEBP [22].", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b292c278f65a7811a7cc05550093e7dd95d81b56786eb901b308f7833c86d24c.jpg", + "image_caption": [ + "Figure 4. Cases of R2C-GPT-4 on open-vocabulary tasks." + ], + "image_footnote": [], + "bbox": [ + 563, + 375, + 849, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Although these specialized models excel in seen scenes, they struggle in unseen environments due to overfitting. In contrast, R2C and other LLM-based methods demonstrate stronger generalization across both seen and unseen environments.", + "bbox": [ + 511, + 508, + 906, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 595, + 666, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform an ablation study to analyze the impact of different R2C modules. As shown in Tab. 3, using ground truth segmentation (GT Seg.) significantly improves performance, highlighting segmentation as a bottleneck, especially in simulation environments. Using ground truth sub-goals (GT Goal) also boosts SR, revealing the impact of ambiguity in natural language instructions. Annotator confusion between categories like desk lamps and floor lamps can hinder task decomposition, though LLMs' strong generalization helps mitigate this.", + "bbox": [ + 511, + 613, + 906, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Removing the CoT-D framework, i.e., forcing the model to directly output position coordinates without rationale, results in a significant performance drop, especially in unseen scenes. This highlights the importance of fine-tuning with CoT-D for better spatial reasoning. Ablating individual subtasks is challenging due to their interdependence. Here, we ablate removing the Selection Analysis part (- SA), where decisions are made without analyzing options and it causes a noticeable performance decline.", + "bbox": [ + 511, + 765, + 908, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19462", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2fbd1535697dae278d6ac2071f728d8aac329473d778aba0b6ac61a6e02645b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 90, + 294, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/66af14fe3725f0ea355129744d40ce9b4053a7cadf8e2088bd57f57ebf20b971.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 90, + 488, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/796f00fd166c3d94b29c8defb9b72cbd8cc59016924d4f245b5da13cf266d905.jpg", + "image_caption": [ + "Figure 5. Visual results of R2C in real-world scenarios. Three tasks are tested in a real-world environment, with the corresponding instructions, third-person trajectories, first-person images, and chessboard visualizations shown for each task." + ], + "image_footnote": [], + "bbox": [ + 94, + 194, + 294, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5467b30963f17942381e4f7ada63edc40d7c776559239836d16b8b5beb18a8d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 194, + 488, + 292 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6153bcbb31c24844ea0013e83f83cecd9795bc48127440445296729567126568.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TaskSpecific Obj.Specific Loc.Nearest CornerCenter BetweenOverall
GPT-4 (90°)66.773.353.380.068.3
GPT-4 (45°)73.373.373.360.070.0
GPT-4o (90°)40.053.333.346.743.3
", + "bbox": [ + 94, + 366, + 488, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Evaluation Across Tasks Types", + "text_level": 1, + "bbox": [ + 89, + 465, + 364, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We analyze R2C's performance across task types using GT Segmentation and GT Goal settings, with task-specific results shown in Tab. 2. R2C shows SR drops on more complex long-horizon tasks, such as \"Heat & Place,\" with average GT step lengths of 63, compared to shorter ones (e.g., Examine: 37). We provide a visualization of two case studies of R2C completing different tasks (\"Examine\" and \"Clean & Place\") in Fig. 3. More failure case analyses are included in the supplementary materials.", + "bbox": [ + 89, + 488, + 483, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Exploration on Open-vocabulary Task", + "text_level": 1, + "bbox": [ + 89, + 635, + 419, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real-world tasks are more diverse and flexible than the predefined, limited tasks in ALFRED. To assess R2C's ability to handle open-vocabulary tasks, we conduct a mini experiment with 60 test trials generated randomly by GPT-4 across 3 room sizes (7x7, 5x9, 5x11), five room layouts, and four task types. 1) Specific Obj.: Move to a specific object (e.g., nearest chair). 2) Specific Loc.: Move to a specific location (e.g., center or corner). 3) Nearest Corner: Move to the nearest corner. 4) Center Between: Move to the center between two objects.", + "bbox": [ + 89, + 657, + 482, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Traditional closed-domain approaches struggle with these tasks, as they are limited to defined tasks in the training set. Meanwhile, high-level LLM planners face challenges in translating them into object-navigation plans. We test R2C with various settings: GPT-4 $(90^{\\circ})$ , GPT-4 $(45^{\\circ})$ which allow 45-degree rotation, and GPT-4o $(90^{\\circ})$ , which", + "bbox": [ + 89, + 810, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/afd5da4a74cbeb468c60dfefbb8411912df2c33513d2663961ec1c4d4f828cc7.jpg", + "table_caption": [ + "Table 4. SR (%) of R2C on open-vocabulary tasks." + ], + "table_footnote": [], + "table_body": "
MethodSAVN [43]S2P [4]R2C
SR (%)40.8646.1652.25
SPL (%)16.1528.0129.56
", + "bbox": [ + 568, + 89, + 851, + 140 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance of R2C on object navigation task.", + "bbox": [ + 542, + 142, + 874, + 156 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "uses visualized chessboards. Results are summarized in Tab. 4, and two task examples are visualized in Fig. 4.", + "bbox": [ + 511, + 169, + 903, + 198 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results demonstrate the potential of R2C in handling open-vocabulary tasks for real-world applications. GPT-4 $(45^{\\circ})$ outperforms the $90^{\\circ}$ -agent, thanks to more efficient diagonal movement, highlighting the expandability of R2C with different action spaces. Both GPT-4 $(90^{\\circ})$ and GPT-4 $(45^{\\circ})$ outperform GPT-4o, as feeding the chessboard directly to the VLM leads to poor spatial grounding and inaccurate path predictions. More results are available in the supplementary materials.", + "bbox": [ + 511, + 199, + 906, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Application in Real-world Scenarios", + "text_level": 1, + "bbox": [ + 511, + 345, + 826, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the real-world applicability of the R2C framework, we design three open-vocabulary tasks to test its performance using the LoCoBot robot in a set-up real-world experiment room. We evaluate R2C-GPT-4 in zero-shot setting. As shown in Fig. 5, the R2C framework, by enabling LLM to generate low-level actions, allows successful task completion in a totally different environment, showcasing its effectiveness and versatility in real-world scenarios. Detailed implementation information can be found in the supplementary materials.", + "bbox": [ + 511, + 368, + 906, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Evaluation on Navigation Task", + "text_level": 1, + "bbox": [ + 511, + 530, + 785, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further evaluate the model's generalization capability across tasks, we extend R2C-Mistral-7B model trained on ALFRED to the AI2THOR ObjectNav task [43] without additional fine-tuning. Results in Tab. 5 show that R2C significantly outperforms S2P [4], another LLM-based planner.", + "bbox": [ + 511, + 551, + 905, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 638, + 633, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce the Room to Chessboard (R2C) framework, which maps the complex room into a chessboard as a communication platform between the LLM and the robot, unlocking the LLM as low-level planner to directly guide the robot to adaptively finish the embodied tasks. To address the spatial reasoning tasks on chessboard, we design a CoT-D fine-tuning paradigm that enhances LLM's ability to make interpretable low-level decisions. Experiments show that R2C outperforms existing LLM-based high-level planners, even in zero-shot settings, and allows 7B models to surpass GPT-4. Furthermore, R2C enables LLMs to tackle open-vocabulary tasks where API-based frameworks fall short. However, R2C still faces challenges, such as handling very large scenes. Future work will focus on optimizing R2C for larger environments and exploring its potential for various open-vocabulary tasks.", + "bbox": [ + 511, + 657, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19463", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is partially supported by National Key R&D Program of China No. 2021ZD0111901, and Natural Science Foundation of China under contracts Nos. 62495082, U21B2025. Ziyi Bai, Hanxuan Li, and Bin Fu contributed equally to this work. Ziyi Bai led the implementation of the overall framework and the evaluation of the ALFRED benchmark and open-vocabulary tasks. Hanxuan Li proposed the R2C and CoT-D fine-tuning methods, validated their feasibility, and took the lead in the design, training, and acceleration of the LLM-based module. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.131, + 0.783, + 0.175 + ], + "angle": 0, + "content": "R2C: Mapping Room to Chessboard to Unlock LLM As Low-Level Action Planner" + }, + { + "type": "text", + "bbox": [ + 0.164, + 0.203, + 0.854, + 0.221 + ], + "angle": 0, + "content": "Ziyi Bai\\(^{1,2}\\), Hanxuan Li\\(^{1,2}\\), Bin Fu\\(^{1,2}\\), Chuyan Xiong\\(^{1,2}\\), Ruiping Wang\\(^{1,2}\\), Xilin Chen\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.222, + 0.79, + 0.257 + ], + "angle": 0, + "content": "1Key Laboratory of AI Safety of Chinese Academy of Sciences (CAS), Institute of Computing Technology, CAS, Beijing, 100190, China" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.257, + 0.785, + 0.275 + ], + "angle": 0, + "content": "\\(^{2}\\)University of Chinese Academy of Sciences, Beijing, 100049, China" + }, + { + "type": "list", + "bbox": [ + 0.232, + 0.222, + 0.79, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.278, + 0.911, + 0.293 + ], + "angle": 0, + "content": "{ziyi.bai,hanxuan.li，bin.fu，chuyan.xiong}@vip1.ict.ac.cn，{wangruiping，xlchen}@ict.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.327, + 0.327, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.36, + 0.486, + 0.829 + ], + "angle": 0, + "content": "This paper explores using large language models (LLMs) as low-level action planners for embodied tasks. While LLMs excel as the robot's \"brain\" for high-level planning, they face challenges in directly controlling the \"body\" by generating precise low-level actions. This limitation arises from LLMs' strength in high-level conceptual understanding but their inability to handle spatial perception effectively, restricting their potential in embodied tasks. To address this, we bridge the gap by enabling LLMs to not only comprehend complex instructions but also produce actionable, low-level plans. We introduce Room to Chessboard (R2C), a novel semantic representation that maps environmental states onto a grid-based chessboard, empowering LLMs to generate specific low-level coordinates and guide the robot in a manner akin to playing a game of chess. To further enhance decision-making, we propose the Chain-of-Thought Decision (CoT-D) paradigm, which improves LLMs' interpretability and context-awareness in spatial reasoning. By jointly training LLMs for high-level task decomposition and low-level action generation, we create a unified \"brain-body\" system capable of handling complex, free-form instructions while producing precise low-level actions, allowing the robot to flexibly control its movements and adapt to varying tasks. We validate R2C using both fine-tuned open-source LLMs and GPT-4, demonstrating effectiveness on the challenging ALFRED benchmark. Results show that with our R2C framework, LLMs can effectively act as low-level planners, generalizing across diverse settings and open-vocabulary robotic tasks. The code and demonstrations are available at: https://vipl-vsu.github.io/Room2Chessboard." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.844, + 0.222, + 0.859 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The pursuit of general embodied agents focuses on developing robust systems capable of understanding natural lan" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.328, + 0.907, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.538, + 0.907, + 0.582 + ], + "angle": 0, + "content": "Figure 1. Comparison of LLM as a high-level versus low-level planner for the task of \"heating eggs\". High-level planner provides subgoals while low-level planner directly provides exact path." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.596, + 0.907, + 0.687 + ], + "angle": 0, + "content": "guage commands to meet diverse human requirements. Traditional robotic learning methods have succeeded in executing complex tasks but struggle to generalize to new environments or tasks due to their reliance on task-specific training and rigid planning. Recently, Large Language Models (LLMs) have emerged as promising embodied agents." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Several pioneering works [8, 13, 14, 37] have explored LLMs as the \"brain\" of embodied systems, leveraging their strong generalization to manage diverse tasks effectively. However, most LLM-based agents [1, 13, 37] focus mainly on high-level task planning, decomposing tasks like \"bring me an egg\" into subgoals (e.g., \"go to egg\") \\(\\rightarrow\\) \"take it back\"). The execution of these subgoals is still delegated to low-level policy networks [5, 16, 18] or deterministic algorithms [7, 31]. While LLMs have extensive world knowledge, they lack spatial awareness of real environments, making it difficult to predict if these plans can be grounded to the physical world accurately. This often leads to frequent re-planning [1, 37], reducing efficiency and success rates, thereby limiting the potential of LLMs as embodied" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19456" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.314, + 0.107 + ], + "angle": 0, + "content": "agents in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.109, + 0.484, + 0.29 + ], + "angle": 0, + "content": "The primary barrier [37, 44] to unlocking the full potential of LLMs lies in the ineffective communication between the LLM (the \"brain\") and the robot (the \"body\"). The robot struggles to convey the updated spatial information about environment, leaving the LLM without a basis for decision-making. As a result, the LLM can only generate high-level subgoal plans, while controlling the robot's movements relies on external navigation APIs. To overcome this challenge, a \"common language\" is needed — a platform that delivers sufficient environmental states, empowering the LLM to generate precise low-level action plans and directly control the robot." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.292, + 0.485, + 0.61 + ], + "angle": 0, + "content": "We propose a novel Room to Chessboard (R2C) framework, which realizes a unified \"brain-body\" system that integrates high-level task understanding with direct low-level action decisions. As shown in Fig. 1, R2C utilizes a grid-based chessboard as an effective communication platform between the robot and the LLM. On one side, the robot can continuously map its observations onto the chessboard, which contains essential information while avoiding information overload. On the other side, the LLM is unlocked as a low-level action planner, directly guiding the robot \"moves\" on the chessboard to complete the task. Specifically, the LLM decomposes long-horizon tasks into sub-goals, which are then addressed through precise low-level planning. At this stage, an Environment Filter maintains task-aware environmental states on a compact chessboard. Since the chessboard grid size is calibrated to match the robot's step length, the LLM can perform low-level planning on the chessboard by predicting the robot's next position. Additionally, the Chain-of-Thought Decision (CoT-D) paradigm is proposed to enhance LLM's spatial reasoning and decision-making capabilities." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.484, + 0.839 + ], + "angle": 0, + "content": "To construct a chessboard representation that fully captures the complex environmental states while remaining manageable for LLMs, we introduce an Environment Filter to abstract the environment states. Initially, new observations are converted into a detailed 2D semantic map. However, such a high-dimensional representation can overwhelm LLMs. To mitigate this, we apply kernel filters to down-sample the map, then flatten it into a 2D chessboard, organized according to the priority of the current subgoal. The object occupancy on the chessboard is further abstracted into object coordinate sets. This representation strikes a balance between semantic richness and simplicity, effectively capturing critical information such as object semantics, object size and scene layout, while enabling efficient low-level action planning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In R2C framework, LLM needs robust long-context understanding capabilities to comprehend the object coordinate sets and spatial reasoning abilities for low-level planning. Despite advancements in LLM capabilities, achiev-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.242 + ], + "angle": 0, + "content": "ing this remains a huge challenge. To enhance LLM's low-level action planning abilities, we design a fine-tuning paradigm and formalize the CoT-D fine-tuning task. CoT-D comprises four subtasks: key information extraction, direction determination, target prediction, and selection analysis. LLM is required to link these subtasks together into a coherent logical chain [42]. These tasks can not only strengthen the long-context understanding of LLM but also enhance its spatial reasoning to generate more interpretable low-level plans." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.907, + 0.41 + ], + "angle": 0, + "content": "We evaluate our R2C framework on the challenging ALFRED [34] benchmark, which features a diverse set of long-horizon tasks. We test both GPT and fine-tuned open-source LLMs using our novel CoT-D. R2C achieves state-of-the-art (SoTA) performance among LLM-based methods. Additionally, LLMs trained with CoT-D exhibit strong spatial reasoning and action planning capabilities. Our LLM-based low-level action planner also demonstrates impressive generalization across open-vocabulary tasks and real-world deployment, highlighting the versatility and robustness of the R2C framework in various application scenarios." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.41, + 0.875, + 0.425 + ], + "angle": 0, + "content": "The main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.426, + 0.905, + 0.485 + ], + "angle": 0, + "content": "- We propose Room to Chessboard (R2C), a unified \"brain-body\" system that enables LLMs to simultaneously understand free-form instructions and generate specific, environment-aware low-level actions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.486, + 0.905, + 0.547 + ], + "angle": 0, + "content": "- We develop the Chain-of-Thought Decision (CoT-D) fine-tuning mechanism, which enhances the spatial reasoning capabilities of LLMs, leading to a significant improvement of \\(11.37\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.547, + 0.905, + 0.606 + ], + "angle": 0, + "content": "- We achieve SoTA performance among LLM-based methods using limited robotic data and demonstrate strong generalization to unseen environments, including real-world scenarios." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.426, + 0.905, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.61, + 0.664, + 0.626 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.636, + 0.755, + 0.652 + ], + "angle": 0, + "content": "2.1. Task Planning In Robotics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.87 + ], + "angle": 0, + "content": "Task planning in robotics [28, 34] involves generating a sequence of actions for robots to execute in the environments to achieve a specific goal. In real-world applications, the instructions are typically complex, resulting in long-horizon tasks that encompass a variety of embodied activities, such as navigation [2, 9] and object interaction [20]. Early approaches [27, 38] simply integrate visual and textual inputs to generate contextually appropriate action sequences. Besides, one widely used approach is reinforcement learning (RL) [11, 24, 39, 41]. Although the above methods have good performance on some specific tasks, they are trained end-to-end using expert trajectories and low-level instructions, resulting in poor generalization to unknown environments [19, 25, 37]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Therefore, some approaches [3, 15, 19, 23, 25] suggest explicitly breaking down the complex task into mul" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19457" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.226 + ], + "angle": 0, + "content": "tiple functional modules. FILM [25] proposes a framework with four submodules including language processing, semantic mapping, semantic search and deterministic policy. ThinkBot [23] presents an additional object localizer based on multimodal transformers to predict the position of target objects. Though they provide more interpretable frameworks, each of their modules need to be fine-tuned with corresponding data, which make them struggle in adapting to novel robotic tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.235, + 0.327, + 0.251 + ], + "angle": 0, + "content": "2.2. Task planning with LLMs" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.257, + 0.483, + 0.378 + ], + "angle": 0, + "content": "To address the above generalization challenges, incorporating Large Language Models (LLMs) into robotic task planning presents a promising pathway [1, 10, 13, 14]. Early attempts [13] adopt LLMs to help with free-form human instruction following by decomposing the task into reasonable subgoals. However, due to LLM's inability to perceive the complex physical world, the generated goals often fail to execute in the environments [1]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.379, + 0.483, + 0.619 + ], + "angle": 0, + "content": "Recent research has delved into integrating environmental states to ground the output of the LLM-based planner. LM-Nav [32] leverages a pre-trained Vision-Language Model (VLM) to generate captions of viewpoints and ground them with landmarks to enhance the executability of navigation plan. Additionally, structured representations such as object-centric scene graphs and topology graphs [6, 10, 29, 46] are commonly employed to improve the LLM's comprehension of relationships among objects and the overall room layout within the environments. Beyond directly translating visual feedback into inputs for LLMs, Say-Can [1] trained a vision-based value function to judge the affordance of the LLM's plan in the environments. Furthermore, some other works [21, 35] involve text-form Planning Domain Definition Language (PDDL) descriptions of scenes, which are easier for LLMs to handle." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.62, + 0.483, + 0.785 + ], + "angle": 0, + "content": "Although the above works address some cases where LLM-generated plans are not executable, they all use LLMs solely as high-level planners. Most works still rely on low-level controllers to translate these high-level plans into executable action sequences. Some recent works [12, 33, 47] train end-to-end models to directly map robot observations to actions on large amounts of robotic trajectory data to achieve generalization. Unlike these approaches, we unlock LLMs to function as both high-level and low-level planners by introducing an interpretable textual representation of the environment." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.791, + 0.19, + 0.807 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.483, + 0.9 + ], + "angle": 0, + "content": "We aim to unlock LLMs as low-level action planners that can directly guide robots to solve long-horizon tasks. We first introduce our newly designed Room to Chessboard framework in Sec. 3.1, and then illustrate the Chain-of-Thought Decision (CoT-D) fine-tuning task formulation in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.712, + 0.106 + ], + "angle": 0, + "content": "3.1. Room to Chessboard" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.114, + 0.907, + 0.31 + ], + "angle": 0, + "content": "We introduce the Room to Chessboard (R2C) framework (Fig. 2), which enables LLMs to perform both High-Level Planning (HLP) and Low-Level Planning (LLP) within a unified framework. First, the LLM conducts HLP, processing step-by-step instructions into a sequence of subgoals. Each subgoal is then handled at the LLP stage. At each timestep, an egocentric RGB-D image is processed by an Environment Filter to generate a chessboard abstraction. The updated chessboard is subsequently converted into object occupancy coordinates, which are fed to the LLM. Acting like a chess player, the LLM predicts the robot's next move on the chessboard, guiding it to navigate or interact with the environment." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.32, + 0.753, + 0.336 + ], + "angle": 0, + "content": "3.1.1. High-Level Planning (HLP)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.907, + 0.476 + ], + "angle": 0, + "content": "At the beginning of an episode, the LLM processes the natural language instruction \\(L\\) into a sequence of high-level subgoals, denoted as \\(\\mathcal{G} = [G_1, G_2, \\dots, G_K]\\). Each subgoal \\(G_k\\) is a tuple (Action, Object), where Action \\(\\in A_H\\) is a primitive action chosen from the set of navigation action (GOTO) or interaction actions (e.g., PICKUP, PUT). The Object refers to the semantic class of the interacted object (e.g., SAFE, CD). These subgoals are executed sequentially during the LLP stage." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.487, + 0.694, + 0.501 + ], + "angle": 0, + "content": "3.1.2. Environment Filter" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.507, + 0.907, + 0.657 + ], + "angle": 0, + "content": "Since the environment is partially observed, the agent has never explored the entire environment and must construct a map based on its own observations online. At each timestep, the Environment Filter \\( F(o_{t}, G_{k}) \\) takes the new observation \\( o_{t} \\) as input to filter out the goal-related environment information conditioned on the current subgoal \\( G_{k} \\). This filtered information is then added to a dynamically updated semantic chessboard \\( \\mathcal{B} \\) to represent the current state of the environment. The computation of \\( F \\) involves two parts: semantic mapping and chessboard building." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.854 + ], + "angle": 0, + "content": "Semantic mapping. We first build an online semantic map of the room, inspired by prior work [25]. At each timestep \\( t \\), the agent receives an egocentric RGB-D observation \\( o_{t} = I_{rgb}, I_{dpt} \\). An off-the-shelf instance segmentation model processes \\( I_{rgb} \\), and, combined with \\( I_{dpt} \\), the observation is converted into a point cloud, with each point labeled with predicted semantic categories. This 3D point cloud is then voxelized and flattened along the Z-axis to form the 2D semantic map \\( \\mathcal{M} \\). The resulting semantic map is represented as \\( (C + 2) \\times M \\times M \\) binary grid, where \\( C \\) is the number of object categories, and two additional channels denote obstacles and explored areas in each cell. Here, \\( M \\) represents the map resolution." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Chessboard building. We further abstract the semantic map into a compact chessboard, i.e., map to chessboard \\((M2C)\\). The \\(M2C\\) function consists of two cascaded kernels." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19458" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.904, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.389, + 0.908, + 0.445 + ], + "angle": 0, + "content": "Figure 2. Overview of R2C framework: The LLM begins by generating high-level subgoals for the task. For each subgoal, the environment filter translates RGB-D observations into an updated grid-based chessboard representation of the environments. The LLM then uses chain-of-thought analysis to integrate this chessboard representation along with game rules, determining the next optimal position, which is finally converted into executable robot actions." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.452, + 0.482, + 0.588 + ], + "angle": 0, + "content": "The first kernel is a dilation kernel \\(\\mathcal{K}_{dila}\\), designed to prevent collisions between the agent and obstacles. Similar to the dilation algorithm in image processing [30], it expands all occupied pixels of obstacles (including objects) outward by \\(\\delta\\) in the map. The second kernel is a max pooling kernel \\(\\mathcal{K}_{pool}\\), which performs max pooling on the map. Then, the map is down-sampled from size \\(M\\) to size \\(W\\), where \\(W = \\left\\lceil \\frac{M}{\\omega} \\right\\rceil\\) and \\(\\omega\\) is the grid size, calibrated to match the length of the agent's step." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.589, + 0.483, + 0.754 + ], + "angle": 0, + "content": "Next, we aggregate this map with multiple object layers into a unified single-layer chessboard. To address the many-to-one projection problem, where overlapping objects might appear in the same grid, e.g., \"apples on a table\", we introduce a Goal-aware Aggregate function \\(\\mathcal{A}(\\cdot)\\). This function prioritizes both the relevance to the current subgoal, i.e., the target object Object in current subgoal \\(G_{k}\\), and the size of the object. The most relevant and smallest objects are placed at the top layer, and then we merge object layers from bottom to top to produce the final chessboard. The overall formulation of the \\(M2C\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.759, + 0.483, + 0.782 + ], + "angle": 0, + "content": "\\[\nM 2 C = \\mathcal {A} \\circ \\mathcal {K} _ {d i l a} \\circ \\mathcal {K} _ {p o o l} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.78, + 0.334, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} = M 2 C (\\mathcal {M}, G _ {k}).\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.806, + 0.325, + 0.822 + ], + "angle": 0, + "content": "3.1.3. Low-Level Planning (LLP)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The chessboard filtered out from the Environment Filter provides compact yet sufficient environmental state information for LLM. We then simulate a \"chess game\" between the LLM and the robot to perform low-level planning. The LLP task is formulated as a single-step generation task for" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.452, + 0.907, + 0.573 + ], + "angle": 0, + "content": "the LLM. As shown in Fig. 2, various state information is collected, including current subgoal \\( G_{k} \\), chessboard state \\( \\mathcal{U} \\), action history \\( \\mathcal{Q} \\) and game rules \\( R \\). Our prompt system \\( \\mathcal{P} \\) organizes such data and feeds them into the LLM to generate the next position prediction \\( w \\). Note that LLP is invoked only for navigation subgoals, as interaction subgoals in ALFRED can be handled by predefined low-level actions once the agent reaches the visible range of the target object." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.577, + 0.906, + 0.711 + ], + "angle": 0, + "content": "Chessboard state. To translate the chessboard state for the LLM, we convert it into textual object occupancy coordinate sets. The chessboard coordinate system originates from the upper left corner, with the X-axis pointing down and the Y-axis to the right. For each object on the chessboard, we gather a set of occupancy coordinates \\(\\mathcal{U}_t^c = \\{x_i,y_i\\}\\), where \\(c\\in [1,C + 2]\\) and \\(x_{i},y_{i}\\in [1,W]\\). The initial agent position \\(w_{0}\\) is predefined in the benchmark." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.717, + 0.906, + 0.837 + ], + "angle": 0, + "content": "Game rules. To assist the LLM in planning, we define key game rules \\( R \\): 1) Basic inputs, including chessboard dimensions \\( W \\), maximum steps \\( T \\), and maximum errors \\( E \\); 2) Action space, simplified to adjacent grids in four directions (up, down, left, right), i.e., the robot is only allowed to move 1 block at a time, due to the limited spatial reasoning ability of current LLMs; 3) Collision rules, where grids occupied by objects or obstacles are considered illegal moves." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Action history. We maintain a queue \\(\\mathcal{Q}\\) with a fixed length \\(\\tau\\) to store recent successful movement coordinates, providing the LLM with contextual information about previous actions. At each step \\(t\\), the prompt system combines" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19459" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.137 + ], + "angle": 0, + "content": "all such information and feeds them to the LLM, which simulates a chess player to decide the next move. The LLP models a policy \\(\\pi\\), defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.14, + 0.483, + 0.157 + ], + "angle": 0, + "content": "\\[\nu _ {t} = \\pi (\\mathcal {P} (G _ {k}, \\mathcal {U} _ {t}, R, \\mathcal {Q} _ {t})), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.164, + 0.484, + 0.24 + ], + "angle": 0, + "content": "where \\( u_{t} = (x_{t},y_{t}) \\) is the predicted next position on the chessboard. According to the defined action space, the available next positions are restricted to the adjacent grids in four directions \\( x_{t + 1}\\in [x_t - 1,x_t + 1] \\) and \\( y_{t + 1}\\in [y_t - 1,y_t + 1] \\), with \\( x_{t + 1},y_{t + 1}\\in [1,W] \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.24, + 0.484, + 0.466 + ], + "angle": 0, + "content": "Since the chessboard grid size is calibrated to match the robot's step length, the predicted adjacency target position \\( u_{t} \\) can be directly converted to a sequence of executable low-level actions \\( \\mathbf{a} = \\{a_{i}\\} \\), \\( a_{i} \\in \\mathbf{A}_{\\text{nav}} \\) in the real-world environments. For example, in the ALFRED benchmark, \\( \\mathbf{A}_{\\text{nav}} \\) includes (MoveForward, 0.25m), (TurnLeft, 90°) and, (TurnRight, 90°). Based on the predicted target position, the movement in any of the four directions can be converted into the corresponding action sequence (e.g., TurnLeft and MoveForward to move to the left adjacent grid). Additionally, if the output \\( w_{t} \\) is within the visible range of the target object Object in the current subgoal, the system moves on to the next subgoal. See more details of the R2C framework in the pseudocode provided in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.477, + 0.442, + 0.493 + ], + "angle": 0, + "content": "3.2. Chain-of-Thought Fine-tuning Paradigm" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.499, + 0.484, + 0.635 + ], + "angle": 0, + "content": "To improve the decision-making capabilities of LLMs in our chess game, we introduce an interpretable fine-tuning paradigm with two core features: 1) simultaneous training of high-level task decomposition and low-level Chain of Thought Decision (CoT-D) tasks, enabling the integration of High-Level Planning (HLP) and Low-Level Planning (LLP) within a single LLM, and 2) structuring the CoT-D process into four distinct parts to enhance the LLM's comprehension of game rules and spatial reasoning." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.643, + 0.36, + 0.658 + ], + "angle": 0, + "content": "3.2.1. Joint Training of HLP and LLP" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.662, + 0.484, + 0.782 + ], + "angle": 0, + "content": "Long-horizon planning often involves compositional tasks that require hierarchical planning capabilities. Therefore, rather than only exploiting the LLM as a high-level planner or training an end-to-end low-level action generation model, we jointly train the model on both HLP and LLP tasks simultaneously. Given the data imbalance between HLP and LLP, we apply data balancing techniques to ensure the model effectively learns skills at both levels." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.791, + 0.387, + 0.807 + ], + "angle": 0, + "content": "3.2.2. Chain of Thought Decision (CoT-D)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "LLM should thoroughly comprehend our chessboard coordinate system and predict the next position based on the semantic information of the chessboard and its inherent common sense. For the given prompt \\(\\mathcal{P}\\) with chessboard state \\(\\mathcal{U}\\), the LLM needs to generate answer sentence \\(S\\) (including next position \\(w\\)) with probabilistic language model \\(p_{LM}\\). If" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.12 + ], + "angle": 0, + "content": "LLM is asked to directly provide coordinates, this process can be formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.116, + 0.905, + 0.158 + ], + "angle": 0, + "content": "\\[\np (\\mathcal {S} \\mid \\mathcal {P}) = \\prod_ {i = 1} ^ {| \\mathcal {S} |} p _ {L M} \\left(s _ {i} \\mid \\mathcal {P}, s _ {< i}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.165, + 0.907, + 0.356 + ], + "angle": 0, + "content": "However, such a complex task is much more challenging than the task decomposition. This requires the LLMs have strong capabilities in long-text comprehension and spatial reasoning. However, the current models are not particularly skilled in these abilities. Consequently, we design the Chain of Thought Decision (CoT-D) tasks to strengthen LLM's rationale \\(\\mathcal{R}\\) in these aspects. The task consists of four subtasks, requiring LLMs to output the result of key information extraction \\(\\mathcal{R}_E\\), direction judgment \\(\\mathcal{R}_D\\), target prediction \\(\\mathcal{R}_T\\), and selection analysis \\(\\mathcal{R}_S\\), respectively. We link these sub-tasks sequentially in natural language to construct a coherent logical chain. The entire task can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.356, + 0.905, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\cdot p (\\mathcal {S} \\mid \\mathcal {P}) = p (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) \\cdot p (\\mathcal {R} \\mid \\mathcal {P}) \\\\ p (\\mathcal {R} \\mid \\mathcal {P}) = \\prod_ {r _ {i} \\in \\left\\{\\mathcal {R} _ {E}, \\mathcal {R} _ {D}, \\mathcal {R} _ {T}, \\mathcal {R} _ {S} \\right\\}} p _ {L M} \\left(r _ {i} \\mid \\mathcal {P}, r _ {< i}\\right) \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.412, + 0.805, + 0.456 + ], + "angle": 0, + "content": "\\[\np (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) = \\prod_ {j = 1} ^ {| \\mathcal {S} |} p _ {L M} (s _ {i} \\mid \\mathcal {P}, \\mathcal {R}, s _ {< j})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.906, + 0.508 + ], + "angle": 0, + "content": "The specific content of the four sub-tasks will be introduced below. Examples can be found in Fig. 2, with details available in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.906, + 0.719 + ], + "angle": 0, + "content": "Key information extraction. Due to the intricate information contained within the chessboard, when textualized, it becomes a lengthy document with substantial information. Considering that LLM often encounters issues such as context loss when comprehending long texts, this task is designed to train LLM in processing task-related long texts and extracting key information. This task requires LLM to extract relevant information about the current coordinates and target objects based on the chessboard information inputs. The form used in data annotation is as follows: The current position of the agent is [COORDS], and the target is [OBJECT NAME], which is located at [COORDS SET]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Direction judgment. The conversion from a chessboard grid image to text is based on a two-dimensional Cartesian coordinate system, and all spatial relationship understanding relies on a good coordinate system understanding. Despite providing clear instructions to establish the coordinate system using prompts like Establish a coordinate system with the top-left grid as (1,1), experiments have shown that the LLM still frequently misunderstands the setup. This could be attributed to the length of the text and the scarcity of spatial reasoning tasks incorporated during the pre-training of contemporary LLM. To ensure LLM's accurate comprehension" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19460" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.101, + 0.09, + 0.585, + 0.262 + ], + "angle": 0, + "content": "
MethodTraining ModeVal SeenVal UnseenΔ SR ↑Δ GC ↑
SR ↑GC ↑SR ↑GC ↑
Specialists, only for ALFRED tasks
E.T. [27]from scratch46.5952.927.3220.87-39.27-32.05
HiTUT [45]from scratch25.2434.8512.4423.71-12.80-11.14
M-TRACK [36]from scratch26.7033.2117.2928.98-9.41-4.23
FILM [25]from scratch24.6337.2020.1032.45-4.53-4.75
LEBP [22]from scratch27.6335.7622.3629.58-5.27-6.18
Generalists, based on LLMs
SayCan [1]few-shot12.3024.529.8822.54-2.42-1.98
LLM-P (GPT) [37]1few-shot16.4530.1115.3629.88-1.09-0.23
R2C-GPT-4 (ours)zero-shot20.0028.4624.0028.24+4.00-0.22
R2C-Llama-7B (ours)fine-tune20.8329.6018.9929.69-1.84+0.09
R2C-Mistral-7B (ours)fine-tune22.3132.4022.3531.97+0.04-0.43
" + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.268, + 0.584, + 0.311 + ], + "angle": 0, + "content": "Table 1. Main results on the ALFRED benchmark. SR and GC are short for success rate and goal-conditioned success rate. \\(\\Delta\\) SR and \\(\\Delta\\) GC represent the performance drops in generalizing from the seen to the unseen environments." + }, + { + "type": "table", + "bbox": [ + 0.61, + 0.089, + 0.885, + 0.219 + ], + "angle": 0, + "content": "
Task TypeVal SeenVal Unseen
SRGCSRGC
Overall48.1855.1353.3358.18
Examine75.8679.3183.3387.96
Pick & Place69.5769.5763.3363.33
Stack & Place29.0337.0045.4546.46
Clean & Place63.8973.8738.8950.45
Cool & Place36.8449.6061.1169.23
Heat & Place23.5341.3828.5741.13
Pick 2 & Place33.3354.4137.5053.70
" + }, + { + "type": "table_caption", + "bbox": [ + 0.597, + 0.227, + 0.896, + 0.31 + ], + "angle": 0, + "content": "Table 2. Performance of R2C on different tasks. The R2C model excels in \"Examine\" tasks, but faces challenges in complex \"Heat & Place\" tasks, where the \"HeatObject\" subgoal alone involves seven interactive steps, increasing the risk of error accumulation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.323, + 0.482, + 0.399 + ], + "angle": 0, + "content": "of the chessboard coordinate system, this task requires LLM to judge the direction between the target and the current coordinates. The format employed in data annotation is as follows: the target is at..., which is on the [DIRECTION] of the agent." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.4, + 0.483, + 0.567 + ], + "angle": 0, + "content": "Target prediction. The locations where different categories of objects appear often have priors. For example, sofas are likely to appear opposite the television. Therefore, we aim to enable LLM to develop the capability of predicting target locations. This can minimize the ineffective or inefficient exploration process for the robot to find target objects, thereby improving the efficiency of the system in accomplishing embodied tasks. The expression utilized in data annotation is: Based on the chessboard analysis, the target is likely located near [COORDS]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.568, + 0.483, + 0.763 + ], + "angle": 0, + "content": "Selection analysis. Based on the above comprehension, we require the LLM to further analyze all potential next positions according to the chessboard rules. During this analysis, the LLM evaluates each possible move, providing a rationale for each choice. The specific format used in the annotation is: [COORDS]: This position is on the [DIRECTION] of the agent, [Reason]. The [Reason] component is generated by GPT-4 based on the agent's current state and the relationship between the chosen position and the correct orientation. For instance: Objects in this direction have already been discovered; we should head to areas that have not been explored." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.811 + ], + "angle": 0, + "content": "These four sub-tasks comprehensively enhance the understanding of chessboard and spatial reasoning ability of the LLMs from different perspectives." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.828, + 0.208, + 0.843 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.284, + 0.864 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Benchmark. We evaluate our method on the challenging ALFRED [34] benchmark, which features long-horizon" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.32, + 0.886, + 0.426 + ], + "angle": 0, + "content": "
MethodVal SeenVal Unseen
SRGCSRGC
Base Model (R2C-Mistral-7B)22.3132.4022.3531.97
+ GT Seg.37.9245.8335.2443.88
+ GT Seg., GT Goal48.1855.1353.3358.18
+ GT Seg., GT Goal, - SA45.9751.7547.4553.03
+ GT Seg., GT Goal, - CoT41.2249.3541.9647.88
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.427, + 0.906, + 0.484 + ], + "angle": 0, + "content": "Table 3. Ablation of R2C. \"GT Seg.\" represents the model using ground-truth segmentation. \"GT Goal\" represents using ground-truth subgoals. \"- SA\" is the model without Selection Analysis part of CoT. \"- CoT\" is the model without all CoT tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.905, + 0.578 + ], + "angle": 0, + "content": "tasks (7 types in total) involving both navigation and interaction across 207 unique environments and 115 different object types. In our experiments, we adhere to the benchmark's settings, including low-level action space, maximum agent steps, and failure limits." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.906, + 0.701 + ], + "angle": 0, + "content": "Chessboard settings. The physical room size \\( D \\) is set to \\( 16m \\), which is the approximate maximum room size, and the grid size \\( \\omega \\) corresponds to the agent's step length, \\( 0.25m \\). Thus, the size of the semantic map and the chessboard is \\( M = 320 \\) and \\( W = 64 \\) separately. However, to represent more complex environments, one can choose a more fine-grained chessboard. We demonstrate this through a simple experiment in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.701, + 0.906, + 0.839 + ], + "angle": 0, + "content": "Model settings. For the zero-shot R2C, we use the public GPT-4-turbo API [26] without any in-context examples. Considering the testing cost, we randomly sample a subset of size 100 covering all 7 types of tasks strictly according to the task distribution of ALFRED. We collected a total of 264,915 data samples for fine-tuning, including 70,000 samples for the Task Decomposition tasks and 194,915 samples for the CoT-D tasks. All data collection was based solely on the training set of ALFRED. During training," + }, + { + "type": "page_footnote", + "bbox": [ + 0.512, + 0.851, + 0.905, + 0.901 + ], + "angle": 0, + "content": "For a fair comparison, we test the performance of the GPT-4 version of LLM-P on the same selected subset as ours, achieving an SR of \\(16.21\\%\\) on seen scenes. Since this work solely employs LLMs for task decomposition, the performance is only slightly different when compared to using GPT-3." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.214, + 0.089, + 0.784, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.336, + 0.907, + 0.365 + ], + "angle": 0, + "content": "Figure 3. Case study of R2C with Mistral model: The model completes an \"Examine\" task in 31 steps (top) but fails to locate the small target object, a bowl, during a \"Clean & Place\" task in a more complex environment (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.378, + 0.484, + 0.468 + ], + "angle": 0, + "content": "we conduct full-parameter fine-tuning on both the Mistral-7B-Instruct-v0.2 model [17] and the Llama-7B-Chat model [40] using all the data. Both models were trained for only one epoch. We conduct all fine-tuning experiments using 4 NVIDIA H100 GPUs, and all evaluations are performed on 4 NVIDIA A40 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.482, + 0.231, + 0.496 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.505, + 0.484, + 0.609 + ], + "angle": 0, + "content": "Tab. 1 presents the evaluation results on the validation set of ALFRED. We compare our R2C framework with both traditional robotic learning methods (specialists) and LLM-based approaches (generalists). R2C achieves state-of-the-art performance among LLM-based methods, with the Mistral-7B excelling in seen environments and GPT-4 in unseen environments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.484, + 0.732 + ], + "angle": 0, + "content": "Compared to SayCan [1] and LLM-P [37], which use LLMs only for high-level planning, R2C integrates high-level and low-level planning, offering a more efficient, end-to-end solution. LLM-P requires 100 instruction-plan pairs for training, while R2C operates in a zero-shot setting without examples. Our CoT-D paradigm enables GPT to analyze the chessboard state comprehensively, improving decision interpretability and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.87 + ], + "angle": 0, + "content": "R2C fine-tuned on open-sourced LLMs achieves competitive results, with \\(2.31\\%\\) improvement in the seen split and \\(1.65\\%\\) drop in the unseen split compared to R2C-GPT-4. This highlights GPT-4's superior generalization to unseen environments. However, with our carefully designed fine-tuning tasks, R2C implemented on much smaller models like LLaMA and Mistral, can still deliver performance comparable to GPT-4. This demonstrates the effectiveness and efficiency of our fine-tuning approach." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Finally, R2C fine-tuned on collected data performs comparably to specialist models like FILM [25] and LEBP [22]." + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.375, + 0.85, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.492, + 0.881, + 0.506 + ], + "angle": 0, + "content": "Figure 4. Cases of R2C-GPT-4 on open-vocabulary tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.907, + 0.584 + ], + "angle": 0, + "content": "Although these specialized models excel in seen scenes, they struggle in unseen environments due to overfitting. In contrast, R2C and other LLM-based methods demonstrate stronger generalization across both seen and unseen environments." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.596, + 0.667, + 0.611 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.765 + ], + "angle": 0, + "content": "We perform an ablation study to analyze the impact of different R2C modules. As shown in Tab. 3, using ground truth segmentation (GT Seg.) significantly improves performance, highlighting segmentation as a bottleneck, especially in simulation environments. Using ground truth sub-goals (GT Goal) also boosts SR, revealing the impact of ambiguity in natural language instructions. Annotator confusion between categories like desk lamps and floor lamps can hinder task decomposition, though LLMs' strong generalization helps mitigate this." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Removing the CoT-D framework, i.e., forcing the model to directly output position coordinates without rationale, results in a significant performance drop, especially in unseen scenes. This highlights the importance of fine-tuning with CoT-D for better spatial reasoning. Ablating individual subtasks is challenging due to their interdependence. Here, we ablate removing the Selection Analysis part (- SA), where decisions are made without analyzing options and it causes a noticeable performance decline." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19462" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.091, + 0.295, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.092, + 0.49, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.195, + 0.295, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.195, + 0.49, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.301, + 0.486, + 0.358 + ], + "angle": 0, + "content": "Figure 5. Visual results of R2C in real-world scenarios. Three tasks are tested in a real-world environment, with the corresponding instructions, third-person trajectories, first-person images, and chessboard visualizations shown for each task." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.367, + 0.49, + 0.435 + ], + "angle": 0, + "content": "
TaskSpecific Obj.Specific Loc.Nearest CornerCenter BetweenOverall
GPT-4 (90°)66.773.353.380.068.3
GPT-4 (45°)73.373.373.360.070.0
GPT-4o (90°)40.053.333.346.743.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.136, + 0.438, + 0.438, + 0.452 + ], + "angle": 0, + "content": "Table 4. SR (%) of R2C on open-vocabulary tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.467, + 0.365, + 0.483 + ], + "angle": 0, + "content": "4.4. Evaluation Across Tasks Types" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.626 + ], + "angle": 0, + "content": "We analyze R2C's performance across task types using GT Segmentation and GT Goal settings, with task-specific results shown in Tab. 2. R2C shows SR drops on more complex long-horizon tasks, such as \"Heat & Place,\" with average GT step lengths of 63, compared to shorter ones (e.g., Examine: 37). We provide a visualization of two case studies of R2C completing different tasks (\"Examine\" and \"Clean & Place\") in Fig. 3. More failure case analyses are included in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.636, + 0.421, + 0.653 + ], + "angle": 0, + "content": "4.5. Exploration on Open-vocabulary Task" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Real-world tasks are more diverse and flexible than the predefined, limited tasks in ALFRED. To assess R2C's ability to handle open-vocabulary tasks, we conduct a mini experiment with 60 test trials generated randomly by GPT-4 across 3 room sizes (7x7, 5x9, 5x11), five room layouts, and four task types. 1) Specific Obj.: Move to a specific object (e.g., nearest chair). 2) Specific Loc.: Move to a specific location (e.g., center or corner). 3) Nearest Corner: Move to the nearest corner. 4) Center Between: Move to the center between two objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Traditional closed-domain approaches struggle with these tasks, as they are limited to defined tasks in the training set. Meanwhile, high-level LLM planners face challenges in translating them into object-navigation plans. We test R2C with various settings: GPT-4 \\((90^{\\circ})\\), GPT-4 \\((45^{\\circ})\\) which allow 45-degree rotation, and GPT-4o \\((90^{\\circ})\\), which" + }, + { + "type": "table", + "bbox": [ + 0.57, + 0.09, + 0.852, + 0.141 + ], + "angle": 0, + "content": "
MethodSAVN [43]S2P [4]R2C
SR (%)40.8646.1652.25
SPL (%)16.1528.0129.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.544, + 0.143, + 0.875, + 0.157 + ], + "angle": 0, + "content": "Table 5. Performance of R2C on object navigation task." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.17, + 0.905, + 0.199 + ], + "angle": 0, + "content": "uses visualized chessboards. Results are summarized in Tab. 4, and two task examples are visualized in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.2, + 0.907, + 0.336 + ], + "angle": 0, + "content": "The results demonstrate the potential of R2C in handling open-vocabulary tasks for real-world applications. GPT-4 \\((45^{\\circ})\\) outperforms the \\(90^{\\circ}\\)-agent, thanks to more efficient diagonal movement, highlighting the expandability of R2C with different action spaces. Both GPT-4 \\((90^{\\circ})\\) and GPT-4 \\((45^{\\circ})\\) outperform GPT-4o, as feeding the chessboard directly to the VLM leads to poor spatial grounding and inaccurate path predictions. More results are available in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.347, + 0.828, + 0.362 + ], + "angle": 0, + "content": "4.6. Application in Real-world Scenarios" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.369, + 0.907, + 0.52 + ], + "angle": 0, + "content": "To evaluate the real-world applicability of the R2C framework, we design three open-vocabulary tasks to test its performance using the LoCoBot robot in a set-up real-world experiment room. We evaluate R2C-GPT-4 in zero-shot setting. As shown in Fig. 5, the R2C framework, by enabling LLM to generate low-level actions, allows successful task completion in a totally different environment, showcasing its effectiveness and versatility in real-world scenarios. Detailed implementation information can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.531, + 0.787, + 0.547 + ], + "angle": 0, + "content": "4.7. Evaluation on Navigation Task" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.63 + ], + "angle": 0, + "content": "To further evaluate the model's generalization capability across tasks, we extend R2C-Mistral-7B model trained on ALFRED to the AI2THOR ObjectNav task [43] without additional fine-tuning. Results in Tab. 5 show that R2C significantly outperforms S2P [4], another LLM-based planner." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.639, + 0.634, + 0.654 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We introduce the Room to Chessboard (R2C) framework, which maps the complex room into a chessboard as a communication platform between the LLM and the robot, unlocking the LLM as low-level planner to directly guide the robot to adaptively finish the embodied tasks. To address the spatial reasoning tasks on chessboard, we design a CoT-D fine-tuning paradigm that enhances LLM's ability to make interpretable low-level decisions. Experiments show that R2C outperforms existing LLM-based high-level planners, even in zero-shot settings, and allows 7B models to surpass GPT-4. Furthermore, R2C enables LLMs to tackle open-vocabulary tasks where API-based frameworks fall short. However, R2C still faces challenges, such as handling very large scenes. Future work will focus on optimizing R2C for larger environments and exploring its potential for various open-vocabulary tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19463" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.314 + ], + "angle": 0, + "content": "Acknowledgement This work is partially supported by National Key R&D Program of China No. 2021ZD0111901, and Natural Science Foundation of China under contracts Nos. 62495082, U21B2025. Ziyi Bai, Hanxuan Li, and Bin Fu contributed equally to this work. Ziyi Bai led the implementation of the overall framework and the evaluation of the ALFRED benchmark and open-vocabulary tasks. Hanxuan Li proposed the R2C and CoT-D fine-tuning methods, validated their feasibility, and took the lead in the design, training, and acceleration of the LLM-based module. 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While LLMs excel as the robot's "brain" for high-level planning, they face challenges in directly controlling the "body" by generating precise low-level actions. This limitation arises from LLMs' strength in high-level conceptual understanding but their inability to handle spatial perception effectively, restricting their potential in embodied tasks. To address this, we bridge the gap by enabling LLMs to not only comprehend complex instructions but also produce actionable, low-level plans. We introduce Room to Chessboard (R2C), a novel semantic representation that maps environmental states onto a grid-based chessboard, empowering LLMs to generate specific low-level coordinates and guide the robot in a manner akin to playing a game of chess. To further enhance decision-making, we propose the Chain-of-Thought Decision (CoT-D) paradigm, which improves LLMs' interpretability and context-awareness in spatial reasoning. By jointly training LLMs for high-level task decomposition and low-level action generation, we create a unified "brain-body" system capable of handling complex, free-form instructions while producing precise low-level actions, allowing the robot to flexibly control its movements and adapt to varying tasks. We validate R2C using both fine-tuned open-source LLMs and GPT-4, demonstrating effectiveness on the challenging ALFRED benchmark. Results show that with our R2C framework, LLMs can effectively act as low-level planners, generalizing across diverse settings and open-vocabulary robotic tasks. The code and demonstrations are available at: https://vipl-vsu.github.io/Room2Chessboard. + +# 1. Introduction + +The pursuit of general embodied agents focuses on developing robust systems capable of understanding natural lan + +![](images/33e7777691d95406c21223740585b937fe4302af0be7e17fef1223ad15dc1970.jpg) +Figure 1. Comparison of LLM as a high-level versus low-level planner for the task of "heating eggs". High-level planner provides subgoals while low-level planner directly provides exact path. + +guage commands to meet diverse human requirements. Traditional robotic learning methods have succeeded in executing complex tasks but struggle to generalize to new environments or tasks due to their reliance on task-specific training and rigid planning. Recently, Large Language Models (LLMs) have emerged as promising embodied agents. + +Several pioneering works [8, 13, 14, 37] have explored LLMs as the "brain" of embodied systems, leveraging their strong generalization to manage diverse tasks effectively. However, most LLM-based agents [1, 13, 37] focus mainly on high-level task planning, decomposing tasks like "bring me an egg" into subgoals (e.g., "go to egg") $\rightarrow$ "take it back"). The execution of these subgoals is still delegated to low-level policy networks [5, 16, 18] or deterministic algorithms [7, 31]. While LLMs have extensive world knowledge, they lack spatial awareness of real environments, making it difficult to predict if these plans can be grounded to the physical world accurately. This often leads to frequent re-planning [1, 37], reducing efficiency and success rates, thereby limiting the potential of LLMs as embodied + +agents in real-world applications. + +The primary barrier [37, 44] to unlocking the full potential of LLMs lies in the ineffective communication between the LLM (the "brain") and the robot (the "body"). The robot struggles to convey the updated spatial information about environment, leaving the LLM without a basis for decision-making. As a result, the LLM can only generate high-level subgoal plans, while controlling the robot's movements relies on external navigation APIs. To overcome this challenge, a "common language" is needed — a platform that delivers sufficient environmental states, empowering the LLM to generate precise low-level action plans and directly control the robot. + +We propose a novel Room to Chessboard (R2C) framework, which realizes a unified "brain-body" system that integrates high-level task understanding with direct low-level action decisions. As shown in Fig. 1, R2C utilizes a grid-based chessboard as an effective communication platform between the robot and the LLM. On one side, the robot can continuously map its observations onto the chessboard, which contains essential information while avoiding information overload. On the other side, the LLM is unlocked as a low-level action planner, directly guiding the robot "moves" on the chessboard to complete the task. Specifically, the LLM decomposes long-horizon tasks into sub-goals, which are then addressed through precise low-level planning. At this stage, an Environment Filter maintains task-aware environmental states on a compact chessboard. Since the chessboard grid size is calibrated to match the robot's step length, the LLM can perform low-level planning on the chessboard by predicting the robot's next position. Additionally, the Chain-of-Thought Decision (CoT-D) paradigm is proposed to enhance LLM's spatial reasoning and decision-making capabilities. + +To construct a chessboard representation that fully captures the complex environmental states while remaining manageable for LLMs, we introduce an Environment Filter to abstract the environment states. Initially, new observations are converted into a detailed 2D semantic map. However, such a high-dimensional representation can overwhelm LLMs. To mitigate this, we apply kernel filters to down-sample the map, then flatten it into a 2D chessboard, organized according to the priority of the current subgoal. The object occupancy on the chessboard is further abstracted into object coordinate sets. This representation strikes a balance between semantic richness and simplicity, effectively capturing critical information such as object semantics, object size and scene layout, while enabling efficient low-level action planning. + +In R2C framework, LLM needs robust long-context understanding capabilities to comprehend the object coordinate sets and spatial reasoning abilities for low-level planning. Despite advancements in LLM capabilities, achiev- + +ing this remains a huge challenge. To enhance LLM's low-level action planning abilities, we design a fine-tuning paradigm and formalize the CoT-D fine-tuning task. CoT-D comprises four subtasks: key information extraction, direction determination, target prediction, and selection analysis. LLM is required to link these subtasks together into a coherent logical chain [42]. These tasks can not only strengthen the long-context understanding of LLM but also enhance its spatial reasoning to generate more interpretable low-level plans. + +We evaluate our R2C framework on the challenging ALFRED [34] benchmark, which features a diverse set of long-horizon tasks. We test both GPT and fine-tuned open-source LLMs using our novel CoT-D. R2C achieves state-of-the-art (SoTA) performance among LLM-based methods. Additionally, LLMs trained with CoT-D exhibit strong spatial reasoning and action planning capabilities. Our LLM-based low-level action planner also demonstrates impressive generalization across open-vocabulary tasks and real-world deployment, highlighting the versatility and robustness of the R2C framework in various application scenarios. + +The main contributions of this paper are as follows: + +- We propose Room to Chessboard (R2C), a unified "brain-body" system that enables LLMs to simultaneously understand free-form instructions and generate specific, environment-aware low-level actions. +- We develop the Chain-of-Thought Decision (CoT-D) fine-tuning mechanism, which enhances the spatial reasoning capabilities of LLMs, leading to a significant improvement of $11.37\%$ . +- We achieve SoTA performance among LLM-based methods using limited robotic data and demonstrate strong generalization to unseen environments, including real-world scenarios. + +# 2. Related Works + +# 2.1. Task Planning In Robotics + +Task planning in robotics [28, 34] involves generating a sequence of actions for robots to execute in the environments to achieve a specific goal. In real-world applications, the instructions are typically complex, resulting in long-horizon tasks that encompass a variety of embodied activities, such as navigation [2, 9] and object interaction [20]. Early approaches [27, 38] simply integrate visual and textual inputs to generate contextually appropriate action sequences. Besides, one widely used approach is reinforcement learning (RL) [11, 24, 39, 41]. Although the above methods have good performance on some specific tasks, they are trained end-to-end using expert trajectories and low-level instructions, resulting in poor generalization to unknown environments [19, 25, 37]. + +Therefore, some approaches [3, 15, 19, 23, 25] suggest explicitly breaking down the complex task into mul + +tiple functional modules. FILM [25] proposes a framework with four submodules including language processing, semantic mapping, semantic search and deterministic policy. ThinkBot [23] presents an additional object localizer based on multimodal transformers to predict the position of target objects. Though they provide more interpretable frameworks, each of their modules need to be fine-tuned with corresponding data, which make them struggle in adapting to novel robotic tasks. + +# 2.2. Task planning with LLMs + +To address the above generalization challenges, incorporating Large Language Models (LLMs) into robotic task planning presents a promising pathway [1, 10, 13, 14]. Early attempts [13] adopt LLMs to help with free-form human instruction following by decomposing the task into reasonable subgoals. However, due to LLM's inability to perceive the complex physical world, the generated goals often fail to execute in the environments [1]. + +Recent research has delved into integrating environmental states to ground the output of the LLM-based planner. LM-Nav [32] leverages a pre-trained Vision-Language Model (VLM) to generate captions of viewpoints and ground them with landmarks to enhance the executability of navigation plan. Additionally, structured representations such as object-centric scene graphs and topology graphs [6, 10, 29, 46] are commonly employed to improve the LLM's comprehension of relationships among objects and the overall room layout within the environments. Beyond directly translating visual feedback into inputs for LLMs, Say-Can [1] trained a vision-based value function to judge the affordance of the LLM's plan in the environments. Furthermore, some other works [21, 35] involve text-form Planning Domain Definition Language (PDDL) descriptions of scenes, which are easier for LLMs to handle. + +Although the above works address some cases where LLM-generated plans are not executable, they all use LLMs solely as high-level planners. Most works still rely on low-level controllers to translate these high-level plans into executable action sequences. Some recent works [12, 33, 47] train end-to-end models to directly map robot observations to actions on large amounts of robotic trajectory data to achieve generalization. Unlike these approaches, we unlock LLMs to function as both high-level and low-level planners by introducing an interpretable textual representation of the environment. + +# 3. Methods + +We aim to unlock LLMs as low-level action planners that can directly guide robots to solve long-horizon tasks. We first introduce our newly designed Room to Chessboard framework in Sec. 3.1, and then illustrate the Chain-of-Thought Decision (CoT-D) fine-tuning task formulation in Sec. 3.2. + +# 3.1. Room to Chessboard + +We introduce the Room to Chessboard (R2C) framework (Fig. 2), which enables LLMs to perform both High-Level Planning (HLP) and Low-Level Planning (LLP) within a unified framework. First, the LLM conducts HLP, processing step-by-step instructions into a sequence of subgoals. Each subgoal is then handled at the LLP stage. At each timestep, an egocentric RGB-D image is processed by an Environment Filter to generate a chessboard abstraction. The updated chessboard is subsequently converted into object occupancy coordinates, which are fed to the LLM. Acting like a chess player, the LLM predicts the robot's next move on the chessboard, guiding it to navigate or interact with the environment. + +# 3.1.1. High-Level Planning (HLP) + +At the beginning of an episode, the LLM processes the natural language instruction $L$ into a sequence of high-level subgoals, denoted as $\mathcal{G} = [G_1, G_2, \dots, G_K]$ . Each subgoal $G_k$ is a tuple (Action, Object), where Action $\in A_H$ is a primitive action chosen from the set of navigation action (GOTO) or interaction actions (e.g., PICKUP, PUT). The Object refers to the semantic class of the interacted object (e.g., SAFE, CD). These subgoals are executed sequentially during the LLP stage. + +# 3.1.2. Environment Filter + +Since the environment is partially observed, the agent has never explored the entire environment and must construct a map based on its own observations online. At each timestep, the Environment Filter $F(o_{t}, G_{k})$ takes the new observation $o_{t}$ as input to filter out the goal-related environment information conditioned on the current subgoal $G_{k}$ . This filtered information is then added to a dynamically updated semantic chessboard $\mathcal{B}$ to represent the current state of the environment. The computation of $F$ involves two parts: semantic mapping and chessboard building. + +Semantic mapping. We first build an online semantic map of the room, inspired by prior work [25]. At each timestep $t$ , the agent receives an egocentric RGB-D observation $o_{t} = I_{rgb}, I_{dpt}$ . An off-the-shelf instance segmentation model processes $I_{rgb}$ , and, combined with $I_{dpt}$ , the observation is converted into a point cloud, with each point labeled with predicted semantic categories. This 3D point cloud is then voxelized and flattened along the Z-axis to form the 2D semantic map $\mathcal{M}$ . The resulting semantic map is represented as $(C + 2) \times M \times M$ binary grid, where $C$ is the number of object categories, and two additional channels denote obstacles and explored areas in each cell. Here, $M$ represents the map resolution. + +Chessboard building. We further abstract the semantic map into a compact chessboard, i.e., map to chessboard $(M2C)$ . The $M2C$ function consists of two cascaded kernels. + +![](images/cd851cc741c27a4a9b736a0e86d20f655dc9f2675fb7d12603da851066e62a89.jpg) +Figure 2. Overview of R2C framework: The LLM begins by generating high-level subgoals for the task. For each subgoal, the environment filter translates RGB-D observations into an updated grid-based chessboard representation of the environments. The LLM then uses chain-of-thought analysis to integrate this chessboard representation along with game rules, determining the next optimal position, which is finally converted into executable robot actions. + +The first kernel is a dilation kernel $\mathcal{K}_{dila}$ , designed to prevent collisions between the agent and obstacles. Similar to the dilation algorithm in image processing [30], it expands all occupied pixels of obstacles (including objects) outward by $\delta$ in the map. The second kernel is a max pooling kernel $\mathcal{K}_{pool}$ , which performs max pooling on the map. Then, the map is down-sampled from size $M$ to size $W$ , where $W = \left\lceil \frac{M}{\omega} \right\rceil$ and $\omega$ is the grid size, calibrated to match the length of the agent's step. + +Next, we aggregate this map with multiple object layers into a unified single-layer chessboard. To address the many-to-one projection problem, where overlapping objects might appear in the same grid, e.g., "apples on a table", we introduce a Goal-aware Aggregate function $\mathcal{A}(\cdot)$ . This function prioritizes both the relevance to the current subgoal, i.e., the target object Object in current subgoal $G_{k}$ , and the size of the object. The most relevant and smallest objects are placed at the top layer, and then we merge object layers from bottom to top to produce the final chessboard. The overall formulation of the $M2C$ is: + +$$ +M 2 C = \mathcal {A} \circ \mathcal {K} _ {d i l a} \circ \mathcal {K} _ {p o o l} \tag {1} +$$ + +$$ +\mathcal {B} = M 2 C (\mathcal {M}, G _ {k}). +$$ + +# 3.1.3. Low-Level Planning (LLP) + +The chessboard filtered out from the Environment Filter provides compact yet sufficient environmental state information for LLM. We then simulate a "chess game" between the LLM and the robot to perform low-level planning. The LLP task is formulated as a single-step generation task for + +the LLM. As shown in Fig. 2, various state information is collected, including current subgoal $G_{k}$ , chessboard state $\mathcal{U}$ , action history $\mathcal{Q}$ and game rules $R$ . Our prompt system $\mathcal{P}$ organizes such data and feeds them into the LLM to generate the next position prediction $w$ . Note that LLP is invoked only for navigation subgoals, as interaction subgoals in ALFRED can be handled by predefined low-level actions once the agent reaches the visible range of the target object. + +Chessboard state. To translate the chessboard state for the LLM, we convert it into textual object occupancy coordinate sets. The chessboard coordinate system originates from the upper left corner, with the X-axis pointing down and the Y-axis to the right. For each object on the chessboard, we gather a set of occupancy coordinates $\mathcal{U}_t^c = \{x_i,y_i\}$ , where $c\in [1,C + 2]$ and $x_{i},y_{i}\in [1,W]$ . The initial agent position $w_{0}$ is predefined in the benchmark. + +Game rules. To assist the LLM in planning, we define key game rules $R$ : 1) Basic inputs, including chessboard dimensions $W$ , maximum steps $T$ , and maximum errors $E$ ; 2) Action space, simplified to adjacent grids in four directions (up, down, left, right), i.e., the robot is only allowed to move 1 block at a time, due to the limited spatial reasoning ability of current LLMs; 3) Collision rules, where grids occupied by objects or obstacles are considered illegal moves. + +Action history. We maintain a queue $\mathcal{Q}$ with a fixed length $\tau$ to store recent successful movement coordinates, providing the LLM with contextual information about previous actions. At each step $t$ , the prompt system combines + +all such information and feeds them to the LLM, which simulates a chess player to decide the next move. The LLP models a policy $\pi$ , defined as: + +$$ +u _ {t} = \pi (\mathcal {P} (G _ {k}, \mathcal {U} _ {t}, R, \mathcal {Q} _ {t})), \tag {2} +$$ + +where $u_{t} = (x_{t},y_{t})$ is the predicted next position on the chessboard. According to the defined action space, the available next positions are restricted to the adjacent grids in four directions $x_{t + 1}\in [x_t - 1,x_t + 1]$ and $y_{t + 1}\in [y_t - 1,y_t + 1]$ , with $x_{t + 1},y_{t + 1}\in [1,W]$ . + +Since the chessboard grid size is calibrated to match the robot's step length, the predicted adjacency target position $u_{t}$ can be directly converted to a sequence of executable low-level actions $\mathbf{a} = \{a_{i}\}$ , $a_{i} \in \mathbf{A}_{\text{nav}}$ in the real-world environments. For example, in the ALFRED benchmark, $\mathbf{A}_{\text{nav}}$ includes (MoveForward, 0.25m), (TurnLeft, 90°) and, (TurnRight, 90°). Based on the predicted target position, the movement in any of the four directions can be converted into the corresponding action sequence (e.g., TurnLeft and MoveForward to move to the left adjacent grid). Additionally, if the output $w_{t}$ is within the visible range of the target object Object in the current subgoal, the system moves on to the next subgoal. See more details of the R2C framework in the pseudocode provided in the supplementary materials. + +# 3.2. Chain-of-Thought Fine-tuning Paradigm + +To improve the decision-making capabilities of LLMs in our chess game, we introduce an interpretable fine-tuning paradigm with two core features: 1) simultaneous training of high-level task decomposition and low-level Chain of Thought Decision (CoT-D) tasks, enabling the integration of High-Level Planning (HLP) and Low-Level Planning (LLP) within a single LLM, and 2) structuring the CoT-D process into four distinct parts to enhance the LLM's comprehension of game rules and spatial reasoning. + +# 3.2.1. Joint Training of HLP and LLP + +Long-horizon planning often involves compositional tasks that require hierarchical planning capabilities. Therefore, rather than only exploiting the LLM as a high-level planner or training an end-to-end low-level action generation model, we jointly train the model on both HLP and LLP tasks simultaneously. Given the data imbalance between HLP and LLP, we apply data balancing techniques to ensure the model effectively learns skills at both levels. + +# 3.2.2. Chain of Thought Decision (CoT-D) + +LLM should thoroughly comprehend our chessboard coordinate system and predict the next position based on the semantic information of the chessboard and its inherent common sense. For the given prompt $\mathcal{P}$ with chessboard state $\mathcal{U}$ , the LLM needs to generate answer sentence $S$ (including next position $w$ ) with probabilistic language model $p_{LM}$ . If + +LLM is asked to directly provide coordinates, this process can be formalized as: + +$$ +p (\mathcal {S} \mid \mathcal {P}) = \prod_ {i = 1} ^ {| \mathcal {S} |} p _ {L M} \left(s _ {i} \mid \mathcal {P}, s _ {< i}\right). \tag {3} +$$ + +However, such a complex task is much more challenging than the task decomposition. This requires the LLMs have strong capabilities in long-text comprehension and spatial reasoning. However, the current models are not particularly skilled in these abilities. Consequently, we design the Chain of Thought Decision (CoT-D) tasks to strengthen LLM's rationale $\mathcal{R}$ in these aspects. The task consists of four subtasks, requiring LLMs to output the result of key information extraction $\mathcal{R}_E$ , direction judgment $\mathcal{R}_D$ , target prediction $\mathcal{R}_T$ , and selection analysis $\mathcal{R}_S$ , respectively. We link these sub-tasks sequentially in natural language to construct a coherent logical chain. The entire task can be represented as: + +$$ +\begin{array}{l} \cdot p (\mathcal {S} \mid \mathcal {P}) = p (\mathcal {S} \mid \mathcal {P}, \mathcal {R}) \cdot p (\mathcal {R} \mid \mathcal {P}) \\ p (\mathcal {R} \mid \mathcal {P}) = \prod_ {r _ {i} \in \left\{\mathcal {R} _ {E}, \mathcal {R} _ {D}, \mathcal {R} _ {T}, \mathcal {R} _ {S} \right\}} p _ {L M} \left(r _ {i} \mid \mathcal {P}, r _ {< i}\right) \tag {4} \\ \end{array} +$$ + +$$ +p (\mathcal {S} \mid \mathcal {P}, \mathcal {R}) = \prod_ {j = 1} ^ {| \mathcal {S} |} p _ {L M} (s _ {i} \mid \mathcal {P}, \mathcal {R}, s _ {< j}) +$$ + +The specific content of the four sub-tasks will be introduced below. Examples can be found in Fig. 2, with details available in the supplementary materials. + +Key information extraction. Due to the intricate information contained within the chessboard, when textualized, it becomes a lengthy document with substantial information. Considering that LLM often encounters issues such as context loss when comprehending long texts, this task is designed to train LLM in processing task-related long texts and extracting key information. This task requires LLM to extract relevant information about the current coordinates and target objects based on the chessboard information inputs. The form used in data annotation is as follows: The current position of the agent is [COORDS], and the target is [OBJECT NAME], which is located at [COORDS SET]. + +Direction judgment. The conversion from a chessboard grid image to text is based on a two-dimensional Cartesian coordinate system, and all spatial relationship understanding relies on a good coordinate system understanding. Despite providing clear instructions to establish the coordinate system using prompts like Establish a coordinate system with the top-left grid as (1,1), experiments have shown that the LLM still frequently misunderstands the setup. This could be attributed to the length of the text and the scarcity of spatial reasoning tasks incorporated during the pre-training of contemporary LLM. To ensure LLM's accurate comprehension + +
MethodTraining ModeVal SeenVal UnseenΔ SR ↑Δ GC ↑
SR ↑GC ↑SR ↑GC ↑
Specialists, only for ALFRED tasks
E.T. [27]from scratch46.5952.927.3220.87-39.27-32.05
HiTUT [45]from scratch25.2434.8512.4423.71-12.80-11.14
M-TRACK [36]from scratch26.7033.2117.2928.98-9.41-4.23
FILM [25]from scratch24.6337.2020.1032.45-4.53-4.75
LEBP [22]from scratch27.6335.7622.3629.58-5.27-6.18
Generalists, based on LLMs
SayCan [1]few-shot12.3024.529.8822.54-2.42-1.98
LLM-P (GPT) [37]1few-shot16.4530.1115.3629.88-1.09-0.23
R2C-GPT-4 (ours)zero-shot20.0028.4624.0028.24+4.00-0.22
R2C-Llama-7B (ours)fine-tune20.8329.6018.9929.69-1.84+0.09
R2C-Mistral-7B (ours)fine-tune22.3132.4022.3531.97+0.04-0.43
+ +Table 1. Main results on the ALFRED benchmark. SR and GC are short for success rate and goal-conditioned success rate. $\Delta$ SR and $\Delta$ GC represent the performance drops in generalizing from the seen to the unseen environments. + +
Task TypeVal SeenVal Unseen
SRGCSRGC
Overall48.1855.1353.3358.18
Examine75.8679.3183.3387.96
Pick & Place69.5769.5763.3363.33
Stack & Place29.0337.0045.4546.46
Clean & Place63.8973.8738.8950.45
Cool & Place36.8449.6061.1169.23
Heat & Place23.5341.3828.5741.13
Pick 2 & Place33.3354.4137.5053.70
+ +of the chessboard coordinate system, this task requires LLM to judge the direction between the target and the current coordinates. The format employed in data annotation is as follows: the target is at..., which is on the [DIRECTION] of the agent. + +Target prediction. The locations where different categories of objects appear often have priors. For example, sofas are likely to appear opposite the television. Therefore, we aim to enable LLM to develop the capability of predicting target locations. This can minimize the ineffective or inefficient exploration process for the robot to find target objects, thereby improving the efficiency of the system in accomplishing embodied tasks. The expression utilized in data annotation is: Based on the chessboard analysis, the target is likely located near [COORDS]. + +Selection analysis. Based on the above comprehension, we require the LLM to further analyze all potential next positions according to the chessboard rules. During this analysis, the LLM evaluates each possible move, providing a rationale for each choice. The specific format used in the annotation is: [COORDS]: This position is on the [DIRECTION] of the agent, [Reason]. The [Reason] component is generated by GPT-4 based on the agent's current state and the relationship between the chosen position and the correct orientation. For instance: Objects in this direction have already been discovered; we should head to areas that have not been explored. + +These four sub-tasks comprehensively enhance the understanding of chessboard and spatial reasoning ability of the LLMs from different perspectives. + +# 4. Evaluation + +# 4.1. Experiment Settings + +Benchmark. We evaluate our method on the challenging ALFRED [34] benchmark, which features long-horizon + +Table 2. Performance of R2C on different tasks. The R2C model excels in "Examine" tasks, but faces challenges in complex "Heat & Place" tasks, where the "HeatObject" subgoal alone involves seven interactive steps, increasing the risk of error accumulation. + +
MethodVal SeenVal Unseen
SRGCSRGC
Base Model (R2C-Mistral-7B)22.3132.4022.3531.97
+ GT Seg.37.9245.8335.2443.88
+ GT Seg., GT Goal48.1855.1353.3358.18
+ GT Seg., GT Goal, - SA45.9751.7547.4553.03
+ GT Seg., GT Goal, - CoT41.2249.3541.9647.88
+ +Table 3. Ablation of R2C. "GT Seg." represents the model using ground-truth segmentation. "GT Goal" represents using ground-truth subgoals. "- SA" is the model without Selection Analysis part of CoT. "- CoT" is the model without all CoT tasks. + +tasks (7 types in total) involving both navigation and interaction across 207 unique environments and 115 different object types. In our experiments, we adhere to the benchmark's settings, including low-level action space, maximum agent steps, and failure limits. + +Chessboard settings. The physical room size $D$ is set to $16m$ , which is the approximate maximum room size, and the grid size $\omega$ corresponds to the agent's step length, $0.25m$ . Thus, the size of the semantic map and the chessboard is $M = 320$ and $W = 64$ separately. However, to represent more complex environments, one can choose a more fine-grained chessboard. We demonstrate this through a simple experiment in the supplementary materials. + +Model settings. For the zero-shot R2C, we use the public GPT-4-turbo API [26] without any in-context examples. Considering the testing cost, we randomly sample a subset of size 100 covering all 7 types of tasks strictly according to the task distribution of ALFRED. We collected a total of 264,915 data samples for fine-tuning, including 70,000 samples for the Task Decomposition tasks and 194,915 samples for the CoT-D tasks. All data collection was based solely on the training set of ALFRED. During training, + +![](images/e4436f41a48d7d371afd859dc4cad439b08c812e31d4757a1ba7f128ab69b883.jpg) +Figure 3. Case study of R2C with Mistral model: The model completes an "Examine" task in 31 steps (top) but fails to locate the small target object, a bowl, during a "Clean & Place" task in a more complex environment (bottom). + +we conduct full-parameter fine-tuning on both the Mistral-7B-Instruct-v0.2 model [17] and the Llama-7B-Chat model [40] using all the data. Both models were trained for only one epoch. We conduct all fine-tuning experiments using 4 NVIDIA H100 GPUs, and all evaluations are performed on 4 NVIDIA A40 GPUs. + +# 4.2. Main Results + +Tab. 1 presents the evaluation results on the validation set of ALFRED. We compare our R2C framework with both traditional robotic learning methods (specialists) and LLM-based approaches (generalists). R2C achieves state-of-the-art performance among LLM-based methods, with the Mistral-7B excelling in seen environments and GPT-4 in unseen environments. + +Compared to SayCan [1] and LLM-P [37], which use LLMs only for high-level planning, R2C integrates high-level and low-level planning, offering a more efficient, end-to-end solution. LLM-P requires 100 instruction-plan pairs for training, while R2C operates in a zero-shot setting without examples. Our CoT-D paradigm enables GPT to analyze the chessboard state comprehensively, improving decision interpretability and efficiency. + +R2C fine-tuned on open-sourced LLMs achieves competitive results, with $2.31\%$ improvement in the seen split and $1.65\%$ drop in the unseen split compared to R2C-GPT-4. This highlights GPT-4's superior generalization to unseen environments. However, with our carefully designed fine-tuning tasks, R2C implemented on much smaller models like LLaMA and Mistral, can still deliver performance comparable to GPT-4. This demonstrates the effectiveness and efficiency of our fine-tuning approach. + +Finally, R2C fine-tuned on collected data performs comparably to specialist models like FILM [25] and LEBP [22]. + +![](images/b292c278f65a7811a7cc05550093e7dd95d81b56786eb901b308f7833c86d24c.jpg) +Figure 4. Cases of R2C-GPT-4 on open-vocabulary tasks. + +Although these specialized models excel in seen scenes, they struggle in unseen environments due to overfitting. In contrast, R2C and other LLM-based methods demonstrate stronger generalization across both seen and unseen environments. + +# 4.3. Ablation Study + +We perform an ablation study to analyze the impact of different R2C modules. As shown in Tab. 3, using ground truth segmentation (GT Seg.) significantly improves performance, highlighting segmentation as a bottleneck, especially in simulation environments. Using ground truth sub-goals (GT Goal) also boosts SR, revealing the impact of ambiguity in natural language instructions. Annotator confusion between categories like desk lamps and floor lamps can hinder task decomposition, though LLMs' strong generalization helps mitigate this. + +Removing the CoT-D framework, i.e., forcing the model to directly output position coordinates without rationale, results in a significant performance drop, especially in unseen scenes. This highlights the importance of fine-tuning with CoT-D for better spatial reasoning. Ablating individual subtasks is challenging due to their interdependence. Here, we ablate removing the Selection Analysis part (- SA), where decisions are made without analyzing options and it causes a noticeable performance decline. + +![](images/c2fbd1535697dae278d6ac2071f728d8aac329473d778aba0b6ac61a6e02645b.jpg) + +![](images/66af14fe3725f0ea355129744d40ce9b4053a7cadf8e2088bd57f57ebf20b971.jpg) + +![](images/796f00fd166c3d94b29c8defb9b72cbd8cc59016924d4f245b5da13cf266d905.jpg) +Figure 5. Visual results of R2C in real-world scenarios. Three tasks are tested in a real-world environment, with the corresponding instructions, third-person trajectories, first-person images, and chessboard visualizations shown for each task. + +![](images/5467b30963f17942381e4f7ada63edc40d7c776559239836d16b8b5beb18a8d3.jpg) + +
TaskSpecific Obj.Specific Loc.Nearest CornerCenter BetweenOverall
GPT-4 (90°)66.773.353.380.068.3
GPT-4 (45°)73.373.373.360.070.0
GPT-4o (90°)40.053.333.346.743.3
+ +# 4.4. Evaluation Across Tasks Types + +We analyze R2C's performance across task types using GT Segmentation and GT Goal settings, with task-specific results shown in Tab. 2. R2C shows SR drops on more complex long-horizon tasks, such as "Heat & Place," with average GT step lengths of 63, compared to shorter ones (e.g., Examine: 37). We provide a visualization of two case studies of R2C completing different tasks ("Examine" and "Clean & Place") in Fig. 3. More failure case analyses are included in the supplementary materials. + +# 4.5. Exploration on Open-vocabulary Task + +Real-world tasks are more diverse and flexible than the predefined, limited tasks in ALFRED. To assess R2C's ability to handle open-vocabulary tasks, we conduct a mini experiment with 60 test trials generated randomly by GPT-4 across 3 room sizes (7x7, 5x9, 5x11), five room layouts, and four task types. 1) Specific Obj.: Move to a specific object (e.g., nearest chair). 2) Specific Loc.: Move to a specific location (e.g., center or corner). 3) Nearest Corner: Move to the nearest corner. 4) Center Between: Move to the center between two objects. + +Traditional closed-domain approaches struggle with these tasks, as they are limited to defined tasks in the training set. Meanwhile, high-level LLM planners face challenges in translating them into object-navigation plans. We test R2C with various settings: GPT-4 $(90^{\circ})$ , GPT-4 $(45^{\circ})$ which allow 45-degree rotation, and GPT-4o $(90^{\circ})$ , which + +Table 4. SR (%) of R2C on open-vocabulary tasks. + +
MethodSAVN [43]S2P [4]R2C
SR (%)40.8646.1652.25
SPL (%)16.1528.0129.56
+ +Table 5. Performance of R2C on object navigation task. + +uses visualized chessboards. Results are summarized in Tab. 4, and two task examples are visualized in Fig. 4. + +The results demonstrate the potential of R2C in handling open-vocabulary tasks for real-world applications. GPT-4 $(45^{\circ})$ outperforms the $90^{\circ}$ -agent, thanks to more efficient diagonal movement, highlighting the expandability of R2C with different action spaces. Both GPT-4 $(90^{\circ})$ and GPT-4 $(45^{\circ})$ outperform GPT-4o, as feeding the chessboard directly to the VLM leads to poor spatial grounding and inaccurate path predictions. More results are available in the supplementary materials. + +# 4.6. Application in Real-world Scenarios + +To evaluate the real-world applicability of the R2C framework, we design three open-vocabulary tasks to test its performance using the LoCoBot robot in a set-up real-world experiment room. We evaluate R2C-GPT-4 in zero-shot setting. As shown in Fig. 5, the R2C framework, by enabling LLM to generate low-level actions, allows successful task completion in a totally different environment, showcasing its effectiveness and versatility in real-world scenarios. Detailed implementation information can be found in the supplementary materials. + +# 4.7. Evaluation on Navigation Task + +To further evaluate the model's generalization capability across tasks, we extend R2C-Mistral-7B model trained on ALFRED to the AI2THOR ObjectNav task [43] without additional fine-tuning. Results in Tab. 5 show that R2C significantly outperforms S2P [4], another LLM-based planner. + +# 5. Conclusion + +We introduce the Room to Chessboard (R2C) framework, which maps the complex room into a chessboard as a communication platform between the LLM and the robot, unlocking the LLM as low-level planner to directly guide the robot to adaptively finish the embodied tasks. To address the spatial reasoning tasks on chessboard, we design a CoT-D fine-tuning paradigm that enhances LLM's ability to make interpretable low-level decisions. Experiments show that R2C outperforms existing LLM-based high-level planners, even in zero-shot settings, and allows 7B models to surpass GPT-4. Furthermore, R2C enables LLMs to tackle open-vocabulary tasks where API-based frameworks fall short. However, R2C still faces challenges, such as handling very large scenes. Future work will focus on optimizing R2C for larger environments and exploring its potential for various open-vocabulary tasks. + +Acknowledgement This work is partially supported by National Key R&D Program of China No. 2021ZD0111901, and Natural Science Foundation of China under contracts Nos. 62495082, U21B2025. Ziyi Bai, Hanxuan Li, and Bin Fu contributed equally to this work. Ziyi Bai led the implementation of the overall framework and the evaluation of the ALFRED benchmark and open-vocabulary tasks. 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While LLMs excel as the robot's \"brain\" for high-level planning, they face challenges in directly controlling the \"body\" by generating precise low-level actions. This limitation arises from LLMs' strength in high-level conceptual understanding but their inability to handle spatial perception effectively, restricting their potential in embodied tasks. To address this, we bridge the gap by enabling LLMs to not only comprehend complex instructions but also produce actionable, low-level plans. We introduce Room to Chessboard (R2C), a novel semantic representation that maps environmental states onto a grid-based chessboard, empowering LLMs to generate specific low-level coordinates and guide the robot in a manner akin to playing a game of chess. To further enhance decision-making, we propose the Chain-of-Thought Decision (CoT-D) paradigm, which improves LLMs' interpretability and context-awareness in spatial reasoning. By jointly training LLMs for high-level task decomposition and low-level action generation, we create a unified \"brain-body\" system capable of handling complex, free-form instructions while producing precise low-level actions, allowing the robot to flexibly control its movements and adapt to varying tasks. We validate R2C using both fine-tuned open-source LLMs and GPT-4, demonstrating effectiveness on the challenging ALFRED benchmark. Results show that with our R2C framework, LLMs can effectively act as low-level planners, generalizing across diverse settings and open-vocabulary robotic tasks. The code and demonstrations are available at: https://vipl-vsu.github.io/Room2Chessboard." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 668, + 135, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 668, + 135, + 680 + ], + "spans": [ + { + "bbox": [ + 55, + 668, + 135, + 680 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "The pursuit of general embodied agents focuses on developing robust systems capable of understanding natural lan" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 319, + 259, + 555, + 414 + ], + "blocks": [ + { + "bbox": [ + 319, + 259, + 555, + 414 + ], + "lines": [ + { + "bbox": [ + 319, + 259, + 555, + 414 + ], + "spans": [ + { + "bbox": [ + 319, + 259, + 555, + 414 + ], + "type": "image", + "image_path": "33e7777691d95406c21223740585b937fe4302af0be7e17fef1223ad15dc1970.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 426, + 555, + 460 + ], + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 460 + ], + "type": "text", + "content": "Figure 1. Comparison of LLM as a high-level versus low-level planner for the task of \"heating eggs\". High-level planner provides subgoals while low-level planner directly provides exact path." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 472, + 555, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 555, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 555, + 544 + ], + "type": "text", + "content": "guage commands to meet diverse human requirements. Traditional robotic learning methods have succeeded in executing complex tasks but struggle to generalize to new environments or tasks due to their reliance on task-specific training and rigid planning. Recently, Large Language Models (LLMs) have emerged as promising embodied agents." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 545, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 556, + 713 + ], + "type": "text", + "content": "Several pioneering works [8, 13, 14, 37] have explored LLMs as the \"brain\" of embodied systems, leveraging their strong generalization to manage diverse tasks effectively. However, most LLM-based agents [1, 13, 37] focus mainly on high-level task planning, decomposing tasks like \"bring me an egg\" into subgoals (e.g., \"go to egg\") " + }, + { + "bbox": [ + 313, + 545, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 545, + 556, + 713 + ], + "type": "text", + "content": " \"take it back\"). The execution of these subgoals is still delegated to low-level policy networks [5, 16, 18] or deterministic algorithms [7, 31]. While LLMs have extensive world knowledge, they lack spatial awareness of real environments, making it difficult to predict if these plans can be grounded to the physical world accurately. This often leads to frequent re-planning [1, 37], reducing efficiency and success rates, thereby limiting the potential of LLMs as embodied" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19456" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 192, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 192, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 192, + 84 + ], + "type": "text", + "content": "agents in real-world applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 86, + 296, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 86, + 296, + 229 + ], + "spans": [ + { + "bbox": [ + 55, + 86, + 296, + 229 + ], + "type": "text", + "content": "The primary barrier [37, 44] to unlocking the full potential of LLMs lies in the ineffective communication between the LLM (the \"brain\") and the robot (the \"body\"). The robot struggles to convey the updated spatial information about environment, leaving the LLM without a basis for decision-making. As a result, the LLM can only generate high-level subgoal plans, while controlling the robot's movements relies on external navigation APIs. To overcome this challenge, a \"common language\" is needed — a platform that delivers sufficient environmental states, empowering the LLM to generate precise low-level action plans and directly control the robot." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 231, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 231, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 56, + 231, + 296, + 483 + ], + "type": "text", + "content": "We propose a novel Room to Chessboard (R2C) framework, which realizes a unified \"brain-body\" system that integrates high-level task understanding with direct low-level action decisions. As shown in Fig. 1, R2C utilizes a grid-based chessboard as an effective communication platform between the robot and the LLM. On one side, the robot can continuously map its observations onto the chessboard, which contains essential information while avoiding information overload. On the other side, the LLM is unlocked as a low-level action planner, directly guiding the robot \"moves\" on the chessboard to complete the task. Specifically, the LLM decomposes long-horizon tasks into sub-goals, which are then addressed through precise low-level planning. At this stage, an Environment Filter maintains task-aware environmental states on a compact chessboard. Since the chessboard grid size is calibrated to match the robot's step length, the LLM can perform low-level planning on the chessboard by predicting the robot's next position. Additionally, the Chain-of-Thought Decision (CoT-D) paradigm is proposed to enhance LLM's spatial reasoning and decision-making capabilities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 484, + 296, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 296, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 296, + 664 + ], + "type": "text", + "content": "To construct a chessboard representation that fully captures the complex environmental states while remaining manageable for LLMs, we introduce an Environment Filter to abstract the environment states. Initially, new observations are converted into a detailed 2D semantic map. However, such a high-dimensional representation can overwhelm LLMs. To mitigate this, we apply kernel filters to down-sample the map, then flatten it into a 2D chessboard, organized according to the priority of the current subgoal. The object occupancy on the chessboard is further abstracted into object coordinate sets. This representation strikes a balance between semantic richness and simplicity, effectively capturing critical information such as object semantics, object size and scene layout, while enabling efficient low-level action planning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "In R2C framework, LLM needs robust long-context understanding capabilities to comprehend the object coordinate sets and spatial reasoning abilities for low-level planning. Despite advancements in LLM capabilities, achiev-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "content": "ing this remains a huge challenge. To enhance LLM's low-level action planning abilities, we design a fine-tuning paradigm and formalize the CoT-D fine-tuning task. CoT-D comprises four subtasks: key information extraction, direction determination, target prediction, and selection analysis. LLM is required to link these subtasks together into a coherent logical chain [42]. These tasks can not only strengthen the long-context understanding of LLM but also enhance its spatial reasoning to generate more interpretable low-level plans." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "type": "text", + "content": "We evaluate our R2C framework on the challenging ALFRED [34] benchmark, which features a diverse set of long-horizon tasks. We test both GPT and fine-tuned open-source LLMs using our novel CoT-D. R2C achieves state-of-the-art (SoTA) performance among LLM-based methods. Additionally, LLMs trained with CoT-D exhibit strong spatial reasoning and action planning capabilities. Our LLM-based low-level action planner also demonstrates impressive generalization across open-vocabulary tasks and real-world deployment, highlighting the versatility and robustness of the R2C framework in various application scenarios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 326, + 324, + 535, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 324, + 535, + 336 + ], + "spans": [ + { + "bbox": [ + 326, + 324, + 535, + 336 + ], + "type": "text", + "content": "The main contributions of this paper are as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 337, + 553, + 479 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 314, + 337, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 337, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 314, + 337, + 553, + 384 + ], + "type": "text", + "content": "- We propose Room to Chessboard (R2C), a unified \"brain-body\" system that enables LLMs to simultaneously understand free-form instructions and generate specific, environment-aware low-level actions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 384, + 553, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 553, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 553, + 433 + ], + "type": "text", + "content": "- We develop the Chain-of-Thought Decision (CoT-D) fine-tuning mechanism, which enhances the spatial reasoning capabilities of LLMs, leading to a significant improvement of " + }, + { + "bbox": [ + 313, + 384, + 553, + 433 + ], + "type": "inline_equation", + "content": "11.37\\%" + }, + { + "bbox": [ + 313, + 384, + 553, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 433, + 553, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 553, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 553, + 479 + ], + "type": "text", + "content": "- We achieve SoTA performance among LLM-based methods using limited robotic data and demonstrate strong generalization to unseen environments, including real-world scenarios." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 483, + 406, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 406, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 406, + 495 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 503, + 462, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 503, + 462, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 462, + 516 + ], + "type": "text", + "content": "2.1. Task Planning In Robotics" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 689 + ], + "type": "text", + "content": "Task planning in robotics [28, 34] involves generating a sequence of actions for robots to execute in the environments to achieve a specific goal. In real-world applications, the instructions are typically complex, resulting in long-horizon tasks that encompass a variety of embodied activities, such as navigation [2, 9] and object interaction [20]. Early approaches [27, 38] simply integrate visual and textual inputs to generate contextually appropriate action sequences. Besides, one widely used approach is reinforcement learning (RL) [11, 24, 39, 41]. Although the above methods have good performance on some specific tasks, they are trained end-to-end using expert trajectories and low-level instructions, resulting in poor generalization to unknown environments [19, 25, 37]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "content": "Therefore, some approaches [3, 15, 19, 23, 25] suggest explicitly breaking down the complex task into mul" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19457" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "content": "tiple functional modules. FILM [25] proposes a framework with four submodules including language processing, semantic mapping, semantic search and deterministic policy. ThinkBot [23] presents an additional object localizer based on multimodal transformers to predict the position of target objects. Though they provide more interpretable frameworks, each of their modules need to be fine-tuned with corresponding data, which make them struggle in adapting to novel robotic tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 186, + 200, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 200, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 200, + 198 + ], + "type": "text", + "content": "2.2. Task planning with LLMs" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 203, + 295, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 203, + 295, + 299 + ], + "spans": [ + { + "bbox": [ + 55, + 203, + 295, + 299 + ], + "type": "text", + "content": "To address the above generalization challenges, incorporating Large Language Models (LLMs) into robotic task planning presents a promising pathway [1, 10, 13, 14]. Early attempts [13] adopt LLMs to help with free-form human instruction following by decomposing the task into reasonable subgoals. However, due to LLM's inability to perceive the complex physical world, the generated goals often fail to execute in the environments [1]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 300, + 295, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 295, + 490 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 295, + 490 + ], + "type": "text", + "content": "Recent research has delved into integrating environmental states to ground the output of the LLM-based planner. LM-Nav [32] leverages a pre-trained Vision-Language Model (VLM) to generate captions of viewpoints and ground them with landmarks to enhance the executability of navigation plan. Additionally, structured representations such as object-centric scene graphs and topology graphs [6, 10, 29, 46] are commonly employed to improve the LLM's comprehension of relationships among objects and the overall room layout within the environments. Beyond directly translating visual feedback into inputs for LLMs, Say-Can [1] trained a vision-based value function to judge the affordance of the LLM's plan in the environments. Furthermore, some other works [21, 35] involve text-form Planning Domain Definition Language (PDDL) descriptions of scenes, which are easier for LLMs to handle." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 491, + 295, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 621 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 621 + ], + "type": "text", + "content": "Although the above works address some cases where LLM-generated plans are not executable, they all use LLMs solely as high-level planners. Most works still rely on low-level controllers to translate these high-level plans into executable action sequences. Some recent works [12, 33, 47] train end-to-end models to directly map robot observations to actions on large amounts of robotic trajectory data to achieve generalization. Unlike these approaches, we unlock LLMs to function as both high-level and low-level planners by introducing an interpretable textual representation of the environment." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 626, + 116, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 626, + 116, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 626, + 116, + 639 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 641, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 295, + 712 + ], + "type": "text", + "content": "We aim to unlock LLMs as low-level action planners that can directly guide robots to solve long-horizon tasks. We first introduce our newly designed Room to Chessboard framework in Sec. 3.1, and then illustrate the Chain-of-Thought Decision (CoT-D) fine-tuning task formulation in Sec. 3.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 72, + 435, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 435, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 435, + 83 + ], + "type": "text", + "content": "3.1. Room to Chessboard" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 90, + 555, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 90, + 555, + 245 + ], + "spans": [ + { + "bbox": [ + 313, + 90, + 555, + 245 + ], + "type": "text", + "content": "We introduce the Room to Chessboard (R2C) framework (Fig. 2), which enables LLMs to perform both High-Level Planning (HLP) and Low-Level Planning (LLP) within a unified framework. First, the LLM conducts HLP, processing step-by-step instructions into a sequence of subgoals. Each subgoal is then handled at the LLP stage. At each timestep, an egocentric RGB-D image is processed by an Environment Filter to generate a chessboard abstraction. The updated chessboard is subsequently converted into object occupancy coordinates, which are fed to the LLM. Acting like a chess player, the LLM predicts the robot's next move on the chessboard, guiding it to navigate or interact with the environment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 253, + 460, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 460, + 266 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 460, + 266 + ], + "type": "text", + "content": "3.1.1. High-Level Planning (HLP)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "content": "At the beginning of an episode, the LLM processes the natural language instruction " + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "content": " into a sequence of high-level subgoals, denoted as " + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = [G_1, G_2, \\dots, G_K]" + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "content": ". Each subgoal " + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "inline_equation", + "content": "G_k" + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "content": " is a tuple (Action, Object), where Action " + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\in A_H" + }, + { + "bbox": [ + 313, + 269, + 555, + 376 + ], + "type": "text", + "content": " is a primitive action chosen from the set of navigation action (GOTO) or interaction actions (e.g., PICKUP, PUT). The Object refers to the semantic class of the interacted object (e.g., SAFE, CD). These subgoals are executed sequentially during the LLP stage." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 385, + 424, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 385, + 424, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 385, + 424, + 396 + ], + "type": "text", + "content": "3.1.2. Environment Filter" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": "Since the environment is partially observed, the agent has never explored the entire environment and must construct a map based on its own observations online. At each timestep, the Environment Filter " + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "inline_equation", + "content": "F(o_{t}, G_{k})" + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": " takes the new observation " + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "inline_equation", + "content": "o_{t}" + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": " as input to filter out the goal-related environment information conditioned on the current subgoal " + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "inline_equation", + "content": "G_{k}" + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": ". This filtered information is then added to a dynamically updated semantic chessboard " + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": " to represent the current state of the environment. The computation of " + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 401, + 555, + 520 + ], + "type": "text", + "content": " involves two parts: semantic mapping and chessboard building." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": "Semantic mapping. We first build an online semantic map of the room, inspired by prior work [25]. At each timestep " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": ", the agent receives an egocentric RGB-D observation " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "o_{t} = I_{rgb}, I_{dpt}" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": ". An off-the-shelf instance segmentation model processes " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "I_{rgb}" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": ", and, combined with " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "I_{dpt}" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": ", the observation is converted into a point cloud, with each point labeled with predicted semantic categories. This 3D point cloud is then voxelized and flattened along the Z-axis to form the 2D semantic map " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": ". The resulting semantic map is represented as " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "(C + 2) \\times M \\times M" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": " binary grid, where " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": " is the number of object categories, and two additional channels denote obstacles and explored areas in each cell. Here, " + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 521, + 555, + 676 + ], + "type": "text", + "content": " represents the map resolution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Chessboard building. We further abstract the semantic map into a compact chessboard, i.e., map to chessboard " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "(M2C)" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "inline_equation", + "content": "M2C" + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": " function consists of two cascaded kernels." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19458" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 553, + 295 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 553, + 295 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 553, + 295 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 553, + 295 + ], + "type": "image", + "image_path": "cd851cc741c27a4a9b736a0e86d20f655dc9f2675fb7d12603da851066e62a89.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 308, + 555, + 352 + ], + "lines": [ + { + "bbox": [ + 54, + 308, + 555, + 352 + ], + "spans": [ + { + "bbox": [ + 54, + 308, + 555, + 352 + ], + "type": "text", + "content": "Figure 2. Overview of R2C framework: The LLM begins by generating high-level subgoals for the task. For each subgoal, the environment filter translates RGB-D observations into an updated grid-based chessboard representation of the environments. The LLM then uses chain-of-thought analysis to integrate this chessboard representation along with game rules, determining the next optimal position, which is finally converted into executable robot actions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "spans": [ + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": "The first kernel is a dilation kernel " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_{dila}" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": ", designed to prevent collisions between the agent and obstacles. Similar to the dilation algorithm in image processing [30], it expands all occupied pixels of obstacles (including objects) outward by " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": " in the map. The second kernel is a max pooling kernel " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_{pool}" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": ", which performs max pooling on the map. Then, the map is down-sampled from size " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": " to size " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "W = \\left\\lceil \\frac{M}{\\omega} \\right\\rceil" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 54, + 357, + 294, + 465 + ], + "type": "text", + "content": " is the grid size, calibrated to match the length of the agent's step." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "text", + "content": "Next, we aggregate this map with multiple object layers into a unified single-layer chessboard. To address the many-to-one projection problem, where overlapping objects might appear in the same grid, e.g., \"apples on a table\", we introduce a Goal-aware Aggregate function " + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "text", + "content": ". This function prioritizes both the relevance to the current subgoal, i.e., the target object Object in current subgoal " + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "G_{k}" + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "text", + "content": ", and the size of the object. The most relevant and smallest objects are placed at the top layer, and then we merge object layers from bottom to top to produce the final chessboard. The overall formulation of the " + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "inline_equation", + "content": "M2C" + }, + { + "bbox": [ + 54, + 466, + 295, + 597 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 121, + 601, + 295, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 601, + 295, + 619 + ], + "spans": [ + { + "bbox": [ + 121, + 601, + 295, + 619 + ], + "type": "interline_equation", + "content": "M 2 C = \\mathcal {A} \\circ \\mathcal {K} _ {d i l a} \\circ \\mathcal {K} _ {p o o l} \\tag {1}", + "image_path": "21db6a478afb762d9be6438b4b14395ef381f389fcf0ef6b4bbe5af36df90c94.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 122, + 617, + 204, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 617, + 204, + 628 + ], + "spans": [ + { + "bbox": [ + 122, + 617, + 204, + 628 + ], + "type": "interline_equation", + "content": "\\mathcal {B} = M 2 C (\\mathcal {M}, G _ {k}).", + "image_path": "cc8804b7ba8bf52ae13a1cc50651839ab530737f8934dd6392cf2c8b82298175.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 638, + 198, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 638, + 198, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 638, + 198, + 651 + ], + "type": "text", + "content": "3.1.3. Low-Level Planning (LLP)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 653, + 296, + 714 + ], + "type": "text", + "content": "The chessboard filtered out from the Environment Filter provides compact yet sufficient environmental state information for LLM. We then simulate a \"chess game\" between the LLM and the robot to perform low-level planning. The LLP task is formulated as a single-step generation task for" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": "the LLM. As shown in Fig. 2, various state information is collected, including current subgoal " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "G_{k}" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": ", chessboard state " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": ", action history " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": " and game rules " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": ". Our prompt system " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": " organizes such data and feeds them into the LLM to generate the next position prediction " + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 357, + 555, + 453 + ], + "type": "text", + "content": ". Note that LLP is invoked only for navigation subgoals, as interaction subgoals in ALFRED can be handled by predefined low-level actions once the agent reaches the visible range of the target object." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "content": "Chessboard state. To translate the chessboard state for the LLM, we convert it into textual object occupancy coordinate sets. The chessboard coordinate system originates from the upper left corner, with the X-axis pointing down and the Y-axis to the right. For each object on the chessboard, we gather a set of occupancy coordinates " + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_t^c = \\{x_i,y_i\\}" + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "inline_equation", + "content": "c\\in [1,C + 2]" + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "inline_equation", + "content": "x_{i},y_{i}\\in [1,W]" + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "content": ". The initial agent position " + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "inline_equation", + "content": "w_{0}" + }, + { + "bbox": [ + 313, + 456, + 554, + 563 + ], + "type": "text", + "content": " is predefined in the benchmark." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "content": "Game rules. To assist the LLM in planning, we define key game rules " + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "content": ": 1) Basic inputs, including chessboard dimensions " + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "content": ", maximum steps " + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "content": ", and maximum errors " + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 567, + 554, + 662 + ], + "type": "text", + "content": "; 2) Action space, simplified to adjacent grids in four directions (up, down, left, right), i.e., the robot is only allowed to move 1 block at a time, due to the limited spatial reasoning ability of current LLMs; 3) Collision rules, where grids occupied by objects or obstacles are considered illegal moves." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Action history. We maintain a queue " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": " with a fixed length " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": " to store recent successful movement coordinates, providing the LLM with contextual information about previous actions. At each step " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": ", the prompt system combines" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19459" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 108 + ], + "type": "text", + "content": "all such information and feeds them to the LLM, which simulates a chess player to decide the next move. The LLP models a policy " + }, + { + "bbox": [ + 55, + 72, + 296, + 108 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 55, + 72, + 296, + 108 + ], + "type": "text", + "content": ", defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 119, + 110, + 295, + 124 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 110, + 295, + 124 + ], + "spans": [ + { + "bbox": [ + 119, + 110, + 295, + 124 + ], + "type": "interline_equation", + "content": "u _ {t} = \\pi (\\mathcal {P} (G _ {k}, \\mathcal {U} _ {t}, R, \\mathcal {Q} _ {t})), \\tag {2}", + "image_path": "a89250536c11150866a4053f348cdedea7a472323dbe6d094ed724444d067872.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "inline_equation", + "content": "u_{t} = (x_{t},y_{t})" + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "content": " is the predicted next position on the chessboard. According to the defined action space, the available next positions are restricted to the adjacent grids in four directions " + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "inline_equation", + "content": "x_{t + 1}\\in [x_t - 1,x_t + 1]" + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "inline_equation", + "content": "y_{t + 1}\\in [y_t - 1,y_t + 1]" + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "inline_equation", + "content": "x_{t + 1},y_{t + 1}\\in [1,W]" + }, + { + "bbox": [ + 55, + 129, + 296, + 190 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": "Since the chessboard grid size is calibrated to match the robot's step length, the predicted adjacency target position " + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "inline_equation", + "content": "u_{t}" + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": " can be directly converted to a sequence of executable low-level actions " + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{a} = \\{a_{i}\\}" + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "inline_equation", + "content": "a_{i} \\in \\mathbf{A}_{\\text{nav}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": " in the real-world environments. For example, in the ALFRED benchmark, " + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\text{nav}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": " includes (MoveForward, 0.25m), (TurnLeft, 90°) and, (TurnRight, 90°). Based on the predicted target position, the movement in any of the four directions can be converted into the corresponding action sequence (e.g., TurnLeft and MoveForward to move to the left adjacent grid). Additionally, if the output " + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 55, + 190, + 296, + 369 + ], + "type": "text", + "content": " is within the visible range of the target object Object in the current subgoal, the system moves on to the next subgoal. See more details of the R2C framework in the pseudocode provided in the supplementary materials." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 377, + 270, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 270, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 270, + 390 + ], + "type": "text", + "content": "3.2. Chain-of-Thought Fine-tuning Paradigm" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 395, + 296, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 296, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 296, + 502 + ], + "type": "text", + "content": "To improve the decision-making capabilities of LLMs in our chess game, we introduce an interpretable fine-tuning paradigm with two core features: 1) simultaneous training of high-level task decomposition and low-level Chain of Thought Decision (CoT-D) tasks, enabling the integration of High-Level Planning (HLP) and Low-Level Planning (LLP) within a single LLM, and 2) structuring the CoT-D process into four distinct parts to enhance the LLM's comprehension of game rules and spatial reasoning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 509, + 220, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 220, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 220, + 521 + ], + "type": "text", + "content": "3.2.1. Joint Training of HLP and LLP" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 524, + 296, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 524, + 296, + 619 + ], + "spans": [ + { + "bbox": [ + 55, + 524, + 296, + 619 + ], + "type": "text", + "content": "Long-horizon planning often involves compositional tasks that require hierarchical planning capabilities. Therefore, rather than only exploiting the LLM as a high-level planner or training an end-to-end low-level action generation model, we jointly train the model on both HLP and LLP tasks simultaneously. Given the data imbalance between HLP and LLP, we apply data balancing techniques to ensure the model effectively learns skills at both levels." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 626, + 236, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 626, + 236, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 626, + 236, + 639 + ], + "type": "text", + "content": "3.2.2. Chain of Thought Decision (CoT-D)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "LLM should thoroughly comprehend our chessboard coordinate system and predict the next position based on the semantic information of the chessboard and its inherent common sense. For the given prompt " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " with chessboard state " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": ", the LLM needs to generate answer sentence " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " (including next position " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": ") with probabilistic language model " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{LM}" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": ". If" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "LLM is asked to directly provide coordinates, this process can be formalized as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 357, + 91, + 553, + 125 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 91, + 553, + 125 + ], + "spans": [ + { + "bbox": [ + 357, + 91, + 553, + 125 + ], + "type": "interline_equation", + "content": "p (\\mathcal {S} \\mid \\mathcal {P}) = \\prod_ {i = 1} ^ {| \\mathcal {S} |} p _ {L M} \\left(s _ {i} \\mid \\mathcal {P}, s _ {< i}\\right). \\tag {3}", + "image_path": "7a09fc1c6436f014b7b4f7cf8d67a620676c861f8ce1e780d04936762da75718.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": "However, such a complex task is much more challenging than the task decomposition. This requires the LLMs have strong capabilities in long-text comprehension and spatial reasoning. However, the current models are not particularly skilled in these abilities. Consequently, we design the Chain of Thought Decision (CoT-D) tasks to strengthen LLM's rationale " + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": " in these aspects. The task consists of four subtasks, requiring LLMs to output the result of key information extraction " + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_E" + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": ", direction judgment " + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_D" + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": ", target prediction " + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_T" + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": ", and selection analysis " + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_S" + }, + { + "bbox": [ + 313, + 130, + 555, + 281 + ], + "type": "text", + "content": ", respectively. We link these sub-tasks sequentially in natural language to construct a coherent logical chain. The entire task can be represented as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 326, + 281, + 553, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 281, + 553, + 326 + ], + "spans": [ + { + "bbox": [ + 326, + 281, + 553, + 326 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\cdot p (\\mathcal {S} \\mid \\mathcal {P}) = p (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) \\cdot p (\\mathcal {R} \\mid \\mathcal {P}) \\\\ p (\\mathcal {R} \\mid \\mathcal {P}) = \\prod_ {r _ {i} \\in \\left\\{\\mathcal {R} _ {E}, \\mathcal {R} _ {D}, \\mathcal {R} _ {T}, \\mathcal {R} _ {S} \\right\\}} p _ {L M} \\left(r _ {i} \\mid \\mathcal {P}, r _ {< i}\\right) \\tag {4} \\\\ \\end{array}", + "image_path": "e1d8ec6d03a34ecf273434e87ee095e41ba574676dd5ac1f78ff2a9a058e9f33.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 326, + 492, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 326, + 492, + 361 + ], + "spans": [ + { + "bbox": [ + 326, + 326, + 492, + 361 + ], + "type": "interline_equation", + "content": "p (\\mathcal {S} \\mid \\mathcal {P}, \\mathcal {R}) = \\prod_ {j = 1} ^ {| \\mathcal {S} |} p _ {L M} (s _ {i} \\mid \\mathcal {P}, \\mathcal {R}, s _ {< j})", + "image_path": "209e0fe2ecd37f95f3dd64e30164345a4d50391c3ab20e509874361027e6c637.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 366, + 554, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 554, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 554, + 402 + ], + "type": "text", + "content": "The specific content of the four sub-tasks will be introduced below. Examples can be found in Fig. 2, with details available in the supplementary materials." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 403, + 554, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 554, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 554, + 569 + ], + "type": "text", + "content": "Key information extraction. Due to the intricate information contained within the chessboard, when textualized, it becomes a lengthy document with substantial information. Considering that LLM often encounters issues such as context loss when comprehending long texts, this task is designed to train LLM in processing task-related long texts and extracting key information. This task requires LLM to extract relevant information about the current coordinates and target objects based on the chessboard information inputs. The form used in data annotation is as follows: The current position of the agent is [COORDS], and the target is [OBJECT NAME], which is located at [COORDS SET]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "Direction judgment. The conversion from a chessboard grid image to text is based on a two-dimensional Cartesian coordinate system, and all spatial relationship understanding relies on a good coordinate system understanding. Despite providing clear instructions to establish the coordinate system using prompts like Establish a coordinate system with the top-left grid as (1,1), experiments have shown that the LLM still frequently misunderstands the setup. This could be attributed to the length of the text and the scarcity of spatial reasoning tasks incorporated during the pre-training of contemporary LLM. To ensure LLM's accurate comprehension" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19460" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 71, + 358, + 207 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 358, + 207 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 358, + 207 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 358, + 207 + ], + "type": "table", + "html": "
MethodTraining ModeVal SeenVal UnseenΔ SR ↑Δ GC ↑
SR ↑GC ↑SR ↑GC ↑
Specialists, only for ALFRED tasks
E.T. [27]from scratch46.5952.927.3220.87-39.27-32.05
HiTUT [45]from scratch25.2434.8512.4423.71-12.80-11.14
M-TRACK [36]from scratch26.7033.2117.2928.98-9.41-4.23
FILM [25]from scratch24.6337.2020.1032.45-4.53-4.75
LEBP [22]from scratch27.6335.7622.3629.58-5.27-6.18
Generalists, based on LLMs
SayCan [1]few-shot12.3024.529.8822.54-2.42-1.98
LLM-P (GPT) [37]1few-shot16.4530.1115.3629.88-1.09-0.23
R2C-GPT-4 (ours)zero-shot20.0028.4624.0028.24+4.00-0.22
R2C-Llama-7B (ours)fine-tune20.8329.6018.9929.69-1.84+0.09
R2C-Mistral-7B (ours)fine-tune22.3132.4022.3531.97+0.04-0.43
", + "image_path": "6e752921d4c9fe7994951f63db8f1349c5558856b92b9675f4dd7f02d8ba860a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 373, + 70, + 541, + 173 + ], + "blocks": [ + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "lines": [ + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "spans": [ + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "type": "text", + "content": "Table 1. Main results on the ALFRED benchmark. SR and GC are short for success rate and goal-conditioned success rate. " + }, + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "type": "text", + "content": " SR and " + }, + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 61, + 212, + 357, + 246 + ], + "type": "text", + "content": " GC represent the performance drops in generalizing from the seen to the unseen environments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 373, + 70, + 541, + 173 + ], + "lines": [ + { + "bbox": [ + 373, + 70, + 541, + 173 + ], + "spans": [ + { + "bbox": [ + 373, + 70, + 541, + 173 + ], + "type": "table", + "html": "
Task TypeVal SeenVal Unseen
SRGCSRGC
Overall48.1855.1353.3358.18
Examine75.8679.3183.3387.96
Pick & Place69.5769.5763.3363.33
Stack & Place29.0337.0045.4546.46
Clean & Place63.8973.8738.8950.45
Cool & Place36.8449.6061.1169.23
Heat & Place23.5341.3828.5741.13
Pick 2 & Place33.3354.4137.5053.70
", + "image_path": "7ad85f7ae661cde6fafb79c7b5422a3e27e507b9942d6d0a734c8ac1087b752c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 255, + 294, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 294, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 294, + 316 + ], + "type": "text", + "content": "of the chessboard coordinate system, this task requires LLM to judge the direction between the target and the current coordinates. The format employed in data annotation is as follows: the target is at..., which is on the [DIRECTION] of the agent." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 316, + 295, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 316, + 295, + 449 + ], + "spans": [ + { + "bbox": [ + 54, + 316, + 295, + 449 + ], + "type": "text", + "content": "Target prediction. The locations where different categories of objects appear often have priors. For example, sofas are likely to appear opposite the television. Therefore, we aim to enable LLM to develop the capability of predicting target locations. This can minimize the ineffective or inefficient exploration process for the robot to find target objects, thereby improving the efficiency of the system in accomplishing embodied tasks. The expression utilized in data annotation is: Based on the chessboard analysis, the target is likely located near [COORDS]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 449, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 295, + 604 + ], + "type": "text", + "content": "Selection analysis. Based on the above comprehension, we require the LLM to further analyze all potential next positions according to the chessboard rules. During this analysis, the LLM evaluates each possible move, providing a rationale for each choice. The specific format used in the annotation is: [COORDS]: This position is on the [DIRECTION] of the agent, [Reason]. The [Reason] component is generated by GPT-4 based on the agent's current state and the relationship between the chosen position and the correct orientation. For instance: Objects in this direction have already been discovered; we should head to areas that have not been explored." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 296, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 642 + ], + "type": "text", + "content": "These four sub-tasks comprehensively enhance the understanding of chessboard and spatial reasoning ability of the LLMs from different perspectives." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 655, + 127, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 655, + 127, + 667 + ], + "spans": [ + { + "bbox": [ + 55, + 655, + 127, + 667 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "Benchmark. We evaluate our method on the challenging ALFRED [34] benchmark, which features long-horizon" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 328, + 253, + 542, + 337 + ], + "blocks": [ + { + "bbox": [ + 365, + 179, + 548, + 245 + ], + "lines": [ + { + "bbox": [ + 365, + 179, + 548, + 245 + ], + "spans": [ + { + "bbox": [ + 365, + 179, + 548, + 245 + ], + "type": "text", + "content": "Table 2. Performance of R2C on different tasks. The R2C model excels in \"Examine\" tasks, but faces challenges in complex \"Heat & Place\" tasks, where the \"HeatObject\" subgoal alone involves seven interactive steps, increasing the risk of error accumulation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 253, + 542, + 337 + ], + "lines": [ + { + "bbox": [ + 328, + 253, + 542, + 337 + ], + "spans": [ + { + "bbox": [ + 328, + 253, + 542, + 337 + ], + "type": "table", + "html": "
MethodVal SeenVal Unseen
SRGCSRGC
Base Model (R2C-Mistral-7B)22.3132.4022.3531.97
+ GT Seg.37.9245.8335.2443.88
+ GT Seg., GT Goal48.1855.1353.3358.18
+ GT Seg., GT Goal, - SA45.9751.7547.4553.03
+ GT Seg., GT Goal, - CoT41.2249.3541.9647.88
", + "image_path": "2be91cc0f55fea700b5ccd577e6c9f39c27506ce242700b6ac1190170b5973ad.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 338, + 554, + 383 + ], + "lines": [ + { + "bbox": [ + 313, + 338, + 554, + 383 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 554, + 383 + ], + "type": "text", + "content": "Table 3. Ablation of R2C. \"GT Seg.\" represents the model using ground-truth segmentation. \"GT Goal\" represents using ground-truth subgoals. \"- SA\" is the model without Selection Analysis part of CoT. \"- CoT\" is the model without all CoT tasks." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 398, + 553, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 553, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 553, + 457 + ], + "type": "text", + "content": "tasks (7 types in total) involving both navigation and interaction across 207 unique environments and 115 different object types. In our experiments, we adhere to the benchmark's settings, including low-level action space, maximum agent steps, and failure limits." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": "Chessboard settings. The physical room size " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "16m" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": ", which is the approximate maximum room size, and the grid size " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": " corresponds to the agent's step length, " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "0.25m" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": ". Thus, the size of the semantic map and the chessboard is " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "M = 320" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "inline_equation", + "content": "W = 64" + }, + { + "bbox": [ + 313, + 459, + 554, + 555 + ], + "type": "text", + "content": " separately. However, to represent more complex environments, one can choose a more fine-grained chessboard. We demonstrate this through a simple experiment in the supplementary materials." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 555, + 554, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 554, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 554, + 664 + ], + "type": "text", + "content": "Model settings. For the zero-shot R2C, we use the public GPT-4-turbo API [26] without any in-context examples. Considering the testing cost, we randomly sample a subset of size 100 covering all 7 types of tasks strictly according to the task distribution of ALFRED. We collected a total of 264,915 data samples for fine-tuning, including 70,000 samples for the Task Decomposition tasks and 194,915 samples for the CoT-D tasks. All data collection was based solely on the training set of ALFRED. During training," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 673, + 553, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 553, + 713 + ], + "type": "text", + "content": "For a fair comparison, we test the performance of the GPT-4 version of LLM-P on the same selected subset as ours, achieving an SR of " + }, + { + "bbox": [ + 313, + 673, + 553, + 713 + ], + "type": "inline_equation", + "content": "16.21\\%" + }, + { + "bbox": [ + 313, + 673, + 553, + 713 + ], + "type": "text", + "content": " on seen scenes. Since this work solely employs LLMs for task decomposition, the performance is only slightly different when compared to using GPT-3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19461" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 70, + 479, + 265 + ], + "blocks": [ + { + "bbox": [ + 130, + 70, + 479, + 265 + ], + "lines": [ + { + "bbox": [ + 130, + 70, + 479, + 265 + ], + "spans": [ + { + "bbox": [ + 130, + 70, + 479, + 265 + ], + "type": "image", + "image_path": "e4436f41a48d7d371afd859dc4cad439b08c812e31d4757a1ba7f128ab69b883.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 266, + 555, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 266, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 555, + 289 + ], + "type": "text", + "content": "Figure 3. Case study of R2C with Mistral model: The model completes an \"Examine\" task in 31 steps (top) but fails to locate the small target object, a bowl, during a \"Clean & Place\" task in a more complex environment (bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 299, + 296, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 299, + 296, + 370 + ], + "spans": [ + { + "bbox": [ + 55, + 299, + 296, + 370 + ], + "type": "text", + "content": "we conduct full-parameter fine-tuning on both the Mistral-7B-Instruct-v0.2 model [17] and the Llama-7B-Chat model [40] using all the data. Both models were trained for only one epoch. We conduct all fine-tuning experiments using 4 NVIDIA H100 GPUs, and all evaluations are performed on 4 NVIDIA A40 GPUs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 381, + 141, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 141, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 141, + 392 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 399, + 296, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 296, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 296, + 482 + ], + "type": "text", + "content": "Tab. 1 presents the evaluation results on the validation set of ALFRED. We compare our R2C framework with both traditional robotic learning methods (specialists) and LLM-based approaches (generalists). R2C achieves state-of-the-art performance among LLM-based methods, with the Mistral-7B excelling in seen environments and GPT-4 in unseen environments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 484, + 296, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 296, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 296, + 579 + ], + "type": "text", + "content": "Compared to SayCan [1] and LLM-P [37], which use LLMs only for high-level planning, R2C integrates high-level and low-level planning, offering a more efficient, end-to-end solution. LLM-P requires 100 instruction-plan pairs for training, while R2C operates in a zero-shot setting without examples. Our CoT-D paradigm enables GPT to analyze the chessboard state comprehensively, improving decision interpretability and efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "text", + "content": "R2C fine-tuned on open-sourced LLMs achieves competitive results, with " + }, + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "inline_equation", + "content": "2.31\\%" + }, + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "text", + "content": " improvement in the seen split and " + }, + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "inline_equation", + "content": "1.65\\%" + }, + { + "bbox": [ + 55, + 581, + 295, + 689 + ], + "type": "text", + "content": " drop in the unseen split compared to R2C-GPT-4. This highlights GPT-4's superior generalization to unseen environments. However, with our carefully designed fine-tuning tasks, R2C implemented on much smaller models like LLaMA and Mistral, can still deliver performance comparable to GPT-4. This demonstrates the effectiveness and efficiency of our fine-tuning approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Finally, R2C fine-tuned on collected data performs comparably to specialist models like FILM [25] and LEBP [22]." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 345, + 297, + 520, + 389 + ], + "blocks": [ + { + "bbox": [ + 345, + 297, + 520, + 389 + ], + "lines": [ + { + "bbox": [ + 345, + 297, + 520, + 389 + ], + "spans": [ + { + "bbox": [ + 345, + 297, + 520, + 389 + ], + "type": "image", + "image_path": "b292c278f65a7811a7cc05550093e7dd95d81b56786eb901b308f7833c86d24c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 389, + 539, + 400 + ], + "lines": [ + { + "bbox": [ + 329, + 389, + 539, + 400 + ], + "spans": [ + { + "bbox": [ + 329, + 389, + 539, + 400 + ], + "type": "text", + "content": "Figure 4. Cases of R2C-GPT-4 on open-vocabulary tasks." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 403, + 555, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 462 + ], + "type": "text", + "content": "Although these specialized models excel in seen scenes, they struggle in unseen environments due to overfitting. In contrast, R2C and other LLM-based methods demonstrate stronger generalization across both seen and unseen environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 472, + 408, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 408, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 408, + 483 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 486, + 555, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 605 + ], + "type": "text", + "content": "We perform an ablation study to analyze the impact of different R2C modules. As shown in Tab. 3, using ground truth segmentation (GT Seg.) significantly improves performance, highlighting segmentation as a bottleneck, especially in simulation environments. Using ground truth sub-goals (GT Goal) also boosts SR, revealing the impact of ambiguity in natural language instructions. Annotator confusion between categories like desk lamps and floor lamps can hinder task decomposition, though LLMs' strong generalization helps mitigate this." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 606, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 556, + 713 + ], + "type": "text", + "content": "Removing the CoT-D framework, i.e., forcing the model to directly output position coordinates without rationale, results in a significant performance drop, especially in unseen scenes. This highlights the importance of fine-tuning with CoT-D for better spatial reasoning. Ablating individual subtasks is challenging due to their interdependence. Here, we ablate removing the Selection Analysis part (- SA), where decisions are made without analyzing options and it causes a noticeable performance decline." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19462" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 72, + 180, + 152 + ], + "blocks": [ + { + "bbox": [ + 58, + 72, + 180, + 152 + ], + "lines": [ + { + "bbox": [ + 58, + 72, + 180, + 152 + ], + "spans": [ + { + "bbox": [ + 58, + 72, + 180, + 152 + ], + "type": "image", + "image_path": "c2fbd1535697dae278d6ac2071f728d8aac329473d778aba0b6ac61a6e02645b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 181, + 72, + 299, + 152 + ], + "blocks": [ + { + "bbox": [ + 181, + 72, + 299, + 152 + ], + "lines": [ + { + "bbox": [ + 181, + 72, + 299, + 152 + ], + "spans": [ + { + "bbox": [ + 181, + 72, + 299, + 152 + ], + "type": "image", + "image_path": "66af14fe3725f0ea355129744d40ce9b4053a7cadf8e2088bd57f57ebf20b971.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 154, + 180, + 232 + ], + "blocks": [ + { + "bbox": [ + 58, + 154, + 180, + 232 + ], + "lines": [ + { + "bbox": [ + 58, + 154, + 180, + 232 + ], + "spans": [ + { + "bbox": [ + 58, + 154, + 180, + 232 + ], + "type": "image", + "image_path": "796f00fd166c3d94b29c8defb9b72cbd8cc59016924d4f245b5da13cf266d905.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 238, + 297, + 283 + ], + "lines": [ + { + "bbox": [ + 55, + 238, + 297, + 283 + ], + "spans": [ + { + "bbox": [ + 55, + 238, + 297, + 283 + ], + "type": "text", + "content": "Figure 5. Visual results of R2C in real-world scenarios. Three tasks are tested in a real-world environment, with the corresponding instructions, third-person trajectories, first-person images, and chessboard visualizations shown for each task." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 181, + 154, + 299, + 232 + ], + "blocks": [ + { + "bbox": [ + 181, + 154, + 299, + 232 + ], + "lines": [ + { + "bbox": [ + 181, + 154, + 299, + 232 + ], + "spans": [ + { + "bbox": [ + 181, + 154, + 299, + 232 + ], + "type": "image", + "image_path": "5467b30963f17942381e4f7ada63edc40d7c776559239836d16b8b5beb18a8d3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 58, + 290, + 299, + 344 + ], + "blocks": [ + { + "bbox": [ + 58, + 290, + 299, + 344 + ], + "lines": [ + { + "bbox": [ + 58, + 290, + 299, + 344 + ], + "spans": [ + { + "bbox": [ + 58, + 290, + 299, + 344 + ], + "type": "table", + "html": "
TaskSpecific Obj.Specific Loc.Nearest CornerCenter BetweenOverall
GPT-4 (90°)66.773.353.380.068.3
GPT-4 (45°)73.373.373.360.070.0
GPT-4o (90°)40.053.333.346.743.3
", + "image_path": "6153bcbb31c24844ea0013e83f83cecd9795bc48127440445296729567126568.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 369, + 223, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 223, + 382 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 223, + 382 + ], + "type": "text", + "content": "4.4. Evaluation Across Tasks Types" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 387, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 495 + ], + "type": "text", + "content": "We analyze R2C's performance across task types using GT Segmentation and GT Goal settings, with task-specific results shown in Tab. 2. R2C shows SR drops on more complex long-horizon tasks, such as \"Heat & Place,\" with average GT step lengths of 63, compared to shorter ones (e.g., Examine: 37). We provide a visualization of two case studies of R2C completing different tasks (\"Examine\" and \"Clean & Place\") in Fig. 3. More failure case analyses are included in the supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 503, + 257, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 257, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 257, + 517 + ], + "type": "text", + "content": "4.5. Exploration on Open-vocabulary Task" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 521, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 640 + ], + "type": "text", + "content": "Real-world tasks are more diverse and flexible than the predefined, limited tasks in ALFRED. To assess R2C's ability to handle open-vocabulary tasks, we conduct a mini experiment with 60 test trials generated randomly by GPT-4 across 3 room sizes (7x7, 5x9, 5x11), five room layouts, and four task types. 1) Specific Obj.: Move to a specific object (e.g., nearest chair). 2) Specific Loc.: Move to a specific location (e.g., center or corner). 3) Nearest Corner: Move to the nearest corner. 4) Center Between: Move to the center between two objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": "Traditional closed-domain approaches struggle with these tasks, as they are limited to defined tasks in the training set. Meanwhile, high-level LLM planners face challenges in translating them into object-navigation plans. We test R2C with various settings: GPT-4 " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "(90^{\\circ})" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": ", GPT-4 " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "(45^{\\circ})" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " which allow 45-degree rotation, and GPT-4o " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "(90^{\\circ})" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": ", which" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 348, + 71, + 521, + 111 + ], + "blocks": [ + { + "bbox": [ + 83, + 346, + 268, + 357 + ], + "lines": [ + { + "bbox": [ + 83, + 346, + 268, + 357 + ], + "spans": [ + { + "bbox": [ + 83, + 346, + 268, + 357 + ], + "type": "text", + "content": "Table 4. SR (%) of R2C on open-vocabulary tasks." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 348, + 71, + 521, + 111 + ], + "lines": [ + { + "bbox": [ + 348, + 71, + 521, + 111 + ], + "spans": [ + { + "bbox": [ + 348, + 71, + 521, + 111 + ], + "type": "table", + "html": "
MethodSAVN [43]S2P [4]R2C
SR (%)40.8646.1652.25
SPL (%)16.1528.0129.56
", + "image_path": "afd5da4a74cbeb468c60dfefbb8411912df2c33513d2663961ec1c4d4f828cc7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 332, + 113, + 535, + 124 + ], + "lines": [ + { + "bbox": [ + 332, + 113, + 535, + 124 + ], + "spans": [ + { + "bbox": [ + 332, + 113, + 535, + 124 + ], + "type": "text", + "content": "Table 5. Performance of R2C on object navigation task." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 134, + 553, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 134, + 553, + 157 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 553, + 157 + ], + "type": "text", + "content": "uses visualized chessboards. Results are summarized in Tab. 4, and two task examples are visualized in Fig. 4." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "spans": [ + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "content": "The results demonstrate the potential of R2C in handling open-vocabulary tasks for real-world applications. GPT-4 " + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "inline_equation", + "content": "(45^{\\circ})" + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "content": " outperforms the " + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "content": "-agent, thanks to more efficient diagonal movement, highlighting the expandability of R2C with different action spaces. Both GPT-4 " + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "inline_equation", + "content": "(90^{\\circ})" + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "content": " and GPT-4 " + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "inline_equation", + "content": "(45^{\\circ})" + }, + { + "bbox": [ + 313, + 158, + 555, + 266 + ], + "type": "text", + "content": " outperform GPT-4o, as feeding the chessboard directly to the VLM leads to poor spatial grounding and inaccurate path predictions. More results are available in the supplementary materials." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 274, + 506, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 506, + 286 + ], + "type": "text", + "content": "4.6. Application in Real-world Scenarios" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 292, + 555, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 292, + 555, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 555, + 411 + ], + "type": "text", + "content": "To evaluate the real-world applicability of the R2C framework, we design three open-vocabulary tasks to test its performance using the LoCoBot robot in a set-up real-world experiment room. We evaluate R2C-GPT-4 in zero-shot setting. As shown in Fig. 5, the R2C framework, by enabling LLM to generate low-level actions, allows successful task completion in a totally different environment, showcasing its effectiveness and versatility in real-world scenarios. Detailed implementation information can be found in the supplementary materials." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 420, + 481, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 481, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 481, + 433 + ], + "type": "text", + "content": "4.7. Evaluation on Navigation Task" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 437, + 554, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 498 + ], + "type": "text", + "content": "To further evaluate the model's generalization capability across tasks, we extend R2C-Mistral-7B model trained on ALFRED to the AI2THOR ObjectNav task [43] without additional fine-tuning. Results in Tab. 5 show that R2C significantly outperforms S2P [4], another LLM-based planner." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "type": "text", + "content": "We introduce the Room to Chessboard (R2C) framework, which maps the complex room into a chessboard as a communication platform between the LLM and the robot, unlocking the LLM as low-level planner to directly guide the robot to adaptively finish the embodied tasks. To address the spatial reasoning tasks on chessboard, we design a CoT-D fine-tuning paradigm that enhances LLM's ability to make interpretable low-level decisions. Experiments show that R2C outperforms existing LLM-based high-level planners, even in zero-shot settings, and allows 7B models to surpass GPT-4. Furthermore, R2C enables LLMs to tackle open-vocabulary tasks where API-based frameworks fall short. However, R2C still faces challenges, such as handling very large scenes. Future work will focus on optimizing R2C for larger environments and exploring its potential for various open-vocabulary tasks." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19463" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "type": "text", + "content": "Acknowledgement This work is partially supported by National Key R&D Program of China No. 2021ZD0111901, and Natural Science Foundation of China under contracts Nos. 62495082, U21B2025. Ziyi Bai, Hanxuan Li, and Bin Fu contributed equally to this work. Ziyi Bai led the implementation of the overall framework and the evaluation of the ALFRED benchmark and open-vocabulary tasks. Hanxuan Li proposed the R2C and CoT-D fine-tuning methods, validated their feasibility, and took the lead in the design, training, and acceleration of the LLM-based module. Bin Fu focused on the implementation of semantic mapping and chessboard construction, led the object navigation evaluation, and also contributed to the ALFRED evaluation. Bin Fu and Hanxuan Li jointly led the system deployment in real-world environments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "spans": [ + { + "bbox": [ + 56, + 259, + 115, + 272 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 279, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 61, + 279, + 294, + 334 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 279, + 294, + 334 + ], + "spans": [ + { + "bbox": [ + 61, + 279, + 294, + 334 + ], + "type": "text", + "content": "[1] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Chuyuan Fu, Keerthana Gopalakrishnan, Karol Hausman, et al. 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PMLR, 2023. 3" + } + ] + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19466" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_content_list.json b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c58d0b6c409a608297c65f9fdae8f5aa9409d60f --- /dev/null +++ b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_content_list.json @@ -0,0 +1,1828 @@ +[ + { + "type": "text", + "text": "RADIOv2.5: Improved Baselines for Agglomerative Vision Foundation Models", + "text_level": 1, + "bbox": [ + 102, + 128, + 897, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Greg Heinrich* Mike Ranzinger* Hongxu (Danny) Yin Yao Lu Jan Kautz Andrew Tao Bryan Catanzaro Pavlo Molchanov NVIDIA", + "bbox": [ + 171, + 180, + 823, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{gheinrich,mranzinger,danny,jkautz,atao,bcatanzaro,pmolchanov}@nvidia.com", + "bbox": [ + 169, + 236, + 823, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 328, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Agglomerative models have recently emerged as a powerful approach to training vision foundation models, leveraging multi-teacher distillation from existing models such as CLIP, DINO, and SAM. This strategy enables the efficient creation of robust models, combining the strengths of individual teachers while significantly reducing computational and resource demands. In this paper, we thoroughly analyze state-of-the-art agglomerative models, identifying critical challenges including resolution mode shifts, teacher imbalance, idiosyncratic teacher artifacts, and an excessive number of output tokens. To address these issues, we propose several novel solutions: multi-resolution training, mosaic augmentation, and improved balancing of teacher loss functions. Specifically, in the context of Vision Language Models, we introduce a token compression technique to maintain high-resolution information within a fixed token count. We release our top-performing variants at multiple scales $(-B, -L, -H, \\text{and} -g)$ , along with inference code and pretrained weights.", + "bbox": [ + 88, + 318, + 485, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Links: Code (on GitHub)—Models (on Hugging Face)", + "bbox": [ + 109, + 611, + 483, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 669, + 223, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The rise of specialized Vision Foundation Models (VFMs) has created a need for methods to consolidate knowledge from multiple models into a unified model. SAM-CLIP [43] addresses this challenge by combining SAM [22] and CLIP [32] to integrate capabilities from both. In another approach, AM-RADIO [35] introduces label-free knowledge distillation from multiple teacher models, enabling knowledge transfer without direct supervision. UNIC [37] adds intermediate teacher matching projectors and dynamic teacher selection. Theia [38] aims to facilitate robot learning by distilling insights from multiple vision teachers. Meanwhile, PHI-S [34] studies the importance of normal", + "bbox": [ + 89, + 695, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "izing the distinct teacher distributions to simplify their balancing. Relatedly, Eagle [39] leverages a mixture of vision encoders to achieve inference-time knowledge aggregation within the context of Vision-Language Models (VLMs).", + "bbox": [ + 511, + 287, + 906, + 348 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite these advancements, this growing body of work on knowledge agglomeration still leaves open several critical challenges:", + "bbox": [ + 511, + 348, + 906, + 393 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Resolution balancing: Teacher models operate at varying resolutions due to different training goals, creating feature granularity inconsistencies. Effective techniques are needed to balance these resolutions in the student model to capture both fine details and broader abstractions.", + "- Teacher distribution balancing: Existing models have different distribution moments and the distillation process should account for this to prevent biased learning.", + "- Generating multi-resolution features for diverse applications: Vision models support various applications requiring different feature resolutions, from image captioning to dense segmentation. A VFM that flexibly produces features at any resolution could serve multiple tasks, reducing the need for separate models and unlocking new opportunities." + ], + "bbox": [ + 514, + 398, + 905, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In our analysis of existing agglomerative models, we study and propose a fix for the notable \"mode switch\" phenomenon in AM-RADIO, where feature distributions shift significantly based on input resolution (Section 3.1). Specifically, low-resolution inputs yield DINO-like features, while high-resolution inputs produce SAM-like features. We trace this behavior to the student learning from different teachers at different resolutions during training. In section 4.2, we introduce a solution to stabilize these mode switches, achieving strong resolution robustness and improved quality scaling.", + "bbox": [ + 511, + 628, + 906, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Equipped with a high-resolution vision encoder, we now focus on Vision-Language Model (VLM) integration. In downstream VL tasks, a key challenge is the token/feature count. High-resolution processing yields more tokens, exacerbating the quadratic complexity of attention in VLMs. To maintain resolution without escalating this issue, we propose using ToMeSD [3] in Section 4.5 to separate vision", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 109, + 887, + 217, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22487", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e72b5c8a0ef08bde93c10da072f0b62a4e62f47d1cb20043654a312c1da51420.jpg", + "image_caption": [ + "Problem: Inconsistent accuracy across resolutions" + ], + "image_footnote": [], + "bbox": [ + 117, + 125, + 205, + 195 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/12b2e341c7e97dc81c48e242f4f5cd28e647b7f6de139afb55acf5a472cbaf61.jpg", + "image_caption": [ + "Cause: Student only sees SAM at high resolution" + ], + "image_footnote": [], + "bbox": [ + 238, + 125, + 325, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/22ec272f96cccaa9842121b05a329fe3727c629d6a425cf2da799e4ec3f699ab.jpg", + "image_caption": [ + "Solution: Multi-Resolution Training" + ], + "image_footnote": [], + "bbox": [ + 117, + 237, + 325, + 348 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ab5a6e93a7e332221acda375049fb95b031fe50f21b90d885a2f2b173007d7b6.jpg", + "image_caption": [ + "Problem: VLM hardly improves at high resolution", + "Cause: Standard local pooling with pixel unshuffling loses details", + "Solution: Global fine-grain token merging" + ], + "image_footnote": [], + "bbox": [ + 351, + 147, + 614, + 234 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bc5f1ddcf587cafd55a3bf60fbca13bd8457b731644def1b34fc68616c9eea20.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 265, + 614, + 345 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f929c59a642bfe2aa33fed545f2c6c36aea00892f569ca50569f28b12b733155.jpg", + "image_caption": [ + "Figure 1. Overview of the main contributions: From left to right, we introduce a multi-resolution training framework that enables our student model to maintain accuracy across all resolutions; we propose using token merging to better retain fine-grained details while merging uninformative tokens; our RADIOv2.5 models improve upon the RADIOv2.1 baseline across all benchmarks, with significant gains on VLM tasks." + ], + "image_footnote": [], + "bbox": [ + 630, + 142, + 897, + 352 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "encoder resolution from the VLM's patch count.", + "bbox": [ + 89, + 460, + 410, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions, illustrated in Figure 1, are:", + "bbox": [ + 89, + 474, + 429, + 489 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A multi-resolution training strategy that fixes mode switching and allows for fully flexible input resolution.", + "- A comprehensive study of feature selection for a range of downstream tasks.", + "- A proposal for vision model feature selection within VLMs, enabling integration with language models while preserving essential information. We demonstrate that RADIOv2.5 disproportionately benefits from this." + ], + "bbox": [ + 89, + 489, + 483, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 89, + 623, + 218, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Knowledge Agglomeration", + "text_level": 1, + "bbox": [ + 89, + 648, + 333, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The assumption underlying knowledge agglomeration is that multiple foundation models exist, each capable of extracting diverse and meaningful representations from a wide range of images, and that knowledge from these models can be distilled into a single agglomerative model.", + "bbox": [ + 89, + 671, + 482, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let $x$ be the input data. The student's shared backbone produces a feature representation:", + "bbox": [ + 89, + 747, + 482, + 777 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} = f (x) = \\left[ z _ {s}, z _ {p} ^ {(1)}, z _ {p} ^ {(2)}, \\dots , z _ {p} ^ {(N)} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 786, + 482, + 813 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $z_{s} \\in \\mathbb{R}^{d}$ is the summary token, $z_{p}^{(i)} \\in \\mathbb{R}^{d}$ for $i = 1, \\dots, N$ are the patch tokens, and $d$ is the student's embedding dimension.", + "bbox": [ + 89, + 823, + 482, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For each teacher $t$ , the student's model includes two adaptor heads: $g_{s}^{(t)}:\\mathbb{R}^{d}\\to \\mathbb{R}^{d_{t}}$ , which projects the sum", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mary token $z_{s}$ into the teacher's embedding space, and $g_p^{(t)}:\\mathbb{R}^d\\to \\mathbb{R}^{dt}$ , which projects each patch token $z_{p}^{(i)}$", + "bbox": [ + 511, + 460, + 903, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adaptor heads, typically simple MLPs, adjust feature dimensions as needed. For teacher $t$ , we define:", + "bbox": [ + 511, + 492, + 903, + 522 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\ng ^ {(t)} (z) = \\operatorname {M L P} ^ {(t)} (z) = \\sigma \\left(W ^ {(t)} z + b ^ {(t)}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 532, + 903, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\sigma (\\cdot)$ is a non-linear activation, and $W^{(t)}$ and $b^{(t)}$ are learnable parameters. Projected features per teacher $t$ are:", + "bbox": [ + 511, + 564, + 906, + 595 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\text {S u m m a r y :} \\hat {z} _ {s} ^ {(t)} = g _ {s} ^ {(t)} \\left(z _ {s}\\right), \\quad \\text {P a t c h :} \\hat {z} _ {p} ^ {(t)} = g _ {p} ^ {(t)} \\left(z _ {p}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 619, + 903, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The training objective aligns student features with teacher features using a loss function that measures their similarity. For teacher $t$ , the loss $\\mathcal{L}_t$ is:", + "bbox": [ + 511, + 651, + 906, + 696 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\ell_ {s} \\left(\\hat {z} _ {s} ^ {(t)}, z _ {s} ^ {(t)}\\right) + \\sum_ {i = 1} ^ {N} \\ell_ {p} \\left(\\hat {z} _ {p} ^ {(t, i)}, z _ {p} ^ {(t, i)}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 708, + 903, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\ell .(\\cdot ,\\cdot)$ is a similarity/distance metric, and $\\ell_{s}$ (summary loss) may differ from $\\ell_p$ (patch loss). The total loss is a weighted average of all $\\mathcal{L}_t$ terms.", + "bbox": [ + 511, + 761, + 906, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Baseline Model", + "text_level": 1, + "bbox": [ + 511, + 816, + 668, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following AM-RADIO[35], our baseline model consists of a Vision Transformer (ViT)[11] backbone, including CPE [21] for multi-resolution support. We use DFN CLIP [15], OpenAI CLIP [32], DINOv2-g-reg [9]", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22488", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/3b2647b1f68f9e002fdce184a90c39c253bc593390a6573e37dce26d75ee6e31.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ConfigurationGoalImageNet1KSegmentationProbe3D[12]Vision-Language (VILA[23])SAM [22]
Zero-shotk-NNADE20kDepthSurfNormalsTextVQAChartQADocVQAInfoVQAOCRBench
A: RADIOv2.1-L*Baseline78.3584.0150.0382.6359.9457.0115.624.1928.8825.60
B: A + multi-resEliminate modes81.2184.0952.8482.3961.0459.4416.633.9929.0229.40
C: B - OpenAICLIP + SigLIPBetter VLM81.0184.6852.9584.760.164.4225.2845.8030.6036.00
D: C + ViT-HBigger backbone82.5185.8153.9785.762.565.8825.9649.7435.1740.90
E: D + Token MergingImprove VLM-----69.7430.4052.3336.2442.90
", + "bbox": [ + 93, + 88, + 903, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Ablation Results. For Probe3D, Depth and Surface Normals metrics are averaged over the buckets defined in the paper. For SAM COCO we use the \"instance all\" bucket. Each incremental change we introduce leads to improved metrics. *We use a ViT-L instead of the ViT-H used in the original AM-RADIO [35] paper.", + "bbox": [ + 89, + 176, + 906, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and SAM-H [22] as teachers. For each teacher to distill from, we augment the backbone with an adaptor for the summarization token, and an adaptor for the patch tokens. Our adaptor is a 2-layer MLP with a LayerNorm[1] and a GeLU[18] in between. We train the student using teacher features generated by inferring images of the DataComp1B[16] dataset. For faster iterations, we replicate AM-RADIO using a ViT-L backbone instead of the original ViT-H backbone and refer to it as RADIOv2.1-L from this point forward. We train the model with a batch size of $1024 + 128$ for $600\\mathrm{k}$ iterations. Training is split into two concurrent partitions: one partition trains the student at a resolution of $432^2$ against CLIP and DINOv2 teachers with batch size 1024, while the other partition trains the student at a resolution of $1024^2$ against SAM with a batch size of 128. This baseline is referred to as $\\mathcal{A}$ in Table 1.", + "bbox": [ + 88, + 231, + 485, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Evaluation Framework", + "text_level": 1, + "bbox": [ + 89, + 482, + 307, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Evaluating foundation model quality across diverse downstream tasks is challenging. We use a rigorous framework to pinpoint improvements and inform design: assessing ImageNet-1k[36] Top-1 accuracy via zero-shot[32] and k-NN[5] classification; probing frozen backbone features for semantic segmentation on ADE20k[50] and PascalVOC[13]; evaluating instance segmentation on COCO[21] with EfficientViT[25] protocols and our SAM adaptor; testing 3D understanding (depth, normals, correspondence) per [12]; pairing with an LLM for Vision-Language reasoning; and probing dense multi-task quality on Pascal Context[30] and NYUDv2[31] as in MLoRE [47].", + "bbox": [ + 89, + 506, + 483, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Challenges", + "text_level": 1, + "bbox": [ + 89, + 700, + 207, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Achieving Multi-Resolution Robustness", + "text_level": 1, + "bbox": [ + 89, + 726, + 429, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although AM-RADIO [35] supports a wide range of input resolutions, we noticed poor quality on high-resolution benchmarks. As illustrated in Figure 2, Zero-Shot Top-1 accuracy drops sharply after inputs are larger than roughly $512\\mathrm{px}$ . This showcases an undesirable property of this model, which is that it doesn't reliably scale to high-resolution images. AM-RADIO hints at this issue in its conclusion: the model exhibits a \"mode switching\" behavior as resolution increases. This prompted us to visualize the features and investigate the effect of a resolution increase. Fig-", + "bbox": [ + 89, + 750, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ure 3 illustrates the issue well: at resolutions lower than or equal to $512^2$ , the features most closely resemble those of DINOv2 and appear to be expressive of depth and semantic content. At higher resolutions, the model starts to behave more like SAM, with features that show sharp delineations around contours and homogeneous contents within. This behavior is intuitive given the fact that in the high-resolution regime the student only sees SAM features. Table 2 shows a quantified measure of feature variance across scales (see implementation in appendix). DINOv2 exhibits much smaller scale variance.", + "bbox": [ + 511, + 231, + 906, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Token Count", + "text_level": 1, + "bbox": [ + 511, + 407, + 650, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dense downstream tasks, such as pixel-level semantic segmentation and depth estimation, benefit from receiving fine features from a vision encoder. However, for vision-language models like LLaVA [24], where visual tokens are integrated into a sequence of text embeddings, an excessive number of vision tokens can negatively impact speed/quality or lead to sequence overflows. Pixel unshuffling, as proposed in InternVL1.5 [7], addresses this by reducing the number of vision tokens, grouping $2 \\times 2$ tokens along the channel dimension. However, this approach cannot adapt to varying information densities within an image. For instance, a text document might have large areas of white background that should be more strongly compressed than areas containing text.", + "bbox": [ + 511, + 430, + 908, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 656, + 604, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Scale Equivariance", + "text_level": 1, + "bbox": [ + 511, + 680, + 697, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We measure scale equivariance of multi-scale features by normalizing and interpolating them to the lowest resolution, then computing the spatial average of variance across scales (see Appendix F). Table 2 shows our baseline student has worse scale equivariance than DINOv2, our only multi-resolution teacher for comparison. VLMs like LLaVa-NeXT[24] and InternVL1.5[7] use tiling to handle high-resolution inputs with fixed-resolution encoders, suggesting scale equivariance may be less critical. However, tiling coarsens increases in resolution and, as tile count grows, limits the encoder's view of the full image, hindering contextual reasoning. In Figure 4, we analyze SigLIP[49] (used in Cambrian[42]) features across tiling setups, revealing", + "bbox": [ + 511, + 704, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22489", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ffc1ab8fad9a4d9f7663e61e2cb4754ec64f4509158e71eb819b973c24c080d9.jpg", + "image_caption": [ + "Figure 2. Zero-Shot Accuracy and teacher matching fidelity metrics as a function of input resolution. AM-RADIO (aka RADIOv2.1, config $\\mathcal{A}$ ), and our \"Multi-Stage Stage 3\" model exhibit mode switching behavior. \"Multi-Stage Stage 2\" doesn't exhibit the behavior, owing to all teachers being trained solely at low resolution, however quality at high resolution quickly degrades. \"Multi-Resolution\" (config $\\mathcal{B}$ ) training fixes the mode switch, and allows the model to be strong across a larger range of resolutions compared to Stage 2." + ], + "image_footnote": [], + "bbox": [ + 99, + 95, + 279, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7eb1b0a2941679a99ef187a2f53db5b5f2416d7e8caae55279208ae1dda21d9d.jpg", + "image_caption": [ + "Finding 1. High-resolution inference through tiling causes the vision encoder to lose global context and exhibit poor scaling equivariance." + ], + "image_footnote": [], + "bbox": [ + 300, + 95, + 480, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0ba186bbf8c58c285a9d49b0863df9c9e0a354af203df6e98f654b9f46039c3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 95, + 684, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f10e355ba79363aeb66436ed0073c861105a88361a82c61abd4a937af4f65488.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 95, + 883, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/65fda17a402052f2557f1a52d76fc580d81793d50d1294f66197bcfe0e0ab5f4.jpg", + "image_caption": [ + "Figure 3. Visualizations of patch token features across input resolutions. We use PCA to map patch tokens to RGB colors. Top: Input image, followed by visualizations of DINOV2, RADIOv2.1 (config $\\mathcal{A}$ ) at $256^2$ , $512^2$ , $1024^2$ resolutions, and SAM. Bottom: RADIOv2.5-H (config $\\mathcal{D}$ ). As resolution increases, RADIOv2.1 features resemble SAM's, even showing VitDet windowing artifacts, while RADIOv2.5 remains more self-consistent and less noisy." + ], + "image_footnote": [], + "bbox": [ + 91, + 297, + 483, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "qualitative inconsistencies and reduced scale equivariance (Table 2). Tiling also boosts vision tokens by up to $12 \\times [7]$ , increasing VLM latency.", + "bbox": [ + 89, + 570, + 482, + 617 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/754fe7c0f6e41dfde5649998d8813672c006c0f0cc117ac9bad88e2e26ee5668.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of tiling and high-resolution inference. Tiling emulates high-res SigLIP inference. Top: From left to right: input, SigLIP features using $1,2 \\times 2$ and $4 \\times 4$ tiles. Bottom: Single-pass inference using RADIOv2.5 (ours) at equivalent image sizes. SigLIP features vary significantly across different tiling arrangements." + ], + "image_footnote": [], + "bbox": [ + 91, + 650, + 482, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Multi-Resolution Training", + "text_level": 1, + "bbox": [ + 513, + 359, + 754, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The previous observations motivate a change in the training schedule: with multi-resolution training we enable the student to learn from all teachers across multiple resolutions. This is easily achieved with DINOv2, since DINOv2 can infer images at any resolution. For CLIP teachers, we feed them with images at the teacher's native resolution, and we feed the student with images at multiple resolutions. We interpolate student features down to the resolution of the teacher's features before applying the loss function. SAM presents an extra challenge, as noted in AM-RADIO[35], since interpolating SAM features significantly deteriorates their quality. Therefore in order to train our student against SAM at lower resolutions than $1024^2$ , we pad smaller images to $1024^2$ , then crop SAM features to the effective size of the unpadded image.", + "bbox": [ + 511, + 383, + 906, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training the student for 600k iterations with a multi-resolution setup is costly. Thus we break down training into three stages:", + "bbox": [ + 511, + 609, + 905, + 655 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- In a first stage, we train the student at low resolution $(256^{2})$ for 300k iterations.", + "- In a second stage, we train the student at medium resolution $(432^{2})$ for 300k iterations.", + "- In the third stage, we train the student simultaneously at $432^{2}$ and $1024^{2}$ resolutions for 300k iterations." + ], + "bbox": [ + 511, + 657, + 903, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-resolution training is illustrated in Figure 5, which depicts four training regimes based on whether the teachers and/or students process low- or high-resolution images. When both the student and teachers use either low- or high-resolution images, no particular challenge arises. However, training a high-resolution student against a low-resolution teacher requires downscaling the student's features to match those of the teacher. Conversely, training a low-resolution student against a high-resolution teacher necessitates a careful augmentation technique, as described in Section 4.3.", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22490", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/f0e3bdf94c52c319d463a61fea52721f617bd4a94cd0ad82938e4286dacb5dfb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelEquivariance ↓
Fine ScaleCoarse Scale
DINOv2-g-reg0.1260.178
AM-RADIO-L0.3570.476
RADIOv2.5-B0.1020.168
RADIOv2.5-L0.1020.165
RADIOv2.5-H0.1190.193
RADIOv2.5-L (tiling)N/A0.369
SigLIP (tiling)N/A0.623
", + "bbox": [ + 135, + 88, + 441, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Scale equivariance, computed over a small dataset of natural images (shown in Appendix). Fine: we scale image resolutions from $384^2$ to $1568^2$ by increments of the model's patch size. Coarse: we scale images from $384^2$ to $1920^2$ by multiples of $384^2$ . For the models that are denoted as \"tiling\", we perform inference over tiles of $384^2$ \" and re-assemble features to produce the high-resolution features.", + "bbox": [ + 89, + 229, + 483, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0fc13bb1c63512edafbd67e4a8db79ca607b649dfe63d1ec5b9cdc10feb07bf1.jpg", + "image_caption": [ + "Figure 5. Illustration of the multi-resolution training setup. The student learns from all teachers at all resolutions. High-res student features are downsampled to match the resolution of low-res teachers. High-res teachers are provided with mosaics of smaller images and their output features are cropped out in order to train a low-res student." + ], + "image_footnote": [], + "bbox": [ + 99, + 343, + 475, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finding 2. For the student model to be consistently accurate across resolutions, it is sufficient to match all teachers at all resolutions, and to train at two resolutions simultaneously in the final training stage.", + "bbox": [ + 107, + 704, + 465, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Mosaic Augmentation", + "text_level": 1, + "bbox": [ + 89, + 786, + 294, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training schedule described in Section 4.2 involves running SAM inference on padded images, using cropped features to train the student against SAM at low resolution. This approach incurs a substantial computational cost, as SAM is the most resource-intensive teacher.", + "bbox": [ + 89, + 809, + 482, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To improve efficiency when training a student at a reso", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "lution $\\leq 512^2$ against SAM, we can instead create a mosaic of $k\\times k$ images, with $k = \\left\\lfloor \\frac{1024}{x}\\right\\rfloor$ and $x$ being the student resolution, resulting in a single $1024^2$ image. We then perform SAM inference on this mosaic and extract $k^2$ individual feature maps to train the student. Mosaic augmentation includes padding as needed to maximize efficiency. For example, to train a student at $432^2$ resolution, we can create a $2\\times 2$ mosaic with 80-pixel padding around each image. Figure 6 shows sample mosaic augmentations under 256 and 432 student resolutions. Qualitatively, we observe cleaner features after applying mosaic augmentation, which we believe is due to the increased diversity in image positions, helping to reduce teacher positional encoding artifacts. We also show SAM's PCA features for these mosaic images in figures 12 and 13 in the appendix.", + "bbox": [ + 511, + 90, + 906, + 318 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/22d3621236937a8b9e215909d8bde9aa7b9597be6d2d03a49902c2fda10cddd8.jpg", + "image_caption": [ + "Figure 6. Sample mosaic augmentations. Grid lines represent $16^{2}$ patches (only shown here for visualization purposes). Left: A $4 \\times 4$ arrangement with a $1024^{2}$ image comprising $16 \\times 256^{2}$ sub-images. Right: A $2 \\times 2$ arrangement comprising $4 \\times 432^{2}$ sub-images, with 80 pixels of padding around each." + ], + "image_footnote": [], + "bbox": [ + 514, + 333, + 694, + 470 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/947576b1e592921b87c5fdd1b5a0caa7583718b24b8deba0f6650fe38df2cdf1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 727, + 333, + 903, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finding 3. Mosaic augmentation greatly reduces the training cost associated with learning from high-resolution teachers and eliminates the need for feature interpolation. Student quality is even improved with this optimization.", + "bbox": [ + 529, + 584, + 888, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Teacher Loss Balancing", + "text_level": 1, + "bbox": [ + 511, + 679, + 732, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In PHI-S [34] we highlighted the significant variations in activation magnitudes among vision foundation models, observing that SAM's activations tend to overshadow those of CLIP and DINOv2 models. We adopt the PCA-Hadamard Isotropic Standardization (PHI-S) method, achieving improved balance among teacher losses. PHI-S rotates teacher activations to evenly distribute variance across all channels and then uniformly scales them to obtain unit variance. This process can be easily inverted by modifying the final linear projection of the adaptor MLP after training. PHI-S enhances training stability and overall benchmark scores. For a given teacher feature map $\\mathbf{X}$ with embedding size $C$ , PHI-S applies the following transformation:", + "bbox": [ + 511, + 703, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22491", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8b6e869e7c6a0505ea883502d1a3fe7c3886ad3896d496a02dd8d674e5e8d3ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 87, + 187, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cee2b6ffc0846e9b8e511114c3f97fd80f30b6cb218199833b33babbb4779c2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 88, + 287, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f96ee98ef295e07f568046c1340b5b7c9af9147c4081caea9943cb7d7f7fa24d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 88, + 383, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a8ec127d93bb31aa68e9c897ade24f15a172dc7ed294d5df1bcee1cedd12bbaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 88, + 482, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cf672b3dc40441d65d77b745c73d4edccf93a502ea74ebfdb6c0602ca8b5f4a.jpg", + "image_caption": [ + "Figure 7. Visualizations of SigLIP and RADIOv2.5-H model features before and after ToMe compression. From left to right: input image; PCA visualization of features; merged tokens; PCA visualization of unmerged tokens. RADIOv2.5 is better able to compress background regions, leaving more tokens available for semantically rich features." + ], + "image_footnote": [], + "bbox": [ + 189, + 164, + 285, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ff01fb5cac81f5703583dc6d000b5ad12c69377965aca4bb905cd45430e89a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 164, + 383, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e7afc103f70c618810c8584cfddc7c3954bc858e18a824308c7b6d8cec7d245d.jpg", + "image_caption": [ + "Figure 8. Illustration of bipartite matching [3] using $2 \\times 2$ strided pattern with $r = 9$ . A: The original tokens, with the red 'T#' squares being assigned as targets, and the green 'S#' squares being assigned as sources. B: We compute the affinity between each source and target. We only consider the maximum affinity for each source (shown in yellow). We find the $r$ highest affinity yellow squares, and merge those into their respective targets. C: The output tokens with merged values when a given 'T#' was assigned one or more sources. D: The final 7 tokens are fed to the LLM. Reconstructed Viz: From (C), we can visualize the compressed original feature map by broadcasting the merged tokens to all of the source locations." + ], + "image_footnote": [], + "bbox": [ + 385, + 164, + 480, + 239 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {i} ^ {\\prime} = \\phi_ {i} ^ {- 1} \\mathbf {R} _ {i} \\mathbf {X} _ {i}, \\quad \\mathbf {R} _ {i} = \\mathbf {H} _ {C} \\mathbf {U} _ {i} ^ {\\intercal}, \\quad \\phi_ {i} = \\sqrt {\\frac {1}{C} \\sum_ {j} ^ {C} \\lambda_ {j}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 382, + 482, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Where $H_{C}$ is a normalized Hadamard matrix of dimension $C \\times C$ , $\\lambda_{j}$ are the eigenvalues of the covariance matrix $\\mathbf{\\Sigma}[\\mathbf{X}]$ , and $\\mathbf{U}$ are the corresponding eigenvectors. $\\phi_{i}$ and $\\mathbf{R}_{i}$ are specific to the $i$ th teacher. PHI-S is a statistical standardization technique, as the expected per-channel variance after PHI-S is 1. However, it is different than vanilla standardization in that it doesn't standardize the channels individually, and thus, doesn't distort the cross-channel variation. We briefly review the key results of [34] in appendix K, but refer the reader to the original paper for deeper understanding.", + "bbox": [ + 89, + 443, + 483, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finding 4. PHI Standardization helps balance the energy spent learning from each teacher.", + "bbox": [ + 106, + 621, + 465, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Token Compression", + "text_level": 1, + "bbox": [ + 89, + 665, + 279, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inspired by ToMeSD[3], we evaluate the use of bipartite soft matching to merge similar tokens. We apply strided partitioning to ensure that each image region retains some representation in the compressed features. For evaluation, we track merged token indices, enabling us to unmerge tokens and measure the reconstruction error and inform hyperparameter selection. The method is illustrated in Figure 8.", + "bbox": [ + 89, + 688, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While ToMe recommends using attention keys for matching, we found that using the features directly reduces reconstruction error. Table 18 in the appendix summarizes our findings. Another slight departure from ToMe's recommendation is that we apply merging at the output of the vision encoder rather than incrementally. As shown in Ta", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/528ba59a844f7cf7cb1d9da6f133256128e82d779e5ccf29711f8aa36f914e1a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 99, + 885, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ble 12, this approach yields an average improvement of $+1.4$ on VLM benchmarks.", + "bbox": [ + 511, + 484, + 906, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also qualitatively evaluate token merging by visualizing feature and token merging outcomes in Figure 7. Token merging is assessed within the context of VLMs, with results reported in Table 1.", + "bbox": [ + 511, + 515, + 905, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further note that token merging can be applied to other vision encoders and demonstrate its application on SigLIP. Interestingly, token merging yields a greater relative improvement on RADIOv2.5 than on SigLIP, a finding that aligns with the feature visualizations in Figure 7 and the measured reconstruction error in Table 18. We hypothesize that SigLIP's higher feature noise makes clustering more error prone.", + "bbox": [ + 511, + 577, + 905, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finding 5. Token Merging is very effective at retaining the most diverse information under high compression ratios.", + "bbox": [ + 529, + 710, + 888, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 511, + 775, + 645, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Evaluation Benchmarks", + "text_level": 1, + "bbox": [ + 511, + 800, + 735, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For Image classification, we report the ImageNet-1k[36] Top-1 classification accuracy using two methods. i) zero-shot[32] classification using the DFN CLIP language model; ii) k-NN[5] classification using the embeddings of the shared backbone.", + "bbox": [ + 511, + 824, + 906, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22492", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ed9c488ccae293c15dc61642b0b66de29a87083c926fb06df49efb450882a638.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ResMethodTokens/imTextVQAChartQADocVQAInfoVQAOCRbench
51222Unshuffle25665.023.745.732.940.2
ToMe r=76825665.725.849.734.941.2
76833Unshuffle25665.825.949.735.240.9
ToMe r=204825669.730.452.336.242.9
102444Unshuffle25666.123.846.634.138.9
ToMe r=384025669.328.149.134.642.7
ToMe r=358451268.931.353.937.044.6
", + "bbox": [ + 94, + 88, + 478, + 258 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. VLM benchmarks across various compression methods. All configurations produce 256 vision tokens per image, except for the last row (512 tokens). Token Merging outperforms Pixel Unshuffling on all benchmarks. $r =$ denotes the number of tokens being merged.", + "bbox": [ + 89, + 270, + 482, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For Instance Segmentation, we use the EfficientViT[25] implementation of a COCO[21] instance segmenter to measure how well our SAM adaptor head can replace SAM.", + "bbox": [ + 89, + 353, + 482, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For Semantic Segmentation, we use the MMSeg[8] framework, and train a linear probe on top of the frozen RADIOv2.5 features. We use the ADE20k[50] dataset. We train the probe at three resolutions $(512^{2}, 768^{2}$ , and $1024^{2}$ ) and report the best result (full results in appendix).", + "bbox": [ + 89, + 398, + 482, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For 3D understanding experiments we use the Probe3D[12] code base and apply a DPT head on top of the frozen backbone features. We train and evaluate on the Navi[19] dataset. We resize images to $512^2$ during both training and evaluation.", + "bbox": [ + 89, + 474, + 483, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For Vision-Language Modeling we follow the same framework as in VILA [23]. We pair our vision encoder with a MN-Minitron-8B[41] LLM. We train all alignment/pretraining/SFT and unfreeze the vision encoder during SFT. We train the model using ShareGPT4v[6] and VFLAN[45] datasets. We leverage insights from Cambrian[42] to select the benchmarks that are most sensitive to the quality of visual features report scores on TextVQA[40], ChartQA[27], DocVQA[29], InfoVQA[28] and OCRBench[26].", + "bbox": [ + 89, + 549, + 482, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 710, + 254, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation studies are summarized in Table 1. Our initial RADIOv2.1-L baseline (config $\\mathcal{A}$ ) is a reproduction of AM-RADIO [35], using a ViT-L backbone and the DataComp1B[16] dataset. Our hyperparameters are detailed in the appendix.", + "bbox": [ + 89, + 733, + 482, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We add multi-resolution training in config $\\mathcal{B}$ , and notice improved results on most dense tasks (+2.8 on ADE20k, +3.4 on average on VLMs). Multi-score robustness is particularly evident in Figure 2, where config $\\mathcal{B}$ exhibits much more consistent results at higher resolutions.", + "bbox": [ + 89, + 810, + 482, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In config $\\mathcal{C}$ , we replace the OpenAI CLIP teacher with", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SigLIP [49] and observe a 6.7-point improvement on VLM benchmarks.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In config $\\mathcal{D}$ , we replace the ViT-L 320M-parameter backbone with a 553M-parameter ViT-H backbone, which improves all metrics significantly.", + "bbox": [ + 511, + 121, + 903, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Config $\\mathcal{E}$ applies only to VLMs, where we replace $2^{2}$ pixel unshuffling with Token Merging. This reduces the number of vision tokens from 576 to 256 and improves VLM scores by an average of 5.9 points. Appendix Table 11 provides a detailed analysis of the trade-off between the number of vision tokens and accuracy, highlighting RA-DIOv2.5's comparative advantage over SigLIP in terms of token merging effectiveness.", + "bbox": [ + 511, + 167, + 906, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparative Results", + "text_level": 1, + "bbox": [ + 511, + 297, + 710, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.1 Dense Task Evaluation", + "text_level": 1, + "bbox": [ + 511, + 321, + 725, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our models in comparison to other agglomerative models of similar size (SAM-CLIP [43], Theia [38], UNIC [37], UNIT [51]). Following MLoRE [47] we report metrics on NYUDv2 and PASCAL Context for our model. We train with a learning rate of $1e - 3$ , and use a weight of 1 for all tasks. We purposefully don't tune any hyperparameters. We keep the backbone model frozen, and use MLoRE's \"conv\" head for each task. The conv head is defined as follows: Conv-3x3 $\\rightarrow$ BatchNorm $\\rightarrow$ GeLU $\\rightarrow$ Conv-1x1.", + "bbox": [ + 511, + 347, + 903, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are reported in Table 4. RADIOv2.5 models exhibit a consistent improvement over previous baselines.", + "bbox": [ + 511, + 498, + 903, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.2 VLM Evaluation", + "text_level": 1, + "bbox": [ + 511, + 549, + 686, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our models against state-of-the-art vision encoders: OpenAI-CLIP [32], RADIoV2.1-H and SigLIPS0400M [49]. We pair the vision encoders with MN-Minitron-8B [41] and train them in VILA [23] using the LLaVA1.6 [24] data mixture. For all vision encoders, we use Token Merging to compress the visual features to 196 tokens in order to ensure a fixed cost to the Language Model. We report results in Table 5. We observe that RADIoV2.5 models consistently exceed the accuracy of other vision encoders.", + "bbox": [ + 511, + 573, + 906, + 723 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Related Work", + "text_level": 1, + "bbox": [ + 511, + 739, + 653, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AM-RADIO[35] and SAM-CLIP[43] pioneered multiteacher distillation for Vision Foundation Models, though AM-RADIO struggles with resolution consistency and SAM-CLIP lacks a strong dense model like DINO, reducing semantic segmentation accuracy. Theia[38] uses a multidistillation framework for robotics, incorporating teachers like DepthAnything[46], while UNIC[37] stabilizes training with expandable projectors and teacher-dropping regularization. Our method, however, employs teacher fea", + "bbox": [ + 511, + 763, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22493", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/23ab0ed66d0216f461ed1b3b2d1c4bdff91fbdeb17b736060ea559d6aed75edb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelParamsADE20k mIoU↑NYUdPascal Context
SemSeg mIoU↑Depth RMSE↓Normal mErr↓SemSeg mIoU↑Parsing mIoU↑Saliency maxF↑Normal mErr↓
SAM-CLIP[43]86M38.4†††††††
Theia [38]86M35.5538.900.637724.1169.8460.6780.6316.94
UNIC-B[37]86M39.642.210.617222.7875.9062.8581.8415.78
RADIOv2.5-B (ours)98M48.9457.190.498020.0481.7571.4981.2616.10
UNIC-L[37]307M48.3058.560.491619.3481.8272.2479.2117.35
RADIOv2.5-L (ours)320M52.9561.420.457718.5782.8774.3281.6516.15
UNIT[51]632M50.1961.440.453819.0782.3673.3478.7017.98
RADIOv2.1-H653M51.3662.760.433918.4382.7874.4278.4817.53
RADIOv2.5-H653M53.9763.820.435317.6783.4375.7581.1916.16
UNIT[51]1B50.6361.620.452719.0782.2073.2278.5117.96
RADIOv2.5-g (ours)1.1B54.5663.460.431817.0882.6575.1880.0817.06
", + "bbox": [ + 93, + 88, + 903, + 251 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1805d3dd212668c57a4df11470593e9f720bd603101b88584a3cd4fd38acc78c.jpg", + "table_caption": [ + "Table 4. Comparison of dense task benchmarks against other agglomerative models. $\\dagger$ Results unavailable due to lack of access to SAM-CLIP model weights. Note: RADIo requires more parameters for a given model class due to a $C \\times {128} \\times {128}$ position embedding buffer coming from CPE, but does not contribute meaningfully to increased FLOPs or representation capacity." + ], + "table_footnote": [], + "table_body": "
Vision EncoderResolutionTokens/fimTextVQAChartQADocVQAInfoVQAOCRBenchGQAPOPEMMESEED(I)MMMUAI2DAverage
OpenAI-CLIP [32]336219663.249.243.427.443162.485.71517.972.743.477.658.55
RADIOv2.1-H [35]512219663.651.740.126.239263.487.31570.673.643.978.958.76
RADIOv2.1-H [35]768219662.849.936.724.836562.787.01517.271.741.973.456.66
SigLIP-SO400M [49]384219664.855.747.929.245263.185.41632.972.941.180.760.95
RADIOv2.5-L (ours)768219666.756.449.229.844163.487.61592.474.043.379.261.21
RADIOv2.5-H (ours)768219668.861.654.230.849863.887.31562.374.144.182.563.19
RADIOv2.5-g (ours)672219669.657.053.330.947963.487.51606.474.341.380.862.39
", + "bbox": [ + 94, + 316, + 903, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Vision Encoder Comparison in VILA[23]. We used MN-Minitron-8B[41] as LLM and the LLaVA1.6[24] data mixture. We use Token Merging to compress all visual features down to 196 tokens. From left to right we report: image resolution, number of tokens per image, TextVQA (with OCR hints) validation accuracy, ChartQA overall, DocVQA validation accuracy, InfoVQA validation accuracy, OCRBench accuracy, GQA (TestDev) accuracy, POPE F1 score, MME perception score, SEED (Image) accuracy, MMMU (validation) accuracy, AI2D (no mask) accuracy, average (calculated after dividing MME score by 20 and OCR score by 10).", + "bbox": [ + 89, + 508, + 906, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ture standardization and multi-resolution training for scale-consistent accuracy, enhancing the original ViT[11] interpolation approach. Unlike FlexiViT[2] and NaViT[10], we use Cropped Position Embeddings (CPE)[21] and distill resolution-robust students from inflexible teachers.", + "bbox": [ + 89, + 590, + 482, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Cambrian-1 [42] integrates multiple vision encoders through a Spatial Vision Aggregator, utilizing learnable latent queries that interact with several layers of a Large Language Model (LLM) via cross-attention. Eagle [39] combines multiple vision experts by concatenating their visual tokens along the channel dimension. BRAVE [20] introduces the Multi-Encoder Querying Transformer, which merges visual features from various encoders into a fixed-length representation, subsequently used as a soft prompt for a frozen language model. In contrast, our method performs multi-vision encoder aggregation as a preliminary step to develop a single, versatile vision encoder suitable for integration into a VLM, but also easily usable outside of a VLM context.", + "bbox": [ + 89, + 688, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 590, + 633, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented RADIOv2.5, a robust framework for multi-teacher vision model distillation that accommodates variations in teacher resolutions, activation magnitudes, and noise patterns. The key differentiating factor in our work is our focus on preserving accuracy across a broad range of resolutions. Our multi-resolution training approach mitigates resolution-dependent quality degradation (mode switching). Our findings show that mosaic augmentation and PHI-S effectively balance computational load and loss contributions from each teacher.", + "bbox": [ + 511, + 637, + 906, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Token compression enables efficient integration with VLMs by preserving critical visual information, even at high compression ratios. Our feature selection study highlighted the advantages of using intermediate activations for dense tasks, particularly when non-linear transformations are used.", + "bbox": [ + 511, + 810, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22494", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. 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Unit: Unifying image and text recognition in one vision encoder, 2024. 7, 8" + ], + "bbox": [ + 91, + 90, + 485, + 219 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22497", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_model.json b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..526f6c2ff05b3312825c1c6e0aac8e27d914df8f --- /dev/null +++ b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_model.json @@ -0,0 +1,2499 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.103, + 0.13, + 0.898, + 0.154 + ], + "angle": 0, + "content": "RADIOv2.5: Improved Baselines for Agglomerative Vision Foundation Models" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.181, + 0.825, + 0.233 + ], + "angle": 0, + "content": "Greg Heinrich* Mike Ranzinger* Hongxu (Danny) Yin Yao Lu Jan Kautz Andrew Tao Bryan Catanzaro Pavlo Molchanov NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.237, + 0.825, + 0.253 + ], + "angle": 0, + "content": "{gheinrich,mranzinger,danny,jkautz,atao,bcatanzaro,pmolchanov}@nvidia.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.329, + 0.304 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.319, + 0.486, + 0.606 + ], + "angle": 0, + "content": "Agglomerative models have recently emerged as a powerful approach to training vision foundation models, leveraging multi-teacher distillation from existing models such as CLIP, DINO, and SAM. This strategy enables the efficient creation of robust models, combining the strengths of individual teachers while significantly reducing computational and resource demands. In this paper, we thoroughly analyze state-of-the-art agglomerative models, identifying critical challenges including resolution mode shifts, teacher imbalance, idiosyncratic teacher artifacts, and an excessive number of output tokens. To address these issues, we propose several novel solutions: multi-resolution training, mosaic augmentation, and improved balancing of teacher loss functions. Specifically, in the context of Vision Language Models, we introduce a token compression technique to maintain high-resolution information within a fixed token count. We release our top-performing variants at multiple scales \\((-B, -L, -H, \\text{and} -g)\\), along with inference code and pretrained weights." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.612, + 0.484, + 0.629 + ], + "angle": 0, + "content": "Links: Code (on GitHub)—Models (on Hugging Face)" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.67, + 0.224, + 0.687 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.696, + 0.485, + 0.877 + ], + "angle": 0, + "content": "The rise of specialized Vision Foundation Models (VFMs) has created a need for methods to consolidate knowledge from multiple models into a unified model. SAM-CLIP [43] addresses this challenge by combining SAM [22] and CLIP [32] to integrate capabilities from both. In another approach, AM-RADIO [35] introduces label-free knowledge distillation from multiple teacher models, enabling knowledge transfer without direct supervision. UNIC [37] adds intermediate teacher matching projectors and dynamic teacher selection. Theia [38] aims to facilitate robot learning by distilling insights from multiple vision teachers. Meanwhile, PHI-S [34] studies the importance of normal" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.907, + 0.349 + ], + "angle": 0, + "content": "izing the distinct teacher distributions to simplify their balancing. Relatedly, Eagle [39] leverages a mixture of vision encoders to achieve inference-time knowledge aggregation within the context of Vision-Language Models (VLMs)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.907, + 0.395 + ], + "angle": 0, + "content": "Despite these advancements, this growing body of work on knowledge agglomeration still leaves open several critical challenges:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.399, + 0.906, + 0.473 + ], + "angle": 0, + "content": "- Resolution balancing: Teacher models operate at varying resolutions due to different training goals, creating feature granularity inconsistencies. Effective techniques are needed to balance these resolutions in the student model to capture both fine details and broader abstractions." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.475, + 0.906, + 0.519 + ], + "angle": 0, + "content": "- Teacher distribution balancing: Existing models have different distribution moments and the distillation process should account for this to prevent biased learning." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.52, + 0.906, + 0.625 + ], + "angle": 0, + "content": "- Generating multi-resolution features for diverse applications: Vision models support various applications requiring different feature resolutions, from image captioning to dense segmentation. A VFM that flexibly produces features at any resolution could serve multiple tasks, reducing the need for separate models and unlocking new opportunities." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.399, + 0.906, + 0.625 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.795 + ], + "angle": 0, + "content": "In our analysis of existing agglomerative models, we study and propose a fix for the notable \"mode switch\" phenomenon in AM-RADIO, where feature distributions shift significantly based on input resolution (Section 3.1). Specifically, low-resolution inputs yield DINO-like features, while high-resolution inputs produce SAM-like features. We trace this behavior to the student learning from different teachers at different resolutions during training. In section 4.2, we introduce a solution to stabilize these mode switches, achieving strong resolution robustness and improved quality scaling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Equipped with a high-resolution vision encoder, we now focus on Vision-Language Model (VLM) integration. In downstream VL tasks, a key challenge is the token/feature count. High-resolution processing yields more tokens, exacerbating the quadratic complexity of attention in VLMs. To maintain resolution without escalating this issue, we propose using ToMeSD [3] in Section 4.5 to separate vision" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.218, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22487" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.101, + 0.316, + 0.123 + ], + "angle": 0, + "content": "Problem: Inconsistent accuracy across resolutions" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.125, + 0.207, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.239, + 0.125, + 0.326, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.201, + 0.317, + 0.223 + ], + "angle": 0, + "content": "Cause: Student only sees SAM at high resolution" + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.224, + 0.294, + 0.236 + ], + "angle": 0, + "content": "Solution: Multi-Resolution Training" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.238, + 0.326, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.096, + 0.562, + 0.118 + ], + "angle": 0, + "content": "Problem: VLM hardly improves at high resolution" + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.118, + 0.569, + 0.141 + ], + "angle": 0, + "content": "Cause: Standard local pooling with pixel unshuffling loses details" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.148, + 0.616, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.355, + 0.241, + 0.576, + 0.255 + ], + "angle": 0, + "content": "Solution: Global fine-grain token merging" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.266, + 0.615, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.143, + 0.898, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.365, + 0.908, + 0.421 + ], + "angle": 0, + "content": "Figure 1. Overview of the main contributions: From left to right, we introduce a multi-resolution training framework that enables our student model to maintain accuracy across all resolutions; we propose using token merging to better retain fine-grained details while merging uninformative tokens; our RADIOv2.5 models improve upon the RADIOv2.1 baseline across all benchmarks, with significant gains on VLM tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.461, + 0.411, + 0.475 + ], + "angle": 0, + "content": "encoder resolution from the VLM's patch count." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.43, + 0.49 + ], + "angle": 0, + "content": "Our main contributions, illustrated in Figure 1, are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.491, + 0.483, + 0.52 + ], + "angle": 0, + "content": "- A multi-resolution training strategy that fixes mode switching and allows for fully flexible input resolution." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.521, + 0.484, + 0.55 + ], + "angle": 0, + "content": "- A comprehensive study of feature selection for a range of downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.551, + 0.484, + 0.611 + ], + "angle": 0, + "content": "- A proposal for vision model feature selection within VLMs, enabling integration with language models while preserving essential information. We demonstrate that RADIOv2.5 disproportionately benefits from this." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.491, + 0.484, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.624, + 0.22, + 0.641 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.649, + 0.334, + 0.666 + ], + "angle": 0, + "content": "2.1. Knowledge Agglomeration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.747 + ], + "angle": 0, + "content": "The assumption underlying knowledge agglomeration is that multiple foundation models exist, each capable of extracting diverse and meaningful representations from a wide range of images, and that knowledge from these models can be distilled into a single agglomerative model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.748, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Let \\( x \\) be the input data. The student's shared backbone produces a feature representation:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.787, + 0.483, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} = f (x) = \\left[ z _ {s}, z _ {p} ^ {(1)}, z _ {p} ^ {(2)}, \\dots , z _ {p} ^ {(N)} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.824, + 0.483, + 0.87 + ], + "angle": 0, + "content": "where \\(z_{s} \\in \\mathbb{R}^{d}\\) is the summary token, \\(z_{p}^{(i)} \\in \\mathbb{R}^{d}\\) for \\(i = 1, \\dots, N\\) are the patch tokens, and \\(d\\) is the student's embedding dimension." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "For each teacher \\(t\\), the student's model includes two adaptor heads: \\(g_{s}^{(t)}:\\mathbb{R}^{d}\\to \\mathbb{R}^{d_{t}}\\), which projects the sum" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.461, + 0.905, + 0.493 + ], + "angle": 0, + "content": "mary token \\(z_{s}\\) into the teacher's embedding space, and \\(g_p^{(t)}:\\mathbb{R}^d\\to \\mathbb{R}^{dt}\\), which projects each patch token \\(z_{p}^{(i)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.493, + 0.905, + 0.523 + ], + "angle": 0, + "content": "Adaptor heads, typically simple MLPs, adjust feature dimensions as needed. For teacher \\( t \\), we define:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.533, + 0.905, + 0.553 + ], + "angle": 0, + "content": "\\[\ng ^ {(t)} (z) = \\operatorname {M L P} ^ {(t)} (z) = \\sigma \\left(W ^ {(t)} z + b ^ {(t)}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.565, + 0.907, + 0.597 + ], + "angle": 0, + "content": "where \\(\\sigma (\\cdot)\\) is a non-linear activation, and \\(W^{(t)}\\) and \\(b^{(t)}\\) are learnable parameters. Projected features per teacher \\(t\\) are:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.621, + 0.905, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\text {S u m m a r y :} \\hat {z} _ {s} ^ {(t)} = g _ {s} ^ {(t)} \\left(z _ {s}\\right), \\quad \\text {P a t c h :} \\hat {z} _ {p} ^ {(t)} = g _ {p} ^ {(t)} \\left(z _ {p}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.652, + 0.907, + 0.698 + ], + "angle": 0, + "content": "The training objective aligns student features with teacher features using a loss function that measures their similarity. For teacher \\( t \\), the loss \\( \\mathcal{L}_t \\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.709, + 0.905, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\ell_ {s} \\left(\\hat {z} _ {s} ^ {(t)}, z _ {s} ^ {(t)}\\right) + \\sum_ {i = 1} ^ {N} \\ell_ {p} \\left(\\hat {z} _ {p} ^ {(t, i)}, z _ {p} ^ {(t, i)}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.762, + 0.907, + 0.808 + ], + "angle": 0, + "content": "where \\(\\ell .(\\cdot ,\\cdot)\\) is a similarity/distance metric, and \\(\\ell_{s}\\) (summary loss) may differ from \\(\\ell_p\\) (patch loss). The total loss is a weighted average of all \\(\\mathcal{L}_t\\) terms." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.669, + 0.832 + ], + "angle": 0, + "content": "2.2. Baseline Model" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Following AM-RADIO[35], our baseline model consists of a Vision Transformer (ViT)[11] backbone, including CPE [21] for multi-resolution support. We use DFN CLIP [15], OpenAI CLIP [32], DINOv2-g-reg [9]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22488" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.168 + ], + "angle": 0, + "content": "
ConfigurationGoalImageNet1KSegmentationProbe3D[12]Vision-Language (VILA[23])SAM [22]
Zero-shotk-NNADE20kDepthSurfNormalsTextVQAChartQADocVQAInfoVQAOCRBench
A: RADIOv2.1-L*Baseline78.3584.0150.0382.6359.9457.0115.624.1928.8825.60
B: A + multi-resEliminate modes81.2184.0952.8482.3961.0459.4416.633.9929.0229.40
C: B - OpenAICLIP + SigLIPBetter VLM81.0184.6852.9584.760.164.4225.2845.8030.6036.00
D: C + ViT-HBigger backbone82.5185.8153.9785.762.565.8825.9649.7435.1740.90
E: D + Token MergingImprove VLM-----69.7430.4052.3336.2442.90
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.178, + 0.907, + 0.22 + ], + "angle": 0, + "content": "Table 1. Ablation Results. For Probe3D, Depth and Surface Normals metrics are averaged over the buckets defined in the paper. For SAM COCO we use the \"instance all\" bucket. Each incremental change we introduce leads to improved metrics. *We use a ViT-L instead of the ViT-H used in the original AM-RADIO [35] paper." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.232, + 0.486, + 0.475 + ], + "angle": 0, + "content": "and SAM-H [22] as teachers. For each teacher to distill from, we augment the backbone with an adaptor for the summarization token, and an adaptor for the patch tokens. Our adaptor is a 2-layer MLP with a LayerNorm[1] and a GeLU[18] in between. We train the student using teacher features generated by inferring images of the DataComp1B[16] dataset. For faster iterations, we replicate AM-RADIO using a ViT-L backbone instead of the original ViT-H backbone and refer to it as RADIOv2.1-L from this point forward. We train the model with a batch size of \\(1024 + 128\\) for \\(600\\mathrm{k}\\) iterations. Training is split into two concurrent partitions: one partition trains the student at a resolution of \\(432^2\\) against CLIP and DINOv2 teachers with batch size 1024, while the other partition trains the student at a resolution of \\(1024^2\\) against SAM with a batch size of 128. This baseline is referred to as \\(\\mathcal{A}\\) in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.483, + 0.308, + 0.499 + ], + "angle": 0, + "content": "2.3. Evaluation Framework" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.507, + 0.485, + 0.691 + ], + "angle": 0, + "content": "Evaluating foundation model quality across diverse downstream tasks is challenging. We use a rigorous framework to pinpoint improvements and inform design: assessing ImageNet-1k[36] Top-1 accuracy via zero-shot[32] and k-NN[5] classification; probing frozen backbone features for semantic segmentation on ADE20k[50] and PascalVOC[13]; evaluating instance segmentation on COCO[21] with EfficientViT[25] protocols and our SAM adaptor; testing 3D understanding (depth, normals, correspondence) per [12]; pairing with an LLM for Vision-Language reasoning; and probing dense multi-task quality on Pascal Context[30] and NYUDv2[31] as in MLoRE [47]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.702, + 0.208, + 0.719 + ], + "angle": 0, + "content": "3. Challenges" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.727, + 0.431, + 0.743 + ], + "angle": 0, + "content": "3.1. Achieving Multi-Resolution Robustness" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Although AM-RADIO [35] supports a wide range of input resolutions, we noticed poor quality on high-resolution benchmarks. As illustrated in Figure 2, Zero-Shot Top-1 accuracy drops sharply after inputs are larger than roughly \\(512\\mathrm{px}\\). This showcases an undesirable property of this model, which is that it doesn't reliably scale to high-resolution images. AM-RADIO hints at this issue in its conclusion: the model exhibits a \"mode switching\" behavior as resolution increases. This prompted us to visualize the features and investigate the effect of a resolution increase. Fig-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.232, + 0.908, + 0.399 + ], + "angle": 0, + "content": "ure 3 illustrates the issue well: at resolutions lower than or equal to \\(512^2\\), the features most closely resemble those of DINOv2 and appear to be expressive of depth and semantic content. At higher resolutions, the model starts to behave more like SAM, with features that show sharp delineations around contours and homogeneous contents within. This behavior is intuitive given the fact that in the high-resolution regime the student only sees SAM features. Table 2 shows a quantified measure of feature variance across scales (see implementation in appendix). DINOv2 exhibits much smaller scale variance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.408, + 0.651, + 0.423 + ], + "angle": 0, + "content": "3.2. Token Count" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.909, + 0.645 + ], + "angle": 0, + "content": "Dense downstream tasks, such as pixel-level semantic segmentation and depth estimation, benefit from receiving fine features from a vision encoder. However, for vision-language models like LLaVA [24], where visual tokens are integrated into a sequence of text embeddings, an excessive number of vision tokens can negatively impact speed/quality or lead to sequence overflows. Pixel unshuffling, as proposed in InternVL1.5 [7], addresses this by reducing the number of vision tokens, grouping \\( 2 \\times 2 \\) tokens along the channel dimension. However, this approach cannot adapt to varying information densities within an image. For instance, a text document might have large areas of white background that should be more strongly compressed than areas containing text." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.657, + 0.606, + 0.672 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.681, + 0.698, + 0.699 + ], + "angle": 0, + "content": "4.1. Scale Equivariance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We measure scale equivariance of multi-scale features by normalizing and interpolating them to the lowest resolution, then computing the spatial average of variance across scales (see Appendix F). Table 2 shows our baseline student has worse scale equivariance than DINOv2, our only multi-resolution teacher for comparison. VLMs like LLaVa-NeXT[24] and InternVL1.5[7] use tiling to handle high-resolution inputs with fixed-resolution encoders, suggesting scale equivariance may be less critical. However, tiling coarsens increases in resolution and, as tile count grows, limits the encoder's view of the full image, hindering contextual reasoning. In Figure 4, we analyze SigLIP[49] (used in Cambrian[42]) features across tiling setups, revealing" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22489" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.096, + 0.28, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.097, + 0.482, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.097, + 0.685, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.097, + 0.885, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.219, + 0.907, + 0.275 + ], + "angle": 0, + "content": "Figure 2. Zero-Shot Accuracy and teacher matching fidelity metrics as a function of input resolution. AM-RADIO (aka RADIOv2.1, config \\(\\mathcal{A}\\)), and our \"Multi-Stage Stage 3\" model exhibit mode switching behavior. \"Multi-Stage Stage 2\" doesn't exhibit the behavior, owing to all teachers being trained solely at low resolution, however quality at high resolution quickly degrades. \"Multi-Resolution\" (config \\(\\mathcal{B}\\)) training fixes the mode switch, and allows the model to be strong across a larger range of resolutions compared to Stage 2." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.298, + 0.485, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.411, + 0.484, + 0.522 + ], + "angle": 0, + "content": "Figure 3. Visualizations of patch token features across input resolutions. We use PCA to map patch tokens to RGB colors. Top: Input image, followed by visualizations of DINOV2, RADIOv2.1 (config \\(\\mathcal{A}\\)) at \\(256^2\\), \\(512^2\\), \\(1024^2\\) resolutions, and SAM. Bottom: RADIOv2.5-H (config \\(\\mathcal{D}\\)). As resolution increases, RADIOv2.1 features resemble SAM's, even showing VitDet windowing artifacts, while RADIOv2.5 remains more self-consistent and less noisy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.571, + 0.483, + 0.618 + ], + "angle": 0, + "content": "qualitative inconsistencies and reduced scale equivariance (Table 2). Tiling also boosts vision tokens by up to \\(12 \\times [7]\\), increasing VLM latency." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.651, + 0.483, + 0.804 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.814, + 0.484, + 0.898 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of tiling and high-resolution inference. Tiling emulates high-res SigLIP inference. Top: From left to right: input, SigLIP features using \\(1,2 \\times 2\\) and \\(4 \\times 4\\) tiles. Bottom: Single-pass inference using RADIOv2.5 (ours) at equivalent image sizes. SigLIP features vary significantly across different tiling arrangements." + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.303, + 0.89, + 0.351 + ], + "angle": 0, + "content": "Finding 1. High-resolution inference through tiling causes the vision encoder to lose global context and exhibit poor scaling equivariance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.361, + 0.755, + 0.377 + ], + "angle": 0, + "content": "4.2. Multi-Resolution Training" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.385, + 0.907, + 0.61 + ], + "angle": 0, + "content": "The previous observations motivate a change in the training schedule: with multi-resolution training we enable the student to learn from all teachers across multiple resolutions. This is easily achieved with DINOv2, since DINOv2 can infer images at any resolution. For CLIP teachers, we feed them with images at the teacher's native resolution, and we feed the student with images at multiple resolutions. We interpolate student features down to the resolution of the teacher's features before applying the loss function. SAM presents an extra challenge, as noted in AM-RADIO[35], since interpolating SAM features significantly deteriorates their quality. Therefore in order to train our student against SAM at lower resolutions than \\(1024^2\\), we pad smaller images to \\(1024^2\\), then crop SAM features to the effective size of the unpadded image." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.611, + 0.906, + 0.656 + ], + "angle": 0, + "content": "Training the student for 600k iterations with a multi-resolution setup is costly. Thus we break down training into three stages:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.658, + 0.905, + 0.687 + ], + "angle": 0, + "content": "- In a first stage, we train the student at low resolution \\((256^{2})\\) for 300k iterations." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.688, + 0.905, + 0.717 + ], + "angle": 0, + "content": "- In a second stage, we train the student at medium resolution \\((432^{2})\\) for 300k iterations." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.718, + 0.905, + 0.747 + ], + "angle": 0, + "content": "- In the third stage, we train the student simultaneously at \\(432^{2}\\) and \\(1024^{2}\\) resolutions for 300k iterations." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.658, + 0.905, + 0.747 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Multi-resolution training is illustrated in Figure 5, which depicts four training regimes based on whether the teachers and/or students process low- or high-resolution images. When both the student and teachers use either low- or high-resolution images, no particular challenge arises. However, training a high-resolution student against a low-resolution teacher requires downscaling the student's features to match those of the teacher. Conversely, training a low-resolution student against a high-resolution teacher necessitates a careful augmentation technique, as described in Section 4.3." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22490" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.136, + 0.089, + 0.442, + 0.22 + ], + "angle": 0, + "content": "
ModelEquivariance ↓
Fine ScaleCoarse Scale
DINOv2-g-reg0.1260.178
AM-RADIO-L0.3570.476
RADIOv2.5-B0.1020.168
RADIOv2.5-L0.1020.165
RADIOv2.5-H0.1190.193
RADIOv2.5-L (tiling)N/A0.369
SigLIP (tiling)N/A0.623
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.231, + 0.484, + 0.327 + ], + "angle": 0, + "content": "Table 2. Scale equivariance, computed over a small dataset of natural images (shown in Appendix). Fine: we scale image resolutions from \\(384^2\\) to \\(1568^2\\) by increments of the model's patch size. Coarse: we scale images from \\(384^2\\) to \\(1920^2\\) by multiples of \\(384^2\\). For the models that are denoted as \"tiling\", we perform inference over tiles of \\(384^2\\)\" and re-assemble features to produce the high-resolution features." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.344, + 0.476, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.593, + 0.484, + 0.676 + ], + "angle": 0, + "content": "Figure 5. Illustration of the multi-resolution training setup. The student learns from all teachers at all resolutions. High-res student features are downsampled to match the resolution of low-res teachers. High-res teachers are provided with mosaics of smaller images and their output features are cropped out in order to train a low-res student." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.705, + 0.466, + 0.767 + ], + "angle": 0, + "content": "Finding 2. For the student model to be consistently accurate across resolutions, it is sufficient to match all teachers at all resolutions, and to train at two resolutions simultaneously in the final training stage." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.787, + 0.295, + 0.803 + ], + "angle": 0, + "content": "4.3. Mosaic Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.483, + 0.884 + ], + "angle": 0, + "content": "The training schedule described in Section 4.2 involves running SAM inference on padded images, using cropped features to train the student against SAM at low resolution. This approach incurs a substantial computational cost, as SAM is the most resource-intensive teacher." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To improve efficiency when training a student at a reso" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.907, + 0.319 + ], + "angle": 0, + "content": "lution \\(\\leq 512^2\\) against SAM, we can instead create a mosaic of \\(k\\times k\\) images, with \\(k = \\left\\lfloor \\frac{1024}{x}\\right\\rfloor\\) and \\(x\\) being the student resolution, resulting in a single \\(1024^2\\) image. We then perform SAM inference on this mosaic and extract \\(k^2\\) individual feature maps to train the student. Mosaic augmentation includes padding as needed to maximize efficiency. For example, to train a student at \\(432^2\\) resolution, we can create a \\(2\\times 2\\) mosaic with 80-pixel padding around each image. Figure 6 shows sample mosaic augmentations under 256 and 432 student resolutions. Qualitatively, we observe cleaner features after applying mosaic augmentation, which we believe is due to the increased diversity in image positions, helping to reduce teacher positional encoding artifacts. We also show SAM's PCA features for these mosaic images in figures 12 and 13 in the appendix." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.334, + 0.695, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.334, + 0.905, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.481, + 0.907, + 0.552 + ], + "angle": 0, + "content": "Figure 6. Sample mosaic augmentations. Grid lines represent \\(16^{2}\\) patches (only shown here for visualization purposes). Left: A \\(4 \\times 4\\) arrangement with a \\(1024^{2}\\) image comprising \\(16 \\times 256^{2}\\) sub-images. Right: A \\(2 \\times 2\\) arrangement comprising \\(4 \\times 432^{2}\\) sub-images, with 80 pixels of padding around each." + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.585, + 0.89, + 0.661 + ], + "angle": 0, + "content": "Finding 3. Mosaic augmentation greatly reduces the training cost associated with learning from high-resolution teachers and eliminates the need for feature interpolation. Student quality is even improved with this optimization." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.68, + 0.733, + 0.696 + ], + "angle": 0, + "content": "4.4. Teacher Loss Balancing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In PHI-S [34] we highlighted the significant variations in activation magnitudes among vision foundation models, observing that SAM's activations tend to overshadow those of CLIP and DINOv2 models. We adopt the PCA-Hadamard Isotropic Standardization (PHI-S) method, achieving improved balance among teacher losses. PHI-S rotates teacher activations to evenly distribute variance across all channels and then uniformly scales them to obtain unit variance. This process can be easily inverted by modifying the final linear projection of the adaptor MLP after training. PHI-S enhances training stability and overall benchmark scores. For a given teacher feature map \\(\\mathbf{X}\\) with embedding size \\(C\\), PHI-S applies the following transformation:" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22491" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.188, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.089, + 0.288, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.385, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.386, + 0.089, + 0.483, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.165, + 0.287, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.165, + 0.385, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.386, + 0.165, + 0.482, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.251, + 0.485, + 0.334 + ], + "angle": 0, + "content": "Figure 7. Visualizations of SigLIP and RADIOv2.5-H model features before and after ToMe compression. From left to right: input image; PCA visualization of features; merged tokens; PCA visualization of unmerged tokens. RADIOv2.5 is better able to compress background regions, leaving more tokens available for semantically rich features." + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.383, + 0.483, + 0.444 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {i} ^ {\\prime} = \\phi_ {i} ^ {- 1} \\mathbf {R} _ {i} \\mathbf {X} _ {i}, \\quad \\mathbf {R} _ {i} = \\mathbf {H} _ {C} \\mathbf {U} _ {i} ^ {\\intercal}, \\quad \\phi_ {i} = \\sqrt {\\frac {1}{C} \\sum_ {j} ^ {C} \\lambda_ {j}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.484, + 0.611 + ], + "angle": 0, + "content": "Where \\( H_{C} \\) is a normalized Hadamard matrix of dimension \\( C \\times C \\), \\( \\lambda_{j} \\) are the eigenvalues of the covariance matrix \\( \\mathbf{\\Sigma}[\\mathbf{X}] \\), and \\( \\mathbf{U} \\) are the corresponding eigenvectors. \\( \\phi_{i} \\) and \\( \\mathbf{R}_{i} \\) are specific to the \\( i \\)th teacher. PHI-S is a statistical standardization technique, as the expected per-channel variance after PHI-S is 1. However, it is different than vanilla standardization in that it doesn't standardize the channels individually, and thus, doesn't distort the cross-channel variation. We briefly review the key results of [34] in appendix K, but refer the reader to the original paper for deeper understanding." + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.622, + 0.466, + 0.654 + ], + "angle": 0, + "content": "Finding 4. PHI Standardization helps balance the energy spent learning from each teacher." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.666, + 0.281, + 0.683 + ], + "angle": 0, + "content": "4.5. Token Compression" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Inspired by ToMeSD[3], we evaluate the use of bipartite soft matching to merge similar tokens. We apply strided partitioning to ensure that each image region retains some representation in the compressed features. For evaluation, we track merged token indices, enabling us to unmerge tokens and measure the reconstruction error and inform hyperparameter selection. The method is illustrated in Figure 8." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "While ToMe recommends using attention keys for matching, we found that using the features directly reduces reconstruction error. Table 18 in the appendix summarizes our findings. Another slight departure from ToMe's recommendation is that we apply merging at the output of the vision encoder rather than incrementally. As shown in Ta" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.1, + 0.887, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.29, + 0.907, + 0.456 + ], + "angle": 0, + "content": "Figure 8. Illustration of bipartite matching [3] using \\(2 \\times 2\\) strided pattern with \\(r = 9\\). A: The original tokens, with the red 'T#' squares being assigned as targets, and the green 'S#' squares being assigned as sources. B: We compute the affinity between each source and target. We only consider the maximum affinity for each source (shown in yellow). We find the \\(r\\) highest affinity yellow squares, and merge those into their respective targets. C: The output tokens with merged values when a given 'T#' was assigned one or more sources. D: The final 7 tokens are fed to the LLM. Reconstructed Viz: From (C), we can visualize the compressed original feature map by broadcasting the merged tokens to all of the source locations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.486, + 0.907, + 0.514 + ], + "angle": 0, + "content": "ble 12, this approach yields an average improvement of \\(+1.4\\) on VLM benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.906, + 0.576 + ], + "angle": 0, + "content": "We also qualitatively evaluate token merging by visualizing feature and token merging outcomes in Figure 7. Token merging is assessed within the context of VLMs, with results reported in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.578, + 0.906, + 0.7 + ], + "angle": 0, + "content": "We further note that token merging can be applied to other vision encoders and demonstrate its application on SigLIP. Interestingly, token merging yields a greater relative improvement on RADIOv2.5 than on SigLIP, a finding that aligns with the feature visualizations in Figure 7 and the measured reconstruction error in Table 18. We hypothesize that SigLIP's higher feature noise makes clustering more error prone." + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.712, + 0.89, + 0.756 + ], + "angle": 0, + "content": "Finding 5. Token Merging is very effective at retaining the most diverse information under high compression ratios." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.776, + 0.646, + 0.793 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.801, + 0.736, + 0.816 + ], + "angle": 0, + "content": "5.1. Evaluation Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.907, + 0.9 + ], + "angle": 0, + "content": "For Image classification, we report the ImageNet-1k[36] Top-1 classification accuracy using two methods. i) zero-shot[32] classification using the DFN CLIP language model; ii) k-NN[5] classification using the embeddings of the shared backbone." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22492" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.48, + 0.26 + ], + "angle": 0, + "content": "
ResMethodTokens/imTextVQAChartQADocVQAInfoVQAOCRbench
51222Unshuffle25665.023.745.732.940.2
ToMe r=76825665.725.849.734.941.2
76833Unshuffle25665.825.949.735.240.9
ToMe r=204825669.730.452.336.242.9
102444Unshuffle25666.123.846.634.138.9
ToMe r=384025669.328.149.134.642.7
ToMe r=358451268.931.353.937.044.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.271, + 0.483, + 0.342 + ], + "angle": 0, + "content": "Table 3. VLM benchmarks across various compression methods. All configurations produce 256 vision tokens per image, except for the last row (512 tokens). Token Merging outperforms Pixel Unshuffling on all benchmarks. \\( r = \\) denotes the number of tokens being merged." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.354, + 0.483, + 0.399 + ], + "angle": 0, + "content": "For Instance Segmentation, we use the EfficientViT[25] implementation of a COCO[21] instance segmenter to measure how well our SAM adaptor head can replace SAM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.483, + 0.475 + ], + "angle": 0, + "content": "For Semantic Segmentation, we use the MMSeg[8] framework, and train a linear probe on top of the frozen RADIOv2.5 features. We use the ADE20k[50] dataset. We train the probe at three resolutions \\((512^{2}, 768^{2}\\), and \\(1024^{2}\\)) and report the best result (full results in appendix)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.475, + 0.484, + 0.55 + ], + "angle": 0, + "content": "For 3D understanding experiments we use the Probe3D[12] code base and apply a DPT head on top of the frozen backbone features. We train and evaluate on the Navi[19] dataset. We resize images to \\(512^2\\) during both training and evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.483, + 0.702 + ], + "angle": 0, + "content": "For Vision-Language Modeling we follow the same framework as in VILA [23]. We pair our vision encoder with a MN-Minitron-8B[41] LLM. We train all alignment/pretraining/SFT and unfreeze the vision encoder during SFT. We train the model using ShareGPT4v[6] and VFLAN[45] datasets. We leverage insights from Cambrian[42] to select the benchmarks that are most sensitive to the quality of visual features report scores on TextVQA[40], ChartQA[27], DocVQA[29], InfoVQA[28] and OCRBench[26]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.711, + 0.255, + 0.726 + ], + "angle": 0, + "content": "5.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.81 + ], + "angle": 0, + "content": "Ablation studies are summarized in Table 1. Our initial RADIOv2.1-L baseline (config \\(\\mathcal{A}\\)) is a reproduction of AM-RADIO [35], using a ViT-L backbone and the DataComp1B[16] dataset. Our hyperparameters are detailed in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.885 + ], + "angle": 0, + "content": "We add multi-resolution training in config \\(\\mathcal{B}\\), and notice improved results on most dense tasks (+2.8 on ADE20k, +3.4 on average on VLMs). Multi-score robustness is particularly evident in Figure 2, where config \\(\\mathcal{B}\\) exhibits much more consistent results at higher resolutions." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In config \\(\\mathcal{C}\\), we replace the OpenAI CLIP teacher with" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "SigLIP [49] and observe a 6.7-point improvement on VLM benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.122, + 0.905, + 0.168 + ], + "angle": 0, + "content": "In config \\(\\mathcal{D}\\), we replace the ViT-L 320M-parameter backbone with a 553M-parameter ViT-H backbone, which improves all metrics significantly." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.907, + 0.289 + ], + "angle": 0, + "content": "Config \\(\\mathcal{E}\\) applies only to VLMs, where we replace \\(2^{2}\\) pixel unshuffling with Token Merging. This reduces the number of vision tokens from 576 to 256 and improves VLM scores by an average of 5.9 points. Appendix Table 11 provides a detailed analysis of the trade-off between the number of vision tokens and accuracy, highlighting RA-DIOv2.5's comparative advantage over SigLIP in terms of token merging effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.299, + 0.712, + 0.315 + ], + "angle": 0, + "content": "5.3. Comparative Results" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.323, + 0.727, + 0.337 + ], + "angle": 0, + "content": "5.3.1 Dense Task Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.348, + 0.905, + 0.497 + ], + "angle": 0, + "content": "We evaluate our models in comparison to other agglomerative models of similar size (SAM-CLIP [43], Theia [38], UNIC [37], UNIT [51]). Following MLoRE [47] we report metrics on NYUDv2 and PASCAL Context for our model. We train with a learning rate of \\( 1e - 3 \\), and use a weight of 1 for all tasks. We purposefully don't tune any hyperparameters. We keep the backbone model frozen, and use MLoRE's \"conv\" head for each task. The conv head is defined as follows: Conv-3x3 \\(\\rightarrow\\) BatchNorm \\(\\rightarrow\\) GeLU \\(\\rightarrow\\) Conv-1x1." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.499, + 0.905, + 0.529 + ], + "angle": 0, + "content": "Results are reported in Table 4. RADIOv2.5 models exhibit a consistent improvement over previous baselines." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.55, + 0.687, + 0.563 + ], + "angle": 0, + "content": "5.3.2 VLM Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.574, + 0.907, + 0.724 + ], + "angle": 0, + "content": "We compare our models against state-of-the-art vision encoders: OpenAI-CLIP [32], RADIoV2.1-H and SigLIPS0400M [49]. We pair the vision encoders with MN-Minitron-8B [41] and train them in VILA [23] using the LLaVA1.6 [24] data mixture. For all vision encoders, we use Token Merging to compress the visual features to 196 tokens in order to ensure a fixed cost to the Language Model. We report results in Table 5. We observe that RADIoV2.5 models consistently exceed the accuracy of other vision encoders." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.74, + 0.655, + 0.755 + ], + "angle": 0, + "content": "6. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.901 + ], + "angle": 0, + "content": "AM-RADIO[35] and SAM-CLIP[43] pioneered multiteacher distillation for Vision Foundation Models, though AM-RADIO struggles with resolution consistency and SAM-CLIP lacks a strong dense model like DINO, reducing semantic segmentation accuracy. Theia[38] uses a multidistillation framework for robotics, incorporating teachers like DepthAnything[46], while UNIC[37] stabilizes training with expandable projectors and teacher-dropping regularization. Our method, however, employs teacher fea" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22493" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.252 + ], + "angle": 0, + "content": "
ModelParamsADE20k mIoU↑NYUdPascal Context
SemSeg mIoU↑Depth RMSE↓Normal mErr↓SemSeg mIoU↑Parsing mIoU↑Saliency maxF↑Normal mErr↓
SAM-CLIP[43]86M38.4†††††††
Theia [38]86M35.5538.900.637724.1169.8460.6780.6316.94
UNIC-B[37]86M39.642.210.617222.7875.9062.8581.8415.78
RADIOv2.5-B (ours)98M48.9457.190.498020.0481.7571.4981.2616.10
UNIC-L[37]307M48.3058.560.491619.3481.8272.2479.2117.35
RADIOv2.5-L (ours)320M52.9561.420.457718.5782.8774.3281.6516.15
UNIT[51]632M50.1961.440.453819.0782.3673.3478.7017.98
RADIOv2.1-H653M51.3662.760.433918.4382.7874.4278.4817.53
RADIOv2.5-H653M53.9763.820.435317.6783.4375.7581.1916.16
UNIT[51]1B50.6361.620.452719.0782.2073.2278.5117.96
RADIOv2.5-g (ours)1.1B54.5663.460.431817.0882.6575.1880.0817.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.261, + 0.907, + 0.304 + ], + "angle": 0, + "content": "Table 4. Comparison of dense task benchmarks against other agglomerative models. \\( \\dagger \\) Results unavailable due to lack of access to SAM-CLIP model weights. Note: RADIo requires more parameters for a given model class due to a \\( C \\times {128} \\times {128} \\) position embedding buffer coming from CPE, but does not contribute meaningfully to increased FLOPs or representation capacity." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.317, + 0.905, + 0.5 + ], + "angle": 0, + "content": "
Vision EncoderResolutionTokens/fimTextVQAChartQADocVQAInfoVQAOCRBenchGQAPOPEMMESEED(I)MMMUAI2DAverage
OpenAI-CLIP [32]336219663.249.243.427.443162.485.71517.972.743.477.658.55
RADIOv2.1-H [35]512219663.651.740.126.239263.487.31570.673.643.978.958.76
RADIOv2.1-H [35]768219662.849.936.724.836562.787.01517.271.741.973.456.66
SigLIP-SO400M [49]384219664.855.747.929.245263.185.41632.972.941.180.760.95
RADIOv2.5-L (ours)768219666.756.449.229.844163.487.61592.474.043.379.261.21
RADIOv2.5-H (ours)768219668.861.654.230.849863.887.31562.374.144.182.563.19
RADIOv2.5-g (ours)672219669.657.053.330.947963.487.51606.474.341.380.862.39
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.51, + 0.907, + 0.581 + ], + "angle": 0, + "content": "Table 5. Vision Encoder Comparison in VILA[23]. We used MN-Minitron-8B[41] as LLM and the LLaVA1.6[24] data mixture. We use Token Merging to compress all visual features down to 196 tokens. From left to right we report: image resolution, number of tokens per image, TextVQA (with OCR hints) validation accuracy, ChartQA overall, DocVQA validation accuracy, InfoVQA validation accuracy, OCRBench accuracy, GQA (TestDev) accuracy, POPE F1 score, MME perception score, SEED (Image) accuracy, MMMU (validation) accuracy, AI2D (no mask) accuracy, average (calculated after dividing MME score by 20 and OCR score by 10)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.592, + 0.483, + 0.669 + ], + "angle": 0, + "content": "ture standardization and multi-resolution training for scale-consistent accuracy, enhancing the original ViT[11] interpolation approach. Unlike FlexiViT[2] and NaViT[10], we use Cropped Position Embeddings (CPE)[21] and distill resolution-robust students from inflexible teachers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Cambrian-1 [42] integrates multiple vision encoders through a Spatial Vision Aggregator, utilizing learnable latent queries that interact with several layers of a Large Language Model (LLM) via cross-attention. Eagle [39] combines multiple vision experts by concatenating their visual tokens along the channel dimension. BRAVE [20] introduces the Multi-Encoder Querying Transformer, which merges visual features from various encoders into a fixed-length representation, subsequently used as a soft prompt for a frozen language model. In contrast, our method performs multi-vision encoder aggregation as a preliminary step to develop a single, versatile vision encoder suitable for integration into a VLM, but also easily usable outside of a VLM context." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.591, + 0.634, + 0.607 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.638, + 0.907, + 0.789 + ], + "angle": 0, + "content": "In this paper, we presented RADIOv2.5, a robust framework for multi-teacher vision model distillation that accommodates variations in teacher resolutions, activation magnitudes, and noise patterns. The key differentiating factor in our work is our focus on preserving accuracy across a broad range of resolutions. Our multi-resolution training approach mitigates resolution-dependent quality degradation (mode switching). Our findings show that mosaic augmentation and PHI-S effectively balance computational load and loss contributions from each teacher." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Token compression enables efficient integration with VLMs by preserving critical visual information, even at high compression ratios. Our feature selection study highlighted the advantages of using intermediate activations for dense tasks, particularly when non-linear transformations are used." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22494" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.482, + 0.143 + ], + "angle": 0, + "content": "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. 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Unit: Unifying image and text recognition in one vision encoder, 2024. 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.486, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22497" + } + ] +] \ No newline at end of file diff --git a/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_origin.pdf b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ba74aac1e0ef6b4d68d6d6682329770cb4f07dbf --- /dev/null +++ b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/f67d7907-0e00-4bb3-98df-d2ff222bce3b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91157a208b646ed45b7634d87a1fbea1b90c27d885a27800955537fa4a58ca04 +size 6256795 diff --git a/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/full.md b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fdaa759be801adedae3582faf0a7e72c84372434 --- /dev/null +++ b/2025/RADIOv2.5_ Improved Baselines for Agglomerative Vision Foundation Models/full.md @@ -0,0 +1,347 @@ +# RADIOv2.5: Improved Baselines for Agglomerative Vision Foundation Models + +Greg Heinrich* Mike Ranzinger* Hongxu (Danny) Yin Yao Lu Jan Kautz Andrew Tao Bryan Catanzaro Pavlo Molchanov NVIDIA + +{gheinrich,mranzinger,danny,jkautz,atao,bcatanzaro,pmolchanov}@nvidia.com + +# Abstract + +Agglomerative models have recently emerged as a powerful approach to training vision foundation models, leveraging multi-teacher distillation from existing models such as CLIP, DINO, and SAM. This strategy enables the efficient creation of robust models, combining the strengths of individual teachers while significantly reducing computational and resource demands. In this paper, we thoroughly analyze state-of-the-art agglomerative models, identifying critical challenges including resolution mode shifts, teacher imbalance, idiosyncratic teacher artifacts, and an excessive number of output tokens. To address these issues, we propose several novel solutions: multi-resolution training, mosaic augmentation, and improved balancing of teacher loss functions. Specifically, in the context of Vision Language Models, we introduce a token compression technique to maintain high-resolution information within a fixed token count. We release our top-performing variants at multiple scales $(-B, -L, -H, \text{and} -g)$ , along with inference code and pretrained weights. + +Links: Code (on GitHub)—Models (on Hugging Face) + +# 1. Introduction + +The rise of specialized Vision Foundation Models (VFMs) has created a need for methods to consolidate knowledge from multiple models into a unified model. SAM-CLIP [43] addresses this challenge by combining SAM [22] and CLIP [32] to integrate capabilities from both. In another approach, AM-RADIO [35] introduces label-free knowledge distillation from multiple teacher models, enabling knowledge transfer without direct supervision. UNIC [37] adds intermediate teacher matching projectors and dynamic teacher selection. Theia [38] aims to facilitate robot learning by distilling insights from multiple vision teachers. Meanwhile, PHI-S [34] studies the importance of normal + +izing the distinct teacher distributions to simplify their balancing. Relatedly, Eagle [39] leverages a mixture of vision encoders to achieve inference-time knowledge aggregation within the context of Vision-Language Models (VLMs). + +Despite these advancements, this growing body of work on knowledge agglomeration still leaves open several critical challenges: + +- Resolution balancing: Teacher models operate at varying resolutions due to different training goals, creating feature granularity inconsistencies. Effective techniques are needed to balance these resolutions in the student model to capture both fine details and broader abstractions. +- Teacher distribution balancing: Existing models have different distribution moments and the distillation process should account for this to prevent biased learning. +- Generating multi-resolution features for diverse applications: Vision models support various applications requiring different feature resolutions, from image captioning to dense segmentation. A VFM that flexibly produces features at any resolution could serve multiple tasks, reducing the need for separate models and unlocking new opportunities. + +In our analysis of existing agglomerative models, we study and propose a fix for the notable "mode switch" phenomenon in AM-RADIO, where feature distributions shift significantly based on input resolution (Section 3.1). Specifically, low-resolution inputs yield DINO-like features, while high-resolution inputs produce SAM-like features. We trace this behavior to the student learning from different teachers at different resolutions during training. In section 4.2, we introduce a solution to stabilize these mode switches, achieving strong resolution robustness and improved quality scaling. + +Equipped with a high-resolution vision encoder, we now focus on Vision-Language Model (VLM) integration. In downstream VL tasks, a key challenge is the token/feature count. High-resolution processing yields more tokens, exacerbating the quadratic complexity of attention in VLMs. To maintain resolution without escalating this issue, we propose using ToMeSD [3] in Section 4.5 to separate vision + +![](images/e72b5c8a0ef08bde93c10da072f0b62a4e62f47d1cb20043654a312c1da51420.jpg) +Problem: Inconsistent accuracy across resolutions + +![](images/12b2e341c7e97dc81c48e242f4f5cd28e647b7f6de139afb55acf5a472cbaf61.jpg) +Cause: Student only sees SAM at high resolution + +![](images/22ec272f96cccaa9842121b05a329fe3727c629d6a425cf2da799e4ec3f699ab.jpg) +Solution: Multi-Resolution Training + +![](images/ab5a6e93a7e332221acda375049fb95b031fe50f21b90d885a2f2b173007d7b6.jpg) +Problem: VLM hardly improves at high resolution +Cause: Standard local pooling with pixel unshuffling loses details +Solution: Global fine-grain token merging + +![](images/bc5f1ddcf587cafd55a3bf60fbca13bd8457b731644def1b34fc68616c9eea20.jpg) + +![](images/f929c59a642bfe2aa33fed545f2c6c36aea00892f569ca50569f28b12b733155.jpg) +Figure 1. Overview of the main contributions: From left to right, we introduce a multi-resolution training framework that enables our student model to maintain accuracy across all resolutions; we propose using token merging to better retain fine-grained details while merging uninformative tokens; our RADIOv2.5 models improve upon the RADIOv2.1 baseline across all benchmarks, with significant gains on VLM tasks. + +encoder resolution from the VLM's patch count. + +Our main contributions, illustrated in Figure 1, are: + +- A multi-resolution training strategy that fixes mode switching and allows for fully flexible input resolution. +- A comprehensive study of feature selection for a range of downstream tasks. +- A proposal for vision model feature selection within VLMs, enabling integration with language models while preserving essential information. We demonstrate that RADIOv2.5 disproportionately benefits from this. + +# 2. Background + +# 2.1. Knowledge Agglomeration + +The assumption underlying knowledge agglomeration is that multiple foundation models exist, each capable of extracting diverse and meaningful representations from a wide range of images, and that knowledge from these models can be distilled into a single agglomerative model. + +Let $x$ be the input data. The student's shared backbone produces a feature representation: + +$$ +\mathbf {z} = f (x) = \left[ z _ {s}, z _ {p} ^ {(1)}, z _ {p} ^ {(2)}, \dots , z _ {p} ^ {(N)} \right], \tag {1} +$$ + +where $z_{s} \in \mathbb{R}^{d}$ is the summary token, $z_{p}^{(i)} \in \mathbb{R}^{d}$ for $i = 1, \dots, N$ are the patch tokens, and $d$ is the student's embedding dimension. + +For each teacher $t$ , the student's model includes two adaptor heads: $g_{s}^{(t)}:\mathbb{R}^{d}\to \mathbb{R}^{d_{t}}$ , which projects the sum + +mary token $z_{s}$ into the teacher's embedding space, and $g_p^{(t)}:\mathbb{R}^d\to \mathbb{R}^{dt}$ , which projects each patch token $z_{p}^{(i)}$ + +Adaptor heads, typically simple MLPs, adjust feature dimensions as needed. For teacher $t$ , we define: + +$$ +g ^ {(t)} (z) = \operatorname {M L P} ^ {(t)} (z) = \sigma \left(W ^ {(t)} z + b ^ {(t)}\right), \tag {2} +$$ + +where $\sigma (\cdot)$ is a non-linear activation, and $W^{(t)}$ and $b^{(t)}$ are learnable parameters. Projected features per teacher $t$ are: + +$$ +\text {S u m m a r y :} \hat {z} _ {s} ^ {(t)} = g _ {s} ^ {(t)} \left(z _ {s}\right), \quad \text {P a t c h :} \hat {z} _ {p} ^ {(t)} = g _ {p} ^ {(t)} \left(z _ {p}\right). \tag {3} +$$ + +The training objective aligns student features with teacher features using a loss function that measures their similarity. For teacher $t$ , the loss $\mathcal{L}_t$ is: + +$$ +\mathcal {L} _ {t} = \ell_ {s} \left(\hat {z} _ {s} ^ {(t)}, z _ {s} ^ {(t)}\right) + \sum_ {i = 1} ^ {N} \ell_ {p} \left(\hat {z} _ {p} ^ {(t, i)}, z _ {p} ^ {(t, i)}\right), \tag {4} +$$ + +where $\ell .(\cdot ,\cdot)$ is a similarity/distance metric, and $\ell_{s}$ (summary loss) may differ from $\ell_p$ (patch loss). The total loss is a weighted average of all $\mathcal{L}_t$ terms. + +# 2.2. Baseline Model + +Following AM-RADIO[35], our baseline model consists of a Vision Transformer (ViT)[11] backbone, including CPE [21] for multi-resolution support. We use DFN CLIP [15], OpenAI CLIP [32], DINOv2-g-reg [9] + +
ConfigurationGoalImageNet1KSegmentationProbe3D[12]Vision-Language (VILA[23])SAM [22]
Zero-shotk-NNADE20kDepthSurfNormalsTextVQAChartQADocVQAInfoVQAOCRBench
A: RADIOv2.1-L*Baseline78.3584.0150.0382.6359.9457.0115.624.1928.8825.60
B: A + multi-resEliminate modes81.2184.0952.8482.3961.0459.4416.633.9929.0229.40
C: B - OpenAICLIP + SigLIPBetter VLM81.0184.6852.9584.760.164.4225.2845.8030.6036.00
D: C + ViT-HBigger backbone82.5185.8153.9785.762.565.8825.9649.7435.1740.90
E: D + Token MergingImprove VLM-----69.7430.4052.3336.2442.90
+ +Table 1. Ablation Results. For Probe3D, Depth and Surface Normals metrics are averaged over the buckets defined in the paper. For SAM COCO we use the "instance all" bucket. Each incremental change we introduce leads to improved metrics. *We use a ViT-L instead of the ViT-H used in the original AM-RADIO [35] paper. + +and SAM-H [22] as teachers. For each teacher to distill from, we augment the backbone with an adaptor for the summarization token, and an adaptor for the patch tokens. Our adaptor is a 2-layer MLP with a LayerNorm[1] and a GeLU[18] in between. We train the student using teacher features generated by inferring images of the DataComp1B[16] dataset. For faster iterations, we replicate AM-RADIO using a ViT-L backbone instead of the original ViT-H backbone and refer to it as RADIOv2.1-L from this point forward. We train the model with a batch size of $1024 + 128$ for $600\mathrm{k}$ iterations. Training is split into two concurrent partitions: one partition trains the student at a resolution of $432^2$ against CLIP and DINOv2 teachers with batch size 1024, while the other partition trains the student at a resolution of $1024^2$ against SAM with a batch size of 128. This baseline is referred to as $\mathcal{A}$ in Table 1. + +# 2.3. Evaluation Framework + +Evaluating foundation model quality across diverse downstream tasks is challenging. We use a rigorous framework to pinpoint improvements and inform design: assessing ImageNet-1k[36] Top-1 accuracy via zero-shot[32] and k-NN[5] classification; probing frozen backbone features for semantic segmentation on ADE20k[50] and PascalVOC[13]; evaluating instance segmentation on COCO[21] with EfficientViT[25] protocols and our SAM adaptor; testing 3D understanding (depth, normals, correspondence) per [12]; pairing with an LLM for Vision-Language reasoning; and probing dense multi-task quality on Pascal Context[30] and NYUDv2[31] as in MLoRE [47]. + +# 3. Challenges + +# 3.1. Achieving Multi-Resolution Robustness + +Although AM-RADIO [35] supports a wide range of input resolutions, we noticed poor quality on high-resolution benchmarks. As illustrated in Figure 2, Zero-Shot Top-1 accuracy drops sharply after inputs are larger than roughly $512\mathrm{px}$ . This showcases an undesirable property of this model, which is that it doesn't reliably scale to high-resolution images. AM-RADIO hints at this issue in its conclusion: the model exhibits a "mode switching" behavior as resolution increases. This prompted us to visualize the features and investigate the effect of a resolution increase. Fig- + +ure 3 illustrates the issue well: at resolutions lower than or equal to $512^2$ , the features most closely resemble those of DINOv2 and appear to be expressive of depth and semantic content. At higher resolutions, the model starts to behave more like SAM, with features that show sharp delineations around contours and homogeneous contents within. This behavior is intuitive given the fact that in the high-resolution regime the student only sees SAM features. Table 2 shows a quantified measure of feature variance across scales (see implementation in appendix). DINOv2 exhibits much smaller scale variance. + +# 3.2. Token Count + +Dense downstream tasks, such as pixel-level semantic segmentation and depth estimation, benefit from receiving fine features from a vision encoder. However, for vision-language models like LLaVA [24], where visual tokens are integrated into a sequence of text embeddings, an excessive number of vision tokens can negatively impact speed/quality or lead to sequence overflows. Pixel unshuffling, as proposed in InternVL1.5 [7], addresses this by reducing the number of vision tokens, grouping $2 \times 2$ tokens along the channel dimension. However, this approach cannot adapt to varying information densities within an image. For instance, a text document might have large areas of white background that should be more strongly compressed than areas containing text. + +# 4. Method + +# 4.1. Scale Equivariance + +We measure scale equivariance of multi-scale features by normalizing and interpolating them to the lowest resolution, then computing the spatial average of variance across scales (see Appendix F). Table 2 shows our baseline student has worse scale equivariance than DINOv2, our only multi-resolution teacher for comparison. VLMs like LLaVa-NeXT[24] and InternVL1.5[7] use tiling to handle high-resolution inputs with fixed-resolution encoders, suggesting scale equivariance may be less critical. However, tiling coarsens increases in resolution and, as tile count grows, limits the encoder's view of the full image, hindering contextual reasoning. In Figure 4, we analyze SigLIP[49] (used in Cambrian[42]) features across tiling setups, revealing + +![](images/ffc1ab8fad9a4d9f7663e61e2cb4754ec64f4509158e71eb819b973c24c080d9.jpg) +Figure 2. Zero-Shot Accuracy and teacher matching fidelity metrics as a function of input resolution. AM-RADIO (aka RADIOv2.1, config $\mathcal{A}$ ), and our "Multi-Stage Stage 3" model exhibit mode switching behavior. "Multi-Stage Stage 2" doesn't exhibit the behavior, owing to all teachers being trained solely at low resolution, however quality at high resolution quickly degrades. "Multi-Resolution" (config $\mathcal{B}$ ) training fixes the mode switch, and allows the model to be strong across a larger range of resolutions compared to Stage 2. + +![](images/7eb1b0a2941679a99ef187a2f53db5b5f2416d7e8caae55279208ae1dda21d9d.jpg) +Finding 1. High-resolution inference through tiling causes the vision encoder to lose global context and exhibit poor scaling equivariance. + +![](images/0ba186bbf8c58c285a9d49b0863df9c9e0a354af203df6e98f654b9f46039c3d.jpg) + +![](images/f10e355ba79363aeb66436ed0073c861105a88361a82c61abd4a937af4f65488.jpg) + +![](images/65fda17a402052f2557f1a52d76fc580d81793d50d1294f66197bcfe0e0ab5f4.jpg) +Figure 3. Visualizations of patch token features across input resolutions. We use PCA to map patch tokens to RGB colors. Top: Input image, followed by visualizations of DINOV2, RADIOv2.1 (config $\mathcal{A}$ ) at $256^2$ , $512^2$ , $1024^2$ resolutions, and SAM. Bottom: RADIOv2.5-H (config $\mathcal{D}$ ). As resolution increases, RADIOv2.1 features resemble SAM's, even showing VitDet windowing artifacts, while RADIOv2.5 remains more self-consistent and less noisy. + +qualitative inconsistencies and reduced scale equivariance (Table 2). Tiling also boosts vision tokens by up to $12 \times [7]$ , increasing VLM latency. + +![](images/754fe7c0f6e41dfde5649998d8813672c006c0f0cc117ac9bad88e2e26ee5668.jpg) +Figure 4. Qualitative comparison of tiling and high-resolution inference. Tiling emulates high-res SigLIP inference. Top: From left to right: input, SigLIP features using $1,2 \times 2$ and $4 \times 4$ tiles. Bottom: Single-pass inference using RADIOv2.5 (ours) at equivalent image sizes. SigLIP features vary significantly across different tiling arrangements. + +# 4.2. Multi-Resolution Training + +The previous observations motivate a change in the training schedule: with multi-resolution training we enable the student to learn from all teachers across multiple resolutions. This is easily achieved with DINOv2, since DINOv2 can infer images at any resolution. For CLIP teachers, we feed them with images at the teacher's native resolution, and we feed the student with images at multiple resolutions. We interpolate student features down to the resolution of the teacher's features before applying the loss function. SAM presents an extra challenge, as noted in AM-RADIO[35], since interpolating SAM features significantly deteriorates their quality. Therefore in order to train our student against SAM at lower resolutions than $1024^2$ , we pad smaller images to $1024^2$ , then crop SAM features to the effective size of the unpadded image. + +Training the student for 600k iterations with a multi-resolution setup is costly. Thus we break down training into three stages: + +- In a first stage, we train the student at low resolution $(256^{2})$ for 300k iterations. +- In a second stage, we train the student at medium resolution $(432^{2})$ for 300k iterations. +- In the third stage, we train the student simultaneously at $432^{2}$ and $1024^{2}$ resolutions for 300k iterations. + +Multi-resolution training is illustrated in Figure 5, which depicts four training regimes based on whether the teachers and/or students process low- or high-resolution images. When both the student and teachers use either low- or high-resolution images, no particular challenge arises. However, training a high-resolution student against a low-resolution teacher requires downscaling the student's features to match those of the teacher. Conversely, training a low-resolution student against a high-resolution teacher necessitates a careful augmentation technique, as described in Section 4.3. + +
ModelEquivariance ↓
Fine ScaleCoarse Scale
DINOv2-g-reg0.1260.178
AM-RADIO-L0.3570.476
RADIOv2.5-B0.1020.168
RADIOv2.5-L0.1020.165
RADIOv2.5-H0.1190.193
RADIOv2.5-L (tiling)N/A0.369
SigLIP (tiling)N/A0.623
+ +Table 2. Scale equivariance, computed over a small dataset of natural images (shown in Appendix). Fine: we scale image resolutions from $384^2$ to $1568^2$ by increments of the model's patch size. Coarse: we scale images from $384^2$ to $1920^2$ by multiples of $384^2$ . For the models that are denoted as "tiling", we perform inference over tiles of $384^2$ " and re-assemble features to produce the high-resolution features. + +![](images/0fc13bb1c63512edafbd67e4a8db79ca607b649dfe63d1ec5b9cdc10feb07bf1.jpg) +Figure 5. Illustration of the multi-resolution training setup. The student learns from all teachers at all resolutions. High-res student features are downsampled to match the resolution of low-res teachers. High-res teachers are provided with mosaics of smaller images and their output features are cropped out in order to train a low-res student. + +Finding 2. For the student model to be consistently accurate across resolutions, it is sufficient to match all teachers at all resolutions, and to train at two resolutions simultaneously in the final training stage. + +# 4.3. Mosaic Augmentation + +The training schedule described in Section 4.2 involves running SAM inference on padded images, using cropped features to train the student against SAM at low resolution. This approach incurs a substantial computational cost, as SAM is the most resource-intensive teacher. + +To improve efficiency when training a student at a reso + +lution $\leq 512^2$ against SAM, we can instead create a mosaic of $k\times k$ images, with $k = \left\lfloor \frac{1024}{x}\right\rfloor$ and $x$ being the student resolution, resulting in a single $1024^2$ image. We then perform SAM inference on this mosaic and extract $k^2$ individual feature maps to train the student. Mosaic augmentation includes padding as needed to maximize efficiency. For example, to train a student at $432^2$ resolution, we can create a $2\times 2$ mosaic with 80-pixel padding around each image. Figure 6 shows sample mosaic augmentations under 256 and 432 student resolutions. Qualitatively, we observe cleaner features after applying mosaic augmentation, which we believe is due to the increased diversity in image positions, helping to reduce teacher positional encoding artifacts. We also show SAM's PCA features for these mosaic images in figures 12 and 13 in the appendix. + +![](images/22d3621236937a8b9e215909d8bde9aa7b9597be6d2d03a49902c2fda10cddd8.jpg) +Figure 6. Sample mosaic augmentations. Grid lines represent $16^{2}$ patches (only shown here for visualization purposes). Left: A $4 \times 4$ arrangement with a $1024^{2}$ image comprising $16 \times 256^{2}$ sub-images. Right: A $2 \times 2$ arrangement comprising $4 \times 432^{2}$ sub-images, with 80 pixels of padding around each. + +![](images/947576b1e592921b87c5fdd1b5a0caa7583718b24b8deba0f6650fe38df2cdf1.jpg) + +Finding 3. Mosaic augmentation greatly reduces the training cost associated with learning from high-resolution teachers and eliminates the need for feature interpolation. Student quality is even improved with this optimization. + +# 4.4. Teacher Loss Balancing + +In PHI-S [34] we highlighted the significant variations in activation magnitudes among vision foundation models, observing that SAM's activations tend to overshadow those of CLIP and DINOv2 models. We adopt the PCA-Hadamard Isotropic Standardization (PHI-S) method, achieving improved balance among teacher losses. PHI-S rotates teacher activations to evenly distribute variance across all channels and then uniformly scales them to obtain unit variance. This process can be easily inverted by modifying the final linear projection of the adaptor MLP after training. PHI-S enhances training stability and overall benchmark scores. For a given teacher feature map $\mathbf{X}$ with embedding size $C$ , PHI-S applies the following transformation: + +![](images/8b6e869e7c6a0505ea883502d1a3fe7c3886ad3896d496a02dd8d674e5e8d3ea.jpg) + +![](images/cee2b6ffc0846e9b8e511114c3f97fd80f30b6cb218199833b33babbb4779c2a.jpg) + +![](images/f96ee98ef295e07f568046c1340b5b7c9af9147c4081caea9943cb7d7f7fa24d.jpg) + +![](images/a8ec127d93bb31aa68e9c897ade24f15a172dc7ed294d5df1bcee1cedd12bbaf.jpg) + +![](images/2cf672b3dc40441d65d77b745c73d4edccf93a502ea74ebfdb6c0602ca8b5f4a.jpg) +Figure 7. Visualizations of SigLIP and RADIOv2.5-H model features before and after ToMe compression. From left to right: input image; PCA visualization of features; merged tokens; PCA visualization of unmerged tokens. RADIOv2.5 is better able to compress background regions, leaving more tokens available for semantically rich features. + +![](images/3ff01fb5cac81f5703583dc6d000b5ad12c69377965aca4bb905cd45430e89a1.jpg) + +![](images/e7afc103f70c618810c8584cfddc7c3954bc858e18a824308c7b6d8cec7d245d.jpg) +Figure 8. Illustration of bipartite matching [3] using $2 \times 2$ strided pattern with $r = 9$ . A: The original tokens, with the red 'T#' squares being assigned as targets, and the green 'S#' squares being assigned as sources. B: We compute the affinity between each source and target. We only consider the maximum affinity for each source (shown in yellow). We find the $r$ highest affinity yellow squares, and merge those into their respective targets. C: The output tokens with merged values when a given 'T#' was assigned one or more sources. D: The final 7 tokens are fed to the LLM. Reconstructed Viz: From (C), we can visualize the compressed original feature map by broadcasting the merged tokens to all of the source locations. + +$$ +\mathbf {X} _ {i} ^ {\prime} = \phi_ {i} ^ {- 1} \mathbf {R} _ {i} \mathbf {X} _ {i}, \quad \mathbf {R} _ {i} = \mathbf {H} _ {C} \mathbf {U} _ {i} ^ {\intercal}, \quad \phi_ {i} = \sqrt {\frac {1}{C} \sum_ {j} ^ {C} \lambda_ {j}} \tag {5} +$$ + +Where $H_{C}$ is a normalized Hadamard matrix of dimension $C \times C$ , $\lambda_{j}$ are the eigenvalues of the covariance matrix $\mathbf{\Sigma}[\mathbf{X}]$ , and $\mathbf{U}$ are the corresponding eigenvectors. $\phi_{i}$ and $\mathbf{R}_{i}$ are specific to the $i$ th teacher. PHI-S is a statistical standardization technique, as the expected per-channel variance after PHI-S is 1. However, it is different than vanilla standardization in that it doesn't standardize the channels individually, and thus, doesn't distort the cross-channel variation. We briefly review the key results of [34] in appendix K, but refer the reader to the original paper for deeper understanding. + +Finding 4. PHI Standardization helps balance the energy spent learning from each teacher. + +# 4.5. Token Compression + +Inspired by ToMeSD[3], we evaluate the use of bipartite soft matching to merge similar tokens. We apply strided partitioning to ensure that each image region retains some representation in the compressed features. For evaluation, we track merged token indices, enabling us to unmerge tokens and measure the reconstruction error and inform hyperparameter selection. The method is illustrated in Figure 8. + +While ToMe recommends using attention keys for matching, we found that using the features directly reduces reconstruction error. Table 18 in the appendix summarizes our findings. Another slight departure from ToMe's recommendation is that we apply merging at the output of the vision encoder rather than incrementally. As shown in Ta + +![](images/528ba59a844f7cf7cb1d9da6f133256128e82d779e5ccf29711f8aa36f914e1a.jpg) + +ble 12, this approach yields an average improvement of $+1.4$ on VLM benchmarks. + +We also qualitatively evaluate token merging by visualizing feature and token merging outcomes in Figure 7. Token merging is assessed within the context of VLMs, with results reported in Table 1. + +We further note that token merging can be applied to other vision encoders and demonstrate its application on SigLIP. Interestingly, token merging yields a greater relative improvement on RADIOv2.5 than on SigLIP, a finding that aligns with the feature visualizations in Figure 7 and the measured reconstruction error in Table 18. We hypothesize that SigLIP's higher feature noise makes clustering more error prone. + +Finding 5. Token Merging is very effective at retaining the most diverse information under high compression ratios. + +# 5. Experiments + +# 5.1. Evaluation Benchmarks + +For Image classification, we report the ImageNet-1k[36] Top-1 classification accuracy using two methods. i) zero-shot[32] classification using the DFN CLIP language model; ii) k-NN[5] classification using the embeddings of the shared backbone. + +
ResMethodTokens/imTextVQAChartQADocVQAInfoVQAOCRbench
51222Unshuffle25665.023.745.732.940.2
ToMe r=76825665.725.849.734.941.2
76833Unshuffle25665.825.949.735.240.9
ToMe r=204825669.730.452.336.242.9
102444Unshuffle25666.123.846.634.138.9
ToMe r=384025669.328.149.134.642.7
ToMe r=358451268.931.353.937.044.6
+ +Table 3. VLM benchmarks across various compression methods. All configurations produce 256 vision tokens per image, except for the last row (512 tokens). Token Merging outperforms Pixel Unshuffling on all benchmarks. $r =$ denotes the number of tokens being merged. + +For Instance Segmentation, we use the EfficientViT[25] implementation of a COCO[21] instance segmenter to measure how well our SAM adaptor head can replace SAM. + +For Semantic Segmentation, we use the MMSeg[8] framework, and train a linear probe on top of the frozen RADIOv2.5 features. We use the ADE20k[50] dataset. We train the probe at three resolutions $(512^{2}, 768^{2}$ , and $1024^{2}$ ) and report the best result (full results in appendix). + +For 3D understanding experiments we use the Probe3D[12] code base and apply a DPT head on top of the frozen backbone features. We train and evaluate on the Navi[19] dataset. We resize images to $512^2$ during both training and evaluation. + +For Vision-Language Modeling we follow the same framework as in VILA [23]. We pair our vision encoder with a MN-Minitron-8B[41] LLM. We train all alignment/pretraining/SFT and unfreeze the vision encoder during SFT. We train the model using ShareGPT4v[6] and VFLAN[45] datasets. We leverage insights from Cambrian[42] to select the benchmarks that are most sensitive to the quality of visual features report scores on TextVQA[40], ChartQA[27], DocVQA[29], InfoVQA[28] and OCRBench[26]. + +# 5.2. Ablation Studies + +Ablation studies are summarized in Table 1. Our initial RADIOv2.1-L baseline (config $\mathcal{A}$ ) is a reproduction of AM-RADIO [35], using a ViT-L backbone and the DataComp1B[16] dataset. Our hyperparameters are detailed in the appendix. + +We add multi-resolution training in config $\mathcal{B}$ , and notice improved results on most dense tasks (+2.8 on ADE20k, +3.4 on average on VLMs). Multi-score robustness is particularly evident in Figure 2, where config $\mathcal{B}$ exhibits much more consistent results at higher resolutions. + +In config $\mathcal{C}$ , we replace the OpenAI CLIP teacher with + +SigLIP [49] and observe a 6.7-point improvement on VLM benchmarks. + +In config $\mathcal{D}$ , we replace the ViT-L 320M-parameter backbone with a 553M-parameter ViT-H backbone, which improves all metrics significantly. + +Config $\mathcal{E}$ applies only to VLMs, where we replace $2^{2}$ pixel unshuffling with Token Merging. This reduces the number of vision tokens from 576 to 256 and improves VLM scores by an average of 5.9 points. Appendix Table 11 provides a detailed analysis of the trade-off between the number of vision tokens and accuracy, highlighting RA-DIOv2.5's comparative advantage over SigLIP in terms of token merging effectiveness. + +# 5.3. Comparative Results + +# 5.3.1 Dense Task Evaluation + +We evaluate our models in comparison to other agglomerative models of similar size (SAM-CLIP [43], Theia [38], UNIC [37], UNIT [51]). Following MLoRE [47] we report metrics on NYUDv2 and PASCAL Context for our model. We train with a learning rate of $1e - 3$ , and use a weight of 1 for all tasks. We purposefully don't tune any hyperparameters. We keep the backbone model frozen, and use MLoRE's "conv" head for each task. The conv head is defined as follows: Conv-3x3 $\rightarrow$ BatchNorm $\rightarrow$ GeLU $\rightarrow$ Conv-1x1. + +Results are reported in Table 4. RADIOv2.5 models exhibit a consistent improvement over previous baselines. + +# 5.3.2 VLM Evaluation + +We compare our models against state-of-the-art vision encoders: OpenAI-CLIP [32], RADIoV2.1-H and SigLIPS0400M [49]. We pair the vision encoders with MN-Minitron-8B [41] and train them in VILA [23] using the LLaVA1.6 [24] data mixture. For all vision encoders, we use Token Merging to compress the visual features to 196 tokens in order to ensure a fixed cost to the Language Model. We report results in Table 5. We observe that RADIoV2.5 models consistently exceed the accuracy of other vision encoders. + +# 6. Related Work + +AM-RADIO[35] and SAM-CLIP[43] pioneered multiteacher distillation for Vision Foundation Models, though AM-RADIO struggles with resolution consistency and SAM-CLIP lacks a strong dense model like DINO, reducing semantic segmentation accuracy. Theia[38] uses a multidistillation framework for robotics, incorporating teachers like DepthAnything[46], while UNIC[37] stabilizes training with expandable projectors and teacher-dropping regularization. Our method, however, employs teacher fea + +
ModelParamsADE20k mIoU↑NYUdPascal Context
SemSeg mIoU↑Depth RMSE↓Normal mErr↓SemSeg mIoU↑Parsing mIoU↑Saliency maxF↑Normal mErr↓
SAM-CLIP[43]86M38.4†††††††
Theia [38]86M35.5538.900.637724.1169.8460.6780.6316.94
UNIC-B[37]86M39.642.210.617222.7875.9062.8581.8415.78
RADIOv2.5-B (ours)98M48.9457.190.498020.0481.7571.4981.2616.10
UNIC-L[37]307M48.3058.560.491619.3481.8272.2479.2117.35
RADIOv2.5-L (ours)320M52.9561.420.457718.5782.8774.3281.6516.15
UNIT[51]632M50.1961.440.453819.0782.3673.3478.7017.98
RADIOv2.1-H653M51.3662.760.433918.4382.7874.4278.4817.53
RADIOv2.5-H653M53.9763.820.435317.6783.4375.7581.1916.16
UNIT[51]1B50.6361.620.452719.0782.2073.2278.5117.96
RADIOv2.5-g (ours)1.1B54.5663.460.431817.0882.6575.1880.0817.06
+ +Table 4. Comparison of dense task benchmarks against other agglomerative models. $\dagger$ Results unavailable due to lack of access to SAM-CLIP model weights. Note: RADIo requires more parameters for a given model class due to a $C \times {128} \times {128}$ position embedding buffer coming from CPE, but does not contribute meaningfully to increased FLOPs or representation capacity. + +
Vision EncoderResolutionTokens/fimTextVQAChartQADocVQAInfoVQAOCRBenchGQAPOPEMMESEED(I)MMMUAI2DAverage
OpenAI-CLIP [32]336219663.249.243.427.443162.485.71517.972.743.477.658.55
RADIOv2.1-H [35]512219663.651.740.126.239263.487.31570.673.643.978.958.76
RADIOv2.1-H [35]768219662.849.936.724.836562.787.01517.271.741.973.456.66
SigLIP-SO400M [49]384219664.855.747.929.245263.185.41632.972.941.180.760.95
RADIOv2.5-L (ours)768219666.756.449.229.844163.487.61592.474.043.379.261.21
RADIOv2.5-H (ours)768219668.861.654.230.849863.887.31562.374.144.182.563.19
RADIOv2.5-g (ours)672219669.657.053.330.947963.487.51606.474.341.380.862.39
+ +Table 5. Vision Encoder Comparison in VILA[23]. We used MN-Minitron-8B[41] as LLM and the LLaVA1.6[24] data mixture. We use Token Merging to compress all visual features down to 196 tokens. From left to right we report: image resolution, number of tokens per image, TextVQA (with OCR hints) validation accuracy, ChartQA overall, DocVQA validation accuracy, InfoVQA validation accuracy, OCRBench accuracy, GQA (TestDev) accuracy, POPE F1 score, MME perception score, SEED (Image) accuracy, MMMU (validation) accuracy, AI2D (no mask) accuracy, average (calculated after dividing MME score by 20 and OCR score by 10). + +ture standardization and multi-resolution training for scale-consistent accuracy, enhancing the original ViT[11] interpolation approach. Unlike FlexiViT[2] and NaViT[10], we use Cropped Position Embeddings (CPE)[21] and distill resolution-robust students from inflexible teachers. + +Cambrian-1 [42] integrates multiple vision encoders through a Spatial Vision Aggregator, utilizing learnable latent queries that interact with several layers of a Large Language Model (LLM) via cross-attention. Eagle [39] combines multiple vision experts by concatenating their visual tokens along the channel dimension. BRAVE [20] introduces the Multi-Encoder Querying Transformer, which merges visual features from various encoders into a fixed-length representation, subsequently used as a soft prompt for a frozen language model. In contrast, our method performs multi-vision encoder aggregation as a preliminary step to develop a single, versatile vision encoder suitable for integration into a VLM, but also easily usable outside of a VLM context. + +# 7. Conclusion + +In this paper, we presented RADIOv2.5, a robust framework for multi-teacher vision model distillation that accommodates variations in teacher resolutions, activation magnitudes, and noise patterns. The key differentiating factor in our work is our focus on preserving accuracy across a broad range of resolutions. Our multi-resolution training approach mitigates resolution-dependent quality degradation (mode switching). Our findings show that mosaic augmentation and PHI-S effectively balance computational load and loss contributions from each teacher. + +Token compression enables efficient integration with VLMs by preserving critical visual information, even at high compression ratios. Our feature selection study highlighted the advantages of using intermediate activations for dense tasks, particularly when non-linear transformations are used. + +# References + +[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. 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This strategy enables the efficient creation of robust models, combining the strengths of individual teachers while significantly reducing computational and resource demands. In this paper, we thoroughly analyze state-of-the-art agglomerative models, identifying critical challenges including resolution mode shifts, teacher imbalance, idiosyncratic teacher artifacts, and an excessive number of output tokens. To address these issues, we propose several novel solutions: multi-resolution training, mosaic augmentation, and improved balancing of teacher loss functions. Specifically, in the context of Vision Language Models, we introduce a token compression technique to maintain high-resolution information within a fixed token count. We release our top-performing variants at multiple scales " + }, + { + "bbox": [ + 54, + 252, + 297, + 479 + ], + "type": "inline_equation", + "content": "(-B, -L, -H, \\text{and} -g)" + }, + { + "bbox": [ + 54, + 252, + 297, + 479 + ], + "type": "text", + "content": ", along with inference code and pretrained weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 484, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 484, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 67, + 484, + 296, + 498 + ], + "type": "text", + "content": "Links: Code (on GitHub)—Models (on Hugging Face)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 530, + 137, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 530, + 137, + 544 + ], + "spans": [ + { + "bbox": [ + 56, + 530, + 137, + 544 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 551, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 551, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 551, + 296, + 694 + ], + "type": "text", + "content": "The rise of specialized Vision Foundation Models (VFMs) has created a need for methods to consolidate knowledge from multiple models into a unified model. SAM-CLIP [43] addresses this challenge by combining SAM [22] and CLIP [32] to integrate capabilities from both. In another approach, AM-RADIO [35] introduces label-free knowledge distillation from multiple teacher models, enabling knowledge transfer without direct supervision. UNIC [37] adds intermediate teacher matching projectors and dynamic teacher selection. Theia [38] aims to facilitate robot learning by distilling insights from multiple vision teachers. Meanwhile, PHI-S [34] studies the importance of normal" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 228, + 555, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 555, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 555, + 276 + ], + "type": "text", + "content": "izing the distinct teacher distributions to simplify their balancing. Relatedly, Eagle [39] leverages a mixture of vision encoders to achieve inference-time knowledge aggregation within the context of Vision-Language Models (VLMs)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 276, + 555, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 555, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 555, + 312 + ], + "type": "text", + "content": "Despite these advancements, this growing body of work on knowledge agglomeration still leaves open several critical challenges:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 316, + 554, + 495 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 315, + 316, + 554, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 316, + 554, + 374 + ], + "spans": [ + { + "bbox": [ + 315, + 316, + 554, + 374 + ], + "type": "text", + "content": "- Resolution balancing: Teacher models operate at varying resolutions due to different training goals, creating feature granularity inconsistencies. Effective techniques are needed to balance these resolutions in the student model to capture both fine details and broader abstractions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 376, + 554, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 376, + 554, + 411 + ], + "spans": [ + { + "bbox": [ + 315, + 376, + 554, + 411 + ], + "type": "text", + "content": "- Teacher distribution balancing: Existing models have different distribution moments and the distillation process should account for this to prevent biased learning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 411, + 554, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 411, + 554, + 495 + ], + "spans": [ + { + "bbox": [ + 315, + 411, + 554, + 495 + ], + "type": "text", + "content": "- Generating multi-resolution features for diverse applications: Vision models support various applications requiring different feature resolutions, from image captioning to dense segmentation. A VFM that flexibly produces features at any resolution could serve multiple tasks, reducing the need for separate models and unlocking new opportunities." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 629 + ], + "type": "text", + "content": "In our analysis of existing agglomerative models, we study and propose a fix for the notable \"mode switch\" phenomenon in AM-RADIO, where feature distributions shift significantly based on input resolution (Section 3.1). Specifically, low-resolution inputs yield DINO-like features, while high-resolution inputs produce SAM-like features. We trace this behavior to the student learning from different teachers at different resolutions during training. In section 4.2, we introduce a solution to stabilize these mode switches, achieving strong resolution robustness and improved quality scaling." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "Equipped with a high-resolution vision encoder, we now focus on Vision-Language Model (VLM) integration. In downstream VL tasks, a key challenge is the token/feature count. 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Overview of the main contributions: From left to right, we introduce a multi-resolution training framework that enables our student model to maintain accuracy across all resolutions; we propose using token merging to better retain fine-grained details while merging uninformative tokens; our RADIOv2.5 models improve upon the RADIOv2.1 baseline across all benchmarks, with significant gains on VLM tasks." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 365, + 251, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 251, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 251, + 376 + ], + "type": "text", + "content": "encoder resolution from the VLM's patch count." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 376, + 263, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 263, + 388 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 263, + 388 + ], + "type": "text", + "content": "Our main contributions, illustrated in Figure 1, are:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 388, + 296, + 483 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 55, + 388, + 295, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 411 + ], + "type": "text", + "content": "- A multi-resolution training strategy that fixes mode switching and allows for fully flexible input resolution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 412, + 296, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 296, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 296, + 435 + ], + "type": "text", + "content": "- A comprehensive study of feature selection for a range of downstream tasks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 436, + 296, + 483 + ], + "type": "text", + "content": "- A proposal for vision model feature selection within VLMs, enabling integration with language models while preserving essential information. We demonstrate that RADIOv2.5 disproportionately benefits from this." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 494, + 134, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 134, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 134, + 507 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 55, + 514, + 204, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 204, + 527 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 204, + 527 + ], + "type": "text", + "content": "2.1. Knowledge Agglomeration" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 55, + 532, + 295, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 591 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 591 + ], + "type": "text", + "content": "The assumption underlying knowledge agglomeration is that multiple foundation models exist, each capable of extracting diverse and meaningful representations from a wide range of images, and that knowledge from these models can be distilled into a single agglomerative model." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 55, + 592, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 592, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 592, + 295, + 616 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 592, + 295, + 616 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 592, + 295, + 616 + ], + "type": "text", + "content": " be the input data. The student's shared backbone produces a feature representation:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 93, + 623, + 295, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 623, + 295, + 644 + ], + "spans": [ + { + "bbox": [ + 93, + 623, + 295, + 644 + ], + "type": "interline_equation", + "content": "\\mathbf {z} = f (x) = \\left[ z _ {s}, z _ {p} ^ {(1)}, z _ {p} ^ {(2)}, \\dots , z _ {p} ^ {(N)} \\right], \\tag {1}", + "image_path": "4ca35e2002ba6c250e92f1e9ce1a8f2d34adbc0d3352e1e3179bde1b3f9f94c8.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "inline_equation", + "content": "z_{s} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "content": " is the summary token, " + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "inline_equation", + "content": "z_{p}^{(i)} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N" + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "content": " are the patch tokens, and " + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 652, + 295, + 689 + ], + "type": "text", + "content": " is the student's embedding dimension." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "For each teacher " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ", the student's model includes two adaptor heads: " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "g_{s}^{(t)}:\\mathbb{R}^{d}\\to \\mathbb{R}^{d_{t}}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ", which projects the sum" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "text", + "content": "mary token " + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "inline_equation", + "content": "z_{s}" + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "text", + "content": " into the teacher's embedding space, and " + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "inline_equation", + "content": "g_p^{(t)}:\\mathbb{R}^d\\to \\mathbb{R}^{dt}" + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "text", + "content": ", which projects each patch token " + }, + { + "bbox": [ + 313, + 365, + 553, + 390 + ], + "type": "inline_equation", + "content": "z_{p}^{(i)}" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 390, + 553, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 553, + 414 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 553, + 414 + ], + "type": "text", + "content": "Adaptor heads, typically simple MLPs, adjust feature dimensions as needed. For teacher " + }, + { + "bbox": [ + 313, + 390, + 553, + 414 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 390, + 553, + 414 + ], + "type": "text", + "content": ", we define:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 347, + 422, + 553, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 422, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 347, + 422, + 553, + 437 + ], + "type": "interline_equation", + "content": "g ^ {(t)} (z) = \\operatorname {M L P} ^ {(t)} (z) = \\sigma \\left(W ^ {(t)} z + b ^ {(t)}\\right), \\tag {2}", + "image_path": "76f958bdd3d3b80835839f3a41649b5a29fa0033abe722aec65e88ffc5217a79.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "content": " is a non-linear activation, and " + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "inline_equation", + "content": "W^{(t)}" + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "inline_equation", + "content": "b^{(t)}" + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "content": " are learnable parameters. Projected features per teacher " + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 447, + 555, + 472 + ], + "type": "text", + "content": " are:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 324, + 491, + 553, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 491, + 553, + 509 + ], + "spans": [ + { + "bbox": [ + 324, + 491, + 553, + 509 + ], + "type": "interline_equation", + "content": "\\text {S u m m a r y :} \\hat {z} _ {s} ^ {(t)} = g _ {s} ^ {(t)} \\left(z _ {s}\\right), \\quad \\text {P a t c h :} \\hat {z} _ {p} ^ {(t)} = g _ {p} ^ {(t)} \\left(z _ {p}\\right). \\tag {3}", + "image_path": "6d6ab4494f3e58de9274bd2fe8afb4e67ade05acc7f4d780251f71bd3295a35f.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 516, + 555, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 555, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 555, + 552 + ], + "type": "text", + "content": "The training objective aligns student features with teacher features using a loss function that measures their similarity. 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ConfigurationGoalImageNet1KSegmentationProbe3D[12]Vision-Language (VILA[23])SAM [22]
Zero-shotk-NNADE20kDepthSurfNormalsTextVQAChartQADocVQAInfoVQAOCRBench
A: RADIOv2.1-L*Baseline78.3584.0150.0382.6359.9457.0115.624.1928.8825.60
B: A + multi-resEliminate modes81.2184.0952.8482.3961.0459.4416.633.9929.0229.40
C: B - OpenAICLIP + SigLIPBetter VLM81.0184.6852.9584.760.164.4225.2845.8030.6036.00
D: C + ViT-HBigger backbone82.5185.8153.9785.762.565.8825.9649.7435.1740.90
E: D + Token MergingImprove VLM-----69.7430.4052.3336.2442.90
", + "image_path": "3b2647b1f68f9e002fdce184a90c39c253bc593390a6573e37dce26d75ee6e31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 140, + 555, + 174 + ], + "lines": [ + { + "bbox": [ + 55, + 140, + 555, + 174 + ], + "spans": [ + { + "bbox": [ + 55, + 140, + 555, + 174 + ], + "type": "text", + "content": "Table 1. Ablation Results. For Probe3D, Depth and Surface Normals metrics are averaged over the buckets defined in the paper. For SAM COCO we use the \"instance all\" bucket. Each incremental change we introduce leads to improved metrics. *We use a ViT-L instead of the ViT-H used in the original AM-RADIO [35] paper." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": "and SAM-H [22] as teachers. For each teacher to distill from, we augment the backbone with an adaptor for the summarization token, and an adaptor for the patch tokens. Our adaptor is a 2-layer MLP with a LayerNorm[1] and a GeLU[18] in between. We train the student using teacher features generated by inferring images of the DataComp1B[16] dataset. For faster iterations, we replicate AM-RADIO using a ViT-L backbone instead of the original ViT-H backbone and refer to it as RADIOv2.1-L from this point forward. We train the model with a batch size of " + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "inline_equation", + "content": "1024 + 128" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "inline_equation", + "content": "600\\mathrm{k}" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": " iterations. Training is split into two concurrent partitions: one partition trains the student at a resolution of " + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "inline_equation", + "content": "432^2" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": " against CLIP and DINOv2 teachers with batch size 1024, while the other partition trains the student at a resolution of " + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": " against SAM with a batch size of 128. This baseline is referred to as " + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 183, + 297, + 376 + ], + "type": "text", + "content": " in Table 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 382, + 188, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 382, + 188, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 188, + 395 + ], + "type": "text", + "content": "2.3. Evaluation Framework" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 401, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 296, + 547 + ], + "type": "text", + "content": "Evaluating foundation model quality across diverse downstream tasks is challenging. We use a rigorous framework to pinpoint improvements and inform design: assessing ImageNet-1k[36] Top-1 accuracy via zero-shot[32] and k-NN[5] classification; probing frozen backbone features for semantic segmentation on ADE20k[50] and PascalVOC[13]; evaluating instance segmentation on COCO[21] with EfficientViT[25] protocols and our SAM adaptor; testing 3D understanding (depth, normals, correspondence) per [12]; pairing with an LLM for Vision-Language reasoning; and probing dense multi-task quality on Pascal Context[30] and NYUDv2[31] as in MLoRE [47]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 555, + 127, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 127, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 127, + 569 + ], + "type": "text", + "content": "3. Challenges" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 575, + 263, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 263, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 263, + 588 + ], + "type": "text", + "content": "3.1. Achieving Multi-Resolution Robustness" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "text", + "content": "Although AM-RADIO [35] supports a wide range of input resolutions, we noticed poor quality on high-resolution benchmarks. As illustrated in Figure 2, Zero-Shot Top-1 accuracy drops sharply after inputs are larger than roughly " + }, + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "inline_equation", + "content": "512\\mathrm{px}" + }, + { + "bbox": [ + 55, + 594, + 296, + 715 + ], + "type": "text", + "content": ". This showcases an undesirable property of this model, which is that it doesn't reliably scale to high-resolution images. AM-RADIO hints at this issue in its conclusion: the model exhibits a \"mode switching\" behavior as resolution increases. This prompted us to visualize the features and investigate the effect of a resolution increase. Fig-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 183, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 183, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 183, + 555, + 316 + ], + "type": "text", + "content": "ure 3 illustrates the issue well: at resolutions lower than or equal to " + }, + { + "bbox": [ + 313, + 183, + 555, + 316 + ], + "type": "inline_equation", + "content": "512^2" + }, + { + "bbox": [ + 313, + 183, + 555, + 316 + ], + "type": "text", + "content": ", the features most closely resemble those of DINOv2 and appear to be expressive of depth and semantic content. At higher resolutions, the model starts to behave more like SAM, with features that show sharp delineations around contours and homogeneous contents within. This behavior is intuitive given the fact that in the high-resolution regime the student only sees SAM features. Table 2 shows a quantified measure of feature variance across scales (see implementation in appendix). DINOv2 exhibits much smaller scale variance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 323, + 398, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 398, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 398, + 335 + ], + "type": "text", + "content": "3.2. Token Count" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 341, + 556, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 556, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 556, + 510 + ], + "type": "text", + "content": "Dense downstream tasks, such as pixel-level semantic segmentation and depth estimation, benefit from receiving fine features from a vision encoder. However, for vision-language models like LLaVA [24], where visual tokens are integrated into a sequence of text embeddings, an excessive number of vision tokens can negatively impact speed/quality or lead to sequence overflows. Pixel unshuffling, as proposed in InternVL1.5 [7], addresses this by reducing the number of vision tokens, grouping " + }, + { + "bbox": [ + 313, + 341, + 556, + 510 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 341, + 556, + 510 + ], + "type": "text", + "content": " tokens along the channel dimension. However, this approach cannot adapt to varying information densities within an image. For instance, a text document might have large areas of white background that should be more strongly compressed than areas containing text." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 520, + 370, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 370, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 370, + 532 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 539, + 427, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 427, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 427, + 553 + ], + "type": "text", + "content": "4.1. Scale Equivariance" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": "We measure scale equivariance of multi-scale features by normalizing and interpolating them to the lowest resolution, then computing the spatial average of variance across scales (see Appendix F). Table 2 shows our baseline student has worse scale equivariance than DINOv2, our only multi-resolution teacher for comparison. VLMs like LLaVa-NeXT[24] and InternVL1.5[7] use tiling to handle high-resolution inputs with fixed-resolution encoders, suggesting scale equivariance may be less critical. However, tiling coarsens increases in resolution and, as tile count grows, limits the encoder's view of the full image, hindering contextual reasoning. In Figure 4, we analyze SigLIP[49] (used in Cambrian[42]) features across tiling setups, revealing" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22489" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 76, + 171, + 163 + ], + "blocks": [ + { + "bbox": [ + 61, + 76, + 171, + 163 + ], + "lines": [ + { + "bbox": [ + 61, + 76, + 171, + 163 + ], + "spans": [ + { + "bbox": [ + 61, + 76, + 171, + 163 + ], + "type": "image", + "image_path": "ffc1ab8fad9a4d9f7663e61e2cb4754ec64f4509158e71eb819b973c24c080d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "lines": [ + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "type": "text", + "content": "Figure 2. Zero-Shot Accuracy and teacher matching fidelity metrics as a function of input resolution. AM-RADIO (aka RADIOv2.1, config " + }, + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "type": "text", + "content": "), and our \"Multi-Stage Stage 3\" model exhibit mode switching behavior. \"Multi-Stage Stage 2\" doesn't exhibit the behavior, owing to all teachers being trained solely at low resolution, however quality at high resolution quickly degrades. \"Multi-Resolution\" (config " + }, + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 173, + 555, + 217 + ], + "type": "text", + "content": ") training fixes the mode switch, and allows the model to be strong across a larger range of resolutions compared to Stage 2." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 184, + 76, + 294, + 163 + ], + "blocks": [ + { + "bbox": [ + 184, + 76, + 294, + 163 + ], + "lines": [ + { + "bbox": [ + 184, + 76, + 294, + 163 + ], + "spans": [ + { + "bbox": [ + 184, + 76, + 294, + 163 + ], + "type": "image", + "image_path": "7eb1b0a2941679a99ef187a2f53db5b5f2416d7e8caae55279208ae1dda21d9d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 239, + 544, + 277 + ], + "lines": [ + { + "bbox": [ + 324, + 239, + 544, + 277 + ], + "spans": [ + { + "bbox": [ + 324, + 239, + 544, + 277 + ], + "type": "text", + "content": "Finding 1. High-resolution inference through tiling causes the vision encoder to lose global context and exhibit poor scaling equivariance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 308, + 76, + 419, + 163 + ], + "blocks": [ + { + "bbox": [ + 308, + 76, + 419, + 163 + ], + "lines": [ + { + "bbox": [ + 308, + 76, + 419, + 163 + ], + "spans": [ + { + "bbox": [ + 308, + 76, + 419, + 163 + ], + "type": "image", + "image_path": "0ba186bbf8c58c285a9d49b0863df9c9e0a354af203df6e98f654b9f46039c3d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 433, + 76, + 541, + 163 + ], + "blocks": [ + { + "bbox": [ + 433, + 76, + 541, + 163 + ], + "lines": [ + { + "bbox": [ + 433, + 76, + 541, + 163 + ], + "spans": [ + { + "bbox": [ + 433, + 76, + 541, + 163 + ], + "type": "image", + "image_path": "f10e355ba79363aeb66436ed0073c861105a88361a82c61abd4a937af4f65488.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 56, + 236, + 296, + 318 + ], + "blocks": [ + { + "bbox": [ + 56, + 236, + 296, + 318 + ], + "lines": [ + { + "bbox": [ + 56, + 236, + 296, + 318 + ], + "spans": [ + { + "bbox": [ + 56, + 236, + 296, + 318 + ], + "type": "image", + "image_path": "65fda17a402052f2557f1a52d76fc580d81793d50d1294f66197bcfe0e0ab5f4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "lines": [ + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": "Figure 3. Visualizations of patch token features across input resolutions. We use PCA to map patch tokens to RGB colors. Top: Input image, followed by visualizations of DINOV2, RADIOv2.1 (config " + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": ") at " + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "inline_equation", + "content": "512^2" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": " resolutions, and SAM. Bottom: RADIOv2.5-H (config " + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 325, + 296, + 413 + ], + "type": "text", + "content": "). As resolution increases, RADIOv2.1 features resemble SAM's, even showing VitDet windowing artifacts, while RADIOv2.5 remains more self-consistent and less noisy." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 452, + 295, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 452, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 452, + 295, + 489 + ], + "type": "text", + "content": "qualitative inconsistencies and reduced scale equivariance (Table 2). Tiling also boosts vision tokens by up to " + }, + { + "bbox": [ + 55, + 452, + 295, + 489 + ], + "type": "inline_equation", + "content": "12 \\times [7]" + }, + { + "bbox": [ + 55, + 452, + 295, + 489 + ], + "type": "text", + "content": ", increasing VLM latency." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 56, + 515, + 295, + 636 + ], + "blocks": [ + { + "bbox": [ + 56, + 515, + 295, + 636 + ], + "lines": [ + { + "bbox": [ + 56, + 515, + 295, + 636 + ], + "spans": [ + { + "bbox": [ + 56, + 515, + 295, + 636 + ], + "type": "image", + "image_path": "754fe7c0f6e41dfde5649998d8813672c006c0f0cc117ac9bad88e2e26ee5668.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "lines": [ + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "spans": [ + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of tiling and high-resolution inference. Tiling emulates high-res SigLIP inference. Top: From left to right: input, SigLIP features using " + }, + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "type": "inline_equation", + "content": "1,2 \\times 2" + }, + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 55, + 644, + 296, + 711 + ], + "type": "text", + "content": " tiles. Bottom: Single-pass inference using RADIOv2.5 (ours) at equivalent image sizes. SigLIP features vary significantly across different tiling arrangements." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 285, + 462, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 285, + 462, + 298 + ], + "spans": [ + { + "bbox": [ + 314, + 285, + 462, + 298 + ], + "type": "text", + "content": "4.2. Multi-Resolution Training" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "text", + "content": "The previous observations motivate a change in the training schedule: with multi-resolution training we enable the student to learn from all teachers across multiple resolutions. This is easily achieved with DINOv2, since DINOv2 can infer images at any resolution. For CLIP teachers, we feed them with images at the teacher's native resolution, and we feed the student with images at multiple resolutions. We interpolate student features down to the resolution of the teacher's features before applying the loss function. SAM presents an extra challenge, as noted in AM-RADIO[35], since interpolating SAM features significantly deteriorates their quality. Therefore in order to train our student against SAM at lower resolutions than " + }, + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "text", + "content": ", we pad smaller images to " + }, + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 313, + 304, + 555, + 483 + ], + "type": "text", + "content": ", then crop SAM features to the effective size of the unpadded image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 483, + 554, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 554, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 554, + 519 + ], + "type": "text", + "content": "Training the student for 600k iterations with a multi-resolution setup is costly. Thus we break down training into three stages:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 553, + 591 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 314, + 521, + 553, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 521, + 553, + 544 + ], + "spans": [ + { + "bbox": [ + 314, + 521, + 553, + 544 + ], + "type": "text", + "content": "- In a first stage, we train the student at low resolution " + }, + { + "bbox": [ + 314, + 521, + 553, + 544 + ], + "type": "inline_equation", + "content": "(256^{2})" + }, + { + "bbox": [ + 314, + 521, + 553, + 544 + ], + "type": "text", + "content": " for 300k iterations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 544, + 553, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 553, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 553, + 567 + ], + "type": "text", + "content": "- In a second stage, we train the student at medium resolution " + }, + { + "bbox": [ + 313, + 544, + 553, + 567 + ], + "type": "inline_equation", + "content": "(432^{2})" + }, + { + "bbox": [ + 313, + 544, + 553, + 567 + ], + "type": "text", + "content": " for 300k iterations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "text", + "content": "- In the third stage, we train the student simultaneously at " + }, + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "inline_equation", + "content": "432^{2}" + }, + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 313, + 568, + 553, + 591 + ], + "type": "text", + "content": " resolutions for 300k iterations." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "Multi-resolution training is illustrated in Figure 5, which depicts four training regimes based on whether the teachers and/or students process low- or high-resolution images. When both the student and teachers use either low- or high-resolution images, no particular challenge arises. However, training a high-resolution student against a low-resolution teacher requires downscaling the student's features to match those of the teacher. Conversely, training a low-resolution student against a high-resolution teacher necessitates a careful augmentation technique, as described in Section 4.3." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22490" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 70, + 270, + 174 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 270, + 174 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 270, + 174 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 270, + 174 + ], + "type": "table", + "html": "
ModelEquivariance ↓
Fine ScaleCoarse Scale
DINOv2-g-reg0.1260.178
AM-RADIO-L0.3570.476
RADIOv2.5-B0.1020.168
RADIOv2.5-L0.1020.165
RADIOv2.5-H0.1190.193
RADIOv2.5-L (tiling)N/A0.369
SigLIP (tiling)N/A0.623
", + "image_path": "f0e3bdf94c52c319d463a61fea52721f617bd4a94cd0ad82938e4286dacb5dfb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "lines": [ + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": "Table 2. Scale equivariance, computed over a small dataset of natural images (shown in Appendix). Fine: we scale image resolutions from " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "384^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "1568^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": " by increments of the model's patch size. Coarse: we scale images from " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "384^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "1920^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": " by multiples of " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "384^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": ". For the models that are denoted as \"tiling\", we perform inference over tiles of " + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "inline_equation", + "content": "384^2" + }, + { + "bbox": [ + 55, + 182, + 296, + 258 + ], + "type": "text", + "content": "\" and re-assemble features to produce the high-resolution features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 61, + 272, + 291, + 459 + ], + "blocks": [ + { + "bbox": [ + 61, + 272, + 291, + 459 + ], + "lines": [ + { + "bbox": [ + 61, + 272, + 291, + 459 + ], + "spans": [ + { + "bbox": [ + 61, + 272, + 291, + 459 + ], + "type": "image", + "image_path": "0fc13bb1c63512edafbd67e4a8db79ca607b649dfe63d1ec5b9cdc10feb07bf1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 469, + 296, + 535 + ], + "lines": [ + { + "bbox": [ + 55, + 469, + 296, + 535 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 296, + 535 + ], + "type": "text", + "content": "Figure 5. Illustration of the multi-resolution training setup. The student learns from all teachers at all resolutions. High-res student features are downsampled to match the resolution of low-res teachers. High-res teachers are provided with mosaics of smaller images and their output features are cropped out in order to train a low-res student." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 558, + 285, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 558, + 285, + 607 + ], + "spans": [ + { + "bbox": [ + 66, + 558, + 285, + 607 + ], + "type": "text", + "content": "Finding 2. For the student model to be consistently accurate across resolutions, it is sufficient to match all teachers at all resolutions, and to train at two resolutions simultaneously in the final training stage." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 180, + 635 + ], + "type": "text", + "content": "4.3. Mosaic Augmentation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 641, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 295, + 700 + ], + "type": "text", + "content": "The training schedule described in Section 4.2 involves running SAM inference on padded images, using cropped features to train the student against SAM at low resolution. This approach incurs a substantial computational cost, as SAM is the most resource-intensive teacher." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "To improve efficiency when training a student at a reso" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": "lution " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "\\leq 512^2" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " against SAM, we can instead create a mosaic of " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "k\\times k" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " images, with " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "k = \\left\\lfloor \\frac{1024}{x}\\right\\rfloor" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " being the student resolution, resulting in a single " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " image. We then perform SAM inference on this mosaic and extract " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "k^2" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " individual feature maps to train the student. Mosaic augmentation includes padding as needed to maximize efficiency. For example, to train a student at " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "432^2" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " resolution, we can create a " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "2\\times 2" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " mosaic with 80-pixel padding around each image. Figure 6 shows sample mosaic augmentations under 256 and 432 student resolutions. Qualitatively, we observe cleaner features after applying mosaic augmentation, which we believe is due to the increased diversity in image positions, helping to reduce teacher positional encoding artifacts. We also show SAM's PCA features for these mosaic images in figures 12 and 13 in the appendix." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 264, + 425, + 373 + ], + "blocks": [ + { + "bbox": [ + 315, + 264, + 425, + 373 + ], + "lines": [ + { + "bbox": [ + 315, + 264, + 425, + 373 + ], + "spans": [ + { + "bbox": [ + 315, + 264, + 425, + 373 + ], + "type": "image", + "image_path": "22d3621236937a8b9e215909d8bde9aa7b9597be6d2d03a49902c2fda10cddd8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": "Figure 6. Sample mosaic augmentations. Grid lines represent " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "16^{2}" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " patches (only shown here for visualization purposes). Left: A " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " arrangement with a " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " image comprising " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "16 \\times 256^{2}" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " sub-images. Right: A " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " arrangement comprising " + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "inline_equation", + "content": "4 \\times 432^{2}" + }, + { + "bbox": [ + 313, + 380, + 555, + 437 + ], + "type": "text", + "content": " sub-images, with 80 pixels of padding around each." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 445, + 264, + 553, + 373 + ], + "blocks": [ + { + "bbox": [ + 445, + 264, + 553, + 373 + ], + "lines": [ + { + "bbox": [ + 445, + 264, + 553, + 373 + ], + "spans": [ + { + "bbox": [ + 445, + 264, + 553, + 373 + ], + "type": "image", + "image_path": "947576b1e592921b87c5fdd1b5a0caa7583718b24b8deba0f6650fe38df2cdf1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 324, + 463, + 544, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 463, + 544, + 523 + ], + "spans": [ + { + "bbox": [ + 324, + 463, + 544, + 523 + ], + "type": "text", + "content": "Finding 3. Mosaic augmentation greatly reduces the training cost associated with learning from high-resolution teachers and eliminates the need for feature interpolation. Student quality is even improved with this optimization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 538, + 448, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 448, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 448, + 551 + ], + "type": "text", + "content": "4.4. Teacher Loss Balancing" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "content": "In PHI-S [34] we highlighted the significant variations in activation magnitudes among vision foundation models, observing that SAM's activations tend to overshadow those of CLIP and DINOv2 models. We adopt the PCA-Hadamard Isotropic Standardization (PHI-S) method, achieving improved balance among teacher losses. PHI-S rotates teacher activations to evenly distribute variance across all channels and then uniformly scales them to obtain unit variance. This process can be easily inverted by modifying the final linear projection of the adaptor MLP after training. PHI-S enhances training stability and overall benchmark scores. For a given teacher feature map " + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "content": " with embedding size " + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "content": ", PHI-S applies the following transformation:" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22491" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 115, + 130 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 115, + 130 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 115, + 130 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 115, + 130 + ], + "type": "image", + "image_path": "8b6e869e7c6a0505ea883502d1a3fe7c3886ad3896d496a02dd8d674e5e8d3ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 116, + 70, + 176, + 130 + ], + "blocks": [ + { + "bbox": [ + 116, + 70, + 176, + 130 + ], + "lines": [ + { + "bbox": [ + 116, + 70, + 176, + 130 + ], + "spans": [ + { + "bbox": [ + 116, + 70, + 176, + 130 + ], + "type": "image", + "image_path": "cee2b6ffc0846e9b8e511114c3f97fd80f30b6cb218199833b33babbb4779c2a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 235, + 130 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 235, + 130 + ], + "lines": [ + { + "bbox": [ + 175, + 70, + 235, + 130 + ], + "spans": [ + { + "bbox": [ + 175, + 70, + 235, + 130 + ], + "type": "image", + "image_path": "f96ee98ef295e07f568046c1340b5b7c9af9147c4081caea9943cb7d7f7fa24d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 236, + 70, + 295, + 130 + ], + "blocks": [ + { + "bbox": [ + 236, + 70, + 295, + 130 + ], + "lines": [ + { + "bbox": [ + 236, + 70, + 295, + 130 + ], + "spans": [ + { + "bbox": [ + 236, + 70, + 295, + 130 + ], + "type": "image", + "image_path": "a8ec127d93bb31aa68e9c897ade24f15a172dc7ed294d5df1bcee1cedd12bbaf.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 116, + 130, + 175, + 190 + ], + "blocks": [ + { + "bbox": [ + 116, + 130, + 175, + 190 + ], + "lines": [ + { + "bbox": [ + 116, + 130, + 175, + 190 + ], + "spans": [ + { + "bbox": [ + 116, + 130, + 175, + 190 + ], + "type": "image", + "image_path": "2cf672b3dc40441d65d77b745c73d4edccf93a502ea74ebfdb6c0602ca8b5f4a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 198, + 296, + 264 + ], + "lines": [ + { + "bbox": [ + 55, + 198, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 296, + 264 + ], + "type": "text", + "content": "Figure 7. Visualizations of SigLIP and RADIOv2.5-H model features before and after ToMe compression. From left to right: input image; PCA visualization of features; merged tokens; PCA visualization of unmerged tokens. RADIOv2.5 is better able to compress background regions, leaving more tokens available for semantically rich features." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 175, + 130, + 235, + 190 + ], + "blocks": [ + { + "bbox": [ + 175, + 130, + 235, + 190 + ], + "lines": [ + { + "bbox": [ + 175, + 130, + 235, + 190 + ], + "spans": [ + { + "bbox": [ + 175, + 130, + 235, + 190 + ], + "type": "image", + "image_path": "3ff01fb5cac81f5703583dc6d000b5ad12c69377965aca4bb905cd45430e89a1.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 236, + 130, + 294, + 190 + ], + "blocks": [ + { + "bbox": [ + 236, + 130, + 294, + 190 + ], + "lines": [ + { + "bbox": [ + 236, + 130, + 294, + 190 + ], + "spans": [ + { + "bbox": [ + 236, + 130, + 294, + 190 + ], + "type": "image", + "image_path": "e7afc103f70c618810c8584cfddc7c3954bc858e18a824308c7b6d8cec7d245d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "text", + "content": "Figure 8. Illustration of bipartite matching [3] using " + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "text", + "content": " strided pattern with " + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "inline_equation", + "content": "r = 9" + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "text", + "content": ". A: The original tokens, with the red 'T#' squares being assigned as targets, and the green 'S#' squares being assigned as sources. B: We compute the affinity between each source and target. We only consider the maximum affinity for each source (shown in yellow). We find the " + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 229, + 555, + 361 + ], + "type": "text", + "content": " highest affinity yellow squares, and merge those into their respective targets. C: The output tokens with merged values when a given 'T#' was assigned one or more sources. D: The final 7 tokens are fed to the LLM. Reconstructed Viz: From (C), we can visualize the compressed original feature map by broadcasting the merged tokens to all of the source locations." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 303, + 295, + 351 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 303, + 295, + 351 + ], + "spans": [ + { + "bbox": [ + 63, + 303, + 295, + 351 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {i} ^ {\\prime} = \\phi_ {i} ^ {- 1} \\mathbf {R} _ {i} \\mathbf {X} _ {i}, \\quad \\mathbf {R} _ {i} = \\mathbf {H} _ {C} \\mathbf {U} _ {i} ^ {\\intercal}, \\quad \\phi_ {i} = \\sqrt {\\frac {1}{C} \\sum_ {j} ^ {C} \\lambda_ {j}} \\tag {5}", + "image_path": "7b8164e456829f992c5e1a862054ae2b21be662468c2d2b9ea7f0b0b2c51f000.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "H_{C}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " is a normalized Hadamard matrix of dimension " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "C \\times C" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\lambda_{j}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " are the eigenvalues of the covariance matrix " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{\\Sigma}[\\mathbf{X}]" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " are the corresponding eigenvectors. " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{i}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " are specific to the " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": "th teacher. PHI-S is a statistical standardization technique, as the expected per-channel variance after PHI-S is 1. However, it is different than vanilla standardization in that it doesn't standardize the channels individually, and thus, doesn't distort the cross-channel variation. We briefly review the key results of [34] in appendix K, but refer the reader to the original paper for deeper understanding." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 65, + 492, + 285, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 492, + 285, + 517 + ], + "spans": [ + { + "bbox": [ + 65, + 492, + 285, + 517 + ], + "type": "text", + "content": "Finding 4. PHI Standardization helps balance the energy spent learning from each teacher." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 527, + 171, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 527, + 171, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 527, + 171, + 540 + ], + "type": "text", + "content": "4.5. Token Compression" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 545, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 640 + ], + "type": "text", + "content": "Inspired by ToMeSD[3], we evaluate the use of bipartite soft matching to merge similar tokens. We apply strided partitioning to ensure that each image region retains some representation in the compressed features. For evaluation, we track merged token indices, enabling us to unmerge tokens and measure the reconstruction error and inform hyperparameter selection. The method is illustrated in Figure 8." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "While ToMe recommends using attention keys for matching, we found that using the features directly reduces reconstruction error. Table 18 in the appendix summarizes our findings. Another slight departure from ToMe's recommendation is that we apply merging at the output of the vision encoder rather than incrementally. As shown in Ta" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 326, + 79, + 542, + 214 + ], + "blocks": [ + { + "bbox": [ + 326, + 79, + 542, + 214 + ], + "lines": [ + { + "bbox": [ + 326, + 79, + 542, + 214 + ], + "spans": [ + { + "bbox": [ + 326, + 79, + 542, + 214 + ], + "type": "image", + "image_path": "528ba59a844f7cf7cb1d9da6f133256128e82d779e5ccf29711f8aa36f914e1a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "type": "text", + "content": "ble 12, this approach yields an average improvement of " + }, + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "type": "inline_equation", + "content": "+1.4" + }, + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "type": "text", + "content": " on VLM benchmarks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 408, + 554, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 554, + 456 + ], + "type": "text", + "content": "We also qualitatively evaluate token merging by visualizing feature and token merging outcomes in Figure 7. Token merging is assessed within the context of VLMs, with results reported in Table 1." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 457, + 554, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 554, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 554, + 554 + ], + "type": "text", + "content": "We further note that token merging can be applied to other vision encoders and demonstrate its application on SigLIP. Interestingly, token merging yields a greater relative improvement on RADIOv2.5 than on SigLIP, a finding that aligns with the feature visualizations in Figure 7 and the measured reconstruction error in Table 18. We hypothesize that SigLIP's higher feature noise makes clustering more error prone." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 324, + 563, + 544, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 563, + 544, + 598 + ], + "spans": [ + { + "bbox": [ + 324, + 563, + 544, + 598 + ], + "type": "text", + "content": "Finding 5. Token Merging is very effective at retaining the most diverse information under high compression ratios." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 614, + 395, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 614, + 395, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 614, + 395, + 628 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 634, + 450, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 450, + 646 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 450, + 646 + ], + "type": "text", + "content": "5.1. Evaluation Benchmarks" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "type": "text", + "content": "For Image classification, we report the ImageNet-1k[36] Top-1 classification accuracy using two methods. i) zero-shot[32] classification using the DFN CLIP language model; ii) k-NN[5] classification using the embeddings of the shared backbone." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22492" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 293, + 205 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 293, + 205 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 293, + 205 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 293, + 205 + ], + "type": "table", + "html": "
ResMethodTokens/imTextVQAChartQADocVQAInfoVQAOCRbench
51222Unshuffle25665.023.745.732.940.2
ToMe r=76825665.725.849.734.941.2
76833Unshuffle25665.825.949.735.240.9
ToMe r=204825669.730.452.336.242.9
102444Unshuffle25666.123.846.634.138.9
ToMe r=384025669.328.149.134.642.7
ToMe r=358451268.931.353.937.044.6
", + "image_path": "ed9c488ccae293c15dc61642b0b66de29a87083c926fb06df49efb450882a638.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 214, + 295, + 270 + ], + "lines": [ + { + "bbox": [ + 55, + 214, + 295, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 214, + 295, + 270 + ], + "type": "text", + "content": "Table 3. VLM benchmarks across various compression methods. All configurations produce 256 vision tokens per image, except for the last row (512 tokens). Token Merging outperforms Pixel Unshuffling on all benchmarks. " + }, + { + "bbox": [ + 55, + 214, + 295, + 270 + ], + "type": "inline_equation", + "content": "r =" + }, + { + "bbox": [ + 55, + 214, + 295, + 270 + ], + "type": "text", + "content": " denotes the number of tokens being merged." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 280, + 295, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 280, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 280, + 295, + 316 + ], + "type": "text", + "content": "For Instance Segmentation, we use the EfficientViT[25] implementation of a COCO[21] instance segmenter to measure how well our SAM adaptor head can replace SAM." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "text", + "content": "For Semantic Segmentation, we use the MMSeg[8] framework, and train a linear probe on top of the frozen RADIOv2.5 features. We use the ADE20k[50] dataset. We train the probe at three resolutions " + }, + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "inline_equation", + "content": "(512^{2}, 768^{2}" + }, + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 55, + 316, + 295, + 376 + ], + "type": "text", + "content": ") and report the best result (full results in appendix)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 376, + 296, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 435 + ], + "type": "text", + "content": "For 3D understanding experiments we use the Probe3D[12] code base and apply a DPT head on top of the frozen backbone features. We train and evaluate on the Navi[19] dataset. We resize images to " + }, + { + "bbox": [ + 55, + 376, + 296, + 435 + ], + "type": "inline_equation", + "content": "512^2" + }, + { + "bbox": [ + 55, + 376, + 296, + 435 + ], + "type": "text", + "content": " during both training and evaluation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 435, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 295, + 555 + ], + "type": "text", + "content": "For Vision-Language Modeling we follow the same framework as in VILA [23]. We pair our vision encoder with a MN-Minitron-8B[41] LLM. We train all alignment/pretraining/SFT and unfreeze the vision encoder during SFT. We train the model using ShareGPT4v[6] and VFLAN[45] datasets. We leverage insights from Cambrian[42] to select the benchmarks that are most sensitive to the quality of visual features report scores on TextVQA[40], ChartQA[27], DocVQA[29], InfoVQA[28] and OCRBench[26]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 563, + 156, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 156, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 156, + 574 + ], + "type": "text", + "content": "5.2. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "content": "Ablation studies are summarized in Table 1. Our initial RADIOv2.1-L baseline (config " + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "content": ") is a reproduction of AM-RADIO [35], using a ViT-L backbone and the DataComp1B[16] dataset. Our hyperparameters are detailed in the appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "text", + "content": "We add multi-resolution training in config " + }, + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "text", + "content": ", and notice improved results on most dense tasks (+2.8 on ADE20k, +3.4 on average on VLMs). Multi-score robustness is particularly evident in Figure 2, where config " + }, + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 55, + 642, + 295, + 700 + ], + "type": "text", + "content": " exhibits much more consistent results at higher resolutions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "In config " + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": ", we replace the OpenAI CLIP teacher with" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "SigLIP [49] and observe a 6.7-point improvement on VLM benchmarks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 96, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 133 + ], + "type": "text", + "content": "In config " + }, + { + "bbox": [ + 313, + 96, + 553, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 96, + 553, + 133 + ], + "type": "text", + "content": ", we replace the ViT-L 320M-parameter backbone with a 553M-parameter ViT-H backbone, which improves all metrics significantly." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "text", + "content": "Config " + }, + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "text", + "content": " applies only to VLMs, where we replace " + }, + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "inline_equation", + "content": "2^{2}" + }, + { + "bbox": [ + 313, + 133, + 555, + 228 + ], + "type": "text", + "content": " pixel unshuffling with Token Merging. This reduces the number of vision tokens from 576 to 256 and improves VLM scores by an average of 5.9 points. Appendix Table 11 provides a detailed analysis of the trade-off between the number of vision tokens and accuracy, highlighting RA-DIOv2.5's comparative advantage over SigLIP in terms of token merging effectiveness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 236, + 435, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 435, + 249 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 435, + 249 + ], + "type": "text", + "content": "5.3. Comparative Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 255, + 444, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 255, + 444, + 266 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 444, + 266 + ], + "type": "text", + "content": "5.3.1 Dense Task Evaluation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "content": "We evaluate our models in comparison to other agglomerative models of similar size (SAM-CLIP [43], Theia [38], UNIC [37], UNIT [51]). Following MLoRE [47] we report metrics on NYUDv2 and PASCAL Context for our model. We train with a learning rate of " + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "inline_equation", + "content": "1e - 3" + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "content": ", and use a weight of 1 for all tasks. We purposefully don't tune any hyperparameters. We keep the backbone model frozen, and use MLoRE's \"conv\" head for each task. The conv head is defined as follows: Conv-3x3 " + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "content": " BatchNorm " + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "content": " GeLU " + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 275, + 553, + 393 + ], + "type": "text", + "content": " Conv-1x1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 395, + 553, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 553, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 553, + 418 + ], + "type": "text", + "content": "Results are reported in Table 4. RADIOv2.5 models exhibit a consistent improvement over previous baselines." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 435, + 420, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 420, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 420, + 445 + ], + "type": "text", + "content": "5.3.2 VLM Evaluation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 454, + 555, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 454, + 555, + 573 + ], + "spans": [ + { + "bbox": [ + 313, + 454, + 555, + 573 + ], + "type": "text", + "content": "We compare our models against state-of-the-art vision encoders: OpenAI-CLIP [32], RADIoV2.1-H and SigLIPS0400M [49]. We pair the vision encoders with MN-Minitron-8B [41] and train them in VILA [23] using the LLaVA1.6 [24] data mixture. For all vision encoders, we use Token Merging to compress the visual features to 196 tokens in order to ensure a fixed cost to the Language Model. We report results in Table 5. We observe that RADIoV2.5 models consistently exceed the accuracy of other vision encoders." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 586, + 400, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 586, + 400, + 597 + ], + "spans": [ + { + "bbox": [ + 313, + 586, + 400, + 597 + ], + "type": "text", + "content": "6. Related Work" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": "AM-RADIO[35] and SAM-CLIP[43] pioneered multiteacher distillation for Vision Foundation Models, though AM-RADIO struggles with resolution consistency and SAM-CLIP lacks a strong dense model like DINO, reducing semantic segmentation accuracy. Theia[38] uses a multidistillation framework for robotics, incorporating teachers like DepthAnything[46], while UNIC[37] stabilizes training with expandable projectors and teacher-dropping regularization. Our method, however, employs teacher fea" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22493" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 553, + 199 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 199 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 199 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 199 + ], + "type": "table", + "html": "
ModelParamsADE20k mIoU↑NYUdPascal Context
SemSeg mIoU↑Depth RMSE↓Normal mErr↓SemSeg mIoU↑Parsing mIoU↑Saliency maxF↑Normal mErr↓
SAM-CLIP[43]86M38.4†††††††
Theia [38]86M35.5538.900.637724.1169.8460.6780.6316.94
UNIC-B[37]86M39.642.210.617222.7875.9062.8581.8415.78
RADIOv2.5-B (ours)98M48.9457.190.498020.0481.7571.4981.2616.10
UNIC-L[37]307M48.3058.560.491619.3481.8272.2479.2117.35
RADIOv2.5-L (ours)320M52.9561.420.457718.5782.8774.3281.6516.15
UNIT[51]632M50.1961.440.453819.0782.3673.3478.7017.98
RADIOv2.1-H653M51.3662.760.433918.4382.7874.4278.4817.53
RADIOv2.5-H653M53.9763.820.435317.6783.4375.7581.1916.16
UNIT[51]1B50.6361.620.452719.0782.2073.2278.5117.96
RADIOv2.5-g (ours)1.1B54.5663.460.431817.0882.6575.1880.0817.06
", + "image_path": "23ab0ed66d0216f461ed1b3b2d1c4bdff91fbdeb17b736060ea559d6aed75edb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 251, + 553, + 396 + ], + "blocks": [ + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "type": "text", + "content": "Table 4. Comparison of dense task benchmarks against other agglomerative models. " + }, + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "type": "text", + "content": " Results unavailable due to lack of access to SAM-CLIP model weights. Note: RADIo requires more parameters for a given model class due to a " + }, + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "type": "inline_equation", + "content": "C \\times {128} \\times {128}" + }, + { + "bbox": [ + 55, + 206, + 555, + 240 + ], + "type": "text", + "content": " position embedding buffer coming from CPE, but does not contribute meaningfully to increased FLOPs or representation capacity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 251, + 553, + 396 + ], + "lines": [ + { + "bbox": [ + 58, + 251, + 553, + 396 + ], + "spans": [ + { + "bbox": [ + 58, + 251, + 553, + 396 + ], + "type": "table", + "html": "
Vision EncoderResolutionTokens/fimTextVQAChartQADocVQAInfoVQAOCRBenchGQAPOPEMMESEED(I)MMMUAI2DAverage
OpenAI-CLIP [32]336219663.249.243.427.443162.485.71517.972.743.477.658.55
RADIOv2.1-H [35]512219663.651.740.126.239263.487.31570.673.643.978.958.76
RADIOv2.1-H [35]768219662.849.936.724.836562.787.01517.271.741.973.456.66
SigLIP-SO400M [49]384219664.855.747.929.245263.185.41632.972.941.180.760.95
RADIOv2.5-L (ours)768219666.756.449.229.844163.487.61592.474.043.379.261.21
RADIOv2.5-H (ours)768219668.861.654.230.849863.887.31562.374.144.182.563.19
RADIOv2.5-g (ours)672219669.657.053.330.947963.487.51606.474.341.380.862.39
", + "image_path": "1805d3dd212668c57a4df11470593e9f720bd603101b88584a3cd4fd38acc78c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 403, + 555, + 460 + ], + "lines": [ + { + "bbox": [ + 55, + 403, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 555, + 460 + ], + "type": "text", + "content": "Table 5. Vision Encoder Comparison in VILA[23]. We used MN-Minitron-8B[41] as LLM and the LLaVA1.6[24] data mixture. We use Token Merging to compress all visual features down to 196 tokens. From left to right we report: image resolution, number of tokens per image, TextVQA (with OCR hints) validation accuracy, ChartQA overall, DocVQA validation accuracy, InfoVQA validation accuracy, OCRBench accuracy, GQA (TestDev) accuracy, POPE F1 score, MME perception score, SEED (Image) accuracy, MMMU (validation) accuracy, AI2D (no mask) accuracy, average (calculated after dividing MME score by 20 and OCR score by 10)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 468, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 295, + 529 + ], + "type": "text", + "content": "ture standardization and multi-resolution training for scale-consistent accuracy, enhancing the original ViT[11] interpolation approach. Unlike FlexiViT[2] and NaViT[10], we use Cropped Position Embeddings (CPE)[21] and distill resolution-robust students from inflexible teachers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "content": "Cambrian-1 [42] integrates multiple vision encoders through a Spatial Vision Aggregator, utilizing learnable latent queries that interact with several layers of a Large Language Model (LLM) via cross-attention. Eagle [39] combines multiple vision experts by concatenating their visual tokens along the channel dimension. BRAVE [20] introduces the Multi-Encoder Querying Transformer, which merges visual features from various encoders into a fixed-length representation, subsequently used as a soft prompt for a frozen language model. In contrast, our method performs multi-vision encoder aggregation as a preliminary step to develop a single, versatile vision encoder suitable for integration into a VLM, but also easily usable outside of a VLM context." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 468, + 388, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 468, + 388, + 480 + ], + "spans": [ + { + "bbox": [ + 314, + 468, + 388, + 480 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 505, + 555, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 505, + 555, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 505, + 555, + 624 + ], + "type": "text", + "content": "In this paper, we presented RADIOv2.5, a robust framework for multi-teacher vision model distillation that accommodates variations in teacher resolutions, activation magnitudes, and noise patterns. The key differentiating factor in our work is our focus on preserving accuracy across a broad range of resolutions. Our multi-resolution training approach mitigates resolution-dependent quality degradation (mode switching). Our findings show that mosaic augmentation and PHI-S effectively balance computational load and loss contributions from each teacher." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "content": "Token compression enables efficient integration with VLMs by preserving critical visual information, even at high compression ratios. Our feature selection study highlighted the advantages of using intermediate activations for dense tasks, particularly when non-linear transformations are used." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22494" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "type": "text", + "content": "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. 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Region-aware diffusion models (RAD) in action." + ], + "image_footnote": [], + "bbox": [ + 151, + 386, + 653, + 535 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a6fc497c0875255d1d7d2c9c688324e5dc142f5c2e42ff3c2b30e360680d64ba.jpg", + "image_caption": [ + "Generated samples" + ], + "image_footnote": [], + "bbox": [ + 653, + 252, + 839, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/df01d18823360cd0b3cd7a0286765680b7dc0f4705fe3c4b07af9af6cc9501ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 402, + 839, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 565, + 326, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, i.e., conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demon", + "bbox": [ + 88, + 598, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "strated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets.", + "bbox": [ + 511, + 566, + 906, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 628, + 645, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Over the past decade, deep generative models [9, 13, 18, 31] have made significant advances in generative learning. Especially, generative adversarial networks (GANs) [9] and diffusion models [13, 31] represent seminal breakthroughs that have changed the paradigm of unsupervised image synthesis. Recently, diffusion models have attracted considerable attention due to their outstanding performance across various applications, such as text-to-image synthesis [23, 28, 30], image editing [3, 22], video frame generation [40], and text-to-3d generation [27, 41].", + "bbox": [ + 511, + 656, + 906, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Denoising diffusion probabilistic models (DDPM) [13, 31], a cornerstone in diffusion models, approximate the distribution of real images by learning to reverse a pre-defined diffusion process in which real images gradually become pure Gaussian noise. Based on the learned reverse process, synthetic images can be generated by iteratively denoising", + "bbox": [ + 511, + 810, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2439", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "arbitrary Gaussian noise. In this process, each reverse step is represented as a Gaussian transition and is modeled with deep networks like U-Net [29]. Even though DDPM had a compelling framework, it initially produced lower fidelity results than GANs. Various studies [24, 26, 37] followed to improve the performance of diffusion models, and Dhariwal et al. [8] proposed the first diffusion model to outperform GANs. Nowadays, diffusion models have become de facto standard for image generation, and numerous applications have been inspired by their well-established theory and outstanding performance.", + "bbox": [ + 88, + 90, + 480, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image inpainting, a problem to fill in missing areas of an image, is such an example that can benefit largely from a powerful generative model. With the notable advancements of deep generative models, many attempts have been made to solve image inpainting based on GANs [19, 34, 36, 43] and diffusion models [6, 21]. Diffusion-based methods have proven effective for various image inpainting or editing tasks, and some approaches utilize conditioned generation techniques based on structural information [20] or text with mask [38, 39, 45, 46]. These methods have advantages in providing more precise control over the result, but they generally require additional modules to process conditions, which add more complexities and computational burdens.", + "bbox": [ + 89, + 260, + 482, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of research focuses on manipulating the generation processes in existing diffusion models. These approaches [1, 2, 4-6, 11, 16, 21, 22, 35] 'hijack' the reverse process of a pretrained diffusion model and devise elaborate procedures for inpainting or editing. These methods do not require any additional training, however, since the plain reverse process is not usually designed for localized generation or editing, the procedures tend to get complicated, e.g., requiring repeated re-evaluation of reverse steps, etc., resulting in significantly extended inference time.", + "bbox": [ + 89, + 459, + 482, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose region-aware diffusion models (RAD), a simple reformulation of the vanilla diffusion models to overcome the aforementioned issues in diffusion-based image inpainting. Unlike conventional diffusion models, which apply noise uniformly across all pixels at each forward step, RAD assigns a different noise schedule to each pixel, enabling some areas to be completely denoised while others retain noise. This spatially variant noise scheduling naturally emulates inpainting by adding noise only to the inpainting region and performing the reverse process. This idea is quite simple, and only minimal changes in the network structures, i.e., 'reshaping' some fully connected (FC) layers into $1 \\times 1$ convolutions, suffice to achieve state-of-the-art (SoTA) performance, demonstrating that existing structures are readily capable of inpainting once the right setting is provided. Unlike the existing methods tempering the noise in diffusion models, such as RePaint [21] and MCG [4], RAD inherently considers the asynchronous generation of pixels, achieving orders of", + "bbox": [ + 89, + 613, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "magnitude improvement in generation speed while maintaining high performance.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "That being said, several issues need to be carefully addressed in RAD. The pixel-wise noise schedules must be designed to represent realistic inpainting patterns and must be somehow informed to the network for effective noise inference. We deal with these issues with simple, novel ideas, i.e., Perlin noise-based schedule generation and spatial noise embedding, respectively. One limitation of the proposed method is that it requires fresh training for the altered diffusion framework; however, we overcome this by employing low-rank adaptation (LoRA) [14] on a pretrained model, greatly reducing computational requirements.", + "bbox": [ + 511, + 121, + 903, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conducted experiments on FFHQ [15], LSUN Bedroom [42], and ImageNet [7], comparing RAD with other SoTA inpainting methods. RAD achieves up to 100 times faster inference time than other SoTA diffusion-based methods and achieves the best FID and LPIPS scores in most cases. In addition, an ablation study shows that the proposed components of RAD, such as the spatially variant noise schedules and the spatial noise embedding technique, are vital for the success of RAD. The contributions of this paper are summarized as follows:", + "bbox": [ + 511, + 287, + 903, + 436 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel reformulation of diffusion models is proposed based on spatially variant noise schedules, allowing asynchronous generation of pixels for inpainting.", + "- Pseudo-realistic noise schedules are presented based on Perlin noise for efficient training.", + "- A spatial noise embedding technique is introduced to provide rich spatial information to the denoiser networks.", + "- Along with the SoTA performance and the exceptional improvement in generation speed, LoRA-based training on pretrained diffusion models is also utilized to reduce the training burdens." + ], + "bbox": [ + 511, + 438, + 903, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 618, + 663, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion model. DDPMs [13, 31] have introduced a novel approach in image generation by employing an iterative denoising process that progressively refines random noise into high-quality images. Unfortunately, DDPMs showed lower image fidelity compared to GANs. To enhance fidelity, various studies [24, 26, 37] have focused on generating high-quality images using diverse datasets such as ImageNet [7], FFHQ [15], and LSUN [42]. Dhariwal and Nichol [24] showed that achieving high log-likelihood on datasets with high diversity, like ImageNet [7], is possible through a hybrid objective. This hybrid objective facilitates learning the variances of the reverse Gaussian transitions that were fixed in DDPM [13]. Meanwhile, Dhariwal et al. [8] introduced ablated diffusion models (ADMs) that use auxiliary classifiers to classify the noisy images generated during the reverse process. This simple class-conditioned generation method, known as classifier guid", + "bbox": [ + 511, + 643, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2440", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ff5df060fc0d4344ae4936a0eaf2954d93dc79639bdb1811e6dd0621c23219aa.jpg", + "image_caption": [ + "Figure 2. An overview of the proposed method. RAD consists of four components: (1) the forward and reverse processes based on pixel-wise noise (Section 3.1); (2) spatially variant noise schedules (Section 3.2); (3) spatial noise embedding (Section 3.3); and (4) the inverse-mapping of $\\bar{b}$ (Section 3.4)." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 464, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ance, mainly enhances the fidelity of generated images by applying strong class conditioning.", + "bbox": [ + 89, + 377, + 482, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion-based inpainting. Recently, many conditional image inpainting/editing methods have been proposed based on diffusion models. Liu et al. [20] used structural information, such as grayscale images or edge maps, to guide an inpainting process. Several studies [38, 39, 45, 46] have incorporated text and mask conditions for image inpainting. These methods typically require additional modules to perform local editing based on the specified conditions, which introduces additional complexity and computational load.", + "bbox": [ + 89, + 426, + 483, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Other approaches leveraged pretrained diffusion models for image inpainting/editing by manipulating their generation processes. Some methods [4, 22] manipulated the reverse SDE procedure of a pretrained score-based model [33]. On the other hand, several works [2, 10, 16, 21, 35] utilize ADM [8]. Notably, Lugmayr et al. [21] proposed RePaint, a method utilizing resampling steps to harmonize mask and non-mask regions. Other studies [1, 5, 6, 11] used the stable diffusion model [28]. Couairon et al. [6] proposed DiffEdit, which employs DDIM inversion for image editing by generating masks based on text prompts to preserve backgrounds.", + "bbox": [ + 89, + 565, + 482, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing methods often require additional modules or extended reverse processes, increasing complexity and inference time. In contrast, RAD utilizes spatially variant noise schedules, inherently allowing detailed generation in specific areas without any additional component or loss. SmartBrush [38], although the problem setting differs from ours, is another method that adds noise only in the inpainting regions. SmartBrush, however, adds several additional modules to a diffusion model to learn this type of noise, unlike ours where the basic framework inherently supports this.", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Region-Aware Diffusion Models", + "text_level": 1, + "bbox": [ + 513, + 89, + 805, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The core of the region-aware diffusion models (RADs) is redefining diffusion models so that each pixel has a different noise schedule, emulating inpainting scenarios. RADs define spatially variant noise schedules based on given masks (Sec. 3.2), which are utilized to establish both the forward and reverse processes based on pixel-wise noise (Sec. 3.1). This involves an element-wise reformulation of DDPM, of which many parts of the derivation naturally follow, however, there are some important points to consider (Secs. 3.3 and 3.4). This section will focus particularly on these critical points. The overview of RAD is shown in Figure 2.", + "bbox": [ + 511, + 114, + 906, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Diffusion Models with Spatially Variant Noise", + "text_level": 1, + "bbox": [ + 511, + 291, + 901, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we explain the basic framework of RAD, along with a brief explanation of DDPM [13]. The goal of a diffusion model is to learn to mimic a data distribution $q(x_0)$ , where $x_0$ denotes a 'clean' image without any noise, based on some model $p_{\\theta}(x_0)$ in an unsupervised manner. This is accomplished by learning an iterative denoising process that reverts a Brownian motion where $x_0$ gradually becomes pure Gaussian. This framework can be more tractable than directly learning $q(x_0)$ because each individual task is to slightly denoise the noisy image at various noise stages.", + "bbox": [ + 511, + 313, + 905, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a noise schedule, a sequence $x_{1}, x_{2}, \\ldots, x_{T}$ can be generated with some $T$ where the image gradually becomes noisier. The forward process governing this is defined as a Markov process with Gaussian transitions:", + "bbox": [ + 511, + 465, + 905, + 526 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t \\geq 1} q \\left(x _ {t} \\mid x _ {t - 1}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 537, + 906, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In DDPM, $q(x_{t}|x_{t - 1}) = \\prod_{i}q(x_{t,i}|x_{t - 1,i})$ , $i$ denoting the element index, is assumed to be i.i.d. for the elements of $x_{t}$ . At this point, RAD takes a different turn from DDPM, assuming the elements have different noise intensities:", + "bbox": [ + 511, + 582, + 905, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t, i} \\mid x _ {t - 1, i}\\right) = N \\left(\\sqrt {1 - b _ {t , i}} x _ {t - 1, i}, b _ {t, i}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 655, + 906, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $b_{t,i}$ is the variance of the $i$ -th element of $x_{t}$ given $x_{t-1}$ , i.e., the covariance matrix of $q(x_{t}|x_{t-1})$ is $\\mathrm{diag}(b_{t})$ . Similarly, the marginal distribution of $x_{t,i}$ can be given as", + "bbox": [ + 511, + 690, + 905, + 737 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t, i} \\mid x _ {0, i}\\right) = N \\left(\\sqrt {\\bar {a} _ {t , i}} x _ {0, i}, 1 - \\bar {a} _ {t, i}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 747, + 906, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $a_{t,i} \\triangleq 1 - b_{t,i}$ , $\\bar{a}_{t,i} \\triangleq \\prod_{s=1}^{t} a_{s,i}$ , and $\\bar{b}_{t,i} \\triangleq 1 - \\bar{a}_{t,i}$ . This spatially variant noise assumption allows asynchronous generation of regions within the image, i.e., different regions can be subjected to different noise intensities so that the individual regions can be generated at different speeds, not affecting already generated ones. This alternate formulation, despite its simplicity, has proven to be quite effective in our experiments.", + "bbox": [ + 511, + 777, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2441", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Even though the forward process is quite simply defined, the reverse process, i.e., the denoising process, has no closed-form solution. The essential reason is that the data distribution $q(x_0)$ is not simple, and hence, the Bayes equation cannot be solved easily. Accordingly, we need to learn a model $p_{\\theta}(x_0)$ that approximates the reverse process. In diffusion models, $p_{\\theta}(x_0)$ is also formulated as a Markov process, starting from $x_T$ , reversing the timesteps:", + "bbox": [ + 89, + 90, + 483, + 212 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {0: T}\\right) = p \\left(x _ {T}\\right) \\prod_ {t \\geq 1} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 222, + 482, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p(x_{T}) = N(0,I)$ is pure Gaussian noise. The reverse transition is also modeled as Gaussian, i.e., $p_{\\theta}(x_{t - 1}|x_t) = N(\\mu_{\\theta ,t}(x_t),\\mathrm{diag}(s_t))$ , however, the mean $\\mu_{\\theta ,t}$ is a learnable function of $x_{t}$ . In practice, the true $\\mu_{t}$ of the denoising process can be expressed in terms of $x_{t}$ and the accumulated noise $\\epsilon_{t}$ (in $x_{t}$ ), $\\epsilon_{\\theta}(x_{t},t)$ is learned to predict $\\epsilon_{t}$ instead:", + "bbox": [ + 89, + 263, + 483, + 369 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta , t, i} \\left(x _ {t}\\right) = \\frac {1}{\\sqrt {a _ {t , i}}} \\left(x _ {t, i} - \\frac {b _ {t , i}}{\\sqrt {1 - \\bar {a} _ {t , i}}} \\epsilon_ {\\theta , i} \\left(x _ {t}, t\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 378, + 482, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Again, this is an element-wise version that can include RAD, while all $a_{t,i}$ , $b_{t,i}$ , and $\\bar{a}_{t,i}$ terms are identical for $i$ in DDPM, and the same goes for $s_t$ as well. In RAD, a division-by-zero can happen in the above equation, i.e., $\\bar{a}_{t,i} = 1$ , if no noise has been added to the $i$ -th pixel until $t$ . In this case, a separate derivation gives $\\mu_{\\theta ,t,i} = x_{t,i}$ .", + "bbox": [ + 89, + 428, + 483, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the above, although the forward process in Eq. (1) has no spatial dependence, $p_{\\theta}(x_{t - 1}|x_t)$ surely has. This is because $q(x_0)$ also likely has strong spatial dependence. Accordingly, $p_{\\theta}$ must take the global context into account in the denoising process. This is why $\\mu_{\\theta ,t,i}(x_t)$ and $\\epsilon_{\\theta ,i}(x_t,t)$ in (5), even though they indicate specific (the $i$ -th) elements of $\\mu_{\\theta ,t}$ and $\\epsilon_{\\theta}$ , respectively, take the entire $x_{t}$ as an input.", + "bbox": [ + 89, + 518, + 483, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the above forward and reverse processes, a variational loss can be defined as", + "bbox": [ + 89, + 625, + 483, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {q} \\left[ \\sum_ {t > 1} D _ {K L} \\left(q \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right) - \\log p _ {\\theta} \\left(x _ {0} \\mid x _ {1}\\right) \\right] \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 659, + 482, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This basically trains $p_{\\theta}(x_{t - 1}|x_t)$ to match the target $q(x_{t - 1}|x_t,x_0)$ , except for $t = 1$ . In [13], a simpler loss has been proposed as", + "bbox": [ + 89, + 696, + 483, + 742 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = \\sum_ {t \\geq 1} \\mathbb {E} _ {q} \\left[ \\left\\| \\epsilon_ {t} - \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\right\\| ^ {2} \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 750, + 482, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which directly trains $\\epsilon_{\\theta}$ to predict $\\epsilon_{t}$ . This has shown to be effective, and in many later works [8, 24], both (6) and (7) have been frequently used. In RAD, the calculation of (6) must be done with the element-wise versions of $q$ and $p_{\\theta}$ . After training, an image can be generated by performing a reverse process based on the learned $p_{\\theta}$ from a randomly generated Gaussian noise.", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As can be seen above, the basic framework of RAD is quite simple, i.e., an element-wise reformulation of DDPM. However, this is an easier part of RAD. For this framework to actually work, there are several important issues to consider: (i) What is an appropriate choice for the spatially variant noise $(b_{t})$ ? (ii) How can $\\epsilon_{\\theta}$ successfully learn from the altered problem setting? (iii) How can we reduce additional efforts in training this alternate formulation? For the rest of the section, we will elaborate on the above points.", + "bbox": [ + 511, + 90, + 905, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Generating Noise Schedules", + "text_level": 1, + "bbox": [ + 511, + 239, + 764, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Seeing RAD, one can quickly notice that the newly introduced flexibility requires careful attention. Unlike DDPM where a fixed noise schedule is applied to all pixels, those are set differently in RAD to allow asynchronous generation of different regions. These schedules must be somehow designed, and they must include various patterns during training so that diverse inpainting scenarios can be handled.", + "bbox": [ + 511, + 263, + 905, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To encompass various noise shapes, we generate $b_{t}$ randomly during training. Now, the noise schedules also form a distribution, and the loss function (6) must include this in the expectation. In other words, we now have $q(x_{0:T}|b_{1:T})$ where $b_{1:T}$ follows some $q(b_{1:T})$ . There are infinite choices for $q(b_{1:T})$ , which becomes important since it can affect training. A naive approach, such as selecting a random schedule for each pixel independently, can be problematic because the resulting noise may not have any distinctive spatial pattern, which is inconsistent with the actual inpainting scenarios. Indeed, this was not very successful in our empirical experience, meaning that having too random a noise pattern can be detrimental to the success of RAD.", + "bbox": [ + 511, + 369, + 905, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering the above point, we limit the possible shapes of $b_{t}$ strictly to the inpainting scenarios. Specifically, we divide the entire diffusion process into two phases, where noise is filled in only for the pixels in a given inpainting mask in Phase 1 and the rest in Phase 2. This adequately represents an inpainting process, where only a part of an image is generated (Phase 1) while the other parts are already present (Phase 2). The order of these phases is set in reverse order because the actual generation is performed in the reverse process. After training, only Phase 1 is utilized in inpainting because this suffices to generate the mask region. In fact, we may only utilize Phase 1 during training as well, but using both phases was better in our experience.", + "bbox": [ + 511, + 566, + 905, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To mimic the noise-filling process of DDPM in each phase, we use the following strategy: Let $T_{1}$ and $T_{2}$ be the numbers of timesteps for Phases 1 and 2, respectively, i.e., $T_{1} + T_{2} = T$ . During each phase, each pixel in or outside the mask is filled in by a scalar noise with variance $\\beta_{t}$ $(1\\leq t\\leq T_1)$ or $\\beta_t^\\prime (1\\leq t\\leq T_2)$ , respectively, with $0 < \\beta_{t},\\beta_{t}^{\\prime} < 1$ . In practice, we use simple linear schedules for $\\beta_{t}$ and $\\beta_{t}^{\\prime}$ as in DDPM. A caveat here is that all pixels must have the same accumulated noise levels after finishing", + "bbox": [ + 511, + 763, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2442", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f7112572ec6b212594c9077c38e331c5f9cab1301f21f76d67b68fc0942ced3c.jpg", + "image_caption": [ + "Figure 3. Examples of inpainting masks based on Perlin noise." + ], + "image_footnote": [], + "bbox": [ + 150, + 87, + 423, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the two phases, which can be satisfied easily by normalizing $\\beta_{t}$ and $\\beta_t^\\prime$ as explained in the supplementary material. Gathering the above pixel-wise noise schedules, we can form $b_{t}$ .", + "bbox": [ + 89, + 287, + 482, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the above strategy, the quality of inpainting masks during training is crucial. Unlike test conditions, numerous masks must be automatically supplied during training. Accessing the true mask distribution is not viable, so we need to find some sort of surrogate that includes diverse natural patterns mimicking real-world inpainting tasks. To this end, we propose to use Perlin noise [25]. Perlin noise, known for its smooth and naturalistic patterns, allows us to create diverse and realistic masks. To generate binary masks, we utilize black-and-white Perlin noise, which can be obtained by simple thresholding. We sample Perlin noise with various spatial scales by uniformly sampling the scale parameter so that the generated patterns have both finer and coarser structures. We also sample the black-and-white conversion threshold to control the overall area of inpainting. Figure 3 shows examples of generated masks. This surrogate distribution is quite effective, providing SoTA performance.", + "bbox": [ + 89, + 335, + 482, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An interesting fact is that, even though there is a sharp separation between the mask and non-mask regions in the above strategy, the inpainting results do not exhibit any noticeable boundary effects. We have also tried blurring the boundaries of the masks, with no meaningful improvement in performance. This suggests that RAD is inherently capable of generating content adaptively to existing regions.", + "bbox": [ + 89, + 592, + 482, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Spatial Noise Embedding", + "text_level": 1, + "bbox": [ + 89, + 708, + 321, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In diffusion models, a deep network $\\epsilon_{\\theta}(x_t,t)$ is trained to estimate the accumulated noise $\\epsilon_{t}$ in $x_{t}$ . RAD does not have any structural difference in this regard, i.e., it shares the same input and output for $\\epsilon_{\\theta}$ . In fact, RAD solves a more difficult problem than that of DDPM, because $\\epsilon_{t}$ becomes more complicated. Hence, using this exact same structure might not be as successful as in DDPM, as also confirmed in our ablation study.", + "bbox": [ + 89, + 729, + 482, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To resolve this issue, we focus on the $t$ input in $\\epsilon_{\\theta}(x_t,t)$ which helps the network handle different steps adaptively. In practice, $t$ undergoes some embedding, comprising a cossin encoding and FC layers, and is added to every pixel of feature maps in the U-Net. Regarding this $t$ input, we conjecture that its main role is to inform $\\epsilon_{\\theta}$ of the overall intensity of $\\epsilon_{t}$ . This is somewhat reasonable because the intensity of $\\epsilon_{t}$ increases as $t$ progresses in DDPM. Accordingly, we propose to use $\\bar{b}_t$ , the pixel-wise intensity of $\\epsilon_{t}$ in RAD, in place of $t$ instead. This is easily accomplished by replacing the FC layers in the embedding module into $1\\times 1$ convolutions. In this way, the pixel-wise noise condition can be directly informed to the network, making it easier to learn the spatially variant $\\epsilon_{t}$ . This actually works without changing any other component, confirming the above conjecture.", + "bbox": [ + 511, + 90, + 903, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above spatial noise embedding can be viewed as an indirect way of spatial conditioning, which has some similarities with conventional conditioning techniques. However, it is more subtle in that it alters the existing $t$ embedding and is completely determined by the noise schedules.", + "bbox": [ + 511, + 318, + 903, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Practical Considerations", + "text_level": 1, + "bbox": [ + 511, + 407, + 738, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although RAD has been explained in terms of DDPM, the proposed approach based on spatially variant noise is not limited to DDPM; it can be similarly applied to other advanced models such as DDIM [32], iDDPM [24], ADM [8], score-based models [33], and stable diffusion [28]. We have successfully tested RAD with many of these. For example, DDIM shares the same training procedure as DDPM, but differs in the reverse process, which we can also apply a similar element-wise reformulation. Similarly, iDDPM and ADM share the forward and reverse processes of DDPM but differ in the denoiser structures and loss functions, which combine (6) and (7). Hence, RAD can be extended to these without an issue, and all examples in the experiments are based on ADM versions. Since the basic framework of RAD is quite simple and universal, we expect it to work on other similar models as well.", + "bbox": [ + 511, + 431, + 906, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One limitation of RAD is that the alternate formulation requires fresh training. Even though this is the reason for the superb generation speed compared to the existing SoTA methods, it can also be a deal-breaker considering the amount of resources required in training. This is why the most recent methods attempt to modify only the generation processes of pretrained models, sacrificing the speed. In this paper, we address this issue by utilizing LoRA [14], which can significantly reduce training efforts by leveraging pretrained models. To train RAD based on LoRA, some minor adjustment is required: The spatial noise embedding in RAD can be too drastic of a change for LoRA. Fortunately, the noise schedules for individual pixels are set to match that in DDPM, so we can inverse-map the elements of $\\bar{b}_t$ to timestep values based on the accumulated noise lev", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "In fact, the difference resides in $\\mu_{\\theta ,t}$ , where $a_{t},b_{t}$ and $\\bar{a}_t$ have different values for each element in RAD as shown in (5). This makes a difference in the generation process where $\\mu_{\\theta ,t}$ is utilized.", + "bbox": [ + 89, + 862, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2443", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "els in the steps of DDPM. We use linear interpolation in this process, meaning that the mapped timestep values can be non-integral. This has proven to be effective in the experiments, where all the examples are actually fine-tuned by LoRA based on pretrained ADMs. This approach makes RAD much more accessible.", + "bbox": [ + 89, + 90, + 480, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In an actual implementation of RAD, singularities in the loss function must be carefully reviewed and avoided. In fact, there is a potential singularity in the variational loss (6), especially in the first step $(t = 1)$ where $p_{\\theta}(x_0|x_1)$ is prone to becoming degenerate. Even though DDPM uses the simplified loss (7) in practice, which has no singularities, later works such as iDDPM and ADM use both (6) and (7), where the singularities become a problem and are handled by some heuristics. This is an often-overlooked problem that can render training unstable, and for RAD, the issue is a little more complicated because the pixels undergo asynchronous noise schedules. The details are explained in the supplementary material.", + "bbox": [ + 89, + 183, + 482, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 393, + 222, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Benchmark Datasets", + "text_level": 1, + "bbox": [ + 89, + 419, + 285, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate RAD on the FFHQ [15], LSUN Bedroom [42], and ImageNet [7]. These datasets are well-suited for training and evaluating high-quality image generation models.", + "bbox": [ + 89, + 441, + 482, + 488 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- FFHQ (Flickr-Faces-HQ) [15] contains a total of 70,000 high-resolution (1024x1024) images of human faces. This dataset provides greater diversity than traditional facial image datasets, encompassing a wide range of ages, genders, ethnicities, hairstyles, and accessories (e.g., glasses, hats, etc.). All images were resized to $256 \\times 256$ .", + "- LSUN Bedroom [42] is a large-scale dataset of indoor scenes, containing over 3M bedroom images. Captured from various angles and perspectives, these images represent complex room structures, enabling algorithms to learn and generate intricate scene layouts. We train RAD with 288K samples of the LSUN Bedroom for convenience. All images were resized to $256 \\times 256$ .", + "- ImageNet [7] is a large-scale image dataset for visual object recognition, containing over 1.2M labeled images across 1,000 categories. This dataset offers extensive diversity, covering a wide range of objects, animals, scenes, and complex visual compositions. All images were resized to $256 \\times 256$ for consistency in our experiments." + ], + "bbox": [ + 91, + 488, + 482, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 787, + 307, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training settings. For all experiments, we set the rank of LoRA [14] to 16 and trained RAD using the Adam optimizer [17] with a learning rate of $10^{-4}$ . We used a batch size of 16 for both FFHQ and ImageNet, while that was eight for LSUN Bedroom. The total diffusion steps was 2000, with the initial 1000 steps dedicated to", + "bbox": [ + 89, + 810, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Phase 1. We used predefined linear noise schedules for $\\beta_{t},\\beta_{t}^{\\prime}\\in (0.0001,0.02)$ . During inpainting, we used 100 sampling steps. FFHQ was trained on four TITAN RTX GPUs, LSUN Bedroom on eight NVIDIA 3090 GPUs, and ImageNet on eight NVIDIA RTX 6000 ADA GPUs. Pretrained ADM models [8] were used for all datasets. RAD was trained for $300\\mathrm{K}$ on FFHQ and LSUN Bedroom, and $700\\mathrm{K}$ on ImageNet. ImageNet was trained using an exponential moving average (EMA) with the decay factor set to 0.999.", + "bbox": [ + 511, + 90, + 903, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Validation settings. For validation, we set aside 1000 images from all datasets. We evaluated RAD across three types of mask configurations: box, extreme, and wide, following the practice in [34]. A box mask randomly removes a $128 \\times 128$ square region. In contrast, an extreme mask retains only a specific $128 \\times 128$ region, removing all other surrounding areas. A wide mask defines irregular missing regions. For inpainting, we used the reverse process of DDPM rather than DDIM due to its superior quality in generating realistic details.", + "bbox": [ + 511, + 248, + 903, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline. We chose various inpainting methods based on GANs and diffusion models. For the GAN-based baseline, we used LaMA [34], and for the diffusion-based baselines, we employed RePaint [21], MCG [4], DDRM [16], DDNM [35], and DeqIR [2]. Publicly available pretrained ADM models [8] were used for all methods. Additionally, each method was evaluated using its publicly available codebase to maintain consistency in performance assessment.", + "bbox": [ + 511, + 407, + 903, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. To evaluate the performance of the proposed method and compare it with existing approaches, we employed Frechet Inception Distance (FID) [12] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] as the inpainting quality measure.", + "bbox": [ + 511, + 535, + 903, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Results", + "text_level": 1, + "bbox": [ + 511, + 621, + 606, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons. Table 1 shows the inpainting performance of various methods. Reported values are either directly quoted from the original papers or computed by us if publicly available pretrained models exist. For LaMa, no pretrained model was available for LSUN Bedroom. Here, RAD achieves the best performance in terms of LPIPS and demonstrates superior FID scores for FFHQ and LSUN Bedroom compared to most baseline methods. Notably, DDNM and DeqIR exhibit relatively weaker performance in our experiments, even though they are relatively newer methods. The main goal of these methods is image restoration, and they are not specifically designed for challenging inpainting scenarios, particularly those involving large missing areas. Consequently, these methods show worse performance under our experimental settings. Figure 4 shows qualitative comparisons on LSUN Bedroom, FFHQ, and ImageNet. Here, all the methods are compared based", + "bbox": [ + 511, + 643, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2444", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8238677c59f7261b63a58fe7129fbb95a5257b2e004ee8a6b073018025ec5bed.jpg", + "table_caption": [ + "Table 1. Performance (FID and LPIPS) on FFHQ and LSUN Bedroom with various mask types. ${}^{ \\dagger }$ indicates that the value is quoted from the original paper. Bold: best,under: second best." + ], + "table_footnote": [], + "table_body": "
MethodFFHQLSUN BedroomImageNet
BoxExtremeWideBoxExtremeWideBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
LaMa [34]27.7†0.086†61.7†0.492†23.2†0.096†------------
Score-SDE [33]30.3†0.135†48.6†0.488†29.8†0.132†23.70.64824.10.64823.20.64457.20.20086.60.49562.00.183
DDRM [16]28.4†0.109†48.1†0.532†27.5†0.113†20.50.16633.10.45026.40.19074.30.224106.90.49275.10.211
RePAINT [21]25.7†0.093†35.9†0.398†24.2†0.108†20.50.17623.50.46121.40.16154.00.17784.00.47959.00.166
MCG [4]23.7†0.089†30.6†0.366†22.1†0.099†19.90.13122.00.39520.90.10848.10.13258.40.44856.90.124
DDNM [35]30.40.08987.70.35330.40.08922.70.15053.30.43123.20.12663.80.18780.60.47664.50.167
DeqIR [2]24.20.09364.20.36827.40.09922.20.17643.90.46122.00.15366.50.19599.50.50568.40.182
RAD (ours)22.10.07433.40.31721.50.07819.20.13121.60.39920.80.10747.00.11857.80.37456.70.104
", + "bbox": [ + 94, + 128, + 903, + 271 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55d7b420e3f98a477e7ecb6f40c73944534dbefbe70a7065a4769f342dcfc8a1.jpg", + "image_caption": [ + "(a) LSUN Bedroom" + ], + "image_footnote": [], + "bbox": [ + 109, + 282, + 361, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/181797860d24e992f32fc1c4de084931f5c3a126b7199825f4c0fd561cd6be2c.jpg", + "image_caption": [ + "(b) FFHQ" + ], + "image_footnote": [], + "bbox": [ + 372, + 282, + 620, + 593 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c4fe0e866e3baa15a6bce66caa3bb35b02afd1e6c646facffd18fe8b86f8f33c.jpg", + "image_caption": [ + "(c) ImageNet", + "Figure 4. Qualitative comparisons. Colored areas indicate inpainting regions (1st/2nd rows: box, 3rd/4th: extreme, 5th/6th: wide)." + ], + "image_footnote": [], + "bbox": [ + 635, + 282, + 883, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "on the same combinations of images and inpainting masks. The results confirm that RAD generally produces more natural images than others and has fewer failure cases.", + "bbox": [ + 89, + 652, + 482, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows the inference time of various methods. We evaluated all methods on $256 \\times 256$ images using a single NVIDIA Titan RTX GPU. Here, RAD is about 100 times faster than RePaint and 15 times faster than MCG while delivering superior performance. Baseline methods other than RePaint and MCG are much faster, but their inpainting quality is significantly worse.", + "bbox": [ + 89, + 696, + 482, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of diversity. Section 4.3 demonstrates that RAD can generate diverse inpaintings across various mask configurations. Each row in the figure shows the input image with a specific mask, followed by multiple inpainting results (Samples 1 to 4) generated by RAD. These results highlight RAD's ability to produce various plausible and contextually", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8fe6f6e2bf0c91a9cd4613f47e45cdebb600b0cdbb116382493ab21f3a77c46a.jpg", + "table_caption": [ + "Table 2. Inference time comparison $\\left( {1 \\times \\text{NVIDIA TITAN RTX}}\\right)$ ." + ], + "table_footnote": [], + "table_body": "
MethodInference time [s]
Score-SDE [33]41.983
DDRM [16]12.291
RePAINT [21]837.136
MCG [4]128.058
DDNM [35]6.566
DeqIR [2]26.443
Ours8.442
", + "bbox": [ + 598, + 674, + 820, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "consistent inpaintings, even under challenging masks.", + "bbox": [ + 511, + 814, + 867, + 829 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study. To verify the effectiveness of the proposed components, we compared RAD with two alternative methods: (1) performing RAD reverse steps directly on a pretrained ADM (i.e., no spatially variant noise training", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2445", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/055bc377a9aaaf760cdb9815790195288ed22a95ab725598128518a4484cb07e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 88, + 447, + 421 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ec9cded712dc8a28a7cbe244e844bbc5b202fe46910f583e8bc2a0dd27f44214.jpg", + "table_caption": [ + "Table 3. Ablation study of RAD on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.)." + ], + "table_footnote": [], + "table_body": "
MethodBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
Cfg. 1128.30.279172.00.44195.70.240
Cfg. 223.50.08637.00.33326.80.085
RAD (ours)22.10.07433.40.31721.50.078
", + "bbox": [ + 94, + 474, + 480, + 553 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and no spatial noise embedding) and (2) RAD without spatial noise embedding (i.e., using $t$ embedding). As shown in Table 3, the RAD reverse steps do not perform well on a pretrained ADM model, which suggests that training with spatially variant noise is vital for RAD. Moreover, $t$ embedding exhibits inferior performance to spatial noise embedding in RAD, showing the effectiveness of the proposed embedding in inpainting tasks. This conclusion is further supported by qualitative results in Figure 5.", + "bbox": [ + 89, + 570, + 482, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 89, + 722, + 212, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A limitation of RAD is that it requires explicit training. The burden of training a diffusion model can be significant, and accordingly, we utilized LoRA to mitigate this issue greatly. Additionally, RAD is trained using a spatially variant noise schedule defined based on masks, making it dependent on the mask distribution. Perlin masks proposed in this paper are effective enough to handle most inpainting scenarios. However, there is a possibility that RePaint or MCG might yield better results in drastic cases even though they take much longer inference time.", + "bbox": [ + 89, + 750, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/68c95cdd20fa2e1e7bcdfd56c8962db2999010a4b6446c668cedf96b8f2e3017.jpg", + "image_caption": [ + "Figure 5. Ablation study examples on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.)." + ], + "image_footnote": [], + "bbox": [ + 560, + 87, + 857, + 276 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 340, + 633, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented a novel inpainting model, RAD, which utilizes a spatially variant noise schedule to allow asynchronous generation of different regions. RAD handles inpainting by selectively adding noise to the regions specified by a given mask, followed by denoising those areas. This approach enables the selective generation of masked regions while preserving the others. The Perlin noise-based mask generation technique has been presented to generate realistic masks during training. Additionally, we proposed spatial noise embedding, significantly enhancing inpainting quality compared to conventional $t$ embedding. RAD can perform seamless inpainting without any additional module, and a plain reverse process is sufficient to produce high-quality results with orders of magnitude faster sampling speed.", + "bbox": [ + 511, + 369, + 906, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While RAD is mainly described in the context of inpainting, the overall framework has broader implications. By extending the pseudo-targets of diffusion models (the denoising distributions) to spatially variant distributions, RAD offers more means to analyze and manipulate spatial interactions in diffusion models, opening interesting future research directions. Combining RAD with conditions such as text will extend the framework to image editing, a direction for future work.", + "bbox": [ + 511, + 584, + 908, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 513, + 746, + 671, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.RS-2022-00155885, Artificial Intelligence Convergence Innovation Human Resources Development (Hanyang University ERICA)) and partly by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2023-NR076576).", + "bbox": [ + 511, + 773, + 908, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2446", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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A task is worth one word: Learning with task prompts for high-quality versatile image inpainting. arXiv preprint arXiv:2312.03594, 2023. 2, 3" + ], + "bbox": [ + 516, + 92, + 903, + 501 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2448", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_model.json b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0f7817cbb74528838a623838978bebe226376774 --- /dev/null +++ b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.197, + 0.131, + 0.803, + 0.154 + ], + "angle": 0, + "content": "RAD: Region-Aware Diffusion Models for Image Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.18, + 0.81, + 0.234 + ], + "angle": 0, + "content": "Sora Kim1, Sungho Suh2,3, Minsik Lee1,4* \n1Hanyang University, 2Korea University, 3DFKI, 4Hanyang University ERICA srk1995@hanyang.ac.kr, sungho_suh@korea.ac.kr, mleepaper@hanyang.ac.kr" + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.253, + 0.655, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.387, + 0.655, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.253, + 0.841, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.39, + 0.797, + 0.4 + ], + "angle": 0, + "content": "Generated samples" + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.404, + 0.841, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.538, + 0.673, + 0.552 + ], + "angle": 0, + "content": "Figure 1. Region-aware diffusion models (RAD) in action." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.566, + 0.327, + 0.582 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.599, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, i.e., conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demon" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.568, + 0.907, + 0.613 + ], + "angle": 0, + "content": "strated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.63, + 0.646, + 0.645 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.657, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Over the past decade, deep generative models [9, 13, 18, 31] have made significant advances in generative learning. Especially, generative adversarial networks (GANs) [9] and diffusion models [13, 31] represent seminal breakthroughs that have changed the paradigm of unsupervised image synthesis. Recently, diffusion models have attracted considerable attention due to their outstanding performance across various applications, such as text-to-image synthesis [23, 28, 30], image editing [3, 22], video frame generation [40], and text-to-3d generation [27, 41]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Denoising diffusion probabilistic models (DDPM) [13, 31], a cornerstone in diffusion models, approximate the distribution of real images by learning to reverse a pre-defined diffusion process in which real images gradually become pure Gaussian noise. Based on the learned reverse process, synthetic images can be generated by iteratively denoising" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2439" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "arbitrary Gaussian noise. In this process, each reverse step is represented as a Gaussian transition and is modeled with deep networks like U-Net [29]. Even though DDPM had a compelling framework, it initially produced lower fidelity results than GANs. Various studies [24, 26, 37] followed to improve the performance of diffusion models, and Dhariwal et al. [8] proposed the first diffusion model to outperform GANs. Nowadays, diffusion models have become de facto standard for image generation, and numerous applications have been inspired by their well-established theory and outstanding performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.261, + 0.483, + 0.457 + ], + "angle": 0, + "content": "Image inpainting, a problem to fill in missing areas of an image, is such an example that can benefit largely from a powerful generative model. With the notable advancements of deep generative models, many attempts have been made to solve image inpainting based on GANs [19, 34, 36, 43] and diffusion models [6, 21]. Diffusion-based methods have proven effective for various image inpainting or editing tasks, and some approaches utilize conditioned generation techniques based on structural information [20] or text with mask [38, 39, 45, 46]. These methods have advantages in providing more precise control over the result, but they generally require additional modules to process conditions, which add more complexities and computational burdens." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.46, + 0.483, + 0.611 + ], + "angle": 0, + "content": "Another line of research focuses on manipulating the generation processes in existing diffusion models. These approaches [1, 2, 4-6, 11, 16, 21, 22, 35] 'hijack' the reverse process of a pretrained diffusion model and devise elaborate procedures for inpainting or editing. These methods do not require any additional training, however, since the plain reverse process is not usually designed for localized generation or editing, the procedures tend to get complicated, e.g., requiring repeated re-evaluation of reverse steps, etc., resulting in significantly extended inference time." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose region-aware diffusion models (RAD), a simple reformulation of the vanilla diffusion models to overcome the aforementioned issues in diffusion-based image inpainting. Unlike conventional diffusion models, which apply noise uniformly across all pixels at each forward step, RAD assigns a different noise schedule to each pixel, enabling some areas to be completely denoised while others retain noise. This spatially variant noise scheduling naturally emulates inpainting by adding noise only to the inpainting region and performing the reverse process. This idea is quite simple, and only minimal changes in the network structures, i.e., 'reshaping' some fully connected (FC) layers into \\(1 \\times 1\\) convolutions, suffice to achieve state-of-the-art (SoTA) performance, demonstrating that existing structures are readily capable of inpainting once the right setting is provided. Unlike the existing methods tempering the noise in diffusion models, such as RePaint [21] and MCG [4], RAD inherently considers the asynchronous generation of pixels, achieving orders of" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "magnitude improvement in generation speed while maintaining high performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.122, + 0.905, + 0.288 + ], + "angle": 0, + "content": "That being said, several issues need to be carefully addressed in RAD. The pixel-wise noise schedules must be designed to represent realistic inpainting patterns and must be somehow informed to the network for effective noise inference. We deal with these issues with simple, novel ideas, i.e., Perlin noise-based schedule generation and spatial noise embedding, respectively. One limitation of the proposed method is that it requires fresh training for the altered diffusion framework; however, we overcome this by employing low-rank adaptation (LoRA) [14] on a pretrained model, greatly reducing computational requirements." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.438 + ], + "angle": 0, + "content": "We conducted experiments on FFHQ [15], LSUN Bedroom [42], and ImageNet [7], comparing RAD with other SoTA inpainting methods. RAD achieves up to 100 times faster inference time than other SoTA diffusion-based methods and achieves the best FID and LPIPS scores in most cases. In addition, an ablation study shows that the proposed components of RAD, such as the spatially variant noise schedules and the spatial noise embedding technique, are vital for the success of RAD. The contributions of this paper are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.439, + 0.905, + 0.484 + ], + "angle": 0, + "content": "- A novel reformulation of diffusion models is proposed based on spatially variant noise schedules, allowing asynchronous generation of pixels for inpainting." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.484, + 0.905, + 0.514 + ], + "angle": 0, + "content": "- Pseudo-realistic noise schedules are presented based on Perlin noise for efficient training." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.514, + 0.905, + 0.544 + ], + "angle": 0, + "content": "- A spatial noise embedding technique is introduced to provide rich spatial information to the denoiser networks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.545, + 0.905, + 0.605 + ], + "angle": 0, + "content": "- Along with the SoTA performance and the exceptional improvement in generation speed, LoRA-based training on pretrained diffusion models is also utilized to reduce the training burdens." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.439, + 0.905, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.619, + 0.665, + 0.635 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Diffusion model. DDPMs [13, 31] have introduced a novel approach in image generation by employing an iterative denoising process that progressively refines random noise into high-quality images. Unfortunately, DDPMs showed lower image fidelity compared to GANs. To enhance fidelity, various studies [24, 26, 37] have focused on generating high-quality images using diverse datasets such as ImageNet [7], FFHQ [15], and LSUN [42]. Dhariwal and Nichol [24] showed that achieving high log-likelihood on datasets with high diversity, like ImageNet [7], is possible through a hybrid objective. This hybrid objective facilitates learning the variances of the reverse Gaussian transitions that were fixed in DDPM [13]. Meanwhile, Dhariwal et al. [8] introduced ablated diffusion models (ADMs) that use auxiliary classifiers to classify the noisy images generated during the reverse process. This simple class-conditioned generation method, known as classifier guid" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2440" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.465, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.283, + 0.485, + 0.354 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed method. RAD consists of four components: (1) the forward and reverse processes based on pixel-wise noise (Section 3.1); (2) spatially variant noise schedules (Section 3.2); (3) spatial noise embedding (Section 3.3); and (4) the inverse-mapping of \\(\\bar{b}\\) (Section 3.4)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.378, + 0.483, + 0.41 + ], + "angle": 0, + "content": "ance, mainly enhances the fidelity of generated images by applying strong class conditioning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.484, + 0.563 + ], + "angle": 0, + "content": "Diffusion-based inpainting. Recently, many conditional image inpainting/editing methods have been proposed based on diffusion models. Liu et al. [20] used structural information, such as grayscale images or edge maps, to guide an inpainting process. Several studies [38, 39, 45, 46] have incorporated text and mask conditions for image inpainting. These methods typically require additional modules to perform local editing based on the specified conditions, which introduces additional complexity and computational load." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.566, + 0.483, + 0.747 + ], + "angle": 0, + "content": "Other approaches leveraged pretrained diffusion models for image inpainting/editing by manipulating their generation processes. Some methods [4, 22] manipulated the reverse SDE procedure of a pretrained score-based model [33]. On the other hand, several works [2, 10, 16, 21, 35] utilize ADM [8]. Notably, Lugmayr et al. [21] proposed RePaint, a method utilizing resampling steps to harmonize mask and non-mask regions. Other studies [1, 5, 6, 11] used the stable diffusion model [28]. Couairon et al. [6] proposed DiffEdit, which employs DDIM inversion for image editing by generating masks based on text prompts to preserve backgrounds." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Existing methods often require additional modules or extended reverse processes, increasing complexity and inference time. In contrast, RAD utilizes spatially variant noise schedules, inherently allowing detailed generation in specific areas without any additional component or loss. SmartBrush [38], although the problem setting differs from ours, is another method that adds noise only in the inpainting regions. SmartBrush, however, adds several additional modules to a diffusion model to learn this type of noise, unlike ours where the basic framework inherently supports this." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.806, + 0.108 + ], + "angle": 0, + "content": "3. Region-Aware Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.907, + 0.283 + ], + "angle": 0, + "content": "The core of the region-aware diffusion models (RADs) is redefining diffusion models so that each pixel has a different noise schedule, emulating inpainting scenarios. RADs define spatially variant noise schedules based on given masks (Sec. 3.2), which are utilized to establish both the forward and reverse processes based on pixel-wise noise (Sec. 3.1). This involves an element-wise reformulation of DDPM, of which many parts of the derivation naturally follow, however, there are some important points to consider (Secs. 3.3 and 3.4). This section will focus particularly on these critical points. The overview of RAD is shown in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.292, + 0.902, + 0.309 + ], + "angle": 0, + "content": "3.1. Diffusion Models with Spatially Variant Noise" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.314, + 0.906, + 0.466 + ], + "angle": 0, + "content": "Here, we explain the basic framework of RAD, along with a brief explanation of DDPM [13]. The goal of a diffusion model is to learn to mimic a data distribution \\( q(x_0) \\), where \\( x_0 \\) denotes a 'clean' image without any noise, based on some model \\( p_{\\theta}(x_0) \\) in an unsupervised manner. This is accomplished by learning an iterative denoising process that reverts a Brownian motion where \\( x_0 \\) gradually becomes pure Gaussian. This framework can be more tractable than directly learning \\( q(x_0) \\) because each individual task is to slightly denoise the noisy image at various noise stages." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.906, + 0.527 + ], + "angle": 0, + "content": "Given a noise schedule, a sequence \\( x_{1}, x_{2}, \\ldots, x_{T} \\) can be generated with some \\( T \\) where the image gradually becomes noisier. The forward process governing this is defined as a Markov process with Gaussian transitions:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.538, + 0.907, + 0.571 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t \\geq 1} q \\left(x _ {t} \\mid x _ {t - 1}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.583, + 0.906, + 0.644 + ], + "angle": 0, + "content": "In DDPM, \\( q(x_{t}|x_{t - 1}) = \\prod_{i}q(x_{t,i}|x_{t - 1,i}) \\), \\( i \\) denoting the element index, is assumed to be i.i.d. for the elements of \\( x_{t} \\). At this point, RAD takes a different turn from DDPM, assuming the elements have different noise intensities:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.656, + 0.907, + 0.681 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t, i} \\mid x _ {t - 1, i}\\right) = N \\left(\\sqrt {1 - b _ {t , i}} x _ {t - 1, i}, b _ {t, i}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.691, + 0.906, + 0.738 + ], + "angle": 0, + "content": "where \\( b_{t,i} \\) is the variance of the \\( i \\)-th element of \\( x_{t} \\) given \\( x_{t-1} \\), i.e., the covariance matrix of \\( q(x_{t}|x_{t-1}) \\) is \\( \\mathrm{diag}(b_{t}) \\). Similarly, the marginal distribution of \\( x_{t,i} \\) can be given as" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.748, + 0.907, + 0.768 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t, i} \\mid x _ {0, i}\\right) = N \\left(\\sqrt {\\bar {a} _ {t , i}} x _ {0, i}, 1 - \\bar {a} _ {t, i}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.779, + 0.907, + 0.901 + ], + "angle": 0, + "content": "with \\( a_{t,i} \\triangleq 1 - b_{t,i} \\), \\( \\bar{a}_{t,i} \\triangleq \\prod_{s=1}^{t} a_{s,i} \\), and \\( \\bar{b}_{t,i} \\triangleq 1 - \\bar{a}_{t,i} \\). This spatially variant noise assumption allows asynchronous generation of regions within the image, i.e., different regions can be subjected to different noise intensities so that the individual regions can be generated at different speeds, not affecting already generated ones. This alternate formulation, despite its simplicity, has proven to be quite effective in our experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2441" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.213 + ], + "angle": 0, + "content": "Even though the forward process is quite simply defined, the reverse process, i.e., the denoising process, has no closed-form solution. The essential reason is that the data distribution \\( q(x_0) \\) is not simple, and hence, the Bayes equation cannot be solved easily. Accordingly, we need to learn a model \\( p_{\\theta}(x_0) \\) that approximates the reverse process. In diffusion models, \\( p_{\\theta}(x_0) \\) is also formulated as a Markov process, starting from \\( x_T \\), reversing the timesteps:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.223, + 0.483, + 0.255 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {0: T}\\right) = p \\left(x _ {T}\\right) \\prod_ {t \\geq 1} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.265, + 0.484, + 0.37 + ], + "angle": 0, + "content": "where \\( p(x_{T}) = N(0,I) \\) is pure Gaussian noise. The reverse transition is also modeled as Gaussian, i.e., \\( p_{\\theta}(x_{t - 1}|x_t) = N(\\mu_{\\theta ,t}(x_t),\\mathrm{diag}(s_t)) \\), however, the mean \\( \\mu_{\\theta ,t} \\) is a learnable function of \\( x_{t} \\). In practice, the true \\( \\mu_{t} \\) of the denoising process can be expressed in terms of \\( x_{t} \\) and the accumulated noise \\( \\epsilon_{t} \\) (in \\( x_{t} \\)), \\( \\epsilon_{\\theta}(x_{t},t) \\) is learned to predict \\( \\epsilon_{t} \\) instead:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.38, + 0.483, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta , t, i} \\left(x _ {t}\\right) = \\frac {1}{\\sqrt {a _ {t , i}}} \\left(x _ {t, i} - \\frac {b _ {t , i}}{\\sqrt {1 - \\bar {a} _ {t , i}}} \\epsilon_ {\\theta , i} \\left(x _ {t}, t\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.429, + 0.484, + 0.519 + ], + "angle": 0, + "content": "Again, this is an element-wise version that can include RAD, while all \\( a_{t,i} \\), \\( b_{t,i} \\), and \\( \\bar{a}_{t,i} \\) terms are identical for \\( i \\) in DDPM, and the same goes for \\( s_t \\) as well. In RAD, a division-by-zero can happen in the above equation, i.e., \\( \\bar{a}_{t,i} = 1 \\), if no noise has been added to the \\( i \\)-th pixel until \\( t \\). In this case, a separate derivation gives \\( \\mu_{\\theta ,t,i} = x_{t,i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.484, + 0.625 + ], + "angle": 0, + "content": "In the above, although the forward process in Eq. (1) has no spatial dependence, \\( p_{\\theta}(x_{t - 1}|x_t) \\) surely has. This is because \\( q(x_0) \\) also likely has strong spatial dependence. Accordingly, \\( p_{\\theta} \\) must take the global context into account in the denoising process. This is why \\( \\mu_{\\theta ,t,i}(x_t) \\) and \\( \\epsilon_{\\theta ,i}(x_t,t) \\) in (5), even though they indicate specific (the \\( i \\)-th) elements of \\( \\mu_{\\theta ,t} \\) and \\( \\epsilon_{\\theta} \\), respectively, take the entire \\( x_{t} \\) as an input." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.626, + 0.484, + 0.654 + ], + "angle": 0, + "content": "Given the above forward and reverse processes, a variational loss can be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.66, + 0.483, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {q} \\left[ \\sum_ {t > 1} D _ {K L} \\left(q \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right) - \\log p _ {\\theta} \\left(x _ {0} \\mid x _ {1}\\right) \\right] \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.484, + 0.743 + ], + "angle": 0, + "content": "This basically trains \\( p_{\\theta}(x_{t - 1}|x_t) \\) to match the target \\( q(x_{t - 1}|x_t,x_0) \\), except for \\( t = 1 \\). In [13], a simpler loss has been proposed as" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.751, + 0.483, + 0.786 + ], + "angle": 0, + "content": "\\[\nL = \\sum_ {t \\geq 1} \\mathbb {E} _ {q} \\left[ \\left\\| \\epsilon_ {t} - \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\right\\| ^ {2} \\right], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "which directly trains \\(\\epsilon_{\\theta}\\) to predict \\(\\epsilon_{t}\\). This has shown to be effective, and in many later works [8, 24], both (6) and (7) have been frequently used. In RAD, the calculation of (6) must be done with the element-wise versions of \\(q\\) and \\(p_{\\theta}\\). After training, an image can be generated by performing a reverse process based on the learned \\(p_{\\theta}\\) from a randomly generated Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.228 + ], + "angle": 0, + "content": "As can be seen above, the basic framework of RAD is quite simple, i.e., an element-wise reformulation of DDPM. However, this is an easier part of RAD. For this framework to actually work, there are several important issues to consider: (i) What is an appropriate choice for the spatially variant noise \\((b_{t})\\)? (ii) How can \\(\\epsilon_{\\theta}\\) successfully learn from the altered problem setting? (iii) How can we reduce additional efforts in training this alternate formulation? For the rest of the section, we will elaborate on the above points." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.24, + 0.766, + 0.257 + ], + "angle": 0, + "content": "3.2. Generating Noise Schedules" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.264, + 0.906, + 0.37 + ], + "angle": 0, + "content": "Seeing RAD, one can quickly notice that the newly introduced flexibility requires careful attention. Unlike DDPM where a fixed noise schedule is applied to all pixels, those are set differently in RAD to allow asynchronous generation of different regions. These schedules must be somehow designed, and they must include various patterns during training so that diverse inpainting scenarios can be handled." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.371, + 0.906, + 0.567 + ], + "angle": 0, + "content": "To encompass various noise shapes, we generate \\( b_{t} \\) randomly during training. Now, the noise schedules also form a distribution, and the loss function (6) must include this in the expectation. In other words, we now have \\( q(x_{0:T}|b_{1:T}) \\) where \\( b_{1:T} \\) follows some \\( q(b_{1:T}) \\). There are infinite choices for \\( q(b_{1:T}) \\), which becomes important since it can affect training. A naive approach, such as selecting a random schedule for each pixel independently, can be problematic because the resulting noise may not have any distinctive spatial pattern, which is inconsistent with the actual inpainting scenarios. Indeed, this was not very successful in our empirical experience, meaning that having too random a noise pattern can be detrimental to the success of RAD." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.906, + 0.764 + ], + "angle": 0, + "content": "Considering the above point, we limit the possible shapes of \\( b_{t} \\) strictly to the inpainting scenarios. Specifically, we divide the entire diffusion process into two phases, where noise is filled in only for the pixels in a given inpainting mask in Phase 1 and the rest in Phase 2. This adequately represents an inpainting process, where only a part of an image is generated (Phase 1) while the other parts are already present (Phase 2). The order of these phases is set in reverse order because the actual generation is performed in the reverse process. After training, only Phase 1 is utilized in inpainting because this suffices to generate the mask region. In fact, we may only utilize Phase 1 during training as well, but using both phases was better in our experience." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.906, + 0.901 + ], + "angle": 0, + "content": "To mimic the noise-filling process of DDPM in each phase, we use the following strategy: Let \\( T_{1} \\) and \\( T_{2} \\) be the numbers of timesteps for Phases 1 and 2, respectively, i.e., \\( T_{1} + T_{2} = T \\). During each phase, each pixel in or outside the mask is filled in by a scalar noise with variance \\( \\beta_{t} \\) \\( (1\\leq t\\leq T_1) \\) or \\( \\beta_t^\\prime (1\\leq t\\leq T_2) \\), respectively, with \\( 0 < \\beta_{t},\\beta_{t}^{\\prime} < 1 \\). In practice, we use simple linear schedules for \\( \\beta_{t} \\) and \\( \\beta_{t}^{\\prime} \\) as in DDPM. A caveat here is that all pixels must have the same accumulated noise levels after finishing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2442" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.151, + 0.088, + 0.424, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.258, + 0.473, + 0.273 + ], + "angle": 0, + "content": "Figure 3. Examples of inpainting masks based on Perlin noise." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.483, + 0.334 + ], + "angle": 0, + "content": "the two phases, which can be satisfied easily by normalizing \\(\\beta_{t}\\) and \\(\\beta_t^\\prime\\) as explained in the supplementary material. Gathering the above pixel-wise noise schedules, we can form \\(b_{t}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.336, + 0.483, + 0.591 + ], + "angle": 0, + "content": "In the above strategy, the quality of inpainting masks during training is crucial. Unlike test conditions, numerous masks must be automatically supplied during training. Accessing the true mask distribution is not viable, so we need to find some sort of surrogate that includes diverse natural patterns mimicking real-world inpainting tasks. To this end, we propose to use Perlin noise [25]. Perlin noise, known for its smooth and naturalistic patterns, allows us to create diverse and realistic masks. To generate binary masks, we utilize black-and-white Perlin noise, which can be obtained by simple thresholding. We sample Perlin noise with various spatial scales by uniformly sampling the scale parameter so that the generated patterns have both finer and coarser structures. We also sample the black-and-white conversion threshold to control the overall area of inpainting. Figure 3 shows examples of generated masks. This surrogate distribution is quite effective, providing SoTA performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.593, + 0.483, + 0.7 + ], + "angle": 0, + "content": "An interesting fact is that, even though there is a sharp separation between the mask and non-mask regions in the above strategy, the inpainting results do not exhibit any noticeable boundary effects. We have also tried blurring the boundaries of the masks, with no meaningful improvement in performance. This suggests that RAD is inherently capable of generating content adaptively to existing regions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.709, + 0.323, + 0.725 + ], + "angle": 0, + "content": "3.3. Spatial Noise Embedding" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.731, + 0.483, + 0.853 + ], + "angle": 0, + "content": "In diffusion models, a deep network \\(\\epsilon_{\\theta}(x_t,t)\\) is trained to estimate the accumulated noise \\(\\epsilon_{t}\\) in \\(x_{t}\\). RAD does not have any structural difference in this regard, i.e., it shares the same input and output for \\(\\epsilon_{\\theta}\\). In fact, RAD solves a more difficult problem than that of DDPM, because \\(\\epsilon_{t}\\) becomes more complicated. Hence, using this exact same structure might not be as successful as in DDPM, as also confirmed in our ablation study." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.318 + ], + "angle": 0, + "content": "To resolve this issue, we focus on the \\(t\\) input in \\(\\epsilon_{\\theta}(x_t,t)\\) which helps the network handle different steps adaptively. In practice, \\(t\\) undergoes some embedding, comprising a cossin encoding and FC layers, and is added to every pixel of feature maps in the U-Net. Regarding this \\(t\\) input, we conjecture that its main role is to inform \\(\\epsilon_{\\theta}\\) of the overall intensity of \\(\\epsilon_{t}\\). This is somewhat reasonable because the intensity of \\(\\epsilon_{t}\\) increases as \\(t\\) progresses in DDPM. Accordingly, we propose to use \\(\\bar{b}_t\\), the pixel-wise intensity of \\(\\epsilon_{t}\\) in RAD, in place of \\(t\\) instead. This is easily accomplished by replacing the FC layers in the embedding module into \\(1\\times 1\\) convolutions. In this way, the pixel-wise noise condition can be directly informed to the network, making it easier to learn the spatially variant \\(\\epsilon_{t}\\). This actually works without changing any other component, confirming the above conjecture." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.319, + 0.905, + 0.396 + ], + "angle": 0, + "content": "The above spatial noise embedding can be viewed as an indirect way of spatial conditioning, which has some similarities with conventional conditioning techniques. However, it is more subtle in that it alters the existing \\(t\\) embedding and is completely determined by the noise schedules." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.409, + 0.74, + 0.423 + ], + "angle": 0, + "content": "3.4. Practical Considerations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.432, + 0.907, + 0.673 + ], + "angle": 0, + "content": "Although RAD has been explained in terms of DDPM, the proposed approach based on spatially variant noise is not limited to DDPM; it can be similarly applied to other advanced models such as DDIM [32], iDDPM [24], ADM [8], score-based models [33], and stable diffusion [28]. We have successfully tested RAD with many of these. For example, DDIM shares the same training procedure as DDPM, but differs in the reverse process, which we can also apply a similar element-wise reformulation. Similarly, iDDPM and ADM share the forward and reverse processes of DDPM but differ in the denoiser structures and loss functions, which combine (6) and (7). Hence, RAD can be extended to these without an issue, and all examples in the experiments are based on ADM versions. Since the basic framework of RAD is quite simple and universal, we expect it to work on other similar models as well." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "One limitation of RAD is that the alternate formulation requires fresh training. Even though this is the reason for the superb generation speed compared to the existing SoTA methods, it can also be a deal-breaker considering the amount of resources required in training. This is why the most recent methods attempt to modify only the generation processes of pretrained models, sacrificing the speed. In this paper, we address this issue by utilizing LoRA [14], which can significantly reduce training efforts by leveraging pretrained models. To train RAD based on LoRA, some minor adjustment is required: The spatial noise embedding in RAD can be too drastic of a change for LoRA. Fortunately, the noise schedules for individual pixels are set to match that in DDPM, so we can inverse-map the elements of \\(\\bar{b}_t\\) to timestep values based on the accumulated noise lev" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.863, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In fact, the difference resides in \\(\\mu_{\\theta ,t}\\), where \\(a_{t},b_{t}\\) and \\(\\bar{a}_t\\) have different values for each element in RAD as shown in (5). This makes a difference in the generation process where \\(\\mu_{\\theta ,t}\\) is utilized." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2443" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.181 + ], + "angle": 0, + "content": "els in the steps of DDPM. We use linear interpolation in this process, meaning that the mapped timestep values can be non-integral. This has proven to be effective in the experiments, where all the examples are actually fine-tuned by LoRA based on pretrained ADMs. This approach makes RAD much more accessible." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.184, + 0.483, + 0.38 + ], + "angle": 0, + "content": "In an actual implementation of RAD, singularities in the loss function must be carefully reviewed and avoided. In fact, there is a potential singularity in the variational loss (6), especially in the first step \\((t = 1)\\) where \\(p_{\\theta}(x_0|x_1)\\) is prone to becoming degenerate. Even though DDPM uses the simplified loss (7) in practice, which has no singularities, later works such as iDDPM and ADM use both (6) and (7), where the singularities become a problem and are handled by some heuristics. This is an often-overlooked problem that can render training unstable, and for RAD, the issue is a little more complicated because the pixels undergo asynchronous noise schedules. The details are explained in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.395, + 0.223, + 0.412 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.42, + 0.286, + 0.435 + ], + "angle": 0, + "content": "4.1. Benchmark Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.443, + 0.483, + 0.489 + ], + "angle": 0, + "content": "We validate RAD on the FFHQ [15], LSUN Bedroom [42], and ImageNet [7]. These datasets are well-suited for training and evaluating high-quality image generation models." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.489, + 0.483, + 0.58 + ], + "angle": 0, + "content": "- FFHQ (Flickr-Faces-HQ) [15] contains a total of 70,000 high-resolution (1024x1024) images of human faces. This dataset provides greater diversity than traditional facial image datasets, encompassing a wide range of ages, genders, ethnicities, hairstyles, and accessories (e.g., glasses, hats, etc.). All images were resized to \\(256 \\times 256\\)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.58, + 0.483, + 0.685 + ], + "angle": 0, + "content": "- LSUN Bedroom [42] is a large-scale dataset of indoor scenes, containing over 3M bedroom images. Captured from various angles and perspectives, these images represent complex room structures, enabling algorithms to learn and generate intricate scene layouts. We train RAD with 288K samples of the LSUN Bedroom for convenience. All images were resized to \\(256 \\times 256\\)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.686, + 0.483, + 0.777 + ], + "angle": 0, + "content": "- ImageNet [7] is a large-scale image dataset for visual object recognition, containing over 1.2M labeled images across 1,000 categories. This dataset offers extensive diversity, covering a wide range of objects, animals, scenes, and complex visual compositions. All images were resized to \\(256 \\times 256\\) for consistency in our experiments." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.489, + 0.483, + 0.777 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.308, + 0.803 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Training settings. For all experiments, we set the rank of LoRA [14] to 16 and trained RAD using the Adam optimizer [17] with a learning rate of \\(10^{-4}\\). We used a batch size of 16 for both FFHQ and ImageNet, while that was eight for LSUN Bedroom. The total diffusion steps was 2000, with the initial 1000 steps dedicated to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.243 + ], + "angle": 0, + "content": "Phase 1. We used predefined linear noise schedules for \\(\\beta_{t},\\beta_{t}^{\\prime}\\in (0.0001,0.02)\\). During inpainting, we used 100 sampling steps. FFHQ was trained on four TITAN RTX GPUs, LSUN Bedroom on eight NVIDIA 3090 GPUs, and ImageNet on eight NVIDIA RTX 6000 ADA GPUs. Pretrained ADM models [8] were used for all datasets. RAD was trained for \\(300\\mathrm{K}\\) on FFHQ and LSUN Bedroom, and \\(700\\mathrm{K}\\) on ImageNet. ImageNet was trained using an exponential moving average (EMA) with the decay factor set to 0.999." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.905, + 0.401 + ], + "angle": 0, + "content": "Validation settings. For validation, we set aside 1000 images from all datasets. We evaluated RAD across three types of mask configurations: box, extreme, and wide, following the practice in [34]. A box mask randomly removes a \\(128 \\times 128\\) square region. In contrast, an extreme mask retains only a specific \\(128 \\times 128\\) region, removing all other surrounding areas. A wide mask defines irregular missing regions. For inpainting, we used the reverse process of DDPM rather than DDIM due to its superior quality in generating realistic details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.408, + 0.905, + 0.528 + ], + "angle": 0, + "content": "Baseline. We chose various inpainting methods based on GANs and diffusion models. For the GAN-based baseline, we used LaMA [34], and for the diffusion-based baselines, we employed RePaint [21], MCG [4], DDRM [16], DDNM [35], and DeqIR [2]. Publicly available pretrained ADM models [8] were used for all methods. Additionally, each method was evaluated using its publicly available codebase to maintain consistency in performance assessment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.536, + 0.905, + 0.611 + ], + "angle": 0, + "content": "Metrics. To evaluate the performance of the proposed method and compare it with existing approaches, we employed Frechet Inception Distance (FID) [12] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] as the inpainting quality measure." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.622, + 0.607, + 0.636 + ], + "angle": 0, + "content": "4.3. Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Comparisons. Table 1 shows the inpainting performance of various methods. Reported values are either directly quoted from the original papers or computed by us if publicly available pretrained models exist. For LaMa, no pretrained model was available for LSUN Bedroom. Here, RAD achieves the best performance in terms of LPIPS and demonstrates superior FID scores for FFHQ and LSUN Bedroom compared to most baseline methods. Notably, DDNM and DeqIR exhibit relatively weaker performance in our experiments, even though they are relatively newer methods. The main goal of these methods is image restoration, and they are not specifically designed for challenging inpainting scenarios, particularly those involving large missing areas. Consequently, these methods show worse performance under our experimental settings. Figure 4 shows qualitative comparisons on LSUN Bedroom, FFHQ, and ImageNet. Here, all the methods are compared based" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2444" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.09, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 1. Performance (FID and LPIPS) on FFHQ and LSUN Bedroom with various mask types. \\( {}^{ \\dagger } \\) indicates that the value is quoted from the original paper. Bold: best,under: second best." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.13, + 0.905, + 0.272 + ], + "angle": 0, + "content": "
MethodFFHQLSUN BedroomImageNet
BoxExtremeWideBoxExtremeWideBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
LaMa [34]27.7†0.086†61.7†0.492†23.2†0.096†------------
Score-SDE [33]30.3†0.135†48.6†0.488†29.8†0.132†23.70.64824.10.64823.20.64457.20.20086.60.49562.00.183
DDRM [16]28.4†0.109†48.1†0.532†27.5†0.113†20.50.16633.10.45026.40.19074.30.224106.90.49275.10.211
RePAINT [21]25.7†0.093†35.9†0.398†24.2†0.108†20.50.17623.50.46121.40.16154.00.17784.00.47959.00.166
MCG [4]23.7†0.089†30.6†0.366†22.1†0.099†19.90.13122.00.39520.90.10848.10.13258.40.44856.90.124
DDNM [35]30.40.08987.70.35330.40.08922.70.15053.30.43123.20.12663.80.18780.60.47664.50.167
DeqIR [2]24.20.09364.20.36827.40.09922.20.17643.90.46122.00.15366.50.19599.50.50568.40.182
RAD (ours)22.10.07433.40.31721.50.07819.20.13121.60.39920.80.10747.00.11857.80.37456.70.104
" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.283, + 0.362, + 0.594 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.598, + 0.29, + 0.61 + ], + "angle": 0, + "content": "(a) LSUN Bedroom" + }, + { + "type": "image", + "bbox": [ + 0.374, + 0.283, + 0.622, + 0.594 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.472, + 0.598, + 0.528, + 0.61 + ], + "angle": 0, + "content": "(b) FFHQ" + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.283, + 0.885, + 0.594 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.726, + 0.598, + 0.798, + 0.61 + ], + "angle": 0, + "content": "(c) ImageNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.623, + 0.882, + 0.637 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparisons. Colored areas indicate inpainting regions (1st/2nd rows: box, 3rd/4th: extreme, 5th/6th: wide)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.653, + 0.483, + 0.697 + ], + "angle": 0, + "content": "on the same combinations of images and inpainting masks. The results confirm that RAD generally produces more natural images than others and has fewer failure cases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.483, + 0.804 + ], + "angle": 0, + "content": "Table 2 shows the inference time of various methods. We evaluated all methods on \\(256 \\times 256\\) images using a single NVIDIA Titan RTX GPU. Here, RAD is about 100 times faster than RePaint and 15 times faster than MCG while delivering superior performance. Baseline methods other than RePaint and MCG are much faster, but their inpainting quality is significantly worse." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Analysis of diversity. Section 4.3 demonstrates that RAD can generate diverse inpaintings across various mask configurations. Each row in the figure shows the input image with a specific mask, followed by multiple inpainting results (Samples 1 to 4) generated by RAD. These results highlight RAD's ability to produce various plausible and contextually" + }, + { + "type": "table_caption", + "bbox": [ + 0.518, + 0.651, + 0.901, + 0.665 + ], + "angle": 0, + "content": "Table 2. Inference time comparison \\( \\left( {1 \\times \\text{NVIDIA TITAN RTX}}\\right) \\) ." + }, + { + "type": "table", + "bbox": [ + 0.599, + 0.675, + 0.821, + 0.801 + ], + "angle": 0, + "content": "
MethodInference time [s]
Score-SDE [33]41.983
DDRM [16]12.291
RePAINT [21]837.136
MCG [4]128.058
DDNM [35]6.566
DeqIR [2]26.443
Ours8.442
" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.815, + 0.868, + 0.83 + ], + "angle": 0, + "content": "consistent inpaintings, even under challenging masks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Ablation study. To verify the effectiveness of the proposed components, we compared RAD with two alternative methods: (1) performing RAD reverse steps directly on a pretrained ADM (i.e., no spatially variant noise training" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2445" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.089, + 0.449, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.437, + 0.483, + 0.465 + ], + "angle": 0, + "content": "Table 3. Ablation study of RAD on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.)." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.476, + 0.481, + 0.554 + ], + "angle": 0, + "content": "
MethodBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
Cfg. 1128.30.279172.00.44195.70.240
Cfg. 223.50.08637.00.33326.80.085
RAD (ours)22.10.07433.40.31721.50.078
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.571, + 0.483, + 0.707 + ], + "angle": 0, + "content": "and no spatial noise embedding) and (2) RAD without spatial noise embedding (i.e., using \\( t \\) embedding). As shown in Table 3, the RAD reverse steps do not perform well on a pretrained ADM model, which suggests that training with spatially variant noise is vital for RAD. Moreover, \\( t \\) embedding exhibits inferior performance to spatial noise embedding in RAD, showing the effectiveness of the proposed embedding in inpainting tasks. This conclusion is further supported by qualitative results in Figure 5." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.723, + 0.214, + 0.739 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.901 + ], + "angle": 0, + "content": "A limitation of RAD is that it requires explicit training. The burden of training a diffusion model can be significant, and accordingly, we utilized LoRA to mitigate this issue greatly. Additionally, RAD is trained using a spatially variant noise schedule defined based on masks, making it dependent on the mask distribution. Perlin masks proposed in this paper are effective enough to handle most inpainting scenarios. However, there is a possibility that RePaint or MCG might yield better results in drastic cases even though they take much longer inference time." + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.088, + 0.859, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.29, + 0.907, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Ablation study examples on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.341, + 0.634, + 0.357 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.37, + 0.907, + 0.583 + ], + "angle": 0, + "content": "We presented a novel inpainting model, RAD, which utilizes a spatially variant noise schedule to allow asynchronous generation of different regions. RAD handles inpainting by selectively adding noise to the regions specified by a given mask, followed by denoising those areas. This approach enables the selective generation of masked regions while preserving the others. The Perlin noise-based mask generation technique has been presented to generate realistic masks during training. Additionally, we proposed spatial noise embedding, significantly enhancing inpainting quality compared to conventional \\( t \\) embedding. RAD can perform seamless inpainting without any additional module, and a plain reverse process is sufficient to produce high-quality results with orders of magnitude faster sampling speed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.909, + 0.721 + ], + "angle": 0, + "content": "While RAD is mainly described in the context of inpainting, the overall framework has broader implications. By extending the pseudo-targets of diffusion models (the denoising distributions) to spatially variant distributions, RAD offers more means to analyze and manipulate spatial interactions in diffusion models, opening interesting future research directions. Combining RAD with conditions such as text will extend the framework to image editing, a direction for future work." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.747, + 0.673, + 0.765 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.909, + 0.889 + ], + "angle": 0, + "content": "This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.RS-2022-00155885, Artificial Intelligence Convergence Innovation Human Resources Development (Hanyang University ERICA)) and partly by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2023-NR076576)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2446" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.156 + ], + "angle": 0, + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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A task is worth one word: Learning with task prompts for high-quality versatile image inpainting. arXiv preprint arXiv:2312.03594, 2023. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2448" + } + ] +] \ No newline at end of file diff --git a/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_origin.pdf b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..592b0a307e8bc9a9bd1c3cfbfd28697a538b2d4d --- /dev/null +++ b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/c3fc017b-fff9-4d44-a432-47bdefc13495_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:911b4c2bae37fa20bfd4539f0c8f4899c36f3f974e80ed348118883fa2ef4ab3 +size 4965582 diff --git a/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/full.md b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/full.md new file mode 100644 index 0000000000000000000000000000000000000000..37edddbe57005e9d39ffdc49d244e61e5647256c --- /dev/null +++ b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/full.md @@ -0,0 +1,289 @@ +# RAD: Region-Aware Diffusion Models for Image Inpainting + +Sora Kim1, Sungho Suh2,3, Minsik Lee1,4* +1Hanyang University, 2Korea University, 3DFKI, 4Hanyang University ERICA srk1995@hanyang.ac.kr, sungho_suh@korea.ac.kr, mleepaper@hanyang.ac.kr + +![](images/10cb934d2e7fc691c1ba6e9d596c491b3ace5deaa67b2a7b5a0ff75cdaf269b6.jpg) + +![](images/8e6326c6ff18e5e387d7432f13d64a19a6a2a44b5e79a874726c36cb2e3cd370.jpg) +Figure 1. Region-aware diffusion models (RAD) in action. + +![](images/a6fc497c0875255d1d7d2c9c688324e5dc142f5c2e42ff3c2b30e360680d64ba.jpg) +Generated samples + +![](images/df01d18823360cd0b3cd7a0286765680b7dc0f4705fe3c4b07af9af6cc9501ac.jpg) + +# Abstract + +Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, i.e., conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demon + +strated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets. + +# 1. Introduction + +Over the past decade, deep generative models [9, 13, 18, 31] have made significant advances in generative learning. Especially, generative adversarial networks (GANs) [9] and diffusion models [13, 31] represent seminal breakthroughs that have changed the paradigm of unsupervised image synthesis. Recently, diffusion models have attracted considerable attention due to their outstanding performance across various applications, such as text-to-image synthesis [23, 28, 30], image editing [3, 22], video frame generation [40], and text-to-3d generation [27, 41]. + +Denoising diffusion probabilistic models (DDPM) [13, 31], a cornerstone in diffusion models, approximate the distribution of real images by learning to reverse a pre-defined diffusion process in which real images gradually become pure Gaussian noise. Based on the learned reverse process, synthetic images can be generated by iteratively denoising + +arbitrary Gaussian noise. In this process, each reverse step is represented as a Gaussian transition and is modeled with deep networks like U-Net [29]. Even though DDPM had a compelling framework, it initially produced lower fidelity results than GANs. Various studies [24, 26, 37] followed to improve the performance of diffusion models, and Dhariwal et al. [8] proposed the first diffusion model to outperform GANs. Nowadays, diffusion models have become de facto standard for image generation, and numerous applications have been inspired by their well-established theory and outstanding performance. + +Image inpainting, a problem to fill in missing areas of an image, is such an example that can benefit largely from a powerful generative model. With the notable advancements of deep generative models, many attempts have been made to solve image inpainting based on GANs [19, 34, 36, 43] and diffusion models [6, 21]. Diffusion-based methods have proven effective for various image inpainting or editing tasks, and some approaches utilize conditioned generation techniques based on structural information [20] or text with mask [38, 39, 45, 46]. These methods have advantages in providing more precise control over the result, but they generally require additional modules to process conditions, which add more complexities and computational burdens. + +Another line of research focuses on manipulating the generation processes in existing diffusion models. These approaches [1, 2, 4-6, 11, 16, 21, 22, 35] 'hijack' the reverse process of a pretrained diffusion model and devise elaborate procedures for inpainting or editing. These methods do not require any additional training, however, since the plain reverse process is not usually designed for localized generation or editing, the procedures tend to get complicated, e.g., requiring repeated re-evaluation of reverse steps, etc., resulting in significantly extended inference time. + +In this paper, we propose region-aware diffusion models (RAD), a simple reformulation of the vanilla diffusion models to overcome the aforementioned issues in diffusion-based image inpainting. Unlike conventional diffusion models, which apply noise uniformly across all pixels at each forward step, RAD assigns a different noise schedule to each pixel, enabling some areas to be completely denoised while others retain noise. This spatially variant noise scheduling naturally emulates inpainting by adding noise only to the inpainting region and performing the reverse process. This idea is quite simple, and only minimal changes in the network structures, i.e., 'reshaping' some fully connected (FC) layers into $1 \times 1$ convolutions, suffice to achieve state-of-the-art (SoTA) performance, demonstrating that existing structures are readily capable of inpainting once the right setting is provided. Unlike the existing methods tempering the noise in diffusion models, such as RePaint [21] and MCG [4], RAD inherently considers the asynchronous generation of pixels, achieving orders of + +magnitude improvement in generation speed while maintaining high performance. + +That being said, several issues need to be carefully addressed in RAD. The pixel-wise noise schedules must be designed to represent realistic inpainting patterns and must be somehow informed to the network for effective noise inference. We deal with these issues with simple, novel ideas, i.e., Perlin noise-based schedule generation and spatial noise embedding, respectively. One limitation of the proposed method is that it requires fresh training for the altered diffusion framework; however, we overcome this by employing low-rank adaptation (LoRA) [14] on a pretrained model, greatly reducing computational requirements. + +We conducted experiments on FFHQ [15], LSUN Bedroom [42], and ImageNet [7], comparing RAD with other SoTA inpainting methods. RAD achieves up to 100 times faster inference time than other SoTA diffusion-based methods and achieves the best FID and LPIPS scores in most cases. In addition, an ablation study shows that the proposed components of RAD, such as the spatially variant noise schedules and the spatial noise embedding technique, are vital for the success of RAD. The contributions of this paper are summarized as follows: + +- A novel reformulation of diffusion models is proposed based on spatially variant noise schedules, allowing asynchronous generation of pixels for inpainting. +- Pseudo-realistic noise schedules are presented based on Perlin noise for efficient training. +- A spatial noise embedding technique is introduced to provide rich spatial information to the denoiser networks. +- Along with the SoTA performance and the exceptional improvement in generation speed, LoRA-based training on pretrained diffusion models is also utilized to reduce the training burdens. + +# 2. Related Works + +Diffusion model. DDPMs [13, 31] have introduced a novel approach in image generation by employing an iterative denoising process that progressively refines random noise into high-quality images. Unfortunately, DDPMs showed lower image fidelity compared to GANs. To enhance fidelity, various studies [24, 26, 37] have focused on generating high-quality images using diverse datasets such as ImageNet [7], FFHQ [15], and LSUN [42]. Dhariwal and Nichol [24] showed that achieving high log-likelihood on datasets with high diversity, like ImageNet [7], is possible through a hybrid objective. This hybrid objective facilitates learning the variances of the reverse Gaussian transitions that were fixed in DDPM [13]. Meanwhile, Dhariwal et al. [8] introduced ablated diffusion models (ADMs) that use auxiliary classifiers to classify the noisy images generated during the reverse process. This simple class-conditioned generation method, known as classifier guid + +![](images/ff5df060fc0d4344ae4936a0eaf2954d93dc79639bdb1811e6dd0621c23219aa.jpg) +Figure 2. An overview of the proposed method. RAD consists of four components: (1) the forward and reverse processes based on pixel-wise noise (Section 3.1); (2) spatially variant noise schedules (Section 3.2); (3) spatial noise embedding (Section 3.3); and (4) the inverse-mapping of $\bar{b}$ (Section 3.4). + +ance, mainly enhances the fidelity of generated images by applying strong class conditioning. + +Diffusion-based inpainting. Recently, many conditional image inpainting/editing methods have been proposed based on diffusion models. Liu et al. [20] used structural information, such as grayscale images or edge maps, to guide an inpainting process. Several studies [38, 39, 45, 46] have incorporated text and mask conditions for image inpainting. These methods typically require additional modules to perform local editing based on the specified conditions, which introduces additional complexity and computational load. + +Other approaches leveraged pretrained diffusion models for image inpainting/editing by manipulating their generation processes. Some methods [4, 22] manipulated the reverse SDE procedure of a pretrained score-based model [33]. On the other hand, several works [2, 10, 16, 21, 35] utilize ADM [8]. Notably, Lugmayr et al. [21] proposed RePaint, a method utilizing resampling steps to harmonize mask and non-mask regions. Other studies [1, 5, 6, 11] used the stable diffusion model [28]. Couairon et al. [6] proposed DiffEdit, which employs DDIM inversion for image editing by generating masks based on text prompts to preserve backgrounds. + +Existing methods often require additional modules or extended reverse processes, increasing complexity and inference time. In contrast, RAD utilizes spatially variant noise schedules, inherently allowing detailed generation in specific areas without any additional component or loss. SmartBrush [38], although the problem setting differs from ours, is another method that adds noise only in the inpainting regions. SmartBrush, however, adds several additional modules to a diffusion model to learn this type of noise, unlike ours where the basic framework inherently supports this. + +# 3. Region-Aware Diffusion Models + +The core of the region-aware diffusion models (RADs) is redefining diffusion models so that each pixel has a different noise schedule, emulating inpainting scenarios. RADs define spatially variant noise schedules based on given masks (Sec. 3.2), which are utilized to establish both the forward and reverse processes based on pixel-wise noise (Sec. 3.1). This involves an element-wise reformulation of DDPM, of which many parts of the derivation naturally follow, however, there are some important points to consider (Secs. 3.3 and 3.4). This section will focus particularly on these critical points. The overview of RAD is shown in Figure 2. + +# 3.1. Diffusion Models with Spatially Variant Noise + +Here, we explain the basic framework of RAD, along with a brief explanation of DDPM [13]. The goal of a diffusion model is to learn to mimic a data distribution $q(x_0)$ , where $x_0$ denotes a 'clean' image without any noise, based on some model $p_{\theta}(x_0)$ in an unsupervised manner. This is accomplished by learning an iterative denoising process that reverts a Brownian motion where $x_0$ gradually becomes pure Gaussian. This framework can be more tractable than directly learning $q(x_0)$ because each individual task is to slightly denoise the noisy image at various noise stages. + +Given a noise schedule, a sequence $x_{1}, x_{2}, \ldots, x_{T}$ can be generated with some $T$ where the image gradually becomes noisier. The forward process governing this is defined as a Markov process with Gaussian transitions: + +$$ +q \left(x _ {1: T} \mid x _ {0}\right) = \prod_ {t \geq 1} q \left(x _ {t} \mid x _ {t - 1}\right). \tag {1} +$$ + +In DDPM, $q(x_{t}|x_{t - 1}) = \prod_{i}q(x_{t,i}|x_{t - 1,i})$ , $i$ denoting the element index, is assumed to be i.i.d. for the elements of $x_{t}$ . At this point, RAD takes a different turn from DDPM, assuming the elements have different noise intensities: + +$$ +q \left(x _ {t, i} \mid x _ {t - 1, i}\right) = N \left(\sqrt {1 - b _ {t , i}} x _ {t - 1, i}, b _ {t, i}\right) \tag {2} +$$ + +where $b_{t,i}$ is the variance of the $i$ -th element of $x_{t}$ given $x_{t-1}$ , i.e., the covariance matrix of $q(x_{t}|x_{t-1})$ is $\mathrm{diag}(b_{t})$ . Similarly, the marginal distribution of $x_{t,i}$ can be given as + +$$ +q \left(x _ {t, i} \mid x _ {0, i}\right) = N \left(\sqrt {\bar {a} _ {t , i}} x _ {0, i}, 1 - \bar {a} _ {t, i}\right) \tag {3} +$$ + +with $a_{t,i} \triangleq 1 - b_{t,i}$ , $\bar{a}_{t,i} \triangleq \prod_{s=1}^{t} a_{s,i}$ , and $\bar{b}_{t,i} \triangleq 1 - \bar{a}_{t,i}$ . This spatially variant noise assumption allows asynchronous generation of regions within the image, i.e., different regions can be subjected to different noise intensities so that the individual regions can be generated at different speeds, not affecting already generated ones. This alternate formulation, despite its simplicity, has proven to be quite effective in our experiments. + +Even though the forward process is quite simply defined, the reverse process, i.e., the denoising process, has no closed-form solution. The essential reason is that the data distribution $q(x_0)$ is not simple, and hence, the Bayes equation cannot be solved easily. Accordingly, we need to learn a model $p_{\theta}(x_0)$ that approximates the reverse process. In diffusion models, $p_{\theta}(x_0)$ is also formulated as a Markov process, starting from $x_T$ , reversing the timesteps: + +$$ +p _ {\theta} \left(x _ {0: T}\right) = p \left(x _ {T}\right) \prod_ {t \geq 1} p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right), \tag {4} +$$ + +where $p(x_{T}) = N(0,I)$ is pure Gaussian noise. The reverse transition is also modeled as Gaussian, i.e., $p_{\theta}(x_{t - 1}|x_t) = N(\mu_{\theta ,t}(x_t),\mathrm{diag}(s_t))$ , however, the mean $\mu_{\theta ,t}$ is a learnable function of $x_{t}$ . In practice, the true $\mu_{t}$ of the denoising process can be expressed in terms of $x_{t}$ and the accumulated noise $\epsilon_{t}$ (in $x_{t}$ ), $\epsilon_{\theta}(x_{t},t)$ is learned to predict $\epsilon_{t}$ instead: + +$$ +\mu_ {\theta , t, i} \left(x _ {t}\right) = \frac {1}{\sqrt {a _ {t , i}}} \left(x _ {t, i} - \frac {b _ {t , i}}{\sqrt {1 - \bar {a} _ {t , i}}} \epsilon_ {\theta , i} \left(x _ {t}, t\right)\right). \tag {5} +$$ + +Again, this is an element-wise version that can include RAD, while all $a_{t,i}$ , $b_{t,i}$ , and $\bar{a}_{t,i}$ terms are identical for $i$ in DDPM, and the same goes for $s_t$ as well. In RAD, a division-by-zero can happen in the above equation, i.e., $\bar{a}_{t,i} = 1$ , if no noise has been added to the $i$ -th pixel until $t$ . In this case, a separate derivation gives $\mu_{\theta ,t,i} = x_{t,i}$ . + +In the above, although the forward process in Eq. (1) has no spatial dependence, $p_{\theta}(x_{t - 1}|x_t)$ surely has. This is because $q(x_0)$ also likely has strong spatial dependence. Accordingly, $p_{\theta}$ must take the global context into account in the denoising process. This is why $\mu_{\theta ,t,i}(x_t)$ and $\epsilon_{\theta ,i}(x_t,t)$ in (5), even though they indicate specific (the $i$ -th) elements of $\mu_{\theta ,t}$ and $\epsilon_{\theta}$ , respectively, take the entire $x_{t}$ as an input. + +Given the above forward and reverse processes, a variational loss can be defined as + +$$ +\mathbb {E} _ {q} \left[ \sum_ {t > 1} D _ {K L} \left(q \left(x _ {t - 1} \mid x _ {t}, x _ {0}\right) \| p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right)\right) - \log p _ {\theta} \left(x _ {0} \mid x _ {1}\right) \right] \tag {6} +$$ + +This basically trains $p_{\theta}(x_{t - 1}|x_t)$ to match the target $q(x_{t - 1}|x_t,x_0)$ , except for $t = 1$ . In [13], a simpler loss has been proposed as + +$$ +L = \sum_ {t \geq 1} \mathbb {E} _ {q} \left[ \left\| \epsilon_ {t} - \epsilon_ {\theta} \left(x _ {t}, t\right) \right\| ^ {2} \right], \tag {7} +$$ + +which directly trains $\epsilon_{\theta}$ to predict $\epsilon_{t}$ . This has shown to be effective, and in many later works [8, 24], both (6) and (7) have been frequently used. In RAD, the calculation of (6) must be done with the element-wise versions of $q$ and $p_{\theta}$ . After training, an image can be generated by performing a reverse process based on the learned $p_{\theta}$ from a randomly generated Gaussian noise. + +As can be seen above, the basic framework of RAD is quite simple, i.e., an element-wise reformulation of DDPM. However, this is an easier part of RAD. For this framework to actually work, there are several important issues to consider: (i) What is an appropriate choice for the spatially variant noise $(b_{t})$ ? (ii) How can $\epsilon_{\theta}$ successfully learn from the altered problem setting? (iii) How can we reduce additional efforts in training this alternate formulation? For the rest of the section, we will elaborate on the above points. + +# 3.2. Generating Noise Schedules + +Seeing RAD, one can quickly notice that the newly introduced flexibility requires careful attention. Unlike DDPM where a fixed noise schedule is applied to all pixels, those are set differently in RAD to allow asynchronous generation of different regions. These schedules must be somehow designed, and they must include various patterns during training so that diverse inpainting scenarios can be handled. + +To encompass various noise shapes, we generate $b_{t}$ randomly during training. Now, the noise schedules also form a distribution, and the loss function (6) must include this in the expectation. In other words, we now have $q(x_{0:T}|b_{1:T})$ where $b_{1:T}$ follows some $q(b_{1:T})$ . There are infinite choices for $q(b_{1:T})$ , which becomes important since it can affect training. A naive approach, such as selecting a random schedule for each pixel independently, can be problematic because the resulting noise may not have any distinctive spatial pattern, which is inconsistent with the actual inpainting scenarios. Indeed, this was not very successful in our empirical experience, meaning that having too random a noise pattern can be detrimental to the success of RAD. + +Considering the above point, we limit the possible shapes of $b_{t}$ strictly to the inpainting scenarios. Specifically, we divide the entire diffusion process into two phases, where noise is filled in only for the pixels in a given inpainting mask in Phase 1 and the rest in Phase 2. This adequately represents an inpainting process, where only a part of an image is generated (Phase 1) while the other parts are already present (Phase 2). The order of these phases is set in reverse order because the actual generation is performed in the reverse process. After training, only Phase 1 is utilized in inpainting because this suffices to generate the mask region. In fact, we may only utilize Phase 1 during training as well, but using both phases was better in our experience. + +To mimic the noise-filling process of DDPM in each phase, we use the following strategy: Let $T_{1}$ and $T_{2}$ be the numbers of timesteps for Phases 1 and 2, respectively, i.e., $T_{1} + T_{2} = T$ . During each phase, each pixel in or outside the mask is filled in by a scalar noise with variance $\beta_{t}$ $(1\leq t\leq T_1)$ or $\beta_t^\prime (1\leq t\leq T_2)$ , respectively, with $0 < \beta_{t},\beta_{t}^{\prime} < 1$ . In practice, we use simple linear schedules for $\beta_{t}$ and $\beta_{t}^{\prime}$ as in DDPM. A caveat here is that all pixels must have the same accumulated noise levels after finishing + +![](images/f7112572ec6b212594c9077c38e331c5f9cab1301f21f76d67b68fc0942ced3c.jpg) +Figure 3. Examples of inpainting masks based on Perlin noise. + +the two phases, which can be satisfied easily by normalizing $\beta_{t}$ and $\beta_t^\prime$ as explained in the supplementary material. Gathering the above pixel-wise noise schedules, we can form $b_{t}$ . + +In the above strategy, the quality of inpainting masks during training is crucial. Unlike test conditions, numerous masks must be automatically supplied during training. Accessing the true mask distribution is not viable, so we need to find some sort of surrogate that includes diverse natural patterns mimicking real-world inpainting tasks. To this end, we propose to use Perlin noise [25]. Perlin noise, known for its smooth and naturalistic patterns, allows us to create diverse and realistic masks. To generate binary masks, we utilize black-and-white Perlin noise, which can be obtained by simple thresholding. We sample Perlin noise with various spatial scales by uniformly sampling the scale parameter so that the generated patterns have both finer and coarser structures. We also sample the black-and-white conversion threshold to control the overall area of inpainting. Figure 3 shows examples of generated masks. This surrogate distribution is quite effective, providing SoTA performance. + +An interesting fact is that, even though there is a sharp separation between the mask and non-mask regions in the above strategy, the inpainting results do not exhibit any noticeable boundary effects. We have also tried blurring the boundaries of the masks, with no meaningful improvement in performance. This suggests that RAD is inherently capable of generating content adaptively to existing regions. + +# 3.3. Spatial Noise Embedding + +In diffusion models, a deep network $\epsilon_{\theta}(x_t,t)$ is trained to estimate the accumulated noise $\epsilon_{t}$ in $x_{t}$ . RAD does not have any structural difference in this regard, i.e., it shares the same input and output for $\epsilon_{\theta}$ . In fact, RAD solves a more difficult problem than that of DDPM, because $\epsilon_{t}$ becomes more complicated. Hence, using this exact same structure might not be as successful as in DDPM, as also confirmed in our ablation study. + +To resolve this issue, we focus on the $t$ input in $\epsilon_{\theta}(x_t,t)$ which helps the network handle different steps adaptively. In practice, $t$ undergoes some embedding, comprising a cossin encoding and FC layers, and is added to every pixel of feature maps in the U-Net. Regarding this $t$ input, we conjecture that its main role is to inform $\epsilon_{\theta}$ of the overall intensity of $\epsilon_{t}$ . This is somewhat reasonable because the intensity of $\epsilon_{t}$ increases as $t$ progresses in DDPM. Accordingly, we propose to use $\bar{b}_t$ , the pixel-wise intensity of $\epsilon_{t}$ in RAD, in place of $t$ instead. This is easily accomplished by replacing the FC layers in the embedding module into $1\times 1$ convolutions. In this way, the pixel-wise noise condition can be directly informed to the network, making it easier to learn the spatially variant $\epsilon_{t}$ . This actually works without changing any other component, confirming the above conjecture. + +The above spatial noise embedding can be viewed as an indirect way of spatial conditioning, which has some similarities with conventional conditioning techniques. However, it is more subtle in that it alters the existing $t$ embedding and is completely determined by the noise schedules. + +# 3.4. Practical Considerations + +Although RAD has been explained in terms of DDPM, the proposed approach based on spatially variant noise is not limited to DDPM; it can be similarly applied to other advanced models such as DDIM [32], iDDPM [24], ADM [8], score-based models [33], and stable diffusion [28]. We have successfully tested RAD with many of these. For example, DDIM shares the same training procedure as DDPM, but differs in the reverse process, which we can also apply a similar element-wise reformulation. Similarly, iDDPM and ADM share the forward and reverse processes of DDPM but differ in the denoiser structures and loss functions, which combine (6) and (7). Hence, RAD can be extended to these without an issue, and all examples in the experiments are based on ADM versions. Since the basic framework of RAD is quite simple and universal, we expect it to work on other similar models as well. + +One limitation of RAD is that the alternate formulation requires fresh training. Even though this is the reason for the superb generation speed compared to the existing SoTA methods, it can also be a deal-breaker considering the amount of resources required in training. This is why the most recent methods attempt to modify only the generation processes of pretrained models, sacrificing the speed. In this paper, we address this issue by utilizing LoRA [14], which can significantly reduce training efforts by leveraging pretrained models. To train RAD based on LoRA, some minor adjustment is required: The spatial noise embedding in RAD can be too drastic of a change for LoRA. Fortunately, the noise schedules for individual pixels are set to match that in DDPM, so we can inverse-map the elements of $\bar{b}_t$ to timestep values based on the accumulated noise lev + +els in the steps of DDPM. We use linear interpolation in this process, meaning that the mapped timestep values can be non-integral. This has proven to be effective in the experiments, where all the examples are actually fine-tuned by LoRA based on pretrained ADMs. This approach makes RAD much more accessible. + +In an actual implementation of RAD, singularities in the loss function must be carefully reviewed and avoided. In fact, there is a potential singularity in the variational loss (6), especially in the first step $(t = 1)$ where $p_{\theta}(x_0|x_1)$ is prone to becoming degenerate. Even though DDPM uses the simplified loss (7) in practice, which has no singularities, later works such as iDDPM and ADM use both (6) and (7), where the singularities become a problem and are handled by some heuristics. This is an often-overlooked problem that can render training unstable, and for RAD, the issue is a little more complicated because the pixels undergo asynchronous noise schedules. The details are explained in the supplementary material. + +# 4. Experiments + +# 4.1. Benchmark Datasets + +We validate RAD on the FFHQ [15], LSUN Bedroom [42], and ImageNet [7]. These datasets are well-suited for training and evaluating high-quality image generation models. + +- FFHQ (Flickr-Faces-HQ) [15] contains a total of 70,000 high-resolution (1024x1024) images of human faces. This dataset provides greater diversity than traditional facial image datasets, encompassing a wide range of ages, genders, ethnicities, hairstyles, and accessories (e.g., glasses, hats, etc.). All images were resized to $256 \times 256$ . +- LSUN Bedroom [42] is a large-scale dataset of indoor scenes, containing over 3M bedroom images. Captured from various angles and perspectives, these images represent complex room structures, enabling algorithms to learn and generate intricate scene layouts. We train RAD with 288K samples of the LSUN Bedroom for convenience. All images were resized to $256 \times 256$ . +- ImageNet [7] is a large-scale image dataset for visual object recognition, containing over 1.2M labeled images across 1,000 categories. This dataset offers extensive diversity, covering a wide range of objects, animals, scenes, and complex visual compositions. All images were resized to $256 \times 256$ for consistency in our experiments. + +# 4.2. Implementation Details + +Training settings. For all experiments, we set the rank of LoRA [14] to 16 and trained RAD using the Adam optimizer [17] with a learning rate of $10^{-4}$ . We used a batch size of 16 for both FFHQ and ImageNet, while that was eight for LSUN Bedroom. The total diffusion steps was 2000, with the initial 1000 steps dedicated to + +Phase 1. We used predefined linear noise schedules for $\beta_{t},\beta_{t}^{\prime}\in (0.0001,0.02)$ . During inpainting, we used 100 sampling steps. FFHQ was trained on four TITAN RTX GPUs, LSUN Bedroom on eight NVIDIA 3090 GPUs, and ImageNet on eight NVIDIA RTX 6000 ADA GPUs. Pretrained ADM models [8] were used for all datasets. RAD was trained for $300\mathrm{K}$ on FFHQ and LSUN Bedroom, and $700\mathrm{K}$ on ImageNet. ImageNet was trained using an exponential moving average (EMA) with the decay factor set to 0.999. + +Validation settings. For validation, we set aside 1000 images from all datasets. We evaluated RAD across three types of mask configurations: box, extreme, and wide, following the practice in [34]. A box mask randomly removes a $128 \times 128$ square region. In contrast, an extreme mask retains only a specific $128 \times 128$ region, removing all other surrounding areas. A wide mask defines irregular missing regions. For inpainting, we used the reverse process of DDPM rather than DDIM due to its superior quality in generating realistic details. + +Baseline. We chose various inpainting methods based on GANs and diffusion models. For the GAN-based baseline, we used LaMA [34], and for the diffusion-based baselines, we employed RePaint [21], MCG [4], DDRM [16], DDNM [35], and DeqIR [2]. Publicly available pretrained ADM models [8] were used for all methods. Additionally, each method was evaluated using its publicly available codebase to maintain consistency in performance assessment. + +Metrics. To evaluate the performance of the proposed method and compare it with existing approaches, we employed Frechet Inception Distance (FID) [12] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] as the inpainting quality measure. + +# 4.3. Results + +Comparisons. Table 1 shows the inpainting performance of various methods. Reported values are either directly quoted from the original papers or computed by us if publicly available pretrained models exist. For LaMa, no pretrained model was available for LSUN Bedroom. Here, RAD achieves the best performance in terms of LPIPS and demonstrates superior FID scores for FFHQ and LSUN Bedroom compared to most baseline methods. Notably, DDNM and DeqIR exhibit relatively weaker performance in our experiments, even though they are relatively newer methods. The main goal of these methods is image restoration, and they are not specifically designed for challenging inpainting scenarios, particularly those involving large missing areas. Consequently, these methods show worse performance under our experimental settings. Figure 4 shows qualitative comparisons on LSUN Bedroom, FFHQ, and ImageNet. Here, all the methods are compared based + +Table 1. Performance (FID and LPIPS) on FFHQ and LSUN Bedroom with various mask types. ${}^{ \dagger }$ indicates that the value is quoted from the original paper. Bold: best,under: second best. + +
MethodFFHQLSUN BedroomImageNet
BoxExtremeWideBoxExtremeWideBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
LaMa [34]27.7†0.086†61.7†0.492†23.2†0.096†------------
Score-SDE [33]30.3†0.135†48.6†0.488†29.8†0.132†23.70.64824.10.64823.20.64457.20.20086.60.49562.00.183
DDRM [16]28.4†0.109†48.1†0.532†27.5†0.113†20.50.16633.10.45026.40.19074.30.224106.90.49275.10.211
RePAINT [21]25.7†0.093†35.9†0.398†24.2†0.108†20.50.17623.50.46121.40.16154.00.17784.00.47959.00.166
MCG [4]23.7†0.089†30.6†0.366†22.1†0.099†19.90.13122.00.39520.90.10848.10.13258.40.44856.90.124
DDNM [35]30.40.08987.70.35330.40.08922.70.15053.30.43123.20.12663.80.18780.60.47664.50.167
DeqIR [2]24.20.09364.20.36827.40.09922.20.17643.90.46122.00.15366.50.19599.50.50568.40.182
RAD (ours)22.10.07433.40.31721.50.07819.20.13121.60.39920.80.10747.00.11857.80.37456.70.104
+ +![](images/55d7b420e3f98a477e7ecb6f40c73944534dbefbe70a7065a4769f342dcfc8a1.jpg) +(a) LSUN Bedroom + +![](images/181797860d24e992f32fc1c4de084931f5c3a126b7199825f4c0fd561cd6be2c.jpg) +(b) FFHQ + +![](images/c4fe0e866e3baa15a6bce66caa3bb35b02afd1e6c646facffd18fe8b86f8f33c.jpg) +(c) ImageNet +Figure 4. Qualitative comparisons. Colored areas indicate inpainting regions (1st/2nd rows: box, 3rd/4th: extreme, 5th/6th: wide). + +on the same combinations of images and inpainting masks. The results confirm that RAD generally produces more natural images than others and has fewer failure cases. + +Table 2 shows the inference time of various methods. We evaluated all methods on $256 \times 256$ images using a single NVIDIA Titan RTX GPU. Here, RAD is about 100 times faster than RePaint and 15 times faster than MCG while delivering superior performance. Baseline methods other than RePaint and MCG are much faster, but their inpainting quality is significantly worse. + +Analysis of diversity. Section 4.3 demonstrates that RAD can generate diverse inpaintings across various mask configurations. Each row in the figure shows the input image with a specific mask, followed by multiple inpainting results (Samples 1 to 4) generated by RAD. These results highlight RAD's ability to produce various plausible and contextually + +Table 2. Inference time comparison $\left( {1 \times \text{NVIDIA TITAN RTX}}\right)$ . + +
MethodInference time [s]
Score-SDE [33]41.983
DDRM [16]12.291
RePAINT [21]837.136
MCG [4]128.058
DDNM [35]6.566
DeqIR [2]26.443
Ours8.442
+ +consistent inpaintings, even under challenging masks. + +Ablation study. To verify the effectiveness of the proposed components, we compared RAD with two alternative methods: (1) performing RAD reverse steps directly on a pretrained ADM (i.e., no spatially variant noise training + +![](images/055bc377a9aaaf760cdb9815790195288ed22a95ab725598128518a4484cb07e.jpg) + +Table 3. Ablation study of RAD on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.). + +
MethodBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
Cfg. 1128.30.279172.00.44195.70.240
Cfg. 223.50.08637.00.33326.80.085
RAD (ours)22.10.07433.40.31721.50.078
+ +and no spatial noise embedding) and (2) RAD without spatial noise embedding (i.e., using $t$ embedding). As shown in Table 3, the RAD reverse steps do not perform well on a pretrained ADM model, which suggests that training with spatially variant noise is vital for RAD. Moreover, $t$ embedding exhibits inferior performance to spatial noise embedding in RAD, showing the effectiveness of the proposed embedding in inpainting tasks. This conclusion is further supported by qualitative results in Figure 5. + +# 5. Limitations + +A limitation of RAD is that it requires explicit training. The burden of training a diffusion model can be significant, and accordingly, we utilized LoRA to mitigate this issue greatly. Additionally, RAD is trained using a spatially variant noise schedule defined based on masks, making it dependent on the mask distribution. Perlin masks proposed in this paper are effective enough to handle most inpainting scenarios. However, there is a possibility that RePaint or MCG might yield better results in drastic cases even though they take much longer inference time. + +![](images/68c95cdd20fa2e1e7bcdfd56c8962db2999010a4b6446c668cedf96b8f2e3017.jpg) +Figure 5. Ablation study examples on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.). + +# 6. Conclusion + +We presented a novel inpainting model, RAD, which utilizes a spatially variant noise schedule to allow asynchronous generation of different regions. RAD handles inpainting by selectively adding noise to the regions specified by a given mask, followed by denoising those areas. This approach enables the selective generation of masked regions while preserving the others. The Perlin noise-based mask generation technique has been presented to generate realistic masks during training. Additionally, we proposed spatial noise embedding, significantly enhancing inpainting quality compared to conventional $t$ embedding. RAD can perform seamless inpainting without any additional module, and a plain reverse process is sufficient to produce high-quality results with orders of magnitude faster sampling speed. + +While RAD is mainly described in the context of inpainting, the overall framework has broader implications. By extending the pseudo-targets of diffusion models (the denoising distributions) to spatially variant distributions, RAD offers more means to analyze and manipulate spatial interactions in diffusion models, opening interesting future research directions. Combining RAD with conditions such as text will extend the framework to image editing, a direction for future work. + +# Acknowledgments + +This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.RS-2022-00155885, Artificial Intelligence Convergence Innovation Human Resources Development (Hanyang University ERICA)) and partly by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2023-NR076576). + +# References + +[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. ACM transactions on graphics (TOG), 42 (4):1-11, 2023. 2, 3 +[2] Jiezhang Cao, Yue Shi, Kai Zhang, Yulun Zhang, Radu Timofte, and Luc Van Gool. Deep equilibrium diffusion restoration with parallel sampling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2824-2834, 2024. 2, 3, 6, 7 +[3] Haiwei Chen and Yajie Zhao. 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Udifftext: A unified framework for high-quality text synthesis in arbitrary images via character-aware diffusion models. In European Conference on Computer Vision, pages 217-233. Springer, 2024. 2, 3 +[46] Junhao Zhuang, Yanhong Zeng, Wenran Liu, Chun Yuan, and Kai Chen. A task is worth one word: Learning with task prompts for high-quality versatile image inpainting. arXiv preprint arXiv:2312.03594, 2023. 2, 3 \ No newline at end of file diff --git a/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/images.zip b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..058e79963d56629d9722060a1c1be1c367990fd2 --- /dev/null +++ b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:077732b8b367895be2276ab48c509da70f3639402f847e8438679231688982b6 +size 686037 diff --git a/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/layout.json b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..66179c5ada436bc4304cc913b802f0d7edcdc304 --- /dev/null +++ b/2025/RAD_ Region-Aware Diffusion Models for Image Inpainting/layout.json @@ -0,0 +1,8735 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 120, + 103, + 491, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 103, + 491, + 121 + ], + "spans": [ + { + "bbox": [ + 120, + 103, + 491, + 121 + ], + "type": "text", + "content": "RAD: Region-Aware Diffusion Models for Image Inpainting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 142, + 495, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 142, + 495, + 185 + ], + "spans": [ + { + "bbox": [ + 115, + 142, + 495, + 185 + ], + "type": "text", + "content": "Sora Kim1, Sungho Suh2,3, Minsik Lee1,4* \n1Hanyang University, 2Korea University, 3DFKI, 4Hanyang University ERICA srk1995@hanyang.ac.kr, sungho_suh@korea.ac.kr, mleepaper@hanyang.ac.kr" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 93, + 200, + 400, + 305 + ], + "blocks": [ + { + "bbox": [ + 93, + 200, + 400, + 305 + ], + "lines": [ + { + "bbox": [ + 93, + 200, + 400, + 305 + ], + "spans": [ + { + "bbox": [ + 93, + 200, + 400, + 305 + ], + "type": "image", + "image_path": "10cb934d2e7fc691c1ba6e9d596c491b3ace5deaa67b2a7b5a0ff75cdaf269b6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 93, + 306, + 400, + 424 + ], + "blocks": [ + { + "bbox": [ + 93, + 306, + 400, + 424 + ], + "lines": [ + { + "bbox": [ + 93, + 306, + 400, + 424 + ], + "spans": [ + { + "bbox": [ + 93, + 306, + 400, + 424 + ], + "type": "image", + "image_path": "8e6326c6ff18e5e387d7432f13d64a19a6a2a44b5e79a874726c36cb2e3cd370.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 426, + 411, + 437 + ], + "lines": [ + { + "bbox": [ + 198, + 426, + 411, + 437 + ], + "spans": [ + { + "bbox": [ + 198, + 426, + 411, + 437 + ], + "type": "text", + "content": "Figure 1. Region-aware diffusion models (RAD) in action." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 400, + 200, + 514, + 306 + ], + "blocks": [ + { + "bbox": [ + 400, + 200, + 514, + 306 + ], + "lines": [ + { + "bbox": [ + 400, + 200, + 514, + 306 + ], + "spans": [ + { + "bbox": [ + 400, + 200, + 514, + 306 + ], + "type": "image", + "image_path": "a6fc497c0875255d1d7d2c9c688324e5dc142f5c2e42ff3c2b30e360680d64ba.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 308, + 487, + 316 + ], + "lines": [ + { + "bbox": [ + 435, + 308, + 487, + 316 + ], + "spans": [ + { + "bbox": [ + 435, + 308, + 487, + 316 + ], + "type": "text", + "content": "Generated samples" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 400, + 319, + 514, + 425 + ], + "blocks": [ + { + "bbox": [ + 400, + 319, + 514, + 425 + ], + "lines": [ + { + "bbox": [ + 400, + 319, + 514, + 425 + ], + "spans": [ + { + "bbox": [ + 400, + 319, + 514, + 425 + ], + "type": "image", + "image_path": "df01d18823360cd0b3cd7a0286765680b7dc0f4705fe3c4b07af9af6cc9501ac.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 152, + 448, + 200, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 448, + 200, + 460 + ], + "spans": [ + { + "bbox": [ + 152, + 448, + 200, + 460 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 474, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 474, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 474, + 297, + 715 + ], + "type": "text", + "content": "Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, i.e., conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demon" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 449, + 555, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 485 + ], + "type": "text", + "content": "strated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 498, + 395, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 498, + 395, + 510 + ], + "spans": [ + { + "bbox": [ + 314, + 498, + 395, + 510 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 520, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 555, + 640 + ], + "type": "text", + "content": "Over the past decade, deep generative models [9, 13, 18, 31] have made significant advances in generative learning. Especially, generative adversarial networks (GANs) [9] and diffusion models [13, 31] represent seminal breakthroughs that have changed the paradigm of unsupervised image synthesis. Recently, diffusion models have attracted considerable attention due to their outstanding performance across various applications, such as text-to-image synthesis [23, 28, 30], image editing [3, 22], video frame generation [40], and text-to-3d generation [27, 41]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": "Denoising diffusion probabilistic models (DDPM) [13, 31], a cornerstone in diffusion models, approximate the distribution of real images by learning to reverse a pre-defined diffusion process in which real images gradually become pure Gaussian noise. Based on the learned reverse process, synthetic images can be generated by iteratively denoising" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2439" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 294, + 204 + ], + "type": "text", + "content": "arbitrary Gaussian noise. In this process, each reverse step is represented as a Gaussian transition and is modeled with deep networks like U-Net [29]. Even though DDPM had a compelling framework, it initially produced lower fidelity results than GANs. Various studies [24, 26, 37] followed to improve the performance of diffusion models, and Dhariwal et al. [8] proposed the first diffusion model to outperform GANs. Nowadays, diffusion models have become de facto standard for image generation, and numerous applications have been inspired by their well-established theory and outstanding performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 206, + 295, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 206, + 295, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 295, + 361 + ], + "type": "text", + "content": "Image inpainting, a problem to fill in missing areas of an image, is such an example that can benefit largely from a powerful generative model. With the notable advancements of deep generative models, many attempts have been made to solve image inpainting based on GANs [19, 34, 36, 43] and diffusion models [6, 21]. Diffusion-based methods have proven effective for various image inpainting or editing tasks, and some approaches utilize conditioned generation techniques based on structural information [20] or text with mask [38, 39, 45, 46]. These methods have advantages in providing more precise control over the result, but they generally require additional modules to process conditions, which add more complexities and computational burdens." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 364, + 295, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 364, + 295, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 364, + 295, + 483 + ], + "type": "text", + "content": "Another line of research focuses on manipulating the generation processes in existing diffusion models. These approaches [1, 2, 4-6, 11, 16, 21, 22, 35] 'hijack' the reverse process of a pretrained diffusion model and devise elaborate procedures for inpainting or editing. These methods do not require any additional training, however, since the plain reverse process is not usually designed for localized generation or editing, the procedures tend to get complicated, e.g., requiring repeated re-evaluation of reverse steps, etc., resulting in significantly extended inference time." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "text", + "content": "In this paper, we propose region-aware diffusion models (RAD), a simple reformulation of the vanilla diffusion models to overcome the aforementioned issues in diffusion-based image inpainting. Unlike conventional diffusion models, which apply noise uniformly across all pixels at each forward step, RAD assigns a different noise schedule to each pixel, enabling some areas to be completely denoised while others retain noise. This spatially variant noise scheduling naturally emulates inpainting by adding noise only to the inpainting region and performing the reverse process. This idea is quite simple, and only minimal changes in the network structures, i.e., 'reshaping' some fully connected (FC) layers into " + }, + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 55, + 486, + 295, + 713 + ], + "type": "text", + "content": " convolutions, suffice to achieve state-of-the-art (SoTA) performance, demonstrating that existing structures are readily capable of inpainting once the right setting is provided. Unlike the existing methods tempering the noise in diffusion models, such as RePaint [21] and MCG [4], RAD inherently considers the asynchronous generation of pixels, achieving orders of" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "magnitude improvement in generation speed while maintaining high performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 96, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 228 + ], + "type": "text", + "content": "That being said, several issues need to be carefully addressed in RAD. The pixel-wise noise schedules must be designed to represent realistic inpainting patterns and must be somehow informed to the network for effective noise inference. We deal with these issues with simple, novel ideas, i.e., Perlin noise-based schedule generation and spatial noise embedding, respectively. One limitation of the proposed method is that it requires fresh training for the altered diffusion framework; however, we overcome this by employing low-rank adaptation (LoRA) [14] on a pretrained model, greatly reducing computational requirements." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 228, + 553, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 346 + ], + "type": "text", + "content": "We conducted experiments on FFHQ [15], LSUN Bedroom [42], and ImageNet [7], comparing RAD with other SoTA inpainting methods. RAD achieves up to 100 times faster inference time than other SoTA diffusion-based methods and achieves the best FID and LPIPS scores in most cases. In addition, an ablation study shows that the proposed components of RAD, such as the spatially variant noise schedules and the spatial noise embedding technique, are vital for the success of RAD. The contributions of this paper are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 347, + 553, + 479 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 313, + 347, + 553, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 553, + 383 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 553, + 383 + ], + "type": "text", + "content": "- A novel reformulation of diffusion models is proposed based on spatially variant noise schedules, allowing asynchronous generation of pixels for inpainting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 383, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 553, + 407 + ], + "type": "text", + "content": "- Pseudo-realistic noise schedules are presented based on Perlin noise for efficient training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 407, + 553, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 553, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 553, + 430 + ], + "type": "text", + "content": "- A spatial noise embedding technique is introduced to provide rich spatial information to the denoiser networks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 431, + 553, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 553, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 553, + 479 + ], + "type": "text", + "content": "- Along with the SoTA performance and the exceptional improvement in generation speed, LoRA-based training on pretrained diffusion models is also utilized to reduce the training burdens." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 490, + 406, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 490, + 406, + 502 + ], + "spans": [ + { + "bbox": [ + 314, + 490, + 406, + 502 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 510, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 715 + ], + "type": "text", + "content": "Diffusion model. DDPMs [13, 31] have introduced a novel approach in image generation by employing an iterative denoising process that progressively refines random noise into high-quality images. Unfortunately, DDPMs showed lower image fidelity compared to GANs. To enhance fidelity, various studies [24, 26, 37] have focused on generating high-quality images using diverse datasets such as ImageNet [7], FFHQ [15], and LSUN [42]. Dhariwal and Nichol [24] showed that achieving high log-likelihood on datasets with high diversity, like ImageNet [7], is possible through a hybrid objective. This hybrid objective facilitates learning the variances of the reverse Gaussian transitions that were fixed in DDPM [13]. Meanwhile, Dhariwal et al. [8] introduced ablated diffusion models (ADMs) that use auxiliary classifiers to classify the noisy images generated during the reverse process. This simple class-conditioned generation method, known as classifier guid" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2440" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 284, + 216 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 284, + 216 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 284, + 216 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 284, + 216 + ], + "type": "image", + "image_path": "ff5df060fc0d4344ae4936a0eaf2954d93dc79639bdb1811e6dd0621c23219aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 224, + 296, + 280 + ], + "lines": [ + { + "bbox": [ + 55, + 224, + 296, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 224, + 296, + 280 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed method. RAD consists of four components: (1) the forward and reverse processes based on pixel-wise noise (Section 3.1); (2) spatially variant noise schedules (Section 3.2); (3) spatial noise embedding (Section 3.3); and (4) the inverse-mapping of " + }, + { + "bbox": [ + 55, + 224, + 296, + 280 + ], + "type": "inline_equation", + "content": "\\bar{b}" + }, + { + "bbox": [ + 55, + 224, + 296, + 280 + ], + "type": "text", + "content": " (Section 3.4)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 299, + 295, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 299, + 295, + 324 + ], + "spans": [ + { + "bbox": [ + 55, + 299, + 295, + 324 + ], + "type": "text", + "content": "ance, mainly enhances the fidelity of generated images by applying strong class conditioning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 338, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 445 + ], + "type": "text", + "content": "Diffusion-based inpainting. Recently, many conditional image inpainting/editing methods have been proposed based on diffusion models. Liu et al. [20] used structural information, such as grayscale images or edge maps, to guide an inpainting process. Several studies [38, 39, 45, 46] have incorporated text and mask conditions for image inpainting. These methods typically require additional modules to perform local editing based on the specified conditions, which introduces additional complexity and computational load." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 448, + 295, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 295, + 591 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 295, + 591 + ], + "type": "text", + "content": "Other approaches leveraged pretrained diffusion models for image inpainting/editing by manipulating their generation processes. Some methods [4, 22] manipulated the reverse SDE procedure of a pretrained score-based model [33]. On the other hand, several works [2, 10, 16, 21, 35] utilize ADM [8]. Notably, Lugmayr et al. [21] proposed RePaint, a method utilizing resampling steps to harmonize mask and non-mask regions. Other studies [1, 5, 6, 11] used the stable diffusion model [28]. Couairon et al. [6] proposed DiffEdit, which employs DDIM inversion for image editing by generating masks based on text prompts to preserve backgrounds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "Existing methods often require additional modules or extended reverse processes, increasing complexity and inference time. In contrast, RAD utilizes spatially variant noise schedules, inherently allowing detailed generation in specific areas without any additional component or loss. SmartBrush [38], although the problem setting differs from ours, is another method that adds noise only in the inpainting regions. SmartBrush, however, adds several additional modules to a diffusion model to learn this type of noise, unlike ours where the basic framework inherently supports this." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 71, + 493, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 493, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 493, + 85 + ], + "type": "text", + "content": "3. Region-Aware Diffusion Models" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 91, + 555, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 224 + ], + "type": "text", + "content": "The core of the region-aware diffusion models (RADs) is redefining diffusion models so that each pixel has a different noise schedule, emulating inpainting scenarios. RADs define spatially variant noise schedules based on given masks (Sec. 3.2), which are utilized to establish both the forward and reverse processes based on pixel-wise noise (Sec. 3.1). This involves an element-wise reformulation of DDPM, of which many parts of the derivation naturally follow, however, there are some important points to consider (Secs. 3.3 and 3.4). This section will focus particularly on these critical points. The overview of RAD is shown in Figure 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 231, + 552, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 231, + 552, + 244 + ], + "spans": [ + { + "bbox": [ + 313, + 231, + 552, + 244 + ], + "type": "text", + "content": "3.1. Diffusion Models with Spatially Variant Noise" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "spans": [ + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": "Here, we explain the basic framework of RAD, along with a brief explanation of DDPM [13]. The goal of a diffusion model is to learn to mimic a data distribution " + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": " denotes a 'clean' image without any noise, based on some model " + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_0)" + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": " in an unsupervised manner. This is accomplished by learning an iterative denoising process that reverts a Brownian motion where " + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": " gradually becomes pure Gaussian. This framework can be more tractable than directly learning " + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 313, + 248, + 554, + 369 + ], + "type": "text", + "content": " because each individual task is to slightly denoise the noisy image at various noise stages." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "text", + "content": "Given a noise schedule, a sequence " + }, + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}, \\ldots, x_{T}" + }, + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "text", + "content": " can be generated with some " + }, + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 369, + 554, + 417 + ], + "type": "text", + "content": " where the image gradually becomes noisier. The forward process governing this is defined as a Markov process with Gaussian transitions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 370, + 426, + 555, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 426, + 555, + 452 + ], + "spans": [ + { + "bbox": [ + 370, + 426, + 555, + 452 + ], + "type": "interline_equation", + "content": "q \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t \\geq 1} q \\left(x _ {t} \\mid x _ {t - 1}\\right). \\tag {1}", + "image_path": "cbf472b9c8fb2aa569666e7ac3f421b4e47e3c2ed4d79dbb3c5cdaf88cd8656a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "text", + "content": "In DDPM, " + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{t - 1}) = \\prod_{i}q(x_{t,i}|x_{t - 1,i})" + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "text", + "content": " denoting the element index, is assumed to be i.i.d. for the elements of " + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 461, + 554, + 510 + ], + "type": "text", + "content": ". At this point, RAD takes a different turn from DDPM, assuming the elements have different noise intensities:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 343, + 519, + 555, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 519, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 343, + 519, + 555, + 539 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t, i} \\mid x _ {t - 1, i}\\right) = N \\left(\\sqrt {1 - b _ {t , i}} x _ {t - 1, i}, b _ {t, i}\\right) \\tag {2}", + "image_path": "3668f20b5076bb39dcc45e0767be2a2308616683a811dd5b7660a277e0c377fd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "b_{t,i}" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": " is the variance of the " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": "-th element of " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": ", i.e., the covariance matrix of " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{t-1})" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "\\mathrm{diag}(b_{t})" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": ". Similarly, the marginal distribution of " + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "inline_equation", + "content": "x_{t,i}" + }, + { + "bbox": [ + 313, + 547, + 554, + 584 + ], + "type": "text", + "content": " can be given as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 354, + 592, + 555, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 592, + 555, + 608 + ], + "spans": [ + { + "bbox": [ + 354, + 592, + 555, + 608 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t, i} \\mid x _ {0, i}\\right) = N \\left(\\sqrt {\\bar {a} _ {t , i}} x _ {0, i}, 1 - \\bar {a} _ {t, i}\\right) \\tag {3}", + "image_path": "6a6407e0fb77a4000de7d7e20a5c9bba49359a09b100497a0735c37eddb8b2c3.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "a_{t,i} \\triangleq 1 - b_{t,i}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\bar{a}_{t,i} \\triangleq \\prod_{s=1}^{t} a_{s,i}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\bar{b}_{t,i} \\triangleq 1 - \\bar{a}_{t,i}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": ". This spatially variant noise assumption allows asynchronous generation of regions within the image, i.e., different regions can be subjected to different noise intensities so that the individual regions can be generated at different speeds, not affecting already generated ones. This alternate formulation, despite its simplicity, has proven to be quite effective in our experiments." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2441" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": "Even though the forward process is quite simply defined, the reverse process, i.e., the denoising process, has no closed-form solution. The essential reason is that the data distribution " + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": " is not simple, and hence, the Bayes equation cannot be solved easily. Accordingly, we need to learn a model " + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_0)" + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": " that approximates the reverse process. In diffusion models, " + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_0)" + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": " is also formulated as a Markov process, starting from " + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": ", reversing the timesteps:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 101, + 176, + 295, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 176, + 295, + 201 + ], + "spans": [ + { + "bbox": [ + 101, + 176, + 295, + 201 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {0: T}\\right) = p \\left(x _ {T}\\right) \\prod_ {t \\geq 1} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right), \\tag {4}", + "image_path": "e9e830762bdeeef877543d2b8c805a2b05a98b37d9c433f532bc3e382a813b43.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "p(x_{T}) = N(0,I)" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " is pure Gaussian noise. The reverse transition is also modeled as Gaussian, i.e., " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t - 1}|x_t) = N(\\mu_{\\theta ,t}(x_t),\\mathrm{diag}(s_t))" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": ", however, the mean " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " is a learnable function of " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": ". In practice, the true " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\mu_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " of the denoising process can be expressed in terms of " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " and the accumulated noise " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " (in " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_{t},t)" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " is learned to predict " + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 209, + 296, + 293 + ], + "type": "text", + "content": " instead:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 300, + 295, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 300, + 295, + 334 + ], + "spans": [ + { + "bbox": [ + 64, + 300, + 295, + 334 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta , t, i} \\left(x _ {t}\\right) = \\frac {1}{\\sqrt {a _ {t , i}}} \\left(x _ {t, i} - \\frac {b _ {t , i}}{\\sqrt {1 - \\bar {a} _ {t , i}}} \\epsilon_ {\\theta , i} \\left(x _ {t}, t\\right)\\right). \\tag {5}", + "image_path": "579749721f25379cf5d53920fa0e9a79e60b7333487123813a193002b92f4e71.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": "Again, this is an element-wise version that can include RAD, while all " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "a_{t,i}" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "b_{t,i}" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\bar{a}_{t,i}" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": " terms are identical for " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": " in DDPM, and the same goes for " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": " as well. In RAD, a division-by-zero can happen in the above equation, i.e., " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\bar{a}_{t,i} = 1" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": ", if no noise has been added to the " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": "-th pixel until " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": ". In this case, a separate derivation gives " + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t,i} = x_{t,i}" + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": "In the above, although the forward process in Eq. (1) has no spatial dependence, " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t - 1}|x_t)" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " surely has. This is because " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " also likely has strong spatial dependence. Accordingly, " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " must take the global context into account in the denoising process. This is why " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t,i}(x_t)" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta ,i}(x_t,t)" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " in (5), even though they indicate specific (the " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": "-th) elements of " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t}" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": ", respectively, take the entire " + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 411, + 296, + 495 + ], + "type": "text", + "content": " as an input." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 495, + 296, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 517 + ], + "type": "text", + "content": "Given the above forward and reverse processes, a variational loss can be defined as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 522, + 295, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 522, + 295, + 546 + ], + "spans": [ + { + "bbox": [ + 63, + 522, + 295, + 546 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {q} \\left[ \\sum_ {t > 1} D _ {K L} \\left(q \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right) - \\log p _ {\\theta} \\left(x _ {0} \\mid x _ {1}\\right) \\right] \\tag {6}", + "image_path": "253038750f1281d97c82317145ce65da5261c119ab552ccea90cdb36786de80d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "text", + "content": "This basically trains " + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t - 1}|x_t)" + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "text", + "content": " to match the target " + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "inline_equation", + "content": "q(x_{t - 1}|x_t,x_0)" + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "text", + "content": ", except for " + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 55, + 552, + 296, + 588 + ], + "type": "text", + "content": ". In [13], a simpler loss has been proposed as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 109, + 594, + 295, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 594, + 295, + 622 + ], + "spans": [ + { + "bbox": [ + 109, + 594, + 295, + 622 + ], + "type": "interline_equation", + "content": "L = \\sum_ {t \\geq 1} \\mathbb {E} _ {q} \\left[ \\left\\| \\epsilon_ {t} - \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\right\\| ^ {2} \\right], \\tag {7}", + "image_path": "708f2f90e2f80a71f5c1cf30e5e96e8396c0c4508a556b283bac150316282a4e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "which directly trains " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " to predict " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ". This has shown to be effective, and in many later works [8, 24], both (6) and (7) have been frequently used. In RAD, the calculation of (6) must be done with the element-wise versions of " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ". After training, an image can be generated by performing a reverse process based on the learned " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " from a randomly generated Gaussian noise." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": "As can be seen above, the basic framework of RAD is quite simple, i.e., an element-wise reformulation of DDPM. However, this is an easier part of RAD. For this framework to actually work, there are several important issues to consider: (i) What is an appropriate choice for the spatially variant noise " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "(b_{t})" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": "? (ii) How can " + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 72, + 554, + 180 + ], + "type": "text", + "content": " successfully learn from the altered problem setting? (iii) How can we reduce additional efforts in training this alternate formulation? For the rest of the section, we will elaborate on the above points." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 190, + 468, + 203 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 468, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 468, + 203 + ], + "type": "text", + "content": "3.2. Generating Noise Schedules" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 209, + 554, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 554, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 554, + 293 + ], + "type": "text", + "content": "Seeing RAD, one can quickly notice that the newly introduced flexibility requires careful attention. Unlike DDPM where a fixed noise schedule is applied to all pixels, those are set differently in RAD to allow asynchronous generation of different regions. These schedules must be somehow designed, and they must include various patterns during training so that diverse inpainting scenarios can be handled." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": "To encompass various noise shapes, we generate " + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "inline_equation", + "content": "b_{t}" + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": " randomly during training. Now, the noise schedules also form a distribution, and the loss function (6) must include this in the expectation. In other words, we now have " + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "inline_equation", + "content": "q(x_{0:T}|b_{1:T})" + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "inline_equation", + "content": "b_{1:T}" + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": " follows some " + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "inline_equation", + "content": "q(b_{1:T})" + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": ". There are infinite choices for " + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "inline_equation", + "content": "q(b_{1:T})" + }, + { + "bbox": [ + 313, + 293, + 554, + 449 + ], + "type": "text", + "content": ", which becomes important since it can affect training. A naive approach, such as selecting a random schedule for each pixel independently, can be problematic because the resulting noise may not have any distinctive spatial pattern, which is inconsistent with the actual inpainting scenarios. Indeed, this was not very successful in our empirical experience, meaning that having too random a noise pattern can be detrimental to the success of RAD." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 449, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 554, + 605 + ], + "type": "text", + "content": "Considering the above point, we limit the possible shapes of " + }, + { + "bbox": [ + 313, + 449, + 554, + 605 + ], + "type": "inline_equation", + "content": "b_{t}" + }, + { + "bbox": [ + 313, + 449, + 554, + 605 + ], + "type": "text", + "content": " strictly to the inpainting scenarios. Specifically, we divide the entire diffusion process into two phases, where noise is filled in only for the pixels in a given inpainting mask in Phase 1 and the rest in Phase 2. This adequately represents an inpainting process, where only a part of an image is generated (Phase 1) while the other parts are already present (Phase 2). The order of these phases is set in reverse order because the actual generation is performed in the reverse process. After training, only Phase 1 is utilized in inpainting because this suffices to generate the mask region. In fact, we may only utilize Phase 1 during training as well, but using both phases was better in our experience." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": "To mimic the noise-filling process of DDPM in each phase, we use the following strategy: Let " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "T_{2}" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": " be the numbers of timesteps for Phases 1 and 2, respectively, i.e., " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "T_{1} + T_{2} = T" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": ". During each phase, each pixel in or outside the mask is filled in by a scalar noise with variance " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "(1\\leq t\\leq T_1)" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\beta_t^\\prime (1\\leq t\\leq T_2)" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": ", respectively, with " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "0 < \\beta_{t},\\beta_{t}^{\\prime} < 1" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": ". In practice, we use simple linear schedules for " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{t}^{\\prime}" + }, + { + "bbox": [ + 313, + 605, + 554, + 713 + ], + "type": "text", + "content": " as in DDPM. A caveat here is that all pixels must have the same accumulated noise levels after finishing" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2442" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 92, + 69, + 259, + 197 + ], + "blocks": [ + { + "bbox": [ + 92, + 69, + 259, + 197 + ], + "lines": [ + { + "bbox": [ + 92, + 69, + 259, + 197 + ], + "spans": [ + { + "bbox": [ + 92, + 69, + 259, + 197 + ], + "type": "image", + "image_path": "f7112572ec6b212594c9077c38e331c5f9cab1301f21f76d67b68fc0942ced3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 204, + 289, + 216 + ], + "lines": [ + { + "bbox": [ + 61, + 204, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 61, + 204, + 289, + 216 + ], + "type": "text", + "content": "Figure 3. Examples of inpainting masks based on Perlin noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "text", + "content": "the two phases, which can be satisfied easily by normalizing " + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "inline_equation", + "content": "\\beta_t^\\prime" + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "text", + "content": " as explained in the supplementary material. Gathering the above pixel-wise noise schedules, we can form " + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "inline_equation", + "content": "b_{t}" + }, + { + "bbox": [ + 55, + 228, + 295, + 264 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 266, + 295, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 295, + 468 + ], + "type": "text", + "content": "In the above strategy, the quality of inpainting masks during training is crucial. Unlike test conditions, numerous masks must be automatically supplied during training. Accessing the true mask distribution is not viable, so we need to find some sort of surrogate that includes diverse natural patterns mimicking real-world inpainting tasks. To this end, we propose to use Perlin noise [25]. Perlin noise, known for its smooth and naturalistic patterns, allows us to create diverse and realistic masks. To generate binary masks, we utilize black-and-white Perlin noise, which can be obtained by simple thresholding. We sample Perlin noise with various spatial scales by uniformly sampling the scale parameter so that the generated patterns have both finer and coarser structures. We also sample the black-and-white conversion threshold to control the overall area of inpainting. Figure 3 shows examples of generated masks. This surrogate distribution is quite effective, providing SoTA performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 469, + 295, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 295, + 554 + ], + "type": "text", + "content": "An interesting fact is that, even though there is a sharp separation between the mask and non-mask regions in the above strategy, the inpainting results do not exhibit any noticeable boundary effects. We have also tried blurring the boundaries of the masks, with no meaningful improvement in performance. This suggests that RAD is inherently capable of generating content adaptively to existing regions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 561, + 197, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 197, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 197, + 574 + ], + "type": "text", + "content": "3.3. Spatial Noise Embedding" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": "In diffusion models, a deep network " + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": " is trained to estimate the accumulated noise " + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": ". RAD does not have any structural difference in this regard, i.e., it shares the same input and output for " + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": ". In fact, RAD solves a more difficult problem than that of DDPM, because " + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 578, + 295, + 675 + ], + "type": "text", + "content": " becomes more complicated. Hence, using this exact same structure might not be as successful as in DDPM, as also confirmed in our ablation study." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": "To resolve this issue, we focus on the " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " input in " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " which helps the network handle different steps adaptively. In practice, " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " undergoes some embedding, comprising a cossin encoding and FC layers, and is added to every pixel of feature maps in the U-Net. Regarding this " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " input, we conjecture that its main role is to inform " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " of the overall intensity of " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": ". This is somewhat reasonable because the intensity of " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " increases as " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " progresses in DDPM. Accordingly, we propose to use " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\bar{b}_t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": ", the pixel-wise intensity of " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " in RAD, in place of " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " instead. This is easily accomplished by replacing the FC layers in the embedding module into " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": " convolutions. In this way, the pixel-wise noise condition can be directly informed to the network, making it easier to learn the spatially variant " + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": ". This actually works without changing any other component, confirming the above conjecture." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 252, + 553, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 553, + 313 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 553, + 313 + ], + "type": "text", + "content": "The above spatial noise embedding can be viewed as an indirect way of spatial conditioning, which has some similarities with conventional conditioning techniques. However, it is more subtle in that it alters the existing " + }, + { + "bbox": [ + 313, + 252, + 553, + 313 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 252, + 553, + 313 + ], + "type": "text", + "content": " embedding and is completely determined by the noise schedules." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 323, + 452, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 452, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 452, + 335 + ], + "type": "text", + "content": "3.4. Practical Considerations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 342, + 555, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 533 + ], + "type": "text", + "content": "Although RAD has been explained in terms of DDPM, the proposed approach based on spatially variant noise is not limited to DDPM; it can be similarly applied to other advanced models such as DDIM [32], iDDPM [24], ADM [8], score-based models [33], and stable diffusion [28]. We have successfully tested RAD with many of these. For example, DDIM shares the same training procedure as DDPM, but differs in the reverse process, which we can also apply a similar element-wise reformulation. Similarly, iDDPM and ADM share the forward and reverse processes of DDPM but differ in the denoiser structures and loss functions, which combine (6) and (7). Hence, RAD can be extended to these without an issue, and all examples in the experiments are based on ADM versions. Since the basic framework of RAD is quite simple and universal, we expect it to work on other similar models as well." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "One limitation of RAD is that the alternate formulation requires fresh training. Even though this is the reason for the superb generation speed compared to the existing SoTA methods, it can also be a deal-breaker considering the amount of resources required in training. This is why the most recent methods attempt to modify only the generation processes of pretrained models, sacrificing the speed. In this paper, we address this issue by utilizing LoRA [14], which can significantly reduce training efforts by leveraging pretrained models. To train RAD based on LoRA, some minor adjustment is required: The spatial noise embedding in RAD can be too drastic of a change for LoRA. Fortunately, the noise schedules for individual pixels are set to match that in DDPM, so we can inverse-map the elements of " + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\bar{b}_t" + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": " to timestep values based on the accumulated noise lev" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": "In fact, the difference resides in " + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t}" + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "inline_equation", + "content": "a_{t},b_{t}" + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\bar{a}_t" + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": " have different values for each element in RAD as shown in (5). This makes a difference in the generation process where " + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta ,t}" + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": " is utilized." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2443" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 143 + ], + "type": "text", + "content": "els in the steps of DDPM. We use linear interpolation in this process, meaning that the mapped timestep values can be non-integral. This has proven to be effective in the experiments, where all the examples are actually fine-tuned by LoRA based on pretrained ADMs. This approach makes RAD much more accessible." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "text", + "content": "In an actual implementation of RAD, singularities in the loss function must be carefully reviewed and avoided. In fact, there is a potential singularity in the variational loss (6), especially in the first step " + }, + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "inline_equation", + "content": "(t = 1)" + }, + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_0|x_1)" + }, + { + "bbox": [ + 55, + 145, + 295, + 300 + ], + "type": "text", + "content": " is prone to becoming degenerate. Even though DDPM uses the simplified loss (7) in practice, which has no singularities, later works such as iDDPM and ADM use both (6) and (7), where the singularities become a problem and are handled by some heuristics. This is an often-overlooked problem that can render training unstable, and for RAD, the issue is a little more complicated because the pixels undergo asynchronous noise schedules. The details are explained in the supplementary material." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 312, + 136, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 136, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 136, + 326 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 332, + 175, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 332, + 175, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 332, + 175, + 344 + ], + "type": "text", + "content": "4.1. Benchmark Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 350, + 295, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 295, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 295, + 387 + ], + "type": "text", + "content": "We validate RAD on the FFHQ [15], LSUN Bedroom [42], and ImageNet [7]. These datasets are well-suited for training and evaluating high-quality image generation models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 387, + 295, + 615 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 56, + 387, + 295, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 387, + 295, + 459 + ], + "spans": [ + { + "bbox": [ + 56, + 387, + 295, + 459 + ], + "type": "text", + "content": "- FFHQ (Flickr-Faces-HQ) [15] contains a total of 70,000 high-resolution (1024x1024) images of human faces. This dataset provides greater diversity than traditional facial image datasets, encompassing a wide range of ages, genders, ethnicities, hairstyles, and accessories (e.g., glasses, hats, etc.). All images were resized to " + }, + { + "bbox": [ + 56, + 387, + 295, + 459 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 56, + 387, + 295, + 459 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 459, + 295, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 459, + 295, + 542 + ], + "spans": [ + { + "bbox": [ + 56, + 459, + 295, + 542 + ], + "type": "text", + "content": "- LSUN Bedroom [42] is a large-scale dataset of indoor scenes, containing over 3M bedroom images. Captured from various angles and perspectives, these images represent complex room structures, enabling algorithms to learn and generate intricate scene layouts. We train RAD with 288K samples of the LSUN Bedroom for convenience. All images were resized to " + }, + { + "bbox": [ + 56, + 459, + 295, + 542 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 56, + 459, + 295, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 543, + 295, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 543, + 295, + 615 + ], + "spans": [ + { + "bbox": [ + 56, + 543, + 295, + 615 + ], + "type": "text", + "content": "- ImageNet [7] is a large-scale image dataset for visual object recognition, containing over 1.2M labeled images across 1,000 categories. This dataset offers extensive diversity, covering a wide range of objects, animals, scenes, and complex visual compositions. All images were resized to " + }, + { + "bbox": [ + 56, + 543, + 295, + 615 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 56, + 543, + 295, + 615 + ], + "type": "text", + "content": " for consistency in our experiments." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 624, + 188, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 188, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 188, + 635 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "content": "Training settings. For all experiments, we set the rank of LoRA [14] to 16 and trained RAD using the Adam optimizer [17] with a learning rate of " + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "content": ". We used a batch size of 16 for both FFHQ and ImageNet, while that was eight for LSUN Bedroom. The total diffusion steps was 2000, with the initial 1000 steps dedicated to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": "Phase 1. We used predefined linear noise schedules for " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "\\beta_{t},\\beta_{t}^{\\prime}\\in (0.0001,0.02)" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": ". During inpainting, we used 100 sampling steps. FFHQ was trained on four TITAN RTX GPUs, LSUN Bedroom on eight NVIDIA 3090 GPUs, and ImageNet on eight NVIDIA RTX 6000 ADA GPUs. Pretrained ADM models [8] were used for all datasets. RAD was trained for " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "300\\mathrm{K}" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": " on FFHQ and LSUN Bedroom, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "700\\mathrm{K}" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": " on ImageNet. ImageNet was trained using an exponential moving average (EMA) with the decay factor set to 0.999." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "text", + "content": "Validation settings. For validation, we set aside 1000 images from all datasets. We evaluated RAD across three types of mask configurations: box, extreme, and wide, following the practice in [34]. A box mask randomly removes a " + }, + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "text", + "content": " square region. In contrast, an extreme mask retains only a specific " + }, + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 313, + 197, + 553, + 317 + ], + "type": "text", + "content": " region, removing all other surrounding areas. A wide mask defines irregular missing regions. For inpainting, we used the reverse process of DDPM rather than DDIM due to its superior quality in generating realistic details." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 323, + 553, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 553, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 553, + 418 + ], + "type": "text", + "content": "Baseline. We chose various inpainting methods based on GANs and diffusion models. For the GAN-based baseline, we used LaMA [34], and for the diffusion-based baselines, we employed RePaint [21], MCG [4], DDRM [16], DDNM [35], and DeqIR [2]. Publicly available pretrained ADM models [8] were used for all methods. Additionally, each method was evaluated using its publicly available codebase to maintain consistency in performance assessment." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 424, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 424, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 424, + 553, + 483 + ], + "type": "text", + "content": "Metrics. To evaluate the performance of the proposed method and compare it with existing approaches, we employed Frechet Inception Distance (FID) [12] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] as the inpainting quality measure." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 492, + 371, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 371, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 371, + 503 + ], + "type": "text", + "content": "4.3. Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 713 + ], + "type": "text", + "content": "Comparisons. Table 1 shows the inpainting performance of various methods. Reported values are either directly quoted from the original papers or computed by us if publicly available pretrained models exist. For LaMa, no pretrained model was available for LSUN Bedroom. Here, RAD achieves the best performance in terms of LPIPS and demonstrates superior FID scores for FFHQ and LSUN Bedroom compared to most baseline methods. Notably, DDNM and DeqIR exhibit relatively weaker performance in our experiments, even though they are relatively newer methods. The main goal of these methods is image restoration, and they are not specifically designed for challenging inpainting scenarios, particularly those involving large missing areas. Consequently, these methods show worse performance under our experimental settings. Figure 4 shows qualitative comparisons on LSUN Bedroom, FFHQ, and ImageNet. Here, all the methods are compared based" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2444" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 102, + 553, + 215 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 555, + 94 + ], + "type": "text", + "content": "Table 1. Performance (FID and LPIPS) on FFHQ and LSUN Bedroom with various mask types. " + }, + { + "bbox": [ + 55, + 71, + 555, + 94 + ], + "type": "inline_equation", + "content": "{}^{ \\dagger }" + }, + { + "bbox": [ + 55, + 71, + 555, + 94 + ], + "type": "text", + "content": " indicates that the value is quoted from the original paper. Bold: best,under: second best." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 102, + 553, + 215 + ], + "lines": [ + { + "bbox": [ + 58, + 102, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 58, + 102, + 553, + 215 + ], + "type": "table", + "html": "
MethodFFHQLSUN BedroomImageNet
BoxExtremeWideBoxExtremeWideBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
LaMa [34]27.7†0.086†61.7†0.492†23.2†0.096†------------
Score-SDE [33]30.3†0.135†48.6†0.488†29.8†0.132†23.70.64824.10.64823.20.64457.20.20086.60.49562.00.183
DDRM [16]28.4†0.109†48.1†0.532†27.5†0.113†20.50.16633.10.45026.40.19074.30.224106.90.49275.10.211
RePAINT [21]25.7†0.093†35.9†0.398†24.2†0.108†20.50.17623.50.46121.40.16154.00.17784.00.47959.00.166
MCG [4]23.7†0.089†30.6†0.366†22.1†0.099†19.90.13122.00.39520.90.10848.10.13258.40.44856.90.124
DDNM [35]30.40.08987.70.35330.40.08922.70.15053.30.43123.20.12663.80.18780.60.47664.50.167
DeqIR [2]24.20.09364.20.36827.40.09922.20.17643.90.46122.00.15366.50.19599.50.50568.40.182
RAD (ours)22.10.07433.40.31721.50.07819.20.13121.60.39920.80.10747.00.11857.80.37456.70.104
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Qualitative comparisons. Colored areas indicate inpainting regions (1st/2nd rows: box, 3rd/4th: extreme, 5th/6th: wide)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 517, + 295, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 295, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 295, + 552 + ], + "type": "text", + "content": "on the same combinations of images and inpainting masks. The results confirm that RAD generally produces more natural images than others and has fewer failure cases." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "text", + "content": "Table 2 shows the inference time of various methods. We evaluated all methods on " + }, + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 552, + 295, + 636 + ], + "type": "text", + "content": " images using a single NVIDIA Titan RTX GPU. Here, RAD is about 100 times faster than RePaint and 15 times faster than MCG while delivering superior performance. Baseline methods other than RePaint and MCG are much faster, but their inpainting quality is significantly worse." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Analysis of diversity. Section 4.3 demonstrates that RAD can generate diverse inpaintings across various mask configurations. Each row in the figure shows the input image with a specific mask, followed by multiple inpainting results (Samples 1 to 4) generated by RAD. These results highlight RAD's ability to produce various plausible and contextually" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 366, + 534, + 502, + 634 + ], + "blocks": [ + { + "bbox": [ + 317, + 515, + 551, + 526 + ], + "lines": [ + { + "bbox": [ + 317, + 515, + 551, + 526 + ], + "spans": [ + { + "bbox": [ + 317, + 515, + 551, + 526 + ], + "type": "text", + "content": "Table 2. Inference time comparison " + }, + { + "bbox": [ + 317, + 515, + 551, + 526 + ], + "type": "inline_equation", + "content": "\\left( {1 \\times \\text{NVIDIA TITAN RTX}}\\right)" + }, + { + "bbox": [ + 317, + 515, + 551, + 526 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 366, + 534, + 502, + 634 + ], + "lines": [ + { + "bbox": [ + 366, + 534, + 502, + 634 + ], + "spans": [ + { + "bbox": [ + 366, + 534, + 502, + 634 + ], + "type": "table", + "html": "
MethodInference time [s]
Score-SDE [33]41.983
DDRM [16]12.291
RePAINT [21]837.136
MCG [4]128.058
DDNM [35]6.566
DeqIR [2]26.443
Ours8.442
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MethodBoxExtremeWide
FID ↓LPIPS ↓FID ↓LPIPS ↓FID ↓LPIPS ↓
Cfg. 1128.30.279172.00.44195.70.240
Cfg. 223.50.08637.00.33326.80.085
RAD (ours)22.10.07433.40.31721.50.078
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Moreover, " + }, + { + "bbox": [ + 55, + 452, + 295, + 559 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 452, + 295, + 559 + ], + "type": "text", + "content": " embedding exhibits inferior performance to spatial noise embedding in RAD, showing the effectiveness of the proposed embedding in inpainting tasks. This conclusion is further supported by qualitative results in Figure 5." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 572, + 130, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 572, + 130, + 585 + ], + "spans": [ + { + "bbox": [ + 55, + 572, + 130, + 585 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 713 + ], + "type": "text", + "content": "A limitation of RAD is that it requires explicit training. The burden of training a diffusion model can be significant, and accordingly, we utilized LoRA to mitigate this issue greatly. Additionally, RAD is trained using a spatially variant noise schedule defined based on masks, making it dependent on the mask distribution. Perlin masks proposed in this paper are effective enough to handle most inpainting scenarios. However, there is a possibility that RePaint or MCG might yield better results in drastic cases even though they take much longer inference time." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 343, + 69, + 525, + 219 + ], + "blocks": [ + { + "bbox": [ + 343, + 69, + 525, + 219 + ], + "lines": [ + { + "bbox": [ + 343, + 69, + 525, + 219 + ], + "spans": [ + { + "bbox": [ + 343, + 69, + 525, + 219 + ], + "type": "image", + "image_path": "68c95cdd20fa2e1e7bcdfd56c8962db2999010a4b6446c668cedf96b8f2e3017.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 229, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 251 + ], + "type": "text", + "content": "Figure 5. Ablation study examples on FFHQ (Cfg. 1: pretrained ADM with RAD reverse steps, Cfg. 2: w/o spatial noise emb.)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 270, + 388, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 270, + 388, + 282 + ], + "spans": [ + { + "bbox": [ + 314, + 270, + 388, + 282 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 293, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 555, + 461 + ], + "type": "text", + "content": "We presented a novel inpainting model, RAD, which utilizes a spatially variant noise schedule to allow asynchronous generation of different regions. RAD handles inpainting by selectively adding noise to the regions specified by a given mask, followed by denoising those areas. This approach enables the selective generation of masked regions while preserving the others. The Perlin noise-based mask generation technique has been presented to generate realistic masks during training. Additionally, we proposed spatial noise embedding, significantly enhancing inpainting quality compared to conventional " + }, + { + "bbox": [ + 313, + 293, + 555, + 461 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 293, + 555, + 461 + ], + "type": "text", + "content": " embedding. RAD can perform seamless inpainting without any additional module, and a plain reverse process is sufficient to produce high-quality results with orders of magnitude faster sampling speed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 463, + 556, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 556, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 556, + 571 + ], + "type": "text", + "content": "While RAD is mainly described in the context of inpainting, the overall framework has broader implications. By extending the pseudo-targets of diffusion models (the denoising distributions) to spatially variant distributions, RAD offers more means to analyze and manipulate spatial interactions in diffusion models, opening interesting future research directions. Combining RAD with conditions such as text will extend the framework to image editing, a direction for future work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 591, + 411, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 591, + 411, + 605 + ], + "spans": [ + { + "bbox": [ + 314, + 591, + 411, + 605 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 613, + 556, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 556, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 556, + 704 + ], + "type": "text", + "content": "This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.RS-2022-00155885, Artificial Intelligence Convergence Innovation Human Resources Development (Hanyang University ERICA)) and partly by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2023-NR076576)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2446" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "text", + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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A task is worth one word: Learning with task prompts for high-quality versatile image inpainting. arXiv preprint arXiv:2312.03594, 2023. 2, 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2448" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_content_list.json b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..706388e41f2802191f3d4d4a9960925aa8cd816d --- /dev/null +++ b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_content_list.json @@ -0,0 +1,1781 @@ +[ + { + "type": "text", + "text": "RAEncoder: A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection", + "text_level": 1, + "bbox": [ + 130, + 128, + 867, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fan Xing, Zhuo Tian, Xuefeng Fan, Xiaoyi Zhou* Hainan University", + "bbox": [ + 297, + 203, + 696, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{xingfan, tianzhuo, xffan, xy.zhou}@hainanu.edu.cn", + "bbox": [ + 274, + 241, + 718, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reversible Adversarial Examples (RAE) are designed to protect the intellectual property of datasets. Such examples can function as imperceptible adversarial examples to erode the model performance of unauthorized users while allowing authorized users to remove the adversarial perturbations and recover the original samples for normal model training. With the rise of Self-Supervised Learning (SSL), an increasing number of unlabeled datasets and pre-trained encoders are available in the community. However, existing RAE methods not only rely on well-labeled datasets for training Supervised Learning (SL) models but also exhibit poor adversarial transferability when attacking SSL pre-trained encoders. To address these challenges, we propose RAEncoder, the first framework for RAEs without the need for labeled samples. RAEncoder aims to generate universal adversarial perturbations by targeting SSL pretrained encoders. Unlike traditional RAE approaches, the pre-trained encoder outputs the feature distribution of the protected dataset rather than classification labels, enhancing both the attack success rate and transferability of RAEs. Extensive experiments are conducted on six pre-trained encoders and four SL models, covering aspects such as imperceptibility and transferability. Our results demonstrate that RAEncoder effectively protects unlabeled datasets from malicious infringements. Additional robustness experiments further confirm the security of RAEncoder in practical application scenarios.", + "bbox": [ + 91, + 325, + 480, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 767, + 220, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reversible Adversarial Examples (RAE) [20, 31-34, 37, 38, 41] are highlighted as a fundamental method for protecting dataset Intellectual Property (IP). Unlike traditional methods for dataset IP protection, such as reversible watermarking [10, 19, 42] and image encryption techniques [11, 35], RAE transforms the dataset into adversarial examples that can mislead model training while allowing authorized users", + "bbox": [ + 89, + 794, + 480, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to remove the adversarial perturbations and restore the original dataset [20]. The adversarial attack methods used in existing RAE schemes focus on targeting specific Supervised Learning (SL) classifiers through optimization-based or gradient-based attacks, which result in a notable limitation: they lose adversarial strength when attacking different model architectures, and the adversarial strength diminishes especially when attacking downstream models trained with Self-Supervised Learning (SSL) pre-trained encoders.", + "bbox": [ + 511, + 292, + 903, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SSL is an emerging paradigm in machine learning. It typically involves pre-training a generic encoder on vast amounts of unlabeled data, and it can then serve as a feature extractor for a wide range of downstream tasks. By utilizing a pre-trained encoder, any resource-constrained user can leverage the advantages of a large model without the need to undertake expensive training from scratch. Considering SSL for RAEs is highly noteworthy because if RAEs exhibit poor transferability when attacking SSL pre-trained encoders, any attacker can leverage them to pre-process RAEs, thereby mitigating the impact of them on the training performance of unauthorized downstream models.", + "bbox": [ + 511, + 430, + 903, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the fact that SSL pre-trained encoders learn feature representations of the data directly rather than feature-label relationships, adversarial attacks against SSL pre-encoders can exhibit excellent transferability across different downstream model architectures [43, 44]. Although this attack process demonstrates significant effectiveness, using it as a method to generate RAEs for protecting dataset IP introduces an additional challenge. Specifically, the protection scheme must address the worst-case scenario—adaptive attacks, where the attacker is assumed to be aware of the detailed steps of the protection scheme [32]. This requires the protection scheme to effectively differentiate between authorized and unauthorized access. To differentiate between authorized and unauthorized users, existing Reversible Data Hiding (RDH)-based RAE methods embed encrypted information in RAEs, ensuring that only users with the correct key can recover original samples. However, embedding any information within RAEs could significantly impact both adversarial strength and vi", + "bbox": [ + 511, + 613, + 903, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20665", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sual quality[20, 31, 32]. Then, without embedding information, how can RAEs be designed to differentiate user authorization and ensure both effectiveness and robustness when attacking SSL encoders?", + "bbox": [ + 89, + 90, + 482, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To bridge the gap between the practical applicability of RAE and real-world needs in the context of SSL's growing popularity, we propose a novel approach, RAEncoder. To be specific, we design a noise encoder with a fixed signature noise as input. It learns the data distribution and generates universal adversarial perturbations by targeting SSL encoder. To effectively differentiate between authorized and unauthorized users, an interference pattern is designed to make the noise encoder insensitive to inputs other than the correct signature noise. By inputting the correct signature noise, authorized users can employ the noise encoder to obtain the recovered perturbation, thereby recovering the original sample. During noise encoder training, we employ high-frequency filters [21, 44] to optimize RAE imperceptibility, as high-frequency perturbations are less detectable than low-frequency ones.", + "bbox": [ + 89, + 152, + 483, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to the existing work, our contributions are as follows:", + "bbox": [ + 89, + 395, + 483, + 422 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A Novel RAEncoder Framework: We introduce RAEncoder to address the limitations of existing RAE frameworks in the context of the growing popularity of SSL. To the best of our knowledge, RAEncoder is the first RAE framework applicable for protecting the IP of unlabeled datasets with $100\\%$ fidelity.", + "- Innovative Noise Encoder: A noise encoder capable of generating RAEs guided by sample texture features is devised to successfully balance imperceptibility with adversarial strength. Additionally, we introduce three losses in the interference pattern to guide adversarial attacks on SSL pre-encoders, ensuring the RAE's robustness.", + "- Extensive Experimental Validation: Through extensive experiments, we compare our RAEncoder with state-of-the-art (SOTA) RAE schemes. The results demonstrate that our RAEncoder outperforms existing methods in various metrics, including imperceptibility, adversarial strength, and transferability." + ], + "bbox": [ + 91, + 426, + 483, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 715, + 232, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. SSL and Its Emerging Threats", + "text_level": 1, + "bbox": [ + 89, + 741, + 362, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SSL uses the inherent information present in unlabeled data to pre-train encoders. These encoders learn to transform complex inputs into generic representations. Once trained, they can extract valuable domain knowledge and serve as versatile tools for solving different specific tasks. With the thriving development of SSL, pre-trained encoders have gained popularity in the industry. Many service providers openly release their pre-trained encoders, such as Google's BYOL [12] and Meta's MoCo [6, 14]. Recently, an increas", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing number of studies begin to investigate adversarial attacks against pre-trained encoders in SSL. Zhou et al. proposed the first attack framework that generates downstream-agnostic adversarial examples based on a cross-modal pretrained encoder for images and text [43]. Zhou et al. proposed the first scheme for generating universal adversarial examples based on pre-trained encoders[44].", + "bbox": [ + 511, + 90, + 905, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Reversible Adversarial Examples", + "text_level": 1, + "bbox": [ + 511, + 205, + 805, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing RAE schemes can be divided into two categories, RDH-based methods[20, 31-34, 37] and generative methods [38, 41], as shown in Figure 1. To generate adversarial examples, recent research endeavors utilize a range of adversarial attacks targeting SL classifier, such as IFGSM[18], DeepFool[23], and C&W[1].", + "bbox": [ + 511, + 227, + 905, + 319 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/315409910f657af6bffe8565f0437ce6e5ed3025234e3a6731932b8cb8d71a85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 330, + 792, + 477 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/56235690c3767c1c604bcb0dc8d61e2b10773c7a2d7c2d34bf8b4e7b212a08d7.jpg", + "image_caption": [ + "Figure 1. Existing methods can be divided into two categories: generative and RDH-based. Our method not only eliminates reliance on classifiers for adversarial attacks but also achieves $100\\%$ fidelity without compromising adversarial strength." + ], + "image_footnote": [], + "bbox": [ + 522, + 477, + 792, + 573 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fef59caab8009d77c7b49ccd92e197d582c9a461924a2d3ff3279eacfae20567.jpg", + "image_caption": [], + "image_footnote": [ + "X' Original sample \n $X'$ Adversarial example \n $X^p$ Protected sample \n $X^r$ Recovered sample \n $\\square$ Classifier \n $\\mathrm{ms}$ Auxiliary Information \n $\\ominus$ Element-wise Subtraction \n $\\oplus$ Element-wise Addition" + ], + "bbox": [ + 792, + 330, + 898, + 497 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given that images contain inherent structures that allow adversarial attacks to be reversed [22], the concept of RAE was first introduced [20] and proposed the first RAE generation method based on RDH technology. Their approach involves embedding the pixel differences between adversarial examples and the original image into the image using RDH, allowing authorized users to achieve $100\\%$ recovery of original samples by extracting the pixel differences. However, this method still has several issues, such as the deterioration of the visual quality of adversarial samples and a reduction in adversarial strength due to embedding information. Thus, reducing the embedded perturbation amount in RAE is a feasible approach. Yin et al. confined perturbations to regions most impactful on adversarial strength[34]. They leveraged the characteristic of the YUV color space, where the human eye is less sensitive to changes in the UV", + "bbox": [ + 511, + 659, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20666", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "channels, by embedding the perturbation differences of the Y channel into the UV channels. Zhang et al. leveraged beam search-based black-box attacks in combination with reversible data hiding featuring grayscale invariance[37]. Xiong et al. proposed PGN, which reduces adversarial perturbations to a sign matrix format and a product with fixed perturbation parameters[31]. Therefore, PGN only needs to record the sign matrix corresponding to pixel differences and embed it with the fixed perturbation parameters, significantly reducing the amount of embedding required. Meanwhile, existing work combined Reversible Image Transformation (RIT)[40] with RDH which involves embedding the reversible transformation information between the original sample and the adversarial example, rather than pixel differences, into the RAEs[32, 33].", + "bbox": [ + 89, + 90, + 483, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the field of generative methods, SRAE [38] developed RAEs using a recoverable generative adversarial network designed to minimize recovery errors while maximizing their effectiveness in adversarial attacks. GEAA [41] utilizes a dual-stream architecture to generate adversarial and recovered samples, ensuring that the distribution of adversarial samples significantly differs from the original.", + "bbox": [ + 89, + 316, + 483, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, RDH-based methods preserve the inverse operation that restores adversarial examples to the original samples, allowing most RDH-based methods to achieve $100\\%$ sample recovery. While generative methods cannot currently achieve $100\\%$ recovery, they do not require any information embedding that might affect adversarial strength. As a result, generative methods exhibit significantly higher adversarial strength compared to RDH-based methods.", + "bbox": [ + 89, + 422, + 483, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is noteworthy that existing work generates RAEs by targeting supervised learning models for adversarial attacks, without addressing the new challenges posed by the popularity of SSL. Consequently, existing RAE solutions are unable to effectively protect unlabeled datasets.", + "bbox": [ + 89, + 544, + 483, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 89, + 633, + 225, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 89, + 657, + 272, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a pre-trained encoder $e_{\\theta}(\\cdot)$ with input $x_{pt}$ in $\\mathcal{D}_{pt}$ , where $\\theta$ represents the parameters of the pre-trained encoder. $\\mathcal{D}_{pt}$ denotes the pre-training dataset. The data owner uses the original sample $x$ in original dataset $\\mathcal{D}$ (remains unattainable for the attacker) to generate universal adversarial perturbation $\\delta$ against the pre-trained encoder. The universal adversarial perturbation $\\delta$ should be sufficiently small and modeled by an upper-bound $\\epsilon$ on the $l_{p}$ norm. The task of finding a perturbation can be formulated as:", + "bbox": [ + 89, + 679, + 483, + 815 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ne _ {\\theta} (x + \\delta) \\neq e _ {\\theta} (x), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 827, + 482, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $||\\cdot ||_p$ is the $l_{p}$ norm.", + "bbox": [ + 89, + 854, + 274, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The data owner's objective is to achieve a universal nontargeted attack to deceive the downstream classifier $f_{\\theta'}$ .", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, the data owner's objective can be formalized as:", + "bbox": [ + 513, + 90, + 903, + 106 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x + \\delta)\\right) \\neq f _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x)\\right), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 132, + 903, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When all original samples $x$ in original dataset $\\mathcal{D}$ are augmented with a universal adversarial perturbation $\\delta$ , it results in a protected dataset $\\mathcal{D}_p$ composed of protected samples (i.e., reversible adversarial examples) $x^p$ . The $\\mathcal{D}_p$ is used as a reference for all users. We assume that any users have access to public pre-trained encoders $e_{\\theta}^{pub}(\\cdot)$ with input $x^{pub}$ in the public dataset $\\mathcal{D}^{pub}$ , which they can obtain through purchase or direct download from public repositories.", + "bbox": [ + 511, + 159, + 906, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The attackers' objective is to encode protected datasets $\\mathcal{D}_p$ using $e_{\\theta}^{pub}(\\cdot)$ to minimize the impact of $\\mathcal{D}_p$ on training performance and then training downstream classifier $f_{\\theta}^{atk}(e_{\\theta}^{pub}(\\cdot))$ . However, as shown in Figure 2, $x^p \\in \\mathcal{D}_p$ is incorrectly encoded into other feature distributions, resulting in a significant degradation in the performance of the obtained downstream classifier which can be formalized as:", + "bbox": [ + 511, + 281, + 905, + 385 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {p}\\right)\\right)\\right) \\ll \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 398, + 903, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{A}(\\cdot)$ denotes the inference accuracy for a classifier.", + "bbox": [ + 511, + 422, + 895, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For authorized users, they can obtain recovered samples $x^{r} \\in \\mathcal{D}_{r}$ which closely resemble the feature distribution of $x$ for normal downstream task training that can be formalized as:", + "bbox": [ + 511, + 438, + 905, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {r}\\right)\\right)\\right) \\approx \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 496, + 903, + 515 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cb1897138eeb6b450cb0e7c393a9aee930f6243b3f8d92cf05375cf680013732.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 519, + 534, + 707, + 608 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1e40f8c8a3556be18f8171fecf431afc6cc4634a4b05a69a6b5bad2d643379f7.jpg", + "image_caption": [ + "(b)", + "Figure 2. Illustrations of sample attributes: (a) The representation of different samples in the feature space. The dashed lines in different colors represent feature representations of various distributions (b) The fit of different samples within the classification decision boundary. The curved lines in different colors indicate the decision boundaries for different classes." + ], + "image_footnote": [], + "bbox": [ + 709, + 535, + 900, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Training Pipeline", + "text_level": 1, + "bbox": [ + 511, + 742, + 684, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The training pipeline of RAEncoder is illustrated in Figure 3. It consists of a noise encoder $E$ , a high-frequency filter $\\mathcal{H}$ , and a target encoder $e_{\\theta}$ . Specifically, we generate a universal adversarial perturbation $\\delta$ applicable to all $x$ in $D$ by inputting a fixed signature noise $S$ into noise encoder $E$ . We then paste $\\delta$ to $x$ to obtain protected sample $x^{p}$ in $D_{p}$ , where high-frequency information of $x^{p}$ is reduced by high-frequency filter $\\mathcal{H}$ . Authorized users can input the signature noise $S$ into the noise encoder $E$ to obtain $\\delta$ . Subtracting $\\delta$", + "bbox": [ + 511, + 763, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20667", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from $x^p$ results in a fully recovered sample $x^r$ identical to the original $x$ , which is achieved for the first time in the previous RAE schemes. During the training process of noise encoder $E$ , we propose an interference pattern to incentivize $E$ to distinguish signature noise $S$ from other noise inputs, aiming to prevent potential attackers from inputting random noise to steal $\\delta$ for image restoration.", + "bbox": [ + 89, + 90, + 483, + 196 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b91bc0be9de2dad9f2c3184a012ad15bd6c207357abc8a6ae035f534431d7868.jpg", + "image_caption": [ + "Figure 3. The training pipeline of RAEncoder." + ], + "image_footnote": [], + "bbox": [ + 98, + 210, + 475, + 371 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1. Noise Encoder.", + "text_level": 1, + "bbox": [ + 89, + 421, + 241, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The noise encoder $E$ takes a fixed input $S$ , designated for different authorized users, to generate a universal adversarial perturbation $\\delta$ , given by:", + "bbox": [ + 89, + 439, + 483, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE (\\mathcal {S}) = \\delta . \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 250, + 498, + 482, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Applying $\\delta$ to original samples $x$ yields $x^p$ . The difference between $x^p$ and $\\delta$ represents the original sample $x$ which can be described as:", + "bbox": [ + 89, + 526, + 483, + 571 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta + x = x ^ {p} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 246, + 585, + 482, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When authorized users want to recover samples, they only need to input their exclusive $S$ into $E$ to obtain $\\delta$ , and original samples can be restored by subtracting $\\delta$ which can be described as:", + "bbox": [ + 89, + 613, + 483, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {r} = x ^ {p} - \\delta = x \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 674, + 480, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss function for optimizing noise encoder $E$ can be described as:", + "bbox": [ + 89, + 696, + 483, + 726 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E} = \\alpha \\mathcal {L} _ {E. a d v} + \\beta \\mathcal {L} _ {E. \\mathcal {H}} + \\lambda \\mathcal {L} _ {E. m s e}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 739, + 482, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 89, + 768, + 137, + 781 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 792, + 482, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E. \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p}\\right) - \\mathcal {H} (x) | | _ {2} ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 844, + 482, + 862 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E \\_ m s e} = | | x ^ {p} - x | | _ {2} ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 883, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\| \\cdot \\| _2$ is the $l_{2}$ norm, $\\langle u\\cdot c\\rangle = u^{\\mathsf{T}}c / \\| u\\| \\| c\\|$ represents the cosine similarity. $i$ represents the $i$ -th sample, with a maximum value of $N$ , while $k$ represents a number not equal to $i$ . $\\tau$ indicates a temperature parameter. $\\mathcal{L}_{E\\_adv}$ drives noise encoder to perform negative pairing between the protected sample $x^{p}$ and $x$ , maximizing the mutual information distance between their features in the feature space by calculating the InfoNCE loss[4, 24]. $\\mathcal{L}_{E\\_H}$ aims to constrain the perturbation intensity in high frequency through the high-frequency filter $\\mathcal{H}$ . $\\mathcal{L}_{E\\_mse}$ aims to make sure the indistinguishability between $x^{p}$ and $x$ .", + "bbox": [ + 511, + 90, + 906, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bb650a516585cc20bc88ed87cb1fe3c3d935a17a0837a9a3da2d97f5d7e3f83d.jpg", + "image_caption": [ + "Figure 4. Visual results of original samples different samples generated from noise encoder without interference pattern employed." + ], + "image_footnote": [], + "bbox": [ + 517, + 267, + 898, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2. Interference Pattern.", + "text_level": 1, + "bbox": [ + 511, + 444, + 705, + 457 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training and optimizing $E$ enables the generation of a highly adversarial universal perturbation $\\delta$ , significantly affecting the model training effectiveness for unauthorized users. However, we discover that guiding the noise encoder $E$ to solely learn the generation of a universal adversarial perturbation $\\delta$ from signature noise $S$ without constraints can lead to vulnerabilities. In the event that the noise encoder $E$ is compromised by attackers, they can potentially acquire a perturbation similar to $\\delta$ for image recovery by feeding noise of the same size as $S$ into the noise encoder $E$ . While the likelihood of the noise encoder $E$ being compromised, particularly when stored in cloud services such as DMCP[32], is minimal in practical scenarios, such an outcome remains unacceptable in cases where the noise encoder $E$ cannot distinguish between inputs from authorized users and attackers. As shown in Figure 4, the images shown in the third column are obtained by subtracting the output of noise encoder $E$ when the protected sample $x^p$ and random noise of the same size as signature noise $S$ are inputted. It can be observed that these samples are very similar to the original images, which completely undermines the security of RAEs. Therefore, an interference pattern is exploited to resolve this problem. The idea is simple: when applying random noise $S' \\neq S$ , noise encoder $E$ should not generate perturbation $\\delta$ , but instead generate an almost blank perturbation $\\delta'$ with hardly any pixel values. The subtraction of perturbation $\\delta'$ from $x^p$ yields $x^{p'}$ which can be described as:", + "bbox": [ + 511, + 463, + 908, + 883 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE \\left(\\mathcal {S} ^ {\\prime}\\right) = \\delta^ {\\prime}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 666, + 883, + 903, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20668", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {p} - \\delta^ {\\prime} = x ^ {p ^ {\\prime}} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 236, + 104, + 480, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, the loss function for optimizing noise encoder E with interference pattern can be described as:", + "bbox": [ + 89, + 126, + 483, + 157 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E \\mathcal {I}} = n \\mathcal {L} _ {I. a d v} + m \\mathcal {L} _ {I. \\mathcal {H}} + \\gamma \\mathcal {L} _ {I. m s e} + \\mathcal {L} _ {E}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 180, + 483, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 224, + 482, + 263 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p ^ {\\prime}}\\right) - \\mathcal {H} \\left(x ^ {p}\\right) | | _ {2} ^ {2}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 272, + 483, + 292 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I. m s e} = \\left\\| x ^ {p} - x ^ {p ^ {\\prime}} \\right\\| _ {2} ^ {2}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 306, + 482, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{I\\_adv}, \\mathcal{L}_{I\\_H}$ and $\\mathcal{L}_{I\\_mse}$ are employed to minimize $\\delta'$ generated from random noise $S'$ towards zero as much as possible.", + "bbox": [ + 89, + 330, + 483, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 387, + 223, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 89, + 411, + 290, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1. Datasets and Models.", + "text_level": 1, + "bbox": [ + 89, + 434, + 284, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilize pre-trained encoders from the solo-learn [8], a well-established self-supervised learning library, as target encoders. These pre-trained encoders were trained on CIFAR10 [17] or ImageNet [25] datasets, employing ResNet18 [13] as the backbone. Among the array of SSL techniques available, we select six pioneering methods: Barlow Twins [36], BYOL [12], DeepCluster v2 [2], DINO [3], MoCo v2+ [5], and NNCLR [9]. We train VGG16[26], ResNet18, Resnet50[13], and DenseNet121[15] as target models. The datasets STL10 [7], GTSRB [28], CIFAR10, and ImageNet were considered as the protected datasets.", + "bbox": [ + 89, + 453, + 483, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2. Training configurations.", + "text_level": 1, + "bbox": [ + 89, + 625, + 303, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The noise encoder consists of multiple consecutive deconvolution layers followed by a convolutional layer. The hyperparameters settings for optimizing the noise encoder $E$ are as follows: $n = \\alpha = 5$ , $m = \\beta = 1$ , $\\gamma = \\lambda = 1$ and $\\varepsilon = 10/255$ , training epochs set to 20 and Adam optimizer [16] is adopted with an initial learning rate of 0.0002. For RDH-based method [32], PGN, and generative method GEAA, SRAE, all experiments conducted were based on their default settings as reported in their respective studies. Since they are not designed for adversarial attacks on pre-trained encoders, for a fair comparison to highlight the advantages of RAEncoder, we connect their target model's classification head to an encoder trained on the same pre-training dataset. Thus, the target model serves as a downstream model connected to the pre-trained encoder. Our experiments are conducted on two NVIDIA GeForce RTX 4090 GPUs.", + "bbox": [ + 89, + 643, + 483, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.3. Evaluation Metrics.", + "text_level": 1, + "bbox": [ + 513, + 90, + 696, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ Structural Similarity Index (SSIM) [30] and Peak Signal-to-Noise Ratio (PSNR) to assess the quality of image. We use Attack Success Rate (ASR) to measure the success rate of samples that deceive the classifier. A higher numerical value indicates stronger attack capability.", + "bbox": [ + 511, + 112, + 906, + 188 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Attack Performance", + "text_level": 1, + "bbox": [ + 513, + 205, + 705, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ six types of SSL pre-trained encoders as target encoders $e_{\\theta}$ . Using two pre-training datasets, CIFAR10 and ImageNet, we generate $x^{p}$ for four downstream datasets and evaluated ASR of $x^{p}$ on the corresponding target encoders. It is worth noting that such experimental setups are deployed to investigate whether the RAEs generated by the RAEncoder possess strong adversarial strength to successfully deceive target encoders. As shown in Table 1, across", + "bbox": [ + 511, + 229, + 906, + 351 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5c480b99f78be208ddc25b557ae3bdee1035b5d020052d72438a1ae07d8e2124.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Different configurations of protected samples' ASR (\\%) are evaluated. $\\mathcal{C}_1 - \\mathcal{C}_4$ represent the downstream datasets CIFAR10, STL10, GTSRB, and ImageNet, respectively, with the encoder's pre-training dataset being CIFAR10. $\\mathcal{I}_1 - \\mathcal{I}_4$ use ImageNet as the pre-training dataset, and the downstream datasets are the same as those in $\\mathcal{C}_1 - \\mathcal{C}_4$ . Barlow Twins and DeepCluster v2 are abbreviated as Barlow and DeepC2, respectively." + ], + "table_body": "
BallowBYOLDeepC2DINOMoCo2+NNCLR
C185.8389.6482.0083.7751.7179.23
C242.5853.4442.9459.0429.3346.89
C381.5288.0781.0680.9370.2581.39
C488.9684.2082.2483.3674.6481.68
I187.6784.8384.7086.5189.1087.77
I266.7660.8468.3366.1863.6163.18
I382.3081.4377.4280.6284.5983.47
I498.9798.9799.0298.9698.9998.96
", + "bbox": [ + 519, + 368, + 901, + 502 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the settings of six pre-trained encoders and four downstream datasets, the ASR of protected samples remains consistently high, with over $80\\%$ achieved in almost all settings. Meanwhile, it is evident that protected samples generated by pretrained encoders trained on corresponding original samples exhibit stronger adversarial attack strength. For example, When the pre-trained dataset is ImageNet and the downstream dataset is also ImageNet, the protected dataset generated by RAEncoder achieved an ASR close to $100\\%$ when attacking encoders pre-trained on ImageNet.", + "bbox": [ + 511, + 632, + 906, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 800, + 666, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we investigate the impact of using different datasets, modules, and attack intensities on RAEncoder when generating the protected dataset. We opt for pretrained encoders on CIFAR10 and select CIFAR10 as the protected dataset for our analysis.", + "bbox": [ + 511, + 824, + 905, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20669", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Effect of Interference Pattern We investigate the impact of the interference pattern. Specifically, as shown in Figure 5a, we examine the cases where noise encoders were deployed with and without the interference pattern, and subjected to random noise inputs to simulate attacks where adversaries aim to steal correct adversarial perturbations $\\delta$ , using random noise attacks. The results depicted in Figure 5a reveal that for noise encoders without interference pattern guidance, the attacked dataset obtained after being subjected to adversaries' random noise attacks has already lost its adversarial strength. However, noise encoders guided by the interference pattern exhibit robust adversarial strength even after undergoing attacks.", + "bbox": [ + 89, + 90, + 483, + 287 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bb35692ba1ef07aa74a9c77f41cc3ed24d77cef9038684b11831782724d4c5ee.jpg", + "image_caption": [ + "Figure 5. Ablation study results of different settings. (a) Impact of deploying the interference pattern on the ASR (\\%) of the protected dataset and attacked dataset generated by the noise encoder. (b) The impact of different upper-bounds on attack performance and visual quality." + ], + "image_footnote": [], + "bbox": [ + 98, + 300, + 285, + 383 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/087444724fdc10f7a26ddb33e0da5d52c5251f5c120cf2af7749795067a183ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 301, + 475, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Effect of $\\epsilon$ We investigate the impact of four different perturbation upper-bounds $\\epsilon$ on the attack performance and visual quality of protected samples. As shown in Figure 5b, different upper bounds influence both the attack performance and visual quality.", + "bbox": [ + 89, + 501, + 483, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Weights of Losses This experiment aims to study the mechanism of our method. From Eq. 9 to 17, we design six losses to train the noise encoder. As our target is to attack pre-trained encoder, the $\\mathcal{L}_{E\\_adv}$ is necessary, and we set its weight to 5 which is the default value as validated in [44].", + "bbox": [ + 89, + 597, + 482, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To more intuitively assess imperceptibility, we introduced a new metric: Learned Perceptual Image Patch Similarity (LPIPS) [39] to evaluate the visual quality of the protected dataset. In contrast to SSIM and PSNR, LPIPS utilizes deep networks and is specifically designed to mimic human perception in image evaluation tasks. A higher LPIPS value indicates that the differences between images are more perceptible to human perception. Table 2 displays results from ablation experiments of $\\mathcal{L}_{E\\cdot \\mathcal{H}}$ and $\\mathcal{L}_{E.mse}$ , demonstrating their importance in enhancing the imperceptibility of adversarial samples.", + "bbox": [ + 89, + 674, + 482, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To better evaluate the importance of the interference pattern, we conduct an ablation study on the values of the three losses introduced in the interference pattern: $\\mathcal{L}_{I\\_adv}$ , $\\mathcal{L}_{I\\_H}$ , and $\\mathcal{L}_{I\\_mse}$ . Specifically, we evaluate the performance of", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a60cf64fcce243d729d53b6619bf3188dddec09b40ea83c03c2dff4eb1aea959.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
L_E_mseL_E_HSSIMPSNRLPIPS
✓X0.8028.220.194
X✓0.8228.240.165
✓✓0.8528.260.148
", + "bbox": [ + 589, + 88, + 834, + 159 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the protected dataset and the attacked dataset, recovered by the attacker using erroneous signature noise inputs to the noise encoder. We denote the ratio of the weights of $\\mathcal{L}_{I\\_adv}$ , $\\mathcal{L}_{I\\_H}$ , and $\\mathcal{L}_{I\\_mse}$ to $\\mathcal{L}_{E\\_adv}$ , $\\mathcal{L}_{E\\_H}$ , and $\\mathcal{L}_{E\\_mse}$ as $\\phi$ , where $n: \\alpha = m: \\beta = \\gamma: \\lambda = \\phi$ . By controlling the value of $\\phi$ , we can adjust the importance of the interference pattern in the learning process of the noise encoder. As shown in Table 3, when $\\phi = 0.5$ , the noise encoder's sensitivity to the interference pattern is reduced, leading to a decrease in $ASR_{Attacked}$ , although the reduction is not substantial. Conversely, when $\\phi = 2$ , the noise encoder focuses more on learning the interference pattern, which increases the $ASR_{Attacked}$ but results in a reduced performance on the protected dataset. Thus, the weight of $\\mathcal{L}_{I\\_adv}$ , $\\mathcal{L}_{I\\_H}$ and $\\mathcal{L}_{I\\_mse}$ used to control the effect of the interference pattern are set to the same value as $\\mathcal{L}_E$ to ensure that the learning of interference patterns is as important as the learning of normal patterns.", + "bbox": [ + 511, + 207, + 906, + 479 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4036617c85bff227abc1880973da1e62b568acf73b085fd12bc510b19ff08614.jpg", + "table_caption": [ + "Table 2. The effect of ${\\mathcal{L}}_{E.mse}$ and ${\\mathcal{L}}_{E\\mathcal{H}}$ on imperceptibility." + ], + "table_footnote": [], + "table_body": "
φASRProtectedASRAttackedSSIMPSNR
0.585.4784.500.8228.22
1(Default)85.8386.110.8528.26
282.1389.500.7626.32
", + "bbox": [ + 519, + 489, + 901, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. The effect of $\\phi$ on interference pattern.", + "bbox": [ + 566, + 569, + 851, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Visualization Results", + "text_level": 1, + "bbox": [ + 511, + 606, + 710, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare the visual quality of protected and recovered samples generated by RAEncoder and existing methods. As shown in Figure 6, under conditions where the adversarial strength is superior, the protected samples produced by RAEncoder still maintain superior imperceptibility when compared to those generated by SRAE. As shown in Table 4, on CIFAR10, the protected dataset generated by RAEncoder achieves higher SSIM and PSNR values compared to the existing RDH-based method by [32] and the generative methods GEAA and SRAE. On ImageNet, the protected dataset generated by RAEncoder outperforms those by [32] and SRAE but is slightly weaker than PGN. However, PGN's visual quality cannot guarantee its adversarial strength which is explained in Section 4.5. Overall, RAEncoder demonstrates its superior imperceptibility, and the recovered dataset obtained through RAEncoder is identical to the original dataset. Importantly, these results are achieved without the need for an additional classification", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20670", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "head, but rather through direct utilization of a pre-trained encoder for the attack.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/485bd38169db6f6def17d5642ffe13a0a044cb504c205173505c7ed30b40cb26.jpg", + "image_caption": [ + "Figure 6. Visualization of the comparison between protected samples and recovered samples generated by our method and SRAE. Best viewed in zoom." + ], + "image_footnote": [], + "bbox": [ + 98, + 132, + 478, + 349 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7d951a4a652ff8074c5eff9af5f0b36c9cdbefe10396b7dd7fc1204aac0de195.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetMethodProtectedRecovered
SSIMPSNRSSIMPSNR
CIFAR10Xue et al. [32]0.7725.760.9956.36
GEAA [41]0.3227.910.9948.11
SRAE[38]0.4214.730.7627.67
Ours0.8528.261.00∞
ImageNetXue et al. [32]0.5820.470.9850.15
PGN [31]0.9434.231.00∞
SRAE[38]0.7627.670.9738.67
Ours0.8230.261.00∞
", + "bbox": [ + 98, + 431, + 478, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Visual performance comparison of protected and recovered datasets from our method and existing methods.", + "bbox": [ + 89, + 590, + 482, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Transferability Study", + "text_level": 1, + "bbox": [ + 89, + 650, + 292, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we delve into the transferability of the RAEncoder from two distinct perspectives: attacks on downstream models trained with different pre-trained encoders, and attacks on various SL models with different network architectures. The downstream models used to evaluate transferability are trained on the corresponding pre-trained datasets of BYOL. The target SL model employed for [32], PGN and SRAE to generate the CIFAR10 protected dataset is ResNet18 and for ImageNet is ResNet50. High ASR is indicative of better adversarial strength and transferability. As shown in Table 5, the protected dataset generated by RAEncoder exhibits strong adversarial strength across various datasets, different SL models, and diverse pre-trained encoder configurations, resulting in significantly high ASR. Furthermore, its transferabil", + "bbox": [ + 88, + 672, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ity across various SL models and pre-trained encoders frequently surpasses existing methods. However, while [32], PGN and SRAE demonstrate equally outstanding transferability across SL models, their ASR dramatically decreases when applied to downstream models trained by pre-trained encoders. It is noteworthy that, when applied to the CIFAR10 dataset, the ASR of SRAE is marginally higher than that of RAEncoder. However, as indicated in the Table 4, this increase in ASR is attained at the expense of image quality. Based on the results presented in Section 4.4 and Table 5, it is evident that our proposed RAEncoder effectively maintains the imperceptibility of protected samples while achieving a high level of adversarial strength.", + "bbox": [ + 511, + 90, + 906, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Robustness Study", + "text_level": 1, + "bbox": [ + 511, + 306, + 686, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6.1. Image Processing Operation", + "text_level": 1, + "bbox": [ + 511, + 332, + 756, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We consider four image processing operations as attack measures from the perspective of attackers, aiming to mitigate the adversarial strength of protected samples. As depicted in Figure 7a, the protected samples generated by our proposed RAEncoder exhibit superior robustness compared to those generated by SRAE. Even after undergoing various image processing operations, the protected samples generated by RAEncoder maintain their adversarial effect, rendering the model incapable of correctly classifying the processed samples. This demonstrates that RAEncoder possesses enhanced robustness.", + "bbox": [ + 511, + 354, + 906, + 521 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2eb4fd1b99cb4b2253676aa0e1e9803449f976264815c462b8ea704da84a8571.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 519, + 539, + 705, + 604 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/30c10c521b7c631141b958aeed421451d40424167dca0606446ae414af9511af.jpg", + "image_caption": [ + "(b)", + "Figure 7. The attack performance of RAEncoder in various settings. (a) From left to right, no disturbance, Center crop(proportion = 90%), Flip(horizontal and vertical), Resize(half of the height and width), Resize (twice the height and width) and JPEG compression(quality factor = 70). (b) Different degree of corruption." + ], + "image_footnote": [], + "bbox": [ + 712, + 539, + 897, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6.2. Corruption", + "text_level": 1, + "bbox": [ + 511, + 757, + 638, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We take into consideration attackers may diminish the adversarial strength by introducing varying degrees of Gaussian blur to the samples, thereby degrading the images. As depicted in Figure 7b, with an increase in the degree of Gaussian perturbation, the ASR decreases. Particularly, when the blur degree reaches 1.25, the ASR of SRAE has dropped to approximately $30\\%$ , whereas our RAEncoder maintains an ASR of over $50\\%$ .", + "bbox": [ + 511, + 779, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20671", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0ac215a51e3e5da27092a5d15f992a488c4ea8e2f8189475ffbeafb457cdff93.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VGG16ResNet18ResNet50Dense121BalowBYOLDeepC2DINOMoCo2+NNCLR
Xue et al. [32]CIFAR1040.1248.5132.1742.4048.9747.6858.1254.8833.8448.96
ImageNet73.0488.1876.4264.2874.1687.5656.640.609.5648.44
PGN [31]CIFAR10----------
ImageNet81.3268.2266.4451.7667.2677.7649.260.589.2434.12
SRAE [38]CIFAR1061.8488.4076.7972.4773.6888.8290.4551.6580.0380.44
ImageNet72.3087.2284.0679.9474.6092.0055.5266.0011.2620.28
OursCIFAR1058.7984.7970.6674.5275.0589.6489.7958.8285.3783.18
ImageNet98.2291.4688.3099.0089.0498.9753.4686.0030.8451.80
", + "bbox": [ + 107, + 88, + 893, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Comparison study of ASR (%) of protected datasets across different SL models and pre-trained encoders. -' denotes experiments not conducted.", + "bbox": [ + 89, + 242, + 906, + 270 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6.3. Adaptive Attack", + "text_level": 1, + "bbox": [ + 89, + 297, + 250, + 313 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We consider the worst-case scenario for security concerns when deploying RAEncoder in practical applications (i.e., adaptive attack [32]). In such a scenario, attackers have full knowledge of the dataset protection methods, with the signature noise being the only unknown factor. The attacker is aware of the specifications of signature noise $S$ . However, due to the presence of the designed interference pattern, attackers are unable to reconstruct the original sample without signature noise $S$ . As shown in Figure 8, attackers are unable to recover the original sample by inputting random noise into the noise encoder and obtaining the output perturbation. Moreover, this even results in deeper levels of sample distortion.", + "bbox": [ + 89, + 316, + 485, + 513 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01532a76d9b96d80507982d2cb1adad059357675d5df36692bd946ea379e666d.jpg", + "image_caption": [ + "Figure 8. Examples of failure in image restoration by the attacker using incorrect signature noise." + ], + "image_footnote": [], + "bbox": [ + 106, + 527, + 464, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Adversarial Strength Explanation", + "text_level": 1, + "bbox": [ + 89, + 756, + 387, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We aim to generate protected samples that are sufficiently distant from the original classes under small perturbations while remaining difficult to detect. As illustrated in Figure 9a and 9b, although PGN and SRAE can push some samples away from the original classes, the protected samples remain very close to the original samples in the feature space. However, as shown in Figure 9c, the method proposed by us, RAEncoder, yields protected samples that", + "bbox": [ + 89, + 780, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cluster together in the feature space, far from all original classes. Meanwhile, there are even cases where protected samples exhibit feature space almost identical to samples from other original classes, demonstrating the superior adversarial strength and imperceptibility of RAEncoder.", + "bbox": [ + 511, + 297, + 906, + 373 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eee3b3a3e64723ba3daaa961dcbaa872012ff97a8a3d5347997ca45816a08882.jpg", + "image_caption": [ + "(a) PGN" + ], + "image_footnote": [], + "bbox": [ + 540, + 398, + 633, + 470 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5553c49baab4b8510109ea3f0b343ea8844fd370a36f6fb2a6109c648c0229ff.jpg", + "image_caption": [ + "(b) SRAE", + "Figure 9. t-SNE [29] visualization of the feature space of protected examples produced by PGN, SRAE and ours. The hollow dots represent original samples and the solid dots represent RAEs." + ], + "image_footnote": [], + "bbox": [ + 666, + 398, + 756, + 470 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0ef08e6fdd9064cabd422dace5824c8efac94ecd8041675ed3ce156cec48f378.jpg", + "image_caption": [ + "(c) Ours" + ], + "image_footnote": [], + "bbox": [ + 792, + 400, + 880, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future work", + "text_level": 1, + "bbox": [ + 511, + 582, + 777, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we highlight the novel challenges posed by the prevalence of SSL on RAEs for the first time. We introduce the first RAE framework applicable to protect the IP of unlabeled datasets. It leverages a noise encoder to generate universal adversarial perturbations for RAE generation, meeting the requirements of adversarial strength and full reversibility. Our RAEncoder exhibits significant performance improvement in all comparative experiments. We also evaluate its robustness against adaptive attacks, highlighting the practical advantages of RAEncoder over existing methods. Future work will include further exploration of balancing visual quality with adversarial strength. We also see new research opportunities in extending the attack approach against variational auto-encoders.", + "bbox": [ + 511, + 607, + 906, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was supported in part by National Natural Science Foundation of China (NFSC, No. 62362025) and Hainan Province Science and Technology Special Fund (No. ZDYF2022GXJS224).", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20672", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 IEEE symposium on security and privacy (sp), pages 39-57. IEEE, 2017. 2", + "[2] Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4345–4355, 2023. 1, 2, 6" + ], + "bbox": [ + 516, + 92, + 903, + 484 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20674", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_model.json b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8667d1c692b7ffa2b31e388cefd08eea9092addb --- /dev/null +++ b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/d38fb843-2f59-4406-8bd2-f601b0c7b2ae_model.json @@ -0,0 +1,2354 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.13, + 0.868, + 0.175 + ], + "angle": 0, + "content": "RAEncoder: A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.204, + 0.697, + 0.24 + ], + "angle": 0, + "content": "Fan Xing, Zhuo Tian, Xuefeng Fan, Xiaoyi Zhou* Hainan University" + }, + { + "type": "text", + "bbox": [ + 0.276, + 0.242, + 0.719, + 0.258 + ], + "angle": 0, + "content": "{xingfan, tianzhuo, xffan, xy.zhou}@hainanu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.326, + 0.482, + 0.733 + ], + "angle": 0, + "content": "Reversible Adversarial Examples (RAE) are designed to protect the intellectual property of datasets. Such examples can function as imperceptible adversarial examples to erode the model performance of unauthorized users while allowing authorized users to remove the adversarial perturbations and recover the original samples for normal model training. With the rise of Self-Supervised Learning (SSL), an increasing number of unlabeled datasets and pre-trained encoders are available in the community. However, existing RAE methods not only rely on well-labeled datasets for training Supervised Learning (SL) models but also exhibit poor adversarial transferability when attacking SSL pre-trained encoders. To address these challenges, we propose RAEncoder, the first framework for RAEs without the need for labeled samples. RAEncoder aims to generate universal adversarial perturbations by targeting SSL pretrained encoders. Unlike traditional RAE approaches, the pre-trained encoder outputs the feature distribution of the protected dataset rather than classification labels, enhancing both the attack success rate and transferability of RAEs. Extensive experiments are conducted on six pre-trained encoders and four SL models, covering aspects such as imperceptibility and transferability. Our results demonstrate that RAEncoder effectively protects unlabeled datasets from malicious infringements. Additional robustness experiments further confirm the security of RAEncoder in practical application scenarios." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.768, + 0.222, + 0.784 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Reversible Adversarial Examples (RAE) [20, 31-34, 37, 38, 41] are highlighted as a fundamental method for protecting dataset Intellectual Property (IP). Unlike traditional methods for dataset IP protection, such as reversible watermarking [10, 19, 42] and image encryption techniques [11, 35], RAE transforms the dataset into adversarial examples that can mislead model training while allowing authorized users" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.293, + 0.905, + 0.43 + ], + "angle": 0, + "content": "to remove the adversarial perturbations and restore the original dataset [20]. The adversarial attack methods used in existing RAE schemes focus on targeting specific Supervised Learning (SL) classifiers through optimization-based or gradient-based attacks, which result in a notable limitation: they lose adversarial strength when attacking different model architectures, and the adversarial strength diminishes especially when attacking downstream models trained with Self-Supervised Learning (SSL) pre-trained encoders." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.905, + 0.612 + ], + "angle": 0, + "content": "SSL is an emerging paradigm in machine learning. It typically involves pre-training a generic encoder on vast amounts of unlabeled data, and it can then serve as a feature extractor for a wide range of downstream tasks. By utilizing a pre-trained encoder, any resource-constrained user can leverage the advantages of a large model without the need to undertake expensive training from scratch. Considering SSL for RAEs is highly noteworthy because if RAEs exhibit poor transferability when attacking SSL pre-trained encoders, any attacker can leverage them to pre-process RAEs, thereby mitigating the impact of them on the training performance of unauthorized downstream models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Due to the fact that SSL pre-trained encoders learn feature representations of the data directly rather than feature-label relationships, adversarial attacks against SSL pre-encoders can exhibit excellent transferability across different downstream model architectures [43, 44]. Although this attack process demonstrates significant effectiveness, using it as a method to generate RAEs for protecting dataset IP introduces an additional challenge. Specifically, the protection scheme must address the worst-case scenario—adaptive attacks, where the attacker is assumed to be aware of the detailed steps of the protection scheme [32]. This requires the protection scheme to effectively differentiate between authorized and unauthorized access. To differentiate between authorized and unauthorized users, existing Reversible Data Hiding (RDH)-based RAE methods embed encrypted information in RAEs, ensuring that only users with the correct key can recover original samples. However, embedding any information within RAEs could significantly impact both adversarial strength and vi" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20665" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.152 + ], + "angle": 0, + "content": "sual quality[20, 31, 32]. Then, without embedding information, how can RAEs be designed to differentiate user authorization and ensure both effectiveness and robustness when attacking SSL encoders?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.484, + 0.395 + ], + "angle": 0, + "content": "To bridge the gap between the practical applicability of RAE and real-world needs in the context of SSL's growing popularity, we propose a novel approach, RAEncoder. To be specific, we design a noise encoder with a fixed signature noise as input. It learns the data distribution and generates universal adversarial perturbations by targeting SSL encoder. To effectively differentiate between authorized and unauthorized users, an interference pattern is designed to make the noise encoder insensitive to inputs other than the correct signature noise. By inputting the correct signature noise, authorized users can employ the noise encoder to obtain the recovered perturbation, thereby recovering the original sample. During noise encoder training, we employ high-frequency filters [21, 44] to optimize RAE imperceptibility, as high-frequency perturbations are less detectable than low-frequency ones." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.396, + 0.484, + 0.424 + ], + "angle": 0, + "content": "Compared to the existing work, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.427, + 0.484, + 0.517 + ], + "angle": 0, + "content": "- A Novel RAEncoder Framework: We introduce RAEncoder to address the limitations of existing RAE frameworks in the context of the growing popularity of SSL. To the best of our knowledge, RAEncoder is the first RAE framework applicable for protecting the IP of unlabeled datasets with \\(100\\%\\) fidelity." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.518, + 0.484, + 0.608 + ], + "angle": 0, + "content": "- Innovative Noise Encoder: A noise encoder capable of generating RAEs guided by sample texture features is devised to successfully balance imperceptibility with adversarial strength. Additionally, we introduce three losses in the interference pattern to guide adversarial attacks on SSL pre-encoders, ensuring the RAE's robustness." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.608, + 0.484, + 0.699 + ], + "angle": 0, + "content": "- Extensive Experimental Validation: Through extensive experiments, we compare our RAEncoder with state-of-the-art (SOTA) RAE schemes. The results demonstrate that our RAEncoder outperforms existing methods in various metrics, including imperceptibility, adversarial strength, and transferability." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.427, + 0.484, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.716, + 0.233, + 0.731 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.363, + 0.759 + ], + "angle": 0, + "content": "2.1. SSL and Its Emerging Threats" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "SSL uses the inherent information present in unlabeled data to pre-train encoders. These encoders learn to transform complex inputs into generic representations. Once trained, they can extract valuable domain knowledge and serve as versatile tools for solving different specific tasks. With the thriving development of SSL, pre-trained encoders have gained popularity in the industry. Many service providers openly release their pre-trained encoders, such as Google's BYOL [12] and Meta's MoCo [6, 14]. Recently, an increas" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.198 + ], + "angle": 0, + "content": "ing number of studies begin to investigate adversarial attacks against pre-trained encoders in SSL. Zhou et al. proposed the first attack framework that generates downstream-agnostic adversarial examples based on a cross-modal pretrained encoder for images and text [43]. Zhou et al. proposed the first scheme for generating universal adversarial examples based on pre-trained encoders[44]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.207, + 0.806, + 0.223 + ], + "angle": 0, + "content": "2.2. Reversible Adversarial Examples" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.906, + 0.32 + ], + "angle": 0, + "content": "Existing RAE schemes can be divided into two categories, RDH-based methods[20, 31-34, 37] and generative methods [38, 41], as shown in Figure 1. To generate adversarial examples, recent research endeavors utilize a range of adversarial attacks targeting SL classifier, such as IFGSM[18], DeepFool[23], and C&W[1]." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.332, + 0.793, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.478, + 0.793, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.332, + 0.9, + 0.498 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.799, + 0.499, + 0.895, + 0.572 + ], + "angle": 0, + "content": "X' Original sample \n\\(X'\\) Adversarial example \n\\(X^p\\) Protected sample \n\\(X^r\\) Recovered sample \n\\(\\square\\) Classifier \n\\(\\mathrm{ms}\\) Auxiliary Information \n\\(\\ominus\\) Element-wise Subtraction \n\\(\\oplus\\) Element-wise Addition" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.587, + 0.906, + 0.644 + ], + "angle": 0, + "content": "Figure 1. Existing methods can be divided into two categories: generative and RDH-based. Our method not only eliminates reliance on classifiers for adversarial attacks but also achieves \\(100\\%\\) fidelity without compromising adversarial strength." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Given that images contain inherent structures that allow adversarial attacks to be reversed [22], the concept of RAE was first introduced [20] and proposed the first RAE generation method based on RDH technology. Their approach involves embedding the pixel differences between adversarial examples and the original image into the image using RDH, allowing authorized users to achieve \\(100\\%\\) recovery of original samples by extracting the pixel differences. However, this method still has several issues, such as the deterioration of the visual quality of adversarial samples and a reduction in adversarial strength due to embedding information. Thus, reducing the embedded perturbation amount in RAE is a feasible approach. Yin et al. confined perturbations to regions most impactful on adversarial strength[34]. They leveraged the characteristic of the YUV color space, where the human eye is less sensitive to changes in the UV" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20666" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.317 + ], + "angle": 0, + "content": "channels, by embedding the perturbation differences of the Y channel into the UV channels. Zhang et al. leveraged beam search-based black-box attacks in combination with reversible data hiding featuring grayscale invariance[37]. Xiong et al. proposed PGN, which reduces adversarial perturbations to a sign matrix format and a product with fixed perturbation parameters[31]. Therefore, PGN only needs to record the sign matrix corresponding to pixel differences and embed it with the fixed perturbation parameters, significantly reducing the amount of embedding required. Meanwhile, existing work combined Reversible Image Transformation (RIT)[40] with RDH which involves embedding the reversible transformation information between the original sample and the adversarial example, rather than pixel differences, into the RAEs[32, 33]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.318, + 0.484, + 0.424 + ], + "angle": 0, + "content": "In the field of generative methods, SRAE [38] developed RAEs using a recoverable generative adversarial network designed to minimize recovery errors while maximizing their effectiveness in adversarial attacks. GEAA [41] utilizes a dual-stream architecture to generate adversarial and recovered samples, ensuring that the distribution of adversarial samples significantly differs from the original." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.484, + 0.544 + ], + "angle": 0, + "content": "In summary, RDH-based methods preserve the inverse operation that restores adversarial examples to the original samples, allowing most RDH-based methods to achieve \\(100\\%\\) sample recovery. While generative methods cannot currently achieve \\(100\\%\\) recovery, they do not require any information embedding that might affect adversarial strength. As a result, generative methods exhibit significantly higher adversarial strength compared to RDH-based methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.545, + 0.484, + 0.621 + ], + "angle": 0, + "content": "It is noteworthy that existing work generates RAEs by targeting supervised learning models for adversarial attacks, without addressing the new challenges posed by the popularity of SSL. Consequently, existing RAE solutions are unable to effectively protect unlabeled datasets." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.634, + 0.226, + 0.65 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.658, + 0.274, + 0.673 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.68, + 0.484, + 0.816 + ], + "angle": 0, + "content": "Given a pre-trained encoder \\( e_{\\theta}(\\cdot) \\) with input \\( x_{pt} \\) in \\( \\mathcal{D}_{pt} \\), where \\( \\theta \\) represents the parameters of the pre-trained encoder. \\( \\mathcal{D}_{pt} \\) denotes the pre-training dataset. The data owner uses the original sample \\( x \\) in original dataset \\( \\mathcal{D} \\) (remains unattainable for the attacker) to generate universal adversarial perturbation \\( \\delta \\) against the pre-trained encoder. The universal adversarial perturbation \\( \\delta \\) should be sufficiently small and modeled by an upper-bound \\( \\epsilon \\) on the \\( l_{p} \\) norm. The task of finding a perturbation can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.828, + 0.483, + 0.845 + ], + "angle": 0, + "content": "\\[\ne _ {\\theta} (x + \\delta) \\neq e _ {\\theta} (x), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.856, + 0.275, + 0.871 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_p\\) is the \\(l_{p}\\) norm." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "The data owner's objective is to achieve a universal nontargeted attack to deceive the downstream classifier \\( f_{\\theta'} \\)." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.107 + ], + "angle": 0, + "content": "Therefore, the data owner's objective can be formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.133, + 0.905, + 0.15 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x + \\delta)\\right) \\neq f _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x)\\right), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.16, + 0.907, + 0.281 + ], + "angle": 0, + "content": "When all original samples \\( x \\) in original dataset \\( \\mathcal{D} \\) are augmented with a universal adversarial perturbation \\( \\delta \\), it results in a protected dataset \\( \\mathcal{D}_p \\) composed of protected samples (i.e., reversible adversarial examples) \\( x^p \\). The \\( \\mathcal{D}_p \\) is used as a reference for all users. We assume that any users have access to public pre-trained encoders \\( e_{\\theta}^{pub}(\\cdot) \\) with input \\( x^{pub} \\) in the public dataset \\( \\mathcal{D}^{pub} \\), which they can obtain through purchase or direct download from public repositories." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.282, + 0.906, + 0.386 + ], + "angle": 0, + "content": "The attackers' objective is to encode protected datasets \\(\\mathcal{D}_p\\) using \\(e_{\\theta}^{pub}(\\cdot)\\) to minimize the impact of \\(\\mathcal{D}_p\\) on training performance and then training downstream classifier \\(f_{\\theta}^{atk}(e_{\\theta}^{pub}(\\cdot))\\). However, as shown in Figure 2, \\(x^p \\in \\mathcal{D}_p\\) is incorrectly encoded into other feature distributions, resulting in a significant degradation in the performance of the obtained downstream classifier which can be formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.4, + 0.905, + 0.419 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {p}\\right)\\right)\\right) \\ll \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.424, + 0.897, + 0.438 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}(\\cdot)\\) denotes the inference accuracy for a classifier." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.439, + 0.906, + 0.496 + ], + "angle": 0, + "content": "For authorized users, they can obtain recovered samples \\( x^{r} \\in \\mathcal{D}_{r} \\) which closely resemble the feature distribution of \\( x \\) for normal downstream task training that can be formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.497, + 0.905, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {r}\\right)\\right)\\right) \\approx \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.535, + 0.709, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.612, + 0.625, + 0.623 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.536, + 0.901, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.611, + 0.815, + 0.623 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.636, + 0.906, + 0.718 + ], + "angle": 0, + "content": "Figure 2. Illustrations of sample attributes: (a) The representation of different samples in the feature space. The dashed lines in different colors represent feature representations of various distributions (b) The fit of different samples within the classification decision boundary. The curved lines in different colors indicate the decision boundaries for different classes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.743, + 0.685, + 0.759 + ], + "angle": 0, + "content": "3.2. Training Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The training pipeline of RAEncoder is illustrated in Figure 3. It consists of a noise encoder \\( E \\), a high-frequency filter \\( \\mathcal{H} \\), and a target encoder \\( e_{\\theta} \\). Specifically, we generate a universal adversarial perturbation \\( \\delta \\) applicable to all \\( x \\) in \\( D \\) by inputting a fixed signature noise \\( S \\) into noise encoder \\( E \\). We then paste \\( \\delta \\) to \\( x \\) to obtain protected sample \\( x^{p} \\) in \\( D_{p} \\), where high-frequency information of \\( x^{p} \\) is reduced by high-frequency filter \\( \\mathcal{H} \\). Authorized users can input the signature noise \\( S \\) into the noise encoder \\( E \\) to obtain \\( \\delta \\). Subtracting \\( \\delta \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20667" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.198 + ], + "angle": 0, + "content": "from \\( x^p \\) results in a fully recovered sample \\( x^r \\) identical to the original \\( x \\), which is achieved for the first time in the previous RAE schemes. During the training process of noise encoder \\( E \\), we propose an interference pattern to incentivize \\( E \\) to distinguish signature noise \\( S \\) from other noise inputs, aiming to prevent potential attackers from inputting random noise to steal \\( \\delta \\) for image restoration." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.211, + 0.476, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.382, + 0.426, + 0.397 + ], + "angle": 0, + "content": "Figure 3. The training pipeline of RAEncoder." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.422, + 0.242, + 0.435 + ], + "angle": 0, + "content": "3.2.1. Noise Encoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.44, + 0.484, + 0.486 + ], + "angle": 0, + "content": "The noise encoder \\( E \\) takes a fixed input \\( S \\), designated for different authorized users, to generate a universal adversarial perturbation \\( \\delta \\), given by:" + }, + { + "type": "equation", + "bbox": [ + 0.25, + 0.499, + 0.483, + 0.515 + ], + "angle": 0, + "content": "\\[\nE (\\mathcal {S}) = \\delta . \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.527, + 0.484, + 0.572 + ], + "angle": 0, + "content": "Applying \\(\\delta\\) to original samples \\(x\\) yields \\(x^p\\). The difference between \\(x^p\\) and \\(\\delta\\) represents the original sample \\(x\\) which can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.247, + 0.586, + 0.483, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\delta + x = x ^ {p} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.673 + ], + "angle": 0, + "content": "When authorized users want to recover samples, they only need to input their exclusive \\(S\\) into \\(E\\) to obtain \\(\\delta\\), and original samples can be restored by subtracting \\(\\delta\\) which can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.675, + 0.482, + 0.69 + ], + "angle": 0, + "content": "\\[\nx ^ {r} = x ^ {p} - \\delta = x \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.484, + 0.727 + ], + "angle": 0, + "content": "The loss function for optimizing noise encoder \\( E \\) can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.741, + 0.483, + 0.757 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E} = \\alpha \\mathcal {L} _ {E. a d v} + \\beta \\mathcal {L} _ {E. \\mathcal {H}} + \\lambda \\mathcal {L} _ {E. m s e}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.77, + 0.138, + 0.782 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.794, + 0.483, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.845, + 0.483, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E. \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p}\\right) - \\mathcal {H} (x) | | _ {2} ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.885, + 0.483, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E \\_ m s e} = | | x ^ {p} - x | | _ {2} ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.907, + 0.259 + ], + "angle": 0, + "content": "\\(\\| \\cdot \\| _2\\) is the \\(l_{2}\\) norm, \\(\\langle u\\cdot c\\rangle = u^{\\mathsf{T}}c / \\| u\\| \\| c\\|\\) represents the cosine similarity. \\(i\\) represents the \\(i\\)-th sample, with a maximum value of \\(N\\), while \\(k\\) represents a number not equal to \\(i\\). \\(\\tau\\) indicates a temperature parameter. \\(\\mathcal{L}_{E\\_adv}\\) drives noise encoder to perform negative pairing between the protected sample \\(x^{p}\\) and \\(x\\), maximizing the mutual information distance between their features in the feature space by calculating the InfoNCE loss[4, 24]. \\(\\mathcal{L}_{E\\_H}\\) aims to constrain the perturbation intensity in high frequency through the high-frequency filter \\(\\mathcal{H}\\). \\(\\mathcal{L}_{E\\_mse}\\) aims to make sure the indistinguishability between \\(x^{p}\\) and \\(x\\)." + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.268, + 0.9, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.397, + 0.907, + 0.425 + ], + "angle": 0, + "content": "Figure 4. Visual results of original samples different samples generated from noise encoder without interference pattern employed." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.445, + 0.706, + 0.458 + ], + "angle": 0, + "content": "3.2.2. Interference Pattern." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.464, + 0.909, + 0.884 + ], + "angle": 0, + "content": "Training and optimizing \\( E \\) enables the generation of a highly adversarial universal perturbation \\( \\delta \\), significantly affecting the model training effectiveness for unauthorized users. However, we discover that guiding the noise encoder \\( E \\) to solely learn the generation of a universal adversarial perturbation \\( \\delta \\) from signature noise \\( S \\) without constraints can lead to vulnerabilities. In the event that the noise encoder \\( E \\) is compromised by attackers, they can potentially acquire a perturbation similar to \\( \\delta \\) for image recovery by feeding noise of the same size as \\( S \\) into the noise encoder \\( E \\). While the likelihood of the noise encoder \\( E \\) being compromised, particularly when stored in cloud services such as DMCP[32], is minimal in practical scenarios, such an outcome remains unacceptable in cases where the noise encoder \\( E \\) cannot distinguish between inputs from authorized users and attackers. As shown in Figure 4, the images shown in the third column are obtained by subtracting the output of noise encoder \\( E \\) when the protected sample \\( x^p \\) and random noise of the same size as signature noise \\( S \\) are inputted. It can be observed that these samples are very similar to the original images, which completely undermines the security of RAEs. Therefore, an interference pattern is exploited to resolve this problem. The idea is simple: when applying random noise \\( S' \\neq S \\), noise encoder \\( E \\) should not generate perturbation \\( \\delta \\), but instead generate an almost blank perturbation \\( \\delta' \\) with hardly any pixel values. The subtraction of perturbation \\( \\delta' \\) from \\( x^p \\) yields \\( x^{p'} \\) which can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.668, + 0.885, + 0.905, + 0.902 + ], + "angle": 0, + "content": "\\[\nE \\left(\\mathcal {S} ^ {\\prime}\\right) = \\delta^ {\\prime}, \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20668" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.238, + 0.105, + 0.482, + 0.122 + ], + "angle": 0, + "content": "\\[\nx ^ {p} - \\delta^ {\\prime} = x ^ {p ^ {\\prime}} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.127, + 0.484, + 0.158 + ], + "angle": 0, + "content": "Thus, the loss function for optimizing noise encoder E with interference pattern can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.181, + 0.484, + 0.199 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E \\mathcal {I}} = n \\mathcal {L} _ {I. a d v} + m \\mathcal {L} _ {I. \\mathcal {H}} + \\gamma \\mathcal {L} _ {I. m s e} + \\mathcal {L} _ {E}, \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.225, + 0.483, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.273, + 0.484, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p ^ {\\prime}}\\right) - \\mathcal {H} \\left(x ^ {p}\\right) | | _ {2} ^ {2}, \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.308, + 0.483, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I. m s e} = \\left\\| x ^ {p} - x ^ {p ^ {\\prime}} \\right\\| _ {2} ^ {2}. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.331, + 0.484, + 0.377 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{I\\_adv}, \\mathcal{L}_{I\\_H}\\) and \\(\\mathcal{L}_{I\\_mse}\\) are employed to minimize \\(\\delta'\\) generated from random noise \\(S'\\) towards zero as much as possible." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.388, + 0.224, + 0.405 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.412, + 0.292, + 0.429 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.435, + 0.285, + 0.449 + ], + "angle": 0, + "content": "4.1.1. Datasets and Models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.454, + 0.484, + 0.621 + ], + "angle": 0, + "content": "We utilize pre-trained encoders from the solo-learn [8], a well-established self-supervised learning library, as target encoders. These pre-trained encoders were trained on CIFAR10 [17] or ImageNet [25] datasets, employing ResNet18 [13] as the backbone. Among the array of SSL techniques available, we select six pioneering methods: Barlow Twins [36], BYOL [12], DeepCluster v2 [2], DINO [3], MoCo v2+ [5], and NNCLR [9]. We train VGG16[26], ResNet18, Resnet50[13], and DenseNet121[15] as target models. The datasets STL10 [7], GTSRB [28], CIFAR10, and ImageNet were considered as the protected datasets." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.626, + 0.305, + 0.641 + ], + "angle": 0, + "content": "4.1.2. Training configurations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.484, + 0.9 + ], + "angle": 0, + "content": "The noise encoder consists of multiple consecutive deconvolution layers followed by a convolutional layer. The hyperparameters settings for optimizing the noise encoder \\( E \\) are as follows: \\( n = \\alpha = 5 \\), \\( m = \\beta = 1 \\), \\( \\gamma = \\lambda = 1 \\) and \\( \\varepsilon = 10/255 \\), training epochs set to 20 and Adam optimizer [16] is adopted with an initial learning rate of 0.0002. For RDH-based method [32], PGN, and generative method GEAA, SRAE, all experiments conducted were based on their default settings as reported in their respective studies. Since they are not designed for adversarial attacks on pre-trained encoders, for a fair comparison to highlight the advantages of RAEncoder, we connect their target model's classification head to an encoder trained on the same pre-training dataset. Thus, the target model serves as a downstream model connected to the pre-trained encoder. Our experiments are conducted on two NVIDIA GeForce RTX 4090 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.092, + 0.697, + 0.106 + ], + "angle": 0, + "content": "4.1.3. Evaluation Metrics." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.113, + 0.907, + 0.189 + ], + "angle": 0, + "content": "We employ Structural Similarity Index (SSIM) [30] and Peak Signal-to-Noise Ratio (PSNR) to assess the quality of image. We use Attack Success Rate (ASR) to measure the success rate of samples that deceive the classifier. A higher numerical value indicates stronger attack capability." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.206, + 0.706, + 0.221 + ], + "angle": 0, + "content": "4.2. Attack Performance" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.23, + 0.907, + 0.352 + ], + "angle": 0, + "content": "We employ six types of SSL pre-trained encoders as target encoders \\( e_{\\theta} \\). Using two pre-training datasets, CIFAR10 and ImageNet, we generate \\( x^{p} \\) for four downstream datasets and evaluated ASR of \\( x^{p} \\) on the corresponding target encoders. It is worth noting that such experimental setups are deployed to investigate whether the RAEs generated by the RAEncoder possess strong adversarial strength to successfully deceive target encoders. As shown in Table 1, across" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.369, + 0.903, + 0.503 + ], + "angle": 0, + "content": "
BallowBYOLDeepC2DINOMoCo2+NNCLR
C185.8389.6482.0083.7751.7179.23
C242.5853.4442.9459.0429.3346.89
C381.5288.0781.0680.9370.2581.39
C488.9684.2082.2483.3674.6481.68
I187.6784.8384.7086.5189.1087.77
I266.7660.8468.3366.1863.6163.18
I382.3081.4377.4280.6284.5983.47
I498.9798.9799.0298.9698.9998.96
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.513, + 0.514, + 0.907, + 0.612 + ], + "angle": 0, + "content": "Table 1. Different configurations of protected samples' ASR (\\%) are evaluated. \\( \\mathcal{C}_1 - \\mathcal{C}_4 \\) represent the downstream datasets CIFAR10, STL10, GTSRB, and ImageNet, respectively, with the encoder's pre-training dataset being CIFAR10. \\( \\mathcal{I}_1 - \\mathcal{I}_4 \\) use ImageNet as the pre-training dataset, and the downstream datasets are the same as those in \\( \\mathcal{C}_1 - \\mathcal{C}_4 \\). Barlow Twins and DeepCluster v2 are abbreviated as Barlow and DeepC2, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.633, + 0.907, + 0.785 + ], + "angle": 0, + "content": "the settings of six pre-trained encoders and four downstream datasets, the ASR of protected samples remains consistently high, with over \\(80\\%\\) achieved in almost all settings. Meanwhile, it is evident that protected samples generated by pretrained encoders trained on corresponding original samples exhibit stronger adversarial attack strength. For example, When the pre-trained dataset is ImageNet and the downstream dataset is also ImageNet, the protected dataset generated by RAEncoder achieved an ASR close to \\(100\\%\\) when attacking encoders pre-trained on ImageNet." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.801, + 0.667, + 0.817 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.903 + ], + "angle": 0, + "content": "In this section, we investigate the impact of using different datasets, modules, and attack intensities on RAEncoder when generating the protected dataset. We opt for pretrained encoders on CIFAR10 and select CIFAR10 as the protected dataset for our analysis." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20669" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.289 + ], + "angle": 0, + "content": "The Effect of Interference Pattern We investigate the impact of the interference pattern. Specifically, as shown in Figure 5a, we examine the cases where noise encoders were deployed with and without the interference pattern, and subjected to random noise inputs to simulate attacks where adversaries aim to steal correct adversarial perturbations \\(\\delta\\), using random noise attacks. The results depicted in Figure 5a reveal that for noise encoders without interference pattern guidance, the attacked dataset obtained after being subjected to adversaries' random noise attacks has already lost its adversarial strength. However, noise encoders guided by the interference pattern exhibit robust adversarial strength even after undergoing attacks." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.301, + 0.287, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.302, + 0.476, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.395, + 0.484, + 0.466 + ], + "angle": 0, + "content": "Figure 5. Ablation study results of different settings. (a) Impact of deploying the interference pattern on the ASR (\\%) of the protected dataset and attacked dataset generated by the noise encoder. (b) The impact of different upper-bounds on attack performance and visual quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.502, + 0.484, + 0.579 + ], + "angle": 0, + "content": "The Effect of \\(\\epsilon\\) We investigate the impact of four different perturbation upper-bounds \\(\\epsilon\\) on the attack performance and visual quality of protected samples. As shown in Figure 5b, different upper bounds influence both the attack performance and visual quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.483, + 0.674 + ], + "angle": 0, + "content": "The Weights of Losses This experiment aims to study the mechanism of our method. From Eq. 9 to 17, we design six losses to train the noise encoder. As our target is to attack pre-trained encoder, the \\(\\mathcal{L}_{E\\_adv}\\) is necessary, and we set its weight to 5 which is the default value as validated in [44]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.84 + ], + "angle": 0, + "content": "To more intuitively assess imperceptibility, we introduced a new metric: Learned Perceptual Image Patch Similarity (LPIPS) [39] to evaluate the visual quality of the protected dataset. In contrast to SSIM and PSNR, LPIPS utilizes deep networks and is specifically designed to mimic human perception in image evaluation tasks. A higher LPIPS value indicates that the differences between images are more perceptible to human perception. Table 2 displays results from ablation experiments of \\(\\mathcal{L}_{E\\cdot \\mathcal{H}}\\) and \\(\\mathcal{L}_{E.mse}\\), demonstrating their importance in enhancing the imperceptibility of adversarial samples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To better evaluate the importance of the interference pattern, we conduct an ablation study on the values of the three losses introduced in the interference pattern: \\(\\mathcal{L}_{I\\_adv}\\), \\(\\mathcal{L}_{I\\_H}\\), and \\(\\mathcal{L}_{I\\_mse}\\). Specifically, we evaluate the performance of" + }, + { + "type": "table", + "bbox": [ + 0.591, + 0.089, + 0.835, + 0.16 + ], + "angle": 0, + "content": "
L_E_mseL_E_HSSIMPSNRLPIPS
✓X0.8028.220.194
X✓0.8228.240.165
✓✓0.8528.260.148
" + }, + { + "type": "table_caption", + "bbox": [ + 0.528, + 0.17, + 0.892, + 0.185 + ], + "angle": 0, + "content": "Table 2. The effect of \\( {\\mathcal{L}}_{E.mse} \\) and \\( {\\mathcal{L}}_{E\\mathcal{H}} \\) on imperceptibility." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.208, + 0.907, + 0.48 + ], + "angle": 0, + "content": "the protected dataset and the attacked dataset, recovered by the attacker using erroneous signature noise inputs to the noise encoder. We denote the ratio of the weights of \\(\\mathcal{L}_{I\\_adv}\\), \\(\\mathcal{L}_{I\\_H}\\), and \\(\\mathcal{L}_{I\\_mse}\\) to \\(\\mathcal{L}_{E\\_adv}\\), \\(\\mathcal{L}_{E\\_H}\\), and \\(\\mathcal{L}_{E\\_mse}\\) as \\(\\phi\\), where \\(n: \\alpha = m: \\beta = \\gamma: \\lambda = \\phi\\). By controlling the value of \\(\\phi\\), we can adjust the importance of the interference pattern in the learning process of the noise encoder. As shown in Table 3, when \\(\\phi = 0.5\\), the noise encoder's sensitivity to the interference pattern is reduced, leading to a decrease in \\(ASR_{Attacked}\\), although the reduction is not substantial. Conversely, when \\(\\phi = 2\\), the noise encoder focuses more on learning the interference pattern, which increases the \\(ASR_{Attacked}\\) but results in a reduced performance on the protected dataset. Thus, the weight of \\(\\mathcal{L}_{I\\_adv}\\), \\(\\mathcal{L}_{I\\_H}\\) and \\(\\mathcal{L}_{I\\_mse}\\) used to control the effect of the interference pattern are set to the same value as \\(\\mathcal{L}_E\\) to ensure that the learning of interference patterns is as important as the learning of normal patterns." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.49, + 0.903, + 0.56 + ], + "angle": 0, + "content": "
φASRProtectedASRAttackedSSIMPSNR
0.585.4784.500.8228.22
1(Default)85.8386.110.8528.26
282.1389.500.7626.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.567, + 0.57, + 0.852, + 0.584 + ], + "angle": 0, + "content": "Table 3. The effect of \\( \\phi \\) on interference pattern." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.607, + 0.712, + 0.621 + ], + "angle": 0, + "content": "4.4. Visualization Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this section, we compare the visual quality of protected and recovered samples generated by RAEncoder and existing methods. As shown in Figure 6, under conditions where the adversarial strength is superior, the protected samples produced by RAEncoder still maintain superior imperceptibility when compared to those generated by SRAE. As shown in Table 4, on CIFAR10, the protected dataset generated by RAEncoder achieves higher SSIM and PSNR values compared to the existing RDH-based method by [32] and the generative methods GEAA and SRAE. On ImageNet, the protected dataset generated by RAEncoder outperforms those by [32] and SRAE but is slightly weaker than PGN. However, PGN's visual quality cannot guarantee its adversarial strength which is explained in Section 4.5. Overall, RAEncoder demonstrates its superior imperceptibility, and the recovered dataset obtained through RAEncoder is identical to the original dataset. Importantly, these results are achieved without the need for an additional classification" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20670" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "head, but rather through direct utilization of a pre-trained encoder for the attack." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.133, + 0.479, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.359, + 0.483, + 0.401 + ], + "angle": 0, + "content": "Figure 6. Visualization of the comparison between protected samples and recovered samples generated by our method and SRAE. Best viewed in zoom." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.432, + 0.479, + 0.582 + ], + "angle": 0, + "content": "
DatasetMethodProtectedRecovered
SSIMPSNRSSIMPSNR
CIFAR10Xue et al. [32]0.7725.760.9956.36
GEAA [41]0.3227.910.9948.11
SRAE[38]0.4214.730.7627.67
Ours0.8528.261.00∞
ImageNetXue et al. [32]0.5820.470.9850.15
PGN [31]0.9434.231.00∞
SRAE[38]0.7627.670.9738.67
Ours0.8230.261.00∞
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.592, + 0.483, + 0.622 + ], + "angle": 0, + "content": "Table 4. Visual performance comparison of protected and recovered datasets from our method and existing methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.651, + 0.294, + 0.669 + ], + "angle": 0, + "content": "4.5. Transferability Study" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.674, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this section, we delve into the transferability of the RAEncoder from two distinct perspectives: attacks on downstream models trained with different pre-trained encoders, and attacks on various SL models with different network architectures. The downstream models used to evaluate transferability are trained on the corresponding pre-trained datasets of BYOL. The target SL model employed for [32], PGN and SRAE to generate the CIFAR10 protected dataset is ResNet18 and for ImageNet is ResNet50. High ASR is indicative of better adversarial strength and transferability. As shown in Table 5, the protected dataset generated by RAEncoder exhibits strong adversarial strength across various datasets, different SL models, and diverse pre-trained encoder configurations, resulting in significantly high ASR. Furthermore, its transferabil" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.289 + ], + "angle": 0, + "content": "ity across various SL models and pre-trained encoders frequently surpasses existing methods. However, while [32], PGN and SRAE demonstrate equally outstanding transferability across SL models, their ASR dramatically decreases when applied to downstream models trained by pre-trained encoders. It is noteworthy that, when applied to the CIFAR10 dataset, the ASR of SRAE is marginally higher than that of RAEncoder. However, as indicated in the Table 4, this increase in ASR is attained at the expense of image quality. Based on the results presented in Section 4.4 and Table 5, it is evident that our proposed RAEncoder effectively maintains the imperceptibility of protected samples while achieving a high level of adversarial strength." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.308, + 0.687, + 0.324 + ], + "angle": 0, + "content": "4.6. Robustness Study" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.333, + 0.757, + 0.349 + ], + "angle": 0, + "content": "4.6.1. Image Processing Operation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.355, + 0.907, + 0.522 + ], + "angle": 0, + "content": "We consider four image processing operations as attack measures from the perspective of attackers, aiming to mitigate the adversarial strength of protected samples. As depicted in Figure 7a, the protected samples generated by our proposed RAEncoder exhibit superior robustness compared to those generated by SRAE. Even after undergoing various image processing operations, the protected samples generated by RAEncoder maintain their adversarial effect, rendering the model incapable of correctly classifying the processed samples. This demonstrates that RAEncoder possesses enhanced robustness." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.54, + 0.707, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.608, + 0.622, + 0.62 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.54, + 0.898, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.608, + 0.814, + 0.62 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.634, + 0.907, + 0.718 + ], + "angle": 0, + "content": "Figure 7. The attack performance of RAEncoder in various settings. (a) From left to right, no disturbance, Center crop(proportion = 90%), Flip(horizontal and vertical), Resize(half of the height and width), Resize (twice the height and width) and JPEG compression(quality factor = 70). (b) Different degree of corruption." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.64, + 0.773 + ], + "angle": 0, + "content": "4.6.2. Corruption" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We take into consideration attackers may diminish the adversarial strength by introducing varying degrees of Gaussian blur to the samples, thereby degrading the images. As depicted in Figure 7b, with an increase in the degree of Gaussian perturbation, the ASR decreases. Particularly, when the blur degree reaches 1.25, the ASR of SRAE has dropped to approximately \\(30\\%\\), whereas our RAEncoder maintains an ASR of over \\(50\\%\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20671" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.108, + 0.089, + 0.895, + 0.234 + ], + "angle": 0, + "content": "
VGG16ResNet18ResNet50Dense121BalowBYOLDeepC2DINOMoCo2+NNCLR
Xue et al. [32]CIFAR1040.1248.5132.1742.4048.9747.6858.1254.8833.8448.96
ImageNet73.0488.1876.4264.2874.1687.5656.640.609.5648.44
PGN [31]CIFAR10----------
ImageNet81.3268.2266.4451.7667.2677.7649.260.589.2434.12
SRAE [38]CIFAR1061.8488.4076.7972.4773.6888.8290.4551.6580.0380.44
ImageNet72.3087.2284.0679.9474.6092.0055.5266.0011.2620.28
OursCIFAR1058.7984.7970.6674.5275.0589.6489.7958.8285.3783.18
ImageNet98.2291.4688.3099.0089.0498.9753.4686.0030.8451.80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.243, + 0.908, + 0.271 + ], + "angle": 0, + "content": "Table 5. Comparison study of ASR (%) of protected datasets across different SL models and pre-trained encoders. -' denotes experiments not conducted." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.298, + 0.251, + 0.314 + ], + "angle": 0, + "content": "4.6.3. Adaptive Attack" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.318, + 0.486, + 0.514 + ], + "angle": 0, + "content": "We consider the worst-case scenario for security concerns when deploying RAEncoder in practical applications (i.e., adaptive attack [32]). In such a scenario, attackers have full knowledge of the dataset protection methods, with the signature noise being the only unknown factor. The attacker is aware of the specifications of signature noise \\( S \\). However, due to the presence of the designed interference pattern, attackers are unable to reconstruct the original sample without signature noise \\( S \\). As shown in Figure 8, attackers are unable to recover the original sample by inputting random noise into the noise encoder and obtaining the output perturbation. Moreover, this even results in deeper levels of sample distortion." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.528, + 0.465, + 0.687 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.699, + 0.483, + 0.727 + ], + "angle": 0, + "content": "Figure 8. Examples of failure in image restoration by the attacker using incorrect signature noise." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.757, + 0.388, + 0.773 + ], + "angle": 0, + "content": "4.7. Adversarial Strength Explanation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We aim to generate protected samples that are sufficiently distant from the original classes under small perturbations while remaining difficult to detect. As illustrated in Figure 9a and 9b, although PGN and SRAE can push some samples away from the original classes, the protected samples remain very close to the original samples in the feature space. However, as shown in Figure 9c, the method proposed by us, RAEncoder, yields protected samples that" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.298, + 0.907, + 0.374 + ], + "angle": 0, + "content": "cluster together in the feature space, far from all original classes. Meanwhile, there are even cases where protected samples exhibit feature space almost identical to samples from other original classes, demonstrating the superior adversarial strength and imperceptibility of RAEncoder." + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.399, + 0.634, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.485, + 0.608, + 0.496 + ], + "angle": 0, + "content": "(a) PGN" + }, + { + "type": "image", + "bbox": [ + 0.667, + 0.4, + 0.758, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.684, + 0.485, + 0.737, + 0.496 + ], + "angle": 0, + "content": "(b) SRAE" + }, + { + "type": "image", + "bbox": [ + 0.793, + 0.401, + 0.882, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.485, + 0.859, + 0.496 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.51, + 0.907, + 0.552 + ], + "angle": 0, + "content": "Figure 9. t-SNE [29] visualization of the feature space of protected examples produced by PGN, SRAE and ours. The hollow dots represent original samples and the solid dots represent RAEs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.583, + 0.779, + 0.599 + ], + "angle": 0, + "content": "5. Conclusion and Future work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.907, + 0.82 + ], + "angle": 0, + "content": "In this paper, we highlight the novel challenges posed by the prevalence of SSL on RAEs for the first time. We introduce the first RAE framework applicable to protect the IP of unlabeled datasets. It leverages a noise encoder to generate universal adversarial perturbations for RAE generation, meeting the requirements of adversarial strength and full reversibility. Our RAEncoder exhibits significant performance improvement in all comparative experiments. We also evaluate its robustness against adaptive attacks, highlighting the practical advantages of RAEncoder over existing methods. Future work will include further exploration of balancing visual quality with adversarial strength. We also see new research opportunities in extending the attack approach against variational auto-encoders." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment. This work was supported in part by National Natural Science Foundation of China (NFSC, No. 62362025) and Hainan Province Science and Technology Special Fund (No. ZDYF2022GXJS224)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20672" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.483, + 0.157 + ], + "angle": 0, + "content": "[1] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. 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Such examples can function as imperceptible adversarial examples to erode the model performance of unauthorized users while allowing authorized users to remove the adversarial perturbations and recover the original samples for normal model training. With the rise of Self-Supervised Learning (SSL), an increasing number of unlabeled datasets and pre-trained encoders are available in the community. However, existing RAE methods not only rely on well-labeled datasets for training Supervised Learning (SL) models but also exhibit poor adversarial transferability when attacking SSL pre-trained encoders. To address these challenges, we propose RAEncoder, the first framework for RAEs without the need for labeled samples. RAEncoder aims to generate universal adversarial perturbations by targeting SSL pretrained encoders. Unlike traditional RAE approaches, the pre-trained encoder outputs the feature distribution of the protected dataset rather than classification labels, enhancing both the attack success rate and transferability of RAEs. Extensive experiments are conducted on six pre-trained encoders and four SL models, covering aspects such as imperceptibility and transferability. Our results demonstrate that RAEncoder effectively protects unlabeled datasets from malicious infringements. Additional robustness experiments further confirm the security of RAEncoder in practical application scenarios. + +# 1. Introduction + +Reversible Adversarial Examples (RAE) [20, 31-34, 37, 38, 41] are highlighted as a fundamental method for protecting dataset Intellectual Property (IP). Unlike traditional methods for dataset IP protection, such as reversible watermarking [10, 19, 42] and image encryption techniques [11, 35], RAE transforms the dataset into adversarial examples that can mislead model training while allowing authorized users + +to remove the adversarial perturbations and restore the original dataset [20]. The adversarial attack methods used in existing RAE schemes focus on targeting specific Supervised Learning (SL) classifiers through optimization-based or gradient-based attacks, which result in a notable limitation: they lose adversarial strength when attacking different model architectures, and the adversarial strength diminishes especially when attacking downstream models trained with Self-Supervised Learning (SSL) pre-trained encoders. + +SSL is an emerging paradigm in machine learning. It typically involves pre-training a generic encoder on vast amounts of unlabeled data, and it can then serve as a feature extractor for a wide range of downstream tasks. By utilizing a pre-trained encoder, any resource-constrained user can leverage the advantages of a large model without the need to undertake expensive training from scratch. Considering SSL for RAEs is highly noteworthy because if RAEs exhibit poor transferability when attacking SSL pre-trained encoders, any attacker can leverage them to pre-process RAEs, thereby mitigating the impact of them on the training performance of unauthorized downstream models. + +Due to the fact that SSL pre-trained encoders learn feature representations of the data directly rather than feature-label relationships, adversarial attacks against SSL pre-encoders can exhibit excellent transferability across different downstream model architectures [43, 44]. Although this attack process demonstrates significant effectiveness, using it as a method to generate RAEs for protecting dataset IP introduces an additional challenge. Specifically, the protection scheme must address the worst-case scenario—adaptive attacks, where the attacker is assumed to be aware of the detailed steps of the protection scheme [32]. This requires the protection scheme to effectively differentiate between authorized and unauthorized access. To differentiate between authorized and unauthorized users, existing Reversible Data Hiding (RDH)-based RAE methods embed encrypted information in RAEs, ensuring that only users with the correct key can recover original samples. However, embedding any information within RAEs could significantly impact both adversarial strength and vi + +sual quality[20, 31, 32]. Then, without embedding information, how can RAEs be designed to differentiate user authorization and ensure both effectiveness and robustness when attacking SSL encoders? + +To bridge the gap between the practical applicability of RAE and real-world needs in the context of SSL's growing popularity, we propose a novel approach, RAEncoder. To be specific, we design a noise encoder with a fixed signature noise as input. It learns the data distribution and generates universal adversarial perturbations by targeting SSL encoder. To effectively differentiate between authorized and unauthorized users, an interference pattern is designed to make the noise encoder insensitive to inputs other than the correct signature noise. By inputting the correct signature noise, authorized users can employ the noise encoder to obtain the recovered perturbation, thereby recovering the original sample. During noise encoder training, we employ high-frequency filters [21, 44] to optimize RAE imperceptibility, as high-frequency perturbations are less detectable than low-frequency ones. + +Compared to the existing work, our contributions are as follows: + +- A Novel RAEncoder Framework: We introduce RAEncoder to address the limitations of existing RAE frameworks in the context of the growing popularity of SSL. To the best of our knowledge, RAEncoder is the first RAE framework applicable for protecting the IP of unlabeled datasets with $100\%$ fidelity. +- Innovative Noise Encoder: A noise encoder capable of generating RAEs guided by sample texture features is devised to successfully balance imperceptibility with adversarial strength. Additionally, we introduce three losses in the interference pattern to guide adversarial attacks on SSL pre-encoders, ensuring the RAE's robustness. +- Extensive Experimental Validation: Through extensive experiments, we compare our RAEncoder with state-of-the-art (SOTA) RAE schemes. The results demonstrate that our RAEncoder outperforms existing methods in various metrics, including imperceptibility, adversarial strength, and transferability. + +# 2. Related Work + +# 2.1. SSL and Its Emerging Threats + +SSL uses the inherent information present in unlabeled data to pre-train encoders. These encoders learn to transform complex inputs into generic representations. Once trained, they can extract valuable domain knowledge and serve as versatile tools for solving different specific tasks. With the thriving development of SSL, pre-trained encoders have gained popularity in the industry. Many service providers openly release their pre-trained encoders, such as Google's BYOL [12] and Meta's MoCo [6, 14]. Recently, an increas + +ing number of studies begin to investigate adversarial attacks against pre-trained encoders in SSL. Zhou et al. proposed the first attack framework that generates downstream-agnostic adversarial examples based on a cross-modal pretrained encoder for images and text [43]. Zhou et al. proposed the first scheme for generating universal adversarial examples based on pre-trained encoders[44]. + +# 2.2. Reversible Adversarial Examples + +Existing RAE schemes can be divided into two categories, RDH-based methods[20, 31-34, 37] and generative methods [38, 41], as shown in Figure 1. To generate adversarial examples, recent research endeavors utilize a range of adversarial attacks targeting SL classifier, such as IFGSM[18], DeepFool[23], and C&W[1]. + +![](images/315409910f657af6bffe8565f0437ce6e5ed3025234e3a6731932b8cb8d71a85.jpg) + +![](images/56235690c3767c1c604bcb0dc8d61e2b10773c7a2d7c2d34bf8b4e7b212a08d7.jpg) +Figure 1. Existing methods can be divided into two categories: generative and RDH-based. Our method not only eliminates reliance on classifiers for adversarial attacks but also achieves $100\%$ fidelity without compromising adversarial strength. + +![](images/fef59caab8009d77c7b49ccd92e197d582c9a461924a2d3ff3279eacfae20567.jpg) +X' Original sample + $X'$ Adversarial example + $X^p$ Protected sample + $X^r$ Recovered sample + $\square$ Classifier + $\mathrm{ms}$ Auxiliary Information + $\ominus$ Element-wise Subtraction + $\oplus$ Element-wise Addition + +Given that images contain inherent structures that allow adversarial attacks to be reversed [22], the concept of RAE was first introduced [20] and proposed the first RAE generation method based on RDH technology. Their approach involves embedding the pixel differences between adversarial examples and the original image into the image using RDH, allowing authorized users to achieve $100\%$ recovery of original samples by extracting the pixel differences. However, this method still has several issues, such as the deterioration of the visual quality of adversarial samples and a reduction in adversarial strength due to embedding information. Thus, reducing the embedded perturbation amount in RAE is a feasible approach. Yin et al. confined perturbations to regions most impactful on adversarial strength[34]. They leveraged the characteristic of the YUV color space, where the human eye is less sensitive to changes in the UV + +channels, by embedding the perturbation differences of the Y channel into the UV channels. Zhang et al. leveraged beam search-based black-box attacks in combination with reversible data hiding featuring grayscale invariance[37]. Xiong et al. proposed PGN, which reduces adversarial perturbations to a sign matrix format and a product with fixed perturbation parameters[31]. Therefore, PGN only needs to record the sign matrix corresponding to pixel differences and embed it with the fixed perturbation parameters, significantly reducing the amount of embedding required. Meanwhile, existing work combined Reversible Image Transformation (RIT)[40] with RDH which involves embedding the reversible transformation information between the original sample and the adversarial example, rather than pixel differences, into the RAEs[32, 33]. + +In the field of generative methods, SRAE [38] developed RAEs using a recoverable generative adversarial network designed to minimize recovery errors while maximizing their effectiveness in adversarial attacks. GEAA [41] utilizes a dual-stream architecture to generate adversarial and recovered samples, ensuring that the distribution of adversarial samples significantly differs from the original. + +In summary, RDH-based methods preserve the inverse operation that restores adversarial examples to the original samples, allowing most RDH-based methods to achieve $100\%$ sample recovery. While generative methods cannot currently achieve $100\%$ recovery, they do not require any information embedding that might affect adversarial strength. As a result, generative methods exhibit significantly higher adversarial strength compared to RDH-based methods. + +It is noteworthy that existing work generates RAEs by targeting supervised learning models for adversarial attacks, without addressing the new challenges posed by the popularity of SSL. Consequently, existing RAE solutions are unable to effectively protect unlabeled datasets. + +# 3. Methodology + +# 3.1. Problem Definition + +Given a pre-trained encoder $e_{\theta}(\cdot)$ with input $x_{pt}$ in $\mathcal{D}_{pt}$ , where $\theta$ represents the parameters of the pre-trained encoder. $\mathcal{D}_{pt}$ denotes the pre-training dataset. The data owner uses the original sample $x$ in original dataset $\mathcal{D}$ (remains unattainable for the attacker) to generate universal adversarial perturbation $\delta$ against the pre-trained encoder. The universal adversarial perturbation $\delta$ should be sufficiently small and modeled by an upper-bound $\epsilon$ on the $l_{p}$ norm. The task of finding a perturbation can be formulated as: + +$$ +e _ {\theta} (x + \delta) \neq e _ {\theta} (x), \quad s. t. | | \delta | | _ {p} \leq \varepsilon \tag {1} +$$ + +where $||\cdot ||_p$ is the $l_{p}$ norm. + +The data owner's objective is to achieve a universal nontargeted attack to deceive the downstream classifier $f_{\theta'}$ . + +Therefore, the data owner's objective can be formalized as: + +$$ +f _ {\theta^ {\prime}} \left(e _ {\theta} (x + \delta)\right) \neq f _ {\theta^ {\prime}} \left(e _ {\theta} (x)\right), \quad s. t. | | \delta | | _ {p} \leq \varepsilon \tag {2} +$$ + +When all original samples $x$ in original dataset $\mathcal{D}$ are augmented with a universal adversarial perturbation $\delta$ , it results in a protected dataset $\mathcal{D}_p$ composed of protected samples (i.e., reversible adversarial examples) $x^p$ . The $\mathcal{D}_p$ is used as a reference for all users. We assume that any users have access to public pre-trained encoders $e_{\theta}^{pub}(\cdot)$ with input $x^{pub}$ in the public dataset $\mathcal{D}^{pub}$ , which they can obtain through purchase or direct download from public repositories. + +The attackers' objective is to encode protected datasets $\mathcal{D}_p$ using $e_{\theta}^{pub}(\cdot)$ to minimize the impact of $\mathcal{D}_p$ on training performance and then training downstream classifier $f_{\theta}^{atk}(e_{\theta}^{pub}(\cdot))$ . However, as shown in Figure 2, $x^p \in \mathcal{D}_p$ is incorrectly encoded into other feature distributions, resulting in a significant degradation in the performance of the obtained downstream classifier which can be formalized as: + +$$ +\mathcal {A} \left(f _ {\theta} ^ {a t k} \left(e _ {\theta} ^ {p u b} \left(x ^ {p}\right)\right)\right) \ll \mathcal {A} \left(f _ {\theta} ^ {a t k} \left(e _ {\theta} ^ {p u b} (x)\right)\right) \tag {3} +$$ + +where $\mathcal{A}(\cdot)$ denotes the inference accuracy for a classifier. + +For authorized users, they can obtain recovered samples $x^{r} \in \mathcal{D}_{r}$ which closely resemble the feature distribution of $x$ for normal downstream task training that can be formalized as: + +$$ +\mathcal {A} \left(f _ {\theta} ^ {a t k} \left(e _ {\theta} ^ {p u b} \left(x ^ {r}\right)\right)\right) \approx \mathcal {A} \left(f _ {\theta} ^ {a t k} \left(e _ {\theta} ^ {p u b} (x)\right)\right) \tag {4} +$$ + +![](images/cb1897138eeb6b450cb0e7c393a9aee930f6243b3f8d92cf05375cf680013732.jpg) +(a) + +![](images/1e40f8c8a3556be18f8171fecf431afc6cc4634a4b05a69a6b5bad2d643379f7.jpg) +(b) +Figure 2. Illustrations of sample attributes: (a) The representation of different samples in the feature space. The dashed lines in different colors represent feature representations of various distributions (b) The fit of different samples within the classification decision boundary. The curved lines in different colors indicate the decision boundaries for different classes. + +# 3.2. Training Pipeline + +The training pipeline of RAEncoder is illustrated in Figure 3. It consists of a noise encoder $E$ , a high-frequency filter $\mathcal{H}$ , and a target encoder $e_{\theta}$ . Specifically, we generate a universal adversarial perturbation $\delta$ applicable to all $x$ in $D$ by inputting a fixed signature noise $S$ into noise encoder $E$ . We then paste $\delta$ to $x$ to obtain protected sample $x^{p}$ in $D_{p}$ , where high-frequency information of $x^{p}$ is reduced by high-frequency filter $\mathcal{H}$ . Authorized users can input the signature noise $S$ into the noise encoder $E$ to obtain $\delta$ . Subtracting $\delta$ + +from $x^p$ results in a fully recovered sample $x^r$ identical to the original $x$ , which is achieved for the first time in the previous RAE schemes. During the training process of noise encoder $E$ , we propose an interference pattern to incentivize $E$ to distinguish signature noise $S$ from other noise inputs, aiming to prevent potential attackers from inputting random noise to steal $\delta$ for image restoration. + +![](images/b91bc0be9de2dad9f2c3184a012ad15bd6c207357abc8a6ae035f534431d7868.jpg) +Figure 3. The training pipeline of RAEncoder. + +# 3.2.1. Noise Encoder. + +The noise encoder $E$ takes a fixed input $S$ , designated for different authorized users, to generate a universal adversarial perturbation $\delta$ , given by: + +$$ +E (\mathcal {S}) = \delta . \tag {5} +$$ + +Applying $\delta$ to original samples $x$ yields $x^p$ . The difference between $x^p$ and $\delta$ represents the original sample $x$ which can be described as: + +$$ +\delta + x = x ^ {p} \tag {6} +$$ + +When authorized users want to recover samples, they only need to input their exclusive $S$ into $E$ to obtain $\delta$ , and original samples can be restored by subtracting $\delta$ which can be described as: + +$$ +x ^ {r} = x ^ {p} - \delta = x \tag {7} +$$ + +The loss function for optimizing noise encoder $E$ can be described as: + +$$ +\mathcal {L} _ {E} = \alpha \mathcal {L} _ {E. a d v} + \beta \mathcal {L} _ {E. \mathcal {H}} + \lambda \mathcal {L} _ {E. m s e}, \tag {8} +$$ + +where + +$$ +\mathcal {L} _ {E. a d v} = \log \frac {\exp \left(\left\langle e _ {\theta} \left(x _ {i} ^ {p}\right) , e _ {\theta} \left(x _ {i}\right) \right\rangle / \tau\right)}{\sum_ {k = 0} ^ {N} \exp \left(\left\langle e _ {\theta} \left(x _ {i} ^ {p}\right) , e _ {\theta} \left(x _ {k}\right) \right\rangle / \tau\right)}, \tag {9} +$$ + +$$ +\mathcal {L} _ {E. \mathcal {H}} = - | | \mathcal {H} \left(x ^ {p}\right) - \mathcal {H} (x) | | _ {2} ^ {2}, \tag {10} +$$ + +$$ +\mathcal {L} _ {E \_ m s e} = | | x ^ {p} - x | | _ {2} ^ {2}, \tag {11} +$$ + +$\| \cdot \| _2$ is the $l_{2}$ norm, $\langle u\cdot c\rangle = u^{\mathsf{T}}c / \| u\| \| c\|$ represents the cosine similarity. $i$ represents the $i$ -th sample, with a maximum value of $N$ , while $k$ represents a number not equal to $i$ . $\tau$ indicates a temperature parameter. $\mathcal{L}_{E\_adv}$ drives noise encoder to perform negative pairing between the protected sample $x^{p}$ and $x$ , maximizing the mutual information distance between their features in the feature space by calculating the InfoNCE loss[4, 24]. $\mathcal{L}_{E\_H}$ aims to constrain the perturbation intensity in high frequency through the high-frequency filter $\mathcal{H}$ . $\mathcal{L}_{E\_mse}$ aims to make sure the indistinguishability between $x^{p}$ and $x$ . + +![](images/bb650a516585cc20bc88ed87cb1fe3c3d935a17a0837a9a3da2d97f5d7e3f83d.jpg) +Figure 4. Visual results of original samples different samples generated from noise encoder without interference pattern employed. + +# 3.2.2. Interference Pattern. + +Training and optimizing $E$ enables the generation of a highly adversarial universal perturbation $\delta$ , significantly affecting the model training effectiveness for unauthorized users. However, we discover that guiding the noise encoder $E$ to solely learn the generation of a universal adversarial perturbation $\delta$ from signature noise $S$ without constraints can lead to vulnerabilities. In the event that the noise encoder $E$ is compromised by attackers, they can potentially acquire a perturbation similar to $\delta$ for image recovery by feeding noise of the same size as $S$ into the noise encoder $E$ . While the likelihood of the noise encoder $E$ being compromised, particularly when stored in cloud services such as DMCP[32], is minimal in practical scenarios, such an outcome remains unacceptable in cases where the noise encoder $E$ cannot distinguish between inputs from authorized users and attackers. As shown in Figure 4, the images shown in the third column are obtained by subtracting the output of noise encoder $E$ when the protected sample $x^p$ and random noise of the same size as signature noise $S$ are inputted. It can be observed that these samples are very similar to the original images, which completely undermines the security of RAEs. Therefore, an interference pattern is exploited to resolve this problem. The idea is simple: when applying random noise $S' \neq S$ , noise encoder $E$ should not generate perturbation $\delta$ , but instead generate an almost blank perturbation $\delta'$ with hardly any pixel values. The subtraction of perturbation $\delta'$ from $x^p$ yields $x^{p'}$ which can be described as: + +$$ +E \left(\mathcal {S} ^ {\prime}\right) = \delta^ {\prime}, \tag {12} +$$ + +$$ +x ^ {p} - \delta^ {\prime} = x ^ {p ^ {\prime}} \tag {13} +$$ + +Thus, the loss function for optimizing noise encoder E with interference pattern can be described as: + +$$ +\mathcal {L} _ {E \mathcal {I}} = n \mathcal {L} _ {I. a d v} + m \mathcal {L} _ {I. \mathcal {H}} + \gamma \mathcal {L} _ {I. m s e} + \mathcal {L} _ {E}, \tag {14} +$$ + +$$ +\mathcal {L} _ {I. a d v} = \log \frac {\exp \left(\left\langle e _ {\theta} \left(x _ {i} ^ {p ^ {\prime}}\right) , e _ {\theta} \left(x _ {i}\right) \right\rangle / \tau\right)}{\sum_ {k = 0} ^ {N} \exp \left(\left\langle e _ {\theta} \left(x _ {i} ^ {p ^ {\prime}}\right) , e _ {\theta} \left(x _ {k}\right) \right\rangle / \tau\right)}, \tag {15} +$$ + +$$ +\mathcal {L} _ {I \mathcal {H}} = - | | \mathcal {H} \left(x ^ {p ^ {\prime}}\right) - \mathcal {H} \left(x ^ {p}\right) | | _ {2} ^ {2}, \tag {16} +$$ + +$$ +\mathcal {L} _ {I. m s e} = \left\| x ^ {p} - x ^ {p ^ {\prime}} \right\| _ {2} ^ {2}. \tag {17} +$$ + +$\mathcal{L}_{I\_adv}, \mathcal{L}_{I\_H}$ and $\mathcal{L}_{I\_mse}$ are employed to minimize $\delta'$ generated from random noise $S'$ towards zero as much as possible. + +# 4. Experiments + +# 4.1. Experimental Setting + +# 4.1.1. Datasets and Models. + +We utilize pre-trained encoders from the solo-learn [8], a well-established self-supervised learning library, as target encoders. These pre-trained encoders were trained on CIFAR10 [17] or ImageNet [25] datasets, employing ResNet18 [13] as the backbone. Among the array of SSL techniques available, we select six pioneering methods: Barlow Twins [36], BYOL [12], DeepCluster v2 [2], DINO [3], MoCo v2+ [5], and NNCLR [9]. We train VGG16[26], ResNet18, Resnet50[13], and DenseNet121[15] as target models. The datasets STL10 [7], GTSRB [28], CIFAR10, and ImageNet were considered as the protected datasets. + +# 4.1.2. Training configurations. + +The noise encoder consists of multiple consecutive deconvolution layers followed by a convolutional layer. The hyperparameters settings for optimizing the noise encoder $E$ are as follows: $n = \alpha = 5$ , $m = \beta = 1$ , $\gamma = \lambda = 1$ and $\varepsilon = 10/255$ , training epochs set to 20 and Adam optimizer [16] is adopted with an initial learning rate of 0.0002. For RDH-based method [32], PGN, and generative method GEAA, SRAE, all experiments conducted were based on their default settings as reported in their respective studies. Since they are not designed for adversarial attacks on pre-trained encoders, for a fair comparison to highlight the advantages of RAEncoder, we connect their target model's classification head to an encoder trained on the same pre-training dataset. Thus, the target model serves as a downstream model connected to the pre-trained encoder. Our experiments are conducted on two NVIDIA GeForce RTX 4090 GPUs. + +# 4.1.3. Evaluation Metrics. + +We employ Structural Similarity Index (SSIM) [30] and Peak Signal-to-Noise Ratio (PSNR) to assess the quality of image. We use Attack Success Rate (ASR) to measure the success rate of samples that deceive the classifier. A higher numerical value indicates stronger attack capability. + +# 4.2. Attack Performance + +We employ six types of SSL pre-trained encoders as target encoders $e_{\theta}$ . Using two pre-training datasets, CIFAR10 and ImageNet, we generate $x^{p}$ for four downstream datasets and evaluated ASR of $x^{p}$ on the corresponding target encoders. It is worth noting that such experimental setups are deployed to investigate whether the RAEs generated by the RAEncoder possess strong adversarial strength to successfully deceive target encoders. As shown in Table 1, across + +
BallowBYOLDeepC2DINOMoCo2+NNCLR
C185.8389.6482.0083.7751.7179.23
C242.5853.4442.9459.0429.3346.89
C381.5288.0781.0680.9370.2581.39
C488.9684.2082.2483.3674.6481.68
I187.6784.8384.7086.5189.1087.77
I266.7660.8468.3366.1863.6163.18
I382.3081.4377.4280.6284.5983.47
I498.9798.9799.0298.9698.9998.96
+ +Table 1. Different configurations of protected samples' ASR (\%) are evaluated. $\mathcal{C}_1 - \mathcal{C}_4$ represent the downstream datasets CIFAR10, STL10, GTSRB, and ImageNet, respectively, with the encoder's pre-training dataset being CIFAR10. $\mathcal{I}_1 - \mathcal{I}_4$ use ImageNet as the pre-training dataset, and the downstream datasets are the same as those in $\mathcal{C}_1 - \mathcal{C}_4$ . Barlow Twins and DeepCluster v2 are abbreviated as Barlow and DeepC2, respectively. + +the settings of six pre-trained encoders and four downstream datasets, the ASR of protected samples remains consistently high, with over $80\%$ achieved in almost all settings. Meanwhile, it is evident that protected samples generated by pretrained encoders trained on corresponding original samples exhibit stronger adversarial attack strength. For example, When the pre-trained dataset is ImageNet and the downstream dataset is also ImageNet, the protected dataset generated by RAEncoder achieved an ASR close to $100\%$ when attacking encoders pre-trained on ImageNet. + +# 4.3. Ablation Study + +In this section, we investigate the impact of using different datasets, modules, and attack intensities on RAEncoder when generating the protected dataset. We opt for pretrained encoders on CIFAR10 and select CIFAR10 as the protected dataset for our analysis. + +The Effect of Interference Pattern We investigate the impact of the interference pattern. Specifically, as shown in Figure 5a, we examine the cases where noise encoders were deployed with and without the interference pattern, and subjected to random noise inputs to simulate attacks where adversaries aim to steal correct adversarial perturbations $\delta$ , using random noise attacks. The results depicted in Figure 5a reveal that for noise encoders without interference pattern guidance, the attacked dataset obtained after being subjected to adversaries' random noise attacks has already lost its adversarial strength. However, noise encoders guided by the interference pattern exhibit robust adversarial strength even after undergoing attacks. + +![](images/bb35692ba1ef07aa74a9c77f41cc3ed24d77cef9038684b11831782724d4c5ee.jpg) +Figure 5. Ablation study results of different settings. (a) Impact of deploying the interference pattern on the ASR (\%) of the protected dataset and attacked dataset generated by the noise encoder. (b) The impact of different upper-bounds on attack performance and visual quality. + +![](images/087444724fdc10f7a26ddb33e0da5d52c5251f5c120cf2af7749795067a183ea.jpg) + +The Effect of $\epsilon$ We investigate the impact of four different perturbation upper-bounds $\epsilon$ on the attack performance and visual quality of protected samples. As shown in Figure 5b, different upper bounds influence both the attack performance and visual quality. + +The Weights of Losses This experiment aims to study the mechanism of our method. From Eq. 9 to 17, we design six losses to train the noise encoder. As our target is to attack pre-trained encoder, the $\mathcal{L}_{E\_adv}$ is necessary, and we set its weight to 5 which is the default value as validated in [44]. + +To more intuitively assess imperceptibility, we introduced a new metric: Learned Perceptual Image Patch Similarity (LPIPS) [39] to evaluate the visual quality of the protected dataset. In contrast to SSIM and PSNR, LPIPS utilizes deep networks and is specifically designed to mimic human perception in image evaluation tasks. A higher LPIPS value indicates that the differences between images are more perceptible to human perception. Table 2 displays results from ablation experiments of $\mathcal{L}_{E\cdot \mathcal{H}}$ and $\mathcal{L}_{E.mse}$ , demonstrating their importance in enhancing the imperceptibility of adversarial samples. + +To better evaluate the importance of the interference pattern, we conduct an ablation study on the values of the three losses introduced in the interference pattern: $\mathcal{L}_{I\_adv}$ , $\mathcal{L}_{I\_H}$ , and $\mathcal{L}_{I\_mse}$ . Specifically, we evaluate the performance of + +
L_E_mseL_E_HSSIMPSNRLPIPS
✓X0.8028.220.194
X✓0.8228.240.165
✓✓0.8528.260.148
+ +the protected dataset and the attacked dataset, recovered by the attacker using erroneous signature noise inputs to the noise encoder. We denote the ratio of the weights of $\mathcal{L}_{I\_adv}$ , $\mathcal{L}_{I\_H}$ , and $\mathcal{L}_{I\_mse}$ to $\mathcal{L}_{E\_adv}$ , $\mathcal{L}_{E\_H}$ , and $\mathcal{L}_{E\_mse}$ as $\phi$ , where $n: \alpha = m: \beta = \gamma: \lambda = \phi$ . By controlling the value of $\phi$ , we can adjust the importance of the interference pattern in the learning process of the noise encoder. As shown in Table 3, when $\phi = 0.5$ , the noise encoder's sensitivity to the interference pattern is reduced, leading to a decrease in $ASR_{Attacked}$ , although the reduction is not substantial. Conversely, when $\phi = 2$ , the noise encoder focuses more on learning the interference pattern, which increases the $ASR_{Attacked}$ but results in a reduced performance on the protected dataset. Thus, the weight of $\mathcal{L}_{I\_adv}$ , $\mathcal{L}_{I\_H}$ and $\mathcal{L}_{I\_mse}$ used to control the effect of the interference pattern are set to the same value as $\mathcal{L}_E$ to ensure that the learning of interference patterns is as important as the learning of normal patterns. + +Table 2. The effect of ${\mathcal{L}}_{E.mse}$ and ${\mathcal{L}}_{E\mathcal{H}}$ on imperceptibility. + +
φASRProtectedASRAttackedSSIMPSNR
0.585.4784.500.8228.22
1(Default)85.8386.110.8528.26
282.1389.500.7626.32
+ +Table 3. The effect of $\phi$ on interference pattern. + +# 4.4. Visualization Results + +In this section, we compare the visual quality of protected and recovered samples generated by RAEncoder and existing methods. As shown in Figure 6, under conditions where the adversarial strength is superior, the protected samples produced by RAEncoder still maintain superior imperceptibility when compared to those generated by SRAE. As shown in Table 4, on CIFAR10, the protected dataset generated by RAEncoder achieves higher SSIM and PSNR values compared to the existing RDH-based method by [32] and the generative methods GEAA and SRAE. On ImageNet, the protected dataset generated by RAEncoder outperforms those by [32] and SRAE but is slightly weaker than PGN. However, PGN's visual quality cannot guarantee its adversarial strength which is explained in Section 4.5. Overall, RAEncoder demonstrates its superior imperceptibility, and the recovered dataset obtained through RAEncoder is identical to the original dataset. Importantly, these results are achieved without the need for an additional classification + +head, but rather through direct utilization of a pre-trained encoder for the attack. + +![](images/485bd38169db6f6def17d5642ffe13a0a044cb504c205173505c7ed30b40cb26.jpg) +Figure 6. Visualization of the comparison between protected samples and recovered samples generated by our method and SRAE. Best viewed in zoom. + +
DatasetMethodProtectedRecovered
SSIMPSNRSSIMPSNR
CIFAR10Xue et al. [32]0.7725.760.9956.36
GEAA [41]0.3227.910.9948.11
SRAE[38]0.4214.730.7627.67
Ours0.8528.261.00∞
ImageNetXue et al. [32]0.5820.470.9850.15
PGN [31]0.9434.231.00∞
SRAE[38]0.7627.670.9738.67
Ours0.8230.261.00∞
+ +Table 4. Visual performance comparison of protected and recovered datasets from our method and existing methods. + +# 4.5. Transferability Study + +In this section, we delve into the transferability of the RAEncoder from two distinct perspectives: attacks on downstream models trained with different pre-trained encoders, and attacks on various SL models with different network architectures. The downstream models used to evaluate transferability are trained on the corresponding pre-trained datasets of BYOL. The target SL model employed for [32], PGN and SRAE to generate the CIFAR10 protected dataset is ResNet18 and for ImageNet is ResNet50. High ASR is indicative of better adversarial strength and transferability. As shown in Table 5, the protected dataset generated by RAEncoder exhibits strong adversarial strength across various datasets, different SL models, and diverse pre-trained encoder configurations, resulting in significantly high ASR. Furthermore, its transferabil + +ity across various SL models and pre-trained encoders frequently surpasses existing methods. However, while [32], PGN and SRAE demonstrate equally outstanding transferability across SL models, their ASR dramatically decreases when applied to downstream models trained by pre-trained encoders. It is noteworthy that, when applied to the CIFAR10 dataset, the ASR of SRAE is marginally higher than that of RAEncoder. However, as indicated in the Table 4, this increase in ASR is attained at the expense of image quality. Based on the results presented in Section 4.4 and Table 5, it is evident that our proposed RAEncoder effectively maintains the imperceptibility of protected samples while achieving a high level of adversarial strength. + +# 4.6. Robustness Study + +# 4.6.1. Image Processing Operation + +We consider four image processing operations as attack measures from the perspective of attackers, aiming to mitigate the adversarial strength of protected samples. As depicted in Figure 7a, the protected samples generated by our proposed RAEncoder exhibit superior robustness compared to those generated by SRAE. Even after undergoing various image processing operations, the protected samples generated by RAEncoder maintain their adversarial effect, rendering the model incapable of correctly classifying the processed samples. This demonstrates that RAEncoder possesses enhanced robustness. + +![](images/2eb4fd1b99cb4b2253676aa0e1e9803449f976264815c462b8ea704da84a8571.jpg) +(a) + +![](images/30c10c521b7c631141b958aeed421451d40424167dca0606446ae414af9511af.jpg) +(b) +Figure 7. The attack performance of RAEncoder in various settings. (a) From left to right, no disturbance, Center crop(proportion = 90%), Flip(horizontal and vertical), Resize(half of the height and width), Resize (twice the height and width) and JPEG compression(quality factor = 70). (b) Different degree of corruption. + +# 4.6.2. Corruption + +We take into consideration attackers may diminish the adversarial strength by introducing varying degrees of Gaussian blur to the samples, thereby degrading the images. As depicted in Figure 7b, with an increase in the degree of Gaussian perturbation, the ASR decreases. Particularly, when the blur degree reaches 1.25, the ASR of SRAE has dropped to approximately $30\%$ , whereas our RAEncoder maintains an ASR of over $50\%$ . + +
VGG16ResNet18ResNet50Dense121BalowBYOLDeepC2DINOMoCo2+NNCLR
Xue et al. [32]CIFAR1040.1248.5132.1742.4048.9747.6858.1254.8833.8448.96
ImageNet73.0488.1876.4264.2874.1687.5656.640.609.5648.44
PGN [31]CIFAR10----------
ImageNet81.3268.2266.4451.7667.2677.7649.260.589.2434.12
SRAE [38]CIFAR1061.8488.4076.7972.4773.6888.8290.4551.6580.0380.44
ImageNet72.3087.2284.0679.9474.6092.0055.5266.0011.2620.28
OursCIFAR1058.7984.7970.6674.5275.0589.6489.7958.8285.3783.18
ImageNet98.2291.4688.3099.0089.0498.9753.4686.0030.8451.80
+ +Table 5. Comparison study of ASR (%) of protected datasets across different SL models and pre-trained encoders. -' denotes experiments not conducted. + +# 4.6.3. Adaptive Attack + +We consider the worst-case scenario for security concerns when deploying RAEncoder in practical applications (i.e., adaptive attack [32]). In such a scenario, attackers have full knowledge of the dataset protection methods, with the signature noise being the only unknown factor. The attacker is aware of the specifications of signature noise $S$ . However, due to the presence of the designed interference pattern, attackers are unable to reconstruct the original sample without signature noise $S$ . As shown in Figure 8, attackers are unable to recover the original sample by inputting random noise into the noise encoder and obtaining the output perturbation. Moreover, this even results in deeper levels of sample distortion. + +![](images/01532a76d9b96d80507982d2cb1adad059357675d5df36692bd946ea379e666d.jpg) +Figure 8. Examples of failure in image restoration by the attacker using incorrect signature noise. + +# 4.7. Adversarial Strength Explanation + +We aim to generate protected samples that are sufficiently distant from the original classes under small perturbations while remaining difficult to detect. As illustrated in Figure 9a and 9b, although PGN and SRAE can push some samples away from the original classes, the protected samples remain very close to the original samples in the feature space. However, as shown in Figure 9c, the method proposed by us, RAEncoder, yields protected samples that + +cluster together in the feature space, far from all original classes. Meanwhile, there are even cases where protected samples exhibit feature space almost identical to samples from other original classes, demonstrating the superior adversarial strength and imperceptibility of RAEncoder. + +![](images/eee3b3a3e64723ba3daaa961dcbaa872012ff97a8a3d5347997ca45816a08882.jpg) +(a) PGN + +![](images/5553c49baab4b8510109ea3f0b343ea8844fd370a36f6fb2a6109c648c0229ff.jpg) +(b) SRAE +Figure 9. t-SNE [29] visualization of the feature space of protected examples produced by PGN, SRAE and ours. The hollow dots represent original samples and the solid dots represent RAEs. + +![](images/0ef08e6fdd9064cabd422dace5824c8efac94ecd8041675ed3ce156cec48f378.jpg) +(c) Ours + +# 5. Conclusion and Future work + +In this paper, we highlight the novel challenges posed by the prevalence of SSL on RAEs for the first time. We introduce the first RAE framework applicable to protect the IP of unlabeled datasets. It leverages a noise encoder to generate universal adversarial perturbations for RAE generation, meeting the requirements of adversarial strength and full reversibility. Our RAEncoder exhibits significant performance improvement in all comparative experiments. We also evaluate its robustness against adaptive attacks, highlighting the practical advantages of RAEncoder over existing methods. Future work will include further exploration of balancing visual quality with adversarial strength. We also see new research opportunities in extending the attack approach against variational auto-encoders. + +Acknowledgment. This work was supported in part by National Natural Science Foundation of China (NFSC, No. 62362025) and Hainan Province Science and Technology Special Fund (No. ZDYF2022GXJS224). + +# References + +[1] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 IEEE symposium on security and privacy (sp), pages 39-57. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4345–4355, 2023. 1, 2, 6 \ No newline at end of file diff --git a/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/images.zip b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..76abc100fa46a9f55c6ccf584710e8d6e2d2ffe3 --- /dev/null +++ b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:71853a93c0918400d960f50eb45901fadf9d5de2df89ae277a8ef525f3cd4c2b +size 540110 diff --git a/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/layout.json b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1c3c5ae3389b7184fd0806474ac6eefb12af28b7 --- /dev/null +++ b/2025/RAEncoder_ A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection/layout.json @@ -0,0 +1,10661 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 80, + 102, + 531, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 102, + 531, + 138 + ], + "spans": [ + { + "bbox": [ + 80, + 102, + 531, + 138 + ], + "type": "text", + "content": "RAEncoder: A Label-Free Reversible Adversarial Examples Encoder for Dataset Intellectual Property Protection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 182, + 161, + 426, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 161, + 426, + 190 + ], + "spans": [ + { + "bbox": [ + 182, + 161, + 426, + 190 + ], + "type": "text", + "content": "Fan Xing, Zhuo Tian, Xuefeng Fan, Xiaoyi Zhou* Hainan University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 168, + 191, + 440, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 191, + 440, + 204 + ], + "spans": [ + { + "bbox": [ + 168, + 191, + 440, + 204 + ], + "type": "text", + "content": "{xingfan, tianzhuo, xffan, xy.zhou}@hainanu.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 258, + 294, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 258, + 294, + 580 + ], + "spans": [ + { + "bbox": [ + 56, + 258, + 294, + 580 + ], + "type": "text", + "content": "Reversible Adversarial Examples (RAE) are designed to protect the intellectual property of datasets. Such examples can function as imperceptible adversarial examples to erode the model performance of unauthorized users while allowing authorized users to remove the adversarial perturbations and recover the original samples for normal model training. With the rise of Self-Supervised Learning (SSL), an increasing number of unlabeled datasets and pre-trained encoders are available in the community. However, existing RAE methods not only rely on well-labeled datasets for training Supervised Learning (SL) models but also exhibit poor adversarial transferability when attacking SSL pre-trained encoders. To address these challenges, we propose RAEncoder, the first framework for RAEs without the need for labeled samples. RAEncoder aims to generate universal adversarial perturbations by targeting SSL pretrained encoders. Unlike traditional RAE approaches, the pre-trained encoder outputs the feature distribution of the protected dataset rather than classification labels, enhancing both the attack success rate and transferability of RAEs. Extensive experiments are conducted on six pre-trained encoders and four SL models, covering aspects such as imperceptibility and transferability. Our results demonstrate that RAEncoder effectively protects unlabeled datasets from malicious infringements. Additional robustness experiments further confirm the security of RAEncoder in practical application scenarios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 608, + 135, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 608, + 135, + 620 + ], + "spans": [ + { + "bbox": [ + 56, + 608, + 135, + 620 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 294, + 713 + ], + "type": "text", + "content": "Reversible Adversarial Examples (RAE) [20, 31-34, 37, 38, 41] are highlighted as a fundamental method for protecting dataset Intellectual Property (IP). Unlike traditional methods for dataset IP protection, such as reversible watermarking [10, 19, 42] and image encryption techniques [11, 35], RAE transforms the dataset into adversarial examples that can mislead model training while allowing authorized users" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 232, + 553, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 553, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 553, + 340 + ], + "type": "text", + "content": "to remove the adversarial perturbations and restore the original dataset [20]. The adversarial attack methods used in existing RAE schemes focus on targeting specific Supervised Learning (SL) classifiers through optimization-based or gradient-based attacks, which result in a notable limitation: they lose adversarial strength when attacking different model architectures, and the adversarial strength diminishes especially when attacking downstream models trained with Self-Supervised Learning (SSL) pre-trained encoders." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 341, + 553, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 553, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 553, + 484 + ], + "type": "text", + "content": "SSL is an emerging paradigm in machine learning. It typically involves pre-training a generic encoder on vast amounts of unlabeled data, and it can then serve as a feature extractor for a wide range of downstream tasks. By utilizing a pre-trained encoder, any resource-constrained user can leverage the advantages of a large model without the need to undertake expensive training from scratch. Considering SSL for RAEs is highly noteworthy because if RAEs exhibit poor transferability when attacking SSL pre-trained encoders, any attacker can leverage them to pre-process RAEs, thereby mitigating the impact of them on the training performance of unauthorized downstream models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 713 + ], + "type": "text", + "content": "Due to the fact that SSL pre-trained encoders learn feature representations of the data directly rather than feature-label relationships, adversarial attacks against SSL pre-encoders can exhibit excellent transferability across different downstream model architectures [43, 44]. Although this attack process demonstrates significant effectiveness, using it as a method to generate RAEs for protecting dataset IP introduces an additional challenge. Specifically, the protection scheme must address the worst-case scenario—adaptive attacks, where the attacker is assumed to be aware of the detailed steps of the protection scheme [32]. This requires the protection scheme to effectively differentiate between authorized and unauthorized access. To differentiate between authorized and unauthorized users, existing Reversible Data Hiding (RDH)-based RAE methods embed encrypted information in RAEs, ensuring that only users with the correct key can recover original samples. However, embedding any information within RAEs could significantly impact both adversarial strength and vi" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20665" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": "sual quality[20, 31, 32]. Then, without embedding information, how can RAEs be designed to differentiate user authorization and ensure both effectiveness and robustness when attacking SSL encoders?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 296, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 296, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 296, + 312 + ], + "type": "text", + "content": "To bridge the gap between the practical applicability of RAE and real-world needs in the context of SSL's growing popularity, we propose a novel approach, RAEncoder. To be specific, we design a noise encoder with a fixed signature noise as input. It learns the data distribution and generates universal adversarial perturbations by targeting SSL encoder. To effectively differentiate between authorized and unauthorized users, an interference pattern is designed to make the noise encoder insensitive to inputs other than the correct signature noise. By inputting the correct signature noise, authorized users can employ the noise encoder to obtain the recovered perturbation, thereby recovering the original sample. During noise encoder training, we employ high-frequency filters [21, 44] to optimize RAE imperceptibility, as high-frequency perturbations are less detectable than low-frequency ones." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 313, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 296, + 335 + ], + "type": "text", + "content": "Compared to the existing work, our contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 338, + 296, + 553 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 56, + 338, + 296, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 338, + 296, + 409 + ], + "spans": [ + { + "bbox": [ + 56, + 338, + 296, + 409 + ], + "type": "text", + "content": "- A Novel RAEncoder Framework: We introduce RAEncoder to address the limitations of existing RAE frameworks in the context of the growing popularity of SSL. To the best of our knowledge, RAEncoder is the first RAE framework applicable for protecting the IP of unlabeled datasets with " + }, + { + "bbox": [ + 56, + 338, + 296, + 409 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 56, + 338, + 296, + 409 + ], + "type": "text", + "content": " fidelity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 410, + 296, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 410, + 296, + 481 + ], + "spans": [ + { + "bbox": [ + 56, + 410, + 296, + 481 + ], + "type": "text", + "content": "- Innovative Noise Encoder: A noise encoder capable of generating RAEs guided by sample texture features is devised to successfully balance imperceptibility with adversarial strength. Additionally, we introduce three losses in the interference pattern to guide adversarial attacks on SSL pre-encoders, ensuring the RAE's robustness." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 481, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 481, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 56, + 481, + 296, + 553 + ], + "type": "text", + "content": "- Extensive Experimental Validation: Through extensive experiments, we compare our RAEncoder with state-of-the-art (SOTA) RAE schemes. The results demonstrate that our RAEncoder outperforms existing methods in various metrics, including imperceptibility, adversarial strength, and transferability." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 567, + 142, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 142, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 142, + 578 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 587, + 222, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 222, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 222, + 601 + ], + "type": "text", + "content": "2.1. SSL and Its Emerging Threats" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "SSL uses the inherent information present in unlabeled data to pre-train encoders. These encoders learn to transform complex inputs into generic representations. Once trained, they can extract valuable domain knowledge and serve as versatile tools for solving different specific tasks. With the thriving development of SSL, pre-trained encoders have gained popularity in the industry. Many service providers openly release their pre-trained encoders, such as Google's BYOL [12] and Meta's MoCo [6, 14]. Recently, an increas" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": "ing number of studies begin to investigate adversarial attacks against pre-trained encoders in SSL. Zhou et al. proposed the first attack framework that generates downstream-agnostic adversarial examples based on a cross-modal pretrained encoder for images and text [43]. Zhou et al. proposed the first scheme for generating universal adversarial examples based on pre-trained encoders[44]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 163, + 493, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 493, + 176 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 493, + 176 + ], + "type": "text", + "content": "2.2. Reversible Adversarial Examples" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 180, + 554, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 554, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 554, + 253 + ], + "type": "text", + "content": "Existing RAE schemes can be divided into two categories, RDH-based methods[20, 31-34, 37] and generative methods [38, 41], as shown in Figure 1. To generate adversarial examples, recent research endeavors utilize a range of adversarial attacks targeting SL classifier, such as IFGSM[18], DeepFool[23], and C&W[1]." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 319, + 262, + 485, + 378 + ], + "blocks": [ + { + "bbox": [ + 319, + 262, + 485, + 378 + ], + "lines": [ + { + "bbox": [ + 319, + 262, + 485, + 378 + ], + "spans": [ + { + "bbox": [ + 319, + 262, + 485, + 378 + ], + "type": "image", + "image_path": "315409910f657af6bffe8565f0437ce6e5ed3025234e3a6731932b8cb8d71a85.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 320, + 378, + 485, + 454 + ], + "blocks": [ + { + "bbox": [ + 320, + 378, + 485, + 454 + ], + "lines": [ + { + "bbox": [ + 320, + 378, + 485, + 454 + ], + "spans": [ + { + "bbox": [ + 320, + 378, + 485, + 454 + ], + "type": "image", + "image_path": "56235690c3767c1c604bcb0dc8d61e2b10773c7a2d7c2d34bf8b4e7b212a08d7.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 464, + 554, + 510 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 510 + ], + "type": "text", + "content": "Figure 1. Existing methods can be divided into two categories: generative and RDH-based. Our method not only eliminates reliance on classifiers for adversarial attacks but also achieves " + }, + { + "bbox": [ + 313, + 464, + 554, + 510 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 464, + 554, + 510 + ], + "type": "text", + "content": " fidelity without compromising adversarial strength." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 485, + 262, + 550, + 394 + ], + "blocks": [ + { + "bbox": [ + 485, + 262, + 550, + 394 + ], + "lines": [ + { + "bbox": [ + 485, + 262, + 550, + 394 + ], + "spans": [ + { + "bbox": [ + 485, + 262, + 550, + 394 + ], + "type": "image", + "image_path": "fef59caab8009d77c7b49ccd92e197d582c9a461924a2d3ff3279eacfae20567.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "lines": [ + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "spans": [ + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": "X' Original sample \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Adversarial example \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "X^p" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Protected sample \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "X^r" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Recovered sample \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "\\square" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Classifier \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "\\mathrm{ms}" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Auxiliary Information \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "\\ominus" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Element-wise Subtraction \n" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 488, + 395, + 547, + 453 + ], + "type": "text", + "content": " Element-wise Addition" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": "Given that images contain inherent structures that allow adversarial attacks to be reversed [22], the concept of RAE was first introduced [20] and proposed the first RAE generation method based on RDH technology. Their approach involves embedding the pixel differences between adversarial examples and the original image into the image using RDH, allowing authorized users to achieve " + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": " recovery of original samples by extracting the pixel differences. However, this method still has several issues, such as the deterioration of the visual quality of adversarial samples and a reduction in adversarial strength due to embedding information. Thus, reducing the embedded perturbation amount in RAE is a feasible approach. Yin et al. confined perturbations to regions most impactful on adversarial strength[34]. They leveraged the characteristic of the YUV color space, where the human eye is less sensitive to changes in the UV" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20666" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 251 + ], + "type": "text", + "content": "channels, by embedding the perturbation differences of the Y channel into the UV channels. Zhang et al. leveraged beam search-based black-box attacks in combination with reversible data hiding featuring grayscale invariance[37]. Xiong et al. proposed PGN, which reduces adversarial perturbations to a sign matrix format and a product with fixed perturbation parameters[31]. Therefore, PGN only needs to record the sign matrix corresponding to pixel differences and embed it with the fixed perturbation parameters, significantly reducing the amount of embedding required. Meanwhile, existing work combined Reversible Image Transformation (RIT)[40] with RDH which involves embedding the reversible transformation information between the original sample and the adversarial example, rather than pixel differences, into the RAEs[32, 33]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "type": "text", + "content": "In the field of generative methods, SRAE [38] developed RAEs using a recoverable generative adversarial network designed to minimize recovery errors while maximizing their effectiveness in adversarial attacks. GEAA [41] utilizes a dual-stream architecture to generate adversarial and recovered samples, ensuring that the distribution of adversarial samples significantly differs from the original." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "content": "In summary, RDH-based methods preserve the inverse operation that restores adversarial examples to the original samples, allowing most RDH-based methods to achieve " + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "content": " sample recovery. While generative methods cannot currently achieve " + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 55, + 335, + 296, + 430 + ], + "type": "text", + "content": " recovery, they do not require any information embedding that might affect adversarial strength. As a result, generative methods exhibit significantly higher adversarial strength compared to RDH-based methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 431, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 296, + 491 + ], + "type": "text", + "content": "It is noteworthy that existing work generates RAEs by targeting supervised learning models for adversarial attacks, without addressing the new challenges posed by the popularity of SSL. Consequently, existing RAE solutions are unable to effectively protect unlabeled datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 502, + 138, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 138, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 138, + 514 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 521, + 167, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 167, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 167, + 533 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "spans": [ + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": "Given a pre-trained encoder " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "e_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " with input " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "x_{pt}" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pt}" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " represents the parameters of the pre-trained encoder. " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pt}" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " denotes the pre-training dataset. The data owner uses the original sample " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " in original dataset " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " (remains unattainable for the attacker) to generate universal adversarial perturbation " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " against the pre-trained encoder. The universal adversarial perturbation " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " should be sufficiently small and modeled by an upper-bound " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "inline_equation", + "content": "l_{p}" + }, + { + "bbox": [ + 55, + 538, + 296, + 646 + ], + "type": "text", + "content": " norm. The task of finding a perturbation can be formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 97, + 655, + 295, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 655, + 295, + 669 + ], + "spans": [ + { + "bbox": [ + 97, + 655, + 295, + 669 + ], + "type": "interline_equation", + "content": "e _ {\\theta} (x + \\delta) \\neq e _ {\\theta} (x), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {1}", + "image_path": "a3add8933671de5959a7308be2e18556f10c848b652ba3edb3a3a8bcc0659ae4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "inline_equation", + "content": "||\\cdot ||_p" + }, + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "inline_equation", + "content": "l_{p}" + }, + { + "bbox": [ + 55, + 677, + 168, + 689 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "The data owner's objective is to achieve a universal nontargeted attack to deceive the downstream classifier " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta'}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 72, + 553, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 84 + ], + "type": "text", + "content": "Therefore, the data owner's objective can be formalized as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 331, + 105, + 553, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 105, + 553, + 118 + ], + "spans": [ + { + "bbox": [ + 331, + 105, + 553, + 118 + ], + "type": "interline_equation", + "content": "f _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x + \\delta)\\right) \\neq f _ {\\theta^ {\\prime}} \\left(e _ {\\theta} (x)\\right), \\quad s. t. | | \\delta | | _ {p} \\leq \\varepsilon \\tag {2}", + "image_path": "4a90516bd2d9b910802fe3f52992182d0e675c4659e7b1f1992d4e6669002112.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": "When all original samples " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " in original dataset " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " are augmented with a universal adversarial perturbation " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": ", it results in a protected dataset " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_p" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " composed of protected samples (i.e., reversible adversarial examples) " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_p" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " is used as a reference for all users. We assume that any users have access to public pre-trained encoders " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "e_{\\theta}^{pub}(\\cdot)" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " with input " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "x^{pub}" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": " in the public dataset " + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^{pub}" + }, + { + "bbox": [ + 313, + 126, + 555, + 222 + ], + "type": "text", + "content": ", which they can obtain through purchase or direct download from public repositories." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "spans": [ + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": "The attackers' objective is to encode protected datasets " + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_p" + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "inline_equation", + "content": "e_{\\theta}^{pub}(\\cdot)" + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": " to minimize the impact of " + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_p" + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": " on training performance and then training downstream classifier " + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "inline_equation", + "content": "f_{\\theta}^{atk}(e_{\\theta}^{pub}(\\cdot))" + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": ". However, as shown in Figure 2, " + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "inline_equation", + "content": "x^p \\in \\mathcal{D}_p" + }, + { + "bbox": [ + 313, + 223, + 554, + 305 + ], + "type": "text", + "content": " is incorrectly encoded into other feature distributions, resulting in a significant degradation in the performance of the obtained downstream classifier which can be formalized as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 316, + 553, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 316, + 553, + 331 + ], + "spans": [ + { + "bbox": [ + 349, + 316, + 553, + 331 + ], + "type": "interline_equation", + "content": "\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {p}\\right)\\right)\\right) \\ll \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {3}", + "image_path": "9108844541237e780b6bf7150bf67efae559fd351c460b5d6f04e44d7e1ce84f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 335, + 548, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 548, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 548, + 346 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 335, + 548, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 313, + 335, + 548, + 346 + ], + "type": "text", + "content": " denotes the inference accuracy for a classifier." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "text", + "content": "For authorized users, they can obtain recovered samples " + }, + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "inline_equation", + "content": "x^{r} \\in \\mathcal{D}_{r}" + }, + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "text", + "content": " which closely resemble the feature distribution of " + }, + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 347, + 554, + 392 + ], + "type": "text", + "content": " for normal downstream task training that can be formalized as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 351, + 393, + 553, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 393, + 553, + 408 + ], + "spans": [ + { + "bbox": [ + 351, + 393, + 553, + 408 + ], + "type": "interline_equation", + "content": "\\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} \\left(x ^ {r}\\right)\\right)\\right) \\approx \\mathcal {A} \\left(f _ {\\theta} ^ {a t k} \\left(e _ {\\theta} ^ {p u b} (x)\\right)\\right) \\tag {4}", + "image_path": "92f02354fbcbf2a50281d4e867bc3197c439d7351d27c49377d7aebbc95eeb66.jpg" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 318, + 423, + 433, + 482 + ], + "blocks": [ + { + "bbox": [ + 318, + 423, + 433, + 482 + ], + "lines": [ + { + "bbox": [ + 318, + 423, + 433, + 482 + ], + "spans": [ + { + "bbox": [ + 318, + 423, + 433, + 482 + ], + "type": "image", + "image_path": "cb1897138eeb6b450cb0e7c393a9aee930f6243b3f8d92cf05375cf680013732.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 484, + 382, + 493 + ], + "lines": [ + { + "bbox": [ + 371, + 484, + 382, + 493 + ], + "spans": [ + { + "bbox": [ + 371, + 484, + 382, + 493 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 434, + 424, + 551, + 482 + ], + "blocks": [ + { + "bbox": [ + 434, + 424, + 551, + 482 + ], + "lines": [ + { + "bbox": [ + 434, + 424, + 551, + 482 + ], + "spans": [ + { + "bbox": [ + 434, + 424, + 551, + 482 + ], + "type": "image", + "image_path": "1e40f8c8a3556be18f8171fecf431afc6cc4634a4b05a69a6b5bad2d643379f7.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 487, + 483, + 498, + 493 + ], + "lines": [ + { + "bbox": [ + 487, + 483, + 498, + 493 + ], + "spans": [ + { + "bbox": [ + 487, + 483, + 498, + 493 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 503, + 554, + 568 + ], + "lines": [ + { + "bbox": [ + 313, + 503, + 554, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 554, + 568 + ], + "type": "text", + "content": "Figure 2. Illustrations of sample attributes: (a) The representation of different samples in the feature space. The dashed lines in different colors represent feature representations of various distributions (b) The fit of different samples within the classification decision boundary. The curved lines in different colors indicate the decision boundaries for different classes." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 588, + 419, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 419, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 419, + 601 + ], + "type": "text", + "content": "3.2. Training Pipeline" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": "The training pipeline of RAEncoder is illustrated in Figure 3. It consists of a noise encoder " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ", a high-frequency filter " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ", and a target encoder " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "e_{\\theta}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ". Specifically, we generate a universal adversarial perturbation " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " applicable to all " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " by inputting a fixed signature noise " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " into noise encoder " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ". We then paste " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " to obtain protected sample " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "D_{p}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ", where high-frequency information of " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " is reduced by high-frequency filter " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ". Authorized users can input the signature noise " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " into the noise encoder " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": ". Subtracting " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20667" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": "from " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " results in a fully recovered sample " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "x^r" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " identical to the original " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": ", which is achieved for the first time in the previous RAE schemes. During the training process of noise encoder " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": ", we propose an interference pattern to incentivize " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " to distinguish signature noise " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " from other noise inputs, aiming to prevent potential attackers from inputting random noise to steal " + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": " for image restoration." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 167, + 291, + 294 + ], + "blocks": [ + { + "bbox": [ + 60, + 167, + 291, + 294 + ], + "lines": [ + { + "bbox": [ + 60, + 167, + 291, + 294 + ], + "spans": [ + { + "bbox": [ + 60, + 167, + 291, + 294 + ], + "type": "image", + "image_path": "b91bc0be9de2dad9f2c3184a012ad15bd6c207357abc8a6ae035f534431d7868.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 90, + 302, + 260, + 314 + ], + "lines": [ + { + "bbox": [ + 90, + 302, + 260, + 314 + ], + "spans": [ + { + "bbox": [ + 90, + 302, + 260, + 314 + ], + "type": "text", + "content": "Figure 3. The training pipeline of RAEncoder." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 334, + 148, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 148, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 148, + 344 + ], + "type": "text", + "content": "3.2.1. 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\\delta = x \\tag {7}", + "image_path": "e4a1eabc3c3ddf555c59c8b89ef40446f24ed704eae091304bd71be4dd6f4aa8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 552, + 296, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 575 + ], + "type": "text", + "content": "The loss function for optimizing noise encoder " + }, + { + "bbox": [ + 55, + 552, + 296, + 575 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 552, + 296, + 575 + ], + "type": "text", + "content": " can be described as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 96, + 586, + 295, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 586, + 295, + 599 + ], + "spans": [ + { + "bbox": [ + 96, + 586, + 295, + 599 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E} = \\alpha \\mathcal {L} _ {E. a d v} + \\beta \\mathcal {L} _ {E. \\mathcal {H}} + \\lambda \\mathcal {L} _ {E. m s e}, \\tag {8}", + "image_path": "4684255be646cbed9a8b238eff93a69f3f2d73e3c69ede82a276a394315cc57e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 609, + 84, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 84, + 619 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 84, + 619 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 79, + 628, + 295, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 628, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 79, + 628, + 295, + 658 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {9}", + "image_path": "322a1485e3444ab0eb021f0d4dc1a8a6db593705977d8cf226679fda2bbb5b49.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 112, + 669, + 295, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 669, + 295, + 683 + ], + "spans": [ + { + "bbox": [ + 112, + 669, + 295, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E. \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p}\\right) - \\mathcal {H} (x) | | _ {2} ^ {2}, \\tag {10}", + "image_path": "16aa8b8cc534165c1b34dd0b1055e2503e8f12f910dde57d86348a221e022dd3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 129, + 700, + 295, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 700, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 129, + 700, + 295, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E \\_ m s e} = | | x ^ {p} - x | | _ {2} ^ {2}, \\tag {11}", + "image_path": "5633f7819b52bbc594e77c91b266ed32cd0e569196944f6291e71614a5c0bc71.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _2" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " norm, " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\langle u\\cdot c\\rangle = u^{\\mathsf{T}}c / \\| u\\| \\| c\\|" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " represents the cosine similarity. " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": "-th sample, with a maximum value of " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " represents a number not equal to " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " indicates a temperature parameter. " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_adv}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " drives noise encoder to perform negative pairing between the protected sample " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": ", maximizing the mutual information distance between their features in the feature space by calculating the InfoNCE loss[4, 24]. " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_H}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " aims to constrain the perturbation intensity in high frequency through the high-frequency filter " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_mse}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " aims to make sure the indistinguishability between " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 72, + 555, + 205 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 317, + 212, + 550, + 305 + ], + "blocks": [ + { + "bbox": [ + 317, + 212, + 550, + 305 + ], + "lines": [ + { + "bbox": [ + 317, + 212, + 550, + 305 + ], + "spans": [ + { + "bbox": [ + 317, + 212, + 550, + 305 + ], + "type": "image", + "image_path": "bb650a516585cc20bc88ed87cb1fe3c3d935a17a0837a9a3da2d97f5d7e3f83d.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 314, + 555, + 336 + ], + "lines": [ + { + "bbox": [ + 313, + 314, + 555, + 336 + ], + "spans": [ + { + "bbox": [ + 313, + 314, + 555, + 336 + ], + "type": "text", + "content": "Figure 4. Visual results of original samples different samples generated from noise encoder without interference pattern employed." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 352, + 432, + 362 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 432, + 362 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 432, + 362 + ], + "type": "text", + "content": "3.2.2. Interference Pattern." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": "Training and optimizing " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " enables the generation of a highly adversarial universal perturbation " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": ", significantly affecting the model training effectiveness for unauthorized users. However, we discover that guiding the noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " to solely learn the generation of a universal adversarial perturbation " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " from signature noise " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " without constraints can lead to vulnerabilities. In the event that the noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " is compromised by attackers, they can potentially acquire a perturbation similar to " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " for image recovery by feeding noise of the same size as " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " into the noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": ". While the likelihood of the noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " being compromised, particularly when stored in cloud services such as DMCP[32], is minimal in practical scenarios, such an outcome remains unacceptable in cases where the noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " cannot distinguish between inputs from authorized users and attackers. As shown in Figure 4, the images shown in the third column are obtained by subtracting the output of noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " when the protected sample " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " and random noise of the same size as signature noise " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " are inputted. It can be observed that these samples are very similar to the original images, which completely undermines the security of RAEs. Therefore, an interference pattern is exploited to resolve this problem. The idea is simple: when applying random noise " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "S' \\neq S" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": ", noise encoder " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " should not generate perturbation " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": ", but instead generate an almost blank perturbation " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta'" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " with hardly any pixel values. The subtraction of perturbation " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "\\delta'" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " yields " + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "inline_equation", + "content": "x^{p'}" + }, + { + "bbox": [ + 313, + 367, + 556, + 700 + ], + "type": "text", + "content": " which can be described as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 408, + 700, + 553, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 700, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 408, + 700, + 553, + 714 + ], + "type": "interline_equation", + "content": "E \\left(\\mathcal {S} ^ {\\prime}\\right) = \\delta^ {\\prime}, \\tag {12}", + "image_path": "fc31d475ee49f4d04e84ddf6f396897d14e0b6f808cfcf180efd2e4f85d54b11.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20668" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 145, + 83, + 294, + 96 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 83, + 294, + 96 + ], + "spans": [ + { + "bbox": [ + 145, + 83, + 294, + 96 + ], + "type": "interline_equation", + "content": "x ^ {p} - \\delta^ {\\prime} = x ^ {p ^ {\\prime}} \\tag {13}", + "image_path": "2d1fb2f6873123c91f9f12f566c225189c11425216ee31c7304dd1181ba12501.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 100, + 296, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 100, + 296, + 125 + ], + "spans": [ + { + "bbox": [ + 55, + 100, + 296, + 125 + ], + "type": "text", + "content": "Thus, the loss function for optimizing noise encoder E with interference pattern can be described as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 73, + 143, + 296, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 143, + 296, + 157 + ], + "spans": [ + { + "bbox": [ + 73, + 143, + 296, + 157 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E \\mathcal {I}} = n \\mathcal {L} _ {I. a d v} + m \\mathcal {L} _ {I. \\mathcal {H}} + \\gamma \\mathcal {L} _ {I. m s e} + \\mathcal {L} _ {E}, \\tag {14}", + "image_path": "93a994ba5f15e235f9be138288e733cdae7efd7b69a7d00aecb591d01bfdc571.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 178, + 295, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 178, + 295, + 209 + ], + "spans": [ + { + "bbox": [ + 70, + 178, + 295, + 209 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I. a d v} = \\log \\frac {\\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {i}\\right) \\right\\rangle / \\tau\\right)}{\\sum_ {k = 0} ^ {N} \\exp \\left(\\left\\langle e _ {\\theta} \\left(x _ {i} ^ {p ^ {\\prime}}\\right) , e _ {\\theta} \\left(x _ {k}\\right) \\right\\rangle / \\tau\\right)}, \\tag {15}", + "image_path": "62eab0069768ad34a54c910fa08ad4b92592f9b3b02ae3758a6e54890a7860c6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 216, + 296, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 216, + 296, + 232 + ], + "spans": [ + { + "bbox": [ + 110, + 216, + 296, + 232 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I \\mathcal {H}} = - | | \\mathcal {H} \\left(x ^ {p ^ {\\prime}}\\right) - \\mathcal {H} \\left(x ^ {p}\\right) | | _ {2} ^ {2}, \\tag {16}", + "image_path": "e0c567abb45f61e855ac96c0bf16208ada956555f4619687767b5033de3cab23.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 126, + 243, + 295, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 243, + 295, + 259 + ], + "spans": [ + { + "bbox": [ + 126, + 243, + 295, + 259 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I. m s e} = \\left\\| x ^ {p} - x ^ {p ^ {\\prime}} \\right\\| _ {2} ^ {2}. \\tag {17}", + "image_path": "af2dbc417006756a7f662a17f03fd8866dbfa36eb486e69a9a0072aee24764a8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_adv}, \\mathcal{L}_{I\\_H}" + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_mse}" + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "text", + "content": " are employed to minimize " + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "inline_equation", + "content": "\\delta'" + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "text", + "content": " generated from random noise " + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "inline_equation", + "content": "S'" + }, + { + "bbox": [ + 55, + 262, + 296, + 298 + ], + "type": "text", + "content": " towards zero as much as possible." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 307, + 137, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 307, + 137, + 320 + ], + "spans": [ + { + "bbox": [ + 55, + 307, + 137, + 320 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 326, + 178, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 326, + 178, + 339 + ], + "spans": [ + { + "bbox": [ + 55, + 326, + 178, + 339 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 344, + 174, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 344, + 174, + 355 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 174, + 355 + ], + "type": "text", + "content": "4.1.1. Datasets and Models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 359, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 359, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 359, + 296, + 491 + ], + "type": "text", + "content": "We utilize pre-trained encoders from the solo-learn [8], a well-established self-supervised learning library, as target encoders. These pre-trained encoders were trained on CIFAR10 [17] or ImageNet [25] datasets, employing ResNet18 [13] as the backbone. Among the array of SSL techniques available, we select six pioneering methods: Barlow Twins [36], BYOL [12], DeepCluster v2 [2], DINO [3], MoCo v2+ [5], and NNCLR [9]. We train VGG16[26], ResNet18, Resnet50[13], and DenseNet121[15] as target models. The datasets STL10 [7], GTSRB [28], CIFAR10, and ImageNet were considered as the protected datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 495, + 186, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 186, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 186, + 507 + ], + "type": "text", + "content": "4.1.2. Training configurations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": "The noise encoder consists of multiple consecutive deconvolution layers followed by a convolutional layer. The hyperparameters settings for optimizing the noise encoder " + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": " are as follows: " + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "inline_equation", + "content": "n = \\alpha = 5" + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "inline_equation", + "content": "m = \\beta = 1" + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "inline_equation", + "content": "\\gamma = \\lambda = 1" + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "inline_equation", + "content": "\\varepsilon = 10/255" + }, + { + "bbox": [ + 55, + 510, + 296, + 712 + ], + "type": "text", + "content": ", training epochs set to 20 and Adam optimizer [16] is adopted with an initial learning rate of 0.0002. For RDH-based method [32], PGN, and generative method GEAA, SRAE, all experiments conducted were based on their default settings as reported in their respective studies. Since they are not designed for adversarial attacks on pre-trained encoders, for a fair comparison to highlight the advantages of RAEncoder, we connect their target model's classification head to an encoder trained on the same pre-training dataset. Thus, the target model serves as a downstream model connected to the pre-trained encoder. Our experiments are conducted on two NVIDIA GeForce RTX 4090 GPUs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 72, + 426, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 426, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 426, + 83 + ], + "type": "text", + "content": "4.1.3. Evaluation Metrics." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 89, + 555, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 555, + 149 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 555, + 149 + ], + "type": "text", + "content": "We employ Structural Similarity Index (SSIM) [30] and Peak Signal-to-Noise Ratio (PSNR) to assess the quality of image. We use Attack Success Rate (ASR) to measure the success rate of samples that deceive the classifier. A higher numerical value indicates stronger attack capability." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 163, + 432, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 163, + 432, + 175 + ], + "spans": [ + { + "bbox": [ + 314, + 163, + 432, + 175 + ], + "type": "text", + "content": "4.2. Attack Performance" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "text", + "content": "We employ six types of SSL pre-trained encoders as target encoders " + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "inline_equation", + "content": "e_{\\theta}" + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "text", + "content": ". Using two pre-training datasets, CIFAR10 and ImageNet, we generate " + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "text", + "content": " for four downstream datasets and evaluated ASR of " + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "inline_equation", + "content": "x^{p}" + }, + { + "bbox": [ + 313, + 182, + 555, + 278 + ], + "type": "text", + "content": " on the corresponding target encoders. It is worth noting that such experimental setups are deployed to investigate whether the RAEs generated by the RAEncoder possess strong adversarial strength to successfully deceive target encoders. As shown in Table 1, across" + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 318, + 292, + 552, + 398 + ], + "blocks": [ + { + "bbox": [ + 318, + 292, + 552, + 398 + ], + "lines": [ + { + "bbox": [ + 318, + 292, + 552, + 398 + ], + "spans": [ + { + "bbox": [ + 318, + 292, + 552, + 398 + ], + "type": "table", + "html": "
BallowBYOLDeepC2DINOMoCo2+NNCLR
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", + "image_path": "5c480b99f78be208ddc25b557ae3bdee1035b5d020052d72438a1ae07d8e2124.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "text", + "content": "Table 1. Different configurations of protected samples' ASR (\\%) are evaluated. " + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1 - \\mathcal{C}_4" + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "text", + "content": " represent the downstream datasets CIFAR10, STL10, GTSRB, and ImageNet, respectively, with the encoder's pre-training dataset being CIFAR10. " + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_1 - \\mathcal{I}_4" + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "text", + "content": " use ImageNet as the pre-training dataset, and the downstream datasets are the same as those in " + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1 - \\mathcal{C}_4" + }, + { + "bbox": [ + 313, + 407, + 555, + 484 + ], + "type": "text", + "content": ". Barlow Twins and DeepCluster v2 are abbreviated as Barlow and DeepC2, respectively." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "text", + "content": "the settings of six pre-trained encoders and four downstream datasets, the ASR of protected samples remains consistently high, with over " + }, + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "text", + "content": " achieved in almost all settings. Meanwhile, it is evident that protected samples generated by pretrained encoders trained on corresponding original samples exhibit stronger adversarial attack strength. For example, When the pre-trained dataset is ImageNet and the downstream dataset is also ImageNet, the protected dataset generated by RAEncoder achieved an ASR close to " + }, + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 501, + 555, + 621 + ], + "type": "text", + "content": " when attacking encoders pre-trained on ImageNet." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 634, + 408, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 408, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 408, + 647 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 715 + ], + "type": "text", + "content": "In this section, we investigate the impact of using different datasets, modules, and attack intensities on RAEncoder when generating the protected dataset. We opt for pretrained encoders on CIFAR10 and select CIFAR10 as the protected dataset for our analysis." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20669" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 228 + ], + "type": "text", + "content": "The Effect of Interference Pattern We investigate the impact of the interference pattern. Specifically, as shown in Figure 5a, we examine the cases where noise encoders were deployed with and without the interference pattern, and subjected to random noise inputs to simulate attacks where adversaries aim to steal correct adversarial perturbations " + }, + { + "bbox": [ + 55, + 72, + 296, + 228 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 72, + 296, + 228 + ], + "type": "text", + "content": ", using random noise attacks. The results depicted in Figure 5a reveal that for noise encoders without interference pattern guidance, the attacked dataset obtained after being subjected to adversaries' random noise attacks has already lost its adversarial strength. However, noise encoders guided by the interference pattern exhibit robust adversarial strength even after undergoing attacks." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 238, + 175, + 304 + ], + "blocks": [ + { + "bbox": [ + 60, + 238, + 175, + 304 + ], + "lines": [ + { + "bbox": [ + 60, + 238, + 175, + 304 + ], + "spans": [ + { + "bbox": [ + 60, + 238, + 175, + 304 + ], + "type": "image", + "image_path": "bb35692ba1ef07aa74a9c77f41cc3ed24d77cef9038684b11831782724d4c5ee.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 312, + 296, + 369 + ], + "lines": [ + { + "bbox": [ + 55, + 312, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 296, + 369 + ], + "type": "text", + "content": "Figure 5. Ablation study results of different settings. (a) Impact of deploying the interference pattern on the ASR (\\%) of the protected dataset and attacked dataset generated by the noise encoder. (b) The impact of different upper-bounds on attack performance and visual quality." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 178, + 239, + 291, + 304 + ], + "blocks": [ + { + "bbox": [ + 178, + 239, + 291, + 304 + ], + "lines": [ + { + "bbox": [ + 178, + 239, + 291, + 304 + ], + "spans": [ + { + "bbox": [ + 178, + 239, + 291, + 304 + ], + "type": "image", + "image_path": "087444724fdc10f7a26ddb33e0da5d52c5251f5c120cf2af7749795067a183ea.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "text", + "content": "The Effect of " + }, + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "text", + "content": " We investigate the impact of four different perturbation upper-bounds " + }, + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 397, + 296, + 458 + ], + "type": "text", + "content": " on the attack performance and visual quality of protected samples. As shown in Figure 5b, different upper bounds influence both the attack performance and visual quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "text", + "content": "The Weights of Losses This experiment aims to study the mechanism of our method. From Eq. 9 to 17, we design six losses to train the noise encoder. As our target is to attack pre-trained encoder, the " + }, + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_adv}" + }, + { + "bbox": [ + 55, + 473, + 295, + 533 + ], + "type": "text", + "content": " is necessary, and we set its weight to 5 which is the default value as validated in [44]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "text", + "content": "To more intuitively assess imperceptibility, we introduced a new metric: Learned Perceptual Image Patch Similarity (LPIPS) [39] to evaluate the visual quality of the protected dataset. In contrast to SSIM and PSNR, LPIPS utilizes deep networks and is specifically designed to mimic human perception in image evaluation tasks. A higher LPIPS value indicates that the differences between images are more perceptible to human perception. Table 2 displays results from ablation experiments of " + }, + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\cdot \\mathcal{H}}" + }, + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E.mse}" + }, + { + "bbox": [ + 55, + 534, + 295, + 665 + ], + "type": "text", + "content": ", demonstrating their importance in enhancing the imperceptibility of adversarial samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "To better evaluate the importance of the interference pattern, we conduct an ablation study on the values of the three losses introduced in the interference pattern: " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_adv}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_H}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_mse}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": ". Specifically, we evaluate the performance of" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 361, + 70, + 511, + 126 + ], + "blocks": [ + { + "bbox": [ + 361, + 70, + 511, + 126 + ], + "lines": [ + { + "bbox": [ + 361, + 70, + 511, + 126 + ], + "spans": [ + { + "bbox": [ + 361, + 70, + 511, + 126 + ], + "type": "table", + "html": "
L_E_mseL_E_HSSIMPSNRLPIPS
✓X0.8028.220.194
X✓0.8228.240.165
✓✓0.8528.260.148
", + "image_path": "a60cf64fcce243d729d53b6619bf3188dddec09b40ea83c03c2dff4eb1aea959.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": "the protected dataset and the attacked dataset, recovered by the attacker using erroneous signature noise inputs to the noise encoder. We denote the ratio of the weights of " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_adv}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_H}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_mse}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_adv}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_H}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{E\\_mse}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "n: \\alpha = m: \\beta = \\gamma: \\lambda = \\phi" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ". By controlling the value of " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", we can adjust the importance of the interference pattern in the learning process of the noise encoder. As shown in Table 3, when " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\phi = 0.5" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", the noise encoder's sensitivity to the interference pattern is reduced, leading to a decrease in " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "ASR_{Attacked}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", although the reduction is not substantial. Conversely, when " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\phi = 2" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", the noise encoder focuses more on learning the interference pattern, which increases the " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "ASR_{Attacked}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " but results in a reduced performance on the protected dataset. Thus, the weight of " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_adv}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_H}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{I\\_mse}" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " used to control the effect of the interference pattern are set to the same value as " + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_E" + }, + { + "bbox": [ + 313, + 164, + 555, + 380 + ], + "type": "text", + "content": " to ensure that the learning of interference patterns is as important as the learning of normal patterns." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 318, + 388, + 552, + 443 + ], + "blocks": [ + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "lines": [ + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "type": "text", + "content": "Table 2. The effect of " + }, + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{E.mse}" + }, + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{E\\mathcal{H}}" + }, + { + "bbox": [ + 323, + 134, + 545, + 146 + ], + "type": "text", + "content": " on imperceptibility." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 388, + 552, + 443 + ], + "lines": [ + { + "bbox": [ + 318, + 388, + 552, + 443 + ], + "spans": [ + { + "bbox": [ + 318, + 388, + 552, + 443 + ], + "type": "table", + "html": "
φASRProtectedASRAttackedSSIMPSNR
0.585.4784.500.8228.22
1(Default)85.8386.110.8528.26
282.1389.500.7626.32
", + "image_path": "4036617c85bff227abc1880973da1e62b568acf73b085fd12bc510b19ff08614.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 451, + 521, + 462 + ], + "lines": [ + { + "bbox": [ + 347, + 451, + 521, + 462 + ], + "spans": [ + { + "bbox": [ + 347, + 451, + 521, + 462 + ], + "type": "text", + "content": "Table 3. The effect of " + }, + { + "bbox": [ + 347, + 451, + 521, + 462 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 347, + 451, + 521, + 462 + ], + "type": "text", + "content": " on interference pattern." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 480, + 435, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 435, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 435, + 491 + ], + "type": "text", + "content": "4.4. Visualization Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "In this section, we compare the visual quality of protected and recovered samples generated by RAEncoder and existing methods. As shown in Figure 6, under conditions where the adversarial strength is superior, the protected samples produced by RAEncoder still maintain superior imperceptibility when compared to those generated by SRAE. As shown in Table 4, on CIFAR10, the protected dataset generated by RAEncoder achieves higher SSIM and PSNR values compared to the existing RDH-based method by [32] and the generative methods GEAA and SRAE. On ImageNet, the protected dataset generated by RAEncoder outperforms those by [32] and SRAE but is slightly weaker than PGN. However, PGN's visual quality cannot guarantee its adversarial strength which is explained in Section 4.5. Overall, RAEncoder demonstrates its superior imperceptibility, and the recovered dataset obtained through RAEncoder is identical to the original dataset. Importantly, these results are achieved without the need for an additional classification" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20670" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "head, but rather through direct utilization of a pre-trained encoder for the attack." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 105, + 293, + 277 + ], + "blocks": [ + { + "bbox": [ + 60, + 105, + 293, + 277 + ], + "lines": [ + { + "bbox": [ + 60, + 105, + 293, + 277 + ], + "spans": [ + { + "bbox": [ + 60, + 105, + 293, + 277 + ], + "type": "image", + "image_path": "485bd38169db6f6def17d5642ffe13a0a044cb504c205173505c7ed30b40cb26.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 284, + 295, + 317 + ], + "lines": [ + { + "bbox": [ + 55, + 284, + 295, + 317 + ], + "spans": [ + { + "bbox": [ + 55, + 284, + 295, + 317 + ], + "type": "text", + "content": "Figure 6. Visualization of the comparison between protected samples and recovered samples generated by our method and SRAE. Best viewed in zoom." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 60, + 342, + 293, + 460 + ], + "blocks": [ + { + "bbox": [ + 60, + 342, + 293, + 460 + ], + "lines": [ + { + "bbox": [ + 60, + 342, + 293, + 460 + ], + "spans": [ + { + "bbox": [ + 60, + 342, + 293, + 460 + ], + "type": "table", + "html": "
DatasetMethodProtectedRecovered
SSIMPSNRSSIMPSNR
CIFAR10Xue et al. [32]0.7725.760.9956.36
GEAA [41]0.3227.910.9948.11
SRAE[38]0.4214.730.7627.67
Ours0.8528.261.00∞
ImageNetXue et al. [32]0.5820.470.9850.15
PGN [31]0.9434.231.00∞
SRAE[38]0.7627.670.9738.67
Ours0.8230.261.00∞
", + "image_path": "7d951a4a652ff8074c5eff9af5f0b36c9cdbefe10396b7dd7fc1204aac0de195.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 468, + 295, + 492 + ], + "lines": [ + { + "bbox": [ + 55, + 468, + 295, + 492 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 295, + 492 + ], + "type": "text", + "content": "Table 4. Visual performance comparison of protected and recovered datasets from our method and existing methods." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 515, + 179, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 179, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 179, + 529 + ], + "type": "text", + "content": "4.5. Transferability Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 533, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 533, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 533, + 295, + 713 + ], + "type": "text", + "content": "In this section, we delve into the transferability of the RAEncoder from two distinct perspectives: attacks on downstream models trained with different pre-trained encoders, and attacks on various SL models with different network architectures. The downstream models used to evaluate transferability are trained on the corresponding pre-trained datasets of BYOL. The target SL model employed for [32], PGN and SRAE to generate the CIFAR10 protected dataset is ResNet18 and for ImageNet is ResNet50. High ASR is indicative of better adversarial strength and transferability. As shown in Table 5, the protected dataset generated by RAEncoder exhibits strong adversarial strength across various datasets, different SL models, and diverse pre-trained encoder configurations, resulting in significantly high ASR. Furthermore, its transferabil" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "type": "text", + "content": "ity across various SL models and pre-trained encoders frequently surpasses existing methods. However, while [32], PGN and SRAE demonstrate equally outstanding transferability across SL models, their ASR dramatically decreases when applied to downstream models trained by pre-trained encoders. It is noteworthy that, when applied to the CIFAR10 dataset, the ASR of SRAE is marginally higher than that of RAEncoder. However, as indicated in the Table 4, this increase in ASR is attained at the expense of image quality. Based on the results presented in Section 4.4 and Table 5, it is evident that our proposed RAEncoder effectively maintains the imperceptibility of protected samples while achieving a high level of adversarial strength." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 243, + 420, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 420, + 256 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 420, + 256 + ], + "type": "text", + "content": "4.6. Robustness Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 263, + 463, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 463, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 463, + 276 + ], + "type": "text", + "content": "4.6.1. Image Processing Operation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 281, + 555, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 413 + ], + "type": "text", + "content": "We consider four image processing operations as attack measures from the perspective of attackers, aiming to mitigate the adversarial strength of protected samples. As depicted in Figure 7a, the protected samples generated by our proposed RAEncoder exhibit superior robustness compared to those generated by SRAE. Even after undergoing various image processing operations, the protected samples generated by RAEncoder maintain their adversarial effect, rendering the model incapable of correctly classifying the processed samples. This demonstrates that RAEncoder possesses enhanced robustness." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 318, + 427, + 432, + 479 + ], + "blocks": [ + { + "bbox": [ + 318, + 427, + 432, + 479 + ], + "lines": [ + { + "bbox": [ + 318, + 427, + 432, + 479 + ], + "spans": [ + { + "bbox": [ + 318, + 427, + 432, + 479 + ], + "type": "image", + "image_path": "2eb4fd1b99cb4b2253676aa0e1e9803449f976264815c462b8ea704da84a8571.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 481, + 380, + 491 + ], + "lines": [ + { + "bbox": [ + 370, + 481, + 380, + 491 + ], + "spans": [ + { + "bbox": [ + 370, + 481, + 380, + 491 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 436, + 427, + 549, + 479 + ], + "blocks": [ + { + "bbox": [ + 436, + 427, + 549, + 479 + ], + "lines": [ + { + "bbox": [ + 436, + 427, + 549, + 479 + ], + "spans": [ + { + "bbox": [ + 436, + 427, + 549, + 479 + ], + "type": "image", + "image_path": "30c10c521b7c631141b958aeed421451d40424167dca0606446ae414af9511af.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 486, + 481, + 498, + 491 + ], + "lines": [ + { + "bbox": [ + 486, + 481, + 498, + 491 + ], + "spans": [ + { + "bbox": [ + 486, + 481, + 498, + 491 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 502, + 555, + 568 + ], + "lines": [ + { + "bbox": [ + 313, + 502, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 555, + 568 + ], + "type": "text", + "content": "Figure 7. The attack performance of RAEncoder in various settings. (a) From left to right, no disturbance, Center crop(proportion = 90%), Flip(horizontal and vertical), Resize(half of the height and width), Resize (twice the height and width) and JPEG compression(quality factor = 70). (b) Different degree of corruption." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 600, + 391, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 391, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 391, + 612 + ], + "type": "text", + "content": "4.6.2. Corruption" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": "We take into consideration attackers may diminish the adversarial strength by introducing varying degrees of Gaussian blur to the samples, thereby degrading the images. As depicted in Figure 7b, with an increase in the degree of Gaussian perturbation, the ASR decreases. Particularly, when the blur degree reaches 1.25, the ASR of SRAE has dropped to approximately " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": ", whereas our RAEncoder maintains an ASR of over " + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20671" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 70, + 547, + 185 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 547, + 185 + ], + "type": "table", + "html": "
VGG16ResNet18ResNet50Dense121BalowBYOLDeepC2DINOMoCo2+NNCLR
Xue et al. [32]CIFAR1040.1248.5132.1742.4048.9747.6858.1254.8833.8448.96
ImageNet73.0488.1876.4264.2874.1687.5656.640.609.5648.44
PGN [31]CIFAR10----------
ImageNet81.3268.2266.4451.7667.2677.7649.260.589.2434.12
SRAE [38]CIFAR1061.8488.4076.7972.4773.6888.8290.4551.6580.0380.44
ImageNet72.3087.2284.0679.9474.6092.0055.5266.0011.2620.28
OursCIFAR1058.7984.7970.6674.5275.0589.6489.7958.8285.3783.18
ImageNet98.2291.4688.3099.0089.0498.9753.4686.0030.8451.80
", + "image_path": "0ac215a51e3e5da27092a5d15f992a488c4ea8e2f8189475ffbeafb457cdff93.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 192, + 555, + 214 + ], + "lines": [ + { + "bbox": [ + 55, + 192, + 555, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 192, + 555, + 214 + ], + "type": "text", + "content": "Table 5. Comparison study of ASR (%) of protected datasets across different SL models and pre-trained encoders. -' denotes experiments not conducted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 236, + 153, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 153, + 248 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 153, + 248 + ], + "type": "text", + "content": "4.6.3. Adaptive Attack" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "text", + "content": "We consider the worst-case scenario for security concerns when deploying RAEncoder in practical applications (i.e., adaptive attack [32]). In such a scenario, attackers have full knowledge of the dataset protection methods, with the signature noise being the only unknown factor. The attacker is aware of the specifications of signature noise " + }, + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "text", + "content": ". However, due to the presence of the designed interference pattern, attackers are unable to reconstruct the original sample without signature noise " + }, + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 251, + 297, + 407 + ], + "type": "text", + "content": ". As shown in Figure 8, attackers are unable to recover the original sample by inputting random noise into the noise encoder and obtaining the output perturbation. Moreover, this even results in deeper levels of sample distortion." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 65, + 418, + 284, + 544 + ], + "blocks": [ + { + "bbox": [ + 65, + 418, + 284, + 544 + ], + "lines": [ + { + "bbox": [ + 65, + 418, + 284, + 544 + ], + "spans": [ + { + "bbox": [ + 65, + 418, + 284, + 544 + ], + "type": "image", + "image_path": "01532a76d9b96d80507982d2cb1adad059357675d5df36692bd946ea379e666d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 553, + 295, + 575 + ], + "lines": [ + { + "bbox": [ + 55, + 553, + 295, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 553, + 295, + 575 + ], + "type": "text", + "content": "Figure 8. Examples of failure in image restoration by the attacker using incorrect signature noise." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 599, + 237, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 599, + 237, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 599, + 237, + 612 + ], + "type": "text", + "content": "4.7. Adversarial Strength Explanation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": "We aim to generate protected samples that are sufficiently distant from the original classes under small perturbations while remaining difficult to detect. As illustrated in Figure 9a and 9b, although PGN and SRAE can push some samples away from the original classes, the protected samples remain very close to the original samples in the feature space. However, as shown in Figure 9c, the method proposed by us, RAEncoder, yields protected samples that" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 236, + 555, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 555, + 296 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 555, + 296 + ], + "type": "text", + "content": "cluster together in the feature space, far from all original classes. Meanwhile, there are even cases where protected samples exhibit feature space almost identical to samples from other original classes, demonstrating the superior adversarial strength and imperceptibility of RAEncoder." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 316, + 388, + 373 + ], + "blocks": [ + { + "bbox": [ + 331, + 316, + 388, + 373 + ], + "lines": [ + { + "bbox": [ + 331, + 316, + 388, + 373 + ], + "spans": [ + { + "bbox": [ + 331, + 316, + 388, + 373 + ], + "type": "image", + "image_path": "eee3b3a3e64723ba3daaa961dcbaa872012ff97a8a3d5347997ca45816a08882.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 384, + 372, + 392 + ], + "lines": [ + { + "bbox": [ + 343, + 384, + 372, + 392 + ], + "spans": [ + { + "bbox": [ + 343, + 384, + 372, + 392 + ], + "type": "text", + "content": "(a) PGN" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 408, + 316, + 463, + 373 + ], + "blocks": [ + { + "bbox": [ + 408, + 316, + 463, + 373 + ], + "lines": [ + { + "bbox": [ + 408, + 316, + 463, + 373 + ], + "spans": [ + { + "bbox": [ + 408, + 316, + 463, + 373 + ], + "type": "image", + "image_path": "5553c49baab4b8510109ea3f0b343ea8844fd370a36f6fb2a6109c648c0229ff.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 418, + 384, + 451, + 392 + ], + "lines": [ + { + "bbox": [ + 418, + 384, + 451, + 392 + ], + "spans": [ + { + "bbox": [ + 418, + 384, + 451, + 392 + ], + "type": "text", + "content": "(b) SRAE" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 403, + 555, + 437 + ], + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 437 + ], + "type": "text", + "content": "Figure 9. t-SNE [29] visualization of the feature space of protected examples produced by PGN, SRAE and ours. The hollow dots represent original samples and the solid dots represent RAEs." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 485, + 317, + 539, + 373 + ], + "blocks": [ + { + "bbox": [ + 485, + 317, + 539, + 373 + ], + "lines": [ + { + "bbox": [ + 485, + 317, + 539, + 373 + ], + "spans": [ + { + "bbox": [ + 485, + 317, + 539, + 373 + ], + "type": "image", + "image_path": "0ef08e6fdd9064cabd422dace5824c8efac94ecd8041675ed3ce156cec48f378.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 497, + 384, + 525, + 392 + ], + "lines": [ + { + "bbox": [ + 497, + 384, + 525, + 392 + ], + "spans": [ + { + "bbox": [ + 497, + 384, + 525, + 392 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 461, + 476, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 476, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 476, + 474 + ], + "type": "text", + "content": "5. Conclusion and Future work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 481, + 555, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 555, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 555, + 649 + ], + "type": "text", + "content": "In this paper, we highlight the novel challenges posed by the prevalence of SSL on RAEs for the first time. We introduce the first RAE framework applicable to protect the IP of unlabeled datasets. It leverages a noise encoder to generate universal adversarial perturbations for RAE generation, meeting the requirements of adversarial strength and full reversibility. Our RAEncoder exhibits significant performance improvement in all comparative experiments. We also evaluate its robustness against adaptive attacks, highlighting the practical advantages of RAEncoder over existing methods. Future work will include further exploration of balancing visual quality with adversarial strength. We also see new research opportunities in extending the attack approach against variational auto-encoders." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "Acknowledgment. This work was supported in part by National Natural Science Foundation of China (NFSC, No. 62362025) and Hainan Province Science and Technology Special Fund (No. ZDYF2022GXJS224)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20672" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 295, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 295, + 124 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 295, + 124 + ], + "type": "text", + "content": "[1] Nicholas Carlini and David Wagner. 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Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to $13.1\\%$ on classification tasks and $0.145R^2$ on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE.", + "bbox": [ + 89, + 320, + 485, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 694, + 220, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several machine learning tasks require the use of geolocation as an input feature. Multiple works have shown the benefits of using geolocation to solve vital ecological, geographical, and geological tasks. SINR [5] used location as input to predict species distribution, Lang et al. [20] used location with satellite image to learn a global canopy height model, and SatCLIP [18] used location to solve several geospatial tasks such as biome classification, population density estimation, housing price prediction, etc. Since location is a ubiquitous input variable in all geospatial settings, finding good representations for it is fundamental when solving geospatial tasks.", + "bbox": [ + 89, + 719, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/11907064e9f0ecfb5447b522b1dfa372540a1f9903864199b9699b02a716a849.jpg", + "image_caption": [ + "Figure 1. Adding explicit visual features allows us to generate more high-resolution location embeddings. We use a retrieval strategy that allows us to generate multi-resolution retrieval-augmented neural field of geo-embeddings (RANGE)." + ], + "image_footnote": [], + "bbox": [ + 521, + 291, + 908, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous work [33] has shown that using location directly (represented as two floating point numbers of latitude and longitude) as an input to a machine learning model yields poor performance. Therefore, several works have attempted to find better ways to represent location data. Some of these approaches [10, 25] use a non-parametric method to encode location. However, recent works [18, 27, 39] have shown that it is possible to learn a general-purpose location representation by learning a parametric model (often a neural network) in a self-supervised setting. There are several strategies that can be used to train the parametric model. A common approach used by state-of-the-art models [18, 27, 39] involves learning visual cues associated with a given geolocation. Two recent state-of-the-art models, GeoCLIP [39] and SatCLIP [18], use contrastive training to align geo-embeddings with co-located images; the former aligns them with ground-level images while the latter aligns them with satellite images. Images of a location capture dense information about the area, such as the landcover, landuse, etc. Therefore, learning location representations that capture this dense information is beneficial for solving geospatial tasks. Prior work [18] has shown that rep", + "bbox": [ + 511, + 568, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24680", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "resentations from such models are extremely powerful and are capable of solving diverse geospatial tasks both on their own and in combination with images. In this work, we argue that the current approaches to learning geo-embeddings using images, while powerful, still fail to preserve all the relevant visual information. The location representations from these models only capture low-resolution shared information between location and image and ignore crucial high-resolution information that is unique to the image. In section 2, we define this problem more formally from the perspective of multi-view redundancy.", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this issue, we propose a retrieval-augmented strategy that approximates the unique visual information present in a location. There are three key ideas to our solution. First, it is possible to approximate the visual features of a given location by strategically combining the visual features of other similar-looking locations. Second, contrastively trained models like SatCLIP [18] and GeoCLIP [39], while lacking in preserving modality-specific information, are excellent in learning modality alignment [13]. Therefore, it is possible to retrieve semantically aligned images, with alignment scores, for a given location using these models. Third, we note that the variance of semantic information visible in satellite images across the Earth is relatively low (as opposed to the wider diversity in consumer photographs). Hence, it is possible to capture a large percentage of unique aerial semantics with a limited number of satellite images. By combining these three key ideas, we propose our retrieval-augmented framework, RANGE (Retrieval-Augmented Neural Fields for Multi-Resolution Geo-Embeddings). Our retriever function uses both semantic and spatial alignment to approximate the visual features of a given location using an auxiliary database of image features. Our function is robust to the database size and works well even in limited sample settings. The hyperparameter in the retriever function can be adjusted to generate geo-embeddings at different frequencies. In summary, these are the main contributions of our paper:", + "bbox": [ + 91, + 279, + 482, + 686 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show why existing image-location contrastive methods result in sub-optimal representations from the perspective of multi-view redundancy.", + "- We propose a novel retrieval-based strategy, RANGE, to generate geo-embeddings that preserve both shared and unique modality information.", + "- We propose a retriever function that estimates the visual embedding of a location using both semantic and spatial alignment. Our retriever function is robust to different database sizes and can generate geo-embeddings at multiple frequencies by enforcing spatial smoothness." + ], + "bbox": [ + 89, + 734, + 478, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Aligning Location and Image is a Multi-View Non-Redundancy Problem", + "text_level": 1, + "bbox": [ + 513, + 89, + 903, + 125 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let (L,H,T) represent location modality, image modality, and geospatial task, respectively. Models like SatCLIP and GeoCLIP align co-located images and locations by minimizing the infoNCE objective. Solving the multimodal infoNCE objective maximizes the lower bound on the mutual information, preserving the shared information within the learned representations [29]. As such, the final learned representations of these models contain only information that is shared across both location and image. This property is useful under the multi-view redundancy assumption which states that the information shared between the two modalities is exactly relevant to solve the underlying task. In other words, the multi-view redundancy setting assumes that any additional unique information from the image or location would not be useful in solving the task T [37]. However, this assumption does not hold in the location-image learning setting as there is high unique information contained in the image modality that is useful for solving downstream tasks. Formally, we argue that location-image learning falls under the multi-view non-redundancy setting: there is unique information in the image modality that is not shared with the location modality, and that information is relevant for solving our geospatial task T. In this case, contrastive training discards valuable task-relevant information from the image, leading to poor downstream performance [23].", + "bbox": [ + 511, + 137, + 903, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Empirically, there is abundant unique information present in the image features that are relevant for solving downstream tasks. The location representations from contrastively trained models like SatCLIP and GeoCLIP only capture the low-resolution shared information, ignoring all the valuable task-relevant information that is unique to the image. To demonstrate this property concretely, we quantitatively show that there are tasks that can be solved more accurately by adding the image representation to the shared image-location representation from SatCLIP [18]. First, we choose 4 tasks: Biome, Ecoregions, Elevation, and Population Density estimation. We download a corresponding Sentinel-2 image for every data point. For each task, we train one model using the SatCLIP features and another model using the SatCLIP features combined with the SatMAE [6] features of the satellite image [6]. The results in Table 1 show that adding image features improves the performance across all tasks. The increase in performance demonstrates that the images contain unique information relevant to solving the task that is lost during contrastive training. Hence, \"location and image\" does not follow the assumption of multi-view redundancy.", + "bbox": [ + 511, + 518, + 903, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although adding corresponding satellite image information to a location embedding improves performance, this is not feasible in practice. For many geospatial tasks, we", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24681", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/4b11cf98d00acbe11412983c7c5255fef1a802d8df87fdfb541c21f43b64b8d2.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. We show that using the image-location shared information from SatCLIP embeddings is sub-optimal to solve some geospatial problems. Adding image features to the embeddings provides useful visual information that improves the accuracy of the task. We show the accuracy for the classification tasks and $\\mathbb{R}^2$ value for the regression tasks. The results indicate that there are valuable visual features that are not captured by the SatCLIP embeddings." + ], + "table_body": "
BiomeEcoregionElevationPopulation
SatMAE58.828.40.3880.600
SatCLIP68.969.30.6660.684
locoplmg74.973.50.7490.765
gain (%)+8.71+6.06+12.46+11.84
", + "bbox": [ + 91, + 88, + 495, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "wish to make predictions across the globe with millions of points. In such cases, using the \"image+location\" framework would require us to retrieve/store/process millions of images. We propose an efficient method for approximating the visual information using a compact database. Our results suggest that this approximation can outperform the use of true visual features in some cases.", + "bbox": [ + 89, + 316, + 483, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Related Works", + "text_level": 1, + "bbox": [ + 89, + 439, + 241, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Learning Representations for Geolocation", + "text_level": 1, + "bbox": [ + 89, + 465, + 447, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning effective representations for geolocation is valuable for diverse downstream geospatial tasks, such as geolocation [39], canopy height prediction [20], fine-grained species classification [25, 34], species distribution modeling [5, 34], geographical question answering [26], soundscape mapping [16], etc. Geolocation in these tasks can be represented using either non-parametric [10, 33] or parametric [18, 27, 39] methods. Rußwurm et al. [33] represents geolocation using spherical harmonic basis functions, and Aodha et al. [25] uses a sine and cosine encoding of geolocation that removes discontinuity at dateline. In recent years, learned representations for geolocation, typically parameterized by neural networks, have been popularized. Some of these methods learn geolocation representations by using self-supervised pre-training strategies that distill visual information from either co-located overhead [18, 27] or ground-level images [27, 39]. The location encoders trained by these methods have demonstrated utility across various downstream geospatial tasks. We use the representations from these location encoders as baselines for our model.", + "bbox": [ + 89, + 488, + 483, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Multimodal Contrastive Learning", + "text_level": 1, + "bbox": [ + 89, + 816, + 387, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive learning is an efficient and scalable pre-training strategy for learning a shared embedding space across multiple modalities [7, 9, 11, 15, 16, 22, 31, 41-43]. As demonstrated by CLIP [31] and more recent works [22, 41, 42] in", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vision-language learning, the shared embedding space can be utilized for zero-shot classification and leveraged across a variety of downstream tasks. Contrastively trained multimodal embedding spaces between geolocation and satellite imagery [18, 27] or ground-level imagery [39], have also demonstrated impressive transferability of both location and visual representations to various geospatial tasks.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite its success, recent works highlight the limitations of multimodal contrastive learning. One such study [23] shows that contrastively trained representations capture the shared information between the two modalities and thus only work best under certain assumptions. Similarly, another work [13] demonstrates that the final layers of encoders in the contrastive learning framework preserve only the information necessary for solving the alignment objective, discarding other modality-specific details. We argue that some of the underlying assumptions of multimodal contrastive training do not hold true in the image-location setting. Therefore, the resulting location representations from these methods are sub-optimal for downstream tasks. To address this issue, we propose a method to approximate the image-specific information for a given location.", + "bbox": [ + 511, + 198, + 906, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Retrieval Augmented Methods", + "text_level": 1, + "bbox": [ + 511, + 435, + 784, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There has been a recent surge in retrieval-augmented generation (RAG) methods, primarily focused on generative tasks [1, 2, 4, 17, 19, 21, 35, 36, 40]. These methods generally consist of three main components: a retriever, an external database, and a generator. For a given query, the retriever selects a set of documents from the database and provides them, along with the original query, to the generator to produce the desired output. RAG has been successfully employed to improve text generation for large language models (LLMs) [2, 21, 36], text-to-image generation [1, 4, 17], text-to-3D generation [35], audio captioning [19], and more. Within the RAG framework, one could also replace the generator with another task-specific component, such as a classifier [24], to enhance performance by leveraging the rich information from the retrieved documents. Inspired by these retrieval-augmented methods, we design our framework, RANGE, which retrieves rich visual information from our database for a given geolocation query and utilizes it for various downstream geospatial tasks.", + "bbox": [ + 511, + 458, + 906, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 761, + 604, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Problem Setup", + "text_level": 1, + "bbox": [ + 511, + 787, + 663, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a dataset with paired geolocations and collocated satellite images $\\{g_i, s_i\\}$ . The goal is to learn a meaningful representation for $g_i$ by aligning it with $s_i$ , which can be done by minimizing the clip objective [18, 31, 39]. We have a trainable geolocation encoder $E$ , a frozen pretrained image encoder $I$ , and a projection layer", + "bbox": [ + 511, + 810, + 905, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24682", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ef4d3962d8b370b6f39e8c9f9198e38c81c7c92acabe103a02cfd1fa0cdbf9ad.jpg", + "image_caption": [ + "Figure 2. Framework of RANGE. (a) In the training stage, a shared embedding space is learned between locations and images. (b) We create a database of low-resolution and high-resolution image embeddings using the trained projection layer and a powerful pretrained image model, respectively. (c) During inference, we use a location as the query, low-resolution image embeddings as keys, and high-resolution image embeddings as values. Using our retriever function, we compute the approximate high-resolution embeddings for the query. We concatenate $(\\oplus)$ the approximated visual feature with our query embedding." + ], + "image_footnote": [], + "bbox": [ + 94, + 92, + 897, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$P$ . Let $G_{i} = E(g_{i})$ represent the location embedding, $S_{i} = I(s_{i})$ represent the frozen image embedding, and $P_{i} = P(I(s_{i})) = P(S_{i})$ represent the image embedding obtained from the projection layer for the $\\mathrm{i}^{th}$ sample. We minimize the objective:", + "bbox": [ + 89, + 497, + 483, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i} ^ {l o c} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {i} \\cdot P _ {j}\\right) / \\tau}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 585, + 482, + 627 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i} ^ {i m g} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {j} \\cdot P _ {i}\\right) / \\tau}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 631, + 482, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i} = \\left(L _ {i} ^ {l o c} + L _ {i} ^ {i m g}\\right) / 2 \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 674, + 480, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training process is shown in Figure 2-(a). We contrastively align the geolocations and satellite images by minimizing their CLIP objective. This formulation is identical to SatCLIP [18], so we use the pretrained SatCLIP image and location encoders for simplicity. For query location $g_{i}$ , $S_{i}$ encodes the high-resolution visual features since $I$ is a powerful pre-trained image encoder. Both $P_{i}$ and $G_{i}$ encode low-resolution shared information between $g_{i}$ and $s_{i}$ . The resulting geo-embedding, $G_{i}$ , is sub-optimal as it loses unique visual information crucial for many downstream tasks. To solve this, we propose a retriever function $R_{\\tau}$ that allows us to approximate the high-resolution information $S_{i}$ given $g_{i}$ . Let $\\epsilon$ denote the deviation from the true", + "bbox": [ + 89, + 704, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "visual embedding. We can then explicitly add the approximate visual information $\\hat{S}_i$ to our location embedding $G_{i}$ :", + "bbox": [ + 511, + 497, + 906, + 530 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\tau} (g _ {i}) = \\hat {S} _ {i} = S _ {i} + \\epsilon \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 547, + 906, + 566 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R A N G E} \\left(g _ {i}\\right) = \\hat {S} _ {i} \\oplus G _ {i} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 568, + 903, + 587 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Retrieval Augmented Neural Fields", + "text_level": 1, + "bbox": [ + 511, + 590, + 821, + 607 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Creating the Retrieval Database: Once the contrastive training is done, we create a retrieval database as shown in Figure 2-(b). We take $\\{g_i,s_i\\}$ sampled uniformly across the globe using the SatCLIP [18] dataset. For every location $g_{i}$ in our data, we compute: a) the shared-information image embedding $R_{i}^{L} = P(I(s_{i}))$ , and b) the high-resolution image embedding $R_{i}^{H} = \\bar{I} (s_{i})$ ; we refer to these sets of embeddings as low-resolution embeddings and high-resolution embeddings, respectively, in the rest of the paper. In practice, $\\bar{I}$ can differ from $I$ ; the only condition is that $\\bar{I}$ is a pretrained image feature extractor. For our purposes, we use SatMAE [6] as $\\bar{I}$ .", + "bbox": [ + 511, + 613, + 906, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Retriever Function: Let $R^L = \\{R_1^L, R_2^L, \\dots, R_N^L\\}$ , and $R^H = \\{R_1^H, R_2^H, \\dots, R_N^H\\}$ represent the set of all low-resolution and high-resolution image embeddings in our database. After creating the database, we need a method to sample appropriate high-resolution image information for a query location. Naively, we can set this as a lookup operation, where $G_i$ is the query, $R^L$ is the set of all keys, and $R^H$", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24683", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is the set of all values. We have a function $\\text{sim}(G_i, R_j^L)$ , which gives the alignment scores between i and j. In our setting, this similarity function is a simple cosine similarity. For a query $G_i$ , we find $R_j^L$ with the highest alignment score and return the key $R_j^H$ . In practice, $R_j^H$ is noisy. The semantically closest image in the database can contain additional information that is irrelevant to the location. Therefore, naively adding $R_j^H$ has the potential of introducing incorrect information to our geo-embeddings.", + "bbox": [ + 89, + 90, + 480, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We instead use a soft selection criteria. First, we compute the query's alignment score with each key in the database using cosine similarity. We use a softmax function to convert the alignment scores to probabilities. We also use a temperature parameter $\\tau$ to slightly reshape the probability distribution; $\\tau$ is extremely robust as it does not need to be fine-tuned for different tasks or for databases with different distributions. We use the resulting probabilities to compute a weighted average across all values, i.e., high-resolution image embeddings in the database. The resulting embedding is an approximation of $S_{i}$ , where the information contributed by each image is weighted by its alignment score with the query. We concatenate this approximate high-resolution image embedding with our original location embedding $G_{i}$ to obtain the multi-resolution RANGE embedding $RANGE_{i}$ . A high-level view of this process is shown in Figure 2-(c).", + "bbox": [ + 91, + 229, + 483, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R A N G E _ {i} = R _ {\\tau} \\left(G _ {i}\\right) \\oplus G _ {i} \\\\ = \\frac {1}{N} \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(G _ {i} , R _ {k} ^ {L}\\right) / \\tau}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(G _ {i} , R _ {j} ^ {L}\\right) / \\tau}} * R _ {k} ^ {H} \\oplus G _ {i} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 518, + 431, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $G_{i}\\in \\mathbb{R}^{M}$ $R_k^L\\in \\mathbb{R}^M$ $R_{k}^{H}\\in \\mathbb{R}^{N}$ (6)", + "bbox": [ + 171, + 582, + 480, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adding smoothness constraints: We also propose another version of our model called $RANG^{+}$ . Here, we additionally use geodesic similarity to approximate the visual features of the location. We convert our query location to 3D cartesian coordinates and use angular distance to find the spatially closest image in the database. This spatial retrieval allows us to impose spatial smoothness on our embeddings since locations close to each other are forced to have similar retrieval, irrespective of the semantics. Similar to $RANG$ , we compute a weighted average across all values in the database using the angular similarity between the query and keys. However, we explicitly mask samples with angular similarity lower than a threshold, i.e., significantly distant samples have no contribution. The spatially retrieved embedding is added to the semantically retrieved embedding and weighted using a $\\beta$ parameter. This $\\beta$ parameter controls the level of spatial smoothness enforced on the $RANG$ embeddings, as shown in Figure 5. Let $g_{i}^{3D}$ be the query location, $l$ be the set of all database locations", + "bbox": [ + 89, + 613, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/271dff7f7c89f2c99b112dd3de7f7923b6736cfb6f29c328e19baa60fb2efa04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 90, + 612, + 156 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f53a9b35396f565ab48b184e96dce97fe315252788be21ffe38b78c2b40c62ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 90, + 710, + 155 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9ff6ea08c79fafa4fd5a4b5aaf23120fdfb4fa9ae9f8e6f0b7b42074b9d505a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 90, + 807, + 155 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c682b55d67a5e896eb3a22092c710ef0741de0399feae8aa97ca2f913ba25716.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 90, + 903, + 156 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9ad5ff47c130c99548fad000019834edfe04b16d0acae91001f11b5bddb5a3fb.jpg", + "image_caption": [ + "Figure 3. Performance of our model with respect to the database size. The results show that compared to RANGE-HAYER, both RANGE and $\\mathrm{RANG}^+$ are very robust to changes in database size. We can maintain the same performance even when only using $10\\%$ of the samples in the database." + ], + "image_footnote": [], + "bbox": [ + 516, + 157, + 614, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f5bc4baa4d4c52621b9698674df02220a94aca9a61d36cea4bbf1a5bcceb038e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 157, + 710, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f6bbbdeae0a2fc624a5692eee038c8f9b04e92976c850296a28c21f76401326c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 157, + 807, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/91eff7d9d5b49662f6a955c719f5e290119abdc2fa6a372a2a1709f99d4577f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 157, + 887, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in 3D cartesian coordinates, and $sim(g_i^{3D},l_k)$ be their angular similarity:", + "bbox": [ + 511, + 339, + 903, + 369 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR A N G E _ {i} ^ {+} = \\frac {1}{N} (\\beta * \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m (G _ {i} , R _ {k} ^ {L}) / \\tau_ {1}}}{\\sum_ {j = 1} ^ {N} e ^ {s i m (G _ {i} , R _ {j} ^ {L}) / \\tau_ {1}}} * R _ {k} ^ {H} +\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 380, + 903, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n(1 - \\beta) \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {k}\\right) / \\tau_ {2}}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {j}\\right) / \\tau_ {2}}} * R _ {k} ^ {H}) \\oplus G _ {i}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 425, + 867, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $G_{i}\\in \\mathbb{R}^{M}$ $g_{i}^{3D}\\in \\mathbb{R}^{3}$ $l_{k}\\in \\mathbb{R}^{3}$ (7)", + "bbox": [ + 609, + 469, + 903, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When $\\beta$ is set to 0, only spatially relevant features are used, and we refer to this setting as RANGE-HAYER.", + "bbox": [ + 511, + 494, + 903, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments and Results", + "text_level": 1, + "bbox": [ + 511, + 536, + 748, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Quantitative Evaluation on Downstream Tasks", + "text_level": 1, + "bbox": [ + 511, + 561, + 903, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the efficacy of RANGE and $\\mathrm{RANG^{+}}$ embeddings on a wide variety of downstream applications. We create our database using the SatCLIP [18] dataset with 82k locations. For $\\mathrm{RANG^{+}}$ , we set $\\beta$ to 0.5. We choose 3 classification tasks and 4 regression tasks for this experiment as used by prior work [18]. The classification tasks are biome classification [8], ecoregion classification [8], and country classification [18]. The regression tasks are air temperature prediction [14], elevation prediction [32], population density prediction [32], and housing price prediction [30]. Results on climate data from ERA5 are shown in Section 10 of the supplementary material. The objective is to learn a linear predictive model that solves the underlying task. For fairness, we use the same hyperparameters for all tasks, i.e., the same $\\tau$ and $\\beta$ parameters for each task. The details of the hyperparameters are listed in the supplementary material. We compare our method with state-of-the-art parametric [5, 18, 27, 28, 39] and non-parametric [10, 25] representations. The results of this experiment are shown in Table 2.", + "bbox": [ + 511, + 582, + 906, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The results show that our method outperforms all state-of-the-art models in the classification tasks with significant", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24684", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/178bc86367d1c89734b32c411086bce04285ed13a2b4c82e09cc43a906e95bbb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BiomeEcoRegionsCountryTemperatureElevationPopulationCali-Housing
Direct29.10.666.90.3810.0250.0530.238
Cartesian_3D30.21.866.90.3620.0300.1620.240
Wrap [25]34.41.169.70.8610.0850.3280.239
Theory [10]33.51.072.50.8490.0930.3300.254
SphereM [28]36.427.372.70.6290.1390.3020.423
SphereM+ [28]58.750.176.10.8860.2940.4210.543
SphereC [28]36.352.972.90.4610.1850.3350.496
SphereC+ [28]53.261.673.60.8420.2600.3920.544
CSP-INat [27]61.157.175.90.7170.3880.5540.462
CSP-FMoW [27]61.458.081.30.8650.3990.5800.541
SINR [5]67.954.988.30.9420.6440.7260.420
GeoCLIP [39]70.271.681.30.9160.6040.6980.708
SatCLIP [18]68.969.382.80.8250.6660.6840.400
RANGE83.375.793.70.8950.8440.7990.422
RANGE+83.375.394.70.9310.8510.8110.336
", + "bbox": [ + 112, + 87, + 883, + 334 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/83a394adae533853ef1fe0c29065fe14ea6143f75c0be2a8f807a177076014df.jpg", + "table_caption": [ + "Table 2. Our model shows improvements over a variety of tasks compared to state-of-the-art models. The first 3 columns are classification tasks with accuracy metrics and the last 4 columns are regression tasks with $\\mathbf{R}^2$ metric. We show improvements with significant margins across many of the tasks. Our model underperforms in the Cali-housing dataset. We further analyze this behavior in our discussions." + ], + "table_footnote": [], + "table_body": "
typetemp.BiomeEcoCountryTemperatureElevationPopulationCali-Housing
SatCLIPbase-model-68.969.382.80.8250.6660.6840.400
RANGEtop-1-75.665.285.60.8170.7660.7420.444
top-k-82.876.890.60.8840.8100.7710.619
soft selectionfixed83.375.793.70.8950.8440.7990.422
soft selectionper task83.575.894.50.9220.8570.8090.465
RANGE+soft selectionfixed83.575.394.70.9310.8510.8110.336
soft selectionper task83.775.994.90.9320.8550.8130.460
gain (%)+21.5+9.5+14.6+12.9+28.37+18.8+15.0
", + "bbox": [ + 91, + 400, + 903, + 539 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6f2e4f9a6becc3144f12ac69a2a275dfc1b17eb0da6a42555f5d276cd5c4a273.jpg", + "table_caption": [ + "Table 3. Ablation of different versions of our model compared with SatCLIP as the base model. Our soft selection using weighted averages over the database performs better than top-k selection. We also find that a single temperature works well for most tasks. Fine-tuning the temperature per task is generally not required as the gain is marginal. The last row shows the difference between the base model and RANGE+." + ], + "table_footnote": [], + "table_body": "
top-1top-3top-5top-10
Img66.183.388.092.2
Img+CSP72.987.991.694.8
Img+GeoCLIP72.988.291.995.2
Img+CSP_INat*74.488.892.294.9
Img+SatCLIP75.188.791.994.5
Img+RANGE75.289.692.995.5
Img+RANGE+75.189.592.895.5
", + "bbox": [ + 109, + 628, + 465, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Top-k classification accuracy on INat-2018 test split: Location information acts as a strong prior in fine-grained species classification. Our method shows competitive top-k results against state-of-the-art models.", + "bbox": [ + 89, + 763, + 482, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "margins. In biome, ecoregion, and country classification, we advance the state-of-the-art by $13.1\\%$ , $4.1\\%$ , and $6.4\\%$ , respectively. Among the regression tasks, we achieve SoTA", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "performance for elevation and population density prediction with significant gains and narrowly come second in the air temperature prediction task. Our method, however, underperforms in the housing price prediction task. We suspect this is because the visual features that define housing change dramatically over time. The standard California housing dataset is based on a 1990 census, while our retrieved visual features are extracted from 2020 Sentinel data. The results also demonstrate that the hyperparameters for our model are robust and do not need to be tuned for specific tasks to achieve good performance. Furthermore, $\\mathrm{RANGE^{+}}$ , on average, outperforms RANGE by a small margin, which can be attributed to the spatial smoothness constraint.", + "bbox": [ + 511, + 631, + 906, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Using Location Embeddings as Geo-prior", + "text_level": 1, + "bbox": [ + 511, + 845, + 867, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our model on the task of fine-grained species classification. We use the iNaturalist 2018 dataset [38],", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24685", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89350c8ac5aa0908ce4dfaab8b96050f574772563113ba5a601db5e99346f42d.jpg", + "image_caption": [ + "Figure 4. We visualize the geo-embeddings from different models by projecting them into a 3-dimensional vector using Independent Component Analysis (ICA). The results suggest that by explicitly adding visual features, our method learns more high-frequency information compared to the existing models." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 906, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8181c7c6f4a81d45ed844755a846983cd81ca06770a39723bc96fe60cbd6f7f5.jpg", + "image_caption": [ + "Figure 5. Interpolating the $\\beta$ parameter in $\\mathrm{RANG}^+$ allows us to control the spatial smoothness of our embeddings. The results show that $\\mathrm{RANG}^+$ can be used to generate neural fields of geo-embeddings at multiple frequencies." + ], + "image_footnote": [], + "bbox": [ + 91, + 388, + 906, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which contains data from 8,142 species. Prior works [18, 25, 33] have shown that adding location information can improve the performance of pretrained image classification models on iNat as knowing the location of an image can provide a strong prior about its content. For our experiment, we follow a similar setup as [33]. We take a pretrained image classification model, which gives us $P(y \\mid I)$ . We then train a linear model that takes as input the pre-trained geo-embeddings and predicts the species categories, i.e., $P(y \\mid G)$ . The final distribution is computed as the product of the two distributions, i.e., $P(y \\mid I, G) = P(y \\mid I) * P(y \\mid G)$ . This experiment also aims to show that location representations obtained using self-supervised training can be eas", + "bbox": [ + 89, + 703, + 485, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ily generalized towards tasks like iNat. Hence, we exclude SINR [5] from this comparison as it is trained in a supervised manner on the iNaturalist data itself.", + "bbox": [ + 511, + 703, + 906, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results of this experiment are shown in Table 4. The performance of the pretrained image classifier is $66.1\\%$ . The addition of location information improves the accuracy across all models. We see that RANGE and $\\mathrm{RANG}^{+}$ achieve competitive scores, narrowly outperforming state-of-the-art models. The results from this experiment highlight the benefits of using good location representations as geo-prior to solve fine-grained image classification tasks.", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24686", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 91, + 90, + 243, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness to Database Size: The RANGE database that we used for our model in Section 5.1 was created using the SatCLIP dataset with 82k locations. However, our method is extremely robust and can be used with much smaller database sizes. We conducted an experiment where we used smaller samples of the SatCLIP data to create our RANGE database. We created a database with $75\\%$ , $50\\%$ , $25\\%$ , and $10\\%$ of the total data. We then trained a linear model for RANGE and $\\mathrm{RANGE^{+}}$ using each of these subsets as our retrieval database. We also trained another version of our method where we only use geodesic distance for retrieval, i.e. $\\beta = 0$ , which we call RANGE-HAYER. We used the same tasks described in Section 5.1 to evaluate these models.", + "bbox": [ + 89, + 112, + 483, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our results from figure 3 show that we can obtain similar performance while using only $10\\%$ of the original database size. In terms of storage, this database only occupies 85 Megabytes in disk, which is very efficient. The results also support our initial claim that there is low variance in satellite images; thus, a small number of satellite images can capture many important semantics across the globe. We see that the performance for both RANGE and $\\mathrm{RANG}^{+}$ is stable across different settings and different tasks. The results also show that RANGE-HAYER, which only relies on spatially retrieved information, can be unstable, as seen in figure 3. These results highlight the pitfalls of depending completely on spatial similarity for retrieval. Locations that are spatially close do not necessarily share similar semantics. Therefore, as you change the sample distribution in the database, you can introduce noisy retrievals, which amplify the noise in the estimated visual embedding. Semantic-based retrieval strategy mitigates such issues.", + "bbox": [ + 89, + 324, + 483, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of architectural components: Table 3 shows the impact of different components of our method compared to SatCLIP as the base model. We also compare our method with two other methods of retrieval: top-1 and top-k (where k was set to 100). The results show that our retriever function generally yields better results than the top-k selection approach. This can be attributed to the fact that top-k averaging does not consider the measure of similarity between query location and keys. We also performed a linear search to find the optimal temperature parameters of RANGE for each task separately. Our results show we are able to make marginal improvements by tuning the temperature parameter for individual tasks. The results indicate the temperature parameters of RANGE are robust and do not need to be fin-tuned for individual tasks in most cases.", + "bbox": [ + 89, + 611, + 482, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Qualitative Evaluation of Geo-embeddings", + "text_level": 1, + "bbox": [ + 89, + 848, + 454, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual comparison of geo-embeddings: We qualitatively compare the RANGE embeddings with other location em", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "beddings. We use Independent Component Analysis (ICA) to project the embeddings to a 3-dimensional vector and use them as RGB channels to visualize them over the globe. Figure 4 shows the visualizations for each model. Qualitatively, we see that models like CSP and SINR are extremely smooth, suggesting that they predominantly capture low-frequency information. GeoCLIP and SatCLIP capture relatively high-frequency information. The visualizations further suggest that RANGE and $\\mathrm{RANG^{+}}$ embeddings are able to capture even higher frequency information.", + "bbox": [ + 511, + 90, + 903, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizing the impact of $\\beta$ parameter: Secondly, we visualize the impact of the $\\beta$ parameter in equation (7). A quantitative evaluation of the $\\beta$ parameter is presented in Section 9 of the supplementary material. Setting $\\beta = 1$ gives us the RANGE embeddings, setting $\\beta = 0$ gives us RANGE-HAYER embeddings, and setting $\\beta = 0.5$ gives the $\\mathrm{RANG}^{+}$ embeddings. This parameter controls the contribution of spatially-retrieved visual information to the semantically-retrieved visual information. This additional information acts as a spatial smoothness constraint on the RANGE embeddings. At $\\beta = 0$ , we add the maximum constraint, which gives us low-frequency embeddings similar to CSP and SINR. As we increase the value of $\\beta$ , we increase the frequency of our embeddings, i.e. locations that are spatially close to each other but are semantically different have different representations. Thus, the $\\beta$ parameter allows us to explicitly control the smoothness of the RANGE embeddings and, therefore, allows generating location embeddings at multiple frequencies.", + "bbox": [ + 511, + 242, + 906, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 511, + 551, + 761, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Self-supervised learning has been a key enabler of the rapid recent progress in computer vision and natural language processing. Representations from models like SimCLR [3], and CLIP [31] have facilitated the creation of many powerful vision and language models. Recent works like SatCLIP [18], GeoCLIP [39], and CSP [27] showed that the same self-supervised techniques can be used to learn powerful representations for geographic locations, which are useful for a broad range of tasks.", + "bbox": [ + 511, + 580, + 903, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced a simple, yet effective strategy for improving such geographic embeddings, moving past previous assumptions of multiview redundancy. We proposed a retrieval-augmented strategy for estimating visual features from an auxiliary database of visual embeddings. Our approach results in significant improvements for a variety of tasks as compared to purely parametric embedding strategies with only a modest increase in storage requirements. Our method is efficient, robust, and multiscale. We hope our insights and results substantiate our recommendation of using RANGE as a general-purpose location encoder for geospatial tasks.", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24687", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 269, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research used the TGI RAILs advanced compute and data resource which is supported by the National Science Foundation (award OAC-2232860) and the Taylor Geospatial Institute.", + "bbox": [ + 89, + 114, + 483, + 175 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 191, + 187, + 207 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Andreas Blattmann, Robin Rombach, Kaan Oktay, Jonas Müller, and Björn Ommer. Retrieval-augmented diffusion models. In NeurIPS, pages 15309-15324, 2022. 3", + "[2] Sebastian Borgeaud, Arthur Mensch, Jordan Hoffmann, Trevor Cai, Eliza Rutherford, Katie Millican, George Bm Van Den Driessche, Jean-Baptiste Lespiau, Bogdan Damoc, Aidan Clark, et al. Improving language models by retrieving from trillions of tokens. 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In CVPR, 2023. 3" + ], + "bbox": [ + 516, + 92, + 903, + 458 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24689", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_model.json b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0b41f0ef42de0f7a25ae2d93e4a31bc49b825690 --- /dev/null +++ b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_model.json @@ -0,0 +1,1804 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.13, + 0.834, + 0.176 + ], + "angle": 0, + "content": "RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.203, + 0.873, + 0.224 + ], + "angle": 0, + "content": "Aayush Dhakal1 Srikumar Sastry1 Subash Khanal1 Adeel Ahmad1,2 Eric Xing1 Nathan Jacobs1" + }, + { + "type": "text", + "bbox": [ + 0.233, + 0.236, + 0.766, + 0.255 + ], + "angle": 0, + "content": "Washington University in St. Louis\\(^{1}\\) Taylor Geospatial Institute\\(^{2}\\)" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.29, + 0.327, + 0.305 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.321, + 0.486, + 0.669 + ], + "angle": 0, + "content": "The choice of representation for geographic location significantly impacts the accuracy of models for a broad range of geospatial tasks, including fine-grained species classification, population density estimation, and biome classification. Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to \\(13.1\\%\\) on classification tasks and \\(0.145R^2\\) on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.695, + 0.222, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Several machine learning tasks require the use of geolocation as an input feature. Multiple works have shown the benefits of using geolocation to solve vital ecological, geographical, and geological tasks. SINR [5] used location as input to predict species distribution, Lang et al. [20] used location with satellite image to learn a global canopy height model, and SatCLIP [18] used location to solve several geospatial tasks such as biome classification, population density estimation, housing price prediction, etc. Since location is a ubiquitous input variable in all geospatial settings, finding good representations for it is fundamental when solving geospatial tasks." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.292, + 0.909, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.484, + 0.909, + 0.541 + ], + "angle": 0, + "content": "Figure 1. Adding explicit visual features allows us to generate more high-resolution location embeddings. We use a retrieval strategy that allows us to generate multi-resolution retrieval-augmented neural field of geo-embeddings (RANGE)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Previous work [33] has shown that using location directly (represented as two floating point numbers of latitude and longitude) as an input to a machine learning model yields poor performance. Therefore, several works have attempted to find better ways to represent location data. Some of these approaches [10, 25] use a non-parametric method to encode location. However, recent works [18, 27, 39] have shown that it is possible to learn a general-purpose location representation by learning a parametric model (often a neural network) in a self-supervised setting. There are several strategies that can be used to train the parametric model. A common approach used by state-of-the-art models [18, 27, 39] involves learning visual cues associated with a given geolocation. Two recent state-of-the-art models, GeoCLIP [39] and SatCLIP [18], use contrastive training to align geo-embeddings with co-located images; the former aligns them with ground-level images while the latter aligns them with satellite images. Images of a location capture dense information about the area, such as the landcover, landuse, etc. Therefore, learning location representations that capture this dense information is beneficial for solving geospatial tasks. Prior work [18] has shown that rep" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24680" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "resentations from such models are extremely powerful and are capable of solving diverse geospatial tasks both on their own and in combination with images. In this work, we argue that the current approaches to learning geo-embeddings using images, while powerful, still fail to preserve all the relevant visual information. The location representations from these models only capture low-resolution shared information between location and image and ignore crucial high-resolution information that is unique to the image. In section 2, we define this problem more formally from the perspective of multi-view redundancy." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.28, + 0.483, + 0.688 + ], + "angle": 0, + "content": "To address this issue, we propose a retrieval-augmented strategy that approximates the unique visual information present in a location. There are three key ideas to our solution. First, it is possible to approximate the visual features of a given location by strategically combining the visual features of other similar-looking locations. Second, contrastively trained models like SatCLIP [18] and GeoCLIP [39], while lacking in preserving modality-specific information, are excellent in learning modality alignment [13]. Therefore, it is possible to retrieve semantically aligned images, with alignment scores, for a given location using these models. Third, we note that the variance of semantic information visible in satellite images across the Earth is relatively low (as opposed to the wider diversity in consumer photographs). Hence, it is possible to capture a large percentage of unique aerial semantics with a limited number of satellite images. By combining these three key ideas, we propose our retrieval-augmented framework, RANGE (Retrieval-Augmented Neural Fields for Multi-Resolution Geo-Embeddings). Our retriever function uses both semantic and spatial alignment to approximate the visual features of a given location using an auxiliary database of image features. Our function is robust to the database size and works well even in limited sample settings. The hyperparameter in the retriever function can be adjusted to generate geo-embeddings at different frequencies. In summary, these are the main contributions of our paper:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.735, + 0.48, + 0.777 + ], + "angle": 0, + "content": "- We show why existing image-location contrastive methods result in sub-optimal representations from the perspective of multi-view redundancy." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.78, + 0.48, + 0.821 + ], + "angle": 0, + "content": "- We propose a novel retrieval-based strategy, RANGE, to generate geo-embeddings that preserve both shared and unique modality information." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.826, + 0.48, + 0.898 + ], + "angle": 0, + "content": "- We propose a retriever function that estimates the visual embedding of a location using both semantic and spatial alignment. Our retriever function is robust to different database sizes and can generate geo-embeddings at multiple frequencies by enforcing spatial smoothness." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.735, + 0.48, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.905, + 0.126 + ], + "angle": 0, + "content": "2. Aligning Location and Image is a Multi-View Non-Redundancy Problem" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.138, + 0.905, + 0.515 + ], + "angle": 0, + "content": "Let (L,H,T) represent location modality, image modality, and geospatial task, respectively. Models like SatCLIP and GeoCLIP align co-located images and locations by minimizing the infoNCE objective. Solving the multimodal infoNCE objective maximizes the lower bound on the mutual information, preserving the shared information within the learned representations [29]. As such, the final learned representations of these models contain only information that is shared across both location and image. This property is useful under the multi-view redundancy assumption which states that the information shared between the two modalities is exactly relevant to solve the underlying task. In other words, the multi-view redundancy setting assumes that any additional unique information from the image or location would not be useful in solving the task T [37]. However, this assumption does not hold in the location-image learning setting as there is high unique information contained in the image modality that is useful for solving downstream tasks. Formally, we argue that location-image learning falls under the multi-view non-redundancy setting: there is unique information in the image modality that is not shared with the location modality, and that information is relevant for solving our geospatial task T. In this case, contrastive training discards valuable task-relevant information from the image, leading to poor downstream performance [23]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.519, + 0.905, + 0.852 + ], + "angle": 0, + "content": "Empirically, there is abundant unique information present in the image features that are relevant for solving downstream tasks. The location representations from contrastively trained models like SatCLIP and GeoCLIP only capture the low-resolution shared information, ignoring all the valuable task-relevant information that is unique to the image. To demonstrate this property concretely, we quantitatively show that there are tasks that can be solved more accurately by adding the image representation to the shared image-location representation from SatCLIP [18]. First, we choose 4 tasks: Biome, Ecoregions, Elevation, and Population Density estimation. We download a corresponding Sentinel-2 image for every data point. For each task, we train one model using the SatCLIP features and another model using the SatCLIP features combined with the SatMAE [6] features of the satellite image [6]. The results in Table 1 show that adding image features improves the performance across all tasks. The increase in performance demonstrates that the images contain unique information relevant to solving the task that is lost during contrastive training. Hence, \"location and image\" does not follow the assumption of multi-view redundancy." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Although adding corresponding satellite image information to a location embedding improves performance, this is not feasible in practice. For many geospatial tasks, we" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24681" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.496, + 0.168 + ], + "angle": 0, + "content": "
BiomeEcoregionElevationPopulation
SatMAE58.828.40.3880.600
SatCLIP68.969.30.6660.684
locoplmg74.973.50.7490.765
gain (%)+8.71+6.06+12.46+11.84
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.179, + 0.483, + 0.29 + ], + "angle": 0, + "content": "Table 1. We show that using the image-location shared information from SatCLIP embeddings is sub-optimal to solve some geospatial problems. Adding image features to the embeddings provides useful visual information that improves the accuracy of the task. We show the accuracy for the classification tasks and \\( \\mathbb{R}^2 \\) value for the regression tasks. The results indicate that there are valuable visual features that are not captured by the SatCLIP embeddings." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.318, + 0.484, + 0.424 + ], + "angle": 0, + "content": "wish to make predictions across the globe with millions of points. In such cases, using the \"image+location\" framework would require us to retrieve/store/process millions of images. We propose an efficient method for approximating the visual information using a compact database. Our results suggest that this approximation can outperform the use of true visual features in some cases." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.44, + 0.242, + 0.456 + ], + "angle": 0, + "content": "3. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.466, + 0.449, + 0.482 + ], + "angle": 0, + "content": "3.1. Learning Representations for Geolocation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.806 + ], + "angle": 0, + "content": "Learning effective representations for geolocation is valuable for diverse downstream geospatial tasks, such as geolocation [39], canopy height prediction [20], fine-grained species classification [25, 34], species distribution modeling [5, 34], geographical question answering [26], soundscape mapping [16], etc. Geolocation in these tasks can be represented using either non-parametric [10, 33] or parametric [18, 27, 39] methods. Rußwurm et al. [33] represents geolocation using spherical harmonic basis functions, and Aodha et al. [25] uses a sine and cosine encoding of geolocation that removes discontinuity at dateline. In recent years, learned representations for geolocation, typically parameterized by neural networks, have been popularized. Some of these methods learn geolocation representations by using self-supervised pre-training strategies that distill visual information from either co-located overhead [18, 27] or ground-level images [27, 39]. The location encoders trained by these methods have demonstrated utility across various downstream geospatial tasks. We use the representations from these location encoders as baselines for our model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.388, + 0.835 + ], + "angle": 0, + "content": "3.2. Multimodal Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Contrastive learning is an efficient and scalable pre-training strategy for learning a shared embedding space across multiple modalities [7, 9, 11, 15, 16, 22, 31, 41-43]. As demonstrated by CLIP [31] and more recent works [22, 41, 42] in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "vision-language learning, the shared embedding space can be utilized for zero-shot classification and leveraged across a variety of downstream tasks. Contrastively trained multimodal embedding spaces between geolocation and satellite imagery [18, 27] or ground-level imagery [39], have also demonstrated impressive transferability of both location and visual representations to various geospatial tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.907, + 0.426 + ], + "angle": 0, + "content": "Despite its success, recent works highlight the limitations of multimodal contrastive learning. One such study [23] shows that contrastively trained representations capture the shared information between the two modalities and thus only work best under certain assumptions. Similarly, another work [13] demonstrates that the final layers of encoders in the contrastive learning framework preserve only the information necessary for solving the alignment objective, discarding other modality-specific details. We argue that some of the underlying assumptions of multimodal contrastive training do not hold true in the image-location setting. Therefore, the resulting location representations from these methods are sub-optimal for downstream tasks. To address this issue, we propose a method to approximate the image-specific information for a given location." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.436, + 0.785, + 0.452 + ], + "angle": 0, + "content": "3.3. Retrieval Augmented Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.907, + 0.747 + ], + "angle": 0, + "content": "There has been a recent surge in retrieval-augmented generation (RAG) methods, primarily focused on generative tasks [1, 2, 4, 17, 19, 21, 35, 36, 40]. These methods generally consist of three main components: a retriever, an external database, and a generator. For a given query, the retriever selects a set of documents from the database and provides them, along with the original query, to the generator to produce the desired output. RAG has been successfully employed to improve text generation for large language models (LLMs) [2, 21, 36], text-to-image generation [1, 4, 17], text-to-3D generation [35], audio captioning [19], and more. Within the RAG framework, one could also replace the generator with another task-specific component, such as a classifier [24], to enhance performance by leveraging the rich information from the retrieved documents. Inspired by these retrieval-augmented methods, we design our framework, RANGE, which retrieves rich visual information from our database for a given geolocation query and utilizes it for various downstream geospatial tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.762, + 0.606, + 0.778 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.665, + 0.804 + ], + "angle": 0, + "content": "4.1. Problem Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.903 + ], + "angle": 0, + "content": "We consider a dataset with paired geolocations and collocated satellite images \\(\\{g_i, s_i\\}\\). The goal is to learn a meaningful representation for \\(g_i\\) by aligning it with \\(s_i\\), which can be done by minimizing the clip objective [18, 31, 39]. We have a trainable geolocation encoder \\(E\\), a frozen pretrained image encoder \\(I\\), and a projection layer" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24682" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.093, + 0.898, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.402, + 0.908, + 0.475 + ], + "angle": 0, + "content": "Figure 2. Framework of RANGE. (a) In the training stage, a shared embedding space is learned between locations and images. (b) We create a database of low-resolution and high-resolution image embeddings using the trained projection layer and a powerful pretrained image model, respectively. (c) During inference, we use a location as the query, low-resolution image embeddings as keys, and high-resolution image embeddings as values. Using our retriever function, we compute the approximate high-resolution embeddings for the query. We concatenate \\((\\oplus)\\) the approximated visual feature with our query embedding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.498, + 0.484, + 0.575 + ], + "angle": 0, + "content": "\\(P\\). Let \\(G_{i} = E(g_{i})\\) represent the location embedding, \\(S_{i} = I(s_{i})\\) represent the frozen image embedding, and \\(P_{i} = P(I(s_{i})) = P(S_{i})\\) represent the image embedding obtained from the projection layer for the \\(\\mathrm{i}^{th}\\) sample. We minimize the objective:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.586, + 0.483, + 0.628 + ], + "angle": 0, + "content": "\\[\nL _ {i} ^ {l o c} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {i} \\cdot P _ {j}\\right) / \\tau}) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.632, + 0.483, + 0.673 + ], + "angle": 0, + "content": "\\[\nL _ {i} ^ {i m g} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {j} \\cdot P _ {i}\\right) / \\tau}) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.675, + 0.482, + 0.695 + ], + "angle": 0, + "content": "\\[\nL _ {i} = \\left(L _ {i} ^ {l o c} + L _ {i} ^ {i m g}\\right) / 2 \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The training process is shown in Figure 2-(a). We contrastively align the geolocations and satellite images by minimizing their CLIP objective. This formulation is identical to SatCLIP [18], so we use the pretrained SatCLIP image and location encoders for simplicity. For query location \\( g_{i} \\), \\( S_{i} \\) encodes the high-resolution visual features since \\( I \\) is a powerful pre-trained image encoder. Both \\( P_{i} \\) and \\( G_{i} \\) encode low-resolution shared information between \\( g_{i} \\) and \\( s_{i} \\). The resulting geo-embedding, \\( G_{i} \\), is sub-optimal as it loses unique visual information crucial for many downstream tasks. To solve this, we propose a retriever function \\( R_{\\tau} \\) that allows us to approximate the high-resolution information \\( S_{i} \\) given \\( g_{i} \\). Let \\( \\epsilon \\) denote the deviation from the true" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.498, + 0.907, + 0.531 + ], + "angle": 0, + "content": "visual embedding. We can then explicitly add the approximate visual information \\(\\hat{S}_i\\) to our location embedding \\(G_{i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.548, + 0.907, + 0.567 + ], + "angle": 0, + "content": "\\[\nR _ {\\tau} (g _ {i}) = \\hat {S} _ {i} = S _ {i} + \\epsilon \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.569, + 0.905, + 0.588 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R A N G E} \\left(g _ {i}\\right) = \\hat {S} _ {i} \\oplus G _ {i} \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.592, + 0.822, + 0.608 + ], + "angle": 0, + "content": "4.2. Retrieval Augmented Neural Fields" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.795 + ], + "angle": 0, + "content": "Creating the Retrieval Database: Once the contrastive training is done, we create a retrieval database as shown in Figure 2-(b). We take \\(\\{g_i,s_i\\}\\) sampled uniformly across the globe using the SatCLIP [18] dataset. For every location \\(g_{i}\\) in our data, we compute: a) the shared-information image embedding \\(R_{i}^{L} = P(I(s_{i}))\\), and b) the high-resolution image embedding \\(R_{i}^{H} = \\bar{I} (s_{i})\\); we refer to these sets of embeddings as low-resolution embeddings and high-resolution embeddings, respectively, in the rest of the paper. In practice, \\(\\bar{I}\\) can differ from \\(I\\); the only condition is that \\(\\bar{I}\\) is a pretrained image feature extractor. For our purposes, we use SatMAE [6] as \\(\\bar{I}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Retriever Function: Let \\( R^L = \\{R_1^L, R_2^L, \\dots, R_N^L\\} \\), and \\( R^H = \\{R_1^H, R_2^H, \\dots, R_N^H\\} \\) represent the set of all low-resolution and high-resolution image embeddings in our database. After creating the database, we need a method to sample appropriate high-resolution image information for a query location. Naively, we can set this as a lookup operation, where \\( G_i \\) is the query, \\( R^L \\) is the set of all keys, and \\( R^H \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24683" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.229 + ], + "angle": 0, + "content": "is the set of all values. We have a function \\( \\text{sim}(G_i, R_j^L) \\), which gives the alignment scores between i and j. In our setting, this similarity function is a simple cosine similarity. For a query \\( G_i \\), we find \\( R_j^L \\) with the highest alignment score and return the key \\( R_j^H \\). In practice, \\( R_j^H \\) is noisy. The semantically closest image in the database can contain additional information that is irrelevant to the location. Therefore, naively adding \\( R_j^H \\) has the potential of introducing incorrect information to our geo-embeddings." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.231, + 0.484, + 0.487 + ], + "angle": 0, + "content": "We instead use a soft selection criteria. First, we compute the query's alignment score with each key in the database using cosine similarity. We use a softmax function to convert the alignment scores to probabilities. We also use a temperature parameter \\(\\tau\\) to slightly reshape the probability distribution; \\(\\tau\\) is extremely robust as it does not need to be fine-tuned for different tasks or for databases with different distributions. We use the resulting probabilities to compute a weighted average across all values, i.e., high-resolution image embeddings in the database. The resulting embedding is an approximation of \\(S_{i}\\), where the information contributed by each image is weighted by its alignment score with the query. We concatenate this approximate high-resolution image embedding with our original location embedding \\(G_{i}\\) to obtain the multi-resolution RANGE embedding \\(RANGE_{i}\\). A high-level view of this process is shown in Figure 2-(c)." + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.519, + 0.433, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R A N G E _ {i} = R _ {\\tau} \\left(G _ {i}\\right) \\oplus G _ {i} \\\\ = \\frac {1}{N} \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(G _ {i} , R _ {k} ^ {L}\\right) / \\tau}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(G _ {i} , R _ {j} ^ {L}\\right) / \\tau}} * R _ {k} ^ {H} \\oplus G _ {i} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.583, + 0.482, + 0.602 + ], + "angle": 0, + "content": "where \\(G_{i}\\in \\mathbb{R}^{M}\\) \\(R_k^L\\in \\mathbb{R}^M\\) \\(R_{k}^{H}\\in \\mathbb{R}^{N}\\) (6)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Adding smoothness constraints: We also propose another version of our model called \\( RANG^{+} \\). Here, we additionally use geodesic similarity to approximate the visual features of the location. We convert our query location to 3D cartesian coordinates and use angular distance to find the spatially closest image in the database. This spatial retrieval allows us to impose spatial smoothness on our embeddings since locations close to each other are forced to have similar retrieval, irrespective of the semantics. Similar to \\( RANG \\), we compute a weighted average across all values in the database using the angular similarity between the query and keys. However, we explicitly mask samples with angular similarity lower than a threshold, i.e., significantly distant samples have no contribution. The spatially retrieved embedding is added to the semantically retrieved embedding and weighted using a \\( \\beta \\) parameter. This \\( \\beta \\) parameter controls the level of spatial smoothness enforced on the \\( RANG \\) embeddings, as shown in Figure 5. Let \\( g_{i}^{3D} \\) be the query location, \\( l \\) be the set of all database locations" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.091, + 0.614, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.091, + 0.712, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.091, + 0.808, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.092, + 0.905, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.158, + 0.615, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.158, + 0.712, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.158, + 0.808, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.809, + 0.158, + 0.888, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.248, + 0.905, + 0.317 + ], + "angle": 0, + "content": "Figure 3. Performance of our model with respect to the database size. The results show that compared to RANGE-HAYER, both RANGE and \\(\\mathrm{RANG}^+\\) are very robust to changes in database size. We can maintain the same performance even when only using \\(10\\%\\) of the samples in the database." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.905, + 0.371 + ], + "angle": 0, + "content": "in 3D cartesian coordinates, and \\(sim(g_i^{3D},l_k)\\) be their angular similarity:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.381, + 0.905, + 0.424 + ], + "angle": 0, + "content": "\\[\nR A N G E _ {i} ^ {+} = \\frac {1}{N} (\\beta * \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m (G _ {i} , R _ {k} ^ {L}) / \\tau_ {1}}}{\\sum_ {j = 1} ^ {N} e ^ {s i m (G _ {i} , R _ {j} ^ {L}) / \\tau_ {1}}} * R _ {k} ^ {H} +\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.426, + 0.868, + 0.468 + ], + "angle": 0, + "content": "\\[\n(1 - \\beta) \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {k}\\right) / \\tau_ {2}}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {j}\\right) / \\tau_ {2}}} * R _ {k} ^ {H}) \\oplus G _ {i}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.611, + 0.47, + 0.905, + 0.488 + ], + "angle": 0, + "content": "where \\(G_{i}\\in \\mathbb{R}^{M}\\) \\(g_{i}^{3D}\\in \\mathbb{R}^{3}\\) \\(l_{k}\\in \\mathbb{R}^{3}\\) (7)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.495, + 0.905, + 0.526 + ], + "angle": 0, + "content": "When \\(\\beta\\) is set to 0, only spatially relevant features are used, and we refer to this setting as RANGE-HAYER." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.537, + 0.749, + 0.554 + ], + "angle": 0, + "content": "5. Experiments and Results" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.562, + 0.905, + 0.578 + ], + "angle": 0, + "content": "5.1. Quantitative Evaluation on Downstream Tasks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.87 + ], + "angle": 0, + "content": "We evaluate the efficacy of RANGE and \\(\\mathrm{RANG^{+}}\\) embeddings on a wide variety of downstream applications. We create our database using the SatCLIP [18] dataset with 82k locations. For \\(\\mathrm{RANG^{+}}\\), we set \\(\\beta\\) to 0.5. We choose 3 classification tasks and 4 regression tasks for this experiment as used by prior work [18]. The classification tasks are biome classification [8], ecoregion classification [8], and country classification [18]. The regression tasks are air temperature prediction [14], elevation prediction [32], population density prediction [32], and housing price prediction [30]. Results on climate data from ERA5 are shown in Section 10 of the supplementary material. The objective is to learn a linear predictive model that solves the underlying task. For fairness, we use the same hyperparameters for all tasks, i.e., the same \\(\\tau\\) and \\(\\beta\\) parameters for each task. The details of the hyperparameters are listed in the supplementary material. We compare our method with state-of-the-art parametric [5, 18, 27, 28, 39] and non-parametric [10, 25] representations. The results of this experiment are shown in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The results show that our method outperforms all state-of-the-art models in the classification tasks with significant" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24684" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.114, + 0.088, + 0.885, + 0.335 + ], + "angle": 0, + "content": "
BiomeEcoRegionsCountryTemperatureElevationPopulationCali-Housing
Direct29.10.666.90.3810.0250.0530.238
Cartesian_3D30.21.866.90.3620.0300.1620.240
Wrap [25]34.41.169.70.8610.0850.3280.239
Theory [10]33.51.072.50.8490.0930.3300.254
SphereM [28]36.427.372.70.6290.1390.3020.423
SphereM+ [28]58.750.176.10.8860.2940.4210.543
SphereC [28]36.352.972.90.4610.1850.3350.496
SphereC+ [28]53.261.673.60.8420.2600.3920.544
CSP-INat [27]61.157.175.90.7170.3880.5540.462
CSP-FMoW [27]61.458.081.30.8650.3990.5800.541
SINR [5]67.954.988.30.9420.6440.7260.420
GeoCLIP [39]70.271.681.30.9160.6040.6980.708
SatCLIP [18]68.969.382.80.8250.6660.6840.400
RANGE83.375.793.70.8950.8440.7990.422
RANGE+83.375.394.70.9310.8510.8110.336
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.346, + 0.907, + 0.389 + ], + "angle": 0, + "content": "Table 2. Our model shows improvements over a variety of tasks compared to state-of-the-art models. The first 3 columns are classification tasks with accuracy metrics and the last 4 columns are regression tasks with \\( \\mathbf{R}^2 \\) metric. We show improvements with significant margins across many of the tasks. Our model underperforms in the Cali-housing dataset. We further analyze this behavior in our discussions." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.401, + 0.905, + 0.54 + ], + "angle": 0, + "content": "
typetemp.BiomeEcoCountryTemperatureElevationPopulationCali-Housing
SatCLIPbase-model-68.969.382.80.8250.6660.6840.400
RANGEtop-1-75.665.285.60.8170.7660.7420.444
top-k-82.876.890.60.8840.8100.7710.619
soft selectionfixed83.375.793.70.8950.8440.7990.422
soft selectionper task83.575.894.50.9220.8570.8090.465
RANGE+soft selectionfixed83.575.394.70.9310.8510.8110.336
soft selectionper task83.775.994.90.9320.8550.8130.460
gain (%)+21.5+9.5+14.6+12.9+28.37+18.8+15.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.549, + 0.907, + 0.604 + ], + "angle": 0, + "content": "Table 3. Ablation of different versions of our model compared with SatCLIP as the base model. Our soft selection using weighted averages over the database performs better than top-k selection. We also find that a single temperature works well for most tasks. Fine-tuning the temperature per task is generally not required as the gain is marginal. The last row shows the difference between the base model and RANGE+." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.629, + 0.466, + 0.755 + ], + "angle": 0, + "content": "
top-1top-3top-5top-10
Img66.183.388.092.2
Img+CSP72.987.991.694.8
Img+GeoCLIP72.988.291.995.2
Img+CSP_INat*74.488.892.294.9
Img+SatCLIP75.188.791.994.5
Img+RANGE75.289.692.995.5
Img+RANGE+75.189.592.895.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.82 + ], + "angle": 0, + "content": "Table 4. Top-k classification accuracy on INat-2018 test split: Location information acts as a strong prior in fine-grained species classification. Our method shows competitive top-k results against state-of-the-art models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "margins. In biome, ecoregion, and country classification, we advance the state-of-the-art by \\(13.1\\%\\), \\(4.1\\%\\), and \\(6.4\\%\\), respectively. Among the regression tasks, we achieve SoTA" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.632, + 0.907, + 0.829 + ], + "angle": 0, + "content": "performance for elevation and population density prediction with significant gains and narrowly come second in the air temperature prediction task. Our method, however, underperforms in the housing price prediction task. We suspect this is because the visual features that define housing change dramatically over time. The standard California housing dataset is based on a 1990 census, while our retrieved visual features are extracted from 2020 Sentinel data. The results also demonstrate that the hyperparameters for our model are robust and do not need to be tuned for specific tasks to achieve good performance. Furthermore, \\(\\mathrm{RANGE^{+}}\\), on average, outperforms RANGE by a small margin, which can be attributed to the spatial smoothness constraint." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.846, + 0.869, + 0.863 + ], + "angle": 0, + "content": "5.2. Using Location Embeddings as Geo-prior" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We evaluate our model on the task of fine-grained species classification. We use the iNaturalist 2018 dataset [38]," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24685" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.907, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.334, + 0.908, + 0.377 + ], + "angle": 0, + "content": "Figure 4. We visualize the geo-embeddings from different models by projecting them into a 3-dimensional vector using Independent Component Analysis (ICA). The results suggest that by explicitly adding visual features, our method learns more high-frequency information compared to the existing models." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.389, + 0.907, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.649, + 0.908, + 0.679 + ], + "angle": 0, + "content": "Figure 5. Interpolating the \\(\\beta\\) parameter in \\(\\mathrm{RANG}^+\\) allows us to control the spatial smoothness of our embeddings. The results show that \\(\\mathrm{RANG}^+\\) can be used to generate neural fields of geo-embeddings at multiple frequencies." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.486, + 0.901 + ], + "angle": 0, + "content": "which contains data from 8,142 species. Prior works [18, 25, 33] have shown that adding location information can improve the performance of pretrained image classification models on iNat as knowing the location of an image can provide a strong prior about its content. For our experiment, we follow a similar setup as [33]. We take a pretrained image classification model, which gives us \\( P(y \\mid I) \\). We then train a linear model that takes as input the pre-trained geo-embeddings and predicts the species categories, i.e., \\( P(y \\mid G) \\). The final distribution is computed as the product of the two distributions, i.e., \\( P(y \\mid I, G) = P(y \\mid I) * P(y \\mid G) \\). This experiment also aims to show that location representations obtained using self-supervised training can be eas" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.749 + ], + "angle": 0, + "content": "ily generalized towards tasks like iNat. Hence, we exclude SINR [5] from this comparison as it is trained in a supervised manner on the iNaturalist data itself." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The results of this experiment are shown in Table 4. The performance of the pretrained image classifier is \\(66.1\\%\\). The addition of location information improves the accuracy across all models. We see that RANGE and \\(\\mathrm{RANG}^{+}\\) achieve competitive scores, narrowly outperforming state-of-the-art models. The results from this experiment highlight the benefits of using good location representations as geo-prior to solve fine-grained image classification tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24686" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.245, + 0.108 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.323 + ], + "angle": 0, + "content": "Robustness to Database Size: The RANGE database that we used for our model in Section 5.1 was created using the SatCLIP dataset with 82k locations. However, our method is extremely robust and can be used with much smaller database sizes. We conducted an experiment where we used smaller samples of the SatCLIP data to create our RANGE database. We created a database with \\(75\\%\\), \\(50\\%\\), \\(25\\%\\), and \\(10\\%\\) of the total data. We then trained a linear model for RANGE and \\(\\mathrm{RANGE^{+}}\\) using each of these subsets as our retrieval database. We also trained another version of our method where we only use geodesic distance for retrieval, i.e. \\(\\beta = 0\\), which we call RANGE-HAYER. We used the same tasks described in Section 5.1 to evaluate these models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.484, + 0.598 + ], + "angle": 0, + "content": "Our results from figure 3 show that we can obtain similar performance while using only \\(10\\%\\) of the original database size. In terms of storage, this database only occupies 85 Megabytes in disk, which is very efficient. The results also support our initial claim that there is low variance in satellite images; thus, a small number of satellite images can capture many important semantics across the globe. We see that the performance for both RANGE and \\(\\mathrm{RANG}^{+}\\) is stable across different settings and different tasks. The results also show that RANGE-HAYER, which only relies on spatially retrieved information, can be unstable, as seen in figure 3. These results highlight the pitfalls of depending completely on spatial similarity for retrieval. Locations that are spatially close do not necessarily share similar semantics. Therefore, as you change the sample distribution in the database, you can introduce noisy retrievals, which amplify the noise in the estimated visual embedding. Semantic-based retrieval strategy mitigates such issues." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.839 + ], + "angle": 0, + "content": "Impact of architectural components: Table 3 shows the impact of different components of our method compared to SatCLIP as the base model. We also compare our method with two other methods of retrieval: top-1 and top-k (where k was set to 100). The results show that our retriever function generally yields better results than the top-k selection approach. This can be attributed to the fact that top-k averaging does not consider the measure of similarity between query location and keys. We also performed a linear search to find the optimal temperature parameters of RANGE for each task separately. Our results show we are able to make marginal improvements by tuning the temperature parameter for individual tasks. The results indicate the temperature parameters of RANGE are robust and do not need to be fin-tuned for individual tasks in most cases." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.455, + 0.866 + ], + "angle": 0, + "content": "5.4. Qualitative Evaluation of Geo-embeddings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Visual comparison of geo-embeddings: We qualitatively compare the RANGE embeddings with other location em" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.242 + ], + "angle": 0, + "content": "beddings. We use Independent Component Analysis (ICA) to project the embeddings to a 3-dimensional vector and use them as RGB channels to visualize them over the globe. Figure 4 shows the visualizations for each model. Qualitatively, we see that models like CSP and SINR are extremely smooth, suggesting that they predominantly capture low-frequency information. GeoCLIP and SatCLIP capture relatively high-frequency information. The visualizations further suggest that RANGE and \\(\\mathrm{RANG^{+}}\\) embeddings are able to capture even higher frequency information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.907, + 0.53 + ], + "angle": 0, + "content": "Visualizing the impact of \\(\\beta\\) parameter: Secondly, we visualize the impact of the \\(\\beta\\) parameter in equation (7). A quantitative evaluation of the \\(\\beta\\) parameter is presented in Section 9 of the supplementary material. Setting \\(\\beta = 1\\) gives us the RANGE embeddings, setting \\(\\beta = 0\\) gives us RANGE-HAYER embeddings, and setting \\(\\beta = 0.5\\) gives the \\(\\mathrm{RANG}^{+}\\) embeddings. This parameter controls the contribution of spatially-retrieved visual information to the semantically-retrieved visual information. This additional information acts as a spatial smoothness constraint on the RANGE embeddings. At \\(\\beta = 0\\), we add the maximum constraint, which gives us low-frequency embeddings similar to CSP and SINR. As we increase the value of \\(\\beta\\), we increase the frequency of our embeddings, i.e. locations that are spatially close to each other but are semantically different have different representations. Thus, the \\(\\beta\\) parameter allows us to explicitly control the smoothness of the RANGE embeddings and, therefore, allows generating location embeddings at multiple frequencies." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.553, + 0.762, + 0.569 + ], + "angle": 0, + "content": "6. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.905, + 0.717 + ], + "angle": 0, + "content": "Self-supervised learning has been a key enabler of the rapid recent progress in computer vision and natural language processing. Representations from models like SimCLR [3], and CLIP [31] have facilitated the creation of many powerful vision and language models. Recent works like SatCLIP [18], GeoCLIP [39], and CSP [27] showed that the same self-supervised techniques can be used to learn powerful representations for geographic locations, which are useful for a broad range of tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduced a simple, yet effective strategy for improving such geographic embeddings, moving past previous assumptions of multiview redundancy. We proposed a retrieval-augmented strategy for estimating visual features from an auxiliary database of visual embeddings. Our approach results in significant improvements for a variety of tasks as compared to purely parametric embedding strategies with only a modest increase in storage requirements. Our method is efficient, robust, and multiscale. We hope our insights and results substantiate our recommendation of using RANGE as a general-purpose location encoder for geospatial tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24687" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.27, + 0.108 + ], + "angle": 0, + "content": "7. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.484, + 0.176 + ], + "angle": 0, + "content": "This research used the TGI RAILs advanced compute and data resource which is supported by the National Science Foundation (award OAC-2232860) and the Taylor Geospatial Institute." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.192, + 0.188, + 0.208 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.217, + 0.484, + 0.259 + ], + "angle": 0, + "content": "[1] Andreas Blattmann, Robin Rombach, Kaan Oktay, Jonas Müller, and Björn Ommer. 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In CVPR, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24689" + } + ] +] \ No newline at end of file diff --git a/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_origin.pdf b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eb2f14f651430fa659450e9dfd4615ff1f79b269 --- /dev/null +++ b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/8a549df3-3427-4bdd-bb2f-4a67986ec4e3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:55734a895949356c360e6bf03175ac9dfeb5bb6327a271eca2022c7c260535ad +size 3434785 diff --git a/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/full.md b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/full.md new file mode 100644 index 0000000000000000000000000000000000000000..03e253bf49ec0b7c68cc3001706f06f84bdb2400 --- /dev/null +++ b/2025/RANGE_ Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings/full.md @@ -0,0 +1,258 @@ +# RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings + +Aayush Dhakal1 Srikumar Sastry1 Subash Khanal1 Adeel Ahmad1,2 Eric Xing1 Nathan Jacobs1 + +Washington University in St. Louis $^{1}$ Taylor Geospatial Institute $^{2}$ + +# Abstract + +The choice of representation for geographic location significantly impacts the accuracy of models for a broad range of geospatial tasks, including fine-grained species classification, population density estimation, and biome classification. Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to $13.1\%$ on classification tasks and $0.145R^2$ on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE. + +# 1. Introduction + +Several machine learning tasks require the use of geolocation as an input feature. Multiple works have shown the benefits of using geolocation to solve vital ecological, geographical, and geological tasks. SINR [5] used location as input to predict species distribution, Lang et al. [20] used location with satellite image to learn a global canopy height model, and SatCLIP [18] used location to solve several geospatial tasks such as biome classification, population density estimation, housing price prediction, etc. Since location is a ubiquitous input variable in all geospatial settings, finding good representations for it is fundamental when solving geospatial tasks. + +![](images/11907064e9f0ecfb5447b522b1dfa372540a1f9903864199b9699b02a716a849.jpg) +Figure 1. Adding explicit visual features allows us to generate more high-resolution location embeddings. We use a retrieval strategy that allows us to generate multi-resolution retrieval-augmented neural field of geo-embeddings (RANGE). + +Previous work [33] has shown that using location directly (represented as two floating point numbers of latitude and longitude) as an input to a machine learning model yields poor performance. Therefore, several works have attempted to find better ways to represent location data. Some of these approaches [10, 25] use a non-parametric method to encode location. However, recent works [18, 27, 39] have shown that it is possible to learn a general-purpose location representation by learning a parametric model (often a neural network) in a self-supervised setting. There are several strategies that can be used to train the parametric model. A common approach used by state-of-the-art models [18, 27, 39] involves learning visual cues associated with a given geolocation. Two recent state-of-the-art models, GeoCLIP [39] and SatCLIP [18], use contrastive training to align geo-embeddings with co-located images; the former aligns them with ground-level images while the latter aligns them with satellite images. Images of a location capture dense information about the area, such as the landcover, landuse, etc. Therefore, learning location representations that capture this dense information is beneficial for solving geospatial tasks. Prior work [18] has shown that rep + +resentations from such models are extremely powerful and are capable of solving diverse geospatial tasks both on their own and in combination with images. In this work, we argue that the current approaches to learning geo-embeddings using images, while powerful, still fail to preserve all the relevant visual information. The location representations from these models only capture low-resolution shared information between location and image and ignore crucial high-resolution information that is unique to the image. In section 2, we define this problem more formally from the perspective of multi-view redundancy. + +To address this issue, we propose a retrieval-augmented strategy that approximates the unique visual information present in a location. There are three key ideas to our solution. First, it is possible to approximate the visual features of a given location by strategically combining the visual features of other similar-looking locations. Second, contrastively trained models like SatCLIP [18] and GeoCLIP [39], while lacking in preserving modality-specific information, are excellent in learning modality alignment [13]. Therefore, it is possible to retrieve semantically aligned images, with alignment scores, for a given location using these models. Third, we note that the variance of semantic information visible in satellite images across the Earth is relatively low (as opposed to the wider diversity in consumer photographs). Hence, it is possible to capture a large percentage of unique aerial semantics with a limited number of satellite images. By combining these three key ideas, we propose our retrieval-augmented framework, RANGE (Retrieval-Augmented Neural Fields for Multi-Resolution Geo-Embeddings). Our retriever function uses both semantic and spatial alignment to approximate the visual features of a given location using an auxiliary database of image features. Our function is robust to the database size and works well even in limited sample settings. The hyperparameter in the retriever function can be adjusted to generate geo-embeddings at different frequencies. In summary, these are the main contributions of our paper: + +- We show why existing image-location contrastive methods result in sub-optimal representations from the perspective of multi-view redundancy. +- We propose a novel retrieval-based strategy, RANGE, to generate geo-embeddings that preserve both shared and unique modality information. +- We propose a retriever function that estimates the visual embedding of a location using both semantic and spatial alignment. Our retriever function is robust to different database sizes and can generate geo-embeddings at multiple frequencies by enforcing spatial smoothness. + +# 2. Aligning Location and Image is a Multi-View Non-Redundancy Problem + +Let (L,H,T) represent location modality, image modality, and geospatial task, respectively. Models like SatCLIP and GeoCLIP align co-located images and locations by minimizing the infoNCE objective. Solving the multimodal infoNCE objective maximizes the lower bound on the mutual information, preserving the shared information within the learned representations [29]. As such, the final learned representations of these models contain only information that is shared across both location and image. This property is useful under the multi-view redundancy assumption which states that the information shared between the two modalities is exactly relevant to solve the underlying task. In other words, the multi-view redundancy setting assumes that any additional unique information from the image or location would not be useful in solving the task T [37]. However, this assumption does not hold in the location-image learning setting as there is high unique information contained in the image modality that is useful for solving downstream tasks. Formally, we argue that location-image learning falls under the multi-view non-redundancy setting: there is unique information in the image modality that is not shared with the location modality, and that information is relevant for solving our geospatial task T. In this case, contrastive training discards valuable task-relevant information from the image, leading to poor downstream performance [23]. + +Empirically, there is abundant unique information present in the image features that are relevant for solving downstream tasks. The location representations from contrastively trained models like SatCLIP and GeoCLIP only capture the low-resolution shared information, ignoring all the valuable task-relevant information that is unique to the image. To demonstrate this property concretely, we quantitatively show that there are tasks that can be solved more accurately by adding the image representation to the shared image-location representation from SatCLIP [18]. First, we choose 4 tasks: Biome, Ecoregions, Elevation, and Population Density estimation. We download a corresponding Sentinel-2 image for every data point. For each task, we train one model using the SatCLIP features and another model using the SatCLIP features combined with the SatMAE [6] features of the satellite image [6]. The results in Table 1 show that adding image features improves the performance across all tasks. The increase in performance demonstrates that the images contain unique information relevant to solving the task that is lost during contrastive training. Hence, "location and image" does not follow the assumption of multi-view redundancy. + +Although adding corresponding satellite image information to a location embedding improves performance, this is not feasible in practice. For many geospatial tasks, we + +
BiomeEcoregionElevationPopulation
SatMAE58.828.40.3880.600
SatCLIP68.969.30.6660.684
locoplmg74.973.50.7490.765
gain (%)+8.71+6.06+12.46+11.84
+ +Table 1. We show that using the image-location shared information from SatCLIP embeddings is sub-optimal to solve some geospatial problems. Adding image features to the embeddings provides useful visual information that improves the accuracy of the task. We show the accuracy for the classification tasks and $\mathbb{R}^2$ value for the regression tasks. The results indicate that there are valuable visual features that are not captured by the SatCLIP embeddings. + +wish to make predictions across the globe with millions of points. In such cases, using the "image+location" framework would require us to retrieve/store/process millions of images. We propose an efficient method for approximating the visual information using a compact database. Our results suggest that this approximation can outperform the use of true visual features in some cases. + +# 3. Related Works + +# 3.1. Learning Representations for Geolocation + +Learning effective representations for geolocation is valuable for diverse downstream geospatial tasks, such as geolocation [39], canopy height prediction [20], fine-grained species classification [25, 34], species distribution modeling [5, 34], geographical question answering [26], soundscape mapping [16], etc. Geolocation in these tasks can be represented using either non-parametric [10, 33] or parametric [18, 27, 39] methods. Rußwurm et al. [33] represents geolocation using spherical harmonic basis functions, and Aodha et al. [25] uses a sine and cosine encoding of geolocation that removes discontinuity at dateline. In recent years, learned representations for geolocation, typically parameterized by neural networks, have been popularized. Some of these methods learn geolocation representations by using self-supervised pre-training strategies that distill visual information from either co-located overhead [18, 27] or ground-level images [27, 39]. The location encoders trained by these methods have demonstrated utility across various downstream geospatial tasks. We use the representations from these location encoders as baselines for our model. + +# 3.2. Multimodal Contrastive Learning + +Contrastive learning is an efficient and scalable pre-training strategy for learning a shared embedding space across multiple modalities [7, 9, 11, 15, 16, 22, 31, 41-43]. As demonstrated by CLIP [31] and more recent works [22, 41, 42] in + +vision-language learning, the shared embedding space can be utilized for zero-shot classification and leveraged across a variety of downstream tasks. Contrastively trained multimodal embedding spaces between geolocation and satellite imagery [18, 27] or ground-level imagery [39], have also demonstrated impressive transferability of both location and visual representations to various geospatial tasks. + +Despite its success, recent works highlight the limitations of multimodal contrastive learning. One such study [23] shows that contrastively trained representations capture the shared information between the two modalities and thus only work best under certain assumptions. Similarly, another work [13] demonstrates that the final layers of encoders in the contrastive learning framework preserve only the information necessary for solving the alignment objective, discarding other modality-specific details. We argue that some of the underlying assumptions of multimodal contrastive training do not hold true in the image-location setting. Therefore, the resulting location representations from these methods are sub-optimal for downstream tasks. To address this issue, we propose a method to approximate the image-specific information for a given location. + +# 3.3. Retrieval Augmented Methods + +There has been a recent surge in retrieval-augmented generation (RAG) methods, primarily focused on generative tasks [1, 2, 4, 17, 19, 21, 35, 36, 40]. These methods generally consist of three main components: a retriever, an external database, and a generator. For a given query, the retriever selects a set of documents from the database and provides them, along with the original query, to the generator to produce the desired output. RAG has been successfully employed to improve text generation for large language models (LLMs) [2, 21, 36], text-to-image generation [1, 4, 17], text-to-3D generation [35], audio captioning [19], and more. Within the RAG framework, one could also replace the generator with another task-specific component, such as a classifier [24], to enhance performance by leveraging the rich information from the retrieved documents. Inspired by these retrieval-augmented methods, we design our framework, RANGE, which retrieves rich visual information from our database for a given geolocation query and utilizes it for various downstream geospatial tasks. + +# 4. Method + +# 4.1. Problem Setup + +We consider a dataset with paired geolocations and collocated satellite images $\{g_i, s_i\}$ . The goal is to learn a meaningful representation for $g_i$ by aligning it with $s_i$ , which can be done by minimizing the clip objective [18, 31, 39]. We have a trainable geolocation encoder $E$ , a frozen pretrained image encoder $I$ , and a projection layer + +![](images/ef4d3962d8b370b6f39e8c9f9198e38c81c7c92acabe103a02cfd1fa0cdbf9ad.jpg) +Figure 2. Framework of RANGE. (a) In the training stage, a shared embedding space is learned between locations and images. (b) We create a database of low-resolution and high-resolution image embeddings using the trained projection layer and a powerful pretrained image model, respectively. (c) During inference, we use a location as the query, low-resolution image embeddings as keys, and high-resolution image embeddings as values. Using our retriever function, we compute the approximate high-resolution embeddings for the query. We concatenate $(\oplus)$ the approximated visual feature with our query embedding. + +$P$ . Let $G_{i} = E(g_{i})$ represent the location embedding, $S_{i} = I(s_{i})$ represent the frozen image embedding, and $P_{i} = P(I(s_{i})) = P(S_{i})$ represent the image embedding obtained from the projection layer for the $\mathrm{i}^{th}$ sample. We minimize the objective: + +$$ +L _ {i} ^ {l o c} = \frac {- 1}{k} \sum_ {i = 1} ^ {k} \log \frac {\exp \left(G _ {i} \cdot P _ {i} / \tau\right)}{\sum_ {j = 1} ^ {k} \exp \left(G _ {i} \cdot P _ {j}\right) / \tau}) \tag {1} +$$ + +$$ +L _ {i} ^ {i m g} = \frac {- 1}{k} \sum_ {i = 1} ^ {k} \log \frac {\exp \left(G _ {i} \cdot P _ {i} / \tau\right)}{\sum_ {j = 1} ^ {k} \exp \left(G _ {j} \cdot P _ {i}\right) / \tau}) \tag {2} +$$ + +$$ +L _ {i} = \left(L _ {i} ^ {l o c} + L _ {i} ^ {i m g}\right) / 2 \tag {3} +$$ + +The training process is shown in Figure 2-(a). We contrastively align the geolocations and satellite images by minimizing their CLIP objective. This formulation is identical to SatCLIP [18], so we use the pretrained SatCLIP image and location encoders for simplicity. For query location $g_{i}$ , $S_{i}$ encodes the high-resolution visual features since $I$ is a powerful pre-trained image encoder. Both $P_{i}$ and $G_{i}$ encode low-resolution shared information between $g_{i}$ and $s_{i}$ . The resulting geo-embedding, $G_{i}$ , is sub-optimal as it loses unique visual information crucial for many downstream tasks. To solve this, we propose a retriever function $R_{\tau}$ that allows us to approximate the high-resolution information $S_{i}$ given $g_{i}$ . Let $\epsilon$ denote the deviation from the true + +visual embedding. We can then explicitly add the approximate visual information $\hat{S}_i$ to our location embedding $G_{i}$ : + +$$ +R _ {\tau} (g _ {i}) = \hat {S} _ {i} = S _ {i} + \epsilon \tag {4} +$$ + +$$ +\operatorname {R A N G E} \left(g _ {i}\right) = \hat {S} _ {i} \oplus G _ {i} \tag {5} +$$ + +# 4.2. Retrieval Augmented Neural Fields + +Creating the Retrieval Database: Once the contrastive training is done, we create a retrieval database as shown in Figure 2-(b). We take $\{g_i,s_i\}$ sampled uniformly across the globe using the SatCLIP [18] dataset. For every location $g_{i}$ in our data, we compute: a) the shared-information image embedding $R_{i}^{L} = P(I(s_{i}))$ , and b) the high-resolution image embedding $R_{i}^{H} = \bar{I} (s_{i})$ ; we refer to these sets of embeddings as low-resolution embeddings and high-resolution embeddings, respectively, in the rest of the paper. In practice, $\bar{I}$ can differ from $I$ ; the only condition is that $\bar{I}$ is a pretrained image feature extractor. For our purposes, we use SatMAE [6] as $\bar{I}$ . + +Retriever Function: Let $R^L = \{R_1^L, R_2^L, \dots, R_N^L\}$ , and $R^H = \{R_1^H, R_2^H, \dots, R_N^H\}$ represent the set of all low-resolution and high-resolution image embeddings in our database. After creating the database, we need a method to sample appropriate high-resolution image information for a query location. Naively, we can set this as a lookup operation, where $G_i$ is the query, $R^L$ is the set of all keys, and $R^H$ + +is the set of all values. We have a function $\text{sim}(G_i, R_j^L)$ , which gives the alignment scores between i and j. In our setting, this similarity function is a simple cosine similarity. For a query $G_i$ , we find $R_j^L$ with the highest alignment score and return the key $R_j^H$ . In practice, $R_j^H$ is noisy. The semantically closest image in the database can contain additional information that is irrelevant to the location. Therefore, naively adding $R_j^H$ has the potential of introducing incorrect information to our geo-embeddings. + +We instead use a soft selection criteria. First, we compute the query's alignment score with each key in the database using cosine similarity. We use a softmax function to convert the alignment scores to probabilities. We also use a temperature parameter $\tau$ to slightly reshape the probability distribution; $\tau$ is extremely robust as it does not need to be fine-tuned for different tasks or for databases with different distributions. We use the resulting probabilities to compute a weighted average across all values, i.e., high-resolution image embeddings in the database. The resulting embedding is an approximation of $S_{i}$ , where the information contributed by each image is weighted by its alignment score with the query. We concatenate this approximate high-resolution image embedding with our original location embedding $G_{i}$ to obtain the multi-resolution RANGE embedding $RANGE_{i}$ . A high-level view of this process is shown in Figure 2-(c). + +$$ +\begin{array}{l} R A N G E _ {i} = R _ {\tau} \left(G _ {i}\right) \oplus G _ {i} \\ = \frac {1}{N} \sum_ {k = 1} ^ {N} \frac {e ^ {s i m \left(G _ {i} , R _ {k} ^ {L}\right) / \tau}}{\sum_ {j = 1} ^ {N} e ^ {s i m \left(G _ {i} , R _ {j} ^ {L}\right) / \tau}} * R _ {k} ^ {H} \oplus G _ {i} \\ \end{array} +$$ + +where $G_{i}\in \mathbb{R}^{M}$ $R_k^L\in \mathbb{R}^M$ $R_{k}^{H}\in \mathbb{R}^{N}$ (6) + +Adding smoothness constraints: We also propose another version of our model called $RANG^{+}$ . Here, we additionally use geodesic similarity to approximate the visual features of the location. We convert our query location to 3D cartesian coordinates and use angular distance to find the spatially closest image in the database. This spatial retrieval allows us to impose spatial smoothness on our embeddings since locations close to each other are forced to have similar retrieval, irrespective of the semantics. Similar to $RANG$ , we compute a weighted average across all values in the database using the angular similarity between the query and keys. However, we explicitly mask samples with angular similarity lower than a threshold, i.e., significantly distant samples have no contribution. The spatially retrieved embedding is added to the semantically retrieved embedding and weighted using a $\beta$ parameter. This $\beta$ parameter controls the level of spatial smoothness enforced on the $RANG$ embeddings, as shown in Figure 5. Let $g_{i}^{3D}$ be the query location, $l$ be the set of all database locations + +![](images/271dff7f7c89f2c99b112dd3de7f7923b6736cfb6f29c328e19baa60fb2efa04.jpg) + +![](images/f53a9b35396f565ab48b184e96dce97fe315252788be21ffe38b78c2b40c62ba.jpg) + +![](images/9ff6ea08c79fafa4fd5a4b5aaf23120fdfb4fa9ae9f8e6f0b7b42074b9d505a8.jpg) + +![](images/c682b55d67a5e896eb3a22092c710ef0741de0399feae8aa97ca2f913ba25716.jpg) + +![](images/9ad5ff47c130c99548fad000019834edfe04b16d0acae91001f11b5bddb5a3fb.jpg) +Figure 3. Performance of our model with respect to the database size. The results show that compared to RANGE-HAYER, both RANGE and $\mathrm{RANG}^+$ are very robust to changes in database size. We can maintain the same performance even when only using $10\%$ of the samples in the database. + +![](images/f5bc4baa4d4c52621b9698674df02220a94aca9a61d36cea4bbf1a5bcceb038e.jpg) + +![](images/f6bbbdeae0a2fc624a5692eee038c8f9b04e92976c850296a28c21f76401326c.jpg) + +![](images/91eff7d9d5b49662f6a955c719f5e290119abdc2fa6a372a2a1709f99d4577f8.jpg) + +in 3D cartesian coordinates, and $sim(g_i^{3D},l_k)$ be their angular similarity: + +$$ +R A N G E _ {i} ^ {+} = \frac {1}{N} (\beta * \sum_ {k = 1} ^ {N} \frac {e ^ {s i m (G _ {i} , R _ {k} ^ {L}) / \tau_ {1}}}{\sum_ {j = 1} ^ {N} e ^ {s i m (G _ {i} , R _ {j} ^ {L}) / \tau_ {1}}} * R _ {k} ^ {H} + +$$ + +$$ +(1 - \beta) \sum_ {k = 1} ^ {N} \frac {e ^ {s i m \left(g _ {i} ^ {3 D} , l _ {k}\right) / \tau_ {2}}}{\sum_ {j = 1} ^ {N} e ^ {s i m \left(g _ {i} ^ {3 D} , l _ {j}\right) / \tau_ {2}}} * R _ {k} ^ {H}) \oplus G _ {i} +$$ + +where $G_{i}\in \mathbb{R}^{M}$ $g_{i}^{3D}\in \mathbb{R}^{3}$ $l_{k}\in \mathbb{R}^{3}$ (7) + +When $\beta$ is set to 0, only spatially relevant features are used, and we refer to this setting as RANGE-HAYER. + +# 5. Experiments and Results + +# 5.1. Quantitative Evaluation on Downstream Tasks + +We evaluate the efficacy of RANGE and $\mathrm{RANG^{+}}$ embeddings on a wide variety of downstream applications. We create our database using the SatCLIP [18] dataset with 82k locations. For $\mathrm{RANG^{+}}$ , we set $\beta$ to 0.5. We choose 3 classification tasks and 4 regression tasks for this experiment as used by prior work [18]. The classification tasks are biome classification [8], ecoregion classification [8], and country classification [18]. The regression tasks are air temperature prediction [14], elevation prediction [32], population density prediction [32], and housing price prediction [30]. Results on climate data from ERA5 are shown in Section 10 of the supplementary material. The objective is to learn a linear predictive model that solves the underlying task. For fairness, we use the same hyperparameters for all tasks, i.e., the same $\tau$ and $\beta$ parameters for each task. The details of the hyperparameters are listed in the supplementary material. We compare our method with state-of-the-art parametric [5, 18, 27, 28, 39] and non-parametric [10, 25] representations. The results of this experiment are shown in Table 2. + +The results show that our method outperforms all state-of-the-art models in the classification tasks with significant + +
BiomeEcoRegionsCountryTemperatureElevationPopulationCali-Housing
Direct29.10.666.90.3810.0250.0530.238
Cartesian_3D30.21.866.90.3620.0300.1620.240
Wrap [25]34.41.169.70.8610.0850.3280.239
Theory [10]33.51.072.50.8490.0930.3300.254
SphereM [28]36.427.372.70.6290.1390.3020.423
SphereM+ [28]58.750.176.10.8860.2940.4210.543
SphereC [28]36.352.972.90.4610.1850.3350.496
SphereC+ [28]53.261.673.60.8420.2600.3920.544
CSP-INat [27]61.157.175.90.7170.3880.5540.462
CSP-FMoW [27]61.458.081.30.8650.3990.5800.541
SINR [5]67.954.988.30.9420.6440.7260.420
GeoCLIP [39]70.271.681.30.9160.6040.6980.708
SatCLIP [18]68.969.382.80.8250.6660.6840.400
RANGE83.375.793.70.8950.8440.7990.422
RANGE+83.375.394.70.9310.8510.8110.336
+ +Table 2. Our model shows improvements over a variety of tasks compared to state-of-the-art models. The first 3 columns are classification tasks with accuracy metrics and the last 4 columns are regression tasks with $\mathbf{R}^2$ metric. We show improvements with significant margins across many of the tasks. Our model underperforms in the Cali-housing dataset. We further analyze this behavior in our discussions. + +
typetemp.BiomeEcoCountryTemperatureElevationPopulationCali-Housing
SatCLIPbase-model-68.969.382.80.8250.6660.6840.400
RANGEtop-1-75.665.285.60.8170.7660.7420.444
top-k-82.876.890.60.8840.8100.7710.619
soft selectionfixed83.375.793.70.8950.8440.7990.422
soft selectionper task83.575.894.50.9220.8570.8090.465
RANGE+soft selectionfixed83.575.394.70.9310.8510.8110.336
soft selectionper task83.775.994.90.9320.8550.8130.460
gain (%)+21.5+9.5+14.6+12.9+28.37+18.8+15.0
+ +Table 3. Ablation of different versions of our model compared with SatCLIP as the base model. Our soft selection using weighted averages over the database performs better than top-k selection. We also find that a single temperature works well for most tasks. Fine-tuning the temperature per task is generally not required as the gain is marginal. The last row shows the difference between the base model and RANGE+. + +
top-1top-3top-5top-10
Img66.183.388.092.2
Img+CSP72.987.991.694.8
Img+GeoCLIP72.988.291.995.2
Img+CSP_INat*74.488.892.294.9
Img+SatCLIP75.188.791.994.5
Img+RANGE75.289.692.995.5
Img+RANGE+75.189.592.895.5
+ +Table 4. Top-k classification accuracy on INat-2018 test split: Location information acts as a strong prior in fine-grained species classification. Our method shows competitive top-k results against state-of-the-art models. + +margins. In biome, ecoregion, and country classification, we advance the state-of-the-art by $13.1\%$ , $4.1\%$ , and $6.4\%$ , respectively. Among the regression tasks, we achieve SoTA + +performance for elevation and population density prediction with significant gains and narrowly come second in the air temperature prediction task. Our method, however, underperforms in the housing price prediction task. We suspect this is because the visual features that define housing change dramatically over time. The standard California housing dataset is based on a 1990 census, while our retrieved visual features are extracted from 2020 Sentinel data. The results also demonstrate that the hyperparameters for our model are robust and do not need to be tuned for specific tasks to achieve good performance. Furthermore, $\mathrm{RANGE^{+}}$ , on average, outperforms RANGE by a small margin, which can be attributed to the spatial smoothness constraint. + +# 5.2. Using Location Embeddings as Geo-prior + +We evaluate our model on the task of fine-grained species classification. We use the iNaturalist 2018 dataset [38], + +![](images/89350c8ac5aa0908ce4dfaab8b96050f574772563113ba5a601db5e99346f42d.jpg) +Figure 4. We visualize the geo-embeddings from different models by projecting them into a 3-dimensional vector using Independent Component Analysis (ICA). The results suggest that by explicitly adding visual features, our method learns more high-frequency information compared to the existing models. + +![](images/8181c7c6f4a81d45ed844755a846983cd81ca06770a39723bc96fe60cbd6f7f5.jpg) +Figure 5. Interpolating the $\beta$ parameter in $\mathrm{RANG}^+$ allows us to control the spatial smoothness of our embeddings. The results show that $\mathrm{RANG}^+$ can be used to generate neural fields of geo-embeddings at multiple frequencies. + +which contains data from 8,142 species. Prior works [18, 25, 33] have shown that adding location information can improve the performance of pretrained image classification models on iNat as knowing the location of an image can provide a strong prior about its content. For our experiment, we follow a similar setup as [33]. We take a pretrained image classification model, which gives us $P(y \mid I)$ . We then train a linear model that takes as input the pre-trained geo-embeddings and predicts the species categories, i.e., $P(y \mid G)$ . The final distribution is computed as the product of the two distributions, i.e., $P(y \mid I, G) = P(y \mid I) * P(y \mid G)$ . This experiment also aims to show that location representations obtained using self-supervised training can be eas + +ily generalized towards tasks like iNat. Hence, we exclude SINR [5] from this comparison as it is trained in a supervised manner on the iNaturalist data itself. + +The results of this experiment are shown in Table 4. The performance of the pretrained image classifier is $66.1\%$ . The addition of location information improves the accuracy across all models. We see that RANGE and $\mathrm{RANG}^{+}$ achieve competitive scores, narrowly outperforming state-of-the-art models. The results from this experiment highlight the benefits of using good location representations as geo-prior to solve fine-grained image classification tasks. + +# 5.3. Ablation Study + +Robustness to Database Size: The RANGE database that we used for our model in Section 5.1 was created using the SatCLIP dataset with 82k locations. However, our method is extremely robust and can be used with much smaller database sizes. We conducted an experiment where we used smaller samples of the SatCLIP data to create our RANGE database. We created a database with $75\%$ , $50\%$ , $25\%$ , and $10\%$ of the total data. We then trained a linear model for RANGE and $\mathrm{RANGE^{+}}$ using each of these subsets as our retrieval database. We also trained another version of our method where we only use geodesic distance for retrieval, i.e. $\beta = 0$ , which we call RANGE-HAYER. We used the same tasks described in Section 5.1 to evaluate these models. + +Our results from figure 3 show that we can obtain similar performance while using only $10\%$ of the original database size. In terms of storage, this database only occupies 85 Megabytes in disk, which is very efficient. The results also support our initial claim that there is low variance in satellite images; thus, a small number of satellite images can capture many important semantics across the globe. We see that the performance for both RANGE and $\mathrm{RANG}^{+}$ is stable across different settings and different tasks. The results also show that RANGE-HAYER, which only relies on spatially retrieved information, can be unstable, as seen in figure 3. These results highlight the pitfalls of depending completely on spatial similarity for retrieval. Locations that are spatially close do not necessarily share similar semantics. Therefore, as you change the sample distribution in the database, you can introduce noisy retrievals, which amplify the noise in the estimated visual embedding. Semantic-based retrieval strategy mitigates such issues. + +Impact of architectural components: Table 3 shows the impact of different components of our method compared to SatCLIP as the base model. We also compare our method with two other methods of retrieval: top-1 and top-k (where k was set to 100). The results show that our retriever function generally yields better results than the top-k selection approach. This can be attributed to the fact that top-k averaging does not consider the measure of similarity between query location and keys. We also performed a linear search to find the optimal temperature parameters of RANGE for each task separately. Our results show we are able to make marginal improvements by tuning the temperature parameter for individual tasks. The results indicate the temperature parameters of RANGE are robust and do not need to be fin-tuned for individual tasks in most cases. + +# 5.4. Qualitative Evaluation of Geo-embeddings + +Visual comparison of geo-embeddings: We qualitatively compare the RANGE embeddings with other location em + +beddings. We use Independent Component Analysis (ICA) to project the embeddings to a 3-dimensional vector and use them as RGB channels to visualize them over the globe. Figure 4 shows the visualizations for each model. Qualitatively, we see that models like CSP and SINR are extremely smooth, suggesting that they predominantly capture low-frequency information. GeoCLIP and SatCLIP capture relatively high-frequency information. The visualizations further suggest that RANGE and $\mathrm{RANG^{+}}$ embeddings are able to capture even higher frequency information. + +Visualizing the impact of $\beta$ parameter: Secondly, we visualize the impact of the $\beta$ parameter in equation (7). A quantitative evaluation of the $\beta$ parameter is presented in Section 9 of the supplementary material. Setting $\beta = 1$ gives us the RANGE embeddings, setting $\beta = 0$ gives us RANGE-HAYER embeddings, and setting $\beta = 0.5$ gives the $\mathrm{RANG}^{+}$ embeddings. This parameter controls the contribution of spatially-retrieved visual information to the semantically-retrieved visual information. This additional information acts as a spatial smoothness constraint on the RANGE embeddings. At $\beta = 0$ , we add the maximum constraint, which gives us low-frequency embeddings similar to CSP and SINR. As we increase the value of $\beta$ , we increase the frequency of our embeddings, i.e. locations that are spatially close to each other but are semantically different have different representations. Thus, the $\beta$ parameter allows us to explicitly control the smoothness of the RANGE embeddings and, therefore, allows generating location embeddings at multiple frequencies. + +# 6. Discussion and Conclusion + +Self-supervised learning has been a key enabler of the rapid recent progress in computer vision and natural language processing. Representations from models like SimCLR [3], and CLIP [31] have facilitated the creation of many powerful vision and language models. Recent works like SatCLIP [18], GeoCLIP [39], and CSP [27] showed that the same self-supervised techniques can be used to learn powerful representations for geographic locations, which are useful for a broad range of tasks. + +In this paper, we introduced a simple, yet effective strategy for improving such geographic embeddings, moving past previous assumptions of multiview redundancy. We proposed a retrieval-augmented strategy for estimating visual features from an auxiliary database of visual embeddings. Our approach results in significant improvements for a variety of tasks as compared to purely parametric embedding strategies with only a modest increase in storage requirements. Our method is efficient, robust, and multiscale. We hope our insights and results substantiate our recommendation of using RANGE as a general-purpose location encoder for geospatial tasks. + +# 7. Acknowledgments + +This research used the TGI RAILs advanced compute and data resource which is supported by the National Science Foundation (award OAC-2232860) and the Taylor Geospatial Institute. + +# References + +[1] Andreas Blattmann, Robin Rombach, Kaan Oktay, Jonas Müller, and Björn Ommer. Retrieval-augmented diffusion models. In NeurIPS, pages 15309-15324, 2022. 3 +[2] Sebastian Borgeaud, Arthur Mensch, Jordan Hoffmann, Trevor Cai, Eliza Rutherford, Katie Millican, George Bm Van Den Driessche, Jean-Baptiste Lespiau, Bogdan Damoc, Aidan Clark, et al. Improving language models by retrieving from trillions of tokens. In ICML, pages 2206-2240, 2022. 3 +[3] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. 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Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to " + }, + { + "bbox": [ + 55, + 254, + 297, + 529 + ], + "type": "inline_equation", + "content": "13.1\\%" + }, + { + "bbox": [ + 55, + 254, + 297, + 529 + ], + "type": "text", + "content": " on classification tasks and " + }, + { + "bbox": [ + 55, + 254, + 297, + 529 + ], + "type": "inline_equation", + "content": "0.145R^2" + }, + { + "bbox": [ + 55, + 254, + 297, + 529 + ], + "type": "text", + "content": " on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": "Several machine learning tasks require the use of geolocation as an input feature. Multiple works have shown the benefits of using geolocation to solve vital ecological, geographical, and geological tasks. SINR [5] used location as input to predict species distribution, Lang et al. [20] used location with satellite image to learn a global canopy height model, and SatCLIP [18] used location to solve several geospatial tasks such as biome classification, population density estimation, housing price prediction, etc. Since location is a ubiquitous input variable in all geospatial settings, finding good representations for it is fundamental when solving geospatial tasks." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 319, + 231, + 556, + 363 + ], + "blocks": [ + { + "bbox": [ + 319, + 231, + 556, + 363 + ], + "lines": [ + { + "bbox": [ + 319, + 231, + 556, + 363 + ], + "spans": [ + { + "bbox": [ + 319, + 231, + 556, + 363 + ], + "type": "image", + "image_path": "11907064e9f0ecfb5447b522b1dfa372540a1f9903864199b9699b02a716a849.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 383, + 556, + 428 + ], + "lines": [ + { + "bbox": [ + 313, + 383, + 556, + 428 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 556, + 428 + ], + "type": "text", + "content": "Figure 1. Adding explicit visual features allows us to generate more high-resolution location embeddings. We use a retrieval strategy that allows us to generate multi-resolution retrieval-augmented neural field of geo-embeddings (RANGE)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": "Previous work [33] has shown that using location directly (represented as two floating point numbers of latitude and longitude) as an input to a machine learning model yields poor performance. Therefore, several works have attempted to find better ways to represent location data. Some of these approaches [10, 25] use a non-parametric method to encode location. However, recent works [18, 27, 39] have shown that it is possible to learn a general-purpose location representation by learning a parametric model (often a neural network) in a self-supervised setting. There are several strategies that can be used to train the parametric model. A common approach used by state-of-the-art models [18, 27, 39] involves learning visual cues associated with a given geolocation. Two recent state-of-the-art models, GeoCLIP [39] and SatCLIP [18], use contrastive training to align geo-embeddings with co-located images; the former aligns them with ground-level images while the latter aligns them with satellite images. Images of a location capture dense information about the area, such as the landcover, landuse, etc. Therefore, learning location representations that capture this dense information is beneficial for solving geospatial tasks. Prior work [18] has shown that rep" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24680" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "resentations from such models are extremely powerful and are capable of solving diverse geospatial tasks both on their own and in combination with images. In this work, we argue that the current approaches to learning geo-embeddings using images, while powerful, still fail to preserve all the relevant visual information. The location representations from these models only capture low-resolution shared information between location and image and ignore crucial high-resolution information that is unique to the image. In section 2, we define this problem more formally from the perspective of multi-view redundancy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 221, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 221, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 56, + 221, + 295, + 544 + ], + "type": "text", + "content": "To address this issue, we propose a retrieval-augmented strategy that approximates the unique visual information present in a location. There are three key ideas to our solution. First, it is possible to approximate the visual features of a given location by strategically combining the visual features of other similar-looking locations. Second, contrastively trained models like SatCLIP [18] and GeoCLIP [39], while lacking in preserving modality-specific information, are excellent in learning modality alignment [13]. Therefore, it is possible to retrieve semantically aligned images, with alignment scores, for a given location using these models. Third, we note that the variance of semantic information visible in satellite images across the Earth is relatively low (as opposed to the wider diversity in consumer photographs). Hence, it is possible to capture a large percentage of unique aerial semantics with a limited number of satellite images. By combining these three key ideas, we propose our retrieval-augmented framework, RANGE (Retrieval-Augmented Neural Fields for Multi-Resolution Geo-Embeddings). Our retriever function uses both semantic and spatial alignment to approximate the visual features of a given location using an auxiliary database of image features. Our function is robust to the database size and works well even in limited sample settings. The hyperparameter in the retriever function can be adjusted to generate geo-embeddings at different frequencies. In summary, these are the main contributions of our paper:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 582, + 293, + 711 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 582, + 293, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 293, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 293, + 615 + ], + "type": "text", + "content": "- We show why existing image-location contrastive methods result in sub-optimal representations from the perspective of multi-view redundancy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 617, + 293, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 293, + 650 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 293, + 650 + ], + "type": "text", + "content": "- We propose a novel retrieval-based strategy, RANGE, to generate geo-embeddings that preserve both shared and unique modality information." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 654, + 293, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 293, + 711 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 293, + 711 + ], + "type": "text", + "content": "- We propose a retriever function that estimates the visual embedding of a location using both semantic and spatial alignment. Our retriever function is robust to different database sizes and can generate geo-embeddings at multiple frequencies by enforcing spatial smoothness." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 553, + 99 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 553, + 99 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 553, + 99 + ], + "type": "text", + "content": "2. Aligning Location and Image is a Multi-View Non-Redundancy Problem" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 109, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 553, + 407 + ], + "type": "text", + "content": "Let (L,H,T) represent location modality, image modality, and geospatial task, respectively. Models like SatCLIP and GeoCLIP align co-located images and locations by minimizing the infoNCE objective. Solving the multimodal infoNCE objective maximizes the lower bound on the mutual information, preserving the shared information within the learned representations [29]. As such, the final learned representations of these models contain only information that is shared across both location and image. This property is useful under the multi-view redundancy assumption which states that the information shared between the two modalities is exactly relevant to solve the underlying task. In other words, the multi-view redundancy setting assumes that any additional unique information from the image or location would not be useful in solving the task T [37]. However, this assumption does not hold in the location-image learning setting as there is high unique information contained in the image modality that is useful for solving downstream tasks. Formally, we argue that location-image learning falls under the multi-view non-redundancy setting: there is unique information in the image modality that is not shared with the location modality, and that information is relevant for solving our geospatial task T. In this case, contrastive training discards valuable task-relevant information from the image, leading to poor downstream performance [23]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 411, + 553, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 553, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 553, + 674 + ], + "type": "text", + "content": "Empirically, there is abundant unique information present in the image features that are relevant for solving downstream tasks. The location representations from contrastively trained models like SatCLIP and GeoCLIP only capture the low-resolution shared information, ignoring all the valuable task-relevant information that is unique to the image. To demonstrate this property concretely, we quantitatively show that there are tasks that can be solved more accurately by adding the image representation to the shared image-location representation from SatCLIP [18]. First, we choose 4 tasks: Biome, Ecoregions, Elevation, and Population Density estimation. We download a corresponding Sentinel-2 image for every data point. For each task, we train one model using the SatCLIP features and another model using the SatCLIP features combined with the SatMAE [6] features of the satellite image [6]. The results in Table 1 show that adding image features improves the performance across all tasks. The increase in performance demonstrates that the images contain unique information relevant to solving the task that is lost during contrastive training. Hence, \"location and image\" does not follow the assumption of multi-view redundancy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "Although adding corresponding satellite image information to a location embedding improves performance, this is not feasible in practice. For many geospatial tasks, we" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24681" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 303, + 133 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 303, + 133 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 303, + 133 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 303, + 133 + ], + "type": "table", + "html": "
BiomeEcoregionElevationPopulation
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", + "image_path": "4b11cf98d00acbe11412983c7c5255fef1a802d8df87fdfb541c21f43b64b8d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 141, + 295, + 229 + ], + "lines": [ + { + "bbox": [ + 55, + 141, + 295, + 229 + ], + "spans": [ + { + "bbox": [ + 55, + 141, + 295, + 229 + ], + "type": "text", + "content": "Table 1. We show that using the image-location shared information from SatCLIP embeddings is sub-optimal to solve some geospatial problems. Adding image features to the embeddings provides useful visual information that improves the accuracy of the task. We show the accuracy for the classification tasks and " + }, + { + "bbox": [ + 55, + 141, + 295, + 229 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2" + }, + { + "bbox": [ + 55, + 141, + 295, + 229 + ], + "type": "text", + "content": " value for the regression tasks. The results indicate that there are valuable visual features that are not captured by the SatCLIP embeddings." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 335 + ], + "type": "text", + "content": "wish to make predictions across the globe with millions of points. In such cases, using the \"image+location\" framework would require us to retrieve/store/process millions of images. We propose an efficient method for approximating the visual information using a compact database. Our results suggest that this approximation can outperform the use of true visual features in some cases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 348, + 148, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 348, + 148, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 348, + 148, + 361 + ], + "type": "text", + "content": "3. Related Works" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 369, + 274, + 381 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 274, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 274, + 381 + ], + "type": "text", + "content": "3.1. Learning Representations for Geolocation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 387, + 296, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 638 + ], + "type": "text", + "content": "Learning effective representations for geolocation is valuable for diverse downstream geospatial tasks, such as geolocation [39], canopy height prediction [20], fine-grained species classification [25, 34], species distribution modeling [5, 34], geographical question answering [26], soundscape mapping [16], etc. Geolocation in these tasks can be represented using either non-parametric [10, 33] or parametric [18, 27, 39] methods. Rußwurm et al. [33] represents geolocation using spherical harmonic basis functions, and Aodha et al. [25] uses a sine and cosine encoding of geolocation that removes discontinuity at dateline. In recent years, learned representations for geolocation, typically parameterized by neural networks, have been popularized. Some of these methods learn geolocation representations by using self-supervised pre-training strategies that distill visual information from either co-located overhead [18, 27] or ground-level images [27, 39]. The location encoders trained by these methods have demonstrated utility across various downstream geospatial tasks. We use the representations from these location encoders as baselines for our model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 647, + 237, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 237, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 237, + 661 + ], + "type": "text", + "content": "3.2. Multimodal Contrastive Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Contrastive learning is an efficient and scalable pre-training strategy for learning a shared embedding space across multiple modalities [7, 9, 11, 15, 16, 22, 31, 41-43]. As demonstrated by CLIP [31] and more recent works [22, 41, 42] in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "vision-language learning, the shared embedding space can be utilized for zero-shot classification and leveraged across a variety of downstream tasks. Contrastively trained multimodal embedding spaces between geolocation and satellite imagery [18, 27] or ground-level imagery [39], have also demonstrated impressive transferability of both location and visual representations to various geospatial tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 157, + 555, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 555, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 555, + 337 + ], + "type": "text", + "content": "Despite its success, recent works highlight the limitations of multimodal contrastive learning. One such study [23] shows that contrastively trained representations capture the shared information between the two modalities and thus only work best under certain assumptions. Similarly, another work [13] demonstrates that the final layers of encoders in the contrastive learning framework preserve only the information necessary for solving the alignment objective, discarding other modality-specific details. We argue that some of the underlying assumptions of multimodal contrastive training do not hold true in the image-location setting. Therefore, the resulting location representations from these methods are sub-optimal for downstream tasks. To address this issue, we propose a method to approximate the image-specific information for a given location." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 345, + 480, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 480, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 480, + 357 + ], + "type": "text", + "content": "3.3. Retrieval Augmented Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 363, + 555, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 591 + ], + "type": "text", + "content": "There has been a recent surge in retrieval-augmented generation (RAG) methods, primarily focused on generative tasks [1, 2, 4, 17, 19, 21, 35, 36, 40]. These methods generally consist of three main components: a retriever, an external database, and a generator. For a given query, the retriever selects a set of documents from the database and provides them, along with the original query, to the generator to produce the desired output. RAG has been successfully employed to improve text generation for large language models (LLMs) [2, 21, 36], text-to-image generation [1, 4, 17], text-to-3D generation [35], audio captioning [19], and more. Within the RAG framework, one could also replace the generator with another task-specific component, such as a classifier [24], to enhance performance by leveraging the rich information from the retrieved documents. Inspired by these retrieval-augmented methods, we design our framework, RANGE, which retrieves rich visual information from our database for a given geolocation query and utilizes it for various downstream geospatial tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 603, + 370, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 370, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 370, + 616 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 624, + 406, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 406, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 406, + 636 + ], + "type": "text", + "content": "4.1. Problem Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": "We consider a dataset with paired geolocations and collocated satellite images " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\{g_i, s_i\\}" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ". The goal is to learn a meaningful representation for " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "g_i" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": " by aligning it with " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ", which can be done by minimizing the clip objective [18, 31, 39]. We have a trainable geolocation encoder " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ", a frozen pretrained image encoder " + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 642, + 554, + 715 + ], + "type": "text", + "content": ", and a projection layer" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24682" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 73, + 549, + 300 + ], + "blocks": [ + { + "bbox": [ + 58, + 73, + 549, + 300 + ], + "lines": [ + { + "bbox": [ + 58, + 73, + 549, + 300 + ], + "spans": [ + { + "bbox": [ + 58, + 73, + 549, + 300 + ], + "type": "image", + "image_path": "ef4d3962d8b370b6f39e8c9f9198e38c81c7c92acabe103a02cfd1fa0cdbf9ad.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 318, + 555, + 376 + ], + "lines": [ + { + "bbox": [ + 54, + 318, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 318, + 555, + 376 + ], + "type": "text", + "content": "Figure 2. Framework of RANGE. (a) In the training stage, a shared embedding space is learned between locations and images. (b) We create a database of low-resolution and high-resolution image embeddings using the trained projection layer and a powerful pretrained image model, respectively. (c) During inference, we use a location as the query, low-resolution image embeddings as keys, and high-resolution image embeddings as values. Using our retriever function, we compute the approximate high-resolution embeddings for the query. We concatenate " + }, + { + "bbox": [ + 54, + 318, + 555, + 376 + ], + "type": "inline_equation", + "content": "(\\oplus)" + }, + { + "bbox": [ + 54, + 318, + 555, + 376 + ], + "type": "text", + "content": " the approximated visual feature with our query embedding." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "inline_equation", + "content": "G_{i} = E(g_{i})" + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "content": " represent the location embedding, " + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "inline_equation", + "content": "S_{i} = I(s_{i})" + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "content": " represent the frozen image embedding, and " + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "inline_equation", + "content": "P_{i} = P(I(s_{i})) = P(S_{i})" + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "content": " represent the image embedding obtained from the projection layer for the " + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "inline_equation", + "content": "\\mathrm{i}^{th}" + }, + { + "bbox": [ + 55, + 394, + 296, + 455 + ], + "type": "text", + "content": " sample. We minimize the objective:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 464, + 295, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 464, + 295, + 497 + ], + "spans": [ + { + "bbox": [ + 85, + 464, + 295, + 497 + ], + "type": "interline_equation", + "content": "L _ {i} ^ {l o c} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {i} \\cdot P _ {j}\\right) / \\tau}) \\tag {1}", + "image_path": "8014a3a35bd93cf958d8c8b01cf22dc1c0a4503cb8d813e4b26cf19838ae9040.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 500, + 295, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 500, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 85, + 500, + 295, + 533 + ], + "type": "interline_equation", + "content": "L _ {i} ^ {i m g} = \\frac {- 1}{k} \\sum_ {i = 1} ^ {k} \\log \\frac {\\exp \\left(G _ {i} \\cdot P _ {i} / \\tau\\right)}{\\sum_ {j = 1} ^ {k} \\exp \\left(G _ {j} \\cdot P _ {i}\\right) / \\tau}) \\tag {2}", + "image_path": "2556e55af894dd2db4fbeffd038c5c18123b6707abf1c8cc427b0d20098b73cb.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 534, + 294, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 534, + 294, + 550 + ], + "spans": [ + { + "bbox": [ + 86, + 534, + 294, + 550 + ], + "type": "interline_equation", + "content": "L _ {i} = \\left(L _ {i} ^ {l o c} + L _ {i} ^ {i m g}\\right) / 2 \\tag {3}", + "image_path": "21f809f1d92478cc66833085f9781c2db5f4010fd9e94a569dd219b0b1c037dd.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": "The training process is shown in Figure 2-(a). We contrastively align the geolocations and satellite images by minimizing their CLIP objective. This formulation is identical to SatCLIP [18], so we use the pretrained SatCLIP image and location encoders for simplicity. For query location " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " encodes the high-resolution visual features since " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " is a powerful pre-trained image encoder. Both " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " encode low-resolution shared information between " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "s_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": ". The resulting geo-embedding, " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": ", is sub-optimal as it loses unique visual information crucial for many downstream tasks. To solve this, we propose a retriever function " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "R_{\\tau}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " that allows us to approximate the high-resolution information " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " denote the deviation from the true" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "text", + "content": "visual embedding. We can then explicitly add the approximate visual information " + }, + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "inline_equation", + "content": "\\hat{S}_i" + }, + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "text", + "content": " to our location embedding " + }, + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 313, + 394, + 555, + 420 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 381, + 434, + 555, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 434, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 381, + 434, + 555, + 449 + ], + "type": "interline_equation", + "content": "R _ {\\tau} (g _ {i}) = \\hat {S} _ {i} = S _ {i} + \\epsilon \\tag {4}", + "image_path": "d3fdff8df2b1ff2f18abfd7da69ef3eeedc6fef55dcee2777c854606ff05ee30.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 382, + 450, + 553, + 465 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 450, + 553, + 465 + ], + "spans": [ + { + "bbox": [ + 382, + 450, + 553, + 465 + ], + "type": "interline_equation", + "content": "\\operatorname {R A N G E} \\left(g _ {i}\\right) = \\hat {S} _ {i} \\oplus G _ {i} \\tag {5}", + "image_path": "d2060124ff3b7fd58abcfc84865eed6fa9a5e57c9ef28f8eab075b8f6728b310.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 468, + 503, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 503, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 503, + 481 + ], + "type": "text", + "content": "4.2. Retrieval Augmented Neural Fields" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": "Creating the Retrieval Database: Once the contrastive training is done, we create a retrieval database as shown in Figure 2-(b). We take " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\{g_i,s_i\\}" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": " sampled uniformly across the globe using the SatCLIP [18] dataset. For every location " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": " in our data, we compute: a) the shared-information image embedding " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "R_{i}^{L} = P(I(s_{i}))" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": ", and b) the high-resolution image embedding " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "R_{i}^{H} = \\bar{I} (s_{i})" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": "; we refer to these sets of embeddings as low-resolution embeddings and high-resolution embeddings, respectively, in the rest of the paper. In practice, " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": " can differ from " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": "; the only condition is that " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": " is a pretrained image feature extractor. For our purposes, we use SatMAE [6] as " + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 313, + 486, + 555, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": "Retriever Function: Let " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "R^L = \\{R_1^L, R_2^L, \\dots, R_N^L\\}" + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "R^H = \\{R_1^H, R_2^H, \\dots, R_N^H\\}" + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": " represent the set of all low-resolution and high-resolution image embeddings in our database. After creating the database, we need a method to sample appropriate high-resolution image information for a query location. Naively, we can set this as a lookup operation, where " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": " is the query, " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "R^L" + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": " is the set of all keys, and " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "R^H" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24683" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": "is the set of all values. We have a function " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "\\text{sim}(G_i, R_j^L)" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": ", which gives the alignment scores between i and j. In our setting, this similarity function is a simple cosine similarity. For a query " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": ", we find " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "R_j^L" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": " with the highest alignment score and return the key " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "R_j^H" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": ". In practice, " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "R_j^H" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": " is noisy. The semantically closest image in the database can contain additional information that is irrelevant to the location. Therefore, naively adding " + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "inline_equation", + "content": "R_j^H" + }, + { + "bbox": [ + 55, + 72, + 294, + 181 + ], + "type": "text", + "content": " has the potential of introducing incorrect information to our geo-embeddings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "spans": [ + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": "We instead use a soft selection criteria. First, we compute the query's alignment score with each key in the database using cosine similarity. We use a softmax function to convert the alignment scores to probabilities. We also use a temperature parameter " + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": " to slightly reshape the probability distribution; " + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": " is extremely robust as it does not need to be fine-tuned for different tasks or for databases with different distributions. We use the resulting probabilities to compute a weighted average across all values, i.e., high-resolution image embeddings in the database. The resulting embedding is an approximation of " + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": ", where the information contributed by each image is weighted by its alignment score with the query. We concatenate this approximate high-resolution image embedding with our original location embedding " + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": " to obtain the multi-resolution RANGE embedding " + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "inline_equation", + "content": "RANGE_{i}" + }, + { + "bbox": [ + 56, + 182, + 296, + 385 + ], + "type": "text", + "content": ". A high-level view of this process is shown in Figure 2-(c)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 411, + 264, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 411, + 264, + 460 + ], + "spans": [ + { + "bbox": [ + 67, + 411, + 264, + 460 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R A N G E _ {i} = R _ {\\tau} \\left(G _ {i}\\right) \\oplus G _ {i} \\\\ = \\frac {1}{N} \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(G _ {i} , R _ {k} ^ {L}\\right) / \\tau}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(G _ {i} , R _ {j} ^ {L}\\right) / \\tau}} * R _ {k} ^ {H} \\oplus G _ {i} \\\\ \\end{array}", + "image_path": "59de78b00f5c22336fe5da7ad654a703f5997ee0b4eecea65137439f892c65c6.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "inline_equation", + "content": "G_{i}\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "inline_equation", + "content": "R_k^L\\in \\mathbb{R}^M" + }, + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "inline_equation", + "content": "R_{k}^{H}\\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 105, + 461, + 294, + 476 + ], + "type": "text", + "content": " (6)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": "Adding smoothness constraints: We also propose another version of our model called " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "RANG^{+}" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": ". Here, we additionally use geodesic similarity to approximate the visual features of the location. We convert our query location to 3D cartesian coordinates and use angular distance to find the spatially closest image in the database. This spatial retrieval allows us to impose spatial smoothness on our embeddings since locations close to each other are forced to have similar retrieval, irrespective of the semantics. Similar to " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "RANG" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": ", we compute a weighted average across all values in the database using the angular similarity between the query and keys. However, we explicitly mask samples with angular similarity lower than a threshold, i.e., significantly distant samples have no contribution. The spatially retrieved embedding is added to the semantically retrieved embedding and weighted using a " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": " parameter. This " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": " parameter controls the level of spatial smoothness enforced on the " + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "inline_equation", + "content": "RANG" + }, + { + "bbox": [ + 55, + 486, + 296, + 713 + ], + "type": "text", + "content": " embeddings, as shown in Figure 5. 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Performance of our model with respect to the database size. The results show that compared to RANGE-HAYER, both RANGE and " + }, + { + "bbox": [ + 313, + 196, + 553, + 251 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^+" + }, + { + "bbox": [ + 313, + 196, + 553, + 251 + ], + "type": "text", + "content": " are very robust to changes in database size. 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\\beta) \\sum_ {k = 1} ^ {N} \\frac {e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {k}\\right) / \\tau_ {2}}}{\\sum_ {j = 1} ^ {N} e ^ {s i m \\left(g _ {i} ^ {3 D} , l _ {j}\\right) / \\tau_ {2}}} * R _ {k} ^ {H}) \\oplus G _ {i}", + "image_path": "abf38e1c4f0a97bb438270528e0610ba7a622231865b2a8090e885390654a290.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "spans": [ + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "inline_equation", + "content": "G_{i}\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "inline_equation", + "content": "g_{i}^{3D}\\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "inline_equation", + "content": "l_{k}\\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 373, + 372, + 553, + 386 + ], + "type": "text", + "content": " (7)" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 392, + 553, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 553, + 416 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 553, + 416 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 313, + 392, + 553, + 416 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 392, + 553, + 416 + ], + "type": "text", + "content": " is set to 0, only spatially relevant features are used, and we refer to this setting as RANGE-HAYER." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 425, + 458, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 458, + 438 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 458, + 438 + ], + "type": "text", + "content": "5. Experiments and Results" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 445, + 553, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 553, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 553, + 457 + ], + "type": "text", + "content": "5.1. Quantitative Evaluation on Downstream Tasks" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": "We evaluate the efficacy of RANGE and " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG^{+}}" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " embeddings on a wide variety of downstream applications. We create our database using the SatCLIP [18] dataset with 82k locations. For " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG^{+}}" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " to 0.5. We choose 3 classification tasks and 4 regression tasks for this experiment as used by prior work [18]. The classification tasks are biome classification [8], ecoregion classification [8], and country classification [18]. The regression tasks are air temperature prediction [14], elevation prediction [32], population density prediction [32], and housing price prediction [30]. Results on climate data from ERA5 are shown in Section 10 of the supplementary material. The objective is to learn a linear predictive model that solves the underlying task. For fairness, we use the same hyperparameters for all tasks, i.e., the same " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " parameters for each task. The details of the hyperparameters are listed in the supplementary material. We compare our method with state-of-the-art parametric [5, 18, 27, 28, 39] and non-parametric [10, 25] representations. The results of this experiment are shown in Table 2." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "The results show that our method outperforms all state-of-the-art models in the classification tasks with significant" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24684" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 69, + 541, + 265 + ], + "blocks": [ + { + "bbox": [ + 69, + 69, + 541, + 265 + ], + "lines": [ + { + "bbox": [ + 69, + 69, + 541, + 265 + ], + "spans": [ + { + "bbox": [ + 69, + 69, + 541, + 265 + ], + "type": "table", + "html": "
BiomeEcoRegionsCountryTemperatureElevationPopulationCali-Housing
Direct29.10.666.90.3810.0250.0530.238
Cartesian_3D30.21.866.90.3620.0300.1620.240
Wrap [25]34.41.169.70.8610.0850.3280.239
Theory [10]33.51.072.50.8490.0930.3300.254
SphereM [28]36.427.372.70.6290.1390.3020.423
SphereM+ [28]58.750.176.10.8860.2940.4210.543
SphereC [28]36.352.972.90.4610.1850.3350.496
SphereC+ [28]53.261.673.60.8420.2600.3920.544
CSP-INat [27]61.157.175.90.7170.3880.5540.462
CSP-FMoW [27]61.458.081.30.8650.3990.5800.541
SINR [5]67.954.988.30.9420.6440.7260.420
GeoCLIP [39]70.271.681.30.9160.6040.6980.708
SatCLIP [18]68.969.382.80.8250.6660.6840.400
RANGE83.375.793.70.8950.8440.7990.422
RANGE+83.375.394.70.9310.8510.8110.336
", + "image_path": "178bc86367d1c89734b32c411086bce04285ed13a2b4c82e09cc43a906e95bbb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 317, + 553, + 427 + ], + "blocks": [ + { + "bbox": [ + 55, + 274, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 55, + 274, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 555, + 308 + ], + "type": "text", + "content": "Table 2. Our model shows improvements over a variety of tasks compared to state-of-the-art models. The first 3 columns are classification tasks with accuracy metrics and the last 4 columns are regression tasks with " + }, + { + "bbox": [ + 55, + 274, + 555, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^2" + }, + { + "bbox": [ + 55, + 274, + 555, + 308 + ], + "type": "text", + "content": " metric. We show improvements with significant margins across many of the tasks. Our model underperforms in the Cali-housing dataset. We further analyze this behavior in our discussions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 317, + 553, + 427 + ], + "lines": [ + { + "bbox": [ + 56, + 317, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 56, + 317, + 553, + 427 + ], + "type": "table", + "html": "
typetemp.BiomeEcoCountryTemperatureElevationPopulationCali-Housing
SatCLIPbase-model-68.969.382.80.8250.6660.6840.400
RANGEtop-1-75.665.285.60.8170.7660.7420.444
top-k-82.876.890.60.8840.8100.7710.619
soft selectionfixed83.375.793.70.8950.8440.7990.422
soft selectionper task83.575.894.50.9220.8570.8090.465
RANGE+soft selectionfixed83.575.394.70.9310.8510.8110.336
soft selectionper task83.775.994.90.9320.8550.8130.460
gain (%)+21.5+9.5+14.6+12.9+28.37+18.8+15.0
", + "image_path": "83a394adae533853ef1fe0c29065fe14ea6143f75c0be2a8f807a177076014df.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 67, + 498, + 285, + 597 + ], + "blocks": [ + { + "bbox": [ + 55, + 434, + 555, + 478 + ], + "lines": [ + { + "bbox": [ + 55, + 434, + 555, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 555, + 478 + ], + "type": "text", + "content": "Table 3. Ablation of different versions of our model compared with SatCLIP as the base model. Our soft selection using weighted averages over the database performs better than top-k selection. We also find that a single temperature works well for most tasks. Fine-tuning the temperature per task is generally not required as the gain is marginal. The last row shows the difference between the base model and RANGE+." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 498, + 285, + 597 + ], + "lines": [ + { + "bbox": [ + 67, + 498, + 285, + 597 + ], + "spans": [ + { + "bbox": [ + 67, + 498, + 285, + 597 + ], + "type": "table", + "html": "
top-1top-3top-5top-10
Img66.183.388.092.2
Img+CSP72.987.991.694.8
Img+GeoCLIP72.988.291.995.2
Img+CSP_INat*74.488.892.294.9
Img+SatCLIP75.188.791.994.5
Img+RANGE75.289.692.995.5
Img+RANGE+75.189.592.895.5
", + "image_path": "6f2e4f9a6becc3144f12ac69a2a275dfc1b17eb0da6a42555f5d276cd5c4a273.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 605, + 295, + 649 + ], + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 649 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 649 + ], + "type": "text", + "content": "Table 4. Top-k classification accuracy on INat-2018 test split: Location information acts as a strong prior in fine-grained species classification. Our method shows competitive top-k results against state-of-the-art models." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "margins. In biome, ecoregion, and country classification, we advance the state-of-the-art by " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "13.1\\%" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "6.4\\%" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": ", respectively. Among the regression tasks, we achieve SoTA" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 500, + 555, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 500, + 555, + 656 + ], + "spans": [ + { + "bbox": [ + 313, + 500, + 555, + 656 + ], + "type": "text", + "content": "performance for elevation and population density prediction with significant gains and narrowly come second in the air temperature prediction task. Our method, however, underperforms in the housing price prediction task. We suspect this is because the visual features that define housing change dramatically over time. The standard California housing dataset is based on a 1990 census, while our retrieved visual features are extracted from 2020 Sentinel data. The results also demonstrate that the hyperparameters for our model are robust and do not need to be tuned for specific tasks to achieve good performance. Furthermore, " + }, + { + "bbox": [ + 313, + 500, + 555, + 656 + ], + "type": "inline_equation", + "content": "\\mathrm{RANGE^{+}}" + }, + { + "bbox": [ + 313, + 500, + 555, + 656 + ], + "type": "text", + "content": ", on average, outperforms RANGE by a small margin, which can be attributed to the spatial smoothness constraint." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 670, + 531, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 531, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 531, + 683 + ], + "type": "text", + "content": "5.2. Using Location Embeddings as Geo-prior" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "We evaluate our model on the task of fine-grained species classification. We use the iNaturalist 2018 dataset [38]," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24685" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 555, + 244 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 244 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 244 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 244 + ], + "type": "image", + "image_path": "89350c8ac5aa0908ce4dfaab8b96050f574772563113ba5a601db5e99346f42d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 264, + 555, + 298 + ], + "lines": [ + { + "bbox": [ + 55, + 264, + 555, + 298 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 555, + 298 + ], + "type": "text", + "content": "Figure 4. We visualize the geo-embeddings from different models by projecting them into a 3-dimensional vector using Independent Component Analysis (ICA). The results suggest that by explicitly adding visual features, our method learns more high-frequency information compared to the existing models." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 308, + 555, + 483 + ], + "blocks": [ + { + "bbox": [ + 56, + 308, + 555, + 483 + ], + "lines": [ + { + "bbox": [ + 56, + 308, + 555, + 483 + ], + "spans": [ + { + "bbox": [ + 56, + 308, + 555, + 483 + ], + "type": "image", + "image_path": "8181c7c6f4a81d45ed844755a846983cd81ca06770a39723bc96fe60cbd6f7f5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "lines": [ + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "text", + "content": "Figure 5. Interpolating the " + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "text", + "content": " parameter in " + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^+" + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "text", + "content": " allows us to control the spatial smoothness of our embeddings. The results show that " + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^+" + }, + { + "bbox": [ + 55, + 514, + 555, + 537 + ], + "type": "text", + "content": " can be used to generate neural fields of geo-embeddings at multiple frequencies." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "text", + "content": "which contains data from 8,142 species. Prior works [18, 25, 33] have shown that adding location information can improve the performance of pretrained image classification models on iNat as knowing the location of an image can provide a strong prior about its content. For our experiment, we follow a similar setup as [33]. We take a pretrained image classification model, which gives us " + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "inline_equation", + "content": "P(y \\mid I)" + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "text", + "content": ". We then train a linear model that takes as input the pre-trained geo-embeddings and predicts the species categories, i.e., " + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "inline_equation", + "content": "P(y \\mid G)" + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "text", + "content": ". The final distribution is computed as the product of the two distributions, i.e., " + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "inline_equation", + "content": "P(y \\mid I, G) = P(y \\mid I) * P(y \\mid G)" + }, + { + "bbox": [ + 55, + 557, + 297, + 713 + ], + "type": "text", + "content": ". This experiment also aims to show that location representations obtained using self-supervised training can be eas" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "type": "text", + "content": "ily generalized towards tasks like iNat. Hence, we exclude SINR [5] from this comparison as it is trained in a supervised manner on the iNaturalist data itself." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "The results of this experiment are shown in Table 4. The performance of the pretrained image classifier is " + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "inline_equation", + "content": "66.1\\%" + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": ". The addition of location information improves the accuracy across all models. We see that RANGE and " + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^{+}" + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": " achieve competitive scores, narrowly outperforming state-of-the-art models. The results from this experiment highlight the benefits of using good location representations as geo-prior to solve fine-grained image classification tasks." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "24686" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": "Robustness to Database Size: The RANGE database that we used for our model in Section 5.1 was created using the SatCLIP dataset with 82k locations. However, our method is extremely robust and can be used with much smaller database sizes. We conducted an experiment where we used smaller samples of the SatCLIP data to create our RANGE database. We created a database with " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": " of the total data. We then trained a linear model for RANGE and " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "\\mathrm{RANGE^{+}}" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": " using each of these subsets as our retrieval database. We also trained another version of our method where we only use geodesic distance for retrieval, i.e. " + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 55, + 89, + 296, + 255 + ], + "type": "text", + "content": ", which we call RANGE-HAYER. We used the same tasks described in Section 5.1 to evaluate these models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "text", + "content": "Our results from figure 3 show that we can obtain similar performance while using only " + }, + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "text", + "content": " of the original database size. In terms of storage, this database only occupies 85 Megabytes in disk, which is very efficient. The results also support our initial claim that there is low variance in satellite images; thus, a small number of satellite images can capture many important semantics across the globe. We see that the performance for both RANGE and " + }, + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^{+}" + }, + { + "bbox": [ + 55, + 257, + 296, + 473 + ], + "type": "text", + "content": " is stable across different settings and different tasks. The results also show that RANGE-HAYER, which only relies on spatially retrieved information, can be unstable, as seen in figure 3. These results highlight the pitfalls of depending completely on spatial similarity for retrieval. Locations that are spatially close do not necessarily share similar semantics. Therefore, as you change the sample distribution in the database, you can introduce noisy retrievals, which amplify the noise in the estimated visual embedding. Semantic-based retrieval strategy mitigates such issues." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 484, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 664 + ], + "type": "text", + "content": "Impact of architectural components: Table 3 shows the impact of different components of our method compared to SatCLIP as the base model. We also compare our method with two other methods of retrieval: top-1 and top-k (where k was set to 100). The results show that our retriever function generally yields better results than the top-k selection approach. This can be attributed to the fact that top-k averaging does not consider the measure of similarity between query location and keys. We also performed a linear search to find the optimal temperature parameters of RANGE for each task separately. Our results show we are able to make marginal improvements by tuning the temperature parameter for individual tasks. The results indicate the temperature parameters of RANGE are robust and do not need to be fin-tuned for individual tasks in most cases." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 672, + 278, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 278, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 278, + 685 + ], + "type": "text", + "content": "5.4. Qualitative Evaluation of Geo-embeddings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "Visual comparison of geo-embeddings: We qualitatively compare the RANGE embeddings with other location em" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "content": "beddings. We use Independent Component Analysis (ICA) to project the embeddings to a 3-dimensional vector and use them as RGB channels to visualize them over the globe. Figure 4 shows the visualizations for each model. Qualitatively, we see that models like CSP and SINR are extremely smooth, suggesting that they predominantly capture low-frequency information. GeoCLIP and SatCLIP capture relatively high-frequency information. The visualizations further suggest that RANGE and " + }, + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG^{+}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "content": " embeddings are able to capture even higher frequency information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": "Visualizing the impact of " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " parameter: Secondly, we visualize the impact of the " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " parameter in equation (7). A quantitative evaluation of the " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " parameter is presented in Section 9 of the supplementary material. Setting " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " gives us the RANGE embeddings, setting " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " gives us RANGE-HAYER embeddings, and setting " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " gives the " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\mathrm{RANG}^{+}" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " embeddings. This parameter controls the contribution of spatially-retrieved visual information to the semantically-retrieved visual information. This additional information acts as a spatial smoothness constraint on the RANGE embeddings. At " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": ", we add the maximum constraint, which gives us low-frequency embeddings similar to CSP and SINR. As we increase the value of " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": ", we increase the frequency of our embeddings, i.e. locations that are spatially close to each other but are semantically different have different representations. Thus, the " + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 192, + 555, + 419 + ], + "type": "text", + "content": " parameter allows us to explicitly control the smoothness of the RANGE embeddings and, therefore, allows generating location embeddings at multiple frequencies." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 437, + 466, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 466, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 466, + 450 + ], + "type": "text", + "content": "6. Discussion and Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 460, + 553, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 553, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 553, + 567 + ], + "type": "text", + "content": "Self-supervised learning has been a key enabler of the rapid recent progress in computer vision and natural language processing. Representations from models like SimCLR [3], and CLIP [31] have facilitated the creation of many powerful vision and language models. Recent works like SatCLIP [18], GeoCLIP [39], and CSP [27] showed that the same self-supervised techniques can be used to learn powerful representations for geographic locations, which are useful for a broad range of tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "In this paper, we introduced a simple, yet effective strategy for improving such geographic embeddings, moving past previous assumptions of multiview redundancy. We proposed a retrieval-augmented strategy for estimating visual features from an auxiliary database of visual embeddings. Our approach results in significant improvements for a variety of tasks as compared to purely parametric embedding strategies with only a modest increase in storage requirements. Our method is efficient, robust, and multiscale. We hope our insights and results substantiate our recommendation of using RANGE as a general-purpose location encoder for geospatial tasks." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24687" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "text", + "content": "7. Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 139 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 139 + ], + "type": "text", + "content": "This research used the TGI RAILs advanced compute and data resource which is supported by the National Science Foundation (award OAC-2232860) and the Taylor Geospatial Institute." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 152, + 115, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 152, + 115, + 164 + ], + "spans": [ + { + "bbox": [ + 56, + 152, + 115, + 164 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 171, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 171, + 296, + 205 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 171, + 296, + 205 + ], + "spans": [ + { + "bbox": [ + 61, + 171, + 296, + 205 + ], + "type": "text", + "content": "[1] Andreas Blattmann, Robin Rombach, Kaan Oktay, Jonas Müller, and Björn Ommer. 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Exif as language: Learning cross-modal associations between images and camera metadata. In CVPR, 2023. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24689" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/7309d551-2983-4b1a-9d3d-bd90263e9ffc_content_list.json b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/7309d551-2983-4b1a-9d3d-bd90263e9ffc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7f41b51a3497ed2983331398748fecac53f5ea53 --- /dev/null +++ b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/7309d551-2983-4b1a-9d3d-bd90263e9ffc_content_list.json @@ -0,0 +1,1206 @@ +[ + { + "type": "text", + "text": "RAP: Retrieval-Augmented Personalization for Multimodal Large Language Models", + "text_level": 1, + "bbox": [ + 166, + 130, + 833, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haoran Hao $^{1,2*}$ , Jiaming Han $^{1*}$ , Changsheng Li $^{3}$ , Yu-Feng Li $^{2}$ , Xiangyu Yue $^{1\\dagger}$", + "bbox": [ + 184, + 202, + 805, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1MMLab, The Chinese University of Hong Kong", + "bbox": [ + 305, + 227, + 692, + 246 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ National Key Laboratory for Novel Software Technology, Nanjing University", + "bbox": [ + 189, + 246, + 807, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Beijing Institute of Technology", + "bbox": [ + 367, + 263, + 622, + 282 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/54ff0a2d69eb20b55923c76be433d65bc0436e42c6238f1a7f0aea4680c3434b.jpg", + "image_caption": [ + "Figure 1. Introduce some user-specific concepts to our RAP-MLLM, it can remember them and achieve excellent performance in a variety of personalized multimodal generation tasks." + ], + "image_footnote": [], + "bbox": [ + 109, + 303, + 883, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 602, + 326, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The development of large language models (LLMs) has significantly enhanced the capabilities of multimodal LLMs (MLLMs) as general assistants. However, lack of user-specific knowledge still restricts their application in human's daily life. In this paper, we introduce the Retrieval Augmented Personalization (RAP) framework for MLLMs' personalization. Starting from a general MLLM, we turn it into a personalized assistant in three steps. (a) Remember: We design a key-value database to store user-related information, e.g., user's name, avatar and other attributes. (b) Retrieve: When the user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts' information are fed into MLLMs to generate personalized, knowledge-augmented responses. Unlike previous methods, RAP allows real-time", + "bbox": [ + 88, + 633, + 485, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "concept editing via updating the external database. To further improve generation quality and alignment with user-specific information, we design a pipeline for data collection and create a specialized dataset for personalized training of MLLMs. Based on the dataset, we train a series of MLLMs as personalized multimodal assistants. By pretraining on large-scale dataset, RAP-MLLMs can generalize to infinite visual concepts without additional finetuning. Our models demonstrate outstanding flexibility and generation quality across a variety of tasks, such as personalized image captioning, question answering and visual recognition. The code, data and models are available at https://hoar012.github.io/RAP-Project/.", + "bbox": [ + 511, + 589, + 908, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 814, + 645, + 829 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, the development of large language models (LLMs) has significantly enhanced their language processing and generating capabilities [60]. Building on this foundation, the integration of visual and textual ability", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution † Corresponding author", + "bbox": [ + 114, + 886, + 357, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14538", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/46e8d4cfb156669005ede69f94812c5c2196df4908bbbbd8abe3c849d8fa6dc9.jpg", + "table_caption": [ + "Table 1. Comparison of Different Personalization Methods. RAP needs only 1 image with its personalized description, showing outstanding convenience and flexibility in practical applications." + ], + "table_footnote": [], + "table_body": "
MethodNumber of ImageData Requirements for PersonalizationSupport
PositiveNegativeCaptionDescriptionQuestion-AnswerRecognitionReal-time editText-only QA
Fine-tuningn-YesYesNoNoX✓
MyVLM [2]n150YesNoYesYesXX
Yo’LLaVA [32]n200NoNoYesYesX✓
RAP(Ours)1-NoYesNoNo✓✓
", + "bbox": [ + 91, + 118, + 906, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "through vision-language alignment brings powerful multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 51, 56]. MLLMs have shown significant improvement in various tasks, such as image description and question answering, highlighting their potential as humans' assistants. However, their lack of user-specific knowledge continues to limit their effectiveness as personalized assistants in daily life.", + "bbox": [ + 88, + 253, + 480, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A qualified personalized assistant first should be able to recognize and remember user-related concepts, such as the dog named $\\langle$ Lala $\\rangle$ adopted by the user. Although existing MLLMs have been trained on large-scale datasets and possess strong recognition and classification capabilities, directly transferring this knowledge to a user's personal concepts remains challenging. For instance, current leading MLLMs cannot remember your dog's name, even if you have mentioned it before, and they lack awareness of your identity and preferences. Furthermore, the assistant should generate responses tailored to the user's preferences and requirements. However, collecting extensive personal data to train a unique assistant for each user is impractical.", + "bbox": [ + 88, + 363, + 482, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this issue, the personalization of MLLMs has gained increasing attention, with several approaches already being proposed. MyVLM [2] utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of vision language models (VLMs) [24, 29]. Another concurrent work, Yo'LLaVA [32], learns a few special tokens to represent each concept. However, both approaches require continuous learning and model updates as new concepts emerge. As shown in Table 1, they require multiple labeled images of the target concept along with a large number of negative images, making data collection a significant challenge. Alternatively, fine-tuning the model for each new concept also incurs substantial computational costs. This presents a challenge in dynamic, ever-changing real-world scenarios, where the computing power of users' personal devices is often limited, and all data must be stored locally for privacy concerns.", + "bbox": [ + 91, + 564, + 482, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose the Retrieval Augmented Personalization (RAP) framework, designed to allow MLLMs to update their supported concepts without additional training. Specifically, RAP works in three key", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "steps. (a) Remember: RAP includes a designed database to help remember each concept via storing its image and basic information, e.g., name, avatar and other attributes. (b) Retrieve: When a user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts information are incorporated into the MLLM's input for personalized, knowledge-augmented generation. As shown in Table 1, our RAP requires only one image per concept with its related information for personalization. At the same time, it allows users to make real-time adjustments to the model's outputs by modifying their personal databases, eliminating the need for retraining. Examples of real-time concept editing are presented in Table 12.", + "bbox": [ + 511, + 253, + 906, + 465 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another significant challenge is the lack of large-scale datasets for training MLLMs' personalized generation capabilities. To address this, we design a pipeline to collect extensive training data and create a comprehensive dataset, which enables to train MLLMs to effectively understand and utilize user-related information for generation. Based on this dataset, we train LLaVA [29] and Phi3-V [36] as novel personalized assistants and evaluate their performance across various tasks, including personalized image captioning, question answering, and visual recognition. Experimental results demonstrate that our RAP-MLLMs excel in a wide range of personalized generation tasks, showcasing excellent generation quality and flexibility.", + "bbox": [ + 511, + 470, + 908, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 531, + 671, + 834, + 685 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the RAP framework for MLLMs' personalization, allowing models pre-trained on our dataset to adapt to diverse users and infinite new concepts without further training.", + "- We develop a pipeline for collecting large-scale data and create a dataset specifically designed for the personalized training and evaluation of MLLMs. This dataset enables us to train a series of MLLMs to function as personalized assistants.", + "- Our models demonstrate exceptional performance across various personalized multimodal generation tasks, including image captioning and question answering. Additionally, they exhibit a strong capability to recognize personal concepts within images." + ], + "bbox": [ + 527, + 686, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14539", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 91, + 89, + 232, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multimodal Large Language Models. Recently, numerous advanced large language models (LLMs) [1, 8, 43, 44, 57] have been proposed, showing remarkable performance in addressing a wide range of tasks. The rapid development of LLMs has led to the emergence of multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 56, 61], which excel in general visual understanding and complex reasoning tasks. For instance, LLaVA [28, 29] and MiniGPT-4 [61] align visual and language modalities through visual instruction tuning, showcasing impressive capabilities in multimodal conversations. GPT4RoI [58] and RegionGPT [13] enhance fine-grained understanding and reasoning for specific regions by training on region-level instruction datasets. Despite these advancements in tasks such as image captioning and question answering, the lack of user-specific knowledge restricts the generation of personalized content. In this work, we focus on the personalization of MLLMs, enabling them to remember and understand user-specific concepts, and generate personalized content tailored to user preferences.", + "bbox": [ + 93, + 114, + 480, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Personalization of MLLMs. In the realm of artificial intelligence, personalization typically refers to the process of customizing a system, application, or model to meet individual needs and preferences [42, 46, 47, 50]. Substantial efforts have been made to generate images of a user's personal objects or within certain contexts [10, 14, 21, 23, 38, 41, 49]. For example, Dreambooth [38] employs transfer learning in text-to-image diffusion models via finetuning all parameters for new concepts. In this paper, we mainly aim at enabling MLLMs to remember and understand user-specific concepts, and generate personalized language outputs. Several studies have focused on the personalization of MLLMs, among which the most relevant works are MyVLM [2] and Yo'LLaVA [32]. MyVLM introduces the task of personalizing VLMs. It utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of VLMs. Yo'LLaVA personalizes LLaVA by extending its vocabulary and learning specific tokens for each concept. However, both approaches require continuous model updates as new concepts emerge, which presents challenges in dynamic real-world applications. In this work, we propose the RAP framework for the personalization of MLLMs, enabling models pre-trained on our dataset to continuously update supported concepts without additional fine-tuning.", + "bbox": [ + 93, + 402, + 480, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Retrieval Augmented Generation. Retrieval-based methods for incorporating external knowledge have been effective in improving generation across various knowledge-intensive tasks [3, 11, 27, 48, 52, 59]. DPR [19] introduces Dense Passage Retrieval, marking a shift from sparse to dense retrieval techniques. Later, MuRAG [5] proposes to use multimodal knowledge to augment language generation. Self-Rag [3] introduces special tokens to make re", + "bbox": [ + 89, + 780, + 480, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "trieval adaptive and controllable. ERAGent [42] presents a comprehensive system for retrieval-augmented language models. With the advancements in MLLMs, RAG has been widely applied to multimodal generative tasks. For instance, FLMR [26] employs multi-dimensional embeddings to capture finer-grained relevance between queries and documents, achieving significant improvement in the RA-VQA setting. While existing methods primarily enhance models' performance by retrieving from external knowledge bases, few of them consider the personalization task. Although RAG has been applied to image generation [4, 55] and image captioning [25, 35], there is currently no existing work that focuses on personalizing MLLMs through RAG, to the best of our knowledge.", + "bbox": [ + 511, + 90, + 903, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Retrieval Augmented Personalization", + "text_level": 1, + "bbox": [ + 511, + 315, + 849, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing MLLMs typically align other modalities with language. For instance, LLaVA [29] projects visual tokens into text space, and then generates subsequent tokens using an LLM. While these MLLMs perform well in various tasks, the lack of memory and comprehension of personal concepts hinders effective user-specific responses. In this work, we mainly focus on personalizing MLLMs to generate tailored language responses, such as creating personalized captions for user's images and answering questions about personal concepts. In this section, we detail the implementation steps of our proposed Retrieval-Augmented Personalization (RAP) framework. Unlike previous approaches that usually necessitate additional data collection and further training to learn new concepts, after pre-training on our dataset, RAP-MLLMs can adapt to diverse users and infinite new concepts without further training. In section 3.1, we present the RAP framework that is applicable to various types of MLLMs, and then in section 3.2, we provide details of the proposed dataset.", + "bbox": [ + 511, + 339, + 903, + 627 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. RAP Framework", + "text_level": 1, + "bbox": [ + 511, + 635, + 683, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "RAP works in three steps: Remember, Retrieve and Generate. An overview of the framework is shown in Figure 2.", + "bbox": [ + 511, + 659, + 903, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Remember. The premise of personalization is that the model can remember personal concepts and relevant information, such as the dog named $\\langle \\mathrm{Lala} \\rangle$ adopted by $\\langle \\mathrm{A} \\rangle$ . To facilitate this, we construct a database $\\mathcal{M}$ to store personal concepts, which comprises an avatar $\\mathbf{I}_j$ , a name along with a brief description $\\mathbf{T}_j$ for each concept. The key $k_i$ for each concept in the database is its visual feature, obtained by feeding its image $\\mathbf{I}_j$ into a pre-trained image encoder $\\mathcal{E}(\\cdot)$ . Examples of our database are presented in Figure 2. When a user initiates a conversation, the input can be represented as $Q = (\\mathbf{X}_v, \\mathbf{X}_q)$ , which may include both image $\\mathbf{X}_v$ and some textual instructions $\\mathbf{X}_q$ . The first step involves identifying possible concepts within the input image that have been previously stored in the database. Previous meth", + "bbox": [ + 511, + 689, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14540", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/59271116909bf394002aea41a1b42506020f150d91dde1ab3b6cd48c2d5c6f35.jpg", + "image_caption": [ + "Figure 2. Retrieval-Augmented Personalization Framework. Region-of-interest detected by an open world detector are used to retrieve concepts from the database. The images and information of the retrieved concepts are then integrated into the input for the MLLM." + ], + "image_footnote": [], + "bbox": [ + 133, + 93, + 848, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ods [2] typically need to learn an external classifier to determine whether a concept appears in the input image, which requires a substantial amount of training data and can only apply to specific concept. To enhance the generalizability of the recognition process, we do not construct specific modules for each concept. Instead, we employ a universal detection model, such asYOLO [37] andYOLO-World [7], as recognition model $\\mathcal{R}(\\cdot)$ . Given the predefined setting $P$ that specifies which categories should be remembered, the region-of-interest can be acquired via $\\mathbf{X}_u = \\mathcal{R}(\\mathbf{X}_v,\\mathbf{X}_q|P)$ .", + "bbox": [ + 88, + 402, + 485, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Retrieve. Identified region-of-interest will be used as query to retrieve from the database. For each recognized component $\\mathbf{X}_u^i$ , we feed the image crop into the image encoder $\\mathcal{E}(\\cdot)$ to get its visual feature $v_{i} = \\mathcal{E}(\\mathbf{X}_{u}^{i})$ , which is a n-dimensional vector. Then we calculate the euclidean distance between the visual feature and each key $k_{j}\\in \\mathcal{M}$ which is calculated as $Dist(v_{i},k_{j}) = \\| v_{i} - k_{j}\\|$ . The Top-K image-text pairs $\\{(I_1,T_1),(I_2,T_2),\\dots (I_K,T_K)\\}$ with the lowest distances are selected from the database. We also introduce retrieval using concept names, such as $\\langle \\mathrm{sks}\\rangle$ for a unique concept. When the user mentions the name of an object documented in the database, our model retrieves its related information from the database. This also enables our model to respond to text-only queries effectively.", + "bbox": [ + 88, + 561, + 483, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generate. Each pair $\\mathbf{M}_j = (\\mathbf{I}_j, \\mathbf{T}_j)$ provides related information about a user's personal concept and will be incorporated into the input of the MLLM. Take LLaVA [29] as an example. The image $\\mathbf{I}_j$ is first encoded by a pre-trained vision encoder, such as CLIP [34], to obtain their visual tokens $\\mathbf{Z}_j$ . These image tokens are then projected by a projector into language tokens $\\mathbf{H}_j^v$ , which could be understood by the language model. Simultaneously, corresponding text", + "bbox": [ + 88, + 779, + 485, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "information $\\mathbf{T}_j$ are transformed into text tokens $\\mathbf{H}_j^q$ . This process is also applied to both $\\mathbf{X}_v$ and $\\mathbf{X}_q$ . All these tokens are incorporated into the MLLM's input to generate language response. During training, we keep parameters of both the detector and retriever frozen, just train the MLLM's parameters $\\theta$ . Given the length $L$ of the output sequence, the probability of the target answer $\\mathbf{X}_a$ is computed as:", + "bbox": [ + 511, + 402, + 908, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\prod_ {i = 1} ^ {L} p _ {\\theta} \\left(\\mathbf {X} _ {a, i} \\mid \\mathbf {X} _ {v}, \\mathbf {X} _ {q}, \\mathbf {M} _ {1}, \\dots \\mathbf {M} _ {K}, \\mathbf {X} _ {a, < i}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 513, + 906, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Personalization Dataset", + "text_level": 1, + "bbox": [ + 511, + 560, + 732, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most existing MLLMs struggle to generate personalized outputs even if additional concept information is provided, and there is currently no large-scale dataset for personalized training of MLLMs. To this end, we design a pipeline for data creation and curate a novel dataset specifically for the personalized training of MLLMs. We use Gemini-1.5 [12] to generate annotations for our dataset. An overview of our pipeline and dataset is presented in Figure 3.", + "bbox": [ + 509, + 583, + 906, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first component of our dataset is dedicated to visual grounding. In this task, an MLLM is trained to determine whether a specific concept is present in an image, particularly identifying if the person or object in a reference image appears in the given image. When a positive match is detected, we also require the model to provide the bounding box for the identified concept. For single-concept grounding, we primarily use the RefCOCO dataset [20]. Based on RefCOCO's annotations, we crop target concepts from the images and assign names to them, which serve as references for specific concepts. We then query Gemini to generate concise descriptions about properties of the concepts in these cropped regions, by which we construct a", + "bbox": [ + 511, + 704, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14541", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/167bae94d523d44fc216bc564799fdbfa76f036afb6eefc6d0b5168fb064558a.jpg", + "image_caption": [ + "Figure 3. Our Pipeline for Data Collection. We first crop the target concept from the image based on the dataset annotations and then query Gemini [12] to generate its personalized description. We also apply data augmentation to diversify these cropped images. Then we combine them with the original image to derive a series of instructions and answers from Gemini. When noise concepts are included in the additional information, the answer remains unchanged, helping to train the MLLMs' ability to filter out irrelevant concepts." + ], + "image_footnote": [], + "bbox": [ + 140, + 95, + 854, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "large-scale database including numerous different concepts. The training data pairs images and these descriptions as queries and the corresponding bounding boxes as outputs. However, data generated in this way is insufficient to simulate the complexity of real-world recognition, especially when the target concept in the reference and input image is captured from different perspectives. To address this, we incorporate the ILSVRC2015-VID video object detection dataset [39], TAO [9] and CustomConcept101 [21] to enrich our dataset. For multi-object grounding, we use the Object365 dataset [40] to construct our training data.", + "bbox": [ + 88, + 430, + 480, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The second component of our dataset is designed for instruction following. This section includes training data for tasks such as image captioning, image description, and question answering. For the image captioning and description data, we provide cropped images of target concepts, accompanied by their names and related information from the large-scale database, then query Gemini to generate a caption or description that reflects the concepts depicted in the entire image. For question answering, we first design a set of seed questions to serve as examples. These examples are used to prompt the annotator, Gemini, to generate new questions and corresponding answers. This iterative process facilitates the creation of a rich and diverse collection of conversations that MLLMs can learn from. We construct such data using RefCOCO [20], Object365 [40], TAO [9] and CustomConcept101 [21] dataset.", + "bbox": [ + 89, + 597, + 482, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To enhance alignment with real-world scenarios, it is essential to collect data featuring the same identity in various environments. Thus, we also include multiple images about the same individual from the CelebA dataset [30] and", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "produce question answering data about the individual. To further diversify the dataset, we apply image editing techniques for data augmentation. This includes performing random rotations and flips on the cropped images, as well as generating novel views of the concepts by diffusion models. Specifically, we use Inpaint-Anything [53] to separate the foreground from the background, and use Wonder3D [31] and SiTH [16] to synthesize novel views of foreground object or person, respectively. Finally, we combine these elements to generate images of the target concept from different perspectives.", + "bbox": [ + 511, + 430, + 906, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To support multi-concept personalized generation, it is necessary to retrieve multiple potential concepts from the database. In the generation step, the MLLM must prioritize accurate and contextually relevant information. Considering that retrieval results can be inaccurate, potentially leading to unreasonable answers, we construct negative samples by adding noise concepts to the input while preserving the original output. This approach trains the model's discrimination ability. By exposing the MLLM to both relevant and irrelevant information during training, it learns to discern and filter out noise concepts, thereby enhancing its robustness during inference. Additionally, we include a subset of the LLaVA-Instruct-665k visual instruction dataset [28] to retain general knowledge from the original MLLM. Further details about our dataset can be found in Appendix D.", + "bbox": [ + 511, + 598, + 908, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 843, + 638, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We conduct experiments on LLaVA-1.5-13B [28] and Phi3-V-3.8B [36], resulting in", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14542", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/235d9d11919bc75793c7d0ae33a93997ee19f1d08ba40a8aaa46cc8627de58ec.jpg", + "table_caption": [ + "Table 2. Qualitative Comparison on Image Captioning. Image examples of target concepts are shown in the left and captions generated are shown in the right. We use green text to denote correct target concepts." + ], + "table_footnote": [], + "table_body": "
ImageCaption
my dogLLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is a very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.LLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.
H\nTLLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping <T> prepare a salad in the kitchen.LLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping < T> prepare a salad in the kitchen.
B\nG\nWPhi3-V: A group of stuffed animals, including a blue one, are sitting on a black surface.\nLLaVA-LoRA: <B>, <G> and <W> are happily exploring the grassland.\nMyVLM: <G> and his crew are always ready to jump into a new adventure.\nRAP-Phi3-V(Ours): <W> is hanging out with <G> and <B> on the lawn. They are having a great time playing!
", + "bbox": [ + 106, + 119, + 890, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "two personalized MLLMs, RAP-LLaVA and RAP-Phi3-V. We select YOLO-Worldv2 [7] as the detector and construct a multimodal retriever using Facebook AI Similarity Search (FAISS) [18], employing a pre-trained CLIP ViT-L/14-336 [34] as the visual encoder. Due to the context length limitation of the backbone language model, for RAP-LLaVA and RAP-Phi3-V, we retrieve the 2 and 3 different concepts with the highest similarity, respectively. More implementation details can be found in Appendix C.", + "bbox": [ + 88, + 551, + 482, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. In the training phase, we skip the recognition and retrieval procedures, instead perform instruction tuning to train the MLLMs. We adhere to most settings from the original experiment of LLaVA [28], except for using a maximum learning rate of 1e-4 and training for 1 epoch. We employ low-rank adapters [17] to reduce the number of trainable parameters, and train our models on 8 A100 GPUs with a valid batch size of 64.", + "bbox": [ + 89, + 686, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Personalized Image Captioning", + "text_level": 1, + "bbox": [ + 89, + 816, + 367, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate our models on generating personalized image captions with user-specific concepts. We extend the dataset introduced by MyVLM [2] via adding 16 new concepts, including both objects and humans, forming", + "bbox": [ + 89, + 840, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "8 concept pairs that appear together. For each pair, there are 8-13 images used for testing. This multi-concept setting presents additional challenges for personalization.", + "bbox": [ + 511, + 551, + 906, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We compare our models with MyVLM [2] and fine-tuning based method LLaVA-LoRA [17]. For LLaVA-LoRA and MyVLM, the training dataset contains 1 image accompanied by 5 captions for each concept. For LLaVA-LoRA, we train it with captions of the training images for 3 epochs, applying low-rank adapters [17] and the same hyperparameters as our models. For MyVLM, following their training process, we first train the classification head with the positive and 150 negative images, then train the corresponding concept embedding with the provided captions for each concept. For our models, we construct a database where each concept is represented by a cropped image and a text description. Details of our database could be found in Appendix H. All remaining images are used as test samples. This evaluation process is repeated three times with different seeds, resulting in a total of 1,182 images used for evaluation, and we report the average results.", + "bbox": [ + 511, + 598, + 908, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Comparison. In Table 2, we present image captions generated by different methods to make a comparison. While LLaVA [28] and Phi3-V [36] generally pro", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14543", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f86b9da2a5d08351098b6502e552da6b5dfaa70832c62e6581dacfbb86fbe9d4.jpg", + "table_caption": [ + "Table 3. Quantitative Evaluation on Image Captioning. We report Recall, Precision and F1-score in the table, the best result in each metric is bold and the second is underlined." + ], + "table_footnote": [], + "table_body": "
MethodLLMRecallPrecisionF1-score
LLaVA [28] + RetrieverVicuna-13B1.26048.762.450
LLaVA-LoRA [17]Vicuna-13B82.9793.2887.82
MyVLM-LLaVA [2]Vicuna-13B84.6586.3785.50
RAP-LLaVAVicuna-13B93.5196.4794.97
RAP-Phi3-VPhi3-V-3.8B88.1495.1091.49
", + "bbox": [ + 91, + 132, + 542, + 252 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bd8c4f97c514daedf20380cee00d32c66f2464f8a99e087bd586504e9f6e539a.jpg", + "image_caption": [ + "Figure 4. Performance under varying number of personalized concepts." + ], + "image_footnote": [], + "bbox": [ + 602, + 119, + 851, + 258 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4803cf969309547aba7b188ee126ef855cc61c82bfe094fa8d93185ec582cab9.jpg", + "table_caption": [ + "Table 4. Quantitative Evaluation on Question Answering and Visual Recognition. The best result in each setting is bold and the second is underlined. Evaluation results of GPT-4V [33] are also provided as reference. Weighted results are computed as arithmetic means." + ], + "table_footnote": [], + "table_body": "
MethodLLMTrain#ImageQuestion AnsweringVisual Recognition
VisualText-onlyWeightedPositiveNegativeWeighted
GPT-4V [33] + PromptGPT-4VX10.8660.9820.9240.8090.9920.901
GPT-4V [33] + PromptGPT-4VX50.8870.9870.9370.8510.9980.925
LLaVA [28]Vicuna-13BX-0.8990.6590.7790.0001.0000.500
LLaVA [28] + RetrieverVicuna-13BX10.9120.8630.8871.0000.0250.513
LLaVA-LoRA [17]Vicuna-13B✓10.9000.5830.7410.9880.6620.825
LLaVA-LoRA [17]Vicuna-13B✓50.9350.6150.7750.9970.4440.721
MyVLM-LLaVA [2]Vicuna-13B✓50.912--0.9940.8450.919
Yo'LLaVA [32]Vicuna-13B✓50.9290.8830.9060.9490.8980.924
RAP-LLaVA(Ours)Vicuna-13BX10.9350.9380.9360.9790.9820.980
RAP-Phi3-V(Ours)Phi3-V-3.8BX10.9410.8500.8960.9220.9880.955
", + "bbox": [ + 98, + 304, + 897, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "vide brief and clear captions for most test images, their lack of understanding of the user-specific concepts restricts them from generating a more personalized caption. LLaVA-LoRA and MyVLM can generate personalized captions, however, the limited training data often results in imprecise outputs, particularly noticeable when multiple concepts are present in the same image. In contrast, our models generate clear and accurate captions based on the database content, which also ensures the reliability of the outputs. Additional examples of personalized captions generated by the models could be found in Appendix E.", + "bbox": [ + 88, + 544, + 482, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Evaluation. We employ recall, precision and the comprehensive metric F1-score as our evaluation metrics. Recall is calculated as the percentage of correct occurrences of target concepts, while precision is the ratio of correct concept names to the total number of concept names presented. The experimental results are shown in Table 3. Notably, the classification heads of MyVLM exhibit higher error rates when the number of positive images is limited, leading to weaker performance. Even with additional concept information provided through retrieval, the vanilla LLaVA [28] still fails to effectively accomplish the personalized generation task, underscoring the necessity of", + "bbox": [ + 88, + 719, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the proposed dataset. Our models demonstrate superior performance in both recall and precision metrics, highlighting the advantages of our RAP-MLLMs in data efficiency.", + "bbox": [ + 511, + 544, + 906, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Personalized Question Answering", + "text_level": 1, + "bbox": [ + 511, + 603, + 808, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Settings. In this section, we evaluate different methods on the benchmark of personalized question answering introduced by Yo'LLaVA [32], which contains both visual and text-only questions about user concepts. For each concept, we generate a description to serve as its information in our database. For LLaVA-LoRA, we feed these descriptions and corresponding images to train the model to describe the concept's properties. Additionally, we incorporate text-only queries and answers to enhance the model's textual understanding. The training dataset for Yo'LLaVA and MyVLM consists of 5 positive images with question answering pairs and 200 negative images per concept. For GPT-4V [33], images and related concept information are provided as a supplementary prompt. The evaluation metric is accuracy. Additional details are provided in Appendix C.", + "bbox": [ + 509, + 627, + 906, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results and Analysis. The experimental results are provided in Table 4. LLaVA and LLaVA-LoRA both perform well in visual based question answering, because substan", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14544", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/28ee32892cecc97ad8cb5c230aa6d84086ef7d97e4e7a1c79bc2c5f378585321.jpg", + "table_caption": [ + "Table 5. We evaluate model's performance with perfect retrieval, and test contributions of text information and dataset components." + ], + "table_footnote": [], + "table_body": "
SettingRecallPrecisionF1-score
RAP-LLaVA93.5196.4794.97
Skip retrieval96.16 (+2.7)100.0 (+3.5)98.04 (+3.1)
- Text information94.91 (+1.4)88.66 (-7.8)91.68 (-3.3)
- Data augmentation89.25 (-4.3)98.01 (+1.5)93.42 (-1.6)
- Negative samples95.74 (+2.2)58.21 (-38.3)72.40 (-22.6)
", + "bbox": [ + 91, + 119, + 483, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tial information of the target concept can be obtained from the images. However, their performance is quite poor when images of the target concept mentioned in the question are not available. MyVLM performs well in visual question answering but does not support text-only question answering. Yo'LLaVA excels in text-only question answering, but its performance is still limited by the insufficient information provided by the learned tokens of a concept. In contrast, our models demonstrate balanced performance in both visual and text-only question answering. By providing a single image, our RAP-LLaVA surpasses baseline methods and achieves performance comparable to that of GPT-4V.", + "bbox": [ + 89, + 244, + 482, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual Recognition. We also evaluate the models' recognition abilities for a more comprehensive comparison. MLLMs are required to determine whether a personal concept is present in an image. We query them with \"Is in the image? Answer with a single word.\", where is replaced by corresponding concept name. For positive images, the desired response is \"Yes\" and \"No\" for negative. Results show that without knowledge of personal concepts, the vanilla LLaVA consistently produces negative responses. After training on target concepts, LLaVA-LoRA, MyVLM and YoLLaVA tend to give positive responses, but struggle to differentiate between similar concepts, resulting in weaker performance on negative images. Our models demonstrate exceptional performance in both positive and negative scenarios, achieving the best overall results.", + "bbox": [ + 89, + 428, + 482, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 665, + 243, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Influence of Number of Learned Concepts. In real-world scenario, users' personal databases typically expand over time. Next, we evaluate the performance of various methods with varying numbers of learned concepts. We extend the database with hundreds of new concepts selected from the RefCOCO dataset [20], ensuring no overlap with the test dataset. For LLaVA-LoRA and MyVLM, we provide images containing the target concepts along with their captions as training data, and assess models' performance on the original test dataset. The results are presented in Figure 4. More learned concepts result in increased recognition errors, leading to a decline in performance for each model. Our RAP-MLLMs maintain the highest performance under different settings.", + "bbox": [ + 89, + 688, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Generation Ability of MLLM. We skip the recognition and retrieval processes, providing the MLLM with relevant information of each concept present in the image to evaluate the generation capability of the trained MLLM. The results, shown in Table 5, indicate that when relevant concept information is supplied, our RAP-LLaVA achieves superior generation performance, obtaining $100\\%$ precision without outputting irrelevant concepts as well as a higher recall rate.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Text Information. We remove additional text information to examine its impact on personalization. The results are shown in Table 5 and 7 (Appendix). This additional text provides extra information that helps the model understand specific concepts, effectively improving the accuracy of the answers and benefiting personalized generation. Furthermore, it is especially helpful for question answering, as it can provide information not directly available from the image, such as a user's age and hobbies, or a pet's preferred food, as shown in the example in Table 12 of the Appendix.", + "bbox": [ + 511, + 210, + 903, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dataset Composition. We conduct experiments to assess the contribution of each component in our dataset. First, we remove data generated through data augmentation and train the model. The results displayed in Table 5 indicate an obvious decrease in the recall metric for image captioning, resulting in a lower overall performance. We further exclude constructed negative samples from the dataset and retrain the model, then we find that it performs poorly on precision metric. This suggests a diminished ability to discriminate against noise concepts not present in the image.", + "bbox": [ + 511, + 363, + 903, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additional Ablation. We conduct ablation studies on retriever's performance, and examine the impact of retrieving different numbers of concepts. We also evaluate models' performance on several multimodal benchmarks, and the results demonstrate that RAP-LLaVA retains most general knowledge of the original LLaVA, while achieving superior performance in knowledge intensive tasks. Due to space limit, we put the results in Appendix Section B.1.", + "bbox": [ + 511, + 513, + 903, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 648, + 633, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce the RAP framework for personalizing MLLMs. This framework enables MLLMs to understand infinite user-specific concepts, generate personalized captions and respond to user-related queries. To enhance the quality of the generated content and better align outputs with user configuration, we curate a large-scale dataset for personalized training of MLLMs and train a series of MLLMs to function as personalized assistants. Experimental results show that RAP-MLLMs achieve exceptional performance in various personalized generation tasks, while allowing real-time adjustments to generation settings.", + "bbox": [ + 511, + 674, + 903, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074).", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14545", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. Phi-3 technical report: A highly capable language model locally on your phone. arXiv preprint arXiv:2404.14219, 2024. 3", + "[2] Yuval Alaluf, Elad Richardson, Sergey Tulyakov, Kfir Aberman, and Daniel Cohen-Or. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.167, + 0.131, + 0.834, + 0.178 + ], + "angle": 0, + "content": "RAP: Retrieval-Augmented Personalization for Multimodal Large Language Models" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.203, + 0.806, + 0.224 + ], + "angle": 0, + "content": "Haoran Hao\\(^{1,2*}\\), Jiaming Han\\(^{1*}\\), Changsheng Li\\(^{3}\\), Yu-Feng Li\\(^{2}\\), Xiangyu Yue\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.306, + 0.228, + 0.694, + 0.247 + ], + "angle": 0, + "content": "1MMLab, The Chinese University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.247, + 0.808, + 0.265 + ], + "angle": 0, + "content": "\\(^{2}\\)National Key Laboratory for Novel Software Technology, Nanjing University" + }, + { + "type": "text", + "bbox": [ + 0.369, + 0.265, + 0.624, + 0.283 + ], + "angle": 0, + "content": "\\(^{3}\\)Beijing Institute of Technology" + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.304, + 0.885, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.547, + 0.908, + 0.577 + ], + "angle": 0, + "content": "Figure 1. Introduce some user-specific concepts to our RAP-MLLM, it can remember them and achieve excellent performance in a variety of personalized multimodal generation tasks." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.603, + 0.327, + 0.619 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.635, + 0.486, + 0.877 + ], + "angle": 0, + "content": "The development of large language models (LLMs) has significantly enhanced the capabilities of multimodal LLMs (MLLMs) as general assistants. However, lack of user-specific knowledge still restricts their application in human's daily life. In this paper, we introduce the Retrieval Augmented Personalization (RAP) framework for MLLMs' personalization. Starting from a general MLLM, we turn it into a personalized assistant in three steps. (a) Remember: We design a key-value database to store user-related information, e.g., user's name, avatar and other attributes. (b) Retrieve: When the user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts' information are fed into MLLMs to generate personalized, knowledge-augmented responses. Unlike previous methods, RAP allows real-time" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.909, + 0.788 + ], + "angle": 0, + "content": "concept editing via updating the external database. To further improve generation quality and alignment with user-specific information, we design a pipeline for data collection and create a specialized dataset for personalized training of MLLMs. Based on the dataset, we train a series of MLLMs as personalized multimodal assistants. By pretraining on large-scale dataset, RAP-MLLMs can generalize to infinite visual concepts without additional finetuning. Our models demonstrate outstanding flexibility and generation quality across a variety of tasks, such as personalized image captioning, question answering and visual recognition. The code, data and models are available at https://hoar012.github.io/RAP-Project/." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.815, + 0.646, + 0.83 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recently, the development of large language models (LLMs) has significantly enhanced their language processing and generating capabilities [60]. Building on this foundation, the integration of visual and textual ability" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.887, + 0.359, + 0.901 + ], + "angle": 0, + "content": "* Equal contribution † Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14538" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.118 + ], + "angle": 0, + "content": "Table 1. Comparison of Different Personalization Methods. RAP needs only 1 image with its personalized description, showing outstanding convenience and flexibility in practical applications." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.119, + 0.907, + 0.233 + ], + "angle": 0, + "content": "
MethodNumber of ImageData Requirements for PersonalizationSupport
PositiveNegativeCaptionDescriptionQuestion-AnswerRecognitionReal-time editText-only QA
Fine-tuningn-YesYesNoNoX✓
MyVLM [2]n150YesNoYesYesXX
Yo’LLaVA [32]n200NoNoYesYesX✓
RAP(Ours)1-NoYesNoNo✓✓
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.254, + 0.482, + 0.36 + ], + "angle": 0, + "content": "through vision-language alignment brings powerful multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 51, 56]. MLLMs have shown significant improvement in various tasks, such as image description and question answering, highlighting their potential as humans' assistants. However, their lack of user-specific knowledge continues to limit their effectiveness as personalized assistants in daily life." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.364, + 0.483, + 0.56 + ], + "angle": 0, + "content": "A qualified personalized assistant first should be able to recognize and remember user-related concepts, such as the dog named \\(\\langle\\) Lala \\(\\rangle\\) adopted by the user. Although existing MLLMs have been trained on large-scale datasets and possess strong recognition and classification capabilities, directly transferring this knowledge to a user's personal concepts remains challenging. For instance, current leading MLLMs cannot remember your dog's name, even if you have mentioned it before, and they lack awareness of your identity and preferences. Furthermore, the assistant should generate responses tailored to the user's preferences and requirements. However, collecting extensive personal data to train a unique assistant for each user is impractical." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.565, + 0.483, + 0.837 + ], + "angle": 0, + "content": "To address this issue, the personalization of MLLMs has gained increasing attention, with several approaches already being proposed. MyVLM [2] utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of vision language models (VLMs) [24, 29]. Another concurrent work, Yo'LLaVA [32], learns a few special tokens to represent each concept. However, both approaches require continuous learning and model updates as new concepts emerge. As shown in Table 1, they require multiple labeled images of the target concept along with a large number of negative images, making data collection a significant challenge. Alternatively, fine-tuning the model for each new concept also incurs substantial computational costs. This presents a challenge in dynamic, ever-changing real-world scenarios, where the computing power of users' personal devices is often limited, and all data must be stored locally for privacy concerns." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.485, + 0.903 + ], + "angle": 0, + "content": "To address these challenges, we propose the Retrieval Augmented Personalization (RAP) framework, designed to allow MLLMs to update their supported concepts without additional training. Specifically, RAP works in three key" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.254, + 0.907, + 0.466 + ], + "angle": 0, + "content": "steps. (a) Remember: RAP includes a designed database to help remember each concept via storing its image and basic information, e.g., name, avatar and other attributes. (b) Retrieve: When a user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts information are incorporated into the MLLM's input for personalized, knowledge-augmented generation. As shown in Table 1, our RAP requires only one image per concept with its related information for personalization. At the same time, it allows users to make real-time adjustments to the model's outputs by modifying their personal databases, eliminating the need for retraining. Examples of real-time concept editing are presented in Table 12." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.471, + 0.909, + 0.669 + ], + "angle": 0, + "content": "Another significant challenge is the lack of large-scale datasets for training MLLMs' personalized generation capabilities. To address this, we design a pipeline to collect extensive training data and create a comprehensive dataset, which enables to train MLLMs to effectively understand and utilize user-related information for generation. Based on this dataset, we train LLaVA [29] and Phi3-V [36] as novel personalized assistants and evaluate their performance across various tasks, including personalized image captioning, question answering, and visual recognition. Experimental results demonstrate that our RAP-MLLMs excel in a wide range of personalized generation tasks, showcasing excellent generation quality and flexibility." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.672, + 0.836, + 0.686 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.687, + 0.905, + 0.746 + ], + "angle": 0, + "content": "- We propose the RAP framework for MLLMs' personalization, allowing models pre-trained on our dataset to adapt to diverse users and infinite new concepts without further training." + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.749, + 0.905, + 0.823 + ], + "angle": 0, + "content": "- We develop a pipeline for collecting large-scale data and create a dataset specifically designed for the personalized training and evaluation of MLLMs. This dataset enables us to train a series of MLLMs to function as personalized assistants." + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.826, + 0.905, + 0.9 + ], + "angle": 0, + "content": "- Our models demonstrate exceptional performance across various personalized multimodal generation tasks, including image captioning and question answering. Additionally, they exhibit a strong capability to recognize personal concepts within images." + }, + { + "type": "list", + "bbox": [ + 0.529, + 0.687, + 0.905, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14539" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.233, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.116, + 0.482, + 0.401 + ], + "angle": 0, + "content": "Multimodal Large Language Models. Recently, numerous advanced large language models (LLMs) [1, 8, 43, 44, 57] have been proposed, showing remarkable performance in addressing a wide range of tasks. The rapid development of LLMs has led to the emergence of multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 56, 61], which excel in general visual understanding and complex reasoning tasks. For instance, LLaVA [28, 29] and MiniGPT-4 [61] align visual and language modalities through visual instruction tuning, showcasing impressive capabilities in multimodal conversations. GPT4RoI [58] and RegionGPT [13] enhance fine-grained understanding and reasoning for specific regions by training on region-level instruction datasets. Despite these advancements in tasks such as image captioning and question answering, the lack of user-specific knowledge restricts the generation of personalized content. In this work, we focus on the personalization of MLLMs, enabling them to remember and understand user-specific concepts, and generate personalized content tailored to user preferences." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.403, + 0.482, + 0.78 + ], + "angle": 0, + "content": "Personalization of MLLMs. In the realm of artificial intelligence, personalization typically refers to the process of customizing a system, application, or model to meet individual needs and preferences [42, 46, 47, 50]. Substantial efforts have been made to generate images of a user's personal objects or within certain contexts [10, 14, 21, 23, 38, 41, 49]. For example, Dreambooth [38] employs transfer learning in text-to-image diffusion models via finetuning all parameters for new concepts. In this paper, we mainly aim at enabling MLLMs to remember and understand user-specific concepts, and generate personalized language outputs. Several studies have focused on the personalization of MLLMs, among which the most relevant works are MyVLM [2] and Yo'LLaVA [32]. MyVLM introduces the task of personalizing VLMs. It utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of VLMs. Yo'LLaVA personalizes LLaVA by extending its vocabulary and learning specific tokens for each concept. However, both approaches require continuous model updates as new concepts emerge, which presents challenges in dynamic real-world applications. In this work, we propose the RAP framework for the personalization of MLLMs, enabling models pre-trained on our dataset to continuously update supported concepts without additional fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.482, + 0.902 + ], + "angle": 0, + "content": "Retrieval Augmented Generation. Retrieval-based methods for incorporating external knowledge have been effective in improving generation across various knowledge-intensive tasks [3, 11, 27, 48, 52, 59]. DPR [19] introduces Dense Passage Retrieval, marking a shift from sparse to dense retrieval techniques. Later, MuRAG [5] proposes to use multimodal knowledge to augment language generation. Self-Rag [3] introduces special tokens to make re" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.304 + ], + "angle": 0, + "content": "trieval adaptive and controllable. ERAGent [42] presents a comprehensive system for retrieval-augmented language models. With the advancements in MLLMs, RAG has been widely applied to multimodal generative tasks. For instance, FLMR [26] employs multi-dimensional embeddings to capture finer-grained relevance between queries and documents, achieving significant improvement in the RA-VQA setting. While existing methods primarily enhance models' performance by retrieving from external knowledge bases, few of them consider the personalization task. Although RAG has been applied to image generation [4, 55] and image captioning [25, 35], there is currently no existing work that focuses on personalizing MLLMs through RAG, to the best of our knowledge." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.316, + 0.851, + 0.333 + ], + "angle": 0, + "content": "3. Retrieval Augmented Personalization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.905, + 0.628 + ], + "angle": 0, + "content": "Existing MLLMs typically align other modalities with language. For instance, LLaVA [29] projects visual tokens into text space, and then generates subsequent tokens using an LLM. While these MLLMs perform well in various tasks, the lack of memory and comprehension of personal concepts hinders effective user-specific responses. In this work, we mainly focus on personalizing MLLMs to generate tailored language responses, such as creating personalized captions for user's images and answering questions about personal concepts. In this section, we detail the implementation steps of our proposed Retrieval-Augmented Personalization (RAP) framework. Unlike previous approaches that usually necessitate additional data collection and further training to learn new concepts, after pre-training on our dataset, RAP-MLLMs can adapt to diverse users and infinite new concepts without further training. In section 3.1, we present the RAP framework that is applicable to various types of MLLMs, and then in section 3.2, we provide details of the proposed dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.636, + 0.684, + 0.651 + ], + "angle": 0, + "content": "3.1. RAP Framework" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.905, + 0.689 + ], + "angle": 0, + "content": "RAP works in three steps: Remember, Retrieve and Generate. An overview of the framework is shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Remember. The premise of personalization is that the model can remember personal concepts and relevant information, such as the dog named \\(\\langle \\mathrm{Lala} \\rangle\\) adopted by \\(\\langle \\mathrm{A} \\rangle\\). To facilitate this, we construct a database \\(\\mathcal{M}\\) to store personal concepts, which comprises an avatar \\(\\mathbf{I}_j\\), a name along with a brief description \\(\\mathbf{T}_j\\) for each concept. The key \\(k_i\\) for each concept in the database is its visual feature, obtained by feeding its image \\(\\mathbf{I}_j\\) into a pre-trained image encoder \\(\\mathcal{E}(\\cdot)\\). Examples of our database are presented in Figure 2. When a user initiates a conversation, the input can be represented as \\(Q = (\\mathbf{X}_v, \\mathbf{X}_q)\\), which may include both image \\(\\mathbf{X}_v\\) and some textual instructions \\(\\mathbf{X}_q\\). The first step involves identifying possible concepts within the input image that have been previously stored in the database. Previous meth" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14540" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.094, + 0.849, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.358, + 0.908, + 0.387 + ], + "angle": 0, + "content": "Figure 2. Retrieval-Augmented Personalization Framework. Region-of-interest detected by an open world detector are used to retrieve concepts from the database. The images and information of the retrieved concepts are then integrated into the input for the MLLM." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.404, + 0.486, + 0.557 + ], + "angle": 0, + "content": "ods [2] typically need to learn an external classifier to determine whether a concept appears in the input image, which requires a substantial amount of training data and can only apply to specific concept. To enhance the generalizability of the recognition process, we do not construct specific modules for each concept. Instead, we employ a universal detection model, such asYOLO [37] andYOLO-World [7], as recognition model \\(\\mathcal{R}(\\cdot)\\). Given the predefined setting \\(P\\) that specifies which categories should be remembered, the region-of-interest can be acquired via \\(\\mathbf{X}_u = \\mathcal{R}(\\mathbf{X}_v,\\mathbf{X}_q|P)\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.562, + 0.485, + 0.775 + ], + "angle": 0, + "content": "Retrieve. Identified region-of-interest will be used as query to retrieve from the database. For each recognized component \\(\\mathbf{X}_u^i\\), we feed the image crop into the image encoder \\(\\mathcal{E}(\\cdot)\\) to get its visual feature \\(v_{i} = \\mathcal{E}(\\mathbf{X}_{u}^{i})\\), which is a n-dimensional vector. Then we calculate the euclidean distance between the visual feature and each key \\(k_{j}\\in \\mathcal{M}\\) which is calculated as \\(Dist(v_{i},k_{j}) = \\| v_{i} - k_{j}\\|\\). The Top-K image-text pairs \\(\\{(I_1,T_1),(I_2,T_2),\\dots (I_K,T_K)\\}\\) with the lowest distances are selected from the database. We also introduce retrieval using concept names, such as \\(\\langle \\mathrm{sks}\\rangle\\) for a unique concept. When the user mentions the name of an object documented in the database, our model retrieves its related information from the database. This also enables our model to respond to text-only queries effectively." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Generate. Each pair \\(\\mathbf{M}_j = (\\mathbf{I}_j, \\mathbf{T}_j)\\) provides related information about a user's personal concept and will be incorporated into the input of the MLLM. Take LLaVA [29] as an example. The image \\(\\mathbf{I}_j\\) is first encoded by a pre-trained vision encoder, such as CLIP [34], to obtain their visual tokens \\(\\mathbf{Z}_j\\). These image tokens are then projected by a projector into language tokens \\(\\mathbf{H}_j^v\\), which could be understood by the language model. Simultaneously, corresponding text" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.404, + 0.909, + 0.512 + ], + "angle": 0, + "content": "information \\(\\mathbf{T}_j\\) are transformed into text tokens \\(\\mathbf{H}_j^q\\). This process is also applied to both \\(\\mathbf{X}_v\\) and \\(\\mathbf{X}_q\\). All these tokens are incorporated into the MLLM's input to generate language response. During training, we keep parameters of both the detector and retriever frozen, just train the MLLM's parameters \\(\\theta\\). Given the length \\(L\\) of the output sequence, the probability of the target answer \\(\\mathbf{X}_a\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.515, + 0.907, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\prod_ {i = 1} ^ {L} p _ {\\theta} \\left(\\mathbf {X} _ {a, i} \\mid \\mathbf {X} _ {v}, \\mathbf {X} _ {q}, \\mathbf {M} _ {1}, \\dots \\mathbf {M} _ {K}, \\mathbf {X} _ {a, < i}\\right). \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.561, + 0.733, + 0.575 + ], + "angle": 0, + "content": "3.2. Personalization Dataset" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.584, + 0.907, + 0.704 + ], + "angle": 0, + "content": "Most existing MLLMs struggle to generate personalized outputs even if additional concept information is provided, and there is currently no large-scale dataset for personalized training of MLLMs. To this end, we design a pipeline for data creation and curate a novel dataset specifically for the personalized training of MLLMs. We use Gemini-1.5 [12] to generate annotations for our dataset. An overview of our pipeline and dataset is presented in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.902 + ], + "angle": 0, + "content": "The first component of our dataset is dedicated to visual grounding. In this task, an MLLM is trained to determine whether a specific concept is present in an image, particularly identifying if the person or object in a reference image appears in the given image. When a positive match is detected, we also require the model to provide the bounding box for the identified concept. For single-concept grounding, we primarily use the RefCOCO dataset [20]. Based on RefCOCO's annotations, we crop target concepts from the images and assign names to them, which serve as references for specific concepts. We then query Gemini to generate concise descriptions about properties of the concepts in these cropped regions, by which we construct a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14541" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.096, + 0.855, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.363, + 0.908, + 0.421 + ], + "angle": 0, + "content": "Figure 3. Our Pipeline for Data Collection. We first crop the target concept from the image based on the dataset annotations and then query Gemini [12] to generate its personalized description. We also apply data augmentation to diversify these cropped images. Then we combine them with the original image to derive a series of instructions and answers from Gemini. When noise concepts are included in the additional information, the answer remains unchanged, helping to train the MLLMs' ability to filter out irrelevant concepts." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.431, + 0.482, + 0.597 + ], + "angle": 0, + "content": "large-scale database including numerous different concepts. The training data pairs images and these descriptions as queries and the corresponding bounding boxes as outputs. However, data generated in this way is insufficient to simulate the complexity of real-world recognition, especially when the target concept in the reference and input image is captured from different perspectives. To address this, we incorporate the ILSVRC2015-VID video object detection dataset [39], TAO [9] and CustomConcept101 [21] to enrich our dataset. For multi-object grounding, we use the Object365 dataset [40] to construct our training data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.483, + 0.839 + ], + "angle": 0, + "content": "The second component of our dataset is designed for instruction following. This section includes training data for tasks such as image captioning, image description, and question answering. For the image captioning and description data, we provide cropped images of target concepts, accompanied by their names and related information from the large-scale database, then query Gemini to generate a caption or description that reflects the concepts depicted in the entire image. For question answering, we first design a set of seed questions to serve as examples. These examples are used to prompt the annotator, Gemini, to generate new questions and corresponding answers. This iterative process facilitates the creation of a rich and diverse collection of conversations that MLLMs can learn from. We construct such data using RefCOCO [20], Object365 [40], TAO [9] and CustomConcept101 [21] dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To enhance alignment with real-world scenarios, it is essential to collect data featuring the same identity in various environments. Thus, we also include multiple images about the same individual from the CelebA dataset [30] and" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.431, + 0.907, + 0.597 + ], + "angle": 0, + "content": "produce question answering data about the individual. To further diversify the dataset, we apply image editing techniques for data augmentation. This includes performing random rotations and flips on the cropped images, as well as generating novel views of the concepts by diffusion models. Specifically, we use Inpaint-Anything [53] to separate the foreground from the background, and use Wonder3D [31] and SiTH [16] to synthesize novel views of foreground object or person, respectively. Finally, we combine these elements to generate images of the target concept from different perspectives." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.827 + ], + "angle": 0, + "content": "To support multi-concept personalized generation, it is necessary to retrieve multiple potential concepts from the database. In the generation step, the MLLM must prioritize accurate and contextually relevant information. Considering that retrieval results can be inaccurate, potentially leading to unreasonable answers, we construct negative samples by adding noise concepts to the input while preserving the original output. This approach trains the model's discrimination ability. By exposing the MLLM to both relevant and irrelevant information during training, it learns to discern and filter out noise concepts, thereby enhancing its robustness during inference. Additionally, we include a subset of the LLaVA-Instruct-665k visual instruction dataset [28] to retain general knowledge from the original MLLM. Further details about our dataset can be found in Appendix D." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.844, + 0.64, + 0.862 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. We conduct experiments on LLaVA-1.5-13B [28] and Phi3-V-3.8B [36], resulting in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14542" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.09, + 0.908, + 0.118 + ], + "angle": 0, + "content": "Table 2. Qualitative Comparison on Image Captioning. Image examples of target concepts are shown in the left and captions generated are shown in the right. We use green text to denote correct target concepts." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.12, + 0.892, + 0.527 + ], + "angle": 0, + "content": "
ImageCaption
my dogLLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is a very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.LLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.
H\nTLLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping <T> prepare a salad in the kitchen.LLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping < T> prepare a salad in the kitchen.
B\nG\nWPhi3-V: A group of stuffed animals, including a blue one, are sitting on a black surface.\nLLaVA-LoRA: <B>, <G> and <W> are happily exploring the grassland.\nMyVLM: <G> and his crew are always ready to jump into a new adventure.\nRAP-Phi3-V(Ours): <W> is hanging out with <G> and <B> on the lawn. They are having a great time playing!
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.553, + 0.483, + 0.688 + ], + "angle": 0, + "content": "two personalized MLLMs, RAP-LLaVA and RAP-Phi3-V. We select YOLO-Worldv2 [7] as the detector and construct a multimodal retriever using Facebook AI Similarity Search (FAISS) [18], employing a pre-trained CLIP ViT-L/14-336 [34] as the visual encoder. Due to the context length limitation of the backbone language model, for RAP-LLaVA and RAP-Phi3-V, we retrieve the 2 and 3 different concepts with the highest similarity, respectively. More implementation details can be found in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Training. In the training phase, we skip the recognition and retrieval procedures, instead perform instruction tuning to train the MLLMs. We adhere to most settings from the original experiment of LLaVA [28], except for using a maximum learning rate of 1e-4 and training for 1 epoch. We employ low-rank adapters [17] to reduce the number of trainable parameters, and train our models on 8 A100 GPUs with a valid batch size of 64." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.369, + 0.835 + ], + "angle": 0, + "content": "4.1. Personalized Image Captioning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In this section, we evaluate our models on generating personalized image captions with user-specific concepts. We extend the dataset introduced by MyVLM [2] via adding 16 new concepts, including both objects and humans, forming" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.907, + 0.598 + ], + "angle": 0, + "content": "8 concept pairs that appear together. For each pair, there are 8-13 images used for testing. This multi-concept setting presents additional challenges for personalization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.854 + ], + "angle": 0, + "content": "Settings. We compare our models with MyVLM [2] and fine-tuning based method LLaVA-LoRA [17]. For LLaVA-LoRA and MyVLM, the training dataset contains 1 image accompanied by 5 captions for each concept. For LLaVA-LoRA, we train it with captions of the training images for 3 epochs, applying low-rank adapters [17] and the same hyperparameters as our models. For MyVLM, following their training process, we first train the classification head with the positive and 150 negative images, then train the corresponding concept embedding with the provided captions for each concept. For our models, we construct a database where each concept is represented by a cropped image and a text description. Details of our database could be found in Appendix H. All remaining images are used as test samples. This evaluation process is repeated three times with different seeds, resulting in a total of 1,182 images used for evaluation, and we report the average results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Qualitative Comparison. In Table 2, we present image captions generated by different methods to make a comparison. While LLaVA [28] and Phi3-V [36] generally pro" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14543" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.544, + 0.13 + ], + "angle": 0, + "content": "Table 3. Quantitative Evaluation on Image Captioning. We report Recall, Precision and F1-score in the table, the best result in each metric is bold and the second is underlined." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.133, + 0.544, + 0.253 + ], + "angle": 0, + "content": "
MethodLLMRecallPrecisionF1-score
LLaVA [28] + RetrieverVicuna-13B1.26048.762.450
LLaVA-LoRA [17]Vicuna-13B82.9793.2887.82
MyVLM-LLaVA [2]Vicuna-13B84.6586.3785.50
RAP-LLaVAVicuna-13B93.5196.4794.97
RAP-Phi3-VPhi3-V-3.8B88.1495.1091.49
" + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Figure 4. Performance under varying number of personalized concepts." + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.121, + 0.852, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.274, + 0.907, + 0.304 + ], + "angle": 0, + "content": "Table 4. Quantitative Evaluation on Question Answering and Visual Recognition. The best result in each setting is bold and the second is underlined. Evaluation results of GPT-4V [33] are also provided as reference. Weighted results are computed as arithmetic means." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.305, + 0.898, + 0.521 + ], + "angle": 0, + "content": "
MethodLLMTrain#ImageQuestion AnsweringVisual Recognition
VisualText-onlyWeightedPositiveNegativeWeighted
GPT-4V [33] + PromptGPT-4VX10.8660.9820.9240.8090.9920.901
GPT-4V [33] + PromptGPT-4VX50.8870.9870.9370.8510.9980.925
LLaVA [28]Vicuna-13BX-0.8990.6590.7790.0001.0000.500
LLaVA [28] + RetrieverVicuna-13BX10.9120.8630.8871.0000.0250.513
LLaVA-LoRA [17]Vicuna-13B✓10.9000.5830.7410.9880.6620.825
LLaVA-LoRA [17]Vicuna-13B✓50.9350.6150.7750.9970.4440.721
MyVLM-LLaVA [2]Vicuna-13B✓50.912--0.9940.8450.919
Yo'LLaVA [32]Vicuna-13B✓50.9290.8830.9060.9490.8980.924
RAP-LLaVA(Ours)Vicuna-13BX10.9350.9380.9360.9790.9820.980
RAP-Phi3-V(Ours)Phi3-V-3.8BX10.9410.8500.8960.9220.9880.955
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.545, + 0.483, + 0.712 + ], + "angle": 0, + "content": "vide brief and clear captions for most test images, their lack of understanding of the user-specific concepts restricts them from generating a more personalized caption. LLaVA-LoRA and MyVLM can generate personalized captions, however, the limited training data often results in imprecise outputs, particularly noticeable when multiple concepts are present in the same image. In contrast, our models generate clear and accurate captions based on the database content, which also ensures the reliability of the outputs. Additional examples of personalized captions generated by the models could be found in Appendix E." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.72, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Quantitative Evaluation. We employ recall, precision and the comprehensive metric F1-score as our evaluation metrics. Recall is calculated as the percentage of correct occurrences of target concepts, while precision is the ratio of correct concept names to the total number of concept names presented. The experimental results are shown in Table 3. Notably, the classification heads of MyVLM exhibit higher error rates when the number of positive images is limited, leading to weaker performance. Even with additional concept information provided through retrieval, the vanilla LLaVA [28] still fails to effectively accomplish the personalized generation task, underscoring the necessity of" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.907, + 0.593 + ], + "angle": 0, + "content": "the proposed dataset. Our models demonstrate superior performance in both recall and precision metrics, highlighting the advantages of our RAP-MLLMs in data efficiency." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.81, + 0.62 + ], + "angle": 0, + "content": "4.2. Personalized Question Answering" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.628, + 0.907, + 0.854 + ], + "angle": 0, + "content": "Settings. In this section, we evaluate different methods on the benchmark of personalized question answering introduced by Yo'LLaVA [32], which contains both visual and text-only questions about user concepts. For each concept, we generate a description to serve as its information in our database. For LLaVA-LoRA, we feed these descriptions and corresponding images to train the model to describe the concept's properties. Additionally, we incorporate text-only queries and answers to enhance the model's textual understanding. The training dataset for Yo'LLaVA and MyVLM consists of 5 positive images with question answering pairs and 200 negative images per concept. For GPT-4V [33], images and related concept information are provided as a supplementary prompt. The evaluation metric is accuracy. Additional details are provided in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Results and Analysis. The experimental results are provided in Table 4. LLaVA and LLaVA-LoRA both perform well in visual based question answering, because substan" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14544" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.118 + ], + "angle": 0, + "content": "Table 5. We evaluate model's performance with perfect retrieval, and test contributions of text information and dataset components." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.12, + 0.485, + 0.226 + ], + "angle": 0, + "content": "
SettingRecallPrecisionF1-score
RAP-LLaVA93.5196.4794.97
Skip retrieval96.16 (+2.7)100.0 (+3.5)98.04 (+3.1)
- Text information94.91 (+1.4)88.66 (-7.8)91.68 (-3.3)
- Data augmentation89.25 (-4.3)98.01 (+1.5)93.42 (-1.6)
- Negative samples95.74 (+2.2)58.21 (-38.3)72.40 (-22.6)
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.246, + 0.483, + 0.427 + ], + "angle": 0, + "content": "tial information of the target concept can be obtained from the images. However, their performance is quite poor when images of the target concept mentioned in the question are not available. MyVLM performs well in visual question answering but does not support text-only question answering. Yo'LLaVA excels in text-only question answering, but its performance is still limited by the insufficient information provided by the learned tokens of a concept. In contrast, our models demonstrate balanced performance in both visual and text-only question answering. By providing a single image, our RAP-LLaVA surpasses baseline methods and achieves performance comparable to that of GPT-4V." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.429, + 0.483, + 0.655 + ], + "angle": 0, + "content": "Visual Recognition. We also evaluate the models' recognition abilities for a more comprehensive comparison. MLLMs are required to determine whether a personal concept is present in an image. We query them with \"Is in the image? Answer with a single word.\", where is replaced by corresponding concept name. For positive images, the desired response is \"Yes\" and \"No\" for negative. Results show that without knowledge of personal concepts, the vanilla LLaVA consistently produces negative responses. After training on target concepts, LLaVA-LoRA, MyVLM and YoLLaVA tend to give positive responses, but struggle to differentiate between similar concepts, resulting in weaker performance on negative images. Our models demonstrate exceptional performance in both positive and negative scenarios, achieving the best overall results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.666, + 0.245, + 0.682 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Influence of Number of Learned Concepts. In real-world scenario, users' personal databases typically expand over time. Next, we evaluate the performance of various methods with varying numbers of learned concepts. We extend the database with hundreds of new concepts selected from the RefCOCO dataset [20], ensuring no overlap with the test dataset. For LLaVA-LoRA and MyVLM, we provide images containing the target concepts along with their captions as training data, and assess models' performance on the original test dataset. The results are presented in Figure 4. More learned concepts result in increased recognition errors, leading to a decline in performance for each model. Our RAP-MLLMs maintain the highest performance under different settings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "Generation Ability of MLLM. We skip the recognition and retrieval processes, providing the MLLM with relevant information of each concept present in the image to evaluate the generation capability of the trained MLLM. The results, shown in Table 5, indicate that when relevant concept information is supplied, our RAP-LLaVA achieves superior generation performance, obtaining \\(100\\%\\) precision without outputting irrelevant concepts as well as a higher recall rate." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.212, + 0.905, + 0.363 + ], + "angle": 0, + "content": "Text Information. We remove additional text information to examine its impact on personalization. The results are shown in Table 5 and 7 (Appendix). This additional text provides extra information that helps the model understand specific concepts, effectively improving the accuracy of the answers and benefiting personalized generation. Furthermore, it is especially helpful for question answering, as it can provide information not directly available from the image, such as a user's age and hobbies, or a pet's preferred food, as shown in the example in Table 12 of the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.364, + 0.905, + 0.514 + ], + "angle": 0, + "content": "Dataset Composition. We conduct experiments to assess the contribution of each component in our dataset. First, we remove data generated through data augmentation and train the model. The results displayed in Table 5 indicate an obvious decrease in the recall metric for image captioning, resulting in a lower overall performance. We further exclude constructed negative samples from the dataset and retrain the model, then we find that it performs poorly on precision metric. This suggests a diminished ability to discriminate against noise concepts not present in the image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.905, + 0.635 + ], + "angle": 0, + "content": "Additional Ablation. We conduct ablation studies on retriever's performance, and examine the impact of retrieving different numbers of concepts. We also evaluate models' performance on several multimodal benchmarks, and the results demonstrate that RAP-LLaVA retains most general knowledge of the original LLaVA, while achieving superior performance in knowledge intensive tasks. Due to space limit, we put the results in Appendix Section B.1." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.649, + 0.634, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.905, + 0.84 + ], + "angle": 0, + "content": "In this paper, we introduce the RAP framework for personalizing MLLMs. This framework enables MLLMs to understand infinite user-specific concepts, generate personalized captions and respond to user-related queries. To enhance the quality of the generated content and better align outputs with user configuration, we curate a large-scale dataset for personalized training of MLLMs and train a series of MLLMs to function as personalized assistants. Experimental results show that RAP-MLLMs achieve exceptional performance in various personalized generation tasks, while allowing real-time adjustments to generation settings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14545" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.185 + ], + "angle": 0, + "content": "[1] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. 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Introduce some user-specific concepts to our RAP-MLLM, it can remember them and achieve excellent performance in a variety of personalized multimodal generation tasks. + +# Abstract + +The development of large language models (LLMs) has significantly enhanced the capabilities of multimodal LLMs (MLLMs) as general assistants. However, lack of user-specific knowledge still restricts their application in human's daily life. In this paper, we introduce the Retrieval Augmented Personalization (RAP) framework for MLLMs' personalization. Starting from a general MLLM, we turn it into a personalized assistant in three steps. (a) Remember: We design a key-value database to store user-related information, e.g., user's name, avatar and other attributes. (b) Retrieve: When the user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts' information are fed into MLLMs to generate personalized, knowledge-augmented responses. Unlike previous methods, RAP allows real-time + +concept editing via updating the external database. To further improve generation quality and alignment with user-specific information, we design a pipeline for data collection and create a specialized dataset for personalized training of MLLMs. Based on the dataset, we train a series of MLLMs as personalized multimodal assistants. By pretraining on large-scale dataset, RAP-MLLMs can generalize to infinite visual concepts without additional finetuning. Our models demonstrate outstanding flexibility and generation quality across a variety of tasks, such as personalized image captioning, question answering and visual recognition. The code, data and models are available at https://hoar012.github.io/RAP-Project/. + +# 1. Introduction + +Recently, the development of large language models (LLMs) has significantly enhanced their language processing and generating capabilities [60]. Building on this foundation, the integration of visual and textual ability + +Table 1. Comparison of Different Personalization Methods. RAP needs only 1 image with its personalized description, showing outstanding convenience and flexibility in practical applications. + +
MethodNumber of ImageData Requirements for PersonalizationSupport
PositiveNegativeCaptionDescriptionQuestion-AnswerRecognitionReal-time editText-only QA
Fine-tuningn-YesYesNoNoX✓
MyVLM [2]n150YesNoYesYesXX
Yo’LLaVA [32]n200NoNoYesYesX✓
RAP(Ours)1-NoYesNoNo✓✓
+ +through vision-language alignment brings powerful multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 51, 56]. MLLMs have shown significant improvement in various tasks, such as image description and question answering, highlighting their potential as humans' assistants. However, their lack of user-specific knowledge continues to limit their effectiveness as personalized assistants in daily life. + +A qualified personalized assistant first should be able to recognize and remember user-related concepts, such as the dog named $\langle$ Lala $\rangle$ adopted by the user. Although existing MLLMs have been trained on large-scale datasets and possess strong recognition and classification capabilities, directly transferring this knowledge to a user's personal concepts remains challenging. For instance, current leading MLLMs cannot remember your dog's name, even if you have mentioned it before, and they lack awareness of your identity and preferences. Furthermore, the assistant should generate responses tailored to the user's preferences and requirements. However, collecting extensive personal data to train a unique assistant for each user is impractical. + +To address this issue, the personalization of MLLMs has gained increasing attention, with several approaches already being proposed. MyVLM [2] utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of vision language models (VLMs) [24, 29]. Another concurrent work, Yo'LLaVA [32], learns a few special tokens to represent each concept. However, both approaches require continuous learning and model updates as new concepts emerge. As shown in Table 1, they require multiple labeled images of the target concept along with a large number of negative images, making data collection a significant challenge. Alternatively, fine-tuning the model for each new concept also incurs substantial computational costs. This presents a challenge in dynamic, ever-changing real-world scenarios, where the computing power of users' personal devices is often limited, and all data must be stored locally for privacy concerns. + +To address these challenges, we propose the Retrieval Augmented Personalization (RAP) framework, designed to allow MLLMs to update their supported concepts without additional training. Specifically, RAP works in three key + +steps. (a) Remember: RAP includes a designed database to help remember each concept via storing its image and basic information, e.g., name, avatar and other attributes. (b) Retrieve: When a user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts information are incorporated into the MLLM's input for personalized, knowledge-augmented generation. As shown in Table 1, our RAP requires only one image per concept with its related information for personalization. At the same time, it allows users to make real-time adjustments to the model's outputs by modifying their personal databases, eliminating the need for retraining. Examples of real-time concept editing are presented in Table 12. + +Another significant challenge is the lack of large-scale datasets for training MLLMs' personalized generation capabilities. To address this, we design a pipeline to collect extensive training data and create a comprehensive dataset, which enables to train MLLMs to effectively understand and utilize user-related information for generation. Based on this dataset, we train LLaVA [29] and Phi3-V [36] as novel personalized assistants and evaluate their performance across various tasks, including personalized image captioning, question answering, and visual recognition. Experimental results demonstrate that our RAP-MLLMs excel in a wide range of personalized generation tasks, showcasing excellent generation quality and flexibility. + +Our contributions are summarized as follows: + +- We propose the RAP framework for MLLMs' personalization, allowing models pre-trained on our dataset to adapt to diverse users and infinite new concepts without further training. +- We develop a pipeline for collecting large-scale data and create a dataset specifically designed for the personalized training and evaluation of MLLMs. This dataset enables us to train a series of MLLMs to function as personalized assistants. +- Our models demonstrate exceptional performance across various personalized multimodal generation tasks, including image captioning and question answering. Additionally, they exhibit a strong capability to recognize personal concepts within images. + +# 2. Related Work + +Multimodal Large Language Models. Recently, numerous advanced large language models (LLMs) [1, 8, 43, 44, 57] have been proposed, showing remarkable performance in addressing a wide range of tasks. The rapid development of LLMs has led to the emergence of multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 56, 61], which excel in general visual understanding and complex reasoning tasks. For instance, LLaVA [28, 29] and MiniGPT-4 [61] align visual and language modalities through visual instruction tuning, showcasing impressive capabilities in multimodal conversations. GPT4RoI [58] and RegionGPT [13] enhance fine-grained understanding and reasoning for specific regions by training on region-level instruction datasets. Despite these advancements in tasks such as image captioning and question answering, the lack of user-specific knowledge restricts the generation of personalized content. In this work, we focus on the personalization of MLLMs, enabling them to remember and understand user-specific concepts, and generate personalized content tailored to user preferences. + +Personalization of MLLMs. In the realm of artificial intelligence, personalization typically refers to the process of customizing a system, application, or model to meet individual needs and preferences [42, 46, 47, 50]. Substantial efforts have been made to generate images of a user's personal objects or within certain contexts [10, 14, 21, 23, 38, 41, 49]. For example, Dreambooth [38] employs transfer learning in text-to-image diffusion models via finetuning all parameters for new concepts. In this paper, we mainly aim at enabling MLLMs to remember and understand user-specific concepts, and generate personalized language outputs. Several studies have focused on the personalization of MLLMs, among which the most relevant works are MyVLM [2] and Yo'LLaVA [32]. MyVLM introduces the task of personalizing VLMs. It utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of VLMs. Yo'LLaVA personalizes LLaVA by extending its vocabulary and learning specific tokens for each concept. However, both approaches require continuous model updates as new concepts emerge, which presents challenges in dynamic real-world applications. In this work, we propose the RAP framework for the personalization of MLLMs, enabling models pre-trained on our dataset to continuously update supported concepts without additional fine-tuning. + +Retrieval Augmented Generation. Retrieval-based methods for incorporating external knowledge have been effective in improving generation across various knowledge-intensive tasks [3, 11, 27, 48, 52, 59]. DPR [19] introduces Dense Passage Retrieval, marking a shift from sparse to dense retrieval techniques. Later, MuRAG [5] proposes to use multimodal knowledge to augment language generation. Self-Rag [3] introduces special tokens to make re + +trieval adaptive and controllable. ERAGent [42] presents a comprehensive system for retrieval-augmented language models. With the advancements in MLLMs, RAG has been widely applied to multimodal generative tasks. For instance, FLMR [26] employs multi-dimensional embeddings to capture finer-grained relevance between queries and documents, achieving significant improvement in the RA-VQA setting. While existing methods primarily enhance models' performance by retrieving from external knowledge bases, few of them consider the personalization task. Although RAG has been applied to image generation [4, 55] and image captioning [25, 35], there is currently no existing work that focuses on personalizing MLLMs through RAG, to the best of our knowledge. + +# 3. Retrieval Augmented Personalization + +Existing MLLMs typically align other modalities with language. For instance, LLaVA [29] projects visual tokens into text space, and then generates subsequent tokens using an LLM. While these MLLMs perform well in various tasks, the lack of memory and comprehension of personal concepts hinders effective user-specific responses. In this work, we mainly focus on personalizing MLLMs to generate tailored language responses, such as creating personalized captions for user's images and answering questions about personal concepts. In this section, we detail the implementation steps of our proposed Retrieval-Augmented Personalization (RAP) framework. Unlike previous approaches that usually necessitate additional data collection and further training to learn new concepts, after pre-training on our dataset, RAP-MLLMs can adapt to diverse users and infinite new concepts without further training. In section 3.1, we present the RAP framework that is applicable to various types of MLLMs, and then in section 3.2, we provide details of the proposed dataset. + +# 3.1. RAP Framework + +RAP works in three steps: Remember, Retrieve and Generate. An overview of the framework is shown in Figure 2. + +Remember. The premise of personalization is that the model can remember personal concepts and relevant information, such as the dog named $\langle \mathrm{Lala} \rangle$ adopted by $\langle \mathrm{A} \rangle$ . To facilitate this, we construct a database $\mathcal{M}$ to store personal concepts, which comprises an avatar $\mathbf{I}_j$ , a name along with a brief description $\mathbf{T}_j$ for each concept. The key $k_i$ for each concept in the database is its visual feature, obtained by feeding its image $\mathbf{I}_j$ into a pre-trained image encoder $\mathcal{E}(\cdot)$ . Examples of our database are presented in Figure 2. When a user initiates a conversation, the input can be represented as $Q = (\mathbf{X}_v, \mathbf{X}_q)$ , which may include both image $\mathbf{X}_v$ and some textual instructions $\mathbf{X}_q$ . The first step involves identifying possible concepts within the input image that have been previously stored in the database. Previous meth + +![](images/59271116909bf394002aea41a1b42506020f150d91dde1ab3b6cd48c2d5c6f35.jpg) +Figure 2. Retrieval-Augmented Personalization Framework. Region-of-interest detected by an open world detector are used to retrieve concepts from the database. The images and information of the retrieved concepts are then integrated into the input for the MLLM. + +ods [2] typically need to learn an external classifier to determine whether a concept appears in the input image, which requires a substantial amount of training data and can only apply to specific concept. To enhance the generalizability of the recognition process, we do not construct specific modules for each concept. Instead, we employ a universal detection model, such asYOLO [37] andYOLO-World [7], as recognition model $\mathcal{R}(\cdot)$ . Given the predefined setting $P$ that specifies which categories should be remembered, the region-of-interest can be acquired via $\mathbf{X}_u = \mathcal{R}(\mathbf{X}_v,\mathbf{X}_q|P)$ . + +Retrieve. Identified region-of-interest will be used as query to retrieve from the database. For each recognized component $\mathbf{X}_u^i$ , we feed the image crop into the image encoder $\mathcal{E}(\cdot)$ to get its visual feature $v_{i} = \mathcal{E}(\mathbf{X}_{u}^{i})$ , which is a n-dimensional vector. Then we calculate the euclidean distance between the visual feature and each key $k_{j}\in \mathcal{M}$ which is calculated as $Dist(v_{i},k_{j}) = \| v_{i} - k_{j}\|$ . The Top-K image-text pairs $\{(I_1,T_1),(I_2,T_2),\dots (I_K,T_K)\}$ with the lowest distances are selected from the database. We also introduce retrieval using concept names, such as $\langle \mathrm{sks}\rangle$ for a unique concept. When the user mentions the name of an object documented in the database, our model retrieves its related information from the database. This also enables our model to respond to text-only queries effectively. + +Generate. Each pair $\mathbf{M}_j = (\mathbf{I}_j, \mathbf{T}_j)$ provides related information about a user's personal concept and will be incorporated into the input of the MLLM. Take LLaVA [29] as an example. The image $\mathbf{I}_j$ is first encoded by a pre-trained vision encoder, such as CLIP [34], to obtain their visual tokens $\mathbf{Z}_j$ . These image tokens are then projected by a projector into language tokens $\mathbf{H}_j^v$ , which could be understood by the language model. Simultaneously, corresponding text + +information $\mathbf{T}_j$ are transformed into text tokens $\mathbf{H}_j^q$ . This process is also applied to both $\mathbf{X}_v$ and $\mathbf{X}_q$ . All these tokens are incorporated into the MLLM's input to generate language response. During training, we keep parameters of both the detector and retriever frozen, just train the MLLM's parameters $\theta$ . Given the length $L$ of the output sequence, the probability of the target answer $\mathbf{X}_a$ is computed as: + +$$ +\prod_ {i = 1} ^ {L} p _ {\theta} \left(\mathbf {X} _ {a, i} \mid \mathbf {X} _ {v}, \mathbf {X} _ {q}, \mathbf {M} _ {1}, \dots \mathbf {M} _ {K}, \mathbf {X} _ {a, < i}\right). \tag {1} +$$ + +# 3.2. Personalization Dataset + +Most existing MLLMs struggle to generate personalized outputs even if additional concept information is provided, and there is currently no large-scale dataset for personalized training of MLLMs. To this end, we design a pipeline for data creation and curate a novel dataset specifically for the personalized training of MLLMs. We use Gemini-1.5 [12] to generate annotations for our dataset. An overview of our pipeline and dataset is presented in Figure 3. + +The first component of our dataset is dedicated to visual grounding. In this task, an MLLM is trained to determine whether a specific concept is present in an image, particularly identifying if the person or object in a reference image appears in the given image. When a positive match is detected, we also require the model to provide the bounding box for the identified concept. For single-concept grounding, we primarily use the RefCOCO dataset [20]. Based on RefCOCO's annotations, we crop target concepts from the images and assign names to them, which serve as references for specific concepts. We then query Gemini to generate concise descriptions about properties of the concepts in these cropped regions, by which we construct a + +![](images/167bae94d523d44fc216bc564799fdbfa76f036afb6eefc6d0b5168fb064558a.jpg) +Figure 3. Our Pipeline for Data Collection. We first crop the target concept from the image based on the dataset annotations and then query Gemini [12] to generate its personalized description. We also apply data augmentation to diversify these cropped images. Then we combine them with the original image to derive a series of instructions and answers from Gemini. When noise concepts are included in the additional information, the answer remains unchanged, helping to train the MLLMs' ability to filter out irrelevant concepts. + +large-scale database including numerous different concepts. The training data pairs images and these descriptions as queries and the corresponding bounding boxes as outputs. However, data generated in this way is insufficient to simulate the complexity of real-world recognition, especially when the target concept in the reference and input image is captured from different perspectives. To address this, we incorporate the ILSVRC2015-VID video object detection dataset [39], TAO [9] and CustomConcept101 [21] to enrich our dataset. For multi-object grounding, we use the Object365 dataset [40] to construct our training data. + +The second component of our dataset is designed for instruction following. This section includes training data for tasks such as image captioning, image description, and question answering. For the image captioning and description data, we provide cropped images of target concepts, accompanied by their names and related information from the large-scale database, then query Gemini to generate a caption or description that reflects the concepts depicted in the entire image. For question answering, we first design a set of seed questions to serve as examples. These examples are used to prompt the annotator, Gemini, to generate new questions and corresponding answers. This iterative process facilitates the creation of a rich and diverse collection of conversations that MLLMs can learn from. We construct such data using RefCOCO [20], Object365 [40], TAO [9] and CustomConcept101 [21] dataset. + +To enhance alignment with real-world scenarios, it is essential to collect data featuring the same identity in various environments. Thus, we also include multiple images about the same individual from the CelebA dataset [30] and + +produce question answering data about the individual. To further diversify the dataset, we apply image editing techniques for data augmentation. This includes performing random rotations and flips on the cropped images, as well as generating novel views of the concepts by diffusion models. Specifically, we use Inpaint-Anything [53] to separate the foreground from the background, and use Wonder3D [31] and SiTH [16] to synthesize novel views of foreground object or person, respectively. Finally, we combine these elements to generate images of the target concept from different perspectives. + +To support multi-concept personalized generation, it is necessary to retrieve multiple potential concepts from the database. In the generation step, the MLLM must prioritize accurate and contextually relevant information. Considering that retrieval results can be inaccurate, potentially leading to unreasonable answers, we construct negative samples by adding noise concepts to the input while preserving the original output. This approach trains the model's discrimination ability. By exposing the MLLM to both relevant and irrelevant information during training, it learns to discern and filter out noise concepts, thereby enhancing its robustness during inference. Additionally, we include a subset of the LLaVA-Instruct-665k visual instruction dataset [28] to retain general knowledge from the original MLLM. Further details about our dataset can be found in Appendix D. + +# 4. Experiment + +Implementation Details. We conduct experiments on LLaVA-1.5-13B [28] and Phi3-V-3.8B [36], resulting in + +Table 2. Qualitative Comparison on Image Captioning. Image examples of target concepts are shown in the left and captions generated are shown in the right. We use green text to denote correct target concepts. + +
ImageCaption
my dogLLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table. +LLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner. +MyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her... +RAP-LLaVA(Ours): <my dog> is a very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.LLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table. +LLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner. +MyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her... +RAP-LLaVA(Ours): <my dog> is very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.
H +TLLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ... +LLaVA-LoRA: <H> and <K> are preparing a meal together. +MyVLM: <T> and her friend <H> are looking very serious as they take in the scenery. +RAP-LLaVA(Ours): <H> is helping <T> prepare a salad in the kitchen.LLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ... +LLaVA-LoRA: <H> and <K> are preparing a meal together. +MyVLM: <T> and her friend <H> are looking very serious as they take in the scenery. +RAP-LLaVA(Ours): <H> is helping < T> prepare a salad in the kitchen.
B +G +WPhi3-V: A group of stuffed animals, including a blue one, are sitting on a black surface. +LLaVA-LoRA: <B>, <G> and <W> are happily exploring the grassland. +MyVLM: <G> and his crew are always ready to jump into a new adventure. +RAP-Phi3-V(Ours): <W> is hanging out with <G> and <B> on the lawn. They are having a great time playing!
+ +two personalized MLLMs, RAP-LLaVA and RAP-Phi3-V. We select YOLO-Worldv2 [7] as the detector and construct a multimodal retriever using Facebook AI Similarity Search (FAISS) [18], employing a pre-trained CLIP ViT-L/14-336 [34] as the visual encoder. Due to the context length limitation of the backbone language model, for RAP-LLaVA and RAP-Phi3-V, we retrieve the 2 and 3 different concepts with the highest similarity, respectively. More implementation details can be found in Appendix C. + +Training. In the training phase, we skip the recognition and retrieval procedures, instead perform instruction tuning to train the MLLMs. We adhere to most settings from the original experiment of LLaVA [28], except for using a maximum learning rate of 1e-4 and training for 1 epoch. We employ low-rank adapters [17] to reduce the number of trainable parameters, and train our models on 8 A100 GPUs with a valid batch size of 64. + +# 4.1. Personalized Image Captioning + +In this section, we evaluate our models on generating personalized image captions with user-specific concepts. We extend the dataset introduced by MyVLM [2] via adding 16 new concepts, including both objects and humans, forming + +8 concept pairs that appear together. For each pair, there are 8-13 images used for testing. This multi-concept setting presents additional challenges for personalization. + +Settings. We compare our models with MyVLM [2] and fine-tuning based method LLaVA-LoRA [17]. For LLaVA-LoRA and MyVLM, the training dataset contains 1 image accompanied by 5 captions for each concept. For LLaVA-LoRA, we train it with captions of the training images for 3 epochs, applying low-rank adapters [17] and the same hyperparameters as our models. For MyVLM, following their training process, we first train the classification head with the positive and 150 negative images, then train the corresponding concept embedding with the provided captions for each concept. For our models, we construct a database where each concept is represented by a cropped image and a text description. Details of our database could be found in Appendix H. All remaining images are used as test samples. This evaluation process is repeated three times with different seeds, resulting in a total of 1,182 images used for evaluation, and we report the average results. + +Qualitative Comparison. In Table 2, we present image captions generated by different methods to make a comparison. While LLaVA [28] and Phi3-V [36] generally pro + +Table 3. Quantitative Evaluation on Image Captioning. We report Recall, Precision and F1-score in the table, the best result in each metric is bold and the second is underlined. + +
MethodLLMRecallPrecisionF1-score
LLaVA [28] + RetrieverVicuna-13B1.26048.762.450
LLaVA-LoRA [17]Vicuna-13B82.9793.2887.82
MyVLM-LLaVA [2]Vicuna-13B84.6586.3785.50
RAP-LLaVAVicuna-13B93.5196.4794.97
RAP-Phi3-VPhi3-V-3.8B88.1495.1091.49
+ +![](images/bd8c4f97c514daedf20380cee00d32c66f2464f8a99e087bd586504e9f6e539a.jpg) +Figure 4. Performance under varying number of personalized concepts. + +Table 4. Quantitative Evaluation on Question Answering and Visual Recognition. The best result in each setting is bold and the second is underlined. Evaluation results of GPT-4V [33] are also provided as reference. Weighted results are computed as arithmetic means. + +
MethodLLMTrain#ImageQuestion AnsweringVisual Recognition
VisualText-onlyWeightedPositiveNegativeWeighted
GPT-4V [33] + PromptGPT-4VX10.8660.9820.9240.8090.9920.901
GPT-4V [33] + PromptGPT-4VX50.8870.9870.9370.8510.9980.925
LLaVA [28]Vicuna-13BX-0.8990.6590.7790.0001.0000.500
LLaVA [28] + RetrieverVicuna-13BX10.9120.8630.8871.0000.0250.513
LLaVA-LoRA [17]Vicuna-13B✓10.9000.5830.7410.9880.6620.825
LLaVA-LoRA [17]Vicuna-13B✓50.9350.6150.7750.9970.4440.721
MyVLM-LLaVA [2]Vicuna-13B✓50.912--0.9940.8450.919
Yo'LLaVA [32]Vicuna-13B✓50.9290.8830.9060.9490.8980.924
RAP-LLaVA(Ours)Vicuna-13BX10.9350.9380.9360.9790.9820.980
RAP-Phi3-V(Ours)Phi3-V-3.8BX10.9410.8500.8960.9220.9880.955
+ +vide brief and clear captions for most test images, their lack of understanding of the user-specific concepts restricts them from generating a more personalized caption. LLaVA-LoRA and MyVLM can generate personalized captions, however, the limited training data often results in imprecise outputs, particularly noticeable when multiple concepts are present in the same image. In contrast, our models generate clear and accurate captions based on the database content, which also ensures the reliability of the outputs. Additional examples of personalized captions generated by the models could be found in Appendix E. + +Quantitative Evaluation. We employ recall, precision and the comprehensive metric F1-score as our evaluation metrics. Recall is calculated as the percentage of correct occurrences of target concepts, while precision is the ratio of correct concept names to the total number of concept names presented. The experimental results are shown in Table 3. Notably, the classification heads of MyVLM exhibit higher error rates when the number of positive images is limited, leading to weaker performance. Even with additional concept information provided through retrieval, the vanilla LLaVA [28] still fails to effectively accomplish the personalized generation task, underscoring the necessity of + +the proposed dataset. Our models demonstrate superior performance in both recall and precision metrics, highlighting the advantages of our RAP-MLLMs in data efficiency. + +# 4.2. Personalized Question Answering + +Settings. In this section, we evaluate different methods on the benchmark of personalized question answering introduced by Yo'LLaVA [32], which contains both visual and text-only questions about user concepts. For each concept, we generate a description to serve as its information in our database. For LLaVA-LoRA, we feed these descriptions and corresponding images to train the model to describe the concept's properties. Additionally, we incorporate text-only queries and answers to enhance the model's textual understanding. The training dataset for Yo'LLaVA and MyVLM consists of 5 positive images with question answering pairs and 200 negative images per concept. For GPT-4V [33], images and related concept information are provided as a supplementary prompt. The evaluation metric is accuracy. Additional details are provided in Appendix C. + +Results and Analysis. The experimental results are provided in Table 4. LLaVA and LLaVA-LoRA both perform well in visual based question answering, because substan + +Table 5. We evaluate model's performance with perfect retrieval, and test contributions of text information and dataset components. + +
SettingRecallPrecisionF1-score
RAP-LLaVA93.5196.4794.97
Skip retrieval96.16 (+2.7)100.0 (+3.5)98.04 (+3.1)
- Text information94.91 (+1.4)88.66 (-7.8)91.68 (-3.3)
- Data augmentation89.25 (-4.3)98.01 (+1.5)93.42 (-1.6)
- Negative samples95.74 (+2.2)58.21 (-38.3)72.40 (-22.6)
+ +tial information of the target concept can be obtained from the images. However, their performance is quite poor when images of the target concept mentioned in the question are not available. MyVLM performs well in visual question answering but does not support text-only question answering. Yo'LLaVA excels in text-only question answering, but its performance is still limited by the insufficient information provided by the learned tokens of a concept. In contrast, our models demonstrate balanced performance in both visual and text-only question answering. By providing a single image, our RAP-LLaVA surpasses baseline methods and achieves performance comparable to that of GPT-4V. + +Visual Recognition. We also evaluate the models' recognition abilities for a more comprehensive comparison. MLLMs are required to determine whether a personal concept is present in an image. We query them with "Is in the image? Answer with a single word.", where is replaced by corresponding concept name. For positive images, the desired response is "Yes" and "No" for negative. Results show that without knowledge of personal concepts, the vanilla LLaVA consistently produces negative responses. After training on target concepts, LLaVA-LoRA, MyVLM and YoLLaVA tend to give positive responses, but struggle to differentiate between similar concepts, resulting in weaker performance on negative images. Our models demonstrate exceptional performance in both positive and negative scenarios, achieving the best overall results. + +# 4.3. Ablation Study + +Influence of Number of Learned Concepts. In real-world scenario, users' personal databases typically expand over time. Next, we evaluate the performance of various methods with varying numbers of learned concepts. We extend the database with hundreds of new concepts selected from the RefCOCO dataset [20], ensuring no overlap with the test dataset. For LLaVA-LoRA and MyVLM, we provide images containing the target concepts along with their captions as training data, and assess models' performance on the original test dataset. The results are presented in Figure 4. More learned concepts result in increased recognition errors, leading to a decline in performance for each model. Our RAP-MLLMs maintain the highest performance under different settings. + +Generation Ability of MLLM. We skip the recognition and retrieval processes, providing the MLLM with relevant information of each concept present in the image to evaluate the generation capability of the trained MLLM. The results, shown in Table 5, indicate that when relevant concept information is supplied, our RAP-LLaVA achieves superior generation performance, obtaining $100\%$ precision without outputting irrelevant concepts as well as a higher recall rate. + +Text Information. We remove additional text information to examine its impact on personalization. The results are shown in Table 5 and 7 (Appendix). This additional text provides extra information that helps the model understand specific concepts, effectively improving the accuracy of the answers and benefiting personalized generation. Furthermore, it is especially helpful for question answering, as it can provide information not directly available from the image, such as a user's age and hobbies, or a pet's preferred food, as shown in the example in Table 12 of the Appendix. + +Dataset Composition. We conduct experiments to assess the contribution of each component in our dataset. First, we remove data generated through data augmentation and train the model. The results displayed in Table 5 indicate an obvious decrease in the recall metric for image captioning, resulting in a lower overall performance. We further exclude constructed negative samples from the dataset and retrain the model, then we find that it performs poorly on precision metric. This suggests a diminished ability to discriminate against noise concepts not present in the image. + +Additional Ablation. We conduct ablation studies on retriever's performance, and examine the impact of retrieving different numbers of concepts. We also evaluate models' performance on several multimodal benchmarks, and the results demonstrate that RAP-LLaVA retains most general knowledge of the original LLaVA, while achieving superior performance in knowledge intensive tasks. Due to space limit, we put the results in Appendix Section B.1. + +# 5. Conclusion + +In this paper, we introduce the RAP framework for personalizing MLLMs. This framework enables MLLMs to understand infinite user-specific concepts, generate personalized captions and respond to user-related queries. To enhance the quality of the generated content and better align outputs with user configuration, we curate a large-scale dataset for personalized training of MLLMs and train a series of MLLMs to function as personalized assistants. Experimental results show that RAP-MLLMs achieve exceptional performance in various personalized generation tasks, while allowing real-time adjustments to generation settings. + +Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074). + +# References + +[1] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 3 \ No newline at end of file diff --git a/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/images.zip b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7280057ea0eb565d9263f2844e298cb77d142374 --- /dev/null +++ b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:96dbfd3de38111344316eab45b286373064261aa70363e76eab42be4150a72b8 +size 721725 diff --git a/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/layout.json b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6b63a69b809ed61a93ff83d0bec321c7aa4e03ed --- /dev/null +++ b/2025/RAP_ Retrieval-Augmented Personalization for Multimodal Large Language Models/layout.json @@ -0,0 +1,6680 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 102, + 103, + 510, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 103, + 510, + 140 + ], + "spans": [ + { + "bbox": [ + 102, + 103, + 510, + 140 + ], + "type": "text", + "content": "RAP: Retrieval-Augmented Personalization for Multimodal Large Language Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "spans": [ + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "content": "Haoran Hao" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "content": ", Jiaming Han" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "content": ", Changsheng Li" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "content": ", Yu-Feng Li" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "text", + "content": ", Xiangyu Yue" + }, + { + "bbox": [ + 113, + 160, + 493, + 177 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 187, + 180, + 424, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 180, + 424, + 195 + ], + "spans": [ + { + "bbox": [ + 187, + 180, + 424, + 195 + ], + "type": "text", + "content": "1MMLab, The Chinese University of Hong Kong" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 195, + 494, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 195, + 494, + 209 + ], + "spans": [ + { + "bbox": [ + 116, + 195, + 494, + 209 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 116, + 195, + 494, + 209 + ], + "type": "text", + "content": "National Key Laboratory for Novel Software Technology, Nanjing University" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 225, + 209, + 381, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 225, + 209, + 381, + 224 + ], + "spans": [ + { + "bbox": [ + 225, + 209, + 381, + 224 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 225, + 209, + 381, + 224 + ], + "type": "text", + "content": "Beijing Institute of Technology" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 67, + 240, + 541, + 426 + ], + "blocks": [ + { + "bbox": [ + 67, + 240, + 541, + 426 + ], + "lines": [ + { + "bbox": [ + 67, + 240, + 541, + 426 + ], + "spans": [ + { + "bbox": [ + 67, + 240, + 541, + 426 + ], + "type": "image", + "image_path": "54ff0a2d69eb20b55923c76be433d65bc0436e42c6238f1a7f0aea4680c3434b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 433, + 555, + 456 + ], + "lines": [ + { + "bbox": [ + 54, + 433, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 54, + 433, + 555, + 456 + ], + "type": "text", + "content": "Figure 1. Introduce some user-specific concepts to our RAP-MLLM, it can remember them and achieve excellent performance in a variety of personalized multimodal generation tasks." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 151, + 477, + 200, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 477, + 200, + 490 + ], + "spans": [ + { + "bbox": [ + 151, + 477, + 200, + 490 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "spans": [ + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "type": "text", + "content": "The development of large language models (LLMs) has significantly enhanced the capabilities of multimodal LLMs (MLLMs) as general assistants. However, lack of user-specific knowledge still restricts their application in human's daily life. In this paper, we introduce the Retrieval Augmented Personalization (RAP) framework for MLLMs' personalization. Starting from a general MLLM, we turn it into a personalized assistant in three steps. (a) Remember: We design a key-value database to store user-related information, e.g., user's name, avatar and other attributes. (b) Retrieve: When the user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts' information are fed into MLLMs to generate personalized, knowledge-augmented responses. Unlike previous methods, RAP allows real-time" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 467, + 556, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 556, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 556, + 624 + ], + "type": "text", + "content": "concept editing via updating the external database. To further improve generation quality and alignment with user-specific information, we design a pipeline for data collection and create a specialized dataset for personalized training of MLLMs. Based on the dataset, we train a series of MLLMs as personalized multimodal assistants. By pretraining on large-scale dataset, RAP-MLLMs can generalize to infinite visual concepts without additional finetuning. Our models demonstrate outstanding flexibility and generation quality across a variety of tasks, such as personalized image captioning, question answering and visual recognition. The code, data and models are available at https://hoar012.github.io/RAP-Project/." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 645, + 395, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 645, + 395, + 657 + ], + "spans": [ + { + "bbox": [ + 314, + 645, + 395, + 657 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Recently, the development of large language models (LLMs) has significantly enhanced their language processing and generating capabilities [60]. Building on this foundation, the integration of visual and textual ability" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "type": "text", + "content": "* Equal contribution † Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14538" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 94, + 555, + 184 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": "Table 1. Comparison of Different Personalization Methods. RAP needs only 1 image with its personalized description, showing outstanding convenience and flexibility in practical applications." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 94, + 555, + 184 + ], + "lines": [ + { + "bbox": [ + 56, + 94, + 555, + 184 + ], + "spans": [ + { + "bbox": [ + 56, + 94, + 555, + 184 + ], + "type": "table", + "html": "
MethodNumber of ImageData Requirements for PersonalizationSupport
PositiveNegativeCaptionDescriptionQuestion-AnswerRecognitionReal-time editText-only QA
Fine-tuningn-YesYesNoNoX✓
MyVLM [2]n150YesNoYesYesXX
Yo’LLaVA [32]n200NoNoYesYesX✓
RAP(Ours)1-NoYesNoNo✓✓
", + "image_path": "46e8d4cfb156669005ede69f94812c5c2196df4908bbbbd8abe3c849d8fa6dc9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 201, + 294, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 201, + 294, + 285 + ], + "spans": [ + { + "bbox": [ + 54, + 201, + 294, + 285 + ], + "type": "text", + "content": "through vision-language alignment brings powerful multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 51, 56]. MLLMs have shown significant improvement in various tasks, such as image description and question answering, highlighting their potential as humans' assistants. However, their lack of user-specific knowledge continues to limit their effectiveness as personalized assistants in daily life." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "spans": [ + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "text", + "content": "A qualified personalized assistant first should be able to recognize and remember user-related concepts, such as the dog named " + }, + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "inline_equation", + "content": "\\langle" + }, + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "text", + "content": " Lala " + }, + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "inline_equation", + "content": "\\rangle" + }, + { + "bbox": [ + 54, + 288, + 295, + 443 + ], + "type": "text", + "content": " adopted by the user. Although existing MLLMs have been trained on large-scale datasets and possess strong recognition and classification capabilities, directly transferring this knowledge to a user's personal concepts remains challenging. For instance, current leading MLLMs cannot remember your dog's name, even if you have mentioned it before, and they lack awareness of your identity and preferences. Furthermore, the assistant should generate responses tailored to the user's preferences and requirements. However, collecting extensive personal data to train a unique assistant for each user is impractical." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 447, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 447, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 56, + 447, + 295, + 662 + ], + "type": "text", + "content": "To address this issue, the personalization of MLLMs has gained increasing attention, with several approaches already being proposed. MyVLM [2] utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of vision language models (VLMs) [24, 29]. Another concurrent work, Yo'LLaVA [32], learns a few special tokens to represent each concept. However, both approaches require continuous learning and model updates as new concepts emerge. As shown in Table 1, they require multiple labeled images of the target concept along with a large number of negative images, making data collection a significant challenge. Alternatively, fine-tuning the model for each new concept also incurs substantial computational costs. This presents a challenge in dynamic, ever-changing real-world scenarios, where the computing power of users' personal devices is often limited, and all data must be stored locally for privacy concerns." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "To address these challenges, we propose the Retrieval Augmented Personalization (RAP) framework, designed to allow MLLMs to update their supported concepts without additional training. Specifically, RAP works in three key" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 201, + 555, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 555, + 369 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 555, + 369 + ], + "type": "text", + "content": "steps. (a) Remember: RAP includes a designed database to help remember each concept via storing its image and basic information, e.g., name, avatar and other attributes. (b) Retrieve: When a user initiates a conversation, RAP will retrieve relevant information from the database using a multimodal retriever. (c) Generate: The input query and retrieved concepts information are incorporated into the MLLM's input for personalized, knowledge-augmented generation. As shown in Table 1, our RAP requires only one image per concept with its related information for personalization. At the same time, it allows users to make real-time adjustments to the model's outputs by modifying their personal databases, eliminating the need for retraining. Examples of real-time concept editing are presented in Table 12." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 373, + 556, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 556, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 556, + 529 + ], + "type": "text", + "content": "Another significant challenge is the lack of large-scale datasets for training MLLMs' personalized generation capabilities. To address this, we design a pipeline to collect extensive training data and create a comprehensive dataset, which enables to train MLLMs to effectively understand and utilize user-related information for generation. Based on this dataset, we train LLaVA [29] and Phi3-V [36] as novel personalized assistants and evaluate their performance across various tasks, including personalized image captioning, question answering, and visual recognition. Experimental results demonstrate that our RAP-MLLMs excel in a wide range of personalized generation tasks, showcasing excellent generation quality and flexibility." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 325, + 532, + 511, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 532, + 511, + 543 + ], + "spans": [ + { + "bbox": [ + 325, + 532, + 511, + 543 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 323, + 544, + 553, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 323, + 544, + 553, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 544, + 553, + 590 + ], + "spans": [ + { + "bbox": [ + 323, + 544, + 553, + 590 + ], + "type": "text", + "content": "- We propose the RAP framework for MLLMs' personalization, allowing models pre-trained on our dataset to adapt to diverse users and infinite new concepts without further training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 323, + 593, + 553, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 593, + 553, + 651 + ], + "spans": [ + { + "bbox": [ + 323, + 593, + 553, + 651 + ], + "type": "text", + "content": "- We develop a pipeline for collecting large-scale data and create a dataset specifically designed for the personalized training and evaluation of MLLMs. This dataset enables us to train a series of MLLMs to function as personalized assistants." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 323, + 654, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 654, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 323, + 654, + 553, + 712 + ], + "type": "text", + "content": "- Our models demonstrate exceptional performance across various personalized multimodal generation tasks, including image captioning and question answering. Additionally, they exhibit a strong capability to recognize personal concepts within images." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14539" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 294, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 91, + 294, + 317 + ], + "spans": [ + { + "bbox": [ + 57, + 91, + 294, + 317 + ], + "type": "text", + "content": "Multimodal Large Language Models. Recently, numerous advanced large language models (LLMs) [1, 8, 43, 44, 57] have been proposed, showing remarkable performance in addressing a wide range of tasks. The rapid development of LLMs has led to the emergence of multimodal LLMs (MLLMs) [12, 15, 29, 33, 45, 56, 61], which excel in general visual understanding and complex reasoning tasks. For instance, LLaVA [28, 29] and MiniGPT-4 [61] align visual and language modalities through visual instruction tuning, showcasing impressive capabilities in multimodal conversations. GPT4RoI [58] and RegionGPT [13] enhance fine-grained understanding and reasoning for specific regions by training on region-level instruction datasets. Despite these advancements in tasks such as image captioning and question answering, the lack of user-specific knowledge restricts the generation of personalized content. In this work, we focus on the personalization of MLLMs, enabling them to remember and understand user-specific concepts, and generate personalized content tailored to user preferences." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 319, + 294, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 319, + 294, + 617 + ], + "spans": [ + { + "bbox": [ + 57, + 319, + 294, + 617 + ], + "type": "text", + "content": "Personalization of MLLMs. In the realm of artificial intelligence, personalization typically refers to the process of customizing a system, application, or model to meet individual needs and preferences [42, 46, 47, 50]. Substantial efforts have been made to generate images of a user's personal objects or within certain contexts [10, 14, 21, 23, 38, 41, 49]. For example, Dreambooth [38] employs transfer learning in text-to-image diffusion models via finetuning all parameters for new concepts. In this paper, we mainly aim at enabling MLLMs to remember and understand user-specific concepts, and generate personalized language outputs. Several studies have focused on the personalization of MLLMs, among which the most relevant works are MyVLM [2] and Yo'LLaVA [32]. MyVLM introduces the task of personalizing VLMs. It utilizes external classification heads to recognize specific concepts, and learns an embedding for each concept to personalize the outputs of VLMs. Yo'LLaVA personalizes LLaVA by extending its vocabulary and learning specific tokens for each concept. However, both approaches require continuous model updates as new concepts emerge, which presents challenges in dynamic real-world applications. In this work, we propose the RAP framework for the personalization of MLLMs, enabling models pre-trained on our dataset to continuously update supported concepts without additional fine-tuning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 618, + 294, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 294, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 294, + 714 + ], + "type": "text", + "content": "Retrieval Augmented Generation. Retrieval-based methods for incorporating external knowledge have been effective in improving generation across various knowledge-intensive tasks [3, 11, 27, 48, 52, 59]. DPR [19] introduces Dense Passage Retrieval, marking a shift from sparse to dense retrieval techniques. Later, MuRAG [5] proposes to use multimodal knowledge to augment language generation. Self-Rag [3] introduces special tokens to make re" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "type": "text", + "content": "trieval adaptive and controllable. ERAGent [42] presents a comprehensive system for retrieval-augmented language models. With the advancements in MLLMs, RAG has been widely applied to multimodal generative tasks. For instance, FLMR [26] employs multi-dimensional embeddings to capture finer-grained relevance between queries and documents, achieving significant improvement in the RA-VQA setting. While existing methods primarily enhance models' performance by retrieving from external knowledge bases, few of them consider the personalization task. Although RAG has been applied to image generation [4, 55] and image captioning [25, 35], there is currently no existing work that focuses on personalizing MLLMs through RAG, to the best of our knowledge." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 250, + 520, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 250, + 520, + 263 + ], + "spans": [ + { + "bbox": [ + 313, + 250, + 520, + 263 + ], + "type": "text", + "content": "3. Retrieval Augmented Personalization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 269, + 553, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 553, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 553, + 497 + ], + "type": "text", + "content": "Existing MLLMs typically align other modalities with language. For instance, LLaVA [29] projects visual tokens into text space, and then generates subsequent tokens using an LLM. While these MLLMs perform well in various tasks, the lack of memory and comprehension of personal concepts hinders effective user-specific responses. In this work, we mainly focus on personalizing MLLMs to generate tailored language responses, such as creating personalized captions for user's images and answering questions about personal concepts. In this section, we detail the implementation steps of our proposed Retrieval-Augmented Personalization (RAP) framework. Unlike previous approaches that usually necessitate additional data collection and further training to learn new concepts, after pre-training on our dataset, RAP-MLLMs can adapt to diverse users and infinite new concepts without further training. In section 3.1, we present the RAP framework that is applicable to various types of MLLMs, and then in section 3.2, we provide details of the proposed dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 503, + 418, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 503, + 418, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 418, + 515 + ], + "type": "text", + "content": "3.1. RAP Framework" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 522, + 553, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 553, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 553, + 545 + ], + "type": "text", + "content": "RAP works in three steps: Remember, Retrieve and Generate. An overview of the framework is shown in Figure 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": "Remember. The premise of personalization is that the model can remember personal concepts and relevant information, such as the dog named " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{Lala} \\rangle" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " adopted by " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{A} \\rangle" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": ". To facilitate this, we construct a database " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " to store personal concepts, which comprises an avatar " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_j" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": ", a name along with a brief description " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " for each concept. The key " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "k_i" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " for each concept in the database is its visual feature, obtained by feeding its image " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_j" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " into a pre-trained image encoder " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\cdot)" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": ". Examples of our database are presented in Figure 2. When a user initiates a conversation, the input can be represented as " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "Q = (\\mathbf{X}_v, \\mathbf{X}_q)" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": ", which may include both image " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_v" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": " and some textual instructions " + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_q" + }, + { + "bbox": [ + 313, + 546, + 553, + 713 + ], + "type": "text", + "content": ". The first step involves identifying possible concepts within the input image that have been previously stored in the database. Previous meth" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14540" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 74, + 519, + 281 + ], + "blocks": [ + { + "bbox": [ + 82, + 74, + 519, + 281 + ], + "lines": [ + { + "bbox": [ + 82, + 74, + 519, + 281 + ], + "spans": [ + { + "bbox": [ + 82, + 74, + 519, + 281 + ], + "type": "image", + "image_path": "59271116909bf394002aea41a1b42506020f150d91dde1ab3b6cd48c2d5c6f35.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 283, + 555, + 306 + ], + "lines": [ + { + "bbox": [ + 54, + 283, + 555, + 306 + ], + "spans": [ + { + "bbox": [ + 54, + 283, + 555, + 306 + ], + "type": "text", + "content": "Figure 2. Retrieval-Augmented Personalization Framework. Region-of-interest detected by an open world detector are used to retrieve concepts from the database. The images and information of the retrieved concepts are then integrated into the input for the MLLM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "spans": [ + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "text", + "content": "ods [2] typically need to learn an external classifier to determine whether a concept appears in the input image, which requires a substantial amount of training data and can only apply to specific concept. To enhance the generalizability of the recognition process, we do not construct specific modules for each concept. Instead, we employ a universal detection model, such asYOLO [37] andYOLO-World [7], as recognition model " + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot)" + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "text", + "content": ". Given the predefined setting " + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "text", + "content": " that specifies which categories should be remembered, the region-of-interest can be acquired via " + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_u = \\mathcal{R}(\\mathbf{X}_v,\\mathbf{X}_q|P)" + }, + { + "bbox": [ + 54, + 319, + 297, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "spans": [ + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": "Retrieve. Identified region-of-interest will be used as query to retrieve from the database. For each recognized component " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_u^i" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": ", we feed the image crop into the image encoder " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\cdot)" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": " to get its visual feature " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "v_{i} = \\mathcal{E}(\\mathbf{X}_{u}^{i})" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": ", which is a n-dimensional vector. Then we calculate the euclidean distance between the visual feature and each key " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "k_{j}\\in \\mathcal{M}" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": " which is calculated as " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "Dist(v_{i},k_{j}) = \\| v_{i} - k_{j}\\|" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": ". The Top-K image-text pairs " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\{(I_1,T_1),(I_2,T_2),\\dots (I_K,T_K)\\}" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": " with the lowest distances are selected from the database. We also introduce retrieval using concept names, such as " + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{sks}\\rangle" + }, + { + "bbox": [ + 54, + 445, + 296, + 613 + ], + "type": "text", + "content": " for a unique concept. When the user mentions the name of an object documented in the database, our model retrieves its related information from the database. This also enables our model to respond to text-only queries effectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "content": "Generate. Each pair " + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_j = (\\mathbf{I}_j, \\mathbf{T}_j)" + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "content": " provides related information about a user's personal concept and will be incorporated into the input of the MLLM. Take LLaVA [29] as an example. The image " + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_j" + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "content": " is first encoded by a pre-trained vision encoder, such as CLIP [34], to obtain their visual tokens " + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_j" + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "content": ". These image tokens are then projected by a projector into language tokens " + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_j^v" + }, + { + "bbox": [ + 54, + 617, + 297, + 715 + ], + "type": "text", + "content": ", which could be understood by the language model. Simultaneously, corresponding text" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": "information " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": " are transformed into text tokens " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_j^q" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": ". This process is also applied to both " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_v" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_q" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": ". All these tokens are incorporated into the MLLM's input to generate language response. During training, we keep parameters of both the detector and retriever frozen, just train the MLLM's parameters " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": ". Given the length " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": " of the output sequence, the probability of the target answer " + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_a" + }, + { + "bbox": [ + 313, + 319, + 556, + 405 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 346, + 407, + 555, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 407, + 555, + 440 + ], + "spans": [ + { + "bbox": [ + 346, + 407, + 555, + 440 + ], + "type": "interline_equation", + "content": "\\prod_ {i = 1} ^ {L} p _ {\\theta} \\left(\\mathbf {X} _ {a, i} \\mid \\mathbf {X} _ {v}, \\mathbf {X} _ {q}, \\mathbf {M} _ {1}, \\dots \\mathbf {M} _ {K}, \\mathbf {X} _ {a, < i}\\right). \\tag {1}", + "image_path": "eccb21ce5ecaf311a6056275af6e7d50e9380e26199c1042d67bcf613c67cfc8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 444, + 448, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 448, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 448, + 455 + ], + "type": "text", + "content": "3.2. Personalization Dataset" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 462, + 555, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 462, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 312, + 462, + 555, + 557 + ], + "type": "text", + "content": "Most existing MLLMs struggle to generate personalized outputs even if additional concept information is provided, and there is currently no large-scale dataset for personalized training of MLLMs. To this end, we design a pipeline for data creation and curate a novel dataset specifically for the personalized training of MLLMs. We use Gemini-1.5 [12] to generate annotations for our dataset. An overview of our pipeline and dataset is presented in Figure 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 714 + ], + "type": "text", + "content": "The first component of our dataset is dedicated to visual grounding. In this task, an MLLM is trained to determine whether a specific concept is present in an image, particularly identifying if the person or object in a reference image appears in the given image. When a positive match is detected, we also require the model to provide the bounding box for the identified concept. For single-concept grounding, we primarily use the RefCOCO dataset [20]. Based on RefCOCO's annotations, we crop target concepts from the images and assign names to them, which serve as references for specific concepts. We then query Gemini to generate concise descriptions about properties of the concepts in these cropped regions, by which we construct a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14541" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 76, + 523, + 284 + ], + "blocks": [ + { + "bbox": [ + 86, + 76, + 523, + 284 + ], + "lines": [ + { + "bbox": [ + 86, + 76, + 523, + 284 + ], + "spans": [ + { + "bbox": [ + 86, + 76, + 523, + 284 + ], + "type": "image", + "image_path": "167bae94d523d44fc216bc564799fdbfa76f036afb6eefc6d0b5168fb064558a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 287, + 555, + 333 + ], + "lines": [ + { + "bbox": [ + 54, + 287, + 555, + 333 + ], + "spans": [ + { + "bbox": [ + 54, + 287, + 555, + 333 + ], + "type": "text", + "content": "Figure 3. Our Pipeline for Data Collection. We first crop the target concept from the image based on the dataset annotations and then query Gemini [12] to generate its personalized description. We also apply data augmentation to diversify these cropped images. Then we combine them with the original image to derive a series of instructions and answers from Gemini. When noise concepts are included in the additional information, the answer remains unchanged, helping to train the MLLMs' ability to filter out irrelevant concepts." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 341, + 294, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 341, + 294, + 472 + ], + "spans": [ + { + "bbox": [ + 54, + 341, + 294, + 472 + ], + "type": "text", + "content": "large-scale database including numerous different concepts. The training data pairs images and these descriptions as queries and the corresponding bounding boxes as outputs. However, data generated in this way is insufficient to simulate the complexity of real-world recognition, especially when the target concept in the reference and input image is captured from different perspectives. To address this, we incorporate the ILSVRC2015-VID video object detection dataset [39], TAO [9] and CustomConcept101 [21] to enrich our dataset. For multi-object grounding, we use the Object365 dataset [40] to construct our training data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 473, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 295, + 664 + ], + "type": "text", + "content": "The second component of our dataset is designed for instruction following. This section includes training data for tasks such as image captioning, image description, and question answering. For the image captioning and description data, we provide cropped images of target concepts, accompanied by their names and related information from the large-scale database, then query Gemini to generate a caption or description that reflects the concepts depicted in the entire image. For question answering, we first design a set of seed questions to serve as examples. These examples are used to prompt the annotator, Gemini, to generate new questions and corresponding answers. This iterative process facilitates the creation of a rich and diverse collection of conversations that MLLMs can learn from. We construct such data using RefCOCO [20], Object365 [40], TAO [9] and CustomConcept101 [21] dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "To enhance alignment with real-world scenarios, it is essential to collect data featuring the same identity in various environments. Thus, we also include multiple images about the same individual from the CelebA dataset [30] and" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 341, + 555, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 341, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 341, + 555, + 472 + ], + "type": "text", + "content": "produce question answering data about the individual. To further diversify the dataset, we apply image editing techniques for data augmentation. This includes performing random rotations and flips on the cropped images, as well as generating novel views of the concepts by diffusion models. Specifically, we use Inpaint-Anything [53] to separate the foreground from the background, and use Wonder3D [31] and SiTH [16] to synthesize novel views of foreground object or person, respectively. Finally, we combine these elements to generate images of the target concept from different perspectives." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 474, + 556, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 654 + ], + "type": "text", + "content": "To support multi-concept personalized generation, it is necessary to retrieve multiple potential concepts from the database. In the generation step, the MLLM must prioritize accurate and contextually relevant information. Considering that retrieval results can be inaccurate, potentially leading to unreasonable answers, we construct negative samples by adding noise concepts to the input while preserving the original output. This approach trains the model's discrimination ability. By exposing the MLLM to both relevant and irrelevant information during training, it learns to discern and filter out noise concepts, thereby enhancing its robustness during inference. Additionally, we include a subset of the LLaVA-Instruct-665k visual instruction dataset [28] to retain general knowledge from the original MLLM. Further details about our dataset can be found in Appendix D." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 668, + 391, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 668, + 391, + 682 + ], + "spans": [ + { + "bbox": [ + 313, + 668, + 391, + 682 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Implementation Details. We conduct experiments on LLaVA-1.5-13B [28] and Phi3-V-3.8B [36], resulting in" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14542" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 95, + 545, + 417 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "type": "text", + "content": "Table 2. Qualitative Comparison on Image Captioning. Image examples of target concepts are shown in the left and captions generated are shown in the right. We use green text to denote correct target concepts." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 95, + 545, + 417 + ], + "lines": [ + { + "bbox": [ + 65, + 95, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 65, + 95, + 545, + 417 + ], + "type": "table", + "html": "
ImageCaption
my dogLLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is a very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.LLaVA: A man is sitting at a table with a dog, and there are wine glasses and a fork on the table.\nLLaVA-LoRA: <collie dog> looking pleased as she shares a meal with her owner.\nMyVLM: <my dog> positioned on a chair by a black table, holding a wine glass in her hand. A white dog sits on the floor beside her...\nRAP-LLaVA(Ours): <my dog> is very good boy, and he loves to sit at a table with his owner. They are enjoying a meal.
H\nTLLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping <T> prepare a salad in the kitchen.LLaVA: A man and a woman are standing in a kitchen, preparing food together. The woman is cutting lettuce on a cutting board, while the man watches her. There are several tomatoes ...\nLLaVA-LoRA: <H> and <K> are preparing a meal together.\nMyVLM: <T> and her friend <H> are looking very serious as they take in the scenery.\nRAP-LLaVA(Ours): <H> is helping < T> prepare a salad in the kitchen.
B\nG\nWPhi3-V: A group of stuffed animals, including a blue one, are sitting on a black surface.\nLLaVA-LoRA: <B>, <G> and <W> are happily exploring the grassland.\nMyVLM: <G> and his crew are always ready to jump into a new adventure.\nRAP-Phi3-V(Ours): <W> is hanging out with <G> and <B> on the lawn. They are having a great time playing!
", + "image_path": "235d9d11919bc75793c7d0ae33a93997ee19f1d08ba40a8aaa46cc8627de58ec.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 544 + ], + "type": "text", + "content": "two personalized MLLMs, RAP-LLaVA and RAP-Phi3-V. We select YOLO-Worldv2 [7] as the detector and construct a multimodal retriever using Facebook AI Similarity Search (FAISS) [18], employing a pre-trained CLIP ViT-L/14-336 [34] as the visual encoder. Due to the context length limitation of the backbone language model, for RAP-LLaVA and RAP-Phi3-V, we retrieve the 2 and 3 different concepts with the highest similarity, respectively. More implementation details can be found in Appendix C." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 544, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 640 + ], + "type": "text", + "content": "Training. In the training phase, we skip the recognition and retrieval procedures, instead perform instruction tuning to train the MLLMs. We adhere to most settings from the original experiment of LLaVA [28], except for using a maximum learning rate of 1e-4 and training for 1 epoch. We employ low-rank adapters [17] to reduce the number of trainable parameters, and train our models on 8 A100 GPUs with a valid batch size of 64." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 647, + 225, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 225, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 225, + 661 + ], + "type": "text", + "content": "4.1. Personalized Image Captioning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 666, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 715 + ], + "type": "text", + "content": "In this section, we evaluate our models on generating personalized image captions with user-specific concepts. We extend the dataset introduced by MyVLM [2] via adding 16 new concepts, including both objects and humans, forming" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 437, + 555, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 473 + ], + "type": "text", + "content": "8 concept pairs that appear together. For each pair, there are 8-13 images used for testing. This multi-concept setting presents additional challenges for personalization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 474, + 556, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 676 + ], + "type": "text", + "content": "Settings. We compare our models with MyVLM [2] and fine-tuning based method LLaVA-LoRA [17]. For LLaVA-LoRA and MyVLM, the training dataset contains 1 image accompanied by 5 captions for each concept. For LLaVA-LoRA, we train it with captions of the training images for 3 epochs, applying low-rank adapters [17] and the same hyperparameters as our models. For MyVLM, following their training process, we first train the classification head with the positive and 150 negative images, then train the corresponding concept embedding with the provided captions for each concept. For our models, we construct a database where each concept is represented by a cropped image and a text description. Details of our database could be found in Appendix H. All remaining images are used as test samples. This evaluation process is repeated three times with different seeds, resulting in a total of 1,182 images used for evaluation, and we report the average results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "Qualitative Comparison. In Table 2, we present image captions generated by different methods to make a comparison. While LLaVA [28] and Phi3-V [36] generally pro" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14543" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 105, + 332, + 200 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 332, + 102 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 332, + 102 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 332, + 102 + ], + "type": "text", + "content": "Table 3. Quantitative Evaluation on Image Captioning. We report Recall, Precision and F1-score in the table, the best result in each metric is bold and the second is underlined." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 105, + 332, + 200 + ], + "lines": [ + { + "bbox": [ + 56, + 105, + 332, + 200 + ], + "spans": [ + { + "bbox": [ + 56, + 105, + 332, + 200 + ], + "type": "table", + "html": "
MethodLLMRecallPrecisionF1-score
LLaVA [28] + RetrieverVicuna-13B1.26048.762.450
LLaVA-LoRA [17]Vicuna-13B82.9793.2887.82
MyVLM-LLaVA [2]Vicuna-13B84.6586.3785.50
RAP-LLaVAVicuna-13B93.5196.4794.97
RAP-Phi3-VPhi3-V-3.8B88.1495.1091.49
", + "image_path": "f86b9da2a5d08351098b6502e552da6b5dfaa70832c62e6581dacfbb86fbe9d4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 369, + 95, + 521, + 205 + ], + "blocks": [ + { + "bbox": [ + 343, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 343, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 343, + 70, + 545, + 93 + ], + "type": "text", + "content": "Figure 4. Performance under varying number of personalized concepts." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 95, + 521, + 205 + ], + "lines": [ + { + "bbox": [ + 369, + 95, + 521, + 205 + ], + "spans": [ + { + "bbox": [ + 369, + 95, + 521, + 205 + ], + "type": "image", + "image_path": "bd8c4f97c514daedf20380cee00d32c66f2464f8a99e087bd586504e9f6e539a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 60, + 241, + 549, + 412 + ], + "blocks": [ + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 555, + 240 + ], + "type": "text", + "content": "Table 4. Quantitative Evaluation on Question Answering and Visual Recognition. The best result in each setting is bold and the second is underlined. Evaluation results of GPT-4V [33] are also provided as reference. Weighted results are computed as arithmetic means." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 241, + 549, + 412 + ], + "lines": [ + { + "bbox": [ + 60, + 241, + 549, + 412 + ], + "spans": [ + { + "bbox": [ + 60, + 241, + 549, + 412 + ], + "type": "table", + "html": "
MethodLLMTrain#ImageQuestion AnsweringVisual Recognition
VisualText-onlyWeightedPositiveNegativeWeighted
GPT-4V [33] + PromptGPT-4VX10.8660.9820.9240.8090.9920.901
GPT-4V [33] + PromptGPT-4VX50.8870.9870.9370.8510.9980.925
LLaVA [28]Vicuna-13BX-0.8990.6590.7790.0001.0000.500
LLaVA [28] + RetrieverVicuna-13BX10.9120.8630.8871.0000.0250.513
LLaVA-LoRA [17]Vicuna-13B✓10.9000.5830.7410.9880.6620.825
LLaVA-LoRA [17]Vicuna-13B✓50.9350.6150.7750.9970.4440.721
MyVLM-LLaVA [2]Vicuna-13B✓50.912--0.9940.8450.919
Yo'LLaVA [32]Vicuna-13B✓50.9290.8830.9060.9490.8980.924
RAP-LLaVA(Ours)Vicuna-13BX10.9350.9380.9360.9790.9820.980
RAP-Phi3-V(Ours)Phi3-V-3.8BX10.9410.8500.8960.9220.9880.955
", + "image_path": "4803cf969309547aba7b188ee126ef855cc61c82bfe094fa8d93185ec582cab9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 431, + 295, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 431, + 295, + 563 + ], + "spans": [ + { + "bbox": [ + 54, + 431, + 295, + 563 + ], + "type": "text", + "content": "vide brief and clear captions for most test images, their lack of understanding of the user-specific concepts restricts them from generating a more personalized caption. LLaVA-LoRA and MyVLM can generate personalized captions, however, the limited training data often results in imprecise outputs, particularly noticeable when multiple concepts are present in the same image. In contrast, our models generate clear and accurate captions based on the database content, which also ensures the reliability of the outputs. Additional examples of personalized captions generated by the models could be found in Appendix E." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 570, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 570, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 570, + 295, + 715 + ], + "type": "text", + "content": "Quantitative Evaluation. We employ recall, precision and the comprehensive metric F1-score as our evaluation metrics. Recall is calculated as the percentage of correct occurrences of target concepts, while precision is the ratio of correct concept names to the total number of concept names presented. The experimental results are shown in Table 3. Notably, the classification heads of MyVLM exhibit higher error rates when the number of positive images is limited, leading to weaker performance. Even with additional concept information provided through retrieval, the vanilla LLaVA [28] still fails to effectively accomplish the personalized generation task, underscoring the necessity of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 431, + 555, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 469 + ], + "type": "text", + "content": "the proposed dataset. Our models demonstrate superior performance in both recall and precision metrics, highlighting the advantages of our RAP-MLLMs in data efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 478, + 495, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 495, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 495, + 491 + ], + "type": "text", + "content": "4.2. Personalized Question Answering" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 497, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 497, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 312, + 497, + 555, + 676 + ], + "type": "text", + "content": "Settings. In this section, we evaluate different methods on the benchmark of personalized question answering introduced by Yo'LLaVA [32], which contains both visual and text-only questions about user concepts. For each concept, we generate a description to serve as its information in our database. For LLaVA-LoRA, we feed these descriptions and corresponding images to train the model to describe the concept's properties. Additionally, we incorporate text-only queries and answers to enhance the model's textual understanding. The training dataset for Yo'LLaVA and MyVLM consists of 5 positive images with question answering pairs and 200 negative images per concept. For GPT-4V [33], images and related concept information are provided as a supplementary prompt. The evaluation metric is accuracy. Additional details are provided in Appendix C." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "Results and Analysis. The experimental results are provided in Table 4. LLaVA and LLaVA-LoRA both perform well in visual based question answering, because substan" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14544" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 95, + 296, + 178 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 93 + ], + "type": "text", + "content": "Table 5. We evaluate model's performance with perfect retrieval, and test contributions of text information and dataset components." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 95, + 296, + 178 + ], + "lines": [ + { + "bbox": [ + 56, + 95, + 296, + 178 + ], + "spans": [ + { + "bbox": [ + 56, + 95, + 296, + 178 + ], + "type": "table", + "html": "
SettingRecallPrecisionF1-score
RAP-LLaVA93.5196.4794.97
Skip retrieval96.16 (+2.7)100.0 (+3.5)98.04 (+3.1)
- Text information94.91 (+1.4)88.66 (-7.8)91.68 (-3.3)
- Data augmentation89.25 (-4.3)98.01 (+1.5)93.42 (-1.6)
- Negative samples95.74 (+2.2)58.21 (-38.3)72.40 (-22.6)
", + "image_path": "28ee32892cecc97ad8cb5c230aa6d84086ef7d97e4e7a1c79bc2c5f378585321.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 194, + 295, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 295, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 295, + 338 + ], + "type": "text", + "content": "tial information of the target concept can be obtained from the images. However, their performance is quite poor when images of the target concept mentioned in the question are not available. MyVLM performs well in visual question answering but does not support text-only question answering. Yo'LLaVA excels in text-only question answering, but its performance is still limited by the insufficient information provided by the learned tokens of a concept. In contrast, our models demonstrate balanced performance in both visual and text-only question answering. By providing a single image, our RAP-LLaVA surpasses baseline methods and achieves performance comparable to that of GPT-4V." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 339, + 295, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 295, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 295, + 518 + ], + "type": "text", + "content": "Visual Recognition. We also evaluate the models' recognition abilities for a more comprehensive comparison. MLLMs are required to determine whether a personal concept is present in an image. We query them with \"Is in the image? Answer with a single word.\", where is replaced by corresponding concept name. For positive images, the desired response is \"Yes\" and \"No\" for negative. Results show that without knowledge of personal concepts, the vanilla LLaVA consistently produces negative responses. After training on target concepts, LLaVA-LoRA, MyVLM and YoLLaVA tend to give positive responses, but struggle to differentiate between similar concepts, resulting in weaker performance on negative images. Our models demonstrate exceptional performance in both positive and negative scenarios, achieving the best overall results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 527, + 149, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 527, + 149, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 527, + 149, + 540 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "content": "Influence of Number of Learned Concepts. In real-world scenario, users' personal databases typically expand over time. Next, we evaluate the performance of various methods with varying numbers of learned concepts. We extend the database with hundreds of new concepts selected from the RefCOCO dataset [20], ensuring no overlap with the test dataset. For LLaVA-LoRA and MyVLM, we provide images containing the target concepts along with their captions as training data, and assess models' performance on the original test dataset. The results are presented in Figure 4. More learned concepts result in increased recognition errors, leading to a decline in performance for each model. Our RAP-MLLMs maintain the highest performance under different settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "Generation Ability of MLLM. We skip the recognition and retrieval processes, providing the MLLM with relevant information of each concept present in the image to evaluate the generation capability of the trained MLLM. The results, shown in Table 5, indicate that when relevant concept information is supplied, our RAP-LLaVA achieves superior generation performance, obtaining " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " precision without outputting irrelevant concepts as well as a higher recall rate." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 167, + 553, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 167, + 553, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 553, + 287 + ], + "type": "text", + "content": "Text Information. We remove additional text information to examine its impact on personalization. The results are shown in Table 5 and 7 (Appendix). This additional text provides extra information that helps the model understand specific concepts, effectively improving the accuracy of the answers and benefiting personalized generation. Furthermore, it is especially helpful for question answering, as it can provide information not directly available from the image, such as a user's age and hobbies, or a pet's preferred food, as shown in the example in Table 12 of the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 288, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 288, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 553, + 407 + ], + "type": "text", + "content": "Dataset Composition. We conduct experiments to assess the contribution of each component in our dataset. First, we remove data generated through data augmentation and train the model. The results displayed in Table 5 indicate an obvious decrease in the recall metric for image captioning, resulting in a lower overall performance. We further exclude constructed negative samples from the dataset and retrain the model, then we find that it performs poorly on precision metric. This suggests a diminished ability to discriminate against noise concepts not present in the image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 407, + 553, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 553, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 553, + 502 + ], + "type": "text", + "content": "Additional Ablation. We conduct ablation studies on retriever's performance, and examine the impact of retrieving different numbers of concepts. We also evaluate models' performance on several multimodal benchmarks, and the results demonstrate that RAP-LLaVA retains most general knowledge of the original LLaVA, while achieving superior performance in knowledge intensive tasks. Due to space limit, we put the results in Appendix Section B.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "spans": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 534, + 553, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 553, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 553, + 665 + ], + "type": "text", + "content": "In this paper, we introduce the RAP framework for personalizing MLLMs. This framework enables MLLMs to understand infinite user-specific concepts, generate personalized captions and respond to user-related queries. To enhance the quality of the generated content and better align outputs with user configuration, we curate a large-scale dataset for personalized training of MLLMs and train a series of MLLMs to function as personalized assistants. Experimental results show that RAP-MLLMs achieve exceptional performance in various personalized generation tasks, while allowing real-time adjustments to generation settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14545" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 146 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 146 + ], + "type": "text", + "content": "[1] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. 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(a) An ensemble of arbitrary shapes casting the shadow of alphabets CVPR and numbers 2025, (b) a set of irregular objects packed inside a face-shaped container, (c) an assembly of parts of a vessel obtained through multi-view shadow guidance via RASP." + ], + "image_footnote": [], + "bbox": [ + 93, + 277, + 903, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 510, + 326, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advancements in learning-based methods have opened new avenues for exploring and interpreting art forms, such as shadow art, origami, and sketch art, through computational models. One notable visual art form is 3D Anamorphic Art in which an ensemble of arbitrarily shaped 3D objects creates a realistic and meaningful expression when observed from a particular viewpoint and loses its coherence over the other viewpoints. In this work, we build on insights from 3D Anamorphic Art to perform 3D object arrangement. We introduce RASP, a differentiable-rendering-based framework to arrange arbitrarily shaped 3D objects within a bounded volume via shadow (or silhouette)-guided optimization with an aim of minimal inter-object spacing and near-maximal occupancy. Furthermore, we propose a novel SDF-based formulation to handle inter-object intersection and container extrusion. We demonstrate that RASP can be extended to part assembly alongside object packing considering 3D objects to be \"parts\" of another 3D object. Finally, we present artistic illustrations of multi-view anamorphic art, achieving meaningful expressions from multiple viewpoints within a single ensemble.", + "bbox": [ + 88, + 542, + 485, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 510, + 643, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For centuries, artists have used their expressions to redefine the boundaries of visual art, demonstrating how art shapes reality and influences human perception. Their work has also broadly impacted technology, design, and engineering. In this work, we explore using a unique visual art form, 3D Anamorphic Art, to tackle challenges in irregular object packing and extend this approach to part assembly.", + "bbox": [ + 511, + 537, + 906, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Interestingly, we are not alone in using (and, in fact, developing) artistic expressions to address applications in computer vision. For example, DeepDream [24] uses GAN-based style transfer to apply the style of classical paintings, like those of Van Gogh or Picasso, to contemporary images. RePaint [34] leverages deep learning and 3D printing to replicate the colors and textures of paintings by optimizing ink layering. ScribGen [7] creates human-like scribbles and hand-strokes in different styles. Beyond images, researchers have expanded artistic techniques into 3D analysis and understanding, as in Shadow Art [23], which uses shadows for 3D reconstruction, sketch-based 3D generation [32], expressive hand movements [8], and the design of knot configurations for realistic visual effects [9]. In this work, we draw upon insights from 3D Anamorphic Art to address an important problem of packing arbitrarily shaped objects within a 3D bounding volume (or container). Packing has", + "bbox": [ + 511, + 643, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution | Project Page", + "bbox": [ + 114, + 887, + 300, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5849", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ed181a5c529501528c2e440f17ff0d4a4513ec74143fc7f7746b7eb152eda7b5.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 171, + 175 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/88fdc997a219ab0533ee43f2da5ec0887af59bcfce7a46d7c892161f3c0d93a5.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 174, + 93, + 246, + 172 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/25570491d4922915444470924dbb9649ea15ce8f2b2c4244bbcb2b9ad4c8b79a.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 248, + 89, + 338, + 175 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dd1afea0c1a4d041de278c0beef03f358d7f7bb7473fe9a9f0bfab652deb438e.jpg", + "image_caption": [ + "(d)", + "Figure 2. Illustration of 3D Anamorphic Art (a, b): Portrait of Nikola Tesla and Bedrich Smetana by Patrick Proško and Shadow Art (c, d): Dirty White Trash and Wild Mood Swing by Tim Nobel and Sue Webster." + ], + "image_footnote": [], + "bbox": [ + 339, + 90, + 478, + 176 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "numerous practical applications, spanning fields such as combinatorial optimization [22, 33], computational geometry [12, 20], computer vision and graphics [2, 18, 31], machine learning [11, 46], robotics [35, 38, 44], and logistics and manufacturing [47].", + "bbox": [ + 89, + 287, + 482, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Anamorphic Art. 3D Anamorphic Art involves arranging objects in 3D space such that the arrangement appears coherent and meaningful only from the specific viewpoint(s). In contrast, from any other view, it appears random. For example, artist Patrick Proško used this technique at the Illusion Art Museum Prague by arranging electrical appliances to form a portrait of Nikola Tesla [28] (Figure 2 (a)) and arranging musical instruments to create a likeness of the musician Bedřich Smetana [29] (Figure 2 (b)). This concept also extends to shadows cast by such arrangements under particular camera-light configurations. For instance, artists Tim Noble and Sue Webster created Dirty White Trash [25] and Wild Mood Swings [26], where carefully arranged trash and wooden pieces cast shadows of people sitting beside each other (see Figure 2 (c, d)). Whether through perspective views from specific viewpoints or shadows created under particular camera-light configurations, these projections reveal valuable insights about the arrangement of objects in 3D space.", + "bbox": [ + 89, + 366, + 482, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Relation with Object Packing. Consider a cuboidal bounding volume (or container), as depicted in Figure 3. When fully packed, this cuboid would appear as a rectangle or square upon being viewed orthographically along any of its faces. Similarly, it would cast rectangular or square shadows under the same viewing configuration. Ideally, gaps between the objects would appear as holes in the shadow from at least one perspective. By considering these shadows (technically binary images or silhouettes of the packed state) as target projections, we aim to arrange arbitrarily shaped elements within a bounding volume, thereby tackling the packing problem.", + "bbox": [ + 89, + 656, + 482, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Interestingly, this approach also allows for bounding volumes of arbitrary shapes, where the target projections are simply the volume's appearance from multiple viewpoints. If the elements to be arranged are whole 3D objects, this", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5a2918fa8318c869725fbaf88d68f2144c7250fc184def3f2792145e819d1578.jpg", + "image_caption": [ + "Objects to be packed" + ], + "image_footnote": [], + "bbox": [ + 516, + 97, + 653, + 161 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/39b96b898f2663589c51511e825836e39c8f9b53620e648fe84db223c87e4b69.jpg", + "image_caption": [ + "Packed arrangement", + "Figure 3. An example depicting the packed state of a cuboidal container and the associated silhouettes/shadows." + ], + "image_footnote": [], + "bbox": [ + 663, + 88, + 803, + 167 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ab13742bc1c0cc2a578b37de99f5514875e75e784c6472d7721d65329eb80aef.jpg", + "image_caption": [ + "Target Shadows" + ], + "image_footnote": [], + "bbox": [ + 813, + 90, + 903, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "approach addresses the irregular object packing problem. However, if these elements are \"parts\" of another object altogether, it naturally extends to the part assembly problem.", + "bbox": [ + 511, + 244, + 903, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key challenge in existing packing methods is managing overlaps or intersections among the elements to be packed. While some methods focus on simple geometries like cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or rely on assumptions of convexity or concavity in polyhedrons [19, 30, 37], often using simple heuristics [17, 27], others handle irregular shapes by employing voxelized representations [1, 6], which tend to be susceptible to approximation errors. This work introduces a signed-distance field (SDF) approach to manage inter-object intersection and container extrusion.", + "bbox": [ + 511, + 291, + 905, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. In this work, we introduce RASP - Revisiting 3D Anamorphic art for Shadow-guided Packing of Irregular Objects. Given a set of arbitrarily shaped objects, a bounding volume (or container), and information about the appearance of its projection/shadows from different viewpoints in the packed state:", + "bbox": [ + 511, + 457, + 905, + 547 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a differentiable rendering-based framework to tackle irregular object packing by drawing inspiration from 3D Anamorphic Art. Our goal is to achieve near-maximal occupancy and minimal inter-object spacing within a known bounding volume.", + "- We present a novel SDF-based approach to manage interobject intersections and object-container extrusions, enhanced by an image-based loss function.", + "- We demonstrate that RASP can also be applied to part assembly without the need for explicit 3D ground truth supervision. Additionally, we illustrate compelling visual effects that cater to multi-view anamorphic art.", + "- To the best of our knowledge, this is the first approach to address packing (and part assembly) using only shadows or projections, guided by the principles of differentiable rendering." + ], + "bbox": [ + 513, + 550, + 903, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through this work, we push the boundaries of 3D anamorphic art to address an important research question: can shadows be used to automatically find an optimal arrangement of arbitrarily shaped 3D objects within a bounded volume? While our framework aims to provide practical solutions, it does not always yield an optimal arrangement due to the NP-hard nature of the packing prob", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5850", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/43a03c5139264eff03d497eda1542f90a6019900a9637102f4e5e015d2e43ad2.jpg", + "image_caption": [ + "Figure 4. The proposed differentiable rendering-based pipeline for RASP. We use Adam optimizer with a learning rate of $1e - 2$ to $1e - 4$ over 1000 iterations. Packing the Kitchen dataset (106 objects, 80000 grid points) takes nearly 17 minutes, and reassembly for each object in the Fantastic Breaks dataset (2 parts, 80000 grid points) takes under 3 minutes." + ], + "image_footnote": [], + "bbox": [ + 101, + 92, + 898, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lem [10]. Nonetheless, this work introduces a new perspective on solving the 3D packing and arrangement problem using shadows as a guiding mechanism.", + "bbox": [ + 88, + 385, + 482, + 433 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 89, + 448, + 241, + 464 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object packing has been addressed using heuristic-based, model-based, learning-based, or policy-based (online) object packing. Several methods have assumed simple object geometries, such as cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or leverage convexity and/or concavity in polyhedrons [19, 30, 37]. This section primarily discusses the methods dealing with irregular object packing.", + "bbox": [ + 88, + 474, + 482, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Heuristic-based Methods. Several previous attempts at object packing were primarily based on heuristic strategies. One method proposed by Wang et al. [40] sequentially places objects employing the Deepest Bottom Left Fill (DBLF) heuristic strategy. However, it is shown to create holes, leading to empty spaces. Later, Wang and Hauser [39] addressed this limitation by reducing unfilled gaps through height-map minimization, which in itself ignores the difference between positions at the same level. HAPE3D [19], another heuristic-based algorithm, deploys the principle of the minimum total potential energy for irregular polyhedrons. Even after allowing free translations and rotations, it fails to achieve high packing density. Lamas et al. [15] voxelized irregular objects and used metaheuristic algorithms to optimize voxel representation that is limited due to memory constraints. Heuristic-based methods generally apply well to objects with only a few facets and struggle to achieve a high packing density while dealing with complex irregular objects.", + "bbox": [ + 89, + 597, + 482, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning-Based Methods. The key challenge for pack", + "bbox": [ + 109, + 885, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing irregular objects is to handle object collision detection or intersection/overlap avoidance. Several different geometric representations of objects (say, objects tightly bound by a sphere or cuboid [45]) have been assumed by different methods for collision detection and packing optimization. Romanova et al. [1] pose the packing problem as a nonlinear optimization problem and propose quasi-phi functions for simple concave polyhedrons to describe nonoverlapping and distance constraints. However, obtaining a local optimum takes longer, even with free translations and rotations. A few works [2, 45] learned to decompose the object into multiple small parts to perform packing to reduce the supporting materials, build time, and assembly costs of 3D printing. While [2] used voxel-based representation, [45] used level sets to represent the object parts.", + "bbox": [ + 511, + 385, + 903, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moreover, Zhao et al. [47] and Zhuang et al. [48] divide the objects into convex shapes for efficient collision detection in physical simulation and pack the objects either using shaking of the container as per the dynamic principle or reinforcement learning in an online manner, respectively. Our work does not focus on online packing. Cui et al. [5] performed efficient collision metric computation in the spectral domain using voxel representation and Fast Fourier Transform (FFT) for discrete placement search. They deploy a greedy strategy to sort objects by volume from largest to smallest and then pack sequentially to minimize the distance between the new and already placed objects at each placement.", + "bbox": [ + 511, + 613, + 903, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The closest to our setting is the work by Ma et al. [20] that optimizes the orientation and position of the objects from their initial placement. However, their approach is multi-stage, involving combinatorial optimization that includes object swapping, enlargement, and replacement to reduce the gaps between the objects. Furthermore, they", + "bbox": [ + 511, + 810, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5851", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/23d7e04cae6d09488f7cad8a252a4a472a6d630402408a73d79c9cfdbfbeb9dc.jpg", + "image_caption": [ + "Figure 5. (a) Target shadow a duck-shaped container, optimized arrangement with mesh intersections. Mesh enclosed within (b) sphere and (c) cube where the intersection region doesn't include object meshes. (d) SDF of two non-intersecting and intersecting objects (intersecting points are marked in red), and SDF transformation within the container." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 343, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/66a5441b7fbc1e7a052ebeb0c6e6958820d35a9ef0999aaf7175501356c335cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 88, + 607, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f78328b8a77e8b1dd193f435661d99942a845baba417f2c3bbb9cc079a3f39f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 89, + 893, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "also minimize the height of a container to obtain an optimal one through binary search. Due to repeated processing, the method is heavily time-consuming. In contrast, given a set of irregular objects, ours is a single-stage end-to-end optimization pipeline that performs packing only via 2D shadow guidance without any intense calculation within the 3D bounding volume. While Ma et al. [20] have the information about the object set and process only one object at a time, sequentially determining the initial placement, our proposed method considers a set of objects at a time.", + "bbox": [ + 88, + 268, + 483, + 420 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 431, + 181, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 89, + 455, + 200, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key idea of our work is to arrange a set $S$ of arbitrarily shaped 3D objects within an arbitrarily shaped container $\\mathcal{C}$ such that the resulting arrangement casts $K$ different shadows (projections) when viewed from $K$ different directions using a differentiable rendering-based optimization pipeline. Interestingly, the problem has two interpretations depending on how we consider the set $S$ .", + "bbox": [ + 88, + 477, + 482, + 583 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) 3D Packing problem: when $S$ contains arbitrarily shaped 3D objects and $C$ is the bounding container within the viewing volume.", + "(b) Part Assembly problem: when $S$ contains \"parts\" of a 3D object $(O)$ where this object $O$ itself is treated as the container $\\mathcal{C}$ ." + ], + "bbox": [ + 89, + 583, + 482, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the case of packing, we might not always have a ground truth or a unique solution, i.e., objects can be arranged in multiple optimal ways to maximize occupancy and minimize spaces. However, we have a ground truth shape in a part assembly whose parts can be assembled only in one way. We demonstrate how this is implemented in Section 4. Overall, we propose a differentiable-rendering-based framework that naturally caters to both these requirements, in addition to generating multi-view anamorphic art. Inspired by computational visual arts, some of the recent works based on shadow art [8, 9, 23] have demonstrated the potential of 3D shape understanding, analysis, and reconstruction through shadows. In this work, we take the first step towards leveraging the benefit of differentiable rendering and principles of visual arts [42] to propose shadow-", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "based 3D packing and part assembly.", + "bbox": [ + 511, + 268, + 759, + 284 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Proposed Approach", + "text_level": 1, + "bbox": [ + 511, + 291, + 702, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The flow of the proposed methodology has been outlined in Figure 4. Consider a set of $N$ arbitrarily shaped objects $\\mathcal{S} = \\{O_1, O_2, \\ldots, O_N\\}$ such that each $O_i$ is represented as a triangular mesh, an arbitrarily shaped bounding container $\\mathcal{C}$ located inside the camera viewing volume $\\mathcal{V}$ , and shadow projection configuration $\\mathcal{X} = \\{X_k = (I_k, P_k) | k = 1, 2, \\ldots, K\\}$ . Here, $\\{I_k\\}_{k=1}^K$ are the target images under the camera configuration $\\{P_k\\}_{k=1}^K$ . Essentially, the camera configuration $P_k = (R_k, t_k)$ corresponds to the camera extrinsic parameters associated with image $I_k$ . With $\\mathcal{S}$ , $\\mathcal{C}$ , and $\\mathcal{X}$ as input to the differentiable renderer $\\mathcal{R}$ , the objective here is to learn the optimal arrangement of objects in set $\\mathcal{S}$ inside the container $\\mathcal{C}$ placed within the viewing volume $\\mathcal{V}$ such that the resulting images $\\{\\widehat{I_k}\\}_{k=1}^K$ rendered under camera configurations $\\{P_k\\}_{k=1}^K$ are close to the corresponding target images $\\{I_k\\}_{k=1}^K$ . From the shadow's perspective, the target images are silhouettes, and we assume that the light (to cast the shadows) will be co-located with the camera. Finding the arrangement of objects is equivalent to finding the rigid transformation, i.e., rotation and translation $\\{R_i, t_i\\}_{i=1}^N$ of each object $O_i$ in set $\\mathcal{S}$ . We use quaternions for obtaining rotations - (a) to avoid gimble lock through other representations like axis-angle rotation or rotation composition of rotation along $x - y - z$ axes, (b) for smooth interpolation, and (c) to learn a smaller number of parameters compared to the rotation matrices. Specifically, we obtain the angle of rotations across each of the coordinate axes and convert them to quaternion representation for optimization.", + "bbox": [ + 511, + 313, + 906, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1. Objective Function", + "text_level": 1, + "bbox": [ + 511, + 757, + 692, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a combined loss function consisting of an SDF-based intersection loss, an image-based loss, and an object-container extrusion loss, as per Equation 1.", + "bbox": [ + 511, + 776, + 905, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s i l}} + \\mathcal {L} _ {\\text {i s}} + \\lambda \\mathcal {L} _ {\\text {e x t}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 830, + 903, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we set $\\lambda = 0.001$", + "bbox": [ + 511, + 854, + 671, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image-based (Silhouette) Loss. A straightforward approach is to optimize each object's rotation and translation", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5852", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/10f7529cc0d25d66feb6ce70bbb867e8f9279a56d418c8cdf2eb1d0b76152541.jpg", + "image_caption": [ + "Figure 6. Visualization of 3D Object packing into a cuboidal container using RASP over four different object categories from [47]. Each instance is labeled with the number of objects packed in the container and the packing density." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 290, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0fd64d3df27779b54491466b2da58f39f9d37047776dc89333f0dcd0c563577d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 308, + 90, + 493, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f4647124650eded28b9ae09d6857990c6a707fa29aa2886cdf0043e894c41543.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 90, + 705, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fbc55d1d0af1854fdf4cf8c1ab759343cc17351ee4a68964e4c00f22017bc840.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 90, + 901, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/921f6060fd13b4bf74514ca2458441bb1ea7753524c5fb180880105ac07f19f5.jpg", + "image_caption": [ + "Figure 7. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + ], + "image_footnote": [], + "bbox": [ + 91, + 292, + 486, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "parameters based on image rendering loss, such as mean squared error, as per Equation 2.", + "bbox": [ + 89, + 518, + 482, + 550 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s i l} = \\frac {1}{M N K} \\sum_ {k = 1} ^ {K} \\sum_ {i = 1} ^ {M N} \\left| \\left| I _ {k} (i) - \\widehat {I} _ {k} (i) \\right| \\right| _ {2} ^ {2} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 560, + 482, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $MN$ is the total number of pixels in the image. As shown in Figure 5 (a), the projection of the arrangement may appear feasible (apart from a few gaps where more objects could fit), but in 3D, objects can still intersect within a duck-shaped container.", + "bbox": [ + 89, + 613, + 483, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the loss functions should penalize mesh intersections. However, handling mesh intersections is complex; some methods [14] detect intersections by evaluating each triangular face of one mesh against others, which is computationally costly and impractical for large numbers of meshes. To simplify intersection computation, some approaches enclose objects within unit spheres or cubes, finding intersections among these simpler bounding shapes [45]. Although faster, this approach often fails with asymmetrically shaped objects, as intersections between bounding spheres or cubes may not correspond to intersections among the actual object meshes, as shown in Figure 5 (b, c). This can lead to excessive penalization of intersections, causing the network to push objects apart and create unnec", + "bbox": [ + 89, + 689, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae6bfa2782cad2693fe2b806d14034a6cdee34d1191fdb7fb886e8c35d38e7b3.jpg", + "image_caption": [ + "Figure 8. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + ], + "image_footnote": [], + "bbox": [ + 514, + 297, + 893, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "essary gaps.", + "bbox": [ + 511, + 551, + 596, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intersection Loss. To overcome these challenges, we propose an SDF-based approach to handle both object-object intersections and object-container extrusion. The signed distance field (SDF) provides the shortest distance from a point to the surface, with a negative sign indicating the point is inside and a positive sign indicating it is outside the object. Specifically, we pre-compute the SDF of each mesh (using [41]) at fixed query points within the container $\\mathcal{C}$ (a few milliseconds on GPU) and deform the SDFs with every update of the learned rotation and translation parameters. Rather than recalculating the SDF for each rigid transformation, we warp the previous SDF using a linear transformation to match the new configuration, as shown in Figure 5 (d). The degree of intersection, thus, can be determined by identifying points where more than one object has a negative SDF value, as marked in red in Figure 5 (d).", + "bbox": [ + 511, + 566, + 906, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let the SDF of the object $O_{i}$ at a point $\\mathbf{p}$ after a rigid transformation (updated rotation and translation) has been applied to $O_{i}$ be denoted by $\\widetilde{S}_{O_i}(\\mathbf{p})$ . One could simply consider the amount of intersection to be proportional to the number of objects under intersection at any point within the container, i.e., $D_{is}(\\mathbf{p}) = |\\{i\\in \\{1,2,\\dots N\\} |\\widetilde{S}_{O_i}(\\mathbf{p}) < 0\\} |.$", + "bbox": [ + 511, + 810, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5853", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/396e46554280870483ff91774d1aace40eea7d52724f729adb772d8da01476ea.jpg", + "image_caption": [ + "Figure 9. Illustration of packing of 24 cubes, each of dimensions $1 \\times 1 \\times 1$ cubic units, into a container of dimensions $6 \\times 6 \\times 6$ cubic units, with varying silhouette widths to simulate physically correct packing for $N < N_{max}$ ." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 472, + 189 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, we observed that considering the SDF value instead of just the count provides smoother guidance to resolve the intersections. Therefore, we define the degree of intersection $D_{is}(\\mathbf{p})$ as the sum of the (negative of) SDFs of the objects that contain point $\\mathbf{p}$ within them at every optimization step, such that,", + "bbox": [ + 89, + 277, + 483, + 369 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {i s} (\\mathbf {p}) = \\sum_ {\\left\\{\\forall O _ {i} \\mid \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) < 0 \\right\\}} - \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 378, + 482, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $D_{is}(\\mathbf{p}) > 1$ indicates that there is an intersection of at least two objects at the point, and $D_{is}(\\mathbf{p}) = 0$ represents that the point $\\mathbf{p}$ is not inside any object. Considering the set of query points $\\mathcal{C}_p$ inside the container $\\mathcal{C}$ , the intersection loss is defined as per Equation 4.", + "bbox": [ + 89, + 430, + 483, + 506 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i s} = \\sum_ {\\mathbf {p} \\in \\mathcal {C} _ {p}} D _ {i s} (\\mathbf {p}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 517, + 482, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Container Extrusion Loss. Let $V_{i}$ be the set of vertices of the triangular mesh corresponding to the object $O_{i}$ and $S_{\\mathcal{C}}$ be the SDF of the container $\\mathcal{C}$ . We define the container extrusion loss as per Equation 5", + "bbox": [ + 89, + 563, + 483, + 625 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e x t} = \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {v} \\in V _ {i}} \\max (- \\epsilon , S _ {\\mathcal {C}} (\\mathbf {v})) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 635, + 482, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $\\epsilon$ , the distance between a vertex and the container's boundary, creates a \"buffer zone\" around the container boundary to control when the extrusion loss begins to be active. While a higher value of $\\epsilon$ hinders the movement of objects inside the container, a very small value leads to portions of objects suddenly extruding out of the container boundary, leading to an unstable optimization. We find $\\epsilon = 0.01$ to be a reasonable value that avoids penalizing objects that are slightly inside the container but still close to the boundary. We observed that in some cases, silhouette loss was just enough to contain the objects with the container, especially for simple shapes. However, for more irregular shapes with asymmetric and skewed spread, extrusion loss proved to be helpful.", + "bbox": [ + 89, + 688, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c4900ca9642bc614d3c51e632f4a02d53ad0b9b6aa71d418888638c25ff28ae3.jpg", + "image_caption": [ + "Figure 10. Illustration of packing arbitrarily shaped objects into arbitrarily shaped containers. The initial containers, the set of object shapes to be packed, and the final packed configuration are shown in the figure." + ], + "image_footnote": [], + "bbox": [ + 517, + 89, + 903, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 289, + 645, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we showcase the results obtained through the RASP framework for irregular object packing drawing parallels with 3D Anamorphic art. Furthermore, we extend RASP to applications like part assembly and creating artistic illustrations.", + "bbox": [ + 511, + 314, + 906, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Irregular Object Packing", + "text_level": 1, + "bbox": [ + 511, + 398, + 745, + 415 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For 3D object packing, we demonstrate the results majorly on the objects from the IR-BPP dataset [47], which contains objects from four categories: General, Kitchen, ABC, and Block Out. A few other illustrations also include objects from the VOLMAP dataset [3] and SilNet dataset [49].", + "bbox": [ + 511, + 419, + 905, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following the existing literature of 3D object packing, we define the packing efficiency/density $(\\rho)$ , as per Equation 6.", + "bbox": [ + 511, + 496, + 905, + 537 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\rho = \\sum_ {O _ {i} \\in \\mathcal {C}} \\frac {\\left| O _ {i} \\right|}{\\left| \\mathcal {C} \\right|} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 537, + 903, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $|O_i|$ and $|\\mathcal{C}|$ are the volume of the $i^{th}$ object and container volume, respectively.", + "bbox": [ + 511, + 579, + 905, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 6, compares the packing density of irregular 3D objects from different categories into a typical cuboidal container. Interestingly, RASP does not require any regularity in object shapes and can handle arbitrary shapes of different sizes, achieving reasonably good packing configurations.", + "bbox": [ + 511, + 609, + 905, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Deciding the number of objects that can be maximally packed within a container is crucial for optimal packing. To start with, we decide the initial number of objects as $N_{init}$ based on the average volume of the objects and the container volume, such that $N_{init} = \\frac{|C|}{|O|_{avg}}$ . Consider $N_{max}$ as an unknown upper bound, i.e., the maximum a physical container can accommodate. If $N_{init} < N_{max}$ , we draw another set of $N_{k}$ objects from the pool (if available) and again optimize the arrangement with $N_{init} + N_{k}$ based on the target silhouettes of projection. In case this exceeds $N_{max}$ , the remaining objects either start extruding out of the container or intersecting heavily within the container depending on the predominance of $\\mathcal{L}_{is}$ or $\\mathcal{L}_{ext}$ , respectively. All the results correspond to $N = N_{max}$ objects that can maximally", + "bbox": [ + 511, + 686, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5854", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c705e941fff4d2853f3443fa07d69bf188b2d458f6d35867b05ea6ef92c980ab.jpg", + "image_caption": [ + "Figure 11. Extending RASP to perform part reassembly of broken objects. The figure showcases the target silhouettes and broken parts reassembled using RASP." + ], + "image_footnote": [], + "bbox": [ + 98, + 93, + 352, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6c567d3784fd3a4a121f8fce875b1ecceb40ab40c31b61e27da633d9ea2ae87d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 370, + 93, + 622, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b03a1eafa78e369b79456ca572fb23e903f9b76a0c0d1344c92d99f07fcf0c5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 95, + 895, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fit inside the container with no intersection, a condition essential for real-world applicability. Moreover, the objects are randomly initialized within the container before optimization. We discuss the effect of different initialization strategies in the supplementary.", + "bbox": [ + 89, + 247, + 482, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Due to silhouette or shadow-guided optimization, the resulting arrangement can sometimes be physically inaccurate. As shown in Figure 9, when the number of objects $N$ is less than the maximum capacity $N_{max}$ , the arrangement often floats within the container rather than settling at the bottom. While such effects are inherent to this type of optimization-based framework, we demonstrate that merely adjusting the width of the silhouettes would effectively constrain the objects to rest at the bottom of the container in Figure 9 progressively.", + "bbox": [ + 89, + 324, + 483, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Arbitrarily Shaped Container. Owing to its design to derive insights from the projected silhouettes, RASP can also accommodate arbitrarily shaped containers, as shown in Figure 1 (b) and Figure 10. Similar to multi-view shape optimization, the target shadows are essentially the silhouettes of the container from 5 different views. Figure 10 depicts the packing on donut-shaped and squirrel-shaped containers.", + "bbox": [ + 89, + 476, + 483, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of loss terms. Figure 8 (top) shows the convergence of each of the loss terms for illustrations in Figure 6 and Figure 10. The intersection density for all the results is zero, offering a multi-view consistent, intersection-free/non-overlapping configuration. Figure 8 (bottom) also illustrates the impact of different loss terms in addition to observations in Figure 5 for $\\mathcal{L}_{sil}$ vs $\\mathcal{L}_{sil} + \\mathcal{L}_{in}$ . Overall, we find that extrusion term $\\mathcal{L}_{ext}$ acts as a regularizer, preventing objects from drifting too far apart to avoid intersections. While the intersection remains zero without $\\mathcal{L}_{ext}$ , its inclusion improves the rendered silhouette by reducing $\\mathcal{L}_{sil}$ . Notably, objects are positioned closer together when $\\mathcal{L}_{ext}$ is applied.", + "bbox": [ + 89, + 598, + 482, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with existing methods. Out of several relevant works on 3D object packing (as described in Section 2), the work by Ma et al. [20] is the closest to our optimization setup (not guided by shadows) whose setup is different from RASP since it involves swapping, replacement with new objects, and object enlargement - which we believe is not practical in a real-world setup where we cannot", + "bbox": [ + 89, + 795, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "alter the object dimensions. However, since their implementation is unavailable online, we choose to quantitatively compare the average packing efficiency across different objects. Although different from ours, we also compared our average packing efficiency of a physically inspired reinforcement learning-based online packing method by Zhao et al. [47] over their dataset to establish the efficacy of our optimization-based methods learning solely from 2D image guidance. Zhao et al. [47] look at only one or a few objects at a time, and packing efficiency is dependent on the sequence in which the objects arrive. Moreover, the object placement is guided by the dynamics and constraints of physics. In contrast, RASP - an offline method, takes a more global standpoint by optimizing all $N \\leq N_{max}$ objects at a time. Overall, RASP obtains an average of $45\\%$ occupancy over the four different categories of the IR-BPP dataset [47] which is better than Ma et al. [20] (34%) and drops below that of Zhao et al. [47] (51.9%) evaluated over the objects from online packing dataset. Moreover, Ma et al. [20] bears an average optimization time of 40.55 minutes while RASP achieves the same in $\\sim 15$ minutes.", + "bbox": [ + 511, + 247, + 906, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For a qualitative comparison over samples from IR-BPP dataset, we adapt [47] to align closest to our setting. Specifically, we generate 100 random sequences of the same set (and same number) of objects from each IR-BPP dataset category (as in Figure 6) and report the best configuration to compare with RASP in Figure. 7. Due to implementation constraints of [47], we could not assign different colors to objects or obtain multiple views of the packed arrangement of [47], and hence, we compared only the top view. RASP performs similar to or slightly better than the physics-aware method for the same object set.", + "bbox": [ + 511, + 565, + 908, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. 3D Part Assembly", + "text_level": 1, + "bbox": [ + 511, + 741, + 689, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Part assembly using RASP also shares similarities with multi-view geometry optimization. However, instead of optimizing a single shape, RASP learns the rigid transformations of different parts of a single shape to obtain a 3D consistent arrangement across all the views. For demonstrating part assembly, we used the *Fantastic Breaks* dataset [16] that consists of paired 3D scans of real-world broken objects and their complete counterparts. Figure 11 demonstrates some qualitative results on reassembling broken ob", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5855", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e4a6c09ceec5c20349d31750e436a4a69642aa3d6d837dede9919d293f5040d3.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 93, + 89, + 272, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cad65da15629067b44ad15720cd42aea7c9af74b27dd7680b2ab487e1c487118.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 90, + 364, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0c7f60b4aa1e1ca7d53310a61bc9251dbff8effbb6882587513f3c768980016f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 90, + 454, + 166 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15d872a65bddc4f51a98d693b5c83ba605dc62690f5ed1ab3d64a9ec77de79a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 460, + 90, + 527, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b062edc091b46cb609c45d6e12c16cda577e5f756169a30590072673d6805e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 169, + 364, + 305 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2a958efa43803a3e1b6ed24124cbdc11b6702edf80ef61602381876d821332d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 169, + 452, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/091ab7586e0e77565a3de9a2338cfbb3b4d181d0c7c21456d8f2c92b77e9a39f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 460, + 169, + 524, + 232 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 292, + 238, + 364, + 305 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/559927167e6cbdf22a2f65657c727fd2899aebd3eead05534a3009430965a73a.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 372, + 238, + 452, + 305 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0de3cd7e3b2b6d868a7d128ad9563cf97fb0b47d0cbe72ec4510d13323d2fd54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 460, + 238, + 524, + 305 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fff5fabb63fd2c94777058a11d01cf1bc72f9ea14d292c015c50562cf45e818b.jpg", + "image_caption": [ + "(c)", + "Figure 12. (a) & (b) use objects from the Kitchen dataset to generate 2-view and 3-view 3D anamorphic art. (c) Multi-view pixelated portraits generated using RASP with artistic texture applied. (d) RASP recreates the famous cover page of the book Gödel, Escher, Bach by Douglas Hofstadter. The 3D and dynamic visualization of these and more related results are provided in the supplementary." + ], + "image_footnote": [], + "bbox": [ + 540, + 90, + 653, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2dffb58bd10748462ab55979316d98cca457b03f4dfc85b4c4d8390b9236a77.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 666, + 117, + 906, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "jects. Notably, it does so solely via silhouette guidance without the need for any explicit 3D ground truth supervision.", + "bbox": [ + 89, + 383, + 482, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Multi-view Anamorphic Art", + "text_level": 1, + "bbox": [ + 89, + 440, + 344, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also leverage RASP to reinterpret and construct different forms of multi-view anamorphic art. Thus far, we have seen that silhouettes or shadows do provide important cues for 3D arrangement. However, these binary images alone cannot create interesting artistic illustrations. Therefore, we also seek guidance from colored or textured images. Take, for example, the portrait of Nikola Tesla shown in Figure 2 (a). One approach would be to search for suitable objects and apply heuristic methods to arrange them in a way that recreates the portrait's appearance. Alternatively, one could collect and randomly arrange objects (like those in Figure 2 (c)) within the outline of the silhouette, then paint the arrangement to revive the essence of the portrait. Following the latter approach, RASP uses a two-stage optimization procedure, where first, it arranges the discrete objects in a 3D space through silhouette matching across a set of views and later performs rendering-based texture optimization (integrated as an add-on) over the finalized arrangement to match the target textures. Figure 12 (a) illustrates how this strategy allows RASP to recreate multi-view portraits of Nikola Tesla and Marie Curie across two non-orthogonal views that are $120^{\\circ}$ apart using objects from the Kitchen dataset. Furthermore, it also generates consistent ensembles that are meaningful across three non-orthogonal views, as shown in Figure 12 (b), giving a visually plausible appearance of Pokémon, Wall-e, and Minion. In figure 12 (c) we obtain 3D arrangements using binary images and then apply artistic textures to create unique 3D illustrations. The resemblance of the textured arrangement and the associated", + "bbox": [ + 89, + 462, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rendered images highlights the creative potential of RASP. In Figure 12 (d) we recreate the famous artistic cover page of the Book by Douglas Hofstadter featuring blocks casting shadows of the first letters of artists – Gödel, Escher, and Bach. Overall, RASP is a versatile optimization pipeline stressing on the fact that shadows do provide limited yet useful cues for 3D understanding and artistic exploration.", + "bbox": [ + 511, + 383, + 906, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 508, + 633, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce RASP, a differentiable rendering-based optimization framework for irregular 3D object packing, part assembly, and recreating artistic illustrations, taking guidance from images, whether in the form of binary silhouettes, textured RGB images, or simple portrait sketches. The current offline strategy does not account for physical dynamics, such as the influence of gravity on object placement. Additionally, RASP struggles with multi-part (more than 2 or 3 parts) part assembly, particularly symmetrical and/or identical parts. An interesting potential extension of this work would be to incorporate physics-based guidance for the packing to be more physically consistent. We believe that there are plenty of untapped capabilities in shadows that drive 3D understanding, and RASP presents a few of them. We anticipate that this work would attract researchers from different domains to use shadows or silhouettes for applications like partitioning and reconfiguration of complex 3D objects into simpler forms, multi-part part assembly, dynamic visual arts, CAD design, and handling non-rigid deformations.", + "bbox": [ + 511, + 536, + 906, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work is supported by the Prime Minister Research Fellowship (PMRF) grant and the Jibaben Patel Chair in Artificial Intelligence. We also thank Prajwal Singh, IIT Gandhinagar, for his valuable inputs.", + "bbox": [ + 511, + 839, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5856", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Thomas Byholm, Martti Toivakka, and Jan Westerholm. Effective packing of 3-dimensional voxel-based arbitrarily shaped particles. Powder Technology, 196(2):139-146, 2009. 2", + "[2] Xuelin Chen, Hao Zhang, Jinjie Lin, Ruizhen Hu, Lin Lu, Qi-Xing Huang, Bedrich Benes, Daniel Cohen-Or, Baoquan Chen, et al. Dapper: decompose-and-pack for 3d printing. ACM Trans. Graph., 34(6):213-1, 2015. 2, 3", + "[3] Gianmarco Cherchi and Marco Livesu. VOLMAP: A large scale benchmark for volume mappings to simple base domains. 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British Machine Vision Association and Society for Pattern Recognition, 2017. 6" + ], + "bbox": [ + 514, + 90, + 903, + 303 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5858", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RASP_ Revisiting 3D Anamorphic Art for Shadow-Guided Packing of Irregular Objects/aef7411d-a9ca-4b1d-a6a0-4ab29fc800b9_model.json b/2025/RASP_ Revisiting 3D Anamorphic Art for Shadow-Guided Packing of Irregular Objects/aef7411d-a9ca-4b1d-a6a0-4ab29fc800b9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1863e89279f89f771bba324c250df509d788b125 --- /dev/null +++ b/2025/RASP_ Revisiting 3D Anamorphic Art for Shadow-Guided Packing of Irregular Objects/aef7411d-a9ca-4b1d-a6a0-4ab29fc800b9_model.json @@ -0,0 +1,2332 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.13, + 0.852, + 0.177 + ], + "angle": 0, + "content": "RASP: Revisiting 3D Anamorphic Art for Shadow-Guided Packing of Irregular Objects" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.203, + 0.865, + 0.24 + ], + "angle": 0, + "content": "Soumyaratna Debnath\\(^{1*}\\) Ashish Tiwari\\(^{1*}\\) Kaustubh Sadekar\\(^{2}\\) Shanmuganathan Raman\\(^{1}\\) \n\\(^{1}\\)Indian Institute of Technology Gandhinagar \\(^{2}\\)Portland State University" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.242, + 0.828, + 0.258 + ], + "angle": 0, + "content": "{debnathsoumyaratna, ashish.tiwari, shanmuga}@iitgn.ac.in, ksadekar@pdx.edu" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.279, + 0.905, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.47, + 0.908, + 0.501 + ], + "angle": 0, + "content": "Figure 1. (a) An ensemble of arbitrary shapes casting the shadow of alphabets CVPR and numbers 2025, (b) a set of irregular objects packed inside a face-shaped container, (c) an assembly of parts of a vessel obtained through multi-view shadow guidance via RASP." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.511, + 0.327, + 0.527 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.544, + 0.486, + 0.862 + ], + "angle": 0, + "content": "Recent advancements in learning-based methods have opened new avenues for exploring and interpreting art forms, such as shadow art, origami, and sketch art, through computational models. One notable visual art form is 3D Anamorphic Art in which an ensemble of arbitrarily shaped 3D objects creates a realistic and meaningful expression when observed from a particular viewpoint and loses its coherence over the other viewpoints. In this work, we build on insights from 3D Anamorphic Art to perform 3D object arrangement. We introduce RASP, a differentiable-rendering-based framework to arrange arbitrarily shaped 3D objects within a bounded volume via shadow (or silhouette)-guided optimization with an aim of minimal inter-object spacing and near-maximal occupancy. Furthermore, we propose a novel SDF-based formulation to handle inter-object intersection and container extrusion. We demonstrate that RASP can be extended to part assembly alongside object packing considering 3D objects to be \"parts\" of another 3D object. Finally, we present artistic illustrations of multi-view anamorphic art, achieving meaningful expressions from multiple viewpoints within a single ensemble." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.511, + 0.645, + 0.527 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.538, + 0.907, + 0.644 + ], + "angle": 0, + "content": "For centuries, artists have used their expressions to redefine the boundaries of visual art, demonstrating how art shapes reality and influences human perception. Their work has also broadly impacted technology, design, and engineering. In this work, we explore using a unique visual art form, 3D Anamorphic Art, to tackle challenges in irregular object packing and extend this approach to part assembly." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Interestingly, we are not alone in using (and, in fact, developing) artistic expressions to address applications in computer vision. For example, DeepDream [24] uses GAN-based style transfer to apply the style of classical paintings, like those of Van Gogh or Picasso, to contemporary images. RePaint [34] leverages deep learning and 3D printing to replicate the colors and textures of paintings by optimizing ink layering. ScribGen [7] creates human-like scribbles and hand-strokes in different styles. Beyond images, researchers have expanded artistic techniques into 3D analysis and understanding, as in Shadow Art [23], which uses shadows for 3D reconstruction, sketch-based 3D generation [32], expressive hand movements [8], and the design of knot configurations for realistic visual effects [9]. In this work, we draw upon insights from 3D Anamorphic Art to address an important problem of packing arbitrarily shaped objects within a 3D bounding volume (or container). Packing has" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.888, + 0.302, + 0.901 + ], + "angle": 0, + "content": "*Equal Contribution | Project Page" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5849" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.172, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.179, + 0.142, + 0.189 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.094, + 0.247, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.179, + 0.218, + 0.189 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.09, + 0.339, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.179, + 0.303, + 0.189 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.091, + 0.48, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.179, + 0.419, + 0.189 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.2, + 0.483, + 0.255 + ], + "angle": 0, + "content": "Figure 2. Illustration of 3D Anamorphic Art (a, b): Portrait of Nikola Tesla and Bedrich Smetana by Patrick Proško and Shadow Art (c, d): Dirty White Trash and Wild Mood Swing by Tim Nobel and Sue Webster." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.289, + 0.483, + 0.365 + ], + "angle": 0, + "content": "numerous practical applications, spanning fields such as combinatorial optimization [22, 33], computational geometry [12, 20], computer vision and graphics [2, 18, 31], machine learning [11, 46], robotics [35, 38, 44], and logistics and manufacturing [47]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.367, + 0.483, + 0.655 + ], + "angle": 0, + "content": "3D Anamorphic Art. 3D Anamorphic Art involves arranging objects in 3D space such that the arrangement appears coherent and meaningful only from the specific viewpoint(s). In contrast, from any other view, it appears random. For example, artist Patrick Proško used this technique at the Illusion Art Museum Prague by arranging electrical appliances to form a portrait of Nikola Tesla [28] (Figure 2 (a)) and arranging musical instruments to create a likeness of the musician Bedřich Smetana [29] (Figure 2 (b)). This concept also extends to shadows cast by such arrangements under particular camera-light configurations. For instance, artists Tim Noble and Sue Webster created Dirty White Trash [25] and Wild Mood Swings [26], where carefully arranged trash and wooden pieces cast shadows of people sitting beside each other (see Figure 2 (c, d)). Whether through perspective views from specific viewpoints or shadows created under particular camera-light configurations, these projections reveal valuable insights about the arrangement of objects in 3D space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.657, + 0.483, + 0.838 + ], + "angle": 0, + "content": "Relation with Object Packing. Consider a cuboidal bounding volume (or container), as depicted in Figure 3. When fully packed, this cuboid would appear as a rectangle or square upon being viewed orthographically along any of its faces. Similarly, it would cast rectangular or square shadows under the same viewing configuration. Ideally, gaps between the objects would appear as holes in the shadow from at least one perspective. By considering these shadows (technically binary images or silhouettes of the packed state) as target projections, we aim to arrange arbitrarily shaped elements within a bounding volume, thereby tackling the packing problem." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Interestingly, this approach also allows for bounding volumes of arbitrary shapes, where the target projections are simply the volume's appearance from multiple viewpoints. If the elements to be arranged are whole 3D objects, this" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.098, + 0.655, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.168, + 0.641, + 0.18 + ], + "angle": 0, + "content": "Objects to be packed" + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.089, + 0.804, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.17, + 0.784, + 0.18 + ], + "angle": 0, + "content": "Packed arrangement" + }, + { + "type": "image", + "bbox": [ + 0.814, + 0.091, + 0.905, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.818, + 0.169, + 0.901, + 0.18 + ], + "angle": 0, + "content": "Target Shadows" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.19, + 0.905, + 0.218 + ], + "angle": 0, + "content": "Figure 3. An example depicting the packed state of a cuboidal container and the associated silhouettes/shadows." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.246, + 0.905, + 0.291 + ], + "angle": 0, + "content": "approach addresses the irregular object packing problem. However, if these elements are \"parts\" of another object altogether, it naturally extends to the part assembly problem." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.292, + 0.906, + 0.457 + ], + "angle": 0, + "content": "A key challenge in existing packing methods is managing overlaps or intersections among the elements to be packed. While some methods focus on simple geometries like cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or rely on assumptions of convexity or concavity in polyhedrons [19, 30, 37], often using simple heuristics [17, 27], others handle irregular shapes by employing voxelized representations [1, 6], which tend to be susceptible to approximation errors. This work introduces a signed-distance field (SDF) approach to manage inter-object intersection and container extrusion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.906, + 0.548 + ], + "angle": 0, + "content": "Contributions. In this work, we introduce RASP - Revisiting 3D Anamorphic art for Shadow-guided Packing of Irregular Objects. Given a set of arbitrarily shaped objects, a bounding volume (or container), and information about the appearance of its projection/shadows from different viewpoints in the packed state:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.551, + 0.905, + 0.627 + ], + "angle": 0, + "content": "- We propose a differentiable rendering-based framework to tackle irregular object packing by drawing inspiration from 3D Anamorphic Art. Our goal is to achieve near-maximal occupancy and minimal inter-object spacing within a known bounding volume." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.627, + 0.905, + 0.671 + ], + "angle": 0, + "content": "- We present a novel SDF-based approach to manage interobject intersections and object-container extrusions, enhanced by an image-based loss function." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.672, + 0.905, + 0.732 + ], + "angle": 0, + "content": "- We demonstrate that RASP can also be applied to part assembly without the need for explicit 3D ground truth supervision. Additionally, we illustrate compelling visual effects that cater to multi-view anamorphic art." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.733, + 0.905, + 0.793 + ], + "angle": 0, + "content": "- To the best of our knowledge, this is the first approach to address packing (and part assembly) using only shadows or projections, guided by the principles of differentiable rendering." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.551, + 0.905, + 0.793 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Through this work, we push the boundaries of 3D anamorphic art to address an important research question: can shadows be used to automatically find an optimal arrangement of arbitrarily shaped 3D objects within a bounded volume? While our framework aims to provide practical solutions, it does not always yield an optimal arrangement due to the NP-hard nature of the packing prob" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5850" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.093, + 0.9, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.318, + 0.908, + 0.361 + ], + "angle": 0, + "content": "Figure 4. The proposed differentiable rendering-based pipeline for RASP. We use Adam optimizer with a learning rate of \\(1e - 2\\) to \\(1e - 4\\) over 1000 iterations. Packing the Kitchen dataset (106 objects, 80000 grid points) takes nearly 17 minutes, and reassembly for each object in the Fantastic Breaks dataset (2 parts, 80000 grid points) takes under 3 minutes." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.386, + 0.483, + 0.434 + ], + "angle": 0, + "content": "lem [10]. Nonetheless, this work introduces a new perspective on solving the 3D packing and arrangement problem using shadows as a guiding mechanism." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.449, + 0.242, + 0.465 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.476, + 0.483, + 0.596 + ], + "angle": 0, + "content": "Object packing has been addressed using heuristic-based, model-based, learning-based, or policy-based (online) object packing. Several methods have assumed simple object geometries, such as cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or leverage convexity and/or concavity in polyhedrons [19, 30, 37]. This section primarily discusses the methods dealing with irregular object packing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Heuristic-based Methods. Several previous attempts at object packing were primarily based on heuristic strategies. One method proposed by Wang et al. [40] sequentially places objects employing the Deepest Bottom Left Fill (DBLF) heuristic strategy. However, it is shown to create holes, leading to empty spaces. Later, Wang and Hauser [39] addressed this limitation by reducing unfilled gaps through height-map minimization, which in itself ignores the difference between positions at the same level. HAPE3D [19], another heuristic-based algorithm, deploys the principle of the minimum total potential energy for irregular polyhedrons. Even after allowing free translations and rotations, it fails to achieve high packing density. Lamas et al. [15] voxelized irregular objects and used metaheuristic algorithms to optimize voxel representation that is limited due to memory constraints. Heuristic-based methods generally apply well to objects with only a few facets and struggle to achieve a high packing density while dealing with complex irregular objects." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Learning-Based Methods. The key challenge for pack" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.386, + 0.905, + 0.612 + ], + "angle": 0, + "content": "ing irregular objects is to handle object collision detection or intersection/overlap avoidance. Several different geometric representations of objects (say, objects tightly bound by a sphere or cuboid [45]) have been assumed by different methods for collision detection and packing optimization. Romanova et al. [1] pose the packing problem as a nonlinear optimization problem and propose quasi-phi functions for simple concave polyhedrons to describe nonoverlapping and distance constraints. However, obtaining a local optimum takes longer, even with free translations and rotations. A few works [2, 45] learned to decompose the object into multiple small parts to perform packing to reduce the supporting materials, build time, and assembly costs of 3D printing. While [2] used voxel-based representation, [45] used level sets to represent the object parts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.809 + ], + "angle": 0, + "content": "Moreover, Zhao et al. [47] and Zhuang et al. [48] divide the objects into convex shapes for efficient collision detection in physical simulation and pack the objects either using shaking of the container as per the dynamic principle or reinforcement learning in an online manner, respectively. Our work does not focus on online packing. Cui et al. [5] performed efficient collision metric computation in the spectral domain using voxel representation and Fast Fourier Transform (FFT) for discrete placement search. They deploy a greedy strategy to sort objects by volume from largest to smallest and then pack sequentially to minimize the distance between the new and already placed objects at each placement." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.902 + ], + "angle": 0, + "content": "The closest to our setting is the work by Ma et al. [20] that optimizes the orientation and position of the objects from their initial placement. However, their approach is multi-stage, involving combinatorial optimization that includes object swapping, enlargement, and replacement to reduce the gaps between the objects. Furthermore, they" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.958 + ], + "angle": 0, + "content": "5851" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.344, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.089, + 0.609, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.09, + 0.895, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.2, + 0.908, + 0.243 + ], + "angle": 0, + "content": "Figure 5. (a) Target shadow a duck-shaped container, optimized arrangement with mesh intersections. Mesh enclosed within (b) sphere and (c) cube where the intersection region doesn't include object meshes. (d) SDF of two non-intersecting and intersecting objects (intersecting points are marked in red), and SDF transformation within the container." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.269, + 0.485, + 0.421 + ], + "angle": 0, + "content": "also minimize the height of a container to obtain an optimal one through binary search. Due to repeated processing, the method is heavily time-consuming. In contrast, given a set of irregular objects, ours is a single-stage end-to-end optimization pipeline that performs packing only via 2D shadow guidance without any intense calculation within the 3D bounding volume. While Ma et al. [20] have the information about the object set and process only one object at a time, sequentially determining the initial placement, our proposed method considers a set of objects at a time." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.432, + 0.182, + 0.447 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.456, + 0.201, + 0.47 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.478, + 0.483, + 0.584 + ], + "angle": 0, + "content": "The key idea of our work is to arrange a set \\( S \\) of arbitrarily shaped 3D objects within an arbitrarily shaped container \\( \\mathcal{C} \\) such that the resulting arrangement casts \\( K \\) different shadows (projections) when viewed from \\( K \\) different directions using a differentiable rendering-based optimization pipeline. Interestingly, the problem has two interpretations depending on how we consider the set \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.483, + 0.629 + ], + "angle": 0, + "content": "(a) 3D Packing problem: when \\( S \\) contains arbitrarily shaped 3D objects and \\( C \\) is the bounding container within the viewing volume." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.674 + ], + "angle": 0, + "content": "(b) Part Assembly problem: when \\( S \\) contains \"parts\" of a 3D object \\( (O) \\) where this object \\( O \\) itself is treated as the container \\( \\mathcal{C} \\)." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.584, + 0.483, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In the case of packing, we might not always have a ground truth or a unique solution, i.e., objects can be arranged in multiple optimal ways to maximize occupancy and minimize spaces. However, we have a ground truth shape in a part assembly whose parts can be assembled only in one way. We demonstrate how this is implemented in Section 4. Overall, we propose a differentiable-rendering-based framework that naturally caters to both these requirements, in addition to generating multi-view anamorphic art. Inspired by computational visual arts, some of the recent works based on shadow art [8, 9, 23] have demonstrated the potential of 3D shape understanding, analysis, and reconstruction through shadows. In this work, we take the first step towards leveraging the benefit of differentiable rendering and principles of visual arts [42] to propose shadow-" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.269, + 0.76, + 0.285 + ], + "angle": 0, + "content": "based 3D packing and part assembly." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.292, + 0.704, + 0.309 + ], + "angle": 0, + "content": "3.2. Proposed Approach" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.314, + 0.907, + 0.752 + ], + "angle": 0, + "content": "The flow of the proposed methodology has been outlined in Figure 4. Consider a set of \\(N\\) arbitrarily shaped objects \\(\\mathcal{S} = \\{O_1, O_2, \\ldots, O_N\\}\\) such that each \\(O_i\\) is represented as a triangular mesh, an arbitrarily shaped bounding container \\(\\mathcal{C}\\) located inside the camera viewing volume \\(\\mathcal{V}\\), and shadow projection configuration \\(\\mathcal{X} = \\{X_k = (I_k, P_k) | k = 1, 2, \\ldots, K\\}\\). Here, \\(\\{I_k\\}_{k=1}^K\\) are the target images under the camera configuration \\(\\{P_k\\}_{k=1}^K\\). Essentially, the camera configuration \\(P_k = (R_k, t_k)\\) corresponds to the camera extrinsic parameters associated with image \\(I_k\\). With \\(\\mathcal{S}\\), \\(\\mathcal{C}\\), and \\(\\mathcal{X}\\) as input to the differentiable renderer \\(\\mathcal{R}\\), the objective here is to learn the optimal arrangement of objects in set \\(\\mathcal{S}\\) inside the container \\(\\mathcal{C}\\) placed within the viewing volume \\(\\mathcal{V}\\) such that the resulting images \\(\\{\\widehat{I_k}\\}_{k=1}^K\\) rendered under camera configurations \\(\\{P_k\\}_{k=1}^K\\) are close to the corresponding target images \\(\\{I_k\\}_{k=1}^K\\). From the shadow's perspective, the target images are silhouettes, and we assume that the light (to cast the shadows) will be co-located with the camera. Finding the arrangement of objects is equivalent to finding the rigid transformation, i.e., rotation and translation \\(\\{R_i, t_i\\}_{i=1}^N\\) of each object \\(O_i\\) in set \\(\\mathcal{S}\\). We use quaternions for obtaining rotations - (a) to avoid gimble lock through other representations like axis-angle rotation or rotation composition of rotation along \\(x - y - z\\) axes, (b) for smooth interpolation, and (c) to learn a smaller number of parameters compared to the rotation matrices. Specifically, we obtain the angle of rotations across each of the coordinate axes and convert them to quaternion representation for optimization." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.694, + 0.773 + ], + "angle": 0, + "content": "3.2.1. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.777, + 0.906, + 0.823 + ], + "angle": 0, + "content": "We propose a combined loss function consisting of an SDF-based intersection loss, an image-based loss, and an object-container extrusion loss, as per Equation 1." + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.832, + 0.905, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s i l}} + \\mathcal {L} _ {\\text {i s}} + \\lambda \\mathcal {L} _ {\\text {e x t}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.672, + 0.87 + ], + "angle": 0, + "content": "Here, we set \\(\\lambda = 0.001\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Image-based (Silhouette) Loss. A straightforward approach is to optimize each object's rotation and translation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5852" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.092, + 0.291, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.092, + 0.495, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.092, + 0.707, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.726, + 0.092, + 0.902, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.241, + 0.908, + 0.271 + ], + "angle": 0, + "content": "Figure 6. Visualization of 3D Object packing into a cuboidal container using RASP over four different object categories from [47]. Each instance is labeled with the number of objects packed in the container and the packing density." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.293, + 0.487, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.451, + 0.483, + 0.493 + ], + "angle": 0, + "content": "Figure 7. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.483, + 0.551 + ], + "angle": 0, + "content": "parameters based on image rendering loss, such as mean squared error, as per Equation 2." + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.561, + 0.483, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s i l} = \\frac {1}{M N K} \\sum_ {k = 1} ^ {K} \\sum_ {i = 1} ^ {M N} \\left| \\left| I _ {k} (i) - \\widehat {I} _ {k} (i) \\right| \\right| _ {2} ^ {2} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.484, + 0.689 + ], + "angle": 0, + "content": "Here, \\(MN\\) is the total number of pixels in the image. As shown in Figure 5 (a), the projection of the arrangement may appear feasible (apart from a few gaps where more objects could fit), but in 3D, objects can still intersect within a duck-shaped container." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Therefore, the loss functions should penalize mesh intersections. However, handling mesh intersections is complex; some methods [14] detect intersections by evaluating each triangular face of one mesh against others, which is computationally costly and impractical for large numbers of meshes. To simplify intersection computation, some approaches enclose objects within unit spheres or cubes, finding intersections among these simpler bounding shapes [45]. Although faster, this approach often fails with asymmetrically shaped objects, as intersections between bounding spheres or cubes may not correspond to intersections among the actual object meshes, as shown in Figure 5 (b, c). This can lead to excessive penalization of intersections, causing the network to push objects apart and create unnec" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.298, + 0.895, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.478, + 0.908, + 0.521 + ], + "angle": 0, + "content": "Figure 8. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.553, + 0.598, + 0.566 + ], + "angle": 0, + "content": "essary gaps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Intersection Loss. To overcome these challenges, we propose an SDF-based approach to handle both object-object intersections and object-container extrusion. The signed distance field (SDF) provides the shortest distance from a point to the surface, with a negative sign indicating the point is inside and a positive sign indicating it is outside the object. Specifically, we pre-compute the SDF of each mesh (using [41]) at fixed query points within the container \\(\\mathcal{C}\\) (a few milliseconds on GPU) and deform the SDFs with every update of the learned rotation and translation parameters. Rather than recalculating the SDF for each rigid transformation, we warp the previous SDF using a linear transformation to match the new configuration, as shown in Figure 5 (d). The degree of intersection, thus, can be determined by identifying points where more than one object has a negative SDF value, as marked in red in Figure 5 (d)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.904 + ], + "angle": 0, + "content": "Let the SDF of the object \\(O_{i}\\) at a point \\(\\mathbf{p}\\) after a rigid transformation (updated rotation and translation) has been applied to \\(O_{i}\\) be denoted by \\(\\widetilde{S}_{O_i}(\\mathbf{p})\\). One could simply consider the amount of intersection to be proportional to the number of objects under intersection at any point within the container, i.e., \\(D_{is}(\\mathbf{p}) = |\\{i\\in \\{1,2,\\dots N\\} |\\widetilde{S}_{O_i}(\\mathbf{p}) < 0\\} |.\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5853" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.473, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.204, + 0.485, + 0.262 + ], + "angle": 0, + "content": "Figure 9. Illustration of packing of 24 cubes, each of dimensions \\(1 \\times 1 \\times 1\\) cubic units, into a container of dimensions \\(6 \\times 6 \\times 6\\) cubic units, with varying silhouette widths to simulate physically correct packing for \\(N < N_{max}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.278, + 0.484, + 0.37 + ], + "angle": 0, + "content": "However, we observed that considering the SDF value instead of just the count provides smoother guidance to resolve the intersections. Therefore, we define the degree of intersection \\( D_{is}(\\mathbf{p}) \\) as the sum of the (negative of) SDFs of the objects that contain point \\( \\mathbf{p} \\) within them at every optimization step, such that," + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.38, + 0.483, + 0.42 + ], + "angle": 0, + "content": "\\[\nD _ {i s} (\\mathbf {p}) = \\sum_ {\\left\\{\\forall O _ {i} \\mid \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) < 0 \\right\\}} - \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.484, + 0.507 + ], + "angle": 0, + "content": "Here, \\( D_{is}(\\mathbf{p}) > 1 \\) indicates that there is an intersection of at least two objects at the point, and \\( D_{is}(\\mathbf{p}) = 0 \\) represents that the point \\( \\mathbf{p} \\) is not inside any object. Considering the set of query points \\( \\mathcal{C}_p \\) inside the container \\( \\mathcal{C} \\), the intersection loss is defined as per Equation 4." + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.518, + 0.483, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i s} = \\sum_ {\\mathbf {p} \\in \\mathcal {C} _ {p}} D _ {i s} (\\mathbf {p}) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.564, + 0.484, + 0.625 + ], + "angle": 0, + "content": "Container Extrusion Loss. Let \\( V_{i} \\) be the set of vertices of the triangular mesh corresponding to the object \\( O_{i} \\) and \\( S_{\\mathcal{C}} \\) be the SDF of the container \\( \\mathcal{C} \\). We define the container extrusion loss as per Equation 5" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.636, + 0.483, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e x t} = \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {v} \\in V _ {i}} \\max (- \\epsilon , S _ {\\mathcal {C}} (\\mathbf {v})) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Here, \\(\\epsilon\\), the distance between a vertex and the container's boundary, creates a \"buffer zone\" around the container boundary to control when the extrusion loss begins to be active. While a higher value of \\(\\epsilon\\) hinders the movement of objects inside the container, a very small value leads to portions of objects suddenly extruding out of the container boundary, leading to an unstable optimization. We find \\(\\epsilon = 0.01\\) to be a reasonable value that avoids penalizing objects that are slightly inside the container but still close to the boundary. We observed that in some cases, silhouette loss was just enough to contain the objects with the container, especially for simple shapes. However, for more irregular shapes with asymmetric and skewed spread, extrusion loss proved to be helpful." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.09, + 0.905, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.211, + 0.908, + 0.268 + ], + "angle": 0, + "content": "Figure 10. Illustration of packing arbitrarily shaped objects into arbitrarily shaped containers. The initial containers, the set of object shapes to be packed, and the final packed configuration are shown in the figure." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.29, + 0.646, + 0.307 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.315, + 0.907, + 0.39 + ], + "angle": 0, + "content": "In this section, we showcase the results obtained through the RASP framework for irregular object packing drawing parallels with 3D Anamorphic art. Furthermore, we extend RASP to applications like part assembly and creating artistic illustrations." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.399, + 0.746, + 0.416 + ], + "angle": 0, + "content": "4.1. Irregular Object Packing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.42, + 0.906, + 0.496 + ], + "angle": 0, + "content": "For 3D object packing, we demonstrate the results majorly on the objects from the IR-BPP dataset [47], which contains objects from four categories: General, Kitchen, ABC, and Block Out. A few other illustrations also include objects from the VOLMAP dataset [3] and SilNet dataset [49]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.497, + 0.906, + 0.539 + ], + "angle": 0, + "content": "Following the existing literature of 3D object packing, we define the packing efficiency/density \\((\\rho)\\), as per Equation 6." + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.539, + 0.905, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\rho = \\sum_ {O _ {i} \\in \\mathcal {C}} \\frac {\\left| O _ {i} \\right|}{\\left| \\mathcal {C} \\right|} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.906, + 0.611 + ], + "angle": 0, + "content": "Here, \\( |O_i| \\) and \\( |\\mathcal{C}| \\) are the volume of the \\( i^{th} \\) object and container volume, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.906, + 0.687 + ], + "angle": 0, + "content": "Figure 6, compares the packing density of irregular 3D objects from different categories into a typical cuboidal container. Interestingly, RASP does not require any regularity in object shapes and can handle arbitrary shapes of different sizes, achieving reasonably good packing configurations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Deciding the number of objects that can be maximally packed within a container is crucial for optimal packing. To start with, we decide the initial number of objects as \\( N_{init} \\) based on the average volume of the objects and the container volume, such that \\( N_{init} = \\frac{|C|}{|O|_{avg}} \\). Consider \\( N_{max} \\) as an unknown upper bound, i.e., the maximum a physical container can accommodate. If \\( N_{init} < N_{max} \\), we draw another set of \\( N_{k} \\) objects from the pool (if available) and again optimize the arrangement with \\( N_{init} + N_{k} \\) based on the target silhouettes of projection. In case this exceeds \\( N_{max} \\), the remaining objects either start extruding out of the container or intersecting heavily within the container depending on the predominance of \\( \\mathcal{L}_{is} \\) or \\( \\mathcal{L}_{ext} \\), respectively. All the results correspond to \\( N = N_{max} \\) objects that can maximally" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5854" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.094, + 0.353, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.094, + 0.624, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.096, + 0.896, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.211, + 0.908, + 0.24 + ], + "angle": 0, + "content": "Figure 11. Extending RASP to perform part reassembly of broken objects. The figure showcases the target silhouettes and broken parts reassembled using RASP." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.248, + 0.483, + 0.324 + ], + "angle": 0, + "content": "fit inside the container with no intersection, a condition essential for real-world applicability. Moreover, the objects are randomly initialized within the container before optimization. We discuss the effect of different initialization strategies in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.484, + 0.476 + ], + "angle": 0, + "content": "Due to silhouette or shadow-guided optimization, the resulting arrangement can sometimes be physically inaccurate. As shown in Figure 9, when the number of objects \\(N\\) is less than the maximum capacity \\(N_{max}\\), the arrangement often floats within the container rather than settling at the bottom. While such effects are inherent to this type of optimization-based framework, we demonstrate that merely adjusting the width of the silhouettes would effectively constrain the objects to rest at the bottom of the container in Figure 9 progressively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.477, + 0.484, + 0.595 + ], + "angle": 0, + "content": "Arbitrarily Shaped Container. Owing to its design to derive insights from the projected silhouettes, RASP can also accommodate arbitrarily shaped containers, as shown in Figure 1 (b) and Figure 10. Similar to multi-view shape optimization, the target shadows are essentially the silhouettes of the container from 5 different views. Figure 10 depicts the packing on donut-shaped and squirrel-shaped containers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.795 + ], + "angle": 0, + "content": "Effect of loss terms. Figure 8 (top) shows the convergence of each of the loss terms for illustrations in Figure 6 and Figure 10. The intersection density for all the results is zero, offering a multi-view consistent, intersection-free/non-overlapping configuration. Figure 8 (bottom) also illustrates the impact of different loss terms in addition to observations in Figure 5 for \\(\\mathcal{L}_{sil}\\) vs \\(\\mathcal{L}_{sil} + \\mathcal{L}_{in}\\). Overall, we find that extrusion term \\(\\mathcal{L}_{ext}\\) acts as a regularizer, preventing objects from drifting too far apart to avoid intersections. While the intersection remains zero without \\(\\mathcal{L}_{ext}\\), its inclusion improves the rendered silhouette by reducing \\(\\mathcal{L}_{sil}\\). Notably, objects are positioned closer together when \\(\\mathcal{L}_{ext}\\) is applied." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Comparison with existing methods. Out of several relevant works on 3D object packing (as described in Section 2), the work by Ma et al. [20] is the closest to our optimization setup (not guided by shadows) whose setup is different from RASP since it involves swapping, replacement with new objects, and object enlargement - which we believe is not practical in a real-world setup where we cannot" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.248, + 0.907, + 0.565 + ], + "angle": 0, + "content": "alter the object dimensions. However, since their implementation is unavailable online, we choose to quantitatively compare the average packing efficiency across different objects. Although different from ours, we also compared our average packing efficiency of a physically inspired reinforcement learning-based online packing method by Zhao et al. [47] over their dataset to establish the efficacy of our optimization-based methods learning solely from 2D image guidance. Zhao et al. [47] look at only one or a few objects at a time, and packing efficiency is dependent on the sequence in which the objects arrive. Moreover, the object placement is guided by the dynamics and constraints of physics. In contrast, RASP - an offline method, takes a more global standpoint by optimizing all \\( N \\leq N_{max} \\) objects at a time. Overall, RASP obtains an average of \\( 45\\% \\) occupancy over the four different categories of the IR-BPP dataset [47] which is better than Ma et al. [20] (34%) and drops below that of Zhao et al. [47] (51.9%) evaluated over the objects from online packing dataset. Moreover, Ma et al. [20] bears an average optimization time of 40.55 minutes while RASP achieves the same in \\( \\sim 15 \\) minutes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.909, + 0.732 + ], + "angle": 0, + "content": "For a qualitative comparison over samples from IR-BPP dataset, we adapt [47] to align closest to our setting. Specifically, we generate 100 random sequences of the same set (and same number) of objects from each IR-BPP dataset category (as in Figure 6) and report the best configuration to compare with RASP in Figure. 7. Due to implementation constraints of [47], we could not assign different colors to objects or obtain multiple views of the packed arrangement of [47], and hence, we compared only the top view. RASP performs similar to or slightly better than the physics-aware method for the same object set." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.742, + 0.691, + 0.759 + ], + "angle": 0, + "content": "4.2. 3D Part Assembly" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Part assembly using RASP also shares similarities with multi-view geometry optimization. However, instead of optimizing a single shape, RASP learns the rigid transformations of different parts of a single shape to obtain a 3D consistent arrangement across all the views. For demonstrating part assembly, we used the *Fantastic Breaks* dataset [16] that consists of paired 3D scans of real-world broken objects and their complete counterparts. Figure 11 demonstrates some qualitative results on reassembling broken ob" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.09, + 0.273, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.311, + 0.194, + 0.323 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.091, + 0.365, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.091, + 0.455, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.461, + 0.091, + 0.528, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.17, + 0.365, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.374, + 0.17, + 0.453, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.461, + 0.17, + 0.525, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.239, + 0.365, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.374, + 0.239, + 0.453, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.461, + 0.239, + 0.525, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.398, + 0.311, + 0.415, + 0.323 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.091, + 0.655, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.311, + 0.616, + 0.323 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.118, + 0.907, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.311, + 0.786, + 0.323 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.334, + 0.907, + 0.378 + ], + "angle": 0, + "content": "Figure 12. (a) & (b) use objects from the Kitchen dataset to generate 2-view and 3-view 3D anamorphic art. (c) Multi-view pixelated portraits generated using RASP with artistic texture applied. (d) RASP recreates the famous cover page of the book Gödel, Escher, Bach by Douglas Hofstadter. The 3D and dynamic visualization of these and more related results are provided in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.385, + 0.483, + 0.43 + ], + "angle": 0, + "content": "jects. Notably, it does so solely via silhouette guidance without the need for any explicit 3D ground truth supervision." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.441, + 0.345, + 0.456 + ], + "angle": 0, + "content": "4.3. Multi-view Anamorphic Art" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We also leverage RASP to reinterpret and construct different forms of multi-view anamorphic art. Thus far, we have seen that silhouettes or shadows do provide important cues for 3D arrangement. However, these binary images alone cannot create interesting artistic illustrations. Therefore, we also seek guidance from colored or textured images. Take, for example, the portrait of Nikola Tesla shown in Figure 2 (a). One approach would be to search for suitable objects and apply heuristic methods to arrange them in a way that recreates the portrait's appearance. Alternatively, one could collect and randomly arrange objects (like those in Figure 2 (c)) within the outline of the silhouette, then paint the arrangement to revive the essence of the portrait. Following the latter approach, RASP uses a two-stage optimization procedure, where first, it arranges the discrete objects in a 3D space through silhouette matching across a set of views and later performs rendering-based texture optimization (integrated as an add-on) over the finalized arrangement to match the target textures. Figure 12 (a) illustrates how this strategy allows RASP to recreate multi-view portraits of Nikola Tesla and Marie Curie across two non-orthogonal views that are \\(120^{\\circ}\\) apart using objects from the Kitchen dataset. Furthermore, it also generates consistent ensembles that are meaningful across three non-orthogonal views, as shown in Figure 12 (b), giving a visually plausible appearance of Pokémon, Wall-e, and Minion. In figure 12 (c) we obtain 3D arrangements using binary images and then apply artistic textures to create unique 3D illustrations. The resemblance of the textured arrangement and the associated" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.385, + 0.907, + 0.492 + ], + "angle": 0, + "content": "rendered images highlights the creative potential of RASP. In Figure 12 (d) we recreate the famous artistic cover page of the Book by Douglas Hofstadter featuring blocks casting shadows of the first letters of artists – Gödel, Escher, and Bach. Overall, RASP is a versatile optimization pipeline stressing on the fact that shadows do provide limited yet useful cues for 3D understanding and artistic exploration." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.51, + 0.634, + 0.525 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.907, + 0.838 + ], + "angle": 0, + "content": "We introduce RASP, a differentiable rendering-based optimization framework for irregular 3D object packing, part assembly, and recreating artistic illustrations, taking guidance from images, whether in the form of binary silhouettes, textured RGB images, or simple portrait sketches. The current offline strategy does not account for physical dynamics, such as the influence of gravity on object placement. Additionally, RASP struggles with multi-part (more than 2 or 3 parts) part assembly, particularly symmetrical and/or identical parts. An interesting potential extension of this work would be to incorporate physics-based guidance for the packing to be more physically consistent. We believe that there are plenty of untapped capabilities in shadows that drive 3D understanding, and RASP presents a few of them. We anticipate that this work would attract researchers from different domains to use shadows or silhouettes for applications like partitioning and reconfiguration of complex 3D objects into simpler forms, multi-part part assembly, dynamic visual arts, CAD design, and handling non-rigid deformations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work is supported by the Prime Minister Research Fellowship (PMRF) grant and the Jibaben Patel Chair in Artificial Intelligence. We also thank Prajwal Singh, IIT Gandhinagar, for his valuable inputs." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5856" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.169 + ], + "angle": 0, + "content": "[1] Thomas Byholm, Martti Toivakka, and Jan Westerholm. Effective packing of 3-dimensional voxel-based arbitrarily shaped particles. Powder Technology, 196(2):139-146, 2009. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.173, + 0.484, + 0.227 + ], + "angle": 0, + "content": "[2] Xuelin Chen, Hao Zhang, Jinjie Lin, Ruizhen Hu, Lin Lu, Qi-Xing Huang, Bedrich Benes, Daniel Cohen-Or, Baoquan Chen, et al. Dapper: decompose-and-pack for 3d printing. ACM Trans. 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(a) An ensemble of arbitrary shapes casting the shadow of alphabets CVPR and numbers 2025, (b) a set of irregular objects packed inside a face-shaped container, (c) an assembly of parts of a vessel obtained through multi-view shadow guidance via RASP. + +# Abstract + +Recent advancements in learning-based methods have opened new avenues for exploring and interpreting art forms, such as shadow art, origami, and sketch art, through computational models. One notable visual art form is 3D Anamorphic Art in which an ensemble of arbitrarily shaped 3D objects creates a realistic and meaningful expression when observed from a particular viewpoint and loses its coherence over the other viewpoints. In this work, we build on insights from 3D Anamorphic Art to perform 3D object arrangement. We introduce RASP, a differentiable-rendering-based framework to arrange arbitrarily shaped 3D objects within a bounded volume via shadow (or silhouette)-guided optimization with an aim of minimal inter-object spacing and near-maximal occupancy. Furthermore, we propose a novel SDF-based formulation to handle inter-object intersection and container extrusion. We demonstrate that RASP can be extended to part assembly alongside object packing considering 3D objects to be "parts" of another 3D object. Finally, we present artistic illustrations of multi-view anamorphic art, achieving meaningful expressions from multiple viewpoints within a single ensemble. + +# 1. Introduction + +For centuries, artists have used their expressions to redefine the boundaries of visual art, demonstrating how art shapes reality and influences human perception. Their work has also broadly impacted technology, design, and engineering. In this work, we explore using a unique visual art form, 3D Anamorphic Art, to tackle challenges in irregular object packing and extend this approach to part assembly. + +Interestingly, we are not alone in using (and, in fact, developing) artistic expressions to address applications in computer vision. For example, DeepDream [24] uses GAN-based style transfer to apply the style of classical paintings, like those of Van Gogh or Picasso, to contemporary images. RePaint [34] leverages deep learning and 3D printing to replicate the colors and textures of paintings by optimizing ink layering. ScribGen [7] creates human-like scribbles and hand-strokes in different styles. Beyond images, researchers have expanded artistic techniques into 3D analysis and understanding, as in Shadow Art [23], which uses shadows for 3D reconstruction, sketch-based 3D generation [32], expressive hand movements [8], and the design of knot configurations for realistic visual effects [9]. In this work, we draw upon insights from 3D Anamorphic Art to address an important problem of packing arbitrarily shaped objects within a 3D bounding volume (or container). Packing has + +![](images/ed181a5c529501528c2e440f17ff0d4a4513ec74143fc7f7746b7eb152eda7b5.jpg) +(a) + +![](images/88fdc997a219ab0533ee43f2da5ec0887af59bcfce7a46d7c892161f3c0d93a5.jpg) +(b) + +![](images/25570491d4922915444470924dbb9649ea15ce8f2b2c4244bbcb2b9ad4c8b79a.jpg) +(c) + +![](images/dd1afea0c1a4d041de278c0beef03f358d7f7bb7473fe9a9f0bfab652deb438e.jpg) +(d) +Figure 2. Illustration of 3D Anamorphic Art (a, b): Portrait of Nikola Tesla and Bedrich Smetana by Patrick Proško and Shadow Art (c, d): Dirty White Trash and Wild Mood Swing by Tim Nobel and Sue Webster. + +numerous practical applications, spanning fields such as combinatorial optimization [22, 33], computational geometry [12, 20], computer vision and graphics [2, 18, 31], machine learning [11, 46], robotics [35, 38, 44], and logistics and manufacturing [47]. + +3D Anamorphic Art. 3D Anamorphic Art involves arranging objects in 3D space such that the arrangement appears coherent and meaningful only from the specific viewpoint(s). In contrast, from any other view, it appears random. For example, artist Patrick Proško used this technique at the Illusion Art Museum Prague by arranging electrical appliances to form a portrait of Nikola Tesla [28] (Figure 2 (a)) and arranging musical instruments to create a likeness of the musician Bedřich Smetana [29] (Figure 2 (b)). This concept also extends to shadows cast by such arrangements under particular camera-light configurations. For instance, artists Tim Noble and Sue Webster created Dirty White Trash [25] and Wild Mood Swings [26], where carefully arranged trash and wooden pieces cast shadows of people sitting beside each other (see Figure 2 (c, d)). Whether through perspective views from specific viewpoints or shadows created under particular camera-light configurations, these projections reveal valuable insights about the arrangement of objects in 3D space. + +Relation with Object Packing. Consider a cuboidal bounding volume (or container), as depicted in Figure 3. When fully packed, this cuboid would appear as a rectangle or square upon being viewed orthographically along any of its faces. Similarly, it would cast rectangular or square shadows under the same viewing configuration. Ideally, gaps between the objects would appear as holes in the shadow from at least one perspective. By considering these shadows (technically binary images or silhouettes of the packed state) as target projections, we aim to arrange arbitrarily shaped elements within a bounding volume, thereby tackling the packing problem. + +Interestingly, this approach also allows for bounding volumes of arbitrary shapes, where the target projections are simply the volume's appearance from multiple viewpoints. If the elements to be arranged are whole 3D objects, this + +![](images/5a2918fa8318c869725fbaf88d68f2144c7250fc184def3f2792145e819d1578.jpg) +Objects to be packed + +![](images/39b96b898f2663589c51511e825836e39c8f9b53620e648fe84db223c87e4b69.jpg) +Packed arrangement +Figure 3. An example depicting the packed state of a cuboidal container and the associated silhouettes/shadows. + +![](images/ab13742bc1c0cc2a578b37de99f5514875e75e784c6472d7721d65329eb80aef.jpg) +Target Shadows + +approach addresses the irregular object packing problem. However, if these elements are "parts" of another object altogether, it naturally extends to the part assembly problem. + +A key challenge in existing packing methods is managing overlaps or intersections among the elements to be packed. While some methods focus on simple geometries like cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or rely on assumptions of convexity or concavity in polyhedrons [19, 30, 37], often using simple heuristics [17, 27], others handle irregular shapes by employing voxelized representations [1, 6], which tend to be susceptible to approximation errors. This work introduces a signed-distance field (SDF) approach to manage inter-object intersection and container extrusion. + +Contributions. In this work, we introduce RASP - Revisiting 3D Anamorphic art for Shadow-guided Packing of Irregular Objects. Given a set of arbitrarily shaped objects, a bounding volume (or container), and information about the appearance of its projection/shadows from different viewpoints in the packed state: + +- We propose a differentiable rendering-based framework to tackle irregular object packing by drawing inspiration from 3D Anamorphic Art. Our goal is to achieve near-maximal occupancy and minimal inter-object spacing within a known bounding volume. +- We present a novel SDF-based approach to manage interobject intersections and object-container extrusions, enhanced by an image-based loss function. +- We demonstrate that RASP can also be applied to part assembly without the need for explicit 3D ground truth supervision. Additionally, we illustrate compelling visual effects that cater to multi-view anamorphic art. +- To the best of our knowledge, this is the first approach to address packing (and part assembly) using only shadows or projections, guided by the principles of differentiable rendering. + +Through this work, we push the boundaries of 3D anamorphic art to address an important research question: can shadows be used to automatically find an optimal arrangement of arbitrarily shaped 3D objects within a bounded volume? While our framework aims to provide practical solutions, it does not always yield an optimal arrangement due to the NP-hard nature of the packing prob + +![](images/43a03c5139264eff03d497eda1542f90a6019900a9637102f4e5e015d2e43ad2.jpg) +Figure 4. The proposed differentiable rendering-based pipeline for RASP. We use Adam optimizer with a learning rate of $1e - 2$ to $1e - 4$ over 1000 iterations. Packing the Kitchen dataset (106 objects, 80000 grid points) takes nearly 17 minutes, and reassembly for each object in the Fantastic Breaks dataset (2 parts, 80000 grid points) takes under 3 minutes. + +lem [10]. Nonetheless, this work introduces a new perspective on solving the 3D packing and arrangement problem using shadows as a guiding mechanism. + +# 2. Related Works + +Object packing has been addressed using heuristic-based, model-based, learning-based, or policy-based (online) object packing. Several methods have assumed simple object geometries, such as cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or leverage convexity and/or concavity in polyhedrons [19, 30, 37]. This section primarily discusses the methods dealing with irregular object packing. + +Heuristic-based Methods. Several previous attempts at object packing were primarily based on heuristic strategies. One method proposed by Wang et al. [40] sequentially places objects employing the Deepest Bottom Left Fill (DBLF) heuristic strategy. However, it is shown to create holes, leading to empty spaces. Later, Wang and Hauser [39] addressed this limitation by reducing unfilled gaps through height-map minimization, which in itself ignores the difference between positions at the same level. HAPE3D [19], another heuristic-based algorithm, deploys the principle of the minimum total potential energy for irregular polyhedrons. Even after allowing free translations and rotations, it fails to achieve high packing density. Lamas et al. [15] voxelized irregular objects and used metaheuristic algorithms to optimize voxel representation that is limited due to memory constraints. Heuristic-based methods generally apply well to objects with only a few facets and struggle to achieve a high packing density while dealing with complex irregular objects. + +Learning-Based Methods. The key challenge for pack + +ing irregular objects is to handle object collision detection or intersection/overlap avoidance. Several different geometric representations of objects (say, objects tightly bound by a sphere or cuboid [45]) have been assumed by different methods for collision detection and packing optimization. Romanova et al. [1] pose the packing problem as a nonlinear optimization problem and propose quasi-phi functions for simple concave polyhedrons to describe nonoverlapping and distance constraints. However, obtaining a local optimum takes longer, even with free translations and rotations. A few works [2, 45] learned to decompose the object into multiple small parts to perform packing to reduce the supporting materials, build time, and assembly costs of 3D printing. While [2] used voxel-based representation, [45] used level sets to represent the object parts. + +Moreover, Zhao et al. [47] and Zhuang et al. [48] divide the objects into convex shapes for efficient collision detection in physical simulation and pack the objects either using shaking of the container as per the dynamic principle or reinforcement learning in an online manner, respectively. Our work does not focus on online packing. Cui et al. [5] performed efficient collision metric computation in the spectral domain using voxel representation and Fast Fourier Transform (FFT) for discrete placement search. They deploy a greedy strategy to sort objects by volume from largest to smallest and then pack sequentially to minimize the distance between the new and already placed objects at each placement. + +The closest to our setting is the work by Ma et al. [20] that optimizes the orientation and position of the objects from their initial placement. However, their approach is multi-stage, involving combinatorial optimization that includes object swapping, enlargement, and replacement to reduce the gaps between the objects. Furthermore, they + +![](images/23d7e04cae6d09488f7cad8a252a4a472a6d630402408a73d79c9cfdbfbeb9dc.jpg) +Figure 5. (a) Target shadow a duck-shaped container, optimized arrangement with mesh intersections. Mesh enclosed within (b) sphere and (c) cube where the intersection region doesn't include object meshes. (d) SDF of two non-intersecting and intersecting objects (intersecting points are marked in red), and SDF transformation within the container. + +![](images/66a5441b7fbc1e7a052ebeb0c6e6958820d35a9ef0999aaf7175501356c335cc.jpg) + +![](images/f78328b8a77e8b1dd193f435661d99942a845baba417f2c3bbb9cc079a3f39f3.jpg) + +also minimize the height of a container to obtain an optimal one through binary search. Due to repeated processing, the method is heavily time-consuming. In contrast, given a set of irregular objects, ours is a single-stage end-to-end optimization pipeline that performs packing only via 2D shadow guidance without any intense calculation within the 3D bounding volume. While Ma et al. [20] have the information about the object set and process only one object at a time, sequentially determining the initial placement, our proposed method considers a set of objects at a time. + +# 3. Method + +# 3.1. Overview + +The key idea of our work is to arrange a set $S$ of arbitrarily shaped 3D objects within an arbitrarily shaped container $\mathcal{C}$ such that the resulting arrangement casts $K$ different shadows (projections) when viewed from $K$ different directions using a differentiable rendering-based optimization pipeline. Interestingly, the problem has two interpretations depending on how we consider the set $S$ . + +(a) 3D Packing problem: when $S$ contains arbitrarily shaped 3D objects and $C$ is the bounding container within the viewing volume. +(b) Part Assembly problem: when $S$ contains "parts" of a 3D object $(O)$ where this object $O$ itself is treated as the container $\mathcal{C}$ . + +In the case of packing, we might not always have a ground truth or a unique solution, i.e., objects can be arranged in multiple optimal ways to maximize occupancy and minimize spaces. However, we have a ground truth shape in a part assembly whose parts can be assembled only in one way. We demonstrate how this is implemented in Section 4. Overall, we propose a differentiable-rendering-based framework that naturally caters to both these requirements, in addition to generating multi-view anamorphic art. Inspired by computational visual arts, some of the recent works based on shadow art [8, 9, 23] have demonstrated the potential of 3D shape understanding, analysis, and reconstruction through shadows. In this work, we take the first step towards leveraging the benefit of differentiable rendering and principles of visual arts [42] to propose shadow- + +based 3D packing and part assembly. + +# 3.2. Proposed Approach + +The flow of the proposed methodology has been outlined in Figure 4. Consider a set of $N$ arbitrarily shaped objects $\mathcal{S} = \{O_1, O_2, \ldots, O_N\}$ such that each $O_i$ is represented as a triangular mesh, an arbitrarily shaped bounding container $\mathcal{C}$ located inside the camera viewing volume $\mathcal{V}$ , and shadow projection configuration $\mathcal{X} = \{X_k = (I_k, P_k) | k = 1, 2, \ldots, K\}$ . Here, $\{I_k\}_{k=1}^K$ are the target images under the camera configuration $\{P_k\}_{k=1}^K$ . Essentially, the camera configuration $P_k = (R_k, t_k)$ corresponds to the camera extrinsic parameters associated with image $I_k$ . With $\mathcal{S}$ , $\mathcal{C}$ , and $\mathcal{X}$ as input to the differentiable renderer $\mathcal{R}$ , the objective here is to learn the optimal arrangement of objects in set $\mathcal{S}$ inside the container $\mathcal{C}$ placed within the viewing volume $\mathcal{V}$ such that the resulting images $\{\widehat{I_k}\}_{k=1}^K$ rendered under camera configurations $\{P_k\}_{k=1}^K$ are close to the corresponding target images $\{I_k\}_{k=1}^K$ . From the shadow's perspective, the target images are silhouettes, and we assume that the light (to cast the shadows) will be co-located with the camera. Finding the arrangement of objects is equivalent to finding the rigid transformation, i.e., rotation and translation $\{R_i, t_i\}_{i=1}^N$ of each object $O_i$ in set $\mathcal{S}$ . We use quaternions for obtaining rotations - (a) to avoid gimble lock through other representations like axis-angle rotation or rotation composition of rotation along $x - y - z$ axes, (b) for smooth interpolation, and (c) to learn a smaller number of parameters compared to the rotation matrices. Specifically, we obtain the angle of rotations across each of the coordinate axes and convert them to quaternion representation for optimization. + +# 3.2.1. Objective Function + +We propose a combined loss function consisting of an SDF-based intersection loss, an image-based loss, and an object-container extrusion loss, as per Equation 1. + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {s i l}} + \mathcal {L} _ {\text {i s}} + \lambda \mathcal {L} _ {\text {e x t}} \tag {1} +$$ + +Here, we set $\lambda = 0.001$ + +Image-based (Silhouette) Loss. A straightforward approach is to optimize each object's rotation and translation + +![](images/10f7529cc0d25d66feb6ce70bbb867e8f9279a56d418c8cdf2eb1d0b76152541.jpg) +Figure 6. Visualization of 3D Object packing into a cuboidal container using RASP over four different object categories from [47]. Each instance is labeled with the number of objects packed in the container and the packing density. + +![](images/0fd64d3df27779b54491466b2da58f39f9d37047776dc89333f0dcd0c563577d.jpg) + +![](images/f4647124650eded28b9ae09d6857990c6a707fa29aa2886cdf0043e894c41543.jpg) + +![](images/fbc55d1d0af1854fdf4cf8c1ab759343cc17351ee4a68964e4c00f22017bc840.jpg) + +![](images/921f6060fd13b4bf74514ca2458441bb1ea7753524c5fb180880105ac07f19f5.jpg) +Figure 7. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom. + +parameters based on image rendering loss, such as mean squared error, as per Equation 2. + +$$ +\mathcal {L} _ {s i l} = \frac {1}{M N K} \sum_ {k = 1} ^ {K} \sum_ {i = 1} ^ {M N} \left| \left| I _ {k} (i) - \widehat {I} _ {k} (i) \right| \right| _ {2} ^ {2} \tag {2} +$$ + +Here, $MN$ is the total number of pixels in the image. As shown in Figure 5 (a), the projection of the arrangement may appear feasible (apart from a few gaps where more objects could fit), but in 3D, objects can still intersect within a duck-shaped container. + +Therefore, the loss functions should penalize mesh intersections. However, handling mesh intersections is complex; some methods [14] detect intersections by evaluating each triangular face of one mesh against others, which is computationally costly and impractical for large numbers of meshes. To simplify intersection computation, some approaches enclose objects within unit spheres or cubes, finding intersections among these simpler bounding shapes [45]. Although faster, this approach often fails with asymmetrically shaped objects, as intersections between bounding spheres or cubes may not correspond to intersections among the actual object meshes, as shown in Figure 5 (b, c). This can lead to excessive penalization of intersections, causing the network to push objects apart and create unnec + +![](images/ae6bfa2782cad2693fe2b806d14034a6cdee34d1191fdb7fb886e8c35d38e7b3.jpg) +Figure 8. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom. + +essary gaps. + +Intersection Loss. To overcome these challenges, we propose an SDF-based approach to handle both object-object intersections and object-container extrusion. The signed distance field (SDF) provides the shortest distance from a point to the surface, with a negative sign indicating the point is inside and a positive sign indicating it is outside the object. Specifically, we pre-compute the SDF of each mesh (using [41]) at fixed query points within the container $\mathcal{C}$ (a few milliseconds on GPU) and deform the SDFs with every update of the learned rotation and translation parameters. Rather than recalculating the SDF for each rigid transformation, we warp the previous SDF using a linear transformation to match the new configuration, as shown in Figure 5 (d). The degree of intersection, thus, can be determined by identifying points where more than one object has a negative SDF value, as marked in red in Figure 5 (d). + +Let the SDF of the object $O_{i}$ at a point $\mathbf{p}$ after a rigid transformation (updated rotation and translation) has been applied to $O_{i}$ be denoted by $\widetilde{S}_{O_i}(\mathbf{p})$ . One could simply consider the amount of intersection to be proportional to the number of objects under intersection at any point within the container, i.e., $D_{is}(\mathbf{p}) = |\{i\in \{1,2,\dots N\} |\widetilde{S}_{O_i}(\mathbf{p}) < 0\} |.$ + +![](images/396e46554280870483ff91774d1aace40eea7d52724f729adb772d8da01476ea.jpg) +Figure 9. Illustration of packing of 24 cubes, each of dimensions $1 \times 1 \times 1$ cubic units, into a container of dimensions $6 \times 6 \times 6$ cubic units, with varying silhouette widths to simulate physically correct packing for $N < N_{max}$ . + +However, we observed that considering the SDF value instead of just the count provides smoother guidance to resolve the intersections. Therefore, we define the degree of intersection $D_{is}(\mathbf{p})$ as the sum of the (negative of) SDFs of the objects that contain point $\mathbf{p}$ within them at every optimization step, such that, + +$$ +D _ {i s} (\mathbf {p}) = \sum_ {\left\{\forall O _ {i} \mid \widetilde {S} _ {O _ {i}} (\mathbf {p}) < 0 \right\}} - \widetilde {S} _ {O _ {i}} (\mathbf {p}) \tag {3} +$$ + +Here, $D_{is}(\mathbf{p}) > 1$ indicates that there is an intersection of at least two objects at the point, and $D_{is}(\mathbf{p}) = 0$ represents that the point $\mathbf{p}$ is not inside any object. Considering the set of query points $\mathcal{C}_p$ inside the container $\mathcal{C}$ , the intersection loss is defined as per Equation 4. + +$$ +\mathcal {L} _ {i s} = \sum_ {\mathbf {p} \in \mathcal {C} _ {p}} D _ {i s} (\mathbf {p}) \tag {4} +$$ + +Container Extrusion Loss. Let $V_{i}$ be the set of vertices of the triangular mesh corresponding to the object $O_{i}$ and $S_{\mathcal{C}}$ be the SDF of the container $\mathcal{C}$ . We define the container extrusion loss as per Equation 5 + +$$ +\mathcal {L} _ {e x t} = \sum_ {i = 1} ^ {N} \sum_ {\mathbf {v} \in V _ {i}} \max (- \epsilon , S _ {\mathcal {C}} (\mathbf {v})) \tag {5} +$$ + +Here, $\epsilon$ , the distance between a vertex and the container's boundary, creates a "buffer zone" around the container boundary to control when the extrusion loss begins to be active. While a higher value of $\epsilon$ hinders the movement of objects inside the container, a very small value leads to portions of objects suddenly extruding out of the container boundary, leading to an unstable optimization. We find $\epsilon = 0.01$ to be a reasonable value that avoids penalizing objects that are slightly inside the container but still close to the boundary. We observed that in some cases, silhouette loss was just enough to contain the objects with the container, especially for simple shapes. However, for more irregular shapes with asymmetric and skewed spread, extrusion loss proved to be helpful. + +![](images/c4900ca9642bc614d3c51e632f4a02d53ad0b9b6aa71d418888638c25ff28ae3.jpg) +Figure 10. Illustration of packing arbitrarily shaped objects into arbitrarily shaped containers. The initial containers, the set of object shapes to be packed, and the final packed configuration are shown in the figure. + +# 4. Experiments + +In this section, we showcase the results obtained through the RASP framework for irregular object packing drawing parallels with 3D Anamorphic art. Furthermore, we extend RASP to applications like part assembly and creating artistic illustrations. + +# 4.1. Irregular Object Packing + +For 3D object packing, we demonstrate the results majorly on the objects from the IR-BPP dataset [47], which contains objects from four categories: General, Kitchen, ABC, and Block Out. A few other illustrations also include objects from the VOLMAP dataset [3] and SilNet dataset [49]. + +Following the existing literature of 3D object packing, we define the packing efficiency/density $(\rho)$ , as per Equation 6. + +$$ +\rho = \sum_ {O _ {i} \in \mathcal {C}} \frac {\left| O _ {i} \right|}{\left| \mathcal {C} \right|} \tag {6} +$$ + +Here, $|O_i|$ and $|\mathcal{C}|$ are the volume of the $i^{th}$ object and container volume, respectively. + +Figure 6, compares the packing density of irregular 3D objects from different categories into a typical cuboidal container. Interestingly, RASP does not require any regularity in object shapes and can handle arbitrary shapes of different sizes, achieving reasonably good packing configurations. + +Deciding the number of objects that can be maximally packed within a container is crucial for optimal packing. To start with, we decide the initial number of objects as $N_{init}$ based on the average volume of the objects and the container volume, such that $N_{init} = \frac{|C|}{|O|_{avg}}$ . Consider $N_{max}$ as an unknown upper bound, i.e., the maximum a physical container can accommodate. If $N_{init} < N_{max}$ , we draw another set of $N_{k}$ objects from the pool (if available) and again optimize the arrangement with $N_{init} + N_{k}$ based on the target silhouettes of projection. In case this exceeds $N_{max}$ , the remaining objects either start extruding out of the container or intersecting heavily within the container depending on the predominance of $\mathcal{L}_{is}$ or $\mathcal{L}_{ext}$ , respectively. All the results correspond to $N = N_{max}$ objects that can maximally + +![](images/c705e941fff4d2853f3443fa07d69bf188b2d458f6d35867b05ea6ef92c980ab.jpg) +Figure 11. Extending RASP to perform part reassembly of broken objects. The figure showcases the target silhouettes and broken parts reassembled using RASP. + +![](images/6c567d3784fd3a4a121f8fce875b1ecceb40ab40c31b61e27da633d9ea2ae87d.jpg) + +![](images/b03a1eafa78e369b79456ca572fb23e903f9b76a0c0d1344c92d99f07fcf0c5d.jpg) + +fit inside the container with no intersection, a condition essential for real-world applicability. Moreover, the objects are randomly initialized within the container before optimization. We discuss the effect of different initialization strategies in the supplementary. + +Due to silhouette or shadow-guided optimization, the resulting arrangement can sometimes be physically inaccurate. As shown in Figure 9, when the number of objects $N$ is less than the maximum capacity $N_{max}$ , the arrangement often floats within the container rather than settling at the bottom. While such effects are inherent to this type of optimization-based framework, we demonstrate that merely adjusting the width of the silhouettes would effectively constrain the objects to rest at the bottom of the container in Figure 9 progressively. + +Arbitrarily Shaped Container. Owing to its design to derive insights from the projected silhouettes, RASP can also accommodate arbitrarily shaped containers, as shown in Figure 1 (b) and Figure 10. Similar to multi-view shape optimization, the target shadows are essentially the silhouettes of the container from 5 different views. Figure 10 depicts the packing on donut-shaped and squirrel-shaped containers. + +Effect of loss terms. Figure 8 (top) shows the convergence of each of the loss terms for illustrations in Figure 6 and Figure 10. The intersection density for all the results is zero, offering a multi-view consistent, intersection-free/non-overlapping configuration. Figure 8 (bottom) also illustrates the impact of different loss terms in addition to observations in Figure 5 for $\mathcal{L}_{sil}$ vs $\mathcal{L}_{sil} + \mathcal{L}_{in}$ . Overall, we find that extrusion term $\mathcal{L}_{ext}$ acts as a regularizer, preventing objects from drifting too far apart to avoid intersections. While the intersection remains zero without $\mathcal{L}_{ext}$ , its inclusion improves the rendered silhouette by reducing $\mathcal{L}_{sil}$ . Notably, objects are positioned closer together when $\mathcal{L}_{ext}$ is applied. + +Comparison with existing methods. Out of several relevant works on 3D object packing (as described in Section 2), the work by Ma et al. [20] is the closest to our optimization setup (not guided by shadows) whose setup is different from RASP since it involves swapping, replacement with new objects, and object enlargement - which we believe is not practical in a real-world setup where we cannot + +alter the object dimensions. However, since their implementation is unavailable online, we choose to quantitatively compare the average packing efficiency across different objects. Although different from ours, we also compared our average packing efficiency of a physically inspired reinforcement learning-based online packing method by Zhao et al. [47] over their dataset to establish the efficacy of our optimization-based methods learning solely from 2D image guidance. Zhao et al. [47] look at only one or a few objects at a time, and packing efficiency is dependent on the sequence in which the objects arrive. Moreover, the object placement is guided by the dynamics and constraints of physics. In contrast, RASP - an offline method, takes a more global standpoint by optimizing all $N \leq N_{max}$ objects at a time. Overall, RASP obtains an average of $45\%$ occupancy over the four different categories of the IR-BPP dataset [47] which is better than Ma et al. [20] (34%) and drops below that of Zhao et al. [47] (51.9%) evaluated over the objects from online packing dataset. Moreover, Ma et al. [20] bears an average optimization time of 40.55 minutes while RASP achieves the same in $\sim 15$ minutes. + +For a qualitative comparison over samples from IR-BPP dataset, we adapt [47] to align closest to our setting. Specifically, we generate 100 random sequences of the same set (and same number) of objects from each IR-BPP dataset category (as in Figure 6) and report the best configuration to compare with RASP in Figure. 7. Due to implementation constraints of [47], we could not assign different colors to objects or obtain multiple views of the packed arrangement of [47], and hence, we compared only the top view. RASP performs similar to or slightly better than the physics-aware method for the same object set. + +# 4.2. 3D Part Assembly + +Part assembly using RASP also shares similarities with multi-view geometry optimization. However, instead of optimizing a single shape, RASP learns the rigid transformations of different parts of a single shape to obtain a 3D consistent arrangement across all the views. For demonstrating part assembly, we used the *Fantastic Breaks* dataset [16] that consists of paired 3D scans of real-world broken objects and their complete counterparts. Figure 11 demonstrates some qualitative results on reassembling broken ob + +![](images/e4a6c09ceec5c20349d31750e436a4a69642aa3d6d837dede9919d293f5040d3.jpg) +(a) + +![](images/cad65da15629067b44ad15720cd42aea7c9af74b27dd7680b2ab487e1c487118.jpg) + +![](images/0c7f60b4aa1e1ca7d53310a61bc9251dbff8effbb6882587513f3c768980016f.jpg) + +![](images/15d872a65bddc4f51a98d693b5c83ba605dc62690f5ed1ab3d64a9ec77de79a7.jpg) + +![](images/6b062edc091b46cb609c45d6e12c16cda577e5f756169a30590072673d6805e3.jpg) + +![](images/2a958efa43803a3e1b6ed24124cbdc11b6702edf80ef61602381876d821332d1.jpg) + +![](images/091ab7586e0e77565a3de9a2338cfbb3b4d181d0c7c21456d8f2c92b77e9a39f.jpg) + +![](images/559927167e6cbdf22a2f65657c727fd2899aebd3eead05534a3009430965a73a.jpg) +(b) + +![](images/0de3cd7e3b2b6d868a7d128ad9563cf97fb0b47d0cbe72ec4510d13323d2fd54.jpg) + +![](images/fff5fabb63fd2c94777058a11d01cf1bc72f9ea14d292c015c50562cf45e818b.jpg) +(c) +Figure 12. (a) & (b) use objects from the Kitchen dataset to generate 2-view and 3-view 3D anamorphic art. (c) Multi-view pixelated portraits generated using RASP with artistic texture applied. (d) RASP recreates the famous cover page of the book Gödel, Escher, Bach by Douglas Hofstadter. The 3D and dynamic visualization of these and more related results are provided in the supplementary. + +![](images/a2dffb58bd10748462ab55979316d98cca457b03f4dfc85b4c4d8390b9236a77.jpg) +(d) + +jects. Notably, it does so solely via silhouette guidance without the need for any explicit 3D ground truth supervision. + +# 4.3. Multi-view Anamorphic Art + +We also leverage RASP to reinterpret and construct different forms of multi-view anamorphic art. Thus far, we have seen that silhouettes or shadows do provide important cues for 3D arrangement. However, these binary images alone cannot create interesting artistic illustrations. Therefore, we also seek guidance from colored or textured images. Take, for example, the portrait of Nikola Tesla shown in Figure 2 (a). One approach would be to search for suitable objects and apply heuristic methods to arrange them in a way that recreates the portrait's appearance. Alternatively, one could collect and randomly arrange objects (like those in Figure 2 (c)) within the outline of the silhouette, then paint the arrangement to revive the essence of the portrait. Following the latter approach, RASP uses a two-stage optimization procedure, where first, it arranges the discrete objects in a 3D space through silhouette matching across a set of views and later performs rendering-based texture optimization (integrated as an add-on) over the finalized arrangement to match the target textures. Figure 12 (a) illustrates how this strategy allows RASP to recreate multi-view portraits of Nikola Tesla and Marie Curie across two non-orthogonal views that are $120^{\circ}$ apart using objects from the Kitchen dataset. Furthermore, it also generates consistent ensembles that are meaningful across three non-orthogonal views, as shown in Figure 12 (b), giving a visually plausible appearance of Pokémon, Wall-e, and Minion. In figure 12 (c) we obtain 3D arrangements using binary images and then apply artistic textures to create unique 3D illustrations. The resemblance of the textured arrangement and the associated + +rendered images highlights the creative potential of RASP. In Figure 12 (d) we recreate the famous artistic cover page of the Book by Douglas Hofstadter featuring blocks casting shadows of the first letters of artists – Gödel, Escher, and Bach. Overall, RASP is a versatile optimization pipeline stressing on the fact that shadows do provide limited yet useful cues for 3D understanding and artistic exploration. + +# 5. Conclusion + +We introduce RASP, a differentiable rendering-based optimization framework for irregular 3D object packing, part assembly, and recreating artistic illustrations, taking guidance from images, whether in the form of binary silhouettes, textured RGB images, or simple portrait sketches. The current offline strategy does not account for physical dynamics, such as the influence of gravity on object placement. Additionally, RASP struggles with multi-part (more than 2 or 3 parts) part assembly, particularly symmetrical and/or identical parts. An interesting potential extension of this work would be to incorporate physics-based guidance for the packing to be more physically consistent. We believe that there are plenty of untapped capabilities in shadows that drive 3D understanding, and RASP presents a few of them. We anticipate that this work would attract researchers from different domains to use shadows or silhouettes for applications like partitioning and reconfiguration of complex 3D objects into simpler forms, multi-part part assembly, dynamic visual arts, CAD design, and handling non-rigid deformations. + +Acknowledgments. This work is supported by the Prime Minister Research Fellowship (PMRF) grant and the Jibaben Patel Chair in Artificial Intelligence. We also thank Prajwal Singh, IIT Gandhinagar, for his valuable inputs. + +# References + +[1] Thomas Byholm, Martti Toivakka, and Jan Westerholm. Effective packing of 3-dimensional voxel-based arbitrarily shaped particles. Powder Technology, 196(2):139-146, 2009. 2 +[2] Xuelin Chen, Hao Zhang, Jinjie Lin, Ruizhen Hu, Lin Lu, Qi-Xing Huang, Bedrich Benes, Daniel Cohen-Or, Baoquan Chen, et al. Dapper: decompose-and-pack for 3d printing. ACM Trans. Graph., 34(6):213-1, 2015. 2, 3 +[3] Gianmarco Cherchi and Marco Livesu. 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(a) An ensemble of arbitrary shapes casting the shadow of alphabets CVPR and numbers 2025, (b) a set of irregular objects packed inside a face-shaped container, (c) an assembly of parts of a vessel obtained through multi-view shadow guidance via RASP." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 404, + 200, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 404, + 200, + 417 + ], + "spans": [ + { + "bbox": [ + 151, + 404, + 200, + 417 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 430, + 297, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 430, + 297, + 682 + ], + "spans": [ + { + "bbox": [ + 54, + 430, + 297, + 682 + ], + "type": "text", + "content": "Recent advancements in learning-based methods have opened new avenues for exploring and interpreting art forms, such as shadow art, origami, and sketch art, through computational models. One notable visual art form is 3D Anamorphic Art in which an ensemble of arbitrarily shaped 3D objects creates a realistic and meaningful expression when observed from a particular viewpoint and loses its coherence over the other viewpoints. In this work, we build on insights from 3D Anamorphic Art to perform 3D object arrangement. We introduce RASP, a differentiable-rendering-based framework to arrange arbitrarily shaped 3D objects within a bounded volume via shadow (or silhouette)-guided optimization with an aim of minimal inter-object spacing and near-maximal occupancy. Furthermore, we propose a novel SDF-based formulation to handle inter-object intersection and container extrusion. We demonstrate that RASP can be extended to part assembly alongside object packing considering 3D objects to be \"parts\" of another 3D object. Finally, we present artistic illustrations of multi-view anamorphic art, achieving meaningful expressions from multiple viewpoints within a single ensemble." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 404, + 394, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 404, + 394, + 417 + ], + "spans": [ + { + "bbox": [ + 315, + 404, + 394, + 417 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "text", + "content": "For centuries, artists have used their expressions to redefine the boundaries of visual art, demonstrating how art shapes reality and influences human perception. Their work has also broadly impacted technology, design, and engineering. In this work, we explore using a unique visual art form, 3D Anamorphic Art, to tackle challenges in irregular object packing and extend this approach to part assembly." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": "Interestingly, we are not alone in using (and, in fact, developing) artistic expressions to address applications in computer vision. For example, DeepDream [24] uses GAN-based style transfer to apply the style of classical paintings, like those of Van Gogh or Picasso, to contemporary images. RePaint [34] leverages deep learning and 3D printing to replicate the colors and textures of paintings by optimizing ink layering. ScribGen [7] creates human-like scribbles and hand-strokes in different styles. Beyond images, researchers have expanded artistic techniques into 3D analysis and understanding, as in Shadow Art [23], which uses shadows for 3D reconstruction, sketch-based 3D generation [32], expressive hand movements [8], and the design of knot configurations for realistic visual effects [9]. In this work, we draw upon insights from 3D Anamorphic Art to address an important problem of packing arbitrarily shaped objects within a 3D bounding volume (or container). Packing has" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. 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Illustration of 3D Anamorphic Art (a, b): Portrait of Nikola Tesla and Bedrich Smetana by Patrick Proško and Shadow Art (c, d): Dirty White Trash and Wild Mood Swing by Tim Nobel and Sue Webster." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 228, + 295, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 295, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 295, + 289 + ], + "type": "text", + "content": "numerous practical applications, spanning fields such as combinatorial optimization [22, 33], computational geometry [12, 20], computer vision and graphics [2, 18, 31], machine learning [11, 46], robotics [35, 38, 44], and logistics and manufacturing [47]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 290, + 295, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 290, + 295, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 290, + 295, + 518 + ], + "type": "text", + "content": "3D Anamorphic Art. 3D Anamorphic Art involves arranging objects in 3D space such that the arrangement appears coherent and meaningful only from the specific viewpoint(s). In contrast, from any other view, it appears random. For example, artist Patrick Proško used this technique at the Illusion Art Museum Prague by arranging electrical appliances to form a portrait of Nikola Tesla [28] (Figure 2 (a)) and arranging musical instruments to create a likeness of the musician Bedřich Smetana [29] (Figure 2 (b)). This concept also extends to shadows cast by such arrangements under particular camera-light configurations. For instance, artists Tim Noble and Sue Webster created Dirty White Trash [25] and Wild Mood Swings [26], where carefully arranged trash and wooden pieces cast shadows of people sitting beside each other (see Figure 2 (c, d)). Whether through perspective views from specific viewpoints or shadows created under particular camera-light configurations, these projections reveal valuable insights about the arrangement of objects in 3D space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 520, + 295, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 520, + 295, + 663 + ], + "spans": [ + { + "bbox": [ + 55, + 520, + 295, + 663 + ], + "type": "text", + "content": "Relation with Object Packing. Consider a cuboidal bounding volume (or container), as depicted in Figure 3. When fully packed, this cuboid would appear as a rectangle or square upon being viewed orthographically along any of its faces. Similarly, it would cast rectangular or square shadows under the same viewing configuration. Ideally, gaps between the objects would appear as holes in the shadow from at least one perspective. By considering these shadows (technically binary images or silhouettes of the packed state) as target projections, we aim to arrange arbitrarily shaped elements within a bounding volume, thereby tackling the packing problem." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Interestingly, this approach also allows for bounding volumes of arbitrary shapes, where the target projections are simply the volume's appearance from multiple viewpoints. If the elements to be arranged are whole 3D objects, this" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 316, + 77, + 400, + 128 + ], + "blocks": [ + { + "bbox": [ + 316, + 77, + 400, + 128 + ], + "lines": [ + { + "bbox": [ + 316, + 77, + 400, + 128 + ], + "spans": [ + { + "bbox": [ + 316, + 77, + 400, + 128 + ], + "type": "image", + "image_path": "5a2918fa8318c869725fbaf88d68f2144c7250fc184def3f2792145e819d1578.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 133, + 392, + 142 + ], + "lines": [ + { + "bbox": [ + 325, + 133, + 392, + 142 + ], + "spans": [ + { + "bbox": [ + 325, + 133, + 392, + 142 + ], + "type": "text", + "content": "Objects to be packed" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 406, + 70, + 492, + 133 + ], + "blocks": [ + { + "bbox": [ + 406, + 70, + 492, + 133 + ], + "lines": [ + { + "bbox": [ + 406, + 70, + 492, + 133 + ], + "spans": [ + { + "bbox": [ + 406, + 70, + 492, + 133 + ], + "type": "image", + "image_path": "39b96b898f2663589c51511e825836e39c8f9b53620e648fe84db223c87e4b69.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 413, + 134, + 479, + 142 + ], + "lines": [ + { + "bbox": [ + 413, + 134, + 479, + 142 + ], + "spans": [ + { + "bbox": [ + 413, + 134, + 479, + 142 + ], + "type": "text", + "content": "Packed arrangement" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 150, + 553, + 172 + ], + "lines": [ + { + "bbox": [ + 313, + 150, + 553, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 150, + 553, + 172 + ], + "type": "text", + "content": "Figure 3. An example depicting the packed state of a cuboidal container and the associated silhouettes/shadows." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 498, + 72, + 553, + 133 + ], + "blocks": [ + { + "bbox": [ + 498, + 72, + 553, + 133 + ], + "lines": [ + { + "bbox": [ + 498, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 498, + 72, + 553, + 133 + ], + "type": "image", + "image_path": "ab13742bc1c0cc2a578b37de99f5514875e75e784c6472d7721d65329eb80aef.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 500, + 133, + 551, + 142 + ], + "lines": [ + { + "bbox": [ + 500, + 133, + 551, + 142 + ], + "spans": [ + { + "bbox": [ + 500, + 133, + 551, + 142 + ], + "type": "text", + "content": "Target Shadows" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 194, + 553, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 553, + 230 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 553, + 230 + ], + "type": "text", + "content": "approach addresses the irregular object packing problem. However, if these elements are \"parts\" of another object altogether, it naturally extends to the part assembly problem." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 231, + 554, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 231, + 554, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 231, + 554, + 361 + ], + "type": "text", + "content": "A key challenge in existing packing methods is managing overlaps or intersections among the elements to be packed. While some methods focus on simple geometries like cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or rely on assumptions of convexity or concavity in polyhedrons [19, 30, 37], often using simple heuristics [17, 27], others handle irregular shapes by employing voxelized representations [1, 6], which tend to be susceptible to approximation errors. This work introduces a signed-distance field (SDF) approach to manage inter-object intersection and container extrusion." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 362, + 554, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 554, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 554, + 434 + ], + "type": "text", + "content": "Contributions. In this work, we introduce RASP - Revisiting 3D Anamorphic art for Shadow-guided Packing of Irregular Objects. Given a set of arbitrarily shaped objects, a bounding volume (or container), and information about the appearance of its projection/shadows from different viewpoints in the packed state:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 436, + 553, + 628 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 314, + 436, + 553, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 436, + 553, + 496 + ], + "spans": [ + { + "bbox": [ + 314, + 436, + 553, + 496 + ], + "type": "text", + "content": "- We propose a differentiable rendering-based framework to tackle irregular object packing by drawing inspiration from 3D Anamorphic Art. Our goal is to achieve near-maximal occupancy and minimal inter-object spacing within a known bounding volume." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 314, + 496, + 553, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 496, + 553, + 531 + ], + "spans": [ + { + "bbox": [ + 314, + 496, + 553, + 531 + ], + "type": "text", + "content": "- We present a novel SDF-based approach to manage interobject intersections and object-container extrusions, enhanced by an image-based loss function." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 314, + 532, + 553, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 532, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 314, + 532, + 553, + 579 + ], + "type": "text", + "content": "- We demonstrate that RASP can also be applied to part assembly without the need for explicit 3D ground truth supervision. Additionally, we illustrate compelling visual effects that cater to multi-view anamorphic art." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 580, + 553, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 580, + 553, + 628 + ], + "spans": [ + { + "bbox": [ + 314, + 580, + 553, + 628 + ], + "type": "text", + "content": "- To the best of our knowledge, this is the first approach to address packing (and part assembly) using only shadows or projections, guided by the principles of differentiable rendering." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Through this work, we push the boundaries of 3D anamorphic art to address an important research question: can shadows be used to automatically find an optimal arrangement of arbitrarily shaped 3D objects within a bounded volume? While our framework aims to provide practical solutions, it does not always yield an optimal arrangement due to the NP-hard nature of the packing prob" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5850" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 73, + 550, + 240 + ], + "blocks": [ + { + "bbox": [ + 62, + 73, + 550, + 240 + ], + "lines": [ + { + "bbox": [ + 62, + 73, + 550, + 240 + ], + "spans": [ + { + "bbox": [ + 62, + 73, + 550, + 240 + ], + "type": "image", + "image_path": "43a03c5139264eff03d497eda1542f90a6019900a9637102f4e5e015d2e43ad2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "lines": [ + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "type": "text", + "content": "Figure 4. The proposed differentiable rendering-based pipeline for RASP. We use Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "type": "inline_equation", + "content": "1e - 2" + }, + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 54, + 251, + 555, + 285 + ], + "type": "text", + "content": " over 1000 iterations. Packing the Kitchen dataset (106 objects, 80000 grid points) takes nearly 17 minutes, and reassembly for each object in the Fantastic Breaks dataset (2 parts, 80000 grid points) takes under 3 minutes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 305, + 295, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 305, + 295, + 343 + ], + "spans": [ + { + "bbox": [ + 54, + 305, + 295, + 343 + ], + "type": "text", + "content": "lem [10]. Nonetheless, this work introduces a new perspective on solving the 3D packing and arrangement problem using shadows as a guiding mechanism." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 355, + 148, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 355, + 148, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 355, + 148, + 368 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 376, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 376, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 54, + 376, + 295, + 472 + ], + "type": "text", + "content": "Object packing has been addressed using heuristic-based, model-based, learning-based, or policy-based (online) object packing. Several methods have assumed simple object geometries, such as cuboids [4, 43], spheres [21], cylinders [36], or ellipsoids [13], or leverage convexity and/or concavity in polyhedrons [19, 30, 37]. This section primarily discusses the methods dealing with irregular object packing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 473, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 295, + 700 + ], + "type": "text", + "content": "Heuristic-based Methods. Several previous attempts at object packing were primarily based on heuristic strategies. One method proposed by Wang et al. [40] sequentially places objects employing the Deepest Bottom Left Fill (DBLF) heuristic strategy. However, it is shown to create holes, leading to empty spaces. Later, Wang and Hauser [39] addressed this limitation by reducing unfilled gaps through height-map minimization, which in itself ignores the difference between positions at the same level. HAPE3D [19], another heuristic-based algorithm, deploys the principle of the minimum total potential energy for irregular polyhedrons. Even after allowing free translations and rotations, it fails to achieve high packing density. Lamas et al. [15] voxelized irregular objects and used metaheuristic algorithms to optimize voxel representation that is limited due to memory constraints. Heuristic-based methods generally apply well to objects with only a few facets and struggle to achieve a high packing density while dealing with complex irregular objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "content": "Learning-Based Methods. The key challenge for pack" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 305, + 553, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 305, + 553, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 305, + 553, + 484 + ], + "type": "text", + "content": "ing irregular objects is to handle object collision detection or intersection/overlap avoidance. Several different geometric representations of objects (say, objects tightly bound by a sphere or cuboid [45]) have been assumed by different methods for collision detection and packing optimization. Romanova et al. [1] pose the packing problem as a nonlinear optimization problem and propose quasi-phi functions for simple concave polyhedrons to describe nonoverlapping and distance constraints. However, obtaining a local optimum takes longer, even with free translations and rotations. A few works [2, 45] learned to decompose the object into multiple small parts to perform packing to reduce the supporting materials, build time, and assembly costs of 3D printing. While [2] used voxel-based representation, [45] used level sets to represent the object parts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 486, + 553, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 640 + ], + "type": "text", + "content": "Moreover, Zhao et al. [47] and Zhuang et al. [48] divide the objects into convex shapes for efficient collision detection in physical simulation and pack the objects either using shaking of the container as per the dynamic principle or reinforcement learning in an online manner, respectively. Our work does not focus on online packing. Cui et al. [5] performed efficient collision metric computation in the spectral domain using voxel representation and Fast Fourier Transform (FFT) for discrete placement search. They deploy a greedy strategy to sort objects by volume from largest to smallest and then pack sequentially to minimize the distance between the new and already placed objects at each placement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "type": "text", + "content": "The closest to our setting is the work by Ma et al. [20] that optimizes the orientation and position of the objects from their initial placement. However, their approach is multi-stage, involving combinatorial optimization that includes object swapping, enlargement, and replacement to reduce the gaps between the objects. Furthermore, they" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "5851" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 210, + 148 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 210, + 148 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 210, + 148 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 210, + 148 + ], + "type": "image", + "image_path": "23d7e04cae6d09488f7cad8a252a4a472a6d630402408a73d79c9cfdbfbeb9dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 158, + 555, + 192 + ], + "lines": [ + { + "bbox": [ + 54, + 158, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 54, + 158, + 555, + 192 + ], + "type": "text", + "content": "Figure 5. (a) Target shadow a duck-shaped container, optimized arrangement with mesh intersections. Mesh enclosed within (b) sphere and (c) cube where the intersection region doesn't include object meshes. (d) SDF of two non-intersecting and intersecting objects (intersecting points are marked in red), and SDF transformation within the container." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 212, + 70, + 372, + 148 + ], + "blocks": [ + { + "bbox": [ + 212, + 70, + 372, + 148 + ], + "lines": [ + { + "bbox": [ + 212, + 70, + 372, + 148 + ], + "spans": [ + { + "bbox": [ + 212, + 70, + 372, + 148 + ], + "type": "image", + "image_path": "66a5441b7fbc1e7a052ebeb0c6e6958820d35a9ef0999aaf7175501356c335cc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 372, + 71, + 547, + 147 + ], + "blocks": [ + { + "bbox": [ + 372, + 71, + 547, + 147 + ], + "lines": [ + { + "bbox": [ + 372, + 71, + 547, + 147 + ], + "spans": [ + { + "bbox": [ + 372, + 71, + 547, + 147 + ], + "type": "image", + "image_path": "f78328b8a77e8b1dd193f435661d99942a845baba417f2c3bbb9cc079a3f39f3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 213, + 296, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 213, + 296, + 333 + ], + "spans": [ + { + "bbox": [ + 54, + 213, + 296, + 333 + ], + "type": "text", + "content": "also minimize the height of a container to obtain an optimal one through binary search. Due to repeated processing, the method is heavily time-consuming. In contrast, given a set of irregular objects, ours is a single-stage end-to-end optimization pipeline that performs packing only via 2D shadow guidance without any intense calculation within the 3D bounding volume. While Ma et al. [20] have the information about the object set and process only one object at a time, sequentially determining the initial placement, our proposed method considers a set of objects at a time." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 342, + 111, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 111, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 111, + 354 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 361, + 123, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 123, + 372 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 123, + 372 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "spans": [ + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": "The key idea of our work is to arrange a set " + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": " of arbitrarily shaped 3D objects within an arbitrarily shaped container " + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": " such that the resulting arrangement casts " + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": " different shadows (projections) when viewed from " + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": " different directions using a differentiable rendering-based optimization pipeline. Interestingly, the problem has two interpretations depending on how we consider the set " + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 54, + 378, + 295, + 462 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 462, + 295, + 533 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "text", + "content": "(a) 3D Packing problem: when " + }, + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "text", + "content": " contains arbitrarily shaped 3D objects and " + }, + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 462, + 295, + 498 + ], + "type": "text", + "content": " is the bounding container within the viewing volume." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "content": "(b) Part Assembly problem: when " + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "content": " contains \"parts\" of a 3D object " + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "inline_equation", + "content": "(O)" + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "content": " where this object " + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "content": " itself is treated as the container " + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 498, + 295, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "In the case of packing, we might not always have a ground truth or a unique solution, i.e., objects can be arranged in multiple optimal ways to maximize occupancy and minimize spaces. However, we have a ground truth shape in a part assembly whose parts can be assembled only in one way. We demonstrate how this is implemented in Section 4. Overall, we propose a differentiable-rendering-based framework that naturally caters to both these requirements, in addition to generating multi-view anamorphic art. Inspired by computational visual arts, some of the recent works based on shadow art [8, 9, 23] have demonstrated the potential of 3D shape understanding, analysis, and reconstruction through shadows. In this work, we take the first step towards leveraging the benefit of differentiable rendering and principles of visual arts [42] to propose shadow-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 213, + 465, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 465, + 225 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 465, + 225 + ], + "type": "text", + "content": "based 3D packing and part assembly." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 231, + 430, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 231, + 430, + 244 + ], + "spans": [ + { + "bbox": [ + 313, + 231, + 430, + 244 + ], + "type": "text", + "content": "3.2. Proposed Approach" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "spans": [ + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": "The flow of the proposed methodology has been outlined in Figure 4. Consider a set of " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " arbitrarily shaped objects " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\{O_1, O_2, \\ldots, O_N\\}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " such that each " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "O_i" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " is represented as a triangular mesh, an arbitrarily shaped bounding container " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " located inside the camera viewing volume " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ", and shadow projection configuration " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\{X_k = (I_k, P_k) | k = 1, 2, \\ldots, K\\}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{I_k\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " are the target images under the camera configuration " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{P_k\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ". Essentially, the camera configuration " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "P_k = (R_k, t_k)" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " corresponds to the camera extrinsic parameters associated with image " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "I_k" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ". With " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " as input to the differentiable renderer " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ", the objective here is to learn the optimal arrangement of objects in set " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " inside the container " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " placed within the viewing volume " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " such that the resulting images " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{\\widehat{I_k}\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " rendered under camera configurations " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{P_k\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " are close to the corresponding target images " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{I_k\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ". From the shadow's perspective, the target images are silhouettes, and we assume that the light (to cast the shadows) will be co-located with the camera. Finding the arrangement of objects is equivalent to finding the rigid transformation, i.e., rotation and translation " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\{R_i, t_i\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " of each object " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "O_i" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " in set " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": ". We use quaternions for obtaining rotations - (a) to avoid gimble lock through other representations like axis-angle rotation or rotation composition of rotation along " + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "inline_equation", + "content": "x - y - z" + }, + { + "bbox": [ + 313, + 248, + 555, + 595 + ], + "type": "text", + "content": " axes, (b) for smooth interpolation, and (c) to learn a smaller number of parameters compared to the rotation matrices. Specifically, we obtain the angle of rotations across each of the coordinate axes and convert them to quaternion representation for optimization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 600, + 424, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 424, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 424, + 612 + ], + "type": "text", + "content": "3.2.1. Objective Function" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 615, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 615, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 615, + 554, + 651 + ], + "type": "text", + "content": "We propose a combined loss function consisting of an SDF-based intersection loss, an image-based loss, and an object-container extrusion loss, as per Equation 1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 374, + 658, + 553, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 658, + 553, + 670 + ], + "spans": [ + { + "bbox": [ + 374, + 658, + 553, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s i l}} + \\mathcal {L} _ {\\text {i s}} + \\lambda \\mathcal {L} _ {\\text {e x t}} \\tag {1}", + "image_path": "fca9ce253e224a1addfcb366c54350e8c6fa7c6285f390a7dd64e4f4122fa2b4.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 411, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 411, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 411, + 689 + ], + "type": "text", + "content": "Here, we set " + }, + { + "bbox": [ + 313, + 677, + 411, + 689 + ], + "type": "inline_equation", + "content": "\\lambda = 0.001" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "Image-based (Silhouette) Loss. A straightforward approach is to optimize each object's rotation and translation" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5852" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 178, + 182 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 178, + 182 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 178, + 182 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 178, + 182 + ], + "type": "image", + "image_path": "10f7529cc0d25d66feb6ce70bbb867e8f9279a56d418c8cdf2eb1d0b76152541.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 190, + 555, + 214 + ], + "lines": [ + { + "bbox": [ + 55, + 190, + 555, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 555, + 214 + ], + "type": "text", + "content": "Figure 6. Visualization of 3D Object packing into a cuboidal container using RASP over four different object categories from [47]. Each instance is labeled with the number of objects packed in the container and the packing density." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 189, + 72, + 302, + 182 + ], + "blocks": [ + { + "bbox": [ + 189, + 72, + 302, + 182 + ], + "lines": [ + { + "bbox": [ + 189, + 72, + 302, + 182 + ], + "spans": [ + { + "bbox": [ + 189, + 72, + 302, + 182 + ], + "type": "image", + "image_path": "0fd64d3df27779b54491466b2da58f39f9d37047776dc89333f0dcd0c563577d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 432, + 182 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 432, + 182 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 432, + 182 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 432, + 182 + ], + "type": "image", + "image_path": "f4647124650eded28b9ae09d6857990c6a707fa29aa2886cdf0043e894c41543.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 444, + 72, + 552, + 182 + ], + "blocks": [ + { + "bbox": [ + 444, + 72, + 552, + 182 + ], + "lines": [ + { + "bbox": [ + 444, + 72, + 552, + 182 + ], + "spans": [ + { + "bbox": [ + 444, + 72, + 552, + 182 + ], + "type": "image", + "image_path": "fbc55d1d0af1854fdf4cf8c1ab759343cc17351ee4a68964e4c00f22017bc840.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 56, + 232, + 298, + 349 + ], + "blocks": [ + { + "bbox": [ + 56, + 232, + 298, + 349 + ], + "lines": [ + { + "bbox": [ + 56, + 232, + 298, + 349 + ], + "spans": [ + { + "bbox": [ + 56, + 232, + 298, + 349 + ], + "type": "image", + "image_path": "921f6060fd13b4bf74514ca2458441bb1ea7753524c5fb180880105ac07f19f5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 357, + 295, + 390 + ], + "lines": [ + { + "bbox": [ + 55, + 357, + 295, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 295, + 390 + ], + "type": "text", + "content": "Figure 7. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": "parameters based on image rendering loss, such as mean squared error, as per Equation 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 444, + 295, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 444, + 295, + 478 + ], + "spans": [ + { + "bbox": [ + 91, + 444, + 295, + 478 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s i l} = \\frac {1}{M N K} \\sum_ {k = 1} ^ {K} \\sum_ {i = 1} ^ {M N} \\left| \\left| I _ {k} (i) - \\widehat {I} _ {k} (i) \\right| \\right| _ {2} ^ {2} \\tag {2}", + "image_path": "2cfaced92826413bb123143900a46932c56957849b8cca70371231d245ff74da.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 486, + 296, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 296, + 545 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 296, + 545 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 486, + 296, + 545 + ], + "type": "inline_equation", + "content": "MN" + }, + { + "bbox": [ + 55, + 486, + 296, + 545 + ], + "type": "text", + "content": " is the total number of pixels in the image. As shown in Figure 5 (a), the projection of the arrangement may appear feasible (apart from a few gaps where more objects could fit), but in 3D, objects can still intersect within a duck-shaped container." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 546, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 296, + 714 + ], + "type": "text", + "content": "Therefore, the loss functions should penalize mesh intersections. However, handling mesh intersections is complex; some methods [14] detect intersections by evaluating each triangular face of one mesh against others, which is computationally costly and impractical for large numbers of meshes. To simplify intersection computation, some approaches enclose objects within unit spheres or cubes, finding intersections among these simpler bounding shapes [45]. Although faster, this approach often fails with asymmetrically shaped objects, as intersections between bounding spheres or cubes may not correspond to intersections among the actual object meshes, as shown in Figure 5 (b, c). This can lead to excessive penalization of intersections, causing the network to push objects apart and create unnec" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 315, + 236, + 547, + 371 + ], + "blocks": [ + { + "bbox": [ + 315, + 236, + 547, + 371 + ], + "lines": [ + { + "bbox": [ + 315, + 236, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 315, + 236, + 547, + 371 + ], + "type": "image", + "image_path": "ae6bfa2782cad2693fe2b806d14034a6cdee34d1191fdb7fb886e8c35d38e7b3.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 378, + 555, + 412 + ], + "lines": [ + { + "bbox": [ + 313, + 378, + 555, + 412 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 555, + 412 + ], + "type": "text", + "content": "Figure 8. (Top) Loss curves for packed configuration in Figure 6 (solid line) & Figure 10 (dashed line). (Bottom) Effect of different loss terms on the packing. Best viewed in pdf with zoom." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 437, + 365, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 365, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 365, + 448 + ], + "type": "text", + "content": "essary gaps." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 449, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 640 + ], + "type": "text", + "content": "Intersection Loss. To overcome these challenges, we propose an SDF-based approach to handle both object-object intersections and object-container extrusion. The signed distance field (SDF) provides the shortest distance from a point to the surface, with a negative sign indicating the point is inside and a positive sign indicating it is outside the object. Specifically, we pre-compute the SDF of each mesh (using [41]) at fixed query points within the container " + }, + { + "bbox": [ + 313, + 449, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 449, + 555, + 640 + ], + "type": "text", + "content": " (a few milliseconds on GPU) and deform the SDFs with every update of the learned rotation and translation parameters. Rather than recalculating the SDF for each rigid transformation, we warp the previous SDF using a linear transformation to match the new configuration, as shown in Figure 5 (d). The degree of intersection, thus, can be determined by identifying points where more than one object has a negative SDF value, as marked in red in Figure 5 (d)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": "Let the SDF of the object " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "O_{i}" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": " at a point " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": " after a rigid transformation (updated rotation and translation) has been applied to " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "O_{i}" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": " be denoted by " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\widetilde{S}_{O_i}(\\mathbf{p})" + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": ". One could simply consider the amount of intersection to be proportional to the number of objects under intersection at any point within the container, i.e., " + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "inline_equation", + "content": "D_{is}(\\mathbf{p}) = |\\{i\\in \\{1,2,\\dots N\\} |\\widetilde{S}_{O_i}(\\mathbf{p}) < 0\\} |." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5853" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 289, + 150 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 289, + 150 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 289, + 150 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 289, + 150 + ], + "type": "image", + "image_path": "396e46554280870483ff91774d1aace40eea7d52724f729adb772d8da01476ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "lines": [ + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "text", + "content": "Figure 9. Illustration of packing of 24 cubes, each of dimensions " + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "text", + "content": " cubic units, into a container of dimensions " + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "inline_equation", + "content": "6 \\times 6 \\times 6" + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "text", + "content": " cubic units, with varying silhouette widths to simulate physically correct packing for " + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "inline_equation", + "content": "N < N_{max}" + }, + { + "bbox": [ + 55, + 161, + 296, + 207 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "text", + "content": "However, we observed that considering the SDF value instead of just the count provides smoother guidance to resolve the intersections. Therefore, we define the degree of intersection " + }, + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "inline_equation", + "content": "D_{is}(\\mathbf{p})" + }, + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "text", + "content": " as the sum of the (negative of) SDFs of the objects that contain point " + }, + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 220, + 296, + 293 + ], + "type": "text", + "content": " within them at every optimization step, such that," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 300, + 295, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 300, + 295, + 332 + ], + "spans": [ + { + "bbox": [ + 102, + 300, + 295, + 332 + ], + "type": "interline_equation", + "content": "D _ {i s} (\\mathbf {p}) = \\sum_ {\\left\\{\\forall O _ {i} \\mid \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) < 0 \\right\\}} - \\widetilde {S} _ {O _ {i}} (\\mathbf {p}) \\tag {3}", + "image_path": "db34bc6821171cf57615d0185a2c862feaf51e3dbbbfa36da0eb254dd6517c14.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "inline_equation", + "content": "D_{is}(\\mathbf{p}) > 1" + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": " indicates that there is an intersection of at least two objects at the point, and " + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "inline_equation", + "content": "D_{is}(\\mathbf{p}) = 0" + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": " represents that the point " + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": " is not inside any object. Considering the set of query points " + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_p" + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": " inside the container " + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 341, + 296, + 401 + ], + "type": "text", + "content": ", the intersection loss is defined as per Equation 4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 410, + 295, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 410, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 134, + 410, + 295, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i s} = \\sum_ {\\mathbf {p} \\in \\mathcal {C} _ {p}} D _ {i s} (\\mathbf {p}) \\tag {4}", + "image_path": "f236a1f637adf0befbe6367fa09c97ade5097937be4037e040030bb7cd774ed3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "content": "Container Extrusion Loss. Let " + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "inline_equation", + "content": "V_{i}" + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "content": " be the set of vertices of the triangular mesh corresponding to the object " + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "inline_equation", + "content": "O_{i}" + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{C}}" + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "content": " be the SDF of the container " + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 446, + 296, + 495 + ], + "type": "text", + "content": ". We define the container extrusion loss as per Equation 5" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 503, + 295, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 503, + 295, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 295, + 537 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e x t} = \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {v} \\in V _ {i}} \\max (- \\epsilon , S _ {\\mathcal {C}} (\\mathbf {v})) \\tag {5}", + "image_path": "d543c1f3d4c759e2f5041364cd7a8330b22bcbd00b5acc27f28f7682bd3ebed0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": ", the distance between a vertex and the container's boundary, creates a \"buffer zone\" around the container boundary to control when the extrusion loss begins to be active. While a higher value of " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": " hinders the movement of objects inside the container, a very small value leads to portions of objects suddenly extruding out of the container boundary, leading to an unstable optimization. We find " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.01" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": " to be a reasonable value that avoids penalizing objects that are slightly inside the container but still close to the boundary. We observed that in some cases, silhouette loss was just enough to contain the objects with the container, especially for simple shapes. However, for more irregular shapes with asymmetric and skewed spread, extrusion loss proved to be helpful." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 71, + 553, + 159 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 553, + 159 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 553, + 159 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 553, + 159 + ], + "type": "image", + "image_path": "c4900ca9642bc614d3c51e632f4a02d53ad0b9b6aa71d418888638c25ff28ae3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 167, + 555, + 212 + ], + "lines": [ + { + "bbox": [ + 313, + 167, + 555, + 212 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 555, + 212 + ], + "type": "text", + "content": "Figure 10. Illustration of packing arbitrarily shaped objects into arbitrarily shaped containers. The initial containers, the set of object shapes to be packed, and the final packed configuration are shown in the figure." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 229, + 395, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 395, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 395, + 243 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 249, + 555, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 249, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 249, + 555, + 308 + ], + "type": "text", + "content": "In this section, we showcase the results obtained through the RASP framework for irregular object packing drawing parallels with 3D Anamorphic art. Furthermore, we extend RASP to applications like part assembly and creating artistic illustrations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 316, + 456, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 456, + 329 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 456, + 329 + ], + "type": "text", + "content": "4.1. Irregular Object Packing" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 332, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 332, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 332, + 554, + 392 + ], + "type": "text", + "content": "For 3D object packing, we demonstrate the results majorly on the objects from the IR-BPP dataset [47], which contains objects from four categories: General, Kitchen, ABC, and Block Out. A few other illustrations also include objects from the VOLMAP dataset [3] and SilNet dataset [49]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 393, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 554, + 426 + ], + "type": "text", + "content": "Following the existing literature of 3D object packing, we define the packing efficiency/density " + }, + { + "bbox": [ + 313, + 393, + 554, + 426 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 313, + 393, + 554, + 426 + ], + "type": "text", + "content": ", as per Equation 6." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 402, + 426, + 553, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 426, + 553, + 455 + ], + "spans": [ + { + "bbox": [ + 402, + 426, + 553, + 455 + ], + "type": "interline_equation", + "content": "\\rho = \\sum_ {O _ {i} \\in \\mathcal {C}} \\frac {\\left| O _ {i} \\right|}{\\left| \\mathcal {C} \\right|} \\tag {6}", + "image_path": "1495f7900ef8f1b2de9fd6919f8cd824e3b5655905b59133995e6b83301db438.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "inline_equation", + "content": "|O_i|" + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}|" + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "text", + "content": " are the volume of the " + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 313, + 459, + 554, + 483 + ], + "type": "text", + "content": " object and container volume, respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 483, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 554, + 544 + ], + "type": "text", + "content": "Figure 6, compares the packing density of irregular 3D objects from different categories into a typical cuboidal container. Interestingly, RASP does not require any regularity in object shapes and can handle arbitrary shapes of different sizes, achieving reasonably good packing configurations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": "Deciding the number of objects that can be maximally packed within a container is crucial for optimal packing. To start with, we decide the initial number of objects as " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{init}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " based on the average volume of the objects and the container volume, such that " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{init} = \\frac{|C|}{|O|_{avg}}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": ". Consider " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{max}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " as an unknown upper bound, i.e., the maximum a physical container can accommodate. If " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{init} < N_{max}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": ", we draw another set of " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{k}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " objects from the pool (if available) and again optimize the arrangement with " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{init} + N_{k}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " based on the target silhouettes of projection. In case this exceeds " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N_{max}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": ", the remaining objects either start extruding out of the container or intersecting heavily within the container depending on the predominance of " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{is}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ext}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": ", respectively. All the results correspond to " + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "inline_equation", + "content": "N = N_{max}" + }, + { + "bbox": [ + 313, + 544, + 555, + 713 + ], + "type": "text", + "content": " objects that can maximally" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5854" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 74, + 216, + 159 + ], + "blocks": [ + { + "bbox": [ + 60, + 74, + 216, + 159 + ], + "lines": [ + { + "bbox": [ + 60, + 74, + 216, + 159 + ], + "spans": [ + { + "bbox": [ + 60, + 74, + 216, + 159 + ], + "type": "image", + "image_path": "c705e941fff4d2853f3443fa07d69bf188b2d458f6d35867b05ea6ef92c980ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 167, + 555, + 190 + ], + "lines": [ + { + "bbox": [ + 55, + 167, + 555, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 555, + 190 + ], + "type": "text", + "content": "Figure 11. Extending RASP to perform part reassembly of broken objects. The figure showcases the target silhouettes and broken parts reassembled using RASP." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 227, + 74, + 381, + 159 + ], + "blocks": [ + { + "bbox": [ + 227, + 74, + 381, + 159 + ], + "lines": [ + { + "bbox": [ + 227, + 74, + 381, + 159 + ], + "spans": [ + { + "bbox": [ + 227, + 74, + 381, + 159 + ], + "type": "image", + "image_path": "6c567d3784fd3a4a121f8fce875b1ecceb40ab40c31b61e27da633d9ea2ae87d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 394, + 76, + 548, + 159 + ], + "blocks": [ + { + "bbox": [ + 394, + 76, + 548, + 159 + ], + "lines": [ + { + "bbox": [ + 394, + 76, + 548, + 159 + ], + "spans": [ + { + "bbox": [ + 394, + 76, + 548, + 159 + ], + "type": "image", + "image_path": "b03a1eafa78e369b79456ca572fb23e903f9b76a0c0d1344c92d99f07fcf0c5d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 196, + 295, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 196, + 295, + 256 + ], + "spans": [ + { + "bbox": [ + 55, + 196, + 295, + 256 + ], + "type": "text", + "content": "fit inside the container with no intersection, a condition essential for real-world applicability. Moreover, the objects are randomly initialized within the container before optimization. We discuss the effect of different initialization strategies in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "text", + "content": "Due to silhouette or shadow-guided optimization, the resulting arrangement can sometimes be physically inaccurate. As shown in Figure 9, when the number of objects " + }, + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "text", + "content": " is less than the maximum capacity " + }, + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "inline_equation", + "content": "N_{max}" + }, + { + "bbox": [ + 55, + 257, + 296, + 376 + ], + "type": "text", + "content": ", the arrangement often floats within the container rather than settling at the bottom. While such effects are inherent to this type of optimization-based framework, we demonstrate that merely adjusting the width of the silhouettes would effectively constrain the objects to rest at the bottom of the container in Figure 9 progressively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 377, + 296, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 296, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 296, + 471 + ], + "type": "text", + "content": "Arbitrarily Shaped Container. Owing to its design to derive insights from the projected silhouettes, RASP can also accommodate arbitrarily shaped containers, as shown in Figure 1 (b) and Figure 10. Similar to multi-view shape optimization, the target shadows are essentially the silhouettes of the container from 5 different views. Figure 10 depicts the packing on donut-shaped and squirrel-shaped containers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": "Effect of loss terms. Figure 8 (top) shows the convergence of each of the loss terms for illustrations in Figure 6 and Figure 10. The intersection density for all the results is zero, offering a multi-view consistent, intersection-free/non-overlapping configuration. Figure 8 (bottom) also illustrates the impact of different loss terms in addition to observations in Figure 5 for " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sil}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sil} + \\mathcal{L}_{in}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": ". Overall, we find that extrusion term " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ext}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": " acts as a regularizer, preventing objects from drifting too far apart to avoid intersections. While the intersection remains zero without " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ext}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": ", its inclusion improves the rendered silhouette by reducing " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sil}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": ". Notably, objects are positioned closer together when " + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ext}" + }, + { + "bbox": [ + 55, + 474, + 295, + 629 + ], + "type": "text", + "content": " is applied." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "content": "Comparison with existing methods. Out of several relevant works on 3D object packing (as described in Section 2), the work by Ma et al. [20] is the closest to our optimization setup (not guided by shadows) whose setup is different from RASP since it involves swapping, replacement with new objects, and object enlargement - which we believe is not practical in a real-world setup where we cannot" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "spans": [ + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "text", + "content": "alter the object dimensions. However, since their implementation is unavailable online, we choose to quantitatively compare the average packing efficiency across different objects. Although different from ours, we also compared our average packing efficiency of a physically inspired reinforcement learning-based online packing method by Zhao et al. [47] over their dataset to establish the efficacy of our optimization-based methods learning solely from 2D image guidance. Zhao et al. [47] look at only one or a few objects at a time, and packing efficiency is dependent on the sequence in which the objects arrive. Moreover, the object placement is guided by the dynamics and constraints of physics. In contrast, RASP - an offline method, takes a more global standpoint by optimizing all " + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "inline_equation", + "content": "N \\leq N_{max}" + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "text", + "content": " objects at a time. Overall, RASP obtains an average of " + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "text", + "content": " occupancy over the four different categories of the IR-BPP dataset [47] which is better than Ma et al. [20] (34%) and drops below that of Zhao et al. [47] (51.9%) evaluated over the objects from online packing dataset. Moreover, Ma et al. [20] bears an average optimization time of 40.55 minutes while RASP achieves the same in " + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "inline_equation", + "content": "\\sim 15" + }, + { + "bbox": [ + 313, + 196, + 555, + 447 + ], + "type": "text", + "content": " minutes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 448, + 556, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 556, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 556, + 579 + ], + "type": "text", + "content": "For a qualitative comparison over samples from IR-BPP dataset, we adapt [47] to align closest to our setting. Specifically, we generate 100 random sequences of the same set (and same number) of objects from each IR-BPP dataset category (as in Figure 6) and report the best configuration to compare with RASP in Figure. 7. Due to implementation constraints of [47], we could not assign different colors to objects or obtain multiple views of the packed arrangement of [47], and hence, we compared only the top view. RASP performs similar to or slightly better than the physics-aware method for the same object set." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "type": "text", + "content": "4.2. 3D Part Assembly" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Part assembly using RASP also shares similarities with multi-view geometry optimization. However, instead of optimizing a single shape, RASP learns the rigid transformations of different parts of a single shape to obtain a 3D consistent arrangement across all the views. For demonstrating part assembly, we used the *Fantastic Breaks* dataset [16] that consists of paired 3D scans of real-world broken objects and their complete counterparts. Figure 11 demonstrates some qualitative results on reassembling broken ob" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5855" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 71, + 167, + 243 + ], + "blocks": [ + { + "bbox": [ + 57, + 71, + 167, + 243 + ], + "lines": [ + { + "bbox": [ + 57, + 71, + 167, + 243 + ], + "spans": [ + { + "bbox": [ + 57, + 71, + 167, + 243 + ], + "type": "image", + "image_path": "e4a6c09ceec5c20349d31750e436a4a69642aa3d6d837dede9919d293f5040d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 246, + 118, + 255 + ], + "lines": [ + { + 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(a) & (b) use objects from the Kitchen dataset to generate 2-view and 3-view 3D anamorphic art. (c) Multi-view pixelated portraits generated using RASP with artistic texture applied. (d) RASP recreates the famous cover page of the book Gödel, Escher, Bach by Douglas Hofstadter. The 3D and dynamic visualization of these and more related results are provided in the supplementary." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 408, + 93, + 555, + 243 + ], + "blocks": [ + { + "bbox": [ + 408, + 93, + 555, + 243 + ], + "lines": [ + { + "bbox": [ + 408, + 93, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 408, + 93, + 555, + 243 + ], + "type": "image", + "image_path": "a2dffb58bd10748462ab55979316d98cca457b03f4dfc85b4c4d8390b9236a77.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 246, + 481, + 255 + ], + "lines": [ + { + "bbox": [ + 470, + 246, + 481, + 255 + ], + "spans": [ + { + "bbox": [ + 470, + 246, + 481, + 255 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 304, + 295, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 295, + 340 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 295, + 340 + ], + "type": "text", + "content": "jects. Notably, it does so solely via silhouette guidance without the need for any explicit 3D ground truth supervision." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 349, + 211, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 211, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 211, + 361 + ], + "type": "text", + "content": "4.3. Multi-view Anamorphic Art" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "content": "We also leverage RASP to reinterpret and construct different forms of multi-view anamorphic art. Thus far, we have seen that silhouettes or shadows do provide important cues for 3D arrangement. However, these binary images alone cannot create interesting artistic illustrations. Therefore, we also seek guidance from colored or textured images. Take, for example, the portrait of Nikola Tesla shown in Figure 2 (a). One approach would be to search for suitable objects and apply heuristic methods to arrange them in a way that recreates the portrait's appearance. Alternatively, one could collect and randomly arrange objects (like those in Figure 2 (c)) within the outline of the silhouette, then paint the arrangement to revive the essence of the portrait. Following the latter approach, RASP uses a two-stage optimization procedure, where first, it arranges the discrete objects in a 3D space through silhouette matching across a set of views and later performs rendering-based texture optimization (integrated as an add-on) over the finalized arrangement to match the target textures. Figure 12 (a) illustrates how this strategy allows RASP to recreate multi-view portraits of Nikola Tesla and Marie Curie across two non-orthogonal views that are " + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "inline_equation", + "content": "120^{\\circ}" + }, + { + "bbox": [ + 55, + 366, + 296, + 713 + ], + "type": "text", + "content": " apart using objects from the Kitchen dataset. Furthermore, it also generates consistent ensembles that are meaningful across three non-orthogonal views, as shown in Figure 12 (b), giving a visually plausible appearance of Pokémon, Wall-e, and Minion. In figure 12 (c) we obtain 3D arrangements using binary images and then apply artistic textures to create unique 3D illustrations. The resemblance of the textured arrangement and the associated" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 304, + 555, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 389 + ], + "type": "text", + "content": "rendered images highlights the creative potential of RASP. In Figure 12 (d) we recreate the famous artistic cover page of the Book by Douglas Hofstadter featuring blocks casting shadows of the first letters of artists – Gödel, Escher, and Bach. Overall, RASP is a versatile optimization pipeline stressing on the fact that shadows do provide limited yet useful cues for 3D understanding and artistic exploration." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 403, + 388, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 388, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 388, + 415 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 425, + 555, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 555, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 555, + 663 + ], + "type": "text", + "content": "We introduce RASP, a differentiable rendering-based optimization framework for irregular 3D object packing, part assembly, and recreating artistic illustrations, taking guidance from images, whether in the form of binary silhouettes, textured RGB images, or simple portrait sketches. The current offline strategy does not account for physical dynamics, such as the influence of gravity on object placement. Additionally, RASP struggles with multi-part (more than 2 or 3 parts) part assembly, particularly symmetrical and/or identical parts. An interesting potential extension of this work would be to incorporate physics-based guidance for the packing to be more physically consistent. We believe that there are plenty of untapped capabilities in shadows that drive 3D understanding, and RASP presents a few of them. We anticipate that this work would attract researchers from different domains to use shadows or silhouettes for applications like partitioning and reconfiguration of complex 3D objects into simpler forms, multi-part part assembly, dynamic visual arts, CAD design, and handling non-rigid deformations." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work is supported by the Prime Minister Research Fellowship (PMRF) grant and the Jibaben Patel Chair in Artificial Intelligence. We also thank Prajwal Singh, IIT Gandhinagar, for his valuable inputs." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5856" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "type": "text", + "content": "[1] Thomas Byholm, Martti Toivakka, and Jan Westerholm. 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Given the significant data sparsity and measurement uncertainty in radar height data, achieving automatic calibration during system operation has long been a challenge. To address the sparsity issue, we propose a Dual-Perspective representation that gathers features from both frontal and bird's-eye views. The frontal view contains rich but sensitive height information, whereas the bird's-eye view provides robust features against height uncertainty. We thereby propose a novel Selective Fusion Mechanism to identify and fuse reliable features from both perspectives, reducing the effect of height uncertainty. Moreover, for each view, we incorporate a Multi-Modal Cross-Attention Mechanism to explicitly find location correspondences through cross-modal matching. During the training phase, we also design a Noise-Resistant Matcher to provide better supervision and enhance the robustness of the matching mechanism against sparsity and height uncertainty. Our experimental results, tested on the nuScenes dataset, demonstrate that our method significantly outperforms previous radar-camera auto-calibration methods, as well as existing state-of-the-art LiDAR-camera calibration techniques, establishing a new benchmark for future research. The code is available at https://github.com/nycuacm/RC-AutoCalib", + "bbox": [ + 88, + 335, + 485, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 744, + 220, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Radars and cameras are increasingly favored in advanced driver-assistance systems (ADAS) due to their cost-effectiveness and robust performance in diverse weather conditions. A critical research area in these systems involves data fusion and multi-modal calibration to ensure reliable functioning in real-world settings [16, 19, 37, 39, 44]. Conventional calibration techniques for 3D radar and cam-", + "bbox": [ + 89, + 770, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ebae9f8891c4527e94ac318400060fa02e23460c96294e20aabd5463d4a770f9.jpg", + "image_caption": [ + "Figure 1. An overview of the proposed RC-AutoCalib method. The approach takes input from radar-camera miscalibration, representing it as feature pairs in Dual-perspective view. These feature representations are then enhanced through feature matching block, from which reliable features are selected to predict the rotation vector and translation." + ], + "image_footnote": [], + "bbox": [ + 517, + 301, + 905, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "eras primarily focus on offline methods, which often rely on specialized calibration targets like checkerboards or corner reflectors, and are generally limited to the radar measurement plane [3, 4, 10-12, 29, 32]. These methods, while effective, require substantial time and manual effort, and they do not account for sensor displacements that can occur under normal operating conditions. This limitation underscores the necessity for online auto-calibration, which can dynamically adjust to changes over time.", + "bbox": [ + 509, + 566, + 906, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Online auto-calibration methods eliminate the need for calibration targets, focusing on matching natural features collected by radar and camera sensors. While this approach offers greater flexibility in real-world scenarios, exploration in this area remains limited, with no established benchmarks using publicly available datasets to date. Only the approach by Schöller et al. [26] utilizes deep learning to address the problem of online auto-calibration for radar and camera. However, their focus remains exclusively on rotational calibration, without addressing translational calibration.", + "bbox": [ + 509, + 704, + 908, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In contrast, online auto-calibration methods for LiDAR and camera [8, 9, 18, 20, 21, 25, 27, 31, 35, 36, 41-43] have", + "bbox": [ + 511, + 869, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 109, + 887, + 233, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6700", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b1376840bc4ef2796da1bf69e5d96931c2180cf0aa47e922ed80c92f95dcbb67.jpg", + "image_caption": [ + "(a) Elevation Ambiguity in Radar Point Clouds [19]." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 331, + 193 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5499c8f13862603e39f3bb8acaf8889cf959e743dcc1cc663e56699082a6601d.jpg", + "image_caption": [ + "(b) Noisy depth measurements and lack of object structures.", + "Figure 2. Challenges of 3D Millimeter-Wave Radar. (a) The green dashed line represents the height plane the radar focuses on. Points A, B, and C denote actual reflection positions, whereas $\\mathbf{A}_{\\mathrm{radar}}$ , $\\mathbf{B}_{\\mathrm{radar}}$ , and $\\mathbf{C}_{\\mathrm{radar}}$ are the positions recorded by the radar. $\\mathbf{D}_{\\mathrm{A}}$ , $\\mathbf{D}_{\\mathrm{B}}$ , and $\\mathbf{D}_{\\mathrm{C}}$ represent the recorded and noisy radar depths. (b) The top image shows a \"LiDAR\" depth map projected onto the camera plane, while the bottom image displays a \"radar\" depth map projected similarly. The red box highlights the issue where depths of points on the same object should be similar, yet significant variations are evident, indicating the presence of noise. Moreover, the green box shows a structural comparison: the \"LiDAR\" point cloud distinctly outlines the object's contour, while the \"radar\" point cloud fails to convey structural information." + ], + "image_footnote": [], + "bbox": [ + 336, + 117, + 478, + 189 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "been extensively explored by researchers and have demonstrated powerful capabilities. Most of these methods share a common concept of using RGB images and mis-calibrated LiDAR data as input, with the overall process divided into feature extraction, feature matching, and parameter regression. Instead of directly extracting features from RGB images [20, 27, 31, 42], some methods have modified the representation of RGB images. For instance, [18, 41] implicitly extract features in the form of semantics and edges, while [35, 43] transform RGB images into depth maps to achieve a unified representation consistent with 3D data. Overall, these methods project 3D data onto the frontal view to fuse with the camera information for further processing. The above-mentioned LiDAR-camera methods provide a reference and comparison for developing radar-camera autocalibration. However, we find that relying solely on a single viewpoint for radar-camera auto-calibration makes achieving high accuracy challenging. As depicted in Fig. 2, the frontal depth map often contains noisy point cloud data due to uncertainty from the lack of radar height information. Additionally, radar data is inherently sparse and lacks object structures. When projecting radar point clouds onto the frontal view to form the depth map, the projected points tend to overlap and become even sparser. To mitigate these challenges, we have introduced a Dual-Perspective representation that leverages attention-based selection to extract more reliable features.", + "bbox": [ + 91, + 444, + 483, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, feature matching between radar and camera is a critical component for auto-calibration. Some methods [27, 35, 43] rely on concatenation followed by several", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "convolutional layers to facilitate feature matching, while others [20] use cost volume to represent the correlation between the two sensors. However, traditional approaches depend solely on implicit supervision from the final calibration loss to guide the matching process. This lack of explicit identification of matched local pairs between sensors renders the calibration process indistinct. To address this, we have developed a Noise-Resistant Matcher that provides direct supervision for feature matching and correspondence finding.", + "bbox": [ + 511, + 90, + 906, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accordingly, as illustrated in Fig. 1, we propose RC-AutoCalib, an end-to-end network for automatic 3D radar and camera calibration, addressing the challenges of sparse and noisy radar data. To counteract these issues, we enhance a Dual-Perspective representation that integrates features from both the frontal view and the bird's eye view (BEV). The frontal view is prone to noise due to missing height information in radar point clouds, while the BEV provides more stable features, unaffected by this limitation. Our model includes a Selective Fusion Mechanism to discern and utilize beneficial features from each perspective. Additionally, we incorporate a Multi-Modal Cross-Attention Mechanism to focus on relevant areas in sparse radar point clouds. To improve calibration accuracy, we introduce Explicit Feature Matching Supervision with a Noise-Resistant Matcher, which helps the model identify and learn from correspondence points between radar and camera, filtering out noise in the process. Our results on the nuScenes dataset demonstrate significant improvements over existing LiDAR-camera calibration methods, as well as previous radar-camera auto-calibration approaches, setting a new benchmark for future research. In summary, our contributions are:", + "bbox": [ + 511, + 253, + 908, + 601 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce RC-AutoCalib, an end-to-end network for calibrating 3D radar and cameras, featuring a Dual-Perspective representation that counters the height information limitations of 3D radar data. This network includes a novel Selective Fusion Mechanism to optimally integrate features from both the frontal view and BEV perspectives.", + "- We develop a feature-matching module incorporating a Multi-Modal Cross-Attention Mechanism to enhance the utilization of radar point clouds. This module integrates a Noise-Resistant Matcher to provide Explicit Feature Matching Supervision. Thereby, RC-AutoCalib can effective filter out noise caused by height inaccuracies and enable robust learning of radar-image correspondences for calibration.", + "- Our approach demonstrates superior experimental results on the nuScenes dataset compared to existing LiDAR-camera calibration methods, establishing a new benchmark for future research." + ], + "bbox": [ + 511, + 613, + 905, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6701", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 91, + 89, + 240, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Offline Calibration", + "text_level": 1, + "bbox": [ + 91, + 114, + 272, + 130 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Offline calibration methods primarily depend on specific calibration targets and cannot address real-time errors. These methods are tailored for fixed environments and necessitate substantial manual effort to achieve precision, rendering them unsuitable for dynamic conditions and generally reserved for controlled settings. Early radar-camera calibration techniques focused on merging radar signals with camera data through homography projection that maps points from the radar's horizontal plane to the camera image plane. Due to inherent noise in radar sensors, these early methods often required specialized trihedral reflectors to establish accurate correspondences [10, 11, 29, 32]. However, the radar's limitation in accurately measuring the elevation of distant targets indicated that reflectors had to be positioned precisely on the radar's horizontal plane [29]. More recent radar calibration algorithms aim to minimize \"reprojection error\" to better synchronize object detection across both sensor fields of view, using techniques like estimating radar-to-camera transformations via reprojection error [12], or intersecting back-projected camera rays with 3D \"arcs\" that conform to radar measurements to determine necessary transformations [4]. Despite improvements, these methods still rely on specific targets and manual input efforts.", + "bbox": [ + 93, + 138, + 483, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Online Calibration", + "text_level": 1, + "bbox": [ + 91, + 497, + 272, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Online methods primarily extract features from natural scenes for calibration, offering greater flexibility and adaptability to various scenarios. The rapid development of deep learning has demonstrated neural networks' powerful feature extraction capabilities. However, due to the aforementioned challenges associated with radar, online calibration methods for radar and cameras are less prevalent. In this paper, we focus on developing an end-to-end architecture for the online auto-calibration of radar and cameras, leveraging robust benchmarks established by LiDAR and camera calibration methods.", + "bbox": [ + 89, + 521, + 482, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LiDAR and Camera. Li et al. [15] categorized targetless calibration methods into information theory-based, feature-based, ego-motion-based, and learning-based approaches. Pandey et al. [22] used mutual information between point cloud intensities and image grayscale values. Taylor and Nieto [30] utilized sensor ego-motion on moving vehicles to estimate extrinsic parameters. Levinson and Thrun [13] as well as Yuan et al. [41] optimized depth-discontinuous and depth-continuous edge features, respectively. Regnet [25] and CalibNet [8] employed deep learning to match features and regress calibration parameters. CalibRCNN [27] combined CNN with LSTM [24] and added pose constraints for accuracy. LCCNet [20] used cost volume for feature correlation. Despite achieving positive results, these methods", + "bbox": [ + 89, + 688, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "do not explicitly learn the correspondence between point clouds and images. In contrast, in this paper, we introduce Explicit Feature Matching Supervision to guide the model in learning the correspondence relationship between point clouds and images more effectively.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Radar and Camera. Peršić et al. [23] proposed an online calibration method based on detecting and tracking moving objects, focusing on rotational calibration. Schöller et al. [26] used deep learning to learn rotational calibration matrices but did not address translational calibration. Additionally, their methods utilize stationary traffic radars fixed on highway positions, differing from ours that employ vehicle-mounted 3D radars moving with the car. Wisec et al. [33] developed a targetless calibration method for 3D radar and cameras, using radar velocity information and motion-based camera pose measurements, solved with nonlinear optimization. Later, the same research team extended their work [33] to include radar ego-velocity estimates and unscaled camera pose measurements in [34] for a more complete spatiotemporal calibration. However, these methods overly rely on radar speed measurements, making them less robust to noise. Additionally, they do not leverage the power of deep learning and fail to explicitly establish the correspondence between radar and images.", + "bbox": [ + 511, + 167, + 903, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 513, + 467, + 612, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall pipeline of the RC-AutoCalib method, depicted in Fig. 3, begins with RGB images and radar point clouds as inputs. These inputs pass through the Data Transform module, yielding the frontal view estimated depth map, frontal view miscalibrated radar depth map, pseudo-BEV image, and miscalibrated radar BEV. Subsequent processing occurs in the Feature Extraction module, where features are extracted. These features are then analyzed in the Feature Matching module to enhance understanding of the correlation between feature pairs. This module incorporates a Multi-Modal Cross-Attention Mechanism, Explicit Feature Matching Supervision, and a Noise-Resistant Matcher. Following this, the Selective Fusion Mechanism aggregates the features, and the system performs parameter regression to predict rotation and translation vectors necessary for autocalibration. Detailed descriptions are provided below.", + "bbox": [ + 511, + 492, + 903, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Transform module", + "text_level": 1, + "bbox": [ + 511, + 742, + 735, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address issues of uncertainty caused by elevation ambiguity and the sparsity of radar data, we propose a DualPerspective feature representation. This approach projects two types of 3D data (i.e., the image plus its depth map and the radar point clouds) onto two different perspectives: bird's-eye view (BEV) and frontal view (FV). The BEV provides a domain where radar data is less impacted by uncertain height and offers more information about the geometry of the scene. Simultaneously, the FV retains rich", + "bbox": [ + 511, + 763, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6702", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0df646f4cd5899ced4affbcd414a36180590c0f655ff202a3fa492697e0109af.jpg", + "image_caption": [ + "Figure 3. Our system flow for iterative online auto-calibration starts with the input image, point cloud, and initial calibration parameters $T_{init}$ , which first pass through the Data Transform module (Sec. 3.1). Here, we obtain the estimated image depth map and miscalibrated radar depth map from the frontal view (FV) perspective, along with the pseudo-BEV image and miscalibrated BEV radar projection. These outputs are then processed in the Feature Extraction module (Sec. 3.2), where features from both FV and BEV perspectives undergo Feature Matching (Sec. 3.3) between the image and radar data. Subsequently, after Feature Matching and Fusion (Sec. 3.4), the Regression Head (Sec. 3.5) generates the rotation and translation vectors that form the transformation matrix, $\\hat{T}_{pred}^{i}$ , to refine calibration. Finally, $\\hat{T}_{pred}^{i}$ is fed back to $T_{init}$ to update the calibration parameters for the next $i$ -th iteration." + ], + "image_footnote": [], + "bbox": [ + 153, + 88, + 841, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "semantic information, preserving important contextual details.", + "bbox": [ + 89, + 496, + 482, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Radar data. Given a random initialized or roughly-estimated extrinsic transformation $T_{init}$ [8, 20, 31, 42], consisting of a rotation matrix $R_{init}$ and a translation vector $t_{init}$ , we transform a 3D radar point $P_r = (X_r, Y_r, Z_r)$ from the radar coordinate to $P_r^c = (X_r^c, Y_r^c, Z_r^c)$ in the camera coordinate using Eq. (1). The projection formula in Eq. (2) is then used to generate mis-calibrated FV and BEV information maps. For the FV map, the recorded pixel value is computed as $I_R^{FV}(u_f, v_f) = Z_r^c$ ; as for the BEV map, the recorded value is determined as $I_R^{BEV}(u_b, v_b) = y_r^c$ , with $y_r^c$ being $Y_r^c$ plus an offset of the camera height (i.e., the distance above the ground) to eliminate negative values. In Eq. (2), $(u_f, v_f)$ and $(u_b, v_b)$ are the coordinates of a radar point $P_r$ projected onto FV and BEV planes using projection matrices $K$ and $K'$ correspondingly. Here, $K$ is the original camera intrinsic matrix. The intrinsic parameters are manually pre-defined for $K'$ based on the map resolution and map center.", + "bbox": [ + 89, + 527, + 483, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {r} ^ {c} = T _ {\\text {i n i t}} \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right] = \\left[ \\begin{array}{c c} R _ {\\text {i n i t}} & t _ {\\text {i n i t}} \\\\ 0 & 1 \\end{array} \\right] \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 809, + 482, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{c} u _ {f} \\\\ v _ {f} \\\\ 1 \\end{array} \\right] = K \\left[ \\begin{array}{c} X _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ Y _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right], a n d \\left[ \\begin{array}{c} u _ {b} \\\\ v _ {b} \\\\ 1 \\end{array} \\right] = K ^ {\\prime} \\left[ \\begin{array}{c} X _ {r} ^ {c} \\\\ Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 854, + 482, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Camera data. For the camera data, the FV information map $I_{I}^{FV}(u_{d}, v_{d})$ is derived using the Metric Depth Estimation module, which predicts the depth image from the input image. This module employs two sequential methods: DepthAnything[40] for relative depth prediction and ZoeDepth[1] for refining it into metric depth, resulting in $I_{I}^{FV}(u_{d}, v_{d})$ . From the depth image, we convert each pixel into a pseudo point cloud $P_{p} = (X_{p}, Y_{p}, Z_{p})$ based on Eq. (3), which are then transformed/projected using matrix $K'$ to form the pseudo-BEV image $I_{I}^{BEV}$ similar to the radar case $I_{R}^{BEV}$ .", + "bbox": [ + 511, + 496, + 906, + 664 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{l l l} X _ {p} & Y _ {p} & Z _ {p} \\end{array} \\right] ^ {\\top} = K ^ {- 1} \\cdot I _ {I} ^ {F V} \\left(u _ {d}, v _ {d}\\right) \\cdot \\left[ \\begin{array}{l l l} u _ {d} & v _ {d} & 1 \\end{array} \\right] ^ {\\top}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 676, + 906, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Feature Extraction", + "text_level": 1, + "bbox": [ + 513, + 724, + 694, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After transforming point clouds and images into two unified representations—FV depth maps $(I_R^{FV}, I_I^{FV} \\in \\mathbb{R}^{H \\times W})$ and BEV maps $(I_I^{BEV}, I_R^{BEV} \\in \\mathbb{R}^{H' \\times W'})$ —we use ResNet [5] and convolutional layers to extract features from these maps. Additionally, to enhance the FV semantic content, context features are extracted from the original image using ResNet18 and are integrated with the features from $I_I^{FV}$ . The resulting feature sets, representing different perspectives for radar and camera, are denoted as $F_R^{FV}$ , $F_I^{FV} \\in \\mathbb{R}^{H/8 \\times W/8 \\times C}$ and $F_R^{BEV}$ , $F_I^{BEV} \\in$", + "bbox": [ + 511, + 748, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6703", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c3d3e842ade00d54ea8d25b509b47472141824f56a48d4eeb1c6f360ae78e966.jpg", + "image_caption": [ + "(a) Cross attention and Explicit Feature Matching Supervision" + ], + "image_footnote": [], + "bbox": [ + 120, + 101, + 488, + 224 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d365f4e01254fb8dbcd67d2c963013eea863a9280a2eed65622cd9f2acdb67a6.jpg", + "image_caption": [ + "(b) 3Dbbox $B$ illustration", + "Figure 4. Illustration of the proposed Feature Matching module." + ], + "image_footnote": [], + "bbox": [ + 511, + 99, + 874, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{H' / 8 \\times W' / 8 \\times C}$ . We detail the network architecture in the supplementary.", + "bbox": [ + 89, + 280, + 482, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Feature Matching", + "text_level": 1, + "bbox": [ + 89, + 321, + 264, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To estimate the 6-DoF (degrees of freedom) extrinsic transformation between radar and camera sensors, our model first focuses on identifying corresponding feature pairs from each sensor's perspective. As illustrated in Fig. 3, we conduct feature matching across two different perspectives. For each perspective, we implement similar matching modules that include a Multi-Modal Cross-Attention Mechanism and an Explicit Feature Matching Supervision. Additionally, in the FV case, we incorporate a Noise-Resistant Matcher.", + "bbox": [ + 89, + 343, + 483, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-Modal Cross-Attention Mechanism. Considering both perspectives, the projected point cloud data from radar is sparse with mostly zero values, while camera data is dense with rich depth information and geometric features. We propose a Multi-Modal Cross-Attention (MCA) Mechanism that enables the model to focus on non-zero feature regions and identify correlations between camera and radar features. As described in Equation Eq. (4), the inputs to the MCA are $F_{I}$ and $F_{R}$ , and the outputs are $O_{I\\leftarrow R}$ and $O_{R\\leftarrow I}$ . These outputs are used to compute the updated features $\\hat{F}_{I}$ and $\\hat{F}_{R}$ as shown in Eq. (5).", + "bbox": [ + 89, + 481, + 483, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left(O _ {I \\leftarrow R}, O _ {R \\leftarrow I}\\right) = \\left(\\Theta \\left(F _ {I}, m _ {I \\leftarrow R}\\right), \\Theta \\left(F _ {R}, m _ {R \\leftarrow I}\\right)\\right) \\tag {4} \\\\ = M C A \\left(F _ {I}, F _ {R}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 659, + 482, + 694 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {F} _ {I} = F _ {I} + O _ {I \\leftarrow R}, \\quad \\hat {F} _ {R} = F _ {R} + O _ {R \\leftarrow I}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 702, + 480, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain $O_{I \\leftarrow R}$ and $O_{R \\leftarrow I}$ in Eq. (4), we first compute the attended features $m_{I \\leftarrow R}$ and $m_{R \\leftarrow I}$ between the radar and image inside MCA. Inspired by [6, 17], we use Eq. (6) to compute attended features $m_{I \\leftarrow R}$ and $m_{R \\leftarrow I}$ , which rely on the cross-attention score $a_{IR}$ computed by Eq. (7).", + "bbox": [ + 89, + 726, + 483, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nm _ {R \\leftarrow I} = \\operatorname {S o f t m a x} \\left(a _ {I R} ^ {\\top}\\right) V _ {I}, m _ {I \\leftarrow R} = \\operatorname {S o f t m a x} \\left(a _ {I R}\\right) V _ {R}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 808, + 483, + 840 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\na _ {I R} = K _ {I} ^ {\\top} K _ {R}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 232, + 845, + 482, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $V_{*}$ and $K_{*}$ are the value and key, respectively, extracted from the feature $F_{*}$ through linear projections. Note", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "that, we reshape $F_{*}$ to $(m \\times c)$ dimension before projection and $* \\in \\{I, R\\}$ . After obtaining these attention maps $m_{I \\leftarrow R}$ and $m_{R \\leftarrow I}$ , we apply the cross-modal feature refinement function $\\Theta$ to calculate the $O_{I \\leftarrow R}$ and $O_{R \\leftarrow I}$ by Eq. (4) given $F_{I}$ and $F_{R}$ . The details of $\\Theta$ can be found in the supplementary material.", + "bbox": [ + 511, + 282, + 903, + 373 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining $\\hat{F}_I$ and $\\hat{F}_R$ , as shown in Fig. 4a, a Residual Conv Block is used to aggregate them into corresponding $F_{view}$ for each perspective branch using Eq. (8), with view $\\in \\{BEV, FV\\}$ .", + "bbox": [ + 511, + 375, + 905, + 436 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} F _ {v i e w} = \\Phi (\\operatorname {c o n v} (\\operatorname {c o n c a t} (\\hat {F} _ {I}, \\hat {F} _ {R})) \\tag {8} \\\\ + \\operatorname {c o n v} \\left(\\operatorname {c o n v} \\left(\\operatorname {c o n c a t} \\left(\\hat {F} _ {I}, \\hat {F} _ {R}\\right)\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 446, + 903, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first term of $\\Phi$ consists of the concatenated features of $\\hat{F}_I$ and $\\hat{F}_R$ after passing through one convolutional layer, while the second term involves passing through two convolutional layers. These terms are then added together to form our Residual Conv Block. Here, \"conv\" denotes a block that includes convolutional layers followed by the leakyReLU [38] activation function. The block $\\Phi$ sequentially applies the leakyReLU activation function, flattens the features, and utilizes a multi-layer perceptron (MLP).", + "bbox": [ + 511, + 502, + 905, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Explicit Feature Matching Supervision. Previously, feature matching was implicitly supervised solely by the final calibration loss to understand overall errors without specifically identifying matched pairs. We find this implicit supervision insufficient and propose directly supervising feature matching using true matching pairs generated from the correct calibration matrix. In other words, we add matching prediction and auxiliary loss during training to enhance the understanding of local feature matching pairs between $\\hat{F}_I$ and $\\hat{F}_R$ .", + "bbox": [ + 511, + 642, + 905, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivated by [17], an extra branch is designed to perform the task of Local Feature Matching during the training phase as shown in Fig. 4a. Assuming each reshaped feature $\\hat{f}_{*} \\in \\mathbb{R}^{m \\times c}$ from $\\hat{F}_{*}$ includes $m$ (i.e., $H / 8 \\times W / 8$ ) keypoints, with each keypoint having a feature descriptor of dimension $c$ . The assignment matrix $P \\in [0,1]^{m \\times m}$ is estimated based on Eq. (9).", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6704", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/83db58cfd827175c831f232a9e3d52dc4675bcda00e328e10d446fbfc9166466.jpg", + "image_caption": [ + "Figure 5. Details of the Selective Fusion Mechanism" + ], + "image_footnote": [], + "bbox": [ + 132, + 88, + 442, + 186 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nP = \\sigma_ {I} ^ {\\top} \\sigma_ {R} \\operatorname {S o f t m a x} \\left(S ^ {\\top}\\right) ^ {\\top} \\operatorname {S o f t m a x} (S), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 239, + 480, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $S \\in \\mathbb{R}^{m \\times m}$ , calculated by equation Eq. (10), is the similarity score matrix between the features extracted from two sensors after the Multi-Modal Cross-Attention step. Meanwhile, $\\sigma_{*} \\in [0, 1]^{1 \\times m}$ is the matchable score of feature points, estimated by equation Eq. (11), where $* \\in \\{I, R\\}$ . A point with a high value of $\\sigma$ means it is more likely to have a corresponding point on another map.", + "bbox": [ + 89, + 265, + 483, + 371 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS = \\operatorname {L i n e a r} \\left(\\hat {f} _ {I}\\right) ^ {\\top} \\operatorname {L i n e a r} \\left(\\hat {f} _ {R}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 382, + 482, + 402 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {*} = \\operatorname {S i g m o i d} \\left(\\operatorname {L i n e a r} \\left(\\hat {f} _ {*}\\right)\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 417, + 480, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the training phase, we use the estimated assignment matrix $P$ and the matching loss defined in Eq. (16) to directly supervise the cross-sensor matching.", + "bbox": [ + 89, + 443, + 482, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Noise-Resistant Matcher. For the FV case, when preparing the ground truth matches matrix $\\mathcal{M}$ to supervise the assignment matrix $P$ , we recognize that the radar training data contains many unreliable data points due to elevation ambiguity. Additionally, radar signals reflected by objects far from the radar plane can lead to unreliable data points. Therefore, we propose using LiDAR data to identify and remove these unreliable data points from the list of true feature matching pairs $\\mathcal{M}$ . First, we transform the LiDAR and radar point clouds into a unified camera coordinate system. For each radar 3D point $P_r^c = (X_r^c, Y_r^c, Z_r^c) \\in \\mathbb{R}^3$ , a neighbor region is created using a 3D bounding box $B$ . If the number of LiDAR point clouds $P_l^c = (X_l^c, Y_l^c, Z_l^c) \\in \\mathbb{R}^3$ within this box $B$ exceeds a threshold $\\tau$ , the radar point cloud $P_r^c$ is considered reliable.", + "bbox": [ + 89, + 489, + 482, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The 3D bounding box $B$ is adaptively designed for each radar point. Denote $\\phi, \\theta$ , and $R$ respectively represent the elevation angle, azimuth angle, and point length relative to a 3D radar point. $(\\Delta x, \\Delta z)$ are the noises caused by elevation ambiguity as defined in the method [28] and $\\Delta s$ is the error between the two sensors. As shown in Fig. 4b, the box height $h_B$ is calculated by Eq. (12) given $\\Delta s, \\phi, R$ , and a predefined parameter $\\delta$ , which represents the allowable height error from a 3D point to the radar plane.", + "bbox": [ + 89, + 715, + 482, + 853 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nh _ {B} = 2 (\\Delta y + \\Delta s) = 2 (\\delta + \\Delta s), a n d \\cos \\phi = \\sqrt {1 - (\\delta / R) ^ {2}}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 868, + 491, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The width $w_{B}$ and depth $d_{B}$ of $B$ , are then calculated by Eqs. (13) and (14). The center of a 3D bounding box $B$ of a radar point $P_{r}^{c}(X_{r}^{c}, Y_{r}^{c}, Z_{r}^{c})$ is determined as: $(X_{r}^{c} - \\Delta x / 2, Y_{r}^{c}, Z_{r}^{c} - \\Delta z / 2)$ .", + "bbox": [ + 511, + 90, + 905, + 152 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nw _ {B} = \\Delta x + 2 \\Delta s = R \\sin \\theta (1 - \\cos \\phi) + 2 \\Delta s, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 165, + 906, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nd _ {B} = \\Delta z + 2 \\Delta s = R \\cos \\theta (1 - \\cos \\phi) + 2 \\Delta s. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 199, + 906, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Due to limited space, we provide additional information and details in the supplementary material.", + "bbox": [ + 511, + 223, + 905, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Selective Fusion Mechanism", + "text_level": 1, + "bbox": [ + 511, + 263, + 766, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After the Feature Matching step, we can extract the features $F_{BEV}$ and $F_{FV}$ in the corresponding perspective branch. To enhance calibration accuracy by leveraging the distinctive contributions of each perspective, we propose a Dual-Perspective View Selective Fusion Mechanism that combines these features influenced by SKNet [14]. As illustrated in Fig. 5, we first calculate the compact feature $z$ from the sum of the two feature vectors using Eq. (15). Subsequently, a channel-wise attention mechanism adaptively selects diverse elements in the corresponding input features, guided by the compact feature descriptor $z$ . The obtained results are then added together to create the final feature $F_{select}$ .", + "bbox": [ + 511, + 286, + 906, + 484 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nz = F _ {f c} \\left(F _ {B E V} + F _ {F V}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 491, + 903, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $F_{fc}$ denotes the use of a fully connected layer, Batch-Norm [7], and the leakyReLU activation function.", + "bbox": [ + 511, + 515, + 905, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Regression Head", + "text_level": 1, + "bbox": [ + 511, + 556, + 679, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To estimate the rotation and translation parameters and form the updated transformation matrix $T_{pred}$ , we leverage the sequence generative decoder from CalibDepth [43]. Specifically, this method employs LSTM [24], where the output is defined as a sequence of actions of length $N$ in an autoregressive manner to address the inherent inaccuracies in the one-shot regression approach. After determining $T_{pred}$ at the current iteration, we update $T_{init} = T_{init} \\cdot T_{pred}^{i}$ , as illustrated in Fig. 3.", + "bbox": [ + 511, + 579, + 905, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.6. Loss Function", + "text_level": 1, + "bbox": [ + 511, + 724, + 658, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our model operates under two supervised tasks. The primary task focuses on auto-calibration, while an auxiliary task centers on local feature matching, which clarifies the correspondence between feature pairs. Consequently, we employ two corresponding loss functions: the matching loss and calibration loss.", + "bbox": [ + 511, + 747, + 905, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Explicit Correspondences Matching. With ground truth match matrix $\\mathcal{M} \\in \\{0,1\\}^{N \\times m \\times m}$ and the predicted matching $P \\in [0,1]^{N \\times m \\times m}$ and $\\sigma_{I}, \\sigma_{R} \\in [0,1]^{N \\times m}$ , the matching loss function is designed to minimize the log-likelihood", + "bbox": [ + 511, + 839, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6705", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the predicted matches as in Eq. (16). Since our calibration includes $N$ iterations, the matching loss term aggregates the loss from all iterations.", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nL _ {M} = - \\sum_ {n} ^ {N} \\left(\\frac {\\lambda}{\\Sigma \\mathcal {M}} L _ {p o s} ^ {n} + \\frac {1 - \\lambda}{\\Sigma \\mathcal {N} _ {\\mathcal {I}} + \\Sigma \\mathcal {N} _ {\\mathcal {R}}} L _ {n e g} ^ {n}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 147, + 482, + 189 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nL _ {p o s} = \\sum_ {i, j} \\log \\left(P ^ {i j}\\right) \\mathcal {M} ^ {i, j}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 200, + 482, + 234 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nL _ {n e g} = \\sum_ {i} \\log \\left(1 - \\sigma_ {I} ^ {i}\\right) \\mathcal {N} _ {I} ^ {i} + \\sum_ {j} \\log \\left(1 - \\sigma_ {R} ^ {j}\\right) \\mathcal {N} _ {R} ^ {j}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 244, + 482, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\lambda$ is the balancing coefficient between positive and negative instances. $\\mathcal{N}_R$ and $\\mathcal{N}_I$ are ground truth for \"No Matchable\" scores for pixels in the radar and camera maps respectively. The true matches matrix $\\mathcal{M}$ between camera and radar maps is dynamically computed based on the true translation $T_{gt}$ between the two sensors and the current, yet imperfect, updated translation $T_{init}$ . $\\mathcal{N}_R$ and $\\mathcal{N}_I$ are derived from $\\mathcal{M}$ by Eq. (19).", + "bbox": [ + 89, + 285, + 483, + 407 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} _ {I} ^ {i} = 1 - \\sum_ {j} \\mathcal {M} _ {i j}, \\quad \\mathcal {N} _ {R} ^ {j} = 1 - \\sum_ {i} \\mathcal {M} _ {i j}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 420, + 482, + 454 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The final matching loss function is then computed as the sum of losses from two perspectives defined as $L_{\\text{matching}} = L_{M_{bev}} + L_{M_{fv}}$ .", + "bbox": [ + 89, + 464, + 483, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Calibration Loss. To both ensure that the calibration results at each iteration step are asymptotic to the ground truth and avoid divergence between different iteration steps, we use the calibration loss $L_{\\text{calib}}$ proposed in [43]. By controlling the weight parameter $\\beta$ , the final total loss consists of the two losses mentioned above, defined as $L_{\\text{total}} = L_{\\text{calib}} + \\beta L_{\\text{matching}}$ .", + "bbox": [ + 89, + 512, + 483, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 636, + 295, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 89, + 662, + 370, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset Preparation. We utilize a subset of images from the nuScenes dataset [2] for our training and testing processes. This subset comprises 12,610 samples for training, 1,628 samples for validation, and 1,623 samples for testing. The training and testing depth range spans from 0 to 200 meters, with input and output resolutions set at $400 \\times 192$ pixels.", + "bbox": [ + 89, + 686, + 482, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Metrics. To facilitate comparison with previous work, we convert the output rotation vector to Euler angles. Then, we calculate the absolute error between the predicted values and the ground truth in all dimensions of angles and translation vectors. For all tables, the best and the second-best results are highlighted in bold and underlined, respectively.", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a4797b4c97c07cd18e6624d9d33a352233a63dbd4de4101b8095ec0b744cac54.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RangeMethodsRotation(°)Translation(cm)
MeanRollPitchYawMeanXY
R1LCCNet-11.6030.1233.1301.55616.53122.99217.648
NetCalib21.2050.3872.2890.94112.29712.53212.076
CalibDepth0.8070.3900.3451.68612.60812.86012.250
Coarse [26]2.0350.5811.5194.004---
Fine [26]1.6920.4420.9393.695---
Ours0.4270.1300.1980.9539.49812.5633.295
R2LCCNet-32.1561.5262.3642.57989.67271.66089.605
LCCNet-51.8980.9192.3142.46188.30274.21685.239
NetCalib22.7781.4654.6882.18071.03776.00157.204
CalibDepth1.6861.1490.8083.10255.38077.14612.918
Coarse [26]4.3881.8663.2518.048---
Fine [26]3.3341.3681.9376.696---
Ours0.8520.35970.44231.754447.53774.7775.415
", + "bbox": [ + 521, + 89, + 903, + 271 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ae81b4afee84c1851c350f0a9f36e7cad1660e3f88229c997f636aaec016febc.jpg", + "table_caption": [ + "Table 1. Comparison with LiDAR-Camera-Based and Radar-Camera-Based Auto-Calibration Methods on the nuScenes dataset. The methods are compared with two mis-calibration ranges, R1 ( $\\pm 10$ , $\\pm 0.25m$ ) and R2 ( $\\pm 20$ , $\\pm 1.5m$ )." + ], + "table_footnote": [], + "table_body": "
FVBEVSFMCAEMSNRRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
✓0.6570.2350.3011.43612.60212.85812.24712.700
✓0.6890.2950.3811.39212.60512.87012.28512.660
✓✓0.5750.2090.2841.23212.31512.86311.41612.667
✓✓✓0.5290.1750.2371.17611.84212.8829.97612.670
✓✓✓✓0.5020.1750.2351.09712.57412.88312.15012.688
✓✓✓✓✓0.4630.1400.2061.0429.62712.5633.68212.636
✓✓✓✓✓✓0.4270.1300.1980.9539.49812.5633.29512.635
", + "bbox": [ + 519, + 347, + 903, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Module Impact Ablation (FV: Front View, BEV: Bird's Eye View, SF: Selective Fusion, MCA: Multi-Modal Cross-Attention Mechanism, EMS: Explicit Feature Matching Supervision, NR: Noise-Resistant Matcher)", + "bbox": [ + 511, + 445, + 905, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Main results", + "text_level": 1, + "bbox": [ + 511, + 527, + 645, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compared it against the method by Schöller et al. [26]. Although this method dates back to 2019 and may not incorporate recent advancements, we have also compared it with state-of-the-art LiDAR-camera-based auto-calibration methods, including LCCNet [20], CalibDepth [43], and NetCalib2 [36]. To ensure a fair comparison, we trained and tested all these methods using the same set of parameters and radar-image dataset. As shown in Sec. 4.2, our focus lies on testing two mis-calibration ranges: $[10^{\\circ}, 0.25\\mathrm{m}]$ and $[20^{\\circ}, 1.5\\mathrm{m}]$ , representing small and large error ranges. For \"LCCNet-number\", the \"number\" corresponds to the number of iteration steps. The achieved results demonstrate that our method exhibits significantly superior average errors in both rotation and translation compared to other methods across both mis-calibration ranges.", + "bbox": [ + 511, + 550, + 906, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 787, + 678, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of each Module. Sec. 4.3 shows the impact of each module on experimental outcomes. Using both FV and BEV perspectives together reduced the mean absolute error in rotation by $12.5\\%$ . The Selective Fusion mechanism further reduced this error by $16.5\\%$ by allowing the model to choose suitable features from each perspective. The multi-", + "bbox": [ + 511, + 809, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6706", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/12b0f381f05cf71cf8978efdf53f88ed4a697b03c11634ad18b14d5180b866de.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Fusion MethodRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
Add Fusion0.6420.2170.3711.33812.54712.83212.09612.714
Concat Fusion0.5750.2090.2841.23212.31512.86311.41612.667
Selective Fusion0.5290.1750.2371.17611.84212.8829.97612.669
", + "bbox": [ + 93, + 88, + 480, + 152 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/318c9665577963d9bc60210cb65ac1992fc4341e98b8ee7aba8266f4d4a966e3.jpg", + "table_caption": [ + "Table 3. Comparison of Dual-Perspective Fusion Methods with Basic Methods" + ], + "table_footnote": [], + "table_body": "
βRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
0.10.4700.1500.2151.04410.30412.5875.68412.640
0.30.4710.1600.2241.02910.37712.5555.94012.637
0.50.4460.1640.2140.96012.11212.54911.15112.637
", + "bbox": [ + 91, + 199, + 480, + 267 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation Study on Weight Impacts in Explicit Feature Matching Loss", + "bbox": [ + 89, + 272, + 482, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "modal cross-attention mechanism also effectively reduced rotation error by $5\\%$ , demonstrating its capability to address the challenges of sparse radar depth maps. However, the mean absolute error in translation did not improve clearly based on the above modules due to the sparse and noisy radar point clouds. Next, introducing Explicit Feature Matching Supervision decreased the translation error by $23.4\\%$ , highlighting the benefit of explicit matching labels in learning correspondences. Finally, the incorporation of the Noise-Resistant Matcher further filtered out highly inaccurate noise points in the FV perspective and aided in translational calibration. As a result, the mean absolute error in rotation decreased by $7.8\\%$", + "bbox": [ + 88, + 320, + 482, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dual-Perspective Fusion Methods. Additionally, we compare our Selective Fusion Mechanism with commonly used methods such as add fusion and concatenation fusion. In Sec. 4.3, the results demonstrate a significant improvement of the proposed method over the conventional fusion methods.", + "bbox": [ + 89, + 518, + 482, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weight of Explicit Feature Matching Loss. In Sec. 4.3, we test three $\\beta$ values: 0.1, 0.3, and 0.5, excluding the noise-resistant matcher module in our method. $\\beta = 0.5$ achieved the lowest rotation error but the highest translation error. $\\beta = 0.1$ provided the best translation accuracy with negligible rotation error. Thus, $\\beta = 0.1$ was selected as the optimal balanced coefficient.", + "bbox": [ + 89, + 611, + 482, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 727, + 272, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method provides accurate calibration results across various initial mis-calibration conditions and scenes. Fig. 6a visualizes these results, showing precise calibration even with significant initial errors and sparse radar points. To highlight the effectiveness of our explicit matching supervision, we compute the cross-attention maps $I_{I\\leftarrow R}$ , $I_{R\\leftarrow I}$ between radar and image features, as visualized in Fig. 6b. The detailed formulas for computing these attention maps are provided in the supplementary material. We represent the attention maps using heatmaps and denote the projected", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f613701e9f918022500c1a109984ee6a4a4036aa3807d4f9a9a53abf078e5c17.jpg", + "image_caption": [ + "Sample 1" + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 705, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ea7d61bd5457fecf10e2ce4e0161df97189fba27b6b62d3b58081f0e6b25878.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 715, + 88, + 903, + 159 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1d843502b4ec6718a490d26cac5cfa6368ddd58c68c6d6c4fde76c60e8f7a69c.jpg", + "image_caption": [ + "Sample 2", + "Figure 6. Results visualization in the front view." + ], + "image_footnote": [], + "bbox": [ + 517, + 176, + 705, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aaa7d1c90b04d14c4144c5634c6e446101888e915155ccb2c72aafada3e1987f.jpg", + "image_caption": [ + "Sample 1", + "Sample 2" + ], + "image_footnote": [], + "bbox": [ + 715, + 175, + 903, + 246 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) Examples of calibration results by projecting radar points onto the frontal-view image. Top-left: input RGB image. Top-right: initial mis-calibrated radar point cloud projection. Bottom-left: network-predicted projection. Bottom-right: ground truth projection.", + "bbox": [ + 511, + 263, + 705, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(b) Examples of cross-attention maps highlighting the important regions the model focuses on. Top: image-attentive radar importance regions. Bottom: radar-attentive image importance regions. Left/Right: Results with and without explicit matching supervision. The projected 3D points are used to highlight the critical regions. With explicit matching supervision, our model can better identify these critical regions.", + "bbox": [ + 712, + 263, + 905, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "radar points with white color to indicate critical regions. Without explicit matching supervision, we observe that due to many zero-value relationships, the image-attentive radar exhibits weaker and less focused attention, while the radar-attentive image focuses on non-critical region, such as the ground. After incorporating explicit matching supervision, the image-attentive radar's attention becomes more concentrated on the non-zero regions, specifically the areas of radar point cloud projection. Meanwhile, the radar-attentive image effectively focuses on crucial regions, such as radar projection locations and vehicle contours, rather than being restricted to non-critical region.", + "bbox": [ + 511, + 462, + 906, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 662, + 633, + 678 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present RC-AutoCalib, an end-to-end network for 3D radar and camera calibration. By incorporating dual perspectives, we address the elevation ambiguity in 3D radar. Our Selective Fusion Mechanism integrates useful features from both FV and BEV perspectives. We also developed a Feature Matching module with a MultiModal Cross-Attention Mechanism to enhance radar point cloud utilization and a Noise-Resistant Matcher to filter out height-inaccurate noise. Our method achieves a calibration error of $0.427^{\\circ}$ in rotation and $9.498\\mathrm{cm}$ in translation on the nuScenes dataset, demonstrating competitive performance with these SOTA auto-calibration methods using dense point clouds and establishing a benchmark for future research in 3D radar and camera calibration.", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6707", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was financially supported in part (project number: 112UA10019) by the Co-creation Platform of the Industry Academia Innovation School, NYCU, under the framework of the National Key Fields Industry-University Cooperation and Skilled Personnel Training Act, from the Ministry of Education (MOE) and industry partners in Taiwan. It also supported in part by the National Science and Technology Council, Taiwan, under Grant NSTC-112-2221-E-A49-089-MY3, Grant NSTC-110-2221-E-A49-066-MY3, Grant NSTC-111-2634-F-A49-010, Grant NSTC-112-2425-H-A49-001, and in part by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and the Ministry of Education (MOE), Taiwan. We also would like to express our gratitude for the support from MediaTek Inc, Hon Hai Research Institute (HHRI), E.SUN Financial Holding Co Ltd, Advantech Co Ltd, Industrial Technology Research Institute (ITRI)", + "bbox": [ + 89, + 90, + 485, + 313 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 330, + 187, + 345 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 16280-16290, 2021. 1" + ], + "bbox": [ + 516, + 90, + 906, + 767 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6709", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RC-AutoCalib_ An End-to-End Radar-Camera Automatic Calibration Network/a8eca73f-f319-47b0-b493-af40482783f5_model.json b/2025/RC-AutoCalib_ An End-to-End Radar-Camera Automatic Calibration Network/a8eca73f-f319-47b0-b493-af40482783f5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..90747ea0d51205f88383d5e0b6cdb8f41e2cca5f --- /dev/null +++ b/2025/RC-AutoCalib_ An End-to-End Radar-Camera Automatic Calibration Network/a8eca73f-f319-47b0-b493-af40482783f5_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.9, + 0.152 + ], + "angle": 0, + "content": "RC-AutoCalib: An End-to-End Radar-Camera Automatic Calibration Network" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.18, + 0.911, + 0.269 + ], + "angle": 0, + "content": "Van-Tin Luu\\(^{1}\\), Yon-Lin Cai\\(^{1}\\), Vu-Hoang Tran\\(^{2}\\), Wei-Chen Chiu\\(^{1}\\), Yi-Ting Chen\\(^{1}\\), Ching-Chun Huang\\(^{1*}\\) \n\\(^{1}\\)National Yang Ming Chiao Tung University, Taiwan \n\\(^{2}\\)Ho Chi Minh City University of Technology and Education, Vietnam \n{tinery.eel2, yukitaka.10, walon, ychen, chingchun}@nycu.edu.tw \nhoangtv@hcmute.edu.vn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.305, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.337, + 0.486, + 0.73 + ], + "angle": 0, + "content": "This paper presents a groundbreaking approach - the first online automatic geometric calibration method for radar and camera systems. Given the significant data sparsity and measurement uncertainty in radar height data, achieving automatic calibration during system operation has long been a challenge. To address the sparsity issue, we propose a Dual-Perspective representation that gathers features from both frontal and bird's-eye views. The frontal view contains rich but sensitive height information, whereas the bird's-eye view provides robust features against height uncertainty. We thereby propose a novel Selective Fusion Mechanism to identify and fuse reliable features from both perspectives, reducing the effect of height uncertainty. Moreover, for each view, we incorporate a Multi-Modal Cross-Attention Mechanism to explicitly find location correspondences through cross-modal matching. During the training phase, we also design a Noise-Resistant Matcher to provide better supervision and enhance the robustness of the matching mechanism against sparsity and height uncertainty. Our experimental results, tested on the nuScenes dataset, demonstrate that our method significantly outperforms previous radar-camera auto-calibration methods, as well as existing state-of-the-art LiDAR-camera calibration techniques, establishing a new benchmark for future research. The code is available at https://github.com/nycuacm/RC-AutoCalib" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.745, + 0.222, + 0.76 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.771, + 0.484, + 0.877 + ], + "angle": 0, + "content": "Radars and cameras are increasingly favored in advanced driver-assistance systems (ADAS) due to their cost-effectiveness and robust performance in diverse weather conditions. A critical research area in these systems involves data fusion and multi-modal calibration to ensure reliable functioning in real-world settings [16, 19, 37, 39, 44]. Conventional calibration techniques for 3D radar and cam-" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.303, + 0.906, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.475, + 0.907, + 0.558 + ], + "angle": 0, + "content": "Figure 1. An overview of the proposed RC-AutoCalib method. The approach takes input from radar-camera miscalibration, representing it as feature pairs in Dual-perspective view. These feature representations are then enhanced through feature matching block, from which reliable features are selected to predict the rotation vector and translation." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.568, + 0.907, + 0.704 + ], + "angle": 0, + "content": "eras primarily focus on offline methods, which often rely on specialized calibration targets like checkerboards or corner reflectors, and are generally limited to the radar measurement plane [3, 4, 10-12, 29, 32]. These methods, while effective, require substantial time and manual effort, and they do not account for sensor displacements that can occur under normal operating conditions. This limitation underscores the necessity for online auto-calibration, which can dynamically adjust to changes over time." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.705, + 0.909, + 0.869 + ], + "angle": 0, + "content": "Online auto-calibration methods eliminate the need for calibration targets, focusing on matching natural features collected by radar and camera sensors. While this approach offers greater flexibility in real-world scenarios, exploration in this area remains limited, with no established benchmarks using publicly available datasets to date. Only the approach by Schöller et al. [26] utilizes deep learning to address the problem of online auto-calibration for radar and camera. However, their focus remains exclusively on rotational calibration, without addressing translational calibration." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.909, + 0.902 + ], + "angle": 0, + "content": "In contrast, online auto-calibration methods for LiDAR and camera [8, 9, 18, 20, 21, 25, 27, 31, 35, 36, 41-43] have" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.235, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6700" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.333, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.197, + 0.333, + 0.222 + ], + "angle": 0, + "content": "(a) Elevation Ambiguity in Radar Point Clouds [19]." + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.118, + 0.48, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.337, + 0.192, + 0.481, + 0.228 + ], + "angle": 0, + "content": "(b) Noisy depth measurements and lack of object structures." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.241, + 0.485, + 0.421 + ], + "angle": 0, + "content": "Figure 2. Challenges of 3D Millimeter-Wave Radar. (a) The green dashed line represents the height plane the radar focuses on. Points A, B, and C denote actual reflection positions, whereas \\(\\mathbf{A}_{\\mathrm{radar}}\\), \\(\\mathbf{B}_{\\mathrm{radar}}\\), and \\(\\mathbf{C}_{\\mathrm{radar}}\\) are the positions recorded by the radar. \\(\\mathbf{D}_{\\mathrm{A}}\\), \\(\\mathbf{D}_{\\mathrm{B}}\\), and \\(\\mathbf{D}_{\\mathrm{C}}\\) represent the recorded and noisy radar depths. (b) The top image shows a \"LiDAR\" depth map projected onto the camera plane, while the bottom image displays a \"radar\" depth map projected similarly. The red box highlights the issue where depths of points on the same object should be similar, yet significant variations are evident, indicating the presence of noise. Moreover, the green box shows a structural comparison: the \"LiDAR\" point cloud distinctly outlines the object's contour, while the \"radar\" point cloud fails to convey structural information." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.445, + 0.485, + 0.852 + ], + "angle": 0, + "content": "been extensively explored by researchers and have demonstrated powerful capabilities. Most of these methods share a common concept of using RGB images and mis-calibrated LiDAR data as input, with the overall process divided into feature extraction, feature matching, and parameter regression. Instead of directly extracting features from RGB images [20, 27, 31, 42], some methods have modified the representation of RGB images. For instance, [18, 41] implicitly extract features in the form of semantics and edges, while [35, 43] transform RGB images into depth maps to achieve a unified representation consistent with 3D data. Overall, these methods project 3D data onto the frontal view to fuse with the camera information for further processing. The above-mentioned LiDAR-camera methods provide a reference and comparison for developing radar-camera autocalibration. However, we find that relying solely on a single viewpoint for radar-camera auto-calibration makes achieving high accuracy challenging. As depicted in Fig. 2, the frontal depth map often contains noisy point cloud data due to uncertainty from the lack of radar height information. Additionally, radar data is inherently sparse and lacks object structures. When projecting radar point clouds onto the frontal view to form the depth map, the projected points tend to overlap and become even sparser. To mitigate these challenges, we have introduced a Dual-Perspective representation that leverages attention-based selection to extract more reliable features." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Furthermore, feature matching between radar and camera is a critical component for auto-calibration. Some methods [27, 35, 43] rely on concatenation followed by several" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.244 + ], + "angle": 0, + "content": "convolutional layers to facilitate feature matching, while others [20] use cost volume to represent the correlation between the two sensors. However, traditional approaches depend solely on implicit supervision from the final calibration loss to guide the matching process. This lack of explicit identification of matched local pairs between sensors renders the calibration process indistinct. To address this, we have developed a Noise-Resistant Matcher that provides direct supervision for feature matching and correspondence finding." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.255, + 0.909, + 0.602 + ], + "angle": 0, + "content": "Accordingly, as illustrated in Fig. 1, we propose RC-AutoCalib, an end-to-end network for automatic 3D radar and camera calibration, addressing the challenges of sparse and noisy radar data. To counteract these issues, we enhance a Dual-Perspective representation that integrates features from both the frontal view and the bird's eye view (BEV). The frontal view is prone to noise due to missing height information in radar point clouds, while the BEV provides more stable features, unaffected by this limitation. Our model includes a Selective Fusion Mechanism to discern and utilize beneficial features from each perspective. Additionally, we incorporate a Multi-Modal Cross-Attention Mechanism to focus on relevant areas in sparse radar point clouds. To improve calibration accuracy, we introduce Explicit Feature Matching Supervision with a Noise-Resistant Matcher, which helps the model identify and learn from correspondence points between radar and camera, filtering out noise in the process. Our results on the nuScenes dataset demonstrate significant improvements over existing LiDAR-camera calibration methods, as well as previous radar-camera auto-calibration approaches, setting a new benchmark for future research. In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.72 + ], + "angle": 0, + "content": "- We introduce RC-AutoCalib, an end-to-end network for calibrating 3D radar and cameras, featuring a Dual-Perspective representation that counters the height information limitations of 3D radar data. This network includes a novel Selective Fusion Mechanism to optimally integrate features from both the frontal view and BEV perspectives." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.84 + ], + "angle": 0, + "content": "- We develop a feature-matching module incorporating a Multi-Modal Cross-Attention Mechanism to enhance the utilization of radar point clouds. This module integrates a Noise-Resistant Matcher to provide Explicit Feature Matching Supervision. Thereby, RC-AutoCalib can effective filter out noise caused by height inaccuracies and enable robust learning of radar-image correspondences for calibration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.905, + 0.9 + ], + "angle": 0, + "content": "- Our approach demonstrates superior experimental results on the nuScenes dataset compared to existing LiDAR-camera calibration methods, establishing a new benchmark for future research." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6701" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.241, + 0.106 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.115, + 0.274, + 0.131 + ], + "angle": 0, + "content": "2.1. Offline Calibration" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.139, + 0.485, + 0.486 + ], + "angle": 0, + "content": "Offline calibration methods primarily depend on specific calibration targets and cannot address real-time errors. These methods are tailored for fixed environments and necessitate substantial manual effort to achieve precision, rendering them unsuitable for dynamic conditions and generally reserved for controlled settings. Early radar-camera calibration techniques focused on merging radar signals with camera data through homography projection that maps points from the radar's horizontal plane to the camera image plane. Due to inherent noise in radar sensors, these early methods often required specialized trihedral reflectors to establish accurate correspondences [10, 11, 29, 32]. However, the radar's limitation in accurately measuring the elevation of distant targets indicated that reflectors had to be positioned precisely on the radar's horizontal plane [29]. More recent radar calibration algorithms aim to minimize \"reprojection error\" to better synchronize object detection across both sensor fields of view, using techniques like estimating radar-to-camera transformations via reprojection error [12], or intersecting back-projected camera rays with 3D \"arcs\" that conform to radar measurements to determine necessary transformations [4]. Despite improvements, these methods still rely on specific targets and manual input efforts." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.498, + 0.274, + 0.513 + ], + "angle": 0, + "content": "2.2. Online Calibration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.522, + 0.483, + 0.687 + ], + "angle": 0, + "content": "Online methods primarily extract features from natural scenes for calibration, offering greater flexibility and adaptability to various scenarios. The rapid development of deep learning has demonstrated neural networks' powerful feature extraction capabilities. However, due to the aforementioned challenges associated with radar, online calibration methods for radar and cameras are less prevalent. In this paper, we focus on developing an end-to-end architecture for the online auto-calibration of radar and cameras, leveraging robust benchmarks established by LiDAR and camera calibration methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "LiDAR and Camera. Li et al. [15] categorized targetless calibration methods into information theory-based, feature-based, ego-motion-based, and learning-based approaches. Pandey et al. [22] used mutual information between point cloud intensities and image grayscale values. Taylor and Nieto [30] utilized sensor ego-motion on moving vehicles to estimate extrinsic parameters. Levinson and Thrun [13] as well as Yuan et al. [41] optimized depth-discontinuous and depth-continuous edge features, respectively. Regnet [25] and CalibNet [8] employed deep learning to match features and regress calibration parameters. CalibRCNN [27] combined CNN with LSTM [24] and added pose constraints for accuracy. LCCNet [20] used cost volume for feature correlation. Despite achieving positive results, these methods" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "do not explicitly learn the correspondence between point clouds and images. In contrast, in this paper, we introduce Explicit Feature Matching Supervision to guide the model in learning the correspondence relationship between point clouds and images more effectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.169, + 0.905, + 0.456 + ], + "angle": 0, + "content": "Radar and Camera. Peršić et al. [23] proposed an online calibration method based on detecting and tracking moving objects, focusing on rotational calibration. Schöller et al. [26] used deep learning to learn rotational calibration matrices but did not address translational calibration. Additionally, their methods utilize stationary traffic radars fixed on highway positions, differing from ours that employ vehicle-mounted 3D radars moving with the car. Wisec et al. [33] developed a targetless calibration method for 3D radar and cameras, using radar velocity information and motion-based camera pose measurements, solved with nonlinear optimization. Later, the same research team extended their work [33] to include radar ego-velocity estimates and unscaled camera pose measurements in [34] for a more complete spatiotemporal calibration. However, these methods overly rely on radar speed measurements, making them less robust to noise. Additionally, they do not leverage the power of deep learning and fail to explicitly establish the correspondence between radar and images." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.468, + 0.613, + 0.484 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.493, + 0.905, + 0.735 + ], + "angle": 0, + "content": "The overall pipeline of the RC-AutoCalib method, depicted in Fig. 3, begins with RGB images and radar point clouds as inputs. These inputs pass through the Data Transform module, yielding the frontal view estimated depth map, frontal view miscalibrated radar depth map, pseudo-BEV image, and miscalibrated radar BEV. Subsequent processing occurs in the Feature Extraction module, where features are extracted. These features are then analyzed in the Feature Matching module to enhance understanding of the correlation between feature pairs. This module incorporates a Multi-Modal Cross-Attention Mechanism, Explicit Feature Matching Supervision, and a Noise-Resistant Matcher. Following this, the Selective Fusion Mechanism aggregates the features, and the system performs parameter regression to predict rotation and translation vectors necessary for autocalibration. Detailed descriptions are provided below." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.743, + 0.736, + 0.758 + ], + "angle": 0, + "content": "3.1. Data Transform module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.903 + ], + "angle": 0, + "content": "To address issues of uncertainty caused by elevation ambiguity and the sparsity of radar data, we propose a DualPerspective feature representation. This approach projects two types of 3D data (i.e., the image plus its depth map and the radar point clouds) onto two different perspectives: bird's-eye view (BEV) and frontal view (FV). The BEV provides a domain where radar data is less impacted by uncertain height and offers more information about the geometry of the scene. Simultaneously, the FV retains rich" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6702" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.154, + 0.089, + 0.843, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.383, + 0.907, + 0.482 + ], + "angle": 0, + "content": "Figure 3. Our system flow for iterative online auto-calibration starts with the input image, point cloud, and initial calibration parameters \\( T_{init} \\), which first pass through the Data Transform module (Sec. 3.1). Here, we obtain the estimated image depth map and miscalibrated radar depth map from the frontal view (FV) perspective, along with the pseudo-BEV image and miscalibrated BEV radar projection. These outputs are then processed in the Feature Extraction module (Sec. 3.2), where features from both FV and BEV perspectives undergo Feature Matching (Sec. 3.3) between the image and radar data. Subsequently, after Feature Matching and Fusion (Sec. 3.4), the Regression Head (Sec. 3.5) generates the rotation and translation vectors that form the transformation matrix, \\( \\hat{T}_{pred}^{i} \\), to refine calibration. Finally, \\( \\hat{T}_{pred}^{i} \\) is fed back to \\( T_{init} \\) to update the calibration parameters for the next \\( i \\)-th iteration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.497, + 0.483, + 0.525 + ], + "angle": 0, + "content": "semantic information, preserving important contextual details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.528, + 0.484, + 0.801 + ], + "angle": 0, + "content": "Radar data. Given a random initialized or roughly-estimated extrinsic transformation \\( T_{init} \\) [8, 20, 31, 42], consisting of a rotation matrix \\( R_{init} \\) and a translation vector \\( t_{init} \\), we transform a 3D radar point \\( P_r = (X_r, Y_r, Z_r) \\) from the radar coordinate to \\( P_r^c = (X_r^c, Y_r^c, Z_r^c) \\) in the camera coordinate using Eq. (1). The projection formula in Eq. (2) is then used to generate mis-calibrated FV and BEV information maps. For the FV map, the recorded pixel value is computed as \\( I_R^{FV}(u_f, v_f) = Z_r^c \\); as for the BEV map, the recorded value is determined as \\( I_R^{BEV}(u_b, v_b) = y_r^c \\), with \\( y_r^c \\) being \\( Y_r^c \\) plus an offset of the camera height (i.e., the distance above the ground) to eliminate negative values. In Eq. (2), \\( (u_f, v_f) \\) and \\( (u_b, v_b) \\) are the coordinates of a radar point \\( P_r \\) projected onto FV and BEV planes using projection matrices \\( K \\) and \\( K' \\) correspondingly. Here, \\( K \\) is the original camera intrinsic matrix. The intrinsic parameters are manually pre-defined for \\( K' \\) based on the map resolution and map center." + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.81, + 0.483, + 0.845 + ], + "angle": 0, + "content": "\\[\nP _ {r} ^ {c} = T _ {\\text {i n i t}} \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right] = \\left[ \\begin{array}{c c} R _ {\\text {i n i t}} & t _ {\\text {i n i t}} \\\\ 0 & 1 \\end{array} \\right] \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right], \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.855, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{c} u _ {f} \\\\ v _ {f} \\\\ 1 \\end{array} \\right] = K \\left[ \\begin{array}{c} X _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ Y _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right], a n d \\left[ \\begin{array}{c} u _ {b} \\\\ v _ {b} \\\\ 1 \\end{array} \\right] = K ^ {\\prime} \\left[ \\begin{array}{c} X _ {r} ^ {c} \\\\ Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.497, + 0.907, + 0.665 + ], + "angle": 0, + "content": "Camera data. For the camera data, the FV information map \\( I_{I}^{FV}(u_{d}, v_{d}) \\) is derived using the Metric Depth Estimation module, which predicts the depth image from the input image. This module employs two sequential methods: DepthAnything[40] for relative depth prediction and ZoeDepth[1] for refining it into metric depth, resulting in \\( I_{I}^{FV}(u_{d}, v_{d}) \\). From the depth image, we convert each pixel into a pseudo point cloud \\( P_{p} = (X_{p}, Y_{p}, Z_{p}) \\) based on Eq. (3), which are then transformed/projected using matrix \\( K' \\) to form the pseudo-BEV image \\( I_{I}^{BEV} \\) similar to the radar case \\( I_{R}^{BEV} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.678, + 0.907, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{l l l} X _ {p} & Y _ {p} & Z _ {p} \\end{array} \\right] ^ {\\top} = K ^ {- 1} \\cdot I _ {I} ^ {F V} \\left(u _ {d}, v _ {d}\\right) \\cdot \\left[ \\begin{array}{l l l} u _ {d} & v _ {d} & 1 \\end{array} \\right] ^ {\\top}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.725, + 0.696, + 0.74 + ], + "angle": 0, + "content": "3.2. Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.907, + 0.903 + ], + "angle": 0, + "content": "After transforming point clouds and images into two unified representations—FV depth maps \\((I_R^{FV}, I_I^{FV} \\in \\mathbb{R}^{H \\times W})\\) and BEV maps \\((I_I^{BEV}, I_R^{BEV} \\in \\mathbb{R}^{H' \\times W'})\\)—we use ResNet [5] and convolutional layers to extract features from these maps. Additionally, to enhance the FV semantic content, context features are extracted from the original image using ResNet18 and are integrated with the features from \\(I_I^{FV}\\). The resulting feature sets, representing different perspectives for radar and camera, are denoted as \\(F_R^{FV}\\), \\(F_I^{FV} \\in \\mathbb{R}^{H/8 \\times W/8 \\times C}\\) and \\(F_R^{BEV}\\), \\(F_I^{BEV} \\in\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6703" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.102, + 0.49, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.228, + 0.468, + 0.242 + ], + "angle": 0, + "content": "(a) Cross attention and Explicit Feature Matching Supervision" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.1, + 0.875, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.228, + 0.764, + 0.24 + ], + "angle": 0, + "content": "(b) 3Dbbox \\(B\\) illustration" + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.253, + 0.688, + 0.267 + ], + "angle": 0, + "content": "Figure 4. Illustration of the proposed Feature Matching module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.281, + 0.483, + 0.315 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{H' / 8 \\times W' / 8 \\times C}\\). We detail the network architecture in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.323, + 0.266, + 0.339 + ], + "angle": 0, + "content": "3.3. Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.344, + 0.484, + 0.48 + ], + "angle": 0, + "content": "To estimate the 6-DoF (degrees of freedom) extrinsic transformation between radar and camera sensors, our model first focuses on identifying corresponding feature pairs from each sensor's perspective. As illustrated in Fig. 3, we conduct feature matching across two different perspectives. For each perspective, we implement similar matching modules that include a Multi-Modal Cross-Attention Mechanism and an Explicit Feature Matching Supervision. Additionally, in the FV case, we incorporate a Noise-Resistant Matcher." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.482, + 0.484, + 0.649 + ], + "angle": 0, + "content": "Multi-Modal Cross-Attention Mechanism. Considering both perspectives, the projected point cloud data from radar is sparse with mostly zero values, while camera data is dense with rich depth information and geometric features. We propose a Multi-Modal Cross-Attention (MCA) Mechanism that enables the model to focus on non-zero feature regions and identify correlations between camera and radar features. As described in Equation Eq. (4), the inputs to the MCA are \\( F_{I} \\) and \\( F_{R} \\), and the outputs are \\( O_{I\\leftarrow R} \\) and \\( O_{R\\leftarrow I} \\). These outputs are used to compute the updated features \\( \\hat{F}_{I} \\) and \\( \\hat{F}_{R} \\) as shown in Eq. (5)." + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.66, + 0.483, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left(O _ {I \\leftarrow R}, O _ {R \\leftarrow I}\\right) = \\left(\\Theta \\left(F _ {I}, m _ {I \\leftarrow R}\\right), \\Theta \\left(F _ {R}, m _ {R \\leftarrow I}\\right)\\right) \\tag {4} \\\\ = M C A \\left(F _ {I}, F _ {R}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.703, + 0.482, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\hat {F} _ {I} = F _ {I} + O _ {I \\leftarrow R}, \\quad \\hat {F} _ {R} = F _ {R} + O _ {R \\leftarrow I}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.484, + 0.803 + ], + "angle": 0, + "content": "To obtain \\( O_{I \\leftarrow R} \\) and \\( O_{R \\leftarrow I} \\) in Eq. (4), we first compute the attended features \\( m_{I \\leftarrow R} \\) and \\( m_{R \\leftarrow I} \\) between the radar and image inside MCA. Inspired by [6, 17], we use Eq. (6) to compute attended features \\( m_{I \\leftarrow R} \\) and \\( m_{R \\leftarrow I} \\), which rely on the cross-attention score \\( a_{IR} \\) computed by Eq. (7)." + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.809, + 0.484, + 0.842 + ], + "angle": 0, + "content": "\\[\nm _ {R \\leftarrow I} = \\operatorname {S o f t m a x} \\left(a _ {I R} ^ {\\top}\\right) V _ {I}, m _ {I \\leftarrow R} = \\operatorname {S o f t m a x} \\left(a _ {I R}\\right) V _ {R}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.233, + 0.846, + 0.483, + 0.865 + ], + "angle": 0, + "content": "\\[\na _ {I R} = K _ {I} ^ {\\top} K _ {R}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(V_{*}\\) and \\(K_{*}\\) are the value and key, respectively, extracted from the feature \\(F_{*}\\) through linear projections. Note" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.283, + 0.905, + 0.374 + ], + "angle": 0, + "content": "that, we reshape \\( F_{*} \\) to \\( (m \\times c) \\) dimension before projection and \\( * \\in \\{I, R\\} \\). After obtaining these attention maps \\( m_{I \\leftarrow R} \\) and \\( m_{R \\leftarrow I} \\), we apply the cross-modal feature refinement function \\( \\Theta \\) to calculate the \\( O_{I \\leftarrow R} \\) and \\( O_{R \\leftarrow I} \\) by Eq. (4) given \\( F_{I} \\) and \\( F_{R} \\). The details of \\( \\Theta \\) can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.376, + 0.906, + 0.437 + ], + "angle": 0, + "content": "After obtaining \\(\\hat{F}_I\\) and \\(\\hat{F}_R\\), as shown in Fig. 4a, a Residual Conv Block is used to aggregate them into corresponding \\(F_{view}\\) for each perspective branch using Eq. (8), with view \\(\\in \\{BEV, FV\\}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.448, + 0.905, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} F _ {v i e w} = \\Phi (\\operatorname {c o n v} (\\operatorname {c o n c a t} (\\hat {F} _ {I}, \\hat {F} _ {R})) \\tag {8} \\\\ + \\operatorname {c o n v} \\left(\\operatorname {c o n v} \\left(\\operatorname {c o n c a t} \\left(\\hat {F} _ {I}, \\hat {F} _ {R}\\right)\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.503, + 0.906, + 0.64 + ], + "angle": 0, + "content": "where the first term of \\(\\Phi\\) consists of the concatenated features of \\(\\hat{F}_I\\) and \\(\\hat{F}_R\\) after passing through one convolutional layer, while the second term involves passing through two convolutional layers. These terms are then added together to form our Residual Conv Block. Here, \"conv\" denotes a block that includes convolutional layers followed by the leakyReLU [38] activation function. The block \\(\\Phi\\) sequentially applies the leakyReLU activation function, flattens the features, and utilizes a multi-layer perceptron (MLP)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.906, + 0.794 + ], + "angle": 0, + "content": "Explicit Feature Matching Supervision. Previously, feature matching was implicitly supervised solely by the final calibration loss to understand overall errors without specifically identifying matched pairs. We find this implicit supervision insufficient and propose directly supervising feature matching using true matching pairs generated from the correct calibration matrix. In other words, we add matching prediction and auxiliary loss during training to enhance the understanding of local feature matching pairs between \\(\\hat{F}_I\\) and \\(\\hat{F}_R\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Motivated by [17], an extra branch is designed to perform the task of Local Feature Matching during the training phase as shown in Fig. 4a. Assuming each reshaped feature \\(\\hat{f}_{*} \\in \\mathbb{R}^{m \\times c}\\) from \\(\\hat{F}_{*}\\) includes \\(m\\) (i.e., \\(H / 8 \\times W / 8\\)) keypoints, with each keypoint having a feature descriptor of dimension \\(c\\). The assignment matrix \\(P \\in [0,1]^{m \\times m}\\) is estimated based on Eq. (9)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6704" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.133, + 0.089, + 0.443, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.196, + 0.444, + 0.21 + ], + "angle": 0, + "content": "Figure 5. Details of the Selective Fusion Mechanism" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.24, + 0.482, + 0.26 + ], + "angle": 0, + "content": "\\[\nP = \\sigma_ {I} ^ {\\top} \\sigma_ {R} \\operatorname {S o f t m a x} \\left(S ^ {\\top}\\right) ^ {\\top} \\operatorname {S o f t m a x} (S), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.266, + 0.484, + 0.372 + ], + "angle": 0, + "content": "where \\(S \\in \\mathbb{R}^{m \\times m}\\), calculated by equation Eq. (10), is the similarity score matrix between the features extracted from two sensors after the Multi-Modal Cross-Attention step. Meanwhile, \\(\\sigma_{*} \\in [0, 1]^{1 \\times m}\\) is the matchable score of feature points, estimated by equation Eq. (11), where \\(* \\in \\{I, R\\}\\). A point with a high value of \\(\\sigma\\) means it is more likely to have a corresponding point on another map." + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.383, + 0.483, + 0.403 + ], + "angle": 0, + "content": "\\[\nS = \\operatorname {L i n e a r} \\left(\\hat {f} _ {I}\\right) ^ {\\top} \\operatorname {L i n e a r} \\left(\\hat {f} _ {R}\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.418, + 0.482, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {*} = \\operatorname {S i g m o i d} \\left(\\operatorname {L i n e a r} \\left(\\hat {f} _ {*}\\right)\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.483, + 0.489 + ], + "angle": 0, + "content": "In the training phase, we use the estimated assignment matrix \\( P \\) and the matching loss defined in Eq. (16) to directly supervise the cross-sensor matching." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.49, + 0.483, + 0.716 + ], + "angle": 0, + "content": "Noise-Resistant Matcher. For the FV case, when preparing the ground truth matches matrix \\(\\mathcal{M}\\) to supervise the assignment matrix \\(P\\), we recognize that the radar training data contains many unreliable data points due to elevation ambiguity. Additionally, radar signals reflected by objects far from the radar plane can lead to unreliable data points. Therefore, we propose using LiDAR data to identify and remove these unreliable data points from the list of true feature matching pairs \\(\\mathcal{M}\\). First, we transform the LiDAR and radar point clouds into a unified camera coordinate system. For each radar 3D point \\(P_r^c = (X_r^c, Y_r^c, Z_r^c) \\in \\mathbb{R}^3\\), a neighbor region is created using a 3D bounding box \\(B\\). If the number of LiDAR point clouds \\(P_l^c = (X_l^c, Y_l^c, Z_l^c) \\in \\mathbb{R}^3\\) within this box \\(B\\) exceeds a threshold \\(\\tau\\), the radar point cloud \\(P_r^c\\) is considered reliable." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.483, + 0.854 + ], + "angle": 0, + "content": "The 3D bounding box \\(B\\) is adaptively designed for each radar point. Denote \\(\\phi, \\theta\\), and \\(R\\) respectively represent the elevation angle, azimuth angle, and point length relative to a 3D radar point. \\((\\Delta x, \\Delta z)\\) are the noises caused by elevation ambiguity as defined in the method [28] and \\(\\Delta s\\) is the error between the two sensors. As shown in Fig. 4b, the box height \\(h_B\\) is calculated by Eq. (12) given \\(\\Delta s, \\phi, R\\), and a predefined parameter \\(\\delta\\), which represents the allowable height error from a 3D point to the radar plane." + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.869, + 0.492, + 0.902 + ], + "angle": 0, + "content": "\\[\nh _ {B} = 2 (\\Delta y + \\Delta s) = 2 (\\delta + \\Delta s), a n d \\cos \\phi = \\sqrt {1 - (\\delta / R) ^ {2}}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.153 + ], + "angle": 0, + "content": "The width \\( w_{B} \\) and depth \\( d_{B} \\) of \\( B \\), are then calculated by Eqs. (13) and (14). The center of a 3D bounding box \\( B \\) of a radar point \\( P_{r}^{c}(X_{r}^{c}, Y_{r}^{c}, Z_{r}^{c}) \\) is determined as: \\( (X_{r}^{c} - \\Delta x / 2, Y_{r}^{c}, Z_{r}^{c} - \\Delta z / 2) \\)." + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.166, + 0.907, + 0.183 + ], + "angle": 0, + "content": "\\[\nw _ {B} = \\Delta x + 2 \\Delta s = R \\sin \\theta (1 - \\cos \\phi) + 2 \\Delta s, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.2, + 0.907, + 0.216 + ], + "angle": 0, + "content": "\\[\nd _ {B} = \\Delta z + 2 \\Delta s = R \\cos \\theta (1 - \\cos \\phi) + 2 \\Delta s. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.224, + 0.906, + 0.255 + ], + "angle": 0, + "content": "Due to limited space, we provide additional information and details in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.265, + 0.767, + 0.279 + ], + "angle": 0, + "content": "3.4. Selective Fusion Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.287, + 0.907, + 0.485 + ], + "angle": 0, + "content": "After the Feature Matching step, we can extract the features \\( F_{BEV} \\) and \\( F_{FV} \\) in the corresponding perspective branch. To enhance calibration accuracy by leveraging the distinctive contributions of each perspective, we propose a Dual-Perspective View Selective Fusion Mechanism that combines these features influenced by SKNet [14]. As illustrated in Fig. 5, we first calculate the compact feature \\( z \\) from the sum of the two feature vectors using Eq. (15). Subsequently, a channel-wise attention mechanism adaptively selects diverse elements in the corresponding input features, guided by the compact feature descriptor \\( z \\). The obtained results are then added together to create the final feature \\( F_{select} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.492, + 0.905, + 0.51 + ], + "angle": 0, + "content": "\\[\nz = F _ {f c} \\left(F _ {B E V} + F _ {F V}\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.906, + 0.547 + ], + "angle": 0, + "content": "where \\( F_{fc} \\) denotes the use of a fully connected layer, Batch-Norm [7], and the leakyReLU activation function." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.557, + 0.681, + 0.573 + ], + "angle": 0, + "content": "3.5. Regression Head" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.906, + 0.716 + ], + "angle": 0, + "content": "To estimate the rotation and translation parameters and form the updated transformation matrix \\( T_{pred} \\), we leverage the sequence generative decoder from CalibDepth [43]. Specifically, this method employs LSTM [24], where the output is defined as a sequence of actions of length \\( N \\) in an autoregressive manner to address the inherent inaccuracies in the one-shot regression approach. After determining \\( T_{pred} \\) at the current iteration, we update \\( T_{init} = T_{init} \\cdot T_{pred}^{i} \\), as illustrated in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.726, + 0.66, + 0.74 + ], + "angle": 0, + "content": "3.6. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.748, + 0.906, + 0.838 + ], + "angle": 0, + "content": "Our model operates under two supervised tasks. The primary task focuses on auto-calibration, while an auxiliary task centers on local feature matching, which clarifies the correspondence between feature pairs. Consequently, we employ two corresponding loss functions: the matching loss and calibration loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Explicit Correspondences Matching. With ground truth match matrix \\(\\mathcal{M} \\in \\{0,1\\}^{N \\times m \\times m}\\) and the predicted matching \\(P \\in [0,1]^{N \\times m \\times m}\\) and \\(\\sigma_{I}, \\sigma_{R} \\in [0,1]^{N \\times m}\\), the matching loss function is designed to minimize the log-likelihood" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6705" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "of the predicted matches as in Eq. (16). Since our calibration includes \\(N\\) iterations, the matching loss term aggregates the loss from all iterations." + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.148, + 0.483, + 0.19 + ], + "angle": 0, + "content": "\\[\nL _ {M} = - \\sum_ {n} ^ {N} \\left(\\frac {\\lambda}{\\Sigma \\mathcal {M}} L _ {p o s} ^ {n} + \\frac {1 - \\lambda}{\\Sigma \\mathcal {N} _ {\\mathcal {I}} + \\Sigma \\mathcal {N} _ {\\mathcal {R}}} L _ {n e g} ^ {n}\\right), \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.202, + 0.483, + 0.235 + ], + "angle": 0, + "content": "\\[\nL _ {p o s} = \\sum_ {i, j} \\log \\left(P ^ {i j}\\right) \\mathcal {M} ^ {i, j}, \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.245, + 0.483, + 0.279 + ], + "angle": 0, + "content": "\\[\nL _ {n e g} = \\sum_ {i} \\log \\left(1 - \\sigma_ {I} ^ {i}\\right) \\mathcal {N} _ {I} ^ {i} + \\sum_ {j} \\log \\left(1 - \\sigma_ {R} ^ {j}\\right) \\mathcal {N} _ {R} ^ {j}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.286, + 0.484, + 0.409 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the balancing coefficient between positive and negative instances. \\(\\mathcal{N}_R\\) and \\(\\mathcal{N}_I\\) are ground truth for \"No Matchable\" scores for pixels in the radar and camera maps respectively. The true matches matrix \\(\\mathcal{M}\\) between camera and radar maps is dynamically computed based on the true translation \\(T_{gt}\\) between the two sensors and the current, yet imperfect, updated translation \\(T_{init}\\). \\(\\mathcal{N}_R\\) and \\(\\mathcal{N}_I\\) are derived from \\(\\mathcal{M}\\) by Eq. (19)." + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.421, + 0.483, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} _ {I} ^ {i} = 1 - \\sum_ {j} \\mathcal {M} _ {i j}, \\quad \\mathcal {N} _ {R} ^ {j} = 1 - \\sum_ {i} \\mathcal {M} _ {i j}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.465, + 0.484, + 0.512 + ], + "angle": 0, + "content": "The final matching loss function is then computed as the sum of losses from two perspectives defined as \\( L_{\\text{matching}} = L_{M_{bev}} + L_{M_{fv}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.513, + 0.484, + 0.621 + ], + "angle": 0, + "content": "Calibration Loss. To both ensure that the calibration results at each iteration step are asymptotic to the ground truth and avoid divergence between different iteration steps, we use the calibration loss \\( L_{\\text{calib}} \\) proposed in [43]. By controlling the weight parameter \\( \\beta \\), the final total loss consists of the two losses mentioned above, defined as \\( L_{\\text{total}} = L_{\\text{calib}} + \\beta L_{\\text{matching}} \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.637, + 0.296, + 0.654 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.663, + 0.371, + 0.679 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.687, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Dataset Preparation. We utilize a subset of images from the nuScenes dataset [2] for our training and testing processes. This subset comprises 12,610 samples for training, 1,628 samples for validation, and 1,623 samples for testing. The training and testing depth range spans from 0 to 200 meters, with input and output resolutions set at \\(400 \\times 192\\) pixels." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Evaluation Metrics. To facilitate comparison with previous work, we convert the output rotation vector to Euler angles. Then, we calculate the absolute error between the predicted values and the ground truth in all dimensions of angles and translation vectors. For all tables, the best and the second-best results are highlighted in bold and underlined, respectively." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.09, + 0.905, + 0.272 + ], + "angle": 0, + "content": "
RangeMethodsRotation(°)Translation(cm)
MeanRollPitchYawMeanXY
R1LCCNet-11.6030.1233.1301.55616.53122.99217.648
NetCalib21.2050.3872.2890.94112.29712.53212.076
CalibDepth0.8070.3900.3451.68612.60812.86012.250
Coarse [26]2.0350.5811.5194.004---
Fine [26]1.6920.4420.9393.695---
Ours0.4270.1300.1980.9539.49812.5633.295
R2LCCNet-32.1561.5262.3642.57989.67271.66089.605
LCCNet-51.8980.9192.3142.46188.30274.21685.239
NetCalib22.7781.4654.6882.18071.03776.00157.204
CalibDepth1.6861.1490.8083.10255.38077.14612.918
Coarse [26]4.3881.8663.2518.048---
Fine [26]3.3341.3681.9376.696---
Ours0.8520.35970.44231.754447.53774.7775.415
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.277, + 0.905, + 0.334 + ], + "angle": 0, + "content": "Table 1. Comparison with LiDAR-Camera-Based and Radar-Camera-Based Auto-Calibration Methods on the nuScenes dataset. The methods are compared with two mis-calibration ranges, R1 (\\(\\pm 10\\), \\(\\pm 0.25m\\)) and R2 (\\(\\pm 20\\), \\(\\pm 1.5m\\))." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.348, + 0.905, + 0.442 + ], + "angle": 0, + "content": "
FVBEVSFMCAEMSNRRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
✓0.6570.2350.3011.43612.60212.85812.24712.700
✓0.6890.2950.3811.39212.60512.87012.28512.660
✓✓0.5750.2090.2841.23212.31512.86311.41612.667
✓✓✓0.5290.1750.2371.17611.84212.8829.97612.670
✓✓✓✓0.5020.1750.2351.09712.57412.88312.15012.688
✓✓✓✓✓0.4630.1400.2061.0429.62712.5633.68212.636
✓✓✓✓✓✓0.4270.1300.1980.9539.49812.5633.29512.635
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.446, + 0.906, + 0.502 + ], + "angle": 0, + "content": "Table 2. Module Impact Ablation (FV: Front View, BEV: Bird's Eye View, SF: Selective Fusion, MCA: Multi-Modal Cross-Attention Mechanism, EMS: Explicit Feature Matching Supervision, NR: Noise-Resistant Matcher)" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.528, + 0.647, + 0.543 + ], + "angle": 0, + "content": "4.2. Main results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.551, + 0.907, + 0.779 + ], + "angle": 0, + "content": "We compared it against the method by Schöller et al. [26]. Although this method dates back to 2019 and may not incorporate recent advancements, we have also compared it with state-of-the-art LiDAR-camera-based auto-calibration methods, including LCCNet [20], CalibDepth [43], and NetCalib2 [36]. To ensure a fair comparison, we trained and tested all these methods using the same set of parameters and radar-image dataset. As shown in Sec. 4.2, our focus lies on testing two mis-calibration ranges: \\([10^{\\circ}, 0.25\\mathrm{m}]\\) and \\([20^{\\circ}, 1.5\\mathrm{m}]\\), representing small and large error ranges. For \"LCCNet-number\", the \"number\" corresponds to the number of iteration steps. The achieved results demonstrate that our method exhibits significantly superior average errors in both rotation and translation compared to other methods across both mis-calibration ranges." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.679, + 0.803 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Impact of each Module. Sec. 4.3 shows the impact of each module on experimental outcomes. Using both FV and BEV perspectives together reduced the mean absolute error in rotation by \\(12.5\\%\\). The Selective Fusion mechanism further reduced this error by \\(16.5\\%\\) by allowing the model to choose suitable features from each perspective. The multi-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6706" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.153 + ], + "angle": 0, + "content": "
Fusion MethodRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
Add Fusion0.6420.2170.3711.33812.54712.83212.09612.714
Concat Fusion0.5750.2090.2841.23212.31512.86311.41612.667
Selective Fusion0.5290.1750.2371.17611.84212.8829.97612.669
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.158, + 0.483, + 0.185 + ], + "angle": 0, + "content": "Table 3. Comparison of Dual-Perspective Fusion Methods with Basic Methods" + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.2, + 0.482, + 0.268 + ], + "angle": 0, + "content": "
βRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
0.10.4700.1500.2151.04410.30412.5875.68412.640
0.30.4710.1600.2241.02910.37712.5555.94012.637
0.50.4460.1640.2140.96012.11212.54911.15112.637
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.273, + 0.483, + 0.302 + ], + "angle": 0, + "content": "Table 4. Ablation Study on Weight Impacts in Explicit Feature Matching Loss" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.321, + 0.483, + 0.518 + ], + "angle": 0, + "content": "modal cross-attention mechanism also effectively reduced rotation error by \\(5\\%\\), demonstrating its capability to address the challenges of sparse radar depth maps. However, the mean absolute error in translation did not improve clearly based on the above modules due to the sparse and noisy radar point clouds. Next, introducing Explicit Feature Matching Supervision decreased the translation error by \\(23.4\\%\\), highlighting the benefit of explicit matching labels in learning correspondences. Finally, the incorporation of the Noise-Resistant Matcher further filtered out highly inaccurate noise points in the FV perspective and aided in translational calibration. As a result, the mean absolute error in rotation decreased by \\(7.8\\%\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.483, + 0.609 + ], + "angle": 0, + "content": "Dual-Perspective Fusion Methods. Additionally, we compare our Selective Fusion Mechanism with commonly used methods such as add fusion and concatenation fusion. In Sec. 4.3, the results demonstrate a significant improvement of the proposed method over the conventional fusion methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.718 + ], + "angle": 0, + "content": "Weight of Explicit Feature Matching Loss. In Sec. 4.3, we test three \\(\\beta\\) values: 0.1, 0.3, and 0.5, excluding the noise-resistant matcher module in our method. \\(\\beta = 0.5\\) achieved the lowest rotation error but the highest translation error. \\(\\beta = 0.1\\) provided the best translation accuracy with negligible rotation error. Thus, \\(\\beta = 0.1\\) was selected as the optimal balanced coefficient." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.728, + 0.274, + 0.743 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Our method provides accurate calibration results across various initial mis-calibration conditions and scenes. Fig. 6a visualizes these results, showing precise calibration even with significant initial errors and sparse radar points. To highlight the effectiveness of our explicit matching supervision, we compute the cross-attention maps \\( I_{I\\leftarrow R} \\), \\( I_{R\\leftarrow I} \\) between radar and image features, as visualized in Fig. 6b. The detailed formulas for computing these attention maps are provided in the supplementary material. We represent the attention maps using heatmaps and denote the projected" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.091, + 0.707, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.164, + 0.636, + 0.175 + ], + "angle": 0, + "content": "Sample 1" + }, + { + "type": "image", + "bbox": [ + 0.716, + 0.089, + 0.905, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.163, + 0.835, + 0.175 + ], + "angle": 0, + "content": "Sample 1" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.177, + 0.706, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.25, + 0.638, + 0.262 + ], + "angle": 0, + "content": "Sample 2" + }, + { + "type": "image", + "bbox": [ + 0.716, + 0.176, + 0.905, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.784, + 0.25, + 0.836, + 0.261 + ], + "angle": 0, + "content": "Sample 2" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.265, + 0.706, + 0.362 + ], + "angle": 0, + "content": "(a) Examples of calibration results by projecting radar points onto the frontal-view image. Top-left: input RGB image. Top-right: initial mis-calibrated radar point cloud projection. Bottom-left: network-predicted projection. Bottom-right: ground truth projection." + }, + { + "type": "text", + "bbox": [ + 0.713, + 0.264, + 0.906, + 0.421 + ], + "angle": 0, + "content": "(b) Examples of cross-attention maps highlighting the important regions the model focuses on. Top: image-attentive radar importance regions. Bottom: radar-attentive image importance regions. Left/Right: Results with and without explicit matching supervision. The projected 3D points are used to highlight the critical regions. With explicit matching supervision, our model can better identify these critical regions." + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.433, + 0.853, + 0.447 + ], + "angle": 0, + "content": "Figure 6. Results visualization in the front view." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.907, + 0.645 + ], + "angle": 0, + "content": "radar points with white color to indicate critical regions. Without explicit matching supervision, we observe that due to many zero-value relationships, the image-attentive radar exhibits weaker and less focused attention, while the radar-attentive image focuses on non-critical region, such as the ground. After incorporating explicit matching supervision, the image-attentive radar's attention becomes more concentrated on the non-zero regions, specifically the areas of radar point cloud projection. Meanwhile, the radar-attentive image effectively focuses on crucial regions, such as radar projection locations and vehicle contours, rather than being restricted to non-critical region." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.663, + 0.634, + 0.679 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this work, we present RC-AutoCalib, an end-to-end network for 3D radar and camera calibration. By incorporating dual perspectives, we address the elevation ambiguity in 3D radar. Our Selective Fusion Mechanism integrates useful features from both FV and BEV perspectives. We also developed a Feature Matching module with a MultiModal Cross-Attention Mechanism to enhance radar point cloud utilization and a Noise-Resistant Matcher to filter out height-inaccurate noise. Our method achieves a calibration error of \\(0.427^{\\circ}\\) in rotation and \\(9.498\\mathrm{cm}\\) in translation on the nuScenes dataset, demonstrating competitive performance with these SOTA auto-calibration methods using dense point clouds and establishing a benchmark for future research in 3D radar and camera calibration." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6707" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.314 + ], + "angle": 0, + "content": "Acknowledgments This work was financially supported in part (project number: 112UA10019) by the Co-creation Platform of the Industry Academia Innovation School, NYCU, under the framework of the National Key Fields Industry-University Cooperation and Skilled Personnel Training Act, from the Ministry of Education (MOE) and industry partners in Taiwan. It also supported in part by the National Science and Technology Council, Taiwan, under Grant NSTC-112-2221-E-A49-089-MY3, Grant NSTC-110-2221-E-A49-066-MY3, Grant NSTC-111-2634-F-A49-010, Grant NSTC-112-2425-H-A49-001, and in part by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and the Ministry of Education (MOE), Taiwan. We also would like to express our gratitude for the support from MediaTek Inc, Hon Hai Research Institute (HHRI), E.SUN Financial Holding Co Ltd, Advantech Co Ltd, Industrial Technology Research Institute (ITRI)" + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.331, + 0.188, + 0.347 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.357, + 0.484, + 0.411 + ], + "angle": 0, + "content": "[1] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. 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Given the significant data sparsity and measurement uncertainty in radar height data, achieving automatic calibration during system operation has long been a challenge. To address the sparsity issue, we propose a Dual-Perspective representation that gathers features from both frontal and bird's-eye views. The frontal view contains rich but sensitive height information, whereas the bird's-eye view provides robust features against height uncertainty. We thereby propose a novel Selective Fusion Mechanism to identify and fuse reliable features from both perspectives, reducing the effect of height uncertainty. Moreover, for each view, we incorporate a Multi-Modal Cross-Attention Mechanism to explicitly find location correspondences through cross-modal matching. During the training phase, we also design a Noise-Resistant Matcher to provide better supervision and enhance the robustness of the matching mechanism against sparsity and height uncertainty. Our experimental results, tested on the nuScenes dataset, demonstrate that our method significantly outperforms previous radar-camera auto-calibration methods, as well as existing state-of-the-art LiDAR-camera calibration techniques, establishing a new benchmark for future research. The code is available at https://github.com/nycuacm/RC-AutoCalib + +# 1. Introduction + +Radars and cameras are increasingly favored in advanced driver-assistance systems (ADAS) due to their cost-effectiveness and robust performance in diverse weather conditions. A critical research area in these systems involves data fusion and multi-modal calibration to ensure reliable functioning in real-world settings [16, 19, 37, 39, 44]. Conventional calibration techniques for 3D radar and cam- + +![](images/ebae9f8891c4527e94ac318400060fa02e23460c96294e20aabd5463d4a770f9.jpg) +Figure 1. An overview of the proposed RC-AutoCalib method. The approach takes input from radar-camera miscalibration, representing it as feature pairs in Dual-perspective view. These feature representations are then enhanced through feature matching block, from which reliable features are selected to predict the rotation vector and translation. + +eras primarily focus on offline methods, which often rely on specialized calibration targets like checkerboards or corner reflectors, and are generally limited to the radar measurement plane [3, 4, 10-12, 29, 32]. These methods, while effective, require substantial time and manual effort, and they do not account for sensor displacements that can occur under normal operating conditions. This limitation underscores the necessity for online auto-calibration, which can dynamically adjust to changes over time. + +Online auto-calibration methods eliminate the need for calibration targets, focusing on matching natural features collected by radar and camera sensors. While this approach offers greater flexibility in real-world scenarios, exploration in this area remains limited, with no established benchmarks using publicly available datasets to date. Only the approach by Schöller et al. [26] utilizes deep learning to address the problem of online auto-calibration for radar and camera. However, their focus remains exclusively on rotational calibration, without addressing translational calibration. + +In contrast, online auto-calibration methods for LiDAR and camera [8, 9, 18, 20, 21, 25, 27, 31, 35, 36, 41-43] have + +![](images/b1376840bc4ef2796da1bf69e5d96931c2180cf0aa47e922ed80c92f95dcbb67.jpg) +(a) Elevation Ambiguity in Radar Point Clouds [19]. + +![](images/5499c8f13862603e39f3bb8acaf8889cf959e743dcc1cc663e56699082a6601d.jpg) +(b) Noisy depth measurements and lack of object structures. +Figure 2. Challenges of 3D Millimeter-Wave Radar. (a) The green dashed line represents the height plane the radar focuses on. Points A, B, and C denote actual reflection positions, whereas $\mathbf{A}_{\mathrm{radar}}$ , $\mathbf{B}_{\mathrm{radar}}$ , and $\mathbf{C}_{\mathrm{radar}}$ are the positions recorded by the radar. $\mathbf{D}_{\mathrm{A}}$ , $\mathbf{D}_{\mathrm{B}}$ , and $\mathbf{D}_{\mathrm{C}}$ represent the recorded and noisy radar depths. (b) The top image shows a "LiDAR" depth map projected onto the camera plane, while the bottom image displays a "radar" depth map projected similarly. The red box highlights the issue where depths of points on the same object should be similar, yet significant variations are evident, indicating the presence of noise. Moreover, the green box shows a structural comparison: the "LiDAR" point cloud distinctly outlines the object's contour, while the "radar" point cloud fails to convey structural information. + +been extensively explored by researchers and have demonstrated powerful capabilities. Most of these methods share a common concept of using RGB images and mis-calibrated LiDAR data as input, with the overall process divided into feature extraction, feature matching, and parameter regression. Instead of directly extracting features from RGB images [20, 27, 31, 42], some methods have modified the representation of RGB images. For instance, [18, 41] implicitly extract features in the form of semantics and edges, while [35, 43] transform RGB images into depth maps to achieve a unified representation consistent with 3D data. Overall, these methods project 3D data onto the frontal view to fuse with the camera information for further processing. The above-mentioned LiDAR-camera methods provide a reference and comparison for developing radar-camera autocalibration. However, we find that relying solely on a single viewpoint for radar-camera auto-calibration makes achieving high accuracy challenging. As depicted in Fig. 2, the frontal depth map often contains noisy point cloud data due to uncertainty from the lack of radar height information. Additionally, radar data is inherently sparse and lacks object structures. When projecting radar point clouds onto the frontal view to form the depth map, the projected points tend to overlap and become even sparser. To mitigate these challenges, we have introduced a Dual-Perspective representation that leverages attention-based selection to extract more reliable features. + +Furthermore, feature matching between radar and camera is a critical component for auto-calibration. Some methods [27, 35, 43] rely on concatenation followed by several + +convolutional layers to facilitate feature matching, while others [20] use cost volume to represent the correlation between the two sensors. However, traditional approaches depend solely on implicit supervision from the final calibration loss to guide the matching process. This lack of explicit identification of matched local pairs between sensors renders the calibration process indistinct. To address this, we have developed a Noise-Resistant Matcher that provides direct supervision for feature matching and correspondence finding. + +Accordingly, as illustrated in Fig. 1, we propose RC-AutoCalib, an end-to-end network for automatic 3D radar and camera calibration, addressing the challenges of sparse and noisy radar data. To counteract these issues, we enhance a Dual-Perspective representation that integrates features from both the frontal view and the bird's eye view (BEV). The frontal view is prone to noise due to missing height information in radar point clouds, while the BEV provides more stable features, unaffected by this limitation. Our model includes a Selective Fusion Mechanism to discern and utilize beneficial features from each perspective. Additionally, we incorporate a Multi-Modal Cross-Attention Mechanism to focus on relevant areas in sparse radar point clouds. To improve calibration accuracy, we introduce Explicit Feature Matching Supervision with a Noise-Resistant Matcher, which helps the model identify and learn from correspondence points between radar and camera, filtering out noise in the process. Our results on the nuScenes dataset demonstrate significant improvements over existing LiDAR-camera calibration methods, as well as previous radar-camera auto-calibration approaches, setting a new benchmark for future research. In summary, our contributions are: + +- We introduce RC-AutoCalib, an end-to-end network for calibrating 3D radar and cameras, featuring a Dual-Perspective representation that counters the height information limitations of 3D radar data. This network includes a novel Selective Fusion Mechanism to optimally integrate features from both the frontal view and BEV perspectives. +- We develop a feature-matching module incorporating a Multi-Modal Cross-Attention Mechanism to enhance the utilization of radar point clouds. This module integrates a Noise-Resistant Matcher to provide Explicit Feature Matching Supervision. Thereby, RC-AutoCalib can effective filter out noise caused by height inaccuracies and enable robust learning of radar-image correspondences for calibration. +- Our approach demonstrates superior experimental results on the nuScenes dataset compared to existing LiDAR-camera calibration methods, establishing a new benchmark for future research. + +# 2. Related Works + +# 2.1. Offline Calibration + +Offline calibration methods primarily depend on specific calibration targets and cannot address real-time errors. These methods are tailored for fixed environments and necessitate substantial manual effort to achieve precision, rendering them unsuitable for dynamic conditions and generally reserved for controlled settings. Early radar-camera calibration techniques focused on merging radar signals with camera data through homography projection that maps points from the radar's horizontal plane to the camera image plane. Due to inherent noise in radar sensors, these early methods often required specialized trihedral reflectors to establish accurate correspondences [10, 11, 29, 32]. However, the radar's limitation in accurately measuring the elevation of distant targets indicated that reflectors had to be positioned precisely on the radar's horizontal plane [29]. More recent radar calibration algorithms aim to minimize "reprojection error" to better synchronize object detection across both sensor fields of view, using techniques like estimating radar-to-camera transformations via reprojection error [12], or intersecting back-projected camera rays with 3D "arcs" that conform to radar measurements to determine necessary transformations [4]. Despite improvements, these methods still rely on specific targets and manual input efforts. + +# 2.2. Online Calibration + +Online methods primarily extract features from natural scenes for calibration, offering greater flexibility and adaptability to various scenarios. The rapid development of deep learning has demonstrated neural networks' powerful feature extraction capabilities. However, due to the aforementioned challenges associated with radar, online calibration methods for radar and cameras are less prevalent. In this paper, we focus on developing an end-to-end architecture for the online auto-calibration of radar and cameras, leveraging robust benchmarks established by LiDAR and camera calibration methods. + +LiDAR and Camera. Li et al. [15] categorized targetless calibration methods into information theory-based, feature-based, ego-motion-based, and learning-based approaches. Pandey et al. [22] used mutual information between point cloud intensities and image grayscale values. Taylor and Nieto [30] utilized sensor ego-motion on moving vehicles to estimate extrinsic parameters. Levinson and Thrun [13] as well as Yuan et al. [41] optimized depth-discontinuous and depth-continuous edge features, respectively. Regnet [25] and CalibNet [8] employed deep learning to match features and regress calibration parameters. CalibRCNN [27] combined CNN with LSTM [24] and added pose constraints for accuracy. LCCNet [20] used cost volume for feature correlation. Despite achieving positive results, these methods + +do not explicitly learn the correspondence between point clouds and images. In contrast, in this paper, we introduce Explicit Feature Matching Supervision to guide the model in learning the correspondence relationship between point clouds and images more effectively. + +Radar and Camera. Peršić et al. [23] proposed an online calibration method based on detecting and tracking moving objects, focusing on rotational calibration. Schöller et al. [26] used deep learning to learn rotational calibration matrices but did not address translational calibration. Additionally, their methods utilize stationary traffic radars fixed on highway positions, differing from ours that employ vehicle-mounted 3D radars moving with the car. Wisec et al. [33] developed a targetless calibration method for 3D radar and cameras, using radar velocity information and motion-based camera pose measurements, solved with nonlinear optimization. Later, the same research team extended their work [33] to include radar ego-velocity estimates and unscaled camera pose measurements in [34] for a more complete spatiotemporal calibration. However, these methods overly rely on radar speed measurements, making them less robust to noise. Additionally, they do not leverage the power of deep learning and fail to explicitly establish the correspondence between radar and images. + +# 3. Methods + +The overall pipeline of the RC-AutoCalib method, depicted in Fig. 3, begins with RGB images and radar point clouds as inputs. These inputs pass through the Data Transform module, yielding the frontal view estimated depth map, frontal view miscalibrated radar depth map, pseudo-BEV image, and miscalibrated radar BEV. Subsequent processing occurs in the Feature Extraction module, where features are extracted. These features are then analyzed in the Feature Matching module to enhance understanding of the correlation between feature pairs. This module incorporates a Multi-Modal Cross-Attention Mechanism, Explicit Feature Matching Supervision, and a Noise-Resistant Matcher. Following this, the Selective Fusion Mechanism aggregates the features, and the system performs parameter regression to predict rotation and translation vectors necessary for autocalibration. Detailed descriptions are provided below. + +# 3.1. Data Transform module + +To address issues of uncertainty caused by elevation ambiguity and the sparsity of radar data, we propose a DualPerspective feature representation. This approach projects two types of 3D data (i.e., the image plus its depth map and the radar point clouds) onto two different perspectives: bird's-eye view (BEV) and frontal view (FV). The BEV provides a domain where radar data is less impacted by uncertain height and offers more information about the geometry of the scene. Simultaneously, the FV retains rich + +![](images/0df646f4cd5899ced4affbcd414a36180590c0f655ff202a3fa492697e0109af.jpg) +Figure 3. Our system flow for iterative online auto-calibration starts with the input image, point cloud, and initial calibration parameters $T_{init}$ , which first pass through the Data Transform module (Sec. 3.1). Here, we obtain the estimated image depth map and miscalibrated radar depth map from the frontal view (FV) perspective, along with the pseudo-BEV image and miscalibrated BEV radar projection. These outputs are then processed in the Feature Extraction module (Sec. 3.2), where features from both FV and BEV perspectives undergo Feature Matching (Sec. 3.3) between the image and radar data. Subsequently, after Feature Matching and Fusion (Sec. 3.4), the Regression Head (Sec. 3.5) generates the rotation and translation vectors that form the transformation matrix, $\hat{T}_{pred}^{i}$ , to refine calibration. Finally, $\hat{T}_{pred}^{i}$ is fed back to $T_{init}$ to update the calibration parameters for the next $i$ -th iteration. + +semantic information, preserving important contextual details. + +Radar data. Given a random initialized or roughly-estimated extrinsic transformation $T_{init}$ [8, 20, 31, 42], consisting of a rotation matrix $R_{init}$ and a translation vector $t_{init}$ , we transform a 3D radar point $P_r = (X_r, Y_r, Z_r)$ from the radar coordinate to $P_r^c = (X_r^c, Y_r^c, Z_r^c)$ in the camera coordinate using Eq. (1). The projection formula in Eq. (2) is then used to generate mis-calibrated FV and BEV information maps. For the FV map, the recorded pixel value is computed as $I_R^{FV}(u_f, v_f) = Z_r^c$ ; as for the BEV map, the recorded value is determined as $I_R^{BEV}(u_b, v_b) = y_r^c$ , with $y_r^c$ being $Y_r^c$ plus an offset of the camera height (i.e., the distance above the ground) to eliminate negative values. In Eq. (2), $(u_f, v_f)$ and $(u_b, v_b)$ are the coordinates of a radar point $P_r$ projected onto FV and BEV planes using projection matrices $K$ and $K'$ correspondingly. Here, $K$ is the original camera intrinsic matrix. The intrinsic parameters are manually pre-defined for $K'$ based on the map resolution and map center. + +$$ +P _ {r} ^ {c} = T _ {\text {i n i t}} \left[ \begin{array}{l} P _ {r} \\ 1 \end{array} \right] = \left[ \begin{array}{c c} R _ {\text {i n i t}} & t _ {\text {i n i t}} \\ 0 & 1 \end{array} \right] \left[ \begin{array}{l} P _ {r} \\ 1 \end{array} \right], \tag {1} +$$ + +$$ +\left[ \begin{array}{c} u _ {f} \\ v _ {f} \\ 1 \end{array} \right] = K \left[ \begin{array}{c} X _ {r} ^ {c} / Z _ {r} ^ {c} \\ Y _ {r} ^ {c} / Z _ {r} ^ {c} \\ 1 \end{array} \right], a n d \left[ \begin{array}{c} u _ {b} \\ v _ {b} \\ 1 \end{array} \right] = K ^ {\prime} \left[ \begin{array}{c} X _ {r} ^ {c} \\ Z _ {r} ^ {c} \\ 1 \end{array} \right]. \tag {2} +$$ + +Camera data. For the camera data, the FV information map $I_{I}^{FV}(u_{d}, v_{d})$ is derived using the Metric Depth Estimation module, which predicts the depth image from the input image. This module employs two sequential methods: DepthAnything[40] for relative depth prediction and ZoeDepth[1] for refining it into metric depth, resulting in $I_{I}^{FV}(u_{d}, v_{d})$ . From the depth image, we convert each pixel into a pseudo point cloud $P_{p} = (X_{p}, Y_{p}, Z_{p})$ based on Eq. (3), which are then transformed/projected using matrix $K'$ to form the pseudo-BEV image $I_{I}^{BEV}$ similar to the radar case $I_{R}^{BEV}$ . + +$$ +\left[ \begin{array}{l l l} X _ {p} & Y _ {p} & Z _ {p} \end{array} \right] ^ {\top} = K ^ {- 1} \cdot I _ {I} ^ {F V} \left(u _ {d}, v _ {d}\right) \cdot \left[ \begin{array}{l l l} u _ {d} & v _ {d} & 1 \end{array} \right] ^ {\top}. \tag {3} +$$ + +# 3.2. Feature Extraction + +After transforming point clouds and images into two unified representations—FV depth maps $(I_R^{FV}, I_I^{FV} \in \mathbb{R}^{H \times W})$ and BEV maps $(I_I^{BEV}, I_R^{BEV} \in \mathbb{R}^{H' \times W'})$ —we use ResNet [5] and convolutional layers to extract features from these maps. Additionally, to enhance the FV semantic content, context features are extracted from the original image using ResNet18 and are integrated with the features from $I_I^{FV}$ . The resulting feature sets, representing different perspectives for radar and camera, are denoted as $F_R^{FV}$ , $F_I^{FV} \in \mathbb{R}^{H/8 \times W/8 \times C}$ and $F_R^{BEV}$ , $F_I^{BEV} \in$ + +![](images/c3d3e842ade00d54ea8d25b509b47472141824f56a48d4eeb1c6f360ae78e966.jpg) +(a) Cross attention and Explicit Feature Matching Supervision + +![](images/d365f4e01254fb8dbcd67d2c963013eea863a9280a2eed65622cd9f2acdb67a6.jpg) +(b) 3Dbbox $B$ illustration +Figure 4. Illustration of the proposed Feature Matching module. + +$\mathbb{R}^{H' / 8 \times W' / 8 \times C}$ . We detail the network architecture in the supplementary. + +# 3.3. Feature Matching + +To estimate the 6-DoF (degrees of freedom) extrinsic transformation between radar and camera sensors, our model first focuses on identifying corresponding feature pairs from each sensor's perspective. As illustrated in Fig. 3, we conduct feature matching across two different perspectives. For each perspective, we implement similar matching modules that include a Multi-Modal Cross-Attention Mechanism and an Explicit Feature Matching Supervision. Additionally, in the FV case, we incorporate a Noise-Resistant Matcher. + +Multi-Modal Cross-Attention Mechanism. Considering both perspectives, the projected point cloud data from radar is sparse with mostly zero values, while camera data is dense with rich depth information and geometric features. We propose a Multi-Modal Cross-Attention (MCA) Mechanism that enables the model to focus on non-zero feature regions and identify correlations between camera and radar features. As described in Equation Eq. (4), the inputs to the MCA are $F_{I}$ and $F_{R}$ , and the outputs are $O_{I\leftarrow R}$ and $O_{R\leftarrow I}$ . These outputs are used to compute the updated features $\hat{F}_{I}$ and $\hat{F}_{R}$ as shown in Eq. (5). + +$$ +\begin{array}{l} \left(O _ {I \leftarrow R}, O _ {R \leftarrow I}\right) = \left(\Theta \left(F _ {I}, m _ {I \leftarrow R}\right), \Theta \left(F _ {R}, m _ {R \leftarrow I}\right)\right) \tag {4} \\ = M C A \left(F _ {I}, F _ {R}\right) \\ \end{array} +$$ + +$$ +\hat {F} _ {I} = F _ {I} + O _ {I \leftarrow R}, \quad \hat {F} _ {R} = F _ {R} + O _ {R \leftarrow I}, \tag {5} +$$ + +To obtain $O_{I \leftarrow R}$ and $O_{R \leftarrow I}$ in Eq. (4), we first compute the attended features $m_{I \leftarrow R}$ and $m_{R \leftarrow I}$ between the radar and image inside MCA. Inspired by [6, 17], we use Eq. (6) to compute attended features $m_{I \leftarrow R}$ and $m_{R \leftarrow I}$ , which rely on the cross-attention score $a_{IR}$ computed by Eq. (7). + +$$ +m _ {R \leftarrow I} = \operatorname {S o f t m a x} \left(a _ {I R} ^ {\top}\right) V _ {I}, m _ {I \leftarrow R} = \operatorname {S o f t m a x} \left(a _ {I R}\right) V _ {R}, \tag {6} +$$ + +$$ +a _ {I R} = K _ {I} ^ {\top} K _ {R}, \tag {7} +$$ + +where $V_{*}$ and $K_{*}$ are the value and key, respectively, extracted from the feature $F_{*}$ through linear projections. Note + +that, we reshape $F_{*}$ to $(m \times c)$ dimension before projection and $* \in \{I, R\}$ . After obtaining these attention maps $m_{I \leftarrow R}$ and $m_{R \leftarrow I}$ , we apply the cross-modal feature refinement function $\Theta$ to calculate the $O_{I \leftarrow R}$ and $O_{R \leftarrow I}$ by Eq. (4) given $F_{I}$ and $F_{R}$ . The details of $\Theta$ can be found in the supplementary material. + +After obtaining $\hat{F}_I$ and $\hat{F}_R$ , as shown in Fig. 4a, a Residual Conv Block is used to aggregate them into corresponding $F_{view}$ for each perspective branch using Eq. (8), with view $\in \{BEV, FV\}$ . + +$$ +\begin{array}{l} F _ {v i e w} = \Phi (\operatorname {c o n v} (\operatorname {c o n c a t} (\hat {F} _ {I}, \hat {F} _ {R})) \tag {8} \\ + \operatorname {c o n v} \left(\operatorname {c o n v} \left(\operatorname {c o n c a t} \left(\hat {F} _ {I}, \hat {F} _ {R}\right)\right)\right), \\ \end{array} +$$ + +where the first term of $\Phi$ consists of the concatenated features of $\hat{F}_I$ and $\hat{F}_R$ after passing through one convolutional layer, while the second term involves passing through two convolutional layers. These terms are then added together to form our Residual Conv Block. Here, "conv" denotes a block that includes convolutional layers followed by the leakyReLU [38] activation function. The block $\Phi$ sequentially applies the leakyReLU activation function, flattens the features, and utilizes a multi-layer perceptron (MLP). + +Explicit Feature Matching Supervision. Previously, feature matching was implicitly supervised solely by the final calibration loss to understand overall errors without specifically identifying matched pairs. We find this implicit supervision insufficient and propose directly supervising feature matching using true matching pairs generated from the correct calibration matrix. In other words, we add matching prediction and auxiliary loss during training to enhance the understanding of local feature matching pairs between $\hat{F}_I$ and $\hat{F}_R$ . + +Motivated by [17], an extra branch is designed to perform the task of Local Feature Matching during the training phase as shown in Fig. 4a. Assuming each reshaped feature $\hat{f}_{*} \in \mathbb{R}^{m \times c}$ from $\hat{F}_{*}$ includes $m$ (i.e., $H / 8 \times W / 8$ ) keypoints, with each keypoint having a feature descriptor of dimension $c$ . The assignment matrix $P \in [0,1]^{m \times m}$ is estimated based on Eq. (9). + +![](images/83db58cfd827175c831f232a9e3d52dc4675bcda00e328e10d446fbfc9166466.jpg) +Figure 5. Details of the Selective Fusion Mechanism + +$$ +P = \sigma_ {I} ^ {\top} \sigma_ {R} \operatorname {S o f t m a x} \left(S ^ {\top}\right) ^ {\top} \operatorname {S o f t m a x} (S), \tag {9} +$$ + +where $S \in \mathbb{R}^{m \times m}$ , calculated by equation Eq. (10), is the similarity score matrix between the features extracted from two sensors after the Multi-Modal Cross-Attention step. Meanwhile, $\sigma_{*} \in [0, 1]^{1 \times m}$ is the matchable score of feature points, estimated by equation Eq. (11), where $* \in \{I, R\}$ . A point with a high value of $\sigma$ means it is more likely to have a corresponding point on another map. + +$$ +S = \operatorname {L i n e a r} \left(\hat {f} _ {I}\right) ^ {\top} \operatorname {L i n e a r} \left(\hat {f} _ {R}\right), \tag {10} +$$ + +$$ +\sigma_ {*} = \operatorname {S i g m o i d} \left(\operatorname {L i n e a r} \left(\hat {f} _ {*}\right)\right). \tag {11} +$$ + +In the training phase, we use the estimated assignment matrix $P$ and the matching loss defined in Eq. (16) to directly supervise the cross-sensor matching. + +Noise-Resistant Matcher. For the FV case, when preparing the ground truth matches matrix $\mathcal{M}$ to supervise the assignment matrix $P$ , we recognize that the radar training data contains many unreliable data points due to elevation ambiguity. Additionally, radar signals reflected by objects far from the radar plane can lead to unreliable data points. Therefore, we propose using LiDAR data to identify and remove these unreliable data points from the list of true feature matching pairs $\mathcal{M}$ . First, we transform the LiDAR and radar point clouds into a unified camera coordinate system. For each radar 3D point $P_r^c = (X_r^c, Y_r^c, Z_r^c) \in \mathbb{R}^3$ , a neighbor region is created using a 3D bounding box $B$ . If the number of LiDAR point clouds $P_l^c = (X_l^c, Y_l^c, Z_l^c) \in \mathbb{R}^3$ within this box $B$ exceeds a threshold $\tau$ , the radar point cloud $P_r^c$ is considered reliable. + +The 3D bounding box $B$ is adaptively designed for each radar point. Denote $\phi, \theta$ , and $R$ respectively represent the elevation angle, azimuth angle, and point length relative to a 3D radar point. $(\Delta x, \Delta z)$ are the noises caused by elevation ambiguity as defined in the method [28] and $\Delta s$ is the error between the two sensors. As shown in Fig. 4b, the box height $h_B$ is calculated by Eq. (12) given $\Delta s, \phi, R$ , and a predefined parameter $\delta$ , which represents the allowable height error from a 3D point to the radar plane. + +$$ +h _ {B} = 2 (\Delta y + \Delta s) = 2 (\delta + \Delta s), a n d \cos \phi = \sqrt {1 - (\delta / R) ^ {2}}. \tag {12} +$$ + +The width $w_{B}$ and depth $d_{B}$ of $B$ , are then calculated by Eqs. (13) and (14). The center of a 3D bounding box $B$ of a radar point $P_{r}^{c}(X_{r}^{c}, Y_{r}^{c}, Z_{r}^{c})$ is determined as: $(X_{r}^{c} - \Delta x / 2, Y_{r}^{c}, Z_{r}^{c} - \Delta z / 2)$ . + +$$ +w _ {B} = \Delta x + 2 \Delta s = R \sin \theta (1 - \cos \phi) + 2 \Delta s, \tag {13} +$$ + +$$ +d _ {B} = \Delta z + 2 \Delta s = R \cos \theta (1 - \cos \phi) + 2 \Delta s. \tag {14} +$$ + +Due to limited space, we provide additional information and details in the supplementary material. + +# 3.4. Selective Fusion Mechanism + +After the Feature Matching step, we can extract the features $F_{BEV}$ and $F_{FV}$ in the corresponding perspective branch. To enhance calibration accuracy by leveraging the distinctive contributions of each perspective, we propose a Dual-Perspective View Selective Fusion Mechanism that combines these features influenced by SKNet [14]. As illustrated in Fig. 5, we first calculate the compact feature $z$ from the sum of the two feature vectors using Eq. (15). Subsequently, a channel-wise attention mechanism adaptively selects diverse elements in the corresponding input features, guided by the compact feature descriptor $z$ . The obtained results are then added together to create the final feature $F_{select}$ . + +$$ +z = F _ {f c} \left(F _ {B E V} + F _ {F V}\right), \tag {15} +$$ + +where $F_{fc}$ denotes the use of a fully connected layer, Batch-Norm [7], and the leakyReLU activation function. + +# 3.5. Regression Head + +To estimate the rotation and translation parameters and form the updated transformation matrix $T_{pred}$ , we leverage the sequence generative decoder from CalibDepth [43]. Specifically, this method employs LSTM [24], where the output is defined as a sequence of actions of length $N$ in an autoregressive manner to address the inherent inaccuracies in the one-shot regression approach. After determining $T_{pred}$ at the current iteration, we update $T_{init} = T_{init} \cdot T_{pred}^{i}$ , as illustrated in Fig. 3. + +# 3.6. Loss Function + +Our model operates under two supervised tasks. The primary task focuses on auto-calibration, while an auxiliary task centers on local feature matching, which clarifies the correspondence between feature pairs. Consequently, we employ two corresponding loss functions: the matching loss and calibration loss. + +Explicit Correspondences Matching. With ground truth match matrix $\mathcal{M} \in \{0,1\}^{N \times m \times m}$ and the predicted matching $P \in [0,1]^{N \times m \times m}$ and $\sigma_{I}, \sigma_{R} \in [0,1]^{N \times m}$ , the matching loss function is designed to minimize the log-likelihood + +of the predicted matches as in Eq. (16). Since our calibration includes $N$ iterations, the matching loss term aggregates the loss from all iterations. + +$$ +L _ {M} = - \sum_ {n} ^ {N} \left(\frac {\lambda}{\Sigma \mathcal {M}} L _ {p o s} ^ {n} + \frac {1 - \lambda}{\Sigma \mathcal {N} _ {\mathcal {I}} + \Sigma \mathcal {N} _ {\mathcal {R}}} L _ {n e g} ^ {n}\right), \tag {16} +$$ + +$$ +L _ {p o s} = \sum_ {i, j} \log \left(P ^ {i j}\right) \mathcal {M} ^ {i, j}, \tag {17} +$$ + +$$ +L _ {n e g} = \sum_ {i} \log \left(1 - \sigma_ {I} ^ {i}\right) \mathcal {N} _ {I} ^ {i} + \sum_ {j} \log \left(1 - \sigma_ {R} ^ {j}\right) \mathcal {N} _ {R} ^ {j}, \tag {18} +$$ + +where $\lambda$ is the balancing coefficient between positive and negative instances. $\mathcal{N}_R$ and $\mathcal{N}_I$ are ground truth for "No Matchable" scores for pixels in the radar and camera maps respectively. The true matches matrix $\mathcal{M}$ between camera and radar maps is dynamically computed based on the true translation $T_{gt}$ between the two sensors and the current, yet imperfect, updated translation $T_{init}$ . $\mathcal{N}_R$ and $\mathcal{N}_I$ are derived from $\mathcal{M}$ by Eq. (19). + +$$ +\mathcal {N} _ {I} ^ {i} = 1 - \sum_ {j} \mathcal {M} _ {i j}, \quad \mathcal {N} _ {R} ^ {j} = 1 - \sum_ {i} \mathcal {M} _ {i j}. \tag {19} +$$ + +The final matching loss function is then computed as the sum of losses from two perspectives defined as $L_{\text{matching}} = L_{M_{bev}} + L_{M_{fv}}$ . + +Calibration Loss. To both ensure that the calibration results at each iteration step are asymptotic to the ground truth and avoid divergence between different iteration steps, we use the calibration loss $L_{\text{calib}}$ proposed in [43]. By controlling the weight parameter $\beta$ , the final total loss consists of the two losses mentioned above, defined as $L_{\text{total}} = L_{\text{calib}} + \beta L_{\text{matching}}$ . + +# 4. Experimental Results + +# 4.1. Dataset and Evaluation Metrics + +Dataset Preparation. We utilize a subset of images from the nuScenes dataset [2] for our training and testing processes. This subset comprises 12,610 samples for training, 1,628 samples for validation, and 1,623 samples for testing. The training and testing depth range spans from 0 to 200 meters, with input and output resolutions set at $400 \times 192$ pixels. + +Evaluation Metrics. To facilitate comparison with previous work, we convert the output rotation vector to Euler angles. Then, we calculate the absolute error between the predicted values and the ground truth in all dimensions of angles and translation vectors. For all tables, the best and the second-best results are highlighted in bold and underlined, respectively. + +
RangeMethodsRotation(°)Translation(cm)
MeanRollPitchYawMeanXY
R1LCCNet-11.6030.1233.1301.55616.53122.99217.648
NetCalib21.2050.3872.2890.94112.29712.53212.076
CalibDepth0.8070.3900.3451.68612.60812.86012.250
Coarse [26]2.0350.5811.5194.004---
Fine [26]1.6920.4420.9393.695---
Ours0.4270.1300.1980.9539.49812.5633.295
R2LCCNet-32.1561.5262.3642.57989.67271.66089.605
LCCNet-51.8980.9192.3142.46188.30274.21685.239
NetCalib22.7781.4654.6882.18071.03776.00157.204
CalibDepth1.6861.1490.8083.10255.38077.14612.918
Coarse [26]4.3881.8663.2518.048---
Fine [26]3.3341.3681.9376.696---
Ours0.8520.35970.44231.754447.53774.7775.415
+ +Table 1. Comparison with LiDAR-Camera-Based and Radar-Camera-Based Auto-Calibration Methods on the nuScenes dataset. The methods are compared with two mis-calibration ranges, R1 ( $\pm 10$ , $\pm 0.25m$ ) and R2 ( $\pm 20$ , $\pm 1.5m$ ). + +
FVBEVSFMCAEMSNRRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
✓0.6570.2350.3011.43612.60212.85812.24712.700
✓0.6890.2950.3811.39212.60512.87012.28512.660
✓✓0.5750.2090.2841.23212.31512.86311.41612.667
✓✓✓0.5290.1750.2371.17611.84212.8829.97612.670
✓✓✓✓0.5020.1750.2351.09712.57412.88312.15012.688
✓✓✓✓✓0.4630.1400.2061.0429.62712.5633.68212.636
✓✓✓✓✓✓0.4270.1300.1980.9539.49812.5633.29512.635
+ +Table 2. Module Impact Ablation (FV: Front View, BEV: Bird's Eye View, SF: Selective Fusion, MCA: Multi-Modal Cross-Attention Mechanism, EMS: Explicit Feature Matching Supervision, NR: Noise-Resistant Matcher) + +# 4.2. Main results + +We compared it against the method by Schöller et al. [26]. Although this method dates back to 2019 and may not incorporate recent advancements, we have also compared it with state-of-the-art LiDAR-camera-based auto-calibration methods, including LCCNet [20], CalibDepth [43], and NetCalib2 [36]. To ensure a fair comparison, we trained and tested all these methods using the same set of parameters and radar-image dataset. As shown in Sec. 4.2, our focus lies on testing two mis-calibration ranges: $[10^{\circ}, 0.25\mathrm{m}]$ and $[20^{\circ}, 1.5\mathrm{m}]$ , representing small and large error ranges. For "LCCNet-number", the "number" corresponds to the number of iteration steps. The achieved results demonstrate that our method exhibits significantly superior average errors in both rotation and translation compared to other methods across both mis-calibration ranges. + +# 4.3. Ablation Studies + +Impact of each Module. Sec. 4.3 shows the impact of each module on experimental outcomes. Using both FV and BEV perspectives together reduced the mean absolute error in rotation by $12.5\%$ . The Selective Fusion mechanism further reduced this error by $16.5\%$ by allowing the model to choose suitable features from each perspective. The multi- + +
Fusion MethodRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
Add Fusion0.6420.2170.3711.33812.54712.83212.09612.714
Concat Fusion0.5750.2090.2841.23212.31512.86311.41612.667
Selective Fusion0.5290.1750.2371.17611.84212.8829.97612.669
+ +Table 3. Comparison of Dual-Perspective Fusion Methods with Basic Methods + +
βRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
0.10.4700.1500.2151.04410.30412.5875.68412.640
0.30.4710.1600.2241.02910.37712.5555.94012.637
0.50.4460.1640.2140.96012.11212.54911.15112.637
+ +Table 4. Ablation Study on Weight Impacts in Explicit Feature Matching Loss + +modal cross-attention mechanism also effectively reduced rotation error by $5\%$ , demonstrating its capability to address the challenges of sparse radar depth maps. However, the mean absolute error in translation did not improve clearly based on the above modules due to the sparse and noisy radar point clouds. Next, introducing Explicit Feature Matching Supervision decreased the translation error by $23.4\%$ , highlighting the benefit of explicit matching labels in learning correspondences. Finally, the incorporation of the Noise-Resistant Matcher further filtered out highly inaccurate noise points in the FV perspective and aided in translational calibration. As a result, the mean absolute error in rotation decreased by $7.8\%$ + +Dual-Perspective Fusion Methods. Additionally, we compare our Selective Fusion Mechanism with commonly used methods such as add fusion and concatenation fusion. In Sec. 4.3, the results demonstrate a significant improvement of the proposed method over the conventional fusion methods. + +Weight of Explicit Feature Matching Loss. In Sec. 4.3, we test three $\beta$ values: 0.1, 0.3, and 0.5, excluding the noise-resistant matcher module in our method. $\beta = 0.5$ achieved the lowest rotation error but the highest translation error. $\beta = 0.1$ provided the best translation accuracy with negligible rotation error. Thus, $\beta = 0.1$ was selected as the optimal balanced coefficient. + +# 4.4. Qualitative Results + +Our method provides accurate calibration results across various initial mis-calibration conditions and scenes. Fig. 6a visualizes these results, showing precise calibration even with significant initial errors and sparse radar points. To highlight the effectiveness of our explicit matching supervision, we compute the cross-attention maps $I_{I\leftarrow R}$ , $I_{R\leftarrow I}$ between radar and image features, as visualized in Fig. 6b. The detailed formulas for computing these attention maps are provided in the supplementary material. We represent the attention maps using heatmaps and denote the projected + +![](images/f613701e9f918022500c1a109984ee6a4a4036aa3807d4f9a9a53abf078e5c17.jpg) +Sample 1 + +![](images/3ea7d61bd5457fecf10e2ce4e0161df97189fba27b6b62d3b58081f0e6b25878.jpg) + +![](images/1d843502b4ec6718a490d26cac5cfa6368ddd58c68c6d6c4fde76c60e8f7a69c.jpg) +Sample 2 +Figure 6. Results visualization in the front view. + +![](images/aaa7d1c90b04d14c4144c5634c6e446101888e915155ccb2c72aafada3e1987f.jpg) +Sample 1 +Sample 2 + +(a) Examples of calibration results by projecting radar points onto the frontal-view image. Top-left: input RGB image. Top-right: initial mis-calibrated radar point cloud projection. Bottom-left: network-predicted projection. Bottom-right: ground truth projection. + +(b) Examples of cross-attention maps highlighting the important regions the model focuses on. Top: image-attentive radar importance regions. Bottom: radar-attentive image importance regions. Left/Right: Results with and without explicit matching supervision. The projected 3D points are used to highlight the critical regions. With explicit matching supervision, our model can better identify these critical regions. + +radar points with white color to indicate critical regions. Without explicit matching supervision, we observe that due to many zero-value relationships, the image-attentive radar exhibits weaker and less focused attention, while the radar-attentive image focuses on non-critical region, such as the ground. After incorporating explicit matching supervision, the image-attentive radar's attention becomes more concentrated on the non-zero regions, specifically the areas of radar point cloud projection. Meanwhile, the radar-attentive image effectively focuses on crucial regions, such as radar projection locations and vehicle contours, rather than being restricted to non-critical region. + +# 5. Conclusion + +In this work, we present RC-AutoCalib, an end-to-end network for 3D radar and camera calibration. By incorporating dual perspectives, we address the elevation ambiguity in 3D radar. Our Selective Fusion Mechanism integrates useful features from both FV and BEV perspectives. We also developed a Feature Matching module with a MultiModal Cross-Attention Mechanism to enhance radar point cloud utilization and a Noise-Resistant Matcher to filter out height-inaccurate noise. Our method achieves a calibration error of $0.427^{\circ}$ in rotation and $9.498\mathrm{cm}$ in translation on the nuScenes dataset, demonstrating competitive performance with these SOTA auto-calibration methods using dense point clouds and establishing a benchmark for future research in 3D radar and camera calibration. + +Acknowledgments This work was financially supported in part (project number: 112UA10019) by the Co-creation Platform of the Industry Academia Innovation School, NYCU, under the framework of the National Key Fields Industry-University Cooperation and Skilled Personnel Training Act, from the Ministry of Education (MOE) and industry partners in Taiwan. It also supported in part by the National Science and Technology Council, Taiwan, under Grant NSTC-112-2221-E-A49-089-MY3, Grant NSTC-110-2221-E-A49-066-MY3, Grant NSTC-111-2634-F-A49-010, Grant NSTC-112-2425-H-A49-001, and in part by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and the Ministry of Education (MOE), Taiwan. We also would like to express our gratitude for the support from MediaTek Inc, Hon Hai Research Institute (HHRI), E.SUN Financial Holding Co Ltd, Advantech Co Ltd, Industrial Technology Research Institute (ITRI) + +# References + +[1] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. Zoedepth: Zero-shot transfer by combining relative and metric depth. arXiv preprint arXiv:2302.12288, 2023. 4 +[2] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscene: A multimodal dataset for autonomous driving. 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Given the significant data sparsity and measurement uncertainty in radar height data, achieving automatic calibration during system operation has long been a challenge. To address the sparsity issue, we propose a Dual-Perspective representation that gathers features from both frontal and bird's-eye views. The frontal view contains rich but sensitive height information, whereas the bird's-eye view provides robust features against height uncertainty. We thereby propose a novel Selective Fusion Mechanism to identify and fuse reliable features from both perspectives, reducing the effect of height uncertainty. Moreover, for each view, we incorporate a Multi-Modal Cross-Attention Mechanism to explicitly find location correspondences through cross-modal matching. During the training phase, we also design a Noise-Resistant Matcher to provide better supervision and enhance the robustness of the matching mechanism against sparsity and height uncertainty. 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These feature representations are then enhanced through feature matching block, from which reliable features are selected to predict the rotation vector and translation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 449, + 555, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 449, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 312, + 449, + 555, + 557 + ], + "type": "text", + "content": "eras primarily focus on offline methods, which often rely on specialized calibration targets like checkerboards or corner reflectors, and are generally limited to the radar measurement plane [3, 4, 10-12, 29, 32]. These methods, while effective, require substantial time and manual effort, and they do not account for sensor displacements that can occur under normal operating conditions. This limitation underscores the necessity for online auto-calibration, which can dynamically adjust to changes over time." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 558, + 556, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 558, + 556, + 688 + ], + "spans": [ + { + "bbox": [ + 312, + 558, + 556, + 688 + ], + "type": "text", + "content": "Online auto-calibration methods eliminate the need for calibration targets, focusing on matching natural features collected by radar and camera sensors. While this approach offers greater flexibility in real-world scenarios, exploration in this area remains limited, with no established benchmarks using publicly available datasets to date. Only the approach by Schöller et al. [26] utilizes deep learning to address the problem of online auto-calibration for radar and camera. However, their focus remains exclusively on rotational calibration, without addressing translational calibration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 714 + ], + "type": "text", + "content": "In contrast, online auto-calibration methods for LiDAR and camera [8, 9, 18, 20, 21, 25, 27, 31, 35, 36, 41-43] have" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6700" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 203, + 153 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 203, + 153 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 203, + 153 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 203, + 153 + ], + "type": "image", + "image_path": "b1376840bc4ef2796da1bf69e5d96931c2180cf0aa47e922ed80c92f95dcbb67.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 57, + 156, + 203, + 175 + ], + "lines": [ + { + "bbox": [ + 57, + 156, + 203, + 175 + ], + "spans": [ + { + "bbox": [ + 57, + 156, + 203, + 175 + ], + "type": "text", + "content": "(a) Elevation Ambiguity in Radar Point Clouds [19]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 206, + 93, + 293, + 150 + ], + "blocks": [ + { + "bbox": [ + 206, + 93, + 293, + 150 + ], + "lines": [ + { + "bbox": [ + 206, + 93, + 293, + 150 + ], + "spans": [ + { + "bbox": [ + 206, + 93, + 293, + 150 + ], + "type": "image", + "image_path": "5499c8f13862603e39f3bb8acaf8889cf959e743dcc1cc663e56699082a6601d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 206, + 152, + 294, + 180 + ], + "lines": [ + { + "bbox": [ + 206, + 152, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 206, + 152, + 294, + 180 + ], + "type": "text", + "content": "(b) Noisy depth measurements and lack of object structures." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "lines": [ + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": "Figure 2. Challenges of 3D Millimeter-Wave Radar. (a) The green dashed line represents the height plane the radar focuses on. Points A, B, and C denote actual reflection positions, whereas " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathrm{radar}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_{\\mathrm{radar}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{radar}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": " are the positions recorded by the radar. " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{A}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{C}}" + }, + { + "bbox": [ + 55, + 190, + 296, + 333 + ], + "type": "text", + "content": " represent the recorded and noisy radar depths. (b) The top image shows a \"LiDAR\" depth map projected onto the camera plane, while the bottom image displays a \"radar\" depth map projected similarly. The red box highlights the issue where depths of points on the same object should be similar, yet significant variations are evident, indicating the presence of noise. Moreover, the green box shows a structural comparison: the \"LiDAR\" point cloud distinctly outlines the object's contour, while the \"radar\" point cloud fails to convey structural information." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 352, + 296, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 352, + 296, + 674 + ], + "spans": [ + { + "bbox": [ + 56, + 352, + 296, + 674 + ], + "type": "text", + "content": "been extensively explored by researchers and have demonstrated powerful capabilities. Most of these methods share a common concept of using RGB images and mis-calibrated LiDAR data as input, with the overall process divided into feature extraction, feature matching, and parameter regression. Instead of directly extracting features from RGB images [20, 27, 31, 42], some methods have modified the representation of RGB images. For instance, [18, 41] implicitly extract features in the form of semantics and edges, while [35, 43] transform RGB images into depth maps to achieve a unified representation consistent with 3D data. Overall, these methods project 3D data onto the frontal view to fuse with the camera information for further processing. The above-mentioned LiDAR-camera methods provide a reference and comparison for developing radar-camera autocalibration. However, we find that relying solely on a single viewpoint for radar-camera auto-calibration makes achieving high accuracy challenging. As depicted in Fig. 2, the frontal depth map often contains noisy point cloud data due to uncertainty from the lack of radar height information. Additionally, radar data is inherently sparse and lacks object structures. When projecting radar point clouds onto the frontal view to form the depth map, the projected points tend to overlap and become even sparser. To mitigate these challenges, we have introduced a Dual-Perspective representation that leverages attention-based selection to extract more reliable features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Furthermore, feature matching between radar and camera is a critical component for auto-calibration. Some methods [27, 35, 43] rely on concatenation followed by several" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": "convolutional layers to facilitate feature matching, while others [20] use cost volume to represent the correlation between the two sensors. However, traditional approaches depend solely on implicit supervision from the final calibration loss to guide the matching process. This lack of explicit identification of matched local pairs between sensors renders the calibration process indistinct. To address this, we have developed a Noise-Resistant Matcher that provides direct supervision for feature matching and correspondence finding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 201, + 556, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 556, + 476 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 556, + 476 + ], + "type": "text", + "content": "Accordingly, as illustrated in Fig. 1, we propose RC-AutoCalib, an end-to-end network for automatic 3D radar and camera calibration, addressing the challenges of sparse and noisy radar data. To counteract these issues, we enhance a Dual-Perspective representation that integrates features from both the frontal view and the bird's eye view (BEV). The frontal view is prone to noise due to missing height information in radar point clouds, while the BEV provides more stable features, unaffected by this limitation. Our model includes a Selective Fusion Mechanism to discern and utilize beneficial features from each perspective. Additionally, we incorporate a Multi-Modal Cross-Attention Mechanism to focus on relevant areas in sparse radar point clouds. To improve calibration accuracy, we introduce Explicit Feature Matching Supervision with a Noise-Resistant Matcher, which helps the model identify and learn from correspondence points between radar and camera, filtering out noise in the process. Our results on the nuScenes dataset demonstrate significant improvements over existing LiDAR-camera calibration methods, as well as previous radar-camera auto-calibration approaches, setting a new benchmark for future research. In summary, our contributions are:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 486, + 554, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "text", + "content": "- We introduce RC-AutoCalib, an end-to-end network for calibrating 3D radar and cameras, featuring a Dual-Perspective representation that counters the height information limitations of 3D radar data. This network includes a novel Selective Fusion Mechanism to optimally integrate features from both the frontal view and BEV perspectives." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "type": "text", + "content": "- We develop a feature-matching module incorporating a Multi-Modal Cross-Attention Mechanism to enhance the utilization of radar point clouds. This module integrates a Noise-Resistant Matcher to provide Explicit Feature Matching Supervision. Thereby, RC-AutoCalib can effective filter out noise caused by height inaccuracies and enable robust learning of radar-image correspondences for calibration." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 666, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 553, + 712 + ], + "type": "text", + "content": "- Our approach demonstrates superior experimental results on the nuScenes dataset compared to existing LiDAR-camera calibration methods, establishing a new benchmark for future research." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6701" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 147, + 83 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 91, + 167, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 91, + 167, + 103 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 167, + 103 + ], + "type": "text", + "content": "2.1. Offline Calibration" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 110, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 110, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 57, + 110, + 296, + 384 + ], + "type": "text", + "content": "Offline calibration methods primarily depend on specific calibration targets and cannot address real-time errors. These methods are tailored for fixed environments and necessitate substantial manual effort to achieve precision, rendering them unsuitable for dynamic conditions and generally reserved for controlled settings. Early radar-camera calibration techniques focused on merging radar signals with camera data through homography projection that maps points from the radar's horizontal plane to the camera image plane. Due to inherent noise in radar sensors, these early methods often required specialized trihedral reflectors to establish accurate correspondences [10, 11, 29, 32]. However, the radar's limitation in accurately measuring the elevation of distant targets indicated that reflectors had to be positioned precisely on the radar's horizontal plane [29]. More recent radar calibration algorithms aim to minimize \"reprojection error\" to better synchronize object detection across both sensor fields of view, using techniques like estimating radar-to-camera transformations via reprojection error [12], or intersecting back-projected camera rays with 3D \"arcs\" that conform to radar measurements to determine necessary transformations [4]. Despite improvements, these methods still rely on specific targets and manual input efforts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 394, + 167, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 394, + 167, + 406 + ], + "spans": [ + { + "bbox": [ + 56, + 394, + 167, + 406 + ], + "type": "text", + "content": "2.2. Online Calibration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 413, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 413, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 295, + 544 + ], + "type": "text", + "content": "Online methods primarily extract features from natural scenes for calibration, offering greater flexibility and adaptability to various scenarios. The rapid development of deep learning has demonstrated neural networks' powerful feature extraction capabilities. However, due to the aforementioned challenges associated with radar, online calibration methods for radar and cameras are less prevalent. In this paper, we focus on developing an end-to-end architecture for the online auto-calibration of radar and cameras, leveraging robust benchmarks established by LiDAR and camera calibration methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 713 + ], + "type": "text", + "content": "LiDAR and Camera. Li et al. [15] categorized targetless calibration methods into information theory-based, feature-based, ego-motion-based, and learning-based approaches. Pandey et al. [22] used mutual information between point cloud intensities and image grayscale values. Taylor and Nieto [30] utilized sensor ego-motion on moving vehicles to estimate extrinsic parameters. Levinson and Thrun [13] as well as Yuan et al. [41] optimized depth-discontinuous and depth-continuous edge features, respectively. Regnet [25] and CalibNet [8] employed deep learning to match features and regress calibration parameters. CalibRCNN [27] combined CNN with LSTM [24] and added pose constraints for accuracy. LCCNet [20] used cost volume for feature correlation. Despite achieving positive results, these methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "do not explicitly learn the correspondence between point clouds and images. In contrast, in this paper, we introduce Explicit Feature Matching Supervision to guide the model in learning the correspondence relationship between point clouds and images more effectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 133, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 553, + 361 + ], + "type": "text", + "content": "Radar and Camera. Peršić et al. [23] proposed an online calibration method based on detecting and tracking moving objects, focusing on rotational calibration. Schöller et al. [26] used deep learning to learn rotational calibration matrices but did not address translational calibration. Additionally, their methods utilize stationary traffic radars fixed on highway positions, differing from ours that employ vehicle-mounted 3D radars moving with the car. Wisec et al. [33] developed a targetless calibration method for 3D radar and cameras, using radar velocity information and motion-based camera pose measurements, solved with nonlinear optimization. Later, the same research team extended their work [33] to include radar ego-velocity estimates and unscaled camera pose measurements in [34] for a more complete spatiotemporal calibration. However, these methods overly rely on radar speed measurements, making them less robust to noise. Additionally, they do not leverage the power of deep learning and fail to explicitly establish the correspondence between radar and images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 370, + 375, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 370, + 375, + 383 + ], + "spans": [ + { + "bbox": [ + 314, + 370, + 375, + 383 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 390, + 553, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 553, + 582 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 553, + 582 + ], + "type": "text", + "content": "The overall pipeline of the RC-AutoCalib method, depicted in Fig. 3, begins with RGB images and radar point clouds as inputs. These inputs pass through the Data Transform module, yielding the frontal view estimated depth map, frontal view miscalibrated radar depth map, pseudo-BEV image, and miscalibrated radar BEV. Subsequent processing occurs in the Feature Extraction module, where features are extracted. These features are then analyzed in the Feature Matching module to enhance understanding of the correlation between feature pairs. This module incorporates a Multi-Modal Cross-Attention Mechanism, Explicit Feature Matching Supervision, and a Noise-Resistant Matcher. Following this, the Selective Fusion Mechanism aggregates the features, and the system performs parameter regression to predict rotation and translation vectors necessary for autocalibration. Detailed descriptions are provided below." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 588, + 450, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 450, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 450, + 600 + ], + "type": "text", + "content": "3.1. Data Transform module" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "content": "To address issues of uncertainty caused by elevation ambiguity and the sparsity of radar data, we propose a DualPerspective feature representation. This approach projects two types of 3D data (i.e., the image plus its depth map and the radar point clouds) onto two different perspectives: bird's-eye view (BEV) and frontal view (FV). The BEV provides a domain where radar data is less impacted by uncertain height and offers more information about the geometry of the scene. Simultaneously, the FV retains rich" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6702" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 94, + 70, + 515, + 293 + ], + "blocks": [ + { + "bbox": [ + 94, + 70, + 515, + 293 + ], + "lines": [ + { + "bbox": [ + 94, + 70, + 515, + 293 + ], + "spans": [ + { + "bbox": [ + 94, + 70, + 515, + 293 + ], + "type": "image", + "image_path": "0df646f4cd5899ced4affbcd414a36180590c0f655ff202a3fa492697e0109af.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": "Figure 3. Our system flow for iterative online auto-calibration starts with the input image, point cloud, and initial calibration parameters " + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "inline_equation", + "content": "T_{init}" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": ", which first pass through the Data Transform module (Sec. 3.1). Here, we obtain the estimated image depth map and miscalibrated radar depth map from the frontal view (FV) perspective, along with the pseudo-BEV image and miscalibrated BEV radar projection. These outputs are then processed in the Feature Extraction module (Sec. 3.2), where features from both FV and BEV perspectives undergo Feature Matching (Sec. 3.3) between the image and radar data. Subsequently, after Feature Matching and Fusion (Sec. 3.4), the Regression Head (Sec. 3.5) generates the rotation and translation vectors that form the transformation matrix, " + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\hat{T}_{pred}^{i}" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": ", to refine calibration. Finally, " + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\hat{T}_{pred}^{i}" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": " is fed back to " + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "inline_equation", + "content": "T_{init}" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": " to update the calibration parameters for the next " + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 303, + 555, + 381 + ], + "type": "text", + "content": "-th iteration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 393, + 295, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 295, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 295, + 415 + ], + "type": "text", + "content": "semantic information, preserving important contextual details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": "Radar data. Given a random initialized or roughly-estimated extrinsic transformation " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "T_{init}" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " [8, 20, 31, 42], consisting of a rotation matrix " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "R_{init}" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " and a translation vector " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "t_{init}" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": ", we transform a 3D radar point " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "P_r = (X_r, Y_r, Z_r)" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " from the radar coordinate to " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "P_r^c = (X_r^c, Y_r^c, Z_r^c)" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " in the camera coordinate using Eq. (1). The projection formula in Eq. (2) is then used to generate mis-calibrated FV and BEV information maps. For the FV map, the recorded pixel value is computed as " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "I_R^{FV}(u_f, v_f) = Z_r^c" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": "; as for the BEV map, the recorded value is determined as " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "I_R^{BEV}(u_b, v_b) = y_r^c" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "y_r^c" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " being " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "Y_r^c" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " plus an offset of the camera height (i.e., the distance above the ground) to eliminate negative values. In Eq. (2), " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "(u_f, v_f)" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "(u_b, v_b)" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " are the coordinates of a radar point " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " projected onto FV and BEV planes using projection matrices " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " correspondingly. Here, " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " is the original camera intrinsic matrix. The intrinsic parameters are manually pre-defined for " + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 55, + 418, + 296, + 634 + ], + "type": "text", + "content": " based on the map resolution and map center." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 89, + 641, + 295, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 641, + 295, + 669 + ], + "spans": [ + { + "bbox": [ + 89, + 641, + 295, + 669 + ], + "type": "interline_equation", + "content": "P _ {r} ^ {c} = T _ {\\text {i n i t}} \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right] = \\left[ \\begin{array}{c c} R _ {\\text {i n i t}} & t _ {\\text {i n i t}} \\\\ 0 & 1 \\end{array} \\right] \\left[ \\begin{array}{l} P _ {r} \\\\ 1 \\end{array} \\right], \\tag {1}", + "image_path": "ace6cd049652554f96a31c9876b5b9b0411ee6a5961bc5598fef561156adc109.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 677, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 677, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 69, + 677, + 295, + 717 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{c} u _ {f} \\\\ v _ {f} \\\\ 1 \\end{array} \\right] = K \\left[ \\begin{array}{c} X _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ Y _ {r} ^ {c} / Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right], a n d \\left[ \\begin{array}{c} u _ {b} \\\\ v _ {b} \\\\ 1 \\end{array} \\right] = K ^ {\\prime} \\left[ \\begin{array}{c} X _ {r} ^ {c} \\\\ Z _ {r} ^ {c} \\\\ 1 \\end{array} \\right]. \\tag {2}", + "image_path": "f342d83b764c3c17bcb69923826216a29de4ecebe68fd500541493532b78a76c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": "Camera data. For the camera data, the FV information map " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "I_{I}^{FV}(u_{d}, v_{d})" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": " is derived using the Metric Depth Estimation module, which predicts the depth image from the input image. This module employs two sequential methods: DepthAnything[40] for relative depth prediction and ZoeDepth[1] for refining it into metric depth, resulting in " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "I_{I}^{FV}(u_{d}, v_{d})" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": ". From the depth image, we convert each pixel into a pseudo point cloud " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "P_{p} = (X_{p}, Y_{p}, Z_{p})" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": " based on Eq. (3), which are then transformed/projected using matrix " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": " to form the pseudo-BEV image " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "I_{I}^{BEV}" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": " similar to the radar case " + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "inline_equation", + "content": "I_{R}^{BEV}" + }, + { + "bbox": [ + 313, + 393, + 555, + 526 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 536, + 555, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 536, + 555, + 566 + ], + "spans": [ + { + "bbox": [ + 317, + 536, + 555, + 566 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{l l l} X _ {p} & Y _ {p} & Z _ {p} \\end{array} \\right] ^ {\\top} = K ^ {- 1} \\cdot I _ {I} ^ {F V} \\left(u _ {d}, v _ {d}\\right) \\cdot \\left[ \\begin{array}{l l l} u _ {d} & v _ {d} & 1 \\end{array} \\right] ^ {\\top}. \\tag {3}", + "image_path": "8caa6df5cbeecbac7d8d99ac70b0a96f377aa4182a4ec5514e4c81118a5dcc92.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 574, + 425, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 574, + 425, + 586 + ], + "spans": [ + { + "bbox": [ + 314, + 574, + 425, + 586 + ], + "type": "text", + "content": "3.2. Feature Extraction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": "After transforming point clouds and images into two unified representations—FV depth maps " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "(I_R^{FV}, I_I^{FV} \\in \\mathbb{R}^{H \\times W})" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": " and BEV maps " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "(I_I^{BEV}, I_R^{BEV} \\in \\mathbb{R}^{H' \\times W'})" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": "—we use ResNet [5] and convolutional layers to extract features from these maps. Additionally, to enhance the FV semantic content, context features are extracted from the original image using ResNet18 and are integrated with the features from " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "I_I^{FV}" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": ". The resulting feature sets, representing different perspectives for radar and camera, are denoted as " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "F_R^{FV}" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "F_I^{FV} \\in \\mathbb{R}^{H/8 \\times W/8 \\times C}" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "F_R^{BEV}" + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 593, + 555, + 715 + ], + "type": "inline_equation", + "content": "F_I^{BEV} \\in" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6703" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 80, + 299, + 178 + ], + "blocks": [ + { + "bbox": [ + 74, + 80, + 299, + 178 + ], + "lines": [ + { + "bbox": [ + 74, + 80, + 299, + 178 + ], + "spans": [ + { + "bbox": [ + 74, + 80, + 299, + 178 + ], + "type": "image", + "image_path": "c3d3e842ade00d54ea8d25b509b47472141824f56a48d4eeb1c6f360ae78e966.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 180, + 286, + 191 + ], + "lines": [ + { + "bbox": [ + 86, + 180, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 86, + 180, + 286, + 191 + ], + "type": "text", + "content": "(a) Cross attention and Explicit Feature Matching Supervision" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 313, + 79, + 535, + 177 + ], + "blocks": [ + { + "bbox": [ + 313, + 79, + 535, + 177 + ], + "lines": [ + { + "bbox": [ + 313, + 79, + 535, + 177 + ], + "spans": [ + { + "bbox": [ + 313, + 79, + 535, + 177 + ], + "type": "image", + "image_path": "d365f4e01254fb8dbcd67d2c963013eea863a9280a2eed65622cd9f2acdb67a6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 381, + 180, + 467, + 190 + ], + "lines": [ + { + "bbox": [ + 381, + 180, + 467, + 190 + ], + "spans": [ + { + "bbox": [ + 381, + 180, + 467, + 190 + ], + "type": "text", + "content": "(b) 3Dbbox " + }, + { + "bbox": [ + 381, + 180, + 467, + 190 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 381, + 180, + 467, + 190 + ], + "type": "text", + "content": " illustration" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 187, + 200, + 421, + 211 + ], + "lines": [ + { + "bbox": [ + 187, + 200, + 421, + 211 + ], + "spans": [ + { + "bbox": [ + 187, + 200, + 421, + 211 + ], + "type": "text", + "content": "Figure 4. Illustration of the proposed Feature Matching module." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 222, + 295, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 222, + 295, + 249 + ], + "spans": [ + { + "bbox": [ + 55, + 222, + 295, + 249 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H' / 8 \\times W' / 8 \\times C}" + }, + { + "bbox": [ + 55, + 222, + 295, + 249 + ], + "type": "text", + "content": ". We detail the network architecture in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 255, + 162, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 162, + 268 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 162, + 268 + ], + "type": "text", + "content": "3.3. Feature Matching" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 272, + 296, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 272, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 272, + 296, + 380 + ], + "type": "text", + "content": "To estimate the 6-DoF (degrees of freedom) extrinsic transformation between radar and camera sensors, our model first focuses on identifying corresponding feature pairs from each sensor's perspective. As illustrated in Fig. 3, we conduct feature matching across two different perspectives. For each perspective, we implement similar matching modules that include a Multi-Modal Cross-Attention Mechanism and an Explicit Feature Matching Supervision. Additionally, in the FV case, we incorporate a Noise-Resistant Matcher." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": "Multi-Modal Cross-Attention Mechanism. Considering both perspectives, the projected point cloud data from radar is sparse with mostly zero values, while camera data is dense with rich depth information and geometric features. We propose a Multi-Modal Cross-Attention (MCA) Mechanism that enables the model to focus on non-zero feature regions and identify correlations between camera and radar features. As described in Equation Eq. (4), the inputs to the MCA are " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "F_{I}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "F_{R}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": ", and the outputs are " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "O_{I\\leftarrow R}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "O_{R\\leftarrow I}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": ". These outputs are used to compute the updated features " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\hat{F}_{I}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\hat{F}_{R}" + }, + { + "bbox": [ + 55, + 381, + 296, + 514 + ], + "type": "text", + "content": " as shown in Eq. (5)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 64, + 522, + 295, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 522, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 64, + 522, + 295, + 550 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left(O _ {I \\leftarrow R}, O _ {R \\leftarrow I}\\right) = \\left(\\Theta \\left(F _ {I}, m _ {I \\leftarrow R}\\right), \\Theta \\left(F _ {R}, m _ {R \\leftarrow I}\\right)\\right) \\tag {4} \\\\ = M C A \\left(F _ {I}, F _ {R}\\right) \\\\ \\end{array}", + "image_path": "3540f5236a09ed93ddc62bd486dc3d3647b5b14f804beb5f0de52f35adf35bf8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 90, + 556, + 294, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 556, + 294, + 571 + ], + "spans": [ + { + "bbox": [ + 90, + 556, + 294, + 571 + ], + "type": "interline_equation", + "content": "\\hat {F} _ {I} = F _ {I} + O _ {I \\leftarrow R}, \\quad \\hat {F} _ {R} = F _ {R} + O _ {R \\leftarrow I}, \\tag {5}", + "image_path": "eb270fcfb3d46b9fe603052931066a7ee1b1385edd2ee32dfb9bbc3f89c9e0b6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": "To obtain " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "O_{I \\leftarrow R}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "O_{R \\leftarrow I}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " in Eq. (4), we first compute the attended features " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "m_{I \\leftarrow R}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "m_{R \\leftarrow I}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " between the radar and image inside MCA. Inspired by [6, 17], we use Eq. (6) to compute attended features " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "m_{I \\leftarrow R}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "m_{R \\leftarrow I}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": ", which rely on the cross-attention score " + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "inline_equation", + "content": "a_{IR}" + }, + { + "bbox": [ + 55, + 575, + 296, + 635 + ], + "type": "text", + "content": " computed by Eq. (7)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 640, + 296, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 640, + 296, + 666 + ], + "spans": [ + { + "bbox": [ + 58, + 640, + 296, + 666 + ], + "type": "interline_equation", + "content": "m _ {R \\leftarrow I} = \\operatorname {S o f t m a x} \\left(a _ {I R} ^ {\\top}\\right) V _ {I}, m _ {I \\leftarrow R} = \\operatorname {S o f t m a x} \\left(a _ {I R}\\right) V _ {R}, \\tag {6}", + "image_path": "16b0fb515037dbe9dd73f47f9e1e967dcb69a8aed0b999e018beb24efb47c0bb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 142, + 670, + 295, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 670, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 142, + 670, + 295, + 685 + ], + "type": "interline_equation", + "content": "a _ {I R} = K _ {I} ^ {\\top} K _ {R}, \\tag {7}", + "image_path": "dec16e4d78cc5a8f3cd0827213e2cb7a81df9ac27c3d47c8ef4e2be17c3924f2.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "V_{*}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "K_{*}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " are the value and key, respectively, extracted from the feature " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "F_{*}" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " through linear projections. Note" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "spans": [ + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": "that, we reshape " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "F_{*}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "(m \\times c)" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " dimension before projection and " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "* \\in \\{I, R\\}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": ". After obtaining these attention maps " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "m_{I \\leftarrow R}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "m_{R \\leftarrow I}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": ", we apply the cross-modal feature refinement function " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " to calculate the " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "O_{I \\leftarrow R}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "O_{R \\leftarrow I}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " by Eq. (4) given " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "F_{I}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "F_{R}" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": ". The details of " + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 313, + 224, + 553, + 296 + ], + "type": "text", + "content": " can be found in the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "content": "After obtaining " + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "inline_equation", + "content": "\\hat{F}_I" + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "inline_equation", + "content": "\\hat{F}_R" + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "content": ", as shown in Fig. 4a, a Residual Conv Block is used to aggregate them into corresponding " + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "inline_equation", + "content": "F_{view}" + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "content": " for each perspective branch using Eq. (8), with view " + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "inline_equation", + "content": "\\in \\{BEV, FV\\}" + }, + { + "bbox": [ + 313, + 297, + 554, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 353, + 354, + 553, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 354, + 553, + 385 + ], + "spans": [ + { + "bbox": [ + 353, + 354, + 553, + 385 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} F _ {v i e w} = \\Phi (\\operatorname {c o n v} (\\operatorname {c o n c a t} (\\hat {F} _ {I}, \\hat {F} _ {R})) \\tag {8} \\\\ + \\operatorname {c o n v} \\left(\\operatorname {c o n v} \\left(\\operatorname {c o n c a t} \\left(\\hat {F} _ {I}, \\hat {F} _ {R}\\right)\\right)\\right), \\\\ \\end{array}", + "image_path": "5c7c57ecfa83842f597e62962de5b8669096b6df47d528ef10a7e6f4a826668f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "content": "where the first term of " + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "content": " consists of the concatenated features of " + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\hat{F}_I" + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\hat{F}_R" + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "content": " after passing through one convolutional layer, while the second term involves passing through two convolutional layers. These terms are then added together to form our Residual Conv Block. Here, \"conv\" denotes a block that includes convolutional layers followed by the leakyReLU [38] activation function. The block " + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 398, + 554, + 506 + ], + "type": "text", + "content": " sequentially applies the leakyReLU activation function, flattens the features, and utilizes a multi-layer perceptron (MLP)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "text", + "content": "Explicit Feature Matching Supervision. Previously, feature matching was implicitly supervised solely by the final calibration loss to understand overall errors without specifically identifying matched pairs. We find this implicit supervision insufficient and propose directly supervising feature matching using true matching pairs generated from the correct calibration matrix. In other words, we add matching prediction and auxiliary loss during training to enhance the understanding of local feature matching pairs between " + }, + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\hat{F}_I" + }, + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\hat{F}_R" + }, + { + "bbox": [ + 313, + 509, + 554, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Motivated by [17], an extra branch is designed to perform the task of Local Feature Matching during the training phase as shown in Fig. 4a. Assuming each reshaped feature " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\hat{f}_{*} \\in \\mathbb{R}^{m \\times c}" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\hat{F}_{*}" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": " includes " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "H / 8 \\times W / 8" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": ") keypoints, with each keypoint having a feature descriptor of dimension " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": ". The assignment matrix " + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "inline_equation", + "content": "P \\in [0,1]^{m \\times m}" + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": " is estimated based on Eq. (9)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6704" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 81, + 70, + 271, + 148 + ], + "blocks": [ + { + "bbox": [ + 81, + 70, + 271, + 148 + ], + "lines": [ + { + "bbox": [ + 81, + 70, + 271, + 148 + ], + "spans": [ + { + "bbox": [ + 81, + 70, + 271, + 148 + ], + "type": "image", + "image_path": "83db58cfd827175c831f232a9e3d52dc4675bcda00e328e10d446fbfc9166466.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 155, + 271, + 166 + ], + "lines": [ + { + "bbox": [ + 78, + 155, + 271, + 166 + ], + "spans": [ + { + "bbox": [ + 78, + 155, + 271, + 166 + ], + "type": "text", + "content": "Figure 5. Details of the Selective Fusion Mechanism" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 91, + 190, + 294, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 190, + 294, + 205 + ], + "spans": [ + { + "bbox": [ + 91, + 190, + 294, + 205 + ], + "type": "interline_equation", + "content": "P = \\sigma_ {I} ^ {\\top} \\sigma_ {R} \\operatorname {S o f t m a x} \\left(S ^ {\\top}\\right) ^ {\\top} \\operatorname {S o f t m a x} (S), \\tag {9}", + "image_path": "f510609c45f0db50b7c153179eba49da88aac6a2a34b9e142c21f091cd5e7f62.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "spans": [ + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{m \\times m}" + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "content": ", calculated by equation Eq. (10), is the similarity score matrix between the features extracted from two sensors after the Multi-Modal Cross-Attention step. Meanwhile, " + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "inline_equation", + "content": "\\sigma_{*} \\in [0, 1]^{1 \\times m}" + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "content": " is the matchable score of feature points, estimated by equation Eq. (11), where " + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "inline_equation", + "content": "* \\in \\{I, R\\}" + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "content": ". A point with a high value of " + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 210, + 296, + 294 + ], + "type": "text", + "content": " means it is more likely to have a corresponding point on another map." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 303, + 295, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 303, + 295, + 319 + ], + "spans": [ + { + "bbox": [ + 115, + 303, + 295, + 319 + ], + "type": "interline_equation", + "content": "S = \\operatorname {L i n e a r} \\left(\\hat {f} _ {I}\\right) ^ {\\top} \\operatorname {L i n e a r} \\left(\\hat {f} _ {R}\\right), \\tag {10}", + "image_path": "e8f8b5e1b8a2b195e70a09c665868f36ab9b7cd417464768a6c8e88de89b875d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 118, + 331, + 294, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 331, + 294, + 345 + ], + "spans": [ + { + "bbox": [ + 118, + 331, + 294, + 345 + ], + "type": "interline_equation", + "content": "\\sigma_ {*} = \\operatorname {S i g m o i d} \\left(\\operatorname {L i n e a r} \\left(\\hat {f} _ {*}\\right)\\right). \\tag {11}", + "image_path": "acd993b61afe81c8d3a5a36a9253afde45859fbdea3c1bf9c84795123e4d06af.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 351, + 295, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 295, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 295, + 387 + ], + "type": "text", + "content": "In the training phase, we use the estimated assignment matrix " + }, + { + "bbox": [ + 55, + 351, + 295, + 387 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 351, + 295, + 387 + ], + "type": "text", + "content": " and the matching loss defined in Eq. (16) to directly supervise the cross-sensor matching." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": "Noise-Resistant Matcher. For the FV case, when preparing the ground truth matches matrix " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": " to supervise the assignment matrix " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": ", we recognize that the radar training data contains many unreliable data points due to elevation ambiguity. Additionally, radar signals reflected by objects far from the radar plane can lead to unreliable data points. Therefore, we propose using LiDAR data to identify and remove these unreliable data points from the list of true feature matching pairs " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": ". First, we transform the LiDAR and radar point clouds into a unified camera coordinate system. For each radar 3D point " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "P_r^c = (X_r^c, Y_r^c, Z_r^c) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": ", a neighbor region is created using a 3D bounding box " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": ". If the number of LiDAR point clouds " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "P_l^c = (X_l^c, Y_l^c, Z_l^c) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": " within this box " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": " exceeds a threshold " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": ", the radar point cloud " + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "inline_equation", + "content": "P_r^c" + }, + { + "bbox": [ + 55, + 388, + 295, + 567 + ], + "type": "text", + "content": " is considered reliable." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": "The 3D bounding box " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": " is adaptively designed for each radar point. Denote " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\phi, \\theta" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": " respectively represent the elevation angle, azimuth angle, and point length relative to a 3D radar point. " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "(\\Delta x, \\Delta z)" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": " are the noises caused by elevation ambiguity as defined in the method [28] and " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\Delta s" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": " is the error between the two sensors. As shown in Fig. 4b, the box height " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "h_B" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": " is calculated by Eq. (12) given " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\Delta s, \\phi, R" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": ", and a predefined parameter " + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 55, + 567, + 295, + 676 + ], + "type": "text", + "content": ", which represents the allowable height error from a 3D point to the radar plane." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 688, + 301, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 688, + 301, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 688, + 301, + 714 + ], + "type": "interline_equation", + "content": "h _ {B} = 2 (\\Delta y + \\Delta s) = 2 (\\delta + \\Delta s), a n d \\cos \\phi = \\sqrt {1 - (\\delta / R) ^ {2}}. \\tag {12}", + "image_path": "5beb91894b34d25b2fc3a3e101463729d16435cd8cfe274aacdcf4b7e612b461.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": "The width " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "w_{B}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "d_{B}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": ", are then calculated by Eqs. (13) and (14). The center of a 3D bounding box " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " of a radar point " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "P_{r}^{c}(X_{r}^{c}, Y_{r}^{c}, Z_{r}^{c})" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " is determined as: " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "(X_{r}^{c} - \\Delta x / 2, Y_{r}^{c}, Z_{r}^{c} - \\Delta z / 2)" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 328, + 131, + 555, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 131, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 328, + 131, + 555, + 144 + ], + "type": "interline_equation", + "content": "w _ {B} = \\Delta x + 2 \\Delta s = R \\sin \\theta (1 - \\cos \\phi) + 2 \\Delta s, \\tag {13}", + "image_path": "0e20c23b39813031765235cf17cda5e327c155db65df81cef8c39458e8d25ee4.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 328, + 158, + 555, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 158, + 555, + 171 + ], + "spans": [ + { + "bbox": [ + 328, + 158, + 555, + 171 + ], + "type": "interline_equation", + "content": "d _ {B} = \\Delta z + 2 \\Delta s = R \\cos \\theta (1 - \\cos \\phi) + 2 \\Delta s. \\tag {14}", + "image_path": "6f1ef9a86494d365fe631fe31c78324344752cf2366b2aca38916ae664ec1133.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 177, + 554, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 177, + 554, + 201 + ], + "spans": [ + { + "bbox": [ + 313, + 177, + 554, + 201 + ], + "type": "text", + "content": "Due to limited space, we provide additional information and details in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 209, + 469, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 469, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 469, + 220 + ], + "type": "text", + "content": "3.4. Selective Fusion Mechanism" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": "After the Feature Matching step, we can extract the features " + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "inline_equation", + "content": "F_{BEV}" + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "inline_equation", + "content": "F_{FV}" + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": " in the corresponding perspective branch. To enhance calibration accuracy by leveraging the distinctive contributions of each perspective, we propose a Dual-Perspective View Selective Fusion Mechanism that combines these features influenced by SKNet [14]. As illustrated in Fig. 5, we first calculate the compact feature " + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": " from the sum of the two feature vectors using Eq. (15). Subsequently, a channel-wise attention mechanism adaptively selects diverse elements in the corresponding input features, guided by the compact feature descriptor " + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": ". The obtained results are then added together to create the final feature " + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "inline_equation", + "content": "F_{select}" + }, + { + "bbox": [ + 313, + 227, + 555, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 381, + 389, + 553, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 389, + 553, + 403 + ], + "spans": [ + { + "bbox": [ + 381, + 389, + 553, + 403 + ], + "type": "interline_equation", + "content": "z = F _ {f c} \\left(F _ {B E V} + F _ {F V}\\right), \\tag {15}", + "image_path": "30e383531db960ea365797b582fca5cfef79f32da537d95fd294ea1baf86f8d8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 408, + 554, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 554, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 554, + 433 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 408, + 554, + 433 + ], + "type": "inline_equation", + "content": "F_{fc}" + }, + { + "bbox": [ + 313, + 408, + 554, + 433 + ], + "type": "text", + "content": " denotes the use of a fully connected layer, Batch-Norm [7], and the leakyReLU activation function." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 441, + 416, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 416, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 416, + 453 + ], + "type": "text", + "content": "3.5. Regression Head" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "content": "To estimate the rotation and translation parameters and form the updated transformation matrix " + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "inline_equation", + "content": "T_{pred}" + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "content": ", we leverage the sequence generative decoder from CalibDepth [43]. Specifically, this method employs LSTM [24], where the output is defined as a sequence of actions of length " + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "content": " in an autoregressive manner to address the inherent inaccuracies in the one-shot regression approach. After determining " + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "inline_equation", + "content": "T_{pred}" + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "content": " at the current iteration, we update " + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "inline_equation", + "content": "T_{init} = T_{init} \\cdot T_{pred}^{i}" + }, + { + "bbox": [ + 313, + 459, + 554, + 567 + ], + "type": "text", + "content": ", as illustrated in Fig. 3." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 574, + 403, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 403, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 403, + 586 + ], + "type": "text", + "content": "3.6. Loss Function" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 592, + 554, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 554, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 554, + 663 + ], + "type": "text", + "content": "Our model operates under two supervised tasks. The primary task focuses on auto-calibration, while an auxiliary task centers on local feature matching, which clarifies the correspondence between feature pairs. Consequently, we employ two corresponding loss functions: the matching loss and calibration loss." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": "Explicit Correspondences Matching. With ground truth match matrix " + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M} \\in \\{0,1\\}^{N \\times m \\times m}" + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": " and the predicted matching " + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "inline_equation", + "content": "P \\in [0,1]^{N \\times m \\times m}" + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{I}, \\sigma_{R} \\in [0,1]^{N \\times m}" + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": ", the matching loss function is designed to minimize the log-likelihood" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6705" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "of the predicted matches as in Eq. (16). Since our calibration includes " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " iterations, the matching loss term aggregates the loss from all iterations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 117, + 295, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 117, + 295, + 150 + ], + "spans": [ + { + "bbox": [ + 69, + 117, + 295, + 150 + ], + "type": "interline_equation", + "content": "L _ {M} = - \\sum_ {n} ^ {N} \\left(\\frac {\\lambda}{\\Sigma \\mathcal {M}} L _ {p o s} ^ {n} + \\frac {1 - \\lambda}{\\Sigma \\mathcal {N} _ {\\mathcal {I}} + \\Sigma \\mathcal {N} _ {\\mathcal {R}}} L _ {n e g} ^ {n}\\right), \\tag {16}", + "image_path": "22b13a60a623a1cdb77a272c6b47586f3dff736f226bf2eb042df7f46f35b578.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 121, + 159, + 295, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 159, + 295, + 186 + ], + "spans": [ + { + "bbox": [ + 121, + 159, + 295, + 186 + ], + "type": "interline_equation", + "content": "L _ {p o s} = \\sum_ {i, j} \\log \\left(P ^ {i j}\\right) \\mathcal {M} ^ {i, j}, \\tag {17}", + "image_path": "a0a5eca2124e1640a6627dbfd46d4416d73a35d389736020edd634f46da114bb.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 194, + 295, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 194, + 295, + 220 + ], + "spans": [ + { + "bbox": [ + 66, + 194, + 295, + 220 + ], + "type": "interline_equation", + "content": "L _ {n e g} = \\sum_ {i} \\log \\left(1 - \\sigma_ {I} ^ {i}\\right) \\mathcal {N} _ {I} ^ {i} + \\sum_ {j} \\log \\left(1 - \\sigma_ {R} ^ {j}\\right) \\mathcal {N} _ {R} ^ {j}, \\tag {18}", + "image_path": "b91502f3245cd17955e189376ea75c2132e3c5708ffd8985a61409b8e0eeff31.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " is the balancing coefficient between positive and negative instances. " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_R" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_I" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " are ground truth for \"No Matchable\" scores for pixels in the radar and camera maps respectively. The true matches matrix " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " between camera and radar maps is dynamically computed based on the true translation " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "T_{gt}" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " between the two sensors and the current, yet imperfect, updated translation " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "T_{init}" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_R" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_I" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " are derived from " + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 226, + 296, + 323 + ], + "type": "text", + "content": " by Eq. (19)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 333, + 295, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 333, + 295, + 360 + ], + "spans": [ + { + "bbox": [ + 77, + 333, + 295, + 360 + ], + "type": "interline_equation", + "content": "\\mathcal {N} _ {I} ^ {i} = 1 - \\sum_ {j} \\mathcal {M} _ {i j}, \\quad \\mathcal {N} _ {R} ^ {j} = 1 - \\sum_ {i} \\mathcal {M} _ {i j}. \\tag {19}", + "image_path": "83fbb0e4cb878de6bde949369b445eefbc8d305dbce400298e2b1504c3084eee.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 368, + 296, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 368, + 296, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 368, + 296, + 405 + ], + "type": "text", + "content": "The final matching loss function is then computed as the sum of losses from two perspectives defined as " + }, + { + "bbox": [ + 55, + 368, + 296, + 405 + ], + "type": "inline_equation", + "content": "L_{\\text{matching}} = L_{M_{bev}} + L_{M_{fv}}" + }, + { + "bbox": [ + 55, + 368, + 296, + 405 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "text", + "content": "Calibration Loss. To both ensure that the calibration results at each iteration step are asymptotic to the ground truth and avoid divergence between different iteration steps, we use the calibration loss " + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "inline_equation", + "content": "L_{\\text{calib}}" + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "text", + "content": " proposed in [43]. By controlling the weight parameter " + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "text", + "content": ", the final total loss consists of the two losses mentioned above, defined as " + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "inline_equation", + "content": "L_{\\text{total}} = L_{\\text{calib}} + \\beta L_{\\text{matching}}" + }, + { + "bbox": [ + 55, + 406, + 296, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 504, + 181, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 504, + 181, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 504, + 181, + 517 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 525, + 227, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 227, + 537 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 227, + 537 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation Metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "text", + "content": "Dataset Preparation. We utilize a subset of images from the nuScenes dataset [2] for our training and testing processes. This subset comprises 12,610 samples for training, 1,628 samples for validation, and 1,623 samples for testing. The training and testing depth range spans from 0 to 200 meters, with input and output resolutions set at " + }, + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "inline_equation", + "content": "400 \\times 192" + }, + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "text", + "content": " pixels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "Evaluation Metrics. To facilitate comparison with previous work, we convert the output rotation vector to Euler angles. Then, we calculate the absolute error between the predicted values and the ground truth in all dimensions of angles and translation vectors. For all tables, the best and the second-best results are highlighted in bold and underlined, respectively." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 319, + 71, + 553, + 215 + ], + "blocks": [ + { + "bbox": [ + 319, + 71, + 553, + 215 + ], + "lines": [ + { + "bbox": [ + 319, + 71, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 319, + 71, + 553, + 215 + ], + "type": "table", + "html": "
RangeMethodsRotation(°)Translation(cm)
MeanRollPitchYawMeanXY
R1LCCNet-11.6030.1233.1301.55616.53122.99217.648
NetCalib21.2050.3872.2890.94112.29712.53212.076
CalibDepth0.8070.3900.3451.68612.60812.86012.250
Coarse [26]2.0350.5811.5194.004---
Fine [26]1.6920.4420.9393.695---
Ours0.4270.1300.1980.9539.49812.5633.295
R2LCCNet-32.1561.5262.3642.57989.67271.66089.605
LCCNet-51.8980.9192.3142.46188.30274.21685.239
NetCalib22.7781.4654.6882.18071.03776.00157.204
CalibDepth1.6861.1490.8083.10255.38077.14612.918
Coarse [26]4.3881.8663.2518.048---
Fine [26]3.3341.3681.9376.696---
Ours0.8520.35970.44231.754447.53774.7775.415
", + "image_path": "a4797b4c97c07cd18e6624d9d33a352233a63dbd4de4101b8095ec0b744cac54.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 318, + 275, + 553, + 350 + ], + "blocks": [ + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "lines": [ + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "text", + "content": "Table 1. Comparison with LiDAR-Camera-Based and Radar-Camera-Based Auto-Calibration Methods on the nuScenes dataset. The methods are compared with two mis-calibration ranges, R1 (" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "inline_equation", + "content": "\\pm 10" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "inline_equation", + "content": "\\pm 0.25m" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "text", + "content": ") and R2 (" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "inline_equation", + "content": "\\pm 20" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "inline_equation", + "content": "\\pm 1.5m" + }, + { + "bbox": [ + 313, + 219, + 553, + 264 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 275, + 553, + 350 + ], + "lines": [ + { + "bbox": [ + 318, + 275, + 553, + 350 + ], + "spans": [ + { + "bbox": [ + 318, + 275, + 553, + 350 + ], + "type": "table", + "html": "
FVBEVSFMCAEMSNRRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
✓0.6570.2350.3011.43612.60212.85812.24712.700
✓0.6890.2950.3811.39212.60512.87012.28512.660
✓✓0.5750.2090.2841.23212.31512.86311.41612.667
✓✓✓0.5290.1750.2371.17611.84212.8829.97612.670
✓✓✓✓0.5020.1750.2351.09712.57412.88312.15012.688
✓✓✓✓✓0.4630.1400.2061.0429.62712.5633.68212.636
✓✓✓✓✓✓0.4270.1300.1980.9539.49812.5633.29512.635
", + "image_path": "ae81b4afee84c1851c350f0a9f36e7cad1660e3f88229c997f636aaec016febc.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 353, + 554, + 397 + ], + "lines": [ + { + "bbox": [ + 313, + 353, + 554, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 554, + 397 + ], + "type": "text", + "content": "Table 2. Module Impact Ablation (FV: Front View, BEV: Bird's Eye View, SF: Selective Fusion, MCA: Multi-Modal Cross-Attention Mechanism, EMS: Explicit Feature Matching Supervision, NR: Noise-Resistant Matcher)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 418, + 395, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 395, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 395, + 430 + ], + "type": "text", + "content": "4.2. Main results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "text", + "content": "We compared it against the method by Schöller et al. [26]. Although this method dates back to 2019 and may not incorporate recent advancements, we have also compared it with state-of-the-art LiDAR-camera-based auto-calibration methods, including LCCNet [20], CalibDepth [43], and NetCalib2 [36]. To ensure a fair comparison, we trained and tested all these methods using the same set of parameters and radar-image dataset. As shown in Sec. 4.2, our focus lies on testing two mis-calibration ranges: " + }, + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "inline_equation", + "content": "[10^{\\circ}, 0.25\\mathrm{m}]" + }, + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "inline_equation", + "content": "[20^{\\circ}, 1.5\\mathrm{m}]" + }, + { + "bbox": [ + 313, + 436, + 555, + 616 + ], + "type": "text", + "content": ", representing small and large error ranges. For \"LCCNet-number\", the \"number\" corresponds to the number of iteration steps. The achieved results demonstrate that our method exhibits significantly superior average errors in both rotation and translation compared to other methods across both mis-calibration ranges." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 624, + 415, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 415, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 415, + 635 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": "Impact of each Module. Sec. 4.3 shows the impact of each module on experimental outcomes. Using both FV and BEV perspectives together reduced the mean absolute error in rotation by " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": ". The Selective Fusion mechanism further reduced this error by " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "16.5\\%" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": " by allowing the model to choose suitable features from each perspective. The multi-" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6706" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 294, + 121 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 121 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 121 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 121 + ], + "type": "table", + "html": "
Fusion MethodRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
Add Fusion0.6420.2170.3711.33812.54712.83212.09612.714
Concat Fusion0.5750.2090.2841.23212.31512.86311.41612.667
Selective Fusion0.5290.1750.2371.17611.84212.8829.97612.669
", + "image_path": "12b0f381f05cf71cf8978efdf53f88ed4a697b03c11634ad18b14d5180b866de.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 158, + 294, + 212 + ], + "blocks": [ + { + "bbox": [ + 56, + 125, + 295, + 146 + ], + "lines": [ + { + "bbox": [ + 56, + 125, + 295, + 146 + ], + "spans": [ + { + "bbox": [ + 56, + 125, + 295, + 146 + ], + "type": "text", + "content": "Table 3. Comparison of Dual-Perspective Fusion Methods with Basic Methods" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 158, + 294, + 212 + ], + "lines": [ + { + "bbox": [ + 56, + 158, + 294, + 212 + ], + "spans": [ + { + "bbox": [ + 56, + 158, + 294, + 212 + ], + "type": "table", + "html": "
βRotation(°)Translation(cm)
MeanRollPitchYawMeanXYZ
0.10.4700.1500.2151.04410.30412.5875.68412.640
0.30.4710.1600.2241.02910.37712.5555.94012.637
0.50.4460.1640.2140.96012.11212.54911.15112.637
", + "image_path": "318c9665577963d9bc60210cb65ac1992fc4341e98b8ee7aba8266f4d4a966e3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 216, + 295, + 239 + ], + "lines": [ + { + "bbox": [ + 55, + 216, + 295, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 295, + 239 + ], + "type": "text", + "content": "Table 4. Ablation Study on Weight Impacts in Explicit Feature Matching Loss" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "text", + "content": "modal cross-attention mechanism also effectively reduced rotation error by " + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "text", + "content": ", demonstrating its capability to address the challenges of sparse radar depth maps. However, the mean absolute error in translation did not improve clearly based on the above modules due to the sparse and noisy radar point clouds. Next, introducing Explicit Feature Matching Supervision decreased the translation error by " + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "inline_equation", + "content": "23.4\\%" + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "text", + "content": ", highlighting the benefit of explicit matching labels in learning correspondences. Finally, the incorporation of the Noise-Resistant Matcher further filtered out highly inaccurate noise points in the FV perspective and aided in translational calibration. As a result, the mean absolute error in rotation decreased by " + }, + { + "bbox": [ + 54, + 254, + 295, + 410 + ], + "type": "inline_equation", + "content": "7.8\\%" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 411, + 295, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 482 + ], + "type": "text", + "content": "Dual-Perspective Fusion Methods. Additionally, we compare our Selective Fusion Mechanism with commonly used methods such as add fusion and concatenation fusion. In Sec. 4.3, the results demonstrate a significant improvement of the proposed method over the conventional fusion methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "content": "Weight of Explicit Feature Matching Loss. In Sec. 4.3, we test three " + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "content": " values: 0.1, 0.3, and 0.5, excluding the noise-resistant matcher module in our method. " + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "content": " achieved the lowest rotation error but the highest translation error. " + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "content": " provided the best translation accuracy with negligible rotation error. Thus, " + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 55, + 484, + 295, + 568 + ], + "type": "text", + "content": " was selected as the optimal balanced coefficient." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 576, + 167, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 167, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 167, + 588 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "Our method provides accurate calibration results across various initial mis-calibration conditions and scenes. Fig. 6a visualizes these results, showing precise calibration even with significant initial errors and sparse radar points. To highlight the effectiveness of our explicit matching supervision, we compute the cross-attention maps " + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "inline_equation", + "content": "I_{I\\leftarrow R}" + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "inline_equation", + "content": "I_{R\\leftarrow I}" + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": " between radar and image features, as visualized in Fig. 6b. The detailed formulas for computing these attention maps are provided in the supplementary material. We represent the attention maps using heatmaps and denote the projected" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 432, + 129 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 432, + 129 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 432, + 129 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 432, + 129 + ], + "type": "image", + "image_path": "f613701e9f918022500c1a109984ee6a4a4036aa3807d4f9a9a53abf078e5c17.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 129, + 389, + 138 + ], + "lines": [ + { + "bbox": [ + 358, + 129, + 389, + 138 + ], + "spans": [ + { + "bbox": [ + 358, + 129, + 389, + 138 + ], + "type": "text", + "content": "Sample 1" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 438, + 70, + 553, + 126 + ], + "blocks": [ + { + "bbox": [ + 438, + 70, + 553, + 126 + ], + "lines": [ + { + "bbox": [ + 438, + 70, + 553, + 126 + ], + "spans": [ + { + "bbox": [ + 438, + 70, + 553, + 126 + ], + "type": "image", + "image_path": "3ea7d61bd5457fecf10e2ce4e0161df97189fba27b6b62d3b58081f0e6b25878.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 317, + 140, + 432, + 196 + ], + "blocks": [ + { + "bbox": [ + 317, + 140, + 432, + 196 + ], + "lines": [ + { + "bbox": [ + 317, + 140, + 432, + 196 + ], + "spans": [ + { + "bbox": [ + 317, + 140, + 432, + 196 + ], + "type": "image", + "image_path": "1d843502b4ec6718a490d26cac5cfa6368ddd58c68c6d6c4fde76c60e8f7a69c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 198, + 390, + 207 + ], + "lines": [ + { + "bbox": [ + 358, + 198, + 390, + 207 + ], + "spans": [ + { + "bbox": [ + 358, + 198, + 390, + 207 + ], + "type": "text", + "content": "Sample 2" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 346, + 342, + 522, + 354 + ], + "lines": [ + { + "bbox": [ + 346, + 342, + 522, + 354 + ], + "spans": [ + { + "bbox": [ + 346, + 342, + 522, + 354 + ], + "type": "text", + "content": "Figure 6. Results visualization in the front view." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 438, + 139, + 553, + 195 + ], + "blocks": [ + { + "bbox": [ + 480, + 129, + 511, + 138 + ], + "lines": [ + { + "bbox": [ + 480, + 129, + 511, + 138 + ], + "spans": [ + { + "bbox": [ + 480, + 129, + 511, + 138 + ], + "type": "text", + "content": "Sample 1" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 438, + 139, + 553, + 195 + ], + "lines": [ + { + "bbox": [ + 438, + 139, + 553, + 195 + ], + "spans": [ + { + "bbox": [ + 438, + 139, + 553, + 195 + ], + "type": "image", + "image_path": "aaa7d1c90b04d14c4144c5634c6e446101888e915155ccb2c72aafada3e1987f.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 198, + 511, + 206 + ], + "lines": [ + { + "bbox": [ + 479, + 198, + 511, + 206 + ], + "spans": [ + { + "bbox": [ + 479, + 198, + 511, + 206 + ], + "type": "text", + "content": "Sample 2" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 209, + 432, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 432, + 286 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 432, + 286 + ], + "type": "text", + "content": "(a) Examples of calibration results by projecting radar points onto the frontal-view image. Top-left: input RGB image. Top-right: initial mis-calibrated radar point cloud projection. Bottom-left: network-predicted projection. Bottom-right: ground truth projection." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 436, + 209, + 554, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 436, + 209, + 554, + 333 + ], + "spans": [ + { + "bbox": [ + 436, + 209, + 554, + 333 + ], + "type": "text", + "content": "(b) Examples of cross-attention maps highlighting the important regions the model focuses on. Top: image-attentive radar importance regions. Bottom: radar-attentive image importance regions. Left/Right: Results with and without explicit matching supervision. The projected 3D points are used to highlight the critical regions. With explicit matching supervision, our model can better identify these critical regions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 555, + 510 + ], + "type": "text", + "content": "radar points with white color to indicate critical regions. Without explicit matching supervision, we observe that due to many zero-value relationships, the image-attentive radar exhibits weaker and less focused attention, while the radar-attentive image focuses on non-critical region, such as the ground. After incorporating explicit matching supervision, the image-attentive radar's attention becomes more concentrated on the non-zero regions, specifically the areas of radar point cloud projection. Meanwhile, the radar-attentive image effectively focuses on crucial regions, such as radar projection locations and vehicle contours, rather than being restricted to non-critical region." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 525, + 388, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 525, + 388, + 537 + ], + "spans": [ + { + "bbox": [ + 314, + 525, + 388, + 537 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "In this work, we present RC-AutoCalib, an end-to-end network for 3D radar and camera calibration. By incorporating dual perspectives, we address the elevation ambiguity in 3D radar. Our Selective Fusion Mechanism integrates useful features from both FV and BEV perspectives. We also developed a Feature Matching module with a MultiModal Cross-Attention Mechanism to enhance radar point cloud utilization and a Noise-Resistant Matcher to filter out height-inaccurate noise. Our method achieves a calibration error of " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "0.427^{\\circ}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " in rotation and " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "9.498\\mathrm{cm}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " in translation on the nuScenes dataset, demonstrating competitive performance with these SOTA auto-calibration methods using dense point clouds and establishing a benchmark for future research in 3D radar and camera calibration." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6707" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 248 + ], + "type": "text", + "content": "Acknowledgments This work was financially supported in part (project number: 112UA10019) by the Co-creation Platform of the Industry Academia Innovation School, NYCU, under the framework of the National Key Fields Industry-University Cooperation and Skilled Personnel Training Act, from the Ministry of Education (MOE) and industry partners in Taiwan. It also supported in part by the National Science and Technology Council, Taiwan, under Grant NSTC-112-2221-E-A49-089-MY3, Grant NSTC-110-2221-E-A49-066-MY3, Grant NSTC-111-2634-F-A49-010, Grant NSTC-112-2425-H-A49-001, and in part by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and the Ministry of Education (MOE), Taiwan. We also would like to express our gratitude for the support from MediaTek Inc, Hon Hai Research Institute (HHRI), E.SUN Financial Holding Co Ltd, Advantech Co Ltd, Industrial Technology Research Institute (ITRI)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 262, + 115, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 262, + 115, + 274 + ], + "spans": [ + { + "bbox": [ + 56, + 262, + 115, + 274 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 282, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 61, + 282, + 296, + 325 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 282, + 296, + 325 + ], + "spans": [ + { + "bbox": [ + 61, + 282, + 296, + 325 + ], + "type": "text", + "content": "[1] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 16280-16290, 2021. 1" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6709" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_content_list.json b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..aa3b6e00865120b96107af54918740b4ecd15f2d --- /dev/null +++ b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_content_list.json @@ -0,0 +1,1688 @@ +[ + { + "type": "text", + "text": "RCP-Bench: Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions", + "text_level": 1, + "bbox": [ + 151, + 128, + 848, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shihang Du $^{1}$ , Sanqing Qu $^{1}$ , Tianhang Wang $^{1}$ , Xudong Zhang $^{1}$ , Yunwei Zhu $^{1}$ , Jian Mao $^{1}$ , Fan Lu $^{1}$ , Qiao Lin $^{2}$ , Guang Chen $^{1*}$ $^{1}$ Tongji University, $^{2}$ EACON Technology Co., Ltd.", + "bbox": [ + 250, + 202, + 746, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Collaborative perception enhances single-vehicle perception by integrating sensory data from multiple connected vehicles. However, existing studies often assume ideal conditions, overlooking resilience to real-world challenges, such as adverse weather and sensor malfunctions, which is critical for safe deployment. To address this gap, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of collaborative detection models under a wide range of real-world corruptions. RCP-Bench includes three new datasets (i.e., OPV2V-C, V2XSet-C, and DAIR-V2X-C) that simulate six collaborative cases and 14 types of camera corruption resulting from external environmental factors, sensor failures, and temporal misalignments. Extensive experiments on 10 leading collaborative perception models reveal that, while these models perform well under ideal conditions, they are significantly affected by corruptions. To improve robustness, we propose two simple yet effective strategies, RCP-Drop and RCP-Mix, based on training regularization and feature augmentation. Additionally, we identify several critical factors influencing robustness, such as backbone architecture, camera number, feature fusion methods, and the number of connected vehicles. We hope that RCP-Bench, along with these strategies and insights, will stimulate future research toward developing more robust collaborative perception models. Our benchmark toolkit is available at https://github.com/LuckyDush/RCP-Bench.", + "bbox": [ + 89, + 321, + 483, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 729, + 220, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Perception is a fundamental capability for robots and autonomous vehicles to accurately interpret their surroundings. Despite significant advancements in perception tasks through deep learning, including object detection [3, 68] and segmentation [19, 27], single-vehicle perception using onboard sensors still faces inherent limitations, such as restricted range, limited field of view, and vulnerability to occlusions [17, 30, 50], resulting in blind spots that hinder full", + "bbox": [ + 89, + 755, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4bc97b7669566de260976936c51864417858c4b405d5beb9155cad444fc52538.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 290, + 696, + 405 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/df586b328085b8f7394033b2cb1f86cbc8d1f78aa00c32488254a90d15875cd3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 704, + 290, + 883, + 405 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c7c7bf465618c359dc71debcdb93a862cd5672f75e3ccaca164b39abbe65263.jpg", + "image_caption": [ + "Figure 1. Comparison of collaborative object detection results (averaged across 10 leading methods) in OPV2V-C across three interference scenarios: Global, Ego, and CAV Interference. The results indicate that perception models are particularly vulnerable to Global Interference, benefit from collaborative compensation under Ego Interference, and experience performance degradation under CAV Interference." + ], + "image_footnote": [ + "or Ego Cor/Clean" + ], + "bbox": [ + 532, + 407, + 696, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d442d202d42f99483db21fca77b678a162e35eaa693541e3830ff02a73b9574.jpg", + "image_caption": [], + "image_footnote": [ + "or CAV Cor/Clean", + "X No CAV" + ], + "bbox": [ + 709, + 407, + 883, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "environmental understanding [5]. Collaborative perception, where perception data are shared among Connected Autonomous Vehicles (CAVs), has shown promise in overcoming these challenges. By leveraging multiple viewpoints, collaborative perception extends perceptual range, enhances spatial coverage, and improves resilience to occlusions [16].", + "bbox": [ + 511, + 642, + 906, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Numerous studies have investigated practical challenges that may impact collaborative performance, such as bandwidth limitations for shared information [15, 32, 33, 44], transmission issues [26, 38, 47, 60], pose estimation errors [24, 34, 43, 66], and heterogeneity among cooperating vehicles [28, 48, 55]. However, current models and evaluations generally assume idealized conditions, such as clear weather and fully functional sensors. In real-world driving scenarios, adverse conditions such as external weather [9, 10, 18] and sensor failures [2, 12] are unavoidable. Although recent efforts address individual robustness", + "bbox": [ + 511, + 734, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: guangchen@tongji.edu.cn", + "bbox": [ + 109, + 886, + 377, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11908", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "challenges, including communication delays [23, 36] and diverse weather conditions [14, 25], a comprehensive assessment of robustness for collaborative perception in real-world scenarios remains an important open challenge.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To bridge this gap, we introduce RCP-Bench, the first benchmark designed to systematically evaluate the reliability of collaborative perception methods under a wide range of corruptions. Specifically, RCP-Bench comprises three new datasets, including OPV2V-C, V2XSet-C and DAIR-V2X-C. These datasets simulate six distinct cases and incorporate 14 types of corruption, incorporating variations in weather conditions, sensor noise or failures, and temporal misalignments, as depicted in Fig. 2. Given that collaborative perception depends on data shared across collaborating CAVs, where corruptions in individual vehicles can propagate throughout the collaborative process, creating diverse and challenging scenarios. RCP-Bench provides a holistic assessment by evaluating robustness across three aspects:", + "bbox": [ + 89, + 152, + 482, + 364 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Global Interference: Both the ego vehicle and collaborating CAVs are affected by diverse corruptions, testing the overall robustness of collaborative perception.", + "- Ego Interference: Only the ego vehicle experiences corruption, assessing the compensatory advantages of collaboration over single-vehicle perception.", + "- CAV Interference: Only the collaborating CAVs are subject to corruptions, evaluating the risk of disruptions compared to single-vehicle perception." + ], + "bbox": [ + 89, + 364, + 482, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Leveraging RCP-Bench, we conduct extensive experiments on 10 collaborative perception models. As shown in Fig. 1, while these models perform well under ideal conditions, their performance significantly degrades in the presence of corruptions. To enhance the robustness, we propose two straightforward strategies tailored for collaborative perception: RCP-Drop and RCP-Mix. Unlike traditional methods [1, 8] that drop features within specific network layers or blocks during training, RCP-Drop operates by randomly discarding data from selected collaborating vehicles, effectively simulating real-world data loss encountered in communication-limited or sensor-failure scenarios. RCP-Mix, inspired by MixStyle [64, 65], probabilistically combines feature statistics, i.e., the means and standard deviations of feature maps, between the ego vehicle and collaborating CAVs, promoting resilience to distribution shifts.", + "bbox": [ + 89, + 503, + 482, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 109, + 746, + 434, + 758 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce RCP-Bench, the first benchmark systematically evaluating collaborative perception robustness across diverse real-world corruptions.", + "- We conduct a comprehensive evaluation of 10 leading collaborative perception models across six scenarios, covering 14 corruption types.", + "- We propose two novel strategies to enhance the robustness of collaborative perception models and highlight key factors affecting resilience." + ], + "bbox": [ + 89, + 761, + 482, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 89, + 656, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Collaborative Perception: Collaborative perception [5, 6, 16, 34, 40, 54, 56, 58, 61, 62] allows vehicles to share perceptual data with connected vehicles, realizing a more comprehensive understanding of the surrounding environment. Existing studies have proposed various techniques to enhance perception performance [42]. For example, Who2com [33] and When2com [32] propose strategies for selecting collaborators and determining the timing of collaboration. Where2comm [15] and What2comm [57] introduce methods for selecting relevant information to be shared. UMC [44] enhances spatiotemporal continuity in collaborative perception by leveraging historical data and multi-scale feature fusion. CoBEVT [51] enables real-time collaborative semantic segmentation by capturing sparse local and global spatial interactions across views and agents. Nevertheless, most of these methods assume ideal conditions, addressing robustness under diverse and challenging conditions remains essential to advancing collaborative perception reliability in practice.", + "bbox": [ + 511, + 114, + 903, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robustness against Corruptions: Perception models are often vulnerable to various sensor corruptions, which can compromise their effectiveness in real-world applications. To evaluate and improve robustness under such conditions, several benchmarks have been developed. ImageNet-C [12] is the first public benchmark to assess object recognition models under a range of corruptions, including noise, blur, adverse weather, and digital interference. For object detection, Michaelis et al. [35] introduce three benchmarks to examine robustness against similar impairments. Recently, benchmarks tailored to driving scenarios have emerged. RoboDepth [20] assesses robustness in monocular depth estimation under corrupted conditions, while RoboBEV [49] introduces a comprehensive benchmark for evaluating BEV perception tasks. Similarly, MapBench [11] is designed to test the robustness of high-definition mapping methods against various sensor corruptions. Although these benchmarks have advanced robustness assessments in single-vehicle perception, they do not account for multi-agent contexts where corruptions may propagate, compounding effects across interconnected systems. Developing collaborative perception specific benchmarks is crucial for evaluating and improving robustness in these multi-vehicle scenarios.", + "bbox": [ + 511, + 402, + 903, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robustness in Collaborative Perception: With the advancement of collaborative perception research [13, 31, 37, 45], increasing attention is being paid to robustness and safety, especially concerning communication challenges between cooperating agents. These challenges include issues in data transmission, such as information loss during communication [26] and communication interruptions [38], timing issues like delays [23, 47, 60] and the reception of outdated or missing collaborative information. While these studies have highlighted potential pitfalls within the collab", + "bbox": [ + 511, + 750, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11909", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/aa5928269343b93675c42739cc8a50a6d33ea44f155602489dbe04e91c67aa79.jpg", + "image_caption": [ + "Figure 2. Definitions of corruption types and evaluation scenarios in RCP-Bench. Our benchmark includes 14 types of camera corruptions, classified into three categories: External Weather, Camera Interior, and Temporal Misalignment. To comprehensively evaluate robustness, we define three interference scenarios: Global Interference (corruptions affecting both the ego vehicle and collaborative vehicles), Ego Interference (corruptions specific to the ego vehicle), and CAV Interference (corruptions isolated to one or more collaborative vehicles). Within the Global Interference scenario, we further examine four cases: Single Corruption, Multiple Corruptions, Heterogeneous Corruptions, and New Scenes with Corruption." + ], + "image_footnote": [], + "bbox": [ + 96, + 66, + 898, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "orative process itself, robustness under diverse environmental and sensor conditions remains underexplored. Recently, a few studies have begun to examine collaborative performance under adverse environmental conditions [14, 25]. Nevertheless, these efforts are primarily limited to extreme sensor failures, without systematically analyzing the benefits and resilience of collaboration across a wider range of realistic sensor corruptions. To the best of our knowledge, this paper is the first to comprehensively examine the robustness and advantages of different collaborative states under diverse sensor corruptions, thereby providing an empirical basis for assessing and improving collaborative perception robustness across various real-world challenges.", + "bbox": [ + 88, + 459, + 485, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. RCP-Bench", + "text_level": 1, + "bbox": [ + 89, + 670, + 215, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Benchmark Design", + "text_level": 1, + "bbox": [ + 89, + 696, + 272, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Collaborative perception relies on information collected by both the ego vehicle and surrounding connected autonomous vehicles (CAVs), each contributing to the final perception outcome. To rigorously evaluate the benefits of shared information and assess model robustness under various corruptions, this study isolates these two information sources and defines three corruption scenarios, as shown in Fig. 2: (1) Global Interference scenario affecting both the ego vehicle and CAVs simultaneously, (2) Ego Interference scenario specific to the ego vehicle, and (3) CAV Interference scenario isolated to one or more CAVs.", + "bbox": [ + 89, + 718, + 482, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given mutual interference among CAVs, independent", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "control of lidar-based corruptions is impractical; therefore, this study focuses exclusively on camera-based corruptions. We categorize these into three groups based on real-world conditions: (1) External environmental factors, like rain, fog, or light; (2) Internal camera issues, such as lens scratches or sensor degradation; (3) Misalignment in capture timing, such as temporal desynchronization between the ego and CAV cameras. We identify 14 distinct types of corruption, following the methodology in [7], and divide each type into five severity levels, resulting in 70 unique corruption conditions. To evaluate collaborative perception model robustness, we create three corruption benchmarks using widely used datasets: DAIR-V2X [59], OPV2V [53], and V2XSet [52]. These corruptions are introduced into the validation sets, producing modified versions: DAIR-V2XC, OPV2V-C, and V2XSet-C.", + "bbox": [ + 511, + 459, + 906, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Typical Corruption Scenarios", + "text_level": 1, + "bbox": [ + 511, + 712, + 777, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Global Interference: In practical applications, it is common for corruptions to affect both the ego vehicle and collaborative vehicles simultaneously. To evaluate model robustness across various types of corruption, we first assess 14 distinct corruptions individually, referring to this as the Single Corruption case. To better reflect real-world complexity, we further define three combined corruption cases. The first, Multiple Corruptions, involves multiple types of corruptions occurring concurrently. For simplicity, we focus on situations where temporal misalignment coincides with either external weather conditions or internal camera", + "bbox": [ + 511, + 734, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11910", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "issues. In the second case, *Heterogeneous Corruptions*, the types of corruption affecting the ego vehicle differ from those impacting the collaborative vehicles, allowing us to examine situations with varying corruption profiles across vehicles. Finally, in the *New Scenes with Corruption* case, we extend prior research on the generalization of collaborative perception by analyzing performance when corruptions are introduced simultaneously in unfamiliar environments.", + "bbox": [ + 89, + 90, + 480, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ego Interference: In real-world scenarios, the ego vehicle may experience unique corruptions that do not affect nearby collaborative vehicles, presenting an opportunity to use uncorrupted data from these vehicles as a compensatory mechanism. To explore this potential, we introduce the concept of \"collaborative compensation.\" Here, when the ego vehicle encounters interference or corruption, we investigate whether reliable information from neighboring collaborative vehicles can help mitigate or even correct these effects. Since some forms of interference, such as adverse weather, are unavoidable and impact all vehicles, we specifically focus on evaluating the advantages of collaborative compensation for the remaining ten types of corruption that are unique to the ego vehicle.", + "bbox": [ + 89, + 213, + 482, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CAV Interference: Similar to Ego Interference, collaborative vehicles may experience unique corruptions that do not directly affect the ego vehicle, creating a potential risk rather than a benefit. To examine this, we introduce the concept of \"collaborative disruption.\" In this scenario, we investigate whether corrupted data from surrounding collaborative vehicles can degrade the perception performance of an otherwise well-functioning ego vehicle. This analysis provides insights into the robustness of collaborative perception systems, highlighting the potential adverse effects of relying on collaborative data when unintentional corruptions are present in the shared information.", + "bbox": [ + 89, + 425, + 482, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 89, + 619, + 274, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In evaluating 3D object detection performance, Average Precision (AP) is commonly used as the primary metric, particularly at Intersection-over-Union (IoU) thresholds of 0.3, 0.5, and 0.7. Building on the evaluation metrics proposed in [7, 41, 67], we introduce two metrics specifically designed to assess the robustness of cooperative perception systems: Corrupted Average Precision $(\\mathrm{AP}_{\\mathrm{cor}})$ and Relative Corruption Error (RCE). To further examine the effects of collaboration under Ego Interference and CAV Interference, we define \"Positive Collaborative\" and \"Negative Collaborative\", and introduce two additional metrics: the Positive Collaborative Coefficient (PosC) and the Negative Collaborative Coefficient (NegC). These four new evaluation metrics are primarily analyzed based on AP@0.5, additional results of AP@0.3 and AP@0.7 are provided in the appendix. Corrupted Average Precision: We denote the performance on the clean, uncorrupted test set as $\\mathrm{AP}_{\\mathrm{clean}}$ . For each cor", + "bbox": [ + 89, + 642, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ruption type $c$ at each severity $l$ , the performance is measured as $\\mathrm{AP}_{c,l}$ . The corruption robustness, $\\mathrm{AP}_{cor}$ is then defined as the average performance across all corruption types and severity levels:", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {A P} _ {c} = \\frac {1}{5} \\sum_ {l = 1} ^ {5} \\mathrm {A P} _ {c, l}, \\mathrm {A P} _ {c o r} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {A P} _ {c}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 152, + 903, + 190 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{C}$ is the set of corruptions in evaluation.", + "bbox": [ + 511, + 190, + 820, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relative Corruption Error: Since $\\mathrm{AP}_{\\mathrm{cor}}$ measures only the absolute performance under corrupted conditions, we define Relative Corruption Error (RCE) as a relative indicator that quantifies the extent to which model performance is retained under corruption:", + "bbox": [ + 511, + 205, + 903, + 280 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {R C E} _ {c} = \\frac {\\mathrm {A P} _ {c l e a n} - \\mathrm {A P} _ {c}}{\\mathrm {A P} _ {c l e a n}}, \\mathrm {m R C E} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {R C E} _ {c}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 282, + 903, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Positive Collaborative Coefficient: To quantify the ability of collaborative information to mitigate corruptions affecting the ego vehicle under Ego Interference, we define the Positive Collaborative Coefficient (PosC), which measures how effectively the model leverages collaborative information from other vehicles to counteract corruptions:", + "bbox": [ + 511, + 319, + 903, + 410 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P o s C} _ {c} = \\frac {\\mathrm {A P} _ {c , 5} - \\mathrm {A P} _ {c , 5} ^ {e g o}}{1 - \\mathrm {A P} _ {c , 5} ^ {e g o}}, \\mathrm {m P o s C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {P o s C} _ {c}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 412, + 903, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{AP}_{\\mathrm{c},5}^{\\mathrm{ego}}$ represents the performance of the ego vehicle under a specific type of corruption at severity 5 in the absence of collaboration.", + "bbox": [ + 511, + 452, + 903, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Negative Collaborative Coefficient: To assess the adverse impact of corrupted collaborative information under CAV Interference, we introduce the Negative Collaborative Coefficient (NegC), which quantifies the negative effects arising from collaborative perception:", + "bbox": [ + 511, + 498, + 903, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {N e g C} _ {c} = \\frac {1 - \\mathrm {A P} _ {c , 5}}{1 - \\mathrm {A P} _ {\\text {c l e a n}} ^ {e g o}}, \\mathrm {m N e g C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {N e g C} _ {c}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 577, + 903, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{AP}_{\\mathrm{clean}}^{\\mathrm{ego}}$ denotes the perception performance of the ego vehicle using only its own clean, uncorrupted data.", + "bbox": [ + 511, + 613, + 903, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Benchmarking Results", + "text_level": 1, + "bbox": [ + 511, + 657, + 728, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we primarily present the results on OPV2VC. Additional results for DAIR-V2X-C and V2XSet-C are provided in the appendix.", + "bbox": [ + 511, + 684, + 903, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Benchmark Setup", + "text_level": 1, + "bbox": [ + 511, + 741, + 689, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our RCP-Bench evaluates a total of 10 leading collaborative perception models and their variants for the detection task, including AttFuse [53], F-Cooper [4], V2X-ViT [52], DiscoNet [29], V2VNet [46], CoBEVT [51], and BM2CP [63]. To ensure a fair comparison, we use official model configurations and public checkpoints from open-source codebases where available or re-train the models using default settings if necessary. For each corruption type, we report metrics by averaging results across five severity levels. To provide a", + "bbox": [ + 511, + 763, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11911", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/16aa1d97ad83ab00855fc16a0a578106b449527c6397dbf2471f49e78562d589.jpg", + "table_caption": [ + "Table 1. Benchmarking results for Global Interference on OPV2V-C. We report the performance under each corruption $\\mathrm{AP}_c$ and the overall corruption robustness $\\mathrm{AP}_{cor}$ averaged over all corruption types. The results are evaluated based on AP@0.5." + ], + "table_footnote": [], + "table_body": "
CortypeAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLateNoFusion
APclean↑37.1334.8558.6147.3446.6440.4945.8768.4135.68
WeatherBright21.399.0543.0633.5536.4223.1827.6651.7625.22
Dark14.0016.6915.5818.487.8414.1213.3322.038.94
Fog10.3011.1515.2315.0215.5810.7811.7312.994.47
Frost7.129.5411.219.622.826.1410.1911.064.21
Snow6.464.7711.1910.427.559.3614.3312.374.75
NoiseGaussian9.178.987.453.102.155.9711.1313.805.23
Impulse9.179.018.112.082.035.6510.5614.915.55
Shot8.5810.558.480.712.274.5111.2615.606.24
BlurZoom18.8521.4426.5721.6815.8918.9523.5231.1012.90
Motion22.0724.8731.1930.1719.2424.5527.5640.5217.22
Defocus18.6417.6521.5721.278.7917.0119.0917.076.55
FailureCrash22.3016.6221.9616.2116.1923.2321.0832.0213.61
ColorQuant26.0121.0341.4835.0933.6825.8633.2748.1323.60
Alignment Tempormis29.7428.0547.9139.3138.7533.3836.8549.2835.68
APcor↑15.9914.9622.2118.3414.9415.9119.4026.6212.44
", + "bbox": [ + 94, + 108, + 897, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/05f24236350c580dd73bb26c42396388afa4ac234f56dda8461e23f6e551b751.jpg", + "image_caption": [ + "(a) $\\mathrm{AP}_{\\text {clean }}$ vs. $\\mathrm{AP}_{\\text {cor }}$" + ], + "image_footnote": [], + "bbox": [ + 96, + 300, + 290, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b4544cb76a25327663fef6f934256369a76890b5bbd133275e3bc131e1967830.jpg", + "image_caption": [ + "(b) $\\mathrm{AP}_{\\text {clean }}$ vs.mRCE" + ], + "image_footnote": [], + "bbox": [ + 300, + 299, + 496, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cc55dfed577bde39a2d1b40d793130791cc27eb0dfce8e96561483555545c1ef.jpg", + "image_caption": [ + "(c) $\\mathrm{AP}_{\\text {clean }}$ vs.mPosC" + ], + "image_footnote": [], + "bbox": [ + 506, + 299, + 699, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8889b8c5b3238ab25547335dec715126d13375861b7c6bb6803908d28496e65a.jpg", + "image_caption": [ + "(d) $\\mathrm{AP}_{\\text {clean }}$ vs.mNegC" + ], + "image_footnote": [], + "bbox": [ + 707, + 300, + 903, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ed00ca8c3d0a1a8d5121feeb0caa0e5ea62501aa71b171f31c7d2ab49de0dc3d.jpg", + "image_caption": [ + "Figure 3. The relationships between baseline performance $(\\mathrm{AP}_{clean})$ and various metrics, including collaborative robustness $(\\mathrm{AP}_{cor}$ , mRCE), collaborative compensation (mPosC) and collaborative disruption (mNegC).", + "Figure 4. The corrupted average precision $(\\mathrm{AP}_c)$ of existing methods across five severity levels of corruption." + ], + "image_footnote": [], + "bbox": [ + 96, + 479, + 472, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "comprehensive robustness evaluation, we also include three non-learning baseline methods: Max, which directly maximizes the feature map for collaboration; Late, which fuses final predictions shared from CAVs; and NoFusion, representing the ego vehicle perception model without collaboration. The NoFusion model is further used to compute the PosC and NegC metrics as defined in Eq. 3 and Eq. 4.", + "bbox": [ + 89, + 726, + 482, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Benchmarking Results for Global Interference", + "text_level": 1, + "bbox": [ + 89, + 845, + 482, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Single Corruption: The performance of collaborative perception models under various corruption types is presented", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in Table 1, with results across different corruption severity levels shown in Fig. 4. The results indicate that existing models experience varying levels of performance degradation depending on the corruption type, with conditions like snow, frost, and noise having particularly severe impacts. The NoFusion model consistently performs the worst, showing significantly lower $\\mathrm{AP}_{cor}$ across all corruption types, underscoring the limitations of single-vehicle perception. Interestingly, the simple Max fusion method outperforms several more complex models in interference scenarios, suggesting that increased model complexity does not necessarily lead to improved robustness against interference. Moreover, the Late fusion methods demonstrate greater adaptability and robustness compared to existing intermediate feature fusion techniques.", + "bbox": [ + 511, + 481, + 906, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further understand the relationship between baseline performance and robustness, we analyze the results in Fig. 3a. The findings suggest that models with higher baseline performance may handle disturbances better, likely due to more robust feature extraction. Similarly, Fig. 3b shows a positive correlation between a model's mRCE and its clean-data performance, indicating that higher-performing models may also experience larger relative performance drops under corruption. With mRCE values generally between $55\\%$ and $70\\%$ , current models exhibit suboptimal robustness, underscoring the need for further improvement.", + "bbox": [ + 511, + 714, + 908, + 880 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multiple Corruptions: As shown in Fig. 5, different types", + "bbox": [ + 511, + 885, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11912", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6538bc1b07f08f4d54d645c544ce4ed84b04e7a36216efcedcef02851632871b.jpg", + "image_caption": [ + "Figure 5. Radar charts for CoBEVT [51] and AttFuse [53] showing performance under single corruptions (labeled as \"Cor\" in the figure) and multiple corruptions that include additional temporal misalignment (labeled as \"Time\" in the figure)." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 279, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/10b1b960c0884413acc9e23ddd386fe2c47a14867bb482f426156ac84cb6d5c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 89, + 470, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2f7ec168eda1e227a6ce8722d8c34e7996bf8cd96e0b80749367eda76e68a4a5.jpg", + "image_caption": [ + "Figure 6. Results of V2VNet [46] and DiscoNet [29] in terms of $\\mathrm{AP}_{cor}$ under heterogeneous corruptions between Ego and CAVs." + ], + "image_footnote": [], + "bbox": [ + 94, + 308, + 285, + 441 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2ee86394488809d0a924e3fe430a370959d9bfdb8f3da22ebaca19d68e69f0dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 306, + 485, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of corruptions have varying impacts on CoBEVT [51] and AttFuse [53], with noise and frost disturbances causing the most significant performance degradation. Adding temporal misalignment to these camera corruptions further intensifies the effects of disturbances such as brightness, motion, and quantization. These results suggest that, in real-world scenarios, the simultaneous occurrence of multiple disturbances presents even greater challenges for model robustness. Please refer to the appendix for more results.", + "bbox": [ + 89, + 477, + 482, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hetero Corruptions: Fig. 6 shows that corruptions impact the Ego vehicle more severely than the CAVs in both DiscoNet [29] and V2VNet [46]. When the Ego vehicle is \"Clean\", the system performs effectively despite various \"CAV corruption\" conditions. However, when both Ego and CAVs are subjected to different types of disturbances, the model's performance declines significantly, particularly when one of them experiences crash corruption, which has the most pronounced impact on overall system performance. More results are included in the appendix.", + "bbox": [ + 89, + 614, + 482, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "New Scenes with Corruption: While collaborative perception models are typically evaluated in familiar environments, real-world deployment demands robustness in diverse, unseen scenes. Table 2 evaluates the model performance in familiar OPV2V scenes (Default) versus previously unseen scenes (Culver). The $\\mathrm{AP}_{\\text {clean }}$ performance of V2X-ViT [52] declines by $47.8\\%$ , indicating that the scene variation significantly impacts model effectiveness. When disturbances and new scenes occur simultaneously, perfor", + "bbox": [ + 89, + 765, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eb939dd491c9754146bfb2509f4e72393de501c69cfd4aefa5350a82f122dbed.jpg", + "table_caption": [ + "Table 2. Performance comparison in the familiar OPV2V scenes (Default) versus the unseen new scenes (Culver)." + ], + "table_footnote": [], + "table_body": "
ModelAPclean↑APcor↑mRCE↓
DefaultCulverDefaultCulverDefaultCulver
AttFuse37.1319.48(↓47.5%)14.937.29(↓51.2%)41.5141.93(↑1.0%)
F-Cooper34.8526.52(↓23.9%)13.958.58(↓38.5%)37.5448.25(↑28.5%)
V2X-ViT58.6130.62(↓47.8%)20.249.11(↓55.0%)46.9451.38(↑9.5%)
DiscoNet47.3428.66(↓39.5%)16.728.31(↓50.3%)49.9453.65(↑7.4%)
V2VNet46.6426.80(↓42.5%)13.116.79(↓48.3%)53.8656.96(↑5.8%)
CoBEVT40.4923.97(↓40.8%)14.567.10(↓51.2%)46.4249.39(↑6.4%)
Max45.8724.97(↓45.6%)18.057.56(↓58.1%)41.9047.95(↑14.4%)
", + "bbox": [ + 516, + 118, + 898, + 219 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mance drops further, with $\\mathrm{AP}_{cor}$ decreasing by $55\\%$ and RCE increasing by $9.5\\%$ . These results highlight the challenges that current collaborative methods encounter in handling disturbed environments with unfamiliar scenes.", + "bbox": [ + 511, + 226, + 903, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Benchmarking Results for Ego Interference", + "text_level": 1, + "bbox": [ + 511, + 296, + 883, + 313 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When the ego vehicle encounters unique corruptions, uncorrupted data from collaborators can offer collaborative compensation. Table 3 verifies this through $\\mathrm{PosC}_c$ and mPosC metrics. Results indicate that the simple Late fusion significantly enhances mPosC compared to other intermediate fusion methods, suggesting that complex fusion models (e.g., attention-based [51-53], graph-based [29, 46]) are effective only when the ego vehicle captures essential information. The compensation stability varies across models and disturbances: V2X-ViT [52] and V2VNet [46] show fluctuations, whereas F-Cooper [4] and CoBEVT [51] exhibit more consistency. Fig. 3c further reveals a positive correlation between collaborative compensation mPosC and baseline performance $\\mathrm{AP}_{clean}$ , suggesting that models with higher baseline results provide stronger compensatory support.", + "bbox": [ + 511, + 316, + 906, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Benchmarking Results for CAV Interference", + "text_level": 1, + "bbox": [ + 511, + 554, + 890, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In scenarios where collaborative vehicles experience unique corruptions not directly affecting the ego vehicle, shared data from these vehicles can introduce \"collaborative disruption.\" Table 3 presents the $\\mathrm{NegC}_c$ and mNegC metrics to quantify this effect. A NegC value over $100\\%$ indicates that corrupted data from collaborators degrades the ego vehicle's performance. The results show that the Late fusion is less vulnerable to these disruptions and often provides positive benefits even under corruption, while intermediate feature fusion methods tend to reduce performance. Additionally, Fig. 3d shows that higher baseline performance $(\\mathrm{AP}_{clean})$ correlates with reduced collaborative disruption, suggesting that models with stronger baseline performance may better handle corrupted collaborative data.", + "bbox": [ + 511, + 575, + 906, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. RCP-Drop & RCP-Mix", + "text_level": 1, + "bbox": [ + 511, + 799, + 735, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To enhance robustness under various corruption scenarios, we develop two simple yet effective strategies specifically for collaborative perception: RCP-Drop and RCP-Mix.", + "bbox": [ + 511, + 825, + 903, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dropout [1, 8] is a widely used regularization technique in deep learning, aimed at reducing model overfitting by", + "bbox": [ + 511, + 869, + 903, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11913", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/738d69d5c018e14945705c60d00fd2e6ccf9007bf5d69380bb8732c49cad6bb6.jpg", + "table_caption": [ + "Table 3. Benchmarking results for Ego Interference and CAV Interference on OPV2V-C. We report collaborative compensation and disruption performance under each corruption type, including $\\mathrm{NegC}_c$ and $\\mathrm{PosC}_c$ , as well as averages across all corruption types, mNegC and mPosC. Results are evaluated based on AP@0.5. Further details are available in the appendix." + ], + "table_footnote": [], + "table_body": "
Cor TypesAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLate
NegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCc
Bright121.278.54115.979.6886.6828.9095.7718.29103.0327.29107.826.24108.7120.6882.4550.82
Dark126.7312.96122.2821.77104.2414.80109.5918.68127.296.43116.0014.97121.5222.1499.9150.81
Zoom117.6319.66116.4321.7493.7229.29100.9620.66107.6223.63107.9817.63104.6825.4188.5051.99
Motion116.6721.12115.5222.5094.5025.8499.3322.52117.469.83106.1919.19102.8325.6790.3051.09
Defocus118.1725.27116.8724.6299.4727.14106.2020.90121.3010.81107.8218.68107.8027.13101.5550.36
Gaussian127.3213.30122.7315.47112.3910.16115.0212.32123.355.81117.9311.545115.8424.7199.7550.83
Impulse127.0415.75122.9814.94112.0611.78115.1311.82123.215.62117.8611.11115.3324.3399.5350.84
Shot126.8713.12122.0117.78112.339.86115.3911.64123.825.95118.1711.81114.0425.7099.8950.82
Crash116.2222.35115.7320.5197.5013.75107.0410.67112.5811.98105.0518.96108.1224.2191.5350.14
Quant118.0317.63113.9122.4999.8622.6998.6021.65110.0020.66110.0012.82110.1425.8398.7648.70
mNegC↓/mPosC↑121.5916.97118.4419.15101.2719.42106.3116.92116.9712.80111.4814.29110.9024.5895.2250.64
", + "bbox": [ + 91, + 122, + 906, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fe7e4b8538757983b82543101f111bc83269e1afd29901788ba314667c5bddce.jpg", + "image_caption": [ + "Figure 7. Overview of the RCP-Drop & RCP-Mix strategies." + ], + "image_footnote": [], + "bbox": [ + 93, + 271, + 480, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "randomly dropping features within certain network layers or blocks during training. In the collaborative perception context, the ego vehicle may encounter incomplete shared perceptual data from CAVs due to communication failures, or CAVs leaving the collaborative queue. Existing collaborative perception models, while beneficial in multi-vehicle setups, often underperform in single-vehicle scenarios due to their learned dependency on supplementary data from other vehicles. To prevent models from being overly reliant on CAVs data and to better equip them for single-vehicle operation, as shown in Fig. 7 we introduce RCP-Drop, which simulates these conditions by selectively discarding information from certain CAVs. Technically, it is defined as:", + "bbox": [ + 88, + 391, + 482, + 588 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nF _ {a g g} ^ {e g o} = \\mathcal {A} \\left(F ^ {e g o}, \\left\\{\\mathbb {1} \\left(p _ {i} < p _ {d r o p}\\right) \\cdot F _ {i} ^ {c a v} \\right\\} _ {i = 1} ^ {N}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 590, + 480, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $F^{ego}$ represents the feature originating from the ego vehicle, $F_{agg}^{ego}$ denotes the aggregated feature after perception information exchange, and $F_{i}^{cav}$ is the feature map shared from the $i$ -th collaborative vehicle. Here, $\\mathcal{A}$ is a specific feature fusion function developed in existing methods [29, 44, 53], $p_i$ is sampled from a uniform distribution between 0 and 1, and $p_{drop}$ is the threshold determining whether data from each collaborative vehicle is discarded.", + "bbox": [ + 89, + 613, + 482, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Rather than keeping the threshold fixed during training, we develop a dynamic adjustment strategy for $p_{drop}$ . Specifically, we start with a high dropout probability, which reduces the number of participating collaborative vehicles and enhances the single-vehicle backbone's feature extraction capabilities. Gradually, we lower the dropout probability to increase the participation of collaborative vehicles, optimizing the collaborative perception performance over time. In this study, we set $p_{drop} = 1.0 - (t / T)^2$ , where $t$ and $T$ are the current and maximum training epoch.", + "bbox": [ + 89, + 733, + 482, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Existing research shows that visual data can be char", + "bbox": [ + 109, + 885, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d76ef14b136669fd1d157f2d76726a8c4b17dbd01aa78aef1c2b41d4748d4037.jpg", + "table_caption": [ + "Table 4. Efficacy of RCP-Drop and RCP-Mix on collaborative robustness, collaborative compensation and collaborative disruption." + ], + "table_footnote": [], + "table_body": "
APclean↑mAPcor↑mNegC↓mPosC↑
CoBEVT [51]40.4915.91111.4814.29
+BN [39]42.7427.87112.9418.28
+BN+RCP-Mix48.2531.83109.1123.44
+BN+RCP-Drop47.8430.68109.4520.07
AttFuse [53]37.1315.99121.5916.97
+BN [39]36.1322.35126.0418.85
+BN+RCP-Mix43.1228.85114.9722.51
+BN+RCP-Drop45.1827.56115.6418.17
", + "bbox": [ + 517, + 303, + 898, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "acterized by feature statistics (i.e., the mean and standard deviation of feature maps). For the same semantic concepts, distinct styles (such as variations in color and texture) correspond to different feature statistics. Inspired by Mixstyle [64, 65], we propose RCP-Mix to enhance model adaptability to varied environmental conditions and styles encountered in collaborative perception. Unlike Mixstyle, which performs random feature statistic mixing across instances within a mini-batch, RCP-Mix probabilistically combines feature statistics between the ego vehicle and collaborating CAVs. Technically, RCP-Mix is defined as:", + "bbox": [ + 511, + 421, + 906, + 588 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mu_ {i}; \\quad \\sigma_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\sigma_ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 589, + 836, + 630 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {i} ^ {\\text {m i x}} = \\lambda \\mu_ {i} + (1 - \\lambda) \\mu_ {\\text {a l l}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 633, + 903, + 652 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {i} ^ {m i x} = \\lambda \\sigma_ {i} + (1 - \\lambda) \\sigma_ {a l l},\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 654, + 767, + 670 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nF _ {i} ^ {m i x} = \\frac {F _ {i} - \\mu_ {i}}{\\sigma_ {i}} * \\sigma_ {i} ^ {m i x} + \\mu_ {i} ^ {m i x},\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 672, + 808, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\mu_{i}$ , $\\sigma_{i}$ are the means and standard deviations of the feature map $F_{i}$ , $\\lambda$ is the weight sampled from the Beta distribution, i.e., $\\lambda \\sim \\text{Beta}(\\alpha, \\alpha)$ , we set $\\alpha = 0.1$ by default.", + "bbox": [ + 511, + 704, + 906, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental Analysis: We selected CoBEVT [51] and AttFuse [53] with online Batch Normalization (BN) Stats Adapt [39] as baselines, integrating them with our RCP-Drop and RCP-Mix strategies. Table 4 demonstrates that, despite their simplicity, both RCP-Drop and RCP-Mix effectively counteract performance degradation from data corruptions. In particular, for $\\mathrm{AP}_{\\text {clean }}$ , these strategies lead to substantial performance improvements compared to the marginal gains or occasional declines observed with the vanilla BN adapt. Moreover, across the three inter-", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11914", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6043a8ad6b3f0f52c378c410952968b4edb0caf6e7529bfb32b648093332e716.jpg", + "table_caption": [ + "Table 5. Ablation on the use of different backbone." + ], + "table_footnote": [], + "table_body": "
MethodbackboneWeatherBlurNoiseQuantCrashAPAPcor
Max○ResNet10111.7922.322.7722.8718.6435.1218.14
Max•EfficientNet-b015.4523.3910.9833.2721.0845.8718.05
V2X-ViT○ResNet10110.9024.6616.6328.7510.4146.2116.73
V2X-ViT•EfficientNet-b019.2526.458.0141.4821.9658.6120.24
", + "bbox": [ + 94, + 104, + 500, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/10a0f9576af382bbfbc0ba3c866e1f04ad63970bac809eeeb6253bb0acea0ff2.jpg", + "image_caption": [ + "Figure 8. Impact of different backbone sizes on model robustness." + ], + "image_footnote": [], + "bbox": [ + 94, + 171, + 285, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/169726178e9aefa41dda1e365e6b9a906493f4b7171f6c77731d60c41249c265.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 172, + 478, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4593dadf21bfb8c1ea3916a8b8dedd6bb6b1bd12af6b922adb05c510eaa17c1e.jpg", + "image_caption": [ + "Figure 9. Effect of CAV number on model robustness." + ], + "image_footnote": [], + "bbox": [ + 94, + 306, + 282, + 422 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22ecded2dd94e7c1ab9da9b21cf29d1c68b88c5e14b3b36ccabd8b1a84c30e9d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 306, + 480, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ference scenarios, Global Interference, Ego Interference, and CAV Interference, our RCP-Drop and RCP-Mix consistently show robust improvements in model resilience under corruption conditions $\\left(\\mathrm{AP}_{cor}\\right)$ , collaborative compensation (mPosC), and reduced collaborative disruption (mNegC). These results further underline the efficacy of our approaches in maintaining model performance and collaborative stability in challenging conditions.", + "bbox": [ + 89, + 450, + 483, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Observation & Discussion", + "text_level": 1, + "bbox": [ + 89, + 587, + 339, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we analyze and discuss the impact of various model configurations and techniques on robustness.", + "bbox": [ + 89, + 613, + 482, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Backbones: Table 5 compares the performance of different backbones, showing that models using EfficientNet-b0 outperform ResNet101 [22] in all conditions except noise disturbances. leading to its use as the backbone for all models in this study. Fig. 8 further compares AttFuse with various backbone sizes, revealing that larger backbones generally improve robustness. Notably, EfficientNetb0 and EfficientNet-b3 [21] show greater stability and robustness across multiple conditions, particularly excelling under \"Noise\" and \"Crash\" scenarios, while EfficientNetb2 performs poorly in these cases.", + "bbox": [ + 89, + 643, + 482, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Fusion: Table 6 shows that multiscale fusion enhances model performance on clean datasets and improves robustness against various perturbations. Additionally, the simple Max Fusion demonstrates greater robustness than attention mechanisms, particularly under noisy conditions, suggesting that more complex mechanisms may be less ef", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4cb4e1498a98c51602a55568b0f6dded03d3b3694a17b3519f4fbdeba779e651.jpg", + "table_caption": [ + "Table 6. Ablation on the use of multiscale fusion." + ], + "table_footnote": [], + "table_body": "
MethodmultiscaleWeatherBlurNoiseQuantCrashAP\\(AP_{cor}\\)
Max○X15.4523.3910.9833.2721.0845.8718.05
Max●✓30.6534.9228.6149.8638.1565.3833.22
AttFuse○X11.8519.858.9726.0122.3037.1314.93
AttFuse●✓23.3631.909.0143.4330.0762.5824.08
", + "bbox": [ + 519, + 104, + 898, + 164 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0eed31304ddb8694b985dbb1e956f9e7dd2033a64fbf5df919052006224ffa03.jpg", + "image_caption": [ + "Figure 10. Effect of camera number on model robustness." + ], + "image_footnote": [], + "bbox": [ + 517, + 171, + 705, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2da14db78e21180b1488787562de78b70bd2f29643b07f934cd773a5ade3426.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 171, + 901, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fective at mitigating certain types of perturbations.", + "bbox": [ + 511, + 316, + 846, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "CAV and Camera Number: Fig. 9 shows that increasing the number of collaborative CAVs generally enhances model performance. Notably, two collaborating vehicles provide a significant improvement over a single vehicle; however, the rate of improvement diminishes once the number of collaborators exceeds four, indicating a diminishing marginal effect. Fig. 10 shows that as camera count increases, both model performance and robustness improve significantly, with a particularly notable boost from three to four cameras.", + "bbox": [ + 511, + 332, + 906, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 497, + 633, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of camera-based collaborative perception models under diverse real-world disturbances. RCP-Bench encompasses 14 corruption types at 5 severity levels across 3 large-scale datasets. We systematically evaluate three collaborative scenarios across six cases to assess robustness in the Global Interference scenario, explore collaborative advantages in the Ego Interference scenario, and examine disturbance risks in the CAV Interference scenario. To improve robustness, we propose two straightforward strategies, RCP-Drop and RCP-Mix, tailored for collaborative perception. Our analysis of backbone architecture, feature fusion, CAV number, and camera number provides key insights for enhancing model resilience. We hope this work offers valuable insights and inspires future research toward more robust collaborative perception models.", + "bbox": [ + 511, + 523, + 906, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment: This work was supported by the National Key Research and Development Program of China (No. 2024YFE0211000), in part by the National Natural Science Foundation of China (No. 62372329), in part by Shanghai Scientific Innovation Foundation (No. 23DZ1203400), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program.", + "bbox": [ + 511, + 780, + 908, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11915", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Pierre Baldi and Peter J Sadowski. 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Proceedings of the IEEE, 111(3):257-276, 2023. 1" + ], + "bbox": [ + 516, + 92, + 903, + 294 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11918", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_model.json b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8a8f1e7f4ecba6ba3654c531f502d66d6ba12406 --- /dev/null +++ b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_model.json @@ -0,0 +1,2587 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.152, + 0.13, + 0.849, + 0.177 + ], + "angle": 0, + "content": "RCP-Bench: Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions" + }, + { + "type": "text", + "bbox": [ + 0.25, + 0.203, + 0.748, + 0.257 + ], + "angle": 0, + "content": "Shihang Du\\(^{1}\\), Sanqing Qu\\(^{1}\\), Tianhang Wang\\(^{1}\\), Xudong Zhang\\(^{1}\\), Yunwei Zhu\\(^{1}\\), Jian Mao\\(^{1}\\), Fan Lu\\(^{1}\\), Qiao Lin\\(^{2}\\), Guang Chen\\(^{1*}\\) \n\\(^{1}\\)Tongji University, \\(^{2}\\)EACON Technology Co., Ltd." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.323, + 0.485, + 0.712 + ], + "angle": 0, + "content": "Collaborative perception enhances single-vehicle perception by integrating sensory data from multiple connected vehicles. However, existing studies often assume ideal conditions, overlooking resilience to real-world challenges, such as adverse weather and sensor malfunctions, which is critical for safe deployment. To address this gap, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of collaborative detection models under a wide range of real-world corruptions. RCP-Bench includes three new datasets (i.e., OPV2V-C, V2XSet-C, and DAIR-V2X-C) that simulate six collaborative cases and 14 types of camera corruption resulting from external environmental factors, sensor failures, and temporal misalignments. Extensive experiments on 10 leading collaborative perception models reveal that, while these models perform well under ideal conditions, they are significantly affected by corruptions. To improve robustness, we propose two simple yet effective strategies, RCP-Drop and RCP-Mix, based on training regularization and feature augmentation. Additionally, we identify several critical factors influencing robustness, such as backbone architecture, camera number, feature fusion methods, and the number of connected vehicles. We hope that RCP-Bench, along with these strategies and insights, will stimulate future research toward developing more robust collaborative perception models. Our benchmark toolkit is available at https://github.com/LuckyDush/RCP-Bench." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.731, + 0.222, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.756, + 0.484, + 0.879 + ], + "angle": 0, + "content": "Perception is a fundamental capability for robots and autonomous vehicles to accurately interpret their surroundings. Despite significant advancements in perception tasks through deep learning, including object detection [3, 68] and segmentation [19, 27], single-vehicle perception using onboard sensors still faces inherent limitations, such as restricted range, limited field of view, and vulnerability to occlusions [17, 30, 50], resulting in blind spots that hinder full" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.291, + 0.697, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.291, + 0.884, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.408, + 0.697, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.408, + 0.884, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.549, + 0.526, + 0.669, + 0.539 + ], + "angle": 0, + "content": "or Ego Cor/Clean" + }, + { + "type": "image_footnote", + "bbox": [ + 0.683, + 0.527, + 0.803, + 0.538 + ], + "angle": 0, + "content": "or CAV Cor/Clean" + }, + { + "type": "image_footnote", + "bbox": [ + 0.817, + 0.527, + 0.877, + 0.538 + ], + "angle": 0, + "content": "X No CAV" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.542, + 0.907, + 0.634 + ], + "angle": 0, + "content": "Figure 1. Comparison of collaborative object detection results (averaged across 10 leading methods) in OPV2V-C across three interference scenarios: Global, Ego, and CAV Interference. The results indicate that perception models are particularly vulnerable to Global Interference, benefit from collaborative compensation under Ego Interference, and experience performance degradation under CAV Interference." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.734 + ], + "angle": 0, + "content": "environmental understanding [5]. Collaborative perception, where perception data are shared among Connected Autonomous Vehicles (CAVs), has shown promise in overcoming these challenges. By leveraging multiple viewpoints, collaborative perception extends perceptual range, enhances spatial coverage, and improves resilience to occlusions [16]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Numerous studies have investigated practical challenges that may impact collaborative performance, such as bandwidth limitations for shared information [15, 32, 33, 44], transmission issues [26, 38, 47, 60], pose estimation errors [24, 34, 43, 66], and heterogeneity among cooperating vehicles [28, 48, 55]. However, current models and evaluations generally assume idealized conditions, such as clear weather and fully functional sensors. In real-world driving scenarios, adverse conditions such as external weather [9, 10, 18] and sensor failures [2, 12] are unavoidable. Although recent efforts address individual robustness" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.378, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: guangchen@tongji.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11908" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "challenges, including communication delays [23, 36] and diverse weather conditions [14, 25], a comprehensive assessment of robustness for collaborative perception in real-world scenarios remains an important open challenge." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.365 + ], + "angle": 0, + "content": "To bridge this gap, we introduce RCP-Bench, the first benchmark designed to systematically evaluate the reliability of collaborative perception methods under a wide range of corruptions. Specifically, RCP-Bench comprises three new datasets, including OPV2V-C, V2XSet-C and DAIR-V2X-C. These datasets simulate six distinct cases and incorporate 14 types of corruption, incorporating variations in weather conditions, sensor noise or failures, and temporal misalignments, as depicted in Fig. 2. Given that collaborative perception depends on data shared across collaborating CAVs, where corruptions in individual vehicles can propagate throughout the collaborative process, creating diverse and challenging scenarios. RCP-Bench provides a holistic assessment by evaluating robustness across three aspects:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.366, + 0.483, + 0.412 + ], + "angle": 0, + "content": "- Global Interference: Both the ego vehicle and collaborating CAVs are affected by diverse corruptions, testing the overall robustness of collaborative perception." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.412, + 0.483, + 0.457 + ], + "angle": 0, + "content": "- Ego Interference: Only the ego vehicle experiences corruption, assessing the compensatory advantages of collaboration over single-vehicle perception." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.457, + 0.483, + 0.502 + ], + "angle": 0, + "content": "- CAV Interference: Only the collaborating CAVs are subject to corruptions, evaluating the risk of disruptions compared to single-vehicle perception." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.366, + 0.483, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.504, + 0.483, + 0.745 + ], + "angle": 0, + "content": "Leveraging RCP-Bench, we conduct extensive experiments on 10 collaborative perception models. As shown in Fig. 1, while these models perform well under ideal conditions, their performance significantly degrades in the presence of corruptions. To enhance the robustness, we propose two straightforward strategies tailored for collaborative perception: RCP-Drop and RCP-Mix. Unlike traditional methods [1, 8] that drop features within specific network layers or blocks during training, RCP-Drop operates by randomly discarding data from selected collaborating vehicles, effectively simulating real-world data loss encountered in communication-limited or sensor-failure scenarios. RCP-Mix, inspired by MixStyle [64, 65], probabilistically combines feature statistics, i.e., the means and standard deviations of feature maps, between the ego vehicle and collaborating CAVs, promoting resilience to distribution shifts." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.747, + 0.436, + 0.76 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.762, + 0.483, + 0.808 + ], + "angle": 0, + "content": "- We introduce RCP-Bench, the first benchmark systematically evaluating collaborative perception robustness across diverse real-world corruptions." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.808, + 0.483, + 0.853 + ], + "angle": 0, + "content": "- We conduct a comprehensive evaluation of 10 leading collaborative perception models across six scenarios, covering 14 corruption types." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.853, + 0.483, + 0.899 + ], + "angle": 0, + "content": "- We propose two novel strategies to enhance the robustness of collaborative perception models and highlight key factors affecting resilience." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.762, + 0.483, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.657, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.905, + 0.403 + ], + "angle": 0, + "content": "Collaborative Perception: Collaborative perception [5, 6, 16, 34, 40, 54, 56, 58, 61, 62] allows vehicles to share perceptual data with connected vehicles, realizing a more comprehensive understanding of the surrounding environment. Existing studies have proposed various techniques to enhance perception performance [42]. For example, Who2com [33] and When2com [32] propose strategies for selecting collaborators and determining the timing of collaboration. Where2comm [15] and What2comm [57] introduce methods for selecting relevant information to be shared. UMC [44] enhances spatiotemporal continuity in collaborative perception by leveraging historical data and multi-scale feature fusion. CoBEVT [51] enables real-time collaborative semantic segmentation by capturing sparse local and global spatial interactions across views and agents. Nevertheless, most of these methods assume ideal conditions, addressing robustness under diverse and challenging conditions remains essential to advancing collaborative perception reliability in practice." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.403, + 0.905, + 0.75 + ], + "angle": 0, + "content": "Robustness against Corruptions: Perception models are often vulnerable to various sensor corruptions, which can compromise their effectiveness in real-world applications. To evaluate and improve robustness under such conditions, several benchmarks have been developed. ImageNet-C [12] is the first public benchmark to assess object recognition models under a range of corruptions, including noise, blur, adverse weather, and digital interference. For object detection, Michaelis et al. [35] introduce three benchmarks to examine robustness against similar impairments. Recently, benchmarks tailored to driving scenarios have emerged. RoboDepth [20] assesses robustness in monocular depth estimation under corrupted conditions, while RoboBEV [49] introduces a comprehensive benchmark for evaluating BEV perception tasks. Similarly, MapBench [11] is designed to test the robustness of high-definition mapping methods against various sensor corruptions. Although these benchmarks have advanced robustness assessments in single-vehicle perception, they do not account for multi-agent contexts where corruptions may propagate, compounding effects across interconnected systems. Developing collaborative perception specific benchmarks is crucial for evaluating and improving robustness in these multi-vehicle scenarios." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.75, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Robustness in Collaborative Perception: With the advancement of collaborative perception research [13, 31, 37, 45], increasing attention is being paid to robustness and safety, especially concerning communication challenges between cooperating agents. These challenges include issues in data transmission, such as information loss during communication [26] and communication interruptions [38], timing issues like delays [23, 47, 60] and the reception of outdated or missing collaborative information. While these studies have highlighted potential pitfalls within the collab" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11909" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.068, + 0.899, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.376, + 0.907, + 0.457 + ], + "angle": 0, + "content": "Figure 2. Definitions of corruption types and evaluation scenarios in RCP-Bench. Our benchmark includes 14 types of camera corruptions, classified into three categories: External Weather, Camera Interior, and Temporal Misalignment. To comprehensively evaluate robustness, we define three interference scenarios: Global Interference (corruptions affecting both the ego vehicle and collaborative vehicles), Ego Interference (corruptions specific to the ego vehicle), and CAV Interference (corruptions isolated to one or more collaborative vehicles). Within the Global Interference scenario, we further examine four cases: Single Corruption, Multiple Corruptions, Heterogeneous Corruptions, and New Scenes with Corruption." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.46, + 0.486, + 0.658 + ], + "angle": 0, + "content": "orative process itself, robustness under diverse environmental and sensor conditions remains underexplored. Recently, a few studies have begun to examine collaborative performance under adverse environmental conditions [14, 25]. Nevertheless, these efforts are primarily limited to extreme sensor failures, without systematically analyzing the benefits and resilience of collaboration across a wider range of realistic sensor corruptions. To the best of our knowledge, this paper is the first to comprehensively examine the robustness and advantages of different collaborative states under diverse sensor corruptions, thereby providing an empirical basis for assessing and improving collaborative perception robustness across various real-world challenges." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.671, + 0.216, + 0.687 + ], + "angle": 0, + "content": "3. RCP-Bench" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.697, + 0.274, + 0.713 + ], + "angle": 0, + "content": "3.1. Benchmark Design" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Collaborative perception relies on information collected by both the ego vehicle and surrounding connected autonomous vehicles (CAVs), each contributing to the final perception outcome. To rigorously evaluate the benefits of shared information and assess model robustness under various corruptions, this study isolates these two information sources and defines three corruption scenarios, as shown in Fig. 2: (1) Global Interference scenario affecting both the ego vehicle and CAVs simultaneously, (2) Ego Interference scenario specific to the ego vehicle, and (3) CAV Interference scenario isolated to one or more CAVs." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Given mutual interference among CAVs, independent" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.907, + 0.702 + ], + "angle": 0, + "content": "control of lidar-based corruptions is impractical; therefore, this study focuses exclusively on camera-based corruptions. We categorize these into three groups based on real-world conditions: (1) External environmental factors, like rain, fog, or light; (2) Internal camera issues, such as lens scratches or sensor degradation; (3) Misalignment in capture timing, such as temporal desynchronization between the ego and CAV cameras. We identify 14 distinct types of corruption, following the methodology in [7], and divide each type into five severity levels, resulting in 70 unique corruption conditions. To evaluate collaborative perception model robustness, we create three corruption benchmarks using widely used datasets: DAIR-V2X [59], OPV2V [53], and V2XSet [52]. These corruptions are introduced into the validation sets, producing modified versions: DAIR-V2XC, OPV2V-C, and V2XSet-C." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.779, + 0.729 + ], + "angle": 0, + "content": "3.2. Typical Corruption Scenarios" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Global Interference: In practical applications, it is common for corruptions to affect both the ego vehicle and collaborative vehicles simultaneously. To evaluate model robustness across various types of corruption, we first assess 14 distinct corruptions individually, referring to this as the Single Corruption case. To better reflect real-world complexity, we further define three combined corruption cases. The first, Multiple Corruptions, involves multiple types of corruptions occurring concurrently. For simplicity, we focus on situations where temporal misalignment coincides with either external weather conditions or internal camera" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11910" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.212 + ], + "angle": 0, + "content": "issues. In the second case, *Heterogeneous Corruptions*, the types of corruption affecting the ego vehicle differ from those impacting the collaborative vehicles, allowing us to examine situations with varying corruption profiles across vehicles. Finally, in the *New Scenes with Corruption* case, we extend prior research on the generalization of collaborative perception by analyzing performance when corruptions are introduced simultaneously in unfamiliar environments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.214, + 0.483, + 0.425 + ], + "angle": 0, + "content": "Ego Interference: In real-world scenarios, the ego vehicle may experience unique corruptions that do not affect nearby collaborative vehicles, presenting an opportunity to use uncorrupted data from these vehicles as a compensatory mechanism. To explore this potential, we introduce the concept of \"collaborative compensation.\" Here, when the ego vehicle encounters interference or corruption, we investigate whether reliable information from neighboring collaborative vehicles can help mitigate or even correct these effects. Since some forms of interference, such as adverse weather, are unavoidable and impact all vehicles, we specifically focus on evaluating the advantages of collaborative compensation for the remaining ten types of corruption that are unique to the ego vehicle." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.426, + 0.483, + 0.609 + ], + "angle": 0, + "content": "CAV Interference: Similar to Ego Interference, collaborative vehicles may experience unique corruptions that do not directly affect the ego vehicle, creating a potential risk rather than a benefit. To examine this, we introduce the concept of \"collaborative disruption.\" In this scenario, we investigate whether corrupted data from surrounding collaborative vehicles can degrade the perception performance of an otherwise well-functioning ego vehicle. This analysis provides insights into the robustness of collaborative perception systems, highlighting the potential adverse effects of relying on collaborative data when unintentional corruptions are present in the shared information." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.62, + 0.276, + 0.635 + ], + "angle": 0, + "content": "3.3. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In evaluating 3D object detection performance, Average Precision (AP) is commonly used as the primary metric, particularly at Intersection-over-Union (IoU) thresholds of 0.3, 0.5, and 0.7. Building on the evaluation metrics proposed in [7, 41, 67], we introduce two metrics specifically designed to assess the robustness of cooperative perception systems: Corrupted Average Precision \\((\\mathrm{AP}_{\\mathrm{cor}})\\) and Relative Corruption Error (RCE). To further examine the effects of collaboration under Ego Interference and CAV Interference, we define \"Positive Collaborative\" and \"Negative Collaborative\", and introduce two additional metrics: the Positive Collaborative Coefficient (PosC) and the Negative Collaborative Coefficient (NegC). These four new evaluation metrics are primarily analyzed based on AP@0.5, additional results of AP@0.3 and AP@0.7 are provided in the appendix. Corrupted Average Precision: We denote the performance on the clean, uncorrupted test set as \\(\\mathrm{AP}_{\\mathrm{clean}}\\). For each cor" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "ruption type \\( c \\) at each severity \\( l \\), the performance is measured as \\( \\mathrm{AP}_{c,l} \\). The corruption robustness, \\( \\mathrm{AP}_{cor} \\) is then defined as the average performance across all corruption types and severity levels:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.153, + 0.905, + 0.191 + ], + "angle": 0, + "content": "\\[\n\\mathrm {A P} _ {c} = \\frac {1}{5} \\sum_ {l = 1} ^ {5} \\mathrm {A P} _ {c, l}, \\mathrm {A P} _ {c o r} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {A P} _ {c}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.191, + 0.821, + 0.205 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}\\) is the set of corruptions in evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.206, + 0.905, + 0.281 + ], + "angle": 0, + "content": "Relative Corruption Error: Since \\(\\mathrm{AP}_{\\mathrm{cor}}\\) measures only the absolute performance under corrupted conditions, we define Relative Corruption Error (RCE) as a relative indicator that quantifies the extent to which model performance is retained under corruption:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.284, + 0.905, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\mathrm {R C E} _ {c} = \\frac {\\mathrm {A P} _ {c l e a n} - \\mathrm {A P} _ {c}}{\\mathrm {A P} _ {c l e a n}}, \\mathrm {m R C E} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {R C E} _ {c}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.32, + 0.905, + 0.411 + ], + "angle": 0, + "content": "Positive Collaborative Coefficient: To quantify the ability of collaborative information to mitigate corruptions affecting the ego vehicle under Ego Interference, we define the Positive Collaborative Coefficient (PosC), which measures how effectively the model leverages collaborative information from other vehicles to counteract corruptions:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.414, + 0.905, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P o s C} _ {c} = \\frac {\\mathrm {A P} _ {c , 5} - \\mathrm {A P} _ {c , 5} ^ {e g o}}{1 - \\mathrm {A P} _ {c , 5} ^ {e g o}}, \\mathrm {m P o s C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {P o s C} _ {c}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.453, + 0.905, + 0.497 + ], + "angle": 0, + "content": "where \\(\\mathrm{AP}_{\\mathrm{c},5}^{\\mathrm{ego}}\\) represents the performance of the ego vehicle under a specific type of corruption at severity 5 in the absence of collaboration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.499, + 0.905, + 0.575 + ], + "angle": 0, + "content": "Negative Collaborative Coefficient: To assess the adverse impact of corrupted collaborative information under CAV Interference, we introduce the Negative Collaborative Coefficient (NegC), which quantifies the negative effects arising from collaborative perception:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.578, + 0.905, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\mathrm {N e g C} _ {c} = \\frac {1 - \\mathrm {A P} _ {c , 5}}{1 - \\mathrm {A P} _ {\\text {c l e a n}} ^ {e g o}}, \\mathrm {m N e g C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {N e g C} _ {c}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.644 + ], + "angle": 0, + "content": "where \\(\\mathrm{AP}_{\\mathrm{clean}}^{\\mathrm{ego}}\\) denotes the perception performance of the ego vehicle using only its own clean, uncorrupted data." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.659, + 0.729, + 0.676 + ], + "angle": 0, + "content": "4. Benchmarking Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.685, + 0.905, + 0.732 + ], + "angle": 0, + "content": "In this section, we primarily present the results on OPV2VC. Additional results for DAIR-V2X-C and V2XSet-C are provided in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.742, + 0.69, + 0.759 + ], + "angle": 0, + "content": "4.1. Benchmark Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Our RCP-Bench evaluates a total of 10 leading collaborative perception models and their variants for the detection task, including AttFuse [53], F-Cooper [4], V2X-ViT [52], DiscoNet [29], V2VNet [46], CoBEVT [51], and BM2CP [63]. To ensure a fair comparison, we use official model configurations and public checkpoints from open-source codebases where available or re-train the models using default settings if necessary. For each corruption type, we report metrics by averaging results across five severity levels. To provide a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11911" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.08, + 0.908, + 0.108 + ], + "angle": 0, + "content": "Table 1. Benchmarking results for Global Interference on OPV2V-C. We report the performance under each corruption \\( \\mathrm{AP}_c \\) and the overall corruption robustness \\( \\mathrm{AP}_{cor} \\) averaged over all corruption types. The results are evaluated based on AP@0.5." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.109, + 0.898, + 0.297 + ], + "angle": 0, + "content": "
CortypeAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLateNoFusion
APclean↑37.1334.8558.6147.3446.6440.4945.8768.4135.68
WeatherBright21.399.0543.0633.5536.4223.1827.6651.7625.22
Dark14.0016.6915.5818.487.8414.1213.3322.038.94
Fog10.3011.1515.2315.0215.5810.7811.7312.994.47
Frost7.129.5411.219.622.826.1410.1911.064.21
Snow6.464.7711.1910.427.559.3614.3312.374.75
NoiseGaussian9.178.987.453.102.155.9711.1313.805.23
Impulse9.179.018.112.082.035.6510.5614.915.55
Shot8.5810.558.480.712.274.5111.2615.606.24
BlurZoom18.8521.4426.5721.6815.8918.9523.5231.1012.90
Motion22.0724.8731.1930.1719.2424.5527.5640.5217.22
Defocus18.6417.6521.5721.278.7917.0119.0917.076.55
FailureCrash22.3016.6221.9616.2116.1923.2321.0832.0213.61
ColorQuant26.0121.0341.4835.0933.6825.8633.2748.1323.60
Alignment Tempormis29.7428.0547.9139.3138.7533.3836.8549.2835.68
APcor↑15.9914.9622.2118.3414.9415.9119.4026.6212.44
" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.301, + 0.291, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.431, + 0.258, + 0.444 + ], + "angle": 0, + "content": "(a) \\(\\mathrm{AP}_{\\text {clean }}\\) vs. \\(\\mathrm{AP}_{\\text {cor }}\\)" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.3, + 0.497, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.333, + 0.431, + 0.464, + 0.444 + ], + "angle": 0, + "content": "(b) \\(\\mathrm{AP}_{\\text {clean }}\\) vs.mRCE" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.3, + 0.7, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.431, + 0.668, + 0.444 + ], + "angle": 0, + "content": "(c) \\(\\mathrm{AP}_{\\text {clean }}\\) vs.mPosC" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.301, + 0.905, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.431, + 0.875, + 0.444 + ], + "angle": 0, + "content": "(d) \\(\\mathrm{AP}_{\\text {clean }}\\) vs.mNegC" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.447, + 0.908, + 0.475 + ], + "angle": 0, + "content": "Figure 3. The relationships between baseline performance \\((\\mathrm{AP}_{clean})\\) and various metrics, including collaborative robustness \\((\\mathrm{AP}_{cor}\\), mRCE), collaborative compensation (mPosC) and collaborative disruption (mNegC)." + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.481, + 0.473, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.696, + 0.483, + 0.723 + ], + "angle": 0, + "content": "Figure 4. The corrupted average precision \\((\\mathrm{AP}_c)\\) of existing methods across five severity levels of corruption." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.483, + 0.834 + ], + "angle": 0, + "content": "comprehensive robustness evaluation, we also include three non-learning baseline methods: Max, which directly maximizes the feature map for collaboration; Late, which fuses final predictions shared from CAVs; and NoFusion, representing the ego vehicle perception model without collaboration. The NoFusion model is further used to compute the PosC and NegC metrics as defined in Eq. 3 and Eq. 4." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.847, + 0.483, + 0.865 + ], + "angle": 0, + "content": "4.2. Benchmarking Results for Global Interference" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Single Corruption: The performance of collaborative perception models under various corruption types is presented" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.482, + 0.907, + 0.709 + ], + "angle": 0, + "content": "in Table 1, with results across different corruption severity levels shown in Fig. 4. The results indicate that existing models experience varying levels of performance degradation depending on the corruption type, with conditions like snow, frost, and noise having particularly severe impacts. The NoFusion model consistently performs the worst, showing significantly lower \\(\\mathrm{AP}_{cor}\\) across all corruption types, underscoring the limitations of single-vehicle perception. Interestingly, the simple Max fusion method outperforms several more complex models in interference scenarios, suggesting that increased model complexity does not necessarily lead to improved robustness against interference. Moreover, the Late fusion methods demonstrate greater adaptability and robustness compared to existing intermediate feature fusion techniques." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.909, + 0.881 + ], + "angle": 0, + "content": "To further understand the relationship between baseline performance and robustness, we analyze the results in Fig. 3a. The findings suggest that models with higher baseline performance may handle disturbances better, likely due to more robust feature extraction. Similarly, Fig. 3b shows a positive correlation between a model's mRCE and its clean-data performance, indicating that higher-performing models may also experience larger relative performance drops under corruption. With mRCE values generally between \\(55\\%\\) and \\(70\\%\\), current models exhibit suboptimal robustness, underscoring the need for further improvement." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.908, + 0.902 + ], + "angle": 0, + "content": "Multiple Corruptions: As shown in Fig. 5, different types" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11912" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.28, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.09, + 0.471, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.248, + 0.483, + 0.302 + ], + "angle": 0, + "content": "Figure 5. Radar charts for CoBEVT [51] and AttFuse [53] showing performance under single corruptions (labeled as \"Cor\" in the figure) and multiple corruptions that include additional temporal misalignment (labeled as \"Time\" in the figure)." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.309, + 0.287, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.308, + 0.486, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.446, + 0.483, + 0.473 + ], + "angle": 0, + "content": "Figure 6. Results of V2VNet [46] and DiscoNet [29] in terms of \\(\\mathrm{AP}_{cor}\\) under heterogeneous corruptions between Ego and CAVs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.478, + 0.483, + 0.613 + ], + "angle": 0, + "content": "of corruptions have varying impacts on CoBEVT [51] and AttFuse [53], with noise and frost disturbances causing the most significant performance degradation. Adding temporal misalignment to these camera corruptions further intensifies the effects of disturbances such as brightness, motion, and quantization. These results suggest that, in real-world scenarios, the simultaneous occurrence of multiple disturbances presents even greater challenges for model robustness. Please refer to the appendix for more results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.615, + 0.483, + 0.765 + ], + "angle": 0, + "content": "Hetero Corruptions: Fig. 6 shows that corruptions impact the Ego vehicle more severely than the CAVs in both DiscoNet [29] and V2VNet [46]. When the Ego vehicle is \"Clean\", the system performs effectively despite various \"CAV corruption\" conditions. However, when both Ego and CAVs are subjected to different types of disturbances, the model's performance declines significantly, particularly when one of them experiences crash corruption, which has the most pronounced impact on overall system performance. More results are included in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.766, + 0.483, + 0.902 + ], + "angle": 0, + "content": "New Scenes with Corruption: While collaborative perception models are typically evaluated in familiar environments, real-world deployment demands robustness in diverse, unseen scenes. Table 2 evaluates the model performance in familiar OPV2V scenes (Default) versus previously unseen scenes (Culver). The \\(\\mathrm{AP}_{\\text {clean }}\\) performance of V2X-ViT [52] declines by \\(47.8\\%\\), indicating that the scene variation significantly impacts model effectiveness. When disturbances and new scenes occur simultaneously, perfor" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.905, + 0.116 + ], + "angle": 0, + "content": "Table 2. Performance comparison in the familiar OPV2V scenes (Default) versus the unseen new scenes (Culver)." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.119, + 0.9, + 0.22 + ], + "angle": 0, + "content": "
ModelAPclean↑APcor↑mRCE↓
DefaultCulverDefaultCulverDefaultCulver
AttFuse37.1319.48(↓47.5%)14.937.29(↓51.2%)41.5141.93(↑1.0%)
F-Cooper34.8526.52(↓23.9%)13.958.58(↓38.5%)37.5448.25(↑28.5%)
V2X-ViT58.6130.62(↓47.8%)20.249.11(↓55.0%)46.9451.38(↑9.5%)
DiscoNet47.3428.66(↓39.5%)16.728.31(↓50.3%)49.9453.65(↑7.4%)
V2VNet46.6426.80(↓42.5%)13.116.79(↓48.3%)53.8656.96(↑5.8%)
CoBEVT40.4923.97(↓40.8%)14.567.10(↓51.2%)46.4249.39(↑6.4%)
Max45.8724.97(↓45.6%)18.057.56(↓58.1%)41.9047.95(↑14.4%)
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.227, + 0.905, + 0.288 + ], + "angle": 0, + "content": "mance drops further, with \\(\\mathrm{AP}_{cor}\\) decreasing by \\(55\\%\\) and RCE increasing by \\(9.5\\%\\). These results highlight the challenges that current collaborative methods encounter in handling disturbed environments with unfamiliar scenes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.297, + 0.885, + 0.314 + ], + "angle": 0, + "content": "4.3. Benchmarking Results for Ego Interference" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.907, + 0.546 + ], + "angle": 0, + "content": "When the ego vehicle encounters unique corruptions, uncorrupted data from collaborators can offer collaborative compensation. Table 3 verifies this through \\(\\mathrm{PosC}_c\\) and mPosC metrics. Results indicate that the simple Late fusion significantly enhances mPosC compared to other intermediate fusion methods, suggesting that complex fusion models (e.g., attention-based [51-53], graph-based [29, 46]) are effective only when the ego vehicle captures essential information. The compensation stability varies across models and disturbances: V2X-ViT [52] and V2VNet [46] show fluctuations, whereas F-Cooper [4] and CoBEVT [51] exhibit more consistency. Fig. 3c further reveals a positive correlation between collaborative compensation mPosC and baseline performance \\(\\mathrm{AP}_{clean}\\), suggesting that models with higher baseline results provide stronger compensatory support." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.555, + 0.892, + 0.571 + ], + "angle": 0, + "content": "4.4. Benchmarking Results for CAV Interference" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.577, + 0.907, + 0.789 + ], + "angle": 0, + "content": "In scenarios where collaborative vehicles experience unique corruptions not directly affecting the ego vehicle, shared data from these vehicles can introduce \"collaborative disruption.\" Table 3 presents the \\(\\mathrm{NegC}_c\\) and mNegC metrics to quantify this effect. A NegC value over \\(100\\%\\) indicates that corrupted data from collaborators degrades the ego vehicle's performance. The results show that the Late fusion is less vulnerable to these disruptions and often provides positive benefits even under corruption, while intermediate feature fusion methods tend to reduce performance. Additionally, Fig. 3d shows that higher baseline performance \\((\\mathrm{AP}_{clean})\\) correlates with reduced collaborative disruption, suggesting that models with stronger baseline performance may better handle corrupted collaborative data." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.8, + 0.736, + 0.817 + ], + "angle": 0, + "content": "5. RCP-Drop & RCP-Mix" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.871 + ], + "angle": 0, + "content": "To enhance robustness under various corruption scenarios, we develop two simple yet effective strategies specifically for collaborative perception: RCP-Drop and RCP-Mix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Dropout [1, 8] is a widely used regularization technique in deep learning, aimed at reducing model overfitting by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11913" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.08, + 0.908, + 0.121 + ], + "angle": 0, + "content": "Table 3. Benchmarking results for Ego Interference and CAV Interference on OPV2V-C. We report collaborative compensation and disruption performance under each corruption type, including \\(\\mathrm{NegC}_c\\) and \\(\\mathrm{PosC}_c\\), as well as averages across all corruption types, mNegC and mPosC. Results are evaluated based on AP@0.5. Further details are available in the appendix." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.123, + 0.907, + 0.265 + ], + "angle": 0, + "content": "
Cor TypesAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLate
NegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCc
Bright121.278.54115.979.6886.6828.9095.7718.29103.0327.29107.826.24108.7120.6882.4550.82
Dark126.7312.96122.2821.77104.2414.80109.5918.68127.296.43116.0014.97121.5222.1499.9150.81
Zoom117.6319.66116.4321.7493.7229.29100.9620.66107.6223.63107.9817.63104.6825.4188.5051.99
Motion116.6721.12115.5222.5094.5025.8499.3322.52117.469.83106.1919.19102.8325.6790.3051.09
Defocus118.1725.27116.8724.6299.4727.14106.2020.90121.3010.81107.8218.68107.8027.13101.5550.36
Gaussian127.3213.30122.7315.47112.3910.16115.0212.32123.355.81117.9311.545115.8424.7199.7550.83
Impulse127.0415.75122.9814.94112.0611.78115.1311.82123.215.62117.8611.11115.3324.3399.5350.84
Shot126.8713.12122.0117.78112.339.86115.3911.64123.825.95118.1711.81114.0425.7099.8950.82
Crash116.2222.35115.7320.5197.5013.75107.0410.67112.5811.98105.0518.96108.1224.2191.5350.14
Quant118.0317.63113.9122.4999.8622.6998.6021.65110.0020.66110.0012.82110.1425.8398.7648.70
mNegC↓/mPosC↑121.5916.97118.4419.15101.2719.42106.3116.92116.9712.80111.4814.29110.9024.5895.2250.64
" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.272, + 0.482, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.368, + 0.468, + 0.383 + ], + "angle": 0, + "content": "Figure 7. Overview of the RCP-Drop & RCP-Mix strategies." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.392, + 0.483, + 0.589 + ], + "angle": 0, + "content": "randomly dropping features within certain network layers or blocks during training. In the collaborative perception context, the ego vehicle may encounter incomplete shared perceptual data from CAVs due to communication failures, or CAVs leaving the collaborative queue. Existing collaborative perception models, while beneficial in multi-vehicle setups, often underperform in single-vehicle scenarios due to their learned dependency on supplementary data from other vehicles. To prevent models from being overly reliant on CAVs data and to better equip them for single-vehicle operation, as shown in Fig. 7 we introduce RCP-Drop, which simulates these conditions by selectively discarding information from certain CAVs. Technically, it is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.592, + 0.482, + 0.613 + ], + "angle": 0, + "content": "\\[\nF _ {a g g} ^ {e g o} = \\mathcal {A} \\left(F ^ {e g o}, \\left\\{\\mathbb {1} \\left(p _ {i} < p _ {d r o p}\\right) \\cdot F _ {i} ^ {c a v} \\right\\} _ {i = 1} ^ {N}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.733 + ], + "angle": 0, + "content": "where \\( F^{ego} \\) represents the feature originating from the ego vehicle, \\( F_{agg}^{ego} \\) denotes the aggregated feature after perception information exchange, and \\( F_{i}^{cav} \\) is the feature map shared from the \\( i \\)-th collaborative vehicle. Here, \\( \\mathcal{A} \\) is a specific feature fusion function developed in existing methods [29, 44, 53], \\( p_i \\) is sampled from a uniform distribution between 0 and 1, and \\( p_{drop} \\) is the threshold determining whether data from each collaborative vehicle is discarded." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Rather than keeping the threshold fixed during training, we develop a dynamic adjustment strategy for \\( p_{drop} \\). Specifically, we start with a high dropout probability, which reduces the number of participating collaborative vehicles and enhances the single-vehicle backbone's feature extraction capabilities. Gradually, we lower the dropout probability to increase the participation of collaborative vehicles, optimizing the collaborative perception performance over time. In this study, we set \\( p_{drop} = 1.0 - (t / T)^2 \\), where \\( t \\) and \\( T \\) are the current and maximum training epoch." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Existing research shows that visual data can be char" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.274, + 0.905, + 0.302 + ], + "angle": 0, + "content": "Table 4. Efficacy of RCP-Drop and RCP-Mix on collaborative robustness, collaborative compensation and collaborative disruption." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.304, + 0.9, + 0.416 + ], + "angle": 0, + "content": "
APclean↑mAPcor↑mNegC↓mPosC↑
CoBEVT [51]40.4915.91111.4814.29
+BN [39]42.7427.87112.9418.28
+BN+RCP-Mix48.2531.83109.1123.44
+BN+RCP-Drop47.8430.68109.4520.07
AttFuse [53]37.1315.99121.5916.97
+BN [39]36.1322.35126.0418.85
+BN+RCP-Mix43.1228.85114.9722.51
+BN+RCP-Drop45.1827.56115.6418.17
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.422, + 0.907, + 0.589 + ], + "angle": 0, + "content": "acterized by feature statistics (i.e., the mean and standard deviation of feature maps). For the same semantic concepts, distinct styles (such as variations in color and texture) correspond to different feature statistics. Inspired by Mixstyle [64, 65], we propose RCP-Mix to enhance model adaptability to varied environmental conditions and styles encountered in collaborative perception. Unlike Mixstyle, which performs random feature statistic mixing across instances within a mini-batch, RCP-Mix probabilistically combines feature statistics between the ego vehicle and collaborating CAVs. Technically, RCP-Mix is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.59, + 0.837, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\mu_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mu_ {i}; \\quad \\sigma_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\sigma_ {i},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.634, + 0.905, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\mu_ {i} ^ {\\text {m i x}} = \\lambda \\mu_ {i} + (1 - \\lambda) \\mu_ {\\text {a l l}}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.655, + 0.768, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {i} ^ {m i x} = \\lambda \\sigma_ {i} + (1 - \\lambda) \\sigma_ {a l l},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.674, + 0.81, + 0.704 + ], + "angle": 0, + "content": "\\[\nF _ {i} ^ {m i x} = \\frac {F _ {i} - \\mu_ {i}}{\\sigma_ {i}} * \\sigma_ {i} ^ {m i x} + \\mu_ {i} ^ {m i x},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.75 + ], + "angle": 0, + "content": "where \\(\\mu_{i}\\), \\(\\sigma_{i}\\) are the means and standard deviations of the feature map \\(F_{i}\\), \\(\\lambda\\) is the weight sampled from the Beta distribution, i.e., \\(\\lambda \\sim \\text{Beta}(\\alpha, \\alpha)\\), we set \\(\\alpha = 0.1\\) by default." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Experimental Analysis: We selected CoBEVT [51] and AttFuse [53] with online Batch Normalization (BN) Stats Adapt [39] as baselines, integrating them with our RCP-Drop and RCP-Mix strategies. Table 4 demonstrates that, despite their simplicity, both RCP-Drop and RCP-Mix effectively counteract performance degradation from data corruptions. In particular, for \\(\\mathrm{AP}_{\\text {clean }}\\), these strategies lead to substantial performance improvements compared to the marginal gains or occasional declines observed with the vanilla BN adapt. Moreover, across the three inter-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11914" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.09, + 0.447, + 0.102 + ], + "angle": 0, + "content": "Table 5. Ablation on the use of different backbone." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.105, + 0.5, + 0.164 + ], + "angle": 0, + "content": "
MethodbackboneWeatherBlurNoiseQuantCrashAPAPcor
Max○ResNet10111.7922.322.7722.8718.6435.1218.14
Max•EfficientNet-b015.4523.3910.9833.2721.0845.8718.05
V2X-ViT○ResNet10110.9024.6616.6328.7510.4146.2116.73
V2X-ViT•EfficientNet-b019.2526.458.0141.4821.9658.6120.24
" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.172, + 0.287, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.173, + 0.48, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.287, + 0.482, + 0.301 + ], + "angle": 0, + "content": "Figure 8. Impact of different backbone sizes on model robustness." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.308, + 0.284, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.307, + 0.481, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.433, + 0.447, + 0.447 + ], + "angle": 0, + "content": "Figure 9. Effect of CAV number on model robustness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.573 + ], + "angle": 0, + "content": "ference scenarios, Global Interference, Ego Interference, and CAV Interference, our RCP-Drop and RCP-Mix consistently show robust improvements in model resilience under corruption conditions \\(\\left(\\mathrm{AP}_{cor}\\right)\\), collaborative compensation (mPosC), and reduced collaborative disruption (mNegC). These results further underline the efficacy of our approaches in maintaining model performance and collaborative stability in challenging conditions." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.588, + 0.34, + 0.604 + ], + "angle": 0, + "content": "6. Observation & Discussion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.643 + ], + "angle": 0, + "content": "In this section, we analyze and discuss the impact of various model configurations and techniques on robustness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Backbones: Table 5 compares the performance of different backbones, showing that models using EfficientNet-b0 outperform ResNet101 [22] in all conditions except noise disturbances. leading to its use as the backbone for all models in this study. Fig. 8 further compares AttFuse with various backbone sizes, revealing that larger backbones generally improve robustness. Notably, EfficientNetb0 and EfficientNet-b3 [21] show greater stability and robustness across multiple conditions, particularly excelling under \"Noise\" and \"Crash\" scenarios, while EfficientNetb2 performs poorly in these cases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Feature Fusion: Table 6 shows that multiscale fusion enhances model performance on clean datasets and improves robustness against various perturbations. Additionally, the simple Max Fusion demonstrates greater robustness than attention mechanisms, particularly under noisy conditions, suggesting that more complex mechanisms may be less ef" + }, + { + "type": "table_caption", + "bbox": [ + 0.563, + 0.09, + 0.857, + 0.103 + ], + "angle": 0, + "content": "Table 6. Ablation on the use of multiscale fusion." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.106, + 0.899, + 0.165 + ], + "angle": 0, + "content": "
MethodmultiscaleWeatherBlurNoiseQuantCrashAP\\(AP_{cor}\\)
Max○X15.4523.3910.9833.2721.0845.8718.05
Max●✓30.6534.9228.6149.8638.1565.3833.22
AttFuse○X11.8519.858.9726.0122.3037.1314.93
AttFuse●✓23.3631.909.0143.4330.0762.5824.08
" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.172, + 0.707, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.172, + 0.903, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.298, + 0.881, + 0.312 + ], + "angle": 0, + "content": "Figure 10. Effect of camera number on model robustness." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.318, + 0.848, + 0.332 + ], + "angle": 0, + "content": "fective at mitigating certain types of perturbations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.333, + 0.907, + 0.483 + ], + "angle": 0, + "content": "CAV and Camera Number: Fig. 9 shows that increasing the number of collaborative CAVs generally enhances model performance. Notably, two collaborating vehicles provide a significant improvement over a single vehicle; however, the rate of improvement diminishes once the number of collaborators exceeds four, indicating a diminishing marginal effect. Fig. 10 shows that as camera count increases, both model performance and robustness improve significantly, with a particularly notable boost from three to four cameras." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.498, + 0.634, + 0.513 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.524, + 0.907, + 0.78 + ], + "angle": 0, + "content": "In this study, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of camera-based collaborative perception models under diverse real-world disturbances. RCP-Bench encompasses 14 corruption types at 5 severity levels across 3 large-scale datasets. We systematically evaluate three collaborative scenarios across six cases to assess robustness in the Global Interference scenario, explore collaborative advantages in the Ego Interference scenario, and examine disturbance risks in the CAV Interference scenario. To improve robustness, we propose two straightforward strategies, RCP-Drop and RCP-Mix, tailored for collaborative perception. Our analysis of backbone architecture, feature fusion, CAV number, and camera number provides key insights for enhancing model resilience. We hope this work offers valuable insights and inspires future research toward more robust collaborative perception models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Acknowledgment: This work was supported by the National Key Research and Development Program of China (No. 2024YFE0211000), in part by the National Natural Science Foundation of China (No. 62372329), in part by Shanghai Scientific Innovation Foundation (No. 23DZ1203400), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11915" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.154 + ], + "angle": 0, + "content": "[1] Pierre Baldi and Peter J Sadowski. 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Proceedings of the IEEE, 111(3):257-276, 2023. 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11918" + } + ] +] \ No newline at end of file diff --git a/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_origin.pdf b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..901df6d38f4adffafa6170472c5899056f433d07 --- /dev/null +++ b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/9170f020-ef41-4783-9545-58730495f413_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b2a28c86521f9af8e2431347656b413273f93904f74c521c514deaebb24a37e4 +size 1392202 diff --git a/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/full.md b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fc809bfc1ba3c933db6b7403a42aea7d2313afa1 --- /dev/null +++ b/2025/RCP-Bench_ Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions/full.md @@ -0,0 +1,353 @@ +# RCP-Bench: Benchmarking Robustness for Collaborative Perception Under Diverse Corruptions + +Shihang Du $^{1}$ , Sanqing Qu $^{1}$ , Tianhang Wang $^{1}$ , Xudong Zhang $^{1}$ , Yunwei Zhu $^{1}$ , Jian Mao $^{1}$ , Fan Lu $^{1}$ , Qiao Lin $^{2}$ , Guang Chen $^{1*}$ $^{1}$ Tongji University, $^{2}$ EACON Technology Co., Ltd. + +# Abstract + +Collaborative perception enhances single-vehicle perception by integrating sensory data from multiple connected vehicles. However, existing studies often assume ideal conditions, overlooking resilience to real-world challenges, such as adverse weather and sensor malfunctions, which is critical for safe deployment. To address this gap, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of collaborative detection models under a wide range of real-world corruptions. RCP-Bench includes three new datasets (i.e., OPV2V-C, V2XSet-C, and DAIR-V2X-C) that simulate six collaborative cases and 14 types of camera corruption resulting from external environmental factors, sensor failures, and temporal misalignments. Extensive experiments on 10 leading collaborative perception models reveal that, while these models perform well under ideal conditions, they are significantly affected by corruptions. To improve robustness, we propose two simple yet effective strategies, RCP-Drop and RCP-Mix, based on training regularization and feature augmentation. Additionally, we identify several critical factors influencing robustness, such as backbone architecture, camera number, feature fusion methods, and the number of connected vehicles. We hope that RCP-Bench, along with these strategies and insights, will stimulate future research toward developing more robust collaborative perception models. Our benchmark toolkit is available at https://github.com/LuckyDush/RCP-Bench. + +# 1. Introduction + +Perception is a fundamental capability for robots and autonomous vehicles to accurately interpret their surroundings. Despite significant advancements in perception tasks through deep learning, including object detection [3, 68] and segmentation [19, 27], single-vehicle perception using onboard sensors still faces inherent limitations, such as restricted range, limited field of view, and vulnerability to occlusions [17, 30, 50], resulting in blind spots that hinder full + +![](images/4bc97b7669566de260976936c51864417858c4b405d5beb9155cad444fc52538.jpg) + +![](images/df586b328085b8f7394033b2cb1f86cbc8d1f78aa00c32488254a90d15875cd3.jpg) + +Figure 1. Comparison of collaborative object detection results (averaged across 10 leading methods) in OPV2V-C across three interference scenarios: Global, Ego, and CAV Interference. The results indicate that perception models are particularly vulnerable to Global Interference, benefit from collaborative compensation under Ego Interference, and experience performance degradation under CAV Interference. +![](images/3c7c7bf465618c359dc71debcdb93a862cd5672f75e3ccaca164b39abbe65263.jpg) +or Ego Cor/Clean + +![](images/4d442d202d42f99483db21fca77b678a162e35eaa693541e3830ff02a73b9574.jpg) +or CAV Cor/Clean +X No CAV + +environmental understanding [5]. Collaborative perception, where perception data are shared among Connected Autonomous Vehicles (CAVs), has shown promise in overcoming these challenges. By leveraging multiple viewpoints, collaborative perception extends perceptual range, enhances spatial coverage, and improves resilience to occlusions [16]. + +Numerous studies have investigated practical challenges that may impact collaborative performance, such as bandwidth limitations for shared information [15, 32, 33, 44], transmission issues [26, 38, 47, 60], pose estimation errors [24, 34, 43, 66], and heterogeneity among cooperating vehicles [28, 48, 55]. However, current models and evaluations generally assume idealized conditions, such as clear weather and fully functional sensors. In real-world driving scenarios, adverse conditions such as external weather [9, 10, 18] and sensor failures [2, 12] are unavoidable. Although recent efforts address individual robustness + +challenges, including communication delays [23, 36] and diverse weather conditions [14, 25], a comprehensive assessment of robustness for collaborative perception in real-world scenarios remains an important open challenge. + +To bridge this gap, we introduce RCP-Bench, the first benchmark designed to systematically evaluate the reliability of collaborative perception methods under a wide range of corruptions. Specifically, RCP-Bench comprises three new datasets, including OPV2V-C, V2XSet-C and DAIR-V2X-C. These datasets simulate six distinct cases and incorporate 14 types of corruption, incorporating variations in weather conditions, sensor noise or failures, and temporal misalignments, as depicted in Fig. 2. Given that collaborative perception depends on data shared across collaborating CAVs, where corruptions in individual vehicles can propagate throughout the collaborative process, creating diverse and challenging scenarios. RCP-Bench provides a holistic assessment by evaluating robustness across three aspects: + +- Global Interference: Both the ego vehicle and collaborating CAVs are affected by diverse corruptions, testing the overall robustness of collaborative perception. +- Ego Interference: Only the ego vehicle experiences corruption, assessing the compensatory advantages of collaboration over single-vehicle perception. +- CAV Interference: Only the collaborating CAVs are subject to corruptions, evaluating the risk of disruptions compared to single-vehicle perception. + +Leveraging RCP-Bench, we conduct extensive experiments on 10 collaborative perception models. As shown in Fig. 1, while these models perform well under ideal conditions, their performance significantly degrades in the presence of corruptions. To enhance the robustness, we propose two straightforward strategies tailored for collaborative perception: RCP-Drop and RCP-Mix. Unlike traditional methods [1, 8] that drop features within specific network layers or blocks during training, RCP-Drop operates by randomly discarding data from selected collaborating vehicles, effectively simulating real-world data loss encountered in communication-limited or sensor-failure scenarios. RCP-Mix, inspired by MixStyle [64, 65], probabilistically combines feature statistics, i.e., the means and standard deviations of feature maps, between the ego vehicle and collaborating CAVs, promoting resilience to distribution shifts. + +Our contributions can be summarized as follows: + +- We introduce RCP-Bench, the first benchmark systematically evaluating collaborative perception robustness across diverse real-world corruptions. +- We conduct a comprehensive evaluation of 10 leading collaborative perception models across six scenarios, covering 14 corruption types. +- We propose two novel strategies to enhance the robustness of collaborative perception models and highlight key factors affecting resilience. + +# 2. Related Work + +Collaborative Perception: Collaborative perception [5, 6, 16, 34, 40, 54, 56, 58, 61, 62] allows vehicles to share perceptual data with connected vehicles, realizing a more comprehensive understanding of the surrounding environment. Existing studies have proposed various techniques to enhance perception performance [42]. For example, Who2com [33] and When2com [32] propose strategies for selecting collaborators and determining the timing of collaboration. Where2comm [15] and What2comm [57] introduce methods for selecting relevant information to be shared. UMC [44] enhances spatiotemporal continuity in collaborative perception by leveraging historical data and multi-scale feature fusion. CoBEVT [51] enables real-time collaborative semantic segmentation by capturing sparse local and global spatial interactions across views and agents. Nevertheless, most of these methods assume ideal conditions, addressing robustness under diverse and challenging conditions remains essential to advancing collaborative perception reliability in practice. + +Robustness against Corruptions: Perception models are often vulnerable to various sensor corruptions, which can compromise their effectiveness in real-world applications. To evaluate and improve robustness under such conditions, several benchmarks have been developed. ImageNet-C [12] is the first public benchmark to assess object recognition models under a range of corruptions, including noise, blur, adverse weather, and digital interference. For object detection, Michaelis et al. [35] introduce three benchmarks to examine robustness against similar impairments. Recently, benchmarks tailored to driving scenarios have emerged. RoboDepth [20] assesses robustness in monocular depth estimation under corrupted conditions, while RoboBEV [49] introduces a comprehensive benchmark for evaluating BEV perception tasks. Similarly, MapBench [11] is designed to test the robustness of high-definition mapping methods against various sensor corruptions. Although these benchmarks have advanced robustness assessments in single-vehicle perception, they do not account for multi-agent contexts where corruptions may propagate, compounding effects across interconnected systems. Developing collaborative perception specific benchmarks is crucial for evaluating and improving robustness in these multi-vehicle scenarios. + +Robustness in Collaborative Perception: With the advancement of collaborative perception research [13, 31, 37, 45], increasing attention is being paid to robustness and safety, especially concerning communication challenges between cooperating agents. These challenges include issues in data transmission, such as information loss during communication [26] and communication interruptions [38], timing issues like delays [23, 47, 60] and the reception of outdated or missing collaborative information. While these studies have highlighted potential pitfalls within the collab + +![](images/aa5928269343b93675c42739cc8a50a6d33ea44f155602489dbe04e91c67aa79.jpg) +Figure 2. Definitions of corruption types and evaluation scenarios in RCP-Bench. Our benchmark includes 14 types of camera corruptions, classified into three categories: External Weather, Camera Interior, and Temporal Misalignment. To comprehensively evaluate robustness, we define three interference scenarios: Global Interference (corruptions affecting both the ego vehicle and collaborative vehicles), Ego Interference (corruptions specific to the ego vehicle), and CAV Interference (corruptions isolated to one or more collaborative vehicles). Within the Global Interference scenario, we further examine four cases: Single Corruption, Multiple Corruptions, Heterogeneous Corruptions, and New Scenes with Corruption. + +orative process itself, robustness under diverse environmental and sensor conditions remains underexplored. Recently, a few studies have begun to examine collaborative performance under adverse environmental conditions [14, 25]. Nevertheless, these efforts are primarily limited to extreme sensor failures, without systematically analyzing the benefits and resilience of collaboration across a wider range of realistic sensor corruptions. To the best of our knowledge, this paper is the first to comprehensively examine the robustness and advantages of different collaborative states under diverse sensor corruptions, thereby providing an empirical basis for assessing and improving collaborative perception robustness across various real-world challenges. + +# 3. RCP-Bench + +# 3.1. Benchmark Design + +Collaborative perception relies on information collected by both the ego vehicle and surrounding connected autonomous vehicles (CAVs), each contributing to the final perception outcome. To rigorously evaluate the benefits of shared information and assess model robustness under various corruptions, this study isolates these two information sources and defines three corruption scenarios, as shown in Fig. 2: (1) Global Interference scenario affecting both the ego vehicle and CAVs simultaneously, (2) Ego Interference scenario specific to the ego vehicle, and (3) CAV Interference scenario isolated to one or more CAVs. + +Given mutual interference among CAVs, independent + +control of lidar-based corruptions is impractical; therefore, this study focuses exclusively on camera-based corruptions. We categorize these into three groups based on real-world conditions: (1) External environmental factors, like rain, fog, or light; (2) Internal camera issues, such as lens scratches or sensor degradation; (3) Misalignment in capture timing, such as temporal desynchronization between the ego and CAV cameras. We identify 14 distinct types of corruption, following the methodology in [7], and divide each type into five severity levels, resulting in 70 unique corruption conditions. To evaluate collaborative perception model robustness, we create three corruption benchmarks using widely used datasets: DAIR-V2X [59], OPV2V [53], and V2XSet [52]. These corruptions are introduced into the validation sets, producing modified versions: DAIR-V2XC, OPV2V-C, and V2XSet-C. + +# 3.2. Typical Corruption Scenarios + +Global Interference: In practical applications, it is common for corruptions to affect both the ego vehicle and collaborative vehicles simultaneously. To evaluate model robustness across various types of corruption, we first assess 14 distinct corruptions individually, referring to this as the Single Corruption case. To better reflect real-world complexity, we further define three combined corruption cases. The first, Multiple Corruptions, involves multiple types of corruptions occurring concurrently. For simplicity, we focus on situations where temporal misalignment coincides with either external weather conditions or internal camera + +issues. In the second case, *Heterogeneous Corruptions*, the types of corruption affecting the ego vehicle differ from those impacting the collaborative vehicles, allowing us to examine situations with varying corruption profiles across vehicles. Finally, in the *New Scenes with Corruption* case, we extend prior research on the generalization of collaborative perception by analyzing performance when corruptions are introduced simultaneously in unfamiliar environments. + +Ego Interference: In real-world scenarios, the ego vehicle may experience unique corruptions that do not affect nearby collaborative vehicles, presenting an opportunity to use uncorrupted data from these vehicles as a compensatory mechanism. To explore this potential, we introduce the concept of "collaborative compensation." Here, when the ego vehicle encounters interference or corruption, we investigate whether reliable information from neighboring collaborative vehicles can help mitigate or even correct these effects. Since some forms of interference, such as adverse weather, are unavoidable and impact all vehicles, we specifically focus on evaluating the advantages of collaborative compensation for the remaining ten types of corruption that are unique to the ego vehicle. + +CAV Interference: Similar to Ego Interference, collaborative vehicles may experience unique corruptions that do not directly affect the ego vehicle, creating a potential risk rather than a benefit. To examine this, we introduce the concept of "collaborative disruption." In this scenario, we investigate whether corrupted data from surrounding collaborative vehicles can degrade the perception performance of an otherwise well-functioning ego vehicle. This analysis provides insights into the robustness of collaborative perception systems, highlighting the potential adverse effects of relying on collaborative data when unintentional corruptions are present in the shared information. + +# 3.3. Evaluation Metrics + +In evaluating 3D object detection performance, Average Precision (AP) is commonly used as the primary metric, particularly at Intersection-over-Union (IoU) thresholds of 0.3, 0.5, and 0.7. Building on the evaluation metrics proposed in [7, 41, 67], we introduce two metrics specifically designed to assess the robustness of cooperative perception systems: Corrupted Average Precision $(\mathrm{AP}_{\mathrm{cor}})$ and Relative Corruption Error (RCE). To further examine the effects of collaboration under Ego Interference and CAV Interference, we define "Positive Collaborative" and "Negative Collaborative", and introduce two additional metrics: the Positive Collaborative Coefficient (PosC) and the Negative Collaborative Coefficient (NegC). These four new evaluation metrics are primarily analyzed based on AP@0.5, additional results of AP@0.3 and AP@0.7 are provided in the appendix. Corrupted Average Precision: We denote the performance on the clean, uncorrupted test set as $\mathrm{AP}_{\mathrm{clean}}$ . For each cor + +ruption type $c$ at each severity $l$ , the performance is measured as $\mathrm{AP}_{c,l}$ . The corruption robustness, $\mathrm{AP}_{cor}$ is then defined as the average performance across all corruption types and severity levels: + +$$ +\mathrm {A P} _ {c} = \frac {1}{5} \sum_ {l = 1} ^ {5} \mathrm {A P} _ {c, l}, \mathrm {A P} _ {c o r} = \frac {1}{| \mathcal {C} |} \sum_ {c \in \mathcal {C}} \mathrm {A P} _ {c}, \tag {1} +$$ + +where $\mathcal{C}$ is the set of corruptions in evaluation. + +Relative Corruption Error: Since $\mathrm{AP}_{\mathrm{cor}}$ measures only the absolute performance under corrupted conditions, we define Relative Corruption Error (RCE) as a relative indicator that quantifies the extent to which model performance is retained under corruption: + +$$ +\mathrm {R C E} _ {c} = \frac {\mathrm {A P} _ {c l e a n} - \mathrm {A P} _ {c}}{\mathrm {A P} _ {c l e a n}}, \mathrm {m R C E} = \frac {1}{| \mathcal {C} |} \sum_ {c \in \mathcal {C}} \mathrm {R C E} _ {c}. \tag {2} +$$ + +Positive Collaborative Coefficient: To quantify the ability of collaborative information to mitigate corruptions affecting the ego vehicle under Ego Interference, we define the Positive Collaborative Coefficient (PosC), which measures how effectively the model leverages collaborative information from other vehicles to counteract corruptions: + +$$ +\mathrm {P o s C} _ {c} = \frac {\mathrm {A P} _ {c , 5} - \mathrm {A P} _ {c , 5} ^ {e g o}}{1 - \mathrm {A P} _ {c , 5} ^ {e g o}}, \mathrm {m P o s C} = \frac {1}{| \mathcal {C} |} \sum_ {c \in \mathcal {C}} \mathrm {P o s C} _ {c}, \tag {3} +$$ + +where $\mathrm{AP}_{\mathrm{c},5}^{\mathrm{ego}}$ represents the performance of the ego vehicle under a specific type of corruption at severity 5 in the absence of collaboration. + +Negative Collaborative Coefficient: To assess the adverse impact of corrupted collaborative information under CAV Interference, we introduce the Negative Collaborative Coefficient (NegC), which quantifies the negative effects arising from collaborative perception: + +$$ +\mathrm {N e g C} _ {c} = \frac {1 - \mathrm {A P} _ {c , 5}}{1 - \mathrm {A P} _ {\text {c l e a n}} ^ {e g o}}, \mathrm {m N e g C} = \frac {1}{| \mathcal {C} |} \sum_ {c \in \mathcal {C}} \mathrm {N e g C} _ {c}, \tag {4} +$$ + +where $\mathrm{AP}_{\mathrm{clean}}^{\mathrm{ego}}$ denotes the perception performance of the ego vehicle using only its own clean, uncorrupted data. + +# 4. Benchmarking Results + +In this section, we primarily present the results on OPV2VC. Additional results for DAIR-V2X-C and V2XSet-C are provided in the appendix. + +# 4.1. Benchmark Setup + +Our RCP-Bench evaluates a total of 10 leading collaborative perception models and their variants for the detection task, including AttFuse [53], F-Cooper [4], V2X-ViT [52], DiscoNet [29], V2VNet [46], CoBEVT [51], and BM2CP [63]. To ensure a fair comparison, we use official model configurations and public checkpoints from open-source codebases where available or re-train the models using default settings if necessary. For each corruption type, we report metrics by averaging results across five severity levels. To provide a + +Table 1. Benchmarking results for Global Interference on OPV2V-C. We report the performance under each corruption $\mathrm{AP}_c$ and the overall corruption robustness $\mathrm{AP}_{cor}$ averaged over all corruption types. The results are evaluated based on AP@0.5. + +
CortypeAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLateNoFusion
APclean↑37.1334.8558.6147.3446.6440.4945.8768.4135.68
WeatherBright21.399.0543.0633.5536.4223.1827.6651.7625.22
Dark14.0016.6915.5818.487.8414.1213.3322.038.94
Fog10.3011.1515.2315.0215.5810.7811.7312.994.47
Frost7.129.5411.219.622.826.1410.1911.064.21
Snow6.464.7711.1910.427.559.3614.3312.374.75
NoiseGaussian9.178.987.453.102.155.9711.1313.805.23
Impulse9.179.018.112.082.035.6510.5614.915.55
Shot8.5810.558.480.712.274.5111.2615.606.24
BlurZoom18.8521.4426.5721.6815.8918.9523.5231.1012.90
Motion22.0724.8731.1930.1719.2424.5527.5640.5217.22
Defocus18.6417.6521.5721.278.7917.0119.0917.076.55
FailureCrash22.3016.6221.9616.2116.1923.2321.0832.0213.61
ColorQuant26.0121.0341.4835.0933.6825.8633.2748.1323.60
Alignment Tempormis29.7428.0547.9139.3138.7533.3836.8549.2835.68
APcor↑15.9914.9622.2118.3414.9415.9119.4026.6212.44
+ +![](images/05f24236350c580dd73bb26c42396388afa4ac234f56dda8461e23f6e551b751.jpg) +(a) $\mathrm{AP}_{\text {clean }}$ vs. $\mathrm{AP}_{\text {cor }}$ + +![](images/b4544cb76a25327663fef6f934256369a76890b5bbd133275e3bc131e1967830.jpg) +(b) $\mathrm{AP}_{\text {clean }}$ vs.mRCE + +![](images/cc55dfed577bde39a2d1b40d793130791cc27eb0dfce8e96561483555545c1ef.jpg) +(c) $\mathrm{AP}_{\text {clean }}$ vs.mPosC + +![](images/8889b8c5b3238ab25547335dec715126d13375861b7c6bb6803908d28496e65a.jpg) +(d) $\mathrm{AP}_{\text {clean }}$ vs.mNegC + +![](images/ed00ca8c3d0a1a8d5121feeb0caa0e5ea62501aa71b171f31c7d2ab49de0dc3d.jpg) +Figure 3. The relationships between baseline performance $(\mathrm{AP}_{clean})$ and various metrics, including collaborative robustness $(\mathrm{AP}_{cor}$ , mRCE), collaborative compensation (mPosC) and collaborative disruption (mNegC). +Figure 4. The corrupted average precision $(\mathrm{AP}_c)$ of existing methods across five severity levels of corruption. + +comprehensive robustness evaluation, we also include three non-learning baseline methods: Max, which directly maximizes the feature map for collaboration; Late, which fuses final predictions shared from CAVs; and NoFusion, representing the ego vehicle perception model without collaboration. The NoFusion model is further used to compute the PosC and NegC metrics as defined in Eq. 3 and Eq. 4. + +# 4.2. Benchmarking Results for Global Interference + +Single Corruption: The performance of collaborative perception models under various corruption types is presented + +in Table 1, with results across different corruption severity levels shown in Fig. 4. The results indicate that existing models experience varying levels of performance degradation depending on the corruption type, with conditions like snow, frost, and noise having particularly severe impacts. The NoFusion model consistently performs the worst, showing significantly lower $\mathrm{AP}_{cor}$ across all corruption types, underscoring the limitations of single-vehicle perception. Interestingly, the simple Max fusion method outperforms several more complex models in interference scenarios, suggesting that increased model complexity does not necessarily lead to improved robustness against interference. Moreover, the Late fusion methods demonstrate greater adaptability and robustness compared to existing intermediate feature fusion techniques. + +To further understand the relationship between baseline performance and robustness, we analyze the results in Fig. 3a. The findings suggest that models with higher baseline performance may handle disturbances better, likely due to more robust feature extraction. Similarly, Fig. 3b shows a positive correlation between a model's mRCE and its clean-data performance, indicating that higher-performing models may also experience larger relative performance drops under corruption. With mRCE values generally between $55\%$ and $70\%$ , current models exhibit suboptimal robustness, underscoring the need for further improvement. + +Multiple Corruptions: As shown in Fig. 5, different types + +![](images/6538bc1b07f08f4d54d645c544ce4ed84b04e7a36216efcedcef02851632871b.jpg) +Figure 5. Radar charts for CoBEVT [51] and AttFuse [53] showing performance under single corruptions (labeled as "Cor" in the figure) and multiple corruptions that include additional temporal misalignment (labeled as "Time" in the figure). + +![](images/10b1b960c0884413acc9e23ddd386fe2c47a14867bb482f426156ac84cb6d5c1.jpg) + +![](images/2f7ec168eda1e227a6ce8722d8c34e7996bf8cd96e0b80749367eda76e68a4a5.jpg) +Figure 6. Results of V2VNet [46] and DiscoNet [29] in terms of $\mathrm{AP}_{cor}$ under heterogeneous corruptions between Ego and CAVs. + +![](images/2ee86394488809d0a924e3fe430a370959d9bfdb8f3da22ebaca19d68e69f0dc.jpg) + +of corruptions have varying impacts on CoBEVT [51] and AttFuse [53], with noise and frost disturbances causing the most significant performance degradation. Adding temporal misalignment to these camera corruptions further intensifies the effects of disturbances such as brightness, motion, and quantization. These results suggest that, in real-world scenarios, the simultaneous occurrence of multiple disturbances presents even greater challenges for model robustness. Please refer to the appendix for more results. + +Hetero Corruptions: Fig. 6 shows that corruptions impact the Ego vehicle more severely than the CAVs in both DiscoNet [29] and V2VNet [46]. When the Ego vehicle is "Clean", the system performs effectively despite various "CAV corruption" conditions. However, when both Ego and CAVs are subjected to different types of disturbances, the model's performance declines significantly, particularly when one of them experiences crash corruption, which has the most pronounced impact on overall system performance. More results are included in the appendix. + +New Scenes with Corruption: While collaborative perception models are typically evaluated in familiar environments, real-world deployment demands robustness in diverse, unseen scenes. Table 2 evaluates the model performance in familiar OPV2V scenes (Default) versus previously unseen scenes (Culver). The $\mathrm{AP}_{\text {clean }}$ performance of V2X-ViT [52] declines by $47.8\%$ , indicating that the scene variation significantly impacts model effectiveness. When disturbances and new scenes occur simultaneously, perfor + +Table 2. Performance comparison in the familiar OPV2V scenes (Default) versus the unseen new scenes (Culver). + +
ModelAPclean↑APcor↑mRCE↓
DefaultCulverDefaultCulverDefaultCulver
AttFuse37.1319.48(↓47.5%)14.937.29(↓51.2%)41.5141.93(↑1.0%)
F-Cooper34.8526.52(↓23.9%)13.958.58(↓38.5%)37.5448.25(↑28.5%)
V2X-ViT58.6130.62(↓47.8%)20.249.11(↓55.0%)46.9451.38(↑9.5%)
DiscoNet47.3428.66(↓39.5%)16.728.31(↓50.3%)49.9453.65(↑7.4%)
V2VNet46.6426.80(↓42.5%)13.116.79(↓48.3%)53.8656.96(↑5.8%)
CoBEVT40.4923.97(↓40.8%)14.567.10(↓51.2%)46.4249.39(↑6.4%)
Max45.8724.97(↓45.6%)18.057.56(↓58.1%)41.9047.95(↑14.4%)
+ +mance drops further, with $\mathrm{AP}_{cor}$ decreasing by $55\%$ and RCE increasing by $9.5\%$ . These results highlight the challenges that current collaborative methods encounter in handling disturbed environments with unfamiliar scenes. + +# 4.3. Benchmarking Results for Ego Interference + +When the ego vehicle encounters unique corruptions, uncorrupted data from collaborators can offer collaborative compensation. Table 3 verifies this through $\mathrm{PosC}_c$ and mPosC metrics. Results indicate that the simple Late fusion significantly enhances mPosC compared to other intermediate fusion methods, suggesting that complex fusion models (e.g., attention-based [51-53], graph-based [29, 46]) are effective only when the ego vehicle captures essential information. The compensation stability varies across models and disturbances: V2X-ViT [52] and V2VNet [46] show fluctuations, whereas F-Cooper [4] and CoBEVT [51] exhibit more consistency. Fig. 3c further reveals a positive correlation between collaborative compensation mPosC and baseline performance $\mathrm{AP}_{clean}$ , suggesting that models with higher baseline results provide stronger compensatory support. + +# 4.4. Benchmarking Results for CAV Interference + +In scenarios where collaborative vehicles experience unique corruptions not directly affecting the ego vehicle, shared data from these vehicles can introduce "collaborative disruption." Table 3 presents the $\mathrm{NegC}_c$ and mNegC metrics to quantify this effect. A NegC value over $100\%$ indicates that corrupted data from collaborators degrades the ego vehicle's performance. The results show that the Late fusion is less vulnerable to these disruptions and often provides positive benefits even under corruption, while intermediate feature fusion methods tend to reduce performance. Additionally, Fig. 3d shows that higher baseline performance $(\mathrm{AP}_{clean})$ correlates with reduced collaborative disruption, suggesting that models with stronger baseline performance may better handle corrupted collaborative data. + +# 5. RCP-Drop & RCP-Mix + +To enhance robustness under various corruption scenarios, we develop two simple yet effective strategies specifically for collaborative perception: RCP-Drop and RCP-Mix. + +Dropout [1, 8] is a widely used regularization technique in deep learning, aimed at reducing model overfitting by + +Table 3. Benchmarking results for Ego Interference and CAV Interference on OPV2V-C. We report collaborative compensation and disruption performance under each corruption type, including $\mathrm{NegC}_c$ and $\mathrm{PosC}_c$ , as well as averages across all corruption types, mNegC and mPosC. Results are evaluated based on AP@0.5. Further details are available in the appendix. + +
Cor TypesAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLate
NegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCc
Bright121.278.54115.979.6886.6828.9095.7718.29103.0327.29107.826.24108.7120.6882.4550.82
Dark126.7312.96122.2821.77104.2414.80109.5918.68127.296.43116.0014.97121.5222.1499.9150.81
Zoom117.6319.66116.4321.7493.7229.29100.9620.66107.6223.63107.9817.63104.6825.4188.5051.99
Motion116.6721.12115.5222.5094.5025.8499.3322.52117.469.83106.1919.19102.8325.6790.3051.09
Defocus118.1725.27116.8724.6299.4727.14106.2020.90121.3010.81107.8218.68107.8027.13101.5550.36
Gaussian127.3213.30122.7315.47112.3910.16115.0212.32123.355.81117.9311.545115.8424.7199.7550.83
Impulse127.0415.75122.9814.94112.0611.78115.1311.82123.215.62117.8611.11115.3324.3399.5350.84
Shot126.8713.12122.0117.78112.339.86115.3911.64123.825.95118.1711.81114.0425.7099.8950.82
Crash116.2222.35115.7320.5197.5013.75107.0410.67112.5811.98105.0518.96108.1224.2191.5350.14
Quant118.0317.63113.9122.4999.8622.6998.6021.65110.0020.66110.0012.82110.1425.8398.7648.70
mNegC↓/mPosC↑121.5916.97118.4419.15101.2719.42106.3116.92116.9712.80111.4814.29110.9024.5895.2250.64
+ +![](images/fe7e4b8538757983b82543101f111bc83269e1afd29901788ba314667c5bddce.jpg) +Figure 7. Overview of the RCP-Drop & RCP-Mix strategies. + +randomly dropping features within certain network layers or blocks during training. In the collaborative perception context, the ego vehicle may encounter incomplete shared perceptual data from CAVs due to communication failures, or CAVs leaving the collaborative queue. Existing collaborative perception models, while beneficial in multi-vehicle setups, often underperform in single-vehicle scenarios due to their learned dependency on supplementary data from other vehicles. To prevent models from being overly reliant on CAVs data and to better equip them for single-vehicle operation, as shown in Fig. 7 we introduce RCP-Drop, which simulates these conditions by selectively discarding information from certain CAVs. Technically, it is defined as: + +$$ +F _ {a g g} ^ {e g o} = \mathcal {A} \left(F ^ {e g o}, \left\{\mathbb {1} \left(p _ {i} < p _ {d r o p}\right) \cdot F _ {i} ^ {c a v} \right\} _ {i = 1} ^ {N}\right), \tag {5} +$$ + +where $F^{ego}$ represents the feature originating from the ego vehicle, $F_{agg}^{ego}$ denotes the aggregated feature after perception information exchange, and $F_{i}^{cav}$ is the feature map shared from the $i$ -th collaborative vehicle. Here, $\mathcal{A}$ is a specific feature fusion function developed in existing methods [29, 44, 53], $p_i$ is sampled from a uniform distribution between 0 and 1, and $p_{drop}$ is the threshold determining whether data from each collaborative vehicle is discarded. + +Rather than keeping the threshold fixed during training, we develop a dynamic adjustment strategy for $p_{drop}$ . Specifically, we start with a high dropout probability, which reduces the number of participating collaborative vehicles and enhances the single-vehicle backbone's feature extraction capabilities. Gradually, we lower the dropout probability to increase the participation of collaborative vehicles, optimizing the collaborative perception performance over time. In this study, we set $p_{drop} = 1.0 - (t / T)^2$ , where $t$ and $T$ are the current and maximum training epoch. + +Existing research shows that visual data can be char + +Table 4. Efficacy of RCP-Drop and RCP-Mix on collaborative robustness, collaborative compensation and collaborative disruption. + +
APclean↑mAPcor↑mNegC↓mPosC↑
CoBEVT [51]40.4915.91111.4814.29
+BN [39]42.7427.87112.9418.28
+BN+RCP-Mix48.2531.83109.1123.44
+BN+RCP-Drop47.8430.68109.4520.07
AttFuse [53]37.1315.99121.5916.97
+BN [39]36.1322.35126.0418.85
+BN+RCP-Mix43.1228.85114.9722.51
+BN+RCP-Drop45.1827.56115.6418.17
+ +acterized by feature statistics (i.e., the mean and standard deviation of feature maps). For the same semantic concepts, distinct styles (such as variations in color and texture) correspond to different feature statistics. Inspired by Mixstyle [64, 65], we propose RCP-Mix to enhance model adaptability to varied environmental conditions and styles encountered in collaborative perception. Unlike Mixstyle, which performs random feature statistic mixing across instances within a mini-batch, RCP-Mix probabilistically combines feature statistics between the ego vehicle and collaborating CAVs. Technically, RCP-Mix is defined as: + +$$ +\mu_ {a l l} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mu_ {i}; \quad \sigma_ {a l l} = \frac {1}{N} \sum_ {i = 1} ^ {N} \sigma_ {i}, +$$ + +$$ +\mu_ {i} ^ {\text {m i x}} = \lambda \mu_ {i} + (1 - \lambda) \mu_ {\text {a l l}}, \tag {6} +$$ + +$$ +\sigma_ {i} ^ {m i x} = \lambda \sigma_ {i} + (1 - \lambda) \sigma_ {a l l}, +$$ + +$$ +F _ {i} ^ {m i x} = \frac {F _ {i} - \mu_ {i}}{\sigma_ {i}} * \sigma_ {i} ^ {m i x} + \mu_ {i} ^ {m i x}, +$$ + +where $\mu_{i}$ , $\sigma_{i}$ are the means and standard deviations of the feature map $F_{i}$ , $\lambda$ is the weight sampled from the Beta distribution, i.e., $\lambda \sim \text{Beta}(\alpha, \alpha)$ , we set $\alpha = 0.1$ by default. + +Experimental Analysis: We selected CoBEVT [51] and AttFuse [53] with online Batch Normalization (BN) Stats Adapt [39] as baselines, integrating them with our RCP-Drop and RCP-Mix strategies. Table 4 demonstrates that, despite their simplicity, both RCP-Drop and RCP-Mix effectively counteract performance degradation from data corruptions. In particular, for $\mathrm{AP}_{\text {clean }}$ , these strategies lead to substantial performance improvements compared to the marginal gains or occasional declines observed with the vanilla BN adapt. Moreover, across the three inter- + +Table 5. Ablation on the use of different backbone. + +
MethodbackboneWeatherBlurNoiseQuantCrashAPAPcor
Max○ResNet10111.7922.322.7722.8718.6435.1218.14
Max•EfficientNet-b015.4523.3910.9833.2721.0845.8718.05
V2X-ViT○ResNet10110.9024.6616.6328.7510.4146.2116.73
V2X-ViT•EfficientNet-b019.2526.458.0141.4821.9658.6120.24
+ +![](images/10a0f9576af382bbfbc0ba3c866e1f04ad63970bac809eeeb6253bb0acea0ff2.jpg) +Figure 8. Impact of different backbone sizes on model robustness. + +![](images/169726178e9aefa41dda1e365e6b9a906493f4b7171f6c77731d60c41249c265.jpg) + +![](images/4593dadf21bfb8c1ea3916a8b8dedd6bb6b1bd12af6b922adb05c510eaa17c1e.jpg) +Figure 9. Effect of CAV number on model robustness. + +![](images/22ecded2dd94e7c1ab9da9b21cf29d1c68b88c5e14b3b36ccabd8b1a84c30e9d.jpg) + +ference scenarios, Global Interference, Ego Interference, and CAV Interference, our RCP-Drop and RCP-Mix consistently show robust improvements in model resilience under corruption conditions $\left(\mathrm{AP}_{cor}\right)$ , collaborative compensation (mPosC), and reduced collaborative disruption (mNegC). These results further underline the efficacy of our approaches in maintaining model performance and collaborative stability in challenging conditions. + +# 6. Observation & Discussion + +In this section, we analyze and discuss the impact of various model configurations and techniques on robustness. + +Backbones: Table 5 compares the performance of different backbones, showing that models using EfficientNet-b0 outperform ResNet101 [22] in all conditions except noise disturbances. leading to its use as the backbone for all models in this study. Fig. 8 further compares AttFuse with various backbone sizes, revealing that larger backbones generally improve robustness. Notably, EfficientNetb0 and EfficientNet-b3 [21] show greater stability and robustness across multiple conditions, particularly excelling under "Noise" and "Crash" scenarios, while EfficientNetb2 performs poorly in these cases. + +Feature Fusion: Table 6 shows that multiscale fusion enhances model performance on clean datasets and improves robustness against various perturbations. Additionally, the simple Max Fusion demonstrates greater robustness than attention mechanisms, particularly under noisy conditions, suggesting that more complex mechanisms may be less ef + +Table 6. Ablation on the use of multiscale fusion. + +
MethodmultiscaleWeatherBlurNoiseQuantCrashAP\(AP_{cor}\)
Max○X15.4523.3910.9833.2721.0845.8718.05
Max●✓30.6534.9228.6149.8638.1565.3833.22
AttFuse○X11.8519.858.9726.0122.3037.1314.93
AttFuse●✓23.3631.909.0143.4330.0762.5824.08
+ +![](images/0eed31304ddb8694b985dbb1e956f9e7dd2033a64fbf5df919052006224ffa03.jpg) +Figure 10. Effect of camera number on model robustness. + +![](images/f2da14db78e21180b1488787562de78b70bd2f29643b07f934cd773a5ade3426.jpg) + +fective at mitigating certain types of perturbations. + +CAV and Camera Number: Fig. 9 shows that increasing the number of collaborative CAVs generally enhances model performance. Notably, two collaborating vehicles provide a significant improvement over a single vehicle; however, the rate of improvement diminishes once the number of collaborators exceeds four, indicating a diminishing marginal effect. Fig. 10 shows that as camera count increases, both model performance and robustness improve significantly, with a particularly notable boost from three to four cameras. + +# 7. Conclusion + +In this study, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of camera-based collaborative perception models under diverse real-world disturbances. RCP-Bench encompasses 14 corruption types at 5 severity levels across 3 large-scale datasets. We systematically evaluate three collaborative scenarios across six cases to assess robustness in the Global Interference scenario, explore collaborative advantages in the Ego Interference scenario, and examine disturbance risks in the CAV Interference scenario. To improve robustness, we propose two straightforward strategies, RCP-Drop and RCP-Mix, tailored for collaborative perception. Our analysis of backbone architecture, feature fusion, CAV number, and camera number provides key insights for enhancing model resilience. We hope this work offers valuable insights and inspires future research toward more robust collaborative perception models. + +Acknowledgment: This work was supported by the National Key Research and Development Program of China (No. 2024YFE0211000), in part by the National Natural Science Foundation of China (No. 62372329), in part by Shanghai Scientific Innovation Foundation (No. 23DZ1203400), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program. + +# References + +[1] Pierre Baldi and Peter J Sadowski. Understanding dropout. Advances in neural information processing systems, 26, 2013. 2, 6 +[2] Alexander Carballo, Jacob Lambert, Abraham Monrroy, David Wong, Patiphon Narksri, Yuki Kitsukawa, Eijiro Takeuchi, Shinpei Kato, and Kazuya Takeda. Libre: The multiple 3d lidar dataset. In 2020 IEEE intelligent vehicles symposium (IV), pages 1094-1101. 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Bm2cp: Efficient collaborative perception with lidar-camera modalities. arXiv preprint arXiv:2310.14702, 2023. 4 +[64] Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang. Domain generalization with mixstyle. In International Conference on Learning Representations (ICLR), 2021. 2, 7 +[65] Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang. Mixstyle neural networks for domain generalization and + +adaptation. International Journal of Computer Vision, 132 (3):822-836, 2024. 2, 7 +[66] Yang Zhou, Jiuhong Xiao, Yue Zhou, and Giuseppe Loianno. Multi-robot collaborative perception with graph neural networks. IEEE Robotics and Automation Letters, 7(2):2289-2296, 2022. 1 +[67] Zijian Zhu, Yichi Zhang, Hai Chen, Yinpeng Dong, Shu Zhao, Wenbo Ding, Jiachen Zhong, and Shibao Zheng. Understanding the robustness of 3d object detection with bird's-eye-view representations in autonomous driving. 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However, existing studies often assume ideal conditions, overlooking resilience to real-world challenges, such as adverse weather and sensor malfunctions, which is critical for safe deployment. To address this gap, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of collaborative detection models under a wide range of real-world corruptions. RCP-Bench includes three new datasets (i.e., OPV2V-C, V2XSet-C, and DAIR-V2X-C) that simulate six collaborative cases and 14 types of camera corruption resulting from external environmental factors, sensor failures, and temporal misalignments. Extensive experiments on 10 leading collaborative perception models reveal that, while these models perform well under ideal conditions, they are significantly affected by corruptions. To improve robustness, we propose two simple yet effective strategies, RCP-Drop and RCP-Mix, based on training regularization and feature augmentation. Additionally, we identify several critical factors influencing robustness, such as backbone architecture, camera number, feature fusion methods, and the number of connected vehicles. We hope that RCP-Bench, along with these strategies and insights, will stimulate future research toward developing more robust collaborative perception models. Our benchmark toolkit is available at https://github.com/LuckyDush/RCP-Bench." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "spans": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 598, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 296, + 696 + ], + "type": "text", + "content": "Perception is a fundamental capability for robots and autonomous vehicles to accurately interpret their surroundings. Despite significant advancements in perception tasks through deep learning, including object detection [3, 68] and segmentation [19, 27], single-vehicle perception using onboard sensors still faces inherent limitations, such as restricted range, limited field of view, and vulnerability to occlusions [17, 30, 50], resulting in blind spots that hinder full" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 230, + 426, + 321 + ], + "blocks": [ + { + "bbox": [ + 326, + 230, + 426, + 321 + ], + "lines": [ + { + "bbox": [ + 326, + 230, + 426, + 321 + ], + "spans": [ + { + "bbox": [ + 326, + 230, + 426, + 321 + ], + "type": "image", + "image_path": "4bc97b7669566de260976936c51864417858c4b405d5beb9155cad444fc52538.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 431, + 230, + 541, + 321 + ], + "blocks": [ + { + "bbox": [ + 431, + 230, + 541, + 321 + ], + "lines": [ + { + "bbox": [ + 431, + 230, + 541, + 321 + ], + "spans": [ + { + "bbox": [ + 431, + 230, + 541, + 321 + ], + "type": "image", + "image_path": "df586b328085b8f7394033b2cb1f86cbc8d1f78aa00c32488254a90d15875cd3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 326, + 323, + 426, + 411 + ], + "blocks": [ + { + "bbox": [ + 326, + 323, + 426, + 411 + ], + "lines": [ + { + "bbox": [ + 326, + 323, + 426, + 411 + ], + "spans": [ + { + "bbox": [ + 326, + 323, + 426, + 411 + ], + "type": "image", + "image_path": "3c7c7bf465618c359dc71debcdb93a862cd5672f75e3ccaca164b39abbe65263.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 335, + 416, + 409, + 426 + ], + "lines": [ + { + "bbox": [ + 335, + 416, + 409, + 426 + ], + "spans": [ + { + "bbox": [ + 335, + 416, + 409, + 426 + ], + "type": "text", + "content": "or Ego Cor/Clean" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 313, + 429, + 555, + 502 + ], + "lines": [ + { + "bbox": [ + 313, + 429, + 555, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 555, + 502 + ], + "type": "text", + "content": "Figure 1. Comparison of collaborative object detection results (averaged across 10 leading methods) in OPV2V-C across three interference scenarios: Global, Ego, and CAV Interference. The results indicate that perception models are particularly vulnerable to Global Interference, benefit from collaborative compensation under Ego Interference, and experience performance degradation under CAV Interference." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 434, + 323, + 541, + 411 + ], + "blocks": [ + { + "bbox": [ + 434, + 323, + 541, + 411 + ], + "lines": [ + { + "bbox": [ + 434, + 323, + 541, + 411 + ], + "spans": [ + { + "bbox": [ + 434, + 323, + 541, + 411 + ], + "type": "image", + "image_path": "4d442d202d42f99483db21fca77b678a162e35eaa693541e3830ff02a73b9574.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 417, + 417, + 491, + 426 + ], + "lines": [ + { + "bbox": [ + 417, + 417, + 491, + 426 + ], + "spans": [ + { + "bbox": [ + 417, + 417, + 491, + 426 + ], + "type": "text", + "content": "or CAV Cor/Clean" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 500, + 417, + 536, + 426 + ], + "lines": [ + { + "bbox": [ + 500, + 417, + 536, + 426 + ], + "spans": [ + { + "bbox": [ + 500, + 417, + 536, + 426 + ], + "type": "text", + "content": "X No CAV" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 509, + 555, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 581 + ], + "type": "text", + "content": "environmental understanding [5]. Collaborative perception, where perception data are shared among Connected Autonomous Vehicles (CAVs), has shown promise in overcoming these challenges. By leveraging multiple viewpoints, collaborative perception extends perceptual range, enhances spatial coverage, and improves resilience to occlusions [16]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": "Numerous studies have investigated practical challenges that may impact collaborative performance, such as bandwidth limitations for shared information [15, 32, 33, 44], transmission issues [26, 38, 47, 60], pose estimation errors [24, 34, 43, 66], and heterogeneity among cooperating vehicles [28, 48, 55]. However, current models and evaluations generally assume idealized conditions, such as clear weather and fully functional sensors. In real-world driving scenarios, adverse conditions such as external weather [9, 10, 18] and sensor failures [2, 12] are unavoidable. Although recent efforts address individual robustness" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 231, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 231, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 231, + 713 + ], + "type": "text", + "content": "*Corresponding author: guangchen@tongji.edu.cn" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11908" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "challenges, including communication delays [23, 36] and diverse weather conditions [14, 25], a comprehensive assessment of robustness for collaborative perception in real-world scenarios remains an important open challenge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 289 + ], + "type": "text", + "content": "To bridge this gap, we introduce RCP-Bench, the first benchmark designed to systematically evaluate the reliability of collaborative perception methods under a wide range of corruptions. Specifically, RCP-Bench comprises three new datasets, including OPV2V-C, V2XSet-C and DAIR-V2X-C. These datasets simulate six distinct cases and incorporate 14 types of corruption, incorporating variations in weather conditions, sensor noise or failures, and temporal misalignments, as depicted in Fig. 2. Given that collaborative perception depends on data shared across collaborating CAVs, where corruptions in individual vehicles can propagate throughout the collaborative process, creating diverse and challenging scenarios. RCP-Bench provides a holistic assessment by evaluating robustness across three aspects:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 289, + 295, + 397 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 289, + 295, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 295, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 295, + 326 + ], + "type": "text", + "content": "- Global Interference: Both the ego vehicle and collaborating CAVs are affected by diverse corruptions, testing the overall robustness of collaborative perception." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 326, + 295, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 326, + 295, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 326, + 295, + 361 + ], + "type": "text", + "content": "- Ego Interference: Only the ego vehicle experiences corruption, assessing the compensatory advantages of collaboration over single-vehicle perception." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 361, + 295, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 295, + 397 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 295, + 397 + ], + "type": "text", + "content": "- CAV Interference: Only the collaborating CAVs are subject to corruptions, evaluating the risk of disruptions compared to single-vehicle perception." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 399, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 295, + 590 + ], + "type": "text", + "content": "Leveraging RCP-Bench, we conduct extensive experiments on 10 collaborative perception models. As shown in Fig. 1, while these models perform well under ideal conditions, their performance significantly degrades in the presence of corruptions. To enhance the robustness, we propose two straightforward strategies tailored for collaborative perception: RCP-Drop and RCP-Mix. Unlike traditional methods [1, 8] that drop features within specific network layers or blocks during training, RCP-Drop operates by randomly discarding data from selected collaborating vehicles, effectively simulating real-world data loss encountered in communication-limited or sensor-failure scenarios. RCP-Mix, inspired by MixStyle [64, 65], probabilistically combines feature statistics, i.e., the means and standard deviations of feature maps, between the ego vehicle and collaborating CAVs, promoting resilience to distribution shifts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 591, + 266, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 591, + 266, + 601 + ], + "spans": [ + { + "bbox": [ + 67, + 591, + 266, + 601 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 603, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 55, + 603, + 295, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 603, + 295, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 603, + 295, + 639 + ], + "type": "text", + "content": "- We introduce RCP-Bench, the first benchmark systematically evaluating collaborative perception robustness across diverse real-world corruptions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 639, + 295, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 639, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 639, + 295, + 675 + ], + "type": "text", + "content": "- We conduct a comprehensive evaluation of 10 leading collaborative perception models across six scenarios, covering 14 corruption types." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 675, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 675, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 675, + 295, + 712 + ], + "type": "text", + "content": "- We propose two novel strategies to enhance the robustness of collaborative perception models and highlight key factors affecting resilience." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 402, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 402, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 402, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 91, + 553, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 319 + ], + "type": "text", + "content": "Collaborative Perception: Collaborative perception [5, 6, 16, 34, 40, 54, 56, 58, 61, 62] allows vehicles to share perceptual data with connected vehicles, realizing a more comprehensive understanding of the surrounding environment. Existing studies have proposed various techniques to enhance perception performance [42]. For example, Who2com [33] and When2com [32] propose strategies for selecting collaborators and determining the timing of collaboration. Where2comm [15] and What2comm [57] introduce methods for selecting relevant information to be shared. UMC [44] enhances spatiotemporal continuity in collaborative perception by leveraging historical data and multi-scale feature fusion. CoBEVT [51] enables real-time collaborative semantic segmentation by capturing sparse local and global spatial interactions across views and agents. Nevertheless, most of these methods assume ideal conditions, addressing robustness under diverse and challenging conditions remains essential to advancing collaborative perception reliability in practice." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 319, + 553, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 553, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 553, + 594 + ], + "type": "text", + "content": "Robustness against Corruptions: Perception models are often vulnerable to various sensor corruptions, which can compromise their effectiveness in real-world applications. To evaluate and improve robustness under such conditions, several benchmarks have been developed. ImageNet-C [12] is the first public benchmark to assess object recognition models under a range of corruptions, including noise, blur, adverse weather, and digital interference. For object detection, Michaelis et al. [35] introduce three benchmarks to examine robustness against similar impairments. Recently, benchmarks tailored to driving scenarios have emerged. RoboDepth [20] assesses robustness in monocular depth estimation under corrupted conditions, while RoboBEV [49] introduces a comprehensive benchmark for evaluating BEV perception tasks. Similarly, MapBench [11] is designed to test the robustness of high-definition mapping methods against various sensor corruptions. Although these benchmarks have advanced robustness assessments in single-vehicle perception, they do not account for multi-agent contexts where corruptions may propagate, compounding effects across interconnected systems. Developing collaborative perception specific benchmarks is crucial for evaluating and improving robustness in these multi-vehicle scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 553, + 713 + ], + "type": "text", + "content": "Robustness in Collaborative Perception: With the advancement of collaborative perception research [13, 31, 37, 45], increasing attention is being paid to robustness and safety, especially concerning communication challenges between cooperating agents. These challenges include issues in data transmission, such as information loss during communication [26] and communication interruptions [38], timing issues like delays [23, 47, 60] and the reception of outdated or missing collaborative information. While these studies have highlighted potential pitfalls within the collab" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11909" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 53, + 550, + 296 + ], + "blocks": [ + { + "bbox": [ + 59, + 53, + 550, + 296 + ], + "lines": [ + { + "bbox": [ + 59, + 53, + 550, + 296 + ], + "spans": [ + { + "bbox": [ + 59, + 53, + 550, + 296 + ], + "type": "image", + "image_path": "aa5928269343b93675c42739cc8a50a6d33ea44f155602489dbe04e91c67aa79.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 297, + 555, + 361 + ], + "lines": [ + { + "bbox": [ + 55, + 297, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 555, + 361 + ], + "type": "text", + "content": "Figure 2. Definitions of corruption types and evaluation scenarios in RCP-Bench. Our benchmark includes 14 types of camera corruptions, classified into three categories: External Weather, Camera Interior, and Temporal Misalignment. To comprehensively evaluate robustness, we define three interference scenarios: Global Interference (corruptions affecting both the ego vehicle and collaborative vehicles), Ego Interference (corruptions specific to the ego vehicle), and CAV Interference (corruptions isolated to one or more collaborative vehicles). Within the Global Interference scenario, we further examine four cases: Single Corruption, Multiple Corruptions, Heterogeneous Corruptions, and New Scenes with Corruption." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 364, + 297, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 364, + 297, + 521 + ], + "spans": [ + { + "bbox": [ + 54, + 364, + 297, + 521 + ], + "type": "text", + "content": "orative process itself, robustness under diverse environmental and sensor conditions remains underexplored. Recently, a few studies have begun to examine collaborative performance under adverse environmental conditions [14, 25]. Nevertheless, these efforts are primarily limited to extreme sensor failures, without systematically analyzing the benefits and resilience of collaboration across a wider range of realistic sensor corruptions. To the best of our knowledge, this paper is the first to comprehensively examine the robustness and advantages of different collaborative states under diverse sensor corruptions, thereby providing an empirical basis for assessing and improving collaborative perception robustness across various real-world challenges." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 531, + 132, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 531, + 132, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 531, + 132, + 544 + ], + "type": "text", + "content": "3. RCP-Bench" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 552, + 167, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 167, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 167, + 564 + ], + "type": "text", + "content": "3.1. Benchmark Design" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "text", + "content": "Collaborative perception relies on information collected by both the ego vehicle and surrounding connected autonomous vehicles (CAVs), each contributing to the final perception outcome. To rigorously evaluate the benefits of shared information and assess model robustness under various corruptions, this study isolates these two information sources and defines three corruption scenarios, as shown in Fig. 2: (1) Global Interference scenario affecting both the ego vehicle and CAVs simultaneously, (2) Ego Interference scenario specific to the ego vehicle, and (3) CAV Interference scenario isolated to one or more CAVs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "Given mutual interference among CAVs, independent" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 364, + 555, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 555, + 555 + ], + "type": "text", + "content": "control of lidar-based corruptions is impractical; therefore, this study focuses exclusively on camera-based corruptions. We categorize these into three groups based on real-world conditions: (1) External environmental factors, like rain, fog, or light; (2) Internal camera issues, such as lens scratches or sensor degradation; (3) Misalignment in capture timing, such as temporal desynchronization between the ego and CAV cameras. We identify 14 distinct types of corruption, following the methodology in [7], and divide each type into five severity levels, resulting in 70 unique corruption conditions. To evaluate collaborative perception model robustness, we create three corruption benchmarks using widely used datasets: DAIR-V2X [59], OPV2V [53], and V2XSet [52]. These corruptions are introduced into the validation sets, producing modified versions: DAIR-V2XC, OPV2V-C, and V2XSet-C." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 564, + 476, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 476, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 476, + 577 + ], + "type": "text", + "content": "3.2. Typical Corruption Scenarios" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "content": "Global Interference: In practical applications, it is common for corruptions to affect both the ego vehicle and collaborative vehicles simultaneously. To evaluate model robustness across various types of corruption, we first assess 14 distinct corruptions individually, referring to this as the Single Corruption case. To better reflect real-world complexity, we further define three combined corruption cases. The first, Multiple Corruptions, involves multiple types of corruptions occurring concurrently. For simplicity, we focus on situations where temporal misalignment coincides with either external weather conditions or internal camera" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11910" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": "issues. In the second case, *Heterogeneous Corruptions*, the types of corruption affecting the ego vehicle differ from those impacting the collaborative vehicles, allowing us to examine situations with varying corruption profiles across vehicles. Finally, in the *New Scenes with Corruption* case, we extend prior research on the generalization of collaborative perception by analyzing performance when corruptions are introduced simultaneously in unfamiliar environments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 169, + 295, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 169, + 295, + 336 + ], + "spans": [ + { + "bbox": [ + 55, + 169, + 295, + 336 + ], + "type": "text", + "content": "Ego Interference: In real-world scenarios, the ego vehicle may experience unique corruptions that do not affect nearby collaborative vehicles, presenting an opportunity to use uncorrupted data from these vehicles as a compensatory mechanism. To explore this potential, we introduce the concept of \"collaborative compensation.\" Here, when the ego vehicle encounters interference or corruption, we investigate whether reliable information from neighboring collaborative vehicles can help mitigate or even correct these effects. Since some forms of interference, such as adverse weather, are unavoidable and impact all vehicles, we specifically focus on evaluating the advantages of collaborative compensation for the remaining ten types of corruption that are unique to the ego vehicle." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 337, + 295, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 295, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 295, + 482 + ], + "type": "text", + "content": "CAV Interference: Similar to Ego Interference, collaborative vehicles may experience unique corruptions that do not directly affect the ego vehicle, creating a potential risk rather than a benefit. To examine this, we introduce the concept of \"collaborative disruption.\" In this scenario, we investigate whether corrupted data from surrounding collaborative vehicles can degrade the perception performance of an otherwise well-functioning ego vehicle. This analysis provides insights into the robustness of collaborative perception systems, highlighting the potential adverse effects of relying on collaborative data when unintentional corruptions are present in the shared information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 491, + 168, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 168, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 168, + 502 + ], + "type": "text", + "content": "3.3. Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "text", + "content": "In evaluating 3D object detection performance, Average Precision (AP) is commonly used as the primary metric, particularly at Intersection-over-Union (IoU) thresholds of 0.3, 0.5, and 0.7. Building on the evaluation metrics proposed in [7, 41, 67], we introduce two metrics specifically designed to assess the robustness of cooperative perception systems: Corrupted Average Precision " + }, + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_{\\mathrm{cor}})" + }, + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "text", + "content": " and Relative Corruption Error (RCE). To further examine the effects of collaboration under Ego Interference and CAV Interference, we define \"Positive Collaborative\" and \"Negative Collaborative\", and introduce two additional metrics: the Positive Collaborative Coefficient (PosC) and the Negative Collaborative Coefficient (NegC). These four new evaluation metrics are primarily analyzed based on AP@0.5, additional results of AP@0.3 and AP@0.7 are provided in the appendix. Corrupted Average Precision: We denote the performance on the clean, uncorrupted test set as " + }, + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 55, + 509, + 295, + 713 + ], + "type": "text", + "content": ". For each cor" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "ruption type " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": " at each severity " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": ", the performance is measured as " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{c,l}" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": ". The corruption robustness, " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": " is then defined as the average performance across all corruption types and severity levels:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 345, + 121, + 553, + 151 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 121, + 553, + 151 + ], + "spans": [ + { + "bbox": [ + 345, + 121, + 553, + 151 + ], + "type": "interline_equation", + "content": "\\mathrm {A P} _ {c} = \\frac {1}{5} \\sum_ {l = 1} ^ {5} \\mathrm {A P} _ {c, l}, \\mathrm {A P} _ {c o r} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {A P} _ {c}, \\tag {1}", + "image_path": "31d240e086851da051776a5ed2a5534c70621aafc46ec9654ed51784112ede41.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 151, + 502, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 151, + 502, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 502, + 162 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 151, + 502, + 162 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 151, + 502, + 162 + ], + "type": "text", + "content": " is the set of corruptions in evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 163, + 553, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 553, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 553, + 222 + ], + "type": "text", + "content": "Relative Corruption Error: Since " + }, + { + "bbox": [ + 313, + 163, + 553, + 222 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{cor}}" + }, + { + "bbox": [ + 313, + 163, + 553, + 222 + ], + "type": "text", + "content": " measures only the absolute performance under corrupted conditions, we define Relative Corruption Error (RCE) as a relative indicator that quantifies the extent to which model performance is retained under corruption:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 324, + 224, + 553, + 252 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 224, + 553, + 252 + ], + "spans": [ + { + "bbox": [ + 324, + 224, + 553, + 252 + ], + "type": "interline_equation", + "content": "\\mathrm {R C E} _ {c} = \\frac {\\mathrm {A P} _ {c l e a n} - \\mathrm {A P} _ {c}}{\\mathrm {A P} _ {c l e a n}}, \\mathrm {m R C E} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {R C E} _ {c}. \\tag {2}", + "image_path": "74f78232a4d6637015e69e20aa793d97cea8a9b47651518bdeebcf572e4c3993.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 253, + 553, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 553, + 325 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 553, + 325 + ], + "type": "text", + "content": "Positive Collaborative Coefficient: To quantify the ability of collaborative information to mitigate corruptions affecting the ego vehicle under Ego Interference, we define the Positive Collaborative Coefficient (PosC), which measures how effectively the model leverages collaborative information from other vehicles to counteract corruptions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 323, + 327, + 553, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 327, + 553, + 357 + ], + "spans": [ + { + "bbox": [ + 323, + 327, + 553, + 357 + ], + "type": "interline_equation", + "content": "\\mathrm {P o s C} _ {c} = \\frac {\\mathrm {A P} _ {c , 5} - \\mathrm {A P} _ {c , 5} ^ {e g o}}{1 - \\mathrm {A P} _ {c , 5} ^ {e g o}}, \\mathrm {m P o s C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {P o s C} _ {c}, \\tag {3}", + "image_path": "3b517b02dc956f51aa287415c63a1eb114c54136ab58f4445c4437b521a6f398.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 358, + 553, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 553, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 553, + 393 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 358, + 553, + 393 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{c},5}^{\\mathrm{ego}}" + }, + { + "bbox": [ + 313, + 358, + 553, + 393 + ], + "type": "text", + "content": " represents the performance of the ego vehicle under a specific type of corruption at severity 5 in the absence of collaboration." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 395, + 553, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 553, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 553, + 455 + ], + "type": "text", + "content": "Negative Collaborative Coefficient: To assess the adverse impact of corrupted collaborative information under CAV Interference, we introduce the Negative Collaborative Coefficient (NegC), which quantifies the negative effects arising from collaborative perception:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 457, + 553, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 457, + 553, + 484 + ], + "spans": [ + { + "bbox": [ + 326, + 457, + 553, + 484 + ], + "type": "interline_equation", + "content": "\\mathrm {N e g C} _ {c} = \\frac {1 - \\mathrm {A P} _ {c , 5}}{1 - \\mathrm {A P} _ {\\text {c l e a n}} ^ {e g o}}, \\mathrm {m N e g C} = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\mathrm {N e g C} _ {c}, \\tag {4}", + "image_path": "92752340139de7ec3b1719dcdb9db72ed96dbb4e43db88368ae76434cf4fc954.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 486, + 553, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 486, + 553, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{clean}}^{\\mathrm{ego}}" + }, + { + "bbox": [ + 313, + 486, + 553, + 510 + ], + "type": "text", + "content": " denotes the perception performance of the ego vehicle using only its own clean, uncorrupted data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 521, + 446, + 535 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 446, + 535 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 446, + 535 + ], + "type": "text", + "content": "4. Benchmarking Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 542, + 553, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 553, + 579 + ], + "type": "text", + "content": "In this section, we primarily present the results on OPV2VC. Additional results for DAIR-V2X-C and V2XSet-C are provided in the appendix." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 587, + 422, + 601 + ], + "type": "text", + "content": "4.1. Benchmark Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "content": "Our RCP-Bench evaluates a total of 10 leading collaborative perception models and their variants for the detection task, including AttFuse [53], F-Cooper [4], V2X-ViT [52], DiscoNet [29], V2VNet [46], CoBEVT [51], and BM2CP [63]. To ensure a fair comparison, we use official model configurations and public checkpoints from open-source codebases where available or re-train the models using default settings if necessary. For each corruption type, we report metrics by averaging results across five severity levels. To provide a" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11911" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 86, + 549, + 235 + ], + "blocks": [ + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "lines": [ + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "type": "text", + "content": "Table 1. Benchmarking results for Global Interference on OPV2V-C. We report the performance under each corruption " + }, + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_c" + }, + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "type": "text", + "content": " and the overall corruption robustness " + }, + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 55, + 63, + 555, + 85 + ], + "type": "text", + "content": " averaged over all corruption types. The results are evaluated based on AP@0.5." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 86, + 549, + 235 + ], + "lines": [ + { + "bbox": [ + 58, + 86, + 549, + 235 + ], + "spans": [ + { + "bbox": [ + 58, + 86, + 549, + 235 + ], + "type": "table", + "html": "
CortypeAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLateNoFusion
APclean↑37.1334.8558.6147.3446.6440.4945.8768.4135.68
WeatherBright21.399.0543.0633.5536.4223.1827.6651.7625.22
Dark14.0016.6915.5818.487.8414.1213.3322.038.94
Fog10.3011.1515.2315.0215.5810.7811.7312.994.47
Frost7.129.5411.219.622.826.1410.1911.064.21
Snow6.464.7711.1910.427.559.3614.3312.374.75
NoiseGaussian9.178.987.453.102.155.9711.1313.805.23
Impulse9.179.018.112.082.035.6510.5614.915.55
Shot8.5810.558.480.712.274.5111.2615.606.24
BlurZoom18.8521.4426.5721.6815.8918.9523.5231.1012.90
Motion22.0724.8731.1930.1719.2424.5527.5640.5217.22
Defocus18.6417.6521.5721.278.7917.0119.0917.076.55
FailureCrash22.3016.6221.9616.2116.1923.2321.0832.0213.61
ColorQuant26.0121.0341.4835.0933.6825.8633.2748.1323.60
Alignment Tempormis29.7428.0547.9139.3138.7533.3836.8549.2835.68
APcor↑15.9914.9622.2118.3414.9415.9119.4026.6212.44
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The relationships between baseline performance " + }, + { + "bbox": [ + 55, + 354, + 555, + 376 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_{clean})" + }, + { + "bbox": [ + 55, + 354, + 555, + 376 + ], + "type": "text", + "content": " and various metrics, including collaborative robustness " + }, + { + "bbox": [ + 55, + 354, + 555, + 376 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 55, + 354, + 555, + 376 + ], + "type": "text", + "content": ", mRCE), collaborative compensation (mPosC) and collaborative disruption (mNegC)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 380, + 289, + 548 + ], + "lines": [ + { + "bbox": [ + 59, + 380, + 289, + 548 + ], + "spans": [ + { + "bbox": [ + 59, + 380, + 289, + 548 + ], + "type": "image", + "image_path": "ed00ca8c3d0a1a8d5121feeb0caa0e5ea62501aa71b171f31c7d2ab49de0dc3d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 551, + 295, + 572 + ], + "lines": [ + { + "bbox": [ + 55, + 551, + 295, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 551, + 295, + 572 + ], + "type": "text", + "content": "Figure 4. The corrupted average precision " + }, + { + "bbox": [ + 55, + 551, + 295, + 572 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_c)" + }, + { + "bbox": [ + 55, + 551, + 295, + 572 + ], + "type": "text", + "content": " of existing methods across five severity levels of corruption." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 575, + 295, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 295, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 295, + 660 + ], + "type": "text", + "content": "comprehensive robustness evaluation, we also include three non-learning baseline methods: Max, which directly maximizes the feature map for collaboration; Late, which fuses final predictions shared from CAVs; and NoFusion, representing the ego vehicle perception model without collaboration. The NoFusion model is further used to compute the PosC and NegC metrics as defined in Eq. 3 and Eq. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 670, + 295, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 670, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 670, + 295, + 685 + ], + "type": "text", + "content": "4.2. Benchmarking Results for Global Interference" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Single Corruption: The performance of collaborative perception models under various corruption types is presented" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 381, + 555, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 555, + 561 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 555, + 561 + ], + "type": "text", + "content": "in Table 1, with results across different corruption severity levels shown in Fig. 4. The results indicate that existing models experience varying levels of performance degradation depending on the corruption type, with conditions like snow, frost, and noise having particularly severe impacts. The NoFusion model consistently performs the worst, showing significantly lower " + }, + { + "bbox": [ + 313, + 381, + 555, + 561 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 313, + 381, + 555, + 561 + ], + "type": "text", + "content": " across all corruption types, underscoring the limitations of single-vehicle perception. Interestingly, the simple Max fusion method outperforms several more complex models in interference scenarios, suggesting that increased model complexity does not necessarily lead to improved robustness against interference. Moreover, the Late fusion methods demonstrate greater adaptability and robustness compared to existing intermediate feature fusion techniques." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "text", + "content": "To further understand the relationship between baseline performance and robustness, we analyze the results in Fig. 3a. The findings suggest that models with higher baseline performance may handle disturbances better, likely due to more robust feature extraction. Similarly, Fig. 3b shows a positive correlation between a model's mRCE and its clean-data performance, indicating that higher-performing models may also experience larger relative performance drops under corruption. With mRCE values generally between " + }, + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "inline_equation", + "content": "55\\%" + }, + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 313, + 566, + 556, + 697 + ], + "type": "text", + "content": ", current models exhibit suboptimal robustness, underscoring the need for further improvement." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 555, + 714 + ], + "type": "text", + "content": "Multiple Corruptions: As shown in Fig. 5, different types" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11912" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 171, + 194 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 171, + 194 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 171, + 194 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 171, + 194 + ], + "type": "image", + "image_path": "6538bc1b07f08f4d54d645c544ce4ed84b04e7a36216efcedcef02851632871b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 196, + 295, + 239 + ], + "lines": [ + { + "bbox": [ + 55, + 196, + 295, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 196, + 295, + 239 + ], + "type": "text", + "content": "Figure 5. Radar charts for CoBEVT [51] and AttFuse [53] showing performance under single corruptions (labeled as \"Cor\" in the figure) and multiple corruptions that include additional temporal misalignment (labeled as \"Time\" in the figure)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 71, + 288, + 194 + ], + "blocks": [ + { + "bbox": [ + 176, + 71, + 288, + 194 + ], + "lines": [ + { + "bbox": [ + 176, + 71, + 288, + 194 + ], + "spans": [ + { + "bbox": [ + 176, + 71, + 288, + 194 + ], + "type": "image", + "image_path": "10b1b960c0884413acc9e23ddd386fe2c47a14867bb482f426156ac84cb6d5c1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 244, + 175, + 350 + ], + "blocks": [ + { + "bbox": [ + 58, + 244, + 175, + 350 + ], + "lines": [ + { + "bbox": [ + 58, + 244, + 175, + 350 + ], + "spans": [ + { + "bbox": [ + 58, + 244, + 175, + 350 + ], + "type": "image", + "image_path": "2f7ec168eda1e227a6ce8722d8c34e7996bf8cd96e0b80749367eda76e68a4a5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "lines": [ + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "type": "text", + "content": "Figure 6. Results of V2VNet [46] and DiscoNet [29] in terms of " + }, + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 55, + 353, + 295, + 374 + ], + "type": "text", + "content": " under heterogeneous corruptions between Ego and CAVs." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 179, + 243, + 297, + 350 + ], + "blocks": [ + { + "bbox": [ + 179, + 243, + 297, + 350 + ], + "lines": [ + { + "bbox": [ + 179, + 243, + 297, + 350 + ], + "spans": [ + { + "bbox": [ + 179, + 243, + 297, + 350 + ], + "type": "image", + "image_path": "2ee86394488809d0a924e3fe430a370959d9bfdb8f3da22ebaca19d68e69f0dc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 378, + 295, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 295, + 485 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 295, + 485 + ], + "type": "text", + "content": "of corruptions have varying impacts on CoBEVT [51] and AttFuse [53], with noise and frost disturbances causing the most significant performance degradation. Adding temporal misalignment to these camera corruptions further intensifies the effects of disturbances such as brightness, motion, and quantization. These results suggest that, in real-world scenarios, the simultaneous occurrence of multiple disturbances presents even greater challenges for model robustness. Please refer to the appendix for more results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 487, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 295, + 605 + ], + "type": "text", + "content": "Hetero Corruptions: Fig. 6 shows that corruptions impact the Ego vehicle more severely than the CAVs in both DiscoNet [29] and V2VNet [46]. When the Ego vehicle is \"Clean\", the system performs effectively despite various \"CAV corruption\" conditions. However, when both Ego and CAVs are subjected to different types of disturbances, the model's performance declines significantly, particularly when one of them experiences crash corruption, which has the most pronounced impact on overall system performance. More results are included in the appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "text", + "content": "New Scenes with Corruption: While collaborative perception models are typically evaluated in familiar environments, real-world deployment demands robustness in diverse, unseen scenes. Table 2 evaluates the model performance in familiar OPV2V scenes (Default) versus previously unseen scenes (Culver). The " + }, + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\text {clean }}" + }, + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "text", + "content": " performance of V2X-ViT [52] declines by " + }, + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "inline_equation", + "content": "47.8\\%" + }, + { + "bbox": [ + 55, + 606, + 295, + 714 + ], + "type": "text", + "content": ", indicating that the scene variation significantly impacts model effectiveness. When disturbances and new scenes occur simultaneously, perfor" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 94, + 550, + 174 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 553, + 91 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 553, + 91 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 553, + 91 + ], + "type": "text", + "content": "Table 2. Performance comparison in the familiar OPV2V scenes (Default) versus the unseen new scenes (Culver)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 94, + 550, + 174 + ], + "lines": [ + { + "bbox": [ + 316, + 94, + 550, + 174 + ], + "spans": [ + { + "bbox": [ + 316, + 94, + 550, + 174 + ], + "type": "table", + "html": "
ModelAPclean↑APcor↑mRCE↓
DefaultCulverDefaultCulverDefaultCulver
AttFuse37.1319.48(↓47.5%)14.937.29(↓51.2%)41.5141.93(↑1.0%)
F-Cooper34.8526.52(↓23.9%)13.958.58(↓38.5%)37.5448.25(↑28.5%)
V2X-ViT58.6130.62(↓47.8%)20.249.11(↓55.0%)46.9451.38(↑9.5%)
DiscoNet47.3428.66(↓39.5%)16.728.31(↓50.3%)49.9453.65(↑7.4%)
V2VNet46.6426.80(↓42.5%)13.116.79(↓48.3%)53.8656.96(↑5.8%)
CoBEVT40.4923.97(↓40.8%)14.567.10(↓51.2%)46.4249.39(↑6.4%)
Max45.8724.97(↓45.6%)18.057.56(↓58.1%)41.9047.95(↑14.4%)
", + "image_path": "eb939dd491c9754146bfb2509f4e72393de501c69cfd4aefa5350a82f122dbed.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "text", + "content": "mance drops further, with " + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{cor}" + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "text", + "content": " decreasing by " + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "inline_equation", + "content": "55\\%" + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "text", + "content": " and RCE increasing by " + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "inline_equation", + "content": "9.5\\%" + }, + { + "bbox": [ + 313, + 179, + 553, + 228 + ], + "type": "text", + "content": ". These results highlight the challenges that current collaborative methods encounter in handling disturbed environments with unfamiliar scenes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 235, + 541, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 235, + 541, + 248 + ], + "spans": [ + { + "bbox": [ + 313, + 235, + 541, + 248 + ], + "type": "text", + "content": "4.3. Benchmarking Results for Ego Interference" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "text", + "content": "When the ego vehicle encounters unique corruptions, uncorrupted data from collaborators can offer collaborative compensation. Table 3 verifies this through " + }, + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "inline_equation", + "content": "\\mathrm{PosC}_c" + }, + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "text", + "content": " and mPosC metrics. Results indicate that the simple Late fusion significantly enhances mPosC compared to other intermediate fusion methods, suggesting that complex fusion models (e.g., attention-based [51-53], graph-based [29, 46]) are effective only when the ego vehicle captures essential information. The compensation stability varies across models and disturbances: V2X-ViT [52] and V2VNet [46] show fluctuations, whereas F-Cooper [4] and CoBEVT [51] exhibit more consistency. Fig. 3c further reveals a positive correlation between collaborative compensation mPosC and baseline performance " + }, + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{clean}" + }, + { + "bbox": [ + 313, + 251, + 555, + 432 + ], + "type": "text", + "content": ", suggesting that models with higher baseline results provide stronger compensatory support." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 439, + 545, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 439, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 439, + 545, + 452 + ], + "type": "text", + "content": "4.4. Benchmarking Results for CAV Interference" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "text", + "content": "In scenarios where collaborative vehicles experience unique corruptions not directly affecting the ego vehicle, shared data from these vehicles can introduce \"collaborative disruption.\" Table 3 presents the " + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "inline_equation", + "content": "\\mathrm{NegC}_c" + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "text", + "content": " and mNegC metrics to quantify this effect. A NegC value over " + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "text", + "content": " indicates that corrupted data from collaborators degrades the ego vehicle's performance. The results show that the Late fusion is less vulnerable to these disruptions and often provides positive benefits even under corruption, while intermediate feature fusion methods tend to reduce performance. Additionally, Fig. 3d shows that higher baseline performance " + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_{clean})" + }, + { + "bbox": [ + 313, + 456, + 555, + 624 + ], + "type": "text", + "content": " correlates with reduced collaborative disruption, suggesting that models with stronger baseline performance may better handle corrupted collaborative data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 633, + 450, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 450, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 450, + 647 + ], + "type": "text", + "content": "5. RCP-Drop & RCP-Mix" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": "To enhance robustness under various corruption scenarios, we develop two simple yet effective strategies specifically for collaborative perception: RCP-Drop and RCP-Mix." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 714 + ], + "type": "text", + "content": "Dropout [1, 8] is a widely used regularization technique in deep learning, aimed at reducing model overfitting by" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11913" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 97, + 555, + 209 + ], + "blocks": [ + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "lines": [ + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "type": "text", + "content": "Table 3. Benchmarking results for Ego Interference and CAV Interference on OPV2V-C. We report collaborative compensation and disruption performance under each corruption type, including " + }, + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "type": "inline_equation", + "content": "\\mathrm{NegC}_c" + }, + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "type": "inline_equation", + "content": "\\mathrm{PosC}_c" + }, + { + "bbox": [ + 55, + 63, + 555, + 95 + ], + "type": "text", + "content": ", as well as averages across all corruption types, mNegC and mPosC. Results are evaluated based on AP@0.5. Further details are available in the appendix." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 97, + 555, + 209 + ], + "lines": [ + { + "bbox": [ + 56, + 97, + 555, + 209 + ], + "spans": [ + { + "bbox": [ + 56, + 97, + 555, + 209 + ], + "type": "table", + "html": "
Cor TypesAttFuse [53]F-Cooper [4]V2X-ViT [52]DiscoNet [29]V2VNet [46]CoBEVT [51]MaxLate
NegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCcNegCcPosCc
Bright121.278.54115.979.6886.6828.9095.7718.29103.0327.29107.826.24108.7120.6882.4550.82
Dark126.7312.96122.2821.77104.2414.80109.5918.68127.296.43116.0014.97121.5222.1499.9150.81
Zoom117.6319.66116.4321.7493.7229.29100.9620.66107.6223.63107.9817.63104.6825.4188.5051.99
Motion116.6721.12115.5222.5094.5025.8499.3322.52117.469.83106.1919.19102.8325.6790.3051.09
Defocus118.1725.27116.8724.6299.4727.14106.2020.90121.3010.81107.8218.68107.8027.13101.5550.36
Gaussian127.3213.30122.7315.47112.3910.16115.0212.32123.355.81117.9311.545115.8424.7199.7550.83
Impulse127.0415.75122.9814.94112.0611.78115.1311.82123.215.62117.8611.11115.3324.3399.5350.84
Shot126.8713.12122.0117.78112.339.86115.3911.64123.825.95118.1711.81114.0425.7099.8950.82
Crash116.2222.35115.7320.5197.5013.75107.0410.67112.5811.98105.0518.96108.1224.2191.5350.14
Quant118.0317.63113.9122.4999.8622.6998.6021.65110.0020.66110.0012.82110.1425.8398.7648.70
mNegC↓/mPosC↑121.5916.97118.4419.15101.2719.42106.3116.92116.9712.80111.4814.29110.9024.5895.2250.64
", + "image_path": "738d69d5c018e14945705c60d00fd2e6ccf9007bf5d69380bb8732c49cad6bb6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 57, + 215, + 294, + 285 + ], + "blocks": [ + { + "bbox": [ + 57, + 215, + 294, + 285 + ], + "lines": [ + { + "bbox": [ + 57, + 215, + 294, + 285 + ], + "spans": [ + { + "bbox": [ + 57, + 215, + 294, + 285 + ], + "type": "image", + "image_path": "fe7e4b8538757983b82543101f111bc83269e1afd29901788ba314667c5bddce.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 291, + 286, + 303 + ], + "lines": [ + { + "bbox": [ + 64, + 291, + 286, + 303 + ], + "spans": [ + { + "bbox": [ + 64, + 291, + 286, + 303 + ], + "type": "text", + "content": "Figure 7. Overview of the RCP-Drop & RCP-Mix strategies." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 310, + 295, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 310, + 295, + 466 + ], + "spans": [ + { + "bbox": [ + 54, + 310, + 295, + 466 + ], + "type": "text", + "content": "randomly dropping features within certain network layers or blocks during training. In the collaborative perception context, the ego vehicle may encounter incomplete shared perceptual data from CAVs due to communication failures, or CAVs leaving the collaborative queue. Existing collaborative perception models, while beneficial in multi-vehicle setups, often underperform in single-vehicle scenarios due to their learned dependency on supplementary data from other vehicles. To prevent models from being overly reliant on CAVs data and to better equip them for single-vehicle operation, as shown in Fig. 7 we introduce RCP-Drop, which simulates these conditions by selectively discarding information from certain CAVs. Technically, it is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 82, + 468, + 294, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 468, + 294, + 485 + ], + "spans": [ + { + "bbox": [ + 82, + 468, + 294, + 485 + ], + "type": "interline_equation", + "content": "F _ {a g g} ^ {e g o} = \\mathcal {A} \\left(F ^ {e g o}, \\left\\{\\mathbb {1} \\left(p _ {i} < p _ {d r o p}\\right) \\cdot F _ {i} ^ {c a v} \\right\\} _ {i = 1} ^ {N}\\right), \\tag {5}", + "image_path": "b4e2c428eb916ee49f6cbfa1f1ad26ec229e233371b76332a4b8b2953b2684e3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "F^{ego}" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " represents the feature originating from the ego vehicle, " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "F_{agg}^{ego}" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " denotes the aggregated feature after perception information exchange, and " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "F_{i}^{cav}" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " is the feature map shared from the " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": "-th collaborative vehicle. Here, " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " is a specific feature fusion function developed in existing methods [29, 44, 53], " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " is sampled from a uniform distribution between 0 and 1, and " + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "inline_equation", + "content": "p_{drop}" + }, + { + "bbox": [ + 55, + 486, + 295, + 580 + ], + "type": "text", + "content": " is the threshold determining whether data from each collaborative vehicle is discarded." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "content": "Rather than keeping the threshold fixed during training, we develop a dynamic adjustment strategy for " + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "inline_equation", + "content": "p_{drop}" + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "content": ". Specifically, we start with a high dropout probability, which reduces the number of participating collaborative vehicles and enhances the single-vehicle backbone's feature extraction capabilities. Gradually, we lower the dropout probability to increase the participation of collaborative vehicles, optimizing the collaborative perception performance over time. In this study, we set " + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "inline_equation", + "content": "p_{drop} = 1.0 - (t / T)^2" + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 581, + 295, + 700 + ], + "type": "text", + "content": " are the current and maximum training epoch." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 713 + ], + "type": "text", + "content": "Existing research shows that visual data can be char" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 240, + 550, + 329 + ], + "blocks": [ + { + "bbox": [ + 313, + 217, + 553, + 239 + ], + "lines": [ + { + "bbox": [ + 313, + 217, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 553, + 239 + ], + "type": "text", + "content": "Table 4. Efficacy of RCP-Drop and RCP-Mix on collaborative robustness, collaborative compensation and collaborative disruption." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 240, + 550, + 329 + ], + "lines": [ + { + "bbox": [ + 317, + 240, + 550, + 329 + ], + "spans": [ + { + "bbox": [ + 317, + 240, + 550, + 329 + ], + "type": "table", + "html": "
APclean↑mAPcor↑mNegC↓mPosC↑
CoBEVT [51]40.4915.91111.4814.29
+BN [39]42.7427.87112.9418.28
+BN+RCP-Mix48.2531.83109.1123.44
+BN+RCP-Drop47.8430.68109.4520.07
AttFuse [53]37.1315.99121.5916.97
+BN [39]36.1322.35126.0418.85
+BN+RCP-Mix43.1228.85114.9722.51
+BN+RCP-Drop45.1827.56115.6418.17
", + "image_path": "d76ef14b136669fd1d157f2d76726a8c4b17dbd01aa78aef1c2b41d4748d4037.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 334, + 555, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 334, + 555, + 466 + ], + "spans": [ + { + "bbox": [ + 313, + 334, + 555, + 466 + ], + "type": "text", + "content": "acterized by feature statistics (i.e., the mean and standard deviation of feature maps). For the same semantic concepts, distinct styles (such as variations in color and texture) correspond to different feature statistics. Inspired by Mixstyle [64, 65], we propose RCP-Mix to enhance model adaptability to varied environmental conditions and styles encountered in collaborative perception. Unlike Mixstyle, which performs random feature statistic mixing across instances within a mini-batch, RCP-Mix probabilistically combines feature statistics between the ego vehicle and collaborating CAVs. Technically, RCP-Mix is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 355, + 467, + 512, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 467, + 512, + 499 + ], + "spans": [ + { + "bbox": [ + 355, + 467, + 512, + 499 + ], + "type": "interline_equation", + "content": "\\mu_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mu_ {i}; \\quad \\sigma_ {a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\sigma_ {i},", + "image_path": "9182057e8ba23bb235f3dbff0b8b3bdddfe20bc70819da8775acefef102cbc35.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 356, + 502, + 553, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 502, + 553, + 517 + ], + "spans": [ + { + "bbox": [ + 356, + 502, + 553, + 517 + ], + "type": "interline_equation", + "content": "\\mu_ {i} ^ {\\text {m i x}} = \\lambda \\mu_ {i} + (1 - \\lambda) \\mu_ {\\text {a l l}}, \\tag {6}", + "image_path": "e79b855cee617fdf6bef4fa4a0338587848cea8ba1b8e017b9051aeb697a0409.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 356, + 518, + 470, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 518, + 470, + 531 + ], + "spans": [ + { + "bbox": [ + 356, + 518, + 470, + 531 + ], + "type": "interline_equation", + "content": "\\sigma_ {i} ^ {m i x} = \\lambda \\sigma_ {i} + (1 - \\lambda) \\sigma_ {a l l},", + "image_path": "dd4bc79a31de92ba6e710a6dd77702d7d6658214fdab7c82391a536e9cad125f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 533, + 495, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 533, + 495, + 557 + ], + "spans": [ + { + "bbox": [ + 356, + 533, + 495, + 557 + ], + "type": "interline_equation", + "content": "F _ {i} ^ {m i x} = \\frac {F _ {i} - \\mu_ {i}}{\\sigma_ {i}} * \\sigma_ {i} ^ {m i x} + \\mu_ {i} ^ {m i x},", + "image_path": "1a1525df54818b08f4f153c9f6755363882c9034b5e33a799465328071dbdb13.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": " are the means and standard deviations of the feature map " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": " is the weight sampled from the Beta distribution, i.e., " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\lambda \\sim \\text{Beta}(\\alpha, \\alpha)" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 313, + 558, + 555, + 594 + ], + "type": "text", + "content": " by default." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "Experimental Analysis: We selected CoBEVT [51] and AttFuse [53] with online Batch Normalization (BN) Stats Adapt [39] as baselines, integrating them with our RCP-Drop and RCP-Mix strategies. Table 4 demonstrates that, despite their simplicity, both RCP-Drop and RCP-Mix effectively counteract performance degradation from data corruptions. In particular, for " + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\text {clean }}" + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": ", these strategies lead to substantial performance improvements compared to the marginal gains or occasional declines observed with the vanilla BN adapt. Moreover, across the three inter-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11914" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 83, + 306, + 129 + ], + "blocks": [ + { + "bbox": [ + 88, + 71, + 273, + 80 + ], + "lines": [ + { + "bbox": [ + 88, + 71, + 273, + 80 + ], + "spans": [ + { + "bbox": [ + 88, + 71, + 273, + 80 + ], + "type": "text", + "content": "Table 5. Ablation on the use of different backbone." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 83, + 306, + 129 + ], + "lines": [ + { + "bbox": [ + 58, + 83, + 306, + 129 + ], + "spans": [ + { + "bbox": [ + 58, + 83, + 306, + 129 + ], + "type": "table", + "html": "
MethodbackboneWeatherBlurNoiseQuantCrashAPAPcor
Max○ResNet10111.7922.322.7722.8718.6435.1218.14
Max•EfficientNet-b015.4523.3910.9833.2721.0845.8718.05
V2X-ViT○ResNet10110.9024.6616.6328.7510.4146.2116.73
V2X-ViT•EfficientNet-b019.2526.458.0141.4821.9658.6120.24
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Impact of different backbone sizes on model robustness." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 175, + 137, + 293, + 222 + ], + "blocks": [ + { + "bbox": [ + 175, + 137, + 293, + 222 + ], + "lines": [ + { + "bbox": [ + 175, + 137, + 293, + 222 + ], + "spans": [ + { + "bbox": [ + 175, + 137, + 293, + 222 + ], + "type": "image", + "image_path": "169726178e9aefa41dda1e365e6b9a906493f4b7171f6c77731d60c41249c265.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 243, + 173, + 335 + ], + "blocks": [ + { + "bbox": [ + 58, + 243, + 173, + 335 + ], + "lines": [ + { + "bbox": [ + 58, + 243, + 173, + 335 + ], + "spans": [ + { + "bbox": [ + 58, + 243, + 173, + 335 + ], + "type": "image", + "image_path": "4593dadf21bfb8c1ea3916a8b8dedd6bb6b1bd12af6b922adb05c510eaa17c1e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 342, + 273, + 354 + ], + "lines": [ + { + "bbox": [ + 76, + 342, + 273, + 354 + ], + "spans": [ + { + "bbox": [ + 76, + 342, + 273, + 354 + ], + "type": "text", + "content": "Figure 9. Effect of CAV number on model robustness." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 175, + 243, + 294, + 335 + ], + "blocks": [ + { + "bbox": [ + 175, + 243, + 294, + 335 + ], + "lines": [ + { + "bbox": [ + 175, + 243, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 175, + 243, + 294, + 335 + ], + "type": "image", + "image_path": "22ecded2dd94e7c1ab9da9b21cf29d1c68b88c5e14b3b36ccabd8b1a84c30e9d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "text", + "content": "ference scenarios, Global Interference, Ego Interference, and CAV Interference, our RCP-Drop and RCP-Mix consistently show robust improvements in model resilience under corruption conditions " + }, + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\left(\\mathrm{AP}_{cor}\\right)" + }, + { + "bbox": [ + 55, + 357, + 296, + 453 + ], + "type": "text", + "content": ", collaborative compensation (mPosC), and reduced collaborative disruption (mNegC). These results further underline the efficacy of our approaches in maintaining model performance and collaborative stability in challenging conditions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 465, + 208, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 208, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 208, + 478 + ], + "type": "text", + "content": "6. Observation & Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 486, + 295, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 509 + ], + "type": "text", + "content": "In this section, we analyze and discuss the impact of various model configurations and techniques on robustness." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 510, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 640 + ], + "type": "text", + "content": "Backbones: Table 5 compares the performance of different backbones, showing that models using EfficientNet-b0 outperform ResNet101 [22] in all conditions except noise disturbances. leading to its use as the backbone for all models in this study. Fig. 8 further compares AttFuse with various backbone sizes, revealing that larger backbones generally improve robustness. Notably, EfficientNetb0 and EfficientNet-b3 [21] show greater stability and robustness across multiple conditions, particularly excelling under \"Noise\" and \"Crash\" scenarios, while EfficientNetb2 performs poorly in these cases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Feature Fusion: Table 6 shows that multiscale fusion enhances model performance on clean datasets and improves robustness against various perturbations. Additionally, the simple Max Fusion demonstrates greater robustness than attention mechanisms, particularly under noisy conditions, suggesting that more complex mechanisms may be less ef" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 318, + 83, + 550, + 130 + ], + "blocks": [ + { + "bbox": [ + 344, + 71, + 524, + 81 + ], + "lines": [ + { + "bbox": [ + 344, + 71, + 524, + 81 + ], + "spans": [ + { + "bbox": [ + 344, + 71, + 524, + 81 + ], + "type": "text", + "content": "Table 6. Ablation on the use of multiscale fusion." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 83, + 550, + 130 + ], + "lines": [ + { + "bbox": [ + 318, + 83, + 550, + 130 + ], + "spans": [ + { + "bbox": [ + 318, + 83, + 550, + 130 + ], + "type": "table", + "html": "
MethodmultiscaleWeatherBlurNoiseQuantCrashAP\\(AP_{cor}\\)
Max○X15.4523.3910.9833.2721.0845.8718.05
Max●✓30.6534.9228.6149.8638.1565.3833.22
AttFuse○X11.8519.858.9726.0122.3037.1314.93
AttFuse●✓23.3631.909.0143.4330.0762.5824.08
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Effect of camera number on model robustness." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 436, + 136, + 552, + 228 + ], + "blocks": [ + { + "bbox": [ + 436, + 136, + 552, + 228 + ], + "lines": [ + { + "bbox": [ + 436, + 136, + 552, + 228 + ], + "spans": [ + { + "bbox": [ + 436, + 136, + 552, + 228 + ], + "type": "image", + "image_path": "f2da14db78e21180b1488787562de78b70bd2f29643b07f934cd773a5ade3426.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 251, + 518, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 518, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 518, + 262 + ], + "type": "text", + "content": "fective at mitigating certain types of perturbations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 263, + 555, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 555, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 555, + 382 + ], + "type": "text", + "content": "CAV and Camera Number: Fig. 9 shows that increasing the number of collaborative CAVs generally enhances model performance. Notably, two collaborating vehicles provide a significant improvement over a single vehicle; however, the rate of improvement diminishes once the number of collaborators exceeds four, indicating a diminishing marginal effect. Fig. 10 shows that as camera count increases, both model performance and robustness improve significantly, with a particularly notable boost from three to four cameras." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 394, + 388, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 394, + 388, + 406 + ], + "spans": [ + { + "bbox": [ + 314, + 394, + 388, + 406 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "type": "text", + "content": "In this study, we introduce RCP-Bench, the first comprehensive benchmark designed to evaluate the robustness of camera-based collaborative perception models under diverse real-world disturbances. RCP-Bench encompasses 14 corruption types at 5 severity levels across 3 large-scale datasets. We systematically evaluate three collaborative scenarios across six cases to assess robustness in the Global Interference scenario, explore collaborative advantages in the Ego Interference scenario, and examine disturbance risks in the CAV Interference scenario. To improve robustness, we propose two straightforward strategies, RCP-Drop and RCP-Mix, tailored for collaborative perception. Our analysis of backbone architecture, feature fusion, CAV number, and camera number provides key insights for enhancing model resilience. We hope this work offers valuable insights and inspires future research toward more robust collaborative perception models." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": "Acknowledgment: This work was supported by the National Key Research and Development Program of China (No. 2024YFE0211000), in part by the National Natural Science Foundation of China (No. 62372329), in part by Shanghai Scientific Innovation Foundation (No. 23DZ1203400), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11915" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 121 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 121 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 121 + ], + "type": "text", + "content": "[1] Pierre Baldi and Peter J Sadowski. 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Proceedings of the IEEE, 111(3):257-276, 2023. 1" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11918" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_content_list.json b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3ffb4109b2381bce30c83117fbfaf74bc9e0fb4c --- /dev/null +++ b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_content_list.json @@ -0,0 +1,1714 @@ +[ + { + "type": "text", + "text": "RDD: Robust Feature Detector and Descriptor using Deformable Transformer", + "text_level": 1, + "bbox": [ + 104, + 130, + 893, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gonglin Chen $^{1,2}$ , Tianwen Fu $^{1,2}$ , Haiwei Chen $^{1,2}$ , Wenbin Teng $^{1,2}$ , Hanyuan Xiao $^{1,2}$ , Yajie Zhao $^{1,2*}$ $^{1}$ Institute for Creative Technologies \n $^{2}$ University of Southern California", + "bbox": [ + 109, + 179, + 890, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{gonglinc, tianwenf}@usc.edu, chenh@ict.usc.edu, {wenbinte, hanyuanx}@usc.edu, zhao@ict.usc.edu", + "bbox": [ + 287, + 218, + 709, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a core step in structure-from-motion and SLAM, robust feature detection and description under challenging scenarios such as significant viewpoint changes remain unresolved despite their ubiquity. While recent works have identified the importance of local features in modeling geometric transformations, these methods fail to learn the visual cues present in long-range relationships. We present Robust Deformable Detector (RDD), a novel and robust keypoint detector/descriptor leveraging the deformable transformer, which captures global context and geometric invariance through deformable self-attention mechanisms. Specifically, we observed that deformable attention focuses on key locations, effectively reducing the search space complexity and modeling the geometric invariance. Furthermore, we collected an Air-to-Ground dataset for training in addition to the standard MegaDepth dataset. Our proposed method outperforms all state-of-the-art keypoint detection/description methods in sparse matching tasks and is also capable of semi-dense matching. To ensure comprehensive evaluation, we introduce two challenging benchmarks: one emphasizing large viewpoint and scale variations, and the other being an Air-to-Ground benchmark — an evaluation setting that has recently gained popularity for 3D reconstruction across different altitudes. Project page: https://xtcpete.github.io/rdd/.", + "bbox": [ + 88, + 316, + 485, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 703, + 220, + 719 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Keypoint detection and description are central to numerous 3D computer vision tasks, including structure-from-motion (SfM), visual localization, and simultaneous localization and mapping (SLAM). These tasks depend on reliable keypoints and descriptors to establish accurate tracks, which are crucial for downstream algorithms to interpret spatial relationships—a requirement in fields from robotics to augmented reality [20]. When applied to real-world tasks, these systems face challenges such as significant viewpoint shifts, lighting variations, and scale changes.", + "bbox": [ + 89, + 729, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dfe1613409498ce448d5ac0074ac4a260bbbbdb34a2af6a67e397f5b0af5d270.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 290, + 901, + 373 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8757cb36584c0083de557fdede5a577b8cdb7380f30992307c59a445582f14f.jpg", + "image_caption": [ + "Figure 1. Our proposed method effectively performs both sparse and semi-dense feature matching, referred to as RDD and $\\mathbf{RDD}^*$ , respectively, as shown in the top section. RDD demonstrates its ability to extract accurate keypoints and robust descriptors, enabling reliable matching even under significant scale and viewpoint variations, as illustrated in the bottom section." + ], + "image_footnote": [], + "bbox": [ + 511, + 378, + 901, + 470 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Historically, feature detection and description methods relied on rule-based techniques such as SIFT, SURF, and ORB [3, 25, 35]. However, these methods often struggled with the aforementioned challenges. To better address these issues, recent works [6, 13, 41, 46] leverage deep neural networks based on data-driven approaches which often extract more robust and discriminative descriptors than the rule-based ones. Despite the enhanced robustness that learning-based methods have, they often rely on regular convolutions to encode images [6, 13, 32, 41, 46], which ignore the geometric invariance and long-distance awareness critical for robust description under challenging conditions. Subsequently, [26, 28, 45] have partially addressed geometric invariance by estimating the scale and orientation of keypoint descriptors to model affine transformations. ALIKED [47] and ASLFeat [28] advanced this approach by using deformable convolutions capable of modeling any geometric transformations. However, these methods are limited to modeling transformations within local windows; features learned with the localized kernels of convolution operators fall short of learning important visual cues that depend on long-range relationships (e.g. vanishing lines).", + "bbox": [ + 509, + 568, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6394", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we focus on feature detection and description in challenging scenarios that haven't been effectively addressed in prior works - specifically, extracting reliable and discriminative keypoints and descriptors across images with large camera baselines, significant illumination variations, and scale changes. We therefore propose RDD: a novel two-branch architecture for keypoint detection and description that can model both geometric invariance and global context at the same time. In particular, we design two dedicated network branches: a fully convolutional architecture to perform keypoint detection and a transformer-based architecture for extracting descriptors: the objectives of keypoint detection and description have previously been found not to align perfectly [21]. We observe that the convolutional neural network excels in detecting sub-pixel keypoints thanks to its expressiveness, whereas a transformer-based architecture is particularly suited for learning features that captures global context and possess geometric invariance through its self-attention mechanism [7, 42]. However, as self-attention layers attend to all spatial locations in the image, they significantly increase computational overhead and may reduce descriptor discriminability. To address this, we have adopted the deformable attention [48] for keypoint description, allowing our designed network to selectively focus on key locations, which greatly reduces time complexity while maintaining the capability to learn geometric invariance and global context.", + "bbox": [ + 93, + 90, + 480, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The two-branch architecture of RDD allows specialized architectures to learn keypoint detection and description independently. Our experiments have found that such design choice accelerates convergence and leads to better overall performance, as proven in Sec. 4.4. Overall, RDD is designed to be robust, achieving competitive performance on challenging imagery and also capable of semi-dense matching Fig. 1. This enhanced capability improves accuracy and stability in 3D vision applications, such as structure-from-motion (SfM) [4] and relative camera pose estimation under difficult imaging conditions. Our approach outperforms current state-of-the-art methods for keypoint detection and description on standard benchmarks, including MegaDepth-1500 [8], HPatches [1], and Aachen-Day-Night [38], across various tasks. However, to the best of our knowledge, no existing benchmarks accurately capture the aftermentioned challenging scenarios. To further validate the robustness of our method and provide a more comprehensive evaluation, we have collected and derived two additional benchmark datasets. The main contributions of our work are:", + "bbox": [ + 93, + 501, + 480, + 801 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel two branch architecture that utilizes a convolutional neural network for detecting accurate keypoints and transformer based network to extract robust descriptors under challenging scenarios, all while maintaining efficient runtime performance.", + "- An innovative refinement module for semi-dense match" + ], + "bbox": [ + 89, + 810, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing, improving matching accuracy and density.", + "bbox": [ + 526, + 92, + 836, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Dataset contribution: MegaDepth-View, derived from MegaDepth [22], specifically focuses on challenging image pairs with large viewpoint and scale variations. Air-to-Ground dataset provides diverse aerial and ground cross view imagery for training and evaluation, enhancing robustness and performance and providing a new evaluation setting.", + "bbox": [ + 514, + 107, + 903, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 227, + 653, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Geometric Invariant Descriptors", + "text_level": 1, + "bbox": [ + 513, + 253, + 800, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In geometric invariance modeling, previous methods have primarily focused on two key aspects: scale and orientation. In traditional hand-crafted methods, SIFT [25] estimates a keypoint's scale and orientation by analyzing histograms of image gradients and subsequently extracts and normalizes image patches around the keypoint to construct scale- and orientation-invariant descriptors. Similarly, ORB [35] computes orientation based on the keypoint's center of mass, followed by rotation of the image patches to ensure orientation invariance.", + "bbox": [ + 511, + 276, + 903, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based methods approach geometric invariance through two primary strategies. The majority of these methods [6, 8, 13, 32, 33, 41] relies heavily on data augmentation techniques to achieve scale and orientation invariance. On the other hand, some learning-based approaches explicitly model scale and orientation. For instance, LIFT [45] mimics SIFT [25] by detecting keypoints, estimating their orientation, and extracting descriptors with different neural networks. Other methods, such as AffNet [30] and LF-Net [31], predict affine transformation parameters and apply these transformations via Spatial Transformer Networks [18] to produce affine-invariant descriptors. These methods generally assume a predefined geometric transformation, typically affine transformations. More recent advancements, such as ASLFeat [28] and ALIKED [47], employ deformable convolutions to directly extract geometric-invariant features, offering a more flexible and adaptive approach to handling geometric variations.", + "bbox": [ + 511, + 428, + 903, + 699 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the use of deformable convolutions in feature description, the proposed network RDD employs deformable attention to extract geometric invariant features that are not restricted by local windows.", + "bbox": [ + 511, + 700, + 903, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Decoupling Keypoint and Descriptor Learning", + "text_level": 1, + "bbox": [ + 511, + 771, + 903, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In traditional handcrafted methods for feature detection and description, such as SIFT [25] and ORB [35], the detection and description processes are performed independently. This decoupled approach was also common in early learning-based methods [2, 29], where keypoint detection and description were treated as separate tasks. However, later works [6, 8, 13, 33] proposed an end-to-end frame", + "bbox": [ + 511, + 794, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6395", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/040bcfe99fa180cce2334932a657b8b8322f3eef3a309cb0778263d9c08693f0.jpg", + "image_caption": [ + "Figure 2. An overview of our network architecture. Descriptor Branch $\\mathcal{F}_D$ and Keypoint Branch $\\mathcal{F}_K$ process an input image $I\\in \\mathbb{R}^{H\\times W\\times 3}$ independently. Descriptor Branch: 4 layers of multiscale feature maps $\\{\\mathbf{x}_{res}^l\\}_{l = 1}^L$ are extracted by passing $I$ through ResNet-50 [15] $\\mathcal{F}_{res}$ . Additional feature map at scale of $1 / 64$ is added by applying a simple CNN on the last feature map and then they are fed to a transformer encoder $\\mathcal{F}_e$ with positional embeddings [42]. We up-sample all feature maps output by $\\mathcal{F}_e$ to size $H / k\\times W / k$ where $k = 4$ is the patch size. Feature maps are then summed together to generate the dense descriptor map $D$ . A classification head $\\mathcal{F}_m$ is applied to the descriptor map to estimate a matchability map $M$ . Keypoint Branch: $I$ passes through a lightweight CNN with residual connection [15] $\\mathcal{F}_{cnn}$ to capture multi-scale features $\\{\\mathbf{x}_{cnn}^l\\}_{l = 1}^L$ . Features are then up-sampled to size $H\\times W$ and concatenated to generate a feature map of $H\\times W\\times 64$ . A score map $S$ is estimated by a classification head $\\mathcal{F}_s$ . Final sub-pixel keypoints are detected using DKD [46]." + ], + "image_footnote": [], + "bbox": [ + 116, + 77, + 872, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "work, jointly optimizing keypoint detection and descriptor extraction. This joint learning approach ensures that the detected keypoints and their descriptors complement each other. Despite the advantages, [21] highlighted a potential drawback of joint training, observing that poorly learned descriptors could negatively impact keypoint detection quality. Subsequently, DeDoDe[10] demonstrated that decoupling keypoint detection and description into two independent networks can significantly improve performance. Similarly, XFeat [32] showed that using task-specific networks provides a better balance between efficiency and accuracy. Inspired by these recent insights, RDD consists of two separate branches for independent keypoint detection and description. We also formulate a training strategy that optimize the descriptor branch first and then the keypoint branch. This design enables both sparse and dense matching and ensures optimized performance across various scenarios.", + "bbox": [ + 91, + 481, + 483, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Efficient Attention Mechanisms", + "text_level": 1, + "bbox": [ + 89, + 770, + 369, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The quadratic complexity of multi-head attention [42] leads to long training schedules and limited spatial resolution for tractability. For 2D images, LR-Net [16] proposed a local relation layer, computing attention in a fixed local window. Linear Transformer [19] proposes to reduce the computation complexity of vanilla attention to linear complexity by substituting the exponential kernel with an alternative ker", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "nel function. Deformable attention [48] further allows the attention window to depend on the query features. With a linear projection predicting a deformable set of displacements from the center and their weight, each pixel in the feature map may attend to a fixed number of pixels of arbitrary distance. Deformable attention [48] is well-suited for our objectives, enabling efficient learning of global context, making it a fitting choice for our approach.", + "bbox": [ + 511, + 481, + 906, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 511, + 614, + 612, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method extracts descriptors and keypoints separately using a descriptor branch and a keypoint branch, as shown in Fig. 2. For an input image $I \\in \\mathbb{R}^{H \\times W \\times 3}$ , the descriptor branch first extracts multi-scale feature maps $\\{x_{res}^l\\}_{l=1}^L$ from $I$ using ResNet-50 [15], denoted as $\\mathcal{F}_{res}$ , and then estimates a descriptor map $D \\in \\mathbb{R}^{H/k \\times W/k}$ through a deformable transformer encoder [48], denoted as $\\mathcal{F}_e$ , where $k = 4$ is the patch size. The matchability map $M \\in \\mathbb{R}^{H/k \\times W/k}$ is then estimated from $D$ with a classification head $\\mathcal{F}_m$ . The keypoint branch $\\mathcal{F}_K$ estimates a scoremap $S \\in \\mathbb{R}^{H \\times W}$ by passing image $I$ through a lightweight CNN with residual connection [15] $\\mathcal{F}_{cnn}$ and a classification head $\\mathcal{F}_s$ , then sub-pixel keypoints $p_s = [x,y]^T$ are detected with differentiable keypoint detection (DKD) [46].", + "bbox": [ + 511, + 642, + 906, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The detected keypoints are used to sample their corresponding descriptors $d \\in \\mathbb{R}^{256}$ from $D$ . In Sec. 3.1, we provide an overview of DKD [46] and deformable attenuated version of the original dataset.", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6396", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion [48]. In Sec. 3.2, we introduce the network architecture. In Sec. 3.3, we discuss how sparse and dense matching are obtained. Finally, the training details and loss functions are presented in Sec. 3.4.", + "bbox": [ + 89, + 90, + 483, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 160, + 230, + 174 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1. Differentiable Keypoint Detection", + "text_level": 1, + "bbox": [ + 89, + 181, + 372, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the scoremap $S$ , DKD detects sub-pixel keypoint locations through partially differentiable operations. First, local maximum scoremap $S_{nms}$ is obtained by non-maximum suppression in local $N \\times N$ windows. Pixel-level keypoints $p_{nms} = [x', y']^T$ are then extracted by applying a threshold to $S_{nms}$ . DKD then selects all scores $s(i, j)$ in the $N \\times N$ windows centered on $p_{nms}$ from $S$ and estimates a sub-pixel-level offset through following steps:", + "bbox": [ + 89, + 200, + 483, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$s(i,j)$ are first normalized with softmax:", + "bbox": [ + 109, + 321, + 380, + 337 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns ^ {\\prime} (i, j) = \\operatorname {s o f t m a x} \\left(\\frac {s (i , j) - s _ {\\max}}{t _ {d e t}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 347, + 482, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t_{det}$ is the temperature. Then $s^{\\prime}(i,j)$ represents the probability of $[i,j]^T$ to be a keypoint within the local window. Thus, the expected position of the keypoint in the local window can be given by integral regression [14, 40]:", + "bbox": [ + 89, + 390, + 483, + 452 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n[ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} ^ {T} = \\sum_ {0 \\leq i, j < N} s ^ {\\prime} (i, j) [ i, j ] ^ {T}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 460, + 482, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final estimated sub-pixel-level keypoint is", + "bbox": [ + 89, + 503, + 398, + 520 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} _ {\\boldsymbol {s}} = \\left[ x, y \\right] ^ {T} = \\left[ x ^ {\\prime}, y ^ {\\prime} \\right] ^ {T} + \\left[ \\hat {i}, \\hat {j} \\right] _ {s o f t} ^ {T}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 527, + 482, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2. Deformable Attention", + "text_level": 1, + "bbox": [ + 89, + 558, + 290, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a feature map $\\mathbf{x} \\in \\{\\mathbf{x}_{res}^{l}\\}_{l=1}^{L}$ , deformable attention selects a small set of sample keys $\\mathbf{p}_q$ corresponding to the query index $q$ and its feature vectors $\\mathbf{z}_q$ . The deformable attention feature $\\mathbf{x}_d$ is calculated by", + "bbox": [ + 89, + 575, + 483, + 636 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\mathbf {x}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 636, + 480, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 89, + 674, + 135, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {m q} = \\sum_ {k = 1} ^ {K} A _ {m q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} \\left(\\mathbf {p} _ {q} + \\Delta \\mathbf {p} _ {m q k}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 689, + 482, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$m$ indexes the attention head, $k$ indexes the sampled keys, and $K$ is the total number of sampled keys. $\\mathbf{W}$ and $\\mathbf{W}'$ are learnable weights. $\\Delta \\mathbf{p}_{mqk}$ and $A_{mqk}$ denote the sampling offset and attention weight of the $k$ -th sampling point in the $m$ -th attention head, where the sampling points are inferred by a linear layer.", + "bbox": [ + 89, + 734, + 483, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most of recent keypoint detection and description frameworks [10, 32, 46, 47] benefit from the use of multi-scale feature maps to capture fine details and broader spatial context. Deformable attention naturally extends to multi-scale feature maps [48], enabling the network to effectively adapt", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to features at different scales. Similar to Eq. (4), multi-scale deformable attention feature $\\mathbf{x}_{msd}$ can be calculated similar to Eq. (4) and Eq. (7)", + "bbox": [ + 511, + 90, + 905, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {m s d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\left\\{\\mathbf {x} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q} ^ {\\prime}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 138, + 903, + 178 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 513, + 179, + 558, + 191 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {m q} ^ {\\prime} = \\left[ \\sum_ {l = 1} ^ {L} \\sum_ {k = 1} ^ {K} A _ {m l q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} _ {l} \\left(f _ {s} \\left(\\hat {p} _ {q}\\right) + \\Delta \\mathbf {p} _ {m l q k}\\right) \\right]. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 205, + 903, + 247 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\hat{p_q} \\in [0,1]^2$ is the normalized coordinates and function $f_s$ re-scales it to match the scale of input feature map of the $l$ -th level.", + "bbox": [ + 511, + 261, + 905, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Network Architecture", + "text_level": 1, + "bbox": [ + 513, + 320, + 718, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Descriptor Branch The descriptor branch $\\mathcal{F}_D$ extracts a dense feature map $D\\in \\mathbb{R}^{H / 4\\times W / 4\\times 256}$ and a matchability map $M$ , which models that probability of a given feature vector can be matched.", + "bbox": [ + 511, + 343, + 905, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using a ResNet-50 [15] as the CNN backbone, $\\mathcal{F}_{res}$ extracts feature maps at 4 scales, each with resolutions of $1/4, 1/8, 1/16, 1/32$ of the original image. An additional feature map at scale of $1/64$ is then included by applying a CNN on the last feature map. These features are positionally encoded and fed into $\\mathcal{F}_e$ with multi-scale deformable attention [48], enabling the network to dynamically attend to relevant spatial locations across multiple scales. We use 4 encoder layers each with 8 attention heads and each head samples 8 points. The entire process of the Descriptor Branch is illustrated in Fig. 2.", + "bbox": [ + 511, + 405, + 906, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Keypoint Branch The keypoint branch is dedicated solely to detecting accurate keypoints without being influenced by descriptor estimation. $\\mathcal{F}_{cnn}$ extracts feature maps at 4 different resolutions, each with a resolution of $1/1, 1/2, 1/8$ , and $1/32$ of the original image and feature dimension of 32. These features are subsequently upsampled to match the original image resolution and concatenated to produce a feature map of size $H \\times W \\times 128$ . Then $\\mathcal{F}_s$ is used to estimate the scoremap. DKD [46] is applied on the scoremap to perform non-maximum suppression and detect the sub-pixel-accurate keypoints. Fig. 2 depicts the entire process of the Keypoint Branch.", + "bbox": [ + 511, + 577, + 906, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Feature Matching", + "text_level": 1, + "bbox": [ + 511, + 771, + 687, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we describe how sparse matches and dense matches are obtained for a given image pair $I^1$ and $I^2$ . Our network outputs sparse keypoints $p_s^{1,2}$ , descriptor maps $D^{1,2}$ , and matchability maps $M^{1,2}$ all in a single forward pass. We bilinearly upsample $D^{1,2}$ to match the original resolution of $I^1$ and $I^2$ . Descriptors $d^{1,2}$ are then sampled from $D^{1,2}$ using $p_s^{1,2}$ .", + "bbox": [ + 511, + 794, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6397", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparse Matching Dual-Softmax operator [34, 41] is used to establish correspondences between two descriptors $d^{1,2}$ . The score matrix $S$ between the descriptors is first calculated by $S(i,j) = \\frac{1}{\\tau} \\cdot \\langle d^1,d^2\\rangle$ , where $\\tau$ is the temperature. We can now apply softmax on both dimensions of $S$ to obtain the probability of soft mutual nearest neighbor (MNN) matching. The matching probability matrix $P$ is obtained by:", + "bbox": [ + 89, + 90, + 480, + 210 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP (i, j) = \\operatorname {s o f t m a x} (S (i, \\cdot)) _ {j} \\cdot \\operatorname {s o f t m a x} (S (\\cdot , j)) _ {i}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 217, + 480, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the confidence matrix $P$ , we select matches $m_{s}$ with confidence higher than a threshold(0.01) to further enforce the mutual nearest neighbor criteria, which filters possible outlier matches.", + "bbox": [ + 89, + 239, + 482, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semi-Dense Matching Recent works [5, 17, 39, 43] demonstrated the benefits of semi-dense feature matching by improving coverage and number of inliers. We propose a novel dense matching module that produces accurate and geometry consistent dense matches.", + "bbox": [ + 89, + 305, + 482, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given images $I^{1}$ and $I^{2}$ , our method can control the memory and computation usage by only selecting the top-K coarse keypoints $p_{c}^{1,2}$ according to their matchability score $M^{1,2}$ . Then we can obtain the coarse matches $m_{c}$ using equation Eq. (8), similar to how we obtain the sparse matches $m_{s}$ . These matches are naturally coarse matches and require refinement for sub-pixel level accuracy as $M$ 's resolution is only $1/4$ of the original resolution. Unlike existing methods [5, 39] that crop fine level features around coarse matches in $I^{1}$ and $I^{2}$ and then predict offset in $I^{2}$ , our work proposes a simple, efficient, and accurate module for semi-dense feature matching, inspired by [4] that utilizes sparse correspondences in guiding semi-dense feature matching.", + "bbox": [ + 89, + 381, + 482, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Differing from [4], which iteratively reassigns the coarse matches of detector-free methods, we adopt a similar idea to refine coarse matches to fine matches. With $m_{s}$ obtained from sparse matching, we use the eight-point method to estimate a fundamental matrix $F$ that relates corresponding points between $I^{1}$ and $I^{2}$ . We keep $p_c^1$ unchanged and refine $p_c^2$ by solving offsets $(\\Delta x, \\Delta y)$ that satisfy the epipolar constraint defined by $F$ . First, we convert $p_c^1$ to homogeneous coordinates $p_h^1$ . Then, epipolar lines $L$ in $I^{2}$ for $p_h^1$ is computed by", + "bbox": [ + 89, + 593, + 482, + 743 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = F \\cdot p _ {h} ^ {1}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 243, + 743, + 480, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where each line is represented by coefficients $a, b$ and $c$ . Offsets $(\\Delta x, \\Delta y)$ are then calculated for each point in $p_c^2$ by solving the linear equation", + "bbox": [ + 89, + 763, + 482, + 808 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\na \\cdot (x + \\Delta x) + b \\cdot (y + \\Delta y) + c = 0 \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 814, + 480, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to enforce the epipolar constraint. Then we can get offsets", + "bbox": [ + 89, + 837, + 475, + 852 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta x = \\frac {b (b x - a y) - a c}{a ^ {2} + b ^ {2} + \\epsilon} - x, \\quad \\Delta y = \\frac {a (a y - b x) - b c}{a ^ {2} + b ^ {2} + \\epsilon} - y, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 857, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(x,y)$ are the pixel coordinates of $p_c^2$ . We finally filter out points with offsets that are larger than the patch size (4) because they are moved outside the matched patch and likely outliers. We then obtain refined dense matches $m_c$ by $(x + \\Delta x, y + \\Delta y)$ . In Sec. 4.4, we show that without this refinement module, the performance of dense matching degrades significantly.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 205, + 730, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train RDD with pseudo ground truth correspondences from the MegaDepth dataset [22] and our Air-to-Ground dataset. We collect data from Internet drone videos and ground images of different famous landmarks, more details can be found in the supplementary. Following [37, 39], we use poses and depths to establish pixel correspondences. For every given image pair $(I^1, I^2)$ with $N$ matching pixels, $m_{gt} \\in R^{N \\times 4}$ is defined such that the first two columns are the pixel coordinates of points in $I^1$ and the last two columns are those in $I^2$ obtained through a warping function $f_{\\text{warp}}$ . We train the descriptor branch and the keypoint branch separately.", + "bbox": [ + 511, + 227, + 906, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Descriptor Branch To supervise the local feature descriptors, we apply focal loss [23] to focus on challenging examples and reduce the influence of easily classified matches. Given descriptor maps $D^{1}$ and $D^{2}$ , we sample descriptor sets $d_{gt}^{1}$ and $d_{gt}^{2}$ based on the ground truth matchability $m_{gt} / k$ , where $k$ is the patch size. The $i$ -th rows, $d_{gt}^{1}(i)$ and $d_{gt}^{2}(i)$ , represent descriptors corresponding to the same points in the images $I^{1}$ and $I^{2}$ , respectively. Using these descriptors, we compute a probability matrix $P$ as described in Eq. (8). Our supervision targets positive correspondences only, represented by the diagonal elements $P_{(i,i)}$ of $P$ . By enforcing $P_{(i,i)}$ to be close to 1, we calculate the focal loss $\\mathcal{L}_{focal}$ as follows:", + "bbox": [ + 511, + 414, + 905, + 611 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f o c a l}} = - \\alpha \\cdot (1 - P _ {(i, i)}) ^ {\\gamma} \\cdot \\log \\left(P _ {(i, i)}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 619, + 903, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha = 0.25$ and $\\gamma = 2$ .", + "bbox": [ + 511, + 646, + 697, + 661 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To supervise the matchability map, we apply a modified focal loss that incorporates binary cross-entropy (BCE) on the matchability map $M^{1,2}$ . The ground truth matchability map $M_{gt}^{1,2}$ is generated using $m_{gt} / k$ . We first compute the binary cross-entropy loss $\\mathcal{L}_{BCE}$ as", + "bbox": [ + 511, + 662, + 905, + 737 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {B C E} = - \\left(M _ {g t} \\cdot \\log (M) + \\left(1 - M _ {g t}\\right) \\cdot \\log (1 - M)\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 747, + 903, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and then replace $P_{(i,i)}$ in Eq. (12) with $\\lambda = e^{-\\mathcal{L}_{BCE}}$ , resulting in the matchability loss $\\mathcal{L}_{\\text{matchability}}$ :", + "bbox": [ + 511, + 772, + 903, + 804 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {m a t c h a b i l i t y}} = - \\alpha \\cdot (1 - \\lambda) ^ {\\gamma} \\cdot \\mathcal {L} _ {B C E}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 814, + 903, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final loss for the descriptor branch is defined as $\\mathcal{L}_D = \\mathcal{L}_{focal} + \\mathcal{L}_{matchability}$ . We train the descriptor branch on the mixture of MegaDepth dataset [22] and collected Air-to-Ground dataset, with images resized to 800.", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6398", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b532cb0dd16e6351e39fc229f0ac8db2d5f914d5f0be0cd34fb345e81ea7ea9f.jpg", + "image_caption": [ + "Figure 3. Qualitative Results on MegaDepth. RDD* and RDD are qualitatively compared to DeDoDe-V2-G [10, 11] ALIKED [47] and XFeat* [32]. RDD* and RDD are more robust compared DeDoDe-G* and ALIKED under challenging scenarios like large scale and viewpoint changes. The red color indicates epipolar error beyond $1 \\times 10^{-4}$ (in the normalized image coordinates)" + ], + "image_footnote": [], + "bbox": [ + 114, + 80, + 869, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training uses a batch size of 32 image pairs and the AdamW optimizer [27]. We use a base learning rate of $1 \\cdot 10^{-4}$ with a step learning rate scheduler that updates the learning rate every 2000 steps after 20000 steps with $\\gamma = 0.5$ . The descriptor branch converges after 1 day of training on 8 NVIDIA H100 GPU.", + "bbox": [ + 89, + 431, + 483, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Keypoint Branch We freeze the weights of descriptor branch once it converges and only supervise the keypoint branch to detect accurate and repeatable keypoints. We apply reprojection loss $\\mathcal{L}_{\\text {reprojection }}$ , reliability loss $\\mathcal{L}_{\\text {reliability }}$ similar to [8, 28, 46] and dispersity peaky loss $\\mathcal{L}_{\\text {peaky }}$ [46] to train repeatable and reliable keypoints.", + "bbox": [ + 89, + 534, + 483, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Given detected keypoint $p_s^1$ from $I^1$ and $p_s^2$ from $I^2$ . We obtain the warped keypoints $p_s^{1\\rightarrow 2}$ using $f_{warp}$ and we find their closest keypoints from $p_s^2$ with distance less than 5 pixels as matched keypoints. Then, $dist_{1\\rightarrow 2}$ is the reprojection distance between the matched $p_s^1$ and $p_s^2$ . We define the reprojection loss in a symmetric way:", + "bbox": [ + 89, + 625, + 483, + 717 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e p r o j e c t i o n}} = \\frac {1}{2} \\left(\\operatorname {d i s t} _ {1 \\rightarrow 2} + \\operatorname {d i s t} _ {2 \\rightarrow 1}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 723, + 480, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For keypoint $p_s^1$ and its warped keypoint $p_s^{1\\rightarrow 2}$ with scores $s^1$ and $s^{1\\rightarrow 2}$ , and the probability map $P$ as described in Sec. 3.3, the reliability map is defined as", + "bbox": [ + 89, + 766, + 483, + 811 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nR = \\exp \\left(\\frac {P - 1}{t _ {r e l}}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 824, + 480, + 858 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $t_{rel}$ is the temperature parameter. Considering all valid $p_s^1$ and warped points $p_s^{1\\rightarrow 2}$ , we sample the reliability", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$r^1$ from $R$ . The reliability loss for $p_s^1$ is then defined as", + "bbox": [ + 511, + 431, + 877, + 448 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} = \\frac {1}{N _ {1}} \\sum_ {p _ {s} ^ {1}, p _ {s} ^ {1 \\rightarrow 2}} \\frac {s ^ {1} \\cdot s ^ {1 \\rightarrow 2}}{\\sum_ {p _ {s} ^ {1} , p _ {s} ^ {1 \\rightarrow 2}} s ^ {1} \\cdot s ^ {1 \\rightarrow 2}} (1 - r ^ {1}). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 458, + 906, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similarly, the total reliability loss is defined symmetrically as", + "bbox": [ + 511, + 510, + 905, + 537 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e l i a b i l i t y}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} + \\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {2}\\right). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 537, + 903, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Eq. (15) optimizes the scores of keypoints in local window through the soft term $[\\hat{i},\\hat{j}]_{soft}^{T}$ of Eq. (3), which might affect the first term $[x',y']_{nms}^{T}$ of the equation. In order to align their optimization direction, we define the dispersity peak loss similar to [46] as", + "bbox": [ + 511, + 571, + 906, + 648 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p e a k y}} = \\frac {1}{N ^ {2}} \\sum_ {0 \\leq i, j < N} d (i, j) s ^ {\\prime} (i, j), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 659, + 903, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 532, + 702, + 578, + 715 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nd (i, j) = \\left\\{\\left| \\left| [ i, j ] - [ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} \\right| \\right| _ {p} \\mid 0 \\leq i, j < N \\right\\}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 724, + 903, + 752 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$N$ is the window size and $s^{\\prime}(i,j)$ are softmax scores defined in Eq. (1).", + "bbox": [ + 511, + 761, + 905, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss for the keypoint branch is defined as $\\mathcal{L}_K = \\mathcal{L}_{projection} + \\mathcal{L}_{reliability} + \\mathcal{L}_{peaky}$ . We use the DKD [46] with a window size of $N = 5$ to detect the top 500 keypoints, and we randomly sample 500 keypoints from non-salient positions. We train the keypoint branch similarly to the descriptor branch, the keypoint branch converges after 4 hours of training on an NVIDIA H100 GPU.", + "bbox": [ + 511, + 792, + 905, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6399", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/61adeca36e5f241e56f4242f62e72265eac69db31d3d161382d7a2aebbbc019a.jpg", + "table_caption": [ + "Table 1. SotA comparison on the MegaDepth [22]. Results are measured in AUC (higher is better). Top 4,096 features used to all sparse matching methods. Best in bold, second best underlined." + ], + "table_footnote": [], + "table_body": "
MethodMegaDepth-1500MegaDepth-View
@5°AUC @10°@20°@5°AUC @10°@20°
Dense
DKM [9] CVPR'2360.474.985.167.480.088.2
RoMa [12] CVPR'2462.676.786.369.981.889.4
Semi-Dense
LoFTR [39] CVPR'2152.869.281.250.665.877.9
ASpanFormer [5] ECCV'2255.371.583.161.375.284.6
ELoFTR [44] CVPR'2456.472.283.560.274.884.7
XFeat* [32] CVPR'2438.656.170.523.937.751.8
RDD*51.367.179.341.555.766.7
Sparse with Learned Matcher
SP [6]+SG [37] CVPR'1949.767.180.651.565.576.9
SP [6]+LG [24] ICCV'2349.967.080.152.467.378.5
Dedode-V2-G [10, 11]+LG [24] ICCV'2344.162.176.541.957.170.0
RDD+LG [24] ICCV'2352.368.981.854.269.380.3
Sparse with MNN
SuperPoint [6] CVPRW'1824.140.054.77.5013.321.1
DISK [41] Neulps'2038.553.766.630.441.951.6
ALIKED [47] TIM'2341.856.869.630.041.853.2
XFeat [32] CVPR'2424.040.155.88.8216.526.8
DeDoDe-V2-G [10, 11] CVPRW'24, 3DV'2447.263.977.533.147.660.2
RDD48.265.278.338.353.165.6
", + "bbox": [ + 91, + 141, + 478, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 406, + 225, + 424 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we demonstrate the performance of our method in Relative Pose Estimation on public benchmark datasets MegaDepth [22] and collected Air-to-Ground dataset, and in Visual Localization using Aachen Day-Night dataset [38]. All experiments are conducted on an NVIDIA H100 GPU.", + "bbox": [ + 89, + 431, + 485, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Relative Pose Estimation", + "text_level": 1, + "bbox": [ + 89, + 534, + 316, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset Following [8, 10, 32], we use the standard MegaDepth-1500 benchmark from D2-Net [8] for outdoor pose estimation and adopt the same test split. To further validate the performance of RDD in challenging scenarios, we construct two benchmark datasets. MegaDepth-View is derived from MegaDepth [22] test scenes, focusing on pairs with large viewpoint and scale changes; additionally, we sampled 1500 pairs from our collected Air-to-Ground dataset. This benchmark is designed to validate feature matching performance for large-baseline outdoor cross-view images, which is naturally challenging because of geometric distortion and significant viewpoint changes.", + "bbox": [ + 89, + 556, + 483, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics and Comparing Methods We report the AUC of recovered pose under threshold of $(5^{\\circ}, 10^{\\circ}$ , and $20^{\\circ}$ ). We use RANSAC to estimate the essential matrix. We compared RDD against the state-of-the-art detector/descriptor methods [6, 10, 13, 32, 41, 46, 47] and learned matching methods [5, 9, 12, 24, 37, 39, 44] on MegaDepth [22] dataset. For Air-to-Ground dataset, RDD is compared against detector/descriptor methods. More results on Air-to-Ground data can be found in the supplementary. For all sparse methods, we use resolution whose larger dimension", + "bbox": [ + 89, + 750, + 485, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/78e5dac39a0eceb11ff19778daf7791d0b8d9a587a0a79678908f83c1872b8d8.jpg", + "table_caption": [ + "Table 2. SotA comparison on proposed Air-to-Ground benchmark. Keypoints and descriptors are matched using dual-softmax MNN. Measured in AUC (higher is better). Best in bold, second best underlined." + ], + "table_footnote": [], + "table_body": "
Method@5°@10°@20°
SuperPoint [6] CVPRW'181.893.566.81
DISK [41] NeurIPS'2019.227.134.6
ALIKED [47] TIM'2312.017.825.8
XFeat [32] CVPR'246.1211.417.5
DeDoDe-V2-G [10, 11] CVPRW'24,3DV'2431.545.358.3
RDD41.456.067.8
", + "bbox": [ + 532, + 156, + 880, + 258 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/86826ff415c3befeeec007e65616d72414358c9dd72ac377fc1c53c877ab28e5.jpg", + "table_caption": [ + "Table 3. Homography estimation on HPatches. All methods perform well for illumination sequences. RDD provides high quality homography estimation especially when there are significant viewpoint changes. Best in bold, second best underlined." + ], + "table_footnote": [], + "table_body": "
MethodIlluminationViewpoint
MHAMHA
@3px@5px@10px@3px@5px@10px
SuperPoint [6] CVPRW'1893.098.099.970.082.087.0
DISK [41] NeurIPS'2096.098.098.072.081.084.0
ALIKED [47] TIM'2397.099.099.078.085.088.0
DeDoDe-G [10] 3DV'2496.099.099.968.077.080.0
XFeat [32] CVPR'2490.096.098.055.072.080.0
RDD93.099.099.976.086.090.0
", + "bbox": [ + 516, + 328, + 901, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is set to 1,600 pixels and use top 4,096 features, while all other learned matching methods follow experiment settings mentioned in their paper.", + "bbox": [ + 511, + 454, + 906, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results The results are presented in Tab. 1 and Tab. 2, and visually in Fig. 3. RDD demonstrates superior performance in the sparse matching setting compared to the state-of-the-art method DeDoDe-V2-G [10, 11], especially in more challenging scenarios. RDD with learned matcher LightGlue [24] also outperforms previous methods.", + "bbox": [ + 511, + 507, + 905, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results on MegaDepth-View and Air-to-Ground prove the effectiveness of our method under challenging scenarios with significant improvements over previous methods. RDD outperforms all previous feature detector/descriptor methods under large viewpoints and scale changes.", + "bbox": [ + 511, + 599, + 905, + 689 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Homography Estimation", + "text_level": 1, + "bbox": [ + 511, + 700, + 741, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets We evaluate the quality of correspondences estimated by RDD on HPatches dataset [1] for Homography Estimation. HPatches contains 52 sequences under significant illumination changes and 56 sequences that exhibit large variation in viewpoints. We use RANSAC to robustly estimate the homography given the estimated correspondences. All images are resized such that their shorter size is equal to 480 pixels.", + "bbox": [ + 511, + 724, + 905, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics and Comparing Methods We follow [32, 46] to estimate the mean homogeneity accuracy (MHA) with a predefined threshold of $\\{3,5,7\\}$ pixels. Accuracy is", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6400", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "computed using the average corner error in pixels by warping reference image corners onto target images using both ground truth and estimated homographies.", + "bbox": [ + 89, + 90, + 480, + 137 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on HPatches In Table 3, RDD shows a similar performance in illumination sequences compared to previous accurate keypoint detectors and descriptors, while outperforming most of the other methods on viewpoint changes, reinforcing the robustness of our proposed method in handling challenging cases such as large baseline pairs.", + "bbox": [ + 89, + 141, + 480, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Visual Localization", + "text_level": 1, + "bbox": [ + 89, + 241, + 274, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dataset We further validate the performance of RDD on the task of visual localization, which estimates the poses of a given query image with respect to the corresponding 3D scene reconstruction. We evaluate RDD on the Aachen Day-Night dataset [38]. It focuses on localizing high-quality night-time images against a day-time 3D model. There are 14,607 images with changing conditions of weather, season, viewpoints, and day-night cycles.", + "bbox": [ + 89, + 262, + 482, + 383 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d73a61ce95ab278646e93e88b7d49be328469cf3a4c775c12549cf3461732ad2.jpg", + "table_caption": [ + "Table 4. Visual Localization on Aachen day-night. RDD outperforms previous state-of-the-art methods with MNN matching for more challenging night setting. Best in bold, second best underlined." + ], + "table_footnote": [], + "table_body": "
MethodsDayNight
(0.25m,2°) / (0.5m,5°) / (1.0m,10°)
SuperPoint [6] CVPRW'1887.4 / 93.2 / 97.077.6 / 85.7 / 95.9
DISK [41] NeurIPS'2086.9 / 95.1 / 97.883.7 / 89.8 / 99.0
ALIKE [46] TM'2285.7 / 92.4 / 96.781.6 / 88.8 / 99.0
ALIKED [47] TIM'2386.5 / 93.4 / 96.885.7 / 91.8 / 96.9
XFeat [32] CVPR'2484.7 / 91.5 / 96.577.6 / 89.8 / 98.0
RDD87.0 / 94.2 / 97.886.7 / 92.9 / 99.0
", + "bbox": [ + 119, + 462, + 447, + 570 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7e2026149aad5539f157423472b5efc4e471a3a498d58f392de7b82e0e4f2c24.jpg", + "table_caption": [ + "Table 5. Ablation study on MegaDepth. We ablate the design choices for architecture and training strategies for relative pose estimation on MegaDepth." + ], + "table_footnote": [], + "table_body": "
VariantAUC@5°
RDDRDD*
Full48.251.3
Larger patch size s = 844.649.4
Less sample points Npq = 446.549.9
No keypoint branch44.1-
Joint training of two branches42.846.9
No match refinement-41.3
Without Air-to-Ground Data47.450.4
", + "bbox": [ + 125, + 631, + 436, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Metrics and Comparing Methods Following [32], HLoc [36] is used to evaluate all approaches [6, 32, 37, 41, 46, 47]. We resize the images such that their longer side is equal to 1,024 pixels and sample the top 4,096 keypoints for all approaches. We use the evaluation tool provided by [38] to calculate the metrics, the AUC of estimated camera poses under threshold of $\\{0.25\\mathrm{m}, 0.5\\mathrm{m}, 5\\mathrm{m}\\}$ for translation errors and $\\{2^{\\circ}, 5^{\\circ}, 10^{\\circ}\\}$ for rotation errors respectively.", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results Tab. 4 presents the results on visual localization. RDD outperforms all approaches in the challenging night setting. These results further validate the effectiveness of RDD.", + "bbox": [ + 511, + 90, + 906, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation", + "text_level": 1, + "bbox": [ + 511, + 162, + 617, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To better understand RDD, we evaluate 5 variants of RDD, with the results shown in Tab. 5: 1) Increasing the patch size of the transformer encoder results in a significant drop in accuracy. 2) Reducing the number of sampled points per query in deformable attention degrades pose estimation accuracy. 3) Removing the keypoint branch and using up-sampled matchability map as keypoint score map with NMS negatively affect the performance. 4) Joint training of the descriptor and keypoint branches leads to a significant drop in performance, as the weights of both branches are updated when only one task fails, making it even harder for the descriptor branch to converge. 5) Simply concatenating the semi-dense matches from matchability results in worse performance. 6) Training without Air-to-Ground dataset slightly damages the performance.", + "bbox": [ + 511, + 181, + 906, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations and Conclusion", + "text_level": 1, + "bbox": [ + 511, + 417, + 769, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present RDD, a robust feature detection and description framework based on deformable transformer, excelling in sparse image matching and demonstrating strong resilience to geometric transformations and varying conditions. By leveraging deformable attention, RDD efficiently extracts geometric-invariant features, enhancing accuracy and adaptability compared to traditional methods. RDD lacks explicit data augmentation during training and depends on confident priors from sparse correspondences which might lead to the failure of semi-dense matching. Training with data augmentation and improving the refinement module with visual features might boost the performance. RDD marks a significant advancement in keypoint detection and description, paving the way for impactful applications in challenging 3D vision tasks like cross-view scene modeling and visual localization.", + "bbox": [ + 511, + 443, + 906, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 511, + 694, + 692, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0075. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. We would like to thank Yayue Chen for her help with visualization.", + "bbox": [ + 511, + 719, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6401", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. Hpatches: A benchmark and evaluation of handcrafted and learned local descriptors. In CVPR, 2017. 2, 7", + "[2] Axel Barroso-Laguna, Edgar Riba, Daniel Ponsa, and Krystian Mikolajczyk. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 2, 3, 4" + ], + "bbox": [ + 91, + 92, + 480, + 883 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6403", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_model.json b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_model.json new file mode 100644 index 0000000000000000000000000000000000000000..791b243f207dde1f3fb5b253380940ac05660a28 --- /dev/null +++ b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_model.json @@ -0,0 +1,2233 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.131, + 0.895, + 0.154 + ], + "angle": 0, + "content": "RDD: Robust Feature Detector and Descriptor using Deformable Transformer" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.18, + 0.892, + 0.217 + ], + "angle": 0, + "content": "Gonglin Chen\\(^{1,2}\\), Tianwen Fu\\(^{1,2}\\), Haiwei Chen\\(^{1,2}\\), Wenbin Teng\\(^{1,2}\\), Hanyuan Xiao\\(^{1,2}\\), Yajie Zhao\\(^{1,2*}\\) \n\\(^{1}\\)Institute for Creative Technologies \n\\(^{2}\\)University of Southern California" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.219, + 0.71, + 0.253 + ], + "angle": 0, + "content": "{gonglinc, tianwenf}@usc.edu, chenh@ict.usc.edu, {wenbinte, hanyuanx}@usc.edu, zhao@ict.usc.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.318, + 0.486, + 0.697 + ], + "angle": 0, + "content": "As a core step in structure-from-motion and SLAM, robust feature detection and description under challenging scenarios such as significant viewpoint changes remain unresolved despite their ubiquity. While recent works have identified the importance of local features in modeling geometric transformations, these methods fail to learn the visual cues present in long-range relationships. We present Robust Deformable Detector (RDD), a novel and robust keypoint detector/descriptor leveraging the deformable transformer, which captures global context and geometric invariance through deformable self-attention mechanisms. Specifically, we observed that deformable attention focuses on key locations, effectively reducing the search space complexity and modeling the geometric invariance. Furthermore, we collected an Air-to-Ground dataset for training in addition to the standard MegaDepth dataset. Our proposed method outperforms all state-of-the-art keypoint detection/description methods in sparse matching tasks and is also capable of semi-dense matching. To ensure comprehensive evaluation, we introduce two challenging benchmarks: one emphasizing large viewpoint and scale variations, and the other being an Air-to-Ground benchmark — an evaluation setting that has recently gained popularity for 3D reconstruction across different altitudes. Project page: https://xtcpete.github.io/rdd/." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.704, + 0.222, + 0.72 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.73, + 0.484, + 0.88 + ], + "angle": 0, + "content": "Keypoint detection and description are central to numerous 3D computer vision tasks, including structure-from-motion (SfM), visual localization, and simultaneous localization and mapping (SLAM). These tasks depend on reliable keypoints and descriptors to establish accurate tracks, which are crucial for downstream algorithms to interpret spatial relationships—a requirement in fields from robotics to augmented reality [20]. When applied to real-world tasks, these systems face challenges such as significant viewpoint shifts, lighting variations, and scale changes." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.291, + 0.902, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.379, + 0.902, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.478, + 0.907, + 0.562 + ], + "angle": 0, + "content": "Figure 1. Our proposed method effectively performs both sparse and semi-dense feature matching, referred to as RDD and \\(\\mathbf{RDD}^*\\), respectively, as shown in the top section. RDD demonstrates its ability to extract accurate keypoints and robust descriptors, enabling reliable matching even under significant scale and viewpoint variations, as illustrated in the bottom section." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.569, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Historically, feature detection and description methods relied on rule-based techniques such as SIFT, SURF, and ORB [3, 25, 35]. However, these methods often struggled with the aforementioned challenges. To better address these issues, recent works [6, 13, 41, 46] leverage deep neural networks based on data-driven approaches which often extract more robust and discriminative descriptors than the rule-based ones. Despite the enhanced robustness that learning-based methods have, they often rely on regular convolutions to encode images [6, 13, 32, 41, 46], which ignore the geometric invariance and long-distance awareness critical for robust description under challenging conditions. Subsequently, [26, 28, 45] have partially addressed geometric invariance by estimating the scale and orientation of keypoint descriptors to model affine transformations. ALIKED [47] and ASLFeat [28] advanced this approach by using deformable convolutions capable of modeling any geometric transformations. However, these methods are limited to modeling transformations within local windows; features learned with the localized kernels of convolution operators fall short of learning important visual cues that depend on long-range relationships (e.g. vanishing lines)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6394" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.497 + ], + "angle": 0, + "content": "In this paper, we focus on feature detection and description in challenging scenarios that haven't been effectively addressed in prior works - specifically, extracting reliable and discriminative keypoints and descriptors across images with large camera baselines, significant illumination variations, and scale changes. We therefore propose RDD: a novel two-branch architecture for keypoint detection and description that can model both geometric invariance and global context at the same time. In particular, we design two dedicated network branches: a fully convolutional architecture to perform keypoint detection and a transformer-based architecture for extracting descriptors: the objectives of keypoint detection and description have previously been found not to align perfectly [21]. We observe that the convolutional neural network excels in detecting sub-pixel keypoints thanks to its expressiveness, whereas a transformer-based architecture is particularly suited for learning features that captures global context and possess geometric invariance through its self-attention mechanism [7, 42]. However, as self-attention layers attend to all spatial locations in the image, they significantly increase computational overhead and may reduce descriptor discriminability. To address this, we have adopted the deformable attention [48] for keypoint description, allowing our designed network to selectively focus on key locations, which greatly reduces time complexity while maintaining the capability to learn geometric invariance and global context." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.502, + 0.482, + 0.802 + ], + "angle": 0, + "content": "The two-branch architecture of RDD allows specialized architectures to learn keypoint detection and description independently. Our experiments have found that such design choice accelerates convergence and leads to better overall performance, as proven in Sec. 4.4. Overall, RDD is designed to be robust, achieving competitive performance on challenging imagery and also capable of semi-dense matching Fig. 1. This enhanced capability improves accuracy and stability in 3D vision applications, such as structure-from-motion (SfM) [4] and relative camera pose estimation under difficult imaging conditions. Our approach outperforms current state-of-the-art methods for keypoint detection and description on standard benchmarks, including MegaDepth-1500 [8], HPatches [1], and Aachen-Day-Night [38], across various tasks. However, to the best of our knowledge, no existing benchmarks accurately capture the aftermentioned challenging scenarios. To further validate the robustness of our method and provide a more comprehensive evaluation, we have collected and derived two additional benchmark datasets. The main contributions of our work are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.481, + 0.884 + ], + "angle": 0, + "content": "- A novel two branch architecture that utilizes a convolutional neural network for detecting accurate keypoints and transformer based network to extract robust descriptors under challenging scenarios, all while maintaining efficient runtime performance." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.481, + 0.899 + ], + "angle": 0, + "content": "- An innovative refinement module for semi-dense match" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.811, + 0.481, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.093, + 0.837, + 0.107 + ], + "angle": 0, + "content": "ing, improving matching accuracy and density." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.108, + 0.905, + 0.212 + ], + "angle": 0, + "content": "- Dataset contribution: MegaDepth-View, derived from MegaDepth [22], specifically focuses on challenging image pairs with large viewpoint and scale variations. Air-to-Ground dataset provides diverse aerial and ground cross view imagery for training and evaluation, enhancing robustness and performance and providing a new evaluation setting." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.228, + 0.655, + 0.244 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.254, + 0.802, + 0.27 + ], + "angle": 0, + "content": "2.1. Geometric Invariant Descriptors" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.277, + 0.905, + 0.427 + ], + "angle": 0, + "content": "In geometric invariance modeling, previous methods have primarily focused on two key aspects: scale and orientation. In traditional hand-crafted methods, SIFT [25] estimates a keypoint's scale and orientation by analyzing histograms of image gradients and subsequently extracts and normalizes image patches around the keypoint to construct scale- and orientation-invariant descriptors. Similarly, ORB [35] computes orientation based on the keypoint's center of mass, followed by rotation of the image patches to ensure orientation invariance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.905, + 0.7 + ], + "angle": 0, + "content": "Learning-based methods approach geometric invariance through two primary strategies. The majority of these methods [6, 8, 13, 32, 33, 41] relies heavily on data augmentation techniques to achieve scale and orientation invariance. On the other hand, some learning-based approaches explicitly model scale and orientation. For instance, LIFT [45] mimics SIFT [25] by detecting keypoints, estimating their orientation, and extracting descriptors with different neural networks. Other methods, such as AffNet [30] and LF-Net [31], predict affine transformation parameters and apply these transformations via Spatial Transformer Networks [18] to produce affine-invariant descriptors. These methods generally assume a predefined geometric transformation, typically affine transformations. More recent advancements, such as ASLFeat [28] and ALIKED [47], employ deformable convolutions to directly extract geometric-invariant features, offering a more flexible and adaptive approach to handling geometric variations." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.701, + 0.905, + 0.761 + ], + "angle": 0, + "content": "Inspired by the use of deformable convolutions in feature description, the proposed network RDD employs deformable attention to extract geometric invariant features that are not restricted by local windows." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.772, + 0.905, + 0.789 + ], + "angle": 0, + "content": "2.2. Decoupling Keypoint and Descriptor Learning" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.795, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In traditional handcrafted methods for feature detection and description, such as SIFT [25] and ORB [35], the detection and description processes are performed independently. This decoupled approach was also common in early learning-based methods [2, 29], where keypoint detection and description were treated as separate tasks. However, later works [6, 8, 13, 33] proposed an end-to-end frame" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6395" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.078, + 0.874, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.356, + 0.907, + 0.469 + ], + "angle": 0, + "content": "Figure 2. An overview of our network architecture. Descriptor Branch \\(\\mathcal{F}_D\\) and Keypoint Branch \\(\\mathcal{F}_K\\) process an input image \\(I\\in \\mathbb{R}^{H\\times W\\times 3}\\) independently. Descriptor Branch: 4 layers of multiscale feature maps \\(\\{\\mathbf{x}_{res}^l\\}_{l = 1}^L\\) are extracted by passing \\(I\\) through ResNet-50 [15] \\(\\mathcal{F}_{res}\\). Additional feature map at scale of \\(1 / 64\\) is added by applying a simple CNN on the last feature map and then they are fed to a transformer encoder \\(\\mathcal{F}_e\\) with positional embeddings [42]. We up-sample all feature maps output by \\(\\mathcal{F}_e\\) to size \\(H / k\\times W / k\\) where \\(k = 4\\) is the patch size. Feature maps are then summed together to generate the dense descriptor map \\(D\\). A classification head \\(\\mathcal{F}_m\\) is applied to the descriptor map to estimate a matchability map \\(M\\). Keypoint Branch: \\(I\\) passes through a lightweight CNN with residual connection [15] \\(\\mathcal{F}_{cnn}\\) to capture multi-scale features \\(\\{\\mathbf{x}_{cnn}^l\\}_{l = 1}^L\\). Features are then up-sampled to size \\(H\\times W\\) and concatenated to generate a feature map of \\(H\\times W\\times 64\\). A score map \\(S\\) is estimated by a classification head \\(\\mathcal{F}_s\\). Final sub-pixel keypoints are detected using DKD [46]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.482, + 0.485, + 0.753 + ], + "angle": 0, + "content": "work, jointly optimizing keypoint detection and descriptor extraction. This joint learning approach ensures that the detected keypoints and their descriptors complement each other. Despite the advantages, [21] highlighted a potential drawback of joint training, observing that poorly learned descriptors could negatively impact keypoint detection quality. Subsequently, DeDoDe[10] demonstrated that decoupling keypoint detection and description into two independent networks can significantly improve performance. Similarly, XFeat [32] showed that using task-specific networks provides a better balance between efficiency and accuracy. Inspired by these recent insights, RDD consists of two separate branches for independent keypoint detection and description. We also formulate a training strategy that optimize the descriptor branch first and then the keypoint branch. This design enables both sparse and dense matching and ensures optimized performance across various scenarios." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.771, + 0.37, + 0.785 + ], + "angle": 0, + "content": "2.3. Efficient Attention Mechanisms" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The quadratic complexity of multi-head attention [42] leads to long training schedules and limited spatial resolution for tractability. For 2D images, LR-Net [16] proposed a local relation layer, computing attention in a fixed local window. Linear Transformer [19] proposes to reduce the computation complexity of vanilla attention to linear complexity by substituting the exponential kernel with an alternative ker" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.482, + 0.907, + 0.604 + ], + "angle": 0, + "content": "nel function. Deformable attention [48] further allows the attention window to depend on the query features. With a linear projection predicting a deformable set of displacements from the center and their weight, each pixel in the feature map may attend to a fixed number of pixels of arbitrary distance. Deformable attention [48] is well-suited for our objectives, enabling efficient learning of global context, making it a fitting choice for our approach." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.615, + 0.613, + 0.631 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.853 + ], + "angle": 0, + "content": "Our method extracts descriptors and keypoints separately using a descriptor branch and a keypoint branch, as shown in Fig. 2. For an input image \\(I \\in \\mathbb{R}^{H \\times W \\times 3}\\), the descriptor branch first extracts multi-scale feature maps \\(\\{x_{res}^l\\}_{l=1}^L\\) from \\(I\\) using ResNet-50 [15], denoted as \\(\\mathcal{F}_{res}\\), and then estimates a descriptor map \\(D \\in \\mathbb{R}^{H/k \\times W/k}\\) through a deformable transformer encoder [48], denoted as \\(\\mathcal{F}_e\\), where \\(k = 4\\) is the patch size. The matchability map \\(M \\in \\mathbb{R}^{H/k \\times W/k}\\) is then estimated from \\(D\\) with a classification head \\(\\mathcal{F}_m\\). The keypoint branch \\(\\mathcal{F}_K\\) estimates a scoremap \\(S \\in \\mathbb{R}^{H \\times W}\\) by passing image \\(I\\) through a lightweight CNN with residual connection [15] \\(\\mathcal{F}_{cnn}\\) and a classification head \\(\\mathcal{F}_s\\), then sub-pixel keypoints \\(p_s = [x,y]^T\\) are detected with differentiable keypoint detection (DKD) [46]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The detected keypoints are used to sample their corresponding descriptors \\(d \\in \\mathbb{R}^{256}\\) from \\(D\\). In Sec. 3.1, we provide an overview of DKD [46] and deformable attenuated version of the original dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6396" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.152 + ], + "angle": 0, + "content": "tion [48]. In Sec. 3.2, we introduce the network architecture. In Sec. 3.3, we discuss how sparse and dense matching are obtained. Finally, the training details and loss functions are presented in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.161, + 0.232, + 0.175 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.183, + 0.373, + 0.199 + ], + "angle": 0, + "content": "3.1.1. Differentiable Keypoint Detection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.201, + 0.484, + 0.322 + ], + "angle": 0, + "content": "Given the scoremap \\( S \\), DKD detects sub-pixel keypoint locations through partially differentiable operations. First, local maximum scoremap \\( S_{nms} \\) is obtained by non-maximum suppression in local \\( N \\times N \\) windows. Pixel-level keypoints \\( p_{nms} = [x', y']^T \\) are then extracted by applying a threshold to \\( S_{nms} \\). DKD then selects all scores \\( s(i, j) \\) in the \\( N \\times N \\) windows centered on \\( p_{nms} \\) from \\( S \\) and estimates a sub-pixel-level offset through following steps:" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.323, + 0.382, + 0.338 + ], + "angle": 0, + "content": "\\(s(i,j)\\) are first normalized with softmax:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.348, + 0.483, + 0.381 + ], + "angle": 0, + "content": "\\[\ns ^ {\\prime} (i, j) = \\operatorname {s o f t m a x} \\left(\\frac {s (i , j) - s _ {\\max}}{t _ {d e t}}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.391, + 0.484, + 0.453 + ], + "angle": 0, + "content": "where \\(t_{det}\\) is the temperature. Then \\(s^{\\prime}(i,j)\\) represents the probability of \\([i,j]^T\\) to be a keypoint within the local window. Thus, the expected position of the keypoint in the local window can be given by integral regression [14, 40]:" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.462, + 0.483, + 0.495 + ], + "angle": 0, + "content": "\\[\n[ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} ^ {T} = \\sum_ {0 \\leq i, j < N} s ^ {\\prime} (i, j) [ i, j ] ^ {T}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.505, + 0.399, + 0.521 + ], + "angle": 0, + "content": "The final estimated sub-pixel-level keypoint is" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.529, + 0.483, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} _ {\\boldsymbol {s}} = \\left[ x, y \\right] ^ {T} = \\left[ x ^ {\\prime}, y ^ {\\prime} \\right] ^ {T} + \\left[ \\hat {i}, \\hat {j} \\right] _ {s o f t} ^ {T}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.559, + 0.291, + 0.572 + ], + "angle": 0, + "content": "3.1.2. Deformable Attention" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.576, + 0.484, + 0.637 + ], + "angle": 0, + "content": "Given a feature map \\(\\mathbf{x} \\in \\{\\mathbf{x}_{res}^{l}\\}_{l=1}^{L}\\), deformable attention selects a small set of sample keys \\(\\mathbf{p}_q\\) corresponding to the query index \\(q\\) and its feature vectors \\(\\mathbf{z}_q\\). The deformable attention feature \\(\\mathbf{x}_d\\) is calculated by" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.637, + 0.482, + 0.676 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\mathbf {x}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.675, + 0.137, + 0.687 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.69, + 0.483, + 0.732 + ], + "angle": 0, + "content": "\\[\nA _ {m q} = \\sum_ {k = 1} ^ {K} A _ {m q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} \\left(\\mathbf {p} _ {q} + \\Delta \\mathbf {p} _ {m q k}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.825 + ], + "angle": 0, + "content": "\\(m\\) indexes the attention head, \\(k\\) indexes the sampled keys, and \\(K\\) is the total number of sampled keys. \\(\\mathbf{W}\\) and \\(\\mathbf{W}'\\) are learnable weights. \\(\\Delta \\mathbf{p}_{mqk}\\) and \\(A_{mqk}\\) denote the sampling offset and attention weight of the \\(k\\)-th sampling point in the \\(m\\)-th attention head, where the sampling points are inferred by a linear layer." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Most of recent keypoint detection and description frameworks [10, 32, 46, 47] benefit from the use of multi-scale feature maps to capture fine details and broader spatial context. Deformable attention naturally extends to multi-scale feature maps [48], enabling the network to effectively adapt" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.137 + ], + "angle": 0, + "content": "to features at different scales. Similar to Eq. (4), multi-scale deformable attention feature \\(\\mathbf{x}_{msd}\\) can be calculated similar to Eq. (4) and Eq. (7)" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.139, + 0.905, + 0.179 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {m s d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\left\\{\\mathbf {x} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q} ^ {\\prime}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.18, + 0.56, + 0.193 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.206, + 0.905, + 0.248 + ], + "angle": 0, + "content": "\\[\nA _ {m q} ^ {\\prime} = \\left[ \\sum_ {l = 1} ^ {L} \\sum_ {k = 1} ^ {K} A _ {m l q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} _ {l} \\left(f _ {s} \\left(\\hat {p} _ {q}\\right) + \\Delta \\mathbf {p} _ {m l q k}\\right) \\right]. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.262, + 0.906, + 0.308 + ], + "angle": 0, + "content": "Here, \\( \\hat{p_q} \\in [0,1]^2 \\) is the normalized coordinates and function \\( f_s \\) re-scales it to match the scale of input feature map of the \\( l \\)-th level." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.321, + 0.72, + 0.336 + ], + "angle": 0, + "content": "3.2. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.344, + 0.906, + 0.403 + ], + "angle": 0, + "content": "Descriptor Branch The descriptor branch \\(\\mathcal{F}_D\\) extracts a dense feature map \\(D\\in \\mathbb{R}^{H / 4\\times W / 4\\times 256}\\) and a matchability map \\(M\\), which models that probability of a given feature vector can be matched." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.406, + 0.907, + 0.572 + ], + "angle": 0, + "content": "Using a ResNet-50 [15] as the CNN backbone, \\(\\mathcal{F}_{res}\\) extracts feature maps at 4 scales, each with resolutions of \\(1/4, 1/8, 1/16, 1/32\\) of the original image. An additional feature map at scale of \\(1/64\\) is then included by applying a CNN on the last feature map. These features are positionally encoded and fed into \\(\\mathcal{F}_e\\) with multi-scale deformable attention [48], enabling the network to dynamically attend to relevant spatial locations across multiple scales. We use 4 encoder layers each with 8 attention heads and each head samples 8 points. The entire process of the Descriptor Branch is illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.578, + 0.907, + 0.76 + ], + "angle": 0, + "content": "Keypoint Branch The keypoint branch is dedicated solely to detecting accurate keypoints without being influenced by descriptor estimation. \\(\\mathcal{F}_{cnn}\\) extracts feature maps at 4 different resolutions, each with a resolution of \\(1/1, 1/2, 1/8\\), and \\(1/32\\) of the original image and feature dimension of 32. These features are subsequently upsampled to match the original image resolution and concatenated to produce a feature map of size \\(H \\times W \\times 128\\). Then \\(\\mathcal{F}_s\\) is used to estimate the scoremap. DKD [46] is applied on the scoremap to perform non-maximum suppression and detect the sub-pixel-accurate keypoints. Fig. 2 depicts the entire process of the Keypoint Branch." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.772, + 0.689, + 0.788 + ], + "angle": 0, + "content": "3.3. Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.902 + ], + "angle": 0, + "content": "In this section, we describe how sparse matches and dense matches are obtained for a given image pair \\( I^1 \\) and \\( I^2 \\). Our network outputs sparse keypoints \\( p_s^{1,2} \\), descriptor maps \\( D^{1,2} \\), and matchability maps \\( M^{1,2} \\) all in a single forward pass. We bilinearly upsample \\( D^{1,2} \\) to match the original resolution of \\( I^1 \\) and \\( I^2 \\). Descriptors \\( d^{1,2} \\) are then sampled from \\( D^{1,2} \\) using \\( p_s^{1,2} \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6397" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.212 + ], + "angle": 0, + "content": "Sparse Matching Dual-Softmax operator [34, 41] is used to establish correspondences between two descriptors \\( d^{1,2} \\). The score matrix \\( S \\) between the descriptors is first calculated by \\( S(i,j) = \\frac{1}{\\tau} \\cdot \\langle d^1,d^2\\rangle \\), where \\( \\tau \\) is the temperature. We can now apply softmax on both dimensions of \\( S \\) to obtain the probability of soft mutual nearest neighbor (MNN) matching. The matching probability matrix \\( P \\) is obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.218, + 0.482, + 0.237 + ], + "angle": 0, + "content": "\\[\nP (i, j) = \\operatorname {s o f t m a x} (S (i, \\cdot)) _ {j} \\cdot \\operatorname {s o f t m a x} (S (\\cdot , j)) _ {i}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.241, + 0.483, + 0.3 + ], + "angle": 0, + "content": "Based on the confidence matrix \\( P \\), we select matches \\( m_{s} \\) with confidence higher than a threshold(0.01) to further enforce the mutual nearest neighbor criteria, which filters possible outlier matches." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.306, + 0.483, + 0.381 + ], + "angle": 0, + "content": "Semi-Dense Matching Recent works [5, 17, 39, 43] demonstrated the benefits of semi-dense feature matching by improving coverage and number of inliers. We propose a novel dense matching module that produces accurate and geometry consistent dense matches." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.382, + 0.483, + 0.593 + ], + "angle": 0, + "content": "Given images \\( I^{1} \\) and \\( I^{2} \\), our method can control the memory and computation usage by only selecting the top-K coarse keypoints \\( p_{c}^{1,2} \\) according to their matchability score \\( M^{1,2} \\). Then we can obtain the coarse matches \\( m_{c} \\) using equation Eq. (8), similar to how we obtain the sparse matches \\( m_{s} \\). These matches are naturally coarse matches and require refinement for sub-pixel level accuracy as \\( M \\)'s resolution is only \\( 1/4 \\) of the original resolution. Unlike existing methods [5, 39] that crop fine level features around coarse matches in \\( I^{1} \\) and \\( I^{2} \\) and then predict offset in \\( I^{2} \\), our work proposes a simple, efficient, and accurate module for semi-dense feature matching, inspired by [4] that utilizes sparse correspondences in guiding semi-dense feature matching." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.594, + 0.483, + 0.744 + ], + "angle": 0, + "content": "Differing from [4], which iteratively reassigns the coarse matches of detector-free methods, we adopt a similar idea to refine coarse matches to fine matches. With \\( m_{s} \\) obtained from sparse matching, we use the eight-point method to estimate a fundamental matrix \\( F \\) that relates corresponding points between \\( I^{1} \\) and \\( I^{2} \\). We keep \\( p_c^1 \\) unchanged and refine \\( p_c^2 \\) by solving offsets \\( (\\Delta x, \\Delta y) \\) that satisfy the epipolar constraint defined by \\( F \\). First, we convert \\( p_c^1 \\) to homogeneous coordinates \\( p_h^1 \\). Then, epipolar lines \\( L \\) in \\( I^{2} \\) for \\( p_h^1 \\) is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.245, + 0.744, + 0.482, + 0.76 + ], + "angle": 0, + "content": "\\[\nL = F \\cdot p _ {h} ^ {1}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.809 + ], + "angle": 0, + "content": "where each line is represented by coefficients \\(a, b\\) and \\(c\\). Offsets \\((\\Delta x, \\Delta y)\\) are then calculated for each point in \\(p_c^2\\) by solving the linear equation" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.815, + 0.482, + 0.831 + ], + "angle": 0, + "content": "\\[\na \\cdot (x + \\Delta x) + b \\cdot (y + \\Delta y) + c = 0 \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.838, + 0.476, + 0.853 + ], + "angle": 0, + "content": "to enforce the epipolar constraint. Then we can get offsets" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.858, + 0.483, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\Delta x = \\frac {b (b x - a y) - a c}{a ^ {2} + b ^ {2} + \\epsilon} - x, \\quad \\Delta y = \\frac {a (a y - b x) - b c}{a ^ {2} + b ^ {2} + \\epsilon} - y, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "where \\((x,y)\\) are the pixel coordinates of \\(p_c^2\\). We finally filter out points with offsets that are larger than the patch size (4) because they are moved outside the matched patch and likely outliers. We then obtain refined dense matches \\(m_c\\) by \\((x + \\Delta x, y + \\Delta y)\\). In Sec. 4.4, we show that without this refinement module, the performance of dense matching degrades significantly." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.206, + 0.731, + 0.221 + ], + "angle": 0, + "content": "3.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.907, + 0.41 + ], + "angle": 0, + "content": "We train RDD with pseudo ground truth correspondences from the MegaDepth dataset [22] and our Air-to-Ground dataset. We collect data from Internet drone videos and ground images of different famous landmarks, more details can be found in the supplementary. Following [37, 39], we use poses and depths to establish pixel correspondences. For every given image pair \\((I^1, I^2)\\) with \\(N\\) matching pixels, \\(m_{gt} \\in R^{N \\times 4}\\) is defined such that the first two columns are the pixel coordinates of points in \\(I^1\\) and the last two columns are those in \\(I^2\\) obtained through a warping function \\(f_{\\text{warp}}\\). We train the descriptor branch and the keypoint branch separately." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.415, + 0.906, + 0.612 + ], + "angle": 0, + "content": "Training Descriptor Branch To supervise the local feature descriptors, we apply focal loss [23] to focus on challenging examples and reduce the influence of easily classified matches. Given descriptor maps \\( D^{1} \\) and \\( D^{2} \\), we sample descriptor sets \\( d_{gt}^{1} \\) and \\( d_{gt}^{2} \\) based on the ground truth matchability \\( m_{gt} / k \\), where \\( k \\) is the patch size. The \\( i \\)-th rows, \\( d_{gt}^{1}(i) \\) and \\( d_{gt}^{2}(i) \\), represent descriptors corresponding to the same points in the images \\( I^{1} \\) and \\( I^{2} \\), respectively. Using these descriptors, we compute a probability matrix \\( P \\) as described in Eq. (8). Our supervision targets positive correspondences only, represented by the diagonal elements \\( P_{(i,i)} \\) of \\( P \\). By enforcing \\( P_{(i,i)} \\) to be close to 1, we calculate the focal loss \\( \\mathcal{L}_{focal} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.621, + 0.905, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f o c a l}} = - \\alpha \\cdot (1 - P _ {(i, i)}) ^ {\\gamma} \\cdot \\log \\left(P _ {(i, i)}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.647, + 0.699, + 0.662 + ], + "angle": 0, + "content": "where \\(\\alpha = 0.25\\) and \\(\\gamma = 2\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.663, + 0.906, + 0.738 + ], + "angle": 0, + "content": "To supervise the matchability map, we apply a modified focal loss that incorporates binary cross-entropy (BCE) on the matchability map \\( M^{1,2} \\). The ground truth matchability map \\( M_{gt}^{1,2} \\) is generated using \\( m_{gt} / k \\). We first compute the binary cross-entropy loss \\( \\mathcal{L}_{BCE} \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.748, + 0.905, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {B C E} = - \\left(M _ {g t} \\cdot \\log (M) + \\left(1 - M _ {g t}\\right) \\cdot \\log (1 - M)\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.773, + 0.905, + 0.805 + ], + "angle": 0, + "content": "and then replace \\(P_{(i,i)}\\) in Eq. (12) with \\(\\lambda = e^{-\\mathcal{L}_{BCE}}\\), resulting in the matchability loss \\(\\mathcal{L}_{\\text{matchability}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.815, + 0.905, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {m a t c h a b i l i t y}} = - \\alpha \\cdot (1 - \\lambda) ^ {\\gamma} \\cdot \\mathcal {L} _ {B C E}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "The final loss for the descriptor branch is defined as \\(\\mathcal{L}_D = \\mathcal{L}_{focal} + \\mathcal{L}_{matchability}\\). We train the descriptor branch on the mixture of MegaDepth dataset [22] and collected Air-to-Ground dataset, with images resized to 800." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6398" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.082, + 0.87, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.376, + 0.907, + 0.42 + ], + "angle": 0, + "content": "Figure 3. Qualitative Results on MegaDepth. RDD* and RDD are qualitatively compared to DeDoDe-V2-G [10, 11] ALIKED [47] and XFeat* [32]. RDD* and RDD are more robust compared DeDoDe-G* and ALIKED under challenging scenarios like large scale and viewpoint changes. The red color indicates epipolar error beyond \\(1 \\times 10^{-4}\\) (in the normalized image coordinates)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.433, + 0.484, + 0.524 + ], + "angle": 0, + "content": "The training uses a batch size of 32 image pairs and the AdamW optimizer [27]. We use a base learning rate of \\(1 \\cdot 10^{-4}\\) with a step learning rate scheduler that updates the learning rate every 2000 steps after 20000 steps with \\(\\gamma = 0.5\\). The descriptor branch converges after 1 day of training on 8 NVIDIA H100 GPU." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.535, + 0.484, + 0.626 + ], + "angle": 0, + "content": "Training Keypoint Branch We freeze the weights of descriptor branch once it converges and only supervise the keypoint branch to detect accurate and repeatable keypoints. We apply reprojection loss \\(\\mathcal{L}_{\\text {reprojection }}\\), reliability loss \\(\\mathcal{L}_{\\text {reliability }}\\) similar to [8, 28, 46] and dispersity peaky loss \\(\\mathcal{L}_{\\text {peaky }}\\) [46] to train repeatable and reliable keypoints." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.626, + 0.484, + 0.718 + ], + "angle": 0, + "content": "Given detected keypoint \\( p_s^1 \\) from \\( I^1 \\) and \\( p_s^2 \\) from \\( I^2 \\). We obtain the warped keypoints \\( p_s^{1\\rightarrow 2} \\) using \\( f_{warp} \\) and we find their closest keypoints from \\( p_s^2 \\) with distance less than 5 pixels as matched keypoints. Then, \\( dist_{1\\rightarrow 2} \\) is the reprojection distance between the matched \\( p_s^1 \\) and \\( p_s^2 \\). We define the reprojection loss in a symmetric way:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.724, + 0.482, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e p r o j e c t i o n}} = \\frac {1}{2} \\left(\\operatorname {d i s t} _ {1 \\rightarrow 2} + \\operatorname {d i s t} _ {2 \\rightarrow 1}\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.484, + 0.813 + ], + "angle": 0, + "content": "For keypoint \\( p_s^1 \\) and its warped keypoint \\( p_s^{1\\rightarrow 2} \\) with scores \\( s^1 \\) and \\( s^{1\\rightarrow 2} \\), and the probability map \\( P \\) as described in Sec. 3.3, the reliability map is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.825, + 0.482, + 0.859 + ], + "angle": 0, + "content": "\\[\nR = \\exp \\left(\\frac {P - 1}{t _ {r e l}}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "where \\( t_{rel} \\) is the temperature parameter. Considering all valid \\( p_s^1 \\) and warped points \\( p_s^{1\\rightarrow 2} \\), we sample the reliability" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.432, + 0.878, + 0.449 + ], + "angle": 0, + "content": "\\(r^1\\) from \\(R\\). The reliability loss for \\(p_s^1\\) is then defined as" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.459, + 0.907, + 0.501 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} = \\frac {1}{N _ {1}} \\sum_ {p _ {s} ^ {1}, p _ {s} ^ {1 \\rightarrow 2}} \\frac {s ^ {1} \\cdot s ^ {1 \\rightarrow 2}}{\\sum_ {p _ {s} ^ {1} , p _ {s} ^ {1 \\rightarrow 2}} s ^ {1} \\cdot s ^ {1 \\rightarrow 2}} (1 - r ^ {1}). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.511, + 0.906, + 0.538 + ], + "angle": 0, + "content": "Similarly, the total reliability loss is defined symmetrically as" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.538, + 0.905, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e l i a b i l i t y}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} + \\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {2}\\right). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.572, + 0.907, + 0.65 + ], + "angle": 0, + "content": "Eq. (15) optimizes the scores of keypoints in local window through the soft term \\([\\hat{i},\\hat{j}]_{soft}^{T}\\) of Eq. (3), which might affect the first term \\([x',y']_{nms}^{T}\\) of the equation. In order to align their optimization direction, we define the dispersity peak loss similar to [46] as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.66, + 0.905, + 0.698 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p e a k y}} = \\frac {1}{N ^ {2}} \\sum_ {0 \\leq i, j < N} d (i, j) s ^ {\\prime} (i, j), \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.703, + 0.58, + 0.716 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.725, + 0.905, + 0.753 + ], + "angle": 0, + "content": "\\[\nd (i, j) = \\left\\{\\left| \\left| [ i, j ] - [ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} \\right| \\right| _ {p} \\mid 0 \\leq i, j < N \\right\\}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.906, + 0.793 + ], + "angle": 0, + "content": "\\(N\\) is the window size and \\(s^{\\prime}(i,j)\\) are softmax scores defined in Eq. (1)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.793, + 0.906, + 0.899 + ], + "angle": 0, + "content": "The overall loss for the keypoint branch is defined as \\(\\mathcal{L}_K = \\mathcal{L}_{projection} + \\mathcal{L}_{reliability} + \\mathcal{L}_{peaky}\\). We use the DKD [46] with a window size of \\(N = 5\\) to detect the top 500 keypoints, and we randomly sample 500 keypoints from non-salient positions. We train the keypoint branch similarly to the descriptor branch, the keypoint branch converges after 4 hours of training on an NVIDIA H100 GPU." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6399" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.486, + 0.133 + ], + "angle": 0, + "content": "Table 1. SotA comparison on the MegaDepth [22]. Results are measured in AUC (higher is better). Top 4,096 features used to all sparse matching methods. Best in bold, second best underlined." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.142, + 0.48, + 0.394 + ], + "angle": 0, + "content": "
MethodMegaDepth-1500MegaDepth-View
@5°AUC @10°@20°@5°AUC @10°@20°
Dense
DKM [9] CVPR'2360.474.985.167.480.088.2
RoMa [12] CVPR'2462.676.786.369.981.889.4
Semi-Dense
LoFTR [39] CVPR'2152.869.281.250.665.877.9
ASpanFormer [5] ECCV'2255.371.583.161.375.284.6
ELoFTR [44] CVPR'2456.472.283.560.274.884.7
XFeat* [32] CVPR'2438.656.170.523.937.751.8
RDD*51.367.179.341.555.766.7
Sparse with Learned Matcher
SP [6]+SG [37] CVPR'1949.767.180.651.565.576.9
SP [6]+LG [24] ICCV'2349.967.080.152.467.378.5
Dedode-V2-G [10, 11]+LG [24] ICCV'2344.162.176.541.957.170.0
RDD+LG [24] ICCV'2352.368.981.854.269.380.3
Sparse with MNN
SuperPoint [6] CVPRW'1824.140.054.77.5013.321.1
DISK [41] Neulps'2038.553.766.630.441.951.6
ALIKED [47] TIM'2341.856.869.630.041.853.2
XFeat [32] CVPR'2424.040.155.88.8216.526.8
DeDoDe-V2-G [10, 11] CVPRW'24, 3DV'2447.263.977.533.147.660.2
RDD48.265.278.338.353.165.6
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.407, + 0.226, + 0.425 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.433, + 0.486, + 0.522 + ], + "angle": 0, + "content": "In this section, we demonstrate the performance of our method in Relative Pose Estimation on public benchmark datasets MegaDepth [22] and collected Air-to-Ground dataset, and in Visual Localization using Aachen Day-Night dataset [38]. All experiments are conducted on an NVIDIA H100 GPU." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.535, + 0.318, + 0.55 + ], + "angle": 0, + "content": "4.1. Relative Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.557, + 0.485, + 0.739 + ], + "angle": 0, + "content": "Dataset Following [8, 10, 32], we use the standard MegaDepth-1500 benchmark from D2-Net [8] for outdoor pose estimation and adopt the same test split. To further validate the performance of RDD in challenging scenarios, we construct two benchmark datasets. MegaDepth-View is derived from MegaDepth [22] test scenes, focusing on pairs with large viewpoint and scale changes; additionally, we sampled 1500 pairs from our collected Air-to-Ground dataset. This benchmark is designed to validate feature matching performance for large-baseline outdoor cross-view images, which is naturally challenging because of geometric distortion and significant viewpoint changes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Metrics and Comparing Methods We report the AUC of recovered pose under threshold of \\((5^{\\circ}, 10^{\\circ}\\), and \\(20^{\\circ}\\)). We use RANSAC to estimate the essential matrix. We compared RDD against the state-of-the-art detector/descriptor methods [6, 10, 13, 32, 41, 46, 47] and learned matching methods [5, 9, 12, 24, 37, 39, 44] on MegaDepth [22] dataset. For Air-to-Ground dataset, RDD is compared against detector/descriptor methods. More results on Air-to-Ground data can be found in the supplementary. For all sparse methods, we use resolution whose larger dimension" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.145 + ], + "angle": 0, + "content": "Table 2. SotA comparison on proposed Air-to-Ground benchmark. Keypoints and descriptors are matched using dual-softmax MNN. Measured in AUC (higher is better). Best in bold, second best underlined." + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.157, + 0.882, + 0.259 + ], + "angle": 0, + "content": "
Method@5°@10°@20°
SuperPoint [6] CVPRW'181.893.566.81
DISK [41] NeurIPS'2019.227.134.6
ALIKED [47] TIM'2312.017.825.8
XFeat [32] CVPR'246.1211.417.5
DeDoDe-V2-G [10, 11] CVPRW'24,3DV'2431.545.358.3
RDD41.456.067.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.262, + 0.907, + 0.319 + ], + "angle": 0, + "content": "Table 3. Homography estimation on HPatches. All methods perform well for illumination sequences. RDD provides high quality homography estimation especially when there are significant viewpoint changes. Best in bold, second best underlined." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.329, + 0.902, + 0.44 + ], + "angle": 0, + "content": "
MethodIlluminationViewpoint
MHAMHA
@3px@5px@10px@3px@5px@10px
SuperPoint [6] CVPRW'1893.098.099.970.082.087.0
DISK [41] NeurIPS'2096.098.098.072.081.084.0
ALIKED [47] TIM'2397.099.099.078.085.088.0
DeDoDe-G [10] 3DV'2496.099.099.968.077.080.0
XFeat [32] CVPR'2490.096.098.055.072.080.0
RDD93.099.099.976.086.090.0
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.455, + 0.907, + 0.502 + ], + "angle": 0, + "content": "is set to 1,600 pixels and use top 4,096 features, while all other learned matching methods follow experiment settings mentioned in their paper." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.906, + 0.599 + ], + "angle": 0, + "content": "Results The results are presented in Tab. 1 and Tab. 2, and visually in Fig. 3. RDD demonstrates superior performance in the sparse matching setting compared to the state-of-the-art method DeDoDe-V2-G [10, 11], especially in more challenging scenarios. RDD with learned matcher LightGlue [24] also outperforms previous methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.6, + 0.906, + 0.69 + ], + "angle": 0, + "content": "The results on MegaDepth-View and Air-to-Ground prove the effectiveness of our method under challenging scenarios with significant improvements over previous methods. RDD outperforms all previous feature detector/descriptor methods under large viewpoints and scale changes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.702, + 0.742, + 0.719 + ], + "angle": 0, + "content": "4.2. Homography Estimation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.725, + 0.906, + 0.846 + ], + "angle": 0, + "content": "Datasets We evaluate the quality of correspondences estimated by RDD on HPatches dataset [1] for Homography Estimation. HPatches contains 52 sequences under significant illumination changes and 56 sequences that exhibit large variation in viewpoints. We use RANSAC to robustly estimate the homography given the estimated correspondences. All images are resized such that their shorter size is equal to 480 pixels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Metrics and Comparing Methods We follow [32, 46] to estimate the mean homogeneity accuracy (MHA) with a predefined threshold of \\(\\{3,5,7\\}\\) pixels. Accuracy is" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6400" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.138 + ], + "angle": 0, + "content": "computed using the average corner error in pixels by warping reference image corners onto target images using both ground truth and estimated homographies." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.142, + 0.482, + 0.234 + ], + "angle": 0, + "content": "Results on HPatches In Table 3, RDD shows a similar performance in illumination sequences compared to previous accurate keypoint detectors and descriptors, while outperforming most of the other methods on viewpoint changes, reinforcing the robustness of our proposed method in handling challenging cases such as large baseline pairs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.242, + 0.276, + 0.258 + ], + "angle": 0, + "content": "4.3. Visual Localization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.263, + 0.483, + 0.385 + ], + "angle": 0, + "content": "Dataset We further validate the performance of RDD on the task of visual localization, which estimates the poses of a given query image with respect to the corresponding 3D scene reconstruction. We evaluate RDD on the Aachen Day-Night dataset [38]. It focuses on localizing high-quality night-time images against a day-time 3D model. There are 14,607 images with changing conditions of weather, season, viewpoints, and day-night cycles." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.397, + 0.483, + 0.452 + ], + "angle": 0, + "content": "Table 4. Visual Localization on Aachen day-night. RDD outperforms previous state-of-the-art methods with MNN matching for more challenging night setting. Best in bold, second best underlined." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.463, + 0.449, + 0.571 + ], + "angle": 0, + "content": "
MethodsDayNight
(0.25m,2°) / (0.5m,5°) / (1.0m,10°)
SuperPoint [6] CVPRW'1887.4 / 93.2 / 97.077.6 / 85.7 / 95.9
DISK [41] NeurIPS'2086.9 / 95.1 / 97.883.7 / 89.8 / 99.0
ALIKE [46] TM'2285.7 / 92.4 / 96.781.6 / 88.8 / 99.0
ALIKED [47] TIM'2386.5 / 93.4 / 96.885.7 / 91.8 / 96.9
XFeat [32] CVPR'2484.7 / 91.5 / 96.577.6 / 89.8 / 98.0
RDD87.0 / 94.2 / 97.886.7 / 92.9 / 99.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.579, + 0.483, + 0.622 + ], + "angle": 0, + "content": "Table 5. Ablation study on MegaDepth. We ablate the design choices for architecture and training strategies for relative pose estimation on MegaDepth." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.632, + 0.437, + 0.773 + ], + "angle": 0, + "content": "
VariantAUC@5°
RDDRDD*
Full48.251.3
Larger patch size s = 844.649.4
Less sample points Npq = 446.549.9
No keypoint branch44.1-
Joint training of two branches42.846.9
No match refinement-41.3
Without Air-to-Ground Data47.450.4
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Metrics and Comparing Methods Following [32], HLoc [36] is used to evaluate all approaches [6, 32, 37, 41, 46, 47]. We resize the images such that their longer side is equal to 1,024 pixels and sample the top 4,096 keypoints for all approaches. We use the evaluation tool provided by [38] to calculate the metrics, the AUC of estimated camera poses under threshold of \\(\\{0.25\\mathrm{m}, 0.5\\mathrm{m}, 5\\mathrm{m}\\}\\) for translation errors and \\(\\{2^{\\circ}, 5^{\\circ}, 10^{\\circ}\\}\\) for rotation errors respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.151 + ], + "angle": 0, + "content": "Results Tab. 4 presents the results on visual localization. RDD outperforms all approaches in the challenging night setting. These results further validate the effectiveness of RDD." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.163, + 0.618, + 0.178 + ], + "angle": 0, + "content": "4.4. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.907, + 0.412 + ], + "angle": 0, + "content": "To better understand RDD, we evaluate 5 variants of RDD, with the results shown in Tab. 5: 1) Increasing the patch size of the transformer encoder results in a significant drop in accuracy. 2) Reducing the number of sampled points per query in deformable attention degrades pose estimation accuracy. 3) Removing the keypoint branch and using up-sampled matchability map as keypoint score map with NMS negatively affect the performance. 4) Joint training of the descriptor and keypoint branches leads to a significant drop in performance, as the weights of both branches are updated when only one task fails, making it even harder for the descriptor branch to converge. 5) Simply concatenating the semi-dense matches from matchability results in worse performance. 6) Training without Air-to-Ground dataset slightly damages the performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.419, + 0.771, + 0.435 + ], + "angle": 0, + "content": "5. Limitations and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.444, + 0.907, + 0.686 + ], + "angle": 0, + "content": "We present RDD, a robust feature detection and description framework based on deformable transformer, excelling in sparse image matching and demonstrating strong resilience to geometric transformations and varying conditions. By leveraging deformable attention, RDD efficiently extracts geometric-invariant features, enhancing accuracy and adaptability compared to traditional methods. RDD lacks explicit data augmentation during training and depends on confident priors from sparse correspondences which might lead to the failure of semi-dense matching. Training with data augmentation and improving the refinement module with visual features might boost the performance. RDD marks a significant advancement in keypoint detection and description, paving the way for impactful applications in challenging 3D vision tasks like cross-view scene modeling and visual localization." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.695, + 0.694, + 0.712 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0075. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. We would like to thank Yayue Chen for her help with visualization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6401" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. Hpatches: A benchmark and evaluation of handcrafted and learned local descriptors. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 2, 3, 4" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.885 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6403" + } + ] +] \ No newline at end of file diff --git a/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_origin.pdf b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9697cb11fd4a4490835a86227faeaea853f91603 --- /dev/null +++ b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/dd7235df-3118-4324-8db3-9be17c94a765_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4be0a76a8c028fee4fa8b3d2963f98e71dd37a7ab8019e07d4613e5c45c21f63 +size 3090175 diff --git a/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/full.md b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a1fbb155751c17cec17b135188b83cb38c92e08d --- /dev/null +++ b/2025/RDD_ Robust Feature Detector and Descriptor using Deformable Transformer/full.md @@ -0,0 +1,359 @@ +# RDD: Robust Feature Detector and Descriptor using Deformable Transformer + +Gonglin Chen $^{1,2}$ , Tianwen Fu $^{1,2}$ , Haiwei Chen $^{1,2}$ , Wenbin Teng $^{1,2}$ , Hanyuan Xiao $^{1,2}$ , Yajie Zhao $^{1,2*}$ $^{1}$ Institute for Creative Technologies + $^{2}$ University of Southern California + +{gonglinc, tianwenf}@usc.edu, chenh@ict.usc.edu, {wenbinte, hanyuanx}@usc.edu, zhao@ict.usc.edu + +# Abstract + +As a core step in structure-from-motion and SLAM, robust feature detection and description under challenging scenarios such as significant viewpoint changes remain unresolved despite their ubiquity. While recent works have identified the importance of local features in modeling geometric transformations, these methods fail to learn the visual cues present in long-range relationships. We present Robust Deformable Detector (RDD), a novel and robust keypoint detector/descriptor leveraging the deformable transformer, which captures global context and geometric invariance through deformable self-attention mechanisms. Specifically, we observed that deformable attention focuses on key locations, effectively reducing the search space complexity and modeling the geometric invariance. Furthermore, we collected an Air-to-Ground dataset for training in addition to the standard MegaDepth dataset. Our proposed method outperforms all state-of-the-art keypoint detection/description methods in sparse matching tasks and is also capable of semi-dense matching. To ensure comprehensive evaluation, we introduce two challenging benchmarks: one emphasizing large viewpoint and scale variations, and the other being an Air-to-Ground benchmark — an evaluation setting that has recently gained popularity for 3D reconstruction across different altitudes. Project page: https://xtcpete.github.io/rdd/. + +# 1. Introduction + +Keypoint detection and description are central to numerous 3D computer vision tasks, including structure-from-motion (SfM), visual localization, and simultaneous localization and mapping (SLAM). These tasks depend on reliable keypoints and descriptors to establish accurate tracks, which are crucial for downstream algorithms to interpret spatial relationships—a requirement in fields from robotics to augmented reality [20]. When applied to real-world tasks, these systems face challenges such as significant viewpoint shifts, lighting variations, and scale changes. + +![](images/dfe1613409498ce448d5ac0074ac4a260bbbbdb34a2af6a67e397f5b0af5d270.jpg) + +![](images/c8757cb36584c0083de557fdede5a577b8cdb7380f30992307c59a445582f14f.jpg) +Figure 1. Our proposed method effectively performs both sparse and semi-dense feature matching, referred to as RDD and $\mathbf{RDD}^*$ , respectively, as shown in the top section. RDD demonstrates its ability to extract accurate keypoints and robust descriptors, enabling reliable matching even under significant scale and viewpoint variations, as illustrated in the bottom section. + +Historically, feature detection and description methods relied on rule-based techniques such as SIFT, SURF, and ORB [3, 25, 35]. However, these methods often struggled with the aforementioned challenges. To better address these issues, recent works [6, 13, 41, 46] leverage deep neural networks based on data-driven approaches which often extract more robust and discriminative descriptors than the rule-based ones. Despite the enhanced robustness that learning-based methods have, they often rely on regular convolutions to encode images [6, 13, 32, 41, 46], which ignore the geometric invariance and long-distance awareness critical for robust description under challenging conditions. Subsequently, [26, 28, 45] have partially addressed geometric invariance by estimating the scale and orientation of keypoint descriptors to model affine transformations. ALIKED [47] and ASLFeat [28] advanced this approach by using deformable convolutions capable of modeling any geometric transformations. However, these methods are limited to modeling transformations within local windows; features learned with the localized kernels of convolution operators fall short of learning important visual cues that depend on long-range relationships (e.g. vanishing lines). + +In this paper, we focus on feature detection and description in challenging scenarios that haven't been effectively addressed in prior works - specifically, extracting reliable and discriminative keypoints and descriptors across images with large camera baselines, significant illumination variations, and scale changes. We therefore propose RDD: a novel two-branch architecture for keypoint detection and description that can model both geometric invariance and global context at the same time. In particular, we design two dedicated network branches: a fully convolutional architecture to perform keypoint detection and a transformer-based architecture for extracting descriptors: the objectives of keypoint detection and description have previously been found not to align perfectly [21]. We observe that the convolutional neural network excels in detecting sub-pixel keypoints thanks to its expressiveness, whereas a transformer-based architecture is particularly suited for learning features that captures global context and possess geometric invariance through its self-attention mechanism [7, 42]. However, as self-attention layers attend to all spatial locations in the image, they significantly increase computational overhead and may reduce descriptor discriminability. To address this, we have adopted the deformable attention [48] for keypoint description, allowing our designed network to selectively focus on key locations, which greatly reduces time complexity while maintaining the capability to learn geometric invariance and global context. + +The two-branch architecture of RDD allows specialized architectures to learn keypoint detection and description independently. Our experiments have found that such design choice accelerates convergence and leads to better overall performance, as proven in Sec. 4.4. Overall, RDD is designed to be robust, achieving competitive performance on challenging imagery and also capable of semi-dense matching Fig. 1. This enhanced capability improves accuracy and stability in 3D vision applications, such as structure-from-motion (SfM) [4] and relative camera pose estimation under difficult imaging conditions. Our approach outperforms current state-of-the-art methods for keypoint detection and description on standard benchmarks, including MegaDepth-1500 [8], HPatches [1], and Aachen-Day-Night [38], across various tasks. However, to the best of our knowledge, no existing benchmarks accurately capture the aftermentioned challenging scenarios. To further validate the robustness of our method and provide a more comprehensive evaluation, we have collected and derived two additional benchmark datasets. The main contributions of our work are: + +- A novel two branch architecture that utilizes a convolutional neural network for detecting accurate keypoints and transformer based network to extract robust descriptors under challenging scenarios, all while maintaining efficient runtime performance. +- An innovative refinement module for semi-dense match + +ing, improving matching accuracy and density. + +- Dataset contribution: MegaDepth-View, derived from MegaDepth [22], specifically focuses on challenging image pairs with large viewpoint and scale variations. Air-to-Ground dataset provides diverse aerial and ground cross view imagery for training and evaluation, enhancing robustness and performance and providing a new evaluation setting. + +# 2. Related Work + +# 2.1. Geometric Invariant Descriptors + +In geometric invariance modeling, previous methods have primarily focused on two key aspects: scale and orientation. In traditional hand-crafted methods, SIFT [25] estimates a keypoint's scale and orientation by analyzing histograms of image gradients and subsequently extracts and normalizes image patches around the keypoint to construct scale- and orientation-invariant descriptors. Similarly, ORB [35] computes orientation based on the keypoint's center of mass, followed by rotation of the image patches to ensure orientation invariance. + +Learning-based methods approach geometric invariance through two primary strategies. The majority of these methods [6, 8, 13, 32, 33, 41] relies heavily on data augmentation techniques to achieve scale and orientation invariance. On the other hand, some learning-based approaches explicitly model scale and orientation. For instance, LIFT [45] mimics SIFT [25] by detecting keypoints, estimating their orientation, and extracting descriptors with different neural networks. Other methods, such as AffNet [30] and LF-Net [31], predict affine transformation parameters and apply these transformations via Spatial Transformer Networks [18] to produce affine-invariant descriptors. These methods generally assume a predefined geometric transformation, typically affine transformations. More recent advancements, such as ASLFeat [28] and ALIKED [47], employ deformable convolutions to directly extract geometric-invariant features, offering a more flexible and adaptive approach to handling geometric variations. + +Inspired by the use of deformable convolutions in feature description, the proposed network RDD employs deformable attention to extract geometric invariant features that are not restricted by local windows. + +# 2.2. Decoupling Keypoint and Descriptor Learning + +In traditional handcrafted methods for feature detection and description, such as SIFT [25] and ORB [35], the detection and description processes are performed independently. This decoupled approach was also common in early learning-based methods [2, 29], where keypoint detection and description were treated as separate tasks. However, later works [6, 8, 13, 33] proposed an end-to-end frame + +![](images/040bcfe99fa180cce2334932a657b8b8322f3eef3a309cb0778263d9c08693f0.jpg) +Figure 2. An overview of our network architecture. Descriptor Branch $\mathcal{F}_D$ and Keypoint Branch $\mathcal{F}_K$ process an input image $I\in \mathbb{R}^{H\times W\times 3}$ independently. Descriptor Branch: 4 layers of multiscale feature maps $\{\mathbf{x}_{res}^l\}_{l = 1}^L$ are extracted by passing $I$ through ResNet-50 [15] $\mathcal{F}_{res}$ . Additional feature map at scale of $1 / 64$ is added by applying a simple CNN on the last feature map and then they are fed to a transformer encoder $\mathcal{F}_e$ with positional embeddings [42]. We up-sample all feature maps output by $\mathcal{F}_e$ to size $H / k\times W / k$ where $k = 4$ is the patch size. Feature maps are then summed together to generate the dense descriptor map $D$ . A classification head $\mathcal{F}_m$ is applied to the descriptor map to estimate a matchability map $M$ . Keypoint Branch: $I$ passes through a lightweight CNN with residual connection [15] $\mathcal{F}_{cnn}$ to capture multi-scale features $\{\mathbf{x}_{cnn}^l\}_{l = 1}^L$ . Features are then up-sampled to size $H\times W$ and concatenated to generate a feature map of $H\times W\times 64$ . A score map $S$ is estimated by a classification head $\mathcal{F}_s$ . Final sub-pixel keypoints are detected using DKD [46]. + +work, jointly optimizing keypoint detection and descriptor extraction. This joint learning approach ensures that the detected keypoints and their descriptors complement each other. Despite the advantages, [21] highlighted a potential drawback of joint training, observing that poorly learned descriptors could negatively impact keypoint detection quality. Subsequently, DeDoDe[10] demonstrated that decoupling keypoint detection and description into two independent networks can significantly improve performance. Similarly, XFeat [32] showed that using task-specific networks provides a better balance between efficiency and accuracy. Inspired by these recent insights, RDD consists of two separate branches for independent keypoint detection and description. We also formulate a training strategy that optimize the descriptor branch first and then the keypoint branch. This design enables both sparse and dense matching and ensures optimized performance across various scenarios. + +# 2.3. Efficient Attention Mechanisms + +The quadratic complexity of multi-head attention [42] leads to long training schedules and limited spatial resolution for tractability. For 2D images, LR-Net [16] proposed a local relation layer, computing attention in a fixed local window. Linear Transformer [19] proposes to reduce the computation complexity of vanilla attention to linear complexity by substituting the exponential kernel with an alternative ker + +nel function. Deformable attention [48] further allows the attention window to depend on the query features. With a linear projection predicting a deformable set of displacements from the center and their weight, each pixel in the feature map may attend to a fixed number of pixels of arbitrary distance. Deformable attention [48] is well-suited for our objectives, enabling efficient learning of global context, making it a fitting choice for our approach. + +# 3. Methods + +Our method extracts descriptors and keypoints separately using a descriptor branch and a keypoint branch, as shown in Fig. 2. For an input image $I \in \mathbb{R}^{H \times W \times 3}$ , the descriptor branch first extracts multi-scale feature maps $\{x_{res}^l\}_{l=1}^L$ from $I$ using ResNet-50 [15], denoted as $\mathcal{F}_{res}$ , and then estimates a descriptor map $D \in \mathbb{R}^{H/k \times W/k}$ through a deformable transformer encoder [48], denoted as $\mathcal{F}_e$ , where $k = 4$ is the patch size. The matchability map $M \in \mathbb{R}^{H/k \times W/k}$ is then estimated from $D$ with a classification head $\mathcal{F}_m$ . The keypoint branch $\mathcal{F}_K$ estimates a scoremap $S \in \mathbb{R}^{H \times W}$ by passing image $I$ through a lightweight CNN with residual connection [15] $\mathcal{F}_{cnn}$ and a classification head $\mathcal{F}_s$ , then sub-pixel keypoints $p_s = [x,y]^T$ are detected with differentiable keypoint detection (DKD) [46]. + +The detected keypoints are used to sample their corresponding descriptors $d \in \mathbb{R}^{256}$ from $D$ . In Sec. 3.1, we provide an overview of DKD [46] and deformable attenuated version of the original dataset. + +tion [48]. In Sec. 3.2, we introduce the network architecture. In Sec. 3.3, we discuss how sparse and dense matching are obtained. Finally, the training details and loss functions are presented in Sec. 3.4. + +# 3.1. Preliminaries + +# 3.1.1. Differentiable Keypoint Detection + +Given the scoremap $S$ , DKD detects sub-pixel keypoint locations through partially differentiable operations. First, local maximum scoremap $S_{nms}$ is obtained by non-maximum suppression in local $N \times N$ windows. Pixel-level keypoints $p_{nms} = [x', y']^T$ are then extracted by applying a threshold to $S_{nms}$ . DKD then selects all scores $s(i, j)$ in the $N \times N$ windows centered on $p_{nms}$ from $S$ and estimates a sub-pixel-level offset through following steps: + +$s(i,j)$ are first normalized with softmax: + +$$ +s ^ {\prime} (i, j) = \operatorname {s o f t m a x} \left(\frac {s (i , j) - s _ {\max}}{t _ {d e t}}\right), \tag {1} +$$ + +where $t_{det}$ is the temperature. Then $s^{\prime}(i,j)$ represents the probability of $[i,j]^T$ to be a keypoint within the local window. Thus, the expected position of the keypoint in the local window can be given by integral regression [14, 40]: + +$$ +[ \hat {i}, \hat {j} ] _ {\text {s o f t}} ^ {T} = \sum_ {0 \leq i, j < N} s ^ {\prime} (i, j) [ i, j ] ^ {T}. \tag {2} +$$ + +The final estimated sub-pixel-level keypoint is + +$$ +\boldsymbol {p} _ {\boldsymbol {s}} = \left[ x, y \right] ^ {T} = \left[ x ^ {\prime}, y ^ {\prime} \right] ^ {T} + \left[ \hat {i}, \hat {j} \right] _ {s o f t} ^ {T}. \tag {3} +$$ + +# 3.1.2. Deformable Attention + +Given a feature map $\mathbf{x} \in \{\mathbf{x}_{res}^{l}\}_{l=1}^{L}$ , deformable attention selects a small set of sample keys $\mathbf{p}_q$ corresponding to the query index $q$ and its feature vectors $\mathbf{z}_q$ . The deformable attention feature $\mathbf{x}_d$ is calculated by + +$$ +\mathbf {x} _ {d} \left(\mathbf {z} _ {q}, \mathbf {p} _ {q}, \mathbf {x}\right) = \sum_ {m = 1} ^ {M} \mathbf {W} _ {m} A _ {m q}, \tag {4} +$$ + +where + +$$ +A _ {m q} = \sum_ {k = 1} ^ {K} A _ {m q k} \cdot \mathbf {W} _ {m} ^ {\prime} \mathbf {x} \left(\mathbf {p} _ {q} + \Delta \mathbf {p} _ {m q k}\right), \tag {5} +$$ + +$m$ indexes the attention head, $k$ indexes the sampled keys, and $K$ is the total number of sampled keys. $\mathbf{W}$ and $\mathbf{W}'$ are learnable weights. $\Delta \mathbf{p}_{mqk}$ and $A_{mqk}$ denote the sampling offset and attention weight of the $k$ -th sampling point in the $m$ -th attention head, where the sampling points are inferred by a linear layer. + +Most of recent keypoint detection and description frameworks [10, 32, 46, 47] benefit from the use of multi-scale feature maps to capture fine details and broader spatial context. Deformable attention naturally extends to multi-scale feature maps [48], enabling the network to effectively adapt + +to features at different scales. Similar to Eq. (4), multi-scale deformable attention feature $\mathbf{x}_{msd}$ can be calculated similar to Eq. (4) and Eq. (7) + +$$ +\mathbf {x} _ {m s d} \left(\mathbf {z} _ {q}, \mathbf {p} _ {q}, \left\{\mathbf {x} ^ {l} \right\} _ {l = 1} ^ {L}\right) = \sum_ {m = 1} ^ {M} \mathbf {W} _ {m} A _ {m q} ^ {\prime}, \tag {6} +$$ + +where + +$$ +A _ {m q} ^ {\prime} = \left[ \sum_ {l = 1} ^ {L} \sum_ {k = 1} ^ {K} A _ {m l q k} \cdot \mathbf {W} _ {m} ^ {\prime} \mathbf {x} _ {l} \left(f _ {s} \left(\hat {p} _ {q}\right) + \Delta \mathbf {p} _ {m l q k}\right) \right]. \tag {7} +$$ + +Here, $\hat{p_q} \in [0,1]^2$ is the normalized coordinates and function $f_s$ re-scales it to match the scale of input feature map of the $l$ -th level. + +# 3.2. Network Architecture + +Descriptor Branch The descriptor branch $\mathcal{F}_D$ extracts a dense feature map $D\in \mathbb{R}^{H / 4\times W / 4\times 256}$ and a matchability map $M$ , which models that probability of a given feature vector can be matched. + +Using a ResNet-50 [15] as the CNN backbone, $\mathcal{F}_{res}$ extracts feature maps at 4 scales, each with resolutions of $1/4, 1/8, 1/16, 1/32$ of the original image. An additional feature map at scale of $1/64$ is then included by applying a CNN on the last feature map. These features are positionally encoded and fed into $\mathcal{F}_e$ with multi-scale deformable attention [48], enabling the network to dynamically attend to relevant spatial locations across multiple scales. We use 4 encoder layers each with 8 attention heads and each head samples 8 points. The entire process of the Descriptor Branch is illustrated in Fig. 2. + +Keypoint Branch The keypoint branch is dedicated solely to detecting accurate keypoints without being influenced by descriptor estimation. $\mathcal{F}_{cnn}$ extracts feature maps at 4 different resolutions, each with a resolution of $1/1, 1/2, 1/8$ , and $1/32$ of the original image and feature dimension of 32. These features are subsequently upsampled to match the original image resolution and concatenated to produce a feature map of size $H \times W \times 128$ . Then $\mathcal{F}_s$ is used to estimate the scoremap. DKD [46] is applied on the scoremap to perform non-maximum suppression and detect the sub-pixel-accurate keypoints. Fig. 2 depicts the entire process of the Keypoint Branch. + +# 3.3. Feature Matching + +In this section, we describe how sparse matches and dense matches are obtained for a given image pair $I^1$ and $I^2$ . Our network outputs sparse keypoints $p_s^{1,2}$ , descriptor maps $D^{1,2}$ , and matchability maps $M^{1,2}$ all in a single forward pass. We bilinearly upsample $D^{1,2}$ to match the original resolution of $I^1$ and $I^2$ . Descriptors $d^{1,2}$ are then sampled from $D^{1,2}$ using $p_s^{1,2}$ . + +Sparse Matching Dual-Softmax operator [34, 41] is used to establish correspondences between two descriptors $d^{1,2}$ . The score matrix $S$ between the descriptors is first calculated by $S(i,j) = \frac{1}{\tau} \cdot \langle d^1,d^2\rangle$ , where $\tau$ is the temperature. We can now apply softmax on both dimensions of $S$ to obtain the probability of soft mutual nearest neighbor (MNN) matching. The matching probability matrix $P$ is obtained by: + +$$ +P (i, j) = \operatorname {s o f t m a x} (S (i, \cdot)) _ {j} \cdot \operatorname {s o f t m a x} (S (\cdot , j)) _ {i}. \tag {8} +$$ + +Based on the confidence matrix $P$ , we select matches $m_{s}$ with confidence higher than a threshold(0.01) to further enforce the mutual nearest neighbor criteria, which filters possible outlier matches. + +Semi-Dense Matching Recent works [5, 17, 39, 43] demonstrated the benefits of semi-dense feature matching by improving coverage and number of inliers. We propose a novel dense matching module that produces accurate and geometry consistent dense matches. + +Given images $I^{1}$ and $I^{2}$ , our method can control the memory and computation usage by only selecting the top-K coarse keypoints $p_{c}^{1,2}$ according to their matchability score $M^{1,2}$ . Then we can obtain the coarse matches $m_{c}$ using equation Eq. (8), similar to how we obtain the sparse matches $m_{s}$ . These matches are naturally coarse matches and require refinement for sub-pixel level accuracy as $M$ 's resolution is only $1/4$ of the original resolution. Unlike existing methods [5, 39] that crop fine level features around coarse matches in $I^{1}$ and $I^{2}$ and then predict offset in $I^{2}$ , our work proposes a simple, efficient, and accurate module for semi-dense feature matching, inspired by [4] that utilizes sparse correspondences in guiding semi-dense feature matching. + +Differing from [4], which iteratively reassigns the coarse matches of detector-free methods, we adopt a similar idea to refine coarse matches to fine matches. With $m_{s}$ obtained from sparse matching, we use the eight-point method to estimate a fundamental matrix $F$ that relates corresponding points between $I^{1}$ and $I^{2}$ . We keep $p_c^1$ unchanged and refine $p_c^2$ by solving offsets $(\Delta x, \Delta y)$ that satisfy the epipolar constraint defined by $F$ . First, we convert $p_c^1$ to homogeneous coordinates $p_h^1$ . Then, epipolar lines $L$ in $I^{2}$ for $p_h^1$ is computed by + +$$ +L = F \cdot p _ {h} ^ {1}, \tag {9} +$$ + +where each line is represented by coefficients $a, b$ and $c$ . Offsets $(\Delta x, \Delta y)$ are then calculated for each point in $p_c^2$ by solving the linear equation + +$$ +a \cdot (x + \Delta x) + b \cdot (y + \Delta y) + c = 0 \tag {10} +$$ + +to enforce the epipolar constraint. Then we can get offsets + +$$ +\Delta x = \frac {b (b x - a y) - a c}{a ^ {2} + b ^ {2} + \epsilon} - x, \quad \Delta y = \frac {a (a y - b x) - b c}{a ^ {2} + b ^ {2} + \epsilon} - y, \tag {11} +$$ + +where $(x,y)$ are the pixel coordinates of $p_c^2$ . We finally filter out points with offsets that are larger than the patch size (4) because they are moved outside the matched patch and likely outliers. We then obtain refined dense matches $m_c$ by $(x + \Delta x, y + \Delta y)$ . In Sec. 4.4, we show that without this refinement module, the performance of dense matching degrades significantly. + +# 3.4. Implementation Details + +We train RDD with pseudo ground truth correspondences from the MegaDepth dataset [22] and our Air-to-Ground dataset. We collect data from Internet drone videos and ground images of different famous landmarks, more details can be found in the supplementary. Following [37, 39], we use poses and depths to establish pixel correspondences. For every given image pair $(I^1, I^2)$ with $N$ matching pixels, $m_{gt} \in R^{N \times 4}$ is defined such that the first two columns are the pixel coordinates of points in $I^1$ and the last two columns are those in $I^2$ obtained through a warping function $f_{\text{warp}}$ . We train the descriptor branch and the keypoint branch separately. + +Training Descriptor Branch To supervise the local feature descriptors, we apply focal loss [23] to focus on challenging examples and reduce the influence of easily classified matches. Given descriptor maps $D^{1}$ and $D^{2}$ , we sample descriptor sets $d_{gt}^{1}$ and $d_{gt}^{2}$ based on the ground truth matchability $m_{gt} / k$ , where $k$ is the patch size. The $i$ -th rows, $d_{gt}^{1}(i)$ and $d_{gt}^{2}(i)$ , represent descriptors corresponding to the same points in the images $I^{1}$ and $I^{2}$ , respectively. Using these descriptors, we compute a probability matrix $P$ as described in Eq. (8). Our supervision targets positive correspondences only, represented by the diagonal elements $P_{(i,i)}$ of $P$ . By enforcing $P_{(i,i)}$ to be close to 1, we calculate the focal loss $\mathcal{L}_{focal}$ as follows: + +$$ +\mathcal {L} _ {\text {f o c a l}} = - \alpha \cdot (1 - P _ {(i, i)}) ^ {\gamma} \cdot \log \left(P _ {(i, i)}\right), \tag {12} +$$ + +where $\alpha = 0.25$ and $\gamma = 2$ . + +To supervise the matchability map, we apply a modified focal loss that incorporates binary cross-entropy (BCE) on the matchability map $M^{1,2}$ . The ground truth matchability map $M_{gt}^{1,2}$ is generated using $m_{gt} / k$ . We first compute the binary cross-entropy loss $\mathcal{L}_{BCE}$ as + +$$ +\mathcal {L} _ {B C E} = - \left(M _ {g t} \cdot \log (M) + \left(1 - M _ {g t}\right) \cdot \log (1 - M)\right), \tag {13} +$$ + +and then replace $P_{(i,i)}$ in Eq. (12) with $\lambda = e^{-\mathcal{L}_{BCE}}$ , resulting in the matchability loss $\mathcal{L}_{\text{matchability}}$ : + +$$ +\mathcal {L} _ {\text {m a t c h a b i l i t y}} = - \alpha \cdot (1 - \lambda) ^ {\gamma} \cdot \mathcal {L} _ {B C E}. \tag {14} +$$ + +The final loss for the descriptor branch is defined as $\mathcal{L}_D = \mathcal{L}_{focal} + \mathcal{L}_{matchability}$ . We train the descriptor branch on the mixture of MegaDepth dataset [22] and collected Air-to-Ground dataset, with images resized to 800. + +![](images/b532cb0dd16e6351e39fc229f0ac8db2d5f914d5f0be0cd34fb345e81ea7ea9f.jpg) +Figure 3. Qualitative Results on MegaDepth. RDD* and RDD are qualitatively compared to DeDoDe-V2-G [10, 11] ALIKED [47] and XFeat* [32]. RDD* and RDD are more robust compared DeDoDe-G* and ALIKED under challenging scenarios like large scale and viewpoint changes. The red color indicates epipolar error beyond $1 \times 10^{-4}$ (in the normalized image coordinates) + +The training uses a batch size of 32 image pairs and the AdamW optimizer [27]. We use a base learning rate of $1 \cdot 10^{-4}$ with a step learning rate scheduler that updates the learning rate every 2000 steps after 20000 steps with $\gamma = 0.5$ . The descriptor branch converges after 1 day of training on 8 NVIDIA H100 GPU. + +Training Keypoint Branch We freeze the weights of descriptor branch once it converges and only supervise the keypoint branch to detect accurate and repeatable keypoints. We apply reprojection loss $\mathcal{L}_{\text {reprojection }}$ , reliability loss $\mathcal{L}_{\text {reliability }}$ similar to [8, 28, 46] and dispersity peaky loss $\mathcal{L}_{\text {peaky }}$ [46] to train repeatable and reliable keypoints. + +Given detected keypoint $p_s^1$ from $I^1$ and $p_s^2$ from $I^2$ . We obtain the warped keypoints $p_s^{1\rightarrow 2}$ using $f_{warp}$ and we find their closest keypoints from $p_s^2$ with distance less than 5 pixels as matched keypoints. Then, $dist_{1\rightarrow 2}$ is the reprojection distance between the matched $p_s^1$ and $p_s^2$ . We define the reprojection loss in a symmetric way: + +$$ +\mathcal {L} _ {\text {r e p r o j e c t i o n}} = \frac {1}{2} \left(\operatorname {d i s t} _ {1 \rightarrow 2} + \operatorname {d i s t} _ {2 \rightarrow 1}\right), \tag {15} +$$ + +For keypoint $p_s^1$ and its warped keypoint $p_s^{1\rightarrow 2}$ with scores $s^1$ and $s^{1\rightarrow 2}$ , and the probability map $P$ as described in Sec. 3.3, the reliability map is defined as + +$$ +R = \exp \left(\frac {P - 1}{t _ {r e l}}\right), \tag {16} +$$ + +where $t_{rel}$ is the temperature parameter. Considering all valid $p_s^1$ and warped points $p_s^{1\rightarrow 2}$ , we sample the reliability + +$r^1$ from $R$ . The reliability loss for $p_s^1$ is then defined as + +$$ +\mathcal {L} _ {\text {r e l i a b i l i t y}} ^ {1} = \frac {1}{N _ {1}} \sum_ {p _ {s} ^ {1}, p _ {s} ^ {1 \rightarrow 2}} \frac {s ^ {1} \cdot s ^ {1 \rightarrow 2}}{\sum_ {p _ {s} ^ {1} , p _ {s} ^ {1 \rightarrow 2}} s ^ {1} \cdot s ^ {1 \rightarrow 2}} (1 - r ^ {1}). \tag {17} +$$ + +Similarly, the total reliability loss is defined symmetrically as + +$$ +\mathcal {L} _ {\text {r e l i a b i l i t y}} = \frac {1}{2} \left(\mathcal {L} _ {\text {r e l i a b i l i t y}} ^ {1} + \mathcal {L} _ {\text {r e l i a b i l i t y}} ^ {2}\right). \tag {18} +$$ + +Eq. (15) optimizes the scores of keypoints in local window through the soft term $[\hat{i},\hat{j}]_{soft}^{T}$ of Eq. (3), which might affect the first term $[x',y']_{nms}^{T}$ of the equation. In order to align their optimization direction, we define the dispersity peak loss similar to [46] as + +$$ +\mathcal {L} _ {\text {p e a k y}} = \frac {1}{N ^ {2}} \sum_ {0 \leq i, j < N} d (i, j) s ^ {\prime} (i, j), \tag {19} +$$ + +where + +$$ +d (i, j) = \left\{\left| \left| [ i, j ] - [ \hat {i}, \hat {j} ] _ {\text {s o f t}} \right| \right| _ {p} \mid 0 \leq i, j < N \right\}, \tag {20} +$$ + +$N$ is the window size and $s^{\prime}(i,j)$ are softmax scores defined in Eq. (1). + +The overall loss for the keypoint branch is defined as $\mathcal{L}_K = \mathcal{L}_{projection} + \mathcal{L}_{reliability} + \mathcal{L}_{peaky}$ . We use the DKD [46] with a window size of $N = 5$ to detect the top 500 keypoints, and we randomly sample 500 keypoints from non-salient positions. We train the keypoint branch similarly to the descriptor branch, the keypoint branch converges after 4 hours of training on an NVIDIA H100 GPU. + +Table 1. SotA comparison on the MegaDepth [22]. Results are measured in AUC (higher is better). Top 4,096 features used to all sparse matching methods. Best in bold, second best underlined. + +
MethodMegaDepth-1500MegaDepth-View
@5°AUC @10°@20°@5°AUC @10°@20°
Dense
DKM [9] CVPR'2360.474.985.167.480.088.2
RoMa [12] CVPR'2462.676.786.369.981.889.4
Semi-Dense
LoFTR [39] CVPR'2152.869.281.250.665.877.9
ASpanFormer [5] ECCV'2255.371.583.161.375.284.6
ELoFTR [44] CVPR'2456.472.283.560.274.884.7
XFeat* [32] CVPR'2438.656.170.523.937.751.8
RDD*51.367.179.341.555.766.7
Sparse with Learned Matcher
SP [6]+SG [37] CVPR'1949.767.180.651.565.576.9
SP [6]+LG [24] ICCV'2349.967.080.152.467.378.5
Dedode-V2-G [10, 11]+LG [24] ICCV'2344.162.176.541.957.170.0
RDD+LG [24] ICCV'2352.368.981.854.269.380.3
Sparse with MNN
SuperPoint [6] CVPRW'1824.140.054.77.5013.321.1
DISK [41] Neulps'2038.553.766.630.441.951.6
ALIKED [47] TIM'2341.856.869.630.041.853.2
XFeat [32] CVPR'2424.040.155.88.8216.526.8
DeDoDe-V2-G [10, 11] CVPRW'24, 3DV'2447.263.977.533.147.660.2
RDD48.265.278.338.353.165.6
+ +# 4. Experiments + +In this section, we demonstrate the performance of our method in Relative Pose Estimation on public benchmark datasets MegaDepth [22] and collected Air-to-Ground dataset, and in Visual Localization using Aachen Day-Night dataset [38]. All experiments are conducted on an NVIDIA H100 GPU. + +# 4.1. Relative Pose Estimation + +Dataset Following [8, 10, 32], we use the standard MegaDepth-1500 benchmark from D2-Net [8] for outdoor pose estimation and adopt the same test split. To further validate the performance of RDD in challenging scenarios, we construct two benchmark datasets. MegaDepth-View is derived from MegaDepth [22] test scenes, focusing on pairs with large viewpoint and scale changes; additionally, we sampled 1500 pairs from our collected Air-to-Ground dataset. This benchmark is designed to validate feature matching performance for large-baseline outdoor cross-view images, which is naturally challenging because of geometric distortion and significant viewpoint changes. + +Metrics and Comparing Methods We report the AUC of recovered pose under threshold of $(5^{\circ}, 10^{\circ}$ , and $20^{\circ}$ ). We use RANSAC to estimate the essential matrix. We compared RDD against the state-of-the-art detector/descriptor methods [6, 10, 13, 32, 41, 46, 47] and learned matching methods [5, 9, 12, 24, 37, 39, 44] on MegaDepth [22] dataset. For Air-to-Ground dataset, RDD is compared against detector/descriptor methods. More results on Air-to-Ground data can be found in the supplementary. For all sparse methods, we use resolution whose larger dimension + +Table 2. SotA comparison on proposed Air-to-Ground benchmark. Keypoints and descriptors are matched using dual-softmax MNN. Measured in AUC (higher is better). Best in bold, second best underlined. + +
Method@5°@10°@20°
SuperPoint [6] CVPRW'181.893.566.81
DISK [41] NeurIPS'2019.227.134.6
ALIKED [47] TIM'2312.017.825.8
XFeat [32] CVPR'246.1211.417.5
DeDoDe-V2-G [10, 11] CVPRW'24,3DV'2431.545.358.3
RDD41.456.067.8
+ +Table 3. Homography estimation on HPatches. All methods perform well for illumination sequences. RDD provides high quality homography estimation especially when there are significant viewpoint changes. Best in bold, second best underlined. + +
MethodIlluminationViewpoint
MHAMHA
@3px@5px@10px@3px@5px@10px
SuperPoint [6] CVPRW'1893.098.099.970.082.087.0
DISK [41] NeurIPS'2096.098.098.072.081.084.0
ALIKED [47] TIM'2397.099.099.078.085.088.0
DeDoDe-G [10] 3DV'2496.099.099.968.077.080.0
XFeat [32] CVPR'2490.096.098.055.072.080.0
RDD93.099.099.976.086.090.0
+ +is set to 1,600 pixels and use top 4,096 features, while all other learned matching methods follow experiment settings mentioned in their paper. + +Results The results are presented in Tab. 1 and Tab. 2, and visually in Fig. 3. RDD demonstrates superior performance in the sparse matching setting compared to the state-of-the-art method DeDoDe-V2-G [10, 11], especially in more challenging scenarios. RDD with learned matcher LightGlue [24] also outperforms previous methods. + +The results on MegaDepth-View and Air-to-Ground prove the effectiveness of our method under challenging scenarios with significant improvements over previous methods. RDD outperforms all previous feature detector/descriptor methods under large viewpoints and scale changes. + +# 4.2. Homography Estimation + +Datasets We evaluate the quality of correspondences estimated by RDD on HPatches dataset [1] for Homography Estimation. HPatches contains 52 sequences under significant illumination changes and 56 sequences that exhibit large variation in viewpoints. We use RANSAC to robustly estimate the homography given the estimated correspondences. All images are resized such that their shorter size is equal to 480 pixels. + +Metrics and Comparing Methods We follow [32, 46] to estimate the mean homogeneity accuracy (MHA) with a predefined threshold of $\{3,5,7\}$ pixels. Accuracy is + +computed using the average corner error in pixels by warping reference image corners onto target images using both ground truth and estimated homographies. + +Results on HPatches In Table 3, RDD shows a similar performance in illumination sequences compared to previous accurate keypoint detectors and descriptors, while outperforming most of the other methods on viewpoint changes, reinforcing the robustness of our proposed method in handling challenging cases such as large baseline pairs. + +# 4.3. Visual Localization + +Dataset We further validate the performance of RDD on the task of visual localization, which estimates the poses of a given query image with respect to the corresponding 3D scene reconstruction. We evaluate RDD on the Aachen Day-Night dataset [38]. It focuses on localizing high-quality night-time images against a day-time 3D model. There are 14,607 images with changing conditions of weather, season, viewpoints, and day-night cycles. + +Table 4. Visual Localization on Aachen day-night. RDD outperforms previous state-of-the-art methods with MNN matching for more challenging night setting. Best in bold, second best underlined. + +
MethodsDayNight
(0.25m,2°) / (0.5m,5°) / (1.0m,10°)
SuperPoint [6] CVPRW'1887.4 / 93.2 / 97.077.6 / 85.7 / 95.9
DISK [41] NeurIPS'2086.9 / 95.1 / 97.883.7 / 89.8 / 99.0
ALIKE [46] TM'2285.7 / 92.4 / 96.781.6 / 88.8 / 99.0
ALIKED [47] TIM'2386.5 / 93.4 / 96.885.7 / 91.8 / 96.9
XFeat [32] CVPR'2484.7 / 91.5 / 96.577.6 / 89.8 / 98.0
RDD87.0 / 94.2 / 97.886.7 / 92.9 / 99.0
+ +Table 5. Ablation study on MegaDepth. We ablate the design choices for architecture and training strategies for relative pose estimation on MegaDepth. + +
VariantAUC@5°
RDDRDD*
Full48.251.3
Larger patch size s = 844.649.4
Less sample points Npq = 446.549.9
No keypoint branch44.1-
Joint training of two branches42.846.9
No match refinement-41.3
Without Air-to-Ground Data47.450.4
+ +Metrics and Comparing Methods Following [32], HLoc [36] is used to evaluate all approaches [6, 32, 37, 41, 46, 47]. We resize the images such that their longer side is equal to 1,024 pixels and sample the top 4,096 keypoints for all approaches. We use the evaluation tool provided by [38] to calculate the metrics, the AUC of estimated camera poses under threshold of $\{0.25\mathrm{m}, 0.5\mathrm{m}, 5\mathrm{m}\}$ for translation errors and $\{2^{\circ}, 5^{\circ}, 10^{\circ}\}$ for rotation errors respectively. + +Results Tab. 4 presents the results on visual localization. RDD outperforms all approaches in the challenging night setting. These results further validate the effectiveness of RDD. + +# 4.4. Ablation + +To better understand RDD, we evaluate 5 variants of RDD, with the results shown in Tab. 5: 1) Increasing the patch size of the transformer encoder results in a significant drop in accuracy. 2) Reducing the number of sampled points per query in deformable attention degrades pose estimation accuracy. 3) Removing the keypoint branch and using up-sampled matchability map as keypoint score map with NMS negatively affect the performance. 4) Joint training of the descriptor and keypoint branches leads to a significant drop in performance, as the weights of both branches are updated when only one task fails, making it even harder for the descriptor branch to converge. 5) Simply concatenating the semi-dense matches from matchability results in worse performance. 6) Training without Air-to-Ground dataset slightly damages the performance. + +# 5. Limitations and Conclusion + +We present RDD, a robust feature detection and description framework based on deformable transformer, excelling in sparse image matching and demonstrating strong resilience to geometric transformations and varying conditions. By leveraging deformable attention, RDD efficiently extracts geometric-invariant features, enhancing accuracy and adaptability compared to traditional methods. RDD lacks explicit data augmentation during training and depends on confident priors from sparse correspondences which might lead to the failure of semi-dense matching. Training with data augmentation and improving the refinement module with visual features might boost the performance. RDD marks a significant advancement in keypoint detection and description, paving the way for impactful applications in challenging 3D vision tasks like cross-view scene modeling and visual localization. + +# 6. Acknowledgement + +Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0075. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. We would like to thank Yayue Chen for her help with visualization. + +# References + +[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. Hpatches: A benchmark and evaluation of handcrafted and learned local descriptors. In CVPR, 2017. 2, 7 +[2] Axel Barroso-Laguna, Edgar Riba, Daniel Ponsa, and Krystian Mikolajczyk. 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Aliked: A lighter keypoint and descriptor extraction network via deformable transformation, 2023. 1, 2, 4, 6, 7, 8 +[48] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 578, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 296, + 696 + ], + "type": "text", + "content": "Keypoint detection and description are central to numerous 3D computer vision tasks, including structure-from-motion (SfM), visual localization, and simultaneous localization and mapping (SLAM). These tasks depend on reliable keypoints and descriptors to establish accurate tracks, which are crucial for downstream algorithms to interpret spatial relationships—a requirement in fields from robotics to augmented reality [20]. 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Our proposed method effectively performs both sparse and semi-dense feature matching, referred to as RDD and " + }, + { + "bbox": [ + 313, + 378, + 555, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{RDD}^*" + }, + { + "bbox": [ + 313, + 378, + 555, + 445 + ], + "type": "text", + "content": ", respectively, as shown in the top section. RDD demonstrates its ability to extract accurate keypoints and robust descriptors, enabling reliable matching even under significant scale and viewpoint variations, as illustrated in the bottom section." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 450, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 450, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 450, + 556, + 715 + ], + "type": "text", + "content": "Historically, feature detection and description methods relied on rule-based techniques such as SIFT, SURF, and ORB [3, 25, 35]. However, these methods often struggled with the aforementioned challenges. To better address these issues, recent works [6, 13, 41, 46] leverage deep neural networks based on data-driven approaches which often extract more robust and discriminative descriptors than the rule-based ones. Despite the enhanced robustness that learning-based methods have, they often rely on regular convolutions to encode images [6, 13, 32, 41, 46], which ignore the geometric invariance and long-distance awareness critical for robust description under challenging conditions. Subsequently, [26, 28, 45] have partially addressed geometric invariance by estimating the scale and orientation of keypoint descriptors to model affine transformations. ALIKED [47] and ASLFeat [28] advanced this approach by using deformable convolutions capable of modeling any geometric transformations. However, these methods are limited to modeling transformations within local windows; features learned with the localized kernels of convolution operators fall short of learning important visual cues that depend on long-range relationships (e.g. vanishing lines)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6394" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 393 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 393 + ], + "type": "text", + "content": "In this paper, we focus on feature detection and description in challenging scenarios that haven't been effectively addressed in prior works - specifically, extracting reliable and discriminative keypoints and descriptors across images with large camera baselines, significant illumination variations, and scale changes. We therefore propose RDD: a novel two-branch architecture for keypoint detection and description that can model both geometric invariance and global context at the same time. In particular, we design two dedicated network branches: a fully convolutional architecture to perform keypoint detection and a transformer-based architecture for extracting descriptors: the objectives of keypoint detection and description have previously been found not to align perfectly [21]. We observe that the convolutional neural network excels in detecting sub-pixel keypoints thanks to its expressiveness, whereas a transformer-based architecture is particularly suited for learning features that captures global context and possess geometric invariance through its self-attention mechanism [7, 42]. However, as self-attention layers attend to all spatial locations in the image, they significantly increase computational overhead and may reduce descriptor discriminability. To address this, we have adopted the deformable attention [48] for keypoint description, allowing our designed network to selectively focus on key locations, which greatly reduces time complexity while maintaining the capability to learn geometric invariance and global context." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 397, + 294, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 397, + 294, + 635 + ], + "spans": [ + { + "bbox": [ + 57, + 397, + 294, + 635 + ], + "type": "text", + "content": "The two-branch architecture of RDD allows specialized architectures to learn keypoint detection and description independently. Our experiments have found that such design choice accelerates convergence and leads to better overall performance, as proven in Sec. 4.4. Overall, RDD is designed to be robust, achieving competitive performance on challenging imagery and also capable of semi-dense matching Fig. 1. This enhanced capability improves accuracy and stability in 3D vision applications, such as structure-from-motion (SfM) [4] and relative camera pose estimation under difficult imaging conditions. Our approach outperforms current state-of-the-art methods for keypoint detection and description on standard benchmarks, including MegaDepth-1500 [8], HPatches [1], and Aachen-Day-Night [38], across various tasks. However, to the best of our knowledge, no existing benchmarks accurately capture the aftermentioned challenging scenarios. To further validate the robustness of our method and provide a more comprehensive evaluation, we have collected and derived two additional benchmark datasets. The main contributions of our work are:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 642, + 294, + 712 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 55, + 642, + 294, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 294, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 294, + 700 + ], + "type": "text", + "content": "- A novel two branch architecture that utilizes a convolutional neural network for detecting accurate keypoints and transformer based network to extract robust descriptors under challenging scenarios, all while maintaining efficient runtime performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 701, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 294, + 712 + ], + "type": "text", + "content": "- An innovative refinement module for semi-dense match" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 322, + 73, + 512, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 73, + 512, + 84 + ], + "spans": [ + { + "bbox": [ + 322, + 73, + 512, + 84 + ], + "type": "text", + "content": "ing, improving matching accuracy and density." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 85, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 85, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 315, + 85, + 553, + 167 + ], + "type": "text", + "content": "- Dataset contribution: MegaDepth-View, derived from MegaDepth [22], specifically focuses on challenging image pairs with large viewpoint and scale variations. Air-to-Ground dataset provides diverse aerial and ground cross view imagery for training and evaluation, enhancing robustness and performance and providing a new evaluation setting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 180, + 400, + 193 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 180, + 400, + 193 + ], + "spans": [ + { + "bbox": [ + 314, + 180, + 400, + 193 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 201, + 490, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 201, + 490, + 213 + ], + "spans": [ + { + "bbox": [ + 314, + 201, + 490, + 213 + ], + "type": "text", + "content": "2.1. Geometric Invariant Descriptors" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 219, + 553, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 553, + 338 + ], + "type": "text", + "content": "In geometric invariance modeling, previous methods have primarily focused on two key aspects: scale and orientation. In traditional hand-crafted methods, SIFT [25] estimates a keypoint's scale and orientation by analyzing histograms of image gradients and subsequently extracts and normalizes image patches around the keypoint to construct scale- and orientation-invariant descriptors. Similarly, ORB [35] computes orientation based on the keypoint's center of mass, followed by rotation of the image patches to ensure orientation invariance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 339, + 553, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 553, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 553, + 554 + ], + "type": "text", + "content": "Learning-based methods approach geometric invariance through two primary strategies. The majority of these methods [6, 8, 13, 32, 33, 41] relies heavily on data augmentation techniques to achieve scale and orientation invariance. On the other hand, some learning-based approaches explicitly model scale and orientation. For instance, LIFT [45] mimics SIFT [25] by detecting keypoints, estimating their orientation, and extracting descriptors with different neural networks. Other methods, such as AffNet [30] and LF-Net [31], predict affine transformation parameters and apply these transformations via Spatial Transformer Networks [18] to produce affine-invariant descriptors. These methods generally assume a predefined geometric transformation, typically affine transformations. More recent advancements, such as ASLFeat [28] and ALIKED [47], employ deformable convolutions to directly extract geometric-invariant features, offering a more flexible and adaptive approach to handling geometric variations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 555, + 553, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 553, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 553, + 602 + ], + "type": "text", + "content": "Inspired by the use of deformable convolutions in feature description, the proposed network RDD employs deformable attention to extract geometric invariant features that are not restricted by local windows." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 611, + 553, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 553, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 553, + 624 + ], + "type": "text", + "content": "2.2. Decoupling Keypoint and Descriptor Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "type": "text", + "content": "In traditional handcrafted methods for feature detection and description, such as SIFT [25] and ORB [35], the detection and description processes are performed independently. This decoupled approach was also common in early learning-based methods [2, 29], where keypoint detection and description were treated as separate tasks. 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An overview of our network architecture. Descriptor Branch " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_D" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " and Keypoint Branch " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_K" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " process an input image " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "I\\in \\mathbb{R}^{H\\times W\\times 3}" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " independently. 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We up-sample all feature maps output by " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_e" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " to size " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "H / k\\times W / k" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "k = 4" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " is the patch size. Feature maps are then summed together to generate the dense descriptor map " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": ". 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Features are then up-sampled to size " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " and concatenated to generate a feature map of " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "H\\times W\\times 64" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": ". A score map " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": " is estimated by a classification head " + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_s" + }, + { + "bbox": [ + 55, + 281, + 555, + 371 + ], + "type": "text", + "content": ". Final sub-pixel keypoints are detected using DKD [46]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 381, + 296, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 381, + 296, + 596 + ], + "spans": [ + { + "bbox": [ + 56, + 381, + 296, + 596 + ], + "type": "text", + "content": "work, jointly optimizing keypoint detection and descriptor extraction. This joint learning approach ensures that the detected keypoints and their descriptors complement each other. Despite the advantages, [21] highlighted a potential drawback of joint training, observing that poorly learned descriptors could negatively impact keypoint detection quality. Subsequently, DeDoDe[10] demonstrated that decoupling keypoint detection and description into two independent networks can significantly improve performance. Similarly, XFeat [32] showed that using task-specific networks provides a better balance between efficiency and accuracy. Inspired by these recent insights, RDD consists of two separate branches for independent keypoint detection and description. We also formulate a training strategy that optimize the descriptor branch first and then the keypoint branch. This design enables both sparse and dense matching and ensures optimized performance across various scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 610, + 226, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 610, + 226, + 621 + ], + "spans": [ + { + "bbox": [ + 55, + 610, + 226, + 621 + ], + "type": "text", + "content": "2.3. Efficient Attention Mechanisms" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "The quadratic complexity of multi-head attention [42] leads to long training schedules and limited spatial resolution for tractability. For 2D images, LR-Net [16] proposed a local relation layer, computing attention in a fixed local window. Linear Transformer [19] proposes to reduce the computation complexity of vanilla attention to linear complexity by substituting the exponential kernel with an alternative ker" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 381, + 555, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 555, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 555, + 478 + ], + "type": "text", + "content": "nel function. Deformable attention [48] further allows the attention window to depend on the query features. With a linear projection predicting a deformable set of displacements from the center and their weight, each pixel in the feature map may attend to a fixed number of pixels of arbitrary distance. Deformable attention [48] is well-suited for our objectives, enabling efficient learning of global context, making it a fitting choice for our approach." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 487, + 375, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 375, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 375, + 499 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": "Our method extracts descriptors and keypoints separately using a descriptor branch and a keypoint branch, as shown in Fig. 2. For an input image " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": ", the descriptor branch first extracts multi-scale feature maps " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\{x_{res}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " using ResNet-50 [15], denoted as " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{res}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": ", and then estimates a descriptor map " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "D \\in \\mathbb{R}^{H/k \\times W/k}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " through a deformable transformer encoder [48], denoted as " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_e" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "k = 4" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " is the patch size. The matchability map " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{H/k \\times W/k}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " is then estimated from " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " with a classification head " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_m" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": ". The keypoint branch " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_K" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " estimates a scoremap " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " by passing image " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " through a lightweight CNN with residual connection [15] " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{cnn}" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " and a classification head " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_s" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": ", then sub-pixel keypoints " + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "inline_equation", + "content": "p_s = [x,y]^T" + }, + { + "bbox": [ + 313, + 509, + 555, + 675 + ], + "type": "text", + "content": " are detected with differentiable keypoint detection (DKD) [46]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "The detected keypoints are used to sample their corresponding descriptors " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "d \\in \\mathbb{R}^{256}" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": ". In Sec. 3.1, we provide an overview of DKD [46] and deformable attenuated version of the original dataset." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6396" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 120 + ], + "type": "text", + "content": "tion [48]. In Sec. 3.2, we introduce the network architecture. In Sec. 3.3, we discuss how sparse and dense matching are obtained. Finally, the training details and loss functions are presented in Sec. 3.4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 127, + 141, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 127, + 141, + 138 + ], + "spans": [ + { + "bbox": [ + 55, + 127, + 141, + 138 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 144, + 228, + 157 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 228, + 157 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 228, + 157 + ], + "type": "text", + "content": "3.1.1. Differentiable Keypoint Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": "Given the scoremap " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": ", DKD detects sub-pixel keypoint locations through partially differentiable operations. First, local maximum scoremap " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "S_{nms}" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " is obtained by non-maximum suppression in local " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " windows. Pixel-level keypoints " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "p_{nms} = [x', y']^T" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " are then extracted by applying a threshold to " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "S_{nms}" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": ". DKD then selects all scores " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "s(i, j)" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " windows centered on " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "p_{nms}" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 159, + 296, + 255 + ], + "type": "text", + "content": " and estimates a sub-pixel-level offset through following steps:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 255, + 233, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 255, + 233, + 267 + ], + "spans": [ + { + "bbox": [ + 67, + 255, + 233, + 267 + ], + "type": "inline_equation", + "content": "s(i,j)" + }, + { + "bbox": [ + 67, + 255, + 233, + 267 + ], + "type": "text", + "content": " are first normalized with softmax:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 93, + 275, + 295, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 275, + 295, + 301 + ], + "spans": [ + { + "bbox": [ + 93, + 275, + 295, + 301 + ], + "type": "interline_equation", + "content": "s ^ {\\prime} (i, j) = \\operatorname {s o f t m a x} \\left(\\frac {s (i , j) - s _ {\\max}}{t _ {d e t}}\\right), \\tag {1}", + "image_path": "19e0f997b00f3a4b358c831fbca00895bdeffc67de5a7c8e74d03878b18863a0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "inline_equation", + "content": "t_{det}" + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "text", + "content": " is the temperature. Then " + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "inline_equation", + "content": "s^{\\prime}(i,j)" + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "text", + "content": " represents the probability of " + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "inline_equation", + "content": "[i,j]^T" + }, + { + "bbox": [ + 55, + 309, + 296, + 358 + ], + "type": "text", + "content": " to be a keypoint within the local window. Thus, the expected position of the keypoint in the local window can be given by integral regression [14, 40]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 365, + 295, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 365, + 295, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 295, + 392 + ], + "type": "interline_equation", + "content": "[ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} ^ {T} = \\sum_ {0 \\leq i, j < N} s ^ {\\prime} (i, j) [ i, j ] ^ {T}. \\tag {2}", + "image_path": "0ff9df1a7675a542363a508c62cfe73377e2209371ac22c7c6dc3cd297f84afe.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 399, + 244, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 244, + 412 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 244, + 412 + ], + "type": "text", + "content": "The final estimated sub-pixel-level keypoint is" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 100, + 418, + 295, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 418, + 295, + 435 + ], + "spans": [ + { + "bbox": [ + 100, + 418, + 295, + 435 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} _ {\\boldsymbol {s}} = \\left[ x, y \\right] ^ {T} = \\left[ x ^ {\\prime}, y ^ {\\prime} \\right] ^ {T} + \\left[ \\hat {i}, \\hat {j} \\right] _ {s o f t} ^ {T}. \\tag {3}", + "image_path": "00986e0a2a3de5d98f905207dd614ab5d8b76ed583f65fbf3aa773699220099d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 442, + 178, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 442, + 178, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 442, + 178, + 453 + ], + "type": "text", + "content": "3.1.2. Deformable Attention" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": "Given a feature map " + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\{\\mathbf{x}_{res}^{l}\\}_{l=1}^{L}" + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": ", deformable attention selects a small set of sample keys " + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_q" + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": " corresponding to the query index " + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": " and its feature vectors " + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_q" + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": ". The deformable attention feature " + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_d" + }, + { + "bbox": [ + 55, + 456, + 296, + 504 + ], + "type": "text", + "content": " is calculated by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 110, + 504, + 294, + 535 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 504, + 294, + 535 + ], + "spans": [ + { + "bbox": [ + 110, + 504, + 294, + 535 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\mathbf {x}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q}, \\tag {4}", + "image_path": "44c9537aef15efd24f42b3a82e4a5a294c0d6c1368aa54097ac5399fc7fe469c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 534, + 83, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 83, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 83, + 544 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 89, + 546, + 295, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 546, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 89, + 546, + 295, + 579 + ], + "type": "interline_equation", + "content": "A _ {m q} = \\sum_ {k = 1} ^ {K} A _ {m q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} \\left(\\mathbf {p} _ {q} + \\Delta \\mathbf {p} _ {m q k}\\right), \\tag {5}", + "image_path": "362d10662a1019d7e0ba1fd452658442384d27fea09aa546c21a4c5bb038d45f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " indexes the attention head, " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " indexes the sampled keys, and " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " is the total number of sampled keys. " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{W}'" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " are learnable weights. " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{p}_{mqk}" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "A_{mqk}" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": " denote the sampling offset and attention weight of the " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": "-th sampling point in the " + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 582, + 296, + 653 + ], + "type": "text", + "content": "-th attention head, where the sampling points are inferred by a linear layer." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "Most of recent keypoint detection and description frameworks [10, 32, 46, 47] benefit from the use of multi-scale feature maps to capture fine details and broader spatial context. Deformable attention naturally extends to multi-scale feature maps [48], enabling the network to effectively adapt" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 72, + 554, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 108 + ], + "type": "text", + "content": "to features at different scales. Similar to Eq. (4), multi-scale deformable attention feature " + }, + { + "bbox": [ + 313, + 72, + 554, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{msd}" + }, + { + "bbox": [ + 313, + 72, + 554, + 108 + ], + "type": "text", + "content": " can be calculated similar to Eq. (4) and Eq. (7)" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 350, + 110, + 553, + 141 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 110, + 553, + 141 + ], + "spans": [ + { + "bbox": [ + 350, + 110, + 553, + 141 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {m s d} \\left(\\mathbf {z} _ {q}, \\mathbf {p} _ {q}, \\left\\{\\mathbf {x} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right) = \\sum_ {m = 1} ^ {M} \\mathbf {W} _ {m} A _ {m q} ^ {\\prime}, \\tag {6}", + "image_path": "e27d866777ccfe508184ce34bbf40ace8546235418c8eece9daa9dae2a9c64cb.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 142, + 342, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 142, + 342, + 152 + ], + "spans": [ + { + "bbox": [ + 314, + 142, + 342, + 152 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 163, + 553, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 163, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 319, + 163, + 553, + 196 + ], + "type": "interline_equation", + "content": "A _ {m q} ^ {\\prime} = \\left[ \\sum_ {l = 1} ^ {L} \\sum_ {k = 1} ^ {K} A _ {m l q k} \\cdot \\mathbf {W} _ {m} ^ {\\prime} \\mathbf {x} _ {l} \\left(f _ {s} \\left(\\hat {p} _ {q}\\right) + \\Delta \\mathbf {p} _ {m l q k}\\right) \\right]. \\tag {7}", + "image_path": "fbd1b48f4f503562ab61805433a887073d0cd7488e76dc3ec8f0626141f1198f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "inline_equation", + "content": "\\hat{p_q} \\in [0,1]^2" + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "text", + "content": " is the normalized coordinates and function " + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "inline_equation", + "content": "f_s" + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "text", + "content": " re-scales it to match the scale of input feature map of the " + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 207, + 554, + 243 + ], + "type": "text", + "content": "-th level." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 314, + 254, + 440, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 254, + 440, + 266 + ], + "spans": [ + { + "bbox": [ + 314, + 254, + 440, + 266 + ], + "type": "text", + "content": "3.2. Network Architecture" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "text", + "content": "Descriptor Branch The descriptor branch " + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_D" + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "text", + "content": " extracts a dense feature map " + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "inline_equation", + "content": "D\\in \\mathbb{R}^{H / 4\\times W / 4\\times 256}" + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "text", + "content": " and a matchability map " + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 272, + 554, + 319 + ], + "type": "text", + "content": ", which models that probability of a given feature vector can be matched." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "content": "Using a ResNet-50 [15] as the CNN backbone, " + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{res}" + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "content": " extracts feature maps at 4 scales, each with resolutions of " + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "inline_equation", + "content": "1/4, 1/8, 1/16, 1/32" + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "content": " of the original image. An additional feature map at scale of " + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "inline_equation", + "content": "1/64" + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "content": " is then included by applying a CNN on the last feature map. These features are positionally encoded and fed into " + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_e" + }, + { + "bbox": [ + 313, + 321, + 555, + 453 + ], + "type": "text", + "content": " with multi-scale deformable attention [48], enabling the network to dynamically attend to relevant spatial locations across multiple scales. We use 4 encoder layers each with 8 attention heads and each head samples 8 points. The entire process of the Descriptor Branch is illustrated in Fig. 2." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": "Keypoint Branch The keypoint branch is dedicated solely to detecting accurate keypoints without being influenced by descriptor estimation. " + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{cnn}" + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": " extracts feature maps at 4 different resolutions, each with a resolution of " + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "inline_equation", + "content": "1/1, 1/2, 1/8" + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "inline_equation", + "content": "1/32" + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": " of the original image and feature dimension of 32. These features are subsequently upsampled to match the original image resolution and concatenated to produce a feature map of size " + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "inline_equation", + "content": "H \\times W \\times 128" + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_s" + }, + { + "bbox": [ + 313, + 457, + 555, + 601 + ], + "type": "text", + "content": " is used to estimate the scoremap. DKD [46] is applied on the scoremap to perform non-maximum suppression and detect the sub-pixel-accurate keypoints. Fig. 2 depicts the entire process of the Keypoint Branch." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 611, + 421, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 421, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 421, + 624 + ], + "type": "text", + "content": "3.3. Feature Matching" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": "In this section, we describe how sparse matches and dense matches are obtained for a given image pair " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "I^1" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "I^2" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": ". Our network outputs sparse keypoints " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "p_s^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": ", descriptor maps " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "D^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": ", and matchability maps " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "M^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " all in a single forward pass. We bilinearly upsample " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "D^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " to match the original resolution of " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "I^1" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "I^2" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": ". Descriptors " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "d^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " are then sampled from " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "D^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "inline_equation", + "content": "p_s^{1,2}" + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6397" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": "Sparse Matching Dual-Softmax operator [34, 41] is used to establish correspondences between two descriptors " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "d^{1,2}" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": ". The score matrix " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": " between the descriptors is first calculated by " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "S(i,j) = \\frac{1}{\\tau} \\cdot \\langle d^1,d^2\\rangle" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": " is the temperature. We can now apply softmax on both dimensions of " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": " to obtain the probability of soft mutual nearest neighbor (MNN) matching. The matching probability matrix " + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": " is obtained by:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 172, + 294, + 187 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 172, + 294, + 187 + ], + "spans": [ + { + "bbox": [ + 67, + 172, + 294, + 187 + ], + "type": "interline_equation", + "content": "P (i, j) = \\operatorname {s o f t m a x} (S (i, \\cdot)) _ {j} \\cdot \\operatorname {s o f t m a x} (S (\\cdot , j)) _ {i}. \\tag {8}", + "image_path": "30386bd783b1675c5fc309e77947eeb376d61582ae6ef0814c858ce617f4a70f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "text", + "content": "Based on the confidence matrix " + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "text", + "content": ", we select matches " + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "inline_equation", + "content": "m_{s}" + }, + { + "bbox": [ + 55, + 190, + 295, + 237 + ], + "type": "text", + "content": " with confidence higher than a threshold(0.01) to further enforce the mutual nearest neighbor criteria, which filters possible outlier matches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 242, + 295, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 242, + 295, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 242, + 295, + 301 + ], + "type": "text", + "content": "Semi-Dense Matching Recent works [5, 17, 39, 43] demonstrated the benefits of semi-dense feature matching by improving coverage and number of inliers. We propose a novel dense matching module that produces accurate and geometry consistent dense matches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": "Given images " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "I^{1}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": ", our method can control the memory and computation usage by only selecting the top-K coarse keypoints " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "p_{c}^{1,2}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " according to their matchability score " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "M^{1,2}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": ". Then we can obtain the coarse matches " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " using equation Eq. (8), similar to how we obtain the sparse matches " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "m_{s}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": ". These matches are naturally coarse matches and require refinement for sub-pixel level accuracy as " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": "'s resolution is only " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " of the original resolution. Unlike existing methods [5, 39] that crop fine level features around coarse matches in " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "I^{1}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": " and then predict offset in " + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 55, + 302, + 295, + 469 + ], + "type": "text", + "content": ", our work proposes a simple, efficient, and accurate module for semi-dense feature matching, inspired by [4] that utilizes sparse correspondences in guiding semi-dense feature matching." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "spans": [ + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": "Differing from [4], which iteratively reassigns the coarse matches of detector-free methods, we adopt a similar idea to refine coarse matches to fine matches. With " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "m_{s}" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " obtained from sparse matching, we use the eight-point method to estimate a fundamental matrix " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " that relates corresponding points between " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "I^{1}" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": ". We keep " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "p_c^1" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " unchanged and refine " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "p_c^2" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " by solving offsets " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "(\\Delta x, \\Delta y)" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " that satisfy the epipolar constraint defined by " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": ". First, we convert " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "p_c^1" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " to homogeneous coordinates " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "p_h^1" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": ". Then, epipolar lines " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "inline_equation", + "content": "p_h^1" + }, + { + "bbox": [ + 55, + 470, + 295, + 589 + ], + "type": "text", + "content": " is computed by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 149, + 589, + 294, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 589, + 294, + 601 + ], + "spans": [ + { + "bbox": [ + 149, + 589, + 294, + 601 + ], + "type": "interline_equation", + "content": "L = F \\cdot p _ {h} ^ {1}, \\tag {9}", + "image_path": "fc654e3ce49e376d69abd10196a41414b239213a6d337a2e0d54649be8dc44dd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": "where each line is represented by coefficients " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "a, b" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": ". Offsets " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "(\\Delta x, \\Delta y)" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " are then calculated for each point in " + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "inline_equation", + "content": "p_c^2" + }, + { + "bbox": [ + 55, + 605, + 295, + 640 + ], + "type": "text", + "content": " by solving the linear equation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 99, + 645, + 294, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 645, + 294, + 658 + ], + "spans": [ + { + "bbox": [ + 99, + 645, + 294, + 658 + ], + "type": "interline_equation", + "content": "a \\cdot (x + \\Delta x) + b \\cdot (y + \\Delta y) + c = 0 \\tag {10}", + "image_path": "a0605ab9020ba43a67756283199fbc0e4f1f0818868a75b7da00bae19b699131.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 663, + 291, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 663, + 291, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 663, + 291, + 675 + ], + "type": "text", + "content": "to enforce the epipolar constraint. Then we can get offsets" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 679, + 295, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 679, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 679, + 295, + 713 + ], + "type": "interline_equation", + "content": "\\Delta x = \\frac {b (b x - a y) - a c}{a ^ {2} + b ^ {2} + \\epsilon} - x, \\quad \\Delta y = \\frac {a (a y - b x) - b c}{a ^ {2} + b ^ {2} + \\epsilon} - y, \\tag {11}", + "image_path": "79293774d23fdfef8237816e0d36975791821d834f6db23455f539a5d480660a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": " are the pixel coordinates of " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "p_c^2" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": ". We finally filter out points with offsets that are larger than the patch size (4) because they are moved outside the matched patch and likely outliers. We then obtain refined dense matches " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "m_c" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "(x + \\Delta x, y + \\Delta y)" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": ". In Sec. 4.4, we show that without this refinement module, the performance of dense matching degrades significantly." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 163, + 447, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 447, + 175 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 447, + 175 + ], + "type": "text", + "content": "3.4. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": "We train RDD with pseudo ground truth correspondences from the MegaDepth dataset [22] and our Air-to-Ground dataset. We collect data from Internet drone videos and ground images of different famous landmarks, more details can be found in the supplementary. Following [37, 39], we use poses and depths to establish pixel correspondences. For every given image pair " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "(I^1, I^2)" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": " matching pixels, " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "m_{gt} \\in R^{N \\times 4}" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": " is defined such that the first two columns are the pixel coordinates of points in " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "I^1" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": " and the last two columns are those in " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "I^2" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": " obtained through a warping function " + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "inline_equation", + "content": "f_{\\text{warp}}" + }, + { + "bbox": [ + 313, + 180, + 555, + 324 + ], + "type": "text", + "content": ". We train the descriptor branch and the keypoint branch separately." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": "Training Descriptor Branch To supervise the local feature descriptors, we apply focal loss [23] to focus on challenging examples and reduce the influence of easily classified matches. Given descriptor maps " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "D^{1}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "D^{2}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": ", we sample descriptor sets " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "d_{gt}^{1}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "d_{gt}^{2}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " based on the ground truth matchability " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "m_{gt} / k" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " is the patch size. The " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": "-th rows, " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "d_{gt}^{1}(i)" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "d_{gt}^{2}(i)" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": ", represent descriptors corresponding to the same points in the images " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "I^{1}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "I^{2}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": ", respectively. Using these descriptors, we compute a probability matrix " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " as described in Eq. (8). Our supervision targets positive correspondences only, represented by the diagonal elements " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "P_{(i,i)}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": ". By enforcing " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "P_{(i,i)}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " to be close to 1, we calculate the focal loss " + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{focal}" + }, + { + "bbox": [ + 313, + 328, + 554, + 484 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 491, + 553, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 491, + 553, + 506 + ], + "spans": [ + { + "bbox": [ + 350, + 491, + 553, + 506 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f o c a l}} = - \\alpha \\cdot (1 - P _ {(i, i)}) ^ {\\gamma} \\cdot \\log \\left(P _ {(i, i)}\\right), \\tag {12}", + "image_path": "ab507227ded1fa163a86474fa67810540c62df450dcd38caf3ac04524af3767f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "inline_equation", + "content": "\\alpha = 0.25" + }, + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "inline_equation", + "content": "\\gamma = 2" + }, + { + "bbox": [ + 313, + 512, + 427, + 524 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "content": "To supervise the matchability map, we apply a modified focal loss that incorporates binary cross-entropy (BCE) on the matchability map " + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "inline_equation", + "content": "M^{1,2}" + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "content": ". The ground truth matchability map " + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "inline_equation", + "content": "M_{gt}^{1,2}" + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "content": " is generated using " + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "inline_equation", + "content": "m_{gt} / k" + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "content": ". We first compute the binary cross-entropy loss " + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{BCE}" + }, + { + "bbox": [ + 313, + 525, + 554, + 584 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 323, + 592, + 553, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 592, + 553, + 605 + ], + "spans": [ + { + "bbox": [ + 323, + 592, + 553, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {B C E} = - \\left(M _ {g t} \\cdot \\log (M) + \\left(1 - M _ {g t}\\right) \\cdot \\log (1 - M)\\right), \\tag {13}", + "image_path": "0c75194b588b72a1af96bb8d9c64677894433dc636749a1444301a51d6fe8a5b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "text", + "content": "and then replace " + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "inline_equation", + "content": "P_{(i,i)}" + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "text", + "content": " in Eq. (12) with " + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "inline_equation", + "content": "\\lambda = e^{-\\mathcal{L}_{BCE}}" + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "text", + "content": ", resulting in the matchability loss " + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{matchability}}" + }, + { + "bbox": [ + 313, + 612, + 553, + 637 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 352, + 645, + 553, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 645, + 553, + 658 + ], + "spans": [ + { + "bbox": [ + 352, + 645, + 553, + 658 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {m a t c h a b i l i t y}} = - \\alpha \\cdot (1 - \\lambda) ^ {\\gamma} \\cdot \\mathcal {L} _ {B C E}. \\tag {14}", + "image_path": "fa26abc7349a84fd834ed97aec6625a30c755d8af03f03c12d4e9987aba4a170.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "The final loss for the descriptor branch is defined as " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D = \\mathcal{L}_{focal} + \\mathcal{L}_{matchability}" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": ". We train the descriptor branch on the mixture of MegaDepth dataset [22] and collected Air-to-Ground dataset, with images resized to 800." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6398" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 64, + 532, + 296 + ], + "blocks": [ + { + "bbox": [ + 70, + 64, + 532, + 296 + ], + "lines": [ + { + "bbox": [ + 70, + 64, + 532, + 296 + ], + "spans": [ + { + "bbox": [ + 70, + 64, + 532, + 296 + ], + "type": "image", + "image_path": "b532cb0dd16e6351e39fc229f0ac8db2d5f914d5f0be0cd34fb345e81ea7ea9f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 297, + 555, + 332 + ], + "lines": [ + { + "bbox": [ + 55, + 297, + 555, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 555, + 332 + ], + "type": "text", + "content": "Figure 3. Qualitative Results on MegaDepth. RDD* and RDD are qualitatively compared to DeDoDe-V2-G [10, 11] ALIKED [47] and XFeat* [32]. RDD* and RDD are more robust compared DeDoDe-G* and ALIKED under challenging scenarios like large scale and viewpoint changes. The red color indicates epipolar error beyond " + }, + { + "bbox": [ + 55, + 297, + 555, + 332 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 55, + 297, + 555, + 332 + ], + "type": "text", + "content": " (in the normalized image coordinates)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "text", + "content": "The training uses a batch size of 32 image pairs and the AdamW optimizer [27]. We use a base learning rate of " + }, + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "inline_equation", + "content": "1 \\cdot 10^{-4}" + }, + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "text", + "content": " with a step learning rate scheduler that updates the learning rate every 2000 steps after 20000 steps with " + }, + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\gamma = 0.5" + }, + { + "bbox": [ + 55, + 342, + 296, + 415 + ], + "type": "text", + "content": ". The descriptor branch converges after 1 day of training on 8 NVIDIA H100 GPU." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "text", + "content": "Training Keypoint Branch We freeze the weights of descriptor branch once it converges and only supervise the keypoint branch to detect accurate and repeatable keypoints. We apply reprojection loss " + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {reprojection }}" + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "text", + "content": ", reliability loss " + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {reliability }}" + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "text", + "content": " similar to [8, 28, 46] and dispersity peaky loss " + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {peaky }}" + }, + { + "bbox": [ + 55, + 423, + 296, + 495 + ], + "type": "text", + "content": " [46] to train repeatable and reliable keypoints." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": "Given detected keypoint " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^1" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "I^1" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^2" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "I^2" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": ". We obtain the warped keypoints " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^{1\\rightarrow 2}" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "f_{warp}" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " and we find their closest keypoints from " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^2" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " with distance less than 5 pixels as matched keypoints. Then, " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "dist_{1\\rightarrow 2}" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " is the reprojection distance between the matched " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^1" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "inline_equation", + "content": "p_s^2" + }, + { + "bbox": [ + 55, + 495, + 296, + 568 + ], + "type": "text", + "content": ". We define the reprojection loss in a symmetric way:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 92, + 573, + 294, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 573, + 294, + 597 + ], + "spans": [ + { + "bbox": [ + 92, + 573, + 294, + 597 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e p r o j e c t i o n}} = \\frac {1}{2} \\left(\\operatorname {d i s t} _ {1 \\rightarrow 2} + \\operatorname {d i s t} _ {2 \\rightarrow 1}\\right), \\tag {15}", + "image_path": "cb467b0abca3580b3d7afa76ea776836dd4f65aec793babe62bd1d01ee7354ac.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": "For keypoint " + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "inline_equation", + "content": "p_s^1" + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": " and its warped keypoint " + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "inline_equation", + "content": "p_s^{1\\rightarrow 2}" + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": " with scores " + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "inline_equation", + "content": "s^1" + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "inline_equation", + "content": "s^{1\\rightarrow 2}" + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": ", and the probability map " + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 607, + 296, + 643 + ], + "type": "text", + "content": " as described in Sec. 3.3, the reliability map is defined as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 131, + 653, + 294, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 653, + 294, + 680 + ], + "spans": [ + { + "bbox": [ + 131, + 653, + 294, + 680 + ], + "type": "interline_equation", + "content": "R = \\exp \\left(\\frac {P - 1}{t _ {r e l}}\\right), \\tag {16}", + "image_path": "27b7543328fb62b1859f291206d7e7a1f7e0b0aebd597efb8692ea464bef56b6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "t_{rel}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " is the temperature parameter. Considering all valid " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "p_s^1" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " and warped points " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "p_s^{1\\rightarrow 2}" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": ", we sample the reliability" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "inline_equation", + "content": "r^1" + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "text", + "content": ". The reliability loss for " + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "inline_equation", + "content": "p_s^1" + }, + { + "bbox": [ + 313, + 342, + 537, + 355 + ], + "type": "text", + "content": " is then defined as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 363, + 555, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 363, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 318, + 363, + 555, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} = \\frac {1}{N _ {1}} \\sum_ {p _ {s} ^ {1}, p _ {s} ^ {1 \\rightarrow 2}} \\frac {s ^ {1} \\cdot s ^ {1 \\rightarrow 2}}{\\sum_ {p _ {s} ^ {1} , p _ {s} ^ {1 \\rightarrow 2}} s ^ {1} \\cdot s ^ {1 \\rightarrow 2}} (1 - r ^ {1}). \\tag {17}", + "image_path": "18927c4ab460a1b654493bba5577bbda3d37fc4b7fe820fa70362b9276c2a3f2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 404, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 404, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 404, + 554, + 426 + ], + "type": "text", + "content": "Similarly, the total reliability loss is defined symmetrically as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 356, + 426, + 553, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 426, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 356, + 426, + 553, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e l i a b i l i t y}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {1} + \\mathcal {L} _ {\\text {r e l i a b i l i t y}} ^ {2}\\right). \\tag {18}", + "image_path": "b7948d711c3bbe47acaf0ba2fc71b79f545b9121318ca07cca976942d460ab49.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "text", + "content": "Eq. (15) optimizes the scores of keypoints in local window through the soft term " + }, + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "inline_equation", + "content": "[\\hat{i},\\hat{j}]_{soft}^{T}" + }, + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "text", + "content": " of Eq. (3), which might affect the first term " + }, + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "inline_equation", + "content": "[x',y']_{nms}^{T}" + }, + { + "bbox": [ + 313, + 453, + 555, + 514 + ], + "type": "text", + "content": " of the equation. In order to align their optimization direction, we define the dispersity peak loss similar to [46] as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 357, + 522, + 553, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 522, + 553, + 552 + ], + "spans": [ + { + "bbox": [ + 357, + 522, + 553, + 552 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p e a k y}} = \\frac {1}{N ^ {2}} \\sum_ {0 \\leq i, j < N} d (i, j) s ^ {\\prime} (i, j), \\tag {19}", + "image_path": "06dc087e15baa978f643124d7c9c32d5a434cd6f7b4bef7447dc541f8b413d66.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 326, + 556, + 354, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 556, + 354, + 567 + ], + "spans": [ + { + "bbox": [ + 326, + 556, + 354, + 567 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 325, + 574, + 553, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 574, + 553, + 596 + ], + "spans": [ + { + "bbox": [ + 325, + 574, + 553, + 596 + ], + "type": "interline_equation", + "content": "d (i, j) = \\left\\{\\left| \\left| [ i, j ] - [ \\hat {i}, \\hat {j} ] _ {\\text {s o f t}} \\right| \\right| _ {p} \\mid 0 \\leq i, j < N \\right\\}, \\tag {20}", + "image_path": "ba9108b0c95b9434af55b66207df23b92b1315dbd3b7124c259ea0e5d5b4552f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "type": "text", + "content": " is the window size and " + }, + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "type": "inline_equation", + "content": "s^{\\prime}(i,j)" + }, + { + "bbox": [ + 313, + 603, + 554, + 628 + ], + "type": "text", + "content": " are softmax scores defined in Eq. (1)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "text", + "content": "The overall loss for the keypoint branch is defined as " + }, + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_K = \\mathcal{L}_{projection} + \\mathcal{L}_{reliability} + \\mathcal{L}_{peaky}" + }, + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "text", + "content": ". We use the DKD [46] with a window size of " + }, + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 313, + 628, + 554, + 712 + ], + "type": "text", + "content": " to detect the top 500 keypoints, and we randomly sample 500 keypoints from non-salient positions. We train the keypoint branch similarly to the descriptor branch, the keypoint branch converges after 4 hours of training on an NVIDIA H100 GPU." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6399" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 112, + 293, + 312 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 105 + ], + "type": "text", + "content": "Table 1. SotA comparison on the MegaDepth [22]. Results are measured in AUC (higher is better). Top 4,096 features used to all sparse matching methods. Best in bold, second best underlined." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 112, + 293, + 312 + ], + "lines": [ + { + "bbox": [ + 56, + 112, + 293, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 112, + 293, + 312 + ], + "type": "table", + "html": "
MethodMegaDepth-1500MegaDepth-View
@5°AUC @10°@20°@5°AUC @10°@20°
Dense
DKM [9] CVPR'2360.474.985.167.480.088.2
RoMa [12] CVPR'2462.676.786.369.981.889.4
Semi-Dense
LoFTR [39] CVPR'2152.869.281.250.665.877.9
ASpanFormer [5] ECCV'2255.371.583.161.375.284.6
ELoFTR [44] CVPR'2456.472.283.560.274.884.7
XFeat* [32] CVPR'2438.656.170.523.937.751.8
RDD*51.367.179.341.555.766.7
Sparse with Learned Matcher
SP [6]+SG [37] CVPR'1949.767.180.651.565.576.9
SP [6]+LG [24] ICCV'2349.967.080.152.467.378.5
Dedode-V2-G [10, 11]+LG [24] ICCV'2344.162.176.541.957.170.0
RDD+LG [24] ICCV'2352.368.981.854.269.380.3
Sparse with MNN
SuperPoint [6] CVPRW'1824.140.054.77.5013.321.1
DISK [41] Neulps'2038.553.766.630.441.951.6
ALIKED [47] TIM'2341.856.869.630.041.853.2
XFeat [32] CVPR'2424.040.155.88.8216.526.8
DeDoDe-V2-G [10, 11] CVPRW'24, 3DV'2447.263.977.533.147.660.2
RDD48.265.278.338.353.165.6
", + "image_path": "61adeca36e5f241e56f4242f62e72265eac69db31d3d161382d7a2aebbbc019a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 322, + 138, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 322, + 138, + 336 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 138, + 336 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 342, + 297, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 297, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 297, + 413 + ], + "type": "text", + "content": "In this section, we demonstrate the performance of our method in Relative Pose Estimation on public benchmark datasets MegaDepth [22] and collected Air-to-Ground dataset, and in Visual Localization using Aachen Day-Night dataset [38]. All experiments are conducted on an NVIDIA H100 GPU." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 423, + 194, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 194, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 194, + 435 + ], + "type": "text", + "content": "4.1. Relative Pose Estimation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 441, + 296, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 296, + 585 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 296, + 585 + ], + "type": "text", + "content": "Dataset Following [8, 10, 32], we use the standard MegaDepth-1500 benchmark from D2-Net [8] for outdoor pose estimation and adopt the same test split. To further validate the performance of RDD in challenging scenarios, we construct two benchmark datasets. MegaDepth-View is derived from MegaDepth [22] test scenes, focusing on pairs with large viewpoint and scale changes; additionally, we sampled 1500 pairs from our collected Air-to-Ground dataset. This benchmark is designed to validate feature matching performance for large-baseline outdoor cross-view images, which is naturally challenging because of geometric distortion and significant viewpoint changes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "content": "Metrics and Comparing Methods We report the AUC of recovered pose under threshold of " + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "inline_equation", + "content": "(5^{\\circ}, 10^{\\circ}" + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "inline_equation", + "content": "20^{\\circ}" + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "content": "). We use RANSAC to estimate the essential matrix. We compared RDD against the state-of-the-art detector/descriptor methods [6, 10, 13, 32, 41, 46, 47] and learned matching methods [5, 9, 12, 24, 37, 39, 44] on MegaDepth [22] dataset. For Air-to-Ground dataset, RDD is compared against detector/descriptor methods. More results on Air-to-Ground data can be found in the supplementary. For all sparse methods, we use resolution whose larger dimension" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 326, + 124, + 539, + 205 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 114 + ], + "type": "text", + "content": "Table 2. SotA comparison on proposed Air-to-Ground benchmark. Keypoints and descriptors are matched using dual-softmax MNN. Measured in AUC (higher is better). Best in bold, second best underlined." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 124, + 539, + 205 + ], + "lines": [ + { + "bbox": [ + 326, + 124, + 539, + 205 + ], + "spans": [ + { + "bbox": [ + 326, + 124, + 539, + 205 + ], + "type": "table", + "html": "
Method@5°@10°@20°
SuperPoint [6] CVPRW'181.893.566.81
DISK [41] NeurIPS'2019.227.134.6
ALIKED [47] TIM'2312.017.825.8
XFeat [32] CVPR'246.1211.417.5
DeDoDe-V2-G [10, 11] CVPRW'24,3DV'2431.545.358.3
RDD41.456.067.8
", + "image_path": "78e5dac39a0eceb11ff19778daf7791d0b8d9a587a0a79678908f83c1872b8d8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 260, + 552, + 348 + ], + "blocks": [ + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "lines": [ + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 555, + 252 + ], + "type": "text", + "content": "Table 3. Homography estimation on HPatches. All methods perform well for illumination sequences. RDD provides high quality homography estimation especially when there are significant viewpoint changes. Best in bold, second best underlined." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 260, + 552, + 348 + ], + "lines": [ + { + "bbox": [ + 316, + 260, + 552, + 348 + ], + "spans": [ + { + "bbox": [ + 316, + 260, + 552, + 348 + ], + "type": "table", + "html": "
MethodIlluminationViewpoint
MHAMHA
@3px@5px@10px@3px@5px@10px
SuperPoint [6] CVPRW'1893.098.099.970.082.087.0
DISK [41] NeurIPS'2096.098.098.072.081.084.0
ALIKED [47] TIM'2397.099.099.078.085.088.0
DeDoDe-G [10] 3DV'2496.099.099.968.077.080.0
XFeat [32] CVPR'2490.096.098.055.072.080.0
RDD93.099.099.976.086.090.0
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RDD demonstrates superior performance in the sparse matching setting compared to the state-of-the-art method DeDoDe-V2-G [10, 11], especially in more challenging scenarios. RDD with learned matcher LightGlue [24] also outperforms previous methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 475, + 554, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 546 + ], + "type": "text", + "content": "The results on MegaDepth-View and Air-to-Ground prove the effectiveness of our method under challenging scenarios with significant improvements over previous methods. RDD outperforms all previous feature detector/descriptor methods under large viewpoints and scale changes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 555, + 454, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 454, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 454, + 569 + ], + "type": "text", + "content": "4.2. Homography Estimation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 574, + 554, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 554, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 554, + 670 + ], + "type": "text", + "content": "Datasets We evaluate the quality of correspondences estimated by RDD on HPatches dataset [1] for Homography Estimation. HPatches contains 52 sequences under significant illumination changes and 56 sequences that exhibit large variation in viewpoints. We use RANSAC to robustly estimate the homography given the estimated correspondences. All images are resized such that their shorter size is equal to 480 pixels." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "Metrics and Comparing Methods We follow [32, 46] to estimate the mean homogeneity accuracy (MHA) with a predefined threshold of " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\{3,5,7\\}" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " pixels. Accuracy is" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6400" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 109 + ], + "type": "text", + "content": "computed using the average corner error in pixels by warping reference image corners onto target images using both ground truth and estimated homographies." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 112, + 294, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 112, + 294, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 112, + 294, + 185 + ], + "type": "text", + "content": "Results on HPatches In Table 3, RDD shows a similar performance in illumination sequences compared to previous accurate keypoint detectors and descriptors, while outperforming most of the other methods on viewpoint changes, reinforcing the robustness of our proposed method in handling challenging cases such as large baseline pairs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 191, + 168, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 191, + 168, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 191, + 168, + 204 + ], + "type": "text", + "content": "4.3. Visual Localization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 208, + 295, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 208, + 295, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 208, + 295, + 304 + ], + "type": "text", + "content": "Dataset We further validate the performance of RDD on the task of visual localization, which estimates the poses of a given query image with respect to the corresponding 3D scene reconstruction. We evaluate RDD on the Aachen Day-Night dataset [38]. It focuses on localizing high-quality night-time images against a day-time 3D model. There are 14,607 images with changing conditions of weather, season, viewpoints, and day-night cycles." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 73, + 366, + 274, + 452 + ], + "blocks": [ + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "lines": [ + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "type": "text", + "content": "Table 4. Visual Localization on Aachen day-night. RDD outperforms previous state-of-the-art methods with MNN matching for more challenging night setting. Best in bold, second best underlined." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 366, + 274, + 452 + ], + "lines": [ + { + "bbox": [ + 73, + 366, + 274, + 452 + ], + "spans": [ + { + "bbox": [ + 73, + 366, + 274, + 452 + ], + "type": "table", + "html": "
MethodsDayNight
(0.25m,2°) / (0.5m,5°) / (1.0m,10°)
SuperPoint [6] CVPRW'1887.4 / 93.2 / 97.077.6 / 85.7 / 95.9
DISK [41] NeurIPS'2086.9 / 95.1 / 97.883.7 / 89.8 / 99.0
ALIKE [46] TM'2285.7 / 92.4 / 96.781.6 / 88.8 / 99.0
ALIKED [47] TIM'2386.5 / 93.4 / 96.885.7 / 91.8 / 96.9
XFeat [32] CVPR'2484.7 / 91.5 / 96.577.6 / 89.8 / 98.0
RDD87.0 / 94.2 / 97.886.7 / 92.9 / 99.0
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VariantAUC@5°
RDDRDD*
Full48.251.3
Larger patch size s = 844.649.4
Less sample points Npq = 446.549.9
No keypoint branch44.1-
Joint training of two branches42.846.9
No match refinement-41.3
Without Air-to-Ground Data47.450.4
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We use the evaluation tool provided by [38] to calculate the metrics, the AUC of estimated camera poses under threshold of " + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\{0.25\\mathrm{m}, 0.5\\mathrm{m}, 5\\mathrm{m}\\}" + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": " for translation errors and " + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\{2^{\\circ}, 5^{\\circ}, 10^{\\circ}\\}" + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": " for rotation errors respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 555, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 119 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 119 + ], + "type": "text", + "content": "Results Tab. 4 presents the results on visual localization. RDD outperforms all approaches in the challenging night setting. These results further validate the effectiveness of RDD." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 129, + 378, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 129, + 378, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 129, + 378, + 140 + ], + "type": "text", + "content": "4.4. Ablation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 144, + 555, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 555, + 326 + ], + "type": "text", + "content": "To better understand RDD, we evaluate 5 variants of RDD, with the results shown in Tab. 5: 1) Increasing the patch size of the transformer encoder results in a significant drop in accuracy. 2) Reducing the number of sampled points per query in deformable attention degrades pose estimation accuracy. 3) Removing the keypoint branch and using up-sampled matchability map as keypoint score map with NMS negatively affect the performance. 4) Joint training of the descriptor and keypoint branches leads to a significant drop in performance, as the weights of both branches are updated when only one task fails, making it even harder for the descriptor branch to converge. 5) Simply concatenating the semi-dense matches from matchability results in worse performance. 6) Training without Air-to-Ground dataset slightly damages the performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 331, + 471, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 471, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 471, + 344 + ], + "type": "text", + "content": "5. Limitations and Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 351, + 555, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 351, + 555, + 543 + ], + "spans": [ + { + "bbox": [ + 313, + 351, + 555, + 543 + ], + "type": "text", + "content": "We present RDD, a robust feature detection and description framework based on deformable transformer, excelling in sparse image matching and demonstrating strong resilience to geometric transformations and varying conditions. By leveraging deformable attention, RDD efficiently extracts geometric-invariant features, enhancing accuracy and adaptability compared to traditional methods. RDD lacks explicit data augmentation during training and depends on confident priors from sparse correspondences which might lead to the failure of semi-dense matching. Training with data augmentation and improving the refinement module with visual features might boost the performance. RDD marks a significant advancement in keypoint detection and description, paving the way for impactful applications in challenging 3D vision tasks like cross-view scene modeling and visual localization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 550, + 424, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 424, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 424, + 563 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 712 + ], + "type": "text", + "content": "Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0075. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. We would like to thank Yayue Chen for her help with visualization." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6401" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. 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Aliked: A lighter keypoint and descriptor extraction network via deformable transformation, 2023. 1, 2, 4, 6, 7, 8" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 56, + 658, + 294, + 700 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 658, + 294, + 700 + ], + "spans": [ + { + "bbox": [ + 56, + 658, + 294, + 700 + ], + "type": "text", + "content": "[48] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 2, 3, 4" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6403" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_content_list.json b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..540efa1d3863b44a7389ce5fb099f87aeeaa03c8 --- /dev/null +++ b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_content_list.json @@ -0,0 +1,1474 @@ +[ + { + "type": "text", + "text": "RELOCATE: A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations", + "text_level": 1, + "bbox": [ + 117, + 128, + 880, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Savya Khosla Sethuraman TV Alexander Schwing Derek Hoiem", + "bbox": [ + 209, + 202, + 787, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Illinois Urbana-Champaign", + "bbox": [ + 375, + 222, + 622, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{savyak2, st34, aschwing, dhoiem}@illinois.edu", + "bbox": [ + 290, + 239, + 697, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 289, + 326, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present RELOCATE, a simple training-free baseline designed to perform the challenging task of visual query localization in long videos. To eliminate the need for task-specific training and efficiently handle long videos, RELOCATE leverages a region-based representation derived from pretrained vision models. At a high level, it follows the classic object localization approach: (1) identify all objects in each video frame, (2) compare the objects with the given query and select the most similar ones, and (3) perform bidirectional tracking to get a spatio-temporal response. However, we propose some key enhancements to handle small objects, cluttered scenes, partial visibility, and varying appearances. Notably, we refine the selected objects for accurate localization and generate additional visual queries to capture visual variations. We evaluate RELOCATE on the challenging Ego4D Visual Query 2D Localization dataset, establishing a new baseline that outperforms prior task-specific methods by $49\\%$ (relative improvement) in spatio-temporal average precision.", + "bbox": [ + 91, + 321, + 483, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 636, + 220, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Query Localization (VQL) requires localizing the last appearance of an object of interest in a long video. The object of interest is specified via a reference image, also known as the visual query. Figure 1 provides illustrative examples. VQL is an important task, e.g., for surveillance, legal investigations, wildlife monitoring, or simply for tracking down a misplaced item. However, the task presents several unique challenges that push the boundaries of contemporary computer vision methods. For instance, unlike classic object detection models that are trained to identify a fixed set of object categories [6, 37], VQL requires localizing an open-ended range of objects. Additionally, while typical object tracking methods are initialized with a bounding box close to the object's temporal location in the video [24, 27, 47], the VQL reference image (visual query) often originates outside the video, i.e., there may be", + "bbox": [ + 89, + 662, + 482, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "no exact or neighboring frame for reliable matching. Further, the object's appearance may vary significantly from the visual query due to changes in orientation, scale, context, lighting, motion blur, and occlusions. Compounding these issues, the object of interest usually appears briefly in a long, untrimmed video.", + "bbox": [ + 511, + 291, + 903, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Classic VQL methods typically use a stage-wise pipeline [17, 45, 46]: (1) identify all objects in each video frame, (2) compare these objects with the given query to select the most similar ones, and (3) perform bidirectional tracking to obtain a spatio-temporal response. While this pipeline is well-grounded in the object localization literature, it is effective only for large, consistently visible objects that closely match the visual query in short video clips. A more recent work [20] has proposed an end-to-end framework that aims to understand the holistic relationship between a given query and the video, performing spatio-temporal localization in a single step. However, this approach requires extensive training on large, annotated datasets, which can be challenging to obtain. Additionally, since such a method learns a holistic video-query relationship, it must process the entire video for each query, even when multiple queries are to be localized in the same video.", + "bbox": [ + 511, + 380, + 903, + 631 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address these limitations, we propose Region-based representations for Localizing Anything in Episodic memory (RELOCATE), a simple training-free baseline for VQL. Being training-free, RELOCATE eliminates the need for extensive task-specific training and large annotated datasets. Moreover, it encodes a video independently of the query, allowing the same video encoding to be reused for multiple queries. This makes the method more suitable for episodic memory tasks, as it enables us to perform the resource-intensive video encoding just once for multiple queries.", + "bbox": [ + 511, + 633, + 903, + 780 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "RELOCATE follows a classic stage-wise setup for object localization while integrating techniques to efficiently encode long videos, handle small and fleeting objects, and manage varying appearances of the query object. Specifically, it begins by extracting region-based representations from the video and searching for candidates that match the visual query. The selected candidates are then refined to improve precision, and the most relevant candidate is tracked", + "bbox": [ + 511, + 782, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3697", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0842be60caf8337dea51dab069c71262e382ae8290c85ab262766d8a9b123a7c.jpg", + "image_caption": [ + "Figure 1. RELOCATE is a training-free framework designed for visual query localization. It can effectively localize target objects in long videos despite challenging conditions such as visual clutter, occlusions, background blending, motion blur, viewpoint changes, and brief object appearances. Here we show visual queries on the left and the successfully localized object appearances marked by cyan bounding boxes on the right." + ], + "image_footnote": [], + "bbox": [ + 112, + 87, + 883, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "across video frames to generate an initial prediction. In a subsequent iteration, this prediction is used to create new visual queries, which are then employed to relocalize the object, aiming to capture appearances that differ significantly from the original visual query.", + "bbox": [ + 89, + 678, + 480, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate RELOCATE using the Ego4D Visual Query 2D (VQ2D) Localization benchmark [17] and observe significant improvements over prior methods. We achieve a $49\\%$ increase in spatio-temporal average precision and a $33\\%$ boost in temporal average precision compared to prior state-of-the-art, all without task-specific training. This demonstrates that simple retrieval methods are effective with region-level tokens derived from pretrained foundation models.", + "bbox": [ + 89, + 767, + 482, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions of this work are:", + "bbox": [ + 532, + 678, + 880, + 693 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose RELOCATE, a training-free method for localizing objects in long videos. Despite no task-specific training, RELOCATE significantly improves upon prior VQL work on the Ego4D VQ2D benchmark.", + "2. We demonstrate the benefits of using region-based representations from pretrained vision models for object localization. Particularly, we show that these representations form a detailed yet compact encoding for long videos. Furthermore, they allow us to efficiently and robustly perform object retrieval using a simple matching function like cosine similarity.", + "3. We propose techniques to improve the robustness and precision of a stage-wise object localization framework." + ], + "bbox": [ + 511, + 707, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3698", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, to enhance localization accuracy, we introduce a refinement step that allows RELOCATE to closely examine the selected candidates and improve their representations, while filtering out incorrect selections. Additionally, we introduce a technique to generate multiple visual queries from a single query, which helps capture varying appearances, changing contexts, and occlusions of objects in a dynamic video setting.", + "bbox": [ + 109, + 90, + 480, + 209 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 223, + 232, + 238 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object Instance Recognition. Early approaches to object instance recognition retrieve images with similar keypoints to the visual query [23, 29, 30, 42]. This works well for objects with distinctive textures, but fails for low-texture, blurry, and highly occluded objects, which are common in the VQL task. Subsequent research shifted towards using features extracted from convolutional neural networks (CNNs) as descriptors for image retrieval [1-3, 8, 35, 36]. However, these early CNN-based methods suffer when faced with large changes in scale, rotation, or viewpoint. To further enhance retrieval performance, query expansion techniques were introduced to iteratively refine the query using information from initial results [12, 16, 44]. The advent of vision foundation models such as CLIP [33], DINO [7], and DINOv2 [31] has enabled new strategies for instance recognition and retrieval. Several works [4, 10, 39, 40] have leveraged the cross-modal capabilities of CLIP for specialized retrieval tasks. However, these approaches are primarily designed for scenarios where query objects occupy a substantial portion of the target frame, which is not the case in VQL. Recent work on region-based representations [41] shows that pooling DINOv2 features over SAM regions provides effective example-based object category retrieval. In this work, we apply a similar approach for our initial search but propose enhancements to refine, track, and expand the initial query. Video Object Tracking. Conventional tracking approaches are initialized with a bounding box in an initial frame of the target video, and they track objects through gradual appearance changes. In contrast, VQL often involves queries from frames outside the target video, leading to significant variations in appearance, viewpoint, and context. Nevertheless, tracking remains crucial in VQL. Early tracking approaches relied on motion and appearance cues, using correlation filters and keypoint matching [18, 21, 38]. More recently, trackers leverage large Transformer models to effectively track one or more objects in long videos [9, 13, 24, 26, 28, 47]. Tracking in egocentric videos introduces additional challenges due to frequent camera motion, occlusions, and object interactions, which have been highlighted in recent benchmarks and studies [5, 14, 15, 49]. Some recent works have also extended SAM [22] for tracking [11, 34, 48]. In this work, we use SAM 2 [34].", + "bbox": [ + 91, + 248, + 483, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Query Localization. The Ego4D benchmark [17]", + "bbox": [ + 91, + 885, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "recently introduced VQ2D, a benchmark for VQL. The initial approach, proposed as a baseline in Ego4D, employs a three-stage detection and tracking framework: performing frame-level detection, identifying the most recent detection peak across time, and applying bi-directional tracking to determine the complete temporal extent of the target object [17]. Subsequent works enhance the framework's performance through various refinements like incorporating negative frame sampling to reduce false positives [45] and leveraging background objects as contextual cues [46]. In this work, we adopt a similar stage-wise framework, introducing key design decisions and refinements that significantly improve the baseline. A more recent effort trains a network to learn the query-video relationship and perform VQL in a single step. However, it relies on a large amount of annotated data, which is costly to obtain. In contrast, we present a training-free solution.", + "bbox": [ + 511, + 90, + 906, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. RELOCATE", + "text_level": 1, + "bbox": [ + 511, + 357, + 635, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We focus on VQL, the task of localizing the last occurrence of a query object in a video. Formally, given a video $\\mathcal{V}$ , a visual query $\\mathcal{Q}$ , and a query time $T$ , the objective is to predict a response track $\\mathcal{R} = \\{b_s, b_{s+1}, \\ldots, b_e\\}$ that localizes and tracks the latest occurrence of the query object prior to time $T$ . Here, $\\mathcal{Q}$ is specified by a bounding box in a reference frame, $s$ and $e \\leq T$ denote the first and the last frames in which the query object is visible, and $b_i$ represents a bounding box around the object in frame $i$ .", + "bbox": [ + 511, + 381, + 906, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, RELOCATE prepares video representations to facilitate a swift search for objects that match the given visual queries. It then refines the search results for better precision and tracks the latest match across frames. After making a prediction, it can reiterate the localization process using the previous prediction for better results.", + "bbox": [ + 511, + 515, + 905, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prepare (Section 3.1). A given video is first distilled into semantically meaningful object-level representations, or object tokens. For this, RELOCATE uses a segmentation model to generate object-wise binary masks for each object across all video frames and a feature extractor to produce dense feature maps for each frame. The features within each object mask are then pooled to produce an object token.", + "bbox": [ + 511, + 604, + 905, + 708 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Search (Section 3.2). After preparing object tokens from the video, RELOCATE creates a similar region-based representation for the visual query, referred to as the query token. It then searches the object tokens for candidates that match the query token.", + "bbox": [ + 511, + 708, + 903, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Refine (Section 3.3). The candidates identified in the initial search are then refined to improve spatial precision and remove any spurious matches. For example, Figure 2 illustrates how refinement enhances spatial precision by capturing the base of the monitor.", + "bbox": [ + 511, + 781, + 903, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Track (Section 3.4). The latest refined search is tracked across video frames using an off-the-shelf tracking model to produce a response track localizing the most recent oc", + "bbox": [ + 511, + 856, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3699", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/32685f46e85948dcc95164e8cf0f81f9da695065679512ea72c1b330acfd14a4.jpg", + "image_caption": [ + "Figure 2. RELOCATE framework: Prepare object tokens from the given video $\\mathcal{V}$ and search for candidates that match the visual query $\\mathcal{Q}$ . Then, refine the search results for better precision and track the latest refined candidate across video frames to get a response track prediction $\\hat{\\mathcal{R}}$ . Finally, use the response track to create additional visual queries and reiterate the search, refinement, and tracking process." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 901, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "currence of the query object in the video.", + "bbox": [ + 89, + 488, + 364, + 502 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reiterate (Section 3.5). To better capture the visual variations of the query object, we leverage the object's appearance in the tracked frames to create more visual queries and then re-apply RELOCATE to the video segment that follows the previously predicted track.", + "bbox": [ + 89, + 503, + 483, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Prepare", + "text_level": 1, + "bbox": [ + 89, + 592, + 191, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address VQL, it is imperative to encode and represent all regions/objects in each frame of a video. However, creating patch-level features for each frame results in an excessive number of tokens for long videos, making the task computationally expensive. To address this issue, we propose using region-based representations [41] to encode each frame. As shown in Table 2, the region-based approach significantly reduces the number of tokens needed to encode a video. Moreover, this produces semantically meaningful object tokens, simplifying entity search for a given query.", + "bbox": [ + 89, + 614, + 483, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Building on this insight, RELOCATE prepares object tokens from a given video as follows:", + "bbox": [ + 89, + 766, + 482, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. Segment Objects. We first generate a binary mask for each region/object in all frames of the video via a segmentation model. Formally, for a frame $f_{t} \\in \\mathbb{R}^{H \\times W \\times 3}$ , we extract a set of binary masks $M_{t} = \\{m_{t1}, m_{t2}, \\ldots\\}$ , one for each region. Here, $m_{ti} \\in \\mathbb{R}^{H \\times W}$ is a binary mask with 1 in the area occupied by the object $i$ and 0 otherwise. In this work, we use SAM ViT-H [22] as the segmentation model,", + "bbox": [ + 89, + 796, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which processes each frame at a resolution of $1024 \\times 1024$ .", + "bbox": [ + 511, + 488, + 903, + 502 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2. Extract Features. We then extract dense features from every frame of the video via a pretrained vision model. Formally, for every frame $f_{t} \\in \\mathbb{R}^{H \\times W \\times 3}$ we compute a high-dimensional feature map $h_{t} \\in \\mathbb{R}^{h \\times w \\times d}$ . In this work, we experiment with different feature extractors and choose DINO ViT-B/8 [7] with a frame resolution of $384 \\times 512$ .", + "3. Resize and Pool. Subsequently, we resize the frame features $h_t \\in \\mathbb{R}^{h \\times w \\times d}$ to $\\overline{h}_t \\in \\mathbb{R}^{H \\times W \\times d}$ to fit the height and width of the masks. We then pool the features within each object mask $m_{ti}$ to get an object token $o_{ti} \\in \\mathbb{R}^d$ . Following the insights from [41], we use bilinear interpolation to resize the features and average pooling to aggregate the features within the mask." + ], + "bbox": [ + 511, + 503, + 906, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Search", + "text_level": 1, + "bbox": [ + 513, + 712, + 604, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Videos spanning tens of minutes and processed at 5 FPS typically involve more than 150,000 object tokens, with only about $0.01\\%$ corresponding to the target response track. To find candidates similar to the visual query, RELOCATE searches over the object tokens. Concretely, given an image and a bounding box localizing the query object, we extract the query token via the process used for video preparation and proceed with the following steps:", + "bbox": [ + 511, + 734, + 906, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. Compute Similarity. We compute pairwise cosine similarity between all object tokens and query tokens. Initially, only one query token is generated from the given visual", + "bbox": [ + 511, + 856, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3700", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "query, but multiple query tokens can be created for the same object. When multiple query tokens are present, we use the maximum similarity score across all tokens as the object score, ensuring that an object is selected if it matches any view of the query. Formally, for the $i^{\\text{th}}$ object token in frame $t$ (i.e., $o_{ti}$ ) and $m$ query tokens $[q_j]_{j=1}^m$ , the similarity score $s_{ti}$ is computed via", + "bbox": [ + 89, + 90, + 480, + 195 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {t i} = \\max _ {j \\in \\{1, \\dots , m \\}} \\frac {o _ {t i} \\cdot q _ {j}}{\\left\\| o _ {t i} \\right\\| \\left\\| q _ {j} \\right\\|}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 200, + 482, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also studied test-time training (TTT) [43], but it performed worse than a simple cosine similarity search due to an insufficient number of query tokens for effective training.", + "bbox": [ + 89, + 234, + 482, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2. Perform Intra-Frame NMS. Given that each frame can contain at most one instance of the query object, we apply non-maximum suppression (NMS) to retain only the highest-scoring object per frame, setting the scores of all other objects to zero. This process results in a single candidate object per frame, yielding a total number of candidate objects equal to the number of frames in the video.", + "bbox": [ + 89, + 279, + 480, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3. Perform Inter-Frame NMS. Since we perform bidirectional tracking at a later stage, selecting one candidate from a potential track is sufficient. So, we perform NMS across consecutive frames to select the highest-scoring match for a query object, suppressing lower-scoring instances in neighboring frames. More precisely, we iteratively select the object with the maximum score and nullify candidate scores in preceding and subsequent frames until the score drops below $80\\%$ of this peak score. As a result, we end up with sparsely selected high-scoring objects across video frames.", + "bbox": [ + 89, + 382, + 482, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Select Candidates. Finally, we select up to $k = 10$ candidate objects that exceed a $t_{\\mathrm{sim}} = 0.7$ similarity threshold, yielding an average of 7.5 candidates per query.", + "bbox": [ + 89, + 530, + 482, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Refine", + "text_level": 1, + "bbox": [ + 89, + 582, + 176, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The objects of interest are often small and situated in cluttered scenes, making it challenging for the segmentation model and feature extractor to produce high-quality object tokens. To address this, we propose refining the selections made after the initial search. We find that this refinement significantly enhances the spatial precision of RELOCATE and helps filter out any spurious selections made after the initial search (see Section 4.3 for an ablation).", + "bbox": [ + 89, + 604, + 482, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We refine the candidates selected from the search in conjunction with the query to generate a more precise set of candidates. This is done as follows:", + "bbox": [ + 89, + 722, + 482, + 766 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Get Object-Centric Crop. We crop the video frames containing the selected candidates and visual queries such that these objects occupy a larger area at the center of the cropped view. These crops are then resized to the original frame dimensions. To prevent pixelation in the case of extremely small objects, we ensure that no frame is cropped with a zoom factor exceeding 2.5 times.", + "2. Generate Refined Token. We process the object-centric crops of candidates and queries using the segmentation" + ], + "bbox": [ + 89, + 767, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model and feature extractor to generate refined object and query tokens. This process yields improved tokens because the segmentation model and feature extractor can produce more accurate masks and detailed features for the objects from the object-centric crop.", + "bbox": [ + 511, + 90, + 903, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3. Recompute Similarity and Filter. We recompute the cosine similarity scores for the selected candidates using the refined object tokens and query tokens, and filter out candidates that have a score below threshold $t_{\\mathrm{sim}} = 0.7$ .", + "bbox": [ + 511, + 167, + 906, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Track", + "text_level": 1, + "bbox": [ + 513, + 246, + 596, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RELOCATE uses an off-the-shelf tracker to bidirectionally track the refined candidate that shows up last in the video, yielding the response track $\\hat{\\mathcal{R}} = \\{b_s,b_{s + 1},\\ldots ,b_e\\}$ . Further, it assigns the similarity score of the candidate as the track score. In this work, we use SAM 2 [34] for tracking.", + "bbox": [ + 511, + 270, + 905, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Reiterate", + "text_level": 1, + "bbox": [ + 513, + 363, + 620, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The query object often appears multiple times in a given video, and RELOCATE is highly successful at localizing at least one of these appearances from a single visual query (see Section 4.1). However, our goal is to identify the latest appearance, which may be heavily occluded or seen from a significantly different viewpoint compared to the visual query. To achieve this, we generate additional visual queries using the response track predicted with the original query and reiterate the process of search, refinement, and tracking. This expanded pool of queries offers diverse views of the object, enhancing the likelihood of detection even when it is obscured or appears in a radically altered form. In practice, we perform this query expansion and reiteration step only once. This is carried out as follows:", + "bbox": [ + 511, + 388, + 906, + 594 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Generate Query Tokens. Given the response track $\\hat{\\mathcal{R}} = \\{b_s, b_{s+1}, \\ldots, b_e\\}$ , we apply the segmentation model and feature extractor to produce region tokens for the objects within the bounding boxes across the frames comprising the response track.", + "2. Filter Queries. We filter out low-quality query tokens generated in the previous step, specifically targeting three types: (1) query tokens with very low cosine similarity (less than 0.5) to the original query token, (2) queries associated with extremely small bounding boxes (occupying less than $0.07\\%$ of the frame area), and (3) queries derived from blurry frames (indicated by a Laplacian operator variance below 100).", + "3. Search, Refine, and Track. After expanding the query pool, we search the video segment following the last frame of the previously predicted response track. The search results are then refined, and the latest refined candidate is tracked across frames to generate a new prediction. If the score of the new prediction exceeds a threshold relative to the previous track score, we update the previous prediction." + ], + "bbox": [ + 511, + 597, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3701", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4f9414bf8ad5806dfe8ca583d9e15f648acf5bbb2185be0e028ff58b3d1bacee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodstAP25tAP25SuccessRecovery
Validation Set
SiamRCNN [17]0.150.2243.232.9
NFM [45]0.190.2647.937.9
CocoFormer [46]0.190.2647.737.7
VQLoC [46]0.220.3155.947.1
RELOCATE0.330.4158.050.5
Test Set
SiamRCNN [17]0.130.2141.634.0
CocoFormer [46]0.180.2648.143.2
VQLoC [46]0.240.3255.945.1
RELOCATE0.350.4360.150.6
", + "bbox": [ + 106, + 88, + 472, + 265 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Results on Ego4D VQ2D benchmark. The validation results are taken from [46], and the test results are obtained from the challenge leaderboard.", + "bbox": [ + 89, + 268, + 482, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 335, + 223, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate RELOCATE (Section 4.1), discuss key design decisions (Section 4.2), and present ablation studies (Section 4.3).", + "bbox": [ + 89, + 362, + 483, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation", + "text_level": 1, + "bbox": [ + 89, + 417, + 210, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We evaluate RELOCATE on the Ego4D VQ2D dataset [17], a large collection of egocentric videos annotated for VQL within episodic memory. On average, the videos in this dataset are 140 seconds long, and the target response tracks last for roughly 3 seconds. The dataset comprises 13,600 training, 4,500 validation, and 4,400 test queries, annotated across 262, 87, and 84 hours of video, respectively. We use the validation set for our development and ablations. To our knowledge, VQ2D is the only publicly available dataset for VQL.", + "bbox": [ + 88, + 439, + 482, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Following the official metrics outlined by the benchmark, we report spatio-temporal average precision $(\\mathrm{stAP}_{25})$ , temporal average precision $(\\mathrm{tAP}_{25})$ , success, and recovery. $\\mathrm{stAP}_{25}$ and $\\mathrm{tAP}_{25}$ evaluate the accuracy of the predicted response tracks' spatio-temporal and temporal extents using an Intersection over Union (IoU) threshold of 0.25. Success measures whether the IoU between predictions and ground truth exceeds 0.05, and recovery measures the proportion of predicted frames where the bounding box achieves an IoU of at least 0.5 with the ground truth.", + "bbox": [ + 88, + 588, + 482, + 736 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Table 1 shows results on the validation and test sets. Despite no task-specific training, RELOCATE outperforms the next-best baseline by $49\\%$ $\\mathrm{stAP}_{25}$ , $33\\%$ $\\mathrm{tAP}_{25}$ , $8\\%$ Success, and $12\\%$ Recovery on the test set. Note, these are relative improvements. Figure 1 shows some qualitative examples of RELOCATE in action.", + "bbox": [ + 88, + 737, + 482, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, a manual analysis of 100 randomly sampled examples from the VQ2D validation set shows that RELOCATE successfully localizes the last occurrence of the object in 61 cases, localizes an earlier instance in 32 cases, and identifies the wrong object in 7 cases. Figure 3 cate", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/051f0c2e771830ec4e20e63a8150144a0fc1254d4cb5be69ec79b67c2a6bbb20.jpg", + "image_caption": [ + "Q", + "Tracked Candidate", + "(a) An object visually similar to the query (blue boxes) is mistakenly tracked instead of the correct query object (green boxes)." + ], + "image_footnote": [], + "bbox": [ + 531, + 103, + 705, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5b32348add231c6ff75c1381f3c0e0f2d6534c7e2216ee36a7a6729903f77f66.jpg", + "image_caption": [ + "Q" + ], + "image_footnote": [], + "bbox": [ + 718, + 103, + 772, + 150 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06236491c658da66239f3c304c53ee2e8e9d6d3e18be8df44535095bb0112242.jpg", + "image_caption": [ + "Tracked Candidate" + ], + "image_footnote": [], + "bbox": [ + 777, + 103, + 892, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/de89fba339e143a26dc1cf26c88e3eb8d7e69b1037b45b79d3ed98044818357d.jpg", + "image_caption": [ + "Q", + "(b) The visual query shows the target object from a distinctly different viewpoint compared to its single appearance in the video (green boxes)." + ], + "image_footnote": [], + "bbox": [ + 531, + 205, + 669, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a90efb841e1f9b7275128baecc6c8134a9036520b7725ddcb2bf5697222a680f.jpg", + "image_caption": [ + "Target response track" + ], + "image_footnote": [], + "bbox": [ + 669, + 205, + 782, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1e67d71ada4a5663d19d7973082b41815c129aca4d117273e8e6c61a1ec7dd5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 784, + 207, + 898, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/29e44d058a59a7361ab39ff6280254c86939ddc4858b34ddb28161fe4f6851aa.jpg", + "image_caption": [ + "Q", + "(c) These visual queries lack discriminative features due to motion blur, low contrast with background, or poor visibility.", + "Figure 3. Examples where a wrong object is localized. Among 100 randomly sampled instances from the VQ2D validation set, RELOCATE localized an instance of the query object in 93 cases, and failed to localize the correct object only under extreme conditions." + ], + "image_footnote": [], + "bbox": [ + 560, + 315, + 612, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f0ac6b220444add6bb64715ff921092d9a5f1fdbede4033e31df6f235a8c56f2.jpg", + "image_caption": [ + "Q" + ], + "image_footnote": [], + "bbox": [ + 627, + 314, + 697, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1791907bafe3a4e82ea2bcc80feb201edc660c2b56012005be8e2499d6ae5807.jpg", + "image_caption": [ + "Q" + ], + "image_footnote": [], + "bbox": [ + 722, + 315, + 781, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/866f733723cbe5f7c5df074d3de3867342e8bbdac9ba4f2718d7974e43a11c95.jpg", + "image_caption": [ + "Q" + ], + "image_footnote": [], + "bbox": [ + 803, + 315, + 864, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "gorizes these failure modes for the cases where RELOCATE localizes the wrong object, highlighting that the framework typically fails to localize the correct object only in extreme situations, such as when the visual query is ambiguous or there exists another object that closely resembles the query. Timing Analysis. On average, preparing a 1000-frame video (i.e., extracting object tokens) takes 1422.5 seconds with our current setup. Subsequent steps are faster: search takes 0.8 seconds, refinement 12.6 seconds, tracking 26.3 seconds, and generating additional queries from a response track is instantaneous. Note that our current implementation is not optimized for speed. For applications requiring faster localization, several simple optimizations can be made with minimal impact on the metrics, such as using HNSW [25] for search, increasing the batch size for feature extraction, using faster SAM variants [32] for region generation, and employing faster trackers. We leave these enhancements for future work.", + "bbox": [ + 511, + 494, + 906, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Design Decisions", + "text_level": 1, + "bbox": [ + 511, + 773, + 679, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Region vs. Patch Representations. Most contemporary approaches to object localization and tracking encode video frames using patch-based representations, where each frame is divided into non-overlapping patches and encoded with a vision transformer. Region-based representations derived from pretrained vision models [41] have recently been proposed as an efficient alternative. These represent", + "bbox": [ + 511, + 797, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3702", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bf160e8ac4f8dae69fecce8ee068be84a5dc44d4565b2b7dfd5778fe6d6e92ad.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Encoding MethodNumber of tokens
384 × 512 Frames1024 × 1024 Frames
Patches3,072,00016,384,000
Regions130,507130,507
", + "bbox": [ + 96, + 88, + 477, + 157 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tations offer both semantic richness and compact encoding—qualities that align with the requirements of VQL.", + "bbox": [ + 89, + 258, + 482, + 290 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, region token count depends on the scene content (detected objects) rather than spatial parameters (image dimensions and patch size). As a result, in most cases, a region-based approach yields fewer tokens than the patch-based approach. As shown in Table 2, a region-based encoding of a 200-second VQ2D video produces $24 \\times$ fewer tokens compared to a patch-based encoding at an image resolution of $384 \\times 512$ with a patch size of 8. Moreover, this difference drastically increases if we increase the resolution; e.g. if the image resolution is increased to $1024 \\times 1024$ , a region-based encoding produces $126 \\times$ fewer tokens than a patch-based encoding. Thus, decoupling of token count from spatial parameters allows the region-based approach to leverage the benefits of smaller patches and high-resolution images without incurring the computational overhead associated with increased token counts.", + "bbox": [ + 88, + 291, + 482, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Beyond their compactness, region-based representations excel at capturing semantic information, enabling spatiotemporal object localization through simple token similarity matching. Figure 4 illustrates this through cosine similarity heatmaps, where region-based representations show precise areas of high similarity for the query objects, while patch-based representations result in less focused similarity distributions. Our comparative analysis reveals that while patch encodings achieve better frame-level retrieval (65% vs. 60%), they perform significantly worse at spatial localization (42% vs. 58%) compared to region-based representations. For specific applications, one could combine patch-based frame retrieval with region-based object localization. For episodic memory tasks, however, we believe that using only region-based representations is advantageous as it avoids the computational overhead of storing and searching through substantially more patch tokens and eliminates the need to generate regions during retrieval.", + "bbox": [ + 89, + 529, + 482, + 796 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature Extraction. To search and retrieve objects that match a given query, VQL requires capturing fine-grained details from each video frame, and the DINO models are particularly well-suited for this task [19, 41]. We compare DINO [7] and DINOv2 [31] using various ViT backbones, with results shown in Table 3. Our findings indicate that DINO ViT-B/8 outperforms ViT-B/16, likely due to its", + "bbox": [ + 89, + 796, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/acf23413dd6443e5af82edc197c0560f3fd9351025534f560bb8c7ede0a779fe.jpg", + "image_caption": [ + "Figure 4. Comparing cosine similarity heatmaps for patch-based and region-based representations. Region-based representations yield distinct, high-similarity matches for query objects (brighter regions), while patch-based representations produce more diffuse similarity patterns." + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 903, + 343 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9675fe1ac3c98ea410fbca7619d08d13ea860721bacba2c80a9a72e439c2ba7e.jpg", + "table_caption": [ + "Table 2. Token count for patch-based and region-based encodings. Region-based representations typically use fewer tokens than the patch-based method, and their token count does not scale with resolution. Token counts are reported for a 1000-frame video, using a patch size of 8 and SAM ViT-H for region-based encoding." + ], + "table_footnote": [], + "table_body": "
ExtractorstAP25tAP25SuccessRecovery
DINO ViT-B/160.2540.30150.047.7
DINOv2 ViT-L/140.3310.45255.845.3
DINO ViT-B/80.3330.40958.050.5
", + "bbox": [ + 524, + 429, + 895, + 493 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b2dead31ce1f3072d740097d25c7a784b2eb711fda5e1bd988c8bcea33efa9e0.jpg", + "table_caption": [ + "Table 3. Performance comparison of feature extractors. DINOv2 ViT-L/14 shows superior frame-level retrieval while DINO ViT-B/8 is better at spatial localization." + ], + "table_footnote": [], + "table_body": "
MethodstAP25tAP25SuccessRecovery
RELOCATE-NoRefine0.2460.36449.139.8
RELOCATE-NoReiter0.2470.29350.948.2
RELOCATE0.3330.40958.050.5
", + "bbox": [ + 514, + 553, + 903, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Impact of refining search results and reiterating after query expansion. Ablating either refinement (RELOCATE-NoRefine) or reiteration (RELOCATE-NoReiter) significantly reduces the performance of RELOCATE.", + "bbox": [ + 511, + 621, + 906, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "smaller patch size enabling finer feature extraction. Additionally, DINOv2 ViT-L/14 shows stronger frame-level retrieval, and DINO ViT-B/8 is better at spatial localization of objects. We choose DINO ViT-B/8 as our feature extractor due to its higher spatio-temporal localization success rate, smaller model size for faster inference, and reduced feature dimensionality requiring less memory.", + "bbox": [ + 511, + 703, + 906, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 818, + 666, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Refining Search Results. Results in Table 4 show that removing search refinement (RELOCATE-NoRefine) from the framework significantly degrades RELOCATE's performance. As illustrated in Figure 5a, refinement enhances", + "bbox": [ + 511, + 840, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3703", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d596021501232916c5574608b668aac80a1fa633b10ad4a3009f89ed1ff2431d.jpg", + "image_caption": [ + "(a) Cropping around objects during refinement helps capture small objects or object parts that full-frame processing might miss.", + "(b) Refinement fixes incorrect selections due to feature bleeding (row 3) and removes false selections by lowering their scores (rows 1 and 2)." + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 885, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/91ece3b8ce80556d9702051f2acbcc872d4c29e21099b963a86e4ef268b326bb.jpg", + "image_caption": [ + "Figure 5. Impact of refining search results. Initial candidates are shown in yellow boxes, and refined candidates are shown in green.", + "Figure 6. Impact of query expansion and reiteration. Using only the initial query $\\mathcal{Q}$ , RELOCATE misses the object's final appearance due to its partial view and low feature similarity. However, the expanded query set $\\mathcal{Q}^+$ captures multiple object perspectives, enabling successful detection of the final occurrence." + ], + "image_footnote": [], + "bbox": [ + 119, + 415, + 875, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "spatial precision for localizing small objects and fine parts by generating regions from an object-centric crop that captures more of the object of interest. Additionally, refinement removes incorrect selections from the initial search by rescoring candidates using region tokens generated from an object-centric crop. Furthermore, for small or thin objects, feature bleeding can result in the selection of an object adjacent to the target object. Object-centered cropping can also help avoid this by providing a clearer view of the target. This is demonstrated in Figure 5b.", + "bbox": [ + 89, + 662, + 482, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Query Expansion and Reiteration. Results in Table 4 show that query expansion and reiteration significantly improve RELOCATE's performance compared to the variant without this step (RELOCATE-NoReiter). Figure 6 shows an example where query expansion using an initial prediction helps capture a wider range of views for the visual query.", + "bbox": [ + 89, + 811, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This, in turn, helps in successfully localizing the final occurrence of the object that was missed when only the initial visual query was used. Additional examples where reiteration after query expansion leads to successful localization are illustrated in rows 2, 5, and 6 of Figure 1.", + "bbox": [ + 511, + 662, + 906, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 755, + 633, + 770 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present RELOCATE, a framework utilizing region-based representations from pretrained vision models to address VQL. Despite a simple design and no task-specific training, RELOCATE can localize target objects in long videos, even under challenging conditions such as clutter, occlusion, blur, and viewpoint changes. On the VQ2D benchmark, it significantly outperforms existing methods that are specifically trained on this dataset.", + "bbox": [ + 511, + 781, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3704", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported in part by ONR N00014-23-1-2383, DARPA HR0011-23-9-0060, NSF 2008387, NSF 2045586, NSF 2106825, NSF MRI 1725729, and NIFA award 2020-67021-32799. 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CVPR, 2023. 3" + ], + "bbox": [ + 514, + 92, + 903, + 521 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3706", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_model.json b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_model.json new file mode 100644 index 0000000000000000000000000000000000000000..809cfb022fa5f01f74e9f6068ba30ec5866ef091 --- /dev/null +++ b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/0b95343c-eb8a-4ffd-99e0-a7265d714a94_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.118, + 0.13, + 0.882, + 0.175 + ], + "angle": 0, + "content": "RELOCATE: A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.203, + 0.788, + 0.221 + ], + "angle": 0, + "content": "Savya Khosla Sethuraman TV Alexander Schwing Derek Hoiem" + }, + { + "type": "text", + "bbox": [ + 0.376, + 0.223, + 0.623, + 0.238 + ], + "angle": 0, + "content": "University of Illinois Urbana-Champaign" + }, + { + "type": "text", + "bbox": [ + 0.292, + 0.24, + 0.698, + 0.255 + ], + "angle": 0, + "content": "{savyak2, st34, aschwing, dhoiem}@illinois.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.29, + 0.327, + 0.306 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.323, + 0.485, + 0.604 + ], + "angle": 0, + "content": "We present RELOCATE, a simple training-free baseline designed to perform the challenging task of visual query localization in long videos. To eliminate the need for task-specific training and efficiently handle long videos, RELOCATE leverages a region-based representation derived from pretrained vision models. At a high level, it follows the classic object localization approach: (1) identify all objects in each video frame, (2) compare the objects with the given query and select the most similar ones, and (3) perform bidirectional tracking to get a spatio-temporal response. However, we propose some key enhancements to handle small objects, cluttered scenes, partial visibility, and varying appearances. Notably, we refine the selected objects for accurate localization and generate additional visual queries to capture visual variations. We evaluate RELOCATE on the challenging Ego4D Visual Query 2D Localization dataset, establishing a new baseline that outperforms prior task-specific methods by \\(49\\%\\) (relative improvement) in spatio-temporal average precision." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.637, + 0.222, + 0.654 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.664, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Visual Query Localization (VQL) requires localizing the last appearance of an object of interest in a long video. The object of interest is specified via a reference image, also known as the visual query. Figure 1 provides illustrative examples. VQL is an important task, e.g., for surveillance, legal investigations, wildlife monitoring, or simply for tracking down a misplaced item. However, the task presents several unique challenges that push the boundaries of contemporary computer vision methods. For instance, unlike classic object detection models that are trained to identify a fixed set of object categories [6, 37], VQL requires localizing an open-ended range of objects. Additionally, while typical object tracking methods are initialized with a bounding box close to the object's temporal location in the video [24, 27, 47], the VQL reference image (visual query) often originates outside the video, i.e., there may be" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.292, + 0.905, + 0.379 + ], + "angle": 0, + "content": "no exact or neighboring frame for reliable matching. Further, the object's appearance may vary significantly from the visual query due to changes in orientation, scale, context, lighting, motion blur, and occlusions. Compounding these issues, the object of interest usually appears briefly in a long, untrimmed video." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.905, + 0.632 + ], + "angle": 0, + "content": "Classic VQL methods typically use a stage-wise pipeline [17, 45, 46]: (1) identify all objects in each video frame, (2) compare these objects with the given query to select the most similar ones, and (3) perform bidirectional tracking to obtain a spatio-temporal response. While this pipeline is well-grounded in the object localization literature, it is effective only for large, consistently visible objects that closely match the visual query in short video clips. A more recent work [20] has proposed an end-to-end framework that aims to understand the holistic relationship between a given query and the video, performing spatio-temporal localization in a single step. However, this approach requires extensive training on large, annotated datasets, which can be challenging to obtain. Additionally, since such a method learns a holistic video-query relationship, it must process the entire video for each query, even when multiple queries are to be localized in the same video." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.634, + 0.905, + 0.781 + ], + "angle": 0, + "content": "To address these limitations, we propose Region-based representations for Localizing Anything in Episodic memory (RELOCATE), a simple training-free baseline for VQL. Being training-free, RELOCATE eliminates the need for extensive task-specific training and large annotated datasets. Moreover, it encodes a video independently of the query, allowing the same video encoding to be reused for multiple queries. This makes the method more suitable for episodic memory tasks, as it enables us to perform the resource-intensive video encoding just once for multiple queries." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.783, + 0.909, + 0.902 + ], + "angle": 0, + "content": "RELOCATE follows a classic stage-wise setup for object localization while integrating techniques to efficiently encode long videos, handle small and fleeting objects, and manage varying appearances of the query object. Specifically, it begins by extracting region-based representations from the video and searching for candidates that match the visual query. The selected candidates are then refined to improve precision, and the most relevant candidate is tracked" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3697" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.088, + 0.885, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.598, + 0.908, + 0.655 + ], + "angle": 0, + "content": "Figure 1. RELOCATE is a training-free framework designed for visual query localization. It can effectively localize target objects in long videos despite challenging conditions such as visual clutter, occlusions, background blending, motion blur, viewpoint changes, and brief object appearances. Here we show visual queries on the left and the successfully localized object appearances marked by cyan bounding boxes on the right." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.679, + 0.482, + 0.755 + ], + "angle": 0, + "content": "across video frames to generate an initial prediction. In a subsequent iteration, this prediction is used to create new visual queries, which are then employed to relocalize the object, aiming to capture appearances that differ significantly from the original visual query." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.768, + 0.483, + 0.9 + ], + "angle": 0, + "content": "We evaluate RELOCATE using the Ego4D Visual Query 2D (VQ2D) Localization benchmark [17] and observe significant improvements over prior methods. We achieve a \\(49\\%\\) increase in spatio-temporal average precision and a \\(33\\%\\) boost in temporal average precision compared to prior state-of-the-art, all without task-specific training. This demonstrates that simple retrieval methods are effective with region-level tokens derived from pretrained foundation models." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.679, + 0.881, + 0.694 + ], + "angle": 0, + "content": "In summary, the main contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.708, + 0.905, + 0.768 + ], + "angle": 0, + "content": "1. We propose RELOCATE, a training-free method for localizing objects in long videos. Despite no task-specific training, RELOCATE significantly improves upon prior VQL work on the Ego4D VQ2D benchmark." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.768, + 0.905, + 0.87 + ], + "angle": 0, + "content": "2. We demonstrate the benefits of using region-based representations from pretrained vision models for object localization. Particularly, we show that these representations form a detailed yet compact encoding for long videos. Furthermore, they allow us to efficiently and robustly perform object retrieval using a simple matching function like cosine similarity." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "3. We propose techniques to improve the robustness and precision of a stage-wise object localization framework." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.708, + 0.905, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3698" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.111, + 0.092, + 0.482, + 0.21 + ], + "angle": 0, + "content": "Specifically, to enhance localization accuracy, we introduce a refinement step that allows RELOCATE to closely examine the selected candidates and improve their representations, while filtering out incorrect selections. Additionally, we introduce a technique to generate multiple visual queries from a single query, which helps capture varying appearances, changing contexts, and occlusions of objects in a dynamic video setting." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.224, + 0.233, + 0.239 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.249, + 0.485, + 0.886 + ], + "angle": 0, + "content": "Object Instance Recognition. Early approaches to object instance recognition retrieve images with similar keypoints to the visual query [23, 29, 30, 42]. This works well for objects with distinctive textures, but fails for low-texture, blurry, and highly occluded objects, which are common in the VQL task. Subsequent research shifted towards using features extracted from convolutional neural networks (CNNs) as descriptors for image retrieval [1-3, 8, 35, 36]. However, these early CNN-based methods suffer when faced with large changes in scale, rotation, or viewpoint. To further enhance retrieval performance, query expansion techniques were introduced to iteratively refine the query using information from initial results [12, 16, 44]. The advent of vision foundation models such as CLIP [33], DINO [7], and DINOv2 [31] has enabled new strategies for instance recognition and retrieval. Several works [4, 10, 39, 40] have leveraged the cross-modal capabilities of CLIP for specialized retrieval tasks. However, these approaches are primarily designed for scenarios where query objects occupy a substantial portion of the target frame, which is not the case in VQL. Recent work on region-based representations [41] shows that pooling DINOv2 features over SAM regions provides effective example-based object category retrieval. In this work, we apply a similar approach for our initial search but propose enhancements to refine, track, and expand the initial query. Video Object Tracking. Conventional tracking approaches are initialized with a bounding box in an initial frame of the target video, and they track objects through gradual appearance changes. In contrast, VQL often involves queries from frames outside the target video, leading to significant variations in appearance, viewpoint, and context. Nevertheless, tracking remains crucial in VQL. Early tracking approaches relied on motion and appearance cues, using correlation filters and keypoint matching [18, 21, 38]. More recently, trackers leverage large Transformer models to effectively track one or more objects in long videos [9, 13, 24, 26, 28, 47]. Tracking in egocentric videos introduces additional challenges due to frequent camera motion, occlusions, and object interactions, which have been highlighted in recent benchmarks and studies [5, 14, 15, 49]. Some recent works have also extended SAM [22] for tracking [11, 34, 48]. In this work, we use SAM 2 [34]." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Visual Query Localization. The Ego4D benchmark [17]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.344 + ], + "angle": 0, + "content": "recently introduced VQ2D, a benchmark for VQL. The initial approach, proposed as a baseline in Ego4D, employs a three-stage detection and tracking framework: performing frame-level detection, identifying the most recent detection peak across time, and applying bi-directional tracking to determine the complete temporal extent of the target object [17]. Subsequent works enhance the framework's performance through various refinements like incorporating negative frame sampling to reduce false positives [45] and leveraging background objects as contextual cues [46]. In this work, we adopt a similar stage-wise framework, introducing key design decisions and refinements that significantly improve the baseline. A more recent effort trains a network to learn the query-video relationship and perform VQL in a single step. However, it relies on a large amount of annotated data, which is costly to obtain. In contrast, we present a training-free solution." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.358, + 0.637, + 0.373 + ], + "angle": 0, + "content": "3. RELOCATE" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.382, + 0.907, + 0.516 + ], + "angle": 0, + "content": "We focus on VQL, the task of localizing the last occurrence of a query object in a video. Formally, given a video \\(\\mathcal{V}\\), a visual query \\(\\mathcal{Q}\\), and a query time \\(T\\), the objective is to predict a response track \\(\\mathcal{R} = \\{b_s, b_{s+1}, \\ldots, b_e\\}\\) that localizes and tracks the latest occurrence of the query object prior to time \\(T\\). Here, \\(\\mathcal{Q}\\) is specified by a bounding box in a reference frame, \\(s\\) and \\(e \\leq T\\) denote the first and the last frames in which the query object is visible, and \\(b_i\\) represents a bounding box around the object in frame \\(i\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.906, + 0.605 + ], + "angle": 0, + "content": "As shown in Figure 2, RELOCATE prepares video representations to facilitate a swift search for objects that match the given visual queries. It then refines the search results for better precision and tracks the latest match across frames. After making a prediction, it can reiterate the localization process using the previous prediction for better results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.605, + 0.906, + 0.709 + ], + "angle": 0, + "content": "Prepare (Section 3.1). A given video is first distilled into semantically meaningful object-level representations, or object tokens. For this, RELOCATE uses a segmentation model to generate object-wise binary masks for each object across all video frames and a feature extractor to produce dense feature maps for each frame. The features within each object mask are then pooled to produce an object token." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.709, + 0.905, + 0.782 + ], + "angle": 0, + "content": "Search (Section 3.2). After preparing object tokens from the video, RELOCATE creates a similar region-based representation for the visual query, referred to as the query token. It then searches the object tokens for candidates that match the query token." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.782, + 0.905, + 0.856 + ], + "angle": 0, + "content": "Refine (Section 3.3). The candidates identified in the initial search are then refined to improve spatial precision and remove any spurious matches. For example, Figure 2 illustrates how refinement enhances spatial precision by capturing the base of the monitor." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.857, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Track (Section 3.4). The latest refined search is tracked across video frames using an off-the-shelf tracking model to produce a response track localizing the most recent oc" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3699" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.903, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.42, + 0.908, + 0.464 + ], + "angle": 0, + "content": "Figure 2. RELOCATE framework: Prepare object tokens from the given video \\(\\mathcal{V}\\) and search for candidates that match the visual query \\(\\mathcal{Q}\\). Then, refine the search results for better precision and track the latest refined candidate across video frames to get a response track prediction \\(\\hat{\\mathcal{R}}\\). Finally, use the response track to create additional visual queries and reiterate the search, refinement, and tracking process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.365, + 0.503 + ], + "angle": 0, + "content": "currence of the query object in the video." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.504, + 0.484, + 0.581 + ], + "angle": 0, + "content": "Reiterate (Section 3.5). To better capture the visual variations of the query object, we leverage the object's appearance in the tracked frames to create more visual queries and then re-apply RELOCATE to the video segment that follows the previously predicted track." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.593, + 0.192, + 0.609 + ], + "angle": 0, + "content": "3.1. Prepare" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.616, + 0.484, + 0.765 + ], + "angle": 0, + "content": "To address VQL, it is imperative to encode and represent all regions/objects in each frame of a video. However, creating patch-level features for each frame results in an excessive number of tokens for long videos, making the task computationally expensive. To address this issue, we propose using region-based representations [41] to encode each frame. As shown in Table 2, the region-based approach significantly reduces the number of tokens needed to encode a video. Moreover, this produces semantically meaningful object tokens, simplifying entity search for a given query." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.483, + 0.796 + ], + "angle": 0, + "content": "Building on this insight, RELOCATE prepares object tokens from a given video as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.797, + 0.484, + 0.902 + ], + "angle": 0, + "content": "1. Segment Objects. We first generate a binary mask for each region/object in all frames of the video via a segmentation model. Formally, for a frame \\( f_{t} \\in \\mathbb{R}^{H \\times W \\times 3} \\), we extract a set of binary masks \\( M_{t} = \\{m_{t1}, m_{t2}, \\ldots\\} \\), one for each region. Here, \\( m_{ti} \\in \\mathbb{R}^{H \\times W} \\) is a binary mask with 1 in the area occupied by the object \\( i \\) and 0 otherwise. In this work, we use SAM ViT-H [22] as the segmentation model," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.489, + 0.905, + 0.503 + ], + "angle": 0, + "content": "which processes each frame at a resolution of \\(1024 \\times 1024\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.505, + 0.906, + 0.594 + ], + "angle": 0, + "content": "2. Extract Features. We then extract dense features from every frame of the video via a pretrained vision model. Formally, for every frame \\( f_{t} \\in \\mathbb{R}^{H \\times W \\times 3} \\) we compute a high-dimensional feature map \\( h_{t} \\in \\mathbb{R}^{h \\times w \\times d} \\). In this work, we experiment with different feature extractors and choose DINO ViT-B/8 [7] with a frame resolution of \\( 384 \\times 512 \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.907, + 0.699 + ], + "angle": 0, + "content": "3. Resize and Pool. Subsequently, we resize the frame features \\( h_t \\in \\mathbb{R}^{h \\times w \\times d} \\) to \\( \\overline{h}_t \\in \\mathbb{R}^{H \\times W \\times d} \\) to fit the height and width of the masks. We then pool the features within each object mask \\( m_{ti} \\) to get an object token \\( o_{ti} \\in \\mathbb{R}^d \\). Following the insights from [41], we use bilinear interpolation to resize the features and average pooling to aggregate the features within the mask." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.505, + 0.907, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.713, + 0.605, + 0.727 + ], + "angle": 0, + "content": "3.2. Search" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.736, + 0.907, + 0.856 + ], + "angle": 0, + "content": "Videos spanning tens of minutes and processed at 5 FPS typically involve more than 150,000 object tokens, with only about \\(0.01\\%\\) corresponding to the target response track. To find candidates similar to the visual query, RELOCATE searches over the object tokens. Concretely, given an image and a bounding box localizing the query object, we extract the query token via the process used for video preparation and proceed with the following steps:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.857, + 0.909, + 0.903 + ], + "angle": 0, + "content": "1. Compute Similarity. We compute pairwise cosine similarity between all object tokens and query tokens. Initially, only one query token is generated from the given visual" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3700" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.196 + ], + "angle": 0, + "content": "query, but multiple query tokens can be created for the same object. When multiple query tokens are present, we use the maximum similarity score across all tokens as the object score, ensuring that an object is selected if it matches any view of the query. Formally, for the \\( i^{\\text{th}} \\) object token in frame \\( t \\) (i.e., \\( o_{ti} \\)) and \\( m \\) query tokens \\( [q_j]_{j=1}^m \\), the similarity score \\( s_{ti} \\) is computed via" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.201, + 0.483, + 0.232 + ], + "angle": 0, + "content": "\\[\ns _ {t i} = \\max _ {j \\in \\{1, \\dots , m \\}} \\frac {o _ {t i} \\cdot q _ {j}}{\\left\\| o _ {t i} \\right\\| \\left\\| q _ {j} \\right\\|}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.235, + 0.483, + 0.28 + ], + "angle": 0, + "content": "We also studied test-time training (TTT) [43], but it performed worse than a simple cosine similarity search due to an insufficient number of query tokens for effective training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.482, + 0.383 + ], + "angle": 0, + "content": "2. Perform Intra-Frame NMS. Given that each frame can contain at most one instance of the query object, we apply non-maximum suppression (NMS) to retain only the highest-scoring object per frame, setting the scores of all other objects to zero. This process results in a single candidate object per frame, yielding a total number of candidate objects equal to the number of frames in the video." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.383, + 0.483, + 0.531 + ], + "angle": 0, + "content": "3. Perform Inter-Frame NMS. Since we perform bidirectional tracking at a later stage, selecting one candidate from a potential track is sufficient. So, we perform NMS across consecutive frames to select the highest-scoring match for a query object, suppressing lower-scoring instances in neighboring frames. More precisely, we iteratively select the object with the maximum score and nullify candidate scores in preceding and subsequent frames until the score drops below \\(80\\%\\) of this peak score. As a result, we end up with sparsely selected high-scoring objects across video frames." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.531, + 0.483, + 0.577 + ], + "angle": 0, + "content": "4. Select Candidates. Finally, we select up to \\( k = 10 \\) candidate objects that exceed a \\( t_{\\mathrm{sim}} = 0.7 \\) similarity threshold, yielding an average of 7.5 candidates per query." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.583, + 0.178, + 0.597 + ], + "angle": 0, + "content": "3.3. Refine" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.605, + 0.483, + 0.722 + ], + "angle": 0, + "content": "The objects of interest are often small and situated in cluttered scenes, making it challenging for the segmentation model and feature extractor to produce high-quality object tokens. To address this, we propose refining the selections made after the initial search. We find that this refinement significantly enhances the spatial precision of RELOCATE and helps filter out any spurious selections made after the initial search (see Section 4.3 for an ablation)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.723, + 0.483, + 0.767 + ], + "angle": 0, + "content": "We refine the candidates selected from the search in conjunction with the query to generate a more precise set of candidates. This is done as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.768, + 0.483, + 0.871 + ], + "angle": 0, + "content": "1. Get Object-Centric Crop. We crop the video frames containing the selected candidates and visual queries such that these objects occupy a larger area at the center of the cropped view. These crops are then resized to the original frame dimensions. To prevent pixelation in the case of extremely small objects, we ensure that no frame is cropped with a zoom factor exceeding 2.5 times." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "2. Generate Refined Token. We process the object-centric crops of candidates and queries using the segmentation" + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.768, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.166 + ], + "angle": 0, + "content": "model and feature extractor to generate refined object and query tokens. This process yields improved tokens because the segmentation model and feature extractor can produce more accurate masks and detailed features for the objects from the object-centric crop." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.169, + 0.907, + 0.229 + ], + "angle": 0, + "content": "3. Recompute Similarity and Filter. We recompute the cosine similarity scores for the selected candidates using the refined object tokens and query tokens, and filter out candidates that have a score below threshold \\( t_{\\mathrm{sim}} = 0.7 \\)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.247, + 0.597, + 0.261 + ], + "angle": 0, + "content": "3.4. Track" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.271, + 0.906, + 0.346 + ], + "angle": 0, + "content": "RELOCATE uses an off-the-shelf tracker to bidirectionally track the refined candidate that shows up last in the video, yielding the response track \\(\\hat{\\mathcal{R}} = \\{b_s,b_{s + 1},\\ldots ,b_e\\}\\). Further, it assigns the similarity score of the candidate as the track score. In this work, we use SAM 2 [34] for tracking." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.364, + 0.622, + 0.378 + ], + "angle": 0, + "content": "3.5. Reiterate" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.907, + 0.595 + ], + "angle": 0, + "content": "The query object often appears multiple times in a given video, and RELOCATE is highly successful at localizing at least one of these appearances from a single visual query (see Section 4.1). However, our goal is to identify the latest appearance, which may be heavily occluded or seen from a significantly different viewpoint compared to the visual query. To achieve this, we generate additional visual queries using the response track predicted with the original query and reiterate the process of search, refinement, and tracking. This expanded pool of queries offers diverse views of the object, enhancing the likelihood of detection even when it is obscured or appears in a radically altered form. In practice, we perform this query expansion and reiteration step only once. This is carried out as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.598, + 0.906, + 0.673 + ], + "angle": 0, + "content": "1. Generate Query Tokens. Given the response track \\(\\hat{\\mathcal{R}} = \\{b_s, b_{s+1}, \\ldots, b_e\\}\\), we apply the segmentation model and feature extractor to produce region tokens for the objects within the bounding boxes across the frames comprising the response track." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.676, + 0.906, + 0.794 + ], + "angle": 0, + "content": "2. Filter Queries. We filter out low-quality query tokens generated in the previous step, specifically targeting three types: (1) query tokens with very low cosine similarity (less than 0.5) to the original query token, (2) queries associated with extremely small bounding boxes (occupying less than \\(0.07\\%\\) of the frame area), and (3) queries derived from blurry frames (indicated by a Laplacian operator variance below 100)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.798, + 0.906, + 0.901 + ], + "angle": 0, + "content": "3. Search, Refine, and Track. After expanding the query pool, we search the video segment following the last frame of the previously predicted response track. The search results are then refined, and the latest refined candidate is tracked across frames to generate a new prediction. If the score of the new prediction exceeds a threshold relative to the previous track score, we update the previous prediction." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.598, + 0.906, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3701" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.473, + 0.266 + ], + "angle": 0, + "content": "
MethodstAP25tAP25SuccessRecovery
Validation Set
SiamRCNN [17]0.150.2243.232.9
NFM [45]0.190.2647.937.9
CocoFormer [46]0.190.2647.737.7
VQLoC [46]0.220.3155.947.1
RELOCATE0.330.4158.050.5
Test Set
SiamRCNN [17]0.130.2141.634.0
CocoFormer [46]0.180.2648.143.2
VQLoC [46]0.240.3255.945.1
RELOCATE0.350.4360.150.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.269, + 0.483, + 0.311 + ], + "angle": 0, + "content": "Table 1. Results on Ego4D VQ2D benchmark. The validation results are taken from [46], and the test results are obtained from the challenge leaderboard." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.337, + 0.224, + 0.354 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.363, + 0.484, + 0.408 + ], + "angle": 0, + "content": "In this section, we evaluate RELOCATE (Section 4.1), discuss key design decisions (Section 4.2), and present ablation studies (Section 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.418, + 0.212, + 0.433 + ], + "angle": 0, + "content": "4.1. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.44, + 0.483, + 0.588 + ], + "angle": 0, + "content": "Dataset. We evaluate RELOCATE on the Ego4D VQ2D dataset [17], a large collection of egocentric videos annotated for VQL within episodic memory. On average, the videos in this dataset are 140 seconds long, and the target response tracks last for roughly 3 seconds. The dataset comprises 13,600 training, 4,500 validation, and 4,400 test queries, annotated across 262, 87, and 84 hours of video, respectively. We use the validation set for our development and ablations. To our knowledge, VQ2D is the only publicly available dataset for VQL." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.589, + 0.483, + 0.737 + ], + "angle": 0, + "content": "Metrics. Following the official metrics outlined by the benchmark, we report spatio-temporal average precision \\((\\mathrm{stAP}_{25})\\), temporal average precision \\((\\mathrm{tAP}_{25})\\), success, and recovery. \\(\\mathrm{stAP}_{25}\\) and \\(\\mathrm{tAP}_{25}\\) evaluate the accuracy of the predicted response tracks' spatio-temporal and temporal extents using an Intersection over Union (IoU) threshold of 0.25. Success measures whether the IoU between predictions and ground truth exceeds 0.05, and recovery measures the proportion of predicted frames where the bounding box achieves an IoU of at least 0.5 with the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.738, + 0.483, + 0.826 + ], + "angle": 0, + "content": "Results. Table 1 shows results on the validation and test sets. Despite no task-specific training, RELOCATE outperforms the next-best baseline by \\(49\\%\\) \\(\\mathrm{stAP}_{25}\\), \\(33\\%\\) \\(\\mathrm{tAP}_{25}\\), \\(8\\%\\) Success, and \\(12\\%\\) Recovery on the test set. Note, these are relative improvements. Figure 1 shows some qualitative examples of RELOCATE in action." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.827, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Additionally, a manual analysis of 100 randomly sampled examples from the VQ2D validation set shows that RELOCATE successfully localizes the last occurrence of the object in 61 cases, localizes an earlier instance in 32 cases, and identifies the wrong object in 7 cases. Figure 3 cate" + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.092, + 0.568, + 0.102 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.092, + 0.688, + 0.102 + ], + "angle": 0, + "content": "Tracked Candidate" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.104, + 0.707, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.092, + 0.754, + 0.102 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.104, + 0.773, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.792, + 0.092, + 0.876, + 0.102 + ], + "angle": 0, + "content": "Tracked Candidate" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.104, + 0.893, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.167, + 0.902, + 0.191 + ], + "angle": 0, + "content": "(a) An object visually similar to the query (blue boxes) is mistakenly tracked instead of the correct query object (green boxes)." + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.195, + 0.547, + 0.204 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.195, + 0.778, + 0.205 + ], + "angle": 0, + "content": "Target response track" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.207, + 0.67, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.207, + 0.784, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.785, + 0.208, + 0.899, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.269, + 0.902, + 0.294 + ], + "angle": 0, + "content": "(b) The visual query shows the target object from a distinctly different viewpoint compared to its single appearance in the video (green boxes)." + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.301, + 0.594, + 0.312 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image", + "bbox": [ + 0.561, + 0.316, + 0.614, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.301, + 0.676, + 0.311 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.315, + 0.699, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.301, + 0.759, + 0.311 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.316, + 0.782, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.829, + 0.301, + 0.842, + 0.311 + ], + "angle": 0, + "content": "Q" + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.316, + 0.866, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.366, + 0.902, + 0.391 + ], + "angle": 0, + "content": "(c) These visual queries lack discriminative features due to motion blur, low contrast with background, or poor visibility." + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.399, + 0.906, + 0.466 + ], + "angle": 0, + "content": "Figure 3. Examples where a wrong object is localized. Among 100 randomly sampled instances from the VQ2D validation set, RELOCATE localized an instance of the query object in 93 cases, and failed to localize the correct object only under extreme conditions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.496, + 0.907, + 0.763 + ], + "angle": 0, + "content": "gorizes these failure modes for the cases where RELOCATE localizes the wrong object, highlighting that the framework typically fails to localize the correct object only in extreme situations, such as when the visual query is ambiguous or there exists another object that closely resembles the query. Timing Analysis. On average, preparing a 1000-frame video (i.e., extracting object tokens) takes 1422.5 seconds with our current setup. Subsequent steps are faster: search takes 0.8 seconds, refinement 12.6 seconds, tracking 26.3 seconds, and generating additional queries from a response track is instantaneous. Note that our current implementation is not optimized for speed. For applications requiring faster localization, several simple optimizations can be made with minimal impact on the metrics, such as using HNSW [25] for search, increasing the batch size for feature extraction, using faster SAM variants [32] for region generation, and employing faster trackers. We leave these enhancements for future work." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.775, + 0.68, + 0.79 + ], + "angle": 0, + "content": "4.2. Design Decisions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.798, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Region vs. Patch Representations. Most contemporary approaches to object localization and tracking encode video frames using patch-based representations, where each frame is divided into non-overlapping patches and encoded with a vision transformer. Region-based representations derived from pretrained vision models [41] have recently been proposed as an efficient alternative. These represent" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3702" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.098, + 0.089, + 0.478, + 0.159 + ], + "angle": 0, + "content": "
Encoding MethodNumber of tokens
384 × 512 Frames1024 × 1024 Frames
Patches3,072,00016,384,000
Regions130,507130,507
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.163, + 0.483, + 0.232 + ], + "angle": 0, + "content": "Table 2. Token count for patch-based and region-based encodings. Region-based representations typically use fewer tokens than the patch-based method, and their token count does not scale with resolution. Token counts are reported for a 1000-frame video, using a patch size of 8 and SAM ViT-H for region-based encoding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.26, + 0.483, + 0.291 + ], + "angle": 0, + "content": "tations offer both semantic richness and compact encoding—qualities that align with the requirements of VQL." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.292, + 0.483, + 0.527 + ], + "angle": 0, + "content": "Notably, region token count depends on the scene content (detected objects) rather than spatial parameters (image dimensions and patch size). As a result, in most cases, a region-based approach yields fewer tokens than the patch-based approach. As shown in Table 2, a region-based encoding of a 200-second VQ2D video produces \\(24 \\times\\) fewer tokens compared to a patch-based encoding at an image resolution of \\(384 \\times 512\\) with a patch size of 8. Moreover, this difference drastically increases if we increase the resolution; e.g. if the image resolution is increased to \\(1024 \\times 1024\\), a region-based encoding produces \\(126 \\times\\) fewer tokens than a patch-based encoding. Thus, decoupling of token count from spatial parameters allows the region-based approach to leverage the benefits of smaller patches and high-resolution images without incurring the computational overhead associated with increased token counts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.53, + 0.483, + 0.797 + ], + "angle": 0, + "content": "Beyond their compactness, region-based representations excel at capturing semantic information, enabling spatiotemporal object localization through simple token similarity matching. Figure 4 illustrates this through cosine similarity heatmaps, where region-based representations show precise areas of high similarity for the query objects, while patch-based representations result in less focused similarity distributions. Our comparative analysis reveals that while patch encodings achieve better frame-level retrieval (65% vs. 60%), they perform significantly worse at spatial localization (42% vs. 58%) compared to region-based representations. For specific applications, one could combine patch-based frame retrieval with region-based object localization. For episodic memory tasks, however, we believe that using only region-based representations is advantageous as it avoids the computational overhead of storing and searching through substantially more patch tokens and eliminates the need to generate regions during retrieval." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.797, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Feature Extraction. To search and retrieve objects that match a given query, VQL requires capturing fine-grained details from each video frame, and the DINO models are particularly well-suited for this task [19, 41]. We compare DINO [7] and DINOv2 [31] using various ViT backbones, with results shown in Table 3. Our findings indicate that DINO ViT-B/8 outperforms ViT-B/16, likely due to its" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.092, + 0.905, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.347, + 0.907, + 0.416 + ], + "angle": 0, + "content": "Figure 4. Comparing cosine similarity heatmaps for patch-based and region-based representations. Region-based representations yield distinct, high-similarity matches for query objects (brighter regions), while patch-based representations produce more diffuse similarity patterns." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.43, + 0.897, + 0.494 + ], + "angle": 0, + "content": "
ExtractorstAP25tAP25SuccessRecovery
DINO ViT-B/160.2540.30150.047.7
DINOv2 ViT-L/140.3310.45255.845.3
DINO ViT-B/80.3330.40958.050.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.498, + 0.907, + 0.54 + ], + "angle": 0, + "content": "Table 3. Performance comparison of feature extractors. DINOv2 ViT-L/14 shows superior frame-level retrieval while DINO ViT-B/8 is better at spatial localization." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.554, + 0.905, + 0.619 + ], + "angle": 0, + "content": "
MethodstAP25tAP25SuccessRecovery
RELOCATE-NoRefine0.2460.36449.139.8
RELOCATE-NoReiter0.2470.29350.948.2
RELOCATE0.3330.40958.050.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.622, + 0.907, + 0.678 + ], + "angle": 0, + "content": "Table 4. Impact of refining search results and reiterating after query expansion. Ablating either refinement (RELOCATE-NoRefine) or reiteration (RELOCATE-NoReiter) significantly reduces the performance of RELOCATE." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.81 + ], + "angle": 0, + "content": "smaller patch size enabling finer feature extraction. Additionally, DINOv2 ViT-L/14 shows stronger frame-level retrieval, and DINO ViT-B/8 is better at spatial localization of objects. We choose DINO ViT-B/8 as our feature extractor due to its higher spatio-temporal localization success rate, smaller model size for faster inference, and reduced feature dimensionality requiring less memory." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.667, + 0.836 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Refining Search Results. Results in Table 4 show that removing search refinement (RELOCATE-NoRefine) from the framework significantly degrades RELOCATE's performance. As illustrated in Figure 5a, refinement enhances" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3703" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.887, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.358, + 0.486, + 0.383 + ], + "angle": 0, + "content": "(a) Cropping around objects during refinement helps capture small objects or object parts that full-frame processing might miss." + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.358, + 0.882, + 0.383 + ], + "angle": 0, + "content": "(b) Refinement fixes incorrect selections due to feature bleeding (row 3) and removes false selections by lowering their scores (rows 1 and 2)." + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.386, + 0.892, + 0.401 + ], + "angle": 0, + "content": "Figure 5. Impact of refining search results. Initial candidates are shown in yellow boxes, and refined candidates are shown in green." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.416, + 0.877, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.596, + 0.907, + 0.637 + ], + "angle": 0, + "content": "Figure 6. Impact of query expansion and reiteration. Using only the initial query \\(\\mathcal{Q}\\), RELOCATE misses the object's final appearance due to its partial view and low feature similarity. However, the expanded query set \\(\\mathcal{Q}^+\\) captures multiple object perspectives, enabling successful detection of the final occurrence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.664, + 0.483, + 0.811 + ], + "angle": 0, + "content": "spatial precision for localizing small objects and fine parts by generating regions from an object-centric crop that captures more of the object of interest. Additionally, refinement removes incorrect selections from the initial search by rescoring candidates using region tokens generated from an object-centric crop. Furthermore, for small or thin objects, feature bleeding can result in the selection of an object adjacent to the target object. Object-centered cropping can also help avoid this by providing a clearer view of the target. This is demonstrated in Figure 5b." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.812, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Query Expansion and Reiteration. Results in Table 4 show that query expansion and reiteration significantly improve RELOCATE's performance compared to the variant without this step (RELOCATE-NoReiter). Figure 6 shows an example where query expansion using an initial prediction helps capture a wider range of views for the visual query." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.664, + 0.907, + 0.739 + ], + "angle": 0, + "content": "This, in turn, helps in successfully localizing the final occurrence of the object that was missed when only the initial visual query was used. Additional examples where reiteration after query expansion leads to successful localization are illustrated in rows 2, 5, and 6 of Figure 1." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.756, + 0.634, + 0.771 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.782, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We present RELOCATE, a framework utilizing region-based representations from pretrained vision models to address VQL. Despite a simple design and no task-specific training, RELOCATE can localize target objects in long videos, even under challenging conditions such as clutter, occlusion, blur, and viewpoint changes. On the VQ2D benchmark, it significantly outperforms existing methods that are specifically trained on this dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3704" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.486, + 0.206 + ], + "angle": 0, + "content": "This work is supported in part by ONR N00014-23-1-2383, DARPA HR0011-23-9-0060, NSF 2008387, NSF 2045586, NSF 2106825, NSF MRI 1725729, and NIFA award 2020-67021-32799. 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To eliminate the need for task-specific training and efficiently handle long videos, RELOCATE leverages a region-based representation derived from pretrained vision models. At a high level, it follows the classic object localization approach: (1) identify all objects in each video frame, (2) compare the objects with the given query and select the most similar ones, and (3) perform bidirectional tracking to get a spatio-temporal response. However, we propose some key enhancements to handle small objects, cluttered scenes, partial visibility, and varying appearances. Notably, we refine the selected objects for accurate localization and generate additional visual queries to capture visual variations. We evaluate RELOCATE on the challenging Ego4D Visual Query 2D Localization dataset, establishing a new baseline that outperforms prior task-specific methods by $49\%$ (relative improvement) in spatio-temporal average precision. + +# 1. Introduction + +Visual Query Localization (VQL) requires localizing the last appearance of an object of interest in a long video. The object of interest is specified via a reference image, also known as the visual query. Figure 1 provides illustrative examples. VQL is an important task, e.g., for surveillance, legal investigations, wildlife monitoring, or simply for tracking down a misplaced item. However, the task presents several unique challenges that push the boundaries of contemporary computer vision methods. For instance, unlike classic object detection models that are trained to identify a fixed set of object categories [6, 37], VQL requires localizing an open-ended range of objects. Additionally, while typical object tracking methods are initialized with a bounding box close to the object's temporal location in the video [24, 27, 47], the VQL reference image (visual query) often originates outside the video, i.e., there may be + +no exact or neighboring frame for reliable matching. Further, the object's appearance may vary significantly from the visual query due to changes in orientation, scale, context, lighting, motion blur, and occlusions. Compounding these issues, the object of interest usually appears briefly in a long, untrimmed video. + +Classic VQL methods typically use a stage-wise pipeline [17, 45, 46]: (1) identify all objects in each video frame, (2) compare these objects with the given query to select the most similar ones, and (3) perform bidirectional tracking to obtain a spatio-temporal response. While this pipeline is well-grounded in the object localization literature, it is effective only for large, consistently visible objects that closely match the visual query in short video clips. A more recent work [20] has proposed an end-to-end framework that aims to understand the holistic relationship between a given query and the video, performing spatio-temporal localization in a single step. However, this approach requires extensive training on large, annotated datasets, which can be challenging to obtain. Additionally, since such a method learns a holistic video-query relationship, it must process the entire video for each query, even when multiple queries are to be localized in the same video. + +To address these limitations, we propose Region-based representations for Localizing Anything in Episodic memory (RELOCATE), a simple training-free baseline for VQL. Being training-free, RELOCATE eliminates the need for extensive task-specific training and large annotated datasets. Moreover, it encodes a video independently of the query, allowing the same video encoding to be reused for multiple queries. This makes the method more suitable for episodic memory tasks, as it enables us to perform the resource-intensive video encoding just once for multiple queries. + +RELOCATE follows a classic stage-wise setup for object localization while integrating techniques to efficiently encode long videos, handle small and fleeting objects, and manage varying appearances of the query object. Specifically, it begins by extracting region-based representations from the video and searching for candidates that match the visual query. The selected candidates are then refined to improve precision, and the most relevant candidate is tracked + +![](images/0842be60caf8337dea51dab069c71262e382ae8290c85ab262766d8a9b123a7c.jpg) +Figure 1. RELOCATE is a training-free framework designed for visual query localization. It can effectively localize target objects in long videos despite challenging conditions such as visual clutter, occlusions, background blending, motion blur, viewpoint changes, and brief object appearances. Here we show visual queries on the left and the successfully localized object appearances marked by cyan bounding boxes on the right. + +across video frames to generate an initial prediction. In a subsequent iteration, this prediction is used to create new visual queries, which are then employed to relocalize the object, aiming to capture appearances that differ significantly from the original visual query. + +We evaluate RELOCATE using the Ego4D Visual Query 2D (VQ2D) Localization benchmark [17] and observe significant improvements over prior methods. We achieve a $49\%$ increase in spatio-temporal average precision and a $33\%$ boost in temporal average precision compared to prior state-of-the-art, all without task-specific training. This demonstrates that simple retrieval methods are effective with region-level tokens derived from pretrained foundation models. + +In summary, the main contributions of this work are: + +1. We propose RELOCATE, a training-free method for localizing objects in long videos. Despite no task-specific training, RELOCATE significantly improves upon prior VQL work on the Ego4D VQ2D benchmark. +2. We demonstrate the benefits of using region-based representations from pretrained vision models for object localization. Particularly, we show that these representations form a detailed yet compact encoding for long videos. Furthermore, they allow us to efficiently and robustly perform object retrieval using a simple matching function like cosine similarity. +3. We propose techniques to improve the robustness and precision of a stage-wise object localization framework. + +Specifically, to enhance localization accuracy, we introduce a refinement step that allows RELOCATE to closely examine the selected candidates and improve their representations, while filtering out incorrect selections. Additionally, we introduce a technique to generate multiple visual queries from a single query, which helps capture varying appearances, changing contexts, and occlusions of objects in a dynamic video setting. + +# 2. Related Work + +Object Instance Recognition. Early approaches to object instance recognition retrieve images with similar keypoints to the visual query [23, 29, 30, 42]. This works well for objects with distinctive textures, but fails for low-texture, blurry, and highly occluded objects, which are common in the VQL task. Subsequent research shifted towards using features extracted from convolutional neural networks (CNNs) as descriptors for image retrieval [1-3, 8, 35, 36]. However, these early CNN-based methods suffer when faced with large changes in scale, rotation, or viewpoint. To further enhance retrieval performance, query expansion techniques were introduced to iteratively refine the query using information from initial results [12, 16, 44]. The advent of vision foundation models such as CLIP [33], DINO [7], and DINOv2 [31] has enabled new strategies for instance recognition and retrieval. Several works [4, 10, 39, 40] have leveraged the cross-modal capabilities of CLIP for specialized retrieval tasks. However, these approaches are primarily designed for scenarios where query objects occupy a substantial portion of the target frame, which is not the case in VQL. Recent work on region-based representations [41] shows that pooling DINOv2 features over SAM regions provides effective example-based object category retrieval. In this work, we apply a similar approach for our initial search but propose enhancements to refine, track, and expand the initial query. Video Object Tracking. Conventional tracking approaches are initialized with a bounding box in an initial frame of the target video, and they track objects through gradual appearance changes. In contrast, VQL often involves queries from frames outside the target video, leading to significant variations in appearance, viewpoint, and context. Nevertheless, tracking remains crucial in VQL. Early tracking approaches relied on motion and appearance cues, using correlation filters and keypoint matching [18, 21, 38]. More recently, trackers leverage large Transformer models to effectively track one or more objects in long videos [9, 13, 24, 26, 28, 47]. Tracking in egocentric videos introduces additional challenges due to frequent camera motion, occlusions, and object interactions, which have been highlighted in recent benchmarks and studies [5, 14, 15, 49]. Some recent works have also extended SAM [22] for tracking [11, 34, 48]. In this work, we use SAM 2 [34]. + +Visual Query Localization. The Ego4D benchmark [17] + +recently introduced VQ2D, a benchmark for VQL. The initial approach, proposed as a baseline in Ego4D, employs a three-stage detection and tracking framework: performing frame-level detection, identifying the most recent detection peak across time, and applying bi-directional tracking to determine the complete temporal extent of the target object [17]. Subsequent works enhance the framework's performance through various refinements like incorporating negative frame sampling to reduce false positives [45] and leveraging background objects as contextual cues [46]. In this work, we adopt a similar stage-wise framework, introducing key design decisions and refinements that significantly improve the baseline. A more recent effort trains a network to learn the query-video relationship and perform VQL in a single step. However, it relies on a large amount of annotated data, which is costly to obtain. In contrast, we present a training-free solution. + +# 3. RELOCATE + +We focus on VQL, the task of localizing the last occurrence of a query object in a video. Formally, given a video $\mathcal{V}$ , a visual query $\mathcal{Q}$ , and a query time $T$ , the objective is to predict a response track $\mathcal{R} = \{b_s, b_{s+1}, \ldots, b_e\}$ that localizes and tracks the latest occurrence of the query object prior to time $T$ . Here, $\mathcal{Q}$ is specified by a bounding box in a reference frame, $s$ and $e \leq T$ denote the first and the last frames in which the query object is visible, and $b_i$ represents a bounding box around the object in frame $i$ . + +As shown in Figure 2, RELOCATE prepares video representations to facilitate a swift search for objects that match the given visual queries. It then refines the search results for better precision and tracks the latest match across frames. After making a prediction, it can reiterate the localization process using the previous prediction for better results. + +Prepare (Section 3.1). A given video is first distilled into semantically meaningful object-level representations, or object tokens. For this, RELOCATE uses a segmentation model to generate object-wise binary masks for each object across all video frames and a feature extractor to produce dense feature maps for each frame. The features within each object mask are then pooled to produce an object token. + +Search (Section 3.2). After preparing object tokens from the video, RELOCATE creates a similar region-based representation for the visual query, referred to as the query token. It then searches the object tokens for candidates that match the query token. + +Refine (Section 3.3). The candidates identified in the initial search are then refined to improve spatial precision and remove any spurious matches. For example, Figure 2 illustrates how refinement enhances spatial precision by capturing the base of the monitor. + +Track (Section 3.4). The latest refined search is tracked across video frames using an off-the-shelf tracking model to produce a response track localizing the most recent oc + +![](images/32685f46e85948dcc95164e8cf0f81f9da695065679512ea72c1b330acfd14a4.jpg) +Figure 2. RELOCATE framework: Prepare object tokens from the given video $\mathcal{V}$ and search for candidates that match the visual query $\mathcal{Q}$ . Then, refine the search results for better precision and track the latest refined candidate across video frames to get a response track prediction $\hat{\mathcal{R}}$ . Finally, use the response track to create additional visual queries and reiterate the search, refinement, and tracking process. + +currence of the query object in the video. + +Reiterate (Section 3.5). To better capture the visual variations of the query object, we leverage the object's appearance in the tracked frames to create more visual queries and then re-apply RELOCATE to the video segment that follows the previously predicted track. + +# 3.1. Prepare + +To address VQL, it is imperative to encode and represent all regions/objects in each frame of a video. However, creating patch-level features for each frame results in an excessive number of tokens for long videos, making the task computationally expensive. To address this issue, we propose using region-based representations [41] to encode each frame. As shown in Table 2, the region-based approach significantly reduces the number of tokens needed to encode a video. Moreover, this produces semantically meaningful object tokens, simplifying entity search for a given query. + +Building on this insight, RELOCATE prepares object tokens from a given video as follows: + +1. Segment Objects. We first generate a binary mask for each region/object in all frames of the video via a segmentation model. Formally, for a frame $f_{t} \in \mathbb{R}^{H \times W \times 3}$ , we extract a set of binary masks $M_{t} = \{m_{t1}, m_{t2}, \ldots\}$ , one for each region. Here, $m_{ti} \in \mathbb{R}^{H \times W}$ is a binary mask with 1 in the area occupied by the object $i$ and 0 otherwise. In this work, we use SAM ViT-H [22] as the segmentation model, + +which processes each frame at a resolution of $1024 \times 1024$ . + +2. Extract Features. We then extract dense features from every frame of the video via a pretrained vision model. Formally, for every frame $f_{t} \in \mathbb{R}^{H \times W \times 3}$ we compute a high-dimensional feature map $h_{t} \in \mathbb{R}^{h \times w \times d}$ . In this work, we experiment with different feature extractors and choose DINO ViT-B/8 [7] with a frame resolution of $384 \times 512$ . +3. Resize and Pool. Subsequently, we resize the frame features $h_t \in \mathbb{R}^{h \times w \times d}$ to $\overline{h}_t \in \mathbb{R}^{H \times W \times d}$ to fit the height and width of the masks. We then pool the features within each object mask $m_{ti}$ to get an object token $o_{ti} \in \mathbb{R}^d$ . Following the insights from [41], we use bilinear interpolation to resize the features and average pooling to aggregate the features within the mask. + +# 3.2. Search + +Videos spanning tens of minutes and processed at 5 FPS typically involve more than 150,000 object tokens, with only about $0.01\%$ corresponding to the target response track. To find candidates similar to the visual query, RELOCATE searches over the object tokens. Concretely, given an image and a bounding box localizing the query object, we extract the query token via the process used for video preparation and proceed with the following steps: + +1. Compute Similarity. We compute pairwise cosine similarity between all object tokens and query tokens. Initially, only one query token is generated from the given visual + +query, but multiple query tokens can be created for the same object. When multiple query tokens are present, we use the maximum similarity score across all tokens as the object score, ensuring that an object is selected if it matches any view of the query. Formally, for the $i^{\text{th}}$ object token in frame $t$ (i.e., $o_{ti}$ ) and $m$ query tokens $[q_j]_{j=1}^m$ , the similarity score $s_{ti}$ is computed via + +$$ +s _ {t i} = \max _ {j \in \{1, \dots , m \}} \frac {o _ {t i} \cdot q _ {j}}{\left\| o _ {t i} \right\| \left\| q _ {j} \right\|}. \tag {1} +$$ + +We also studied test-time training (TTT) [43], but it performed worse than a simple cosine similarity search due to an insufficient number of query tokens for effective training. + +2. Perform Intra-Frame NMS. Given that each frame can contain at most one instance of the query object, we apply non-maximum suppression (NMS) to retain only the highest-scoring object per frame, setting the scores of all other objects to zero. This process results in a single candidate object per frame, yielding a total number of candidate objects equal to the number of frames in the video. + +3. Perform Inter-Frame NMS. Since we perform bidirectional tracking at a later stage, selecting one candidate from a potential track is sufficient. So, we perform NMS across consecutive frames to select the highest-scoring match for a query object, suppressing lower-scoring instances in neighboring frames. More precisely, we iteratively select the object with the maximum score and nullify candidate scores in preceding and subsequent frames until the score drops below $80\%$ of this peak score. As a result, we end up with sparsely selected high-scoring objects across video frames. + +4. Select Candidates. Finally, we select up to $k = 10$ candidate objects that exceed a $t_{\mathrm{sim}} = 0.7$ similarity threshold, yielding an average of 7.5 candidates per query. + +# 3.3. Refine + +The objects of interest are often small and situated in cluttered scenes, making it challenging for the segmentation model and feature extractor to produce high-quality object tokens. To address this, we propose refining the selections made after the initial search. We find that this refinement significantly enhances the spatial precision of RELOCATE and helps filter out any spurious selections made after the initial search (see Section 4.3 for an ablation). + +We refine the candidates selected from the search in conjunction with the query to generate a more precise set of candidates. This is done as follows: + +1. Get Object-Centric Crop. We crop the video frames containing the selected candidates and visual queries such that these objects occupy a larger area at the center of the cropped view. These crops are then resized to the original frame dimensions. To prevent pixelation in the case of extremely small objects, we ensure that no frame is cropped with a zoom factor exceeding 2.5 times. +2. Generate Refined Token. We process the object-centric crops of candidates and queries using the segmentation + +model and feature extractor to generate refined object and query tokens. This process yields improved tokens because the segmentation model and feature extractor can produce more accurate masks and detailed features for the objects from the object-centric crop. + +3. Recompute Similarity and Filter. We recompute the cosine similarity scores for the selected candidates using the refined object tokens and query tokens, and filter out candidates that have a score below threshold $t_{\mathrm{sim}} = 0.7$ . + +# 3.4. Track + +RELOCATE uses an off-the-shelf tracker to bidirectionally track the refined candidate that shows up last in the video, yielding the response track $\hat{\mathcal{R}} = \{b_s,b_{s + 1},\ldots ,b_e\}$ . Further, it assigns the similarity score of the candidate as the track score. In this work, we use SAM 2 [34] for tracking. + +# 3.5. Reiterate + +The query object often appears multiple times in a given video, and RELOCATE is highly successful at localizing at least one of these appearances from a single visual query (see Section 4.1). However, our goal is to identify the latest appearance, which may be heavily occluded or seen from a significantly different viewpoint compared to the visual query. To achieve this, we generate additional visual queries using the response track predicted with the original query and reiterate the process of search, refinement, and tracking. This expanded pool of queries offers diverse views of the object, enhancing the likelihood of detection even when it is obscured or appears in a radically altered form. In practice, we perform this query expansion and reiteration step only once. This is carried out as follows: + +1. Generate Query Tokens. Given the response track $\hat{\mathcal{R}} = \{b_s, b_{s+1}, \ldots, b_e\}$ , we apply the segmentation model and feature extractor to produce region tokens for the objects within the bounding boxes across the frames comprising the response track. +2. Filter Queries. We filter out low-quality query tokens generated in the previous step, specifically targeting three types: (1) query tokens with very low cosine similarity (less than 0.5) to the original query token, (2) queries associated with extremely small bounding boxes (occupying less than $0.07\%$ of the frame area), and (3) queries derived from blurry frames (indicated by a Laplacian operator variance below 100). +3. Search, Refine, and Track. After expanding the query pool, we search the video segment following the last frame of the previously predicted response track. The search results are then refined, and the latest refined candidate is tracked across frames to generate a new prediction. If the score of the new prediction exceeds a threshold relative to the previous track score, we update the previous prediction. + +
MethodstAP25tAP25SuccessRecovery
Validation Set
SiamRCNN [17]0.150.2243.232.9
NFM [45]0.190.2647.937.9
CocoFormer [46]0.190.2647.737.7
VQLoC [46]0.220.3155.947.1
RELOCATE0.330.4158.050.5
Test Set
SiamRCNN [17]0.130.2141.634.0
CocoFormer [46]0.180.2648.143.2
VQLoC [46]0.240.3255.945.1
RELOCATE0.350.4360.150.6
+ +Table 1. Results on Ego4D VQ2D benchmark. The validation results are taken from [46], and the test results are obtained from the challenge leaderboard. + +# 4. Experiments + +In this section, we evaluate RELOCATE (Section 4.1), discuss key design decisions (Section 4.2), and present ablation studies (Section 4.3). + +# 4.1. Evaluation + +Dataset. We evaluate RELOCATE on the Ego4D VQ2D dataset [17], a large collection of egocentric videos annotated for VQL within episodic memory. On average, the videos in this dataset are 140 seconds long, and the target response tracks last for roughly 3 seconds. The dataset comprises 13,600 training, 4,500 validation, and 4,400 test queries, annotated across 262, 87, and 84 hours of video, respectively. We use the validation set for our development and ablations. To our knowledge, VQ2D is the only publicly available dataset for VQL. + +Metrics. Following the official metrics outlined by the benchmark, we report spatio-temporal average precision $(\mathrm{stAP}_{25})$ , temporal average precision $(\mathrm{tAP}_{25})$ , success, and recovery. $\mathrm{stAP}_{25}$ and $\mathrm{tAP}_{25}$ evaluate the accuracy of the predicted response tracks' spatio-temporal and temporal extents using an Intersection over Union (IoU) threshold of 0.25. Success measures whether the IoU between predictions and ground truth exceeds 0.05, and recovery measures the proportion of predicted frames where the bounding box achieves an IoU of at least 0.5 with the ground truth. + +Results. Table 1 shows results on the validation and test sets. Despite no task-specific training, RELOCATE outperforms the next-best baseline by $49\%$ $\mathrm{stAP}_{25}$ , $33\%$ $\mathrm{tAP}_{25}$ , $8\%$ Success, and $12\%$ Recovery on the test set. Note, these are relative improvements. Figure 1 shows some qualitative examples of RELOCATE in action. + +Additionally, a manual analysis of 100 randomly sampled examples from the VQ2D validation set shows that RELOCATE successfully localizes the last occurrence of the object in 61 cases, localizes an earlier instance in 32 cases, and identifies the wrong object in 7 cases. Figure 3 cate + +![](images/051f0c2e771830ec4e20e63a8150144a0fc1254d4cb5be69ec79b67c2a6bbb20.jpg) +Q +Tracked Candidate +(a) An object visually similar to the query (blue boxes) is mistakenly tracked instead of the correct query object (green boxes). + +![](images/5b32348add231c6ff75c1381f3c0e0f2d6534c7e2216ee36a7a6729903f77f66.jpg) +Q + +![](images/06236491c658da66239f3c304c53ee2e8e9d6d3e18be8df44535095bb0112242.jpg) +Tracked Candidate + +![](images/de89fba339e143a26dc1cf26c88e3eb8d7e69b1037b45b79d3ed98044818357d.jpg) +Q +(b) The visual query shows the target object from a distinctly different viewpoint compared to its single appearance in the video (green boxes). + +![](images/a90efb841e1f9b7275128baecc6c8134a9036520b7725ddcb2bf5697222a680f.jpg) +Target response track + +![](images/1e67d71ada4a5663d19d7973082b41815c129aca4d117273e8e6c61a1ec7dd5d.jpg) + +![](images/29e44d058a59a7361ab39ff6280254c86939ddc4858b34ddb28161fe4f6851aa.jpg) +Q +(c) These visual queries lack discriminative features due to motion blur, low contrast with background, or poor visibility. +Figure 3. Examples where a wrong object is localized. Among 100 randomly sampled instances from the VQ2D validation set, RELOCATE localized an instance of the query object in 93 cases, and failed to localize the correct object only under extreme conditions. + +![](images/f0ac6b220444add6bb64715ff921092d9a5f1fdbede4033e31df6f235a8c56f2.jpg) +Q + +![](images/1791907bafe3a4e82ea2bcc80feb201edc660c2b56012005be8e2499d6ae5807.jpg) +Q + +![](images/866f733723cbe5f7c5df074d3de3867342e8bbdac9ba4f2718d7974e43a11c95.jpg) +Q + +gorizes these failure modes for the cases where RELOCATE localizes the wrong object, highlighting that the framework typically fails to localize the correct object only in extreme situations, such as when the visual query is ambiguous or there exists another object that closely resembles the query. Timing Analysis. On average, preparing a 1000-frame video (i.e., extracting object tokens) takes 1422.5 seconds with our current setup. Subsequent steps are faster: search takes 0.8 seconds, refinement 12.6 seconds, tracking 26.3 seconds, and generating additional queries from a response track is instantaneous. Note that our current implementation is not optimized for speed. For applications requiring faster localization, several simple optimizations can be made with minimal impact on the metrics, such as using HNSW [25] for search, increasing the batch size for feature extraction, using faster SAM variants [32] for region generation, and employing faster trackers. We leave these enhancements for future work. + +# 4.2. Design Decisions + +Region vs. Patch Representations. Most contemporary approaches to object localization and tracking encode video frames using patch-based representations, where each frame is divided into non-overlapping patches and encoded with a vision transformer. Region-based representations derived from pretrained vision models [41] have recently been proposed as an efficient alternative. These represent + +
Encoding MethodNumber of tokens
384 × 512 Frames1024 × 1024 Frames
Patches3,072,00016,384,000
Regions130,507130,507
+ +tations offer both semantic richness and compact encoding—qualities that align with the requirements of VQL. + +Notably, region token count depends on the scene content (detected objects) rather than spatial parameters (image dimensions and patch size). As a result, in most cases, a region-based approach yields fewer tokens than the patch-based approach. As shown in Table 2, a region-based encoding of a 200-second VQ2D video produces $24 \times$ fewer tokens compared to a patch-based encoding at an image resolution of $384 \times 512$ with a patch size of 8. Moreover, this difference drastically increases if we increase the resolution; e.g. if the image resolution is increased to $1024 \times 1024$ , a region-based encoding produces $126 \times$ fewer tokens than a patch-based encoding. Thus, decoupling of token count from spatial parameters allows the region-based approach to leverage the benefits of smaller patches and high-resolution images without incurring the computational overhead associated with increased token counts. + +Beyond their compactness, region-based representations excel at capturing semantic information, enabling spatiotemporal object localization through simple token similarity matching. Figure 4 illustrates this through cosine similarity heatmaps, where region-based representations show precise areas of high similarity for the query objects, while patch-based representations result in less focused similarity distributions. Our comparative analysis reveals that while patch encodings achieve better frame-level retrieval (65% vs. 60%), they perform significantly worse at spatial localization (42% vs. 58%) compared to region-based representations. For specific applications, one could combine patch-based frame retrieval with region-based object localization. For episodic memory tasks, however, we believe that using only region-based representations is advantageous as it avoids the computational overhead of storing and searching through substantially more patch tokens and eliminates the need to generate regions during retrieval. + +Feature Extraction. To search and retrieve objects that match a given query, VQL requires capturing fine-grained details from each video frame, and the DINO models are particularly well-suited for this task [19, 41]. We compare DINO [7] and DINOv2 [31] using various ViT backbones, with results shown in Table 3. Our findings indicate that DINO ViT-B/8 outperforms ViT-B/16, likely due to its + +![](images/acf23413dd6443e5af82edc197c0560f3fd9351025534f560bb8c7ede0a779fe.jpg) +Figure 4. Comparing cosine similarity heatmaps for patch-based and region-based representations. Region-based representations yield distinct, high-similarity matches for query objects (brighter regions), while patch-based representations produce more diffuse similarity patterns. + +Table 2. Token count for patch-based and region-based encodings. Region-based representations typically use fewer tokens than the patch-based method, and their token count does not scale with resolution. Token counts are reported for a 1000-frame video, using a patch size of 8 and SAM ViT-H for region-based encoding. + +
ExtractorstAP25tAP25SuccessRecovery
DINO ViT-B/160.2540.30150.047.7
DINOv2 ViT-L/140.3310.45255.845.3
DINO ViT-B/80.3330.40958.050.5
+ +Table 3. Performance comparison of feature extractors. DINOv2 ViT-L/14 shows superior frame-level retrieval while DINO ViT-B/8 is better at spatial localization. + +
MethodstAP25tAP25SuccessRecovery
RELOCATE-NoRefine0.2460.36449.139.8
RELOCATE-NoReiter0.2470.29350.948.2
RELOCATE0.3330.40958.050.5
+ +Table 4. Impact of refining search results and reiterating after query expansion. Ablating either refinement (RELOCATE-NoRefine) or reiteration (RELOCATE-NoReiter) significantly reduces the performance of RELOCATE. + +smaller patch size enabling finer feature extraction. Additionally, DINOv2 ViT-L/14 shows stronger frame-level retrieval, and DINO ViT-B/8 is better at spatial localization of objects. We choose DINO ViT-B/8 as our feature extractor due to its higher spatio-temporal localization success rate, smaller model size for faster inference, and reduced feature dimensionality requiring less memory. + +# 4.3. Ablation Study + +Refining Search Results. Results in Table 4 show that removing search refinement (RELOCATE-NoRefine) from the framework significantly degrades RELOCATE's performance. As illustrated in Figure 5a, refinement enhances + +![](images/d596021501232916c5574608b668aac80a1fa633b10ad4a3009f89ed1ff2431d.jpg) +(a) Cropping around objects during refinement helps capture small objects or object parts that full-frame processing might miss. +(b) Refinement fixes incorrect selections due to feature bleeding (row 3) and removes false selections by lowering their scores (rows 1 and 2). + +![](images/91ece3b8ce80556d9702051f2acbcc872d4c29e21099b963a86e4ef268b326bb.jpg) +Figure 5. Impact of refining search results. Initial candidates are shown in yellow boxes, and refined candidates are shown in green. +Figure 6. Impact of query expansion and reiteration. Using only the initial query $\mathcal{Q}$ , RELOCATE misses the object's final appearance due to its partial view and low feature similarity. However, the expanded query set $\mathcal{Q}^+$ captures multiple object perspectives, enabling successful detection of the final occurrence. + +spatial precision for localizing small objects and fine parts by generating regions from an object-centric crop that captures more of the object of interest. Additionally, refinement removes incorrect selections from the initial search by rescoring candidates using region tokens generated from an object-centric crop. Furthermore, for small or thin objects, feature bleeding can result in the selection of an object adjacent to the target object. Object-centered cropping can also help avoid this by providing a clearer view of the target. This is demonstrated in Figure 5b. + +Query Expansion and Reiteration. Results in Table 4 show that query expansion and reiteration significantly improve RELOCATE's performance compared to the variant without this step (RELOCATE-NoReiter). Figure 6 shows an example where query expansion using an initial prediction helps capture a wider range of views for the visual query. + +This, in turn, helps in successfully localizing the final occurrence of the object that was missed when only the initial visual query was used. Additional examples where reiteration after query expansion leads to successful localization are illustrated in rows 2, 5, and 6 of Figure 1. + +# 5. Conclusion + +We present RELOCATE, a framework utilizing region-based representations from pretrained vision models to address VQL. Despite a simple design and no task-specific training, RELOCATE can localize target objects in long videos, even under challenging conditions such as clutter, occlusion, blur, and viewpoint changes. On the VQ2D benchmark, it significantly outperforms existing methods that are specifically trained on this dataset. + +# Acknowledgements + +This work is supported in part by ONR N00014-23-1-2383, DARPA HR0011-23-9-0060, NSF 2008387, NSF 2045586, NSF 2106825, NSF MRI 1725729, and NIFA award 2020-67021-32799. The views and conclusions expressed are those of the authors, and not necessarily representative of the US Government or its agencies. + +# References + +[1] Hossein Azizpour, Ali Sharif Razavian, Josephine Sullivan, Atsuto Maki, and Stefan Carlsson. From generic to specific deep representations for visual recognition. In CVPRW, 2014. 3 +[2] Artem Babenko and Victor S. Lempitsky. Aggregating local deep features for image retrieval. In ICCV, 2015. +[3] Artem Babenko, Anton Slesarev, Alexander Chigorin, and Victor S. Lempitsky. Neural codes for image retrieval. In ECCV, 2014. 3 +[4] Alberto Baldrati, Marco Bertini, Tiberio Uricchio, and A. Bimbo. 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CVPR, 2023. 3 \ No newline at end of file diff --git a/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/images.zip b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fa109eda4ff82868e9f3c22b9c8f143b4ef1facc --- /dev/null +++ b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:507d6d1d7342ad74a9cd332d9141e92fccd9a98ff351e01ab5fb98be6620cabb +size 715947 diff --git a/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/layout.json b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..280a60d71a06319fbecbae3ffc0fad0b40b54421 --- /dev/null +++ b/2025/RELOCATE_ A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations/layout.json @@ -0,0 +1,7937 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 72, + 102, + 539, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 102, + 539, + 138 + ], + "spans": [ + { + "bbox": [ + 72, + 102, + 539, + 138 + ], + "type": "text", + "content": "RELOCATE: A Simple Training-Free Baseline for Visual Query Localization Using Region-Based Representations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 128, + 160, + 482, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 160, + 482, + 175 + ], + "spans": [ + { + "bbox": [ + 128, + 160, + 482, + 175 + ], + "type": "text", + "content": "Savya Khosla Sethuraman TV Alexander Schwing Derek Hoiem" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 230, + 176, + 381, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 230, + 176, + 381, + 188 + ], + "spans": [ + { + "bbox": [ + 230, + 176, + 381, + 188 + ], + "type": "text", + "content": "University of Illinois Urbana-Champaign" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 178, + 190, + 427, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 190, + 427, + 201 + ], + "spans": [ + { + "bbox": [ + 178, + 190, + 427, + 201 + ], + "type": "text", + "content": "{savyak2, st34, aschwing, dhoiem}@illinois.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 229, + 200, + 242 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 229, + 200, + 242 + ], + "spans": [ + { + "bbox": [ + 151, + 229, + 200, + 242 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 255, + 296, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 255, + 296, + 478 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 296, + 478 + ], + "type": "text", + "content": "We present RELOCATE, a simple training-free baseline designed to perform the challenging task of visual query localization in long videos. To eliminate the need for task-specific training and efficiently handle long videos, RELOCATE leverages a region-based representation derived from pretrained vision models. At a high level, it follows the classic object localization approach: (1) identify all objects in each video frame, (2) compare the objects with the given query and select the most similar ones, and (3) perform bidirectional tracking to get a spatio-temporal response. However, we propose some key enhancements to handle small objects, cluttered scenes, partial visibility, and varying appearances. Notably, we refine the selected objects for accurate localization and generate additional visual queries to capture visual variations. We evaluate RELOCATE on the challenging Ego4D Visual Query 2D Localization dataset, establishing a new baseline that outperforms prior task-specific methods by " + }, + { + "bbox": [ + 56, + 255, + 296, + 478 + ], + "type": "inline_equation", + "content": "49\\%" + }, + { + "bbox": [ + 56, + 255, + 296, + 478 + ], + "type": "text", + "content": " (relative improvement) in spatio-temporal average precision." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 504, + 135, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 504, + 135, + 517 + ], + "spans": [ + { + "bbox": [ + 56, + 504, + 135, + 517 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 525, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 295, + 714 + ], + "type": "text", + "content": "Visual Query Localization (VQL) requires localizing the last appearance of an object of interest in a long video. The object of interest is specified via a reference image, also known as the visual query. Figure 1 provides illustrative examples. VQL is an important task, e.g., for surveillance, legal investigations, wildlife monitoring, or simply for tracking down a misplaced item. However, the task presents several unique challenges that push the boundaries of contemporary computer vision methods. For instance, unlike classic object detection models that are trained to identify a fixed set of object categories [6, 37], VQL requires localizing an open-ended range of objects. Additionally, while typical object tracking methods are initialized with a bounding box close to the object's temporal location in the video [24, 27, 47], the VQL reference image (visual query) often originates outside the video, i.e., there may be" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 231, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 231, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 231, + 553, + 300 + ], + "type": "text", + "content": "no exact or neighboring frame for reliable matching. Further, the object's appearance may vary significantly from the visual query due to changes in orientation, scale, context, lighting, motion blur, and occlusions. Compounding these issues, the object of interest usually appears briefly in a long, untrimmed video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 301, + 553, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 553, + 500 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 553, + 500 + ], + "type": "text", + "content": "Classic VQL methods typically use a stage-wise pipeline [17, 45, 46]: (1) identify all objects in each video frame, (2) compare these objects with the given query to select the most similar ones, and (3) perform bidirectional tracking to obtain a spatio-temporal response. While this pipeline is well-grounded in the object localization literature, it is effective only for large, consistently visible objects that closely match the visual query in short video clips. A more recent work [20] has proposed an end-to-end framework that aims to understand the holistic relationship between a given query and the video, performing spatio-temporal localization in a single step. However, this approach requires extensive training on large, annotated datasets, which can be challenging to obtain. Additionally, since such a method learns a holistic video-query relationship, it must process the entire video for each query, even when multiple queries are to be localized in the same video." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 502, + 553, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 553, + 618 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 553, + 618 + ], + "type": "text", + "content": "To address these limitations, we propose Region-based representations for Localizing Anything in Episodic memory (RELOCATE), a simple training-free baseline for VQL. Being training-free, RELOCATE eliminates the need for extensive task-specific training and large annotated datasets. Moreover, it encodes a video independently of the query, allowing the same video encoding to be reused for multiple queries. This makes the method more suitable for episodic memory tasks, as it enables us to perform the resource-intensive video encoding just once for multiple queries." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 620, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 620, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 620, + 556, + 714 + ], + "type": "text", + "content": "RELOCATE follows a classic stage-wise setup for object localization while integrating techniques to efficiently encode long videos, handle small and fleeting objects, and manage varying appearances of the query object. Specifically, it begins by extracting region-based representations from the video and searching for candidates that match the visual query. The selected candidates are then refined to improve precision, and the most relevant candidate is tracked" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3697" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 69, + 541, + 466 + ], + "blocks": [ + { + "bbox": [ + 69, + 69, + 541, + 466 + ], + "lines": [ + { + "bbox": [ + 69, + 69, + 541, + 466 + ], + "spans": [ + { + "bbox": [ + 69, + 69, + 541, + 466 + ], + "type": "image", + "image_path": "0842be60caf8337dea51dab069c71262e382ae8290c85ab262766d8a9b123a7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 473, + 555, + 518 + ], + "lines": [ + { + "bbox": [ + 55, + 473, + 555, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 555, + 518 + ], + "type": "text", + "content": "Figure 1. RELOCATE is a training-free framework designed for visual query localization. It can effectively localize target objects in long videos despite challenging conditions such as visual clutter, occlusions, background blending, motion blur, viewpoint changes, and brief object appearances. Here we show visual queries on the left and the successfully localized object appearances marked by cyan bounding boxes on the right." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 537, + 294, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 537, + 294, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 537, + 294, + 597 + ], + "type": "text", + "content": "across video frames to generate an initial prediction. In a subsequent iteration, this prediction is used to create new visual queries, which are then employed to relocalize the object, aiming to capture appearances that differ significantly from the original visual query." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "text", + "content": "We evaluate RELOCATE using the Ego4D Visual Query 2D (VQ2D) Localization benchmark [17] and observe significant improvements over prior methods. We achieve a " + }, + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "inline_equation", + "content": "49\\%" + }, + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "text", + "content": " increase in spatio-temporal average precision and a " + }, + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 55, + 608, + 295, + 712 + ], + "type": "text", + "content": " boost in temporal average precision compared to prior state-of-the-art, all without task-specific training. This demonstrates that simple retrieval methods are effective with region-level tokens derived from pretrained foundation models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 326, + 537, + 539, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 537, + 539, + 549 + ], + "spans": [ + { + "bbox": [ + 326, + 537, + 539, + 549 + ], + "type": "text", + "content": "In summary, the main contributions of this work are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 560, + 553, + 713 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 315, + 560, + 553, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 560, + 553, + 608 + ], + "spans": [ + { + "bbox": [ + 315, + 560, + 553, + 608 + ], + "type": "text", + "content": "1. We propose RELOCATE, a training-free method for localizing objects in long videos. Despite no task-specific training, RELOCATE significantly improves upon prior VQL work on the Ego4D VQ2D benchmark." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 608, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 553, + 689 + ], + "type": "text", + "content": "2. We demonstrate the benefits of using region-based representations from pretrained vision models for object localization. Particularly, we show that these representations form a detailed yet compact encoding for long videos. Furthermore, they allow us to efficiently and robustly perform object retrieval using a simple matching function like cosine similarity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "3. We propose techniques to improve the robustness and precision of a stage-wise object localization framework." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "3698" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 294, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 294, + 166 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 294, + 166 + ], + "type": "text", + "content": "Specifically, to enhance localization accuracy, we introduce a refinement step that allows RELOCATE to closely examine the selected candidates and improve their representations, while filtering out incorrect selections. Additionally, we introduce a technique to generate multiple visual queries from a single query, which helps capture varying appearances, changing contexts, and occlusions of objects in a dynamic video setting." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 177, + 142, + 189 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 177, + 142, + 189 + ], + "spans": [ + { + "bbox": [ + 55, + 177, + 142, + 189 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 197, + 296, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 197, + 296, + 701 + ], + "spans": [ + { + "bbox": [ + 56, + 197, + 296, + 701 + ], + "type": "text", + "content": "Object Instance Recognition. Early approaches to object instance recognition retrieve images with similar keypoints to the visual query [23, 29, 30, 42]. This works well for objects with distinctive textures, but fails for low-texture, blurry, and highly occluded objects, which are common in the VQL task. Subsequent research shifted towards using features extracted from convolutional neural networks (CNNs) as descriptors for image retrieval [1-3, 8, 35, 36]. However, these early CNN-based methods suffer when faced with large changes in scale, rotation, or viewpoint. To further enhance retrieval performance, query expansion techniques were introduced to iteratively refine the query using information from initial results [12, 16, 44]. The advent of vision foundation models such as CLIP [33], DINO [7], and DINOv2 [31] has enabled new strategies for instance recognition and retrieval. Several works [4, 10, 39, 40] have leveraged the cross-modal capabilities of CLIP for specialized retrieval tasks. However, these approaches are primarily designed for scenarios where query objects occupy a substantial portion of the target frame, which is not the case in VQL. Recent work on region-based representations [41] shows that pooling DINOv2 features over SAM regions provides effective example-based object category retrieval. In this work, we apply a similar approach for our initial search but propose enhancements to refine, track, and expand the initial query. Video Object Tracking. Conventional tracking approaches are initialized with a bounding box in an initial frame of the target video, and they track objects through gradual appearance changes. In contrast, VQL often involves queries from frames outside the target video, leading to significant variations in appearance, viewpoint, and context. Nevertheless, tracking remains crucial in VQL. Early tracking approaches relied on motion and appearance cues, using correlation filters and keypoint matching [18, 21, 38]. More recently, trackers leverage large Transformer models to effectively track one or more objects in long videos [9, 13, 24, 26, 28, 47]. Tracking in egocentric videos introduces additional challenges due to frequent camera motion, occlusions, and object interactions, which have been highlighted in recent benchmarks and studies [5, 14, 15, 49]. Some recent works have also extended SAM [22] for tracking [11, 34, 48]. In this work, we use SAM 2 [34]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 701, + 295, + 714 + ], + "type": "text", + "content": "Visual Query Localization. The Ego4D benchmark [17]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 555, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 272 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 272 + ], + "type": "text", + "content": "recently introduced VQ2D, a benchmark for VQL. The initial approach, proposed as a baseline in Ego4D, employs a three-stage detection and tracking framework: performing frame-level detection, identifying the most recent detection peak across time, and applying bi-directional tracking to determine the complete temporal extent of the target object [17]. Subsequent works enhance the framework's performance through various refinements like incorporating negative frame sampling to reduce false positives [45] and leveraging background objects as contextual cues [46]. In this work, we adopt a similar stage-wise framework, introducing key design decisions and refinements that significantly improve the baseline. A more recent effort trains a network to learn the query-video relationship and perform VQL in a single step. However, it relies on a large amount of annotated data, which is costly to obtain. In contrast, we present a training-free solution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 283, + 389, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 283, + 389, + 295 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 389, + 295 + ], + "type": "text", + "content": "3. RELOCATE" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "spans": [ + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": "We focus on VQL, the task of localizing the last occurrence of a query object in a video. Formally, given a video " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": ", a visual query " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": ", and a query time " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": ", the objective is to predict a response track " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{b_s, b_{s+1}, \\ldots, b_e\\}" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": " that localizes and tracks the latest occurrence of the query object prior to time " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": " is specified by a bounding box in a reference frame, " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "e \\leq T" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": " denote the first and the last frames in which the query object is visible, and " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "b_i" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": " represents a bounding box around the object in frame " + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 302, + 555, + 408 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 554, + 479 + ], + "type": "text", + "content": "As shown in Figure 2, RELOCATE prepares video representations to facilitate a swift search for objects that match the given visual queries. It then refines the search results for better precision and tracks the latest match across frames. After making a prediction, it can reiterate the localization process using the previous prediction for better results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 479, + 554, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 554, + 561 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 554, + 561 + ], + "type": "text", + "content": "Prepare (Section 3.1). A given video is first distilled into semantically meaningful object-level representations, or object tokens. For this, RELOCATE uses a segmentation model to generate object-wise binary masks for each object across all video frames and a feature extractor to produce dense feature maps for each frame. The features within each object mask are then pooled to produce an object token." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 561, + 553, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 553, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 553, + 619 + ], + "type": "text", + "content": "Search (Section 3.2). After preparing object tokens from the video, RELOCATE creates a similar region-based representation for the visual query, referred to as the query token. It then searches the object tokens for candidates that match the query token." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 619, + 553, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 619, + 553, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 619, + 553, + 677 + ], + "type": "text", + "content": "Refine (Section 3.3). The candidates identified in the initial search are then refined to improve spatial precision and remove any spurious matches. For example, Figure 2 illustrates how refinement enhances spatial precision by capturing the base of the monitor." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 678, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 678, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 678, + 553, + 713 + ], + "type": "text", + "content": "Track (Section 3.4). The latest refined search is tracked across video frames using an off-the-shelf tracking model to produce a response track localizing the most recent oc" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3699" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 552, + 324 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 552, + 324 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 552, + 324 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 552, + 324 + ], + "type": "image", + "image_path": "32685f46e85948dcc95164e8cf0f81f9da695065679512ea72c1b330acfd14a4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "lines": [ + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "text", + "content": "Figure 2. RELOCATE framework: Prepare object tokens from the given video " + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "text", + "content": " and search for candidates that match the visual query " + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "text", + "content": ". Then, refine the search results for better precision and track the latest refined candidate across video frames to get a response track prediction " + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}}" + }, + { + "bbox": [ + 55, + 332, + 555, + 367 + ], + "type": "text", + "content": ". Finally, use the response track to create additional visual queries and reiterate the search, refinement, and tracking process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 387, + 223, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 223, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 223, + 398 + ], + "type": "text", + "content": "currence of the query object in the video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 399, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 296, + 460 + ], + "type": "text", + "content": "Reiterate (Section 3.5). To better capture the visual variations of the query object, we leverage the object's appearance in the tracked frames to create more visual queries and then re-apply RELOCATE to the video segment that follows the previously predicted track." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 469, + 117, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 117, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 117, + 482 + ], + "type": "text", + "content": "3.1. Prepare" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 487, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 296, + 605 + ], + "type": "text", + "content": "To address VQL, it is imperative to encode and represent all regions/objects in each frame of a video. However, creating patch-level features for each frame results in an excessive number of tokens for long videos, making the task computationally expensive. To address this issue, we propose using region-based representations [41] to encode each frame. As shown in Table 2, the region-based approach significantly reduces the number of tokens needed to encode a video. Moreover, this produces semantically meaningful object tokens, simplifying entity search for a given query." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 607, + 295, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 295, + 630 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 295, + 630 + ], + "type": "text", + "content": "Building on this insight, RELOCATE prepares object tokens from a given video as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "content": "1. Segment Objects. We first generate a binary mask for each region/object in all frames of the video via a segmentation model. Formally, for a frame " + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_{t} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "content": ", we extract a set of binary masks " + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "inline_equation", + "content": "M_{t} = \\{m_{t1}, m_{t2}, \\ldots\\}" + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "content": ", one for each region. Here, " + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "inline_equation", + "content": "m_{ti} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "content": " is a binary mask with 1 in the area occupied by the object " + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 631, + 296, + 714 + ], + "type": "text", + "content": " and 0 otherwise. In this work, we use SAM ViT-H [22] as the segmentation model," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 387, + 553, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 553, + 398 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 553, + 398 + ], + "type": "text", + "content": "which processes each frame at a resolution of " + }, + { + "bbox": [ + 313, + 387, + 553, + 398 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 313, + 387, + 553, + 398 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 399, + 555, + 553 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "text", + "content": "2. Extract Features. We then extract dense features from every frame of the video via a pretrained vision model. Formally, for every frame " + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "inline_equation", + "content": "f_{t} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "text", + "content": " we compute a high-dimensional feature map " + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "inline_equation", + "content": "h_{t} \\in \\mathbb{R}^{h \\times w \\times d}" + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "text", + "content": ". In this work, we experiment with different feature extractors and choose DINO ViT-B/8 [7] with a frame resolution of " + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "inline_equation", + "content": "384 \\times 512" + }, + { + "bbox": [ + 313, + 399, + 554, + 470 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "content": "3. Resize and Pool. Subsequently, we resize the frame features " + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "inline_equation", + "content": "h_t \\in \\mathbb{R}^{h \\times w \\times d}" + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "inline_equation", + "content": "\\overline{h}_t \\in \\mathbb{R}^{H \\times W \\times d}" + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "content": " to fit the height and width of the masks. We then pool the features within each object mask " + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "inline_equation", + "content": "m_{ti}" + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "content": " to get an object token " + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "inline_equation", + "content": "o_{ti} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 471, + 555, + 553 + ], + "type": "text", + "content": ". Following the insights from [41], we use bilinear interpolation to resize the features and average pooling to aggregate the features within the mask." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 564, + 370, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 564, + 370, + 575 + ], + "spans": [ + { + "bbox": [ + 314, + 564, + 370, + 575 + ], + "type": "text", + "content": "3.2. Search" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 582, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 677 + ], + "type": "text", + "content": "Videos spanning tens of minutes and processed at 5 FPS typically involve more than 150,000 object tokens, with only about " + }, + { + "bbox": [ + 313, + 582, + 555, + 677 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 313, + 582, + 555, + 677 + ], + "type": "text", + "content": " corresponding to the target response track. To find candidates similar to the visual query, RELOCATE searches over the object tokens. Concretely, given an image and a bounding box localizing the query object, we extract the query token via the process used for video preparation and proceed with the following steps:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 678, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 678, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 678, + 556, + 715 + ], + "type": "text", + "content": "1. Compute Similarity. We compute pairwise cosine similarity between all object tokens and query tokens. Initially, only one query token is generated from the given visual" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3700" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": "query, but multiple query tokens can be created for the same object. When multiple query tokens are present, we use the maximum similarity score across all tokens as the object score, ensuring that an object is selected if it matches any view of the query. Formally, for the " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "i^{\\text{th}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": " object token in frame " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "o_{ti}" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": " query tokens " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "[q_j]_{j=1}^m" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": ", the similarity score " + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "inline_equation", + "content": "s_{ti}" + }, + { + "bbox": [ + 55, + 72, + 294, + 155 + ], + "type": "text", + "content": " is computed via" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 118, + 159, + 295, + 183 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 159, + 295, + 183 + ], + "spans": [ + { + "bbox": [ + 118, + 159, + 295, + 183 + ], + "type": "interline_equation", + "content": "s _ {t i} = \\max _ {j \\in \\{1, \\dots , m \\}} \\frac {o _ {t i} \\cdot q _ {j}}{\\left\\| o _ {t i} \\right\\| \\left\\| q _ {j} \\right\\|}. \\tag {1}", + "image_path": "800fdfa3b77b0fa9dbc249afc0cb6cf120c56a99226494c0ad55482d249ff6e6.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 186, + 295, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 295, + 221 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 295, + 221 + ], + "type": "text", + "content": "We also studied test-time training (TTT) [43], but it performed worse than a simple cosine similarity search due to an insufficient number of query tokens for effective training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 221, + 294, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 294, + 303 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 294, + 303 + ], + "type": "text", + "content": "2. Perform Intra-Frame NMS. Given that each frame can contain at most one instance of the query object, we apply non-maximum suppression (NMS) to retain only the highest-scoring object per frame, setting the scores of all other objects to zero. This process results in a single candidate object per frame, yielding a total number of candidate objects equal to the number of frames in the video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 303, + 295, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 303, + 295, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 303, + 295, + 420 + ], + "type": "text", + "content": "3. Perform Inter-Frame NMS. Since we perform bidirectional tracking at a later stage, selecting one candidate from a potential track is sufficient. So, we perform NMS across consecutive frames to select the highest-scoring match for a query object, suppressing lower-scoring instances in neighboring frames. More precisely, we iteratively select the object with the maximum score and nullify candidate scores in preceding and subsequent frames until the score drops below " + }, + { + "bbox": [ + 55, + 303, + 295, + 420 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 55, + 303, + 295, + 420 + ], + "type": "text", + "content": " of this peak score. As a result, we end up with sparsely selected high-scoring objects across video frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "content": "4. Select Candidates. Finally, we select up to " + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "content": " candidate objects that exceed a " + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{sim}} = 0.7" + }, + { + "bbox": [ + 55, + 420, + 295, + 456 + ], + "type": "text", + "content": " similarity threshold, yielding an average of 7.5 candidates per query." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 461, + 108, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 108, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 108, + 472 + ], + "type": "text", + "content": "3.3. Refine" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 479, + 295, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 295, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 295, + 571 + ], + "type": "text", + "content": "The objects of interest are often small and situated in cluttered scenes, making it challenging for the segmentation model and feature extractor to produce high-quality object tokens. To address this, we propose refining the selections made after the initial search. We find that this refinement significantly enhances the spatial precision of RELOCATE and helps filter out any spurious selections made after the initial search (see Section 4.3 for an ablation)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 572, + 295, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 572, + 295, + 607 + ], + "spans": [ + { + "bbox": [ + 55, + 572, + 295, + 607 + ], + "type": "text", + "content": "We refine the candidates selected from the search in conjunction with the query to generate a more precise set of candidates. This is done as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 608, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 55, + 608, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 608, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 608, + 295, + 689 + ], + "type": "text", + "content": "1. Get Object-Centric Crop. We crop the video frames containing the selected candidates and visual queries such that these objects occupy a larger area at the center of the cropped view. These crops are then resized to the original frame dimensions. To prevent pixelation in the case of extremely small objects, we ensure that no frame is cropped with a zoom factor exceeding 2.5 times." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "2. Generate Refined Token. We process the object-centric crops of candidates and queries using the segmentation" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 553, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 131 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 131 + ], + "type": "text", + "content": "model and feature extractor to generate refined object and query tokens. This process yields improved tokens because the segmentation model and feature extractor can produce more accurate masks and detailed features for the objects from the object-centric crop." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 133, + 555, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 181 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 181 + ], + "type": "text", + "content": "3. Recompute Similarity and Filter. We recompute the cosine similarity scores for the selected candidates using the refined object tokens and query tokens, and filter out candidates that have a score below threshold " + }, + { + "bbox": [ + 313, + 133, + 555, + 181 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{sim}} = 0.7" + }, + { + "bbox": [ + 313, + 133, + 555, + 181 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 195, + 365, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 195, + 365, + 206 + ], + "spans": [ + { + "bbox": [ + 314, + 195, + 365, + 206 + ], + "type": "text", + "content": "3.4. Track" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 214, + 554, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 214, + 554, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 214, + 554, + 274 + ], + "type": "text", + "content": "RELOCATE uses an off-the-shelf tracker to bidirectionally track the refined candidate that shows up last in the video, yielding the response track " + }, + { + "bbox": [ + 313, + 214, + 554, + 274 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}} = \\{b_s,b_{s + 1},\\ldots ,b_e\\}" + }, + { + "bbox": [ + 313, + 214, + 554, + 274 + ], + "type": "text", + "content": ". Further, it assigns the similarity score of the candidate as the track score. In this work, we use SAM 2 [34] for tracking." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 288, + 380, + 299 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 288, + 380, + 299 + ], + "spans": [ + { + "bbox": [ + 314, + 288, + 380, + 299 + ], + "type": "text", + "content": "3.5. Reiterate" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 308, + 555, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 471 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 471 + ], + "type": "text", + "content": "The query object often appears multiple times in a given video, and RELOCATE is highly successful at localizing at least one of these appearances from a single visual query (see Section 4.1). However, our goal is to identify the latest appearance, which may be heavily occluded or seen from a significantly different viewpoint compared to the visual query. To achieve this, we generate additional visual queries using the response track predicted with the original query and reiterate the process of search, refinement, and tracking. This expanded pool of queries offers diverse views of the object, enhancing the likelihood of detection even when it is obscured or appears in a radically altered form. In practice, we perform this query expansion and reiteration step only once. This is carried out as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 473, + 554, + 713 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 313, + 473, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 554, + 533 + ], + "type": "text", + "content": "1. Generate Query Tokens. Given the response track " + }, + { + "bbox": [ + 313, + 473, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}} = \\{b_s, b_{s+1}, \\ldots, b_e\\}" + }, + { + "bbox": [ + 313, + 473, + 554, + 533 + ], + "type": "text", + "content": ", we apply the segmentation model and feature extractor to produce region tokens for the objects within the bounding boxes across the frames comprising the response track." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 535, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 535, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 535, + 554, + 628 + ], + "type": "text", + "content": "2. Filter Queries. We filter out low-quality query tokens generated in the previous step, specifically targeting three types: (1) query tokens with very low cosine similarity (less than 0.5) to the original query token, (2) queries associated with extremely small bounding boxes (occupying less than " + }, + { + "bbox": [ + 313, + 535, + 554, + 628 + ], + "type": "inline_equation", + "content": "0.07\\%" + }, + { + "bbox": [ + 313, + 535, + 554, + 628 + ], + "type": "text", + "content": " of the frame area), and (3) queries derived from blurry frames (indicated by a Laplacian operator variance below 100)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "type": "text", + "content": "3. Search, Refine, and Track. After expanding the query pool, we search the video segment following the last frame of the previously predicted response track. The search results are then refined, and the latest refined candidate is tracked across frames to generate a new prediction. If the score of the new prediction exceeds a threshold relative to the previous track score, we update the previous prediction." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3701" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 289, + 210 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 289, + 210 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 289, + 210 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 289, + 210 + ], + "type": "table", + "html": "
MethodstAP25tAP25SuccessRecovery
Validation Set
SiamRCNN [17]0.150.2243.232.9
NFM [45]0.190.2647.937.9
CocoFormer [46]0.190.2647.737.7
VQLoC [46]0.220.3155.947.1
RELOCATE0.330.4158.050.5
Test Set
SiamRCNN [17]0.130.2141.634.0
CocoFormer [46]0.180.2648.143.2
VQLoC [46]0.240.3255.945.1
RELOCATE0.350.4360.150.6
", + "image_path": "4f9414bf8ad5806dfe8ca583d9e15f648acf5bbb2185be0e028ff58b3d1bacee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "type": "text", + "content": "Table 1. Results on Ego4D VQ2D benchmark. The validation results are taken from [46], and the test results are obtained from the challenge leaderboard." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 266, + 137, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 137, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 137, + 280 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 287, + 296, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 287, + 296, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 287, + 296, + 323 + ], + "type": "text", + "content": "In this section, we evaluate RELOCATE (Section 4.1), discuss key design decisions (Section 4.2), and present ablation studies (Section 4.3)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 331, + 129, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 129, + 342 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 129, + 342 + ], + "type": "text", + "content": "4.1. Evaluation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 348, + 295, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 348, + 295, + 465 + ], + "spans": [ + { + "bbox": [ + 54, + 348, + 295, + 465 + ], + "type": "text", + "content": "Dataset. We evaluate RELOCATE on the Ego4D VQ2D dataset [17], a large collection of egocentric videos annotated for VQL within episodic memory. On average, the videos in this dataset are 140 seconds long, and the target response tracks last for roughly 3 seconds. The dataset comprises 13,600 training, 4,500 validation, and 4,400 test queries, annotated across 262, 87, and 84 hours of video, respectively. We use the validation set for our development and ablations. To our knowledge, VQ2D is the only publicly available dataset for VQL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "content": "Metrics. Following the official metrics outlined by the benchmark, we report spatio-temporal average precision " + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "inline_equation", + "content": "(\\mathrm{stAP}_{25})" + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "content": ", temporal average precision " + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "inline_equation", + "content": "(\\mathrm{tAP}_{25})" + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "content": ", success, and recovery. " + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "inline_equation", + "content": "\\mathrm{stAP}_{25}" + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "inline_equation", + "content": "\\mathrm{tAP}_{25}" + }, + { + "bbox": [ + 54, + 466, + 295, + 583 + ], + "type": "text", + "content": " evaluate the accuracy of the predicted response tracks' spatio-temporal and temporal extents using an Intersection over Union (IoU) threshold of 0.25. Success measures whether the IoU between predictions and ground truth exceeds 0.05, and recovery measures the proportion of predicted frames where the bounding box achieves an IoU of at least 0.5 with the ground truth." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "spans": [ + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "content": "Results. Table 1 shows results on the validation and test sets. Despite no task-specific training, RELOCATE outperforms the next-best baseline by " + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "49\\%" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{stAP}_{25}" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{tAP}_{25}" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "content": " Success, and " + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 54, + 584, + 295, + 654 + ], + "type": "text", + "content": " Recovery on the test set. Note, these are relative improvements. Figure 1 shows some qualitative examples of RELOCATE in action." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "Additionally, a manual analysis of 100 randomly sampled examples from the VQ2D validation set shows that RELOCATE successfully localizes the last occurrence of the object in 61 cases, localizes an earlier instance in 32 cases, and identifies the wrong object in 7 cases. Figure 3 cate" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 325, + 82, + 432, + 129 + ], + "blocks": [ + { + "bbox": [ + 323, + 72, + 347, + 80 + ], + "lines": [ + { + "bbox": [ + 323, + 72, + 347, + 80 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 347, + 80 + ], + "type": "text", + "content": "Q" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 72, + 421, + 80 + ], + "lines": [ + { + "bbox": [ + 369, + 72, + 421, + 80 + ], + "spans": [ + { + "bbox": [ + 369, + 72, + 421, + 80 + ], + "type": "text", + "content": "Tracked Candidate" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 325, + 82, + 432, + 129 + ], + "lines": [ + { + "bbox": [ + 325, + 82, + 432, + 129 + ], + "spans": [ + { + "bbox": [ + 325, + 82, + 432, + 129 + ], + "type": "image", + "image_path": "051f0c2e771830ec4e20e63a8150144a0fc1254d4cb5be69ec79b67c2a6bbb20.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 132, + 552, + 151 + ], + "lines": [ + { + "bbox": [ + 315, + 132, + 552, + 151 + ], + "spans": [ + { + "bbox": [ + 315, + 132, + 552, + 151 + ], + "type": "text", + "content": "(a) An object visually similar to the query (blue boxes) is mistakenly tracked instead of the correct query object (green boxes)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 440, + 82, + 473, + 119 + ], + "blocks": [ + { + "bbox": [ + 453, + 72, + 461, + 80 + ], + "lines": [ + { + "bbox": [ + 453, + 72, + 461, + 80 + ], + "spans": [ + { + "bbox": [ + 453, + 72, + 461, + 80 + ], + "type": "text", + "content": "Q" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 440, + 82, + 473, + 119 + ], + "lines": [ + { + "bbox": [ + 440, + 82, + 473, + 119 + ], + "spans": [ + { + "bbox": [ + 440, + 82, + 473, + 119 + ], + "type": "image", + "image_path": "5b32348add231c6ff75c1381f3c0e0f2d6534c7e2216ee36a7a6729903f77f66.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 476, + 82, + 546, + 129 + ], + "blocks": [ + { + "bbox": [ + 484, + 72, + 536, + 80 + ], + "lines": [ + { + "bbox": [ + 484, + 72, + 536, + 80 + ], + "spans": [ + { + "bbox": [ + 484, + 72, + 536, + 80 + ], + "type": "text", + "content": "Tracked Candidate" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 476, + 82, + 546, + 129 + ], + "lines": [ + { + "bbox": [ + 476, + 82, + 546, + 129 + ], + "spans": [ + { + "bbox": [ + 476, + 82, + 546, + 129 + ], + "type": "image", + "image_path": "06236491c658da66239f3c304c53ee2e8e9d6d3e18be8df44535095bb0112242.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 325, + 163, + 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"angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 289, + 552, + 309 + ], + "lines": [ + { + "bbox": [ + 315, + 289, + 552, + 309 + ], + "spans": [ + { + "bbox": [ + 315, + 289, + 552, + 309 + ], + "type": "text", + "content": "(c) These visual queries lack discriminative features due to motion blur, low contrast with background, or poor visibility." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 316, + 554, + 369 + ], + "lines": [ + { + "bbox": [ + 313, + 316, + 554, + 369 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 554, + 369 + ], + "type": "text", + "content": "Figure 3. Examples where a wrong object is localized. Among 100 randomly sampled instances from the VQ2D validation set, RELOCATE localized an instance of the query object in 93 cases, and failed to localize the correct object only under extreme conditions." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 384, + 249, + 427, + 285 + ], + "blocks": [ + { + "bbox": [ + 406, + 238, + 413, + 246 + ], + "lines": [ + { + "bbox": [ + 406, + 238, + 413, + 246 + ], + "spans": [ + { + "bbox": [ + 406, + 238, + 413, + 246 + ], + "type": "text", + "content": "Q" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 384, + 249, + 427, + 285 + ], + "lines": [ + { + "bbox": [ + 384, + 249, + 427, + 285 + ], + "spans": [ + { + "bbox": [ + 384, + 249, + 427, + 285 + ], + "type": "image", + "image_path": "f0ac6b220444add6bb64715ff921092d9a5f1fdbede4033e31df6f235a8c56f2.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 442, + 250, + 478, + 285 + ], + "blocks": [ + { + "bbox": [ + 457, + 238, + 464, + 246 + ], + "lines": [ + { + "bbox": [ + 457, + 238, + 464, + 246 + ], + "spans": [ + { + "bbox": [ + 457, + 238, + 464, + 246 + ], + "type": "text", + "content": "Q" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 442, + 250, + 478, + 285 + ], + "lines": [ + { + "bbox": [ + 442, + 250, + 478, + 285 + ], + "spans": [ + { + "bbox": [ + 442, + 250, + 478, + 285 + ], + "type": "image", + "image_path": "1791907bafe3a4e82ea2bcc80feb201edc660c2b56012005be8e2499d6ae5807.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 492, + 250, + 529, + 285 + ], + "blocks": [ + { + "bbox": [ + 507, + 238, + 515, + 246 + ], + "lines": [ + { + "bbox": [ + 507, + 238, + 515, + 246 + ], + "spans": [ + { + "bbox": [ + 507, + 238, + 515, + 246 + ], + "type": "text", + "content": "Q" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 492, + 250, + 529, + 285 + ], + "lines": [ + { + "bbox": [ + 492, + 250, + 529, + 285 + ], + "spans": [ + { + "bbox": [ + 492, + 250, + 529, + 285 + ], + "type": "image", + "image_path": "866f733723cbe5f7c5df074d3de3867342e8bbdac9ba4f2718d7974e43a11c95.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 392, + 555, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 604 + ], + "type": "text", + "content": "gorizes these failure modes for the cases where RELOCATE localizes the wrong object, highlighting that the framework typically fails to localize the correct object only in extreme situations, such as when the visual query is ambiguous or there exists another object that closely resembles the query. Timing Analysis. On average, preparing a 1000-frame video (i.e., extracting object tokens) takes 1422.5 seconds with our current setup. Subsequent steps are faster: search takes 0.8 seconds, refinement 12.6 seconds, tracking 26.3 seconds, and generating additional queries from a response track is instantaneous. Note that our current implementation is not optimized for speed. For applications requiring faster localization, several simple optimizations can be made with minimal impact on the metrics, such as using HNSW [25] for search, increasing the batch size for feature extraction, using faster SAM variants [32] for region generation, and employing faster trackers. We leave these enhancements for future work." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 313, + 613, + 416, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 416, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 416, + 625 + ], + "type": "text", + "content": "4.2. Design Decisions" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 554, + 713 + ], + "type": "text", + "content": "Region vs. Patch Representations. Most contemporary approaches to object localization and tracking encode video frames using patch-based representations, where each frame is divided into non-overlapping patches and encoded with a vision transformer. Region-based representations derived from pretrained vision models [41] have recently been proposed as an efficient alternative. These represent" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3702" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 292, + 125 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 292, + 125 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 292, + 125 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 292, + 125 + ], + "type": "table", + "html": "
Encoding MethodNumber of tokens
384 × 512 Frames1024 × 1024 Frames
Patches3,072,00016,384,000
Regions130,507130,507
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As a result, in most cases, a region-based approach yields fewer tokens than the patch-based approach. As shown in Table 2, a region-based encoding of a 200-second VQ2D video produces " + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "inline_equation", + "content": "24 \\times" + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "text", + "content": " fewer tokens compared to a patch-based encoding at an image resolution of " + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "inline_equation", + "content": "384 \\times 512" + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "text", + "content": " with a patch size of 8. Moreover, this difference drastically increases if we increase the resolution; e.g. if the image resolution is increased to " + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "text", + "content": ", a region-based encoding produces " + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "inline_equation", + "content": "126 \\times" + }, + { + "bbox": [ + 54, + 231, + 295, + 417 + ], + "type": "text", + "content": " fewer tokens than a patch-based encoding. Thus, decoupling of token count from spatial parameters allows the region-based approach to leverage the benefits of smaller patches and high-resolution images without incurring the computational overhead associated with increased token counts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 419, + 295, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 295, + 631 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 295, + 631 + ], + "type": "text", + "content": "Beyond their compactness, region-based representations excel at capturing semantic information, enabling spatiotemporal object localization through simple token similarity matching. Figure 4 illustrates this through cosine similarity heatmaps, where region-based representations show precise areas of high similarity for the query objects, while patch-based representations result in less focused similarity distributions. Our comparative analysis reveals that while patch encodings achieve better frame-level retrieval (65% vs. 60%), they perform significantly worse at spatial localization (42% vs. 58%) compared to region-based representations. For specific applications, one could combine patch-based frame retrieval with region-based object localization. For episodic memory tasks, however, we believe that using only region-based representations is advantageous as it avoids the computational overhead of storing and searching through substantially more patch tokens and eliminates the need to generate regions during retrieval." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 631, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 631, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 631, + 295, + 714 + ], + "type": "text", + "content": "Feature Extraction. To search and retrieve objects that match a given query, VQL requires capturing fine-grained details from each video frame, and the DINO models are particularly well-suited for this task [19, 41]. We compare DINO [7] and DINOv2 [31] using various ViT backbones, with results shown in Table 3. Our findings indicate that DINO ViT-B/8 outperforms ViT-B/16, likely due to its" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 553, + 272 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 553, + 272 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 553, + 272 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 553, + 272 + ], + "type": "image", + "image_path": "acf23413dd6443e5af82edc197c0560f3fd9351025534f560bb8c7ede0a779fe.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 274, + 555, + 329 + ], + "lines": [ + { + "bbox": [ + 313, + 274, + 555, + 329 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 555, + 329 + ], + "type": "text", + "content": "Figure 4. Comparing cosine similarity heatmaps for patch-based and region-based representations. Region-based representations yield distinct, high-similarity matches for query objects (brighter regions), while patch-based representations produce more diffuse similarity patterns." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 321, + 340, + 548, + 391 + ], + "blocks": [ + { + "bbox": [ + 55, + 129, + 295, + 183 + ], + "lines": [ + { + "bbox": [ + 55, + 129, + 295, + 183 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 295, + 183 + ], + "type": "text", + "content": "Table 2. Token count for patch-based and region-based encodings. Region-based representations typically use fewer tokens than the patch-based method, and their token count does not scale with resolution. Token counts are reported for a 1000-frame video, using a patch size of 8 and SAM ViT-H for region-based encoding." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 340, + 548, + 391 + ], + "lines": [ + { + "bbox": [ + 321, + 340, + 548, + 391 + ], + "spans": [ + { + "bbox": [ + 321, + 340, + 548, + 391 + ], + "type": "table", + "html": "
ExtractorstAP25tAP25SuccessRecovery
DINO ViT-B/160.2540.30150.047.7
DINOv2 ViT-L/140.3310.45255.845.3
DINO ViT-B/80.3330.40958.050.5
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MethodstAP25tAP25SuccessRecovery
RELOCATE-NoRefine0.2460.36449.139.8
RELOCATE-NoReiter0.2470.29350.948.2
RELOCATE0.3330.40958.050.5
", + "image_path": "b2dead31ce1f3072d740097d25c7a784b2eb711fda5e1bd988c8bcea33efa9e0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 492, + 555, + 536 + ], + "lines": [ + { + "bbox": [ + 313, + 492, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 555, + 536 + ], + "type": "text", + "content": "Table 4. Impact of refining search results and reiterating after query expansion. Ablating either refinement (RELOCATE-NoRefine) or reiteration (RELOCATE-NoReiter) significantly reduces the performance of RELOCATE." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": "smaller patch size enabling finer feature extraction. Additionally, DINOv2 ViT-L/14 shows stronger frame-level retrieval, and DINO ViT-B/8 is better at spatial localization of objects. We choose DINO ViT-B/8 as our feature extractor due to its higher spatio-temporal localization success rate, smaller model size for faster inference, and reduced feature dimensionality requiring less memory." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 648, + 408, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 408, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 408, + 662 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "content": "Refining Search Results. Results in Table 4 show that removing search refinement (RELOCATE-NoRefine) from the framework significantly degrades RELOCATE's performance. As illustrated in Figure 5a, refinement enhances" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3703" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 71, + 542, + 281 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 542, + 281 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 542, + 281 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 542, + 281 + ], + "type": "image", + "image_path": "d596021501232916c5574608b668aac80a1fa633b10ad4a3009f89ed1ff2431d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 283, + 297, + 303 + ], + "lines": [ + { + "bbox": [ + 66, + 283, + 297, + 303 + ], + "spans": [ + { + "bbox": [ + 66, + 283, + 297, + 303 + ], + "type": "text", + "content": "(a) Cropping around objects during refinement helps capture small objects or object parts that full-frame processing might miss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 283, + 539, + 303 + ], + "lines": [ + { + "bbox": [ + 310, + 283, + 539, + 303 + ], + "spans": [ + { + "bbox": [ + 310, + 283, + 539, + 303 + ], + "type": "text", + "content": "(b) Refinement fixes incorrect selections due to feature bleeding (row 3) and removes false selections by lowering their scores (rows 1 and 2)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 73, + 329, + 536, + 467 + ], + "blocks": [ + { + "bbox": [ + 63, + 305, + 545, + 317 + ], + "lines": [ + { + "bbox": [ + 63, + 305, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 63, + 305, + 545, + 317 + ], + "type": "text", + "content": "Figure 5. Impact of refining search results. Initial candidates are shown in yellow boxes, and refined candidates are shown in green." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 73, + 329, + 536, + 467 + ], + "lines": [ + { + "bbox": [ + 73, + 329, + 536, + 467 + ], + "spans": [ + { + "bbox": [ + 73, + 329, + 536, + 467 + ], + "type": "image", + "image_path": "91ece3b8ce80556d9702051f2acbcc872d4c29e21099b963a86e4ef268b326bb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "lines": [ + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "type": "text", + "content": "Figure 6. Impact of query expansion and reiteration. Using only the initial query " + }, + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "type": "text", + "content": ", RELOCATE misses the object's final appearance due to its partial view and low feature similarity. However, the expanded query set " + }, + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}^+" + }, + { + "bbox": [ + 55, + 472, + 555, + 504 + ], + "type": "text", + "content": " captures multiple object perspectives, enabling successful detection of the final occurrence." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 525, + 295, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 295, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 295, + 642 + ], + "type": "text", + "content": "spatial precision for localizing small objects and fine parts by generating regions from an object-centric crop that captures more of the object of interest. Additionally, refinement removes incorrect selections from the initial search by rescoring candidates using region tokens generated from an object-centric crop. Furthermore, for small or thin objects, feature bleeding can result in the selection of an object adjacent to the target object. Object-centered cropping can also help avoid this by providing a clearer view of the target. This is demonstrated in Figure 5b." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 643, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 643, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 643, + 295, + 714 + ], + "type": "text", + "content": "Query Expansion and Reiteration. Results in Table 4 show that query expansion and reiteration significantly improve RELOCATE's performance compared to the variant without this step (RELOCATE-NoReiter). Figure 6 shows an example where query expansion using an initial prediction helps capture a wider range of views for the visual query." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 525, + 555, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 555, + 585 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 555, + 585 + ], + "type": "text", + "content": "This, in turn, helps in successfully localizing the final occurrence of the object that was missed when only the initial visual query was used. Additional examples where reiteration after query expansion leads to successful localization are illustrated in rows 2, 5, and 6 of Figure 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 598, + 388, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 598, + 388, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 598, + 388, + 610 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 619, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 619, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 619, + 555, + 713 + ], + "type": "text", + "content": "We present RELOCATE, a framework utilizing region-based representations from pretrained vision models to address VQL. Despite a simple design and no task-specific training, RELOCATE can localize target objects in long videos, even under challenging conditions such as clutter, occlusion, blur, and viewpoint changes. On the VQ2D benchmark, it significantly outperforms existing methods that are specifically trained on this dataset." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3704" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 163 + ], + "type": "text", + "content": "This work is supported in part by ONR N00014-23-1-2383, DARPA HR0011-23-9-0060, NSF 2008387, NSF 2045586, NSF 2106825, NSF MRI 1725729, and NIFA award 2020-67021-32799. 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